Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.698857\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.43091 | 1.71891 | 0.859456 | − | 0.511210i | \(-0.170803\pi\) | ||||
0.859456 | + | 0.511210i | \(0.170803\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.90931 | 1.95466 | ||||||||
\(5\) | 3.43091 | 1.53435 | 0.767174 | − | 0.641439i | \(-0.221662\pi\) | ||||
0.767174 | + | 0.641439i | \(0.221662\pi\) | |||||||
\(6\) | −2.43091 | −0.992414 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 4.64136 | 1.64097 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.34022 | 2.63741 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.90931 | −1.12852 | ||||||||
\(13\) | −6.11977 | −1.69732 | −0.848659 | − | 0.528940i | \(-0.822590\pi\) | ||||
−0.848659 | + | 0.528940i | \(0.822590\pi\) | |||||||
\(14\) | 2.43091 | 0.649687 | ||||||||
\(15\) | −3.43091 | −0.885857 | ||||||||
\(16\) | 3.46410 | 0.866025 | ||||||||
\(17\) | 3.21046 | 0.778650 | 0.389325 | − | 0.921100i | \(-0.372708\pi\) | ||||
0.389325 | + | 0.921100i | \(0.372708\pi\) | |||||||
\(18\) | 2.43091 | 0.572970 | ||||||||
\(19\) | 6.34022 | 1.45455 | 0.727273 | − | 0.686348i | \(-0.240787\pi\) | ||||
0.727273 | + | 0.686348i | \(0.240787\pi\) | |||||||
\(20\) | 13.4125 | 2.99912 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.210456 | −0.0438831 | −0.0219415 | − | 0.999759i | \(-0.506985\pi\) | ||||
−0.0219415 | + | 0.999759i | \(0.506985\pi\) | |||||||
\(24\) | −4.64136 | −0.947414 | ||||||||
\(25\) | 6.77113 | 1.35423 | ||||||||
\(26\) | −14.8766 | −2.91754 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.90931 | 0.738791 | ||||||||
\(29\) | 2.74635 | 0.509985 | 0.254993 | − | 0.966943i | \(-0.417927\pi\) | ||||
0.254993 | + | 0.966943i | \(0.417927\pi\) | |||||||
\(30\) | −8.34022 | −1.52271 | ||||||||
\(31\) | 4.64136 | 0.833614 | 0.416807 | − | 0.908995i | \(-0.363149\pi\) | ||||
0.416807 | + | 0.908995i | \(0.363149\pi\) | |||||||
\(32\) | −0.861816 | −0.152349 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.80432 | 1.33843 | ||||||||
\(35\) | 3.43091 | 0.579929 | ||||||||
\(36\) | 3.90931 | 0.651552 | ||||||||
\(37\) | −9.37341 | −1.54098 | −0.770490 | − | 0.637452i | \(-0.779988\pi\) | ||||
−0.770490 | + | 0.637452i | \(0.779988\pi\) | |||||||
\(38\) | 15.4125 | 2.50024 | ||||||||
\(39\) | 6.11977 | 0.979947 | ||||||||
\(40\) | 15.9241 | 2.51782 | ||||||||
\(41\) | 11.9484 | 1.86603 | 0.933013 | − | 0.359844i | \(-0.117170\pi\) | ||||
0.933013 | + | 0.359844i | \(0.117170\pi\) | |||||||
\(42\) | −2.43091 | −0.375097 | ||||||||
\(43\) | 7.12976 | 1.08728 | 0.543639 | − | 0.839319i | \(-0.317046\pi\) | ||||
0.543639 | + | 0.839319i | \(0.317046\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.43091 | 0.511450 | ||||||||
\(46\) | −0.511599 | −0.0754311 | ||||||||
\(47\) | −5.91520 | −0.862820 | −0.431410 | − | 0.902156i | \(-0.641984\pi\) | ||||
−0.431410 | + | 0.902156i | \(0.641984\pi\) | |||||||
\(48\) | −3.46410 | −0.500000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 16.4600 | 2.32779 | ||||||||
\(51\) | −3.21046 | −0.449554 | ||||||||
\(52\) | −23.9241 | −3.31767 | ||||||||
\(53\) | −6.35452 | −0.872861 | −0.436431 | − | 0.899738i | \(-0.643758\pi\) | ||||
−0.436431 | + | 0.899738i | \(0.643758\pi\) | |||||||
\(54\) | −2.43091 | −0.330805 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.64136 | 0.620228 | ||||||||
\(57\) | −6.34022 | −0.839783 | ||||||||
\(58\) | 6.67613 | 0.876619 | ||||||||
\(59\) | −11.8232 | −1.53925 | −0.769626 | − | 0.638495i | \(-0.779557\pi\) | ||||
−0.769626 | + | 0.638495i | \(0.779557\pi\) | |||||||
\(60\) | −13.4125 | −1.73155 | ||||||||
\(61\) | 9.20204 | 1.17820 | 0.589100 | − | 0.808060i | \(-0.299482\pi\) | ||||
0.589100 | + | 0.808060i | \(0.299482\pi\) | |||||||
\(62\) | 11.2827 | 1.43291 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −9.02320 | −1.12790 | ||||||||
\(65\) | −20.9964 | −2.60428 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.89042 | −0.475291 | −0.237645 | − | 0.971352i | \(-0.576376\pi\) | ||||
−0.237645 | + | 0.971352i | \(0.576376\pi\) | |||||||
\(68\) | 12.5507 | 1.52199 | ||||||||
\(69\) | 0.210456 | 0.0253359 | ||||||||
\(70\) | 8.34022 | 0.996847 | ||||||||
\(71\) | −5.19458 | −0.616483 | −0.308241 | − | 0.951308i | \(-0.599740\pi\) | ||||
−0.308241 | + | 0.951308i | \(0.599740\pi\) | |||||||
\(72\) | 4.64136 | 0.546990 | ||||||||
\(73\) | −13.1747 | −1.54199 | −0.770993 | − | 0.636844i | \(-0.780239\pi\) | ||||
−0.770993 | + | 0.636844i | \(0.780239\pi\) | |||||||
\(74\) | −22.7859 | −2.64881 | ||||||||
\(75\) | −6.77113 | −0.781863 | ||||||||
\(76\) | 24.7859 | 2.84314 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 14.8766 | 1.68444 | ||||||||
\(79\) | −4.33022 | −0.487188 | −0.243594 | − | 0.969877i | \(-0.578326\pi\) | ||||
−0.243594 | + | 0.969877i | \(0.578326\pi\) | |||||||
\(80\) | 11.8850 | 1.32878 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 29.0454 | 3.20753 | ||||||||
\(83\) | −0.737935 | −0.0809989 | −0.0404994 | − | 0.999180i | \(-0.512895\pi\) | ||||
−0.0404994 | + | 0.999180i | \(0.512895\pi\) | |||||||
\(84\) | −3.90931 | −0.426541 | ||||||||
\(85\) | 11.0148 | 1.19472 | ||||||||
\(86\) | 17.3318 | 1.86894 | ||||||||
\(87\) | −2.74635 | −0.294440 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.34453 | −0.990518 | −0.495259 | − | 0.868745i | \(-0.664927\pi\) | ||||
−0.495259 | + | 0.868745i | \(0.664927\pi\) | |||||||
\(90\) | 8.34022 | 0.879136 | ||||||||
\(91\) | −6.11977 | −0.641526 | ||||||||
\(92\) | −0.822738 | −0.0857764 | ||||||||
\(93\) | −4.64136 | −0.481287 | ||||||||
\(94\) | −14.3793 | −1.48311 | ||||||||
\(95\) | 21.7527 | 2.23178 | ||||||||
\(96\) | 0.861816 | 0.0879587 | ||||||||
\(97\) | 12.0534 | 1.22384 | 0.611918 | − | 0.790921i | \(-0.290398\pi\) | ||||
0.611918 | + | 0.790921i | \(0.290398\pi\) | |||||||
\(98\) | 2.43091 | 0.245559 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.4705 | 2.64705 | ||||||||
\(101\) | −1.58798 | −0.158010 | −0.0790051 | − | 0.996874i | \(-0.525174\pi\) | ||||
−0.0790051 | + | 0.996874i | \(0.525174\pi\) | |||||||
\(102\) | −7.80432 | −0.772743 | ||||||||
\(103\) | 9.42249 | 0.928425 | 0.464213 | − | 0.885724i | \(-0.346337\pi\) | ||||
0.464213 | + | 0.885724i | \(0.346337\pi\) | |||||||
\(104\) | −28.4041 | −2.78525 | ||||||||
\(105\) | −3.43091 | −0.334822 | ||||||||
\(106\) | −15.4473 | −1.50037 | ||||||||
\(107\) | 7.03319 | 0.679925 | 0.339962 | − | 0.940439i | \(-0.389586\pi\) | ||||
0.339962 | + | 0.940439i | \(0.389586\pi\) | |||||||
\(108\) | −3.90931 | −0.376174 | ||||||||
\(109\) | −2.37040 | −0.227044 | −0.113522 | − | 0.993536i | \(-0.536213\pi\) | ||||
−0.113522 | + | 0.993536i | \(0.536213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.37341 | 0.889685 | ||||||||
\(112\) | 3.46410 | 0.327327 | ||||||||
\(113\) | 0.409144 | 0.0384890 | 0.0192445 | − | 0.999815i | \(-0.493874\pi\) | ||||
0.0192445 | + | 0.999815i | \(0.493874\pi\) | |||||||
\(114\) | −15.4125 | −1.44351 | ||||||||
\(115\) | −0.722055 | −0.0673320 | ||||||||
\(116\) | 10.7364 | 0.996846 | ||||||||
\(117\) | −6.11977 | −0.565773 | ||||||||
\(118\) | −28.7411 | −2.64584 | ||||||||
\(119\) | 3.21046 | 0.294302 | ||||||||
\(120\) | −15.9241 | −1.45366 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 22.3693 | 2.02522 | ||||||||
\(123\) | −11.9484 | −1.07735 | ||||||||
\(124\) | 18.1445 | 1.62943 | ||||||||
\(125\) | 6.07658 | 0.543506 | ||||||||
\(126\) | 2.43091 | 0.216562 | ||||||||
\(127\) | −19.5307 | −1.73307 | −0.866534 | − | 0.499118i | \(-0.833657\pi\) | ||||
−0.866534 | + | 0.499118i | \(0.833657\pi\) | |||||||
\(128\) | −20.2109 | −1.78641 | ||||||||
\(129\) | −7.12976 | −0.627741 | ||||||||
\(130\) | −51.0402 | −4.47652 | ||||||||
\(131\) | 19.3750 | 1.69280 | 0.846400 | − | 0.532547i | \(-0.178765\pi\) | ||||
0.846400 | + | 0.532547i | \(0.178765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.34022 | 0.549767 | ||||||||
\(134\) | −9.45726 | −0.816983 | ||||||||
\(135\) | −3.43091 | −0.295286 | ||||||||
\(136\) | 14.9009 | 1.27774 | ||||||||
\(137\) | −6.14277 | −0.524812 | −0.262406 | − | 0.964958i | \(-0.584516\pi\) | ||||
−0.262406 | + | 0.964958i | \(0.584516\pi\) | |||||||
\(138\) | 0.511599 | 0.0435502 | ||||||||
\(139\) | 6.77065 | 0.574279 | 0.287140 | − | 0.957889i | \(-0.407296\pi\) | ||||
0.287140 | + | 0.957889i | \(0.407296\pi\) | |||||||
\(140\) | 13.4125 | 1.13356 | ||||||||
\(141\) | 5.91520 | 0.498149 | ||||||||
\(142\) | −12.6275 | −1.05968 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.46410 | 0.288675 | ||||||||
\(145\) | 9.42249 | 0.782495 | ||||||||
\(146\) | −32.0265 | −2.65054 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −36.6436 | −3.01209 | ||||||||
\(149\) | −17.8204 | −1.45990 | −0.729952 | − | 0.683498i | \(-0.760458\pi\) | ||||
−0.729952 | + | 0.683498i | \(0.760458\pi\) | |||||||
\(150\) | −16.4600 | −1.34395 | ||||||||
\(151\) | 0.610705 | 0.0496985 | 0.0248493 | − | 0.999691i | \(-0.492089\pi\) | ||||
0.0248493 | + | 0.999691i | \(0.492089\pi\) | |||||||
\(152\) | 29.4273 | 2.38687 | ||||||||
\(153\) | 3.21046 | 0.259550 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.9241 | 1.27905 | ||||||||
\(156\) | 23.9241 | 1.91546 | ||||||||
\(157\) | 6.82274 | 0.544514 | 0.272257 | − | 0.962225i | \(-0.412230\pi\) | ||||
0.272257 | + | 0.962225i | \(0.412230\pi\) | |||||||
\(158\) | −10.5264 | −0.837434 | ||||||||
\(159\) | 6.35452 | 0.503947 | ||||||||
\(160\) | −2.95681 | −0.233756 | ||||||||
\(161\) | −0.210456 | −0.0165862 | ||||||||
\(162\) | 2.43091 | 0.190990 | ||||||||
\(163\) | −12.0738 | −0.945697 | −0.472848 | − | 0.881144i | \(-0.656774\pi\) | ||||
−0.472848 | + | 0.881144i | \(0.656774\pi\) | |||||||
\(164\) | 46.7100 | 3.64744 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.79385 | −0.139230 | ||||||||
\(167\) | −2.89932 | −0.224356 | −0.112178 | − | 0.993688i | \(-0.535783\pi\) | ||||
−0.112178 | + | 0.993688i | \(0.535783\pi\) | |||||||
\(168\) | −4.64136 | −0.358089 | ||||||||
\(169\) | 24.4516 | 1.88089 | ||||||||
\(170\) | 26.7759 | 2.05362 | ||||||||
\(171\) | 6.34022 | 0.484849 | ||||||||
\(172\) | 27.8725 | 2.12526 | ||||||||
\(173\) | −14.5713 | −1.10784 | −0.553919 | − | 0.832570i | \(-0.686868\pi\) | ||||
−0.553919 | + | 0.832570i | \(0.686868\pi\) | |||||||
\(174\) | −6.67613 | −0.506116 | ||||||||
\(175\) | 6.77113 | 0.511849 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.8232 | 0.888687 | ||||||||
\(178\) | −22.7157 | −1.70261 | ||||||||
\(179\) | 18.9082 | 1.41327 | 0.706633 | − | 0.707580i | \(-0.250213\pi\) | ||||
0.706633 | + | 0.707580i | \(0.250213\pi\) | |||||||
\(180\) | 13.4125 | 0.999708 | ||||||||
\(181\) | 15.7713 | 1.17227 | 0.586137 | − | 0.810212i | \(-0.300648\pi\) | ||||
0.586137 | + | 0.810212i | \(0.300648\pi\) | |||||||
\(182\) | −14.8766 | −1.10273 | ||||||||
\(183\) | −9.20204 | −0.680234 | ||||||||
\(184\) | −0.976802 | −0.0720108 | ||||||||
\(185\) | −32.1593 | −2.36440 | ||||||||
\(186\) | −11.2827 | −0.827290 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −23.1244 | −1.68652 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 52.8788 | 3.83623 | ||||||||
\(191\) | −19.5132 | −1.41192 | −0.705962 | − | 0.708250i | \(-0.749485\pi\) | ||||
−0.705962 | + | 0.708250i | \(0.749485\pi\) | |||||||
\(192\) | 9.02320 | 0.651193 | ||||||||
\(193\) | −22.9830 | −1.65435 | −0.827177 | − | 0.561942i | \(-0.810055\pi\) | ||||
−0.827177 | + | 0.561942i | \(0.810055\pi\) | |||||||
\(194\) | 29.3007 | 2.10366 | ||||||||
\(195\) | 20.9964 | 1.50358 | ||||||||
\(196\) | 3.90931 | 0.279237 | ||||||||
\(197\) | 11.3218 | 0.806645 | 0.403323 | − | 0.915058i | \(-0.367855\pi\) | ||||
0.403323 | + | 0.915058i | \(0.367855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.43837 | −0.456404 | −0.228202 | − | 0.973614i | \(-0.573285\pi\) | ||||
−0.228202 | + | 0.973614i | \(0.573285\pi\) | |||||||
\(200\) | 31.4273 | 2.22224 | ||||||||
\(201\) | 3.89042 | 0.274409 | ||||||||
\(202\) | −3.86024 | −0.271605 | ||||||||
\(203\) | 2.74635 | 0.192756 | ||||||||
\(204\) | −12.5507 | −0.878723 | ||||||||
\(205\) | 40.9938 | 2.86313 | ||||||||
\(206\) | 22.9052 | 1.59588 | ||||||||
\(207\) | −0.210456 | −0.0146277 | ||||||||
\(208\) | −21.1995 | −1.46992 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −8.34022 | −0.575530 | ||||||||
\(211\) | 20.1287 | 1.38571 | 0.692857 | − | 0.721075i | \(-0.256352\pi\) | ||||
0.692857 | + | 0.721075i | \(0.256352\pi\) | |||||||
\(212\) | −24.8418 | −1.70614 | ||||||||
\(213\) | 5.19458 | 0.355926 | ||||||||
\(214\) | 17.0970 | 1.16873 | ||||||||
\(215\) | 24.4616 | 1.66826 | ||||||||
\(216\) | −4.64136 | −0.315805 | ||||||||
\(217\) | 4.64136 | 0.315076 | ||||||||
\(218\) | −5.76223 | −0.390268 | ||||||||
\(219\) | 13.1747 | 0.890266 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.6472 | −1.32162 | ||||||||
\(222\) | 22.7859 | 1.52929 | ||||||||
\(223\) | −20.8691 | −1.39750 | −0.698750 | − | 0.715366i | \(-0.746260\pi\) | ||||
−0.698750 | + | 0.715366i | \(0.746260\pi\) | |||||||
\(224\) | −0.861816 | −0.0575825 | ||||||||
\(225\) | 6.77113 | 0.451409 | ||||||||
\(226\) | 0.994591 | 0.0661592 | ||||||||
\(227\) | 3.06892 | 0.203692 | 0.101846 | − | 0.994800i | \(-0.467525\pi\) | ||||
0.101846 | + | 0.994800i | \(0.467525\pi\) | |||||||
\(228\) | −24.7859 | −1.64149 | ||||||||
\(229\) | −8.35768 | −0.552291 | −0.276145 | − | 0.961116i | \(-0.589057\pi\) | ||||
−0.276145 | + | 0.961116i | \(0.589057\pi\) | |||||||
\(230\) | −1.75525 | −0.115738 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.7468 | 0.836870 | ||||||||
\(233\) | −5.50270 | −0.360494 | −0.180247 | − | 0.983621i | \(-0.557690\pi\) | ||||
−0.180247 | + | 0.983621i | \(0.557690\pi\) | |||||||
\(234\) | −14.8766 | −0.972513 | ||||||||
\(235\) | −20.2945 | −1.32387 | ||||||||
\(236\) | −46.2206 | −3.00871 | ||||||||
\(237\) | 4.33022 | 0.281278 | ||||||||
\(238\) | 7.80432 | 0.505879 | ||||||||
\(239\) | 2.30368 | 0.149013 | 0.0745063 | − | 0.997221i | \(-0.476262\pi\) | ||||
0.0745063 | + | 0.997221i | \(0.476262\pi\) | |||||||
\(240\) | −11.8850 | −0.767174 | ||||||||
\(241\) | −10.3602 | −0.667360 | −0.333680 | − | 0.942686i | \(-0.608290\pi\) | ||||
−0.333680 | + | 0.942686i | \(0.608290\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 35.9736 | 2.30298 | ||||||||
\(245\) | 3.43091 | 0.219193 | ||||||||
\(246\) | −29.0454 | −1.85187 | ||||||||
\(247\) | −38.8007 | −2.46883 | ||||||||
\(248\) | 21.5423 | 1.36793 | ||||||||
\(249\) | 0.737935 | 0.0467647 | ||||||||
\(250\) | 14.7716 | 0.934238 | ||||||||
\(251\) | 11.2627 | 0.710898 | 0.355449 | − | 0.934696i | \(-0.384328\pi\) | ||||
0.355449 | + | 0.934696i | \(0.384328\pi\) | |||||||
\(252\) | 3.90931 | 0.246264 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −47.4773 | −2.97899 | ||||||||
\(255\) | −11.0148 | −0.689772 | ||||||||
\(256\) | −31.0845 | −1.94278 | ||||||||
\(257\) | −15.2643 | −0.952162 | −0.476081 | − | 0.879402i | \(-0.657943\pi\) | ||||
−0.476081 | + | 0.879402i | \(0.657943\pi\) | |||||||
\(258\) | −17.3318 | −1.07903 | ||||||||
\(259\) | −9.37341 | −0.582436 | ||||||||
\(260\) | −82.0814 | −5.09047 | ||||||||
\(261\) | 2.74635 | 0.169995 | ||||||||
\(262\) | 47.0988 | 2.90977 | ||||||||
\(263\) | −8.45315 | −0.521243 | −0.260622 | − | 0.965441i | \(-0.583928\pi\) | ||||
−0.260622 | + | 0.965441i | \(0.583928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8018 | −1.33927 | ||||||||
\(266\) | 15.4125 | 0.945001 | ||||||||
\(267\) | 9.34453 | 0.571876 | ||||||||
\(268\) | −15.2089 | −0.929030 | ||||||||
\(269\) | −21.3987 | −1.30470 | −0.652350 | − | 0.757918i | \(-0.726217\pi\) | ||||
−0.652350 | + | 0.757918i | \(0.726217\pi\) | |||||||
\(270\) | −8.34022 | −0.507570 | ||||||||
\(271\) | 26.2414 | 1.59405 | 0.797026 | − | 0.603946i | \(-0.206406\pi\) | ||||
0.797026 | + | 0.603946i | \(0.206406\pi\) | |||||||
\(272\) | 11.1213 | 0.674331 | ||||||||
\(273\) | 6.11977 | 0.370385 | ||||||||
\(274\) | −14.9325 | −0.902106 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.822738 | 0.0495230 | ||||||||
\(277\) | −18.5696 | −1.11574 | −0.557869 | − | 0.829929i | \(-0.688381\pi\) | ||||
−0.557869 | + | 0.829929i | \(0.688381\pi\) | |||||||
\(278\) | 16.4588 | 0.987135 | ||||||||
\(279\) | 4.64136 | 0.277871 | ||||||||
\(280\) | 15.9241 | 0.951646 | ||||||||
\(281\) | 4.24906 | 0.253478 | 0.126739 | − | 0.991936i | \(-0.459549\pi\) | ||||
0.126739 | + | 0.991936i | \(0.459549\pi\) | |||||||
\(282\) | 14.3793 | 0.856275 | ||||||||
\(283\) | 20.5277 | 1.22024 | 0.610122 | − | 0.792308i | \(-0.291121\pi\) | ||||
0.610122 | + | 0.792308i | \(0.291121\pi\) | |||||||
\(284\) | −20.3072 | −1.20501 | ||||||||
\(285\) | −21.7527 | −1.28852 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.9484 | 0.705291 | ||||||||
\(288\) | −0.861816 | −0.0507830 | ||||||||
\(289\) | −6.69297 | −0.393704 | ||||||||
\(290\) | 22.9052 | 1.34504 | ||||||||
\(291\) | −12.0534 | −0.706582 | ||||||||
\(292\) | −51.5041 | −3.01405 | ||||||||
\(293\) | −21.2022 | −1.23865 | −0.619324 | − | 0.785136i | \(-0.712593\pi\) | ||||
−0.619324 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(294\) | −2.43091 | −0.141773 | ||||||||
\(295\) | −40.5644 | −2.36175 | ||||||||
\(296\) | −43.5054 | −2.52870 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −43.3197 | −2.50945 | ||||||||
\(299\) | 1.28794 | 0.0744836 | ||||||||
\(300\) | −26.4705 | −1.52827 | ||||||||
\(301\) | 7.12976 | 0.410953 | ||||||||
\(302\) | 1.48457 | 0.0854273 | ||||||||
\(303\) | 1.58798 | 0.0912272 | ||||||||
\(304\) | 21.9632 | 1.25967 | ||||||||
\(305\) | 31.5713 | 1.80777 | ||||||||
\(306\) | 7.80432 | 0.446143 | ||||||||
\(307\) | 23.0007 | 1.31272 | 0.656359 | − | 0.754449i | \(-0.272096\pi\) | ||||
0.656359 | + | 0.754449i | \(0.272096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.42249 | −0.536027 | ||||||||
\(310\) | 38.7100 | 2.19858 | ||||||||
\(311\) | 7.36753 | 0.417774 | 0.208887 | − | 0.977940i | \(-0.433016\pi\) | ||||
0.208887 | + | 0.977940i | \(0.433016\pi\) | |||||||
\(312\) | 28.4041 | 1.60806 | ||||||||
\(313\) | −4.80590 | −0.271645 | −0.135823 | − | 0.990733i | \(-0.543368\pi\) | ||||
−0.135823 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(314\) | 16.5854 | 0.935971 | ||||||||
\(315\) | 3.43091 | 0.193310 | ||||||||
\(316\) | −16.9282 | −0.952286 | ||||||||
\(317\) | −1.54178 | −0.0865951 | −0.0432976 | − | 0.999062i | \(-0.513786\pi\) | ||||
−0.0432976 | + | 0.999062i | \(0.513786\pi\) | |||||||
\(318\) | 15.4473 | 0.866239 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −30.9578 | −1.73059 | ||||||||
\(321\) | −7.03319 | −0.392555 | ||||||||
\(322\) | −0.511599 | −0.0285103 | ||||||||
\(323\) | 20.3550 | 1.13258 | ||||||||
\(324\) | 3.90931 | 0.217184 | ||||||||
\(325\) | −41.4377 | −2.29855 | ||||||||
\(326\) | −29.3504 | −1.62557 | ||||||||
\(327\) | 2.37040 | 0.131084 | ||||||||
\(328\) | 55.4568 | 3.06209 | ||||||||
\(329\) | −5.91520 | −0.326115 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8925 | −0.708634 | −0.354317 | − | 0.935125i | \(-0.615287\pi\) | ||||
−0.354317 | + | 0.935125i | \(0.615287\pi\) | |||||||
\(332\) | −2.88482 | −0.158325 | ||||||||
\(333\) | −9.37341 | −0.513660 | ||||||||
\(334\) | −7.04797 | −0.385648 | ||||||||
\(335\) | −13.3477 | −0.729262 | ||||||||
\(336\) | −3.46410 | −0.188982 | ||||||||
\(337\) | −18.6475 | −1.01580 | −0.507898 | − | 0.861417i | \(-0.669577\pi\) | ||||
−0.507898 | + | 0.861417i | \(0.669577\pi\) | |||||||
\(338\) | 59.4395 | 3.23308 | ||||||||
\(339\) | −0.409144 | −0.0222216 | ||||||||
\(340\) | 43.0602 | 2.33527 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 15.4125 | 0.833412 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 33.0918 | 1.78419 | ||||||||
\(345\) | 0.722055 | 0.0388741 | ||||||||
\(346\) | −35.4216 | −1.90428 | ||||||||
\(347\) | 12.4700 | 0.669424 | 0.334712 | − | 0.942320i | \(-0.391361\pi\) | ||||
0.334712 | + | 0.942320i | \(0.391361\pi\) | |||||||
\(348\) | −10.7364 | −0.575529 | ||||||||
\(349\) | 5.11087 | 0.273579 | 0.136789 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136789 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(350\) | 16.4600 | 0.879823 | ||||||||
\(351\) | 6.11977 | 0.326649 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7386 | 1.42315 | 0.711576 | − | 0.702609i | \(-0.247982\pi\) | ||||
0.711576 | + | 0.702609i | \(0.247982\pi\) | |||||||
\(354\) | 28.7411 | 1.52757 | ||||||||
\(355\) | −17.8221 | −0.945899 | ||||||||
\(356\) | −36.5307 | −1.93612 | ||||||||
\(357\) | −3.21046 | −0.169915 | ||||||||
\(358\) | 45.9641 | 2.42928 | ||||||||
\(359\) | 0.873109 | 0.0460809 | 0.0230405 | − | 0.999735i | \(-0.492665\pi\) | ||||
0.0230405 | + | 0.999735i | \(0.492665\pi\) | |||||||
\(360\) | 15.9241 | 0.839273 | ||||||||
\(361\) | 21.1984 | 1.11571 | ||||||||
\(362\) | 38.3386 | 2.01503 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.9241 | −1.25396 | ||||||||
\(365\) | −45.2013 | −2.36594 | ||||||||
\(366\) | −22.3693 | −1.16926 | ||||||||
\(367\) | 12.4644 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(368\) | −0.729041 | −0.0380039 | ||||||||
\(369\) | 11.9484 | 0.622008 | ||||||||
\(370\) | −78.1763 | −4.06419 | ||||||||
\(371\) | −6.35452 | −0.329910 | ||||||||
\(372\) | −18.1445 | −0.940751 | ||||||||
\(373\) | −2.27617 | −0.117856 | −0.0589279 | − | 0.998262i | \(-0.518768\pi\) | ||||
−0.0589279 | + | 0.998262i | \(0.518768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.07658 | −0.313793 | ||||||||
\(376\) | −27.4546 | −1.41586 | ||||||||
\(377\) | −16.8071 | −0.865607 | ||||||||
\(378\) | −2.43091 | −0.125032 | ||||||||
\(379\) | 20.7575 | 1.06624 | 0.533120 | − | 0.846039i | \(-0.321019\pi\) | ||||
0.533120 | + | 0.846039i | \(0.321019\pi\) | |||||||
\(380\) | 85.0382 | 4.36237 | ||||||||
\(381\) | 19.5307 | 1.00059 | ||||||||
\(382\) | −47.4347 | −2.42697 | ||||||||
\(383\) | −17.8498 | −0.912080 | −0.456040 | − | 0.889959i | \(-0.650733\pi\) | ||||
−0.456040 | + | 0.889959i | \(0.650733\pi\) | |||||||
\(384\) | 20.2109 | 1.03138 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −55.8696 | −2.84369 | ||||||||
\(387\) | 7.12976 | 0.362426 | ||||||||
\(388\) | 47.1204 | 2.39218 | ||||||||
\(389\) | −8.23954 | −0.417761 | −0.208881 | − | 0.977941i | \(-0.566982\pi\) | ||||
−0.208881 | + | 0.977941i | \(0.566982\pi\) | |||||||
\(390\) | 51.0402 | 2.58452 | ||||||||
\(391\) | −0.675659 | −0.0341696 | ||||||||
\(392\) | 4.64136 | 0.234424 | ||||||||
\(393\) | −19.3750 | −0.977339 | ||||||||
\(394\) | 27.5223 | 1.38655 | ||||||||
\(395\) | −14.8566 | −0.747517 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.1445 | −0.810271 | −0.405136 | − | 0.914257i | \(-0.632776\pi\) | ||||
−0.405136 | + | 0.914257i | \(0.632776\pi\) | |||||||
\(398\) | −15.6511 | −0.784518 | ||||||||
\(399\) | −6.34022 | −0.317408 | ||||||||
\(400\) | 23.4559 | 1.17279 | ||||||||
\(401\) | 27.5236 | 1.37446 | 0.687231 | − | 0.726439i | \(-0.258826\pi\) | ||||
0.687231 | + | 0.726439i | \(0.258826\pi\) | |||||||
\(402\) | 9.45726 | 0.471685 | ||||||||
\(403\) | −28.4041 | −1.41491 | ||||||||
\(404\) | −6.20792 | −0.308856 | ||||||||
\(405\) | 3.43091 | 0.170483 | ||||||||
\(406\) | 6.67613 | 0.331331 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.9009 | −0.737704 | ||||||||
\(409\) | −17.1270 | −0.846877 | −0.423439 | − | 0.905925i | \(-0.639177\pi\) | ||||
−0.423439 | + | 0.905925i | \(0.639177\pi\) | |||||||
\(410\) | 99.6522 | 4.92147 | ||||||||
\(411\) | 6.14277 | 0.303001 | ||||||||
\(412\) | 36.8355 | 1.81475 | ||||||||
\(413\) | −11.8232 | −0.581782 | ||||||||
\(414\) | −0.511599 | −0.0251437 | ||||||||
\(415\) | −2.53179 | −0.124281 | ||||||||
\(416\) | 5.27411 | 0.258585 | ||||||||
\(417\) | −6.77065 | −0.331560 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3995 | 0.703461 | 0.351730 | − | 0.936101i | \(-0.385593\pi\) | ||||
0.351730 | + | 0.936101i | \(0.385593\pi\) | |||||||
\(420\) | −13.4125 | −0.654463 | ||||||||
\(421\) | −11.0695 | −0.539496 | −0.269748 | − | 0.962931i | \(-0.586940\pi\) | ||||
−0.269748 | + | 0.962931i | \(0.586940\pi\) | |||||||
\(422\) | 48.9309 | 2.38192 | ||||||||
\(423\) | −5.91520 | −0.287607 | ||||||||
\(424\) | −29.4937 | −1.43234 | ||||||||
\(425\) | 21.7384 | 1.05447 | ||||||||
\(426\) | 12.6275 | 0.611806 | ||||||||
\(427\) | 9.20204 | 0.445318 | ||||||||
\(428\) | 27.4950 | 1.32902 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 59.4638 | 2.86760 | ||||||||
\(431\) | 15.6173 | 0.752257 | 0.376128 | − | 0.926568i | \(-0.377255\pi\) | ||||
0.376128 | + | 0.926568i | \(0.377255\pi\) | |||||||
\(432\) | −3.46410 | −0.166667 | ||||||||
\(433\) | 2.17439 | 0.104494 | 0.0522472 | − | 0.998634i | \(-0.483362\pi\) | ||||
0.0522472 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(434\) | 11.2827 | 0.541588 | ||||||||
\(435\) | −9.42249 | −0.451774 | ||||||||
\(436\) | −9.26665 | −0.443792 | ||||||||
\(437\) | −1.33434 | −0.0638300 | ||||||||
\(438\) | 32.0265 | 1.53029 | ||||||||
\(439\) | −9.44726 | −0.450893 | −0.225447 | − | 0.974256i | \(-0.572384\pi\) | ||||
−0.225447 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −47.7606 | −2.27174 | ||||||||
\(443\) | 8.08725 | 0.384237 | 0.192118 | − | 0.981372i | \(-0.438464\pi\) | ||||
0.192118 | + | 0.981372i | \(0.438464\pi\) | |||||||
\(444\) | 36.6436 | 1.73903 | ||||||||
\(445\) | −32.0602 | −1.51980 | ||||||||
\(446\) | −50.7309 | −2.40218 | ||||||||
\(447\) | 17.8204 | 0.842876 | ||||||||
\(448\) | −9.02320 | −0.426306 | ||||||||
\(449\) | −28.5845 | −1.34899 | −0.674494 | − | 0.738280i | \(-0.735638\pi\) | ||||
−0.674494 | + | 0.738280i | \(0.735638\pi\) | |||||||
\(450\) | 16.4600 | 0.775931 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.59947 | 0.0752328 | ||||||||
\(453\) | −0.610705 | −0.0286934 | ||||||||
\(454\) | 7.46027 | 0.350128 | ||||||||
\(455\) | −20.9964 | −0.984325 | ||||||||
\(456\) | −29.4273 | −1.37806 | ||||||||
\(457\) | 8.25713 | 0.386252 | 0.193126 | − | 0.981174i | \(-0.438137\pi\) | ||||
0.193126 | + | 0.981174i | \(0.438137\pi\) | |||||||
\(458\) | −20.3167 | −0.949339 | ||||||||
\(459\) | −3.21046 | −0.149851 | ||||||||
\(460\) | −2.82274 | −0.131611 | ||||||||
\(461\) | −13.3346 | −0.621055 | −0.310527 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310527 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.6479 | 1.23843 | 0.619217 | − | 0.785220i | \(-0.287450\pi\) | ||||
0.619217 | + | 0.785220i | \(0.287450\pi\) | |||||||
\(464\) | 9.51365 | 0.441660 | ||||||||
\(465\) | −15.9241 | −0.738462 | ||||||||
\(466\) | −13.3766 | −0.619658 | ||||||||
\(467\) | 28.8194 | 1.33360 | 0.666801 | − | 0.745236i | \(-0.267663\pi\) | ||||
0.666801 | + | 0.745236i | \(0.267663\pi\) | |||||||
\(468\) | −23.9241 | −1.10589 | ||||||||
\(469\) | −3.89042 | −0.179643 | ||||||||
\(470\) | −49.3340 | −2.27561 | ||||||||
\(471\) | −6.82274 | −0.314375 | ||||||||
\(472\) | −54.8758 | −2.52586 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 10.5264 | 0.483493 | ||||||||
\(475\) | 42.9304 | 1.96978 | ||||||||
\(476\) | 12.5507 | 0.575259 | ||||||||
\(477\) | −6.35452 | −0.290954 | ||||||||
\(478\) | 5.60003 | 0.256139 | ||||||||
\(479\) | 7.03430 | 0.321405 | 0.160703 | − | 0.987003i | \(-0.448624\pi\) | ||||
0.160703 | + | 0.987003i | \(0.448624\pi\) | |||||||
\(480\) | 2.95681 | 0.134959 | ||||||||
\(481\) | 57.3631 | 2.61553 | ||||||||
\(482\) | −25.1847 | −1.14713 | ||||||||
\(483\) | 0.210456 | 0.00957607 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.3540 | 1.87779 | ||||||||
\(486\) | −2.43091 | −0.110268 | ||||||||
\(487\) | −15.1823 | −0.687977 | −0.343988 | − | 0.938974i | \(-0.611778\pi\) | ||||
−0.343988 | + | 0.938974i | \(0.611778\pi\) | |||||||
\(488\) | 42.7100 | 1.93339 | ||||||||
\(489\) | 12.0738 | 0.545998 | ||||||||
\(490\) | 8.34022 | 0.376773 | ||||||||
\(491\) | −15.6173 | −0.704801 | −0.352400 | − | 0.935849i | \(-0.614634\pi\) | ||||
−0.352400 | + | 0.935849i | \(0.614634\pi\) | |||||||
\(492\) | −46.7100 | −2.10585 | ||||||||
\(493\) | 8.81705 | 0.397100 | ||||||||
\(494\) | −94.3209 | −4.24370 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.0782 | 0.721930 | ||||||||
\(497\) | −5.19458 | −0.233009 | ||||||||
\(498\) | 1.79385 | 0.0803844 | ||||||||
\(499\) | 9.99383 | 0.447385 | 0.223693 | − | 0.974660i | \(-0.428189\pi\) | ||||
0.223693 | + | 0.974660i | \(0.428189\pi\) | |||||||
\(500\) | 23.7552 | 1.06237 | ||||||||
\(501\) | 2.89932 | 0.129532 | ||||||||
\(502\) | 27.3787 | 1.22197 | ||||||||
\(503\) | −13.6115 | −0.606908 | −0.303454 | − | 0.952846i | \(-0.598140\pi\) | ||||
−0.303454 | + | 0.952846i | \(0.598140\pi\) | |||||||
\(504\) | 4.64136 | 0.206743 | ||||||||
\(505\) | −5.44822 | −0.242443 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.4516 | −1.08593 | ||||||||
\(508\) | −76.3516 | −3.38755 | ||||||||
\(509\) | −20.5379 | −0.910325 | −0.455162 | − | 0.890408i | \(-0.650419\pi\) | ||||
−0.455162 | + | 0.890408i | \(0.650419\pi\) | |||||||
\(510\) | −26.7759 | −1.18566 | ||||||||
\(511\) | −13.1747 | −0.582816 | ||||||||
\(512\) | −35.1417 | −1.55306 | ||||||||
\(513\) | −6.34022 | −0.279928 | ||||||||
\(514\) | −37.1061 | −1.63668 | ||||||||
\(515\) | 32.3277 | 1.42453 | ||||||||
\(516\) | −27.8725 | −1.22702 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −22.7859 | −1.00116 | ||||||||
\(519\) | 14.5713 | 0.639611 | ||||||||
\(520\) | −97.4518 | −4.27354 | ||||||||
\(521\) | 14.7483 | 0.646133 | 0.323067 | − | 0.946376i | \(-0.395286\pi\) | ||||
0.323067 | + | 0.946376i | \(0.395286\pi\) | |||||||
\(522\) | 6.67613 | 0.292206 | ||||||||
\(523\) | −22.1029 | −0.966494 | −0.483247 | − | 0.875484i | \(-0.660543\pi\) | ||||
−0.483247 | + | 0.875484i | \(0.660543\pi\) | |||||||
\(524\) | 75.7429 | 3.30884 | ||||||||
\(525\) | −6.77113 | −0.295516 | ||||||||
\(526\) | −20.5488 | −0.895971 | ||||||||
\(527\) | 14.9009 | 0.649093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9557 | −0.998074 | ||||||||
\(530\) | −52.9981 | −2.30209 | ||||||||
\(531\) | −11.8232 | −0.513084 | ||||||||
\(532\) | 24.7859 | 1.07461 | ||||||||
\(533\) | −73.1214 | −3.16724 | ||||||||
\(534\) | 22.7157 | 0.983004 | ||||||||
\(535\) | 24.1302 | 1.04324 | ||||||||
\(536\) | −18.0569 | −0.779938 | ||||||||
\(537\) | −18.9082 | −0.815950 | ||||||||
\(538\) | −52.0182 | −2.24266 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.4125 | −0.577182 | ||||||||
\(541\) | 6.86201 | 0.295021 | 0.147510 | − | 0.989060i | \(-0.452874\pi\) | ||||
0.147510 | + | 0.989060i | \(0.452874\pi\) | |||||||
\(542\) | 63.7904 | 2.74003 | ||||||||
\(543\) | −15.7713 | −0.676812 | ||||||||
\(544\) | −2.76682 | −0.118626 | ||||||||
\(545\) | −8.13264 | −0.348364 | ||||||||
\(546\) | 14.8766 | 0.636659 | ||||||||
\(547\) | −24.7425 | −1.05791 | −0.528957 | − | 0.848649i | \(-0.677417\pi\) | ||||
−0.528957 | + | 0.848649i | \(0.677417\pi\) | |||||||
\(548\) | −24.0140 | −1.02583 | ||||||||
\(549\) | 9.20204 | 0.392733 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.4125 | 0.741797 | ||||||||
\(552\) | 0.976802 | 0.0415755 | ||||||||
\(553\) | −4.33022 | −0.184140 | ||||||||
\(554\) | −45.1409 | −1.91785 | ||||||||
\(555\) | 32.1593 | 1.36509 | ||||||||
\(556\) | 26.4686 | 1.12252 | ||||||||
\(557\) | 4.14961 | 0.175825 | 0.0879124 | − | 0.996128i | \(-0.471980\pi\) | ||||
0.0879124 | + | 0.996128i | \(0.471980\pi\) | |||||||
\(558\) | 11.2827 | 0.477636 | ||||||||
\(559\) | −43.6325 | −1.84546 | ||||||||
\(560\) | 11.8850 | 0.502233 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.3291 | 0.435706 | ||||||||
\(563\) | −2.86455 | −0.120726 | −0.0603631 | − | 0.998176i | \(-0.519226\pi\) | ||||
−0.0603631 | + | 0.998176i | \(0.519226\pi\) | |||||||
\(564\) | 23.1244 | 0.973711 | ||||||||
\(565\) | 1.40373 | 0.0590556 | ||||||||
\(566\) | 49.9009 | 2.09749 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −24.1099 | −1.01163 | ||||||||
\(569\) | −10.5736 | −0.443268 | −0.221634 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221634 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(570\) | −52.8788 | −2.21485 | ||||||||
\(571\) | 27.2490 | 1.14034 | 0.570169 | − | 0.821528i | \(-0.306878\pi\) | ||||
0.570169 | + | 0.821528i | \(0.306878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.5132 | 0.815175 | ||||||||
\(574\) | 29.0454 | 1.21233 | ||||||||
\(575\) | −1.42502 | −0.0594276 | ||||||||
\(576\) | −9.02320 | −0.375967 | ||||||||
\(577\) | −29.8593 | −1.24306 | −0.621530 | − | 0.783390i | \(-0.713489\pi\) | ||||
−0.621530 | + | 0.783390i | \(0.713489\pi\) | |||||||
\(578\) | −16.2700 | −0.676743 | ||||||||
\(579\) | 22.9830 | 0.955142 | ||||||||
\(580\) | 36.8355 | 1.52951 | ||||||||
\(581\) | −0.737935 | −0.0306147 | ||||||||
\(582\) | −29.3007 | −1.21455 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −61.1487 | −2.53035 | ||||||||
\(585\) | −20.9964 | −0.868093 | ||||||||
\(586\) | −51.5407 | −2.12913 | ||||||||
\(587\) | 10.4659 | 0.431973 | 0.215986 | − | 0.976396i | \(-0.430703\pi\) | ||||
0.215986 | + | 0.976396i | \(0.430703\pi\) | |||||||
\(588\) | −3.90931 | −0.161217 | ||||||||
\(589\) | 29.4273 | 1.21253 | ||||||||
\(590\) | −98.6082 | −4.05964 | ||||||||
\(591\) | −11.3218 | −0.465717 | ||||||||
\(592\) | −32.4705 | −1.33453 | ||||||||
\(593\) | 36.5059 | 1.49912 | 0.749559 | − | 0.661938i | \(-0.230266\pi\) | ||||
0.749559 | + | 0.661938i | \(0.230266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0148 | 0.451562 | ||||||||
\(596\) | −69.6655 | −2.85361 | ||||||||
\(597\) | 6.43837 | 0.263505 | ||||||||
\(598\) | 3.13087 | 0.128031 | ||||||||
\(599\) | 9.49586 | 0.387990 | 0.193995 | − | 0.981002i | \(-0.437855\pi\) | ||||
0.193995 | + | 0.981002i | \(0.437855\pi\) | |||||||
\(600\) | −31.4273 | −1.28301 | ||||||||
\(601\) | −7.98125 | −0.325562 | −0.162781 | − | 0.986662i | \(-0.552046\pi\) | ||||
−0.162781 | + | 0.986662i | \(0.552046\pi\) | |||||||
\(602\) | 17.3318 | 0.706391 | ||||||||
\(603\) | −3.89042 | −0.158430 | ||||||||
\(604\) | 2.38744 | 0.0971435 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.86024 | 0.156811 | ||||||||
\(607\) | 32.4406 | 1.31672 | 0.658362 | − | 0.752701i | \(-0.271250\pi\) | ||||
0.658362 | + | 0.752701i | \(0.271250\pi\) | |||||||
\(608\) | −5.46410 | −0.221599 | ||||||||
\(609\) | −2.74635 | −0.111288 | ||||||||
\(610\) | 76.7470 | 3.10740 | ||||||||
\(611\) | 36.1996 | 1.46448 | ||||||||
\(612\) | 12.5507 | 0.507331 | ||||||||
\(613\) | 33.0240 | 1.33382 | 0.666912 | − | 0.745136i | \(-0.267616\pi\) | ||||
0.666912 | + | 0.745136i | \(0.267616\pi\) | |||||||
\(614\) | 55.9125 | 2.25645 | ||||||||
\(615\) | −40.9938 | −1.65303 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.7478 | 1.96251 | 0.981256 | − | 0.192710i | \(-0.0617275\pi\) | ||||
0.981256 | + | 0.192710i | \(0.0617275\pi\) | |||||||
\(618\) | −22.9052 | −0.921382 | ||||||||
\(619\) | −1.29320 | −0.0519780 | −0.0259890 | − | 0.999662i | \(-0.508273\pi\) | ||||
−0.0259890 | + | 0.999662i | \(0.508273\pi\) | |||||||
\(620\) | 62.2523 | 2.50011 | ||||||||
\(621\) | 0.210456 | 0.00844530 | ||||||||
\(622\) | 17.9098 | 0.718117 | ||||||||
\(623\) | −9.34453 | −0.374381 | ||||||||
\(624\) | 21.1995 | 0.848659 | ||||||||
\(625\) | −13.0075 | −0.520298 | ||||||||
\(626\) | −11.6827 | −0.466935 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.6722 | 1.06434 | ||||||||
\(629\) | −30.0929 | −1.19988 | ||||||||
\(630\) | 8.34022 | 0.332282 | ||||||||
\(631\) | −18.7715 | −0.747280 | −0.373640 | − | 0.927574i | \(-0.621891\pi\) | ||||
−0.373640 | + | 0.927574i | \(0.621891\pi\) | |||||||
\(632\) | −20.0981 | −0.799461 | ||||||||
\(633\) | −20.1287 | −0.800043 | ||||||||
\(634\) | −3.74793 | −0.148849 | ||||||||
\(635\) | −67.0080 | −2.65913 | ||||||||
\(636\) | 24.8418 | 0.985042 | ||||||||
\(637\) | −6.11977 | −0.242474 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.19458 | −0.205494 | ||||||||
\(640\) | −69.3418 | −2.74098 | ||||||||
\(641\) | −17.9563 | −0.709232 | −0.354616 | − | 0.935012i | \(-0.615388\pi\) | ||||
−0.354616 | + | 0.935012i | \(0.615388\pi\) | |||||||
\(642\) | −17.0970 | −0.674767 | ||||||||
\(643\) | 23.2796 | 0.918057 | 0.459028 | − | 0.888422i | \(-0.348198\pi\) | ||||
0.459028 | + | 0.888422i | \(0.348198\pi\) | |||||||
\(644\) | −0.822738 | −0.0324204 | ||||||||
\(645\) | −24.4616 | −0.963173 | ||||||||
\(646\) | 49.4811 | 1.94681 | ||||||||
\(647\) | −42.2211 | −1.65988 | −0.829942 | − | 0.557850i | \(-0.811626\pi\) | ||||
−0.829942 | + | 0.557850i | \(0.811626\pi\) | |||||||
\(648\) | 4.64136 | 0.182330 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −100.731 | −3.95101 | ||||||||
\(651\) | −4.64136 | −0.181909 | ||||||||
\(652\) | −47.2005 | −1.84851 | ||||||||
\(653\) | −1.27048 | −0.0497179 | −0.0248590 | − | 0.999691i | \(-0.507914\pi\) | ||||
−0.0248590 | + | 0.999691i | \(0.507914\pi\) | |||||||
\(654\) | 5.76223 | 0.225321 | ||||||||
\(655\) | 66.4738 | 2.59735 | ||||||||
\(656\) | 41.3904 | 1.61603 | ||||||||
\(657\) | −13.1747 | −0.513995 | ||||||||
\(658\) | −14.3793 | −0.560563 | ||||||||
\(659\) | 35.1838 | 1.37056 | 0.685282 | − | 0.728278i | \(-0.259679\pi\) | ||||
0.685282 | + | 0.728278i | \(0.259679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.90089 | 0.112832 | 0.0564158 | − | 0.998407i | \(-0.482033\pi\) | ||||
0.0564158 | + | 0.998407i | \(0.482033\pi\) | |||||||
\(662\) | −31.3404 | −1.21808 | ||||||||
\(663\) | 19.6472 | 0.763036 | ||||||||
\(664\) | −3.42502 | −0.132917 | ||||||||
\(665\) | 21.7527 | 0.843534 | ||||||||
\(666\) | −22.7859 | −0.882936 | ||||||||
\(667\) | −0.577986 | −0.0223797 | ||||||||
\(668\) | −11.3343 | −0.438539 | ||||||||
\(669\) | 20.8691 | 0.806847 | ||||||||
\(670\) | −32.4470 | −1.25354 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.861816 | 0.0332453 | ||||||||
\(673\) | 37.1846 | 1.43336 | 0.716680 | − | 0.697402i | \(-0.245661\pi\) | ||||
0.716680 | + | 0.697402i | \(0.245661\pi\) | |||||||
\(674\) | −45.3304 | −1.74606 | ||||||||
\(675\) | −6.77113 | −0.260621 | ||||||||
\(676\) | 95.5888 | 3.67649 | ||||||||
\(677\) | 26.7675 | 1.02876 | 0.514379 | − | 0.857563i | \(-0.328022\pi\) | ||||
0.514379 | + | 0.857563i | \(0.328022\pi\) | |||||||
\(678\) | −0.994591 | −0.0381970 | ||||||||
\(679\) | 12.0534 | 0.462566 | ||||||||
\(680\) | 51.1236 | 1.96050 | ||||||||
\(681\) | −3.06892 | −0.117601 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.9076 | 1.56529 | 0.782643 | − | 0.622471i | \(-0.213871\pi\) | ||||
0.782643 | + | 0.622471i | \(0.213871\pi\) | |||||||
\(684\) | 24.7859 | 0.947713 | ||||||||
\(685\) | −21.0753 | −0.805245 | ||||||||
\(686\) | 2.43091 | 0.0928125 | ||||||||
\(687\) | 8.35768 | 0.318865 | ||||||||
\(688\) | 24.6982 | 0.941611 | ||||||||
\(689\) | 38.8882 | 1.48152 | ||||||||
\(690\) | 1.75525 | 0.0668212 | ||||||||
\(691\) | 41.0267 | 1.56073 | 0.780365 | − | 0.625324i | \(-0.215033\pi\) | ||||
0.780365 | + | 0.625324i | \(0.215033\pi\) | |||||||
\(692\) | −56.9639 | −2.16544 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3134 | 1.15068 | ||||||||
\(695\) | 23.2295 | 0.881145 | ||||||||
\(696\) | −12.7468 | −0.483167 | ||||||||
\(697\) | 38.3598 | 1.45298 | ||||||||
\(698\) | 12.4241 | 0.470258 | ||||||||
\(699\) | 5.50270 | 0.208131 | ||||||||
\(700\) | 26.4705 | 1.00049 | ||||||||
\(701\) | 18.6482 | 0.704333 | 0.352167 | − | 0.935937i | \(-0.385445\pi\) | ||||
0.352167 | + | 0.935937i | \(0.385445\pi\) | |||||||
\(702\) | 14.8766 | 0.561481 | ||||||||
\(703\) | −59.4295 | −2.24143 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.2945 | 0.764335 | ||||||||
\(706\) | 64.9991 | 2.44627 | ||||||||
\(707\) | −1.58798 | −0.0597222 | ||||||||
\(708\) | 46.2206 | 1.73708 | ||||||||
\(709\) | −35.4041 | −1.32963 | −0.664814 | − | 0.747009i | \(-0.731489\pi\) | ||||
−0.664814 | + | 0.747009i | \(0.731489\pi\) | |||||||
\(710\) | −43.3239 | −1.62592 | ||||||||
\(711\) | −4.33022 | −0.162396 | ||||||||
\(712\) | −43.3714 | −1.62541 | ||||||||
\(713\) | −0.976802 | −0.0365815 | ||||||||
\(714\) | −7.80432 | −0.292069 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 73.9181 | 2.76245 | ||||||||
\(717\) | −2.30368 | −0.0860324 | ||||||||
\(718\) | 2.12245 | 0.0792090 | ||||||||
\(719\) | 22.9482 | 0.855823 | 0.427912 | − | 0.903821i | \(-0.359249\pi\) | ||||
0.427912 | + | 0.903821i | \(0.359249\pi\) | |||||||
\(720\) | 11.8850 | 0.442928 | ||||||||
\(721\) | 9.42249 | 0.350912 | ||||||||
\(722\) | 51.5314 | 1.91780 | ||||||||
\(723\) | 10.3602 | 0.385300 | ||||||||
\(724\) | 61.6550 | 2.29139 | ||||||||
\(725\) | 18.5959 | 0.690635 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.75027 | 0.176178 | 0.0880889 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880889 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(728\) | −28.4041 | −1.05272 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −109.880 | −4.06685 | ||||||||
\(731\) | 22.8898 | 0.846610 | ||||||||
\(732\) | −35.9736 | −1.32962 | ||||||||
\(733\) | −26.7529 | −0.988141 | −0.494071 | − | 0.869422i | \(-0.664492\pi\) | ||||
−0.494071 | + | 0.869422i | \(0.664492\pi\) | |||||||
\(734\) | 30.2998 | 1.11838 | ||||||||
\(735\) | −3.43091 | −0.126551 | ||||||||
\(736\) | 0.181374 | 0.00668554 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 29.0454 | 1.06918 | ||||||||
\(739\) | −4.44616 | −0.163555 | −0.0817773 | − | 0.996651i | \(-0.526060\pi\) | ||||
−0.0817773 | + | 0.996651i | \(0.526060\pi\) | |||||||
\(740\) | −125.721 | −4.62159 | ||||||||
\(741\) | 38.8007 | 1.42538 | ||||||||
\(742\) | −15.4473 | −0.567087 | ||||||||
\(743\) | 8.17268 | 0.299826 | 0.149913 | − | 0.988699i | \(-0.452101\pi\) | ||||
0.149913 | + | 0.988699i | \(0.452101\pi\) | |||||||
\(744\) | −21.5423 | −0.789777 | ||||||||
\(745\) | −61.1401 | −2.24000 | ||||||||
\(746\) | −5.53317 | −0.202584 | ||||||||
\(747\) | −0.737935 | −0.0269996 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.03319 | 0.256987 | ||||||||
\(750\) | −14.7716 | −0.539383 | ||||||||
\(751\) | −23.9396 | −0.873568 | −0.436784 | − | 0.899566i | \(-0.643883\pi\) | ||||
−0.436784 | + | 0.899566i | \(0.643883\pi\) | |||||||
\(752\) | −20.4908 | −0.747224 | ||||||||
\(753\) | −11.2627 | −0.410437 | ||||||||
\(754\) | −40.8564 | −1.48790 | ||||||||
\(755\) | 2.09527 | 0.0762548 | ||||||||
\(756\) | −3.90931 | −0.142180 | ||||||||
\(757\) | 19.9431 | 0.724845 | 0.362423 | − | 0.932014i | \(-0.381950\pi\) | ||||
0.362423 | + | 0.932014i | \(0.381950\pi\) | |||||||
\(758\) | 50.4596 | 1.83277 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 100.962 | 3.66229 | ||||||||
\(761\) | 10.2909 | 0.373044 | 0.186522 | − | 0.982451i | \(-0.440278\pi\) | ||||
0.186522 | + | 0.982451i | \(0.440278\pi\) | |||||||
\(762\) | 47.4773 | 1.71992 | ||||||||
\(763\) | −2.37040 | −0.0858144 | ||||||||
\(764\) | −76.2831 | −2.75983 | ||||||||
\(765\) | 11.0148 | 0.398240 | ||||||||
\(766\) | −43.3911 | −1.56778 | ||||||||
\(767\) | 72.3553 | 2.61260 | ||||||||
\(768\) | 31.0845 | 1.12167 | ||||||||
\(769\) | −39.4073 | −1.42106 | −0.710531 | − | 0.703665i | \(-0.751545\pi\) | ||||
−0.710531 | + | 0.703665i | \(0.751545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2643 | 0.549731 | ||||||||
\(772\) | −89.8478 | −3.23369 | ||||||||
\(773\) | 22.7516 | 0.818317 | 0.409158 | − | 0.912463i | \(-0.365822\pi\) | ||||
0.409158 | + | 0.912463i | \(0.365822\pi\) | |||||||
\(774\) | 17.3318 | 0.622979 | ||||||||
\(775\) | 31.4273 | 1.12890 | ||||||||
\(776\) | 55.9441 | 2.00828 | ||||||||
\(777\) | 9.37341 | 0.336269 | ||||||||
\(778\) | −20.0296 | −0.718094 | ||||||||
\(779\) | 75.7554 | 2.71422 | ||||||||
\(780\) | 82.0814 | 2.93898 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.64247 | −0.0587344 | ||||||||
\(783\) | −2.74635 | −0.0981467 | ||||||||
\(784\) | 3.46410 | 0.123718 | ||||||||
\(785\) | 23.4082 | 0.835474 | ||||||||
\(786\) | −47.0988 | −1.67996 | ||||||||
\(787\) | −36.2328 | −1.29156 | −0.645780 | − | 0.763524i | \(-0.723467\pi\) | ||||
−0.645780 | + | 0.763524i | \(0.723467\pi\) | |||||||
\(788\) | 44.2605 | 1.57671 | ||||||||
\(789\) | 8.45315 | 0.300940 | ||||||||
\(790\) | −36.1150 | −1.28492 | ||||||||
\(791\) | 0.409144 | 0.0145475 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.3143 | −1.99978 | ||||||||
\(794\) | −39.2459 | −1.39278 | ||||||||
\(795\) | 21.8018 | 0.773230 | ||||||||
\(796\) | −25.1696 | −0.892113 | ||||||||
\(797\) | 21.3161 | 0.755054 | 0.377527 | − | 0.925999i | \(-0.376775\pi\) | ||||
0.377527 | + | 0.925999i | \(0.376775\pi\) | |||||||
\(798\) | −15.4125 | −0.545596 | ||||||||
\(799\) | −18.9905 | −0.671835 | ||||||||
\(800\) | −5.83546 | −0.206315 | ||||||||
\(801\) | −9.34453 | −0.330173 | ||||||||
\(802\) | 66.9072 | 2.36258 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.2089 | 0.536376 | ||||||||
\(805\) | −0.722055 | −0.0254491 | ||||||||
\(806\) | −69.0477 | −2.43210 | ||||||||
\(807\) | 21.3987 | 0.753269 | ||||||||
\(808\) | −7.37040 | −0.259290 | ||||||||
\(809\) | −37.6282 | −1.32294 | −0.661469 | − | 0.749973i | \(-0.730067\pi\) | ||||
−0.661469 | + | 0.749973i | \(0.730067\pi\) | |||||||
\(810\) | 8.34022 | 0.293045 | ||||||||
\(811\) | −3.04195 | −0.106817 | −0.0534087 | − | 0.998573i | \(-0.517009\pi\) | ||||
−0.0534087 | + | 0.998573i | \(0.517009\pi\) | |||||||
\(812\) | 10.7364 | 0.376772 | ||||||||
\(813\) | −26.2414 | −0.920326 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.4243 | −1.45103 | ||||||||
\(816\) | −11.1213 | −0.389325 | ||||||||
\(817\) | 45.2043 | 1.58150 | ||||||||
\(818\) | −41.6342 | −1.45571 | ||||||||
\(819\) | −6.11977 | −0.213842 | ||||||||
\(820\) | 160.258 | 5.59644 | ||||||||
\(821\) | 37.2094 | 1.29862 | 0.649309 | − | 0.760525i | \(-0.275058\pi\) | ||||
0.649309 | + | 0.760525i | \(0.275058\pi\) | |||||||
\(822\) | 14.9325 | 0.520831 | ||||||||
\(823\) | −36.4957 | −1.27216 | −0.636080 | − | 0.771623i | \(-0.719445\pi\) | ||||
−0.636080 | + | 0.771623i | \(0.719445\pi\) | |||||||
\(824\) | 43.7332 | 1.52352 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.7411 | −1.00003 | ||||||||
\(827\) | 52.8436 | 1.83755 | 0.918776 | − | 0.394779i | \(-0.129179\pi\) | ||||
0.918776 | + | 0.394779i | \(0.129179\pi\) | |||||||
\(828\) | −0.822738 | −0.0285921 | ||||||||
\(829\) | −43.4225 | −1.50813 | −0.754063 | − | 0.656802i | \(-0.771909\pi\) | ||||
−0.754063 | + | 0.656802i | \(0.771909\pi\) | |||||||
\(830\) | −6.15454 | −0.213627 | ||||||||
\(831\) | 18.5696 | 0.644171 | ||||||||
\(832\) | 55.2199 | 1.91441 | ||||||||
\(833\) | 3.21046 | 0.111236 | ||||||||
\(834\) | −16.4588 | −0.569923 | ||||||||
\(835\) | −9.94729 | −0.344240 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.64136 | −0.160429 | ||||||||
\(838\) | 35.0038 | 1.20919 | ||||||||
\(839\) | 27.6102 | 0.953211 | 0.476605 | − | 0.879117i | \(-0.341867\pi\) | ||||
0.476605 | + | 0.879117i | \(0.341867\pi\) | |||||||
\(840\) | −15.9241 | −0.549433 | ||||||||
\(841\) | −21.4575 | −0.739915 | ||||||||
\(842\) | −26.9090 | −0.927347 | ||||||||
\(843\) | −4.24906 | −0.146345 | ||||||||
\(844\) | 78.6892 | 2.70860 | ||||||||
\(845\) | 83.8911 | 2.88594 | ||||||||
\(846\) | −14.3793 | −0.494370 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22.0127 | −0.755920 | ||||||||
\(849\) | −20.5277 | −0.704508 | ||||||||
\(850\) | 52.8441 | 1.81254 | ||||||||
\(851\) | 1.97269 | 0.0676229 | ||||||||
\(852\) | 20.3072 | 0.695714 | ||||||||
\(853\) | 22.4005 | 0.766980 | 0.383490 | − | 0.923545i | \(-0.374722\pi\) | ||||
0.383490 | + | 0.923545i | \(0.374722\pi\) | |||||||
\(854\) | 22.3693 | 0.765462 | ||||||||
\(855\) | 21.7527 | 0.743927 | ||||||||
\(856\) | 32.6436 | 1.11574 | ||||||||
\(857\) | −8.30018 | −0.283529 | −0.141764 | − | 0.989900i | \(-0.545278\pi\) | ||||
−0.141764 | + | 0.989900i | \(0.545278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.09088 | 0.173699 | 0.0868493 | − | 0.996221i | \(-0.472320\pi\) | ||||
0.0868493 | + | 0.996221i | \(0.472320\pi\) | |||||||
\(860\) | 95.6279 | 3.26088 | ||||||||
\(861\) | −11.9484 | −0.407200 | ||||||||
\(862\) | 37.9641 | 1.29306 | ||||||||
\(863\) | 44.7322 | 1.52270 | 0.761352 | − | 0.648339i | \(-0.224536\pi\) | ||||
0.761352 | + | 0.648339i | \(0.224536\pi\) | |||||||
\(864\) | 0.861816 | 0.0293196 | ||||||||
\(865\) | −49.9929 | −1.69981 | ||||||||
\(866\) | 5.28574 | 0.179617 | ||||||||
\(867\) | 6.69297 | 0.227305 | ||||||||
\(868\) | 18.1445 | 0.615866 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −22.9052 | −0.776559 | ||||||||
\(871\) | 23.8085 | 0.806720 | ||||||||
\(872\) | −11.0019 | −0.372572 | ||||||||
\(873\) | 12.0534 | 0.407945 | ||||||||
\(874\) | −3.24365 | −0.109718 | ||||||||
\(875\) | 6.07658 | 0.205426 | ||||||||
\(876\) | 51.5041 | 1.74016 | ||||||||
\(877\) | −8.54938 | −0.288692 | −0.144346 | − | 0.989527i | \(-0.546108\pi\) | ||||
−0.144346 | + | 0.989527i | \(0.546108\pi\) | |||||||
\(878\) | −22.9654 | −0.775046 | ||||||||
\(879\) | 21.2022 | 0.715134 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.1169 | 1.28419 | 0.642095 | − | 0.766625i | \(-0.278065\pi\) | ||||
0.642095 | + | 0.766625i | \(0.278065\pi\) | |||||||
\(882\) | 2.43091 | 0.0818529 | ||||||||
\(883\) | 2.36088 | 0.0794500 | 0.0397250 | − | 0.999211i | \(-0.487352\pi\) | ||||
0.0397250 | + | 0.999211i | \(0.487352\pi\) | |||||||
\(884\) | −76.8072 | −2.58331 | ||||||||
\(885\) | 40.5644 | 1.36356 | ||||||||
\(886\) | 19.6593 | 0.660469 | ||||||||
\(887\) | 11.5996 | 0.389477 | 0.194738 | − | 0.980855i | \(-0.437614\pi\) | ||||
0.194738 | + | 0.980855i | \(0.437614\pi\) | |||||||
\(888\) | 43.5054 | 1.45995 | ||||||||
\(889\) | −19.5307 | −0.655038 | ||||||||
\(890\) | −77.9354 | −2.61240 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −81.5840 | −2.73163 | ||||||||
\(893\) | −37.5037 | −1.25501 | ||||||||
\(894\) | 43.3197 | 1.44883 | ||||||||
\(895\) | 64.8723 | 2.16844 | ||||||||
\(896\) | −20.2109 | −0.675200 | ||||||||
\(897\) | −1.28794 | −0.0430031 | ||||||||
\(898\) | −69.4864 | −2.31879 | ||||||||
\(899\) | 12.7468 | 0.425131 | ||||||||
\(900\) | 26.4705 | 0.882349 | ||||||||
\(901\) | −20.4009 | −0.679653 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.12976 | −0.237264 | ||||||||
\(904\) | 1.89899 | 0.0631593 | ||||||||
\(905\) | 54.1100 | 1.79868 | ||||||||
\(906\) | −1.48457 | −0.0493215 | ||||||||
\(907\) | −5.25241 | −0.174403 | −0.0872017 | − | 0.996191i | \(-0.527792\pi\) | ||||
−0.0872017 | + | 0.996191i | \(0.527792\pi\) | |||||||
\(908\) | 11.9974 | 0.398147 | ||||||||
\(909\) | −1.58798 | −0.0526701 | ||||||||
\(910\) | −51.0402 | −1.69197 | ||||||||
\(911\) | 14.4254 | 0.477934 | 0.238967 | − | 0.971028i | \(-0.423191\pi\) | ||||
0.238967 | + | 0.971028i | \(0.423191\pi\) | |||||||
\(912\) | −21.9632 | −0.727273 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 20.0723 | 0.663933 | ||||||||
\(915\) | −31.5713 | −1.04372 | ||||||||
\(916\) | −32.6728 | −1.07954 | ||||||||
\(917\) | 19.3750 | 0.639819 | ||||||||
\(918\) | −7.80432 | −0.257581 | ||||||||
\(919\) | −0.440140 | −0.0145189 | −0.00725945 | − | 0.999974i | \(-0.502311\pi\) | ||||
−0.00725945 | + | 0.999974i | \(0.502311\pi\) | |||||||
\(920\) | −3.35132 | −0.110490 | ||||||||
\(921\) | −23.0007 | −0.757898 | ||||||||
\(922\) | −32.4152 | −1.06754 | ||||||||
\(923\) | 31.7896 | 1.04637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −63.4686 | −2.08683 | ||||||||
\(926\) | 64.7786 | 2.12876 | ||||||||
\(927\) | 9.42249 | 0.309475 | ||||||||
\(928\) | −2.36685 | −0.0776957 | ||||||||
\(929\) | −44.8443 | −1.47130 | −0.735648 | − | 0.677364i | \(-0.763122\pi\) | ||||
−0.735648 | + | 0.677364i | \(0.763122\pi\) | |||||||
\(930\) | −38.7100 | −1.26935 | ||||||||
\(931\) | 6.34022 | 0.207792 | ||||||||
\(932\) | −21.5118 | −0.704642 | ||||||||
\(933\) | −7.36753 | −0.241202 | ||||||||
\(934\) | 70.0573 | 2.29234 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −28.4041 | −0.928416 | ||||||||
\(937\) | −25.6547 | −0.838103 | −0.419051 | − | 0.907963i | \(-0.637637\pi\) | ||||
−0.419051 | + | 0.907963i | \(0.637637\pi\) | |||||||
\(938\) | −9.45726 | −0.308790 | ||||||||
\(939\) | 4.80590 | 0.156835 | ||||||||
\(940\) | −79.3375 | −2.58771 | ||||||||
\(941\) | 47.6122 | 1.55211 | 0.776056 | − | 0.630663i | \(-0.217217\pi\) | ||||
0.776056 | + | 0.630663i | \(0.217217\pi\) | |||||||
\(942\) | −16.5854 | −0.540383 | ||||||||
\(943\) | −2.51461 | −0.0818869 | ||||||||
\(944\) | −40.9568 | −1.33303 | ||||||||
\(945\) | −3.43091 | −0.111607 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.8549 | −1.42509 | −0.712546 | − | 0.701625i | \(-0.752458\pi\) | ||||
−0.712546 | + | 0.701625i | \(0.752458\pi\) | |||||||
\(948\) | 16.9282 | 0.549802 | ||||||||
\(949\) | 80.6263 | 2.61724 | ||||||||
\(950\) | 104.360 | 3.38588 | ||||||||
\(951\) | 1.54178 | 0.0499957 | ||||||||
\(952\) | 14.9009 | 0.482941 | ||||||||
\(953\) | 30.5035 | 0.988106 | 0.494053 | − | 0.869432i | \(-0.335515\pi\) | ||||
0.494053 | + | 0.869432i | \(0.335515\pi\) | |||||||
\(954\) | −15.4473 | −0.500124 | ||||||||
\(955\) | −66.9479 | −2.16638 | ||||||||
\(956\) | 9.00580 | 0.291268 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.0997 | 0.552467 | ||||||||
\(959\) | −6.14277 | −0.198360 | ||||||||
\(960\) | 30.9578 | 0.999157 | ||||||||
\(961\) | −9.45774 | −0.305088 | ||||||||
\(962\) | 139.444 | 4.49587 | ||||||||
\(963\) | 7.03319 | 0.226642 | ||||||||
\(964\) | −40.5013 | −1.30446 | ||||||||
\(965\) | −78.8526 | −2.53836 | ||||||||
\(966\) | 0.511599 | 0.0164604 | ||||||||
\(967\) | 14.1404 | 0.454726 | 0.227363 | − | 0.973810i | \(-0.426990\pi\) | ||||
0.227363 | + | 0.973810i | \(0.426990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.3550 | −0.653897 | ||||||||
\(970\) | 100.528 | 3.22776 | ||||||||
\(971\) | 18.1712 | 0.583141 | 0.291571 | − | 0.956549i | \(-0.405822\pi\) | ||||
0.291571 | + | 0.956549i | \(0.405822\pi\) | |||||||
\(972\) | −3.90931 | −0.125391 | ||||||||
\(973\) | 6.77065 | 0.217057 | ||||||||
\(974\) | −36.9068 | −1.18257 | ||||||||
\(975\) | 41.4377 | 1.32707 | ||||||||
\(976\) | 31.8768 | 1.02035 | ||||||||
\(977\) | 47.4599 | 1.51838 | 0.759188 | − | 0.650871i | \(-0.225596\pi\) | ||||
0.759188 | + | 0.650871i | \(0.225596\pi\) | |||||||
\(978\) | 29.3504 | 0.938523 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 13.4125 | 0.428446 | ||||||||
\(981\) | −2.37040 | −0.0756812 | ||||||||
\(982\) | −37.9643 | −1.21149 | ||||||||
\(983\) | 53.8977 | 1.71907 | 0.859535 | − | 0.511076i | \(-0.170753\pi\) | ||||
0.859535 | + | 0.511076i | \(0.170753\pi\) | |||||||
\(984\) | −55.4568 | −1.76790 | ||||||||
\(985\) | 38.8441 | 1.23767 | ||||||||
\(986\) | 21.4334 | 0.682580 | ||||||||
\(987\) | 5.91520 | 0.188283 | ||||||||
\(988\) | −151.684 | −4.82571 | ||||||||
\(989\) | −1.50050 | −0.0477132 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.06529 | −0.160904 | −0.0804521 | − | 0.996758i | \(-0.525636\pi\) | ||||
−0.0804521 | + | 0.996758i | \(0.525636\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | 12.8925 | 0.409130 | ||||||||
\(994\) | −12.6275 | −0.400521 | ||||||||
\(995\) | −22.0894 | −0.700283 | ||||||||
\(996\) | 2.88482 | 0.0914090 | ||||||||
\(997\) | 14.8081 | 0.468979 | 0.234489 | − | 0.972119i | \(-0.424658\pi\) | ||||
0.234489 | + | 0.972119i | \(0.424658\pi\) | |||||||
\(998\) | 24.2941 | 0.769015 | ||||||||
\(999\) | 9.37341 | 0.296562 |
(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 | 2541.2.a.bo.1.4 | yes | 4 | |
3.2 | odd | 2 | 7623.2.a.cf.1.1 | 4 | |||
11.10 | odd | 2 | 2541.2.a.bk.1.1 | ✓ | 4 | ||
33.32 | even | 2 | 7623.2.a.cm.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bk.1.1 | ✓ | 4 | 11.10 | odd | 2 | ||
2541.2.a.bo.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
7623.2.a.cf.1.1 | 4 | 3.2 | odd | 2 | |||
7623.2.a.cm.1.4 | 4 | 33.32 | even | 2 |