Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.64420 | 1.16263 | 0.581314 | − | 0.813680i | \(-0.302539\pi\) | ||||
0.581314 | + | 0.813680i | \(0.302539\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.703405 | 0.351702 | ||||||||
\(5\) | −3.28206 | −1.46778 | −0.733891 | − | 0.679267i | \(-0.762298\pi\) | ||||
−0.733891 | + | 0.679267i | \(0.762298\pi\) | |||||||
\(6\) | −1.64420 | −0.671243 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.13187 | −0.753729 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.39638 | −1.70648 | ||||||||
\(11\) | −3.35789 | −1.01244 | −0.506221 | − | 0.862404i | \(-0.668958\pi\) | ||||
−0.506221 | + | 0.862404i | \(0.668958\pi\) | |||||||
\(12\) | −0.703405 | −0.203055 | ||||||||
\(13\) | −5.75857 | −1.59714 | −0.798571 | − | 0.601901i | \(-0.794410\pi\) | ||||
−0.798571 | + | 0.601901i | \(0.794410\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.28206 | 0.847425 | ||||||||
\(16\) | −4.91203 | −1.22801 | ||||||||
\(17\) | −6.12943 | −1.48661 | −0.743303 | − | 0.668955i | \(-0.766742\pi\) | ||||
−0.743303 | + | 0.668955i | \(0.766742\pi\) | |||||||
\(18\) | 1.64420 | 0.387542 | ||||||||
\(19\) | −3.14030 | −0.720434 | −0.360217 | − | 0.932869i | \(-0.617297\pi\) | ||||
−0.360217 | + | 0.932869i | \(0.617297\pi\) | |||||||
\(20\) | −2.30862 | −0.516223 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.52106 | −1.17709 | ||||||||
\(23\) | −9.17799 | −1.91374 | −0.956871 | − | 0.290512i | \(-0.906174\pi\) | ||||
−0.956871 | + | 0.290512i | \(0.906174\pi\) | |||||||
\(24\) | 2.13187 | 0.435165 | ||||||||
\(25\) | 5.77193 | 1.15439 | ||||||||
\(26\) | −9.46827 | −1.85688 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.986050 | 0.183105 | 0.0915524 | − | 0.995800i | \(-0.470817\pi\) | ||||
0.0915524 | + | 0.995800i | \(0.470817\pi\) | |||||||
\(30\) | 5.39638 | 0.985239 | ||||||||
\(31\) | 4.50254 | 0.808680 | 0.404340 | − | 0.914609i | \(-0.367501\pi\) | ||||
0.404340 | + | 0.914609i | \(0.367501\pi\) | |||||||
\(32\) | −3.81265 | −0.673987 | ||||||||
\(33\) | 3.35789 | 0.584534 | ||||||||
\(34\) | −10.0780 | −1.72837 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.703405 | 0.117234 | ||||||||
\(37\) | 11.7958 | 1.93922 | 0.969611 | − | 0.244651i | \(-0.0786733\pi\) | ||||
0.969611 | + | 0.244651i | \(0.0786733\pi\) | |||||||
\(38\) | −5.16329 | −0.837596 | ||||||||
\(39\) | 5.75857 | 0.922110 | ||||||||
\(40\) | 6.99692 | 1.10631 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.67969 | 1.17114 | 0.585571 | − | 0.810621i | \(-0.300870\pi\) | ||||
0.585571 | + | 0.810621i | \(0.300870\pi\) | |||||||
\(44\) | −2.36196 | −0.356078 | ||||||||
\(45\) | −3.28206 | −0.489261 | ||||||||
\(46\) | −15.0905 | −2.22497 | ||||||||
\(47\) | −12.0154 | −1.75262 | −0.876311 | − | 0.481746i | \(-0.840003\pi\) | ||||
−0.876311 | + | 0.481746i | \(0.840003\pi\) | |||||||
\(48\) | 4.91203 | 0.708991 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.49023 | 1.34212 | ||||||||
\(51\) | 6.12943 | 0.858292 | ||||||||
\(52\) | −4.05061 | −0.561718 | ||||||||
\(53\) | −2.61317 | −0.358947 | −0.179473 | − | 0.983763i | \(-0.557439\pi\) | ||||
−0.179473 | + | 0.983763i | \(0.557439\pi\) | |||||||
\(54\) | −1.64420 | −0.223748 | ||||||||
\(55\) | 11.0208 | 1.48605 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.14030 | 0.415943 | ||||||||
\(58\) | 1.62127 | 0.212883 | ||||||||
\(59\) | −11.2245 | −1.46131 | −0.730654 | − | 0.682748i | \(-0.760785\pi\) | ||||
−0.730654 | + | 0.682748i | \(0.760785\pi\) | |||||||
\(60\) | 2.30862 | 0.298041 | ||||||||
\(61\) | −1.80269 | −0.230810 | −0.115405 | − | 0.993319i | \(-0.536817\pi\) | ||||
−0.115405 | + | 0.993319i | \(0.536817\pi\) | |||||||
\(62\) | 7.40309 | 0.940194 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.55530 | 0.444412 | ||||||||
\(65\) | 18.9000 | 2.34426 | ||||||||
\(66\) | 5.52106 | 0.679595 | ||||||||
\(67\) | −13.1550 | −1.60714 | −0.803571 | − | 0.595209i | \(-0.797069\pi\) | ||||
−0.803571 | + | 0.595209i | \(0.797069\pi\) | |||||||
\(68\) | −4.31147 | −0.522843 | ||||||||
\(69\) | 9.17799 | 1.10490 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.92317 | −0.702951 | −0.351475 | − | 0.936197i | \(-0.614320\pi\) | ||||
−0.351475 | + | 0.936197i | \(0.614320\pi\) | |||||||
\(72\) | −2.13187 | −0.251243 | ||||||||
\(73\) | 9.66466 | 1.13116 | 0.565581 | − | 0.824692i | \(-0.308652\pi\) | ||||
0.565581 | + | 0.824692i | \(0.308652\pi\) | |||||||
\(74\) | 19.3947 | 2.25459 | ||||||||
\(75\) | −5.77193 | −0.666485 | ||||||||
\(76\) | −2.20890 | −0.253378 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.46827 | 1.07207 | ||||||||
\(79\) | −8.44944 | −0.950637 | −0.475318 | − | 0.879814i | \(-0.657667\pi\) | ||||
−0.475318 | + | 0.879814i | \(0.657667\pi\) | |||||||
\(80\) | 16.1216 | 1.80245 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.64420 | 0.181572 | ||||||||
\(83\) | −5.92934 | −0.650830 | −0.325415 | − | 0.945571i | \(-0.605504\pi\) | ||||
−0.325415 | + | 0.945571i | \(0.605504\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.1172 | 2.18201 | ||||||||
\(86\) | 12.6270 | 1.36160 | ||||||||
\(87\) | −0.986050 | −0.105716 | ||||||||
\(88\) | 7.15857 | 0.763107 | ||||||||
\(89\) | −11.3923 | −1.20758 | −0.603788 | − | 0.797145i | \(-0.706343\pi\) | ||||
−0.603788 | + | 0.797145i | \(0.706343\pi\) | |||||||
\(90\) | −5.39638 | −0.568828 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.45584 | −0.673068 | ||||||||
\(93\) | −4.50254 | −0.466892 | ||||||||
\(94\) | −19.7557 | −2.03765 | ||||||||
\(95\) | 10.3067 | 1.05744 | ||||||||
\(96\) | 3.81265 | 0.389127 | ||||||||
\(97\) | 11.7824 | 1.19632 | 0.598160 | − | 0.801377i | \(-0.295899\pi\) | ||||
0.598160 | + | 0.801377i | \(0.295899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.35789 | −0.337481 | ||||||||
\(100\) | 4.06001 | 0.406001 | ||||||||
\(101\) | 4.37589 | 0.435417 | 0.217708 | − | 0.976014i | \(-0.430142\pi\) | ||||
0.217708 | + | 0.976014i | \(0.430142\pi\) | |||||||
\(102\) | 10.0780 | 0.997874 | ||||||||
\(103\) | −7.57841 | −0.746723 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(104\) | 12.2765 | 1.20381 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.29659 | −0.417321 | ||||||||
\(107\) | 20.3029 | 1.96276 | 0.981380 | − | 0.192078i | \(-0.0615226\pi\) | ||||
0.981380 | + | 0.192078i | \(0.0615226\pi\) | |||||||
\(108\) | −0.703405 | −0.0676852 | ||||||||
\(109\) | −6.23589 | −0.597290 | −0.298645 | − | 0.954364i | \(-0.596535\pi\) | ||||
−0.298645 | + | 0.954364i | \(0.596535\pi\) | |||||||
\(110\) | 18.1204 | 1.72772 | ||||||||
\(111\) | −11.7958 | −1.11961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.17038 | −0.298245 | −0.149122 | − | 0.988819i | \(-0.547645\pi\) | ||||
−0.149122 | + | 0.988819i | \(0.547645\pi\) | |||||||
\(114\) | 5.16329 | 0.483586 | ||||||||
\(115\) | 30.1227 | 2.80896 | ||||||||
\(116\) | 0.693592 | 0.0643984 | ||||||||
\(117\) | −5.75857 | −0.532380 | ||||||||
\(118\) | −18.4554 | −1.69896 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.99692 | −0.638728 | ||||||||
\(121\) | 0.275433 | 0.0250393 | ||||||||
\(122\) | −2.96398 | −0.268346 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 3.16711 | 0.284415 | ||||||||
\(125\) | −2.53353 | −0.226606 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.07325 | 0.716385 | 0.358193 | − | 0.933648i | \(-0.383393\pi\) | ||||
0.358193 | + | 0.933648i | \(0.383393\pi\) | |||||||
\(128\) | 13.4709 | 1.19067 | ||||||||
\(129\) | −7.67969 | −0.676159 | ||||||||
\(130\) | 31.0754 | 2.72550 | ||||||||
\(131\) | 9.14130 | 0.798679 | 0.399340 | − | 0.916803i | \(-0.369239\pi\) | ||||
0.399340 | + | 0.916803i | \(0.369239\pi\) | |||||||
\(132\) | 2.36196 | 0.205582 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −21.6295 | −1.86851 | ||||||||
\(135\) | 3.28206 | 0.282475 | ||||||||
\(136\) | 13.0671 | 1.12050 | ||||||||
\(137\) | −6.53936 | −0.558695 | −0.279348 | − | 0.960190i | \(-0.590118\pi\) | ||||
−0.279348 | + | 0.960190i | \(0.590118\pi\) | |||||||
\(138\) | 15.0905 | 1.28459 | ||||||||
\(139\) | −8.98420 | −0.762030 | −0.381015 | − | 0.924569i | \(-0.624425\pi\) | ||||
−0.381015 | + | 0.924569i | \(0.624425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0154 | 1.01188 | ||||||||
\(142\) | −9.73890 | −0.817270 | ||||||||
\(143\) | 19.3367 | 1.61701 | ||||||||
\(144\) | −4.91203 | −0.409336 | ||||||||
\(145\) | −3.23628 | −0.268758 | ||||||||
\(146\) | 15.8907 | 1.31512 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.29724 | 0.682029 | ||||||||
\(149\) | 0.272952 | 0.0223611 | 0.0111805 | − | 0.999937i | \(-0.496441\pi\) | ||||
0.0111805 | + | 0.999937i | \(0.496441\pi\) | |||||||
\(150\) | −9.49023 | −0.774874 | ||||||||
\(151\) | −6.62811 | −0.539388 | −0.269694 | − | 0.962946i | \(-0.586923\pi\) | ||||
−0.269694 | + | 0.962946i | \(0.586923\pi\) | |||||||
\(152\) | 6.69470 | 0.543011 | ||||||||
\(153\) | −6.12943 | −0.495535 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.7776 | −1.18697 | ||||||||
\(156\) | 4.05061 | 0.324308 | ||||||||
\(157\) | −23.3131 | −1.86058 | −0.930292 | − | 0.366819i | \(-0.880447\pi\) | ||||
−0.930292 | + | 0.366819i | \(0.880447\pi\) | |||||||
\(158\) | −13.8926 | −1.10524 | ||||||||
\(159\) | 2.61317 | 0.207238 | ||||||||
\(160\) | 12.5133 | 0.989266 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.64420 | 0.129181 | ||||||||
\(163\) | −21.0309 | −1.64727 | −0.823634 | − | 0.567122i | \(-0.808057\pi\) | ||||
−0.823634 | + | 0.567122i | \(0.808057\pi\) | |||||||
\(164\) | 0.703405 | 0.0549267 | ||||||||
\(165\) | −11.0208 | −0.857969 | ||||||||
\(166\) | −9.74905 | −0.756673 | ||||||||
\(167\) | 3.40709 | 0.263648 | 0.131824 | − | 0.991273i | \(-0.457917\pi\) | ||||
0.131824 | + | 0.991273i | \(0.457917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.1612 | 1.55086 | ||||||||
\(170\) | 33.0767 | 2.53687 | ||||||||
\(171\) | −3.14030 | −0.240145 | ||||||||
\(172\) | 5.40193 | 0.411893 | ||||||||
\(173\) | −4.48482 | −0.340974 | −0.170487 | − | 0.985360i | \(-0.554534\pi\) | ||||
−0.170487 | + | 0.985360i | \(0.554534\pi\) | |||||||
\(174\) | −1.62127 | −0.122908 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.4941 | 1.24329 | ||||||||
\(177\) | 11.2245 | 0.843687 | ||||||||
\(178\) | −18.7312 | −1.40396 | ||||||||
\(179\) | 13.9561 | 1.04313 | 0.521565 | − | 0.853211i | \(-0.325348\pi\) | ||||
0.521565 | + | 0.853211i | \(0.325348\pi\) | |||||||
\(180\) | −2.30862 | −0.172074 | ||||||||
\(181\) | 9.21198 | 0.684721 | 0.342361 | − | 0.939569i | \(-0.388774\pi\) | ||||
0.342361 | + | 0.939569i | \(0.388774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.80269 | 0.133258 | ||||||||
\(184\) | 19.5662 | 1.44244 | ||||||||
\(185\) | −38.7147 | −2.84636 | ||||||||
\(186\) | −7.40309 | −0.542821 | ||||||||
\(187\) | 20.5820 | 1.50510 | ||||||||
\(188\) | −8.45167 | −0.616401 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.9462 | 1.22941 | ||||||||
\(191\) | −18.9462 | −1.37090 | −0.685451 | − | 0.728119i | \(-0.740395\pi\) | ||||
−0.685451 | + | 0.728119i | \(0.740395\pi\) | |||||||
\(192\) | −3.55530 | −0.256581 | ||||||||
\(193\) | −15.5168 | −1.11692 | −0.558461 | − | 0.829531i | \(-0.688608\pi\) | ||||
−0.558461 | + | 0.829531i | \(0.688608\pi\) | |||||||
\(194\) | 19.3726 | 1.39087 | ||||||||
\(195\) | −18.9000 | −1.35346 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.07929 | 0.219390 | 0.109695 | − | 0.993965i | \(-0.465013\pi\) | ||||
0.109695 | + | 0.993965i | \(0.465013\pi\) | |||||||
\(198\) | −5.52106 | −0.392364 | ||||||||
\(199\) | −5.82235 | −0.412736 | −0.206368 | − | 0.978474i | \(-0.566164\pi\) | ||||
−0.206368 | + | 0.978474i | \(0.566164\pi\) | |||||||
\(200\) | −12.3050 | −0.870094 | ||||||||
\(201\) | 13.1550 | 0.927884 | ||||||||
\(202\) | 7.19485 | 0.506228 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.31147 | 0.301863 | ||||||||
\(205\) | −3.28206 | −0.229229 | ||||||||
\(206\) | −12.4604 | −0.868160 | ||||||||
\(207\) | −9.17799 | −0.637914 | ||||||||
\(208\) | 28.2863 | 1.96130 | ||||||||
\(209\) | 10.5448 | 0.729398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.1035 | −1.31514 | −0.657569 | − | 0.753394i | \(-0.728415\pi\) | ||||
−0.657569 | + | 0.753394i | \(0.728415\pi\) | |||||||
\(212\) | −1.83812 | −0.126242 | ||||||||
\(213\) | 5.92317 | 0.405849 | ||||||||
\(214\) | 33.3822 | 2.28196 | ||||||||
\(215\) | −25.2052 | −1.71898 | ||||||||
\(216\) | 2.13187 | 0.145055 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.2531 | −0.694426 | ||||||||
\(219\) | −9.66466 | −0.653077 | ||||||||
\(220\) | 7.75209 | 0.522646 | ||||||||
\(221\) | 35.2968 | 2.37432 | ||||||||
\(222\) | −19.3947 | −1.30169 | ||||||||
\(223\) | 27.3295 | 1.83012 | 0.915059 | − | 0.403320i | \(-0.132144\pi\) | ||||
0.915059 | + | 0.403320i | \(0.132144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.77193 | 0.384796 | ||||||||
\(226\) | −5.21275 | −0.346747 | ||||||||
\(227\) | −6.27102 | −0.416222 | −0.208111 | − | 0.978105i | \(-0.566732\pi\) | ||||
−0.208111 | + | 0.978105i | \(0.566732\pi\) | |||||||
\(228\) | 2.20890 | 0.146288 | ||||||||
\(229\) | 7.57515 | 0.500580 | 0.250290 | − | 0.968171i | \(-0.419474\pi\) | ||||
0.250290 | + | 0.968171i | \(0.419474\pi\) | |||||||
\(230\) | 49.5279 | 3.26577 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.10213 | −0.138011 | ||||||||
\(233\) | −1.10598 | −0.0724553 | −0.0362276 | − | 0.999344i | \(-0.511534\pi\) | ||||
−0.0362276 | + | 0.999344i | \(0.511534\pi\) | |||||||
\(234\) | −9.46827 | −0.618960 | ||||||||
\(235\) | 39.4352 | 2.57247 | ||||||||
\(236\) | −7.89538 | −0.513946 | ||||||||
\(237\) | 8.44944 | 0.548850 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.1910 | 1.17668 | 0.588339 | − | 0.808615i | \(-0.299782\pi\) | ||||
0.588339 | + | 0.808615i | \(0.299782\pi\) | |||||||
\(240\) | −16.1216 | −1.04064 | ||||||||
\(241\) | −20.6913 | −1.33284 | −0.666422 | − | 0.745575i | \(-0.732175\pi\) | ||||
−0.666422 | + | 0.745575i | \(0.732175\pi\) | |||||||
\(242\) | 0.452867 | 0.0291114 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.26802 | −0.0811765 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.64420 | −0.104831 | ||||||||
\(247\) | 18.0836 | 1.15063 | ||||||||
\(248\) | −9.59882 | −0.609525 | ||||||||
\(249\) | 5.92934 | 0.375757 | ||||||||
\(250\) | −4.16564 | −0.263458 | ||||||||
\(251\) | 2.49992 | 0.157793 | 0.0788967 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788967 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.8187 | 1.93755 | ||||||||
\(254\) | 13.2741 | 0.832889 | ||||||||
\(255\) | −20.1172 | −1.25979 | ||||||||
\(256\) | 15.0383 | 0.939896 | ||||||||
\(257\) | −12.6110 | −0.786650 | −0.393325 | − | 0.919400i | \(-0.628675\pi\) | ||||
−0.393325 | + | 0.919400i | \(0.628675\pi\) | |||||||
\(258\) | −12.6270 | −0.786121 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.2943 | 0.824481 | ||||||||
\(261\) | 0.986050 | 0.0610350 | ||||||||
\(262\) | 15.0302 | 0.928566 | ||||||||
\(263\) | −21.2852 | −1.31250 | −0.656250 | − | 0.754544i | \(-0.727858\pi\) | ||||
−0.656250 | + | 0.754544i | \(0.727858\pi\) | |||||||
\(264\) | −7.15857 | −0.440580 | ||||||||
\(265\) | 8.57659 | 0.526856 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.3923 | 0.697195 | ||||||||
\(268\) | −9.25331 | −0.565236 | ||||||||
\(269\) | 26.5602 | 1.61940 | 0.809701 | − | 0.586842i | \(-0.199629\pi\) | ||||
0.809701 | + | 0.586842i | \(0.199629\pi\) | |||||||
\(270\) | 5.39638 | 0.328413 | ||||||||
\(271\) | −11.8390 | −0.719170 | −0.359585 | − | 0.933112i | \(-0.617082\pi\) | ||||
−0.359585 | + | 0.933112i | \(0.617082\pi\) | |||||||
\(272\) | 30.1080 | 1.82556 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.7520 | −0.649555 | ||||||||
\(275\) | −19.3815 | −1.16875 | ||||||||
\(276\) | 6.45584 | 0.388596 | ||||||||
\(277\) | −19.3182 | −1.16072 | −0.580360 | − | 0.814360i | \(-0.697088\pi\) | ||||
−0.580360 | + | 0.814360i | \(0.697088\pi\) | |||||||
\(278\) | −14.7718 | −0.885957 | ||||||||
\(279\) | 4.50254 | 0.269560 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2205 | −1.02729 | −0.513645 | − | 0.858003i | \(-0.671705\pi\) | ||||
−0.513645 | + | 0.858003i | \(0.671705\pi\) | |||||||
\(282\) | 19.7557 | 1.17644 | ||||||||
\(283\) | 21.7400 | 1.29231 | 0.646156 | − | 0.763206i | \(-0.276376\pi\) | ||||
0.646156 | + | 0.763206i | \(0.276376\pi\) | |||||||
\(284\) | −4.16639 | −0.247230 | ||||||||
\(285\) | −10.3067 | −0.610513 | ||||||||
\(286\) | 31.7934 | 1.87998 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.81265 | −0.224662 | ||||||||
\(289\) | 20.5699 | 1.20999 | ||||||||
\(290\) | −5.32110 | −0.312466 | ||||||||
\(291\) | −11.7824 | −0.690696 | ||||||||
\(292\) | 6.79817 | 0.397833 | ||||||||
\(293\) | 3.46874 | 0.202646 | 0.101323 | − | 0.994854i | \(-0.467692\pi\) | ||||
0.101323 | + | 0.994854i | \(0.467692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.8396 | 2.14488 | ||||||||
\(296\) | −25.1471 | −1.46165 | ||||||||
\(297\) | 3.35789 | 0.194845 | ||||||||
\(298\) | 0.448788 | 0.0259976 | ||||||||
\(299\) | 52.8521 | 3.05652 | ||||||||
\(300\) | −4.06001 | −0.234405 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.8980 | −0.627107 | ||||||||
\(303\) | −4.37589 | −0.251388 | ||||||||
\(304\) | 15.4252 | 0.884698 | ||||||||
\(305\) | 5.91653 | 0.338779 | ||||||||
\(306\) | −10.0780 | −0.576123 | ||||||||
\(307\) | 26.8694 | 1.53352 | 0.766758 | − | 0.641937i | \(-0.221869\pi\) | ||||
0.766758 | + | 0.641937i | \(0.221869\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.57841 | 0.431121 | ||||||||
\(310\) | −24.2974 | −1.38000 | ||||||||
\(311\) | −28.0423 | −1.59013 | −0.795066 | − | 0.606523i | \(-0.792564\pi\) | ||||
−0.795066 | + | 0.606523i | \(0.792564\pi\) | |||||||
\(312\) | −12.2765 | −0.695021 | ||||||||
\(313\) | −14.1597 | −0.800356 | −0.400178 | − | 0.916438i | \(-0.631052\pi\) | ||||
−0.400178 | + | 0.916438i | \(0.631052\pi\) | |||||||
\(314\) | −38.3314 | −2.16317 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.94338 | −0.334341 | ||||||||
\(317\) | 31.4411 | 1.76591 | 0.882955 | − | 0.469458i | \(-0.155551\pi\) | ||||
0.882955 | + | 0.469458i | \(0.155551\pi\) | |||||||
\(318\) | 4.29659 | 0.240941 | ||||||||
\(319\) | −3.31105 | −0.185383 | ||||||||
\(320\) | −11.6687 | −0.652301 | ||||||||
\(321\) | −20.3029 | −1.13320 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.2482 | 1.07100 | ||||||||
\(324\) | 0.703405 | 0.0390780 | ||||||||
\(325\) | −33.2381 | −1.84372 | ||||||||
\(326\) | −34.5791 | −1.91516 | ||||||||
\(327\) | 6.23589 | 0.344845 | ||||||||
\(328\) | −2.13187 | −0.117713 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −18.1204 | −0.997498 | ||||||||
\(331\) | −13.1862 | −0.724778 | −0.362389 | − | 0.932027i | \(-0.618039\pi\) | ||||
−0.362389 | + | 0.932027i | \(0.618039\pi\) | |||||||
\(332\) | −4.17073 | −0.228898 | ||||||||
\(333\) | 11.7958 | 0.646408 | ||||||||
\(334\) | 5.60195 | 0.306525 | ||||||||
\(335\) | 43.1756 | 2.35894 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.19410 | 0.0650470 | 0.0325235 | − | 0.999471i | \(-0.489646\pi\) | ||||
0.0325235 | + | 0.999471i | \(0.489646\pi\) | |||||||
\(338\) | 33.1491 | 1.80307 | ||||||||
\(339\) | 3.17038 | 0.172192 | ||||||||
\(340\) | 14.1505 | 0.767419 | ||||||||
\(341\) | −15.1190 | −0.818742 | ||||||||
\(342\) | −5.16329 | −0.279199 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −16.3721 | −0.882723 | ||||||||
\(345\) | −30.1227 | −1.62175 | ||||||||
\(346\) | −7.37395 | −0.396426 | ||||||||
\(347\) | −1.39245 | −0.0747507 | −0.0373753 | − | 0.999301i | \(-0.511900\pi\) | ||||
−0.0373753 | + | 0.999301i | \(0.511900\pi\) | |||||||
\(348\) | −0.693592 | −0.0371804 | ||||||||
\(349\) | −1.98813 | −0.106422 | −0.0532112 | − | 0.998583i | \(-0.516946\pi\) | ||||
−0.0532112 | + | 0.998583i | \(0.516946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.75857 | 0.307370 | ||||||||
\(352\) | 12.8024 | 0.682373 | ||||||||
\(353\) | −19.9677 | −1.06277 | −0.531387 | − | 0.847129i | \(-0.678329\pi\) | ||||
−0.531387 | + | 0.847129i | \(0.678329\pi\) | |||||||
\(354\) | 18.4554 | 0.980894 | ||||||||
\(355\) | 19.4402 | 1.03178 | ||||||||
\(356\) | −8.01337 | −0.424708 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9467 | 1.21277 | ||||||||
\(359\) | 18.9529 | 1.00029 | 0.500147 | − | 0.865940i | \(-0.333279\pi\) | ||||
0.500147 | + | 0.865940i | \(0.333279\pi\) | |||||||
\(360\) | 6.99692 | 0.368770 | ||||||||
\(361\) | −9.13853 | −0.480975 | ||||||||
\(362\) | 15.1464 | 0.796076 | ||||||||
\(363\) | −0.275433 | −0.0144565 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.7200 | −1.66030 | ||||||||
\(366\) | 2.96398 | 0.154930 | ||||||||
\(367\) | 3.57715 | 0.186726 | 0.0933630 | − | 0.995632i | \(-0.470238\pi\) | ||||
0.0933630 | + | 0.995632i | \(0.470238\pi\) | |||||||
\(368\) | 45.0826 | 2.35009 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −63.6548 | −3.30925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.16711 | −0.164207 | ||||||||
\(373\) | 22.8399 | 1.18261 | 0.591303 | − | 0.806450i | \(-0.298614\pi\) | ||||
0.591303 | + | 0.806450i | \(0.298614\pi\) | |||||||
\(374\) | 33.8409 | 1.74987 | ||||||||
\(375\) | 2.53353 | 0.130831 | ||||||||
\(376\) | 25.6152 | 1.32100 | ||||||||
\(377\) | −5.67824 | −0.292444 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3056 | −1.24849 | −0.624247 | − | 0.781227i | \(-0.714594\pi\) | ||||
−0.624247 | + | 0.781227i | \(0.714594\pi\) | |||||||
\(380\) | 7.24975 | 0.371904 | ||||||||
\(381\) | −8.07325 | −0.413605 | ||||||||
\(382\) | −31.1515 | −1.59385 | ||||||||
\(383\) | 14.8477 | 0.758682 | 0.379341 | − | 0.925257i | \(-0.376151\pi\) | ||||
0.379341 | + | 0.925257i | \(0.376151\pi\) | |||||||
\(384\) | −13.4709 | −0.687435 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.5127 | −1.29856 | ||||||||
\(387\) | 7.67969 | 0.390380 | ||||||||
\(388\) | 8.28779 | 0.420749 | ||||||||
\(389\) | −30.2374 | −1.53310 | −0.766548 | − | 0.642188i | \(-0.778027\pi\) | ||||
−0.766548 | + | 0.642188i | \(0.778027\pi\) | |||||||
\(390\) | −31.0754 | −1.57357 | ||||||||
\(391\) | 56.2558 | 2.84498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.14130 | −0.461118 | ||||||||
\(394\) | 5.06298 | 0.255069 | ||||||||
\(395\) | 27.7316 | 1.39533 | ||||||||
\(396\) | −2.36196 | −0.118693 | ||||||||
\(397\) | 16.8983 | 0.848101 | 0.424051 | − | 0.905639i | \(-0.360608\pi\) | ||||
0.424051 | + | 0.905639i | \(0.360608\pi\) | |||||||
\(398\) | −9.57313 | −0.479858 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −28.3519 | −1.41760 | ||||||||
\(401\) | −27.9165 | −1.39408 | −0.697042 | − | 0.717030i | \(-0.745501\pi\) | ||||
−0.697042 | + | 0.717030i | \(0.745501\pi\) | |||||||
\(402\) | 21.6295 | 1.07878 | ||||||||
\(403\) | −25.9282 | −1.29158 | ||||||||
\(404\) | 3.07802 | 0.153137 | ||||||||
\(405\) | −3.28206 | −0.163087 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −39.6091 | −1.96335 | ||||||||
\(408\) | −13.0671 | −0.646919 | ||||||||
\(409\) | −29.3409 | −1.45081 | −0.725407 | − | 0.688320i | \(-0.758349\pi\) | ||||
−0.725407 | + | 0.688320i | \(0.758349\pi\) | |||||||
\(410\) | −5.39638 | −0.266508 | ||||||||
\(411\) | 6.53936 | 0.322563 | ||||||||
\(412\) | −5.33069 | −0.262624 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −15.0905 | −0.741656 | ||||||||
\(415\) | 19.4605 | 0.955277 | ||||||||
\(416\) | 21.9554 | 1.07645 | ||||||||
\(417\) | 8.98420 | 0.439958 | ||||||||
\(418\) | 17.3378 | 0.848018 | ||||||||
\(419\) | 9.50190 | 0.464198 | 0.232099 | − | 0.972692i | \(-0.425441\pi\) | ||||
0.232099 | + | 0.972692i | \(0.425441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.34695 | −0.309331 | −0.154666 | − | 0.987967i | \(-0.549430\pi\) | ||||
−0.154666 | + | 0.987967i | \(0.549430\pi\) | |||||||
\(422\) | −31.4100 | −1.52902 | ||||||||
\(423\) | −12.0154 | −0.584207 | ||||||||
\(424\) | 5.57093 | 0.270548 | ||||||||
\(425\) | −35.3787 | −1.71612 | ||||||||
\(426\) | 9.73890 | 0.471851 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.2812 | 0.690307 | ||||||||
\(429\) | −19.3367 | −0.933583 | ||||||||
\(430\) | −41.4425 | −1.99853 | ||||||||
\(431\) | 5.67814 | 0.273507 | 0.136753 | − | 0.990605i | \(-0.456333\pi\) | ||||
0.136753 | + | 0.990605i | \(0.456333\pi\) | |||||||
\(432\) | 4.91203 | 0.236330 | ||||||||
\(433\) | 22.8926 | 1.10015 | 0.550075 | − | 0.835116i | \(-0.314599\pi\) | ||||
0.550075 | + | 0.835116i | \(0.314599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.23628 | 0.155168 | ||||||||
\(436\) | −4.38635 | −0.210068 | ||||||||
\(437\) | 28.8216 | 1.37872 | ||||||||
\(438\) | −15.8907 | −0.759285 | ||||||||
\(439\) | −13.8291 | −0.660027 | −0.330014 | − | 0.943976i | \(-0.607053\pi\) | ||||
−0.330014 | + | 0.943976i | \(0.607053\pi\) | |||||||
\(440\) | −23.4949 | −1.12007 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 58.0351 | 2.76045 | ||||||||
\(443\) | −20.1776 | −0.958669 | −0.479334 | − | 0.877632i | \(-0.659122\pi\) | ||||
−0.479334 | + | 0.877632i | \(0.659122\pi\) | |||||||
\(444\) | −8.29724 | −0.393770 | ||||||||
\(445\) | 37.3901 | 1.77246 | ||||||||
\(446\) | 44.9352 | 2.12775 | ||||||||
\(447\) | −0.272952 | −0.0129102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.97663 | 0.140476 | 0.0702379 | − | 0.997530i | \(-0.477624\pi\) | ||||
0.0702379 | + | 0.997530i | \(0.477624\pi\) | |||||||
\(450\) | 9.49023 | 0.447374 | ||||||||
\(451\) | −3.35789 | −0.158117 | ||||||||
\(452\) | −2.23006 | −0.104893 | ||||||||
\(453\) | 6.62811 | 0.311416 | ||||||||
\(454\) | −10.3108 | −0.483912 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.69470 | −0.313508 | ||||||||
\(457\) | 1.48861 | 0.0696341 | 0.0348171 | − | 0.999394i | \(-0.488915\pi\) | ||||
0.0348171 | + | 0.999394i | \(0.488915\pi\) | |||||||
\(458\) | 12.4551 | 0.581988 | ||||||||
\(459\) | 6.12943 | 0.286097 | ||||||||
\(460\) | 21.1885 | 0.987917 | ||||||||
\(461\) | −26.5341 | −1.23581 | −0.617907 | − | 0.786251i | \(-0.712019\pi\) | ||||
−0.617907 | + | 0.786251i | \(0.712019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3359 | 0.666245 | 0.333123 | − | 0.942883i | \(-0.391898\pi\) | ||||
0.333123 | + | 0.942883i | \(0.391898\pi\) | |||||||
\(464\) | −4.84351 | −0.224854 | ||||||||
\(465\) | 14.7776 | 0.685296 | ||||||||
\(466\) | −1.81846 | −0.0842385 | ||||||||
\(467\) | 26.7495 | 1.23782 | 0.618909 | − | 0.785462i | \(-0.287575\pi\) | ||||
0.618909 | + | 0.785462i | \(0.287575\pi\) | |||||||
\(468\) | −4.05061 | −0.187239 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 64.8395 | 2.99082 | ||||||||
\(471\) | 23.3131 | 1.07421 | ||||||||
\(472\) | 23.9292 | 1.10143 | ||||||||
\(473\) | −25.7876 | −1.18571 | ||||||||
\(474\) | 13.8926 | 0.638108 | ||||||||
\(475\) | −18.1256 | −0.831659 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.61317 | −0.119649 | ||||||||
\(478\) | 29.9097 | 1.36804 | ||||||||
\(479\) | 16.7956 | 0.767410 | 0.383705 | − | 0.923456i | \(-0.374648\pi\) | ||||
0.383705 | + | 0.923456i | \(0.374648\pi\) | |||||||
\(480\) | −12.5133 | −0.571153 | ||||||||
\(481\) | −67.9272 | −3.09721 | ||||||||
\(482\) | −34.0207 | −1.54960 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.193741 | 0.00880639 | ||||||||
\(485\) | −38.6705 | −1.75594 | ||||||||
\(486\) | −1.64420 | −0.0745826 | ||||||||
\(487\) | −11.1089 | −0.503392 | −0.251696 | − | 0.967806i | \(-0.580988\pi\) | ||||
−0.251696 | + | 0.967806i | \(0.580988\pi\) | |||||||
\(488\) | 3.84309 | 0.173968 | ||||||||
\(489\) | 21.0309 | 0.951050 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.5338 | −1.55849 | −0.779244 | − | 0.626720i | \(-0.784397\pi\) | ||||
−0.779244 | + | 0.626720i | \(0.784397\pi\) | |||||||
\(492\) | −0.703405 | −0.0317119 | ||||||||
\(493\) | −6.04392 | −0.272205 | ||||||||
\(494\) | 29.7332 | 1.33776 | ||||||||
\(495\) | 11.0208 | 0.495348 | ||||||||
\(496\) | −22.1166 | −0.993066 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.74905 | 0.436865 | ||||||||
\(499\) | −1.84774 | −0.0827161 | −0.0413580 | − | 0.999144i | \(-0.513168\pi\) | ||||
−0.0413580 | + | 0.999144i | \(0.513168\pi\) | |||||||
\(500\) | −1.78210 | −0.0796979 | ||||||||
\(501\) | −3.40709 | −0.152218 | ||||||||
\(502\) | 4.11037 | 0.183455 | ||||||||
\(503\) | 7.20636 | 0.321316 | 0.160658 | − | 0.987010i | \(-0.448638\pi\) | ||||
0.160658 | + | 0.987010i | \(0.448638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.3619 | −0.639098 | ||||||||
\(506\) | 50.6722 | 2.25265 | ||||||||
\(507\) | −20.1612 | −0.895389 | ||||||||
\(508\) | 5.67876 | 0.251954 | ||||||||
\(509\) | −9.61401 | −0.426134 | −0.213067 | − | 0.977038i | \(-0.568345\pi\) | ||||
−0.213067 | + | 0.977038i | \(0.568345\pi\) | |||||||
\(510\) | −33.0767 | −1.46466 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.21575 | −0.0979233 | ||||||||
\(513\) | 3.14030 | 0.138648 | ||||||||
\(514\) | −20.7350 | −0.914581 | ||||||||
\(515\) | 24.8728 | 1.09603 | ||||||||
\(516\) | −5.40193 | −0.237807 | ||||||||
\(517\) | 40.3463 | 1.77443 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.48482 | 0.196862 | ||||||||
\(520\) | −40.2923 | −1.76693 | ||||||||
\(521\) | 16.5470 | 0.724936 | 0.362468 | − | 0.931996i | \(-0.381934\pi\) | ||||
0.362468 | + | 0.931996i | \(0.381934\pi\) | |||||||
\(522\) | 1.62127 | 0.0709609 | ||||||||
\(523\) | −26.9120 | −1.17678 | −0.588390 | − | 0.808577i | \(-0.700238\pi\) | ||||
−0.588390 | + | 0.808577i | \(0.700238\pi\) | |||||||
\(524\) | 6.43003 | 0.280897 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.9972 | −1.52595 | ||||||||
\(527\) | −27.5980 | −1.20219 | ||||||||
\(528\) | −16.4941 | −0.717812 | ||||||||
\(529\) | 61.2354 | 2.66241 | ||||||||
\(530\) | 14.1017 | 0.612537 | ||||||||
\(531\) | −11.2245 | −0.487103 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.75857 | −0.249432 | ||||||||
\(534\) | 18.7312 | 0.810578 | ||||||||
\(535\) | −66.6355 | −2.88090 | ||||||||
\(536\) | 28.0448 | 1.21135 | ||||||||
\(537\) | −13.9561 | −0.602252 | ||||||||
\(538\) | 43.6703 | 1.88276 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.30862 | 0.0993471 | ||||||||
\(541\) | −22.1189 | −0.950965 | −0.475483 | − | 0.879725i | \(-0.657727\pi\) | ||||
−0.475483 | + | 0.879725i | \(0.657727\pi\) | |||||||
\(542\) | −19.4658 | −0.836126 | ||||||||
\(543\) | −9.21198 | −0.395324 | ||||||||
\(544\) | 23.3693 | 1.00195 | ||||||||
\(545\) | 20.4666 | 0.876692 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.32996 | 0.398920 | 0.199460 | − | 0.979906i | \(-0.436081\pi\) | ||||
0.199460 | + | 0.979906i | \(0.436081\pi\) | |||||||
\(548\) | −4.59982 | −0.196495 | ||||||||
\(549\) | −1.80269 | −0.0769368 | ||||||||
\(550\) | −31.8672 | −1.35882 | ||||||||
\(551\) | −3.09649 | −0.131915 | ||||||||
\(552\) | −19.5662 | −0.832795 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −31.7631 | −1.34948 | ||||||||
\(555\) | 38.7147 | 1.64335 | ||||||||
\(556\) | −6.31953 | −0.268008 | ||||||||
\(557\) | 35.5298 | 1.50545 | 0.752723 | − | 0.658338i | \(-0.228740\pi\) | ||||
0.752723 | + | 0.658338i | \(0.228740\pi\) | |||||||
\(558\) | 7.40309 | 0.313398 | ||||||||
\(559\) | −44.2241 | −1.87048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.5820 | −0.868971 | ||||||||
\(562\) | −28.3141 | −1.19436 | ||||||||
\(563\) | 11.6691 | 0.491795 | 0.245897 | − | 0.969296i | \(-0.420917\pi\) | ||||
0.245897 | + | 0.969296i | \(0.420917\pi\) | |||||||
\(564\) | 8.45167 | 0.355879 | ||||||||
\(565\) | 10.4054 | 0.437758 | ||||||||
\(566\) | 35.7450 | 1.50248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.6274 | 0.529834 | ||||||||
\(569\) | 10.1162 | 0.424095 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(570\) | −16.9462 | −0.709800 | ||||||||
\(571\) | −7.08972 | −0.296696 | −0.148348 | − | 0.988935i | \(-0.547395\pi\) | ||||
−0.148348 | + | 0.988935i | \(0.547395\pi\) | |||||||
\(572\) | 13.6015 | 0.568707 | ||||||||
\(573\) | 18.9462 | 0.791491 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −52.9747 | −2.20920 | ||||||||
\(576\) | 3.55530 | 0.148137 | ||||||||
\(577\) | 16.7129 | 0.695767 | 0.347884 | − | 0.937538i | \(-0.386900\pi\) | ||||
0.347884 | + | 0.937538i | \(0.386900\pi\) | |||||||
\(578\) | 33.8211 | 1.40677 | ||||||||
\(579\) | 15.5168 | 0.644855 | ||||||||
\(580\) | −2.27641 | −0.0945229 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −19.3726 | −0.803022 | ||||||||
\(583\) | 8.77475 | 0.363413 | ||||||||
\(584\) | −20.6038 | −0.852590 | ||||||||
\(585\) | 18.9000 | 0.781419 | ||||||||
\(586\) | 5.70332 | 0.235602 | ||||||||
\(587\) | −18.0499 | −0.745000 | −0.372500 | − | 0.928032i | \(-0.621499\pi\) | ||||
−0.372500 | + | 0.928032i | \(0.621499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.1393 | −0.582601 | ||||||||
\(590\) | 60.5718 | 2.49370 | ||||||||
\(591\) | −3.07929 | −0.126665 | ||||||||
\(592\) | −57.9415 | −2.38138 | ||||||||
\(593\) | 2.63006 | 0.108004 | 0.0540018 | − | 0.998541i | \(-0.482802\pi\) | ||||
0.0540018 | + | 0.998541i | \(0.482802\pi\) | |||||||
\(594\) | 5.52106 | 0.226532 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.191996 | 0.00786444 | ||||||||
\(597\) | 5.82235 | 0.238293 | ||||||||
\(598\) | 86.8996 | 3.55359 | ||||||||
\(599\) | −41.3763 | −1.69059 | −0.845296 | − | 0.534299i | \(-0.820576\pi\) | ||||
−0.845296 | + | 0.534299i | \(0.820576\pi\) | |||||||
\(600\) | 12.3050 | 0.502349 | ||||||||
\(601\) | 7.93199 | 0.323552 | 0.161776 | − | 0.986827i | \(-0.448278\pi\) | ||||
0.161776 | + | 0.986827i | \(0.448278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.1550 | −0.535714 | ||||||||
\(604\) | −4.66224 | −0.189704 | ||||||||
\(605\) | −0.903987 | −0.0367523 | ||||||||
\(606\) | −7.19485 | −0.292271 | ||||||||
\(607\) | −25.0957 | −1.01860 | −0.509302 | − | 0.860588i | \(-0.670096\pi\) | ||||
−0.509302 | + | 0.860588i | \(0.670096\pi\) | |||||||
\(608\) | 11.9728 | 0.485563 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.72798 | 0.393874 | ||||||||
\(611\) | 69.1914 | 2.79918 | ||||||||
\(612\) | −4.31147 | −0.174281 | ||||||||
\(613\) | 39.5202 | 1.59621 | 0.798103 | − | 0.602521i | \(-0.205837\pi\) | ||||
0.798103 | + | 0.602521i | \(0.205837\pi\) | |||||||
\(614\) | 44.1787 | 1.78291 | ||||||||
\(615\) | 3.28206 | 0.132346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0390 | −0.645705 | −0.322853 | − | 0.946449i | \(-0.604642\pi\) | ||||
−0.322853 | + | 0.946449i | \(0.604642\pi\) | |||||||
\(618\) | 12.4604 | 0.501233 | ||||||||
\(619\) | 4.05138 | 0.162839 | 0.0814194 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814194 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(620\) | −10.3946 | −0.417459 | ||||||||
\(621\) | 9.17799 | 0.368300 | ||||||||
\(622\) | −46.1072 | −1.84873 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −28.2863 | −1.13236 | ||||||||
\(625\) | −20.5445 | −0.821778 | ||||||||
\(626\) | −23.2815 | −0.930515 | ||||||||
\(627\) | −10.5448 | −0.421118 | ||||||||
\(628\) | −16.3985 | −0.654372 | ||||||||
\(629\) | −72.3017 | −2.88286 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7081 | −1.42152 | −0.710759 | − | 0.703436i | \(-0.751648\pi\) | ||||
−0.710759 | + | 0.703436i | \(0.751648\pi\) | |||||||
\(632\) | 18.0131 | 0.716522 | ||||||||
\(633\) | 19.1035 | 0.759295 | ||||||||
\(634\) | 51.6956 | 2.05310 | ||||||||
\(635\) | −26.4969 | −1.05150 | ||||||||
\(636\) | 1.83812 | 0.0728861 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.44404 | −0.215531 | ||||||||
\(639\) | −5.92317 | −0.234317 | ||||||||
\(640\) | −44.2124 | −1.74765 | ||||||||
\(641\) | 16.1373 | 0.637383 | 0.318692 | − | 0.947858i | \(-0.396757\pi\) | ||||
0.318692 | + | 0.947858i | \(0.396757\pi\) | |||||||
\(642\) | −33.3822 | −1.31749 | ||||||||
\(643\) | 17.6523 | 0.696137 | 0.348068 | − | 0.937469i | \(-0.386838\pi\) | ||||
0.348068 | + | 0.937469i | \(0.386838\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.2052 | 0.992454 | ||||||||
\(646\) | 31.6480 | 1.24517 | ||||||||
\(647\) | 0.0105799 | 0.000415939 0 | 0.000207970 | − | 1.00000i | \(-0.499934\pi\) | ||||
0.000207970 | 1.00000i | \(0.499934\pi\) | ||||||||
\(648\) | −2.13187 | −0.0837476 | ||||||||
\(649\) | 37.6907 | 1.47949 | ||||||||
\(650\) | −54.6502 | −2.14356 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7932 | −0.579348 | ||||||||
\(653\) | −35.3931 | −1.38504 | −0.692519 | − | 0.721399i | \(-0.743499\pi\) | ||||
−0.692519 | + | 0.721399i | \(0.743499\pi\) | |||||||
\(654\) | 10.2531 | 0.400927 | ||||||||
\(655\) | −30.0023 | −1.17229 | ||||||||
\(656\) | −4.91203 | −0.191783 | ||||||||
\(657\) | 9.66466 | 0.377054 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.98465 | 0.116266 | 0.0581328 | − | 0.998309i | \(-0.481485\pi\) | ||||
0.0581328 | + | 0.998309i | \(0.481485\pi\) | |||||||
\(660\) | −7.75209 | −0.301750 | ||||||||
\(661\) | −46.2120 | −1.79744 | −0.898718 | − | 0.438526i | \(-0.855501\pi\) | ||||
−0.898718 | + | 0.438526i | \(0.855501\pi\) | |||||||
\(662\) | −21.6807 | −0.842646 | ||||||||
\(663\) | −35.2968 | −1.37081 | ||||||||
\(664\) | 12.6406 | 0.490549 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.3947 | 0.751531 | ||||||||
\(667\) | −9.04995 | −0.350416 | ||||||||
\(668\) | 2.39656 | 0.0927258 | ||||||||
\(669\) | −27.3295 | −1.05662 | ||||||||
\(670\) | 70.9895 | 2.74256 | ||||||||
\(671\) | 6.05322 | 0.233682 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0235 | −0.540565 | −0.270282 | − | 0.962781i | \(-0.587117\pi\) | ||||
−0.270282 | + | 0.962781i | \(0.587117\pi\) | |||||||
\(674\) | 1.96335 | 0.0756254 | ||||||||
\(675\) | −5.77193 | −0.222162 | ||||||||
\(676\) | 14.1815 | 0.545441 | ||||||||
\(677\) | 2.26496 | 0.0870497 | 0.0435248 | − | 0.999052i | \(-0.486141\pi\) | ||||
0.0435248 | + | 0.999052i | \(0.486141\pi\) | |||||||
\(678\) | 5.21275 | 0.200195 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −42.8871 | −1.64465 | ||||||||
\(681\) | 6.27102 | 0.240306 | ||||||||
\(682\) | −24.8588 | −0.951892 | ||||||||
\(683\) | −3.25047 | −0.124376 | −0.0621879 | − | 0.998064i | \(-0.519808\pi\) | ||||
−0.0621879 | + | 0.998064i | \(0.519808\pi\) | |||||||
\(684\) | −2.20890 | −0.0844594 | ||||||||
\(685\) | 21.4626 | 0.820044 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.57515 | −0.289010 | ||||||||
\(688\) | −37.7229 | −1.43817 | ||||||||
\(689\) | 15.0481 | 0.573289 | ||||||||
\(690\) | −49.5279 | −1.88549 | ||||||||
\(691\) | 5.13808 | 0.195462 | 0.0977309 | − | 0.995213i | \(-0.468842\pi\) | ||||
0.0977309 | + | 0.995213i | \(0.468842\pi\) | |||||||
\(692\) | −3.15464 | −0.119921 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.28947 | −0.0869072 | ||||||||
\(695\) | 29.4867 | 1.11849 | ||||||||
\(696\) | 2.10213 | 0.0796809 | ||||||||
\(697\) | −6.12943 | −0.232169 | ||||||||
\(698\) | −3.26890 | −0.123730 | ||||||||
\(699\) | 1.10598 | 0.0418321 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.0426 | 1.24800 | 0.624001 | − | 0.781424i | \(-0.285506\pi\) | ||||
0.624001 | + | 0.781424i | \(0.285506\pi\) | |||||||
\(702\) | 9.46827 | 0.357357 | ||||||||
\(703\) | −37.0424 | −1.39708 | ||||||||
\(704\) | −11.9383 | −0.449942 | ||||||||
\(705\) | −39.4352 | −1.48522 | ||||||||
\(706\) | −32.8310 | −1.23561 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.89538 | 0.296727 | ||||||||
\(709\) | −40.5637 | −1.52340 | −0.761701 | − | 0.647928i | \(-0.775636\pi\) | ||||
−0.761701 | + | 0.647928i | \(0.775636\pi\) | |||||||
\(710\) | 31.9637 | 1.19957 | ||||||||
\(711\) | −8.44944 | −0.316879 | ||||||||
\(712\) | 24.2868 | 0.910185 | ||||||||
\(713\) | −41.3243 | −1.54761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −63.4641 | −2.37342 | ||||||||
\(716\) | 9.81682 | 0.366872 | ||||||||
\(717\) | −18.1910 | −0.679355 | ||||||||
\(718\) | 31.1624 | 1.16297 | ||||||||
\(719\) | −18.0190 | −0.671994 | −0.335997 | − | 0.941863i | \(-0.609073\pi\) | ||||
−0.335997 | + | 0.941863i | \(0.609073\pi\) | |||||||
\(720\) | 16.1216 | 0.600816 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0256 | −0.559195 | ||||||||
\(723\) | 20.6913 | 0.769517 | ||||||||
\(724\) | 6.47975 | 0.240818 | ||||||||
\(725\) | 5.69141 | 0.211374 | ||||||||
\(726\) | −0.452867 | −0.0168075 | ||||||||
\(727\) | −10.1884 | −0.377868 | −0.188934 | − | 0.981990i | \(-0.560503\pi\) | ||||
−0.188934 | + | 0.981990i | \(0.560503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −52.1542 | −1.93031 | ||||||||
\(731\) | −47.0721 | −1.74102 | ||||||||
\(732\) | 1.26802 | 0.0468673 | ||||||||
\(733\) | 42.6537 | 1.57545 | 0.787726 | − | 0.616026i | \(-0.211258\pi\) | ||||
0.787726 | + | 0.616026i | \(0.211258\pi\) | |||||||
\(734\) | 5.88157 | 0.217093 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.9924 | 1.28984 | ||||||||
\(737\) | 44.1731 | 1.62714 | ||||||||
\(738\) | 1.64420 | 0.0605240 | ||||||||
\(739\) | 16.1174 | 0.592887 | 0.296444 | − | 0.955050i | \(-0.404199\pi\) | ||||
0.296444 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(740\) | −27.2321 | −1.00107 | ||||||||
\(741\) | −18.0836 | −0.664319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.9584 | −1.02569 | −0.512846 | − | 0.858480i | \(-0.671409\pi\) | ||||
−0.512846 | + | 0.858480i | \(0.671409\pi\) | |||||||
\(744\) | 9.59882 | 0.351910 | ||||||||
\(745\) | −0.895844 | −0.0328212 | ||||||||
\(746\) | 37.5534 | 1.37493 | ||||||||
\(747\) | −5.92934 | −0.216943 | ||||||||
\(748\) | 14.4774 | 0.529348 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.16564 | 0.152108 | ||||||||
\(751\) | 17.5578 | 0.640695 | 0.320347 | − | 0.947300i | \(-0.396200\pi\) | ||||
0.320347 | + | 0.947300i | \(0.396200\pi\) | |||||||
\(752\) | 59.0199 | 2.15223 | ||||||||
\(753\) | −2.49992 | −0.0911020 | ||||||||
\(754\) | −9.33618 | −0.340004 | ||||||||
\(755\) | 21.7539 | 0.791704 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.87592 | −0.213564 | −0.106782 | − | 0.994282i | \(-0.534055\pi\) | ||||
−0.106782 | + | 0.994282i | \(0.534055\pi\) | |||||||
\(758\) | −39.9633 | −1.45153 | ||||||||
\(759\) | −30.8187 | −1.11865 | ||||||||
\(760\) | −21.9724 | −0.797023 | ||||||||
\(761\) | −26.4642 | −0.959326 | −0.479663 | − | 0.877453i | \(-0.659241\pi\) | ||||
−0.479663 | + | 0.877453i | \(0.659241\pi\) | |||||||
\(762\) | −13.2741 | −0.480869 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.3269 | −0.482150 | ||||||||
\(765\) | 20.1172 | 0.727338 | ||||||||
\(766\) | 24.4126 | 0.882065 | ||||||||
\(767\) | 64.6373 | 2.33392 | ||||||||
\(768\) | −15.0383 | −0.542649 | ||||||||
\(769\) | −30.5496 | −1.10165 | −0.550823 | − | 0.834622i | \(-0.685686\pi\) | ||||
−0.550823 | + | 0.834622i | \(0.685686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.6110 | 0.454173 | ||||||||
\(772\) | −10.9146 | −0.392824 | ||||||||
\(773\) | 33.4890 | 1.20452 | 0.602258 | − | 0.798302i | \(-0.294268\pi\) | ||||
0.602258 | + | 0.798302i | \(0.294268\pi\) | |||||||
\(774\) | 12.6270 | 0.453867 | ||||||||
\(775\) | 25.9884 | 0.933530 | ||||||||
\(776\) | −25.1185 | −0.901701 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −49.7164 | −1.78242 | ||||||||
\(779\) | −3.14030 | −0.112513 | ||||||||
\(780\) | −13.2943 | −0.476014 | ||||||||
\(781\) | 19.8894 | 0.711697 | ||||||||
\(782\) | 92.4960 | 3.30765 | ||||||||
\(783\) | −0.986050 | −0.0352386 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 76.5149 | 2.73093 | ||||||||
\(786\) | −15.0302 | −0.536108 | ||||||||
\(787\) | −6.84173 | −0.243881 | −0.121941 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121941 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(788\) | 2.16599 | 0.0771601 | ||||||||
\(789\) | 21.2852 | 0.757772 | ||||||||
\(790\) | 45.5964 | 1.62225 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.15857 | 0.254369 | ||||||||
\(793\) | 10.3809 | 0.368637 | ||||||||
\(794\) | 27.7842 | 0.986026 | ||||||||
\(795\) | −8.57659 | −0.304180 | ||||||||
\(796\) | −4.09547 | −0.145160 | ||||||||
\(797\) | 9.72791 | 0.344580 | 0.172290 | − | 0.985046i | \(-0.444883\pi\) | ||||
0.172290 | + | 0.985046i | \(0.444883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73.6474 | 2.60546 | ||||||||
\(800\) | −22.0063 | −0.778041 | ||||||||
\(801\) | −11.3923 | −0.402526 | ||||||||
\(802\) | −45.9004 | −1.62080 | ||||||||
\(803\) | −32.4529 | −1.14524 | ||||||||
\(804\) | 9.25331 | 0.326339 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.6313 | −1.50162 | ||||||||
\(807\) | −26.5602 | −0.934963 | ||||||||
\(808\) | −9.32880 | −0.328186 | ||||||||
\(809\) | 23.9599 | 0.842386 | 0.421193 | − | 0.906971i | \(-0.361611\pi\) | ||||
0.421193 | + | 0.906971i | \(0.361611\pi\) | |||||||
\(810\) | −5.39638 | −0.189609 | ||||||||
\(811\) | −30.6208 | −1.07524 | −0.537622 | − | 0.843186i | \(-0.680677\pi\) | ||||
−0.537622 | + | 0.843186i | \(0.680677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.8390 | 0.415213 | ||||||||
\(814\) | −65.1254 | −2.28265 | ||||||||
\(815\) | 69.0247 | 2.41783 | ||||||||
\(816\) | −30.1080 | −1.05399 | ||||||||
\(817\) | −24.1165 | −0.843730 | ||||||||
\(818\) | −48.2424 | −1.68676 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.30862 | −0.0806204 | ||||||||
\(821\) | 19.7037 | 0.687662 | 0.343831 | − | 0.939031i | \(-0.388275\pi\) | ||||
0.343831 | + | 0.939031i | \(0.388275\pi\) | |||||||
\(822\) | 10.7520 | 0.375021 | ||||||||
\(823\) | −26.6490 | −0.928926 | −0.464463 | − | 0.885593i | \(-0.653753\pi\) | ||||
−0.464463 | + | 0.885593i | \(0.653753\pi\) | |||||||
\(824\) | 16.1562 | 0.562826 | ||||||||
\(825\) | 19.3815 | 0.674778 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.60475 | 0.0905761 | 0.0452881 | − | 0.998974i | \(-0.485579\pi\) | ||||
0.0452881 | + | 0.998974i | \(0.485579\pi\) | |||||||
\(828\) | −6.45584 | −0.224356 | ||||||||
\(829\) | −7.20154 | −0.250120 | −0.125060 | − | 0.992149i | \(-0.539912\pi\) | ||||
−0.125060 | + | 0.992149i | \(0.539912\pi\) | |||||||
\(830\) | 31.9970 | 1.11063 | ||||||||
\(831\) | 19.3182 | 0.670142 | ||||||||
\(832\) | −20.4734 | −0.709789 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.7718 | 0.511507 | ||||||||
\(835\) | −11.1823 | −0.386979 | ||||||||
\(836\) | 7.41725 | 0.256531 | ||||||||
\(837\) | −4.50254 | −0.155631 | ||||||||
\(838\) | 15.6231 | 0.539689 | ||||||||
\(839\) | 3.36252 | 0.116087 | 0.0580436 | − | 0.998314i | \(-0.481514\pi\) | ||||
0.0580436 | + | 0.998314i | \(0.481514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0277 | −0.966473 | ||||||||
\(842\) | −10.4357 | −0.359637 | ||||||||
\(843\) | 17.2205 | 0.593107 | ||||||||
\(844\) | −13.4375 | −0.462537 | ||||||||
\(845\) | −66.1702 | −2.27633 | ||||||||
\(846\) | −19.7557 | −0.679215 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.8360 | 0.440789 | ||||||||
\(849\) | −21.7400 | −0.746116 | ||||||||
\(850\) | −58.1697 | −1.99520 | ||||||||
\(851\) | −108.262 | −3.71117 | ||||||||
\(852\) | 4.16639 | 0.142738 | ||||||||
\(853\) | −4.03938 | −0.138306 | −0.0691529 | − | 0.997606i | \(-0.522030\pi\) | ||||
−0.0691529 | + | 0.997606i | \(0.522030\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.3067 | 0.352480 | ||||||||
\(856\) | −43.2832 | −1.47939 | ||||||||
\(857\) | −21.4868 | −0.733975 | −0.366987 | − | 0.930226i | \(-0.619611\pi\) | ||||
−0.366987 | + | 0.930226i | \(0.619611\pi\) | |||||||
\(858\) | −31.7934 | −1.08541 | ||||||||
\(859\) | 24.7283 | 0.843717 | 0.421859 | − | 0.906662i | \(-0.361378\pi\) | ||||
0.421859 | + | 0.906662i | \(0.361378\pi\) | |||||||
\(860\) | −17.7295 | −0.604570 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.33602 | 0.317986 | ||||||||
\(863\) | −0.835485 | −0.0284402 | −0.0142201 | − | 0.999899i | \(-0.504527\pi\) | ||||
−0.0142201 | + | 0.999899i | \(0.504527\pi\) | |||||||
\(864\) | 3.81265 | 0.129709 | ||||||||
\(865\) | 14.7194 | 0.500476 | ||||||||
\(866\) | 37.6401 | 1.27906 | ||||||||
\(867\) | −20.5699 | −0.698591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.3723 | 0.962465 | ||||||||
\(870\) | 5.32110 | 0.180402 | ||||||||
\(871\) | 75.7542 | 2.56683 | ||||||||
\(872\) | 13.2941 | 0.450194 | ||||||||
\(873\) | 11.7824 | 0.398774 | ||||||||
\(874\) | 47.3886 | 1.60294 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.79817 | −0.229689 | ||||||||
\(877\) | −43.9609 | −1.48445 | −0.742227 | − | 0.670148i | \(-0.766230\pi\) | ||||
−0.742227 | + | 0.670148i | \(0.766230\pi\) | |||||||
\(878\) | −22.7379 | −0.767366 | ||||||||
\(879\) | −3.46874 | −0.116998 | ||||||||
\(880\) | −54.1346 | −1.82488 | ||||||||
\(881\) | −49.2250 | −1.65843 | −0.829217 | − | 0.558927i | \(-0.811213\pi\) | ||||
−0.829217 | + | 0.558927i | \(0.811213\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.1493 | −0.947300 | −0.473650 | − | 0.880713i | \(-0.657064\pi\) | ||||
−0.473650 | + | 0.880713i | \(0.657064\pi\) | |||||||
\(884\) | 24.8279 | 0.835053 | ||||||||
\(885\) | −36.8396 | −1.23835 | ||||||||
\(886\) | −33.1761 | −1.11457 | ||||||||
\(887\) | −39.1184 | −1.31347 | −0.656733 | − | 0.754123i | \(-0.728062\pi\) | ||||
−0.656733 | + | 0.754123i | \(0.728062\pi\) | |||||||
\(888\) | 25.1471 | 0.843883 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 61.4769 | 2.06071 | ||||||||
\(891\) | −3.35789 | −0.112494 | ||||||||
\(892\) | 19.2237 | 0.643657 | ||||||||
\(893\) | 37.7318 | 1.26265 | ||||||||
\(894\) | −0.448788 | −0.0150097 | ||||||||
\(895\) | −45.8049 | −1.53109 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −52.8521 | −1.76468 | ||||||||
\(898\) | 4.89418 | 0.163321 | ||||||||
\(899\) | 4.43973 | 0.148073 | ||||||||
\(900\) | 4.06001 | 0.135334 | ||||||||
\(901\) | 16.0173 | 0.533612 | ||||||||
\(902\) | −5.52106 | −0.183831 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.75883 | 0.224795 | ||||||||
\(905\) | −30.2343 | −1.00502 | ||||||||
\(906\) | 10.8980 | 0.362061 | ||||||||
\(907\) | −35.8670 | −1.19094 | −0.595472 | − | 0.803376i | \(-0.703035\pi\) | ||||
−0.595472 | + | 0.803376i | \(0.703035\pi\) | |||||||
\(908\) | −4.41107 | −0.146386 | ||||||||
\(909\) | 4.37589 | 0.145139 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.2869 | −0.572741 | −0.286371 | − | 0.958119i | \(-0.592449\pi\) | ||||
−0.286371 | + | 0.958119i | \(0.592449\pi\) | |||||||
\(912\) | −15.4252 | −0.510781 | ||||||||
\(913\) | 19.9101 | 0.658928 | ||||||||
\(914\) | 2.44757 | 0.0809585 | ||||||||
\(915\) | −5.91653 | −0.195594 | ||||||||
\(916\) | 5.32840 | 0.176055 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.0780 | 0.332625 | ||||||||
\(919\) | −22.0788 | −0.728312 | −0.364156 | − | 0.931338i | \(-0.618643\pi\) | ||||
−0.364156 | + | 0.931338i | \(0.618643\pi\) | |||||||
\(920\) | −64.2176 | −2.11719 | ||||||||
\(921\) | −26.8694 | −0.885376 | ||||||||
\(922\) | −43.6274 | −1.43679 | ||||||||
\(923\) | 34.1090 | 1.12271 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 68.0847 | 2.23861 | ||||||||
\(926\) | 23.5711 | 0.774595 | ||||||||
\(927\) | −7.57841 | −0.248908 | ||||||||
\(928\) | −3.75946 | −0.123410 | ||||||||
\(929\) | −33.4705 | −1.09813 | −0.549066 | − | 0.835779i | \(-0.685016\pi\) | ||||
−0.549066 | + | 0.835779i | \(0.685016\pi\) | |||||||
\(930\) | 24.2974 | 0.796744 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.777953 | −0.0254827 | ||||||||
\(933\) | 28.0423 | 0.918063 | ||||||||
\(934\) | 43.9816 | 1.43912 | ||||||||
\(935\) | −67.5513 | −2.20916 | ||||||||
\(936\) | 12.2765 | 0.401270 | ||||||||
\(937\) | 34.1088 | 1.11429 | 0.557143 | − | 0.830416i | \(-0.311897\pi\) | ||||
0.557143 | + | 0.830416i | \(0.311897\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1597 | 0.462086 | ||||||||
\(940\) | 27.7389 | 0.904743 | ||||||||
\(941\) | 2.69587 | 0.0878829 | 0.0439415 | − | 0.999034i | \(-0.486008\pi\) | ||||
0.0439415 | + | 0.999034i | \(0.486008\pi\) | |||||||
\(942\) | 38.3314 | 1.24890 | ||||||||
\(943\) | −9.17799 | −0.298876 | ||||||||
\(944\) | 55.1352 | 1.79450 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.4000 | −1.37854 | ||||||||
\(947\) | 24.9949 | 0.812226 | 0.406113 | − | 0.913823i | \(-0.366884\pi\) | ||||
0.406113 | + | 0.913823i | \(0.366884\pi\) | |||||||
\(948\) | 5.94338 | 0.193032 | ||||||||
\(949\) | −55.6547 | −1.80663 | ||||||||
\(950\) | −29.8022 | −0.966910 | ||||||||
\(951\) | −31.4411 | −1.01955 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.7561 | −0.963895 | −0.481948 | − | 0.876200i | \(-0.660070\pi\) | ||||
−0.481948 | + | 0.876200i | \(0.660070\pi\) | |||||||
\(954\) | −4.29659 | −0.139107 | ||||||||
\(955\) | 62.1828 | 2.01219 | ||||||||
\(956\) | 12.7956 | 0.413840 | ||||||||
\(957\) | 3.31105 | 0.107031 | ||||||||
\(958\) | 27.6154 | 0.892212 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 11.6687 | 0.376606 | ||||||||
\(961\) | −10.7271 | −0.346036 | ||||||||
\(962\) | −111.686 | −3.60090 | ||||||||
\(963\) | 20.3029 | 0.654253 | ||||||||
\(964\) | −14.5544 | −0.468764 | ||||||||
\(965\) | 50.9270 | 1.63940 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3371 | 1.29715 | 0.648577 | − | 0.761149i | \(-0.275364\pi\) | ||||
0.648577 | + | 0.761149i | \(0.275364\pi\) | |||||||
\(968\) | −0.587185 | −0.0188729 | ||||||||
\(969\) | −19.2482 | −0.618342 | ||||||||
\(970\) | −63.5822 | −2.04150 | ||||||||
\(971\) | −57.5004 | −1.84527 | −0.922637 | − | 0.385669i | \(-0.873971\pi\) | ||||
−0.922637 | + | 0.385669i | \(0.873971\pi\) | |||||||
\(972\) | −0.703405 | −0.0225617 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.2653 | −0.585258 | ||||||||
\(975\) | 33.2381 | 1.06447 | ||||||||
\(976\) | 8.85485 | 0.283437 | ||||||||
\(977\) | 40.1369 | 1.28409 | 0.642047 | − | 0.766665i | \(-0.278085\pi\) | ||||
0.642047 | + | 0.766665i | \(0.278085\pi\) | |||||||
\(978\) | 34.5791 | 1.10572 | ||||||||
\(979\) | 38.2540 | 1.22260 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.23589 | −0.199097 | ||||||||
\(982\) | −56.7806 | −1.81194 | ||||||||
\(983\) | 7.02052 | 0.223920 | 0.111960 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111960 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(984\) | 2.13187 | 0.0679614 | ||||||||
\(985\) | −10.1064 | −0.322017 | ||||||||
\(986\) | −9.93744 | −0.316473 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.7201 | 0.404681 | ||||||||
\(989\) | −70.4841 | −2.24126 | ||||||||
\(990\) | 18.1204 | 0.575906 | ||||||||
\(991\) | −1.28810 | −0.0409177 | −0.0204589 | − | 0.999791i | \(-0.506513\pi\) | ||||
−0.0204589 | + | 0.999791i | \(0.506513\pi\) | |||||||
\(992\) | −17.1666 | −0.545040 | ||||||||
\(993\) | 13.1862 | 0.418450 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.1093 | 0.605806 | ||||||||
\(996\) | 4.17073 | 0.132155 | ||||||||
\(997\) | 24.1834 | 0.765895 | 0.382948 | − | 0.923770i | \(-0.374909\pi\) | ||||
0.382948 | + | 0.923770i | \(0.374909\pi\) | |||||||
\(998\) | −3.03805 | −0.0961679 | ||||||||
\(999\) | −11.7958 | −0.373204 |
(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 | 6027.2.a.bn.1.17 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.17 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.17 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.17 | yes | 24 | 7.6 | odd | 2 |