Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, 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("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 9x^{5} + 34x^{4} - 19x^{3} - 27x^{2} + 11x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 445) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.66289\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.66289 | 1.17584 | 0.587921 | − | 0.808918i | \(-0.299947\pi\) | ||||
0.587921 | + | 0.808918i | \(0.299947\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.765209 | 0.382604 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.19579 | −0.451964 | −0.225982 | − | 0.974131i | \(-0.572559\pi\) | ||||
−0.225982 | + | 0.974131i | \(0.572559\pi\) | |||||||
\(8\) | −2.05332 | −0.725960 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.66289 | 0.525853 | ||||||||
\(11\) | 1.71622 | 0.517459 | 0.258729 | − | 0.965950i | \(-0.416696\pi\) | ||||
0.258729 | + | 0.965950i | \(0.416696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.71750 | −1.86310 | −0.931550 | − | 0.363614i | \(-0.881543\pi\) | ||||
−0.931550 | + | 0.363614i | \(0.881543\pi\) | |||||||
\(14\) | −1.98846 | −0.531439 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.94487 | −1.23622 | ||||||||
\(17\) | −0.198198 | −0.0480700 | −0.0240350 | − | 0.999711i | \(-0.507651\pi\) | ||||
−0.0240350 | + | 0.999711i | \(0.507651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.88536 | 1.35019 | 0.675097 | − | 0.737729i | \(-0.264102\pi\) | ||||
0.675097 | + | 0.737729i | \(0.264102\pi\) | |||||||
\(20\) | 0.765209 | 0.171106 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.85388 | 0.608449 | ||||||||
\(23\) | 5.52172 | 1.15136 | 0.575679 | − | 0.817676i | \(-0.304738\pi\) | ||||
0.575679 | + | 0.817676i | \(0.304738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.1705 | −2.19071 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.915025 | −0.172924 | ||||||||
\(29\) | −9.07040 | −1.68433 | −0.842165 | − | 0.539219i | \(-0.818719\pi\) | ||||
−0.842165 | + | 0.539219i | \(0.818719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.91047 | 0.522735 | 0.261368 | − | 0.965239i | \(-0.415827\pi\) | ||||
0.261368 | + | 0.965239i | \(0.415827\pi\) | |||||||
\(32\) | −4.11614 | −0.727638 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.329581 | −0.0565227 | ||||||||
\(35\) | −1.19579 | −0.202125 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00129 | 0.164610 | 0.0823052 | − | 0.996607i | \(-0.473772\pi\) | ||||
0.0823052 | + | 0.996607i | \(0.473772\pi\) | |||||||
\(38\) | 9.78671 | 1.58761 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.05332 | −0.324659 | ||||||||
\(41\) | −9.69562 | −1.51420 | −0.757101 | − | 0.653298i | \(-0.773385\pi\) | ||||
−0.757101 | + | 0.653298i | \(0.773385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.27832 | −0.957435 | −0.478718 | − | 0.877969i | \(-0.658898\pi\) | ||||
−0.478718 | + | 0.877969i | \(0.658898\pi\) | |||||||
\(44\) | 1.31326 | 0.197982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.18202 | 1.35381 | ||||||||
\(47\) | −4.24748 | −0.619559 | −0.309780 | − | 0.950808i | \(-0.600255\pi\) | ||||
−0.309780 | + | 0.950808i | \(0.600255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.57010 | −0.795728 | ||||||||
\(50\) | 1.66289 | 0.235168 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.14029 | −0.712830 | ||||||||
\(53\) | −8.93237 | −1.22696 | −0.613478 | − | 0.789712i | \(-0.710230\pi\) | ||||
−0.613478 | + | 0.789712i | \(0.710230\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.71622 | 0.231415 | ||||||||
\(56\) | 2.45534 | 0.328108 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.0831 | −1.98051 | ||||||||
\(59\) | −3.20445 | −0.417184 | −0.208592 | − | 0.978003i | \(-0.566888\pi\) | ||||
−0.208592 | + | 0.978003i | \(0.566888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8563 | −1.39001 | −0.695004 | − | 0.719006i | \(-0.744598\pi\) | ||||
−0.695004 | + | 0.719006i | \(0.744598\pi\) | |||||||
\(62\) | 4.83979 | 0.614654 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.04505 | 0.380632 | ||||||||
\(65\) | −6.71750 | −0.833204 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.0366 | 1.83701 | 0.918505 | − | 0.395409i | \(-0.129397\pi\) | ||||
0.918505 | + | 0.395409i | \(0.129397\pi\) | |||||||
\(68\) | −0.151663 | −0.0183918 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.98846 | −0.237667 | ||||||||
\(71\) | −3.52924 | −0.418843 | −0.209422 | − | 0.977825i | \(-0.567158\pi\) | ||||
−0.209422 | + | 0.977825i | \(0.567158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.36638 | −0.394004 | −0.197002 | − | 0.980403i | \(-0.563121\pi\) | ||||
−0.197002 | + | 0.980403i | \(0.563121\pi\) | |||||||
\(74\) | 1.66503 | 0.193556 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.50353 | 0.516590 | ||||||||
\(77\) | −2.05223 | −0.233873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.21235 | −0.586435 | −0.293217 | − | 0.956046i | \(-0.594726\pi\) | ||||
−0.293217 | + | 0.956046i | \(0.594726\pi\) | |||||||
\(80\) | −4.94487 | −0.552854 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.1228 | −1.78046 | ||||||||
\(83\) | −11.4175 | −1.25323 | −0.626616 | − | 0.779328i | \(-0.715560\pi\) | ||||
−0.626616 | + | 0.779328i | \(0.715560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.198198 | −0.0214976 | ||||||||
\(86\) | −10.4402 | −1.12579 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.52395 | −0.375654 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.03269 | 0.842055 | ||||||||
\(92\) | 4.22526 | 0.440514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.06310 | −0.728504 | ||||||||
\(95\) | 5.88536 | 0.603825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3533 | −1.25429 | −0.627145 | − | 0.778903i | \(-0.715777\pi\) | ||||
−0.627145 | + | 0.778903i | \(0.715777\pi\) | |||||||
\(98\) | −9.26247 | −0.935651 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.765209 | 0.0765209 | ||||||||
\(101\) | 13.8431 | 1.37744 | 0.688719 | − | 0.725029i | \(-0.258174\pi\) | ||||
0.688719 | + | 0.725029i | \(0.258174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82296 | −0.278155 | −0.139077 | − | 0.990282i | \(-0.544414\pi\) | ||||
−0.139077 | + | 0.990282i | \(0.544414\pi\) | |||||||
\(104\) | 13.7932 | 1.35254 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.8536 | −1.44271 | ||||||||
\(107\) | −14.4241 | −1.39443 | −0.697214 | − | 0.716863i | \(-0.745577\pi\) | ||||
−0.697214 | + | 0.716863i | \(0.745577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2682 | −1.07929 | −0.539647 | − | 0.841892i | \(-0.681442\pi\) | ||||
−0.539647 | + | 0.841892i | \(0.681442\pi\) | |||||||
\(110\) | 2.85388 | 0.272107 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.91301 | 0.558727 | ||||||||
\(113\) | 6.97824 | 0.656458 | 0.328229 | − | 0.944598i | \(-0.393548\pi\) | ||||
0.328229 | + | 0.944598i | \(0.393548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.52172 | 0.514903 | ||||||||
\(116\) | −6.94075 | −0.644432 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.32866 | −0.490543 | ||||||||
\(119\) | 0.237002 | 0.0217259 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.05460 | −0.732237 | ||||||||
\(122\) | −18.0529 | −1.63443 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.22711 | 0.200001 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7488 | 1.13127 | 0.565636 | − | 0.824655i | \(-0.308631\pi\) | ||||
0.565636 | + | 0.824655i | \(0.308631\pi\) | |||||||
\(128\) | 13.2959 | 1.17520 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.1705 | −0.979716 | ||||||||
\(131\) | −14.2498 | −1.24501 | −0.622505 | − | 0.782616i | \(-0.713885\pi\) | ||||
−0.622505 | + | 0.782616i | \(0.713885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.03763 | −0.610240 | ||||||||
\(134\) | 25.0042 | 2.16003 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.406964 | 0.0348969 | ||||||||
\(137\) | −12.5956 | −1.07611 | −0.538055 | − | 0.842909i | \(-0.680841\pi\) | ||||
−0.538055 | + | 0.842909i | \(0.680841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.2156 | 1.71466 | 0.857330 | − | 0.514766i | \(-0.172121\pi\) | ||||
0.857330 | + | 0.514766i | \(0.172121\pi\) | |||||||
\(140\) | −0.915025 | −0.0773338 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.86874 | −0.492493 | ||||||||
\(143\) | −11.5287 | −0.964077 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.07040 | −0.753256 | ||||||||
\(146\) | −5.59792 | −0.463287 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.766192 | 0.0629806 | ||||||||
\(149\) | 21.1805 | 1.73518 | 0.867588 | − | 0.497283i | \(-0.165669\pi\) | ||||
0.867588 | + | 0.497283i | \(0.165669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.83007 | 0.555824 | 0.277912 | − | 0.960607i | \(-0.410358\pi\) | ||||
0.277912 | + | 0.960607i | \(0.410358\pi\) | |||||||
\(152\) | −12.0846 | −0.980187 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.41263 | −0.274998 | ||||||||
\(155\) | 2.91047 | 0.233774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.11228 | 0.647430 | 0.323715 | − | 0.946155i | \(-0.395068\pi\) | ||||
0.323715 | + | 0.946155i | \(0.395068\pi\) | |||||||
\(158\) | −8.66757 | −0.689555 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.11614 | −0.325409 | ||||||||
\(161\) | −6.60279 | −0.520373 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.775772 | 0.0607632 | 0.0303816 | − | 0.999538i | \(-0.490328\pi\) | ||||
0.0303816 | + | 0.999538i | \(0.490328\pi\) | |||||||
\(164\) | −7.41917 | −0.579340 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.9860 | −1.47360 | ||||||||
\(167\) | 8.31329 | 0.643302 | 0.321651 | − | 0.946858i | \(-0.395762\pi\) | ||||
0.321651 | + | 0.946858i | \(0.395762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.1248 | 2.47114 | ||||||||
\(170\) | −0.329581 | −0.0252777 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.80423 | −0.366319 | ||||||||
\(173\) | −2.84871 | −0.216584 | −0.108292 | − | 0.994119i | \(-0.534538\pi\) | ||||
−0.108292 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.19579 | −0.0903929 | ||||||||
\(176\) | −8.48647 | −0.639692 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.66289 | −0.124639 | ||||||||
\(179\) | 11.2580 | 0.841461 | 0.420730 | − | 0.907186i | \(-0.361774\pi\) | ||||
0.420730 | + | 0.907186i | \(0.361774\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.89728 | 0.512671 | 0.256336 | − | 0.966588i | \(-0.417485\pi\) | ||||
0.256336 | + | 0.966588i | \(0.417485\pi\) | |||||||
\(182\) | 13.3575 | 0.990123 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.3379 | −0.835839 | ||||||||
\(185\) | 1.00129 | 0.0736160 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.340150 | −0.0248742 | ||||||||
\(188\) | −3.25021 | −0.237046 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.78671 | 0.710003 | ||||||||
\(191\) | 14.6743 | 1.06179 | 0.530897 | − | 0.847436i | \(-0.321855\pi\) | ||||
0.530897 | + | 0.847436i | \(0.321855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.6706 | −0.840068 | −0.420034 | − | 0.907508i | \(-0.637982\pi\) | ||||
−0.420034 | + | 0.907508i | \(0.637982\pi\) | |||||||
\(194\) | −20.5422 | −1.47485 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.26229 | −0.304449 | ||||||||
\(197\) | −13.1956 | −0.940147 | −0.470074 | − | 0.882627i | \(-0.655773\pi\) | ||||
−0.470074 | + | 0.882627i | \(0.655773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1226 | 0.717575 | 0.358788 | − | 0.933419i | \(-0.383190\pi\) | ||||
0.358788 | + | 0.933419i | \(0.383190\pi\) | |||||||
\(200\) | −2.05332 | −0.145192 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 23.0195 | 1.61965 | ||||||||
\(203\) | 10.8463 | 0.761258 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.69562 | −0.677172 | ||||||||
\(206\) | −4.69428 | −0.327066 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 33.2172 | 2.30320 | ||||||||
\(209\) | 10.1005 | 0.698669 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8961 | 0.887802 | 0.443901 | − | 0.896076i | \(-0.353594\pi\) | ||||
0.443901 | + | 0.896076i | \(0.353594\pi\) | |||||||
\(212\) | −6.83513 | −0.469438 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.9857 | −1.63963 | ||||||||
\(215\) | −6.27832 | −0.428178 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.48029 | −0.236258 | ||||||||
\(218\) | −18.7377 | −1.26908 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.31326 | 0.0885402 | ||||||||
\(221\) | 1.33139 | 0.0895592 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2759 | 0.755090 | 0.377545 | − | 0.925991i | \(-0.376768\pi\) | ||||
0.377545 | + | 0.925991i | \(0.376768\pi\) | |||||||
\(224\) | 4.92202 | 0.328866 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.6041 | 0.771891 | ||||||||
\(227\) | −5.26072 | −0.349167 | −0.174583 | − | 0.984642i | \(-0.555858\pi\) | ||||
−0.174583 | + | 0.984642i | \(0.555858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.7381 | 1.83298 | 0.916492 | − | 0.400054i | \(-0.131008\pi\) | ||||
0.916492 | + | 0.400054i | \(0.131008\pi\) | |||||||
\(230\) | 9.18202 | 0.605444 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.6245 | 1.22276 | ||||||||
\(233\) | −12.9676 | −0.849533 | −0.424766 | − | 0.905303i | \(-0.639644\pi\) | ||||
−0.424766 | + | 0.905303i | \(0.639644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.24748 | −0.277075 | ||||||||
\(236\) | −2.45207 | −0.159616 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.394109 | 0.0255463 | ||||||||
\(239\) | 2.84490 | 0.184021 | 0.0920106 | − | 0.995758i | \(-0.470671\pi\) | ||||
0.0920106 | + | 0.995758i | \(0.470671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4580 | 0.995736 | 0.497868 | − | 0.867253i | \(-0.334116\pi\) | ||||
0.497868 | + | 0.867253i | \(0.334116\pi\) | |||||||
\(242\) | −13.3939 | −0.860995 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.30735 | −0.531823 | ||||||||
\(245\) | −5.57010 | −0.355860 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.5349 | −2.51555 | ||||||||
\(248\) | −5.97613 | −0.379485 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.66289 | 0.105171 | ||||||||
\(251\) | −15.5422 | −0.981016 | −0.490508 | − | 0.871437i | \(-0.663189\pi\) | ||||
−0.490508 | + | 0.871437i | \(0.663189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.47646 | 0.595780 | ||||||||
\(254\) | 21.1999 | 1.33020 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0195 | 1.00122 | ||||||||
\(257\) | 18.4372 | 1.15008 | 0.575040 | − | 0.818125i | \(-0.304986\pi\) | ||||
0.575040 | + | 0.818125i | \(0.304986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.19732 | −0.0743980 | ||||||||
\(260\) | −5.14029 | −0.318787 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −23.6959 | −1.46394 | ||||||||
\(263\) | −1.37018 | −0.0844891 | −0.0422445 | − | 0.999107i | \(-0.513451\pi\) | ||||
−0.0422445 | + | 0.999107i | \(0.513451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.93237 | −0.548711 | ||||||||
\(266\) | −11.7028 | −0.717545 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.5061 | 0.702848 | ||||||||
\(269\) | −12.6384 | −0.770580 | −0.385290 | − | 0.922796i | \(-0.625899\pi\) | ||||
−0.385290 | + | 0.922796i | \(0.625899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8509 | −0.780635 | −0.390317 | − | 0.920680i | \(-0.627635\pi\) | ||||
−0.390317 | + | 0.920680i | \(0.627635\pi\) | |||||||
\(272\) | 0.980063 | 0.0594250 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.9450 | −1.26534 | ||||||||
\(275\) | 1.71622 | 0.103492 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.5069 | −1.53256 | −0.766279 | − | 0.642508i | \(-0.777894\pi\) | ||||
−0.766279 | + | 0.642508i | \(0.777894\pi\) | |||||||
\(278\) | 33.6163 | 2.01617 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.45534 | 0.146734 | ||||||||
\(281\) | 10.0582 | 0.600022 | 0.300011 | − | 0.953936i | \(-0.403010\pi\) | ||||
0.300011 | + | 0.953936i | \(0.403010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8405 | −0.703848 | −0.351924 | − | 0.936029i | \(-0.614472\pi\) | ||||
−0.351924 | + | 0.936029i | \(0.614472\pi\) | |||||||
\(284\) | −2.70060 | −0.160251 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.1710 | −1.13360 | ||||||||
\(287\) | 11.5939 | 0.684365 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9607 | −0.997689 | ||||||||
\(290\) | −15.0831 | −0.885710 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.57598 | −0.150748 | ||||||||
\(293\) | −19.8376 | −1.15893 | −0.579463 | − | 0.814999i | \(-0.696738\pi\) | ||||
−0.579463 | + | 0.814999i | \(0.696738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.20445 | −0.186570 | ||||||||
\(296\) | −2.05596 | −0.119500 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 35.2209 | 2.04029 | ||||||||
\(299\) | −37.0921 | −2.14509 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.50753 | 0.432727 | ||||||||
\(302\) | 11.3577 | 0.653561 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29.1024 | −1.66913 | ||||||||
\(305\) | −10.8563 | −0.621631 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.32228 | −0.189613 | −0.0948064 | − | 0.995496i | \(-0.530223\pi\) | ||||
−0.0948064 | + | 0.995496i | \(0.530223\pi\) | |||||||
\(308\) | −1.57038 | −0.0894808 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.83979 | 0.274882 | ||||||||
\(311\) | −10.8962 | −0.617869 | −0.308934 | − | 0.951083i | \(-0.599972\pi\) | ||||
−0.308934 | + | 0.951083i | \(0.599972\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.60276 | 0.203640 | 0.101820 | − | 0.994803i | \(-0.467533\pi\) | ||||
0.101820 | + | 0.994803i | \(0.467533\pi\) | |||||||
\(314\) | 13.4898 | 0.761276 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.98853 | −0.224372 | ||||||||
\(317\) | −8.70500 | −0.488921 | −0.244461 | − | 0.969659i | \(-0.578611\pi\) | ||||
−0.244461 | + | 0.969659i | \(0.578611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5668 | −0.871571 | ||||||||
\(320\) | 3.04505 | 0.170224 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.9797 | −0.611876 | ||||||||
\(323\) | −1.16647 | −0.0649039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.71750 | −0.372620 | ||||||||
\(326\) | 1.29003 | 0.0714479 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 19.9083 | 1.09925 | ||||||||
\(329\) | 5.07908 | 0.280019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.9163 | −1.58938 | −0.794691 | − | 0.607014i | \(-0.792367\pi\) | ||||
−0.794691 | + | 0.607014i | \(0.792367\pi\) | |||||||
\(332\) | −8.73676 | −0.479492 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.8241 | 0.756421 | ||||||||
\(335\) | 15.0366 | 0.821536 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.14680 | −0.171417 | −0.0857085 | − | 0.996320i | \(-0.527315\pi\) | ||||
−0.0857085 | + | 0.996320i | \(0.527315\pi\) | |||||||
\(338\) | 53.4201 | 2.90567 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.151663 | −0.00822506 | ||||||||
\(341\) | 4.99499 | 0.270494 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0311 | 0.811605 | ||||||||
\(344\) | 12.8914 | 0.695060 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.73710 | −0.254668 | ||||||||
\(347\) | 15.4128 | 0.827405 | 0.413702 | − | 0.910412i | \(-0.364235\pi\) | ||||
0.413702 | + | 0.910412i | \(0.364235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5617 | 1.10064 | 0.550322 | − | 0.834952i | \(-0.314505\pi\) | ||||
0.550322 | + | 0.834952i | \(0.314505\pi\) | |||||||
\(350\) | −1.98846 | −0.106288 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.06418 | −0.376522 | ||||||||
\(353\) | −33.5463 | −1.78549 | −0.892745 | − | 0.450563i | \(-0.851223\pi\) | ||||
−0.892745 | + | 0.450563i | \(0.851223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.52924 | −0.187312 | ||||||||
\(356\) | −0.765209 | −0.0405560 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.7208 | 0.989425 | ||||||||
\(359\) | 17.2671 | 0.911321 | 0.455660 | − | 0.890154i | \(-0.349403\pi\) | ||||
0.455660 | + | 0.890154i | \(0.349403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.6375 | 0.823024 | ||||||||
\(362\) | 11.4694 | 0.602820 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.14668 | 0.322174 | ||||||||
\(365\) | −3.36638 | −0.176204 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8203 | 0.669215 | 0.334608 | − | 0.942358i | \(-0.391396\pi\) | ||||
0.334608 | + | 0.942358i | \(0.391396\pi\) | |||||||
\(368\) | −27.3042 | −1.42333 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.66503 | 0.0865608 | ||||||||
\(371\) | 10.6812 | 0.554540 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.0233 | 1.19210 | 0.596051 | − | 0.802947i | \(-0.296736\pi\) | ||||
0.596051 | + | 0.802947i | \(0.296736\pi\) | |||||||
\(374\) | −0.565633 | −0.0292482 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.72146 | 0.449775 | ||||||||
\(377\) | 60.9304 | 3.13808 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.39286 | −0.174279 | −0.0871397 | − | 0.996196i | \(-0.527773\pi\) | ||||
−0.0871397 | + | 0.996196i | \(0.527773\pi\) | |||||||
\(380\) | 4.50353 | 0.231026 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.4017 | 1.24850 | ||||||||
\(383\) | 20.1762 | 1.03096 | 0.515479 | − | 0.856902i | \(-0.327614\pi\) | ||||
0.515479 | + | 0.856902i | \(0.327614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.05223 | −0.104591 | ||||||||
\(386\) | −19.4069 | −0.987787 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.45287 | −0.479897 | ||||||||
\(389\) | 7.30763 | 0.370512 | 0.185256 | − | 0.982690i | \(-0.440689\pi\) | ||||
0.185256 | + | 0.982690i | \(0.440689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.09439 | −0.0553458 | ||||||||
\(392\) | 11.4372 | 0.577667 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.9428 | −1.10546 | ||||||||
\(395\) | −5.21235 | −0.262262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.5261 | −1.18074 | −0.590372 | − | 0.807131i | \(-0.701019\pi\) | ||||
−0.590372 | + | 0.807131i | \(0.701019\pi\) | |||||||
\(398\) | 16.8329 | 0.843755 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.94487 | −0.247244 | ||||||||
\(401\) | 25.2928 | 1.26306 | 0.631531 | − | 0.775351i | \(-0.282427\pi\) | ||||
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5511 | −0.973908 | ||||||||
\(404\) | 10.5928 | 0.527013 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0361 | 0.895119 | ||||||||
\(407\) | 1.71842 | 0.0851790 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0516 | −0.744252 | −0.372126 | − | 0.928182i | \(-0.621371\pi\) | ||||
−0.372126 | + | 0.928182i | \(0.621371\pi\) | |||||||
\(410\) | −16.1228 | −0.796247 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.16016 | −0.106423 | ||||||||
\(413\) | 3.83184 | 0.188552 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.4175 | −0.560462 | ||||||||
\(416\) | 27.6502 | 1.35566 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.7961 | 0.821525 | ||||||||
\(419\) | −16.8945 | −0.825352 | −0.412676 | − | 0.910878i | \(-0.635406\pi\) | ||||
−0.412676 | + | 0.910878i | \(0.635406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0518 | 1.46464 | 0.732319 | − | 0.680962i | \(-0.238438\pi\) | ||||
0.732319 | + | 0.680962i | \(0.238438\pi\) | |||||||
\(422\) | 21.4448 | 1.04391 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.3411 | 0.890720 | ||||||||
\(425\) | −0.198198 | −0.00961400 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9818 | 0.628234 | ||||||||
\(428\) | −11.0374 | −0.533514 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.4402 | −0.503470 | ||||||||
\(431\) | −30.4221 | −1.46538 | −0.732690 | − | 0.680562i | \(-0.761736\pi\) | ||||
−0.732690 | + | 0.680562i | \(0.761736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.56731 | −0.171434 | −0.0857169 | − | 0.996320i | \(-0.527318\pi\) | ||||
−0.0857169 | + | 0.996320i | \(0.527318\pi\) | |||||||
\(434\) | −5.78735 | −0.277802 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.62249 | −0.412942 | ||||||||
\(437\) | 32.4973 | 1.55456 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.6626 | 1.27254 | 0.636269 | − | 0.771467i | \(-0.280477\pi\) | ||||
0.636269 | + | 0.771467i | \(0.280477\pi\) | |||||||
\(440\) | −3.52395 | −0.167998 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.21396 | 0.105308 | ||||||||
\(443\) | −28.8940 | −1.37280 | −0.686398 | − | 0.727226i | \(-0.740809\pi\) | ||||
−0.686398 | + | 0.727226i | \(0.740809\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | −0.0474045 | ||||||||
\(446\) | 18.7506 | 0.887867 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.64123 | −0.172032 | ||||||||
\(449\) | 0.202083 | 0.00953690 | 0.00476845 | − | 0.999989i | \(-0.498482\pi\) | ||||
0.00476845 | + | 0.999989i | \(0.498482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.6398 | −0.783537 | ||||||||
\(452\) | 5.33981 | 0.251164 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.74801 | −0.410565 | ||||||||
\(455\) | 8.03269 | 0.376578 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.8993 | 1.49219 | 0.746094 | − | 0.665841i | \(-0.231927\pi\) | ||||
0.746094 | + | 0.665841i | \(0.231927\pi\) | |||||||
\(458\) | 46.1254 | 2.15530 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.22526 | 0.197004 | ||||||||
\(461\) | −14.8233 | −0.690390 | −0.345195 | − | 0.938531i | \(-0.612187\pi\) | ||||
−0.345195 | + | 0.938531i | \(0.612187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0952 | −0.701532 | −0.350766 | − | 0.936463i | \(-0.614079\pi\) | ||||
−0.350766 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(464\) | 44.8520 | 2.08220 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.5636 | −0.998916 | ||||||||
\(467\) | −26.4862 | −1.22564 | −0.612818 | − | 0.790224i | \(-0.709964\pi\) | ||||
−0.612818 | + | 0.790224i | \(0.709964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.9805 | −0.830264 | ||||||||
\(470\) | −7.06310 | −0.325797 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.57978 | 0.302859 | ||||||||
\(473\) | −10.7750 | −0.495433 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.88536 | 0.270039 | ||||||||
\(476\) | 0.181356 | 0.00831244 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.73076 | 0.216380 | ||||||||
\(479\) | 38.6539 | 1.76614 | 0.883071 | − | 0.469240i | \(-0.155472\pi\) | ||||
0.883071 | + | 0.469240i | \(0.155472\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.72614 | −0.306685 | ||||||||
\(482\) | 25.7050 | 1.17083 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.16345 | −0.280157 | ||||||||
\(485\) | −12.3533 | −0.560936 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.2894 | 1.96163 | 0.980814 | − | 0.194946i | \(-0.0624531\pi\) | ||||
0.980814 | + | 0.194946i | \(0.0624531\pi\) | |||||||
\(488\) | 22.2915 | 1.00909 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.26247 | −0.418436 | ||||||||
\(491\) | −6.88098 | −0.310534 | −0.155267 | − | 0.987873i | \(-0.549624\pi\) | ||||
−0.155267 | + | 0.987873i | \(0.549624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.79773 | 0.0809658 | ||||||||
\(494\) | −65.7423 | −2.95788 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.3919 | −0.646215 | ||||||||
\(497\) | 4.22021 | 0.189302 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.61190 | 0.340756 | 0.170378 | − | 0.985379i | \(-0.445501\pi\) | ||||
0.170378 | + | 0.985379i | \(0.445501\pi\) | |||||||
\(500\) | 0.765209 | 0.0342212 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.8450 | −1.15352 | ||||||||
\(503\) | 1.51948 | 0.0677503 | 0.0338752 | − | 0.999426i | \(-0.489215\pi\) | ||||
0.0338752 | + | 0.999426i | \(0.489215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.8431 | 0.616009 | ||||||||
\(506\) | 15.7583 | 0.700543 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.75549 | 0.432830 | ||||||||
\(509\) | −0.581726 | −0.0257845 | −0.0128923 | − | 0.999917i | \(-0.504104\pi\) | ||||
−0.0128923 | + | 0.999917i | \(0.504104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.02546 | 0.178076 | ||||||||
\(512\) | 0.0469310 | 0.00207408 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.6590 | 1.35231 | ||||||||
\(515\) | −2.82296 | −0.124395 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.28960 | −0.320596 | ||||||||
\(518\) | −1.99102 | −0.0874803 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.7932 | 0.604872 | ||||||||
\(521\) | −24.8734 | −1.08972 | −0.544862 | − | 0.838526i | \(-0.683418\pi\) | ||||
−0.544862 | + | 0.838526i | \(0.683418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.87994 | 0.169658 | 0.0848290 | − | 0.996396i | \(-0.472966\pi\) | ||||
0.0848290 | + | 0.996396i | \(0.472966\pi\) | |||||||
\(524\) | −10.9041 | −0.476346 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.27847 | −0.0993458 | ||||||||
\(527\) | −0.576848 | −0.0251279 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.48935 | 0.325624 | ||||||||
\(530\) | −14.8536 | −0.645198 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.38525 | −0.233480 | ||||||||
\(533\) | 65.1304 | 2.82111 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4241 | −0.623607 | ||||||||
\(536\) | −30.8750 | −1.33360 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.0164 | −0.906080 | ||||||||
\(539\) | −9.55949 | −0.411756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.04133 | −0.0877634 | −0.0438817 | − | 0.999037i | \(-0.513972\pi\) | ||||
−0.0438817 | + | 0.999037i | \(0.513972\pi\) | |||||||
\(542\) | −21.3696 | −0.917903 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.815810 | 0.0349776 | ||||||||
\(545\) | −11.2682 | −0.482675 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.56220 | −0.109552 | −0.0547760 | − | 0.998499i | \(-0.517444\pi\) | ||||
−0.0547760 | + | 0.998499i | \(0.517444\pi\) | |||||||
\(548\) | −9.63823 | −0.411725 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.85388 | 0.121690 | ||||||||
\(551\) | −53.3826 | −2.27417 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.23285 | 0.265048 | ||||||||
\(554\) | −42.4151 | −1.80205 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.4691 | 0.656037 | ||||||||
\(557\) | −17.4626 | −0.739913 | −0.369957 | − | 0.929049i | \(-0.620627\pi\) | ||||
−0.369957 | + | 0.929049i | \(0.620627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.1746 | 1.78380 | ||||||||
\(560\) | 5.91301 | 0.249870 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.7257 | 0.705531 | ||||||||
\(563\) | −28.7597 | −1.21208 | −0.606039 | − | 0.795435i | \(-0.707243\pi\) | ||||
−0.606039 | + | 0.795435i | \(0.707243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.97824 | 0.293577 | ||||||||
\(566\) | −19.6895 | −0.827613 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.24667 | 0.304063 | ||||||||
\(569\) | −15.4946 | −0.649566 | −0.324783 | − | 0.945789i | \(-0.605291\pi\) | ||||
−0.324783 | + | 0.945789i | \(0.605291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.95093 | −0.249039 | −0.124519 | − | 0.992217i | \(-0.539739\pi\) | ||||
−0.124519 | + | 0.992217i | \(0.539739\pi\) | |||||||
\(572\) | −8.82185 | −0.368860 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.2794 | 0.804706 | ||||||||
\(575\) | 5.52172 | 0.230271 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.1544 | −0.672517 | −0.336258 | − | 0.941770i | \(-0.609162\pi\) | ||||
−0.336258 | + | 0.941770i | \(0.609162\pi\) | |||||||
\(578\) | −28.2038 | −1.17312 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.94075 | −0.288199 | ||||||||
\(581\) | 13.6529 | 0.566416 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.3299 | −0.634899 | ||||||||
\(584\) | 6.91226 | 0.286031 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.9878 | −1.36271 | ||||||||
\(587\) | −11.3500 | −0.468467 | −0.234233 | − | 0.972180i | \(-0.575258\pi\) | ||||
−0.234233 | + | 0.972180i | \(0.575258\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1291 | 0.705794 | ||||||||
\(590\) | −5.32866 | −0.219377 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.95123 | −0.203494 | ||||||||
\(593\) | −41.0239 | −1.68465 | −0.842325 | − | 0.538970i | \(-0.818814\pi\) | ||||
−0.842325 | + | 0.538970i | \(0.818814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.237002 | 0.00971614 | ||||||||
\(596\) | 16.2075 | 0.663886 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −61.6802 | −2.52229 | ||||||||
\(599\) | 27.9781 | 1.14316 | 0.571578 | − | 0.820548i | \(-0.306331\pi\) | ||||
0.571578 | + | 0.820548i | \(0.306331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6344 | 0.515367 | 0.257683 | − | 0.966229i | \(-0.417041\pi\) | ||||
0.257683 | + | 0.966229i | \(0.417041\pi\) | |||||||
\(602\) | 12.4842 | 0.508818 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.22643 | 0.212660 | ||||||||
\(605\) | −8.05460 | −0.327466 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.4981 | −0.588459 | −0.294229 | − | 0.955735i | \(-0.595063\pi\) | ||||
−0.294229 | + | 0.955735i | \(0.595063\pi\) | |||||||
\(608\) | −24.2250 | −0.982452 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0529 | −0.730940 | ||||||||
\(611\) | 28.5325 | 1.15430 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.5975 | −0.589589 | −0.294794 | − | 0.955561i | \(-0.595251\pi\) | ||||
−0.294794 | + | 0.955561i | \(0.595251\pi\) | |||||||
\(614\) | −5.52460 | −0.222955 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.21389 | 0.169782 | ||||||||
\(617\) | −16.4323 | −0.661541 | −0.330771 | − | 0.943711i | \(-0.607309\pi\) | ||||
−0.330771 | + | 0.943711i | \(0.607309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.9391 | 1.20335 | 0.601677 | − | 0.798740i | \(-0.294500\pi\) | ||||
0.601677 | + | 0.798740i | \(0.294500\pi\) | |||||||
\(620\) | 2.22711 | 0.0894431 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.1193 | −0.726516 | ||||||||
\(623\) | 1.19579 | 0.0479081 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.99100 | 0.239448 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.20758 | 0.247710 | ||||||||
\(629\) | −0.198453 | −0.00791282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8242 | −0.709571 | −0.354786 | − | 0.934948i | \(-0.615446\pi\) | ||||
−0.354786 | + | 0.934948i | \(0.615446\pi\) | |||||||
\(632\) | 10.7026 | 0.425728 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.4755 | −0.574894 | ||||||||
\(635\) | 12.7488 | 0.505920 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.4171 | 1.48252 | ||||||||
\(638\) | −25.8858 | −1.02483 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13.2959 | 0.525565 | ||||||||
\(641\) | −8.57421 | −0.338661 | −0.169330 | − | 0.985559i | \(-0.554160\pi\) | ||||
−0.169330 | + | 0.985559i | \(0.554160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.12722 | 0.0444531 | 0.0222266 | − | 0.999753i | \(-0.492924\pi\) | ||||
0.0222266 | + | 0.999753i | \(0.492924\pi\) | |||||||
\(644\) | −5.05251 | −0.199097 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.93971 | −0.0763167 | ||||||||
\(647\) | −3.85176 | −0.151428 | −0.0757141 | − | 0.997130i | \(-0.524124\pi\) | ||||
−0.0757141 | + | 0.997130i | \(0.524124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.49953 | −0.215875 | ||||||||
\(650\) | −11.1705 | −0.438142 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.593628 | 0.0232483 | ||||||||
\(653\) | 27.7221 | 1.08485 | 0.542426 | − | 0.840104i | \(-0.317506\pi\) | ||||
0.542426 | + | 0.840104i | \(0.317506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2498 | −0.556786 | ||||||||
\(656\) | 47.9436 | 1.87188 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.44596 | 0.329258 | ||||||||
\(659\) | 15.6657 | 0.610249 | 0.305125 | − | 0.952312i | \(-0.401302\pi\) | ||||
0.305125 | + | 0.952312i | \(0.401302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.3528 | 1.76402 | 0.882009 | − | 0.471233i | \(-0.156191\pi\) | ||||
0.882009 | + | 0.471233i | \(0.156191\pi\) | |||||||
\(662\) | −48.0847 | −1.86886 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.4438 | 0.909796 | ||||||||
\(665\) | −7.03763 | −0.272907 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.0842 | −1.93927 | ||||||||
\(668\) | 6.36140 | 0.246130 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25.0042 | 0.965997 | ||||||||
\(671\) | −18.6318 | −0.719272 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.0019 | 1.73470 | 0.867348 | − | 0.497702i | \(-0.165823\pi\) | ||||
0.867348 | + | 0.497702i | \(0.165823\pi\) | |||||||
\(674\) | −5.23278 | −0.201559 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.5822 | 0.945469 | ||||||||
\(677\) | −9.10467 | −0.349921 | −0.174960 | − | 0.984575i | \(-0.555980\pi\) | ||||
−0.174960 | + | 0.984575i | \(0.555980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.7719 | 0.566894 | ||||||||
\(680\) | 0.406964 | 0.0156064 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.30613 | 0.318058 | ||||||||
\(683\) | 16.3302 | 0.624856 | 0.312428 | − | 0.949941i | \(-0.398858\pi\) | ||||
0.312428 | + | 0.949941i | \(0.398858\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.5956 | −0.481251 | ||||||||
\(686\) | 24.9952 | 0.954320 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.0455 | 1.18360 | ||||||||
\(689\) | 60.0032 | 2.28594 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.41243 | −0.358066 | −0.179033 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179033 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(692\) | −2.17986 | −0.0828659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.6299 | 0.972897 | ||||||||
\(695\) | 20.2156 | 0.766820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.92165 | 0.0727877 | ||||||||
\(698\) | 34.1919 | 1.29418 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.915025 | −0.0345847 | ||||||||
\(701\) | 19.5729 | 0.739257 | 0.369628 | − | 0.929180i | \(-0.379485\pi\) | ||||
0.369628 | + | 0.929180i | \(0.379485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.89293 | 0.222256 | ||||||||
\(704\) | 5.22597 | 0.196961 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −55.7839 | −2.09945 | ||||||||
\(707\) | −16.5533 | −0.622553 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.6409 | 0.775187 | 0.387593 | − | 0.921830i | \(-0.373307\pi\) | ||||
0.387593 | + | 0.921830i | \(0.373307\pi\) | |||||||
\(710\) | −5.86874 | −0.220250 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.05332 | 0.0769516 | ||||||||
\(713\) | 16.0708 | 0.601855 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5287 | −0.431148 | ||||||||
\(716\) | 8.61470 | 0.321946 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.7133 | 1.07157 | ||||||||
\(719\) | −1.99007 | −0.0742169 | −0.0371085 | − | 0.999311i | \(-0.511815\pi\) | ||||
−0.0371085 | + | 0.999311i | \(0.511815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.37566 | 0.125716 | ||||||||
\(722\) | 26.0034 | 0.967746 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.27786 | 0.196150 | ||||||||
\(725\) | −9.07040 | −0.336866 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.1638 | 0.822009 | 0.411005 | − | 0.911633i | \(-0.365178\pi\) | ||||
0.411005 | + | 0.911633i | \(0.365178\pi\) | |||||||
\(728\) | −16.4937 | −0.611298 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.59792 | −0.207188 | ||||||||
\(731\) | 1.24435 | 0.0460239 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.4198 | 0.938903 | 0.469452 | − | 0.882958i | \(-0.344452\pi\) | ||||
0.469452 | + | 0.882958i | \(0.344452\pi\) | |||||||
\(734\) | 21.3188 | 0.786891 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.7282 | −0.837771 | ||||||||
\(737\) | 25.8060 | 0.950577 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.8759 | −0.841502 | −0.420751 | − | 0.907176i | \(-0.638233\pi\) | ||||
−0.420751 | + | 0.907176i | \(0.638233\pi\) | |||||||
\(740\) | 0.766192 | 0.0281658 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.7617 | 0.652052 | ||||||||
\(743\) | −33.2907 | −1.22132 | −0.610658 | − | 0.791894i | \(-0.709095\pi\) | ||||
−0.610658 | + | 0.791894i | \(0.709095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.1805 | 0.775994 | ||||||||
\(746\) | 38.2852 | 1.40172 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.260286 | −0.00951699 | ||||||||
\(749\) | 17.2481 | 0.630232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.3081 | −1.03298 | −0.516488 | − | 0.856294i | \(-0.672761\pi\) | ||||
−0.516488 | + | 0.856294i | \(0.672761\pi\) | |||||||
\(752\) | 21.0033 | 0.765910 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 101.321 | 3.68988 | ||||||||
\(755\) | 6.83007 | 0.248572 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.0207 | −1.16381 | −0.581906 | − | 0.813256i | \(-0.697693\pi\) | ||||
−0.581906 | + | 0.813256i | \(0.697693\pi\) | |||||||
\(758\) | −5.64196 | −0.204925 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0846 | −0.438353 | ||||||||
\(761\) | −8.64233 | −0.313284 | −0.156642 | − | 0.987655i | \(-0.550067\pi\) | ||||
−0.156642 | + | 0.987655i | \(0.550067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.4743 | 0.487802 | ||||||||
\(764\) | 11.2289 | 0.406247 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.5509 | 1.21224 | ||||||||
\(767\) | 21.5259 | 0.777255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.1270 | −1.44702 | −0.723509 | − | 0.690315i | \(-0.757472\pi\) | ||||
−0.723509 | + | 0.690315i | \(0.757472\pi\) | |||||||
\(770\) | −3.41263 | −0.122983 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.93044 | −0.321414 | ||||||||
\(773\) | 2.23597 | 0.0804221 | 0.0402111 | − | 0.999191i | \(-0.487197\pi\) | ||||
0.0402111 | + | 0.999191i | \(0.487197\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.91047 | 0.104547 | ||||||||
\(776\) | 25.3654 | 0.910564 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.1518 | 0.435663 | ||||||||
\(779\) | −57.0622 | −2.04447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.05693 | −0.216734 | ||||||||
\(782\) | −1.81986 | −0.0650779 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.5434 | 0.983694 | ||||||||
\(785\) | 8.11228 | 0.289540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.85057 | −0.315489 | −0.157744 | − | 0.987480i | \(-0.550422\pi\) | ||||
−0.157744 | + | 0.987480i | \(0.550422\pi\) | |||||||
\(788\) | −10.0974 | −0.359704 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.66757 | −0.308378 | ||||||||
\(791\) | −8.34448 | −0.296696 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 72.9273 | 2.58972 | ||||||||
\(794\) | −39.1214 | −1.38837 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.74593 | 0.274547 | ||||||||
\(797\) | 9.35770 | 0.331467 | 0.165733 | − | 0.986171i | \(-0.447001\pi\) | ||||
0.165733 | + | 0.986171i | \(0.447001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.841842 | 0.0297822 | ||||||||
\(800\) | −4.11614 | −0.145528 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 42.0592 | 1.48516 | ||||||||
\(803\) | −5.77743 | −0.203881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.60279 | −0.232718 | ||||||||
\(806\) | −32.5113 | −1.14516 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.4243 | −0.999964 | ||||||||
\(809\) | 11.3616 | 0.399452 | 0.199726 | − | 0.979852i | \(-0.435995\pi\) | ||||
0.199726 | + | 0.979852i | \(0.435995\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.473846 | −0.0166390 | −0.00831950 | − | 0.999965i | \(-0.502648\pi\) | ||||
−0.00831950 | + | 0.999965i | \(0.502648\pi\) | |||||||
\(812\) | 8.29964 | 0.291260 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.85755 | 0.100157 | ||||||||
\(815\) | 0.775772 | 0.0271741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.9502 | −1.29272 | ||||||||
\(818\) | −25.0291 | −0.875122 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.41917 | −0.259089 | ||||||||
\(821\) | 20.7434 | 0.723950 | 0.361975 | − | 0.932188i | \(-0.382103\pi\) | ||||
0.361975 | + | 0.932188i | \(0.382103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.18591 | −0.0413381 | −0.0206691 | − | 0.999786i | \(-0.506580\pi\) | ||||
−0.0206691 | + | 0.999786i | \(0.506580\pi\) | |||||||
\(824\) | 5.79646 | 0.201929 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.37193 | 0.221708 | ||||||||
\(827\) | 3.91986 | 0.136307 | 0.0681535 | − | 0.997675i | \(-0.478289\pi\) | ||||
0.0681535 | + | 0.997675i | \(0.478289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.6555 | −0.786858 | −0.393429 | − | 0.919355i | \(-0.628711\pi\) | ||||
−0.393429 | + | 0.919355i | \(0.628711\pi\) | |||||||
\(830\) | −18.9860 | −0.659015 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.4551 | −0.709154 | ||||||||
\(833\) | 1.10398 | 0.0382507 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.31329 | 0.287693 | ||||||||
\(836\) | 7.72903 | 0.267314 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.0938 | −0.970484 | ||||||||
\(839\) | 19.8509 | 0.685330 | 0.342665 | − | 0.939458i | \(-0.388670\pi\) | ||||
0.342665 | + | 0.939458i | \(0.388670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.2721 | 1.83697 | ||||||||
\(842\) | 49.9730 | 1.72218 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.86818 | 0.339677 | ||||||||
\(845\) | 32.1248 | 1.10513 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.63158 | 0.330945 | ||||||||
\(848\) | 44.1694 | 1.51678 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.329581 | −0.0113045 | ||||||||
\(851\) | 5.52881 | 0.189525 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.6566 | 0.844224 | 0.422112 | − | 0.906544i | \(-0.361289\pi\) | ||||
0.422112 | + | 0.906544i | \(0.361289\pi\) | |||||||
\(854\) | 21.5874 | 0.738704 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6173 | 1.01230 | ||||||||
\(857\) | −38.0292 | −1.29905 | −0.649526 | − | 0.760339i | \(-0.725033\pi\) | ||||
−0.649526 | + | 0.760339i | \(0.725033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.74130 | 0.0935321 | 0.0467660 | − | 0.998906i | \(-0.485108\pi\) | ||||
0.0467660 | + | 0.998906i | \(0.485108\pi\) | |||||||
\(860\) | −4.80423 | −0.163823 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −50.5887 | −1.72306 | ||||||||
\(863\) | 55.9189 | 1.90350 | 0.951750 | − | 0.306874i | \(-0.0992831\pi\) | ||||
0.951750 | + | 0.306874i | \(0.0992831\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.84871 | −0.0968592 | ||||||||
\(866\) | −5.93204 | −0.201579 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.66315 | −0.0903932 | ||||||||
\(869\) | −8.94551 | −0.303456 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −101.008 | −3.42253 | ||||||||
\(872\) | 23.1372 | 0.783524 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 54.0395 | 1.82791 | ||||||||
\(875\) | −1.19579 | −0.0404249 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.89562 | 0.300384 | 0.150192 | − | 0.988657i | \(-0.452011\pi\) | ||||
0.150192 | + | 0.988657i | \(0.452011\pi\) | |||||||
\(878\) | 44.3371 | 1.49630 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.48647 | −0.286079 | ||||||||
\(881\) | −36.7358 | −1.23766 | −0.618831 | − | 0.785524i | \(-0.712393\pi\) | ||||
−0.618831 | + | 0.785524i | \(0.712393\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.5930 | −1.09684 | −0.548422 | − | 0.836202i | \(-0.684771\pi\) | ||||
−0.548422 | + | 0.836202i | \(0.684771\pi\) | |||||||
\(884\) | 1.01879 | 0.0342658 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48.0476 | −1.61419 | ||||||||
\(887\) | −17.7696 | −0.596646 | −0.298323 | − | 0.954465i | \(-0.596427\pi\) | ||||
−0.298323 | + | 0.954465i | \(0.596427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.2448 | −0.511295 | ||||||||
\(890\) | −1.66289 | −0.0557403 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.62842 | 0.288901 | ||||||||
\(893\) | −24.9980 | −0.836525 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2580 | 0.376313 | ||||||||
\(896\) | −15.8990 | −0.531149 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.336043 | 0.0112139 | ||||||||
\(899\) | −26.3991 | −0.880459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.77038 | 0.0589798 | ||||||||
\(902\) | −27.6702 | −0.921315 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.3286 | −0.476562 | ||||||||
\(905\) | 6.89728 | 0.229273 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.2038 | 1.13572 | 0.567860 | − | 0.823125i | \(-0.307772\pi\) | ||||
0.567860 | + | 0.823125i | \(0.307772\pi\) | |||||||
\(908\) | −4.02555 | −0.133593 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.3575 | 0.442797 | ||||||||
\(911\) | 4.05202 | 0.134249 | 0.0671246 | − | 0.997745i | \(-0.478617\pi\) | ||||
0.0671246 | + | 0.997745i | \(0.478617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5949 | −0.648495 | ||||||||
\(914\) | 53.0451 | 1.75458 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.2254 | 0.701307 | ||||||||
\(917\) | 17.0397 | 0.562700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.2709 | 0.932571 | 0.466285 | − | 0.884634i | \(-0.345592\pi\) | ||||
0.466285 | + | 0.884634i | \(0.345592\pi\) | |||||||
\(920\) | −11.3379 | −0.373799 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.6495 | −0.811790 | ||||||||
\(923\) | 23.7076 | 0.780347 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00129 | 0.0329221 | ||||||||
\(926\) | −25.1016 | −0.824890 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37.3350 | 1.22558 | ||||||||
\(929\) | 36.5851 | 1.20032 | 0.600159 | − | 0.799881i | \(-0.295104\pi\) | ||||
0.600159 | + | 0.799881i | \(0.295104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.7820 | −1.07439 | ||||||||
\(932\) | −9.92289 | −0.325035 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −44.0437 | −1.44115 | ||||||||
\(935\) | −0.340150 | −0.0111241 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.3092 | 0.892153 | 0.446076 | − | 0.894995i | \(-0.352821\pi\) | ||||
0.446076 | + | 0.894995i | \(0.352821\pi\) | |||||||
\(938\) | −29.8997 | −0.976259 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.25021 | −0.106010 | ||||||||
\(941\) | 22.8368 | 0.744457 | 0.372228 | − | 0.928141i | \(-0.378594\pi\) | ||||
0.372228 | + | 0.928141i | \(0.378594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53.5365 | −1.74339 | ||||||||
\(944\) | 15.8456 | 0.515731 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.9176 | −0.582551 | ||||||||
\(947\) | −9.04038 | −0.293773 | −0.146887 | − | 0.989153i | \(-0.546925\pi\) | ||||
−0.146887 | + | 0.989153i | \(0.546925\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.6136 | 0.734070 | ||||||||
\(950\) | 9.78671 | 0.317523 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.486642 | −0.0157722 | ||||||||
\(953\) | 34.7105 | 1.12438 | 0.562192 | − | 0.827007i | \(-0.309958\pi\) | ||||
0.562192 | + | 0.827007i | \(0.309958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6743 | 0.474849 | ||||||||
\(956\) | 2.17694 | 0.0704073 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 64.2772 | 2.07670 | ||||||||
\(959\) | 15.0616 | 0.486364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5292 | −0.726748 | ||||||||
\(962\) | −11.1848 | −0.360614 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.8286 | 0.380973 | ||||||||
\(965\) | −11.6706 | −0.375690 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.0870 | −1.54637 | −0.773187 | − | 0.634178i | \(-0.781339\pi\) | ||||
−0.773187 | + | 0.634178i | \(0.781339\pi\) | |||||||
\(968\) | 16.5387 | 0.531574 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.5422 | −0.659572 | ||||||||
\(971\) | −60.5323 | −1.94257 | −0.971287 | − | 0.237912i | \(-0.923537\pi\) | ||||
−0.971287 | + | 0.237912i | \(0.923537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.1735 | −0.774966 | ||||||||
\(974\) | 71.9855 | 2.30656 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 53.6831 | 1.71835 | ||||||||
\(977\) | 34.0996 | 1.09094 | 0.545472 | − | 0.838129i | \(-0.316351\pi\) | ||||
0.545472 | + | 0.838129i | \(0.316351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.71622 | −0.0548505 | ||||||||
\(980\) | −4.26229 | −0.136154 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.4423 | −0.365139 | ||||||||
\(983\) | 38.6982 | 1.23428 | 0.617141 | − | 0.786853i | \(-0.288291\pi\) | ||||
0.617141 | + | 0.786853i | \(0.288291\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1956 | −0.420447 | ||||||||
\(986\) | 2.98943 | 0.0952030 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.2525 | −0.962459 | ||||||||
\(989\) | −34.6671 | −1.10235 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.87602 | −0.186658 | −0.0933290 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933290 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(992\) | −11.9799 | −0.380362 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.01775 | 0.222590 | ||||||||
\(995\) | 10.1226 | 0.320909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.1823 | −1.33593 | −0.667963 | − | 0.744195i | \(-0.732834\pi\) | ||||
−0.667963 | + | 0.744195i | \(0.732834\pi\) | |||||||
\(998\) | 12.6578 | 0.400675 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4005.2.a.p.1.7 | 8 | ||
3.2 | odd | 2 | 445.2.a.g.1.2 | ✓ | 8 | ||
12.11 | even | 2 | 7120.2.a.bk.1.7 | 8 | |||
15.14 | odd | 2 | 2225.2.a.l.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.g.1.2 | ✓ | 8 | 3.2 | odd | 2 | ||
2225.2.a.l.1.7 | 8 | 15.14 | odd | 2 | |||
4005.2.a.p.1.7 | 8 | 1.1 | even | 1 | trivial | ||
7120.2.a.bk.1.7 | 8 | 12.11 | even | 2 |