Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-2.02621\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.02621 | 1.43275 | 0.716373 | − | 0.697718i | \(-0.245801\pi\) | ||||
0.716373 | + | 0.697718i | \(0.245801\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.10552 | 1.05276 | ||||||||
\(5\) | −3.48073 | −1.55663 | −0.778314 | − | 0.627875i | \(-0.783925\pi\) | ||||
−0.778314 | + | 0.627875i | \(0.783925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.37004 | 0.517828 | 0.258914 | − | 0.965900i | \(-0.416635\pi\) | ||||
0.258914 | + | 0.965900i | \(0.416635\pi\) | |||||||
\(8\) | 0.213806 | 0.0755918 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.05267 | −2.23025 | ||||||||
\(11\) | −0.191564 | −0.0577588 | −0.0288794 | − | 0.999583i | \(-0.509194\pi\) | ||||
−0.0288794 | + | 0.999583i | \(0.509194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24334 | 1.17689 | 0.588445 | − | 0.808537i | \(-0.299740\pi\) | ||||
0.588445 | + | 0.808537i | \(0.299740\pi\) | |||||||
\(14\) | 2.77599 | 0.741915 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.77782 | −0.944456 | ||||||||
\(17\) | −4.07863 | −0.989214 | −0.494607 | − | 0.869117i | \(-0.664688\pi\) | ||||
−0.494607 | + | 0.869117i | \(0.664688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.16823 | −1.18567 | −0.592837 | − | 0.805323i | \(-0.701992\pi\) | ||||
−0.592837 | + | 0.805323i | \(0.701992\pi\) | |||||||
\(20\) | −7.32874 | −1.63876 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.388149 | −0.0827536 | ||||||||
\(23\) | −0.978985 | −0.204132 | −0.102066 | − | 0.994778i | \(-0.532545\pi\) | ||||
−0.102066 | + | 0.994778i | \(0.532545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.11545 | 1.42309 | ||||||||
\(26\) | 8.59789 | 1.68619 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.88465 | 0.545148 | ||||||||
\(29\) | −10.0111 | −1.85901 | −0.929507 | − | 0.368806i | \(-0.879767\pi\) | ||||
−0.929507 | + | 0.368806i | \(0.879767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04813 | −0.727065 | −0.363533 | − | 0.931582i | \(-0.618429\pi\) | ||||
−0.363533 | + | 0.931582i | \(0.618429\pi\) | |||||||
\(32\) | −8.08227 | −1.42876 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.26416 | −1.41729 | ||||||||
\(35\) | −4.76874 | −0.806065 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.15163 | 0.353726 | 0.176863 | − | 0.984235i | \(-0.443405\pi\) | ||||
0.176863 | + | 0.984235i | \(0.443405\pi\) | |||||||
\(38\) | −10.4719 | −1.69877 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.744200 | −0.117668 | ||||||||
\(41\) | −0.0317692 | −0.00496152 | −0.00248076 | − | 0.999997i | \(-0.500790\pi\) | ||||
−0.00248076 | + | 0.999997i | \(0.500790\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.77809 | 0.423654 | 0.211827 | − | 0.977307i | \(-0.432059\pi\) | ||||
0.211827 | + | 0.977307i | \(0.432059\pi\) | |||||||
\(44\) | −0.403342 | −0.0608061 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.98363 | −0.292470 | ||||||||
\(47\) | −0.680962 | −0.0993286 | −0.0496643 | − | 0.998766i | \(-0.515815\pi\) | ||||
−0.0496643 | + | 0.998766i | \(0.515815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.12298 | −0.731854 | ||||||||
\(50\) | 14.4174 | 2.03893 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.93444 | 1.23898 | ||||||||
\(53\) | −4.91306 | −0.674861 | −0.337431 | − | 0.941350i | \(-0.609558\pi\) | ||||
−0.337431 | + | 0.941350i | \(0.609558\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.666782 | 0.0899089 | ||||||||
\(56\) | 0.292924 | 0.0391436 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20.2846 | −2.66349 | ||||||||
\(59\) | −3.94941 | −0.514169 | −0.257085 | − | 0.966389i | \(-0.582762\pi\) | ||||
−0.257085 | + | 0.966389i | \(0.582762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.63175 | 0.464997 | 0.232499 | − | 0.972597i | \(-0.425310\pi\) | ||||
0.232499 | + | 0.972597i | \(0.425310\pi\) | |||||||
\(62\) | −8.20235 | −1.04170 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.82072 | −1.10259 | ||||||||
\(65\) | −14.7699 | −1.83198 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.37197 | 0.656290 | 0.328145 | − | 0.944627i | \(-0.393576\pi\) | ||||
0.328145 | + | 0.944627i | \(0.393576\pi\) | |||||||
\(68\) | −8.58765 | −1.04141 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.66247 | −1.15489 | ||||||||
\(71\) | 8.95527 | 1.06279 | 0.531397 | − | 0.847123i | \(-0.321667\pi\) | ||||
0.531397 | + | 0.847123i | \(0.321667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.76915 | −0.909310 | −0.454655 | − | 0.890668i | \(-0.650237\pi\) | ||||
−0.454655 | + | 0.890668i | \(0.650237\pi\) | |||||||
\(74\) | 4.35966 | 0.506800 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.8818 | −1.24823 | ||||||||
\(77\) | −0.262451 | −0.0299091 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9221 | −1.45385 | −0.726924 | − | 0.686718i | \(-0.759051\pi\) | ||||
−0.726924 | + | 0.686718i | \(0.759051\pi\) | |||||||
\(80\) | 13.1496 | 1.47017 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.0643711 | −0.00710860 | ||||||||
\(83\) | −2.22931 | −0.244698 | −0.122349 | − | 0.992487i | \(-0.539043\pi\) | ||||
−0.122349 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.1966 | 1.53984 | ||||||||
\(86\) | 5.62898 | 0.606989 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0409576 | −0.00436609 | ||||||||
\(89\) | 9.94855 | 1.05454 | 0.527272 | − | 0.849696i | \(-0.323215\pi\) | ||||
0.527272 | + | 0.849696i | \(0.323215\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.81356 | 0.609427 | ||||||||
\(92\) | −2.06127 | −0.214903 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.37977 | −0.142313 | ||||||||
\(95\) | 17.9892 | 1.84565 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.84284 | −0.491715 | −0.245858 | − | 0.969306i | \(-0.579070\pi\) | ||||
−0.245858 | + | 0.969306i | \(0.579070\pi\) | |||||||
\(98\) | −10.3802 | −1.04856 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.9817 | 1.49817 | ||||||||
\(101\) | −12.8427 | −1.27790 | −0.638950 | − | 0.769249i | \(-0.720631\pi\) | ||||
−0.638950 | + | 0.769249i | \(0.720631\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.83159 | −0.968736 | −0.484368 | − | 0.874864i | \(-0.660950\pi\) | ||||
−0.484368 | + | 0.874864i | \(0.660950\pi\) | |||||||
\(104\) | 0.907252 | 0.0889634 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.95489 | −0.966904 | ||||||||
\(107\) | −6.72004 | −0.649650 | −0.324825 | − | 0.945774i | \(-0.605305\pi\) | ||||
−0.324825 | + | 0.945774i | \(0.605305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0804 | 1.63601 | 0.818005 | − | 0.575211i | \(-0.195080\pi\) | ||||
0.818005 | + | 0.575211i | \(0.195080\pi\) | |||||||
\(110\) | 1.35104 | 0.128817 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.17578 | −0.489066 | ||||||||
\(113\) | 12.2581 | 1.15315 | 0.576574 | − | 0.817045i | \(-0.304389\pi\) | ||||
0.576574 | + | 0.817045i | \(0.304389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.40758 | 0.317758 | ||||||||
\(116\) | −21.0786 | −1.95709 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.00233 | −0.736674 | ||||||||
\(119\) | −5.58791 | −0.512243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9633 | −0.996664 | ||||||||
\(122\) | 7.35867 | 0.666223 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.52341 | −0.765425 | ||||||||
\(125\) | −7.36330 | −0.658593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4140 | −1.19030 | −0.595151 | − | 0.803614i | \(-0.702908\pi\) | ||||
−0.595151 | + | 0.803614i | \(0.702908\pi\) | |||||||
\(128\) | −1.70807 | −0.150973 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −29.9269 | −2.62476 | ||||||||
\(131\) | 15.1828 | 1.32652 | 0.663262 | − | 0.748387i | \(-0.269171\pi\) | ||||
0.663262 | + | 0.748387i | \(0.269171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.08070 | −0.613974 | ||||||||
\(134\) | 10.8847 | 0.940297 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.872037 | −0.0747765 | ||||||||
\(137\) | −6.50914 | −0.556113 | −0.278057 | − | 0.960565i | \(-0.589690\pi\) | ||||
−0.278057 | + | 0.960565i | \(0.589690\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.06206 | −0.429359 | −0.214679 | − | 0.976685i | \(-0.568871\pi\) | ||||
−0.214679 | + | 0.976685i | \(0.568871\pi\) | |||||||
\(140\) | −10.0407 | −0.848593 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.1452 | 1.52271 | ||||||||
\(143\) | −0.812872 | −0.0679758 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.8459 | 2.89379 | ||||||||
\(146\) | −15.7419 | −1.30281 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.53031 | 0.372389 | ||||||||
\(149\) | 10.6906 | 0.875805 | 0.437903 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437903 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4018 | 1.25338 | 0.626691 | − | 0.779268i | \(-0.284409\pi\) | ||||
0.626691 | + | 0.779268i | \(0.284409\pi\) | |||||||
\(152\) | −1.10500 | −0.0896272 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.531781 | −0.0428521 | ||||||||
\(155\) | 14.0904 | 1.13177 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.81548 | −0.304509 | −0.152254 | − | 0.988341i | \(-0.548653\pi\) | ||||
−0.152254 | + | 0.988341i | \(0.548653\pi\) | |||||||
\(158\) | −26.1828 | −2.08299 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.1322 | 2.22404 | ||||||||
\(161\) | −1.34125 | −0.105705 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4217 | 0.816292 | 0.408146 | − | 0.912917i | \(-0.366175\pi\) | ||||
0.408146 | + | 0.912917i | \(0.366175\pi\) | |||||||
\(164\) | −0.0668908 | −0.00522329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.51705 | −0.350591 | ||||||||
\(167\) | −1.09246 | −0.0845374 | −0.0422687 | − | 0.999106i | \(-0.513459\pi\) | ||||
−0.0422687 | + | 0.999106i | \(0.513459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00594 | 0.385072 | ||||||||
\(170\) | 28.7653 | 2.20620 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.84932 | 0.446006 | ||||||||
\(173\) | −10.4717 | −0.796148 | −0.398074 | − | 0.917353i | \(-0.630321\pi\) | ||||
−0.398074 | + | 0.917353i | \(0.630321\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.74847 | 0.736915 | ||||||||
\(176\) | 0.723696 | 0.0545506 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.1578 | 1.51089 | ||||||||
\(179\) | 21.7287 | 1.62408 | 0.812041 | − | 0.583600i | \(-0.198357\pi\) | ||||
0.812041 | + | 0.583600i | \(0.198357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6108 | 0.937351 | 0.468676 | − | 0.883370i | \(-0.344731\pi\) | ||||
0.468676 | + | 0.883370i | \(0.344731\pi\) | |||||||
\(182\) | 11.7795 | 0.873153 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.209313 | −0.0154308 | ||||||||
\(185\) | −7.48924 | −0.550620 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.781320 | 0.0571358 | ||||||||
\(188\) | −1.43378 | −0.104569 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 36.4498 | 2.64435 | ||||||||
\(191\) | −5.93669 | −0.429564 | −0.214782 | − | 0.976662i | \(-0.568904\pi\) | ||||
−0.214782 | + | 0.976662i | \(0.568904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.5726 | 1.48085 | 0.740426 | − | 0.672138i | \(-0.234624\pi\) | ||||
0.740426 | + | 0.672138i | \(0.234624\pi\) | |||||||
\(194\) | −9.81259 | −0.704503 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.7865 | −0.770467 | ||||||||
\(197\) | −3.06174 | −0.218140 | −0.109070 | − | 0.994034i | \(-0.534787\pi\) | ||||
−0.109070 | + | 0.994034i | \(0.534787\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.1755 | 1.64286 | 0.821432 | − | 0.570306i | \(-0.193175\pi\) | ||||
0.821432 | + | 0.570306i | \(0.193175\pi\) | |||||||
\(200\) | 1.52133 | 0.107574 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −26.0220 | −1.83090 | ||||||||
\(203\) | −13.7156 | −0.962649 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.110580 | 0.00772324 | ||||||||
\(206\) | −19.9209 | −1.38795 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0306 | −1.11152 | ||||||||
\(209\) | 0.990047 | 0.0684830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.22027 | 0.221693 | 0.110846 | − | 0.993838i | \(-0.464644\pi\) | ||||
0.110846 | + | 0.993838i | \(0.464644\pi\) | |||||||
\(212\) | −10.3446 | −0.710467 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.6162 | −0.930784 | ||||||||
\(215\) | −9.66976 | −0.659472 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.54611 | −0.376494 | ||||||||
\(218\) | 34.6085 | 2.34399 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.40392 | 0.0946525 | ||||||||
\(221\) | −17.3070 | −1.16420 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.78961 | 0.186806 | 0.0934032 | − | 0.995628i | \(-0.470225\pi\) | ||||
0.0934032 | + | 0.995628i | \(0.470225\pi\) | |||||||
\(224\) | −11.0731 | −0.739850 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.8375 | 1.65217 | ||||||||
\(227\) | −15.2465 | −1.01195 | −0.505975 | − | 0.862548i | \(-0.668867\pi\) | ||||
−0.505975 | + | 0.862548i | \(0.668867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.2752 | 1.14158 | 0.570788 | − | 0.821097i | \(-0.306638\pi\) | ||||
0.570788 | + | 0.821097i | \(0.306638\pi\) | |||||||
\(230\) | 6.90446 | 0.455267 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.14043 | −0.140526 | ||||||||
\(233\) | 12.5824 | 0.824298 | 0.412149 | − | 0.911116i | \(-0.364778\pi\) | ||||
0.412149 | + | 0.911116i | \(0.364778\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.37024 | 0.154618 | ||||||||
\(236\) | −8.31556 | −0.541297 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.3223 | −0.733913 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.658194 | −0.0423980 | −0.0211990 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211990 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(242\) | −22.2139 | −1.42797 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.64671 | 0.489531 | ||||||||
\(245\) | 17.8317 | 1.13922 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.9306 | −1.39541 | ||||||||
\(248\) | −0.865514 | −0.0549602 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.9196 | −0.943597 | ||||||||
\(251\) | −18.5453 | −1.17057 | −0.585283 | − | 0.810829i | \(-0.699017\pi\) | ||||
−0.585283 | + | 0.810829i | \(0.699017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.187538 | 0.0117904 | ||||||||
\(254\) | −27.1796 | −1.70540 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.1805 | 0.886283 | ||||||||
\(257\) | −23.0065 | −1.43511 | −0.717555 | − | 0.696502i | \(-0.754739\pi\) | ||||
−0.717555 | + | 0.696502i | \(0.754739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.94783 | 0.183169 | ||||||||
\(260\) | −31.0983 | −1.92864 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 30.7634 | 1.90057 | ||||||||
\(263\) | −3.78505 | −0.233396 | −0.116698 | − | 0.993167i | \(-0.537231\pi\) | ||||
−0.116698 | + | 0.993167i | \(0.537231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.1010 | 1.05051 | ||||||||
\(266\) | −14.3470 | −0.879669 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.3108 | 0.690916 | ||||||||
\(269\) | 2.62526 | 0.160065 | 0.0800325 | − | 0.996792i | \(-0.474498\pi\) | ||||
0.0800325 | + | 0.996792i | \(0.474498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6427 | −0.707242 | −0.353621 | − | 0.935389i | \(-0.615050\pi\) | ||||
−0.353621 | + | 0.935389i | \(0.615050\pi\) | |||||||
\(272\) | 15.4084 | 0.934270 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.1889 | −0.796769 | ||||||||
\(275\) | −1.36306 | −0.0821959 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.72065 | 0.283636 | 0.141818 | − | 0.989893i | \(-0.454705\pi\) | ||||
0.141818 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(278\) | −10.2568 | −0.615162 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.01959 | −0.0609319 | ||||||||
\(281\) | 25.0192 | 1.49252 | 0.746260 | − | 0.665654i | \(-0.231847\pi\) | ||||
0.746260 | + | 0.665654i | \(0.231847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.85106 | −0.585585 | −0.292792 | − | 0.956176i | \(-0.594584\pi\) | ||||
−0.292792 | + | 0.956176i | \(0.594584\pi\) | |||||||
\(284\) | 18.8555 | 1.11887 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.64705 | −0.0973920 | ||||||||
\(287\) | −0.0435252 | −0.00256921 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.364740 | −0.0214553 | ||||||||
\(290\) | 70.6050 | 4.14607 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.3581 | −0.957285 | ||||||||
\(293\) | 21.2915 | 1.24386 | 0.621932 | − | 0.783071i | \(-0.286348\pi\) | ||||
0.621932 | + | 0.783071i | \(0.286348\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7468 | 0.800370 | ||||||||
\(296\) | 0.460032 | 0.0267388 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.6613 | 1.25481 | ||||||||
\(299\) | −4.15417 | −0.240242 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.80610 | 0.219380 | ||||||||
\(302\) | 31.2073 | 1.79578 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19.5247 | 1.11982 | ||||||||
\(305\) | −12.6411 | −0.723828 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0413 | −0.972597 | −0.486299 | − | 0.873793i | \(-0.661653\pi\) | ||||
−0.486299 | + | 0.873793i | \(0.661653\pi\) | |||||||
\(308\) | −0.552596 | −0.0314871 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 28.5501 | 1.62154 | ||||||||
\(311\) | −22.1896 | −1.25826 | −0.629130 | − | 0.777300i | \(-0.716589\pi\) | ||||
−0.629130 | + | 0.777300i | \(0.716589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.79466 | −0.271010 | −0.135505 | − | 0.990777i | \(-0.543266\pi\) | ||||
−0.135505 | + | 0.990777i | \(0.543266\pi\) | |||||||
\(314\) | −7.73096 | −0.436283 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.2077 | −1.53055 | ||||||||
\(317\) | 10.5786 | 0.594152 | 0.297076 | − | 0.954854i | \(-0.403988\pi\) | ||||
0.297076 | + | 0.954854i | \(0.403988\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.91777 | 0.107374 | ||||||||
\(320\) | 30.7025 | 1.71632 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.71766 | −0.151449 | ||||||||
\(323\) | 21.0793 | 1.17288 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.1933 | 1.67482 | ||||||||
\(326\) | 21.1166 | 1.16954 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.00679245 | −0.000375050 0 | ||||||||
\(329\) | −0.932948 | −0.0514351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.0018 | 1.81394 | 0.906972 | − | 0.421192i | \(-0.138388\pi\) | ||||
0.906972 | + | 0.421192i | \(0.138388\pi\) | |||||||
\(332\) | −4.69386 | −0.257609 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.21356 | −0.121121 | ||||||||
\(335\) | −18.6983 | −1.02160 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.0856 | −1.69334 | −0.846671 | − | 0.532116i | \(-0.821397\pi\) | ||||
−0.846671 | + | 0.532116i | \(0.821397\pi\) | |||||||
\(338\) | 10.1431 | 0.551711 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 29.8912 | 1.62108 | ||||||||
\(341\) | 0.775476 | 0.0419944 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.6090 | −0.896802 | ||||||||
\(344\) | 0.593972 | 0.0320248 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.2178 | −1.14068 | ||||||||
\(347\) | 22.9937 | 1.23436 | 0.617182 | − | 0.786820i | \(-0.288274\pi\) | ||||
0.617182 | + | 0.786820i | \(0.288274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7700 | 0.951208 | 0.475604 | − | 0.879659i | \(-0.342230\pi\) | ||||
0.475604 | + | 0.879659i | \(0.342230\pi\) | |||||||
\(350\) | 19.7524 | 1.05581 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.54827 | 0.0825233 | ||||||||
\(353\) | 13.9632 | 0.743188 | 0.371594 | − | 0.928395i | \(-0.378811\pi\) | ||||
0.371594 | + | 0.928395i | \(0.378811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.1708 | −1.65438 | ||||||||
\(356\) | 20.9469 | 1.11018 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 44.0269 | 2.32690 | ||||||||
\(359\) | −21.7844 | −1.14974 | −0.574869 | − | 0.818245i | \(-0.694947\pi\) | ||||
−0.574869 | + | 0.818245i | \(0.694947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.71060 | 0.405821 | ||||||||
\(362\) | 25.5521 | 1.34299 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.2406 | 0.641580 | ||||||||
\(365\) | 27.0423 | 1.41546 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.31876 | 0.277637 | 0.138818 | − | 0.990318i | \(-0.455670\pi\) | ||||
0.138818 | + | 0.990318i | \(0.455670\pi\) | |||||||
\(368\) | 3.69843 | 0.192794 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.1748 | −0.788898 | ||||||||
\(371\) | −6.73111 | −0.349462 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1559 | −1.19897 | −0.599484 | − | 0.800387i | \(-0.704628\pi\) | ||||
−0.599484 | + | 0.800387i | \(0.704628\pi\) | |||||||
\(374\) | 1.58312 | 0.0818610 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.145594 | −0.00750843 | ||||||||
\(377\) | −42.4805 | −2.18786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.92833 | −0.304518 | −0.152259 | − | 0.988341i | \(-0.548655\pi\) | ||||
−0.152259 | + | 0.988341i | \(0.548655\pi\) | |||||||
\(380\) | 37.8766 | 1.94303 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0290 | −0.615456 | ||||||||
\(383\) | −34.8364 | −1.78006 | −0.890029 | − | 0.455903i | \(-0.849316\pi\) | ||||
−0.890029 | + | 0.455903i | \(0.849316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.913520 | 0.0465573 | ||||||||
\(386\) | 41.6845 | 2.12168 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.1967 | −0.517658 | ||||||||
\(389\) | −1.77761 | −0.0901285 | −0.0450643 | − | 0.998984i | \(-0.514349\pi\) | ||||
−0.0450643 | + | 0.998984i | \(0.514349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.99292 | 0.201931 | ||||||||
\(392\) | −1.09532 | −0.0553222 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.20373 | −0.312540 | ||||||||
\(395\) | 44.9782 | 2.26310 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.8987 | −0.647365 | −0.323682 | − | 0.946166i | \(-0.604921\pi\) | ||||
−0.323682 | + | 0.946166i | \(0.604921\pi\) | |||||||
\(398\) | 46.9583 | 2.35381 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.8809 | −1.34405 | ||||||||
\(401\) | −25.4445 | −1.27064 | −0.635319 | − | 0.772250i | \(-0.719131\pi\) | ||||
−0.635319 | + | 0.772250i | \(0.719131\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1776 | −0.855676 | ||||||||
\(404\) | −27.0406 | −1.34532 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.7907 | −1.37923 | ||||||||
\(407\) | −0.412176 | −0.0204308 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.1140 | −1.63738 | −0.818690 | − | 0.574235i | \(-0.805299\pi\) | ||||
−0.818690 | + | 0.574235i | \(0.805299\pi\) | |||||||
\(410\) | 0.224058 | 0.0110654 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.7006 | −1.01985 | ||||||||
\(413\) | −5.41086 | −0.266251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.75961 | 0.380904 | ||||||||
\(416\) | −34.2958 | −1.68149 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.00604 | 0.0981187 | ||||||||
\(419\) | −33.1423 | −1.61911 | −0.809553 | − | 0.587047i | \(-0.800290\pi\) | ||||
−0.809553 | + | 0.587047i | \(0.800290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.3129 | −0.697570 | −0.348785 | − | 0.937203i | \(-0.613406\pi\) | ||||
−0.348785 | + | 0.937203i | \(0.613406\pi\) | |||||||
\(422\) | 6.52495 | 0.317629 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.05044 | −0.0510140 | ||||||||
\(425\) | −29.0213 | −1.40774 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.97565 | 0.240789 | ||||||||
\(428\) | −14.1492 | −0.683926 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.5929 | −0.944856 | ||||||||
\(431\) | −24.1655 | −1.16401 | −0.582006 | − | 0.813185i | \(-0.697732\pi\) | ||||
−0.582006 | + | 0.813185i | \(0.697732\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.95559 | −0.238150 | −0.119075 | − | 0.992885i | \(-0.537993\pi\) | ||||
−0.119075 | + | 0.992885i | \(0.537993\pi\) | |||||||
\(434\) | −11.2376 | −0.539421 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 35.9632 | 1.72233 | ||||||||
\(437\) | 5.05962 | 0.242034 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9535 | −1.00005 | −0.500027 | − | 0.866010i | \(-0.666677\pi\) | ||||
−0.500027 | + | 0.866010i | \(0.666677\pi\) | |||||||
\(440\) | 0.142562 | 0.00679638 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −35.0677 | −1.66800 | ||||||||
\(443\) | −3.09007 | −0.146814 | −0.0734069 | − | 0.997302i | \(-0.523387\pi\) | ||||
−0.0734069 | + | 0.997302i | \(0.523387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.6282 | −1.64153 | ||||||||
\(446\) | 5.65234 | 0.267646 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.0848 | −0.570952 | ||||||||
\(449\) | −7.59148 | −0.358264 | −0.179132 | − | 0.983825i | \(-0.557329\pi\) | ||||
−0.179132 | + | 0.983825i | \(0.557329\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.00608585 | 0.000286571 0 | ||||||||
\(452\) | 25.8097 | 1.21399 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.8927 | −1.44987 | ||||||||
\(455\) | −20.2354 | −0.948650 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.8554 | −1.16269 | −0.581344 | − | 0.813658i | \(-0.697473\pi\) | ||||
−0.581344 | + | 0.813658i | \(0.697473\pi\) | |||||||
\(458\) | 35.0031 | 1.63559 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.17472 | 0.334523 | ||||||||
\(461\) | 6.55243 | 0.305177 | 0.152589 | − | 0.988290i | \(-0.451239\pi\) | ||||
0.152589 | + | 0.988290i | \(0.451239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.94066 | 0.322560 | 0.161280 | − | 0.986909i | \(-0.448438\pi\) | ||||
0.161280 | + | 0.986909i | \(0.448438\pi\) | |||||||
\(464\) | 37.8202 | 1.75576 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.4945 | 1.18101 | ||||||||
\(467\) | −39.0558 | −1.80729 | −0.903644 | − | 0.428285i | \(-0.859118\pi\) | ||||
−0.903644 | + | 0.428285i | \(0.859118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.35983 | 0.339845 | ||||||||
\(470\) | 4.80261 | 0.221528 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.844407 | −0.0388670 | ||||||||
\(473\) | −0.532182 | −0.0244697 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.7743 | −1.68732 | ||||||||
\(476\) | −11.7654 | −0.539268 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.02621 | −0.0926766 | ||||||||
\(479\) | 18.4393 | 0.842513 | 0.421257 | − | 0.906942i | \(-0.361589\pi\) | ||||
0.421257 | + | 0.906942i | \(0.361589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.13011 | 0.416297 | ||||||||
\(482\) | −1.33364 | −0.0607456 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.0835 | −1.04925 | ||||||||
\(485\) | 16.8566 | 0.765418 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.3485 | 1.69242 | 0.846212 | − | 0.532846i | \(-0.178878\pi\) | ||||
0.846212 | + | 0.532846i | \(0.178878\pi\) | |||||||
\(488\) | 0.776489 | 0.0351500 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 36.1307 | 1.63222 | ||||||||
\(491\) | 33.4616 | 1.51010 | 0.755050 | − | 0.655668i | \(-0.227613\pi\) | ||||
0.755050 | + | 0.655668i | \(0.227613\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.8316 | 1.83896 | ||||||||
\(494\) | −44.4359 | −1.99926 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.2931 | 0.686681 | ||||||||
\(497\) | 12.2691 | 0.550345 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.5621 | −1.45768 | −0.728841 | − | 0.684684i | \(-0.759940\pi\) | ||||
−0.728841 | + | 0.684684i | \(0.759940\pi\) | |||||||
\(500\) | −15.5036 | −0.693341 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −37.5766 | −1.67712 | ||||||||
\(503\) | −4.28613 | −0.191109 | −0.0955545 | − | 0.995424i | \(-0.530462\pi\) | ||||
−0.0955545 | + | 0.995424i | \(0.530462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.7020 | 1.98921 | ||||||||
\(506\) | 0.379992 | 0.0168927 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.2435 | −1.25310 | ||||||||
\(509\) | −28.3767 | −1.25777 | −0.628887 | − | 0.777497i | \(-0.716489\pi\) | ||||
−0.628887 | + | 0.777497i | \(0.716489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6441 | −0.470866 | ||||||||
\(512\) | 32.1489 | 1.42079 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −46.6161 | −2.05615 | ||||||||
\(515\) | 34.2211 | 1.50796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.130448 | 0.00573710 | ||||||||
\(518\) | 5.97292 | 0.262435 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.15789 | −0.138483 | ||||||||
\(521\) | 33.0835 | 1.44941 | 0.724706 | − | 0.689058i | \(-0.241976\pi\) | ||||
0.724706 | + | 0.689058i | \(0.241976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.8785 | 1.61258 | 0.806292 | − | 0.591517i | \(-0.201471\pi\) | ||||
0.806292 | + | 0.591517i | \(0.201471\pi\) | |||||||
\(524\) | 31.9676 | 1.39651 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.66931 | −0.334398 | ||||||||
\(527\) | 16.5108 | 0.719223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0416 | −0.958330 | ||||||||
\(530\) | 34.6502 | 1.50511 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9086 | −0.646368 | ||||||||
\(533\) | −0.134808 | −0.00583917 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3906 | 1.01126 | ||||||||
\(536\) | 1.14856 | 0.0496102 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.31932 | 0.229332 | ||||||||
\(539\) | 0.981380 | 0.0422710 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.7829 | 1.19448 | 0.597241 | − | 0.802062i | \(-0.296264\pi\) | ||||
0.597241 | + | 0.802062i | \(0.296264\pi\) | |||||||
\(542\) | −23.5905 | −1.01330 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.9646 | 1.41335 | ||||||||
\(545\) | −59.4523 | −2.54666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.6920 | −1.01300 | −0.506498 | − | 0.862241i | \(-0.669060\pi\) | ||||
−0.506498 | + | 0.862241i | \(0.669060\pi\) | |||||||
\(548\) | −13.7051 | −0.585454 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.76185 | −0.117766 | ||||||||
\(551\) | 51.7396 | 2.20418 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.7038 | −0.752843 | ||||||||
\(554\) | 9.56502 | 0.406379 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6583 | −0.452012 | ||||||||
\(557\) | −16.2888 | −0.690178 | −0.345089 | − | 0.938570i | \(-0.612151\pi\) | ||||
−0.345089 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.7884 | 0.498595 | ||||||||
\(560\) | 18.0155 | 0.761293 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 50.6941 | 2.13840 | ||||||||
\(563\) | 0.216197 | 0.00911160 | 0.00455580 | − | 0.999990i | \(-0.498550\pi\) | ||||
0.00455580 | + | 0.999990i | \(0.498550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.6672 | −1.79502 | ||||||||
\(566\) | −19.9603 | −0.838994 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.91469 | 0.0803386 | ||||||||
\(569\) | −13.6370 | −0.571691 | −0.285845 | − | 0.958276i | \(-0.592274\pi\) | ||||
−0.285845 | + | 0.958276i | \(0.592274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2641 | −0.722482 | −0.361241 | − | 0.932473i | \(-0.617647\pi\) | ||||
−0.361241 | + | 0.932473i | \(0.617647\pi\) | |||||||
\(572\) | −1.71152 | −0.0715622 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0881912 | −0.00368103 | ||||||||
\(575\) | −6.96592 | −0.290499 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.0478 | −1.87537 | −0.937683 | − | 0.347493i | \(-0.887033\pi\) | ||||
−0.937683 | + | 0.347493i | \(0.887033\pi\) | |||||||
\(578\) | −0.739039 | −0.0307400 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 73.3687 | 3.04647 | ||||||||
\(581\) | −3.05425 | −0.126712 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.941167 | 0.0389791 | ||||||||
\(584\) | −1.66109 | −0.0687364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.1411 | 1.78214 | ||||||||
\(587\) | −6.87236 | −0.283653 | −0.141826 | − | 0.989892i | \(-0.545297\pi\) | ||||
−0.141826 | + | 0.989892i | \(0.545297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.9216 | 0.862062 | ||||||||
\(590\) | 27.8539 | 1.14673 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.12849 | −0.334079 | ||||||||
\(593\) | 11.7147 | 0.481067 | 0.240534 | − | 0.970641i | \(-0.422678\pi\) | ||||
0.240534 | + | 0.970641i | \(0.422678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.4500 | 0.797371 | ||||||||
\(596\) | 22.5092 | 0.922013 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.41721 | −0.344205 | ||||||||
\(599\) | −29.8786 | −1.22081 | −0.610403 | − | 0.792091i | \(-0.708992\pi\) | ||||
−0.610403 | + | 0.792091i | \(0.708992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7040 | 0.885324 | 0.442662 | − | 0.896688i | \(-0.354034\pi\) | ||||
0.442662 | + | 0.896688i | \(0.354034\pi\) | |||||||
\(602\) | 7.71195 | 0.314316 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.4288 | 1.31951 | ||||||||
\(605\) | 38.1602 | 1.55143 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5826 | −0.510713 | −0.255357 | − | 0.966847i | \(-0.582193\pi\) | ||||
−0.255357 | + | 0.966847i | \(0.582193\pi\) | |||||||
\(608\) | 41.7710 | 1.69404 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.6135 | −1.03706 | ||||||||
\(611\) | −2.88956 | −0.116899 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.3210 | −0.497642 | −0.248821 | − | 0.968549i | \(-0.580043\pi\) | ||||
−0.248821 | + | 0.968549i | \(0.580043\pi\) | |||||||
\(614\) | −34.5292 | −1.39348 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0561136 | −0.00226088 | ||||||||
\(617\) | 48.6690 | 1.95934 | 0.979670 | − | 0.200617i | \(-0.0642947\pi\) | ||||
0.979670 | + | 0.200617i | \(0.0642947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.9465 | −1.64578 | −0.822890 | − | 0.568201i | \(-0.807640\pi\) | ||||
−0.822890 | + | 0.568201i | \(0.807640\pi\) | |||||||
\(620\) | 29.6677 | 1.19148 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −44.9608 | −1.80277 | ||||||||
\(623\) | 13.6299 | 0.546072 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.94763 | −0.397905 | ||||||||
\(626\) | −9.71497 | −0.388288 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.03357 | −0.320574 | ||||||||
\(629\) | −8.77572 | −0.349911 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.4459 | −0.893558 | −0.446779 | − | 0.894644i | \(-0.647429\pi\) | ||||
−0.446779 | + | 0.894644i | \(0.647429\pi\) | |||||||
\(632\) | −2.76282 | −0.109899 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.4344 | 0.851269 | ||||||||
\(635\) | 46.6905 | 1.85286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.7386 | −0.861313 | ||||||||
\(638\) | 3.88579 | 0.153840 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.94531 | 0.235009 | ||||||||
\(641\) | −11.9975 | −0.473872 | −0.236936 | − | 0.971525i | \(-0.576143\pi\) | ||||
−0.236936 | + | 0.971525i | \(0.576143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.5278 | −1.59826 | −0.799130 | − | 0.601158i | \(-0.794706\pi\) | ||||
−0.799130 | + | 0.601158i | \(0.794706\pi\) | |||||||
\(644\) | −2.82403 | −0.111282 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 42.7111 | 1.68045 | ||||||||
\(647\) | 10.4001 | 0.408871 | 0.204435 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204435 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.756565 | 0.0296978 | ||||||||
\(650\) | 61.1779 | 2.39959 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.9431 | 0.859359 | ||||||||
\(653\) | −2.80015 | −0.109578 | −0.0547891 | − | 0.998498i | \(-0.517449\pi\) | ||||
−0.0547891 | + | 0.998498i | \(0.517449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.8470 | −2.06490 | ||||||||
\(656\) | 0.120019 | 0.00468594 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.89035 | −0.0736934 | ||||||||
\(659\) | 28.1624 | 1.09705 | 0.548525 | − | 0.836134i | \(-0.315189\pi\) | ||||
0.548525 | + | 0.836134i | \(0.315189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9663 | 0.621016 | 0.310508 | − | 0.950571i | \(-0.399501\pi\) | ||||
0.310508 | + | 0.950571i | \(0.399501\pi\) | |||||||
\(662\) | 66.8685 | 2.59892 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.476640 | −0.0184972 | ||||||||
\(665\) | 24.6460 | 0.955730 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.80071 | 0.379485 | ||||||||
\(668\) | −2.30020 | −0.0889976 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −37.8867 | −1.46369 | ||||||||
\(671\) | −0.695712 | −0.0268577 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0409 | 0.772519 | 0.386260 | − | 0.922390i | \(-0.373767\pi\) | ||||
0.386260 | + | 0.922390i | \(0.373767\pi\) | |||||||
\(674\) | −62.9860 | −2.42613 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5401 | 0.405389 | ||||||||
\(677\) | −36.8324 | −1.41558 | −0.707791 | − | 0.706422i | \(-0.750308\pi\) | ||||
−0.707791 | + | 0.706422i | \(0.750308\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.63489 | −0.254624 | ||||||||
\(680\) | 3.03532 | 0.116399 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.57128 | 0.0601673 | ||||||||
\(683\) | 25.9817 | 0.994161 | 0.497080 | − | 0.867705i | \(-0.334405\pi\) | ||||
0.497080 | + | 0.867705i | \(0.334405\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.6565 | 0.865661 | ||||||||
\(686\) | −33.6533 | −1.28489 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.4951 | −0.400123 | ||||||||
\(689\) | −20.8478 | −0.794238 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.84083 | −0.298279 | −0.149140 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149140 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(692\) | −22.0483 | −0.838152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.5900 | 1.76853 | ||||||||
\(695\) | 17.6196 | 0.668351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.129575 | 0.00490801 | ||||||||
\(698\) | 36.0058 | 1.36284 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.5256 | 0.775795 | ||||||||
\(701\) | −28.2197 | −1.06584 | −0.532921 | − | 0.846165i | \(-0.678906\pi\) | ||||
−0.532921 | + | 0.846165i | \(0.678906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.1201 | −0.419404 | ||||||||
\(704\) | 1.68973 | 0.0636842 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.2924 | 1.06480 | ||||||||
\(707\) | −17.5951 | −0.661732 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.9221 | 0.823303 | 0.411652 | − | 0.911341i | \(-0.364952\pi\) | ||||
0.411652 | + | 0.911341i | \(0.364952\pi\) | |||||||
\(710\) | −63.1586 | −2.37030 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.12706 | 0.0797150 | ||||||||
\(713\) | 3.96306 | 0.148418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.82938 | 0.105813 | ||||||||
\(716\) | 45.7503 | 1.70977 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −44.1398 | −1.64728 | ||||||||
\(719\) | 51.4814 | 1.91993 | 0.959966 | − | 0.280118i | \(-0.0903735\pi\) | ||||
0.959966 | + | 0.280118i | \(0.0903735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4697 | −0.501638 | ||||||||
\(722\) | 15.6233 | 0.581438 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.5522 | 0.986806 | ||||||||
\(725\) | −71.2334 | −2.64554 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.61082 | −0.171006 | −0.0855030 | − | 0.996338i | \(-0.527250\pi\) | ||||
−0.0855030 | + | 0.996338i | \(0.527250\pi\) | |||||||
\(728\) | 1.24297 | 0.0460677 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 54.7933 | 2.02799 | ||||||||
\(731\) | −11.3308 | −0.419085 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.26928 | −0.120754 | −0.0603768 | − | 0.998176i | \(-0.519230\pi\) | ||||
−0.0603768 | + | 0.998176i | \(0.519230\pi\) | |||||||
\(734\) | 10.7769 | 0.397783 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.91242 | 0.291656 | ||||||||
\(737\) | −1.02908 | −0.0379065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.3375 | 1.29991 | 0.649956 | − | 0.759972i | \(-0.274787\pi\) | ||||
0.649956 | + | 0.759972i | \(0.274787\pi\) | |||||||
\(740\) | −15.7688 | −0.579671 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.6386 | −0.500690 | ||||||||
\(743\) | 45.5076 | 1.66951 | 0.834757 | − | 0.550619i | \(-0.185608\pi\) | ||||
0.834757 | + | 0.550619i | \(0.185608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.2109 | −1.36330 | ||||||||
\(746\) | −46.9187 | −1.71782 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.64509 | 0.0601503 | ||||||||
\(749\) | −9.20674 | −0.336407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.6081 | 1.40883 | 0.704415 | − | 0.709789i | \(-0.251210\pi\) | ||||
0.704415 | + | 0.709789i | \(0.251210\pi\) | |||||||
\(752\) | 2.57256 | 0.0938115 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −86.0743 | −3.13464 | ||||||||
\(755\) | −53.6095 | −1.95105 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.4991 | 0.454288 | 0.227144 | − | 0.973861i | \(-0.427061\pi\) | ||||
0.227144 | + | 0.973861i | \(0.427061\pi\) | |||||||
\(758\) | −12.0120 | −0.436297 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.84620 | 0.139516 | ||||||||
\(761\) | −42.9165 | −1.55572 | −0.777862 | − | 0.628435i | \(-0.783696\pi\) | ||||
−0.777862 | + | 0.628435i | \(0.783696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.4010 | 0.847171 | ||||||||
\(764\) | −12.4998 | −0.452228 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −70.5859 | −2.55037 | ||||||||
\(767\) | −16.7587 | −0.605121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.9328 | −1.51214 | −0.756068 | − | 0.654493i | \(-0.772882\pi\) | ||||
−0.756068 | + | 0.654493i | \(0.772882\pi\) | |||||||
\(770\) | 1.85098 | 0.0667048 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 43.3161 | 1.55898 | ||||||||
\(773\) | −17.1599 | −0.617200 | −0.308600 | − | 0.951192i | \(-0.599860\pi\) | ||||
−0.308600 | + | 0.951192i | \(0.599860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.8042 | −1.03468 | ||||||||
\(776\) | −1.03543 | −0.0371697 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.60181 | −0.129131 | ||||||||
\(779\) | 0.164191 | 0.00588274 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.71551 | −0.0613857 | ||||||||
\(782\) | 8.09049 | 0.289315 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.3537 | 0.691205 | ||||||||
\(785\) | 13.2806 | 0.474006 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.35629 | 0.297870 | 0.148935 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148935 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(788\) | −6.44657 | −0.229649 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 91.1353 | 3.24245 | ||||||||
\(791\) | 16.7942 | 0.597132 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4107 | 0.547251 | ||||||||
\(794\) | −26.1354 | −0.927509 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 48.7964 | 1.72954 | ||||||||
\(797\) | 50.4354 | 1.78651 | 0.893257 | − | 0.449547i | \(-0.148415\pi\) | ||||
0.893257 | + | 0.449547i | \(0.148415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.77740 | 0.0982572 | ||||||||
\(800\) | −57.5090 | −2.03325 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −51.5559 | −1.82050 | ||||||||
\(803\) | 1.48829 | 0.0525206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.66853 | 0.164544 | ||||||||
\(806\) | −34.8054 | −1.22597 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.74585 | −0.0965988 | ||||||||
\(809\) | 37.4116 | 1.31532 | 0.657661 | − | 0.753314i | \(-0.271546\pi\) | ||||
0.657661 | + | 0.753314i | \(0.271546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.9470 | 1.22716 | 0.613578 | − | 0.789634i | \(-0.289730\pi\) | ||||
0.613578 | + | 0.789634i | \(0.289730\pi\) | |||||||
\(812\) | −28.8785 | −1.01344 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.835154 | −0.0292721 | ||||||||
\(815\) | −36.2751 | −1.27066 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.3578 | −0.502316 | ||||||||
\(818\) | −67.0958 | −2.34595 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.232828 | 0.00813072 | ||||||||
\(821\) | −51.6588 | −1.80291 | −0.901453 | − | 0.432877i | \(-0.857499\pi\) | ||||
−0.901453 | + | 0.432877i | \(0.857499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.3085 | −0.812484 | −0.406242 | − | 0.913765i | \(-0.633161\pi\) | ||||
−0.406242 | + | 0.913765i | \(0.633161\pi\) | |||||||
\(824\) | −2.10205 | −0.0732285 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.9635 | −0.381470 | ||||||||
\(827\) | −0.139400 | −0.00484741 | −0.00242370 | − | 0.999997i | \(-0.500771\pi\) | ||||
−0.00242370 | + | 0.999997i | \(0.500771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.55617 | −0.297168 | −0.148584 | − | 0.988900i | \(-0.547472\pi\) | ||||
−0.148584 | + | 0.988900i | \(0.547472\pi\) | |||||||
\(830\) | 15.7226 | 0.545739 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.4293 | −1.29763 | ||||||||
\(833\) | 20.8948 | 0.723961 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.80257 | 0.131593 | ||||||||
\(836\) | 2.08456 | 0.0720962 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −67.1532 | −2.31977 | ||||||||
\(839\) | −7.49954 | −0.258913 | −0.129456 | − | 0.991585i | \(-0.541323\pi\) | ||||
−0.129456 | + | 0.991585i | \(0.541323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.2220 | 2.45593 | ||||||||
\(842\) | −29.0010 | −0.999440 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.78035 | 0.233389 | ||||||||
\(845\) | −17.4243 | −0.599414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.0202 | −0.516100 | ||||||||
\(848\) | 18.5607 | 0.637377 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −58.8032 | −2.01693 | ||||||||
\(851\) | −2.10642 | −0.0722070 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.83193 | 0.268160 | 0.134080 | − | 0.990971i | \(-0.457192\pi\) | ||||
0.134080 | + | 0.990971i | \(0.457192\pi\) | |||||||
\(854\) | 10.0817 | 0.344989 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.43678 | −0.0491083 | ||||||||
\(857\) | 9.69988 | 0.331342 | 0.165671 | − | 0.986181i | \(-0.447021\pi\) | ||||
0.165671 | + | 0.986181i | \(0.447021\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.41295 | −0.116448 | −0.0582242 | − | 0.998304i | \(-0.518544\pi\) | ||||
−0.0582242 | + | 0.998304i | \(0.518544\pi\) | |||||||
\(860\) | −20.3599 | −0.694266 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −48.9643 | −1.66773 | ||||||||
\(863\) | −37.9282 | −1.29109 | −0.645545 | − | 0.763722i | \(-0.723370\pi\) | ||||
−0.645545 | + | 0.763722i | \(0.723370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.4491 | 1.23931 | ||||||||
\(866\) | −10.0411 | −0.341209 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.6774 | −0.396358 | ||||||||
\(869\) | 2.47541 | 0.0839725 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.7951 | 0.772382 | ||||||||
\(872\) | 3.65190 | 0.123669 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.2518 | 0.346774 | ||||||||
\(875\) | −10.0880 | −0.341038 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.6999 | 1.50941 | 0.754704 | − | 0.656066i | \(-0.227781\pi\) | ||||
0.754704 | + | 0.656066i | \(0.227781\pi\) | |||||||
\(878\) | −42.4561 | −1.43282 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.51899 | −0.0849150 | ||||||||
\(881\) | −32.1877 | −1.08443 | −0.542216 | − | 0.840239i | \(-0.682414\pi\) | ||||
−0.542216 | + | 0.840239i | \(0.682414\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.4253 | 1.83156 | 0.915778 | − | 0.401685i | \(-0.131575\pi\) | ||||
0.915778 | + | 0.401685i | \(0.131575\pi\) | |||||||
\(884\) | −36.4403 | −1.22562 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.26113 | −0.210347 | ||||||||
\(887\) | 32.7726 | 1.10040 | 0.550198 | − | 0.835034i | \(-0.314552\pi\) | ||||
0.550198 | + | 0.835034i | \(0.314552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.3778 | −0.616371 | ||||||||
\(890\) | −70.1639 | −2.35190 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.87359 | 0.196662 | ||||||||
\(893\) | 3.51937 | 0.117771 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −75.6318 | −2.52809 | ||||||||
\(896\) | −2.34013 | −0.0781781 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.3819 | −0.513301 | ||||||||
\(899\) | 40.5262 | 1.35162 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0386 | 0.667582 | ||||||||
\(902\) | 0.0123312 | 0.000410584 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.62086 | 0.0871685 | ||||||||
\(905\) | −43.8946 | −1.45911 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.5122 | 0.647890 | 0.323945 | − | 0.946076i | \(-0.394991\pi\) | ||||
0.323945 | + | 0.946076i | \(0.394991\pi\) | |||||||
\(908\) | −32.1019 | −1.06534 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −41.0011 | −1.35917 | ||||||||
\(911\) | 12.5747 | 0.416618 | 0.208309 | − | 0.978063i | \(-0.433204\pi\) | ||||
0.208309 | + | 0.978063i | \(0.433204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.427056 | 0.0141335 | ||||||||
\(914\) | −50.3623 | −1.66584 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.3733 | 1.20181 | ||||||||
\(917\) | 20.8010 | 0.686911 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2431 | −0.832693 | −0.416347 | − | 0.909206i | \(-0.636690\pi\) | ||||
−0.416347 | + | 0.909206i | \(0.636690\pi\) | |||||||
\(920\) | 0.728561 | 0.0240199 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.2766 | 0.437241 | ||||||||
\(923\) | 38.0003 | 1.25079 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.3098 | 0.503384 | ||||||||
\(926\) | 14.0632 | 0.462146 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 80.9124 | 2.65608 | ||||||||
\(929\) | 14.4960 | 0.475599 | 0.237799 | − | 0.971314i | \(-0.423574\pi\) | ||||
0.237799 | + | 0.971314i | \(0.423574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.4767 | 0.867740 | ||||||||
\(932\) | 26.4924 | 0.867789 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −79.1352 | −2.58938 | ||||||||
\(935\) | −2.71956 | −0.0889391 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.7602 | −0.449525 | −0.224762 | − | 0.974414i | \(-0.572161\pi\) | ||||
−0.224762 | + | 0.974414i | \(0.572161\pi\) | |||||||
\(938\) | 14.9125 | 0.486912 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.99059 | 0.162775 | ||||||||
\(941\) | −34.3696 | −1.12042 | −0.560209 | − | 0.828351i | \(-0.689279\pi\) | ||||
−0.560209 | + | 0.828351i | \(0.689279\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0311016 | 0.00101281 | ||||||||
\(944\) | 14.9202 | 0.485610 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.07831 | −0.0350589 | ||||||||
\(947\) | 5.24589 | 0.170469 | 0.0852343 | − | 0.996361i | \(-0.472836\pi\) | ||||
0.0852343 | + | 0.996361i | \(0.472836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.9671 | −1.07016 | ||||||||
\(950\) | −74.5123 | −2.41750 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.19473 | −0.0387214 | ||||||||
\(953\) | 28.2817 | 0.916135 | 0.458068 | − | 0.888917i | \(-0.348542\pi\) | ||||
0.458068 | + | 0.888917i | \(0.348542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.6640 | 0.668671 | ||||||||
\(956\) | −2.10552 | −0.0680974 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.3619 | 1.20711 | ||||||||
\(959\) | −8.91780 | −0.287971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6127 | −0.471376 | ||||||||
\(962\) | 18.4995 | 0.596448 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.38584 | −0.0446349 | ||||||||
\(965\) | −71.6077 | −2.30513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.52394 | 0.113322 | 0.0566611 | − | 0.998393i | \(-0.481955\pi\) | ||||
0.0566611 | + | 0.998393i | \(0.481955\pi\) | |||||||
\(968\) | −2.34402 | −0.0753397 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.1549 | 1.09665 | ||||||||
\(971\) | 30.9946 | 0.994665 | 0.497333 | − | 0.867560i | \(-0.334313\pi\) | ||||
0.497333 | + | 0.867560i | \(0.334313\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.93525 | −0.222334 | ||||||||
\(974\) | 75.6759 | 2.42481 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.7201 | −0.439170 | ||||||||
\(977\) | −44.4189 | −1.42109 | −0.710543 | − | 0.703653i | \(-0.751551\pi\) | ||||
−0.710543 | + | 0.703653i | \(0.751551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.90579 | −0.0609092 | ||||||||
\(980\) | 37.5450 | 1.19933 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 67.8001 | 2.16359 | ||||||||
\(983\) | 28.7370 | 0.916568 | 0.458284 | − | 0.888806i | \(-0.348464\pi\) | ||||
0.458284 | + | 0.888806i | \(0.348464\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6571 | 0.339563 | ||||||||
\(986\) | 82.7333 | 2.63477 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −46.1752 | −1.46903 | ||||||||
\(989\) | −2.71971 | −0.0864816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3353 | 0.582441 | 0.291220 | − | 0.956656i | \(-0.405939\pi\) | ||||
0.291220 | + | 0.956656i | \(0.405939\pi\) | |||||||
\(992\) | 32.7181 | 1.03880 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.8598 | 0.788504 | ||||||||
\(995\) | −80.6674 | −2.55733 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7618 | 0.594192 | 0.297096 | − | 0.954848i | \(-0.403982\pi\) | ||||
0.297096 | + | 0.954848i | \(0.403982\pi\) | |||||||
\(998\) | −65.9777 | −2.08849 | ||||||||
\(999\) | 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 | 2151.2.a.j.1.18 | ✓ | 20 | |
3.2 | odd | 2 | 2151.2.a.k.1.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.18 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2151.2.a.k.1.3 | yes | 20 | 3.2 | odd | 2 |