Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.69963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69963 | 1.90893 | 0.954463 | − | 0.298330i | \(-0.0964297\pi\) | ||||
0.954463 | + | 0.298330i | \(0.0964297\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.28799 | 2.64400 | ||||||||
\(5\) | −1.58836 | −0.710338 | −0.355169 | − | 0.934802i | \(-0.615577\pi\) | ||||
−0.355169 | + | 0.934802i | \(0.615577\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.87636 | 3.13827 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.28799 | −1.35598 | ||||||||
\(11\) | 0.300372 | 0.0905655 | 0.0452828 | − | 0.998974i | \(-0.485581\pi\) | ||||
0.0452828 | + | 0.998974i | \(0.485581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81089 | 0.779601 | 0.389801 | − | 0.920899i | \(-0.372544\pi\) | ||||
0.389801 | + | 0.920899i | \(0.372544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.3869 | 3.34672 | ||||||||
\(17\) | 5.87636 | 1.42523 | 0.712613 | − | 0.701557i | \(-0.247512\pi\) | ||||
0.712613 | + | 0.701557i | \(0.247512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.28799 | −0.524901 | −0.262451 | − | 0.964945i | \(-0.584531\pi\) | ||||
−0.262451 | + | 0.964945i | \(0.584531\pi\) | |||||||
\(20\) | −8.39926 | −1.87813 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.810892 | 0.172883 | ||||||||
\(23\) | 1.88874 | 0.393829 | 0.196914 | − | 0.980421i | \(-0.436908\pi\) | ||||
0.196914 | + | 0.980421i | \(0.436908\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.47710 | −0.495420 | ||||||||
\(26\) | 7.58836 | 1.48820 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.52290 | 0.468491 | 0.234245 | − | 0.972178i | \(-0.424738\pi\) | ||||
0.234245 | + | 0.972178i | \(0.424738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.81089 | −0.864062 | −0.432031 | − | 0.901859i | \(-0.642203\pi\) | ||||
−0.432031 | + | 0.901859i | \(0.642203\pi\) | |||||||
\(32\) | 18.3869 | 3.25037 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.8640 | 2.72065 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47710 | −0.736031 | −0.368015 | − | 0.929820i | \(-0.619963\pi\) | ||||
−0.368015 | + | 0.929820i | \(0.619963\pi\) | |||||||
\(38\) | −6.17673 | −1.00200 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.0989 | −2.22923 | ||||||||
\(41\) | 8.90978 | 1.39147 | 0.695737 | − | 0.718297i | \(-0.255078\pi\) | ||||
0.695737 | + | 0.718297i | \(0.255078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.09888 | −1.38757 | −0.693783 | − | 0.720184i | \(-0.744058\pi\) | ||||
−0.693783 | + | 0.720184i | \(0.744058\pi\) | |||||||
\(44\) | 1.58836 | 0.239455 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.09888 | 0.751789 | ||||||||
\(47\) | −3.21015 | −0.468248 | −0.234124 | − | 0.972207i | \(-0.575222\pi\) | ||||
−0.234124 | + | 0.972207i | \(0.575222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.68725 | −0.945720 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14.8640 | 2.06126 | ||||||||
\(53\) | 2.01238 | 0.276422 | 0.138211 | − | 0.990403i | \(-0.455865\pi\) | ||||
0.138211 | + | 0.990403i | \(0.455865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.477100 | −0.0643321 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.81089 | 0.894314 | ||||||||
\(59\) | −4.88874 | −0.636459 | −0.318230 | − | 0.948014i | \(-0.603088\pi\) | ||||
−0.318230 | + | 0.948014i | \(0.603088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.57598 | 0.970005 | 0.485003 | − | 0.874513i | \(-0.338819\pi\) | ||||
0.485003 | + | 0.874513i | \(0.338819\pi\) | |||||||
\(62\) | −12.9876 | −1.64943 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 22.8640 | 2.85800 | ||||||||
\(65\) | −4.46472 | −0.553780 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.712008 | 0.0869856 | 0.0434928 | − | 0.999054i | \(-0.486151\pi\) | ||||
0.0434928 | + | 0.999054i | \(0.486151\pi\) | |||||||
\(68\) | 31.0741 | 3.76829 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8640 | −1.52667 | −0.763337 | − | 0.646001i | \(-0.776440\pi\) | ||||
−0.763337 | + | 0.646001i | \(0.776440\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6749 | −1.36644 | −0.683220 | − | 0.730213i | \(-0.739421\pi\) | ||||
−0.683220 | + | 0.730213i | \(0.739421\pi\) | |||||||
\(74\) | −12.0865 | −1.40503 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.0989 | −1.38784 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.66621 | 0.187463 | 0.0937315 | − | 0.995598i | \(-0.470120\pi\) | ||||
0.0937315 | + | 0.995598i | \(0.470120\pi\) | |||||||
\(80\) | −21.2632 | −2.37730 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 24.0531 | 2.65622 | ||||||||
\(83\) | −5.43268 | −0.596314 | −0.298157 | − | 0.954517i | \(-0.596372\pi\) | ||||
−0.298157 | + | 0.954517i | \(0.596372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.33379 | −1.01239 | ||||||||
\(86\) | −24.5636 | −2.64876 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.66621 | 0.284219 | ||||||||
\(89\) | −9.35346 | −0.991464 | −0.495732 | − | 0.868475i | \(-0.665100\pi\) | ||||
−0.495732 | + | 0.868475i | \(0.665100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.98762 | 1.04128 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.66621 | −0.893851 | ||||||||
\(95\) | 3.63416 | 0.372857 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.5760 | −1.27690 | −0.638449 | − | 0.769664i | \(-0.720424\pi\) | ||||
−0.638449 | + | 0.769664i | \(0.720424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.0989 | −1.30989 | ||||||||
\(101\) | −14.6094 | −1.45369 | −0.726845 | − | 0.686801i | \(-0.759014\pi\) | ||||
−0.726845 | + | 0.686801i | \(0.759014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.19777 | 0.906283 | 0.453142 | − | 0.891439i | \(-0.350303\pi\) | ||||
0.453142 | + | 0.891439i | \(0.350303\pi\) | |||||||
\(104\) | 24.9505 | 2.44660 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.43268 | 0.527668 | ||||||||
\(107\) | 12.5105 | 1.20944 | 0.604719 | − | 0.796439i | \(-0.293285\pi\) | ||||
0.604719 | + | 0.796439i | \(0.293285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.04580 | −0.291735 | −0.145867 | − | 0.989304i | \(-0.546597\pi\) | ||||
−0.145867 | + | 0.989304i | \(0.546597\pi\) | |||||||
\(110\) | −1.28799 | −0.122805 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.95420 | 0.936412 | 0.468206 | − | 0.883619i | \(-0.344900\pi\) | ||||
0.468206 | + | 0.883619i | \(0.344900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | 13.3411 | 1.23869 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.1978 | −1.21495 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9098 | −0.991798 | ||||||||
\(122\) | 20.4523 | 1.85167 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −25.4400 | −2.28458 | ||||||||
\(125\) | 11.8764 | 1.06225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4400 | −1.19260 | −0.596302 | − | 0.802760i | \(-0.703364\pi\) | ||||
−0.596302 | + | 0.802760i | \(0.703364\pi\) | |||||||
\(128\) | 24.9505 | 2.20533 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0531 | −1.05713 | ||||||||
\(131\) | 11.2756 | 0.985155 | 0.492577 | − | 0.870269i | \(-0.336055\pi\) | ||||
0.492577 | + | 0.870269i | \(0.336055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.92216 | 0.166049 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 52.1606 | 4.47274 | ||||||||
\(137\) | 3.77747 | 0.322731 | 0.161366 | − | 0.986895i | \(-0.448410\pi\) | ||||
0.161366 | + | 0.986895i | \(0.448410\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7193 | 1.41811 | 0.709056 | − | 0.705152i | \(-0.249121\pi\) | ||||
0.709056 | + | 0.705152i | \(0.249121\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −34.7280 | −2.91431 | ||||||||
\(143\) | 0.844313 | 0.0706050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00728 | −0.332787 | ||||||||
\(146\) | −31.5178 | −2.60843 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.6749 | −1.94606 | ||||||||
\(149\) | 10.8887 | 0.892040 | 0.446020 | − | 0.895023i | \(-0.352841\pi\) | ||||
0.446020 | + | 0.895023i | \(0.352841\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0989 | −0.984593 | −0.492297 | − | 0.870427i | \(-0.663842\pi\) | ||||
−0.492297 | + | 0.870427i | \(0.663842\pi\) | |||||||
\(152\) | −20.3090 | −1.64728 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.64145 | 0.613776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.189108 | −0.0150924 | −0.00754622 | − | 0.999972i | \(-0.502402\pi\) | ||||
−0.00754622 | + | 0.999972i | \(0.502402\pi\) | |||||||
\(158\) | 4.49814 | 0.357853 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −29.2051 | −2.30886 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.95558 | −0.701455 | −0.350727 | − | 0.936478i | \(-0.614066\pi\) | ||||
−0.350727 | + | 0.936478i | \(0.614066\pi\) | |||||||
\(164\) | 47.1148 | 3.67905 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6662 | −1.13832 | ||||||||
\(167\) | −4.34108 | −0.335923 | −0.167961 | − | 0.985794i | \(-0.553718\pi\) | ||||
−0.167961 | + | 0.985794i | \(0.553718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.09888 | −0.392222 | ||||||||
\(170\) | −25.1978 | −1.93258 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −48.1148 | −3.66872 | ||||||||
\(173\) | −6.30037 | −0.479008 | −0.239504 | − | 0.970895i | \(-0.576985\pi\) | ||||
−0.239504 | + | 0.970895i | \(0.576985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.02104 | 0.303097 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.2509 | −1.89263 | ||||||||
\(179\) | −13.9418 | −1.04206 | −0.521030 | − | 0.853538i | \(-0.674452\pi\) | ||||
−0.521030 | + | 0.853538i | \(0.674452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3411 | 1.36328 | 0.681641 | − | 0.731687i | \(-0.261267\pi\) | ||||
0.681641 | + | 0.731687i | \(0.261267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.7651 | 1.23594 | ||||||||
\(185\) | 7.11126 | 0.522831 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.76509 | 0.129076 | ||||||||
\(188\) | −16.9752 | −1.23805 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.81089 | 0.711757 | ||||||||
\(191\) | 7.60803 | 0.550498 | 0.275249 | − | 0.961373i | \(-0.411240\pi\) | ||||
0.275249 | + | 0.961373i | \(0.411240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.66621 | 0.551826 | 0.275913 | − | 0.961183i | \(-0.411020\pi\) | ||||
0.275913 | + | 0.961183i | \(0.411020\pi\) | |||||||
\(194\) | −33.9505 | −2.43750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3869 | 1.31001 | 0.655005 | − | 0.755624i | \(-0.272666\pi\) | ||||
0.655005 | + | 0.755624i | \(0.272666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.95420 | 0.422082 | 0.211041 | − | 0.977477i | \(-0.432315\pi\) | ||||
0.211041 | + | 0.977477i | \(0.432315\pi\) | |||||||
\(200\) | −21.9876 | −1.55476 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −39.4400 | −2.77499 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.1520 | −0.988416 | ||||||||
\(206\) | 24.8306 | 1.73003 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 37.6291 | 2.60911 | ||||||||
\(209\) | −0.687248 | −0.0475380 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.67487 | 0.459517 | 0.229758 | − | 0.973248i | \(-0.426206\pi\) | ||||
0.229758 | + | 0.973248i | \(0.426206\pi\) | |||||||
\(212\) | 10.6414 | 0.730858 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 33.7738 | 2.30873 | ||||||||
\(215\) | 14.4523 | 0.985641 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.22253 | −0.556900 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.52290 | −0.170094 | ||||||||
\(221\) | 16.5178 | 1.11111 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.34108 | 0.424630 | 0.212315 | − | 0.977201i | \(-0.431900\pi\) | ||||
0.212315 | + | 0.977201i | \(0.431900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.8726 | 1.78754 | ||||||||
\(227\) | −27.0865 | −1.79779 | −0.898897 | − | 0.438160i | \(-0.855630\pi\) | ||||
−0.898897 | + | 0.438160i | \(0.855630\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.19639 | 0.541633 | 0.270816 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270816 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(230\) | −8.09888 | −0.534025 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.3942 | 1.47025 | ||||||||
\(233\) | 27.4203 | 1.79636 | 0.898182 | − | 0.439624i | \(-0.144888\pi\) | ||||
0.898182 | + | 0.439624i | \(0.144888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.09888 | 0.332615 | ||||||||
\(236\) | −25.8516 | −1.68280 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.8640 | −1.80237 | −0.901185 | − | 0.433434i | \(-0.857302\pi\) | ||||
−0.901185 | + | 0.433434i | \(0.857302\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.5302 | −1.45130 | −0.725648 | − | 0.688066i | \(-0.758460\pi\) | ||||
−0.725648 | + | 0.688066i | \(0.758460\pi\) | |||||||
\(242\) | −29.4523 | −1.89327 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 40.0617 | 2.56469 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.43130 | −0.409214 | ||||||||
\(248\) | −42.7032 | −2.71166 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 32.0617 | 2.02776 | ||||||||
\(251\) | 31.2509 | 1.97254 | 0.986268 | − | 0.165152i | \(-0.0528114\pi\) | ||||
0.986268 | + | 0.165152i | \(0.0528114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.567323 | 0.0356673 | ||||||||
\(254\) | −36.2829 | −2.27659 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 21.6291 | 1.35182 | ||||||||
\(257\) | −10.2015 | −0.636351 | −0.318176 | − | 0.948032i | \(-0.603070\pi\) | ||||
−0.318176 | + | 0.948032i | \(0.603070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −23.6094 | −1.46419 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 30.4400 | 1.88059 | ||||||||
\(263\) | 28.4610 | 1.75498 | 0.877490 | − | 0.479594i | \(-0.159216\pi\) | ||||
0.877490 | + | 0.479594i | \(0.159216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.19639 | −0.196353 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.76509 | 0.229990 | ||||||||
\(269\) | 14.8764 | 0.907027 | 0.453514 | − | 0.891249i | \(-0.350170\pi\) | ||||
0.453514 | + | 0.891249i | \(0.350170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0444229 | 0.00269850 | 0.00134925 | − | 0.999999i | \(-0.499571\pi\) | ||||
0.00134925 | + | 0.999999i | \(0.499571\pi\) | |||||||
\(272\) | 78.6661 | 4.76983 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1978 | 0.616070 | ||||||||
\(275\) | −0.744051 | −0.0448680 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.6749 | 0.941812 | 0.470906 | − | 0.882184i | \(-0.343927\pi\) | ||||
0.470906 | + | 0.882184i | \(0.343927\pi\) | |||||||
\(278\) | 45.1359 | 2.70707 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9098 | 0.710478 | 0.355239 | − | 0.934776i | \(-0.384400\pi\) | ||||
0.355239 | + | 0.934776i | \(0.384400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00728 | 0.357096 | 0.178548 | − | 0.983931i | \(-0.442860\pi\) | ||||
0.178548 | + | 0.983931i | \(0.442860\pi\) | |||||||
\(284\) | −68.0246 | −4.03652 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.27933 | 0.134780 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.5316 | 1.03127 | ||||||||
\(290\) | −10.8182 | −0.635265 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −61.7366 | −3.61286 | ||||||||
\(293\) | −4.95558 | −0.289508 | −0.144754 | − | 0.989468i | \(-0.546239\pi\) | ||||
−0.144754 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.76509 | 0.452101 | ||||||||
\(296\) | −39.7403 | −2.30986 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 29.3955 | 1.70284 | ||||||||
\(299\) | 5.30903 | 0.307029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −32.6625 | −1.87952 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −30.6291 | −1.75670 | ||||||||
\(305\) | −12.0334 | −0.689032 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0531 | −1.25864 | −0.629318 | − | 0.777148i | \(-0.716666\pi\) | ||||
−0.629318 | + | 0.777148i | \(0.716666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.6291 | 1.17165 | ||||||||
\(311\) | 7.97524 | 0.452234 | 0.226117 | − | 0.974100i | \(-0.427397\pi\) | ||||
0.226117 | + | 0.974100i | \(0.427397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5302 | −1.27348 | −0.636741 | − | 0.771078i | \(-0.719718\pi\) | ||||
−0.636741 | + | 0.771078i | \(0.719718\pi\) | |||||||
\(314\) | −0.510520 | −0.0288103 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.81089 | 0.495651 | ||||||||
\(317\) | −19.9381 | −1.11984 | −0.559918 | − | 0.828548i | \(-0.689167\pi\) | ||||
−0.559918 | + | 0.828548i | \(0.689167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.757808 | 0.0424291 | ||||||||
\(320\) | −36.3163 | −2.03014 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.4451 | −0.748103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.96286 | −0.386230 | ||||||||
\(326\) | −24.1767 | −1.33903 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 79.0864 | 4.36681 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6304 | 1.29885 | 0.649423 | − | 0.760427i | \(-0.275010\pi\) | ||||
0.649423 | + | 0.760427i | \(0.275010\pi\) | |||||||
\(332\) | −28.7280 | −1.57665 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.7193 | −0.641251 | ||||||||
\(335\) | −1.13093 | −0.0617892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3855 | −0.674681 | −0.337341 | − | 0.941383i | \(-0.609527\pi\) | ||||
−0.337341 | + | 0.941383i | \(0.609527\pi\) | |||||||
\(338\) | −13.7651 | −0.748722 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −49.3570 | −2.67676 | ||||||||
\(341\) | −1.44506 | −0.0782542 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −80.7649 | −4.35455 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.0087 | −0.914391 | ||||||||
\(347\) | −3.84431 | −0.206374 | −0.103187 | − | 0.994662i | \(-0.532904\pi\) | ||||
−0.103187 | + | 0.994662i | \(0.532904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.1891 | −0.652468 | −0.326234 | − | 0.945289i | \(-0.605780\pi\) | ||||
−0.326234 | + | 0.945289i | \(0.605780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.52290 | 0.294372 | ||||||||
\(353\) | −3.56360 | −0.189672 | −0.0948358 | − | 0.995493i | \(-0.530233\pi\) | ||||
−0.0948358 | + | 0.995493i | \(0.530233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.4327 | 1.08445 | ||||||||
\(356\) | −49.4610 | −2.62143 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −37.6377 | −1.98922 | ||||||||
\(359\) | −0.967957 | −0.0510868 | −0.0255434 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255434 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7651 | −0.724479 | ||||||||
\(362\) | 49.5141 | 2.60240 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.5439 | 0.970634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.9542 | 1.09380 | 0.546900 | − | 0.837198i | \(-0.315808\pi\) | ||||
0.546900 | + | 0.837198i | \(0.315808\pi\) | |||||||
\(368\) | 25.2843 | 1.31803 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.1978 | 0.998044 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | 4.76509 | 0.246397 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −28.4944 | −1.46949 | ||||||||
\(377\) | 7.09160 | 0.365236 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.14331 | −0.366927 | −0.183464 | − | 0.983027i | \(-0.558731\pi\) | ||||
−0.183464 | + | 0.983027i | \(0.558731\pi\) | |||||||
\(380\) | 19.2174 | 0.985833 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.5388 | 1.05086 | ||||||||
\(383\) | −11.9766 | −0.611977 | −0.305988 | − | 0.952035i | \(-0.598987\pi\) | ||||
−0.305988 | + | 0.952035i | \(0.598987\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.6959 | 1.05339 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −66.5017 | −3.37611 | ||||||||
\(389\) | 13.7788 | 0.698615 | 0.349308 | − | 0.937008i | \(-0.386417\pi\) | ||||
0.349308 | + | 0.937008i | \(0.386417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0989 | 0.561295 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 49.6377 | 2.50071 | ||||||||
\(395\) | −2.64654 | −0.133162 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.38688 | 0.420925 | 0.210463 | − | 0.977602i | \(-0.432503\pi\) | ||||
0.210463 | + | 0.977602i | \(0.432503\pi\) | |||||||
\(398\) | 16.0741 | 0.805723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −33.1606 | −1.65803 | ||||||||
\(401\) | 27.6167 | 1.37911 | 0.689556 | − | 0.724233i | \(-0.257806\pi\) | ||||
0.689556 | + | 0.724233i | \(0.257806\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.5229 | −0.673624 | ||||||||
\(404\) | −77.2544 | −3.84355 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.34479 | −0.0666590 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5316 | 1.50969 | 0.754844 | − | 0.655904i | \(-0.227712\pi\) | ||||
0.754844 | + | 0.655904i | \(0.227712\pi\) | |||||||
\(410\) | −38.2051 | −1.88681 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 48.6377 | 2.39621 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.62907 | 0.423584 | ||||||||
\(416\) | 51.6835 | 2.53399 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.85532 | −0.0907464 | ||||||||
\(419\) | 21.0000 | 1.02592 | 0.512959 | − | 0.858413i | \(-0.328549\pi\) | ||||
0.512959 | + | 0.858413i | \(0.328549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.7293 | 1.69260 | 0.846302 | − | 0.532703i | \(-0.178824\pi\) | ||||
0.846302 | + | 0.532703i | \(0.178824\pi\) | |||||||
\(422\) | 18.0197 | 0.877183 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.8626 | 0.867484 | ||||||||
\(425\) | −14.5563 | −0.706085 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 66.1555 | 3.19775 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.0159 | 1.88152 | ||||||||
\(431\) | 31.6043 | 1.52233 | 0.761163 | − | 0.648561i | \(-0.224629\pi\) | ||||
0.761163 | + | 0.648561i | \(0.224629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.48576 | −0.311686 | −0.155843 | − | 0.987782i | \(-0.549809\pi\) | ||||
−0.155843 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1062 | −0.771346 | ||||||||
\(437\) | −4.32141 | −0.206721 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5760 | −0.743401 | −0.371701 | − | 0.928353i | \(-0.621225\pi\) | ||||
−0.371701 | + | 0.928353i | \(0.621225\pi\) | |||||||
\(440\) | −4.23491 | −0.201891 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 44.5919 | 2.12102 | ||||||||
\(443\) | −25.0741 | −1.19131 | −0.595654 | − | 0.803241i | \(-0.703107\pi\) | ||||
−0.595654 | + | 0.803241i | \(0.703107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.8567 | 0.704275 | ||||||||
\(446\) | 17.1185 | 0.810587 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.2967 | −0.721894 | −0.360947 | − | 0.932586i | \(-0.617546\pi\) | ||||
−0.360947 | + | 0.932586i | \(0.617546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.67625 | 0.126020 | ||||||||
\(452\) | 52.6377 | 2.47587 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −73.1235 | −3.43186 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4400 | 0.956141 | 0.478071 | − | 0.878321i | \(-0.341336\pi\) | ||||
0.478071 | + | 0.878321i | \(0.341336\pi\) | |||||||
\(458\) | 22.1272 | 1.03394 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.8640 | −0.739662 | ||||||||
\(461\) | −40.8182 | −1.90109 | −0.950546 | − | 0.310584i | \(-0.899475\pi\) | ||||
−0.950546 | + | 0.310584i | \(0.899475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.90840 | 0.460482 | 0.230241 | − | 0.973134i | \(-0.426048\pi\) | ||||
0.230241 | + | 0.973134i | \(0.426048\pi\) | |||||||
\(464\) | 33.7738 | 1.56791 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 74.0246 | 3.42912 | ||||||||
\(467\) | −17.7390 | −0.820861 | −0.410430 | − | 0.911892i | \(-0.634622\pi\) | ||||
−0.410430 | + | 0.911892i | \(0.634622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.7651 | 0.634936 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −43.3942 | −1.99738 | ||||||||
\(473\) | −2.73305 | −0.125666 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.66758 | 0.260047 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −75.2224 | −3.44059 | ||||||||
\(479\) | −23.6094 | −1.07874 | −0.539371 | − | 0.842068i | \(-0.681338\pi\) | ||||
−0.539371 | + | 0.842068i | \(0.681338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5846 | −0.573810 | ||||||||
\(482\) | −60.8231 | −2.77042 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −57.6908 | −2.62231 | ||||||||
\(485\) | 19.9752 | 0.907029 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.8726 | 1.58023 | 0.790115 | − | 0.612959i | \(-0.210021\pi\) | ||||
0.790115 | + | 0.612959i | \(0.210021\pi\) | |||||||
\(488\) | 67.2471 | 3.04413 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.2051 | 1.04723 | 0.523615 | − | 0.851955i | \(-0.324583\pi\) | ||||
0.523615 | + | 0.851955i | \(0.324583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.8255 | 0.667705 | ||||||||
\(494\) | −17.3621 | −0.781159 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −64.4028 | −2.89177 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.32513 | −0.238386 | −0.119193 | − | 0.992871i | \(-0.538031\pi\) | ||||
−0.119193 | + | 0.992871i | \(0.538031\pi\) | |||||||
\(500\) | 62.8021 | 2.80859 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 84.3657 | 3.76542 | ||||||||
\(503\) | −10.4313 | −0.465109 | −0.232554 | − | 0.972583i | \(-0.574708\pi\) | ||||
−0.232554 | + | 0.972583i | \(0.574708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.2051 | 1.03261 | ||||||||
\(506\) | 1.53156 | 0.0680862 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −71.0704 | −3.15324 | ||||||||
\(509\) | 1.50186 | 0.0665687 | 0.0332844 | − | 0.999446i | \(-0.489403\pi\) | ||||
0.0332844 | + | 0.999446i | \(0.489403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.48948 | 0.375186 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.5402 | −1.21475 | ||||||||
\(515\) | −14.6094 | −0.643767 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.964238 | −0.0424072 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.6304 | −1.73791 | ||||||||
\(521\) | 37.7417 | 1.65349 | 0.826747 | − | 0.562574i | \(-0.190189\pi\) | ||||
0.826747 | + | 0.562574i | \(0.190189\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.9556 | −0.785143 | −0.392571 | − | 0.919722i | \(-0.628414\pi\) | ||||
−0.392571 | + | 0.919722i | \(0.628414\pi\) | |||||||
\(524\) | 59.6253 | 2.60475 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 76.8341 | 3.35013 | ||||||||
\(527\) | −28.2705 | −1.23148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.4327 | −0.844899 | ||||||||
\(530\) | −8.62907 | −0.374823 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.0444 | 1.08479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.8713 | −0.859109 | ||||||||
\(536\) | 6.32004 | 0.272984 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.1606 | 1.73145 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.37093 | 0.359894 | 0.179947 | − | 0.983676i | \(-0.442407\pi\) | ||||
0.179947 | + | 0.983676i | \(0.442407\pi\) | |||||||
\(542\) | 0.119925 | 0.00515123 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 108.048 | 4.63251 | ||||||||
\(545\) | 4.83784 | 0.207230 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1075 | 1.28731 | 0.643653 | − | 0.765318i | \(-0.277418\pi\) | ||||
0.643653 | + | 0.765318i | \(0.277418\pi\) | |||||||
\(548\) | 19.9752 | 0.853300 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00866 | −0.0856496 | ||||||||
\(551\) | −5.77238 | −0.245911 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 42.3163 | 1.79785 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 88.4115 | 3.74948 | ||||||||
\(557\) | 16.5353 | 0.700622 | 0.350311 | − | 0.936633i | \(-0.386076\pi\) | ||||
0.350311 | + | 0.936633i | \(0.386076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5760 | −1.08175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.1520 | 1.35625 | ||||||||
\(563\) | −22.2312 | −0.936933 | −0.468466 | − | 0.883481i | \(-0.655193\pi\) | ||||
−0.468466 | + | 0.883481i | \(0.655193\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.8109 | −0.665169 | ||||||||
\(566\) | 16.2174 | 0.681670 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −114.185 | −4.79111 | ||||||||
\(569\) | 2.31275 | 0.0969556 | 0.0484778 | − | 0.998824i | \(-0.484563\pi\) | ||||
0.0484778 | + | 0.998824i | \(0.484563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.09888 | −0.255230 | −0.127615 | − | 0.991824i | \(-0.540732\pi\) | ||||
−0.127615 | + | 0.991824i | \(0.540732\pi\) | |||||||
\(572\) | 4.46472 | 0.186679 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.67859 | −0.195111 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.2064 | 0.841205 | 0.420602 | − | 0.907245i | \(-0.361819\pi\) | ||||
0.420602 | + | 0.907245i | \(0.361819\pi\) | |||||||
\(578\) | 47.3287 | 1.96861 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.1905 | −0.879887 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.604462 | 0.0250343 | ||||||||
\(584\) | −103.630 | −4.28825 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.3782 | −0.552649 | ||||||||
\(587\) | 38.6822 | 1.59658 | 0.798292 | − | 0.602271i | \(-0.205737\pi\) | ||||
0.798292 | + | 0.602271i | \(0.205737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.0073 | 0.453547 | ||||||||
\(590\) | 20.9629 | 0.863027 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −59.9344 | −2.46329 | ||||||||
\(593\) | 23.7156 | 0.973882 | 0.486941 | − | 0.873435i | \(-0.338113\pi\) | ||||
0.486941 | + | 0.873435i | \(0.338113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 57.5795 | 2.35855 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.3324 | 0.586096 | ||||||||
\(599\) | −34.4807 | −1.40884 | −0.704421 | − | 0.709783i | \(-0.748793\pi\) | ||||
−0.704421 | + | 0.709783i | \(0.748793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.28071 | −0.296986 | −0.148493 | − | 0.988913i | \(-0.547442\pi\) | ||||
−0.148493 | + | 0.988913i | \(0.547442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −63.9788 | −2.60326 | ||||||||
\(605\) | 17.3287 | 0.704512 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.1593 | −1.02118 | −0.510591 | − | 0.859824i | \(-0.670573\pi\) | ||||
−0.510591 | + | 0.859824i | \(0.670573\pi\) | |||||||
\(608\) | −42.0690 | −1.70612 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.4858 | −1.31531 | ||||||||
\(611\) | −9.02338 | −0.365047 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.5461 | −1.51647 | −0.758237 | − | 0.651979i | \(-0.773939\pi\) | ||||
−0.758237 | + | 0.651979i | \(0.773939\pi\) | |||||||
\(614\) | −59.5351 | −2.40264 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7280 | −0.552667 | −0.276333 | − | 0.961062i | \(-0.589119\pi\) | ||||
−0.276333 | + | 0.961062i | \(0.589119\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8109 | 0.474720 | 0.237360 | − | 0.971422i | \(-0.423718\pi\) | ||||
0.237360 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(620\) | 40.4079 | 1.62282 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.5302 | 0.863282 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.47848 | −0.259139 | ||||||||
\(626\) | −60.8231 | −2.43098 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | −0.0399043 | ||||||||
\(629\) | −26.3090 | −1.04901 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6304 | 1.17957 | 0.589785 | − | 0.807561i | \(-0.299213\pi\) | ||||
0.589785 | + | 0.807561i | \(0.299213\pi\) | |||||||
\(632\) | 14.7899 | 0.588309 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −53.8255 | −2.13768 | ||||||||
\(635\) | 21.3475 | 0.847152 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.04580 | 0.0809940 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −39.6304 | −1.56653 | ||||||||
\(641\) | −14.6525 | −0.578737 | −0.289368 | − | 0.957218i | \(-0.593445\pi\) | ||||
−0.289368 | + | 0.957218i | \(0.593445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.03714 | 0.0803369 | 0.0401685 | − | 0.999193i | \(-0.487211\pi\) | ||||
0.0401685 | + | 0.999193i | \(0.487211\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.2967 | −1.42807 | ||||||||
\(647\) | 11.7861 | 0.463361 | 0.231680 | − | 0.972792i | \(-0.425578\pi\) | ||||
0.231680 | + | 0.972792i | \(0.425578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.46844 | −0.0576413 | ||||||||
\(650\) | −18.7971 | −0.737284 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −47.3570 | −1.85464 | ||||||||
\(653\) | 34.1840 | 1.33772 | 0.668862 | − | 0.743387i | \(-0.266782\pi\) | ||||
0.668862 | + | 0.743387i | \(0.266782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.9098 | −0.699793 | ||||||||
\(656\) | 119.274 | 4.65687 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.8640 | −0.968563 | −0.484282 | − | 0.874912i | \(-0.660919\pi\) | ||||
−0.484282 | + | 0.874912i | \(0.660919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5388 | 0.993346 | 0.496673 | − | 0.867938i | \(-0.334555\pi\) | ||||
0.496673 | + | 0.867938i | \(0.334555\pi\) | |||||||
\(662\) | 63.7934 | 2.47940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −48.2224 | −1.87139 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.76509 | 0.184505 | ||||||||
\(668\) | −22.9556 | −0.888178 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.05308 | −0.117951 | ||||||||
\(671\) | 2.27561 | 0.0878490 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.81955 | −0.147233 | −0.0736165 | − | 0.997287i | \(-0.523454\pi\) | ||||
−0.0736165 | + | 0.997287i | \(0.523454\pi\) | |||||||
\(674\) | −33.4362 | −1.28792 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.9629 | −1.03703 | ||||||||
\(677\) | 17.2225 | 0.661916 | 0.330958 | − | 0.943646i | \(-0.392628\pi\) | ||||
0.330958 | + | 0.943646i | \(0.392628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −82.8501 | −3.17715 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.90112 | −0.149381 | ||||||||
\(683\) | −33.7170 | −1.29014 | −0.645072 | − | 0.764122i | \(-0.723172\pi\) | ||||
−0.645072 | + | 0.764122i | \(0.723172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −121.806 | −4.64380 | ||||||||
\(689\) | 5.65658 | 0.215499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4930 | −0.969801 | −0.484901 | − | 0.874569i | \(-0.661144\pi\) | ||||
−0.484901 | + | 0.874569i | \(0.661144\pi\) | |||||||
\(692\) | −33.3163 | −1.26650 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.3782 | −0.393952 | ||||||||
\(695\) | −26.5563 | −1.00734 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.3570 | 1.98316 | ||||||||
\(698\) | −32.9061 | −1.24551 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1606 | −0.383762 | −0.191881 | − | 0.981418i | \(-0.561459\pi\) | ||||
−0.191881 | + | 0.981418i | \(0.561459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2436 | 0.386344 | ||||||||
\(704\) | 6.86769 | 0.258836 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.62041 | −0.362069 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.9469 | −0.598899 | −0.299449 | − | 0.954112i | \(-0.596803\pi\) | ||||
−0.299449 | + | 0.954112i | \(0.596803\pi\) | |||||||
\(710\) | 55.1606 | 2.07014 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −83.0246 | −3.11148 | ||||||||
\(713\) | −9.08650 | −0.340292 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.34108 | −0.0501534 | ||||||||
\(716\) | −73.7242 | −2.75520 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.61312 | −0.0975209 | ||||||||
\(719\) | 16.4175 | 0.612271 | 0.306136 | − | 0.951988i | \(-0.400964\pi\) | ||||
0.306136 | + | 0.951988i | \(0.400964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37.1606 | −1.38298 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 96.9875 | 3.60451 | ||||||||
\(725\) | −6.24948 | −0.232100 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.8282 | −1.32879 | −0.664397 | − | 0.747379i | \(-0.731312\pi\) | ||||
−0.664397 | + | 0.747379i | \(0.731312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 50.0617 | 1.85287 | ||||||||
\(731\) | −53.4683 | −1.97760 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.2880 | 1.45114 | 0.725568 | − | 0.688151i | \(-0.241577\pi\) | ||||
0.725568 | + | 0.688151i | \(0.241577\pi\) | |||||||
\(734\) | 56.5685 | 2.08798 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.7280 | 1.28009 | ||||||||
\(737\) | 0.213867 | 0.00787790 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.09022 | 0.0768901 | 0.0384451 | − | 0.999261i | \(-0.487760\pi\) | ||||
0.0384451 | + | 0.999261i | \(0.487760\pi\) | |||||||
\(740\) | 37.6043 | 1.38236 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.7266 | −1.12725 | −0.563624 | − | 0.826031i | \(-0.690593\pi\) | ||||
−0.563624 | + | 0.826031i | \(0.690593\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.2953 | −0.633650 | ||||||||
\(746\) | 5.39926 | 0.197681 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.33379 | 0.341277 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7738 | 0.758045 | 0.379023 | − | 0.925387i | \(-0.376260\pi\) | ||||
0.379023 | + | 0.925387i | \(0.376260\pi\) | |||||||
\(752\) | −42.9739 | −1.56710 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.1447 | 0.697208 | ||||||||
\(755\) | 19.2174 | 0.699394 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.9257 | 0.615176 | 0.307588 | − | 0.951520i | \(-0.400478\pi\) | ||||
0.307588 | + | 0.951520i | \(0.400478\pi\) | |||||||
\(758\) | −19.2843 | −0.700436 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 32.2581 | 1.17013 | ||||||||
\(761\) | −32.8392 | −1.19042 | −0.595210 | − | 0.803570i | \(-0.702931\pi\) | ||||
−0.595210 | + | 0.803570i | \(0.702931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 40.2312 | 1.45551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.3324 | −1.16822 | ||||||||
\(767\) | −13.7417 | −0.496184 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.7293 | 1.14419 | 0.572094 | − | 0.820188i | \(-0.306131\pi\) | ||||
0.572094 | + | 0.820188i | \(0.306131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40.5388 | 1.45902 | ||||||||
\(773\) | −6.37312 | −0.229225 | −0.114613 | − | 0.993410i | \(-0.536563\pi\) | ||||
−0.114613 | + | 0.993410i | \(0.536563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.9171 | 0.428073 | ||||||||
\(776\) | −111.629 | −4.00724 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.1978 | 1.33360 | ||||||||
\(779\) | −20.3855 | −0.730386 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.86398 | −0.138264 | ||||||||
\(782\) | 29.9629 | 1.07147 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.300372 | 0.0107207 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8799 | −0.708643 | −0.354321 | − | 0.935124i | \(-0.615288\pi\) | ||||
−0.354321 | + | 0.935124i | \(0.615288\pi\) | |||||||
\(788\) | 97.2297 | 3.46366 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.14468 | −0.254196 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.2953 | 0.756217 | ||||||||
\(794\) | 22.6414 | 0.803515 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.4858 | 1.11598 | ||||||||
\(797\) | 5.81955 | 0.206139 | 0.103070 | − | 0.994674i | \(-0.467134\pi\) | ||||
0.103070 | + | 0.994674i | \(0.467134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8640 | −0.667360 | ||||||||
\(800\) | −45.5461 | −1.61030 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 74.5548 | 2.63262 | ||||||||
\(803\) | −3.50680 | −0.123752 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.5068 | −1.28590 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −129.678 | −4.56207 | ||||||||
\(809\) | −2.12227 | −0.0746149 | −0.0373075 | − | 0.999304i | \(-0.511878\pi\) | ||||
−0.0373075 | + | 0.999304i | \(0.511878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4327 | −0.647259 | −0.323629 | − | 0.946184i | \(-0.604903\pi\) | ||||
−0.323629 | + | 0.946184i | \(0.604903\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.63045 | −0.127247 | ||||||||
\(815\) | 14.2247 | 0.498270 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.8182 | 0.728336 | ||||||||
\(818\) | 82.4239 | 2.88188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −74.8355 | −2.61337 | ||||||||
\(821\) | 45.1555 | 1.57594 | 0.787969 | − | 0.615714i | \(-0.211132\pi\) | ||||
0.787969 | + | 0.615714i | \(0.211132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0517 | 0.873248 | 0.436624 | − | 0.899644i | \(-0.356174\pi\) | ||||
0.436624 | + | 0.899644i | \(0.356174\pi\) | |||||||
\(824\) | 81.6427 | 2.84416 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.2953 | 0.497095 | 0.248548 | − | 0.968620i | \(-0.420047\pi\) | ||||
0.248548 | + | 0.968620i | \(0.420047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.8255 | 1.10534 | 0.552672 | − | 0.833399i | \(-0.313608\pi\) | ||||
0.552672 | + | 0.833399i | \(0.313608\pi\) | |||||||
\(830\) | 23.2953 | 0.808591 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 64.2682 | 2.22810 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.89521 | 0.238619 | ||||||||
\(836\) | −3.63416 | −0.125690 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 56.6922 | 1.95840 | ||||||||
\(839\) | −16.4785 | −0.568900 | −0.284450 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284450 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6350 | −0.780516 | ||||||||
\(842\) | 93.7563 | 3.23105 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.2967 | 1.21496 | ||||||||
\(845\) | 8.09888 | 0.278610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 26.9395 | 0.925106 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −39.2967 | −1.34786 | ||||||||
\(851\) | −8.45606 | −0.289870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.9986 | −0.924415 | −0.462208 | − | 0.886772i | \(-0.652943\pi\) | ||||
−0.462208 | + | 0.886772i | \(0.652943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 111.048 | 3.79554 | ||||||||
\(857\) | 39.1630 | 1.33778 | 0.668891 | − | 0.743361i | \(-0.266769\pi\) | ||||
0.668891 | + | 0.743361i | \(0.266769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.46844 | 0.323059 | 0.161529 | − | 0.986868i | \(-0.448357\pi\) | ||||
0.161529 | + | 0.986868i | \(0.448357\pi\) | |||||||
\(860\) | 76.4239 | 2.60603 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 85.3199 | 2.90601 | ||||||||
\(863\) | −2.01238 | −0.0685022 | −0.0342511 | − | 0.999413i | \(-0.510905\pi\) | ||||
−0.0342511 | + | 0.999413i | \(0.510905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0073 | 0.340258 | ||||||||
\(866\) | −17.5091 | −0.594985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.500482 | 0.0169777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00138 | 0.0678141 | ||||||||
\(872\) | −27.0356 | −0.915541 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.6662 | −0.394615 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.6995 | 1.50939 | 0.754697 | − | 0.656073i | \(-0.227784\pi\) | ||||
0.754697 | + | 0.656073i | \(0.227784\pi\) | |||||||
\(878\) | −42.0494 | −1.41910 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.38688 | −0.215302 | ||||||||
\(881\) | −12.7047 | −0.428033 | −0.214017 | − | 0.976830i | \(-0.568655\pi\) | ||||
−0.214017 | + | 0.976830i | \(0.568655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0014 | −0.572142 | −0.286071 | − | 0.958208i | \(-0.592349\pi\) | ||||
−0.286071 | + | 0.958208i | \(0.592349\pi\) | |||||||
\(884\) | 87.3460 | 2.93776 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −67.6908 | −2.27412 | ||||||||
\(887\) | −1.20149 | −0.0403420 | −0.0201710 | − | 0.999797i | \(-0.506421\pi\) | ||||
−0.0201710 | + | 0.999797i | \(0.506421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 40.1075 | 1.34441 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.5316 | 1.12272 | ||||||||
\(893\) | 7.34479 | 0.245784 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.1447 | 0.740215 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.2953 | −1.37804 | ||||||||
\(899\) | −12.1374 | −0.404805 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8255 | 0.393963 | ||||||||
\(902\) | 7.22487 | 0.240562 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 88.3570 | 2.93871 | ||||||||
\(905\) | −29.1323 | −0.968391 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0631 | 0.566572 | 0.283286 | − | 0.959036i | \(-0.408575\pi\) | ||||
0.283286 | + | 0.959036i | \(0.408575\pi\) | |||||||
\(908\) | −143.233 | −4.75336 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0014 | −0.728938 | −0.364469 | − | 0.931215i | \(-0.618750\pi\) | ||||
−0.364469 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.63182 | −0.0540055 | ||||||||
\(914\) | 55.1803 | 1.82520 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.3425 | 1.43207 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.5906 | −0.976102 | −0.488051 | − | 0.872815i | \(-0.662292\pi\) | ||||
−0.488051 | + | 0.872815i | \(0.662292\pi\) | |||||||
\(920\) | −26.6291 | −0.877934 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −110.194 | −3.62904 | ||||||||
\(923\) | −36.1593 | −1.19020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0902 | 0.364644 | ||||||||
\(926\) | 26.7490 | 0.879026 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 46.3883 | 1.52277 | ||||||||
\(929\) | 2.69963 | 0.0885719 | 0.0442860 | − | 0.999019i | \(-0.485899\pi\) | ||||
0.0442860 | + | 0.999019i | \(0.485899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 144.998 | 4.74958 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −47.8886 | −1.56696 | ||||||||
\(935\) | −2.80361 | −0.0916878 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.4472 | 1.28869 | 0.644343 | − | 0.764737i | \(-0.277131\pi\) | ||||
0.644343 | + | 0.764737i | \(0.277131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 26.9629 | 0.879432 | ||||||||
\(941\) | 39.7244 | 1.29498 | 0.647489 | − | 0.762075i | \(-0.275819\pi\) | ||||
0.647489 | + | 0.762075i | \(0.275819\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.8282 | 0.548002 | ||||||||
\(944\) | −65.4449 | −2.13005 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.37822 | −0.239886 | ||||||||
\(947\) | −15.7303 | −0.511166 | −0.255583 | − | 0.966787i | \(-0.582267\pi\) | ||||
−0.255583 | + | 0.966787i | \(0.582267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.8168 | −1.06528 | ||||||||
\(950\) | 15.3004 | 0.496410 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.2064 | 0.978482 | 0.489241 | − | 0.872149i | \(-0.337274\pi\) | ||||
0.489241 | + | 0.872149i | \(0.337274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0843 | −0.391039 | ||||||||
\(956\) | −147.344 | −4.76546 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −63.7366 | −2.05924 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.85532 | −0.253397 | ||||||||
\(962\) | −33.9739 | −1.09536 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −119.139 | −3.83722 | ||||||||
\(965\) | −12.1767 | −0.391983 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.18911 | −0.199028 | −0.0995141 | − | 0.995036i | \(-0.531729\pi\) | ||||
−0.0995141 | + | 0.995036i | \(0.531729\pi\) | |||||||
\(968\) | −96.8391 | −3.11253 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 53.9257 | 1.73145 | ||||||||
\(971\) | −2.17163 | −0.0696910 | −0.0348455 | − | 0.999393i | \(-0.511094\pi\) | ||||
−0.0348455 | + | 0.999393i | \(0.511094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 94.1432 | 3.01654 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 101.419 | 3.24634 | ||||||||
\(977\) | −11.4561 | −0.366512 | −0.183256 | − | 0.983065i | \(-0.558664\pi\) | ||||
−0.183256 | + | 0.983065i | \(0.558664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.80951 | −0.0897925 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 62.6450 | 1.99908 | ||||||||
\(983\) | 44.8021 | 1.42896 | 0.714482 | − | 0.699654i | \(-0.246662\pi\) | ||||
0.714482 | + | 0.699654i | \(0.246662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.2051 | −0.930550 | ||||||||
\(986\) | 40.0232 | 1.27460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −34.0087 | −1.08196 | ||||||||
\(989\) | −17.1854 | −0.546464 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2953 | −0.771765 | −0.385882 | − | 0.922548i | \(-0.626103\pi\) | ||||
−0.385882 | + | 0.922548i | \(0.626103\pi\) | |||||||
\(992\) | −88.4573 | −2.80852 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.45744 | −0.299821 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.3251 | −0.358671 | −0.179335 | − | 0.983788i | \(-0.557395\pi\) | ||||
−0.179335 | + | 0.983788i | \(0.557395\pi\) | |||||||
\(998\) | −14.3759 | −0.455060 | ||||||||
\(999\) | 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 | 1323.2.a.ba.1.3 | 3 | ||
3.2 | odd | 2 | 1323.2.a.x.1.1 | 3 | |||
7.2 | even | 3 | 189.2.e.e.109.1 | ✓ | 6 | ||
7.4 | even | 3 | 189.2.e.e.163.1 | yes | 6 | ||
7.6 | odd | 2 | 1323.2.a.z.1.3 | 3 | |||
21.2 | odd | 6 | 189.2.e.f.109.3 | yes | 6 | ||
21.11 | odd | 6 | 189.2.e.f.163.3 | yes | 6 | ||
21.20 | even | 2 | 1323.2.a.y.1.1 | 3 | |||
63.2 | odd | 6 | 567.2.g.i.109.3 | 6 | |||
63.4 | even | 3 | 567.2.g.h.541.1 | 6 | |||
63.11 | odd | 6 | 567.2.h.h.352.1 | 6 | |||
63.16 | even | 3 | 567.2.g.h.109.1 | 6 | |||
63.23 | odd | 6 | 567.2.h.h.298.1 | 6 | |||
63.25 | even | 3 | 567.2.h.i.352.3 | 6 | |||
63.32 | odd | 6 | 567.2.g.i.541.3 | 6 | |||
63.58 | even | 3 | 567.2.h.i.298.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.e.109.1 | ✓ | 6 | 7.2 | even | 3 | ||
189.2.e.e.163.1 | yes | 6 | 7.4 | even | 3 | ||
189.2.e.f.109.3 | yes | 6 | 21.2 | odd | 6 | ||
189.2.e.f.163.3 | yes | 6 | 21.11 | odd | 6 | ||
567.2.g.h.109.1 | 6 | 63.16 | even | 3 | |||
567.2.g.h.541.1 | 6 | 63.4 | even | 3 | |||
567.2.g.i.109.3 | 6 | 63.2 | odd | 6 | |||
567.2.g.i.541.3 | 6 | 63.32 | odd | 6 | |||
567.2.h.h.298.1 | 6 | 63.23 | odd | 6 | |||
567.2.h.h.352.1 | 6 | 63.11 | odd | 6 | |||
567.2.h.i.298.3 | 6 | 63.58 | even | 3 | |||
567.2.h.i.352.3 | 6 | 63.25 | even | 3 | |||
1323.2.a.x.1.1 | 3 | 3.2 | odd | 2 | |||
1323.2.a.y.1.1 | 3 | 21.20 | even | 2 | |||
1323.2.a.z.1.3 | 3 | 7.6 | odd | 2 | |||
1323.2.a.ba.1.3 | 3 | 1.1 | even | 1 | trivial |