Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
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 475) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.37720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37720 | −1.68094 | −0.840468 | − | 0.541861i | \(-0.817720\pi\) | ||||
−0.840468 | + | 0.541861i | \(0.817720\pi\) | |||||||
\(3\) | −1.27389 | −0.735481 | −0.367741 | − | 0.929928i | \(-0.619869\pi\) | ||||
−0.367741 | + | 0.929928i | \(0.619869\pi\) | |||||||
\(4\) | 3.65109 | 1.82555 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.02830 | 1.23630 | ||||||||
\(7\) | 0.726109 | 0.274444 | 0.137222 | − | 0.990540i | \(-0.456183\pi\) | ||||
0.137222 | + | 0.990540i | \(0.456183\pi\) | |||||||
\(8\) | −3.92498 | −1.38769 | ||||||||
\(9\) | −1.37720 | −0.459068 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.273891 | −0.0825811 | −0.0412906 | − | 0.999147i | \(-0.513147\pi\) | ||||
−0.0412906 | + | 0.999147i | \(0.513147\pi\) | |||||||
\(12\) | −4.65109 | −1.34266 | ||||||||
\(13\) | 5.95328 | 1.65114 | 0.825571 | − | 0.564298i | \(-0.190853\pi\) | ||||
0.825571 | + | 0.564298i | \(0.190853\pi\) | |||||||
\(14\) | −1.72611 | −0.461322 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.02830 | 0.507074 | ||||||||
\(17\) | 5.27389 | 1.27911 | 0.639553 | − | 0.768747i | \(-0.279119\pi\) | ||||
0.639553 | + | 0.768747i | \(0.279119\pi\) | |||||||
\(18\) | 3.27389 | 0.771663 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.924984 | −0.201848 | ||||||||
\(22\) | 0.651093 | 0.138814 | ||||||||
\(23\) | −3.67939 | −0.767206 | −0.383603 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383603 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(24\) | 5.00000 | 1.02062 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.1522 | −2.77547 | ||||||||
\(27\) | 5.57608 | 1.07312 | ||||||||
\(28\) | 2.65109 | 0.501010 | ||||||||
\(29\) | 2.27389 | 0.422251 | 0.211125 | − | 0.977459i | \(-0.432287\pi\) | ||||
0.211125 | + | 0.977459i | \(0.432287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19887 | −0.574535 | −0.287267 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287267 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(32\) | 3.02830 | 0.535332 | ||||||||
\(33\) | 0.348907 | 0.0607368 | ||||||||
\(34\) | −12.5371 | −2.15010 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.02830 | −0.838049 | ||||||||
\(37\) | −8.12386 | −1.33555 | −0.667777 | − | 0.744361i | \(-0.732754\pi\) | ||||
−0.667777 | + | 0.744361i | \(0.732754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.58383 | −1.21438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.43380 | 1.47331 | 0.736656 | − | 0.676268i | \(-0.236404\pi\) | ||||
0.736656 | + | 0.676268i | \(0.236404\pi\) | |||||||
\(42\) | 2.19887 | 0.339294 | ||||||||
\(43\) | 9.81100 | 1.49616 | 0.748082 | − | 0.663607i | \(-0.230975\pi\) | ||||
0.748082 | + | 0.663607i | \(0.230975\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.74666 | 1.28962 | ||||||||
\(47\) | 12.1599 | 1.77370 | 0.886852 | − | 0.462053i | \(-0.152887\pi\) | ||||
0.886852 | + | 0.462053i | \(0.152887\pi\) | |||||||
\(48\) | −2.58383 | −0.372943 | ||||||||
\(49\) | −6.47277 | −0.924681 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.71836 | −0.940758 | ||||||||
\(52\) | 21.7360 | 3.01424 | ||||||||
\(53\) | −5.69781 | −0.782655 | −0.391327 | − | 0.920252i | \(-0.627984\pi\) | ||||
−0.391327 | + | 0.920252i | \(0.627984\pi\) | |||||||
\(54\) | −13.2555 | −1.80384 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.84997 | −0.380843 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.40550 | −0.709777 | ||||||||
\(59\) | 4.20662 | 0.547656 | 0.273828 | − | 0.961779i | \(-0.411710\pi\) | ||||
0.273828 | + | 0.961779i | \(0.411710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.103312 | −0.0132278 | −0.00661389 | − | 0.999978i | \(-0.502105\pi\) | ||||
−0.00661389 | + | 0.999978i | \(0.502105\pi\) | |||||||
\(62\) | 7.60437 | 0.965756 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −11.2555 | −1.40693 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.829422 | −0.102095 | ||||||||
\(67\) | 11.7827 | 1.43949 | 0.719743 | − | 0.694241i | \(-0.244260\pi\) | ||||
0.719743 | + | 0.694241i | \(0.244260\pi\) | |||||||
\(68\) | 19.2555 | 2.33507 | ||||||||
\(69\) | 4.68714 | 0.564265 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.75441 | −0.682922 | −0.341461 | − | 0.939896i | \(-0.610922\pi\) | ||||
−0.341461 | + | 0.939896i | \(0.610922\pi\) | |||||||
\(72\) | 5.40550 | 0.637044 | ||||||||
\(73\) | 6.67939 | 0.781763 | 0.390882 | − | 0.920441i | \(-0.372170\pi\) | ||||
0.390882 | + | 0.920441i | \(0.372170\pi\) | |||||||
\(74\) | 19.3121 | 2.24498 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.198875 | −0.0226639 | ||||||||
\(78\) | 18.0283 | 2.04130 | ||||||||
\(79\) | −3.87826 | −0.436339 | −0.218169 | − | 0.975911i | \(-0.570009\pi\) | ||||
−0.218169 | + | 0.975911i | \(0.570009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.97170 | −0.330189 | ||||||||
\(82\) | −22.4260 | −2.47654 | ||||||||
\(83\) | −0.488265 | −0.0535941 | −0.0267970 | − | 0.999641i | \(-0.508531\pi\) | ||||
−0.0267970 | + | 0.999641i | \(0.508531\pi\) | |||||||
\(84\) | −3.37720 | −0.368483 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −23.3227 | −2.51495 | ||||||||
\(87\) | −2.89669 | −0.310558 | ||||||||
\(88\) | 1.07502 | 0.114597 | ||||||||
\(89\) | 16.4338 | 1.74198 | 0.870989 | − | 0.491302i | \(-0.163479\pi\) | ||||
0.870989 | + | 0.491302i | \(0.163479\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.32273 | 0.453146 | ||||||||
\(92\) | −13.4338 | −1.40057 | ||||||||
\(93\) | 4.07502 | 0.422559 | ||||||||
\(94\) | −28.9066 | −2.98148 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.85772 | −0.393727 | ||||||||
\(97\) | 4.44447 | 0.451267 | 0.225634 | − | 0.974212i | \(-0.427555\pi\) | ||||
0.225634 | + | 0.974212i | \(0.427555\pi\) | |||||||
\(98\) | 15.3871 | 1.55433 | ||||||||
\(99\) | 0.377203 | 0.0379103 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.38495 | 0.436319 | 0.218160 | − | 0.975913i | \(-0.429995\pi\) | ||||
0.218160 | + | 0.975913i | \(0.429995\pi\) | |||||||
\(102\) | 15.9709 | 1.58136 | ||||||||
\(103\) | −3.33048 | −0.328162 | −0.164081 | − | 0.986447i | \(-0.552466\pi\) | ||||
−0.164081 | + | 0.986447i | \(0.552466\pi\) | |||||||
\(104\) | −23.3665 | −2.29128 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.5449 | 1.31559 | ||||||||
\(107\) | −16.4904 | −1.59419 | −0.797093 | − | 0.603857i | \(-0.793630\pi\) | ||||
−0.797093 | + | 0.603857i | \(0.793630\pi\) | |||||||
\(108\) | 20.3588 | 1.95902 | ||||||||
\(109\) | −7.79045 | −0.746190 | −0.373095 | − | 0.927793i | \(-0.621703\pi\) | ||||
−0.373095 | + | 0.927793i | \(0.621703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3489 | 0.982275 | ||||||||
\(112\) | 1.47277 | 0.139163 | ||||||||
\(113\) | 0.142282 | 0.0133848 | 0.00669238 | − | 0.999978i | \(-0.497870\pi\) | ||||
0.00669238 | + | 0.999978i | \(0.497870\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.30219 | 0.770839 | ||||||||
\(117\) | −8.19887 | −0.757986 | ||||||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | 3.82942 | 0.351043 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9250 | −0.993180 | ||||||||
\(122\) | 0.245594 | 0.0222351 | ||||||||
\(123\) | −12.0176 | −1.08359 | ||||||||
\(124\) | −11.6794 | −1.04884 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.37720 | 0.211778 | ||||||||
\(127\) | 15.1316 | 1.34271 | 0.671357 | − | 0.741135i | \(-0.265712\pi\) | ||||
0.671357 | + | 0.741135i | \(0.265712\pi\) | |||||||
\(128\) | 20.6999 | 1.82963 | ||||||||
\(129\) | −12.4981 | −1.10040 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.58383 | 0.487861 | 0.243931 | − | 0.969793i | \(-0.421563\pi\) | ||||
0.243931 | + | 0.969793i | \(0.421563\pi\) | |||||||
\(132\) | 1.27389 | 0.110878 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −28.0099 | −2.41968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.6999 | −1.77500 | ||||||||
\(137\) | 12.8294 | 1.09609 | 0.548046 | − | 0.836448i | \(-0.315372\pi\) | ||||
0.548046 | + | 0.836448i | \(0.315372\pi\) | |||||||
\(138\) | −11.1423 | −0.948494 | ||||||||
\(139\) | −15.2477 | −1.29329 | −0.646647 | − | 0.762789i | \(-0.723829\pi\) | ||||
−0.646647 | + | 0.762789i | \(0.723829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.4904 | −1.30453 | ||||||||
\(142\) | 13.6794 | 1.14795 | ||||||||
\(143\) | −1.63055 | −0.136353 | ||||||||
\(144\) | −2.79338 | −0.232781 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.8783 | −1.31409 | ||||||||
\(147\) | 8.24559 | 0.680085 | ||||||||
\(148\) | −29.6610 | −2.43812 | ||||||||
\(149\) | 13.8315 | 1.13312 | 0.566562 | − | 0.824019i | \(-0.308273\pi\) | ||||
0.566562 | + | 0.824019i | \(0.308273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7077 | 0.952758 | 0.476379 | − | 0.879240i | \(-0.341949\pi\) | ||||
0.476379 | + | 0.879240i | \(0.341949\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.26322 | −0.587196 | ||||||||
\(154\) | 0.472765 | 0.0380965 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −27.6893 | −2.21692 | ||||||||
\(157\) | −4.79045 | −0.382320 | −0.191160 | − | 0.981559i | \(-0.561225\pi\) | ||||
−0.191160 | + | 0.981559i | \(0.561225\pi\) | |||||||
\(158\) | 9.21942 | 0.733458 | ||||||||
\(159\) | 7.25839 | 0.575628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.67164 | −0.210555 | ||||||||
\(162\) | 7.06434 | 0.555027 | ||||||||
\(163\) | 12.8011 | 1.00266 | 0.501331 | − | 0.865256i | \(-0.332844\pi\) | ||||
0.501331 | + | 0.865256i | \(0.332844\pi\) | |||||||
\(164\) | 34.4437 | 2.68960 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.16071 | 0.0900882 | ||||||||
\(167\) | 20.9426 | 1.62059 | 0.810294 | − | 0.586024i | \(-0.199308\pi\) | ||||
0.810294 | + | 0.586024i | \(0.199308\pi\) | |||||||
\(168\) | 3.63055 | 0.280103 | ||||||||
\(169\) | 22.4415 | 1.72627 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 35.8209 | 2.73132 | ||||||||
\(173\) | −15.7282 | −1.19580 | −0.597898 | − | 0.801572i | \(-0.703997\pi\) | ||||
−0.597898 | + | 0.801572i | \(0.703997\pi\) | |||||||
\(174\) | 6.88601 | 0.522027 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.555531 | −0.0418747 | ||||||||
\(177\) | −5.35878 | −0.402791 | ||||||||
\(178\) | −39.0665 | −2.92816 | ||||||||
\(179\) | −3.41325 | −0.255118 | −0.127559 | − | 0.991831i | \(-0.540714\pi\) | ||||
−0.127559 | + | 0.991831i | \(0.540714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.5109 | −1.74755 | −0.873777 | − | 0.486327i | \(-0.838336\pi\) | ||||
−0.873777 | + | 0.486327i | \(0.838336\pi\) | |||||||
\(182\) | −10.2760 | −0.761709 | ||||||||
\(183\) | 0.131609 | 0.00972878 | ||||||||
\(184\) | 14.4415 | 1.06464 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.68714 | −0.710296 | ||||||||
\(187\) | −1.44447 | −0.105630 | ||||||||
\(188\) | 44.3969 | 3.23798 | ||||||||
\(189\) | 4.04884 | 0.294510 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4650 | 0.901937 | 0.450968 | − | 0.892540i | \(-0.351079\pi\) | ||||
0.450968 | + | 0.892540i | \(0.351079\pi\) | |||||||
\(192\) | 14.3382 | 1.03477 | ||||||||
\(193\) | −19.2993 | −1.38919 | −0.694596 | − | 0.719400i | \(-0.744417\pi\) | ||||
−0.694596 | + | 0.719400i | \(0.744417\pi\) | |||||||
\(194\) | −10.5654 | −0.758552 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.6327 | −1.68805 | ||||||||
\(197\) | 6.63055 | 0.472407 | 0.236203 | − | 0.971704i | \(-0.424097\pi\) | ||||
0.236203 | + | 0.971704i | \(0.424097\pi\) | |||||||
\(198\) | −0.896688 | −0.0637248 | ||||||||
\(199\) | −23.0849 | −1.63644 | −0.818222 | − | 0.574902i | \(-0.805040\pi\) | ||||
−0.818222 | + | 0.574902i | \(0.805040\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0099 | −1.05871 | ||||||||
\(202\) | −10.4239 | −0.733425 | ||||||||
\(203\) | 1.65109 | 0.115884 | ||||||||
\(204\) | −24.5294 | −1.71740 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.91723 | 0.551620 | ||||||||
\(207\) | 5.06727 | 0.352199 | ||||||||
\(208\) | 12.0750 | 0.837252 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.54778 | 0.519611 | 0.259805 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259805 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(212\) | −20.8032 | −1.42877 | ||||||||
\(213\) | 7.33048 | 0.502276 | ||||||||
\(214\) | 39.2010 | 2.67973 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −21.8860 | −1.48915 | ||||||||
\(217\) | −2.32273 | −0.157677 | ||||||||
\(218\) | 18.5195 | 1.25430 | ||||||||
\(219\) | −8.50881 | −0.574972 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.3969 | 2.11199 | ||||||||
\(222\) | −24.6015 | −1.65114 | ||||||||
\(223\) | 1.09344 | 0.0732221 | 0.0366111 | − | 0.999330i | \(-0.488344\pi\) | ||||
0.0366111 | + | 0.999330i | \(0.488344\pi\) | |||||||
\(224\) | 2.19887 | 0.146918 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.338233 | −0.0224989 | ||||||||
\(227\) | 20.1316 | 1.33618 | 0.668091 | − | 0.744080i | \(-0.267112\pi\) | ||||
0.668091 | + | 0.744080i | \(0.267112\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.51656 | −0.364545 | −0.182272 | − | 0.983248i | \(-0.558345\pi\) | ||||
−0.182272 | + | 0.983248i | \(0.558345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.253344 | 0.0166688 | ||||||||
\(232\) | −8.92498 | −0.585954 | ||||||||
\(233\) | −18.1805 | −1.19104 | −0.595520 | − | 0.803340i | \(-0.703054\pi\) | ||||
−0.595520 | + | 0.803340i | \(0.703054\pi\) | |||||||
\(234\) | 19.4904 | 1.27413 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.3588 | 0.999771 | ||||||||
\(237\) | 4.94048 | 0.320919 | ||||||||
\(238\) | −9.10331 | −0.590080 | ||||||||
\(239\) | 21.9164 | 1.41766 | 0.708828 | − | 0.705381i | \(-0.249224\pi\) | ||||
0.708828 | + | 0.705381i | \(0.249224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1882 | 1.81576 | 0.907881 | − | 0.419228i | \(-0.137699\pi\) | ||||
0.907881 | + | 0.419228i | \(0.137699\pi\) | |||||||
\(242\) | 25.9709 | 1.66947 | ||||||||
\(243\) | −12.9426 | −0.830269 | ||||||||
\(244\) | −0.377203 | −0.0241479 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 28.5683 | 1.82145 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.5555 | 0.797277 | ||||||||
\(249\) | 0.621996 | 0.0394174 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00987 | 0.568698 | 0.284349 | − | 0.958721i | \(-0.408223\pi\) | ||||
0.284349 | + | 0.958721i | \(0.408223\pi\) | |||||||
\(252\) | −3.65109 | −0.229997 | ||||||||
\(253\) | 1.00775 | 0.0633567 | ||||||||
\(254\) | −35.9709 | −2.25702 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.6970 | −1.66856 | ||||||||
\(257\) | −6.86064 | −0.427955 | −0.213978 | − | 0.976839i | \(-0.568642\pi\) | ||||
−0.213978 | + | 0.976839i | \(0.568642\pi\) | |||||||
\(258\) | 29.7106 | 1.84970 | ||||||||
\(259\) | −5.89881 | −0.366534 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.13161 | −0.193842 | ||||||||
\(262\) | −13.2739 | −0.820064 | ||||||||
\(263\) | −9.25547 | −0.570717 | −0.285358 | − | 0.958421i | \(-0.592113\pi\) | ||||
−0.285358 | + | 0.958421i | \(0.592113\pi\) | |||||||
\(264\) | −1.36945 | −0.0842840 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.9349 | −1.28119 | ||||||||
\(268\) | 43.0197 | 2.62785 | ||||||||
\(269\) | −0.498939 | −0.0304208 | −0.0152104 | − | 0.999884i | \(-0.504842\pi\) | ||||
−0.0152104 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.71061 | 0.225403 | 0.112702 | − | 0.993629i | \(-0.464050\pi\) | ||||
0.112702 | + | 0.993629i | \(0.464050\pi\) | |||||||
\(272\) | 10.6970 | 0.648602 | ||||||||
\(273\) | −5.50669 | −0.333280 | ||||||||
\(274\) | −30.4981 | −1.84246 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 17.1132 | 1.03009 | ||||||||
\(277\) | 4.58675 | 0.275591 | 0.137796 | − | 0.990461i | \(-0.455998\pi\) | ||||
0.137796 | + | 0.990461i | \(0.455998\pi\) | |||||||
\(278\) | 36.2469 | 2.17395 | ||||||||
\(279\) | 4.40550 | 0.263750 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.2653 | −1.62651 | −0.813257 | − | 0.581905i | \(-0.802308\pi\) | ||||
−0.813257 | + | 0.581905i | \(0.802308\pi\) | |||||||
\(282\) | 36.8238 | 2.19283 | ||||||||
\(283\) | −10.2661 | −0.610259 | −0.305129 | − | 0.952311i | \(-0.598700\pi\) | ||||
−0.305129 | + | 0.952311i | \(0.598700\pi\) | |||||||
\(284\) | −21.0099 | −1.24671 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.87614 | 0.229201 | ||||||||
\(287\) | 6.84997 | 0.404341 | ||||||||
\(288\) | −4.17058 | −0.245754 | ||||||||
\(289\) | 10.8139 | 0.636113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.66177 | −0.331899 | ||||||||
\(292\) | 24.3871 | 1.42715 | ||||||||
\(293\) | 1.87051 | 0.109277 | 0.0546383 | − | 0.998506i | \(-0.482599\pi\) | ||||
0.0546383 | + | 0.998506i | \(0.482599\pi\) | |||||||
\(294\) | −19.6015 | −1.14318 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 31.8860 | 1.85334 | ||||||||
\(297\) | −1.52723 | −0.0886192 | ||||||||
\(298\) | −32.8804 | −1.90471 | ||||||||
\(299\) | −21.9044 | −1.26677 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.12386 | 0.410612 | ||||||||
\(302\) | −27.8315 | −1.60153 | ||||||||
\(303\) | −5.58595 | −0.320904 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 17.2661 | 0.987040 | ||||||||
\(307\) | −0.227171 | −0.0129653 | −0.00648266 | − | 0.999979i | \(-0.502064\pi\) | ||||
−0.00648266 | + | 0.999979i | \(0.502064\pi\) | |||||||
\(308\) | −0.726109 | −0.0413739 | ||||||||
\(309\) | 4.24267 | 0.241357 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9554 | 1.18827 | 0.594136 | − | 0.804365i | \(-0.297494\pi\) | ||||
0.594136 | + | 0.804365i | \(0.297494\pi\) | |||||||
\(312\) | 29.7664 | 1.68519 | ||||||||
\(313\) | −11.2349 | −0.635035 | −0.317518 | − | 0.948252i | \(-0.602849\pi\) | ||||
−0.317518 | + | 0.948252i | \(0.602849\pi\) | |||||||
\(314\) | 11.3879 | 0.642655 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.1599 | −0.796557 | ||||||||
\(317\) | −18.6228 | −1.04596 | −0.522980 | − | 0.852345i | \(-0.675180\pi\) | ||||
−0.522980 | + | 0.852345i | \(0.675180\pi\) | |||||||
\(318\) | −17.2547 | −0.967594 | ||||||||
\(319\) | −0.622797 | −0.0348699 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.0069 | 1.17249 | ||||||||
\(322\) | 6.35103 | 0.353929 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −10.8500 | −0.602776 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.4309 | −1.68541 | ||||||||
\(327\) | 9.92418 | 0.548809 | ||||||||
\(328\) | −37.0275 | −2.04450 | ||||||||
\(329\) | 8.82942 | 0.486782 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1054 | 0.775305 | 0.387652 | − | 0.921806i | \(-0.373286\pi\) | ||||
0.387652 | + | 0.921806i | \(0.373286\pi\) | |||||||
\(332\) | −1.78270 | −0.0978385 | ||||||||
\(333\) | 11.1882 | 0.613110 | ||||||||
\(334\) | −49.7848 | −2.72410 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.87614 | −0.102352 | ||||||||
\(337\) | −22.9709 | −1.25130 | −0.625652 | − | 0.780102i | \(-0.715167\pi\) | ||||
−0.625652 | + | 0.780102i | \(0.715167\pi\) | |||||||
\(338\) | −53.3481 | −2.90175 | ||||||||
\(339\) | −0.181252 | −0.00984424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.876142 | 0.0474457 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.78270 | −0.528216 | ||||||||
\(344\) | −38.5080 | −2.07621 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 37.3892 | 2.01006 | ||||||||
\(347\) | −3.93273 | −0.211120 | −0.105560 | − | 0.994413i | \(-0.533664\pi\) | ||||
−0.105560 | + | 0.994413i | \(0.533664\pi\) | |||||||
\(348\) | −10.5761 | −0.566937 | ||||||||
\(349\) | −34.4252 | −1.84274 | −0.921371 | − | 0.388685i | \(-0.872929\pi\) | ||||
−0.921371 | + | 0.388685i | \(0.872929\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.1960 | 1.77187 | ||||||||
\(352\) | −0.829422 | −0.0442083 | ||||||||
\(353\) | −4.25547 | −0.226496 | −0.113248 | − | 0.993567i | \(-0.536125\pi\) | ||||
−0.113248 | + | 0.993567i | \(0.536125\pi\) | |||||||
\(354\) | 12.7389 | 0.677065 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 60.0013 | 3.18006 | ||||||||
\(357\) | −4.87826 | −0.258185 | ||||||||
\(358\) | 8.11399 | 0.428837 | ||||||||
\(359\) | −20.2944 | −1.07110 | −0.535550 | − | 0.844504i | \(-0.679896\pi\) | ||||
−0.535550 | + | 0.844504i | \(0.679896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 55.8903 | 2.93753 | ||||||||
\(363\) | 13.9172 | 0.730465 | ||||||||
\(364\) | 15.7827 | 0.827238 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.312860 | −0.0163535 | ||||||||
\(367\) | 3.85289 | 0.201119 | 0.100560 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100560 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(368\) | −7.46289 | −0.389030 | ||||||||
\(369\) | −12.9922 | −0.676350 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.13724 | −0.214795 | ||||||||
\(372\) | 14.8783 | 0.771402 | ||||||||
\(373\) | −14.6356 | −0.757802 | −0.378901 | − | 0.925437i | \(-0.623698\pi\) | ||||
−0.378901 | + | 0.925437i | \(0.623698\pi\) | |||||||
\(374\) | 3.43380 | 0.177557 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −47.7274 | −2.46135 | ||||||||
\(377\) | 13.5371 | 0.697197 | ||||||||
\(378\) | −9.62492 | −0.495052 | ||||||||
\(379\) | 22.0099 | 1.13057 | 0.565286 | − | 0.824895i | \(-0.308766\pi\) | ||||
0.565286 | + | 0.824895i | \(0.308766\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.2760 | −0.987540 | ||||||||
\(382\) | −29.6319 | −1.51610 | ||||||||
\(383\) | 3.08569 | 0.157671 | 0.0788357 | − | 0.996888i | \(-0.474880\pi\) | ||||
0.0788357 | + | 0.996888i | \(0.474880\pi\) | |||||||
\(384\) | −26.3695 | −1.34566 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 45.8783 | 2.33514 | ||||||||
\(387\) | −13.5117 | −0.686840 | ||||||||
\(388\) | 16.2272 | 0.823810 | ||||||||
\(389\) | 8.77203 | 0.444760 | 0.222380 | − | 0.974960i | \(-0.428618\pi\) | ||||
0.222380 | + | 0.974960i | \(0.428618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.4047 | −0.981338 | ||||||||
\(392\) | 25.4055 | 1.28317 | ||||||||
\(393\) | −7.11319 | −0.358813 | ||||||||
\(394\) | −15.7622 | −0.794086 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.37720 | 0.0692070 | ||||||||
\(397\) | −1.59450 | −0.0800257 | −0.0400129 | − | 0.999199i | \(-0.512740\pi\) | ||||
−0.0400129 | + | 0.999199i | \(0.512740\pi\) | |||||||
\(398\) | 54.8775 | 2.75076 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5526 | 0.876535 | 0.438268 | − | 0.898844i | \(-0.355592\pi\) | ||||
0.438268 | + | 0.898844i | \(0.355592\pi\) | |||||||
\(402\) | 35.6815 | 1.77963 | ||||||||
\(403\) | −19.0438 | −0.948639 | ||||||||
\(404\) | 16.0099 | 0.796521 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.92498 | −0.194794 | ||||||||
\(407\) | 2.22505 | 0.110292 | ||||||||
\(408\) | 26.3695 | 1.30548 | ||||||||
\(409\) | −36.6815 | −1.81378 | −0.906892 | − | 0.421363i | \(-0.861552\pi\) | ||||
−0.906892 | + | 0.421363i | \(0.861552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.3433 | −0.806155 | ||||||||
\(412\) | −12.1599 | −0.599076 | ||||||||
\(413\) | 3.05447 | 0.150301 | ||||||||
\(414\) | −12.0459 | −0.592025 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 18.0283 | 0.883910 | ||||||||
\(417\) | 19.4239 | 0.951194 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.8187 | −0.919356 | −0.459678 | − | 0.888086i | \(-0.652035\pi\) | ||||
−0.459678 | + | 0.888086i | \(0.652035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7819 | 1.64643 | 0.823215 | − | 0.567730i | \(-0.192178\pi\) | ||||
0.823215 | + | 0.567730i | \(0.192178\pi\) | |||||||
\(422\) | −17.9426 | −0.873432 | ||||||||
\(423\) | −16.7467 | −0.814250 | ||||||||
\(424\) | 22.3638 | 1.08608 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −17.4260 | −0.844295 | ||||||||
\(427\) | −0.0750160 | −0.00363028 | ||||||||
\(428\) | −60.2079 | −2.91026 | ||||||||
\(429\) | 2.07714 | 0.100285 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7651 | 0.614872 | 0.307436 | − | 0.951569i | \(-0.400529\pi\) | ||||
0.307436 | + | 0.951569i | \(0.400529\pi\) | |||||||
\(432\) | 11.3099 | 0.544150 | ||||||||
\(433\) | 16.0771 | 0.772618 | 0.386309 | − | 0.922369i | \(-0.373750\pi\) | ||||
0.386309 | + | 0.922369i | \(0.373750\pi\) | |||||||
\(434\) | 5.52161 | 0.265046 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.4437 | −1.36220 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 20.2272 | 0.966492 | ||||||||
\(439\) | −1.36945 | −0.0653604 | −0.0326802 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326802 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.91431 | 0.424491 | ||||||||
\(442\) | −74.6369 | −3.55012 | ||||||||
\(443\) | 4.62280 | 0.219636 | 0.109818 | − | 0.993952i | \(-0.464973\pi\) | ||||
0.109818 | + | 0.993952i | \(0.464973\pi\) | |||||||
\(444\) | 37.7848 | 1.79319 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.59933 | −0.123082 | ||||||||
\(447\) | −17.6199 | −0.833391 | ||||||||
\(448\) | −8.17270 | −0.386124 | ||||||||
\(449\) | −23.2555 | −1.09749 | −0.548747 | − | 0.835989i | \(-0.684895\pi\) | ||||
−0.548747 | + | 0.835989i | \(0.684895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.58383 | −0.121668 | ||||||||
\(452\) | 0.519485 | 0.0244345 | ||||||||
\(453\) | −14.9143 | −0.700735 | ||||||||
\(454\) | −47.8569 | −2.24604 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.8443 | −1.67673 | −0.838364 | − | 0.545111i | \(-0.816487\pi\) | ||||
−0.838364 | + | 0.545111i | \(0.816487\pi\) | |||||||
\(458\) | 13.1140 | 0.612776 | ||||||||
\(459\) | 29.4076 | 1.37263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.8812 | −0.693086 | −0.346543 | − | 0.938034i | \(-0.612645\pi\) | ||||
−0.346543 | + | 0.938034i | \(0.612645\pi\) | |||||||
\(462\) | −0.602251 | −0.0280193 | ||||||||
\(463\) | −29.9554 | −1.39215 | −0.696073 | − | 0.717971i | \(-0.745071\pi\) | ||||
−0.696073 | + | 0.717971i | \(0.745071\pi\) | |||||||
\(464\) | 4.61212 | 0.214112 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.2186 | 2.00206 | ||||||||
\(467\) | −6.73598 | −0.311704 | −0.155852 | − | 0.987780i | \(-0.549812\pi\) | ||||
−0.155852 | + | 0.987780i | \(0.549812\pi\) | |||||||
\(468\) | −29.9349 | −1.38374 | ||||||||
\(469\) | 8.55553 | 0.395058 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.10251 | 0.281189 | ||||||||
\(472\) | −16.5109 | −0.759977 | ||||||||
\(473\) | −2.68714 | −0.123555 | ||||||||
\(474\) | −11.7445 | −0.539444 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.9816 | 0.640845 | ||||||||
\(477\) | 7.84704 | 0.359291 | ||||||||
\(478\) | −52.0998 | −2.38299 | ||||||||
\(479\) | 16.6978 | 0.762943 | 0.381471 | − | 0.924381i | \(-0.375418\pi\) | ||||
0.381471 | + | 0.924381i | \(0.375418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.3636 | −2.20519 | ||||||||
\(482\) | −67.0091 | −3.05218 | ||||||||
\(483\) | 3.40338 | 0.154859 | ||||||||
\(484\) | −39.8881 | −1.81310 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 30.7672 | 1.39563 | ||||||||
\(487\) | −3.64042 | −0.164963 | −0.0824816 | − | 0.996593i | \(-0.526285\pi\) | ||||
−0.0824816 | + | 0.996593i | \(0.526285\pi\) | |||||||
\(488\) | 0.405499 | 0.0183561 | ||||||||
\(489\) | −16.3072 | −0.737439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.3249 | −1.50393 | −0.751965 | − | 0.659203i | \(-0.770894\pi\) | ||||
−0.751965 | + | 0.659203i | \(0.770894\pi\) | |||||||
\(492\) | −43.8775 | −1.97815 | ||||||||
\(493\) | 11.9922 | 0.540104 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.48827 | −0.291332 | ||||||||
\(497\) | −4.17833 | −0.187424 | ||||||||
\(498\) | −1.47861 | −0.0662582 | ||||||||
\(499\) | −37.9914 | −1.70073 | −0.850365 | − | 0.526193i | \(-0.823619\pi\) | ||||
−0.850365 | + | 0.526193i | \(0.823619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.6786 | −1.19191 | ||||||||
\(502\) | −21.4183 | −0.955945 | ||||||||
\(503\) | −42.1826 | −1.88083 | −0.940414 | − | 0.340032i | \(-0.889562\pi\) | ||||
−0.940414 | + | 0.340032i | \(0.889562\pi\) | |||||||
\(504\) | 3.92498 | 0.174833 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.39563 | −0.106499 | ||||||||
\(507\) | −28.5881 | −1.26964 | ||||||||
\(508\) | 55.2469 | 2.45119 | ||||||||
\(509\) | 21.9971 | 0.975003 | 0.487502 | − | 0.873122i | \(-0.337908\pi\) | ||||
0.487502 | + | 0.873122i | \(0.337908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.84997 | 0.214550 | ||||||||
\(512\) | 22.0643 | 0.975115 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.3091 | 0.719365 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −45.6319 | −2.00883 | ||||||||
\(517\) | −3.33048 | −0.146474 | ||||||||
\(518\) | 14.0227 | 0.616121 | ||||||||
\(519\) | 20.0360 | 0.879485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0977 | −0.880496 | −0.440248 | − | 0.897876i | \(-0.645109\pi\) | ||||
−0.440248 | + | 0.897876i | \(0.645109\pi\) | |||||||
\(522\) | 7.44447 | 0.325836 | ||||||||
\(523\) | 4.64817 | 0.203250 | 0.101625 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101625 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(524\) | 20.3871 | 0.890614 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.0021 | 0.959338 | ||||||||
\(527\) | −16.8705 | −0.734891 | ||||||||
\(528\) | 0.707686 | 0.0307981 | ||||||||
\(529\) | −9.46209 | −0.411395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.79338 | −0.251411 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 56.1620 | 2.43265 | ||||||||
\(534\) | 49.7664 | 2.15360 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −46.2469 | −1.99756 | ||||||||
\(537\) | 4.34811 | 0.187635 | ||||||||
\(538\) | 1.18608 | 0.0511355 | ||||||||
\(539\) | 1.77283 | 0.0763612 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0673 | 0.862759 | 0.431380 | − | 0.902171i | \(-0.358027\pi\) | ||||
0.431380 | + | 0.902171i | \(0.358027\pi\) | |||||||
\(542\) | −8.82087 | −0.378889 | ||||||||
\(543\) | 29.9504 | 1.28529 | ||||||||
\(544\) | 15.9709 | 0.684747 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.0905 | 0.560222 | ||||||||
\(547\) | 37.2010 | 1.59060 | 0.795300 | − | 0.606216i | \(-0.207313\pi\) | ||||
0.795300 | + | 0.606216i | \(0.207313\pi\) | |||||||
\(548\) | 46.8414 | 2.00097 | ||||||||
\(549\) | 0.142282 | 0.00607245 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −18.3969 | −0.783026 | ||||||||
\(553\) | −2.81604 | −0.119750 | ||||||||
\(554\) | −10.9036 | −0.463251 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −55.6708 | −2.36097 | ||||||||
\(557\) | 44.8393 | 1.89990 | 0.949951 | − | 0.312399i | \(-0.101133\pi\) | ||||
0.949951 | + | 0.312399i | \(0.101133\pi\) | |||||||
\(558\) | −10.4728 | −0.443347 | ||||||||
\(559\) | 58.4076 | 2.47038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.84010 | 0.0776889 | ||||||||
\(562\) | 64.8152 | 2.73407 | ||||||||
\(563\) | 21.9172 | 0.923701 | 0.461851 | − | 0.886958i | \(-0.347186\pi\) | ||||
0.461851 | + | 0.886958i | \(0.347186\pi\) | |||||||
\(564\) | −56.5569 | −2.38147 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.4047 | 1.02581 | ||||||||
\(567\) | −2.15778 | −0.0906183 | ||||||||
\(568\) | 22.5860 | 0.947685 | ||||||||
\(569\) | −9.90656 | −0.415305 | −0.207652 | − | 0.978203i | \(-0.566582\pi\) | ||||
−0.207652 | + | 0.978203i | \(0.566582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6404 | 0.738229 | 0.369114 | − | 0.929384i | \(-0.379661\pi\) | ||||
0.369114 | + | 0.929384i | \(0.379661\pi\) | |||||||
\(572\) | −5.95328 | −0.248919 | ||||||||
\(573\) | −15.8791 | −0.663357 | ||||||||
\(574\) | −16.2838 | −0.679671 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.5011 | 0.645878 | ||||||||
\(577\) | −12.7048 | −0.528906 | −0.264453 | − | 0.964399i | \(-0.585191\pi\) | ||||
−0.264453 | + | 0.964399i | \(0.585191\pi\) | |||||||
\(578\) | −25.7069 | −1.06927 | ||||||||
\(579\) | 24.5851 | 1.02172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.354534 | −0.0147085 | ||||||||
\(582\) | 13.4592 | 0.557900 | ||||||||
\(583\) | 1.56058 | 0.0646325 | ||||||||
\(584\) | −26.2165 | −1.08485 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.44659 | −0.183687 | ||||||||
\(587\) | 15.0438 | 0.620924 | 0.310462 | − | 0.950586i | \(-0.399516\pi\) | ||||
0.310462 | + | 0.950586i | \(0.399516\pi\) | |||||||
\(588\) | 30.1054 | 1.24153 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.44659 | −0.347446 | ||||||||
\(592\) | −16.4776 | −0.677225 | ||||||||
\(593\) | −16.4231 | −0.674417 | −0.337208 | − | 0.941430i | \(-0.609483\pi\) | ||||
−0.337208 | + | 0.941430i | \(0.609483\pi\) | |||||||
\(594\) | 3.63055 | 0.148963 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 50.5003 | 2.06857 | ||||||||
\(597\) | 29.4076 | 1.20357 | ||||||||
\(598\) | 52.0713 | 2.12935 | ||||||||
\(599\) | 19.1260 | 0.781466 | 0.390733 | − | 0.920504i | \(-0.372222\pi\) | ||||
0.390733 | + | 0.920504i | \(0.372222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.4124 | −1.28134 | −0.640670 | − | 0.767816i | \(-0.721343\pi\) | ||||
−0.640670 | + | 0.767816i | \(0.721343\pi\) | |||||||
\(602\) | −16.9349 | −0.690213 | ||||||||
\(603\) | −16.2272 | −0.660821 | ||||||||
\(604\) | 42.7459 | 1.73930 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.2789 | 0.539420 | ||||||||
\(607\) | 41.5315 | 1.68571 | 0.842855 | − | 0.538140i | \(-0.180873\pi\) | ||||
0.842855 | + | 0.538140i | \(0.180873\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.10331 | −0.0852305 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 72.3913 | 2.92864 | ||||||||
\(612\) | −26.5187 | −1.07195 | ||||||||
\(613\) | 21.7274 | 0.877563 | 0.438781 | − | 0.898594i | \(-0.355410\pi\) | ||||
0.438781 | + | 0.898594i | \(0.355410\pi\) | |||||||
\(614\) | 0.540031 | 0.0217939 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.780579 | 0.0314504 | ||||||||
\(617\) | 33.6065 | 1.35295 | 0.676473 | − | 0.736467i | \(-0.263507\pi\) | ||||
0.676473 | + | 0.736467i | \(0.263507\pi\) | |||||||
\(618\) | −10.0857 | −0.405706 | ||||||||
\(619\) | −27.6036 | −1.10948 | −0.554741 | − | 0.832023i | \(-0.687183\pi\) | ||||
−0.554741 | + | 0.832023i | \(0.687183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.5166 | −0.823301 | ||||||||
\(622\) | −49.8152 | −1.99741 | ||||||||
\(623\) | 11.9327 | 0.478075 | ||||||||
\(624\) | −15.3822 | −0.615783 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.7077 | 1.06745 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.4904 | −0.697942 | ||||||||
\(629\) | −42.8443 | −1.70832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.94048 | 0.0772495 | 0.0386247 | − | 0.999254i | \(-0.487702\pi\) | ||||
0.0386247 | + | 0.999254i | \(0.487702\pi\) | |||||||
\(632\) | 15.2221 | 0.605504 | ||||||||
\(633\) | −9.61505 | −0.382164 | ||||||||
\(634\) | 44.2702 | 1.75819 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 26.5011 | 1.05084 | ||||||||
\(637\) | −38.5342 | −1.52678 | ||||||||
\(638\) | 1.48052 | 0.0586142 | ||||||||
\(639\) | 7.92498 | 0.313508 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.01975 | −0.0402775 | −0.0201388 | − | 0.999797i | \(-0.506411\pi\) | ||||
−0.0201388 | + | 0.999797i | \(0.506411\pi\) | |||||||
\(642\) | −49.9378 | −1.97089 | ||||||||
\(643\) | 36.9866 | 1.45861 | 0.729305 | − | 0.684189i | \(-0.239844\pi\) | ||||
0.729305 | + | 0.684189i | \(0.239844\pi\) | |||||||
\(644\) | −9.75441 | −0.384377 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.1182 | 0.948186 | 0.474093 | − | 0.880475i | \(-0.342776\pi\) | ||||
0.474093 | + | 0.880475i | \(0.342776\pi\) | |||||||
\(648\) | 11.6639 | 0.458201 | ||||||||
\(649\) | −1.15215 | −0.0452260 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.95891 | 0.115969 | ||||||||
\(652\) | 46.7381 | 1.83041 | ||||||||
\(653\) | 37.2603 | 1.45811 | 0.729054 | − | 0.684456i | \(-0.239960\pi\) | ||||
0.729054 | + | 0.684456i | \(0.239960\pi\) | |||||||
\(654\) | −23.5918 | −0.922512 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.1345 | 0.747078 | ||||||||
\(657\) | −9.19887 | −0.358882 | ||||||||
\(658\) | −20.9893 | −0.818249 | ||||||||
\(659\) | −21.4386 | −0.835130 | −0.417565 | − | 0.908647i | \(-0.637116\pi\) | ||||
−0.417565 | + | 0.908647i | \(0.637116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.783503 | −0.0304747 | −0.0152374 | − | 0.999884i | \(-0.504850\pi\) | ||||
−0.0152374 | + | 0.999884i | \(0.504850\pi\) | |||||||
\(662\) | −33.5315 | −1.30324 | ||||||||
\(663\) | −39.9963 | −1.55333 | ||||||||
\(664\) | 1.91643 | 0.0743720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.5966 | −1.03060 | ||||||||
\(667\) | −8.36653 | −0.323953 | ||||||||
\(668\) | 76.4634 | 2.95846 | ||||||||
\(669\) | −1.39292 | −0.0538535 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0282963 | 0.00109237 | ||||||||
\(672\) | −2.80113 | −0.108056 | ||||||||
\(673\) | 50.1903 | 1.93469 | 0.967347 | − | 0.253454i | \(-0.0815667\pi\) | ||||
0.967347 | + | 0.253454i | \(0.0815667\pi\) | |||||||
\(674\) | 54.6065 | 2.10336 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 81.9362 | 3.15139 | ||||||||
\(677\) | 29.8804 | 1.14840 | 0.574198 | − | 0.818716i | \(-0.305314\pi\) | ||||
0.574198 | + | 0.818716i | \(0.305314\pi\) | |||||||
\(678\) | 0.430872 | 0.0165475 | ||||||||
\(679\) | 3.22717 | 0.123847 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.6455 | −0.982736 | ||||||||
\(682\) | −2.08277 | −0.0797532 | ||||||||
\(683\) | −12.3326 | −0.471894 | −0.235947 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235947 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.2555 | 0.887898 | ||||||||
\(687\) | 7.02750 | 0.268116 | ||||||||
\(688\) | 19.8996 | 0.758666 | ||||||||
\(689\) | −33.9207 | −1.29227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.62200 | 0.137787 | 0.0688936 | − | 0.997624i | \(-0.478053\pi\) | ||||
0.0688936 | + | 0.997624i | \(0.478053\pi\) | |||||||
\(692\) | −57.4252 | −2.18298 | ||||||||
\(693\) | 0.273891 | 0.0104042 | ||||||||
\(694\) | 9.34891 | 0.354880 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.3695 | 0.430958 | ||||||||
\(697\) | 49.7528 | 1.88452 | ||||||||
\(698\) | 81.8358 | 3.09753 | ||||||||
\(699\) | 23.1599 | 0.875988 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.1209 | 1.28873 | 0.644365 | − | 0.764718i | \(-0.277122\pi\) | ||||
0.644365 | + | 0.764718i | \(0.277122\pi\) | |||||||
\(702\) | −78.9135 | −2.97840 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.08277 | 0.116186 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.1161 | 0.380725 | ||||||||
\(707\) | 3.18396 | 0.119745 | ||||||||
\(708\) | −19.5654 | −0.735313 | ||||||||
\(709\) | −17.1209 | −0.642990 | −0.321495 | − | 0.946911i | \(-0.604185\pi\) | ||||
−0.321495 | + | 0.946911i | \(0.604185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.34116 | 0.200309 | ||||||||
\(712\) | −64.5024 | −2.41733 | ||||||||
\(713\) | 11.7699 | 0.440786 | ||||||||
\(714\) | 11.5966 | 0.433993 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.4621 | −0.465730 | ||||||||
\(717\) | −27.9191 | −1.04266 | ||||||||
\(718\) | 48.2440 | 1.80045 | ||||||||
\(719\) | −7.02750 | −0.262081 | −0.131041 | − | 0.991377i | \(-0.541832\pi\) | ||||
−0.131041 | + | 0.991377i | \(0.541832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.41830 | −0.0900620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.9087 | −1.33546 | ||||||||
\(724\) | −85.8406 | −3.19024 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −33.0841 | −1.22787 | ||||||||
\(727\) | −11.8938 | −0.441115 | −0.220558 | − | 0.975374i | \(-0.570788\pi\) | ||||
−0.220558 | + | 0.975374i | \(0.570788\pi\) | |||||||
\(728\) | −16.9667 | −0.628826 | ||||||||
\(729\) | 25.4026 | 0.940836 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.7421 | 1.91375 | ||||||||
\(732\) | 0.480515 | 0.0177604 | ||||||||
\(733\) | 20.7154 | 0.765142 | 0.382571 | − | 0.923926i | \(-0.375039\pi\) | ||||
0.382571 | + | 0.923926i | \(0.375039\pi\) | |||||||
\(734\) | −9.15910 | −0.338069 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.1423 | −0.410710 | ||||||||
\(737\) | −3.22717 | −0.118874 | ||||||||
\(738\) | 30.8852 | 1.13690 | ||||||||
\(739\) | 33.8620 | 1.24563 | 0.622816 | − | 0.782368i | \(-0.285988\pi\) | ||||
0.622816 | + | 0.782368i | \(0.285988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.83505 | 0.361056 | ||||||||
\(743\) | −42.7381 | −1.56791 | −0.783955 | − | 0.620818i | \(-0.786800\pi\) | ||||
−0.783955 | + | 0.620818i | \(0.786800\pi\) | |||||||
\(744\) | −15.9944 | −0.586382 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34.7918 | 1.27382 | ||||||||
\(747\) | 0.672440 | 0.0246033 | ||||||||
\(748\) | −5.27389 | −0.192833 | ||||||||
\(749\) | −11.9738 | −0.437514 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.9581 | −0.436358 | −0.218179 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218179 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(752\) | 24.6639 | 0.899400 | ||||||||
\(753\) | −11.4776 | −0.418267 | ||||||||
\(754\) | −32.1805 | −1.17194 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.7827 | 0.537642 | ||||||||
\(757\) | 29.1103 | 1.05803 | 0.529015 | − | 0.848612i | \(-0.322561\pi\) | ||||
0.529015 | + | 0.848612i | \(0.322561\pi\) | |||||||
\(758\) | −52.3219 | −1.90042 | ||||||||
\(759\) | −1.28376 | −0.0465977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.3014 | −0.808425 | −0.404212 | − | 0.914665i | \(-0.632454\pi\) | ||||
−0.404212 | + | 0.914665i | \(0.632454\pi\) | |||||||
\(762\) | 45.8230 | 1.65999 | ||||||||
\(763\) | −5.65672 | −0.204787 | ||||||||
\(764\) | 45.5109 | 1.64653 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.33531 | −0.265036 | ||||||||
\(767\) | 25.0432 | 0.904258 | ||||||||
\(768\) | 34.0091 | 1.22720 | ||||||||
\(769\) | 3.95891 | 0.142762 | 0.0713809 | − | 0.997449i | \(-0.477259\pi\) | ||||
0.0713809 | + | 0.997449i | \(0.477259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.73971 | 0.314753 | ||||||||
\(772\) | −70.4634 | −2.53603 | ||||||||
\(773\) | −27.8139 | −1.00040 | −0.500199 | − | 0.865911i | \(-0.666740\pi\) | ||||
−0.500199 | + | 0.865911i | \(0.666740\pi\) | |||||||
\(774\) | 32.1201 | 1.15453 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.4445 | −0.626220 | ||||||||
\(777\) | 7.51444 | 0.269579 | ||||||||
\(778\) | −20.8529 | −0.747612 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.57608 | 0.0563965 | ||||||||
\(782\) | 46.1289 | 1.64957 | ||||||||
\(783\) | 12.6794 | 0.453124 | ||||||||
\(784\) | −13.1287 | −0.468882 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.9095 | 0.603141 | ||||||||
\(787\) | 1.82460 | 0.0650398 | 0.0325199 | − | 0.999471i | \(-0.489647\pi\) | ||||
0.0325199 | + | 0.999471i | \(0.489647\pi\) | |||||||
\(788\) | 24.2087 | 0.862401 | ||||||||
\(789\) | 11.7905 | 0.419751 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.103312 | 0.00367336 | ||||||||
\(792\) | −1.48052 | −0.0526078 | ||||||||
\(793\) | −0.615047 | −0.0218410 | ||||||||
\(794\) | 3.79045 | 0.134518 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −84.2851 | −2.98741 | ||||||||
\(797\) | 21.0360 | 0.745135 | 0.372567 | − | 0.928005i | \(-0.378478\pi\) | ||||
0.372567 | + | 0.928005i | \(0.378478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.1300 | 2.26876 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6327 | −0.799686 | ||||||||
\(802\) | −41.7261 | −1.47340 | ||||||||
\(803\) | −1.82942 | −0.0645589 | ||||||||
\(804\) | −54.8024 | −1.93273 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 45.2710 | 1.59460 | ||||||||
\(807\) | 0.635593 | 0.0223739 | ||||||||
\(808\) | −17.2109 | −0.605476 | ||||||||
\(809\) | −0.0819654 | −0.00288175 | −0.00144088 | − | 0.999999i | \(-0.500459\pi\) | ||||
−0.00144088 | + | 0.999999i | \(0.500459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.72531 | 0.236158 | 0.118079 | − | 0.993004i | \(-0.462326\pi\) | ||||
0.118079 | + | 0.993004i | \(0.462326\pi\) | |||||||
\(812\) | 6.02830 | 0.211552 | ||||||||
\(813\) | −4.72691 | −0.165780 | ||||||||
\(814\) | −5.28939 | −0.185393 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.6268 | −0.477034 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 87.1994 | 3.04886 | ||||||||
\(819\) | −5.95328 | −0.208024 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9426 | 1.07990 | 0.539952 | − | 0.841696i | \(-0.318442\pi\) | ||||
0.539952 | + | 0.841696i | \(0.318442\pi\) | |||||||
\(822\) | 38.8513 | 1.35509 | ||||||||
\(823\) | 26.5908 | 0.926896 | 0.463448 | − | 0.886124i | \(-0.346612\pi\) | ||||
0.463448 | + | 0.886124i | \(0.346612\pi\) | |||||||
\(824\) | 13.0721 | 0.455388 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.26109 | −0.252646 | ||||||||
\(827\) | 5.57900 | 0.194001 | 0.0970004 | − | 0.995284i | \(-0.469075\pi\) | ||||
0.0970004 | + | 0.995284i | \(0.469075\pi\) | |||||||
\(828\) | 18.5011 | 0.642956 | ||||||||
\(829\) | −18.9765 | −0.659082 | −0.329541 | − | 0.944141i | \(-0.606894\pi\) | ||||
−0.329541 | + | 0.944141i | \(0.606894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.84302 | −0.202692 | ||||||||
\(832\) | −67.0069 | −2.32305 | ||||||||
\(833\) | −34.1367 | −1.18276 | ||||||||
\(834\) | −46.1746 | −1.59890 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.8372 | −0.616543 | ||||||||
\(838\) | 44.7360 | 1.54538 | ||||||||
\(839\) | −12.9143 | −0.445852 | −0.222926 | − | 0.974835i | \(-0.571561\pi\) | ||||
−0.222926 | + | 0.974835i | \(0.571561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8294 | −0.821704 | ||||||||
\(842\) | −80.3064 | −2.76754 | ||||||||
\(843\) | 34.7331 | 1.19627 | ||||||||
\(844\) | 27.5577 | 0.948574 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 39.8102 | 1.36870 | ||||||||
\(847\) | −7.93273 | −0.272572 | ||||||||
\(848\) | −11.5569 | −0.396864 | ||||||||
\(849\) | 13.0779 | 0.448834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.8908 | 1.02464 | ||||||||
\(852\) | 26.7643 | 0.916929 | ||||||||
\(853\) | 6.46077 | 0.221213 | 0.110606 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110606 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(854\) | 0.178328 | 0.00610227 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 64.7245 | 2.21224 | ||||||||
\(857\) | 12.4055 | 0.423764 | 0.211882 | − | 0.977295i | \(-0.432041\pi\) | ||||
0.211882 | + | 0.977295i | \(0.432041\pi\) | |||||||
\(858\) | −4.93778 | −0.168573 | ||||||||
\(859\) | 40.3425 | 1.37647 | 0.688234 | − | 0.725489i | \(-0.258386\pi\) | ||||
0.688234 | + | 0.725489i | \(0.258386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.72611 | −0.297385 | ||||||||
\(862\) | −30.3452 | −1.03356 | ||||||||
\(863\) | −1.83235 | −0.0623738 | −0.0311869 | − | 0.999514i | \(-0.509929\pi\) | ||||
−0.0311869 | + | 0.999514i | \(0.509929\pi\) | |||||||
\(864\) | 16.8860 | 0.574474 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −38.2186 | −1.29872 | ||||||||
\(867\) | −13.7758 | −0.467849 | ||||||||
\(868\) | −8.48052 | −0.287847 | ||||||||
\(869\) | 1.06222 | 0.0360333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.1457 | 2.37680 | ||||||||
\(872\) | 30.5774 | 1.03548 | ||||||||
\(873\) | −6.12094 | −0.207162 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.0665 | −1.04964 | ||||||||
\(877\) | 8.14419 | 0.275010 | 0.137505 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137505 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(878\) | 3.25547 | 0.109867 | ||||||||
\(879\) | −2.38283 | −0.0803709 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1706 | 0.410037 | 0.205019 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205019 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(882\) | −21.1911 | −0.713542 | ||||||||
\(883\) | 46.7614 | 1.57364 | 0.786822 | − | 0.617179i | \(-0.211725\pi\) | ||||
0.786822 | + | 0.617179i | \(0.211725\pi\) | |||||||
\(884\) | 114.633 | 3.85553 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9893 | −0.369194 | ||||||||
\(887\) | 34.8804 | 1.17117 | 0.585584 | − | 0.810611i | \(-0.300865\pi\) | ||||
0.585584 | + | 0.810611i | \(0.300865\pi\) | |||||||
\(888\) | −40.6193 | −1.36309 | ||||||||
\(889\) | 10.9872 | 0.368499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.813922 | 0.0272674 | ||||||||
\(892\) | 3.99225 | 0.133670 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 41.8860 | 1.40088 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.0304 | 0.502131 | ||||||||
\(897\) | 27.9039 | 0.931683 | ||||||||
\(898\) | 55.2830 | 1.84482 | ||||||||
\(899\) | −7.27389 | −0.242598 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.0496 | −1.00110 | ||||||||
\(902\) | 6.14228 | 0.204516 | ||||||||
\(903\) | −9.07502 | −0.301998 | ||||||||
\(904\) | −0.558455 | −0.0185739 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35.4543 | 1.17789 | ||||||||
\(907\) | 25.5080 | 0.846980 | 0.423490 | − | 0.905901i | \(-0.360805\pi\) | ||||
0.423490 | + | 0.905901i | \(0.360805\pi\) | |||||||
\(908\) | 73.5024 | 2.43926 | ||||||||
\(909\) | −6.03897 | −0.200300 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5032 | 0.712432 | 0.356216 | − | 0.934404i | \(-0.384067\pi\) | ||||
0.356216 | + | 0.934404i | \(0.384067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.133731 | 0.00442586 | ||||||||
\(914\) | 85.2093 | 2.81847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.1415 | −0.665493 | ||||||||
\(917\) | 4.05447 | 0.133890 | ||||||||
\(918\) | −69.9079 | −2.30730 | ||||||||
\(919\) | 37.1386 | 1.22509 | 0.612544 | − | 0.790436i | \(-0.290146\pi\) | ||||
0.612544 | + | 0.790436i | \(0.290146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.289391 | 0.00953575 | ||||||||
\(922\) | 35.3756 | 1.16503 | ||||||||
\(923\) | −34.2576 | −1.12760 | ||||||||
\(924\) | 0.924984 | 0.0304297 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 71.2101 | 2.34011 | ||||||||
\(927\) | 4.58675 | 0.150649 | ||||||||
\(928\) | 6.88601 | 0.226044 | ||||||||
\(929\) | −3.36170 | −0.110294 | −0.0551469 | − | 0.998478i | \(-0.517563\pi\) | ||||
−0.0551469 | + | 0.998478i | \(0.517563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −66.3785 | −2.17430 | ||||||||
\(933\) | −26.6949 | −0.873951 | ||||||||
\(934\) | 16.0128 | 0.523955 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 32.1805 | 1.05185 | ||||||||
\(937\) | 10.0694 | 0.328953 | 0.164476 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164476 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(938\) | −20.3382 | −0.664067 | ||||||||
\(939\) | 14.3121 | 0.467056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8139 | −0.678514 | −0.339257 | − | 0.940694i | \(-0.610176\pi\) | ||||
−0.339257 | + | 0.940694i | \(0.610176\pi\) | |||||||
\(942\) | −14.5069 | −0.472661 | ||||||||
\(943\) | −34.7106 | −1.13033 | ||||||||
\(944\) | 8.53228 | 0.277702 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.38788 | 0.207688 | ||||||||
\(947\) | −30.4904 | −0.990804 | −0.495402 | − | 0.868664i | \(-0.664979\pi\) | ||||
−0.495402 | + | 0.868664i | \(0.664979\pi\) | |||||||
\(948\) | 18.0382 | 0.585852 | ||||||||
\(949\) | 39.7643 | 1.29080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.7234 | 0.769284 | ||||||||
\(952\) | −15.0304 | −0.487139 | ||||||||
\(953\) | −7.58383 | −0.245664 | −0.122832 | − | 0.992427i | \(-0.539198\pi\) | ||||
−0.122832 | + | 0.992427i | \(0.539198\pi\) | |||||||
\(954\) | −18.6540 | −0.603946 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 80.0189 | 2.58800 | ||||||||
\(957\) | 0.793375 | 0.0256462 | ||||||||
\(958\) | −39.6941 | −1.28246 | ||||||||
\(959\) | 9.31556 | 0.300815 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7672 | −0.669910 | ||||||||
\(962\) | 114.970 | 3.70678 | ||||||||
\(963\) | 22.7106 | 0.731839 | ||||||||
\(964\) | 102.918 | 3.31476 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.09052 | −0.260308 | ||||||||
\(967\) | 54.6687 | 1.75803 | 0.879014 | − | 0.476797i | \(-0.158202\pi\) | ||||
0.879014 | + | 0.476797i | \(0.158202\pi\) | |||||||
\(968\) | 42.8804 | 1.37823 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9632 | 1.28248 | 0.641239 | − | 0.767341i | \(-0.278421\pi\) | ||||
0.641239 | + | 0.767341i | \(0.278421\pi\) | |||||||
\(972\) | −47.2547 | −1.51569 | ||||||||
\(973\) | −11.0715 | −0.354936 | ||||||||
\(974\) | 8.65402 | 0.277293 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.209548 | −0.00670747 | ||||||||
\(977\) | −15.2400 | −0.487570 | −0.243785 | − | 0.969829i | \(-0.578389\pi\) | ||||
−0.243785 | + | 0.969829i | \(0.578389\pi\) | |||||||
\(978\) | 38.7656 | 1.23959 | ||||||||
\(979\) | −4.50106 | −0.143855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7290 | 0.342552 | ||||||||
\(982\) | 79.2199 | 2.52801 | ||||||||
\(983\) | 45.3609 | 1.44679 | 0.723394 | − | 0.690435i | \(-0.242581\pi\) | ||||
0.723394 | + | 0.690435i | \(0.242581\pi\) | |||||||
\(984\) | 47.1690 | 1.50369 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −28.5080 | −0.907880 | ||||||||
\(987\) | −11.2477 | −0.358019 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0985 | −1.14787 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.3537 | 0.519493 | 0.259747 | − | 0.965677i | \(-0.416361\pi\) | ||||
0.259747 | + | 0.965677i | \(0.416361\pi\) | |||||||
\(992\) | −9.68714 | −0.307567 | ||||||||
\(993\) | −17.9688 | −0.570222 | ||||||||
\(994\) | 9.93273 | 0.315047 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.27097 | 0.0719583 | ||||||||
\(997\) | −33.2037 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(998\) | 90.3134 | 2.85882 | ||||||||
\(999\) | −45.2993 | −1.43321 |
(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 | 9025.2.a.y.1.1 | 3 | ||
5.4 | even | 2 | 9025.2.a.bc.1.3 | 3 | |||
19.18 | odd | 2 | 475.2.a.g.1.3 | yes | 3 | ||
57.56 | even | 2 | 4275.2.a.ba.1.1 | 3 | |||
76.75 | even | 2 | 7600.2.a.bh.1.2 | 3 | |||
95.18 | even | 4 | 475.2.b.b.324.1 | 6 | |||
95.37 | even | 4 | 475.2.b.b.324.6 | 6 | |||
95.94 | odd | 2 | 475.2.a.e.1.1 | ✓ | 3 | ||
285.284 | even | 2 | 4275.2.a.bm.1.3 | 3 | |||
380.379 | even | 2 | 7600.2.a.cc.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.e.1.1 | ✓ | 3 | 95.94 | odd | 2 | ||
475.2.a.g.1.3 | yes | 3 | 19.18 | odd | 2 | ||
475.2.b.b.324.1 | 6 | 95.18 | even | 4 | |||
475.2.b.b.324.6 | 6 | 95.37 | even | 4 | |||
4275.2.a.ba.1.1 | 3 | 57.56 | even | 2 | |||
4275.2.a.bm.1.3 | 3 | 285.284 | even | 2 | |||
7600.2.a.bh.1.2 | 3 | 76.75 | even | 2 | |||
7600.2.a.cc.1.2 | 3 | 380.379 | even | 2 | |||
9025.2.a.y.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9025.2.a.bc.1.3 | 3 | 5.4 | even | 2 |