Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8085,2,Mod(1,8085)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8085, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8085.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8085.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: | \(64.5590500342\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.127775712.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 20x^{2} - 2x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1155) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.33025\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8085.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33025 | 1.64773 | 0.823867 | − | 0.566783i | \(-0.191812\pi\) | ||||
0.823867 | + | 0.566783i | \(0.191812\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.43006 | 1.71503 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.33025 | 0.951320 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.33238 | 1.17818 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.33025 | −0.736889 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.43006 | 0.990172 | ||||||||
\(13\) | −6.56567 | −1.82099 | −0.910494 | − | 0.413522i | \(-0.864299\pi\) | ||||
−0.910494 | + | 0.413522i | \(0.864299\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0.905171 | 0.226293 | ||||||||
\(17\) | −2.55550 | −0.619799 | −0.309899 | − | 0.950769i | \(-0.600295\pi\) | ||||
−0.309899 | + | 0.950769i | \(0.600295\pi\) | |||||||
\(18\) | 2.33025 | 0.549245 | ||||||||
\(19\) | −2.38844 | −0.547947 | −0.273973 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273973 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(20\) | −3.43006 | −0.766984 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.33025 | 0.496811 | ||||||||
\(23\) | −3.71869 | −0.775401 | −0.387700 | − | 0.921785i | \(-0.626730\pi\) | ||||
−0.387700 | + | 0.921785i | \(0.626730\pi\) | |||||||
\(24\) | 3.33238 | 0.680220 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −15.2996 | −3.00050 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.34552 | −0.806943 | −0.403472 | − | 0.914992i | \(-0.632197\pi\) | ||||
−0.403472 | + | 0.914992i | \(0.632197\pi\) | |||||||
\(30\) | −2.33025 | −0.425443 | ||||||||
\(31\) | −9.27917 | −1.66659 | −0.833294 | − | 0.552830i | \(-0.813548\pi\) | ||||
−0.833294 | + | 0.552830i | \(0.813548\pi\) | |||||||
\(32\) | −4.55550 | −0.805306 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −5.95494 | −1.02126 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.43006 | 0.571676 | ||||||||
\(37\) | 6.98686 | 1.14863 | 0.574316 | − | 0.818634i | \(-0.305268\pi\) | ||||
0.574316 | + | 0.818634i | \(0.305268\pi\) | |||||||
\(38\) | −5.56567 | −0.902870 | ||||||||
\(39\) | −6.56567 | −1.05135 | ||||||||
\(40\) | −3.33238 | −0.526896 | ||||||||
\(41\) | 5.85125 | 0.913811 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.577059 | −0.0880007 | −0.0440004 | − | 0.999032i | \(-0.514010\pi\) | ||||
−0.0440004 | + | 0.999032i | \(0.514010\pi\) | |||||||
\(44\) | 3.43006 | 0.517100 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −8.66547 | −1.27765 | ||||||||
\(47\) | 1.22008 | 0.177967 | 0.0889835 | − | 0.996033i | \(-0.471638\pi\) | ||||
0.0889835 | + | 0.996033i | \(0.471638\pi\) | |||||||
\(48\) | 0.905171 | 0.130650 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.33025 | 0.329547 | ||||||||
\(51\) | −2.55550 | −0.357841 | ||||||||
\(52\) | −22.5206 | −3.12305 | ||||||||
\(53\) | 1.71564 | 0.235661 | 0.117830 | − | 0.993034i | \(-0.462406\pi\) | ||||
0.117830 | + | 0.993034i | \(0.462406\pi\) | |||||||
\(54\) | 2.33025 | 0.317107 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.38844 | −0.316357 | ||||||||
\(58\) | −10.1261 | −1.32963 | ||||||||
\(59\) | −11.7696 | −1.53227 | −0.766133 | − | 0.642682i | \(-0.777822\pi\) | ||||
−0.766133 | + | 0.642682i | \(0.777822\pi\) | |||||||
\(60\) | −3.43006 | −0.442818 | ||||||||
\(61\) | 10.1078 | 1.29418 | 0.647088 | − | 0.762415i | \(-0.275987\pi\) | ||||
0.647088 | + | 0.762415i | \(0.275987\pi\) | |||||||
\(62\) | −21.6228 | −2.74609 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4258 | −1.55322 | ||||||||
\(65\) | 6.56567 | 0.814371 | ||||||||
\(66\) | 2.33025 | 0.286834 | ||||||||
\(67\) | −12.1037 | −1.47870 | −0.739350 | − | 0.673321i | \(-0.764867\pi\) | ||||
−0.739350 | + | 0.673321i | \(0.764867\pi\) | |||||||
\(68\) | −8.76550 | −1.06297 | ||||||||
\(69\) | −3.71869 | −0.447678 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.12615 | 0.133649 | 0.0668245 | − | 0.997765i | \(-0.478713\pi\) | ||||
0.0668245 | + | 0.997765i | \(0.478713\pi\) | |||||||
\(72\) | 3.33238 | 0.392725 | ||||||||
\(73\) | 7.66678 | 0.897329 | 0.448664 | − | 0.893700i | \(-0.351900\pi\) | ||||
0.448664 | + | 0.893700i | \(0.351900\pi\) | |||||||
\(74\) | 16.2811 | 1.89264 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −8.19250 | −0.939744 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −15.2996 | −1.73234 | ||||||||
\(79\) | 0.744325 | 0.0837431 | 0.0418716 | − | 0.999123i | \(-0.486668\pi\) | ||||
0.0418716 | + | 0.999123i | \(0.486668\pi\) | |||||||
\(80\) | −0.905171 | −0.101201 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.6349 | 1.50572 | ||||||||
\(83\) | −12.9061 | −1.41663 | −0.708313 | − | 0.705898i | \(-0.750544\pi\) | ||||
−0.708313 | + | 0.705898i | \(0.750544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.55550 | 0.277183 | ||||||||
\(86\) | −1.34469 | −0.145002 | ||||||||
\(87\) | −4.34552 | −0.465889 | ||||||||
\(88\) | 3.33238 | 0.355233 | ||||||||
\(89\) | −16.0765 | −1.70411 | −0.852054 | − | 0.523454i | \(-0.824643\pi\) | ||||
−0.852054 | + | 0.523454i | \(0.824643\pi\) | |||||||
\(90\) | −2.33025 | −0.245630 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.7553 | −1.32983 | ||||||||
\(93\) | −9.27917 | −0.962205 | ||||||||
\(94\) | 2.84309 | 0.293242 | ||||||||
\(95\) | 2.38844 | 0.245049 | ||||||||
\(96\) | −4.55550 | −0.464943 | ||||||||
\(97\) | −4.43219 | −0.450021 | −0.225010 | − | 0.974356i | \(-0.572242\pi\) | ||||
−0.225010 | + | 0.974356i | \(0.572242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 3.43006 | 0.343006 | ||||||||
\(101\) | 10.5424 | 1.04900 | 0.524502 | − | 0.851409i | \(-0.324252\pi\) | ||||
0.524502 | + | 0.851409i | \(0.324252\pi\) | |||||||
\(102\) | −5.95494 | −0.589627 | ||||||||
\(103\) | 5.93083 | 0.584382 | 0.292191 | − | 0.956360i | \(-0.405616\pi\) | ||||
0.292191 | + | 0.956360i | \(0.405616\pi\) | |||||||
\(104\) | −21.8793 | −2.14544 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.99786 | 0.388306 | ||||||||
\(107\) | 16.7846 | 1.62263 | 0.811317 | − | 0.584607i | \(-0.198751\pi\) | ||||
0.811317 | + | 0.584607i | \(0.198751\pi\) | |||||||
\(108\) | 3.43006 | 0.330057 | ||||||||
\(109\) | −16.5688 | −1.58701 | −0.793504 | − | 0.608566i | \(-0.791745\pi\) | ||||
−0.793504 | + | 0.608566i | \(0.791745\pi\) | |||||||
\(110\) | −2.33025 | −0.222180 | ||||||||
\(111\) | 6.98686 | 0.663163 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2975 | 1.62721 | 0.813606 | − | 0.581417i | \(-0.197502\pi\) | ||||
0.813606 | + | 0.581417i | \(0.197502\pi\) | |||||||
\(114\) | −5.56567 | −0.521272 | ||||||||
\(115\) | 3.71869 | 0.346770 | ||||||||
\(116\) | −14.9054 | −1.38393 | ||||||||
\(117\) | −6.56567 | −0.606996 | ||||||||
\(118\) | −27.4260 | −2.52477 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.33238 | −0.304204 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 23.5538 | 2.13246 | ||||||||
\(123\) | 5.85125 | 0.527589 | ||||||||
\(124\) | −31.8281 | −2.85824 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.96467 | −0.618015 | −0.309007 | − | 0.951060i | \(-0.599997\pi\) | ||||
−0.309007 | + | 0.951060i | \(0.599997\pi\) | |||||||
\(128\) | −19.8442 | −1.75399 | ||||||||
\(129\) | −0.577059 | −0.0508072 | ||||||||
\(130\) | 15.2996 | 1.34187 | ||||||||
\(131\) | −15.6096 | −1.36382 | −0.681910 | − | 0.731436i | \(-0.738850\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738850\pi\) | |||||||
\(132\) | 3.43006 | 0.298548 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −28.2046 | −2.43651 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −8.51590 | −0.730232 | ||||||||
\(137\) | 2.23737 | 0.191151 | 0.0955757 | − | 0.995422i | \(-0.469531\pi\) | ||||
0.0955757 | + | 0.995422i | \(0.469531\pi\) | |||||||
\(138\) | −8.66547 | −0.737654 | ||||||||
\(139\) | −12.3721 | −1.04939 | −0.524693 | − | 0.851292i | \(-0.675820\pi\) | ||||
−0.524693 | + | 0.851292i | \(0.675820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22008 | 0.102749 | ||||||||
\(142\) | 2.62420 | 0.220218 | ||||||||
\(143\) | −6.56567 | −0.549049 | ||||||||
\(144\) | 0.905171 | 0.0754309 | ||||||||
\(145\) | 4.34552 | 0.360876 | ||||||||
\(146\) | 17.8655 | 1.47856 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.9653 | 1.96994 | ||||||||
\(149\) | 3.39043 | 0.277755 | 0.138878 | − | 0.990310i | \(-0.455651\pi\) | ||||
0.138878 | + | 0.990310i | \(0.455651\pi\) | |||||||
\(150\) | 2.33025 | 0.190264 | ||||||||
\(151\) | −0.920629 | −0.0749197 | −0.0374599 | − | 0.999298i | \(-0.511927\pi\) | ||||
−0.0374599 | + | 0.999298i | \(0.511927\pi\) | |||||||
\(152\) | −7.95921 | −0.645577 | ||||||||
\(153\) | −2.55550 | −0.206600 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.27917 | 0.745321 | ||||||||
\(156\) | −22.5206 | −1.80309 | ||||||||
\(157\) | 19.6247 | 1.56623 | 0.783113 | − | 0.621880i | \(-0.213631\pi\) | ||||
0.783113 | + | 0.621880i | \(0.213631\pi\) | |||||||
\(158\) | 1.73446 | 0.137986 | ||||||||
\(159\) | 1.71564 | 0.136059 | ||||||||
\(160\) | 4.55550 | 0.360144 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.33025 | 0.183082 | ||||||||
\(163\) | 10.1961 | 0.798617 | 0.399309 | − | 0.916817i | \(-0.369250\pi\) | ||||
0.399309 | + | 0.916817i | \(0.369250\pi\) | |||||||
\(164\) | 20.0701 | 1.56721 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −30.0744 | −2.33422 | ||||||||
\(167\) | 0.708129 | 0.0547967 | 0.0273983 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273983 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.1080 | 2.31600 | ||||||||
\(170\) | 5.95494 | 0.456723 | ||||||||
\(171\) | −2.38844 | −0.182649 | ||||||||
\(172\) | −1.97935 | −0.150924 | ||||||||
\(173\) | 13.5334 | 1.02893 | 0.514464 | − | 0.857512i | \(-0.327991\pi\) | ||||
0.514464 | + | 0.857512i | \(0.327991\pi\) | |||||||
\(174\) | −10.1261 | −0.767661 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.905171 | 0.0682298 | ||||||||
\(177\) | −11.7696 | −0.884654 | ||||||||
\(178\) | −37.4623 | −2.80792 | ||||||||
\(179\) | −13.9753 | −1.04456 | −0.522281 | − | 0.852774i | \(-0.674919\pi\) | ||||
−0.522281 | + | 0.852774i | \(0.674919\pi\) | |||||||
\(180\) | −3.43006 | −0.255661 | ||||||||
\(181\) | −9.94639 | −0.739309 | −0.369655 | − | 0.929169i | \(-0.620524\pi\) | ||||
−0.369655 | + | 0.929169i | \(0.620524\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.1078 | 0.747193 | ||||||||
\(184\) | −12.3921 | −0.913559 | ||||||||
\(185\) | −6.98686 | −0.513684 | ||||||||
\(186\) | −21.6228 | −1.58546 | ||||||||
\(187\) | −2.55550 | −0.186876 | ||||||||
\(188\) | 4.18494 | 0.305218 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.56567 | 0.403776 | ||||||||
\(191\) | 12.4829 | 0.903230 | 0.451615 | − | 0.892213i | \(-0.350848\pi\) | ||||
0.451615 | + | 0.892213i | \(0.350848\pi\) | |||||||
\(192\) | −12.4258 | −0.896753 | ||||||||
\(193\) | 1.71866 | 0.123712 | 0.0618561 | − | 0.998085i | \(-0.480298\pi\) | ||||
0.0618561 | + | 0.998085i | \(0.480298\pi\) | |||||||
\(194\) | −10.3281 | −0.741515 | ||||||||
\(195\) | 6.56567 | 0.470177 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0590259 | 0.00420542 | 0.00210271 | − | 0.999998i | \(-0.499331\pi\) | ||||
0.00210271 | + | 0.999998i | \(0.499331\pi\) | |||||||
\(198\) | 2.33025 | 0.165604 | ||||||||
\(199\) | 21.3818 | 1.51571 | 0.757856 | − | 0.652422i | \(-0.226247\pi\) | ||||
0.757856 | + | 0.652422i | \(0.226247\pi\) | |||||||
\(200\) | 3.33238 | 0.235635 | ||||||||
\(201\) | −12.1037 | −0.853728 | ||||||||
\(202\) | 24.5663 | 1.72848 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.76550 | −0.613707 | ||||||||
\(205\) | −5.85125 | −0.408669 | ||||||||
\(206\) | 13.8203 | 0.962906 | ||||||||
\(207\) | −3.71869 | −0.258467 | ||||||||
\(208\) | −5.94305 | −0.412076 | ||||||||
\(209\) | −2.38844 | −0.165212 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1643 | 1.11280 | 0.556398 | − | 0.830916i | \(-0.312183\pi\) | ||||
0.556398 | + | 0.830916i | \(0.312183\pi\) | |||||||
\(212\) | 5.88473 | 0.404165 | ||||||||
\(213\) | 1.12615 | 0.0771623 | ||||||||
\(214\) | 39.1124 | 2.67367 | ||||||||
\(215\) | 0.577059 | 0.0393551 | ||||||||
\(216\) | 3.33238 | 0.226740 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −38.6095 | −2.61497 | ||||||||
\(219\) | 7.66678 | 0.518073 | ||||||||
\(220\) | −3.43006 | −0.231254 | ||||||||
\(221\) | 16.7785 | 1.12865 | ||||||||
\(222\) | 16.2811 | 1.09272 | ||||||||
\(223\) | −9.06835 | −0.607262 | −0.303631 | − | 0.952790i | \(-0.598199\pi\) | ||||
−0.303631 | + | 0.952790i | \(0.598199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 40.3074 | 2.68121 | ||||||||
\(227\) | −13.3174 | −0.883904 | −0.441952 | − | 0.897039i | \(-0.645714\pi\) | ||||
−0.441952 | + | 0.897039i | \(0.645714\pi\) | |||||||
\(228\) | −8.19250 | −0.542561 | ||||||||
\(229\) | 17.9433 | 1.18573 | 0.592864 | − | 0.805303i | \(-0.297997\pi\) | ||||
0.592864 | + | 0.805303i | \(0.297997\pi\) | |||||||
\(230\) | 8.66547 | 0.571384 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.4809 | −0.950721 | ||||||||
\(233\) | 8.66091 | 0.567395 | 0.283698 | − | 0.958914i | \(-0.408439\pi\) | ||||
0.283698 | + | 0.958914i | \(0.408439\pi\) | |||||||
\(234\) | −15.2996 | −1.00017 | ||||||||
\(235\) | −1.22008 | −0.0795893 | ||||||||
\(236\) | −40.3702 | −2.62788 | ||||||||
\(237\) | 0.744325 | 0.0483491 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.89784 | −0.381499 | −0.190750 | − | 0.981639i | \(-0.561092\pi\) | ||||
−0.190750 | + | 0.981639i | \(0.561092\pi\) | |||||||
\(240\) | −0.905171 | −0.0584285 | ||||||||
\(241\) | 25.7444 | 1.65834 | 0.829170 | − | 0.558997i | \(-0.188814\pi\) | ||||
0.829170 | + | 0.558997i | \(0.188814\pi\) | |||||||
\(242\) | 2.33025 | 0.149794 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 34.6704 | 2.21955 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.6349 | 0.869327 | ||||||||
\(247\) | 15.6817 | 0.997804 | ||||||||
\(248\) | −30.9218 | −1.96353 | ||||||||
\(249\) | −12.9061 | −0.817890 | ||||||||
\(250\) | −2.33025 | −0.147378 | ||||||||
\(251\) | −20.9817 | −1.32435 | −0.662176 | − | 0.749348i | \(-0.730367\pi\) | ||||
−0.662176 | + | 0.749348i | \(0.730367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.71869 | −0.233792 | ||||||||
\(254\) | −16.2294 | −1.01832 | ||||||||
\(255\) | 2.55550 | 0.160031 | ||||||||
\(256\) | −21.3902 | −1.33689 | ||||||||
\(257\) | −13.7452 | −0.857404 | −0.428702 | − | 0.903446i | \(-0.641029\pi\) | ||||
−0.428702 | + | 0.903446i | \(0.641029\pi\) | |||||||
\(258\) | −1.34469 | −0.0837168 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 22.5206 | 1.39667 | ||||||||
\(261\) | −4.34552 | −0.268981 | ||||||||
\(262\) | −36.3743 | −2.24721 | ||||||||
\(263\) | −26.4249 | −1.62943 | −0.814713 | − | 0.579864i | \(-0.803106\pi\) | ||||
−0.814713 | + | 0.579864i | \(0.803106\pi\) | |||||||
\(264\) | 3.33238 | 0.205094 | ||||||||
\(265\) | −1.71564 | −0.105391 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.0765 | −0.983867 | ||||||||
\(268\) | −41.5163 | −2.53601 | ||||||||
\(269\) | −21.5035 | −1.31109 | −0.655546 | − | 0.755155i | \(-0.727562\pi\) | ||||
−0.655546 | + | 0.755155i | \(0.727562\pi\) | |||||||
\(270\) | −2.33025 | −0.141814 | ||||||||
\(271\) | 12.9964 | 0.789473 | 0.394736 | − | 0.918794i | \(-0.370836\pi\) | ||||
0.394736 | + | 0.918794i | \(0.370836\pi\) | |||||||
\(272\) | −2.31316 | −0.140256 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.21363 | 0.314967 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −12.7553 | −0.767780 | ||||||||
\(277\) | −15.1834 | −0.912285 | −0.456142 | − | 0.889907i | \(-0.650769\pi\) | ||||
−0.456142 | + | 0.889907i | \(0.650769\pi\) | |||||||
\(278\) | −28.8300 | −1.72911 | ||||||||
\(279\) | −9.27917 | −0.555529 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.45336 | 0.563940 | 0.281970 | − | 0.959423i | \(-0.409012\pi\) | ||||
0.281970 | + | 0.959423i | \(0.409012\pi\) | |||||||
\(282\) | 2.84309 | 0.169304 | ||||||||
\(283\) | −18.1802 | −1.08070 | −0.540351 | − | 0.841440i | \(-0.681708\pi\) | ||||
−0.540351 | + | 0.841440i | \(0.681708\pi\) | |||||||
\(284\) | 3.86274 | 0.229212 | ||||||||
\(285\) | 2.38844 | 0.141479 | ||||||||
\(286\) | −15.2996 | −0.904686 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.55550 | −0.268435 | ||||||||
\(289\) | −10.4694 | −0.615849 | ||||||||
\(290\) | 10.1261 | 0.594628 | ||||||||
\(291\) | −4.43219 | −0.259820 | ||||||||
\(292\) | 26.2975 | 1.53894 | ||||||||
\(293\) | 28.7950 | 1.68222 | 0.841112 | − | 0.540862i | \(-0.181902\pi\) | ||||
0.841112 | + | 0.540862i | \(0.181902\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7696 | 0.685250 | ||||||||
\(296\) | 23.2829 | 1.35329 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 7.90055 | 0.457667 | ||||||||
\(299\) | 24.4157 | 1.41200 | ||||||||
\(300\) | 3.43006 | 0.198034 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.14529 | −0.123448 | ||||||||
\(303\) | 10.5424 | 0.605642 | ||||||||
\(304\) | −2.16195 | −0.123996 | ||||||||
\(305\) | −10.1078 | −0.578773 | ||||||||
\(306\) | −5.95494 | −0.340421 | ||||||||
\(307\) | −25.7537 | −1.46984 | −0.734920 | − | 0.678154i | \(-0.762780\pi\) | ||||
−0.734920 | + | 0.678154i | \(0.762780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.93083 | 0.337393 | ||||||||
\(310\) | 21.6228 | 1.22809 | ||||||||
\(311\) | −6.95499 | −0.394381 | −0.197191 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197191 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(312\) | −21.8793 | −1.23867 | ||||||||
\(313\) | −15.9445 | −0.901235 | −0.450618 | − | 0.892717i | \(-0.648796\pi\) | ||||
−0.450618 | + | 0.892717i | \(0.648796\pi\) | |||||||
\(314\) | 45.7305 | 2.58072 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.55308 | 0.143622 | ||||||||
\(317\) | 6.11558 | 0.343485 | 0.171743 | − | 0.985142i | \(-0.445060\pi\) | ||||
0.171743 | + | 0.985142i | \(0.445060\pi\) | |||||||
\(318\) | 3.99786 | 0.224189 | ||||||||
\(319\) | −4.34552 | −0.243302 | ||||||||
\(320\) | 12.4258 | 0.694622 | ||||||||
\(321\) | 16.7846 | 0.936828 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.10366 | 0.339617 | ||||||||
\(324\) | 3.43006 | 0.190559 | ||||||||
\(325\) | −6.56567 | −0.364198 | ||||||||
\(326\) | 23.7594 | 1.31591 | ||||||||
\(327\) | −16.5688 | −0.916259 | ||||||||
\(328\) | 19.4986 | 1.07663 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.33025 | −0.128276 | ||||||||
\(331\) | 2.21500 | 0.121747 | 0.0608737 | − | 0.998145i | \(-0.480611\pi\) | ||||
0.0608737 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(332\) | −44.2686 | −2.42955 | ||||||||
\(333\) | 6.98686 | 0.382878 | ||||||||
\(334\) | 1.65012 | 0.0902904 | ||||||||
\(335\) | 12.1037 | 0.661295 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9876 | −0.707480 | −0.353740 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353740 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(338\) | 70.1591 | 3.81615 | ||||||||
\(339\) | 17.2975 | 0.939471 | ||||||||
\(340\) | 8.76550 | 0.475376 | ||||||||
\(341\) | −9.27917 | −0.502495 | ||||||||
\(342\) | −5.56567 | −0.300957 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.92298 | −0.103680 | ||||||||
\(345\) | 3.71869 | 0.200208 | ||||||||
\(346\) | 31.5362 | 1.69540 | ||||||||
\(347\) | −5.86289 | −0.314736 | −0.157368 | − | 0.987540i | \(-0.550301\pi\) | ||||
−0.157368 | + | 0.987540i | \(0.550301\pi\) | |||||||
\(348\) | −14.9054 | −0.799012 | ||||||||
\(349\) | 9.96125 | 0.533213 | 0.266607 | − | 0.963805i | \(-0.414098\pi\) | ||||
0.266607 | + | 0.963805i | \(0.414098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.56567 | −0.350449 | ||||||||
\(352\) | −4.55550 | −0.242809 | ||||||||
\(353\) | 6.91306 | 0.367945 | 0.183973 | − | 0.982931i | \(-0.441104\pi\) | ||||
0.183973 | + | 0.982931i | \(0.441104\pi\) | |||||||
\(354\) | −27.4260 | −1.45767 | ||||||||
\(355\) | −1.12615 | −0.0597696 | ||||||||
\(356\) | −55.1434 | −2.92259 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −32.5659 | −1.72116 | ||||||||
\(359\) | 5.09607 | 0.268960 | 0.134480 | − | 0.990916i | \(-0.457064\pi\) | ||||
0.134480 | + | 0.990916i | \(0.457064\pi\) | |||||||
\(360\) | −3.33238 | −0.175632 | ||||||||
\(361\) | −13.2953 | −0.699754 | ||||||||
\(362\) | −23.1776 | −1.21819 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.66678 | −0.401298 | ||||||||
\(366\) | 23.5538 | 1.23118 | ||||||||
\(367\) | −15.6679 | −0.817858 | −0.408929 | − | 0.912566i | \(-0.634098\pi\) | ||||
−0.408929 | + | 0.912566i | \(0.634098\pi\) | |||||||
\(368\) | −3.36605 | −0.175468 | ||||||||
\(369\) | 5.85125 | 0.304604 | ||||||||
\(370\) | −16.2811 | −0.846415 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −31.8281 | −1.65021 | ||||||||
\(373\) | −22.0542 | −1.14192 | −0.570962 | − | 0.820976i | \(-0.693430\pi\) | ||||
−0.570962 | + | 0.820976i | \(0.693430\pi\) | |||||||
\(374\) | −5.95494 | −0.307923 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 4.06578 | 0.209676 | ||||||||
\(377\) | 28.5312 | 1.46943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.40055 | 0.380141 | 0.190070 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190070 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(380\) | 8.19250 | 0.420266 | ||||||||
\(381\) | −6.96467 | −0.356811 | ||||||||
\(382\) | 29.0882 | 1.48828 | ||||||||
\(383\) | −16.8001 | −0.858445 | −0.429223 | − | 0.903199i | \(-0.641212\pi\) | ||||
−0.429223 | + | 0.903199i | \(0.641212\pi\) | |||||||
\(384\) | −19.8442 | −1.01267 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.00491 | 0.203845 | ||||||||
\(387\) | −0.577059 | −0.0293336 | ||||||||
\(388\) | −15.2027 | −0.771798 | ||||||||
\(389\) | −17.9625 | −0.910737 | −0.455369 | − | 0.890303i | \(-0.650493\pi\) | ||||
−0.455369 | + | 0.890303i | \(0.650493\pi\) | |||||||
\(390\) | 15.2996 | 0.774727 | ||||||||
\(391\) | 9.50310 | 0.480593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.6096 | −0.787402 | ||||||||
\(394\) | 0.137545 | 0.00692941 | ||||||||
\(395\) | −0.744325 | −0.0374511 | ||||||||
\(396\) | 3.43006 | 0.172367 | ||||||||
\(397\) | −0.443236 | −0.0222454 | −0.0111227 | − | 0.999938i | \(-0.503541\pi\) | ||||
−0.0111227 | + | 0.999938i | \(0.503541\pi\) | |||||||
\(398\) | 49.8248 | 2.49749 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.905171 | 0.0452585 | ||||||||
\(401\) | 29.6287 | 1.47959 | 0.739793 | − | 0.672834i | \(-0.234923\pi\) | ||||
0.739793 | + | 0.672834i | \(0.234923\pi\) | |||||||
\(402\) | −28.2046 | −1.40672 | ||||||||
\(403\) | 60.9239 | 3.03484 | ||||||||
\(404\) | 36.1609 | 1.79907 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.98686 | 0.346326 | ||||||||
\(408\) | −8.51590 | −0.421600 | ||||||||
\(409\) | 8.99186 | 0.444619 | 0.222310 | − | 0.974976i | \(-0.428640\pi\) | ||||
0.222310 | + | 0.974976i | \(0.428640\pi\) | |||||||
\(410\) | −13.6349 | −0.673378 | ||||||||
\(411\) | 2.23737 | 0.110361 | ||||||||
\(412\) | 20.3431 | 1.00223 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.66547 | −0.425885 | ||||||||
\(415\) | 12.9061 | 0.633535 | ||||||||
\(416\) | 29.9099 | 1.46645 | ||||||||
\(417\) | −12.3721 | −0.605863 | ||||||||
\(418\) | −5.56567 | −0.272226 | ||||||||
\(419\) | 16.4514 | 0.803704 | 0.401852 | − | 0.915705i | \(-0.368367\pi\) | ||||
0.401852 | + | 0.915705i | \(0.368367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.4904 | −1.38854 | −0.694268 | − | 0.719717i | \(-0.744272\pi\) | ||||
−0.694268 | + | 0.719717i | \(0.744272\pi\) | |||||||
\(422\) | 37.6668 | 1.83359 | ||||||||
\(423\) | 1.22008 | 0.0593223 | ||||||||
\(424\) | 5.71716 | 0.277650 | ||||||||
\(425\) | −2.55550 | −0.123960 | ||||||||
\(426\) | 2.62420 | 0.127143 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 57.5723 | 2.78286 | ||||||||
\(429\) | −6.56567 | −0.316993 | ||||||||
\(430\) | 1.34469 | 0.0648468 | ||||||||
\(431\) | 27.6688 | 1.33276 | 0.666379 | − | 0.745613i | \(-0.267843\pi\) | ||||
0.666379 | + | 0.745613i | \(0.267843\pi\) | |||||||
\(432\) | 0.905171 | 0.0435500 | ||||||||
\(433\) | −31.9507 | −1.53545 | −0.767727 | − | 0.640777i | \(-0.778612\pi\) | ||||
−0.767727 | + | 0.640777i | \(0.778612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.34552 | 0.208352 | ||||||||
\(436\) | −56.8321 | −2.72176 | ||||||||
\(437\) | 8.88189 | 0.424878 | ||||||||
\(438\) | 17.8655 | 0.853647 | ||||||||
\(439\) | 34.0895 | 1.62701 | 0.813503 | − | 0.581561i | \(-0.197558\pi\) | ||||
0.813503 | + | 0.581561i | \(0.197558\pi\) | |||||||
\(440\) | −3.33238 | −0.158865 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 39.0982 | 1.85971 | ||||||||
\(443\) | −41.1418 | −1.95471 | −0.977353 | − | 0.211615i | \(-0.932128\pi\) | ||||
−0.977353 | + | 0.211615i | \(0.932128\pi\) | |||||||
\(444\) | 23.9653 | 1.13734 | ||||||||
\(445\) | 16.0765 | 0.762100 | ||||||||
\(446\) | −21.1315 | −1.00061 | ||||||||
\(447\) | 3.39043 | 0.160362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.0369 | −1.51191 | −0.755957 | − | 0.654621i | \(-0.772828\pi\) | ||||
−0.755957 | + | 0.654621i | \(0.772828\pi\) | |||||||
\(450\) | 2.33025 | 0.109849 | ||||||||
\(451\) | 5.85125 | 0.275524 | ||||||||
\(452\) | 59.3314 | 2.79071 | ||||||||
\(453\) | −0.920629 | −0.0432549 | ||||||||
\(454\) | −31.0327 | −1.45644 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.95921 | −0.372724 | ||||||||
\(457\) | −21.5638 | −1.00871 | −0.504357 | − | 0.863495i | \(-0.668270\pi\) | ||||
−0.504357 | + | 0.863495i | \(0.668270\pi\) | |||||||
\(458\) | 41.8124 | 1.95376 | ||||||||
\(459\) | −2.55550 | −0.119280 | ||||||||
\(460\) | 12.7553 | 0.594720 | ||||||||
\(461\) | −23.9259 | −1.11434 | −0.557171 | − | 0.830398i | \(-0.688113\pi\) | ||||
−0.557171 | + | 0.830398i | \(0.688113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7595 | −0.732407 | −0.366203 | − | 0.930535i | \(-0.619343\pi\) | ||||
−0.366203 | + | 0.930535i | \(0.619343\pi\) | |||||||
\(464\) | −3.93344 | −0.182605 | ||||||||
\(465\) | 9.27917 | 0.430311 | ||||||||
\(466\) | 20.1821 | 0.934916 | ||||||||
\(467\) | 0.419691 | 0.0194210 | 0.00971050 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00971050 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(468\) | −22.5206 | −1.04102 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.84309 | −0.131142 | ||||||||
\(471\) | 19.6247 | 0.904261 | ||||||||
\(472\) | −39.2207 | −1.80528 | ||||||||
\(473\) | −0.577059 | −0.0265332 | ||||||||
\(474\) | 1.73446 | 0.0796665 | ||||||||
\(475\) | −2.38844 | −0.109589 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.71564 | 0.0785536 | ||||||||
\(478\) | −13.7434 | −0.628610 | ||||||||
\(479\) | 31.9291 | 1.45888 | 0.729439 | − | 0.684046i | \(-0.239781\pi\) | ||||
0.729439 | + | 0.684046i | \(0.239781\pi\) | |||||||
\(480\) | 4.55550 | 0.207929 | ||||||||
\(481\) | −45.8734 | −2.09165 | ||||||||
\(482\) | 59.9907 | 2.73250 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.43006 | 0.155912 | ||||||||
\(485\) | 4.43219 | 0.201255 | ||||||||
\(486\) | 2.33025 | 0.105702 | ||||||||
\(487\) | 9.01768 | 0.408630 | 0.204315 | − | 0.978905i | \(-0.434503\pi\) | ||||
0.204315 | + | 0.978905i | \(0.434503\pi\) | |||||||
\(488\) | 33.6832 | 1.52477 | ||||||||
\(489\) | 10.1961 | 0.461082 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8024 | 1.20957 | 0.604787 | − | 0.796388i | \(-0.293258\pi\) | ||||
0.604787 | + | 0.796388i | \(0.293258\pi\) | |||||||
\(492\) | 20.0701 | 0.904830 | ||||||||
\(493\) | 11.1050 | 0.500142 | ||||||||
\(494\) | 36.5423 | 1.64412 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −8.39923 | −0.377137 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −30.0744 | −1.34767 | ||||||||
\(499\) | −13.4874 | −0.603780 | −0.301890 | − | 0.953343i | \(-0.597618\pi\) | ||||
−0.301890 | + | 0.953343i | \(0.597618\pi\) | |||||||
\(500\) | −3.43006 | −0.153397 | ||||||||
\(501\) | 0.708129 | 0.0316369 | ||||||||
\(502\) | −48.8925 | −2.18218 | ||||||||
\(503\) | 0.989318 | 0.0441115 | 0.0220557 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220557 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5424 | −0.469129 | ||||||||
\(506\) | −8.66547 | −0.385227 | ||||||||
\(507\) | 30.1080 | 1.33714 | ||||||||
\(508\) | −23.8892 | −1.05991 | ||||||||
\(509\) | −13.6416 | −0.604655 | −0.302328 | − | 0.953204i | \(-0.597764\pi\) | ||||
−0.302328 | + | 0.953204i | \(0.597764\pi\) | |||||||
\(510\) | 5.95494 | 0.263689 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.1563 | −0.448847 | ||||||||
\(513\) | −2.38844 | −0.105452 | ||||||||
\(514\) | −32.0298 | −1.41277 | ||||||||
\(515\) | −5.93083 | −0.261343 | ||||||||
\(516\) | −1.97935 | −0.0871358 | ||||||||
\(517\) | 1.22008 | 0.0536591 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5334 | 0.594051 | ||||||||
\(520\) | 21.8793 | 0.959472 | ||||||||
\(521\) | 30.3215 | 1.32841 | 0.664204 | − | 0.747552i | \(-0.268771\pi\) | ||||
0.664204 | + | 0.747552i | \(0.268771\pi\) | |||||||
\(522\) | −10.1261 | −0.443209 | ||||||||
\(523\) | −9.56645 | −0.418312 | −0.209156 | − | 0.977882i | \(-0.567072\pi\) | ||||
−0.209156 | + | 0.977882i | \(0.567072\pi\) | |||||||
\(524\) | −53.5419 | −2.33899 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −61.5765 | −2.68486 | ||||||||
\(527\) | 23.7129 | 1.03295 | ||||||||
\(528\) | 0.905171 | 0.0393925 | ||||||||
\(529\) | −9.17133 | −0.398753 | ||||||||
\(530\) | −3.99786 | −0.173656 | ||||||||
\(531\) | −11.7696 | −0.510755 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.4173 | −1.66404 | ||||||||
\(534\) | −37.4623 | −1.62115 | ||||||||
\(535\) | −16.7846 | −0.725664 | ||||||||
\(536\) | −40.3341 | −1.74217 | ||||||||
\(537\) | −13.9753 | −0.603078 | ||||||||
\(538\) | −50.1085 | −2.16033 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.43006 | −0.147606 | ||||||||
\(541\) | 22.7800 | 0.979390 | 0.489695 | − | 0.871894i | \(-0.337108\pi\) | ||||
0.489695 | + | 0.871894i | \(0.337108\pi\) | |||||||
\(542\) | 30.2847 | 1.30084 | ||||||||
\(543\) | −9.94639 | −0.426840 | ||||||||
\(544\) | 11.6416 | 0.499128 | ||||||||
\(545\) | 16.5688 | 0.709731 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.7796 | −1.78637 | −0.893184 | − | 0.449691i | \(-0.851534\pi\) | ||||
−0.893184 | + | 0.449691i | \(0.851534\pi\) | |||||||
\(548\) | 7.67430 | 0.327830 | ||||||||
\(549\) | 10.1078 | 0.431392 | ||||||||
\(550\) | 2.33025 | 0.0993621 | ||||||||
\(551\) | 10.3790 | 0.442162 | ||||||||
\(552\) | −12.3921 | −0.527443 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35.3812 | −1.50320 | ||||||||
\(555\) | −6.98686 | −0.296576 | ||||||||
\(556\) | −42.4369 | −1.79973 | ||||||||
\(557\) | −14.6582 | −0.621090 | −0.310545 | − | 0.950559i | \(-0.600511\pi\) | ||||
−0.310545 | + | 0.950559i | \(0.600511\pi\) | |||||||
\(558\) | −21.6228 | −0.915364 | ||||||||
\(559\) | 3.78878 | 0.160248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.55550 | −0.107893 | ||||||||
\(562\) | 22.0287 | 0.929224 | ||||||||
\(563\) | 10.5178 | 0.443274 | 0.221637 | − | 0.975129i | \(-0.428860\pi\) | ||||
0.221637 | + | 0.975129i | \(0.428860\pi\) | |||||||
\(564\) | 4.18494 | 0.176218 | ||||||||
\(565\) | −17.2975 | −0.727711 | ||||||||
\(566\) | −42.3644 | −1.78071 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.75275 | 0.157462 | ||||||||
\(569\) | −5.00689 | −0.209900 | −0.104950 | − | 0.994478i | \(-0.533468\pi\) | ||||
−0.104950 | + | 0.994478i | \(0.533468\pi\) | |||||||
\(570\) | 5.56567 | 0.233120 | ||||||||
\(571\) | −8.53669 | −0.357249 | −0.178625 | − | 0.983917i | \(-0.557165\pi\) | ||||
−0.178625 | + | 0.983917i | \(0.557165\pi\) | |||||||
\(572\) | −22.5206 | −0.941634 | ||||||||
\(573\) | 12.4829 | 0.521480 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.71869 | −0.155080 | ||||||||
\(576\) | −12.4258 | −0.517741 | ||||||||
\(577\) | 7.15949 | 0.298054 | 0.149027 | − | 0.988833i | \(-0.452386\pi\) | ||||
0.149027 | + | 0.988833i | \(0.452386\pi\) | |||||||
\(578\) | −24.3964 | −1.01476 | ||||||||
\(579\) | 1.71866 | 0.0714252 | ||||||||
\(580\) | 14.9054 | 0.618912 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.3281 | −0.428114 | ||||||||
\(583\) | 1.71564 | 0.0710544 | ||||||||
\(584\) | 25.5487 | 1.05721 | ||||||||
\(585\) | 6.56567 | 0.271457 | ||||||||
\(586\) | 67.0995 | 2.77186 | ||||||||
\(587\) | 29.4112 | 1.21393 | 0.606964 | − | 0.794729i | \(-0.292387\pi\) | ||||
0.606964 | + | 0.794729i | \(0.292387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1628 | 0.913201 | ||||||||
\(590\) | 27.4260 | 1.12911 | ||||||||
\(591\) | 0.0590259 | 0.00242800 | ||||||||
\(592\) | 6.32430 | 0.259927 | ||||||||
\(593\) | 1.54545 | 0.0634642 | 0.0317321 | − | 0.999496i | \(-0.489898\pi\) | ||||
0.0317321 | + | 0.999496i | \(0.489898\pi\) | |||||||
\(594\) | 2.33025 | 0.0956112 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.6294 | 0.476358 | ||||||||
\(597\) | 21.3818 | 0.875097 | ||||||||
\(598\) | 56.8946 | 2.32659 | ||||||||
\(599\) | 10.5213 | 0.429890 | 0.214945 | − | 0.976626i | \(-0.431043\pi\) | ||||
0.214945 | + | 0.976626i | \(0.431043\pi\) | |||||||
\(600\) | 3.33238 | 0.136044 | ||||||||
\(601\) | −35.8037 | −1.46046 | −0.730232 | − | 0.683199i | \(-0.760588\pi\) | ||||
−0.730232 | + | 0.683199i | \(0.760588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.1037 | −0.492900 | ||||||||
\(604\) | −3.15781 | −0.128489 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 24.5663 | 0.997938 | ||||||||
\(607\) | 0.564007 | 0.0228923 | 0.0114462 | − | 0.999934i | \(-0.496356\pi\) | ||||
0.0114462 | + | 0.999934i | \(0.496356\pi\) | |||||||
\(608\) | 10.8805 | 0.441264 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.5538 | −0.953664 | ||||||||
\(611\) | −8.01064 | −0.324076 | ||||||||
\(612\) | −8.76550 | −0.354324 | ||||||||
\(613\) | −13.6564 | −0.551576 | −0.275788 | − | 0.961218i | \(-0.588939\pi\) | ||||
−0.275788 | + | 0.961218i | \(0.588939\pi\) | |||||||
\(614\) | −60.0124 | −2.42190 | ||||||||
\(615\) | −5.85125 | −0.235945 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.4948 | −1.06664 | −0.533320 | − | 0.845913i | \(-0.679056\pi\) | ||||
−0.533320 | + | 0.845913i | \(0.679056\pi\) | |||||||
\(618\) | 13.8203 | 0.555934 | ||||||||
\(619\) | 12.2166 | 0.491025 | 0.245513 | − | 0.969393i | \(-0.421044\pi\) | ||||
0.245513 | + | 0.969393i | \(0.421044\pi\) | |||||||
\(620\) | 31.8281 | 1.27825 | ||||||||
\(621\) | −3.71869 | −0.149226 | ||||||||
\(622\) | −16.2069 | −0.649836 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.94305 | −0.237912 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −37.1546 | −1.48500 | ||||||||
\(627\) | −2.38844 | −0.0953853 | ||||||||
\(628\) | 67.3140 | 2.68612 | ||||||||
\(629\) | −17.8549 | −0.711921 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4089 | −0.613417 | −0.306709 | − | 0.951803i | \(-0.599228\pi\) | ||||
−0.306709 | + | 0.951803i | \(0.599228\pi\) | |||||||
\(632\) | 2.48038 | 0.0986641 | ||||||||
\(633\) | 16.1643 | 0.642473 | ||||||||
\(634\) | 14.2508 | 0.565973 | ||||||||
\(635\) | 6.96467 | 0.276385 | ||||||||
\(636\) | 5.88473 | 0.233345 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.1261 | −0.400898 | ||||||||
\(639\) | 1.12615 | 0.0445497 | ||||||||
\(640\) | 19.8442 | 0.784409 | ||||||||
\(641\) | −13.9149 | −0.549607 | −0.274803 | − | 0.961500i | \(-0.588613\pi\) | ||||
−0.274803 | + | 0.961500i | \(0.588613\pi\) | |||||||
\(642\) | 39.1124 | 1.54364 | ||||||||
\(643\) | −16.1658 | −0.637519 | −0.318759 | − | 0.947836i | \(-0.603266\pi\) | ||||
−0.318759 | + | 0.947836i | \(0.603266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.577059 | 0.0227217 | ||||||||
\(646\) | 14.2230 | 0.559598 | ||||||||
\(647\) | −29.6850 | −1.16704 | −0.583519 | − | 0.812100i | \(-0.698325\pi\) | ||||
−0.583519 | + | 0.812100i | \(0.698325\pi\) | |||||||
\(648\) | 3.33238 | 0.130908 | ||||||||
\(649\) | −11.7696 | −0.461995 | ||||||||
\(650\) | −15.2996 | −0.600101 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 34.9731 | 1.36965 | ||||||||
\(653\) | −0.310300 | −0.0121430 | −0.00607149 | − | 0.999982i | \(-0.501933\pi\) | ||||
−0.00607149 | + | 0.999982i | \(0.501933\pi\) | |||||||
\(654\) | −38.6095 | −1.50975 | ||||||||
\(655\) | 15.6096 | 0.609919 | ||||||||
\(656\) | 5.29638 | 0.206789 | ||||||||
\(657\) | 7.66678 | 0.299110 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0773 | 0.860008 | 0.430004 | − | 0.902827i | \(-0.358512\pi\) | ||||
0.430004 | + | 0.902827i | \(0.358512\pi\) | |||||||
\(660\) | −3.43006 | −0.133515 | ||||||||
\(661\) | 44.4597 | 1.72928 | 0.864641 | − | 0.502390i | \(-0.167546\pi\) | ||||
0.864641 | + | 0.502390i | \(0.167546\pi\) | |||||||
\(662\) | 5.16150 | 0.200607 | ||||||||
\(663\) | 16.7785 | 0.651624 | ||||||||
\(664\) | −43.0080 | −1.66904 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.2811 | 0.630880 | ||||||||
\(667\) | 16.1597 | 0.625704 | ||||||||
\(668\) | 2.42892 | 0.0939779 | ||||||||
\(669\) | −9.06835 | −0.350603 | ||||||||
\(670\) | 28.2046 | 1.08964 | ||||||||
\(671\) | 10.1078 | 0.390209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.27727 | −0.203424 | −0.101712 | − | 0.994814i | \(-0.532432\pi\) | ||||
−0.101712 | + | 0.994814i | \(0.532432\pi\) | |||||||
\(674\) | −30.2643 | −1.16574 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 103.272 | 3.97200 | ||||||||
\(677\) | 47.1912 | 1.81371 | 0.906853 | − | 0.421447i | \(-0.138478\pi\) | ||||
0.906853 | + | 0.421447i | \(0.138478\pi\) | |||||||
\(678\) | 40.3074 | 1.54800 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.51590 | 0.326570 | ||||||||
\(681\) | −13.3174 | −0.510322 | ||||||||
\(682\) | −21.6228 | −0.827978 | ||||||||
\(683\) | −16.9902 | −0.650113 | −0.325057 | − | 0.945695i | \(-0.605383\pi\) | ||||
−0.325057 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(684\) | −8.19250 | −0.313248 | ||||||||
\(685\) | −2.23737 | −0.0854855 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.9433 | 0.684580 | ||||||||
\(688\) | −0.522337 | −0.0199139 | ||||||||
\(689\) | −11.2643 | −0.429136 | ||||||||
\(690\) | 8.66547 | 0.329889 | ||||||||
\(691\) | 11.6357 | 0.442642 | 0.221321 | − | 0.975201i | \(-0.428963\pi\) | ||||
0.221321 | + | 0.975201i | \(0.428963\pi\) | |||||||
\(692\) | 46.4204 | 1.76464 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.6620 | −0.518602 | ||||||||
\(695\) | 12.3721 | 0.469299 | ||||||||
\(696\) | −14.4809 | −0.548899 | ||||||||
\(697\) | −14.9528 | −0.566379 | ||||||||
\(698\) | 23.2122 | 0.878594 | ||||||||
\(699\) | 8.66091 | 0.327586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.31631 | 0.238564 | 0.119282 | − | 0.992860i | \(-0.461941\pi\) | ||||
0.119282 | + | 0.992860i | \(0.461941\pi\) | |||||||
\(702\) | −15.2996 | −0.577447 | ||||||||
\(703\) | −16.6877 | −0.629389 | ||||||||
\(704\) | −12.4258 | −0.468314 | ||||||||
\(705\) | −1.22008 | −0.0459509 | ||||||||
\(706\) | 16.1091 | 0.606276 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −40.3702 | −1.51721 | ||||||||
\(709\) | 16.9654 | 0.637147 | 0.318574 | − | 0.947898i | \(-0.396796\pi\) | ||||
0.318574 | + | 0.947898i | \(0.396796\pi\) | |||||||
\(710\) | −2.62420 | −0.0984845 | ||||||||
\(711\) | 0.744325 | 0.0279144 | ||||||||
\(712\) | −53.5731 | −2.00774 | ||||||||
\(713\) | 34.5064 | 1.29227 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.56567 | 0.245542 | ||||||||
\(716\) | −47.9360 | −1.79145 | ||||||||
\(717\) | −5.89784 | −0.220259 | ||||||||
\(718\) | 11.8751 | 0.443175 | ||||||||
\(719\) | −9.53294 | −0.355519 | −0.177759 | − | 0.984074i | \(-0.556885\pi\) | ||||
−0.177759 | + | 0.984074i | \(0.556885\pi\) | |||||||
\(720\) | −0.905171 | −0.0337337 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −30.9814 | −1.15301 | ||||||||
\(723\) | 25.7444 | 0.957443 | ||||||||
\(724\) | −34.1167 | −1.26794 | ||||||||
\(725\) | −4.34552 | −0.161389 | ||||||||
\(726\) | 2.33025 | 0.0864836 | ||||||||
\(727\) | 45.7753 | 1.69771 | 0.848855 | − | 0.528625i | \(-0.177292\pi\) | ||||
0.848855 | + | 0.528625i | \(0.177292\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.8655 | −0.661232 | ||||||||
\(731\) | 1.47467 | 0.0545427 | ||||||||
\(732\) | 34.6704 | 1.28146 | ||||||||
\(733\) | 6.54970 | 0.241919 | 0.120959 | − | 0.992657i | \(-0.461403\pi\) | ||||
0.120959 | + | 0.992657i | \(0.461403\pi\) | |||||||
\(734\) | −36.5101 | −1.34761 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.9405 | 0.624435 | ||||||||
\(737\) | −12.1037 | −0.445845 | ||||||||
\(738\) | 13.6349 | 0.501906 | ||||||||
\(739\) | −20.6539 | −0.759768 | −0.379884 | − | 0.925034i | \(-0.624036\pi\) | ||||
−0.379884 | + | 0.925034i | \(0.624036\pi\) | |||||||
\(740\) | −23.9653 | −0.880983 | ||||||||
\(741\) | 15.6817 | 0.576083 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7387 | 1.45787 | 0.728936 | − | 0.684582i | \(-0.240015\pi\) | ||||
0.728936 | + | 0.684582i | \(0.240015\pi\) | |||||||
\(744\) | −30.9218 | −1.13365 | ||||||||
\(745\) | −3.39043 | −0.124216 | ||||||||
\(746\) | −51.3918 | −1.88159 | ||||||||
\(747\) | −12.9061 | −0.472209 | ||||||||
\(748\) | −8.76550 | −0.320498 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.33025 | −0.0850886 | ||||||||
\(751\) | 42.5246 | 1.55175 | 0.775873 | − | 0.630889i | \(-0.217310\pi\) | ||||
0.775873 | + | 0.630889i | \(0.217310\pi\) | |||||||
\(752\) | 1.10438 | 0.0402726 | ||||||||
\(753\) | −20.9817 | −0.764615 | ||||||||
\(754\) | 66.4849 | 2.42124 | ||||||||
\(755\) | 0.920629 | 0.0335051 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.5157 | −1.36353 | −0.681767 | − | 0.731570i | \(-0.738788\pi\) | ||||
−0.681767 | + | 0.731570i | \(0.738788\pi\) | |||||||
\(758\) | 17.2451 | 0.626371 | ||||||||
\(759\) | −3.71869 | −0.134980 | ||||||||
\(760\) | 7.95921 | 0.288711 | ||||||||
\(761\) | 44.9932 | 1.63100 | 0.815501 | − | 0.578755i | \(-0.196461\pi\) | ||||
0.815501 | + | 0.578755i | \(0.196461\pi\) | |||||||
\(762\) | −16.2294 | −0.587930 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 42.8170 | 1.54906 | ||||||||
\(765\) | 2.55550 | 0.0923942 | ||||||||
\(766\) | −39.1484 | −1.41449 | ||||||||
\(767\) | 77.2750 | 2.79024 | ||||||||
\(768\) | −21.3902 | −0.771854 | ||||||||
\(769\) | 0.330307 | 0.0119112 | 0.00595559 | − | 0.999982i | \(-0.498104\pi\) | ||||
0.00595559 | + | 0.999982i | \(0.498104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.7452 | −0.495023 | ||||||||
\(772\) | 5.89511 | 0.212170 | ||||||||
\(773\) | 7.69570 | 0.276795 | 0.138398 | − | 0.990377i | \(-0.455805\pi\) | ||||
0.138398 | + | 0.990377i | \(0.455805\pi\) | |||||||
\(774\) | −1.34469 | −0.0483339 | ||||||||
\(775\) | −9.27917 | −0.333318 | ||||||||
\(776\) | −14.7698 | −0.530204 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.8572 | −1.50065 | ||||||||
\(779\) | −13.9754 | −0.500720 | ||||||||
\(780\) | 22.5206 | 0.806367 | ||||||||
\(781\) | 1.12615 | 0.0402967 | ||||||||
\(782\) | 22.1446 | 0.791889 | ||||||||
\(783\) | −4.34552 | −0.155296 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.6247 | −0.700437 | ||||||||
\(786\) | −36.3743 | −1.29743 | ||||||||
\(787\) | −27.0391 | −0.963839 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(788\) | 0.202462 | 0.00721241 | ||||||||
\(789\) | −26.4249 | −0.940750 | ||||||||
\(790\) | −1.73446 | −0.0617094 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.33238 | 0.118411 | ||||||||
\(793\) | −66.3647 | −2.35668 | ||||||||
\(794\) | −1.03285 | −0.0366545 | ||||||||
\(795\) | −1.71564 | −0.0608474 | ||||||||
\(796\) | 73.3406 | 2.59949 | ||||||||
\(797\) | −13.7899 | −0.488465 | −0.244232 | − | 0.969717i | \(-0.578536\pi\) | ||||
−0.244232 | + | 0.969717i | \(0.578536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.11791 | −0.110304 | ||||||||
\(800\) | −4.55550 | −0.161061 | ||||||||
\(801\) | −16.0765 | −0.568036 | ||||||||
\(802\) | 69.0422 | 2.43796 | ||||||||
\(803\) | 7.66678 | 0.270555 | ||||||||
\(804\) | −41.5163 | −1.46417 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 141.968 | 5.00060 | ||||||||
\(807\) | −21.5035 | −0.756960 | ||||||||
\(808\) | 35.1312 | 1.23591 | ||||||||
\(809\) | 24.3164 | 0.854919 | 0.427460 | − | 0.904034i | \(-0.359409\pi\) | ||||
0.427460 | + | 0.904034i | \(0.359409\pi\) | |||||||
\(810\) | −2.33025 | −0.0818766 | ||||||||
\(811\) | 25.5442 | 0.896978 | 0.448489 | − | 0.893788i | \(-0.351962\pi\) | ||||
0.448489 | + | 0.893788i | \(0.351962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9964 | 0.455802 | ||||||||
\(814\) | 16.2811 | 0.570653 | ||||||||
\(815\) | −10.1961 | −0.357153 | ||||||||
\(816\) | −2.31316 | −0.0809768 | ||||||||
\(817\) | 1.37827 | 0.0482197 | ||||||||
\(818\) | 20.9533 | 0.732614 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.0701 | −0.700878 | ||||||||
\(821\) | 32.5200 | 1.13496 | 0.567478 | − | 0.823389i | \(-0.307919\pi\) | ||||
0.567478 | + | 0.823389i | \(0.307919\pi\) | |||||||
\(822\) | 5.21363 | 0.181846 | ||||||||
\(823\) | −46.8394 | −1.63272 | −0.816359 | − | 0.577544i | \(-0.804011\pi\) | ||||
−0.816359 | + | 0.577544i | \(0.804011\pi\) | |||||||
\(824\) | 19.7638 | 0.688504 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.2843 | 1.26173 | 0.630864 | − | 0.775893i | \(-0.282701\pi\) | ||||
0.630864 | + | 0.775893i | \(0.282701\pi\) | |||||||
\(828\) | −12.7553 | −0.443278 | ||||||||
\(829\) | −38.5594 | −1.33922 | −0.669612 | − | 0.742711i | \(-0.733539\pi\) | ||||
−0.669612 | + | 0.742711i | \(0.733539\pi\) | |||||||
\(830\) | 30.0744 | 1.04390 | ||||||||
\(831\) | −15.1834 | −0.526708 | ||||||||
\(832\) | 81.5835 | 2.82840 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −28.8300 | −0.998301 | ||||||||
\(835\) | −0.708129 | −0.0245058 | ||||||||
\(836\) | −8.19250 | −0.283343 | ||||||||
\(837\) | −9.27917 | −0.320735 | ||||||||
\(838\) | 38.3358 | 1.32429 | ||||||||
\(839\) | −40.9551 | −1.41393 | −0.706964 | − | 0.707249i | \(-0.749936\pi\) | ||||
−0.706964 | + | 0.707249i | \(0.749936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.1164 | −0.348843 | ||||||||
\(842\) | −66.3896 | −2.28794 | ||||||||
\(843\) | 9.45336 | 0.325591 | ||||||||
\(844\) | 55.4445 | 1.90848 | ||||||||
\(845\) | −30.1080 | −1.03575 | ||||||||
\(846\) | 2.84309 | 0.0977474 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.55294 | 0.0533283 | ||||||||
\(849\) | −18.1802 | −0.623943 | ||||||||
\(850\) | −5.95494 | −0.204253 | ||||||||
\(851\) | −25.9820 | −0.890651 | ||||||||
\(852\) | 3.86274 | 0.132335 | ||||||||
\(853\) | 55.8708 | 1.91298 | 0.956489 | − | 0.291768i | \(-0.0942436\pi\) | ||||
0.956489 | + | 0.291768i | \(0.0942436\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.38844 | 0.0816831 | ||||||||
\(856\) | 55.9329 | 1.91175 | ||||||||
\(857\) | 6.09782 | 0.208298 | 0.104149 | − | 0.994562i | \(-0.466788\pi\) | ||||
0.104149 | + | 0.994562i | \(0.466788\pi\) | |||||||
\(858\) | −15.2996 | −0.522321 | ||||||||
\(859\) | 27.9037 | 0.952062 | 0.476031 | − | 0.879428i | \(-0.342075\pi\) | ||||
0.476031 | + | 0.879428i | \(0.342075\pi\) | |||||||
\(860\) | 1.97935 | 0.0674951 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 64.4751 | 2.19603 | ||||||||
\(863\) | −30.5230 | −1.03901 | −0.519507 | − | 0.854466i | \(-0.673885\pi\) | ||||
−0.519507 | + | 0.854466i | \(0.673885\pi\) | |||||||
\(864\) | −4.55550 | −0.154981 | ||||||||
\(865\) | −13.5334 | −0.460150 | ||||||||
\(866\) | −74.4531 | −2.53002 | ||||||||
\(867\) | −10.4694 | −0.355561 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.744325 | 0.0252495 | ||||||||
\(870\) | 10.1261 | 0.343308 | ||||||||
\(871\) | 79.4688 | 2.69270 | ||||||||
\(872\) | −55.2138 | −1.86977 | ||||||||
\(873\) | −4.43219 | −0.150007 | ||||||||
\(874\) | 20.6970 | 0.700086 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.2975 | 0.888510 | ||||||||
\(877\) | −36.1262 | −1.21989 | −0.609947 | − | 0.792442i | \(-0.708809\pi\) | ||||
−0.609947 | + | 0.792442i | \(0.708809\pi\) | |||||||
\(878\) | 79.4371 | 2.68087 | ||||||||
\(879\) | 28.7950 | 0.971232 | ||||||||
\(880\) | −0.905171 | −0.0305133 | ||||||||
\(881\) | −42.0321 | −1.41610 | −0.708048 | − | 0.706164i | \(-0.750424\pi\) | ||||
−0.708048 | + | 0.706164i | \(0.750424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.1106 | −1.24887 | −0.624436 | − | 0.781076i | \(-0.714671\pi\) | ||||
−0.624436 | + | 0.781076i | \(0.714671\pi\) | |||||||
\(884\) | 57.5513 | 1.93566 | ||||||||
\(885\) | 11.7696 | 0.395629 | ||||||||
\(886\) | −95.8706 | −3.22084 | ||||||||
\(887\) | 27.8091 | 0.933738 | 0.466869 | − | 0.884326i | \(-0.345382\pi\) | ||||
0.466869 | + | 0.884326i | \(0.345382\pi\) | |||||||
\(888\) | 23.2829 | 0.781323 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 37.4623 | 1.25574 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −31.1049 | −1.04147 | ||||||||
\(893\) | −2.91409 | −0.0975164 | ||||||||
\(894\) | 7.90055 | 0.264234 | ||||||||
\(895\) | 13.9753 | 0.467142 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.4157 | 0.815216 | ||||||||
\(898\) | −74.6539 | −2.49123 | ||||||||
\(899\) | 40.3228 | 1.34484 | ||||||||
\(900\) | 3.43006 | 0.114335 | ||||||||
\(901\) | −4.38430 | −0.146062 | ||||||||
\(902\) | 13.6349 | 0.453991 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 57.6419 | 1.91714 | ||||||||
\(905\) | 9.94639 | 0.330629 | ||||||||
\(906\) | −2.14529 | −0.0712726 | ||||||||
\(907\) | 14.9836 | 0.497523 | 0.248761 | − | 0.968565i | \(-0.419977\pi\) | ||||
0.248761 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(908\) | −45.6793 | −1.51592 | ||||||||
\(909\) | 10.5424 | 0.349668 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.1417 | −0.799851 | −0.399925 | − | 0.916548i | \(-0.630964\pi\) | ||||
−0.399925 | + | 0.916548i | \(0.630964\pi\) | |||||||
\(912\) | −2.16195 | −0.0715893 | ||||||||
\(913\) | −12.9061 | −0.427129 | ||||||||
\(914\) | −50.2491 | −1.66209 | ||||||||
\(915\) | −10.1078 | −0.334155 | ||||||||
\(916\) | 61.5466 | 2.03356 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.95494 | −0.196542 | ||||||||
\(919\) | −27.3335 | −0.901649 | −0.450825 | − | 0.892613i | \(-0.648870\pi\) | ||||
−0.450825 | + | 0.892613i | \(0.648870\pi\) | |||||||
\(920\) | 12.3921 | 0.408556 | ||||||||
\(921\) | −25.7537 | −0.848612 | ||||||||
\(922\) | −55.7534 | −1.83614 | ||||||||
\(923\) | −7.39390 | −0.243373 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.98686 | 0.229727 | ||||||||
\(926\) | −36.7236 | −1.20681 | ||||||||
\(927\) | 5.93083 | 0.194794 | ||||||||
\(928\) | 19.7960 | 0.649836 | ||||||||
\(929\) | −9.52488 | −0.312501 | −0.156251 | − | 0.987717i | \(-0.549941\pi\) | ||||
−0.156251 | + | 0.987717i | \(0.549941\pi\) | |||||||
\(930\) | 21.6228 | 0.709038 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.7074 | 0.973099 | ||||||||
\(933\) | −6.95499 | −0.227696 | ||||||||
\(934\) | 0.977984 | 0.0320006 | ||||||||
\(935\) | 2.55550 | 0.0835737 | ||||||||
\(936\) | −21.8793 | −0.715148 | ||||||||
\(937\) | 9.95761 | 0.325301 | 0.162650 | − | 0.986684i | \(-0.447996\pi\) | ||||
0.162650 | + | 0.986684i | \(0.447996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.9445 | −0.520328 | ||||||||
\(940\) | −4.18494 | −0.136498 | ||||||||
\(941\) | 21.2617 | 0.693113 | 0.346556 | − | 0.938029i | \(-0.387351\pi\) | ||||
0.346556 | + | 0.938029i | \(0.387351\pi\) | |||||||
\(942\) | 45.7305 | 1.48998 | ||||||||
\(943\) | −21.7590 | −0.708570 | ||||||||
\(944\) | −10.6535 | −0.346741 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.34469 | −0.0437197 | ||||||||
\(947\) | −9.61638 | −0.312491 | −0.156245 | − | 0.987718i | \(-0.549939\pi\) | ||||
−0.156245 | + | 0.987718i | \(0.549939\pi\) | |||||||
\(948\) | 2.55308 | 0.0829201 | ||||||||
\(949\) | −50.3375 | −1.63403 | ||||||||
\(950\) | −5.56567 | −0.180574 | ||||||||
\(951\) | 6.11558 | 0.198311 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.6598 | −0.539665 | −0.269833 | − | 0.962907i | \(-0.586968\pi\) | ||||
−0.269833 | + | 0.962907i | \(0.586968\pi\) | |||||||
\(954\) | 3.99786 | 0.129435 | ||||||||
\(955\) | −12.4829 | −0.403937 | ||||||||
\(956\) | −20.2299 | −0.654282 | ||||||||
\(957\) | −4.34552 | −0.140471 | ||||||||
\(958\) | 74.4027 | 2.40384 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 12.4258 | 0.401040 | ||||||||
\(961\) | 55.1029 | 1.77751 | ||||||||
\(962\) | −106.896 | −3.44648 | ||||||||
\(963\) | 16.7846 | 0.540878 | ||||||||
\(964\) | 88.3046 | 2.84410 | ||||||||
\(965\) | −1.71866 | −0.0553257 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.39085 | 0.269831 | 0.134916 | − | 0.990857i | \(-0.456924\pi\) | ||||
0.134916 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(968\) | 3.33238 | 0.107107 | ||||||||
\(969\) | 6.10366 | 0.196078 | ||||||||
\(970\) | 10.3281 | 0.331616 | ||||||||
\(971\) | 47.8541 | 1.53571 | 0.767855 | − | 0.640623i | \(-0.221324\pi\) | ||||
0.767855 | + | 0.640623i | \(0.221324\pi\) | |||||||
\(972\) | 3.43006 | 0.110019 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.0134 | 0.673314 | ||||||||
\(975\) | −6.56567 | −0.210270 | ||||||||
\(976\) | 9.14932 | 0.292863 | ||||||||
\(977\) | 27.5644 | 0.881862 | 0.440931 | − | 0.897541i | \(-0.354648\pi\) | ||||
0.440931 | + | 0.897541i | \(0.354648\pi\) | |||||||
\(978\) | 23.7594 | 0.759740 | ||||||||
\(979\) | −16.0765 | −0.513808 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.5688 | −0.529002 | ||||||||
\(982\) | 62.4561 | 1.99306 | ||||||||
\(983\) | 14.6530 | 0.467359 | 0.233680 | − | 0.972314i | \(-0.424923\pi\) | ||||
0.233680 | + | 0.972314i | \(0.424923\pi\) | |||||||
\(984\) | 19.4986 | 0.621593 | ||||||||
\(985\) | −0.0590259 | −0.00188072 | ||||||||
\(986\) | 25.8773 | 0.824102 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 53.7892 | 1.71126 | ||||||||
\(989\) | 2.14591 | 0.0682358 | ||||||||
\(990\) | −2.33025 | −0.0740601 | ||||||||
\(991\) | 47.0503 | 1.49460 | 0.747301 | − | 0.664486i | \(-0.231349\pi\) | ||||
0.747301 | + | 0.664486i | \(0.231349\pi\) | |||||||
\(992\) | 42.2712 | 1.34211 | ||||||||
\(993\) | 2.21500 | 0.0702909 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.3818 | −0.677847 | ||||||||
\(996\) | −44.2686 | −1.40270 | ||||||||
\(997\) | 9.86987 | 0.312582 | 0.156291 | − | 0.987711i | \(-0.450046\pi\) | ||||
0.156291 | + | 0.987711i | \(0.450046\pi\) | |||||||
\(998\) | −31.4291 | −0.994869 | ||||||||
\(999\) | 6.98686 | 0.221054 |
(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 | 8085.2.a.bz.1.6 | 6 | ||
7.2 | even | 3 | 1155.2.q.h.991.1 | yes | 12 | ||
7.4 | even | 3 | 1155.2.q.h.331.1 | ✓ | 12 | ||
7.6 | odd | 2 | 8085.2.a.bx.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.q.h.331.1 | ✓ | 12 | 7.4 | even | 3 | ||
1155.2.q.h.991.1 | yes | 12 | 7.2 | even | 3 | ||
8085.2.a.bx.1.6 | 6 | 7.6 | odd | 2 | |||
8085.2.a.bz.1.6 | 6 | 1.1 | even | 1 | trivial |