Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.990574 | −0.571908 | −0.285954 | − | 0.958243i | \(-0.592310\pi\) | ||||
−0.285954 | + | 0.958243i | \(0.592310\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.23904 | 1.89576 | 0.947879 | − | 0.318631i | \(-0.103223\pi\) | ||||
0.947879 | + | 0.318631i | \(0.103223\pi\) | |||||||
\(6\) | −0.990574 | −0.404400 | ||||||||
\(7\) | −4.18696 | −1.58252 | −0.791261 | − | 0.611478i | \(-0.790575\pi\) | ||||
−0.791261 | + | 0.611478i | \(0.790575\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.01876 | −0.672921 | ||||||||
\(10\) | 4.23904 | 1.34050 | ||||||||
\(11\) | −4.64963 | −1.40192 | −0.700958 | − | 0.713203i | \(-0.747244\pi\) | ||||
−0.700958 | + | 0.713203i | \(0.747244\pi\) | |||||||
\(12\) | −0.990574 | −0.285954 | ||||||||
\(13\) | −2.88609 | −0.800456 | −0.400228 | − | 0.916416i | \(-0.631069\pi\) | ||||
−0.400228 | + | 0.916416i | \(0.631069\pi\) | |||||||
\(14\) | −4.18696 | −1.11901 | ||||||||
\(15\) | −4.19909 | −1.08420 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.19917 | 1.50352 | 0.751760 | − | 0.659437i | \(-0.229205\pi\) | ||||
0.751760 | + | 0.659437i | \(0.229205\pi\) | |||||||
\(18\) | −2.01876 | −0.475827 | ||||||||
\(19\) | 4.17285 | 0.957317 | 0.478659 | − | 0.878001i | \(-0.341123\pi\) | ||||
0.478659 | + | 0.878001i | \(0.341123\pi\) | |||||||
\(20\) | 4.23904 | 0.947879 | ||||||||
\(21\) | 4.14750 | 0.905058 | ||||||||
\(22\) | −4.64963 | −0.991304 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −0.990574 | −0.202200 | ||||||||
\(25\) | 12.9695 | 2.59390 | ||||||||
\(26\) | −2.88609 | −0.566008 | ||||||||
\(27\) | 4.97146 | 0.956757 | ||||||||
\(28\) | −4.18696 | −0.791261 | ||||||||
\(29\) | −3.53526 | −0.656481 | −0.328240 | − | 0.944594i | \(-0.606456\pi\) | ||||
−0.328240 | + | 0.944594i | \(0.606456\pi\) | |||||||
\(30\) | −4.19909 | −0.766645 | ||||||||
\(31\) | −6.53898 | −1.17444 | −0.587218 | − | 0.809429i | \(-0.699777\pi\) | ||||
−0.587218 | + | 0.809429i | \(0.699777\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.60580 | 0.801767 | ||||||||
\(34\) | 6.19917 | 1.06315 | ||||||||
\(35\) | −17.7487 | −3.00008 | ||||||||
\(36\) | −2.01876 | −0.336460 | ||||||||
\(37\) | 8.77913 | 1.44328 | 0.721640 | − | 0.692268i | \(-0.243389\pi\) | ||||
0.721640 | + | 0.692268i | \(0.243389\pi\) | |||||||
\(38\) | 4.17285 | 0.676925 | ||||||||
\(39\) | 2.85888 | 0.457788 | ||||||||
\(40\) | 4.23904 | 0.670252 | ||||||||
\(41\) | 0.889308 | 0.138887 | 0.0694433 | − | 0.997586i | \(-0.477878\pi\) | ||||
0.0694433 | + | 0.997586i | \(0.477878\pi\) | |||||||
\(42\) | 4.14750 | 0.639973 | ||||||||
\(43\) | 9.47962 | 1.44563 | 0.722814 | − | 0.691042i | \(-0.242848\pi\) | ||||
0.722814 | + | 0.691042i | \(0.242848\pi\) | |||||||
\(44\) | −4.64963 | −0.700958 | ||||||||
\(45\) | −8.55762 | −1.27569 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 3.37309 | 0.492015 | 0.246008 | − | 0.969268i | \(-0.420881\pi\) | ||||
0.246008 | + | 0.969268i | \(0.420881\pi\) | |||||||
\(48\) | −0.990574 | −0.142977 | ||||||||
\(49\) | 10.5307 | 1.50438 | ||||||||
\(50\) | 12.9695 | 1.83416 | ||||||||
\(51\) | −6.14074 | −0.859875 | ||||||||
\(52\) | −2.88609 | −0.400228 | ||||||||
\(53\) | −5.23757 | −0.719435 | −0.359718 | − | 0.933061i | \(-0.617127\pi\) | ||||
−0.359718 | + | 0.933061i | \(0.617127\pi\) | |||||||
\(54\) | 4.97146 | 0.676530 | ||||||||
\(55\) | −19.7100 | −2.65769 | ||||||||
\(56\) | −4.18696 | −0.559506 | ||||||||
\(57\) | −4.13352 | −0.547498 | ||||||||
\(58\) | −3.53526 | −0.464202 | ||||||||
\(59\) | −14.4993 | −1.88764 | −0.943822 | − | 0.330453i | \(-0.892798\pi\) | ||||
−0.943822 | + | 0.330453i | \(0.892798\pi\) | |||||||
\(60\) | −4.19909 | −0.542100 | ||||||||
\(61\) | 5.45134 | 0.697973 | 0.348986 | − | 0.937128i | \(-0.386526\pi\) | ||||
0.348986 | + | 0.937128i | \(0.386526\pi\) | |||||||
\(62\) | −6.53898 | −0.830452 | ||||||||
\(63\) | 8.45248 | 1.06491 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.2342 | −1.51747 | ||||||||
\(66\) | 4.60580 | 0.566935 | ||||||||
\(67\) | 12.4749 | 1.52405 | 0.762027 | − | 0.647545i | \(-0.224204\pi\) | ||||
0.762027 | + | 0.647545i | \(0.224204\pi\) | |||||||
\(68\) | 6.19917 | 0.751760 | ||||||||
\(69\) | −0.990574 | −0.119251 | ||||||||
\(70\) | −17.7487 | −2.12138 | ||||||||
\(71\) | −8.58867 | −1.01929 | −0.509644 | − | 0.860386i | \(-0.670223\pi\) | ||||
−0.509644 | + | 0.860386i | \(0.670223\pi\) | |||||||
\(72\) | −2.01876 | −0.237913 | ||||||||
\(73\) | 5.07471 | 0.593950 | 0.296975 | − | 0.954885i | \(-0.404022\pi\) | ||||
0.296975 | + | 0.954885i | \(0.404022\pi\) | |||||||
\(74\) | 8.77913 | 1.02055 | ||||||||
\(75\) | −12.8472 | −1.48347 | ||||||||
\(76\) | 4.17285 | 0.478659 | ||||||||
\(77\) | 19.4678 | 2.21856 | ||||||||
\(78\) | 2.85888 | 0.323705 | ||||||||
\(79\) | −7.35263 | −0.827235 | −0.413618 | − | 0.910451i | \(-0.635735\pi\) | ||||
−0.413618 | + | 0.910451i | \(0.635735\pi\) | |||||||
\(80\) | 4.23904 | 0.473939 | ||||||||
\(81\) | 1.13169 | 0.125744 | ||||||||
\(82\) | 0.889308 | 0.0982077 | ||||||||
\(83\) | 2.15419 | 0.236453 | 0.118227 | − | 0.992987i | \(-0.462279\pi\) | ||||
0.118227 | + | 0.992987i | \(0.462279\pi\) | |||||||
\(84\) | 4.14750 | 0.452529 | ||||||||
\(85\) | 26.2785 | 2.85031 | ||||||||
\(86\) | 9.47962 | 1.02221 | ||||||||
\(87\) | 3.50193 | 0.375447 | ||||||||
\(88\) | −4.64963 | −0.495652 | ||||||||
\(89\) | 13.5167 | 1.43276 | 0.716381 | − | 0.697709i | \(-0.245797\pi\) | ||||
0.716381 | + | 0.697709i | \(0.245797\pi\) | |||||||
\(90\) | −8.55762 | −0.902053 | ||||||||
\(91\) | 12.0839 | 1.26674 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 6.47735 | 0.671670 | ||||||||
\(94\) | 3.37309 | 0.347907 | ||||||||
\(95\) | 17.6889 | 1.81484 | ||||||||
\(96\) | −0.990574 | −0.101100 | ||||||||
\(97\) | 11.9593 | 1.21428 | 0.607142 | − | 0.794594i | \(-0.292316\pi\) | ||||
0.607142 | + | 0.794594i | \(0.292316\pi\) | |||||||
\(98\) | 10.5307 | 1.06376 | ||||||||
\(99\) | 9.38650 | 0.943379 | ||||||||
\(100\) | 12.9695 | 1.29695 | ||||||||
\(101\) | −6.15687 | −0.612632 | −0.306316 | − | 0.951930i | \(-0.599096\pi\) | ||||
−0.306316 | + | 0.951930i | \(0.599096\pi\) | |||||||
\(102\) | −6.14074 | −0.608024 | ||||||||
\(103\) | 13.1874 | 1.29939 | 0.649695 | − | 0.760195i | \(-0.274897\pi\) | ||||
0.649695 | + | 0.760195i | \(0.274897\pi\) | |||||||
\(104\) | −2.88609 | −0.283004 | ||||||||
\(105\) | 17.5814 | 1.71577 | ||||||||
\(106\) | −5.23757 | −0.508717 | ||||||||
\(107\) | 6.11832 | 0.591481 | 0.295740 | − | 0.955268i | \(-0.404434\pi\) | ||||
0.295740 | + | 0.955268i | \(0.404434\pi\) | |||||||
\(108\) | 4.97146 | 0.478379 | ||||||||
\(109\) | 8.00174 | 0.766427 | 0.383214 | − | 0.923660i | \(-0.374817\pi\) | ||||
0.383214 | + | 0.923660i | \(0.374817\pi\) | |||||||
\(110\) | −19.7100 | −1.87927 | ||||||||
\(111\) | −8.69638 | −0.825424 | ||||||||
\(112\) | −4.18696 | −0.395631 | ||||||||
\(113\) | 0.262047 | 0.0246513 | 0.0123256 | − | 0.999924i | \(-0.496077\pi\) | ||||
0.0123256 | + | 0.999924i | \(0.496077\pi\) | |||||||
\(114\) | −4.13352 | −0.387139 | ||||||||
\(115\) | 4.23904 | 0.395293 | ||||||||
\(116\) | −3.53526 | −0.328240 | ||||||||
\(117\) | 5.82632 | 0.538644 | ||||||||
\(118\) | −14.4993 | −1.33477 | ||||||||
\(119\) | −25.9557 | −2.37935 | ||||||||
\(120\) | −4.19909 | −0.383322 | ||||||||
\(121\) | 10.6191 | 0.965369 | ||||||||
\(122\) | 5.45134 | 0.493541 | ||||||||
\(123\) | −0.880926 | −0.0794304 | ||||||||
\(124\) | −6.53898 | −0.587218 | ||||||||
\(125\) | 33.7830 | 3.02164 | ||||||||
\(126\) | 8.45248 | 0.753007 | ||||||||
\(127\) | 8.67904 | 0.770140 | 0.385070 | − | 0.922887i | \(-0.374177\pi\) | ||||
0.385070 | + | 0.922887i | \(0.374177\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.39027 | −0.826767 | ||||||||
\(130\) | −12.2342 | −1.07301 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 4.60580 | 0.400884 | ||||||||
\(133\) | −17.4716 | −1.51498 | ||||||||
\(134\) | 12.4749 | 1.07767 | ||||||||
\(135\) | 21.0742 | 1.81378 | ||||||||
\(136\) | 6.19917 | 0.531574 | ||||||||
\(137\) | 1.77806 | 0.151910 | 0.0759549 | − | 0.997111i | \(-0.475800\pi\) | ||||
0.0759549 | + | 0.997111i | \(0.475800\pi\) | |||||||
\(138\) | −0.990574 | −0.0843233 | ||||||||
\(139\) | 2.19802 | 0.186433 | 0.0932167 | − | 0.995646i | \(-0.470285\pi\) | ||||
0.0932167 | + | 0.995646i | \(0.470285\pi\) | |||||||
\(140\) | −17.7487 | −1.50004 | ||||||||
\(141\) | −3.34129 | −0.281388 | ||||||||
\(142\) | −8.58867 | −0.720745 | ||||||||
\(143\) | 13.4192 | 1.12217 | ||||||||
\(144\) | −2.01876 | −0.168230 | ||||||||
\(145\) | −14.9861 | −1.24453 | ||||||||
\(146\) | 5.07471 | 0.419986 | ||||||||
\(147\) | −10.4314 | −0.860367 | ||||||||
\(148\) | 8.77913 | 0.721640 | ||||||||
\(149\) | 0.185406 | 0.0151891 | 0.00759454 | − | 0.999971i | \(-0.497583\pi\) | ||||
0.00759454 | + | 0.999971i | \(0.497583\pi\) | |||||||
\(150\) | −12.8472 | −1.04897 | ||||||||
\(151\) | 11.8553 | 0.964771 | 0.482385 | − | 0.875959i | \(-0.339771\pi\) | ||||
0.482385 | + | 0.875959i | \(0.339771\pi\) | |||||||
\(152\) | 4.17285 | 0.338463 | ||||||||
\(153\) | −12.5147 | −1.01175 | ||||||||
\(154\) | 19.4678 | 1.56876 | ||||||||
\(155\) | −27.7190 | −2.22645 | ||||||||
\(156\) | 2.85888 | 0.228894 | ||||||||
\(157\) | −4.19281 | −0.334622 | −0.167311 | − | 0.985904i | \(-0.553508\pi\) | ||||
−0.167311 | + | 0.985904i | \(0.553508\pi\) | |||||||
\(158\) | −7.35263 | −0.584944 | ||||||||
\(159\) | 5.18820 | 0.411451 | ||||||||
\(160\) | 4.23904 | 0.335126 | ||||||||
\(161\) | −4.18696 | −0.329979 | ||||||||
\(162\) | 1.13169 | 0.0889141 | ||||||||
\(163\) | 7.63248 | 0.597822 | 0.298911 | − | 0.954281i | \(-0.403377\pi\) | ||||
0.298911 | + | 0.954281i | \(0.403377\pi\) | |||||||
\(164\) | 0.889308 | 0.0694433 | ||||||||
\(165\) | 19.5242 | 1.51996 | ||||||||
\(166\) | 2.15419 | 0.167198 | ||||||||
\(167\) | 8.43220 | 0.652503 | 0.326252 | − | 0.945283i | \(-0.394214\pi\) | ||||
0.326252 | + | 0.945283i | \(0.394214\pi\) | |||||||
\(168\) | 4.14750 | 0.319986 | ||||||||
\(169\) | −4.67050 | −0.359270 | ||||||||
\(170\) | 26.2785 | 2.01547 | ||||||||
\(171\) | −8.42399 | −0.644199 | ||||||||
\(172\) | 9.47962 | 0.722814 | ||||||||
\(173\) | −15.3308 | −1.16558 | −0.582789 | − | 0.812624i | \(-0.698039\pi\) | ||||
−0.582789 | + | 0.812624i | \(0.698039\pi\) | |||||||
\(174\) | 3.50193 | 0.265481 | ||||||||
\(175\) | −54.3027 | −4.10490 | ||||||||
\(176\) | −4.64963 | −0.350479 | ||||||||
\(177\) | 14.3626 | 1.07956 | ||||||||
\(178\) | 13.5167 | 1.01312 | ||||||||
\(179\) | −3.86562 | −0.288930 | −0.144465 | − | 0.989510i | \(-0.546146\pi\) | ||||
−0.144465 | + | 0.989510i | \(0.546146\pi\) | |||||||
\(180\) | −8.55762 | −0.637847 | ||||||||
\(181\) | 22.9661 | 1.70706 | 0.853530 | − | 0.521043i | \(-0.174457\pi\) | ||||
0.853530 | + | 0.521043i | \(0.174457\pi\) | |||||||
\(182\) | 12.0839 | 0.895721 | ||||||||
\(183\) | −5.39996 | −0.399176 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 37.2151 | 2.73611 | ||||||||
\(186\) | 6.47735 | 0.474942 | ||||||||
\(187\) | −28.8238 | −2.10781 | ||||||||
\(188\) | 3.37309 | 0.246008 | ||||||||
\(189\) | −20.8153 | −1.51409 | ||||||||
\(190\) | 17.6889 | 1.28329 | ||||||||
\(191\) | 7.94271 | 0.574714 | 0.287357 | − | 0.957824i | \(-0.407223\pi\) | ||||
0.287357 | + | 0.957824i | \(0.407223\pi\) | |||||||
\(192\) | −0.990574 | −0.0714885 | ||||||||
\(193\) | −13.3411 | −0.960311 | −0.480155 | − | 0.877183i | \(-0.659420\pi\) | ||||
−0.480155 | + | 0.877183i | \(0.659420\pi\) | |||||||
\(194\) | 11.9593 | 0.858628 | ||||||||
\(195\) | 12.1189 | 0.867854 | ||||||||
\(196\) | 10.5307 | 0.752189 | ||||||||
\(197\) | 11.8119 | 0.841562 | 0.420781 | − | 0.907162i | \(-0.361756\pi\) | ||||
0.420781 | + | 0.907162i | \(0.361756\pi\) | |||||||
\(198\) | 9.38650 | 0.667069 | ||||||||
\(199\) | 19.4517 | 1.37890 | 0.689449 | − | 0.724334i | \(-0.257853\pi\) | ||||
0.689449 | + | 0.724334i | \(0.257853\pi\) | |||||||
\(200\) | 12.9695 | 0.917081 | ||||||||
\(201\) | −12.3573 | −0.871619 | ||||||||
\(202\) | −6.15687 | −0.433196 | ||||||||
\(203\) | 14.8020 | 1.03890 | ||||||||
\(204\) | −6.14074 | −0.429938 | ||||||||
\(205\) | 3.76982 | 0.263295 | ||||||||
\(206\) | 13.1874 | 0.918807 | ||||||||
\(207\) | −2.01876 | −0.140314 | ||||||||
\(208\) | −2.88609 | −0.200114 | ||||||||
\(209\) | −19.4022 | −1.34208 | ||||||||
\(210\) | 17.5814 | 1.21323 | ||||||||
\(211\) | −10.1748 | −0.700462 | −0.350231 | − | 0.936663i | \(-0.613897\pi\) | ||||
−0.350231 | + | 0.936663i | \(0.613897\pi\) | |||||||
\(212\) | −5.23757 | −0.359718 | ||||||||
\(213\) | 8.50771 | 0.582939 | ||||||||
\(214\) | 6.11832 | 0.418240 | ||||||||
\(215\) | 40.1845 | 2.74056 | ||||||||
\(216\) | 4.97146 | 0.338265 | ||||||||
\(217\) | 27.3785 | 1.85857 | ||||||||
\(218\) | 8.00174 | 0.541946 | ||||||||
\(219\) | −5.02688 | −0.339685 | ||||||||
\(220\) | −19.7100 | −1.32885 | ||||||||
\(221\) | −17.8913 | −1.20350 | ||||||||
\(222\) | −8.69638 | −0.583663 | ||||||||
\(223\) | 8.12936 | 0.544382 | 0.272191 | − | 0.962243i | \(-0.412252\pi\) | ||||
0.272191 | + | 0.962243i | \(0.412252\pi\) | |||||||
\(224\) | −4.18696 | −0.279753 | ||||||||
\(225\) | −26.1823 | −1.74549 | ||||||||
\(226\) | 0.262047 | 0.0174311 | ||||||||
\(227\) | 6.67700 | 0.443168 | 0.221584 | − | 0.975141i | \(-0.428877\pi\) | ||||
0.221584 | + | 0.975141i | \(0.428877\pi\) | |||||||
\(228\) | −4.13352 | −0.273749 | ||||||||
\(229\) | −21.8855 | −1.44623 | −0.723116 | − | 0.690727i | \(-0.757291\pi\) | ||||
−0.723116 | + | 0.690727i | \(0.757291\pi\) | |||||||
\(230\) | 4.23904 | 0.279514 | ||||||||
\(231\) | −19.2843 | −1.26882 | ||||||||
\(232\) | −3.53526 | −0.232101 | ||||||||
\(233\) | −13.8846 | −0.909611 | −0.454805 | − | 0.890591i | \(-0.650291\pi\) | ||||
−0.454805 | + | 0.890591i | \(0.650291\pi\) | |||||||
\(234\) | 5.82632 | 0.380879 | ||||||||
\(235\) | 14.2987 | 0.932742 | ||||||||
\(236\) | −14.4993 | −0.943822 | ||||||||
\(237\) | 7.28332 | 0.473103 | ||||||||
\(238\) | −25.9557 | −1.68246 | ||||||||
\(239\) | −17.2121 | −1.11336 | −0.556679 | − | 0.830727i | \(-0.687925\pi\) | ||||
−0.556679 | + | 0.830727i | \(0.687925\pi\) | |||||||
\(240\) | −4.19909 | −0.271050 | ||||||||
\(241\) | 24.4972 | 1.57800 | 0.789001 | − | 0.614392i | \(-0.210599\pi\) | ||||
0.789001 | + | 0.614392i | \(0.210599\pi\) | |||||||
\(242\) | 10.6191 | 0.682619 | ||||||||
\(243\) | −16.0354 | −1.02867 | ||||||||
\(244\) | 5.45134 | 0.348986 | ||||||||
\(245\) | 44.6399 | 2.85194 | ||||||||
\(246\) | −0.880926 | −0.0561658 | ||||||||
\(247\) | −12.0432 | −0.766291 | ||||||||
\(248\) | −6.53898 | −0.415226 | ||||||||
\(249\) | −2.13389 | −0.135230 | ||||||||
\(250\) | 33.7830 | 2.13662 | ||||||||
\(251\) | −22.3581 | −1.41123 | −0.705616 | − | 0.708594i | \(-0.749330\pi\) | ||||
−0.705616 | + | 0.708594i | \(0.749330\pi\) | |||||||
\(252\) | 8.45248 | 0.532456 | ||||||||
\(253\) | −4.64963 | −0.292320 | ||||||||
\(254\) | 8.67904 | 0.544572 | ||||||||
\(255\) | −26.0308 | −1.63011 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.722583 | −0.0450735 | −0.0225367 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225367 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(258\) | −9.39027 | −0.584612 | ||||||||
\(259\) | −36.7579 | −2.28402 | ||||||||
\(260\) | −12.2342 | −0.758736 | ||||||||
\(261\) | 7.13685 | 0.441760 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −9.82028 | −0.605544 | −0.302772 | − | 0.953063i | \(-0.597912\pi\) | ||||
−0.302772 | + | 0.953063i | \(0.597912\pi\) | |||||||
\(264\) | 4.60580 | 0.283468 | ||||||||
\(265\) | −22.2023 | −1.36387 | ||||||||
\(266\) | −17.4716 | −1.07125 | ||||||||
\(267\) | −13.3893 | −0.819409 | ||||||||
\(268\) | 12.4749 | 0.762027 | ||||||||
\(269\) | 2.99155 | 0.182398 | 0.0911991 | − | 0.995833i | \(-0.470930\pi\) | ||||
0.0911991 | + | 0.995833i | \(0.470930\pi\) | |||||||
\(270\) | 21.0742 | 1.28254 | ||||||||
\(271\) | 2.70639 | 0.164401 | 0.0822007 | − | 0.996616i | \(-0.473805\pi\) | ||||
0.0822007 | + | 0.996616i | \(0.473805\pi\) | |||||||
\(272\) | 6.19917 | 0.375880 | ||||||||
\(273\) | −11.9700 | −0.724459 | ||||||||
\(274\) | 1.77806 | 0.107416 | ||||||||
\(275\) | −60.3033 | −3.63643 | ||||||||
\(276\) | −0.990574 | −0.0596256 | ||||||||
\(277\) | 4.32473 | 0.259848 | 0.129924 | − | 0.991524i | \(-0.458527\pi\) | ||||
0.129924 | + | 0.991524i | \(0.458527\pi\) | |||||||
\(278\) | 2.19802 | 0.131828 | ||||||||
\(279\) | 13.2007 | 0.790302 | ||||||||
\(280\) | −17.7487 | −1.06069 | ||||||||
\(281\) | −26.3102 | −1.56954 | −0.784768 | − | 0.619790i | \(-0.787218\pi\) | ||||
−0.784768 | + | 0.619790i | \(0.787218\pi\) | |||||||
\(282\) | −3.34129 | −0.198971 | ||||||||
\(283\) | −18.0689 | −1.07409 | −0.537043 | − | 0.843555i | \(-0.680459\pi\) | ||||
−0.537043 | + | 0.843555i | \(0.680459\pi\) | |||||||
\(284\) | −8.58867 | −0.509644 | ||||||||
\(285\) | −17.5221 | −1.03792 | ||||||||
\(286\) | 13.4192 | 0.793496 | ||||||||
\(287\) | −3.72350 | −0.219791 | ||||||||
\(288\) | −2.01876 | −0.118957 | ||||||||
\(289\) | 21.4297 | 1.26057 | ||||||||
\(290\) | −14.9861 | −0.880015 | ||||||||
\(291\) | −11.8466 | −0.694459 | ||||||||
\(292\) | 5.07471 | 0.296975 | ||||||||
\(293\) | 31.1941 | 1.82238 | 0.911191 | − | 0.411985i | \(-0.135164\pi\) | ||||
0.911191 | + | 0.411985i | \(0.135164\pi\) | |||||||
\(294\) | −10.4314 | −0.608371 | ||||||||
\(295\) | −61.4630 | −3.57852 | ||||||||
\(296\) | 8.77913 | 0.510277 | ||||||||
\(297\) | −23.1154 | −1.34129 | ||||||||
\(298\) | 0.185406 | 0.0107403 | ||||||||
\(299\) | −2.88609 | −0.166907 | ||||||||
\(300\) | −12.8472 | −0.741735 | ||||||||
\(301\) | −39.6908 | −2.28774 | ||||||||
\(302\) | 11.8553 | 0.682196 | ||||||||
\(303\) | 6.09884 | 0.350369 | ||||||||
\(304\) | 4.17285 | 0.239329 | ||||||||
\(305\) | 23.1085 | 1.32319 | ||||||||
\(306\) | −12.5147 | −0.715415 | ||||||||
\(307\) | 26.0459 | 1.48652 | 0.743258 | − | 0.669005i | \(-0.233280\pi\) | ||||
0.743258 | + | 0.669005i | \(0.233280\pi\) | |||||||
\(308\) | 19.4678 | 1.10928 | ||||||||
\(309\) | −13.0631 | −0.743132 | ||||||||
\(310\) | −27.7190 | −1.57433 | ||||||||
\(311\) | 15.2963 | 0.867371 | 0.433685 | − | 0.901064i | \(-0.357213\pi\) | ||||
0.433685 | + | 0.901064i | \(0.357213\pi\) | |||||||
\(312\) | 2.85888 | 0.161852 | ||||||||
\(313\) | −4.01954 | −0.227198 | −0.113599 | − | 0.993527i | \(-0.536238\pi\) | ||||
−0.113599 | + | 0.993527i | \(0.536238\pi\) | |||||||
\(314\) | −4.19281 | −0.236614 | ||||||||
\(315\) | 35.8304 | 2.01882 | ||||||||
\(316\) | −7.35263 | −0.413618 | ||||||||
\(317\) | 10.9815 | 0.616783 | 0.308392 | − | 0.951260i | \(-0.400209\pi\) | ||||
0.308392 | + | 0.951260i | \(0.400209\pi\) | |||||||
\(318\) | 5.18820 | 0.290940 | ||||||||
\(319\) | 16.4376 | 0.920331 | ||||||||
\(320\) | 4.23904 | 0.236970 | ||||||||
\(321\) | −6.06065 | −0.338273 | ||||||||
\(322\) | −4.18696 | −0.233330 | ||||||||
\(323\) | 25.8682 | 1.43934 | ||||||||
\(324\) | 1.13169 | 0.0628718 | ||||||||
\(325\) | −37.4311 | −2.07630 | ||||||||
\(326\) | 7.63248 | 0.422724 | ||||||||
\(327\) | −7.92631 | −0.438326 | ||||||||
\(328\) | 0.889308 | 0.0491038 | ||||||||
\(329\) | −14.1230 | −0.778626 | ||||||||
\(330\) | 19.5242 | 1.07477 | ||||||||
\(331\) | 8.54084 | 0.469447 | 0.234723 | − | 0.972062i | \(-0.424582\pi\) | ||||
0.234723 | + | 0.972062i | \(0.424582\pi\) | |||||||
\(332\) | 2.15419 | 0.118227 | ||||||||
\(333\) | −17.7230 | −0.971214 | ||||||||
\(334\) | 8.43220 | 0.461389 | ||||||||
\(335\) | 52.8817 | 2.88924 | ||||||||
\(336\) | 4.14750 | 0.226264 | ||||||||
\(337\) | 32.5556 | 1.77342 | 0.886708 | − | 0.462329i | \(-0.152986\pi\) | ||||
0.886708 | + | 0.462329i | \(0.152986\pi\) | |||||||
\(338\) | −4.67050 | −0.254042 | ||||||||
\(339\) | −0.259577 | −0.0140983 | ||||||||
\(340\) | 26.2785 | 1.42515 | ||||||||
\(341\) | 30.4038 | 1.64646 | ||||||||
\(342\) | −8.42399 | −0.455517 | ||||||||
\(343\) | −14.7827 | −0.798191 | ||||||||
\(344\) | 9.47962 | 0.511107 | ||||||||
\(345\) | −4.19909 | −0.226071 | ||||||||
\(346\) | −15.3308 | −0.824188 | ||||||||
\(347\) | −19.9106 | −1.06886 | −0.534428 | − | 0.845214i | \(-0.679473\pi\) | ||||
−0.534428 | + | 0.845214i | \(0.679473\pi\) | |||||||
\(348\) | 3.50193 | 0.187723 | ||||||||
\(349\) | 3.41373 | 0.182733 | 0.0913663 | − | 0.995817i | \(-0.470877\pi\) | ||||
0.0913663 | + | 0.995817i | \(0.470877\pi\) | |||||||
\(350\) | −54.3027 | −2.90260 | ||||||||
\(351\) | −14.3481 | −0.765843 | ||||||||
\(352\) | −4.64963 | −0.247826 | ||||||||
\(353\) | −16.9942 | −0.904508 | −0.452254 | − | 0.891889i | \(-0.649380\pi\) | ||||
−0.452254 | + | 0.891889i | \(0.649380\pi\) | |||||||
\(354\) | 14.3626 | 0.763364 | ||||||||
\(355\) | −36.4077 | −1.93232 | ||||||||
\(356\) | 13.5167 | 0.716381 | ||||||||
\(357\) | 25.7110 | 1.36077 | ||||||||
\(358\) | −3.86562 | −0.204304 | ||||||||
\(359\) | 18.8551 | 0.995132 | 0.497566 | − | 0.867426i | \(-0.334227\pi\) | ||||
0.497566 | + | 0.867426i | \(0.334227\pi\) | |||||||
\(360\) | −8.55762 | −0.451026 | ||||||||
\(361\) | −1.58734 | −0.0835441 | ||||||||
\(362\) | 22.9661 | 1.20707 | ||||||||
\(363\) | −10.5190 | −0.552102 | ||||||||
\(364\) | 12.0839 | 0.633370 | ||||||||
\(365\) | 21.5119 | 1.12599 | ||||||||
\(366\) | −5.39996 | −0.282260 | ||||||||
\(367\) | −21.3435 | −1.11412 | −0.557062 | − | 0.830471i | \(-0.688071\pi\) | ||||
−0.557062 | + | 0.830471i | \(0.688071\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.79530 | −0.0934597 | ||||||||
\(370\) | 37.2151 | 1.93472 | ||||||||
\(371\) | 21.9295 | 1.13852 | ||||||||
\(372\) | 6.47735 | 0.335835 | ||||||||
\(373\) | −16.3289 | −0.845481 | −0.422740 | − | 0.906251i | \(-0.638932\pi\) | ||||
−0.422740 | + | 0.906251i | \(0.638932\pi\) | |||||||
\(374\) | −28.8238 | −1.49045 | ||||||||
\(375\) | −33.4645 | −1.72810 | ||||||||
\(376\) | 3.37309 | 0.173954 | ||||||||
\(377\) | 10.2031 | 0.525484 | ||||||||
\(378\) | −20.8153 | −1.07062 | ||||||||
\(379\) | −14.7023 | −0.755204 | −0.377602 | − | 0.925968i | \(-0.623251\pi\) | ||||
−0.377602 | + | 0.925968i | \(0.623251\pi\) | |||||||
\(380\) | 17.6889 | 0.907420 | ||||||||
\(381\) | −8.59724 | −0.440450 | ||||||||
\(382\) | 7.94271 | 0.406384 | ||||||||
\(383\) | 7.52661 | 0.384592 | 0.192296 | − | 0.981337i | \(-0.438407\pi\) | ||||
0.192296 | + | 0.981337i | \(0.438407\pi\) | |||||||
\(384\) | −0.990574 | −0.0505500 | ||||||||
\(385\) | 82.5249 | 4.20586 | ||||||||
\(386\) | −13.3411 | −0.679042 | ||||||||
\(387\) | −19.1371 | −0.972794 | ||||||||
\(388\) | 11.9593 | 0.607142 | ||||||||
\(389\) | 18.3954 | 0.932682 | 0.466341 | − | 0.884605i | \(-0.345572\pi\) | ||||
0.466341 | + | 0.884605i | \(0.345572\pi\) | |||||||
\(390\) | 12.1189 | 0.613666 | ||||||||
\(391\) | 6.19917 | 0.313505 | ||||||||
\(392\) | 10.5307 | 0.531878 | ||||||||
\(393\) | −0.990574 | −0.0499679 | ||||||||
\(394\) | 11.8119 | 0.595074 | ||||||||
\(395\) | −31.1681 | −1.56824 | ||||||||
\(396\) | 9.38650 | 0.471689 | ||||||||
\(397\) | −35.9896 | −1.80627 | −0.903133 | − | 0.429360i | \(-0.858739\pi\) | ||||
−0.903133 | + | 0.429360i | \(0.858739\pi\) | |||||||
\(398\) | 19.4517 | 0.975028 | ||||||||
\(399\) | 17.3069 | 0.866427 | ||||||||
\(400\) | 12.9695 | 0.648474 | ||||||||
\(401\) | −29.8552 | −1.49090 | −0.745449 | − | 0.666563i | \(-0.767765\pi\) | ||||
−0.745449 | + | 0.666563i | \(0.767765\pi\) | |||||||
\(402\) | −12.3573 | −0.616328 | ||||||||
\(403\) | 18.8721 | 0.940085 | ||||||||
\(404\) | −6.15687 | −0.306316 | ||||||||
\(405\) | 4.79729 | 0.238379 | ||||||||
\(406\) | 14.8020 | 0.734610 | ||||||||
\(407\) | −40.8197 | −2.02336 | ||||||||
\(408\) | −6.14074 | −0.304012 | ||||||||
\(409\) | −0.985581 | −0.0487338 | −0.0243669 | − | 0.999703i | \(-0.507757\pi\) | ||||
−0.0243669 | + | 0.999703i | \(0.507757\pi\) | |||||||
\(410\) | 3.76982 | 0.186178 | ||||||||
\(411\) | −1.76130 | −0.0868785 | ||||||||
\(412\) | 13.1874 | 0.649695 | ||||||||
\(413\) | 60.7079 | 2.98724 | ||||||||
\(414\) | −2.01876 | −0.0992168 | ||||||||
\(415\) | 9.13171 | 0.448258 | ||||||||
\(416\) | −2.88609 | −0.141502 | ||||||||
\(417\) | −2.17730 | −0.106623 | ||||||||
\(418\) | −19.4022 | −0.948993 | ||||||||
\(419\) | −3.91510 | −0.191265 | −0.0956326 | − | 0.995417i | \(-0.530487\pi\) | ||||
−0.0956326 | + | 0.995417i | \(0.530487\pi\) | |||||||
\(420\) | 17.5814 | 0.857885 | ||||||||
\(421\) | 12.1728 | 0.593264 | 0.296632 | − | 0.954992i | \(-0.404137\pi\) | ||||
0.296632 | + | 0.954992i | \(0.404137\pi\) | |||||||
\(422\) | −10.1748 | −0.495302 | ||||||||
\(423\) | −6.80947 | −0.331088 | ||||||||
\(424\) | −5.23757 | −0.254359 | ||||||||
\(425\) | 80.4000 | 3.89997 | ||||||||
\(426\) | 8.50771 | 0.412200 | ||||||||
\(427\) | −22.8246 | −1.10456 | ||||||||
\(428\) | 6.11832 | 0.295740 | ||||||||
\(429\) | −13.2927 | −0.641780 | ||||||||
\(430\) | 40.1845 | 1.93787 | ||||||||
\(431\) | 29.0274 | 1.39820 | 0.699101 | − | 0.715023i | \(-0.253584\pi\) | ||||
0.699101 | + | 0.715023i | \(0.253584\pi\) | |||||||
\(432\) | 4.97146 | 0.239189 | ||||||||
\(433\) | −22.4980 | −1.08118 | −0.540592 | − | 0.841285i | \(-0.681800\pi\) | ||||
−0.540592 | + | 0.841285i | \(0.681800\pi\) | |||||||
\(434\) | 27.3785 | 1.31421 | ||||||||
\(435\) | 14.8449 | 0.711756 | ||||||||
\(436\) | 8.00174 | 0.383214 | ||||||||
\(437\) | 4.17285 | 0.199614 | ||||||||
\(438\) | −5.02688 | −0.240194 | ||||||||
\(439\) | 36.4289 | 1.73865 | 0.869327 | − | 0.494237i | \(-0.164552\pi\) | ||||
0.869327 | + | 0.494237i | \(0.164552\pi\) | |||||||
\(440\) | −19.7100 | −0.939636 | ||||||||
\(441\) | −21.2589 | −1.01233 | ||||||||
\(442\) | −17.8913 | −0.851004 | ||||||||
\(443\) | 7.15995 | 0.340180 | 0.170090 | − | 0.985429i | \(-0.445594\pi\) | ||||
0.170090 | + | 0.985429i | \(0.445594\pi\) | |||||||
\(444\) | −8.69638 | −0.412712 | ||||||||
\(445\) | 57.2977 | 2.71617 | ||||||||
\(446\) | 8.12936 | 0.384936 | ||||||||
\(447\) | −0.183659 | −0.00868676 | ||||||||
\(448\) | −4.18696 | −0.197815 | ||||||||
\(449\) | −25.0404 | −1.18173 | −0.590866 | − | 0.806770i | \(-0.701214\pi\) | ||||
−0.590866 | + | 0.806770i | \(0.701214\pi\) | |||||||
\(450\) | −26.1823 | −1.23425 | ||||||||
\(451\) | −4.13495 | −0.194707 | ||||||||
\(452\) | 0.262047 | 0.0123256 | ||||||||
\(453\) | −11.7436 | −0.551760 | ||||||||
\(454\) | 6.67700 | 0.313367 | ||||||||
\(455\) | 51.2243 | 2.40143 | ||||||||
\(456\) | −4.13352 | −0.193570 | ||||||||
\(457\) | −6.46099 | −0.302233 | −0.151116 | − | 0.988516i | \(-0.548287\pi\) | ||||
−0.151116 | + | 0.988516i | \(0.548287\pi\) | |||||||
\(458\) | −21.8855 | −1.02264 | ||||||||
\(459\) | 30.8189 | 1.43850 | ||||||||
\(460\) | 4.23904 | 0.197646 | ||||||||
\(461\) | 8.90625 | 0.414806 | 0.207403 | − | 0.978256i | \(-0.433499\pi\) | ||||
0.207403 | + | 0.978256i | \(0.433499\pi\) | |||||||
\(462\) | −19.2843 | −0.897188 | ||||||||
\(463\) | 0.254866 | 0.0118446 | 0.00592232 | − | 0.999982i | \(-0.498115\pi\) | ||||
0.00592232 | + | 0.999982i | \(0.498115\pi\) | |||||||
\(464\) | −3.53526 | −0.164120 | ||||||||
\(465\) | 27.4577 | 1.27332 | ||||||||
\(466\) | −13.8846 | −0.643192 | ||||||||
\(467\) | 1.67439 | 0.0774815 | 0.0387407 | − | 0.999249i | \(-0.487665\pi\) | ||||
0.0387407 | + | 0.999249i | \(0.487665\pi\) | |||||||
\(468\) | 5.82632 | 0.269322 | ||||||||
\(469\) | −52.2320 | −2.41185 | ||||||||
\(470\) | 14.2987 | 0.659548 | ||||||||
\(471\) | 4.15328 | 0.191373 | ||||||||
\(472\) | −14.4993 | −0.667383 | ||||||||
\(473\) | −44.0767 | −2.02665 | ||||||||
\(474\) | 7.28332 | 0.334534 | ||||||||
\(475\) | 54.1197 | 2.48318 | ||||||||
\(476\) | −25.9557 | −1.18968 | ||||||||
\(477\) | 10.5734 | 0.484123 | ||||||||
\(478\) | −17.2121 | −0.787264 | ||||||||
\(479\) | 16.1791 | 0.739244 | 0.369622 | − | 0.929182i | \(-0.379487\pi\) | ||||
0.369622 | + | 0.929182i | \(0.379487\pi\) | |||||||
\(480\) | −4.19909 | −0.191661 | ||||||||
\(481\) | −25.3373 | −1.15528 | ||||||||
\(482\) | 24.4972 | 1.11582 | ||||||||
\(483\) | 4.14750 | 0.188718 | ||||||||
\(484\) | 10.6191 | 0.482684 | ||||||||
\(485\) | 50.6960 | 2.30199 | ||||||||
\(486\) | −16.0354 | −0.727380 | ||||||||
\(487\) | −36.3583 | −1.64755 | −0.823775 | − | 0.566917i | \(-0.808136\pi\) | ||||
−0.823775 | + | 0.566917i | \(0.808136\pi\) | |||||||
\(488\) | 5.45134 | 0.246771 | ||||||||
\(489\) | −7.56054 | −0.341899 | ||||||||
\(490\) | 44.6399 | 2.01662 | ||||||||
\(491\) | −2.02395 | −0.0913395 | −0.0456698 | − | 0.998957i | \(-0.514542\pi\) | ||||
−0.0456698 | + | 0.998957i | \(0.514542\pi\) | |||||||
\(492\) | −0.880926 | −0.0397152 | ||||||||
\(493\) | −21.9157 | −0.987032 | ||||||||
\(494\) | −12.0432 | −0.541849 | ||||||||
\(495\) | 39.7898 | 1.78842 | ||||||||
\(496\) | −6.53898 | −0.293609 | ||||||||
\(497\) | 35.9604 | 1.61305 | ||||||||
\(498\) | −2.13389 | −0.0956217 | ||||||||
\(499\) | 3.92126 | 0.175540 | 0.0877699 | − | 0.996141i | \(-0.472026\pi\) | ||||
0.0877699 | + | 0.996141i | \(0.472026\pi\) | |||||||
\(500\) | 33.7830 | 1.51082 | ||||||||
\(501\) | −8.35272 | −0.373172 | ||||||||
\(502\) | −22.3581 | −0.997892 | ||||||||
\(503\) | 7.59484 | 0.338637 | 0.169319 | − | 0.985561i | \(-0.445843\pi\) | ||||
0.169319 | + | 0.985561i | \(0.445843\pi\) | |||||||
\(504\) | 8.45248 | 0.376504 | ||||||||
\(505\) | −26.0992 | −1.16140 | ||||||||
\(506\) | −4.64963 | −0.206701 | ||||||||
\(507\) | 4.62648 | 0.205469 | ||||||||
\(508\) | 8.67904 | 0.385070 | ||||||||
\(509\) | −38.3098 | −1.69805 | −0.849026 | − | 0.528350i | \(-0.822811\pi\) | ||||
−0.849026 | + | 0.528350i | \(0.822811\pi\) | |||||||
\(510\) | −26.0308 | −1.15267 | ||||||||
\(511\) | −21.2476 | −0.939940 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 20.7451 | 0.915920 | ||||||||
\(514\) | −0.722583 | −0.0318717 | ||||||||
\(515\) | 55.9018 | 2.46333 | ||||||||
\(516\) | −9.39027 | −0.413383 | ||||||||
\(517\) | −15.6836 | −0.689764 | ||||||||
\(518\) | −36.7579 | −1.61505 | ||||||||
\(519\) | 15.1863 | 0.666604 | ||||||||
\(520\) | −12.2342 | −0.536507 | ||||||||
\(521\) | 8.63269 | 0.378205 | 0.189102 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189102 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(522\) | 7.13685 | 0.312371 | ||||||||
\(523\) | −7.44523 | −0.325557 | −0.162779 | − | 0.986663i | \(-0.552046\pi\) | ||||
−0.162779 | + | 0.986663i | \(0.552046\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 53.7909 | 2.34763 | ||||||||
\(526\) | −9.82028 | −0.428184 | ||||||||
\(527\) | −40.5363 | −1.76579 | ||||||||
\(528\) | 4.60580 | 0.200442 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −22.2023 | −0.964405 | ||||||||
\(531\) | 29.2706 | 1.27024 | ||||||||
\(532\) | −17.4716 | −0.757488 | ||||||||
\(533\) | −2.56662 | −0.111173 | ||||||||
\(534\) | −13.3893 | −0.579410 | ||||||||
\(535\) | 25.9358 | 1.12130 | ||||||||
\(536\) | 12.4749 | 0.538834 | ||||||||
\(537\) | 3.82918 | 0.165241 | ||||||||
\(538\) | 2.99155 | 0.128975 | ||||||||
\(539\) | −48.9636 | −2.10901 | ||||||||
\(540\) | 21.0742 | 0.906890 | ||||||||
\(541\) | −12.2464 | −0.526515 | −0.263257 | − | 0.964726i | \(-0.584797\pi\) | ||||
−0.263257 | + | 0.964726i | \(0.584797\pi\) | |||||||
\(542\) | 2.70639 | 0.116249 | ||||||||
\(543\) | −22.7497 | −0.976282 | ||||||||
\(544\) | 6.19917 | 0.265787 | ||||||||
\(545\) | 33.9197 | 1.45296 | ||||||||
\(546\) | −11.9700 | −0.512270 | ||||||||
\(547\) | −23.8729 | −1.02073 | −0.510366 | − | 0.859957i | \(-0.670490\pi\) | ||||
−0.510366 | + | 0.859957i | \(0.670490\pi\) | |||||||
\(548\) | 1.77806 | 0.0759549 | ||||||||
\(549\) | −11.0050 | −0.469680 | ||||||||
\(550\) | −60.3033 | −2.57134 | ||||||||
\(551\) | −14.7521 | −0.628460 | ||||||||
\(552\) | −0.990574 | −0.0421616 | ||||||||
\(553\) | 30.7852 | 1.30912 | ||||||||
\(554\) | 4.32473 | 0.183740 | ||||||||
\(555\) | −36.8643 | −1.56480 | ||||||||
\(556\) | 2.19802 | 0.0932167 | ||||||||
\(557\) | −13.8877 | −0.588441 | −0.294220 | − | 0.955738i | \(-0.595060\pi\) | ||||
−0.294220 | + | 0.955738i | \(0.595060\pi\) | |||||||
\(558\) | 13.2007 | 0.558828 | ||||||||
\(559\) | −27.3590 | −1.15716 | ||||||||
\(560\) | −17.7487 | −0.750020 | ||||||||
\(561\) | 28.5521 | 1.20547 | ||||||||
\(562\) | −26.3102 | −1.10983 | ||||||||
\(563\) | −0.309278 | −0.0130345 | −0.00651726 | − | 0.999979i | \(-0.502075\pi\) | ||||
−0.00651726 | + | 0.999979i | \(0.502075\pi\) | |||||||
\(564\) | −3.34129 | −0.140694 | ||||||||
\(565\) | 1.11083 | 0.0467328 | ||||||||
\(566\) | −18.0689 | −0.759494 | ||||||||
\(567\) | −4.73835 | −0.198992 | ||||||||
\(568\) | −8.58867 | −0.360372 | ||||||||
\(569\) | −22.8905 | −0.959621 | −0.479811 | − | 0.877372i | \(-0.659295\pi\) | ||||
−0.479811 | + | 0.877372i | \(0.659295\pi\) | |||||||
\(570\) | −17.5221 | −0.733922 | ||||||||
\(571\) | 10.2796 | 0.430187 | 0.215094 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215094 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(572\) | 13.4192 | 0.561086 | ||||||||
\(573\) | −7.86784 | −0.328684 | ||||||||
\(574\) | −3.72350 | −0.155416 | ||||||||
\(575\) | 12.9695 | 0.540865 | ||||||||
\(576\) | −2.01876 | −0.0841151 | ||||||||
\(577\) | 27.5574 | 1.14723 | 0.573614 | − | 0.819126i | \(-0.305541\pi\) | ||||
0.573614 | + | 0.819126i | \(0.305541\pi\) | |||||||
\(578\) | 21.4297 | 0.891358 | ||||||||
\(579\) | 13.2153 | 0.549210 | ||||||||
\(580\) | −14.9861 | −0.622264 | ||||||||
\(581\) | −9.01952 | −0.374193 | ||||||||
\(582\) | −11.8466 | −0.491056 | ||||||||
\(583\) | 24.3527 | 1.00859 | ||||||||
\(584\) | 5.07471 | 0.209993 | ||||||||
\(585\) | 24.6980 | 1.02114 | ||||||||
\(586\) | 31.1941 | 1.28862 | ||||||||
\(587\) | −26.2100 | −1.08180 | −0.540901 | − | 0.841086i | \(-0.681917\pi\) | ||||
−0.540901 | + | 0.841086i | \(0.681917\pi\) | |||||||
\(588\) | −10.4314 | −0.430183 | ||||||||
\(589\) | −27.2862 | −1.12431 | ||||||||
\(590\) | −61.4630 | −2.53039 | ||||||||
\(591\) | −11.7005 | −0.481296 | ||||||||
\(592\) | 8.77913 | 0.360820 | ||||||||
\(593\) | −18.2345 | −0.748803 | −0.374401 | − | 0.927267i | \(-0.622152\pi\) | ||||
−0.374401 | + | 0.927267i | \(0.622152\pi\) | |||||||
\(594\) | −23.1154 | −0.948438 | ||||||||
\(595\) | −110.027 | −4.51068 | ||||||||
\(596\) | 0.185406 | 0.00759454 | ||||||||
\(597\) | −19.2684 | −0.788603 | ||||||||
\(598\) | −2.88609 | −0.118021 | ||||||||
\(599\) | 21.6096 | 0.882946 | 0.441473 | − | 0.897275i | \(-0.354456\pi\) | ||||
0.441473 | + | 0.897275i | \(0.354456\pi\) | |||||||
\(600\) | −12.8472 | −0.524486 | ||||||||
\(601\) | 32.0050 | 1.30551 | 0.652756 | − | 0.757568i | \(-0.273613\pi\) | ||||
0.652756 | + | 0.757568i | \(0.273613\pi\) | |||||||
\(602\) | −39.6908 | −1.61768 | ||||||||
\(603\) | −25.1839 | −1.02557 | ||||||||
\(604\) | 11.8553 | 0.482385 | ||||||||
\(605\) | 45.0146 | 1.83010 | ||||||||
\(606\) | 6.09884 | 0.247748 | ||||||||
\(607\) | −0.0175697 | −0.000713133 0 | −0.000356567 | − | 1.00000i | \(-0.500113\pi\) | ||||
−0.000356567 | 1.00000i | \(0.500113\pi\) | ||||||||
\(608\) | 4.17285 | 0.169231 | ||||||||
\(609\) | −14.6625 | −0.594153 | ||||||||
\(610\) | 23.1085 | 0.935634 | ||||||||
\(611\) | −9.73503 | −0.393837 | ||||||||
\(612\) | −12.5147 | −0.505875 | ||||||||
\(613\) | 44.0824 | 1.78047 | 0.890236 | − | 0.455499i | \(-0.150539\pi\) | ||||
0.890236 | + | 0.455499i | \(0.150539\pi\) | |||||||
\(614\) | 26.0459 | 1.05113 | ||||||||
\(615\) | −3.73428 | −0.150581 | ||||||||
\(616\) | 19.4678 | 0.784381 | ||||||||
\(617\) | −34.7123 | −1.39746 | −0.698731 | − | 0.715384i | \(-0.746252\pi\) | ||||
−0.698731 | + | 0.715384i | \(0.746252\pi\) | |||||||
\(618\) | −13.0631 | −0.525474 | ||||||||
\(619\) | 46.2712 | 1.85980 | 0.929898 | − | 0.367818i | \(-0.119895\pi\) | ||||
0.929898 | + | 0.367818i | \(0.119895\pi\) | |||||||
\(620\) | −27.7190 | −1.11322 | ||||||||
\(621\) | 4.97146 | 0.199498 | ||||||||
\(622\) | 15.2963 | 0.613324 | ||||||||
\(623\) | −56.5937 | −2.26738 | ||||||||
\(624\) | 2.85888 | 0.114447 | ||||||||
\(625\) | 78.3601 | 3.13440 | ||||||||
\(626\) | −4.01954 | −0.160653 | ||||||||
\(627\) | 19.2193 | 0.767546 | ||||||||
\(628\) | −4.19281 | −0.167311 | ||||||||
\(629\) | 54.4233 | 2.17000 | ||||||||
\(630\) | 35.8304 | 1.42752 | ||||||||
\(631\) | 31.5763 | 1.25703 | 0.628517 | − | 0.777796i | \(-0.283662\pi\) | ||||
0.628517 | + | 0.777796i | \(0.283662\pi\) | |||||||
\(632\) | −7.35263 | −0.292472 | ||||||||
\(633\) | 10.0789 | 0.400600 | ||||||||
\(634\) | 10.9815 | 0.436131 | ||||||||
\(635\) | 36.7908 | 1.46000 | ||||||||
\(636\) | 5.18820 | 0.205725 | ||||||||
\(637\) | −30.3924 | −1.20419 | ||||||||
\(638\) | 16.4376 | 0.650772 | ||||||||
\(639\) | 17.3385 | 0.685900 | ||||||||
\(640\) | 4.23904 | 0.167563 | ||||||||
\(641\) | −31.0538 | −1.22655 | −0.613276 | − | 0.789869i | \(-0.710149\pi\) | ||||
−0.613276 | + | 0.789869i | \(0.710149\pi\) | |||||||
\(642\) | −6.06065 | −0.239195 | ||||||||
\(643\) | −42.4715 | −1.67491 | −0.837457 | − | 0.546504i | \(-0.815958\pi\) | ||||
−0.837457 | + | 0.546504i | \(0.815958\pi\) | |||||||
\(644\) | −4.18696 | −0.164989 | ||||||||
\(645\) | −39.8057 | −1.56735 | ||||||||
\(646\) | 25.8682 | 1.01777 | ||||||||
\(647\) | 34.9220 | 1.37292 | 0.686462 | − | 0.727165i | \(-0.259163\pi\) | ||||
0.686462 | + | 0.727165i | \(0.259163\pi\) | |||||||
\(648\) | 1.13169 | 0.0444571 | ||||||||
\(649\) | 67.4163 | 2.64632 | ||||||||
\(650\) | −37.4311 | −1.46817 | ||||||||
\(651\) | −27.1204 | −1.06293 | ||||||||
\(652\) | 7.63248 | 0.298911 | ||||||||
\(653\) | 45.4001 | 1.77664 | 0.888322 | − | 0.459222i | \(-0.151872\pi\) | ||||
0.888322 | + | 0.459222i | \(0.151872\pi\) | |||||||
\(654\) | −7.92631 | −0.309943 | ||||||||
\(655\) | 4.23904 | 0.165633 | ||||||||
\(656\) | 0.889308 | 0.0347217 | ||||||||
\(657\) | −10.2446 | −0.399682 | ||||||||
\(658\) | −14.1230 | −0.550572 | ||||||||
\(659\) | −17.5372 | −0.683153 | −0.341577 | − | 0.939854i | \(-0.610961\pi\) | ||||
−0.341577 | + | 0.939854i | \(0.610961\pi\) | |||||||
\(660\) | 19.5242 | 0.759978 | ||||||||
\(661\) | 18.6886 | 0.726902 | 0.363451 | − | 0.931613i | \(-0.381598\pi\) | ||||
0.363451 | + | 0.931613i | \(0.381598\pi\) | |||||||
\(662\) | 8.54084 | 0.331949 | ||||||||
\(663\) | 17.7227 | 0.688293 | ||||||||
\(664\) | 2.15419 | 0.0835988 | ||||||||
\(665\) | −74.0627 | −2.87203 | ||||||||
\(666\) | −17.7230 | −0.686752 | ||||||||
\(667\) | −3.53526 | −0.136886 | ||||||||
\(668\) | 8.43220 | 0.326252 | ||||||||
\(669\) | −8.05273 | −0.311337 | ||||||||
\(670\) | 52.8817 | 2.04300 | ||||||||
\(671\) | −25.3467 | −0.978499 | ||||||||
\(672\) | 4.14750 | 0.159993 | ||||||||
\(673\) | −43.4269 | −1.67398 | −0.836992 | − | 0.547215i | \(-0.815688\pi\) | ||||
−0.836992 | + | 0.547215i | \(0.815688\pi\) | |||||||
\(674\) | 32.5556 | 1.25400 | ||||||||
\(675\) | 64.4772 | 2.48173 | ||||||||
\(676\) | −4.67050 | −0.179635 | ||||||||
\(677\) | 47.7304 | 1.83443 | 0.917214 | − | 0.398395i | \(-0.130433\pi\) | ||||
0.917214 | + | 0.398395i | \(0.130433\pi\) | |||||||
\(678\) | −0.259577 | −0.00996898 | ||||||||
\(679\) | −50.0731 | −1.92163 | ||||||||
\(680\) | 26.2785 | 1.00774 | ||||||||
\(681\) | −6.61406 | −0.253451 | ||||||||
\(682\) | 30.4038 | 1.16422 | ||||||||
\(683\) | −39.4114 | −1.50804 | −0.754018 | − | 0.656854i | \(-0.771887\pi\) | ||||
−0.754018 | + | 0.656854i | \(0.771887\pi\) | |||||||
\(684\) | −8.42399 | −0.322099 | ||||||||
\(685\) | 7.53726 | 0.287984 | ||||||||
\(686\) | −14.7827 | −0.564406 | ||||||||
\(687\) | 21.6792 | 0.827112 | ||||||||
\(688\) | 9.47962 | 0.361407 | ||||||||
\(689\) | 15.1161 | 0.575876 | ||||||||
\(690\) | −4.19909 | −0.159856 | ||||||||
\(691\) | −10.5570 | −0.401606 | −0.200803 | − | 0.979632i | \(-0.564355\pi\) | ||||
−0.200803 | + | 0.979632i | \(0.564355\pi\) | |||||||
\(692\) | −15.3308 | −0.582789 | ||||||||
\(693\) | −39.3009 | −1.49292 | ||||||||
\(694\) | −19.9106 | −0.755795 | ||||||||
\(695\) | 9.31749 | 0.353433 | ||||||||
\(696\) | 3.50193 | 0.132740 | ||||||||
\(697\) | 5.51297 | 0.208819 | ||||||||
\(698\) | 3.41373 | 0.129211 | ||||||||
\(699\) | 13.7537 | 0.520214 | ||||||||
\(700\) | −54.3027 | −2.05245 | ||||||||
\(701\) | −21.6842 | −0.818999 | −0.409500 | − | 0.912310i | \(-0.634297\pi\) | ||||
−0.409500 | + | 0.912310i | \(0.634297\pi\) | |||||||
\(702\) | −14.3481 | −0.541532 | ||||||||
\(703\) | 36.6340 | 1.38168 | ||||||||
\(704\) | −4.64963 | −0.175240 | ||||||||
\(705\) | −14.1639 | −0.533443 | ||||||||
\(706\) | −16.9942 | −0.639584 | ||||||||
\(707\) | 25.7786 | 0.969504 | ||||||||
\(708\) | 14.3626 | 0.539780 | ||||||||
\(709\) | 25.4200 | 0.954669 | 0.477335 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477335 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(710\) | −36.4077 | −1.36636 | ||||||||
\(711\) | 14.8432 | 0.556664 | ||||||||
\(712\) | 13.5167 | 0.506558 | ||||||||
\(713\) | −6.53898 | −0.244887 | ||||||||
\(714\) | 25.7110 | 0.962211 | ||||||||
\(715\) | 56.8847 | 2.12737 | ||||||||
\(716\) | −3.86562 | −0.144465 | ||||||||
\(717\) | 17.0499 | 0.636739 | ||||||||
\(718\) | 18.8551 | 0.703664 | ||||||||
\(719\) | −24.5047 | −0.913871 | −0.456936 | − | 0.889500i | \(-0.651053\pi\) | ||||
−0.456936 | + | 0.889500i | \(0.651053\pi\) | |||||||
\(720\) | −8.55762 | −0.318924 | ||||||||
\(721\) | −55.2150 | −2.05631 | ||||||||
\(722\) | −1.58734 | −0.0590746 | ||||||||
\(723\) | −24.2663 | −0.902472 | ||||||||
\(724\) | 22.9661 | 0.853530 | ||||||||
\(725\) | −45.8505 | −1.70284 | ||||||||
\(726\) | −10.5190 | −0.390395 | ||||||||
\(727\) | 10.8062 | 0.400781 | 0.200391 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200391 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(728\) | 12.0839 | 0.447860 | ||||||||
\(729\) | 12.4892 | 0.462562 | ||||||||
\(730\) | 21.5119 | 0.796192 | ||||||||
\(731\) | 58.7658 | 2.17353 | ||||||||
\(732\) | −5.39996 | −0.199588 | ||||||||
\(733\) | 9.98461 | 0.368790 | 0.184395 | − | 0.982852i | \(-0.440967\pi\) | ||||
0.184395 | + | 0.982852i | \(0.440967\pi\) | |||||||
\(734\) | −21.3435 | −0.787804 | ||||||||
\(735\) | −44.2191 | −1.63105 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −58.0037 | −2.13660 | ||||||||
\(738\) | −1.79530 | −0.0660860 | ||||||||
\(739\) | −5.77419 | −0.212407 | −0.106204 | − | 0.994344i | \(-0.533870\pi\) | ||||
−0.106204 | + | 0.994344i | \(0.533870\pi\) | |||||||
\(740\) | 37.2151 | 1.36805 | ||||||||
\(741\) | 11.9297 | 0.438248 | ||||||||
\(742\) | 21.9295 | 0.805057 | ||||||||
\(743\) | −39.5518 | −1.45102 | −0.725508 | − | 0.688214i | \(-0.758395\pi\) | ||||
−0.725508 | + | 0.688214i | \(0.758395\pi\) | |||||||
\(744\) | 6.47735 | 0.237471 | ||||||||
\(745\) | 0.785946 | 0.0287948 | ||||||||
\(746\) | −16.3289 | −0.597845 | ||||||||
\(747\) | −4.34880 | −0.159114 | ||||||||
\(748\) | −28.8238 | −1.05390 | ||||||||
\(749\) | −25.6172 | −0.936032 | ||||||||
\(750\) | −33.4645 | −1.22195 | ||||||||
\(751\) | −44.8947 | −1.63823 | −0.819116 | − | 0.573628i | \(-0.805536\pi\) | ||||
−0.819116 | + | 0.573628i | \(0.805536\pi\) | |||||||
\(752\) | 3.37309 | 0.123004 | ||||||||
\(753\) | 22.1474 | 0.807095 | ||||||||
\(754\) | 10.2031 | 0.371574 | ||||||||
\(755\) | 50.2551 | 1.82897 | ||||||||
\(756\) | −20.8153 | −0.757045 | ||||||||
\(757\) | −4.44653 | −0.161612 | −0.0808059 | − | 0.996730i | \(-0.525749\pi\) | ||||
−0.0808059 | + | 0.996730i | \(0.525749\pi\) | |||||||
\(758\) | −14.7023 | −0.534010 | ||||||||
\(759\) | 4.60580 | 0.167180 | ||||||||
\(760\) | 17.6889 | 0.641643 | ||||||||
\(761\) | 15.4999 | 0.561870 | 0.280935 | − | 0.959727i | \(-0.409356\pi\) | ||||
0.280935 | + | 0.959727i | \(0.409356\pi\) | |||||||
\(762\) | −8.59724 | −0.311445 | ||||||||
\(763\) | −33.5030 | −1.21289 | ||||||||
\(764\) | 7.94271 | 0.287357 | ||||||||
\(765\) | −53.0501 | −1.91803 | ||||||||
\(766\) | 7.52661 | 0.271947 | ||||||||
\(767\) | 41.8462 | 1.51098 | ||||||||
\(768\) | −0.990574 | −0.0357443 | ||||||||
\(769\) | −43.8962 | −1.58294 | −0.791470 | − | 0.611209i | \(-0.790684\pi\) | ||||
−0.791470 | + | 0.611209i | \(0.790684\pi\) | |||||||
\(770\) | 82.5249 | 2.97399 | ||||||||
\(771\) | 0.715772 | 0.0257779 | ||||||||
\(772\) | −13.3411 | −0.480155 | ||||||||
\(773\) | 31.7418 | 1.14167 | 0.570837 | − | 0.821063i | \(-0.306619\pi\) | ||||
0.570837 | + | 0.821063i | \(0.306619\pi\) | |||||||
\(774\) | −19.1371 | −0.687869 | ||||||||
\(775\) | −84.8072 | −3.04637 | ||||||||
\(776\) | 11.9593 | 0.429314 | ||||||||
\(777\) | 36.4114 | 1.30625 | ||||||||
\(778\) | 18.3954 | 0.659506 | ||||||||
\(779\) | 3.71095 | 0.132959 | ||||||||
\(780\) | 12.1189 | 0.433927 | ||||||||
\(781\) | 39.9341 | 1.42896 | ||||||||
\(782\) | 6.19917 | 0.221682 | ||||||||
\(783\) | −17.5754 | −0.628093 | ||||||||
\(784\) | 10.5307 | 0.376095 | ||||||||
\(785\) | −17.7735 | −0.634363 | ||||||||
\(786\) | −0.990574 | −0.0353326 | ||||||||
\(787\) | −54.7862 | −1.95292 | −0.976458 | − | 0.215708i | \(-0.930794\pi\) | ||||
−0.976458 | + | 0.215708i | \(0.930794\pi\) | |||||||
\(788\) | 11.8119 | 0.420781 | ||||||||
\(789\) | 9.72771 | 0.346316 | ||||||||
\(790\) | −31.1681 | −1.10891 | ||||||||
\(791\) | −1.09718 | −0.0390112 | ||||||||
\(792\) | 9.38650 | 0.333535 | ||||||||
\(793\) | −15.7330 | −0.558697 | ||||||||
\(794\) | −35.9896 | −1.27722 | ||||||||
\(795\) | 21.9930 | 0.780011 | ||||||||
\(796\) | 19.4517 | 0.689449 | ||||||||
\(797\) | 7.67887 | 0.272000 | 0.136000 | − | 0.990709i | \(-0.456575\pi\) | ||||
0.136000 | + | 0.990709i | \(0.456575\pi\) | |||||||
\(798\) | 17.3069 | 0.612657 | ||||||||
\(799\) | 20.9103 | 0.739755 | ||||||||
\(800\) | 12.9695 | 0.458540 | ||||||||
\(801\) | −27.2869 | −0.964136 | ||||||||
\(802\) | −29.8552 | −1.05422 | ||||||||
\(803\) | −23.5955 | −0.832668 | ||||||||
\(804\) | −12.3573 | −0.435809 | ||||||||
\(805\) | −17.7487 | −0.625560 | ||||||||
\(806\) | 18.8721 | 0.664740 | ||||||||
\(807\) | −2.96335 | −0.104315 | ||||||||
\(808\) | −6.15687 | −0.216598 | ||||||||
\(809\) | 11.5713 | 0.406825 | 0.203413 | − | 0.979093i | \(-0.434797\pi\) | ||||
0.203413 | + | 0.979093i | \(0.434797\pi\) | |||||||
\(810\) | 4.79729 | 0.168560 | ||||||||
\(811\) | 48.2486 | 1.69424 | 0.847118 | − | 0.531404i | \(-0.178336\pi\) | ||||
0.847118 | + | 0.531404i | \(0.178336\pi\) | |||||||
\(812\) | 14.8020 | 0.519448 | ||||||||
\(813\) | −2.68088 | −0.0940225 | ||||||||
\(814\) | −40.8197 | −1.43073 | ||||||||
\(815\) | 32.3544 | 1.13333 | ||||||||
\(816\) | −6.14074 | −0.214969 | ||||||||
\(817\) | 39.5570 | 1.38392 | ||||||||
\(818\) | −0.985581 | −0.0344600 | ||||||||
\(819\) | −24.3946 | −0.852416 | ||||||||
\(820\) | 3.76982 | 0.131648 | ||||||||
\(821\) | 25.0746 | 0.875108 | 0.437554 | − | 0.899192i | \(-0.355845\pi\) | ||||
0.437554 | + | 0.899192i | \(0.355845\pi\) | |||||||
\(822\) | −1.76130 | −0.0614323 | ||||||||
\(823\) | 44.0536 | 1.53561 | 0.767807 | − | 0.640682i | \(-0.221348\pi\) | ||||
0.767807 | + | 0.640682i | \(0.221348\pi\) | |||||||
\(824\) | 13.1874 | 0.459404 | ||||||||
\(825\) | 59.7349 | 2.07970 | ||||||||
\(826\) | 60.7079 | 2.11230 | ||||||||
\(827\) | −41.3204 | −1.43685 | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695603i | \(0.755137\pi\) | |||||||
\(828\) | −2.01876 | −0.0701569 | ||||||||
\(829\) | 31.5601 | 1.09613 | 0.548064 | − | 0.836437i | \(-0.315365\pi\) | ||||
0.548064 | + | 0.836437i | \(0.315365\pi\) | |||||||
\(830\) | 9.13171 | 0.316966 | ||||||||
\(831\) | −4.28397 | −0.148609 | ||||||||
\(832\) | −2.88609 | −0.100057 | ||||||||
\(833\) | 65.2813 | 2.26186 | ||||||||
\(834\) | −2.17730 | −0.0753937 | ||||||||
\(835\) | 35.7445 | 1.23699 | ||||||||
\(836\) | −19.4022 | −0.671039 | ||||||||
\(837\) | −32.5083 | −1.12365 | ||||||||
\(838\) | −3.91510 | −0.135245 | ||||||||
\(839\) | −36.8533 | −1.27232 | −0.636159 | − | 0.771558i | \(-0.719478\pi\) | ||||
−0.636159 | + | 0.771558i | \(0.719478\pi\) | |||||||
\(840\) | 17.5814 | 0.606616 | ||||||||
\(841\) | −16.5020 | −0.569033 | ||||||||
\(842\) | 12.1728 | 0.419501 | ||||||||
\(843\) | 26.0622 | 0.897630 | ||||||||
\(844\) | −10.1748 | −0.350231 | ||||||||
\(845\) | −19.7985 | −0.681088 | ||||||||
\(846\) | −6.80947 | −0.234114 | ||||||||
\(847\) | −44.4616 | −1.52772 | ||||||||
\(848\) | −5.23757 | −0.179859 | ||||||||
\(849\) | 17.8986 | 0.614279 | ||||||||
\(850\) | 80.4000 | 2.75770 | ||||||||
\(851\) | 8.77913 | 0.300945 | ||||||||
\(852\) | 8.50771 | 0.291469 | ||||||||
\(853\) | 32.4495 | 1.11105 | 0.555525 | − | 0.831500i | \(-0.312517\pi\) | ||||
0.555525 | + | 0.831500i | \(0.312517\pi\) | |||||||
\(854\) | −22.8246 | −0.781040 | ||||||||
\(855\) | −35.7097 | −1.22124 | ||||||||
\(856\) | 6.11832 | 0.209120 | ||||||||
\(857\) | 14.7119 | 0.502549 | 0.251274 | − | 0.967916i | \(-0.419150\pi\) | ||||
0.251274 | + | 0.967916i | \(0.419150\pi\) | |||||||
\(858\) | −13.2927 | −0.453807 | ||||||||
\(859\) | −53.6414 | −1.83022 | −0.915111 | − | 0.403202i | \(-0.867897\pi\) | ||||
−0.915111 | + | 0.403202i | \(0.867897\pi\) | |||||||
\(860\) | 40.1845 | 1.37028 | ||||||||
\(861\) | 3.68840 | 0.125700 | ||||||||
\(862\) | 29.0274 | 0.988678 | ||||||||
\(863\) | −19.0429 | −0.648228 | −0.324114 | − | 0.946018i | \(-0.605066\pi\) | ||||
−0.324114 | + | 0.946018i | \(0.605066\pi\) | |||||||
\(864\) | 4.97146 | 0.169132 | ||||||||
\(865\) | −64.9878 | −2.20965 | ||||||||
\(866\) | −22.4980 | −0.764512 | ||||||||
\(867\) | −21.2277 | −0.720931 | ||||||||
\(868\) | 27.3785 | 0.929286 | ||||||||
\(869\) | 34.1870 | 1.15971 | ||||||||
\(870\) | 14.8449 | 0.503288 | ||||||||
\(871\) | −36.0037 | −1.21994 | ||||||||
\(872\) | 8.00174 | 0.270973 | ||||||||
\(873\) | −24.1430 | −0.817117 | ||||||||
\(874\) | 4.17285 | 0.141149 | ||||||||
\(875\) | −141.448 | −4.78182 | ||||||||
\(876\) | −5.02688 | −0.169843 | ||||||||
\(877\) | −32.1103 | −1.08429 | −0.542144 | − | 0.840286i | \(-0.682387\pi\) | ||||
−0.542144 | + | 0.840286i | \(0.682387\pi\) | |||||||
\(878\) | 36.4289 | 1.22941 | ||||||||
\(879\) | −30.9001 | −1.04223 | ||||||||
\(880\) | −19.7100 | −0.664423 | ||||||||
\(881\) | 38.3259 | 1.29123 | 0.645617 | − | 0.763662i | \(-0.276600\pi\) | ||||
0.645617 | + | 0.763662i | \(0.276600\pi\) | |||||||
\(882\) | −21.2589 | −0.715824 | ||||||||
\(883\) | −46.9520 | −1.58006 | −0.790030 | − | 0.613068i | \(-0.789935\pi\) | ||||
−0.790030 | + | 0.613068i | \(0.789935\pi\) | |||||||
\(884\) | −17.8913 | −0.601751 | ||||||||
\(885\) | 60.8837 | 2.04658 | ||||||||
\(886\) | 7.15995 | 0.240543 | ||||||||
\(887\) | −20.8413 | −0.699784 | −0.349892 | − | 0.936790i | \(-0.613782\pi\) | ||||
−0.349892 | + | 0.936790i | \(0.613782\pi\) | |||||||
\(888\) | −8.69638 | −0.291831 | ||||||||
\(889\) | −36.3388 | −1.21876 | ||||||||
\(890\) | 57.2977 | 1.92062 | ||||||||
\(891\) | −5.26195 | −0.176282 | ||||||||
\(892\) | 8.12936 | 0.272191 | ||||||||
\(893\) | 14.0754 | 0.471015 | ||||||||
\(894\) | −0.183659 | −0.00614247 | ||||||||
\(895\) | −16.3865 | −0.547741 | ||||||||
\(896\) | −4.18696 | −0.139877 | ||||||||
\(897\) | 2.85888 | 0.0954553 | ||||||||
\(898\) | −25.0404 | −0.835610 | ||||||||
\(899\) | 23.1170 | 0.770995 | ||||||||
\(900\) | −26.1823 | −0.872744 | ||||||||
\(901\) | −32.4686 | −1.08168 | ||||||||
\(902\) | −4.13495 | −0.137679 | ||||||||
\(903\) | 39.3167 | 1.30838 | ||||||||
\(904\) | 0.262047 | 0.00871554 | ||||||||
\(905\) | 97.3545 | 3.23617 | ||||||||
\(906\) | −11.7436 | −0.390153 | ||||||||
\(907\) | −17.7743 | −0.590185 | −0.295092 | − | 0.955469i | \(-0.595350\pi\) | ||||
−0.295092 | + | 0.955469i | \(0.595350\pi\) | |||||||
\(908\) | 6.67700 | 0.221584 | ||||||||
\(909\) | 12.4293 | 0.412253 | ||||||||
\(910\) | 51.2243 | 1.69807 | ||||||||
\(911\) | −42.0898 | −1.39450 | −0.697248 | − | 0.716830i | \(-0.745592\pi\) | ||||
−0.697248 | + | 0.716830i | \(0.745592\pi\) | |||||||
\(912\) | −4.13352 | −0.136874 | ||||||||
\(913\) | −10.0162 | −0.331488 | ||||||||
\(914\) | −6.46099 | −0.213711 | ||||||||
\(915\) | −22.8906 | −0.756742 | ||||||||
\(916\) | −21.8855 | −0.723116 | ||||||||
\(917\) | −4.18696 | −0.138266 | ||||||||
\(918\) | 30.8189 | 1.01718 | ||||||||
\(919\) | 57.6152 | 1.90055 | 0.950274 | − | 0.311414i | \(-0.100803\pi\) | ||||
0.950274 | + | 0.311414i | \(0.100803\pi\) | |||||||
\(920\) | 4.23904 | 0.139757 | ||||||||
\(921\) | −25.8004 | −0.850151 | ||||||||
\(922\) | 8.90625 | 0.293312 | ||||||||
\(923\) | 24.7876 | 0.815895 | ||||||||
\(924\) | −19.2843 | −0.634408 | ||||||||
\(925\) | 113.861 | 3.74372 | ||||||||
\(926\) | 0.254866 | 0.00837543 | ||||||||
\(927\) | −26.6222 | −0.874387 | ||||||||
\(928\) | −3.53526 | −0.116051 | ||||||||
\(929\) | 2.85572 | 0.0936932 | 0.0468466 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468466 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(930\) | 27.4577 | 0.900375 | ||||||||
\(931\) | 43.9428 | 1.44017 | ||||||||
\(932\) | −13.8846 | −0.454805 | ||||||||
\(933\) | −15.1521 | −0.496057 | ||||||||
\(934\) | 1.67439 | 0.0547877 | ||||||||
\(935\) | −122.185 | −3.99589 | ||||||||
\(936\) | 5.82632 | 0.190439 | ||||||||
\(937\) | −1.60737 | −0.0525105 | −0.0262553 | − | 0.999655i | \(-0.508358\pi\) | ||||
−0.0262553 | + | 0.999655i | \(0.508358\pi\) | |||||||
\(938\) | −52.2320 | −1.70544 | ||||||||
\(939\) | 3.98165 | 0.129936 | ||||||||
\(940\) | 14.2987 | 0.466371 | ||||||||
\(941\) | 8.19586 | 0.267177 | 0.133589 | − | 0.991037i | \(-0.457350\pi\) | ||||
0.133589 | + | 0.991037i | \(0.457350\pi\) | |||||||
\(942\) | 4.15328 | 0.135321 | ||||||||
\(943\) | 0.889308 | 0.0289599 | ||||||||
\(944\) | −14.4993 | −0.471911 | ||||||||
\(945\) | −88.2370 | −2.87035 | ||||||||
\(946\) | −44.0767 | −1.43306 | ||||||||
\(947\) | −0.322617 | −0.0104836 | −0.00524182 | − | 0.999986i | \(-0.501669\pi\) | ||||
−0.00524182 | + | 0.999986i | \(0.501669\pi\) | |||||||
\(948\) | 7.28332 | 0.236551 | ||||||||
\(949\) | −14.6461 | −0.475431 | ||||||||
\(950\) | 54.1197 | 1.75587 | ||||||||
\(951\) | −10.8780 | −0.352743 | ||||||||
\(952\) | −25.9557 | −0.841229 | ||||||||
\(953\) | 43.3459 | 1.40411 | 0.702056 | − | 0.712122i | \(-0.252266\pi\) | ||||
0.702056 | + | 0.712122i | \(0.252266\pi\) | |||||||
\(954\) | 10.5734 | 0.342327 | ||||||||
\(955\) | 33.6695 | 1.08952 | ||||||||
\(956\) | −17.2121 | −0.556679 | ||||||||
\(957\) | −16.2827 | −0.526345 | ||||||||
\(958\) | 16.1791 | 0.522724 | ||||||||
\(959\) | −7.44466 | −0.240401 | ||||||||
\(960\) | −4.19909 | −0.135525 | ||||||||
\(961\) | 11.7583 | 0.379299 | ||||||||
\(962\) | −25.3373 | −0.816908 | ||||||||
\(963\) | −12.3514 | −0.398020 | ||||||||
\(964\) | 24.4972 | 0.789001 | ||||||||
\(965\) | −56.5533 | −1.82052 | ||||||||
\(966\) | 4.14750 | 0.133444 | ||||||||
\(967\) | 51.0793 | 1.64260 | 0.821299 | − | 0.570498i | \(-0.193250\pi\) | ||||
0.821299 | + | 0.570498i | \(0.193250\pi\) | |||||||
\(968\) | 10.6191 | 0.341309 | ||||||||
\(969\) | −25.6244 | −0.823173 | ||||||||
\(970\) | 50.6960 | 1.62775 | ||||||||
\(971\) | 31.3491 | 1.00604 | 0.503021 | − | 0.864274i | \(-0.332222\pi\) | ||||
0.503021 | + | 0.864274i | \(0.332222\pi\) | |||||||
\(972\) | −16.0354 | −0.514336 | ||||||||
\(973\) | −9.20302 | −0.295035 | ||||||||
\(974\) | −36.3583 | −1.16499 | ||||||||
\(975\) | 37.0782 | 1.18745 | ||||||||
\(976\) | 5.45134 | 0.174493 | ||||||||
\(977\) | 50.6186 | 1.61943 | 0.809717 | − | 0.586821i | \(-0.199621\pi\) | ||||
0.809717 | + | 0.586821i | \(0.199621\pi\) | |||||||
\(978\) | −7.56054 | −0.241759 | ||||||||
\(979\) | −62.8475 | −2.00861 | ||||||||
\(980\) | 44.6399 | 1.42597 | ||||||||
\(981\) | −16.1536 | −0.515745 | ||||||||
\(982\) | −2.02395 | −0.0645868 | ||||||||
\(983\) | 39.5002 | 1.25986 | 0.629930 | − | 0.776652i | \(-0.283083\pi\) | ||||
0.629930 | + | 0.776652i | \(0.283083\pi\) | |||||||
\(984\) | −0.880926 | −0.0280829 | ||||||||
\(985\) | 50.0711 | 1.59540 | ||||||||
\(986\) | −21.9157 | −0.697937 | ||||||||
\(987\) | 13.9899 | 0.445303 | ||||||||
\(988\) | −12.0432 | −0.383145 | ||||||||
\(989\) | 9.47962 | 0.301434 | ||||||||
\(990\) | 39.7898 | 1.26460 | ||||||||
\(991\) | −43.8891 | −1.39418 | −0.697092 | − | 0.716982i | \(-0.745523\pi\) | ||||
−0.697092 | + | 0.716982i | \(0.745523\pi\) | |||||||
\(992\) | −6.53898 | −0.207613 | ||||||||
\(993\) | −8.46033 | −0.268481 | ||||||||
\(994\) | 35.9604 | 1.14060 | ||||||||
\(995\) | 82.4568 | 2.61406 | ||||||||
\(996\) | −2.13389 | −0.0676148 | ||||||||
\(997\) | −1.28493 | −0.0406942 | −0.0203471 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203471 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(998\) | 3.92126 | 0.124125 | ||||||||
\(999\) | 43.6451 | 1.38087 |
(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 | 6026.2.a.m.1.15 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.m.1.15 | ✓ | 41 | 1.1 | even | 1 | trivial |