Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} - 2118 x^{6} - 710 x^{5} + 1113 x^{4} + 243 x^{3} - 183 x^{2} - 10 x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.291985\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.291985 | −0.206464 | −0.103232 | − | 0.994657i | \(-0.532918\pi\) | ||||
−0.103232 | + | 0.994657i | \(0.532918\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.91474 | −0.957372 | ||||||||
\(5\) | −3.42004 | −1.52949 | −0.764745 | − | 0.644333i | \(-0.777135\pi\) | ||||
−0.764745 | + | 0.644333i | \(0.777135\pi\) | |||||||
\(6\) | −0.291985 | −0.119202 | ||||||||
\(7\) | −3.90865 | −1.47733 | −0.738666 | − | 0.674072i | \(-0.764544\pi\) | ||||
−0.738666 | + | 0.674072i | \(0.764544\pi\) | |||||||
\(8\) | 1.14305 | 0.404128 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.998600 | 0.315785 | ||||||||
\(11\) | 4.06263 | 1.22493 | 0.612465 | − | 0.790498i | \(-0.290178\pi\) | ||||
0.612465 | + | 0.790498i | \(0.290178\pi\) | |||||||
\(12\) | −1.91474 | −0.552739 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.14127 | 0.305016 | ||||||||
\(15\) | −3.42004 | −0.883051 | ||||||||
\(16\) | 3.49574 | 0.873935 | ||||||||
\(17\) | −0.751286 | −0.182214 | −0.0911068 | − | 0.995841i | \(-0.529040\pi\) | ||||
−0.0911068 | + | 0.995841i | \(0.529040\pi\) | |||||||
\(18\) | −0.291985 | −0.0688215 | ||||||||
\(19\) | 5.37839 | 1.23389 | 0.616944 | − | 0.787007i | \(-0.288371\pi\) | ||||
0.616944 | + | 0.787007i | \(0.288371\pi\) | |||||||
\(20\) | 6.54851 | 1.46429 | ||||||||
\(21\) | −3.90865 | −0.852938 | ||||||||
\(22\) | −1.18623 | −0.252904 | ||||||||
\(23\) | −8.24911 | −1.72006 | −0.860029 | − | 0.510245i | \(-0.829555\pi\) | ||||
−0.860029 | + | 0.510245i | \(0.829555\pi\) | |||||||
\(24\) | 1.14305 | 0.233323 | ||||||||
\(25\) | 6.69670 | 1.33934 | ||||||||
\(26\) | 0.291985 | 0.0572629 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 7.48407 | 1.41436 | ||||||||
\(29\) | 8.16240 | 1.51572 | 0.757860 | − | 0.652417i | \(-0.226245\pi\) | ||||
0.757860 | + | 0.652417i | \(0.226245\pi\) | |||||||
\(30\) | 0.998600 | 0.182319 | ||||||||
\(31\) | 1.89795 | 0.340881 | 0.170441 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170441 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(32\) | −3.30679 | −0.584564 | ||||||||
\(33\) | 4.06263 | 0.707214 | ||||||||
\(34\) | 0.219364 | 0.0376206 | ||||||||
\(35\) | 13.3678 | 2.25956 | ||||||||
\(36\) | −1.91474 | −0.319124 | ||||||||
\(37\) | −4.14408 | −0.681283 | −0.340641 | − | 0.940193i | \(-0.610644\pi\) | ||||
−0.340641 | + | 0.940193i | \(0.610644\pi\) | |||||||
\(38\) | −1.57041 | −0.254754 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −3.90927 | −0.618109 | ||||||||
\(41\) | 0.461243 | 0.0720341 | 0.0360170 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360170 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(42\) | 1.14127 | 0.176101 | ||||||||
\(43\) | 0.847965 | 0.129314 | 0.0646568 | − | 0.997908i | \(-0.479405\pi\) | ||||
0.0646568 | + | 0.997908i | \(0.479405\pi\) | |||||||
\(44\) | −7.77891 | −1.17271 | ||||||||
\(45\) | −3.42004 | −0.509830 | ||||||||
\(46\) | 2.40861 | 0.355131 | ||||||||
\(47\) | 8.10038 | 1.18156 | 0.590781 | − | 0.806832i | \(-0.298820\pi\) | ||||
0.590781 | + | 0.806832i | \(0.298820\pi\) | |||||||
\(48\) | 3.49574 | 0.504566 | ||||||||
\(49\) | 8.27757 | 1.18251 | ||||||||
\(50\) | −1.95533 | −0.276526 | ||||||||
\(51\) | −0.751286 | −0.105201 | ||||||||
\(52\) | 1.91474 | 0.265527 | ||||||||
\(53\) | 2.55597 | 0.351089 | 0.175545 | − | 0.984471i | \(-0.443831\pi\) | ||||
0.175545 | + | 0.984471i | \(0.443831\pi\) | |||||||
\(54\) | −0.291985 | −0.0397341 | ||||||||
\(55\) | −13.8944 | −1.87352 | ||||||||
\(56\) | −4.46777 | −0.597031 | ||||||||
\(57\) | 5.37839 | 0.712385 | ||||||||
\(58\) | −2.38330 | −0.312942 | ||||||||
\(59\) | −5.39458 | −0.702315 | −0.351157 | − | 0.936316i | \(-0.614212\pi\) | ||||
−0.351157 | + | 0.936316i | \(0.614212\pi\) | |||||||
\(60\) | 6.54851 | 0.845409 | ||||||||
\(61\) | −1.43944 | −0.184302 | −0.0921509 | − | 0.995745i | \(-0.529374\pi\) | ||||
−0.0921509 | + | 0.995745i | \(0.529374\pi\) | |||||||
\(62\) | −0.554172 | −0.0703799 | ||||||||
\(63\) | −3.90865 | −0.492444 | ||||||||
\(64\) | −6.02594 | −0.753243 | ||||||||
\(65\) | 3.42004 | 0.424204 | ||||||||
\(66\) | −1.18623 | −0.146014 | ||||||||
\(67\) | 5.33432 | 0.651690 | 0.325845 | − | 0.945423i | \(-0.394351\pi\) | ||||
0.325845 | + | 0.945423i | \(0.394351\pi\) | |||||||
\(68\) | 1.43852 | 0.174446 | ||||||||
\(69\) | −8.24911 | −0.993076 | ||||||||
\(70\) | −3.90318 | −0.466519 | ||||||||
\(71\) | −1.28042 | −0.151958 | −0.0759790 | − | 0.997109i | \(-0.524208\pi\) | ||||
−0.0759790 | + | 0.997109i | \(0.524208\pi\) | |||||||
\(72\) | 1.14305 | 0.134709 | ||||||||
\(73\) | 5.97616 | 0.699456 | 0.349728 | − | 0.936851i | \(-0.386274\pi\) | ||||
0.349728 | + | 0.936851i | \(0.386274\pi\) | |||||||
\(74\) | 1.21001 | 0.140661 | ||||||||
\(75\) | 6.69670 | 0.773268 | ||||||||
\(76\) | −10.2982 | −1.18129 | ||||||||
\(77\) | −15.8794 | −1.80963 | ||||||||
\(78\) | 0.291985 | 0.0330608 | ||||||||
\(79\) | −8.83363 | −0.993861 | −0.496930 | − | 0.867790i | \(-0.665540\pi\) | ||||
−0.496930 | + | 0.867790i | \(0.665540\pi\) | |||||||
\(80\) | −11.9556 | −1.33667 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.134676 | −0.0148725 | ||||||||
\(83\) | 11.3247 | 1.24305 | 0.621524 | − | 0.783395i | \(-0.286514\pi\) | ||||
0.621524 | + | 0.783395i | \(0.286514\pi\) | |||||||
\(84\) | 7.48407 | 0.816579 | ||||||||
\(85\) | 2.56943 | 0.278694 | ||||||||
\(86\) | −0.247593 | −0.0266986 | ||||||||
\(87\) | 8.16240 | 0.875101 | ||||||||
\(88\) | 4.64378 | 0.495028 | ||||||||
\(89\) | −12.6221 | −1.33794 | −0.668972 | − | 0.743288i | \(-0.733265\pi\) | ||||
−0.668972 | + | 0.743288i | \(0.733265\pi\) | |||||||
\(90\) | 0.998600 | 0.105262 | ||||||||
\(91\) | 3.90865 | 0.409738 | ||||||||
\(92\) | 15.7949 | 1.64674 | ||||||||
\(93\) | 1.89795 | 0.196808 | ||||||||
\(94\) | −2.36519 | −0.243950 | ||||||||
\(95\) | −18.3943 | −1.88722 | ||||||||
\(96\) | −3.30679 | −0.337498 | ||||||||
\(97\) | −4.26288 | −0.432829 | −0.216415 | − | 0.976302i | \(-0.569436\pi\) | ||||
−0.216415 | + | 0.976302i | \(0.569436\pi\) | |||||||
\(98\) | −2.41692 | −0.244146 | ||||||||
\(99\) | 4.06263 | 0.408310 | ||||||||
\(100\) | −12.8225 | −1.28225 | ||||||||
\(101\) | −3.27285 | −0.325661 | −0.162830 | − | 0.986654i | \(-0.552062\pi\) | ||||
−0.162830 | + | 0.986654i | \(0.552062\pi\) | |||||||
\(102\) | 0.219364 | 0.0217203 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.14305 | −0.112085 | ||||||||
\(105\) | 13.3678 | 1.30456 | ||||||||
\(106\) | −0.746304 | −0.0724874 | ||||||||
\(107\) | −18.1309 | −1.75278 | −0.876392 | − | 0.481599i | \(-0.840056\pi\) | ||||
−0.876392 | + | 0.481599i | \(0.840056\pi\) | |||||||
\(108\) | −1.91474 | −0.184246 | ||||||||
\(109\) | 3.57733 | 0.342646 | 0.171323 | − | 0.985215i | \(-0.445196\pi\) | ||||
0.171323 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(110\) | 4.05695 | 0.386815 | ||||||||
\(111\) | −4.14408 | −0.393339 | ||||||||
\(112\) | −13.6636 | −1.29109 | ||||||||
\(113\) | 7.41181 | 0.697244 | 0.348622 | − | 0.937263i | \(-0.386650\pi\) | ||||
0.348622 | + | 0.937263i | \(0.386650\pi\) | |||||||
\(114\) | −1.57041 | −0.147082 | ||||||||
\(115\) | 28.2123 | 2.63081 | ||||||||
\(116\) | −15.6289 | −1.45111 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 1.57514 | 0.145003 | ||||||||
\(119\) | 2.93652 | 0.269190 | ||||||||
\(120\) | −3.90927 | −0.356865 | ||||||||
\(121\) | 5.50499 | 0.500454 | ||||||||
\(122\) | 0.420295 | 0.0380517 | ||||||||
\(123\) | 0.461243 | 0.0415889 | ||||||||
\(124\) | −3.63409 | −0.326350 | ||||||||
\(125\) | −5.80277 | −0.519016 | ||||||||
\(126\) | 1.14127 | 0.101672 | ||||||||
\(127\) | −11.5345 | −1.02352 | −0.511761 | − | 0.859128i | \(-0.671007\pi\) | ||||
−0.511761 | + | 0.859128i | \(0.671007\pi\) | |||||||
\(128\) | 8.37307 | 0.740082 | ||||||||
\(129\) | 0.847965 | 0.0746592 | ||||||||
\(130\) | −0.998600 | −0.0875830 | ||||||||
\(131\) | −10.3087 | −0.900677 | −0.450339 | − | 0.892858i | \(-0.648697\pi\) | ||||
−0.450339 | + | 0.892858i | \(0.648697\pi\) | |||||||
\(132\) | −7.77891 | −0.677067 | ||||||||
\(133\) | −21.0223 | −1.82286 | ||||||||
\(134\) | −1.55754 | −0.134551 | ||||||||
\(135\) | −3.42004 | −0.294350 | ||||||||
\(136\) | −0.858755 | −0.0736376 | ||||||||
\(137\) | −0.280481 | −0.0239631 | −0.0119815 | − | 0.999928i | \(-0.503814\pi\) | ||||
−0.0119815 | + | 0.999928i | \(0.503814\pi\) | |||||||
\(138\) | 2.40861 | 0.205035 | ||||||||
\(139\) | 16.5220 | 1.40137 | 0.700687 | − | 0.713469i | \(-0.252877\pi\) | ||||
0.700687 | + | 0.713469i | \(0.252877\pi\) | |||||||
\(140\) | −25.5959 | −2.16324 | ||||||||
\(141\) | 8.10038 | 0.682175 | ||||||||
\(142\) | 0.373863 | 0.0313739 | ||||||||
\(143\) | −4.06263 | −0.339735 | ||||||||
\(144\) | 3.49574 | 0.291312 | ||||||||
\(145\) | −27.9158 | −2.31828 | ||||||||
\(146\) | −1.74495 | −0.144413 | ||||||||
\(147\) | 8.27757 | 0.682722 | ||||||||
\(148\) | 7.93486 | 0.652241 | ||||||||
\(149\) | 3.22493 | 0.264196 | 0.132098 | − | 0.991237i | \(-0.457829\pi\) | ||||
0.132098 | + | 0.991237i | \(0.457829\pi\) | |||||||
\(150\) | −1.95533 | −0.159652 | ||||||||
\(151\) | −12.1172 | −0.986085 | −0.493043 | − | 0.870005i | \(-0.664115\pi\) | ||||
−0.493043 | + | 0.870005i | \(0.664115\pi\) | |||||||
\(152\) | 6.14775 | 0.498648 | ||||||||
\(153\) | −0.751286 | −0.0607379 | ||||||||
\(154\) | 4.63655 | 0.373624 | ||||||||
\(155\) | −6.49106 | −0.521375 | ||||||||
\(156\) | 1.91474 | 0.153302 | ||||||||
\(157\) | −6.90402 | −0.551001 | −0.275501 | − | 0.961301i | \(-0.588844\pi\) | ||||
−0.275501 | + | 0.961301i | \(0.588844\pi\) | |||||||
\(158\) | 2.57928 | 0.205197 | ||||||||
\(159\) | 2.55597 | 0.202702 | ||||||||
\(160\) | 11.3094 | 0.894085 | ||||||||
\(161\) | 32.2429 | 2.54110 | ||||||||
\(162\) | −0.291985 | −0.0229405 | ||||||||
\(163\) | −10.0169 | −0.784585 | −0.392293 | − | 0.919840i | \(-0.628318\pi\) | ||||
−0.392293 | + | 0.919840i | \(0.628318\pi\) | |||||||
\(164\) | −0.883163 | −0.0689635 | ||||||||
\(165\) | −13.8944 | −1.08168 | ||||||||
\(166\) | −3.30664 | −0.256645 | ||||||||
\(167\) | −3.84284 | −0.297368 | −0.148684 | − | 0.988885i | \(-0.547504\pi\) | ||||
−0.148684 | + | 0.988885i | \(0.547504\pi\) | |||||||
\(168\) | −4.46777 | −0.344696 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.750235 | −0.0575404 | ||||||||
\(171\) | 5.37839 | 0.411296 | ||||||||
\(172\) | −1.62364 | −0.123801 | ||||||||
\(173\) | −18.6286 | −1.41631 | −0.708154 | − | 0.706058i | \(-0.750472\pi\) | ||||
−0.708154 | + | 0.706058i | \(0.750472\pi\) | |||||||
\(174\) | −2.38330 | −0.180677 | ||||||||
\(175\) | −26.1751 | −1.97865 | ||||||||
\(176\) | 14.2019 | 1.07051 | ||||||||
\(177\) | −5.39458 | −0.405482 | ||||||||
\(178\) | 3.68547 | 0.276238 | ||||||||
\(179\) | −20.6618 | −1.54433 | −0.772166 | − | 0.635421i | \(-0.780827\pi\) | ||||
−0.772166 | + | 0.635421i | \(0.780827\pi\) | |||||||
\(180\) | 6.54851 | 0.488097 | ||||||||
\(181\) | −21.6202 | −1.60701 | −0.803507 | − | 0.595295i | \(-0.797035\pi\) | ||||
−0.803507 | + | 0.595295i | \(0.797035\pi\) | |||||||
\(182\) | −1.14127 | −0.0845963 | ||||||||
\(183\) | −1.43944 | −0.106407 | ||||||||
\(184\) | −9.42911 | −0.695123 | ||||||||
\(185\) | 14.1729 | 1.04202 | ||||||||
\(186\) | −0.554172 | −0.0406338 | ||||||||
\(187\) | −3.05220 | −0.223199 | ||||||||
\(188\) | −15.5102 | −1.13119 | ||||||||
\(189\) | −3.90865 | −0.284313 | ||||||||
\(190\) | 5.37086 | 0.389643 | ||||||||
\(191\) | 16.0629 | 1.16227 | 0.581134 | − | 0.813808i | \(-0.302609\pi\) | ||||
0.581134 | + | 0.813808i | \(0.302609\pi\) | |||||||
\(192\) | −6.02594 | −0.434885 | ||||||||
\(193\) | −1.18317 | −0.0851665 | −0.0425832 | − | 0.999093i | \(-0.513559\pi\) | ||||
−0.0425832 | + | 0.999093i | \(0.513559\pi\) | |||||||
\(194\) | 1.24469 | 0.0893638 | ||||||||
\(195\) | 3.42004 | 0.244914 | ||||||||
\(196\) | −15.8494 | −1.13210 | ||||||||
\(197\) | −21.1485 | −1.50677 | −0.753383 | − | 0.657582i | \(-0.771579\pi\) | ||||
−0.753383 | + | 0.657582i | \(0.771579\pi\) | |||||||
\(198\) | −1.18623 | −0.0843015 | ||||||||
\(199\) | −10.8945 | −0.772287 | −0.386144 | − | 0.922439i | \(-0.626193\pi\) | ||||
−0.386144 | + | 0.922439i | \(0.626193\pi\) | |||||||
\(200\) | 7.65463 | 0.541264 | ||||||||
\(201\) | 5.33432 | 0.376254 | ||||||||
\(202\) | 0.955622 | 0.0672374 | ||||||||
\(203\) | −31.9040 | −2.23922 | ||||||||
\(204\) | 1.43852 | 0.100717 | ||||||||
\(205\) | −1.57747 | −0.110175 | ||||||||
\(206\) | −0.291985 | −0.0203435 | ||||||||
\(207\) | −8.24911 | −0.573353 | ||||||||
\(208\) | −3.49574 | −0.242386 | ||||||||
\(209\) | 21.8504 | 1.51143 | ||||||||
\(210\) | −3.90318 | −0.269345 | ||||||||
\(211\) | 1.53355 | 0.105574 | 0.0527869 | − | 0.998606i | \(-0.483190\pi\) | ||||
0.0527869 | + | 0.998606i | \(0.483190\pi\) | |||||||
\(212\) | −4.89403 | −0.336123 | ||||||||
\(213\) | −1.28042 | −0.0877330 | ||||||||
\(214\) | 5.29396 | 0.361887 | ||||||||
\(215\) | −2.90008 | −0.197784 | ||||||||
\(216\) | 1.14305 | 0.0777744 | ||||||||
\(217\) | −7.41842 | −0.503595 | ||||||||
\(218\) | −1.04452 | −0.0707441 | ||||||||
\(219\) | 5.97616 | 0.403831 | ||||||||
\(220\) | 26.6042 | 1.79365 | ||||||||
\(221\) | 0.751286 | 0.0505370 | ||||||||
\(222\) | 1.21001 | 0.0812104 | ||||||||
\(223\) | −7.27176 | −0.486953 | −0.243476 | − | 0.969907i | \(-0.578288\pi\) | ||||
−0.243476 | + | 0.969907i | \(0.578288\pi\) | |||||||
\(224\) | 12.9251 | 0.863595 | ||||||||
\(225\) | 6.69670 | 0.446446 | ||||||||
\(226\) | −2.16413 | −0.143956 | ||||||||
\(227\) | −19.6771 | −1.30602 | −0.653008 | − | 0.757351i | \(-0.726493\pi\) | ||||
−0.653008 | + | 0.757351i | \(0.726493\pi\) | |||||||
\(228\) | −10.2982 | −0.682018 | ||||||||
\(229\) | −12.7100 | −0.839899 | −0.419949 | − | 0.907548i | \(-0.637952\pi\) | ||||
−0.419949 | + | 0.907548i | \(0.637952\pi\) | |||||||
\(230\) | −8.23757 | −0.543169 | ||||||||
\(231\) | −15.8794 | −1.04479 | ||||||||
\(232\) | 9.33000 | 0.612544 | ||||||||
\(233\) | 11.1281 | 0.729029 | 0.364515 | − | 0.931198i | \(-0.381235\pi\) | ||||
0.364515 | + | 0.931198i | \(0.381235\pi\) | |||||||
\(234\) | 0.291985 | 0.0190876 | ||||||||
\(235\) | −27.7037 | −1.80719 | ||||||||
\(236\) | 10.3292 | 0.672377 | ||||||||
\(237\) | −8.83363 | −0.573806 | ||||||||
\(238\) | −0.857418 | −0.0555782 | ||||||||
\(239\) | 23.2690 | 1.50514 | 0.752572 | − | 0.658510i | \(-0.228813\pi\) | ||||
0.752572 | + | 0.658510i | \(0.228813\pi\) | |||||||
\(240\) | −11.9556 | −0.771729 | ||||||||
\(241\) | −7.36801 | −0.474616 | −0.237308 | − | 0.971435i | \(-0.576265\pi\) | ||||
−0.237308 | + | 0.971435i | \(0.576265\pi\) | |||||||
\(242\) | −1.60737 | −0.103326 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.75617 | 0.176445 | ||||||||
\(245\) | −28.3096 | −1.80864 | ||||||||
\(246\) | −0.134676 | −0.00858663 | ||||||||
\(247\) | −5.37839 | −0.342219 | ||||||||
\(248\) | 2.16944 | 0.137760 | ||||||||
\(249\) | 11.3247 | 0.717674 | ||||||||
\(250\) | 1.69432 | 0.107158 | ||||||||
\(251\) | 7.87972 | 0.497364 | 0.248682 | − | 0.968585i | \(-0.420003\pi\) | ||||
0.248682 | + | 0.968585i | \(0.420003\pi\) | |||||||
\(252\) | 7.48407 | 0.471452 | ||||||||
\(253\) | −33.5131 | −2.10695 | ||||||||
\(254\) | 3.36790 | 0.211321 | ||||||||
\(255\) | 2.56943 | 0.160904 | ||||||||
\(256\) | 9.60708 | 0.600442 | ||||||||
\(257\) | 6.16495 | 0.384559 | 0.192280 | − | 0.981340i | \(-0.438412\pi\) | ||||
0.192280 | + | 0.981340i | \(0.438412\pi\) | |||||||
\(258\) | −0.247593 | −0.0154145 | ||||||||
\(259\) | 16.1978 | 1.00648 | ||||||||
\(260\) | −6.54851 | −0.406121 | ||||||||
\(261\) | 8.16240 | 0.505240 | ||||||||
\(262\) | 3.00999 | 0.185958 | ||||||||
\(263\) | 10.4331 | 0.643330 | 0.321665 | − | 0.946853i | \(-0.395757\pi\) | ||||
0.321665 | + | 0.946853i | \(0.395757\pi\) | |||||||
\(264\) | 4.64378 | 0.285805 | ||||||||
\(265\) | −8.74152 | −0.536988 | ||||||||
\(266\) | 6.13818 | 0.376356 | ||||||||
\(267\) | −12.6221 | −0.772462 | ||||||||
\(268\) | −10.2139 | −0.623910 | ||||||||
\(269\) | 2.25633 | 0.137571 | 0.0687853 | − | 0.997631i | \(-0.478088\pi\) | ||||
0.0687853 | + | 0.997631i | \(0.478088\pi\) | |||||||
\(270\) | 0.998600 | 0.0607729 | ||||||||
\(271\) | −7.93979 | −0.482308 | −0.241154 | − | 0.970487i | \(-0.577526\pi\) | ||||
−0.241154 | + | 0.970487i | \(0.577526\pi\) | |||||||
\(272\) | −2.62630 | −0.159243 | ||||||||
\(273\) | 3.90865 | 0.236562 | ||||||||
\(274\) | 0.0818961 | 0.00494752 | ||||||||
\(275\) | 27.2062 | 1.64060 | ||||||||
\(276\) | 15.7949 | 0.950744 | ||||||||
\(277\) | −24.1539 | −1.45127 | −0.725635 | − | 0.688080i | \(-0.758454\pi\) | ||||
−0.725635 | + | 0.688080i | \(0.758454\pi\) | |||||||
\(278\) | −4.82416 | −0.289334 | ||||||||
\(279\) | 1.89795 | 0.113627 | ||||||||
\(280\) | 15.2800 | 0.913152 | ||||||||
\(281\) | 26.4669 | 1.57888 | 0.789441 | − | 0.613827i | \(-0.210371\pi\) | ||||
0.789441 | + | 0.613827i | \(0.210371\pi\) | |||||||
\(282\) | −2.36519 | −0.140845 | ||||||||
\(283\) | −5.24325 | −0.311679 | −0.155839 | − | 0.987782i | \(-0.549808\pi\) | ||||
−0.155839 | + | 0.987782i | \(0.549808\pi\) | |||||||
\(284\) | 2.45168 | 0.145480 | ||||||||
\(285\) | −18.3943 | −1.08959 | ||||||||
\(286\) | 1.18623 | 0.0701431 | ||||||||
\(287\) | −1.80284 | −0.106418 | ||||||||
\(288\) | −3.30679 | −0.194855 | ||||||||
\(289\) | −16.4356 | −0.966798 | ||||||||
\(290\) | 8.15097 | 0.478642 | ||||||||
\(291\) | −4.26288 | −0.249894 | ||||||||
\(292\) | −11.4428 | −0.669640 | ||||||||
\(293\) | 27.1084 | 1.58369 | 0.791845 | − | 0.610722i | \(-0.209121\pi\) | ||||
0.791845 | + | 0.610722i | \(0.209121\pi\) | |||||||
\(294\) | −2.41692 | −0.140958 | ||||||||
\(295\) | 18.4497 | 1.07418 | ||||||||
\(296\) | −4.73687 | −0.275325 | ||||||||
\(297\) | 4.06263 | 0.235738 | ||||||||
\(298\) | −0.941629 | −0.0545471 | ||||||||
\(299\) | 8.24911 | 0.477058 | ||||||||
\(300\) | −12.8225 | −0.740305 | ||||||||
\(301\) | −3.31440 | −0.191039 | ||||||||
\(302\) | 3.53804 | 0.203591 | ||||||||
\(303\) | −3.27285 | −0.188020 | ||||||||
\(304\) | 18.8014 | 1.07834 | ||||||||
\(305\) | 4.92296 | 0.281888 | ||||||||
\(306\) | 0.219364 | 0.0125402 | ||||||||
\(307\) | 29.6254 | 1.69081 | 0.845404 | − | 0.534127i | \(-0.179359\pi\) | ||||
0.845404 | + | 0.534127i | \(0.179359\pi\) | |||||||
\(308\) | 30.4050 | 1.73249 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 1.89529 | 0.107645 | ||||||||
\(311\) | 27.3840 | 1.55280 | 0.776402 | − | 0.630238i | \(-0.217043\pi\) | ||||
0.776402 | + | 0.630238i | \(0.217043\pi\) | |||||||
\(312\) | −1.14305 | −0.0647122 | ||||||||
\(313\) | −3.74737 | −0.211814 | −0.105907 | − | 0.994376i | \(-0.533775\pi\) | ||||
−0.105907 | + | 0.994376i | \(0.533775\pi\) | |||||||
\(314\) | 2.01587 | 0.113762 | ||||||||
\(315\) | 13.3678 | 0.753188 | ||||||||
\(316\) | 16.9141 | 0.951495 | ||||||||
\(317\) | 27.9021 | 1.56714 | 0.783569 | − | 0.621304i | \(-0.213397\pi\) | ||||
0.783569 | + | 0.621304i | \(0.213397\pi\) | |||||||
\(318\) | −0.746304 | −0.0418506 | ||||||||
\(319\) | 33.1608 | 1.85665 | ||||||||
\(320\) | 20.6090 | 1.15208 | ||||||||
\(321\) | −18.1309 | −1.01197 | ||||||||
\(322\) | −9.41444 | −0.524646 | ||||||||
\(323\) | −4.04071 | −0.224831 | ||||||||
\(324\) | −1.91474 | −0.106375 | ||||||||
\(325\) | −6.69670 | −0.371466 | ||||||||
\(326\) | 2.92479 | 0.161989 | ||||||||
\(327\) | 3.57733 | 0.197827 | ||||||||
\(328\) | 0.527222 | 0.0291110 | ||||||||
\(329\) | −31.6616 | −1.74556 | ||||||||
\(330\) | 4.05695 | 0.223328 | ||||||||
\(331\) | −16.3140 | −0.896699 | −0.448350 | − | 0.893858i | \(-0.647988\pi\) | ||||
−0.448350 | + | 0.893858i | \(0.647988\pi\) | |||||||
\(332\) | −21.6839 | −1.19006 | ||||||||
\(333\) | −4.14408 | −0.227094 | ||||||||
\(334\) | 1.12205 | 0.0613958 | ||||||||
\(335\) | −18.2436 | −0.996754 | ||||||||
\(336\) | −13.6636 | −0.745412 | ||||||||
\(337\) | −9.27981 | −0.505504 | −0.252752 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252752 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(338\) | −0.291985 | −0.0158819 | ||||||||
\(339\) | 7.41181 | 0.402554 | ||||||||
\(340\) | −4.91981 | −0.266814 | ||||||||
\(341\) | 7.71066 | 0.417556 | ||||||||
\(342\) | −1.57041 | −0.0849179 | ||||||||
\(343\) | −4.99356 | −0.269627 | ||||||||
\(344\) | 0.969263 | 0.0522592 | ||||||||
\(345\) | 28.2123 | 1.51890 | ||||||||
\(346\) | 5.43927 | 0.292417 | ||||||||
\(347\) | −24.4834 | −1.31434 | −0.657169 | − | 0.753743i | \(-0.728246\pi\) | ||||
−0.657169 | + | 0.753743i | \(0.728246\pi\) | |||||||
\(348\) | −15.6289 | −0.837798 | ||||||||
\(349\) | −20.5689 | −1.10103 | −0.550514 | − | 0.834826i | \(-0.685568\pi\) | ||||
−0.550514 | + | 0.834826i | \(0.685568\pi\) | |||||||
\(350\) | 7.64272 | 0.408520 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −13.4343 | −0.716050 | ||||||||
\(353\) | 9.75708 | 0.519317 | 0.259659 | − | 0.965700i | \(-0.416390\pi\) | ||||
0.259659 | + | 0.965700i | \(0.416390\pi\) | |||||||
\(354\) | 1.57514 | 0.0837175 | ||||||||
\(355\) | 4.37909 | 0.232418 | ||||||||
\(356\) | 24.1682 | 1.28091 | ||||||||
\(357\) | 2.93652 | 0.155417 | ||||||||
\(358\) | 6.03292 | 0.318850 | ||||||||
\(359\) | 28.4144 | 1.49965 | 0.749827 | − | 0.661634i | \(-0.230137\pi\) | ||||
0.749827 | + | 0.661634i | \(0.230137\pi\) | |||||||
\(360\) | −3.90927 | −0.206036 | ||||||||
\(361\) | 9.92708 | 0.522478 | ||||||||
\(362\) | 6.31276 | 0.331791 | ||||||||
\(363\) | 5.50499 | 0.288937 | ||||||||
\(364\) | −7.48407 | −0.392272 | ||||||||
\(365\) | −20.4387 | −1.06981 | ||||||||
\(366\) | 0.420295 | 0.0219692 | ||||||||
\(367\) | −28.0983 | −1.46672 | −0.733359 | − | 0.679841i | \(-0.762049\pi\) | ||||
−0.733359 | + | 0.679841i | \(0.762049\pi\) | |||||||
\(368\) | −28.8367 | −1.50322 | ||||||||
\(369\) | 0.461243 | 0.0240114 | ||||||||
\(370\) | −4.13828 | −0.215139 | ||||||||
\(371\) | −9.99039 | −0.518675 | ||||||||
\(372\) | −3.63409 | −0.188419 | ||||||||
\(373\) | −19.8663 | −1.02864 | −0.514319 | − | 0.857599i | \(-0.671955\pi\) | ||||
−0.514319 | + | 0.857599i | \(0.671955\pi\) | |||||||
\(374\) | 0.891196 | 0.0460826 | ||||||||
\(375\) | −5.80277 | −0.299654 | ||||||||
\(376\) | 9.25911 | 0.477502 | ||||||||
\(377\) | −8.16240 | −0.420385 | ||||||||
\(378\) | 1.14127 | 0.0587004 | ||||||||
\(379\) | 10.7347 | 0.551406 | 0.275703 | − | 0.961243i | \(-0.411089\pi\) | ||||
0.275703 | + | 0.961243i | \(0.411089\pi\) | |||||||
\(380\) | 35.2204 | 1.80677 | ||||||||
\(381\) | −11.5345 | −0.590931 | ||||||||
\(382\) | −4.69011 | −0.239967 | ||||||||
\(383\) | 14.5351 | 0.742710 | 0.371355 | − | 0.928491i | \(-0.378893\pi\) | ||||
0.371355 | + | 0.928491i | \(0.378893\pi\) | |||||||
\(384\) | 8.37307 | 0.427286 | ||||||||
\(385\) | 54.3083 | 2.76781 | ||||||||
\(386\) | 0.345468 | 0.0175838 | ||||||||
\(387\) | 0.847965 | 0.0431045 | ||||||||
\(388\) | 8.16232 | 0.414379 | ||||||||
\(389\) | 37.4501 | 1.89879 | 0.949397 | − | 0.314080i | \(-0.101696\pi\) | ||||
0.949397 | + | 0.314080i | \(0.101696\pi\) | |||||||
\(390\) | −0.998600 | −0.0505661 | ||||||||
\(391\) | 6.19744 | 0.313418 | ||||||||
\(392\) | 9.46164 | 0.477885 | ||||||||
\(393\) | −10.3087 | −0.520006 | ||||||||
\(394\) | 6.17503 | 0.311093 | ||||||||
\(395\) | 30.2114 | 1.52010 | ||||||||
\(396\) | −7.77891 | −0.390905 | ||||||||
\(397\) | −16.5911 | −0.832683 | −0.416342 | − | 0.909208i | \(-0.636688\pi\) | ||||
−0.416342 | + | 0.909208i | \(0.636688\pi\) | |||||||
\(398\) | 3.18101 | 0.159450 | ||||||||
\(399\) | −21.0223 | −1.05243 | ||||||||
\(400\) | 23.4099 | 1.17049 | ||||||||
\(401\) | −34.1489 | −1.70531 | −0.852656 | − | 0.522472i | \(-0.825010\pi\) | ||||
−0.852656 | + | 0.522472i | \(0.825010\pi\) | |||||||
\(402\) | −1.55754 | −0.0776830 | ||||||||
\(403\) | −1.89795 | −0.0945435 | ||||||||
\(404\) | 6.26667 | 0.311779 | ||||||||
\(405\) | −3.42004 | −0.169943 | ||||||||
\(406\) | 9.31548 | 0.462319 | ||||||||
\(407\) | −16.8359 | −0.834524 | ||||||||
\(408\) | −0.858755 | −0.0425147 | ||||||||
\(409\) | −12.3348 | −0.609917 | −0.304958 | − | 0.952366i | \(-0.598643\pi\) | ||||
−0.304958 | + | 0.952366i | \(0.598643\pi\) | |||||||
\(410\) | 0.460598 | 0.0227473 | ||||||||
\(411\) | −0.280481 | −0.0138351 | ||||||||
\(412\) | −1.91474 | −0.0943327 | ||||||||
\(413\) | 21.0855 | 1.03755 | ||||||||
\(414\) | 2.40861 | 0.118377 | ||||||||
\(415\) | −38.7310 | −1.90123 | ||||||||
\(416\) | 3.30679 | 0.162129 | ||||||||
\(417\) | 16.5220 | 0.809084 | ||||||||
\(418\) | −6.37999 | −0.312056 | ||||||||
\(419\) | 22.7240 | 1.11014 | 0.555070 | − | 0.831804i | \(-0.312692\pi\) | ||||
0.555070 | + | 0.831804i | \(0.312692\pi\) | |||||||
\(420\) | −25.5959 | −1.24895 | ||||||||
\(421\) | 30.5654 | 1.48967 | 0.744833 | − | 0.667251i | \(-0.232529\pi\) | ||||
0.744833 | + | 0.667251i | \(0.232529\pi\) | |||||||
\(422\) | −0.447773 | −0.0217972 | ||||||||
\(423\) | 8.10038 | 0.393854 | ||||||||
\(424\) | 2.92159 | 0.141885 | ||||||||
\(425\) | −5.03114 | −0.244046 | ||||||||
\(426\) | 0.373863 | 0.0181137 | ||||||||
\(427\) | 5.62628 | 0.272275 | ||||||||
\(428\) | 34.7161 | 1.67807 | ||||||||
\(429\) | −4.06263 | −0.196146 | ||||||||
\(430\) | 0.846778 | 0.0408353 | ||||||||
\(431\) | −15.5146 | −0.747314 | −0.373657 | − | 0.927567i | \(-0.621896\pi\) | ||||
−0.373657 | + | 0.927567i | \(0.621896\pi\) | |||||||
\(432\) | 3.49574 | 0.168189 | ||||||||
\(433\) | −17.7167 | −0.851409 | −0.425704 | − | 0.904862i | \(-0.639974\pi\) | ||||
−0.425704 | + | 0.904862i | \(0.639974\pi\) | |||||||
\(434\) | 2.16606 | 0.103974 | ||||||||
\(435\) | −27.9158 | −1.33846 | ||||||||
\(436\) | −6.84967 | −0.328039 | ||||||||
\(437\) | −44.3669 | −2.12236 | ||||||||
\(438\) | −1.74495 | −0.0833767 | ||||||||
\(439\) | 24.4918 | 1.16893 | 0.584464 | − | 0.811419i | \(-0.301305\pi\) | ||||
0.584464 | + | 0.811419i | \(0.301305\pi\) | |||||||
\(440\) | −15.8819 | −0.757141 | ||||||||
\(441\) | 8.27757 | 0.394170 | ||||||||
\(442\) | −0.219364 | −0.0104341 | ||||||||
\(443\) | 14.0806 | 0.668988 | 0.334494 | − | 0.942398i | \(-0.391435\pi\) | ||||
0.334494 | + | 0.942398i | \(0.391435\pi\) | |||||||
\(444\) | 7.93486 | 0.376572 | ||||||||
\(445\) | 43.1683 | 2.04637 | ||||||||
\(446\) | 2.12324 | 0.100538 | ||||||||
\(447\) | 3.22493 | 0.152534 | ||||||||
\(448\) | 23.5533 | 1.11279 | ||||||||
\(449\) | 26.2006 | 1.23648 | 0.618241 | − | 0.785989i | \(-0.287846\pi\) | ||||
0.618241 | + | 0.785989i | \(0.287846\pi\) | |||||||
\(450\) | −1.95533 | −0.0921753 | ||||||||
\(451\) | 1.87386 | 0.0882367 | ||||||||
\(452\) | −14.1917 | −0.667522 | ||||||||
\(453\) | −12.1172 | −0.569317 | ||||||||
\(454\) | 5.74542 | 0.269646 | ||||||||
\(455\) | −13.3678 | −0.626690 | ||||||||
\(456\) | 6.14775 | 0.287895 | ||||||||
\(457\) | 24.4187 | 1.14226 | 0.571129 | − | 0.820860i | \(-0.306505\pi\) | ||||
0.571129 | + | 0.820860i | \(0.306505\pi\) | |||||||
\(458\) | 3.71112 | 0.173409 | ||||||||
\(459\) | −0.751286 | −0.0350670 | ||||||||
\(460\) | −54.0194 | −2.51867 | ||||||||
\(461\) | −2.64630 | −0.123250 | −0.0616252 | − | 0.998099i | \(-0.519628\pi\) | ||||
−0.0616252 | + | 0.998099i | \(0.519628\pi\) | |||||||
\(462\) | 4.63655 | 0.215712 | ||||||||
\(463\) | −8.27785 | −0.384704 | −0.192352 | − | 0.981326i | \(-0.561612\pi\) | ||||
−0.192352 | + | 0.981326i | \(0.561612\pi\) | |||||||
\(464\) | 28.5336 | 1.32464 | ||||||||
\(465\) | −6.49106 | −0.301016 | ||||||||
\(466\) | −3.24925 | −0.150519 | ||||||||
\(467\) | 6.41694 | 0.296941 | 0.148470 | − | 0.988917i | \(-0.452565\pi\) | ||||
0.148470 | + | 0.988917i | \(0.452565\pi\) | |||||||
\(468\) | 1.91474 | 0.0885091 | ||||||||
\(469\) | −20.8500 | −0.962763 | ||||||||
\(470\) | 8.08904 | 0.373120 | ||||||||
\(471\) | −6.90402 | −0.318121 | ||||||||
\(472\) | −6.16625 | −0.283825 | ||||||||
\(473\) | 3.44497 | 0.158400 | ||||||||
\(474\) | 2.57928 | 0.118470 | ||||||||
\(475\) | 36.0174 | 1.65259 | ||||||||
\(476\) | −5.62268 | −0.257715 | ||||||||
\(477\) | 2.55597 | 0.117030 | ||||||||
\(478\) | −6.79418 | −0.310759 | ||||||||
\(479\) | −18.2673 | −0.834653 | −0.417327 | − | 0.908757i | \(-0.637033\pi\) | ||||
−0.417327 | + | 0.908757i | \(0.637033\pi\) | |||||||
\(480\) | 11.3094 | 0.516200 | ||||||||
\(481\) | 4.14408 | 0.188954 | ||||||||
\(482\) | 2.15135 | 0.0979912 | ||||||||
\(483\) | 32.2429 | 1.46710 | ||||||||
\(484\) | −10.5407 | −0.479121 | ||||||||
\(485\) | 14.5792 | 0.662008 | ||||||||
\(486\) | −0.291985 | −0.0132447 | ||||||||
\(487\) | 20.5854 | 0.932814 | 0.466407 | − | 0.884570i | \(-0.345548\pi\) | ||||
0.466407 | + | 0.884570i | \(0.345548\pi\) | |||||||
\(488\) | −1.64535 | −0.0744814 | ||||||||
\(489\) | −10.0169 | −0.452981 | ||||||||
\(490\) | 8.26598 | 0.373419 | ||||||||
\(491\) | −35.2613 | −1.59132 | −0.795660 | − | 0.605743i | \(-0.792876\pi\) | ||||
−0.795660 | + | 0.605743i | \(0.792876\pi\) | |||||||
\(492\) | −0.883163 | −0.0398161 | ||||||||
\(493\) | −6.13230 | −0.276185 | ||||||||
\(494\) | 1.57041 | 0.0706560 | ||||||||
\(495\) | −13.8944 | −0.624506 | ||||||||
\(496\) | 6.63473 | 0.297908 | ||||||||
\(497\) | 5.00472 | 0.224492 | ||||||||
\(498\) | −3.30664 | −0.148174 | ||||||||
\(499\) | 12.3590 | 0.553267 | 0.276633 | − | 0.960976i | \(-0.410781\pi\) | ||||
0.276633 | + | 0.960976i | \(0.410781\pi\) | |||||||
\(500\) | 11.1108 | 0.496891 | ||||||||
\(501\) | −3.84284 | −0.171685 | ||||||||
\(502\) | −2.30076 | −0.102688 | ||||||||
\(503\) | 8.11879 | 0.361999 | 0.180999 | − | 0.983483i | \(-0.442067\pi\) | ||||
0.180999 | + | 0.983483i | \(0.442067\pi\) | |||||||
\(504\) | −4.46777 | −0.199010 | ||||||||
\(505\) | 11.1933 | 0.498095 | ||||||||
\(506\) | 9.78532 | 0.435010 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 22.0856 | 0.979892 | ||||||||
\(509\) | −1.23756 | −0.0548540 | −0.0274270 | − | 0.999624i | \(-0.508731\pi\) | ||||
−0.0274270 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(510\) | −0.750235 | −0.0332210 | ||||||||
\(511\) | −23.3587 | −1.03333 | ||||||||
\(512\) | −19.5513 | −0.864052 | ||||||||
\(513\) | 5.37839 | 0.237462 | ||||||||
\(514\) | −1.80007 | −0.0793978 | ||||||||
\(515\) | −3.42004 | −0.150705 | ||||||||
\(516\) | −1.62364 | −0.0714767 | ||||||||
\(517\) | 32.9089 | 1.44733 | ||||||||
\(518\) | −4.72950 | −0.207802 | ||||||||
\(519\) | −18.6286 | −0.817705 | ||||||||
\(520\) | 3.90927 | 0.171433 | ||||||||
\(521\) | 25.9861 | 1.13847 | 0.569236 | − | 0.822174i | \(-0.307239\pi\) | ||||
0.569236 | + | 0.822174i | \(0.307239\pi\) | |||||||
\(522\) | −2.38330 | −0.104314 | ||||||||
\(523\) | 8.85525 | 0.387213 | 0.193606 | − | 0.981079i | \(-0.437982\pi\) | ||||
0.193606 | + | 0.981079i | \(0.437982\pi\) | |||||||
\(524\) | 19.7386 | 0.862283 | ||||||||
\(525\) | −26.1751 | −1.14237 | ||||||||
\(526\) | −3.04630 | −0.132825 | ||||||||
\(527\) | −1.42590 | −0.0621133 | ||||||||
\(528\) | 14.2019 | 0.618059 | ||||||||
\(529\) | 45.0478 | 1.95860 | ||||||||
\(530\) | 2.55239 | 0.110869 | ||||||||
\(531\) | −5.39458 | −0.234105 | ||||||||
\(532\) | 40.2523 | 1.74516 | ||||||||
\(533\) | −0.461243 | −0.0199787 | ||||||||
\(534\) | 3.68547 | 0.159486 | ||||||||
\(535\) | 62.0086 | 2.68086 | ||||||||
\(536\) | 6.09737 | 0.263366 | ||||||||
\(537\) | −20.6618 | −0.891620 | ||||||||
\(538\) | −0.658813 | −0.0284034 | ||||||||
\(539\) | 33.6287 | 1.44849 | ||||||||
\(540\) | 6.54851 | 0.281803 | ||||||||
\(541\) | −1.98118 | −0.0851774 | −0.0425887 | − | 0.999093i | \(-0.513561\pi\) | ||||
−0.0425887 | + | 0.999093i | \(0.513561\pi\) | |||||||
\(542\) | 2.31830 | 0.0995795 | ||||||||
\(543\) | −21.6202 | −0.927810 | ||||||||
\(544\) | 2.48435 | 0.106516 | ||||||||
\(545\) | −12.2346 | −0.524073 | ||||||||
\(546\) | −1.14127 | −0.0488417 | ||||||||
\(547\) | −38.2448 | −1.63523 | −0.817615 | − | 0.575765i | \(-0.804704\pi\) | ||||
−0.817615 | + | 0.575765i | \(0.804704\pi\) | |||||||
\(548\) | 0.537049 | 0.0229416 | ||||||||
\(549\) | −1.43944 | −0.0614339 | ||||||||
\(550\) | −7.94380 | −0.338725 | ||||||||
\(551\) | 43.9006 | 1.87023 | ||||||||
\(552\) | −9.42911 | −0.401330 | ||||||||
\(553\) | 34.5276 | 1.46826 | ||||||||
\(554\) | 7.05258 | 0.299636 | ||||||||
\(555\) | 14.1729 | 0.601608 | ||||||||
\(556\) | −31.6353 | −1.34164 | ||||||||
\(557\) | 18.2115 | 0.771646 | 0.385823 | − | 0.922573i | \(-0.373918\pi\) | ||||
0.385823 | + | 0.922573i | \(0.373918\pi\) | |||||||
\(558\) | −0.554172 | −0.0234600 | ||||||||
\(559\) | −0.847965 | −0.0358651 | ||||||||
\(560\) | 46.7302 | 1.97471 | ||||||||
\(561\) | −3.05220 | −0.128864 | ||||||||
\(562\) | −7.72792 | −0.325983 | ||||||||
\(563\) | −28.3927 | −1.19661 | −0.598305 | − | 0.801269i | \(-0.704159\pi\) | ||||
−0.598305 | + | 0.801269i | \(0.704159\pi\) | |||||||
\(564\) | −15.5102 | −0.653096 | ||||||||
\(565\) | −25.3487 | −1.06643 | ||||||||
\(566\) | 1.53095 | 0.0643505 | ||||||||
\(567\) | −3.90865 | −0.164148 | ||||||||
\(568\) | −1.46358 | −0.0614104 | ||||||||
\(569\) | −12.0751 | −0.506214 | −0.253107 | − | 0.967438i | \(-0.581452\pi\) | ||||
−0.253107 | + | 0.967438i | \(0.581452\pi\) | |||||||
\(570\) | 5.37086 | 0.224961 | ||||||||
\(571\) | −4.87460 | −0.203996 | −0.101998 | − | 0.994785i | \(-0.532523\pi\) | ||||
−0.101998 | + | 0.994785i | \(0.532523\pi\) | |||||||
\(572\) | 7.77891 | 0.325252 | ||||||||
\(573\) | 16.0629 | 0.671036 | ||||||||
\(574\) | 0.526402 | 0.0219716 | ||||||||
\(575\) | −55.2418 | −2.30374 | ||||||||
\(576\) | −6.02594 | −0.251081 | ||||||||
\(577\) | −3.94288 | −0.164144 | −0.0820721 | − | 0.996626i | \(-0.526154\pi\) | ||||
−0.0820721 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(578\) | 4.79893 | 0.199609 | ||||||||
\(579\) | −1.18317 | −0.0491709 | ||||||||
\(580\) | 53.4516 | 2.21946 | ||||||||
\(581\) | −44.2644 | −1.83639 | ||||||||
\(582\) | 1.24469 | 0.0515942 | ||||||||
\(583\) | 10.3840 | 0.430060 | ||||||||
\(584\) | 6.83102 | 0.282670 | ||||||||
\(585\) | 3.42004 | 0.141401 | ||||||||
\(586\) | −7.91524 | −0.326975 | ||||||||
\(587\) | −6.69981 | −0.276531 | −0.138265 | − | 0.990395i | \(-0.544153\pi\) | ||||
−0.138265 | + | 0.990395i | \(0.544153\pi\) | |||||||
\(588\) | −15.8494 | −0.653619 | ||||||||
\(589\) | 10.2079 | 0.420609 | ||||||||
\(590\) | −5.38703 | −0.221781 | ||||||||
\(591\) | −21.1485 | −0.869932 | ||||||||
\(592\) | −14.4866 | −0.595397 | ||||||||
\(593\) | −35.9666 | −1.47697 | −0.738486 | − | 0.674269i | \(-0.764459\pi\) | ||||
−0.738486 | + | 0.674269i | \(0.764459\pi\) | |||||||
\(594\) | −1.18623 | −0.0486715 | ||||||||
\(595\) | −10.0430 | −0.411723 | ||||||||
\(596\) | −6.17491 | −0.252934 | ||||||||
\(597\) | −10.8945 | −0.445880 | ||||||||
\(598\) | −2.40861 | −0.0984956 | ||||||||
\(599\) | −44.9990 | −1.83861 | −0.919304 | − | 0.393547i | \(-0.871248\pi\) | ||||
−0.919304 | + | 0.393547i | \(0.871248\pi\) | |||||||
\(600\) | 7.65463 | 0.312499 | ||||||||
\(601\) | −41.4206 | −1.68958 | −0.844791 | − | 0.535097i | \(-0.820275\pi\) | ||||
−0.844791 | + | 0.535097i | \(0.820275\pi\) | |||||||
\(602\) | 0.967755 | 0.0394427 | ||||||||
\(603\) | 5.33432 | 0.217230 | ||||||||
\(604\) | 23.2014 | 0.944051 | ||||||||
\(605\) | −18.8273 | −0.765439 | ||||||||
\(606\) | 0.955622 | 0.0388195 | ||||||||
\(607\) | −34.4093 | −1.39663 | −0.698316 | − | 0.715789i | \(-0.746067\pi\) | ||||
−0.698316 | + | 0.715789i | \(0.746067\pi\) | |||||||
\(608\) | −17.7852 | −0.721286 | ||||||||
\(609\) | −31.9040 | −1.29281 | ||||||||
\(610\) | −1.43743 | −0.0581998 | ||||||||
\(611\) | −8.10038 | −0.327706 | ||||||||
\(612\) | 1.43852 | 0.0581488 | ||||||||
\(613\) | −8.32488 | −0.336239 | −0.168119 | − | 0.985767i | \(-0.553769\pi\) | ||||
−0.168119 | + | 0.985767i | \(0.553769\pi\) | |||||||
\(614\) | −8.65015 | −0.349092 | ||||||||
\(615\) | −1.57747 | −0.0636098 | ||||||||
\(616\) | −18.1509 | −0.731321 | ||||||||
\(617\) | −5.27308 | −0.212286 | −0.106143 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106143 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(618\) | −0.291985 | −0.0117453 | ||||||||
\(619\) | 1.41263 | 0.0567785 | 0.0283892 | − | 0.999597i | \(-0.490962\pi\) | ||||
0.0283892 | + | 0.999597i | \(0.490962\pi\) | |||||||
\(620\) | 12.4287 | 0.499150 | ||||||||
\(621\) | −8.24911 | −0.331025 | ||||||||
\(622\) | −7.99571 | −0.320599 | ||||||||
\(623\) | 49.3356 | 1.97659 | ||||||||
\(624\) | −3.49574 | −0.139942 | ||||||||
\(625\) | −13.6377 | −0.545510 | ||||||||
\(626\) | 1.09417 | 0.0437320 | ||||||||
\(627\) | 21.8504 | 0.872622 | ||||||||
\(628\) | 13.2194 | 0.527513 | ||||||||
\(629\) | 3.11339 | 0.124139 | ||||||||
\(630\) | −3.90318 | −0.155506 | ||||||||
\(631\) | −3.73469 | −0.148675 | −0.0743377 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743377 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(632\) | −10.0972 | −0.401647 | ||||||||
\(633\) | 1.53355 | 0.0609531 | ||||||||
\(634\) | −8.14699 | −0.323558 | ||||||||
\(635\) | 39.4485 | 1.56547 | ||||||||
\(636\) | −4.89403 | −0.194061 | ||||||||
\(637\) | −8.27757 | −0.327969 | ||||||||
\(638\) | −9.68246 | −0.383332 | ||||||||
\(639\) | −1.28042 | −0.0506527 | ||||||||
\(640\) | −28.6363 | −1.13195 | ||||||||
\(641\) | 7.40940 | 0.292654 | 0.146327 | − | 0.989236i | \(-0.453255\pi\) | ||||
0.146327 | + | 0.989236i | \(0.453255\pi\) | |||||||
\(642\) | 5.29396 | 0.208936 | ||||||||
\(643\) | −25.2640 | −0.996316 | −0.498158 | − | 0.867086i | \(-0.665990\pi\) | ||||
−0.498158 | + | 0.867086i | \(0.665990\pi\) | |||||||
\(644\) | −61.7370 | −2.43278 | ||||||||
\(645\) | −2.90008 | −0.114190 | ||||||||
\(646\) | 1.17983 | 0.0464196 | ||||||||
\(647\) | −14.8010 | −0.581887 | −0.290944 | − | 0.956740i | \(-0.593969\pi\) | ||||
−0.290944 | + | 0.956740i | \(0.593969\pi\) | |||||||
\(648\) | 1.14305 | 0.0449031 | ||||||||
\(649\) | −21.9162 | −0.860286 | ||||||||
\(650\) | 1.95533 | 0.0766945 | ||||||||
\(651\) | −7.41842 | −0.290751 | ||||||||
\(652\) | 19.1798 | 0.751140 | ||||||||
\(653\) | −19.8418 | −0.776469 | −0.388234 | − | 0.921561i | \(-0.626915\pi\) | ||||
−0.388234 | + | 0.921561i | \(0.626915\pi\) | |||||||
\(654\) | −1.04452 | −0.0408441 | ||||||||
\(655\) | 35.2563 | 1.37758 | ||||||||
\(656\) | 1.61239 | 0.0629531 | ||||||||
\(657\) | 5.97616 | 0.233152 | ||||||||
\(658\) | 9.24470 | 0.360396 | ||||||||
\(659\) | −26.6577 | −1.03844 | −0.519219 | − | 0.854641i | \(-0.673777\pi\) | ||||
−0.519219 | + | 0.854641i | \(0.673777\pi\) | |||||||
\(660\) | 26.6042 | 1.03557 | ||||||||
\(661\) | −39.6098 | −1.54064 | −0.770321 | − | 0.637656i | \(-0.779904\pi\) | ||||
−0.770321 | + | 0.637656i | \(0.779904\pi\) | |||||||
\(662\) | 4.76344 | 0.185136 | ||||||||
\(663\) | 0.751286 | 0.0291775 | ||||||||
\(664\) | 12.9447 | 0.502350 | ||||||||
\(665\) | 71.8970 | 2.78805 | ||||||||
\(666\) | 1.21001 | 0.0468869 | ||||||||
\(667\) | −67.3325 | −2.60713 | ||||||||
\(668\) | 7.35805 | 0.284692 | ||||||||
\(669\) | −7.27176 | −0.281142 | ||||||||
\(670\) | 5.32685 | 0.205794 | ||||||||
\(671\) | −5.84793 | −0.225757 | ||||||||
\(672\) | 12.9251 | 0.498597 | ||||||||
\(673\) | −47.7062 | −1.83894 | −0.919469 | − | 0.393163i | \(-0.871381\pi\) | ||||
−0.919469 | + | 0.393163i | \(0.871381\pi\) | |||||||
\(674\) | 2.70956 | 0.104368 | ||||||||
\(675\) | 6.69670 | 0.257756 | ||||||||
\(676\) | −1.91474 | −0.0736440 | ||||||||
\(677\) | −26.2074 | −1.00723 | −0.503615 | − | 0.863928i | \(-0.667997\pi\) | ||||
−0.503615 | + | 0.863928i | \(0.667997\pi\) | |||||||
\(678\) | −2.16413 | −0.0831131 | ||||||||
\(679\) | 16.6621 | 0.639433 | ||||||||
\(680\) | 2.93698 | 0.112628 | ||||||||
\(681\) | −19.6771 | −0.754029 | ||||||||
\(682\) | −2.25140 | −0.0862104 | ||||||||
\(683\) | 4.31379 | 0.165063 | 0.0825314 | − | 0.996588i | \(-0.473700\pi\) | ||||
0.0825314 | + | 0.996588i | \(0.473700\pi\) | |||||||
\(684\) | −10.2982 | −0.393763 | ||||||||
\(685\) | 0.959256 | 0.0366513 | ||||||||
\(686\) | 1.45804 | 0.0556683 | ||||||||
\(687\) | −12.7100 | −0.484916 | ||||||||
\(688\) | 2.96426 | 0.113012 | ||||||||
\(689\) | −2.55597 | −0.0973747 | ||||||||
\(690\) | −8.23757 | −0.313599 | ||||||||
\(691\) | −5.79495 | −0.220450 | −0.110225 | − | 0.993907i | \(-0.535157\pi\) | ||||
−0.110225 | + | 0.993907i | \(0.535157\pi\) | |||||||
\(692\) | 35.6690 | 1.35593 | ||||||||
\(693\) | −15.8794 | −0.603209 | ||||||||
\(694\) | 7.14878 | 0.271364 | ||||||||
\(695\) | −56.5058 | −2.14339 | ||||||||
\(696\) | 9.33000 | 0.353653 | ||||||||
\(697\) | −0.346526 | −0.0131256 | ||||||||
\(698\) | 6.00581 | 0.227323 | ||||||||
\(699\) | 11.1281 | 0.420905 | ||||||||
\(700\) | 50.1186 | 1.89430 | ||||||||
\(701\) | −10.8920 | −0.411386 | −0.205693 | − | 0.978617i | \(-0.565945\pi\) | ||||
−0.205693 | + | 0.978617i | \(0.565945\pi\) | |||||||
\(702\) | 0.291985 | 0.0110203 | ||||||||
\(703\) | −22.2885 | −0.840626 | ||||||||
\(704\) | −24.4812 | −0.922670 | ||||||||
\(705\) | −27.7037 | −1.04338 | ||||||||
\(706\) | −2.84892 | −0.107220 | ||||||||
\(707\) | 12.7924 | 0.481109 | ||||||||
\(708\) | 10.3292 | 0.388197 | ||||||||
\(709\) | 22.8349 | 0.857582 | 0.428791 | − | 0.903404i | \(-0.358940\pi\) | ||||
0.428791 | + | 0.903404i | \(0.358940\pi\) | |||||||
\(710\) | −1.27863 | −0.0479861 | ||||||||
\(711\) | −8.83363 | −0.331287 | ||||||||
\(712\) | −14.4277 | −0.540700 | ||||||||
\(713\) | −15.6564 | −0.586336 | ||||||||
\(714\) | −0.857418 | −0.0320881 | ||||||||
\(715\) | 13.8944 | 0.519620 | ||||||||
\(716\) | 39.5620 | 1.47850 | ||||||||
\(717\) | 23.2690 | 0.868996 | ||||||||
\(718\) | −8.29657 | −0.309625 | ||||||||
\(719\) | 18.6716 | 0.696332 | 0.348166 | − | 0.937433i | \(-0.386805\pi\) | ||||
0.348166 | + | 0.937433i | \(0.386805\pi\) | |||||||
\(720\) | −11.9556 | −0.445558 | ||||||||
\(721\) | −3.90865 | −0.145566 | ||||||||
\(722\) | −2.89855 | −0.107873 | ||||||||
\(723\) | −7.36801 | −0.274019 | ||||||||
\(724\) | 41.3971 | 1.53851 | ||||||||
\(725\) | 54.6611 | 2.03006 | ||||||||
\(726\) | −1.60737 | −0.0596552 | ||||||||
\(727\) | −9.24966 | −0.343051 | −0.171525 | − | 0.985180i | \(-0.554870\pi\) | ||||
−0.171525 | + | 0.985180i | \(0.554870\pi\) | |||||||
\(728\) | 4.46777 | 0.165587 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.96779 | 0.220878 | ||||||||
\(731\) | −0.637065 | −0.0235627 | ||||||||
\(732\) | 2.75617 | 0.101871 | ||||||||
\(733\) | 7.64093 | 0.282224 | 0.141112 | − | 0.989994i | \(-0.454932\pi\) | ||||
0.141112 | + | 0.989994i | \(0.454932\pi\) | |||||||
\(734\) | 8.20427 | 0.302825 | ||||||||
\(735\) | −28.3096 | −1.04422 | ||||||||
\(736\) | 27.2781 | 1.00548 | ||||||||
\(737\) | 21.6714 | 0.798275 | ||||||||
\(738\) | −0.134676 | −0.00495749 | ||||||||
\(739\) | 52.5423 | 1.93280 | 0.966399 | − | 0.257045i | \(-0.0827488\pi\) | ||||
0.966399 | + | 0.257045i | \(0.0827488\pi\) | |||||||
\(740\) | −27.1376 | −0.997596 | ||||||||
\(741\) | −5.37839 | −0.197580 | ||||||||
\(742\) | 2.91704 | 0.107088 | ||||||||
\(743\) | 14.8996 | 0.546613 | 0.273306 | − | 0.961927i | \(-0.411883\pi\) | ||||
0.273306 | + | 0.961927i | \(0.411883\pi\) | |||||||
\(744\) | 2.16944 | 0.0795355 | ||||||||
\(745\) | −11.0294 | −0.404086 | ||||||||
\(746\) | 5.80066 | 0.212377 | ||||||||
\(747\) | 11.3247 | 0.414349 | ||||||||
\(748\) | 5.84419 | 0.213685 | ||||||||
\(749\) | 70.8675 | 2.58944 | ||||||||
\(750\) | 1.69432 | 0.0618678 | ||||||||
\(751\) | −50.0771 | −1.82734 | −0.913669 | − | 0.406458i | \(-0.866764\pi\) | ||||
−0.913669 | + | 0.406458i | \(0.866764\pi\) | |||||||
\(752\) | 28.3168 | 1.03261 | ||||||||
\(753\) | 7.87972 | 0.287153 | ||||||||
\(754\) | 2.38330 | 0.0867945 | ||||||||
\(755\) | 41.4414 | 1.50821 | ||||||||
\(756\) | 7.48407 | 0.272193 | ||||||||
\(757\) | −12.5890 | −0.457555 | −0.228777 | − | 0.973479i | \(-0.573473\pi\) | ||||
−0.228777 | + | 0.973479i | \(0.573473\pi\) | |||||||
\(758\) | −3.13437 | −0.113846 | ||||||||
\(759\) | −33.5131 | −1.21645 | ||||||||
\(760\) | −21.0256 | −0.762677 | ||||||||
\(761\) | −10.7172 | −0.388497 | −0.194248 | − | 0.980952i | \(-0.562227\pi\) | ||||
−0.194248 | + | 0.980952i | \(0.562227\pi\) | |||||||
\(762\) | 3.36790 | 0.122006 | ||||||||
\(763\) | −13.9825 | −0.506201 | ||||||||
\(764\) | −30.7563 | −1.11272 | ||||||||
\(765\) | 2.56943 | 0.0928980 | ||||||||
\(766\) | −4.24404 | −0.153343 | ||||||||
\(767\) | 5.39458 | 0.194787 | ||||||||
\(768\) | 9.60708 | 0.346666 | ||||||||
\(769\) | 3.80655 | 0.137268 | 0.0686338 | − | 0.997642i | \(-0.478136\pi\) | ||||
0.0686338 | + | 0.997642i | \(0.478136\pi\) | |||||||
\(770\) | −15.8572 | −0.571454 | ||||||||
\(771\) | 6.16495 | 0.222025 | ||||||||
\(772\) | 2.26547 | 0.0815360 | ||||||||
\(773\) | −35.4403 | −1.27470 | −0.637349 | − | 0.770575i | \(-0.719969\pi\) | ||||
−0.637349 | + | 0.770575i | \(0.719969\pi\) | |||||||
\(774\) | −0.247593 | −0.00889954 | ||||||||
\(775\) | 12.7100 | 0.456556 | ||||||||
\(776\) | −4.87266 | −0.174918 | ||||||||
\(777\) | 16.1978 | 0.581092 | ||||||||
\(778\) | −10.9348 | −0.392033 | ||||||||
\(779\) | 2.48075 | 0.0888819 | ||||||||
\(780\) | −6.54851 | −0.234474 | ||||||||
\(781\) | −5.20188 | −0.186138 | ||||||||
\(782\) | −1.80956 | −0.0647097 | ||||||||
\(783\) | 8.16240 | 0.291700 | ||||||||
\(784\) | 28.9362 | 1.03344 | ||||||||
\(785\) | 23.6121 | 0.842751 | ||||||||
\(786\) | 3.00999 | 0.107363 | ||||||||
\(787\) | 6.93573 | 0.247232 | 0.123616 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123616 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(788\) | 40.4939 | 1.44254 | ||||||||
\(789\) | 10.4331 | 0.371427 | ||||||||
\(790\) | −8.82126 | −0.313846 | ||||||||
\(791\) | −28.9702 | −1.03006 | ||||||||
\(792\) | 4.64378 | 0.165009 | ||||||||
\(793\) | 1.43944 | 0.0511161 | ||||||||
\(794\) | 4.84435 | 0.171919 | ||||||||
\(795\) | −8.74152 | −0.310030 | ||||||||
\(796\) | 20.8601 | 0.739366 | ||||||||
\(797\) | 13.4366 | 0.475950 | 0.237975 | − | 0.971271i | \(-0.423516\pi\) | ||||
0.237975 | + | 0.971271i | \(0.423516\pi\) | |||||||
\(798\) | 6.13818 | 0.217289 | ||||||||
\(799\) | −6.08571 | −0.215297 | ||||||||
\(800\) | −22.1446 | −0.782929 | ||||||||
\(801\) | −12.6221 | −0.445981 | ||||||||
\(802\) | 9.97095 | 0.352086 | ||||||||
\(803\) | 24.2789 | 0.856785 | ||||||||
\(804\) | −10.2139 | −0.360215 | ||||||||
\(805\) | −110.272 | −3.88658 | ||||||||
\(806\) | 0.554172 | 0.0195199 | ||||||||
\(807\) | 2.25633 | 0.0794264 | ||||||||
\(808\) | −3.74102 | −0.131609 | ||||||||
\(809\) | −23.5074 | −0.826475 | −0.413237 | − | 0.910623i | \(-0.635602\pi\) | ||||
−0.413237 | + | 0.910623i | \(0.635602\pi\) | |||||||
\(810\) | 0.998600 | 0.0350872 | ||||||||
\(811\) | −25.7091 | −0.902768 | −0.451384 | − | 0.892330i | \(-0.649070\pi\) | ||||
−0.451384 | + | 0.892330i | \(0.649070\pi\) | |||||||
\(812\) | 61.0880 | 2.14377 | ||||||||
\(813\) | −7.93979 | −0.278461 | ||||||||
\(814\) | 4.91582 | 0.172299 | ||||||||
\(815\) | 34.2583 | 1.20002 | ||||||||
\(816\) | −2.62630 | −0.0919389 | ||||||||
\(817\) | 4.56069 | 0.159558 | ||||||||
\(818\) | 3.60157 | 0.125926 | ||||||||
\(819\) | 3.90865 | 0.136579 | ||||||||
\(820\) | 3.02046 | 0.105479 | ||||||||
\(821\) | −41.0294 | −1.43194 | −0.715968 | − | 0.698133i | \(-0.754015\pi\) | ||||
−0.715968 | + | 0.698133i | \(0.754015\pi\) | |||||||
\(822\) | 0.0818961 | 0.00285645 | ||||||||
\(823\) | −2.30228 | −0.0802525 | −0.0401262 | − | 0.999195i | \(-0.512776\pi\) | ||||
−0.0401262 | + | 0.999195i | \(0.512776\pi\) | |||||||
\(824\) | 1.14305 | 0.0398199 | ||||||||
\(825\) | 27.2062 | 0.947199 | ||||||||
\(826\) | −6.15666 | −0.214217 | ||||||||
\(827\) | 27.3361 | 0.950571 | 0.475285 | − | 0.879832i | \(-0.342345\pi\) | ||||
0.475285 | + | 0.879832i | \(0.342345\pi\) | |||||||
\(828\) | 15.7949 | 0.548912 | ||||||||
\(829\) | 44.5572 | 1.54754 | 0.773768 | − | 0.633469i | \(-0.218370\pi\) | ||||
0.773768 | + | 0.633469i | \(0.218370\pi\) | |||||||
\(830\) | 11.3089 | 0.392536 | ||||||||
\(831\) | −24.1539 | −0.837891 | ||||||||
\(832\) | 6.02594 | 0.208912 | ||||||||
\(833\) | −6.21882 | −0.215469 | ||||||||
\(834\) | −4.82416 | −0.167047 | ||||||||
\(835\) | 13.1427 | 0.454821 | ||||||||
\(836\) | −41.8380 | −1.44700 | ||||||||
\(837\) | 1.89795 | 0.0656027 | ||||||||
\(838\) | −6.63506 | −0.229204 | ||||||||
\(839\) | 7.92724 | 0.273679 | 0.136839 | − | 0.990593i | \(-0.456306\pi\) | ||||
0.136839 | + | 0.990593i | \(0.456306\pi\) | |||||||
\(840\) | 15.2800 | 0.527209 | ||||||||
\(841\) | 37.6248 | 1.29741 | ||||||||
\(842\) | −8.92463 | −0.307563 | ||||||||
\(843\) | 26.4669 | 0.911567 | ||||||||
\(844\) | −2.93635 | −0.101073 | ||||||||
\(845\) | −3.42004 | −0.117653 | ||||||||
\(846\) | −2.36519 | −0.0813168 | ||||||||
\(847\) | −21.5171 | −0.739337 | ||||||||
\(848\) | 8.93500 | 0.306829 | ||||||||
\(849\) | −5.24325 | −0.179948 | ||||||||
\(850\) | 1.46901 | 0.0503868 | ||||||||
\(851\) | 34.1850 | 1.17185 | ||||||||
\(852\) | 2.45168 | 0.0839931 | ||||||||
\(853\) | −18.8584 | −0.645700 | −0.322850 | − | 0.946450i | \(-0.604641\pi\) | ||||
−0.322850 | + | 0.946450i | \(0.604641\pi\) | |||||||
\(854\) | −1.64279 | −0.0562151 | ||||||||
\(855\) | −18.3943 | −0.629073 | ||||||||
\(856\) | −20.7245 | −0.708348 | ||||||||
\(857\) | −7.48466 | −0.255671 | −0.127836 | − | 0.991795i | \(-0.540803\pi\) | ||||
−0.127836 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(858\) | 1.18623 | 0.0404971 | ||||||||
\(859\) | −0.276798 | −0.00944423 | −0.00472211 | − | 0.999989i | \(-0.501503\pi\) | ||||
−0.00472211 | + | 0.999989i | \(0.501503\pi\) | |||||||
\(860\) | 5.55291 | 0.189353 | ||||||||
\(861\) | −1.80284 | −0.0614406 | ||||||||
\(862\) | 4.53004 | 0.154294 | ||||||||
\(863\) | −25.5255 | −0.868897 | −0.434448 | − | 0.900697i | \(-0.643057\pi\) | ||||
−0.434448 | + | 0.900697i | \(0.643057\pi\) | |||||||
\(864\) | −3.30679 | −0.112499 | ||||||||
\(865\) | 63.7107 | 2.16623 | ||||||||
\(866\) | 5.17300 | 0.175786 | ||||||||
\(867\) | −16.4356 | −0.558181 | ||||||||
\(868\) | 14.2044 | 0.482128 | ||||||||
\(869\) | −35.8878 | −1.21741 | ||||||||
\(870\) | 8.15097 | 0.276344 | ||||||||
\(871\) | −5.33432 | −0.180746 | ||||||||
\(872\) | 4.08905 | 0.138473 | ||||||||
\(873\) | −4.26288 | −0.144276 | ||||||||
\(874\) | 12.9545 | 0.438191 | ||||||||
\(875\) | 22.6810 | 0.766758 | ||||||||
\(876\) | −11.4428 | −0.386617 | ||||||||
\(877\) | −20.1987 | −0.682063 | −0.341032 | − | 0.940052i | \(-0.610776\pi\) | ||||
−0.341032 | + | 0.940052i | \(0.610776\pi\) | |||||||
\(878\) | −7.15122 | −0.241342 | ||||||||
\(879\) | 27.1084 | 0.914344 | ||||||||
\(880\) | −48.5711 | −1.63733 | ||||||||
\(881\) | −10.8204 | −0.364550 | −0.182275 | − | 0.983248i | \(-0.558346\pi\) | ||||
−0.182275 | + | 0.983248i | \(0.558346\pi\) | |||||||
\(882\) | −2.41692 | −0.0813820 | ||||||||
\(883\) | −41.9002 | −1.41005 | −0.705027 | − | 0.709181i | \(-0.749065\pi\) | ||||
−0.705027 | + | 0.709181i | \(0.749065\pi\) | |||||||
\(884\) | −1.43852 | −0.0483827 | ||||||||
\(885\) | 18.4497 | 0.620180 | ||||||||
\(886\) | −4.11131 | −0.138122 | ||||||||
\(887\) | 12.0341 | 0.404066 | 0.202033 | − | 0.979379i | \(-0.435245\pi\) | ||||
0.202033 | + | 0.979379i | \(0.435245\pi\) | |||||||
\(888\) | −4.73687 | −0.158959 | ||||||||
\(889\) | 45.0844 | 1.51208 | ||||||||
\(890\) | −12.6045 | −0.422503 | ||||||||
\(891\) | 4.06263 | 0.136103 | ||||||||
\(892\) | 13.9236 | 0.466195 | ||||||||
\(893\) | 43.5670 | 1.45791 | ||||||||
\(894\) | −0.941629 | −0.0314928 | ||||||||
\(895\) | 70.6641 | 2.36204 | ||||||||
\(896\) | −32.7274 | −1.09335 | ||||||||
\(897\) | 8.24911 | 0.275430 | ||||||||
\(898\) | −7.65017 | −0.255289 | ||||||||
\(899\) | 15.4918 | 0.516681 | ||||||||
\(900\) | −12.8225 | −0.427415 | ||||||||
\(901\) | −1.92026 | −0.0639733 | ||||||||
\(902\) | −0.547139 | −0.0182177 | ||||||||
\(903\) | −3.31440 | −0.110296 | ||||||||
\(904\) | 8.47203 | 0.281776 | ||||||||
\(905\) | 73.9419 | 2.45791 | ||||||||
\(906\) | 3.53804 | 0.117544 | ||||||||
\(907\) | 8.55232 | 0.283975 | 0.141987 | − | 0.989868i | \(-0.454651\pi\) | ||||
0.141987 | + | 0.989868i | \(0.454651\pi\) | |||||||
\(908\) | 37.6767 | 1.25034 | ||||||||
\(909\) | −3.27285 | −0.108554 | ||||||||
\(910\) | 3.90318 | 0.129389 | ||||||||
\(911\) | −15.7307 | −0.521182 | −0.260591 | − | 0.965449i | \(-0.583917\pi\) | ||||
−0.260591 | + | 0.965449i | \(0.583917\pi\) | |||||||
\(912\) | 18.8014 | 0.622578 | ||||||||
\(913\) | 46.0081 | 1.52265 | ||||||||
\(914\) | −7.12989 | −0.235836 | ||||||||
\(915\) | 4.92296 | 0.162748 | ||||||||
\(916\) | 24.3364 | 0.804096 | ||||||||
\(917\) | 40.2932 | 1.33060 | ||||||||
\(918\) | 0.219364 | 0.00724009 | ||||||||
\(919\) | −40.0281 | −1.32040 | −0.660202 | − | 0.751088i | \(-0.729529\pi\) | ||||
−0.660202 | + | 0.751088i | \(0.729529\pi\) | |||||||
\(920\) | 32.2480 | 1.06318 | ||||||||
\(921\) | 29.6254 | 0.976189 | ||||||||
\(922\) | 0.772678 | 0.0254468 | ||||||||
\(923\) | 1.28042 | 0.0421456 | ||||||||
\(924\) | 30.4050 | 1.00025 | ||||||||
\(925\) | −27.7516 | −0.912469 | ||||||||
\(926\) | 2.41701 | 0.0794278 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −26.9914 | −0.886035 | ||||||||
\(929\) | 22.5677 | 0.740422 | 0.370211 | − | 0.928948i | \(-0.379285\pi\) | ||||
0.370211 | + | 0.928948i | \(0.379285\pi\) | |||||||
\(930\) | 1.89529 | 0.0621490 | ||||||||
\(931\) | 44.5200 | 1.45908 | ||||||||
\(932\) | −21.3076 | −0.697952 | ||||||||
\(933\) | 27.3840 | 0.896512 | ||||||||
\(934\) | −1.87365 | −0.0613077 | ||||||||
\(935\) | 10.4387 | 0.341381 | ||||||||
\(936\) | −1.14305 | −0.0373616 | ||||||||
\(937\) | 58.2171 | 1.90187 | 0.950935 | − | 0.309389i | \(-0.100125\pi\) | ||||
0.950935 | + | 0.309389i | \(0.100125\pi\) | |||||||
\(938\) | 6.08788 | 0.198776 | ||||||||
\(939\) | −3.74737 | −0.122291 | ||||||||
\(940\) | 53.0454 | 1.73015 | ||||||||
\(941\) | −55.5396 | −1.81054 | −0.905270 | − | 0.424837i | \(-0.860332\pi\) | ||||
−0.905270 | + | 0.424837i | \(0.860332\pi\) | |||||||
\(942\) | 2.01587 | 0.0656806 | ||||||||
\(943\) | −3.80485 | −0.123903 | ||||||||
\(944\) | −18.8580 | −0.613777 | ||||||||
\(945\) | 13.3678 | 0.434853 | ||||||||
\(946\) | −1.00588 | −0.0327040 | ||||||||
\(947\) | −45.9699 | −1.49382 | −0.746910 | − | 0.664925i | \(-0.768463\pi\) | ||||
−0.746910 | + | 0.664925i | \(0.768463\pi\) | |||||||
\(948\) | 16.9141 | 0.549346 | ||||||||
\(949\) | −5.97616 | −0.193994 | ||||||||
\(950\) | −10.5165 | −0.341202 | ||||||||
\(951\) | 27.9021 | 0.904788 | ||||||||
\(952\) | 3.35657 | 0.108787 | ||||||||
\(953\) | −11.0045 | −0.356471 | −0.178235 | − | 0.983988i | \(-0.557039\pi\) | ||||
−0.178235 | + | 0.983988i | \(0.557039\pi\) | |||||||
\(954\) | −0.746304 | −0.0241625 | ||||||||
\(955\) | −54.9357 | −1.77768 | ||||||||
\(956\) | −44.5541 | −1.44098 | ||||||||
\(957\) | 33.1608 | 1.07194 | ||||||||
\(958\) | 5.33377 | 0.172326 | ||||||||
\(959\) | 1.09630 | 0.0354014 | ||||||||
\(960\) | 20.6090 | 0.665152 | ||||||||
\(961\) | −27.3978 | −0.883800 | ||||||||
\(962\) | −1.21001 | −0.0390122 | ||||||||
\(963\) | −18.1309 | −0.584261 | ||||||||
\(964\) | 14.1079 | 0.454384 | ||||||||
\(965\) | 4.04649 | 0.130261 | ||||||||
\(966\) | −9.41444 | −0.302905 | ||||||||
\(967\) | 20.3983 | 0.655966 | 0.327983 | − | 0.944684i | \(-0.393631\pi\) | ||||
0.327983 | + | 0.944684i | \(0.393631\pi\) | |||||||
\(968\) | 6.29246 | 0.202247 | ||||||||
\(969\) | −4.04071 | −0.129806 | ||||||||
\(970\) | −4.25691 | −0.136681 | ||||||||
\(971\) | −39.5917 | −1.27056 | −0.635278 | − | 0.772283i | \(-0.719115\pi\) | ||||
−0.635278 | + | 0.772283i | \(0.719115\pi\) | |||||||
\(972\) | −1.91474 | −0.0614155 | ||||||||
\(973\) | −64.5786 | −2.07029 | ||||||||
\(974\) | −6.01063 | −0.192593 | ||||||||
\(975\) | −6.69670 | −0.214466 | ||||||||
\(976\) | −5.03191 | −0.161068 | ||||||||
\(977\) | −45.1151 | −1.44336 | −0.721679 | − | 0.692227i | \(-0.756630\pi\) | ||||
−0.721679 | + | 0.692227i | \(0.756630\pi\) | |||||||
\(978\) | 2.92479 | 0.0935244 | ||||||||
\(979\) | −51.2791 | −1.63889 | ||||||||
\(980\) | 54.2057 | 1.73154 | ||||||||
\(981\) | 3.57733 | 0.114215 | ||||||||
\(982\) | 10.2958 | 0.328551 | ||||||||
\(983\) | −43.7929 | −1.39678 | −0.698388 | − | 0.715720i | \(-0.746099\pi\) | ||||
−0.698388 | + | 0.715720i | \(0.746099\pi\) | |||||||
\(984\) | 0.527222 | 0.0168072 | ||||||||
\(985\) | 72.3287 | 2.30458 | ||||||||
\(986\) | 1.79054 | 0.0570223 | ||||||||
\(987\) | −31.6616 | −1.00780 | ||||||||
\(988\) | 10.2982 | 0.327631 | ||||||||
\(989\) | −6.99496 | −0.222427 | ||||||||
\(990\) | 4.05695 | 0.128938 | ||||||||
\(991\) | 23.1871 | 0.736562 | 0.368281 | − | 0.929714i | \(-0.379946\pi\) | ||||
0.368281 | + | 0.929714i | \(0.379946\pi\) | |||||||
\(992\) | −6.27612 | −0.199267 | ||||||||
\(993\) | −16.3140 | −0.517710 | ||||||||
\(994\) | −1.46130 | −0.0463497 | ||||||||
\(995\) | 37.2595 | 1.18121 | ||||||||
\(996\) | −21.6839 | −0.687082 | ||||||||
\(997\) | −1.26380 | −0.0400248 | −0.0200124 | − | 0.999800i | \(-0.506371\pi\) | ||||
−0.0200124 | + | 0.999800i | \(0.506371\pi\) | |||||||
\(998\) | −3.60865 | −0.114230 | ||||||||
\(999\) | −4.14408 | −0.131113 |
(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 | 4017.2.a.e.1.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.e.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial |