Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8038,2,Mod(1,8038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1837531447\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8038.1 |
$q$-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 | ||||||||
\(3\) | −2.67211 | −1.54275 | −0.771373 | − | 0.636383i | \(-0.780430\pi\) | ||||
−0.771373 | + | 0.636383i | \(0.780430\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.54258 | 0.689863 | 0.344931 | − | 0.938628i | \(-0.387902\pi\) | ||||
0.344931 | + | 0.938628i | \(0.387902\pi\) | |||||||
\(6\) | −2.67211 | −1.09089 | ||||||||
\(7\) | 1.53058 | 0.578505 | 0.289252 | − | 0.957253i | \(-0.406593\pi\) | ||||
0.289252 | + | 0.957253i | \(0.406593\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.14019 | 1.38006 | ||||||||
\(10\) | 1.54258 | 0.487807 | ||||||||
\(11\) | −0.242994 | −0.0732655 | −0.0366328 | − | 0.999329i | \(-0.511663\pi\) | ||||
−0.0366328 | + | 0.999329i | \(0.511663\pi\) | |||||||
\(12\) | −2.67211 | −0.771373 | ||||||||
\(13\) | 2.26336 | 0.627742 | 0.313871 | − | 0.949466i | \(-0.398374\pi\) | ||||
0.313871 | + | 0.949466i | \(0.398374\pi\) | |||||||
\(14\) | 1.53058 | 0.409065 | ||||||||
\(15\) | −4.12195 | −1.06428 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.48447 | −0.360036 | −0.180018 | − | 0.983663i | \(-0.557616\pi\) | ||||
−0.180018 | + | 0.983663i | \(0.557616\pi\) | |||||||
\(18\) | 4.14019 | 0.975853 | ||||||||
\(19\) | 4.72739 | 1.08454 | 0.542269 | − | 0.840205i | \(-0.317565\pi\) | ||||
0.542269 | + | 0.840205i | \(0.317565\pi\) | |||||||
\(20\) | 1.54258 | 0.344931 | ||||||||
\(21\) | −4.08988 | −0.892486 | ||||||||
\(22\) | −0.242994 | −0.0518065 | ||||||||
\(23\) | −5.72536 | −1.19382 | −0.596910 | − | 0.802308i | \(-0.703605\pi\) | ||||
−0.596910 | + | 0.802308i | \(0.703605\pi\) | |||||||
\(24\) | −2.67211 | −0.545443 | ||||||||
\(25\) | −2.62045 | −0.524089 | ||||||||
\(26\) | 2.26336 | 0.443881 | ||||||||
\(27\) | −3.04673 | −0.586343 | ||||||||
\(28\) | 1.53058 | 0.289252 | ||||||||
\(29\) | 7.61807 | 1.41464 | 0.707320 | − | 0.706893i | \(-0.249904\pi\) | ||||
0.707320 | + | 0.706893i | \(0.249904\pi\) | |||||||
\(30\) | −4.12195 | −0.752562 | ||||||||
\(31\) | 7.13459 | 1.28141 | 0.640705 | − | 0.767787i | \(-0.278642\pi\) | ||||
0.640705 | + | 0.767787i | \(0.278642\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.649308 | 0.113030 | ||||||||
\(34\) | −1.48447 | −0.254584 | ||||||||
\(35\) | 2.36104 | 0.399089 | ||||||||
\(36\) | 4.14019 | 0.690032 | ||||||||
\(37\) | −0.190629 | −0.0313391 | −0.0156696 | − | 0.999877i | \(-0.504988\pi\) | ||||
−0.0156696 | + | 0.999877i | \(0.504988\pi\) | |||||||
\(38\) | 4.72739 | 0.766884 | ||||||||
\(39\) | −6.04795 | −0.968447 | ||||||||
\(40\) | 1.54258 | 0.243903 | ||||||||
\(41\) | −0.786097 | −0.122768 | −0.0613839 | − | 0.998114i | \(-0.519551\pi\) | ||||
−0.0613839 | + | 0.998114i | \(0.519551\pi\) | |||||||
\(42\) | −4.08988 | −0.631083 | ||||||||
\(43\) | 6.26489 | 0.955387 | 0.477693 | − | 0.878527i | \(-0.341473\pi\) | ||||
0.477693 | + | 0.878527i | \(0.341473\pi\) | |||||||
\(44\) | −0.242994 | −0.0366328 | ||||||||
\(45\) | 6.38658 | 0.952055 | ||||||||
\(46\) | −5.72536 | −0.844158 | ||||||||
\(47\) | −1.31794 | −0.192241 | −0.0961207 | − | 0.995370i | \(-0.530643\pi\) | ||||
−0.0961207 | + | 0.995370i | \(0.530643\pi\) | |||||||
\(48\) | −2.67211 | −0.385686 | ||||||||
\(49\) | −4.65733 | −0.665332 | ||||||||
\(50\) | −2.62045 | −0.370587 | ||||||||
\(51\) | 3.96666 | 0.555444 | ||||||||
\(52\) | 2.26336 | 0.313871 | ||||||||
\(53\) | −3.84781 | −0.528538 | −0.264269 | − | 0.964449i | \(-0.585131\pi\) | ||||
−0.264269 | + | 0.964449i | \(0.585131\pi\) | |||||||
\(54\) | −3.04673 | −0.414607 | ||||||||
\(55\) | −0.374838 | −0.0505432 | ||||||||
\(56\) | 1.53058 | 0.204532 | ||||||||
\(57\) | −12.6321 | −1.67317 | ||||||||
\(58\) | 7.61807 | 1.00030 | ||||||||
\(59\) | −7.45997 | −0.971206 | −0.485603 | − | 0.874179i | \(-0.661400\pi\) | ||||
−0.485603 | + | 0.874179i | \(0.661400\pi\) | |||||||
\(60\) | −4.12195 | −0.532142 | ||||||||
\(61\) | 2.26563 | 0.290085 | 0.145042 | − | 0.989425i | \(-0.453668\pi\) | ||||
0.145042 | + | 0.989425i | \(0.453668\pi\) | |||||||
\(62\) | 7.13459 | 0.906094 | ||||||||
\(63\) | 6.33690 | 0.798374 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.49141 | 0.433056 | ||||||||
\(66\) | 0.649308 | 0.0799243 | ||||||||
\(67\) | 16.1002 | 1.96695 | 0.983476 | − | 0.181038i | \(-0.0579458\pi\) | ||||
0.983476 | + | 0.181038i | \(0.0579458\pi\) | |||||||
\(68\) | −1.48447 | −0.180018 | ||||||||
\(69\) | 15.2988 | 1.84176 | ||||||||
\(70\) | 2.36104 | 0.282199 | ||||||||
\(71\) | 5.96809 | 0.708282 | 0.354141 | − | 0.935192i | \(-0.384773\pi\) | ||||
0.354141 | + | 0.935192i | \(0.384773\pi\) | |||||||
\(72\) | 4.14019 | 0.487927 | ||||||||
\(73\) | −2.58683 | −0.302766 | −0.151383 | − | 0.988475i | \(-0.548373\pi\) | ||||
−0.151383 | + | 0.988475i | \(0.548373\pi\) | |||||||
\(74\) | −0.190629 | −0.0221601 | ||||||||
\(75\) | 7.00213 | 0.808536 | ||||||||
\(76\) | 4.72739 | 0.542269 | ||||||||
\(77\) | −0.371922 | −0.0423844 | ||||||||
\(78\) | −6.04795 | −0.684795 | ||||||||
\(79\) | 1.81227 | 0.203897 | 0.101948 | − | 0.994790i | \(-0.467492\pi\) | ||||
0.101948 | + | 0.994790i | \(0.467492\pi\) | |||||||
\(80\) | 1.54258 | 0.172466 | ||||||||
\(81\) | −4.27938 | −0.475486 | ||||||||
\(82\) | −0.786097 | −0.0868099 | ||||||||
\(83\) | 16.5019 | 1.81132 | 0.905658 | − | 0.424009i | \(-0.139377\pi\) | ||||
0.905658 | + | 0.424009i | \(0.139377\pi\) | |||||||
\(84\) | −4.08988 | −0.446243 | ||||||||
\(85\) | −2.28991 | −0.248375 | ||||||||
\(86\) | 6.26489 | 0.675560 | ||||||||
\(87\) | −20.3564 | −2.18243 | ||||||||
\(88\) | −0.242994 | −0.0259033 | ||||||||
\(89\) | 10.2315 | 1.08453 | 0.542266 | − | 0.840207i | \(-0.317567\pi\) | ||||
0.542266 | + | 0.840207i | \(0.317567\pi\) | |||||||
\(90\) | 6.38658 | 0.673205 | ||||||||
\(91\) | 3.46425 | 0.363152 | ||||||||
\(92\) | −5.72536 | −0.596910 | ||||||||
\(93\) | −19.0644 | −1.97689 | ||||||||
\(94\) | −1.31794 | −0.135935 | ||||||||
\(95\) | 7.29238 | 0.748182 | ||||||||
\(96\) | −2.67211 | −0.272722 | ||||||||
\(97\) | 3.87448 | 0.393394 | 0.196697 | − | 0.980464i | \(-0.436979\pi\) | ||||
0.196697 | + | 0.980464i | \(0.436979\pi\) | |||||||
\(98\) | −4.65733 | −0.470461 | ||||||||
\(99\) | −1.00604 | −0.101111 | ||||||||
\(100\) | −2.62045 | −0.262045 | ||||||||
\(101\) | −3.08877 | −0.307345 | −0.153672 | − | 0.988122i | \(-0.549110\pi\) | ||||
−0.153672 | + | 0.988122i | \(0.549110\pi\) | |||||||
\(102\) | 3.96666 | 0.392758 | ||||||||
\(103\) | −16.1878 | −1.59503 | −0.797515 | − | 0.603299i | \(-0.793852\pi\) | ||||
−0.797515 | + | 0.603299i | \(0.793852\pi\) | |||||||
\(104\) | 2.26336 | 0.221940 | ||||||||
\(105\) | −6.30897 | −0.615693 | ||||||||
\(106\) | −3.84781 | −0.373733 | ||||||||
\(107\) | 1.97161 | 0.190603 | 0.0953016 | − | 0.995448i | \(-0.469618\pi\) | ||||
0.0953016 | + | 0.995448i | \(0.469618\pi\) | |||||||
\(108\) | −3.04673 | −0.293172 | ||||||||
\(109\) | −16.5660 | −1.58674 | −0.793368 | − | 0.608742i | \(-0.791674\pi\) | ||||
−0.793368 | + | 0.608742i | \(0.791674\pi\) | |||||||
\(110\) | −0.374838 | −0.0357394 | ||||||||
\(111\) | 0.509381 | 0.0483483 | ||||||||
\(112\) | 1.53058 | 0.144626 | ||||||||
\(113\) | 10.8064 | 1.01658 | 0.508289 | − | 0.861187i | \(-0.330278\pi\) | ||||
0.508289 | + | 0.861187i | \(0.330278\pi\) | |||||||
\(114\) | −12.6321 | −1.18311 | ||||||||
\(115\) | −8.83182 | −0.823572 | ||||||||
\(116\) | 7.61807 | 0.707320 | ||||||||
\(117\) | 9.37074 | 0.866325 | ||||||||
\(118\) | −7.45997 | −0.686746 | ||||||||
\(119\) | −2.27209 | −0.208282 | ||||||||
\(120\) | −4.12195 | −0.376281 | ||||||||
\(121\) | −10.9410 | −0.994632 | ||||||||
\(122\) | 2.26563 | 0.205121 | ||||||||
\(123\) | 2.10054 | 0.189399 | ||||||||
\(124\) | 7.13459 | 0.640705 | ||||||||
\(125\) | −11.7552 | −1.05141 | ||||||||
\(126\) | 6.33690 | 0.564536 | ||||||||
\(127\) | −10.3670 | −0.919921 | −0.459960 | − | 0.887939i | \(-0.652136\pi\) | ||||
−0.459960 | + | 0.887939i | \(0.652136\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.7405 | −1.47392 | ||||||||
\(130\) | 3.49141 | 0.306217 | ||||||||
\(131\) | −2.35300 | −0.205583 | −0.102791 | − | 0.994703i | \(-0.532777\pi\) | ||||
−0.102791 | + | 0.994703i | \(0.532777\pi\) | |||||||
\(132\) | 0.649308 | 0.0565150 | ||||||||
\(133\) | 7.23565 | 0.627410 | ||||||||
\(134\) | 16.1002 | 1.39085 | ||||||||
\(135\) | −4.69982 | −0.404496 | ||||||||
\(136\) | −1.48447 | −0.127292 | ||||||||
\(137\) | 11.5805 | 0.989391 | 0.494696 | − | 0.869066i | \(-0.335280\pi\) | ||||
0.494696 | + | 0.869066i | \(0.335280\pi\) | |||||||
\(138\) | 15.2988 | 1.30232 | ||||||||
\(139\) | 1.66475 | 0.141202 | 0.0706011 | − | 0.997505i | \(-0.477508\pi\) | ||||
0.0706011 | + | 0.997505i | \(0.477508\pi\) | |||||||
\(140\) | 2.36104 | 0.199544 | ||||||||
\(141\) | 3.52169 | 0.296580 | ||||||||
\(142\) | 5.96809 | 0.500831 | ||||||||
\(143\) | −0.549983 | −0.0459919 | ||||||||
\(144\) | 4.14019 | 0.345016 | ||||||||
\(145\) | 11.7515 | 0.975908 | ||||||||
\(146\) | −2.58683 | −0.214088 | ||||||||
\(147\) | 12.4449 | 1.02644 | ||||||||
\(148\) | −0.190629 | −0.0156696 | ||||||||
\(149\) | 16.1436 | 1.32253 | 0.661267 | − | 0.750151i | \(-0.270019\pi\) | ||||
0.661267 | + | 0.750151i | \(0.270019\pi\) | |||||||
\(150\) | 7.00213 | 0.571721 | ||||||||
\(151\) | −22.7807 | −1.85387 | −0.926935 | − | 0.375222i | \(-0.877567\pi\) | ||||
−0.926935 | + | 0.375222i | \(0.877567\pi\) | |||||||
\(152\) | 4.72739 | 0.383442 | ||||||||
\(153\) | −6.14597 | −0.496873 | ||||||||
\(154\) | −0.371922 | −0.0299703 | ||||||||
\(155\) | 11.0057 | 0.883997 | ||||||||
\(156\) | −6.04795 | −0.484223 | ||||||||
\(157\) | 2.41265 | 0.192550 | 0.0962752 | − | 0.995355i | \(-0.469307\pi\) | ||||
0.0962752 | + | 0.995355i | \(0.469307\pi\) | |||||||
\(158\) | 1.81227 | 0.144177 | ||||||||
\(159\) | 10.2818 | 0.815400 | ||||||||
\(160\) | 1.54258 | 0.121952 | ||||||||
\(161\) | −8.76311 | −0.690630 | ||||||||
\(162\) | −4.27938 | −0.336220 | ||||||||
\(163\) | 12.4319 | 0.973743 | 0.486872 | − | 0.873474i | \(-0.338138\pi\) | ||||
0.486872 | + | 0.873474i | \(0.338138\pi\) | |||||||
\(164\) | −0.786097 | −0.0613839 | ||||||||
\(165\) | 1.00161 | 0.0779753 | ||||||||
\(166\) | 16.5019 | 1.28079 | ||||||||
\(167\) | −6.10802 | −0.472653 | −0.236326 | − | 0.971674i | \(-0.575943\pi\) | ||||
−0.236326 | + | 0.971674i | \(0.575943\pi\) | |||||||
\(168\) | −4.08988 | −0.315541 | ||||||||
\(169\) | −7.87722 | −0.605940 | ||||||||
\(170\) | −2.28991 | −0.175628 | ||||||||
\(171\) | 19.5723 | 1.49673 | ||||||||
\(172\) | 6.26489 | 0.477693 | ||||||||
\(173\) | −5.94113 | −0.451696 | −0.225848 | − | 0.974163i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974163i | \(0.572515\pi\) | |||||||
\(174\) | −20.3564 | −1.54321 | ||||||||
\(175\) | −4.01080 | −0.303188 | ||||||||
\(176\) | −0.242994 | −0.0183164 | ||||||||
\(177\) | 19.9339 | 1.49832 | ||||||||
\(178\) | 10.2315 | 0.766880 | ||||||||
\(179\) | 17.5073 | 1.30855 | 0.654277 | − | 0.756255i | \(-0.272973\pi\) | ||||
0.654277 | + | 0.756255i | \(0.272973\pi\) | |||||||
\(180\) | 6.38658 | 0.476028 | ||||||||
\(181\) | −14.2484 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(182\) | 3.46425 | 0.256787 | ||||||||
\(183\) | −6.05403 | −0.447527 | ||||||||
\(184\) | −5.72536 | −0.422079 | ||||||||
\(185\) | −0.294060 | −0.0216197 | ||||||||
\(186\) | −19.0644 | −1.39787 | ||||||||
\(187\) | 0.360717 | 0.0263782 | ||||||||
\(188\) | −1.31794 | −0.0961207 | ||||||||
\(189\) | −4.66326 | −0.339202 | ||||||||
\(190\) | 7.29238 | 0.529045 | ||||||||
\(191\) | 21.1591 | 1.53102 | 0.765508 | − | 0.643427i | \(-0.222488\pi\) | ||||
0.765508 | + | 0.643427i | \(0.222488\pi\) | |||||||
\(192\) | −2.67211 | −0.192843 | ||||||||
\(193\) | 23.0206 | 1.65706 | 0.828531 | − | 0.559943i | \(-0.189177\pi\) | ||||
0.828531 | + | 0.559943i | \(0.189177\pi\) | |||||||
\(194\) | 3.87448 | 0.278171 | ||||||||
\(195\) | −9.32945 | −0.668096 | ||||||||
\(196\) | −4.65733 | −0.332666 | ||||||||
\(197\) | −4.98388 | −0.355087 | −0.177543 | − | 0.984113i | \(-0.556815\pi\) | ||||
−0.177543 | + | 0.984113i | \(0.556815\pi\) | |||||||
\(198\) | −1.00604 | −0.0714964 | ||||||||
\(199\) | −9.49186 | −0.672860 | −0.336430 | − | 0.941708i | \(-0.609220\pi\) | ||||
−0.336430 | + | 0.941708i | \(0.609220\pi\) | |||||||
\(200\) | −2.62045 | −0.185293 | ||||||||
\(201\) | −43.0216 | −3.03451 | ||||||||
\(202\) | −3.08877 | −0.217325 | ||||||||
\(203\) | 11.6601 | 0.818376 | ||||||||
\(204\) | 3.96666 | 0.277722 | ||||||||
\(205\) | −1.21262 | −0.0846929 | ||||||||
\(206\) | −16.1878 | −1.12786 | ||||||||
\(207\) | −23.7041 | −1.64755 | ||||||||
\(208\) | 2.26336 | 0.156936 | ||||||||
\(209\) | −1.14873 | −0.0794592 | ||||||||
\(210\) | −6.30897 | −0.435361 | ||||||||
\(211\) | 5.28526 | 0.363852 | 0.181926 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181926 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(212\) | −3.84781 | −0.264269 | ||||||||
\(213\) | −15.9474 | −1.09270 | ||||||||
\(214\) | 1.97161 | 0.134777 | ||||||||
\(215\) | 9.66409 | 0.659086 | ||||||||
\(216\) | −3.04673 | −0.207304 | ||||||||
\(217\) | 10.9201 | 0.741302 | ||||||||
\(218\) | −16.5660 | −1.12199 | ||||||||
\(219\) | 6.91231 | 0.467091 | ||||||||
\(220\) | −0.374838 | −0.0252716 | ||||||||
\(221\) | −3.35988 | −0.226010 | ||||||||
\(222\) | 0.509381 | 0.0341874 | ||||||||
\(223\) | 5.79143 | 0.387823 | 0.193911 | − | 0.981019i | \(-0.437883\pi\) | ||||
0.193911 | + | 0.981019i | \(0.437883\pi\) | |||||||
\(224\) | 1.53058 | 0.102266 | ||||||||
\(225\) | −10.8492 | −0.723277 | ||||||||
\(226\) | 10.8064 | 0.718829 | ||||||||
\(227\) | −0.143720 | −0.00953905 | −0.00476952 | − | 0.999989i | \(-0.501518\pi\) | ||||
−0.00476952 | + | 0.999989i | \(0.501518\pi\) | |||||||
\(228\) | −12.6321 | −0.836583 | ||||||||
\(229\) | −20.0353 | −1.32397 | −0.661986 | − | 0.749516i | \(-0.730286\pi\) | ||||
−0.661986 | + | 0.749516i | \(0.730286\pi\) | |||||||
\(230\) | −8.83182 | −0.582353 | ||||||||
\(231\) | 0.993818 | 0.0653884 | ||||||||
\(232\) | 7.61807 | 0.500151 | ||||||||
\(233\) | 18.4254 | 1.20709 | 0.603546 | − | 0.797329i | \(-0.293754\pi\) | ||||
0.603546 | + | 0.797329i | \(0.293754\pi\) | |||||||
\(234\) | 9.37074 | 0.612584 | ||||||||
\(235\) | −2.03303 | −0.132620 | ||||||||
\(236\) | −7.45997 | −0.485603 | ||||||||
\(237\) | −4.84261 | −0.314561 | ||||||||
\(238\) | −2.27209 | −0.147278 | ||||||||
\(239\) | 17.9629 | 1.16192 | 0.580961 | − | 0.813931i | \(-0.302677\pi\) | ||||
0.580961 | + | 0.813931i | \(0.302677\pi\) | |||||||
\(240\) | −4.12195 | −0.266071 | ||||||||
\(241\) | −22.0437 | −1.41996 | −0.709981 | − | 0.704221i | \(-0.751297\pi\) | ||||
−0.709981 | + | 0.704221i | \(0.751297\pi\) | |||||||
\(242\) | −10.9410 | −0.703311 | ||||||||
\(243\) | 20.5752 | 1.31990 | ||||||||
\(244\) | 2.26563 | 0.145042 | ||||||||
\(245\) | −7.18430 | −0.458988 | ||||||||
\(246\) | 2.10054 | 0.133926 | ||||||||
\(247\) | 10.6998 | 0.680810 | ||||||||
\(248\) | 7.13459 | 0.453047 | ||||||||
\(249\) | −44.0949 | −2.79440 | ||||||||
\(250\) | −11.7552 | −0.743461 | ||||||||
\(251\) | 2.84013 | 0.179268 | 0.0896338 | − | 0.995975i | \(-0.471430\pi\) | ||||
0.0896338 | + | 0.995975i | \(0.471430\pi\) | |||||||
\(252\) | 6.33690 | 0.399187 | ||||||||
\(253\) | 1.39123 | 0.0874658 | ||||||||
\(254\) | −10.3670 | −0.650482 | ||||||||
\(255\) | 6.11889 | 0.383180 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.5053 | −0.967191 | −0.483596 | − | 0.875291i | \(-0.660669\pi\) | ||||
−0.483596 | + | 0.875291i | \(0.660669\pi\) | |||||||
\(258\) | −16.7405 | −1.04222 | ||||||||
\(259\) | −0.291772 | −0.0181298 | ||||||||
\(260\) | 3.49141 | 0.216528 | ||||||||
\(261\) | 31.5403 | 1.95229 | ||||||||
\(262\) | −2.35300 | −0.145369 | ||||||||
\(263\) | 16.8989 | 1.04203 | 0.521017 | − | 0.853547i | \(-0.325553\pi\) | ||||
0.521017 | + | 0.853547i | \(0.325553\pi\) | |||||||
\(264\) | 0.649308 | 0.0399622 | ||||||||
\(265\) | −5.93556 | −0.364619 | ||||||||
\(266\) | 7.23565 | 0.443646 | ||||||||
\(267\) | −27.3396 | −1.67316 | ||||||||
\(268\) | 16.1002 | 0.983476 | ||||||||
\(269\) | −10.7604 | −0.656073 | −0.328037 | − | 0.944665i | \(-0.606387\pi\) | ||||
−0.328037 | + | 0.944665i | \(0.606387\pi\) | |||||||
\(270\) | −4.69982 | −0.286022 | ||||||||
\(271\) | −2.92423 | −0.177634 | −0.0888172 | − | 0.996048i | \(-0.528309\pi\) | ||||
−0.0888172 | + | 0.996048i | \(0.528309\pi\) | |||||||
\(272\) | −1.48447 | −0.0900089 | ||||||||
\(273\) | −9.25687 | −0.560251 | ||||||||
\(274\) | 11.5805 | 0.699605 | ||||||||
\(275\) | 0.636753 | 0.0383977 | ||||||||
\(276\) | 15.2988 | 0.920880 | ||||||||
\(277\) | 16.7942 | 1.00907 | 0.504533 | − | 0.863392i | \(-0.331665\pi\) | ||||
0.504533 | + | 0.863392i | \(0.331665\pi\) | |||||||
\(278\) | 1.66475 | 0.0998450 | ||||||||
\(279\) | 29.5386 | 1.76843 | ||||||||
\(280\) | 2.36104 | 0.141099 | ||||||||
\(281\) | −7.84228 | −0.467831 | −0.233916 | − | 0.972257i | \(-0.575154\pi\) | ||||
−0.233916 | + | 0.972257i | \(0.575154\pi\) | |||||||
\(282\) | 3.52169 | 0.209714 | ||||||||
\(283\) | 22.5405 | 1.33990 | 0.669948 | − | 0.742408i | \(-0.266316\pi\) | ||||
0.669948 | + | 0.742408i | \(0.266316\pi\) | |||||||
\(284\) | 5.96809 | 0.354141 | ||||||||
\(285\) | −19.4861 | −1.15425 | ||||||||
\(286\) | −0.549983 | −0.0325212 | ||||||||
\(287\) | −1.20318 | −0.0710217 | ||||||||
\(288\) | 4.14019 | 0.243963 | ||||||||
\(289\) | −14.7964 | −0.870374 | ||||||||
\(290\) | 11.7515 | 0.690071 | ||||||||
\(291\) | −10.3531 | −0.606907 | ||||||||
\(292\) | −2.58683 | −0.151383 | ||||||||
\(293\) | 31.0174 | 1.81206 | 0.906028 | − | 0.423218i | \(-0.139100\pi\) | ||||
0.906028 | + | 0.423218i | \(0.139100\pi\) | |||||||
\(294\) | 12.4449 | 0.725802 | ||||||||
\(295\) | −11.5076 | −0.669999 | ||||||||
\(296\) | −0.190629 | −0.0110801 | ||||||||
\(297\) | 0.740337 | 0.0429587 | ||||||||
\(298\) | 16.1436 | 0.935172 | ||||||||
\(299\) | −12.9585 | −0.749411 | ||||||||
\(300\) | 7.00213 | 0.404268 | ||||||||
\(301\) | 9.58891 | 0.552696 | ||||||||
\(302\) | −22.7807 | −1.31088 | ||||||||
\(303\) | 8.25356 | 0.474154 | ||||||||
\(304\) | 4.72739 | 0.271134 | ||||||||
\(305\) | 3.49492 | 0.200119 | ||||||||
\(306\) | −6.14597 | −0.351342 | ||||||||
\(307\) | 14.6953 | 0.838704 | 0.419352 | − | 0.907824i | \(-0.362257\pi\) | ||||
0.419352 | + | 0.907824i | \(0.362257\pi\) | |||||||
\(308\) | −0.371922 | −0.0211922 | ||||||||
\(309\) | 43.2556 | 2.46073 | ||||||||
\(310\) | 11.0057 | 0.625080 | ||||||||
\(311\) | 13.2704 | 0.752495 | 0.376248 | − | 0.926519i | \(-0.377214\pi\) | ||||
0.376248 | + | 0.926519i | \(0.377214\pi\) | |||||||
\(312\) | −6.04795 | −0.342398 | ||||||||
\(313\) | 11.7200 | 0.662453 | 0.331226 | − | 0.943551i | \(-0.392538\pi\) | ||||
0.331226 | + | 0.943551i | \(0.392538\pi\) | |||||||
\(314\) | 2.41265 | 0.136154 | ||||||||
\(315\) | 9.77517 | 0.550769 | ||||||||
\(316\) | 1.81227 | 0.101948 | ||||||||
\(317\) | −21.0946 | −1.18479 | −0.592394 | − | 0.805648i | \(-0.701817\pi\) | ||||
−0.592394 | + | 0.805648i | \(0.701817\pi\) | |||||||
\(318\) | 10.2818 | 0.576575 | ||||||||
\(319\) | −1.85115 | −0.103644 | ||||||||
\(320\) | 1.54258 | 0.0862329 | ||||||||
\(321\) | −5.26838 | −0.294052 | ||||||||
\(322\) | −8.76311 | −0.488349 | ||||||||
\(323\) | −7.01765 | −0.390472 | ||||||||
\(324\) | −4.27938 | −0.237743 | ||||||||
\(325\) | −5.93100 | −0.328993 | ||||||||
\(326\) | 12.4319 | 0.688540 | ||||||||
\(327\) | 44.2663 | 2.44793 | ||||||||
\(328\) | −0.786097 | −0.0434050 | ||||||||
\(329\) | −2.01721 | −0.111213 | ||||||||
\(330\) | 1.00161 | 0.0551368 | ||||||||
\(331\) | −7.80058 | −0.428759 | −0.214379 | − | 0.976750i | \(-0.568773\pi\) | ||||
−0.214379 | + | 0.976750i | \(0.568773\pi\) | |||||||
\(332\) | 16.5019 | 0.905658 | ||||||||
\(333\) | −0.789239 | −0.0432500 | ||||||||
\(334\) | −6.10802 | −0.334216 | ||||||||
\(335\) | 24.8358 | 1.35693 | ||||||||
\(336\) | −4.08988 | −0.223121 | ||||||||
\(337\) | 17.4264 | 0.949277 | 0.474639 | − | 0.880181i | \(-0.342579\pi\) | ||||
0.474639 | + | 0.880181i | \(0.342579\pi\) | |||||||
\(338\) | −7.87722 | −0.428464 | ||||||||
\(339\) | −28.8758 | −1.56832 | ||||||||
\(340\) | −2.28991 | −0.124188 | ||||||||
\(341\) | −1.73366 | −0.0938832 | ||||||||
\(342\) | 19.5723 | 1.05835 | ||||||||
\(343\) | −17.8425 | −0.963403 | ||||||||
\(344\) | 6.26489 | 0.337780 | ||||||||
\(345\) | 23.5996 | 1.27056 | ||||||||
\(346\) | −5.94113 | −0.319397 | ||||||||
\(347\) | 5.48709 | 0.294562 | 0.147281 | − | 0.989095i | \(-0.452948\pi\) | ||||
0.147281 | + | 0.989095i | \(0.452948\pi\) | |||||||
\(348\) | −20.3564 | −1.09122 | ||||||||
\(349\) | 12.9415 | 0.692741 | 0.346371 | − | 0.938098i | \(-0.387414\pi\) | ||||
0.346371 | + | 0.938098i | \(0.387414\pi\) | |||||||
\(350\) | −4.01080 | −0.214386 | ||||||||
\(351\) | −6.89583 | −0.368072 | ||||||||
\(352\) | −0.242994 | −0.0129516 | ||||||||
\(353\) | −26.9966 | −1.43688 | −0.718441 | − | 0.695588i | \(-0.755144\pi\) | ||||
−0.718441 | + | 0.695588i | \(0.755144\pi\) | |||||||
\(354\) | 19.9339 | 1.05947 | ||||||||
\(355\) | 9.20625 | 0.488617 | ||||||||
\(356\) | 10.2315 | 0.542266 | ||||||||
\(357\) | 6.07129 | 0.321327 | ||||||||
\(358\) | 17.5073 | 0.925288 | ||||||||
\(359\) | 14.3007 | 0.754762 | 0.377381 | − | 0.926058i | \(-0.376825\pi\) | ||||
0.377381 | + | 0.926058i | \(0.376825\pi\) | |||||||
\(360\) | 6.38658 | 0.336602 | ||||||||
\(361\) | 3.34821 | 0.176221 | ||||||||
\(362\) | −14.2484 | −0.748877 | ||||||||
\(363\) | 29.2355 | 1.53446 | ||||||||
\(364\) | 3.46425 | 0.181576 | ||||||||
\(365\) | −3.99040 | −0.208867 | ||||||||
\(366\) | −6.05403 | −0.316449 | ||||||||
\(367\) | 29.0059 | 1.51410 | 0.757048 | − | 0.653359i | \(-0.226641\pi\) | ||||
0.757048 | + | 0.653359i | \(0.226641\pi\) | |||||||
\(368\) | −5.72536 | −0.298455 | ||||||||
\(369\) | −3.25460 | −0.169427 | ||||||||
\(370\) | −0.294060 | −0.0152874 | ||||||||
\(371\) | −5.88939 | −0.305762 | ||||||||
\(372\) | −19.0644 | −0.988445 | ||||||||
\(373\) | −21.6104 | −1.11894 | −0.559472 | − | 0.828849i | \(-0.688996\pi\) | ||||
−0.559472 | + | 0.828849i | \(0.688996\pi\) | |||||||
\(374\) | 0.360717 | 0.0186522 | ||||||||
\(375\) | 31.4111 | 1.62206 | ||||||||
\(376\) | −1.31794 | −0.0679676 | ||||||||
\(377\) | 17.2424 | 0.888029 | ||||||||
\(378\) | −4.66326 | −0.239852 | ||||||||
\(379\) | −18.4146 | −0.945894 | −0.472947 | − | 0.881091i | \(-0.656810\pi\) | ||||
−0.472947 | + | 0.881091i | \(0.656810\pi\) | |||||||
\(380\) | 7.29238 | 0.374091 | ||||||||
\(381\) | 27.7018 | 1.41920 | ||||||||
\(382\) | 21.1591 | 1.08259 | ||||||||
\(383\) | 13.7101 | 0.700556 | 0.350278 | − | 0.936646i | \(-0.386087\pi\) | ||||
0.350278 | + | 0.936646i | \(0.386087\pi\) | |||||||
\(384\) | −2.67211 | −0.136361 | ||||||||
\(385\) | −0.573720 | −0.0292395 | ||||||||
\(386\) | 23.0206 | 1.17172 | ||||||||
\(387\) | 25.9379 | 1.31850 | ||||||||
\(388\) | 3.87448 | 0.196697 | ||||||||
\(389\) | −9.24988 | −0.468988 | −0.234494 | − | 0.972118i | \(-0.575343\pi\) | ||||
−0.234494 | + | 0.972118i | \(0.575343\pi\) | |||||||
\(390\) | −9.32945 | −0.472415 | ||||||||
\(391\) | 8.49910 | 0.429818 | ||||||||
\(392\) | −4.65733 | −0.235230 | ||||||||
\(393\) | 6.28749 | 0.317162 | ||||||||
\(394\) | −4.98388 | −0.251084 | ||||||||
\(395\) | 2.79558 | 0.140661 | ||||||||
\(396\) | −1.00604 | −0.0505556 | ||||||||
\(397\) | 12.0435 | 0.604447 | 0.302223 | − | 0.953237i | \(-0.402271\pi\) | ||||
0.302223 | + | 0.953237i | \(0.402271\pi\) | |||||||
\(398\) | −9.49186 | −0.475784 | ||||||||
\(399\) | −19.3345 | −0.967934 | ||||||||
\(400\) | −2.62045 | −0.131022 | ||||||||
\(401\) | 17.7224 | 0.885014 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(402\) | −43.0216 | −2.14572 | ||||||||
\(403\) | 16.1481 | 0.804395 | ||||||||
\(404\) | −3.08877 | −0.153672 | ||||||||
\(405\) | −6.60128 | −0.328020 | ||||||||
\(406\) | 11.6601 | 0.578679 | ||||||||
\(407\) | 0.0463216 | 0.00229608 | ||||||||
\(408\) | 3.96666 | 0.196379 | ||||||||
\(409\) | 31.5590 | 1.56049 | 0.780246 | − | 0.625473i | \(-0.215094\pi\) | ||||
0.780246 | + | 0.625473i | \(0.215094\pi\) | |||||||
\(410\) | −1.21262 | −0.0598870 | ||||||||
\(411\) | −30.9445 | −1.52638 | ||||||||
\(412\) | −16.1878 | −0.797515 | ||||||||
\(413\) | −11.4181 | −0.561847 | ||||||||
\(414\) | −23.7041 | −1.16499 | ||||||||
\(415\) | 25.4555 | 1.24956 | ||||||||
\(416\) | 2.26336 | 0.110970 | ||||||||
\(417\) | −4.44840 | −0.217839 | ||||||||
\(418\) | −1.14873 | −0.0561861 | ||||||||
\(419\) | −16.1235 | −0.787685 | −0.393842 | − | 0.919178i | \(-0.628854\pi\) | ||||
−0.393842 | + | 0.919178i | \(0.628854\pi\) | |||||||
\(420\) | −6.30897 | −0.307846 | ||||||||
\(421\) | 10.0250 | 0.488590 | 0.244295 | − | 0.969701i | \(-0.421444\pi\) | ||||
0.244295 | + | 0.969701i | \(0.421444\pi\) | |||||||
\(422\) | 5.28526 | 0.257282 | ||||||||
\(423\) | −5.45653 | −0.265306 | ||||||||
\(424\) | −3.84781 | −0.186866 | ||||||||
\(425\) | 3.88996 | 0.188691 | ||||||||
\(426\) | −15.9474 | −0.772654 | ||||||||
\(427\) | 3.46773 | 0.167815 | ||||||||
\(428\) | 1.97161 | 0.0953016 | ||||||||
\(429\) | 1.46962 | 0.0709537 | ||||||||
\(430\) | 9.66409 | 0.466044 | ||||||||
\(431\) | 16.0663 | 0.773884 | 0.386942 | − | 0.922104i | \(-0.373531\pi\) | ||||
0.386942 | + | 0.922104i | \(0.373531\pi\) | |||||||
\(432\) | −3.04673 | −0.146586 | ||||||||
\(433\) | 28.1134 | 1.35105 | 0.675523 | − | 0.737339i | \(-0.263918\pi\) | ||||
0.675523 | + | 0.737339i | \(0.263918\pi\) | |||||||
\(434\) | 10.9201 | 0.524179 | ||||||||
\(435\) | −31.4013 | −1.50558 | ||||||||
\(436\) | −16.5660 | −0.793368 | ||||||||
\(437\) | −27.0660 | −1.29474 | ||||||||
\(438\) | 6.91231 | 0.330283 | ||||||||
\(439\) | −9.34301 | −0.445918 | −0.222959 | − | 0.974828i | \(-0.571572\pi\) | ||||
−0.222959 | + | 0.974828i | \(0.571572\pi\) | |||||||
\(440\) | −0.374838 | −0.0178697 | ||||||||
\(441\) | −19.2822 | −0.918202 | ||||||||
\(442\) | −3.35988 | −0.159813 | ||||||||
\(443\) | 5.51180 | 0.261873 | 0.130937 | − | 0.991391i | \(-0.458202\pi\) | ||||
0.130937 | + | 0.991391i | \(0.458202\pi\) | |||||||
\(444\) | 0.509381 | 0.0241742 | ||||||||
\(445\) | 15.7828 | 0.748178 | ||||||||
\(446\) | 5.79143 | 0.274232 | ||||||||
\(447\) | −43.1375 | −2.04033 | ||||||||
\(448\) | 1.53058 | 0.0723131 | ||||||||
\(449\) | 29.0429 | 1.37062 | 0.685311 | − | 0.728251i | \(-0.259666\pi\) | ||||
0.685311 | + | 0.728251i | \(0.259666\pi\) | |||||||
\(450\) | −10.8492 | −0.511434 | ||||||||
\(451\) | 0.191017 | 0.00899465 | ||||||||
\(452\) | 10.8064 | 0.508289 | ||||||||
\(453\) | 60.8727 | 2.86005 | ||||||||
\(454\) | −0.143720 | −0.00674512 | ||||||||
\(455\) | 5.34388 | 0.250525 | ||||||||
\(456\) | −12.6321 | −0.591553 | ||||||||
\(457\) | −32.0699 | −1.50017 | −0.750083 | − | 0.661343i | \(-0.769987\pi\) | ||||
−0.750083 | + | 0.661343i | \(0.769987\pi\) | |||||||
\(458\) | −20.0353 | −0.936190 | ||||||||
\(459\) | 4.52276 | 0.211104 | ||||||||
\(460\) | −8.83182 | −0.411786 | ||||||||
\(461\) | 15.1934 | 0.707627 | 0.353813 | − | 0.935316i | \(-0.384885\pi\) | ||||
0.353813 | + | 0.935316i | \(0.384885\pi\) | |||||||
\(462\) | 0.993818 | 0.0462366 | ||||||||
\(463\) | 11.7465 | 0.545906 | 0.272953 | − | 0.962027i | \(-0.412000\pi\) | ||||
0.272953 | + | 0.962027i | \(0.412000\pi\) | |||||||
\(464\) | 7.61807 | 0.353660 | ||||||||
\(465\) | −29.4084 | −1.36378 | ||||||||
\(466\) | 18.4254 | 0.853542 | ||||||||
\(467\) | 39.0470 | 1.80688 | 0.903439 | − | 0.428717i | \(-0.141034\pi\) | ||||
0.903439 | + | 0.428717i | \(0.141034\pi\) | |||||||
\(468\) | 9.37074 | 0.433162 | ||||||||
\(469\) | 24.6426 | 1.13789 | ||||||||
\(470\) | −2.03303 | −0.0937767 | ||||||||
\(471\) | −6.44687 | −0.297056 | ||||||||
\(472\) | −7.45997 | −0.343373 | ||||||||
\(473\) | −1.52233 | −0.0699969 | ||||||||
\(474\) | −4.84261 | −0.222428 | ||||||||
\(475\) | −12.3879 | −0.568394 | ||||||||
\(476\) | −2.27209 | −0.104141 | ||||||||
\(477\) | −15.9307 | −0.729417 | ||||||||
\(478\) | 17.9629 | 0.821604 | ||||||||
\(479\) | 11.0464 | 0.504725 | 0.252362 | − | 0.967633i | \(-0.418793\pi\) | ||||
0.252362 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(480\) | −4.12195 | −0.188140 | ||||||||
\(481\) | −0.431460 | −0.0196729 | ||||||||
\(482\) | −22.0437 | −1.00407 | ||||||||
\(483\) | 23.4160 | 1.06547 | ||||||||
\(484\) | −10.9410 | −0.497316 | ||||||||
\(485\) | 5.97670 | 0.271388 | ||||||||
\(486\) | 20.5752 | 0.933309 | ||||||||
\(487\) | −33.7729 | −1.53039 | −0.765197 | − | 0.643796i | \(-0.777358\pi\) | ||||
−0.765197 | + | 0.643796i | \(0.777358\pi\) | |||||||
\(488\) | 2.26563 | 0.102560 | ||||||||
\(489\) | −33.2195 | −1.50224 | ||||||||
\(490\) | −7.18430 | −0.324554 | ||||||||
\(491\) | 28.0685 | 1.26671 | 0.633356 | − | 0.773861i | \(-0.281677\pi\) | ||||
0.633356 | + | 0.773861i | \(0.281677\pi\) | |||||||
\(492\) | 2.10054 | 0.0946997 | ||||||||
\(493\) | −11.3088 | −0.509321 | ||||||||
\(494\) | 10.6998 | 0.481405 | ||||||||
\(495\) | −1.55190 | −0.0697528 | ||||||||
\(496\) | 7.13459 | 0.320352 | ||||||||
\(497\) | 9.13463 | 0.409744 | ||||||||
\(498\) | −44.0949 | −1.97594 | ||||||||
\(499\) | 3.28146 | 0.146898 | 0.0734491 | − | 0.997299i | \(-0.476599\pi\) | ||||
0.0734491 | + | 0.997299i | \(0.476599\pi\) | |||||||
\(500\) | −11.7552 | −0.525706 | ||||||||
\(501\) | 16.3213 | 0.729183 | ||||||||
\(502\) | 2.84013 | 0.126761 | ||||||||
\(503\) | 25.2809 | 1.12722 | 0.563609 | − | 0.826042i | \(-0.309413\pi\) | ||||
0.563609 | + | 0.826042i | \(0.309413\pi\) | |||||||
\(504\) | 6.33690 | 0.282268 | ||||||||
\(505\) | −4.76468 | −0.212026 | ||||||||
\(506\) | 1.39123 | 0.0618477 | ||||||||
\(507\) | 21.0488 | 0.934811 | ||||||||
\(508\) | −10.3670 | −0.459960 | ||||||||
\(509\) | −19.3461 | −0.857501 | −0.428750 | − | 0.903423i | \(-0.641046\pi\) | ||||
−0.428750 | + | 0.903423i | \(0.641046\pi\) | |||||||
\(510\) | 6.11889 | 0.270949 | ||||||||
\(511\) | −3.95935 | −0.175151 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −14.4031 | −0.635911 | ||||||||
\(514\) | −15.5053 | −0.683908 | ||||||||
\(515\) | −24.9710 | −1.10035 | ||||||||
\(516\) | −16.7405 | −0.736959 | ||||||||
\(517\) | 0.320252 | 0.0140847 | ||||||||
\(518\) | −0.291772 | −0.0128197 | ||||||||
\(519\) | 15.8754 | 0.696852 | ||||||||
\(520\) | 3.49141 | 0.153108 | ||||||||
\(521\) | 25.3534 | 1.11075 | 0.555376 | − | 0.831600i | \(-0.312575\pi\) | ||||
0.555376 | + | 0.831600i | \(0.312575\pi\) | |||||||
\(522\) | 31.5403 | 1.38048 | ||||||||
\(523\) | 9.07012 | 0.396609 | 0.198304 | − | 0.980140i | \(-0.436457\pi\) | ||||
0.198304 | + | 0.980140i | \(0.436457\pi\) | |||||||
\(524\) | −2.35300 | −0.102791 | ||||||||
\(525\) | 10.7173 | 0.467742 | ||||||||
\(526\) | 16.8989 | 0.736829 | ||||||||
\(527\) | −10.5910 | −0.461353 | ||||||||
\(528\) | 0.649308 | 0.0282575 | ||||||||
\(529\) | 9.77971 | 0.425205 | ||||||||
\(530\) | −5.93556 | −0.257824 | ||||||||
\(531\) | −30.8857 | −1.34033 | ||||||||
\(532\) | 7.23565 | 0.313705 | ||||||||
\(533\) | −1.77922 | −0.0770665 | ||||||||
\(534\) | −27.3396 | −1.18310 | ||||||||
\(535\) | 3.04137 | 0.131490 | ||||||||
\(536\) | 16.1002 | 0.695423 | ||||||||
\(537\) | −46.7814 | −2.01877 | ||||||||
\(538\) | −10.7604 | −0.463914 | ||||||||
\(539\) | 1.13170 | 0.0487459 | ||||||||
\(540\) | −4.69982 | −0.202248 | ||||||||
\(541\) | −20.6935 | −0.889683 | −0.444841 | − | 0.895609i | \(-0.646740\pi\) | ||||
−0.444841 | + | 0.895609i | \(0.646740\pi\) | |||||||
\(542\) | −2.92423 | −0.125607 | ||||||||
\(543\) | 38.0732 | 1.63388 | ||||||||
\(544\) | −1.48447 | −0.0636459 | ||||||||
\(545\) | −25.5544 | −1.09463 | ||||||||
\(546\) | −9.25687 | −0.396157 | ||||||||
\(547\) | −6.35946 | −0.271911 | −0.135956 | − | 0.990715i | \(-0.543410\pi\) | ||||
−0.135956 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(548\) | 11.5805 | 0.494696 | ||||||||
\(549\) | 9.38017 | 0.400336 | ||||||||
\(550\) | 0.636753 | 0.0271512 | ||||||||
\(551\) | 36.0136 | 1.53423 | ||||||||
\(552\) | 15.2988 | 0.651160 | ||||||||
\(553\) | 2.77383 | 0.117955 | ||||||||
\(554\) | 16.7942 | 0.713518 | ||||||||
\(555\) | 0.785762 | 0.0333537 | ||||||||
\(556\) | 1.66475 | 0.0706011 | ||||||||
\(557\) | −0.833740 | −0.0353267 | −0.0176633 | − | 0.999844i | \(-0.505623\pi\) | ||||
−0.0176633 | + | 0.999844i | \(0.505623\pi\) | |||||||
\(558\) | 29.5386 | 1.25047 | ||||||||
\(559\) | 14.1797 | 0.599736 | ||||||||
\(560\) | 2.36104 | 0.0997722 | ||||||||
\(561\) | −0.963876 | −0.0406949 | ||||||||
\(562\) | −7.84228 | −0.330807 | ||||||||
\(563\) | 31.4592 | 1.32585 | 0.662924 | − | 0.748687i | \(-0.269315\pi\) | ||||
0.662924 | + | 0.748687i | \(0.269315\pi\) | |||||||
\(564\) | 3.52169 | 0.148290 | ||||||||
\(565\) | 16.6697 | 0.701299 | ||||||||
\(566\) | 22.5405 | 0.947450 | ||||||||
\(567\) | −6.54993 | −0.275071 | ||||||||
\(568\) | 5.96809 | 0.250415 | ||||||||
\(569\) | 0.772276 | 0.0323755 | 0.0161877 | − | 0.999869i | \(-0.494847\pi\) | ||||
0.0161877 | + | 0.999869i | \(0.494847\pi\) | |||||||
\(570\) | −19.4861 | −0.816182 | ||||||||
\(571\) | −12.5757 | −0.526276 | −0.263138 | − | 0.964758i | \(-0.584757\pi\) | ||||
−0.263138 | + | 0.964758i | \(0.584757\pi\) | |||||||
\(572\) | −0.549983 | −0.0229959 | ||||||||
\(573\) | −56.5394 | −2.36197 | ||||||||
\(574\) | −1.20318 | −0.0502200 | ||||||||
\(575\) | 15.0030 | 0.625668 | ||||||||
\(576\) | 4.14019 | 0.172508 | ||||||||
\(577\) | 18.9705 | 0.789752 | 0.394876 | − | 0.918734i | \(-0.370788\pi\) | ||||
0.394876 | + | 0.918734i | \(0.370788\pi\) | |||||||
\(578\) | −14.7964 | −0.615448 | ||||||||
\(579\) | −61.5138 | −2.55643 | ||||||||
\(580\) | 11.7515 | 0.487954 | ||||||||
\(581\) | 25.2574 | 1.04786 | ||||||||
\(582\) | −10.3531 | −0.429148 | ||||||||
\(583\) | 0.934997 | 0.0387236 | ||||||||
\(584\) | −2.58683 | −0.107044 | ||||||||
\(585\) | 14.4551 | 0.597645 | ||||||||
\(586\) | 31.0174 | 1.28132 | ||||||||
\(587\) | 28.6600 | 1.18293 | 0.591463 | − | 0.806332i | \(-0.298551\pi\) | ||||
0.591463 | + | 0.806332i | \(0.298551\pi\) | |||||||
\(588\) | 12.4449 | 0.513219 | ||||||||
\(589\) | 33.7280 | 1.38974 | ||||||||
\(590\) | −11.5076 | −0.473761 | ||||||||
\(591\) | 13.3175 | 0.547808 | ||||||||
\(592\) | −0.190629 | −0.00783479 | ||||||||
\(593\) | 20.6639 | 0.848565 | 0.424283 | − | 0.905530i | \(-0.360526\pi\) | ||||
0.424283 | + | 0.905530i | \(0.360526\pi\) | |||||||
\(594\) | 0.740337 | 0.0303764 | ||||||||
\(595\) | −3.50489 | −0.143686 | ||||||||
\(596\) | 16.1436 | 0.661267 | ||||||||
\(597\) | 25.3633 | 1.03805 | ||||||||
\(598\) | −12.9585 | −0.529914 | ||||||||
\(599\) | −31.2557 | −1.27707 | −0.638537 | − | 0.769591i | \(-0.720460\pi\) | ||||
−0.638537 | + | 0.769591i | \(0.720460\pi\) | |||||||
\(600\) | 7.00213 | 0.285861 | ||||||||
\(601\) | 9.92625 | 0.404900 | 0.202450 | − | 0.979293i | \(-0.435110\pi\) | ||||
0.202450 | + | 0.979293i | \(0.435110\pi\) | |||||||
\(602\) | 9.58891 | 0.390815 | ||||||||
\(603\) | 66.6579 | 2.71452 | ||||||||
\(604\) | −22.7807 | −0.926935 | ||||||||
\(605\) | −16.8773 | −0.686160 | ||||||||
\(606\) | 8.25356 | 0.335278 | ||||||||
\(607\) | −5.74153 | −0.233042 | −0.116521 | − | 0.993188i | \(-0.537174\pi\) | ||||
−0.116521 | + | 0.993188i | \(0.537174\pi\) | |||||||
\(608\) | 4.72739 | 0.191721 | ||||||||
\(609\) | −31.1570 | −1.26255 | ||||||||
\(610\) | 3.49492 | 0.141505 | ||||||||
\(611\) | −2.98297 | −0.120678 | ||||||||
\(612\) | −6.14597 | −0.248436 | ||||||||
\(613\) | −19.5719 | −0.790502 | −0.395251 | − | 0.918573i | \(-0.629342\pi\) | ||||
−0.395251 | + | 0.918573i | \(0.629342\pi\) | |||||||
\(614\) | 14.6953 | 0.593054 | ||||||||
\(615\) | 3.24025 | 0.130660 | ||||||||
\(616\) | −0.371922 | −0.0149852 | ||||||||
\(617\) | 10.8255 | 0.435820 | 0.217910 | − | 0.975969i | \(-0.430076\pi\) | ||||
0.217910 | + | 0.975969i | \(0.430076\pi\) | |||||||
\(618\) | 43.2556 | 1.74000 | ||||||||
\(619\) | 25.4720 | 1.02380 | 0.511902 | − | 0.859044i | \(-0.328941\pi\) | ||||
0.511902 | + | 0.859044i | \(0.328941\pi\) | |||||||
\(620\) | 11.0057 | 0.441999 | ||||||||
\(621\) | 17.4436 | 0.699988 | ||||||||
\(622\) | 13.2704 | 0.532095 | ||||||||
\(623\) | 15.6601 | 0.627407 | ||||||||
\(624\) | −6.04795 | −0.242112 | ||||||||
\(625\) | −5.03104 | −0.201242 | ||||||||
\(626\) | 11.7200 | 0.468425 | ||||||||
\(627\) | 3.06953 | 0.122585 | ||||||||
\(628\) | 2.41265 | 0.0962752 | ||||||||
\(629\) | 0.282982 | 0.0112832 | ||||||||
\(630\) | 9.77517 | 0.389452 | ||||||||
\(631\) | −31.2230 | −1.24297 | −0.621485 | − | 0.783426i | \(-0.713470\pi\) | ||||
−0.621485 | + | 0.783426i | \(0.713470\pi\) | |||||||
\(632\) | 1.81227 | 0.0720884 | ||||||||
\(633\) | −14.1228 | −0.561331 | ||||||||
\(634\) | −21.0946 | −0.837772 | ||||||||
\(635\) | −15.9919 | −0.634619 | ||||||||
\(636\) | 10.2818 | 0.407700 | ||||||||
\(637\) | −10.5412 | −0.417657 | ||||||||
\(638\) | −1.85115 | −0.0732876 | ||||||||
\(639\) | 24.7090 | 0.977474 | ||||||||
\(640\) | 1.54258 | 0.0609758 | ||||||||
\(641\) | 37.3744 | 1.47620 | 0.738101 | − | 0.674690i | \(-0.235723\pi\) | ||||
0.738101 | + | 0.674690i | \(0.235723\pi\) | |||||||
\(642\) | −5.26838 | −0.207926 | ||||||||
\(643\) | −13.2381 | −0.522061 | −0.261030 | − | 0.965331i | \(-0.584062\pi\) | ||||
−0.261030 | + | 0.965331i | \(0.584062\pi\) | |||||||
\(644\) | −8.76311 | −0.345315 | ||||||||
\(645\) | −25.8236 | −1.01680 | ||||||||
\(646\) | −7.01765 | −0.276106 | ||||||||
\(647\) | 14.1610 | 0.556728 | 0.278364 | − | 0.960476i | \(-0.410208\pi\) | ||||
0.278364 | + | 0.960476i | \(0.410208\pi\) | |||||||
\(648\) | −4.27938 | −0.168110 | ||||||||
\(649\) | 1.81273 | 0.0711559 | ||||||||
\(650\) | −5.93100 | −0.232633 | ||||||||
\(651\) | −29.1796 | −1.14364 | ||||||||
\(652\) | 12.4319 | 0.486872 | ||||||||
\(653\) | −19.6330 | −0.768298 | −0.384149 | − | 0.923271i | \(-0.625505\pi\) | ||||
−0.384149 | + | 0.923271i | \(0.625505\pi\) | |||||||
\(654\) | 44.2663 | 1.73095 | ||||||||
\(655\) | −3.62970 | −0.141824 | ||||||||
\(656\) | −0.786097 | −0.0306919 | ||||||||
\(657\) | −10.7100 | −0.417836 | ||||||||
\(658\) | −2.01721 | −0.0786392 | ||||||||
\(659\) | −31.9992 | −1.24651 | −0.623256 | − | 0.782018i | \(-0.714190\pi\) | ||||
−0.623256 | + | 0.782018i | \(0.714190\pi\) | |||||||
\(660\) | 1.00161 | 0.0389876 | ||||||||
\(661\) | 24.0835 | 0.936740 | 0.468370 | − | 0.883532i | \(-0.344841\pi\) | ||||
0.468370 | + | 0.883532i | \(0.344841\pi\) | |||||||
\(662\) | −7.80058 | −0.303178 | ||||||||
\(663\) | 8.97797 | 0.348675 | ||||||||
\(664\) | 16.5019 | 0.640397 | ||||||||
\(665\) | 11.1616 | 0.432827 | ||||||||
\(666\) | −0.789239 | −0.0305824 | ||||||||
\(667\) | −43.6162 | −1.68882 | ||||||||
\(668\) | −6.10802 | −0.236326 | ||||||||
\(669\) | −15.4754 | −0.598312 | ||||||||
\(670\) | 24.8358 | 0.959493 | ||||||||
\(671\) | −0.550536 | −0.0212532 | ||||||||
\(672\) | −4.08988 | −0.157771 | ||||||||
\(673\) | −40.5342 | −1.56248 | −0.781239 | − | 0.624232i | \(-0.785412\pi\) | ||||
−0.781239 | + | 0.624232i | \(0.785412\pi\) | |||||||
\(674\) | 17.4264 | 0.671240 | ||||||||
\(675\) | 7.98378 | 0.307296 | ||||||||
\(676\) | −7.87722 | −0.302970 | ||||||||
\(677\) | −13.7315 | −0.527745 | −0.263872 | − | 0.964558i | \(-0.585000\pi\) | ||||
−0.263872 | + | 0.964558i | \(0.585000\pi\) | |||||||
\(678\) | −28.8758 | −1.10897 | ||||||||
\(679\) | 5.93020 | 0.227580 | ||||||||
\(680\) | −2.28991 | −0.0878139 | ||||||||
\(681\) | 0.384037 | 0.0147163 | ||||||||
\(682\) | −1.73366 | −0.0663854 | ||||||||
\(683\) | 41.1233 | 1.57354 | 0.786769 | − | 0.617247i | \(-0.211752\pi\) | ||||
0.786769 | + | 0.617247i | \(0.211752\pi\) | |||||||
\(684\) | 19.5723 | 0.748366 | ||||||||
\(685\) | 17.8639 | 0.682544 | ||||||||
\(686\) | −17.8425 | −0.681228 | ||||||||
\(687\) | 53.5367 | 2.04255 | ||||||||
\(688\) | 6.26489 | 0.238847 | ||||||||
\(689\) | −8.70898 | −0.331786 | ||||||||
\(690\) | 23.5996 | 0.898423 | ||||||||
\(691\) | 21.7571 | 0.827678 | 0.413839 | − | 0.910350i | \(-0.364188\pi\) | ||||
0.413839 | + | 0.910350i | \(0.364188\pi\) | |||||||
\(692\) | −5.94113 | −0.225848 | ||||||||
\(693\) | −1.53983 | −0.0584933 | ||||||||
\(694\) | 5.48709 | 0.208287 | ||||||||
\(695\) | 2.56801 | 0.0974102 | ||||||||
\(696\) | −20.3564 | −0.771606 | ||||||||
\(697\) | 1.16693 | 0.0442008 | ||||||||
\(698\) | 12.9415 | 0.489842 | ||||||||
\(699\) | −49.2349 | −1.86223 | ||||||||
\(700\) | −4.01080 | −0.151594 | ||||||||
\(701\) | −34.9552 | −1.32024 | −0.660120 | − | 0.751160i | \(-0.729495\pi\) | ||||
−0.660120 | + | 0.751160i | \(0.729495\pi\) | |||||||
\(702\) | −6.89583 | −0.260266 | ||||||||
\(703\) | −0.901175 | −0.0339885 | ||||||||
\(704\) | −0.242994 | −0.00915819 | ||||||||
\(705\) | 5.43249 | 0.204599 | ||||||||
\(706\) | −26.9966 | −1.01603 | ||||||||
\(707\) | −4.72761 | −0.177800 | ||||||||
\(708\) | 19.9339 | 0.749162 | ||||||||
\(709\) | −8.07009 | −0.303079 | −0.151539 | − | 0.988451i | \(-0.548423\pi\) | ||||
−0.151539 | + | 0.988451i | \(0.548423\pi\) | |||||||
\(710\) | 9.20625 | 0.345505 | ||||||||
\(711\) | 7.50317 | 0.281391 | ||||||||
\(712\) | 10.2315 | 0.383440 | ||||||||
\(713\) | −40.8481 | −1.52977 | ||||||||
\(714\) | 6.07129 | 0.227212 | ||||||||
\(715\) | −0.848393 | −0.0317281 | ||||||||
\(716\) | 17.5073 | 0.654277 | ||||||||
\(717\) | −47.9989 | −1.79255 | ||||||||
\(718\) | 14.3007 | 0.533697 | ||||||||
\(719\) | 15.2286 | 0.567930 | 0.283965 | − | 0.958835i | \(-0.408350\pi\) | ||||
0.283965 | + | 0.958835i | \(0.408350\pi\) | |||||||
\(720\) | 6.38658 | 0.238014 | ||||||||
\(721\) | −24.7767 | −0.922732 | ||||||||
\(722\) | 3.34821 | 0.124607 | ||||||||
\(723\) | 58.9034 | 2.19064 | ||||||||
\(724\) | −14.2484 | −0.529536 | ||||||||
\(725\) | −19.9627 | −0.741397 | ||||||||
\(726\) | 29.2355 | 1.08503 | ||||||||
\(727\) | −38.2184 | −1.41744 | −0.708720 | − | 0.705490i | \(-0.750727\pi\) | ||||
−0.708720 | + | 0.705490i | \(0.750727\pi\) | |||||||
\(728\) | 3.46425 | 0.128394 | ||||||||
\(729\) | −42.1411 | −1.56078 | ||||||||
\(730\) | −3.99040 | −0.147691 | ||||||||
\(731\) | −9.30001 | −0.343973 | ||||||||
\(732\) | −6.05403 | −0.223764 | ||||||||
\(733\) | −30.3110 | −1.11956 | −0.559782 | − | 0.828640i | \(-0.689115\pi\) | ||||
−0.559782 | + | 0.828640i | \(0.689115\pi\) | |||||||
\(734\) | 29.0059 | 1.07063 | ||||||||
\(735\) | 19.1973 | 0.708102 | ||||||||
\(736\) | −5.72536 | −0.211039 | ||||||||
\(737\) | −3.91225 | −0.144110 | ||||||||
\(738\) | −3.25460 | −0.119803 | ||||||||
\(739\) | −32.0927 | −1.18055 | −0.590275 | − | 0.807202i | \(-0.700981\pi\) | ||||
−0.590275 | + | 0.807202i | \(0.700981\pi\) | |||||||
\(740\) | −0.294060 | −0.0108099 | ||||||||
\(741\) | −28.5910 | −1.05032 | ||||||||
\(742\) | −5.88939 | −0.216206 | ||||||||
\(743\) | −29.4066 | −1.07882 | −0.539411 | − | 0.842043i | \(-0.681353\pi\) | ||||
−0.539411 | + | 0.842043i | \(0.681353\pi\) | |||||||
\(744\) | −19.0644 | −0.698936 | ||||||||
\(745\) | 24.9028 | 0.912367 | ||||||||
\(746\) | −21.6104 | −0.791212 | ||||||||
\(747\) | 68.3210 | 2.49973 | ||||||||
\(748\) | 0.360717 | 0.0131891 | ||||||||
\(749\) | 3.01771 | 0.110265 | ||||||||
\(750\) | 31.4111 | 1.14697 | ||||||||
\(751\) | −21.0248 | −0.767205 | −0.383603 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383603 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(752\) | −1.31794 | −0.0480604 | ||||||||
\(753\) | −7.58916 | −0.276564 | ||||||||
\(754\) | 17.2424 | 0.627932 | ||||||||
\(755\) | −35.1411 | −1.27892 | ||||||||
\(756\) | −4.66326 | −0.169601 | ||||||||
\(757\) | 47.0354 | 1.70953 | 0.854766 | − | 0.519014i | \(-0.173701\pi\) | ||||
0.854766 | + | 0.519014i | \(0.173701\pi\) | |||||||
\(758\) | −18.4146 | −0.668848 | ||||||||
\(759\) | −3.71752 | −0.134938 | ||||||||
\(760\) | 7.29238 | 0.264522 | ||||||||
\(761\) | −4.77882 | −0.173232 | −0.0866160 | − | 0.996242i | \(-0.527605\pi\) | ||||
−0.0866160 | + | 0.996242i | \(0.527605\pi\) | |||||||
\(762\) | 27.7018 | 1.00353 | ||||||||
\(763\) | −25.3556 | −0.917934 | ||||||||
\(764\) | 21.1591 | 0.765508 | ||||||||
\(765\) | −9.48066 | −0.342774 | ||||||||
\(766\) | 13.7101 | 0.495368 | ||||||||
\(767\) | −16.8846 | −0.609667 | ||||||||
\(768\) | −2.67211 | −0.0964216 | ||||||||
\(769\) | 34.0944 | 1.22948 | 0.614738 | − | 0.788732i | \(-0.289262\pi\) | ||||
0.614738 | + | 0.788732i | \(0.289262\pi\) | |||||||
\(770\) | −0.573720 | −0.0206754 | ||||||||
\(771\) | 41.4318 | 1.49213 | ||||||||
\(772\) | 23.0206 | 0.828531 | ||||||||
\(773\) | −11.3643 | −0.408746 | −0.204373 | − | 0.978893i | \(-0.565515\pi\) | ||||
−0.204373 | + | 0.978893i | \(0.565515\pi\) | |||||||
\(774\) | 25.9379 | 0.932317 | ||||||||
\(775\) | −18.6958 | −0.671573 | ||||||||
\(776\) | 3.87448 | 0.139086 | ||||||||
\(777\) | 0.779649 | 0.0279697 | ||||||||
\(778\) | −9.24988 | −0.331624 | ||||||||
\(779\) | −3.71619 | −0.133146 | ||||||||
\(780\) | −9.32945 | −0.334048 | ||||||||
\(781\) | −1.45021 | −0.0518926 | ||||||||
\(782\) | 8.49910 | 0.303927 | ||||||||
\(783\) | −23.2102 | −0.829464 | ||||||||
\(784\) | −4.65733 | −0.166333 | ||||||||
\(785\) | 3.72171 | 0.132833 | ||||||||
\(786\) | 6.28749 | 0.224267 | ||||||||
\(787\) | 28.9099 | 1.03053 | 0.515263 | − | 0.857032i | \(-0.327694\pi\) | ||||
0.515263 | + | 0.857032i | \(0.327694\pi\) | |||||||
\(788\) | −4.98388 | −0.177543 | ||||||||
\(789\) | −45.1559 | −1.60759 | ||||||||
\(790\) | 2.79558 | 0.0994623 | ||||||||
\(791\) | 16.5400 | 0.588095 | ||||||||
\(792\) | −1.00604 | −0.0357482 | ||||||||
\(793\) | 5.12794 | 0.182098 | ||||||||
\(794\) | 12.0435 | 0.427408 | ||||||||
\(795\) | 15.8605 | 0.562514 | ||||||||
\(796\) | −9.49186 | −0.336430 | ||||||||
\(797\) | 4.08869 | 0.144829 | 0.0724145 | − | 0.997375i | \(-0.476930\pi\) | ||||
0.0724145 | + | 0.997375i | \(0.476930\pi\) | |||||||
\(798\) | −19.3345 | −0.684433 | ||||||||
\(799\) | 1.95644 | 0.0692138 | ||||||||
\(800\) | −2.62045 | −0.0926467 | ||||||||
\(801\) | 42.3602 | 1.49672 | ||||||||
\(802\) | 17.7224 | 0.625799 | ||||||||
\(803\) | 0.628585 | 0.0221823 | ||||||||
\(804\) | −43.0216 | −1.51725 | ||||||||
\(805\) | −13.5178 | −0.476440 | ||||||||
\(806\) | 16.1481 | 0.568793 | ||||||||
\(807\) | 28.7530 | 1.01215 | ||||||||
\(808\) | −3.08877 | −0.108663 | ||||||||
\(809\) | −35.5127 | −1.24856 | −0.624280 | − | 0.781201i | \(-0.714607\pi\) | ||||
−0.624280 | + | 0.781201i | \(0.714607\pi\) | |||||||
\(810\) | −6.60128 | −0.231945 | ||||||||
\(811\) | 39.9971 | 1.40449 | 0.702245 | − | 0.711936i | \(-0.252181\pi\) | ||||
0.702245 | + | 0.711936i | \(0.252181\pi\) | |||||||
\(812\) | 11.6601 | 0.409188 | ||||||||
\(813\) | 7.81388 | 0.274045 | ||||||||
\(814\) | 0.0463216 | 0.00162357 | ||||||||
\(815\) | 19.1772 | 0.671749 | ||||||||
\(816\) | 3.96666 | 0.138861 | ||||||||
\(817\) | 29.6166 | 1.03615 | ||||||||
\(818\) | 31.5590 | 1.10343 | ||||||||
\(819\) | 14.3427 | 0.501173 | ||||||||
\(820\) | −1.21262 | −0.0423465 | ||||||||
\(821\) | 48.2818 | 1.68505 | 0.842523 | − | 0.538661i | \(-0.181070\pi\) | ||||
0.842523 | + | 0.538661i | \(0.181070\pi\) | |||||||
\(822\) | −30.9445 | −1.07931 | ||||||||
\(823\) | −12.0786 | −0.421035 | −0.210517 | − | 0.977590i | \(-0.567515\pi\) | ||||
−0.210517 | + | 0.977590i | \(0.567515\pi\) | |||||||
\(824\) | −16.1878 | −0.563928 | ||||||||
\(825\) | −1.70148 | −0.0592378 | ||||||||
\(826\) | −11.4181 | −0.397286 | ||||||||
\(827\) | −3.75611 | −0.130613 | −0.0653063 | − | 0.997865i | \(-0.520802\pi\) | ||||
−0.0653063 | + | 0.997865i | \(0.520802\pi\) | |||||||
\(828\) | −23.7041 | −0.823774 | ||||||||
\(829\) | −25.7300 | −0.893641 | −0.446821 | − | 0.894624i | \(-0.647444\pi\) | ||||
−0.446821 | + | 0.894624i | \(0.647444\pi\) | |||||||
\(830\) | 25.4555 | 0.883572 | ||||||||
\(831\) | −44.8761 | −1.55673 | ||||||||
\(832\) | 2.26336 | 0.0784678 | ||||||||
\(833\) | 6.91364 | 0.239543 | ||||||||
\(834\) | −4.44840 | −0.154035 | ||||||||
\(835\) | −9.42211 | −0.326066 | ||||||||
\(836\) | −1.14873 | −0.0397296 | ||||||||
\(837\) | −21.7371 | −0.751346 | ||||||||
\(838\) | −16.1235 | −0.556977 | ||||||||
\(839\) | −31.2929 | −1.08035 | −0.540176 | − | 0.841552i | \(-0.681642\pi\) | ||||
−0.540176 | + | 0.841552i | \(0.681642\pi\) | |||||||
\(840\) | −6.30897 | −0.217680 | ||||||||
\(841\) | 29.0350 | 1.00121 | ||||||||
\(842\) | 10.0250 | 0.345485 | ||||||||
\(843\) | 20.9555 | 0.721745 | ||||||||
\(844\) | 5.28526 | 0.181926 | ||||||||
\(845\) | −12.1512 | −0.418015 | ||||||||
\(846\) | −5.45653 | −0.187599 | ||||||||
\(847\) | −16.7460 | −0.575399 | ||||||||
\(848\) | −3.84781 | −0.132134 | ||||||||
\(849\) | −60.2309 | −2.06712 | ||||||||
\(850\) | 3.88996 | 0.133425 | ||||||||
\(851\) | 1.09142 | 0.0374133 | ||||||||
\(852\) | −15.9474 | −0.546349 | ||||||||
\(853\) | −15.0589 | −0.515606 | −0.257803 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257803 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(854\) | 3.46773 | 0.118663 | ||||||||
\(855\) | 30.1919 | 1.03254 | ||||||||
\(856\) | 1.97161 | 0.0673884 | ||||||||
\(857\) | −25.9501 | −0.886438 | −0.443219 | − | 0.896413i | \(-0.646164\pi\) | ||||
−0.443219 | + | 0.896413i | \(0.646164\pi\) | |||||||
\(858\) | 1.46962 | 0.0501719 | ||||||||
\(859\) | 10.3571 | 0.353380 | 0.176690 | − | 0.984267i | \(-0.443461\pi\) | ||||
0.176690 | + | 0.984267i | \(0.443461\pi\) | |||||||
\(860\) | 9.66409 | 0.329543 | ||||||||
\(861\) | 3.21505 | 0.109568 | ||||||||
\(862\) | 16.0663 | 0.547219 | ||||||||
\(863\) | −37.7296 | −1.28433 | −0.642165 | − | 0.766567i | \(-0.721963\pi\) | ||||
−0.642165 | + | 0.766567i | \(0.721963\pi\) | |||||||
\(864\) | −3.04673 | −0.103652 | ||||||||
\(865\) | −9.16467 | −0.311608 | ||||||||
\(866\) | 28.1134 | 0.955333 | ||||||||
\(867\) | 39.5376 | 1.34277 | ||||||||
\(868\) | 10.9201 | 0.370651 | ||||||||
\(869\) | −0.440372 | −0.0149386 | ||||||||
\(870\) | −31.4013 | −1.06460 | ||||||||
\(871\) | 36.4405 | 1.23474 | ||||||||
\(872\) | −16.5660 | −0.560996 | ||||||||
\(873\) | 16.0411 | 0.542909 | ||||||||
\(874\) | −27.0660 | −0.915521 | ||||||||
\(875\) | −17.9922 | −0.608247 | ||||||||
\(876\) | 6.91231 | 0.233545 | ||||||||
\(877\) | −23.2710 | −0.785806 | −0.392903 | − | 0.919580i | \(-0.628529\pi\) | ||||
−0.392903 | + | 0.919580i | \(0.628529\pi\) | |||||||
\(878\) | −9.34301 | −0.315311 | ||||||||
\(879\) | −82.8820 | −2.79554 | ||||||||
\(880\) | −0.374838 | −0.0126358 | ||||||||
\(881\) | 27.7617 | 0.935314 | 0.467657 | − | 0.883910i | \(-0.345098\pi\) | ||||
0.467657 | + | 0.883910i | \(0.345098\pi\) | |||||||
\(882\) | −19.2822 | −0.649267 | ||||||||
\(883\) | −22.5632 | −0.759311 | −0.379655 | − | 0.925128i | \(-0.623957\pi\) | ||||
−0.379655 | + | 0.925128i | \(0.623957\pi\) | |||||||
\(884\) | −3.35988 | −0.113005 | ||||||||
\(885\) | 30.7496 | 1.03364 | ||||||||
\(886\) | 5.51180 | 0.185172 | ||||||||
\(887\) | −18.2737 | −0.613572 | −0.306786 | − | 0.951778i | \(-0.599254\pi\) | ||||
−0.306786 | + | 0.951778i | \(0.599254\pi\) | |||||||
\(888\) | 0.509381 | 0.0170937 | ||||||||
\(889\) | −15.8675 | −0.532178 | ||||||||
\(890\) | 15.7828 | 0.529042 | ||||||||
\(891\) | 1.03986 | 0.0348368 | ||||||||
\(892\) | 5.79143 | 0.193911 | ||||||||
\(893\) | −6.23042 | −0.208493 | ||||||||
\(894\) | −43.1375 | −1.44273 | ||||||||
\(895\) | 27.0064 | 0.902723 | ||||||||
\(896\) | 1.53058 | 0.0511331 | ||||||||
\(897\) | 34.6267 | 1.15615 | ||||||||
\(898\) | 29.0429 | 0.969175 | ||||||||
\(899\) | 54.3518 | 1.81273 | ||||||||
\(900\) | −10.8492 | −0.361638 | ||||||||
\(901\) | 5.71195 | 0.190293 | ||||||||
\(902\) | 0.191017 | 0.00636017 | ||||||||
\(903\) | −25.6227 | −0.852669 | ||||||||
\(904\) | 10.8064 | 0.359414 | ||||||||
\(905\) | −21.9792 | −0.730615 | ||||||||
\(906\) | 60.8727 | 2.02236 | ||||||||
\(907\) | −34.5036 | −1.14567 | −0.572837 | − | 0.819670i | \(-0.694157\pi\) | ||||
−0.572837 | + | 0.819670i | \(0.694157\pi\) | |||||||
\(908\) | −0.143720 | −0.00476952 | ||||||||
\(909\) | −12.7881 | −0.424155 | ||||||||
\(910\) | 5.34388 | 0.177148 | ||||||||
\(911\) | −14.8868 | −0.493223 | −0.246611 | − | 0.969114i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969114i | \(0.579317\pi\) | |||||||
\(912\) | −12.6321 | −0.418291 | ||||||||
\(913\) | −4.00986 | −0.132707 | ||||||||
\(914\) | −32.0699 | −1.06078 | ||||||||
\(915\) | −9.33883 | −0.308732 | ||||||||
\(916\) | −20.0353 | −0.661986 | ||||||||
\(917\) | −3.60146 | −0.118931 | ||||||||
\(918\) | 4.52276 | 0.149273 | ||||||||
\(919\) | −43.4869 | −1.43450 | −0.717250 | − | 0.696816i | \(-0.754599\pi\) | ||||
−0.717250 | + | 0.696816i | \(0.754599\pi\) | |||||||
\(920\) | −8.83182 | −0.291177 | ||||||||
\(921\) | −39.2675 | −1.29391 | ||||||||
\(922\) | 15.1934 | 0.500368 | ||||||||
\(923\) | 13.5079 | 0.444618 | ||||||||
\(924\) | 0.993818 | 0.0326942 | ||||||||
\(925\) | 0.499532 | 0.0164245 | ||||||||
\(926\) | 11.7465 | 0.386014 | ||||||||
\(927\) | −67.0206 | −2.20124 | ||||||||
\(928\) | 7.61807 | 0.250075 | ||||||||
\(929\) | −19.1943 | −0.629745 | −0.314872 | − | 0.949134i | \(-0.601962\pi\) | ||||
−0.314872 | + | 0.949134i | \(0.601962\pi\) | |||||||
\(930\) | −29.4084 | −0.964340 | ||||||||
\(931\) | −22.0170 | −0.721578 | ||||||||
\(932\) | 18.4254 | 0.603546 | ||||||||
\(933\) | −35.4600 | −1.16091 | ||||||||
\(934\) | 39.0470 | 1.27766 | ||||||||
\(935\) | 0.556434 | 0.0181973 | ||||||||
\(936\) | 9.37074 | 0.306292 | ||||||||
\(937\) | 51.8095 | 1.69254 | 0.846271 | − | 0.532753i | \(-0.178842\pi\) | ||||
0.846271 | + | 0.532753i | \(0.178842\pi\) | |||||||
\(938\) | 24.6426 | 0.804610 | ||||||||
\(939\) | −31.3171 | −1.02200 | ||||||||
\(940\) | −2.03303 | −0.0663101 | ||||||||
\(941\) | −24.9201 | −0.812372 | −0.406186 | − | 0.913790i | \(-0.633141\pi\) | ||||
−0.406186 | + | 0.913790i | \(0.633141\pi\) | |||||||
\(942\) | −6.44687 | −0.210050 | ||||||||
\(943\) | 4.50069 | 0.146563 | ||||||||
\(944\) | −7.45997 | −0.242801 | ||||||||
\(945\) | −7.19345 | −0.234003 | ||||||||
\(946\) | −1.52233 | −0.0494953 | ||||||||
\(947\) | −46.6989 | −1.51751 | −0.758755 | − | 0.651377i | \(-0.774192\pi\) | ||||
−0.758755 | + | 0.651377i | \(0.774192\pi\) | |||||||
\(948\) | −4.84261 | −0.157281 | ||||||||
\(949\) | −5.85492 | −0.190059 | ||||||||
\(950\) | −12.3879 | −0.401915 | ||||||||
\(951\) | 56.3671 | 1.82783 | ||||||||
\(952\) | −2.27209 | −0.0736389 | ||||||||
\(953\) | −11.9124 | −0.385881 | −0.192941 | − | 0.981210i | \(-0.561802\pi\) | ||||
−0.192941 | + | 0.981210i | \(0.561802\pi\) | |||||||
\(954\) | −15.9307 | −0.515775 | ||||||||
\(955\) | 32.6395 | 1.05619 | ||||||||
\(956\) | 17.9629 | 0.580961 | ||||||||
\(957\) | 4.94648 | 0.159897 | ||||||||
\(958\) | 11.0464 | 0.356894 | ||||||||
\(959\) | 17.7249 | 0.572368 | ||||||||
\(960\) | −4.12195 | −0.133035 | ||||||||
\(961\) | 19.9023 | 0.642011 | ||||||||
\(962\) | −0.431460 | −0.0139108 | ||||||||
\(963\) | 8.16287 | 0.263045 | ||||||||
\(964\) | −22.0437 | −0.709981 | ||||||||
\(965\) | 35.5112 | 1.14315 | ||||||||
\(966\) | 23.4160 | 0.753399 | ||||||||
\(967\) | 55.8604 | 1.79635 | 0.898175 | − | 0.439637i | \(-0.144893\pi\) | ||||
0.898175 | + | 0.439637i | \(0.144893\pi\) | |||||||
\(968\) | −10.9410 | −0.351656 | ||||||||
\(969\) | 18.7520 | 0.602399 | ||||||||
\(970\) | 5.97670 | 0.191900 | ||||||||
\(971\) | 0.470325 | 0.0150935 | 0.00754673 | − | 0.999972i | \(-0.497598\pi\) | ||||
0.00754673 | + | 0.999972i | \(0.497598\pi\) | |||||||
\(972\) | 20.5752 | 0.659949 | ||||||||
\(973\) | 2.54803 | 0.0816861 | ||||||||
\(974\) | −33.7729 | −1.08215 | ||||||||
\(975\) | 15.8483 | 0.507552 | ||||||||
\(976\) | 2.26563 | 0.0725212 | ||||||||
\(977\) | −39.5221 | −1.26442 | −0.632212 | − | 0.774795i | \(-0.717853\pi\) | ||||
−0.632212 | + | 0.774795i | \(0.717853\pi\) | |||||||
\(978\) | −33.2195 | −1.06224 | ||||||||
\(979\) | −2.48618 | −0.0794588 | ||||||||
\(980\) | −7.18430 | −0.229494 | ||||||||
\(981\) | −68.5865 | −2.18980 | ||||||||
\(982\) | 28.0685 | 0.895701 | ||||||||
\(983\) | 1.34196 | 0.0428018 | 0.0214009 | − | 0.999771i | \(-0.493187\pi\) | ||||
0.0214009 | + | 0.999771i | \(0.493187\pi\) | |||||||
\(984\) | 2.10054 | 0.0669628 | ||||||||
\(985\) | −7.68803 | −0.244961 | ||||||||
\(986\) | −11.3088 | −0.360144 | ||||||||
\(987\) | 5.39023 | 0.171573 | ||||||||
\(988\) | 10.6998 | 0.340405 | ||||||||
\(989\) | −35.8687 | −1.14056 | ||||||||
\(990\) | −1.55190 | −0.0493227 | ||||||||
\(991\) | −14.8177 | −0.470699 | −0.235350 | − | 0.971911i | \(-0.575624\pi\) | ||||
−0.235350 | + | 0.971911i | \(0.575624\pi\) | |||||||
\(992\) | 7.13459 | 0.226523 | ||||||||
\(993\) | 20.8440 | 0.661466 | ||||||||
\(994\) | 9.13463 | 0.289733 | ||||||||
\(995\) | −14.6420 | −0.464181 | ||||||||
\(996\) | −44.0949 | −1.39720 | ||||||||
\(997\) | −12.8721 | −0.407664 | −0.203832 | − | 0.979006i | \(-0.565340\pi\) | ||||
−0.203832 | + | 0.979006i | \(0.565340\pi\) | |||||||
\(998\) | 3.28146 | 0.103873 | ||||||||
\(999\) | 0.580793 | 0.0183755 |
(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 | 8038.2.a.d.1.7 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8038.2.a.d.1.7 | ✓ | 92 | 1.1 | even | 1 | trivial |