Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} - 5452 x^{7} - 4098 x^{6} + 9986 x^{5} + 850 x^{4} - 7216 x^{3} + 1688 x^{2} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.679191\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −3.00420 | −1.73448 | −0.867239 | − | 0.497892i | \(-0.834108\pi\) | ||||
−0.867239 | + | 0.497892i | \(0.834108\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.00420 | 1.22646 | ||||||||
\(7\) | −4.38135 | −1.65599 | −0.827997 | − | 0.560733i | \(-0.810520\pi\) | ||||
−0.827997 | + | 0.560733i | \(0.810520\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.02524 | 2.00841 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.27120 | −0.986304 | −0.493152 | − | 0.869943i | \(-0.664155\pi\) | ||||
−0.493152 | + | 0.869943i | \(0.664155\pi\) | |||||||
\(12\) | −3.00420 | −0.867239 | ||||||||
\(13\) | −2.26078 | −0.627027 | −0.313513 | − | 0.949584i | \(-0.601506\pi\) | ||||
−0.313513 | + | 0.949584i | \(0.601506\pi\) | |||||||
\(14\) | 4.38135 | 1.17096 | ||||||||
\(15\) | 3.00420 | 0.775682 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.368220 | 0.0893064 | 0.0446532 | − | 0.999003i | \(-0.485782\pi\) | ||||
0.0446532 | + | 0.999003i | \(0.485782\pi\) | |||||||
\(18\) | −6.02524 | −1.42016 | ||||||||
\(19\) | −1.86184 | −0.427136 | −0.213568 | − | 0.976928i | \(-0.568509\pi\) | ||||
−0.213568 | + | 0.976928i | \(0.568509\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 13.1625 | 2.87229 | ||||||||
\(22\) | 3.27120 | 0.697422 | ||||||||
\(23\) | −0.625538 | −0.130434 | −0.0652168 | − | 0.997871i | \(-0.520774\pi\) | ||||
−0.0652168 | + | 0.997871i | \(0.520774\pi\) | |||||||
\(24\) | 3.00420 | 0.613231 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.26078 | 0.443375 | ||||||||
\(27\) | −9.08845 | −1.74907 | ||||||||
\(28\) | −4.38135 | −0.827997 | ||||||||
\(29\) | 0.824083 | 0.153028 | 0.0765142 | − | 0.997068i | \(-0.475621\pi\) | ||||
0.0765142 | + | 0.997068i | \(0.475621\pi\) | |||||||
\(30\) | −3.00420 | −0.548490 | ||||||||
\(31\) | 2.48127 | 0.445649 | 0.222824 | − | 0.974859i | \(-0.428472\pi\) | ||||
0.222824 | + | 0.974859i | \(0.428472\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 9.82735 | 1.71072 | ||||||||
\(34\) | −0.368220 | −0.0631492 | ||||||||
\(35\) | 4.38135 | 0.740583 | ||||||||
\(36\) | 6.02524 | 1.00421 | ||||||||
\(37\) | −3.19737 | −0.525644 | −0.262822 | − | 0.964844i | \(-0.584653\pi\) | ||||
−0.262822 | + | 0.964844i | \(0.584653\pi\) | |||||||
\(38\) | 1.86184 | 0.302031 | ||||||||
\(39\) | 6.79184 | 1.08756 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 4.93053 | 0.770019 | 0.385010 | − | 0.922913i | \(-0.374198\pi\) | ||||
0.385010 | + | 0.922913i | \(0.374198\pi\) | |||||||
\(42\) | −13.1625 | −2.03101 | ||||||||
\(43\) | 5.23037 | 0.797624 | 0.398812 | − | 0.917033i | \(-0.369423\pi\) | ||||
0.398812 | + | 0.917033i | \(0.369423\pi\) | |||||||
\(44\) | −3.27120 | −0.493152 | ||||||||
\(45\) | −6.02524 | −0.898190 | ||||||||
\(46\) | 0.625538 | 0.0922305 | ||||||||
\(47\) | −1.07028 | −0.156117 | −0.0780585 | − | 0.996949i | \(-0.524872\pi\) | ||||
−0.0780585 | + | 0.996949i | \(0.524872\pi\) | |||||||
\(48\) | −3.00420 | −0.433620 | ||||||||
\(49\) | 12.1962 | 1.74232 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.10621 | −0.154900 | ||||||||
\(52\) | −2.26078 | −0.313513 | ||||||||
\(53\) | 0.543690 | 0.0746816 | 0.0373408 | − | 0.999303i | \(-0.488111\pi\) | ||||
0.0373408 | + | 0.999303i | \(0.488111\pi\) | |||||||
\(54\) | 9.08845 | 1.23678 | ||||||||
\(55\) | 3.27120 | 0.441088 | ||||||||
\(56\) | 4.38135 | 0.585482 | ||||||||
\(57\) | 5.59336 | 0.740859 | ||||||||
\(58\) | −0.824083 | −0.108207 | ||||||||
\(59\) | 1.14090 | 0.148532 | 0.0742660 | − | 0.997238i | \(-0.476339\pi\) | ||||
0.0742660 | + | 0.997238i | \(0.476339\pi\) | |||||||
\(60\) | 3.00420 | 0.387841 | ||||||||
\(61\) | −6.83722 | −0.875416 | −0.437708 | − | 0.899117i | \(-0.644210\pi\) | ||||
−0.437708 | + | 0.899117i | \(0.644210\pi\) | |||||||
\(62\) | −2.48127 | −0.315121 | ||||||||
\(63\) | −26.3987 | −3.32592 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.26078 | 0.280415 | ||||||||
\(66\) | −9.82735 | −1.20966 | ||||||||
\(67\) | −4.96537 | −0.606616 | −0.303308 | − | 0.952893i | \(-0.598091\pi\) | ||||
−0.303308 | + | 0.952893i | \(0.598091\pi\) | |||||||
\(68\) | 0.368220 | 0.0446532 | ||||||||
\(69\) | 1.87924 | 0.226234 | ||||||||
\(70\) | −4.38135 | −0.523671 | ||||||||
\(71\) | 5.72963 | 0.679982 | 0.339991 | − | 0.940429i | \(-0.389576\pi\) | ||||
0.339991 | + | 0.940429i | \(0.389576\pi\) | |||||||
\(72\) | −6.02524 | −0.710082 | ||||||||
\(73\) | 16.8546 | 1.97268 | 0.986342 | − | 0.164713i | \(-0.0526698\pi\) | ||||
0.986342 | + | 0.164713i | \(0.0526698\pi\) | |||||||
\(74\) | 3.19737 | 0.371687 | ||||||||
\(75\) | −3.00420 | −0.346896 | ||||||||
\(76\) | −1.86184 | −0.213568 | ||||||||
\(77\) | 14.3323 | 1.63331 | ||||||||
\(78\) | −6.79184 | −0.769024 | ||||||||
\(79\) | 8.03970 | 0.904537 | 0.452269 | − | 0.891882i | \(-0.350615\pi\) | ||||
0.452269 | + | 0.891882i | \(0.350615\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 9.22783 | 1.02531 | ||||||||
\(82\) | −4.93053 | −0.544486 | ||||||||
\(83\) | −14.4168 | −1.58245 | −0.791224 | − | 0.611526i | \(-0.790556\pi\) | ||||
−0.791224 | + | 0.611526i | \(0.790556\pi\) | |||||||
\(84\) | 13.1625 | 1.43614 | ||||||||
\(85\) | −0.368220 | −0.0399391 | ||||||||
\(86\) | −5.23037 | −0.564006 | ||||||||
\(87\) | −2.47572 | −0.265425 | ||||||||
\(88\) | 3.27120 | 0.348711 | ||||||||
\(89\) | −0.445164 | −0.0471872 | −0.0235936 | − | 0.999722i | \(-0.507511\pi\) | ||||
−0.0235936 | + | 0.999722i | \(0.507511\pi\) | |||||||
\(90\) | 6.02524 | 0.635116 | ||||||||
\(91\) | 9.90525 | 1.03835 | ||||||||
\(92\) | −0.625538 | −0.0652168 | ||||||||
\(93\) | −7.45423 | −0.772968 | ||||||||
\(94\) | 1.07028 | 0.110391 | ||||||||
\(95\) | 1.86184 | 0.191021 | ||||||||
\(96\) | 3.00420 | 0.306615 | ||||||||
\(97\) | 13.9251 | 1.41388 | 0.706939 | − | 0.707275i | \(-0.250076\pi\) | ||||
0.706939 | + | 0.707275i | \(0.250076\pi\) | |||||||
\(98\) | −12.1962 | −1.23200 | ||||||||
\(99\) | −19.7098 | −1.98091 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 19.3713 | 1.92752 | 0.963758 | − | 0.266777i | \(-0.0859588\pi\) | ||||
0.963758 | + | 0.266777i | \(0.0859588\pi\) | |||||||
\(102\) | 1.10621 | 0.109531 | ||||||||
\(103\) | 2.38314 | 0.234818 | 0.117409 | − | 0.993084i | \(-0.462541\pi\) | ||||
0.117409 | + | 0.993084i | \(0.462541\pi\) | |||||||
\(104\) | 2.26078 | 0.221687 | ||||||||
\(105\) | −13.1625 | −1.28453 | ||||||||
\(106\) | −0.543690 | −0.0528078 | ||||||||
\(107\) | 9.76789 | 0.944298 | 0.472149 | − | 0.881519i | \(-0.343478\pi\) | ||||
0.472149 | + | 0.881519i | \(0.343478\pi\) | |||||||
\(108\) | −9.08845 | −0.874536 | ||||||||
\(109\) | −0.0384553 | −0.00368335 | −0.00184167 | − | 0.999998i | \(-0.500586\pi\) | ||||
−0.00184167 | + | 0.999998i | \(0.500586\pi\) | |||||||
\(110\) | −3.27120 | −0.311897 | ||||||||
\(111\) | 9.60555 | 0.911719 | ||||||||
\(112\) | −4.38135 | −0.413998 | ||||||||
\(113\) | −3.13526 | −0.294940 | −0.147470 | − | 0.989066i | \(-0.547113\pi\) | ||||
−0.147470 | + | 0.989066i | \(0.547113\pi\) | |||||||
\(114\) | −5.59336 | −0.523866 | ||||||||
\(115\) | 0.625538 | 0.0583317 | ||||||||
\(116\) | 0.824083 | 0.0765142 | ||||||||
\(117\) | −13.6217 | −1.25933 | ||||||||
\(118\) | −1.14090 | −0.105028 | ||||||||
\(119\) | −1.61330 | −0.147891 | ||||||||
\(120\) | −3.00420 | −0.274245 | ||||||||
\(121\) | −0.299252 | −0.0272047 | ||||||||
\(122\) | 6.83722 | 0.619012 | ||||||||
\(123\) | −14.8123 | −1.33558 | ||||||||
\(124\) | 2.48127 | 0.222824 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 26.3987 | 2.35178 | ||||||||
\(127\) | −4.70586 | −0.417578 | −0.208789 | − | 0.977961i | \(-0.566952\pi\) | ||||
−0.208789 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −15.7131 | −1.38346 | ||||||||
\(130\) | −2.26078 | −0.198283 | ||||||||
\(131\) | −0.648468 | −0.0566569 | −0.0283285 | − | 0.999599i | \(-0.509018\pi\) | ||||
−0.0283285 | + | 0.999599i | \(0.509018\pi\) | |||||||
\(132\) | 9.82735 | 0.855361 | ||||||||
\(133\) | 8.15739 | 0.707335 | ||||||||
\(134\) | 4.96537 | 0.428943 | ||||||||
\(135\) | 9.08845 | 0.782209 | ||||||||
\(136\) | −0.368220 | −0.0315746 | ||||||||
\(137\) | −4.79646 | −0.409789 | −0.204894 | − | 0.978784i | \(-0.565685\pi\) | ||||
−0.204894 | + | 0.978784i | \(0.565685\pi\) | |||||||
\(138\) | −1.87924 | −0.159972 | ||||||||
\(139\) | 3.91350 | 0.331939 | 0.165969 | − | 0.986131i | \(-0.446925\pi\) | ||||
0.165969 | + | 0.986131i | \(0.446925\pi\) | |||||||
\(140\) | 4.38135 | 0.370292 | ||||||||
\(141\) | 3.21535 | 0.270781 | ||||||||
\(142\) | −5.72963 | −0.480820 | ||||||||
\(143\) | 7.39545 | 0.618439 | ||||||||
\(144\) | 6.02524 | 0.502104 | ||||||||
\(145\) | −0.824083 | −0.0684364 | ||||||||
\(146\) | −16.8546 | −1.39490 | ||||||||
\(147\) | −36.6399 | −3.02201 | ||||||||
\(148\) | −3.19737 | −0.262822 | ||||||||
\(149\) | −7.54191 | −0.617857 | −0.308929 | − | 0.951085i | \(-0.599970\pi\) | ||||
−0.308929 | + | 0.951085i | \(0.599970\pi\) | |||||||
\(150\) | 3.00420 | 0.245292 | ||||||||
\(151\) | 3.11492 | 0.253489 | 0.126744 | − | 0.991935i | \(-0.459547\pi\) | ||||
0.126744 | + | 0.991935i | \(0.459547\pi\) | |||||||
\(152\) | 1.86184 | 0.151016 | ||||||||
\(153\) | 2.21861 | 0.179364 | ||||||||
\(154\) | −14.3323 | −1.15493 | ||||||||
\(155\) | −2.48127 | −0.199300 | ||||||||
\(156\) | 6.79184 | 0.543782 | ||||||||
\(157\) | 4.02861 | 0.321518 | 0.160759 | − | 0.986994i | \(-0.448606\pi\) | ||||
0.160759 | + | 0.986994i | \(0.448606\pi\) | |||||||
\(158\) | −8.03970 | −0.639605 | ||||||||
\(159\) | −1.63336 | −0.129534 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.74070 | 0.215997 | ||||||||
\(162\) | −9.22783 | −0.725007 | ||||||||
\(163\) | −16.9126 | −1.32469 | −0.662347 | − | 0.749197i | \(-0.730440\pi\) | ||||
−0.662347 | + | 0.749197i | \(0.730440\pi\) | |||||||
\(164\) | 4.93053 | 0.385010 | ||||||||
\(165\) | −9.82735 | −0.765058 | ||||||||
\(166\) | 14.4168 | 1.11896 | ||||||||
\(167\) | 4.31707 | 0.334065 | 0.167033 | − | 0.985951i | \(-0.446581\pi\) | ||||
0.167033 | + | 0.985951i | \(0.446581\pi\) | |||||||
\(168\) | −13.1625 | −1.01551 | ||||||||
\(169\) | −7.88889 | −0.606837 | ||||||||
\(170\) | 0.368220 | 0.0282412 | ||||||||
\(171\) | −11.2181 | −0.857867 | ||||||||
\(172\) | 5.23037 | 0.398812 | ||||||||
\(173\) | 24.6465 | 1.87384 | 0.936920 | − | 0.349543i | \(-0.113663\pi\) | ||||
0.936920 | + | 0.349543i | \(0.113663\pi\) | |||||||
\(174\) | 2.47572 | 0.187683 | ||||||||
\(175\) | −4.38135 | −0.331199 | ||||||||
\(176\) | −3.27120 | −0.246576 | ||||||||
\(177\) | −3.42749 | −0.257626 | ||||||||
\(178\) | 0.445164 | 0.0333664 | ||||||||
\(179\) | 8.59930 | 0.642742 | 0.321371 | − | 0.946953i | \(-0.395856\pi\) | ||||
0.321371 | + | 0.946953i | \(0.395856\pi\) | |||||||
\(180\) | −6.02524 | −0.449095 | ||||||||
\(181\) | 7.47920 | 0.555924 | 0.277962 | − | 0.960592i | \(-0.410341\pi\) | ||||
0.277962 | + | 0.960592i | \(0.410341\pi\) | |||||||
\(182\) | −9.90525 | −0.734226 | ||||||||
\(183\) | 20.5404 | 1.51839 | ||||||||
\(184\) | 0.625538 | 0.0461153 | ||||||||
\(185\) | 3.19737 | 0.235075 | ||||||||
\(186\) | 7.45423 | 0.546571 | ||||||||
\(187\) | −1.20452 | −0.0880833 | ||||||||
\(188\) | −1.07028 | −0.0780585 | ||||||||
\(189\) | 39.8197 | 2.89645 | ||||||||
\(190\) | −1.86184 | −0.135072 | ||||||||
\(191\) | 17.4327 | 1.26138 | 0.630692 | − | 0.776033i | \(-0.282771\pi\) | ||||
0.630692 | + | 0.776033i | \(0.282771\pi\) | |||||||
\(192\) | −3.00420 | −0.216810 | ||||||||
\(193\) | 2.95323 | 0.212578 | 0.106289 | − | 0.994335i | \(-0.466103\pi\) | ||||
0.106289 | + | 0.994335i | \(0.466103\pi\) | |||||||
\(194\) | −13.9251 | −0.999763 | ||||||||
\(195\) | −6.79184 | −0.486374 | ||||||||
\(196\) | 12.1962 | 0.871158 | ||||||||
\(197\) | 4.24292 | 0.302296 | 0.151148 | − | 0.988511i | \(-0.451703\pi\) | ||||
0.151148 | + | 0.988511i | \(0.451703\pi\) | |||||||
\(198\) | 19.7098 | 1.40071 | ||||||||
\(199\) | −14.8029 | −1.04935 | −0.524677 | − | 0.851302i | \(-0.675814\pi\) | ||||
−0.524677 | + | 0.851302i | \(0.675814\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 14.9170 | 1.05216 | ||||||||
\(202\) | −19.3713 | −1.36296 | ||||||||
\(203\) | −3.61060 | −0.253414 | ||||||||
\(204\) | −1.10621 | −0.0774500 | ||||||||
\(205\) | −4.93053 | −0.344363 | ||||||||
\(206\) | −2.38314 | −0.166041 | ||||||||
\(207\) | −3.76902 | −0.261965 | ||||||||
\(208\) | −2.26078 | −0.156757 | ||||||||
\(209\) | 6.09047 | 0.421286 | ||||||||
\(210\) | 13.1625 | 0.908296 | ||||||||
\(211\) | −24.5294 | −1.68867 | −0.844336 | − | 0.535814i | \(-0.820005\pi\) | ||||
−0.844336 | + | 0.535814i | \(0.820005\pi\) | |||||||
\(212\) | 0.543690 | 0.0373408 | ||||||||
\(213\) | −17.2130 | −1.17941 | ||||||||
\(214\) | −9.76789 | −0.667720 | ||||||||
\(215\) | −5.23037 | −0.356708 | ||||||||
\(216\) | 9.08845 | 0.618391 | ||||||||
\(217\) | −10.8713 | −0.737992 | ||||||||
\(218\) | 0.0384553 | 0.00260452 | ||||||||
\(219\) | −50.6347 | −3.42158 | ||||||||
\(220\) | 3.27120 | 0.220544 | ||||||||
\(221\) | −0.832463 | −0.0559975 | ||||||||
\(222\) | −9.60555 | −0.644682 | ||||||||
\(223\) | −25.8383 | −1.73026 | −0.865129 | − | 0.501550i | \(-0.832763\pi\) | ||||
−0.865129 | + | 0.501550i | \(0.832763\pi\) | |||||||
\(224\) | 4.38135 | 0.292741 | ||||||||
\(225\) | 6.02524 | 0.401683 | ||||||||
\(226\) | 3.13526 | 0.208554 | ||||||||
\(227\) | −4.05065 | −0.268851 | −0.134426 | − | 0.990924i | \(-0.542919\pi\) | ||||
−0.134426 | + | 0.990924i | \(0.542919\pi\) | |||||||
\(228\) | 5.59336 | 0.370429 | ||||||||
\(229\) | 14.0087 | 0.925723 | 0.462861 | − | 0.886431i | \(-0.346823\pi\) | ||||
0.462861 | + | 0.886431i | \(0.346823\pi\) | |||||||
\(230\) | −0.625538 | −0.0412467 | ||||||||
\(231\) | −43.0571 | −2.83295 | ||||||||
\(232\) | −0.824083 | −0.0541037 | ||||||||
\(233\) | 0.268423 | 0.0175850 | 0.00879249 | − | 0.999961i | \(-0.497201\pi\) | ||||
0.00879249 | + | 0.999961i | \(0.497201\pi\) | |||||||
\(234\) | 13.6217 | 0.890481 | ||||||||
\(235\) | 1.07028 | 0.0698176 | ||||||||
\(236\) | 1.14090 | 0.0742660 | ||||||||
\(237\) | −24.1529 | −1.56890 | ||||||||
\(238\) | 1.61330 | 0.104575 | ||||||||
\(239\) | 7.07729 | 0.457792 | 0.228896 | − | 0.973451i | \(-0.426488\pi\) | ||||
0.228896 | + | 0.973451i | \(0.426488\pi\) | |||||||
\(240\) | 3.00420 | 0.193921 | ||||||||
\(241\) | −17.3121 | −1.11517 | −0.557584 | − | 0.830121i | \(-0.688271\pi\) | ||||
−0.557584 | + | 0.830121i | \(0.688271\pi\) | |||||||
\(242\) | 0.299252 | 0.0192366 | ||||||||
\(243\) | −0.456932 | −0.0293122 | ||||||||
\(244\) | −6.83722 | −0.437708 | ||||||||
\(245\) | −12.1962 | −0.779187 | ||||||||
\(246\) | 14.8123 | 0.944399 | ||||||||
\(247\) | 4.20922 | 0.267826 | ||||||||
\(248\) | −2.48127 | −0.157561 | ||||||||
\(249\) | 43.3110 | 2.74472 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −14.4545 | −0.912360 | −0.456180 | − | 0.889888i | \(-0.650783\pi\) | ||||
−0.456180 | + | 0.889888i | \(0.650783\pi\) | |||||||
\(252\) | −26.3987 | −1.66296 | ||||||||
\(253\) | 2.04626 | 0.128647 | ||||||||
\(254\) | 4.70586 | 0.295272 | ||||||||
\(255\) | 1.10621 | 0.0692734 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0459 | 1.12567 | 0.562836 | − | 0.826569i | \(-0.309710\pi\) | ||||
0.562836 | + | 0.826569i | \(0.309710\pi\) | |||||||
\(258\) | 15.7131 | 0.978255 | ||||||||
\(259\) | 14.0088 | 0.870464 | ||||||||
\(260\) | 2.26078 | 0.140207 | ||||||||
\(261\) | 4.96530 | 0.307345 | ||||||||
\(262\) | 0.648468 | 0.0400625 | ||||||||
\(263\) | −9.64450 | −0.594705 | −0.297353 | − | 0.954768i | \(-0.596104\pi\) | ||||
−0.297353 | + | 0.954768i | \(0.596104\pi\) | |||||||
\(264\) | −9.82735 | −0.604832 | ||||||||
\(265\) | −0.543690 | −0.0333986 | ||||||||
\(266\) | −8.15739 | −0.500162 | ||||||||
\(267\) | 1.33736 | 0.0818452 | ||||||||
\(268\) | −4.96537 | −0.303308 | ||||||||
\(269\) | 2.99229 | 0.182443 | 0.0912215 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912215 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(270\) | −9.08845 | −0.553105 | ||||||||
\(271\) | 4.85673 | 0.295026 | 0.147513 | − | 0.989060i | \(-0.452873\pi\) | ||||
0.147513 | + | 0.989060i | \(0.452873\pi\) | |||||||
\(272\) | 0.368220 | 0.0223266 | ||||||||
\(273\) | −29.7574 | −1.80100 | ||||||||
\(274\) | 4.79646 | 0.289764 | ||||||||
\(275\) | −3.27120 | −0.197261 | ||||||||
\(276\) | 1.87924 | 0.113117 | ||||||||
\(277\) | 3.53360 | 0.212313 | 0.106157 | − | 0.994349i | \(-0.466145\pi\) | ||||
0.106157 | + | 0.994349i | \(0.466145\pi\) | |||||||
\(278\) | −3.91350 | −0.234716 | ||||||||
\(279\) | 14.9502 | 0.895047 | ||||||||
\(280\) | −4.38135 | −0.261836 | ||||||||
\(281\) | −28.1683 | −1.68038 | −0.840188 | − | 0.542295i | \(-0.817556\pi\) | ||||
−0.840188 | + | 0.542295i | \(0.817556\pi\) | |||||||
\(282\) | −3.21535 | −0.191471 | ||||||||
\(283\) | 16.2124 | 0.963726 | 0.481863 | − | 0.876247i | \(-0.339960\pi\) | ||||
0.481863 | + | 0.876247i | \(0.339960\pi\) | |||||||
\(284\) | 5.72963 | 0.339991 | ||||||||
\(285\) | −5.59336 | −0.331322 | ||||||||
\(286\) | −7.39545 | −0.437302 | ||||||||
\(287\) | −21.6024 | −1.27515 | ||||||||
\(288\) | −6.02524 | −0.355041 | ||||||||
\(289\) | −16.8644 | −0.992024 | ||||||||
\(290\) | 0.824083 | 0.0483918 | ||||||||
\(291\) | −41.8338 | −2.45234 | ||||||||
\(292\) | 16.8546 | 0.986342 | ||||||||
\(293\) | −13.7452 | −0.803004 | −0.401502 | − | 0.915858i | \(-0.631512\pi\) | ||||
−0.401502 | + | 0.915858i | \(0.631512\pi\) | |||||||
\(294\) | 36.6399 | 2.13688 | ||||||||
\(295\) | −1.14090 | −0.0664256 | ||||||||
\(296\) | 3.19737 | 0.185843 | ||||||||
\(297\) | 29.7301 | 1.72512 | ||||||||
\(298\) | 7.54191 | 0.436891 | ||||||||
\(299\) | 1.41420 | 0.0817854 | ||||||||
\(300\) | −3.00420 | −0.173448 | ||||||||
\(301\) | −22.9161 | −1.32086 | ||||||||
\(302\) | −3.11492 | −0.179243 | ||||||||
\(303\) | −58.1953 | −3.34324 | ||||||||
\(304\) | −1.86184 | −0.106784 | ||||||||
\(305\) | 6.83722 | 0.391498 | ||||||||
\(306\) | −2.21861 | −0.126830 | ||||||||
\(307\) | −19.0088 | −1.08489 | −0.542445 | − | 0.840091i | \(-0.682501\pi\) | ||||
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(308\) | 14.3323 | 0.816657 | ||||||||
\(309\) | −7.15945 | −0.407287 | ||||||||
\(310\) | 2.48127 | 0.140927 | ||||||||
\(311\) | 13.1742 | 0.747041 | 0.373520 | − | 0.927622i | \(-0.378151\pi\) | ||||
0.373520 | + | 0.927622i | \(0.378151\pi\) | |||||||
\(312\) | −6.79184 | −0.384512 | ||||||||
\(313\) | 3.86799 | 0.218632 | 0.109316 | − | 0.994007i | \(-0.465134\pi\) | ||||
0.109316 | + | 0.994007i | \(0.465134\pi\) | |||||||
\(314\) | −4.02861 | −0.227348 | ||||||||
\(315\) | 26.3987 | 1.48740 | ||||||||
\(316\) | 8.03970 | 0.452269 | ||||||||
\(317\) | −18.5368 | −1.04113 | −0.520564 | − | 0.853823i | \(-0.674278\pi\) | ||||
−0.520564 | + | 0.853823i | \(0.674278\pi\) | |||||||
\(318\) | 1.63336 | 0.0915941 | ||||||||
\(319\) | −2.69574 | −0.150933 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −29.3448 | −1.63786 | ||||||||
\(322\) | −2.74070 | −0.152733 | ||||||||
\(323\) | −0.685568 | −0.0381460 | ||||||||
\(324\) | 9.22783 | 0.512657 | ||||||||
\(325\) | −2.26078 | −0.125405 | ||||||||
\(326\) | 16.9126 | 0.936700 | ||||||||
\(327\) | 0.115528 | 0.00638869 | ||||||||
\(328\) | −4.93053 | −0.272243 | ||||||||
\(329\) | 4.68929 | 0.258529 | ||||||||
\(330\) | 9.82735 | 0.540978 | ||||||||
\(331\) | −25.1409 | −1.38187 | −0.690934 | − | 0.722918i | \(-0.742800\pi\) | ||||
−0.690934 | + | 0.722918i | \(0.742800\pi\) | |||||||
\(332\) | −14.4168 | −0.791224 | ||||||||
\(333\) | −19.2649 | −1.05571 | ||||||||
\(334\) | −4.31707 | −0.236220 | ||||||||
\(335\) | 4.96537 | 0.271287 | ||||||||
\(336\) | 13.1625 | 0.718071 | ||||||||
\(337\) | 12.4506 | 0.678228 | 0.339114 | − | 0.940745i | \(-0.389873\pi\) | ||||
0.339114 | + | 0.940745i | \(0.389873\pi\) | |||||||
\(338\) | 7.88889 | 0.429099 | ||||||||
\(339\) | 9.41896 | 0.511568 | ||||||||
\(340\) | −0.368220 | −0.0199695 | ||||||||
\(341\) | −8.11672 | −0.439545 | ||||||||
\(342\) | 11.2181 | 0.606604 | ||||||||
\(343\) | −22.7664 | −1.22927 | ||||||||
\(344\) | −5.23037 | −0.282003 | ||||||||
\(345\) | −1.87924 | −0.101175 | ||||||||
\(346\) | −24.6465 | −1.32501 | ||||||||
\(347\) | 13.9023 | 0.746317 | 0.373159 | − | 0.927768i | \(-0.378275\pi\) | ||||
0.373159 | + | 0.927768i | \(0.378275\pi\) | |||||||
\(348\) | −2.47572 | −0.132712 | ||||||||
\(349\) | −5.12796 | −0.274494 | −0.137247 | − | 0.990537i | \(-0.543825\pi\) | ||||
−0.137247 | + | 0.990537i | \(0.543825\pi\) | |||||||
\(350\) | 4.38135 | 0.234193 | ||||||||
\(351\) | 20.5470 | 1.09672 | ||||||||
\(352\) | 3.27120 | 0.174356 | ||||||||
\(353\) | −13.7457 | −0.731612 | −0.365806 | − | 0.930691i | \(-0.619207\pi\) | ||||
−0.365806 | + | 0.930691i | \(0.619207\pi\) | |||||||
\(354\) | 3.42749 | 0.182169 | ||||||||
\(355\) | −5.72963 | −0.304097 | ||||||||
\(356\) | −0.445164 | −0.0235936 | ||||||||
\(357\) | 4.84668 | 0.256514 | ||||||||
\(358\) | −8.59930 | −0.454487 | ||||||||
\(359\) | −24.2421 | −1.27945 | −0.639725 | − | 0.768604i | \(-0.720952\pi\) | ||||
−0.639725 | + | 0.768604i | \(0.720952\pi\) | |||||||
\(360\) | 6.02524 | 0.317558 | ||||||||
\(361\) | −15.5335 | −0.817554 | ||||||||
\(362\) | −7.47920 | −0.393098 | ||||||||
\(363\) | 0.899013 | 0.0471859 | ||||||||
\(364\) | 9.90525 | 0.519176 | ||||||||
\(365\) | −16.8546 | −0.882211 | ||||||||
\(366\) | −20.5404 | −1.07366 | ||||||||
\(367\) | −8.27488 | −0.431945 | −0.215972 | − | 0.976399i | \(-0.569292\pi\) | ||||
−0.215972 | + | 0.976399i | \(0.569292\pi\) | |||||||
\(368\) | −0.625538 | −0.0326084 | ||||||||
\(369\) | 29.7076 | 1.54652 | ||||||||
\(370\) | −3.19737 | −0.166223 | ||||||||
\(371\) | −2.38210 | −0.123672 | ||||||||
\(372\) | −7.45423 | −0.386484 | ||||||||
\(373\) | −24.9657 | −1.29268 | −0.646338 | − | 0.763051i | \(-0.723701\pi\) | ||||
−0.646338 | + | 0.763051i | \(0.723701\pi\) | |||||||
\(374\) | 1.20452 | 0.0622843 | ||||||||
\(375\) | 3.00420 | 0.155136 | ||||||||
\(376\) | 1.07028 | 0.0551957 | ||||||||
\(377\) | −1.86307 | −0.0959530 | ||||||||
\(378\) | −39.8197 | −2.04810 | ||||||||
\(379\) | 5.76871 | 0.296319 | 0.148159 | − | 0.988963i | \(-0.452665\pi\) | ||||
0.148159 | + | 0.988963i | \(0.452665\pi\) | |||||||
\(380\) | 1.86184 | 0.0955106 | ||||||||
\(381\) | 14.1374 | 0.724280 | ||||||||
\(382\) | −17.4327 | −0.891934 | ||||||||
\(383\) | 31.1789 | 1.59317 | 0.796584 | − | 0.604527i | \(-0.206638\pi\) | ||||
0.796584 | + | 0.604527i | \(0.206638\pi\) | |||||||
\(384\) | 3.00420 | 0.153308 | ||||||||
\(385\) | −14.3323 | −0.730440 | ||||||||
\(386\) | −2.95323 | −0.150316 | ||||||||
\(387\) | 31.5143 | 1.60196 | ||||||||
\(388\) | 13.9251 | 0.706939 | ||||||||
\(389\) | 15.8001 | 0.801096 | 0.400548 | − | 0.916276i | \(-0.368820\pi\) | ||||
0.400548 | + | 0.916276i | \(0.368820\pi\) | |||||||
\(390\) | 6.79184 | 0.343918 | ||||||||
\(391\) | −0.230335 | −0.0116486 | ||||||||
\(392\) | −12.1962 | −0.616002 | ||||||||
\(393\) | 1.94813 | 0.0982702 | ||||||||
\(394\) | −4.24292 | −0.213755 | ||||||||
\(395\) | −8.03970 | −0.404521 | ||||||||
\(396\) | −19.7098 | −0.990453 | ||||||||
\(397\) | −1.32833 | −0.0666672 | −0.0333336 | − | 0.999444i | \(-0.510612\pi\) | ||||
−0.0333336 | + | 0.999444i | \(0.510612\pi\) | |||||||
\(398\) | 14.8029 | 0.742005 | ||||||||
\(399\) | −24.5065 | −1.22686 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −14.9170 | −0.743992 | ||||||||
\(403\) | −5.60959 | −0.279434 | ||||||||
\(404\) | 19.3713 | 0.963758 | ||||||||
\(405\) | −9.22783 | −0.458534 | ||||||||
\(406\) | 3.61060 | 0.179191 | ||||||||
\(407\) | 10.4592 | 0.518445 | ||||||||
\(408\) | 1.10621 | 0.0547654 | ||||||||
\(409\) | 8.99084 | 0.444568 | 0.222284 | − | 0.974982i | \(-0.428649\pi\) | ||||
0.222284 | + | 0.974982i | \(0.428649\pi\) | |||||||
\(410\) | 4.93053 | 0.243501 | ||||||||
\(411\) | 14.4095 | 0.710770 | ||||||||
\(412\) | 2.38314 | 0.117409 | ||||||||
\(413\) | −4.99867 | −0.245968 | ||||||||
\(414\) | 3.76902 | 0.185237 | ||||||||
\(415\) | 14.4168 | 0.707692 | ||||||||
\(416\) | 2.26078 | 0.110844 | ||||||||
\(417\) | −11.7570 | −0.575740 | ||||||||
\(418\) | −6.09047 | −0.297894 | ||||||||
\(419\) | −17.4387 | −0.851936 | −0.425968 | − | 0.904738i | \(-0.640066\pi\) | ||||
−0.425968 | + | 0.904738i | \(0.640066\pi\) | |||||||
\(420\) | −13.1625 | −0.642263 | ||||||||
\(421\) | −19.2201 | −0.936729 | −0.468365 | − | 0.883535i | \(-0.655157\pi\) | ||||
−0.468365 | + | 0.883535i | \(0.655157\pi\) | |||||||
\(422\) | 24.5294 | 1.19407 | ||||||||
\(423\) | −6.44872 | −0.313547 | ||||||||
\(424\) | −0.543690 | −0.0264039 | ||||||||
\(425\) | 0.368220 | 0.0178613 | ||||||||
\(426\) | 17.2130 | 0.833971 | ||||||||
\(427\) | 29.9562 | 1.44968 | ||||||||
\(428\) | 9.76789 | 0.472149 | ||||||||
\(429\) | −22.2175 | −1.07267 | ||||||||
\(430\) | 5.23037 | 0.252231 | ||||||||
\(431\) | 2.69307 | 0.129720 | 0.0648602 | − | 0.997894i | \(-0.479340\pi\) | ||||
0.0648602 | + | 0.997894i | \(0.479340\pi\) | |||||||
\(432\) | −9.08845 | −0.437268 | ||||||||
\(433\) | −21.8698 | −1.05100 | −0.525498 | − | 0.850795i | \(-0.676121\pi\) | ||||
−0.525498 | + | 0.850795i | \(0.676121\pi\) | |||||||
\(434\) | 10.8713 | 0.521839 | ||||||||
\(435\) | 2.47572 | 0.118701 | ||||||||
\(436\) | −0.0384553 | −0.00184167 | ||||||||
\(437\) | 1.16465 | 0.0557130 | ||||||||
\(438\) | 50.6347 | 2.41942 | ||||||||
\(439\) | −1.52968 | −0.0730075 | −0.0365038 | − | 0.999334i | \(-0.511622\pi\) | ||||
−0.0365038 | + | 0.999334i | \(0.511622\pi\) | |||||||
\(440\) | −3.27120 | −0.155948 | ||||||||
\(441\) | 73.4851 | 3.49929 | ||||||||
\(442\) | 0.832463 | 0.0395962 | ||||||||
\(443\) | −7.30305 | −0.346979 | −0.173489 | − | 0.984836i | \(-0.555504\pi\) | ||||
−0.173489 | + | 0.984836i | \(0.555504\pi\) | |||||||
\(444\) | 9.60555 | 0.455859 | ||||||||
\(445\) | 0.445164 | 0.0211028 | ||||||||
\(446\) | 25.8383 | 1.22348 | ||||||||
\(447\) | 22.6574 | 1.07166 | ||||||||
\(448\) | −4.38135 | −0.206999 | ||||||||
\(449\) | 10.7673 | 0.508142 | 0.254071 | − | 0.967186i | \(-0.418230\pi\) | ||||
0.254071 | + | 0.967186i | \(0.418230\pi\) | |||||||
\(450\) | −6.02524 | −0.284033 | ||||||||
\(451\) | −16.1287 | −0.759473 | ||||||||
\(452\) | −3.13526 | −0.147470 | ||||||||
\(453\) | −9.35785 | −0.439670 | ||||||||
\(454\) | 4.05065 | 0.190107 | ||||||||
\(455\) | −9.90525 | −0.464365 | ||||||||
\(456\) | −5.59336 | −0.261933 | ||||||||
\(457\) | 27.1707 | 1.27099 | 0.635496 | − | 0.772104i | \(-0.280796\pi\) | ||||
0.635496 | + | 0.772104i | \(0.280796\pi\) | |||||||
\(458\) | −14.0087 | −0.654585 | ||||||||
\(459\) | −3.34655 | −0.156203 | ||||||||
\(460\) | 0.625538 | 0.0291658 | ||||||||
\(461\) | −9.07414 | −0.422625 | −0.211312 | − | 0.977419i | \(-0.567774\pi\) | ||||
−0.211312 | + | 0.977419i | \(0.567774\pi\) | |||||||
\(462\) | 43.0571 | 2.00320 | ||||||||
\(463\) | −23.5550 | −1.09469 | −0.547347 | − | 0.836906i | \(-0.684362\pi\) | ||||
−0.547347 | + | 0.836906i | \(0.684362\pi\) | |||||||
\(464\) | 0.824083 | 0.0382571 | ||||||||
\(465\) | 7.45423 | 0.345682 | ||||||||
\(466\) | −0.268423 | −0.0124345 | ||||||||
\(467\) | 17.4498 | 0.807482 | 0.403741 | − | 0.914873i | \(-0.367710\pi\) | ||||
0.403741 | + | 0.914873i | \(0.367710\pi\) | |||||||
\(468\) | −13.6217 | −0.629665 | ||||||||
\(469\) | 21.7550 | 1.00455 | ||||||||
\(470\) | −1.07028 | −0.0493685 | ||||||||
\(471\) | −12.1028 | −0.557667 | ||||||||
\(472\) | −1.14090 | −0.0525140 | ||||||||
\(473\) | −17.1096 | −0.786700 | ||||||||
\(474\) | 24.1529 | 1.10938 | ||||||||
\(475\) | −1.86184 | −0.0854273 | ||||||||
\(476\) | −1.61330 | −0.0739455 | ||||||||
\(477\) | 3.27587 | 0.149992 | ||||||||
\(478\) | −7.07729 | −0.323708 | ||||||||
\(479\) | 9.78078 | 0.446895 | 0.223448 | − | 0.974716i | \(-0.428269\pi\) | ||||
0.223448 | + | 0.974716i | \(0.428269\pi\) | |||||||
\(480\) | −3.00420 | −0.137123 | ||||||||
\(481\) | 7.22854 | 0.329593 | ||||||||
\(482\) | 17.3121 | 0.788542 | ||||||||
\(483\) | −8.23362 | −0.374643 | ||||||||
\(484\) | −0.299252 | −0.0136023 | ||||||||
\(485\) | −13.9251 | −0.632305 | ||||||||
\(486\) | 0.456932 | 0.0207269 | ||||||||
\(487\) | 24.3102 | 1.10160 | 0.550801 | − | 0.834637i | \(-0.314322\pi\) | ||||
0.550801 | + | 0.834637i | \(0.314322\pi\) | |||||||
\(488\) | 6.83722 | 0.309506 | ||||||||
\(489\) | 50.8088 | 2.29765 | ||||||||
\(490\) | 12.1962 | 0.550969 | ||||||||
\(491\) | −18.0341 | −0.813869 | −0.406934 | − | 0.913457i | \(-0.633402\pi\) | ||||
−0.406934 | + | 0.913457i | \(0.633402\pi\) | |||||||
\(492\) | −14.8123 | −0.667791 | ||||||||
\(493\) | 0.303444 | 0.0136664 | ||||||||
\(494\) | −4.20922 | −0.189382 | ||||||||
\(495\) | 19.7098 | 0.885889 | ||||||||
\(496\) | 2.48127 | 0.111412 | ||||||||
\(497\) | −25.1035 | −1.12605 | ||||||||
\(498\) | −43.3110 | −1.94081 | ||||||||
\(499\) | 22.4604 | 1.00547 | 0.502734 | − | 0.864441i | \(-0.332328\pi\) | ||||
0.502734 | + | 0.864441i | \(0.332328\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −12.9694 | −0.579429 | ||||||||
\(502\) | 14.4545 | 0.645136 | ||||||||
\(503\) | 24.7026 | 1.10144 | 0.550718 | − | 0.834691i | \(-0.314354\pi\) | ||||
0.550718 | + | 0.834691i | \(0.314354\pi\) | |||||||
\(504\) | 26.3987 | 1.17589 | ||||||||
\(505\) | −19.3713 | −0.862012 | ||||||||
\(506\) | −2.04626 | −0.0909673 | ||||||||
\(507\) | 23.6998 | 1.05255 | ||||||||
\(508\) | −4.70586 | −0.208789 | ||||||||
\(509\) | 32.9928 | 1.46238 | 0.731191 | − | 0.682173i | \(-0.238965\pi\) | ||||
0.731191 | + | 0.682173i | \(0.238965\pi\) | |||||||
\(510\) | −1.10621 | −0.0489837 | ||||||||
\(511\) | −73.8459 | −3.26675 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.9213 | 0.747093 | ||||||||
\(514\) | −18.0459 | −0.795970 | ||||||||
\(515\) | −2.38314 | −0.105014 | ||||||||
\(516\) | −15.7131 | −0.691731 | ||||||||
\(517\) | 3.50111 | 0.153979 | ||||||||
\(518\) | −14.0088 | −0.615511 | ||||||||
\(519\) | −74.0432 | −3.25014 | ||||||||
\(520\) | −2.26078 | −0.0991417 | ||||||||
\(521\) | 25.0471 | 1.09733 | 0.548666 | − | 0.836042i | \(-0.315136\pi\) | ||||
0.548666 | + | 0.836042i | \(0.315136\pi\) | |||||||
\(522\) | −4.96530 | −0.217325 | ||||||||
\(523\) | −33.1723 | −1.45052 | −0.725262 | − | 0.688473i | \(-0.758281\pi\) | ||||
−0.725262 | + | 0.688473i | \(0.758281\pi\) | |||||||
\(524\) | −0.648468 | −0.0283285 | ||||||||
\(525\) | 13.1625 | 0.574457 | ||||||||
\(526\) | 9.64450 | 0.420520 | ||||||||
\(527\) | 0.913652 | 0.0397993 | ||||||||
\(528\) | 9.82735 | 0.427681 | ||||||||
\(529\) | −22.6087 | −0.982987 | ||||||||
\(530\) | 0.543690 | 0.0236164 | ||||||||
\(531\) | 6.87418 | 0.298314 | ||||||||
\(532\) | 8.15739 | 0.353668 | ||||||||
\(533\) | −11.1468 | −0.482823 | ||||||||
\(534\) | −1.33736 | −0.0578733 | ||||||||
\(535\) | −9.76789 | −0.422303 | ||||||||
\(536\) | 4.96537 | 0.214471 | ||||||||
\(537\) | −25.8341 | −1.11482 | ||||||||
\(538\) | −2.99229 | −0.129007 | ||||||||
\(539\) | −39.8962 | −1.71845 | ||||||||
\(540\) | 9.08845 | 0.391105 | ||||||||
\(541\) | −40.0342 | −1.72121 | −0.860603 | − | 0.509276i | \(-0.829913\pi\) | ||||
−0.860603 | + | 0.509276i | \(0.829913\pi\) | |||||||
\(542\) | −4.85673 | −0.208615 | ||||||||
\(543\) | −22.4690 | −0.964239 | ||||||||
\(544\) | −0.368220 | −0.0157873 | ||||||||
\(545\) | 0.0384553 | 0.00164724 | ||||||||
\(546\) | 29.7574 | 1.27350 | ||||||||
\(547\) | 35.0640 | 1.49923 | 0.749614 | − | 0.661876i | \(-0.230239\pi\) | ||||
0.749614 | + | 0.661876i | \(0.230239\pi\) | |||||||
\(548\) | −4.79646 | −0.204894 | ||||||||
\(549\) | −41.1959 | −1.75820 | ||||||||
\(550\) | 3.27120 | 0.139484 | ||||||||
\(551\) | −1.53432 | −0.0653640 | ||||||||
\(552\) | −1.87924 | −0.0799859 | ||||||||
\(553\) | −35.2247 | −1.49791 | ||||||||
\(554\) | −3.53360 | −0.150128 | ||||||||
\(555\) | −9.60555 | −0.407733 | ||||||||
\(556\) | 3.91350 | 0.165969 | ||||||||
\(557\) | −42.6982 | −1.80918 | −0.904591 | − | 0.426281i | \(-0.859823\pi\) | ||||
−0.904591 | + | 0.426281i | \(0.859823\pi\) | |||||||
\(558\) | −14.9502 | −0.632894 | ||||||||
\(559\) | −11.8247 | −0.500132 | ||||||||
\(560\) | 4.38135 | 0.185146 | ||||||||
\(561\) | 3.61863 | 0.152779 | ||||||||
\(562\) | 28.1683 | 1.18821 | ||||||||
\(563\) | 3.47846 | 0.146600 | 0.0732998 | − | 0.997310i | \(-0.476647\pi\) | ||||
0.0732998 | + | 0.997310i | \(0.476647\pi\) | |||||||
\(564\) | 3.21535 | 0.135391 | ||||||||
\(565\) | 3.13526 | 0.131901 | ||||||||
\(566\) | −16.2124 | −0.681457 | ||||||||
\(567\) | −40.4303 | −1.69791 | ||||||||
\(568\) | −5.72963 | −0.240410 | ||||||||
\(569\) | 16.9175 | 0.709219 | 0.354610 | − | 0.935014i | \(-0.384614\pi\) | ||||
0.354610 | + | 0.935014i | \(0.384614\pi\) | |||||||
\(570\) | 5.59336 | 0.234280 | ||||||||
\(571\) | −3.92420 | −0.164223 | −0.0821113 | − | 0.996623i | \(-0.526166\pi\) | ||||
−0.0821113 | + | 0.996623i | \(0.526166\pi\) | |||||||
\(572\) | 7.39545 | 0.309220 | ||||||||
\(573\) | −52.3713 | −2.18784 | ||||||||
\(574\) | 21.6024 | 0.901665 | ||||||||
\(575\) | −0.625538 | −0.0260867 | ||||||||
\(576\) | 6.02524 | 0.251052 | ||||||||
\(577\) | 1.47636 | 0.0614616 | 0.0307308 | − | 0.999528i | \(-0.490217\pi\) | ||||
0.0307308 | + | 0.999528i | \(0.490217\pi\) | |||||||
\(578\) | 16.8644 | 0.701467 | ||||||||
\(579\) | −8.87212 | −0.368713 | ||||||||
\(580\) | −0.824083 | −0.0342182 | ||||||||
\(581\) | 63.1650 | 2.62052 | ||||||||
\(582\) | 41.8338 | 1.73407 | ||||||||
\(583\) | −1.77852 | −0.0736587 | ||||||||
\(584\) | −16.8546 | −0.697449 | ||||||||
\(585\) | 13.6217 | 0.563189 | ||||||||
\(586\) | 13.7452 | 0.567809 | ||||||||
\(587\) | −42.4425 | −1.75179 | −0.875895 | − | 0.482501i | \(-0.839728\pi\) | ||||
−0.875895 | + | 0.482501i | \(0.839728\pi\) | |||||||
\(588\) | −36.6399 | −1.51100 | ||||||||
\(589\) | −4.61973 | −0.190353 | ||||||||
\(590\) | 1.14090 | 0.0469700 | ||||||||
\(591\) | −12.7466 | −0.524325 | ||||||||
\(592\) | −3.19737 | −0.131411 | ||||||||
\(593\) | −9.06297 | −0.372172 | −0.186086 | − | 0.982534i | \(-0.559580\pi\) | ||||
−0.186086 | + | 0.982534i | \(0.559580\pi\) | |||||||
\(594\) | −29.7301 | −1.21984 | ||||||||
\(595\) | 1.61330 | 0.0661388 | ||||||||
\(596\) | −7.54191 | −0.308929 | ||||||||
\(597\) | 44.4711 | 1.82008 | ||||||||
\(598\) | −1.41420 | −0.0578310 | ||||||||
\(599\) | 24.3541 | 0.995081 | 0.497541 | − | 0.867441i | \(-0.334237\pi\) | ||||
0.497541 | + | 0.867441i | \(0.334237\pi\) | |||||||
\(600\) | 3.00420 | 0.122646 | ||||||||
\(601\) | −19.8389 | −0.809245 | −0.404622 | − | 0.914484i | \(-0.632597\pi\) | ||||
−0.404622 | + | 0.914484i | \(0.632597\pi\) | |||||||
\(602\) | 22.9161 | 0.933990 | ||||||||
\(603\) | −29.9176 | −1.21834 | ||||||||
\(604\) | 3.11492 | 0.126744 | ||||||||
\(605\) | 0.299252 | 0.0121663 | ||||||||
\(606\) | 58.1953 | 2.36402 | ||||||||
\(607\) | 25.7922 | 1.04687 | 0.523437 | − | 0.852064i | \(-0.324650\pi\) | ||||
0.523437 | + | 0.852064i | \(0.324650\pi\) | |||||||
\(608\) | 1.86184 | 0.0755078 | ||||||||
\(609\) | 10.8470 | 0.439541 | ||||||||
\(610\) | −6.83722 | −0.276831 | ||||||||
\(611\) | 2.41967 | 0.0978895 | ||||||||
\(612\) | 2.21861 | 0.0896822 | ||||||||
\(613\) | 26.6350 | 1.07578 | 0.537889 | − | 0.843015i | \(-0.319222\pi\) | ||||
0.537889 | + | 0.843015i | \(0.319222\pi\) | |||||||
\(614\) | 19.0088 | 0.767133 | ||||||||
\(615\) | 14.8123 | 0.597290 | ||||||||
\(616\) | −14.3323 | −0.577463 | ||||||||
\(617\) | 18.5084 | 0.745122 | 0.372561 | − | 0.928008i | \(-0.378480\pi\) | ||||
0.372561 | + | 0.928008i | \(0.378480\pi\) | |||||||
\(618\) | 7.15945 | 0.287995 | ||||||||
\(619\) | 18.1508 | 0.729540 | 0.364770 | − | 0.931098i | \(-0.381148\pi\) | ||||
0.364770 | + | 0.931098i | \(0.381148\pi\) | |||||||
\(620\) | −2.48127 | −0.0996501 | ||||||||
\(621\) | 5.68517 | 0.228138 | ||||||||
\(622\) | −13.1742 | −0.528238 | ||||||||
\(623\) | 1.95042 | 0.0781418 | ||||||||
\(624\) | 6.79184 | 0.271891 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.86799 | −0.154596 | ||||||||
\(627\) | −18.2970 | −0.730712 | ||||||||
\(628\) | 4.02861 | 0.160759 | ||||||||
\(629\) | −1.17734 | −0.0469434 | ||||||||
\(630\) | −26.3987 | −1.05175 | ||||||||
\(631\) | −14.9828 | −0.596454 | −0.298227 | − | 0.954495i | \(-0.596395\pi\) | ||||
−0.298227 | + | 0.954495i | \(0.596395\pi\) | |||||||
\(632\) | −8.03970 | −0.319802 | ||||||||
\(633\) | 73.6913 | 2.92896 | ||||||||
\(634\) | 18.5368 | 0.736189 | ||||||||
\(635\) | 4.70586 | 0.186747 | ||||||||
\(636\) | −1.63336 | −0.0647668 | ||||||||
\(637\) | −27.5729 | −1.09248 | ||||||||
\(638\) | 2.69574 | 0.106725 | ||||||||
\(639\) | 34.5224 | 1.36569 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −14.6679 | −0.579346 | −0.289673 | − | 0.957126i | \(-0.593547\pi\) | ||||
−0.289673 | + | 0.957126i | \(0.593547\pi\) | |||||||
\(642\) | 29.3448 | 1.15814 | ||||||||
\(643\) | 12.6029 | 0.497009 | 0.248504 | − | 0.968631i | \(-0.420061\pi\) | ||||
0.248504 | + | 0.968631i | \(0.420061\pi\) | |||||||
\(644\) | 2.74070 | 0.107999 | ||||||||
\(645\) | 15.7131 | 0.618703 | ||||||||
\(646\) | 0.685568 | 0.0269733 | ||||||||
\(647\) | 26.6210 | 1.04658 | 0.523291 | − | 0.852154i | \(-0.324704\pi\) | ||||
0.523291 | + | 0.852154i | \(0.324704\pi\) | |||||||
\(648\) | −9.22783 | −0.362503 | ||||||||
\(649\) | −3.73210 | −0.146498 | ||||||||
\(650\) | 2.26078 | 0.0886750 | ||||||||
\(651\) | 32.6596 | 1.28003 | ||||||||
\(652\) | −16.9126 | −0.662347 | ||||||||
\(653\) | 36.0372 | 1.41024 | 0.705122 | − | 0.709086i | \(-0.250892\pi\) | ||||
0.705122 | + | 0.709086i | \(0.250892\pi\) | |||||||
\(654\) | −0.115528 | −0.00451748 | ||||||||
\(655\) | 0.648468 | 0.0253377 | ||||||||
\(656\) | 4.93053 | 0.192505 | ||||||||
\(657\) | 101.553 | 3.96197 | ||||||||
\(658\) | −4.68929 | −0.182807 | ||||||||
\(659\) | 49.0391 | 1.91029 | 0.955147 | − | 0.296133i | \(-0.0956972\pi\) | ||||
0.955147 | + | 0.296133i | \(0.0956972\pi\) | |||||||
\(660\) | −9.82735 | −0.382529 | ||||||||
\(661\) | −30.3035 | −1.17867 | −0.589334 | − | 0.807889i | \(-0.700610\pi\) | ||||
−0.589334 | + | 0.807889i | \(0.700610\pi\) | |||||||
\(662\) | 25.1409 | 0.977128 | ||||||||
\(663\) | 2.50089 | 0.0971265 | ||||||||
\(664\) | 14.4168 | 0.559480 | ||||||||
\(665\) | −8.15739 | −0.316330 | ||||||||
\(666\) | 19.2649 | 0.746501 | ||||||||
\(667\) | −0.515495 | −0.0199601 | ||||||||
\(668\) | 4.31707 | 0.167033 | ||||||||
\(669\) | 77.6234 | 3.00109 | ||||||||
\(670\) | −4.96537 | −0.191829 | ||||||||
\(671\) | 22.3659 | 0.863426 | ||||||||
\(672\) | −13.1625 | −0.507753 | ||||||||
\(673\) | −39.8737 | −1.53702 | −0.768510 | − | 0.639838i | \(-0.779001\pi\) | ||||
−0.768510 | + | 0.639838i | \(0.779001\pi\) | |||||||
\(674\) | −12.4506 | −0.479580 | ||||||||
\(675\) | −9.08845 | −0.349815 | ||||||||
\(676\) | −7.88889 | −0.303419 | ||||||||
\(677\) | 37.1772 | 1.42884 | 0.714418 | − | 0.699719i | \(-0.246691\pi\) | ||||
0.714418 | + | 0.699719i | \(0.246691\pi\) | |||||||
\(678\) | −9.41896 | −0.361733 | ||||||||
\(679\) | −61.0106 | −2.34137 | ||||||||
\(680\) | 0.368220 | 0.0141206 | ||||||||
\(681\) | 12.1690 | 0.466317 | ||||||||
\(682\) | 8.11672 | 0.310805 | ||||||||
\(683\) | 13.5008 | 0.516594 | 0.258297 | − | 0.966066i | \(-0.416839\pi\) | ||||
0.258297 | + | 0.966066i | \(0.416839\pi\) | |||||||
\(684\) | −11.2181 | −0.428933 | ||||||||
\(685\) | 4.79646 | 0.183263 | ||||||||
\(686\) | 22.7664 | 0.869226 | ||||||||
\(687\) | −42.0851 | −1.60565 | ||||||||
\(688\) | 5.23037 | 0.199406 | ||||||||
\(689\) | −1.22916 | −0.0468274 | ||||||||
\(690\) | 1.87924 | 0.0715416 | ||||||||
\(691\) | −15.2582 | −0.580450 | −0.290225 | − | 0.956958i | \(-0.593730\pi\) | ||||
−0.290225 | + | 0.956958i | \(0.593730\pi\) | |||||||
\(692\) | 24.6465 | 0.936920 | ||||||||
\(693\) | 86.3554 | 3.28037 | ||||||||
\(694\) | −13.9023 | −0.527726 | ||||||||
\(695\) | −3.91350 | −0.148447 | ||||||||
\(696\) | 2.47572 | 0.0938417 | ||||||||
\(697\) | 1.81552 | 0.0687677 | ||||||||
\(698\) | 5.12796 | 0.194096 | ||||||||
\(699\) | −0.806398 | −0.0305008 | ||||||||
\(700\) | −4.38135 | −0.165599 | ||||||||
\(701\) | −24.7375 | −0.934324 | −0.467162 | − | 0.884172i | \(-0.654723\pi\) | ||||
−0.467162 | + | 0.884172i | \(0.654723\pi\) | |||||||
\(702\) | −20.5470 | −0.775495 | ||||||||
\(703\) | 5.95301 | 0.224522 | ||||||||
\(704\) | −3.27120 | −0.123288 | ||||||||
\(705\) | −3.21535 | −0.121097 | ||||||||
\(706\) | 13.7457 | 0.517328 | ||||||||
\(707\) | −84.8724 | −3.19196 | ||||||||
\(708\) | −3.42749 | −0.128813 | ||||||||
\(709\) | 41.9924 | 1.57706 | 0.788529 | − | 0.614998i | \(-0.210843\pi\) | ||||
0.788529 | + | 0.614998i | \(0.210843\pi\) | |||||||
\(710\) | 5.72963 | 0.215029 | ||||||||
\(711\) | 48.4412 | 1.81669 | ||||||||
\(712\) | 0.445164 | 0.0166832 | ||||||||
\(713\) | −1.55213 | −0.0581276 | ||||||||
\(714\) | −4.84668 | −0.181383 | ||||||||
\(715\) | −7.39545 | −0.276574 | ||||||||
\(716\) | 8.59930 | 0.321371 | ||||||||
\(717\) | −21.2616 | −0.794030 | ||||||||
\(718\) | 24.2421 | 0.904707 | ||||||||
\(719\) | 4.68575 | 0.174749 | 0.0873744 | − | 0.996176i | \(-0.472152\pi\) | ||||
0.0873744 | + | 0.996176i | \(0.472152\pi\) | |||||||
\(720\) | −6.02524 | −0.224548 | ||||||||
\(721\) | −10.4414 | −0.388857 | ||||||||
\(722\) | 15.5335 | 0.578098 | ||||||||
\(723\) | 52.0089 | 1.93423 | ||||||||
\(724\) | 7.47920 | 0.277962 | ||||||||
\(725\) | 0.824083 | 0.0306057 | ||||||||
\(726\) | −0.899013 | −0.0333655 | ||||||||
\(727\) | 27.9141 | 1.03527 | 0.517637 | − | 0.855600i | \(-0.326812\pi\) | ||||
0.517637 | + | 0.855600i | \(0.326812\pi\) | |||||||
\(728\) | −9.90525 | −0.367113 | ||||||||
\(729\) | −26.3108 | −0.974473 | ||||||||
\(730\) | 16.8546 | 0.623817 | ||||||||
\(731\) | 1.92593 | 0.0712330 | ||||||||
\(732\) | 20.5404 | 0.759195 | ||||||||
\(733\) | 34.5426 | 1.27586 | 0.637930 | − | 0.770095i | \(-0.279791\pi\) | ||||
0.637930 | + | 0.770095i | \(0.279791\pi\) | |||||||
\(734\) | 8.27488 | 0.305431 | ||||||||
\(735\) | 36.6399 | 1.35148 | ||||||||
\(736\) | 0.625538 | 0.0230576 | ||||||||
\(737\) | 16.2427 | 0.598308 | ||||||||
\(738\) | −29.7076 | −1.09355 | ||||||||
\(739\) | −18.9705 | −0.697840 | −0.348920 | − | 0.937152i | \(-0.613452\pi\) | ||||
−0.348920 | + | 0.937152i | \(0.613452\pi\) | |||||||
\(740\) | 3.19737 | 0.117538 | ||||||||
\(741\) | −12.6453 | −0.464538 | ||||||||
\(742\) | 2.38210 | 0.0874495 | ||||||||
\(743\) | 15.3973 | 0.564871 | 0.282436 | − | 0.959286i | \(-0.408858\pi\) | ||||
0.282436 | + | 0.959286i | \(0.408858\pi\) | |||||||
\(744\) | 7.45423 | 0.273285 | ||||||||
\(745\) | 7.54191 | 0.276314 | ||||||||
\(746\) | 24.9657 | 0.914061 | ||||||||
\(747\) | −86.8647 | −3.17821 | ||||||||
\(748\) | −1.20452 | −0.0440416 | ||||||||
\(749\) | −42.7965 | −1.56375 | ||||||||
\(750\) | −3.00420 | −0.109698 | ||||||||
\(751\) | 46.5683 | 1.69930 | 0.849651 | − | 0.527346i | \(-0.176813\pi\) | ||||
0.849651 | + | 0.527346i | \(0.176813\pi\) | |||||||
\(752\) | −1.07028 | −0.0390292 | ||||||||
\(753\) | 43.4243 | 1.58247 | ||||||||
\(754\) | 1.86307 | 0.0678490 | ||||||||
\(755\) | −3.11492 | −0.113364 | ||||||||
\(756\) | 39.8197 | 1.44823 | ||||||||
\(757\) | 27.9286 | 1.01508 | 0.507540 | − | 0.861628i | \(-0.330555\pi\) | ||||
0.507540 | + | 0.861628i | \(0.330555\pi\) | |||||||
\(758\) | −5.76871 | −0.209529 | ||||||||
\(759\) | −6.14738 | −0.223136 | ||||||||
\(760\) | −1.86184 | −0.0675362 | ||||||||
\(761\) | −25.2055 | −0.913700 | −0.456850 | − | 0.889544i | \(-0.651022\pi\) | ||||
−0.456850 | + | 0.889544i | \(0.651022\pi\) | |||||||
\(762\) | −14.1374 | −0.512143 | ||||||||
\(763\) | 0.168486 | 0.00609960 | ||||||||
\(764\) | 17.4327 | 0.630692 | ||||||||
\(765\) | −2.21861 | −0.0802142 | ||||||||
\(766\) | −31.1789 | −1.12654 | ||||||||
\(767\) | −2.57931 | −0.0931336 | ||||||||
\(768\) | −3.00420 | −0.108405 | ||||||||
\(769\) | 35.1757 | 1.26847 | 0.634233 | − | 0.773142i | \(-0.281316\pi\) | ||||
0.634233 | + | 0.773142i | \(0.281316\pi\) | |||||||
\(770\) | 14.3323 | 0.516499 | ||||||||
\(771\) | −54.2135 | −1.95245 | ||||||||
\(772\) | 2.95323 | 0.106289 | ||||||||
\(773\) | 5.98674 | 0.215328 | 0.107664 | − | 0.994187i | \(-0.465663\pi\) | ||||
0.107664 | + | 0.994187i | \(0.465663\pi\) | |||||||
\(774\) | −31.5143 | −1.13276 | ||||||||
\(775\) | 2.48127 | 0.0891298 | ||||||||
\(776\) | −13.9251 | −0.499881 | ||||||||
\(777\) | −42.0853 | −1.50980 | ||||||||
\(778\) | −15.8001 | −0.566461 | ||||||||
\(779\) | −9.17988 | −0.328903 | ||||||||
\(780\) | −6.79184 | −0.243187 | ||||||||
\(781\) | −18.7428 | −0.670669 | ||||||||
\(782\) | 0.230335 | 0.00823678 | ||||||||
\(783\) | −7.48964 | −0.267658 | ||||||||
\(784\) | 12.1962 | 0.435579 | ||||||||
\(785\) | −4.02861 | −0.143787 | ||||||||
\(786\) | −1.94813 | −0.0694875 | ||||||||
\(787\) | 0.564328 | 0.0201161 | 0.0100581 | − | 0.999949i | \(-0.496798\pi\) | ||||
0.0100581 | + | 0.999949i | \(0.496798\pi\) | |||||||
\(788\) | 4.24292 | 0.151148 | ||||||||
\(789\) | 28.9741 | 1.03150 | ||||||||
\(790\) | 8.03970 | 0.286040 | ||||||||
\(791\) | 13.7367 | 0.488420 | ||||||||
\(792\) | 19.7098 | 0.700356 | ||||||||
\(793\) | 15.4574 | 0.548909 | ||||||||
\(794\) | 1.32833 | 0.0471408 | ||||||||
\(795\) | 1.63336 | 0.0579292 | ||||||||
\(796\) | −14.8029 | −0.524677 | ||||||||
\(797\) | −5.57121 | −0.197342 | −0.0986712 | − | 0.995120i | \(-0.531459\pi\) | ||||
−0.0986712 | + | 0.995120i | \(0.531459\pi\) | |||||||
\(798\) | 24.5065 | 0.867519 | ||||||||
\(799\) | −0.394100 | −0.0139422 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −2.68222 | −0.0947715 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −55.1348 | −1.94566 | ||||||||
\(804\) | 14.9170 | 0.526081 | ||||||||
\(805\) | −2.74070 | −0.0965969 | ||||||||
\(806\) | 5.60959 | 0.197589 | ||||||||
\(807\) | −8.98944 | −0.316443 | ||||||||
\(808\) | −19.3713 | −0.681480 | ||||||||
\(809\) | 3.85000 | 0.135359 | 0.0676795 | − | 0.997707i | \(-0.478440\pi\) | ||||
0.0676795 | + | 0.997707i | \(0.478440\pi\) | |||||||
\(810\) | 9.22783 | 0.324233 | ||||||||
\(811\) | −7.46901 | −0.262272 | −0.131136 | − | 0.991364i | \(-0.541863\pi\) | ||||
−0.131136 | + | 0.991364i | \(0.541863\pi\) | |||||||
\(812\) | −3.61060 | −0.126707 | ||||||||
\(813\) | −14.5906 | −0.511715 | ||||||||
\(814\) | −10.4592 | −0.366596 | ||||||||
\(815\) | 16.9126 | 0.592421 | ||||||||
\(816\) | −1.10621 | −0.0387250 | ||||||||
\(817\) | −9.73814 | −0.340694 | ||||||||
\(818\) | −8.99084 | −0.314357 | ||||||||
\(819\) | 59.6816 | 2.08544 | ||||||||
\(820\) | −4.93053 | −0.172182 | ||||||||
\(821\) | 18.0808 | 0.631025 | 0.315512 | − | 0.948921i | \(-0.397824\pi\) | ||||
0.315512 | + | 0.948921i | \(0.397824\pi\) | |||||||
\(822\) | −14.4095 | −0.502590 | ||||||||
\(823\) | −13.5500 | −0.472323 | −0.236162 | − | 0.971714i | \(-0.575889\pi\) | ||||
−0.236162 | + | 0.971714i | \(0.575889\pi\) | |||||||
\(824\) | −2.38314 | −0.0830207 | ||||||||
\(825\) | 9.82735 | 0.342145 | ||||||||
\(826\) | 4.99867 | 0.173926 | ||||||||
\(827\) | 6.20103 | 0.215631 | 0.107815 | − | 0.994171i | \(-0.465614\pi\) | ||||
0.107815 | + | 0.994171i | \(0.465614\pi\) | |||||||
\(828\) | −3.76902 | −0.130982 | ||||||||
\(829\) | −21.4092 | −0.743572 | −0.371786 | − | 0.928318i | \(-0.621254\pi\) | ||||
−0.371786 | + | 0.928318i | \(0.621254\pi\) | |||||||
\(830\) | −14.4168 | −0.500414 | ||||||||
\(831\) | −10.6157 | −0.368253 | ||||||||
\(832\) | −2.26078 | −0.0783784 | ||||||||
\(833\) | 4.49089 | 0.155600 | ||||||||
\(834\) | 11.7570 | 0.407110 | ||||||||
\(835\) | −4.31707 | −0.149398 | ||||||||
\(836\) | 6.09047 | 0.210643 | ||||||||
\(837\) | −22.5509 | −0.779472 | ||||||||
\(838\) | 17.4387 | 0.602410 | ||||||||
\(839\) | −45.2264 | −1.56139 | −0.780695 | − | 0.624912i | \(-0.785135\pi\) | ||||
−0.780695 | + | 0.624912i | \(0.785135\pi\) | |||||||
\(840\) | 13.1625 | 0.454148 | ||||||||
\(841\) | −28.3209 | −0.976582 | ||||||||
\(842\) | 19.2201 | 0.662368 | ||||||||
\(843\) | 84.6232 | 2.91458 | ||||||||
\(844\) | −24.5294 | −0.844336 | ||||||||
\(845\) | 7.88889 | 0.271386 | ||||||||
\(846\) | 6.44872 | 0.221712 | ||||||||
\(847\) | 1.31113 | 0.0450508 | ||||||||
\(848\) | 0.543690 | 0.0186704 | ||||||||
\(849\) | −48.7053 | −1.67156 | ||||||||
\(850\) | −0.368220 | −0.0126298 | ||||||||
\(851\) | 2.00008 | 0.0685617 | ||||||||
\(852\) | −17.2130 | −0.589707 | ||||||||
\(853\) | 4.77907 | 0.163632 | 0.0818160 | − | 0.996647i | \(-0.473928\pi\) | ||||
0.0818160 | + | 0.996647i | \(0.473928\pi\) | |||||||
\(854\) | −29.9562 | −1.02508 | ||||||||
\(855\) | 11.2181 | 0.383650 | ||||||||
\(856\) | −9.76789 | −0.333860 | ||||||||
\(857\) | 19.5735 | 0.668619 | 0.334310 | − | 0.942463i | \(-0.391497\pi\) | ||||
0.334310 | + | 0.942463i | \(0.391497\pi\) | |||||||
\(858\) | 22.2175 | 0.758491 | ||||||||
\(859\) | 28.6355 | 0.977030 | 0.488515 | − | 0.872555i | \(-0.337539\pi\) | ||||
0.488515 | + | 0.872555i | \(0.337539\pi\) | |||||||
\(860\) | −5.23037 | −0.178354 | ||||||||
\(861\) | 64.8979 | 2.21171 | ||||||||
\(862\) | −2.69307 | −0.0917262 | ||||||||
\(863\) | 45.8524 | 1.56083 | 0.780417 | − | 0.625259i | \(-0.215007\pi\) | ||||
0.780417 | + | 0.625259i | \(0.215007\pi\) | |||||||
\(864\) | 9.08845 | 0.309195 | ||||||||
\(865\) | −24.6465 | −0.838007 | ||||||||
\(866\) | 21.8698 | 0.743167 | ||||||||
\(867\) | 50.6641 | 1.72064 | ||||||||
\(868\) | −10.8713 | −0.368996 | ||||||||
\(869\) | −26.2995 | −0.892149 | ||||||||
\(870\) | −2.47572 | −0.0839346 | ||||||||
\(871\) | 11.2256 | 0.380365 | ||||||||
\(872\) | 0.0384553 | 0.00130226 | ||||||||
\(873\) | 83.9020 | 2.83965 | ||||||||
\(874\) | −1.16465 | −0.0393950 | ||||||||
\(875\) | 4.38135 | 0.148117 | ||||||||
\(876\) | −50.6347 | −1.71079 | ||||||||
\(877\) | −39.3654 | −1.32928 | −0.664638 | − | 0.747165i | \(-0.731414\pi\) | ||||
−0.664638 | + | 0.747165i | \(0.731414\pi\) | |||||||
\(878\) | 1.52968 | 0.0516241 | ||||||||
\(879\) | 41.2934 | 1.39279 | ||||||||
\(880\) | 3.27120 | 0.110272 | ||||||||
\(881\) | −9.49150 | −0.319777 | −0.159888 | − | 0.987135i | \(-0.551113\pi\) | ||||
−0.159888 | + | 0.987135i | \(0.551113\pi\) | |||||||
\(882\) | −73.4851 | −2.47437 | ||||||||
\(883\) | 15.7979 | 0.531641 | 0.265821 | − | 0.964023i | \(-0.414357\pi\) | ||||
0.265821 | + | 0.964023i | \(0.414357\pi\) | |||||||
\(884\) | −0.832463 | −0.0279988 | ||||||||
\(885\) | 3.42749 | 0.115214 | ||||||||
\(886\) | 7.30305 | 0.245351 | ||||||||
\(887\) | 30.2187 | 1.01464 | 0.507322 | − | 0.861757i | \(-0.330636\pi\) | ||||
0.507322 | + | 0.861757i | \(0.330636\pi\) | |||||||
\(888\) | −9.60555 | −0.322341 | ||||||||
\(889\) | 20.6180 | 0.691507 | ||||||||
\(890\) | −0.445164 | −0.0149219 | ||||||||
\(891\) | −30.1861 | −1.01127 | ||||||||
\(892\) | −25.8383 | −0.865129 | ||||||||
\(893\) | 1.99270 | 0.0666832 | ||||||||
\(894\) | −22.6574 | −0.757778 | ||||||||
\(895\) | −8.59930 | −0.287443 | ||||||||
\(896\) | 4.38135 | 0.146371 | ||||||||
\(897\) | −4.24855 | −0.141855 | ||||||||
\(898\) | −10.7673 | −0.359310 | ||||||||
\(899\) | 2.04477 | 0.0681969 | ||||||||
\(900\) | 6.02524 | 0.200841 | ||||||||
\(901\) | 0.200198 | 0.00666955 | ||||||||
\(902\) | 16.1287 | 0.537028 | ||||||||
\(903\) | 68.8446 | 2.29100 | ||||||||
\(904\) | 3.13526 | 0.104277 | ||||||||
\(905\) | −7.47920 | −0.248617 | ||||||||
\(906\) | 9.35785 | 0.310894 | ||||||||
\(907\) | 29.1017 | 0.966308 | 0.483154 | − | 0.875535i | \(-0.339491\pi\) | ||||
0.483154 | + | 0.875535i | \(0.339491\pi\) | |||||||
\(908\) | −4.05065 | −0.134426 | ||||||||
\(909\) | 116.717 | 3.87125 | ||||||||
\(910\) | 9.90525 | 0.328356 | ||||||||
\(911\) | −45.1221 | −1.49496 | −0.747481 | − | 0.664283i | \(-0.768737\pi\) | ||||
−0.747481 | + | 0.664283i | \(0.768737\pi\) | |||||||
\(912\) | 5.59336 | 0.185215 | ||||||||
\(913\) | 47.1602 | 1.56077 | ||||||||
\(914\) | −27.1707 | −0.898728 | ||||||||
\(915\) | −20.5404 | −0.679044 | ||||||||
\(916\) | 14.0087 | 0.462861 | ||||||||
\(917\) | 2.84116 | 0.0938235 | ||||||||
\(918\) | 3.34655 | 0.110453 | ||||||||
\(919\) | 3.90777 | 0.128905 | 0.0644527 | − | 0.997921i | \(-0.479470\pi\) | ||||
0.0644527 | + | 0.997921i | \(0.479470\pi\) | |||||||
\(920\) | −0.625538 | −0.0206234 | ||||||||
\(921\) | 57.1063 | 1.88172 | ||||||||
\(922\) | 9.07414 | 0.298841 | ||||||||
\(923\) | −12.9534 | −0.426367 | ||||||||
\(924\) | −43.0571 | −1.41647 | ||||||||
\(925\) | −3.19737 | −0.105129 | ||||||||
\(926\) | 23.5550 | 0.774066 | ||||||||
\(927\) | 14.3590 | 0.471612 | ||||||||
\(928\) | −0.824083 | −0.0270519 | ||||||||
\(929\) | 4.84819 | 0.159064 | 0.0795319 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795319 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(930\) | −7.45423 | −0.244434 | ||||||||
\(931\) | −22.7075 | −0.744207 | ||||||||
\(932\) | 0.268423 | 0.00879249 | ||||||||
\(933\) | −39.5780 | −1.29573 | ||||||||
\(934\) | −17.4498 | −0.570976 | ||||||||
\(935\) | 1.20452 | 0.0393920 | ||||||||
\(936\) | 13.6217 | 0.445240 | ||||||||
\(937\) | −17.0699 | −0.557650 | −0.278825 | − | 0.960342i | \(-0.589945\pi\) | ||||
−0.278825 | + | 0.960342i | \(0.589945\pi\) | |||||||
\(938\) | −21.7550 | −0.710326 | ||||||||
\(939\) | −11.6202 | −0.379212 | ||||||||
\(940\) | 1.07028 | 0.0349088 | ||||||||
\(941\) | 42.5380 | 1.38670 | 0.693350 | − | 0.720601i | \(-0.256134\pi\) | ||||
0.693350 | + | 0.720601i | \(0.256134\pi\) | |||||||
\(942\) | 12.1028 | 0.394330 | ||||||||
\(943\) | −3.08423 | −0.100436 | ||||||||
\(944\) | 1.14090 | 0.0371330 | ||||||||
\(945\) | −39.8197 | −1.29533 | ||||||||
\(946\) | 17.1096 | 0.556281 | ||||||||
\(947\) | 9.23495 | 0.300096 | 0.150048 | − | 0.988679i | \(-0.452057\pi\) | ||||
0.150048 | + | 0.988679i | \(0.452057\pi\) | |||||||
\(948\) | −24.1529 | −0.784450 | ||||||||
\(949\) | −38.1045 | −1.23693 | ||||||||
\(950\) | 1.86184 | 0.0604062 | ||||||||
\(951\) | 55.6882 | 1.80581 | ||||||||
\(952\) | 1.61330 | 0.0522873 | ||||||||
\(953\) | −23.6660 | −0.766617 | −0.383309 | − | 0.923620i | \(-0.625215\pi\) | ||||
−0.383309 | + | 0.923620i | \(0.625215\pi\) | |||||||
\(954\) | −3.27587 | −0.106060 | ||||||||
\(955\) | −17.4327 | −0.564108 | ||||||||
\(956\) | 7.07729 | 0.228896 | ||||||||
\(957\) | 8.09856 | 0.261789 | ||||||||
\(958\) | −9.78078 | −0.316003 | ||||||||
\(959\) | 21.0149 | 0.678608 | ||||||||
\(960\) | 3.00420 | 0.0969603 | ||||||||
\(961\) | −24.8433 | −0.801397 | ||||||||
\(962\) | −7.22854 | −0.233058 | ||||||||
\(963\) | 58.8539 | 1.89654 | ||||||||
\(964\) | −17.3121 | −0.557584 | ||||||||
\(965\) | −2.95323 | −0.0950680 | ||||||||
\(966\) | 8.23362 | 0.264912 | ||||||||
\(967\) | 41.3149 | 1.32860 | 0.664300 | − | 0.747466i | \(-0.268730\pi\) | ||||
0.664300 | + | 0.747466i | \(0.268730\pi\) | |||||||
\(968\) | 0.299252 | 0.00961831 | ||||||||
\(969\) | 2.05959 | 0.0661635 | ||||||||
\(970\) | 13.9251 | 0.447107 | ||||||||
\(971\) | −50.7255 | −1.62786 | −0.813929 | − | 0.580964i | \(-0.802676\pi\) | ||||
−0.813929 | + | 0.580964i | \(0.802676\pi\) | |||||||
\(972\) | −0.456932 | −0.0146561 | ||||||||
\(973\) | −17.1464 | −0.549688 | ||||||||
\(974\) | −24.3102 | −0.778950 | ||||||||
\(975\) | 6.79184 | 0.217513 | ||||||||
\(976\) | −6.83722 | −0.218854 | ||||||||
\(977\) | 55.0815 | 1.76221 | 0.881107 | − | 0.472917i | \(-0.156799\pi\) | ||||
0.881107 | + | 0.472917i | \(0.156799\pi\) | |||||||
\(978\) | −50.8088 | −1.62469 | ||||||||
\(979\) | 1.45622 | 0.0465410 | ||||||||
\(980\) | −12.1962 | −0.389594 | ||||||||
\(981\) | −0.231702 | −0.00739769 | ||||||||
\(982\) | 18.0341 | 0.575492 | ||||||||
\(983\) | 14.4805 | 0.461856 | 0.230928 | − | 0.972971i | \(-0.425824\pi\) | ||||
0.230928 | + | 0.972971i | \(0.425824\pi\) | |||||||
\(984\) | 14.8123 | 0.472199 | ||||||||
\(985\) | −4.24292 | −0.135191 | ||||||||
\(986\) | −0.303444 | −0.00966362 | ||||||||
\(987\) | −14.0876 | −0.448412 | ||||||||
\(988\) | 4.20922 | 0.133913 | ||||||||
\(989\) | −3.27180 | −0.104037 | ||||||||
\(990\) | −19.7098 | −0.626418 | ||||||||
\(991\) | 52.7667 | 1.67619 | 0.838095 | − | 0.545524i | \(-0.183669\pi\) | ||||
0.838095 | + | 0.545524i | \(0.183669\pi\) | |||||||
\(992\) | −2.48127 | −0.0787803 | ||||||||
\(993\) | 75.5283 | 2.39682 | ||||||||
\(994\) | 25.1035 | 0.796235 | ||||||||
\(995\) | 14.8029 | 0.469285 | ||||||||
\(996\) | 43.3110 | 1.37236 | ||||||||
\(997\) | −29.4070 | −0.931329 | −0.465665 | − | 0.884961i | \(-0.654185\pi\) | ||||
−0.465665 | + | 0.884961i | \(0.654185\pi\) | |||||||
\(998\) | −22.4604 | −0.710973 | ||||||||
\(999\) | 29.0591 | 0.919390 |
(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 | 4010.2.a.k.1.2 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.2 | ✓ | 15 | 1.1 | even | 1 | trivial |