Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1519,2,Mod(1,1519)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1519, 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("1519.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1519 = 7^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1519.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: | \(12.1292760670\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 5 x^{12} - 9 x^{11} + 76 x^{10} - 17 x^{9} - 387 x^{8} + 332 x^{7} + 758 x^{6} - 875 x^{5} + \cdots + 21 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 217) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.64321\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1519.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.64321 | 1.86903 | 0.934514 | − | 0.355925i | \(-0.115834\pi\) | ||||
0.934514 | + | 0.355925i | \(0.115834\pi\) | |||||||
\(3\) | 2.32634 | 1.34311 | 0.671556 | − | 0.740953i | \(-0.265626\pi\) | ||||
0.671556 | + | 0.740953i | \(0.265626\pi\) | |||||||
\(4\) | 4.98654 | 2.49327 | ||||||||
\(5\) | 0.354419 | 0.158501 | 0.0792506 | − | 0.996855i | \(-0.474747\pi\) | ||||
0.0792506 | + | 0.996855i | \(0.474747\pi\) | |||||||
\(6\) | 6.14899 | 2.51032 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.89404 | 2.79096 | ||||||||
\(9\) | 2.41186 | 0.803952 | ||||||||
\(10\) | 0.936803 | 0.296243 | ||||||||
\(11\) | −2.17674 | −0.656311 | −0.328156 | − | 0.944624i | \(-0.606427\pi\) | ||||
−0.328156 | + | 0.944624i | \(0.606427\pi\) | |||||||
\(12\) | 11.6004 | 3.34874 | ||||||||
\(13\) | −4.99524 | −1.38543 | −0.692715 | − | 0.721211i | \(-0.743586\pi\) | ||||
−0.692715 | + | 0.721211i | \(0.743586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.824500 | 0.212885 | ||||||||
\(16\) | 10.8925 | 2.72312 | ||||||||
\(17\) | −6.28607 | −1.52460 | −0.762298 | − | 0.647226i | \(-0.775929\pi\) | ||||
−0.762298 | + | 0.647226i | \(0.775929\pi\) | |||||||
\(18\) | 6.37503 | 1.50261 | ||||||||
\(19\) | 2.83131 | 0.649548 | 0.324774 | − | 0.945792i | \(-0.394712\pi\) | ||||
0.324774 | + | 0.945792i | \(0.394712\pi\) | |||||||
\(20\) | 1.76733 | 0.395186 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.75357 | −1.22666 | ||||||||
\(23\) | 2.91448 | 0.607712 | 0.303856 | − | 0.952718i | \(-0.401726\pi\) | ||||
0.303856 | + | 0.952718i | \(0.401726\pi\) | |||||||
\(24\) | 18.3642 | 3.74858 | ||||||||
\(25\) | −4.87439 | −0.974877 | ||||||||
\(26\) | −13.2035 | −2.58941 | ||||||||
\(27\) | −1.36822 | −0.263315 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.51280 | 1.76648 | 0.883241 | − | 0.468919i | \(-0.155356\pi\) | ||||
0.883241 | + | 0.468919i | \(0.155356\pi\) | |||||||
\(30\) | 2.17932 | 0.397888 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 13.0030 | 2.29863 | ||||||||
\(33\) | −5.06383 | −0.881500 | ||||||||
\(34\) | −16.6154 | −2.84951 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.0268 | 2.00447 | ||||||||
\(37\) | 4.77815 | 0.785523 | 0.392761 | − | 0.919640i | \(-0.371520\pi\) | ||||
0.392761 | + | 0.919640i | \(0.371520\pi\) | |||||||
\(38\) | 7.48374 | 1.21402 | ||||||||
\(39\) | −11.6206 | −1.86079 | ||||||||
\(40\) | 2.79780 | 0.442371 | ||||||||
\(41\) | −2.71610 | −0.424183 | −0.212092 | − | 0.977250i | \(-0.568028\pi\) | ||||
−0.212092 | + | 0.977250i | \(0.568028\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.143225 | −0.0218415 | −0.0109208 | − | 0.999940i | \(-0.503476\pi\) | ||||
−0.0109208 | + | 0.999940i | \(0.503476\pi\) | |||||||
\(44\) | −10.8544 | −1.63636 | ||||||||
\(45\) | 0.854808 | 0.127427 | ||||||||
\(46\) | 7.70358 | 1.13583 | ||||||||
\(47\) | −3.53184 | −0.515171 | −0.257586 | − | 0.966255i | \(-0.582927\pi\) | ||||
−0.257586 | + | 0.966255i | \(0.582927\pi\) | |||||||
\(48\) | 25.3396 | 3.65746 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.8840 | −1.82207 | ||||||||
\(51\) | −14.6235 | −2.04770 | ||||||||
\(52\) | −24.9090 | −3.45425 | ||||||||
\(53\) | −9.99332 | −1.37269 | −0.686344 | − | 0.727277i | \(-0.740786\pi\) | ||||
−0.686344 | + | 0.727277i | \(0.740786\pi\) | |||||||
\(54\) | −3.61650 | −0.492143 | ||||||||
\(55\) | −0.771478 | −0.104026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.58659 | 0.872416 | ||||||||
\(58\) | 25.1443 | 3.30161 | ||||||||
\(59\) | 9.02557 | 1.17503 | 0.587514 | − | 0.809214i | \(-0.300107\pi\) | ||||
0.587514 | + | 0.809214i | \(0.300107\pi\) | |||||||
\(60\) | 4.11140 | 0.530779 | ||||||||
\(61\) | −4.62165 | −0.591742 | −0.295871 | − | 0.955228i | \(-0.595610\pi\) | ||||
−0.295871 | + | 0.955228i | \(0.595610\pi\) | |||||||
\(62\) | 2.64321 | 0.335688 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.5847 | 1.57309 | ||||||||
\(65\) | −1.77041 | −0.219592 | ||||||||
\(66\) | −13.3848 | −1.64755 | ||||||||
\(67\) | 14.0369 | 1.71488 | 0.857441 | − | 0.514582i | \(-0.172053\pi\) | ||||
0.857441 | + | 0.514582i | \(0.172053\pi\) | |||||||
\(68\) | −31.3457 | −3.80123 | ||||||||
\(69\) | 6.78008 | 0.816226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.11202 | −0.962719 | −0.481360 | − | 0.876523i | \(-0.659857\pi\) | ||||
−0.481360 | + | 0.876523i | \(0.659857\pi\) | |||||||
\(72\) | 19.0393 | 2.24380 | ||||||||
\(73\) | −7.54534 | −0.883116 | −0.441558 | − | 0.897233i | \(-0.645574\pi\) | ||||
−0.441558 | + | 0.897233i | \(0.645574\pi\) | |||||||
\(74\) | 12.6296 | 1.46816 | ||||||||
\(75\) | −11.3395 | −1.30937 | ||||||||
\(76\) | 14.1185 | 1.61950 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −30.7157 | −3.47787 | ||||||||
\(79\) | −5.31173 | −0.597616 | −0.298808 | − | 0.954313i | \(-0.596589\pi\) | ||||
−0.298808 | + | 0.954313i | \(0.596589\pi\) | |||||||
\(80\) | 3.86051 | 0.431618 | ||||||||
\(81\) | −10.4185 | −1.15761 | ||||||||
\(82\) | −7.17921 | −0.792811 | ||||||||
\(83\) | 8.37314 | 0.919071 | 0.459536 | − | 0.888159i | \(-0.348016\pi\) | ||||
0.459536 | + | 0.888159i | \(0.348016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.22790 | −0.241650 | ||||||||
\(86\) | −0.378572 | −0.0408225 | ||||||||
\(87\) | 22.1300 | 2.37259 | ||||||||
\(88\) | −17.1833 | −1.83174 | ||||||||
\(89\) | 3.38479 | 0.358787 | 0.179394 | − | 0.983777i | \(-0.442586\pi\) | ||||
0.179394 | + | 0.983777i | \(0.442586\pi\) | |||||||
\(90\) | 2.25943 | 0.238165 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.5332 | 1.51519 | ||||||||
\(93\) | 2.32634 | 0.241230 | ||||||||
\(94\) | −9.33537 | −0.962870 | ||||||||
\(95\) | 1.00347 | 0.102954 | ||||||||
\(96\) | 30.2495 | 3.08732 | ||||||||
\(97\) | −2.32530 | −0.236098 | −0.118049 | − | 0.993008i | \(-0.537664\pi\) | ||||
−0.118049 | + | 0.993008i | \(0.537664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.24998 | −0.527643 | ||||||||
\(100\) | −24.3063 | −2.43063 | ||||||||
\(101\) | 8.90630 | 0.886210 | 0.443105 | − | 0.896470i | \(-0.353877\pi\) | ||||
0.443105 | + | 0.896470i | \(0.353877\pi\) | |||||||
\(102\) | −38.6530 | −3.82722 | ||||||||
\(103\) | 9.65162 | 0.951003 | 0.475501 | − | 0.879715i | \(-0.342267\pi\) | ||||
0.475501 | + | 0.879715i | \(0.342267\pi\) | |||||||
\(104\) | −39.4326 | −3.86669 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.4144 | −2.56559 | ||||||||
\(107\) | 15.1675 | 1.46630 | 0.733149 | − | 0.680068i | \(-0.238050\pi\) | ||||
0.733149 | + | 0.680068i | \(0.238050\pi\) | |||||||
\(108\) | −6.82270 | −0.656515 | ||||||||
\(109\) | 8.56409 | 0.820291 | 0.410146 | − | 0.912020i | \(-0.365478\pi\) | ||||
0.410146 | + | 0.912020i | \(0.365478\pi\) | |||||||
\(110\) | −2.03918 | −0.194428 | ||||||||
\(111\) | 11.1156 | 1.05505 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6566 | 1.00249 | 0.501243 | − | 0.865306i | \(-0.332876\pi\) | ||||
0.501243 | + | 0.865306i | \(0.332876\pi\) | |||||||
\(114\) | 17.4097 | 1.63057 | ||||||||
\(115\) | 1.03295 | 0.0963230 | ||||||||
\(116\) | 47.4359 | 4.40432 | ||||||||
\(117\) | −12.0478 | −1.11382 | ||||||||
\(118\) | 23.8564 | 2.19616 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.50863 | 0.594154 | ||||||||
\(121\) | −6.26181 | −0.569255 | ||||||||
\(122\) | −12.2160 | −1.10598 | ||||||||
\(123\) | −6.31857 | −0.569726 | ||||||||
\(124\) | 4.98654 | 0.447804 | ||||||||
\(125\) | −3.49967 | −0.313020 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.25322 | 0.111205 | 0.0556025 | − | 0.998453i | \(-0.482292\pi\) | ||||
0.0556025 | + | 0.998453i | \(0.482292\pi\) | |||||||
\(128\) | 7.25789 | 0.641513 | ||||||||
\(129\) | −0.333189 | −0.0293356 | ||||||||
\(130\) | −4.67956 | −0.410424 | ||||||||
\(131\) | 10.9897 | 0.960179 | 0.480089 | − | 0.877220i | \(-0.340604\pi\) | ||||
0.480089 | + | 0.877220i | \(0.340604\pi\) | |||||||
\(132\) | −25.2510 | −2.19782 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 37.1025 | 3.20517 | ||||||||
\(135\) | −0.484925 | −0.0417357 | ||||||||
\(136\) | −49.6225 | −4.25509 | ||||||||
\(137\) | −22.0369 | −1.88274 | −0.941370 | − | 0.337376i | \(-0.890461\pi\) | ||||
−0.941370 | + | 0.337376i | \(0.890461\pi\) | |||||||
\(138\) | 17.9211 | 1.52555 | ||||||||
\(139\) | 15.0380 | 1.27551 | 0.637754 | − | 0.770240i | \(-0.279864\pi\) | ||||
0.637754 | + | 0.770240i | \(0.279864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.21625 | −0.691933 | ||||||||
\(142\) | −21.4417 | −1.79935 | ||||||||
\(143\) | 10.8733 | 0.909274 | ||||||||
\(144\) | 26.2711 | 2.18926 | ||||||||
\(145\) | 3.37152 | 0.279989 | ||||||||
\(146\) | −19.9439 | −1.65057 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.8264 | 1.95852 | ||||||||
\(149\) | 1.69025 | 0.138471 | 0.0692354 | − | 0.997600i | \(-0.477944\pi\) | ||||
0.0692354 | + | 0.997600i | \(0.477944\pi\) | |||||||
\(150\) | −29.9726 | −2.44725 | ||||||||
\(151\) | 9.58645 | 0.780134 | 0.390067 | − | 0.920787i | \(-0.372452\pi\) | ||||
0.390067 | + | 0.920787i | \(0.372452\pi\) | |||||||
\(152\) | 22.3505 | 1.81286 | ||||||||
\(153\) | −15.1611 | −1.22570 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.354419 | 0.0284676 | ||||||||
\(156\) | −57.9467 | −4.63945 | ||||||||
\(157\) | 16.2134 | 1.29397 | 0.646987 | − | 0.762501i | \(-0.276029\pi\) | ||||
0.646987 | + | 0.762501i | \(0.276029\pi\) | |||||||
\(158\) | −14.0400 | −1.11696 | ||||||||
\(159\) | −23.2479 | −1.84367 | ||||||||
\(160\) | 4.60852 | 0.364336 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −27.5383 | −2.16361 | ||||||||
\(163\) | −13.0689 | −1.02364 | −0.511819 | − | 0.859093i | \(-0.671028\pi\) | ||||
−0.511819 | + | 0.859093i | \(0.671028\pi\) | |||||||
\(164\) | −13.5439 | −1.05760 | ||||||||
\(165\) | −1.79472 | −0.139719 | ||||||||
\(166\) | 22.1319 | 1.71777 | ||||||||
\(167\) | −8.26882 | −0.639860 | −0.319930 | − | 0.947441i | \(-0.603659\pi\) | ||||
−0.319930 | + | 0.947441i | \(0.603659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9524 | 0.919419 | ||||||||
\(170\) | −5.88881 | −0.451651 | ||||||||
\(171\) | 6.82872 | 0.522205 | ||||||||
\(172\) | −0.714195 | −0.0544568 | ||||||||
\(173\) | −2.35772 | −0.179254 | −0.0896272 | − | 0.995975i | \(-0.528568\pi\) | ||||
−0.0896272 | + | 0.995975i | \(0.528568\pi\) | |||||||
\(174\) | 58.4942 | 4.43443 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −23.7101 | −1.78722 | ||||||||
\(177\) | 20.9965 | 1.57820 | ||||||||
\(178\) | 8.94670 | 0.670584 | ||||||||
\(179\) | −6.84472 | −0.511599 | −0.255799 | − | 0.966730i | \(-0.582339\pi\) | ||||
−0.255799 | + | 0.966730i | \(0.582339\pi\) | |||||||
\(180\) | 4.26253 | 0.317710 | ||||||||
\(181\) | 16.4144 | 1.22007 | 0.610035 | − | 0.792375i | \(-0.291156\pi\) | ||||
0.610035 | + | 0.792375i | \(0.291156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7515 | −0.794776 | ||||||||
\(184\) | 23.0070 | 1.69610 | ||||||||
\(185\) | 1.69347 | 0.124506 | ||||||||
\(186\) | 6.14899 | 0.450866 | ||||||||
\(187\) | 13.6831 | 1.00061 | ||||||||
\(188\) | −17.6116 | −1.28446 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.65238 | 0.192424 | ||||||||
\(191\) | −1.87210 | −0.135461 | −0.0677303 | − | 0.997704i | \(-0.521576\pi\) | ||||
−0.0677303 | + | 0.997704i | \(0.521576\pi\) | |||||||
\(192\) | 29.2763 | 2.11283 | ||||||||
\(193\) | −14.2628 | −1.02666 | −0.513329 | − | 0.858192i | \(-0.671588\pi\) | ||||
−0.513329 | + | 0.858192i | \(0.671588\pi\) | |||||||
\(194\) | −6.14624 | −0.441274 | ||||||||
\(195\) | −4.11858 | −0.294937 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.9854 | −0.996419 | −0.498209 | − | 0.867057i | \(-0.666009\pi\) | ||||
−0.498209 | + | 0.867057i | \(0.666009\pi\) | |||||||
\(198\) | −13.8768 | −0.986179 | ||||||||
\(199\) | −13.6559 | −0.968040 | −0.484020 | − | 0.875057i | \(-0.660824\pi\) | ||||
−0.484020 | + | 0.875057i | \(0.660824\pi\) | |||||||
\(200\) | −38.4786 | −2.72085 | ||||||||
\(201\) | 32.6546 | 2.30328 | ||||||||
\(202\) | 23.5412 | 1.65635 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −72.9208 | −5.10548 | ||||||||
\(205\) | −0.962638 | −0.0672335 | ||||||||
\(206\) | 25.5112 | 1.77745 | ||||||||
\(207\) | 7.02931 | 0.488571 | ||||||||
\(208\) | −54.4106 | −3.77270 | ||||||||
\(209\) | −6.16303 | −0.426306 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2135 | −1.52924 | −0.764619 | − | 0.644483i | \(-0.777073\pi\) | ||||
−0.764619 | + | 0.644483i | \(0.777073\pi\) | |||||||
\(212\) | −49.8321 | −3.42248 | ||||||||
\(213\) | −18.8713 | −1.29304 | ||||||||
\(214\) | 40.0908 | 2.74055 | ||||||||
\(215\) | −0.0507615 | −0.00346191 | ||||||||
\(216\) | −10.8008 | −0.734902 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 22.6367 | 1.53315 | ||||||||
\(219\) | −17.5530 | −1.18612 | ||||||||
\(220\) | −3.84701 | −0.259365 | ||||||||
\(221\) | 31.4004 | 2.11222 | ||||||||
\(222\) | 29.3808 | 1.97191 | ||||||||
\(223\) | −21.7578 | −1.45701 | −0.728505 | − | 0.685040i | \(-0.759785\pi\) | ||||
−0.728505 | + | 0.685040i | \(0.759785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.7563 | −0.783754 | ||||||||
\(226\) | 28.1675 | 1.87368 | ||||||||
\(227\) | −1.54952 | −0.102845 | −0.0514226 | − | 0.998677i | \(-0.516376\pi\) | ||||
−0.0514226 | + | 0.998677i | \(0.516376\pi\) | |||||||
\(228\) | 32.8443 | 2.17517 | ||||||||
\(229\) | 1.69033 | 0.111700 | 0.0558502 | − | 0.998439i | \(-0.482213\pi\) | ||||
0.0558502 | + | 0.998439i | \(0.482213\pi\) | |||||||
\(230\) | 2.73030 | 0.180031 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 75.0944 | 4.93019 | ||||||||
\(233\) | −5.77383 | −0.378256 | −0.189128 | − | 0.981952i | \(-0.560566\pi\) | ||||
−0.189128 | + | 0.981952i | \(0.560566\pi\) | |||||||
\(234\) | −31.8448 | −2.08176 | ||||||||
\(235\) | −1.25175 | −0.0816552 | ||||||||
\(236\) | 45.0063 | 2.92966 | ||||||||
\(237\) | −12.3569 | −0.802666 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.6926 | 1.59723 | 0.798615 | − | 0.601842i | \(-0.205566\pi\) | ||||
0.798615 | + | 0.601842i | \(0.205566\pi\) | |||||||
\(240\) | 8.98085 | 0.579712 | ||||||||
\(241\) | −2.24466 | −0.144591 | −0.0722957 | − | 0.997383i | \(-0.523033\pi\) | ||||
−0.0722957 | + | 0.997383i | \(0.523033\pi\) | |||||||
\(242\) | −16.5513 | −1.06395 | ||||||||
\(243\) | −20.1323 | −1.29149 | ||||||||
\(244\) | −23.0460 | −1.47537 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.7013 | −1.06483 | ||||||||
\(247\) | −14.1431 | −0.899903 | ||||||||
\(248\) | 7.89404 | 0.501272 | ||||||||
\(249\) | 19.4788 | 1.23442 | ||||||||
\(250\) | −9.25036 | −0.585044 | ||||||||
\(251\) | 28.5981 | 1.80510 | 0.902549 | − | 0.430588i | \(-0.141694\pi\) | ||||
0.902549 | + | 0.430588i | \(0.141694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.34407 | −0.398848 | ||||||||
\(254\) | 3.31251 | 0.207845 | ||||||||
\(255\) | −5.18286 | −0.324563 | ||||||||
\(256\) | −5.98529 | −0.374081 | ||||||||
\(257\) | −19.2512 | −1.20086 | −0.600429 | − | 0.799678i | \(-0.705004\pi\) | ||||
−0.600429 | + | 0.799678i | \(0.705004\pi\) | |||||||
\(258\) | −0.880687 | −0.0548292 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.82822 | −0.547503 | ||||||||
\(261\) | 22.9435 | 1.42017 | ||||||||
\(262\) | 29.0482 | 1.79460 | ||||||||
\(263\) | 11.7553 | 0.724865 | 0.362433 | − | 0.932010i | \(-0.381946\pi\) | ||||
0.362433 | + | 0.932010i | \(0.381946\pi\) | |||||||
\(264\) | −39.9741 | −2.46023 | ||||||||
\(265\) | −3.54183 | −0.217573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.87418 | 0.481892 | ||||||||
\(268\) | 69.9956 | 4.27566 | ||||||||
\(269\) | −10.4927 | −0.639753 | −0.319876 | − | 0.947459i | \(-0.603641\pi\) | ||||
−0.319876 | + | 0.947459i | \(0.603641\pi\) | |||||||
\(270\) | −1.28176 | −0.0780052 | ||||||||
\(271\) | −8.69159 | −0.527976 | −0.263988 | − | 0.964526i | \(-0.585038\pi\) | ||||
−0.263988 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(272\) | −68.4709 | −4.15166 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −58.2481 | −3.51890 | ||||||||
\(275\) | 10.6103 | 0.639823 | ||||||||
\(276\) | 33.8091 | 2.03507 | ||||||||
\(277\) | −5.99620 | −0.360277 | −0.180139 | − | 0.983641i | \(-0.557655\pi\) | ||||
−0.180139 | + | 0.983641i | \(0.557655\pi\) | |||||||
\(278\) | 39.7486 | 2.38396 | ||||||||
\(279\) | 2.41186 | 0.144394 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3627 | 1.51301 | 0.756506 | − | 0.653986i | \(-0.226905\pi\) | ||||
0.756506 | + | 0.653986i | \(0.226905\pi\) | |||||||
\(282\) | −21.7172 | −1.29324 | ||||||||
\(283\) | 6.67371 | 0.396711 | 0.198356 | − | 0.980130i | \(-0.436440\pi\) | ||||
0.198356 | + | 0.980130i | \(0.436440\pi\) | |||||||
\(284\) | −40.4509 | −2.40032 | ||||||||
\(285\) | 2.33442 | 0.138279 | ||||||||
\(286\) | 28.7405 | 1.69946 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 31.3614 | 1.84799 | ||||||||
\(289\) | 22.5147 | 1.32439 | ||||||||
\(290\) | 8.91162 | 0.523308 | ||||||||
\(291\) | −5.40943 | −0.317106 | ||||||||
\(292\) | −37.6251 | −2.20185 | ||||||||
\(293\) | 4.55839 | 0.266304 | 0.133152 | − | 0.991096i | \(-0.457490\pi\) | ||||
0.133152 | + | 0.991096i | \(0.457490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.19883 | 0.186243 | ||||||||
\(296\) | 37.7189 | 2.19237 | ||||||||
\(297\) | 2.97827 | 0.172817 | ||||||||
\(298\) | 4.46768 | 0.258806 | ||||||||
\(299\) | −14.5586 | −0.841943 | ||||||||
\(300\) | −56.5448 | −3.26461 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 25.3390 | 1.45809 | ||||||||
\(303\) | 20.7191 | 1.19028 | ||||||||
\(304\) | 30.8401 | 1.76880 | ||||||||
\(305\) | −1.63800 | −0.0937918 | ||||||||
\(306\) | −40.0739 | −2.29087 | ||||||||
\(307\) | 30.0271 | 1.71374 | 0.856869 | − | 0.515534i | \(-0.172407\pi\) | ||||
0.856869 | + | 0.515534i | \(0.172407\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.4529 | 1.27730 | ||||||||
\(310\) | 0.936803 | 0.0532068 | ||||||||
\(311\) | −18.9801 | −1.07626 | −0.538131 | − | 0.842861i | \(-0.680870\pi\) | ||||
−0.538131 | + | 0.842861i | \(0.680870\pi\) | |||||||
\(312\) | −91.7337 | −5.19340 | ||||||||
\(313\) | −10.8415 | −0.612799 | −0.306399 | − | 0.951903i | \(-0.599124\pi\) | ||||
−0.306399 | + | 0.951903i | \(0.599124\pi\) | |||||||
\(314\) | 42.8555 | 2.41847 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.4871 | −1.49002 | ||||||||
\(317\) | −2.74924 | −0.154413 | −0.0772063 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772063 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(318\) | −61.4489 | −3.44588 | ||||||||
\(319\) | −20.7069 | −1.15936 | ||||||||
\(320\) | 4.46026 | 0.249336 | ||||||||
\(321\) | 35.2848 | 1.96940 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.7978 | −0.990298 | ||||||||
\(324\) | −51.9524 | −2.88624 | ||||||||
\(325\) | 24.3487 | 1.35063 | ||||||||
\(326\) | −34.5439 | −1.91321 | ||||||||
\(327\) | 19.9230 | 1.10174 | ||||||||
\(328\) | −21.4410 | −1.18388 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.74381 | −0.261138 | ||||||||
\(331\) | −24.0874 | −1.32396 | −0.661981 | − | 0.749521i | \(-0.730284\pi\) | ||||
−0.661981 | + | 0.749521i | \(0.730284\pi\) | |||||||
\(332\) | 41.7530 | 2.29149 | ||||||||
\(333\) | 11.5242 | 0.631522 | ||||||||
\(334\) | −21.8562 | −1.19592 | ||||||||
\(335\) | 4.97496 | 0.271811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50464 | 0.245383 | 0.122692 | − | 0.992445i | \(-0.460847\pi\) | ||||
0.122692 | + | 0.992445i | \(0.460847\pi\) | |||||||
\(338\) | 31.5928 | 1.71842 | ||||||||
\(339\) | 24.7908 | 1.34645 | ||||||||
\(340\) | −11.1095 | −0.602499 | ||||||||
\(341\) | −2.17674 | −0.117877 | ||||||||
\(342\) | 18.0497 | 0.976016 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.13062 | −0.0609589 | ||||||||
\(345\) | 2.40299 | 0.129373 | ||||||||
\(346\) | −6.23195 | −0.335032 | ||||||||
\(347\) | −0.446505 | −0.0239697 | −0.0119848 | − | 0.999928i | \(-0.503815\pi\) | ||||
−0.0119848 | + | 0.999928i | \(0.503815\pi\) | |||||||
\(348\) | 110.352 | 5.91549 | ||||||||
\(349\) | −11.7175 | −0.627221 | −0.313611 | − | 0.949552i | \(-0.601539\pi\) | ||||
−0.313611 | + | 0.949552i | \(0.601539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.83461 | 0.364805 | ||||||||
\(352\) | −28.3042 | −1.50862 | ||||||||
\(353\) | 16.3366 | 0.869510 | 0.434755 | − | 0.900549i | \(-0.356835\pi\) | ||||
0.434755 | + | 0.900549i | \(0.356835\pi\) | |||||||
\(354\) | 55.4982 | 2.94969 | ||||||||
\(355\) | −2.87505 | −0.152592 | ||||||||
\(356\) | 16.8784 | 0.894553 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.0920 | −0.956193 | ||||||||
\(359\) | −3.86854 | −0.204174 | −0.102087 | − | 0.994775i | \(-0.532552\pi\) | ||||
−0.102087 | + | 0.994775i | \(0.532552\pi\) | |||||||
\(360\) | 6.74789 | 0.355645 | ||||||||
\(361\) | −10.9837 | −0.578088 | ||||||||
\(362\) | 43.3865 | 2.28034 | ||||||||
\(363\) | −14.5671 | −0.764574 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.67422 | −0.139975 | ||||||||
\(366\) | −28.4185 | −1.48546 | ||||||||
\(367\) | −1.67607 | −0.0874901 | −0.0437451 | − | 0.999043i | \(-0.513929\pi\) | ||||
−0.0437451 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(368\) | 31.7460 | 1.65487 | ||||||||
\(369\) | −6.55084 | −0.341023 | ||||||||
\(370\) | 4.47618 | 0.232706 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 11.6004 | 0.601452 | ||||||||
\(373\) | −10.0023 | −0.517898 | −0.258949 | − | 0.965891i | \(-0.583376\pi\) | ||||
−0.258949 | + | 0.965891i | \(0.583376\pi\) | |||||||
\(374\) | 36.1673 | 1.87017 | ||||||||
\(375\) | −8.14143 | −0.420422 | ||||||||
\(376\) | −27.8804 | −1.43782 | ||||||||
\(377\) | −47.5187 | −2.44734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.64969 | 0.238839 | 0.119419 | − | 0.992844i | \(-0.461897\pi\) | ||||
0.119419 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(380\) | 5.00385 | 0.256692 | ||||||||
\(381\) | 2.91541 | 0.149361 | ||||||||
\(382\) | −4.94836 | −0.253180 | ||||||||
\(383\) | −9.65621 | −0.493409 | −0.246705 | − | 0.969091i | \(-0.579348\pi\) | ||||
−0.246705 | + | 0.969091i | \(0.579348\pi\) | |||||||
\(384\) | 16.8843 | 0.861624 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.6995 | −1.91885 | ||||||||
\(387\) | −0.345437 | −0.0175595 | ||||||||
\(388\) | −11.5952 | −0.588656 | ||||||||
\(389\) | 8.28222 | 0.419925 | 0.209963 | − | 0.977709i | \(-0.432666\pi\) | ||||
0.209963 | + | 0.977709i | \(0.432666\pi\) | |||||||
\(390\) | −10.8862 | −0.551246 | ||||||||
\(391\) | −18.3206 | −0.926515 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.5659 | 1.28963 | ||||||||
\(394\) | −36.9663 | −1.86234 | ||||||||
\(395\) | −1.88258 | −0.0947228 | ||||||||
\(396\) | −26.1792 | −1.31556 | ||||||||
\(397\) | −7.08145 | −0.355408 | −0.177704 | − | 0.984084i | \(-0.556867\pi\) | ||||
−0.177704 | + | 0.984084i | \(0.556867\pi\) | |||||||
\(398\) | −36.0953 | −1.80929 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −53.0942 | −2.65471 | ||||||||
\(401\) | 5.70335 | 0.284812 | 0.142406 | − | 0.989808i | \(-0.454516\pi\) | ||||
0.142406 | + | 0.989808i | \(0.454516\pi\) | |||||||
\(402\) | 86.3129 | 4.30490 | ||||||||
\(403\) | −4.99524 | −0.248831 | ||||||||
\(404\) | 44.4116 | 2.20956 | ||||||||
\(405\) | −3.69252 | −0.183483 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4008 | −0.515547 | ||||||||
\(408\) | −115.439 | −5.71507 | ||||||||
\(409\) | 6.64606 | 0.328626 | 0.164313 | − | 0.986408i | \(-0.447459\pi\) | ||||
0.164313 | + | 0.986408i | \(0.447459\pi\) | |||||||
\(410\) | −2.54445 | −0.125661 | ||||||||
\(411\) | −51.2653 | −2.52873 | ||||||||
\(412\) | 48.1282 | 2.37111 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.5799 | 0.913154 | ||||||||
\(415\) | 2.96760 | 0.145674 | ||||||||
\(416\) | −64.9533 | −3.18460 | ||||||||
\(417\) | 34.9835 | 1.71315 | ||||||||
\(418\) | −16.2902 | −0.796777 | ||||||||
\(419\) | 9.06221 | 0.442718 | 0.221359 | − | 0.975192i | \(-0.428951\pi\) | ||||
0.221359 | + | 0.975192i | \(0.428951\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.93098 | −0.240321 | −0.120161 | − | 0.992754i | \(-0.538341\pi\) | ||||
−0.120161 | + | 0.992754i | \(0.538341\pi\) | |||||||
\(422\) | −58.7147 | −2.85819 | ||||||||
\(423\) | −8.51828 | −0.414173 | ||||||||
\(424\) | −78.8877 | −3.83112 | ||||||||
\(425\) | 30.6407 | 1.48629 | ||||||||
\(426\) | −49.8807 | −2.41673 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 75.6333 | 3.65588 | ||||||||
\(429\) | 25.2951 | 1.22126 | ||||||||
\(430\) | −0.134173 | −0.00647041 | ||||||||
\(431\) | 25.4703 | 1.22686 | 0.613430 | − | 0.789749i | \(-0.289789\pi\) | ||||
0.613430 | + | 0.789749i | \(0.289789\pi\) | |||||||
\(432\) | −14.9034 | −0.717039 | ||||||||
\(433\) | 9.39902 | 0.451688 | 0.225844 | − | 0.974163i | \(-0.427486\pi\) | ||||
0.225844 | + | 0.974163i | \(0.427486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.84330 | 0.376057 | ||||||||
\(436\) | 42.7052 | 2.04521 | ||||||||
\(437\) | 8.25182 | 0.394738 | ||||||||
\(438\) | −46.3963 | −2.21690 | ||||||||
\(439\) | 39.9665 | 1.90749 | 0.953747 | − | 0.300609i | \(-0.0971900\pi\) | ||||
0.953747 | + | 0.300609i | \(0.0971900\pi\) | |||||||
\(440\) | −6.09008 | −0.290333 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 82.9978 | 3.94780 | ||||||||
\(443\) | 14.2263 | 0.675911 | 0.337955 | − | 0.941162i | \(-0.390265\pi\) | ||||
0.337955 | + | 0.941162i | \(0.390265\pi\) | |||||||
\(444\) | 55.4283 | 2.63051 | ||||||||
\(445\) | 1.19964 | 0.0568682 | ||||||||
\(446\) | −57.5104 | −2.72320 | ||||||||
\(447\) | 3.93210 | 0.185982 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.38464 | −0.0653451 | −0.0326726 | − | 0.999466i | \(-0.510402\pi\) | ||||
−0.0326726 | + | 0.999466i | \(0.510402\pi\) | |||||||
\(450\) | −31.0744 | −1.46486 | ||||||||
\(451\) | 5.91224 | 0.278396 | ||||||||
\(452\) | 53.1395 | 2.49947 | ||||||||
\(453\) | 22.3013 | 1.04781 | ||||||||
\(454\) | −4.09570 | −0.192221 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 51.9948 | 2.43488 | ||||||||
\(457\) | −17.5760 | −0.822168 | −0.411084 | − | 0.911597i | \(-0.634850\pi\) | ||||
−0.411084 | + | 0.911597i | \(0.634850\pi\) | |||||||
\(458\) | 4.46790 | 0.208771 | ||||||||
\(459\) | 8.60075 | 0.401449 | ||||||||
\(460\) | 5.15084 | 0.240159 | ||||||||
\(461\) | −27.1063 | −1.26247 | −0.631234 | − | 0.775593i | \(-0.717451\pi\) | ||||
−0.631234 | + | 0.775593i | \(0.717451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.7308 | −0.870494 | −0.435247 | − | 0.900311i | \(-0.643339\pi\) | ||||
−0.435247 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(464\) | 103.618 | 4.81035 | ||||||||
\(465\) | 0.824500 | 0.0382353 | ||||||||
\(466\) | −15.2614 | −0.706972 | ||||||||
\(467\) | −10.2196 | −0.472904 | −0.236452 | − | 0.971643i | \(-0.575985\pi\) | ||||
−0.236452 | + | 0.971643i | \(0.575985\pi\) | |||||||
\(468\) | −60.0768 | −2.77705 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.30863 | −0.152616 | ||||||||
\(471\) | 37.7180 | 1.73795 | ||||||||
\(472\) | 71.2482 | 3.27946 | ||||||||
\(473\) | 0.311762 | 0.0143348 | ||||||||
\(474\) | −32.6618 | −1.50021 | ||||||||
\(475\) | −13.8009 | −0.633229 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.1024 | −1.10358 | ||||||||
\(478\) | 65.2676 | 2.98527 | ||||||||
\(479\) | −24.4638 | −1.11778 | −0.558889 | − | 0.829242i | \(-0.688772\pi\) | ||||
−0.558889 | + | 0.829242i | \(0.688772\pi\) | |||||||
\(480\) | 10.7210 | 0.489344 | ||||||||
\(481\) | −23.8680 | −1.08829 | ||||||||
\(482\) | −5.93310 | −0.270245 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.2248 | −1.41931 | ||||||||
\(485\) | −0.824130 | −0.0374218 | ||||||||
\(486\) | −53.2139 | −2.41383 | ||||||||
\(487\) | 4.39995 | 0.199381 | 0.0996905 | − | 0.995018i | \(-0.468215\pi\) | ||||
0.0996905 | + | 0.995018i | \(0.468215\pi\) | |||||||
\(488\) | −36.4835 | −1.65153 | ||||||||
\(489\) | −30.4028 | −1.37486 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9170 | 1.21475 | 0.607374 | − | 0.794416i | \(-0.292223\pi\) | ||||
0.607374 | + | 0.794416i | \(0.292223\pi\) | |||||||
\(492\) | −31.5078 | −1.42048 | ||||||||
\(493\) | −59.7981 | −2.69317 | ||||||||
\(494\) | −37.3831 | −1.68195 | ||||||||
\(495\) | −1.86069 | −0.0836320 | ||||||||
\(496\) | 10.8925 | 0.489087 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 51.4864 | 2.30716 | ||||||||
\(499\) | 0.0837718 | 0.00375014 | 0.00187507 | − | 0.999998i | \(-0.499403\pi\) | ||||
0.00187507 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(500\) | −17.4513 | −0.780444 | ||||||||
\(501\) | −19.2361 | −0.859404 | ||||||||
\(502\) | 75.5907 | 3.37378 | ||||||||
\(503\) | −3.94084 | −0.175713 | −0.0878566 | − | 0.996133i | \(-0.528002\pi\) | ||||
−0.0878566 | + | 0.996133i | \(0.528002\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.15657 | 0.140465 | ||||||||
\(506\) | −16.7687 | −0.745459 | ||||||||
\(507\) | 27.8054 | 1.23488 | ||||||||
\(508\) | 6.24921 | 0.277264 | ||||||||
\(509\) | −8.81784 | −0.390844 | −0.195422 | − | 0.980719i | \(-0.562608\pi\) | ||||
−0.195422 | + | 0.980719i | \(0.562608\pi\) | |||||||
\(510\) | −13.6994 | −0.606618 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −30.3361 | −1.34068 | ||||||||
\(513\) | −3.87387 | −0.171036 | ||||||||
\(514\) | −50.8850 | −2.24444 | ||||||||
\(515\) | 3.42072 | 0.150735 | ||||||||
\(516\) | −1.66146 | −0.0731417 | ||||||||
\(517\) | 7.68788 | 0.338113 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.48486 | −0.240759 | ||||||||
\(520\) | −13.9757 | −0.612874 | ||||||||
\(521\) | −13.4148 | −0.587712 | −0.293856 | − | 0.955850i | \(-0.594939\pi\) | ||||
−0.293856 | + | 0.955850i | \(0.594939\pi\) | |||||||
\(522\) | 60.6444 | 2.65433 | ||||||||
\(523\) | −17.7610 | −0.776635 | −0.388318 | − | 0.921526i | \(-0.626944\pi\) | ||||
−0.388318 | + | 0.921526i | \(0.626944\pi\) | |||||||
\(524\) | 54.8008 | 2.39398 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.0718 | 1.35479 | ||||||||
\(527\) | −6.28607 | −0.273825 | ||||||||
\(528\) | −55.1578 | −2.40043 | ||||||||
\(529\) | −14.5058 | −0.630686 | ||||||||
\(530\) | −9.36178 | −0.406650 | ||||||||
\(531\) | 21.7684 | 0.944666 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5676 | 0.587677 | ||||||||
\(534\) | 20.8131 | 0.900670 | ||||||||
\(535\) | 5.37566 | 0.232410 | ||||||||
\(536\) | 110.808 | 4.78618 | ||||||||
\(537\) | −15.9231 | −0.687135 | ||||||||
\(538\) | −27.7344 | −1.19572 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.41810 | −0.104058 | ||||||||
\(541\) | −10.5221 | −0.452378 | −0.226189 | − | 0.974083i | \(-0.572627\pi\) | ||||
−0.226189 | + | 0.974083i | \(0.572627\pi\) | |||||||
\(542\) | −22.9737 | −0.986803 | ||||||||
\(543\) | 38.1854 | 1.63869 | ||||||||
\(544\) | −81.7379 | −3.50448 | ||||||||
\(545\) | 3.03528 | 0.130017 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2290 | 1.03596 | 0.517978 | − | 0.855394i | \(-0.326685\pi\) | ||||
0.517978 | + | 0.855394i | \(0.326685\pi\) | |||||||
\(548\) | −109.888 | −4.69418 | ||||||||
\(549\) | −11.1468 | −0.475732 | ||||||||
\(550\) | 28.0451 | 1.19585 | ||||||||
\(551\) | 26.9337 | 1.14741 | ||||||||
\(552\) | 53.5222 | 2.27806 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.8492 | −0.673368 | ||||||||
\(555\) | 3.93958 | 0.167226 | ||||||||
\(556\) | 74.9877 | 3.18019 | ||||||||
\(557\) | −22.7619 | −0.964453 | −0.482227 | − | 0.876047i | \(-0.660172\pi\) | ||||
−0.482227 | + | 0.876047i | \(0.660172\pi\) | |||||||
\(558\) | 6.37503 | 0.269877 | ||||||||
\(559\) | 0.715441 | 0.0302599 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.8316 | 1.34393 | ||||||||
\(562\) | 67.0389 | 2.82786 | ||||||||
\(563\) | −18.6412 | −0.785633 | −0.392816 | − | 0.919617i | \(-0.628499\pi\) | ||||
−0.392816 | + | 0.919617i | \(0.628499\pi\) | |||||||
\(564\) | −40.9706 | −1.72518 | ||||||||
\(565\) | 3.77690 | 0.158895 | ||||||||
\(566\) | 17.6400 | 0.741465 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −64.0366 | −2.68691 | ||||||||
\(569\) | 19.7690 | 0.828760 | 0.414380 | − | 0.910104i | \(-0.363999\pi\) | ||||
0.414380 | + | 0.910104i | \(0.363999\pi\) | |||||||
\(570\) | 6.17034 | 0.258447 | ||||||||
\(571\) | −19.6037 | −0.820391 | −0.410196 | − | 0.911998i | \(-0.634540\pi\) | ||||
−0.410196 | + | 0.911998i | \(0.634540\pi\) | |||||||
\(572\) | 54.2203 | 2.26707 | ||||||||
\(573\) | −4.35515 | −0.181939 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.2063 | −0.592445 | ||||||||
\(576\) | 30.3525 | 1.26469 | ||||||||
\(577\) | 2.06307 | 0.0858865 | 0.0429433 | − | 0.999078i | \(-0.486327\pi\) | ||||
0.0429433 | + | 0.999078i | \(0.486327\pi\) | |||||||
\(578\) | 59.5109 | 2.47533 | ||||||||
\(579\) | −33.1801 | −1.37892 | ||||||||
\(580\) | 16.8122 | 0.698089 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −14.2982 | −0.592681 | ||||||||
\(583\) | 21.7528 | 0.900911 | ||||||||
\(584\) | −59.5632 | −2.46474 | ||||||||
\(585\) | −4.26997 | −0.176542 | ||||||||
\(586\) | 12.0488 | 0.497729 | ||||||||
\(587\) | 9.20613 | 0.379978 | 0.189989 | − | 0.981786i | \(-0.439155\pi\) | ||||
0.189989 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.83131 | 0.116662 | ||||||||
\(590\) | 8.45518 | 0.348094 | ||||||||
\(591\) | −32.5348 | −1.33830 | ||||||||
\(592\) | 52.0459 | 2.13907 | ||||||||
\(593\) | 42.7927 | 1.75729 | 0.878643 | − | 0.477479i | \(-0.158449\pi\) | ||||
0.878643 | + | 0.477479i | \(0.158449\pi\) | |||||||
\(594\) | 7.87217 | 0.322999 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.42850 | 0.345245 | ||||||||
\(597\) | −31.7682 | −1.30019 | ||||||||
\(598\) | −38.4813 | −1.57362 | ||||||||
\(599\) | 14.9797 | 0.612052 | 0.306026 | − | 0.952023i | \(-0.401000\pi\) | ||||
0.306026 | + | 0.952023i | \(0.401000\pi\) | |||||||
\(600\) | −89.5143 | −3.65440 | ||||||||
\(601\) | 35.5248 | 1.44909 | 0.724544 | − | 0.689228i | \(-0.242050\pi\) | ||||
0.724544 | + | 0.689228i | \(0.242050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.8550 | 1.37868 | ||||||||
\(604\) | 47.8032 | 1.94508 | ||||||||
\(605\) | −2.21931 | −0.0902276 | ||||||||
\(606\) | 54.7648 | 2.22467 | ||||||||
\(607\) | −33.2770 | −1.35067 | −0.675336 | − | 0.737510i | \(-0.736001\pi\) | ||||
−0.675336 | + | 0.737510i | \(0.736001\pi\) | |||||||
\(608\) | 36.8156 | 1.49307 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.32958 | −0.175300 | ||||||||
\(611\) | 17.6424 | 0.713734 | ||||||||
\(612\) | −75.6014 | −3.05600 | ||||||||
\(613\) | 40.1397 | 1.62123 | 0.810614 | − | 0.585581i | \(-0.199134\pi\) | ||||
0.810614 | + | 0.585581i | \(0.199134\pi\) | |||||||
\(614\) | 79.3679 | 3.20303 | ||||||||
\(615\) | −2.23942 | −0.0903022 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.7106 | −0.793518 | −0.396759 | − | 0.917923i | \(-0.629865\pi\) | ||||
−0.396759 | + | 0.917923i | \(0.629865\pi\) | |||||||
\(618\) | 59.3478 | 2.38732 | ||||||||
\(619\) | 19.5282 | 0.784906 | 0.392453 | − | 0.919772i | \(-0.371627\pi\) | ||||
0.392453 | + | 0.919772i | \(0.371627\pi\) | |||||||
\(620\) | 1.76733 | 0.0709775 | ||||||||
\(621\) | −3.98767 | −0.160020 | ||||||||
\(622\) | −50.1683 | −2.01157 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −126.578 | −5.06716 | ||||||||
\(625\) | 23.1316 | 0.925263 | ||||||||
\(626\) | −28.6564 | −1.14534 | ||||||||
\(627\) | −14.3373 | −0.572576 | ||||||||
\(628\) | 80.8489 | 3.22622 | ||||||||
\(629\) | −30.0358 | −1.19760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8837 | −0.512891 | −0.256446 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256446 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(632\) | −41.9310 | −1.66793 | ||||||||
\(633\) | −51.6760 | −2.05394 | ||||||||
\(634\) | −7.26680 | −0.288601 | ||||||||
\(635\) | 0.444164 | 0.0176261 | ||||||||
\(636\) | −115.926 | −4.59678 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −54.7325 | −2.16688 | ||||||||
\(639\) | −19.5650 | −0.773980 | ||||||||
\(640\) | 2.57234 | 0.101680 | ||||||||
\(641\) | 40.3069 | 1.59203 | 0.796013 | − | 0.605280i | \(-0.206939\pi\) | ||||
0.796013 | + | 0.605280i | \(0.206939\pi\) | |||||||
\(642\) | 93.2649 | 3.68087 | ||||||||
\(643\) | −4.71734 | −0.186034 | −0.0930169 | − | 0.995665i | \(-0.529651\pi\) | ||||
−0.0930169 | + | 0.995665i | \(0.529651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.118089 | −0.00464973 | ||||||||
\(646\) | −47.0433 | −1.85089 | ||||||||
\(647\) | 12.1692 | 0.478420 | 0.239210 | − | 0.970968i | \(-0.423112\pi\) | ||||
0.239210 | + | 0.970968i | \(0.423112\pi\) | |||||||
\(648\) | −82.2442 | −3.23086 | ||||||||
\(649\) | −19.6463 | −0.771185 | ||||||||
\(650\) | 64.3588 | 2.52436 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −65.1687 | −2.55220 | ||||||||
\(653\) | 5.64254 | 0.220810 | 0.110405 | − | 0.993887i | \(-0.464785\pi\) | ||||
0.110405 | + | 0.993887i | \(0.464785\pi\) | |||||||
\(654\) | 52.6605 | 2.05919 | ||||||||
\(655\) | 3.89498 | 0.152189 | ||||||||
\(656\) | −29.5851 | −1.15510 | ||||||||
\(657\) | −18.1983 | −0.709982 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.3995 | −0.716742 | −0.358371 | − | 0.933579i | \(-0.616668\pi\) | ||||
−0.358371 | + | 0.933579i | \(0.616668\pi\) | |||||||
\(660\) | −8.94944 | −0.348357 | ||||||||
\(661\) | −29.4676 | −1.14616 | −0.573079 | − | 0.819500i | \(-0.694251\pi\) | ||||
−0.573079 | + | 0.819500i | \(0.694251\pi\) | |||||||
\(662\) | −63.6679 | −2.47452 | ||||||||
\(663\) | 73.0481 | 2.83695 | ||||||||
\(664\) | 66.0979 | 2.56510 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.4608 | 1.18033 | ||||||||
\(667\) | 27.7249 | 1.07351 | ||||||||
\(668\) | −41.2328 | −1.59534 | ||||||||
\(669\) | −50.6160 | −1.95693 | ||||||||
\(670\) | 13.1498 | 0.508022 | ||||||||
\(671\) | 10.0601 | 0.388367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.7875 | 0.916940 | 0.458470 | − | 0.888710i | \(-0.348398\pi\) | ||||
0.458470 | + | 0.888710i | \(0.348398\pi\) | |||||||
\(674\) | 11.9067 | 0.458628 | ||||||||
\(675\) | 6.66925 | 0.256700 | ||||||||
\(676\) | 59.6013 | 2.29236 | ||||||||
\(677\) | −17.6902 | −0.679891 | −0.339945 | − | 0.940445i | \(-0.610409\pi\) | ||||
−0.339945 | + | 0.940445i | \(0.610409\pi\) | |||||||
\(678\) | 65.5273 | 2.51656 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −17.5872 | −0.674437 | ||||||||
\(681\) | −3.60471 | −0.138133 | ||||||||
\(682\) | −5.75357 | −0.220316 | ||||||||
\(683\) | −15.6996 | −0.600728 | −0.300364 | − | 0.953825i | \(-0.597108\pi\) | ||||
−0.300364 | + | 0.953825i | \(0.597108\pi\) | |||||||
\(684\) | 34.0517 | 1.30200 | ||||||||
\(685\) | −7.81031 | −0.298416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.93229 | 0.150026 | ||||||||
\(688\) | −1.56007 | −0.0594772 | ||||||||
\(689\) | 49.9191 | 1.90176 | ||||||||
\(690\) | 6.35160 | 0.241801 | ||||||||
\(691\) | 45.6324 | 1.73594 | 0.867969 | − | 0.496618i | \(-0.165425\pi\) | ||||
0.867969 | + | 0.496618i | \(0.165425\pi\) | |||||||
\(692\) | −11.7569 | −0.446929 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.18021 | −0.0448000 | ||||||||
\(695\) | 5.32976 | 0.202169 | ||||||||
\(696\) | 174.695 | 6.62180 | ||||||||
\(697\) | 17.0736 | 0.646708 | ||||||||
\(698\) | −30.9717 | −1.17230 | ||||||||
\(699\) | −13.4319 | −0.508041 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.6332 | 1.61023 | 0.805116 | − | 0.593117i | \(-0.202103\pi\) | ||||
0.805116 | + | 0.593117i | \(0.202103\pi\) | |||||||
\(702\) | 18.0653 | 0.681830 | ||||||||
\(703\) | 13.5284 | 0.510234 | ||||||||
\(704\) | −27.3936 | −1.03243 | ||||||||
\(705\) | −2.91200 | −0.109672 | ||||||||
\(706\) | 43.1810 | 1.62514 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 104.700 | 3.93487 | ||||||||
\(709\) | −11.5388 | −0.433351 | −0.216675 | − | 0.976244i | \(-0.569521\pi\) | ||||
−0.216675 | + | 0.976244i | \(0.569521\pi\) | |||||||
\(710\) | −7.59936 | −0.285199 | ||||||||
\(711\) | −12.8111 | −0.480455 | ||||||||
\(712\) | 26.7197 | 1.00136 | ||||||||
\(713\) | 2.91448 | 0.109148 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.85372 | 0.144121 | ||||||||
\(716\) | −34.1315 | −1.27555 | ||||||||
\(717\) | 57.4433 | 2.14526 | ||||||||
\(718\) | −10.2254 | −0.381607 | ||||||||
\(719\) | −9.19248 | −0.342822 | −0.171411 | − | 0.985200i | \(-0.554833\pi\) | ||||
−0.171411 | + | 0.985200i | \(0.554833\pi\) | |||||||
\(720\) | 9.31099 | 0.347000 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29.0321 | −1.08046 | ||||||||
\(723\) | −5.22185 | −0.194203 | ||||||||
\(724\) | 81.8508 | 3.04196 | ||||||||
\(725\) | −46.3691 | −1.72210 | ||||||||
\(726\) | −38.5038 | −1.42901 | ||||||||
\(727\) | −31.3235 | −1.16172 | −0.580862 | − | 0.814002i | \(-0.697284\pi\) | ||||
−0.580862 | + | 0.814002i | \(0.697284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.5791 | −0.577004 | ||||||||
\(730\) | −7.06850 | −0.261617 | ||||||||
\(731\) | 0.900319 | 0.0332995 | ||||||||
\(732\) | −53.6129 | −1.98159 | ||||||||
\(733\) | 39.9736 | 1.47646 | 0.738229 | − | 0.674550i | \(-0.235662\pi\) | ||||
0.738229 | + | 0.674550i | \(0.235662\pi\) | |||||||
\(734\) | −4.43020 | −0.163522 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.8971 | 1.39691 | ||||||||
\(737\) | −30.5547 | −1.12550 | ||||||||
\(738\) | −17.3152 | −0.637382 | ||||||||
\(739\) | −6.97061 | −0.256418 | −0.128209 | − | 0.991747i | \(-0.540923\pi\) | ||||
−0.128209 | + | 0.991747i | \(0.540923\pi\) | |||||||
\(740\) | 8.44454 | 0.310428 | ||||||||
\(741\) | −32.9016 | −1.20867 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0493 | −0.442046 | −0.221023 | − | 0.975269i | \(-0.570940\pi\) | ||||
−0.221023 | + | 0.975269i | \(0.570940\pi\) | |||||||
\(744\) | 18.3642 | 0.673265 | ||||||||
\(745\) | 0.599058 | 0.0219478 | ||||||||
\(746\) | −26.4381 | −0.967967 | ||||||||
\(747\) | 20.1948 | 0.738889 | ||||||||
\(748\) | 68.2314 | 2.49479 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −21.5195 | −0.785780 | ||||||||
\(751\) | −9.96963 | −0.363797 | −0.181898 | − | 0.983317i | \(-0.558224\pi\) | ||||
−0.181898 | + | 0.983317i | \(0.558224\pi\) | |||||||
\(752\) | −38.4705 | −1.40287 | ||||||||
\(753\) | 66.5289 | 2.42445 | ||||||||
\(754\) | −125.602 | −4.57415 | ||||||||
\(755\) | 3.39762 | 0.123652 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.7659 | −1.88146 | −0.940732 | − | 0.339151i | \(-0.889860\pi\) | ||||
−0.940732 | + | 0.339151i | \(0.889860\pi\) | |||||||
\(758\) | 12.2901 | 0.446396 | ||||||||
\(759\) | −14.7585 | −0.535698 | ||||||||
\(760\) | 7.92144 | 0.287341 | ||||||||
\(761\) | −21.8136 | −0.790741 | −0.395371 | − | 0.918522i | \(-0.629384\pi\) | ||||
−0.395371 | + | 0.918522i | \(0.629384\pi\) | |||||||
\(762\) | 7.70602 | 0.279160 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.33532 | −0.337740 | ||||||||
\(765\) | −5.37338 | −0.194275 | ||||||||
\(766\) | −25.5233 | −0.922196 | ||||||||
\(767\) | −45.0849 | −1.62792 | ||||||||
\(768\) | −13.9238 | −0.502433 | ||||||||
\(769\) | −33.2768 | −1.19999 | −0.599995 | − | 0.800003i | \(-0.704831\pi\) | ||||
−0.599995 | + | 0.800003i | \(0.704831\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.7849 | −1.61289 | ||||||||
\(772\) | −71.1219 | −2.55973 | ||||||||
\(773\) | −12.6696 | −0.455694 | −0.227847 | − | 0.973697i | \(-0.573169\pi\) | ||||
−0.227847 | + | 0.973697i | \(0.573169\pi\) | |||||||
\(774\) | −0.913061 | −0.0328193 | ||||||||
\(775\) | −4.87439 | −0.175093 | ||||||||
\(776\) | −18.3560 | −0.658941 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.8916 | 0.784852 | ||||||||
\(779\) | −7.69012 | −0.275527 | ||||||||
\(780\) | −20.5374 | −0.735358 | ||||||||
\(781\) | 17.6577 | 0.631844 | ||||||||
\(782\) | −48.4252 | −1.73168 | ||||||||
\(783\) | −13.0156 | −0.465141 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.74635 | 0.205096 | ||||||||
\(786\) | 67.5759 | 2.41035 | ||||||||
\(787\) | −33.0489 | −1.17807 | −0.589033 | − | 0.808109i | \(-0.700491\pi\) | ||||
−0.589033 | + | 0.808109i | \(0.700491\pi\) | |||||||
\(788\) | −69.7387 | −2.48434 | ||||||||
\(789\) | 27.3469 | 0.973576 | ||||||||
\(790\) | −4.97605 | −0.177040 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −41.4435 | −1.47263 | ||||||||
\(793\) | 23.0863 | 0.819818 | ||||||||
\(794\) | −18.7177 | −0.664267 | ||||||||
\(795\) | −8.23949 | −0.292225 | ||||||||
\(796\) | −68.0956 | −2.41358 | ||||||||
\(797\) | −31.1760 | −1.10431 | −0.552156 | − | 0.833741i | \(-0.686195\pi\) | ||||
−0.552156 | + | 0.833741i | \(0.686195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.2014 | 0.785428 | ||||||||
\(800\) | −63.3818 | −2.24088 | ||||||||
\(801\) | 8.16363 | 0.288448 | ||||||||
\(802\) | 15.0751 | 0.532321 | ||||||||
\(803\) | 16.4242 | 0.579599 | ||||||||
\(804\) | 162.834 | 5.74270 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2035 | −0.465072 | ||||||||
\(807\) | −24.4096 | −0.859260 | ||||||||
\(808\) | 70.3067 | 2.47338 | ||||||||
\(809\) | −0.770850 | −0.0271016 | −0.0135508 | − | 0.999908i | \(-0.504313\pi\) | ||||
−0.0135508 | + | 0.999908i | \(0.504313\pi\) | |||||||
\(810\) | −9.76010 | −0.342935 | ||||||||
\(811\) | 41.1256 | 1.44412 | 0.722058 | − | 0.691832i | \(-0.243196\pi\) | ||||
0.722058 | + | 0.691832i | \(0.243196\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.2196 | −0.709132 | ||||||||
\(814\) | −27.4914 | −0.963573 | ||||||||
\(815\) | −4.63188 | −0.162248 | ||||||||
\(816\) | −159.287 | −5.57615 | ||||||||
\(817\) | −0.405513 | −0.0141871 | ||||||||
\(818\) | 17.5669 | 0.614212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.80023 | −0.167631 | ||||||||
\(821\) | −3.56797 | −0.124523 | −0.0622615 | − | 0.998060i | \(-0.519831\pi\) | ||||
−0.0622615 | + | 0.998060i | \(0.519831\pi\) | |||||||
\(822\) | −135.505 | −4.72627 | ||||||||
\(823\) | 18.2856 | 0.637396 | 0.318698 | − | 0.947856i | \(-0.396754\pi\) | ||||
0.318698 | + | 0.947856i | \(0.396754\pi\) | |||||||
\(824\) | 76.1903 | 2.65421 | ||||||||
\(825\) | 24.6831 | 0.859355 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.17728 | −0.180032 | −0.0900159 | − | 0.995940i | \(-0.528692\pi\) | ||||
−0.0900159 | + | 0.995940i | \(0.528692\pi\) | |||||||
\(828\) | 35.0519 | 1.21814 | ||||||||
\(829\) | −35.6623 | −1.23860 | −0.619302 | − | 0.785153i | \(-0.712584\pi\) | ||||
−0.619302 | + | 0.785153i | \(0.712584\pi\) | |||||||
\(830\) | 7.84398 | 0.272269 | ||||||||
\(831\) | −13.9492 | −0.483893 | ||||||||
\(832\) | −62.8636 | −2.17940 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 92.4687 | 3.20193 | ||||||||
\(835\) | −2.93063 | −0.101419 | ||||||||
\(836\) | −30.7322 | −1.06289 | ||||||||
\(837\) | −1.36822 | −0.0472927 | ||||||||
\(838\) | 23.9533 | 0.827452 | ||||||||
\(839\) | 33.2844 | 1.14910 | 0.574552 | − | 0.818468i | \(-0.305176\pi\) | ||||
0.574552 | + | 0.818468i | \(0.305176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.4934 | 2.12046 | ||||||||
\(842\) | −13.0336 | −0.449167 | ||||||||
\(843\) | 59.0023 | 2.03215 | ||||||||
\(844\) | −110.768 | −3.81280 | ||||||||
\(845\) | 4.23618 | 0.145729 | ||||||||
\(846\) | −22.5156 | −0.774101 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −108.852 | −3.73800 | ||||||||
\(849\) | 15.5253 | 0.532828 | ||||||||
\(850\) | 80.9898 | 2.77793 | ||||||||
\(851\) | 13.9258 | 0.477371 | ||||||||
\(852\) | −94.1025 | −3.22390 | ||||||||
\(853\) | −19.9660 | −0.683623 | −0.341811 | − | 0.939769i | \(-0.611040\pi\) | ||||
−0.341811 | + | 0.939769i | \(0.611040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.42023 | 0.0827701 | ||||||||
\(856\) | 119.733 | 4.09238 | ||||||||
\(857\) | 38.0655 | 1.30029 | 0.650146 | − | 0.759809i | \(-0.274708\pi\) | ||||
0.650146 | + | 0.759809i | \(0.274708\pi\) | |||||||
\(858\) | 66.8601 | 2.28257 | ||||||||
\(859\) | 34.3211 | 1.17102 | 0.585511 | − | 0.810664i | \(-0.300894\pi\) | ||||
0.585511 | + | 0.810664i | \(0.300894\pi\) | |||||||
\(860\) | −0.253124 | −0.00863147 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 67.3232 | 2.29304 | ||||||||
\(863\) | −31.7584 | −1.08107 | −0.540534 | − | 0.841322i | \(-0.681778\pi\) | ||||
−0.540534 | + | 0.841322i | \(0.681778\pi\) | |||||||
\(864\) | −17.7911 | −0.605264 | ||||||||
\(865\) | −0.835623 | −0.0284120 | ||||||||
\(866\) | 24.8436 | 0.844218 | ||||||||
\(867\) | 52.3767 | 1.77881 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5622 | 0.392222 | ||||||||
\(870\) | 20.7315 | 0.702862 | ||||||||
\(871\) | −70.1178 | −2.37585 | ||||||||
\(872\) | 67.6053 | 2.28940 | ||||||||
\(873\) | −5.60828 | −0.189812 | ||||||||
\(874\) | 21.8113 | 0.737777 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −87.5289 | −2.95733 | ||||||||
\(877\) | −50.6498 | −1.71032 | −0.855161 | − | 0.518363i | \(-0.826542\pi\) | ||||
−0.855161 | + | 0.518363i | \(0.826542\pi\) | |||||||
\(878\) | 105.640 | 3.56516 | ||||||||
\(879\) | 10.6044 | 0.357676 | ||||||||
\(880\) | −8.40332 | −0.283276 | ||||||||
\(881\) | −8.31830 | −0.280251 | −0.140125 | − | 0.990134i | \(-0.544751\pi\) | ||||
−0.140125 | + | 0.990134i | \(0.544751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.6299 | −1.83844 | −0.919221 | − | 0.393743i | \(-0.871180\pi\) | ||||
−0.919221 | + | 0.393743i | \(0.871180\pi\) | |||||||
\(884\) | 156.579 | 5.26634 | ||||||||
\(885\) | 7.44158 | 0.250146 | ||||||||
\(886\) | 37.6030 | 1.26330 | ||||||||
\(887\) | 10.7364 | 0.360493 | 0.180246 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180246 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(888\) | 87.7469 | 2.94459 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.17088 | 0.106288 | ||||||||
\(891\) | 22.6784 | 0.759755 | ||||||||
\(892\) | −108.496 | −3.63272 | ||||||||
\(893\) | −9.99973 | −0.334628 | ||||||||
\(894\) | 10.3933 | 0.347605 | ||||||||
\(895\) | −2.42590 | −0.0810890 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.8681 | −1.13082 | ||||||||
\(898\) | −3.65989 | −0.122132 | ||||||||
\(899\) | 9.51280 | 0.317270 | ||||||||
\(900\) | −58.6233 | −1.95411 | ||||||||
\(901\) | 62.8187 | 2.09279 | ||||||||
\(902\) | 15.6273 | 0.520331 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 84.1235 | 2.79790 | ||||||||
\(905\) | 5.81756 | 0.193382 | ||||||||
\(906\) | 58.9470 | 1.95838 | ||||||||
\(907\) | 20.0274 | 0.664999 | 0.332500 | − | 0.943103i | \(-0.392108\pi\) | ||||
0.332500 | + | 0.943103i | \(0.392108\pi\) | |||||||
\(908\) | −7.72674 | −0.256421 | ||||||||
\(909\) | 21.4807 | 0.712470 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7955 | 0.655854 | 0.327927 | − | 0.944703i | \(-0.393650\pi\) | ||||
0.327927 | + | 0.944703i | \(0.393650\pi\) | |||||||
\(912\) | 71.7444 | 2.37570 | ||||||||
\(913\) | −18.2261 | −0.603197 | ||||||||
\(914\) | −46.4569 | −1.53666 | ||||||||
\(915\) | −3.81055 | −0.125973 | ||||||||
\(916\) | 8.42891 | 0.278499 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 22.7336 | 0.750319 | ||||||||
\(919\) | −40.3280 | −1.33030 | −0.665150 | − | 0.746710i | \(-0.731632\pi\) | ||||
−0.665150 | + | 0.746710i | \(0.731632\pi\) | |||||||
\(920\) | 8.15414 | 0.268834 | ||||||||
\(921\) | 69.8533 | 2.30174 | ||||||||
\(922\) | −71.6476 | −2.35959 | ||||||||
\(923\) | 40.5215 | 1.33378 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.2905 | −0.765788 | ||||||||
\(926\) | −49.5094 | −1.62698 | ||||||||
\(927\) | 23.2783 | 0.764560 | ||||||||
\(928\) | 123.695 | 4.06049 | ||||||||
\(929\) | 5.36391 | 0.175984 | 0.0879921 | − | 0.996121i | \(-0.471955\pi\) | ||||
0.0879921 | + | 0.996121i | \(0.471955\pi\) | |||||||
\(930\) | 2.17932 | 0.0714628 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28.7914 | −0.943095 | ||||||||
\(933\) | −44.1542 | −1.44554 | ||||||||
\(934\) | −27.0124 | −0.883872 | ||||||||
\(935\) | 4.84956 | 0.158598 | ||||||||
\(936\) | −95.1058 | −3.10863 | ||||||||
\(937\) | 48.2187 | 1.57524 | 0.787619 | − | 0.616163i | \(-0.211314\pi\) | ||||
0.787619 | + | 0.616163i | \(0.211314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.2211 | −0.823058 | ||||||||
\(940\) | −6.24190 | −0.203588 | ||||||||
\(941\) | 24.9474 | 0.813264 | 0.406632 | − | 0.913592i | \(-0.366703\pi\) | ||||
0.406632 | + | 0.913592i | \(0.366703\pi\) | |||||||
\(942\) | 99.6963 | 3.24828 | ||||||||
\(943\) | −7.91603 | −0.257781 | ||||||||
\(944\) | 98.3109 | 3.19975 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.824052 | 0.0267922 | ||||||||
\(947\) | 2.03448 | 0.0661117 | 0.0330558 | − | 0.999454i | \(-0.489476\pi\) | ||||
0.0330558 | + | 0.999454i | \(0.489476\pi\) | |||||||
\(948\) | −61.6181 | −2.00126 | ||||||||
\(949\) | 37.6908 | 1.22350 | ||||||||
\(950\) | −36.4787 | −1.18352 | ||||||||
\(951\) | −6.39566 | −0.207393 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.39082 | −0.174626 | −0.0873130 | − | 0.996181i | \(-0.527828\pi\) | ||||
−0.0873130 | + | 0.996181i | \(0.527828\pi\) | |||||||
\(954\) | −63.7077 | −2.06261 | ||||||||
\(955\) | −0.663510 | −0.0214707 | ||||||||
\(956\) | 123.130 | 3.98232 | ||||||||
\(957\) | −48.1712 | −1.55715 | ||||||||
\(958\) | −64.6628 | −2.08916 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10.3761 | 0.334886 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −63.0881 | −2.03404 | ||||||||
\(963\) | 36.5818 | 1.17883 | ||||||||
\(964\) | −11.1931 | −0.360505 | ||||||||
\(965\) | −5.05501 | −0.162726 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4887 | 0.337295 | 0.168647 | − | 0.985676i | \(-0.446060\pi\) | ||||
0.168647 | + | 0.985676i | \(0.446060\pi\) | |||||||
\(968\) | −49.4310 | −1.58877 | ||||||||
\(969\) | −41.4038 | −1.33008 | ||||||||
\(970\) | −2.17835 | −0.0699425 | ||||||||
\(971\) | 53.3663 | 1.71260 | 0.856302 | − | 0.516475i | \(-0.172756\pi\) | ||||
0.856302 | + | 0.516475i | \(0.172756\pi\) | |||||||
\(972\) | −100.391 | −3.22003 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.6300 | 0.372649 | ||||||||
\(975\) | 56.6434 | 1.81404 | ||||||||
\(976\) | −50.3413 | −1.61139 | ||||||||
\(977\) | 58.2089 | 1.86227 | 0.931134 | − | 0.364677i | \(-0.118821\pi\) | ||||
0.931134 | + | 0.364677i | \(0.118821\pi\) | |||||||
\(978\) | −80.3608 | −2.56966 | ||||||||
\(979\) | −7.36781 | −0.235476 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6553 | 0.659474 | ||||||||
\(982\) | 71.1472 | 2.27040 | ||||||||
\(983\) | 26.8145 | 0.855251 | 0.427626 | − | 0.903956i | \(-0.359350\pi\) | ||||
0.427626 | + | 0.903956i | \(0.359350\pi\) | |||||||
\(984\) | −49.8790 | −1.59008 | ||||||||
\(985\) | −4.95670 | −0.157933 | ||||||||
\(986\) | −158.059 | −5.03362 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −70.5251 | −2.24370 | ||||||||
\(989\) | −0.417426 | −0.0132734 | ||||||||
\(990\) | −4.91820 | −0.156311 | ||||||||
\(991\) | −51.2497 | −1.62800 | −0.814000 | − | 0.580864i | \(-0.802715\pi\) | ||||
−0.814000 | + | 0.580864i | \(0.802715\pi\) | |||||||
\(992\) | 13.0030 | 0.412846 | ||||||||
\(993\) | −56.0354 | −1.77823 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.83991 | −0.153435 | ||||||||
\(996\) | 97.1316 | 3.07773 | ||||||||
\(997\) | 29.8303 | 0.944735 | 0.472367 | − | 0.881402i | \(-0.343400\pi\) | ||||
0.472367 | + | 0.881402i | \(0.343400\pi\) | |||||||
\(998\) | 0.221426 | 0.00700912 | ||||||||
\(999\) | −6.53758 | −0.206840 |
(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 | 1519.2.a.k.1.13 | 13 | ||
7.2 | even | 3 | 217.2.f.b.32.1 | ✓ | 26 | ||
7.4 | even | 3 | 217.2.f.b.156.1 | yes | 26 | ||
7.6 | odd | 2 | 1519.2.a.j.1.13 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
217.2.f.b.32.1 | ✓ | 26 | 7.2 | even | 3 | ||
217.2.f.b.156.1 | yes | 26 | 7.4 | even | 3 | ||
1519.2.a.j.1.13 | 13 | 7.6 | odd | 2 | |||
1519.2.a.k.1.13 | 13 | 1.1 | even | 1 | trivial |