Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.61063\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.40749 | 0.629450 | 0.314725 | − | 0.949183i | \(-0.398088\pi\) | ||||
0.314725 | + | 0.949183i | \(0.398088\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.998879 | −0.377541 | −0.188770 | − | 0.982021i | \(-0.560450\pi\) | ||||
−0.188770 | + | 0.982021i | \(0.560450\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.40749 | −0.445089 | ||||||||
\(11\) | 4.83053 | 1.45646 | 0.728230 | − | 0.685333i | \(-0.240343\pi\) | ||||
0.728230 | + | 0.685333i | \(0.240343\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.998879 | 0.266962 | ||||||||
\(15\) | 1.40749 | 0.363413 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.95365 | −0.716365 | −0.358183 | − | 0.933652i | \(-0.616603\pi\) | ||||
−0.358183 | + | 0.933652i | \(0.616603\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.88860 | 0.433274 | 0.216637 | − | 0.976252i | \(-0.430491\pi\) | ||||
0.216637 | + | 0.976252i | \(0.430491\pi\) | |||||||
\(20\) | 1.40749 | 0.314725 | ||||||||
\(21\) | −0.998879 | −0.217973 | ||||||||
\(22\) | −4.83053 | −1.02987 | ||||||||
\(23\) | −2.84489 | −0.593200 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.01896 | −0.603792 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.998879 | −0.188770 | ||||||||
\(29\) | −5.72981 | −1.06400 | −0.532000 | − | 0.846744i | \(-0.678559\pi\) | ||||
−0.532000 | + | 0.846744i | \(0.678559\pi\) | |||||||
\(30\) | −1.40749 | −0.256972 | ||||||||
\(31\) | −10.1479 | −1.82261 | −0.911305 | − | 0.411731i | \(-0.864924\pi\) | ||||
−0.911305 | + | 0.411731i | \(0.864924\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.83053 | 0.840888 | ||||||||
\(34\) | 2.95365 | 0.506547 | ||||||||
\(35\) | −1.40592 | −0.237643 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.75750 | −0.782128 | −0.391064 | − | 0.920363i | \(-0.627893\pi\) | ||||
−0.391064 | + | 0.920363i | \(0.627893\pi\) | |||||||
\(38\) | −1.88860 | −0.306371 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.40749 | −0.222544 | ||||||||
\(41\) | −4.77235 | −0.745315 | −0.372658 | − | 0.927969i | \(-0.621553\pi\) | ||||
−0.372658 | + | 0.927969i | \(0.621553\pi\) | |||||||
\(42\) | 0.998879 | 0.154130 | ||||||||
\(43\) | 9.75344 | 1.48739 | 0.743693 | − | 0.668521i | \(-0.233072\pi\) | ||||
0.743693 | + | 0.668521i | \(0.233072\pi\) | |||||||
\(44\) | 4.83053 | 0.728230 | ||||||||
\(45\) | 1.40749 | 0.209817 | ||||||||
\(46\) | 2.84489 | 0.419456 | ||||||||
\(47\) | −2.46105 | −0.358981 | −0.179491 | − | 0.983760i | \(-0.557445\pi\) | ||||
−0.179491 | + | 0.983760i | \(0.557445\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.00224 | −0.857463 | ||||||||
\(50\) | 3.01896 | 0.426946 | ||||||||
\(51\) | −2.95365 | −0.413594 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −8.38795 | −1.15217 | −0.576087 | − | 0.817389i | \(-0.695421\pi\) | ||||
−0.576087 | + | 0.817389i | \(0.695421\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 6.79894 | 0.916769 | ||||||||
\(56\) | 0.998879 | 0.133481 | ||||||||
\(57\) | 1.88860 | 0.250151 | ||||||||
\(58\) | 5.72981 | 0.752362 | ||||||||
\(59\) | −8.26441 | −1.07593 | −0.537967 | − | 0.842966i | \(-0.680808\pi\) | ||||
−0.537967 | + | 0.842966i | \(0.680808\pi\) | |||||||
\(60\) | 1.40749 | 0.181707 | ||||||||
\(61\) | −6.11324 | −0.782720 | −0.391360 | − | 0.920238i | \(-0.627995\pi\) | ||||
−0.391360 | + | 0.920238i | \(0.627995\pi\) | |||||||
\(62\) | 10.1479 | 1.28878 | ||||||||
\(63\) | −0.998879 | −0.125847 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.40749 | 0.174578 | ||||||||
\(66\) | −4.83053 | −0.594597 | ||||||||
\(67\) | −4.55266 | −0.556196 | −0.278098 | − | 0.960553i | \(-0.589704\pi\) | ||||
−0.278098 | + | 0.960553i | \(0.589704\pi\) | |||||||
\(68\) | −2.95365 | −0.358183 | ||||||||
\(69\) | −2.84489 | −0.342484 | ||||||||
\(70\) | 1.40592 | 0.168039 | ||||||||
\(71\) | −3.66759 | −0.435262 | −0.217631 | − | 0.976031i | \(-0.569833\pi\) | ||||
−0.217631 | + | 0.976031i | \(0.569833\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.4965 | −1.57964 | −0.789821 | − | 0.613337i | \(-0.789827\pi\) | ||||
−0.789821 | + | 0.613337i | \(0.789827\pi\) | |||||||
\(74\) | 4.75750 | 0.553048 | ||||||||
\(75\) | −3.01896 | −0.348600 | ||||||||
\(76\) | 1.88860 | 0.216637 | ||||||||
\(77\) | −4.82512 | −0.549873 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −11.1098 | −1.24995 | −0.624977 | − | 0.780643i | \(-0.714892\pi\) | ||||
−0.624977 | + | 0.780643i | \(0.714892\pi\) | |||||||
\(80\) | 1.40749 | 0.157363 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.77235 | 0.527018 | ||||||||
\(83\) | 1.76274 | 0.193486 | 0.0967429 | − | 0.995309i | \(-0.469158\pi\) | ||||
0.0967429 | + | 0.995309i | \(0.469158\pi\) | |||||||
\(84\) | −0.998879 | −0.108987 | ||||||||
\(85\) | −4.15724 | −0.450916 | ||||||||
\(86\) | −9.75344 | −1.05174 | ||||||||
\(87\) | −5.72981 | −0.614301 | ||||||||
\(88\) | −4.83053 | −0.514936 | ||||||||
\(89\) | −0.860992 | −0.0912650 | −0.0456325 | − | 0.998958i | \(-0.514530\pi\) | ||||
−0.0456325 | + | 0.998958i | \(0.514530\pi\) | |||||||
\(90\) | −1.40749 | −0.148363 | ||||||||
\(91\) | −0.998879 | −0.104711 | ||||||||
\(92\) | −2.84489 | −0.296600 | ||||||||
\(93\) | −10.1479 | −1.05228 | ||||||||
\(94\) | 2.46105 | 0.253838 | ||||||||
\(95\) | 2.65819 | 0.272725 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −5.09415 | −0.517232 | −0.258616 | − | 0.965980i | \(-0.583266\pi\) | ||||
−0.258616 | + | 0.965980i | \(0.583266\pi\) | |||||||
\(98\) | 6.00224 | 0.606318 | ||||||||
\(99\) | 4.83053 | 0.485487 | ||||||||
\(100\) | −3.01896 | −0.301896 | ||||||||
\(101\) | −5.83551 | −0.580655 | −0.290327 | − | 0.956927i | \(-0.593764\pi\) | ||||
−0.290327 | + | 0.956927i | \(0.593764\pi\) | |||||||
\(102\) | 2.95365 | 0.292455 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −1.40592 | −0.137203 | ||||||||
\(106\) | 8.38795 | 0.814710 | ||||||||
\(107\) | 13.0054 | 1.25728 | 0.628642 | − | 0.777695i | \(-0.283611\pi\) | ||||
0.628642 | + | 0.777695i | \(0.283611\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.24549 | −0.119297 | −0.0596484 | − | 0.998219i | \(-0.518998\pi\) | ||||
−0.0596484 | + | 0.998219i | \(0.518998\pi\) | |||||||
\(110\) | −6.79894 | −0.648254 | ||||||||
\(111\) | −4.75750 | −0.451562 | ||||||||
\(112\) | −0.998879 | −0.0943852 | ||||||||
\(113\) | 9.96193 | 0.937139 | 0.468570 | − | 0.883427i | \(-0.344770\pi\) | ||||
0.468570 | + | 0.883427i | \(0.344770\pi\) | |||||||
\(114\) | −1.88860 | −0.176883 | ||||||||
\(115\) | −4.00416 | −0.373390 | ||||||||
\(116\) | −5.72981 | −0.532000 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 8.26441 | 0.760801 | ||||||||
\(119\) | 2.95034 | 0.270457 | ||||||||
\(120\) | −1.40749 | −0.128486 | ||||||||
\(121\) | 12.3340 | 1.12128 | ||||||||
\(122\) | 6.11324 | 0.553466 | ||||||||
\(123\) | −4.77235 | −0.430308 | ||||||||
\(124\) | −10.1479 | −0.911305 | ||||||||
\(125\) | −11.2866 | −1.00951 | ||||||||
\(126\) | 0.998879 | 0.0889872 | ||||||||
\(127\) | 3.66487 | 0.325204 | 0.162602 | − | 0.986692i | \(-0.448011\pi\) | ||||
0.162602 | + | 0.986692i | \(0.448011\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.75344 | 0.858743 | ||||||||
\(130\) | −1.40749 | −0.123445 | ||||||||
\(131\) | 11.9908 | 1.04764 | 0.523822 | − | 0.851827i | \(-0.324506\pi\) | ||||
0.523822 | + | 0.851827i | \(0.324506\pi\) | |||||||
\(132\) | 4.83053 | 0.420444 | ||||||||
\(133\) | −1.88648 | −0.163579 | ||||||||
\(134\) | 4.55266 | 0.393290 | ||||||||
\(135\) | 1.40749 | 0.121138 | ||||||||
\(136\) | 2.95365 | 0.253273 | ||||||||
\(137\) | 11.6193 | 0.992702 | 0.496351 | − | 0.868122i | \(-0.334673\pi\) | ||||
0.496351 | + | 0.868122i | \(0.334673\pi\) | |||||||
\(138\) | 2.84489 | 0.242173 | ||||||||
\(139\) | 10.1782 | 0.863301 | 0.431650 | − | 0.902041i | \(-0.357931\pi\) | ||||
0.431650 | + | 0.902041i | \(0.357931\pi\) | |||||||
\(140\) | −1.40592 | −0.118822 | ||||||||
\(141\) | −2.46105 | −0.207258 | ||||||||
\(142\) | 3.66759 | 0.307777 | ||||||||
\(143\) | 4.83053 | 0.403949 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −8.06468 | −0.669735 | ||||||||
\(146\) | 13.4965 | 1.11698 | ||||||||
\(147\) | −6.00224 | −0.495056 | ||||||||
\(148\) | −4.75750 | −0.391064 | ||||||||
\(149\) | 17.0885 | 1.39995 | 0.699973 | − | 0.714169i | \(-0.253195\pi\) | ||||
0.699973 | + | 0.714169i | \(0.253195\pi\) | |||||||
\(150\) | 3.01896 | 0.246497 | ||||||||
\(151\) | 13.2289 | 1.07655 | 0.538277 | − | 0.842768i | \(-0.319076\pi\) | ||||
0.538277 | + | 0.842768i | \(0.319076\pi\) | |||||||
\(152\) | −1.88860 | −0.153186 | ||||||||
\(153\) | −2.95365 | −0.238788 | ||||||||
\(154\) | 4.82512 | 0.388819 | ||||||||
\(155\) | −14.2831 | −1.14724 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 9.61127 | 0.767062 | 0.383531 | − | 0.923528i | \(-0.374708\pi\) | ||||
0.383531 | + | 0.923528i | \(0.374708\pi\) | |||||||
\(158\) | 11.1098 | 0.883852 | ||||||||
\(159\) | −8.38795 | −0.665208 | ||||||||
\(160\) | −1.40749 | −0.111272 | ||||||||
\(161\) | 2.84170 | 0.223957 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.98844 | −0.625703 | −0.312851 | − | 0.949802i | \(-0.601284\pi\) | ||||
−0.312851 | + | 0.949802i | \(0.601284\pi\) | |||||||
\(164\) | −4.77235 | −0.372658 | ||||||||
\(165\) | 6.79894 | 0.529297 | ||||||||
\(166\) | −1.76274 | −0.136815 | ||||||||
\(167\) | 3.41720 | 0.264431 | 0.132215 | − | 0.991221i | \(-0.457791\pi\) | ||||
0.132215 | + | 0.991221i | \(0.457791\pi\) | |||||||
\(168\) | 0.998879 | 0.0770652 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.15724 | 0.318846 | ||||||||
\(171\) | 1.88860 | 0.144425 | ||||||||
\(172\) | 9.75344 | 0.743693 | ||||||||
\(173\) | −24.4518 | −1.85904 | −0.929519 | − | 0.368773i | \(-0.879778\pi\) | ||||
−0.929519 | + | 0.368773i | \(0.879778\pi\) | |||||||
\(174\) | 5.72981 | 0.434376 | ||||||||
\(175\) | 3.01558 | 0.227956 | ||||||||
\(176\) | 4.83053 | 0.364115 | ||||||||
\(177\) | −8.26441 | −0.621191 | ||||||||
\(178\) | 0.860992 | 0.0645341 | ||||||||
\(179\) | −11.6219 | −0.868664 | −0.434332 | − | 0.900753i | \(-0.643015\pi\) | ||||
−0.434332 | + | 0.900753i | \(0.643015\pi\) | |||||||
\(180\) | 1.40749 | 0.104908 | ||||||||
\(181\) | 16.1688 | 1.20181 | 0.600907 | − | 0.799319i | \(-0.294806\pi\) | ||||
0.600907 | + | 0.799319i | \(0.294806\pi\) | |||||||
\(182\) | 0.998879 | 0.0740418 | ||||||||
\(183\) | −6.11324 | −0.451903 | ||||||||
\(184\) | 2.84489 | 0.209728 | ||||||||
\(185\) | −6.69615 | −0.492311 | ||||||||
\(186\) | 10.1479 | 0.744078 | ||||||||
\(187\) | −14.2677 | −1.04336 | ||||||||
\(188\) | −2.46105 | −0.179491 | ||||||||
\(189\) | −0.998879 | −0.0726578 | ||||||||
\(190\) | −2.65819 | −0.192845 | ||||||||
\(191\) | −15.3479 | −1.11054 | −0.555269 | − | 0.831671i | \(-0.687385\pi\) | ||||
−0.555269 | + | 0.831671i | \(0.687385\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 5.62711 | 0.405048 | 0.202524 | − | 0.979277i | \(-0.435086\pi\) | ||||
0.202524 | + | 0.979277i | \(0.435086\pi\) | |||||||
\(194\) | 5.09415 | 0.365739 | ||||||||
\(195\) | 1.40749 | 0.100793 | ||||||||
\(196\) | −6.00224 | −0.428731 | ||||||||
\(197\) | −8.91051 | −0.634848 | −0.317424 | − | 0.948284i | \(-0.602818\pi\) | ||||
−0.317424 | + | 0.948284i | \(0.602818\pi\) | |||||||
\(198\) | −4.83053 | −0.343291 | ||||||||
\(199\) | −21.5100 | −1.52480 | −0.762401 | − | 0.647105i | \(-0.775980\pi\) | ||||
−0.762401 | + | 0.647105i | \(0.775980\pi\) | |||||||
\(200\) | 3.01896 | 0.213473 | ||||||||
\(201\) | −4.55266 | −0.321120 | ||||||||
\(202\) | 5.83551 | 0.410585 | ||||||||
\(203\) | 5.72339 | 0.401703 | ||||||||
\(204\) | −2.95365 | −0.206797 | ||||||||
\(205\) | −6.71705 | −0.469139 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −2.84489 | −0.197733 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 9.12294 | 0.631047 | ||||||||
\(210\) | 1.40592 | 0.0970174 | ||||||||
\(211\) | 25.6510 | 1.76589 | 0.882945 | − | 0.469476i | \(-0.155557\pi\) | ||||
0.882945 | + | 0.469476i | \(0.155557\pi\) | |||||||
\(212\) | −8.38795 | −0.576087 | ||||||||
\(213\) | −3.66759 | −0.251299 | ||||||||
\(214\) | −13.0054 | −0.889034 | ||||||||
\(215\) | 13.7279 | 0.936235 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.1365 | 0.688110 | ||||||||
\(218\) | 1.24549 | 0.0843555 | ||||||||
\(219\) | −13.4965 | −0.912007 | ||||||||
\(220\) | 6.79894 | 0.458385 | ||||||||
\(221\) | −2.95365 | −0.198684 | ||||||||
\(222\) | 4.75750 | 0.319302 | ||||||||
\(223\) | 12.8137 | 0.858069 | 0.429034 | − | 0.903288i | \(-0.358854\pi\) | ||||
0.429034 | + | 0.903288i | \(0.358854\pi\) | |||||||
\(224\) | 0.998879 | 0.0667404 | ||||||||
\(225\) | −3.01896 | −0.201264 | ||||||||
\(226\) | −9.96193 | −0.662657 | ||||||||
\(227\) | −12.3807 | −0.821736 | −0.410868 | − | 0.911695i | \(-0.634774\pi\) | ||||
−0.410868 | + | 0.911695i | \(0.634774\pi\) | |||||||
\(228\) | 1.88860 | 0.125076 | ||||||||
\(229\) | 12.8890 | 0.851726 | 0.425863 | − | 0.904788i | \(-0.359971\pi\) | ||||
0.425863 | + | 0.904788i | \(0.359971\pi\) | |||||||
\(230\) | 4.00416 | 0.264026 | ||||||||
\(231\) | −4.82512 | −0.317469 | ||||||||
\(232\) | 5.72981 | 0.376181 | ||||||||
\(233\) | −6.27793 | −0.411281 | −0.205641 | − | 0.978628i | \(-0.565928\pi\) | ||||
−0.205641 | + | 0.978628i | \(0.565928\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −3.46391 | −0.225961 | ||||||||
\(236\) | −8.26441 | −0.537967 | ||||||||
\(237\) | −11.1098 | −0.721662 | ||||||||
\(238\) | −2.95034 | −0.191242 | ||||||||
\(239\) | −20.3261 | −1.31478 | −0.657392 | − | 0.753549i | \(-0.728341\pi\) | ||||
−0.657392 | + | 0.753549i | \(0.728341\pi\) | |||||||
\(240\) | 1.40749 | 0.0908533 | ||||||||
\(241\) | −5.81756 | −0.374742 | −0.187371 | − | 0.982289i | \(-0.559997\pi\) | ||||
−0.187371 | + | 0.982289i | \(0.559997\pi\) | |||||||
\(242\) | −12.3340 | −0.792862 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.11324 | −0.391360 | ||||||||
\(245\) | −8.44812 | −0.539730 | ||||||||
\(246\) | 4.77235 | 0.304274 | ||||||||
\(247\) | 1.88860 | 0.120169 | ||||||||
\(248\) | 10.1479 | 0.644390 | ||||||||
\(249\) | 1.76274 | 0.111709 | ||||||||
\(250\) | 11.2866 | 0.713830 | ||||||||
\(251\) | 10.3172 | 0.651215 | 0.325607 | − | 0.945505i | \(-0.394431\pi\) | ||||
0.325607 | + | 0.945505i | \(0.394431\pi\) | |||||||
\(252\) | −0.998879 | −0.0629235 | ||||||||
\(253\) | −13.7423 | −0.863972 | ||||||||
\(254\) | −3.66487 | −0.229954 | ||||||||
\(255\) | −4.15724 | −0.260337 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.22415 | 0.201117 | 0.100558 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100558 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(258\) | −9.75344 | −0.607223 | ||||||||
\(259\) | 4.75217 | 0.295285 | ||||||||
\(260\) | 1.40749 | 0.0872890 | ||||||||
\(261\) | −5.72981 | −0.354667 | ||||||||
\(262\) | −11.9908 | −0.740797 | ||||||||
\(263\) | −27.8650 | −1.71823 | −0.859115 | − | 0.511782i | \(-0.828986\pi\) | ||||
−0.859115 | + | 0.511782i | \(0.828986\pi\) | |||||||
\(264\) | −4.83053 | −0.297299 | ||||||||
\(265\) | −11.8060 | −0.725236 | ||||||||
\(266\) | 1.88648 | 0.115668 | ||||||||
\(267\) | −0.860992 | −0.0526918 | ||||||||
\(268\) | −4.55266 | −0.278098 | ||||||||
\(269\) | −5.47995 | −0.334119 | −0.167059 | − | 0.985947i | \(-0.553427\pi\) | ||||
−0.167059 | + | 0.985947i | \(0.553427\pi\) | |||||||
\(270\) | −1.40749 | −0.0856573 | ||||||||
\(271\) | 25.0590 | 1.52223 | 0.761114 | − | 0.648618i | \(-0.224653\pi\) | ||||
0.761114 | + | 0.648618i | \(0.224653\pi\) | |||||||
\(272\) | −2.95365 | −0.179091 | ||||||||
\(273\) | −0.998879 | −0.0604549 | ||||||||
\(274\) | −11.6193 | −0.701947 | ||||||||
\(275\) | −14.5832 | −0.879399 | ||||||||
\(276\) | −2.84489 | −0.171242 | ||||||||
\(277\) | 4.14155 | 0.248841 | 0.124421 | − | 0.992230i | \(-0.460293\pi\) | ||||
0.124421 | + | 0.992230i | \(0.460293\pi\) | |||||||
\(278\) | −10.1782 | −0.610446 | ||||||||
\(279\) | −10.1479 | −0.607537 | ||||||||
\(280\) | 1.40592 | 0.0840195 | ||||||||
\(281\) | −2.03599 | −0.121457 | −0.0607284 | − | 0.998154i | \(-0.519342\pi\) | ||||
−0.0607284 | + | 0.998154i | \(0.519342\pi\) | |||||||
\(282\) | 2.46105 | 0.146553 | ||||||||
\(283\) | 10.5521 | 0.627256 | 0.313628 | − | 0.949546i | \(-0.398455\pi\) | ||||
0.313628 | + | 0.949546i | \(0.398455\pi\) | |||||||
\(284\) | −3.66759 | −0.217631 | ||||||||
\(285\) | 2.65819 | 0.157458 | ||||||||
\(286\) | −4.83053 | −0.285635 | ||||||||
\(287\) | 4.76700 | 0.281387 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −8.27596 | −0.486821 | ||||||||
\(290\) | 8.06468 | 0.473574 | ||||||||
\(291\) | −5.09415 | −0.298624 | ||||||||
\(292\) | −13.4965 | −0.789821 | ||||||||
\(293\) | 20.2309 | 1.18190 | 0.590950 | − | 0.806708i | \(-0.298753\pi\) | ||||
0.590950 | + | 0.806708i | \(0.298753\pi\) | |||||||
\(294\) | 6.00224 | 0.350058 | ||||||||
\(295\) | −11.6321 | −0.677248 | ||||||||
\(296\) | 4.75750 | 0.276524 | ||||||||
\(297\) | 4.83053 | 0.280296 | ||||||||
\(298\) | −17.0885 | −0.989912 | ||||||||
\(299\) | −2.84489 | −0.164524 | ||||||||
\(300\) | −3.01896 | −0.174300 | ||||||||
\(301\) | −9.74251 | −0.561549 | ||||||||
\(302\) | −13.2289 | −0.761238 | ||||||||
\(303\) | −5.83551 | −0.335241 | ||||||||
\(304\) | 1.88860 | 0.108319 | ||||||||
\(305\) | −8.60434 | −0.492683 | ||||||||
\(306\) | 2.95365 | 0.168849 | ||||||||
\(307\) | 9.28706 | 0.530041 | 0.265020 | − | 0.964243i | \(-0.414621\pi\) | ||||
0.265020 | + | 0.964243i | \(0.414621\pi\) | |||||||
\(308\) | −4.82512 | −0.274937 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 14.2831 | 0.811223 | ||||||||
\(311\) | 18.0200 | 1.02182 | 0.510910 | − | 0.859634i | \(-0.329309\pi\) | ||||
0.510910 | + | 0.859634i | \(0.329309\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 26.1537 | 1.47829 | 0.739146 | − | 0.673545i | \(-0.235229\pi\) | ||||
0.739146 | + | 0.673545i | \(0.235229\pi\) | |||||||
\(314\) | −9.61127 | −0.542395 | ||||||||
\(315\) | −1.40592 | −0.0792144 | ||||||||
\(316\) | −11.1098 | −0.624977 | ||||||||
\(317\) | 7.89534 | 0.443447 | 0.221723 | − | 0.975110i | \(-0.428832\pi\) | ||||
0.221723 | + | 0.975110i | \(0.428832\pi\) | |||||||
\(318\) | 8.38795 | 0.470373 | ||||||||
\(319\) | −27.6780 | −1.54967 | ||||||||
\(320\) | 1.40749 | 0.0786813 | ||||||||
\(321\) | 13.0054 | 0.725893 | ||||||||
\(322\) | −2.84170 | −0.158362 | ||||||||
\(323\) | −5.57826 | −0.310383 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.01896 | −0.167462 | ||||||||
\(326\) | 7.98844 | 0.442439 | ||||||||
\(327\) | −1.24549 | −0.0688760 | ||||||||
\(328\) | 4.77235 | 0.263509 | ||||||||
\(329\) | 2.45829 | 0.135530 | ||||||||
\(330\) | −6.79894 | −0.374269 | ||||||||
\(331\) | 21.0364 | 1.15627 | 0.578134 | − | 0.815942i | \(-0.303781\pi\) | ||||
0.578134 | + | 0.815942i | \(0.303781\pi\) | |||||||
\(332\) | 1.76274 | 0.0967429 | ||||||||
\(333\) | −4.75750 | −0.260709 | ||||||||
\(334\) | −3.41720 | −0.186981 | ||||||||
\(335\) | −6.40784 | −0.350098 | ||||||||
\(336\) | −0.998879 | −0.0544933 | ||||||||
\(337\) | 26.1538 | 1.42469 | 0.712344 | − | 0.701831i | \(-0.247634\pi\) | ||||
0.712344 | + | 0.701831i | \(0.247634\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 9.96193 | 0.541058 | ||||||||
\(340\) | −4.15724 | −0.225458 | ||||||||
\(341\) | −49.0196 | −2.65456 | ||||||||
\(342\) | −1.88860 | −0.102124 | ||||||||
\(343\) | 12.9877 | 0.701268 | ||||||||
\(344\) | −9.75344 | −0.525870 | ||||||||
\(345\) | −4.00416 | −0.215577 | ||||||||
\(346\) | 24.4518 | 1.31454 | ||||||||
\(347\) | −20.9493 | −1.12462 | −0.562308 | − | 0.826928i | \(-0.690087\pi\) | ||||
−0.562308 | + | 0.826928i | \(0.690087\pi\) | |||||||
\(348\) | −5.72981 | −0.307150 | ||||||||
\(349\) | 33.7856 | 1.80850 | 0.904251 | − | 0.427002i | \(-0.140430\pi\) | ||||
0.904251 | + | 0.427002i | \(0.140430\pi\) | |||||||
\(350\) | −3.01558 | −0.161189 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.83053 | −0.257468 | ||||||||
\(353\) | −8.70939 | −0.463554 | −0.231777 | − | 0.972769i | \(-0.574454\pi\) | ||||
−0.231777 | + | 0.972769i | \(0.574454\pi\) | |||||||
\(354\) | 8.26441 | 0.439249 | ||||||||
\(355\) | −5.16210 | −0.273976 | ||||||||
\(356\) | −0.860992 | −0.0456325 | ||||||||
\(357\) | 2.95034 | 0.156148 | ||||||||
\(358\) | 11.6219 | 0.614238 | ||||||||
\(359\) | −26.5369 | −1.40056 | −0.700281 | − | 0.713867i | \(-0.746942\pi\) | ||||
−0.700281 | + | 0.713867i | \(0.746942\pi\) | |||||||
\(360\) | −1.40749 | −0.0741814 | ||||||||
\(361\) | −15.4332 | −0.812273 | ||||||||
\(362\) | −16.1688 | −0.849811 | ||||||||
\(363\) | 12.3340 | 0.647369 | ||||||||
\(364\) | −0.998879 | −0.0523555 | ||||||||
\(365\) | −18.9962 | −0.994306 | ||||||||
\(366\) | 6.11324 | 0.319544 | ||||||||
\(367\) | 9.83164 | 0.513207 | 0.256604 | − | 0.966517i | \(-0.417396\pi\) | ||||
0.256604 | + | 0.966517i | \(0.417396\pi\) | |||||||
\(368\) | −2.84489 | −0.148300 | ||||||||
\(369\) | −4.77235 | −0.248438 | ||||||||
\(370\) | 6.69615 | 0.348116 | ||||||||
\(371\) | 8.37855 | 0.434992 | ||||||||
\(372\) | −10.1479 | −0.526142 | ||||||||
\(373\) | −36.6010 | −1.89513 | −0.947565 | − | 0.319563i | \(-0.896464\pi\) | ||||
−0.947565 | + | 0.319563i | \(0.896464\pi\) | |||||||
\(374\) | 14.2677 | 0.737765 | ||||||||
\(375\) | −11.2866 | −0.582839 | ||||||||
\(376\) | 2.46105 | 0.126919 | ||||||||
\(377\) | −5.72981 | −0.295100 | ||||||||
\(378\) | 0.998879 | 0.0513768 | ||||||||
\(379\) | −23.6372 | −1.21416 | −0.607080 | − | 0.794640i | \(-0.707659\pi\) | ||||
−0.607080 | + | 0.794640i | \(0.707659\pi\) | |||||||
\(380\) | 2.65819 | 0.136362 | ||||||||
\(381\) | 3.66487 | 0.187757 | ||||||||
\(382\) | 15.3479 | 0.785269 | ||||||||
\(383\) | 29.2380 | 1.49399 | 0.746996 | − | 0.664829i | \(-0.231496\pi\) | ||||
0.746996 | + | 0.664829i | \(0.231496\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −6.79132 | −0.346118 | ||||||||
\(386\) | −5.62711 | −0.286412 | ||||||||
\(387\) | 9.75344 | 0.495795 | ||||||||
\(388\) | −5.09415 | −0.258616 | ||||||||
\(389\) | 9.48255 | 0.480784 | 0.240392 | − | 0.970676i | \(-0.422724\pi\) | ||||
0.240392 | + | 0.970676i | \(0.422724\pi\) | |||||||
\(390\) | −1.40749 | −0.0712712 | ||||||||
\(391\) | 8.40279 | 0.424948 | ||||||||
\(392\) | 6.00224 | 0.303159 | ||||||||
\(393\) | 11.9908 | 0.604858 | ||||||||
\(394\) | 8.91051 | 0.448905 | ||||||||
\(395\) | −15.6370 | −0.786784 | ||||||||
\(396\) | 4.83053 | 0.242743 | ||||||||
\(397\) | 6.03291 | 0.302783 | 0.151392 | − | 0.988474i | \(-0.451625\pi\) | ||||
0.151392 | + | 0.988474i | \(0.451625\pi\) | |||||||
\(398\) | 21.5100 | 1.07820 | ||||||||
\(399\) | −1.88648 | −0.0944422 | ||||||||
\(400\) | −3.01896 | −0.150948 | ||||||||
\(401\) | −10.9056 | −0.544601 | −0.272300 | − | 0.962212i | \(-0.587784\pi\) | ||||
−0.272300 | + | 0.962212i | \(0.587784\pi\) | |||||||
\(402\) | 4.55266 | 0.227066 | ||||||||
\(403\) | −10.1479 | −0.505501 | ||||||||
\(404\) | −5.83551 | −0.290327 | ||||||||
\(405\) | 1.40749 | 0.0699389 | ||||||||
\(406\) | −5.72339 | −0.284047 | ||||||||
\(407\) | −22.9812 | −1.13914 | ||||||||
\(408\) | 2.95365 | 0.146227 | ||||||||
\(409\) | −20.6537 | −1.02126 | −0.510631 | − | 0.859800i | \(-0.670588\pi\) | ||||
−0.510631 | + | 0.859800i | \(0.670588\pi\) | |||||||
\(410\) | 6.71705 | 0.331731 | ||||||||
\(411\) | 11.6193 | 0.573137 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 8.25515 | 0.406209 | ||||||||
\(414\) | 2.84489 | 0.139819 | ||||||||
\(415\) | 2.48104 | 0.121790 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 10.1782 | 0.498427 | ||||||||
\(418\) | −9.12294 | −0.446217 | ||||||||
\(419\) | 27.0666 | 1.32229 | 0.661145 | − | 0.750258i | \(-0.270071\pi\) | ||||
0.661145 | + | 0.750258i | \(0.270071\pi\) | |||||||
\(420\) | −1.40592 | −0.0686017 | ||||||||
\(421\) | −25.4862 | −1.24212 | −0.621062 | − | 0.783762i | \(-0.713298\pi\) | ||||
−0.621062 | + | 0.783762i | \(0.713298\pi\) | |||||||
\(422\) | −25.6510 | −1.24867 | ||||||||
\(423\) | −2.46105 | −0.119660 | ||||||||
\(424\) | 8.38795 | 0.407355 | ||||||||
\(425\) | 8.91695 | 0.432536 | ||||||||
\(426\) | 3.66759 | 0.177695 | ||||||||
\(427\) | 6.10638 | 0.295509 | ||||||||
\(428\) | 13.0054 | 0.628642 | ||||||||
\(429\) | 4.83053 | 0.233220 | ||||||||
\(430\) | −13.7279 | −0.662018 | ||||||||
\(431\) | 30.4313 | 1.46582 | 0.732911 | − | 0.680324i | \(-0.238161\pi\) | ||||
0.732911 | + | 0.680324i | \(0.238161\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 37.2374 | 1.78952 | 0.894758 | − | 0.446551i | \(-0.147348\pi\) | ||||
0.894758 | + | 0.446551i | \(0.147348\pi\) | |||||||
\(434\) | −10.1365 | −0.486567 | ||||||||
\(435\) | −8.06468 | −0.386672 | ||||||||
\(436\) | −1.24549 | −0.0596484 | ||||||||
\(437\) | −5.37285 | −0.257018 | ||||||||
\(438\) | 13.4965 | 0.644886 | ||||||||
\(439\) | −28.7436 | −1.37186 | −0.685929 | − | 0.727668i | \(-0.740604\pi\) | ||||
−0.685929 | + | 0.727668i | \(0.740604\pi\) | |||||||
\(440\) | −6.79894 | −0.324127 | ||||||||
\(441\) | −6.00224 | −0.285821 | ||||||||
\(442\) | 2.95365 | 0.140491 | ||||||||
\(443\) | −9.15518 | −0.434976 | −0.217488 | − | 0.976063i | \(-0.569786\pi\) | ||||
−0.217488 | + | 0.976063i | \(0.569786\pi\) | |||||||
\(444\) | −4.75750 | −0.225781 | ||||||||
\(445\) | −1.21184 | −0.0574468 | ||||||||
\(446\) | −12.8137 | −0.606746 | ||||||||
\(447\) | 17.0885 | 0.808260 | ||||||||
\(448\) | −0.998879 | −0.0471926 | ||||||||
\(449\) | 35.7192 | 1.68569 | 0.842847 | − | 0.538154i | \(-0.180878\pi\) | ||||
0.842847 | + | 0.538154i | \(0.180878\pi\) | |||||||
\(450\) | 3.01896 | 0.142315 | ||||||||
\(451\) | −23.0530 | −1.08552 | ||||||||
\(452\) | 9.96193 | 0.468570 | ||||||||
\(453\) | 13.2289 | 0.621548 | ||||||||
\(454\) | 12.3807 | 0.581055 | ||||||||
\(455\) | −1.40592 | −0.0659104 | ||||||||
\(456\) | −1.88860 | −0.0884417 | ||||||||
\(457\) | 22.8348 | 1.06817 | 0.534083 | − | 0.845432i | \(-0.320657\pi\) | ||||
0.534083 | + | 0.845432i | \(0.320657\pi\) | |||||||
\(458\) | −12.8890 | −0.602261 | ||||||||
\(459\) | −2.95365 | −0.137865 | ||||||||
\(460\) | −4.00416 | −0.186695 | ||||||||
\(461\) | −24.7047 | −1.15061 | −0.575305 | − | 0.817939i | \(-0.695117\pi\) | ||||
−0.575305 | + | 0.817939i | \(0.695117\pi\) | |||||||
\(462\) | 4.82512 | 0.224485 | ||||||||
\(463\) | 9.59246 | 0.445799 | 0.222900 | − | 0.974841i | \(-0.428448\pi\) | ||||
0.222900 | + | 0.974841i | \(0.428448\pi\) | |||||||
\(464\) | −5.72981 | −0.266000 | ||||||||
\(465\) | −14.2831 | −0.662361 | ||||||||
\(466\) | 6.27793 | 0.290820 | ||||||||
\(467\) | −20.3961 | −0.943817 | −0.471908 | − | 0.881648i | \(-0.656435\pi\) | ||||
−0.471908 | + | 0.881648i | \(0.656435\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 4.54756 | 0.209987 | ||||||||
\(470\) | 3.46391 | 0.159778 | ||||||||
\(471\) | 9.61127 | 0.442864 | ||||||||
\(472\) | 8.26441 | 0.380400 | ||||||||
\(473\) | 47.1143 | 2.16632 | ||||||||
\(474\) | 11.1098 | 0.510292 | ||||||||
\(475\) | −5.70161 | −0.261608 | ||||||||
\(476\) | 2.95034 | 0.135229 | ||||||||
\(477\) | −8.38795 | −0.384058 | ||||||||
\(478\) | 20.3261 | 0.929693 | ||||||||
\(479\) | −6.02670 | −0.275367 | −0.137684 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137684 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(480\) | −1.40749 | −0.0642430 | ||||||||
\(481\) | −4.75750 | −0.216923 | ||||||||
\(482\) | 5.81756 | 0.264983 | ||||||||
\(483\) | 2.84170 | 0.129302 | ||||||||
\(484\) | 12.3340 | 0.560638 | ||||||||
\(485\) | −7.16998 | −0.325572 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 23.6141 | 1.07006 | 0.535029 | − | 0.844834i | \(-0.320301\pi\) | ||||
0.535029 | + | 0.844834i | \(0.320301\pi\) | |||||||
\(488\) | 6.11324 | 0.276733 | ||||||||
\(489\) | −7.98844 | −0.361250 | ||||||||
\(490\) | 8.44812 | 0.381647 | ||||||||
\(491\) | −18.4702 | −0.833550 | −0.416775 | − | 0.909010i | \(-0.636840\pi\) | ||||
−0.416775 | + | 0.909010i | \(0.636840\pi\) | |||||||
\(492\) | −4.77235 | −0.215154 | ||||||||
\(493\) | 16.9239 | 0.762212 | ||||||||
\(494\) | −1.88860 | −0.0849721 | ||||||||
\(495\) | 6.79894 | 0.305590 | ||||||||
\(496\) | −10.1479 | −0.455653 | ||||||||
\(497\) | 3.66347 | 0.164329 | ||||||||
\(498\) | −1.76274 | −0.0789902 | ||||||||
\(499\) | 24.8331 | 1.11168 | 0.555841 | − | 0.831288i | \(-0.312396\pi\) | ||||
0.555841 | + | 0.831288i | \(0.312396\pi\) | |||||||
\(500\) | −11.2866 | −0.504754 | ||||||||
\(501\) | 3.41720 | 0.152669 | ||||||||
\(502\) | −10.3172 | −0.460478 | ||||||||
\(503\) | −21.4279 | −0.955423 | −0.477712 | − | 0.878517i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878517i | \(0.658534\pi\) | |||||||
\(504\) | 0.998879 | 0.0444936 | ||||||||
\(505\) | −8.21344 | −0.365493 | ||||||||
\(506\) | 13.7423 | 0.610920 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 3.66487 | 0.162602 | ||||||||
\(509\) | −44.6685 | −1.97989 | −0.989947 | − | 0.141437i | \(-0.954828\pi\) | ||||
−0.989947 | + | 0.141437i | \(0.954828\pi\) | |||||||
\(510\) | 4.15724 | 0.184086 | ||||||||
\(511\) | 13.4813 | 0.596379 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.88860 | 0.0833837 | ||||||||
\(514\) | −3.22415 | −0.142211 | ||||||||
\(515\) | −1.40749 | −0.0620216 | ||||||||
\(516\) | 9.75344 | 0.429371 | ||||||||
\(517\) | −11.8882 | −0.522841 | ||||||||
\(518\) | −4.75217 | −0.208798 | ||||||||
\(519\) | −24.4518 | −1.07332 | ||||||||
\(520\) | −1.40749 | −0.0617227 | ||||||||
\(521\) | 23.6255 | 1.03505 | 0.517525 | − | 0.855668i | \(-0.326853\pi\) | ||||
0.517525 | + | 0.855668i | \(0.326853\pi\) | |||||||
\(522\) | 5.72981 | 0.250787 | ||||||||
\(523\) | −14.6631 | −0.641175 | −0.320587 | − | 0.947219i | \(-0.603880\pi\) | ||||
−0.320587 | + | 0.947219i | \(0.603880\pi\) | |||||||
\(524\) | 11.9908 | 0.523822 | ||||||||
\(525\) | 3.01558 | 0.131611 | ||||||||
\(526\) | 27.8650 | 1.21497 | ||||||||
\(527\) | 29.9732 | 1.30565 | ||||||||
\(528\) | 4.83053 | 0.210222 | ||||||||
\(529\) | −14.9066 | −0.648114 | ||||||||
\(530\) | 11.8060 | 0.512819 | ||||||||
\(531\) | −8.26441 | −0.358645 | ||||||||
\(532\) | −1.88648 | −0.0817894 | ||||||||
\(533\) | −4.77235 | −0.206713 | ||||||||
\(534\) | 0.860992 | 0.0372588 | ||||||||
\(535\) | 18.3051 | 0.791398 | ||||||||
\(536\) | 4.55266 | 0.196645 | ||||||||
\(537\) | −11.6219 | −0.501523 | ||||||||
\(538\) | 5.47995 | 0.236258 | ||||||||
\(539\) | −28.9940 | −1.24886 | ||||||||
\(540\) | 1.40749 | 0.0605689 | ||||||||
\(541\) | −14.5293 | −0.624663 | −0.312331 | − | 0.949973i | \(-0.601110\pi\) | ||||
−0.312331 | + | 0.949973i | \(0.601110\pi\) | |||||||
\(542\) | −25.0590 | −1.07638 | ||||||||
\(543\) | 16.1688 | 0.693868 | ||||||||
\(544\) | 2.95365 | 0.126637 | ||||||||
\(545\) | −1.75303 | −0.0750914 | ||||||||
\(546\) | 0.998879 | 0.0427481 | ||||||||
\(547\) | 7.36417 | 0.314869 | 0.157435 | − | 0.987529i | \(-0.449678\pi\) | ||||
0.157435 | + | 0.987529i | \(0.449678\pi\) | |||||||
\(548\) | 11.6193 | 0.496351 | ||||||||
\(549\) | −6.11324 | −0.260907 | ||||||||
\(550\) | 14.5832 | 0.621829 | ||||||||
\(551\) | −10.8213 | −0.461004 | ||||||||
\(552\) | 2.84489 | 0.121086 | ||||||||
\(553\) | 11.0974 | 0.471909 | ||||||||
\(554\) | −4.14155 | −0.175957 | ||||||||
\(555\) | −6.69615 | −0.284236 | ||||||||
\(556\) | 10.1782 | 0.431650 | ||||||||
\(557\) | 31.0943 | 1.31751 | 0.658753 | − | 0.752359i | \(-0.271084\pi\) | ||||
0.658753 | + | 0.752359i | \(0.271084\pi\) | |||||||
\(558\) | 10.1479 | 0.429593 | ||||||||
\(559\) | 9.75344 | 0.412527 | ||||||||
\(560\) | −1.40592 | −0.0594108 | ||||||||
\(561\) | −14.2677 | −0.602383 | ||||||||
\(562\) | 2.03599 | 0.0858830 | ||||||||
\(563\) | −14.1457 | −0.596171 | −0.298086 | − | 0.954539i | \(-0.596348\pi\) | ||||
−0.298086 | + | 0.954539i | \(0.596348\pi\) | |||||||
\(564\) | −2.46105 | −0.103629 | ||||||||
\(565\) | 14.0213 | 0.589883 | ||||||||
\(566\) | −10.5521 | −0.443537 | ||||||||
\(567\) | −0.998879 | −0.0419490 | ||||||||
\(568\) | 3.66759 | 0.153888 | ||||||||
\(569\) | −29.1790 | −1.22325 | −0.611623 | − | 0.791149i | \(-0.709483\pi\) | ||||
−0.611623 | + | 0.791149i | \(0.709483\pi\) | |||||||
\(570\) | −2.65819 | −0.111339 | ||||||||
\(571\) | −28.3905 | −1.18810 | −0.594052 | − | 0.804426i | \(-0.702473\pi\) | ||||
−0.594052 | + | 0.804426i | \(0.702473\pi\) | |||||||
\(572\) | 4.83053 | 0.201975 | ||||||||
\(573\) | −15.3479 | −0.641169 | ||||||||
\(574\) | −4.76700 | −0.198971 | ||||||||
\(575\) | 8.58860 | 0.358169 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 24.1055 | 1.00352 | 0.501762 | − | 0.865006i | \(-0.332685\pi\) | ||||
0.501762 | + | 0.865006i | \(0.332685\pi\) | |||||||
\(578\) | 8.27596 | 0.344234 | ||||||||
\(579\) | 5.62711 | 0.233855 | ||||||||
\(580\) | −8.06468 | −0.334868 | ||||||||
\(581\) | −1.76076 | −0.0730488 | ||||||||
\(582\) | 5.09415 | 0.211159 | ||||||||
\(583\) | −40.5182 | −1.67809 | ||||||||
\(584\) | 13.4965 | 0.558488 | ||||||||
\(585\) | 1.40749 | 0.0581927 | ||||||||
\(586\) | −20.2309 | −0.835729 | ||||||||
\(587\) | −20.9165 | −0.863318 | −0.431659 | − | 0.902037i | \(-0.642072\pi\) | ||||
−0.431659 | + | 0.902037i | \(0.642072\pi\) | |||||||
\(588\) | −6.00224 | −0.247528 | ||||||||
\(589\) | −19.1653 | −0.789690 | ||||||||
\(590\) | 11.6321 | 0.478886 | ||||||||
\(591\) | −8.91051 | −0.366529 | ||||||||
\(592\) | −4.75750 | −0.195532 | ||||||||
\(593\) | 31.4689 | 1.29227 | 0.646137 | − | 0.763222i | \(-0.276384\pi\) | ||||
0.646137 | + | 0.763222i | \(0.276384\pi\) | |||||||
\(594\) | −4.83053 | −0.198199 | ||||||||
\(595\) | 4.15258 | 0.170239 | ||||||||
\(596\) | 17.0885 | 0.699973 | ||||||||
\(597\) | −21.5100 | −0.880345 | ||||||||
\(598\) | 2.84489 | 0.116336 | ||||||||
\(599\) | −23.6003 | −0.964284 | −0.482142 | − | 0.876093i | \(-0.660141\pi\) | ||||
−0.482142 | + | 0.876093i | \(0.660141\pi\) | |||||||
\(600\) | 3.01896 | 0.123249 | ||||||||
\(601\) | 31.7300 | 1.29429 | 0.647147 | − | 0.762365i | \(-0.275962\pi\) | ||||
0.647147 | + | 0.762365i | \(0.275962\pi\) | |||||||
\(602\) | 9.74251 | 0.397075 | ||||||||
\(603\) | −4.55266 | −0.185399 | ||||||||
\(604\) | 13.2289 | 0.538277 | ||||||||
\(605\) | 17.3601 | 0.705787 | ||||||||
\(606\) | 5.83551 | 0.237051 | ||||||||
\(607\) | −14.8494 | −0.602718 | −0.301359 | − | 0.953511i | \(-0.597440\pi\) | ||||
−0.301359 | + | 0.953511i | \(0.597440\pi\) | |||||||
\(608\) | −1.88860 | −0.0765928 | ||||||||
\(609\) | 5.72339 | 0.231924 | ||||||||
\(610\) | 8.60434 | 0.348380 | ||||||||
\(611\) | −2.46105 | −0.0995634 | ||||||||
\(612\) | −2.95365 | −0.119394 | ||||||||
\(613\) | 23.6567 | 0.955484 | 0.477742 | − | 0.878500i | \(-0.341455\pi\) | ||||
0.477742 | + | 0.878500i | \(0.341455\pi\) | |||||||
\(614\) | −9.28706 | −0.374795 | ||||||||
\(615\) | −6.71705 | −0.270858 | ||||||||
\(616\) | 4.82512 | 0.194409 | ||||||||
\(617\) | −9.47246 | −0.381347 | −0.190673 | − | 0.981654i | \(-0.561067\pi\) | ||||
−0.190673 | + | 0.981654i | \(0.561067\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 26.5081 | 1.06545 | 0.532726 | − | 0.846288i | \(-0.321168\pi\) | ||||
0.532726 | + | 0.846288i | \(0.321168\pi\) | |||||||
\(620\) | −14.2831 | −0.573621 | ||||||||
\(621\) | −2.84489 | −0.114161 | ||||||||
\(622\) | −18.0200 | −0.722536 | ||||||||
\(623\) | 0.860027 | 0.0344562 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −0.791061 | −0.0316424 | ||||||||
\(626\) | −26.1537 | −1.04531 | ||||||||
\(627\) | 9.12294 | 0.364335 | ||||||||
\(628\) | 9.61127 | 0.383531 | ||||||||
\(629\) | 14.0520 | 0.560289 | ||||||||
\(630\) | 1.40592 | 0.0560130 | ||||||||
\(631\) | 38.7613 | 1.54306 | 0.771531 | − | 0.636192i | \(-0.219491\pi\) | ||||
0.771531 | + | 0.636192i | \(0.219491\pi\) | |||||||
\(632\) | 11.1098 | 0.441926 | ||||||||
\(633\) | 25.6510 | 1.01954 | ||||||||
\(634\) | −7.89534 | −0.313564 | ||||||||
\(635\) | 5.15828 | 0.204700 | ||||||||
\(636\) | −8.38795 | −0.332604 | ||||||||
\(637\) | −6.00224 | −0.237817 | ||||||||
\(638\) | 27.6780 | 1.09578 | ||||||||
\(639\) | −3.66759 | −0.145087 | ||||||||
\(640\) | −1.40749 | −0.0556361 | ||||||||
\(641\) | 21.2063 | 0.837600 | 0.418800 | − | 0.908079i | \(-0.362451\pi\) | ||||
0.418800 | + | 0.908079i | \(0.362451\pi\) | |||||||
\(642\) | −13.0054 | −0.513284 | ||||||||
\(643\) | −15.7977 | −0.622999 | −0.311500 | − | 0.950246i | \(-0.600831\pi\) | ||||
−0.311500 | + | 0.950246i | \(0.600831\pi\) | |||||||
\(644\) | 2.84170 | 0.111979 | ||||||||
\(645\) | 13.7279 | 0.540536 | ||||||||
\(646\) | 5.57826 | 0.219474 | ||||||||
\(647\) | −31.0349 | −1.22011 | −0.610054 | − | 0.792360i | \(-0.708852\pi\) | ||||
−0.610054 | + | 0.792360i | \(0.708852\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −39.9215 | −1.56706 | ||||||||
\(650\) | 3.01896 | 0.118413 | ||||||||
\(651\) | 10.1365 | 0.397280 | ||||||||
\(652\) | −7.98844 | −0.312851 | ||||||||
\(653\) | −35.0335 | −1.37097 | −0.685483 | − | 0.728089i | \(-0.740409\pi\) | ||||
−0.685483 | + | 0.728089i | \(0.740409\pi\) | |||||||
\(654\) | 1.24549 | 0.0487027 | ||||||||
\(655\) | 16.8770 | 0.659440 | ||||||||
\(656\) | −4.77235 | −0.186329 | ||||||||
\(657\) | −13.4965 | −0.526547 | ||||||||
\(658\) | −2.45829 | −0.0958342 | ||||||||
\(659\) | −49.0836 | −1.91202 | −0.956012 | − | 0.293327i | \(-0.905237\pi\) | ||||
−0.956012 | + | 0.293327i | \(0.905237\pi\) | |||||||
\(660\) | 6.79894 | 0.264648 | ||||||||
\(661\) | −24.0650 | −0.936020 | −0.468010 | − | 0.883723i | \(-0.655029\pi\) | ||||
−0.468010 | + | 0.883723i | \(0.655029\pi\) | |||||||
\(662\) | −21.0364 | −0.817605 | ||||||||
\(663\) | −2.95365 | −0.114710 | ||||||||
\(664\) | −1.76274 | −0.0684076 | ||||||||
\(665\) | −2.65521 | −0.102965 | ||||||||
\(666\) | 4.75750 | 0.184349 | ||||||||
\(667\) | 16.3007 | 0.631164 | ||||||||
\(668\) | 3.41720 | 0.132215 | ||||||||
\(669\) | 12.8137 | 0.495406 | ||||||||
\(670\) | 6.40784 | 0.247556 | ||||||||
\(671\) | −29.5302 | −1.14000 | ||||||||
\(672\) | 0.998879 | 0.0385326 | ||||||||
\(673\) | 9.91676 | 0.382263 | 0.191131 | − | 0.981564i | \(-0.438784\pi\) | ||||
0.191131 | + | 0.981564i | \(0.438784\pi\) | |||||||
\(674\) | −26.1538 | −1.00741 | ||||||||
\(675\) | −3.01896 | −0.116200 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 17.8633 | 0.686543 | 0.343272 | − | 0.939236i | \(-0.388465\pi\) | ||||
0.343272 | + | 0.939236i | \(0.388465\pi\) | |||||||
\(678\) | −9.96193 | −0.382585 | ||||||||
\(679\) | 5.08844 | 0.195276 | ||||||||
\(680\) | 4.15724 | 0.159423 | ||||||||
\(681\) | −12.3807 | −0.474429 | ||||||||
\(682\) | 49.0196 | 1.87706 | ||||||||
\(683\) | 3.17969 | 0.121668 | 0.0608338 | − | 0.998148i | \(-0.480624\pi\) | ||||
0.0608338 | + | 0.998148i | \(0.480624\pi\) | |||||||
\(684\) | 1.88860 | 0.0722124 | ||||||||
\(685\) | 16.3541 | 0.624857 | ||||||||
\(686\) | −12.9877 | −0.495871 | ||||||||
\(687\) | 12.8890 | 0.491744 | ||||||||
\(688\) | 9.75344 | 0.371846 | ||||||||
\(689\) | −8.38795 | −0.319555 | ||||||||
\(690\) | 4.00416 | 0.152436 | ||||||||
\(691\) | 22.1457 | 0.842462 | 0.421231 | − | 0.906953i | \(-0.361598\pi\) | ||||
0.421231 | + | 0.906953i | \(0.361598\pi\) | |||||||
\(692\) | −24.4518 | −0.929519 | ||||||||
\(693\) | −4.82512 | −0.183291 | ||||||||
\(694\) | 20.9493 | 0.795224 | ||||||||
\(695\) | 14.3257 | 0.543405 | ||||||||
\(696\) | 5.72981 | 0.217188 | ||||||||
\(697\) | 14.0958 | 0.533918 | ||||||||
\(698\) | −33.7856 | −1.27880 | ||||||||
\(699\) | −6.27793 | −0.237453 | ||||||||
\(700\) | 3.01558 | 0.113978 | ||||||||
\(701\) | −21.3476 | −0.806289 | −0.403144 | − | 0.915136i | \(-0.632083\pi\) | ||||
−0.403144 | + | 0.915136i | \(0.632083\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −8.98501 | −0.338876 | ||||||||
\(704\) | 4.83053 | 0.182057 | ||||||||
\(705\) | −3.46391 | −0.130458 | ||||||||
\(706\) | 8.70939 | 0.327782 | ||||||||
\(707\) | 5.82897 | 0.219221 | ||||||||
\(708\) | −8.26441 | −0.310596 | ||||||||
\(709\) | 16.7407 | 0.628709 | 0.314355 | − | 0.949306i | \(-0.398212\pi\) | ||||
0.314355 | + | 0.949306i | \(0.398212\pi\) | |||||||
\(710\) | 5.16210 | 0.193730 | ||||||||
\(711\) | −11.1098 | −0.416652 | ||||||||
\(712\) | 0.860992 | 0.0322670 | ||||||||
\(713\) | 28.8695 | 1.08117 | ||||||||
\(714\) | −2.95034 | −0.110414 | ||||||||
\(715\) | 6.79894 | 0.254266 | ||||||||
\(716\) | −11.6219 | −0.434332 | ||||||||
\(717\) | −20.3261 | −0.759091 | ||||||||
\(718\) | 26.5369 | 0.990347 | ||||||||
\(719\) | 13.5812 | 0.506494 | 0.253247 | − | 0.967402i | \(-0.418502\pi\) | ||||
0.253247 | + | 0.967402i | \(0.418502\pi\) | |||||||
\(720\) | 1.40749 | 0.0524542 | ||||||||
\(721\) | 0.998879 | 0.0372002 | ||||||||
\(722\) | 15.4332 | 0.574364 | ||||||||
\(723\) | −5.81756 | −0.216357 | ||||||||
\(724\) | 16.1688 | 0.600907 | ||||||||
\(725\) | 17.2981 | 0.642435 | ||||||||
\(726\) | −12.3340 | −0.457759 | ||||||||
\(727\) | 20.6522 | 0.765947 | 0.382974 | − | 0.923759i | \(-0.374900\pi\) | ||||
0.382974 | + | 0.923759i | \(0.374900\pi\) | |||||||
\(728\) | 0.998879 | 0.0370209 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.9962 | 0.703081 | ||||||||
\(731\) | −28.8082 | −1.06551 | ||||||||
\(732\) | −6.11324 | −0.225952 | ||||||||
\(733\) | −24.6696 | −0.911194 | −0.455597 | − | 0.890186i | \(-0.650574\pi\) | ||||
−0.455597 | + | 0.890186i | \(0.650574\pi\) | |||||||
\(734\) | −9.83164 | −0.362892 | ||||||||
\(735\) | −8.44812 | −0.311613 | ||||||||
\(736\) | 2.84489 | 0.104864 | ||||||||
\(737\) | −21.9918 | −0.810077 | ||||||||
\(738\) | 4.77235 | 0.175673 | ||||||||
\(739\) | 30.0209 | 1.10434 | 0.552169 | − | 0.833732i | \(-0.313800\pi\) | ||||
0.552169 | + | 0.833732i | \(0.313800\pi\) | |||||||
\(740\) | −6.69615 | −0.246155 | ||||||||
\(741\) | 1.88860 | 0.0693794 | ||||||||
\(742\) | −8.37855 | −0.307586 | ||||||||
\(743\) | −27.9466 | −1.02526 | −0.512631 | − | 0.858609i | \(-0.671329\pi\) | ||||
−0.512631 | + | 0.858609i | \(0.671329\pi\) | |||||||
\(744\) | 10.1479 | 0.372039 | ||||||||
\(745\) | 24.0520 | 0.881197 | ||||||||
\(746\) | 36.6010 | 1.34006 | ||||||||
\(747\) | 1.76274 | 0.0644953 | ||||||||
\(748\) | −14.2677 | −0.521679 | ||||||||
\(749\) | −12.9909 | −0.474676 | ||||||||
\(750\) | 11.2866 | 0.412130 | ||||||||
\(751\) | −1.09991 | −0.0401365 | −0.0200682 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200682 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(752\) | −2.46105 | −0.0897453 | ||||||||
\(753\) | 10.3172 | 0.375979 | ||||||||
\(754\) | 5.72981 | 0.208668 | ||||||||
\(755\) | 18.6196 | 0.677637 | ||||||||
\(756\) | −0.998879 | −0.0363289 | ||||||||
\(757\) | 47.2731 | 1.71817 | 0.859084 | − | 0.511834i | \(-0.171034\pi\) | ||||
0.859084 | + | 0.511834i | \(0.171034\pi\) | |||||||
\(758\) | 23.6372 | 0.858541 | ||||||||
\(759\) | −13.7423 | −0.498814 | ||||||||
\(760\) | −2.65819 | −0.0964227 | ||||||||
\(761\) | −48.2098 | −1.74760 | −0.873802 | − | 0.486282i | \(-0.838353\pi\) | ||||
−0.873802 | + | 0.486282i | \(0.838353\pi\) | |||||||
\(762\) | −3.66487 | −0.132764 | ||||||||
\(763\) | 1.24410 | 0.0450394 | ||||||||
\(764\) | −15.3479 | −0.555269 | ||||||||
\(765\) | −4.15724 | −0.150305 | ||||||||
\(766\) | −29.2380 | −1.05641 | ||||||||
\(767\) | −8.26441 | −0.298411 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −44.9515 | −1.62099 | −0.810497 | − | 0.585743i | \(-0.800803\pi\) | ||||
−0.810497 | + | 0.585743i | \(0.800803\pi\) | |||||||
\(770\) | 6.79132 | 0.244742 | ||||||||
\(771\) | 3.22415 | 0.116115 | ||||||||
\(772\) | 5.62711 | 0.202524 | ||||||||
\(773\) | 20.0462 | 0.721011 | 0.360506 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360506 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(774\) | −9.75344 | −0.350580 | ||||||||
\(775\) | 30.6360 | 1.10048 | ||||||||
\(776\) | 5.09415 | 0.182869 | ||||||||
\(777\) | 4.75217 | 0.170483 | ||||||||
\(778\) | −9.48255 | −0.339966 | ||||||||
\(779\) | −9.01305 | −0.322926 | ||||||||
\(780\) | 1.40749 | 0.0503964 | ||||||||
\(781\) | −17.7164 | −0.633942 | ||||||||
\(782\) | −8.40279 | −0.300483 | ||||||||
\(783\) | −5.72981 | −0.204767 | ||||||||
\(784\) | −6.00224 | −0.214366 | ||||||||
\(785\) | 13.5278 | 0.482828 | ||||||||
\(786\) | −11.9908 | −0.427699 | ||||||||
\(787\) | −14.6857 | −0.523489 | −0.261744 | − | 0.965137i | \(-0.584298\pi\) | ||||
−0.261744 | + | 0.965137i | \(0.584298\pi\) | |||||||
\(788\) | −8.91051 | −0.317424 | ||||||||
\(789\) | −27.8650 | −0.992021 | ||||||||
\(790\) | 15.6370 | 0.556341 | ||||||||
\(791\) | −9.95076 | −0.353808 | ||||||||
\(792\) | −4.83053 | −0.171645 | ||||||||
\(793\) | −6.11324 | −0.217087 | ||||||||
\(794\) | −6.03291 | −0.214100 | ||||||||
\(795\) | −11.8060 | −0.418715 | ||||||||
\(796\) | −21.5100 | −0.762401 | ||||||||
\(797\) | 37.0049 | 1.31078 | 0.655391 | − | 0.755290i | \(-0.272504\pi\) | ||||
0.655391 | + | 0.755290i | \(0.272504\pi\) | |||||||
\(798\) | 1.88648 | 0.0667807 | ||||||||
\(799\) | 7.26908 | 0.257161 | ||||||||
\(800\) | 3.01896 | 0.106736 | ||||||||
\(801\) | −0.860992 | −0.0304217 | ||||||||
\(802\) | 10.9056 | 0.385091 | ||||||||
\(803\) | −65.1951 | −2.30069 | ||||||||
\(804\) | −4.55266 | −0.160560 | ||||||||
\(805\) | 3.99967 | 0.140970 | ||||||||
\(806\) | 10.1479 | 0.357443 | ||||||||
\(807\) | −5.47995 | −0.192904 | ||||||||
\(808\) | 5.83551 | 0.205292 | ||||||||
\(809\) | −34.4491 | −1.21117 | −0.605583 | − | 0.795782i | \(-0.707060\pi\) | ||||
−0.605583 | + | 0.795782i | \(0.707060\pi\) | |||||||
\(810\) | −1.40749 | −0.0494543 | ||||||||
\(811\) | −25.1527 | −0.883230 | −0.441615 | − | 0.897205i | \(-0.645594\pi\) | ||||
−0.441615 | + | 0.897205i | \(0.645594\pi\) | |||||||
\(812\) | 5.72339 | 0.200852 | ||||||||
\(813\) | 25.0590 | 0.878859 | ||||||||
\(814\) | 22.9812 | 0.805492 | ||||||||
\(815\) | −11.2437 | −0.393849 | ||||||||
\(816\) | −2.95365 | −0.103398 | ||||||||
\(817\) | 18.4203 | 0.644446 | ||||||||
\(818\) | 20.6537 | 0.722141 | ||||||||
\(819\) | −0.998879 | −0.0349037 | ||||||||
\(820\) | −6.71705 | −0.234569 | ||||||||
\(821\) | 51.1856 | 1.78639 | 0.893194 | − | 0.449671i | \(-0.148459\pi\) | ||||
0.893194 | + | 0.449671i | \(0.148459\pi\) | |||||||
\(822\) | −11.6193 | −0.405269 | ||||||||
\(823\) | 9.93393 | 0.346275 | 0.173138 | − | 0.984898i | \(-0.444609\pi\) | ||||
0.173138 | + | 0.984898i | \(0.444609\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −14.5832 | −0.507721 | ||||||||
\(826\) | −8.25515 | −0.287233 | ||||||||
\(827\) | −4.04881 | −0.140791 | −0.0703954 | − | 0.997519i | \(-0.522426\pi\) | ||||
−0.0703954 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(828\) | −2.84489 | −0.0988666 | ||||||||
\(829\) | −44.1314 | −1.53275 | −0.766374 | − | 0.642395i | \(-0.777941\pi\) | ||||
−0.766374 | + | 0.642395i | \(0.777941\pi\) | |||||||
\(830\) | −2.48104 | −0.0861183 | ||||||||
\(831\) | 4.14155 | 0.143669 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 17.7285 | 0.614257 | ||||||||
\(834\) | −10.1782 | −0.352441 | ||||||||
\(835\) | 4.80969 | 0.166446 | ||||||||
\(836\) | 9.12294 | 0.315523 | ||||||||
\(837\) | −10.1479 | −0.350762 | ||||||||
\(838\) | −27.0666 | −0.935001 | ||||||||
\(839\) | −25.9048 | −0.894332 | −0.447166 | − | 0.894451i | \(-0.647567\pi\) | ||||
−0.447166 | + | 0.894451i | \(0.647567\pi\) | |||||||
\(840\) | 1.40592 | 0.0485087 | ||||||||
\(841\) | 3.83078 | 0.132096 | ||||||||
\(842\) | 25.4862 | 0.878314 | ||||||||
\(843\) | −2.03599 | −0.0701231 | ||||||||
\(844\) | 25.6510 | 0.882945 | ||||||||
\(845\) | 1.40749 | 0.0484193 | ||||||||
\(846\) | 2.46105 | 0.0846126 | ||||||||
\(847\) | −12.3202 | −0.423327 | ||||||||
\(848\) | −8.38795 | −0.288043 | ||||||||
\(849\) | 10.5521 | 0.362147 | ||||||||
\(850\) | −8.91695 | −0.305849 | ||||||||
\(851\) | 13.5345 | 0.463958 | ||||||||
\(852\) | −3.66759 | −0.125649 | ||||||||
\(853\) | 9.38918 | 0.321479 | 0.160740 | − | 0.986997i | \(-0.448612\pi\) | ||||
0.160740 | + | 0.986997i | \(0.448612\pi\) | |||||||
\(854\) | −6.10638 | −0.208956 | ||||||||
\(855\) | 2.65819 | 0.0909082 | ||||||||
\(856\) | −13.0054 | −0.444517 | ||||||||
\(857\) | −22.2294 | −0.759342 | −0.379671 | − | 0.925122i | \(-0.623963\pi\) | ||||
−0.379671 | + | 0.925122i | \(0.623963\pi\) | |||||||
\(858\) | −4.83053 | −0.164912 | ||||||||
\(859\) | 37.6415 | 1.28431 | 0.642156 | − | 0.766574i | \(-0.278040\pi\) | ||||
0.642156 | + | 0.766574i | \(0.278040\pi\) | |||||||
\(860\) | 13.7279 | 0.468118 | ||||||||
\(861\) | 4.76700 | 0.162459 | ||||||||
\(862\) | −30.4313 | −1.03649 | ||||||||
\(863\) | 33.2589 | 1.13215 | 0.566073 | − | 0.824355i | \(-0.308462\pi\) | ||||
0.566073 | + | 0.824355i | \(0.308462\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −34.4158 | −1.17017 | ||||||||
\(866\) | −37.2374 | −1.26538 | ||||||||
\(867\) | −8.27596 | −0.281066 | ||||||||
\(868\) | 10.1365 | 0.344055 | ||||||||
\(869\) | −53.6664 | −1.82051 | ||||||||
\(870\) | 8.06468 | 0.273418 | ||||||||
\(871\) | −4.55266 | −0.154261 | ||||||||
\(872\) | 1.24549 | 0.0421778 | ||||||||
\(873\) | −5.09415 | −0.172411 | ||||||||
\(874\) | 5.37285 | 0.181739 | ||||||||
\(875\) | 11.2740 | 0.381130 | ||||||||
\(876\) | −13.4965 | −0.456003 | ||||||||
\(877\) | −35.4445 | −1.19688 | −0.598438 | − | 0.801169i | \(-0.704212\pi\) | ||||
−0.598438 | + | 0.801169i | \(0.704212\pi\) | |||||||
\(878\) | 28.7436 | 0.970050 | ||||||||
\(879\) | 20.2309 | 0.682370 | ||||||||
\(880\) | 6.79894 | 0.229192 | ||||||||
\(881\) | −9.58825 | −0.323036 | −0.161518 | − | 0.986870i | \(-0.551639\pi\) | ||||
−0.161518 | + | 0.986870i | \(0.551639\pi\) | |||||||
\(882\) | 6.00224 | 0.202106 | ||||||||
\(883\) | −31.9681 | −1.07581 | −0.537907 | − | 0.843004i | \(-0.680785\pi\) | ||||
−0.537907 | + | 0.843004i | \(0.680785\pi\) | |||||||
\(884\) | −2.95365 | −0.0993420 | ||||||||
\(885\) | −11.6321 | −0.391009 | ||||||||
\(886\) | 9.15518 | 0.307574 | ||||||||
\(887\) | 25.2887 | 0.849113 | 0.424556 | − | 0.905402i | \(-0.360430\pi\) | ||||
0.424556 | + | 0.905402i | \(0.360430\pi\) | |||||||
\(888\) | 4.75750 | 0.159651 | ||||||||
\(889\) | −3.66076 | −0.122778 | ||||||||
\(890\) | 1.21184 | 0.0406210 | ||||||||
\(891\) | 4.83053 | 0.161829 | ||||||||
\(892\) | 12.8137 | 0.429034 | ||||||||
\(893\) | −4.64794 | −0.155537 | ||||||||
\(894\) | −17.0885 | −0.571526 | ||||||||
\(895\) | −16.3578 | −0.546781 | ||||||||
\(896\) | 0.998879 | 0.0333702 | ||||||||
\(897\) | −2.84489 | −0.0949880 | ||||||||
\(898\) | −35.7192 | −1.19197 | ||||||||
\(899\) | 58.1454 | 1.93926 | ||||||||
\(900\) | −3.01896 | −0.100632 | ||||||||
\(901\) | 24.7751 | 0.825377 | ||||||||
\(902\) | 23.0530 | 0.767580 | ||||||||
\(903\) | −9.74251 | −0.324210 | ||||||||
\(904\) | −9.96193 | −0.331329 | ||||||||
\(905\) | 22.7574 | 0.756482 | ||||||||
\(906\) | −13.2289 | −0.439501 | ||||||||
\(907\) | 24.8400 | 0.824798 | 0.412399 | − | 0.911003i | \(-0.364691\pi\) | ||||
0.412399 | + | 0.911003i | \(0.364691\pi\) | |||||||
\(908\) | −12.3807 | −0.410868 | ||||||||
\(909\) | −5.83551 | −0.193552 | ||||||||
\(910\) | 1.40592 | 0.0466057 | ||||||||
\(911\) | −52.5136 | −1.73985 | −0.869926 | − | 0.493182i | \(-0.835834\pi\) | ||||
−0.869926 | + | 0.493182i | \(0.835834\pi\) | |||||||
\(912\) | 1.88860 | 0.0625378 | ||||||||
\(913\) | 8.51497 | 0.281804 | ||||||||
\(914\) | −22.8348 | −0.755307 | ||||||||
\(915\) | −8.60434 | −0.284451 | ||||||||
\(916\) | 12.8890 | 0.425863 | ||||||||
\(917\) | −11.9774 | −0.395529 | ||||||||
\(918\) | 2.95365 | 0.0974850 | ||||||||
\(919\) | −17.4881 | −0.576878 | −0.288439 | − | 0.957498i | \(-0.593136\pi\) | ||||
−0.288439 | + | 0.957498i | \(0.593136\pi\) | |||||||
\(920\) | 4.00416 | 0.132013 | ||||||||
\(921\) | 9.28706 | 0.306019 | ||||||||
\(922\) | 24.7047 | 0.813605 | ||||||||
\(923\) | −3.66759 | −0.120720 | ||||||||
\(924\) | −4.82512 | −0.158735 | ||||||||
\(925\) | 14.3627 | 0.472243 | ||||||||
\(926\) | −9.59246 | −0.315228 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 5.72981 | 0.188090 | ||||||||
\(929\) | −7.34782 | −0.241074 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(930\) | 14.2831 | 0.468360 | ||||||||
\(931\) | −11.3358 | −0.371517 | ||||||||
\(932\) | −6.27793 | −0.205641 | ||||||||
\(933\) | 18.0200 | 0.589948 | ||||||||
\(934\) | 20.3961 | 0.667379 | ||||||||
\(935\) | −20.0817 | −0.656741 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 36.0157 | 1.17658 | 0.588291 | − | 0.808649i | \(-0.299801\pi\) | ||||
0.588291 | + | 0.808649i | \(0.299801\pi\) | |||||||
\(938\) | −4.54756 | −0.148483 | ||||||||
\(939\) | 26.1537 | 0.853493 | ||||||||
\(940\) | −3.46391 | −0.112980 | ||||||||
\(941\) | 2.80335 | 0.0913865 | 0.0456933 | − | 0.998956i | \(-0.485450\pi\) | ||||
0.0456933 | + | 0.998956i | \(0.485450\pi\) | |||||||
\(942\) | −9.61127 | −0.313152 | ||||||||
\(943\) | 13.5768 | 0.442121 | ||||||||
\(944\) | −8.26441 | −0.268984 | ||||||||
\(945\) | −1.40592 | −0.0457345 | ||||||||
\(946\) | −47.1143 | −1.53182 | ||||||||
\(947\) | −17.8646 | −0.580522 | −0.290261 | − | 0.956947i | \(-0.593742\pi\) | ||||
−0.290261 | + | 0.956947i | \(0.593742\pi\) | |||||||
\(948\) | −11.1098 | −0.360831 | ||||||||
\(949\) | −13.4965 | −0.438114 | ||||||||
\(950\) | 5.70161 | 0.184985 | ||||||||
\(951\) | 7.89534 | 0.256024 | ||||||||
\(952\) | −2.95034 | −0.0956210 | ||||||||
\(953\) | 37.0971 | 1.20169 | 0.600846 | − | 0.799365i | \(-0.294831\pi\) | ||||
0.600846 | + | 0.799365i | \(0.294831\pi\) | |||||||
\(954\) | 8.38795 | 0.271570 | ||||||||
\(955\) | −21.6021 | −0.699028 | ||||||||
\(956\) | −20.3261 | −0.657392 | ||||||||
\(957\) | −27.6780 | −0.894704 | ||||||||
\(958\) | 6.02670 | 0.194714 | ||||||||
\(959\) | −11.6063 | −0.374786 | ||||||||
\(960\) | 1.40749 | 0.0454267 | ||||||||
\(961\) | 71.9792 | 2.32191 | ||||||||
\(962\) | 4.75750 | 0.153388 | ||||||||
\(963\) | 13.0054 | 0.419095 | ||||||||
\(964\) | −5.81756 | −0.187371 | ||||||||
\(965\) | 7.92013 | 0.254958 | ||||||||
\(966\) | −2.84170 | −0.0914301 | ||||||||
\(967\) | −12.1837 | −0.391800 | −0.195900 | − | 0.980624i | \(-0.562763\pi\) | ||||
−0.195900 | + | 0.980624i | \(0.562763\pi\) | |||||||
\(968\) | −12.3340 | −0.396431 | ||||||||
\(969\) | −5.57826 | −0.179199 | ||||||||
\(970\) | 7.16998 | 0.230214 | ||||||||
\(971\) | −57.5801 | −1.84783 | −0.923917 | − | 0.382592i | \(-0.875031\pi\) | ||||
−0.923917 | + | 0.382592i | \(0.875031\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −10.1668 | −0.325931 | ||||||||
\(974\) | −23.6141 | −0.756645 | ||||||||
\(975\) | −3.01896 | −0.0966842 | ||||||||
\(976\) | −6.11324 | −0.195680 | ||||||||
\(977\) | −32.1063 | −1.02717 | −0.513585 | − | 0.858039i | \(-0.671683\pi\) | ||||
−0.513585 | + | 0.858039i | \(0.671683\pi\) | |||||||
\(978\) | 7.98844 | 0.255442 | ||||||||
\(979\) | −4.15905 | −0.132924 | ||||||||
\(980\) | −8.44812 | −0.269865 | ||||||||
\(981\) | −1.24549 | −0.0397656 | ||||||||
\(982\) | 18.4702 | 0.589409 | ||||||||
\(983\) | 42.9319 | 1.36931 | 0.684657 | − | 0.728865i | \(-0.259952\pi\) | ||||
0.684657 | + | 0.728865i | \(0.259952\pi\) | |||||||
\(984\) | 4.77235 | 0.152137 | ||||||||
\(985\) | −12.5415 | −0.399605 | ||||||||
\(986\) | −16.9239 | −0.538966 | ||||||||
\(987\) | 2.45829 | 0.0782483 | ||||||||
\(988\) | 1.88860 | 0.0600843 | ||||||||
\(989\) | −27.7474 | −0.882317 | ||||||||
\(990\) | −6.79894 | −0.216085 | ||||||||
\(991\) | −26.2680 | −0.834429 | −0.417215 | − | 0.908808i | \(-0.636994\pi\) | ||||
−0.417215 | + | 0.908808i | \(0.636994\pi\) | |||||||
\(992\) | 10.1479 | 0.322195 | ||||||||
\(993\) | 21.0364 | 0.667571 | ||||||||
\(994\) | −3.66347 | −0.116198 | ||||||||
\(995\) | −30.2752 | −0.959787 | ||||||||
\(996\) | 1.76274 | 0.0558545 | ||||||||
\(997\) | −60.1384 | −1.90460 | −0.952301 | − | 0.305160i | \(-0.901290\pi\) | ||||
−0.952301 | + | 0.305160i | \(0.901290\pi\) | |||||||
\(998\) | −24.8331 | −0.786078 | ||||||||
\(999\) | −4.75750 | −0.150521 |
(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 | 8034.2.a.w.1.8 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial |