Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.70928 | 1.91575 | 0.957873 | − | 0.287190i | \(-0.0927213\pi\) | ||||
0.957873 | + | 0.287190i | \(0.0927213\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.34017 | 2.67009 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.70928 | −1.10606 | ||||||||
\(7\) | −1.07838 | −0.407588 | −0.203794 | − | 0.979014i | \(-0.565327\pi\) | ||||
−0.203794 | + | 0.979014i | \(0.565327\pi\) | |||||||
\(8\) | 9.04945 | 3.19946 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −5.34017 | −1.54158 | ||||||||
\(13\) | 4.34017 | 1.20375 | 0.601874 | − | 0.798591i | \(-0.294421\pi\) | ||||
0.601874 | + | 0.798591i | \(0.294421\pi\) | |||||||
\(14\) | −2.92162 | −0.780836 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.8371 | 3.45928 | ||||||||
\(17\) | −7.75872 | −1.88177 | −0.940883 | − | 0.338730i | \(-0.890003\pi\) | ||||
−0.940883 | + | 0.338730i | \(0.890003\pi\) | |||||||
\(18\) | 2.70928 | 0.638582 | ||||||||
\(19\) | 5.26180 | 1.20714 | 0.603569 | − | 0.797311i | \(-0.293745\pi\) | ||||
0.603569 | + | 0.797311i | \(0.293745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.07838 | 0.235321 | ||||||||
\(22\) | 2.70928 | 0.577619 | ||||||||
\(23\) | 2.15676 | 0.449715 | 0.224857 | − | 0.974392i | \(-0.427808\pi\) | ||||
0.224857 | + | 0.974392i | \(0.427808\pi\) | |||||||
\(24\) | −9.04945 | −1.84721 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.7587 | 2.30608 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.75872 | −1.08830 | ||||||||
\(29\) | 1.41855 | 0.263418 | 0.131709 | − | 0.991288i | \(-0.457954\pi\) | ||||
0.131709 | + | 0.991288i | \(0.457954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.68035 | −0.840615 | −0.420307 | − | 0.907382i | \(-0.638078\pi\) | ||||
−0.420307 | + | 0.907382i | \(0.638078\pi\) | |||||||
\(32\) | 19.3896 | 3.42763 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −21.0205 | −3.60499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.34017 | 0.890029 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 14.2557 | 2.31257 | ||||||||
\(39\) | −4.34017 | −0.694984 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.41855 | −1.47093 | −0.735465 | − | 0.677562i | \(-0.763036\pi\) | ||||
−0.735465 | + | 0.677562i | \(0.763036\pi\) | |||||||
\(42\) | 2.92162 | 0.450816 | ||||||||
\(43\) | −7.60197 | −1.15929 | −0.579645 | − | 0.814869i | \(-0.696809\pi\) | ||||
−0.579645 | + | 0.814869i | \(0.696809\pi\) | |||||||
\(44\) | 5.34017 | 0.805061 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.84324 | 0.861539 | ||||||||
\(47\) | −4.68035 | −0.682699 | −0.341349 | − | 0.939937i | \(-0.610884\pi\) | ||||
−0.341349 | + | 0.939937i | \(0.610884\pi\) | |||||||
\(48\) | −13.8371 | −1.99721 | ||||||||
\(49\) | −5.83710 | −0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.75872 | 1.08644 | ||||||||
\(52\) | 23.1773 | 3.21411 | ||||||||
\(53\) | −0.156755 | −0.0215320 | −0.0107660 | − | 0.999942i | \(-0.503427\pi\) | ||||
−0.0107660 | + | 0.999942i | \(0.503427\pi\) | |||||||
\(54\) | −2.70928 | −0.368686 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.75872 | −1.30406 | ||||||||
\(57\) | −5.26180 | −0.696942 | ||||||||
\(58\) | 3.84324 | 0.504643 | ||||||||
\(59\) | 6.15676 | 0.801541 | 0.400771 | − | 0.916178i | \(-0.368742\pi\) | ||||
0.400771 | + | 0.916178i | \(0.368742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.15676 | −0.532218 | −0.266109 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266109 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(62\) | −12.6803 | −1.61041 | ||||||||
\(63\) | −1.07838 | −0.135863 | ||||||||
\(64\) | 24.8576 | 3.10720 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.70928 | −0.333489 | ||||||||
\(67\) | 8.68035 | 1.06047 | 0.530237 | − | 0.847850i | \(-0.322103\pi\) | ||||
0.530237 | + | 0.847850i | \(0.322103\pi\) | |||||||
\(68\) | −41.4329 | −5.02448 | ||||||||
\(69\) | −2.15676 | −0.259643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.68035 | −0.555455 | −0.277727 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277727 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(72\) | 9.04945 | 1.06649 | ||||||||
\(73\) | 10.4969 | 1.22857 | 0.614286 | − | 0.789083i | \(-0.289444\pi\) | ||||
0.614286 | + | 0.789083i | \(0.289444\pi\) | |||||||
\(74\) | 5.41855 | 0.629894 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.0989 | 3.22316 | ||||||||
\(77\) | −1.07838 | −0.122893 | ||||||||
\(78\) | −11.7587 | −1.33141 | ||||||||
\(79\) | −8.09890 | −0.911197 | −0.455599 | − | 0.890185i | \(-0.650575\pi\) | ||||
−0.455599 | + | 0.890185i | \(0.650575\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −25.5174 | −2.81793 | ||||||||
\(83\) | 11.0205 | 1.20966 | 0.604830 | − | 0.796355i | \(-0.293241\pi\) | ||||
0.604830 | + | 0.796355i | \(0.293241\pi\) | |||||||
\(84\) | 5.75872 | 0.628328 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −20.5958 | −2.22090 | ||||||||
\(87\) | −1.41855 | −0.152085 | ||||||||
\(88\) | 9.04945 | 0.964674 | ||||||||
\(89\) | −12.8371 | −1.36073 | −0.680365 | − | 0.732873i | \(-0.738179\pi\) | ||||
−0.680365 | + | 0.732873i | \(0.738179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.68035 | −0.490634 | ||||||||
\(92\) | 11.5174 | 1.20078 | ||||||||
\(93\) | 4.68035 | 0.485329 | ||||||||
\(94\) | −12.6803 | −1.30788 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −19.3896 | −1.97894 | ||||||||
\(97\) | −14.6803 | −1.49056 | −0.745282 | − | 0.666750i | \(-0.767685\pi\) | ||||
−0.745282 | + | 0.666750i | \(0.767685\pi\) | |||||||
\(98\) | −15.8143 | −1.59749 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5753 | −1.54980 | −0.774900 | − | 0.632083i | \(-0.782200\pi\) | ||||
−0.774900 | + | 0.632083i | \(0.782200\pi\) | |||||||
\(102\) | 21.0205 | 2.08134 | ||||||||
\(103\) | −6.83710 | −0.673680 | −0.336840 | − | 0.941562i | \(-0.609358\pi\) | ||||
−0.336840 | + | 0.941562i | \(0.609358\pi\) | |||||||
\(104\) | 39.2762 | 3.85135 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.424694 | −0.0412499 | ||||||||
\(107\) | −6.34017 | −0.612928 | −0.306464 | − | 0.951882i | \(-0.599146\pi\) | ||||
−0.306464 | + | 0.951882i | \(0.599146\pi\) | |||||||
\(108\) | −5.34017 | −0.513858 | ||||||||
\(109\) | 2.31351 | 0.221594 | 0.110797 | − | 0.993843i | \(-0.464660\pi\) | ||||
0.110797 | + | 0.993843i | \(0.464660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | −14.9216 | −1.40996 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | −14.2557 | −1.33516 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.57531 | 0.703350 | ||||||||
\(117\) | 4.34017 | 0.401249 | ||||||||
\(118\) | 16.6803 | 1.53555 | ||||||||
\(119\) | 8.36683 | 0.766987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.2618 | −1.01960 | ||||||||
\(123\) | 9.41855 | 0.849242 | ||||||||
\(124\) | −24.9939 | −2.24451 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.92162 | −0.260279 | ||||||||
\(127\) | 2.24128 | 0.198881 | 0.0994406 | − | 0.995044i | \(-0.468295\pi\) | ||||
0.0994406 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(128\) | 28.5669 | 2.52498 | ||||||||
\(129\) | 7.60197 | 0.669316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68035 | 0.758405 | 0.379203 | − | 0.925314i | \(-0.376198\pi\) | ||||
0.379203 | + | 0.925314i | \(0.376198\pi\) | |||||||
\(132\) | −5.34017 | −0.464802 | ||||||||
\(133\) | −5.67420 | −0.492016 | ||||||||
\(134\) | 23.5174 | 2.03160 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −70.2122 | −6.02064 | ||||||||
\(137\) | 15.3607 | 1.31235 | 0.656176 | − | 0.754608i | \(-0.272173\pi\) | ||||
0.656176 | + | 0.754608i | \(0.272173\pi\) | |||||||
\(138\) | −5.84324 | −0.497410 | ||||||||
\(139\) | 8.58145 | 0.727869 | 0.363935 | − | 0.931425i | \(-0.381433\pi\) | ||||
0.363935 | + | 0.931425i | \(0.381433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.68035 | 0.394156 | ||||||||
\(142\) | −12.6803 | −1.06411 | ||||||||
\(143\) | 4.34017 | 0.362943 | ||||||||
\(144\) | 13.8371 | 1.15309 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 28.4391 | 2.35363 | ||||||||
\(147\) | 5.83710 | 0.481436 | ||||||||
\(148\) | 10.6803 | 0.877919 | ||||||||
\(149\) | −18.0989 | −1.48272 | −0.741360 | − | 0.671108i | \(-0.765819\pi\) | ||||
−0.741360 | + | 0.671108i | \(0.765819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9360 | 1.86651 | 0.933253 | − | 0.359221i | \(-0.116958\pi\) | ||||
0.933253 | + | 0.359221i | \(0.116958\pi\) | |||||||
\(152\) | 47.6163 | 3.86220 | ||||||||
\(153\) | −7.75872 | −0.627256 | ||||||||
\(154\) | −2.92162 | −0.235431 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −23.1773 | −1.85567 | ||||||||
\(157\) | 10.9939 | 0.877405 | 0.438703 | − | 0.898632i | \(-0.355438\pi\) | ||||
0.438703 | + | 0.898632i | \(0.355438\pi\) | |||||||
\(158\) | −21.9421 | −1.74562 | ||||||||
\(159\) | 0.156755 | 0.0124315 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.32580 | −0.183298 | ||||||||
\(162\) | 2.70928 | 0.212861 | ||||||||
\(163\) | 6.52359 | 0.510967 | 0.255484 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255484 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(164\) | −50.2967 | −3.92751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.8576 | 2.31740 | ||||||||
\(167\) | −1.97334 | −0.152701 | −0.0763507 | − | 0.997081i | \(-0.524327\pi\) | ||||
−0.0763507 | + | 0.997081i | \(0.524327\pi\) | |||||||
\(168\) | 9.75872 | 0.752902 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.26180 | 0.402380 | ||||||||
\(172\) | −40.5958 | −3.09540 | ||||||||
\(173\) | −3.75872 | −0.285770 | −0.142885 | − | 0.989739i | \(-0.545638\pi\) | ||||
−0.142885 | + | 0.989739i | \(0.545638\pi\) | |||||||
\(174\) | −3.84324 | −0.291356 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.8371 | 1.04301 | ||||||||
\(177\) | −6.15676 | −0.462770 | ||||||||
\(178\) | −34.7792 | −2.60681 | ||||||||
\(179\) | 15.1506 | 1.13241 | 0.566205 | − | 0.824264i | \(-0.308411\pi\) | ||||
0.566205 | + | 0.824264i | \(0.308411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.83710 | 0.359539 | 0.179769 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179769 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(182\) | −12.6803 | −0.939930 | ||||||||
\(183\) | 4.15676 | 0.307276 | ||||||||
\(184\) | 19.5174 | 1.43885 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.6803 | 0.929768 | ||||||||
\(187\) | −7.75872 | −0.567374 | ||||||||
\(188\) | −24.9939 | −1.82286 | ||||||||
\(189\) | 1.07838 | 0.0784404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.52359 | 0.182601 | 0.0913003 | − | 0.995823i | \(-0.470898\pi\) | ||||
0.0913003 | + | 0.995823i | \(0.470898\pi\) | |||||||
\(192\) | −24.8576 | −1.79394 | ||||||||
\(193\) | −0.0266620 | −0.00191917 | −0.000959586 | − | 1.00000i | \(-0.500305\pi\) | ||||
−0.000959586 | 1.00000i | \(0.500305\pi\) | ||||||||
\(194\) | −39.7731 | −2.85554 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.1711 | −2.22651 | ||||||||
\(197\) | −21.1194 | −1.50470 | −0.752348 | − | 0.658766i | \(-0.771079\pi\) | ||||
−0.752348 | + | 0.658766i | \(0.771079\pi\) | |||||||
\(198\) | 2.70928 | 0.192540 | ||||||||
\(199\) | 10.5236 | 0.745998 | 0.372999 | − | 0.927832i | \(-0.378330\pi\) | ||||
0.372999 | + | 0.927832i | \(0.378330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.68035 | −0.612264 | ||||||||
\(202\) | −42.1978 | −2.96903 | ||||||||
\(203\) | −1.52973 | −0.107366 | ||||||||
\(204\) | 41.4329 | 2.90089 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.5236 | −1.29060 | ||||||||
\(207\) | 2.15676 | 0.149905 | ||||||||
\(208\) | 60.0554 | 4.16409 | ||||||||
\(209\) | 5.26180 | 0.363966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.57531 | 0.659191 | 0.329596 | − | 0.944122i | \(-0.393088\pi\) | ||||
0.329596 | + | 0.944122i | \(0.393088\pi\) | |||||||
\(212\) | −0.837101 | −0.0574924 | ||||||||
\(213\) | 4.68035 | 0.320692 | ||||||||
\(214\) | −17.1773 | −1.17421 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.04945 | −0.615737 | ||||||||
\(217\) | 5.04718 | 0.342625 | ||||||||
\(218\) | 6.26794 | 0.424518 | ||||||||
\(219\) | −10.4969 | −0.709317 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.6742 | −2.26517 | ||||||||
\(222\) | −5.41855 | −0.363669 | ||||||||
\(223\) | 2.15676 | 0.144427 | 0.0722135 | − | 0.997389i | \(-0.476994\pi\) | ||||
0.0722135 | + | 0.997389i | \(0.476994\pi\) | |||||||
\(224\) | −20.9093 | −1.39706 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.2557 | 1.08131 | ||||||||
\(227\) | −9.65983 | −0.641145 | −0.320573 | − | 0.947224i | \(-0.603875\pi\) | ||||
−0.320573 | + | 0.947224i | \(0.603875\pi\) | |||||||
\(228\) | −28.0989 | −1.86089 | ||||||||
\(229\) | −3.36069 | −0.222081 | −0.111040 | − | 0.993816i | \(-0.535418\pi\) | ||||
−0.111040 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.07838 | 0.0709520 | ||||||||
\(232\) | 12.8371 | 0.842797 | ||||||||
\(233\) | 2.39803 | 0.157100 | 0.0785501 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785501 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(234\) | 11.7587 | 0.768692 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.8781 | 2.14018 | ||||||||
\(237\) | 8.09890 | 0.526080 | ||||||||
\(238\) | 22.6681 | 1.46935 | ||||||||
\(239\) | −7.20394 | −0.465984 | −0.232992 | − | 0.972479i | \(-0.574852\pi\) | ||||
−0.232992 | + | 0.972479i | \(0.574852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.20394 | −0.335215 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(242\) | 2.70928 | 0.174159 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −22.1978 | −1.42107 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 25.5174 | 1.62693 | ||||||||
\(247\) | 22.8371 | 1.45309 | ||||||||
\(248\) | −42.3545 | −2.68952 | ||||||||
\(249\) | −11.0205 | −0.698397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3197 | 0.966968 | 0.483484 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483484 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(252\) | −5.75872 | −0.362765 | ||||||||
\(253\) | 2.15676 | 0.135594 | ||||||||
\(254\) | 6.07223 | 0.381006 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 27.6803 | 1.73002 | ||||||||
\(257\) | −4.15676 | −0.259291 | −0.129646 | − | 0.991560i | \(-0.541384\pi\) | ||||
−0.129646 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(258\) | 20.5958 | 1.28224 | ||||||||
\(259\) | −2.15676 | −0.134014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41855 | 0.0878061 | ||||||||
\(262\) | 23.5174 | 1.45291 | ||||||||
\(263\) | 18.7070 | 1.15352 | 0.576762 | − | 0.816912i | \(-0.304316\pi\) | ||||
0.576762 | + | 0.816912i | \(0.304316\pi\) | |||||||
\(264\) | −9.04945 | −0.556955 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.3730 | −0.942578 | ||||||||
\(267\) | 12.8371 | 0.785618 | ||||||||
\(268\) | 46.3545 | 2.83155 | ||||||||
\(269\) | 23.3607 | 1.42433 | 0.712163 | − | 0.702014i | \(-0.247716\pi\) | ||||
0.712163 | + | 0.702014i | \(0.247716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.57531 | −0.338676 | −0.169338 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169338 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(272\) | −107.358 | −6.50955 | ||||||||
\(273\) | 4.68035 | 0.283267 | ||||||||
\(274\) | 41.6163 | 2.51414 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.5174 | −0.693269 | ||||||||
\(277\) | 26.0144 | 1.56305 | 0.781526 | − | 0.623872i | \(-0.214442\pi\) | ||||
0.781526 | + | 0.623872i | \(0.214442\pi\) | |||||||
\(278\) | 23.2495 | 1.39441 | ||||||||
\(279\) | −4.68035 | −0.280205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.41855 | −0.561864 | −0.280932 | − | 0.959728i | \(-0.590643\pi\) | ||||
−0.280932 | + | 0.959728i | \(0.590643\pi\) | |||||||
\(282\) | 12.6803 | 0.755104 | ||||||||
\(283\) | −14.2413 | −0.846556 | −0.423278 | − | 0.906000i | \(-0.639121\pi\) | ||||
−0.423278 | + | 0.906000i | \(0.639121\pi\) | |||||||
\(284\) | −24.9939 | −1.48311 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7587 | 0.695308 | ||||||||
\(287\) | 10.1568 | 0.599534 | ||||||||
\(288\) | 19.3896 | 1.14254 | ||||||||
\(289\) | 43.1978 | 2.54105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6803 | 0.860577 | ||||||||
\(292\) | 56.0554 | 3.28039 | ||||||||
\(293\) | 15.7587 | 0.920634 | 0.460317 | − | 0.887754i | \(-0.347736\pi\) | ||||
0.460317 | + | 0.887754i | \(0.347736\pi\) | |||||||
\(294\) | 15.8143 | 0.922310 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.0989 | 1.05198 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −49.0349 | −2.84052 | ||||||||
\(299\) | 9.36069 | 0.541343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.19779 | 0.472513 | ||||||||
\(302\) | 62.1399 | 3.57575 | ||||||||
\(303\) | 15.5753 | 0.894778 | ||||||||
\(304\) | 72.8080 | 4.17582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.0205 | −1.20166 | ||||||||
\(307\) | 18.9216 | 1.07991 | 0.539957 | − | 0.841693i | \(-0.318440\pi\) | ||||
0.539957 | + | 0.841693i | \(0.318440\pi\) | |||||||
\(308\) | −5.75872 | −0.328134 | ||||||||
\(309\) | 6.83710 | 0.388949 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8781 | −1.18389 | −0.591945 | − | 0.805978i | \(-0.701640\pi\) | ||||
−0.591945 | + | 0.805978i | \(0.701640\pi\) | |||||||
\(312\) | −39.2762 | −2.22358 | ||||||||
\(313\) | −6.31351 | −0.356861 | −0.178430 | − | 0.983953i | \(-0.557102\pi\) | ||||
−0.178430 | + | 0.983953i | \(0.557102\pi\) | |||||||
\(314\) | 29.7854 | 1.68089 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.2495 | −2.43297 | ||||||||
\(317\) | −31.3607 | −1.76139 | −0.880696 | − | 0.473682i | \(-0.842925\pi\) | ||||
−0.880696 | + | 0.473682i | \(0.842925\pi\) | |||||||
\(318\) | 0.424694 | 0.0238156 | ||||||||
\(319\) | 1.41855 | 0.0794236 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.34017 | 0.353874 | ||||||||
\(322\) | −6.30122 | −0.351154 | ||||||||
\(323\) | −40.8248 | −2.27155 | ||||||||
\(324\) | 5.34017 | 0.296676 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.6742 | 0.978884 | ||||||||
\(327\) | −2.31351 | −0.127937 | ||||||||
\(328\) | −85.2327 | −4.70619 | ||||||||
\(329\) | 5.04718 | 0.278260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2039 | 1.05554 | 0.527772 | − | 0.849386i | \(-0.323028\pi\) | ||||
0.527772 | + | 0.849386i | \(0.323028\pi\) | |||||||
\(332\) | 58.8515 | 3.22989 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | −5.34632 | −0.292537 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.9216 | 0.814041 | ||||||||
\(337\) | −13.5031 | −0.735559 | −0.367780 | − | 0.929913i | \(-0.619882\pi\) | ||||
−0.367780 | + | 0.929913i | \(0.619882\pi\) | |||||||
\(338\) | 15.8143 | 0.860185 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.68035 | −0.253455 | ||||||||
\(342\) | 14.2557 | 0.770857 | ||||||||
\(343\) | 13.8432 | 0.747465 | ||||||||
\(344\) | −68.7936 | −3.70910 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.1834 | −0.547464 | ||||||||
\(347\) | −6.34017 | −0.340358 | −0.170179 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170179 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(348\) | −7.57531 | −0.406079 | ||||||||
\(349\) | 16.1568 | 0.864851 | 0.432426 | − | 0.901670i | \(-0.357658\pi\) | ||||
0.432426 | + | 0.901670i | \(0.357658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.34017 | −0.231661 | ||||||||
\(352\) | 19.3896 | 1.03347 | ||||||||
\(353\) | 13.2039 | 0.702775 | 0.351387 | − | 0.936230i | \(-0.385710\pi\) | ||||
0.351387 | + | 0.936230i | \(0.385710\pi\) | |||||||
\(354\) | −16.6803 | −0.886550 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −68.5523 | −3.63327 | ||||||||
\(357\) | −8.36683 | −0.442820 | ||||||||
\(358\) | 41.0472 | 2.16941 | ||||||||
\(359\) | 3.31965 | 0.175205 | 0.0876023 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876023 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68649 | 0.457184 | ||||||||
\(362\) | 13.1050 | 0.688786 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −24.9939 | −1.31003 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.2618 | 0.588663 | ||||||||
\(367\) | 36.1445 | 1.88673 | 0.943363 | − | 0.331762i | \(-0.107643\pi\) | ||||
0.943363 | + | 0.331762i | \(0.107643\pi\) | |||||||
\(368\) | 29.8432 | 1.55569 | ||||||||
\(369\) | −9.41855 | −0.490310 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.169042 | 0.00877620 | ||||||||
\(372\) | 24.9939 | 1.29587 | ||||||||
\(373\) | 2.81044 | 0.145519 | 0.0727595 | − | 0.997350i | \(-0.476819\pi\) | ||||
0.0727595 | + | 0.997350i | \(0.476819\pi\) | |||||||
\(374\) | −21.0205 | −1.08695 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −42.3545 | −2.18427 | ||||||||
\(377\) | 6.15676 | 0.317089 | ||||||||
\(378\) | 2.92162 | 0.150272 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.24128 | −0.114824 | ||||||||
\(382\) | 6.83710 | 0.349817 | ||||||||
\(383\) | −33.5585 | −1.71476 | −0.857379 | − | 0.514685i | \(-0.827909\pi\) | ||||
−0.857379 | + | 0.514685i | \(0.827909\pi\) | |||||||
\(384\) | −28.5669 | −1.45780 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.0722347 | −0.00367665 | ||||||||
\(387\) | −7.60197 | −0.386430 | ||||||||
\(388\) | −78.3956 | −3.97993 | ||||||||
\(389\) | 12.8371 | 0.650867 | 0.325433 | − | 0.945565i | \(-0.394490\pi\) | ||||
0.325433 | + | 0.945565i | \(0.394490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7337 | −0.846258 | ||||||||
\(392\) | −52.8225 | −2.66794 | ||||||||
\(393\) | −8.68035 | −0.437866 | ||||||||
\(394\) | −57.2183 | −2.88262 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.34017 | 0.268354 | ||||||||
\(397\) | 5.31965 | 0.266986 | 0.133493 | − | 0.991050i | \(-0.457381\pi\) | ||||
0.133493 | + | 0.991050i | \(0.457381\pi\) | |||||||
\(398\) | 28.5113 | 1.42914 | ||||||||
\(399\) | 5.67420 | 0.284065 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | −23.5174 | −1.17294 | ||||||||
\(403\) | −20.3135 | −1.01189 | ||||||||
\(404\) | −83.1748 | −4.13810 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.14447 | −0.205687 | ||||||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 70.2122 | 3.47602 | ||||||||
\(409\) | 26.1978 | 1.29540 | 0.647699 | − | 0.761897i | \(-0.275732\pi\) | ||||
0.647699 | + | 0.761897i | \(0.275732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.3607 | −0.757687 | ||||||||
\(412\) | −36.5113 | −1.79878 | ||||||||
\(413\) | −6.63931 | −0.326699 | ||||||||
\(414\) | 5.84324 | 0.287180 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 84.1543 | 4.12600 | ||||||||
\(417\) | −8.58145 | −0.420235 | ||||||||
\(418\) | 14.2557 | 0.697267 | ||||||||
\(419\) | −2.83710 | −0.138601 | −0.0693007 | − | 0.997596i | \(-0.522077\pi\) | ||||
−0.0693007 | + | 0.997596i | \(0.522077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4764 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(422\) | 25.9421 | 1.26284 | ||||||||
\(423\) | −4.68035 | −0.227566 | ||||||||
\(424\) | −1.41855 | −0.0688909 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.6803 | 0.614365 | ||||||||
\(427\) | 4.48255 | 0.216926 | ||||||||
\(428\) | −33.8576 | −1.63657 | ||||||||
\(429\) | −4.34017 | −0.209546 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.5708 | 1.13536 | 0.567682 | − | 0.823248i | \(-0.307840\pi\) | ||||
0.567682 | + | 0.823248i | \(0.307840\pi\) | |||||||
\(432\) | −13.8371 | −0.665738 | ||||||||
\(433\) | 14.9939 | 0.720559 | 0.360279 | − | 0.932844i | \(-0.382681\pi\) | ||||
0.360279 | + | 0.932844i | \(0.382681\pi\) | |||||||
\(434\) | 13.6742 | 0.656383 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3545 | 0.591676 | ||||||||
\(437\) | 11.3484 | 0.542868 | ||||||||
\(438\) | −28.4391 | −1.35887 | ||||||||
\(439\) | 4.77924 | 0.228101 | 0.114050 | − | 0.993475i | \(-0.463617\pi\) | ||||
0.114050 | + | 0.993475i | \(0.463617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.83710 | −0.277957 | ||||||||
\(442\) | −91.2327 | −4.33950 | ||||||||
\(443\) | −20.1978 | −0.959626 | −0.479813 | − | 0.877371i | \(-0.659296\pi\) | ||||
−0.479813 | + | 0.877371i | \(0.659296\pi\) | |||||||
\(444\) | −10.6803 | −0.506867 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.84324 | 0.276686 | ||||||||
\(447\) | 18.0989 | 0.856048 | ||||||||
\(448\) | −26.8059 | −1.26646 | ||||||||
\(449\) | −21.5708 | −1.01799 | −0.508994 | − | 0.860770i | \(-0.669982\pi\) | ||||
−0.508994 | + | 0.860770i | \(0.669982\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.41855 | −0.443502 | ||||||||
\(452\) | 32.0410 | 1.50708 | ||||||||
\(453\) | −22.9360 | −1.07763 | ||||||||
\(454\) | −26.1711 | −1.22827 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −47.6163 | −2.22984 | ||||||||
\(457\) | −28.1711 | −1.31779 | −0.658895 | − | 0.752235i | \(-0.728976\pi\) | ||||
−0.658895 | + | 0.752235i | \(0.728976\pi\) | |||||||
\(458\) | −9.10504 | −0.425451 | ||||||||
\(459\) | 7.75872 | 0.362146 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.47187 | −0.0685520 | −0.0342760 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342760 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(462\) | 2.92162 | 0.135926 | ||||||||
\(463\) | 23.2039 | 1.07838 | 0.539189 | − | 0.842185i | \(-0.318731\pi\) | ||||
0.539189 | + | 0.842185i | \(0.318731\pi\) | |||||||
\(464\) | 19.6286 | 0.911236 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.49693 | 0.300964 | ||||||||
\(467\) | −14.1568 | −0.655097 | −0.327548 | − | 0.944834i | \(-0.606222\pi\) | ||||
−0.327548 | + | 0.944834i | \(0.606222\pi\) | |||||||
\(468\) | 23.1773 | 1.07137 | ||||||||
\(469\) | −9.36069 | −0.432237 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9939 | −0.506570 | ||||||||
\(472\) | 55.7152 | 2.56450 | ||||||||
\(473\) | −7.60197 | −0.349539 | ||||||||
\(474\) | 21.9421 | 1.00784 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 44.6803 | 2.04792 | ||||||||
\(477\) | −0.156755 | −0.00717734 | ||||||||
\(478\) | −19.5174 | −0.892707 | ||||||||
\(479\) | −13.8432 | −0.632514 | −0.316257 | − | 0.948674i | \(-0.602426\pi\) | ||||
−0.316257 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68035 | 0.395790 | ||||||||
\(482\) | −14.0989 | −0.642187 | ||||||||
\(483\) | 2.32580 | 0.105827 | ||||||||
\(484\) | 5.34017 | 0.242735 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.70928 | −0.122895 | ||||||||
\(487\) | 40.9939 | 1.85761 | 0.928804 | − | 0.370570i | \(-0.120838\pi\) | ||||
0.928804 | + | 0.370570i | \(0.120838\pi\) | |||||||
\(488\) | −37.6163 | −1.70281 | ||||||||
\(489\) | −6.52359 | −0.295007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8371 | 1.57218 | 0.786088 | − | 0.618114i | \(-0.212103\pi\) | ||||
0.786088 | + | 0.618114i | \(0.212103\pi\) | |||||||
\(492\) | 50.2967 | 2.26755 | ||||||||
\(493\) | −11.0061 | −0.495692 | ||||||||
\(494\) | 61.8720 | 2.78375 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −64.7624 | −2.90792 | ||||||||
\(497\) | 5.04718 | 0.226397 | ||||||||
\(498\) | −29.8576 | −1.33795 | ||||||||
\(499\) | 15.1506 | 0.678235 | 0.339117 | − | 0.940744i | \(-0.389872\pi\) | ||||
0.339117 | + | 0.940744i | \(0.389872\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.97334 | 0.0881622 | ||||||||
\(502\) | 41.5052 | 1.85247 | ||||||||
\(503\) | 6.65368 | 0.296673 | 0.148337 | − | 0.988937i | \(-0.452608\pi\) | ||||
0.148337 | + | 0.988937i | \(0.452608\pi\) | |||||||
\(504\) | −9.75872 | −0.434688 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.84324 | 0.259764 | ||||||||
\(507\) | −5.83710 | −0.259235 | ||||||||
\(508\) | 11.9688 | 0.531030 | ||||||||
\(509\) | 41.3484 | 1.83274 | 0.916368 | − | 0.400337i | \(-0.131107\pi\) | ||||
0.916368 | + | 0.400337i | \(0.131107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3197 | −0.500752 | ||||||||
\(512\) | 17.8599 | 0.789303 | ||||||||
\(513\) | −5.26180 | −0.232314 | ||||||||
\(514\) | −11.2618 | −0.496736 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.5958 | 1.78713 | ||||||||
\(517\) | −4.68035 | −0.205841 | ||||||||
\(518\) | −5.84324 | −0.256737 | ||||||||
\(519\) | 3.75872 | 0.164990 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.67420 | 0.336213 | 0.168106 | − | 0.985769i | \(-0.446235\pi\) | ||||
0.168106 | + | 0.985769i | \(0.446235\pi\) | |||||||
\(522\) | 3.84324 | 0.168214 | ||||||||
\(523\) | −23.2351 | −1.01600 | −0.508001 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(524\) | 46.3545 | 2.02501 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 50.6824 | 2.20986 | ||||||||
\(527\) | 36.3135 | 1.58184 | ||||||||
\(528\) | −13.8371 | −0.602183 | ||||||||
\(529\) | −18.3484 | −0.797757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.15676 | 0.267180 | ||||||||
\(532\) | −30.3012 | −1.31372 | ||||||||
\(533\) | −40.8781 | −1.77063 | ||||||||
\(534\) | 34.7792 | 1.50505 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 78.5523 | 3.39294 | ||||||||
\(537\) | −15.1506 | −0.653797 | ||||||||
\(538\) | 63.2905 | 2.72865 | ||||||||
\(539\) | −5.83710 | −0.251422 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | −15.1050 | −0.648817 | ||||||||
\(543\) | −4.83710 | −0.207580 | ||||||||
\(544\) | −150.439 | −6.45001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.6803 | 0.542669 | ||||||||
\(547\) | 23.0661 | 0.986235 | 0.493117 | − | 0.869963i | \(-0.335857\pi\) | ||||
0.493117 | + | 0.869963i | \(0.335857\pi\) | |||||||
\(548\) | 82.0288 | 3.50409 | ||||||||
\(549\) | −4.15676 | −0.177406 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.46412 | 0.317982 | ||||||||
\(552\) | −19.5174 | −0.830718 | ||||||||
\(553\) | 8.73367 | 0.371393 | ||||||||
\(554\) | 70.4801 | 2.99441 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 45.8264 | 1.94347 | ||||||||
\(557\) | −10.5958 | −0.448960 | −0.224480 | − | 0.974479i | \(-0.572068\pi\) | ||||
−0.224480 | + | 0.974479i | \(0.572068\pi\) | |||||||
\(558\) | −12.6803 | −0.536802 | ||||||||
\(559\) | −32.9939 | −1.39549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.75872 | 0.327574 | ||||||||
\(562\) | −25.5174 | −1.07639 | ||||||||
\(563\) | 36.2122 | 1.52616 | 0.763080 | − | 0.646303i | \(-0.223686\pi\) | ||||
0.763080 | + | 0.646303i | \(0.223686\pi\) | |||||||
\(564\) | 24.9939 | 1.05243 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −38.5835 | −1.62179 | ||||||||
\(567\) | −1.07838 | −0.0452876 | ||||||||
\(568\) | −42.3545 | −1.77716 | ||||||||
\(569\) | −27.5753 | −1.15602 | −0.578008 | − | 0.816031i | \(-0.696170\pi\) | ||||
−0.578008 | + | 0.816031i | \(0.696170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.9299 | −1.16883 | −0.584414 | − | 0.811456i | \(-0.698676\pi\) | ||||
−0.584414 | + | 0.811456i | \(0.698676\pi\) | |||||||
\(572\) | 23.1773 | 0.969091 | ||||||||
\(573\) | −2.52359 | −0.105425 | ||||||||
\(574\) | 27.5174 | 1.14856 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.8576 | 1.03573 | ||||||||
\(577\) | −41.4017 | −1.72358 | −0.861788 | − | 0.507268i | \(-0.830655\pi\) | ||||
−0.861788 | + | 0.507268i | \(0.830655\pi\) | |||||||
\(578\) | 117.035 | 4.86800 | ||||||||
\(579\) | 0.0266620 | 0.00110803 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8843 | −0.493043 | ||||||||
\(582\) | 39.7731 | 1.64865 | ||||||||
\(583\) | −0.156755 | −0.00649215 | ||||||||
\(584\) | 94.9914 | 3.93077 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.6947 | 1.76370 | ||||||||
\(587\) | −8.48255 | −0.350112 | −0.175056 | − | 0.984558i | \(-0.556011\pi\) | ||||
−0.175056 | + | 0.984558i | \(0.556011\pi\) | |||||||
\(588\) | 31.1711 | 1.28548 | ||||||||
\(589\) | −24.6270 | −1.01474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1194 | 0.868737 | ||||||||
\(592\) | 27.6742 | 1.13740 | ||||||||
\(593\) | −7.56093 | −0.310490 | −0.155245 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155245 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(594\) | −2.70928 | −0.111163 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −96.6512 | −3.95899 | ||||||||
\(597\) | −10.5236 | −0.430702 | ||||||||
\(598\) | 25.3607 | 1.03708 | ||||||||
\(599\) | 5.67420 | 0.231842 | 0.115921 | − | 0.993258i | \(-0.463018\pi\) | ||||
0.115921 | + | 0.993258i | \(0.463018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.31965 | −0.0538298 | −0.0269149 | − | 0.999638i | \(-0.508568\pi\) | ||||
−0.0269149 | + | 0.999638i | \(0.508568\pi\) | |||||||
\(602\) | 22.2101 | 0.905215 | ||||||||
\(603\) | 8.68035 | 0.353491 | ||||||||
\(604\) | 122.482 | 4.98373 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 42.1978 | 1.71417 | ||||||||
\(607\) | 2.24128 | 0.0909706 | 0.0454853 | − | 0.998965i | \(-0.485517\pi\) | ||||
0.0454853 | + | 0.998965i | \(0.485517\pi\) | |||||||
\(608\) | 102.024 | 4.13763 | ||||||||
\(609\) | 1.52973 | 0.0619879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.3135 | −0.821797 | ||||||||
\(612\) | −41.4329 | −1.67483 | ||||||||
\(613\) | −42.8638 | −1.73125 | −0.865626 | − | 0.500692i | \(-0.833079\pi\) | ||||
−0.865626 | + | 0.500692i | \(0.833079\pi\) | |||||||
\(614\) | 51.2639 | 2.06884 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.75872 | −0.393190 | ||||||||
\(617\) | −11.3607 | −0.457364 | −0.228682 | − | 0.973501i | \(-0.573442\pi\) | ||||
−0.228682 | + | 0.973501i | \(0.573442\pi\) | |||||||
\(618\) | 18.5236 | 0.745128 | ||||||||
\(619\) | −45.1917 | −1.81641 | −0.908203 | − | 0.418530i | \(-0.862545\pi\) | ||||
−0.908203 | + | 0.418530i | \(0.862545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.15676 | −0.0865476 | ||||||||
\(622\) | −56.5646 | −2.26803 | ||||||||
\(623\) | 13.8432 | 0.554618 | ||||||||
\(624\) | −60.0554 | −2.40414 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.1050 | −0.683655 | ||||||||
\(627\) | −5.26180 | −0.210136 | ||||||||
\(628\) | 58.7091 | 2.34275 | ||||||||
\(629\) | −15.5174 | −0.618721 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.78992 | −0.389731 | −0.194865 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194865 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(632\) | −73.2905 | −2.91534 | ||||||||
\(633\) | −9.57531 | −0.380584 | ||||||||
\(634\) | −84.9647 | −3.37438 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.837101 | 0.0331932 | ||||||||
\(637\) | −25.3340 | −1.00377 | ||||||||
\(638\) | 3.84324 | 0.152156 | ||||||||
\(639\) | −4.68035 | −0.185152 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.210079 | 0.00829764 | 0.00414882 | − | 0.999991i | \(-0.498679\pi\) | ||||
0.00414882 | + | 0.999991i | \(0.498679\pi\) | |||||||
\(642\) | 17.1773 | 0.677933 | ||||||||
\(643\) | −14.5236 | −0.572754 | −0.286377 | − | 0.958117i | \(-0.592451\pi\) | ||||
−0.286377 | + | 0.958117i | \(0.592451\pi\) | |||||||
\(644\) | −12.4202 | −0.489423 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −110.606 | −4.35172 | ||||||||
\(647\) | −15.4641 | −0.607957 | −0.303979 | − | 0.952679i | \(-0.598315\pi\) | ||||
−0.303979 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(648\) | 9.04945 | 0.355496 | ||||||||
\(649\) | 6.15676 | 0.241674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.04718 | −0.197815 | ||||||||
\(652\) | 34.8371 | 1.36433 | ||||||||
\(653\) | 17.8310 | 0.697779 | 0.348890 | − | 0.937164i | \(-0.386559\pi\) | ||||
0.348890 | + | 0.937164i | \(0.386559\pi\) | |||||||
\(654\) | −6.26794 | −0.245096 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −130.325 | −5.08835 | ||||||||
\(657\) | 10.4969 | 0.409524 | ||||||||
\(658\) | 13.6742 | 0.533076 | ||||||||
\(659\) | −32.3135 | −1.25876 | −0.629378 | − | 0.777099i | \(-0.716690\pi\) | ||||
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.68649 | −0.221179 | −0.110589 | − | 0.993866i | \(-0.535274\pi\) | ||||
−0.110589 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(662\) | 52.0288 | 2.02215 | ||||||||
\(663\) | 33.6742 | 1.30780 | ||||||||
\(664\) | 99.7296 | 3.87026 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.41855 | 0.209965 | ||||||||
\(667\) | 3.05947 | 0.118463 | ||||||||
\(668\) | −10.5380 | −0.407726 | ||||||||
\(669\) | −2.15676 | −0.0833850 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15676 | −0.160470 | ||||||||
\(672\) | 20.9093 | 0.806595 | ||||||||
\(673\) | 21.0205 | 0.810281 | 0.405141 | − | 0.914254i | \(-0.367223\pi\) | ||||
0.405141 | + | 0.914254i | \(0.367223\pi\) | |||||||
\(674\) | −36.5835 | −1.40915 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.1711 | 1.19889 | ||||||||
\(677\) | −36.7526 | −1.41252 | −0.706258 | − | 0.707954i | \(-0.749618\pi\) | ||||
−0.706258 | + | 0.707954i | \(0.749618\pi\) | |||||||
\(678\) | −16.2557 | −0.624295 | ||||||||
\(679\) | 15.8310 | 0.607536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.65983 | 0.370165 | ||||||||
\(682\) | −12.6803 | −0.485556 | ||||||||
\(683\) | 17.3074 | 0.662248 | 0.331124 | − | 0.943587i | \(-0.392572\pi\) | ||||
0.331124 | + | 0.943587i | \(0.392572\pi\) | |||||||
\(684\) | 28.0989 | 1.07439 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 37.5052 | 1.43195 | ||||||||
\(687\) | 3.36069 | 0.128218 | ||||||||
\(688\) | −105.189 | −4.01030 | ||||||||
\(689\) | −0.680346 | −0.0259191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6742 | 0.672358 | 0.336179 | − | 0.941798i | \(-0.390865\pi\) | ||||
0.336179 | + | 0.941798i | \(0.390865\pi\) | |||||||
\(692\) | −20.0722 | −0.763032 | ||||||||
\(693\) | −1.07838 | −0.0409642 | ||||||||
\(694\) | −17.1773 | −0.652040 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.8371 | −0.486589 | ||||||||
\(697\) | 73.0759 | 2.76795 | ||||||||
\(698\) | 43.7731 | 1.65684 | ||||||||
\(699\) | −2.39803 | −0.0907019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.1050 | −0.646048 | −0.323024 | − | 0.946391i | \(-0.604700\pi\) | ||||
−0.323024 | + | 0.946391i | \(0.604700\pi\) | |||||||
\(702\) | −11.7587 | −0.443804 | ||||||||
\(703\) | 10.5236 | 0.396905 | ||||||||
\(704\) | 24.8576 | 0.936857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.7731 | 1.34634 | ||||||||
\(707\) | 16.7961 | 0.631681 | ||||||||
\(708\) | −32.8781 | −1.23564 | ||||||||
\(709\) | 25.1506 | 0.944551 | 0.472276 | − | 0.881451i | \(-0.343433\pi\) | ||||
0.472276 | + | 0.881451i | \(0.343433\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.09890 | −0.303732 | ||||||||
\(712\) | −116.169 | −4.35361 | ||||||||
\(713\) | −10.0944 | −0.378037 | ||||||||
\(714\) | −22.6681 | −0.848331 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 80.9069 | 3.02363 | ||||||||
\(717\) | 7.20394 | 0.269036 | ||||||||
\(718\) | 8.99386 | 0.335648 | ||||||||
\(719\) | −1.78992 | −0.0667528 | −0.0333764 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333764 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.37298 | 0.274584 | ||||||||
\(722\) | 23.5341 | 0.875848 | ||||||||
\(723\) | 5.20394 | 0.193536 | ||||||||
\(724\) | 25.8310 | 0.960000 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.70928 | −0.100551 | ||||||||
\(727\) | −25.9877 | −0.963831 | −0.481915 | − | 0.876218i | \(-0.660059\pi\) | ||||
−0.481915 | + | 0.876218i | \(0.660059\pi\) | |||||||
\(728\) | −42.3545 | −1.56976 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.9816 | 2.18151 | ||||||||
\(732\) | 22.1978 | 0.820454 | ||||||||
\(733\) | 41.0205 | 1.51513 | 0.757564 | − | 0.652761i | \(-0.226390\pi\) | ||||
0.757564 | + | 0.652761i | \(0.226390\pi\) | |||||||
\(734\) | 97.9253 | 3.61449 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.8187 | 1.54146 | ||||||||
\(737\) | 8.68035 | 0.319745 | ||||||||
\(738\) | −25.5174 | −0.939310 | ||||||||
\(739\) | −47.6163 | −1.75160 | −0.875798 | − | 0.482678i | \(-0.839664\pi\) | ||||
−0.875798 | + | 0.482678i | \(0.839664\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.8371 | −0.838942 | ||||||||
\(742\) | 0.457980 | 0.0168130 | ||||||||
\(743\) | −0.550252 | −0.0201868 | −0.0100934 | − | 0.999949i | \(-0.503213\pi\) | ||||
−0.0100934 | + | 0.999949i | \(0.503213\pi\) | |||||||
\(744\) | 42.3545 | 1.55279 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.61425 | 0.278778 | ||||||||
\(747\) | 11.0205 | 0.403220 | ||||||||
\(748\) | −41.4329 | −1.51494 | ||||||||
\(749\) | 6.83710 | 0.249822 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.5585 | 1.51649 | 0.758245 | − | 0.651969i | \(-0.226057\pi\) | ||||
0.758245 | + | 0.651969i | \(0.226057\pi\) | |||||||
\(752\) | −64.7624 | −2.36164 | ||||||||
\(753\) | −15.3197 | −0.558279 | ||||||||
\(754\) | 16.6803 | 0.607462 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.75872 | 0.209443 | ||||||||
\(757\) | −1.31965 | −0.0479636 | −0.0239818 | − | 0.999712i | \(-0.507634\pi\) | ||||
−0.0239818 | + | 0.999712i | \(0.507634\pi\) | |||||||
\(758\) | −54.1855 | −1.96811 | ||||||||
\(759\) | −2.15676 | −0.0782853 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.21461 | −0.0802797 | −0.0401399 | − | 0.999194i | \(-0.512780\pi\) | ||||
−0.0401399 | + | 0.999194i | \(0.512780\pi\) | |||||||
\(762\) | −6.07223 | −0.219974 | ||||||||
\(763\) | −2.49484 | −0.0903192 | ||||||||
\(764\) | 13.4764 | 0.487559 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −90.9192 | −3.28504 | ||||||||
\(767\) | 26.7214 | 0.964853 | ||||||||
\(768\) | −27.6803 | −0.998828 | ||||||||
\(769\) | −14.3668 | −0.518081 | −0.259041 | − | 0.965866i | \(-0.583406\pi\) | ||||
−0.259041 | + | 0.965866i | \(0.583406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.15676 | 0.149702 | ||||||||
\(772\) | −0.142380 | −0.00512436 | ||||||||
\(773\) | −40.1568 | −1.44434 | −0.722169 | − | 0.691717i | \(-0.756855\pi\) | ||||
−0.722169 | + | 0.691717i | \(0.756855\pi\) | |||||||
\(774\) | −20.5958 | −0.740302 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −132.849 | −4.76900 | ||||||||
\(777\) | 2.15676 | 0.0773732 | ||||||||
\(778\) | 34.7792 | 1.24690 | ||||||||
\(779\) | −49.5585 | −1.77562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.68035 | −0.167476 | ||||||||
\(782\) | −45.3361 | −1.62122 | ||||||||
\(783\) | −1.41855 | −0.0506949 | ||||||||
\(784\) | −80.7686 | −2.88459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.5174 | −0.838840 | ||||||||
\(787\) | −49.5897 | −1.76768 | −0.883841 | − | 0.467788i | \(-0.845051\pi\) | ||||
−0.883841 | + | 0.467788i | \(0.845051\pi\) | |||||||
\(788\) | −112.781 | −4.01767 | ||||||||
\(789\) | −18.7070 | −0.665987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.47027 | −0.230056 | ||||||||
\(792\) | 9.04945 | 0.321558 | ||||||||
\(793\) | −18.0410 | −0.640656 | ||||||||
\(794\) | 14.4124 | 0.511477 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 56.1978 | 1.99188 | ||||||||
\(797\) | 46.7091 | 1.65452 | 0.827261 | − | 0.561818i | \(-0.189898\pi\) | ||||
0.827261 | + | 0.561818i | \(0.189898\pi\) | |||||||
\(798\) | 15.3730 | 0.544198 | ||||||||
\(799\) | 36.3135 | 1.28468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8371 | −0.453577 | ||||||||
\(802\) | 5.41855 | 0.191336 | ||||||||
\(803\) | 10.4969 | 0.370429 | ||||||||
\(804\) | −46.3545 | −1.63480 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55.0349 | −1.93852 | ||||||||
\(807\) | −23.3607 | −0.822335 | ||||||||
\(808\) | −140.948 | −4.95853 | ||||||||
\(809\) | −18.5814 | −0.653289 | −0.326644 | − | 0.945147i | \(-0.605918\pi\) | ||||
−0.326644 | + | 0.945147i | \(0.605918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.3028 | 0.958732 | 0.479366 | − | 0.877615i | \(-0.340867\pi\) | ||||
0.479366 | + | 0.877615i | \(0.340867\pi\) | |||||||
\(812\) | −8.16904 | −0.286677 | ||||||||
\(813\) | 5.57531 | 0.195535 | ||||||||
\(814\) | 5.41855 | 0.189920 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 107.358 | 3.75829 | ||||||||
\(817\) | −40.0000 | −1.39942 | ||||||||
\(818\) | 70.9770 | 2.48165 | ||||||||
\(819\) | −4.68035 | −0.163545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.2085 | −1.08918 | −0.544592 | − | 0.838701i | \(-0.683315\pi\) | ||||
−0.544592 | + | 0.838701i | \(0.683315\pi\) | |||||||
\(822\) | −41.6163 | −1.45154 | ||||||||
\(823\) | 50.1855 | 1.74936 | 0.874678 | − | 0.484704i | \(-0.161073\pi\) | ||||
0.874678 | + | 0.484704i | \(0.161073\pi\) | |||||||
\(824\) | −61.8720 | −2.15541 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.9877 | −0.625873 | ||||||||
\(827\) | −27.3874 | −0.952352 | −0.476176 | − | 0.879350i | \(-0.657977\pi\) | ||||
−0.476176 | + | 0.879350i | \(0.657977\pi\) | |||||||
\(828\) | 11.5174 | 0.400259 | ||||||||
\(829\) | −26.1978 | −0.909887 | −0.454943 | − | 0.890520i | \(-0.650341\pi\) | ||||
−0.454943 | + | 0.890520i | \(0.650341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.0144 | −0.902429 | ||||||||
\(832\) | 107.886 | 3.74029 | ||||||||
\(833\) | 45.2885 | 1.56915 | ||||||||
\(834\) | −23.2495 | −0.805065 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 28.0989 | 0.971821 | ||||||||
\(837\) | 4.68035 | 0.161776 | ||||||||
\(838\) | −7.68649 | −0.265525 | ||||||||
\(839\) | 7.20394 | 0.248708 | 0.124354 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124354 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9877 | −0.930611 | ||||||||
\(842\) | 31.0928 | 1.07153 | ||||||||
\(843\) | 9.41855 | 0.324392 | ||||||||
\(844\) | 51.1338 | 1.76010 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.6803 | −0.435959 | ||||||||
\(847\) | −1.07838 | −0.0370535 | ||||||||
\(848\) | −2.16904 | −0.0744852 | ||||||||
\(849\) | 14.2413 | 0.488759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.31351 | 0.147865 | ||||||||
\(852\) | 24.9939 | 0.856275 | ||||||||
\(853\) | −39.8043 | −1.36287 | −0.681437 | − | 0.731877i | \(-0.738644\pi\) | ||||
−0.681437 | + | 0.731877i | \(0.738644\pi\) | |||||||
\(854\) | 12.1445 | 0.415575 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −57.3751 | −1.96104 | ||||||||
\(857\) | 36.9504 | 1.26220 | 0.631100 | − | 0.775701i | \(-0.282604\pi\) | ||||
0.631100 | + | 0.775701i | \(0.282604\pi\) | |||||||
\(858\) | −11.7587 | −0.401436 | ||||||||
\(859\) | 57.5052 | 1.96205 | 0.981025 | − | 0.193879i | \(-0.0621070\pi\) | ||||
0.981025 | + | 0.193879i | \(0.0621070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.1568 | −0.346141 | ||||||||
\(862\) | 63.8597 | 2.17507 | ||||||||
\(863\) | 1.89657 | 0.0645599 | 0.0322800 | − | 0.999479i | \(-0.489723\pi\) | ||||
0.0322800 | + | 0.999479i | \(0.489723\pi\) | |||||||
\(864\) | −19.3896 | −0.659648 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 40.6225 | 1.38041 | ||||||||
\(867\) | −43.1978 | −1.46707 | ||||||||
\(868\) | 26.9528 | 0.914838 | ||||||||
\(869\) | −8.09890 | −0.274736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.6742 | 1.27654 | ||||||||
\(872\) | 20.9360 | 0.708982 | ||||||||
\(873\) | −14.6803 | −0.496854 | ||||||||
\(874\) | 30.7460 | 1.04000 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −56.0554 | −1.89394 | ||||||||
\(877\) | −32.5380 | −1.09873 | −0.549365 | − | 0.835583i | \(-0.685130\pi\) | ||||
−0.549365 | + | 0.835583i | \(0.685130\pi\) | |||||||
\(878\) | 12.9483 | 0.436983 | ||||||||
\(879\) | −15.7587 | −0.531529 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.1978 | 0.613099 | 0.306550 | − | 0.951855i | \(-0.400825\pi\) | ||||
0.306550 | + | 0.951855i | \(0.400825\pi\) | |||||||
\(882\) | −15.8143 | −0.532496 | ||||||||
\(883\) | −36.3956 | −1.22481 | −0.612405 | − | 0.790545i | \(-0.709798\pi\) | ||||
−0.612405 | + | 0.790545i | \(0.709798\pi\) | |||||||
\(884\) | −179.826 | −6.04821 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −54.7214 | −1.83840 | ||||||||
\(887\) | −27.8699 | −0.935780 | −0.467890 | − | 0.883787i | \(-0.654986\pi\) | ||||
−0.467890 | + | 0.883787i | \(0.654986\pi\) | |||||||
\(888\) | −18.0989 | −0.607359 | ||||||||
\(889\) | −2.41694 | −0.0810616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 11.5174 | 0.385633 | ||||||||
\(893\) | −24.6270 | −0.824112 | ||||||||
\(894\) | 49.0349 | 1.63997 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −30.8059 | −1.02915 | ||||||||
\(897\) | −9.36069 | −0.312544 | ||||||||
\(898\) | −58.4412 | −1.95021 | ||||||||
\(899\) | −6.63931 | −0.221433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21622 | 0.0405182 | ||||||||
\(902\) | −25.5174 | −0.849638 | ||||||||
\(903\) | −8.19779 | −0.272805 | ||||||||
\(904\) | 54.2967 | 1.80588 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −62.1399 | −2.06446 | ||||||||
\(907\) | 27.9376 | 0.927653 | 0.463826 | − | 0.885926i | \(-0.346476\pi\) | ||||
0.463826 | + | 0.885926i | \(0.346476\pi\) | |||||||
\(908\) | −51.5851 | −1.71191 | ||||||||
\(909\) | −15.5753 | −0.516600 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8843 | −0.393744 | −0.196872 | − | 0.980429i | \(-0.563078\pi\) | ||||
−0.196872 | + | 0.980429i | \(0.563078\pi\) | |||||||
\(912\) | −72.8080 | −2.41091 | ||||||||
\(913\) | 11.0205 | 0.364726 | ||||||||
\(914\) | −76.3234 | −2.52455 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.9467 | −0.592975 | ||||||||
\(917\) | −9.36069 | −0.309117 | ||||||||
\(918\) | 21.0205 | 0.693781 | ||||||||
\(919\) | −45.6041 | −1.50434 | −0.752170 | − | 0.658970i | \(-0.770993\pi\) | ||||
−0.752170 | + | 0.658970i | \(0.770993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.9216 | −0.623489 | ||||||||
\(922\) | −3.98771 | −0.131328 | ||||||||
\(923\) | −20.3135 | −0.668627 | ||||||||
\(924\) | 5.75872 | 0.189448 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 62.8659 | 2.06590 | ||||||||
\(927\) | −6.83710 | −0.224560 | ||||||||
\(928\) | 27.5052 | 0.902901 | ||||||||
\(929\) | −25.1506 | −0.825165 | −0.412582 | − | 0.910920i | \(-0.635373\pi\) | ||||
−0.412582 | + | 0.910920i | \(0.635373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.7136 | −1.00660 | ||||||||
\(932\) | 12.8059 | 0.419471 | ||||||||
\(933\) | 20.8781 | 0.683520 | ||||||||
\(934\) | −38.3545 | −1.25500 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 39.2762 | 1.28378 | ||||||||
\(937\) | −5.33403 | −0.174255 | −0.0871276 | − | 0.996197i | \(-0.527769\pi\) | ||||
−0.0871276 | + | 0.996197i | \(0.527769\pi\) | |||||||
\(938\) | −25.3607 | −0.828056 | ||||||||
\(939\) | 6.31351 | 0.206034 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.8203 | 1.85229 | 0.926144 | − | 0.377170i | \(-0.123103\pi\) | ||||
0.926144 | + | 0.377170i | \(0.123103\pi\) | |||||||
\(942\) | −29.7854 | −0.970460 | ||||||||
\(943\) | −20.3135 | −0.661499 | ||||||||
\(944\) | 85.1917 | 2.77275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.5958 | −0.669628 | ||||||||
\(947\) | 20.9939 | 0.682209 | 0.341104 | − | 0.940025i | \(-0.389199\pi\) | ||||
0.341104 | + | 0.940025i | \(0.389199\pi\) | |||||||
\(948\) | 43.2495 | 1.40468 | ||||||||
\(949\) | 45.5585 | 1.47889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.3607 | 1.01694 | ||||||||
\(952\) | 75.7152 | 2.45395 | ||||||||
\(953\) | 25.2351 | 0.817446 | 0.408723 | − | 0.912658i | \(-0.365974\pi\) | ||||
0.408723 | + | 0.912658i | \(0.365974\pi\) | |||||||
\(954\) | −0.424694 | −0.0137500 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −38.4703 | −1.24422 | ||||||||
\(957\) | −1.41855 | −0.0458552 | ||||||||
\(958\) | −37.5052 | −1.21174 | ||||||||
\(959\) | −16.5646 | −0.534900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | 23.5174 | 0.758233 | ||||||||
\(963\) | −6.34017 | −0.204309 | ||||||||
\(964\) | −27.7899 | −0.895053 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.30122 | 0.202739 | ||||||||
\(967\) | −13.1317 | −0.422287 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(968\) | 9.04945 | 0.290860 | ||||||||
\(969\) | 40.8248 | 1.31148 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.94053 | 0.286915 | 0.143458 | − | 0.989656i | \(-0.454178\pi\) | ||||
0.143458 | + | 0.989656i | \(0.454178\pi\) | |||||||
\(972\) | −5.34017 | −0.171286 | ||||||||
\(973\) | −9.25404 | −0.296671 | ||||||||
\(974\) | 111.064 | 3.55871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.5174 | −1.84109 | ||||||||
\(977\) | −50.3956 | −1.61230 | −0.806149 | − | 0.591713i | \(-0.798452\pi\) | ||||
−0.806149 | + | 0.591713i | \(0.798452\pi\) | |||||||
\(978\) | −17.6742 | −0.565159 | ||||||||
\(979\) | −12.8371 | −0.410276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.31351 | 0.0738647 | ||||||||
\(982\) | 94.3833 | 3.01189 | ||||||||
\(983\) | 32.1978 | 1.02695 | 0.513475 | − | 0.858105i | \(-0.328358\pi\) | ||||
0.513475 | + | 0.858105i | \(0.328358\pi\) | |||||||
\(984\) | 85.2327 | 2.71712 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.8187 | −0.949620 | ||||||||
\(987\) | −5.04718 | −0.160654 | ||||||||
\(988\) | 121.954 | 3.87988 | ||||||||
\(989\) | −16.3956 | −0.521349 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.7747 | −1.48585 | −0.742924 | − | 0.669376i | \(-0.766562\pi\) | ||||
−0.742924 | + | 0.669376i | \(0.766562\pi\) | |||||||
\(992\) | −90.7501 | −2.88132 | ||||||||
\(993\) | −19.2039 | −0.609419 | ||||||||
\(994\) | 13.6742 | 0.433719 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −58.8515 | −1.86478 | ||||||||
\(997\) | −38.2122 | −1.21019 | −0.605096 | − | 0.796153i | \(-0.706865\pi\) | ||||
−0.605096 | + | 0.796153i | \(0.706865\pi\) | |||||||
\(998\) | 41.0472 | 1.29933 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 825.2.a.k.1.3 | 3 | ||
3.2 | odd | 2 | 2475.2.a.bb.1.1 | 3 | |||
5.2 | odd | 4 | 825.2.c.g.199.6 | 6 | |||
5.3 | odd | 4 | 825.2.c.g.199.1 | 6 | |||
5.4 | even | 2 | 165.2.a.c.1.1 | ✓ | 3 | ||
11.10 | odd | 2 | 9075.2.a.cf.1.1 | 3 | |||
15.2 | even | 4 | 2475.2.c.r.199.1 | 6 | |||
15.8 | even | 4 | 2475.2.c.r.199.6 | 6 | |||
15.14 | odd | 2 | 495.2.a.e.1.3 | 3 | |||
20.19 | odd | 2 | 2640.2.a.be.1.2 | 3 | |||
35.34 | odd | 2 | 8085.2.a.bk.1.1 | 3 | |||
55.54 | odd | 2 | 1815.2.a.m.1.3 | 3 | |||
60.59 | even | 2 | 7920.2.a.cj.1.2 | 3 | |||
165.164 | even | 2 | 5445.2.a.z.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
495.2.a.e.1.3 | 3 | 15.14 | odd | 2 | |||
825.2.a.k.1.3 | 3 | 1.1 | even | 1 | trivial | ||
825.2.c.g.199.1 | 6 | 5.3 | odd | 4 | |||
825.2.c.g.199.6 | 6 | 5.2 | odd | 4 | |||
1815.2.a.m.1.3 | 3 | 55.54 | odd | 2 | |||
2475.2.a.bb.1.1 | 3 | 3.2 | odd | 2 | |||
2475.2.c.r.199.1 | 6 | 15.2 | even | 4 | |||
2475.2.c.r.199.6 | 6 | 15.8 | even | 4 | |||
2640.2.a.be.1.2 | 3 | 20.19 | odd | 2 | |||
5445.2.a.z.1.1 | 3 | 165.164 | even | 2 | |||
7920.2.a.cj.1.2 | 3 | 60.59 | even | 2 | |||
8085.2.a.bk.1.1 | 3 | 35.34 | odd | 2 | |||
9075.2.a.cf.1.1 | 3 | 11.10 | odd | 2 |