Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.546984493056.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 20x^{6} + 129x^{4} - 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.25511\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.66933 | 1.19376 | 0.596880 | − | 0.802331i | \(-0.296407\pi\) | ||||
0.596880 | + | 0.802331i | \(0.296407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.18696 | 1.20456 | 0.602280 | − | 0.798285i | \(-0.294259\pi\) | ||||
0.602280 | + | 0.798285i | \(0.294259\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.66933 | 0.844115 | ||||||||
\(11\) | 5.51998 | 1.66434 | 0.832169 | − | 0.554522i | \(-0.187099\pi\) | ||||
0.832169 | + | 0.554522i | \(0.187099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64969 | 0.734893 | 0.367446 | − | 0.930045i | \(-0.380232\pi\) | ||||
0.367446 | + | 0.930045i | \(0.380232\pi\) | |||||||
\(14\) | 3.18696 | 0.851752 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.74723 | −0.908838 | −0.454419 | − | 0.890788i | \(-0.650153\pi\) | ||||
−0.454419 | + | 0.890788i | \(0.650153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.37393 | 1.46228 | 0.731140 | − | 0.682228i | \(-0.238989\pi\) | ||||
0.731140 | + | 0.682228i | \(0.238989\pi\) | |||||||
\(20\) | 2.66933 | 0.596880 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.51998 | 1.17686 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12530 | 0.425061 | ||||||||
\(26\) | 2.64969 | 0.519648 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.18696 | 0.602280 | ||||||||
\(29\) | −5.50705 | −1.02263 | −0.511317 | − | 0.859392i | \(-0.670842\pi\) | ||||
−0.511317 | + | 0.859392i | \(0.670842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.6638 | −1.91527 | −0.957637 | − | 0.287979i | \(-0.907017\pi\) | ||||
−0.957637 | + | 0.287979i | \(0.907017\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.74723 | −0.642645 | ||||||||
\(35\) | 8.50705 | 1.43795 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.36329 | −1.53932 | −0.769658 | − | 0.638457i | \(-0.779573\pi\) | ||||
−0.769658 | + | 0.638457i | \(0.779573\pi\) | |||||||
\(38\) | 6.37393 | 1.03399 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.66933 | 0.422058 | ||||||||
\(41\) | −0.424692 | −0.0663257 | −0.0331629 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331629 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.38311 | 0.820917 | 0.410459 | − | 0.911879i | \(-0.365369\pi\) | ||||
0.410459 | + | 0.911879i | \(0.365369\pi\) | |||||||
\(44\) | 5.51998 | 0.832169 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.38528 | 1.36898 | 0.684492 | − | 0.729020i | \(-0.260024\pi\) | ||||
0.684492 | + | 0.729020i | \(0.260024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.15674 | 0.450963 | ||||||||
\(50\) | 2.12530 | 0.300563 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.64969 | 0.367446 | ||||||||
\(53\) | 11.6296 | 1.59745 | 0.798725 | − | 0.601696i | \(-0.205508\pi\) | ||||
0.798725 | + | 0.601696i | \(0.205508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.7346 | 1.98682 | ||||||||
\(56\) | 3.18696 | 0.425876 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.50705 | −0.723111 | ||||||||
\(59\) | 5.64969 | 0.735528 | 0.367764 | − | 0.929919i | \(-0.380124\pi\) | ||||
0.367764 | + | 0.929919i | \(0.380124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.39110 | 0.946333 | 0.473167 | − | 0.880973i | \(-0.343111\pi\) | ||||
0.473167 | + | 0.880973i | \(0.343111\pi\) | |||||||
\(62\) | −10.6638 | −1.35430 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.07290 | 0.877285 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.30338 | 0.525741 | 0.262871 | − | 0.964831i | \(-0.415331\pi\) | ||||
0.262871 | + | 0.964831i | \(0.415331\pi\) | |||||||
\(68\) | −3.74723 | −0.454419 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.50705 | 1.01679 | ||||||||
\(71\) | 1.91411 | 0.227163 | 0.113581 | − | 0.993529i | \(-0.463768\pi\) | ||||
0.113581 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.37377 | −0.628953 | −0.314476 | − | 0.949265i | \(-0.601829\pi\) | ||||
−0.314476 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(74\) | −9.36329 | −1.08846 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.37393 | 0.731140 | ||||||||
\(77\) | 17.5920 | 2.00479 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.61099 | −0.743795 | −0.371897 | − | 0.928274i | \(-0.621293\pi\) | ||||
−0.371897 | + | 0.928274i | \(0.621293\pi\) | |||||||
\(80\) | 2.66933 | 0.298440 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.424692 | −0.0468994 | ||||||||
\(83\) | −5.15732 | −0.566090 | −0.283045 | − | 0.959107i | \(-0.591345\pi\) | ||||
−0.283045 | + | 0.959107i | \(0.591345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0026 | −1.08493 | ||||||||
\(86\) | 5.38311 | 0.580476 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.51998 | 0.588432 | ||||||||
\(89\) | −14.9168 | −1.58117 | −0.790587 | − | 0.612349i | \(-0.790225\pi\) | ||||
−0.790587 | + | 0.612349i | \(0.790225\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.44448 | 0.885222 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.38528 | 0.968018 | ||||||||
\(95\) | 17.0141 | 1.74561 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8109 | 1.30075 | 0.650374 | − | 0.759614i | \(-0.274612\pi\) | ||||
0.650374 | + | 0.759614i | \(0.274612\pi\) | |||||||
\(98\) | 3.15674 | 0.318879 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.12530 | 0.212530 | ||||||||
\(101\) | −6.74615 | −0.671267 | −0.335633 | − | 0.941993i | \(-0.608950\pi\) | ||||
−0.335633 | + | 0.941993i | \(0.608950\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21661 | 0.119876 | 0.0599380 | − | 0.998202i | \(-0.480910\pi\) | ||||
0.0599380 | + | 0.998202i | \(0.480910\pi\) | |||||||
\(104\) | 2.64969 | 0.259824 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.6296 | 1.12957 | ||||||||
\(107\) | −6.63640 | −0.641565 | −0.320782 | − | 0.947153i | \(-0.603946\pi\) | ||||
−0.320782 | + | 0.947153i | \(0.603946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.8759 | −1.61641 | −0.808207 | − | 0.588898i | \(-0.799562\pi\) | ||||
−0.808207 | + | 0.588898i | \(0.799562\pi\) | |||||||
\(110\) | 14.7346 | 1.40489 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.18696 | 0.301140 | ||||||||
\(113\) | −8.31491 | −0.782201 | −0.391100 | − | 0.920348i | \(-0.627905\pi\) | ||||
−0.391100 | + | 0.920348i | \(0.627905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.50705 | −0.511317 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.64969 | 0.520097 | ||||||||
\(119\) | −11.9423 | −1.09475 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.4702 | 1.77002 | ||||||||
\(122\) | 7.39110 | 0.669159 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.6638 | −0.957637 | ||||||||
\(125\) | −7.67350 | −0.686339 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.6429 | −1.12188 | −0.560938 | − | 0.827857i | \(-0.689560\pi\) | ||||
−0.560938 | + | 0.827857i | \(0.689560\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.07290 | 0.620334 | ||||||||
\(131\) | −4.07085 | −0.355672 | −0.177836 | − | 0.984060i | \(-0.556910\pi\) | ||||
−0.177836 | + | 0.984060i | \(0.556910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.3135 | 1.76140 | ||||||||
\(134\) | 4.30338 | 0.371755 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.74723 | −0.321323 | ||||||||
\(137\) | −10.4983 | −0.896928 | −0.448464 | − | 0.893801i | \(-0.648029\pi\) | ||||
−0.448464 | + | 0.893801i | \(0.648029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.71471 | 0.823991 | 0.411995 | − | 0.911186i | \(-0.364832\pi\) | ||||
0.411995 | + | 0.911186i | \(0.364832\pi\) | |||||||
\(140\) | 8.50705 | 0.718977 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.91411 | 0.160628 | ||||||||
\(143\) | 14.6263 | 1.22311 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.7001 | −1.22078 | ||||||||
\(146\) | −5.37377 | −0.444737 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.36329 | −0.769658 | ||||||||
\(149\) | −11.3155 | −0.927005 | −0.463503 | − | 0.886096i | \(-0.653408\pi\) | ||||
−0.463503 | + | 0.886096i | \(0.653408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.75552 | −0.712514 | −0.356257 | − | 0.934388i | \(-0.615947\pi\) | ||||
−0.356257 | + | 0.934388i | \(0.615947\pi\) | |||||||
\(152\) | 6.37393 | 0.516994 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.5920 | 1.41760 | ||||||||
\(155\) | −28.4651 | −2.28637 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.69959 | −0.774112 | −0.387056 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387056 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(158\) | −6.61099 | −0.525942 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.66933 | 0.211029 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.01410 | −0.392734 | −0.196367 | − | 0.980530i | \(-0.562914\pi\) | ||||
−0.196367 | + | 0.980530i | \(0.562914\pi\) | |||||||
\(164\) | −0.424692 | −0.0331629 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.15732 | −0.400286 | ||||||||
\(167\) | −10.5988 | −0.820158 | −0.410079 | − | 0.912050i | \(-0.634499\pi\) | ||||
−0.410079 | + | 0.912050i | \(0.634499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.97912 | −0.459932 | ||||||||
\(170\) | −10.0026 | −0.767164 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.38311 | 0.410459 | ||||||||
\(173\) | −11.9773 | −0.910615 | −0.455308 | − | 0.890334i | \(-0.650471\pi\) | ||||
−0.455308 | + | 0.890334i | \(0.650471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.77327 | 0.512011 | ||||||||
\(176\) | 5.51998 | 0.416084 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.9168 | −1.11806 | ||||||||
\(179\) | 24.6429 | 1.84190 | 0.920949 | − | 0.389683i | \(-0.127416\pi\) | ||||
0.920949 | + | 0.389683i | \(0.127416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9599 | −1.48361 | −0.741805 | − | 0.670616i | \(-0.766030\pi\) | ||||
−0.741805 | + | 0.670616i | \(0.766030\pi\) | |||||||
\(182\) | 8.44448 | 0.625947 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.9937 | −1.83757 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.6847 | −1.51261 | ||||||||
\(188\) | 9.38528 | 0.684492 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.0141 | 1.23433 | ||||||||
\(191\) | 15.1004 | 1.09263 | 0.546313 | − | 0.837581i | \(-0.316031\pi\) | ||||
0.546313 | + | 0.837581i | \(0.316031\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.60321 | 0.187383 | 0.0936916 | − | 0.995601i | \(-0.470133\pi\) | ||||
0.0936916 | + | 0.995601i | \(0.470133\pi\) | |||||||
\(194\) | 12.8109 | 0.919768 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.15674 | 0.225482 | ||||||||
\(197\) | −2.24169 | −0.159714 | −0.0798568 | − | 0.996806i | \(-0.525446\pi\) | ||||
−0.0798568 | + | 0.996806i | \(0.525446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.43816 | −0.243725 | −0.121862 | − | 0.992547i | \(-0.538887\pi\) | ||||
−0.121862 | + | 0.992547i | \(0.538887\pi\) | |||||||
\(200\) | 2.12530 | 0.150282 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.74615 | −0.474657 | ||||||||
\(203\) | −17.5508 | −1.23182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.13364 | −0.0791769 | ||||||||
\(206\) | 1.21661 | 0.0847651 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.64969 | 0.183723 | ||||||||
\(209\) | 35.1840 | 2.43373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.22759 | 0.428725 | 0.214363 | − | 0.976754i | \(-0.431233\pi\) | ||||
0.214363 | + | 0.976754i | \(0.431233\pi\) | |||||||
\(212\) | 11.6296 | 0.798725 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.63640 | −0.453655 | ||||||||
\(215\) | 14.3693 | 0.979977 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.9851 | −2.30706 | ||||||||
\(218\) | −16.8759 | −1.14298 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.7346 | 0.993409 | ||||||||
\(221\) | −9.92902 | −0.667898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6429 | −1.38235 | −0.691176 | − | 0.722687i | \(-0.742907\pi\) | ||||
−0.691176 | + | 0.722687i | \(0.742907\pi\) | |||||||
\(224\) | 3.18696 | 0.212938 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.31491 | −0.553099 | ||||||||
\(227\) | −21.7031 | −1.44049 | −0.720244 | − | 0.693721i | \(-0.755970\pi\) | ||||
−0.720244 | + | 0.693721i | \(0.755970\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.76768 | −0.579385 | −0.289692 | − | 0.957120i | \(-0.593553\pi\) | ||||
−0.289692 | + | 0.957120i | \(0.593553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.50705 | −0.361555 | ||||||||
\(233\) | −6.98878 | −0.457850 | −0.228925 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228925 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.0524 | 1.63424 | ||||||||
\(236\) | 5.64969 | 0.367764 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.9423 | −0.774104 | ||||||||
\(239\) | 26.3417 | 1.70390 | 0.851951 | − | 0.523622i | \(-0.175420\pi\) | ||||
0.851951 | + | 0.523622i | \(0.175420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3769 | 0.926098 | 0.463049 | − | 0.886333i | \(-0.346755\pi\) | ||||
0.463049 | + | 0.886333i | \(0.346755\pi\) | |||||||
\(242\) | 19.4702 | 1.25159 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.39110 | 0.473167 | ||||||||
\(245\) | 8.42638 | 0.538341 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.8890 | 1.07462 | ||||||||
\(248\) | −10.6638 | −0.677151 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.67350 | −0.485315 | ||||||||
\(251\) | 27.8370 | 1.75706 | 0.878528 | − | 0.477692i | \(-0.158526\pi\) | ||||
0.878528 | + | 0.477692i | \(0.158526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.6429 | −0.793287 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.1882 | 0.947413 | 0.473706 | − | 0.880683i | \(-0.342916\pi\) | ||||
0.473706 | + | 0.880683i | \(0.342916\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.8405 | −1.85420 | ||||||||
\(260\) | 7.07290 | 0.438643 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.07085 | −0.251498 | ||||||||
\(263\) | 29.3640 | 1.81066 | 0.905331 | − | 0.424706i | \(-0.139623\pi\) | ||||
0.905331 | + | 0.424706i | \(0.139623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.0432 | 1.90697 | ||||||||
\(266\) | 20.3135 | 1.24550 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.30338 | 0.262871 | ||||||||
\(269\) | 16.5062 | 1.00640 | 0.503199 | − | 0.864171i | \(-0.332156\pi\) | ||||
0.503199 | + | 0.864171i | \(0.332156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.22854 | 0.439102 | 0.219551 | − | 0.975601i | \(-0.429541\pi\) | ||||
0.219551 | + | 0.975601i | \(0.429541\pi\) | |||||||
\(272\) | −3.74723 | −0.227209 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4983 | −0.634224 | ||||||||
\(275\) | 11.7316 | 0.707445 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21349 | 0.0729118 | 0.0364559 | − | 0.999335i | \(-0.488393\pi\) | ||||
0.0364559 | + | 0.999335i | \(0.488393\pi\) | |||||||
\(278\) | 9.71471 | 0.582649 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.50705 | 0.508393 | ||||||||
\(281\) | −6.88927 | −0.410980 | −0.205490 | − | 0.978659i | \(-0.565879\pi\) | ||||
−0.205490 | + | 0.978659i | \(0.565879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.24316 | −0.549449 | −0.274724 | − | 0.961523i | \(-0.588587\pi\) | ||||
−0.274724 | + | 0.961523i | \(0.588587\pi\) | |||||||
\(284\) | 1.91411 | 0.113581 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.6263 | 0.864870 | ||||||||
\(287\) | −1.35348 | −0.0798933 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.95824 | −0.174014 | ||||||||
\(290\) | −14.7001 | −0.863220 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.37377 | −0.314476 | ||||||||
\(293\) | −14.3366 | −0.837551 | −0.418776 | − | 0.908090i | \(-0.637541\pi\) | ||||
−0.418776 | + | 0.908090i | \(0.637541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0809 | 0.878043 | ||||||||
\(296\) | −9.36329 | −0.544230 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.3155 | −0.655492 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.1558 | 0.988844 | ||||||||
\(302\) | −8.75552 | −0.503824 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.37393 | 0.365570 | ||||||||
\(305\) | 19.7293 | 1.12969 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0423 | 0.858509 | 0.429254 | − | 0.903184i | \(-0.358776\pi\) | ||||
0.429254 | + | 0.903184i | \(0.358776\pi\) | |||||||
\(308\) | 17.5920 | 1.00240 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.4651 | −1.61671 | ||||||||
\(311\) | −5.01410 | −0.284323 | −0.142162 | − | 0.989843i | \(-0.545405\pi\) | ||||
−0.142162 | + | 0.989843i | \(0.545405\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.36031 | 0.0768893 | 0.0384446 | − | 0.999261i | \(-0.487760\pi\) | ||||
0.0384446 | + | 0.999261i | \(0.487760\pi\) | |||||||
\(314\) | −9.69959 | −0.547380 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.61099 | −0.371897 | ||||||||
\(317\) | 29.9622 | 1.68285 | 0.841423 | − | 0.540377i | \(-0.181718\pi\) | ||||
0.841423 | + | 0.540377i | \(0.181718\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.3988 | −1.70201 | ||||||||
\(320\) | 2.66933 | 0.149220 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.8846 | −1.32897 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.63140 | 0.312374 | ||||||||
\(326\) | −5.01410 | −0.277705 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.424692 | −0.0234497 | ||||||||
\(329\) | 29.9106 | 1.64902 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.7288 | 1.24929 | 0.624644 | − | 0.780910i | \(-0.285244\pi\) | ||||
0.624644 | + | 0.780910i | \(0.285244\pi\) | |||||||
\(332\) | −5.15732 | −0.283045 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.5988 | −0.579939 | ||||||||
\(335\) | 11.4871 | 0.627608 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7294 | 1.56499 | 0.782496 | − | 0.622656i | \(-0.213946\pi\) | ||||
0.782496 | + | 0.622656i | \(0.213946\pi\) | |||||||
\(338\) | −5.97912 | −0.325221 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.0026 | −0.542467 | ||||||||
\(341\) | −58.8640 | −3.18766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.2483 | −0.661347 | ||||||||
\(344\) | 5.38311 | 0.290238 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.9773 | −0.643902 | ||||||||
\(347\) | −17.1990 | −0.923292 | −0.461646 | − | 0.887064i | \(-0.652741\pi\) | ||||
−0.461646 | + | 0.887064i | \(0.652741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.1540 | 1.61410 | 0.807052 | − | 0.590480i | \(-0.201062\pi\) | ||||
0.807052 | + | 0.590480i | \(0.201062\pi\) | |||||||
\(350\) | 6.77327 | 0.362046 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.51998 | 0.294216 | ||||||||
\(353\) | 32.5920 | 1.73470 | 0.867348 | − | 0.497701i | \(-0.165822\pi\) | ||||
0.867348 | + | 0.497701i | \(0.165822\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.10937 | 0.271177 | ||||||||
\(356\) | −14.9168 | −0.790587 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.6429 | 1.30242 | ||||||||
\(359\) | 10.9584 | 0.578361 | 0.289180 | − | 0.957275i | \(-0.406617\pi\) | ||||
0.289180 | + | 0.957275i | \(0.406617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.6270 | 1.13826 | ||||||||
\(362\) | −19.9599 | −1.04907 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.44448 | 0.442611 | ||||||||
\(365\) | −14.3444 | −0.750818 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6009 | 0.762159 | 0.381080 | − | 0.924542i | \(-0.375552\pi\) | ||||
0.381080 | + | 0.924542i | \(0.375552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.9937 | −1.29936 | ||||||||
\(371\) | 37.0632 | 1.92422 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.9805 | −1.81122 | −0.905610 | − | 0.424111i | \(-0.860587\pi\) | ||||
−0.905610 | + | 0.424111i | \(0.860587\pi\) | |||||||
\(374\) | −20.6847 | −1.06958 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.38528 | 0.484009 | ||||||||
\(377\) | −14.5920 | −0.751526 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.9184 | −0.663573 | −0.331786 | − | 0.943355i | \(-0.607651\pi\) | ||||
−0.331786 | + | 0.943355i | \(0.607651\pi\) | |||||||
\(380\) | 17.0141 | 0.872805 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.1004 | 0.772604 | ||||||||
\(383\) | −3.50470 | −0.179082 | −0.0895409 | − | 0.995983i | \(-0.528540\pi\) | ||||
−0.0895409 | + | 0.995983i | \(0.528540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.9588 | 2.39324 | ||||||||
\(386\) | 2.60321 | 0.132500 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.8109 | 0.650374 | ||||||||
\(389\) | −35.8835 | −1.81936 | −0.909682 | − | 0.415305i | \(-0.863675\pi\) | ||||
−0.909682 | + | 0.415305i | \(0.863675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.15674 | 0.159440 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.24169 | −0.112935 | ||||||||
\(395\) | −17.6469 | −0.887912 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.7061 | −1.64147 | −0.820736 | − | 0.571308i | \(-0.806436\pi\) | ||||
−0.820736 | + | 0.571308i | \(0.806436\pi\) | |||||||
\(398\) | −3.43816 | −0.172339 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.12530 | 0.106265 | ||||||||
\(401\) | 33.1293 | 1.65440 | 0.827200 | − | 0.561907i | \(-0.189932\pi\) | ||||
0.827200 | + | 0.561907i | \(0.189932\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.2558 | −1.40752 | ||||||||
\(404\) | −6.74615 | −0.335633 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5508 | −0.871030 | ||||||||
\(407\) | −51.6852 | −2.56194 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6760 | −1.61573 | −0.807863 | − | 0.589370i | \(-0.799376\pi\) | ||||
−0.807863 | + | 0.589370i | \(0.799376\pi\) | |||||||
\(410\) | −1.13364 | −0.0559865 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.21661 | 0.0599380 | ||||||||
\(413\) | 18.0054 | 0.885987 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7666 | −0.675775 | ||||||||
\(416\) | 2.64969 | 0.129912 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35.1840 | 1.72091 | ||||||||
\(419\) | 8.40048 | 0.410390 | 0.205195 | − | 0.978721i | \(-0.434217\pi\) | ||||
0.205195 | + | 0.978721i | \(0.434217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.81779 | 0.283542 | 0.141771 | − | 0.989900i | \(-0.454720\pi\) | ||||
0.141771 | + | 0.989900i | \(0.454720\pi\) | |||||||
\(422\) | 6.22759 | 0.303154 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.6296 | 0.564784 | ||||||||
\(425\) | −7.96401 | −0.386311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.5552 | 1.13991 | ||||||||
\(428\) | −6.63640 | −0.320782 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.3693 | 0.692949 | ||||||||
\(431\) | −20.4753 | −0.986259 | −0.493129 | − | 0.869956i | \(-0.664147\pi\) | ||||
−0.493129 | + | 0.869956i | \(0.664147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.5736 | −1.27705 | −0.638523 | − | 0.769602i | \(-0.720454\pi\) | ||||
−0.638523 | + | 0.769602i | \(0.720454\pi\) | |||||||
\(434\) | −33.9851 | −1.63134 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.8759 | −0.808207 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.807385 | −0.0385344 | −0.0192672 | − | 0.999814i | \(-0.506133\pi\) | ||||
−0.0192672 | + | 0.999814i | \(0.506133\pi\) | |||||||
\(440\) | 14.7346 | 0.702446 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.92902 | −0.472275 | ||||||||
\(443\) | 15.1349 | 0.719082 | 0.359541 | − | 0.933129i | \(-0.382933\pi\) | ||||
0.359541 | + | 0.933129i | \(0.382933\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.8177 | −1.88754 | ||||||||
\(446\) | −20.6429 | −0.977470 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.18696 | 0.150570 | ||||||||
\(449\) | 6.19710 | 0.292459 | 0.146230 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146230 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.34429 | −0.110388 | ||||||||
\(452\) | −8.31491 | −0.391100 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.7031 | −1.01858 | ||||||||
\(455\) | 22.5411 | 1.05674 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.24075 | −0.245152 | −0.122576 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122576 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(458\) | −8.76768 | −0.409687 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.47112 | −0.347965 | −0.173982 | − | 0.984749i | \(-0.555664\pi\) | ||||
−0.173982 | + | 0.984749i | \(0.555664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.63375 | 0.261823 | 0.130911 | − | 0.991394i | \(-0.458210\pi\) | ||||
0.130911 | + | 0.991394i | \(0.458210\pi\) | |||||||
\(464\) | −5.50705 | −0.255658 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.98878 | −0.323749 | ||||||||
\(467\) | −20.1267 | −0.931354 | −0.465677 | − | 0.884955i | \(-0.654189\pi\) | ||||
−0.465677 | + | 0.884955i | \(0.654189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7147 | 0.633286 | ||||||||
\(470\) | 25.0524 | 1.15558 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.64969 | 0.260048 | ||||||||
\(473\) | 29.7147 | 1.36628 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.5465 | 0.621558 | ||||||||
\(476\) | −11.9423 | −0.547374 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.3417 | 1.20484 | ||||||||
\(479\) | 17.1402 | 0.783154 | 0.391577 | − | 0.920145i | \(-0.371930\pi\) | ||||
0.391577 | + | 0.920145i | \(0.371930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.8098 | −1.13123 | ||||||||
\(482\) | 14.3769 | 0.654850 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.4702 | 0.885010 | ||||||||
\(485\) | 34.1964 | 1.55278 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2644 | −0.555754 | −0.277877 | − | 0.960617i | \(-0.589631\pi\) | ||||
−0.277877 | + | 0.960617i | \(0.589631\pi\) | |||||||
\(488\) | 7.39110 | 0.334579 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.42638 | 0.380665 | ||||||||
\(491\) | −6.37029 | −0.287487 | −0.143744 | − | 0.989615i | \(-0.545914\pi\) | ||||
−0.143744 | + | 0.989615i | \(0.545914\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.6362 | 0.929408 | ||||||||
\(494\) | 16.8890 | 0.759870 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.6638 | −0.478818 | ||||||||
\(497\) | 6.10019 | 0.273631 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.9981 | −0.984770 | −0.492385 | − | 0.870377i | \(-0.663875\pi\) | ||||
−0.492385 | + | 0.870377i | \(0.663875\pi\) | |||||||
\(500\) | −7.67350 | −0.343170 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.8370 | 1.24243 | ||||||||
\(503\) | −19.2333 | −0.857568 | −0.428784 | − | 0.903407i | \(-0.641058\pi\) | ||||
−0.428784 | + | 0.903407i | \(0.641058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0077 | −0.801331 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.6429 | −0.560938 | ||||||||
\(509\) | 23.2616 | 1.03105 | 0.515527 | − | 0.856874i | \(-0.327596\pi\) | ||||
0.515527 | + | 0.856874i | \(0.327596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.1260 | −0.757611 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.1882 | 0.669922 | ||||||||
\(515\) | 3.24752 | 0.143103 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.8066 | 2.27845 | ||||||||
\(518\) | −29.8405 | −1.31111 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.07290 | 0.310167 | ||||||||
\(521\) | 27.6565 | 1.21165 | 0.605827 | − | 0.795596i | \(-0.292842\pi\) | ||||
0.605827 | + | 0.795596i | \(0.292842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8574 | 1.17439 | 0.587197 | − | 0.809444i | \(-0.300231\pi\) | ||||
0.587197 | + | 0.809444i | \(0.300231\pi\) | |||||||
\(524\) | −4.07085 | −0.177836 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.3640 | 1.28033 | ||||||||
\(527\) | 39.9597 | 1.74067 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 31.0432 | 1.34843 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.3135 | 0.880701 | ||||||||
\(533\) | −1.12530 | −0.0487423 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.7147 | −0.765874 | ||||||||
\(536\) | 4.30338 | 0.185878 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.5062 | 0.711631 | ||||||||
\(539\) | 17.4252 | 0.750555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.9222 | −1.54441 | −0.772207 | − | 0.635371i | \(-0.780847\pi\) | ||||
−0.772207 | + | 0.635371i | \(0.780847\pi\) | |||||||
\(542\) | 7.22854 | 0.310492 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.74723 | −0.160661 | ||||||||
\(545\) | −45.0472 | −1.92961 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.51531 | 0.406845 | 0.203423 | − | 0.979091i | \(-0.434793\pi\) | ||||
0.203423 | + | 0.979091i | \(0.434793\pi\) | |||||||
\(548\) | −10.4983 | −0.448464 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.7316 | 0.500239 | ||||||||
\(551\) | −35.1015 | −1.49538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.0690 | −0.895945 | ||||||||
\(554\) | 1.21349 | 0.0515565 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.71471 | 0.411995 | ||||||||
\(557\) | 39.2924 | 1.66487 | 0.832437 | − | 0.554120i | \(-0.186945\pi\) | ||||
0.832437 | + | 0.554120i | \(0.186945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2636 | 0.603286 | ||||||||
\(560\) | 8.50705 | 0.359488 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.88927 | −0.290606 | ||||||||
\(563\) | −1.85603 | −0.0782224 | −0.0391112 | − | 0.999235i | \(-0.512453\pi\) | ||||
−0.0391112 | + | 0.999235i | \(0.512453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.1952 | −0.933759 | ||||||||
\(566\) | −9.24316 | −0.388519 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.91411 | 0.0803141 | ||||||||
\(569\) | 30.4311 | 1.27574 | 0.637868 | − | 0.770146i | \(-0.279816\pi\) | ||||
0.637868 | + | 0.770146i | \(0.279816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.2231 | −1.39034 | −0.695172 | − | 0.718843i | \(-0.744672\pi\) | ||||
−0.695172 | + | 0.718843i | \(0.744672\pi\) | |||||||
\(572\) | 14.6263 | 0.611555 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.35348 | −0.0564931 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00095 | −0.374714 | −0.187357 | − | 0.982292i | \(-0.559992\pi\) | ||||
−0.187357 | + | 0.982292i | \(0.559992\pi\) | |||||||
\(578\) | −2.95824 | −0.123047 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.7001 | −0.610389 | ||||||||
\(581\) | −16.4362 | −0.681888 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64.1953 | 2.65870 | ||||||||
\(584\) | −5.37377 | −0.222368 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.3366 | −0.592238 | ||||||||
\(587\) | 35.0840 | 1.44807 | 0.724037 | − | 0.689761i | \(-0.242285\pi\) | ||||
0.724037 | + | 0.689761i | \(0.242285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.9702 | −2.80067 | ||||||||
\(590\) | 15.0809 | 0.620870 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.36329 | −0.384829 | ||||||||
\(593\) | −0.355244 | −0.0145881 | −0.00729406 | − | 0.999973i | \(-0.502322\pi\) | ||||
−0.00729406 | + | 0.999973i | \(0.502322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31.8779 | −1.30687 | ||||||||
\(596\) | −11.3155 | −0.463503 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.61472 | −0.106834 | −0.0534172 | − | 0.998572i | \(-0.517011\pi\) | ||||
−0.0534172 | + | 0.998572i | \(0.517011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.9109 | −0.771390 | −0.385695 | − | 0.922626i | \(-0.626038\pi\) | ||||
−0.385695 | + | 0.922626i | \(0.626038\pi\) | |||||||
\(602\) | 17.1558 | 0.699218 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.75552 | −0.356257 | ||||||||
\(605\) | 51.9724 | 2.11298 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.40033 | −0.300370 | −0.150185 | − | 0.988658i | \(-0.547987\pi\) | ||||
−0.150185 | + | 0.988658i | \(0.547987\pi\) | |||||||
\(608\) | 6.37393 | 0.258497 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.7293 | 0.798814 | ||||||||
\(611\) | 24.8681 | 1.00606 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1742 | 0.855219 | 0.427610 | − | 0.903963i | \(-0.359356\pi\) | ||||
0.427610 | + | 0.903963i | \(0.359356\pi\) | |||||||
\(614\) | 15.0423 | 0.607057 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.5920 | 0.708802 | ||||||||
\(617\) | 23.1202 | 0.930785 | 0.465392 | − | 0.885104i | \(-0.345913\pi\) | ||||
0.465392 | + | 0.885104i | \(0.345913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2953 | 0.534385 | 0.267192 | − | 0.963643i | \(-0.413904\pi\) | ||||
0.267192 | + | 0.963643i | \(0.413904\pi\) | |||||||
\(620\) | −28.4651 | −1.14319 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.01410 | −0.201047 | ||||||||
\(623\) | −47.5392 | −1.90462 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1096 | −1.24438 | ||||||||
\(626\) | 1.36031 | 0.0543689 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.69959 | −0.387056 | ||||||||
\(629\) | 35.0864 | 1.39899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6775 | −1.02221 | −0.511103 | − | 0.859520i | \(-0.670763\pi\) | ||||
−0.511103 | + | 0.859520i | \(0.670763\pi\) | |||||||
\(632\) | −6.61099 | −0.262971 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.9622 | 1.18995 | ||||||||
\(635\) | −33.7481 | −1.33925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.36440 | 0.331410 | ||||||||
\(638\) | −30.3988 | −1.20350 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.66933 | 0.105514 | ||||||||
\(641\) | −6.19355 | −0.244631 | −0.122315 | − | 0.992491i | \(-0.539032\pi\) | ||||
−0.122315 | + | 0.992491i | \(0.539032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2528 | 0.995872 | 0.497936 | − | 0.867214i | \(-0.334091\pi\) | ||||
0.497936 | + | 0.867214i | \(0.334091\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.8846 | −0.939727 | ||||||||
\(647\) | −11.5969 | −0.455922 | −0.227961 | − | 0.973670i | \(-0.573206\pi\) | ||||
−0.227961 | + | 0.973670i | \(0.573206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.1862 | 1.22417 | ||||||||
\(650\) | 5.63140 | 0.220882 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.01410 | −0.196367 | ||||||||
\(653\) | −33.4707 | −1.30981 | −0.654904 | − | 0.755712i | \(-0.727291\pi\) | ||||
−0.654904 | + | 0.755712i | \(0.727291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8664 | −0.424586 | ||||||||
\(656\) | −0.424692 | −0.0165814 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29.9106 | 1.16604 | ||||||||
\(659\) | 37.9004 | 1.47639 | 0.738196 | − | 0.674587i | \(-0.235678\pi\) | ||||
0.738196 | + | 0.674587i | \(0.235678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6084 | 0.412619 | 0.206309 | − | 0.978487i | \(-0.433855\pi\) | ||||
0.206309 | + | 0.978487i | \(0.433855\pi\) | |||||||
\(662\) | 22.7288 | 0.883380 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.15732 | −0.200143 | ||||||||
\(665\) | 54.2233 | 2.10269 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −10.5988 | −0.410079 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.4871 | 0.443786 | ||||||||
\(671\) | 40.7988 | 1.57502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.9337 | 1.46224 | 0.731118 | − | 0.682251i | \(-0.238999\pi\) | ||||
0.731118 | + | 0.682251i | \(0.238999\pi\) | |||||||
\(674\) | 28.7294 | 1.10662 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.97912 | −0.229966 | ||||||||
\(677\) | 3.28167 | 0.126125 | 0.0630624 | − | 0.998010i | \(-0.479913\pi\) | ||||
0.0630624 | + | 0.998010i | \(0.479913\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.8278 | 1.56683 | ||||||||
\(680\) | −10.0026 | −0.383582 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −58.8640 | −2.25402 | ||||||||
\(683\) | −3.48285 | −0.133267 | −0.0666337 | − | 0.997778i | \(-0.521226\pi\) | ||||
−0.0666337 | + | 0.997778i | \(0.521226\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.0233 | −1.07072 | ||||||||
\(686\) | −12.2483 | −0.467643 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.38311 | 0.205229 | ||||||||
\(689\) | 30.8149 | 1.17396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2135 | −0.502665 | −0.251333 | − | 0.967901i | \(-0.580869\pi\) | ||||
−0.251333 | + | 0.967901i | \(0.580869\pi\) | |||||||
\(692\) | −11.9773 | −0.455308 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.1990 | −0.652866 | ||||||||
\(695\) | 25.9317 | 0.983646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.59142 | 0.0602793 | ||||||||
\(698\) | 30.1540 | 1.14134 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.77327 | 0.256005 | ||||||||
\(701\) | 0.552017 | 0.0208494 | 0.0104247 | − | 0.999946i | \(-0.496682\pi\) | ||||
0.0104247 | + | 0.999946i | \(0.496682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −59.6809 | −2.25091 | ||||||||
\(704\) | 5.51998 | 0.208042 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.5920 | 1.22662 | ||||||||
\(707\) | −21.4997 | −0.808581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.35489 | −0.276219 | −0.138109 | − | 0.990417i | \(-0.544103\pi\) | ||||
−0.138109 | + | 0.990417i | \(0.544103\pi\) | |||||||
\(710\) | 5.10937 | 0.191751 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.9168 | −0.559030 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.0423 | 1.46010 | ||||||||
\(716\) | 24.6429 | 0.920949 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.9584 | 0.408963 | ||||||||
\(719\) | −28.9564 | −1.07989 | −0.539946 | − | 0.841700i | \(-0.681555\pi\) | ||||
−0.539946 | + | 0.841700i | \(0.681555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.87729 | 0.144398 | ||||||||
\(722\) | 21.6270 | 0.804872 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.9599 | −0.741805 | ||||||||
\(725\) | −11.7041 | −0.434681 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.6754 | 1.13769 | 0.568844 | − | 0.822445i | \(-0.307391\pi\) | ||||
0.568844 | + | 0.822445i | \(0.307391\pi\) | |||||||
\(728\) | 8.44448 | 0.312973 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.3444 | −0.530909 | ||||||||
\(731\) | −20.1718 | −0.746080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.9225 | 0.809727 | 0.404863 | − | 0.914377i | \(-0.367319\pi\) | ||||
0.404863 | + | 0.914377i | \(0.367319\pi\) | |||||||
\(734\) | 14.6009 | 0.538928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7546 | 0.875011 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.0840 | −0.996303 | −0.498151 | − | 0.867090i | \(-0.665988\pi\) | ||||
−0.498151 | + | 0.867090i | \(0.665988\pi\) | |||||||
\(740\) | −24.9937 | −0.918786 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 37.0632 | 1.36063 | ||||||||
\(743\) | 39.3316 | 1.44294 | 0.721468 | − | 0.692448i | \(-0.243468\pi\) | ||||
0.721468 | + | 0.692448i | \(0.243468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.2049 | −1.10662 | ||||||||
\(746\) | −34.9805 | −1.28073 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.6847 | −0.756306 | ||||||||
\(749\) | −21.1500 | −0.772803 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.33934 | −0.267816 | −0.133908 | − | 0.990994i | \(-0.542753\pi\) | ||||
−0.133908 | + | 0.990994i | \(0.542753\pi\) | |||||||
\(752\) | 9.38528 | 0.342246 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.5920 | −0.531409 | ||||||||
\(755\) | −23.3713 | −0.850570 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.00496 | −0.290945 | −0.145473 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145473 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(758\) | −12.9184 | −0.469217 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.0141 | 0.617166 | ||||||||
\(761\) | 48.5601 | 1.76030 | 0.880151 | − | 0.474693i | \(-0.157441\pi\) | ||||
0.880151 | + | 0.474693i | \(0.157441\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −53.7828 | −1.94707 | ||||||||
\(764\) | 15.1004 | 0.546313 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.50470 | −0.126630 | ||||||||
\(767\) | 14.9700 | 0.540534 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.81228 | −0.0653526 | −0.0326763 | − | 0.999466i | \(-0.510403\pi\) | ||||
−0.0326763 | + | 0.999466i | \(0.510403\pi\) | |||||||
\(770\) | 46.9588 | 1.69228 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.60321 | 0.0936916 | ||||||||
\(773\) | 8.27640 | 0.297682 | 0.148841 | − | 0.988861i | \(-0.452446\pi\) | ||||
0.148841 | + | 0.988861i | \(0.452446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.6638 | −0.814107 | ||||||||
\(776\) | 12.8109 | 0.459884 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.8835 | −1.28648 | ||||||||
\(779\) | −2.70696 | −0.0969867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5658 | 0.378075 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.15674 | 0.112741 | ||||||||
\(785\) | −25.8914 | −0.924103 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.23096 | 0.115171 | 0.0575857 | − | 0.998341i | \(-0.481660\pi\) | ||||
0.0575857 | + | 0.998341i | \(0.481660\pi\) | |||||||
\(788\) | −2.24169 | −0.0798568 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.6469 | −0.627849 | ||||||||
\(791\) | −26.4993 | −0.942207 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5842 | 0.695454 | ||||||||
\(794\) | −32.7061 | −1.16070 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.43816 | −0.121862 | ||||||||
\(797\) | −14.6545 | −0.519088 | −0.259544 | − | 0.965731i | \(-0.583572\pi\) | ||||
−0.259544 | + | 0.965731i | \(0.583572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.1688 | −1.24418 | ||||||||
\(800\) | 2.12530 | 0.0751408 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.1293 | 1.16984 | ||||||||
\(803\) | −29.6632 | −1.04679 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.2558 | −0.995268 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.74615 | −0.237329 | ||||||||
\(809\) | 37.2257 | 1.30879 | 0.654394 | − | 0.756154i | \(-0.272924\pi\) | ||||
0.654394 | + | 0.756154i | \(0.272924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.5135 | 0.369178 | 0.184589 | − | 0.982816i | \(-0.440905\pi\) | ||||
0.184589 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(812\) | −17.5508 | −0.615911 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −51.6852 | −1.81157 | ||||||||
\(815\) | −13.3843 | −0.468830 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.3116 | 1.20041 | ||||||||
\(818\) | −32.6760 | −1.14249 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.13364 | −0.0395885 | ||||||||
\(821\) | 2.43266 | 0.0849005 | 0.0424503 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424503 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2576 | −0.950141 | −0.475071 | − | 0.879948i | \(-0.657577\pi\) | ||||
−0.475071 | + | 0.879948i | \(0.657577\pi\) | |||||||
\(824\) | 1.21661 | 0.0423825 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0054 | 0.626487 | ||||||||
\(827\) | −50.7147 | −1.76352 | −0.881761 | − | 0.471697i | \(-0.843642\pi\) | ||||
−0.881761 | + | 0.471697i | \(0.843642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5670 | 1.20056 | 0.600280 | − | 0.799790i | \(-0.295056\pi\) | ||||
0.600280 | + | 0.799790i | \(0.295056\pi\) | |||||||
\(830\) | −13.7666 | −0.477845 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.64969 | 0.0918616 | ||||||||
\(833\) | −11.8291 | −0.409852 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.2916 | −0.979071 | ||||||||
\(836\) | 35.1840 | 1.21686 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.40048 | 0.290190 | ||||||||
\(839\) | 7.91222 | 0.273160 | 0.136580 | − | 0.990629i | \(-0.456389\pi\) | ||||
0.136580 | + | 0.990629i | \(0.456389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.32758 | 0.0457787 | ||||||||
\(842\) | 5.81779 | 0.200494 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.22759 | 0.214363 | ||||||||
\(845\) | −15.9602 | −0.549048 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 62.0509 | 2.13209 | ||||||||
\(848\) | 11.6296 | 0.399363 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.96401 | −0.273163 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4693 | 0.529658 | 0.264829 | − | 0.964295i | \(-0.414684\pi\) | ||||
0.264829 | + | 0.964295i | \(0.414684\pi\) | |||||||
\(854\) | 23.5552 | 0.806041 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.63640 | −0.226827 | ||||||||
\(857\) | 17.0835 | 0.583563 | 0.291781 | − | 0.956485i | \(-0.405752\pi\) | ||||
0.291781 | + | 0.956485i | \(0.405752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5987 | 0.532222 | 0.266111 | − | 0.963942i | \(-0.414261\pi\) | ||||
0.266111 | + | 0.963942i | \(0.414261\pi\) | |||||||
\(860\) | 14.3693 | 0.489989 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.4753 | −0.697390 | ||||||||
\(863\) | 43.1680 | 1.46946 | 0.734729 | − | 0.678361i | \(-0.237309\pi\) | ||||
0.734729 | + | 0.678361i | \(0.237309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.9713 | −1.08706 | ||||||||
\(866\) | −26.5736 | −0.903008 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33.9851 | −1.15353 | ||||||||
\(869\) | −36.4926 | −1.23793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.4026 | 0.386363 | ||||||||
\(872\) | −16.8759 | −0.571489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.4552 | −0.826736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.673001 | 0.0227256 | 0.0113628 | − | 0.999935i | \(-0.496383\pi\) | ||||
0.0113628 | + | 0.999935i | \(0.496383\pi\) | |||||||
\(878\) | −0.807385 | −0.0272479 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.7346 | 0.496705 | ||||||||
\(881\) | −23.1728 | −0.780711 | −0.390355 | − | 0.920664i | \(-0.627648\pi\) | ||||
−0.390355 | + | 0.920664i | \(0.627648\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.9841 | −1.48018 | −0.740091 | − | 0.672507i | \(-0.765217\pi\) | ||||
−0.740091 | + | 0.672507i | \(0.765217\pi\) | |||||||
\(884\) | −9.92902 | −0.333949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.1349 | 0.508467 | ||||||||
\(887\) | −7.47118 | −0.250858 | −0.125429 | − | 0.992103i | \(-0.540031\pi\) | ||||
−0.125429 | + | 0.992103i | \(0.540031\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.2925 | −1.35137 | ||||||||
\(890\) | −39.8177 | −1.33469 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.6429 | −0.691176 | ||||||||
\(893\) | 59.8211 | 2.00184 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.7800 | 2.19878 | ||||||||
\(896\) | 3.18696 | 0.106469 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.19710 | 0.206800 | ||||||||
\(899\) | 58.7260 | 1.95862 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.5789 | −1.45182 | ||||||||
\(902\) | −2.34429 | −0.0780564 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.31491 | −0.276550 | ||||||||
\(905\) | −53.2795 | −1.77107 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.6253 | −0.518831 | −0.259415 | − | 0.965766i | \(-0.583530\pi\) | ||||
−0.259415 | + | 0.965766i | \(0.583530\pi\) | |||||||
\(908\) | −21.7031 | −0.720244 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.5411 | 0.747229 | ||||||||
\(911\) | −21.0891 | −0.698714 | −0.349357 | − | 0.936990i | \(-0.613600\pi\) | ||||
−0.349357 | + | 0.936990i | \(0.613600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.4683 | −0.942164 | ||||||||
\(914\) | −5.24075 | −0.173349 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.76768 | −0.289692 | ||||||||
\(917\) | −12.9737 | −0.428428 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4325 | 0.575045 | 0.287522 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287522 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.47112 | −0.246048 | ||||||||
\(923\) | 5.07180 | 0.166940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8998 | −0.654302 | ||||||||
\(926\) | 5.63375 | 0.185137 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.50705 | −0.180778 | ||||||||
\(929\) | −25.9963 | −0.852911 | −0.426456 | − | 0.904508i | \(-0.640238\pi\) | ||||
−0.426456 | + | 0.904508i | \(0.640238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.1209 | 0.659434 | ||||||||
\(932\) | −6.98878 | −0.228925 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.1267 | −0.658567 | ||||||||
\(935\) | −55.2141 | −1.80570 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1080 | 0.526224 | 0.263112 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263112 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(938\) | 13.7147 | 0.447801 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.0524 | 0.817119 | ||||||||
\(941\) | −24.7832 | −0.807909 | −0.403954 | − | 0.914779i | \(-0.632365\pi\) | ||||
−0.403954 | + | 0.914779i | \(0.632365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 5.64969 | 0.183882 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.7147 | 0.966109 | ||||||||
\(947\) | 33.7002 | 1.09511 | 0.547555 | − | 0.836769i | \(-0.315559\pi\) | ||||
0.547555 | + | 0.836769i | \(0.315559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.2389 | −0.462213 | ||||||||
\(950\) | 13.5465 | 0.439508 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.9423 | −0.387052 | ||||||||
\(953\) | 26.7114 | 0.865266 | 0.432633 | − | 0.901570i | \(-0.357585\pi\) | ||||
0.432633 | + | 0.901570i | \(0.357585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.3079 | 1.30433 | ||||||||
\(956\) | 26.3417 | 0.851951 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.1402 | 0.553773 | ||||||||
\(959\) | −33.4576 | −1.08040 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.7164 | 2.66827 | ||||||||
\(962\) | −24.8098 | −0.799902 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.3769 | 0.463049 | ||||||||
\(965\) | 6.94882 | 0.223690 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.4502 | −0.593320 | −0.296660 | − | 0.954983i | \(-0.595873\pi\) | ||||
−0.296660 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(968\) | 19.4702 | 0.625797 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.1964 | 1.09798 | ||||||||
\(971\) | −43.0914 | −1.38287 | −0.691435 | − | 0.722439i | \(-0.743021\pi\) | ||||
−0.691435 | + | 0.722439i | \(0.743021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.9604 | 0.992546 | ||||||||
\(974\) | −12.2644 | −0.392977 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.39110 | 0.236583 | ||||||||
\(977\) | −54.0937 | −1.73061 | −0.865306 | − | 0.501244i | \(-0.832876\pi\) | ||||
−0.865306 | + | 0.501244i | \(0.832876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −82.3404 | −2.63161 | ||||||||
\(980\) | 8.42638 | 0.269171 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.37029 | −0.203284 | ||||||||
\(983\) | −1.46495 | −0.0467245 | −0.0233623 | − | 0.999727i | \(-0.507437\pi\) | ||||
−0.0233623 | + | 0.999727i | \(0.507437\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.98380 | −0.190660 | ||||||||
\(986\) | 20.6362 | 0.657190 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.8890 | 0.537309 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.2490 | 0.738529 | 0.369264 | − | 0.929324i | \(-0.379610\pi\) | ||||
0.369264 | + | 0.929324i | \(0.379610\pi\) | |||||||
\(992\) | −10.6638 | −0.338576 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.10019 | 0.193486 | ||||||||
\(995\) | −9.17757 | −0.290949 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.4158 | −1.18497 | −0.592485 | − | 0.805582i | \(-0.701853\pi\) | ||||
−0.592485 | + | 0.805582i | \(0.701853\pi\) | |||||||
\(998\) | −21.9981 | −0.696338 | ||||||||
\(999\) | 0 | 0 |
(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 | 9522.2.a.cf.1.7 | yes | 8 | |
3.2 | odd | 2 | 9522.2.a.cd.1.2 | ✓ | 8 | ||
23.22 | odd | 2 | inner | 9522.2.a.cf.1.2 | yes | 8 | |
69.68 | even | 2 | 9522.2.a.cd.1.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9522.2.a.cd.1.2 | ✓ | 8 | 3.2 | odd | 2 | ||
9522.2.a.cd.1.7 | yes | 8 | 69.68 | even | 2 | ||
9522.2.a.cf.1.2 | yes | 8 | 23.22 | odd | 2 | inner | |
9522.2.a.cf.1.7 | yes | 8 | 1.1 | even | 1 | trivial |