Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 \) |
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 | \(-0.182716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.30349 | 1.90727 | 0.953635 | − | 0.300966i | \(-0.0973089\pi\) | ||||
0.953635 | + | 0.300966i | \(0.0973089\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.88260 | 0.841926 | 0.420963 | − | 0.907078i | \(-0.361692\pi\) | ||||
0.420963 | + | 0.907078i | \(0.361692\pi\) | |||||||
\(6\) | −3.30349 | −1.34864 | ||||||||
\(7\) | −2.41197 | −0.911640 | −0.455820 | − | 0.890072i | \(-0.650654\pi\) | ||||
−0.455820 | + | 0.890072i | \(0.650654\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.91304 | 2.63768 | ||||||||
\(10\) | −1.88260 | −0.595332 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.30349 | 0.953635 | ||||||||
\(13\) | 3.16592 | 0.878068 | 0.439034 | − | 0.898470i | \(-0.355321\pi\) | ||||
0.439034 | + | 0.898470i | \(0.355321\pi\) | |||||||
\(14\) | 2.41197 | 0.644627 | ||||||||
\(15\) | 6.21916 | 1.60578 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0684367 | 0.0165983 | 0.00829916 | − | 0.999966i | \(-0.497358\pi\) | ||||
0.00829916 | + | 0.999966i | \(0.497358\pi\) | |||||||
\(18\) | −7.91304 | −1.86512 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.88260 | 0.420963 | ||||||||
\(21\) | −7.96793 | −1.73874 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.39138 | −1.54121 | −0.770605 | − | 0.637313i | \(-0.780046\pi\) | ||||
−0.770605 | + | 0.637313i | \(0.780046\pi\) | |||||||
\(24\) | −3.30349 | −0.674322 | ||||||||
\(25\) | −1.45580 | −0.291160 | ||||||||
\(26\) | −3.16592 | −0.620888 | ||||||||
\(27\) | 16.2302 | 3.12350 | ||||||||
\(28\) | −2.41197 | −0.455820 | ||||||||
\(29\) | 7.11637 | 1.32148 | 0.660738 | − | 0.750616i | \(-0.270243\pi\) | ||||
0.660738 | + | 0.750616i | \(0.270243\pi\) | |||||||
\(30\) | −6.21916 | −1.13546 | ||||||||
\(31\) | −5.53983 | −0.994982 | −0.497491 | − | 0.867469i | \(-0.665745\pi\) | ||||
−0.497491 | + | 0.867469i | \(0.665745\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.0684367 | −0.0117368 | ||||||||
\(35\) | −4.54079 | −0.767534 | ||||||||
\(36\) | 7.91304 | 1.31884 | ||||||||
\(37\) | 8.71254 | 1.43233 | 0.716166 | − | 0.697930i | \(-0.245895\pi\) | ||||
0.716166 | + | 0.697930i | \(0.245895\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 10.4586 | 1.67471 | ||||||||
\(40\) | −1.88260 | −0.297666 | ||||||||
\(41\) | −2.36137 | −0.368783 | −0.184392 | − | 0.982853i | \(-0.559031\pi\) | ||||
−0.184392 | + | 0.982853i | \(0.559031\pi\) | |||||||
\(42\) | 7.96793 | 1.22948 | ||||||||
\(43\) | 1.76442 | 0.269072 | 0.134536 | − | 0.990909i | \(-0.457046\pi\) | ||||
0.134536 | + | 0.990909i | \(0.457046\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.8971 | 2.22073 | ||||||||
\(46\) | 7.39138 | 1.08980 | ||||||||
\(47\) | 9.11437 | 1.32947 | 0.664734 | − | 0.747080i | \(-0.268545\pi\) | ||||
0.664734 | + | 0.747080i | \(0.268545\pi\) | |||||||
\(48\) | 3.30349 | 0.476818 | ||||||||
\(49\) | −1.18238 | −0.168912 | ||||||||
\(50\) | 1.45580 | 0.205881 | ||||||||
\(51\) | 0.226080 | 0.0316575 | ||||||||
\(52\) | 3.16592 | 0.439034 | ||||||||
\(53\) | 8.63343 | 1.18589 | 0.592947 | − | 0.805242i | \(-0.297964\pi\) | ||||
0.592947 | + | 0.805242i | \(0.297964\pi\) | |||||||
\(54\) | −16.2302 | −2.20865 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.41197 | 0.322314 | ||||||||
\(57\) | 3.30349 | 0.437558 | ||||||||
\(58\) | −7.11637 | −0.934425 | ||||||||
\(59\) | 5.32542 | 0.693311 | 0.346655 | − | 0.937993i | \(-0.387317\pi\) | ||||
0.346655 | + | 0.937993i | \(0.387317\pi\) | |||||||
\(60\) | 6.21916 | 0.802891 | ||||||||
\(61\) | 14.3424 | 1.83636 | 0.918179 | − | 0.396165i | \(-0.129659\pi\) | ||||
0.918179 | + | 0.396165i | \(0.129659\pi\) | |||||||
\(62\) | 5.53983 | 0.703559 | ||||||||
\(63\) | −19.0860 | −2.40461 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.96017 | 0.739269 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3594 | 1.38777 | 0.693883 | − | 0.720088i | \(-0.255898\pi\) | ||||
0.693883 | + | 0.720088i | \(0.255898\pi\) | |||||||
\(68\) | 0.0684367 | 0.00829916 | ||||||||
\(69\) | −24.4173 | −2.93950 | ||||||||
\(70\) | 4.54079 | 0.542729 | ||||||||
\(71\) | −13.1580 | −1.56156 | −0.780782 | − | 0.624803i | \(-0.785179\pi\) | ||||
−0.780782 | + | 0.624803i | \(0.785179\pi\) | |||||||
\(72\) | −7.91304 | −0.932560 | ||||||||
\(73\) | −5.34443 | −0.625519 | −0.312759 | − | 0.949832i | \(-0.601253\pi\) | ||||
−0.312759 | + | 0.949832i | \(0.601253\pi\) | |||||||
\(74\) | −8.71254 | −1.01281 | ||||||||
\(75\) | −4.80922 | −0.555320 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.4586 | −1.18420 | ||||||||
\(79\) | 3.95165 | 0.444595 | 0.222298 | − | 0.974979i | \(-0.428644\pi\) | ||||
0.222298 | + | 0.974979i | \(0.428644\pi\) | |||||||
\(80\) | 1.88260 | 0.210482 | ||||||||
\(81\) | 29.8770 | 3.31967 | ||||||||
\(82\) | 2.36137 | 0.260769 | ||||||||
\(83\) | 5.25612 | 0.576934 | 0.288467 | − | 0.957490i | \(-0.406854\pi\) | ||||
0.288467 | + | 0.957490i | \(0.406854\pi\) | |||||||
\(84\) | −7.96793 | −0.869372 | ||||||||
\(85\) | 0.128839 | 0.0139746 | ||||||||
\(86\) | −1.76442 | −0.190262 | ||||||||
\(87\) | 23.5089 | 2.52041 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.41191 | 0.679661 | 0.339831 | − | 0.940487i | \(-0.389630\pi\) | ||||
0.339831 | + | 0.940487i | \(0.389630\pi\) | |||||||
\(90\) | −14.8971 | −1.57029 | ||||||||
\(91\) | −7.63611 | −0.800482 | ||||||||
\(92\) | −7.39138 | −0.770605 | ||||||||
\(93\) | −18.3008 | −1.89770 | ||||||||
\(94\) | −9.11437 | −0.940075 | ||||||||
\(95\) | 1.88260 | 0.193151 | ||||||||
\(96\) | −3.30349 | −0.337161 | ||||||||
\(97\) | −2.67951 | −0.272063 | −0.136032 | − | 0.990704i | \(-0.543435\pi\) | ||||
−0.136032 | + | 0.990704i | \(0.543435\pi\) | |||||||
\(98\) | 1.18238 | 0.119439 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.45580 | −0.145580 | ||||||||
\(101\) | 11.8482 | 1.17894 | 0.589471 | − | 0.807789i | \(-0.299336\pi\) | ||||
0.589471 | + | 0.807789i | \(0.299336\pi\) | |||||||
\(102\) | −0.226080 | −0.0223852 | ||||||||
\(103\) | −11.8327 | −1.16591 | −0.582957 | − | 0.812503i | \(-0.698104\pi\) | ||||
−0.582957 | + | 0.812503i | \(0.698104\pi\) | |||||||
\(104\) | −3.16592 | −0.310444 | ||||||||
\(105\) | −15.0005 | −1.46389 | ||||||||
\(106\) | −8.63343 | −0.838553 | ||||||||
\(107\) | −8.26216 | −0.798733 | −0.399367 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399367 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(108\) | 16.2302 | 1.56175 | ||||||||
\(109\) | −4.92876 | −0.472090 | −0.236045 | − | 0.971742i | \(-0.575851\pi\) | ||||
−0.236045 | + | 0.971742i | \(0.575851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.7818 | 2.73184 | ||||||||
\(112\) | −2.41197 | −0.227910 | ||||||||
\(113\) | −19.1454 | −1.80105 | −0.900524 | − | 0.434807i | \(-0.856817\pi\) | ||||
−0.900524 | + | 0.434807i | \(0.856817\pi\) | |||||||
\(114\) | −3.30349 | −0.309400 | ||||||||
\(115\) | −13.9151 | −1.29759 | ||||||||
\(116\) | 7.11637 | 0.660738 | ||||||||
\(117\) | 25.0520 | 2.31606 | ||||||||
\(118\) | −5.32542 | −0.490245 | ||||||||
\(119\) | −0.165067 | −0.0151317 | ||||||||
\(120\) | −6.21916 | −0.567729 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −14.3424 | −1.29850 | ||||||||
\(123\) | −7.80074 | −0.703369 | ||||||||
\(124\) | −5.53983 | −0.497491 | ||||||||
\(125\) | −12.1537 | −1.08706 | ||||||||
\(126\) | 19.0860 | 1.70032 | ||||||||
\(127\) | 1.25227 | 0.111121 | 0.0555606 | − | 0.998455i | \(-0.482305\pi\) | ||||
0.0555606 | + | 0.998455i | \(0.482305\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.82874 | 0.513192 | ||||||||
\(130\) | −5.96017 | −0.522742 | ||||||||
\(131\) | −13.7739 | −1.20343 | −0.601714 | − | 0.798711i | \(-0.705515\pi\) | ||||
−0.601714 | + | 0.798711i | \(0.705515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.41197 | −0.209145 | ||||||||
\(134\) | −11.3594 | −0.981299 | ||||||||
\(135\) | 30.5550 | 2.62975 | ||||||||
\(136\) | −0.0684367 | −0.00586839 | ||||||||
\(137\) | 1.83597 | 0.156858 | 0.0784289 | − | 0.996920i | \(-0.475010\pi\) | ||||
0.0784289 | + | 0.996920i | \(0.475010\pi\) | |||||||
\(138\) | 24.4173 | 2.07854 | ||||||||
\(139\) | 15.9172 | 1.35008 | 0.675039 | − | 0.737782i | \(-0.264127\pi\) | ||||
0.675039 | + | 0.737782i | \(0.264127\pi\) | |||||||
\(140\) | −4.54079 | −0.383767 | ||||||||
\(141\) | 30.1092 | 2.53565 | ||||||||
\(142\) | 13.1580 | 1.10419 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.91304 | 0.659420 | ||||||||
\(145\) | 13.3973 | 1.11259 | ||||||||
\(146\) | 5.34443 | 0.442308 | ||||||||
\(147\) | −3.90598 | −0.322160 | ||||||||
\(148\) | 8.71254 | 0.716166 | ||||||||
\(149\) | 3.08074 | 0.252384 | 0.126192 | − | 0.992006i | \(-0.459724\pi\) | ||||
0.126192 | + | 0.992006i | \(0.459724\pi\) | |||||||
\(150\) | 4.80922 | 0.392671 | ||||||||
\(151\) | −17.4026 | −1.41620 | −0.708101 | − | 0.706112i | \(-0.750448\pi\) | ||||
−0.708101 | + | 0.706112i | \(0.750448\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0.541542 | 0.0437811 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.4293 | −0.837702 | ||||||||
\(156\) | 10.4586 | 0.837356 | ||||||||
\(157\) | 8.92808 | 0.712538 | 0.356269 | − | 0.934383i | \(-0.384049\pi\) | ||||
0.356269 | + | 0.934383i | \(0.384049\pi\) | |||||||
\(158\) | −3.95165 | −0.314376 | ||||||||
\(159\) | 28.5205 | 2.26182 | ||||||||
\(160\) | −1.88260 | −0.148833 | ||||||||
\(161\) | 17.8278 | 1.40503 | ||||||||
\(162\) | −29.8770 | −2.34736 | ||||||||
\(163\) | −3.61306 | −0.282997 | −0.141498 | − | 0.989938i | \(-0.545192\pi\) | ||||
−0.141498 | + | 0.989938i | \(0.545192\pi\) | |||||||
\(164\) | −2.36137 | −0.184392 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.25612 | −0.407954 | ||||||||
\(167\) | 24.7026 | 1.91154 | 0.955771 | − | 0.294112i | \(-0.0950238\pi\) | ||||
0.955771 | + | 0.294112i | \(0.0950238\pi\) | |||||||
\(168\) | 7.96793 | 0.614739 | ||||||||
\(169\) | −2.97696 | −0.228997 | ||||||||
\(170\) | −0.128839 | −0.00988151 | ||||||||
\(171\) | 7.91304 | 0.605125 | ||||||||
\(172\) | 1.76442 | 0.134536 | ||||||||
\(173\) | −14.2517 | −1.08354 | −0.541770 | − | 0.840527i | \(-0.682246\pi\) | ||||
−0.541770 | + | 0.840527i | \(0.682246\pi\) | |||||||
\(174\) | −23.5089 | −1.78220 | ||||||||
\(175\) | 3.51135 | 0.265433 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.5925 | 1.32233 | ||||||||
\(178\) | −6.41191 | −0.480593 | ||||||||
\(179\) | −12.3954 | −0.926475 | −0.463237 | − | 0.886234i | \(-0.653312\pi\) | ||||
−0.463237 | + | 0.886234i | \(0.653312\pi\) | |||||||
\(180\) | 14.8971 | 1.11037 | ||||||||
\(181\) | 9.78871 | 0.727589 | 0.363795 | − | 0.931479i | \(-0.381481\pi\) | ||||
0.363795 | + | 0.931479i | \(0.381481\pi\) | |||||||
\(182\) | 7.63611 | 0.566026 | ||||||||
\(183\) | 47.3800 | 3.50243 | ||||||||
\(184\) | 7.39138 | 0.544900 | ||||||||
\(185\) | 16.4023 | 1.20592 | ||||||||
\(186\) | 18.3008 | 1.34188 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.11437 | 0.664734 | ||||||||
\(189\) | −39.1467 | −2.84751 | ||||||||
\(190\) | −1.88260 | −0.136579 | ||||||||
\(191\) | 4.26597 | 0.308674 | 0.154337 | − | 0.988018i | \(-0.450676\pi\) | ||||
0.154337 | + | 0.988018i | \(0.450676\pi\) | |||||||
\(192\) | 3.30349 | 0.238409 | ||||||||
\(193\) | 10.3339 | 0.743854 | 0.371927 | − | 0.928262i | \(-0.378697\pi\) | ||||
0.371927 | + | 0.928262i | \(0.378697\pi\) | |||||||
\(194\) | 2.67951 | 0.192378 | ||||||||
\(195\) | 19.6894 | 1.40998 | ||||||||
\(196\) | −1.18238 | −0.0844558 | ||||||||
\(197\) | −12.8943 | −0.918683 | −0.459342 | − | 0.888260i | \(-0.651915\pi\) | ||||
−0.459342 | + | 0.888260i | \(0.651915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1491 | 0.932117 | 0.466059 | − | 0.884754i | \(-0.345674\pi\) | ||||
0.466059 | + | 0.884754i | \(0.345674\pi\) | |||||||
\(200\) | 1.45580 | 0.102941 | ||||||||
\(201\) | 37.5255 | 2.64684 | ||||||||
\(202\) | −11.8482 | −0.833638 | ||||||||
\(203\) | −17.1645 | −1.20471 | ||||||||
\(204\) | 0.226080 | 0.0158287 | ||||||||
\(205\) | −4.44552 | −0.310488 | ||||||||
\(206\) | 11.8327 | 0.824426 | ||||||||
\(207\) | −58.4883 | −4.06522 | ||||||||
\(208\) | 3.16592 | 0.219517 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 15.0005 | 1.03513 | ||||||||
\(211\) | −26.5013 | −1.82442 | −0.912212 | − | 0.409719i | \(-0.865627\pi\) | ||||
−0.912212 | + | 0.409719i | \(0.865627\pi\) | |||||||
\(212\) | 8.63343 | 0.592947 | ||||||||
\(213\) | −43.4672 | −2.97833 | ||||||||
\(214\) | 8.26216 | 0.564790 | ||||||||
\(215\) | 3.32171 | 0.226539 | ||||||||
\(216\) | −16.2302 | −1.10432 | ||||||||
\(217\) | 13.3619 | 0.907066 | ||||||||
\(218\) | 4.92876 | 0.333818 | ||||||||
\(219\) | −17.6553 | −1.19303 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.216665 | 0.0145745 | ||||||||
\(222\) | −28.7818 | −1.93171 | ||||||||
\(223\) | −29.7656 | −1.99325 | −0.996625 | − | 0.0820854i | \(-0.973842\pi\) | ||||
−0.996625 | + | 0.0820854i | \(0.973842\pi\) | |||||||
\(224\) | 2.41197 | 0.161157 | ||||||||
\(225\) | −11.5198 | −0.767986 | ||||||||
\(226\) | 19.1454 | 1.27353 | ||||||||
\(227\) | −24.0754 | −1.59794 | −0.798969 | − | 0.601372i | \(-0.794621\pi\) | ||||
−0.798969 | + | 0.601372i | \(0.794621\pi\) | |||||||
\(228\) | 3.30349 | 0.218779 | ||||||||
\(229\) | 7.85068 | 0.518787 | 0.259394 | − | 0.965772i | \(-0.416477\pi\) | ||||
0.259394 | + | 0.965772i | \(0.416477\pi\) | |||||||
\(230\) | 13.9151 | 0.917531 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.11637 | −0.467213 | ||||||||
\(233\) | 22.1903 | 1.45374 | 0.726869 | − | 0.686776i | \(-0.240975\pi\) | ||||
0.726869 | + | 0.686776i | \(0.240975\pi\) | |||||||
\(234\) | −25.0520 | −1.63770 | ||||||||
\(235\) | 17.1588 | 1.11931 | ||||||||
\(236\) | 5.32542 | 0.346655 | ||||||||
\(237\) | 13.0542 | 0.847963 | ||||||||
\(238\) | 0.165067 | 0.0106997 | ||||||||
\(239\) | 2.33473 | 0.151021 | 0.0755107 | − | 0.997145i | \(-0.475941\pi\) | ||||
0.0755107 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(240\) | 6.21916 | 0.401445 | ||||||||
\(241\) | −28.6284 | −1.84412 | −0.922060 | − | 0.387046i | \(-0.873495\pi\) | ||||
−0.922060 | + | 0.387046i | \(0.873495\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 50.0080 | 3.20801 | ||||||||
\(244\) | 14.3424 | 0.918179 | ||||||||
\(245\) | −2.22596 | −0.142211 | ||||||||
\(246\) | 7.80074 | 0.497357 | ||||||||
\(247\) | 3.16592 | 0.201443 | ||||||||
\(248\) | 5.53983 | 0.351779 | ||||||||
\(249\) | 17.3635 | 1.10037 | ||||||||
\(250\) | 12.1537 | 0.768669 | ||||||||
\(251\) | 5.69434 | 0.359424 | 0.179712 | − | 0.983719i | \(-0.442483\pi\) | ||||
0.179712 | + | 0.983719i | \(0.442483\pi\) | |||||||
\(252\) | −19.0860 | −1.20231 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.25227 | −0.0785746 | ||||||||
\(255\) | 0.425619 | 0.0266533 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.4196 | −0.899473 | −0.449737 | − | 0.893161i | \(-0.648482\pi\) | ||||
−0.449737 | + | 0.893161i | \(0.648482\pi\) | |||||||
\(258\) | −5.82874 | −0.362882 | ||||||||
\(259\) | −21.0144 | −1.30577 | ||||||||
\(260\) | 5.96017 | 0.369634 | ||||||||
\(261\) | 56.3121 | 3.48563 | ||||||||
\(262\) | 13.7739 | 0.850953 | ||||||||
\(263\) | 6.25442 | 0.385664 | 0.192832 | − | 0.981232i | \(-0.438233\pi\) | ||||
0.192832 | + | 0.981232i | \(0.438233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2533 | 0.998435 | ||||||||
\(266\) | 2.41197 | 0.147888 | ||||||||
\(267\) | 21.1817 | 1.29630 | ||||||||
\(268\) | 11.3594 | 0.693883 | ||||||||
\(269\) | 16.9603 | 1.03409 | 0.517043 | − | 0.855960i | \(-0.327033\pi\) | ||||
0.517043 | + | 0.855960i | \(0.327033\pi\) | |||||||
\(270\) | −30.5550 | −1.85952 | ||||||||
\(271\) | −10.9294 | −0.663912 | −0.331956 | − | 0.943295i | \(-0.607709\pi\) | ||||
−0.331956 | + | 0.943295i | \(0.607709\pi\) | |||||||
\(272\) | 0.0684367 | 0.00414958 | ||||||||
\(273\) | −25.2258 | −1.52674 | ||||||||
\(274\) | −1.83597 | −0.110915 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −24.4173 | −1.46975 | ||||||||
\(277\) | −17.4179 | −1.04654 | −0.523271 | − | 0.852166i | \(-0.675289\pi\) | ||||
−0.523271 | + | 0.852166i | \(0.675289\pi\) | |||||||
\(278\) | −15.9172 | −0.954649 | ||||||||
\(279\) | −43.8368 | −2.62444 | ||||||||
\(280\) | 4.54079 | 0.271364 | ||||||||
\(281\) | −11.8423 | −0.706451 | −0.353225 | − | 0.935538i | \(-0.614915\pi\) | ||||
−0.353225 | + | 0.935538i | \(0.614915\pi\) | |||||||
\(282\) | −30.1092 | −1.79298 | ||||||||
\(283\) | −3.87917 | −0.230593 | −0.115296 | − | 0.993331i | \(-0.536782\pi\) | ||||
−0.115296 | + | 0.993331i | \(0.536782\pi\) | |||||||
\(284\) | −13.1580 | −0.780782 | ||||||||
\(285\) | 6.21916 | 0.368391 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.69555 | 0.336198 | ||||||||
\(288\) | −7.91304 | −0.466280 | ||||||||
\(289\) | −16.9953 | −0.999724 | ||||||||
\(290\) | −13.3973 | −0.786717 | ||||||||
\(291\) | −8.85174 | −0.518898 | ||||||||
\(292\) | −5.34443 | −0.312759 | ||||||||
\(293\) | 0.882661 | 0.0515656 | 0.0257828 | − | 0.999668i | \(-0.491792\pi\) | ||||
0.0257828 | + | 0.999668i | \(0.491792\pi\) | |||||||
\(294\) | 3.90598 | 0.227802 | ||||||||
\(295\) | 10.0257 | 0.583717 | ||||||||
\(296\) | −8.71254 | −0.506406 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.08074 | −0.178462 | ||||||||
\(299\) | −23.4005 | −1.35329 | ||||||||
\(300\) | −4.80922 | −0.277660 | ||||||||
\(301\) | −4.25574 | −0.245297 | ||||||||
\(302\) | 17.4026 | 1.00141 | ||||||||
\(303\) | 39.1405 | 2.24856 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 27.0011 | 1.54608 | ||||||||
\(306\) | −0.541542 | −0.0309579 | ||||||||
\(307\) | −21.8100 | −1.24476 | −0.622380 | − | 0.782715i | \(-0.713834\pi\) | ||||
−0.622380 | + | 0.782715i | \(0.713834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.0893 | −2.22371 | ||||||||
\(310\) | 10.4293 | 0.592345 | ||||||||
\(311\) | 7.08973 | 0.402022 | 0.201011 | − | 0.979589i | \(-0.435577\pi\) | ||||
0.201011 | + | 0.979589i | \(0.435577\pi\) | |||||||
\(312\) | −10.4586 | −0.592100 | ||||||||
\(313\) | 7.51385 | 0.424708 | 0.212354 | − | 0.977193i | \(-0.431887\pi\) | ||||
0.212354 | + | 0.977193i | \(0.431887\pi\) | |||||||
\(314\) | −8.92808 | −0.503841 | ||||||||
\(315\) | −35.9315 | −2.02451 | ||||||||
\(316\) | 3.95165 | 0.222298 | ||||||||
\(317\) | 15.4744 | 0.869131 | 0.434566 | − | 0.900640i | \(-0.356902\pi\) | ||||
0.434566 | + | 0.900640i | \(0.356902\pi\) | |||||||
\(318\) | −28.5205 | −1.59935 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.88260 | 0.105241 | ||||||||
\(321\) | −27.2940 | −1.52340 | ||||||||
\(322\) | −17.8278 | −0.993506 | ||||||||
\(323\) | 0.0684367 | 0.00380792 | ||||||||
\(324\) | 29.8770 | 1.65984 | ||||||||
\(325\) | −4.60894 | −0.255658 | ||||||||
\(326\) | 3.61306 | 0.200109 | ||||||||
\(327\) | −16.2821 | −0.900402 | ||||||||
\(328\) | 2.36137 | 0.130385 | ||||||||
\(329\) | −21.9836 | −1.21200 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.4405 | 0.573864 | 0.286932 | − | 0.957951i | \(-0.407365\pi\) | ||||
0.286932 | + | 0.957951i | \(0.407365\pi\) | |||||||
\(332\) | 5.25612 | 0.288467 | ||||||||
\(333\) | 68.9426 | 3.77803 | ||||||||
\(334\) | −24.7026 | −1.35166 | ||||||||
\(335\) | 21.3852 | 1.16840 | ||||||||
\(336\) | −7.96793 | −0.434686 | ||||||||
\(337\) | 26.5055 | 1.44385 | 0.721924 | − | 0.691972i | \(-0.243258\pi\) | ||||
0.721924 | + | 0.691972i | \(0.243258\pi\) | |||||||
\(338\) | 2.97696 | 0.161925 | ||||||||
\(339\) | −63.2466 | −3.43508 | ||||||||
\(340\) | 0.128839 | 0.00698729 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.91304 | −0.427888 | ||||||||
\(343\) | 19.7357 | 1.06563 | ||||||||
\(344\) | −1.76442 | −0.0951312 | ||||||||
\(345\) | −45.9682 | −2.47485 | ||||||||
\(346\) | 14.2517 | 0.766179 | ||||||||
\(347\) | −23.8096 | −1.27817 | −0.639084 | − | 0.769137i | \(-0.720686\pi\) | ||||
−0.639084 | + | 0.769137i | \(0.720686\pi\) | |||||||
\(348\) | 23.5089 | 1.26021 | ||||||||
\(349\) | 21.0247 | 1.12543 | 0.562714 | − | 0.826652i | \(-0.309757\pi\) | ||||
0.562714 | + | 0.826652i | \(0.309757\pi\) | |||||||
\(350\) | −3.51135 | −0.187690 | ||||||||
\(351\) | 51.3834 | 2.74264 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4736 | 0.983253 | 0.491626 | − | 0.870806i | \(-0.336403\pi\) | ||||
0.491626 | + | 0.870806i | \(0.336403\pi\) | |||||||
\(354\) | −17.5925 | −0.935029 | ||||||||
\(355\) | −24.7713 | −1.31472 | ||||||||
\(356\) | 6.41191 | 0.339831 | ||||||||
\(357\) | −0.545298 | −0.0288603 | ||||||||
\(358\) | 12.3954 | 0.655117 | ||||||||
\(359\) | −34.8001 | −1.83668 | −0.918341 | − | 0.395791i | \(-0.870471\pi\) | ||||
−0.918341 | + | 0.395791i | \(0.870471\pi\) | |||||||
\(360\) | −14.8971 | −0.785147 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.78871 | −0.514483 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.63611 | −0.400241 | ||||||||
\(365\) | −10.0615 | −0.526641 | ||||||||
\(366\) | −47.3800 | −2.47659 | ||||||||
\(367\) | −10.0520 | −0.524713 | −0.262356 | − | 0.964971i | \(-0.584500\pi\) | ||||
−0.262356 | + | 0.964971i | \(0.584500\pi\) | |||||||
\(368\) | −7.39138 | −0.385302 | ||||||||
\(369\) | −18.6856 | −0.972732 | ||||||||
\(370\) | −16.4023 | −0.852713 | ||||||||
\(371\) | −20.8236 | −1.08111 | ||||||||
\(372\) | −18.3008 | −0.948850 | ||||||||
\(373\) | 20.6591 | 1.06969 | 0.534843 | − | 0.844951i | \(-0.320371\pi\) | ||||
0.534843 | + | 0.844951i | \(0.320371\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −40.1497 | −2.07332 | ||||||||
\(376\) | −9.11437 | −0.470038 | ||||||||
\(377\) | 22.5299 | 1.16035 | ||||||||
\(378\) | 39.1467 | 2.01349 | ||||||||
\(379\) | 11.5387 | 0.592704 | 0.296352 | − | 0.955079i | \(-0.404230\pi\) | ||||
0.296352 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(380\) | 1.88260 | 0.0965756 | ||||||||
\(381\) | 4.13687 | 0.211938 | ||||||||
\(382\) | −4.26597 | −0.218266 | ||||||||
\(383\) | 5.30452 | 0.271048 | 0.135524 | − | 0.990774i | \(-0.456728\pi\) | ||||
0.135524 | + | 0.990774i | \(0.456728\pi\) | |||||||
\(384\) | −3.30349 | −0.168580 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.3339 | −0.525984 | ||||||||
\(387\) | 13.9619 | 0.709725 | ||||||||
\(388\) | −2.67951 | −0.136032 | ||||||||
\(389\) | −22.9500 | −1.16361 | −0.581805 | − | 0.813328i | \(-0.697653\pi\) | ||||
−0.581805 | + | 0.813328i | \(0.697653\pi\) | |||||||
\(390\) | −19.6894 | −0.997010 | ||||||||
\(391\) | −0.505842 | −0.0255815 | ||||||||
\(392\) | 1.18238 | 0.0597193 | ||||||||
\(393\) | −45.5018 | −2.29526 | ||||||||
\(394\) | 12.8943 | 0.649607 | ||||||||
\(395\) | 7.43939 | 0.374316 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.483759 | 0.0242792 | 0.0121396 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121396 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(398\) | −13.1491 | −0.659106 | ||||||||
\(399\) | −7.96793 | −0.398895 | ||||||||
\(400\) | −1.45580 | −0.0727900 | ||||||||
\(401\) | −36.1672 | −1.80610 | −0.903051 | − | 0.429532i | \(-0.858678\pi\) | ||||
−0.903051 | + | 0.429532i | \(0.858678\pi\) | |||||||
\(402\) | −37.5255 | −1.87160 | ||||||||
\(403\) | −17.5386 | −0.873662 | ||||||||
\(404\) | 11.8482 | 0.589471 | ||||||||
\(405\) | 56.2467 | 2.79492 | ||||||||
\(406\) | 17.1645 | 0.851860 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.226080 | −0.0111926 | ||||||||
\(409\) | −12.0788 | −0.597256 | −0.298628 | − | 0.954370i | \(-0.596529\pi\) | ||||
−0.298628 | + | 0.954370i | \(0.596529\pi\) | |||||||
\(410\) | 4.44552 | 0.219548 | ||||||||
\(411\) | 6.06512 | 0.299170 | ||||||||
\(412\) | −11.8327 | −0.582957 | ||||||||
\(413\) | −12.8448 | −0.632050 | ||||||||
\(414\) | 58.4883 | 2.87454 | ||||||||
\(415\) | 9.89520 | 0.485736 | ||||||||
\(416\) | −3.16592 | −0.155222 | ||||||||
\(417\) | 52.5822 | 2.57496 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4844 | −0.707611 | −0.353806 | − | 0.935319i | \(-0.615113\pi\) | ||||
−0.353806 | + | 0.935319i | \(0.615113\pi\) | |||||||
\(420\) | −15.0005 | −0.731947 | ||||||||
\(421\) | 8.74595 | 0.426252 | 0.213126 | − | 0.977025i | \(-0.431636\pi\) | ||||
0.213126 | + | 0.977025i | \(0.431636\pi\) | |||||||
\(422\) | 26.5013 | 1.29006 | ||||||||
\(423\) | 72.1223 | 3.50671 | ||||||||
\(424\) | −8.63343 | −0.419277 | ||||||||
\(425\) | −0.0996300 | −0.00483277 | ||||||||
\(426\) | 43.4672 | 2.10599 | ||||||||
\(427\) | −34.5935 | −1.67410 | ||||||||
\(428\) | −8.26216 | −0.399367 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.32171 | −0.160187 | ||||||||
\(431\) | −18.0983 | −0.871763 | −0.435881 | − | 0.900004i | \(-0.643563\pi\) | ||||
−0.435881 | + | 0.900004i | \(0.643563\pi\) | |||||||
\(432\) | 16.2302 | 0.780874 | ||||||||
\(433\) | 19.3031 | 0.927648 | 0.463824 | − | 0.885927i | \(-0.346477\pi\) | ||||
0.463824 | + | 0.885927i | \(0.346477\pi\) | |||||||
\(434\) | −13.3619 | −0.641392 | ||||||||
\(435\) | 44.2579 | 2.12200 | ||||||||
\(436\) | −4.92876 | −0.236045 | ||||||||
\(437\) | −7.39138 | −0.353578 | ||||||||
\(438\) | 17.6553 | 0.843602 | ||||||||
\(439\) | 0.543248 | 0.0259278 | 0.0129639 | − | 0.999916i | \(-0.495873\pi\) | ||||
0.0129639 | + | 0.999916i | \(0.495873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.35623 | −0.445535 | ||||||||
\(442\) | −0.216665 | −0.0103057 | ||||||||
\(443\) | −24.5763 | −1.16765 | −0.583827 | − | 0.811878i | \(-0.698445\pi\) | ||||
−0.583827 | + | 0.811878i | \(0.698445\pi\) | |||||||
\(444\) | 28.7818 | 1.36592 | ||||||||
\(445\) | 12.0711 | 0.572225 | ||||||||
\(446\) | 29.7656 | 1.40944 | ||||||||
\(447\) | 10.1772 | 0.481365 | ||||||||
\(448\) | −2.41197 | −0.113955 | ||||||||
\(449\) | 30.2173 | 1.42604 | 0.713022 | − | 0.701141i | \(-0.247326\pi\) | ||||
0.713022 | + | 0.701141i | \(0.247326\pi\) | |||||||
\(450\) | 11.5198 | 0.543048 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −19.1454 | −0.900524 | ||||||||
\(453\) | −57.4892 | −2.70108 | ||||||||
\(454\) | 24.0754 | 1.12991 | ||||||||
\(455\) | −14.3758 | −0.673947 | ||||||||
\(456\) | −3.30349 | −0.154700 | ||||||||
\(457\) | −34.7631 | −1.62615 | −0.813073 | − | 0.582161i | \(-0.802207\pi\) | ||||
−0.813073 | + | 0.582161i | \(0.802207\pi\) | |||||||
\(458\) | −7.85068 | −0.366838 | ||||||||
\(459\) | 1.11074 | 0.0518448 | ||||||||
\(460\) | −13.9151 | −0.648793 | ||||||||
\(461\) | −10.2206 | −0.476019 | −0.238010 | − | 0.971263i | \(-0.576495\pi\) | ||||
−0.238010 | + | 0.971263i | \(0.576495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.73645 | −0.266596 | −0.133298 | − | 0.991076i | \(-0.542557\pi\) | ||||
−0.133298 | + | 0.991076i | \(0.542557\pi\) | |||||||
\(464\) | 7.11637 | 0.330369 | ||||||||
\(465\) | −34.4531 | −1.59772 | ||||||||
\(466\) | −22.1903 | −1.02795 | ||||||||
\(467\) | −25.2965 | −1.17058 | −0.585292 | − | 0.810823i | \(-0.699020\pi\) | ||||
−0.585292 | + | 0.810823i | \(0.699020\pi\) | |||||||
\(468\) | 25.0520 | 1.15803 | ||||||||
\(469\) | −27.3985 | −1.26514 | ||||||||
\(470\) | −17.1588 | −0.791474 | ||||||||
\(471\) | 29.4938 | 1.35900 | ||||||||
\(472\) | −5.32542 | −0.245122 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −13.0542 | −0.599600 | ||||||||
\(475\) | −1.45580 | −0.0667966 | ||||||||
\(476\) | −0.165067 | −0.00756585 | ||||||||
\(477\) | 68.3167 | 3.12801 | ||||||||
\(478\) | −2.33473 | −0.106788 | ||||||||
\(479\) | 6.51483 | 0.297670 | 0.148835 | − | 0.988862i | \(-0.452448\pi\) | ||||
0.148835 | + | 0.988862i | \(0.452448\pi\) | |||||||
\(480\) | −6.21916 | −0.283865 | ||||||||
\(481\) | 27.5832 | 1.25769 | ||||||||
\(482\) | 28.6284 | 1.30399 | ||||||||
\(483\) | 58.8940 | 2.67977 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.04446 | −0.229057 | ||||||||
\(486\) | −50.0080 | −2.26841 | ||||||||
\(487\) | −26.5992 | −1.20532 | −0.602662 | − | 0.797997i | \(-0.705893\pi\) | ||||
−0.602662 | + | 0.797997i | \(0.705893\pi\) | |||||||
\(488\) | −14.3424 | −0.649251 | ||||||||
\(489\) | −11.9357 | −0.539751 | ||||||||
\(490\) | 2.22596 | 0.100559 | ||||||||
\(491\) | 16.5430 | 0.746576 | 0.373288 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373288 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(492\) | −7.80074 | −0.351685 | ||||||||
\(493\) | 0.487021 | 0.0219343 | ||||||||
\(494\) | −3.16592 | −0.142441 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.53983 | −0.248746 | ||||||||
\(497\) | 31.7367 | 1.42359 | ||||||||
\(498\) | −17.3635 | −0.778079 | ||||||||
\(499\) | 8.60654 | 0.385282 | 0.192641 | − | 0.981269i | \(-0.438295\pi\) | ||||
0.192641 | + | 0.981269i | \(0.438295\pi\) | |||||||
\(500\) | −12.1537 | −0.543531 | ||||||||
\(501\) | 81.6047 | 3.64583 | ||||||||
\(502\) | −5.69434 | −0.254151 | ||||||||
\(503\) | 10.3371 | 0.460906 | 0.230453 | − | 0.973083i | \(-0.425979\pi\) | ||||
0.230453 | + | 0.973083i | \(0.425979\pi\) | |||||||
\(504\) | 19.0860 | 0.850160 | ||||||||
\(505\) | 22.3055 | 0.992583 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.83434 | −0.436758 | ||||||||
\(508\) | 1.25227 | 0.0555606 | ||||||||
\(509\) | −35.1873 | −1.55965 | −0.779825 | − | 0.625997i | \(-0.784692\pi\) | ||||
−0.779825 | + | 0.625997i | \(0.784692\pi\) | |||||||
\(510\) | −0.425619 | −0.0188467 | ||||||||
\(511\) | 12.8906 | 0.570248 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.2302 | 0.716579 | ||||||||
\(514\) | 14.4196 | 0.636023 | ||||||||
\(515\) | −22.2764 | −0.981614 | ||||||||
\(516\) | 5.82874 | 0.256596 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 21.0144 | 0.923320 | ||||||||
\(519\) | −47.0805 | −2.06660 | ||||||||
\(520\) | −5.96017 | −0.261371 | ||||||||
\(521\) | 9.17004 | 0.401747 | 0.200873 | − | 0.979617i | \(-0.435622\pi\) | ||||
0.200873 | + | 0.979617i | \(0.435622\pi\) | |||||||
\(522\) | −56.3121 | −2.46471 | ||||||||
\(523\) | 40.4012 | 1.76662 | 0.883311 | − | 0.468788i | \(-0.155309\pi\) | ||||
0.883311 | + | 0.468788i | \(0.155309\pi\) | |||||||
\(524\) | −13.7739 | −0.601714 | ||||||||
\(525\) | 11.5997 | 0.506253 | ||||||||
\(526\) | −6.25442 | −0.272706 | ||||||||
\(527\) | −0.379127 | −0.0165150 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.6325 | 1.37533 | ||||||||
\(530\) | −16.2533 | −0.706000 | ||||||||
\(531\) | 42.1402 | 1.82873 | ||||||||
\(532\) | −2.41197 | −0.104572 | ||||||||
\(533\) | −7.47589 | −0.323817 | ||||||||
\(534\) | −21.1817 | −0.916620 | ||||||||
\(535\) | −15.5544 | −0.672475 | ||||||||
\(536\) | −11.3594 | −0.490649 | ||||||||
\(537\) | −40.9480 | −1.76704 | ||||||||
\(538\) | −16.9603 | −0.731209 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 30.5550 | 1.31488 | ||||||||
\(541\) | 22.9546 | 0.986895 | 0.493447 | − | 0.869776i | \(-0.335737\pi\) | ||||
0.493447 | + | 0.869776i | \(0.335737\pi\) | |||||||
\(542\) | 10.9294 | 0.469456 | ||||||||
\(543\) | 32.3369 | 1.38771 | ||||||||
\(544\) | −0.0684367 | −0.00293420 | ||||||||
\(545\) | −9.27891 | −0.397465 | ||||||||
\(546\) | 25.2258 | 1.07957 | ||||||||
\(547\) | 22.0926 | 0.944611 | 0.472306 | − | 0.881435i | \(-0.343422\pi\) | ||||
0.472306 | + | 0.881435i | \(0.343422\pi\) | |||||||
\(548\) | 1.83597 | 0.0784289 | ||||||||
\(549\) | 113.492 | 4.84373 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.11637 | 0.303168 | ||||||||
\(552\) | 24.4173 | 1.03927 | ||||||||
\(553\) | −9.53127 | −0.405311 | ||||||||
\(554\) | 17.4179 | 0.740017 | ||||||||
\(555\) | 54.1847 | 2.30001 | ||||||||
\(556\) | 15.9172 | 0.675039 | ||||||||
\(557\) | 1.14809 | 0.0486463 | 0.0243232 | − | 0.999704i | \(-0.492257\pi\) | ||||
0.0243232 | + | 0.999704i | \(0.492257\pi\) | |||||||
\(558\) | 43.8368 | 1.85576 | ||||||||
\(559\) | 5.58601 | 0.236263 | ||||||||
\(560\) | −4.54079 | −0.191884 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.8423 | 0.499536 | ||||||||
\(563\) | 40.9190 | 1.72453 | 0.862265 | − | 0.506458i | \(-0.169046\pi\) | ||||
0.862265 | + | 0.506458i | \(0.169046\pi\) | |||||||
\(564\) | 30.1092 | 1.26783 | ||||||||
\(565\) | −36.0432 | −1.51635 | ||||||||
\(566\) | 3.87917 | 0.163054 | ||||||||
\(567\) | −72.0626 | −3.02635 | ||||||||
\(568\) | 13.1580 | 0.552097 | ||||||||
\(569\) | −7.10111 | −0.297694 | −0.148847 | − | 0.988860i | \(-0.547556\pi\) | ||||
−0.148847 | + | 0.988860i | \(0.547556\pi\) | |||||||
\(570\) | −6.21916 | −0.260492 | ||||||||
\(571\) | −21.1001 | −0.883012 | −0.441506 | − | 0.897258i | \(-0.645556\pi\) | ||||
−0.441506 | + | 0.897258i | \(0.645556\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0926 | 0.588725 | ||||||||
\(574\) | −5.69555 | −0.237728 | ||||||||
\(575\) | 10.7604 | 0.448738 | ||||||||
\(576\) | 7.91304 | 0.329710 | ||||||||
\(577\) | −24.3512 | −1.01375 | −0.506877 | − | 0.862018i | \(-0.669200\pi\) | ||||
−0.506877 | + | 0.862018i | \(0.669200\pi\) | |||||||
\(578\) | 16.9953 | 0.706912 | ||||||||
\(579\) | 34.1381 | 1.41873 | ||||||||
\(580\) | 13.3973 | 0.556293 | ||||||||
\(581\) | −12.6776 | −0.525957 | ||||||||
\(582\) | 8.85174 | 0.366916 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 5.34443 | 0.221154 | ||||||||
\(585\) | 47.1631 | 1.94995 | ||||||||
\(586\) | −0.882661 | −0.0364624 | ||||||||
\(587\) | 10.9498 | 0.451946 | 0.225973 | − | 0.974134i | \(-0.427444\pi\) | ||||
0.225973 | + | 0.974134i | \(0.427444\pi\) | |||||||
\(588\) | −3.90598 | −0.161080 | ||||||||
\(589\) | −5.53983 | −0.228265 | ||||||||
\(590\) | −10.0257 | −0.412750 | ||||||||
\(591\) | −42.5963 | −1.75218 | ||||||||
\(592\) | 8.71254 | 0.358083 | ||||||||
\(593\) | −34.8544 | −1.43130 | −0.715649 | − | 0.698461i | \(-0.753869\pi\) | ||||
−0.715649 | + | 0.698461i | \(0.753869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.310757 | −0.0127398 | ||||||||
\(596\) | 3.08074 | 0.126192 | ||||||||
\(597\) | 43.4380 | 1.77780 | ||||||||
\(598\) | 23.4005 | 0.956918 | ||||||||
\(599\) | 12.0037 | 0.490460 | 0.245230 | − | 0.969465i | \(-0.421137\pi\) | ||||
0.245230 | + | 0.969465i | \(0.421137\pi\) | |||||||
\(600\) | 4.80922 | 0.196335 | ||||||||
\(601\) | 15.7288 | 0.641591 | 0.320795 | − | 0.947148i | \(-0.396050\pi\) | ||||
0.320795 | + | 0.947148i | \(0.396050\pi\) | |||||||
\(602\) | 4.25574 | 0.173451 | ||||||||
\(603\) | 89.8870 | 3.66048 | ||||||||
\(604\) | −17.4026 | −0.708101 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −39.1405 | −1.58997 | ||||||||
\(607\) | 25.9881 | 1.05482 | 0.527412 | − | 0.849610i | \(-0.323163\pi\) | ||||
0.527412 | + | 0.849610i | \(0.323163\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −56.7027 | −2.29771 | ||||||||
\(610\) | −27.0011 | −1.09324 | ||||||||
\(611\) | 28.8554 | 1.16736 | ||||||||
\(612\) | 0.541542 | 0.0218905 | ||||||||
\(613\) | −38.5286 | −1.55616 | −0.778078 | − | 0.628168i | \(-0.783805\pi\) | ||||
−0.778078 | + | 0.628168i | \(0.783805\pi\) | |||||||
\(614\) | 21.8100 | 0.880178 | ||||||||
\(615\) | −14.6857 | −0.592185 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.01409 | 0.0408255 | 0.0204128 | − | 0.999792i | \(-0.493502\pi\) | ||||
0.0204128 | + | 0.999792i | \(0.493502\pi\) | |||||||
\(618\) | 39.0893 | 1.57240 | ||||||||
\(619\) | 23.3860 | 0.939964 | 0.469982 | − | 0.882676i | \(-0.344260\pi\) | ||||
0.469982 | + | 0.882676i | \(0.344260\pi\) | |||||||
\(620\) | −10.4293 | −0.418851 | ||||||||
\(621\) | −119.963 | −4.81396 | ||||||||
\(622\) | −7.08973 | −0.284272 | ||||||||
\(623\) | −15.4654 | −0.619606 | ||||||||
\(624\) | 10.4586 | 0.418678 | ||||||||
\(625\) | −15.6017 | −0.624066 | ||||||||
\(626\) | −7.51385 | −0.300314 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.92808 | 0.356269 | ||||||||
\(629\) | 0.596257 | 0.0237743 | ||||||||
\(630\) | 35.9315 | 1.43154 | ||||||||
\(631\) | 11.2632 | 0.448382 | 0.224191 | − | 0.974545i | \(-0.428026\pi\) | ||||
0.224191 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(632\) | −3.95165 | −0.157188 | ||||||||
\(633\) | −87.5467 | −3.47967 | ||||||||
\(634\) | −15.4744 | −0.614569 | ||||||||
\(635\) | 2.35753 | 0.0935559 | ||||||||
\(636\) | 28.5205 | 1.13091 | ||||||||
\(637\) | −3.74333 | −0.148316 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −104.120 | −4.11891 | ||||||||
\(640\) | −1.88260 | −0.0744165 | ||||||||
\(641\) | −12.1252 | −0.478918 | −0.239459 | − | 0.970906i | \(-0.576970\pi\) | ||||
−0.239459 | + | 0.970906i | \(0.576970\pi\) | |||||||
\(642\) | 27.2940 | 1.07721 | ||||||||
\(643\) | 9.15192 | 0.360916 | 0.180458 | − | 0.983583i | \(-0.442242\pi\) | ||||
0.180458 | + | 0.983583i | \(0.442242\pi\) | |||||||
\(644\) | 17.8278 | 0.702515 | ||||||||
\(645\) | 10.9732 | 0.432070 | ||||||||
\(646\) | −0.0684367 | −0.00269260 | ||||||||
\(647\) | 24.1081 | 0.947788 | 0.473894 | − | 0.880582i | \(-0.342848\pi\) | ||||
0.473894 | + | 0.880582i | \(0.342848\pi\) | |||||||
\(648\) | −29.8770 | −1.17368 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.60894 | 0.180778 | ||||||||
\(651\) | 44.1409 | 1.73002 | ||||||||
\(652\) | −3.61306 | −0.141498 | ||||||||
\(653\) | −14.8121 | −0.579642 | −0.289821 | − | 0.957081i | \(-0.593596\pi\) | ||||
−0.289821 | + | 0.957081i | \(0.593596\pi\) | |||||||
\(654\) | 16.2821 | 0.636681 | ||||||||
\(655\) | −25.9308 | −1.01320 | ||||||||
\(656\) | −2.36137 | −0.0921958 | ||||||||
\(657\) | −42.2907 | −1.64992 | ||||||||
\(658\) | 21.9836 | 0.857011 | ||||||||
\(659\) | −21.6275 | −0.842489 | −0.421244 | − | 0.906947i | \(-0.638407\pi\) | ||||
−0.421244 | + | 0.906947i | \(0.638407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.88808 | 0.306811 | 0.153405 | − | 0.988163i | \(-0.450976\pi\) | ||||
0.153405 | + | 0.988163i | \(0.450976\pi\) | |||||||
\(662\) | −10.4405 | −0.405783 | ||||||||
\(663\) | 0.715750 | 0.0277974 | ||||||||
\(664\) | −5.25612 | −0.203977 | ||||||||
\(665\) | −4.54079 | −0.176084 | ||||||||
\(666\) | −68.9426 | −2.67147 | ||||||||
\(667\) | −52.5998 | −2.03667 | ||||||||
\(668\) | 24.7026 | 0.955771 | ||||||||
\(669\) | −98.3302 | −3.80167 | ||||||||
\(670\) | −21.3852 | −0.826181 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 7.96793 | 0.307370 | ||||||||
\(673\) | 29.4014 | 1.13334 | 0.566669 | − | 0.823945i | \(-0.308232\pi\) | ||||
0.566669 | + | 0.823945i | \(0.308232\pi\) | |||||||
\(674\) | −26.5055 | −1.02095 | ||||||||
\(675\) | −23.6279 | −0.909437 | ||||||||
\(676\) | −2.97696 | −0.114498 | ||||||||
\(677\) | 27.6599 | 1.06306 | 0.531528 | − | 0.847041i | \(-0.321618\pi\) | ||||
0.531528 | + | 0.847041i | \(0.321618\pi\) | |||||||
\(678\) | 63.2466 | 2.42897 | ||||||||
\(679\) | 6.46291 | 0.248024 | ||||||||
\(680\) | −0.128839 | −0.00494076 | ||||||||
\(681\) | −79.5327 | −3.04770 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0143 | −1.64589 | −0.822947 | − | 0.568117i | \(-0.807672\pi\) | ||||
−0.822947 | + | 0.568117i | \(0.807672\pi\) | |||||||
\(684\) | 7.91304 | 0.302563 | ||||||||
\(685\) | 3.45641 | 0.132063 | ||||||||
\(686\) | −19.7357 | −0.753512 | ||||||||
\(687\) | 25.9346 | 0.989468 | ||||||||
\(688\) | 1.76442 | 0.0672679 | ||||||||
\(689\) | 27.3328 | 1.04129 | ||||||||
\(690\) | 45.9682 | 1.74998 | ||||||||
\(691\) | −22.3751 | −0.851190 | −0.425595 | − | 0.904914i | \(-0.639935\pi\) | ||||
−0.425595 | + | 0.904914i | \(0.639935\pi\) | |||||||
\(692\) | −14.2517 | −0.541770 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.8096 | 0.903801 | ||||||||
\(695\) | 29.9658 | 1.13667 | ||||||||
\(696\) | −23.5089 | −0.891101 | ||||||||
\(697\) | −0.161604 | −0.00612119 | ||||||||
\(698\) | −21.0247 | −0.795798 | ||||||||
\(699\) | 73.3055 | 2.77267 | ||||||||
\(700\) | 3.51135 | 0.132717 | ||||||||
\(701\) | −16.8504 | −0.636430 | −0.318215 | − | 0.948019i | \(-0.603083\pi\) | ||||
−0.318215 | + | 0.948019i | \(0.603083\pi\) | |||||||
\(702\) | −51.3834 | −1.93934 | ||||||||
\(703\) | 8.71254 | 0.328600 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 56.6838 | 2.13483 | ||||||||
\(706\) | −18.4736 | −0.695265 | ||||||||
\(707\) | −28.5776 | −1.07477 | ||||||||
\(708\) | 17.5925 | 0.661165 | ||||||||
\(709\) | 1.44052 | 0.0541000 | 0.0270500 | − | 0.999634i | \(-0.491389\pi\) | ||||
0.0270500 | + | 0.999634i | \(0.491389\pi\) | |||||||
\(710\) | 24.7713 | 0.929649 | ||||||||
\(711\) | 31.2695 | 1.17270 | ||||||||
\(712\) | −6.41191 | −0.240296 | ||||||||
\(713\) | 40.9470 | 1.53348 | ||||||||
\(714\) | 0.545298 | 0.0204073 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.3954 | −0.463237 | ||||||||
\(717\) | 7.71277 | 0.288039 | ||||||||
\(718\) | 34.8001 | 1.29873 | ||||||||
\(719\) | −20.5362 | −0.765870 | −0.382935 | − | 0.923775i | \(-0.625087\pi\) | ||||
−0.382935 | + | 0.923775i | \(0.625087\pi\) | |||||||
\(720\) | 14.8971 | 0.555183 | ||||||||
\(721\) | 28.5403 | 1.06289 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −94.5738 | −3.51724 | ||||||||
\(724\) | 9.78871 | 0.363795 | ||||||||
\(725\) | −10.3600 | −0.384761 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6689 | 0.544041 | 0.272021 | − | 0.962291i | \(-0.412308\pi\) | ||||
0.272021 | + | 0.962291i | \(0.412308\pi\) | |||||||
\(728\) | 7.63611 | 0.283013 | ||||||||
\(729\) | 75.5697 | 2.79888 | ||||||||
\(730\) | 10.0615 | 0.372391 | ||||||||
\(731\) | 0.120751 | 0.00446614 | ||||||||
\(732\) | 47.3800 | 1.75122 | ||||||||
\(733\) | −49.7416 | −1.83725 | −0.918623 | − | 0.395135i | \(-0.870698\pi\) | ||||
−0.918623 | + | 0.395135i | \(0.870698\pi\) | |||||||
\(734\) | 10.0520 | 0.371028 | ||||||||
\(735\) | −7.35343 | −0.271235 | ||||||||
\(736\) | 7.39138 | 0.272450 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.6856 | 0.687825 | ||||||||
\(739\) | −42.1810 | −1.55165 | −0.775826 | − | 0.630947i | \(-0.782667\pi\) | ||||
−0.775826 | + | 0.630947i | \(0.782667\pi\) | |||||||
\(740\) | 16.4023 | 0.602959 | ||||||||
\(741\) | 10.4586 | 0.384205 | ||||||||
\(742\) | 20.8236 | 0.764459 | ||||||||
\(743\) | −4.83219 | −0.177276 | −0.0886380 | − | 0.996064i | \(-0.528251\pi\) | ||||
−0.0886380 | + | 0.996064i | \(0.528251\pi\) | |||||||
\(744\) | 18.3008 | 0.670938 | ||||||||
\(745\) | 5.79982 | 0.212489 | ||||||||
\(746\) | −20.6591 | −0.756383 | ||||||||
\(747\) | 41.5919 | 1.52177 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.9281 | 0.728158 | ||||||||
\(750\) | 40.1497 | 1.46606 | ||||||||
\(751\) | 28.9857 | 1.05770 | 0.528851 | − | 0.848714i | \(-0.322623\pi\) | ||||
0.528851 | + | 0.848714i | \(0.322623\pi\) | |||||||
\(752\) | 9.11437 | 0.332367 | ||||||||
\(753\) | 18.8112 | 0.685518 | ||||||||
\(754\) | −22.5299 | −0.820489 | ||||||||
\(755\) | −32.7622 | −1.19234 | ||||||||
\(756\) | −39.1467 | −1.42375 | ||||||||
\(757\) | 32.3975 | 1.17751 | 0.588753 | − | 0.808313i | \(-0.299619\pi\) | ||||
0.588753 | + | 0.808313i | \(0.299619\pi\) | |||||||
\(758\) | −11.5387 | −0.419105 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.88260 | −0.0682893 | ||||||||
\(761\) | −20.0438 | −0.726587 | −0.363293 | − | 0.931675i | \(-0.618348\pi\) | ||||
−0.363293 | + | 0.931675i | \(0.618348\pi\) | |||||||
\(762\) | −4.13687 | −0.149863 | ||||||||
\(763\) | 11.8880 | 0.430376 | ||||||||
\(764\) | 4.26597 | 0.154337 | ||||||||
\(765\) | 1.01951 | 0.0368604 | ||||||||
\(766\) | −5.30452 | −0.191660 | ||||||||
\(767\) | 16.8598 | 0.608774 | ||||||||
\(768\) | 3.30349 | 0.119204 | ||||||||
\(769\) | −25.6006 | −0.923182 | −0.461591 | − | 0.887093i | \(-0.652721\pi\) | ||||
−0.461591 | + | 0.887093i | \(0.652721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −47.6351 | −1.71554 | ||||||||
\(772\) | 10.3339 | 0.371927 | ||||||||
\(773\) | 33.8041 | 1.21585 | 0.607925 | − | 0.793995i | \(-0.292002\pi\) | ||||
0.607925 | + | 0.793995i | \(0.292002\pi\) | |||||||
\(774\) | −13.9619 | −0.501851 | ||||||||
\(775\) | 8.06487 | 0.289699 | ||||||||
\(776\) | 2.67951 | 0.0961889 | ||||||||
\(777\) | −69.4209 | −2.49046 | ||||||||
\(778\) | 22.9500 | 0.822796 | ||||||||
\(779\) | −2.36137 | −0.0846047 | ||||||||
\(780\) | 19.6894 | 0.704992 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.505842 | 0.0180889 | ||||||||
\(783\) | 115.500 | 4.12763 | ||||||||
\(784\) | −1.18238 | −0.0422279 | ||||||||
\(785\) | 16.8080 | 0.599905 | ||||||||
\(786\) | 45.5018 | 1.62300 | ||||||||
\(787\) | −18.3654 | −0.654656 | −0.327328 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327328 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(788\) | −12.8943 | −0.459342 | ||||||||
\(789\) | 20.6614 | 0.735566 | ||||||||
\(790\) | −7.43939 | −0.264682 | ||||||||
\(791\) | 46.1782 | 1.64191 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.4069 | 1.61245 | ||||||||
\(794\) | −0.483759 | −0.0171680 | ||||||||
\(795\) | 53.6927 | 1.90429 | ||||||||
\(796\) | 13.1491 | 0.466059 | ||||||||
\(797\) | −32.4974 | −1.15112 | −0.575559 | − | 0.817760i | \(-0.695215\pi\) | ||||
−0.575559 | + | 0.817760i | \(0.695215\pi\) | |||||||
\(798\) | 7.96793 | 0.282062 | ||||||||
\(799\) | 0.623757 | 0.0220669 | ||||||||
\(800\) | 1.45580 | 0.0514703 | ||||||||
\(801\) | 50.7377 | 1.79273 | ||||||||
\(802\) | 36.1672 | 1.27711 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 37.5255 | 1.32342 | ||||||||
\(805\) | 33.5627 | 1.18293 | ||||||||
\(806\) | 17.5386 | 0.617772 | ||||||||
\(807\) | 56.0280 | 1.97228 | ||||||||
\(808\) | −11.8482 | −0.416819 | ||||||||
\(809\) | −36.7995 | −1.29380 | −0.646901 | − | 0.762574i | \(-0.723935\pi\) | ||||
−0.646901 | + | 0.762574i | \(0.723935\pi\) | |||||||
\(810\) | −56.2467 | −1.97631 | ||||||||
\(811\) | 27.2780 | 0.957862 | 0.478931 | − | 0.877853i | \(-0.341024\pi\) | ||||
0.478931 | + | 0.877853i | \(0.341024\pi\) | |||||||
\(812\) | −17.1645 | −0.602356 | ||||||||
\(813\) | −36.1050 | −1.26626 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.80196 | −0.238262 | ||||||||
\(816\) | 0.226080 | 0.00791437 | ||||||||
\(817\) | 1.76442 | 0.0617293 | ||||||||
\(818\) | 12.0788 | 0.422324 | ||||||||
\(819\) | −60.4249 | −2.11142 | ||||||||
\(820\) | −4.44552 | −0.155244 | ||||||||
\(821\) | −1.63228 | −0.0569669 | −0.0284835 | − | 0.999594i | \(-0.509068\pi\) | ||||
−0.0284835 | + | 0.999594i | \(0.509068\pi\) | |||||||
\(822\) | −6.06512 | −0.211545 | ||||||||
\(823\) | 53.4082 | 1.86169 | 0.930846 | − | 0.365412i | \(-0.119072\pi\) | ||||
0.930846 | + | 0.365412i | \(0.119072\pi\) | |||||||
\(824\) | 11.8327 | 0.412213 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.8448 | 0.446927 | ||||||||
\(827\) | −4.12284 | −0.143365 | −0.0716825 | − | 0.997427i | \(-0.522837\pi\) | ||||
−0.0716825 | + | 0.997427i | \(0.522837\pi\) | |||||||
\(828\) | −58.4883 | −2.03261 | ||||||||
\(829\) | 12.8328 | 0.445702 | 0.222851 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222851 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(830\) | −9.89520 | −0.343467 | ||||||||
\(831\) | −57.5400 | −1.99604 | ||||||||
\(832\) | 3.16592 | 0.109758 | ||||||||
\(833\) | −0.0809183 | −0.00280365 | ||||||||
\(834\) | −52.5822 | −1.82077 | ||||||||
\(835\) | 46.5052 | 1.60938 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −89.9123 | −3.10782 | ||||||||
\(838\) | 14.4844 | 0.500357 | ||||||||
\(839\) | −16.9755 | −0.586058 | −0.293029 | − | 0.956104i | \(-0.594663\pi\) | ||||
−0.293029 | + | 0.956104i | \(0.594663\pi\) | |||||||
\(840\) | 15.0005 | 0.517565 | ||||||||
\(841\) | 21.6427 | 0.746301 | ||||||||
\(842\) | −8.74595 | −0.301405 | ||||||||
\(843\) | −39.1208 | −1.34739 | ||||||||
\(844\) | −26.5013 | −0.912212 | ||||||||
\(845\) | −5.60443 | −0.192798 | ||||||||
\(846\) | −72.1223 | −2.47962 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.63343 | 0.296473 | ||||||||
\(849\) | −12.8148 | −0.439803 | ||||||||
\(850\) | 0.0996300 | 0.00341728 | ||||||||
\(851\) | −64.3977 | −2.20752 | ||||||||
\(852\) | −43.4672 | −1.48916 | ||||||||
\(853\) | 18.3348 | 0.627771 | 0.313886 | − | 0.949461i | \(-0.398369\pi\) | ||||
0.313886 | + | 0.949461i | \(0.398369\pi\) | |||||||
\(854\) | 34.5935 | 1.18377 | ||||||||
\(855\) | 14.8971 | 0.509471 | ||||||||
\(856\) | 8.26216 | 0.282395 | ||||||||
\(857\) | −9.14446 | −0.312369 | −0.156184 | − | 0.987728i | \(-0.549919\pi\) | ||||
−0.156184 | + | 0.987728i | \(0.549919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.1013 | 1.91415 | 0.957076 | − | 0.289836i | \(-0.0936007\pi\) | ||||
0.957076 | + | 0.289836i | \(0.0936007\pi\) | |||||||
\(860\) | 3.32171 | 0.113269 | ||||||||
\(861\) | 18.8152 | 0.641220 | ||||||||
\(862\) | 18.0983 | 0.616429 | ||||||||
\(863\) | 9.49783 | 0.323310 | 0.161655 | − | 0.986847i | \(-0.448317\pi\) | ||||
0.161655 | + | 0.986847i | \(0.448317\pi\) | |||||||
\(864\) | −16.2302 | −0.552161 | ||||||||
\(865\) | −26.8304 | −0.912261 | ||||||||
\(866\) | −19.3031 | −0.655946 | ||||||||
\(867\) | −56.1438 | −1.90674 | ||||||||
\(868\) | 13.3619 | 0.453533 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −44.2579 | −1.50048 | ||||||||
\(871\) | 35.9628 | 1.21855 | ||||||||
\(872\) | 4.92876 | 0.166909 | ||||||||
\(873\) | −21.2031 | −0.717616 | ||||||||
\(874\) | 7.39138 | 0.250017 | ||||||||
\(875\) | 29.3145 | 0.991009 | ||||||||
\(876\) | −17.6553 | −0.596516 | ||||||||
\(877\) | 49.0925 | 1.65773 | 0.828867 | − | 0.559445i | \(-0.188986\pi\) | ||||
0.828867 | + | 0.559445i | \(0.188986\pi\) | |||||||
\(878\) | −0.543248 | −0.0183337 | ||||||||
\(879\) | 2.91586 | 0.0983495 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.3645 | −1.25884 | −0.629422 | − | 0.777064i | \(-0.716708\pi\) | ||||
−0.629422 | + | 0.777064i | \(0.716708\pi\) | |||||||
\(882\) | 9.35623 | 0.315041 | ||||||||
\(883\) | 22.6572 | 0.762476 | 0.381238 | − | 0.924477i | \(-0.375498\pi\) | ||||
0.381238 | + | 0.924477i | \(0.375498\pi\) | |||||||
\(884\) | 0.216665 | 0.00728723 | ||||||||
\(885\) | 33.1197 | 1.11330 | ||||||||
\(886\) | 24.5763 | 0.825656 | ||||||||
\(887\) | 31.0484 | 1.04250 | 0.521251 | − | 0.853403i | \(-0.325465\pi\) | ||||
0.521251 | + | 0.853403i | \(0.325465\pi\) | |||||||
\(888\) | −28.7818 | −0.965853 | ||||||||
\(889\) | −3.02045 | −0.101303 | ||||||||
\(890\) | −12.0711 | −0.404624 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.7656 | −0.996625 | ||||||||
\(893\) | 9.11437 | 0.305001 | ||||||||
\(894\) | −10.1772 | −0.340376 | ||||||||
\(895\) | −23.3356 | −0.780024 | ||||||||
\(896\) | 2.41197 | 0.0805784 | ||||||||
\(897\) | −77.3034 | −2.58108 | ||||||||
\(898\) | −30.2173 | −1.00837 | ||||||||
\(899\) | −39.4235 | −1.31485 | ||||||||
\(900\) | −11.5198 | −0.383993 | ||||||||
\(901\) | 0.590843 | 0.0196838 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.0588 | −0.467847 | ||||||||
\(904\) | 19.1454 | 0.636767 | ||||||||
\(905\) | 18.4283 | 0.612577 | ||||||||
\(906\) | 57.4892 | 1.90995 | ||||||||
\(907\) | −11.8840 | −0.394603 | −0.197301 | − | 0.980343i | \(-0.563218\pi\) | ||||
−0.197301 | + | 0.980343i | \(0.563218\pi\) | |||||||
\(908\) | −24.0754 | −0.798969 | ||||||||
\(909\) | 93.7554 | 3.10967 | ||||||||
\(910\) | 14.3758 | 0.476553 | ||||||||
\(911\) | −33.5828 | −1.11265 | −0.556324 | − | 0.830966i | \(-0.687788\pi\) | ||||
−0.556324 | + | 0.830966i | \(0.687788\pi\) | |||||||
\(912\) | 3.30349 | 0.109389 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.7631 | 1.14986 | ||||||||
\(915\) | 89.1979 | 2.94879 | ||||||||
\(916\) | 7.85068 | 0.259394 | ||||||||
\(917\) | 33.2222 | 1.09709 | ||||||||
\(918\) | −1.11074 | −0.0366598 | ||||||||
\(919\) | 3.27575 | 0.108057 | 0.0540285 | − | 0.998539i | \(-0.482794\pi\) | ||||
0.0540285 | + | 0.998539i | \(0.482794\pi\) | |||||||
\(920\) | 13.9151 | 0.458766 | ||||||||
\(921\) | −72.0489 | −2.37409 | ||||||||
\(922\) | 10.2206 | 0.336597 | ||||||||
\(923\) | −41.6571 | −1.37116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.6837 | −0.417038 | ||||||||
\(926\) | 5.73645 | 0.188512 | ||||||||
\(927\) | −93.6329 | −3.07531 | ||||||||
\(928\) | −7.11637 | −0.233606 | ||||||||
\(929\) | −0.192133 | −0.00630369 | −0.00315185 | − | 0.999995i | \(-0.501003\pi\) | ||||
−0.00315185 | + | 0.999995i | \(0.501003\pi\) | |||||||
\(930\) | 34.4531 | 1.12976 | ||||||||
\(931\) | −1.18238 | −0.0387510 | ||||||||
\(932\) | 22.1903 | 0.726869 | ||||||||
\(933\) | 23.4208 | 0.766764 | ||||||||
\(934\) | 25.2965 | 0.827728 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25.0520 | −0.818851 | ||||||||
\(937\) | −8.33878 | −0.272416 | −0.136208 | − | 0.990680i | \(-0.543492\pi\) | ||||
−0.136208 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(938\) | 27.3985 | 0.894592 | ||||||||
\(939\) | 24.8219 | 0.810032 | ||||||||
\(940\) | 17.1588 | 0.559657 | ||||||||
\(941\) | −32.4537 | −1.05796 | −0.528980 | − | 0.848634i | \(-0.677425\pi\) | ||||
−0.528980 | + | 0.848634i | \(0.677425\pi\) | |||||||
\(942\) | −29.4938 | −0.960960 | ||||||||
\(943\) | 17.4538 | 0.568373 | ||||||||
\(944\) | 5.32542 | 0.173328 | ||||||||
\(945\) | −73.6978 | −2.39739 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.7033 | 1.29018 | 0.645092 | − | 0.764105i | \(-0.276819\pi\) | ||||
0.645092 | + | 0.764105i | \(0.276819\pi\) | |||||||
\(948\) | 13.0542 | 0.423982 | ||||||||
\(949\) | −16.9200 | −0.549248 | ||||||||
\(950\) | 1.45580 | 0.0472324 | ||||||||
\(951\) | 51.1196 | 1.65767 | ||||||||
\(952\) | 0.165067 | 0.00534987 | ||||||||
\(953\) | −28.2036 | −0.913604 | −0.456802 | − | 0.889568i | \(-0.651005\pi\) | ||||
−0.456802 | + | 0.889568i | \(0.651005\pi\) | |||||||
\(954\) | −68.3167 | −2.21183 | ||||||||
\(955\) | 8.03113 | 0.259881 | ||||||||
\(956\) | 2.33473 | 0.0755107 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.51483 | −0.210485 | ||||||||
\(959\) | −4.42832 | −0.142998 | ||||||||
\(960\) | 6.21916 | 0.200723 | ||||||||
\(961\) | −0.310330 | −0.0100106 | ||||||||
\(962\) | −27.5832 | −0.889318 | ||||||||
\(963\) | −65.3788 | −2.10680 | ||||||||
\(964\) | −28.6284 | −0.922060 | ||||||||
\(965\) | 19.4547 | 0.626270 | ||||||||
\(966\) | −58.8940 | −1.89488 | ||||||||
\(967\) | 50.9270 | 1.63770 | 0.818851 | − | 0.574006i | \(-0.194611\pi\) | ||||
0.818851 | + | 0.574006i | \(0.194611\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.226080 | 0.00726273 | ||||||||
\(970\) | 5.04446 | 0.161968 | ||||||||
\(971\) | −25.2762 | −0.811151 | −0.405576 | − | 0.914062i | \(-0.632929\pi\) | ||||
−0.405576 | + | 0.914062i | \(0.632929\pi\) | |||||||
\(972\) | 50.0080 | 1.60401 | ||||||||
\(973\) | −38.3918 | −1.23079 | ||||||||
\(974\) | 26.5992 | 0.852293 | ||||||||
\(975\) | −15.2256 | −0.487609 | ||||||||
\(976\) | 14.3424 | 0.459090 | ||||||||
\(977\) | −51.5477 | −1.64916 | −0.824579 | − | 0.565747i | \(-0.808588\pi\) | ||||
−0.824579 | + | 0.565747i | \(0.808588\pi\) | |||||||
\(978\) | 11.9357 | 0.381662 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.22596 | −0.0711056 | ||||||||
\(981\) | −39.0015 | −1.24522 | ||||||||
\(982\) | −16.5430 | −0.527909 | ||||||||
\(983\) | −8.63287 | −0.275346 | −0.137673 | − | 0.990478i | \(-0.543962\pi\) | ||||
−0.137673 | + | 0.990478i | \(0.543962\pi\) | |||||||
\(984\) | 7.80074 | 0.248679 | ||||||||
\(985\) | −24.2749 | −0.773464 | ||||||||
\(986\) | −0.487021 | −0.0155099 | ||||||||
\(987\) | −72.6226 | −2.31160 | ||||||||
\(988\) | 3.16592 | 0.100721 | ||||||||
\(989\) | −13.0415 | −0.414696 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8596 | −0.757925 | −0.378962 | − | 0.925412i | \(-0.623719\pi\) | ||||
−0.378962 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(992\) | 5.53983 | 0.175890 | ||||||||
\(993\) | 34.4902 | 1.09451 | ||||||||
\(994\) | −31.7367 | −1.00663 | ||||||||
\(995\) | 24.7546 | 0.784774 | ||||||||
\(996\) | 17.3635 | 0.550185 | ||||||||
\(997\) | 15.9135 | 0.503987 | 0.251993 | − | 0.967729i | \(-0.418914\pi\) | ||||
0.251993 | + | 0.967729i | \(0.418914\pi\) | |||||||
\(998\) | −8.60654 | −0.272435 | ||||||||
\(999\) | 141.406 | 4.47388 |
(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 | 4598.2.a.by.1.7 | ✓ | 8 | |
11.10 | odd | 2 | 4598.2.a.cb.1.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.by.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4598.2.a.cb.1.7 | yes | 8 | 11.10 | odd | 2 |