Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(1,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.1 |
$q$-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 | ||||||||
\(3\) | 2.73205 | 1.57735 | 0.788675 | − | 0.614810i | \(-0.210767\pi\) | ||||
0.788675 | + | 0.614810i | \(0.210767\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.73205 | −1.11536 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.73205 | 0.788675 | ||||||||
\(13\) | −1.46410 | −0.406069 | −0.203034 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203034 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.73205 | 0.705412 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | −4.46410 | −1.05220 | ||||||||
\(19\) | −2.73205 | −0.626775 | −0.313388 | − | 0.949625i | \(-0.601464\pi\) | ||||
−0.313388 | + | 0.949625i | \(0.601464\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.73205 | 0.596182 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.26795 | 0.264386 | 0.132193 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132193 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(24\) | −2.73205 | −0.557678 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.46410 | 0.287134 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.73205 | −0.878720 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(30\) | −2.73205 | −0.498802 | ||||||||
\(31\) | 8.92820 | 1.60355 | 0.801776 | − | 0.597624i | \(-0.203889\pi\) | ||||
0.801776 | + | 0.597624i | \(0.203889\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.73205 | 0.475589 | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | 3.26795 | 0.537248 | 0.268624 | − | 0.963245i | \(-0.413431\pi\) | ||||
0.268624 | + | 0.963245i | \(0.413431\pi\) | |||||||
\(38\) | 2.73205 | 0.443197 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.73205 | −0.739022 | −0.369511 | − | 0.929226i | \(-0.620475\pi\) | ||||
−0.369511 | + | 0.929226i | \(0.620475\pi\) | |||||||
\(42\) | −2.73205 | −0.421565 | ||||||||
\(43\) | −4.92820 | −0.751544 | −0.375772 | − | 0.926712i | \(-0.622622\pi\) | ||||
−0.375772 | + | 0.926712i | \(0.622622\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 4.46410 | 0.665469 | ||||||||
\(46\) | −1.26795 | −0.186949 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 2.73205 | 0.394338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 9.46410 | 1.32524 | ||||||||
\(52\) | −1.46410 | −0.203034 | ||||||||
\(53\) | −4.73205 | −0.649997 | −0.324999 | − | 0.945715i | \(-0.605364\pi\) | ||||
−0.324999 | + | 0.945715i | \(0.605364\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −7.46410 | −0.988644 | ||||||||
\(58\) | 4.73205 | 0.621349 | ||||||||
\(59\) | −13.8564 | −1.80395 | −0.901975 | − | 0.431788i | \(-0.857883\pi\) | ||||
−0.901975 | + | 0.431788i | \(0.857883\pi\) | |||||||
\(60\) | 2.73205 | 0.352706 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −8.92820 | −1.13388 | ||||||||
\(63\) | 4.46410 | 0.562424 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.46410 | −0.181599 | ||||||||
\(66\) | −2.73205 | −0.336292 | ||||||||
\(67\) | −10.9282 | −1.33509 | −0.667546 | − | 0.744568i | \(-0.732655\pi\) | ||||
−0.667546 | + | 0.744568i | \(0.732655\pi\) | |||||||
\(68\) | 3.46410 | 0.420084 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 9.46410 | 1.12318 | 0.561591 | − | 0.827415i | \(-0.310189\pi\) | ||||
0.561591 | + | 0.827415i | \(0.310189\pi\) | |||||||
\(72\) | −4.46410 | −0.526099 | ||||||||
\(73\) | 11.4641 | 1.34177 | 0.670886 | − | 0.741561i | \(-0.265914\pi\) | ||||
0.670886 | + | 0.741561i | \(0.265914\pi\) | |||||||
\(74\) | −3.26795 | −0.379891 | ||||||||
\(75\) | 2.73205 | 0.315470 | ||||||||
\(76\) | −2.73205 | −0.313388 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 6.73205 | 0.757415 | 0.378707 | − | 0.925516i | \(-0.376369\pi\) | ||||
0.378707 | + | 0.925516i | \(0.376369\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 4.73205 | 0.522568 | ||||||||
\(83\) | −4.39230 | −0.482118 | −0.241059 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241059 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(84\) | 2.73205 | 0.298091 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 4.92820 | 0.531422 | ||||||||
\(87\) | −12.9282 | −1.38605 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −15.4641 | −1.63919 | −0.819596 | − | 0.572942i | \(-0.805802\pi\) | ||||
−0.819596 | + | 0.572942i | \(0.805802\pi\) | |||||||
\(90\) | −4.46410 | −0.470558 | ||||||||
\(91\) | −1.46410 | −0.153480 | ||||||||
\(92\) | 1.26795 | 0.132193 | ||||||||
\(93\) | 24.3923 | 2.52936 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.73205 | −0.280302 | ||||||||
\(96\) | −2.73205 | −0.278839 | ||||||||
\(97\) | 5.80385 | 0.589291 | 0.294646 | − | 0.955607i | \(-0.404798\pi\) | ||||
0.294646 | + | 0.955607i | \(0.404798\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.46410 | 0.448659 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | −9.46410 | −0.937086 | ||||||||
\(103\) | 10.5359 | 1.03813 | 0.519066 | − | 0.854734i | \(-0.326280\pi\) | ||||
0.519066 | + | 0.854734i | \(0.326280\pi\) | |||||||
\(104\) | 1.46410 | 0.143567 | ||||||||
\(105\) | 2.73205 | 0.266621 | ||||||||
\(106\) | 4.73205 | 0.459617 | ||||||||
\(107\) | 0.928203 | 0.0897328 | 0.0448664 | − | 0.998993i | \(-0.485714\pi\) | ||||
0.0448664 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −1.80385 | −0.172777 | −0.0863886 | − | 0.996262i | \(-0.527533\pi\) | ||||
−0.0863886 | + | 0.996262i | \(0.527533\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 8.92820 | 0.847428 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 12.9282 | 1.21618 | 0.608092 | − | 0.793867i | \(-0.291935\pi\) | ||||
0.608092 | + | 0.793867i | \(0.291935\pi\) | |||||||
\(114\) | 7.46410 | 0.699077 | ||||||||
\(115\) | 1.26795 | 0.118237 | ||||||||
\(116\) | −4.73205 | −0.439360 | ||||||||
\(117\) | −6.53590 | −0.604244 | ||||||||
\(118\) | 13.8564 | 1.27559 | ||||||||
\(119\) | 3.46410 | 0.317554 | ||||||||
\(120\) | −2.73205 | −0.249401 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | −12.9282 | −1.16570 | ||||||||
\(124\) | 8.92820 | 0.801776 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.46410 | −0.397694 | ||||||||
\(127\) | 9.85641 | 0.874615 | 0.437307 | − | 0.899312i | \(-0.355932\pi\) | ||||
0.437307 | + | 0.899312i | \(0.355932\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −13.4641 | −1.18545 | ||||||||
\(130\) | 1.46410 | 0.128410 | ||||||||
\(131\) | −17.6603 | −1.54298 | −0.771492 | − | 0.636239i | \(-0.780489\pi\) | ||||
−0.771492 | + | 0.636239i | \(0.780489\pi\) | |||||||
\(132\) | 2.73205 | 0.237795 | ||||||||
\(133\) | −2.73205 | −0.236899 | ||||||||
\(134\) | 10.9282 | 0.944053 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | −3.46410 | −0.297044 | ||||||||
\(137\) | 7.85641 | 0.671218 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(138\) | −3.46410 | −0.294884 | ||||||||
\(139\) | 4.19615 | 0.355913 | 0.177957 | − | 0.984038i | \(-0.443051\pi\) | ||||
0.177957 | + | 0.984038i | \(0.443051\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.46410 | −0.794210 | ||||||||
\(143\) | −1.46410 | −0.122434 | ||||||||
\(144\) | 4.46410 | 0.372008 | ||||||||
\(145\) | −4.73205 | −0.392975 | ||||||||
\(146\) | −11.4641 | −0.948776 | ||||||||
\(147\) | 2.73205 | 0.225336 | ||||||||
\(148\) | 3.26795 | 0.268624 | ||||||||
\(149\) | −7.26795 | −0.595414 | −0.297707 | − | 0.954657i | \(-0.596222\pi\) | ||||
−0.297707 | + | 0.954657i | \(0.596222\pi\) | |||||||
\(150\) | −2.73205 | −0.223071 | ||||||||
\(151\) | −7.80385 | −0.635068 | −0.317534 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317534 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(152\) | 2.73205 | 0.221599 | ||||||||
\(153\) | 15.4641 | 1.25020 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 8.92820 | 0.717131 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | 6.39230 | 0.510161 | 0.255081 | − | 0.966920i | \(-0.417898\pi\) | ||||
0.255081 | + | 0.966920i | \(0.417898\pi\) | |||||||
\(158\) | −6.73205 | −0.535573 | ||||||||
\(159\) | −12.9282 | −1.02527 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.26795 | 0.0999284 | ||||||||
\(162\) | 2.46410 | 0.193598 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | −4.73205 | −0.369511 | ||||||||
\(165\) | 2.73205 | 0.212690 | ||||||||
\(166\) | 4.39230 | 0.340909 | ||||||||
\(167\) | −13.8564 | −1.07224 | −0.536120 | − | 0.844141i | \(-0.680111\pi\) | ||||
−0.536120 | + | 0.844141i | \(0.680111\pi\) | |||||||
\(168\) | −2.73205 | −0.210782 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | −3.46410 | −0.265684 | ||||||||
\(171\) | −12.1962 | −0.932663 | ||||||||
\(172\) | −4.92820 | −0.375772 | ||||||||
\(173\) | 0.928203 | 0.0705700 | 0.0352850 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352850 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(174\) | 12.9282 | 0.980085 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −37.8564 | −2.84546 | ||||||||
\(178\) | 15.4641 | 1.15908 | ||||||||
\(179\) | −19.8564 | −1.48414 | −0.742069 | − | 0.670324i | \(-0.766155\pi\) | ||||
−0.742069 | + | 0.670324i | \(0.766155\pi\) | |||||||
\(180\) | 4.46410 | 0.332734 | ||||||||
\(181\) | −11.8564 | −0.881280 | −0.440640 | − | 0.897684i | \(-0.645248\pi\) | ||||
−0.440640 | + | 0.897684i | \(0.645248\pi\) | |||||||
\(182\) | 1.46410 | 0.108526 | ||||||||
\(183\) | 5.46410 | 0.403918 | ||||||||
\(184\) | −1.26795 | −0.0934745 | ||||||||
\(185\) | 3.26795 | 0.240264 | ||||||||
\(186\) | −24.3923 | −1.78853 | ||||||||
\(187\) | 3.46410 | 0.253320 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | 2.73205 | 0.198204 | ||||||||
\(191\) | 6.92820 | 0.501307 | 0.250654 | − | 0.968077i | \(-0.419354\pi\) | ||||
0.250654 | + | 0.968077i | \(0.419354\pi\) | |||||||
\(192\) | 2.73205 | 0.197169 | ||||||||
\(193\) | −25.4641 | −1.83295 | −0.916473 | − | 0.400096i | \(-0.868977\pi\) | ||||
−0.916473 | + | 0.400096i | \(0.868977\pi\) | |||||||
\(194\) | −5.80385 | −0.416692 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −22.3923 | −1.59539 | −0.797693 | − | 0.603064i | \(-0.793946\pi\) | ||||
−0.797693 | + | 0.603064i | \(0.793946\pi\) | |||||||
\(198\) | −4.46410 | −0.317250 | ||||||||
\(199\) | −24.7846 | −1.75693 | −0.878467 | − | 0.477803i | \(-0.841433\pi\) | ||||
−0.878467 | + | 0.477803i | \(0.841433\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −29.8564 | −2.10591 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | −4.73205 | −0.332125 | ||||||||
\(204\) | 9.46410 | 0.662620 | ||||||||
\(205\) | −4.73205 | −0.330501 | ||||||||
\(206\) | −10.5359 | −0.734071 | ||||||||
\(207\) | 5.66025 | 0.393415 | ||||||||
\(208\) | −1.46410 | −0.101517 | ||||||||
\(209\) | −2.73205 | −0.188980 | ||||||||
\(210\) | −2.73205 | −0.188529 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −4.73205 | −0.324999 | ||||||||
\(213\) | 25.8564 | 1.77165 | ||||||||
\(214\) | −0.928203 | −0.0634507 | ||||||||
\(215\) | −4.92820 | −0.336101 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 8.92820 | 0.606086 | ||||||||
\(218\) | 1.80385 | 0.122172 | ||||||||
\(219\) | 31.3205 | 2.11644 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −5.07180 | −0.341166 | ||||||||
\(222\) | −8.92820 | −0.599222 | ||||||||
\(223\) | −8.39230 | −0.561990 | −0.280995 | − | 0.959709i | \(-0.590664\pi\) | ||||
−0.280995 | + | 0.959709i | \(0.590664\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | −12.9282 | −0.859971 | ||||||||
\(227\) | 13.8564 | 0.919682 | 0.459841 | − | 0.888001i | \(-0.347906\pi\) | ||||
0.459841 | + | 0.888001i | \(0.347906\pi\) | |||||||
\(228\) | −7.46410 | −0.494322 | ||||||||
\(229\) | −13.4641 | −0.889733 | −0.444866 | − | 0.895597i | \(-0.646749\pi\) | ||||
−0.444866 | + | 0.895597i | \(0.646749\pi\) | |||||||
\(230\) | −1.26795 | −0.0836061 | ||||||||
\(231\) | 2.73205 | 0.179756 | ||||||||
\(232\) | 4.73205 | 0.310674 | ||||||||
\(233\) | 7.85641 | 0.514690 | 0.257345 | − | 0.966320i | \(-0.417152\pi\) | ||||
0.257345 | + | 0.966320i | \(0.417152\pi\) | |||||||
\(234\) | 6.53590 | 0.427265 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.8564 | −0.901975 | ||||||||
\(237\) | 18.3923 | 1.19471 | ||||||||
\(238\) | −3.46410 | −0.224544 | ||||||||
\(239\) | −3.80385 | −0.246050 | −0.123025 | − | 0.992404i | \(-0.539260\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539260\pi\) | |||||||
\(240\) | 2.73205 | 0.176353 | ||||||||
\(241\) | −18.1962 | −1.17212 | −0.586059 | − | 0.810269i | \(-0.699321\pi\) | ||||
−0.586059 | + | 0.810269i | \(0.699321\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −18.7321 | −1.20166 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 12.9282 | 0.824272 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | −8.92820 | −0.566941 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 4.46410 | 0.281212 | ||||||||
\(253\) | 1.26795 | 0.0797153 | ||||||||
\(254\) | −9.85641 | −0.618446 | ||||||||
\(255\) | 9.46410 | 0.592665 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.9808 | 1.43350 | 0.716750 | − | 0.697330i | \(-0.245629\pi\) | ||||
0.716750 | + | 0.697330i | \(0.245629\pi\) | |||||||
\(258\) | 13.4641 | 0.838238 | ||||||||
\(259\) | 3.26795 | 0.203060 | ||||||||
\(260\) | −1.46410 | −0.0907997 | ||||||||
\(261\) | −21.1244 | −1.30756 | ||||||||
\(262\) | 17.6603 | 1.09105 | ||||||||
\(263\) | 18.9282 | 1.16716 | 0.583582 | − | 0.812055i | \(-0.301651\pi\) | ||||
0.583582 | + | 0.812055i | \(0.301651\pi\) | |||||||
\(264\) | −2.73205 | −0.168146 | ||||||||
\(265\) | −4.73205 | −0.290688 | ||||||||
\(266\) | 2.73205 | 0.167513 | ||||||||
\(267\) | −42.2487 | −2.58558 | ||||||||
\(268\) | −10.9282 | −0.667546 | ||||||||
\(269\) | 4.39230 | 0.267804 | 0.133902 | − | 0.990995i | \(-0.457249\pi\) | ||||
0.133902 | + | 0.990995i | \(0.457249\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | 24.3923 | 1.48173 | 0.740863 | − | 0.671656i | \(-0.234417\pi\) | ||||
0.740863 | + | 0.671656i | \(0.234417\pi\) | |||||||
\(272\) | 3.46410 | 0.210042 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | −7.85641 | −0.474623 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 3.46410 | 0.208514 | ||||||||
\(277\) | 27.8564 | 1.67373 | 0.836865 | − | 0.547410i | \(-0.184386\pi\) | ||||
0.836865 | + | 0.547410i | \(0.184386\pi\) | |||||||
\(278\) | −4.19615 | −0.251668 | ||||||||
\(279\) | 39.8564 | 2.38614 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −10.3923 | −0.619953 | −0.309976 | − | 0.950744i | \(-0.600321\pi\) | ||||
−0.309976 | + | 0.950744i | \(0.600321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9282 | −0.649614 | −0.324807 | − | 0.945780i | \(-0.605299\pi\) | ||||
−0.324807 | + | 0.945780i | \(0.605299\pi\) | |||||||
\(284\) | 9.46410 | 0.561591 | ||||||||
\(285\) | −7.46410 | −0.442135 | ||||||||
\(286\) | 1.46410 | 0.0865741 | ||||||||
\(287\) | −4.73205 | −0.279324 | ||||||||
\(288\) | −4.46410 | −0.263050 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 4.73205 | 0.277876 | ||||||||
\(291\) | 15.8564 | 0.929519 | ||||||||
\(292\) | 11.4641 | 0.670886 | ||||||||
\(293\) | −2.53590 | −0.148149 | −0.0740744 | − | 0.997253i | \(-0.523600\pi\) | ||||
−0.0740744 | + | 0.997253i | \(0.523600\pi\) | |||||||
\(294\) | −2.73205 | −0.159336 | ||||||||
\(295\) | −13.8564 | −0.806751 | ||||||||
\(296\) | −3.26795 | −0.189946 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 7.26795 | 0.421021 | ||||||||
\(299\) | −1.85641 | −0.107359 | ||||||||
\(300\) | 2.73205 | 0.157735 | ||||||||
\(301\) | −4.92820 | −0.284057 | ||||||||
\(302\) | 7.80385 | 0.449061 | ||||||||
\(303\) | −16.3923 | −0.941713 | ||||||||
\(304\) | −2.73205 | −0.156694 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | −15.4641 | −0.884024 | ||||||||
\(307\) | 31.3205 | 1.78756 | 0.893778 | − | 0.448510i | \(-0.148045\pi\) | ||||
0.893778 | + | 0.448510i | \(0.148045\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 28.7846 | 1.63750 | ||||||||
\(310\) | −8.92820 | −0.507088 | ||||||||
\(311\) | 7.85641 | 0.445496 | 0.222748 | − | 0.974876i | \(-0.428497\pi\) | ||||
0.222748 | + | 0.974876i | \(0.428497\pi\) | |||||||
\(312\) | 4.00000 | 0.226455 | ||||||||
\(313\) | 27.2679 | 1.54128 | 0.770638 | − | 0.637273i | \(-0.219938\pi\) | ||||
0.770638 | + | 0.637273i | \(0.219938\pi\) | |||||||
\(314\) | −6.39230 | −0.360739 | ||||||||
\(315\) | 4.46410 | 0.251524 | ||||||||
\(316\) | 6.73205 | 0.378707 | ||||||||
\(317\) | −32.4449 | −1.82229 | −0.911143 | − | 0.412091i | \(-0.864798\pi\) | ||||
−0.911143 | + | 0.412091i | \(0.864798\pi\) | |||||||
\(318\) | 12.9282 | 0.724978 | ||||||||
\(319\) | −4.73205 | −0.264944 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 2.53590 | 0.141540 | ||||||||
\(322\) | −1.26795 | −0.0706600 | ||||||||
\(323\) | −9.46410 | −0.526597 | ||||||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | −1.46410 | −0.0812137 | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | −4.92820 | −0.272530 | ||||||||
\(328\) | 4.73205 | 0.261284 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.73205 | −0.150394 | ||||||||
\(331\) | −4.92820 | −0.270879 | −0.135439 | − | 0.990786i | \(-0.543245\pi\) | ||||
−0.135439 | + | 0.990786i | \(0.543245\pi\) | |||||||
\(332\) | −4.39230 | −0.241059 | ||||||||
\(333\) | 14.5885 | 0.799443 | ||||||||
\(334\) | 13.8564 | 0.758189 | ||||||||
\(335\) | −10.9282 | −0.597072 | ||||||||
\(336\) | 2.73205 | 0.149046 | ||||||||
\(337\) | −30.7846 | −1.67694 | −0.838472 | − | 0.544944i | \(-0.816551\pi\) | ||||
−0.838472 | + | 0.544944i | \(0.816551\pi\) | |||||||
\(338\) | 10.8564 | 0.590511 | ||||||||
\(339\) | 35.3205 | 1.91835 | ||||||||
\(340\) | 3.46410 | 0.187867 | ||||||||
\(341\) | 8.92820 | 0.483489 | ||||||||
\(342\) | 12.1962 | 0.659492 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.92820 | 0.265711 | ||||||||
\(345\) | 3.46410 | 0.186501 | ||||||||
\(346\) | −0.928203 | −0.0499005 | ||||||||
\(347\) | 7.85641 | 0.421754 | 0.210877 | − | 0.977513i | \(-0.432368\pi\) | ||||
0.210877 | + | 0.977513i | \(0.432368\pi\) | |||||||
\(348\) | −12.9282 | −0.693024 | ||||||||
\(349\) | 30.3923 | 1.62686 | 0.813431 | − | 0.581661i | \(-0.197597\pi\) | ||||
0.813431 | + | 0.581661i | \(0.197597\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −5.85641 | −0.312592 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −32.4449 | −1.72687 | −0.863433 | − | 0.504464i | \(-0.831690\pi\) | ||||
−0.863433 | + | 0.504464i | \(0.831690\pi\) | |||||||
\(354\) | 37.8564 | 2.01205 | ||||||||
\(355\) | 9.46410 | 0.502302 | ||||||||
\(356\) | −15.4641 | −0.819596 | ||||||||
\(357\) | 9.46410 | 0.500893 | ||||||||
\(358\) | 19.8564 | 1.04944 | ||||||||
\(359\) | −1.26795 | −0.0669198 | −0.0334599 | − | 0.999440i | \(-0.510653\pi\) | ||||
−0.0334599 | + | 0.999440i | \(0.510653\pi\) | |||||||
\(360\) | −4.46410 | −0.235279 | ||||||||
\(361\) | −11.5359 | −0.607153 | ||||||||
\(362\) | 11.8564 | 0.623159 | ||||||||
\(363\) | 2.73205 | 0.143395 | ||||||||
\(364\) | −1.46410 | −0.0767398 | ||||||||
\(365\) | 11.4641 | 0.600059 | ||||||||
\(366\) | −5.46410 | −0.285613 | ||||||||
\(367\) | 29.4641 | 1.53801 | 0.769007 | − | 0.639241i | \(-0.220751\pi\) | ||||
0.769007 | + | 0.639241i | \(0.220751\pi\) | |||||||
\(368\) | 1.26795 | 0.0660964 | ||||||||
\(369\) | −21.1244 | −1.09969 | ||||||||
\(370\) | −3.26795 | −0.169893 | ||||||||
\(371\) | −4.73205 | −0.245676 | ||||||||
\(372\) | 24.3923 | 1.26468 | ||||||||
\(373\) | 30.3923 | 1.57365 | 0.786827 | − | 0.617174i | \(-0.211722\pi\) | ||||
0.786827 | + | 0.617174i | \(0.211722\pi\) | |||||||
\(374\) | −3.46410 | −0.179124 | ||||||||
\(375\) | 2.73205 | 0.141082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.92820 | 0.356821 | ||||||||
\(378\) | −4.00000 | −0.205738 | ||||||||
\(379\) | 23.7128 | 1.21805 | 0.609023 | − | 0.793153i | \(-0.291562\pi\) | ||||
0.609023 | + | 0.793153i | \(0.291562\pi\) | |||||||
\(380\) | −2.73205 | −0.140151 | ||||||||
\(381\) | 26.9282 | 1.37957 | ||||||||
\(382\) | −6.92820 | −0.354478 | ||||||||
\(383\) | 16.3923 | 0.837608 | 0.418804 | − | 0.908077i | \(-0.362449\pi\) | ||||
0.418804 | + | 0.908077i | \(0.362449\pi\) | |||||||
\(384\) | −2.73205 | −0.139419 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 25.4641 | 1.29609 | ||||||||
\(387\) | −22.0000 | −1.11832 | ||||||||
\(388\) | 5.80385 | 0.294646 | ||||||||
\(389\) | −24.2487 | −1.22946 | −0.614729 | − | 0.788738i | \(-0.710735\pi\) | ||||
−0.614729 | + | 0.788738i | \(0.710735\pi\) | |||||||
\(390\) | 4.00000 | 0.202548 | ||||||||
\(391\) | 4.39230 | 0.222128 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −48.2487 | −2.43383 | ||||||||
\(394\) | 22.3923 | 1.12811 | ||||||||
\(395\) | 6.73205 | 0.338726 | ||||||||
\(396\) | 4.46410 | 0.224330 | ||||||||
\(397\) | −38.3923 | −1.92685 | −0.963427 | − | 0.267970i | \(-0.913647\pi\) | ||||
−0.963427 | + | 0.267970i | \(0.913647\pi\) | |||||||
\(398\) | 24.7846 | 1.24234 | ||||||||
\(399\) | −7.46410 | −0.373672 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −25.1769 | −1.25728 | −0.628638 | − | 0.777698i | \(-0.716387\pi\) | ||||
−0.628638 | + | 0.777698i | \(0.716387\pi\) | |||||||
\(402\) | 29.8564 | 1.48910 | ||||||||
\(403\) | −13.0718 | −0.651153 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | −2.46410 | −0.122442 | ||||||||
\(406\) | 4.73205 | 0.234848 | ||||||||
\(407\) | 3.26795 | 0.161986 | ||||||||
\(408\) | −9.46410 | −0.468543 | ||||||||
\(409\) | 22.1962 | 1.09753 | 0.548765 | − | 0.835977i | \(-0.315098\pi\) | ||||
0.548765 | + | 0.835977i | \(0.315098\pi\) | |||||||
\(410\) | 4.73205 | 0.233699 | ||||||||
\(411\) | 21.4641 | 1.05875 | ||||||||
\(412\) | 10.5359 | 0.519066 | ||||||||
\(413\) | −13.8564 | −0.681829 | ||||||||
\(414\) | −5.66025 | −0.278186 | ||||||||
\(415\) | −4.39230 | −0.215610 | ||||||||
\(416\) | 1.46410 | 0.0717835 | ||||||||
\(417\) | 11.4641 | 0.561399 | ||||||||
\(418\) | 2.73205 | 0.133629 | ||||||||
\(419\) | 32.7846 | 1.60163 | 0.800816 | − | 0.598910i | \(-0.204399\pi\) | ||||
0.800816 | + | 0.598910i | \(0.204399\pi\) | |||||||
\(420\) | 2.73205 | 0.133310 | ||||||||
\(421\) | 10.7846 | 0.525610 | 0.262805 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262805 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.73205 | 0.229809 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | −25.8564 | −1.25275 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | 0.928203 | 0.0448664 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 4.92820 | 0.237659 | ||||||||
\(431\) | 18.3397 | 0.883394 | 0.441697 | − | 0.897164i | \(-0.354377\pi\) | ||||
0.441697 | + | 0.897164i | \(0.354377\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 0.732051 | 0.0351801 | 0.0175901 | − | 0.999845i | \(-0.494401\pi\) | ||||
0.0175901 | + | 0.999845i | \(0.494401\pi\) | |||||||
\(434\) | −8.92820 | −0.428567 | ||||||||
\(435\) | −12.9282 | −0.619860 | ||||||||
\(436\) | −1.80385 | −0.0863886 | ||||||||
\(437\) | −3.46410 | −0.165710 | ||||||||
\(438\) | −31.3205 | −1.49655 | ||||||||
\(439\) | 36.3923 | 1.73691 | 0.868455 | − | 0.495768i | \(-0.165113\pi\) | ||||
0.868455 | + | 0.495768i | \(0.165113\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 4.46410 | 0.212576 | ||||||||
\(442\) | 5.07180 | 0.241241 | ||||||||
\(443\) | 20.7846 | 0.987507 | 0.493753 | − | 0.869602i | \(-0.335625\pi\) | ||||
0.493753 | + | 0.869602i | \(0.335625\pi\) | |||||||
\(444\) | 8.92820 | 0.423714 | ||||||||
\(445\) | −15.4641 | −0.733069 | ||||||||
\(446\) | 8.39230 | 0.397387 | ||||||||
\(447\) | −19.8564 | −0.939176 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −35.3205 | −1.66688 | −0.833439 | − | 0.552612i | \(-0.813631\pi\) | ||||
−0.833439 | + | 0.552612i | \(0.813631\pi\) | |||||||
\(450\) | −4.46410 | −0.210440 | ||||||||
\(451\) | −4.73205 | −0.222824 | ||||||||
\(452\) | 12.9282 | 0.608092 | ||||||||
\(453\) | −21.3205 | −1.00172 | ||||||||
\(454\) | −13.8564 | −0.650313 | ||||||||
\(455\) | −1.46410 | −0.0686381 | ||||||||
\(456\) | 7.46410 | 0.349539 | ||||||||
\(457\) | −34.0000 | −1.59045 | −0.795226 | − | 0.606313i | \(-0.792648\pi\) | ||||
−0.795226 | + | 0.606313i | \(0.792648\pi\) | |||||||
\(458\) | 13.4641 | 0.629136 | ||||||||
\(459\) | 13.8564 | 0.646762 | ||||||||
\(460\) | 1.26795 | 0.0591184 | ||||||||
\(461\) | 29.3205 | 1.36559 | 0.682796 | − | 0.730609i | \(-0.260764\pi\) | ||||
0.682796 | + | 0.730609i | \(0.260764\pi\) | |||||||
\(462\) | −2.73205 | −0.127107 | ||||||||
\(463\) | 12.9808 | 0.603267 | 0.301634 | − | 0.953424i | \(-0.402468\pi\) | ||||
0.301634 | + | 0.953424i | \(0.402468\pi\) | |||||||
\(464\) | −4.73205 | −0.219680 | ||||||||
\(465\) | 24.3923 | 1.13117 | ||||||||
\(466\) | −7.85641 | −0.363941 | ||||||||
\(467\) | 17.6603 | 0.817219 | 0.408610 | − | 0.912709i | \(-0.366014\pi\) | ||||
0.408610 | + | 0.912709i | \(0.366014\pi\) | |||||||
\(468\) | −6.53590 | −0.302122 | ||||||||
\(469\) | −10.9282 | −0.504618 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.4641 | 0.804703 | ||||||||
\(472\) | 13.8564 | 0.637793 | ||||||||
\(473\) | −4.92820 | −0.226599 | ||||||||
\(474\) | −18.3923 | −0.844787 | ||||||||
\(475\) | −2.73205 | −0.125355 | ||||||||
\(476\) | 3.46410 | 0.158777 | ||||||||
\(477\) | −21.1244 | −0.967218 | ||||||||
\(478\) | 3.80385 | 0.173984 | ||||||||
\(479\) | 13.8564 | 0.633115 | 0.316558 | − | 0.948573i | \(-0.397473\pi\) | ||||
0.316558 | + | 0.948573i | \(0.397473\pi\) | |||||||
\(480\) | −2.73205 | −0.124700 | ||||||||
\(481\) | −4.78461 | −0.218159 | ||||||||
\(482\) | 18.1962 | 0.828812 | ||||||||
\(483\) | 3.46410 | 0.157622 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 5.80385 | 0.263539 | ||||||||
\(486\) | 18.7321 | 0.849703 | ||||||||
\(487\) | 4.87564 | 0.220937 | 0.110468 | − | 0.993880i | \(-0.464765\pi\) | ||||
0.110468 | + | 0.993880i | \(0.464765\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 21.8564 | 0.988381 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 42.9282 | 1.93732 | 0.968661 | − | 0.248385i | \(-0.0798999\pi\) | ||||
0.968661 | + | 0.248385i | \(0.0798999\pi\) | |||||||
\(492\) | −12.9282 | −0.582848 | ||||||||
\(493\) | −16.3923 | −0.738272 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 4.46410 | 0.200646 | ||||||||
\(496\) | 8.92820 | 0.400888 | ||||||||
\(497\) | 9.46410 | 0.424523 | ||||||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | 2.00000 | 0.0895323 | 0.0447661 | − | 0.998997i | \(-0.485746\pi\) | ||||
0.0447661 | + | 0.998997i | \(0.485746\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −37.8564 | −1.69130 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9282 | −0.843967 | −0.421983 | − | 0.906604i | \(-0.638666\pi\) | ||||
−0.421983 | + | 0.906604i | \(0.638666\pi\) | |||||||
\(504\) | −4.46410 | −0.198847 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −1.26795 | −0.0563672 | ||||||||
\(507\) | −29.6603 | −1.31726 | ||||||||
\(508\) | 9.85641 | 0.437307 | ||||||||
\(509\) | 2.78461 | 0.123426 | 0.0617128 | − | 0.998094i | \(-0.480344\pi\) | ||||
0.0617128 | + | 0.998094i | \(0.480344\pi\) | |||||||
\(510\) | −9.46410 | −0.419077 | ||||||||
\(511\) | 11.4641 | 0.507142 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.9282 | −0.482492 | ||||||||
\(514\) | −22.9808 | −1.01364 | ||||||||
\(515\) | 10.5359 | 0.464267 | ||||||||
\(516\) | −13.4641 | −0.592724 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.26795 | −0.143585 | ||||||||
\(519\) | 2.53590 | 0.111314 | ||||||||
\(520\) | 1.46410 | 0.0642051 | ||||||||
\(521\) | 10.3923 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(522\) | 21.1244 | 0.924588 | ||||||||
\(523\) | 19.3205 | 0.844827 | 0.422413 | − | 0.906403i | \(-0.361183\pi\) | ||||
0.422413 | + | 0.906403i | \(0.361183\pi\) | |||||||
\(524\) | −17.6603 | −0.771492 | ||||||||
\(525\) | 2.73205 | 0.119236 | ||||||||
\(526\) | −18.9282 | −0.825309 | ||||||||
\(527\) | 30.9282 | 1.34725 | ||||||||
\(528\) | 2.73205 | 0.118897 | ||||||||
\(529\) | −21.3923 | −0.930100 | ||||||||
\(530\) | 4.73205 | 0.205547 | ||||||||
\(531\) | −61.8564 | −2.68434 | ||||||||
\(532\) | −2.73205 | −0.118449 | ||||||||
\(533\) | 6.92820 | 0.300094 | ||||||||
\(534\) | 42.2487 | 1.82828 | ||||||||
\(535\) | 0.928203 | 0.0401297 | ||||||||
\(536\) | 10.9282 | 0.472026 | ||||||||
\(537\) | −54.2487 | −2.34100 | ||||||||
\(538\) | −4.39230 | −0.189366 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | 17.1244 | 0.736234 | 0.368117 | − | 0.929780i | \(-0.380003\pi\) | ||||
0.368117 | + | 0.929780i | \(0.380003\pi\) | |||||||
\(542\) | −24.3923 | −1.04774 | ||||||||
\(543\) | −32.3923 | −1.39009 | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | −1.80385 | −0.0772683 | ||||||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | 4.78461 | 0.204575 | 0.102288 | − | 0.994755i | \(-0.467384\pi\) | ||||
0.102288 | + | 0.994755i | \(0.467384\pi\) | |||||||
\(548\) | 7.85641 | 0.335609 | ||||||||
\(549\) | 8.92820 | 0.381046 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 12.9282 | 0.550760 | ||||||||
\(552\) | −3.46410 | −0.147442 | ||||||||
\(553\) | 6.73205 | 0.286276 | ||||||||
\(554\) | −27.8564 | −1.18351 | ||||||||
\(555\) | 8.92820 | 0.378981 | ||||||||
\(556\) | 4.19615 | 0.177957 | ||||||||
\(557\) | −12.2487 | −0.518995 | −0.259497 | − | 0.965744i | \(-0.583557\pi\) | ||||
−0.259497 | + | 0.965744i | \(0.583557\pi\) | |||||||
\(558\) | −39.8564 | −1.68726 | ||||||||
\(559\) | 7.21539 | 0.305178 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 9.46410 | 0.399575 | ||||||||
\(562\) | 10.3923 | 0.438373 | ||||||||
\(563\) | −20.7846 | −0.875967 | −0.437983 | − | 0.898983i | \(-0.644307\pi\) | ||||
−0.437983 | + | 0.898983i | \(0.644307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.9282 | 0.543894 | ||||||||
\(566\) | 10.9282 | 0.459347 | ||||||||
\(567\) | −2.46410 | −0.103483 | ||||||||
\(568\) | −9.46410 | −0.397105 | ||||||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 7.46410 | 0.312637 | ||||||||
\(571\) | −20.3923 | −0.853391 | −0.426696 | − | 0.904395i | \(-0.640322\pi\) | ||||
−0.426696 | + | 0.904395i | \(0.640322\pi\) | |||||||
\(572\) | −1.46410 | −0.0612172 | ||||||||
\(573\) | 18.9282 | 0.790737 | ||||||||
\(574\) | 4.73205 | 0.197512 | ||||||||
\(575\) | 1.26795 | 0.0528771 | ||||||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | 8.33975 | 0.347188 | 0.173594 | − | 0.984817i | \(-0.444462\pi\) | ||||
0.173594 | + | 0.984817i | \(0.444462\pi\) | |||||||
\(578\) | 5.00000 | 0.207973 | ||||||||
\(579\) | −69.5692 | −2.89120 | ||||||||
\(580\) | −4.73205 | −0.196488 | ||||||||
\(581\) | −4.39230 | −0.182224 | ||||||||
\(582\) | −15.8564 | −0.657269 | ||||||||
\(583\) | −4.73205 | −0.195982 | ||||||||
\(584\) | −11.4641 | −0.474388 | ||||||||
\(585\) | −6.53590 | −0.270226 | ||||||||
\(586\) | 2.53590 | 0.104757 | ||||||||
\(587\) | −28.9808 | −1.19616 | −0.598082 | − | 0.801435i | \(-0.704070\pi\) | ||||
−0.598082 | + | 0.801435i | \(0.704070\pi\) | |||||||
\(588\) | 2.73205 | 0.112668 | ||||||||
\(589\) | −24.3923 | −1.00507 | ||||||||
\(590\) | 13.8564 | 0.570459 | ||||||||
\(591\) | −61.1769 | −2.51648 | ||||||||
\(592\) | 3.26795 | 0.134312 | ||||||||
\(593\) | 32.5359 | 1.33609 | 0.668045 | − | 0.744121i | \(-0.267132\pi\) | ||||
0.668045 | + | 0.744121i | \(0.267132\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 3.46410 | 0.142014 | ||||||||
\(596\) | −7.26795 | −0.297707 | ||||||||
\(597\) | −67.7128 | −2.77130 | ||||||||
\(598\) | 1.85641 | 0.0759141 | ||||||||
\(599\) | −32.1051 | −1.31178 | −0.655890 | − | 0.754857i | \(-0.727706\pi\) | ||||
−0.655890 | + | 0.754857i | \(0.727706\pi\) | |||||||
\(600\) | −2.73205 | −0.111536 | ||||||||
\(601\) | 28.4449 | 1.16029 | 0.580145 | − | 0.814513i | \(-0.302996\pi\) | ||||
0.580145 | + | 0.814513i | \(0.302996\pi\) | |||||||
\(602\) | 4.92820 | 0.200859 | ||||||||
\(603\) | −48.7846 | −1.98666 | ||||||||
\(604\) | −7.80385 | −0.317534 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 16.3923 | 0.665892 | ||||||||
\(607\) | 34.7846 | 1.41186 | 0.705932 | − | 0.708280i | \(-0.250528\pi\) | ||||
0.705932 | + | 0.708280i | \(0.250528\pi\) | |||||||
\(608\) | 2.73205 | 0.110799 | ||||||||
\(609\) | −12.9282 | −0.523877 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.4641 | 0.625099 | ||||||||
\(613\) | 27.1769 | 1.09767 | 0.548833 | − | 0.835932i | \(-0.315072\pi\) | ||||
0.548833 | + | 0.835932i | \(0.315072\pi\) | |||||||
\(614\) | −31.3205 | −1.26399 | ||||||||
\(615\) | −12.9282 | −0.521315 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 8.53590 | 0.343642 | 0.171821 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171821 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(618\) | −28.7846 | −1.15789 | ||||||||
\(619\) | −10.9282 | −0.439242 | −0.219621 | − | 0.975585i | \(-0.570482\pi\) | ||||
−0.219621 | + | 0.975585i | \(0.570482\pi\) | |||||||
\(620\) | 8.92820 | 0.358565 | ||||||||
\(621\) | 5.07180 | 0.203524 | ||||||||
\(622\) | −7.85641 | −0.315013 | ||||||||
\(623\) | −15.4641 | −0.619556 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −27.2679 | −1.08985 | ||||||||
\(627\) | −7.46410 | −0.298088 | ||||||||
\(628\) | 6.39230 | 0.255081 | ||||||||
\(629\) | 11.3205 | 0.451378 | ||||||||
\(630\) | −4.46410 | −0.177854 | ||||||||
\(631\) | −12.7846 | −0.508947 | −0.254474 | − | 0.967080i | \(-0.581902\pi\) | ||||
−0.254474 | + | 0.967080i | \(0.581902\pi\) | |||||||
\(632\) | −6.73205 | −0.267787 | ||||||||
\(633\) | 21.8564 | 0.868714 | ||||||||
\(634\) | 32.4449 | 1.28855 | ||||||||
\(635\) | 9.85641 | 0.391140 | ||||||||
\(636\) | −12.9282 | −0.512637 | ||||||||
\(637\) | −1.46410 | −0.0580098 | ||||||||
\(638\) | 4.73205 | 0.187344 | ||||||||
\(639\) | 42.2487 | 1.67133 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 19.8564 | 0.784281 | 0.392140 | − | 0.919905i | \(-0.371735\pi\) | ||||
0.392140 | + | 0.919905i | \(0.371735\pi\) | |||||||
\(642\) | −2.53590 | −0.100084 | ||||||||
\(643\) | −14.7321 | −0.580975 | −0.290488 | − | 0.956879i | \(-0.593818\pi\) | ||||
−0.290488 | + | 0.956879i | \(0.593818\pi\) | |||||||
\(644\) | 1.26795 | 0.0499642 | ||||||||
\(645\) | −13.4641 | −0.530148 | ||||||||
\(646\) | 9.46410 | 0.372360 | ||||||||
\(647\) | 37.1769 | 1.46158 | 0.730788 | − | 0.682605i | \(-0.239153\pi\) | ||||
0.730788 | + | 0.682605i | \(0.239153\pi\) | |||||||
\(648\) | 2.46410 | 0.0967991 | ||||||||
\(649\) | −13.8564 | −0.543912 | ||||||||
\(650\) | 1.46410 | 0.0574268 | ||||||||
\(651\) | 24.3923 | 0.956010 | ||||||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | −9.80385 | −0.383654 | −0.191827 | − | 0.981429i | \(-0.561441\pi\) | ||||
−0.191827 | + | 0.981429i | \(0.561441\pi\) | |||||||
\(654\) | 4.92820 | 0.192708 | ||||||||
\(655\) | −17.6603 | −0.690043 | ||||||||
\(656\) | −4.73205 | −0.184756 | ||||||||
\(657\) | 51.1769 | 1.99660 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.24871 | 0.243415 | 0.121708 | − | 0.992566i | \(-0.461163\pi\) | ||||
0.121708 | + | 0.992566i | \(0.461163\pi\) | |||||||
\(660\) | 2.73205 | 0.106345 | ||||||||
\(661\) | 3.85641 | 0.149997 | 0.0749984 | − | 0.997184i | \(-0.476105\pi\) | ||||
0.0749984 | + | 0.997184i | \(0.476105\pi\) | |||||||
\(662\) | 4.92820 | 0.191540 | ||||||||
\(663\) | −13.8564 | −0.538138 | ||||||||
\(664\) | 4.39230 | 0.170454 | ||||||||
\(665\) | −2.73205 | −0.105944 | ||||||||
\(666\) | −14.5885 | −0.565291 | ||||||||
\(667\) | −6.00000 | −0.232321 | ||||||||
\(668\) | −13.8564 | −0.536120 | ||||||||
\(669\) | −22.9282 | −0.886456 | ||||||||
\(670\) | 10.9282 | 0.422193 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | −2.73205 | −0.105391 | ||||||||
\(673\) | −20.1436 | −0.776478 | −0.388239 | − | 0.921559i | \(-0.626917\pi\) | ||||
−0.388239 | + | 0.921559i | \(0.626917\pi\) | |||||||
\(674\) | 30.7846 | 1.18578 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | 19.8564 | 0.763144 | 0.381572 | − | 0.924339i | \(-0.375383\pi\) | ||||
0.381572 | + | 0.924339i | \(0.375383\pi\) | |||||||
\(678\) | −35.3205 | −1.35648 | ||||||||
\(679\) | 5.80385 | 0.222731 | ||||||||
\(680\) | −3.46410 | −0.132842 | ||||||||
\(681\) | 37.8564 | 1.45066 | ||||||||
\(682\) | −8.92820 | −0.341879 | ||||||||
\(683\) | 42.2487 | 1.61660 | 0.808301 | − | 0.588769i | \(-0.200387\pi\) | ||||
0.808301 | + | 0.588769i | \(0.200387\pi\) | |||||||
\(684\) | −12.1962 | −0.466332 | ||||||||
\(685\) | 7.85641 | 0.300178 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −36.7846 | −1.40342 | ||||||||
\(688\) | −4.92820 | −0.187886 | ||||||||
\(689\) | 6.92820 | 0.263944 | ||||||||
\(690\) | −3.46410 | −0.131876 | ||||||||
\(691\) | 31.3205 | 1.19149 | 0.595744 | − | 0.803174i | \(-0.296857\pi\) | ||||
0.595744 | + | 0.803174i | \(0.296857\pi\) | |||||||
\(692\) | 0.928203 | 0.0352850 | ||||||||
\(693\) | 4.46410 | 0.169577 | ||||||||
\(694\) | −7.85641 | −0.298225 | ||||||||
\(695\) | 4.19615 | 0.159169 | ||||||||
\(696\) | 12.9282 | 0.490042 | ||||||||
\(697\) | −16.3923 | −0.620903 | ||||||||
\(698\) | −30.3923 | −1.15037 | ||||||||
\(699\) | 21.4641 | 0.811847 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 14.1962 | 0.536181 | 0.268091 | − | 0.963394i | \(-0.413607\pi\) | ||||
0.268091 | + | 0.963394i | \(0.413607\pi\) | |||||||
\(702\) | 5.85641 | 0.221036 | ||||||||
\(703\) | −8.92820 | −0.336734 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.4449 | 1.22108 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | −37.8564 | −1.42273 | ||||||||
\(709\) | −2.39230 | −0.0898449 | −0.0449224 | − | 0.998990i | \(-0.514304\pi\) | ||||
−0.0449224 | + | 0.998990i | \(0.514304\pi\) | |||||||
\(710\) | −9.46410 | −0.355181 | ||||||||
\(711\) | 30.0526 | 1.12706 | ||||||||
\(712\) | 15.4641 | 0.579542 | ||||||||
\(713\) | 11.3205 | 0.423956 | ||||||||
\(714\) | −9.46410 | −0.354185 | ||||||||
\(715\) | −1.46410 | −0.0547543 | ||||||||
\(716\) | −19.8564 | −0.742069 | ||||||||
\(717\) | −10.3923 | −0.388108 | ||||||||
\(718\) | 1.26795 | 0.0473194 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 4.46410 | 0.166367 | ||||||||
\(721\) | 10.5359 | 0.392377 | ||||||||
\(722\) | 11.5359 | 0.429322 | ||||||||
\(723\) | −49.7128 | −1.84884 | ||||||||
\(724\) | −11.8564 | −0.440640 | ||||||||
\(725\) | −4.73205 | −0.175744 | ||||||||
\(726\) | −2.73205 | −0.101396 | ||||||||
\(727\) | −38.6410 | −1.43312 | −0.716558 | − | 0.697528i | \(-0.754283\pi\) | ||||
−0.716558 | + | 0.697528i | \(0.754283\pi\) | |||||||
\(728\) | 1.46410 | 0.0542632 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | −11.4641 | −0.424305 | ||||||||
\(731\) | −17.0718 | −0.631423 | ||||||||
\(732\) | 5.46410 | 0.201959 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | −29.4641 | −1.08754 | ||||||||
\(735\) | 2.73205 | 0.100773 | ||||||||
\(736\) | −1.26795 | −0.0467372 | ||||||||
\(737\) | −10.9282 | −0.402546 | ||||||||
\(738\) | 21.1244 | 0.777598 | ||||||||
\(739\) | 18.1436 | 0.667423 | 0.333711 | − | 0.942675i | \(-0.391699\pi\) | ||||
0.333711 | + | 0.942675i | \(0.391699\pi\) | |||||||
\(740\) | 3.26795 | 0.120132 | ||||||||
\(741\) | 10.9282 | 0.401458 | ||||||||
\(742\) | 4.73205 | 0.173719 | ||||||||
\(743\) | 3.71281 | 0.136210 | 0.0681049 | − | 0.997678i | \(-0.478305\pi\) | ||||
0.0681049 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(744\) | −24.3923 | −0.894265 | ||||||||
\(745\) | −7.26795 | −0.266277 | ||||||||
\(746\) | −30.3923 | −1.11274 | ||||||||
\(747\) | −19.6077 | −0.717408 | ||||||||
\(748\) | 3.46410 | 0.126660 | ||||||||
\(749\) | 0.928203 | 0.0339158 | ||||||||
\(750\) | −2.73205 | −0.0997604 | ||||||||
\(751\) | 2.24871 | 0.0820566 | 0.0410283 | − | 0.999158i | \(-0.486937\pi\) | ||||
0.0410283 | + | 0.999158i | \(0.486937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.92820 | −0.252310 | ||||||||
\(755\) | −7.80385 | −0.284011 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | 23.3731 | 0.849509 | 0.424754 | − | 0.905309i | \(-0.360360\pi\) | ||||
0.424754 | + | 0.905309i | \(0.360360\pi\) | |||||||
\(758\) | −23.7128 | −0.861288 | ||||||||
\(759\) | 3.46410 | 0.125739 | ||||||||
\(760\) | 2.73205 | 0.0991019 | ||||||||
\(761\) | 19.2679 | 0.698463 | 0.349231 | − | 0.937037i | \(-0.386443\pi\) | ||||
0.349231 | + | 0.937037i | \(0.386443\pi\) | |||||||
\(762\) | −26.9282 | −0.975506 | ||||||||
\(763\) | −1.80385 | −0.0653037 | ||||||||
\(764\) | 6.92820 | 0.250654 | ||||||||
\(765\) | 15.4641 | 0.559106 | ||||||||
\(766\) | −16.3923 | −0.592278 | ||||||||
\(767\) | 20.2872 | 0.732528 | ||||||||
\(768\) | 2.73205 | 0.0985844 | ||||||||
\(769\) | −24.4449 | −0.881504 | −0.440752 | − | 0.897629i | \(-0.645288\pi\) | ||||
−0.440752 | + | 0.897629i | \(0.645288\pi\) | |||||||
\(770\) | −1.00000 | −0.0360375 | ||||||||
\(771\) | 62.7846 | 2.26113 | ||||||||
\(772\) | −25.4641 | −0.916473 | ||||||||
\(773\) | 30.0000 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(774\) | 22.0000 | 0.790774 | ||||||||
\(775\) | 8.92820 | 0.320711 | ||||||||
\(776\) | −5.80385 | −0.208346 | ||||||||
\(777\) | 8.92820 | 0.320298 | ||||||||
\(778\) | 24.2487 | 0.869358 | ||||||||
\(779\) | 12.9282 | 0.463201 | ||||||||
\(780\) | −4.00000 | −0.143223 | ||||||||
\(781\) | 9.46410 | 0.338652 | ||||||||
\(782\) | −4.39230 | −0.157069 | ||||||||
\(783\) | −18.9282 | −0.676439 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 6.39230 | 0.228151 | ||||||||
\(786\) | 48.2487 | 1.72097 | ||||||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | −22.3923 | −0.797693 | ||||||||
\(789\) | 51.7128 | 1.84102 | ||||||||
\(790\) | −6.73205 | −0.239516 | ||||||||
\(791\) | 12.9282 | 0.459674 | ||||||||
\(792\) | −4.46410 | −0.158625 | ||||||||
\(793\) | −2.92820 | −0.103984 | ||||||||
\(794\) | 38.3923 | 1.36249 | ||||||||
\(795\) | −12.9282 | −0.458516 | ||||||||
\(796\) | −24.7846 | −0.878467 | ||||||||
\(797\) | 6.67949 | 0.236600 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(798\) | 7.46410 | 0.264226 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −69.0333 | −2.43917 | ||||||||
\(802\) | 25.1769 | 0.889028 | ||||||||
\(803\) | 11.4641 | 0.404559 | ||||||||
\(804\) | −29.8564 | −1.05295 | ||||||||
\(805\) | 1.26795 | 0.0446893 | ||||||||
\(806\) | 13.0718 | 0.460434 | ||||||||
\(807\) | 12.0000 | 0.422420 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | 5.32051 | 0.187059 | 0.0935296 | − | 0.995617i | \(-0.470185\pi\) | ||||
0.0935296 | + | 0.995617i | \(0.470185\pi\) | |||||||
\(810\) | 2.46410 | 0.0865797 | ||||||||
\(811\) | −4.58846 | −0.161123 | −0.0805613 | − | 0.996750i | \(-0.525671\pi\) | ||||
−0.0805613 | + | 0.996750i | \(0.525671\pi\) | |||||||
\(812\) | −4.73205 | −0.166062 | ||||||||
\(813\) | 66.6410 | 2.33720 | ||||||||
\(814\) | −3.26795 | −0.114542 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | 9.46410 | 0.331310 | ||||||||
\(817\) | 13.4641 | 0.471049 | ||||||||
\(818\) | −22.1962 | −0.776070 | ||||||||
\(819\) | −6.53590 | −0.228383 | ||||||||
\(820\) | −4.73205 | −0.165250 | ||||||||
\(821\) | 52.0526 | 1.81665 | 0.908323 | − | 0.418269i | \(-0.137363\pi\) | ||||
0.908323 | + | 0.418269i | \(0.137363\pi\) | |||||||
\(822\) | −21.4641 | −0.748647 | ||||||||
\(823\) | −24.1962 | −0.843425 | −0.421712 | − | 0.906730i | \(-0.638571\pi\) | ||||
−0.421712 | + | 0.906730i | \(0.638571\pi\) | |||||||
\(824\) | −10.5359 | −0.367035 | ||||||||
\(825\) | 2.73205 | 0.0951178 | ||||||||
\(826\) | 13.8564 | 0.482126 | ||||||||
\(827\) | 53.5692 | 1.86278 | 0.931392 | − | 0.364017i | \(-0.118595\pi\) | ||||
0.931392 | + | 0.364017i | \(0.118595\pi\) | |||||||
\(828\) | 5.66025 | 0.196707 | ||||||||
\(829\) | 40.1051 | 1.39291 | 0.696454 | − | 0.717601i | \(-0.254760\pi\) | ||||
0.696454 | + | 0.717601i | \(0.254760\pi\) | |||||||
\(830\) | 4.39230 | 0.152459 | ||||||||
\(831\) | 76.1051 | 2.64006 | ||||||||
\(832\) | −1.46410 | −0.0507586 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | −11.4641 | −0.396969 | ||||||||
\(835\) | −13.8564 | −0.479521 | ||||||||
\(836\) | −2.73205 | −0.0944900 | ||||||||
\(837\) | 35.7128 | 1.23442 | ||||||||
\(838\) | −32.7846 | −1.13253 | ||||||||
\(839\) | −38.7846 | −1.33899 | −0.669497 | − | 0.742815i | \(-0.733490\pi\) | ||||
−0.669497 | + | 0.742815i | \(0.733490\pi\) | |||||||
\(840\) | −2.73205 | −0.0942647 | ||||||||
\(841\) | −6.60770 | −0.227852 | ||||||||
\(842\) | −10.7846 | −0.371662 | ||||||||
\(843\) | −28.3923 | −0.977883 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | −10.8564 | −0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −4.73205 | −0.162499 | ||||||||
\(849\) | −29.8564 | −1.02467 | ||||||||
\(850\) | −3.46410 | −0.118818 | ||||||||
\(851\) | 4.14359 | 0.142041 | ||||||||
\(852\) | 25.8564 | 0.885826 | ||||||||
\(853\) | 20.9282 | 0.716568 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | −12.1962 | −0.417100 | ||||||||
\(856\) | −0.928203 | −0.0317253 | ||||||||
\(857\) | −19.1769 | −0.655071 | −0.327535 | − | 0.944839i | \(-0.606218\pi\) | ||||
−0.327535 | + | 0.944839i | \(0.606218\pi\) | |||||||
\(858\) | 4.00000 | 0.136558 | ||||||||
\(859\) | 40.7846 | 1.39155 | 0.695776 | − | 0.718258i | \(-0.255060\pi\) | ||||
0.695776 | + | 0.718258i | \(0.255060\pi\) | |||||||
\(860\) | −4.92820 | −0.168050 | ||||||||
\(861\) | −12.9282 | −0.440592 | ||||||||
\(862\) | −18.3397 | −0.624654 | ||||||||
\(863\) | 24.5885 | 0.837001 | 0.418500 | − | 0.908217i | \(-0.362556\pi\) | ||||
0.418500 | + | 0.908217i | \(0.362556\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | 0.928203 | 0.0315599 | ||||||||
\(866\) | −0.732051 | −0.0248761 | ||||||||
\(867\) | −13.6603 | −0.463927 | ||||||||
\(868\) | 8.92820 | 0.303043 | ||||||||
\(869\) | 6.73205 | 0.228369 | ||||||||
\(870\) | 12.9282 | 0.438307 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | 1.80385 | 0.0610860 | ||||||||
\(873\) | 25.9090 | 0.876886 | ||||||||
\(874\) | 3.46410 | 0.117175 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 31.3205 | 1.05822 | ||||||||
\(877\) | −23.1769 | −0.782629 | −0.391314 | − | 0.920257i | \(-0.627979\pi\) | ||||
−0.391314 | + | 0.920257i | \(0.627979\pi\) | |||||||
\(878\) | −36.3923 | −1.22818 | ||||||||
\(879\) | −6.92820 | −0.233682 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 24.9282 | 0.839853 | 0.419926 | − | 0.907558i | \(-0.362056\pi\) | ||||
0.419926 | + | 0.907558i | \(0.362056\pi\) | |||||||
\(882\) | −4.46410 | −0.150314 | ||||||||
\(883\) | −41.1769 | −1.38571 | −0.692857 | − | 0.721075i | \(-0.743648\pi\) | ||||
−0.692857 | + | 0.721075i | \(0.743648\pi\) | |||||||
\(884\) | −5.07180 | −0.170583 | ||||||||
\(885\) | −37.8564 | −1.27253 | ||||||||
\(886\) | −20.7846 | −0.698273 | ||||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | −8.92820 | −0.299611 | ||||||||
\(889\) | 9.85641 | 0.330573 | ||||||||
\(890\) | 15.4641 | 0.518358 | ||||||||
\(891\) | −2.46410 | −0.0825505 | ||||||||
\(892\) | −8.39230 | −0.280995 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 19.8564 | 0.664098 | ||||||||
\(895\) | −19.8564 | −0.663726 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −5.07180 | −0.169342 | ||||||||
\(898\) | 35.3205 | 1.17866 | ||||||||
\(899\) | −42.2487 | −1.40907 | ||||||||
\(900\) | 4.46410 | 0.148803 | ||||||||
\(901\) | −16.3923 | −0.546107 | ||||||||
\(902\) | 4.73205 | 0.157560 | ||||||||
\(903\) | −13.4641 | −0.448057 | ||||||||
\(904\) | −12.9282 | −0.429986 | ||||||||
\(905\) | −11.8564 | −0.394120 | ||||||||
\(906\) | 21.3205 | 0.708326 | ||||||||
\(907\) | −15.3205 | −0.508709 | −0.254355 | − | 0.967111i | \(-0.581863\pi\) | ||||
−0.254355 | + | 0.967111i | \(0.581863\pi\) | |||||||
\(908\) | 13.8564 | 0.459841 | ||||||||
\(909\) | −26.7846 | −0.888389 | ||||||||
\(910\) | 1.46410 | 0.0485345 | ||||||||
\(911\) | 14.5359 | 0.481596 | 0.240798 | − | 0.970575i | \(-0.422591\pi\) | ||||
0.240798 | + | 0.970575i | \(0.422591\pi\) | |||||||
\(912\) | −7.46410 | −0.247161 | ||||||||
\(913\) | −4.39230 | −0.145364 | ||||||||
\(914\) | 34.0000 | 1.12462 | ||||||||
\(915\) | 5.46410 | 0.180638 | ||||||||
\(916\) | −13.4641 | −0.444866 | ||||||||
\(917\) | −17.6603 | −0.583193 | ||||||||
\(918\) | −13.8564 | −0.457330 | ||||||||
\(919\) | 24.9808 | 0.824039 | 0.412020 | − | 0.911175i | \(-0.364824\pi\) | ||||
0.412020 | + | 0.911175i | \(0.364824\pi\) | |||||||
\(920\) | −1.26795 | −0.0418030 | ||||||||
\(921\) | 85.5692 | 2.81960 | ||||||||
\(922\) | −29.3205 | −0.965620 | ||||||||
\(923\) | −13.8564 | −0.456089 | ||||||||
\(924\) | 2.73205 | 0.0898779 | ||||||||
\(925\) | 3.26795 | 0.107450 | ||||||||
\(926\) | −12.9808 | −0.426574 | ||||||||
\(927\) | 47.0333 | 1.54478 | ||||||||
\(928\) | 4.73205 | 0.155337 | ||||||||
\(929\) | 26.1051 | 0.856481 | 0.428241 | − | 0.903665i | \(-0.359134\pi\) | ||||
0.428241 | + | 0.903665i | \(0.359134\pi\) | |||||||
\(930\) | −24.3923 | −0.799855 | ||||||||
\(931\) | −2.73205 | −0.0895393 | ||||||||
\(932\) | 7.85641 | 0.257345 | ||||||||
\(933\) | 21.4641 | 0.702703 | ||||||||
\(934\) | −17.6603 | −0.577861 | ||||||||
\(935\) | 3.46410 | 0.113288 | ||||||||
\(936\) | 6.53590 | 0.213633 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 10.9282 | 0.356818 | ||||||||
\(939\) | 74.4974 | 2.43113 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.5692 | −1.15952 | −0.579762 | − | 0.814786i | \(-0.696854\pi\) | ||||
−0.579762 | + | 0.814786i | \(0.696854\pi\) | |||||||
\(942\) | −17.4641 | −0.569011 | ||||||||
\(943\) | −6.00000 | −0.195387 | ||||||||
\(944\) | −13.8564 | −0.450988 | ||||||||
\(945\) | 4.00000 | 0.130120 | ||||||||
\(946\) | 4.92820 | 0.160230 | ||||||||
\(947\) | −25.1769 | −0.818140 | −0.409070 | − | 0.912503i | \(-0.634147\pi\) | ||||
−0.409070 | + | 0.912503i | \(0.634147\pi\) | |||||||
\(948\) | 18.3923 | 0.597354 | ||||||||
\(949\) | −16.7846 | −0.544851 | ||||||||
\(950\) | 2.73205 | 0.0886394 | ||||||||
\(951\) | −88.6410 | −2.87438 | ||||||||
\(952\) | −3.46410 | −0.112272 | ||||||||
\(953\) | −11.3205 | −0.366707 | −0.183354 | − | 0.983047i | \(-0.558695\pi\) | ||||
−0.183354 | + | 0.983047i | \(0.558695\pi\) | |||||||
\(954\) | 21.1244 | 0.683926 | ||||||||
\(955\) | 6.92820 | 0.224191 | ||||||||
\(956\) | −3.80385 | −0.123025 | ||||||||
\(957\) | −12.9282 | −0.417909 | ||||||||
\(958\) | −13.8564 | −0.447680 | ||||||||
\(959\) | 7.85641 | 0.253697 | ||||||||
\(960\) | 2.73205 | 0.0881766 | ||||||||
\(961\) | 48.7128 | 1.57138 | ||||||||
\(962\) | 4.78461 | 0.154262 | ||||||||
\(963\) | 4.14359 | 0.133525 | ||||||||
\(964\) | −18.1962 | −0.586059 | ||||||||
\(965\) | −25.4641 | −0.819718 | ||||||||
\(966\) | −3.46410 | −0.111456 | ||||||||
\(967\) | −26.1436 | −0.840721 | −0.420361 | − | 0.907357i | \(-0.638096\pi\) | ||||
−0.420361 | + | 0.907357i | \(0.638096\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −25.8564 | −0.830627 | ||||||||
\(970\) | −5.80385 | −0.186350 | ||||||||
\(971\) | 49.8564 | 1.59997 | 0.799984 | − | 0.600021i | \(-0.204841\pi\) | ||||
0.799984 | + | 0.600021i | \(0.204841\pi\) | |||||||
\(972\) | −18.7321 | −0.600831 | ||||||||
\(973\) | 4.19615 | 0.134522 | ||||||||
\(974\) | −4.87564 | −0.156226 | ||||||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −0.928203 | −0.0296959 | −0.0148479 | − | 0.999890i | \(-0.504726\pi\) | ||||
−0.0148479 | + | 0.999890i | \(0.504726\pi\) | |||||||
\(978\) | −21.8564 | −0.698891 | ||||||||
\(979\) | −15.4641 | −0.494235 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −8.05256 | −0.257098 | ||||||||
\(982\) | −42.9282 | −1.36989 | ||||||||
\(983\) | −7.60770 | −0.242648 | −0.121324 | − | 0.992613i | \(-0.538714\pi\) | ||||
−0.121324 | + | 0.992613i | \(0.538714\pi\) | |||||||
\(984\) | 12.9282 | 0.412136 | ||||||||
\(985\) | −22.3923 | −0.713478 | ||||||||
\(986\) | 16.3923 | 0.522037 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | −6.24871 | −0.198697 | ||||||||
\(990\) | −4.46410 | −0.141878 | ||||||||
\(991\) | −22.9282 | −0.728338 | −0.364169 | − | 0.931333i | \(-0.618647\pi\) | ||||
−0.364169 | + | 0.931333i | \(0.618647\pi\) | |||||||
\(992\) | −8.92820 | −0.283471 | ||||||||
\(993\) | −13.4641 | −0.427270 | ||||||||
\(994\) | −9.46410 | −0.300183 | ||||||||
\(995\) | −24.7846 | −0.785725 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | −23.8564 | −0.755540 | −0.377770 | − | 0.925899i | \(-0.623309\pi\) | ||||
−0.377770 | + | 0.925899i | \(0.623309\pi\) | |||||||
\(998\) | −2.00000 | −0.0633089 | ||||||||
\(999\) | 13.0718 | 0.413573 |
(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 | 770.2.a.h.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6930.2.a.ca.1.1 | 2 | |||
4.3 | odd | 2 | 6160.2.a.v.1.1 | 2 | |||
5.2 | odd | 4 | 3850.2.c.s.1849.1 | 4 | |||
5.3 | odd | 4 | 3850.2.c.s.1849.4 | 4 | |||
5.4 | even | 2 | 3850.2.a.bm.1.1 | 2 | |||
7.6 | odd | 2 | 5390.2.a.bk.1.1 | 2 | |||
11.10 | odd | 2 | 8470.2.a.ce.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.h.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3850.2.a.bm.1.1 | 2 | 5.4 | even | 2 | |||
3850.2.c.s.1849.1 | 4 | 5.2 | odd | 4 | |||
3850.2.c.s.1849.4 | 4 | 5.3 | odd | 4 | |||
5390.2.a.bk.1.1 | 2 | 7.6 | odd | 2 | |||
6160.2.a.v.1.1 | 2 | 4.3 | odd | 2 | |||
6930.2.a.ca.1.1 | 2 | 3.2 | odd | 2 | |||
8470.2.a.ce.1.2 | 2 | 11.10 | odd | 2 |