Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.19898000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.86564\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | −2.86564 | −1.65448 | −0.827238 | − | 0.561852i | \(-0.810089\pi\) | ||||
−0.827238 | + | 0.561852i | \(0.810089\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.86564 | −1.16989 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.21187 | 1.73729 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.86564 | −0.827238 | ||||||||
\(13\) | 5.63670 | 1.56334 | 0.781669 | − | 0.623693i | \(-0.214369\pi\) | ||||
0.781669 | + | 0.623693i | \(0.214369\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.86564 | −0.739904 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.32986 | 0.565074 | 0.282537 | − | 0.959256i | \(-0.408824\pi\) | ||||
0.282537 | + | 0.959256i | \(0.408824\pi\) | |||||||
\(18\) | 5.21187 | 1.22845 | ||||||||
\(19\) | 7.81494 | 1.79287 | 0.896435 | − | 0.443175i | \(-0.146148\pi\) | ||||
0.896435 | + | 0.443175i | \(0.146148\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.86564 | 0.625333 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.98434 | 1.66485 | 0.832425 | − | 0.554138i | \(-0.186952\pi\) | ||||
0.832425 | + | 0.554138i | \(0.186952\pi\) | |||||||
\(24\) | −2.86564 | −0.584945 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.63670 | 1.10545 | ||||||||
\(27\) | −6.33840 | −1.21983 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.99446 | −0.556057 | −0.278029 | − | 0.960573i | \(-0.589681\pi\) | ||||
−0.278029 | + | 0.960573i | \(0.589681\pi\) | |||||||
\(30\) | −2.86564 | −0.523191 | ||||||||
\(31\) | 5.08533 | 0.913352 | 0.456676 | − | 0.889633i | \(-0.349040\pi\) | ||||
0.456676 | + | 0.889633i | \(0.349040\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.32986 | 0.399567 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 5.21187 | 0.868644 | ||||||||
\(37\) | −1.38681 | −0.227989 | −0.113995 | − | 0.993481i | \(-0.536365\pi\) | ||||
−0.113995 | + | 0.993481i | \(0.536365\pi\) | |||||||
\(38\) | 7.81494 | 1.26775 | ||||||||
\(39\) | −16.1527 | −2.58650 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −6.90154 | −1.07784 | −0.538920 | − | 0.842357i | \(-0.681167\pi\) | ||||
−0.538920 | + | 0.842357i | \(0.681167\pi\) | |||||||
\(42\) | 2.86564 | 0.442177 | ||||||||
\(43\) | 11.5492 | 1.76124 | 0.880622 | − | 0.473820i | \(-0.157125\pi\) | ||||
0.880622 | + | 0.473820i | \(0.157125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.21187 | 0.776939 | ||||||||
\(46\) | 7.98434 | 1.17723 | ||||||||
\(47\) | −5.14520 | −0.750504 | −0.375252 | − | 0.926923i | \(-0.622444\pi\) | ||||
−0.375252 | + | 0.926923i | \(0.622444\pi\) | |||||||
\(48\) | −2.86564 | −0.413619 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.67652 | −0.934900 | ||||||||
\(52\) | 5.63670 | 0.781669 | ||||||||
\(53\) | 0.582695 | 0.0800393 | 0.0400196 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400196 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(54\) | −6.33840 | −0.862547 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −22.3948 | −2.96626 | ||||||||
\(58\) | −2.99446 | −0.393192 | ||||||||
\(59\) | 13.8292 | 1.80041 | 0.900204 | − | 0.435468i | \(-0.143417\pi\) | ||||
0.900204 | + | 0.435468i | \(0.143417\pi\) | |||||||
\(60\) | −2.86564 | −0.369952 | ||||||||
\(61\) | −7.82443 | −1.00182 | −0.500908 | − | 0.865501i | \(-0.667000\pi\) | ||||
−0.500908 | + | 0.865501i | \(0.667000\pi\) | |||||||
\(62\) | 5.08533 | 0.645838 | ||||||||
\(63\) | −5.21187 | −0.656633 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.63670 | 0.699146 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0485769 | −0.00593462 | −0.00296731 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00296731 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(68\) | 2.32986 | 0.282537 | ||||||||
\(69\) | −22.8802 | −2.75445 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 4.45361 | 0.528546 | 0.264273 | − | 0.964448i | \(-0.414868\pi\) | ||||
0.264273 | + | 0.964448i | \(0.414868\pi\) | |||||||
\(72\) | 5.21187 | 0.614224 | ||||||||
\(73\) | 0.336814 | 0.0394210 | 0.0197105 | − | 0.999806i | \(-0.493726\pi\) | ||||
0.0197105 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(74\) | −1.38681 | −0.161213 | ||||||||
\(75\) | −2.86564 | −0.330895 | ||||||||
\(76\) | 7.81494 | 0.896435 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −16.1527 | −1.82893 | ||||||||
\(79\) | −1.05291 | −0.118462 | −0.0592308 | − | 0.998244i | \(-0.518865\pi\) | ||||
−0.0592308 | + | 0.998244i | \(0.518865\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 2.52795 | 0.280883 | ||||||||
\(82\) | −6.90154 | −0.762148 | ||||||||
\(83\) | −10.8315 | −1.18891 | −0.594455 | − | 0.804129i | \(-0.702632\pi\) | ||||
−0.594455 | + | 0.804129i | \(0.702632\pi\) | |||||||
\(84\) | 2.86564 | 0.312666 | ||||||||
\(85\) | 2.32986 | 0.252709 | ||||||||
\(86\) | 11.5492 | 1.24539 | ||||||||
\(87\) | 8.58103 | 0.919983 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.5268 | −1.96384 | −0.981921 | − | 0.189291i | \(-0.939381\pi\) | ||||
−0.981921 | + | 0.189291i | \(0.939381\pi\) | |||||||
\(90\) | 5.21187 | 0.549379 | ||||||||
\(91\) | −5.63670 | −0.590886 | ||||||||
\(92\) | 7.98434 | 0.832425 | ||||||||
\(93\) | −14.5727 | −1.51112 | ||||||||
\(94\) | −5.14520 | −0.530686 | ||||||||
\(95\) | 7.81494 | 0.801796 | ||||||||
\(96\) | −2.86564 | −0.292473 | ||||||||
\(97\) | −5.33180 | −0.541362 | −0.270681 | − | 0.962669i | \(-0.587249\pi\) | ||||
−0.270681 | + | 0.962669i | \(0.587249\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.2701 | 1.81795 | 0.908973 | − | 0.416854i | \(-0.136867\pi\) | ||||
0.908973 | + | 0.416854i | \(0.136867\pi\) | |||||||
\(102\) | −6.67652 | −0.661074 | ||||||||
\(103\) | −11.2347 | −1.10699 | −0.553495 | − | 0.832852i | \(-0.686706\pi\) | ||||
−0.553495 | + | 0.832852i | \(0.686706\pi\) | |||||||
\(104\) | 5.63670 | 0.552723 | ||||||||
\(105\) | 2.86564 | 0.279657 | ||||||||
\(106\) | 0.582695 | 0.0565963 | ||||||||
\(107\) | −4.89157 | −0.472886 | −0.236443 | − | 0.971645i | \(-0.575982\pi\) | ||||
−0.236443 | + | 0.971645i | \(0.575982\pi\) | |||||||
\(108\) | −6.33840 | −0.609913 | ||||||||
\(109\) | −6.26442 | −0.600023 | −0.300011 | − | 0.953936i | \(-0.596991\pi\) | ||||
−0.300011 | + | 0.953936i | \(0.596991\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.97408 | 0.377203 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.1651 | 0.956251 | 0.478126 | − | 0.878291i | \(-0.341316\pi\) | ||||
0.478126 | + | 0.878291i | \(0.341316\pi\) | |||||||
\(114\) | −22.3948 | −2.09746 | ||||||||
\(115\) | 7.98434 | 0.744544 | ||||||||
\(116\) | −2.99446 | −0.278029 | ||||||||
\(117\) | 29.3777 | 2.71597 | ||||||||
\(118\) | 13.8292 | 1.27308 | ||||||||
\(119\) | −2.32986 | −0.213578 | ||||||||
\(120\) | −2.86564 | −0.261596 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −7.82443 | −0.708391 | ||||||||
\(123\) | 19.7773 | 1.78326 | ||||||||
\(124\) | 5.08533 | 0.456676 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.21187 | −0.464310 | ||||||||
\(127\) | −6.58727 | −0.584526 | −0.292263 | − | 0.956338i | \(-0.594408\pi\) | ||||
−0.292263 | + | 0.956338i | \(0.594408\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −33.0959 | −2.91393 | ||||||||
\(130\) | 5.63670 | 0.494371 | ||||||||
\(131\) | −1.20821 | −0.105562 | −0.0527808 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527808 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.81494 | −0.677641 | ||||||||
\(134\) | −0.0485769 | −0.00419641 | ||||||||
\(135\) | −6.33840 | −0.545523 | ||||||||
\(136\) | 2.32986 | 0.199784 | ||||||||
\(137\) | 14.0829 | 1.20318 | 0.601590 | − | 0.798805i | \(-0.294534\pi\) | ||||
0.601590 | + | 0.798805i | \(0.294534\pi\) | |||||||
\(138\) | −22.8802 | −1.94769 | ||||||||
\(139\) | −2.74290 | −0.232650 | −0.116325 | − | 0.993211i | \(-0.537111\pi\) | ||||
−0.116325 | + | 0.993211i | \(0.537111\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 14.7443 | 1.24169 | ||||||||
\(142\) | 4.45361 | 0.373739 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.21187 | 0.434322 | ||||||||
\(145\) | −2.99446 | −0.248676 | ||||||||
\(146\) | 0.336814 | 0.0278749 | ||||||||
\(147\) | −2.86564 | −0.236354 | ||||||||
\(148\) | −1.38681 | −0.113995 | ||||||||
\(149\) | 17.1642 | 1.40615 | 0.703075 | − | 0.711116i | \(-0.251810\pi\) | ||||
0.703075 | + | 0.711116i | \(0.251810\pi\) | |||||||
\(150\) | −2.86564 | −0.233978 | ||||||||
\(151\) | −5.94304 | −0.483637 | −0.241819 | − | 0.970321i | \(-0.577744\pi\) | ||||
−0.241819 | + | 0.970321i | \(0.577744\pi\) | |||||||
\(152\) | 7.81494 | 0.633875 | ||||||||
\(153\) | 12.1429 | 0.981696 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.08533 | 0.408464 | ||||||||
\(156\) | −16.1527 | −1.29325 | ||||||||
\(157\) | −16.7947 | −1.34037 | −0.670183 | − | 0.742196i | \(-0.733784\pi\) | ||||
−0.670183 | + | 0.742196i | \(0.733784\pi\) | |||||||
\(158\) | −1.05291 | −0.0837650 | ||||||||
\(159\) | −1.66979 | −0.132423 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −7.98434 | −0.629254 | ||||||||
\(162\) | 2.52795 | 0.198614 | ||||||||
\(163\) | 2.43041 | 0.190364 | 0.0951821 | − | 0.995460i | \(-0.469657\pi\) | ||||
0.0951821 | + | 0.995460i | \(0.469657\pi\) | |||||||
\(164\) | −6.90154 | −0.538920 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8315 | −0.840686 | ||||||||
\(167\) | 11.0306 | 0.853572 | 0.426786 | − | 0.904353i | \(-0.359646\pi\) | ||||
0.426786 | + | 0.904353i | \(0.359646\pi\) | |||||||
\(168\) | 2.86564 | 0.221089 | ||||||||
\(169\) | 18.7723 | 1.44403 | ||||||||
\(170\) | 2.32986 | 0.178692 | ||||||||
\(171\) | 40.7304 | 3.11473 | ||||||||
\(172\) | 11.5492 | 0.880622 | ||||||||
\(173\) | −14.6947 | −1.11721 | −0.558607 | − | 0.829433i | \(-0.688664\pi\) | ||||
−0.558607 | + | 0.829433i | \(0.688664\pi\) | |||||||
\(174\) | 8.58103 | 0.650526 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −39.6294 | −2.97873 | ||||||||
\(178\) | −18.5268 | −1.38865 | ||||||||
\(179\) | 4.51392 | 0.337387 | 0.168693 | − | 0.985669i | \(-0.446045\pi\) | ||||
0.168693 | + | 0.985669i | \(0.446045\pi\) | |||||||
\(180\) | 5.21187 | 0.388470 | ||||||||
\(181\) | −10.1770 | −0.756451 | −0.378225 | − | 0.925714i | \(-0.623466\pi\) | ||||
−0.378225 | + | 0.925714i | \(0.623466\pi\) | |||||||
\(182\) | −5.63670 | −0.417820 | ||||||||
\(183\) | 22.4220 | 1.65748 | ||||||||
\(184\) | 7.98434 | 0.588613 | ||||||||
\(185\) | −1.38681 | −0.101960 | ||||||||
\(186\) | −14.5727 | −1.06852 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.14520 | −0.375252 | ||||||||
\(189\) | 6.33840 | 0.461051 | ||||||||
\(190\) | 7.81494 | 0.566955 | ||||||||
\(191\) | 11.9914 | 0.867669 | 0.433834 | − | 0.900993i | \(-0.357160\pi\) | ||||
0.433834 | + | 0.900993i | \(0.357160\pi\) | |||||||
\(192\) | −2.86564 | −0.206809 | ||||||||
\(193\) | 17.8748 | 1.28666 | 0.643330 | − | 0.765589i | \(-0.277552\pi\) | ||||
0.643330 | + | 0.765589i | \(0.277552\pi\) | |||||||
\(194\) | −5.33180 | −0.382801 | ||||||||
\(195\) | −16.1527 | −1.15672 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.7871 | 0.839795 | 0.419897 | − | 0.907572i | \(-0.362066\pi\) | ||||
0.419897 | + | 0.907572i | \(0.362066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.9342 | −0.987767 | −0.493884 | − | 0.869528i | \(-0.664423\pi\) | ||||
−0.493884 | + | 0.869528i | \(0.664423\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0.139204 | 0.00981868 | ||||||||
\(202\) | 18.2701 | 1.28548 | ||||||||
\(203\) | 2.99446 | 0.210170 | ||||||||
\(204\) | −6.67652 | −0.467450 | ||||||||
\(205\) | −6.90154 | −0.482025 | ||||||||
\(206\) | −11.2347 | −0.782760 | ||||||||
\(207\) | 41.6133 | 2.89233 | ||||||||
\(208\) | 5.63670 | 0.390835 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.86564 | 0.197748 | ||||||||
\(211\) | −26.4497 | −1.82087 | −0.910435 | − | 0.413653i | \(-0.864253\pi\) | ||||
−0.910435 | + | 0.413653i | \(0.864253\pi\) | |||||||
\(212\) | 0.582695 | 0.0400196 | ||||||||
\(213\) | −12.7624 | −0.874467 | ||||||||
\(214\) | −4.89157 | −0.334381 | ||||||||
\(215\) | 11.5492 | 0.787652 | ||||||||
\(216\) | −6.33840 | −0.431274 | ||||||||
\(217\) | −5.08533 | −0.345215 | ||||||||
\(218\) | −6.26442 | −0.424280 | ||||||||
\(219\) | −0.965185 | −0.0652211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.1327 | 0.883401 | ||||||||
\(222\) | 3.97408 | 0.266723 | ||||||||
\(223\) | 24.5893 | 1.64662 | 0.823311 | − | 0.567591i | \(-0.192124\pi\) | ||||
0.823311 | + | 0.567591i | \(0.192124\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 5.21187 | 0.347458 | ||||||||
\(226\) | 10.1651 | 0.676172 | ||||||||
\(227\) | 5.59242 | 0.371182 | 0.185591 | − | 0.982627i | \(-0.440580\pi\) | ||||
0.185591 | + | 0.982627i | \(0.440580\pi\) | |||||||
\(228\) | −22.3948 | −1.48313 | ||||||||
\(229\) | −8.10340 | −0.535488 | −0.267744 | − | 0.963490i | \(-0.586278\pi\) | ||||
−0.267744 | + | 0.963490i | \(0.586278\pi\) | |||||||
\(230\) | 7.98434 | 0.526472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.99446 | −0.196596 | ||||||||
\(233\) | −11.9807 | −0.784882 | −0.392441 | − | 0.919777i | \(-0.628369\pi\) | ||||
−0.392441 | + | 0.919777i | \(0.628369\pi\) | |||||||
\(234\) | 29.3777 | 1.92048 | ||||||||
\(235\) | −5.14520 | −0.335636 | ||||||||
\(236\) | 13.8292 | 0.900204 | ||||||||
\(237\) | 3.01726 | 0.195992 | ||||||||
\(238\) | −2.32986 | −0.151022 | ||||||||
\(239\) | 6.46612 | 0.418258 | 0.209129 | − | 0.977888i | \(-0.432937\pi\) | ||||
0.209129 | + | 0.977888i | \(0.432937\pi\) | |||||||
\(240\) | −2.86564 | −0.184976 | ||||||||
\(241\) | −20.3441 | −1.31048 | −0.655238 | − | 0.755423i | \(-0.727432\pi\) | ||||
−0.655238 | + | 0.755423i | \(0.727432\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7710 | 0.755112 | ||||||||
\(244\) | −7.82443 | −0.500908 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 19.7773 | 1.26096 | ||||||||
\(247\) | 44.0504 | 2.80286 | ||||||||
\(248\) | 5.08533 | 0.322919 | ||||||||
\(249\) | 31.0391 | 1.96702 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 12.5842 | 0.794311 | 0.397155 | − | 0.917751i | \(-0.369997\pi\) | ||||
0.397155 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(252\) | −5.21187 | −0.328317 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.58727 | −0.413322 | ||||||||
\(255\) | −6.67652 | −0.418100 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.45995 | 0.215826 | 0.107913 | − | 0.994160i | \(-0.465583\pi\) | ||||
0.107913 | + | 0.994160i | \(0.465583\pi\) | |||||||
\(258\) | −33.0959 | −2.06046 | ||||||||
\(259\) | 1.38681 | 0.0861719 | ||||||||
\(260\) | 5.63670 | 0.349573 | ||||||||
\(261\) | −15.6067 | −0.966032 | ||||||||
\(262\) | −1.20821 | −0.0746434 | ||||||||
\(263\) | 8.01789 | 0.494404 | 0.247202 | − | 0.968964i | \(-0.420489\pi\) | ||||
0.247202 | + | 0.968964i | \(0.420489\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.582695 | 0.0357946 | ||||||||
\(266\) | −7.81494 | −0.479165 | ||||||||
\(267\) | 53.0912 | 3.24913 | ||||||||
\(268\) | −0.0485769 | −0.00296731 | ||||||||
\(269\) | −18.5650 | −1.13193 | −0.565964 | − | 0.824430i | \(-0.691496\pi\) | ||||
−0.565964 | + | 0.824430i | \(0.691496\pi\) | |||||||
\(270\) | −6.33840 | −0.385743 | ||||||||
\(271\) | −25.2051 | −1.53110 | −0.765552 | − | 0.643375i | \(-0.777534\pi\) | ||||
−0.765552 | + | 0.643375i | \(0.777534\pi\) | |||||||
\(272\) | 2.32986 | 0.141268 | ||||||||
\(273\) | 16.1527 | 0.977607 | ||||||||
\(274\) | 14.0829 | 0.850777 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −22.8802 | −1.37723 | ||||||||
\(277\) | 12.2281 | 0.734714 | 0.367357 | − | 0.930080i | \(-0.380263\pi\) | ||||
0.367357 | + | 0.930080i | \(0.380263\pi\) | |||||||
\(278\) | −2.74290 | −0.164508 | ||||||||
\(279\) | 26.5041 | 1.58676 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −26.5934 | −1.58643 | −0.793216 | − | 0.608941i | \(-0.791595\pi\) | ||||
−0.793216 | + | 0.608941i | \(0.791595\pi\) | |||||||
\(282\) | 14.7443 | 0.878008 | ||||||||
\(283\) | 13.7220 | 0.815689 | 0.407845 | − | 0.913051i | \(-0.366281\pi\) | ||||
0.407845 | + | 0.913051i | \(0.366281\pi\) | |||||||
\(284\) | 4.45361 | 0.264273 | ||||||||
\(285\) | −22.3948 | −1.32655 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.90154 | 0.407385 | ||||||||
\(288\) | 5.21187 | 0.307112 | ||||||||
\(289\) | −11.5718 | −0.680692 | ||||||||
\(290\) | −2.99446 | −0.175841 | ||||||||
\(291\) | 15.2790 | 0.895670 | ||||||||
\(292\) | 0.336814 | 0.0197105 | ||||||||
\(293\) | −0.714463 | −0.0417394 | −0.0208697 | − | 0.999782i | \(-0.506644\pi\) | ||||
−0.0208697 | + | 0.999782i | \(0.506644\pi\) | |||||||
\(294\) | −2.86564 | −0.167127 | ||||||||
\(295\) | 13.8292 | 0.805167 | ||||||||
\(296\) | −1.38681 | −0.0806064 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.1642 | 0.994298 | ||||||||
\(299\) | 45.0053 | 2.60272 | ||||||||
\(300\) | −2.86564 | −0.165448 | ||||||||
\(301\) | −11.5492 | −0.665688 | ||||||||
\(302\) | −5.94304 | −0.341983 | ||||||||
\(303\) | −52.3556 | −3.00775 | ||||||||
\(304\) | 7.81494 | 0.448218 | ||||||||
\(305\) | −7.82443 | −0.448026 | ||||||||
\(306\) | 12.1429 | 0.694164 | ||||||||
\(307\) | 19.3442 | 1.10403 | 0.552015 | − | 0.833834i | \(-0.313859\pi\) | ||||
0.552015 | + | 0.833834i | \(0.313859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.1946 | 1.83149 | ||||||||
\(310\) | 5.08533 | 0.288827 | ||||||||
\(311\) | 1.82729 | 0.103616 | 0.0518080 | − | 0.998657i | \(-0.483502\pi\) | ||||
0.0518080 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(312\) | −16.1527 | −0.914467 | ||||||||
\(313\) | −9.83108 | −0.555686 | −0.277843 | − | 0.960627i | \(-0.589619\pi\) | ||||
−0.277843 | + | 0.960627i | \(0.589619\pi\) | |||||||
\(314\) | −16.7947 | −0.947782 | ||||||||
\(315\) | −5.21187 | −0.293655 | ||||||||
\(316\) | −1.05291 | −0.0592308 | ||||||||
\(317\) | −13.8545 | −0.778146 | −0.389073 | − | 0.921207i | \(-0.627205\pi\) | ||||
−0.389073 | + | 0.921207i | \(0.627205\pi\) | |||||||
\(318\) | −1.66979 | −0.0936372 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 14.0175 | 0.782378 | ||||||||
\(322\) | −7.98434 | −0.444950 | ||||||||
\(323\) | 18.2077 | 1.01310 | ||||||||
\(324\) | 2.52795 | 0.140442 | ||||||||
\(325\) | 5.63670 | 0.312668 | ||||||||
\(326\) | 2.43041 | 0.134608 | ||||||||
\(327\) | 17.9516 | 0.992723 | ||||||||
\(328\) | −6.90154 | −0.381074 | ||||||||
\(329\) | 5.14520 | 0.283664 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.02084 | 0.440865 | 0.220433 | − | 0.975402i | \(-0.429253\pi\) | ||||
0.220433 | + | 0.975402i | \(0.429253\pi\) | |||||||
\(332\) | −10.8315 | −0.594455 | ||||||||
\(333\) | −7.22784 | −0.396083 | ||||||||
\(334\) | 11.0306 | 0.603567 | ||||||||
\(335\) | −0.0485769 | −0.00265404 | ||||||||
\(336\) | 2.86564 | 0.156333 | ||||||||
\(337\) | 11.6060 | 0.632218 | 0.316109 | − | 0.948723i | \(-0.397624\pi\) | ||||
0.316109 | + | 0.948723i | \(0.397624\pi\) | |||||||
\(338\) | 18.7723 | 1.02108 | ||||||||
\(339\) | −29.1294 | −1.58209 | ||||||||
\(340\) | 2.32986 | 0.126354 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 40.7304 | 2.20245 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.5492 | 0.622694 | ||||||||
\(345\) | −22.8802 | −1.23183 | ||||||||
\(346\) | −14.6947 | −0.789989 | ||||||||
\(347\) | 26.4301 | 1.41884 | 0.709420 | − | 0.704786i | \(-0.248957\pi\) | ||||
0.709420 | + | 0.704786i | \(0.248957\pi\) | |||||||
\(348\) | 8.58103 | 0.459991 | ||||||||
\(349\) | −27.3777 | −1.46549 | −0.732747 | − | 0.680501i | \(-0.761762\pi\) | ||||
−0.732747 | + | 0.680501i | \(0.761762\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −35.7276 | −1.90700 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3772 | 1.13779 | 0.568897 | − | 0.822409i | \(-0.307370\pi\) | ||||
0.568897 | + | 0.822409i | \(0.307370\pi\) | |||||||
\(354\) | −39.6294 | −2.10628 | ||||||||
\(355\) | 4.45361 | 0.236373 | ||||||||
\(356\) | −18.5268 | −0.981921 | ||||||||
\(357\) | 6.67652 | 0.353359 | ||||||||
\(358\) | 4.51392 | 0.238568 | ||||||||
\(359\) | 10.8904 | 0.574774 | 0.287387 | − | 0.957815i | \(-0.407213\pi\) | ||||
0.287387 | + | 0.957815i | \(0.407213\pi\) | |||||||
\(360\) | 5.21187 | 0.274689 | ||||||||
\(361\) | 42.0733 | 2.21439 | ||||||||
\(362\) | −10.1770 | −0.534891 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.63670 | −0.295443 | ||||||||
\(365\) | 0.336814 | 0.0176296 | ||||||||
\(366\) | 22.4220 | 1.17201 | ||||||||
\(367\) | 11.3108 | 0.590416 | 0.295208 | − | 0.955433i | \(-0.404611\pi\) | ||||
0.295208 | + | 0.955433i | \(0.404611\pi\) | |||||||
\(368\) | 7.98434 | 0.416213 | ||||||||
\(369\) | −35.9699 | −1.87252 | ||||||||
\(370\) | −1.38681 | −0.0720966 | ||||||||
\(371\) | −0.582695 | −0.0302520 | ||||||||
\(372\) | −14.5727 | −0.755559 | ||||||||
\(373\) | −11.6658 | −0.604034 | −0.302017 | − | 0.953303i | \(-0.597660\pi\) | ||||
−0.302017 | + | 0.953303i | \(0.597660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.86564 | −0.147981 | ||||||||
\(376\) | −5.14520 | −0.265343 | ||||||||
\(377\) | −16.8789 | −0.869305 | ||||||||
\(378\) | 6.33840 | 0.326012 | ||||||||
\(379\) | 0.617088 | 0.0316977 | 0.0158488 | − | 0.999874i | \(-0.494955\pi\) | ||||
0.0158488 | + | 0.999874i | \(0.494955\pi\) | |||||||
\(380\) | 7.81494 | 0.400898 | ||||||||
\(381\) | 18.8767 | 0.967084 | ||||||||
\(382\) | 11.9914 | 0.613535 | ||||||||
\(383\) | −26.4471 | −1.35138 | −0.675692 | − | 0.737184i | \(-0.736155\pi\) | ||||
−0.675692 | + | 0.737184i | \(0.736155\pi\) | |||||||
\(384\) | −2.86564 | −0.146236 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.8748 | 0.909806 | ||||||||
\(387\) | 60.1931 | 3.05979 | ||||||||
\(388\) | −5.33180 | −0.270681 | ||||||||
\(389\) | 1.60446 | 0.0813492 | 0.0406746 | − | 0.999172i | \(-0.487049\pi\) | ||||
0.0406746 | + | 0.999172i | \(0.487049\pi\) | |||||||
\(390\) | −16.1527 | −0.817924 | ||||||||
\(391\) | 18.6024 | 0.940763 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 3.46228 | 0.174649 | ||||||||
\(394\) | 11.7871 | 0.593825 | ||||||||
\(395\) | −1.05291 | −0.0529776 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.28819 | 0.265407 | 0.132703 | − | 0.991156i | \(-0.457634\pi\) | ||||
0.132703 | + | 0.991156i | \(0.457634\pi\) | |||||||
\(398\) | −13.9342 | −0.698457 | ||||||||
\(399\) | 22.3948 | 1.12114 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −13.6059 | −0.679446 | −0.339723 | − | 0.940526i | \(-0.610333\pi\) | ||||
−0.339723 | + | 0.940526i | \(0.610333\pi\) | |||||||
\(402\) | 0.139204 | 0.00694285 | ||||||||
\(403\) | 28.6645 | 1.42788 | ||||||||
\(404\) | 18.2701 | 0.908973 | ||||||||
\(405\) | 2.52795 | 0.125615 | ||||||||
\(406\) | 2.99446 | 0.148613 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.67652 | −0.330537 | ||||||||
\(409\) | 3.40230 | 0.168233 | 0.0841164 | − | 0.996456i | \(-0.473193\pi\) | ||||
0.0841164 | + | 0.996456i | \(0.473193\pi\) | |||||||
\(410\) | −6.90154 | −0.340843 | ||||||||
\(411\) | −40.3564 | −1.99063 | ||||||||
\(412\) | −11.2347 | −0.553495 | ||||||||
\(413\) | −13.8292 | −0.680490 | ||||||||
\(414\) | 41.6133 | 2.04518 | ||||||||
\(415\) | −10.8315 | −0.531697 | ||||||||
\(416\) | 5.63670 | 0.276362 | ||||||||
\(417\) | 7.86016 | 0.384914 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.5263 | −1.93099 | −0.965493 | − | 0.260428i | \(-0.916136\pi\) | ||||
−0.965493 | + | 0.260428i | \(0.916136\pi\) | |||||||
\(420\) | 2.86564 | 0.139829 | ||||||||
\(421\) | −15.6617 | −0.763304 | −0.381652 | − | 0.924306i | \(-0.624645\pi\) | ||||
−0.381652 | + | 0.924306i | \(0.624645\pi\) | |||||||
\(422\) | −26.4497 | −1.28755 | ||||||||
\(423\) | −26.8161 | −1.30384 | ||||||||
\(424\) | 0.582695 | 0.0282982 | ||||||||
\(425\) | 2.32986 | 0.113015 | ||||||||
\(426\) | −12.7624 | −0.618341 | ||||||||
\(427\) | 7.82443 | 0.378651 | ||||||||
\(428\) | −4.89157 | −0.236443 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.5492 | 0.556954 | ||||||||
\(431\) | −5.63150 | −0.271260 | −0.135630 | − | 0.990760i | \(-0.543306\pi\) | ||||
−0.135630 | + | 0.990760i | \(0.543306\pi\) | |||||||
\(432\) | −6.33840 | −0.304956 | ||||||||
\(433\) | −34.5223 | −1.65903 | −0.829517 | − | 0.558481i | \(-0.811384\pi\) | ||||
−0.829517 | + | 0.558481i | \(0.811384\pi\) | |||||||
\(434\) | −5.08533 | −0.244104 | ||||||||
\(435\) | 8.58103 | 0.411429 | ||||||||
\(436\) | −6.26442 | −0.300011 | ||||||||
\(437\) | 62.3972 | 2.98486 | ||||||||
\(438\) | −0.965185 | −0.0461183 | ||||||||
\(439\) | −30.0533 | −1.43437 | −0.717184 | − | 0.696884i | \(-0.754569\pi\) | ||||
−0.717184 | + | 0.696884i | \(0.754569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.21187 | 0.248184 | ||||||||
\(442\) | 13.1327 | 0.624659 | ||||||||
\(443\) | −32.0651 | −1.52346 | −0.761730 | − | 0.647894i | \(-0.775650\pi\) | ||||
−0.761730 | + | 0.647894i | \(0.775650\pi\) | |||||||
\(444\) | 3.97408 | 0.188601 | ||||||||
\(445\) | −18.5268 | −0.878257 | ||||||||
\(446\) | 24.5893 | 1.16434 | ||||||||
\(447\) | −49.1865 | −2.32644 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −9.27706 | −0.437811 | −0.218906 | − | 0.975746i | \(-0.570249\pi\) | ||||
−0.218906 | + | 0.975746i | \(0.570249\pi\) | |||||||
\(450\) | 5.21187 | 0.245690 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.1651 | 0.478126 | ||||||||
\(453\) | 17.0306 | 0.800166 | ||||||||
\(454\) | 5.59242 | 0.262465 | ||||||||
\(455\) | −5.63670 | −0.264252 | ||||||||
\(456\) | −22.3948 | −1.04873 | ||||||||
\(457\) | 20.0782 | 0.939217 | 0.469608 | − | 0.882875i | \(-0.344395\pi\) | ||||
0.469608 | + | 0.882875i | \(0.344395\pi\) | |||||||
\(458\) | −8.10340 | −0.378647 | ||||||||
\(459\) | −14.7676 | −0.689291 | ||||||||
\(460\) | 7.98434 | 0.372272 | ||||||||
\(461\) | −14.6490 | −0.682272 | −0.341136 | − | 0.940014i | \(-0.610812\pi\) | ||||
−0.341136 | + | 0.940014i | \(0.610812\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0973 | 0.515737 | 0.257869 | − | 0.966180i | \(-0.416980\pi\) | ||||
0.257869 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(464\) | −2.99446 | −0.139014 | ||||||||
\(465\) | −14.5727 | −0.675793 | ||||||||
\(466\) | −11.9807 | −0.554995 | ||||||||
\(467\) | 24.6923 | 1.14262 | 0.571311 | − | 0.820734i | \(-0.306435\pi\) | ||||
0.571311 | + | 0.820734i | \(0.306435\pi\) | |||||||
\(468\) | 29.3777 | 1.35798 | ||||||||
\(469\) | 0.0485769 | 0.00224307 | ||||||||
\(470\) | −5.14520 | −0.237330 | ||||||||
\(471\) | 48.1276 | 2.21760 | ||||||||
\(472\) | 13.8292 | 0.636540 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.01726 | 0.138587 | ||||||||
\(475\) | 7.81494 | 0.358574 | ||||||||
\(476\) | −2.32986 | −0.106789 | ||||||||
\(477\) | 3.03693 | 0.139051 | ||||||||
\(478\) | 6.46612 | 0.295753 | ||||||||
\(479\) | 31.2114 | 1.42608 | 0.713042 | − | 0.701121i | \(-0.247317\pi\) | ||||
0.713042 | + | 0.701121i | \(0.247317\pi\) | |||||||
\(480\) | −2.86564 | −0.130798 | ||||||||
\(481\) | −7.81700 | −0.356424 | ||||||||
\(482\) | −20.3441 | −0.926646 | ||||||||
\(483\) | 22.8802 | 1.04109 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.33180 | −0.242104 | ||||||||
\(486\) | 11.7710 | 0.533945 | ||||||||
\(487\) | 3.02777 | 0.137201 | 0.0686007 | − | 0.997644i | \(-0.478147\pi\) | ||||
0.0686007 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(488\) | −7.82443 | −0.354195 | ||||||||
\(489\) | −6.96466 | −0.314953 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 14.8069 | 0.668228 | 0.334114 | − | 0.942533i | \(-0.391563\pi\) | ||||
0.334114 | + | 0.942533i | \(0.391563\pi\) | |||||||
\(492\) | 19.7773 | 0.891630 | ||||||||
\(493\) | −6.97666 | −0.314213 | ||||||||
\(494\) | 44.0504 | 1.98192 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.08533 | 0.228338 | ||||||||
\(497\) | −4.45361 | −0.199772 | ||||||||
\(498\) | 31.0391 | 1.39089 | ||||||||
\(499\) | −6.99445 | −0.313115 | −0.156557 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156557 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −31.6096 | −1.41221 | ||||||||
\(502\) | 12.5842 | 0.561663 | ||||||||
\(503\) | 1.93800 | 0.0864112 | 0.0432056 | − | 0.999066i | \(-0.486243\pi\) | ||||
0.0432056 | + | 0.999066i | \(0.486243\pi\) | |||||||
\(504\) | −5.21187 | −0.232155 | ||||||||
\(505\) | 18.2701 | 0.813011 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −53.7947 | −2.38910 | ||||||||
\(508\) | −6.58727 | −0.292263 | ||||||||
\(509\) | 12.9518 | 0.574081 | 0.287040 | − | 0.957919i | \(-0.407329\pi\) | ||||
0.287040 | + | 0.957919i | \(0.407329\pi\) | |||||||
\(510\) | −6.67652 | −0.295641 | ||||||||
\(511\) | −0.336814 | −0.0148998 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −49.5342 | −2.18699 | ||||||||
\(514\) | 3.45995 | 0.152612 | ||||||||
\(515\) | −11.2347 | −0.495061 | ||||||||
\(516\) | −33.0959 | −1.45697 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.38681 | 0.0609327 | ||||||||
\(519\) | 42.1095 | 1.84840 | ||||||||
\(520\) | 5.63670 | 0.247185 | ||||||||
\(521\) | −5.90459 | −0.258685 | −0.129342 | − | 0.991600i | \(-0.541287\pi\) | ||||
−0.129342 | + | 0.991600i | \(0.541287\pi\) | |||||||
\(522\) | −15.6067 | −0.683088 | ||||||||
\(523\) | 18.1944 | 0.795587 | 0.397794 | − | 0.917475i | \(-0.369776\pi\) | ||||
0.397794 | + | 0.917475i | \(0.369776\pi\) | |||||||
\(524\) | −1.20821 | −0.0527808 | ||||||||
\(525\) | 2.86564 | 0.125067 | ||||||||
\(526\) | 8.01789 | 0.349597 | ||||||||
\(527\) | 11.8481 | 0.516111 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.7497 | 1.77173 | ||||||||
\(530\) | 0.582695 | 0.0253106 | ||||||||
\(531\) | 72.0759 | 3.12783 | ||||||||
\(532\) | −7.81494 | −0.338821 | ||||||||
\(533\) | −38.9019 | −1.68503 | ||||||||
\(534\) | 53.0912 | 2.29748 | ||||||||
\(535\) | −4.89157 | −0.211481 | ||||||||
\(536\) | −0.0485769 | −0.00209820 | ||||||||
\(537\) | −12.9353 | −0.558198 | ||||||||
\(538\) | −18.5650 | −0.800393 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.33840 | −0.272761 | ||||||||
\(541\) | 15.1525 | 0.651457 | 0.325729 | − | 0.945463i | \(-0.394390\pi\) | ||||
0.325729 | + | 0.945463i | \(0.394390\pi\) | |||||||
\(542\) | −25.2051 | −1.08265 | ||||||||
\(543\) | 29.1636 | 1.25153 | ||||||||
\(544\) | 2.32986 | 0.0998918 | ||||||||
\(545\) | −6.26442 | −0.268338 | ||||||||
\(546\) | 16.1527 | 0.691272 | ||||||||
\(547\) | 10.3369 | 0.441975 | 0.220988 | − | 0.975277i | \(-0.429072\pi\) | ||||
0.220988 | + | 0.975277i | \(0.429072\pi\) | |||||||
\(548\) | 14.0829 | 0.601590 | ||||||||
\(549\) | −40.7799 | −1.74044 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.4015 | −0.996938 | ||||||||
\(552\) | −22.8802 | −0.973846 | ||||||||
\(553\) | 1.05291 | 0.0447743 | ||||||||
\(554\) | 12.2281 | 0.519521 | ||||||||
\(555\) | 3.97408 | 0.168690 | ||||||||
\(556\) | −2.74290 | −0.116325 | ||||||||
\(557\) | 6.41056 | 0.271624 | 0.135812 | − | 0.990735i | \(-0.456636\pi\) | ||||
0.135812 | + | 0.990735i | \(0.456636\pi\) | |||||||
\(558\) | 26.5041 | 1.12201 | ||||||||
\(559\) | 65.0996 | 2.75342 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.5934 | −1.12178 | ||||||||
\(563\) | 36.3501 | 1.53197 | 0.765986 | − | 0.642857i | \(-0.222251\pi\) | ||||
0.765986 | + | 0.642857i | \(0.222251\pi\) | |||||||
\(564\) | 14.7443 | 0.620845 | ||||||||
\(565\) | 10.1651 | 0.427649 | ||||||||
\(566\) | 13.7220 | 0.576779 | ||||||||
\(567\) | −2.52795 | −0.106164 | ||||||||
\(568\) | 4.45361 | 0.186869 | ||||||||
\(569\) | 45.1901 | 1.89447 | 0.947234 | − | 0.320544i | \(-0.103866\pi\) | ||||
0.947234 | + | 0.320544i | \(0.103866\pi\) | |||||||
\(570\) | −22.3948 | −0.938014 | ||||||||
\(571\) | −24.7479 | −1.03567 | −0.517834 | − | 0.855481i | \(-0.673262\pi\) | ||||
−0.517834 | + | 0.855481i | \(0.673262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.3630 | −1.43554 | ||||||||
\(574\) | 6.90154 | 0.288065 | ||||||||
\(575\) | 7.98434 | 0.332970 | ||||||||
\(576\) | 5.21187 | 0.217161 | ||||||||
\(577\) | −2.62695 | −0.109361 | −0.0546807 | − | 0.998504i | \(-0.517414\pi\) | ||||
−0.0546807 | + | 0.998504i | \(0.517414\pi\) | |||||||
\(578\) | −11.5718 | −0.481322 | ||||||||
\(579\) | −51.2228 | −2.12875 | ||||||||
\(580\) | −2.99446 | −0.124338 | ||||||||
\(581\) | 10.8315 | 0.449366 | ||||||||
\(582\) | 15.2790 | 0.633334 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.336814 | 0.0139374 | ||||||||
\(585\) | 29.3777 | 1.21462 | ||||||||
\(586\) | −0.714463 | −0.0295142 | ||||||||
\(587\) | 12.8971 | 0.532319 | 0.266159 | − | 0.963929i | \(-0.414245\pi\) | ||||
0.266159 | + | 0.963929i | \(0.414245\pi\) | |||||||
\(588\) | −2.86564 | −0.118177 | ||||||||
\(589\) | 39.7416 | 1.63752 | ||||||||
\(590\) | 13.8292 | 0.569339 | ||||||||
\(591\) | −33.7775 | −1.38942 | ||||||||
\(592\) | −1.38681 | −0.0569973 | ||||||||
\(593\) | 33.4157 | 1.37222 | 0.686110 | − | 0.727498i | \(-0.259317\pi\) | ||||
0.686110 | + | 0.727498i | \(0.259317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.32986 | −0.0955149 | ||||||||
\(596\) | 17.1642 | 0.703075 | ||||||||
\(597\) | 39.9303 | 1.63424 | ||||||||
\(598\) | 45.0053 | 1.84040 | ||||||||
\(599\) | 34.4823 | 1.40891 | 0.704455 | − | 0.709749i | \(-0.251192\pi\) | ||||
0.704455 | + | 0.709749i | \(0.251192\pi\) | |||||||
\(600\) | −2.86564 | −0.116989 | ||||||||
\(601\) | 32.7460 | 1.33574 | 0.667869 | − | 0.744279i | \(-0.267207\pi\) | ||||
0.667869 | + | 0.744279i | \(0.267207\pi\) | |||||||
\(602\) | −11.5492 | −0.470712 | ||||||||
\(603\) | −0.253176 | −0.0103101 | ||||||||
\(604\) | −5.94304 | −0.241819 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −52.3556 | −2.12680 | ||||||||
\(607\) | 5.79559 | 0.235236 | 0.117618 | − | 0.993059i | \(-0.462474\pi\) | ||||
0.117618 | + | 0.993059i | \(0.462474\pi\) | |||||||
\(608\) | 7.81494 | 0.316938 | ||||||||
\(609\) | −8.58103 | −0.347721 | ||||||||
\(610\) | −7.82443 | −0.316802 | ||||||||
\(611\) | −29.0019 | −1.17329 | ||||||||
\(612\) | 12.1429 | 0.490848 | ||||||||
\(613\) | 39.3606 | 1.58976 | 0.794879 | − | 0.606767i | \(-0.207534\pi\) | ||||
0.794879 | + | 0.606767i | \(0.207534\pi\) | |||||||
\(614\) | 19.3442 | 0.780667 | ||||||||
\(615\) | 19.7773 | 0.797498 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3175 | −0.656918 | −0.328459 | − | 0.944518i | \(-0.606529\pi\) | ||||
−0.328459 | + | 0.944518i | \(0.606529\pi\) | |||||||
\(618\) | 32.1946 | 1.29506 | ||||||||
\(619\) | −44.7221 | −1.79753 | −0.898767 | − | 0.438427i | \(-0.855536\pi\) | ||||
−0.898767 | + | 0.438427i | \(0.855536\pi\) | |||||||
\(620\) | 5.08533 | 0.204232 | ||||||||
\(621\) | −50.6079 | −2.03083 | ||||||||
\(622\) | 1.82729 | 0.0732675 | ||||||||
\(623\) | 18.5268 | 0.742263 | ||||||||
\(624\) | −16.1527 | −0.646626 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.83108 | −0.392929 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.7947 | −0.670183 | ||||||||
\(629\) | −3.23106 | −0.128831 | ||||||||
\(630\) | −5.21187 | −0.207646 | ||||||||
\(631\) | −30.1105 | −1.19868 | −0.599340 | − | 0.800495i | \(-0.704570\pi\) | ||||
−0.599340 | + | 0.800495i | \(0.704570\pi\) | |||||||
\(632\) | −1.05291 | −0.0418825 | ||||||||
\(633\) | 75.7951 | 3.01258 | ||||||||
\(634\) | −13.8545 | −0.550232 | ||||||||
\(635\) | −6.58727 | −0.261408 | ||||||||
\(636\) | −1.66979 | −0.0662115 | ||||||||
\(637\) | 5.63670 | 0.223334 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.2116 | 0.918237 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.937781 | −0.0370401 | −0.0185201 | − | 0.999828i | \(-0.505895\pi\) | ||||
−0.0185201 | + | 0.999828i | \(0.505895\pi\) | |||||||
\(642\) | 14.0175 | 0.553225 | ||||||||
\(643\) | 44.9904 | 1.77425 | 0.887125 | − | 0.461529i | \(-0.152699\pi\) | ||||
0.887125 | + | 0.461529i | \(0.152699\pi\) | |||||||
\(644\) | −7.98434 | −0.314627 | ||||||||
\(645\) | −33.0959 | −1.30315 | ||||||||
\(646\) | 18.2077 | 0.716373 | ||||||||
\(647\) | −32.9160 | −1.29406 | −0.647032 | − | 0.762463i | \(-0.723990\pi\) | ||||
−0.647032 | + | 0.762463i | \(0.723990\pi\) | |||||||
\(648\) | 2.52795 | 0.0993072 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.63670 | 0.221089 | ||||||||
\(651\) | 14.5727 | 0.571149 | ||||||||
\(652\) | 2.43041 | 0.0951821 | ||||||||
\(653\) | −3.32100 | −0.129961 | −0.0649804 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649804 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(654\) | 17.9516 | 0.701961 | ||||||||
\(655\) | −1.20821 | −0.0472086 | ||||||||
\(656\) | −6.90154 | −0.269460 | ||||||||
\(657\) | 1.75543 | 0.0684857 | ||||||||
\(658\) | 5.14520 | 0.200581 | ||||||||
\(659\) | 20.5642 | 0.801069 | 0.400535 | − | 0.916282i | \(-0.368824\pi\) | ||||
0.400535 | + | 0.916282i | \(0.368824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.9387 | −1.70902 | −0.854508 | − | 0.519438i | \(-0.826141\pi\) | ||||
−0.854508 | + | 0.519438i | \(0.826141\pi\) | |||||||
\(662\) | 8.02084 | 0.311739 | ||||||||
\(663\) | −37.6335 | −1.46157 | ||||||||
\(664\) | −10.8315 | −0.420343 | ||||||||
\(665\) | −7.81494 | −0.303050 | ||||||||
\(666\) | −7.22784 | −0.280073 | ||||||||
\(667\) | −23.9088 | −0.925752 | ||||||||
\(668\) | 11.0306 | 0.426786 | ||||||||
\(669\) | −70.4640 | −2.72430 | ||||||||
\(670\) | −0.0485769 | −0.00187669 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.86564 | 0.110544 | ||||||||
\(673\) | 0.623385 | 0.0240297 | 0.0120149 | − | 0.999928i | \(-0.496175\pi\) | ||||
0.0120149 | + | 0.999928i | \(0.496175\pi\) | |||||||
\(674\) | 11.6060 | 0.447045 | ||||||||
\(675\) | −6.33840 | −0.243965 | ||||||||
\(676\) | 18.7723 | 0.722013 | ||||||||
\(677\) | 30.6611 | 1.17840 | 0.589200 | − | 0.807987i | \(-0.299443\pi\) | ||||
0.589200 | + | 0.807987i | \(0.299443\pi\) | |||||||
\(678\) | −29.1294 | −1.11871 | ||||||||
\(679\) | 5.33180 | 0.204616 | ||||||||
\(680\) | 2.32986 | 0.0893460 | ||||||||
\(681\) | −16.0258 | −0.614112 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.08570 | −0.156335 | −0.0781676 | − | 0.996940i | \(-0.524907\pi\) | ||||
−0.0781676 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(684\) | 40.7304 | 1.55737 | ||||||||
\(685\) | 14.0829 | 0.538079 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 23.2214 | 0.885951 | ||||||||
\(688\) | 11.5492 | 0.440311 | ||||||||
\(689\) | 3.28447 | 0.125128 | ||||||||
\(690\) | −22.8802 | −0.871035 | ||||||||
\(691\) | −9.75385 | −0.371054 | −0.185527 | − | 0.982639i | \(-0.559399\pi\) | ||||
−0.185527 | + | 0.982639i | \(0.559399\pi\) | |||||||
\(692\) | −14.6947 | −0.558607 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.4301 | 1.00327 | ||||||||
\(695\) | −2.74290 | −0.104044 | ||||||||
\(696\) | 8.58103 | 0.325263 | ||||||||
\(697\) | −16.0796 | −0.609059 | ||||||||
\(698\) | −27.3777 | −1.03626 | ||||||||
\(699\) | 34.3323 | 1.29857 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 8.34928 | 0.315348 | 0.157674 | − | 0.987491i | \(-0.449600\pi\) | ||||
0.157674 | + | 0.987491i | \(0.449600\pi\) | |||||||
\(702\) | −35.7276 | −1.34845 | ||||||||
\(703\) | −10.8378 | −0.408755 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7443 | 0.555301 | ||||||||
\(706\) | 21.3772 | 0.804541 | ||||||||
\(707\) | −18.2701 | −0.687119 | ||||||||
\(708\) | −39.6294 | −1.48937 | ||||||||
\(709\) | 41.6502 | 1.56421 | 0.782103 | − | 0.623149i | \(-0.214147\pi\) | ||||
0.782103 | + | 0.623149i | \(0.214147\pi\) | |||||||
\(710\) | 4.45361 | 0.167141 | ||||||||
\(711\) | −5.48763 | −0.205802 | ||||||||
\(712\) | −18.5268 | −0.694323 | ||||||||
\(713\) | 40.6030 | 1.52059 | ||||||||
\(714\) | 6.67652 | 0.249863 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.51392 | 0.168693 | ||||||||
\(717\) | −18.5295 | −0.691998 | ||||||||
\(718\) | 10.8904 | 0.406427 | ||||||||
\(719\) | 27.1930 | 1.01413 | 0.507064 | − | 0.861909i | \(-0.330731\pi\) | ||||
0.507064 | + | 0.861909i | \(0.330731\pi\) | |||||||
\(720\) | 5.21187 | 0.194235 | ||||||||
\(721\) | 11.2347 | 0.418403 | ||||||||
\(722\) | 42.0733 | 1.56581 | ||||||||
\(723\) | 58.2986 | 2.16815 | ||||||||
\(724\) | −10.1770 | −0.378225 | ||||||||
\(725\) | −2.99446 | −0.111211 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.4443 | 0.980766 | 0.490383 | − | 0.871507i | \(-0.336857\pi\) | ||||
0.490383 | + | 0.871507i | \(0.336857\pi\) | |||||||
\(728\) | −5.63670 | −0.208910 | ||||||||
\(729\) | −41.3153 | −1.53020 | ||||||||
\(730\) | 0.336814 | 0.0124660 | ||||||||
\(731\) | 26.9081 | 0.995232 | ||||||||
\(732\) | 22.4220 | 0.828740 | ||||||||
\(733\) | −25.1965 | −0.930653 | −0.465326 | − | 0.885139i | \(-0.654063\pi\) | ||||
−0.465326 | + | 0.885139i | \(0.654063\pi\) | |||||||
\(734\) | 11.3108 | 0.417487 | ||||||||
\(735\) | −2.86564 | −0.105701 | ||||||||
\(736\) | 7.98434 | 0.294307 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −35.9699 | −1.32407 | ||||||||
\(739\) | −5.90682 | −0.217286 | −0.108643 | − | 0.994081i | \(-0.534651\pi\) | ||||
−0.108643 | + | 0.994081i | \(0.534651\pi\) | |||||||
\(740\) | −1.38681 | −0.0509800 | ||||||||
\(741\) | −126.233 | −4.63727 | ||||||||
\(742\) | −0.582695 | −0.0213914 | ||||||||
\(743\) | −19.5944 | −0.718847 | −0.359424 | − | 0.933175i | \(-0.617027\pi\) | ||||
−0.359424 | + | 0.933175i | \(0.617027\pi\) | |||||||
\(744\) | −14.5727 | −0.534261 | ||||||||
\(745\) | 17.1642 | 0.628849 | ||||||||
\(746\) | −11.6658 | −0.427116 | ||||||||
\(747\) | −56.4523 | −2.06548 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.89157 | 0.178734 | ||||||||
\(750\) | −2.86564 | −0.104638 | ||||||||
\(751\) | 0.465285 | 0.0169785 | 0.00848925 | − | 0.999964i | \(-0.497298\pi\) | ||||
0.00848925 | + | 0.999964i | \(0.497298\pi\) | |||||||
\(752\) | −5.14520 | −0.187626 | ||||||||
\(753\) | −36.0619 | −1.31417 | ||||||||
\(754\) | −16.8789 | −0.614692 | ||||||||
\(755\) | −5.94304 | −0.216289 | ||||||||
\(756\) | 6.33840 | 0.230525 | ||||||||
\(757\) | −6.85681 | −0.249215 | −0.124607 | − | 0.992206i | \(-0.539767\pi\) | ||||
−0.124607 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(758\) | 0.617088 | 0.0224136 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.81494 | 0.283478 | ||||||||
\(761\) | −41.5119 | −1.50481 | −0.752403 | − | 0.658703i | \(-0.771105\pi\) | ||||
−0.752403 | + | 0.658703i | \(0.771105\pi\) | |||||||
\(762\) | 18.8767 | 0.683831 | ||||||||
\(763\) | 6.26442 | 0.226787 | ||||||||
\(764\) | 11.9914 | 0.433834 | ||||||||
\(765\) | 12.1429 | 0.439028 | ||||||||
\(766\) | −26.4471 | −0.955573 | ||||||||
\(767\) | 77.9510 | 2.81465 | ||||||||
\(768\) | −2.86564 | −0.103405 | ||||||||
\(769\) | 17.8632 | 0.644164 | 0.322082 | − | 0.946712i | \(-0.395617\pi\) | ||||
0.322082 | + | 0.946712i | \(0.395617\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.91495 | −0.357078 | ||||||||
\(772\) | 17.8748 | 0.643330 | ||||||||
\(773\) | 9.91463 | 0.356604 | 0.178302 | − | 0.983976i | \(-0.442940\pi\) | ||||
0.178302 | + | 0.983976i | \(0.442940\pi\) | |||||||
\(774\) | 60.1931 | 2.16360 | ||||||||
\(775\) | 5.08533 | 0.182670 | ||||||||
\(776\) | −5.33180 | −0.191400 | ||||||||
\(777\) | −3.97408 | −0.142569 | ||||||||
\(778\) | 1.60446 | 0.0575226 | ||||||||
\(779\) | −53.9352 | −1.93243 | ||||||||
\(780\) | −16.1527 | −0.578360 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 18.6024 | 0.665220 | ||||||||
\(783\) | 18.9801 | 0.678293 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −16.7947 | −0.599430 | ||||||||
\(786\) | 3.46228 | 0.123496 | ||||||||
\(787\) | 0.812618 | 0.0289667 | 0.0144834 | − | 0.999895i | \(-0.495390\pi\) | ||||
0.0144834 | + | 0.999895i | \(0.495390\pi\) | |||||||
\(788\) | 11.7871 | 0.419897 | ||||||||
\(789\) | −22.9763 | −0.817979 | ||||||||
\(790\) | −1.05291 | −0.0374609 | ||||||||
\(791\) | −10.1651 | −0.361429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.1039 | −1.56618 | ||||||||
\(794\) | 5.28819 | 0.187671 | ||||||||
\(795\) | −1.66979 | −0.0592214 | ||||||||
\(796\) | −13.9342 | −0.493884 | ||||||||
\(797\) | 32.3331 | 1.14530 | 0.572649 | − | 0.819800i | \(-0.305916\pi\) | ||||
0.572649 | + | 0.819800i | \(0.305916\pi\) | |||||||
\(798\) | 22.3948 | 0.792766 | ||||||||
\(799\) | −11.9876 | −0.424090 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −96.5595 | −3.41176 | ||||||||
\(802\) | −13.6059 | −0.480441 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.139204 | 0.00490934 | ||||||||
\(805\) | −7.98434 | −0.281411 | ||||||||
\(806\) | 28.6645 | 1.00966 | ||||||||
\(807\) | 53.2005 | 1.87275 | ||||||||
\(808\) | 18.2701 | 0.642741 | ||||||||
\(809\) | 24.5501 | 0.863135 | 0.431568 | − | 0.902081i | \(-0.357961\pi\) | ||||
0.431568 | + | 0.902081i | \(0.357961\pi\) | |||||||
\(810\) | 2.52795 | 0.0888230 | ||||||||
\(811\) | −41.3394 | −1.45162 | −0.725812 | − | 0.687893i | \(-0.758536\pi\) | ||||
−0.725812 | + | 0.687893i | \(0.758536\pi\) | |||||||
\(812\) | 2.99446 | 0.105085 | ||||||||
\(813\) | 72.2287 | 2.53317 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.43041 | 0.0851335 | ||||||||
\(816\) | −6.67652 | −0.233725 | ||||||||
\(817\) | 90.2567 | 3.15768 | ||||||||
\(818\) | 3.40230 | 0.118959 | ||||||||
\(819\) | −29.3777 | −1.02654 | ||||||||
\(820\) | −6.90154 | −0.241012 | ||||||||
\(821\) | −16.0197 | −0.559090 | −0.279545 | − | 0.960133i | \(-0.590184\pi\) | ||||
−0.279545 | + | 0.960133i | \(0.590184\pi\) | |||||||
\(822\) | −40.3564 | −1.40759 | ||||||||
\(823\) | 19.3583 | 0.674787 | 0.337394 | − | 0.941364i | \(-0.390455\pi\) | ||||
0.337394 | + | 0.941364i | \(0.390455\pi\) | |||||||
\(824\) | −11.2347 | −0.391380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.8292 | −0.481179 | ||||||||
\(827\) | −43.1757 | −1.50136 | −0.750682 | − | 0.660663i | \(-0.770275\pi\) | ||||
−0.750682 | + | 0.660663i | \(0.770275\pi\) | |||||||
\(828\) | 41.6133 | 1.44616 | ||||||||
\(829\) | −38.5839 | −1.34007 | −0.670037 | − | 0.742327i | \(-0.733722\pi\) | ||||
−0.670037 | + | 0.742327i | \(0.733722\pi\) | |||||||
\(830\) | −10.8315 | −0.375966 | ||||||||
\(831\) | −35.0412 | −1.21557 | ||||||||
\(832\) | 5.63670 | 0.195417 | ||||||||
\(833\) | 2.32986 | 0.0807248 | ||||||||
\(834\) | 7.86016 | 0.272175 | ||||||||
\(835\) | 11.0306 | 0.381729 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.2329 | −1.11413 | ||||||||
\(838\) | −39.5263 | −1.36541 | ||||||||
\(839\) | 9.31984 | 0.321757 | 0.160878 | − | 0.986974i | \(-0.448567\pi\) | ||||
0.160878 | + | 0.986974i | \(0.448567\pi\) | |||||||
\(840\) | 2.86564 | 0.0988738 | ||||||||
\(841\) | −20.0332 | −0.690800 | ||||||||
\(842\) | −15.6617 | −0.539738 | ||||||||
\(843\) | 76.2071 | 2.62471 | ||||||||
\(844\) | −26.4497 | −0.910435 | ||||||||
\(845\) | 18.7723 | 0.645788 | ||||||||
\(846\) | −26.8161 | −0.921956 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.582695 | 0.0200098 | ||||||||
\(849\) | −39.3223 | −1.34954 | ||||||||
\(850\) | 2.32986 | 0.0799135 | ||||||||
\(851\) | −11.0727 | −0.379568 | ||||||||
\(852\) | −12.7624 | −0.437233 | ||||||||
\(853\) | −9.65688 | −0.330645 | −0.165323 | − | 0.986240i | \(-0.552867\pi\) | ||||
−0.165323 | + | 0.986240i | \(0.552867\pi\) | |||||||
\(854\) | 7.82443 | 0.267747 | ||||||||
\(855\) | 40.7304 | 1.39295 | ||||||||
\(856\) | −4.89157 | −0.167190 | ||||||||
\(857\) | −7.88344 | −0.269293 | −0.134647 | − | 0.990894i | \(-0.542990\pi\) | ||||
−0.134647 | + | 0.990894i | \(0.542990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.00176 | 0.307136 | 0.153568 | − | 0.988138i | \(-0.450924\pi\) | ||||
0.153568 | + | 0.988138i | \(0.450924\pi\) | |||||||
\(860\) | 11.5492 | 0.393826 | ||||||||
\(861\) | −19.7773 | −0.674009 | ||||||||
\(862\) | −5.63150 | −0.191810 | ||||||||
\(863\) | −14.5890 | −0.496616 | −0.248308 | − | 0.968681i | \(-0.579874\pi\) | ||||
−0.248308 | + | 0.968681i | \(0.579874\pi\) | |||||||
\(864\) | −6.33840 | −0.215637 | ||||||||
\(865\) | −14.6947 | −0.499633 | ||||||||
\(866\) | −34.5223 | −1.17311 | ||||||||
\(867\) | 33.1604 | 1.12619 | ||||||||
\(868\) | −5.08533 | −0.172607 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8.58103 | 0.290924 | ||||||||
\(871\) | −0.273813 | −0.00927781 | ||||||||
\(872\) | −6.26442 | −0.212140 | ||||||||
\(873\) | −27.7886 | −0.940502 | ||||||||
\(874\) | 62.3972 | 2.11062 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −0.965185 | −0.0326106 | ||||||||
\(877\) | −17.0812 | −0.576791 | −0.288396 | − | 0.957511i | \(-0.593122\pi\) | ||||
−0.288396 | + | 0.957511i | \(0.593122\pi\) | |||||||
\(878\) | −30.0533 | −1.01425 | ||||||||
\(879\) | 2.04739 | 0.0690568 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.9541 | −1.04287 | −0.521435 | − | 0.853291i | \(-0.674603\pi\) | ||||
−0.521435 | + | 0.853291i | \(0.674603\pi\) | |||||||
\(882\) | 5.21187 | 0.175493 | ||||||||
\(883\) | −13.5966 | −0.457561 | −0.228781 | − | 0.973478i | \(-0.573474\pi\) | ||||
−0.228781 | + | 0.973478i | \(0.573474\pi\) | |||||||
\(884\) | 13.1327 | 0.441700 | ||||||||
\(885\) | −39.6294 | −1.33213 | ||||||||
\(886\) | −32.0651 | −1.07725 | ||||||||
\(887\) | −17.1901 | −0.577188 | −0.288594 | − | 0.957452i | \(-0.593188\pi\) | ||||
−0.288594 | + | 0.957452i | \(0.593188\pi\) | |||||||
\(888\) | 3.97408 | 0.133361 | ||||||||
\(889\) | 6.58727 | 0.220930 | ||||||||
\(890\) | −18.5268 | −0.621021 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.5893 | 0.823311 | ||||||||
\(893\) | −40.2094 | −1.34556 | ||||||||
\(894\) | −49.1865 | −1.64504 | ||||||||
\(895\) | 4.51392 | 0.150884 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −128.969 | −4.30614 | ||||||||
\(898\) | −9.27706 | −0.309579 | ||||||||
\(899\) | −15.2278 | −0.507876 | ||||||||
\(900\) | 5.21187 | 0.173729 | ||||||||
\(901\) | 1.35760 | 0.0452281 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.0959 | 1.10136 | ||||||||
\(904\) | 10.1651 | 0.338086 | ||||||||
\(905\) | −10.1770 | −0.338295 | ||||||||
\(906\) | 17.0306 | 0.565803 | ||||||||
\(907\) | −23.5921 | −0.783363 | −0.391682 | − | 0.920101i | \(-0.628107\pi\) | ||||
−0.391682 | + | 0.920101i | \(0.628107\pi\) | |||||||
\(908\) | 5.59242 | 0.185591 | ||||||||
\(909\) | 95.2215 | 3.15830 | ||||||||
\(910\) | −5.63670 | −0.186855 | ||||||||
\(911\) | 50.0697 | 1.65888 | 0.829441 | − | 0.558594i | \(-0.188659\pi\) | ||||
0.829441 | + | 0.558594i | \(0.188659\pi\) | |||||||
\(912\) | −22.3948 | −0.741565 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 20.0782 | 0.664127 | ||||||||
\(915\) | 22.4220 | 0.741247 | ||||||||
\(916\) | −8.10340 | −0.267744 | ||||||||
\(917\) | 1.20821 | 0.0398985 | ||||||||
\(918\) | −14.7676 | −0.487403 | ||||||||
\(919\) | 13.1628 | 0.434200 | 0.217100 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217100 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(920\) | 7.98434 | 0.263236 | ||||||||
\(921\) | −55.4333 | −1.82659 | ||||||||
\(922\) | −14.6490 | −0.482439 | ||||||||
\(923\) | 25.1036 | 0.826296 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.38681 | −0.0455979 | ||||||||
\(926\) | 11.0973 | 0.364681 | ||||||||
\(927\) | −58.5539 | −1.92316 | ||||||||
\(928\) | −2.99446 | −0.0982979 | ||||||||
\(929\) | −9.87262 | −0.323910 | −0.161955 | − | 0.986798i | \(-0.551780\pi\) | ||||
−0.161955 | + | 0.986798i | \(0.551780\pi\) | |||||||
\(930\) | −14.5727 | −0.477858 | ||||||||
\(931\) | 7.81494 | 0.256124 | ||||||||
\(932\) | −11.9807 | −0.392441 | ||||||||
\(933\) | −5.23634 | −0.171430 | ||||||||
\(934\) | 24.6923 | 0.807956 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 29.3777 | 0.960240 | ||||||||
\(937\) | −4.81983 | −0.157457 | −0.0787285 | − | 0.996896i | \(-0.525086\pi\) | ||||
−0.0787285 | + | 0.996896i | \(0.525086\pi\) | |||||||
\(938\) | 0.0485769 | 0.00158609 | ||||||||
\(939\) | 28.1723 | 0.919368 | ||||||||
\(940\) | −5.14520 | −0.167818 | ||||||||
\(941\) | 57.3904 | 1.87087 | 0.935437 | − | 0.353493i | \(-0.115006\pi\) | ||||
0.935437 | + | 0.353493i | \(0.115006\pi\) | |||||||
\(942\) | 48.1276 | 1.56808 | ||||||||
\(943\) | −55.1043 | −1.79444 | ||||||||
\(944\) | 13.8292 | 0.450102 | ||||||||
\(945\) | 6.33840 | 0.206188 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.22221 | −0.137203 | −0.0686017 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686017 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(948\) | 3.01726 | 0.0979959 | ||||||||
\(949\) | 1.89852 | 0.0616284 | ||||||||
\(950\) | 7.81494 | 0.253550 | ||||||||
\(951\) | 39.7019 | 1.28742 | ||||||||
\(952\) | −2.32986 | −0.0755111 | ||||||||
\(953\) | 5.10500 | 0.165367 | 0.0826836 | − | 0.996576i | \(-0.473651\pi\) | ||||
0.0826836 | + | 0.996576i | \(0.473651\pi\) | |||||||
\(954\) | 3.03693 | 0.0983241 | ||||||||
\(955\) | 11.9914 | 0.388033 | ||||||||
\(956\) | 6.46612 | 0.209129 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.2114 | 1.00839 | ||||||||
\(959\) | −14.0829 | −0.454759 | ||||||||
\(960\) | −2.86564 | −0.0924880 | ||||||||
\(961\) | −5.13941 | −0.165787 | ||||||||
\(962\) | −7.81700 | −0.252030 | ||||||||
\(963\) | −25.4942 | −0.821539 | ||||||||
\(964\) | −20.3441 | −0.655238 | ||||||||
\(965\) | 17.8748 | 0.575412 | ||||||||
\(966\) | 22.8802 | 0.736159 | ||||||||
\(967\) | −61.6521 | −1.98260 | −0.991298 | − | 0.131633i | \(-0.957978\pi\) | ||||
−0.991298 | + | 0.131633i | \(0.957978\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −52.1766 | −1.67616 | ||||||||
\(970\) | −5.33180 | −0.171194 | ||||||||
\(971\) | −26.0709 | −0.836656 | −0.418328 | − | 0.908296i | \(-0.637384\pi\) | ||||
−0.418328 | + | 0.908296i | \(0.637384\pi\) | |||||||
\(972\) | 11.7710 | 0.377556 | ||||||||
\(973\) | 2.74290 | 0.0879334 | ||||||||
\(974\) | 3.02777 | 0.0970160 | ||||||||
\(975\) | −16.1527 | −0.517301 | ||||||||
\(976\) | −7.82443 | −0.250454 | ||||||||
\(977\) | 19.0437 | 0.609261 | 0.304631 | − | 0.952471i | \(-0.401467\pi\) | ||||
0.304631 | + | 0.952471i | \(0.401467\pi\) | |||||||
\(978\) | −6.96466 | −0.222705 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −32.6493 | −1.04241 | ||||||||
\(982\) | 14.8069 | 0.472509 | ||||||||
\(983\) | −19.3347 | −0.616681 | −0.308340 | − | 0.951276i | \(-0.599774\pi\) | ||||
−0.308340 | + | 0.951276i | \(0.599774\pi\) | |||||||
\(984\) | 19.7773 | 0.630478 | ||||||||
\(985\) | 11.7871 | 0.375568 | ||||||||
\(986\) | −6.97666 | −0.222182 | ||||||||
\(987\) | −14.7443 | −0.469315 | ||||||||
\(988\) | 44.0504 | 1.40143 | ||||||||
\(989\) | 92.2131 | 2.93221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.4567 | −0.903958 | −0.451979 | − | 0.892029i | \(-0.649282\pi\) | ||||
−0.451979 | + | 0.892029i | \(0.649282\pi\) | |||||||
\(992\) | 5.08533 | 0.161459 | ||||||||
\(993\) | −22.9848 | −0.729401 | ||||||||
\(994\) | −4.45361 | −0.141260 | ||||||||
\(995\) | −13.9342 | −0.441743 | ||||||||
\(996\) | 31.0391 | 0.983511 | ||||||||
\(997\) | −14.1144 | −0.447008 | −0.223504 | − | 0.974703i | \(-0.571750\pi\) | ||||
−0.223504 | + | 0.974703i | \(0.571750\pi\) | |||||||
\(998\) | −6.99445 | −0.221406 | ||||||||
\(999\) | 8.79013 | 0.278107 |
(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 | 8470.2.a.dc.1.1 | 6 | ||
11.7 | odd | 10 | 770.2.n.j.71.3 | ✓ | 12 | ||
11.8 | odd | 10 | 770.2.n.j.141.3 | yes | 12 | ||
11.10 | odd | 2 | 8470.2.a.cw.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.j.71.3 | ✓ | 12 | 11.7 | odd | 10 | ||
770.2.n.j.141.3 | yes | 12 | 11.8 | odd | 10 | ||
8470.2.a.cw.1.1 | 6 | 11.10 | odd | 2 | |||
8470.2.a.dc.1.1 | 6 | 1.1 | even | 1 | trivial |