Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1019601.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 10x^{3} - x^{2} + 24x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.298978\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 | ||||||||
\(3\) | 2.44245 | 1.41015 | 0.705074 | − | 0.709134i | \(-0.250914\pi\) | ||||
0.705074 | + | 0.709134i | \(0.250914\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.14347 | −1.85302 | −0.926508 | − | 0.376276i | \(-0.877205\pi\) | ||||
−0.926508 | + | 0.376276i | \(0.877205\pi\) | |||||||
\(6\) | 2.44245 | 0.997125 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.96555 | 0.988516 | ||||||||
\(10\) | −4.14347 | −1.31028 | ||||||||
\(11\) | −4.70697 | −1.41921 | −0.709603 | − | 0.704602i | \(-0.751126\pi\) | ||||
−0.709603 | + | 0.704602i | \(0.751126\pi\) | |||||||
\(12\) | 2.44245 | 0.705074 | ||||||||
\(13\) | 1.91061 | 0.529908 | 0.264954 | − | 0.964261i | \(-0.414643\pi\) | ||||
0.264954 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.1202 | −2.61302 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.76714 | −0.671131 | −0.335565 | − | 0.942017i | \(-0.608927\pi\) | ||||
−0.335565 | + | 0.942017i | \(0.608927\pi\) | |||||||
\(18\) | 2.96555 | 0.698986 | ||||||||
\(19\) | −4.04040 | −0.926932 | −0.463466 | − | 0.886115i | \(-0.653394\pi\) | ||||
−0.463466 | + | 0.886115i | \(0.653394\pi\) | |||||||
\(20\) | −4.14347 | −0.926508 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.70697 | −1.00353 | ||||||||
\(23\) | −2.17268 | −0.453036 | −0.226518 | − | 0.974007i | \(-0.572734\pi\) | ||||
−0.226518 | + | 0.974007i | \(0.572734\pi\) | |||||||
\(24\) | 2.44245 | 0.498562 | ||||||||
\(25\) | 12.1683 | 2.43367 | ||||||||
\(26\) | 1.91061 | 0.374702 | ||||||||
\(27\) | −0.0841506 | −0.0161948 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −10.1202 | −1.84769 | ||||||||
\(31\) | 0.969044 | 0.174045 | 0.0870227 | − | 0.996206i | \(-0.472265\pi\) | ||||
0.0870227 | + | 0.996206i | \(0.472265\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −11.4965 | −2.00129 | ||||||||
\(34\) | −2.76714 | −0.474561 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.96555 | 0.494258 | ||||||||
\(37\) | −1.47340 | −0.242226 | −0.121113 | − | 0.992639i | \(-0.538646\pi\) | ||||
−0.121113 | + | 0.992639i | \(0.538646\pi\) | |||||||
\(38\) | −4.04040 | −0.655440 | ||||||||
\(39\) | 4.66657 | 0.747249 | ||||||||
\(40\) | −4.14347 | −0.655140 | ||||||||
\(41\) | −10.4741 | −1.63578 | −0.817891 | − | 0.575373i | \(-0.804857\pi\) | ||||
−0.817891 | + | 0.575373i | \(0.804857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.84520 | 1.19638 | 0.598191 | − | 0.801353i | \(-0.295886\pi\) | ||||
0.598191 | + | 0.801353i | \(0.295886\pi\) | |||||||
\(44\) | −4.70697 | −0.709603 | ||||||||
\(45\) | −12.2876 | −1.83173 | ||||||||
\(46\) | −2.17268 | −0.320345 | ||||||||
\(47\) | −11.7294 | −1.71091 | −0.855453 | − | 0.517880i | \(-0.826721\pi\) | ||||
−0.855453 | + | 0.517880i | \(0.826721\pi\) | |||||||
\(48\) | 2.44245 | 0.352537 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12.1683 | 1.72086 | ||||||||
\(51\) | −6.75860 | −0.946393 | ||||||||
\(52\) | 1.91061 | 0.264954 | ||||||||
\(53\) | −2.78082 | −0.381975 | −0.190988 | − | 0.981592i | \(-0.561169\pi\) | ||||
−0.190988 | + | 0.981592i | \(0.561169\pi\) | |||||||
\(54\) | −0.0841506 | −0.0114514 | ||||||||
\(55\) | 19.5032 | 2.62981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.86847 | −1.30711 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −3.41673 | −0.444820 | −0.222410 | − | 0.974953i | \(-0.571392\pi\) | ||||
−0.222410 | + | 0.974953i | \(0.571392\pi\) | |||||||
\(60\) | −10.1202 | −1.30651 | ||||||||
\(61\) | −11.4192 | −1.46208 | −0.731038 | − | 0.682337i | \(-0.760964\pi\) | ||||
−0.731038 | + | 0.682337i | \(0.760964\pi\) | |||||||
\(62\) | 0.969044 | 0.123069 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.91656 | −0.981929 | ||||||||
\(66\) | −11.4965 | −1.41512 | ||||||||
\(67\) | −2.27575 | −0.278027 | −0.139014 | − | 0.990290i | \(-0.544393\pi\) | ||||
−0.139014 | + | 0.990290i | \(0.544393\pi\) | |||||||
\(68\) | −2.76714 | −0.335565 | ||||||||
\(69\) | −5.30667 | −0.638848 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.24653 | −0.741327 | −0.370664 | − | 0.928767i | \(-0.620870\pi\) | ||||
−0.370664 | + | 0.928767i | \(0.620870\pi\) | |||||||
\(72\) | 2.96555 | 0.349493 | ||||||||
\(73\) | 13.5230 | 1.58274 | 0.791371 | − | 0.611336i | \(-0.209368\pi\) | ||||
0.791371 | + | 0.611336i | \(0.209368\pi\) | |||||||
\(74\) | −1.47340 | −0.171280 | ||||||||
\(75\) | 29.7205 | 3.43183 | ||||||||
\(76\) | −4.04040 | −0.463466 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.66657 | 0.528385 | ||||||||
\(79\) | −4.46293 | −0.502119 | −0.251059 | − | 0.967972i | \(-0.580779\pi\) | ||||
−0.251059 | + | 0.967972i | \(0.580779\pi\) | |||||||
\(80\) | −4.14347 | −0.463254 | ||||||||
\(81\) | −9.10217 | −1.01135 | ||||||||
\(82\) | −10.4741 | −1.15667 | ||||||||
\(83\) | 6.06003 | 0.665175 | 0.332587 | − | 0.943072i | \(-0.392078\pi\) | ||||
0.332587 | + | 0.943072i | \(0.392078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4656 | 1.24362 | ||||||||
\(86\) | 7.84520 | 0.845970 | ||||||||
\(87\) | −2.44245 | −0.261858 | ||||||||
\(88\) | −4.70697 | −0.501765 | ||||||||
\(89\) | −13.2662 | −1.40621 | −0.703105 | − | 0.711086i | \(-0.748204\pi\) | ||||
−0.703105 | + | 0.711086i | \(0.748204\pi\) | |||||||
\(90\) | −12.2876 | −1.29523 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.17268 | −0.226518 | ||||||||
\(93\) | 2.36684 | 0.245430 | ||||||||
\(94\) | −11.7294 | −1.20979 | ||||||||
\(95\) | 16.7413 | 1.71762 | ||||||||
\(96\) | 2.44245 | 0.249281 | ||||||||
\(97\) | −16.8452 | −1.71037 | −0.855186 | − | 0.518322i | \(-0.826557\pi\) | ||||
−0.855186 | + | 0.518322i | \(0.826557\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.9587 | −1.40291 | ||||||||
\(100\) | 12.1683 | 1.21683 | ||||||||
\(101\) | 12.4261 | 1.23644 | 0.618219 | − | 0.786006i | \(-0.287854\pi\) | ||||
0.618219 | + | 0.786006i | \(0.287854\pi\) | |||||||
\(102\) | −6.75860 | −0.669201 | ||||||||
\(103\) | 16.1718 | 1.59346 | 0.796729 | − | 0.604337i | \(-0.206562\pi\) | ||||
0.796729 | + | 0.604337i | \(0.206562\pi\) | |||||||
\(104\) | 1.91061 | 0.187351 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.78082 | −0.270097 | ||||||||
\(107\) | 10.6246 | 1.02712 | 0.513558 | − | 0.858055i | \(-0.328327\pi\) | ||||
0.513558 | + | 0.858055i | \(0.328327\pi\) | |||||||
\(108\) | −0.0841506 | −0.00809739 | ||||||||
\(109\) | 6.09884 | 0.584162 | 0.292081 | − | 0.956394i | \(-0.405652\pi\) | ||||
0.292081 | + | 0.956394i | \(0.405652\pi\) | |||||||
\(110\) | 19.5032 | 1.85956 | ||||||||
\(111\) | −3.59871 | −0.341574 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.5875 | 1.37228 | 0.686139 | − | 0.727471i | \(-0.259304\pi\) | ||||
0.686139 | + | 0.727471i | \(0.259304\pi\) | |||||||
\(114\) | −9.86847 | −0.924267 | ||||||||
\(115\) | 9.00245 | 0.839483 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 5.66601 | 0.523823 | ||||||||
\(118\) | −3.41673 | −0.314535 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.1202 | −0.923844 | ||||||||
\(121\) | 11.1556 | 1.01414 | ||||||||
\(122\) | −11.4192 | −1.03384 | ||||||||
\(123\) | −25.5825 | −2.30669 | ||||||||
\(124\) | 0.969044 | 0.0870227 | ||||||||
\(125\) | −29.7018 | −2.65661 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.46381 | 0.484835 | 0.242418 | − | 0.970172i | \(-0.422060\pi\) | ||||
0.242418 | + | 0.970172i | \(0.422060\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 19.1615 | 1.68708 | ||||||||
\(130\) | −7.91656 | −0.694328 | ||||||||
\(131\) | 13.4182 | 1.17235 | 0.586176 | − | 0.810184i | \(-0.300633\pi\) | ||||
0.586176 | + | 0.810184i | \(0.300633\pi\) | |||||||
\(132\) | −11.4965 | −1.00064 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.27575 | −0.196595 | ||||||||
\(135\) | 0.348675 | 0.0300092 | ||||||||
\(136\) | −2.76714 | −0.237281 | ||||||||
\(137\) | 17.1032 | 1.46123 | 0.730613 | − | 0.682791i | \(-0.239234\pi\) | ||||
0.730613 | + | 0.682791i | \(0.239234\pi\) | |||||||
\(138\) | −5.30667 | −0.451734 | ||||||||
\(139\) | 3.90711 | 0.331397 | 0.165699 | − | 0.986176i | \(-0.447012\pi\) | ||||
0.165699 | + | 0.986176i | \(0.447012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.6484 | −2.41263 | ||||||||
\(142\) | −6.24653 | −0.524198 | ||||||||
\(143\) | −8.99320 | −0.752049 | ||||||||
\(144\) | 2.96555 | 0.247129 | ||||||||
\(145\) | 4.14347 | 0.344096 | ||||||||
\(146\) | 13.5230 | 1.11917 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.47340 | −0.121113 | ||||||||
\(149\) | −7.49827 | −0.614282 | −0.307141 | − | 0.951664i | \(-0.599372\pi\) | ||||
−0.307141 | + | 0.951664i | \(0.599372\pi\) | |||||||
\(150\) | 29.7205 | 2.42667 | ||||||||
\(151\) | 9.41817 | 0.766440 | 0.383220 | − | 0.923657i | \(-0.374815\pi\) | ||||
0.383220 | + | 0.923657i | \(0.374815\pi\) | |||||||
\(152\) | −4.04040 | −0.327720 | ||||||||
\(153\) | −8.20609 | −0.663423 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.01520 | −0.322509 | ||||||||
\(156\) | 4.66657 | 0.373625 | ||||||||
\(157\) | −17.8286 | −1.42288 | −0.711439 | − | 0.702747i | \(-0.751956\pi\) | ||||
−0.711439 | + | 0.702747i | \(0.751956\pi\) | |||||||
\(158\) | −4.46293 | −0.355051 | ||||||||
\(159\) | −6.79201 | −0.538641 | ||||||||
\(160\) | −4.14347 | −0.327570 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9.10217 | −0.715134 | ||||||||
\(163\) | −10.8789 | −0.852102 | −0.426051 | − | 0.904699i | \(-0.640096\pi\) | ||||
−0.426051 | + | 0.904699i | \(0.640096\pi\) | |||||||
\(164\) | −10.4741 | −0.817891 | ||||||||
\(165\) | 47.6355 | 3.70842 | ||||||||
\(166\) | 6.06003 | 0.470350 | ||||||||
\(167\) | −16.0326 | −1.24064 | −0.620318 | − | 0.784350i | \(-0.712997\pi\) | ||||
−0.620318 | + | 0.784350i | \(0.712997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.34956 | −0.719197 | ||||||||
\(170\) | 11.4656 | 0.879369 | ||||||||
\(171\) | −11.9820 | −0.916287 | ||||||||
\(172\) | 7.84520 | 0.598191 | ||||||||
\(173\) | 6.18878 | 0.470524 | 0.235262 | − | 0.971932i | \(-0.424405\pi\) | ||||
0.235262 | + | 0.971932i | \(0.424405\pi\) | |||||||
\(174\) | −2.44245 | −0.185161 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.70697 | −0.354801 | ||||||||
\(177\) | −8.34518 | −0.627262 | ||||||||
\(178\) | −13.2662 | −0.994341 | ||||||||
\(179\) | 1.20540 | 0.0900957 | 0.0450479 | − | 0.998985i | \(-0.485656\pi\) | ||||
0.0450479 | + | 0.998985i | \(0.485656\pi\) | |||||||
\(180\) | −12.2876 | −0.915867 | ||||||||
\(181\) | −6.95105 | −0.516668 | −0.258334 | − | 0.966056i | \(-0.583173\pi\) | ||||
−0.258334 | + | 0.966056i | \(0.583173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.8907 | −2.06174 | ||||||||
\(184\) | −2.17268 | −0.160172 | ||||||||
\(185\) | 6.10500 | 0.448848 | ||||||||
\(186\) | 2.36684 | 0.173545 | ||||||||
\(187\) | 13.0249 | 0.952472 | ||||||||
\(188\) | −11.7294 | −0.855453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.7413 | 1.21454 | ||||||||
\(191\) | −6.80847 | −0.492644 | −0.246322 | − | 0.969188i | \(-0.579222\pi\) | ||||
−0.246322 | + | 0.969188i | \(0.579222\pi\) | |||||||
\(192\) | 2.44245 | 0.176268 | ||||||||
\(193\) | −3.89664 | −0.280486 | −0.140243 | − | 0.990117i | \(-0.544788\pi\) | ||||
−0.140243 | + | 0.990117i | \(0.544788\pi\) | |||||||
\(194\) | −16.8452 | −1.20942 | ||||||||
\(195\) | −19.3358 | −1.38466 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5624 | 1.10877 | 0.554386 | − | 0.832260i | \(-0.312953\pi\) | ||||
0.554386 | + | 0.832260i | \(0.312953\pi\) | |||||||
\(198\) | −13.9587 | −0.992005 | ||||||||
\(199\) | −24.5735 | −1.74197 | −0.870986 | − | 0.491308i | \(-0.836519\pi\) | ||||
−0.870986 | + | 0.491308i | \(0.836519\pi\) | |||||||
\(200\) | 12.1683 | 0.860431 | ||||||||
\(201\) | −5.55840 | −0.392059 | ||||||||
\(202\) | 12.4261 | 0.874294 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.75860 | −0.473197 | ||||||||
\(205\) | 43.3992 | 3.03113 | ||||||||
\(206\) | 16.1718 | 1.12674 | ||||||||
\(207\) | −6.44320 | −0.447833 | ||||||||
\(208\) | 1.91061 | 0.132477 | ||||||||
\(209\) | 19.0181 | 1.31551 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.65646 | 0.595935 | 0.297968 | − | 0.954576i | \(-0.403691\pi\) | ||||
0.297968 | + | 0.954576i | \(0.403691\pi\) | |||||||
\(212\) | −2.78082 | −0.190988 | ||||||||
\(213\) | −15.2568 | −1.04538 | ||||||||
\(214\) | 10.6246 | 0.726281 | ||||||||
\(215\) | −32.5064 | −2.21691 | ||||||||
\(216\) | −0.0841506 | −0.00572572 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.09884 | 0.413065 | ||||||||
\(219\) | 33.0291 | 2.23190 | ||||||||
\(220\) | 19.5032 | 1.31490 | ||||||||
\(221\) | −5.28694 | −0.355638 | ||||||||
\(222\) | −3.59871 | −0.241529 | ||||||||
\(223\) | 10.9191 | 0.731194 | 0.365597 | − | 0.930773i | \(-0.380865\pi\) | ||||
0.365597 | + | 0.930773i | \(0.380865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.0858 | 2.40572 | ||||||||
\(226\) | 14.5875 | 0.970347 | ||||||||
\(227\) | 10.4951 | 0.696583 | 0.348292 | − | 0.937386i | \(-0.386762\pi\) | ||||
0.348292 | + | 0.937386i | \(0.386762\pi\) | |||||||
\(228\) | −9.86847 | −0.653555 | ||||||||
\(229\) | 7.51525 | 0.496622 | 0.248311 | − | 0.968680i | \(-0.420125\pi\) | ||||
0.248311 | + | 0.968680i | \(0.420125\pi\) | |||||||
\(230\) | 9.00245 | 0.593604 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 5.14262 | 0.336904 | 0.168452 | − | 0.985710i | \(-0.446123\pi\) | ||||
0.168452 | + | 0.985710i | \(0.446123\pi\) | |||||||
\(234\) | 5.66601 | 0.370399 | ||||||||
\(235\) | 48.6003 | 3.17034 | ||||||||
\(236\) | −3.41673 | −0.222410 | ||||||||
\(237\) | −10.9005 | −0.708061 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.749673 | 0.0484923 | 0.0242462 | − | 0.999706i | \(-0.492281\pi\) | ||||
0.0242462 | + | 0.999706i | \(0.492281\pi\) | |||||||
\(240\) | −10.1202 | −0.653256 | ||||||||
\(241\) | 9.01959 | 0.581003 | 0.290501 | − | 0.956875i | \(-0.406178\pi\) | ||||
0.290501 | + | 0.956875i | \(0.406178\pi\) | |||||||
\(242\) | 11.1556 | 0.717108 | ||||||||
\(243\) | −21.9791 | −1.40996 | ||||||||
\(244\) | −11.4192 | −0.731038 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −25.5825 | −1.63108 | ||||||||
\(247\) | −7.71964 | −0.491189 | ||||||||
\(248\) | 0.969044 | 0.0615344 | ||||||||
\(249\) | 14.8013 | 0.937994 | ||||||||
\(250\) | −29.7018 | −1.87850 | ||||||||
\(251\) | 29.1169 | 1.83784 | 0.918921 | − | 0.394441i | \(-0.129062\pi\) | ||||
0.918921 | + | 0.394441i | \(0.129062\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2268 | 0.642951 | ||||||||
\(254\) | 5.46381 | 0.342830 | ||||||||
\(255\) | 28.0041 | 1.75368 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.2275 | 1.44889 | 0.724447 | − | 0.689330i | \(-0.242095\pi\) | ||||
0.724447 | + | 0.689330i | \(0.242095\pi\) | |||||||
\(258\) | 19.1615 | 1.19294 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.91656 | −0.490964 | ||||||||
\(261\) | −2.96555 | −0.183563 | ||||||||
\(262\) | 13.4182 | 0.828978 | ||||||||
\(263\) | −20.5033 | −1.26429 | −0.632145 | − | 0.774850i | \(-0.717825\pi\) | ||||
−0.632145 | + | 0.774850i | \(0.717825\pi\) | |||||||
\(264\) | −11.4965 | −0.707562 | ||||||||
\(265\) | 11.5222 | 0.707806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.4019 | −1.98296 | ||||||||
\(268\) | −2.27575 | −0.139014 | ||||||||
\(269\) | 11.3952 | 0.694778 | 0.347389 | − | 0.937721i | \(-0.387068\pi\) | ||||
0.347389 | + | 0.937721i | \(0.387068\pi\) | |||||||
\(270\) | 0.348675 | 0.0212197 | ||||||||
\(271\) | −17.9751 | −1.09191 | −0.545954 | − | 0.837815i | \(-0.683833\pi\) | ||||
−0.545954 | + | 0.837815i | \(0.683833\pi\) | |||||||
\(272\) | −2.76714 | −0.167783 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.1032 | 1.03324 | ||||||||
\(275\) | −57.2760 | −3.45387 | ||||||||
\(276\) | −5.30667 | −0.319424 | ||||||||
\(277\) | −2.08032 | −0.124994 | −0.0624971 | − | 0.998045i | \(-0.519906\pi\) | ||||
−0.0624971 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(278\) | 3.90711 | 0.234333 | ||||||||
\(279\) | 2.87375 | 0.172047 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.35741 | 0.438906 | 0.219453 | − | 0.975623i | \(-0.429573\pi\) | ||||
0.219453 | + | 0.975623i | \(0.429573\pi\) | |||||||
\(282\) | −28.6484 | −1.70599 | ||||||||
\(283\) | 6.08053 | 0.361450 | 0.180725 | − | 0.983534i | \(-0.442156\pi\) | ||||
0.180725 | + | 0.983534i | \(0.442156\pi\) | |||||||
\(284\) | −6.24653 | −0.370664 | ||||||||
\(285\) | 40.8897 | 2.42210 | ||||||||
\(286\) | −8.99320 | −0.531779 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.96555 | 0.174747 | ||||||||
\(289\) | −9.34292 | −0.549583 | ||||||||
\(290\) | 4.14347 | 0.243313 | ||||||||
\(291\) | −41.1435 | −2.41188 | ||||||||
\(292\) | 13.5230 | 0.791371 | ||||||||
\(293\) | −13.7159 | −0.801291 | −0.400646 | − | 0.916233i | \(-0.631214\pi\) | ||||
−0.400646 | + | 0.916233i | \(0.631214\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1571 | 0.824259 | ||||||||
\(296\) | −1.47340 | −0.0856398 | ||||||||
\(297\) | 0.396094 | 0.0229837 | ||||||||
\(298\) | −7.49827 | −0.434363 | ||||||||
\(299\) | −4.15116 | −0.240068 | ||||||||
\(300\) | 29.7205 | 1.71591 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.41817 | 0.541955 | ||||||||
\(303\) | 30.3500 | 1.74356 | ||||||||
\(304\) | −4.04040 | −0.231733 | ||||||||
\(305\) | 47.3150 | 2.70925 | ||||||||
\(306\) | −8.20609 | −0.469111 | ||||||||
\(307\) | −7.64494 | −0.436320 | −0.218160 | − | 0.975913i | \(-0.570005\pi\) | ||||
−0.218160 | + | 0.975913i | \(0.570005\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.4988 | 2.24701 | ||||||||
\(310\) | −4.01520 | −0.228048 | ||||||||
\(311\) | −24.4252 | −1.38502 | −0.692512 | − | 0.721406i | \(-0.743496\pi\) | ||||
−0.692512 | + | 0.721406i | \(0.743496\pi\) | |||||||
\(312\) | 4.66657 | 0.264192 | ||||||||
\(313\) | 18.2645 | 1.03237 | 0.516185 | − | 0.856477i | \(-0.327352\pi\) | ||||
0.516185 | + | 0.856477i | \(0.327352\pi\) | |||||||
\(314\) | −17.8286 | −1.00613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.46293 | −0.251059 | ||||||||
\(317\) | −10.4217 | −0.585342 | −0.292671 | − | 0.956213i | \(-0.594544\pi\) | ||||
−0.292671 | + | 0.956213i | \(0.594544\pi\) | |||||||
\(318\) | −6.79201 | −0.380877 | ||||||||
\(319\) | 4.70697 | 0.263540 | ||||||||
\(320\) | −4.14347 | −0.231627 | ||||||||
\(321\) | 25.9500 | 1.44839 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1804 | 0.622093 | ||||||||
\(324\) | −9.10217 | −0.505676 | ||||||||
\(325\) | 23.2490 | 1.28962 | ||||||||
\(326\) | −10.8789 | −0.602527 | ||||||||
\(327\) | 14.8961 | 0.823755 | ||||||||
\(328\) | −10.4741 | −0.578336 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 47.6355 | 2.62225 | ||||||||
\(331\) | 4.68351 | 0.257429 | 0.128715 | − | 0.991682i | \(-0.458915\pi\) | ||||
0.128715 | + | 0.991682i | \(0.458915\pi\) | |||||||
\(332\) | 6.06003 | 0.332587 | ||||||||
\(333\) | −4.36944 | −0.239444 | ||||||||
\(334\) | −16.0326 | −0.877262 | ||||||||
\(335\) | 9.42950 | 0.515189 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.3719 | −1.38210 | −0.691048 | − | 0.722809i | \(-0.742851\pi\) | ||||
−0.691048 | + | 0.722809i | \(0.742851\pi\) | |||||||
\(338\) | −9.34956 | −0.508549 | ||||||||
\(339\) | 35.6292 | 1.93511 | ||||||||
\(340\) | 11.4656 | 0.621808 | ||||||||
\(341\) | −4.56126 | −0.247006 | ||||||||
\(342\) | −11.9820 | −0.647913 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.84520 | 0.422985 | ||||||||
\(345\) | 21.9880 | 1.18379 | ||||||||
\(346\) | 6.18878 | 0.332711 | ||||||||
\(347\) | −1.93057 | −0.103639 | −0.0518193 | − | 0.998656i | \(-0.516502\pi\) | ||||
−0.0518193 | + | 0.998656i | \(0.516502\pi\) | |||||||
\(348\) | −2.44245 | −0.130929 | ||||||||
\(349\) | −1.95782 | −0.104800 | −0.0523998 | − | 0.998626i | \(-0.516687\pi\) | ||||
−0.0523998 | + | 0.998626i | \(0.516687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.160779 | −0.00858175 | ||||||||
\(352\) | −4.70697 | −0.250882 | ||||||||
\(353\) | 16.3330 | 0.869317 | 0.434658 | − | 0.900595i | \(-0.356869\pi\) | ||||
0.434658 | + | 0.900595i | \(0.356869\pi\) | |||||||
\(354\) | −8.34518 | −0.443541 | ||||||||
\(355\) | 25.8823 | 1.37369 | ||||||||
\(356\) | −13.2662 | −0.703105 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.20540 | 0.0637073 | ||||||||
\(359\) | −11.7801 | −0.621729 | −0.310865 | − | 0.950454i | \(-0.600619\pi\) | ||||
−0.310865 | + | 0.950454i | \(0.600619\pi\) | |||||||
\(360\) | −12.2876 | −0.647616 | ||||||||
\(361\) | −2.67514 | −0.140797 | ||||||||
\(362\) | −6.95105 | −0.365339 | ||||||||
\(363\) | 27.2469 | 1.43009 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −56.0320 | −2.93285 | ||||||||
\(366\) | −27.8907 | −1.45787 | ||||||||
\(367\) | −35.6438 | −1.86059 | −0.930295 | − | 0.366813i | \(-0.880449\pi\) | ||||
−0.930295 | + | 0.366813i | \(0.880449\pi\) | |||||||
\(368\) | −2.17268 | −0.113259 | ||||||||
\(369\) | −31.0615 | −1.61700 | ||||||||
\(370\) | 6.10500 | 0.317384 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.36684 | 0.122715 | ||||||||
\(373\) | 17.7483 | 0.918971 | 0.459486 | − | 0.888185i | \(-0.348034\pi\) | ||||
0.459486 | + | 0.888185i | \(0.348034\pi\) | |||||||
\(374\) | 13.0249 | 0.673500 | ||||||||
\(375\) | −72.5450 | −3.74621 | ||||||||
\(376\) | −11.7294 | −0.604897 | ||||||||
\(377\) | −1.91061 | −0.0984015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2263 | −0.782124 | −0.391062 | − | 0.920364i | \(-0.627892\pi\) | ||||
−0.391062 | + | 0.920364i | \(0.627892\pi\) | |||||||
\(380\) | 16.7413 | 0.858810 | ||||||||
\(381\) | 13.3451 | 0.683689 | ||||||||
\(382\) | −6.80847 | −0.348352 | ||||||||
\(383\) | 15.8118 | 0.807943 | 0.403971 | − | 0.914772i | \(-0.367629\pi\) | ||||
0.403971 | + | 0.914772i | \(0.367629\pi\) | |||||||
\(384\) | 2.44245 | 0.124641 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.89664 | −0.198334 | ||||||||
\(387\) | 23.2653 | 1.18264 | ||||||||
\(388\) | −16.8452 | −0.855186 | ||||||||
\(389\) | −21.7172 | −1.10110 | −0.550552 | − | 0.834801i | \(-0.685583\pi\) | ||||
−0.550552 | + | 0.834801i | \(0.685583\pi\) | |||||||
\(390\) | −19.3358 | −0.979105 | ||||||||
\(391\) | 6.01213 | 0.304047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.7732 | 1.65319 | ||||||||
\(394\) | 15.5624 | 0.784020 | ||||||||
\(395\) | 18.4920 | 0.930434 | ||||||||
\(396\) | −13.9587 | −0.701453 | ||||||||
\(397\) | −1.26033 | −0.0632543 | −0.0316272 | − | 0.999500i | \(-0.510069\pi\) | ||||
−0.0316272 | + | 0.999500i | \(0.510069\pi\) | |||||||
\(398\) | −24.5735 | −1.23176 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.1683 | 0.608417 | ||||||||
\(401\) | −1.91181 | −0.0954713 | −0.0477356 | − | 0.998860i | \(-0.515201\pi\) | ||||
−0.0477356 | + | 0.998860i | \(0.515201\pi\) | |||||||
\(402\) | −5.55840 | −0.277228 | ||||||||
\(403\) | 1.85147 | 0.0922282 | ||||||||
\(404\) | 12.4261 | 0.618219 | ||||||||
\(405\) | 37.7146 | 1.87405 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.93526 | 0.343768 | ||||||||
\(408\) | −6.75860 | −0.334601 | ||||||||
\(409\) | 3.01815 | 0.149238 | 0.0746189 | − | 0.997212i | \(-0.476226\pi\) | ||||
0.0746189 | + | 0.997212i | \(0.476226\pi\) | |||||||
\(410\) | 43.3992 | 2.14333 | ||||||||
\(411\) | 41.7737 | 2.06054 | ||||||||
\(412\) | 16.1718 | 0.796729 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.44320 | −0.316666 | ||||||||
\(415\) | −25.1095 | −1.23258 | ||||||||
\(416\) | 1.91061 | 0.0936755 | ||||||||
\(417\) | 9.54292 | 0.467319 | ||||||||
\(418\) | 19.0181 | 0.930204 | ||||||||
\(419\) | −4.64504 | −0.226925 | −0.113463 | − | 0.993542i | \(-0.536194\pi\) | ||||
−0.113463 | + | 0.993542i | \(0.536194\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.6202 | −1.29739 | −0.648695 | − | 0.761048i | \(-0.724685\pi\) | ||||
−0.648695 | + | 0.761048i | \(0.724685\pi\) | |||||||
\(422\) | 8.65646 | 0.421390 | ||||||||
\(423\) | −34.7840 | −1.69126 | ||||||||
\(424\) | −2.78082 | −0.135049 | ||||||||
\(425\) | −33.6715 | −1.63331 | ||||||||
\(426\) | −15.2568 | −0.739196 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.6246 | 0.513558 | ||||||||
\(429\) | −21.9654 | −1.06050 | ||||||||
\(430\) | −32.5064 | −1.56760 | ||||||||
\(431\) | −9.63869 | −0.464279 | −0.232140 | − | 0.972682i | \(-0.574573\pi\) | ||||
−0.232140 | + | 0.972682i | \(0.574573\pi\) | |||||||
\(432\) | −0.0841506 | −0.00404870 | ||||||||
\(433\) | 3.16466 | 0.152084 | 0.0760420 | − | 0.997105i | \(-0.475772\pi\) | ||||
0.0760420 | + | 0.997105i | \(0.475772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.1202 | 0.485227 | ||||||||
\(436\) | 6.09884 | 0.292081 | ||||||||
\(437\) | 8.77852 | 0.419934 | ||||||||
\(438\) | 33.0291 | 1.57819 | ||||||||
\(439\) | −13.8900 | −0.662933 | −0.331467 | − | 0.943467i | \(-0.607543\pi\) | ||||
−0.331467 | + | 0.943467i | \(0.607543\pi\) | |||||||
\(440\) | 19.5032 | 0.929778 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.28694 | −0.251474 | ||||||||
\(443\) | 20.3708 | 0.967845 | 0.483923 | − | 0.875111i | \(-0.339212\pi\) | ||||
0.483923 | + | 0.875111i | \(0.339212\pi\) | |||||||
\(444\) | −3.59871 | −0.170787 | ||||||||
\(445\) | 54.9679 | 2.60573 | ||||||||
\(446\) | 10.9191 | 0.517032 | ||||||||
\(447\) | −18.3141 | −0.866228 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1442 | 1.56417 | 0.782086 | − | 0.623170i | \(-0.214156\pi\) | ||||
0.782086 | + | 0.623170i | \(0.214156\pi\) | |||||||
\(450\) | 36.0858 | 1.70110 | ||||||||
\(451\) | 49.3014 | 2.32151 | ||||||||
\(452\) | 14.5875 | 0.686139 | ||||||||
\(453\) | 23.0034 | 1.08079 | ||||||||
\(454\) | 10.4951 | 0.492559 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.86847 | −0.462133 | ||||||||
\(457\) | −18.2087 | −0.851767 | −0.425883 | − | 0.904778i | \(-0.640037\pi\) | ||||
−0.425883 | + | 0.904778i | \(0.640037\pi\) | |||||||
\(458\) | 7.51525 | 0.351165 | ||||||||
\(459\) | 0.232857 | 0.0108688 | ||||||||
\(460\) | 9.00245 | 0.419741 | ||||||||
\(461\) | 3.52484 | 0.164168 | 0.0820841 | − | 0.996625i | \(-0.473842\pi\) | ||||
0.0820841 | + | 0.996625i | \(0.473842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.7653 | 0.500304 | 0.250152 | − | 0.968207i | \(-0.419519\pi\) | ||||
0.250152 | + | 0.968207i | \(0.419519\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −9.80692 | −0.454785 | ||||||||
\(466\) | 5.14262 | 0.238227 | ||||||||
\(467\) | −12.0199 | −0.556214 | −0.278107 | − | 0.960550i | \(-0.589707\pi\) | ||||
−0.278107 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(468\) | 5.66601 | 0.261911 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 48.6003 | 2.24177 | ||||||||
\(471\) | −43.5455 | −2.00647 | ||||||||
\(472\) | −3.41673 | −0.157268 | ||||||||
\(473\) | −36.9271 | −1.69791 | ||||||||
\(474\) | −10.9005 | −0.500675 | ||||||||
\(475\) | −49.1650 | −2.25584 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.24666 | −0.377588 | ||||||||
\(478\) | 0.749673 | 0.0342893 | ||||||||
\(479\) | −8.29202 | −0.378872 | −0.189436 | − | 0.981893i | \(-0.560666\pi\) | ||||
−0.189436 | + | 0.981893i | \(0.560666\pi\) | |||||||
\(480\) | −10.1202 | −0.461922 | ||||||||
\(481\) | −2.81510 | −0.128358 | ||||||||
\(482\) | 9.01959 | 0.410831 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.1556 | 0.507072 | ||||||||
\(485\) | 69.7976 | 3.16934 | ||||||||
\(486\) | −21.9791 | −0.996993 | ||||||||
\(487\) | 7.89345 | 0.357687 | 0.178843 | − | 0.983878i | \(-0.442764\pi\) | ||||
0.178843 | + | 0.983878i | \(0.442764\pi\) | |||||||
\(488\) | −11.4192 | −0.516922 | ||||||||
\(489\) | −26.5711 | −1.20159 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.7250 | −1.70250 | −0.851252 | − | 0.524757i | \(-0.824156\pi\) | ||||
−0.851252 | + | 0.524757i | \(0.824156\pi\) | |||||||
\(492\) | −25.5825 | −1.15335 | ||||||||
\(493\) | 2.76714 | 0.124626 | ||||||||
\(494\) | −7.71964 | −0.347323 | ||||||||
\(495\) | 57.8376 | 2.59961 | ||||||||
\(496\) | 0.969044 | 0.0435114 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.8013 | 0.663262 | ||||||||
\(499\) | −8.47942 | −0.379591 | −0.189796 | − | 0.981824i | \(-0.560783\pi\) | ||||
−0.189796 | + | 0.981824i | \(0.560783\pi\) | |||||||
\(500\) | −29.7018 | −1.32830 | ||||||||
\(501\) | −39.1587 | −1.74948 | ||||||||
\(502\) | 29.1169 | 1.29955 | ||||||||
\(503\) | 25.2796 | 1.12716 | 0.563581 | − | 0.826061i | \(-0.309423\pi\) | ||||
0.563581 | + | 0.826061i | \(0.309423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.4870 | −2.29114 | ||||||||
\(506\) | 10.2268 | 0.454635 | ||||||||
\(507\) | −22.8358 | −1.01417 | ||||||||
\(508\) | 5.46381 | 0.242418 | ||||||||
\(509\) | −4.96964 | −0.220275 | −0.110138 | − | 0.993916i | \(-0.535129\pi\) | ||||
−0.110138 | + | 0.993916i | \(0.535129\pi\) | |||||||
\(510\) | 28.0041 | 1.24004 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.340002 | 0.0150115 | ||||||||
\(514\) | 23.2275 | 1.02452 | ||||||||
\(515\) | −67.0075 | −2.95270 | ||||||||
\(516\) | 19.1615 | 0.843538 | ||||||||
\(517\) | 55.2099 | 2.42813 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.1158 | 0.663508 | ||||||||
\(520\) | −7.91656 | −0.347164 | ||||||||
\(521\) | −26.9628 | −1.18126 | −0.590631 | − | 0.806942i | \(-0.701121\pi\) | ||||
−0.590631 | + | 0.806942i | \(0.701121\pi\) | |||||||
\(522\) | −2.96555 | −0.129798 | ||||||||
\(523\) | 10.4899 | 0.458691 | 0.229345 | − | 0.973345i | \(-0.426341\pi\) | ||||
0.229345 | + | 0.973345i | \(0.426341\pi\) | |||||||
\(524\) | 13.4182 | 0.586176 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.5033 | −0.893988 | ||||||||
\(527\) | −2.68148 | −0.116807 | ||||||||
\(528\) | −11.4965 | −0.500322 | ||||||||
\(529\) | −18.2794 | −0.794758 | ||||||||
\(530\) | 11.5222 | 0.500494 | ||||||||
\(531\) | −10.1325 | −0.439712 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.0120 | −0.866815 | ||||||||
\(534\) | −32.4019 | −1.40217 | ||||||||
\(535\) | −44.0226 | −1.90326 | ||||||||
\(536\) | −2.27575 | −0.0982975 | ||||||||
\(537\) | 2.94412 | 0.127048 | ||||||||
\(538\) | 11.3952 | 0.491282 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.348675 | 0.0150046 | ||||||||
\(541\) | −44.5694 | −1.91619 | −0.958093 | − | 0.286456i | \(-0.907523\pi\) | ||||
−0.958093 | + | 0.286456i | \(0.907523\pi\) | |||||||
\(542\) | −17.9751 | −0.772095 | ||||||||
\(543\) | −16.9776 | −0.728578 | ||||||||
\(544\) | −2.76714 | −0.118640 | ||||||||
\(545\) | −25.2703 | −1.08246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8005 | 1.48796 | 0.743980 | − | 0.668202i | \(-0.232936\pi\) | ||||
0.743980 | + | 0.668202i | \(0.232936\pi\) | |||||||
\(548\) | 17.1032 | 0.730613 | ||||||||
\(549\) | −33.8641 | −1.44529 | ||||||||
\(550\) | −57.2760 | −2.44226 | ||||||||
\(551\) | 4.04040 | 0.172127 | ||||||||
\(552\) | −5.30667 | −0.225867 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.08032 | −0.0883843 | ||||||||
\(555\) | 14.9111 | 0.632942 | ||||||||
\(556\) | 3.90711 | 0.165699 | ||||||||
\(557\) | −33.7665 | −1.43073 | −0.715365 | − | 0.698751i | \(-0.753740\pi\) | ||||
−0.715365 | + | 0.698751i | \(0.753740\pi\) | |||||||
\(558\) | 2.87375 | 0.121655 | ||||||||
\(559\) | 14.9891 | 0.633973 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.8125 | 1.34313 | ||||||||
\(562\) | 7.35741 | 0.310354 | ||||||||
\(563\) | −41.2408 | −1.73809 | −0.869047 | − | 0.494730i | \(-0.835267\pi\) | ||||
−0.869047 | + | 0.494730i | \(0.835267\pi\) | |||||||
\(564\) | −28.6484 | −1.20632 | ||||||||
\(565\) | −60.4429 | −2.54285 | ||||||||
\(566\) | 6.08053 | 0.255584 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.24653 | −0.262099 | ||||||||
\(569\) | −25.9185 | −1.08656 | −0.543281 | − | 0.839551i | \(-0.682818\pi\) | ||||
−0.543281 | + | 0.839551i | \(0.682818\pi\) | |||||||
\(570\) | 40.8897 | 1.71268 | ||||||||
\(571\) | 15.8953 | 0.665196 | 0.332598 | − | 0.943069i | \(-0.392075\pi\) | ||||
0.332598 | + | 0.943069i | \(0.392075\pi\) | |||||||
\(572\) | −8.99320 | −0.376024 | ||||||||
\(573\) | −16.6293 | −0.694700 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.4380 | −1.10254 | ||||||||
\(576\) | 2.96555 | 0.123564 | ||||||||
\(577\) | 10.2723 | 0.427639 | 0.213820 | − | 0.976873i | \(-0.431409\pi\) | ||||
0.213820 | + | 0.976873i | \(0.431409\pi\) | |||||||
\(578\) | −9.34292 | −0.388614 | ||||||||
\(579\) | −9.51734 | −0.395527 | ||||||||
\(580\) | 4.14347 | 0.172048 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −41.1435 | −1.70545 | ||||||||
\(583\) | 13.0892 | 0.542101 | ||||||||
\(584\) | 13.5230 | 0.559584 | ||||||||
\(585\) | −23.4769 | −0.970652 | ||||||||
\(586\) | −13.7159 | −0.566599 | ||||||||
\(587\) | 23.9902 | 0.990183 | 0.495091 | − | 0.868841i | \(-0.335135\pi\) | ||||
0.495091 | + | 0.868841i | \(0.335135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.91533 | −0.161328 | ||||||||
\(590\) | 14.1571 | 0.582839 | ||||||||
\(591\) | 38.0102 | 1.56353 | ||||||||
\(592\) | −1.47340 | −0.0605565 | ||||||||
\(593\) | 15.5367 | 0.638014 | 0.319007 | − | 0.947752i | \(-0.396651\pi\) | ||||
0.319007 | + | 0.947752i | \(0.396651\pi\) | |||||||
\(594\) | 0.396094 | 0.0162519 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.49827 | −0.307141 | ||||||||
\(597\) | −60.0196 | −2.45644 | ||||||||
\(598\) | −4.15116 | −0.169753 | ||||||||
\(599\) | −20.8308 | −0.851122 | −0.425561 | − | 0.904930i | \(-0.639923\pi\) | ||||
−0.425561 | + | 0.904930i | \(0.639923\pi\) | |||||||
\(600\) | 29.7205 | 1.21333 | ||||||||
\(601\) | −17.7149 | −0.722606 | −0.361303 | − | 0.932448i | \(-0.617668\pi\) | ||||
−0.361303 | + | 0.932448i | \(0.617668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.74884 | −0.274834 | ||||||||
\(604\) | 9.41817 | 0.383220 | ||||||||
\(605\) | −46.2228 | −1.87922 | ||||||||
\(606\) | 30.3500 | 1.23288 | ||||||||
\(607\) | 2.44517 | 0.0992466 | 0.0496233 | − | 0.998768i | \(-0.484198\pi\) | ||||
0.0496233 | + | 0.998768i | \(0.484198\pi\) | |||||||
\(608\) | −4.04040 | −0.163860 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 47.3150 | 1.91573 | ||||||||
\(611\) | −22.4103 | −0.906624 | ||||||||
\(612\) | −8.20609 | −0.331712 | ||||||||
\(613\) | −1.80610 | −0.0729477 | −0.0364739 | − | 0.999335i | \(-0.511613\pi\) | ||||
−0.0364739 | + | 0.999335i | \(0.511613\pi\) | |||||||
\(614\) | −7.64494 | −0.308525 | ||||||||
\(615\) | 106.000 | 4.27434 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0917 | −0.607567 | −0.303784 | − | 0.952741i | \(-0.598250\pi\) | ||||
−0.303784 | + | 0.952741i | \(0.598250\pi\) | |||||||
\(618\) | 39.4988 | 1.58888 | ||||||||
\(619\) | 44.5910 | 1.79227 | 0.896133 | − | 0.443786i | \(-0.146365\pi\) | ||||
0.896133 | + | 0.443786i | \(0.146365\pi\) | |||||||
\(620\) | −4.01520 | −0.161254 | ||||||||
\(621\) | 0.182833 | 0.00733682 | ||||||||
\(622\) | −24.4252 | −0.979360 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.66657 | 0.186812 | ||||||||
\(625\) | 62.2267 | 2.48907 | ||||||||
\(626\) | 18.2645 | 0.729996 | ||||||||
\(627\) | 46.4506 | 1.85506 | ||||||||
\(628\) | −17.8286 | −0.711439 | ||||||||
\(629\) | 4.07712 | 0.162565 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.3265 | −0.570328 | −0.285164 | − | 0.958479i | \(-0.592048\pi\) | ||||
−0.285164 | + | 0.958479i | \(0.592048\pi\) | |||||||
\(632\) | −4.46293 | −0.177526 | ||||||||
\(633\) | 21.1429 | 0.840357 | ||||||||
\(634\) | −10.4217 | −0.413899 | ||||||||
\(635\) | −22.6391 | −0.898407 | ||||||||
\(636\) | −6.79201 | −0.269321 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.70697 | 0.186351 | ||||||||
\(639\) | −18.5244 | −0.732814 | ||||||||
\(640\) | −4.14347 | −0.163785 | ||||||||
\(641\) | −17.4354 | −0.688658 | −0.344329 | − | 0.938849i | \(-0.611894\pi\) | ||||
−0.344329 | + | 0.938849i | \(0.611894\pi\) | |||||||
\(642\) | 25.9500 | 1.02416 | ||||||||
\(643\) | 6.99067 | 0.275685 | 0.137843 | − | 0.990454i | \(-0.455983\pi\) | ||||
0.137843 | + | 0.990454i | \(0.455983\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.3950 | −3.12618 | ||||||||
\(646\) | 11.1804 | 0.439886 | ||||||||
\(647\) | 16.2341 | 0.638227 | 0.319113 | − | 0.947717i | \(-0.396615\pi\) | ||||
0.319113 | + | 0.947717i | \(0.396615\pi\) | |||||||
\(648\) | −9.10217 | −0.357567 | ||||||||
\(649\) | 16.0824 | 0.631291 | ||||||||
\(650\) | 23.2490 | 0.911899 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.8789 | −0.426051 | ||||||||
\(653\) | 22.5201 | 0.881281 | 0.440641 | − | 0.897684i | \(-0.354751\pi\) | ||||
0.440641 | + | 0.897684i | \(0.354751\pi\) | |||||||
\(654\) | 14.8961 | 0.582483 | ||||||||
\(655\) | −55.5978 | −2.17239 | ||||||||
\(656\) | −10.4741 | −0.408945 | ||||||||
\(657\) | 40.1030 | 1.56457 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.71682 | −0.261650 | −0.130825 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130825 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(660\) | 47.6355 | 1.85421 | ||||||||
\(661\) | 35.3608 | 1.37538 | 0.687689 | − | 0.726006i | \(-0.258625\pi\) | ||||
0.687689 | + | 0.726006i | \(0.258625\pi\) | |||||||
\(662\) | 4.68351 | 0.182030 | ||||||||
\(663\) | −12.9131 | −0.501502 | ||||||||
\(664\) | 6.06003 | 0.235175 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.36944 | −0.169313 | ||||||||
\(667\) | 2.17268 | 0.0841267 | ||||||||
\(668\) | −16.0326 | −0.620318 | ||||||||
\(669\) | 26.6692 | 1.03109 | ||||||||
\(670\) | 9.42950 | 0.364293 | ||||||||
\(671\) | 53.7498 | 2.07499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1388 | −0.891935 | −0.445967 | − | 0.895049i | \(-0.647140\pi\) | ||||
−0.445967 | + | 0.895049i | \(0.647140\pi\) | |||||||
\(674\) | −25.3719 | −0.977290 | ||||||||
\(675\) | −1.02397 | −0.0394127 | ||||||||
\(676\) | −9.34956 | −0.359599 | ||||||||
\(677\) | −22.7344 | −0.873755 | −0.436878 | − | 0.899521i | \(-0.643916\pi\) | ||||
−0.436878 | + | 0.899521i | \(0.643916\pi\) | |||||||
\(678\) | 35.6292 | 1.36833 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.4656 | 0.439685 | ||||||||
\(681\) | 25.6337 | 0.982285 | ||||||||
\(682\) | −4.56126 | −0.174660 | ||||||||
\(683\) | 20.2928 | 0.776483 | 0.388242 | − | 0.921558i | \(-0.373083\pi\) | ||||
0.388242 | + | 0.921558i | \(0.373083\pi\) | |||||||
\(684\) | −11.9820 | −0.458143 | ||||||||
\(685\) | −70.8667 | −2.70768 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.3556 | 0.700310 | ||||||||
\(688\) | 7.84520 | 0.299096 | ||||||||
\(689\) | −5.31307 | −0.202412 | ||||||||
\(690\) | 21.9880 | 0.837069 | ||||||||
\(691\) | −2.01180 | −0.0765324 | −0.0382662 | − | 0.999268i | \(-0.512183\pi\) | ||||
−0.0382662 | + | 0.999268i | \(0.512183\pi\) | |||||||
\(692\) | 6.18878 | 0.235262 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.93057 | −0.0732836 | ||||||||
\(695\) | −16.1890 | −0.614084 | ||||||||
\(696\) | −2.44245 | −0.0925807 | ||||||||
\(697\) | 28.9834 | 1.09782 | ||||||||
\(698\) | −1.95782 | −0.0741045 | ||||||||
\(699\) | 12.5606 | 0.475084 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.02432 | −0.114227 | −0.0571136 | − | 0.998368i | \(-0.518190\pi\) | ||||
−0.0571136 | + | 0.998368i | \(0.518190\pi\) | |||||||
\(702\) | −0.160779 | −0.00606822 | ||||||||
\(703\) | 5.95314 | 0.224527 | ||||||||
\(704\) | −4.70697 | −0.177401 | ||||||||
\(705\) | 118.704 | 4.47064 | ||||||||
\(706\) | 16.3330 | 0.614700 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.34518 | −0.313631 | ||||||||
\(709\) | −45.4669 | −1.70754 | −0.853772 | − | 0.520647i | \(-0.825691\pi\) | ||||
−0.853772 | + | 0.520647i | \(0.825691\pi\) | |||||||
\(710\) | 25.8823 | 0.971346 | ||||||||
\(711\) | −13.2350 | −0.496352 | ||||||||
\(712\) | −13.2662 | −0.497170 | ||||||||
\(713\) | −2.10543 | −0.0788489 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.2630 | 1.39356 | ||||||||
\(716\) | 1.20540 | 0.0450479 | ||||||||
\(717\) | 1.83104 | 0.0683813 | ||||||||
\(718\) | −11.7801 | −0.439629 | ||||||||
\(719\) | −30.1441 | −1.12418 | −0.562092 | − | 0.827075i | \(-0.690003\pi\) | ||||
−0.562092 | + | 0.827075i | \(0.690003\pi\) | |||||||
\(720\) | −12.2876 | −0.457934 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.67514 | −0.0995585 | ||||||||
\(723\) | 22.0299 | 0.819300 | ||||||||
\(724\) | −6.95105 | −0.258334 | ||||||||
\(725\) | −12.1683 | −0.451921 | ||||||||
\(726\) | 27.2469 | 1.01123 | ||||||||
\(727\) | −45.6599 | −1.69343 | −0.846717 | − | 0.532044i | \(-0.821424\pi\) | ||||
−0.846717 | + | 0.532044i | \(0.821424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.3763 | −0.976901 | ||||||||
\(730\) | −56.0320 | −2.07384 | ||||||||
\(731\) | −21.7088 | −0.802929 | ||||||||
\(732\) | −27.8907 | −1.03087 | ||||||||
\(733\) | 27.3458 | 1.01004 | 0.505020 | − | 0.863107i | \(-0.331485\pi\) | ||||
0.505020 | + | 0.863107i | \(0.331485\pi\) | |||||||
\(734\) | −35.6438 | −1.31564 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.17268 | −0.0800862 | ||||||||
\(737\) | 10.7119 | 0.394578 | ||||||||
\(738\) | −31.0615 | −1.14339 | ||||||||
\(739\) | 49.9166 | 1.83621 | 0.918106 | − | 0.396335i | \(-0.129718\pi\) | ||||
0.918106 | + | 0.396335i | \(0.129718\pi\) | |||||||
\(740\) | 6.10500 | 0.224424 | ||||||||
\(741\) | −18.8548 | −0.692649 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.6655 | 1.05164 | 0.525818 | − | 0.850597i | \(-0.323759\pi\) | ||||
0.525818 | + | 0.850597i | \(0.323759\pi\) | |||||||
\(744\) | 2.36684 | 0.0867725 | ||||||||
\(745\) | 31.0688 | 1.13827 | ||||||||
\(746\) | 17.7483 | 0.649811 | ||||||||
\(747\) | 17.9713 | 0.657536 | ||||||||
\(748\) | 13.0249 | 0.476236 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −72.5450 | −2.64897 | ||||||||
\(751\) | −19.0316 | −0.694473 | −0.347236 | − | 0.937778i | \(-0.612880\pi\) | ||||
−0.347236 | + | 0.937778i | \(0.612880\pi\) | |||||||
\(752\) | −11.7294 | −0.427727 | ||||||||
\(753\) | 71.1165 | 2.59163 | ||||||||
\(754\) | −1.91061 | −0.0695804 | ||||||||
\(755\) | −39.0239 | −1.42023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.39694 | −0.341538 | −0.170769 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170769 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(758\) | −15.2263 | −0.553045 | ||||||||
\(759\) | 24.9783 | 0.906656 | ||||||||
\(760\) | 16.7413 | 0.607270 | ||||||||
\(761\) | 10.7493 | 0.389661 | 0.194831 | − | 0.980837i | \(-0.437584\pi\) | ||||
0.194831 | + | 0.980837i | \(0.437584\pi\) | |||||||
\(762\) | 13.3451 | 0.483441 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.80847 | −0.246322 | ||||||||
\(765\) | 34.0017 | 1.22933 | ||||||||
\(766\) | 15.8118 | 0.571302 | ||||||||
\(767\) | −6.52804 | −0.235714 | ||||||||
\(768\) | 2.44245 | 0.0881342 | ||||||||
\(769\) | −39.3774 | −1.41998 | −0.709992 | − | 0.704209i | \(-0.751302\pi\) | ||||
−0.709992 | + | 0.704209i | \(0.751302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.7321 | 2.04316 | ||||||||
\(772\) | −3.89664 | −0.140243 | ||||||||
\(773\) | 19.0471 | 0.685078 | 0.342539 | − | 0.939504i | \(-0.388713\pi\) | ||||
0.342539 | + | 0.939504i | \(0.388713\pi\) | |||||||
\(774\) | 23.2653 | 0.836254 | ||||||||
\(775\) | 11.7917 | 0.423569 | ||||||||
\(776\) | −16.8452 | −0.604708 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.7172 | −0.778598 | ||||||||
\(779\) | 42.3196 | 1.51626 | ||||||||
\(780\) | −19.3358 | −0.692332 | ||||||||
\(781\) | 29.4023 | 1.05210 | ||||||||
\(782\) | 6.01213 | 0.214993 | ||||||||
\(783\) | 0.0841506 | 0.00300730 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 73.8723 | 2.63662 | ||||||||
\(786\) | 32.7732 | 1.16898 | ||||||||
\(787\) | −26.4446 | −0.942650 | −0.471325 | − | 0.881960i | \(-0.656224\pi\) | ||||
−0.471325 | + | 0.881960i | \(0.656224\pi\) | |||||||
\(788\) | 15.5624 | 0.554386 | ||||||||
\(789\) | −50.0783 | −1.78283 | ||||||||
\(790\) | 18.4920 | 0.657916 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.9587 | −0.496002 | ||||||||
\(793\) | −21.8176 | −0.774767 | ||||||||
\(794\) | −1.26033 | −0.0447275 | ||||||||
\(795\) | 28.1425 | 0.998111 | ||||||||
\(796\) | −24.5735 | −0.870986 | ||||||||
\(797\) | 42.8772 | 1.51879 | 0.759395 | − | 0.650630i | \(-0.225495\pi\) | ||||
0.759395 | + | 0.650630i | \(0.225495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.4569 | 1.14824 | ||||||||
\(800\) | 12.1683 | 0.430216 | ||||||||
\(801\) | −39.3414 | −1.39006 | ||||||||
\(802\) | −1.91181 | −0.0675084 | ||||||||
\(803\) | −63.6522 | −2.24624 | ||||||||
\(804\) | −5.55840 | −0.196030 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.85147 | 0.0652152 | ||||||||
\(807\) | 27.8322 | 0.979739 | ||||||||
\(808\) | 12.4261 | 0.437147 | ||||||||
\(809\) | −1.72392 | −0.0606097 | −0.0303048 | − | 0.999541i | \(-0.509648\pi\) | ||||
−0.0303048 | + | 0.999541i | \(0.509648\pi\) | |||||||
\(810\) | 37.7146 | 1.32515 | ||||||||
\(811\) | −7.23311 | −0.253989 | −0.126995 | − | 0.991903i | \(-0.540533\pi\) | ||||
−0.126995 | + | 0.991903i | \(0.540533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.9031 | −1.53975 | ||||||||
\(814\) | 6.93526 | 0.243081 | ||||||||
\(815\) | 45.0764 | 1.57896 | ||||||||
\(816\) | −6.75860 | −0.236598 | ||||||||
\(817\) | −31.6978 | −1.10896 | ||||||||
\(818\) | 3.01815 | 0.105527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 43.3992 | 1.51556 | ||||||||
\(821\) | 30.7040 | 1.07158 | 0.535789 | − | 0.844352i | \(-0.320014\pi\) | ||||
0.535789 | + | 0.844352i | \(0.320014\pi\) | |||||||
\(822\) | 41.7737 | 1.45703 | ||||||||
\(823\) | −9.58578 | −0.334139 | −0.167070 | − | 0.985945i | \(-0.553430\pi\) | ||||
−0.167070 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(824\) | 16.1718 | 0.563372 | ||||||||
\(825\) | −139.894 | −4.87047 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.26986 | −0.218025 | −0.109012 | − | 0.994040i | \(-0.534769\pi\) | ||||
−0.109012 | + | 0.994040i | \(0.534769\pi\) | |||||||
\(828\) | −6.44320 | −0.223917 | ||||||||
\(829\) | −11.2898 | −0.392110 | −0.196055 | − | 0.980593i | \(-0.562813\pi\) | ||||
−0.196055 | + | 0.980593i | \(0.562813\pi\) | |||||||
\(830\) | −25.1095 | −0.871565 | ||||||||
\(831\) | −5.08107 | −0.176260 | ||||||||
\(832\) | 1.91061 | 0.0662386 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.54292 | 0.330444 | ||||||||
\(835\) | 66.4304 | 2.29892 | ||||||||
\(836\) | 19.0181 | 0.657753 | ||||||||
\(837\) | −0.0815456 | −0.00281863 | ||||||||
\(838\) | −4.64504 | −0.160460 | ||||||||
\(839\) | 44.0101 | 1.51940 | 0.759698 | − | 0.650276i | \(-0.225347\pi\) | ||||
0.759698 | + | 0.650276i | \(0.225347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −26.6202 | −0.917394 | ||||||||
\(843\) | 17.9701 | 0.618923 | ||||||||
\(844\) | 8.65646 | 0.297968 | ||||||||
\(845\) | 38.7396 | 1.33268 | ||||||||
\(846\) | −34.7840 | −1.19590 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.78082 | −0.0954938 | ||||||||
\(849\) | 14.8514 | 0.509698 | ||||||||
\(850\) | −33.6715 | −1.15492 | ||||||||
\(851\) | 3.20124 | 0.109737 | ||||||||
\(852\) | −15.2568 | −0.522690 | ||||||||
\(853\) | −10.9272 | −0.374141 | −0.187070 | − | 0.982347i | \(-0.559899\pi\) | ||||
−0.187070 | + | 0.982347i | \(0.559899\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 49.6471 | 1.69789 | ||||||||
\(856\) | 10.6246 | 0.363141 | ||||||||
\(857\) | −29.2754 | −1.00003 | −0.500015 | − | 0.866017i | \(-0.666672\pi\) | ||||
−0.500015 | + | 0.866017i | \(0.666672\pi\) | |||||||
\(858\) | −21.9654 | −0.749887 | ||||||||
\(859\) | 43.3222 | 1.47813 | 0.739067 | − | 0.673632i | \(-0.235267\pi\) | ||||
0.739067 | + | 0.673632i | \(0.235267\pi\) | |||||||
\(860\) | −32.5064 | −1.10846 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.63869 | −0.328295 | ||||||||
\(863\) | −43.8381 | −1.49227 | −0.746133 | − | 0.665797i | \(-0.768092\pi\) | ||||
−0.746133 | + | 0.665797i | \(0.768092\pi\) | |||||||
\(864\) | −0.0841506 | −0.00286286 | ||||||||
\(865\) | −25.6430 | −0.871888 | ||||||||
\(866\) | 3.16466 | 0.107540 | ||||||||
\(867\) | −22.8196 | −0.774994 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0069 | 0.712609 | ||||||||
\(870\) | 10.1202 | 0.343107 | ||||||||
\(871\) | −4.34808 | −0.147329 | ||||||||
\(872\) | 6.09884 | 0.206533 | ||||||||
\(873\) | −49.9552 | −1.69073 | ||||||||
\(874\) | 8.77852 | 0.296938 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 33.0291 | 1.11595 | ||||||||
\(877\) | 29.5072 | 0.996388 | 0.498194 | − | 0.867066i | \(-0.333997\pi\) | ||||
0.498194 | + | 0.867066i | \(0.333997\pi\) | |||||||
\(878\) | −13.8900 | −0.468764 | ||||||||
\(879\) | −33.5004 | −1.12994 | ||||||||
\(880\) | 19.5032 | 0.657452 | ||||||||
\(881\) | 13.1060 | 0.441554 | 0.220777 | − | 0.975324i | \(-0.429141\pi\) | ||||
0.220777 | + | 0.975324i | \(0.429141\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.44435 | −0.250522 | −0.125261 | − | 0.992124i | \(-0.539977\pi\) | ||||
−0.125261 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(884\) | −5.28694 | −0.177819 | ||||||||
\(885\) | 34.5780 | 1.16233 | ||||||||
\(886\) | 20.3708 | 0.684370 | ||||||||
\(887\) | −38.6833 | −1.29886 | −0.649430 | − | 0.760422i | \(-0.724992\pi\) | ||||
−0.649430 | + | 0.760422i | \(0.724992\pi\) | |||||||
\(888\) | −3.59871 | −0.120765 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 54.9679 | 1.84253 | ||||||||
\(891\) | 42.8437 | 1.43532 | ||||||||
\(892\) | 10.9191 | 0.365597 | ||||||||
\(893\) | 47.3914 | 1.58589 | ||||||||
\(894\) | −18.3141 | −0.612516 | ||||||||
\(895\) | −4.99453 | −0.166949 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.1390 | −0.338531 | ||||||||
\(898\) | 33.1442 | 1.10604 | ||||||||
\(899\) | −0.969044 | −0.0323194 | ||||||||
\(900\) | 36.0858 | 1.20286 | ||||||||
\(901\) | 7.69493 | 0.256355 | ||||||||
\(902\) | 49.3014 | 1.64156 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.5875 | 0.485173 | ||||||||
\(905\) | 28.8015 | 0.957393 | ||||||||
\(906\) | 23.0034 | 0.764236 | ||||||||
\(907\) | 2.42625 | 0.0805624 | 0.0402812 | − | 0.999188i | \(-0.487175\pi\) | ||||
0.0402812 | + | 0.999188i | \(0.487175\pi\) | |||||||
\(908\) | 10.4951 | 0.348292 | ||||||||
\(909\) | 36.8500 | 1.22224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.86661 | −0.0618435 | −0.0309218 | − | 0.999522i | \(-0.509844\pi\) | ||||
−0.0309218 | + | 0.999522i | \(0.509844\pi\) | |||||||
\(912\) | −9.86847 | −0.326778 | ||||||||
\(913\) | −28.5244 | −0.944020 | ||||||||
\(914\) | −18.2087 | −0.602290 | ||||||||
\(915\) | 115.564 | 3.82044 | ||||||||
\(916\) | 7.51525 | 0.248311 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.232857 | 0.00768542 | ||||||||
\(919\) | 27.4057 | 0.904031 | 0.452015 | − | 0.892010i | \(-0.350705\pi\) | ||||
0.452015 | + | 0.892010i | \(0.350705\pi\) | |||||||
\(920\) | 9.00245 | 0.296802 | ||||||||
\(921\) | −18.6724 | −0.615275 | ||||||||
\(922\) | 3.52484 | 0.116084 | ||||||||
\(923\) | −11.9347 | −0.392836 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9289 | −0.589497 | ||||||||
\(926\) | 10.7653 | 0.353768 | ||||||||
\(927\) | 47.9583 | 1.57516 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −43.9595 | −1.44227 | −0.721133 | − | 0.692797i | \(-0.756378\pi\) | ||||
−0.721133 | + | 0.692797i | \(0.756378\pi\) | |||||||
\(930\) | −9.80692 | −0.321582 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.14262 | 0.168452 | ||||||||
\(933\) | −59.6572 | −1.95309 | ||||||||
\(934\) | −12.0199 | −0.393303 | ||||||||
\(935\) | −53.9681 | −1.76495 | ||||||||
\(936\) | 5.66601 | 0.185199 | ||||||||
\(937\) | 29.9446 | 0.978246 | 0.489123 | − | 0.872215i | \(-0.337317\pi\) | ||||
0.489123 | + | 0.872215i | \(0.337317\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.6101 | 1.45579 | ||||||||
\(940\) | 48.6003 | 1.58517 | ||||||||
\(941\) | −21.5723 | −0.703236 | −0.351618 | − | 0.936144i | \(-0.614368\pi\) | ||||
−0.351618 | + | 0.936144i | \(0.614368\pi\) | |||||||
\(942\) | −43.5455 | −1.41879 | ||||||||
\(943\) | 22.7570 | 0.741068 | ||||||||
\(944\) | −3.41673 | −0.111205 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.9271 | −1.20061 | ||||||||
\(947\) | 4.39212 | 0.142725 | 0.0713624 | − | 0.997450i | \(-0.477265\pi\) | ||||
0.0713624 | + | 0.997450i | \(0.477265\pi\) | |||||||
\(948\) | −10.9005 | −0.354031 | ||||||||
\(949\) | 25.8371 | 0.838709 | ||||||||
\(950\) | −49.1650 | −1.59512 | ||||||||
\(951\) | −25.4545 | −0.825418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.9052 | 1.06591 | 0.532953 | − | 0.846145i | \(-0.321082\pi\) | ||||
0.532953 | + | 0.846145i | \(0.321082\pi\) | |||||||
\(954\) | −8.24666 | −0.266995 | ||||||||
\(955\) | 28.2107 | 0.912876 | ||||||||
\(956\) | 0.749673 | 0.0242462 | ||||||||
\(957\) | 11.4965 | 0.371630 | ||||||||
\(958\) | −8.29202 | −0.267903 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.1202 | −0.326628 | ||||||||
\(961\) | −30.0610 | −0.969708 | ||||||||
\(962\) | −2.81510 | −0.0907625 | ||||||||
\(963\) | 31.5077 | 1.01532 | ||||||||
\(964\) | 9.01959 | 0.290501 | ||||||||
\(965\) | 16.1456 | 0.519745 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.50365 | 0.144827 | 0.0724137 | − | 0.997375i | \(-0.476930\pi\) | ||||
0.0724137 | + | 0.997375i | \(0.476930\pi\) | |||||||
\(968\) | 11.1556 | 0.358554 | ||||||||
\(969\) | 27.3075 | 0.877242 | ||||||||
\(970\) | 69.7976 | 2.24107 | ||||||||
\(971\) | −30.4189 | −0.976187 | −0.488094 | − | 0.872791i | \(-0.662308\pi\) | ||||
−0.488094 | + | 0.872791i | \(0.662308\pi\) | |||||||
\(972\) | −21.9791 | −0.704981 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.89345 | 0.252923 | ||||||||
\(975\) | 56.7844 | 1.81856 | ||||||||
\(976\) | −11.4192 | −0.365519 | ||||||||
\(977\) | 37.5202 | 1.20038 | 0.600189 | − | 0.799858i | \(-0.295092\pi\) | ||||
0.600189 | + | 0.799858i | \(0.295092\pi\) | |||||||
\(978\) | −26.5711 | −0.849652 | ||||||||
\(979\) | 62.4434 | 1.99570 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0864 | 0.577454 | ||||||||
\(982\) | −37.7250 | −1.20385 | ||||||||
\(983\) | −43.4878 | −1.38705 | −0.693523 | − | 0.720435i | \(-0.743942\pi\) | ||||
−0.693523 | + | 0.720435i | \(0.743942\pi\) | |||||||
\(984\) | −25.5825 | −0.815539 | ||||||||
\(985\) | −64.4821 | −2.05457 | ||||||||
\(986\) | 2.76714 | 0.0881238 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.71964 | −0.245595 | ||||||||
\(989\) | −17.0452 | −0.542004 | ||||||||
\(990\) | 57.8376 | 1.83820 | ||||||||
\(991\) | −55.4198 | −1.76047 | −0.880233 | − | 0.474541i | \(-0.842614\pi\) | ||||
−0.880233 | + | 0.474541i | \(0.842614\pi\) | |||||||
\(992\) | 0.969044 | 0.0307672 | ||||||||
\(993\) | 11.4392 | 0.363013 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 101.820 | 3.22790 | ||||||||
\(996\) | 14.8013 | 0.468997 | ||||||||
\(997\) | 23.8889 | 0.756570 | 0.378285 | − | 0.925689i | \(-0.376514\pi\) | ||||
0.378285 | + | 0.925689i | \(0.376514\pi\) | |||||||
\(998\) | −8.47942 | −0.268411 | ||||||||
\(999\) | 0.123988 | 0.00392280 |
(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 | 2842.2.a.x.1.5 | 5 | ||
7.3 | odd | 6 | 406.2.e.a.233.5 | ✓ | 10 | ||
7.5 | odd | 6 | 406.2.e.a.291.5 | yes | 10 | ||
7.6 | odd | 2 | 2842.2.a.z.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.a.233.5 | ✓ | 10 | 7.3 | odd | 6 | ||
406.2.e.a.291.5 | yes | 10 | 7.5 | odd | 6 | ||
2842.2.a.x.1.5 | 5 | 1.1 | even | 1 | trivial | ||
2842.2.a.z.1.1 | 5 | 7.6 | odd | 2 |