Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.368135 | 0.260311 | 0.130155 | − | 0.991494i | \(-0.458452\pi\) | ||||
0.130155 | + | 0.991494i | \(0.458452\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.86448 | −0.932238 | ||||||||
\(5\) | 0.572097 | 0.255850 | 0.127925 | − | 0.991784i | \(-0.459168\pi\) | ||||
0.127925 | + | 0.991784i | \(0.459168\pi\) | |||||||
\(6\) | −0.368135 | −0.150291 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.42265 | −0.502983 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.210609 | 0.0666005 | ||||||||
\(11\) | 5.73282 | 1.72851 | 0.864255 | − | 0.503055i | \(-0.167791\pi\) | ||||
0.864255 | + | 0.503055i | \(0.167791\pi\) | |||||||
\(12\) | 1.86448 | 0.538228 | ||||||||
\(13\) | 3.53946 | 0.981671 | 0.490835 | − | 0.871252i | \(-0.336692\pi\) | ||||
0.490835 | + | 0.871252i | \(0.336692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.572097 | −0.147715 | ||||||||
\(16\) | 3.20522 | 0.801306 | ||||||||
\(17\) | 1.83305 | 0.444579 | 0.222289 | − | 0.974981i | \(-0.428647\pi\) | ||||
0.222289 | + | 0.974981i | \(0.428647\pi\) | |||||||
\(18\) | 0.368135 | 0.0867703 | ||||||||
\(19\) | 5.95881 | 1.36704 | 0.683522 | − | 0.729930i | \(-0.260447\pi\) | ||||
0.683522 | + | 0.729930i | \(0.260447\pi\) | |||||||
\(20\) | −1.06666 | −0.238513 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.11045 | 0.449950 | ||||||||
\(23\) | 3.12066 | 0.650703 | 0.325351 | − | 0.945593i | \(-0.394517\pi\) | ||||
0.325351 | + | 0.945593i | \(0.394517\pi\) | |||||||
\(24\) | 1.42265 | 0.290397 | ||||||||
\(25\) | −4.67270 | −0.934541 | ||||||||
\(26\) | 1.30300 | 0.255540 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0143419 | −0.00266322 | −0.00133161 | − | 0.999999i | \(-0.500424\pi\) | ||||
−0.00133161 | + | 0.999999i | \(0.500424\pi\) | |||||||
\(30\) | −0.210609 | −0.0384518 | ||||||||
\(31\) | −6.00517 | −1.07856 | −0.539281 | − | 0.842126i | \(-0.681304\pi\) | ||||
−0.539281 | + | 0.842126i | \(0.681304\pi\) | |||||||
\(32\) | 4.02526 | 0.711572 | ||||||||
\(33\) | −5.73282 | −0.997955 | ||||||||
\(34\) | 0.674809 | 0.115729 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.86448 | −0.310746 | ||||||||
\(37\) | 7.68699 | 1.26373 | 0.631867 | − | 0.775077i | \(-0.282289\pi\) | ||||
0.631867 | + | 0.775077i | \(0.282289\pi\) | |||||||
\(38\) | 2.19365 | 0.355857 | ||||||||
\(39\) | −3.53946 | −0.566768 | ||||||||
\(40\) | −0.813895 | −0.128688 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.01972 | 0.917999 | 0.459000 | − | 0.888436i | \(-0.348208\pi\) | ||||
0.459000 | + | 0.888436i | \(0.348208\pi\) | |||||||
\(44\) | −10.6887 | −1.61138 | ||||||||
\(45\) | 0.572097 | 0.0852833 | ||||||||
\(46\) | 1.14883 | 0.169385 | ||||||||
\(47\) | 6.07970 | 0.886815 | 0.443407 | − | 0.896320i | \(-0.353769\pi\) | ||||
0.443407 | + | 0.896320i | \(0.353769\pi\) | |||||||
\(48\) | −3.20522 | −0.462634 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.72019 | −0.243271 | ||||||||
\(51\) | −1.83305 | −0.256678 | ||||||||
\(52\) | −6.59925 | −0.915151 | ||||||||
\(53\) | −0.555156 | −0.0762566 | −0.0381283 | − | 0.999273i | \(-0.512140\pi\) | ||||
−0.0381283 | + | 0.999273i | \(0.512140\pi\) | |||||||
\(54\) | −0.368135 | −0.0500969 | ||||||||
\(55\) | 3.27973 | 0.442239 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.95881 | −0.789263 | ||||||||
\(58\) | −0.00527975 | −0.000693265 0 | ||||||||
\(59\) | 7.46748 | 0.972182 | 0.486091 | − | 0.873908i | \(-0.338422\pi\) | ||||
0.486091 | + | 0.873908i | \(0.338422\pi\) | |||||||
\(60\) | 1.06666 | 0.137705 | ||||||||
\(61\) | −10.8150 | −1.38472 | −0.692360 | − | 0.721552i | \(-0.743429\pi\) | ||||
−0.692360 | + | 0.721552i | \(0.743429\pi\) | |||||||
\(62\) | −2.21072 | −0.280761 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.92861 | −0.616076 | ||||||||
\(65\) | 2.02492 | 0.251160 | ||||||||
\(66\) | −2.11045 | −0.259779 | ||||||||
\(67\) | 3.12025 | 0.381199 | 0.190600 | − | 0.981668i | \(-0.438957\pi\) | ||||
0.190600 | + | 0.981668i | \(0.438957\pi\) | |||||||
\(68\) | −3.41767 | −0.414453 | ||||||||
\(69\) | −3.12066 | −0.375683 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.70596 | −1.03321 | −0.516603 | − | 0.856225i | \(-0.672804\pi\) | ||||
−0.516603 | + | 0.856225i | \(0.672804\pi\) | |||||||
\(72\) | −1.42265 | −0.167661 | ||||||||
\(73\) | 8.02113 | 0.938803 | 0.469401 | − | 0.882985i | \(-0.344470\pi\) | ||||
0.469401 | + | 0.882985i | \(0.344470\pi\) | |||||||
\(74\) | 2.82985 | 0.328964 | ||||||||
\(75\) | 4.67270 | 0.539557 | ||||||||
\(76\) | −11.1101 | −1.27441 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.30300 | −0.147536 | ||||||||
\(79\) | 5.75556 | 0.647551 | 0.323775 | − | 0.946134i | \(-0.395048\pi\) | ||||
0.323775 | + | 0.946134i | \(0.395048\pi\) | |||||||
\(80\) | 1.83370 | 0.205014 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.368135 | 0.0406537 | ||||||||
\(83\) | −13.4857 | −1.48025 | −0.740124 | − | 0.672470i | \(-0.765233\pi\) | ||||
−0.740124 | + | 0.672470i | \(0.765233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.04868 | 0.113745 | ||||||||
\(86\) | 2.21607 | 0.238965 | ||||||||
\(87\) | 0.0143419 | 0.00153761 | ||||||||
\(88\) | −8.15579 | −0.869410 | ||||||||
\(89\) | −2.84026 | −0.301067 | −0.150534 | − | 0.988605i | \(-0.548099\pi\) | ||||
−0.150534 | + | 0.988605i | \(0.548099\pi\) | |||||||
\(90\) | 0.210609 | 0.0222002 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.81840 | −0.606610 | ||||||||
\(93\) | 6.00517 | 0.622708 | ||||||||
\(94\) | 2.23815 | 0.230848 | ||||||||
\(95\) | 3.40902 | 0.349758 | ||||||||
\(96\) | −4.02526 | −0.410826 | ||||||||
\(97\) | −17.0640 | −1.73259 | −0.866295 | − | 0.499533i | \(-0.833505\pi\) | ||||
−0.866295 | + | 0.499533i | \(0.833505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.73282 | 0.576170 | ||||||||
\(100\) | 8.71215 | 0.871215 | ||||||||
\(101\) | 4.47011 | 0.444793 | 0.222396 | − | 0.974956i | \(-0.428612\pi\) | ||||
0.222396 | + | 0.974956i | \(0.428612\pi\) | |||||||
\(102\) | −0.674809 | −0.0668160 | ||||||||
\(103\) | −14.9268 | −1.47078 | −0.735389 | − | 0.677645i | \(-0.763001\pi\) | ||||
−0.735389 | + | 0.677645i | \(0.763001\pi\) | |||||||
\(104\) | −5.03542 | −0.493764 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.204373 | −0.0198504 | ||||||||
\(107\) | −7.58526 | −0.733294 | −0.366647 | − | 0.930360i | \(-0.619494\pi\) | ||||
−0.366647 | + | 0.930360i | \(0.619494\pi\) | |||||||
\(108\) | 1.86448 | 0.179409 | ||||||||
\(109\) | −10.2791 | −0.984555 | −0.492277 | − | 0.870438i | \(-0.663835\pi\) | ||||
−0.492277 | + | 0.870438i | \(0.663835\pi\) | |||||||
\(110\) | 1.20738 | 0.115120 | ||||||||
\(111\) | −7.68699 | −0.729617 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.2306 | 1.15056 | 0.575278 | − | 0.817958i | \(-0.304894\pi\) | ||||
0.575278 | + | 0.817958i | \(0.304894\pi\) | |||||||
\(114\) | −2.19365 | −0.205454 | ||||||||
\(115\) | 1.78532 | 0.166482 | ||||||||
\(116\) | 0.0267401 | 0.00248275 | ||||||||
\(117\) | 3.53946 | 0.327224 | ||||||||
\(118\) | 2.74904 | 0.253070 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.813895 | 0.0742981 | ||||||||
\(121\) | 21.8652 | 1.98774 | ||||||||
\(122\) | −3.98139 | −0.360458 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 11.1965 | 1.00548 | ||||||||
\(125\) | −5.53373 | −0.494952 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.17403 | −0.370386 | −0.185193 | − | 0.982702i | \(-0.559291\pi\) | ||||
−0.185193 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(128\) | −9.86491 | −0.871943 | ||||||||
\(129\) | −6.01972 | −0.530007 | ||||||||
\(130\) | 0.745444 | 0.0653798 | ||||||||
\(131\) | 9.28498 | 0.811233 | 0.405616 | − | 0.914043i | \(-0.367057\pi\) | ||||
0.405616 | + | 0.914043i | \(0.367057\pi\) | |||||||
\(132\) | 10.6887 | 0.930332 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.14867 | 0.0992303 | ||||||||
\(135\) | −0.572097 | −0.0492383 | ||||||||
\(136\) | −2.60778 | −0.223615 | ||||||||
\(137\) | −7.86277 | −0.671762 | −0.335881 | − | 0.941904i | \(-0.609034\pi\) | ||||
−0.335881 | + | 0.941904i | \(0.609034\pi\) | |||||||
\(138\) | −1.14883 | −0.0977945 | ||||||||
\(139\) | −15.5406 | −1.31814 | −0.659068 | − | 0.752084i | \(-0.729049\pi\) | ||||
−0.659068 | + | 0.752084i | \(0.729049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.07970 | −0.512003 | ||||||||
\(142\) | −3.20497 | −0.268955 | ||||||||
\(143\) | 20.2911 | 1.69683 | ||||||||
\(144\) | 3.20522 | 0.267102 | ||||||||
\(145\) | −0.00820495 | −0.000681384 0 | ||||||||
\(146\) | 2.95286 | 0.244381 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.3322 | −1.17810 | ||||||||
\(149\) | 13.5549 | 1.11046 | 0.555231 | − | 0.831696i | \(-0.312630\pi\) | ||||
0.555231 | + | 0.831696i | \(0.312630\pi\) | |||||||
\(150\) | 1.72019 | 0.140453 | ||||||||
\(151\) | 11.5360 | 0.938787 | 0.469393 | − | 0.882989i | \(-0.344473\pi\) | ||||
0.469393 | + | 0.882989i | \(0.344473\pi\) | |||||||
\(152\) | −8.47730 | −0.687600 | ||||||||
\(153\) | 1.83305 | 0.148193 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.43554 | −0.275950 | ||||||||
\(156\) | 6.59925 | 0.528363 | ||||||||
\(157\) | 19.5905 | 1.56349 | 0.781744 | − | 0.623599i | \(-0.214330\pi\) | ||||
0.781744 | + | 0.623599i | \(0.214330\pi\) | |||||||
\(158\) | 2.11882 | 0.168565 | ||||||||
\(159\) | 0.555156 | 0.0440268 | ||||||||
\(160\) | 2.30284 | 0.182055 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.368135 | 0.0289234 | ||||||||
\(163\) | 15.5597 | 1.21873 | 0.609366 | − | 0.792889i | \(-0.291424\pi\) | ||||
0.609366 | + | 0.792889i | \(0.291424\pi\) | |||||||
\(164\) | −1.86448 | −0.145591 | ||||||||
\(165\) | −3.27973 | −0.255327 | ||||||||
\(166\) | −4.96456 | −0.385325 | ||||||||
\(167\) | −5.56934 | −0.430968 | −0.215484 | − | 0.976507i | \(-0.569133\pi\) | ||||
−0.215484 | + | 0.976507i | \(0.569133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.472192 | −0.0363224 | ||||||||
\(170\) | 0.386056 | 0.0296092 | ||||||||
\(171\) | 5.95881 | 0.455681 | ||||||||
\(172\) | −11.2236 | −0.855794 | ||||||||
\(173\) | −6.77107 | −0.514795 | −0.257397 | − | 0.966306i | \(-0.582865\pi\) | ||||
−0.257397 | + | 0.966306i | \(0.582865\pi\) | |||||||
\(174\) | 0.00527975 | 0.000400257 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.3750 | 1.38507 | ||||||||
\(177\) | −7.46748 | −0.561290 | ||||||||
\(178\) | −1.04560 | −0.0783711 | ||||||||
\(179\) | 21.2999 | 1.59203 | 0.796014 | − | 0.605278i | \(-0.206938\pi\) | ||||
0.796014 | + | 0.605278i | \(0.206938\pi\) | |||||||
\(180\) | −1.06666 | −0.0795043 | ||||||||
\(181\) | 1.68236 | 0.125049 | 0.0625246 | − | 0.998043i | \(-0.480085\pi\) | ||||
0.0625246 | + | 0.998043i | \(0.480085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8150 | 0.799468 | ||||||||
\(184\) | −4.43961 | −0.327292 | ||||||||
\(185\) | 4.39771 | 0.323326 | ||||||||
\(186\) | 2.21072 | 0.162098 | ||||||||
\(187\) | 10.5085 | 0.768458 | ||||||||
\(188\) | −11.3355 | −0.826723 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.25498 | 0.0910458 | ||||||||
\(191\) | 23.4936 | 1.69994 | 0.849968 | − | 0.526834i | \(-0.176621\pi\) | ||||
0.849968 | + | 0.526834i | \(0.176621\pi\) | |||||||
\(192\) | 4.92861 | 0.355692 | ||||||||
\(193\) | −0.472321 | −0.0339984 | −0.0169992 | − | 0.999856i | \(-0.505411\pi\) | ||||
−0.0169992 | + | 0.999856i | \(0.505411\pi\) | |||||||
\(194\) | −6.28187 | −0.451012 | ||||||||
\(195\) | −2.02492 | −0.145007 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4501 | −0.744536 | −0.372268 | − | 0.928125i | \(-0.621420\pi\) | ||||
−0.372268 | + | 0.928125i | \(0.621420\pi\) | |||||||
\(198\) | 2.11045 | 0.149983 | ||||||||
\(199\) | 17.6063 | 1.24808 | 0.624038 | − | 0.781394i | \(-0.285491\pi\) | ||||
0.624038 | + | 0.781394i | \(0.285491\pi\) | |||||||
\(200\) | 6.64762 | 0.470058 | ||||||||
\(201\) | −3.12025 | −0.220085 | ||||||||
\(202\) | 1.64561 | 0.115784 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.41767 | 0.239285 | ||||||||
\(205\) | 0.572097 | 0.0399570 | ||||||||
\(206\) | −5.49507 | −0.382860 | ||||||||
\(207\) | 3.12066 | 0.216901 | ||||||||
\(208\) | 11.3448 | 0.786619 | ||||||||
\(209\) | 34.1607 | 2.36295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.47455 | −0.170355 | −0.0851774 | − | 0.996366i | \(-0.527146\pi\) | ||||
−0.0851774 | + | 0.996366i | \(0.527146\pi\) | |||||||
\(212\) | 1.03508 | 0.0710893 | ||||||||
\(213\) | 8.70596 | 0.596522 | ||||||||
\(214\) | −2.79240 | −0.190885 | ||||||||
\(215\) | 3.44387 | 0.234870 | ||||||||
\(216\) | 1.42265 | 0.0967991 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.78408 | −0.256290 | ||||||||
\(219\) | −8.02113 | −0.542018 | ||||||||
\(220\) | −6.11498 | −0.412272 | ||||||||
\(221\) | 6.48800 | 0.436430 | ||||||||
\(222\) | −2.82985 | −0.189927 | ||||||||
\(223\) | 9.68745 | 0.648720 | 0.324360 | − | 0.945934i | \(-0.394851\pi\) | ||||
0.324360 | + | 0.945934i | \(0.394851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.67270 | −0.311514 | ||||||||
\(226\) | 4.50251 | 0.299502 | ||||||||
\(227\) | −16.5132 | −1.09602 | −0.548011 | − | 0.836471i | \(-0.684615\pi\) | ||||
−0.548011 | + | 0.836471i | \(0.684615\pi\) | |||||||
\(228\) | 11.1101 | 0.735781 | ||||||||
\(229\) | −4.68553 | −0.309629 | −0.154814 | − | 0.987944i | \(-0.549478\pi\) | ||||
−0.154814 | + | 0.987944i | \(0.549478\pi\) | |||||||
\(230\) | 0.657240 | 0.0433371 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0204035 | 0.00133955 | ||||||||
\(233\) | 15.5025 | 1.01560 | 0.507800 | − | 0.861475i | \(-0.330459\pi\) | ||||
0.507800 | + | 0.861475i | \(0.330459\pi\) | |||||||
\(234\) | 1.30300 | 0.0851799 | ||||||||
\(235\) | 3.47818 | 0.226891 | ||||||||
\(236\) | −13.9229 | −0.906306 | ||||||||
\(237\) | −5.75556 | −0.373864 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.7726 | 1.73178 | 0.865889 | − | 0.500236i | \(-0.166753\pi\) | ||||
0.865889 | + | 0.500236i | \(0.166753\pi\) | |||||||
\(240\) | −1.83370 | −0.118365 | ||||||||
\(241\) | 10.1181 | 0.651766 | 0.325883 | − | 0.945410i | \(-0.394338\pi\) | ||||
0.325883 | + | 0.945410i | \(0.394338\pi\) | |||||||
\(242\) | 8.04935 | 0.517432 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 20.1643 | 1.29089 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.368135 | −0.0234715 | ||||||||
\(247\) | 21.0910 | 1.34199 | ||||||||
\(248\) | 8.54326 | 0.542498 | ||||||||
\(249\) | 13.4857 | 0.854622 | ||||||||
\(250\) | −2.03716 | −0.128841 | ||||||||
\(251\) | −18.7939 | −1.18626 | −0.593130 | − | 0.805107i | \(-0.702108\pi\) | ||||
−0.593130 | + | 0.805107i | \(0.702108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.8902 | 1.12475 | ||||||||
\(254\) | −1.53661 | −0.0964155 | ||||||||
\(255\) | −1.04868 | −0.0656709 | ||||||||
\(256\) | 6.22560 | 0.389100 | ||||||||
\(257\) | 9.48014 | 0.591355 | 0.295677 | − | 0.955288i | \(-0.404455\pi\) | ||||
0.295677 | + | 0.955288i | \(0.404455\pi\) | |||||||
\(258\) | −2.21607 | −0.137967 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.77541 | −0.234141 | ||||||||
\(261\) | −0.0143419 | −0.000887740 0 | ||||||||
\(262\) | 3.41813 | 0.211173 | ||||||||
\(263\) | 26.2738 | 1.62011 | 0.810055 | − | 0.586354i | \(-0.199437\pi\) | ||||
0.810055 | + | 0.586354i | \(0.199437\pi\) | |||||||
\(264\) | 8.15579 | 0.501954 | ||||||||
\(265\) | −0.317604 | −0.0195102 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.84026 | 0.173821 | ||||||||
\(268\) | −5.81763 | −0.355368 | ||||||||
\(269\) | −7.74464 | −0.472199 | −0.236099 | − | 0.971729i | \(-0.575869\pi\) | ||||
−0.236099 | + | 0.971729i | \(0.575869\pi\) | |||||||
\(270\) | −0.210609 | −0.0128173 | ||||||||
\(271\) | −19.3834 | −1.17746 | −0.588729 | − | 0.808331i | \(-0.700371\pi\) | ||||
−0.588729 | + | 0.808331i | \(0.700371\pi\) | |||||||
\(272\) | 5.87532 | 0.356244 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.89456 | −0.174867 | ||||||||
\(275\) | −26.7878 | −1.61536 | ||||||||
\(276\) | 5.81840 | 0.350226 | ||||||||
\(277\) | 2.76321 | 0.166025 | 0.0830125 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830125 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(278\) | −5.72104 | −0.343125 | ||||||||
\(279\) | −6.00517 | −0.359520 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.5677 | 1.40593 | 0.702967 | − | 0.711223i | \(-0.251858\pi\) | ||||
0.702967 | + | 0.711223i | \(0.251858\pi\) | |||||||
\(282\) | −2.23815 | −0.133280 | ||||||||
\(283\) | −30.7005 | −1.82495 | −0.912476 | − | 0.409130i | \(-0.865832\pi\) | ||||
−0.912476 | + | 0.409130i | \(0.865832\pi\) | |||||||
\(284\) | 16.2320 | 0.963195 | ||||||||
\(285\) | −3.40902 | −0.201933 | ||||||||
\(286\) | 7.46987 | 0.441703 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.02526 | 0.237191 | ||||||||
\(289\) | −13.6399 | −0.802350 | ||||||||
\(290\) | −0.00302053 | −0.000177372 0 | ||||||||
\(291\) | 17.0640 | 1.00031 | ||||||||
\(292\) | −14.9552 | −0.875188 | ||||||||
\(293\) | −2.03371 | −0.118810 | −0.0594052 | − | 0.998234i | \(-0.518920\pi\) | ||||
−0.0594052 | + | 0.998234i | \(0.518920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.27212 | 0.248733 | ||||||||
\(296\) | −10.9359 | −0.635637 | ||||||||
\(297\) | −5.73282 | −0.332652 | ||||||||
\(298\) | 4.99005 | 0.289066 | ||||||||
\(299\) | 11.0455 | 0.638776 | ||||||||
\(300\) | −8.71215 | −0.502996 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.24681 | 0.244376 | ||||||||
\(303\) | −4.47011 | −0.256801 | ||||||||
\(304\) | 19.0993 | 1.09542 | ||||||||
\(305\) | −6.18724 | −0.354280 | ||||||||
\(306\) | 0.674809 | 0.0385762 | ||||||||
\(307\) | 1.78236 | 0.101725 | 0.0508623 | − | 0.998706i | \(-0.483803\pi\) | ||||
0.0508623 | + | 0.998706i | \(0.483803\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9268 | 0.849154 | ||||||||
\(310\) | −1.26475 | −0.0718327 | ||||||||
\(311\) | −12.2745 | −0.696021 | −0.348011 | − | 0.937491i | \(-0.613143\pi\) | ||||
−0.348011 | + | 0.937491i | \(0.613143\pi\) | |||||||
\(312\) | 5.03542 | 0.285075 | ||||||||
\(313\) | −3.15436 | −0.178295 | −0.0891475 | − | 0.996018i | \(-0.528414\pi\) | ||||
−0.0891475 | + | 0.996018i | \(0.528414\pi\) | |||||||
\(314\) | 7.21194 | 0.406993 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7311 | −0.603672 | ||||||||
\(317\) | −6.09319 | −0.342228 | −0.171114 | − | 0.985251i | \(-0.554737\pi\) | ||||
−0.171114 | + | 0.985251i | \(0.554737\pi\) | |||||||
\(318\) | 0.204373 | 0.0114607 | ||||||||
\(319\) | −0.0822193 | −0.00460340 | ||||||||
\(320\) | −2.81965 | −0.157623 | ||||||||
\(321\) | 7.58526 | 0.423368 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.9228 | 0.607759 | ||||||||
\(324\) | −1.86448 | −0.103582 | ||||||||
\(325\) | −16.5389 | −0.917412 | ||||||||
\(326\) | 5.72809 | 0.317249 | ||||||||
\(327\) | 10.2791 | 0.568433 | ||||||||
\(328\) | −1.42265 | −0.0785527 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.20738 | −0.0664643 | ||||||||
\(331\) | 30.2082 | 1.66039 | 0.830195 | − | 0.557473i | \(-0.188229\pi\) | ||||
0.830195 | + | 0.557473i | \(0.188229\pi\) | |||||||
\(332\) | 25.1438 | 1.37994 | ||||||||
\(333\) | 7.68699 | 0.421245 | ||||||||
\(334\) | −2.05027 | −0.112186 | ||||||||
\(335\) | 1.78509 | 0.0975297 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4472 | −0.841463 | −0.420731 | − | 0.907185i | \(-0.638227\pi\) | ||||
−0.420731 | + | 0.907185i | \(0.638227\pi\) | |||||||
\(338\) | −0.173830 | −0.00945513 | ||||||||
\(339\) | −12.2306 | −0.664274 | ||||||||
\(340\) | −1.95524 | −0.106038 | ||||||||
\(341\) | −34.4266 | −1.86430 | ||||||||
\(342\) | 2.19365 | 0.118619 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.56396 | −0.461738 | ||||||||
\(345\) | −1.78532 | −0.0961185 | ||||||||
\(346\) | −2.49267 | −0.134007 | ||||||||
\(347\) | −31.1378 | −1.67156 | −0.835781 | − | 0.549062i | \(-0.814985\pi\) | ||||
−0.835781 | + | 0.549062i | \(0.814985\pi\) | |||||||
\(348\) | −0.0267401 | −0.00143342 | ||||||||
\(349\) | 14.4496 | 0.773470 | 0.386735 | − | 0.922191i | \(-0.373603\pi\) | ||||
0.386735 | + | 0.922191i | \(0.373603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.53946 | −0.188923 | ||||||||
\(352\) | 23.0761 | 1.22996 | ||||||||
\(353\) | 17.1005 | 0.910169 | 0.455085 | − | 0.890448i | \(-0.349609\pi\) | ||||
0.455085 | + | 0.890448i | \(0.349609\pi\) | |||||||
\(354\) | −2.74904 | −0.146110 | ||||||||
\(355\) | −4.98066 | −0.264346 | ||||||||
\(356\) | 5.29560 | 0.280666 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.84124 | 0.414423 | ||||||||
\(359\) | 28.1115 | 1.48367 | 0.741833 | − | 0.670585i | \(-0.233957\pi\) | ||||
0.741833 | + | 0.670585i | \(0.233957\pi\) | |||||||
\(360\) | −0.813895 | −0.0428960 | ||||||||
\(361\) | 16.5074 | 0.868810 | ||||||||
\(362\) | 0.619337 | 0.0325517 | ||||||||
\(363\) | −21.8652 | −1.14762 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.58887 | 0.240192 | ||||||||
\(366\) | 3.98139 | 0.208110 | ||||||||
\(367\) | 8.76594 | 0.457578 | 0.228789 | − | 0.973476i | \(-0.426523\pi\) | ||||
0.228789 | + | 0.973476i | \(0.426523\pi\) | |||||||
\(368\) | 10.0024 | 0.521412 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 1.61895 | 0.0841653 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.1965 | −0.580512 | ||||||||
\(373\) | 4.95495 | 0.256558 | 0.128279 | − | 0.991738i | \(-0.459055\pi\) | ||||
0.128279 | + | 0.991738i | \(0.459055\pi\) | |||||||
\(374\) | 3.86855 | 0.200038 | ||||||||
\(375\) | 5.53373 | 0.285761 | ||||||||
\(376\) | −8.64928 | −0.446053 | ||||||||
\(377\) | −0.0507625 | −0.00261440 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.2578 | −0.937841 | −0.468921 | − | 0.883240i | \(-0.655357\pi\) | ||||
−0.468921 | + | 0.883240i | \(0.655357\pi\) | |||||||
\(380\) | −6.35603 | −0.326058 | ||||||||
\(381\) | 4.17403 | 0.213842 | ||||||||
\(382\) | 8.64882 | 0.442512 | ||||||||
\(383\) | 4.11599 | 0.210317 | 0.105159 | − | 0.994455i | \(-0.466465\pi\) | ||||
0.105159 | + | 0.994455i | \(0.466465\pi\) | |||||||
\(384\) | 9.86491 | 0.503417 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.173878 | −0.00885016 | ||||||||
\(387\) | 6.01972 | 0.306000 | ||||||||
\(388\) | 31.8155 | 1.61519 | ||||||||
\(389\) | −38.8864 | −1.97162 | −0.985809 | − | 0.167870i | \(-0.946311\pi\) | ||||
−0.985809 | + | 0.167870i | \(0.946311\pi\) | |||||||
\(390\) | −0.745444 | −0.0377470 | ||||||||
\(391\) | 5.72031 | 0.289289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.28498 | −0.468365 | ||||||||
\(394\) | −3.84704 | −0.193811 | ||||||||
\(395\) | 3.29274 | 0.165676 | ||||||||
\(396\) | −10.6887 | −0.537127 | ||||||||
\(397\) | −7.84996 | −0.393978 | −0.196989 | − | 0.980406i | \(-0.563116\pi\) | ||||
−0.196989 | + | 0.980406i | \(0.563116\pi\) | |||||||
\(398\) | 6.48149 | 0.324888 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.9771 | −0.748853 | ||||||||
\(401\) | 12.7903 | 0.638717 | 0.319358 | − | 0.947634i | \(-0.396533\pi\) | ||||
0.319358 | + | 0.947634i | \(0.396533\pi\) | |||||||
\(402\) | −1.14867 | −0.0572907 | ||||||||
\(403\) | −21.2551 | −1.05879 | ||||||||
\(404\) | −8.33442 | −0.414653 | ||||||||
\(405\) | 0.572097 | 0.0284278 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.0681 | 2.18438 | ||||||||
\(408\) | 2.60778 | 0.129104 | ||||||||
\(409\) | −16.1403 | −0.798086 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(410\) | 0.210609 | 0.0104013 | ||||||||
\(411\) | 7.86277 | 0.387842 | ||||||||
\(412\) | 27.8306 | 1.37112 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.14883 | 0.0564617 | ||||||||
\(415\) | −7.71513 | −0.378721 | ||||||||
\(416\) | 14.2473 | 0.698529 | ||||||||
\(417\) | 15.5406 | 0.761026 | ||||||||
\(418\) | 12.5758 | 0.615101 | ||||||||
\(419\) | −20.6228 | −1.00749 | −0.503745 | − | 0.863852i | \(-0.668045\pi\) | ||||
−0.503745 | + | 0.863852i | \(0.668045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8239 | 1.06363 | 0.531815 | − | 0.846861i | \(-0.321510\pi\) | ||||
0.531815 | + | 0.846861i | \(0.321510\pi\) | |||||||
\(422\) | −0.910968 | −0.0443452 | ||||||||
\(423\) | 6.07970 | 0.295605 | ||||||||
\(424\) | 0.789794 | 0.0383558 | ||||||||
\(425\) | −8.56528 | −0.415477 | ||||||||
\(426\) | 3.20497 | 0.155281 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.1425 | 0.683605 | ||||||||
\(429\) | −20.2911 | −0.979664 | ||||||||
\(430\) | 1.26781 | 0.0611392 | ||||||||
\(431\) | −32.1389 | −1.54808 | −0.774039 | − | 0.633138i | \(-0.781766\pi\) | ||||
−0.774039 | + | 0.633138i | \(0.781766\pi\) | |||||||
\(432\) | −3.20522 | −0.154211 | ||||||||
\(433\) | 5.26215 | 0.252883 | 0.126441 | − | 0.991974i | \(-0.459644\pi\) | ||||
0.126441 | + | 0.991974i | \(0.459644\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.00820495 | 0.000393397 0 | ||||||||
\(436\) | 19.1651 | 0.917839 | ||||||||
\(437\) | 18.5954 | 0.889539 | ||||||||
\(438\) | −2.95286 | −0.141093 | ||||||||
\(439\) | −4.85141 | −0.231545 | −0.115773 | − | 0.993276i | \(-0.536934\pi\) | ||||
−0.115773 | + | 0.993276i | \(0.536934\pi\) | |||||||
\(440\) | −4.66591 | −0.222438 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.38846 | 0.113608 | ||||||||
\(443\) | 1.60189 | 0.0761083 | 0.0380541 | − | 0.999276i | \(-0.487884\pi\) | ||||
0.0380541 | + | 0.999276i | \(0.487884\pi\) | |||||||
\(444\) | 14.3322 | 0.680177 | ||||||||
\(445\) | −1.62491 | −0.0770280 | ||||||||
\(446\) | 3.56629 | 0.168869 | ||||||||
\(447\) | −13.5549 | −0.641126 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.340029 | −0.0160470 | −0.00802348 | − | 0.999968i | \(-0.502554\pi\) | ||||
−0.00802348 | + | 0.999968i | \(0.502554\pi\) | |||||||
\(450\) | −1.72019 | −0.0810904 | ||||||||
\(451\) | 5.73282 | 0.269948 | ||||||||
\(452\) | −22.8036 | −1.07259 | ||||||||
\(453\) | −11.5360 | −0.542009 | ||||||||
\(454\) | −6.07911 | −0.285307 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.47730 | 0.396986 | ||||||||
\(457\) | 5.27444 | 0.246728 | 0.123364 | − | 0.992362i | \(-0.460632\pi\) | ||||
0.123364 | + | 0.992362i | \(0.460632\pi\) | |||||||
\(458\) | −1.72491 | −0.0805997 | ||||||||
\(459\) | −1.83305 | −0.0855592 | ||||||||
\(460\) | −3.32869 | −0.155201 | ||||||||
\(461\) | 19.2751 | 0.897731 | 0.448866 | − | 0.893599i | \(-0.351828\pi\) | ||||
0.448866 | + | 0.893599i | \(0.351828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5289 | 1.69764 | 0.848820 | − | 0.528682i | \(-0.177314\pi\) | ||||
0.848820 | + | 0.528682i | \(0.177314\pi\) | |||||||
\(464\) | −0.0459689 | −0.00213405 | ||||||||
\(465\) | 3.43554 | 0.159320 | ||||||||
\(466\) | 5.70700 | 0.264372 | ||||||||
\(467\) | −28.2161 | −1.30569 | −0.652843 | − | 0.757493i | \(-0.726424\pi\) | ||||
−0.652843 | + | 0.757493i | \(0.726424\pi\) | |||||||
\(468\) | −6.59925 | −0.305050 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.28044 | 0.0590623 | ||||||||
\(471\) | −19.5905 | −0.902681 | ||||||||
\(472\) | −10.6236 | −0.488991 | ||||||||
\(473\) | 34.5100 | 1.58677 | ||||||||
\(474\) | −2.11882 | −0.0973208 | ||||||||
\(475\) | −27.8437 | −1.27756 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.555156 | −0.0254189 | ||||||||
\(478\) | 9.85595 | 0.450801 | ||||||||
\(479\) | −21.9430 | −1.00260 | −0.501300 | − | 0.865274i | \(-0.667145\pi\) | ||||
−0.501300 | + | 0.865274i | \(0.667145\pi\) | |||||||
\(480\) | −2.30284 | −0.105110 | ||||||||
\(481\) | 27.2078 | 1.24057 | ||||||||
\(482\) | 3.72484 | 0.169662 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −40.7671 | −1.85305 | ||||||||
\(485\) | −9.76229 | −0.443283 | ||||||||
\(486\) | −0.368135 | −0.0166990 | ||||||||
\(487\) | −21.5895 | −0.978314 | −0.489157 | − | 0.872196i | \(-0.662696\pi\) | ||||
−0.489157 | + | 0.872196i | \(0.662696\pi\) | |||||||
\(488\) | 15.3860 | 0.696490 | ||||||||
\(489\) | −15.5597 | −0.703636 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.4173 | −1.73375 | −0.866874 | − | 0.498527i | \(-0.833874\pi\) | ||||
−0.866874 | + | 0.498527i | \(0.833874\pi\) | |||||||
\(492\) | 1.86448 | 0.0840571 | ||||||||
\(493\) | −0.0262893 | −0.00118401 | ||||||||
\(494\) | 7.76434 | 0.349334 | ||||||||
\(495\) | 3.27973 | 0.147413 | ||||||||
\(496\) | −19.2479 | −0.864258 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.96456 | 0.222467 | ||||||||
\(499\) | −11.8858 | −0.532083 | −0.266042 | − | 0.963962i | \(-0.585716\pi\) | ||||
−0.266042 | + | 0.963962i | \(0.585716\pi\) | |||||||
\(500\) | 10.3175 | 0.461413 | ||||||||
\(501\) | 5.56934 | 0.248820 | ||||||||
\(502\) | −6.91869 | −0.308796 | ||||||||
\(503\) | −8.91377 | −0.397445 | −0.198723 | − | 0.980056i | \(-0.563679\pi\) | ||||
−0.198723 | + | 0.980056i | \(0.563679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.55734 | 0.113800 | ||||||||
\(506\) | 6.58601 | 0.292784 | ||||||||
\(507\) | 0.472192 | 0.0209708 | ||||||||
\(508\) | 7.78239 | 0.345288 | ||||||||
\(509\) | 22.7887 | 1.01009 | 0.505046 | − | 0.863093i | \(-0.331476\pi\) | ||||
0.505046 | + | 0.863093i | \(0.331476\pi\) | |||||||
\(510\) | −0.386056 | −0.0170949 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.0217 | 0.973230 | ||||||||
\(513\) | −5.95881 | −0.263088 | ||||||||
\(514\) | 3.48997 | 0.153936 | ||||||||
\(515\) | −8.53957 | −0.376298 | ||||||||
\(516\) | 11.2236 | 0.494093 | ||||||||
\(517\) | 34.8538 | 1.53287 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.77107 | 0.297217 | ||||||||
\(520\) | −2.88075 | −0.126329 | ||||||||
\(521\) | 21.7252 | 0.951800 | 0.475900 | − | 0.879499i | \(-0.342122\pi\) | ||||
0.475900 | + | 0.879499i | \(0.342122\pi\) | |||||||
\(522\) | −0.00527975 | −0.000231088 0 | ||||||||
\(523\) | 44.0260 | 1.92512 | 0.962562 | − | 0.271061i | \(-0.0873746\pi\) | ||||
0.962562 | + | 0.271061i | \(0.0873746\pi\) | |||||||
\(524\) | −17.3116 | −0.756262 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.67230 | 0.421733 | ||||||||
\(527\) | −11.0078 | −0.479505 | ||||||||
\(528\) | −18.3750 | −0.799668 | ||||||||
\(529\) | −13.2615 | −0.576586 | ||||||||
\(530\) | −0.116921 | −0.00507873 | ||||||||
\(531\) | 7.46748 | 0.324061 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.53946 | 0.153311 | ||||||||
\(534\) | 1.04560 | 0.0452476 | ||||||||
\(535\) | −4.33951 | −0.187613 | ||||||||
\(536\) | −4.43902 | −0.191737 | ||||||||
\(537\) | −21.2999 | −0.919158 | ||||||||
\(538\) | −2.85107 | −0.122919 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.06666 | 0.0459018 | ||||||||
\(541\) | 28.2078 | 1.21275 | 0.606373 | − | 0.795180i | \(-0.292624\pi\) | ||||
0.606373 | + | 0.795180i | \(0.292624\pi\) | |||||||
\(542\) | −7.13571 | −0.306505 | ||||||||
\(543\) | −1.68236 | −0.0721971 | ||||||||
\(544\) | 7.37848 | 0.316350 | ||||||||
\(545\) | −5.88062 | −0.251898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0668 | 0.558694 | 0.279347 | − | 0.960190i | \(-0.409882\pi\) | ||||
0.279347 | + | 0.960190i | \(0.409882\pi\) | |||||||
\(548\) | 14.6600 | 0.626242 | ||||||||
\(549\) | −10.8150 | −0.461573 | ||||||||
\(550\) | −9.86152 | −0.420497 | ||||||||
\(551\) | −0.0854605 | −0.00364074 | ||||||||
\(552\) | 4.43961 | 0.188962 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.01723 | 0.0432181 | ||||||||
\(555\) | −4.39771 | −0.186672 | ||||||||
\(556\) | 28.9751 | 1.22882 | ||||||||
\(557\) | −0.655721 | −0.0277838 | −0.0138919 | − | 0.999904i | \(-0.504422\pi\) | ||||
−0.0138919 | + | 0.999904i | \(0.504422\pi\) | |||||||
\(558\) | −2.21072 | −0.0935871 | ||||||||
\(559\) | 21.3066 | 0.901173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.5085 | −0.443670 | ||||||||
\(562\) | 8.67612 | 0.365980 | ||||||||
\(563\) | −11.5086 | −0.485028 | −0.242514 | − | 0.970148i | \(-0.577972\pi\) | ||||
−0.242514 | + | 0.970148i | \(0.577972\pi\) | |||||||
\(564\) | 11.3355 | 0.477309 | ||||||||
\(565\) | 6.99708 | 0.294369 | ||||||||
\(566\) | −11.3019 | −0.475055 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.3855 | 0.519685 | ||||||||
\(569\) | −21.4649 | −0.899854 | −0.449927 | − | 0.893065i | \(-0.648550\pi\) | ||||
−0.449927 | + | 0.893065i | \(0.648550\pi\) | |||||||
\(570\) | −1.25498 | −0.0525653 | ||||||||
\(571\) | −4.64258 | −0.194286 | −0.0971429 | − | 0.995270i | \(-0.530970\pi\) | ||||
−0.0971429 | + | 0.995270i | \(0.530970\pi\) | |||||||
\(572\) | −37.8323 | −1.58185 | ||||||||
\(573\) | −23.4936 | −0.981459 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.5819 | −0.608108 | ||||||||
\(576\) | −4.92861 | −0.205359 | ||||||||
\(577\) | −7.53651 | −0.313749 | −0.156875 | − | 0.987619i | \(-0.550142\pi\) | ||||
−0.156875 | + | 0.987619i | \(0.550142\pi\) | |||||||
\(578\) | −5.02135 | −0.208860 | ||||||||
\(579\) | 0.472321 | 0.0196290 | ||||||||
\(580\) | 0.0152979 | 0.000635212 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.28187 | 0.260392 | ||||||||
\(583\) | −3.18261 | −0.131810 | ||||||||
\(584\) | −11.4113 | −0.472202 | ||||||||
\(585\) | 2.02492 | 0.0837201 | ||||||||
\(586\) | −0.748679 | −0.0309277 | ||||||||
\(587\) | −27.6511 | −1.14128 | −0.570641 | − | 0.821200i | \(-0.693305\pi\) | ||||
−0.570641 | + | 0.821200i | \(0.693305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.7837 | −1.47444 | ||||||||
\(590\) | 1.57272 | 0.0647478 | ||||||||
\(591\) | 10.4501 | 0.429858 | ||||||||
\(592\) | 24.6385 | 1.01264 | ||||||||
\(593\) | −15.7715 | −0.647658 | −0.323829 | − | 0.946116i | \(-0.604970\pi\) | ||||
−0.323829 | + | 0.946116i | \(0.604970\pi\) | |||||||
\(594\) | −2.11045 | −0.0865929 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.2728 | −1.03522 | ||||||||
\(597\) | −17.6063 | −0.720577 | ||||||||
\(598\) | 4.06623 | 0.166280 | ||||||||
\(599\) | −23.6599 | −0.966716 | −0.483358 | − | 0.875423i | \(-0.660583\pi\) | ||||
−0.483358 | + | 0.875423i | \(0.660583\pi\) | |||||||
\(600\) | −6.64762 | −0.271388 | ||||||||
\(601\) | 28.5440 | 1.16433 | 0.582166 | − | 0.813070i | \(-0.302205\pi\) | ||||
0.582166 | + | 0.813070i | \(0.302205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.12025 | 0.127066 | ||||||||
\(604\) | −21.5086 | −0.875173 | ||||||||
\(605\) | 12.5090 | 0.508564 | ||||||||
\(606\) | −1.64561 | −0.0668482 | ||||||||
\(607\) | −8.51374 | −0.345562 | −0.172781 | − | 0.984960i | \(-0.555275\pi\) | ||||
−0.172781 | + | 0.984960i | \(0.555275\pi\) | |||||||
\(608\) | 23.9857 | 0.972750 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.27774 | −0.0922230 | ||||||||
\(611\) | 21.5189 | 0.870560 | ||||||||
\(612\) | −3.41767 | −0.138151 | ||||||||
\(613\) | −2.53249 | −0.102286 | −0.0511431 | − | 0.998691i | \(-0.516286\pi\) | ||||
−0.0511431 | + | 0.998691i | \(0.516286\pi\) | |||||||
\(614\) | 0.656149 | 0.0264800 | ||||||||
\(615\) | −0.572097 | −0.0230692 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.5279 | −0.665387 | −0.332694 | − | 0.943035i | \(-0.607957\pi\) | ||||
−0.332694 | + | 0.943035i | \(0.607957\pi\) | |||||||
\(618\) | 5.49507 | 0.221044 | ||||||||
\(619\) | 17.3928 | 0.699075 | 0.349537 | − | 0.936922i | \(-0.386339\pi\) | ||||
0.349537 | + | 0.936922i | \(0.386339\pi\) | |||||||
\(620\) | 6.40549 | 0.257251 | ||||||||
\(621\) | −3.12066 | −0.125228 | ||||||||
\(622\) | −4.51867 | −0.181182 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11.3448 | −0.454155 | ||||||||
\(625\) | 20.1977 | 0.807908 | ||||||||
\(626\) | −1.16123 | −0.0464122 | ||||||||
\(627\) | −34.1607 | −1.36425 | ||||||||
\(628\) | −36.5259 | −1.45754 | ||||||||
\(629\) | 14.0906 | 0.561829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.3799 | −1.52788 | −0.763940 | − | 0.645287i | \(-0.776738\pi\) | ||||
−0.763940 | + | 0.645287i | \(0.776738\pi\) | |||||||
\(632\) | −8.18815 | −0.325707 | ||||||||
\(633\) | 2.47455 | 0.0983544 | ||||||||
\(634\) | −2.24312 | −0.0890857 | ||||||||
\(635\) | −2.38795 | −0.0947631 | ||||||||
\(636\) | −1.03508 | −0.0410434 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0302678 | −0.00119832 | ||||||||
\(639\) | −8.70596 | −0.344402 | ||||||||
\(640\) | −5.64369 | −0.223086 | ||||||||
\(641\) | 12.4300 | 0.490955 | 0.245477 | − | 0.969402i | \(-0.421055\pi\) | ||||
0.245477 | + | 0.969402i | \(0.421055\pi\) | |||||||
\(642\) | 2.79240 | 0.110207 | ||||||||
\(643\) | 15.1428 | 0.597172 | 0.298586 | − | 0.954383i | \(-0.403485\pi\) | ||||
0.298586 | + | 0.954383i | \(0.403485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.44387 | −0.135602 | ||||||||
\(646\) | 4.02105 | 0.158206 | ||||||||
\(647\) | −12.5947 | −0.495149 | −0.247574 | − | 0.968869i | \(-0.579633\pi\) | ||||
−0.247574 | + | 0.968869i | \(0.579633\pi\) | |||||||
\(648\) | −1.42265 | −0.0558870 | ||||||||
\(649\) | 42.8097 | 1.68043 | ||||||||
\(650\) | −6.08854 | −0.238812 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.0108 | −1.13615 | ||||||||
\(653\) | −20.3273 | −0.795467 | −0.397734 | − | 0.917501i | \(-0.630203\pi\) | ||||
−0.397734 | + | 0.917501i | \(0.630203\pi\) | |||||||
\(654\) | 3.78408 | 0.147969 | ||||||||
\(655\) | 5.31191 | 0.207554 | ||||||||
\(656\) | 3.20522 | 0.125143 | ||||||||
\(657\) | 8.02113 | 0.312934 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.2304 | 0.788063 | 0.394031 | − | 0.919097i | \(-0.371080\pi\) | ||||
0.394031 | + | 0.919097i | \(0.371080\pi\) | |||||||
\(660\) | 6.11498 | 0.238025 | ||||||||
\(661\) | 29.3691 | 1.14233 | 0.571163 | − | 0.820837i | \(-0.306492\pi\) | ||||
0.571163 | + | 0.820837i | \(0.306492\pi\) | |||||||
\(662\) | 11.1207 | 0.432218 | ||||||||
\(663\) | −6.48800 | −0.251973 | ||||||||
\(664\) | 19.1854 | 0.744539 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.82985 | 0.109655 | ||||||||
\(667\) | −0.0447561 | −0.00173296 | ||||||||
\(668\) | 10.3839 | 0.401765 | ||||||||
\(669\) | −9.68745 | −0.374539 | ||||||||
\(670\) | 0.657154 | 0.0253881 | ||||||||
\(671\) | −62.0005 | −2.39350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.9695 | 1.27088 | 0.635441 | − | 0.772150i | \(-0.280818\pi\) | ||||
0.635441 | + | 0.772150i | \(0.280818\pi\) | |||||||
\(674\) | −5.68666 | −0.219042 | ||||||||
\(675\) | 4.67270 | 0.179852 | ||||||||
\(676\) | 0.880390 | 0.0338612 | ||||||||
\(677\) | 31.1088 | 1.19561 | 0.597805 | − | 0.801642i | \(-0.296040\pi\) | ||||
0.597805 | + | 0.801642i | \(0.296040\pi\) | |||||||
\(678\) | −4.50251 | −0.172918 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.49191 | −0.0572120 | ||||||||
\(681\) | 16.5132 | 0.632789 | ||||||||
\(682\) | −12.6736 | −0.485298 | ||||||||
\(683\) | 27.6060 | 1.05632 | 0.528158 | − | 0.849146i | \(-0.322883\pi\) | ||||
0.528158 | + | 0.849146i | \(0.322883\pi\) | |||||||
\(684\) | −11.1101 | −0.424804 | ||||||||
\(685\) | −4.49827 | −0.171870 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.68553 | 0.178764 | ||||||||
\(688\) | 19.2946 | 0.735599 | ||||||||
\(689\) | −1.96496 | −0.0748589 | ||||||||
\(690\) | −0.657240 | −0.0250207 | ||||||||
\(691\) | 12.7292 | 0.484240 | 0.242120 | − | 0.970246i | \(-0.422157\pi\) | ||||
0.242120 | + | 0.970246i | \(0.422157\pi\) | |||||||
\(692\) | 12.6245 | 0.479911 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4629 | −0.435126 | ||||||||
\(695\) | −8.89073 | −0.337245 | ||||||||
\(696\) | −0.0204035 | −0.000773392 0 | ||||||||
\(697\) | 1.83305 | 0.0694315 | ||||||||
\(698\) | 5.31942 | 0.201343 | ||||||||
\(699\) | −15.5025 | −0.586357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.6716 | −1.30953 | −0.654765 | − | 0.755832i | \(-0.727232\pi\) | ||||
−0.654765 | + | 0.755832i | \(0.727232\pi\) | |||||||
\(702\) | −1.30300 | −0.0491786 | ||||||||
\(703\) | 45.8053 | 1.72758 | ||||||||
\(704\) | −28.2548 | −1.06489 | ||||||||
\(705\) | −3.47818 | −0.130996 | ||||||||
\(706\) | 6.29531 | 0.236927 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.9229 | 0.523256 | ||||||||
\(709\) | −25.5878 | −0.960969 | −0.480484 | − | 0.877003i | \(-0.659539\pi\) | ||||
−0.480484 | + | 0.877003i | \(0.659539\pi\) | |||||||
\(710\) | −1.83356 | −0.0688121 | ||||||||
\(711\) | 5.75556 | 0.215850 | ||||||||
\(712\) | 4.04070 | 0.151432 | ||||||||
\(713\) | −18.7401 | −0.701823 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6085 | 0.434133 | ||||||||
\(716\) | −39.7131 | −1.48415 | ||||||||
\(717\) | −26.7726 | −0.999843 | ||||||||
\(718\) | 10.3488 | 0.386215 | ||||||||
\(719\) | −16.6471 | −0.620832 | −0.310416 | − | 0.950601i | \(-0.600468\pi\) | ||||
−0.310416 | + | 0.950601i | \(0.600468\pi\) | |||||||
\(720\) | 1.83370 | 0.0683380 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.07695 | 0.226161 | ||||||||
\(723\) | −10.1181 | −0.376297 | ||||||||
\(724\) | −3.13673 | −0.116576 | ||||||||
\(725\) | 0.0670153 | 0.00248889 | ||||||||
\(726\) | −8.04935 | −0.298739 | ||||||||
\(727\) | 49.3359 | 1.82977 | 0.914883 | − | 0.403720i | \(-0.132283\pi\) | ||||
0.914883 | + | 0.403720i | \(0.132283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.68933 | 0.0625247 | ||||||||
\(731\) | 11.0344 | 0.408123 | ||||||||
\(732\) | −20.1643 | −0.745295 | ||||||||
\(733\) | 35.2802 | 1.30311 | 0.651553 | − | 0.758603i | \(-0.274118\pi\) | ||||
0.651553 | + | 0.758603i | \(0.274118\pi\) | |||||||
\(734\) | 3.22705 | 0.119113 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.5615 | 0.463022 | ||||||||
\(737\) | 17.8878 | 0.658906 | ||||||||
\(738\) | 0.368135 | 0.0135512 | ||||||||
\(739\) | −13.1321 | −0.483071 | −0.241535 | − | 0.970392i | \(-0.577651\pi\) | ||||
−0.241535 | + | 0.970392i | \(0.577651\pi\) | |||||||
\(740\) | −8.19943 | −0.301417 | ||||||||
\(741\) | −21.0910 | −0.774797 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.4339 | −1.29994 | −0.649971 | − | 0.759959i | \(-0.725219\pi\) | ||||
−0.649971 | + | 0.759959i | \(0.725219\pi\) | |||||||
\(744\) | −8.54326 | −0.313211 | ||||||||
\(745\) | 7.75474 | 0.284112 | ||||||||
\(746\) | 1.82409 | 0.0667848 | ||||||||
\(747\) | −13.4857 | −0.493416 | ||||||||
\(748\) | −19.5929 | −0.716386 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.03716 | 0.0743866 | ||||||||
\(751\) | 34.6635 | 1.26489 | 0.632445 | − | 0.774606i | \(-0.282052\pi\) | ||||
0.632445 | + | 0.774606i | \(0.282052\pi\) | |||||||
\(752\) | 19.4868 | 0.710610 | ||||||||
\(753\) | 18.7939 | 0.684887 | ||||||||
\(754\) | −0.0186875 | −0.000680558 0 | ||||||||
\(755\) | 6.59972 | 0.240188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.3224 | 1.61093 | 0.805463 | − | 0.592646i | \(-0.201917\pi\) | ||||
0.805463 | + | 0.592646i | \(0.201917\pi\) | |||||||
\(758\) | −6.72135 | −0.244130 | ||||||||
\(759\) | −17.8902 | −0.649372 | ||||||||
\(760\) | −4.84984 | −0.175922 | ||||||||
\(761\) | −5.89442 | −0.213673 | −0.106836 | − | 0.994277i | \(-0.534072\pi\) | ||||
−0.106836 | + | 0.994277i | \(0.534072\pi\) | |||||||
\(762\) | 1.53661 | 0.0556655 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −43.8032 | −1.58475 | ||||||||
\(765\) | 1.04868 | 0.0379151 | ||||||||
\(766\) | 1.51524 | 0.0547479 | ||||||||
\(767\) | 26.4309 | 0.954363 | ||||||||
\(768\) | −6.22560 | −0.224647 | ||||||||
\(769\) | −23.7197 | −0.855355 | −0.427678 | − | 0.903931i | \(-0.640668\pi\) | ||||
−0.427678 | + | 0.903931i | \(0.640668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.48014 | −0.341419 | ||||||||
\(772\) | 0.880632 | 0.0316946 | ||||||||
\(773\) | 31.9035 | 1.14749 | 0.573745 | − | 0.819034i | \(-0.305490\pi\) | ||||
0.573745 | + | 0.819034i | \(0.305490\pi\) | |||||||
\(774\) | 2.21607 | 0.0796551 | ||||||||
\(775\) | 28.0604 | 1.00796 | ||||||||
\(776\) | 24.2762 | 0.871463 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.3155 | −0.513234 | ||||||||
\(779\) | 5.95881 | 0.213496 | ||||||||
\(780\) | 3.77541 | 0.135181 | ||||||||
\(781\) | −49.9096 | −1.78591 | ||||||||
\(782\) | 2.10585 | 0.0753050 | ||||||||
\(783\) | 0.0143419 | 0.000512537 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.2077 | 0.400018 | ||||||||
\(786\) | −3.41813 | −0.121921 | ||||||||
\(787\) | 29.8518 | 1.06410 | 0.532050 | − | 0.846713i | \(-0.321422\pi\) | ||||
0.532050 | + | 0.846713i | \(0.321422\pi\) | |||||||
\(788\) | 19.4839 | 0.694085 | ||||||||
\(789\) | −26.2738 | −0.935371 | ||||||||
\(790\) | 1.21217 | 0.0431272 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8.15579 | −0.289803 | ||||||||
\(793\) | −38.2793 | −1.35934 | ||||||||
\(794\) | −2.88985 | −0.102557 | ||||||||
\(795\) | 0.317604 | 0.0112642 | ||||||||
\(796\) | −32.8265 | −1.16350 | ||||||||
\(797\) | −12.8988 | −0.456898 | −0.228449 | − | 0.973556i | \(-0.573365\pi\) | ||||
−0.228449 | + | 0.973556i | \(0.573365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1444 | 0.394259 | ||||||||
\(800\) | −18.8088 | −0.664993 | ||||||||
\(801\) | −2.84026 | −0.100356 | ||||||||
\(802\) | 4.70856 | 0.166265 | ||||||||
\(803\) | 45.9837 | 1.62273 | ||||||||
\(804\) | 5.81763 | 0.205172 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.82475 | −0.275615 | ||||||||
\(807\) | 7.74464 | 0.272624 | ||||||||
\(808\) | −6.35941 | −0.223723 | ||||||||
\(809\) | −46.4983 | −1.63479 | −0.817396 | − | 0.576075i | \(-0.804583\pi\) | ||||
−0.817396 | + | 0.576075i | \(0.804583\pi\) | |||||||
\(810\) | 0.210609 | 0.00740006 | ||||||||
\(811\) | −35.2925 | −1.23929 | −0.619643 | − | 0.784883i | \(-0.712723\pi\) | ||||
−0.619643 | + | 0.784883i | \(0.712723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.3834 | 0.679805 | ||||||||
\(814\) | 16.2230 | 0.568617 | ||||||||
\(815\) | 8.90168 | 0.311812 | ||||||||
\(816\) | −5.87532 | −0.205677 | ||||||||
\(817\) | 35.8704 | 1.25495 | ||||||||
\(818\) | −5.94181 | −0.207751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.06666 | −0.0372495 | ||||||||
\(821\) | −16.2632 | −0.567590 | −0.283795 | − | 0.958885i | \(-0.591594\pi\) | ||||
−0.283795 | + | 0.958885i | \(0.591594\pi\) | |||||||
\(822\) | 2.89456 | 0.100960 | ||||||||
\(823\) | 28.4263 | 0.990880 | 0.495440 | − | 0.868642i | \(-0.335007\pi\) | ||||
0.495440 | + | 0.868642i | \(0.335007\pi\) | |||||||
\(824\) | 21.2356 | 0.739776 | ||||||||
\(825\) | 26.7878 | 0.932630 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3536 | 1.26414 | 0.632070 | − | 0.774911i | \(-0.282205\pi\) | ||||
0.632070 | + | 0.774911i | \(0.282205\pi\) | |||||||
\(828\) | −5.81840 | −0.202203 | ||||||||
\(829\) | −43.8325 | −1.52236 | −0.761182 | − | 0.648538i | \(-0.775381\pi\) | ||||
−0.761182 | + | 0.648538i | \(0.775381\pi\) | |||||||
\(830\) | −2.84021 | −0.0985853 | ||||||||
\(831\) | −2.76321 | −0.0958545 | ||||||||
\(832\) | −17.4446 | −0.604784 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.72104 | 0.198103 | ||||||||
\(835\) | −3.18620 | −0.110263 | ||||||||
\(836\) | −63.6919 | −2.20283 | ||||||||
\(837\) | 6.00517 | 0.207569 | ||||||||
\(838\) | −7.59198 | −0.262261 | ||||||||
\(839\) | 35.7789 | 1.23523 | 0.617613 | − | 0.786482i | \(-0.288100\pi\) | ||||
0.617613 | + | 0.786482i | \(0.288100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9998 | −0.999993 | ||||||||
\(842\) | 8.03413 | 0.276874 | ||||||||
\(843\) | −23.5677 | −0.811716 | ||||||||
\(844\) | 4.61373 | 0.158811 | ||||||||
\(845\) | −0.270140 | −0.00929309 | ||||||||
\(846\) | 2.23815 | 0.0769492 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.77940 | −0.0611049 | ||||||||
\(849\) | 30.7005 | 1.05364 | ||||||||
\(850\) | −3.15318 | −0.108153 | ||||||||
\(851\) | 23.9885 | 0.822315 | ||||||||
\(852\) | −16.2320 | −0.556101 | ||||||||
\(853\) | 9.95627 | 0.340896 | 0.170448 | − | 0.985367i | \(-0.445478\pi\) | ||||
0.170448 | + | 0.985367i | \(0.445478\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.40902 | 0.116586 | ||||||||
\(856\) | 10.7912 | 0.368834 | ||||||||
\(857\) | −39.7735 | −1.35864 | −0.679319 | − | 0.733843i | \(-0.737725\pi\) | ||||
−0.679319 | + | 0.733843i | \(0.737725\pi\) | |||||||
\(858\) | −7.46987 | −0.255017 | ||||||||
\(859\) | 21.4817 | 0.732947 | 0.366474 | − | 0.930428i | \(-0.380565\pi\) | ||||
0.366474 | + | 0.930428i | \(0.380565\pi\) | |||||||
\(860\) | −6.42101 | −0.218955 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.8315 | −0.402982 | ||||||||
\(863\) | 14.9202 | 0.507889 | 0.253945 | − | 0.967219i | \(-0.418272\pi\) | ||||
0.253945 | + | 0.967219i | \(0.418272\pi\) | |||||||
\(864\) | −4.02526 | −0.136942 | ||||||||
\(865\) | −3.87371 | −0.131710 | ||||||||
\(866\) | 1.93718 | 0.0658282 | ||||||||
\(867\) | 13.6399 | 0.463237 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.9956 | 1.11930 | ||||||||
\(870\) | 0.00302053 | 0.000102406 0 | ||||||||
\(871\) | 11.0440 | 0.374212 | ||||||||
\(872\) | 14.6235 | 0.495214 | ||||||||
\(873\) | −17.0640 | −0.577530 | ||||||||
\(874\) | 6.84563 | 0.231557 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.9552 | 0.505290 | ||||||||
\(877\) | 14.4102 | 0.486599 | 0.243299 | − | 0.969951i | \(-0.421770\pi\) | ||||
0.243299 | + | 0.969951i | \(0.421770\pi\) | |||||||
\(878\) | −1.78598 | −0.0602738 | ||||||||
\(879\) | 2.03371 | 0.0685952 | ||||||||
\(880\) | 10.5123 | 0.354369 | ||||||||
\(881\) | 16.5606 | 0.557942 | 0.278971 | − | 0.960300i | \(-0.410007\pi\) | ||||
0.278971 | + | 0.960300i | \(0.410007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.1125 | −1.51815 | −0.759077 | − | 0.651000i | \(-0.774350\pi\) | ||||
−0.759077 | + | 0.651000i | \(0.774350\pi\) | |||||||
\(884\) | −12.0967 | −0.406857 | ||||||||
\(885\) | −4.27212 | −0.143606 | ||||||||
\(886\) | 0.589714 | 0.0198118 | ||||||||
\(887\) | 1.62359 | 0.0545150 | 0.0272575 | − | 0.999628i | \(-0.491323\pi\) | ||||
0.0272575 | + | 0.999628i | \(0.491323\pi\) | |||||||
\(888\) | 10.9359 | 0.366985 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.598186 | −0.0200512 | ||||||||
\(891\) | 5.73282 | 0.192057 | ||||||||
\(892\) | −18.0620 | −0.604761 | ||||||||
\(893\) | 36.2277 | 1.21232 | ||||||||
\(894\) | −4.99005 | −0.166892 | ||||||||
\(895\) | 12.1856 | 0.407320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.0455 | −0.368797 | ||||||||
\(898\) | −0.125177 | −0.00417720 | ||||||||
\(899\) | 0.0861254 | 0.00287244 | ||||||||
\(900\) | 8.71215 | 0.290405 | ||||||||
\(901\) | −1.01763 | −0.0339021 | ||||||||
\(902\) | 2.11045 | 0.0702704 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.3998 | −0.578710 | ||||||||
\(905\) | 0.962476 | 0.0319938 | ||||||||
\(906\) | −4.24681 | −0.141091 | ||||||||
\(907\) | −51.5666 | −1.71224 | −0.856120 | − | 0.516777i | \(-0.827132\pi\) | ||||
−0.856120 | + | 0.516777i | \(0.827132\pi\) | |||||||
\(908\) | 30.7885 | 1.02175 | ||||||||
\(909\) | 4.47011 | 0.148264 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.8580 | 1.28742 | 0.643712 | − | 0.765268i | \(-0.277394\pi\) | ||||
0.643712 | + | 0.765268i | \(0.277394\pi\) | |||||||
\(912\) | −19.0993 | −0.632442 | ||||||||
\(913\) | −77.3110 | −2.55862 | ||||||||
\(914\) | 1.94171 | 0.0642259 | ||||||||
\(915\) | 6.18724 | 0.204544 | ||||||||
\(916\) | 8.73606 | 0.288648 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.674809 | −0.0222720 | ||||||||
\(919\) | −9.94808 | −0.328157 | −0.164078 | − | 0.986447i | \(-0.552465\pi\) | ||||
−0.164078 | + | 0.986447i | \(0.552465\pi\) | |||||||
\(920\) | −2.53989 | −0.0837377 | ||||||||
\(921\) | −1.78236 | −0.0587307 | ||||||||
\(922\) | 7.09585 | 0.233689 | ||||||||
\(923\) | −30.8144 | −1.01427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.9191 | −1.18101 | ||||||||
\(926\) | 13.4476 | 0.441914 | ||||||||
\(927\) | −14.9268 | −0.490259 | ||||||||
\(928\) | −0.0577297 | −0.00189507 | ||||||||
\(929\) | −35.2695 | −1.15715 | −0.578577 | − | 0.815628i | \(-0.696392\pi\) | ||||
−0.578577 | + | 0.815628i | \(0.696392\pi\) | |||||||
\(930\) | 1.26475 | 0.0414726 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28.9040 | −0.946781 | ||||||||
\(933\) | 12.2745 | 0.401848 | ||||||||
\(934\) | −10.3874 | −0.339885 | ||||||||
\(935\) | 6.01189 | 0.196610 | ||||||||
\(936\) | −5.03542 | −0.164588 | ||||||||
\(937\) | 31.4143 | 1.02626 | 0.513131 | − | 0.858311i | \(-0.328486\pi\) | ||||
0.513131 | + | 0.858311i | \(0.328486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.15436 | 0.102939 | ||||||||
\(940\) | −6.48498 | −0.211517 | ||||||||
\(941\) | 54.8731 | 1.78881 | 0.894405 | − | 0.447258i | \(-0.147599\pi\) | ||||
0.894405 | + | 0.447258i | \(0.147599\pi\) | |||||||
\(942\) | −7.21194 | −0.234978 | ||||||||
\(943\) | 3.12066 | 0.101623 | ||||||||
\(944\) | 23.9349 | 0.779016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.7043 | 0.413054 | ||||||||
\(947\) | −20.2918 | −0.659396 | −0.329698 | − | 0.944086i | \(-0.606947\pi\) | ||||
−0.329698 | + | 0.944086i | \(0.606947\pi\) | |||||||
\(948\) | 10.7311 | 0.348530 | ||||||||
\(949\) | 28.3905 | 0.921595 | ||||||||
\(950\) | −10.2503 | −0.332563 | ||||||||
\(951\) | 6.09319 | 0.197585 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.54182 | 0.244303 | 0.122152 | − | 0.992511i | \(-0.461021\pi\) | ||||
0.122152 | + | 0.992511i | \(0.461021\pi\) | |||||||
\(954\) | −0.204373 | −0.00661681 | ||||||||
\(955\) | 13.4406 | 0.434928 | ||||||||
\(956\) | −49.9170 | −1.61443 | ||||||||
\(957\) | 0.0822193 | 0.00265777 | ||||||||
\(958\) | −8.07798 | −0.260988 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.81965 | 0.0910037 | ||||||||
\(961\) | 5.06211 | 0.163294 | ||||||||
\(962\) | 10.0162 | 0.322934 | ||||||||
\(963\) | −7.58526 | −0.244431 | ||||||||
\(964\) | −18.8650 | −0.607601 | ||||||||
\(965\) | −0.270214 | −0.00869849 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.0827 | −1.70702 | −0.853512 | − | 0.521073i | \(-0.825532\pi\) | ||||
−0.853512 | + | 0.521073i | \(0.825532\pi\) | |||||||
\(968\) | −31.1065 | −0.999801 | ||||||||
\(969\) | −10.9228 | −0.350890 | ||||||||
\(970\) | −3.59384 | −0.115391 | ||||||||
\(971\) | −41.4620 | −1.33058 | −0.665290 | − | 0.746585i | \(-0.731692\pi\) | ||||
−0.665290 | + | 0.746585i | \(0.731692\pi\) | |||||||
\(972\) | 1.86448 | 0.0598031 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.94786 | −0.254666 | ||||||||
\(975\) | 16.5389 | 0.529668 | ||||||||
\(976\) | −34.6645 | −1.10958 | ||||||||
\(977\) | 58.5821 | 1.87421 | 0.937103 | − | 0.349053i | \(-0.113497\pi\) | ||||
0.937103 | + | 0.349053i | \(0.113497\pi\) | |||||||
\(978\) | −5.72809 | −0.183164 | ||||||||
\(979\) | −16.2827 | −0.520398 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.2791 | −0.328185 | ||||||||
\(982\) | −14.1428 | −0.451314 | ||||||||
\(983\) | −42.8900 | −1.36798 | −0.683990 | − | 0.729492i | \(-0.739757\pi\) | ||||
−0.683990 | + | 0.729492i | \(0.739757\pi\) | |||||||
\(984\) | 1.42265 | 0.0453524 | ||||||||
\(985\) | −5.97845 | −0.190489 | ||||||||
\(986\) | −0.00967802 | −0.000308211 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −39.3236 | −1.25105 | ||||||||
\(989\) | 18.7855 | 0.597345 | ||||||||
\(990\) | 1.20738 | 0.0383732 | ||||||||
\(991\) | 11.9612 | 0.379960 | 0.189980 | − | 0.981788i | \(-0.439158\pi\) | ||||
0.189980 | + | 0.981788i | \(0.439158\pi\) | |||||||
\(992\) | −24.1724 | −0.767473 | ||||||||
\(993\) | −30.2082 | −0.958627 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0725 | 0.319320 | ||||||||
\(996\) | −25.1438 | −0.796711 | ||||||||
\(997\) | −16.9681 | −0.537386 | −0.268693 | − | 0.963226i | \(-0.586592\pi\) | ||||
−0.268693 | + | 0.963226i | \(0.586592\pi\) | |||||||
\(998\) | −4.37560 | −0.138507 | ||||||||
\(999\) | −7.68699 | −0.243206 |
(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 | 6027.2.a.bn.1.13 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.13 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.13 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.13 | yes | 24 | 7.6 | odd | 2 |