Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81819 | −1.28566 | −0.642828 | − | 0.766010i | \(-0.722239\pi\) | ||||
−0.642828 | + | 0.766010i | \(0.722239\pi\) | |||||||
\(3\) | 1.88652 | 1.08918 | 0.544590 | − | 0.838702i | \(-0.316685\pi\) | ||||
0.544590 | + | 0.838702i | \(0.316685\pi\) | |||||||
\(4\) | 1.30583 | 0.652913 | ||||||||
\(5\) | −3.78374 | −1.69214 | −0.846070 | − | 0.533071i | \(-0.821038\pi\) | ||||
−0.846070 | + | 0.533071i | \(0.821038\pi\) | |||||||
\(6\) | −3.43005 | −1.40031 | ||||||||
\(7\) | 2.14600 | 0.811113 | 0.405557 | − | 0.914070i | \(-0.367078\pi\) | ||||
0.405557 | + | 0.914070i | \(0.367078\pi\) | |||||||
\(8\) | 1.26214 | 0.446234 | ||||||||
\(9\) | 0.558942 | 0.186314 | ||||||||
\(10\) | 6.87957 | 2.17551 | ||||||||
\(11\) | −3.52159 | −1.06180 | −0.530899 | − | 0.847435i | \(-0.678146\pi\) | ||||
−0.530899 | + | 0.847435i | \(0.678146\pi\) | |||||||
\(12\) | 2.46346 | 0.711140 | ||||||||
\(13\) | 6.24903 | 1.73317 | 0.866584 | − | 0.499031i | \(-0.166311\pi\) | ||||
0.866584 | + | 0.499031i | \(0.166311\pi\) | |||||||
\(14\) | −3.90185 | −1.04281 | ||||||||
\(15\) | −7.13809 | −1.84305 | ||||||||
\(16\) | −4.90647 | −1.22662 | ||||||||
\(17\) | −3.30498 | −0.801576 | −0.400788 | − | 0.916171i | \(-0.631264\pi\) | ||||
−0.400788 | + | 0.916171i | \(0.631264\pi\) | |||||||
\(18\) | −1.01626 | −0.239536 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.94091 | −1.10482 | ||||||||
\(21\) | 4.04847 | 0.883449 | ||||||||
\(22\) | 6.40292 | 1.36511 | ||||||||
\(23\) | −0.0872254 | −0.0181878 | −0.00909388 | − | 0.999959i | \(-0.502895\pi\) | ||||
−0.00909388 | + | 0.999959i | \(0.502895\pi\) | |||||||
\(24\) | 2.38105 | 0.486030 | ||||||||
\(25\) | 9.31670 | 1.86334 | ||||||||
\(26\) | −11.3619 | −2.22826 | ||||||||
\(27\) | −4.60509 | −0.886251 | ||||||||
\(28\) | 2.80231 | 0.529587 | ||||||||
\(29\) | −3.48115 | −0.646433 | −0.323217 | − | 0.946325i | \(-0.604764\pi\) | ||||
−0.323217 | + | 0.946325i | \(0.604764\pi\) | |||||||
\(30\) | 12.9784 | 2.36953 | ||||||||
\(31\) | 8.80857 | 1.58207 | 0.791033 | − | 0.611774i | \(-0.209544\pi\) | ||||
0.791033 | + | 0.611774i | \(0.209544\pi\) | |||||||
\(32\) | 6.39663 | 1.13077 | ||||||||
\(33\) | −6.64353 | −1.15649 | ||||||||
\(34\) | 6.00910 | 1.03055 | ||||||||
\(35\) | −8.11993 | −1.37252 | ||||||||
\(36\) | 0.729881 | 0.121647 | ||||||||
\(37\) | 4.61409 | 0.758552 | 0.379276 | − | 0.925284i | \(-0.376173\pi\) | ||||
0.379276 | + | 0.925284i | \(0.376173\pi\) | |||||||
\(38\) | 1.81819 | 0.294950 | ||||||||
\(39\) | 11.7889 | 1.88773 | ||||||||
\(40\) | −4.77562 | −0.755091 | ||||||||
\(41\) | −3.33867 | −0.521413 | −0.260706 | − | 0.965418i | \(-0.583955\pi\) | ||||
−0.260706 | + | 0.965418i | \(0.583955\pi\) | |||||||
\(42\) | −7.36090 | −1.13581 | ||||||||
\(43\) | −6.44056 | −0.982177 | −0.491088 | − | 0.871110i | \(-0.663401\pi\) | ||||
−0.491088 | + | 0.871110i | \(0.663401\pi\) | |||||||
\(44\) | −4.59858 | −0.693262 | ||||||||
\(45\) | −2.11489 | −0.315269 | ||||||||
\(46\) | 0.158593 | 0.0233832 | ||||||||
\(47\) | 12.1176 | 1.76754 | 0.883768 | − | 0.467925i | \(-0.154998\pi\) | ||||
0.883768 | + | 0.467925i | \(0.154998\pi\) | |||||||
\(48\) | −9.25613 | −1.33601 | ||||||||
\(49\) | −2.39466 | −0.342095 | ||||||||
\(50\) | −16.9396 | −2.39562 | ||||||||
\(51\) | −6.23490 | −0.873061 | ||||||||
\(52\) | 8.16015 | 1.13161 | ||||||||
\(53\) | 4.45724 | 0.612249 | 0.306125 | − | 0.951991i | \(-0.400968\pi\) | ||||
0.306125 | + | 0.951991i | \(0.400968\pi\) | |||||||
\(54\) | 8.37295 | 1.13941 | ||||||||
\(55\) | 13.3248 | 1.79671 | ||||||||
\(56\) | 2.70856 | 0.361947 | ||||||||
\(57\) | −1.88652 | −0.249875 | ||||||||
\(58\) | 6.32940 | 0.831091 | ||||||||
\(59\) | −1.45966 | −0.190031 | −0.0950157 | − | 0.995476i | \(-0.530290\pi\) | ||||
−0.0950157 | + | 0.995476i | \(0.530290\pi\) | |||||||
\(60\) | −9.32111 | −1.20335 | ||||||||
\(61\) | −8.89957 | −1.13947 | −0.569736 | − | 0.821827i | \(-0.692955\pi\) | ||||
−0.569736 | + | 0.821827i | \(0.692955\pi\) | |||||||
\(62\) | −16.0157 | −2.03399 | ||||||||
\(63\) | 1.19949 | 0.151122 | ||||||||
\(64\) | −1.81737 | −0.227171 | ||||||||
\(65\) | −23.6447 | −2.93277 | ||||||||
\(66\) | 12.0792 | 1.48685 | ||||||||
\(67\) | 7.80761 | 0.953851 | 0.476925 | − | 0.878944i | \(-0.341751\pi\) | ||||
0.476925 | + | 0.878944i | \(0.341751\pi\) | |||||||
\(68\) | −4.31574 | −0.523360 | ||||||||
\(69\) | −0.164552 | −0.0198098 | ||||||||
\(70\) | 14.7636 | 1.76459 | ||||||||
\(71\) | −15.2885 | −1.81441 | −0.907205 | − | 0.420690i | \(-0.861788\pi\) | ||||
−0.907205 | + | 0.420690i | \(0.861788\pi\) | |||||||
\(72\) | 0.705464 | 0.0831397 | ||||||||
\(73\) | −10.5444 | −1.23413 | −0.617066 | − | 0.786911i | \(-0.711679\pi\) | ||||
−0.617066 | + | 0.786911i | \(0.711679\pi\) | |||||||
\(74\) | −8.38931 | −0.975238 | ||||||||
\(75\) | 17.5761 | 2.02951 | ||||||||
\(76\) | −1.30583 | −0.149789 | ||||||||
\(77\) | −7.55734 | −0.861239 | ||||||||
\(78\) | −21.4345 | −2.42698 | ||||||||
\(79\) | −5.94661 | −0.669046 | −0.334523 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334523 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(80\) | 18.5648 | 2.07561 | ||||||||
\(81\) | −10.3644 | −1.15160 | ||||||||
\(82\) | 6.07035 | 0.670358 | ||||||||
\(83\) | −10.8558 | −1.19157 | −0.595787 | − | 0.803142i | \(-0.703160\pi\) | ||||
−0.595787 | + | 0.803142i | \(0.703160\pi\) | |||||||
\(84\) | 5.28660 | 0.576815 | ||||||||
\(85\) | 12.5052 | 1.35638 | ||||||||
\(86\) | 11.7102 | 1.26274 | ||||||||
\(87\) | −6.56724 | −0.704082 | ||||||||
\(88\) | −4.44474 | −0.473811 | ||||||||
\(89\) | 15.9439 | 1.69005 | 0.845026 | − | 0.534725i | \(-0.179585\pi\) | ||||
0.845026 | + | 0.534725i | \(0.179585\pi\) | |||||||
\(90\) | 3.84528 | 0.405328 | ||||||||
\(91\) | 13.4104 | 1.40580 | ||||||||
\(92\) | −0.113901 | −0.0118750 | ||||||||
\(93\) | 16.6175 | 1.72315 | ||||||||
\(94\) | −22.0322 | −2.27245 | ||||||||
\(95\) | 3.78374 | 0.388204 | ||||||||
\(96\) | 12.0673 | 1.23162 | ||||||||
\(97\) | −4.28346 | −0.434920 | −0.217460 | − | 0.976069i | \(-0.569777\pi\) | ||||
−0.217460 | + | 0.976069i | \(0.569777\pi\) | |||||||
\(98\) | 4.35396 | 0.439817 | ||||||||
\(99\) | −1.96836 | −0.197828 | ||||||||
\(100\) | 12.1660 | 1.21660 | ||||||||
\(101\) | 11.8193 | 1.17606 | 0.588031 | − | 0.808838i | \(-0.299903\pi\) | ||||
0.588031 | + | 0.808838i | \(0.299903\pi\) | |||||||
\(102\) | 11.3363 | 1.12246 | ||||||||
\(103\) | 13.8456 | 1.36425 | 0.682123 | − | 0.731237i | \(-0.261057\pi\) | ||||
0.682123 | + | 0.731237i | \(0.261057\pi\) | |||||||
\(104\) | 7.88716 | 0.773399 | ||||||||
\(105\) | −15.3184 | −1.49492 | ||||||||
\(106\) | −8.10413 | −0.787143 | ||||||||
\(107\) | −7.33755 | −0.709348 | −0.354674 | − | 0.934990i | \(-0.615408\pi\) | ||||
−0.354674 | + | 0.934990i | \(0.615408\pi\) | |||||||
\(108\) | −6.01346 | −0.578645 | ||||||||
\(109\) | 16.3469 | 1.56575 | 0.782875 | − | 0.622179i | \(-0.213752\pi\) | ||||
0.782875 | + | 0.622179i | \(0.213752\pi\) | |||||||
\(110\) | −24.2270 | −2.30996 | ||||||||
\(111\) | 8.70456 | 0.826200 | ||||||||
\(112\) | −10.5293 | −0.994926 | ||||||||
\(113\) | 1.73388 | 0.163110 | 0.0815549 | − | 0.996669i | \(-0.474011\pi\) | ||||
0.0815549 | + | 0.996669i | \(0.474011\pi\) | |||||||
\(114\) | 3.43005 | 0.321254 | ||||||||
\(115\) | 0.330039 | 0.0307763 | ||||||||
\(116\) | −4.54578 | −0.422065 | ||||||||
\(117\) | 3.49284 | 0.322913 | ||||||||
\(118\) | 2.65394 | 0.244315 | ||||||||
\(119\) | −7.09251 | −0.650169 | ||||||||
\(120\) | −9.00928 | −0.822431 | ||||||||
\(121\) | 1.40157 | 0.127416 | ||||||||
\(122\) | 16.1811 | 1.46497 | ||||||||
\(123\) | −6.29846 | −0.567913 | ||||||||
\(124\) | 11.5025 | 1.03295 | ||||||||
\(125\) | −16.3333 | −1.46089 | ||||||||
\(126\) | −2.18091 | −0.194291 | ||||||||
\(127\) | −7.80232 | −0.692344 | −0.346172 | − | 0.938171i | \(-0.612519\pi\) | ||||
−0.346172 | + | 0.938171i | \(0.612519\pi\) | |||||||
\(128\) | −9.48893 | −0.838711 | ||||||||
\(129\) | −12.1502 | −1.06977 | ||||||||
\(130\) | 42.9907 | 3.77053 | ||||||||
\(131\) | 11.5203 | 1.00653 | 0.503266 | − | 0.864132i | \(-0.332132\pi\) | ||||
0.503266 | + | 0.864132i | \(0.332132\pi\) | |||||||
\(132\) | −8.67530 | −0.755088 | ||||||||
\(133\) | −2.14600 | −0.186082 | ||||||||
\(134\) | −14.1957 | −1.22632 | ||||||||
\(135\) | 17.4245 | 1.49966 | ||||||||
\(136\) | −4.17136 | −0.357691 | ||||||||
\(137\) | −18.7466 | −1.60163 | −0.800817 | − | 0.598909i | \(-0.795601\pi\) | ||||
−0.800817 | + | 0.598909i | \(0.795601\pi\) | |||||||
\(138\) | 0.299188 | 0.0254685 | ||||||||
\(139\) | −18.6995 | −1.58607 | −0.793034 | − | 0.609177i | \(-0.791500\pi\) | ||||
−0.793034 | + | 0.609177i | \(0.791500\pi\) | |||||||
\(140\) | −10.6032 | −0.896135 | ||||||||
\(141\) | 22.8601 | 1.92517 | ||||||||
\(142\) | 27.7974 | 2.33271 | ||||||||
\(143\) | −22.0065 | −1.84028 | ||||||||
\(144\) | −2.74243 | −0.228536 | ||||||||
\(145\) | 13.1718 | 1.09386 | ||||||||
\(146\) | 19.1718 | 1.58667 | ||||||||
\(147\) | −4.51757 | −0.372603 | ||||||||
\(148\) | 6.02521 | 0.495269 | ||||||||
\(149\) | 6.53410 | 0.535295 | 0.267647 | − | 0.963517i | \(-0.413754\pi\) | ||||
0.267647 | + | 0.963517i | \(0.413754\pi\) | |||||||
\(150\) | −31.9568 | −2.60926 | ||||||||
\(151\) | −10.2148 | −0.831265 | −0.415633 | − | 0.909533i | \(-0.636440\pi\) | ||||
−0.415633 | + | 0.909533i | \(0.636440\pi\) | |||||||
\(152\) | −1.26214 | −0.102373 | ||||||||
\(153\) | −1.84729 | −0.149345 | ||||||||
\(154\) | 13.7407 | 1.10726 | ||||||||
\(155\) | −33.3293 | −2.67708 | ||||||||
\(156\) | 15.3942 | 1.23253 | ||||||||
\(157\) | 20.3842 | 1.62684 | 0.813419 | − | 0.581678i | \(-0.197604\pi\) | ||||
0.813419 | + | 0.581678i | \(0.197604\pi\) | |||||||
\(158\) | 10.8121 | 0.860164 | ||||||||
\(159\) | 8.40866 | 0.666850 | ||||||||
\(160\) | −24.2032 | −1.91343 | ||||||||
\(161\) | −0.187186 | −0.0147523 | ||||||||
\(162\) | 18.8445 | 1.48056 | ||||||||
\(163\) | −7.16401 | −0.561129 | −0.280564 | − | 0.959835i | \(-0.590522\pi\) | ||||
−0.280564 | + | 0.959835i | \(0.590522\pi\) | |||||||
\(164\) | −4.35973 | −0.340437 | ||||||||
\(165\) | 25.1374 | 1.95694 | ||||||||
\(166\) | 19.7379 | 1.53196 | ||||||||
\(167\) | −11.2907 | −0.873703 | −0.436851 | − | 0.899534i | \(-0.643906\pi\) | ||||
−0.436851 | + | 0.899534i | \(0.643906\pi\) | |||||||
\(168\) | 5.10974 | 0.394225 | ||||||||
\(169\) | 26.0504 | 2.00387 | ||||||||
\(170\) | −22.7369 | −1.74384 | ||||||||
\(171\) | −0.558942 | −0.0427433 | ||||||||
\(172\) | −8.41026 | −0.641276 | ||||||||
\(173\) | −11.6872 | −0.888560 | −0.444280 | − | 0.895888i | \(-0.646540\pi\) | ||||
−0.444280 | + | 0.895888i | \(0.646540\pi\) | |||||||
\(174\) | 11.9405 | 0.905208 | ||||||||
\(175\) | 19.9937 | 1.51138 | ||||||||
\(176\) | 17.2786 | 1.30242 | ||||||||
\(177\) | −2.75367 | −0.206978 | ||||||||
\(178\) | −28.9891 | −2.17283 | ||||||||
\(179\) | −20.6659 | −1.54465 | −0.772323 | − | 0.635230i | \(-0.780905\pi\) | ||||
−0.772323 | + | 0.635230i | \(0.780905\pi\) | |||||||
\(180\) | −2.76168 | −0.205844 | ||||||||
\(181\) | −17.6451 | −1.31155 | −0.655776 | − | 0.754955i | \(-0.727659\pi\) | ||||
−0.655776 | + | 0.754955i | \(0.727659\pi\) | |||||||
\(182\) | −24.3828 | −1.80737 | ||||||||
\(183\) | −16.7892 | −1.24109 | ||||||||
\(184\) | −0.110091 | −0.00811600 | ||||||||
\(185\) | −17.4585 | −1.28358 | ||||||||
\(186\) | −30.2138 | −2.21538 | ||||||||
\(187\) | 11.6388 | 0.851112 | ||||||||
\(188\) | 15.8235 | 1.15405 | ||||||||
\(189\) | −9.88255 | −0.718850 | ||||||||
\(190\) | −6.87957 | −0.499097 | ||||||||
\(191\) | 23.3851 | 1.69209 | 0.846044 | − | 0.533113i | \(-0.178978\pi\) | ||||
0.846044 | + | 0.533113i | \(0.178978\pi\) | |||||||
\(192\) | −3.42849 | −0.247430 | ||||||||
\(193\) | −25.7480 | −1.85339 | −0.926693 | − | 0.375820i | \(-0.877361\pi\) | ||||
−0.926693 | + | 0.375820i | \(0.877361\pi\) | |||||||
\(194\) | 7.78816 | 0.559157 | ||||||||
\(195\) | −44.6061 | −3.19431 | ||||||||
\(196\) | −3.12702 | −0.223358 | ||||||||
\(197\) | 3.15279 | 0.224627 | 0.112313 | − | 0.993673i | \(-0.464174\pi\) | ||||
0.112313 | + | 0.993673i | \(0.464174\pi\) | |||||||
\(198\) | 3.57886 | 0.254339 | ||||||||
\(199\) | −19.5289 | −1.38437 | −0.692183 | − | 0.721722i | \(-0.743351\pi\) | ||||
−0.692183 | + | 0.721722i | \(0.743351\pi\) | |||||||
\(200\) | 11.7590 | 0.831487 | ||||||||
\(201\) | 14.7292 | 1.03892 | ||||||||
\(202\) | −21.4897 | −1.51201 | ||||||||
\(203\) | −7.47056 | −0.524331 | ||||||||
\(204\) | −8.14170 | −0.570033 | ||||||||
\(205\) | 12.6327 | 0.882304 | ||||||||
\(206\) | −25.1740 | −1.75395 | ||||||||
\(207\) | −0.0487539 | −0.00338863 | ||||||||
\(208\) | −30.6607 | −2.12593 | ||||||||
\(209\) | 3.52159 | 0.243593 | ||||||||
\(210\) | 27.8518 | 1.92195 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 5.82039 | 0.399746 | ||||||||
\(213\) | −28.8420 | −1.97622 | ||||||||
\(214\) | 13.3411 | 0.911978 | ||||||||
\(215\) | 24.3694 | 1.66198 | ||||||||
\(216\) | −5.81228 | −0.395476 | ||||||||
\(217\) | 18.9032 | 1.28323 | ||||||||
\(218\) | −29.7218 | −2.01302 | ||||||||
\(219\) | −19.8922 | −1.34419 | ||||||||
\(220\) | 17.3998 | 1.17310 | ||||||||
\(221\) | −20.6529 | −1.38927 | ||||||||
\(222\) | −15.8266 | −1.06221 | ||||||||
\(223\) | −20.1782 | −1.35123 | −0.675616 | − | 0.737253i | \(-0.736122\pi\) | ||||
−0.675616 | + | 0.737253i | \(0.736122\pi\) | |||||||
\(224\) | 13.7272 | 0.917187 | ||||||||
\(225\) | 5.20749 | 0.347166 | ||||||||
\(226\) | −3.15253 | −0.209703 | ||||||||
\(227\) | −5.97763 | −0.396749 | −0.198375 | − | 0.980126i | \(-0.563566\pi\) | ||||
−0.198375 | + | 0.980126i | \(0.563566\pi\) | |||||||
\(228\) | −2.46346 | −0.163147 | ||||||||
\(229\) | −20.8444 | −1.37744 | −0.688718 | − | 0.725029i | \(-0.741826\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(230\) | −0.600074 | −0.0395677 | ||||||||
\(231\) | −14.2570 | −0.938044 | ||||||||
\(232\) | −4.39370 | −0.288461 | ||||||||
\(233\) | 17.2137 | 1.12771 | 0.563853 | − | 0.825875i | \(-0.309318\pi\) | ||||
0.563853 | + | 0.825875i | \(0.309318\pi\) | |||||||
\(234\) | −6.35066 | −0.415156 | ||||||||
\(235\) | −45.8499 | −2.99092 | ||||||||
\(236\) | −1.90606 | −0.124074 | ||||||||
\(237\) | −11.2184 | −0.728712 | ||||||||
\(238\) | 12.8956 | 0.835895 | ||||||||
\(239\) | −7.56793 | −0.489529 | −0.244764 | − | 0.969583i | \(-0.578711\pi\) | ||||
−0.244764 | + | 0.969583i | \(0.578711\pi\) | |||||||
\(240\) | 35.0228 | 2.26071 | ||||||||
\(241\) | −17.2128 | −1.10877 | −0.554386 | − | 0.832260i | \(-0.687047\pi\) | ||||
−0.554386 | + | 0.832260i | \(0.687047\pi\) | |||||||
\(242\) | −2.54833 | −0.163813 | ||||||||
\(243\) | −5.73734 | −0.368050 | ||||||||
\(244\) | −11.6213 | −0.743977 | ||||||||
\(245\) | 9.06079 | 0.578873 | ||||||||
\(246\) | 11.4518 | 0.730141 | ||||||||
\(247\) | −6.24903 | −0.397616 | ||||||||
\(248\) | 11.1177 | 0.705972 | ||||||||
\(249\) | −20.4796 | −1.29784 | ||||||||
\(250\) | 29.6971 | 1.87821 | ||||||||
\(251\) | 20.6586 | 1.30396 | 0.651979 | − | 0.758237i | \(-0.273939\pi\) | ||||
0.651979 | + | 0.758237i | \(0.273939\pi\) | |||||||
\(252\) | 1.56633 | 0.0986694 | ||||||||
\(253\) | 0.307172 | 0.0193117 | ||||||||
\(254\) | 14.1861 | 0.890116 | ||||||||
\(255\) | 23.5913 | 1.47734 | ||||||||
\(256\) | 20.8874 | 1.30547 | ||||||||
\(257\) | −12.2927 | −0.766801 | −0.383400 | − | 0.923582i | \(-0.625247\pi\) | ||||
−0.383400 | + | 0.923582i | \(0.625247\pi\) | |||||||
\(258\) | 22.0915 | 1.37535 | ||||||||
\(259\) | 9.90186 | 0.615272 | ||||||||
\(260\) | −30.8759 | −1.91484 | ||||||||
\(261\) | −1.94576 | −0.120439 | ||||||||
\(262\) | −20.9461 | −1.29405 | ||||||||
\(263\) | −11.6250 | −0.716829 | −0.358415 | − | 0.933562i | \(-0.616683\pi\) | ||||
−0.358415 | + | 0.933562i | \(0.616683\pi\) | |||||||
\(264\) | −8.38507 | −0.516066 | ||||||||
\(265\) | −16.8651 | −1.03601 | ||||||||
\(266\) | 3.90185 | 0.239238 | ||||||||
\(267\) | 30.0785 | 1.84077 | ||||||||
\(268\) | 10.1954 | 0.622782 | ||||||||
\(269\) | 4.58603 | 0.279615 | 0.139808 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139808 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(270\) | −31.6811 | −1.92805 | ||||||||
\(271\) | −13.9745 | −0.848891 | −0.424446 | − | 0.905453i | \(-0.639531\pi\) | ||||
−0.424446 | + | 0.905453i | \(0.639531\pi\) | |||||||
\(272\) | 16.2158 | 0.983228 | ||||||||
\(273\) | 25.2990 | 1.53117 | ||||||||
\(274\) | 34.0850 | 2.05915 | ||||||||
\(275\) | −32.8096 | −1.97849 | ||||||||
\(276\) | −0.214877 | −0.0129341 | ||||||||
\(277\) | 24.6601 | 1.48168 | 0.740840 | − | 0.671682i | \(-0.234428\pi\) | ||||
0.740840 | + | 0.671682i | \(0.234428\pi\) | |||||||
\(278\) | 33.9992 | 2.03914 | ||||||||
\(279\) | 4.92348 | 0.294761 | ||||||||
\(280\) | −10.2485 | −0.612465 | ||||||||
\(281\) | 30.7544 | 1.83465 | 0.917327 | − | 0.398135i | \(-0.130342\pi\) | ||||
0.917327 | + | 0.398135i | \(0.130342\pi\) | |||||||
\(282\) | −41.5640 | −2.47510 | ||||||||
\(283\) | −14.4297 | −0.857757 | −0.428878 | − | 0.903362i | \(-0.641091\pi\) | ||||
−0.428878 | + | 0.903362i | \(0.641091\pi\) | |||||||
\(284\) | −19.9641 | −1.18465 | ||||||||
\(285\) | 7.13809 | 0.422824 | ||||||||
\(286\) | 40.0121 | 2.36596 | ||||||||
\(287\) | −7.16480 | −0.422925 | ||||||||
\(288\) | 3.57534 | 0.210679 | ||||||||
\(289\) | −6.07708 | −0.357475 | ||||||||
\(290\) | −23.9488 | −1.40632 | ||||||||
\(291\) | −8.08082 | −0.473706 | ||||||||
\(292\) | −13.7692 | −0.805782 | ||||||||
\(293\) | −9.80388 | −0.572749 | −0.286374 | − | 0.958118i | \(-0.592450\pi\) | ||||
−0.286374 | + | 0.958118i | \(0.592450\pi\) | |||||||
\(294\) | 8.21382 | 0.479040 | ||||||||
\(295\) | 5.52297 | 0.321560 | ||||||||
\(296\) | 5.82364 | 0.338492 | ||||||||
\(297\) | 16.2172 | 0.941020 | ||||||||
\(298\) | −11.8803 | −0.688205 | ||||||||
\(299\) | −0.545074 | −0.0315225 | ||||||||
\(300\) | 22.9513 | 1.32510 | ||||||||
\(301\) | −13.8215 | −0.796657 | ||||||||
\(302\) | 18.5724 | 1.06872 | ||||||||
\(303\) | 22.2972 | 1.28094 | ||||||||
\(304\) | 4.90647 | 0.281405 | ||||||||
\(305\) | 33.6737 | 1.92815 | ||||||||
\(306\) | 3.35874 | 0.192006 | ||||||||
\(307\) | −15.6236 | −0.891686 | −0.445843 | − | 0.895111i | \(-0.647096\pi\) | ||||
−0.445843 | + | 0.895111i | \(0.647096\pi\) | |||||||
\(308\) | −9.86858 | −0.562314 | ||||||||
\(309\) | 26.1199 | 1.48591 | ||||||||
\(310\) | 60.5992 | 3.44180 | ||||||||
\(311\) | 2.66454 | 0.151092 | 0.0755460 | − | 0.997142i | \(-0.475930\pi\) | ||||
0.0755460 | + | 0.997142i | \(0.475930\pi\) | |||||||
\(312\) | 14.8792 | 0.842371 | ||||||||
\(313\) | −23.4143 | −1.32345 | −0.661727 | − | 0.749745i | \(-0.730176\pi\) | ||||
−0.661727 | + | 0.749745i | \(0.730176\pi\) | |||||||
\(314\) | −37.0625 | −2.09156 | ||||||||
\(315\) | −4.53857 | −0.255719 | ||||||||
\(316\) | −7.76525 | −0.436829 | ||||||||
\(317\) | −14.2156 | −0.798429 | −0.399215 | − | 0.916858i | \(-0.630717\pi\) | ||||
−0.399215 | + | 0.916858i | \(0.630717\pi\) | |||||||
\(318\) | −15.2886 | −0.857340 | ||||||||
\(319\) | 12.2592 | 0.686382 | ||||||||
\(320\) | 6.87644 | 0.384405 | ||||||||
\(321\) | −13.8424 | −0.772608 | ||||||||
\(322\) | 0.340341 | 0.0189664 | ||||||||
\(323\) | 3.30498 | 0.183894 | ||||||||
\(324\) | −13.5341 | −0.751896 | ||||||||
\(325\) | 58.2203 | 3.22948 | ||||||||
\(326\) | 13.0256 | 0.721419 | ||||||||
\(327\) | 30.8387 | 1.70538 | ||||||||
\(328\) | −4.21388 | −0.232672 | ||||||||
\(329\) | 26.0045 | 1.43367 | ||||||||
\(330\) | −45.7046 | −2.51596 | ||||||||
\(331\) | 29.3083 | 1.61093 | 0.805465 | − | 0.592644i | \(-0.201916\pi\) | ||||
0.805465 | + | 0.592644i | \(0.201916\pi\) | |||||||
\(332\) | −14.1757 | −0.777995 | ||||||||
\(333\) | 2.57901 | 0.141329 | ||||||||
\(334\) | 20.5287 | 1.12328 | ||||||||
\(335\) | −29.5420 | −1.61405 | ||||||||
\(336\) | −19.8637 | −1.08365 | ||||||||
\(337\) | 8.76941 | 0.477700 | 0.238850 | − | 0.971056i | \(-0.423230\pi\) | ||||
0.238850 | + | 0.971056i | \(0.423230\pi\) | |||||||
\(338\) | −47.3646 | −2.57629 | ||||||||
\(339\) | 3.27099 | 0.177656 | ||||||||
\(340\) | 16.3296 | 0.885599 | ||||||||
\(341\) | −31.0201 | −1.67983 | ||||||||
\(342\) | 1.01626 | 0.0549533 | ||||||||
\(343\) | −20.1610 | −1.08859 | ||||||||
\(344\) | −8.12890 | −0.438281 | ||||||||
\(345\) | 0.622623 | 0.0335209 | ||||||||
\(346\) | 21.2496 | 1.14238 | ||||||||
\(347\) | −35.5073 | −1.90613 | −0.953067 | − | 0.302760i | \(-0.902092\pi\) | ||||
−0.953067 | + | 0.302760i | \(0.902092\pi\) | |||||||
\(348\) | −8.57568 | −0.459705 | ||||||||
\(349\) | −15.4167 | −0.825237 | −0.412618 | − | 0.910904i | \(-0.635386\pi\) | ||||
−0.412618 | + | 0.910904i | \(0.635386\pi\) | |||||||
\(350\) | −36.3524 | −1.94312 | ||||||||
\(351\) | −28.7774 | −1.53602 | ||||||||
\(352\) | −22.5263 | −1.20065 | ||||||||
\(353\) | −20.1960 | −1.07492 | −0.537461 | − | 0.843289i | \(-0.680617\pi\) | ||||
−0.537461 | + | 0.843289i | \(0.680617\pi\) | |||||||
\(354\) | 5.00670 | 0.266103 | ||||||||
\(355\) | 57.8477 | 3.07024 | ||||||||
\(356\) | 20.8200 | 1.10346 | ||||||||
\(357\) | −13.3801 | −0.708152 | ||||||||
\(358\) | 37.5747 | 1.98588 | ||||||||
\(359\) | 21.3925 | 1.12905 | 0.564526 | − | 0.825415i | \(-0.309059\pi\) | ||||
0.564526 | + | 0.825415i | \(0.309059\pi\) | |||||||
\(360\) | −2.66929 | −0.140684 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 32.0823 | 1.68621 | ||||||||
\(363\) | 2.64408 | 0.138778 | ||||||||
\(364\) | 17.5117 | 0.917863 | ||||||||
\(365\) | 39.8974 | 2.08833 | ||||||||
\(366\) | 30.5260 | 1.59562 | ||||||||
\(367\) | 8.09352 | 0.422478 | 0.211239 | − | 0.977434i | \(-0.432250\pi\) | ||||
0.211239 | + | 0.977434i | \(0.432250\pi\) | |||||||
\(368\) | 0.427969 | 0.0223094 | ||||||||
\(369\) | −1.86612 | −0.0971465 | ||||||||
\(370\) | 31.7430 | 1.65024 | ||||||||
\(371\) | 9.56526 | 0.496604 | ||||||||
\(372\) | 21.6996 | 1.12507 | ||||||||
\(373\) | −8.76341 | −0.453752 | −0.226876 | − | 0.973924i | \(-0.572851\pi\) | ||||
−0.226876 | + | 0.973924i | \(0.572851\pi\) | |||||||
\(374\) | −21.1616 | −1.09424 | ||||||||
\(375\) | −30.8130 | −1.59118 | ||||||||
\(376\) | 15.2941 | 0.788736 | ||||||||
\(377\) | −21.7538 | −1.12038 | ||||||||
\(378\) | 17.9684 | 0.924194 | ||||||||
\(379\) | −14.3162 | −0.735371 | −0.367686 | − | 0.929950i | \(-0.619850\pi\) | ||||
−0.367686 | + | 0.929950i | \(0.619850\pi\) | |||||||
\(380\) | 4.94091 | 0.253463 | ||||||||
\(381\) | −14.7192 | −0.754087 | ||||||||
\(382\) | −42.5187 | −2.17544 | ||||||||
\(383\) | 16.6973 | 0.853191 | 0.426595 | − | 0.904443i | \(-0.359713\pi\) | ||||
0.426595 | + | 0.904443i | \(0.359713\pi\) | |||||||
\(384\) | −17.9010 | −0.913508 | ||||||||
\(385\) | 28.5950 | 1.45734 | ||||||||
\(386\) | 46.8149 | 2.38282 | ||||||||
\(387\) | −3.59990 | −0.182993 | ||||||||
\(388\) | −5.59346 | −0.283965 | ||||||||
\(389\) | 3.40403 | 0.172591 | 0.0862956 | − | 0.996270i | \(-0.472497\pi\) | ||||
0.0862956 | + | 0.996270i | \(0.472497\pi\) | |||||||
\(390\) | 81.1025 | 4.10679 | ||||||||
\(391\) | 0.288279 | 0.0145789 | ||||||||
\(392\) | −3.02241 | −0.152655 | ||||||||
\(393\) | 21.7332 | 1.09629 | ||||||||
\(394\) | −5.73238 | −0.288793 | ||||||||
\(395\) | 22.5005 | 1.13212 | ||||||||
\(396\) | −2.57034 | −0.129164 | ||||||||
\(397\) | 14.0888 | 0.707096 | 0.353548 | − | 0.935416i | \(-0.384975\pi\) | ||||
0.353548 | + | 0.935416i | \(0.384975\pi\) | |||||||
\(398\) | 35.5073 | 1.77982 | ||||||||
\(399\) | −4.04847 | −0.202677 | ||||||||
\(400\) | −45.7121 | −2.28561 | ||||||||
\(401\) | −33.0010 | −1.64799 | −0.823995 | − | 0.566596i | \(-0.808260\pi\) | ||||
−0.823995 | + | 0.566596i | \(0.808260\pi\) | |||||||
\(402\) | −26.7805 | −1.33569 | ||||||||
\(403\) | 55.0450 | 2.74199 | ||||||||
\(404\) | 15.4339 | 0.767866 | ||||||||
\(405\) | 39.2163 | 1.94867 | ||||||||
\(406\) | 13.5829 | 0.674109 | ||||||||
\(407\) | −16.2489 | −0.805429 | ||||||||
\(408\) | −7.86933 | −0.389590 | ||||||||
\(409\) | −37.2366 | −1.84123 | −0.920615 | − | 0.390471i | \(-0.872312\pi\) | ||||
−0.920615 | + | 0.390471i | \(0.872312\pi\) | |||||||
\(410\) | −22.9686 | −1.13434 | ||||||||
\(411\) | −35.3658 | −1.74447 | ||||||||
\(412\) | 18.0799 | 0.890735 | ||||||||
\(413\) | −3.13243 | −0.154137 | ||||||||
\(414\) | 0.0886441 | 0.00435662 | ||||||||
\(415\) | 41.0754 | 2.01631 | ||||||||
\(416\) | 39.9727 | 1.95982 | ||||||||
\(417\) | −35.2768 | −1.72751 | ||||||||
\(418\) | −6.40292 | −0.313177 | ||||||||
\(419\) | 37.5041 | 1.83219 | 0.916096 | − | 0.400958i | \(-0.131323\pi\) | ||||
0.916096 | + | 0.400958i | \(0.131323\pi\) | |||||||
\(420\) | −20.0031 | −0.976053 | ||||||||
\(421\) | −4.93622 | −0.240577 | −0.120288 | − | 0.992739i | \(-0.538382\pi\) | ||||
−0.120288 | + | 0.992739i | \(0.538382\pi\) | |||||||
\(422\) | 1.81819 | 0.0885083 | ||||||||
\(423\) | 6.77304 | 0.329317 | ||||||||
\(424\) | 5.62567 | 0.273207 | ||||||||
\(425\) | −30.7916 | −1.49361 | ||||||||
\(426\) | 52.4403 | 2.54074 | ||||||||
\(427\) | −19.0985 | −0.924242 | ||||||||
\(428\) | −9.58157 | −0.463143 | ||||||||
\(429\) | −41.5156 | −2.00439 | ||||||||
\(430\) | −44.3083 | −2.13674 | ||||||||
\(431\) | −18.7461 | −0.902968 | −0.451484 | − | 0.892279i | \(-0.649105\pi\) | ||||
−0.451484 | + | 0.892279i | \(0.649105\pi\) | |||||||
\(432\) | 22.5948 | 1.08709 | ||||||||
\(433\) | −40.2284 | −1.93326 | −0.966628 | − | 0.256186i | \(-0.917534\pi\) | ||||
−0.966628 | + | 0.256186i | \(0.917534\pi\) | |||||||
\(434\) | −34.3697 | −1.64980 | ||||||||
\(435\) | 24.8488 | 1.19141 | ||||||||
\(436\) | 21.3462 | 1.02230 | ||||||||
\(437\) | 0.0872254 | 0.00417256 | ||||||||
\(438\) | 36.1679 | 1.72817 | ||||||||
\(439\) | −4.00275 | −0.191041 | −0.0955204 | − | 0.995427i | \(-0.530452\pi\) | ||||
−0.0955204 | + | 0.995427i | \(0.530452\pi\) | |||||||
\(440\) | 16.8177 | 0.801755 | ||||||||
\(441\) | −1.33848 | −0.0637371 | ||||||||
\(442\) | 37.5510 | 1.78612 | ||||||||
\(443\) | −17.3114 | −0.822491 | −0.411245 | − | 0.911525i | \(-0.634906\pi\) | ||||
−0.411245 | + | 0.911525i | \(0.634906\pi\) | |||||||
\(444\) | 11.3666 | 0.539437 | ||||||||
\(445\) | −60.3277 | −2.85981 | ||||||||
\(446\) | 36.6879 | 1.73722 | ||||||||
\(447\) | 12.3267 | 0.583032 | ||||||||
\(448\) | −3.90007 | −0.184261 | ||||||||
\(449\) | −25.2442 | −1.19135 | −0.595675 | − | 0.803226i | \(-0.703115\pi\) | ||||
−0.595675 | + | 0.803226i | \(0.703115\pi\) | |||||||
\(450\) | −9.46823 | −0.446337 | ||||||||
\(451\) | 11.7574 | 0.553635 | ||||||||
\(452\) | 2.26415 | 0.106497 | ||||||||
\(453\) | −19.2703 | −0.905398 | ||||||||
\(454\) | 10.8685 | 0.510083 | ||||||||
\(455\) | −50.7417 | −2.37881 | ||||||||
\(456\) | −2.38105 | −0.111503 | ||||||||
\(457\) | 6.40939 | 0.299819 | 0.149909 | − | 0.988700i | \(-0.452102\pi\) | ||||
0.149909 | + | 0.988700i | \(0.452102\pi\) | |||||||
\(458\) | 37.8991 | 1.77091 | ||||||||
\(459\) | 15.2198 | 0.710398 | ||||||||
\(460\) | 0.430973 | 0.0200942 | ||||||||
\(461\) | 13.0392 | 0.607296 | 0.303648 | − | 0.952784i | \(-0.401795\pi\) | ||||
0.303648 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(462\) | 25.9221 | 1.20600 | ||||||||
\(463\) | 3.34924 | 0.155652 | 0.0778261 | − | 0.996967i | \(-0.475202\pi\) | ||||
0.0778261 | + | 0.996967i | \(0.475202\pi\) | |||||||
\(464\) | 17.0802 | 0.792926 | ||||||||
\(465\) | −62.8763 | −2.91582 | ||||||||
\(466\) | −31.2978 | −1.44984 | ||||||||
\(467\) | 2.15818 | 0.0998687 | 0.0499343 | − | 0.998753i | \(-0.484099\pi\) | ||||
0.0499343 | + | 0.998753i | \(0.484099\pi\) | |||||||
\(468\) | 4.56105 | 0.210834 | ||||||||
\(469\) | 16.7552 | 0.773681 | ||||||||
\(470\) | 83.3641 | 3.84530 | ||||||||
\(471\) | 38.4552 | 1.77192 | ||||||||
\(472\) | −1.84230 | −0.0847985 | ||||||||
\(473\) | 22.6810 | 1.04287 | ||||||||
\(474\) | 20.3972 | 0.936874 | ||||||||
\(475\) | −9.31670 | −0.427480 | ||||||||
\(476\) | −9.26159 | −0.424504 | ||||||||
\(477\) | 2.49134 | 0.114071 | ||||||||
\(478\) | 13.7600 | 0.629366 | ||||||||
\(479\) | −15.5214 | −0.709192 | −0.354596 | − | 0.935020i | \(-0.615382\pi\) | ||||
−0.354596 | + | 0.935020i | \(0.615382\pi\) | |||||||
\(480\) | −45.6597 | −2.08407 | ||||||||
\(481\) | 28.8336 | 1.31470 | ||||||||
\(482\) | 31.2961 | 1.42550 | ||||||||
\(483\) | −0.353130 | −0.0160680 | ||||||||
\(484\) | 1.83021 | 0.0831913 | ||||||||
\(485\) | 16.2075 | 0.735945 | ||||||||
\(486\) | 10.4316 | 0.473186 | ||||||||
\(487\) | −5.32544 | −0.241319 | −0.120659 | − | 0.992694i | \(-0.538501\pi\) | ||||
−0.120659 | + | 0.992694i | \(0.538501\pi\) | |||||||
\(488\) | −11.2325 | −0.508472 | ||||||||
\(489\) | −13.5150 | −0.611171 | ||||||||
\(490\) | −16.4743 | −0.744232 | ||||||||
\(491\) | −19.2453 | −0.868526 | −0.434263 | − | 0.900786i | \(-0.642991\pi\) | ||||
−0.434263 | + | 0.900786i | \(0.642991\pi\) | |||||||
\(492\) | −8.22469 | −0.370798 | ||||||||
\(493\) | 11.5051 | 0.518166 | ||||||||
\(494\) | 11.3619 | 0.511198 | ||||||||
\(495\) | 7.44777 | 0.334752 | ||||||||
\(496\) | −43.2190 | −1.94059 | ||||||||
\(497\) | −32.8092 | −1.47169 | ||||||||
\(498\) | 37.2358 | 1.66858 | ||||||||
\(499\) | 41.3501 | 1.85108 | 0.925542 | − | 0.378644i | \(-0.123610\pi\) | ||||
0.925542 | + | 0.378644i | \(0.123610\pi\) | |||||||
\(500\) | −21.3284 | −0.953837 | ||||||||
\(501\) | −21.3001 | −0.951620 | ||||||||
\(502\) | −37.5613 | −1.67644 | ||||||||
\(503\) | −25.2654 | −1.12653 | −0.563264 | − | 0.826277i | \(-0.690455\pi\) | ||||
−0.563264 | + | 0.826277i | \(0.690455\pi\) | |||||||
\(504\) | 1.51393 | 0.0674357 | ||||||||
\(505\) | −44.7211 | −1.99006 | ||||||||
\(506\) | −0.558498 | −0.0248283 | ||||||||
\(507\) | 49.1444 | 2.18258 | ||||||||
\(508\) | −10.1885 | −0.452040 | ||||||||
\(509\) | 14.2475 | 0.631511 | 0.315756 | − | 0.948841i | \(-0.397742\pi\) | ||||
0.315756 | + | 0.948841i | \(0.397742\pi\) | |||||||
\(510\) | −42.8935 | −1.89936 | ||||||||
\(511\) | −22.6284 | −1.00102 | ||||||||
\(512\) | −18.9995 | −0.839669 | ||||||||
\(513\) | 4.60509 | 0.203320 | ||||||||
\(514\) | 22.3506 | 0.985842 | ||||||||
\(515\) | −52.3881 | −2.30850 | ||||||||
\(516\) | −15.8661 | −0.698465 | ||||||||
\(517\) | −42.6732 | −1.87677 | ||||||||
\(518\) | −18.0035 | −0.791029 | ||||||||
\(519\) | −22.0481 | −0.967802 | ||||||||
\(520\) | −29.8430 | −1.30870 | ||||||||
\(521\) | 33.8855 | 1.48455 | 0.742275 | − | 0.670095i | \(-0.233747\pi\) | ||||
0.742275 | + | 0.670095i | \(0.233747\pi\) | |||||||
\(522\) | 3.53777 | 0.154844 | ||||||||
\(523\) | 19.3119 | 0.844449 | 0.422225 | − | 0.906491i | \(-0.361249\pi\) | ||||
0.422225 | + | 0.906491i | \(0.361249\pi\) | |||||||
\(524\) | 15.0435 | 0.657178 | ||||||||
\(525\) | 37.7184 | 1.64617 | ||||||||
\(526\) | 21.1365 | 0.921597 | ||||||||
\(527\) | −29.1122 | −1.26815 | ||||||||
\(528\) | 32.5963 | 1.41857 | ||||||||
\(529\) | −22.9924 | −0.999669 | ||||||||
\(530\) | 30.6639 | 1.33196 | ||||||||
\(531\) | −0.815864 | −0.0354055 | ||||||||
\(532\) | −2.80231 | −0.121496 | ||||||||
\(533\) | −20.8634 | −0.903696 | ||||||||
\(534\) | −54.6884 | −2.36660 | ||||||||
\(535\) | 27.7634 | 1.20032 | ||||||||
\(536\) | 9.85430 | 0.425641 | ||||||||
\(537\) | −38.9866 | −1.68240 | ||||||||
\(538\) | −8.33829 | −0.359489 | ||||||||
\(539\) | 8.43302 | 0.363236 | ||||||||
\(540\) | 22.7534 | 0.979149 | ||||||||
\(541\) | 13.9238 | 0.598633 | 0.299316 | − | 0.954154i | \(-0.403241\pi\) | ||||
0.299316 | + | 0.954154i | \(0.403241\pi\) | |||||||
\(542\) | 25.4084 | 1.09138 | ||||||||
\(543\) | −33.2878 | −1.42852 | ||||||||
\(544\) | −21.1408 | −0.906402 | ||||||||
\(545\) | −61.8525 | −2.64947 | ||||||||
\(546\) | −45.9985 | −1.96855 | ||||||||
\(547\) | 3.43145 | 0.146718 | 0.0733591 | − | 0.997306i | \(-0.476628\pi\) | ||||
0.0733591 | + | 0.997306i | \(0.476628\pi\) | |||||||
\(548\) | −24.4799 | −1.04573 | ||||||||
\(549\) | −4.97434 | −0.212300 | ||||||||
\(550\) | 59.6541 | 2.54366 | ||||||||
\(551\) | 3.48115 | 0.148302 | ||||||||
\(552\) | −0.207688 | −0.00883979 | ||||||||
\(553\) | −12.7615 | −0.542673 | ||||||||
\(554\) | −44.8368 | −1.90493 | ||||||||
\(555\) | −32.9358 | −1.39805 | ||||||||
\(556\) | −24.4183 | −1.03556 | ||||||||
\(557\) | −41.7985 | −1.77106 | −0.885530 | − | 0.464582i | \(-0.846205\pi\) | ||||
−0.885530 | + | 0.464582i | \(0.846205\pi\) | |||||||
\(558\) | −8.95183 | −0.378961 | ||||||||
\(559\) | −40.2473 | −1.70228 | ||||||||
\(560\) | 39.8402 | 1.68355 | ||||||||
\(561\) | 21.9568 | 0.927015 | ||||||||
\(562\) | −55.9174 | −2.35873 | ||||||||
\(563\) | −27.1922 | −1.14601 | −0.573007 | − | 0.819551i | \(-0.694223\pi\) | ||||
−0.573007 | + | 0.819551i | \(0.694223\pi\) | |||||||
\(564\) | 29.8513 | 1.25697 | ||||||||
\(565\) | −6.56056 | −0.276005 | ||||||||
\(566\) | 26.2360 | 1.10278 | ||||||||
\(567\) | −22.2421 | −0.934079 | ||||||||
\(568\) | −19.2962 | −0.809652 | ||||||||
\(569\) | −2.74307 | −0.114995 | −0.0574977 | − | 0.998346i | \(-0.518312\pi\) | ||||
−0.0574977 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(570\) | −12.9784 | −0.543606 | ||||||||
\(571\) | 20.2442 | 0.847192 | 0.423596 | − | 0.905851i | \(-0.360768\pi\) | ||||
0.423596 | + | 0.905851i | \(0.360768\pi\) | |||||||
\(572\) | −28.7367 | −1.20154 | ||||||||
\(573\) | 44.1164 | 1.84299 | ||||||||
\(574\) | 13.0270 | 0.543736 | ||||||||
\(575\) | −0.812654 | −0.0338900 | ||||||||
\(576\) | −1.01580 | −0.0423251 | ||||||||
\(577\) | −4.21073 | −0.175295 | −0.0876475 | − | 0.996152i | \(-0.527935\pi\) | ||||
−0.0876475 | + | 0.996152i | \(0.527935\pi\) | |||||||
\(578\) | 11.0493 | 0.459590 | ||||||||
\(579\) | −48.5741 | −2.01867 | ||||||||
\(580\) | 17.2000 | 0.714193 | ||||||||
\(581\) | −23.2965 | −0.966502 | ||||||||
\(582\) | 14.6925 | 0.609023 | ||||||||
\(583\) | −15.6966 | −0.650085 | ||||||||
\(584\) | −13.3086 | −0.550713 | ||||||||
\(585\) | −13.2160 | −0.546415 | ||||||||
\(586\) | 17.8254 | 0.736359 | ||||||||
\(587\) | 17.0714 | 0.704614 | 0.352307 | − | 0.935885i | \(-0.385397\pi\) | ||||
0.352307 | + | 0.935885i | \(0.385397\pi\) | |||||||
\(588\) | −5.89917 | −0.243278 | ||||||||
\(589\) | −8.80857 | −0.362951 | ||||||||
\(590\) | −10.0418 | −0.413416 | ||||||||
\(591\) | 5.94779 | 0.244659 | ||||||||
\(592\) | −22.6389 | −0.930453 | ||||||||
\(593\) | −25.5945 | −1.05104 | −0.525520 | − | 0.850781i | \(-0.676129\pi\) | ||||
−0.525520 | + | 0.850781i | \(0.676129\pi\) | |||||||
\(594\) | −29.4861 | −1.20983 | ||||||||
\(595\) | 26.8362 | 1.10018 | ||||||||
\(596\) | 8.53241 | 0.349501 | ||||||||
\(597\) | −36.8416 | −1.50782 | ||||||||
\(598\) | 0.991050 | 0.0405271 | ||||||||
\(599\) | 33.9046 | 1.38530 | 0.692652 | − | 0.721272i | \(-0.256442\pi\) | ||||
0.692652 | + | 0.721272i | \(0.256442\pi\) | |||||||
\(600\) | 22.1835 | 0.905639 | ||||||||
\(601\) | −11.6557 | −0.475446 | −0.237723 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237723 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(602\) | 25.1301 | 1.02423 | ||||||||
\(603\) | 4.36400 | 0.177716 | ||||||||
\(604\) | −13.3387 | −0.542744 | ||||||||
\(605\) | −5.30318 | −0.215605 | ||||||||
\(606\) | −40.5407 | −1.64685 | ||||||||
\(607\) | −24.4378 | −0.991900 | −0.495950 | − | 0.868351i | \(-0.665180\pi\) | ||||
−0.495950 | + | 0.868351i | \(0.665180\pi\) | |||||||
\(608\) | −6.39663 | −0.259418 | ||||||||
\(609\) | −14.0933 | −0.571091 | ||||||||
\(610\) | −61.2252 | −2.47894 | ||||||||
\(611\) | 75.7233 | 3.06344 | ||||||||
\(612\) | −2.41225 | −0.0975092 | ||||||||
\(613\) | 15.7222 | 0.635016 | 0.317508 | − | 0.948256i | \(-0.397154\pi\) | ||||
0.317508 | + | 0.948256i | \(0.397154\pi\) | |||||||
\(614\) | 28.4067 | 1.14640 | ||||||||
\(615\) | 23.8317 | 0.960988 | ||||||||
\(616\) | −9.53843 | −0.384314 | ||||||||
\(617\) | 20.5305 | 0.826529 | 0.413264 | − | 0.910611i | \(-0.364389\pi\) | ||||
0.413264 | + | 0.910611i | \(0.364389\pi\) | |||||||
\(618\) | −47.4911 | −1.91037 | ||||||||
\(619\) | 2.77815 | 0.111663 | 0.0558317 | − | 0.998440i | \(-0.482219\pi\) | ||||
0.0558317 | + | 0.998440i | \(0.482219\pi\) | |||||||
\(620\) | −43.5223 | −1.74790 | ||||||||
\(621\) | 0.401681 | 0.0161189 | ||||||||
\(622\) | −4.84464 | −0.194253 | ||||||||
\(623\) | 34.2157 | 1.37082 | ||||||||
\(624\) | −57.8418 | −2.31553 | ||||||||
\(625\) | 15.2174 | 0.608698 | ||||||||
\(626\) | 42.5717 | 1.70151 | ||||||||
\(627\) | 6.64353 | 0.265317 | ||||||||
\(628\) | 26.6183 | 1.06218 | ||||||||
\(629\) | −15.2495 | −0.608038 | ||||||||
\(630\) | 8.25199 | 0.328767 | ||||||||
\(631\) | −25.7245 | −1.02407 | −0.512037 | − | 0.858963i | \(-0.671109\pi\) | ||||
−0.512037 | + | 0.858963i | \(0.671109\pi\) | |||||||
\(632\) | −7.50547 | −0.298552 | ||||||||
\(633\) | −1.88652 | −0.0749823 | ||||||||
\(634\) | 25.8468 | 1.02651 | ||||||||
\(635\) | 29.5220 | 1.17154 | ||||||||
\(636\) | 10.9803 | 0.435395 | ||||||||
\(637\) | −14.9643 | −0.592908 | ||||||||
\(638\) | −22.2895 | −0.882451 | ||||||||
\(639\) | −8.54537 | −0.338050 | ||||||||
\(640\) | 35.9037 | 1.41922 | ||||||||
\(641\) | 2.04248 | 0.0806733 | 0.0403366 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403366 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(642\) | 25.1682 | 0.993308 | ||||||||
\(643\) | 21.4216 | 0.844785 | 0.422393 | − | 0.906413i | \(-0.361190\pi\) | ||||
0.422393 | + | 0.906413i | \(0.361190\pi\) | |||||||
\(644\) | −0.244433 | −0.00963200 | ||||||||
\(645\) | 45.9733 | 1.81020 | ||||||||
\(646\) | −6.00910 | −0.236425 | ||||||||
\(647\) | 47.7010 | 1.87532 | 0.937660 | − | 0.347554i | \(-0.112988\pi\) | ||||
0.937660 | + | 0.347554i | \(0.112988\pi\) | |||||||
\(648\) | −13.0814 | −0.513884 | ||||||||
\(649\) | 5.14031 | 0.201775 | ||||||||
\(650\) | −105.856 | −4.15201 | ||||||||
\(651\) | 35.6612 | 1.39767 | ||||||||
\(652\) | −9.35496 | −0.366368 | ||||||||
\(653\) | −25.5713 | −1.00068 | −0.500340 | − | 0.865829i | \(-0.666792\pi\) | ||||
−0.500340 | + | 0.865829i | \(0.666792\pi\) | |||||||
\(654\) | −56.0707 | −2.19254 | ||||||||
\(655\) | −43.5898 | −1.70319 | ||||||||
\(656\) | 16.3811 | 0.639574 | ||||||||
\(657\) | −5.89373 | −0.229936 | ||||||||
\(658\) | −47.2811 | −1.84321 | ||||||||
\(659\) | 17.7872 | 0.692891 | 0.346445 | − | 0.938070i | \(-0.387389\pi\) | ||||
0.346445 | + | 0.938070i | \(0.387389\pi\) | |||||||
\(660\) | 32.8251 | 1.27771 | ||||||||
\(661\) | 23.7433 | 0.923508 | 0.461754 | − | 0.887008i | \(-0.347220\pi\) | ||||
0.461754 | + | 0.887008i | \(0.347220\pi\) | |||||||
\(662\) | −53.2881 | −2.07110 | ||||||||
\(663\) | −38.9621 | −1.51316 | ||||||||
\(664\) | −13.7015 | −0.531721 | ||||||||
\(665\) | 8.11993 | 0.314877 | ||||||||
\(666\) | −4.68914 | −0.181700 | ||||||||
\(667\) | 0.303645 | 0.0117572 | ||||||||
\(668\) | −14.7437 | −0.570452 | ||||||||
\(669\) | −38.0665 | −1.47174 | ||||||||
\(670\) | 53.7130 | 2.07511 | ||||||||
\(671\) | 31.3406 | 1.20989 | ||||||||
\(672\) | 25.8966 | 0.998982 | ||||||||
\(673\) | 34.2055 | 1.31853 | 0.659263 | − | 0.751912i | \(-0.270868\pi\) | ||||
0.659263 | + | 0.751912i | \(0.270868\pi\) | |||||||
\(674\) | −15.9445 | −0.614158 | ||||||||
\(675\) | −42.9043 | −1.65139 | ||||||||
\(676\) | 34.0172 | 1.30836 | ||||||||
\(677\) | 30.8872 | 1.18709 | 0.593546 | − | 0.804800i | \(-0.297727\pi\) | ||||
0.593546 | + | 0.804800i | \(0.297727\pi\) | |||||||
\(678\) | −5.94730 | −0.228405 | ||||||||
\(679\) | −9.19233 | −0.352769 | ||||||||
\(680\) | 15.7833 | 0.605263 | ||||||||
\(681\) | −11.2769 | −0.432131 | ||||||||
\(682\) | 56.4006 | 2.15969 | ||||||||
\(683\) | −8.81030 | −0.337117 | −0.168558 | − | 0.985692i | \(-0.553911\pi\) | ||||
−0.168558 | + | 0.985692i | \(0.553911\pi\) | |||||||
\(684\) | −0.729881 | −0.0279077 | ||||||||
\(685\) | 70.9325 | 2.71019 | ||||||||
\(686\) | 36.6566 | 1.39955 | ||||||||
\(687\) | −39.3233 | −1.50028 | ||||||||
\(688\) | 31.6004 | 1.20476 | ||||||||
\(689\) | 27.8534 | 1.06113 | ||||||||
\(690\) | −1.13205 | −0.0430964 | ||||||||
\(691\) | −44.7478 | −1.70229 | −0.851143 | − | 0.524934i | \(-0.824090\pi\) | ||||
−0.851143 | + | 0.524934i | \(0.824090\pi\) | |||||||
\(692\) | −15.2614 | −0.580153 | ||||||||
\(693\) | −4.22411 | −0.160461 | ||||||||
\(694\) | 64.5592 | 2.45063 | ||||||||
\(695\) | 70.7540 | 2.68385 | ||||||||
\(696\) | −8.28879 | −0.314186 | ||||||||
\(697\) | 11.0343 | 0.417952 | ||||||||
\(698\) | 28.0305 | 1.06097 | ||||||||
\(699\) | 32.4739 | 1.22828 | ||||||||
\(700\) | 26.1083 | 0.986801 | ||||||||
\(701\) | −26.9443 | −1.01767 | −0.508836 | − | 0.860863i | \(-0.669924\pi\) | ||||
−0.508836 | + | 0.860863i | \(0.669924\pi\) | |||||||
\(702\) | 52.3228 | 1.97480 | ||||||||
\(703\) | −4.61409 | −0.174024 | ||||||||
\(704\) | 6.40001 | 0.241209 | ||||||||
\(705\) | −86.4966 | −3.25765 | ||||||||
\(706\) | 36.7202 | 1.38198 | ||||||||
\(707\) | 25.3642 | 0.953920 | ||||||||
\(708\) | −3.59581 | −0.135139 | ||||||||
\(709\) | 25.5134 | 0.958174 | 0.479087 | − | 0.877767i | \(-0.340968\pi\) | ||||
0.479087 | + | 0.877767i | \(0.340968\pi\) | |||||||
\(710\) | −105.178 | −3.94727 | ||||||||
\(711\) | −3.32381 | −0.124653 | ||||||||
\(712\) | 20.1235 | 0.754159 | ||||||||
\(713\) | −0.768331 | −0.0287742 | ||||||||
\(714\) | 24.3277 | 0.910440 | ||||||||
\(715\) | 83.2669 | 3.11401 | ||||||||
\(716\) | −26.9861 | −1.00852 | ||||||||
\(717\) | −14.2770 | −0.533185 | ||||||||
\(718\) | −38.8957 | −1.45157 | ||||||||
\(719\) | −36.2519 | −1.35197 | −0.675984 | − | 0.736916i | \(-0.736281\pi\) | ||||
−0.675984 | + | 0.736916i | \(0.736281\pi\) | |||||||
\(720\) | 10.3767 | 0.386715 | ||||||||
\(721\) | 29.7127 | 1.10656 | ||||||||
\(722\) | −1.81819 | −0.0676661 | ||||||||
\(723\) | −32.4722 | −1.20765 | ||||||||
\(724\) | −23.0415 | −0.856330 | ||||||||
\(725\) | −32.4328 | −1.20453 | ||||||||
\(726\) | −4.80746 | −0.178421 | ||||||||
\(727\) | 50.7667 | 1.88283 | 0.941417 | − | 0.337244i | \(-0.109495\pi\) | ||||
0.941417 | + | 0.337244i | \(0.109495\pi\) | |||||||
\(728\) | 16.9259 | 0.627315 | ||||||||
\(729\) | 20.2697 | 0.750728 | ||||||||
\(730\) | −72.5412 | −2.68487 | ||||||||
\(731\) | 21.2860 | 0.787290 | ||||||||
\(732\) | −21.9238 | −0.810325 | ||||||||
\(733\) | −15.4256 | −0.569758 | −0.284879 | − | 0.958564i | \(-0.591953\pi\) | ||||
−0.284879 | + | 0.958564i | \(0.591953\pi\) | |||||||
\(734\) | −14.7156 | −0.543162 | ||||||||
\(735\) | 17.0933 | 0.630497 | ||||||||
\(736\) | −0.557949 | −0.0205663 | ||||||||
\(737\) | −27.4952 | −1.01280 | ||||||||
\(738\) | 3.39297 | 0.124897 | ||||||||
\(739\) | 4.15378 | 0.152799 | 0.0763996 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763996 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(740\) | −22.7978 | −0.838065 | ||||||||
\(741\) | −11.7889 | −0.433076 | ||||||||
\(742\) | −17.3915 | −0.638462 | ||||||||
\(743\) | −24.4746 | −0.897887 | −0.448944 | − | 0.893560i | \(-0.648200\pi\) | ||||
−0.448944 | + | 0.893560i | \(0.648200\pi\) | |||||||
\(744\) | 20.9736 | 0.768931 | ||||||||
\(745\) | −24.7234 | −0.905794 | ||||||||
\(746\) | 15.9336 | 0.583369 | ||||||||
\(747\) | −6.06774 | −0.222007 | ||||||||
\(748\) | 15.1982 | 0.555703 | ||||||||
\(749\) | −15.7464 | −0.575362 | ||||||||
\(750\) | 56.0240 | 2.04571 | ||||||||
\(751\) | −1.63410 | −0.0596291 | −0.0298145 | − | 0.999555i | \(-0.509492\pi\) | ||||
−0.0298145 | + | 0.999555i | \(0.509492\pi\) | |||||||
\(752\) | −59.4547 | −2.16809 | ||||||||
\(753\) | 38.9728 | 1.42025 | ||||||||
\(754\) | 39.5526 | 1.44042 | ||||||||
\(755\) | 38.6500 | 1.40662 | ||||||||
\(756\) | −12.9049 | −0.469347 | ||||||||
\(757\) | 12.8912 | 0.468539 | 0.234269 | − | 0.972172i | \(-0.424730\pi\) | ||||
0.234269 | + | 0.972172i | \(0.424730\pi\) | |||||||
\(758\) | 26.0295 | 0.945435 | ||||||||
\(759\) | 0.579485 | 0.0210340 | ||||||||
\(760\) | 4.77562 | 0.173230 | ||||||||
\(761\) | −25.5146 | −0.924905 | −0.462452 | − | 0.886644i | \(-0.653030\pi\) | ||||
−0.462452 | + | 0.886644i | \(0.653030\pi\) | |||||||
\(762\) | 26.7623 | 0.969497 | ||||||||
\(763\) | 35.0805 | 1.27000 | ||||||||
\(764\) | 30.5369 | 1.10479 | ||||||||
\(765\) | 6.98968 | 0.252713 | ||||||||
\(766\) | −30.3589 | −1.09691 | ||||||||
\(767\) | −9.12145 | −0.329356 | ||||||||
\(768\) | 39.4045 | 1.42189 | ||||||||
\(769\) | 4.82978 | 0.174166 | 0.0870832 | − | 0.996201i | \(-0.472245\pi\) | ||||
0.0870832 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(770\) | −51.9913 | −1.87364 | ||||||||
\(771\) | −23.1905 | −0.835184 | ||||||||
\(772\) | −33.6225 | −1.21010 | ||||||||
\(773\) | 17.5314 | 0.630561 | 0.315280 | − | 0.948999i | \(-0.397901\pi\) | ||||
0.315280 | + | 0.948999i | \(0.397901\pi\) | |||||||
\(774\) | 6.54531 | 0.235266 | ||||||||
\(775\) | 82.0668 | 2.94793 | ||||||||
\(776\) | −5.40633 | −0.194076 | ||||||||
\(777\) | 18.6800 | 0.670142 | ||||||||
\(778\) | −6.18918 | −0.221893 | ||||||||
\(779\) | 3.33867 | 0.119620 | ||||||||
\(780\) | −58.2479 | −2.08561 | ||||||||
\(781\) | 53.8397 | 1.92654 | ||||||||
\(782\) | −0.524146 | −0.0187434 | ||||||||
\(783\) | 16.0310 | 0.572902 | ||||||||
\(784\) | 11.7494 | 0.419620 | ||||||||
\(785\) | −77.1286 | −2.75284 | ||||||||
\(786\) | −39.5151 | −1.40946 | ||||||||
\(787\) | 5.85732 | 0.208791 | 0.104395 | − | 0.994536i | \(-0.466709\pi\) | ||||
0.104395 | + | 0.994536i | \(0.466709\pi\) | |||||||
\(788\) | 4.11700 | 0.146662 | ||||||||
\(789\) | −21.9308 | −0.780757 | ||||||||
\(790\) | −40.9102 | −1.45552 | ||||||||
\(791\) | 3.72092 | 0.132301 | ||||||||
\(792\) | −2.48435 | −0.0882776 | ||||||||
\(793\) | −55.6137 | −1.97490 | ||||||||
\(794\) | −25.6161 | −0.909083 | ||||||||
\(795\) | −31.8162 | −1.12840 | ||||||||
\(796\) | −25.5013 | −0.903871 | ||||||||
\(797\) | 11.2661 | 0.399067 | 0.199534 | − | 0.979891i | \(-0.436057\pi\) | ||||
0.199534 | + | 0.979891i | \(0.436057\pi\) | |||||||
\(798\) | 7.36090 | 0.260573 | ||||||||
\(799\) | −40.0485 | −1.41682 | ||||||||
\(800\) | 59.5955 | 2.10702 | ||||||||
\(801\) | 8.91172 | 0.314880 | ||||||||
\(802\) | 60.0022 | 2.11875 | ||||||||
\(803\) | 37.1331 | 1.31040 | ||||||||
\(804\) | 19.2337 | 0.678322 | ||||||||
\(805\) | 0.708264 | 0.0249630 | ||||||||
\(806\) | −100.082 | −3.52525 | ||||||||
\(807\) | 8.65162 | 0.304552 | ||||||||
\(808\) | 14.9176 | 0.524799 | ||||||||
\(809\) | 50.6521 | 1.78083 | 0.890417 | − | 0.455145i | \(-0.150413\pi\) | ||||
0.890417 | + | 0.455145i | \(0.150413\pi\) | |||||||
\(810\) | −71.3027 | −2.50532 | ||||||||
\(811\) | 23.0634 | 0.809865 | 0.404932 | − | 0.914347i | \(-0.367295\pi\) | ||||
0.404932 | + | 0.914347i | \(0.367295\pi\) | |||||||
\(812\) | −9.75526 | −0.342342 | ||||||||
\(813\) | −26.3631 | −0.924596 | ||||||||
\(814\) | 29.5437 | 1.03551 | ||||||||
\(815\) | 27.1068 | 0.949509 | ||||||||
\(816\) | 30.5914 | 1.07091 | ||||||||
\(817\) | 6.44056 | 0.225327 | ||||||||
\(818\) | 67.7033 | 2.36719 | ||||||||
\(819\) | 7.49566 | 0.261919 | ||||||||
\(820\) | 16.4961 | 0.576068 | ||||||||
\(821\) | 13.7686 | 0.480526 | 0.240263 | − | 0.970708i | \(-0.422766\pi\) | ||||
0.240263 | + | 0.970708i | \(0.422766\pi\) | |||||||
\(822\) | 64.3019 | 2.24279 | ||||||||
\(823\) | 31.4555 | 1.09647 | 0.548235 | − | 0.836324i | \(-0.315300\pi\) | ||||
0.548235 | + | 0.836324i | \(0.315300\pi\) | |||||||
\(824\) | 17.4751 | 0.608774 | ||||||||
\(825\) | −61.8958 | −2.15493 | ||||||||
\(826\) | 5.69537 | 0.198167 | ||||||||
\(827\) | −0.989139 | −0.0343957 | −0.0171979 | − | 0.999852i | \(-0.505475\pi\) | ||||
−0.0171979 | + | 0.999852i | \(0.505475\pi\) | |||||||
\(828\) | −0.0636642 | −0.00221248 | ||||||||
\(829\) | 18.0885 | 0.628241 | 0.314121 | − | 0.949383i | \(-0.398290\pi\) | ||||
0.314121 | + | 0.949383i | \(0.398290\pi\) | |||||||
\(830\) | −74.6830 | −2.59228 | ||||||||
\(831\) | 46.5216 | 1.61382 | ||||||||
\(832\) | −11.3568 | −0.393725 | ||||||||
\(833\) | 7.91433 | 0.274215 | ||||||||
\(834\) | 64.1401 | 2.22099 | ||||||||
\(835\) | 42.7212 | 1.47843 | ||||||||
\(836\) | 4.59858 | 0.159045 | ||||||||
\(837\) | −40.5643 | −1.40211 | ||||||||
\(838\) | −68.1896 | −2.35557 | ||||||||
\(839\) | −27.6926 | −0.956054 | −0.478027 | − | 0.878345i | \(-0.658648\pi\) | ||||
−0.478027 | + | 0.878345i | \(0.658648\pi\) | |||||||
\(840\) | −19.3340 | −0.667085 | ||||||||
\(841\) | −16.8816 | −0.582124 | ||||||||
\(842\) | 8.97500 | 0.309299 | ||||||||
\(843\) | 58.0187 | 1.99827 | ||||||||
\(844\) | −1.30583 | −0.0449484 | ||||||||
\(845\) | −98.5678 | −3.39084 | ||||||||
\(846\) | −12.3147 | −0.423388 | ||||||||
\(847\) | 3.00778 | 0.103348 | ||||||||
\(848\) | −21.8693 | −0.750996 | ||||||||
\(849\) | −27.2219 | −0.934252 | ||||||||
\(850\) | 55.9850 | 1.92027 | ||||||||
\(851\) | −0.402466 | −0.0137964 | ||||||||
\(852\) | −37.6626 | −1.29030 | ||||||||
\(853\) | −27.9079 | −0.955547 | −0.477773 | − | 0.878483i | \(-0.658556\pi\) | ||||
−0.477773 | + | 0.878483i | \(0.658556\pi\) | |||||||
\(854\) | 34.7248 | 1.18826 | ||||||||
\(855\) | 2.11489 | 0.0723278 | ||||||||
\(856\) | −9.26103 | −0.316535 | ||||||||
\(857\) | 10.0300 | 0.342620 | 0.171310 | − | 0.985217i | \(-0.445200\pi\) | ||||
0.171310 | + | 0.985217i | \(0.445200\pi\) | |||||||
\(858\) | 75.4834 | 2.57696 | ||||||||
\(859\) | −26.9727 | −0.920298 | −0.460149 | − | 0.887842i | \(-0.652204\pi\) | ||||
−0.460149 | + | 0.887842i | \(0.652204\pi\) | |||||||
\(860\) | 31.8222 | 1.08513 | ||||||||
\(861\) | −13.5165 | −0.460642 | ||||||||
\(862\) | 34.0840 | 1.16091 | ||||||||
\(863\) | −22.7753 | −0.775280 | −0.387640 | − | 0.921811i | \(-0.626710\pi\) | ||||
−0.387640 | + | 0.921811i | \(0.626710\pi\) | |||||||
\(864\) | −29.4571 | −1.00215 | ||||||||
\(865\) | 44.2213 | 1.50357 | ||||||||
\(866\) | 73.1431 | 2.48550 | ||||||||
\(867\) | −11.4645 | −0.389355 | ||||||||
\(868\) | 24.6843 | 0.837841 | ||||||||
\(869\) | 20.9415 | 0.710392 | ||||||||
\(870\) | −45.1798 | −1.53174 | ||||||||
\(871\) | 48.7899 | 1.65318 | ||||||||
\(872\) | 20.6321 | 0.698691 | ||||||||
\(873\) | −2.39421 | −0.0810316 | ||||||||
\(874\) | −0.158593 | −0.00536448 | ||||||||
\(875\) | −35.0513 | −1.18495 | ||||||||
\(876\) | −25.9758 | −0.877642 | ||||||||
\(877\) | 40.4512 | 1.36594 | 0.682970 | − | 0.730447i | \(-0.260688\pi\) | ||||
0.682970 | + | 0.730447i | \(0.260688\pi\) | |||||||
\(878\) | 7.27777 | 0.245613 | ||||||||
\(879\) | −18.4952 | −0.623827 | ||||||||
\(880\) | −65.3776 | −2.20388 | ||||||||
\(881\) | −40.3640 | −1.35990 | −0.679948 | − | 0.733260i | \(-0.737998\pi\) | ||||
−0.679948 | + | 0.733260i | \(0.737998\pi\) | |||||||
\(882\) | 2.43361 | 0.0819440 | ||||||||
\(883\) | −43.6647 | −1.46943 | −0.734717 | − | 0.678373i | \(-0.762685\pi\) | ||||
−0.734717 | + | 0.678373i | \(0.762685\pi\) | |||||||
\(884\) | −26.9692 | −0.907071 | ||||||||
\(885\) | 10.4192 | 0.350237 | ||||||||
\(886\) | 31.4755 | 1.05744 | ||||||||
\(887\) | 46.1981 | 1.55118 | 0.775590 | − | 0.631238i | \(-0.217453\pi\) | ||||
0.775590 | + | 0.631238i | \(0.217453\pi\) | |||||||
\(888\) | 10.9864 | 0.368679 | ||||||||
\(889\) | −16.7438 | −0.561569 | ||||||||
\(890\) | 109.687 | 3.67673 | ||||||||
\(891\) | 36.4992 | 1.22277 | ||||||||
\(892\) | −26.3492 | −0.882238 | ||||||||
\(893\) | −12.1176 | −0.405501 | ||||||||
\(894\) | −22.4123 | −0.749580 | ||||||||
\(895\) | 78.1946 | 2.61376 | ||||||||
\(896\) | −20.3633 | −0.680290 | ||||||||
\(897\) | −1.02829 | −0.0343336 | ||||||||
\(898\) | 45.8989 | 1.53167 | ||||||||
\(899\) | −30.6639 | −1.02270 | ||||||||
\(900\) | 6.80008 | 0.226669 | ||||||||
\(901\) | −14.7311 | −0.490765 | ||||||||
\(902\) | −21.3773 | −0.711785 | ||||||||
\(903\) | −26.0744 | −0.867703 | ||||||||
\(904\) | 2.18840 | 0.0727852 | ||||||||
\(905\) | 66.7646 | 2.21933 | ||||||||
\(906\) | 35.0371 | 1.16403 | ||||||||
\(907\) | 39.4830 | 1.31101 | 0.655506 | − | 0.755190i | \(-0.272456\pi\) | ||||
0.655506 | + | 0.755190i | \(0.272456\pi\) | |||||||
\(908\) | −7.80575 | −0.259043 | ||||||||
\(909\) | 6.60629 | 0.219117 | ||||||||
\(910\) | 92.2581 | 3.05833 | ||||||||
\(911\) | −5.38896 | −0.178544 | −0.0892721 | − | 0.996007i | \(-0.528454\pi\) | ||||
−0.0892721 | + | 0.996007i | \(0.528454\pi\) | |||||||
\(912\) | 9.25613 | 0.306501 | ||||||||
\(913\) | 38.2295 | 1.26521 | ||||||||
\(914\) | −11.6535 | −0.385464 | ||||||||
\(915\) | 63.5259 | 2.10010 | ||||||||
\(916\) | −27.2192 | −0.899346 | ||||||||
\(917\) | 24.7226 | 0.816411 | ||||||||
\(918\) | −27.6725 | −0.913328 | ||||||||
\(919\) | −0.567009 | −0.0187039 | −0.00935195 | − | 0.999956i | \(-0.502977\pi\) | ||||
−0.00935195 | + | 0.999956i | \(0.502977\pi\) | |||||||
\(920\) | 0.416555 | 0.0137334 | ||||||||
\(921\) | −29.4742 | −0.971207 | ||||||||
\(922\) | −23.7078 | −0.780775 | ||||||||
\(923\) | −95.5382 | −3.14468 | ||||||||
\(924\) | −18.6172 | −0.612462 | ||||||||
\(925\) | 42.9881 | 1.41344 | ||||||||
\(926\) | −6.08956 | −0.200115 | ||||||||
\(927\) | 7.73888 | 0.254178 | ||||||||
\(928\) | −22.2676 | −0.730970 | ||||||||
\(929\) | 20.4719 | 0.671663 | 0.335831 | − | 0.941922i | \(-0.390983\pi\) | ||||
0.335831 | + | 0.941922i | \(0.390983\pi\) | |||||||
\(930\) | 114.321 | 3.74874 | ||||||||
\(931\) | 2.39466 | 0.0784820 | ||||||||
\(932\) | 22.4781 | 0.736294 | ||||||||
\(933\) | 5.02669 | 0.164566 | ||||||||
\(934\) | −3.92399 | −0.128397 | ||||||||
\(935\) | −44.0382 | −1.44020 | ||||||||
\(936\) | 4.40846 | 0.144095 | ||||||||
\(937\) | 23.7189 | 0.774862 | 0.387431 | − | 0.921899i | \(-0.373363\pi\) | ||||
0.387431 | + | 0.921899i | \(0.373363\pi\) | |||||||
\(938\) | −30.4641 | −0.994689 | ||||||||
\(939\) | −44.1714 | −1.44148 | ||||||||
\(940\) | −59.8721 | −1.95281 | ||||||||
\(941\) | 23.1721 | 0.755389 | 0.377695 | − | 0.925930i | \(-0.376717\pi\) | ||||
0.377695 | + | 0.925930i | \(0.376717\pi\) | |||||||
\(942\) | −69.9189 | −2.27808 | ||||||||
\(943\) | 0.291217 | 0.00948333 | ||||||||
\(944\) | 7.16177 | 0.233096 | ||||||||
\(945\) | 37.3930 | 1.21640 | ||||||||
\(946\) | −41.2384 | −1.34078 | ||||||||
\(947\) | −32.0394 | −1.04114 | −0.520570 | − | 0.853819i | \(-0.674281\pi\) | ||||
−0.520570 | + | 0.853819i | \(0.674281\pi\) | |||||||
\(948\) | −14.6493 | −0.475786 | ||||||||
\(949\) | −65.8925 | −2.13896 | ||||||||
\(950\) | 16.9396 | 0.549592 | ||||||||
\(951\) | −26.8180 | −0.869633 | ||||||||
\(952\) | −8.95175 | −0.290128 | ||||||||
\(953\) | 4.37101 | 0.141591 | 0.0707955 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707955 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(954\) | −4.52974 | −0.146656 | ||||||||
\(955\) | −88.4832 | −2.86325 | ||||||||
\(956\) | −9.88241 | −0.319620 | ||||||||
\(957\) | 23.1271 | 0.747593 | ||||||||
\(958\) | 28.2210 | 0.911778 | ||||||||
\(959\) | −40.2304 | −1.29911 | ||||||||
\(960\) | 12.9725 | 0.418686 | ||||||||
\(961\) | 46.5908 | 1.50293 | ||||||||
\(962\) | −52.4251 | −1.69025 | ||||||||
\(963\) | −4.10126 | −0.132161 | ||||||||
\(964\) | −22.4769 | −0.723932 | ||||||||
\(965\) | 97.4240 | 3.13619 | ||||||||
\(966\) | 0.642058 | 0.0206579 | ||||||||
\(967\) | 45.9585 | 1.47793 | 0.738963 | − | 0.673746i | \(-0.235316\pi\) | ||||
0.738963 | + | 0.673746i | \(0.235316\pi\) | |||||||
\(968\) | 1.76898 | 0.0568572 | ||||||||
\(969\) | 6.23490 | 0.200294 | ||||||||
\(970\) | −29.4684 | −0.946173 | ||||||||
\(971\) | 12.1510 | 0.389944 | 0.194972 | − | 0.980809i | \(-0.437538\pi\) | ||||
0.194972 | + | 0.980809i | \(0.437538\pi\) | |||||||
\(972\) | −7.49197 | −0.240305 | ||||||||
\(973\) | −40.1291 | −1.28648 | ||||||||
\(974\) | 9.68267 | 0.310253 | ||||||||
\(975\) | 109.834 | 3.51749 | ||||||||
\(976\) | 43.6655 | 1.39770 | ||||||||
\(977\) | 3.10719 | 0.0994078 | 0.0497039 | − | 0.998764i | \(-0.484172\pi\) | ||||
0.0497039 | + | 0.998764i | \(0.484172\pi\) | |||||||
\(978\) | 24.5729 | 0.785755 | ||||||||
\(979\) | −56.1479 | −1.79449 | ||||||||
\(980\) | 11.8318 | 0.377954 | ||||||||
\(981\) | 9.13697 | 0.291721 | ||||||||
\(982\) | 34.9916 | 1.11663 | ||||||||
\(983\) | 7.46232 | 0.238011 | 0.119006 | − | 0.992894i | \(-0.462029\pi\) | ||||
0.119006 | + | 0.992894i | \(0.462029\pi\) | |||||||
\(984\) | −7.94954 | −0.253422 | ||||||||
\(985\) | −11.9293 | −0.380101 | ||||||||
\(986\) | −20.9186 | −0.666183 | ||||||||
\(987\) | 49.0578 | 1.56153 | ||||||||
\(988\) | −8.16015 | −0.259609 | ||||||||
\(989\) | 0.561781 | 0.0178636 | ||||||||
\(990\) | −13.5415 | −0.430377 | ||||||||
\(991\) | −25.2984 | −0.803630 | −0.401815 | − | 0.915721i | \(-0.631620\pi\) | ||||
−0.401815 | + | 0.915721i | \(0.631620\pi\) | |||||||
\(992\) | 56.3451 | 1.78896 | ||||||||
\(993\) | 55.2906 | 1.75459 | ||||||||
\(994\) | 59.6534 | 1.89209 | ||||||||
\(995\) | 73.8923 | 2.34254 | ||||||||
\(996\) | −26.7427 | −0.847376 | ||||||||
\(997\) | −10.5323 | −0.333560 | −0.166780 | − | 0.985994i | \(-0.553337\pi\) | ||||
−0.166780 | + | 0.985994i | \(0.553337\pi\) | |||||||
\(998\) | −75.1825 | −2.37986 | ||||||||
\(999\) | −21.2483 | −0.672268 |
(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 | 4009.2.a.d.1.16 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.d.1.16 | ✓ | 75 | 1.1 | even | 1 | trivial |