Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.31 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.49464 | 1.76398 | 0.881989 | − | 0.471270i | \(-0.156204\pi\) | ||||
0.881989 | + | 0.471270i | \(0.156204\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.22324 | 2.11162 | ||||||||
\(5\) | 0.373762 | 0.167151 | 0.0835757 | − | 0.996501i | \(-0.473366\pi\) | ||||
0.0835757 | + | 0.996501i | \(0.473366\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 5.54618 | 1.96087 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.932401 | 0.294851 | ||||||||
\(11\) | −6.40807 | −1.93210 | −0.966052 | − | 0.258346i | \(-0.916823\pi\) | ||||
−0.966052 | + | 0.258346i | \(0.916823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.54237 | 0.705127 | 0.352564 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352564 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(14\) | −2.49464 | −0.666721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.38926 | 1.34731 | ||||||||
\(17\) | 4.88897 | 1.18575 | 0.592875 | − | 0.805295i | \(-0.297993\pi\) | ||||
0.592875 | + | 0.805295i | \(0.297993\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.83201 | −1.33796 | −0.668978 | − | 0.743283i | \(-0.733268\pi\) | ||||
−0.668978 | + | 0.743283i | \(0.733268\pi\) | |||||||
\(20\) | 1.57848 | 0.352960 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.9858 | −3.40819 | ||||||||
\(23\) | −8.35556 | −1.74225 | −0.871127 | − | 0.491058i | \(-0.836610\pi\) | ||||
−0.871127 | + | 0.491058i | \(0.836610\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86030 | −0.972060 | ||||||||
\(26\) | 6.34231 | 1.24383 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.22324 | −0.798117 | ||||||||
\(29\) | −1.63505 | −0.303620 | −0.151810 | − | 0.988410i | \(-0.548510\pi\) | ||||
−0.151810 | + | 0.988410i | \(0.548510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.96821 | −1.25153 | −0.625764 | − | 0.780013i | \(-0.715213\pi\) | ||||
−0.625764 | + | 0.780013i | \(0.715213\pi\) | |||||||
\(32\) | 2.35191 | 0.415763 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.1962 | 2.09164 | ||||||||
\(35\) | −0.373762 | −0.0631773 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.46339 | 1.22697 | 0.613487 | − | 0.789705i | \(-0.289766\pi\) | ||||
0.613487 | + | 0.789705i | \(0.289766\pi\) | |||||||
\(38\) | −14.5488 | −2.36012 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.07295 | 0.327762 | ||||||||
\(41\) | −9.02251 | −1.40908 | −0.704540 | − | 0.709664i | \(-0.748847\pi\) | ||||
−0.704540 | + | 0.709664i | \(0.748847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.64100 | −1.16524 | −0.582621 | − | 0.812744i | \(-0.697973\pi\) | ||||
−0.582621 | + | 0.812744i | \(0.697973\pi\) | |||||||
\(44\) | −27.0628 | −4.07987 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.8441 | −3.07330 | ||||||||
\(47\) | 6.14673 | 0.896592 | 0.448296 | − | 0.893885i | \(-0.352031\pi\) | ||||
0.448296 | + | 0.893885i | \(0.352031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −12.1247 | −1.71469 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.7370 | 1.48896 | ||||||||
\(53\) | −2.53581 | −0.348321 | −0.174160 | − | 0.984717i | \(-0.555721\pi\) | ||||
−0.174160 | + | 0.984717i | \(0.555721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.39509 | −0.322954 | ||||||||
\(56\) | −5.54618 | −0.741140 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.07885 | −0.535580 | ||||||||
\(59\) | 1.55774 | 0.202800 | 0.101400 | − | 0.994846i | \(-0.467668\pi\) | ||||
0.101400 | + | 0.994846i | \(0.467668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0709 | −1.41749 | −0.708745 | − | 0.705465i | \(-0.750738\pi\) | ||||
−0.708745 | + | 0.705465i | \(0.750738\pi\) | |||||||
\(62\) | −17.3832 | −2.20767 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.91135 | −0.613918 | ||||||||
\(65\) | 0.950241 | 0.117863 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4944 | 1.40427 | 0.702134 | − | 0.712045i | \(-0.252231\pi\) | ||||
0.702134 | + | 0.712045i | \(0.252231\pi\) | |||||||
\(68\) | 20.6473 | 2.50385 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.932401 | −0.111443 | ||||||||
\(71\) | 7.04746 | 0.836380 | 0.418190 | − | 0.908360i | \(-0.362665\pi\) | ||||
0.418190 | + | 0.908360i | \(0.362665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.49704 | 0.643380 | 0.321690 | − | 0.946845i | \(-0.395749\pi\) | ||||
0.321690 | + | 0.946845i | \(0.395749\pi\) | |||||||
\(74\) | 18.6185 | 2.16436 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.6300 | −2.82525 | ||||||||
\(77\) | 6.40807 | 0.730267 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.21739 | −0.812020 | −0.406010 | − | 0.913869i | \(-0.633080\pi\) | ||||
−0.406010 | + | 0.913869i | \(0.633080\pi\) | |||||||
\(80\) | 2.01430 | 0.225205 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −22.5079 | −2.48559 | ||||||||
\(83\) | 4.98747 | 0.547445 | 0.273723 | − | 0.961809i | \(-0.411745\pi\) | ||||
0.273723 | + | 0.961809i | \(0.411745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.82731 | 0.198200 | ||||||||
\(86\) | −19.0616 | −2.05546 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −35.5403 | −3.78861 | ||||||||
\(89\) | 6.29176 | 0.666925 | 0.333463 | − | 0.942763i | \(-0.391783\pi\) | ||||
0.333463 | + | 0.942763i | \(0.391783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.54237 | −0.266513 | ||||||||
\(92\) | −35.2875 | −3.67898 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.3339 | 1.58157 | ||||||||
\(95\) | −2.17978 | −0.223641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3484 | −1.55840 | −0.779199 | − | 0.626776i | \(-0.784374\pi\) | ||||
−0.779199 | + | 0.626776i | \(0.784374\pi\) | |||||||
\(98\) | 2.49464 | 0.251997 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −20.5262 | −2.05262 | ||||||||
\(101\) | 14.8823 | 1.48085 | 0.740424 | − | 0.672140i | \(-0.234625\pi\) | ||||
0.740424 | + | 0.672140i | \(0.234625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5754 | 1.04203 | 0.521013 | − | 0.853548i | \(-0.325554\pi\) | ||||
0.521013 | + | 0.853548i | \(0.325554\pi\) | |||||||
\(104\) | 14.1005 | 1.38266 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.32594 | −0.614430 | ||||||||
\(107\) | 14.1331 | 1.36630 | 0.683150 | − | 0.730278i | \(-0.260609\pi\) | ||||
0.683150 | + | 0.730278i | \(0.260609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.01182 | 0.671610 | 0.335805 | − | 0.941932i | \(-0.390992\pi\) | ||||
0.335805 | + | 0.941932i | \(0.390992\pi\) | |||||||
\(110\) | −5.97489 | −0.569684 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.38926 | −0.509237 | ||||||||
\(113\) | 14.2300 | 1.33865 | 0.669325 | − | 0.742970i | \(-0.266583\pi\) | ||||
0.669325 | + | 0.742970i | \(0.266583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.12299 | −0.291220 | ||||||||
\(116\) | −6.90519 | −0.641130 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.88600 | 0.357735 | ||||||||
\(119\) | −4.88897 | −0.448171 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.0633 | 2.73303 | ||||||||
\(122\) | −27.6181 | −2.50042 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −29.4284 | −2.64275 | ||||||||
\(125\) | −3.68540 | −0.329632 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −16.9559 | −1.49870 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.37051 | 0.207908 | ||||||||
\(131\) | −19.2456 | −1.68150 | −0.840750 | − | 0.541424i | \(-0.817885\pi\) | ||||
−0.840750 | + | 0.541424i | \(0.817885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.83201 | 0.505700 | ||||||||
\(134\) | 28.6745 | 2.47710 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.1151 | 2.32510 | ||||||||
\(137\) | −0.417270 | −0.0356498 | −0.0178249 | − | 0.999841i | \(-0.505674\pi\) | ||||
−0.0178249 | + | 0.999841i | \(0.505674\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.80248 | −0.661798 | −0.330899 | − | 0.943666i | \(-0.607352\pi\) | ||||
−0.330899 | + | 0.943666i | \(0.607352\pi\) | |||||||
\(140\) | −1.57848 | −0.133406 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.5809 | 1.47536 | ||||||||
\(143\) | −16.2917 | −1.36238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.611117 | −0.0507505 | ||||||||
\(146\) | 13.7132 | 1.13491 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 31.5197 | 2.59090 | ||||||||
\(149\) | 0.799730 | 0.0655165 | 0.0327582 | − | 0.999463i | \(-0.489571\pi\) | ||||
0.0327582 | + | 0.999463i | \(0.489571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4297 | −1.41841 | −0.709204 | − | 0.705003i | \(-0.750946\pi\) | ||||
−0.709204 | + | 0.705003i | \(0.750946\pi\) | |||||||
\(152\) | −32.3454 | −2.62356 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.9858 | 1.28817 | ||||||||
\(155\) | −2.60445 | −0.209194 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3819 | −1.78627 | −0.893133 | − | 0.449792i | \(-0.851498\pi\) | ||||
−0.893133 | + | 0.449792i | \(0.851498\pi\) | |||||||
\(158\) | −18.0048 | −1.43238 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.879054 | 0.0694953 | ||||||||
\(161\) | 8.35556 | 0.658510 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1243 | 1.34128 | 0.670638 | − | 0.741785i | \(-0.266021\pi\) | ||||
0.670638 | + | 0.741785i | \(0.266021\pi\) | |||||||
\(164\) | −38.1042 | −2.97544 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.4419 | 0.965682 | ||||||||
\(167\) | 8.64194 | 0.668734 | 0.334367 | − | 0.942443i | \(-0.391478\pi\) | ||||
0.334367 | + | 0.942443i | \(0.391478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.53634 | −0.502796 | ||||||||
\(170\) | 4.55848 | 0.349620 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −32.2697 | −2.46055 | ||||||||
\(173\) | −25.8065 | −1.96203 | −0.981016 | − | 0.193925i | \(-0.937878\pi\) | ||||
−0.981016 | + | 0.193925i | \(0.937878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.86030 | 0.367404 | ||||||||
\(176\) | −34.5347 | −2.60315 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.6957 | 1.17644 | ||||||||
\(179\) | 14.0778 | 1.05222 | 0.526111 | − | 0.850416i | \(-0.323649\pi\) | ||||
0.526111 | + | 0.850416i | \(0.323649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7679 | −1.24635 | −0.623174 | − | 0.782083i | \(-0.714157\pi\) | ||||
−0.623174 | + | 0.782083i | \(0.714157\pi\) | |||||||
\(182\) | −6.34231 | −0.470123 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −46.3414 | −3.41634 | ||||||||
\(185\) | 2.78953 | 0.205090 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.3289 | −2.29099 | ||||||||
\(188\) | 25.9591 | 1.89326 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.43778 | −0.394498 | ||||||||
\(191\) | −22.6982 | −1.64238 | −0.821191 | − | 0.570653i | \(-0.806690\pi\) | ||||
−0.821191 | + | 0.570653i | \(0.806690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.65402 | 0.119059 | 0.0595296 | − | 0.998227i | \(-0.481040\pi\) | ||||
0.0595296 | + | 0.998227i | \(0.481040\pi\) | |||||||
\(194\) | −38.2889 | −2.74898 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.22324 | 0.301660 | ||||||||
\(197\) | −12.5827 | −0.896481 | −0.448241 | − | 0.893913i | \(-0.647949\pi\) | ||||
−0.448241 | + | 0.893913i | \(0.647949\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6610 | 0.755737 | 0.377869 | − | 0.925859i | \(-0.376657\pi\) | ||||
0.377869 | + | 0.925859i | \(0.376657\pi\) | |||||||
\(200\) | −26.9561 | −1.90609 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 37.1261 | 2.61218 | ||||||||
\(203\) | 1.63505 | 0.114758 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.37227 | −0.235529 | ||||||||
\(206\) | 26.3819 | 1.83811 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.7015 | 0.950028 | ||||||||
\(209\) | 37.3719 | 2.58507 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.06656 | −0.555325 | −0.277662 | − | 0.960679i | \(-0.589560\pi\) | ||||
−0.277662 | + | 0.960679i | \(0.589560\pi\) | |||||||
\(212\) | −10.7093 | −0.735520 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 35.2571 | 2.41012 | ||||||||
\(215\) | −2.85591 | −0.194772 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.96821 | 0.473033 | ||||||||
\(218\) | 17.4920 | 1.18471 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.1150 | −0.681955 | ||||||||
\(221\) | 12.4296 | 0.836104 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.52281 | −0.235905 | −0.117952 | − | 0.993019i | \(-0.537633\pi\) | ||||
−0.117952 | + | 0.993019i | \(0.537633\pi\) | |||||||
\(224\) | −2.35191 | −0.157144 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.4989 | 2.36135 | ||||||||
\(227\) | 11.6455 | 0.772938 | 0.386469 | − | 0.922302i | \(-0.373695\pi\) | ||||
0.386469 | + | 0.922302i | \(0.373695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.3408 | 1.41024 | 0.705120 | − | 0.709088i | \(-0.250893\pi\) | ||||
0.705120 | + | 0.709088i | \(0.250893\pi\) | |||||||
\(230\) | −7.79073 | −0.513706 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.06826 | −0.595360 | ||||||||
\(233\) | 3.63820 | 0.238346 | 0.119173 | − | 0.992873i | \(-0.461976\pi\) | ||||
0.119173 | + | 0.992873i | \(0.461976\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.29741 | 0.149867 | ||||||||
\(236\) | 6.57870 | 0.428237 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.1962 | −0.790564 | ||||||||
\(239\) | 3.73257 | 0.241440 | 0.120720 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120720 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.73060 | 0.369141 | 0.184570 | − | 0.982819i | \(-0.440911\pi\) | ||||
0.184570 | + | 0.982819i | \(0.440911\pi\) | |||||||
\(242\) | 74.9972 | 4.82100 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −46.7552 | −2.99320 | ||||||||
\(245\) | 0.373762 | 0.0238788 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.8271 | −0.943429 | ||||||||
\(248\) | −38.6470 | −2.45408 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.19376 | −0.581464 | ||||||||
\(251\) | 11.4934 | 0.725458 | 0.362729 | − | 0.931895i | \(-0.381845\pi\) | ||||
0.362729 | + | 0.931895i | \(0.381845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 53.5430 | 3.36622 | ||||||||
\(254\) | −2.49464 | −0.156528 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.4761 | −2.02976 | ||||||||
\(257\) | −24.9218 | −1.55458 | −0.777290 | − | 0.629143i | \(-0.783406\pi\) | ||||
−0.777290 | + | 0.629143i | \(0.783406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.46339 | −0.463753 | ||||||||
\(260\) | 4.01309 | 0.248882 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −48.0110 | −2.96613 | ||||||||
\(263\) | −22.7571 | −1.40326 | −0.701632 | − | 0.712539i | \(-0.747545\pi\) | ||||
−0.701632 | + | 0.712539i | \(0.747545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.947789 | −0.0582222 | ||||||||
\(266\) | 14.5488 | 0.892043 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 48.5437 | 2.96528 | ||||||||
\(269\) | 6.75574 | 0.411905 | 0.205952 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205952 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8092 | −1.26407 | −0.632036 | − | 0.774939i | \(-0.717780\pi\) | ||||
−0.632036 | + | 0.774939i | \(0.717780\pi\) | |||||||
\(272\) | 26.3479 | 1.59758 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.04094 | −0.0628854 | ||||||||
\(275\) | 31.1451 | 1.87812 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4321 | 0.987311 | 0.493655 | − | 0.869658i | \(-0.335660\pi\) | ||||
0.493655 | + | 0.869658i | \(0.335660\pi\) | |||||||
\(278\) | −19.4644 | −1.16740 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.07295 | −0.123882 | ||||||||
\(281\) | 17.3979 | 1.03787 | 0.518935 | − | 0.854814i | \(-0.326329\pi\) | ||||
0.518935 | + | 0.854814i | \(0.326329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.8735 | −1.24080 | −0.620400 | − | 0.784285i | \(-0.713030\pi\) | ||||
−0.620400 | + | 0.784285i | \(0.713030\pi\) | |||||||
\(284\) | 29.7631 | 1.76612 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −40.6419 | −2.40321 | ||||||||
\(287\) | 9.02251 | 0.532582 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.90205 | 0.406003 | ||||||||
\(290\) | −1.52452 | −0.0895228 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 23.2153 | 1.35857 | ||||||||
\(293\) | 2.66238 | 0.155538 | 0.0777690 | − | 0.996971i | \(-0.475220\pi\) | ||||
0.0777690 | + | 0.996971i | \(0.475220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.582223 | 0.0338984 | ||||||||
\(296\) | 41.3933 | 2.40594 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.99504 | 0.115570 | ||||||||
\(299\) | −21.2429 | −1.22851 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.64100 | 0.440420 | ||||||||
\(302\) | −43.4808 | −2.50204 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −31.4302 | −1.80265 | ||||||||
\(305\) | −4.13790 | −0.236935 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1541 | −1.09318 | −0.546592 | − | 0.837399i | \(-0.684075\pi\) | ||||
−0.546592 | + | 0.837399i | \(0.684075\pi\) | |||||||
\(308\) | 27.0628 | 1.54205 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.49717 | −0.369014 | ||||||||
\(311\) | 17.6665 | 1.00177 | 0.500887 | − | 0.865513i | \(-0.333007\pi\) | ||||
0.500887 | + | 0.865513i | \(0.333007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.4016 | −1.20969 | −0.604846 | − | 0.796343i | \(-0.706765\pi\) | ||||
−0.604846 | + | 0.796343i | \(0.706765\pi\) | |||||||
\(314\) | −55.8347 | −3.15094 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.4807 | −1.71468 | ||||||||
\(317\) | −11.4317 | −0.642070 | −0.321035 | − | 0.947067i | \(-0.604031\pi\) | ||||
−0.321035 | + | 0.947067i | \(0.604031\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4775 | 0.586626 | ||||||||
\(320\) | −1.83567 | −0.102617 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20.8441 | 1.16160 | ||||||||
\(323\) | −28.5125 | −1.58648 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.3567 | −0.685426 | ||||||||
\(326\) | 42.7189 | 2.36598 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −50.0405 | −2.76302 | ||||||||
\(329\) | −6.14673 | −0.338880 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5607 | 1.40494 | 0.702472 | − | 0.711711i | \(-0.252079\pi\) | ||||
0.702472 | + | 0.711711i | \(0.252079\pi\) | |||||||
\(332\) | 21.0633 | 1.15600 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.5586 | 1.17963 | ||||||||
\(335\) | 4.29618 | 0.234725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.321760 | −0.0175274 | −0.00876370 | − | 0.999962i | \(-0.502790\pi\) | ||||
−0.00876370 | + | 0.999962i | \(0.502790\pi\) | |||||||
\(338\) | −16.3058 | −0.886921 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.71717 | 0.418522 | ||||||||
\(341\) | 44.6528 | 2.41808 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −42.3784 | −2.28489 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −64.3780 | −3.46098 | ||||||||
\(347\) | −11.5029 | −0.617507 | −0.308753 | − | 0.951142i | \(-0.599912\pi\) | ||||
−0.308753 | + | 0.951142i | \(0.599912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3049 | 0.819252 | 0.409626 | − | 0.912254i | \(-0.365659\pi\) | ||||
0.409626 | + | 0.912254i | \(0.365659\pi\) | |||||||
\(350\) | 12.1247 | 0.648093 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.0712 | −0.803298 | ||||||||
\(353\) | −7.04701 | −0.375075 | −0.187537 | − | 0.982257i | \(-0.560051\pi\) | ||||
−0.187537 | + | 0.982257i | \(0.560051\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.63407 | 0.139802 | ||||||||
\(356\) | 26.5716 | 1.40829 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 35.1190 | 1.85610 | ||||||||
\(359\) | 17.9118 | 0.945350 | 0.472675 | − | 0.881237i | \(-0.343289\pi\) | ||||
0.472675 | + | 0.881237i | \(0.343289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0124 | 0.790124 | ||||||||
\(362\) | −41.8299 | −2.19853 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.7370 | −0.562774 | ||||||||
\(365\) | 2.05458 | 0.107542 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.13230 | 0.111305 | 0.0556527 | − | 0.998450i | \(-0.482276\pi\) | ||||
0.0556527 | + | 0.998450i | \(0.482276\pi\) | |||||||
\(368\) | −45.0303 | −2.34736 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.95888 | 0.361775 | ||||||||
\(371\) | 2.53581 | 0.131653 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.0911 | −1.50628 | −0.753140 | − | 0.657861i | \(-0.771462\pi\) | ||||
−0.753140 | + | 0.657861i | \(0.771462\pi\) | |||||||
\(374\) | −78.1543 | −4.04126 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.0909 | 1.75810 | ||||||||
\(377\) | −4.15689 | −0.214091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7521 | −1.01460 | −0.507298 | − | 0.861771i | \(-0.669356\pi\) | ||||
−0.507298 | + | 0.861771i | \(0.669356\pi\) | |||||||
\(380\) | −9.20574 | −0.472244 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −56.6238 | −2.89713 | ||||||||
\(383\) | −13.0295 | −0.665776 | −0.332888 | − | 0.942966i | \(-0.608023\pi\) | ||||
−0.332888 | + | 0.942966i | \(0.608023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.39509 | 0.122065 | ||||||||
\(386\) | 4.12619 | 0.210018 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −64.8201 | −3.29074 | ||||||||
\(389\) | 27.0519 | 1.37159 | 0.685794 | − | 0.727796i | \(-0.259455\pi\) | ||||
0.685794 | + | 0.727796i | \(0.259455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.8501 | −2.06588 | ||||||||
\(392\) | 5.54618 | 0.280124 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −31.3894 | −1.58137 | ||||||||
\(395\) | −2.69758 | −0.135730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.86212 | −0.394589 | −0.197294 | − | 0.980344i | \(-0.563215\pi\) | ||||
−0.197294 | + | 0.980344i | \(0.563215\pi\) | |||||||
\(398\) | 26.5953 | 1.33310 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.1934 | −1.30967 | ||||||||
\(401\) | 7.53993 | 0.376526 | 0.188263 | − | 0.982119i | \(-0.439714\pi\) | ||||
0.188263 | + | 0.982119i | \(0.439714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.7158 | −0.882486 | ||||||||
\(404\) | 62.8517 | 3.12699 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.07885 | 0.202430 | ||||||||
\(407\) | −47.8259 | −2.37064 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.18427 | −0.256346 | −0.128173 | − | 0.991752i | \(-0.540911\pi\) | ||||
−0.128173 | + | 0.991752i | \(0.540911\pi\) | |||||||
\(410\) | −8.41260 | −0.415469 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44.6625 | 2.20036 | ||||||||
\(413\) | −1.55774 | −0.0766514 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.86412 | 0.0915062 | ||||||||
\(416\) | 5.97943 | 0.293166 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 93.2296 | 4.56001 | ||||||||
\(419\) | −23.7502 | −1.16028 | −0.580138 | − | 0.814518i | \(-0.697001\pi\) | ||||
−0.580138 | + | 0.814518i | \(0.697001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3466 | 0.845419 | 0.422710 | − | 0.906265i | \(-0.361079\pi\) | ||||
0.422710 | + | 0.906265i | \(0.361079\pi\) | |||||||
\(422\) | −20.1232 | −0.979581 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.0641 | −0.683012 | ||||||||
\(425\) | −23.7619 | −1.15262 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0709 | 0.535761 | ||||||||
\(428\) | 59.6875 | 2.88511 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.12448 | −0.343573 | ||||||||
\(431\) | −18.6704 | −0.899324 | −0.449662 | − | 0.893199i | \(-0.648456\pi\) | ||||
−0.449662 | + | 0.893199i | \(0.648456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6587 | 0.656398 | 0.328199 | − | 0.944609i | \(-0.393558\pi\) | ||||
0.328199 | + | 0.944609i | \(0.393558\pi\) | |||||||
\(434\) | 17.3832 | 0.834420 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.6126 | 1.41818 | ||||||||
\(437\) | 48.7297 | 2.33106 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1317 | 1.19947 | 0.599736 | − | 0.800198i | \(-0.295272\pi\) | ||||
0.599736 | + | 0.800198i | \(0.295272\pi\) | |||||||
\(440\) | −13.2836 | −0.633271 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.0074 | 1.47487 | ||||||||
\(443\) | −26.5215 | −1.26008 | −0.630038 | − | 0.776565i | \(-0.716961\pi\) | ||||
−0.630038 | + | 0.776565i | \(0.716961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.35162 | 0.111477 | ||||||||
\(446\) | −8.78815 | −0.416131 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.91135 | 0.232039 | ||||||||
\(449\) | 16.1644 | 0.762843 | 0.381422 | − | 0.924401i | \(-0.375435\pi\) | ||||
0.381422 | + | 0.924401i | \(0.375435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 57.8169 | 2.72249 | ||||||||
\(452\) | 60.0968 | 2.82672 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 29.0513 | 1.36345 | ||||||||
\(455\) | −0.950241 | −0.0445480 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.04113 | −0.142258 | −0.0711290 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711290 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(458\) | 53.2377 | 2.48763 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.1891 | −0.614946 | ||||||||
\(461\) | 21.0282 | 0.979379 | 0.489689 | − | 0.871897i | \(-0.337110\pi\) | ||||
0.489689 | + | 0.871897i | \(0.337110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6609 | 0.634877 | 0.317439 | − | 0.948279i | \(-0.397177\pi\) | ||||
0.317439 | + | 0.948279i | \(0.397177\pi\) | |||||||
\(464\) | −8.81169 | −0.409072 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.07601 | 0.420438 | ||||||||
\(467\) | −11.9422 | −0.552619 | −0.276310 | − | 0.961069i | \(-0.589112\pi\) | ||||
−0.276310 | + | 0.961069i | \(0.589112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4944 | −0.530763 | ||||||||
\(470\) | 5.73122 | 0.264361 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.63951 | 0.397665 | ||||||||
\(473\) | 48.9640 | 2.25137 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.3453 | 1.30057 | ||||||||
\(476\) | −20.6473 | −0.946367 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.31144 | 0.425895 | ||||||||
\(479\) | 2.43999 | 0.111486 | 0.0557430 | − | 0.998445i | \(-0.482247\pi\) | ||||
0.0557430 | + | 0.998445i | \(0.482247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9747 | 0.865173 | ||||||||
\(482\) | 14.2958 | 0.651156 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 126.965 | 5.77112 | ||||||||
\(485\) | −5.73666 | −0.260488 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2175 | 1.50523 | 0.752613 | − | 0.658463i | \(-0.228793\pi\) | ||||
0.752613 | + | 0.658463i | \(0.228793\pi\) | |||||||
\(488\) | −61.4015 | −2.77951 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.932401 | 0.0421216 | ||||||||
\(491\) | −31.9094 | −1.44005 | −0.720025 | − | 0.693948i | \(-0.755870\pi\) | ||||
−0.720025 | + | 0.693948i | \(0.755870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.99369 | −0.360018 | ||||||||
\(494\) | −36.9884 | −1.66419 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.5535 | −1.68620 | ||||||||
\(497\) | −7.04746 | −0.316122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.0736 | 1.74917 | 0.874586 | − | 0.484870i | \(-0.161133\pi\) | ||||
0.874586 | + | 0.484870i | \(0.161133\pi\) | |||||||
\(500\) | −15.5643 | −0.696058 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.6719 | 1.27969 | ||||||||
\(503\) | 1.41048 | 0.0628903 | 0.0314451 | − | 0.999505i | \(-0.489989\pi\) | ||||
0.0314451 | + | 0.999505i | \(0.489989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.56245 | 0.247526 | ||||||||
\(506\) | 133.571 | 5.93793 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.22324 | −0.187376 | ||||||||
\(509\) | 21.3887 | 0.948036 | 0.474018 | − | 0.880515i | \(-0.342803\pi\) | ||||
0.474018 | + | 0.880515i | \(0.342803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.49704 | −0.243175 | ||||||||
\(512\) | −47.1046 | −2.08175 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −62.1710 | −2.74224 | ||||||||
\(515\) | 3.95269 | 0.174176 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.3886 | −1.73231 | ||||||||
\(518\) | −18.6185 | −0.818049 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.27021 | 0.231114 | ||||||||
\(521\) | 8.11999 | 0.355743 | 0.177872 | − | 0.984054i | \(-0.443079\pi\) | ||||
0.177872 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.7403 | −0.863184 | −0.431592 | − | 0.902069i | \(-0.642048\pi\) | ||||
−0.431592 | + | 0.902069i | \(0.642048\pi\) | |||||||
\(524\) | −81.2789 | −3.55069 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.7709 | −2.47533 | ||||||||
\(527\) | −34.0674 | −1.48400 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.8153 | 2.03545 | ||||||||
\(530\) | −2.36440 | −0.102703 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.6300 | 1.06784 | ||||||||
\(533\) | −22.9386 | −0.993580 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.28242 | 0.228379 | ||||||||
\(536\) | 63.7502 | 2.75359 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.8532 | 0.726591 | ||||||||
\(539\) | −6.40807 | −0.276015 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.35211 | −0.316092 | −0.158046 | − | 0.987432i | \(-0.550519\pi\) | ||||
−0.158046 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(542\) | −51.9116 | −2.22979 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11.4984 | 0.492991 | ||||||||
\(545\) | 2.62075 | 0.112261 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8879 | −0.764831 | −0.382416 | − | 0.923990i | \(-0.624908\pi\) | ||||
−0.382416 | + | 0.923990i | \(0.624908\pi\) | |||||||
\(548\) | −1.76223 | −0.0752787 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 77.6960 | 3.31297 | ||||||||
\(551\) | 9.53561 | 0.406230 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.21739 | 0.306915 | ||||||||
\(554\) | 40.9923 | 1.74159 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −32.9517 | −1.39746 | ||||||||
\(557\) | 11.6752 | 0.494693 | 0.247346 | − | 0.968927i | \(-0.420441\pi\) | ||||
0.247346 | + | 0.968927i | \(0.420441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.4263 | −0.821643 | ||||||||
\(560\) | −2.01430 | −0.0851197 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 43.4014 | 1.83078 | ||||||||
\(563\) | −23.7886 | −1.00257 | −0.501285 | − | 0.865282i | \(-0.667139\pi\) | ||||
−0.501285 | + | 0.865282i | \(0.667139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.31864 | 0.223757 | ||||||||
\(566\) | −52.0719 | −2.18874 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 39.0865 | 1.64003 | ||||||||
\(569\) | −3.67726 | −0.154159 | −0.0770794 | − | 0.997025i | \(-0.524560\pi\) | ||||
−0.0770794 | + | 0.997025i | \(0.524560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.7874 | −1.74875 | −0.874375 | − | 0.485251i | \(-0.838728\pi\) | ||||
−0.874375 | + | 0.485251i | \(0.838728\pi\) | |||||||
\(572\) | −68.8037 | −2.87683 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.5079 | 0.939463 | ||||||||
\(575\) | 40.6105 | 1.69358 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.4826 | 1.47716 | 0.738579 | − | 0.674167i | \(-0.235497\pi\) | ||||
0.738579 | + | 0.674167i | \(0.235497\pi\) | |||||||
\(578\) | 17.2181 | 0.716180 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.58089 | −0.107166 | ||||||||
\(581\) | −4.98747 | −0.206915 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.2497 | 0.672992 | ||||||||
\(584\) | 30.4876 | 1.26159 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.64169 | 0.274366 | ||||||||
\(587\) | 18.7445 | 0.773669 | 0.386834 | − | 0.922149i | \(-0.373569\pi\) | ||||
0.386834 | + | 0.922149i | \(0.373569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.6387 | 1.67449 | ||||||||
\(590\) | 1.45244 | 0.0597960 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.2222 | 1.65312 | ||||||||
\(593\) | −15.6452 | −0.642470 | −0.321235 | − | 0.947000i | \(-0.604098\pi\) | ||||
−0.321235 | + | 0.947000i | \(0.604098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.82731 | −0.0749124 | ||||||||
\(596\) | 3.37745 | 0.138346 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −52.9935 | −2.16707 | ||||||||
\(599\) | 21.2278 | 0.867343 | 0.433672 | − | 0.901071i | \(-0.357218\pi\) | ||||
0.433672 | + | 0.901071i | \(0.357218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.5015 | −0.469154 | −0.234577 | − | 0.972098i | \(-0.575371\pi\) | ||||
−0.234577 | + | 0.972098i | \(0.575371\pi\) | |||||||
\(602\) | 19.0616 | 0.776891 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −73.6097 | −2.99514 | ||||||||
\(605\) | 11.2365 | 0.456829 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.5860 | −1.20086 | −0.600430 | − | 0.799677i | \(-0.705004\pi\) | ||||
−0.600430 | + | 0.799677i | \(0.705004\pi\) | |||||||
\(608\) | −13.7164 | −0.556272 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.3226 | −0.417949 | ||||||||
\(611\) | 15.6273 | 0.632212 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0162 | 0.646888 | 0.323444 | − | 0.946247i | \(-0.395159\pi\) | ||||
0.323444 | + | 0.946247i | \(0.395159\pi\) | |||||||
\(614\) | −47.7827 | −1.92835 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 35.5403 | 1.43196 | ||||||||
\(617\) | 32.3833 | 1.30370 | 0.651851 | − | 0.758347i | \(-0.273993\pi\) | ||||
0.651851 | + | 0.758347i | \(0.273993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.74750 | −0.271205 | −0.135602 | − | 0.990763i | \(-0.543297\pi\) | ||||
−0.135602 | + | 0.990763i | \(0.543297\pi\) | |||||||
\(620\) | −10.9992 | −0.441739 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 44.0715 | 1.76711 | ||||||||
\(623\) | −6.29176 | −0.252074 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.9240 | 0.916962 | ||||||||
\(626\) | −53.3894 | −2.13387 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −94.5239 | −3.77191 | ||||||||
\(629\) | 36.4883 | 1.45488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4499 | −1.09276 | −0.546381 | − | 0.837537i | \(-0.683995\pi\) | ||||
−0.546381 | + | 0.837537i | \(0.683995\pi\) | |||||||
\(632\) | −40.0289 | −1.59227 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.5181 | −1.13260 | ||||||||
\(635\) | −0.373762 | −0.0148323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.54237 | 0.100732 | ||||||||
\(638\) | 26.1376 | 1.03480 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.33745 | −0.250510 | ||||||||
\(641\) | 25.6205 | 1.01195 | 0.505975 | − | 0.862548i | \(-0.331133\pi\) | ||||
0.505975 | + | 0.862548i | \(0.331133\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0718 | −0.988735 | −0.494368 | − | 0.869253i | \(-0.664600\pi\) | ||||
−0.494368 | + | 0.869253i | \(0.664600\pi\) | |||||||
\(644\) | 35.2875 | 1.39052 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −71.1286 | −2.79852 | ||||||||
\(647\) | −26.5116 | −1.04228 | −0.521139 | − | 0.853472i | \(-0.674493\pi\) | ||||
−0.521139 | + | 0.853472i | \(0.674493\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.98210 | −0.391832 | ||||||||
\(650\) | −30.8255 | −1.20908 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 72.3198 | 2.83226 | ||||||||
\(653\) | 0.745988 | 0.0291928 | 0.0145964 | − | 0.999893i | \(-0.495354\pi\) | ||||
0.0145964 | + | 0.999893i | \(0.495354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.19328 | −0.281065 | ||||||||
\(656\) | −48.6247 | −1.89847 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.3339 | −0.597777 | ||||||||
\(659\) | 50.1415 | 1.95324 | 0.976619 | − | 0.214979i | \(-0.0689685\pi\) | ||||
0.976619 | + | 0.214979i | \(0.0689685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0074 | −0.428138 | −0.214069 | − | 0.976819i | \(-0.568672\pi\) | ||||
−0.214069 | + | 0.976819i | \(0.568672\pi\) | |||||||
\(662\) | 63.7649 | 2.47829 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.6614 | 1.07347 | ||||||||
\(665\) | 2.17978 | 0.0845283 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6617 | 0.528984 | ||||||||
\(668\) | 36.4970 | 1.41211 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.7174 | 0.414050 | ||||||||
\(671\) | 70.9434 | 2.73874 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4045 | −1.17201 | −0.586003 | − | 0.810309i | \(-0.699299\pi\) | ||||
−0.586003 | + | 0.810309i | \(0.699299\pi\) | |||||||
\(674\) | −0.802676 | −0.0309179 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27.6045 | −1.06171 | ||||||||
\(677\) | 27.3555 | 1.05136 | 0.525679 | − | 0.850683i | \(-0.323811\pi\) | ||||
0.525679 | + | 0.850683i | \(0.323811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3484 | 0.589019 | ||||||||
\(680\) | 10.1346 | 0.388644 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 111.393 | 4.26544 | ||||||||
\(683\) | −17.0233 | −0.651379 | −0.325689 | − | 0.945477i | \(-0.605596\pi\) | ||||
−0.325689 | + | 0.945477i | \(0.605596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.155960 | −0.00595891 | ||||||||
\(686\) | −2.49464 | −0.0952459 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −41.1793 | −1.56995 | ||||||||
\(689\) | −6.44698 | −0.245610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.1416 | −1.83139 | −0.915696 | − | 0.401871i | \(-0.868360\pi\) | ||||
−0.915696 | + | 0.401871i | \(0.868360\pi\) | |||||||
\(692\) | −108.987 | −4.14307 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.6956 | −1.08927 | ||||||||
\(695\) | −2.91627 | −0.110620 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.1108 | −1.67082 | ||||||||
\(698\) | 38.1802 | 1.44514 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.5262 | 0.775818 | ||||||||
\(701\) | 36.9208 | 1.39448 | 0.697240 | − | 0.716837i | \(-0.254411\pi\) | ||||
0.697240 | + | 0.716837i | \(0.254411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.5266 | −1.64164 | ||||||||
\(704\) | 31.4722 | 1.18615 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.5798 | −0.661623 | ||||||||
\(707\) | −14.8823 | −0.559708 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1340 | −0.380592 | −0.190296 | − | 0.981727i | \(-0.560945\pi\) | ||||
−0.190296 | + | 0.981727i | \(0.560945\pi\) | |||||||
\(710\) | 6.57107 | 0.246608 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.8952 | 1.30775 | ||||||||
\(713\) | 58.2233 | 2.18048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.08921 | −0.227724 | ||||||||
\(716\) | 59.4538 | 2.22189 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 44.6836 | 1.66758 | ||||||||
\(719\) | 6.11067 | 0.227890 | 0.113945 | − | 0.993487i | \(-0.463651\pi\) | ||||
0.113945 | + | 0.993487i | \(0.463651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5754 | −0.393849 | ||||||||
\(722\) | 37.4505 | 1.39376 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −70.8148 | −2.63181 | ||||||||
\(725\) | 7.94682 | 0.295137 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.9229 | 1.22104 | 0.610521 | − | 0.792000i | \(-0.290960\pi\) | ||||
0.610521 | + | 0.792000i | \(0.290960\pi\) | |||||||
\(728\) | −14.1005 | −0.522598 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.12545 | 0.189701 | ||||||||
\(731\) | −37.3566 | −1.38168 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5829 | 0.427823 | 0.213912 | − | 0.976853i | \(-0.431380\pi\) | ||||
0.213912 | + | 0.976853i | \(0.431380\pi\) | |||||||
\(734\) | 5.31933 | 0.196340 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.6515 | −0.724365 | ||||||||
\(737\) | −73.6571 | −2.71319 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.8534 | −1.20853 | −0.604267 | − | 0.796782i | \(-0.706534\pi\) | ||||
−0.604267 | + | 0.796782i | \(0.706534\pi\) | |||||||
\(740\) | 11.7808 | 0.433073 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.32594 | 0.232233 | ||||||||
\(743\) | 16.3217 | 0.598783 | 0.299392 | − | 0.954130i | \(-0.403216\pi\) | ||||
0.299392 | + | 0.954130i | \(0.403216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.298909 | 0.0109512 | ||||||||
\(746\) | −72.5718 | −2.65704 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −132.309 | −4.83770 | ||||||||
\(749\) | −14.1331 | −0.516413 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.51082 | −0.237583 | −0.118792 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118792 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(752\) | 33.1263 | 1.20799 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.3700 | −0.377652 | ||||||||
\(755\) | −6.51455 | −0.237089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.1014 | 1.02136 | 0.510682 | − | 0.859770i | \(-0.329393\pi\) | ||||
0.510682 | + | 0.859770i | \(0.329393\pi\) | |||||||
\(758\) | −49.2744 | −1.78973 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0895 | −0.438531 | ||||||||
\(761\) | −17.9070 | −0.649130 | −0.324565 | − | 0.945863i | \(-0.605218\pi\) | ||||
−0.324565 | + | 0.945863i | \(0.605218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.01182 | −0.253845 | ||||||||
\(764\) | −95.8598 | −3.46809 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.5039 | −1.17441 | ||||||||
\(767\) | 3.96035 | 0.143000 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.1782 | −1.12432 | −0.562158 | − | 0.827030i | \(-0.690029\pi\) | ||||
−0.562158 | + | 0.827030i | \(0.690029\pi\) | |||||||
\(770\) | 5.97489 | 0.215320 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.98533 | 0.251408 | ||||||||
\(773\) | 28.7394 | 1.03368 | 0.516842 | − | 0.856081i | \(-0.327108\pi\) | ||||
0.516842 | + | 0.856081i | \(0.327108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.8676 | 1.21656 | ||||||||
\(776\) | −85.1252 | −3.05582 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 67.4849 | 2.41945 | ||||||||
\(779\) | 52.6194 | 1.88529 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.1606 | −1.61597 | ||||||||
\(782\) | −101.906 | −3.64416 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.38926 | 0.192474 | ||||||||
\(785\) | −8.36548 | −0.298577 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.8508 | 1.13536 | 0.567680 | − | 0.823249i | \(-0.307841\pi\) | ||||
0.567680 | + | 0.823249i | \(0.307841\pi\) | |||||||
\(788\) | −53.1398 | −1.89303 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.72950 | −0.239425 | ||||||||
\(791\) | −14.2300 | −0.505962 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.1465 | −0.999511 | ||||||||
\(794\) | −19.6132 | −0.696046 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.0239 | 1.59583 | ||||||||
\(797\) | −7.35905 | −0.260671 | −0.130335 | − | 0.991470i | \(-0.541605\pi\) | ||||
−0.130335 | + | 0.991470i | \(0.541605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0512 | 1.06313 | ||||||||
\(800\) | −11.4310 | −0.404147 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.8094 | 0.664184 | ||||||||
\(803\) | −35.2254 | −1.24308 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.12299 | 0.110071 | ||||||||
\(806\) | −44.1945 | −1.55669 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 82.5402 | 2.90375 | ||||||||
\(809\) | 37.0239 | 1.30169 | 0.650846 | − | 0.759210i | \(-0.274414\pi\) | ||||
0.650846 | + | 0.759210i | \(0.274414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.7240 | −1.92162 | −0.960809 | − | 0.277212i | \(-0.910590\pi\) | ||||
−0.960809 | + | 0.277212i | \(0.910590\pi\) | |||||||
\(812\) | 6.90519 | 0.242325 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −119.309 | −4.18176 | ||||||||
\(815\) | 6.40039 | 0.224196 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.5624 | 1.55904 | ||||||||
\(818\) | −12.9329 | −0.452188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.2419 | −0.497348 | ||||||||
\(821\) | 9.67818 | 0.337771 | 0.168885 | − | 0.985636i | \(-0.445983\pi\) | ||||
0.168885 | + | 0.985636i | \(0.445983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.7237 | −0.408663 | −0.204331 | − | 0.978902i | \(-0.565502\pi\) | ||||
−0.204331 | + | 0.978902i | \(0.565502\pi\) | |||||||
\(824\) | 58.6532 | 2.04328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.88600 | −0.135211 | ||||||||
\(827\) | −26.6769 | −0.927646 | −0.463823 | − | 0.885928i | \(-0.653523\pi\) | ||||
−0.463823 | + | 0.885928i | \(0.653523\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.20281 | 0.284895 | 0.142448 | − | 0.989802i | \(-0.454503\pi\) | ||||
0.142448 | + | 0.989802i | \(0.454503\pi\) | |||||||
\(830\) | 4.65032 | 0.161415 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.4865 | −0.432890 | ||||||||
\(833\) | 4.88897 | 0.169393 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.23003 | 0.111780 | ||||||||
\(836\) | 157.830 | 5.45868 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −59.2484 | −2.04670 | ||||||||
\(839\) | −32.8245 | −1.13323 | −0.566614 | − | 0.823983i | \(-0.691747\pi\) | ||||
−0.566614 | + | 0.823983i | \(0.691747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3266 | −0.907815 | ||||||||
\(842\) | 43.2734 | 1.49130 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34.0670 | −1.17263 | ||||||||
\(845\) | −2.44303 | −0.0840430 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.0633 | −1.03299 | ||||||||
\(848\) | −13.6661 | −0.469298 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −59.2774 | −2.03320 | ||||||||
\(851\) | −62.3608 | −2.13770 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.2937 | −1.10571 | −0.552857 | − | 0.833276i | \(-0.686462\pi\) | ||||
−0.552857 | + | 0.833276i | \(0.686462\pi\) | |||||||
\(854\) | 27.6181 | 0.945070 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 78.3849 | 2.67914 | ||||||||
\(857\) | 27.3034 | 0.932668 | 0.466334 | − | 0.884609i | \(-0.345575\pi\) | ||||
0.466334 | + | 0.884609i | \(0.345575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.1565 | −1.74544 | −0.872718 | − | 0.488225i | \(-0.837645\pi\) | ||||
−0.872718 | + | 0.488225i | \(0.837645\pi\) | |||||||
\(860\) | −12.0612 | −0.411283 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.5761 | −1.58639 | ||||||||
\(863\) | 38.4182 | 1.30777 | 0.653885 | − | 0.756594i | \(-0.273138\pi\) | ||||
0.653885 | + | 0.756594i | \(0.273138\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.64549 | −0.327956 | ||||||||
\(866\) | 34.0737 | 1.15787 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 29.4284 | 0.998865 | ||||||||
\(869\) | 46.2495 | 1.56891 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.2231 | 0.990187 | ||||||||
\(872\) | 38.8888 | 1.31694 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 121.563 | 4.11194 | ||||||||
\(875\) | 3.68540 | 0.124589 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.3936 | −1.80298 | −0.901488 | − | 0.432805i | \(-0.857524\pi\) | ||||
−0.901488 | + | 0.432805i | \(0.857524\pi\) | |||||||
\(878\) | 62.6947 | 2.11584 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.9078 | −0.435121 | ||||||||
\(881\) | −3.49548 | −0.117766 | −0.0588828 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588828 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.75544 | −0.0927281 | −0.0463640 | − | 0.998925i | \(-0.514763\pi\) | ||||
−0.0463640 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(884\) | 52.4931 | 1.76553 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −66.1617 | −2.22275 | ||||||||
\(887\) | 53.5674 | 1.79862 | 0.899308 | − | 0.437315i | \(-0.144071\pi\) | ||||
0.899308 | + | 0.437315i | \(0.144071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 5.86644 | 0.196644 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.8777 | −0.498141 | ||||||||
\(893\) | −35.8478 | −1.19960 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.26174 | 0.175880 | ||||||||
\(896\) | 16.9559 | 0.566456 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.3243 | 1.34564 | ||||||||
\(899\) | 11.3933 | 0.379989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.3975 | −0.413021 | ||||||||
\(902\) | 144.232 | 4.80241 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 78.9224 | 2.62492 | ||||||||
\(905\) | −6.26720 | −0.208329 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.2461 | 0.373422 | 0.186711 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186711 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(908\) | 49.1816 | 1.63215 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.37051 | −0.0785817 | ||||||||
\(911\) | −42.0363 | −1.39272 | −0.696362 | − | 0.717690i | \(-0.745199\pi\) | ||||
−0.696362 | + | 0.717690i | \(0.745199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.9600 | −1.05772 | ||||||||
\(914\) | −7.58653 | −0.250940 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 90.1273 | 2.97789 | ||||||||
\(917\) | 19.2456 | 0.635547 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.6524 | −0.681261 | −0.340630 | − | 0.940197i | \(-0.610641\pi\) | ||||
−0.340630 | + | 0.940197i | \(0.610641\pi\) | |||||||
\(920\) | −17.3207 | −0.571045 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 52.4577 | 1.72760 | ||||||||
\(923\) | 17.9173 | 0.589754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.2743 | −1.19269 | ||||||||
\(926\) | 34.0791 | 1.11991 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.84548 | −0.126234 | ||||||||
\(929\) | −8.98955 | −0.294937 | −0.147469 | − | 0.989067i | \(-0.547113\pi\) | ||||
−0.147469 | + | 0.989067i | \(0.547113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.83201 | −0.191136 | ||||||||
\(932\) | 15.3650 | 0.503297 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.7915 | −0.974808 | ||||||||
\(935\) | −11.7095 | −0.382942 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7903 | −0.613853 | −0.306927 | − | 0.951733i | \(-0.599301\pi\) | ||||
−0.306927 | + | 0.951733i | \(0.599301\pi\) | |||||||
\(938\) | −28.6745 | −0.936255 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.70251 | 0.316461 | ||||||||
\(941\) | −34.8758 | −1.13692 | −0.568459 | − | 0.822712i | \(-0.692460\pi\) | ||||
−0.568459 | + | 0.822712i | \(0.692460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75.3881 | 2.45497 | ||||||||
\(944\) | 8.39506 | 0.273236 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 122.148 | 3.97136 | ||||||||
\(947\) | 57.7138 | 1.87545 | 0.937723 | − | 0.347383i | \(-0.112929\pi\) | ||||
0.937723 | + | 0.347383i | \(0.112929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.9755 | 0.453665 | ||||||||
\(950\) | 70.7115 | 2.29418 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −27.1151 | −0.878806 | ||||||||
\(953\) | −0.231947 | −0.00751349 | −0.00375675 | − | 0.999993i | \(-0.501196\pi\) | ||||
−0.00375675 | + | 0.999993i | \(0.501196\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.48371 | −0.274526 | ||||||||
\(956\) | 15.7635 | 0.509830 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.08690 | 0.196659 | ||||||||
\(959\) | 0.417270 | 0.0134744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.5559 | 0.566321 | ||||||||
\(962\) | 47.3351 | 1.52615 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2017 | 0.779484 | ||||||||
\(965\) | 0.618210 | 0.0199009 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.3332 | −0.653871 | −0.326935 | − | 0.945047i | \(-0.606016\pi\) | ||||
−0.326935 | + | 0.945047i | \(0.606016\pi\) | |||||||
\(968\) | 166.737 | 5.35912 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.3109 | −0.459496 | ||||||||
\(971\) | 18.7408 | 0.601421 | 0.300711 | − | 0.953715i | \(-0.402776\pi\) | ||||
0.300711 | + | 0.953715i | \(0.402776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.80248 | 0.250136 | ||||||||
\(974\) | 82.8657 | 2.65519 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −59.6642 | −1.90981 | ||||||||
\(977\) | −17.7823 | −0.568906 | −0.284453 | − | 0.958690i | \(-0.591812\pi\) | ||||
−0.284453 | + | 0.958690i | \(0.591812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.3180 | −1.28857 | ||||||||
\(980\) | 1.57848 | 0.0504228 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −79.6025 | −2.54022 | ||||||||
\(983\) | 54.0319 | 1.72335 | 0.861675 | − | 0.507460i | \(-0.169416\pi\) | ||||
0.861675 | + | 0.507460i | \(0.169416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.70294 | −0.149848 | ||||||||
\(986\) | −19.9414 | −0.635064 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −62.6185 | −1.99216 | ||||||||
\(989\) | 63.8448 | 2.03015 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9862 | −0.412519 | −0.206259 | − | 0.978497i | \(-0.566129\pi\) | ||||
−0.206259 | + | 0.978497i | \(0.566129\pi\) | |||||||
\(992\) | −16.3886 | −0.520339 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.5809 | −0.557632 | ||||||||
\(995\) | 3.98467 | 0.126323 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.65694 | 0.305838 | 0.152919 | − | 0.988239i | \(-0.451133\pi\) | ||||
0.152919 | + | 0.988239i | \(0.451133\pi\) | |||||||
\(998\) | 97.4745 | 3.08550 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.z.1.31 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.2 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.2 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.31 | yes | 32 | 1.1 | even | 1 | trivial |