Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12129 | −1.49998 | −0.749988 | − | 0.661451i | \(-0.769941\pi\) | ||||
−0.749988 | + | 0.661451i | \(0.769941\pi\) | |||||||
\(3\) | 1.35005 | 0.779449 | 0.389725 | − | 0.920931i | \(-0.372570\pi\) | ||||
0.389725 | + | 0.920931i | \(0.372570\pi\) | |||||||
\(4\) | 2.49986 | 1.24993 | ||||||||
\(5\) | −1.60395 | −0.717308 | −0.358654 | − | 0.933471i | \(-0.616764\pi\) | ||||
−0.358654 | + | 0.933471i | \(0.616764\pi\) | |||||||
\(6\) | −2.86383 | −1.16916 | ||||||||
\(7\) | −4.53308 | −1.71334 | −0.856671 | − | 0.515863i | \(-0.827471\pi\) | ||||
−0.856671 | + | 0.515863i | \(0.827471\pi\) | |||||||
\(8\) | −1.06034 | −0.374888 | ||||||||
\(9\) | −1.17738 | −0.392459 | ||||||||
\(10\) | 3.40244 | 1.07594 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.37492 | 0.974257 | ||||||||
\(13\) | 0.894770 | 0.248164 | 0.124082 | − | 0.992272i | \(-0.460401\pi\) | ||||
0.124082 | + | 0.992272i | \(0.460401\pi\) | |||||||
\(14\) | 9.61596 | 2.56997 | ||||||||
\(15\) | −2.16540 | −0.559105 | ||||||||
\(16\) | −2.75042 | −0.687606 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 2.49755 | 0.588679 | ||||||||
\(19\) | 5.74568 | 1.31815 | 0.659074 | − | 0.752078i | \(-0.270948\pi\) | ||||
0.659074 | + | 0.752078i | \(0.270948\pi\) | |||||||
\(20\) | −4.00965 | −0.896584 | ||||||||
\(21\) | −6.11986 | −1.33546 | ||||||||
\(22\) | 2.12129 | 0.452260 | ||||||||
\(23\) | −5.62341 | −1.17256 | −0.586281 | − | 0.810108i | \(-0.699408\pi\) | ||||
−0.586281 | + | 0.810108i | \(0.699408\pi\) | |||||||
\(24\) | −1.43151 | −0.292206 | ||||||||
\(25\) | −2.42735 | −0.485470 | ||||||||
\(26\) | −1.89806 | −0.372241 | ||||||||
\(27\) | −5.63965 | −1.08535 | ||||||||
\(28\) | −11.3321 | −2.14156 | ||||||||
\(29\) | −3.02816 | −0.562314 | −0.281157 | − | 0.959662i | \(-0.590718\pi\) | ||||
−0.281157 | + | 0.959662i | \(0.590718\pi\) | |||||||
\(30\) | 4.59344 | 0.838644 | ||||||||
\(31\) | 6.20713 | 1.11483 | 0.557417 | − | 0.830233i | \(-0.311793\pi\) | ||||
0.557417 | + | 0.830233i | \(0.311793\pi\) | |||||||
\(32\) | 7.95513 | 1.40628 | ||||||||
\(33\) | −1.35005 | −0.235013 | ||||||||
\(34\) | −2.12129 | −0.363798 | ||||||||
\(35\) | 7.27082 | 1.22899 | ||||||||
\(36\) | −2.94328 | −0.490546 | ||||||||
\(37\) | 6.17491 | 1.01515 | 0.507575 | − | 0.861608i | \(-0.330542\pi\) | ||||
0.507575 | + | 0.861608i | \(0.330542\pi\) | |||||||
\(38\) | −12.1882 | −1.97719 | ||||||||
\(39\) | 1.20798 | 0.193432 | ||||||||
\(40\) | 1.70074 | 0.268910 | ||||||||
\(41\) | 11.3513 | 1.77277 | 0.886387 | − | 0.462946i | \(-0.153208\pi\) | ||||
0.886387 | + | 0.462946i | \(0.153208\pi\) | |||||||
\(42\) | 12.9820 | 2.00316 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −2.49986 | −0.376868 | ||||||||
\(45\) | 1.88845 | 0.281514 | ||||||||
\(46\) | 11.9289 | 1.75881 | ||||||||
\(47\) | 3.38378 | 0.493575 | 0.246788 | − | 0.969070i | \(-0.420625\pi\) | ||||
0.246788 | + | 0.969070i | \(0.420625\pi\) | |||||||
\(48\) | −3.71320 | −0.535954 | ||||||||
\(49\) | 13.5488 | 1.93554 | ||||||||
\(50\) | 5.14910 | 0.728193 | ||||||||
\(51\) | 1.35005 | 0.189044 | ||||||||
\(52\) | 2.23680 | 0.310188 | ||||||||
\(53\) | 3.66404 | 0.503294 | 0.251647 | − | 0.967819i | \(-0.419028\pi\) | ||||
0.251647 | + | 0.967819i | \(0.419028\pi\) | |||||||
\(54\) | 11.9633 | 1.62800 | ||||||||
\(55\) | 1.60395 | 0.216276 | ||||||||
\(56\) | 4.80662 | 0.642312 | ||||||||
\(57\) | 7.75693 | 1.02743 | ||||||||
\(58\) | 6.42359 | 0.843458 | ||||||||
\(59\) | −8.84019 | −1.15089 | −0.575447 | − | 0.817839i | \(-0.695172\pi\) | ||||
−0.575447 | + | 0.817839i | \(0.695172\pi\) | |||||||
\(60\) | −5.41320 | −0.698842 | ||||||||
\(61\) | −10.1961 | −1.30548 | −0.652739 | − | 0.757583i | \(-0.726380\pi\) | ||||
−0.652739 | + | 0.757583i | \(0.726380\pi\) | |||||||
\(62\) | −13.1671 | −1.67222 | ||||||||
\(63\) | 5.33714 | 0.672416 | ||||||||
\(64\) | −11.3743 | −1.42178 | ||||||||
\(65\) | −1.43516 | −0.178010 | ||||||||
\(66\) | 2.86383 | 0.352514 | ||||||||
\(67\) | 2.85720 | 0.349063 | 0.174532 | − | 0.984652i | \(-0.444159\pi\) | ||||
0.174532 | + | 0.984652i | \(0.444159\pi\) | |||||||
\(68\) | 2.49986 | 0.303152 | ||||||||
\(69\) | −7.59185 | −0.913952 | ||||||||
\(70\) | −15.4235 | −1.84346 | ||||||||
\(71\) | 0.715674 | 0.0849349 | 0.0424675 | − | 0.999098i | \(-0.486478\pi\) | ||||
0.0424675 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(72\) | 1.24843 | 0.147128 | ||||||||
\(73\) | 9.17039 | 1.07331 | 0.536657 | − | 0.843801i | \(-0.319687\pi\) | ||||
0.536657 | + | 0.843801i | \(0.319687\pi\) | |||||||
\(74\) | −13.0988 | −1.52270 | ||||||||
\(75\) | −3.27703 | −0.378399 | ||||||||
\(76\) | 14.3634 | 1.64759 | ||||||||
\(77\) | 4.53308 | 0.516592 | ||||||||
\(78\) | −2.56247 | −0.290143 | ||||||||
\(79\) | −15.9552 | −1.79510 | −0.897550 | − | 0.440912i | \(-0.854655\pi\) | ||||
−0.897550 | + | 0.440912i | \(0.854655\pi\) | |||||||
\(80\) | 4.41154 | 0.493225 | ||||||||
\(81\) | −4.08165 | −0.453517 | ||||||||
\(82\) | −24.0793 | −2.65912 | ||||||||
\(83\) | −12.3232 | −1.35265 | −0.676325 | − | 0.736603i | \(-0.736429\pi\) | ||||
−0.676325 | + | 0.736603i | \(0.736429\pi\) | |||||||
\(84\) | −15.2988 | −1.66923 | ||||||||
\(85\) | −1.60395 | −0.173973 | ||||||||
\(86\) | −2.12129 | −0.228744 | ||||||||
\(87\) | −4.08815 | −0.438295 | ||||||||
\(88\) | 1.06034 | 0.113033 | ||||||||
\(89\) | 6.18834 | 0.655963 | 0.327982 | − | 0.944684i | \(-0.393632\pi\) | ||||
0.327982 | + | 0.944684i | \(0.393632\pi\) | |||||||
\(90\) | −4.00595 | −0.422264 | ||||||||
\(91\) | −4.05606 | −0.425191 | ||||||||
\(92\) | −14.0577 | −1.46562 | ||||||||
\(93\) | 8.37991 | 0.868956 | ||||||||
\(94\) | −7.17797 | −0.740351 | ||||||||
\(95\) | −9.21577 | −0.945518 | ||||||||
\(96\) | 10.7398 | 1.09612 | ||||||||
\(97\) | 18.0060 | 1.82823 | 0.914114 | − | 0.405457i | \(-0.132888\pi\) | ||||
0.914114 | + | 0.405457i | \(0.132888\pi\) | |||||||
\(98\) | −28.7409 | −2.90327 | ||||||||
\(99\) | 1.17738 | 0.118331 | ||||||||
\(100\) | −6.06803 | −0.606803 | ||||||||
\(101\) | 10.1588 | 1.01084 | 0.505421 | − | 0.862873i | \(-0.331337\pi\) | ||||
0.505421 | + | 0.862873i | \(0.331337\pi\) | |||||||
\(102\) | −2.86383 | −0.283562 | ||||||||
\(103\) | 11.8307 | 1.16571 | 0.582857 | − | 0.812575i | \(-0.301935\pi\) | ||||
0.582857 | + | 0.812575i | \(0.301935\pi\) | |||||||
\(104\) | −0.948764 | −0.0930340 | ||||||||
\(105\) | 9.81594 | 0.957938 | ||||||||
\(106\) | −7.77248 | −0.754930 | ||||||||
\(107\) | 7.66772 | 0.741267 | 0.370633 | − | 0.928779i | \(-0.379141\pi\) | ||||
0.370633 | + | 0.928779i | \(0.379141\pi\) | |||||||
\(108\) | −14.0983 | −1.35661 | ||||||||
\(109\) | 1.24366 | 0.119121 | 0.0595607 | − | 0.998225i | \(-0.481030\pi\) | ||||
0.0595607 | + | 0.998225i | \(0.481030\pi\) | |||||||
\(110\) | −3.40244 | −0.324409 | ||||||||
\(111\) | 8.33641 | 0.791257 | ||||||||
\(112\) | 12.4679 | 1.17810 | ||||||||
\(113\) | 3.81585 | 0.358965 | 0.179483 | − | 0.983761i | \(-0.442558\pi\) | ||||
0.179483 | + | 0.983761i | \(0.442558\pi\) | |||||||
\(114\) | −16.4547 | −1.54112 | ||||||||
\(115\) | 9.01965 | 0.841087 | ||||||||
\(116\) | −7.56996 | −0.702853 | ||||||||
\(117\) | −1.05348 | −0.0973944 | ||||||||
\(118\) | 18.7526 | 1.72632 | ||||||||
\(119\) | −4.53308 | −0.415546 | ||||||||
\(120\) | 2.29607 | 0.209602 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 21.6289 | 1.95819 | ||||||||
\(123\) | 15.3248 | 1.38179 | ||||||||
\(124\) | 15.5170 | 1.39346 | ||||||||
\(125\) | 11.9131 | 1.06554 | ||||||||
\(126\) | −11.3216 | −1.00861 | ||||||||
\(127\) | −14.8361 | −1.31649 | −0.658243 | − | 0.752805i | \(-0.728700\pi\) | ||||
−0.658243 | + | 0.752805i | \(0.728700\pi\) | |||||||
\(128\) | 8.21782 | 0.726359 | ||||||||
\(129\) | 1.35005 | 0.118865 | ||||||||
\(130\) | 3.04440 | 0.267011 | ||||||||
\(131\) | 7.44224 | 0.650231 | 0.325116 | − | 0.945674i | \(-0.394597\pi\) | ||||
0.325116 | + | 0.945674i | \(0.394597\pi\) | |||||||
\(132\) | −3.37492 | −0.293749 | ||||||||
\(133\) | −26.0456 | −2.25844 | ||||||||
\(134\) | −6.06095 | −0.523586 | ||||||||
\(135\) | 9.04571 | 0.778531 | ||||||||
\(136\) | −1.06034 | −0.0909238 | ||||||||
\(137\) | −21.9270 | −1.87335 | −0.936675 | − | 0.350201i | \(-0.886113\pi\) | ||||
−0.936675 | + | 0.350201i | \(0.886113\pi\) | |||||||
\(138\) | 16.1045 | 1.37091 | ||||||||
\(139\) | 7.16231 | 0.607499 | 0.303750 | − | 0.952752i | \(-0.401761\pi\) | ||||
0.303750 | + | 0.952752i | \(0.401761\pi\) | |||||||
\(140\) | 18.1760 | 1.53615 | ||||||||
\(141\) | 4.56826 | 0.384717 | ||||||||
\(142\) | −1.51815 | −0.127400 | ||||||||
\(143\) | −0.894770 | −0.0748244 | ||||||||
\(144\) | 3.23828 | 0.269857 | ||||||||
\(145\) | 4.85701 | 0.403352 | ||||||||
\(146\) | −19.4530 | −1.60994 | ||||||||
\(147\) | 18.2915 | 1.50866 | ||||||||
\(148\) | 15.4364 | 1.26886 | ||||||||
\(149\) | 8.18872 | 0.670846 | 0.335423 | − | 0.942068i | \(-0.391121\pi\) | ||||
0.335423 | + | 0.942068i | \(0.391121\pi\) | |||||||
\(150\) | 6.95153 | 0.567590 | ||||||||
\(151\) | −18.1026 | −1.47317 | −0.736584 | − | 0.676347i | \(-0.763562\pi\) | ||||
−0.736584 | + | 0.676347i | \(0.763562\pi\) | |||||||
\(152\) | −6.09240 | −0.494159 | ||||||||
\(153\) | −1.17738 | −0.0951853 | ||||||||
\(154\) | −9.61596 | −0.774876 | ||||||||
\(155\) | −9.95592 | −0.799679 | ||||||||
\(156\) | 3.01978 | 0.241776 | ||||||||
\(157\) | 17.1521 | 1.36889 | 0.684444 | − | 0.729065i | \(-0.260045\pi\) | ||||
0.684444 | + | 0.729065i | \(0.260045\pi\) | |||||||
\(158\) | 33.8456 | 2.69261 | ||||||||
\(159\) | 4.94662 | 0.392292 | ||||||||
\(160\) | −12.7596 | −1.00874 | ||||||||
\(161\) | 25.4913 | 2.00900 | ||||||||
\(162\) | 8.65836 | 0.680265 | ||||||||
\(163\) | 0.737702 | 0.0577813 | 0.0288906 | − | 0.999583i | \(-0.490803\pi\) | ||||
0.0288906 | + | 0.999583i | \(0.490803\pi\) | |||||||
\(164\) | 28.3766 | 2.21584 | ||||||||
\(165\) | 2.16540 | 0.168576 | ||||||||
\(166\) | 26.1411 | 2.02894 | ||||||||
\(167\) | 4.70137 | 0.363803 | 0.181901 | − | 0.983317i | \(-0.441775\pi\) | ||||
0.181901 | + | 0.983317i | \(0.441775\pi\) | |||||||
\(168\) | 6.48916 | 0.500650 | ||||||||
\(169\) | −12.1994 | −0.938414 | ||||||||
\(170\) | 3.40244 | 0.260955 | ||||||||
\(171\) | −6.76483 | −0.517319 | ||||||||
\(172\) | 2.49986 | 0.190612 | ||||||||
\(173\) | −17.7514 | −1.34962 | −0.674809 | − | 0.737993i | \(-0.735774\pi\) | ||||
−0.674809 | + | 0.737993i | \(0.735774\pi\) | |||||||
\(174\) | 8.67214 | 0.657433 | ||||||||
\(175\) | 11.0034 | 0.831776 | ||||||||
\(176\) | 2.75042 | 0.207321 | ||||||||
\(177\) | −11.9347 | −0.897064 | ||||||||
\(178\) | −13.1273 | −0.983929 | ||||||||
\(179\) | 4.16077 | 0.310991 | 0.155495 | − | 0.987837i | \(-0.450303\pi\) | ||||
0.155495 | + | 0.987837i | \(0.450303\pi\) | |||||||
\(180\) | 4.72086 | 0.351872 | ||||||||
\(181\) | 17.0430 | 1.26680 | 0.633399 | − | 0.773826i | \(-0.281659\pi\) | ||||
0.633399 | + | 0.773826i | \(0.281659\pi\) | |||||||
\(182\) | 8.60407 | 0.637776 | ||||||||
\(183\) | −13.7652 | −1.01755 | ||||||||
\(184\) | 5.96275 | 0.439580 | ||||||||
\(185\) | −9.90424 | −0.728174 | ||||||||
\(186\) | −17.7762 | −1.30341 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 8.45898 | 0.616934 | ||||||||
\(189\) | 25.5650 | 1.85958 | ||||||||
\(190\) | 19.5493 | 1.41825 | ||||||||
\(191\) | 9.68610 | 0.700861 | 0.350431 | − | 0.936589i | \(-0.386035\pi\) | ||||
0.350431 | + | 0.936589i | \(0.386035\pi\) | |||||||
\(192\) | −15.3558 | −1.10821 | ||||||||
\(193\) | 6.74611 | 0.485596 | 0.242798 | − | 0.970077i | \(-0.421935\pi\) | ||||
0.242798 | + | 0.970077i | \(0.421935\pi\) | |||||||
\(194\) | −38.1958 | −2.74230 | ||||||||
\(195\) | −1.93754 | −0.138750 | ||||||||
\(196\) | 33.8701 | 2.41929 | ||||||||
\(197\) | −7.49347 | −0.533888 | −0.266944 | − | 0.963712i | \(-0.586014\pi\) | ||||
−0.266944 | + | 0.963712i | \(0.586014\pi\) | |||||||
\(198\) | −2.49755 | −0.177493 | ||||||||
\(199\) | −16.1205 | −1.14275 | −0.571375 | − | 0.820689i | \(-0.693590\pi\) | ||||
−0.571375 | + | 0.820689i | \(0.693590\pi\) | |||||||
\(200\) | 2.57383 | 0.181997 | ||||||||
\(201\) | 3.85736 | 0.272077 | ||||||||
\(202\) | −21.5498 | −1.51624 | ||||||||
\(203\) | 13.7269 | 0.963437 | ||||||||
\(204\) | 3.37492 | 0.236292 | ||||||||
\(205\) | −18.2069 | −1.27162 | ||||||||
\(206\) | −25.0963 | −1.74854 | ||||||||
\(207\) | 6.62087 | 0.460182 | ||||||||
\(208\) | −2.46100 | −0.170639 | ||||||||
\(209\) | −5.74568 | −0.397437 | ||||||||
\(210\) | −20.8224 | −1.43688 | ||||||||
\(211\) | −19.7117 | −1.35701 | −0.678504 | − | 0.734597i | \(-0.737371\pi\) | ||||
−0.678504 | + | 0.734597i | \(0.737371\pi\) | |||||||
\(212\) | 9.15958 | 0.629082 | ||||||||
\(213\) | 0.966193 | 0.0662025 | ||||||||
\(214\) | −16.2654 | −1.11188 | ||||||||
\(215\) | −1.60395 | −0.109388 | ||||||||
\(216\) | 5.97997 | 0.406885 | ||||||||
\(217\) | −28.1374 | −1.91009 | ||||||||
\(218\) | −2.63817 | −0.178679 | ||||||||
\(219\) | 12.3804 | 0.836593 | ||||||||
\(220\) | 4.00965 | 0.270330 | ||||||||
\(221\) | 0.894770 | 0.0601887 | ||||||||
\(222\) | −17.6839 | −1.18687 | ||||||||
\(223\) | 12.4905 | 0.836428 | 0.418214 | − | 0.908348i | \(-0.362656\pi\) | ||||
0.418214 | + | 0.908348i | \(0.362656\pi\) | |||||||
\(224\) | −36.0612 | −2.40944 | ||||||||
\(225\) | 2.85790 | 0.190527 | ||||||||
\(226\) | −8.09452 | −0.538440 | ||||||||
\(227\) | −11.3312 | −0.752081 | −0.376041 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376041 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(228\) | 19.3912 | 1.28421 | ||||||||
\(229\) | 0.800643 | 0.0529080 | 0.0264540 | − | 0.999650i | \(-0.491578\pi\) | ||||
0.0264540 | + | 0.999650i | \(0.491578\pi\) | |||||||
\(230\) | −19.1333 | −1.26161 | ||||||||
\(231\) | 6.11986 | 0.402657 | ||||||||
\(232\) | 3.21089 | 0.210805 | ||||||||
\(233\) | −0.607229 | −0.0397809 | −0.0198904 | − | 0.999802i | \(-0.506332\pi\) | ||||
−0.0198904 | + | 0.999802i | \(0.506332\pi\) | |||||||
\(234\) | 2.23474 | 0.146089 | ||||||||
\(235\) | −5.42741 | −0.354045 | ||||||||
\(236\) | −22.0992 | −1.43854 | ||||||||
\(237\) | −21.5403 | −1.39919 | ||||||||
\(238\) | 9.61596 | 0.623310 | ||||||||
\(239\) | −11.4642 | −0.741556 | −0.370778 | − | 0.928722i | \(-0.620909\pi\) | ||||
−0.370778 | + | 0.928722i | \(0.620909\pi\) | |||||||
\(240\) | 5.95578 | 0.384444 | ||||||||
\(241\) | −11.3964 | −0.734105 | −0.367053 | − | 0.930200i | \(-0.619633\pi\) | ||||
−0.367053 | + | 0.930200i | \(0.619633\pi\) | |||||||
\(242\) | −2.12129 | −0.136361 | ||||||||
\(243\) | 11.4085 | 0.731858 | ||||||||
\(244\) | −25.4888 | −1.63175 | ||||||||
\(245\) | −21.7316 | −1.38838 | ||||||||
\(246\) | −32.5082 | −2.07265 | ||||||||
\(247\) | 5.14106 | 0.327118 | ||||||||
\(248\) | −6.58170 | −0.417938 | ||||||||
\(249\) | −16.6369 | −1.05432 | ||||||||
\(250\) | −25.2711 | −1.59828 | ||||||||
\(251\) | −14.0964 | −0.889757 | −0.444879 | − | 0.895591i | \(-0.646753\pi\) | ||||
−0.444879 | + | 0.895591i | \(0.646753\pi\) | |||||||
\(252\) | 13.3421 | 0.840473 | ||||||||
\(253\) | 5.62341 | 0.353541 | ||||||||
\(254\) | 31.4715 | 1.97470 | ||||||||
\(255\) | −2.16540 | −0.135603 | ||||||||
\(256\) | 5.31617 | 0.332260 | ||||||||
\(257\) | −24.3319 | −1.51778 | −0.758890 | − | 0.651219i | \(-0.774258\pi\) | ||||
−0.758890 | + | 0.651219i | \(0.774258\pi\) | |||||||
\(258\) | −2.86383 | −0.178295 | ||||||||
\(259\) | −27.9913 | −1.73930 | ||||||||
\(260\) | −3.58771 | −0.222500 | ||||||||
\(261\) | 3.56528 | 0.220685 | ||||||||
\(262\) | −15.7871 | −0.975332 | ||||||||
\(263\) | 8.06694 | 0.497429 | 0.248714 | − | 0.968577i | \(-0.419992\pi\) | ||||
0.248714 | + | 0.968577i | \(0.419992\pi\) | |||||||
\(264\) | 1.43151 | 0.0881036 | ||||||||
\(265\) | −5.87693 | −0.361017 | ||||||||
\(266\) | 55.2502 | 3.38761 | ||||||||
\(267\) | 8.35455 | 0.511290 | ||||||||
\(268\) | 7.14261 | 0.436304 | ||||||||
\(269\) | −5.22515 | −0.318583 | −0.159292 | − | 0.987232i | \(-0.550921\pi\) | ||||
−0.159292 | + | 0.987232i | \(0.550921\pi\) | |||||||
\(270\) | −19.1885 | −1.16778 | ||||||||
\(271\) | −16.8716 | −1.02488 | −0.512438 | − | 0.858724i | \(-0.671258\pi\) | ||||
−0.512438 | + | 0.858724i | \(0.671258\pi\) | |||||||
\(272\) | −2.75042 | −0.166769 | ||||||||
\(273\) | −5.47587 | −0.331414 | ||||||||
\(274\) | 46.5134 | 2.80998 | ||||||||
\(275\) | 2.42735 | 0.146375 | ||||||||
\(276\) | −18.9786 | −1.14238 | ||||||||
\(277\) | 21.8995 | 1.31581 | 0.657905 | − | 0.753101i | \(-0.271443\pi\) | ||||
0.657905 | + | 0.753101i | \(0.271443\pi\) | |||||||
\(278\) | −15.1933 | −0.911235 | ||||||||
\(279\) | −7.30813 | −0.437526 | ||||||||
\(280\) | −7.70958 | −0.460735 | ||||||||
\(281\) | 9.16234 | 0.546579 | 0.273290 | − | 0.961932i | \(-0.411888\pi\) | ||||
0.273290 | + | 0.961932i | \(0.411888\pi\) | |||||||
\(282\) | −9.69059 | −0.577066 | ||||||||
\(283\) | −2.28900 | −0.136067 | −0.0680336 | − | 0.997683i | \(-0.521673\pi\) | ||||
−0.0680336 | + | 0.997683i | \(0.521673\pi\) | |||||||
\(284\) | 1.78909 | 0.106163 | ||||||||
\(285\) | −12.4417 | −0.736983 | ||||||||
\(286\) | 1.89806 | 0.112235 | ||||||||
\(287\) | −51.4563 | −3.03737 | ||||||||
\(288\) | −9.36618 | −0.551908 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −10.3031 | −0.605019 | ||||||||
\(291\) | 24.3089 | 1.42501 | ||||||||
\(292\) | 22.9247 | 1.34157 | ||||||||
\(293\) | −21.8462 | −1.27627 | −0.638134 | − | 0.769925i | \(-0.720293\pi\) | ||||
−0.638134 | + | 0.769925i | \(0.720293\pi\) | |||||||
\(294\) | −38.8015 | −2.26295 | ||||||||
\(295\) | 14.1792 | 0.825546 | ||||||||
\(296\) | −6.54753 | −0.380568 | ||||||||
\(297\) | 5.63965 | 0.327246 | ||||||||
\(298\) | −17.3706 | −1.00625 | ||||||||
\(299\) | −5.03165 | −0.290988 | ||||||||
\(300\) | −8.19212 | −0.472972 | ||||||||
\(301\) | −4.53308 | −0.261282 | ||||||||
\(302\) | 38.4008 | 2.20972 | ||||||||
\(303\) | 13.7149 | 0.787900 | ||||||||
\(304\) | −15.8030 | −0.906367 | ||||||||
\(305\) | 16.3540 | 0.936429 | ||||||||
\(306\) | 2.49755 | 0.142776 | ||||||||
\(307\) | −27.0810 | −1.54559 | −0.772797 | − | 0.634653i | \(-0.781143\pi\) | ||||
−0.772797 | + | 0.634653i | \(0.781143\pi\) | |||||||
\(308\) | 11.3321 | 0.645704 | ||||||||
\(309\) | 15.9720 | 0.908614 | ||||||||
\(310\) | 21.1194 | 1.19950 | ||||||||
\(311\) | −1.20649 | −0.0684139 | −0.0342069 | − | 0.999415i | \(-0.510891\pi\) | ||||
−0.0342069 | + | 0.999415i | \(0.510891\pi\) | |||||||
\(312\) | −1.28087 | −0.0725153 | ||||||||
\(313\) | 9.18903 | 0.519395 | 0.259697 | − | 0.965690i | \(-0.416377\pi\) | ||||
0.259697 | + | 0.965690i | \(0.416377\pi\) | |||||||
\(314\) | −36.3846 | −2.05330 | ||||||||
\(315\) | −8.56050 | −0.482329 | ||||||||
\(316\) | −39.8858 | −2.24375 | ||||||||
\(317\) | 4.75104 | 0.266845 | 0.133422 | − | 0.991059i | \(-0.457403\pi\) | ||||
0.133422 | + | 0.991059i | \(0.457403\pi\) | |||||||
\(318\) | −10.4932 | −0.588429 | ||||||||
\(319\) | 3.02816 | 0.169544 | ||||||||
\(320\) | 18.2437 | 1.01986 | ||||||||
\(321\) | 10.3518 | 0.577780 | ||||||||
\(322\) | −54.0744 | −3.01345 | ||||||||
\(323\) | 5.74568 | 0.319698 | ||||||||
\(324\) | −10.2036 | −0.566864 | ||||||||
\(325\) | −2.17192 | −0.120476 | ||||||||
\(326\) | −1.56488 | −0.0866706 | ||||||||
\(327\) | 1.67900 | 0.0928491 | ||||||||
\(328\) | −12.0363 | −0.664592 | ||||||||
\(329\) | −15.3389 | −0.845663 | ||||||||
\(330\) | −4.59344 | −0.252861 | ||||||||
\(331\) | 27.1099 | 1.49009 | 0.745047 | − | 0.667012i | \(-0.232427\pi\) | ||||
0.745047 | + | 0.667012i | \(0.232427\pi\) | |||||||
\(332\) | −30.8063 | −1.69072 | ||||||||
\(333\) | −7.27020 | −0.398404 | ||||||||
\(334\) | −9.97295 | −0.545696 | ||||||||
\(335\) | −4.58281 | −0.250386 | ||||||||
\(336\) | 16.8322 | 0.918272 | ||||||||
\(337\) | −11.5539 | −0.629380 | −0.314690 | − | 0.949195i | \(-0.601901\pi\) | ||||
−0.314690 | + | 0.949195i | \(0.601901\pi\) | |||||||
\(338\) | 25.8784 | 1.40760 | ||||||||
\(339\) | 5.15158 | 0.279795 | ||||||||
\(340\) | −4.00965 | −0.217454 | ||||||||
\(341\) | −6.20713 | −0.336135 | ||||||||
\(342\) | 14.3501 | 0.775967 | ||||||||
\(343\) | −29.6862 | −1.60290 | ||||||||
\(344\) | −1.06034 | −0.0571699 | ||||||||
\(345\) | 12.1769 | 0.655585 | ||||||||
\(346\) | 37.6559 | 2.02439 | ||||||||
\(347\) | 22.9132 | 1.23004 | 0.615022 | − | 0.788510i | \(-0.289147\pi\) | ||||
0.615022 | + | 0.788510i | \(0.289147\pi\) | |||||||
\(348\) | −10.2198 | −0.547838 | ||||||||
\(349\) | −26.0383 | −1.39380 | −0.696898 | − | 0.717170i | \(-0.745437\pi\) | ||||
−0.696898 | + | 0.717170i | \(0.745437\pi\) | |||||||
\(350\) | −23.3413 | −1.24764 | ||||||||
\(351\) | −5.04619 | −0.269346 | ||||||||
\(352\) | −7.95513 | −0.424010 | ||||||||
\(353\) | −0.901560 | −0.0479852 | −0.0239926 | − | 0.999712i | \(-0.507638\pi\) | ||||
−0.0239926 | + | 0.999712i | \(0.507638\pi\) | |||||||
\(354\) | 25.3168 | 1.34558 | ||||||||
\(355\) | −1.14790 | −0.0609245 | ||||||||
\(356\) | 15.4700 | 0.819908 | ||||||||
\(357\) | −6.11986 | −0.323897 | ||||||||
\(358\) | −8.82619 | −0.466479 | ||||||||
\(359\) | −17.8974 | −0.944588 | −0.472294 | − | 0.881441i | \(-0.656574\pi\) | ||||
−0.472294 | + | 0.881441i | \(0.656574\pi\) | |||||||
\(360\) | −2.00241 | −0.105536 | ||||||||
\(361\) | 14.0128 | 0.737516 | ||||||||
\(362\) | −36.1531 | −1.90017 | ||||||||
\(363\) | 1.35005 | 0.0708590 | ||||||||
\(364\) | −10.1396 | −0.531458 | ||||||||
\(365\) | −14.7088 | −0.769896 | ||||||||
\(366\) | 29.2000 | 1.52631 | ||||||||
\(367\) | 35.5802 | 1.85727 | 0.928635 | − | 0.370995i | \(-0.120983\pi\) | ||||
0.928635 | + | 0.370995i | \(0.120983\pi\) | |||||||
\(368\) | 15.4667 | 0.806260 | ||||||||
\(369\) | −13.3647 | −0.695741 | ||||||||
\(370\) | 21.0097 | 1.09224 | ||||||||
\(371\) | −16.6094 | −0.862315 | ||||||||
\(372\) | 20.9486 | 1.08613 | ||||||||
\(373\) | 35.2062 | 1.82291 | 0.911455 | − | 0.411401i | \(-0.134960\pi\) | ||||
0.911455 | + | 0.411401i | \(0.134960\pi\) | |||||||
\(374\) | 2.12129 | 0.109689 | ||||||||
\(375\) | 16.0832 | 0.830533 | ||||||||
\(376\) | −3.58797 | −0.185036 | ||||||||
\(377\) | −2.70950 | −0.139546 | ||||||||
\(378\) | −54.2306 | −2.78932 | ||||||||
\(379\) | 18.9428 | 0.973026 | 0.486513 | − | 0.873673i | \(-0.338269\pi\) | ||||
0.486513 | + | 0.873673i | \(0.338269\pi\) | |||||||
\(380\) | −23.0381 | −1.18183 | ||||||||
\(381\) | −20.0293 | −1.02613 | ||||||||
\(382\) | −20.5470 | −1.05128 | ||||||||
\(383\) | −4.24810 | −0.217068 | −0.108534 | − | 0.994093i | \(-0.534616\pi\) | ||||
−0.108534 | + | 0.994093i | \(0.534616\pi\) | |||||||
\(384\) | 11.0944 | 0.566160 | ||||||||
\(385\) | −7.27082 | −0.370555 | ||||||||
\(386\) | −14.3104 | −0.728382 | ||||||||
\(387\) | −1.17738 | −0.0598494 | ||||||||
\(388\) | 45.0124 | 2.28516 | ||||||||
\(389\) | −28.5944 | −1.44979 | −0.724897 | − | 0.688857i | \(-0.758113\pi\) | ||||
−0.724897 | + | 0.688857i | \(0.758113\pi\) | |||||||
\(390\) | 4.11007 | 0.208122 | ||||||||
\(391\) | −5.62341 | −0.284388 | ||||||||
\(392\) | −14.3664 | −0.725612 | ||||||||
\(393\) | 10.0474 | 0.506822 | ||||||||
\(394\) | 15.8958 | 0.800819 | ||||||||
\(395\) | 25.5913 | 1.28764 | ||||||||
\(396\) | 2.94328 | 0.147905 | ||||||||
\(397\) | −21.7445 | −1.09133 | −0.545664 | − | 0.838004i | \(-0.683722\pi\) | ||||
−0.545664 | + | 0.838004i | \(0.683722\pi\) | |||||||
\(398\) | 34.1961 | 1.71410 | ||||||||
\(399\) | −35.1627 | −1.76034 | ||||||||
\(400\) | 6.67624 | 0.333812 | ||||||||
\(401\) | −20.6726 | −1.03234 | −0.516169 | − | 0.856487i | \(-0.672643\pi\) | ||||
−0.516169 | + | 0.856487i | \(0.672643\pi\) | |||||||
\(402\) | −8.18256 | −0.408109 | ||||||||
\(403\) | 5.55395 | 0.276662 | ||||||||
\(404\) | 25.3957 | 1.26348 | ||||||||
\(405\) | 6.54676 | 0.325311 | ||||||||
\(406\) | −29.1186 | −1.44513 | ||||||||
\(407\) | −6.17491 | −0.306079 | ||||||||
\(408\) | −1.43151 | −0.0708705 | ||||||||
\(409\) | −14.9278 | −0.738131 | −0.369066 | − | 0.929403i | \(-0.620322\pi\) | ||||
−0.369066 | + | 0.929403i | \(0.620322\pi\) | |||||||
\(410\) | 38.6220 | 1.90741 | ||||||||
\(411\) | −29.6024 | −1.46018 | ||||||||
\(412\) | 29.5751 | 1.45706 | ||||||||
\(413\) | 40.0733 | 1.97188 | ||||||||
\(414\) | −14.0448 | −0.690262 | ||||||||
\(415\) | 19.7658 | 0.970267 | ||||||||
\(416\) | 7.11801 | 0.348989 | ||||||||
\(417\) | 9.66945 | 0.473515 | ||||||||
\(418\) | 12.1882 | 0.596146 | ||||||||
\(419\) | −20.0504 | −0.979528 | −0.489764 | − | 0.871855i | \(-0.662917\pi\) | ||||
−0.489764 | + | 0.871855i | \(0.662917\pi\) | |||||||
\(420\) | 24.5385 | 1.19735 | ||||||||
\(421\) | −26.6335 | −1.29804 | −0.649018 | − | 0.760773i | \(-0.724820\pi\) | ||||
−0.649018 | + | 0.760773i | \(0.724820\pi\) | |||||||
\(422\) | 41.8141 | 2.03548 | ||||||||
\(423\) | −3.98399 | −0.193708 | ||||||||
\(424\) | −3.88514 | −0.188679 | ||||||||
\(425\) | −2.42735 | −0.117744 | ||||||||
\(426\) | −2.04957 | −0.0993021 | ||||||||
\(427\) | 46.2197 | 2.23673 | ||||||||
\(428\) | 19.1682 | 0.926531 | ||||||||
\(429\) | −1.20798 | −0.0583218 | ||||||||
\(430\) | 3.40244 | 0.164080 | ||||||||
\(431\) | −38.6023 | −1.85941 | −0.929704 | − | 0.368307i | \(-0.879937\pi\) | ||||
−0.929704 | + | 0.368307i | \(0.879937\pi\) | |||||||
\(432\) | 15.5114 | 0.746294 | ||||||||
\(433\) | 15.3579 | 0.738056 | 0.369028 | − | 0.929418i | \(-0.379691\pi\) | ||||
0.369028 | + | 0.929418i | \(0.379691\pi\) | |||||||
\(434\) | 59.6875 | 2.86509 | ||||||||
\(435\) | 6.55718 | 0.314393 | ||||||||
\(436\) | 3.10898 | 0.148893 | ||||||||
\(437\) | −32.3103 | −1.54561 | ||||||||
\(438\) | −26.2625 | −1.25487 | ||||||||
\(439\) | 17.0823 | 0.815292 | 0.407646 | − | 0.913140i | \(-0.366350\pi\) | ||||
0.407646 | + | 0.913140i | \(0.366350\pi\) | |||||||
\(440\) | −1.70074 | −0.0810795 | ||||||||
\(441\) | −15.9520 | −0.759620 | ||||||||
\(442\) | −1.89806 | −0.0902817 | ||||||||
\(443\) | 0.699711 | 0.0332443 | 0.0166221 | − | 0.999862i | \(-0.494709\pi\) | ||||
0.0166221 | + | 0.999862i | \(0.494709\pi\) | |||||||
\(444\) | 20.8399 | 0.989016 | ||||||||
\(445\) | −9.92578 | −0.470527 | ||||||||
\(446\) | −26.4960 | −1.25462 | ||||||||
\(447\) | 11.0552 | 0.522891 | ||||||||
\(448\) | 51.5604 | 2.43600 | ||||||||
\(449\) | 20.5926 | 0.971827 | 0.485913 | − | 0.874007i | \(-0.338487\pi\) | ||||
0.485913 | + | 0.874007i | \(0.338487\pi\) | |||||||
\(450\) | −6.06244 | −0.285786 | ||||||||
\(451\) | −11.3513 | −0.534511 | ||||||||
\(452\) | 9.53910 | 0.448681 | ||||||||
\(453\) | −24.4393 | −1.14826 | ||||||||
\(454\) | 24.0368 | 1.12810 | ||||||||
\(455\) | 6.50571 | 0.304992 | ||||||||
\(456\) | −8.22501 | −0.385172 | ||||||||
\(457\) | 7.34008 | 0.343354 | 0.171677 | − | 0.985153i | \(-0.445081\pi\) | ||||
0.171677 | + | 0.985153i | \(0.445081\pi\) | |||||||
\(458\) | −1.69839 | −0.0793608 | ||||||||
\(459\) | −5.63965 | −0.263236 | ||||||||
\(460\) | 22.5479 | 1.05130 | ||||||||
\(461\) | −22.4511 | −1.04565 | −0.522827 | − | 0.852439i | \(-0.675122\pi\) | ||||
−0.522827 | + | 0.852439i | \(0.675122\pi\) | |||||||
\(462\) | −12.9820 | −0.603976 | ||||||||
\(463\) | −32.2725 | −1.49983 | −0.749915 | − | 0.661534i | \(-0.769906\pi\) | ||||
−0.749915 | + | 0.661534i | \(0.769906\pi\) | |||||||
\(464\) | 8.32871 | 0.386651 | ||||||||
\(465\) | −13.4409 | −0.623309 | ||||||||
\(466\) | 1.28811 | 0.0596704 | ||||||||
\(467\) | 1.93299 | 0.0894482 | 0.0447241 | − | 0.998999i | \(-0.485759\pi\) | ||||
0.0447241 | + | 0.998999i | \(0.485759\pi\) | |||||||
\(468\) | −2.63355 | −0.121736 | ||||||||
\(469\) | −12.9519 | −0.598065 | ||||||||
\(470\) | 11.5131 | 0.531060 | ||||||||
\(471\) | 23.1561 | 1.06698 | ||||||||
\(472\) | 9.37365 | 0.431457 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 45.6931 | 2.09875 | ||||||||
\(475\) | −13.9468 | −0.639921 | ||||||||
\(476\) | −11.3321 | −0.519404 | ||||||||
\(477\) | −4.31395 | −0.197522 | ||||||||
\(478\) | 24.3188 | 1.11232 | ||||||||
\(479\) | −30.1508 | −1.37763 | −0.688813 | − | 0.724939i | \(-0.741868\pi\) | ||||
−0.688813 | + | 0.724939i | \(0.741868\pi\) | |||||||
\(480\) | −17.2261 | −0.786258 | ||||||||
\(481\) | 5.52512 | 0.251924 | ||||||||
\(482\) | 24.1750 | 1.10114 | ||||||||
\(483\) | 34.4145 | 1.56591 | ||||||||
\(484\) | 2.49986 | 0.113630 | ||||||||
\(485\) | −28.8806 | −1.31140 | ||||||||
\(486\) | −24.2008 | −1.09777 | ||||||||
\(487\) | 21.3503 | 0.967473 | 0.483736 | − | 0.875214i | \(-0.339279\pi\) | ||||
0.483736 | + | 0.875214i | \(0.339279\pi\) | |||||||
\(488\) | 10.8114 | 0.489408 | ||||||||
\(489\) | 0.995932 | 0.0450376 | ||||||||
\(490\) | 46.0989 | 2.08253 | ||||||||
\(491\) | 4.90253 | 0.221248 | 0.110624 | − | 0.993862i | \(-0.464715\pi\) | ||||
0.110624 | + | 0.993862i | \(0.464715\pi\) | |||||||
\(492\) | 38.3097 | 1.72714 | ||||||||
\(493\) | −3.02816 | −0.136381 | ||||||||
\(494\) | −10.9057 | −0.490669 | ||||||||
\(495\) | −1.88845 | −0.0848796 | ||||||||
\(496\) | −17.0722 | −0.766566 | ||||||||
\(497\) | −3.24421 | −0.145523 | ||||||||
\(498\) | 35.2917 | 1.58146 | ||||||||
\(499\) | 25.7276 | 1.15172 | 0.575862 | − | 0.817547i | \(-0.304666\pi\) | ||||
0.575862 | + | 0.817547i | \(0.304666\pi\) | |||||||
\(500\) | 29.7810 | 1.33185 | ||||||||
\(501\) | 6.34706 | 0.283566 | ||||||||
\(502\) | 29.9025 | 1.33462 | ||||||||
\(503\) | 2.70094 | 0.120429 | 0.0602144 | − | 0.998185i | \(-0.480822\pi\) | ||||
0.0602144 | + | 0.998185i | \(0.480822\pi\) | |||||||
\(504\) | −5.65921 | −0.252081 | ||||||||
\(505\) | −16.2943 | −0.725085 | ||||||||
\(506\) | −11.9289 | −0.530302 | ||||||||
\(507\) | −16.4697 | −0.731446 | ||||||||
\(508\) | −37.0880 | −1.64552 | ||||||||
\(509\) | −40.2878 | −1.78572 | −0.892862 | − | 0.450331i | \(-0.851306\pi\) | ||||
−0.892862 | + | 0.450331i | \(0.851306\pi\) | |||||||
\(510\) | 4.59344 | 0.203401 | ||||||||
\(511\) | −41.5701 | −1.83895 | ||||||||
\(512\) | −27.7128 | −1.22474 | ||||||||
\(513\) | −32.4036 | −1.43065 | ||||||||
\(514\) | 51.6149 | 2.27663 | ||||||||
\(515\) | −18.9758 | −0.836175 | ||||||||
\(516\) | 3.37492 | 0.148573 | ||||||||
\(517\) | −3.38378 | −0.148819 | ||||||||
\(518\) | 59.3777 | 2.60891 | ||||||||
\(519\) | −23.9653 | −1.05196 | ||||||||
\(520\) | 1.52177 | 0.0667340 | ||||||||
\(521\) | −37.5481 | −1.64501 | −0.822506 | − | 0.568756i | \(-0.807425\pi\) | ||||
−0.822506 | + | 0.568756i | \(0.807425\pi\) | |||||||
\(522\) | −7.56298 | −0.331023 | ||||||||
\(523\) | 10.6478 | 0.465597 | 0.232799 | − | 0.972525i | \(-0.425212\pi\) | ||||
0.232799 | + | 0.972525i | \(0.425212\pi\) | |||||||
\(524\) | 18.6045 | 0.812743 | ||||||||
\(525\) | 14.8550 | 0.648327 | ||||||||
\(526\) | −17.1123 | −0.746131 | ||||||||
\(527\) | 6.20713 | 0.270387 | ||||||||
\(528\) | 3.71320 | 0.161596 | ||||||||
\(529\) | 8.62269 | 0.374900 | ||||||||
\(530\) | 12.4667 | 0.541517 | ||||||||
\(531\) | 10.4082 | 0.451679 | ||||||||
\(532\) | −65.1103 | −2.82289 | ||||||||
\(533\) | 10.1568 | 0.439939 | ||||||||
\(534\) | −17.7224 | −0.766923 | ||||||||
\(535\) | −12.2986 | −0.531716 | ||||||||
\(536\) | −3.02962 | −0.130860 | ||||||||
\(537\) | 5.61723 | 0.242401 | ||||||||
\(538\) | 11.0840 | 0.477867 | ||||||||
\(539\) | −13.5488 | −0.583588 | ||||||||
\(540\) | 22.6130 | 0.973108 | ||||||||
\(541\) | 9.70174 | 0.417110 | 0.208555 | − | 0.978011i | \(-0.433124\pi\) | ||||
0.208555 | + | 0.978011i | \(0.433124\pi\) | |||||||
\(542\) | 35.7895 | 1.53729 | ||||||||
\(543\) | 23.0089 | 0.987404 | ||||||||
\(544\) | 7.95513 | 0.341073 | ||||||||
\(545\) | −1.99477 | −0.0854467 | ||||||||
\(546\) | 11.6159 | 0.497114 | ||||||||
\(547\) | −14.2489 | −0.609241 | −0.304620 | − | 0.952474i | \(-0.598530\pi\) | ||||
−0.304620 | + | 0.952474i | \(0.598530\pi\) | |||||||
\(548\) | −54.8144 | −2.34155 | ||||||||
\(549\) | 12.0047 | 0.512346 | ||||||||
\(550\) | −5.14910 | −0.219559 | ||||||||
\(551\) | −17.3988 | −0.741214 | ||||||||
\(552\) | 8.04998 | 0.342630 | ||||||||
\(553\) | 72.3262 | 3.07562 | ||||||||
\(554\) | −46.4550 | −1.97368 | ||||||||
\(555\) | −13.3712 | −0.567575 | ||||||||
\(556\) | 17.9048 | 0.759331 | ||||||||
\(557\) | −4.01900 | −0.170291 | −0.0851453 | − | 0.996369i | \(-0.527135\pi\) | ||||
−0.0851453 | + | 0.996369i | \(0.527135\pi\) | |||||||
\(558\) | 15.5026 | 0.656279 | ||||||||
\(559\) | 0.894770 | 0.0378447 | ||||||||
\(560\) | −19.9978 | −0.845063 | ||||||||
\(561\) | −1.35005 | −0.0569990 | ||||||||
\(562\) | −19.4360 | −0.819856 | ||||||||
\(563\) | 24.5602 | 1.03509 | 0.517544 | − | 0.855657i | \(-0.326846\pi\) | ||||
0.517544 | + | 0.855657i | \(0.326846\pi\) | |||||||
\(564\) | 11.4200 | 0.480869 | ||||||||
\(565\) | −6.12044 | −0.257489 | ||||||||
\(566\) | 4.85564 | 0.204098 | ||||||||
\(567\) | 18.5024 | 0.777030 | ||||||||
\(568\) | −0.758861 | −0.0318411 | ||||||||
\(569\) | −8.81938 | −0.369728 | −0.184864 | − | 0.982764i | \(-0.559184\pi\) | ||||
−0.184864 | + | 0.982764i | \(0.559184\pi\) | |||||||
\(570\) | 26.3924 | 1.10546 | ||||||||
\(571\) | −36.1769 | −1.51396 | −0.756978 | − | 0.653440i | \(-0.773325\pi\) | ||||
−0.756978 | + | 0.653440i | \(0.773325\pi\) | |||||||
\(572\) | −2.23680 | −0.0935252 | ||||||||
\(573\) | 13.0767 | 0.546286 | ||||||||
\(574\) | 109.153 | 4.55598 | ||||||||
\(575\) | 13.6500 | 0.569243 | ||||||||
\(576\) | 13.3918 | 0.557991 | ||||||||
\(577\) | −4.71121 | −0.196130 | −0.0980652 | − | 0.995180i | \(-0.531265\pi\) | ||||
−0.0980652 | + | 0.995180i | \(0.531265\pi\) | |||||||
\(578\) | −2.12129 | −0.0882339 | ||||||||
\(579\) | 9.10756 | 0.378497 | ||||||||
\(580\) | 12.1418 | 0.504162 | ||||||||
\(581\) | 55.8622 | 2.31755 | ||||||||
\(582\) | −51.5661 | −2.13748 | ||||||||
\(583\) | −3.66404 | −0.151749 | ||||||||
\(584\) | −9.72377 | −0.402373 | ||||||||
\(585\) | 1.68973 | 0.0698617 | ||||||||
\(586\) | 46.3420 | 1.91437 | ||||||||
\(587\) | 23.8581 | 0.984729 | 0.492364 | − | 0.870389i | \(-0.336133\pi\) | ||||
0.492364 | + | 0.870389i | \(0.336133\pi\) | |||||||
\(588\) | 45.7261 | 1.88571 | ||||||||
\(589\) | 35.6642 | 1.46952 | ||||||||
\(590\) | −30.0782 | −1.23830 | ||||||||
\(591\) | −10.1165 | −0.416138 | ||||||||
\(592\) | −16.9836 | −0.698022 | ||||||||
\(593\) | 36.8701 | 1.51408 | 0.757038 | − | 0.653371i | \(-0.226646\pi\) | ||||
0.757038 | + | 0.653371i | \(0.226646\pi\) | |||||||
\(594\) | −11.9633 | −0.490861 | ||||||||
\(595\) | 7.27082 | 0.298075 | ||||||||
\(596\) | 20.4707 | 0.838511 | ||||||||
\(597\) | −21.7634 | −0.890715 | ||||||||
\(598\) | 10.6736 | 0.436475 | ||||||||
\(599\) | −3.24023 | −0.132392 | −0.0661962 | − | 0.997807i | \(-0.521086\pi\) | ||||
−0.0661962 | + | 0.997807i | \(0.521086\pi\) | |||||||
\(600\) | 3.47478 | 0.141857 | ||||||||
\(601\) | 19.1314 | 0.780386 | 0.390193 | − | 0.920733i | \(-0.372408\pi\) | ||||
0.390193 | + | 0.920733i | \(0.372408\pi\) | |||||||
\(602\) | 9.61596 | 0.391917 | ||||||||
\(603\) | −3.36401 | −0.136993 | ||||||||
\(604\) | −45.2539 | −1.84135 | ||||||||
\(605\) | −1.60395 | −0.0652098 | ||||||||
\(606\) | −29.0932 | −1.18183 | ||||||||
\(607\) | −20.9200 | −0.849117 | −0.424558 | − | 0.905401i | \(-0.639571\pi\) | ||||
−0.424558 | + | 0.905401i | \(0.639571\pi\) | |||||||
\(608\) | 45.7076 | 1.85369 | ||||||||
\(609\) | 18.5319 | 0.750950 | ||||||||
\(610\) | −34.6916 | −1.40462 | ||||||||
\(611\) | 3.02771 | 0.122488 | ||||||||
\(612\) | −2.94328 | −0.118975 | ||||||||
\(613\) | −34.5619 | −1.39594 | −0.697971 | − | 0.716126i | \(-0.745913\pi\) | ||||
−0.697971 | + | 0.716126i | \(0.745913\pi\) | |||||||
\(614\) | 57.4466 | 2.31835 | ||||||||
\(615\) | −24.5801 | −0.991166 | ||||||||
\(616\) | −4.80662 | −0.193664 | ||||||||
\(617\) | −19.9308 | −0.802384 | −0.401192 | − | 0.915994i | \(-0.631404\pi\) | ||||
−0.401192 | + | 0.915994i | \(0.631404\pi\) | |||||||
\(618\) | −33.8812 | −1.36290 | ||||||||
\(619\) | 30.8898 | 1.24157 | 0.620784 | − | 0.783982i | \(-0.286815\pi\) | ||||
0.620784 | + | 0.783982i | \(0.286815\pi\) | |||||||
\(620\) | −24.8884 | −0.999542 | ||||||||
\(621\) | 31.7140 | 1.27264 | ||||||||
\(622\) | 2.55931 | 0.102619 | ||||||||
\(623\) | −28.0522 | −1.12389 | ||||||||
\(624\) | −3.32246 | −0.133005 | ||||||||
\(625\) | −6.97123 | −0.278849 | ||||||||
\(626\) | −19.4926 | −0.779080 | ||||||||
\(627\) | −7.75693 | −0.309782 | ||||||||
\(628\) | 42.8779 | 1.71101 | ||||||||
\(629\) | 6.17491 | 0.246210 | ||||||||
\(630\) | 18.1593 | 0.723483 | ||||||||
\(631\) | 8.18195 | 0.325718 | 0.162859 | − | 0.986649i | \(-0.447928\pi\) | ||||
0.162859 | + | 0.986649i | \(0.447928\pi\) | |||||||
\(632\) | 16.9180 | 0.672962 | ||||||||
\(633\) | −26.6117 | −1.05772 | ||||||||
\(634\) | −10.0783 | −0.400261 | ||||||||
\(635\) | 23.7963 | 0.944326 | ||||||||
\(636\) | 12.3658 | 0.490338 | ||||||||
\(637\) | 12.1230 | 0.480332 | ||||||||
\(638\) | −6.42359 | −0.254312 | ||||||||
\(639\) | −0.842619 | −0.0333335 | ||||||||
\(640\) | −13.1810 | −0.521023 | ||||||||
\(641\) | 45.0270 | 1.77846 | 0.889229 | − | 0.457462i | \(-0.151241\pi\) | ||||
0.889229 | + | 0.457462i | \(0.151241\pi\) | |||||||
\(642\) | −21.9591 | −0.866656 | ||||||||
\(643\) | 3.21875 | 0.126935 | 0.0634675 | − | 0.997984i | \(-0.479784\pi\) | ||||
0.0634675 | + | 0.997984i | \(0.479784\pi\) | |||||||
\(644\) | 63.7247 | 2.51111 | ||||||||
\(645\) | −2.16540 | −0.0852627 | ||||||||
\(646\) | −12.1882 | −0.479539 | ||||||||
\(647\) | −29.7823 | −1.17086 | −0.585432 | − | 0.810721i | \(-0.699075\pi\) | ||||
−0.585432 | + | 0.810721i | \(0.699075\pi\) | |||||||
\(648\) | 4.32796 | 0.170018 | ||||||||
\(649\) | 8.84019 | 0.347008 | ||||||||
\(650\) | 4.60726 | 0.180712 | ||||||||
\(651\) | −37.9868 | −1.48882 | ||||||||
\(652\) | 1.84415 | 0.0722226 | ||||||||
\(653\) | 16.2837 | 0.637232 | 0.318616 | − | 0.947884i | \(-0.396782\pi\) | ||||
0.318616 | + | 0.947884i | \(0.396782\pi\) | |||||||
\(654\) | −3.56165 | −0.139271 | ||||||||
\(655\) | −11.9370 | −0.466416 | ||||||||
\(656\) | −31.2208 | −1.21897 | ||||||||
\(657\) | −10.7970 | −0.421231 | ||||||||
\(658\) | 32.5383 | 1.26848 | ||||||||
\(659\) | −1.47647 | −0.0575149 | −0.0287575 | − | 0.999586i | \(-0.509155\pi\) | ||||
−0.0287575 | + | 0.999586i | \(0.509155\pi\) | |||||||
\(660\) | 5.41320 | 0.210709 | ||||||||
\(661\) | 29.7457 | 1.15697 | 0.578487 | − | 0.815692i | \(-0.303643\pi\) | ||||
0.578487 | + | 0.815692i | \(0.303643\pi\) | |||||||
\(662\) | −57.5078 | −2.23511 | ||||||||
\(663\) | 1.20798 | 0.0469141 | ||||||||
\(664\) | 13.0669 | 0.507093 | ||||||||
\(665\) | 41.7758 | 1.62000 | ||||||||
\(666\) | 15.4222 | 0.597597 | ||||||||
\(667\) | 17.0285 | 0.659348 | ||||||||
\(668\) | 11.7528 | 0.454728 | ||||||||
\(669\) | 16.8628 | 0.651953 | ||||||||
\(670\) | 9.72146 | 0.375573 | ||||||||
\(671\) | 10.1961 | 0.393616 | ||||||||
\(672\) | −48.6843 | −1.87804 | ||||||||
\(673\) | 6.11258 | 0.235623 | 0.117811 | − | 0.993036i | \(-0.462412\pi\) | ||||
0.117811 | + | 0.993036i | \(0.462412\pi\) | |||||||
\(674\) | 24.5091 | 0.944055 | ||||||||
\(675\) | 13.6894 | 0.526905 | ||||||||
\(676\) | −30.4967 | −1.17295 | ||||||||
\(677\) | −40.0929 | −1.54090 | −0.770448 | − | 0.637503i | \(-0.779968\pi\) | ||||
−0.770448 | + | 0.637503i | \(0.779968\pi\) | |||||||
\(678\) | −10.9280 | −0.419686 | ||||||||
\(679\) | −81.6224 | −3.13238 | ||||||||
\(680\) | 1.70074 | 0.0652203 | ||||||||
\(681\) | −15.2977 | −0.586209 | ||||||||
\(682\) | 13.1671 | 0.504195 | ||||||||
\(683\) | 24.9039 | 0.952921 | 0.476461 | − | 0.879196i | \(-0.341919\pi\) | ||||
0.476461 | + | 0.879196i | \(0.341919\pi\) | |||||||
\(684\) | −16.9111 | −0.646613 | ||||||||
\(685\) | 35.1698 | 1.34377 | ||||||||
\(686\) | 62.9729 | 2.40431 | ||||||||
\(687\) | 1.08091 | 0.0412391 | ||||||||
\(688\) | −2.75042 | −0.104859 | ||||||||
\(689\) | 3.27847 | 0.124900 | ||||||||
\(690\) | −25.8308 | −0.983362 | ||||||||
\(691\) | 16.5740 | 0.630504 | 0.315252 | − | 0.949008i | \(-0.397911\pi\) | ||||
0.315252 | + | 0.949008i | \(0.397911\pi\) | |||||||
\(692\) | −44.3761 | −1.68693 | ||||||||
\(693\) | −5.33714 | −0.202741 | ||||||||
\(694\) | −48.6054 | −1.84504 | ||||||||
\(695\) | −11.4880 | −0.435764 | ||||||||
\(696\) | 4.33484 | 0.164312 | ||||||||
\(697\) | 11.3513 | 0.429961 | ||||||||
\(698\) | 55.2346 | 2.09066 | ||||||||
\(699\) | −0.819787 | −0.0310072 | ||||||||
\(700\) | 27.5068 | 1.03966 | ||||||||
\(701\) | −11.7750 | −0.444737 | −0.222369 | − | 0.974963i | \(-0.571379\pi\) | ||||
−0.222369 | + | 0.974963i | \(0.571379\pi\) | |||||||
\(702\) | 10.7044 | 0.404012 | ||||||||
\(703\) | 35.4790 | 1.33812 | ||||||||
\(704\) | 11.3743 | 0.428684 | ||||||||
\(705\) | −7.32725 | −0.275960 | ||||||||
\(706\) | 1.91247 | 0.0719766 | ||||||||
\(707\) | −46.0508 | −1.73192 | ||||||||
\(708\) | −29.8350 | −1.12127 | ||||||||
\(709\) | 30.7825 | 1.15606 | 0.578031 | − | 0.816015i | \(-0.303821\pi\) | ||||
0.578031 | + | 0.816015i | \(0.303821\pi\) | |||||||
\(710\) | 2.43504 | 0.0913853 | ||||||||
\(711\) | 18.7853 | 0.704503 | ||||||||
\(712\) | −6.56177 | −0.245913 | ||||||||
\(713\) | −34.9052 | −1.30721 | ||||||||
\(714\) | 12.9820 | 0.485838 | ||||||||
\(715\) | 1.43516 | 0.0536721 | ||||||||
\(716\) | 10.4013 | 0.388716 | ||||||||
\(717\) | −15.4772 | −0.578005 | ||||||||
\(718\) | 37.9655 | 1.41686 | ||||||||
\(719\) | 6.01929 | 0.224482 | 0.112241 | − | 0.993681i | \(-0.464197\pi\) | ||||
0.112241 | + | 0.993681i | \(0.464197\pi\) | |||||||
\(720\) | −5.19404 | −0.193571 | ||||||||
\(721\) | −53.6295 | −1.99727 | ||||||||
\(722\) | −29.7252 | −1.10626 | ||||||||
\(723\) | −15.3856 | −0.572198 | ||||||||
\(724\) | 42.6051 | 1.58341 | ||||||||
\(725\) | 7.35039 | 0.272987 | ||||||||
\(726\) | −2.86383 | −0.106287 | ||||||||
\(727\) | −42.3690 | −1.57138 | −0.785690 | − | 0.618621i | \(-0.787692\pi\) | ||||
−0.785690 | + | 0.618621i | \(0.787692\pi\) | |||||||
\(728\) | 4.30082 | 0.159399 | ||||||||
\(729\) | 27.6470 | 1.02396 | ||||||||
\(730\) | 31.2017 | 1.15483 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −34.4111 | −1.27187 | ||||||||
\(733\) | 11.1677 | 0.412487 | 0.206243 | − | 0.978501i | \(-0.433876\pi\) | ||||
0.206243 | + | 0.978501i | \(0.433876\pi\) | |||||||
\(734\) | −75.4757 | −2.78586 | ||||||||
\(735\) | −29.3386 | −1.08217 | ||||||||
\(736\) | −44.7349 | −1.64895 | ||||||||
\(737\) | −2.85720 | −0.105246 | ||||||||
\(738\) | 28.3505 | 1.04359 | ||||||||
\(739\) | 27.3680 | 1.00675 | 0.503374 | − | 0.864069i | \(-0.332092\pi\) | ||||
0.503374 | + | 0.864069i | \(0.332092\pi\) | |||||||
\(740\) | −24.7592 | −0.910167 | ||||||||
\(741\) | 6.94066 | 0.254972 | ||||||||
\(742\) | 35.2332 | 1.29345 | ||||||||
\(743\) | −35.1915 | −1.29105 | −0.645525 | − | 0.763739i | \(-0.723361\pi\) | ||||
−0.645525 | + | 0.763739i | \(0.723361\pi\) | |||||||
\(744\) | −8.88559 | −0.325762 | ||||||||
\(745\) | −13.1343 | −0.481203 | ||||||||
\(746\) | −74.6825 | −2.73432 | ||||||||
\(747\) | 14.5091 | 0.530860 | ||||||||
\(748\) | −2.49986 | −0.0914039 | ||||||||
\(749\) | −34.7584 | −1.27004 | ||||||||
\(750\) | −34.1171 | −1.24578 | ||||||||
\(751\) | −17.4790 | −0.637819 | −0.318910 | − | 0.947785i | \(-0.603317\pi\) | ||||
−0.318910 | + | 0.947785i | \(0.603317\pi\) | |||||||
\(752\) | −9.30683 | −0.339385 | ||||||||
\(753\) | −19.0308 | −0.693521 | ||||||||
\(754\) | 5.74763 | 0.209316 | ||||||||
\(755\) | 29.0356 | 1.05671 | ||||||||
\(756\) | 63.9088 | 2.32434 | ||||||||
\(757\) | −37.1050 | −1.34860 | −0.674302 | − | 0.738456i | \(-0.735555\pi\) | ||||
−0.674302 | + | 0.738456i | \(0.735555\pi\) | |||||||
\(758\) | −40.1831 | −1.45952 | ||||||||
\(759\) | 7.59185 | 0.275567 | ||||||||
\(760\) | 9.77189 | 0.354464 | ||||||||
\(761\) | −22.6338 | −0.820476 | −0.410238 | − | 0.911978i | \(-0.634554\pi\) | ||||
−0.410238 | + | 0.911978i | \(0.634554\pi\) | |||||||
\(762\) | 42.4880 | 1.53918 | ||||||||
\(763\) | −5.63762 | −0.204096 | ||||||||
\(764\) | 24.2139 | 0.876027 | ||||||||
\(765\) | 1.88845 | 0.0682771 | ||||||||
\(766\) | 9.01144 | 0.325596 | ||||||||
\(767\) | −7.90994 | −0.285611 | ||||||||
\(768\) | 7.17707 | 0.258980 | ||||||||
\(769\) | 12.5856 | 0.453848 | 0.226924 | − | 0.973912i | \(-0.427133\pi\) | ||||
0.226924 | + | 0.973912i | \(0.427133\pi\) | |||||||
\(770\) | 15.4235 | 0.555824 | ||||||||
\(771\) | −32.8491 | −1.18303 | ||||||||
\(772\) | 16.8643 | 0.606960 | ||||||||
\(773\) | 16.3638 | 0.588566 | 0.294283 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294283 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(774\) | 2.49755 | 0.0897727 | ||||||||
\(775\) | −15.0669 | −0.541218 | ||||||||
\(776\) | −19.0925 | −0.685382 | ||||||||
\(777\) | −37.7896 | −1.35569 | ||||||||
\(778\) | 60.6570 | 2.17466 | ||||||||
\(779\) | 65.2208 | 2.33678 | ||||||||
\(780\) | −4.84357 | −0.173428 | ||||||||
\(781\) | −0.715674 | −0.0256088 | ||||||||
\(782\) | 11.9289 | 0.426575 | ||||||||
\(783\) | 17.0777 | 0.610308 | ||||||||
\(784\) | −37.2649 | −1.33089 | ||||||||
\(785\) | −27.5111 | −0.981914 | ||||||||
\(786\) | −21.3133 | −0.760222 | ||||||||
\(787\) | 1.59031 | 0.0566884 | 0.0283442 | − | 0.999598i | \(-0.490977\pi\) | ||||
0.0283442 | + | 0.999598i | \(0.490977\pi\) | |||||||
\(788\) | −18.7326 | −0.667322 | ||||||||
\(789\) | 10.8907 | 0.387720 | ||||||||
\(790\) | −54.2865 | −1.93143 | ||||||||
\(791\) | −17.2976 | −0.615031 | ||||||||
\(792\) | −1.24843 | −0.0443609 | ||||||||
\(793\) | −9.12317 | −0.323973 | ||||||||
\(794\) | 46.1264 | 1.63697 | ||||||||
\(795\) | −7.93412 | −0.281394 | ||||||||
\(796\) | −40.2989 | −1.42836 | ||||||||
\(797\) | −23.4033 | −0.828987 | −0.414494 | − | 0.910052i | \(-0.636041\pi\) | ||||
−0.414494 | + | 0.910052i | \(0.636041\pi\) | |||||||
\(798\) | 74.5903 | 2.64047 | ||||||||
\(799\) | 3.38378 | 0.119710 | ||||||||
\(800\) | −19.3099 | −0.682707 | ||||||||
\(801\) | −7.28601 | −0.257439 | ||||||||
\(802\) | 43.8525 | 1.54848 | ||||||||
\(803\) | −9.17039 | −0.323616 | ||||||||
\(804\) | 9.64285 | 0.340077 | ||||||||
\(805\) | −40.8868 | −1.44107 | ||||||||
\(806\) | −11.7815 | −0.414987 | ||||||||
\(807\) | −7.05419 | −0.248319 | ||||||||
\(808\) | −10.7719 | −0.378953 | ||||||||
\(809\) | 34.6676 | 1.21885 | 0.609424 | − | 0.792844i | \(-0.291401\pi\) | ||||
0.609424 | + | 0.792844i | \(0.291401\pi\) | |||||||
\(810\) | −13.8876 | −0.487959 | ||||||||
\(811\) | −25.8975 | −0.909384 | −0.454692 | − | 0.890649i | \(-0.650251\pi\) | ||||
−0.454692 | + | 0.890649i | \(0.650251\pi\) | |||||||
\(812\) | 34.3152 | 1.20423 | ||||||||
\(813\) | −22.7774 | −0.798839 | ||||||||
\(814\) | 13.0988 | 0.459111 | ||||||||
\(815\) | −1.18324 | −0.0414470 | ||||||||
\(816\) | −3.71320 | −0.129988 | ||||||||
\(817\) | 5.74568 | 0.201016 | ||||||||
\(818\) | 31.6661 | 1.10718 | ||||||||
\(819\) | 4.77551 | 0.166870 | ||||||||
\(820\) | −45.5146 | −1.58944 | ||||||||
\(821\) | 47.8939 | 1.67151 | 0.835755 | − | 0.549103i | \(-0.185030\pi\) | ||||
0.835755 | + | 0.549103i | \(0.185030\pi\) | |||||||
\(822\) | 62.7953 | 2.19024 | ||||||||
\(823\) | −21.5145 | −0.749949 | −0.374975 | − | 0.927035i | \(-0.622349\pi\) | ||||
−0.374975 | + | 0.927035i | \(0.622349\pi\) | |||||||
\(824\) | −12.5446 | −0.437012 | ||||||||
\(825\) | 3.27703 | 0.114092 | ||||||||
\(826\) | −85.0069 | −2.95777 | ||||||||
\(827\) | −50.8283 | −1.76747 | −0.883737 | − | 0.467983i | \(-0.844981\pi\) | ||||
−0.883737 | + | 0.467983i | \(0.844981\pi\) | |||||||
\(828\) | 16.5512 | 0.575195 | ||||||||
\(829\) | −1.79519 | −0.0623494 | −0.0311747 | − | 0.999514i | \(-0.509925\pi\) | ||||
−0.0311747 | + | 0.999514i | \(0.509925\pi\) | |||||||
\(830\) | −41.9290 | −1.45538 | ||||||||
\(831\) | 29.5653 | 1.02561 | ||||||||
\(832\) | −10.1773 | −0.352836 | ||||||||
\(833\) | 13.5488 | 0.469438 | ||||||||
\(834\) | −20.5117 | −0.710261 | ||||||||
\(835\) | −7.54075 | −0.260958 | ||||||||
\(836\) | −14.3634 | −0.496768 | ||||||||
\(837\) | −35.0060 | −1.20999 | ||||||||
\(838\) | 42.5328 | 1.46927 | ||||||||
\(839\) | −52.1184 | −1.79933 | −0.899664 | − | 0.436582i | \(-0.856189\pi\) | ||||
−0.899664 | + | 0.436582i | \(0.856189\pi\) | |||||||
\(840\) | −10.4083 | −0.359120 | ||||||||
\(841\) | −19.8303 | −0.683803 | ||||||||
\(842\) | 56.4972 | 1.94702 | ||||||||
\(843\) | 12.3696 | 0.426031 | ||||||||
\(844\) | −49.2764 | −1.69616 | ||||||||
\(845\) | 19.5672 | 0.673132 | ||||||||
\(846\) | 8.45118 | 0.290558 | ||||||||
\(847\) | −4.53308 | −0.155758 | ||||||||
\(848\) | −10.0777 | −0.346068 | ||||||||
\(849\) | −3.09026 | −0.106057 | ||||||||
\(850\) | 5.14910 | 0.176613 | ||||||||
\(851\) | −34.7240 | −1.19032 | ||||||||
\(852\) | 2.41535 | 0.0827484 | ||||||||
\(853\) | −14.2140 | −0.486678 | −0.243339 | − | 0.969941i | \(-0.578243\pi\) | ||||
−0.243339 | + | 0.969941i | \(0.578243\pi\) | |||||||
\(854\) | −98.0453 | −3.35504 | ||||||||
\(855\) | 10.8504 | 0.371077 | ||||||||
\(856\) | −8.13042 | −0.277892 | ||||||||
\(857\) | −8.13322 | −0.277825 | −0.138913 | − | 0.990305i | \(-0.544361\pi\) | ||||
−0.138913 | + | 0.990305i | \(0.544361\pi\) | |||||||
\(858\) | 2.56247 | 0.0874814 | ||||||||
\(859\) | 14.3524 | 0.489698 | 0.244849 | − | 0.969561i | \(-0.421262\pi\) | ||||
0.244849 | + | 0.969561i | \(0.421262\pi\) | |||||||
\(860\) | −4.00965 | −0.136728 | ||||||||
\(861\) | −69.4683 | −2.36747 | ||||||||
\(862\) | 81.8866 | 2.78907 | ||||||||
\(863\) | 55.1946 | 1.87885 | 0.939423 | − | 0.342760i | \(-0.111362\pi\) | ||||
0.939423 | + | 0.342760i | \(0.111362\pi\) | |||||||
\(864\) | −44.8641 | −1.52631 | ||||||||
\(865\) | 28.4724 | 0.968091 | ||||||||
\(866\) | −32.5786 | −1.10707 | ||||||||
\(867\) | 1.35005 | 0.0458500 | ||||||||
\(868\) | −70.3395 | −2.38748 | ||||||||
\(869\) | 15.9552 | 0.541243 | ||||||||
\(870\) | −13.9097 | −0.471582 | ||||||||
\(871\) | 2.55654 | 0.0866251 | ||||||||
\(872\) | −1.31871 | −0.0446572 | ||||||||
\(873\) | −21.1998 | −0.717505 | ||||||||
\(874\) | 68.5394 | 2.31838 | ||||||||
\(875\) | −54.0029 | −1.82563 | ||||||||
\(876\) | 30.9494 | 1.04568 | ||||||||
\(877\) | 53.2848 | 1.79930 | 0.899650 | − | 0.436611i | \(-0.143822\pi\) | ||||
0.899650 | + | 0.436611i | \(0.143822\pi\) | |||||||
\(878\) | −36.2364 | −1.22292 | ||||||||
\(879\) | −29.4933 | −0.994786 | ||||||||
\(880\) | −4.41154 | −0.148713 | ||||||||
\(881\) | −9.74148 | −0.328199 | −0.164099 | − | 0.986444i | \(-0.552472\pi\) | ||||
−0.164099 | + | 0.986444i | \(0.552472\pi\) | |||||||
\(882\) | 33.8388 | 1.13941 | ||||||||
\(883\) | −1.20413 | −0.0405222 | −0.0202611 | − | 0.999795i | \(-0.506450\pi\) | ||||
−0.0202611 | + | 0.999795i | \(0.506450\pi\) | |||||||
\(884\) | 2.23680 | 0.0752317 | ||||||||
\(885\) | 19.1426 | 0.643471 | ||||||||
\(886\) | −1.48429 | −0.0498656 | ||||||||
\(887\) | −27.4999 | −0.923356 | −0.461678 | − | 0.887048i | \(-0.652752\pi\) | ||||
−0.461678 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(888\) | −8.83947 | −0.296633 | ||||||||
\(889\) | 67.2530 | 2.25559 | ||||||||
\(890\) | 21.0554 | 0.705780 | ||||||||
\(891\) | 4.08165 | 0.136741 | ||||||||
\(892\) | 31.2246 | 1.04548 | ||||||||
\(893\) | 19.4421 | 0.650606 | ||||||||
\(894\) | −23.4512 | −0.784324 | ||||||||
\(895\) | −6.67366 | −0.223076 | ||||||||
\(896\) | −37.2520 | −1.24450 | ||||||||
\(897\) | −6.79296 | −0.226810 | ||||||||
\(898\) | −43.6829 | −1.45772 | ||||||||
\(899\) | −18.7962 | −0.626887 | ||||||||
\(900\) | 7.14436 | 0.238145 | ||||||||
\(901\) | 3.66404 | 0.122067 | ||||||||
\(902\) | 24.0793 | 0.801754 | ||||||||
\(903\) | −6.11986 | −0.203656 | ||||||||
\(904\) | −4.04612 | −0.134572 | ||||||||
\(905\) | −27.3361 | −0.908683 | ||||||||
\(906\) | 51.8428 | 1.72236 | ||||||||
\(907\) | 5.75278 | 0.191018 | 0.0955089 | − | 0.995429i | \(-0.469552\pi\) | ||||
0.0955089 | + | 0.995429i | \(0.469552\pi\) | |||||||
\(908\) | −28.3265 | −0.940049 | ||||||||
\(909\) | −11.9608 | −0.396714 | ||||||||
\(910\) | −13.8005 | −0.457482 | ||||||||
\(911\) | −25.8306 | −0.855806 | −0.427903 | − | 0.903825i | \(-0.640748\pi\) | ||||
−0.427903 | + | 0.903825i | \(0.640748\pi\) | |||||||
\(912\) | −21.3348 | −0.706467 | ||||||||
\(913\) | 12.3232 | 0.407840 | ||||||||
\(914\) | −15.5704 | −0.515023 | ||||||||
\(915\) | 22.0787 | 0.729899 | ||||||||
\(916\) | 2.00150 | 0.0661313 | ||||||||
\(917\) | −33.7362 | −1.11407 | ||||||||
\(918\) | 11.9633 | 0.394848 | ||||||||
\(919\) | 59.1823 | 1.95224 | 0.976122 | − | 0.217224i | \(-0.0697003\pi\) | ||||
0.976122 | + | 0.217224i | \(0.0697003\pi\) | |||||||
\(920\) | −9.56394 | −0.315314 | ||||||||
\(921\) | −36.5606 | −1.20471 | ||||||||
\(922\) | 47.6253 | 1.56846 | ||||||||
\(923\) | 0.640364 | 0.0210778 | ||||||||
\(924\) | 15.2988 | 0.503293 | ||||||||
\(925\) | −14.9887 | −0.492824 | ||||||||
\(926\) | 68.4592 | 2.24971 | ||||||||
\(927\) | −13.9292 | −0.457495 | ||||||||
\(928\) | −24.0894 | −0.790772 | ||||||||
\(929\) | 53.6562 | 1.76040 | 0.880201 | − | 0.474602i | \(-0.157408\pi\) | ||||
0.880201 | + | 0.474602i | \(0.157408\pi\) | |||||||
\(930\) | 28.5121 | 0.934949 | ||||||||
\(931\) | 77.8469 | 2.55133 | ||||||||
\(932\) | −1.51799 | −0.0497233 | ||||||||
\(933\) | −1.62882 | −0.0533251 | ||||||||
\(934\) | −4.10043 | −0.134170 | ||||||||
\(935\) | 1.60395 | 0.0524547 | ||||||||
\(936\) | 1.11705 | 0.0365120 | ||||||||
\(937\) | 21.5314 | 0.703401 | 0.351701 | − | 0.936113i | \(-0.385604\pi\) | ||||
0.351701 | + | 0.936113i | \(0.385604\pi\) | |||||||
\(938\) | 27.4748 | 0.897083 | ||||||||
\(939\) | 12.4056 | 0.404842 | ||||||||
\(940\) | −13.5678 | −0.442532 | ||||||||
\(941\) | −7.49397 | −0.244296 | −0.122148 | − | 0.992512i | \(-0.538978\pi\) | ||||
−0.122148 | + | 0.992512i | \(0.538978\pi\) | |||||||
\(942\) | −49.1208 | −1.60044 | ||||||||
\(943\) | −63.8329 | −2.07869 | ||||||||
\(944\) | 24.3143 | 0.791362 | ||||||||
\(945\) | −41.0049 | −1.33389 | ||||||||
\(946\) | 2.12129 | 0.0689690 | ||||||||
\(947\) | −61.1766 | −1.98797 | −0.993987 | − | 0.109500i | \(-0.965075\pi\) | ||||
−0.993987 | + | 0.109500i | \(0.965075\pi\) | |||||||
\(948\) | −53.8476 | −1.74889 | ||||||||
\(949\) | 8.20539 | 0.266358 | ||||||||
\(950\) | 29.5851 | 0.959867 | ||||||||
\(951\) | 6.41411 | 0.207992 | ||||||||
\(952\) | 4.80662 | 0.155784 | ||||||||
\(953\) | −34.1480 | −1.10616 | −0.553082 | − | 0.833127i | \(-0.686548\pi\) | ||||
−0.553082 | + | 0.833127i | \(0.686548\pi\) | |||||||
\(954\) | 9.15113 | 0.296279 | ||||||||
\(955\) | −15.5360 | −0.502733 | ||||||||
\(956\) | −28.6588 | −0.926892 | ||||||||
\(957\) | 4.08815 | 0.132151 | ||||||||
\(958\) | 63.9585 | 2.06641 | ||||||||
\(959\) | 99.3967 | 3.20969 | ||||||||
\(960\) | 24.6299 | 0.794925 | ||||||||
\(961\) | 7.52848 | 0.242854 | ||||||||
\(962\) | −11.7204 | −0.377880 | ||||||||
\(963\) | −9.02780 | −0.290917 | ||||||||
\(964\) | −28.4893 | −0.917580 | ||||||||
\(965\) | −10.8204 | −0.348321 | ||||||||
\(966\) | −73.0030 | −2.34883 | ||||||||
\(967\) | −21.5863 | −0.694169 | −0.347084 | − | 0.937834i | \(-0.612828\pi\) | ||||
−0.347084 | + | 0.937834i | \(0.612828\pi\) | |||||||
\(968\) | −1.06034 | −0.0340808 | ||||||||
\(969\) | 7.75693 | 0.249188 | ||||||||
\(970\) | 61.2641 | 1.96707 | ||||||||
\(971\) | −21.9094 | −0.703106 | −0.351553 | − | 0.936168i | \(-0.614346\pi\) | ||||
−0.351553 | + | 0.936168i | \(0.614346\pi\) | |||||||
\(972\) | 28.5197 | 0.914770 | ||||||||
\(973\) | −32.4673 | −1.04085 | ||||||||
\(974\) | −45.2900 | −1.45119 | ||||||||
\(975\) | −2.93219 | −0.0939052 | ||||||||
\(976\) | 28.0436 | 0.897654 | ||||||||
\(977\) | 6.59345 | 0.210943 | 0.105472 | − | 0.994422i | \(-0.466365\pi\) | ||||
0.105472 | + | 0.994422i | \(0.466365\pi\) | |||||||
\(978\) | −2.11266 | −0.0675553 | ||||||||
\(979\) | −6.18834 | −0.197780 | ||||||||
\(980\) | −54.3258 | −1.73537 | ||||||||
\(981\) | −1.46426 | −0.0467503 | ||||||||
\(982\) | −10.3997 | −0.331867 | ||||||||
\(983\) | −17.2978 | −0.551713 | −0.275857 | − | 0.961199i | \(-0.588962\pi\) | ||||
−0.275857 | + | 0.961199i | \(0.588962\pi\) | |||||||
\(984\) | −16.2495 | −0.518016 | ||||||||
\(985\) | 12.0191 | 0.382962 | ||||||||
\(986\) | 6.42359 | 0.204569 | ||||||||
\(987\) | −20.7083 | −0.659152 | ||||||||
\(988\) | 12.8519 | 0.408874 | ||||||||
\(989\) | −5.62341 | −0.178814 | ||||||||
\(990\) | 4.00595 | 0.127317 | ||||||||
\(991\) | 34.2575 | 1.08823 | 0.544113 | − | 0.839012i | \(-0.316866\pi\) | ||||
0.544113 | + | 0.839012i | \(0.316866\pi\) | |||||||
\(992\) | 49.3785 | 1.56777 | ||||||||
\(993\) | 36.5996 | 1.16145 | ||||||||
\(994\) | 6.88189 | 0.218280 | ||||||||
\(995\) | 25.8564 | 0.819703 | ||||||||
\(996\) | −41.5900 | −1.31783 | ||||||||
\(997\) | 8.48372 | 0.268682 | 0.134341 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134341 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(998\) | −54.5756 | −1.72756 | ||||||||
\(999\) | −34.8243 | −1.10179 |
(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 | 8041.2.a.g.1.12 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.12 | ✓ | 69 | 1.1 | even | 1 | trivial |