Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.308797 | −0.218352 | −0.109176 | − | 0.994022i | \(-0.534821\pi\) | ||||
−0.109176 | + | 0.994022i | \(0.534821\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.90464 | −0.952322 | ||||||||
\(5\) | 0.898648 | 0.401888 | 0.200944 | − | 0.979603i | \(-0.435599\pi\) | ||||
0.200944 | + | 0.979603i | \(0.435599\pi\) | |||||||
\(6\) | 0.308797 | 0.126066 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.20574 | 0.426294 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.277499 | −0.0877530 | ||||||||
\(11\) | 1.38960 | 0.418980 | 0.209490 | − | 0.977811i | \(-0.432820\pi\) | ||||
0.209490 | + | 0.977811i | \(0.432820\pi\) | |||||||
\(12\) | 1.90464 | 0.549824 | ||||||||
\(13\) | −6.64217 | −1.84221 | −0.921103 | − | 0.389319i | \(-0.872711\pi\) | ||||
−0.921103 | + | 0.389319i | \(0.872711\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.898648 | −0.232030 | ||||||||
\(16\) | 3.43696 | 0.859240 | ||||||||
\(17\) | −6.17243 | −1.49703 | −0.748517 | − | 0.663115i | \(-0.769234\pi\) | ||||
−0.748517 | + | 0.663115i | \(0.769234\pi\) | |||||||
\(18\) | −0.308797 | −0.0727841 | ||||||||
\(19\) | −5.46842 | −1.25454 | −0.627271 | − | 0.778801i | \(-0.715828\pi\) | ||||
−0.627271 | + | 0.778801i | \(0.715828\pi\) | |||||||
\(20\) | −1.71160 | −0.382726 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.429104 | −0.0914852 | ||||||||
\(23\) | 4.76671 | 0.993927 | 0.496964 | − | 0.867771i | \(-0.334448\pi\) | ||||
0.496964 | + | 0.867771i | \(0.334448\pi\) | |||||||
\(24\) | −1.20574 | −0.246121 | ||||||||
\(25\) | −4.19243 | −0.838486 | ||||||||
\(26\) | 2.05108 | 0.402250 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.78706 | −1.26033 | −0.630163 | − | 0.776463i | \(-0.717012\pi\) | ||||
−0.630163 | + | 0.776463i | \(0.717012\pi\) | |||||||
\(30\) | 0.277499 | 0.0506642 | ||||||||
\(31\) | 6.37461 | 1.14491 | 0.572457 | − | 0.819935i | \(-0.305991\pi\) | ||||
0.572457 | + | 0.819935i | \(0.305991\pi\) | |||||||
\(32\) | −3.47280 | −0.613911 | ||||||||
\(33\) | −1.38960 | −0.241898 | ||||||||
\(34\) | 1.90603 | 0.326881 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.90464 | −0.317441 | ||||||||
\(37\) | 7.16373 | 1.17771 | 0.588855 | − | 0.808239i | \(-0.299579\pi\) | ||||
0.588855 | + | 0.808239i | \(0.299579\pi\) | |||||||
\(38\) | 1.68863 | 0.273932 | ||||||||
\(39\) | 6.64217 | 1.06360 | ||||||||
\(40\) | 1.08354 | 0.171322 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00164 | −0.915241 | −0.457620 | − | 0.889148i | \(-0.651298\pi\) | ||||
−0.457620 | + | 0.889148i | \(0.651298\pi\) | |||||||
\(44\) | −2.64669 | −0.399004 | ||||||||
\(45\) | 0.898648 | 0.133963 | ||||||||
\(46\) | −1.47194 | −0.217026 | ||||||||
\(47\) | −6.21931 | −0.907180 | −0.453590 | − | 0.891211i | \(-0.649857\pi\) | ||||
−0.453590 | + | 0.891211i | \(0.649857\pi\) | |||||||
\(48\) | −3.43696 | −0.496082 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.29461 | 0.183085 | ||||||||
\(51\) | 6.17243 | 0.864313 | ||||||||
\(52\) | 12.6510 | 1.75437 | ||||||||
\(53\) | 10.4055 | 1.42930 | 0.714650 | − | 0.699483i | \(-0.246586\pi\) | ||||
0.714650 | + | 0.699483i | \(0.246586\pi\) | |||||||
\(54\) | 0.308797 | 0.0420219 | ||||||||
\(55\) | 1.24876 | 0.168383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.46842 | 0.724310 | ||||||||
\(58\) | 2.09582 | 0.275195 | ||||||||
\(59\) | 4.50432 | 0.586413 | 0.293207 | − | 0.956049i | \(-0.405278\pi\) | ||||
0.293207 | + | 0.956049i | \(0.405278\pi\) | |||||||
\(60\) | 1.71160 | 0.220967 | ||||||||
\(61\) | −13.3304 | −1.70678 | −0.853391 | − | 0.521272i | \(-0.825458\pi\) | ||||
−0.853391 | + | 0.521272i | \(0.825458\pi\) | |||||||
\(62\) | −1.96846 | −0.249994 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.80153 | −0.725191 | ||||||||
\(65\) | −5.96897 | −0.740360 | ||||||||
\(66\) | 0.429104 | 0.0528190 | ||||||||
\(67\) | −4.95916 | −0.605857 | −0.302929 | − | 0.953013i | \(-0.597964\pi\) | ||||
−0.302929 | + | 0.953013i | \(0.597964\pi\) | |||||||
\(68\) | 11.7563 | 1.42566 | ||||||||
\(69\) | −4.76671 | −0.573844 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9115 | 1.29496 | 0.647481 | − | 0.762082i | \(-0.275823\pi\) | ||||
0.647481 | + | 0.762082i | \(0.275823\pi\) | |||||||
\(72\) | 1.20574 | 0.142098 | ||||||||
\(73\) | −4.36211 | −0.510547 | −0.255273 | − | 0.966869i | \(-0.582165\pi\) | ||||
−0.255273 | + | 0.966869i | \(0.582165\pi\) | |||||||
\(74\) | −2.21214 | −0.257156 | ||||||||
\(75\) | 4.19243 | 0.484100 | ||||||||
\(76\) | 10.4154 | 1.19473 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.05108 | −0.232239 | ||||||||
\(79\) | −8.63992 | −0.972067 | −0.486034 | − | 0.873940i | \(-0.661557\pi\) | ||||
−0.486034 | + | 0.873940i | \(0.661557\pi\) | |||||||
\(80\) | 3.08862 | 0.345318 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.308797 | −0.0341009 | ||||||||
\(83\) | 9.05009 | 0.993376 | 0.496688 | − | 0.867929i | \(-0.334549\pi\) | ||||
0.496688 | + | 0.867929i | \(0.334549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.54684 | −0.601640 | ||||||||
\(86\) | 1.85329 | 0.199845 | ||||||||
\(87\) | 6.78706 | 0.727649 | ||||||||
\(88\) | 1.67550 | 0.178609 | ||||||||
\(89\) | 1.29949 | 0.137746 | 0.0688729 | − | 0.997625i | \(-0.478060\pi\) | ||||
0.0688729 | + | 0.997625i | \(0.478060\pi\) | |||||||
\(90\) | −0.277499 | −0.0292510 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.07888 | −0.946539 | ||||||||
\(93\) | −6.37461 | −0.661016 | ||||||||
\(94\) | 1.92050 | 0.198085 | ||||||||
\(95\) | −4.91418 | −0.504184 | ||||||||
\(96\) | 3.47280 | 0.354442 | ||||||||
\(97\) | −7.81362 | −0.793353 | −0.396677 | − | 0.917958i | \(-0.629837\pi\) | ||||
−0.396677 | + | 0.917958i | \(0.629837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38960 | 0.139660 | ||||||||
\(100\) | 7.98509 | 0.798509 | ||||||||
\(101\) | 12.5977 | 1.25352 | 0.626759 | − | 0.779213i | \(-0.284381\pi\) | ||||
0.626759 | + | 0.779213i | \(0.284381\pi\) | |||||||
\(102\) | −1.90603 | −0.188725 | ||||||||
\(103\) | 18.5097 | 1.82381 | 0.911906 | − | 0.410399i | \(-0.134611\pi\) | ||||
0.911906 | + | 0.410399i | \(0.134611\pi\) | |||||||
\(104\) | −8.00874 | −0.785321 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.21317 | −0.312091 | ||||||||
\(107\) | 3.77779 | 0.365213 | 0.182607 | − | 0.983186i | \(-0.441547\pi\) | ||||
0.182607 | + | 0.983186i | \(0.441547\pi\) | |||||||
\(108\) | 1.90464 | 0.183275 | ||||||||
\(109\) | −5.31301 | −0.508894 | −0.254447 | − | 0.967087i | \(-0.581893\pi\) | ||||
−0.254447 | + | 0.967087i | \(0.581893\pi\) | |||||||
\(110\) | −0.385613 | −0.0367668 | ||||||||
\(111\) | −7.16373 | −0.679951 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.6298 | −1.56440 | −0.782200 | − | 0.623028i | \(-0.785902\pi\) | ||||
−0.782200 | + | 0.623028i | \(0.785902\pi\) | |||||||
\(114\) | −1.68863 | −0.158155 | ||||||||
\(115\) | 4.28359 | 0.399447 | ||||||||
\(116\) | 12.9269 | 1.20024 | ||||||||
\(117\) | −6.64217 | −0.614069 | ||||||||
\(118\) | −1.39092 | −0.128045 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.08354 | −0.0989129 | ||||||||
\(121\) | −9.06901 | −0.824456 | ||||||||
\(122\) | 4.11638 | 0.372680 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −12.1414 | −1.09033 | ||||||||
\(125\) | −8.26076 | −0.738865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.11991 | −0.631790 | −0.315895 | − | 0.948794i | \(-0.602305\pi\) | ||||
−0.315895 | + | 0.948794i | \(0.602305\pi\) | |||||||
\(128\) | 8.73710 | 0.772258 | ||||||||
\(129\) | 6.00164 | 0.528415 | ||||||||
\(130\) | 1.84320 | 0.161659 | ||||||||
\(131\) | 1.76987 | 0.154635 | 0.0773173 | − | 0.997007i | \(-0.475365\pi\) | ||||
0.0773173 | + | 0.997007i | \(0.475365\pi\) | |||||||
\(132\) | 2.64669 | 0.230365 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.53137 | 0.132290 | ||||||||
\(135\) | −0.898648 | −0.0773433 | ||||||||
\(136\) | −7.44236 | −0.638177 | ||||||||
\(137\) | 16.2543 | 1.38870 | 0.694348 | − | 0.719640i | \(-0.255693\pi\) | ||||
0.694348 | + | 0.719640i | \(0.255693\pi\) | |||||||
\(138\) | 1.47194 | 0.125300 | ||||||||
\(139\) | −10.8156 | −0.917370 | −0.458685 | − | 0.888599i | \(-0.651679\pi\) | ||||
−0.458685 | + | 0.888599i | \(0.651679\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.21931 | 0.523760 | ||||||||
\(142\) | −3.36945 | −0.282758 | ||||||||
\(143\) | −9.22996 | −0.771848 | ||||||||
\(144\) | 3.43696 | 0.286413 | ||||||||
\(145\) | −6.09918 | −0.506509 | ||||||||
\(146\) | 1.34701 | 0.111479 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.6444 | −1.12156 | ||||||||
\(149\) | 6.94118 | 0.568644 | 0.284322 | − | 0.958729i | \(-0.408232\pi\) | ||||
0.284322 | + | 0.958729i | \(0.408232\pi\) | |||||||
\(150\) | −1.29461 | −0.105704 | ||||||||
\(151\) | −15.9874 | −1.30103 | −0.650516 | − | 0.759492i | \(-0.725447\pi\) | ||||
−0.650516 | + | 0.759492i | \(0.725447\pi\) | |||||||
\(152\) | −6.59350 | −0.534803 | ||||||||
\(153\) | −6.17243 | −0.499012 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.72853 | 0.460126 | ||||||||
\(156\) | −12.6510 | −1.01289 | ||||||||
\(157\) | 7.87899 | 0.628812 | 0.314406 | − | 0.949289i | \(-0.398195\pi\) | ||||
0.314406 | + | 0.949289i | \(0.398195\pi\) | |||||||
\(158\) | 2.66798 | 0.212253 | ||||||||
\(159\) | −10.4055 | −0.825206 | ||||||||
\(160\) | −3.12083 | −0.246723 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.308797 | −0.0242614 | ||||||||
\(163\) | 23.6380 | 1.85147 | 0.925735 | − | 0.378172i | \(-0.123447\pi\) | ||||
0.925735 | + | 0.378172i | \(0.123447\pi\) | |||||||
\(164\) | −1.90464 | −0.148728 | ||||||||
\(165\) | −1.24876 | −0.0972159 | ||||||||
\(166\) | −2.79464 | −0.216906 | ||||||||
\(167\) | −13.3089 | −1.02988 | −0.514938 | − | 0.857227i | \(-0.672185\pi\) | ||||
−0.514938 | + | 0.857227i | \(0.672185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.1184 | 2.39372 | ||||||||
\(170\) | 1.71285 | 0.131369 | ||||||||
\(171\) | −5.46842 | −0.418180 | ||||||||
\(172\) | 11.4310 | 0.871604 | ||||||||
\(173\) | −6.99173 | −0.531571 | −0.265786 | − | 0.964032i | \(-0.585631\pi\) | ||||
−0.265786 | + | 0.964032i | \(0.585631\pi\) | |||||||
\(174\) | −2.09582 | −0.158884 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.77600 | 0.360004 | ||||||||
\(177\) | −4.50432 | −0.338566 | ||||||||
\(178\) | −0.401279 | −0.0300771 | ||||||||
\(179\) | −6.32731 | −0.472925 | −0.236463 | − | 0.971641i | \(-0.575988\pi\) | ||||
−0.236463 | + | 0.971641i | \(0.575988\pi\) | |||||||
\(180\) | −1.71160 | −0.127575 | ||||||||
\(181\) | −6.94382 | −0.516130 | −0.258065 | − | 0.966128i | \(-0.583085\pi\) | ||||
−0.258065 | + | 0.966128i | \(0.583085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3304 | 0.985411 | ||||||||
\(184\) | 5.74742 | 0.423705 | ||||||||
\(185\) | 6.43767 | 0.473307 | ||||||||
\(186\) | 1.96846 | 0.144334 | ||||||||
\(187\) | −8.57721 | −0.627228 | ||||||||
\(188\) | 11.8456 | 0.863927 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.51748 | 0.110090 | ||||||||
\(191\) | 19.9797 | 1.44568 | 0.722842 | − | 0.691014i | \(-0.242836\pi\) | ||||
0.722842 | + | 0.691014i | \(0.242836\pi\) | |||||||
\(192\) | 5.80153 | 0.418689 | ||||||||
\(193\) | 10.2929 | 0.740897 | 0.370448 | − | 0.928853i | \(-0.379204\pi\) | ||||
0.370448 | + | 0.928853i | \(0.379204\pi\) | |||||||
\(194\) | 2.41282 | 0.173230 | ||||||||
\(195\) | 5.96897 | 0.427447 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.5794 | −1.96495 | −0.982477 | − | 0.186383i | \(-0.940323\pi\) | ||||
−0.982477 | + | 0.186383i | \(0.940323\pi\) | |||||||
\(198\) | −0.429104 | −0.0304951 | ||||||||
\(199\) | −15.6115 | −1.10667 | −0.553335 | − | 0.832959i | \(-0.686645\pi\) | ||||
−0.553335 | + | 0.832959i | \(0.686645\pi\) | |||||||
\(200\) | −5.05499 | −0.357442 | ||||||||
\(201\) | 4.95916 | 0.349792 | ||||||||
\(202\) | −3.89013 | −0.273708 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.7563 | −0.823105 | ||||||||
\(205\) | 0.898648 | 0.0627643 | ||||||||
\(206\) | −5.71573 | −0.398233 | ||||||||
\(207\) | 4.76671 | 0.331309 | ||||||||
\(208\) | −22.8289 | −1.58290 | ||||||||
\(209\) | −7.59891 | −0.525628 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4853 | 1.41026 | 0.705132 | − | 0.709076i | \(-0.250888\pi\) | ||||
0.705132 | + | 0.709076i | \(0.250888\pi\) | |||||||
\(212\) | −19.8187 | −1.36115 | ||||||||
\(213\) | −10.9115 | −0.747646 | ||||||||
\(214\) | −1.16657 | −0.0797451 | ||||||||
\(215\) | −5.39336 | −0.367824 | ||||||||
\(216\) | −1.20574 | −0.0820403 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.64064 | 0.111118 | ||||||||
\(219\) | 4.36211 | 0.294764 | ||||||||
\(220\) | −2.37845 | −0.160355 | ||||||||
\(221\) | 40.9983 | 2.75785 | ||||||||
\(222\) | 2.21214 | 0.148469 | ||||||||
\(223\) | 15.7327 | 1.05354 | 0.526771 | − | 0.850007i | \(-0.323403\pi\) | ||||
0.526771 | + | 0.850007i | \(0.323403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.19243 | −0.279495 | ||||||||
\(226\) | 5.13523 | 0.341590 | ||||||||
\(227\) | 14.8282 | 0.984183 | 0.492092 | − | 0.870543i | \(-0.336232\pi\) | ||||
0.492092 | + | 0.870543i | \(0.336232\pi\) | |||||||
\(228\) | −10.4154 | −0.689776 | ||||||||
\(229\) | 7.20918 | 0.476396 | 0.238198 | − | 0.971217i | \(-0.423443\pi\) | ||||
0.238198 | + | 0.971217i | \(0.423443\pi\) | |||||||
\(230\) | −1.32276 | −0.0872201 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.18344 | −0.537269 | ||||||||
\(233\) | 4.00163 | 0.262156 | 0.131078 | − | 0.991372i | \(-0.458156\pi\) | ||||
0.131078 | + | 0.991372i | \(0.458156\pi\) | |||||||
\(234\) | 2.05108 | 0.134083 | ||||||||
\(235\) | −5.58897 | −0.364584 | ||||||||
\(236\) | −8.57914 | −0.558454 | ||||||||
\(237\) | 8.63992 | 0.561223 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.64792 | 0.171280 | 0.0856399 | − | 0.996326i | \(-0.472707\pi\) | ||||
0.0856399 | + | 0.996326i | \(0.472707\pi\) | |||||||
\(240\) | −3.08862 | −0.199369 | ||||||||
\(241\) | −9.68840 | −0.624085 | −0.312042 | − | 0.950068i | \(-0.601013\pi\) | ||||
−0.312042 | + | 0.950068i | \(0.601013\pi\) | |||||||
\(242\) | 2.80048 | 0.180022 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 25.3897 | 1.62541 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.308797 | 0.0196882 | ||||||||
\(247\) | 36.3222 | 2.31112 | ||||||||
\(248\) | 7.68613 | 0.488070 | ||||||||
\(249\) | −9.05009 | −0.573526 | ||||||||
\(250\) | 2.55090 | 0.161333 | ||||||||
\(251\) | −21.2826 | −1.34335 | −0.671674 | − | 0.740847i | \(-0.734424\pi\) | ||||
−0.671674 | + | 0.740847i | \(0.734424\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.62381 | 0.416436 | ||||||||
\(254\) | 2.19861 | 0.137953 | ||||||||
\(255\) | 5.54684 | 0.347357 | ||||||||
\(256\) | 8.90507 | 0.556567 | ||||||||
\(257\) | −28.2476 | −1.76204 | −0.881019 | − | 0.473081i | \(-0.843142\pi\) | ||||
−0.881019 | + | 0.473081i | \(0.843142\pi\) | |||||||
\(258\) | −1.85329 | −0.115380 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.3688 | 0.705061 | ||||||||
\(261\) | −6.78706 | −0.420109 | ||||||||
\(262\) | −0.546531 | −0.0337648 | ||||||||
\(263\) | −5.67723 | −0.350073 | −0.175036 | − | 0.984562i | \(-0.556004\pi\) | ||||
−0.175036 | + | 0.984562i | \(0.556004\pi\) | |||||||
\(264\) | −1.67550 | −0.103120 | ||||||||
\(265\) | 9.35084 | 0.574418 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.29949 | −0.0795276 | ||||||||
\(268\) | 9.44543 | 0.576971 | ||||||||
\(269\) | 0.465240 | 0.0283662 | 0.0141831 | − | 0.999899i | \(-0.495485\pi\) | ||||
0.0141831 | + | 0.999899i | \(0.495485\pi\) | |||||||
\(270\) | 0.277499 | 0.0168881 | ||||||||
\(271\) | 8.51652 | 0.517342 | 0.258671 | − | 0.965965i | \(-0.416715\pi\) | ||||
0.258671 | + | 0.965965i | \(0.416715\pi\) | |||||||
\(272\) | −21.2144 | −1.28631 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.01926 | −0.303225 | ||||||||
\(275\) | −5.82580 | −0.351309 | ||||||||
\(276\) | 9.07888 | 0.546485 | ||||||||
\(277\) | −0.909276 | −0.0546331 | −0.0273165 | − | 0.999627i | \(-0.508696\pi\) | ||||
−0.0273165 | + | 0.999627i | \(0.508696\pi\) | |||||||
\(278\) | 3.33983 | 0.200310 | ||||||||
\(279\) | 6.37461 | 0.381638 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6460 | 1.47026 | 0.735128 | − | 0.677928i | \(-0.237122\pi\) | ||||
0.735128 | + | 0.677928i | \(0.237122\pi\) | |||||||
\(282\) | −1.92050 | −0.114364 | ||||||||
\(283\) | 27.0805 | 1.60977 | 0.804885 | − | 0.593430i | \(-0.202227\pi\) | ||||
0.804885 | + | 0.593430i | \(0.202227\pi\) | |||||||
\(284\) | −20.7826 | −1.23322 | ||||||||
\(285\) | 4.91418 | 0.291091 | ||||||||
\(286\) | 2.85018 | 0.168535 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.47280 | −0.204637 | ||||||||
\(289\) | 21.0989 | 1.24111 | ||||||||
\(290\) | 1.88341 | 0.110597 | ||||||||
\(291\) | 7.81362 | 0.458043 | ||||||||
\(292\) | 8.30827 | 0.486205 | ||||||||
\(293\) | 31.1849 | 1.82184 | 0.910921 | − | 0.412581i | \(-0.135373\pi\) | ||||
0.910921 | + | 0.412581i | \(0.135373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.04780 | 0.235672 | ||||||||
\(296\) | 8.63761 | 0.502051 | ||||||||
\(297\) | −1.38960 | −0.0806327 | ||||||||
\(298\) | −2.14341 | −0.124165 | ||||||||
\(299\) | −31.6613 | −1.83102 | ||||||||
\(300\) | −7.98509 | −0.461020 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.93684 | 0.284083 | ||||||||
\(303\) | −12.5977 | −0.723719 | ||||||||
\(304\) | −18.7947 | −1.07795 | ||||||||
\(305\) | −11.9793 | −0.685934 | ||||||||
\(306\) | 1.90603 | 0.108960 | ||||||||
\(307\) | 25.2868 | 1.44319 | 0.721596 | − | 0.692314i | \(-0.243409\pi\) | ||||
0.721596 | + | 0.692314i | \(0.243409\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.5097 | −1.05298 | ||||||||
\(310\) | −1.76895 | −0.100470 | ||||||||
\(311\) | 8.85487 | 0.502113 | 0.251057 | − | 0.967972i | \(-0.419222\pi\) | ||||
0.251057 | + | 0.967972i | \(0.419222\pi\) | |||||||
\(312\) | 8.00874 | 0.453406 | ||||||||
\(313\) | 3.62015 | 0.204623 | 0.102312 | − | 0.994752i | \(-0.467376\pi\) | ||||
0.102312 | + | 0.994752i | \(0.467376\pi\) | |||||||
\(314\) | −2.43301 | −0.137303 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.4560 | 0.925721 | ||||||||
\(317\) | 12.1660 | 0.683312 | 0.341656 | − | 0.939825i | \(-0.389012\pi\) | ||||
0.341656 | + | 0.939825i | \(0.389012\pi\) | |||||||
\(318\) | 3.21317 | 0.180186 | ||||||||
\(319\) | −9.43130 | −0.528051 | ||||||||
\(320\) | −5.21353 | −0.291445 | ||||||||
\(321\) | −3.77779 | −0.210856 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.7534 | 1.87809 | ||||||||
\(324\) | −1.90464 | −0.105814 | ||||||||
\(325\) | 27.8468 | 1.54466 | ||||||||
\(326\) | −7.29934 | −0.404273 | ||||||||
\(327\) | 5.31301 | 0.293810 | ||||||||
\(328\) | 1.20574 | 0.0665759 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.385613 | 0.0212273 | ||||||||
\(331\) | 2.91507 | 0.160227 | 0.0801135 | − | 0.996786i | \(-0.474472\pi\) | ||||
0.0801135 | + | 0.996786i | \(0.474472\pi\) | |||||||
\(332\) | −17.2372 | −0.946014 | ||||||||
\(333\) | 7.16373 | 0.392570 | ||||||||
\(334\) | 4.10976 | 0.224876 | ||||||||
\(335\) | −4.45654 | −0.243487 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6448 | 0.797753 | 0.398877 | − | 0.917005i | \(-0.369400\pi\) | ||||
0.398877 | + | 0.917005i | \(0.369400\pi\) | |||||||
\(338\) | −9.60926 | −0.522675 | ||||||||
\(339\) | 16.6298 | 0.903207 | ||||||||
\(340\) | 10.5648 | 0.572955 | ||||||||
\(341\) | 8.85815 | 0.479696 | ||||||||
\(342\) | 1.68863 | 0.0913106 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.23642 | −0.390162 | ||||||||
\(345\) | −4.28359 | −0.230621 | ||||||||
\(346\) | 2.15902 | 0.116070 | ||||||||
\(347\) | 26.4588 | 1.42039 | 0.710193 | − | 0.704007i | \(-0.248608\pi\) | ||||
0.710193 | + | 0.704007i | \(0.248608\pi\) | |||||||
\(348\) | −12.9269 | −0.692957 | ||||||||
\(349\) | −4.11366 | −0.220199 | −0.110099 | − | 0.993921i | \(-0.535117\pi\) | ||||
−0.110099 | + | 0.993921i | \(0.535117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.64217 | 0.354533 | ||||||||
\(352\) | −4.82581 | −0.257216 | ||||||||
\(353\) | 35.9977 | 1.91596 | 0.957982 | − | 0.286829i | \(-0.0926012\pi\) | ||||
0.957982 | + | 0.286829i | \(0.0926012\pi\) | |||||||
\(354\) | 1.39092 | 0.0739266 | ||||||||
\(355\) | 9.80563 | 0.520429 | ||||||||
\(356\) | −2.47507 | −0.131178 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.95385 | 0.103264 | ||||||||
\(359\) | −14.7022 | −0.775951 | −0.387976 | − | 0.921670i | \(-0.626826\pi\) | ||||
−0.387976 | + | 0.921670i | \(0.626826\pi\) | |||||||
\(360\) | 1.08354 | 0.0571074 | ||||||||
\(361\) | 10.9036 | 0.573874 | ||||||||
\(362\) | 2.14423 | 0.112698 | ||||||||
\(363\) | 9.06901 | 0.476000 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.92000 | −0.205182 | ||||||||
\(366\) | −4.11638 | −0.215167 | ||||||||
\(367\) | −4.99355 | −0.260661 | −0.130331 | − | 0.991471i | \(-0.541604\pi\) | ||||
−0.130331 | + | 0.991471i | \(0.541604\pi\) | |||||||
\(368\) | 16.3830 | 0.854022 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −1.98793 | −0.103348 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.1414 | 0.629500 | ||||||||
\(373\) | 26.6906 | 1.38199 | 0.690993 | − | 0.722862i | \(-0.257174\pi\) | ||||
0.690993 | + | 0.722862i | \(0.257174\pi\) | |||||||
\(374\) | 2.64861 | 0.136957 | ||||||||
\(375\) | 8.26076 | 0.426584 | ||||||||
\(376\) | −7.49888 | −0.386725 | ||||||||
\(377\) | 45.0808 | 2.32178 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.64461 | 0.0844778 | 0.0422389 | − | 0.999108i | \(-0.486551\pi\) | ||||
0.0422389 | + | 0.999108i | \(0.486551\pi\) | |||||||
\(380\) | 9.35977 | 0.480146 | ||||||||
\(381\) | 7.11991 | 0.364764 | ||||||||
\(382\) | −6.16968 | −0.315668 | ||||||||
\(383\) | −10.6131 | −0.542306 | −0.271153 | − | 0.962536i | \(-0.587405\pi\) | ||||
−0.271153 | + | 0.962536i | \(0.587405\pi\) | |||||||
\(384\) | −8.73710 | −0.445863 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.17840 | −0.161776 | ||||||||
\(387\) | −6.00164 | −0.305080 | ||||||||
\(388\) | 14.8822 | 0.755528 | ||||||||
\(389\) | 26.4309 | 1.34010 | 0.670049 | − | 0.742317i | \(-0.266273\pi\) | ||||
0.670049 | + | 0.742317i | \(0.266273\pi\) | |||||||
\(390\) | −1.84320 | −0.0933340 | ||||||||
\(391\) | −29.4222 | −1.48794 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.76987 | −0.0892783 | ||||||||
\(394\) | 8.51644 | 0.429052 | ||||||||
\(395\) | −7.76425 | −0.390662 | ||||||||
\(396\) | −2.64669 | −0.133001 | ||||||||
\(397\) | 14.6264 | 0.734080 | 0.367040 | − | 0.930205i | \(-0.380371\pi\) | ||||
0.367040 | + | 0.930205i | \(0.380371\pi\) | |||||||
\(398\) | 4.82078 | 0.241644 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.4092 | −0.720461 | ||||||||
\(401\) | −24.7129 | −1.23410 | −0.617051 | − | 0.786923i | \(-0.711673\pi\) | ||||
−0.617051 | + | 0.786923i | \(0.711673\pi\) | |||||||
\(402\) | −1.53137 | −0.0763778 | ||||||||
\(403\) | −42.3412 | −2.10917 | ||||||||
\(404\) | −23.9941 | −1.19375 | ||||||||
\(405\) | 0.898648 | 0.0446542 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.95472 | 0.493437 | ||||||||
\(408\) | 7.44236 | 0.368452 | ||||||||
\(409\) | −9.79226 | −0.484196 | −0.242098 | − | 0.970252i | \(-0.577836\pi\) | ||||
−0.242098 | + | 0.970252i | \(0.577836\pi\) | |||||||
\(410\) | −0.277499 | −0.0137047 | ||||||||
\(411\) | −16.2543 | −0.801764 | ||||||||
\(412\) | −35.2543 | −1.73686 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.47194 | −0.0723421 | ||||||||
\(415\) | 8.13284 | 0.399226 | ||||||||
\(416\) | 23.0670 | 1.13095 | ||||||||
\(417\) | 10.8156 | 0.529644 | ||||||||
\(418\) | 2.34652 | 0.114772 | ||||||||
\(419\) | −1.56318 | −0.0763662 | −0.0381831 | − | 0.999271i | \(-0.512157\pi\) | ||||
−0.0381831 | + | 0.999271i | \(0.512157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0323 | −1.22000 | −0.610000 | − | 0.792401i | \(-0.708831\pi\) | ||||
−0.610000 | + | 0.792401i | \(0.708831\pi\) | |||||||
\(422\) | −6.32578 | −0.307934 | ||||||||
\(423\) | −6.21931 | −0.302393 | ||||||||
\(424\) | 12.5463 | 0.609302 | ||||||||
\(425\) | 25.8775 | 1.25524 | ||||||||
\(426\) | 3.36945 | 0.163250 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.19536 | −0.347801 | ||||||||
\(429\) | 9.22996 | 0.445626 | ||||||||
\(430\) | 1.66545 | 0.0803152 | ||||||||
\(431\) | 12.4377 | 0.599101 | 0.299550 | − | 0.954081i | \(-0.403163\pi\) | ||||
0.299550 | + | 0.954081i | \(0.403163\pi\) | |||||||
\(432\) | −3.43696 | −0.165361 | ||||||||
\(433\) | 0.0273710 | 0.00131537 | 0.000657683 | − | 1.00000i | \(-0.499791\pi\) | ||||
0.000657683 | 1.00000i | \(0.499791\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.09918 | 0.292433 | ||||||||
\(436\) | 10.1194 | 0.484631 | ||||||||
\(437\) | −26.0664 | −1.24692 | ||||||||
\(438\) | −1.34701 | −0.0643624 | ||||||||
\(439\) | 33.9319 | 1.61948 | 0.809740 | − | 0.586789i | \(-0.199608\pi\) | ||||
0.809740 | + | 0.586789i | \(0.199608\pi\) | |||||||
\(440\) | 1.50568 | 0.0717806 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.6602 | −0.602182 | ||||||||
\(443\) | 19.8639 | 0.943760 | 0.471880 | − | 0.881663i | \(-0.343575\pi\) | ||||
0.471880 | + | 0.881663i | \(0.343575\pi\) | |||||||
\(444\) | 13.6444 | 0.647533 | ||||||||
\(445\) | 1.16779 | 0.0553583 | ||||||||
\(446\) | −4.85822 | −0.230043 | ||||||||
\(447\) | −6.94118 | −0.328307 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0360 | 0.662399 | 0.331200 | − | 0.943561i | \(-0.392547\pi\) | ||||
0.331200 | + | 0.943561i | \(0.392547\pi\) | |||||||
\(450\) | 1.29461 | 0.0610285 | ||||||||
\(451\) | 1.38960 | 0.0654337 | ||||||||
\(452\) | 31.6739 | 1.48981 | ||||||||
\(453\) | 15.9874 | 0.751152 | ||||||||
\(454\) | −4.57890 | −0.214899 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.59350 | 0.308769 | ||||||||
\(457\) | 23.3867 | 1.09399 | 0.546993 | − | 0.837137i | \(-0.315773\pi\) | ||||
0.546993 | + | 0.837137i | \(0.315773\pi\) | |||||||
\(458\) | −2.22617 | −0.104022 | ||||||||
\(459\) | 6.17243 | 0.288104 | ||||||||
\(460\) | −8.15872 | −0.380402 | ||||||||
\(461\) | −23.2004 | −1.08055 | −0.540275 | − | 0.841488i | \(-0.681680\pi\) | ||||
−0.540275 | + | 0.841488i | \(0.681680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.4318 | −0.670702 | −0.335351 | − | 0.942093i | \(-0.608855\pi\) | ||||
−0.335351 | + | 0.942093i | \(0.608855\pi\) | |||||||
\(464\) | −23.3269 | −1.08292 | ||||||||
\(465\) | −5.72853 | −0.265654 | ||||||||
\(466\) | −1.23569 | −0.0572423 | ||||||||
\(467\) | 21.6092 | 0.999955 | 0.499977 | − | 0.866039i | \(-0.333342\pi\) | ||||
0.499977 | + | 0.866039i | \(0.333342\pi\) | |||||||
\(468\) | 12.6510 | 0.584791 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.72586 | 0.0796078 | ||||||||
\(471\) | −7.87899 | −0.363045 | ||||||||
\(472\) | 5.43105 | 0.249984 | ||||||||
\(473\) | −8.33987 | −0.383468 | ||||||||
\(474\) | −2.66798 | −0.122544 | ||||||||
\(475\) | 22.9260 | 1.05192 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4055 | 0.476433 | ||||||||
\(478\) | −0.817669 | −0.0373993 | ||||||||
\(479\) | 6.91726 | 0.316057 | 0.158029 | − | 0.987435i | \(-0.449486\pi\) | ||||
0.158029 | + | 0.987435i | \(0.449486\pi\) | |||||||
\(480\) | 3.12083 | 0.142446 | ||||||||
\(481\) | −47.5827 | −2.16959 | ||||||||
\(482\) | 2.99175 | 0.136270 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.2732 | 0.785148 | ||||||||
\(485\) | −7.02169 | −0.318839 | ||||||||
\(486\) | 0.308797 | 0.0140073 | ||||||||
\(487\) | 15.0820 | 0.683430 | 0.341715 | − | 0.939804i | \(-0.388992\pi\) | ||||
0.341715 | + | 0.939804i | \(0.388992\pi\) | |||||||
\(488\) | −16.0730 | −0.727591 | ||||||||
\(489\) | −23.6380 | −1.06895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.3627 | 1.09948 | 0.549738 | − | 0.835337i | \(-0.314728\pi\) | ||||
0.549738 | + | 0.835337i | \(0.314728\pi\) | |||||||
\(492\) | 1.90464 | 0.0858680 | ||||||||
\(493\) | 41.8927 | 1.88675 | ||||||||
\(494\) | −11.2162 | −0.504639 | ||||||||
\(495\) | 1.24876 | 0.0561276 | ||||||||
\(496\) | 21.9093 | 0.983755 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.79464 | 0.125231 | ||||||||
\(499\) | 1.21709 | 0.0544843 | 0.0272421 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272421 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(500\) | 15.7338 | 0.703637 | ||||||||
\(501\) | 13.3089 | 0.594599 | ||||||||
\(502\) | 6.57201 | 0.293323 | ||||||||
\(503\) | −37.9289 | −1.69117 | −0.845583 | − | 0.533845i | \(-0.820747\pi\) | ||||
−0.845583 | + | 0.533845i | \(0.820747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.3209 | 0.503773 | ||||||||
\(506\) | −2.04541 | −0.0909297 | ||||||||
\(507\) | −31.1184 | −1.38202 | ||||||||
\(508\) | 13.5609 | 0.601668 | ||||||||
\(509\) | −27.0118 | −1.19728 | −0.598638 | − | 0.801020i | \(-0.704291\pi\) | ||||
−0.598638 | + | 0.801020i | \(0.704291\pi\) | |||||||
\(510\) | −1.71285 | −0.0758461 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.2241 | −0.893786 | ||||||||
\(513\) | 5.46842 | 0.241437 | ||||||||
\(514\) | 8.72277 | 0.384745 | ||||||||
\(515\) | 16.6337 | 0.732967 | ||||||||
\(516\) | −11.4310 | −0.503221 | ||||||||
\(517\) | −8.64235 | −0.380090 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.99173 | 0.306903 | ||||||||
\(520\) | −7.19704 | −0.315611 | ||||||||
\(521\) | −41.0082 | −1.79660 | −0.898300 | − | 0.439383i | \(-0.855197\pi\) | ||||
−0.898300 | + | 0.439383i | \(0.855197\pi\) | |||||||
\(522\) | 2.09582 | 0.0917316 | ||||||||
\(523\) | 37.2325 | 1.62807 | 0.814033 | − | 0.580819i | \(-0.197268\pi\) | ||||
0.814033 | + | 0.580819i | \(0.197268\pi\) | |||||||
\(524\) | −3.37098 | −0.147262 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.75311 | 0.0764392 | ||||||||
\(527\) | −39.3468 | −1.71397 | ||||||||
\(528\) | −4.77600 | −0.207849 | ||||||||
\(529\) | −0.278497 | −0.0121086 | ||||||||
\(530\) | −2.88751 | −0.125425 | ||||||||
\(531\) | 4.50432 | 0.195471 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.64217 | −0.287704 | ||||||||
\(534\) | 0.401279 | 0.0173650 | ||||||||
\(535\) | 3.39491 | 0.146775 | ||||||||
\(536\) | −5.97946 | −0.258273 | ||||||||
\(537\) | 6.32731 | 0.273044 | ||||||||
\(538\) | −0.143664 | −0.00619381 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.71160 | 0.0736557 | ||||||||
\(541\) | −18.6657 | −0.802500 | −0.401250 | − | 0.915969i | \(-0.631424\pi\) | ||||
−0.401250 | + | 0.915969i | \(0.631424\pi\) | |||||||
\(542\) | −2.62987 | −0.112963 | ||||||||
\(543\) | 6.94382 | 0.297988 | ||||||||
\(544\) | 21.4357 | 0.919046 | ||||||||
\(545\) | −4.77452 | −0.204518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.4706 | 0.960775 | 0.480388 | − | 0.877056i | \(-0.340496\pi\) | ||||
0.480388 | + | 0.877056i | \(0.340496\pi\) | |||||||
\(548\) | −30.9586 | −1.32249 | ||||||||
\(549\) | −13.3304 | −0.568927 | ||||||||
\(550\) | 1.79899 | 0.0767091 | ||||||||
\(551\) | 37.1145 | 1.58113 | ||||||||
\(552\) | −5.74742 | −0.244626 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.280781 | 0.0119293 | ||||||||
\(555\) | −6.43767 | −0.273264 | ||||||||
\(556\) | 20.5999 | 0.873632 | ||||||||
\(557\) | 1.44517 | 0.0612339 | 0.0306170 | − | 0.999531i | \(-0.490253\pi\) | ||||
0.0306170 | + | 0.999531i | \(0.490253\pi\) | |||||||
\(558\) | −1.96846 | −0.0833314 | ||||||||
\(559\) | 39.8639 | 1.68606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.57721 | 0.362130 | ||||||||
\(562\) | −7.61060 | −0.321034 | ||||||||
\(563\) | 33.4355 | 1.40914 | 0.704568 | − | 0.709636i | \(-0.251141\pi\) | ||||
0.704568 | + | 0.709636i | \(0.251141\pi\) | |||||||
\(564\) | −11.8456 | −0.498789 | ||||||||
\(565\) | −14.9443 | −0.628713 | ||||||||
\(566\) | −8.36238 | −0.351497 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.1565 | 0.552034 | ||||||||
\(569\) | 32.2954 | 1.35389 | 0.676946 | − | 0.736033i | \(-0.263303\pi\) | ||||
0.676946 | + | 0.736033i | \(0.263303\pi\) | |||||||
\(570\) | −1.51748 | −0.0635604 | ||||||||
\(571\) | −23.7959 | −0.995829 | −0.497915 | − | 0.867226i | \(-0.665901\pi\) | ||||
−0.497915 | + | 0.867226i | \(0.665901\pi\) | |||||||
\(572\) | 17.5798 | 0.735048 | ||||||||
\(573\) | −19.9797 | −0.834666 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.9841 | −0.833394 | ||||||||
\(576\) | −5.80153 | −0.241730 | ||||||||
\(577\) | −14.7145 | −0.612574 | −0.306287 | − | 0.951939i | \(-0.599087\pi\) | ||||
−0.306287 | + | 0.951939i | \(0.599087\pi\) | |||||||
\(578\) | −6.51528 | −0.271000 | ||||||||
\(579\) | −10.2929 | −0.427757 | ||||||||
\(580\) | 11.6168 | 0.482360 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.41282 | −0.100015 | ||||||||
\(583\) | 14.4594 | 0.598848 | ||||||||
\(584\) | −5.25958 | −0.217643 | ||||||||
\(585\) | −5.96897 | −0.246787 | ||||||||
\(586\) | −9.62980 | −0.397803 | ||||||||
\(587\) | −3.04010 | −0.125479 | −0.0627393 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627393 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.8590 | −1.43634 | ||||||||
\(590\) | −1.24995 | −0.0514595 | ||||||||
\(591\) | 27.5794 | 1.13447 | ||||||||
\(592\) | 24.6215 | 1.01194 | ||||||||
\(593\) | 42.2287 | 1.73413 | 0.867063 | − | 0.498198i | \(-0.166005\pi\) | ||||
0.867063 | + | 0.498198i | \(0.166005\pi\) | |||||||
\(594\) | 0.429104 | 0.0176063 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.2205 | −0.541532 | ||||||||
\(597\) | 15.6115 | 0.638936 | ||||||||
\(598\) | 9.77690 | 0.399807 | ||||||||
\(599\) | −41.9943 | −1.71584 | −0.857920 | − | 0.513783i | \(-0.828243\pi\) | ||||
−0.857920 | + | 0.513783i | \(0.828243\pi\) | |||||||
\(600\) | 5.05499 | 0.206369 | ||||||||
\(601\) | 29.4544 | 1.20147 | 0.600735 | − | 0.799448i | \(-0.294875\pi\) | ||||
0.600735 | + | 0.799448i | \(0.294875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.95916 | −0.201952 | ||||||||
\(604\) | 30.4502 | 1.23900 | ||||||||
\(605\) | −8.14985 | −0.331339 | ||||||||
\(606\) | 3.89013 | 0.158026 | ||||||||
\(607\) | −20.7083 | −0.840526 | −0.420263 | − | 0.907402i | \(-0.638062\pi\) | ||||
−0.420263 | + | 0.907402i | \(0.638062\pi\) | |||||||
\(608\) | 18.9907 | 0.770177 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.69918 | 0.149775 | ||||||||
\(611\) | 41.3097 | 1.67121 | ||||||||
\(612\) | 11.7563 | 0.475220 | ||||||||
\(613\) | −41.4706 | −1.67498 | −0.837491 | − | 0.546451i | \(-0.815978\pi\) | ||||
−0.837491 | + | 0.546451i | \(0.815978\pi\) | |||||||
\(614\) | −7.80847 | −0.315124 | ||||||||
\(615\) | −0.898648 | −0.0362370 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.76644 | 0.111373 | 0.0556863 | − | 0.998448i | \(-0.482265\pi\) | ||||
0.0556863 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(618\) | 5.71573 | 0.229920 | ||||||||
\(619\) | 0.990969 | 0.0398304 | 0.0199152 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199152 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(620\) | −10.9108 | −0.438189 | ||||||||
\(621\) | −4.76671 | −0.191281 | ||||||||
\(622\) | −2.73435 | −0.109638 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 22.8289 | 0.913886 | ||||||||
\(625\) | 13.5386 | 0.541546 | ||||||||
\(626\) | −1.11789 | −0.0446799 | ||||||||
\(627\) | 7.59891 | 0.303471 | ||||||||
\(628\) | −15.0067 | −0.598832 | ||||||||
\(629\) | −44.2177 | −1.76307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.46880 | −0.177900 | −0.0889500 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889500 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(632\) | −10.4175 | −0.414386 | ||||||||
\(633\) | −20.4853 | −0.814217 | ||||||||
\(634\) | −3.75683 | −0.149203 | ||||||||
\(635\) | −6.39830 | −0.253909 | ||||||||
\(636\) | 19.8187 | 0.785862 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.91235 | 0.115301 | ||||||||
\(639\) | 10.9115 | 0.431654 | ||||||||
\(640\) | 7.85158 | 0.310361 | ||||||||
\(641\) | −30.9202 | −1.22127 | −0.610637 | − | 0.791911i | \(-0.709086\pi\) | ||||
−0.610637 | + | 0.791911i | \(0.709086\pi\) | |||||||
\(642\) | 1.16657 | 0.0460409 | ||||||||
\(643\) | −9.54896 | −0.376574 | −0.188287 | − | 0.982114i | \(-0.560294\pi\) | ||||
−0.188287 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.39336 | 0.212363 | ||||||||
\(646\) | −10.4230 | −0.410086 | ||||||||
\(647\) | −38.0623 | −1.49638 | −0.748191 | − | 0.663484i | \(-0.769077\pi\) | ||||
−0.748191 | + | 0.663484i | \(0.769077\pi\) | |||||||
\(648\) | 1.20574 | 0.0473660 | ||||||||
\(649\) | 6.25921 | 0.245695 | ||||||||
\(650\) | −8.59901 | −0.337281 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −45.0220 | −1.76320 | ||||||||
\(653\) | 27.2830 | 1.06767 | 0.533833 | − | 0.845590i | \(-0.320751\pi\) | ||||
0.533833 | + | 0.845590i | \(0.320751\pi\) | |||||||
\(654\) | −1.64064 | −0.0641540 | ||||||||
\(655\) | 1.59049 | 0.0621457 | ||||||||
\(656\) | 3.43696 | 0.134191 | ||||||||
\(657\) | −4.36211 | −0.170182 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.31532 | −0.362873 | −0.181437 | − | 0.983403i | \(-0.558075\pi\) | ||||
−0.181437 | + | 0.983403i | \(0.558075\pi\) | |||||||
\(660\) | 2.37845 | 0.0925809 | ||||||||
\(661\) | 14.6419 | 0.569502 | 0.284751 | − | 0.958601i | \(-0.408089\pi\) | ||||
0.284751 | + | 0.958601i | \(0.408089\pi\) | |||||||
\(662\) | −0.900165 | −0.0349859 | ||||||||
\(663\) | −40.9983 | −1.59224 | ||||||||
\(664\) | 10.9121 | 0.423470 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.21214 | −0.0857186 | ||||||||
\(667\) | −32.3519 | −1.25267 | ||||||||
\(668\) | 25.3488 | 0.980774 | ||||||||
\(669\) | −15.7327 | −0.608263 | ||||||||
\(670\) | 1.37616 | 0.0531658 | ||||||||
\(671\) | −18.5239 | −0.715107 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.2730 | −1.08984 | −0.544921 | − | 0.838487i | \(-0.683441\pi\) | ||||
−0.544921 | + | 0.838487i | \(0.683441\pi\) | |||||||
\(674\) | −4.52227 | −0.174191 | ||||||||
\(675\) | 4.19243 | 0.161367 | ||||||||
\(676\) | −59.2695 | −2.27960 | ||||||||
\(677\) | 25.4582 | 0.978437 | 0.489218 | − | 0.872161i | \(-0.337282\pi\) | ||||
0.489218 | + | 0.872161i | \(0.337282\pi\) | |||||||
\(678\) | −5.13523 | −0.197217 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.68806 | −0.256475 | ||||||||
\(681\) | −14.8282 | −0.568219 | ||||||||
\(682\) | −2.73537 | −0.104743 | ||||||||
\(683\) | −51.8529 | −1.98410 | −0.992048 | − | 0.125861i | \(-0.959831\pi\) | ||||
−0.992048 | + | 0.125861i | \(0.959831\pi\) | |||||||
\(684\) | 10.4154 | 0.398243 | ||||||||
\(685\) | 14.6069 | 0.558099 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.20918 | −0.275048 | ||||||||
\(688\) | −20.6274 | −0.786412 | ||||||||
\(689\) | −69.1148 | −2.63306 | ||||||||
\(690\) | 1.32276 | 0.0503566 | ||||||||
\(691\) | 47.1718 | 1.79450 | 0.897249 | − | 0.441524i | \(-0.145562\pi\) | ||||
0.897249 | + | 0.441524i | \(0.145562\pi\) | |||||||
\(692\) | 13.3168 | 0.506227 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.17040 | −0.310144 | ||||||||
\(695\) | −9.71944 | −0.368679 | ||||||||
\(696\) | 8.18344 | 0.310193 | ||||||||
\(697\) | −6.17243 | −0.233798 | ||||||||
\(698\) | 1.27028 | 0.0480809 | ||||||||
\(699\) | −4.00163 | −0.151356 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.7588 | 1.50167 | 0.750834 | − | 0.660491i | \(-0.229652\pi\) | ||||
0.750834 | + | 0.660491i | \(0.229652\pi\) | |||||||
\(702\) | −2.05108 | −0.0774130 | ||||||||
\(703\) | −39.1743 | −1.47749 | ||||||||
\(704\) | −8.06180 | −0.303841 | ||||||||
\(705\) | 5.58897 | 0.210493 | ||||||||
\(706\) | −11.1160 | −0.418355 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.57914 | 0.322424 | ||||||||
\(709\) | −11.4500 | −0.430016 | −0.215008 | − | 0.976612i | \(-0.568978\pi\) | ||||
−0.215008 | + | 0.976612i | \(0.568978\pi\) | |||||||
\(710\) | −3.02795 | −0.113637 | ||||||||
\(711\) | −8.63992 | −0.324022 | ||||||||
\(712\) | 1.56685 | 0.0587202 | ||||||||
\(713\) | 30.3859 | 1.13796 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.29448 | −0.310196 | ||||||||
\(716\) | 12.0513 | 0.450377 | ||||||||
\(717\) | −2.64792 | −0.0988884 | ||||||||
\(718\) | 4.53998 | 0.169431 | ||||||||
\(719\) | −42.0567 | −1.56845 | −0.784226 | − | 0.620476i | \(-0.786940\pi\) | ||||
−0.784226 | + | 0.620476i | \(0.786940\pi\) | |||||||
\(720\) | 3.08862 | 0.115106 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.36700 | −0.125307 | ||||||||
\(723\) | 9.68840 | 0.360315 | ||||||||
\(724\) | 13.2255 | 0.491522 | ||||||||
\(725\) | 28.4543 | 1.05677 | ||||||||
\(726\) | −2.80048 | −0.103936 | ||||||||
\(727\) | 24.0062 | 0.890342 | 0.445171 | − | 0.895446i | \(-0.353143\pi\) | ||||
0.445171 | + | 0.895446i | \(0.353143\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.21048 | 0.0448020 | ||||||||
\(731\) | 37.0447 | 1.37015 | ||||||||
\(732\) | −25.3897 | −0.938429 | ||||||||
\(733\) | 45.8010 | 1.69170 | 0.845849 | − | 0.533423i | \(-0.179095\pi\) | ||||
0.845849 | + | 0.533423i | \(0.179095\pi\) | |||||||
\(734\) | 1.54199 | 0.0569159 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.5538 | −0.610183 | ||||||||
\(737\) | −6.89124 | −0.253842 | ||||||||
\(738\) | −0.308797 | −0.0113670 | ||||||||
\(739\) | 27.6295 | 1.01637 | 0.508184 | − | 0.861248i | \(-0.330317\pi\) | ||||
0.508184 | + | 0.861248i | \(0.330317\pi\) | |||||||
\(740\) | −12.2615 | −0.450741 | ||||||||
\(741\) | −36.3222 | −1.33433 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.43601 | −0.199428 | −0.0997139 | − | 0.995016i | \(-0.531793\pi\) | ||||
−0.0997139 | + | 0.995016i | \(0.531793\pi\) | |||||||
\(744\) | −7.68613 | −0.281787 | ||||||||
\(745\) | 6.23768 | 0.228531 | ||||||||
\(746\) | −8.24196 | −0.301760 | ||||||||
\(747\) | 9.05009 | 0.331125 | ||||||||
\(748\) | 16.3365 | 0.597323 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.55090 | −0.0931455 | ||||||||
\(751\) | 2.55797 | 0.0933416 | 0.0466708 | − | 0.998910i | \(-0.485139\pi\) | ||||
0.0466708 | + | 0.998910i | \(0.485139\pi\) | |||||||
\(752\) | −21.3755 | −0.779485 | ||||||||
\(753\) | 21.2826 | 0.775582 | ||||||||
\(754\) | −13.9208 | −0.506966 | ||||||||
\(755\) | −14.3670 | −0.522869 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.4360 | 0.488339 | 0.244170 | − | 0.969733i | \(-0.421485\pi\) | ||||
0.244170 | + | 0.969733i | \(0.421485\pi\) | |||||||
\(758\) | −0.507849 | −0.0184459 | ||||||||
\(759\) | −6.62381 | −0.240429 | ||||||||
\(760\) | −5.92523 | −0.214931 | ||||||||
\(761\) | −19.8756 | −0.720489 | −0.360245 | − | 0.932858i | \(-0.617307\pi\) | ||||
−0.360245 | + | 0.932858i | \(0.617307\pi\) | |||||||
\(762\) | −2.19861 | −0.0796471 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −38.0543 | −1.37676 | ||||||||
\(765\) | −5.54684 | −0.200547 | ||||||||
\(766\) | 3.27730 | 0.118414 | ||||||||
\(767\) | −29.9185 | −1.08029 | ||||||||
\(768\) | −8.90507 | −0.321334 | ||||||||
\(769\) | 54.3254 | 1.95902 | 0.979512 | − | 0.201384i | \(-0.0645441\pi\) | ||||
0.979512 | + | 0.201384i | \(0.0645441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.2476 | 1.01731 | ||||||||
\(772\) | −19.6043 | −0.705572 | ||||||||
\(773\) | −23.4861 | −0.844737 | −0.422368 | − | 0.906424i | \(-0.638801\pi\) | ||||
−0.422368 | + | 0.906424i | \(0.638801\pi\) | |||||||
\(774\) | 1.85329 | 0.0666150 | ||||||||
\(775\) | −26.7251 | −0.959994 | ||||||||
\(776\) | −9.42121 | −0.338202 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.16176 | −0.292613 | ||||||||
\(779\) | −5.46842 | −0.195926 | ||||||||
\(780\) | −11.3688 | −0.407067 | ||||||||
\(781\) | 15.1627 | 0.542563 | ||||||||
\(782\) | 9.08547 | 0.324896 | ||||||||
\(783\) | 6.78706 | 0.242550 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.08044 | 0.252712 | ||||||||
\(786\) | 0.546531 | 0.0194941 | ||||||||
\(787\) | −21.1427 | −0.753655 | −0.376828 | − | 0.926283i | \(-0.622985\pi\) | ||||
−0.376828 | + | 0.926283i | \(0.622985\pi\) | |||||||
\(788\) | 52.5290 | 1.87127 | ||||||||
\(789\) | 5.67723 | 0.202115 | ||||||||
\(790\) | 2.39757 | 0.0853018 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.67550 | 0.0595362 | ||||||||
\(793\) | 88.5427 | 3.14424 | ||||||||
\(794\) | −4.51660 | −0.160288 | ||||||||
\(795\) | −9.35084 | −0.331640 | ||||||||
\(796\) | 29.7343 | 1.05391 | ||||||||
\(797\) | −31.1992 | −1.10513 | −0.552566 | − | 0.833469i | \(-0.686351\pi\) | ||||
−0.552566 | + | 0.833469i | \(0.686351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.3883 | 1.35808 | ||||||||
\(800\) | 14.5595 | 0.514756 | ||||||||
\(801\) | 1.29949 | 0.0459153 | ||||||||
\(802\) | 7.63126 | 0.269469 | ||||||||
\(803\) | −6.06159 | −0.213909 | ||||||||
\(804\) | −9.44543 | −0.333115 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.0748 | 0.460541 | ||||||||
\(807\) | −0.465240 | −0.0163772 | ||||||||
\(808\) | 15.1896 | 0.534367 | ||||||||
\(809\) | −15.7021 | −0.552058 | −0.276029 | − | 0.961149i | \(-0.589019\pi\) | ||||
−0.276029 | + | 0.961149i | \(0.589019\pi\) | |||||||
\(810\) | −0.277499 | −0.00975034 | ||||||||
\(811\) | −23.2522 | −0.816496 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.51652 | −0.298687 | ||||||||
\(814\) | −3.07398 | −0.107743 | ||||||||
\(815\) | 21.2422 | 0.744083 | ||||||||
\(816\) | 21.2144 | 0.742653 | ||||||||
\(817\) | 32.8195 | 1.14821 | ||||||||
\(818\) | 3.02382 | 0.105725 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.71160 | −0.0597718 | ||||||||
\(821\) | 51.4928 | 1.79711 | 0.898555 | − | 0.438861i | \(-0.144618\pi\) | ||||
0.898555 | + | 0.438861i | \(0.144618\pi\) | |||||||
\(822\) | 5.01926 | 0.175067 | ||||||||
\(823\) | −7.46987 | −0.260383 | −0.130192 | − | 0.991489i | \(-0.541559\pi\) | ||||
−0.130192 | + | 0.991489i | \(0.541559\pi\) | |||||||
\(824\) | 22.3179 | 0.777480 | ||||||||
\(825\) | 5.82580 | 0.202828 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.08519 | −0.0725090 | −0.0362545 | − | 0.999343i | \(-0.511543\pi\) | ||||
−0.0362545 | + | 0.999343i | \(0.511543\pi\) | |||||||
\(828\) | −9.07888 | −0.315513 | ||||||||
\(829\) | 35.6611 | 1.23856 | 0.619280 | − | 0.785170i | \(-0.287425\pi\) | ||||
0.619280 | + | 0.785170i | \(0.287425\pi\) | |||||||
\(830\) | −2.51140 | −0.0871718 | ||||||||
\(831\) | 0.909276 | 0.0315424 | ||||||||
\(832\) | 38.5347 | 1.33595 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.33983 | −0.115649 | ||||||||
\(835\) | −11.9600 | −0.413895 | ||||||||
\(836\) | 14.4732 | 0.500567 | ||||||||
\(837\) | −6.37461 | −0.220339 | ||||||||
\(838\) | 0.482704 | 0.0166747 | ||||||||
\(839\) | −28.7416 | −0.992271 | −0.496136 | − | 0.868245i | \(-0.665248\pi\) | ||||
−0.496136 | + | 0.868245i | \(0.665248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0642 | 0.588421 | ||||||||
\(842\) | 7.72989 | 0.266390 | ||||||||
\(843\) | −24.6460 | −0.848853 | ||||||||
\(844\) | −39.0172 | −1.34303 | ||||||||
\(845\) | 27.9645 | 0.962008 | ||||||||
\(846\) | 1.92050 | 0.0660282 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 35.7631 | 1.22811 | ||||||||
\(849\) | −27.0805 | −0.929402 | ||||||||
\(850\) | −7.99089 | −0.274085 | ||||||||
\(851\) | 34.1474 | 1.17056 | ||||||||
\(852\) | 20.7826 | 0.712000 | ||||||||
\(853\) | 10.3798 | 0.355399 | 0.177700 | − | 0.984085i | \(-0.443134\pi\) | ||||
0.177700 | + | 0.984085i | \(0.443134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.91418 | −0.168061 | ||||||||
\(856\) | 4.55504 | 0.155688 | ||||||||
\(857\) | 17.1959 | 0.587400 | 0.293700 | − | 0.955898i | \(-0.405113\pi\) | ||||
0.293700 | + | 0.955898i | \(0.405113\pi\) | |||||||
\(858\) | −2.85018 | −0.0973035 | ||||||||
\(859\) | 20.5963 | 0.702738 | 0.351369 | − | 0.936237i | \(-0.385716\pi\) | ||||
0.351369 | + | 0.936237i | \(0.385716\pi\) | |||||||
\(860\) | 10.2724 | 0.350287 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.84071 | −0.130815 | ||||||||
\(863\) | −3.01849 | −0.102750 | −0.0513752 | − | 0.998679i | \(-0.516360\pi\) | ||||
−0.0513752 | + | 0.998679i | \(0.516360\pi\) | |||||||
\(864\) | 3.47280 | 0.118147 | ||||||||
\(865\) | −6.28310 | −0.213632 | ||||||||
\(866\) | −0.00845207 | −0.000287213 0 | ||||||||
\(867\) | −21.0989 | −0.716557 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0060 | −0.407277 | ||||||||
\(870\) | −1.88341 | −0.0638535 | ||||||||
\(871\) | 32.9396 | 1.11611 | ||||||||
\(872\) | −6.40611 | −0.216938 | ||||||||
\(873\) | −7.81362 | −0.264451 | ||||||||
\(874\) | 8.04920 | 0.272268 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.30827 | −0.280711 | ||||||||
\(877\) | 14.5978 | 0.492933 | 0.246466 | − | 0.969151i | \(-0.420731\pi\) | ||||
0.246466 | + | 0.969151i | \(0.420731\pi\) | |||||||
\(878\) | −10.4780 | −0.353617 | ||||||||
\(879\) | −31.1849 | −1.05184 | ||||||||
\(880\) | 4.29194 | 0.144681 | ||||||||
\(881\) | −8.66646 | −0.291981 | −0.145990 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145990 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.6380 | −0.425304 | −0.212652 | − | 0.977128i | \(-0.568210\pi\) | ||||
−0.212652 | + | 0.977128i | \(0.568210\pi\) | |||||||
\(884\) | −78.0873 | −2.62636 | ||||||||
\(885\) | −4.04780 | −0.136065 | ||||||||
\(886\) | −6.13389 | −0.206072 | ||||||||
\(887\) | −21.8225 | −0.732729 | −0.366364 | − | 0.930472i | \(-0.619398\pi\) | ||||
−0.366364 | + | 0.930472i | \(0.619398\pi\) | |||||||
\(888\) | −8.63761 | −0.289859 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.360608 | −0.0120876 | ||||||||
\(891\) | 1.38960 | 0.0465533 | ||||||||
\(892\) | −29.9653 | −1.00331 | ||||||||
\(893\) | 34.0098 | 1.13809 | ||||||||
\(894\) | 2.14341 | 0.0716865 | ||||||||
\(895\) | −5.68602 | −0.190063 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.6613 | 1.05714 | ||||||||
\(898\) | −4.33427 | −0.144636 | ||||||||
\(899\) | −43.2648 | −1.44296 | ||||||||
\(900\) | 7.98509 | 0.266170 | ||||||||
\(901\) | −64.2270 | −2.13971 | ||||||||
\(902\) | −0.429104 | −0.0142876 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.0512 | −0.666894 | ||||||||
\(905\) | −6.24005 | −0.207426 | ||||||||
\(906\) | −4.93684 | −0.164016 | ||||||||
\(907\) | 8.54997 | 0.283897 | 0.141949 | − | 0.989874i | \(-0.454663\pi\) | ||||
0.141949 | + | 0.989874i | \(0.454663\pi\) | |||||||
\(908\) | −28.2425 | −0.937260 | ||||||||
\(909\) | 12.5977 | 0.417839 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.92067 | −0.163029 | −0.0815145 | − | 0.996672i | \(-0.525976\pi\) | ||||
−0.0815145 | + | 0.996672i | \(0.525976\pi\) | |||||||
\(912\) | 18.7947 | 0.622356 | ||||||||
\(913\) | 12.5760 | 0.416205 | ||||||||
\(914\) | −7.22175 | −0.238874 | ||||||||
\(915\) | 11.9793 | 0.396024 | ||||||||
\(916\) | −13.7309 | −0.453683 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.90603 | −0.0629083 | ||||||||
\(919\) | −54.5333 | −1.79889 | −0.899444 | − | 0.437037i | \(-0.856028\pi\) | ||||
−0.899444 | + | 0.437037i | \(0.856028\pi\) | |||||||
\(920\) | 5.16490 | 0.170282 | ||||||||
\(921\) | −25.2868 | −0.833228 | ||||||||
\(922\) | 7.16420 | 0.235941 | ||||||||
\(923\) | −72.4763 | −2.38559 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.0335 | −0.987494 | ||||||||
\(926\) | 4.45649 | 0.146449 | ||||||||
\(927\) | 18.5097 | 0.607937 | ||||||||
\(928\) | 23.5701 | 0.773728 | ||||||||
\(929\) | −2.13381 | −0.0700080 | −0.0350040 | − | 0.999387i | \(-0.511144\pi\) | ||||
−0.0350040 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(930\) | 1.76895 | 0.0580062 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.62169 | −0.249657 | ||||||||
\(933\) | −8.85487 | −0.289895 | ||||||||
\(934\) | −6.67285 | −0.218342 | ||||||||
\(935\) | −7.70789 | −0.252075 | ||||||||
\(936\) | −8.00874 | −0.261774 | ||||||||
\(937\) | 6.22159 | 0.203250 | 0.101625 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101625 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.62015 | −0.118139 | ||||||||
\(940\) | 10.6450 | 0.347202 | ||||||||
\(941\) | −10.0787 | −0.328555 | −0.164278 | − | 0.986414i | \(-0.552529\pi\) | ||||
−0.164278 | + | 0.986414i | \(0.552529\pi\) | |||||||
\(942\) | 2.43301 | 0.0792716 | ||||||||
\(943\) | 4.76671 | 0.155225 | ||||||||
\(944\) | 15.4812 | 0.503870 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.57532 | 0.0837310 | ||||||||
\(947\) | −46.3131 | −1.50497 | −0.752486 | − | 0.658608i | \(-0.771146\pi\) | ||||
−0.752486 | + | 0.658608i | \(0.771146\pi\) | |||||||
\(948\) | −16.4560 | −0.534465 | ||||||||
\(949\) | 28.9739 | 0.940532 | ||||||||
\(950\) | −7.07946 | −0.229688 | ||||||||
\(951\) | −12.1660 | −0.394510 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.1172 | 0.651659 | 0.325829 | − | 0.945429i | \(-0.394356\pi\) | ||||
0.325829 | + | 0.945429i | \(0.394356\pi\) | |||||||
\(954\) | −3.21317 | −0.104030 | ||||||||
\(955\) | 17.9548 | 0.581002 | ||||||||
\(956\) | −5.04335 | −0.163114 | ||||||||
\(957\) | 9.43130 | 0.304871 | ||||||||
\(958\) | −2.13603 | −0.0690119 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.21353 | 0.168266 | ||||||||
\(961\) | 9.63561 | 0.310826 | ||||||||
\(962\) | 14.6934 | 0.473734 | ||||||||
\(963\) | 3.77779 | 0.121738 | ||||||||
\(964\) | 18.4530 | 0.594330 | ||||||||
\(965\) | 9.24966 | 0.297757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.4719 | −1.10854 | −0.554271 | − | 0.832336i | \(-0.687003\pi\) | ||||
−0.554271 | + | 0.832336i | \(0.687003\pi\) | |||||||
\(968\) | −10.9349 | −0.351460 | ||||||||
\(969\) | −33.7534 | −1.08432 | ||||||||
\(970\) | 2.16828 | 0.0696191 | ||||||||
\(971\) | 15.7013 | 0.503880 | 0.251940 | − | 0.967743i | \(-0.418931\pi\) | ||||
0.251940 | + | 0.967743i | \(0.418931\pi\) | |||||||
\(972\) | 1.90464 | 0.0610915 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.65727 | −0.149229 | ||||||||
\(975\) | −27.8468 | −0.891813 | ||||||||
\(976\) | −45.8160 | −1.46653 | ||||||||
\(977\) | −13.7257 | −0.439123 | −0.219561 | − | 0.975599i | \(-0.570463\pi\) | ||||
−0.219561 | + | 0.975599i | \(0.570463\pi\) | |||||||
\(978\) | 7.29934 | 0.233407 | ||||||||
\(979\) | 1.80577 | 0.0577127 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.31301 | −0.169631 | ||||||||
\(982\) | −7.52314 | −0.240073 | ||||||||
\(983\) | −31.3146 | −0.998781 | −0.499391 | − | 0.866377i | \(-0.666443\pi\) | ||||
−0.499391 | + | 0.866377i | \(0.666443\pi\) | |||||||
\(984\) | −1.20574 | −0.0384376 | ||||||||
\(985\) | −24.7842 | −0.789691 | ||||||||
\(986\) | −12.9363 | −0.411976 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −69.1808 | −2.20093 | ||||||||
\(989\) | −28.6080 | −0.909683 | ||||||||
\(990\) | −0.385613 | −0.0122556 | ||||||||
\(991\) | −4.10511 | −0.130403 | −0.0652016 | − | 0.997872i | \(-0.520769\pi\) | ||||
−0.0652016 | + | 0.997872i | \(0.520769\pi\) | |||||||
\(992\) | −22.1378 | −0.702875 | ||||||||
\(993\) | −2.91507 | −0.0925071 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0292 | −0.444757 | ||||||||
\(996\) | 17.2372 | 0.546182 | ||||||||
\(997\) | −56.9183 | −1.80262 | −0.901311 | − | 0.433173i | \(-0.857394\pi\) | ||||
−0.901311 | + | 0.433173i | \(0.857394\pi\) | |||||||
\(998\) | −0.375832 | −0.0118968 | ||||||||
\(999\) | −7.16373 | −0.226650 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6027.2.a.bn.1.10 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.10 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.10 | yes | 24 | 7.6 | odd | 2 |