Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32322 | −1.64276 | −0.821381 | − | 0.570381i | \(-0.806796\pi\) | ||||
−0.821381 | + | 0.570381i | \(0.806796\pi\) | |||||||
\(3\) | 2.41590 | 1.39482 | 0.697410 | − | 0.716672i | \(-0.254336\pi\) | ||||
0.697410 | + | 0.716672i | \(0.254336\pi\) | |||||||
\(4\) | 3.39733 | 1.69866 | ||||||||
\(5\) | 0.249961 | 0.111786 | 0.0558929 | − | 0.998437i | \(-0.482199\pi\) | ||||
0.0558929 | + | 0.998437i | \(0.482199\pi\) | |||||||
\(6\) | −5.61265 | −2.29136 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.24629 | −1.14774 | ||||||||
\(9\) | 2.83657 | 0.945524 | ||||||||
\(10\) | −0.580712 | −0.183637 | ||||||||
\(11\) | 3.91510 | 1.18045 | 0.590224 | − | 0.807240i | \(-0.299040\pi\) | ||||
0.590224 | + | 0.807240i | \(0.299040\pi\) | |||||||
\(12\) | 8.20760 | 2.36933 | ||||||||
\(13\) | 0.778528 | 0.215925 | 0.107962 | − | 0.994155i | \(-0.465567\pi\) | ||||
0.107962 | + | 0.994155i | \(0.465567\pi\) | |||||||
\(14\) | −2.32322 | −0.620905 | ||||||||
\(15\) | 0.603880 | 0.155921 | ||||||||
\(16\) | 0.747183 | 0.186796 | ||||||||
\(17\) | 3.22662 | 0.782569 | 0.391285 | − | 0.920270i | \(-0.372031\pi\) | ||||
0.391285 | + | 0.920270i | \(0.372031\pi\) | |||||||
\(18\) | −6.58997 | −1.55327 | ||||||||
\(19\) | 6.57430 | 1.50825 | 0.754124 | − | 0.656732i | \(-0.228062\pi\) | ||||
0.754124 | + | 0.656732i | \(0.228062\pi\) | |||||||
\(20\) | 0.849198 | 0.189886 | ||||||||
\(21\) | 2.41590 | 0.527193 | ||||||||
\(22\) | −9.09562 | −1.93919 | ||||||||
\(23\) | −3.71094 | −0.773785 | −0.386892 | − | 0.922125i | \(-0.626452\pi\) | ||||
−0.386892 | + | 0.922125i | \(0.626452\pi\) | |||||||
\(24\) | −7.84272 | −1.60089 | ||||||||
\(25\) | −4.93752 | −0.987504 | ||||||||
\(26\) | −1.80869 | −0.354713 | ||||||||
\(27\) | −0.394827 | −0.0759845 | ||||||||
\(28\) | 3.39733 | 0.642035 | ||||||||
\(29\) | 9.52419 | 1.76860 | 0.884299 | − | 0.466922i | \(-0.154637\pi\) | ||||
0.884299 | + | 0.466922i | \(0.154637\pi\) | |||||||
\(30\) | −1.40294 | −0.256141 | ||||||||
\(31\) | 7.29397 | 1.31004 | 0.655018 | − | 0.755614i | \(-0.272661\pi\) | ||||
0.655018 | + | 0.755614i | \(0.272661\pi\) | |||||||
\(32\) | 4.75672 | 0.840878 | ||||||||
\(33\) | 9.45849 | 1.64651 | ||||||||
\(34\) | −7.49612 | −1.28557 | ||||||||
\(35\) | 0.249961 | 0.0422510 | ||||||||
\(36\) | 9.63676 | 1.60613 | ||||||||
\(37\) | −8.87264 | −1.45865 | −0.729327 | − | 0.684166i | \(-0.760166\pi\) | ||||
−0.729327 | + | 0.684166i | \(0.760166\pi\) | |||||||
\(38\) | −15.2735 | −2.47769 | ||||||||
\(39\) | 1.88085 | 0.301177 | ||||||||
\(40\) | −0.811446 | −0.128301 | ||||||||
\(41\) | 4.01810 | 0.627521 | 0.313761 | − | 0.949502i | \(-0.398411\pi\) | ||||
0.313761 | + | 0.949502i | \(0.398411\pi\) | |||||||
\(42\) | −5.61265 | −0.866051 | ||||||||
\(43\) | 2.12465 | 0.324005 | 0.162003 | − | 0.986790i | \(-0.448205\pi\) | ||||
0.162003 | + | 0.986790i | \(0.448205\pi\) | |||||||
\(44\) | 13.3009 | 2.00518 | ||||||||
\(45\) | 0.709031 | 0.105696 | ||||||||
\(46\) | 8.62132 | 1.27114 | ||||||||
\(47\) | −13.2644 | −1.93482 | −0.967408 | − | 0.253223i | \(-0.918509\pi\) | ||||
−0.967408 | + | 0.253223i | \(0.918509\pi\) | |||||||
\(48\) | 1.80512 | 0.260546 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 11.4709 | 1.62223 | ||||||||
\(51\) | 7.79518 | 1.09154 | ||||||||
\(52\) | 2.64492 | 0.366784 | ||||||||
\(53\) | 4.92230 | 0.676130 | 0.338065 | − | 0.941123i | \(-0.390228\pi\) | ||||
0.338065 | + | 0.941123i | \(0.390228\pi\) | |||||||
\(54\) | 0.917268 | 0.124824 | ||||||||
\(55\) | 0.978621 | 0.131957 | ||||||||
\(56\) | −3.24629 | −0.433804 | ||||||||
\(57\) | 15.8829 | 2.10374 | ||||||||
\(58\) | −22.1267 | −2.90538 | ||||||||
\(59\) | −3.00791 | −0.391596 | −0.195798 | − | 0.980644i | \(-0.562730\pi\) | ||||
−0.195798 | + | 0.980644i | \(0.562730\pi\) | |||||||
\(60\) | 2.05158 | 0.264858 | ||||||||
\(61\) | 7.07562 | 0.905941 | 0.452970 | − | 0.891526i | \(-0.350364\pi\) | ||||
0.452970 | + | 0.891526i | \(0.350364\pi\) | |||||||
\(62\) | −16.9455 | −2.15207 | ||||||||
\(63\) | 2.83657 | 0.357374 | ||||||||
\(64\) | −12.5453 | −1.56816 | ||||||||
\(65\) | 0.194601 | 0.0241373 | ||||||||
\(66\) | −21.9741 | −2.70483 | ||||||||
\(67\) | 9.24765 | 1.12978 | 0.564890 | − | 0.825166i | \(-0.308918\pi\) | ||||
0.564890 | + | 0.825166i | \(0.308918\pi\) | |||||||
\(68\) | 10.9619 | 1.32932 | ||||||||
\(69\) | −8.96526 | −1.07929 | ||||||||
\(70\) | −0.580712 | −0.0694084 | ||||||||
\(71\) | 13.4447 | 1.59559 | 0.797795 | − | 0.602928i | \(-0.206000\pi\) | ||||
0.797795 | + | 0.602928i | \(0.206000\pi\) | |||||||
\(72\) | −9.20835 | −1.08521 | ||||||||
\(73\) | 3.92772 | 0.459705 | 0.229852 | − | 0.973226i | \(-0.426176\pi\) | ||||
0.229852 | + | 0.973226i | \(0.426176\pi\) | |||||||
\(74\) | 20.6131 | 2.39622 | ||||||||
\(75\) | −11.9286 | −1.37739 | ||||||||
\(76\) | 22.3351 | 2.56201 | ||||||||
\(77\) | 3.91510 | 0.446167 | ||||||||
\(78\) | −4.36961 | −0.494761 | ||||||||
\(79\) | 9.95908 | 1.12048 | 0.560242 | − | 0.828329i | \(-0.310708\pi\) | ||||
0.560242 | + | 0.828329i | \(0.310708\pi\) | |||||||
\(80\) | 0.186766 | 0.0208811 | ||||||||
\(81\) | −9.46358 | −1.05151 | ||||||||
\(82\) | −9.33490 | −1.03087 | ||||||||
\(83\) | −17.4886 | −1.91963 | −0.959813 | − | 0.280639i | \(-0.909454\pi\) | ||||
−0.959813 | + | 0.280639i | \(0.909454\pi\) | |||||||
\(84\) | 8.20760 | 0.895523 | ||||||||
\(85\) | 0.806527 | 0.0874801 | ||||||||
\(86\) | −4.93601 | −0.532263 | ||||||||
\(87\) | 23.0095 | 2.46688 | ||||||||
\(88\) | −12.7096 | −1.35484 | ||||||||
\(89\) | −1.86575 | −0.197769 | −0.0988844 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988844 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(90\) | −1.64723 | −0.173633 | ||||||||
\(91\) | 0.778528 | 0.0816120 | ||||||||
\(92\) | −12.6073 | −1.31440 | ||||||||
\(93\) | 17.6215 | 1.82726 | ||||||||
\(94\) | 30.8161 | 3.17844 | ||||||||
\(95\) | 1.64332 | 0.168601 | ||||||||
\(96\) | 11.4918 | 1.17287 | ||||||||
\(97\) | 3.66925 | 0.372556 | 0.186278 | − | 0.982497i | \(-0.440357\pi\) | ||||
0.186278 | + | 0.982497i | \(0.440357\pi\) | |||||||
\(98\) | −2.32322 | −0.234680 | ||||||||
\(99\) | 11.1055 | 1.11614 | ||||||||
\(100\) | −16.7744 | −1.67744 | ||||||||
\(101\) | −7.99220 | −0.795254 | −0.397627 | − | 0.917547i | \(-0.630166\pi\) | ||||
−0.397627 | + | 0.917547i | \(0.630166\pi\) | |||||||
\(102\) | −18.1099 | −1.79315 | ||||||||
\(103\) | −9.14245 | −0.900832 | −0.450416 | − | 0.892819i | \(-0.648724\pi\) | ||||
−0.450416 | + | 0.892819i | \(0.648724\pi\) | |||||||
\(104\) | −2.52733 | −0.247825 | ||||||||
\(105\) | 0.603880 | 0.0589326 | ||||||||
\(106\) | −11.4356 | −1.11072 | ||||||||
\(107\) | 2.38360 | 0.230431 | 0.115216 | − | 0.993341i | \(-0.463244\pi\) | ||||
0.115216 | + | 0.993341i | \(0.463244\pi\) | |||||||
\(108\) | −1.34136 | −0.129072 | ||||||||
\(109\) | 1.05016 | 0.100587 | 0.0502934 | − | 0.998734i | \(-0.483984\pi\) | ||||
0.0502934 | + | 0.998734i | \(0.483984\pi\) | |||||||
\(110\) | −2.27355 | −0.216774 | ||||||||
\(111\) | −21.4354 | −2.03456 | ||||||||
\(112\) | 0.747183 | 0.0706021 | ||||||||
\(113\) | −15.7834 | −1.48478 | −0.742389 | − | 0.669969i | \(-0.766307\pi\) | ||||
−0.742389 | + | 0.669969i | \(0.766307\pi\) | |||||||
\(114\) | −36.8993 | −3.45594 | ||||||||
\(115\) | −0.927589 | −0.0864981 | ||||||||
\(116\) | 32.3568 | 3.00425 | ||||||||
\(117\) | 2.20835 | 0.204162 | ||||||||
\(118\) | 6.98802 | 0.643299 | ||||||||
\(119\) | 3.22662 | 0.295783 | ||||||||
\(120\) | −1.96037 | −0.178957 | ||||||||
\(121\) | 4.32801 | 0.393455 | ||||||||
\(122\) | −16.4382 | −1.48824 | ||||||||
\(123\) | 9.70732 | 0.875279 | ||||||||
\(124\) | 24.7800 | 2.22531 | ||||||||
\(125\) | −2.48399 | −0.222175 | ||||||||
\(126\) | −6.58997 | −0.587081 | ||||||||
\(127\) | −7.24116 | −0.642549 | −0.321274 | − | 0.946986i | \(-0.604111\pi\) | ||||
−0.321274 | + | 0.946986i | \(0.604111\pi\) | |||||||
\(128\) | 19.6319 | 1.73523 | ||||||||
\(129\) | 5.13293 | 0.451929 | ||||||||
\(130\) | −0.452101 | −0.0396519 | ||||||||
\(131\) | 20.9396 | 1.82950 | 0.914752 | − | 0.404016i | \(-0.132386\pi\) | ||||
0.914752 | + | 0.404016i | \(0.132386\pi\) | |||||||
\(132\) | 32.1336 | 2.79687 | ||||||||
\(133\) | 6.57430 | 0.570064 | ||||||||
\(134\) | −21.4843 | −1.85596 | ||||||||
\(135\) | −0.0986911 | −0.00849398 | ||||||||
\(136\) | −10.4745 | −0.898185 | ||||||||
\(137\) | −19.9137 | −1.70134 | −0.850669 | − | 0.525701i | \(-0.823803\pi\) | ||||
−0.850669 | + | 0.525701i | \(0.823803\pi\) | |||||||
\(138\) | 20.8282 | 1.77302 | ||||||||
\(139\) | −13.6921 | −1.16135 | −0.580675 | − | 0.814135i | \(-0.697211\pi\) | ||||
−0.580675 | + | 0.814135i | \(0.697211\pi\) | |||||||
\(140\) | 0.849198 | 0.0717703 | ||||||||
\(141\) | −32.0455 | −2.69872 | ||||||||
\(142\) | −31.2349 | −2.62117 | ||||||||
\(143\) | 3.04802 | 0.254888 | ||||||||
\(144\) | 2.11944 | 0.176620 | ||||||||
\(145\) | 2.38067 | 0.197704 | ||||||||
\(146\) | −9.12493 | −0.755185 | ||||||||
\(147\) | 2.41590 | 0.199260 | ||||||||
\(148\) | −30.1433 | −2.47776 | ||||||||
\(149\) | 11.9358 | 0.977819 | 0.488909 | − | 0.872335i | \(-0.337395\pi\) | ||||
0.488909 | + | 0.872335i | \(0.337395\pi\) | |||||||
\(150\) | 27.7126 | 2.26272 | ||||||||
\(151\) | 0.0794979 | 0.00646945 | 0.00323472 | − | 0.999995i | \(-0.498970\pi\) | ||||
0.00323472 | + | 0.999995i | \(0.498970\pi\) | |||||||
\(152\) | −21.3421 | −1.73107 | ||||||||
\(153\) | 9.15252 | 0.739938 | ||||||||
\(154\) | −9.09562 | −0.732946 | ||||||||
\(155\) | 1.82320 | 0.146443 | ||||||||
\(156\) | 6.38985 | 0.511598 | ||||||||
\(157\) | −4.64293 | −0.370546 | −0.185273 | − | 0.982687i | \(-0.559317\pi\) | ||||
−0.185273 | + | 0.982687i | \(0.559317\pi\) | |||||||
\(158\) | −23.1371 | −1.84069 | ||||||||
\(159\) | 11.8918 | 0.943079 | ||||||||
\(160\) | 1.18899 | 0.0939981 | ||||||||
\(161\) | −3.71094 | −0.292463 | ||||||||
\(162\) | 21.9859 | 1.72738 | ||||||||
\(163\) | 16.1775 | 1.26712 | 0.633558 | − | 0.773695i | \(-0.281594\pi\) | ||||
0.633558 | + | 0.773695i | \(0.281594\pi\) | |||||||
\(164\) | 13.6508 | 1.06595 | ||||||||
\(165\) | 2.36425 | 0.184057 | ||||||||
\(166\) | 40.6298 | 3.15349 | ||||||||
\(167\) | −6.40110 | −0.495332 | −0.247666 | − | 0.968845i | \(-0.579664\pi\) | ||||
−0.247666 | + | 0.968845i | \(0.579664\pi\) | |||||||
\(168\) | −7.84272 | −0.605079 | ||||||||
\(169\) | −12.3939 | −0.953376 | ||||||||
\(170\) | −1.87373 | −0.143709 | ||||||||
\(171\) | 18.6485 | 1.42608 | ||||||||
\(172\) | 7.21812 | 0.550376 | ||||||||
\(173\) | −15.3410 | −1.16635 | −0.583177 | − | 0.812345i | \(-0.698191\pi\) | ||||
−0.583177 | + | 0.812345i | \(0.698191\pi\) | |||||||
\(174\) | −53.4560 | −4.05249 | ||||||||
\(175\) | −4.93752 | −0.373241 | ||||||||
\(176\) | 2.92530 | 0.220502 | ||||||||
\(177\) | −7.26681 | −0.546207 | ||||||||
\(178\) | 4.33453 | 0.324887 | ||||||||
\(179\) | 20.0212 | 1.49645 | 0.748227 | − | 0.663443i | \(-0.230905\pi\) | ||||
0.748227 | + | 0.663443i | \(0.230905\pi\) | |||||||
\(180\) | 2.40881 | 0.179542 | ||||||||
\(181\) | 14.5407 | 1.08080 | 0.540402 | − | 0.841407i | \(-0.318272\pi\) | ||||
0.540402 | + | 0.841407i | \(0.318272\pi\) | |||||||
\(182\) | −1.80869 | −0.134069 | ||||||||
\(183\) | 17.0940 | 1.26362 | ||||||||
\(184\) | 12.0468 | 0.888102 | ||||||||
\(185\) | −2.21781 | −0.163057 | ||||||||
\(186\) | −40.9385 | −3.00176 | ||||||||
\(187\) | 12.6325 | 0.923781 | ||||||||
\(188\) | −45.0636 | −3.28660 | ||||||||
\(189\) | −0.394827 | −0.0287194 | ||||||||
\(190\) | −3.81778 | −0.276971 | ||||||||
\(191\) | −8.15118 | −0.589799 | −0.294899 | − | 0.955528i | \(-0.595286\pi\) | ||||
−0.294899 | + | 0.955528i | \(0.595286\pi\) | |||||||
\(192\) | −30.3081 | −2.18730 | ||||||||
\(193\) | 16.3978 | 1.18034 | 0.590168 | − | 0.807280i | \(-0.299061\pi\) | ||||
0.590168 | + | 0.807280i | \(0.299061\pi\) | |||||||
\(194\) | −8.52446 | −0.612021 | ||||||||
\(195\) | 0.470138 | 0.0336672 | ||||||||
\(196\) | 3.39733 | 0.242666 | ||||||||
\(197\) | 10.7579 | 0.766472 | 0.383236 | − | 0.923650i | \(-0.374810\pi\) | ||||
0.383236 | + | 0.923650i | \(0.374810\pi\) | |||||||
\(198\) | −25.8004 | −1.83355 | ||||||||
\(199\) | 26.3198 | 1.86576 | 0.932882 | − | 0.360182i | \(-0.117285\pi\) | ||||
0.932882 | + | 0.360182i | \(0.117285\pi\) | |||||||
\(200\) | 16.0286 | 1.13340 | ||||||||
\(201\) | 22.3414 | 1.57584 | ||||||||
\(202\) | 18.5676 | 1.30641 | ||||||||
\(203\) | 9.52419 | 0.668467 | ||||||||
\(204\) | 26.4828 | 1.85417 | ||||||||
\(205\) | 1.00437 | 0.0701479 | ||||||||
\(206\) | 21.2399 | 1.47985 | ||||||||
\(207\) | −10.5264 | −0.731632 | ||||||||
\(208\) | 0.581703 | 0.0403338 | ||||||||
\(209\) | 25.7391 | 1.78041 | ||||||||
\(210\) | −1.40294 | −0.0968122 | ||||||||
\(211\) | −18.4210 | −1.26815 | −0.634076 | − | 0.773271i | \(-0.718619\pi\) | ||||
−0.634076 | + | 0.773271i | \(0.718619\pi\) | |||||||
\(212\) | 16.7227 | 1.14852 | ||||||||
\(213\) | 32.4810 | 2.22556 | ||||||||
\(214\) | −5.53761 | −0.378543 | ||||||||
\(215\) | 0.531078 | 0.0362192 | ||||||||
\(216\) | 1.28172 | 0.0872103 | ||||||||
\(217\) | 7.29397 | 0.495147 | ||||||||
\(218\) | −2.43974 | −0.165240 | ||||||||
\(219\) | 9.48897 | 0.641205 | ||||||||
\(220\) | 3.32470 | 0.224151 | ||||||||
\(221\) | 2.51201 | 0.168976 | ||||||||
\(222\) | 49.7991 | 3.34229 | ||||||||
\(223\) | −1.18338 | −0.0792452 | −0.0396226 | − | 0.999215i | \(-0.512616\pi\) | ||||
−0.0396226 | + | 0.999215i | \(0.512616\pi\) | |||||||
\(224\) | 4.75672 | 0.317822 | ||||||||
\(225\) | −14.0056 | −0.933709 | ||||||||
\(226\) | 36.6683 | 2.43914 | ||||||||
\(227\) | 0.425661 | 0.0282521 | 0.0141261 | − | 0.999900i | \(-0.495503\pi\) | ||||
0.0141261 | + | 0.999900i | \(0.495503\pi\) | |||||||
\(228\) | 53.9593 | 3.57354 | ||||||||
\(229\) | 17.1475 | 1.13314 | 0.566569 | − | 0.824015i | \(-0.308271\pi\) | ||||
0.566569 | + | 0.824015i | \(0.308271\pi\) | |||||||
\(230\) | 2.15499 | 0.142096 | ||||||||
\(231\) | 9.45849 | 0.622323 | ||||||||
\(232\) | −30.9183 | −2.02989 | ||||||||
\(233\) | −27.5273 | −1.80338 | −0.901688 | − | 0.432387i | \(-0.857671\pi\) | ||||
−0.901688 | + | 0.432387i | \(0.857671\pi\) | |||||||
\(234\) | −5.13048 | −0.335390 | ||||||||
\(235\) | −3.31558 | −0.216285 | ||||||||
\(236\) | −10.2189 | −0.665191 | ||||||||
\(237\) | 24.0601 | 1.56287 | ||||||||
\(238\) | −7.49612 | −0.485901 | ||||||||
\(239\) | −6.62922 | −0.428808 | −0.214404 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214404 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(240\) | 0.451208 | 0.0291254 | ||||||||
\(241\) | 20.7738 | 1.33816 | 0.669080 | − | 0.743190i | \(-0.266688\pi\) | ||||
0.669080 | + | 0.743190i | \(0.266688\pi\) | |||||||
\(242\) | −10.0549 | −0.646353 | ||||||||
\(243\) | −21.6786 | −1.39068 | ||||||||
\(244\) | 24.0382 | 1.53889 | ||||||||
\(245\) | 0.249961 | 0.0159694 | ||||||||
\(246\) | −22.5522 | −1.43788 | ||||||||
\(247\) | 5.11828 | 0.325668 | ||||||||
\(248\) | −23.6784 | −1.50358 | ||||||||
\(249\) | −42.2508 | −2.67753 | ||||||||
\(250\) | 5.77084 | 0.364980 | ||||||||
\(251\) | −22.0828 | −1.39386 | −0.696928 | − | 0.717141i | \(-0.745450\pi\) | ||||
−0.696928 | + | 0.717141i | \(0.745450\pi\) | |||||||
\(252\) | 9.63676 | 0.607059 | ||||||||
\(253\) | −14.5287 | −0.913412 | ||||||||
\(254\) | 16.8228 | 1.05555 | ||||||||
\(255\) | 1.94849 | 0.122019 | ||||||||
\(256\) | −20.5186 | −1.28241 | ||||||||
\(257\) | −6.24116 | −0.389313 | −0.194656 | − | 0.980872i | \(-0.562359\pi\) | ||||
−0.194656 | + | 0.980872i | \(0.562359\pi\) | |||||||
\(258\) | −11.9249 | −0.742412 | ||||||||
\(259\) | −8.87264 | −0.551319 | ||||||||
\(260\) | 0.661125 | 0.0410012 | ||||||||
\(261\) | 27.0160 | 1.67225 | ||||||||
\(262\) | −48.6473 | −3.00544 | ||||||||
\(263\) | −5.24927 | −0.323684 | −0.161842 | − | 0.986817i | \(-0.551743\pi\) | ||||
−0.161842 | + | 0.986817i | \(0.551743\pi\) | |||||||
\(264\) | −30.7050 | −1.88976 | ||||||||
\(265\) | 1.23038 | 0.0755817 | ||||||||
\(266\) | −15.2735 | −0.936480 | ||||||||
\(267\) | −4.50746 | −0.275852 | ||||||||
\(268\) | 31.4173 | 1.91912 | ||||||||
\(269\) | 13.0845 | 0.797779 | 0.398889 | − | 0.916999i | \(-0.369396\pi\) | ||||
0.398889 | + | 0.916999i | \(0.369396\pi\) | |||||||
\(270\) | 0.229281 | 0.0139536 | ||||||||
\(271\) | 6.80852 | 0.413588 | 0.206794 | − | 0.978384i | \(-0.433697\pi\) | ||||
0.206794 | + | 0.978384i | \(0.433697\pi\) | |||||||
\(272\) | 2.41087 | 0.146181 | ||||||||
\(273\) | 1.88085 | 0.113834 | ||||||||
\(274\) | 46.2637 | 2.79489 | ||||||||
\(275\) | −19.3309 | −1.16570 | ||||||||
\(276\) | −30.4579 | −1.83335 | ||||||||
\(277\) | 10.0423 | 0.603386 | 0.301693 | − | 0.953405i | \(-0.402448\pi\) | ||||
0.301693 | + | 0.953405i | \(0.402448\pi\) | |||||||
\(278\) | 31.8097 | 1.90782 | ||||||||
\(279\) | 20.6899 | 1.23867 | ||||||||
\(280\) | −0.811446 | −0.0484931 | ||||||||
\(281\) | −5.98701 | −0.357155 | −0.178578 | − | 0.983926i | \(-0.557150\pi\) | ||||
−0.178578 | + | 0.983926i | \(0.557150\pi\) | |||||||
\(282\) | 74.4487 | 4.43335 | ||||||||
\(283\) | −0.833588 | −0.0495517 | −0.0247758 | − | 0.999693i | \(-0.507887\pi\) | ||||
−0.0247758 | + | 0.999693i | \(0.507887\pi\) | |||||||
\(284\) | 45.6760 | 2.71037 | ||||||||
\(285\) | 3.97009 | 0.235168 | ||||||||
\(286\) | −7.08120 | −0.418720 | ||||||||
\(287\) | 4.01810 | 0.237181 | ||||||||
\(288\) | 13.4928 | 0.795070 | ||||||||
\(289\) | −6.58895 | −0.387586 | ||||||||
\(290\) | −5.53081 | −0.324781 | ||||||||
\(291\) | 8.86454 | 0.519649 | ||||||||
\(292\) | 13.3437 | 0.780884 | ||||||||
\(293\) | −4.29442 | −0.250882 | −0.125441 | − | 0.992101i | \(-0.540035\pi\) | ||||
−0.125441 | + | 0.992101i | \(0.540035\pi\) | |||||||
\(294\) | −5.61265 | −0.327337 | ||||||||
\(295\) | −0.751859 | −0.0437749 | ||||||||
\(296\) | 28.8032 | 1.67415 | ||||||||
\(297\) | −1.54579 | −0.0896956 | ||||||||
\(298\) | −27.7294 | −1.60632 | ||||||||
\(299\) | −2.88907 | −0.167079 | ||||||||
\(300\) | −40.5252 | −2.33972 | ||||||||
\(301\) | 2.12465 | 0.122463 | ||||||||
\(302\) | −0.184691 | −0.0106278 | ||||||||
\(303\) | −19.3084 | −1.10924 | ||||||||
\(304\) | 4.91221 | 0.281734 | ||||||||
\(305\) | 1.76863 | 0.101271 | ||||||||
\(306\) | −21.2633 | −1.21554 | ||||||||
\(307\) | −13.5745 | −0.774738 | −0.387369 | − | 0.921925i | \(-0.626616\pi\) | ||||
−0.387369 | + | 0.921925i | \(0.626616\pi\) | |||||||
\(308\) | 13.3009 | 0.757888 | ||||||||
\(309\) | −22.0872 | −1.25650 | ||||||||
\(310\) | −4.23570 | −0.240571 | ||||||||
\(311\) | −7.87348 | −0.446464 | −0.223232 | − | 0.974765i | \(-0.571661\pi\) | ||||
−0.223232 | + | 0.974765i | \(0.571661\pi\) | |||||||
\(312\) | −6.10578 | −0.345672 | ||||||||
\(313\) | 6.78714 | 0.383632 | 0.191816 | − | 0.981431i | \(-0.438562\pi\) | ||||
0.191816 | + | 0.981431i | \(0.438562\pi\) | |||||||
\(314\) | 10.7865 | 0.608719 | ||||||||
\(315\) | 0.709031 | 0.0399494 | ||||||||
\(316\) | 33.8343 | 1.90333 | ||||||||
\(317\) | 6.98076 | 0.392079 | 0.196039 | − | 0.980596i | \(-0.437192\pi\) | ||||
0.196039 | + | 0.980596i | \(0.437192\pi\) | |||||||
\(318\) | −27.6272 | −1.54925 | ||||||||
\(319\) | 37.2882 | 2.08774 | ||||||||
\(320\) | −3.13582 | −0.175298 | ||||||||
\(321\) | 5.75854 | 0.321410 | ||||||||
\(322\) | 8.62132 | 0.480447 | ||||||||
\(323\) | 21.2127 | 1.18031 | ||||||||
\(324\) | −32.1509 | −1.78616 | ||||||||
\(325\) | −3.84400 | −0.213227 | ||||||||
\(326\) | −37.5837 | −2.08157 | ||||||||
\(327\) | 2.53707 | 0.140300 | ||||||||
\(328\) | −13.0439 | −0.720230 | ||||||||
\(329\) | −13.2644 | −0.731292 | ||||||||
\(330\) | −5.49266 | −0.302361 | ||||||||
\(331\) | −18.4003 | −1.01137 | −0.505685 | − | 0.862718i | \(-0.668760\pi\) | ||||
−0.505685 | + | 0.862718i | \(0.668760\pi\) | |||||||
\(332\) | −59.4146 | −3.26080 | ||||||||
\(333\) | −25.1679 | −1.37919 | ||||||||
\(334\) | 14.8711 | 0.813713 | ||||||||
\(335\) | 2.31155 | 0.126293 | ||||||||
\(336\) | 1.80512 | 0.0984773 | ||||||||
\(337\) | 11.1747 | 0.608724 | 0.304362 | − | 0.952556i | \(-0.401557\pi\) | ||||
0.304362 | + | 0.952556i | \(0.401557\pi\) | |||||||
\(338\) | 28.7937 | 1.56617 | ||||||||
\(339\) | −38.1311 | −2.07100 | ||||||||
\(340\) | 2.74004 | 0.148599 | ||||||||
\(341\) | 28.5566 | 1.54643 | ||||||||
\(342\) | −43.3244 | −2.34272 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.89722 | −0.371873 | ||||||||
\(345\) | −2.24096 | −0.120649 | ||||||||
\(346\) | 35.6404 | 1.91604 | ||||||||
\(347\) | −3.12443 | −0.167728 | −0.0838642 | − | 0.996477i | \(-0.526726\pi\) | ||||
−0.0838642 | + | 0.996477i | \(0.526726\pi\) | |||||||
\(348\) | 78.1708 | 4.19039 | ||||||||
\(349\) | 0.948338 | 0.0507634 | 0.0253817 | − | 0.999678i | \(-0.491920\pi\) | ||||
0.0253817 | + | 0.999678i | \(0.491920\pi\) | |||||||
\(350\) | 11.4709 | 0.613146 | ||||||||
\(351\) | −0.307384 | −0.0164069 | ||||||||
\(352\) | 18.6230 | 0.992611 | ||||||||
\(353\) | −27.6077 | −1.46941 | −0.734706 | − | 0.678386i | \(-0.762680\pi\) | ||||
−0.734706 | + | 0.678386i | \(0.762680\pi\) | |||||||
\(354\) | 16.8824 | 0.897287 | ||||||||
\(355\) | 3.36064 | 0.178364 | ||||||||
\(356\) | −6.33855 | −0.335943 | ||||||||
\(357\) | 7.79518 | 0.412565 | ||||||||
\(358\) | −46.5135 | −2.45832 | ||||||||
\(359\) | −6.73201 | −0.355302 | −0.177651 | − | 0.984094i | \(-0.556850\pi\) | ||||
−0.177651 | + | 0.984094i | \(0.556850\pi\) | |||||||
\(360\) | −2.30172 | −0.121311 | ||||||||
\(361\) | 24.2215 | 1.27481 | ||||||||
\(362\) | −33.7812 | −1.77550 | ||||||||
\(363\) | 10.4560 | 0.548800 | ||||||||
\(364\) | 2.64492 | 0.138631 | ||||||||
\(365\) | 0.981774 | 0.0513884 | ||||||||
\(366\) | −39.7130 | −2.07583 | ||||||||
\(367\) | 25.3040 | 1.32086 | 0.660428 | − | 0.750889i | \(-0.270375\pi\) | ||||
0.660428 | + | 0.750889i | \(0.270375\pi\) | |||||||
\(368\) | −2.77275 | −0.144540 | ||||||||
\(369\) | 11.3976 | 0.593336 | ||||||||
\(370\) | 5.15245 | 0.267863 | ||||||||
\(371\) | 4.92230 | 0.255553 | ||||||||
\(372\) | 59.8660 | 3.10391 | ||||||||
\(373\) | −5.91183 | −0.306103 | −0.153051 | − | 0.988218i | \(-0.548910\pi\) | ||||
−0.153051 | + | 0.988218i | \(0.548910\pi\) | |||||||
\(374\) | −29.3481 | −1.51755 | ||||||||
\(375\) | −6.00107 | −0.309894 | ||||||||
\(376\) | 43.0602 | 2.22066 | ||||||||
\(377\) | 7.41485 | 0.381884 | ||||||||
\(378\) | 0.917268 | 0.0471792 | ||||||||
\(379\) | 3.53866 | 0.181769 | 0.0908843 | − | 0.995861i | \(-0.471031\pi\) | ||||
0.0908843 | + | 0.995861i | \(0.471031\pi\) | |||||||
\(380\) | 5.58289 | 0.286396 | ||||||||
\(381\) | −17.4939 | −0.896240 | ||||||||
\(382\) | 18.9369 | 0.968898 | ||||||||
\(383\) | 23.0661 | 1.17862 | 0.589310 | − | 0.807907i | \(-0.299400\pi\) | ||||
0.589310 | + | 0.807907i | \(0.299400\pi\) | |||||||
\(384\) | 47.4286 | 2.42033 | ||||||||
\(385\) | 0.978621 | 0.0498751 | ||||||||
\(386\) | −38.0955 | −1.93901 | ||||||||
\(387\) | 6.02671 | 0.306355 | ||||||||
\(388\) | 12.4657 | 0.632848 | ||||||||
\(389\) | 8.30924 | 0.421295 | 0.210647 | − | 0.977562i | \(-0.432443\pi\) | ||||
0.210647 | + | 0.977562i | \(0.432443\pi\) | |||||||
\(390\) | −1.09223 | −0.0553072 | ||||||||
\(391\) | −11.9738 | −0.605540 | ||||||||
\(392\) | −3.24629 | −0.163963 | ||||||||
\(393\) | 50.5880 | 2.55183 | ||||||||
\(394\) | −24.9930 | −1.25913 | ||||||||
\(395\) | 2.48938 | 0.125254 | ||||||||
\(396\) | 37.7289 | 1.89595 | ||||||||
\(397\) | 22.9321 | 1.15093 | 0.575466 | − | 0.817826i | \(-0.304821\pi\) | ||||
0.575466 | + | 0.817826i | \(0.304821\pi\) | |||||||
\(398\) | −61.1466 | −3.06500 | ||||||||
\(399\) | 15.8829 | 0.795137 | ||||||||
\(400\) | −3.68923 | −0.184461 | ||||||||
\(401\) | −12.2159 | −0.610031 | −0.305016 | − | 0.952347i | \(-0.598662\pi\) | ||||
−0.305016 | + | 0.952347i | \(0.598662\pi\) | |||||||
\(402\) | −51.9039 | −2.58873 | ||||||||
\(403\) | 5.67856 | 0.282869 | ||||||||
\(404\) | −27.1521 | −1.35087 | ||||||||
\(405\) | −2.36552 | −0.117544 | ||||||||
\(406\) | −22.1267 | −1.09813 | ||||||||
\(407\) | −34.7373 | −1.72186 | ||||||||
\(408\) | −25.3054 | −1.25281 | ||||||||
\(409\) | 11.5517 | 0.571195 | 0.285597 | − | 0.958350i | \(-0.407808\pi\) | ||||
0.285597 | + | 0.958350i | \(0.407808\pi\) | |||||||
\(410\) | −2.33336 | −0.115236 | ||||||||
\(411\) | −48.1094 | −2.37306 | ||||||||
\(412\) | −31.0599 | −1.53021 | ||||||||
\(413\) | −3.00791 | −0.148010 | ||||||||
\(414\) | 24.4550 | 1.20190 | ||||||||
\(415\) | −4.37147 | −0.214587 | ||||||||
\(416\) | 3.70324 | 0.181566 | ||||||||
\(417\) | −33.0788 | −1.61988 | ||||||||
\(418\) | −59.7974 | −2.92478 | ||||||||
\(419\) | −30.7824 | −1.50382 | −0.751909 | − | 0.659266i | \(-0.770867\pi\) | ||||
−0.751909 | + | 0.659266i | \(0.770867\pi\) | |||||||
\(420\) | 2.05158 | 0.100107 | ||||||||
\(421\) | 0.890721 | 0.0434111 | 0.0217056 | − | 0.999764i | \(-0.493090\pi\) | ||||
0.0217056 | + | 0.999764i | \(0.493090\pi\) | |||||||
\(422\) | 42.7959 | 2.08327 | ||||||||
\(423\) | −37.6255 | −1.82941 | ||||||||
\(424\) | −15.9792 | −0.776020 | ||||||||
\(425\) | −15.9315 | −0.772790 | ||||||||
\(426\) | −75.4604 | −3.65607 | ||||||||
\(427\) | 7.07562 | 0.342413 | ||||||||
\(428\) | 8.09787 | 0.391425 | ||||||||
\(429\) | 7.36370 | 0.355523 | ||||||||
\(430\) | −1.23381 | −0.0594995 | ||||||||
\(431\) | −22.2770 | −1.07304 | −0.536521 | − | 0.843887i | \(-0.680262\pi\) | ||||
−0.536521 | + | 0.843887i | \(0.680262\pi\) | |||||||
\(432\) | −0.295008 | −0.0141936 | ||||||||
\(433\) | 4.00513 | 0.192474 | 0.0962371 | − | 0.995358i | \(-0.469319\pi\) | ||||
0.0962371 | + | 0.995358i | \(0.469319\pi\) | |||||||
\(434\) | −16.9455 | −0.813408 | ||||||||
\(435\) | 5.75146 | 0.275762 | ||||||||
\(436\) | 3.56773 | 0.170863 | ||||||||
\(437\) | −24.3969 | −1.16706 | ||||||||
\(438\) | −22.0449 | −1.05335 | ||||||||
\(439\) | −25.6374 | −1.22361 | −0.611804 | − | 0.791009i | \(-0.709556\pi\) | ||||
−0.611804 | + | 0.791009i | \(0.709556\pi\) | |||||||
\(440\) | −3.17689 | −0.151452 | ||||||||
\(441\) | 2.83657 | 0.135075 | ||||||||
\(442\) | −5.83594 | −0.277588 | ||||||||
\(443\) | −3.71944 | −0.176716 | −0.0883579 | − | 0.996089i | \(-0.528162\pi\) | ||||
−0.0883579 | + | 0.996089i | \(0.528162\pi\) | |||||||
\(444\) | −72.8231 | −3.45603 | ||||||||
\(445\) | −0.466363 | −0.0221077 | ||||||||
\(446\) | 2.74925 | 0.130181 | ||||||||
\(447\) | 28.8357 | 1.36388 | ||||||||
\(448\) | −12.5453 | −0.592708 | ||||||||
\(449\) | 22.2992 | 1.05236 | 0.526182 | − | 0.850372i | \(-0.323623\pi\) | ||||
0.526182 | + | 0.850372i | \(0.323623\pi\) | |||||||
\(450\) | 32.5381 | 1.53386 | ||||||||
\(451\) | 15.7313 | 0.740756 | ||||||||
\(452\) | −53.6214 | −2.52214 | ||||||||
\(453\) | 0.192059 | 0.00902372 | ||||||||
\(454\) | −0.988902 | −0.0464115 | ||||||||
\(455\) | 0.194601 | 0.00912306 | ||||||||
\(456\) | −51.5604 | −2.41454 | ||||||||
\(457\) | 1.95251 | 0.0913345 | 0.0456672 | − | 0.998957i | \(-0.485459\pi\) | ||||
0.0456672 | + | 0.998957i | \(0.485459\pi\) | |||||||
\(458\) | −39.8373 | −1.86147 | ||||||||
\(459\) | −1.27395 | −0.0594631 | ||||||||
\(460\) | −3.15132 | −0.146931 | ||||||||
\(461\) | −6.21417 | −0.289423 | −0.144711 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144711 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(462\) | −21.9741 | −1.02233 | ||||||||
\(463\) | −2.94314 | −0.136779 | −0.0683897 | − | 0.997659i | \(-0.521786\pi\) | ||||
−0.0683897 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(464\) | 7.11631 | 0.330366 | ||||||||
\(465\) | 4.40468 | 0.204262 | ||||||||
\(466\) | 63.9519 | 2.96252 | ||||||||
\(467\) | −3.36550 | −0.155737 | −0.0778683 | − | 0.996964i | \(-0.524811\pi\) | ||||
−0.0778683 | + | 0.996964i | \(0.524811\pi\) | |||||||
\(468\) | 7.50250 | 0.346803 | ||||||||
\(469\) | 9.24765 | 0.427017 | ||||||||
\(470\) | 7.70282 | 0.355304 | ||||||||
\(471\) | −11.2169 | −0.516846 | ||||||||
\(472\) | 9.76456 | 0.449450 | ||||||||
\(473\) | 8.31820 | 0.382471 | ||||||||
\(474\) | −55.8969 | −2.56743 | ||||||||
\(475\) | −32.4607 | −1.48940 | ||||||||
\(476\) | 10.9619 | 0.502437 | ||||||||
\(477\) | 13.9625 | 0.639297 | ||||||||
\(478\) | 15.4011 | 0.704430 | ||||||||
\(479\) | 6.62083 | 0.302513 | 0.151257 | − | 0.988495i | \(-0.451668\pi\) | ||||
0.151257 | + | 0.988495i | \(0.451668\pi\) | |||||||
\(480\) | 2.87249 | 0.131111 | ||||||||
\(481\) | −6.90760 | −0.314960 | ||||||||
\(482\) | −48.2621 | −2.19828 | ||||||||
\(483\) | −8.96526 | −0.407934 | ||||||||
\(484\) | 14.7037 | 0.668348 | ||||||||
\(485\) | 0.917168 | 0.0416465 | ||||||||
\(486\) | 50.3640 | 2.28456 | ||||||||
\(487\) | 10.8426 | 0.491326 | 0.245663 | − | 0.969355i | \(-0.420994\pi\) | ||||
0.245663 | + | 0.969355i | \(0.420994\pi\) | |||||||
\(488\) | −22.9696 | −1.03978 | ||||||||
\(489\) | 39.0831 | 1.76740 | ||||||||
\(490\) | −0.580712 | −0.0262339 | ||||||||
\(491\) | −14.2737 | −0.644164 | −0.322082 | − | 0.946712i | \(-0.604383\pi\) | ||||
−0.322082 | + | 0.946712i | \(0.604383\pi\) | |||||||
\(492\) | 32.9789 | 1.48681 | ||||||||
\(493\) | 30.7309 | 1.38405 | ||||||||
\(494\) | −11.8909 | −0.534995 | ||||||||
\(495\) | 2.77593 | 0.124769 | ||||||||
\(496\) | 5.44993 | 0.244709 | ||||||||
\(497\) | 13.4447 | 0.603077 | ||||||||
\(498\) | 98.1576 | 4.39855 | ||||||||
\(499\) | −26.4167 | −1.18257 | −0.591286 | − | 0.806462i | \(-0.701380\pi\) | ||||
−0.591286 | + | 0.806462i | \(0.701380\pi\) | |||||||
\(500\) | −8.43892 | −0.377400 | ||||||||
\(501\) | −15.4644 | −0.690900 | ||||||||
\(502\) | 51.3032 | 2.28977 | ||||||||
\(503\) | 16.1977 | 0.722219 | 0.361110 | − | 0.932523i | \(-0.382398\pi\) | ||||
0.361110 | + | 0.932523i | \(0.382398\pi\) | |||||||
\(504\) | −9.20835 | −0.410172 | ||||||||
\(505\) | −1.99774 | −0.0888981 | ||||||||
\(506\) | 33.7533 | 1.50052 | ||||||||
\(507\) | −29.9424 | −1.32979 | ||||||||
\(508\) | −24.6006 | −1.09147 | ||||||||
\(509\) | 7.46534 | 0.330895 | 0.165448 | − | 0.986219i | \(-0.447093\pi\) | ||||
0.165448 | + | 0.986219i | \(0.447093\pi\) | |||||||
\(510\) | −4.52676 | −0.200448 | ||||||||
\(511\) | 3.92772 | 0.173752 | ||||||||
\(512\) | 8.40529 | 0.371465 | ||||||||
\(513\) | −2.59571 | −0.114603 | ||||||||
\(514\) | 14.4995 | 0.639548 | ||||||||
\(515\) | −2.28525 | −0.100700 | ||||||||
\(516\) | 17.4382 | 0.767676 | ||||||||
\(517\) | −51.9316 | −2.28395 | ||||||||
\(518\) | 20.6131 | 0.905686 | ||||||||
\(519\) | −37.0623 | −1.62686 | ||||||||
\(520\) | −0.631733 | −0.0277033 | ||||||||
\(521\) | −22.5064 | −0.986025 | −0.493012 | − | 0.870022i | \(-0.664104\pi\) | ||||
−0.493012 | + | 0.870022i | \(0.664104\pi\) | |||||||
\(522\) | −62.7641 | −2.74711 | ||||||||
\(523\) | 6.29048 | 0.275063 | 0.137532 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137532 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(524\) | 71.1388 | 3.10771 | ||||||||
\(525\) | −11.9286 | −0.520605 | ||||||||
\(526\) | 12.1952 | 0.531736 | ||||||||
\(527\) | 23.5348 | 1.02519 | ||||||||
\(528\) | 7.06722 | 0.307561 | ||||||||
\(529\) | −9.22891 | −0.401257 | ||||||||
\(530\) | −2.85844 | −0.124163 | ||||||||
\(531\) | −8.53215 | −0.370264 | ||||||||
\(532\) | 22.3351 | 0.968348 | ||||||||
\(533\) | 3.12820 | 0.135497 | ||||||||
\(534\) | 10.4718 | 0.453159 | ||||||||
\(535\) | 0.595806 | 0.0257589 | ||||||||
\(536\) | −30.0206 | −1.29669 | ||||||||
\(537\) | 48.3692 | 2.08728 | ||||||||
\(538\) | −30.3982 | −1.31056 | ||||||||
\(539\) | 3.91510 | 0.168635 | ||||||||
\(540\) | −0.335286 | −0.0144284 | ||||||||
\(541\) | −18.1700 | −0.781191 | −0.390596 | − | 0.920562i | \(-0.627731\pi\) | ||||
−0.390596 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(542\) | −15.8177 | −0.679427 | ||||||||
\(543\) | 35.1289 | 1.50753 | ||||||||
\(544\) | 15.3481 | 0.658045 | ||||||||
\(545\) | 0.262498 | 0.0112442 | ||||||||
\(546\) | −4.36961 | −0.187002 | ||||||||
\(547\) | 25.8143 | 1.10374 | 0.551869 | − | 0.833931i | \(-0.313915\pi\) | ||||
0.551869 | + | 0.833931i | \(0.313915\pi\) | |||||||
\(548\) | −67.6532 | −2.89000 | ||||||||
\(549\) | 20.0705 | 0.856588 | ||||||||
\(550\) | 44.9098 | 1.91496 | ||||||||
\(551\) | 62.6149 | 2.66748 | ||||||||
\(552\) | 29.1039 | 1.23874 | ||||||||
\(553\) | 9.95908 | 0.423503 | ||||||||
\(554\) | −23.3305 | −0.991219 | ||||||||
\(555\) | −5.35801 | −0.227435 | ||||||||
\(556\) | −46.5166 | −1.97274 | ||||||||
\(557\) | 5.72328 | 0.242503 | 0.121252 | − | 0.992622i | \(-0.461309\pi\) | ||||
0.121252 | + | 0.992622i | \(0.461309\pi\) | |||||||
\(558\) | −48.0670 | −2.03484 | ||||||||
\(559\) | 1.65410 | 0.0699608 | ||||||||
\(560\) | 0.186766 | 0.00789231 | ||||||||
\(561\) | 30.5189 | 1.28851 | ||||||||
\(562\) | 13.9091 | 0.586721 | ||||||||
\(563\) | 9.19731 | 0.387620 | 0.193810 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193810 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(564\) | −108.869 | −4.58422 | ||||||||
\(565\) | −3.94523 | −0.165977 | ||||||||
\(566\) | 1.93660 | 0.0814016 | ||||||||
\(567\) | −9.46358 | −0.397433 | ||||||||
\(568\) | −43.6454 | −1.83132 | ||||||||
\(569\) | −19.1641 | −0.803403 | −0.401701 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401701 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(570\) | −9.22337 | −0.386324 | ||||||||
\(571\) | −12.6880 | −0.530975 | −0.265487 | − | 0.964114i | \(-0.585533\pi\) | ||||
−0.265487 | + | 0.964114i | \(0.585533\pi\) | |||||||
\(572\) | 10.3551 | 0.432969 | ||||||||
\(573\) | −19.6924 | −0.822663 | ||||||||
\(574\) | −9.33490 | −0.389631 | ||||||||
\(575\) | 18.3228 | 0.764116 | ||||||||
\(576\) | −35.5855 | −1.48273 | ||||||||
\(577\) | −29.8813 | −1.24397 | −0.621987 | − | 0.783028i | \(-0.713674\pi\) | ||||
−0.621987 | + | 0.783028i | \(0.713674\pi\) | |||||||
\(578\) | 15.3076 | 0.636710 | ||||||||
\(579\) | 39.6153 | 1.64636 | ||||||||
\(580\) | 8.08792 | 0.335833 | ||||||||
\(581\) | −17.4886 | −0.725551 | ||||||||
\(582\) | −20.5942 | −0.853659 | ||||||||
\(583\) | 19.2713 | 0.798135 | ||||||||
\(584\) | −12.7505 | −0.527620 | ||||||||
\(585\) | 0.552001 | 0.0228224 | ||||||||
\(586\) | 9.97685 | 0.412140 | ||||||||
\(587\) | 33.1092 | 1.36656 | 0.683282 | − | 0.730155i | \(-0.260552\pi\) | ||||
0.683282 | + | 0.730155i | \(0.260552\pi\) | |||||||
\(588\) | 8.20760 | 0.338476 | ||||||||
\(589\) | 47.9527 | 1.97586 | ||||||||
\(590\) | 1.74673 | 0.0719117 | ||||||||
\(591\) | 25.9901 | 1.06909 | ||||||||
\(592\) | −6.62948 | −0.272470 | ||||||||
\(593\) | 6.38519 | 0.262208 | 0.131104 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131104 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(594\) | 3.59119 | 0.147348 | ||||||||
\(595\) | 0.806527 | 0.0330644 | ||||||||
\(596\) | 40.5498 | 1.66099 | ||||||||
\(597\) | 63.5861 | 2.60241 | ||||||||
\(598\) | 6.71194 | 0.274472 | ||||||||
\(599\) | −20.2403 | −0.826998 | −0.413499 | − | 0.910505i | \(-0.635693\pi\) | ||||
−0.413499 | + | 0.910505i | \(0.635693\pi\) | |||||||
\(600\) | 38.7236 | 1.58088 | ||||||||
\(601\) | −0.800381 | −0.0326482 | −0.0163241 | − | 0.999867i | \(-0.505196\pi\) | ||||
−0.0163241 | + | 0.999867i | \(0.505196\pi\) | |||||||
\(602\) | −4.93601 | −0.201177 | ||||||||
\(603\) | 26.2316 | 1.06823 | ||||||||
\(604\) | 0.270081 | 0.0109894 | ||||||||
\(605\) | 1.08183 | 0.0439827 | ||||||||
\(606\) | 44.8575 | 1.82221 | ||||||||
\(607\) | 41.9841 | 1.70408 | 0.852040 | − | 0.523476i | \(-0.175365\pi\) | ||||
0.852040 | + | 0.523476i | \(0.175365\pi\) | |||||||
\(608\) | 31.2721 | 1.26825 | ||||||||
\(609\) | 23.0095 | 0.932391 | ||||||||
\(610\) | −4.10890 | −0.166365 | ||||||||
\(611\) | −10.3267 | −0.417775 | ||||||||
\(612\) | 31.0941 | 1.25691 | ||||||||
\(613\) | 16.9583 | 0.684941 | 0.342470 | − | 0.939529i | \(-0.388736\pi\) | ||||
0.342470 | + | 0.939529i | \(0.388736\pi\) | |||||||
\(614\) | 31.5365 | 1.27271 | ||||||||
\(615\) | 2.42645 | 0.0978438 | ||||||||
\(616\) | −12.7096 | −0.512083 | ||||||||
\(617\) | −14.9102 | −0.600261 | −0.300131 | − | 0.953898i | \(-0.597030\pi\) | ||||
−0.300131 | + | 0.953898i | \(0.597030\pi\) | |||||||
\(618\) | 51.3134 | 2.06413 | ||||||||
\(619\) | −9.52969 | −0.383031 | −0.191515 | − | 0.981490i | \(-0.561340\pi\) | ||||
−0.191515 | + | 0.981490i | \(0.561340\pi\) | |||||||
\(620\) | 6.19402 | 0.248758 | ||||||||
\(621\) | 1.46518 | 0.0587956 | ||||||||
\(622\) | 18.2918 | 0.733434 | ||||||||
\(623\) | −1.86575 | −0.0747496 | ||||||||
\(624\) | 1.40534 | 0.0562585 | ||||||||
\(625\) | 24.0667 | 0.962668 | ||||||||
\(626\) | −15.7680 | −0.630215 | ||||||||
\(627\) | 62.1830 | 2.48335 | ||||||||
\(628\) | −15.7736 | −0.629434 | ||||||||
\(629\) | −28.6286 | −1.14150 | ||||||||
\(630\) | −1.64723 | −0.0656273 | ||||||||
\(631\) | −16.6968 | −0.664688 | −0.332344 | − | 0.943158i | \(-0.607839\pi\) | ||||
−0.332344 | + | 0.943158i | \(0.607839\pi\) | |||||||
\(632\) | −32.3301 | −1.28602 | ||||||||
\(633\) | −44.5032 | −1.76884 | ||||||||
\(634\) | −16.2178 | −0.644092 | ||||||||
\(635\) | −1.81000 | −0.0718278 | ||||||||
\(636\) | 40.4003 | 1.60198 | ||||||||
\(637\) | 0.778528 | 0.0308464 | ||||||||
\(638\) | −86.6284 | −3.42965 | ||||||||
\(639\) | 38.1368 | 1.50867 | ||||||||
\(640\) | 4.90720 | 0.193974 | ||||||||
\(641\) | 26.5122 | 1.04717 | 0.523585 | − | 0.851973i | \(-0.324594\pi\) | ||||
0.523585 | + | 0.851973i | \(0.324594\pi\) | |||||||
\(642\) | −13.3783 | −0.528000 | ||||||||
\(643\) | 39.4211 | 1.55462 | 0.777309 | − | 0.629119i | \(-0.216584\pi\) | ||||
0.777309 | + | 0.629119i | \(0.216584\pi\) | |||||||
\(644\) | −12.6073 | −0.496797 | ||||||||
\(645\) | 1.28303 | 0.0505193 | ||||||||
\(646\) | −49.2818 | −1.93897 | ||||||||
\(647\) | −34.4890 | −1.35590 | −0.677951 | − | 0.735107i | \(-0.737132\pi\) | ||||
−0.677951 | + | 0.735107i | \(0.737132\pi\) | |||||||
\(648\) | 30.7216 | 1.20686 | ||||||||
\(649\) | −11.7763 | −0.462259 | ||||||||
\(650\) | 8.93044 | 0.350281 | ||||||||
\(651\) | 17.6215 | 0.690641 | ||||||||
\(652\) | 54.9601 | 2.15241 | ||||||||
\(653\) | 27.1351 | 1.06188 | 0.530939 | − | 0.847410i | \(-0.321839\pi\) | ||||
0.530939 | + | 0.847410i | \(0.321839\pi\) | |||||||
\(654\) | −5.89417 | −0.230480 | ||||||||
\(655\) | 5.23408 | 0.204513 | ||||||||
\(656\) | 3.00225 | 0.117218 | ||||||||
\(657\) | 11.1413 | 0.434662 | ||||||||
\(658\) | 30.8161 | 1.20134 | ||||||||
\(659\) | 42.3125 | 1.64826 | 0.824131 | − | 0.566399i | \(-0.191664\pi\) | ||||
0.824131 | + | 0.566399i | \(0.191664\pi\) | |||||||
\(660\) | 8.03213 | 0.312650 | ||||||||
\(661\) | −25.9655 | −1.00994 | −0.504970 | − | 0.863137i | \(-0.668497\pi\) | ||||
−0.504970 | + | 0.863137i | \(0.668497\pi\) | |||||||
\(662\) | 42.7477 | 1.66144 | ||||||||
\(663\) | 6.06877 | 0.235691 | ||||||||
\(664\) | 56.7732 | 2.20323 | ||||||||
\(665\) | 1.64332 | 0.0637251 | ||||||||
\(666\) | 58.4704 | 2.26568 | ||||||||
\(667\) | −35.3437 | −1.36851 | ||||||||
\(668\) | −21.7467 | −0.841403 | ||||||||
\(669\) | −2.85894 | −0.110533 | ||||||||
\(670\) | −5.37023 | −0.207470 | ||||||||
\(671\) | 27.7018 | 1.06941 | ||||||||
\(672\) | 11.4918 | 0.443304 | ||||||||
\(673\) | −5.54953 | −0.213919 | −0.106959 | − | 0.994263i | \(-0.534111\pi\) | ||||
−0.106959 | + | 0.994263i | \(0.534111\pi\) | |||||||
\(674\) | −25.9612 | −0.999988 | ||||||||
\(675\) | 1.94947 | 0.0750349 | ||||||||
\(676\) | −42.1061 | −1.61947 | ||||||||
\(677\) | 38.3481 | 1.47384 | 0.736918 | − | 0.675982i | \(-0.236280\pi\) | ||||
0.736918 | + | 0.675982i | \(0.236280\pi\) | |||||||
\(678\) | 88.5868 | 3.40216 | ||||||||
\(679\) | 3.66925 | 0.140813 | ||||||||
\(680\) | −2.61822 | −0.100404 | ||||||||
\(681\) | 1.02835 | 0.0394066 | ||||||||
\(682\) | −66.3431 | −2.54041 | ||||||||
\(683\) | 41.5552 | 1.59007 | 0.795033 | − | 0.606566i | \(-0.207454\pi\) | ||||
0.795033 | + | 0.606566i | \(0.207454\pi\) | |||||||
\(684\) | 63.3550 | 2.42244 | ||||||||
\(685\) | −4.97763 | −0.190185 | ||||||||
\(686\) | −2.32322 | −0.0887008 | ||||||||
\(687\) | 41.4266 | 1.58052 | ||||||||
\(688\) | 1.58750 | 0.0605228 | ||||||||
\(689\) | 3.83215 | 0.145993 | ||||||||
\(690\) | 5.20624 | 0.198198 | ||||||||
\(691\) | 32.4489 | 1.23441 | 0.617207 | − | 0.786801i | \(-0.288264\pi\) | ||||
0.617207 | + | 0.786801i | \(0.288264\pi\) | |||||||
\(692\) | −52.1184 | −1.98125 | ||||||||
\(693\) | 11.1055 | 0.421862 | ||||||||
\(694\) | 7.25873 | 0.275538 | ||||||||
\(695\) | −3.42249 | −0.129822 | ||||||||
\(696\) | −74.6956 | −2.83133 | ||||||||
\(697\) | 12.9649 | 0.491079 | ||||||||
\(698\) | −2.20319 | −0.0833921 | ||||||||
\(699\) | −66.5033 | −2.51539 | ||||||||
\(700\) | −16.7744 | −0.634012 | ||||||||
\(701\) | 20.5210 | 0.775068 | 0.387534 | − | 0.921855i | \(-0.373327\pi\) | ||||
0.387534 | + | 0.921855i | \(0.373327\pi\) | |||||||
\(702\) | 0.714119 | 0.0269527 | ||||||||
\(703\) | −58.3314 | −2.20001 | ||||||||
\(704\) | −49.1159 | −1.85113 | ||||||||
\(705\) | −8.01012 | −0.301679 | ||||||||
\(706\) | 64.1387 | 2.41389 | ||||||||
\(707\) | −7.99220 | −0.300578 | ||||||||
\(708\) | −24.6877 | −0.927822 | ||||||||
\(709\) | 25.5778 | 0.960593 | 0.480297 | − | 0.877106i | \(-0.340529\pi\) | ||||
0.480297 | + | 0.877106i | \(0.340529\pi\) | |||||||
\(710\) | −7.80749 | −0.293010 | ||||||||
\(711\) | 28.2496 | 1.05944 | ||||||||
\(712\) | 6.05676 | 0.226987 | ||||||||
\(713\) | −27.0675 | −1.01369 | ||||||||
\(714\) | −18.1099 | −0.677745 | ||||||||
\(715\) | 0.761884 | 0.0284928 | ||||||||
\(716\) | 68.0186 | 2.54197 | ||||||||
\(717\) | −16.0155 | −0.598111 | ||||||||
\(718\) | 15.6399 | 0.583676 | ||||||||
\(719\) | −19.9240 | −0.743040 | −0.371520 | − | 0.928425i | \(-0.621163\pi\) | ||||
−0.371520 | + | 0.928425i | \(0.621163\pi\) | |||||||
\(720\) | 0.529776 | 0.0197436 | ||||||||
\(721\) | −9.14245 | −0.340483 | ||||||||
\(722\) | −56.2716 | −2.09421 | ||||||||
\(723\) | 50.1875 | 1.86649 | ||||||||
\(724\) | 49.3996 | 1.83592 | ||||||||
\(725\) | −47.0259 | −1.74650 | ||||||||
\(726\) | −24.2916 | −0.901546 | ||||||||
\(727\) | 4.38569 | 0.162656 | 0.0813280 | − | 0.996687i | \(-0.474084\pi\) | ||||
0.0813280 | + | 0.996687i | \(0.474084\pi\) | |||||||
\(728\) | −2.52733 | −0.0936692 | ||||||||
\(729\) | −23.9825 | −0.888242 | ||||||||
\(730\) | −2.28087 | −0.0844189 | ||||||||
\(731\) | 6.85541 | 0.253557 | ||||||||
\(732\) | 58.0739 | 2.14647 | ||||||||
\(733\) | −36.0771 | −1.33254 | −0.666270 | − | 0.745711i | \(-0.732110\pi\) | ||||
−0.666270 | + | 0.745711i | \(0.732110\pi\) | |||||||
\(734\) | −58.7865 | −2.16985 | ||||||||
\(735\) | 0.603880 | 0.0222744 | ||||||||
\(736\) | −17.6519 | −0.650658 | ||||||||
\(737\) | 36.2055 | 1.33365 | ||||||||
\(738\) | −26.4791 | −0.974710 | ||||||||
\(739\) | −42.0234 | −1.54585 | −0.772927 | − | 0.634495i | \(-0.781208\pi\) | ||||
−0.772927 | + | 0.634495i | \(0.781208\pi\) | |||||||
\(740\) | −7.53463 | −0.276979 | ||||||||
\(741\) | 12.3653 | 0.454249 | ||||||||
\(742\) | −11.4356 | −0.419813 | ||||||||
\(743\) | −50.9812 | −1.87032 | −0.935160 | − | 0.354225i | \(-0.884745\pi\) | ||||
−0.935160 | + | 0.354225i | \(0.884745\pi\) | |||||||
\(744\) | −57.2045 | −2.09722 | ||||||||
\(745\) | 2.98348 | 0.109306 | ||||||||
\(746\) | 13.7345 | 0.502854 | ||||||||
\(747\) | −49.6078 | −1.81505 | ||||||||
\(748\) | 42.9168 | 1.56919 | ||||||||
\(749\) | 2.38360 | 0.0870948 | ||||||||
\(750\) | 13.9418 | 0.509081 | ||||||||
\(751\) | −26.6313 | −0.971790 | −0.485895 | − | 0.874017i | \(-0.661506\pi\) | ||||
−0.485895 | + | 0.874017i | \(0.661506\pi\) | |||||||
\(752\) | −9.91095 | −0.361415 | ||||||||
\(753\) | −53.3499 | −1.94418 | ||||||||
\(754\) | −17.2263 | −0.627345 | ||||||||
\(755\) | 0.0198713 | 0.000723192 0 | ||||||||
\(756\) | −1.34136 | −0.0487847 | ||||||||
\(757\) | 46.4929 | 1.68981 | 0.844907 | − | 0.534914i | \(-0.179656\pi\) | ||||
0.844907 | + | 0.534914i | \(0.179656\pi\) | |||||||
\(758\) | −8.22106 | −0.298602 | ||||||||
\(759\) | −35.0999 | −1.27405 | ||||||||
\(760\) | −5.33469 | −0.193509 | ||||||||
\(761\) | −10.3478 | −0.375106 | −0.187553 | − | 0.982254i | \(-0.560056\pi\) | ||||
−0.187553 | + | 0.982254i | \(0.560056\pi\) | |||||||
\(762\) | 40.6421 | 1.47231 | ||||||||
\(763\) | 1.05016 | 0.0380182 | ||||||||
\(764\) | −27.6922 | −1.00187 | ||||||||
\(765\) | 2.28777 | 0.0827145 | ||||||||
\(766\) | −53.5874 | −1.93619 | ||||||||
\(767\) | −2.34174 | −0.0845554 | ||||||||
\(768\) | −49.5708 | −1.78873 | ||||||||
\(769\) | 41.4044 | 1.49308 | 0.746541 | − | 0.665340i | \(-0.231713\pi\) | ||||
0.746541 | + | 0.665340i | \(0.231713\pi\) | |||||||
\(770\) | −2.27355 | −0.0819329 | ||||||||
\(771\) | −15.0780 | −0.543021 | ||||||||
\(772\) | 55.7086 | 2.00500 | ||||||||
\(773\) | −22.4816 | −0.808605 | −0.404303 | − | 0.914625i | \(-0.632486\pi\) | ||||
−0.404303 | + | 0.914625i | \(0.632486\pi\) | |||||||
\(774\) | −14.0013 | −0.503268 | ||||||||
\(775\) | −36.0141 | −1.29366 | ||||||||
\(776\) | −11.9115 | −0.427597 | ||||||||
\(777\) | −21.4354 | −0.768991 | ||||||||
\(778\) | −19.3041 | −0.692087 | ||||||||
\(779\) | 26.4162 | 0.946458 | ||||||||
\(780\) | 1.59721 | 0.0571893 | ||||||||
\(781\) | 52.6373 | 1.88351 | ||||||||
\(782\) | 27.8177 | 0.994758 | ||||||||
\(783\) | −3.76041 | −0.134386 | ||||||||
\(784\) | 0.747183 | 0.0266851 | ||||||||
\(785\) | −1.16055 | −0.0414218 | ||||||||
\(786\) | −117.527 | −4.19205 | ||||||||
\(787\) | 9.60789 | 0.342484 | 0.171242 | − | 0.985229i | \(-0.445222\pi\) | ||||
0.171242 | + | 0.985229i | \(0.445222\pi\) | |||||||
\(788\) | 36.5483 | 1.30198 | ||||||||
\(789\) | −12.6817 | −0.451481 | ||||||||
\(790\) | −5.78336 | −0.205763 | ||||||||
\(791\) | −15.7834 | −0.561193 | ||||||||
\(792\) | −36.0516 | −1.28104 | ||||||||
\(793\) | 5.50857 | 0.195615 | ||||||||
\(794\) | −53.2763 | −1.89071 | ||||||||
\(795\) | 2.97248 | 0.105423 | ||||||||
\(796\) | 89.4171 | 3.16931 | ||||||||
\(797\) | 35.9437 | 1.27319 | 0.636596 | − | 0.771198i | \(-0.280342\pi\) | ||||
0.636596 | + | 0.771198i | \(0.280342\pi\) | |||||||
\(798\) | −36.8993 | −1.30622 | ||||||||
\(799\) | −42.7992 | −1.51413 | ||||||||
\(800\) | −23.4864 | −0.830370 | ||||||||
\(801\) | −5.29232 | −0.186995 | ||||||||
\(802\) | 28.3801 | 1.00214 | ||||||||
\(803\) | 15.3774 | 0.542657 | ||||||||
\(804\) | 75.9011 | 2.67682 | ||||||||
\(805\) | −0.927589 | −0.0326932 | ||||||||
\(806\) | −13.1925 | −0.464687 | ||||||||
\(807\) | 31.6109 | 1.11276 | ||||||||
\(808\) | 25.9450 | 0.912743 | ||||||||
\(809\) | 7.44846 | 0.261874 | 0.130937 | − | 0.991391i | \(-0.458201\pi\) | ||||
0.130937 | + | 0.991391i | \(0.458201\pi\) | |||||||
\(810\) | 5.49561 | 0.193096 | ||||||||
\(811\) | −17.3304 | −0.608552 | −0.304276 | − | 0.952584i | \(-0.598414\pi\) | ||||
−0.304276 | + | 0.952584i | \(0.598414\pi\) | |||||||
\(812\) | 32.3568 | 1.13550 | ||||||||
\(813\) | 16.4487 | 0.576881 | ||||||||
\(814\) | 80.7022 | 2.82861 | ||||||||
\(815\) | 4.04373 | 0.141646 | ||||||||
\(816\) | 5.82442 | 0.203896 | ||||||||
\(817\) | 13.9681 | 0.488681 | ||||||||
\(818\) | −26.8371 | −0.938336 | ||||||||
\(819\) | 2.20835 | 0.0771661 | ||||||||
\(820\) | 3.41216 | 0.119158 | ||||||||
\(821\) | −40.4372 | −1.41127 | −0.705634 | − | 0.708577i | \(-0.749338\pi\) | ||||
−0.705634 | + | 0.708577i | \(0.749338\pi\) | |||||||
\(822\) | 111.768 | 3.89837 | ||||||||
\(823\) | −10.8949 | −0.379772 | −0.189886 | − | 0.981806i | \(-0.560812\pi\) | ||||
−0.189886 | + | 0.981806i | \(0.560812\pi\) | |||||||
\(824\) | 29.6791 | 1.03392 | ||||||||
\(825\) | −46.7015 | −1.62594 | ||||||||
\(826\) | 6.98802 | 0.243144 | ||||||||
\(827\) | −25.3817 | −0.882608 | −0.441304 | − | 0.897358i | \(-0.645484\pi\) | ||||
−0.441304 | + | 0.897358i | \(0.645484\pi\) | |||||||
\(828\) | −35.7615 | −1.24280 | ||||||||
\(829\) | 14.4419 | 0.501587 | 0.250793 | − | 0.968041i | \(-0.419309\pi\) | ||||
0.250793 | + | 0.968041i | \(0.419309\pi\) | |||||||
\(830\) | 10.1559 | 0.352515 | ||||||||
\(831\) | 24.2613 | 0.841615 | ||||||||
\(832\) | −9.76684 | −0.338604 | ||||||||
\(833\) | 3.22662 | 0.111796 | ||||||||
\(834\) | 76.8492 | 2.66107 | ||||||||
\(835\) | −1.60002 | −0.0553711 | ||||||||
\(836\) | 87.4440 | 3.02431 | ||||||||
\(837\) | −2.87985 | −0.0995423 | ||||||||
\(838\) | 71.5141 | 2.47042 | ||||||||
\(839\) | 36.7760 | 1.26965 | 0.634824 | − | 0.772657i | \(-0.281073\pi\) | ||||
0.634824 | + | 0.772657i | \(0.281073\pi\) | |||||||
\(840\) | −1.96037 | −0.0676392 | ||||||||
\(841\) | 61.7102 | 2.12794 | ||||||||
\(842\) | −2.06934 | −0.0713141 | ||||||||
\(843\) | −14.4640 | −0.498167 | ||||||||
\(844\) | −62.5821 | −2.15417 | ||||||||
\(845\) | −3.09798 | −0.106574 | ||||||||
\(846\) | 87.4121 | 3.00529 | ||||||||
\(847\) | 4.32801 | 0.148712 | ||||||||
\(848\) | 3.67786 | 0.126298 | ||||||||
\(849\) | −2.01387 | −0.0691157 | ||||||||
\(850\) | 37.0122 | 1.26951 | ||||||||
\(851\) | 32.9259 | 1.12868 | ||||||||
\(852\) | 110.349 | 3.78048 | ||||||||
\(853\) | 22.3193 | 0.764200 | 0.382100 | − | 0.924121i | \(-0.375201\pi\) | ||||
0.382100 | + | 0.924121i | \(0.375201\pi\) | |||||||
\(854\) | −16.4382 | −0.562503 | ||||||||
\(855\) | 4.66138 | 0.159416 | ||||||||
\(856\) | −7.73786 | −0.264475 | ||||||||
\(857\) | 34.9241 | 1.19298 | 0.596491 | − | 0.802619i | \(-0.296561\pi\) | ||||
0.596491 | + | 0.802619i | \(0.296561\pi\) | |||||||
\(858\) | −17.1075 | −0.584039 | ||||||||
\(859\) | −18.2717 | −0.623423 | −0.311711 | − | 0.950177i | \(-0.600902\pi\) | ||||
−0.311711 | + | 0.950177i | \(0.600902\pi\) | |||||||
\(860\) | 1.80424 | 0.0615242 | ||||||||
\(861\) | 9.70732 | 0.330825 | ||||||||
\(862\) | 51.7541 | 1.76275 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −1.87808 | −0.0638936 | ||||||||
\(865\) | −3.83465 | −0.130382 | ||||||||
\(866\) | −9.30477 | −0.316189 | ||||||||
\(867\) | −15.9183 | −0.540612 | ||||||||
\(868\) | 24.7800 | 0.841088 | ||||||||
\(869\) | 38.9908 | 1.32267 | ||||||||
\(870\) | −13.3619 | −0.453010 | ||||||||
\(871\) | 7.19956 | 0.243948 | ||||||||
\(872\) | −3.40912 | −0.115447 | ||||||||
\(873\) | 10.4081 | 0.352261 | ||||||||
\(874\) | 56.6791 | 1.91720 | ||||||||
\(875\) | −2.48399 | −0.0839741 | ||||||||
\(876\) | 32.2371 | 1.08919 | ||||||||
\(877\) | 45.5877 | 1.53939 | 0.769694 | − | 0.638413i | \(-0.220409\pi\) | ||||
0.769694 | + | 0.638413i | \(0.220409\pi\) | |||||||
\(878\) | 59.5613 | 2.01010 | ||||||||
\(879\) | −10.3749 | −0.349936 | ||||||||
\(880\) | 0.731208 | 0.0246490 | ||||||||
\(881\) | −5.12342 | −0.172612 | −0.0863062 | − | 0.996269i | \(-0.527506\pi\) | ||||
−0.0863062 | + | 0.996269i | \(0.527506\pi\) | |||||||
\(882\) | −6.58997 | −0.221896 | ||||||||
\(883\) | −9.79563 | −0.329649 | −0.164825 | − | 0.986323i | \(-0.552706\pi\) | ||||
−0.164825 | + | 0.986323i | \(0.552706\pi\) | |||||||
\(884\) | 8.53413 | 0.287034 | ||||||||
\(885\) | −1.81642 | −0.0610581 | ||||||||
\(886\) | 8.64105 | 0.290302 | ||||||||
\(887\) | 34.6144 | 1.16224 | 0.581119 | − | 0.813819i | \(-0.302615\pi\) | ||||
0.581119 | + | 0.813819i | \(0.302615\pi\) | |||||||
\(888\) | 69.5856 | 2.33514 | ||||||||
\(889\) | −7.24116 | −0.242861 | ||||||||
\(890\) | 1.08346 | 0.0363177 | ||||||||
\(891\) | −37.0508 | −1.24125 | ||||||||
\(892\) | −4.02034 | −0.134611 | ||||||||
\(893\) | −87.2044 | −2.91818 | ||||||||
\(894\) | −66.9915 | −2.24053 | ||||||||
\(895\) | 5.00451 | 0.167282 | ||||||||
\(896\) | 19.6319 | 0.655855 | ||||||||
\(897\) | −6.97971 | −0.233046 | ||||||||
\(898\) | −51.8058 | −1.72878 | ||||||||
\(899\) | 69.4691 | 2.31692 | ||||||||
\(900\) | −47.5817 | −1.58606 | ||||||||
\(901\) | 15.8824 | 0.529118 | ||||||||
\(902\) | −36.5471 | −1.21688 | ||||||||
\(903\) | 5.13293 | 0.170813 | ||||||||
\(904\) | 51.2376 | 1.70414 | ||||||||
\(905\) | 3.63461 | 0.120819 | ||||||||
\(906\) | −0.446194 | −0.0148238 | ||||||||
\(907\) | −8.11052 | −0.269305 | −0.134653 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134653 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(908\) | 1.44611 | 0.0479909 | ||||||||
\(909\) | −22.6705 | −0.751932 | ||||||||
\(910\) | −0.452101 | −0.0149870 | ||||||||
\(911\) | −41.5161 | −1.37549 | −0.687746 | − | 0.725952i | \(-0.741400\pi\) | ||||
−0.687746 | + | 0.725952i | \(0.741400\pi\) | |||||||
\(912\) | 11.8674 | 0.392969 | ||||||||
\(913\) | −68.4697 | −2.26602 | ||||||||
\(914\) | −4.53610 | −0.150041 | ||||||||
\(915\) | 4.27282 | 0.141255 | ||||||||
\(916\) | 58.2556 | 1.92482 | ||||||||
\(917\) | 20.9396 | 0.691488 | ||||||||
\(918\) | 2.95967 | 0.0976836 | ||||||||
\(919\) | −9.47738 | −0.312630 | −0.156315 | − | 0.987707i | \(-0.549961\pi\) | ||||
−0.156315 | + | 0.987707i | \(0.549961\pi\) | |||||||
\(920\) | 3.01123 | 0.0992772 | ||||||||
\(921\) | −32.7946 | −1.08062 | ||||||||
\(922\) | 14.4369 | 0.475453 | ||||||||
\(923\) | 10.4671 | 0.344528 | ||||||||
\(924\) | 32.1336 | 1.05712 | ||||||||
\(925\) | 43.8088 | 1.44043 | ||||||||
\(926\) | 6.83755 | 0.224696 | ||||||||
\(927\) | −25.9332 | −0.851758 | ||||||||
\(928\) | 45.3039 | 1.48717 | ||||||||
\(929\) | 57.2899 | 1.87962 | 0.939810 | − | 0.341697i | \(-0.111002\pi\) | ||||
0.939810 | + | 0.341697i | \(0.111002\pi\) | |||||||
\(930\) | −10.2330 | −0.335554 | ||||||||
\(931\) | 6.57430 | 0.215464 | ||||||||
\(932\) | −93.5194 | −3.06333 | ||||||||
\(933\) | −19.0215 | −0.622737 | ||||||||
\(934\) | 7.81877 | 0.255838 | ||||||||
\(935\) | 3.15763 | 0.103266 | ||||||||
\(936\) | −7.16896 | −0.234325 | ||||||||
\(937\) | 36.7691 | 1.20119 | 0.600597 | − | 0.799552i | \(-0.294930\pi\) | ||||
0.600597 | + | 0.799552i | \(0.294930\pi\) | |||||||
\(938\) | −21.4843 | −0.701487 | ||||||||
\(939\) | 16.3970 | 0.535097 | ||||||||
\(940\) | −11.2641 | −0.367395 | ||||||||
\(941\) | 51.1660 | 1.66796 | 0.833982 | − | 0.551792i | \(-0.186056\pi\) | ||||
0.833982 | + | 0.551792i | \(0.186056\pi\) | |||||||
\(942\) | 26.0592 | 0.849054 | ||||||||
\(943\) | −14.9109 | −0.485566 | ||||||||
\(944\) | −2.24746 | −0.0731485 | ||||||||
\(945\) | −0.0986911 | −0.00321042 | ||||||||
\(946\) | −19.3250 | −0.628309 | ||||||||
\(947\) | 54.9177 | 1.78458 | 0.892292 | − | 0.451459i | \(-0.149096\pi\) | ||||
0.892292 | + | 0.451459i | \(0.149096\pi\) | |||||||
\(948\) | 81.7402 | 2.65480 | ||||||||
\(949\) | 3.05784 | 0.0992617 | ||||||||
\(950\) | 75.4133 | 2.44673 | ||||||||
\(951\) | 16.8648 | 0.546879 | ||||||||
\(952\) | −10.4745 | −0.339482 | ||||||||
\(953\) | 29.9073 | 0.968792 | 0.484396 | − | 0.874849i | \(-0.339039\pi\) | ||||
0.484396 | + | 0.874849i | \(0.339039\pi\) | |||||||
\(954\) | −32.4378 | −1.05021 | ||||||||
\(955\) | −2.03747 | −0.0659311 | ||||||||
\(956\) | −22.5216 | −0.728401 | ||||||||
\(957\) | 90.0844 | 2.91202 | ||||||||
\(958\) | −15.3816 | −0.496957 | ||||||||
\(959\) | −19.9137 | −0.643046 | ||||||||
\(960\) | −7.57582 | −0.244509 | ||||||||
\(961\) | 22.2020 | 0.716192 | ||||||||
\(962\) | 16.0478 | 0.517403 | ||||||||
\(963\) | 6.76125 | 0.217878 | ||||||||
\(964\) | 70.5755 | 2.27308 | ||||||||
\(965\) | 4.09879 | 0.131945 | ||||||||
\(966\) | 20.8282 | 0.670137 | ||||||||
\(967\) | 48.2573 | 1.55185 | 0.775925 | − | 0.630825i | \(-0.217284\pi\) | ||||
0.775925 | + | 0.630825i | \(0.217284\pi\) | |||||||
\(968\) | −14.0500 | −0.451584 | ||||||||
\(969\) | 51.2479 | 1.64632 | ||||||||
\(970\) | −2.13078 | −0.0684152 | ||||||||
\(971\) | −21.8317 | −0.700612 | −0.350306 | − | 0.936635i | \(-0.613922\pi\) | ||||
−0.350306 | + | 0.936635i | \(0.613922\pi\) | |||||||
\(972\) | −73.6492 | −2.36230 | ||||||||
\(973\) | −13.6921 | −0.438949 | ||||||||
\(974\) | −25.1898 | −0.807132 | ||||||||
\(975\) | −9.28672 | −0.297413 | ||||||||
\(976\) | 5.28678 | 0.169226 | ||||||||
\(977\) | −50.8131 | −1.62566 | −0.812828 | − | 0.582504i | \(-0.802073\pi\) | ||||
−0.812828 | + | 0.582504i | \(0.802073\pi\) | |||||||
\(978\) | −90.7985 | −2.90342 | ||||||||
\(979\) | −7.30459 | −0.233456 | ||||||||
\(980\) | 0.849198 | 0.0271266 | ||||||||
\(981\) | 2.97884 | 0.0951072 | ||||||||
\(982\) | 33.1609 | 1.05821 | ||||||||
\(983\) | −62.2006 | −1.98389 | −0.991945 | − | 0.126668i | \(-0.959572\pi\) | ||||
−0.991945 | + | 0.126668i | \(0.959572\pi\) | |||||||
\(984\) | −31.5128 | −1.00459 | ||||||||
\(985\) | 2.68906 | 0.0856807 | ||||||||
\(986\) | −71.3945 | −2.27366 | ||||||||
\(987\) | −32.0455 | −1.02002 | ||||||||
\(988\) | 17.3885 | 0.553201 | ||||||||
\(989\) | −7.88443 | −0.250710 | ||||||||
\(990\) | −6.44908 | −0.204965 | ||||||||
\(991\) | 22.4166 | 0.712088 | 0.356044 | − | 0.934469i | \(-0.384125\pi\) | ||||
0.356044 | + | 0.934469i | \(0.384125\pi\) | |||||||
\(992\) | 34.6954 | 1.10158 | ||||||||
\(993\) | −44.4532 | −1.41068 | ||||||||
\(994\) | −31.2349 | −0.990711 | ||||||||
\(995\) | 6.57892 | 0.208566 | ||||||||
\(996\) | −143.540 | −4.54823 | ||||||||
\(997\) | 62.2275 | 1.97076 | 0.985382 | − | 0.170361i | \(-0.0544935\pi\) | ||||
0.985382 | + | 0.170361i | \(0.0544935\pi\) | |||||||
\(998\) | 61.3716 | 1.94268 | ||||||||
\(999\) | 3.50316 | 0.110835 |
(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 | 6041.2.a.f.1.16 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.16 | ✓ | 132 | 1.1 | even | 1 | trivial |