Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31084 | −1.63401 | −0.817006 | − | 0.576629i | \(-0.804368\pi\) | ||||
−0.817006 | + | 0.576629i | \(0.804368\pi\) | |||||||
\(3\) | 0.814794 | 0.470422 | 0.235211 | − | 0.971944i | \(-0.424422\pi\) | ||||
0.235211 | + | 0.971944i | \(0.424422\pi\) | |||||||
\(4\) | 3.33999 | 1.67000 | ||||||||
\(5\) | −0.287417 | −0.128537 | −0.0642683 | − | 0.997933i | \(-0.520471\pi\) | ||||
−0.0642683 | + | 0.997933i | \(0.520471\pi\) | |||||||
\(6\) | −1.88286 | −0.768674 | ||||||||
\(7\) | −2.20640 | −0.833942 | −0.416971 | − | 0.908920i | \(-0.636908\pi\) | ||||
−0.416971 | + | 0.908920i | \(0.636908\pi\) | |||||||
\(8\) | −3.09651 | −1.09478 | ||||||||
\(9\) | −2.33611 | −0.778704 | ||||||||
\(10\) | 0.664174 | 0.210030 | ||||||||
\(11\) | 0.898242 | 0.270830 | 0.135415 | − | 0.990789i | \(-0.456763\pi\) | ||||
0.135415 | + | 0.990789i | \(0.456763\pi\) | |||||||
\(12\) | 2.72140 | 0.785602 | ||||||||
\(13\) | 1.31308 | 0.364182 | 0.182091 | − | 0.983282i | \(-0.441713\pi\) | ||||
0.182091 | + | 0.983282i | \(0.441713\pi\) | |||||||
\(14\) | 5.09865 | 1.36267 | ||||||||
\(15\) | −0.234185 | −0.0604664 | ||||||||
\(16\) | 0.475556 | 0.118889 | ||||||||
\(17\) | 4.29513 | 1.04172 | 0.520861 | − | 0.853641i | \(-0.325611\pi\) | ||||
0.520861 | + | 0.853641i | \(0.325611\pi\) | |||||||
\(18\) | 5.39838 | 1.27241 | ||||||||
\(19\) | 5.16079 | 1.18397 | 0.591983 | − | 0.805951i | \(-0.298345\pi\) | ||||
0.591983 | + | 0.805951i | \(0.298345\pi\) | |||||||
\(20\) | −0.959968 | −0.214655 | ||||||||
\(21\) | −1.79776 | −0.392304 | ||||||||
\(22\) | −2.07570 | −0.442540 | ||||||||
\(23\) | 3.20752 | 0.668814 | 0.334407 | − | 0.942429i | \(-0.391464\pi\) | ||||
0.334407 | + | 0.942429i | \(0.391464\pi\) | |||||||
\(24\) | −2.52302 | −0.515008 | ||||||||
\(25\) | −4.91739 | −0.983478 | ||||||||
\(26\) | −3.03431 | −0.595077 | ||||||||
\(27\) | −4.34783 | −0.836740 | ||||||||
\(28\) | −7.36936 | −1.39268 | ||||||||
\(29\) | 0.736008 | 0.136673 | 0.0683366 | − | 0.997662i | \(-0.478231\pi\) | ||||
0.0683366 | + | 0.997662i | \(0.478231\pi\) | |||||||
\(30\) | 0.541165 | 0.0988028 | ||||||||
\(31\) | 9.07661 | 1.63021 | 0.815103 | − | 0.579316i | \(-0.196680\pi\) | ||||
0.815103 | + | 0.579316i | \(0.196680\pi\) | |||||||
\(32\) | 5.09408 | 0.900514 | ||||||||
\(33\) | 0.731883 | 0.127404 | ||||||||
\(34\) | −9.92537 | −1.70219 | ||||||||
\(35\) | 0.634157 | 0.107192 | ||||||||
\(36\) | −7.80259 | −1.30043 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −11.9258 | −1.93461 | ||||||||
\(39\) | 1.06989 | 0.171319 | ||||||||
\(40\) | 0.889987 | 0.140719 | ||||||||
\(41\) | 0.873864 | 0.136475 | 0.0682373 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682373 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(42\) | 4.15435 | 0.641030 | ||||||||
\(43\) | 6.76802 | 1.03211 | 0.516056 | − | 0.856555i | \(-0.327400\pi\) | ||||
0.516056 | + | 0.856555i | \(0.327400\pi\) | |||||||
\(44\) | 3.00012 | 0.452285 | ||||||||
\(45\) | 0.671437 | 0.100092 | ||||||||
\(46\) | −7.41207 | −1.09285 | ||||||||
\(47\) | −5.62094 | −0.819898 | −0.409949 | − | 0.912108i | \(-0.634454\pi\) | ||||
−0.409949 | + | 0.912108i | \(0.634454\pi\) | |||||||
\(48\) | 0.387480 | 0.0559280 | ||||||||
\(49\) | −2.13179 | −0.304541 | ||||||||
\(50\) | 11.3633 | 1.60702 | ||||||||
\(51\) | 3.49965 | 0.490049 | ||||||||
\(52\) | 4.38566 | 0.608182 | ||||||||
\(53\) | −11.0462 | −1.51731 | −0.758656 | − | 0.651491i | \(-0.774144\pi\) | ||||
−0.758656 | + | 0.651491i | \(0.774144\pi\) | |||||||
\(54\) | 10.0472 | 1.36724 | ||||||||
\(55\) | −0.258170 | −0.0348116 | ||||||||
\(56\) | 6.83214 | 0.912983 | ||||||||
\(57\) | 4.20498 | 0.556963 | ||||||||
\(58\) | −1.70080 | −0.223326 | ||||||||
\(59\) | −13.7616 | −1.79161 | −0.895806 | − | 0.444446i | \(-0.853401\pi\) | ||||
−0.895806 | + | 0.444446i | \(0.853401\pi\) | |||||||
\(60\) | −0.782177 | −0.100979 | ||||||||
\(61\) | −12.2127 | −1.56368 | −0.781838 | − | 0.623481i | \(-0.785718\pi\) | ||||
−0.781838 | + | 0.623481i | \(0.785718\pi\) | |||||||
\(62\) | −20.9746 | −2.66378 | ||||||||
\(63\) | 5.15440 | 0.649393 | ||||||||
\(64\) | −12.7227 | −1.59034 | ||||||||
\(65\) | −0.377400 | −0.0468107 | ||||||||
\(66\) | −1.69126 | −0.208180 | ||||||||
\(67\) | −3.02677 | −0.369779 | −0.184889 | − | 0.982759i | \(-0.559193\pi\) | ||||
−0.184889 | + | 0.982759i | \(0.559193\pi\) | |||||||
\(68\) | 14.3457 | 1.73967 | ||||||||
\(69\) | 2.61347 | 0.314624 | ||||||||
\(70\) | −1.46544 | −0.175153 | ||||||||
\(71\) | 2.86657 | 0.340199 | 0.170099 | − | 0.985427i | \(-0.445591\pi\) | ||||
0.170099 | + | 0.985427i | \(0.445591\pi\) | |||||||
\(72\) | 7.23378 | 0.852509 | ||||||||
\(73\) | 2.37897 | 0.278437 | 0.139219 | − | 0.990262i | \(-0.455541\pi\) | ||||
0.139219 | + | 0.990262i | \(0.455541\pi\) | |||||||
\(74\) | −2.31084 | −0.268630 | ||||||||
\(75\) | −4.00666 | −0.462649 | ||||||||
\(76\) | 17.2370 | 1.97722 | ||||||||
\(77\) | −1.98188 | −0.225857 | ||||||||
\(78\) | −2.47234 | −0.279937 | ||||||||
\(79\) | −8.37285 | −0.942020 | −0.471010 | − | 0.882128i | \(-0.656110\pi\) | ||||
−0.471010 | + | 0.882128i | \(0.656110\pi\) | |||||||
\(80\) | −0.136683 | −0.0152816 | ||||||||
\(81\) | 3.46575 | 0.385083 | ||||||||
\(82\) | −2.01936 | −0.223001 | ||||||||
\(83\) | −12.8847 | −1.41428 | −0.707139 | − | 0.707075i | \(-0.750014\pi\) | ||||
−0.707139 | + | 0.707075i | \(0.750014\pi\) | |||||||
\(84\) | −6.00451 | −0.655146 | ||||||||
\(85\) | −1.23449 | −0.133899 | ||||||||
\(86\) | −15.6398 | −1.68648 | ||||||||
\(87\) | 0.599695 | 0.0642941 | ||||||||
\(88\) | −2.78141 | −0.296500 | ||||||||
\(89\) | 17.4249 | 1.84703 | 0.923517 | − | 0.383557i | \(-0.125301\pi\) | ||||
0.923517 | + | 0.383557i | \(0.125301\pi\) | |||||||
\(90\) | −1.55158 | −0.163551 | ||||||||
\(91\) | −2.89717 | −0.303706 | ||||||||
\(92\) | 10.7131 | 1.11692 | ||||||||
\(93\) | 7.39556 | 0.766884 | ||||||||
\(94\) | 12.9891 | 1.33972 | ||||||||
\(95\) | −1.48329 | −0.152183 | ||||||||
\(96\) | 4.15062 | 0.423621 | ||||||||
\(97\) | 11.0293 | 1.11986 | 0.559929 | − | 0.828541i | \(-0.310828\pi\) | ||||
0.559929 | + | 0.828541i | \(0.310828\pi\) | |||||||
\(98\) | 4.92622 | 0.497624 | ||||||||
\(99\) | −2.09839 | −0.210896 | ||||||||
\(100\) | −16.4240 | −1.64240 | ||||||||
\(101\) | 18.0000 | 1.79107 | 0.895534 | − | 0.444994i | \(-0.146794\pi\) | ||||
0.895534 | + | 0.444994i | \(0.146794\pi\) | |||||||
\(102\) | −8.08713 | −0.800746 | ||||||||
\(103\) | −3.63892 | −0.358554 | −0.179277 | − | 0.983799i | \(-0.557376\pi\) | ||||
−0.179277 | + | 0.983799i | \(0.557376\pi\) | |||||||
\(104\) | −4.06595 | −0.398699 | ||||||||
\(105\) | 0.516707 | 0.0504254 | ||||||||
\(106\) | 25.5260 | 2.47931 | ||||||||
\(107\) | 0.0678228 | 0.00655668 | 0.00327834 | − | 0.999995i | \(-0.498956\pi\) | ||||
0.00327834 | + | 0.999995i | \(0.498956\pi\) | |||||||
\(108\) | −14.5217 | −1.39735 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 0.596589 | 0.0568826 | ||||||||
\(111\) | 0.814794 | 0.0773368 | ||||||||
\(112\) | −1.04927 | −0.0991465 | ||||||||
\(113\) | 20.3004 | 1.90970 | 0.954852 | − | 0.297081i | \(-0.0960130\pi\) | ||||
0.954852 | + | 0.297081i | \(0.0960130\pi\) | |||||||
\(114\) | −9.71704 | −0.910084 | ||||||||
\(115\) | −0.921894 | −0.0859670 | ||||||||
\(116\) | 2.45826 | 0.228244 | ||||||||
\(117\) | −3.06749 | −0.283590 | ||||||||
\(118\) | 31.8010 | 2.92751 | ||||||||
\(119\) | −9.47679 | −0.868736 | ||||||||
\(120\) | 0.725156 | 0.0661974 | ||||||||
\(121\) | −10.1932 | −0.926651 | ||||||||
\(122\) | 28.2216 | 2.55507 | ||||||||
\(123\) | 0.712019 | 0.0642006 | ||||||||
\(124\) | 30.3158 | 2.72244 | ||||||||
\(125\) | 2.85042 | 0.254950 | ||||||||
\(126\) | −11.9110 | −1.06112 | ||||||||
\(127\) | 4.10139 | 0.363939 | 0.181970 | − | 0.983304i | \(-0.441753\pi\) | ||||
0.181970 | + | 0.983304i | \(0.441753\pi\) | |||||||
\(128\) | 19.2120 | 1.69812 | ||||||||
\(129\) | 5.51454 | 0.485528 | ||||||||
\(130\) | 0.872111 | 0.0764892 | ||||||||
\(131\) | 0.864195 | 0.0755051 | 0.0377525 | − | 0.999287i | \(-0.487980\pi\) | ||||
0.0377525 | + | 0.999287i | \(0.487980\pi\) | |||||||
\(132\) | 2.44448 | 0.212765 | ||||||||
\(133\) | −11.3868 | −0.987358 | ||||||||
\(134\) | 6.99438 | 0.604223 | ||||||||
\(135\) | 1.24964 | 0.107552 | ||||||||
\(136\) | −13.2999 | −1.14046 | ||||||||
\(137\) | 14.4554 | 1.23501 | 0.617505 | − | 0.786567i | \(-0.288144\pi\) | ||||
0.617505 | + | 0.786567i | \(0.288144\pi\) | |||||||
\(138\) | −6.03931 | −0.514100 | ||||||||
\(139\) | 8.07612 | 0.685008 | 0.342504 | − | 0.939516i | \(-0.388725\pi\) | ||||
0.342504 | + | 0.939516i | \(0.388725\pi\) | |||||||
\(140\) | 2.11808 | 0.179010 | ||||||||
\(141\) | −4.57991 | −0.385698 | ||||||||
\(142\) | −6.62418 | −0.555889 | ||||||||
\(143\) | 1.17946 | 0.0986314 | ||||||||
\(144\) | −1.11095 | −0.0925793 | ||||||||
\(145\) | −0.211541 | −0.0175675 | ||||||||
\(146\) | −5.49742 | −0.454970 | ||||||||
\(147\) | −1.73697 | −0.143263 | ||||||||
\(148\) | 3.33999 | 0.274546 | ||||||||
\(149\) | 21.3137 | 1.74609 | 0.873044 | − | 0.487641i | \(-0.162143\pi\) | ||||
0.873044 | + | 0.487641i | \(0.162143\pi\) | |||||||
\(150\) | 9.25876 | 0.755975 | ||||||||
\(151\) | 13.2986 | 1.08222 | 0.541112 | − | 0.840950i | \(-0.318003\pi\) | ||||
0.541112 | + | 0.840950i | \(0.318003\pi\) | |||||||
\(152\) | −15.9804 | −1.29618 | ||||||||
\(153\) | −10.0339 | −0.811193 | ||||||||
\(154\) | 4.57982 | 0.369053 | ||||||||
\(155\) | −2.60877 | −0.209541 | ||||||||
\(156\) | 3.57341 | 0.286102 | ||||||||
\(157\) | 2.79588 | 0.223136 | 0.111568 | − | 0.993757i | \(-0.464413\pi\) | ||||
0.111568 | + | 0.993757i | \(0.464413\pi\) | |||||||
\(158\) | 19.3483 | 1.53927 | ||||||||
\(159\) | −9.00038 | −0.713777 | ||||||||
\(160\) | −1.46412 | −0.115749 | ||||||||
\(161\) | −7.07708 | −0.557752 | ||||||||
\(162\) | −8.00879 | −0.629230 | ||||||||
\(163\) | −9.71610 | −0.761024 | −0.380512 | − | 0.924776i | \(-0.624252\pi\) | ||||
−0.380512 | + | 0.924776i | \(0.624252\pi\) | |||||||
\(164\) | 2.91870 | 0.227912 | ||||||||
\(165\) | −0.210355 | −0.0163761 | ||||||||
\(166\) | 29.7745 | 2.31095 | ||||||||
\(167\) | 19.3468 | 1.49710 | 0.748551 | − | 0.663077i | \(-0.230750\pi\) | ||||
0.748551 | + | 0.663077i | \(0.230750\pi\) | |||||||
\(168\) | 5.56679 | 0.429487 | ||||||||
\(169\) | −11.2758 | −0.867372 | ||||||||
\(170\) | 2.85272 | 0.218793 | ||||||||
\(171\) | −12.0562 | −0.921958 | ||||||||
\(172\) | 22.6051 | 1.72362 | ||||||||
\(173\) | 2.78884 | 0.212032 | 0.106016 | − | 0.994364i | \(-0.466191\pi\) | ||||
0.106016 | + | 0.994364i | \(0.466191\pi\) | |||||||
\(174\) | −1.38580 | −0.105057 | ||||||||
\(175\) | 10.8497 | 0.820164 | ||||||||
\(176\) | 0.427165 | 0.0321987 | ||||||||
\(177\) | −11.2129 | −0.842813 | ||||||||
\(178\) | −40.2662 | −3.01808 | ||||||||
\(179\) | −22.2048 | −1.65967 | −0.829833 | − | 0.558011i | \(-0.811565\pi\) | ||||
−0.829833 | + | 0.558011i | \(0.811565\pi\) | |||||||
\(180\) | 2.24259 | 0.167153 | ||||||||
\(181\) | 0.0302952 | 0.00225183 | 0.00112591 | − | 0.999999i | \(-0.499642\pi\) | ||||
0.00112591 | + | 0.999999i | \(0.499642\pi\) | |||||||
\(182\) | 6.69491 | 0.496260 | ||||||||
\(183\) | −9.95084 | −0.735587 | ||||||||
\(184\) | −9.93210 | −0.732204 | ||||||||
\(185\) | −0.287417 | −0.0211313 | ||||||||
\(186\) | −17.0900 | −1.25310 | ||||||||
\(187\) | 3.85807 | 0.282130 | ||||||||
\(188\) | −18.7739 | −1.36923 | ||||||||
\(189\) | 9.59307 | 0.697793 | ||||||||
\(190\) | 3.42766 | 0.248669 | ||||||||
\(191\) | 18.0105 | 1.30319 | 0.651596 | − | 0.758566i | \(-0.274100\pi\) | ||||
0.651596 | + | 0.758566i | \(0.274100\pi\) | |||||||
\(192\) | −10.3664 | −0.748130 | ||||||||
\(193\) | 13.6294 | 0.981063 | 0.490531 | − | 0.871424i | \(-0.336803\pi\) | ||||
0.490531 | + | 0.871424i | \(0.336803\pi\) | |||||||
\(194\) | −25.4870 | −1.82986 | ||||||||
\(195\) | −0.307503 | −0.0220207 | ||||||||
\(196\) | −7.12015 | −0.508582 | ||||||||
\(197\) | 6.56154 | 0.467490 | 0.233745 | − | 0.972298i | \(-0.424902\pi\) | ||||
0.233745 | + | 0.972298i | \(0.424902\pi\) | |||||||
\(198\) | 4.84906 | 0.344607 | ||||||||
\(199\) | −3.06411 | −0.217209 | −0.108605 | − | 0.994085i | \(-0.534638\pi\) | ||||
−0.108605 | + | 0.994085i | \(0.534638\pi\) | |||||||
\(200\) | 15.2267 | 1.07669 | ||||||||
\(201\) | −2.46619 | −0.173952 | ||||||||
\(202\) | −41.5952 | −2.92663 | ||||||||
\(203\) | −1.62393 | −0.113978 | ||||||||
\(204\) | 11.6888 | 0.818379 | ||||||||
\(205\) | −0.251163 | −0.0175420 | ||||||||
\(206\) | 8.40897 | 0.585881 | ||||||||
\(207\) | −7.49312 | −0.520808 | ||||||||
\(208\) | 0.624441 | 0.0432972 | ||||||||
\(209\) | 4.63564 | 0.320654 | ||||||||
\(210\) | −1.19403 | −0.0823958 | ||||||||
\(211\) | −1.57453 | −0.108395 | −0.0541976 | − | 0.998530i | \(-0.517260\pi\) | ||||
−0.0541976 | + | 0.998530i | \(0.517260\pi\) | |||||||
\(212\) | −36.8942 | −2.53391 | ||||||||
\(213\) | 2.33566 | 0.160037 | ||||||||
\(214\) | −0.156728 | −0.0107137 | ||||||||
\(215\) | −1.94524 | −0.132664 | ||||||||
\(216\) | 13.4631 | 0.916047 | ||||||||
\(217\) | −20.0266 | −1.35950 | ||||||||
\(218\) | 2.31084 | 0.156510 | ||||||||
\(219\) | 1.93837 | 0.130983 | ||||||||
\(220\) | −0.862284 | −0.0581352 | ||||||||
\(221\) | 5.63983 | 0.379376 | ||||||||
\(222\) | −1.88286 | −0.126369 | ||||||||
\(223\) | −5.10551 | −0.341890 | −0.170945 | − | 0.985281i | \(-0.554682\pi\) | ||||
−0.170945 | + | 0.985281i | \(0.554682\pi\) | |||||||
\(224\) | −11.2396 | −0.750977 | ||||||||
\(225\) | 11.4876 | 0.765838 | ||||||||
\(226\) | −46.9111 | −3.12048 | ||||||||
\(227\) | −4.90101 | −0.325291 | −0.162646 | − | 0.986685i | \(-0.552003\pi\) | ||||
−0.162646 | + | 0.986685i | \(0.552003\pi\) | |||||||
\(228\) | 14.0446 | 0.930125 | ||||||||
\(229\) | −13.5248 | −0.893744 | −0.446872 | − | 0.894598i | \(-0.647462\pi\) | ||||
−0.446872 | + | 0.894598i | \(0.647462\pi\) | |||||||
\(230\) | 2.13035 | 0.140471 | ||||||||
\(231\) | −1.61483 | −0.106248 | ||||||||
\(232\) | −2.27905 | −0.149627 | ||||||||
\(233\) | 13.4359 | 0.880215 | 0.440108 | − | 0.897945i | \(-0.354940\pi\) | ||||
0.440108 | + | 0.897945i | \(0.354940\pi\) | |||||||
\(234\) | 7.08849 | 0.463389 | ||||||||
\(235\) | 1.61555 | 0.105387 | ||||||||
\(236\) | −45.9637 | −2.99198 | ||||||||
\(237\) | −6.82215 | −0.443146 | ||||||||
\(238\) | 21.8994 | 1.41952 | ||||||||
\(239\) | 7.30707 | 0.472655 | 0.236328 | − | 0.971673i | \(-0.424056\pi\) | ||||
0.236328 | + | 0.971673i | \(0.424056\pi\) | |||||||
\(240\) | −0.111368 | −0.00718879 | ||||||||
\(241\) | 20.0435 | 1.29112 | 0.645558 | − | 0.763711i | \(-0.276625\pi\) | ||||
0.645558 | + | 0.763711i | \(0.276625\pi\) | |||||||
\(242\) | 23.5548 | 1.51416 | ||||||||
\(243\) | 15.8674 | 1.01789 | ||||||||
\(244\) | −40.7903 | −2.61133 | ||||||||
\(245\) | 0.612711 | 0.0391447 | ||||||||
\(246\) | −1.64536 | −0.104905 | ||||||||
\(247\) | 6.77650 | 0.431179 | ||||||||
\(248\) | −28.1058 | −1.78472 | ||||||||
\(249\) | −10.4984 | −0.665307 | ||||||||
\(250\) | −6.58687 | −0.416591 | ||||||||
\(251\) | 6.70412 | 0.423160 | 0.211580 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211580 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(252\) | 17.2156 | 1.08448 | ||||||||
\(253\) | 2.88113 | 0.181135 | ||||||||
\(254\) | −9.47766 | −0.594681 | ||||||||
\(255\) | −1.00586 | −0.0629892 | ||||||||
\(256\) | −18.9506 | −1.18441 | ||||||||
\(257\) | 7.55207 | 0.471085 | 0.235543 | − | 0.971864i | \(-0.424313\pi\) | ||||
0.235543 | + | 0.971864i | \(0.424313\pi\) | |||||||
\(258\) | −12.7432 | −0.793359 | ||||||||
\(259\) | −2.20640 | −0.137099 | ||||||||
\(260\) | −1.26051 | −0.0781736 | ||||||||
\(261\) | −1.71940 | −0.106428 | ||||||||
\(262\) | −1.99702 | −0.123376 | ||||||||
\(263\) | 29.6449 | 1.82798 | 0.913992 | − | 0.405733i | \(-0.132984\pi\) | ||||
0.913992 | + | 0.405733i | \(0.132984\pi\) | |||||||
\(264\) | −2.26628 | −0.139480 | ||||||||
\(265\) | 3.17486 | 0.195030 | ||||||||
\(266\) | 26.3130 | 1.61336 | ||||||||
\(267\) | 14.1977 | 0.868885 | ||||||||
\(268\) | −10.1094 | −0.617528 | ||||||||
\(269\) | 21.6719 | 1.32136 | 0.660679 | − | 0.750668i | \(-0.270268\pi\) | ||||
0.660679 | + | 0.750668i | \(0.270268\pi\) | |||||||
\(270\) | −2.88772 | −0.175741 | ||||||||
\(271\) | −12.5636 | −0.763184 | −0.381592 | − | 0.924331i | \(-0.624624\pi\) | ||||
−0.381592 | + | 0.924331i | \(0.624624\pi\) | |||||||
\(272\) | 2.04258 | 0.123849 | ||||||||
\(273\) | −2.36060 | −0.142870 | ||||||||
\(274\) | −33.4042 | −2.01802 | ||||||||
\(275\) | −4.41701 | −0.266356 | ||||||||
\(276\) | 8.72895 | 0.525421 | ||||||||
\(277\) | −6.30526 | −0.378846 | −0.189423 | − | 0.981896i | \(-0.560662\pi\) | ||||
−0.189423 | + | 0.981896i | \(0.560662\pi\) | |||||||
\(278\) | −18.6626 | −1.11931 | ||||||||
\(279\) | −21.2040 | −1.26945 | ||||||||
\(280\) | −1.96367 | −0.117352 | ||||||||
\(281\) | −3.68004 | −0.219533 | −0.109767 | − | 0.993957i | \(-0.535010\pi\) | ||||
−0.109767 | + | 0.993957i | \(0.535010\pi\) | |||||||
\(282\) | 10.5834 | 0.630235 | ||||||||
\(283\) | 24.5825 | 1.46128 | 0.730639 | − | 0.682764i | \(-0.239222\pi\) | ||||
0.730639 | + | 0.682764i | \(0.239222\pi\) | |||||||
\(284\) | 9.57430 | 0.568130 | ||||||||
\(285\) | −1.20858 | −0.0715901 | ||||||||
\(286\) | −2.72555 | −0.161165 | ||||||||
\(287\) | −1.92810 | −0.113812 | ||||||||
\(288\) | −11.9003 | −0.701234 | ||||||||
\(289\) | 1.44816 | 0.0851858 | ||||||||
\(290\) | 0.488838 | 0.0287055 | ||||||||
\(291\) | 8.98662 | 0.526805 | ||||||||
\(292\) | 7.94573 | 0.464989 | ||||||||
\(293\) | −12.3358 | −0.720663 | −0.360332 | − | 0.932824i | \(-0.617336\pi\) | ||||
−0.360332 | + | 0.932824i | \(0.617336\pi\) | |||||||
\(294\) | 4.01386 | 0.234093 | ||||||||
\(295\) | 3.95532 | 0.230288 | ||||||||
\(296\) | −3.09651 | −0.179981 | ||||||||
\(297\) | −3.90541 | −0.226615 | ||||||||
\(298\) | −49.2526 | −2.85313 | ||||||||
\(299\) | 4.21172 | 0.243570 | ||||||||
\(300\) | −13.3822 | −0.772622 | ||||||||
\(301\) | −14.9330 | −0.860722 | ||||||||
\(302\) | −30.7310 | −1.76837 | ||||||||
\(303\) | 14.6663 | 0.842557 | ||||||||
\(304\) | 2.45424 | 0.140760 | ||||||||
\(305\) | 3.51013 | 0.200990 | ||||||||
\(306\) | 23.1868 | 1.32550 | ||||||||
\(307\) | −7.42348 | −0.423680 | −0.211840 | − | 0.977304i | \(-0.567946\pi\) | ||||
−0.211840 | + | 0.977304i | \(0.567946\pi\) | |||||||
\(308\) | −6.61948 | −0.377180 | ||||||||
\(309\) | −2.96497 | −0.168671 | ||||||||
\(310\) | 6.02845 | 0.342393 | ||||||||
\(311\) | 28.1145 | 1.59423 | 0.797115 | − | 0.603828i | \(-0.206359\pi\) | ||||
0.797115 | + | 0.603828i | \(0.206359\pi\) | |||||||
\(312\) | −3.31291 | −0.187557 | ||||||||
\(313\) | −13.4692 | −0.761322 | −0.380661 | − | 0.924715i | \(-0.624303\pi\) | ||||
−0.380661 | + | 0.924715i | \(0.624303\pi\) | |||||||
\(314\) | −6.46084 | −0.364606 | ||||||||
\(315\) | −1.48146 | −0.0834708 | ||||||||
\(316\) | −27.9652 | −1.57317 | ||||||||
\(317\) | 14.2437 | 0.800008 | 0.400004 | − | 0.916513i | \(-0.369009\pi\) | ||||
0.400004 | + | 0.916513i | \(0.369009\pi\) | |||||||
\(318\) | 20.7985 | 1.16632 | ||||||||
\(319\) | 0.661114 | 0.0370153 | ||||||||
\(320\) | 3.65672 | 0.204417 | ||||||||
\(321\) | 0.0552616 | 0.00308440 | ||||||||
\(322\) | 16.3540 | 0.911373 | ||||||||
\(323\) | 22.1663 | 1.23336 | ||||||||
\(324\) | 11.5756 | 0.643086 | ||||||||
\(325\) | −6.45691 | −0.358165 | ||||||||
\(326\) | 22.4524 | 1.24352 | ||||||||
\(327\) | −0.814794 | −0.0450582 | ||||||||
\(328\) | −2.70593 | −0.149410 | ||||||||
\(329\) | 12.4021 | 0.683747 | ||||||||
\(330\) | 0.486097 | 0.0267588 | ||||||||
\(331\) | 3.00918 | 0.165399 | 0.0826997 | − | 0.996575i | \(-0.473646\pi\) | ||||
0.0826997 | + | 0.996575i | \(0.473646\pi\) | |||||||
\(332\) | −43.0347 | −2.36184 | ||||||||
\(333\) | −2.33611 | −0.128018 | ||||||||
\(334\) | −44.7075 | −2.44628 | ||||||||
\(335\) | 0.869943 | 0.0475301 | ||||||||
\(336\) | −0.854937 | −0.0466407 | ||||||||
\(337\) | −32.7664 | −1.78490 | −0.892449 | − | 0.451148i | \(-0.851015\pi\) | ||||
−0.892449 | + | 0.451148i | \(0.851015\pi\) | |||||||
\(338\) | 26.0567 | 1.41730 | ||||||||
\(339\) | 16.5407 | 0.898366 | ||||||||
\(340\) | −4.12319 | −0.223611 | ||||||||
\(341\) | 8.15299 | 0.441509 | ||||||||
\(342\) | 27.8599 | 1.50649 | ||||||||
\(343\) | 20.1484 | 1.08791 | ||||||||
\(344\) | −20.9572 | −1.12994 | ||||||||
\(345\) | −0.751154 | −0.0404407 | ||||||||
\(346\) | −6.44458 | −0.346463 | ||||||||
\(347\) | 6.80346 | 0.365229 | 0.182615 | − | 0.983185i | \(-0.441544\pi\) | ||||
0.182615 | + | 0.983185i | \(0.441544\pi\) | |||||||
\(348\) | 2.00298 | 0.107371 | ||||||||
\(349\) | 3.04624 | 0.163061 | 0.0815306 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815306 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(350\) | −25.0720 | −1.34016 | ||||||||
\(351\) | −5.70903 | −0.304726 | ||||||||
\(352\) | 4.57572 | 0.243887 | ||||||||
\(353\) | 9.09743 | 0.484207 | 0.242104 | − | 0.970250i | \(-0.422163\pi\) | ||||
0.242104 | + | 0.970250i | \(0.422163\pi\) | |||||||
\(354\) | 25.9112 | 1.37717 | ||||||||
\(355\) | −0.823898 | −0.0437280 | ||||||||
\(356\) | 58.1990 | 3.08454 | ||||||||
\(357\) | −7.72163 | −0.408672 | ||||||||
\(358\) | 51.3118 | 2.71192 | ||||||||
\(359\) | −26.5807 | −1.40287 | −0.701437 | − | 0.712732i | \(-0.747458\pi\) | ||||
−0.701437 | + | 0.712732i | \(0.747458\pi\) | |||||||
\(360\) | −2.07911 | −0.109579 | ||||||||
\(361\) | 7.63370 | 0.401774 | ||||||||
\(362\) | −0.0700075 | −0.00367951 | ||||||||
\(363\) | −8.30533 | −0.435917 | ||||||||
\(364\) | −9.67653 | −0.507188 | ||||||||
\(365\) | −0.683755 | −0.0357894 | ||||||||
\(366\) | 22.9948 | 1.20196 | ||||||||
\(367\) | 28.6879 | 1.49749 | 0.748747 | − | 0.662855i | \(-0.230656\pi\) | ||||
0.748747 | + | 0.662855i | \(0.230656\pi\) | |||||||
\(368\) | 1.52535 | 0.0795146 | ||||||||
\(369\) | −2.04144 | −0.106273 | ||||||||
\(370\) | 0.664174 | 0.0345288 | ||||||||
\(371\) | 24.3724 | 1.26535 | ||||||||
\(372\) | 24.7011 | 1.28069 | ||||||||
\(373\) | −13.4992 | −0.698964 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(374\) | −8.91539 | −0.461004 | ||||||||
\(375\) | 2.32251 | 0.119934 | ||||||||
\(376\) | 17.4053 | 0.897609 | ||||||||
\(377\) | 0.966435 | 0.0497739 | ||||||||
\(378\) | −22.1681 | −1.14020 | ||||||||
\(379\) | −24.3828 | −1.25246 | −0.626231 | − | 0.779638i | \(-0.715403\pi\) | ||||
−0.626231 | + | 0.779638i | \(0.715403\pi\) | |||||||
\(380\) | −4.95419 | −0.254145 | ||||||||
\(381\) | 3.34179 | 0.171205 | ||||||||
\(382\) | −41.6194 | −2.12943 | ||||||||
\(383\) | 10.8263 | 0.553200 | 0.276600 | − | 0.960985i | \(-0.410792\pi\) | ||||
0.276600 | + | 0.960985i | \(0.410792\pi\) | |||||||
\(384\) | 15.6539 | 0.798833 | ||||||||
\(385\) | 0.569626 | 0.0290308 | ||||||||
\(386\) | −31.4953 | −1.60307 | ||||||||
\(387\) | −15.8108 | −0.803710 | ||||||||
\(388\) | 36.8378 | 1.87016 | ||||||||
\(389\) | 0.846100 | 0.0428990 | 0.0214495 | − | 0.999770i | \(-0.493172\pi\) | ||||
0.0214495 | + | 0.999770i | \(0.493172\pi\) | |||||||
\(390\) | 0.710591 | 0.0359822 | ||||||||
\(391\) | 13.7767 | 0.696718 | ||||||||
\(392\) | 6.60109 | 0.333406 | ||||||||
\(393\) | 0.704141 | 0.0355192 | ||||||||
\(394\) | −15.1627 | −0.763885 | ||||||||
\(395\) | 2.40650 | 0.121084 | ||||||||
\(396\) | −7.00862 | −0.352196 | ||||||||
\(397\) | 29.2462 | 1.46782 | 0.733912 | − | 0.679245i | \(-0.237693\pi\) | ||||
0.733912 | + | 0.679245i | \(0.237693\pi\) | |||||||
\(398\) | 7.08068 | 0.354923 | ||||||||
\(399\) | −9.27787 | −0.464475 | ||||||||
\(400\) | −2.33850 | −0.116925 | ||||||||
\(401\) | 27.7390 | 1.38522 | 0.692610 | − | 0.721312i | \(-0.256461\pi\) | ||||
0.692610 | + | 0.721312i | \(0.256461\pi\) | |||||||
\(402\) | 5.69898 | 0.284239 | ||||||||
\(403\) | 11.9183 | 0.593691 | ||||||||
\(404\) | 60.1198 | 2.99107 | ||||||||
\(405\) | −0.996112 | −0.0494972 | ||||||||
\(406\) | 3.75265 | 0.186241 | ||||||||
\(407\) | 0.898242 | 0.0445242 | ||||||||
\(408\) | −10.8367 | −0.536496 | ||||||||
\(409\) | −9.01240 | −0.445635 | −0.222817 | − | 0.974860i | \(-0.571525\pi\) | ||||
−0.222817 | + | 0.974860i | \(0.571525\pi\) | |||||||
\(410\) | 0.580398 | 0.0286638 | ||||||||
\(411\) | 11.7782 | 0.580975 | ||||||||
\(412\) | −12.1540 | −0.598783 | ||||||||
\(413\) | 30.3637 | 1.49410 | ||||||||
\(414\) | 17.3154 | 0.851006 | ||||||||
\(415\) | 3.70327 | 0.181786 | ||||||||
\(416\) | 6.68891 | 0.327951 | ||||||||
\(417\) | 6.58038 | 0.322242 | ||||||||
\(418\) | −10.7122 | −0.523952 | ||||||||
\(419\) | 23.4981 | 1.14796 | 0.573978 | − | 0.818871i | \(-0.305399\pi\) | ||||
0.573978 | + | 0.818871i | \(0.305399\pi\) | |||||||
\(420\) | 1.72580 | 0.0842102 | ||||||||
\(421\) | −30.7833 | −1.50029 | −0.750144 | − | 0.661274i | \(-0.770016\pi\) | ||||
−0.750144 | + | 0.661274i | \(0.770016\pi\) | |||||||
\(422\) | 3.63849 | 0.177119 | ||||||||
\(423\) | 13.1311 | 0.638458 | ||||||||
\(424\) | 34.2046 | 1.66112 | ||||||||
\(425\) | −21.1208 | −1.02451 | ||||||||
\(426\) | −5.39734 | −0.261502 | ||||||||
\(427\) | 26.9461 | 1.30402 | ||||||||
\(428\) | 0.226528 | 0.0109496 | ||||||||
\(429\) | 0.961017 | 0.0463984 | ||||||||
\(430\) | 4.49514 | 0.216775 | ||||||||
\(431\) | 11.7164 | 0.564359 | 0.282179 | − | 0.959362i | \(-0.408943\pi\) | ||||
0.282179 | + | 0.959362i | \(0.408943\pi\) | |||||||
\(432\) | −2.06764 | −0.0994793 | ||||||||
\(433\) | 9.27250 | 0.445608 | 0.222804 | − | 0.974863i | \(-0.428479\pi\) | ||||
0.222804 | + | 0.974863i | \(0.428479\pi\) | |||||||
\(434\) | 46.2784 | 2.22143 | ||||||||
\(435\) | −0.172362 | −0.00826414 | ||||||||
\(436\) | −3.33999 | −0.159957 | ||||||||
\(437\) | 16.5533 | 0.791852 | ||||||||
\(438\) | −4.47926 | −0.214028 | ||||||||
\(439\) | 27.8010 | 1.32687 | 0.663434 | − | 0.748235i | \(-0.269098\pi\) | ||||
0.663434 | + | 0.748235i | \(0.269098\pi\) | |||||||
\(440\) | 0.799424 | 0.0381111 | ||||||||
\(441\) | 4.98009 | 0.237147 | ||||||||
\(442\) | −13.0328 | −0.619905 | ||||||||
\(443\) | 19.2136 | 0.912866 | 0.456433 | − | 0.889758i | \(-0.349127\pi\) | ||||
0.456433 | + | 0.889758i | \(0.349127\pi\) | |||||||
\(444\) | 2.72140 | 0.129152 | ||||||||
\(445\) | −5.00820 | −0.237411 | ||||||||
\(446\) | 11.7980 | 0.558653 | ||||||||
\(447\) | 17.3663 | 0.821398 | ||||||||
\(448\) | 28.0714 | 1.32625 | ||||||||
\(449\) | −41.5434 | −1.96055 | −0.980277 | − | 0.197631i | \(-0.936675\pi\) | ||||
−0.980277 | + | 0.197631i | \(0.936675\pi\) | |||||||
\(450\) | −26.5460 | −1.25139 | ||||||||
\(451\) | 0.784942 | 0.0369615 | ||||||||
\(452\) | 67.8033 | 3.18920 | ||||||||
\(453\) | 10.8356 | 0.509102 | ||||||||
\(454\) | 11.3255 | 0.531530 | ||||||||
\(455\) | 0.832696 | 0.0390374 | ||||||||
\(456\) | −13.0207 | −0.609752 | ||||||||
\(457\) | −25.9963 | −1.21605 | −0.608027 | − | 0.793916i | \(-0.708039\pi\) | ||||
−0.608027 | + | 0.793916i | \(0.708039\pi\) | |||||||
\(458\) | 31.2537 | 1.46039 | ||||||||
\(459\) | −18.6745 | −0.871651 | ||||||||
\(460\) | −3.07912 | −0.143565 | ||||||||
\(461\) | −24.3920 | −1.13605 | −0.568025 | − | 0.823012i | \(-0.692292\pi\) | ||||
−0.568025 | + | 0.823012i | \(0.692292\pi\) | |||||||
\(462\) | 3.73161 | 0.173610 | ||||||||
\(463\) | 20.4853 | 0.952031 | 0.476015 | − | 0.879437i | \(-0.342081\pi\) | ||||
0.476015 | + | 0.879437i | \(0.342081\pi\) | |||||||
\(464\) | 0.350013 | 0.0162490 | ||||||||
\(465\) | −2.12561 | −0.0985727 | ||||||||
\(466\) | −31.0483 | −1.43828 | ||||||||
\(467\) | −8.32520 | −0.385244 | −0.192622 | − | 0.981273i | \(-0.561699\pi\) | ||||
−0.192622 | + | 0.981273i | \(0.561699\pi\) | |||||||
\(468\) | −10.2454 | −0.473593 | ||||||||
\(469\) | 6.67827 | 0.308374 | ||||||||
\(470\) | −3.73328 | −0.172203 | ||||||||
\(471\) | 2.27807 | 0.104968 | ||||||||
\(472\) | 42.6130 | 1.96142 | ||||||||
\(473\) | 6.07932 | 0.279527 | ||||||||
\(474\) | 15.7649 | 0.724106 | ||||||||
\(475\) | −25.3776 | −1.16440 | ||||||||
\(476\) | −31.6524 | −1.45078 | ||||||||
\(477\) | 25.8052 | 1.18154 | ||||||||
\(478\) | −16.8855 | −0.772324 | ||||||||
\(479\) | −13.4689 | −0.615408 | −0.307704 | − | 0.951482i | \(-0.599561\pi\) | ||||
−0.307704 | + | 0.951482i | \(0.599561\pi\) | |||||||
\(480\) | −1.19296 | −0.0544508 | ||||||||
\(481\) | 1.31308 | 0.0598711 | ||||||||
\(482\) | −46.3174 | −2.10970 | ||||||||
\(483\) | −5.76636 | −0.262378 | ||||||||
\(484\) | −34.0451 | −1.54750 | ||||||||
\(485\) | −3.17001 | −0.143943 | ||||||||
\(486\) | −36.6670 | −1.66325 | ||||||||
\(487\) | −6.69308 | −0.303292 | −0.151646 | − | 0.988435i | \(-0.548457\pi\) | ||||
−0.151646 | + | 0.988435i | \(0.548457\pi\) | |||||||
\(488\) | 37.8167 | 1.71188 | ||||||||
\(489\) | −7.91662 | −0.358002 | ||||||||
\(490\) | −1.41588 | −0.0639629 | ||||||||
\(491\) | 13.0608 | 0.589424 | 0.294712 | − | 0.955586i | \(-0.404776\pi\) | ||||
0.294712 | + | 0.955586i | \(0.404776\pi\) | |||||||
\(492\) | 2.37814 | 0.107215 | ||||||||
\(493\) | 3.16125 | 0.142376 | ||||||||
\(494\) | −15.6594 | −0.704551 | ||||||||
\(495\) | 0.603113 | 0.0271079 | ||||||||
\(496\) | 4.31643 | 0.193814 | ||||||||
\(497\) | −6.32480 | −0.283706 | ||||||||
\(498\) | 24.2601 | 1.08712 | ||||||||
\(499\) | 11.5792 | 0.518357 | 0.259179 | − | 0.965829i | \(-0.416548\pi\) | ||||
0.259179 | + | 0.965829i | \(0.416548\pi\) | |||||||
\(500\) | 9.52038 | 0.425764 | ||||||||
\(501\) | 15.7637 | 0.704269 | ||||||||
\(502\) | −15.4922 | −0.691449 | ||||||||
\(503\) | −8.48039 | −0.378122 | −0.189061 | − | 0.981965i | \(-0.560544\pi\) | ||||
−0.189061 | + | 0.981965i | \(0.560544\pi\) | |||||||
\(504\) | −15.9606 | −0.710943 | ||||||||
\(505\) | −5.17350 | −0.230218 | ||||||||
\(506\) | −6.65783 | −0.295977 | ||||||||
\(507\) | −9.18748 | −0.408030 | ||||||||
\(508\) | 13.6986 | 0.607777 | ||||||||
\(509\) | −28.4189 | −1.25964 | −0.629822 | − | 0.776739i | \(-0.716872\pi\) | ||||
−0.629822 | + | 0.776739i | \(0.716872\pi\) | |||||||
\(510\) | 2.32438 | 0.102925 | ||||||||
\(511\) | −5.24896 | −0.232200 | ||||||||
\(512\) | 5.36764 | 0.237219 | ||||||||
\(513\) | −22.4382 | −0.990672 | ||||||||
\(514\) | −17.4517 | −0.769759 | ||||||||
\(515\) | 1.04589 | 0.0460873 | ||||||||
\(516\) | 18.4185 | 0.810830 | ||||||||
\(517\) | −5.04897 | −0.222053 | ||||||||
\(518\) | 5.09865 | 0.224022 | ||||||||
\(519\) | 2.27233 | 0.0997444 | ||||||||
\(520\) | 1.16862 | 0.0512474 | ||||||||
\(521\) | 21.8034 | 0.955223 | 0.477611 | − | 0.878571i | \(-0.341503\pi\) | ||||
0.477611 | + | 0.878571i | \(0.341503\pi\) | |||||||
\(522\) | 3.97325 | 0.173905 | ||||||||
\(523\) | −26.4063 | −1.15467 | −0.577334 | − | 0.816508i | \(-0.695907\pi\) | ||||
−0.577334 | + | 0.816508i | \(0.695907\pi\) | |||||||
\(524\) | 2.88640 | 0.126093 | ||||||||
\(525\) | 8.84031 | 0.385823 | ||||||||
\(526\) | −68.5047 | −2.98695 | ||||||||
\(527\) | 38.9852 | 1.69822 | ||||||||
\(528\) | 0.348051 | 0.0151470 | ||||||||
\(529\) | −12.7118 | −0.552688 | ||||||||
\(530\) | −7.33660 | −0.318682 | ||||||||
\(531\) | 32.1487 | 1.39513 | ||||||||
\(532\) | −38.0317 | −1.64888 | ||||||||
\(533\) | 1.14745 | 0.0497016 | ||||||||
\(534\) | −32.8086 | −1.41977 | ||||||||
\(535\) | −0.0194934 | −0.000842773 0 | ||||||||
\(536\) | 9.37241 | 0.404826 | ||||||||
\(537\) | −18.0924 | −0.780743 | ||||||||
\(538\) | −50.0803 | −2.15912 | ||||||||
\(539\) | −1.91486 | −0.0824789 | ||||||||
\(540\) | 4.17378 | 0.179611 | ||||||||
\(541\) | 12.6031 | 0.541849 | 0.270925 | − | 0.962601i | \(-0.412671\pi\) | ||||
0.270925 | + | 0.962601i | \(0.412671\pi\) | |||||||
\(542\) | 29.0325 | 1.24705 | ||||||||
\(543\) | 0.0246844 | 0.00105931 | ||||||||
\(544\) | 21.8797 | 0.938086 | ||||||||
\(545\) | 0.287417 | 0.0123116 | ||||||||
\(546\) | 5.45497 | 0.233451 | ||||||||
\(547\) | 19.3293 | 0.826463 | 0.413231 | − | 0.910626i | \(-0.364400\pi\) | ||||
0.413231 | + | 0.910626i | \(0.364400\pi\) | |||||||
\(548\) | 48.2810 | 2.06246 | ||||||||
\(549\) | 28.5302 | 1.21764 | ||||||||
\(550\) | 10.2070 | 0.435228 | ||||||||
\(551\) | 3.79838 | 0.161816 | ||||||||
\(552\) | −8.09262 | −0.344445 | ||||||||
\(553\) | 18.4739 | 0.785589 | ||||||||
\(554\) | 14.5705 | 0.619040 | ||||||||
\(555\) | −0.234185 | −0.00994061 | ||||||||
\(556\) | 26.9742 | 1.14396 | ||||||||
\(557\) | 30.1331 | 1.27678 | 0.638391 | − | 0.769713i | \(-0.279600\pi\) | ||||
0.638391 | + | 0.769713i | \(0.279600\pi\) | |||||||
\(558\) | 48.9990 | 2.07429 | ||||||||
\(559\) | 8.88692 | 0.375877 | ||||||||
\(560\) | 0.301577 | 0.0127440 | ||||||||
\(561\) | 3.14353 | 0.132720 | ||||||||
\(562\) | 8.50400 | 0.358720 | ||||||||
\(563\) | 24.1584 | 1.01815 | 0.509077 | − | 0.860721i | \(-0.329987\pi\) | ||||
0.509077 | + | 0.860721i | \(0.329987\pi\) | |||||||
\(564\) | −15.2968 | −0.644114 | ||||||||
\(565\) | −5.83468 | −0.245467 | ||||||||
\(566\) | −56.8062 | −2.38774 | ||||||||
\(567\) | −7.64683 | −0.321137 | ||||||||
\(568\) | −8.87634 | −0.372443 | ||||||||
\(569\) | 41.0380 | 1.72040 | 0.860202 | − | 0.509953i | \(-0.170337\pi\) | ||||
0.860202 | + | 0.509953i | \(0.170337\pi\) | |||||||
\(570\) | 2.79284 | 0.116979 | ||||||||
\(571\) | 25.2461 | 1.05652 | 0.528259 | − | 0.849084i | \(-0.322845\pi\) | ||||
0.528259 | + | 0.849084i | \(0.322845\pi\) | |||||||
\(572\) | 3.93939 | 0.164714 | ||||||||
\(573\) | 14.6748 | 0.613050 | ||||||||
\(574\) | 4.45552 | 0.185970 | ||||||||
\(575\) | −15.7726 | −0.657764 | ||||||||
\(576\) | 29.7217 | 1.23840 | ||||||||
\(577\) | 41.0081 | 1.70719 | 0.853595 | − | 0.520937i | \(-0.174417\pi\) | ||||
0.853595 | + | 0.520937i | \(0.174417\pi\) | |||||||
\(578\) | −3.34647 | −0.139195 | ||||||||
\(579\) | 11.1051 | 0.461513 | ||||||||
\(580\) | −0.706545 | −0.0293377 | ||||||||
\(581\) | 28.4288 | 1.17943 | ||||||||
\(582\) | −20.7667 | −0.860806 | ||||||||
\(583\) | −9.92217 | −0.410934 | ||||||||
\(584\) | −7.36649 | −0.304828 | ||||||||
\(585\) | 0.881647 | 0.0364516 | ||||||||
\(586\) | 28.5060 | 1.17757 | ||||||||
\(587\) | −22.2761 | −0.919434 | −0.459717 | − | 0.888065i | \(-0.652049\pi\) | ||||
−0.459717 | + | 0.888065i | \(0.652049\pi\) | |||||||
\(588\) | −5.80146 | −0.239248 | ||||||||
\(589\) | 46.8424 | 1.93011 | ||||||||
\(590\) | −9.14012 | −0.376293 | ||||||||
\(591\) | 5.34630 | 0.219917 | ||||||||
\(592\) | 0.475556 | 0.0195452 | ||||||||
\(593\) | −31.4364 | −1.29094 | −0.645469 | − | 0.763787i | \(-0.723338\pi\) | ||||
−0.645469 | + | 0.763787i | \(0.723338\pi\) | |||||||
\(594\) | 9.02478 | 0.370291 | ||||||||
\(595\) | 2.72379 | 0.111664 | ||||||||
\(596\) | 71.1876 | 2.91596 | ||||||||
\(597\) | −2.49662 | −0.102180 | ||||||||
\(598\) | −9.73261 | −0.397996 | ||||||||
\(599\) | −18.0834 | −0.738869 | −0.369434 | − | 0.929257i | \(-0.620449\pi\) | ||||
−0.369434 | + | 0.929257i | \(0.620449\pi\) | |||||||
\(600\) | 12.4067 | 0.506500 | ||||||||
\(601\) | 42.0147 | 1.71382 | 0.856908 | − | 0.515469i | \(-0.172382\pi\) | ||||
0.856908 | + | 0.515469i | \(0.172382\pi\) | |||||||
\(602\) | 34.5077 | 1.40643 | ||||||||
\(603\) | 7.07086 | 0.287948 | ||||||||
\(604\) | 44.4172 | 1.80731 | ||||||||
\(605\) | 2.92968 | 0.119109 | ||||||||
\(606\) | −33.8915 | −1.37675 | ||||||||
\(607\) | −10.4174 | −0.422829 | −0.211415 | − | 0.977396i | \(-0.567807\pi\) | ||||
−0.211415 | + | 0.977396i | \(0.567807\pi\) | |||||||
\(608\) | 26.2894 | 1.06618 | ||||||||
\(609\) | −1.32317 | −0.0536175 | ||||||||
\(610\) | −8.11136 | −0.328420 | ||||||||
\(611\) | −7.38072 | −0.298592 | ||||||||
\(612\) | −33.5131 | −1.35469 | ||||||||
\(613\) | −33.2254 | −1.34196 | −0.670980 | − | 0.741475i | \(-0.734126\pi\) | ||||
−0.670980 | + | 0.741475i | \(0.734126\pi\) | |||||||
\(614\) | 17.1545 | 0.692298 | ||||||||
\(615\) | −0.204646 | −0.00825213 | ||||||||
\(616\) | 6.13692 | 0.247263 | ||||||||
\(617\) | 10.1943 | 0.410407 | 0.205203 | − | 0.978719i | \(-0.434214\pi\) | ||||
0.205203 | + | 0.978719i | \(0.434214\pi\) | |||||||
\(618\) | 6.85158 | 0.275611 | ||||||||
\(619\) | 38.9238 | 1.56448 | 0.782240 | − | 0.622977i | \(-0.214077\pi\) | ||||
0.782240 | + | 0.622977i | \(0.214077\pi\) | |||||||
\(620\) | −8.71325 | −0.349933 | ||||||||
\(621\) | −13.9457 | −0.559624 | ||||||||
\(622\) | −64.9682 | −2.60499 | ||||||||
\(623\) | −38.4463 | −1.54032 | ||||||||
\(624\) | 0.508791 | 0.0203679 | ||||||||
\(625\) | 23.7677 | 0.950708 | ||||||||
\(626\) | 31.1251 | 1.24401 | ||||||||
\(627\) | 3.77709 | 0.150842 | ||||||||
\(628\) | 9.33822 | 0.372636 | ||||||||
\(629\) | 4.29513 | 0.171258 | ||||||||
\(630\) | 3.42342 | 0.136392 | ||||||||
\(631\) | 33.2773 | 1.32475 | 0.662374 | − | 0.749173i | \(-0.269549\pi\) | ||||
0.662374 | + | 0.749173i | \(0.269549\pi\) | |||||||
\(632\) | 25.9266 | 1.03130 | ||||||||
\(633\) | −1.28292 | −0.0509915 | ||||||||
\(634\) | −32.9150 | −1.30722 | ||||||||
\(635\) | −1.17881 | −0.0467795 | ||||||||
\(636\) | −30.0612 | −1.19200 | ||||||||
\(637\) | −2.79920 | −0.110908 | ||||||||
\(638\) | −1.52773 | −0.0604834 | ||||||||
\(639\) | −6.69662 | −0.264914 | ||||||||
\(640\) | −5.52186 | −0.218271 | ||||||||
\(641\) | −27.5964 | −1.08999 | −0.544997 | − | 0.838438i | \(-0.683469\pi\) | ||||
−0.544997 | + | 0.838438i | \(0.683469\pi\) | |||||||
\(642\) | −0.127701 | −0.00503995 | ||||||||
\(643\) | 5.46781 | 0.215629 | 0.107815 | − | 0.994171i | \(-0.465615\pi\) | ||||
0.107815 | + | 0.994171i | \(0.465615\pi\) | |||||||
\(644\) | −23.6374 | −0.931443 | ||||||||
\(645\) | −1.58497 | −0.0624081 | ||||||||
\(646\) | −51.2227 | −2.01533 | ||||||||
\(647\) | 13.8578 | 0.544808 | 0.272404 | − | 0.962183i | \(-0.412181\pi\) | ||||
0.272404 | + | 0.962183i | \(0.412181\pi\) | |||||||
\(648\) | −10.7317 | −0.421581 | ||||||||
\(649\) | −12.3613 | −0.485223 | ||||||||
\(650\) | 14.9209 | 0.585246 | ||||||||
\(651\) | −16.3176 | −0.639537 | ||||||||
\(652\) | −32.4517 | −1.27091 | ||||||||
\(653\) | 41.5317 | 1.62526 | 0.812630 | − | 0.582780i | \(-0.198035\pi\) | ||||
0.812630 | + | 0.582780i | \(0.198035\pi\) | |||||||
\(654\) | 1.88286 | 0.0736257 | ||||||||
\(655\) | −0.248384 | −0.00970516 | ||||||||
\(656\) | 0.415571 | 0.0162253 | ||||||||
\(657\) | −5.55753 | −0.216820 | ||||||||
\(658\) | −28.6592 | −1.11725 | ||||||||
\(659\) | −26.7706 | −1.04284 | −0.521418 | − | 0.853302i | \(-0.674597\pi\) | ||||
−0.521418 | + | 0.853302i | \(0.674597\pi\) | |||||||
\(660\) | −0.702584 | −0.0273481 | ||||||||
\(661\) | −24.5489 | −0.954843 | −0.477421 | − | 0.878674i | \(-0.658429\pi\) | ||||
−0.477421 | + | 0.878674i | \(0.658429\pi\) | |||||||
\(662\) | −6.95374 | −0.270265 | ||||||||
\(663\) | 4.59530 | 0.178467 | ||||||||
\(664\) | 39.8975 | 1.54832 | ||||||||
\(665\) | 3.27275 | 0.126912 | ||||||||
\(666\) | 5.39838 | 0.209183 | ||||||||
\(667\) | 2.36076 | 0.0914090 | ||||||||
\(668\) | 64.6182 | 2.50015 | ||||||||
\(669\) | −4.15994 | −0.160833 | ||||||||
\(670\) | −2.01030 | −0.0776647 | ||||||||
\(671\) | −10.9700 | −0.423491 | ||||||||
\(672\) | −9.15795 | −0.353276 | ||||||||
\(673\) | 17.0851 | 0.658581 | 0.329290 | − | 0.944229i | \(-0.393191\pi\) | ||||
0.329290 | + | 0.944229i | \(0.393191\pi\) | |||||||
\(674\) | 75.7179 | 2.91655 | ||||||||
\(675\) | 21.3800 | 0.822916 | ||||||||
\(676\) | −37.6612 | −1.44851 | ||||||||
\(677\) | 32.0785 | 1.23288 | 0.616439 | − | 0.787403i | \(-0.288575\pi\) | ||||
0.616439 | + | 0.787403i | \(0.288575\pi\) | |||||||
\(678\) | −38.2229 | −1.46794 | ||||||||
\(679\) | −24.3351 | −0.933896 | ||||||||
\(680\) | 3.82261 | 0.146590 | ||||||||
\(681\) | −3.99331 | −0.153024 | ||||||||
\(682\) | −18.8403 | −0.721431 | ||||||||
\(683\) | 14.0085 | 0.536022 | 0.268011 | − | 0.963416i | \(-0.413634\pi\) | ||||
0.268011 | + | 0.963416i | \(0.413634\pi\) | |||||||
\(684\) | −40.2675 | −1.53967 | ||||||||
\(685\) | −4.15473 | −0.158744 | ||||||||
\(686\) | −46.5598 | −1.77766 | ||||||||
\(687\) | −11.0199 | −0.420437 | ||||||||
\(688\) | 3.21857 | 0.122707 | ||||||||
\(689\) | −14.5045 | −0.552578 | ||||||||
\(690\) | 1.73580 | 0.0660807 | ||||||||
\(691\) | −31.9275 | −1.21458 | −0.607289 | − | 0.794481i | \(-0.707743\pi\) | ||||
−0.607289 | + | 0.794481i | \(0.707743\pi\) | |||||||
\(692\) | 9.31471 | 0.354092 | ||||||||
\(693\) | 4.62990 | 0.175875 | ||||||||
\(694\) | −15.7217 | −0.596789 | ||||||||
\(695\) | −2.32121 | −0.0880485 | ||||||||
\(696\) | −1.85696 | −0.0703879 | ||||||||
\(697\) | 3.75336 | 0.142169 | ||||||||
\(698\) | −7.03937 | −0.266444 | ||||||||
\(699\) | 10.9475 | 0.414072 | ||||||||
\(700\) | 36.2380 | 1.36967 | ||||||||
\(701\) | −39.3670 | −1.48687 | −0.743435 | − | 0.668808i | \(-0.766805\pi\) | ||||
−0.743435 | + | 0.668808i | \(0.766805\pi\) | |||||||
\(702\) | 13.1927 | 0.497925 | ||||||||
\(703\) | 5.16079 | 0.194643 | ||||||||
\(704\) | −11.4281 | −0.430712 | ||||||||
\(705\) | 1.31634 | 0.0495763 | ||||||||
\(706\) | −21.0227 | −0.791200 | ||||||||
\(707\) | −39.7153 | −1.49365 | ||||||||
\(708\) | −37.4510 | −1.40749 | ||||||||
\(709\) | −26.4138 | −0.991992 | −0.495996 | − | 0.868325i | \(-0.665197\pi\) | ||||
−0.495996 | + | 0.868325i | \(0.665197\pi\) | |||||||
\(710\) | 1.90390 | 0.0714521 | ||||||||
\(711\) | 19.5599 | 0.733554 | ||||||||
\(712\) | −53.9563 | −2.02210 | ||||||||
\(713\) | 29.1134 | 1.09030 | ||||||||
\(714\) | 17.8435 | 0.667775 | ||||||||
\(715\) | −0.338996 | −0.0126777 | ||||||||
\(716\) | −74.1639 | −2.77164 | ||||||||
\(717\) | 5.95376 | 0.222347 | ||||||||
\(718\) | 61.4237 | 2.29231 | ||||||||
\(719\) | −32.4146 | −1.20886 | −0.604430 | − | 0.796658i | \(-0.706599\pi\) | ||||
−0.604430 | + | 0.796658i | \(0.706599\pi\) | |||||||
\(720\) | 0.319306 | 0.0118998 | ||||||||
\(721\) | 8.02893 | 0.299013 | ||||||||
\(722\) | −17.6403 | −0.656503 | ||||||||
\(723\) | 16.3313 | 0.607369 | ||||||||
\(724\) | 0.101186 | 0.00376054 | ||||||||
\(725\) | −3.61924 | −0.134415 | ||||||||
\(726\) | 19.1923 | 0.712293 | ||||||||
\(727\) | −45.1672 | −1.67516 | −0.837579 | − | 0.546316i | \(-0.816030\pi\) | ||||
−0.837579 | + | 0.546316i | \(0.816030\pi\) | |||||||
\(728\) | 8.97112 | 0.332492 | ||||||||
\(729\) | 2.53140 | 0.0937554 | ||||||||
\(730\) | 1.58005 | 0.0584802 | ||||||||
\(731\) | 29.0695 | 1.07517 | ||||||||
\(732\) | −33.2357 | −1.22843 | ||||||||
\(733\) | 19.6790 | 0.726859 | 0.363430 | − | 0.931622i | \(-0.381606\pi\) | ||||
0.363430 | + | 0.931622i | \(0.381606\pi\) | |||||||
\(734\) | −66.2931 | −2.44692 | ||||||||
\(735\) | 0.499233 | 0.0184145 | ||||||||
\(736\) | 16.3393 | 0.602276 | ||||||||
\(737\) | −2.71877 | −0.100147 | ||||||||
\(738\) | 4.71745 | 0.173652 | ||||||||
\(739\) | −29.6765 | −1.09167 | −0.545833 | − | 0.837894i | \(-0.683787\pi\) | ||||
−0.545833 | + | 0.837894i | \(0.683787\pi\) | |||||||
\(740\) | −0.959968 | −0.0352891 | ||||||||
\(741\) | 5.52145 | 0.202836 | ||||||||
\(742\) | −56.3207 | −2.06760 | ||||||||
\(743\) | −18.4315 | −0.676186 | −0.338093 | − | 0.941113i | \(-0.609782\pi\) | ||||
−0.338093 | + | 0.941113i | \(0.609782\pi\) | |||||||
\(744\) | −22.9004 | −0.839570 | ||||||||
\(745\) | −6.12592 | −0.224436 | ||||||||
\(746\) | 31.1946 | 1.14212 | ||||||||
\(747\) | 30.1000 | 1.10130 | ||||||||
\(748\) | 12.8859 | 0.471156 | ||||||||
\(749\) | −0.149644 | −0.00546789 | ||||||||
\(750\) | −5.36695 | −0.195973 | ||||||||
\(751\) | 31.6294 | 1.15417 | 0.577087 | − | 0.816683i | \(-0.304189\pi\) | ||||
0.577087 | + | 0.816683i | \(0.304189\pi\) | |||||||
\(752\) | −2.67307 | −0.0974769 | ||||||||
\(753\) | 5.46248 | 0.199064 | ||||||||
\(754\) | −2.23328 | −0.0813312 | ||||||||
\(755\) | −3.82224 | −0.139105 | ||||||||
\(756\) | 32.0408 | 1.16531 | ||||||||
\(757\) | 46.2602 | 1.68135 | 0.840677 | − | 0.541536i | \(-0.182157\pi\) | ||||
0.840677 | + | 0.541536i | \(0.182157\pi\) | |||||||
\(758\) | 56.3448 | 2.04654 | ||||||||
\(759\) | 2.34753 | 0.0852098 | ||||||||
\(760\) | 4.59303 | 0.166607 | ||||||||
\(761\) | −0.517494 | −0.0187591 | −0.00937957 | − | 0.999956i | \(-0.502986\pi\) | ||||
−0.00937957 | + | 0.999956i | \(0.502986\pi\) | |||||||
\(762\) | −7.72234 | −0.279751 | ||||||||
\(763\) | 2.20640 | 0.0798771 | ||||||||
\(764\) | 60.1549 | 2.17633 | ||||||||
\(765\) | 2.88391 | 0.104268 | ||||||||
\(766\) | −25.0180 | −0.903936 | ||||||||
\(767\) | −18.0701 | −0.652472 | ||||||||
\(768\) | −15.4408 | −0.557172 | ||||||||
\(769\) | 29.5329 | 1.06498 | 0.532492 | − | 0.846435i | \(-0.321256\pi\) | ||||
0.532492 | + | 0.846435i | \(0.321256\pi\) | |||||||
\(770\) | −1.31632 | −0.0474367 | ||||||||
\(771\) | 6.15339 | 0.221609 | ||||||||
\(772\) | 45.5219 | 1.63837 | ||||||||
\(773\) | −14.7516 | −0.530578 | −0.265289 | − | 0.964169i | \(-0.585467\pi\) | ||||
−0.265289 | + | 0.964169i | \(0.585467\pi\) | |||||||
\(774\) | 36.5363 | 1.31327 | ||||||||
\(775\) | −44.6332 | −1.60327 | ||||||||
\(776\) | −34.1524 | −1.22600 | ||||||||
\(777\) | −1.79776 | −0.0644944 | ||||||||
\(778\) | −1.95520 | −0.0700975 | ||||||||
\(779\) | 4.50982 | 0.161581 | ||||||||
\(780\) | −1.02706 | −0.0367745 | ||||||||
\(781\) | 2.57487 | 0.0921361 | ||||||||
\(782\) | −31.8358 | −1.13845 | ||||||||
\(783\) | −3.20004 | −0.114360 | ||||||||
\(784\) | −1.01378 | −0.0362066 | ||||||||
\(785\) | −0.803583 | −0.0286811 | ||||||||
\(786\) | −1.62716 | −0.0580388 | ||||||||
\(787\) | 37.3630 | 1.33185 | 0.665924 | − | 0.746019i | \(-0.268037\pi\) | ||||
0.665924 | + | 0.746019i | \(0.268037\pi\) | |||||||
\(788\) | 21.9155 | 0.780707 | ||||||||
\(789\) | 24.1545 | 0.859923 | ||||||||
\(790\) | −5.56103 | −0.197853 | ||||||||
\(791\) | −44.7909 | −1.59258 | ||||||||
\(792\) | 6.49769 | 0.230885 | ||||||||
\(793\) | −16.0362 | −0.569463 | ||||||||
\(794\) | −67.5833 | −2.39844 | ||||||||
\(795\) | 2.58686 | 0.0917464 | ||||||||
\(796\) | −10.2341 | −0.362738 | ||||||||
\(797\) | −7.09162 | −0.251198 | −0.125599 | − | 0.992081i | \(-0.540085\pi\) | ||||
−0.125599 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(798\) | 21.4397 | 0.758957 | ||||||||
\(799\) | −24.1427 | −0.854106 | ||||||||
\(800\) | −25.0496 | −0.885636 | ||||||||
\(801\) | −40.7065 | −1.43829 | ||||||||
\(802\) | −64.1005 | −2.26347 | ||||||||
\(803\) | 2.13689 | 0.0754092 | ||||||||
\(804\) | −8.23706 | −0.290499 | ||||||||
\(805\) | 2.03407 | 0.0716915 | ||||||||
\(806\) | −27.5412 | −0.970099 | ||||||||
\(807\) | 17.6581 | 0.621596 | ||||||||
\(808\) | −55.7371 | −1.96083 | ||||||||
\(809\) | −22.7574 | −0.800109 | −0.400055 | − | 0.916491i | \(-0.631009\pi\) | ||||
−0.400055 | + | 0.916491i | \(0.631009\pi\) | |||||||
\(810\) | 2.30186 | 0.0808791 | ||||||||
\(811\) | −39.0587 | −1.37154 | −0.685768 | − | 0.727820i | \(-0.740534\pi\) | ||||
−0.685768 | + | 0.727820i | \(0.740534\pi\) | |||||||
\(812\) | −5.42391 | −0.190342 | ||||||||
\(813\) | −10.2367 | −0.359018 | ||||||||
\(814\) | −2.07570 | −0.0727531 | ||||||||
\(815\) | 2.79257 | 0.0978194 | ||||||||
\(816\) | 1.66428 | 0.0582614 | ||||||||
\(817\) | 34.9283 | 1.22199 | ||||||||
\(818\) | 20.8262 | 0.728172 | ||||||||
\(819\) | 6.76812 | 0.236497 | ||||||||
\(820\) | −0.838882 | −0.0292950 | ||||||||
\(821\) | −15.3867 | −0.537000 | −0.268500 | − | 0.963280i | \(-0.586528\pi\) | ||||
−0.268500 | + | 0.963280i | \(0.586528\pi\) | |||||||
\(822\) | −27.2175 | −0.949320 | ||||||||
\(823\) | 1.82397 | 0.0635795 | 0.0317897 | − | 0.999495i | \(-0.489879\pi\) | ||||
0.0317897 | + | 0.999495i | \(0.489879\pi\) | |||||||
\(824\) | 11.2679 | 0.392537 | ||||||||
\(825\) | −3.59895 | −0.125299 | ||||||||
\(826\) | −70.1657 | −2.44138 | ||||||||
\(827\) | 20.8658 | 0.725576 | 0.362788 | − | 0.931872i | \(-0.381825\pi\) | ||||
0.362788 | + | 0.931872i | \(0.381825\pi\) | |||||||
\(828\) | −25.0269 | −0.869746 | ||||||||
\(829\) | −19.1267 | −0.664297 | −0.332148 | − | 0.943227i | \(-0.607773\pi\) | ||||
−0.332148 | + | 0.943227i | \(0.607773\pi\) | |||||||
\(830\) | −8.55767 | −0.297041 | ||||||||
\(831\) | −5.13749 | −0.178218 | ||||||||
\(832\) | −16.7059 | −0.579173 | ||||||||
\(833\) | −9.15631 | −0.317247 | ||||||||
\(834\) | −15.2062 | −0.526548 | ||||||||
\(835\) | −5.56060 | −0.192432 | ||||||||
\(836\) | 15.4830 | 0.535490 | ||||||||
\(837\) | −39.4635 | −1.36406 | ||||||||
\(838\) | −54.3003 | −1.87577 | ||||||||
\(839\) | 3.67858 | 0.126999 | 0.0634993 | − | 0.997982i | \(-0.479774\pi\) | ||||
0.0634993 | + | 0.997982i | \(0.479774\pi\) | |||||||
\(840\) | −1.59999 | −0.0552048 | ||||||||
\(841\) | −28.4583 | −0.981320 | ||||||||
\(842\) | 71.1354 | 2.45149 | ||||||||
\(843\) | −2.99848 | −0.103273 | ||||||||
\(844\) | −5.25892 | −0.181020 | ||||||||
\(845\) | 3.24086 | 0.111489 | ||||||||
\(846\) | −30.3440 | −1.04325 | ||||||||
\(847\) | 22.4902 | 0.772773 | ||||||||
\(848\) | −5.25309 | −0.180392 | ||||||||
\(849\) | 20.0297 | 0.687416 | ||||||||
\(850\) | 48.8069 | 1.67406 | ||||||||
\(851\) | 3.20752 | 0.109952 | ||||||||
\(852\) | 7.80109 | 0.267261 | ||||||||
\(853\) | −1.41418 | −0.0484205 | −0.0242103 | − | 0.999707i | \(-0.507707\pi\) | ||||
−0.0242103 | + | 0.999707i | \(0.507707\pi\) | |||||||
\(854\) | −62.2683 | −2.13078 | ||||||||
\(855\) | 3.46514 | 0.118505 | ||||||||
\(856\) | −0.210014 | −0.00717812 | ||||||||
\(857\) | −14.6219 | −0.499476 | −0.249738 | − | 0.968313i | \(-0.580344\pi\) | ||||
−0.249738 | + | 0.968313i | \(0.580344\pi\) | |||||||
\(858\) | −2.22076 | −0.0758155 | ||||||||
\(859\) | −17.7215 | −0.604651 | −0.302325 | − | 0.953205i | \(-0.597763\pi\) | ||||
−0.302325 | + | 0.953205i | \(0.597763\pi\) | |||||||
\(860\) | −6.49708 | −0.221549 | ||||||||
\(861\) | −1.57100 | −0.0535396 | ||||||||
\(862\) | −27.0747 | −0.922169 | ||||||||
\(863\) | 24.3375 | 0.828458 | 0.414229 | − | 0.910173i | \(-0.364051\pi\) | ||||
0.414229 | + | 0.910173i | \(0.364051\pi\) | |||||||
\(864\) | −22.1482 | −0.753497 | ||||||||
\(865\) | −0.801560 | −0.0272538 | ||||||||
\(866\) | −21.4273 | −0.728129 | ||||||||
\(867\) | 1.17995 | 0.0400732 | ||||||||
\(868\) | −66.8888 | −2.27035 | ||||||||
\(869\) | −7.52085 | −0.255127 | ||||||||
\(870\) | 0.398302 | 0.0135037 | ||||||||
\(871\) | −3.97438 | −0.134667 | ||||||||
\(872\) | 3.09651 | 0.104861 | ||||||||
\(873\) | −25.7657 | −0.872037 | ||||||||
\(874\) | −38.2521 | −1.29390 | ||||||||
\(875\) | −6.28918 | −0.212613 | ||||||||
\(876\) | 6.47413 | 0.218741 | ||||||||
\(877\) | −17.4631 | −0.589686 | −0.294843 | − | 0.955546i | \(-0.595267\pi\) | ||||
−0.294843 | + | 0.955546i | \(0.595267\pi\) | |||||||
\(878\) | −64.2436 | −2.16812 | ||||||||
\(879\) | −10.0511 | −0.339016 | ||||||||
\(880\) | −0.122774 | −0.00413872 | ||||||||
\(881\) | −51.4068 | −1.73194 | −0.865970 | − | 0.500096i | \(-0.833298\pi\) | ||||
−0.865970 | + | 0.500096i | \(0.833298\pi\) | |||||||
\(882\) | −11.5082 | −0.387501 | ||||||||
\(883\) | 32.6339 | 1.09822 | 0.549109 | − | 0.835751i | \(-0.314967\pi\) | ||||
0.549109 | + | 0.835751i | \(0.314967\pi\) | |||||||
\(884\) | 18.8370 | 0.633557 | ||||||||
\(885\) | 3.22277 | 0.108332 | ||||||||
\(886\) | −44.3996 | −1.49163 | ||||||||
\(887\) | −12.8326 | −0.430877 | −0.215439 | − | 0.976517i | \(-0.569118\pi\) | ||||
−0.215439 | + | 0.976517i | \(0.569118\pi\) | |||||||
\(888\) | −2.52302 | −0.0846668 | ||||||||
\(889\) | −9.04931 | −0.303504 | ||||||||
\(890\) | 11.5732 | 0.387933 | ||||||||
\(891\) | 3.11308 | 0.104292 | ||||||||
\(892\) | −17.0524 | −0.570955 | ||||||||
\(893\) | −29.0085 | −0.970731 | ||||||||
\(894\) | −40.1308 | −1.34217 | ||||||||
\(895\) | 6.38203 | 0.213328 | ||||||||
\(896\) | −42.3895 | −1.41613 | ||||||||
\(897\) | 3.43168 | 0.114580 | ||||||||
\(898\) | 96.0002 | 3.20357 | ||||||||
\(899\) | 6.68046 | 0.222806 | ||||||||
\(900\) | 38.3684 | 1.27895 | ||||||||
\(901\) | −47.4449 | −1.58062 | ||||||||
\(902\) | −1.81388 | −0.0603955 | ||||||||
\(903\) | −12.1673 | −0.404902 | ||||||||
\(904\) | −62.8604 | −2.09071 | ||||||||
\(905\) | −0.00870735 | −0.000289442 0 | ||||||||
\(906\) | −25.0394 | −0.831879 | ||||||||
\(907\) | 46.2552 | 1.53588 | 0.767939 | − | 0.640523i | \(-0.221282\pi\) | ||||
0.767939 | + | 0.640523i | \(0.221282\pi\) | |||||||
\(908\) | −16.3693 | −0.543235 | ||||||||
\(909\) | −42.0500 | −1.39471 | ||||||||
\(910\) | −1.92423 | −0.0637875 | ||||||||
\(911\) | 57.7968 | 1.91489 | 0.957447 | − | 0.288608i | \(-0.0931926\pi\) | ||||
0.957447 | + | 0.288608i | \(0.0931926\pi\) | |||||||
\(912\) | 1.99970 | 0.0662168 | ||||||||
\(913\) | −11.5736 | −0.383029 | ||||||||
\(914\) | 60.0733 | 1.98705 | ||||||||
\(915\) | 2.86004 | 0.0945499 | ||||||||
\(916\) | −45.1727 | −1.49255 | ||||||||
\(917\) | −1.90676 | −0.0629668 | ||||||||
\(918\) | 43.1538 | 1.42429 | ||||||||
\(919\) | 24.9878 | 0.824271 | 0.412135 | − | 0.911123i | \(-0.364783\pi\) | ||||
0.412135 | + | 0.911123i | \(0.364783\pi\) | |||||||
\(920\) | 2.85465 | 0.0941150 | ||||||||
\(921\) | −6.04860 | −0.199308 | ||||||||
\(922\) | 56.3661 | 1.85632 | ||||||||
\(923\) | 3.76402 | 0.123894 | ||||||||
\(924\) | −5.39351 | −0.177433 | ||||||||
\(925\) | −4.91739 | −0.161683 | ||||||||
\(926\) | −47.3382 | −1.55563 | ||||||||
\(927\) | 8.50092 | 0.279207 | ||||||||
\(928\) | 3.74928 | 0.123076 | ||||||||
\(929\) | −60.8275 | −1.99568 | −0.997842 | − | 0.0656572i | \(-0.979086\pi\) | ||||
−0.997842 | + | 0.0656572i | \(0.979086\pi\) | |||||||
\(930\) | 4.91194 | 0.161069 | ||||||||
\(931\) | −11.0017 | −0.360566 | ||||||||
\(932\) | 44.8758 | 1.46996 | ||||||||
\(933\) | 22.9076 | 0.749960 | ||||||||
\(934\) | 19.2382 | 0.629494 | ||||||||
\(935\) | −1.10887 | −0.0362640 | ||||||||
\(936\) | 9.49851 | 0.310468 | ||||||||
\(937\) | −6.01124 | −0.196379 | −0.0981893 | − | 0.995168i | \(-0.531305\pi\) | ||||
−0.0981893 | + | 0.995168i | \(0.531305\pi\) | |||||||
\(938\) | −15.4324 | −0.503886 | ||||||||
\(939\) | −10.9746 | −0.358142 | ||||||||
\(940\) | 5.39592 | 0.175996 | ||||||||
\(941\) | −10.1643 | −0.331347 | −0.165673 | − | 0.986181i | \(-0.552980\pi\) | ||||
−0.165673 | + | 0.986181i | \(0.552980\pi\) | |||||||
\(942\) | −5.26426 | −0.171519 | ||||||||
\(943\) | 2.80293 | 0.0912761 | ||||||||
\(944\) | −6.54443 | −0.213003 | ||||||||
\(945\) | −2.75721 | −0.0896919 | ||||||||
\(946\) | −14.0483 | −0.456751 | ||||||||
\(947\) | −49.0757 | −1.59474 | −0.797372 | − | 0.603488i | \(-0.793777\pi\) | ||||
−0.797372 | + | 0.603488i | \(0.793777\pi\) | |||||||
\(948\) | −22.7859 | −0.740052 | ||||||||
\(949\) | 3.12377 | 0.101402 | ||||||||
\(950\) | 58.6436 | 1.90265 | ||||||||
\(951\) | 11.6057 | 0.376341 | ||||||||
\(952\) | 29.3449 | 0.951075 | ||||||||
\(953\) | 8.21968 | 0.266262 | 0.133131 | − | 0.991098i | \(-0.457497\pi\) | ||||
0.133131 | + | 0.991098i | \(0.457497\pi\) | |||||||
\(954\) | −59.6316 | −1.93065 | ||||||||
\(955\) | −5.17651 | −0.167508 | ||||||||
\(956\) | 24.4056 | 0.789332 | ||||||||
\(957\) | 0.538672 | 0.0174128 | ||||||||
\(958\) | 31.1244 | 1.00558 | ||||||||
\(959\) | −31.8945 | −1.02993 | ||||||||
\(960\) | 2.97947 | 0.0961621 | ||||||||
\(961\) | 51.3848 | 1.65757 | ||||||||
\(962\) | −3.03431 | −0.0978301 | ||||||||
\(963\) | −0.158442 | −0.00510571 | ||||||||
\(964\) | 66.9451 | 2.15616 | ||||||||
\(965\) | −3.91730 | −0.126102 | ||||||||
\(966\) | 13.3251 | 0.428730 | ||||||||
\(967\) | −53.8311 | −1.73109 | −0.865545 | − | 0.500831i | \(-0.833028\pi\) | ||||
−0.865545 | + | 0.500831i | \(0.833028\pi\) | |||||||
\(968\) | 31.5632 | 1.01448 | ||||||||
\(969\) | 18.0609 | 0.580201 | ||||||||
\(970\) | 7.32539 | 0.235204 | ||||||||
\(971\) | 0.515998 | 0.0165592 | 0.00827958 | − | 0.999966i | \(-0.497364\pi\) | ||||
0.00827958 | + | 0.999966i | \(0.497364\pi\) | |||||||
\(972\) | 52.9968 | 1.69987 | ||||||||
\(973\) | −17.8192 | −0.571256 | ||||||||
\(974\) | 15.4667 | 0.495584 | ||||||||
\(975\) | −5.26105 | −0.168488 | ||||||||
\(976\) | −5.80783 | −0.185904 | ||||||||
\(977\) | 7.24138 | 0.231672 | 0.115836 | − | 0.993268i | \(-0.463045\pi\) | ||||
0.115836 | + | 0.993268i | \(0.463045\pi\) | |||||||
\(978\) | 18.2941 | 0.584979 | ||||||||
\(979\) | 15.6518 | 0.500233 | ||||||||
\(980\) | 2.04645 | 0.0653714 | ||||||||
\(981\) | 2.33611 | 0.0745863 | ||||||||
\(982\) | −30.1813 | −0.963125 | ||||||||
\(983\) | −61.2524 | −1.95365 | −0.976824 | − | 0.214043i | \(-0.931337\pi\) | ||||
−0.976824 | + | 0.214043i | \(0.931337\pi\) | |||||||
\(984\) | −2.20477 | −0.0702856 | ||||||||
\(985\) | −1.88589 | −0.0600896 | ||||||||
\(986\) | −7.30515 | −0.232643 | ||||||||
\(987\) | 10.1051 | 0.321650 | ||||||||
\(988\) | 22.6335 | 0.720066 | ||||||||
\(989\) | 21.7085 | 0.690291 | ||||||||
\(990\) | −1.39370 | −0.0442947 | ||||||||
\(991\) | −8.97907 | −0.285230 | −0.142615 | − | 0.989778i | \(-0.545551\pi\) | ||||
−0.142615 | + | 0.989778i | \(0.545551\pi\) | |||||||
\(992\) | 46.2369 | 1.46802 | ||||||||
\(993\) | 2.45186 | 0.0778075 | ||||||||
\(994\) | 14.6156 | 0.463579 | ||||||||
\(995\) | 0.880677 | 0.0279193 | ||||||||
\(996\) | −35.0644 | −1.11106 | ||||||||
\(997\) | 1.91311 | 0.0605888 | 0.0302944 | − | 0.999541i | \(-0.490356\pi\) | ||||
0.0302944 | + | 0.999541i | \(0.490356\pi\) | |||||||
\(998\) | −26.7577 | −0.847002 | ||||||||
\(999\) | −4.34783 | −0.137559 |
(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 | 4033.2.a.f.1.8 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.8 | ✓ | 85 | 1.1 | even | 1 | trivial |