Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25548 | −0.887762 | −0.443881 | − | 0.896086i | \(-0.646399\pi\) | ||||
−0.443881 | + | 0.896086i | \(0.646399\pi\) | |||||||
\(3\) | −0.219421 | −0.126683 | −0.0633414 | − | 0.997992i | \(-0.520176\pi\) | ||||
−0.0633414 | + | 0.997992i | \(0.520176\pi\) | |||||||
\(4\) | −0.423759 | −0.211879 | ||||||||
\(5\) | 4.17472 | 1.86699 | 0.933496 | − | 0.358588i | \(-0.116742\pi\) | ||||
0.933496 | + | 0.358588i | \(0.116742\pi\) | |||||||
\(6\) | 0.275480 | 0.112464 | ||||||||
\(7\) | −0.198048 | −0.0748551 | −0.0374275 | − | 0.999299i | \(-0.511916\pi\) | ||||
−0.0374275 | + | 0.999299i | \(0.511916\pi\) | |||||||
\(8\) | 3.04299 | 1.07586 | ||||||||
\(9\) | −2.95185 | −0.983951 | ||||||||
\(10\) | −5.24130 | −1.65744 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.0929815 | 0.0268415 | ||||||||
\(13\) | 0.262830 | 0.0728960 | 0.0364480 | − | 0.999336i | \(-0.488396\pi\) | ||||
0.0364480 | + | 0.999336i | \(0.488396\pi\) | |||||||
\(14\) | 0.248646 | 0.0664534 | ||||||||
\(15\) | −0.916021 | −0.236516 | ||||||||
\(16\) | −2.97291 | −0.743228 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 3.70601 | 0.873514 | ||||||||
\(19\) | −5.47442 | −1.25592 | −0.627959 | − | 0.778247i | \(-0.716109\pi\) | ||||
−0.627959 | + | 0.778247i | \(0.716109\pi\) | |||||||
\(20\) | −1.76907 | −0.395577 | ||||||||
\(21\) | 0.0434558 | 0.00948284 | ||||||||
\(22\) | 1.25548 | 0.267670 | ||||||||
\(23\) | 5.47926 | 1.14251 | 0.571253 | − | 0.820774i | \(-0.306458\pi\) | ||||
0.571253 | + | 0.820774i | \(0.306458\pi\) | |||||||
\(24\) | −0.667696 | −0.136293 | ||||||||
\(25\) | 12.4283 | 2.48566 | ||||||||
\(26\) | −0.329979 | −0.0647143 | ||||||||
\(27\) | 1.30596 | 0.251332 | ||||||||
\(28\) | 0.0839245 | 0.0158602 | ||||||||
\(29\) | 1.57962 | 0.293329 | 0.146664 | − | 0.989186i | \(-0.453146\pi\) | ||||
0.146664 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(30\) | 1.15005 | 0.209969 | ||||||||
\(31\) | −0.491859 | −0.0883405 | −0.0441703 | − | 0.999024i | \(-0.514064\pi\) | ||||
−0.0441703 | + | 0.999024i | \(0.514064\pi\) | |||||||
\(32\) | −2.35354 | −0.416051 | ||||||||
\(33\) | 0.219421 | 0.0381963 | ||||||||
\(34\) | −1.25548 | −0.215314 | ||||||||
\(35\) | −0.826794 | −0.139754 | ||||||||
\(36\) | 1.25087 | 0.208479 | ||||||||
\(37\) | −4.40751 | −0.724590 | −0.362295 | − | 0.932063i | \(-0.618007\pi\) | ||||
−0.362295 | + | 0.932063i | \(0.618007\pi\) | |||||||
\(38\) | 6.87304 | 1.11496 | ||||||||
\(39\) | −0.0576705 | −0.00923467 | ||||||||
\(40\) | 12.7036 | 2.00862 | ||||||||
\(41\) | 2.47972 | 0.387267 | 0.193633 | − | 0.981074i | \(-0.437973\pi\) | ||||
0.193633 | + | 0.981074i | \(0.437973\pi\) | |||||||
\(42\) | −0.0545581 | −0.00841850 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 0.423759 | 0.0638840 | ||||||||
\(45\) | −12.3232 | −1.83703 | ||||||||
\(46\) | −6.87913 | −1.01427 | ||||||||
\(47\) | 1.03795 | 0.151400 | 0.0757001 | − | 0.997131i | \(-0.475881\pi\) | ||||
0.0757001 | + | 0.997131i | \(0.475881\pi\) | |||||||
\(48\) | 0.652319 | 0.0941541 | ||||||||
\(49\) | −6.96078 | −0.994397 | ||||||||
\(50\) | −15.6035 | −2.20667 | ||||||||
\(51\) | −0.219421 | −0.0307251 | ||||||||
\(52\) | −0.111377 | −0.0154452 | ||||||||
\(53\) | −1.96523 | −0.269945 | −0.134973 | − | 0.990849i | \(-0.543095\pi\) | ||||
−0.134973 | + | 0.990849i | \(0.543095\pi\) | |||||||
\(54\) | −1.63961 | −0.223123 | ||||||||
\(55\) | −4.17472 | −0.562919 | ||||||||
\(56\) | −0.602658 | −0.0805336 | ||||||||
\(57\) | 1.20120 | 0.159103 | ||||||||
\(58\) | −1.98319 | −0.260406 | ||||||||
\(59\) | 4.48629 | 0.584065 | 0.292032 | − | 0.956408i | \(-0.405669\pi\) | ||||
0.292032 | + | 0.956408i | \(0.405669\pi\) | |||||||
\(60\) | 0.388172 | 0.0501128 | ||||||||
\(61\) | 0.162668 | 0.0208275 | 0.0104137 | − | 0.999946i | \(-0.496685\pi\) | ||||
0.0104137 | + | 0.999946i | \(0.496685\pi\) | |||||||
\(62\) | 0.617522 | 0.0784253 | ||||||||
\(63\) | 0.584608 | 0.0736537 | ||||||||
\(64\) | 8.90065 | 1.11258 | ||||||||
\(65\) | 1.09724 | 0.136096 | ||||||||
\(66\) | −0.275480 | −0.0339092 | ||||||||
\(67\) | 5.02953 | 0.614455 | 0.307228 | − | 0.951636i | \(-0.400599\pi\) | ||||
0.307228 | + | 0.951636i | \(0.400599\pi\) | |||||||
\(68\) | −0.423759 | −0.0513883 | ||||||||
\(69\) | −1.20227 | −0.144736 | ||||||||
\(70\) | 1.03803 | 0.124068 | ||||||||
\(71\) | −4.99462 | −0.592752 | −0.296376 | − | 0.955071i | \(-0.595778\pi\) | ||||
−0.296376 | + | 0.955071i | \(0.595778\pi\) | |||||||
\(72\) | −8.98247 | −1.05859 | ||||||||
\(73\) | 15.8803 | 1.85864 | 0.929322 | − | 0.369271i | \(-0.120393\pi\) | ||||
0.929322 | + | 0.369271i | \(0.120393\pi\) | |||||||
\(74\) | 5.53356 | 0.643263 | ||||||||
\(75\) | −2.72703 | −0.314890 | ||||||||
\(76\) | 2.31983 | 0.266103 | ||||||||
\(77\) | 0.198048 | 0.0225696 | ||||||||
\(78\) | 0.0724044 | 0.00819818 | ||||||||
\(79\) | 6.86933 | 0.772859 | 0.386430 | − | 0.922319i | \(-0.373708\pi\) | ||||
0.386430 | + | 0.922319i | \(0.373708\pi\) | |||||||
\(80\) | −12.4111 | −1.38760 | ||||||||
\(81\) | 8.56901 | 0.952112 | ||||||||
\(82\) | −3.11325 | −0.343800 | ||||||||
\(83\) | 0.608284 | 0.0667679 | 0.0333839 | − | 0.999443i | \(-0.489372\pi\) | ||||
0.0333839 | + | 0.999443i | \(0.489372\pi\) | |||||||
\(84\) | −0.0184148 | −0.00200922 | ||||||||
\(85\) | 4.17472 | 0.452812 | ||||||||
\(86\) | 1.25548 | 0.135382 | ||||||||
\(87\) | −0.346603 | −0.0371597 | ||||||||
\(88\) | −3.04299 | −0.324384 | ||||||||
\(89\) | −16.7625 | −1.77683 | −0.888413 | − | 0.459045i | \(-0.848192\pi\) | ||||
−0.888413 | + | 0.459045i | \(0.848192\pi\) | |||||||
\(90\) | 15.4715 | 1.63084 | ||||||||
\(91\) | −0.0520530 | −0.00545664 | ||||||||
\(92\) | −2.32189 | −0.242073 | ||||||||
\(93\) | 0.107924 | 0.0111912 | ||||||||
\(94\) | −1.30313 | −0.134407 | ||||||||
\(95\) | −22.8542 | −2.34479 | ||||||||
\(96\) | 0.516416 | 0.0527065 | ||||||||
\(97\) | −16.8484 | −1.71070 | −0.855349 | − | 0.518052i | \(-0.826657\pi\) | ||||
−0.855349 | + | 0.518052i | \(0.826657\pi\) | |||||||
\(98\) | 8.73915 | 0.882787 | ||||||||
\(99\) | 2.95185 | 0.296673 | ||||||||
\(100\) | −5.26660 | −0.526660 | ||||||||
\(101\) | 0.894331 | 0.0889893 | 0.0444946 | − | 0.999010i | \(-0.485832\pi\) | ||||
0.0444946 | + | 0.999010i | \(0.485832\pi\) | |||||||
\(102\) | 0.275480 | 0.0272765 | ||||||||
\(103\) | 1.97313 | 0.194419 | 0.0972094 | − | 0.995264i | \(-0.469008\pi\) | ||||
0.0972094 | + | 0.995264i | \(0.469008\pi\) | |||||||
\(104\) | 0.799791 | 0.0784259 | ||||||||
\(105\) | 0.181416 | 0.0177044 | ||||||||
\(106\) | 2.46732 | 0.239647 | ||||||||
\(107\) | 6.29149 | 0.608222 | 0.304111 | − | 0.952637i | \(-0.401641\pi\) | ||||
0.304111 | + | 0.952637i | \(0.401641\pi\) | |||||||
\(108\) | −0.553413 | −0.0532521 | ||||||||
\(109\) | −4.93109 | −0.472312 | −0.236156 | − | 0.971715i | \(-0.575888\pi\) | ||||
−0.236156 | + | 0.971715i | \(0.575888\pi\) | |||||||
\(110\) | 5.24130 | 0.499738 | ||||||||
\(111\) | 0.967100 | 0.0917930 | ||||||||
\(112\) | 0.588779 | 0.0556344 | ||||||||
\(113\) | 13.1299 | 1.23516 | 0.617578 | − | 0.786509i | \(-0.288114\pi\) | ||||
0.617578 | + | 0.786509i | \(0.288114\pi\) | |||||||
\(114\) | −1.50809 | −0.141246 | ||||||||
\(115\) | 22.8744 | 2.13305 | ||||||||
\(116\) | −0.669379 | −0.0621503 | ||||||||
\(117\) | −0.775837 | −0.0717262 | ||||||||
\(118\) | −5.63246 | −0.518510 | ||||||||
\(119\) | −0.198048 | −0.0181550 | ||||||||
\(120\) | −2.78744 | −0.254458 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.204227 | −0.0184898 | ||||||||
\(123\) | −0.544102 | −0.0490600 | ||||||||
\(124\) | 0.208430 | 0.0187175 | ||||||||
\(125\) | 31.0110 | 2.77371 | ||||||||
\(126\) | −0.733967 | −0.0653870 | ||||||||
\(127\) | 14.7165 | 1.30587 | 0.652937 | − | 0.757412i | \(-0.273536\pi\) | ||||
0.652937 | + | 0.757412i | \(0.273536\pi\) | |||||||
\(128\) | −6.46755 | −0.571656 | ||||||||
\(129\) | 0.219421 | 0.0193189 | ||||||||
\(130\) | −1.37757 | −0.120821 | ||||||||
\(131\) | 19.2655 | 1.68323 | 0.841617 | − | 0.540075i | \(-0.181604\pi\) | ||||
0.841617 | + | 0.540075i | \(0.181604\pi\) | |||||||
\(132\) | −0.0929815 | −0.00809300 | ||||||||
\(133\) | 1.08420 | 0.0940118 | ||||||||
\(134\) | −6.31450 | −0.545490 | ||||||||
\(135\) | 5.45202 | 0.469235 | ||||||||
\(136\) | 3.04299 | 0.260934 | ||||||||
\(137\) | 9.71081 | 0.829650 | 0.414825 | − | 0.909901i | \(-0.363843\pi\) | ||||
0.414825 | + | 0.909901i | \(0.363843\pi\) | |||||||
\(138\) | 1.50943 | 0.128491 | ||||||||
\(139\) | 1.88200 | 0.159629 | 0.0798147 | − | 0.996810i | \(-0.474567\pi\) | ||||
0.0798147 | + | 0.996810i | \(0.474567\pi\) | |||||||
\(140\) | 0.350361 | 0.0296109 | ||||||||
\(141\) | −0.227748 | −0.0191798 | ||||||||
\(142\) | 6.27066 | 0.526222 | ||||||||
\(143\) | −0.262830 | −0.0219790 | ||||||||
\(144\) | 8.77560 | 0.731300 | ||||||||
\(145\) | 6.59449 | 0.547642 | ||||||||
\(146\) | −19.9374 | −1.65003 | ||||||||
\(147\) | 1.52734 | 0.125973 | ||||||||
\(148\) | 1.86772 | 0.153526 | ||||||||
\(149\) | −22.4773 | −1.84142 | −0.920708 | − | 0.390253i | \(-0.872387\pi\) | ||||
−0.920708 | + | 0.390253i | \(0.872387\pi\) | |||||||
\(150\) | 3.42374 | 0.279547 | ||||||||
\(151\) | 20.0317 | 1.63016 | 0.815079 | − | 0.579350i | \(-0.196694\pi\) | ||||
0.815079 | + | 0.579350i | \(0.196694\pi\) | |||||||
\(152\) | −16.6586 | −1.35119 | ||||||||
\(153\) | −2.95185 | −0.238643 | ||||||||
\(154\) | −0.248646 | −0.0200365 | ||||||||
\(155\) | −2.05337 | −0.164931 | ||||||||
\(156\) | 0.0244384 | 0.00195664 | ||||||||
\(157\) | 21.5385 | 1.71896 | 0.859481 | − | 0.511168i | \(-0.170787\pi\) | ||||
0.859481 | + | 0.511168i | \(0.170787\pi\) | |||||||
\(158\) | −8.62433 | −0.686115 | ||||||||
\(159\) | 0.431213 | 0.0341974 | ||||||||
\(160\) | −9.82537 | −0.776764 | ||||||||
\(161\) | −1.08516 | −0.0855223 | ||||||||
\(162\) | −10.7583 | −0.845248 | ||||||||
\(163\) | 2.91228 | 0.228107 | 0.114054 | − | 0.993475i | \(-0.463616\pi\) | ||||
0.114054 | + | 0.993475i | \(0.463616\pi\) | |||||||
\(164\) | −1.05080 | −0.0820538 | ||||||||
\(165\) | 0.916021 | 0.0713121 | ||||||||
\(166\) | −0.763691 | −0.0592740 | ||||||||
\(167\) | 23.6474 | 1.82989 | 0.914946 | − | 0.403575i | \(-0.132233\pi\) | ||||
0.914946 | + | 0.403575i | \(0.132233\pi\) | |||||||
\(168\) | 0.132236 | 0.0102022 | ||||||||
\(169\) | −12.9309 | −0.994686 | ||||||||
\(170\) | −5.24130 | −0.401989 | ||||||||
\(171\) | 16.1597 | 1.23576 | ||||||||
\(172\) | 0.423759 | 0.0323113 | ||||||||
\(173\) | 3.99111 | 0.303438 | 0.151719 | − | 0.988424i | \(-0.451519\pi\) | ||||
0.151719 | + | 0.988424i | \(0.451519\pi\) | |||||||
\(174\) | 0.435154 | 0.0329889 | ||||||||
\(175\) | −2.46140 | −0.186064 | ||||||||
\(176\) | 2.97291 | 0.224092 | ||||||||
\(177\) | −0.984385 | −0.0739909 | ||||||||
\(178\) | 21.0451 | 1.57740 | ||||||||
\(179\) | −9.55519 | −0.714189 | −0.357094 | − | 0.934068i | \(-0.616233\pi\) | ||||
−0.357094 | + | 0.934068i | \(0.616233\pi\) | |||||||
\(180\) | 5.22205 | 0.389229 | ||||||||
\(181\) | −1.14049 | −0.0847719 | −0.0423860 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423860 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(182\) | 0.0653517 | 0.00484419 | ||||||||
\(183\) | −0.0356927 | −0.00263848 | ||||||||
\(184\) | 16.6734 | 1.22918 | ||||||||
\(185\) | −18.4001 | −1.35280 | ||||||||
\(186\) | −0.135497 | −0.00993513 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −0.439840 | −0.0320786 | ||||||||
\(189\) | −0.258643 | −0.0188135 | ||||||||
\(190\) | 28.6930 | 2.08161 | ||||||||
\(191\) | 17.2310 | 1.24679 | 0.623397 | − | 0.781905i | \(-0.285752\pi\) | ||||
0.623397 | + | 0.781905i | \(0.285752\pi\) | |||||||
\(192\) | −1.95299 | −0.140945 | ||||||||
\(193\) | −3.30315 | −0.237766 | −0.118883 | − | 0.992908i | \(-0.537931\pi\) | ||||
−0.118883 | + | 0.992908i | \(0.537931\pi\) | |||||||
\(194\) | 21.1529 | 1.51869 | ||||||||
\(195\) | −0.240758 | −0.0172410 | ||||||||
\(196\) | 2.94969 | 0.210692 | ||||||||
\(197\) | 8.69059 | 0.619179 | 0.309590 | − | 0.950870i | \(-0.399808\pi\) | ||||
0.309590 | + | 0.950870i | \(0.399808\pi\) | |||||||
\(198\) | −3.70601 | −0.263374 | ||||||||
\(199\) | 3.17087 | 0.224777 | 0.112388 | − | 0.993664i | \(-0.464150\pi\) | ||||
0.112388 | + | 0.993664i | \(0.464150\pi\) | |||||||
\(200\) | 37.8192 | 2.67422 | ||||||||
\(201\) | −1.10358 | −0.0778408 | ||||||||
\(202\) | −1.12282 | −0.0790013 | ||||||||
\(203\) | −0.312841 | −0.0219571 | ||||||||
\(204\) | 0.0929815 | 0.00651001 | ||||||||
\(205\) | 10.3521 | 0.723024 | ||||||||
\(206\) | −2.47724 | −0.172597 | ||||||||
\(207\) | −16.1740 | −1.12417 | ||||||||
\(208\) | −0.781371 | −0.0541784 | ||||||||
\(209\) | 5.47442 | 0.378673 | ||||||||
\(210\) | −0.227765 | −0.0157173 | ||||||||
\(211\) | 6.68616 | 0.460294 | 0.230147 | − | 0.973156i | \(-0.426079\pi\) | ||||
0.230147 | + | 0.973156i | \(0.426079\pi\) | |||||||
\(212\) | 0.832784 | 0.0571958 | ||||||||
\(213\) | 1.09592 | 0.0750914 | ||||||||
\(214\) | −7.89887 | −0.539956 | ||||||||
\(215\) | −4.17472 | −0.284714 | ||||||||
\(216\) | 3.97403 | 0.270398 | ||||||||
\(217\) | 0.0974117 | 0.00661273 | ||||||||
\(218\) | 6.19090 | 0.419301 | ||||||||
\(219\) | −3.48446 | −0.235458 | ||||||||
\(220\) | 1.76907 | 0.119271 | ||||||||
\(221\) | 0.262830 | 0.0176799 | ||||||||
\(222\) | −1.21418 | −0.0814903 | ||||||||
\(223\) | 4.16096 | 0.278639 | 0.139319 | − | 0.990247i | \(-0.455509\pi\) | ||||
0.139319 | + | 0.990247i | \(0.455509\pi\) | |||||||
\(224\) | 0.466113 | 0.0311435 | ||||||||
\(225\) | −36.6865 | −2.44577 | ||||||||
\(226\) | −16.4844 | −1.09652 | ||||||||
\(227\) | −18.7600 | −1.24514 | −0.622571 | − | 0.782563i | \(-0.713912\pi\) | ||||
−0.622571 | + | 0.782563i | \(0.713912\pi\) | |||||||
\(228\) | −0.509020 | −0.0337106 | ||||||||
\(229\) | −7.01865 | −0.463806 | −0.231903 | − | 0.972739i | \(-0.574495\pi\) | ||||
−0.231903 | + | 0.972739i | \(0.574495\pi\) | |||||||
\(230\) | −28.7184 | −1.89364 | ||||||||
\(231\) | −0.0434558 | −0.00285918 | ||||||||
\(232\) | 4.80678 | 0.315581 | ||||||||
\(233\) | −14.2957 | −0.936543 | −0.468272 | − | 0.883585i | \(-0.655123\pi\) | ||||
−0.468272 | + | 0.883585i | \(0.655123\pi\) | |||||||
\(234\) | 0.974051 | 0.0636757 | ||||||||
\(235\) | 4.33314 | 0.282663 | ||||||||
\(236\) | −1.90110 | −0.123751 | ||||||||
\(237\) | −1.50727 | −0.0979079 | ||||||||
\(238\) | 0.248646 | 0.0161173 | ||||||||
\(239\) | −17.0906 | −1.10550 | −0.552749 | − | 0.833348i | \(-0.686421\pi\) | ||||
−0.552749 | + | 0.833348i | \(0.686421\pi\) | |||||||
\(240\) | 2.72325 | 0.175785 | ||||||||
\(241\) | −11.2551 | −0.725002 | −0.362501 | − | 0.931983i | \(-0.618077\pi\) | ||||
−0.362501 | + | 0.931983i | \(0.618077\pi\) | |||||||
\(242\) | −1.25548 | −0.0807056 | ||||||||
\(243\) | −5.79810 | −0.371949 | ||||||||
\(244\) | −0.0689318 | −0.00441291 | ||||||||
\(245\) | −29.0593 | −1.85653 | ||||||||
\(246\) | 0.683111 | 0.0435536 | ||||||||
\(247\) | −1.43884 | −0.0915514 | ||||||||
\(248\) | −1.49672 | −0.0950420 | ||||||||
\(249\) | −0.133470 | −0.00845834 | ||||||||
\(250\) | −38.9339 | −2.46239 | ||||||||
\(251\) | −18.2278 | −1.15053 | −0.575264 | − | 0.817968i | \(-0.695101\pi\) | ||||
−0.575264 | + | 0.817968i | \(0.695101\pi\) | |||||||
\(252\) | −0.247733 | −0.0156057 | ||||||||
\(253\) | −5.47926 | −0.344478 | ||||||||
\(254\) | −18.4763 | −1.15931 | ||||||||
\(255\) | −0.916021 | −0.0573635 | ||||||||
\(256\) | −9.68139 | −0.605087 | ||||||||
\(257\) | 21.0290 | 1.31175 | 0.655876 | − | 0.754868i | \(-0.272299\pi\) | ||||
0.655876 | + | 0.754868i | \(0.272299\pi\) | |||||||
\(258\) | −0.275480 | −0.0171506 | ||||||||
\(259\) | 0.872898 | 0.0542392 | ||||||||
\(260\) | −0.464966 | −0.0288360 | ||||||||
\(261\) | −4.66282 | −0.288621 | ||||||||
\(262\) | −24.1875 | −1.49431 | ||||||||
\(263\) | 2.84048 | 0.175152 | 0.0875759 | − | 0.996158i | \(-0.472088\pi\) | ||||
0.0875759 | + | 0.996158i | \(0.472088\pi\) | |||||||
\(264\) | 0.667696 | 0.0410938 | ||||||||
\(265\) | −8.20429 | −0.503985 | ||||||||
\(266\) | −1.36119 | −0.0834600 | ||||||||
\(267\) | 3.67805 | 0.225093 | ||||||||
\(268\) | −2.13131 | −0.130190 | ||||||||
\(269\) | −13.5930 | −0.828780 | −0.414390 | − | 0.910099i | \(-0.636005\pi\) | ||||
−0.414390 | + | 0.910099i | \(0.636005\pi\) | |||||||
\(270\) | −6.84493 | −0.416569 | ||||||||
\(271\) | 10.4699 | 0.636000 | 0.318000 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.318000 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(272\) | −2.97291 | −0.180259 | ||||||||
\(273\) | 0.0114215 | 0.000691262 0 | ||||||||
\(274\) | −12.1918 | −0.736532 | ||||||||
\(275\) | −12.4283 | −0.749454 | ||||||||
\(276\) | 0.509470 | 0.0306665 | ||||||||
\(277\) | 13.2330 | 0.795092 | 0.397546 | − | 0.917582i | \(-0.369862\pi\) | ||||
0.397546 | + | 0.917582i | \(0.369862\pi\) | |||||||
\(278\) | −2.36282 | −0.141713 | ||||||||
\(279\) | 1.45190 | 0.0869228 | ||||||||
\(280\) | −2.51593 | −0.150355 | ||||||||
\(281\) | −7.82870 | −0.467021 | −0.233511 | − | 0.972354i | \(-0.575021\pi\) | ||||
−0.233511 | + | 0.972354i | \(0.575021\pi\) | |||||||
\(282\) | 0.285933 | 0.0170271 | ||||||||
\(283\) | 28.6242 | 1.70153 | 0.850767 | − | 0.525543i | \(-0.176138\pi\) | ||||
0.850767 | + | 0.525543i | \(0.176138\pi\) | |||||||
\(284\) | 2.11651 | 0.125592 | ||||||||
\(285\) | 5.01468 | 0.297044 | ||||||||
\(286\) | 0.329979 | 0.0195121 | ||||||||
\(287\) | −0.491103 | −0.0289889 | ||||||||
\(288\) | 6.94731 | 0.409374 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.27928 | −0.486176 | ||||||||
\(291\) | 3.69690 | 0.216716 | ||||||||
\(292\) | −6.72940 | −0.393808 | ||||||||
\(293\) | 5.23654 | 0.305922 | 0.152961 | − | 0.988232i | \(-0.451119\pi\) | ||||
0.152961 | + | 0.988232i | \(0.451119\pi\) | |||||||
\(294\) | −1.91755 | −0.111834 | ||||||||
\(295\) | 18.7290 | 1.09044 | ||||||||
\(296\) | −13.4120 | −0.779557 | ||||||||
\(297\) | −1.30596 | −0.0757796 | ||||||||
\(298\) | 28.2199 | 1.63474 | ||||||||
\(299\) | 1.44012 | 0.0832841 | ||||||||
\(300\) | 1.15560 | 0.0667187 | ||||||||
\(301\) | 0.198048 | 0.0114153 | ||||||||
\(302\) | −25.1495 | −1.44719 | ||||||||
\(303\) | −0.196235 | −0.0112734 | ||||||||
\(304\) | 16.2750 | 0.933433 | ||||||||
\(305\) | 0.679092 | 0.0388847 | ||||||||
\(306\) | 3.70601 | 0.211858 | ||||||||
\(307\) | 13.8668 | 0.791422 | 0.395711 | − | 0.918375i | \(-0.370498\pi\) | ||||
0.395711 | + | 0.918375i | \(0.370498\pi\) | |||||||
\(308\) | −0.0839245 | −0.00478204 | ||||||||
\(309\) | −0.432947 | −0.0246295 | ||||||||
\(310\) | 2.57798 | 0.146419 | ||||||||
\(311\) | −21.6256 | −1.22628 | −0.613138 | − | 0.789976i | \(-0.710093\pi\) | ||||
−0.613138 | + | 0.789976i | \(0.710093\pi\) | |||||||
\(312\) | −0.175491 | −0.00993521 | ||||||||
\(313\) | 23.6956 | 1.33935 | 0.669676 | − | 0.742653i | \(-0.266433\pi\) | ||||
0.669676 | + | 0.742653i | \(0.266433\pi\) | |||||||
\(314\) | −27.0413 | −1.52603 | ||||||||
\(315\) | 2.44058 | 0.137511 | ||||||||
\(316\) | −2.91094 | −0.163753 | ||||||||
\(317\) | 27.9898 | 1.57206 | 0.786032 | − | 0.618185i | \(-0.212132\pi\) | ||||
0.786032 | + | 0.618185i | \(0.212132\pi\) | |||||||
\(318\) | −0.541381 | −0.0303591 | ||||||||
\(319\) | −1.57962 | −0.0884420 | ||||||||
\(320\) | 37.1577 | 2.07718 | ||||||||
\(321\) | −1.38049 | −0.0770512 | ||||||||
\(322\) | 1.36240 | 0.0759234 | ||||||||
\(323\) | −5.47442 | −0.304605 | ||||||||
\(324\) | −3.63119 | −0.201733 | ||||||||
\(325\) | 3.26653 | 0.181195 | ||||||||
\(326\) | −3.65632 | −0.202505 | ||||||||
\(327\) | 1.08198 | 0.0598338 | ||||||||
\(328\) | 7.54576 | 0.416645 | ||||||||
\(329\) | −0.205563 | −0.0113331 | ||||||||
\(330\) | −1.15005 | −0.0633082 | ||||||||
\(331\) | 20.5936 | 1.13193 | 0.565965 | − | 0.824430i | \(-0.308504\pi\) | ||||
0.565965 | + | 0.824430i | \(0.308504\pi\) | |||||||
\(332\) | −0.257766 | −0.0141467 | ||||||||
\(333\) | 13.0103 | 0.712961 | ||||||||
\(334\) | −29.6890 | −1.62451 | ||||||||
\(335\) | 20.9969 | 1.14718 | ||||||||
\(336\) | −0.129190 | −0.00704791 | ||||||||
\(337\) | −11.0382 | −0.601289 | −0.300644 | − | 0.953736i | \(-0.597202\pi\) | ||||
−0.300644 | + | 0.953736i | \(0.597202\pi\) | |||||||
\(338\) | 16.2346 | 0.883044 | ||||||||
\(339\) | −2.88097 | −0.156473 | ||||||||
\(340\) | −1.76907 | −0.0959415 | ||||||||
\(341\) | 0.491859 | 0.0266357 | ||||||||
\(342\) | −20.2882 | −1.09706 | ||||||||
\(343\) | 2.76490 | 0.149291 | ||||||||
\(344\) | −3.04299 | −0.164067 | ||||||||
\(345\) | −5.01912 | −0.270220 | ||||||||
\(346\) | −5.01078 | −0.269381 | ||||||||
\(347\) | 10.0228 | 0.538054 | 0.269027 | − | 0.963133i | \(-0.413298\pi\) | ||||
0.269027 | + | 0.963133i | \(0.413298\pi\) | |||||||
\(348\) | 0.146876 | 0.00787337 | ||||||||
\(349\) | −16.3768 | −0.876631 | −0.438315 | − | 0.898821i | \(-0.644425\pi\) | ||||
−0.438315 | + | 0.898821i | \(0.644425\pi\) | |||||||
\(350\) | 3.09024 | 0.165181 | ||||||||
\(351\) | 0.343246 | 0.0183211 | ||||||||
\(352\) | 2.35354 | 0.125444 | ||||||||
\(353\) | −25.6068 | −1.36291 | −0.681456 | − | 0.731859i | \(-0.738653\pi\) | ||||
−0.681456 | + | 0.731859i | \(0.738653\pi\) | |||||||
\(354\) | 1.23588 | 0.0656863 | ||||||||
\(355\) | −20.8511 | −1.10666 | ||||||||
\(356\) | 7.10328 | 0.376473 | ||||||||
\(357\) | 0.0434558 | 0.00229993 | ||||||||
\(358\) | 11.9964 | 0.634029 | ||||||||
\(359\) | −19.4853 | −1.02840 | −0.514198 | − | 0.857672i | \(-0.671910\pi\) | ||||
−0.514198 | + | 0.857672i | \(0.671910\pi\) | |||||||
\(360\) | −37.4993 | −1.97639 | ||||||||
\(361\) | 10.9692 | 0.577328 | ||||||||
\(362\) | 1.43187 | 0.0752573 | ||||||||
\(363\) | −0.219421 | −0.0115166 | ||||||||
\(364\) | 0.0220579 | 0.00115615 | ||||||||
\(365\) | 66.2956 | 3.47007 | ||||||||
\(366\) | 0.0448116 | 0.00234234 | ||||||||
\(367\) | 31.7509 | 1.65738 | 0.828692 | − | 0.559705i | \(-0.189086\pi\) | ||||
0.828692 | + | 0.559705i | \(0.189086\pi\) | |||||||
\(368\) | −16.2894 | −0.849142 | ||||||||
\(369\) | −7.31976 | −0.381052 | ||||||||
\(370\) | 23.1011 | 1.20097 | ||||||||
\(371\) | 0.389210 | 0.0202068 | ||||||||
\(372\) | −0.0457338 | −0.00237119 | ||||||||
\(373\) | −4.50240 | −0.233125 | −0.116563 | − | 0.993183i | \(-0.537188\pi\) | ||||
−0.116563 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(374\) | 1.25548 | 0.0649196 | ||||||||
\(375\) | −6.80447 | −0.351381 | ||||||||
\(376\) | 3.15847 | 0.162886 | ||||||||
\(377\) | 0.415173 | 0.0213825 | ||||||||
\(378\) | 0.324722 | 0.0167019 | ||||||||
\(379\) | −31.7529 | −1.63104 | −0.815519 | − | 0.578731i | \(-0.803548\pi\) | ||||
−0.815519 | + | 0.578731i | \(0.803548\pi\) | |||||||
\(380\) | 9.68465 | 0.496812 | ||||||||
\(381\) | −3.22910 | −0.165432 | ||||||||
\(382\) | −21.6333 | −1.10686 | ||||||||
\(383\) | 0.324770 | 0.0165950 | 0.00829749 | − | 0.999966i | \(-0.497359\pi\) | ||||
0.00829749 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(384\) | 1.41912 | 0.0724190 | ||||||||
\(385\) | 0.826794 | 0.0421373 | ||||||||
\(386\) | 4.14706 | 0.211080 | ||||||||
\(387\) | 2.95185 | 0.150051 | ||||||||
\(388\) | 7.13967 | 0.362462 | ||||||||
\(389\) | −35.2287 | −1.78617 | −0.893084 | − | 0.449890i | \(-0.851463\pi\) | ||||
−0.893084 | + | 0.449890i | \(0.851463\pi\) | |||||||
\(390\) | 0.302268 | 0.0153059 | ||||||||
\(391\) | 5.47926 | 0.277098 | ||||||||
\(392\) | −21.1816 | −1.06983 | ||||||||
\(393\) | −4.22725 | −0.213237 | ||||||||
\(394\) | −10.9109 | −0.549684 | ||||||||
\(395\) | 28.6775 | 1.44292 | ||||||||
\(396\) | −1.25087 | −0.0628588 | ||||||||
\(397\) | −0.994514 | −0.0499132 | −0.0249566 | − | 0.999689i | \(-0.507945\pi\) | ||||
−0.0249566 | + | 0.999689i | \(0.507945\pi\) | |||||||
\(398\) | −3.98098 | −0.199548 | ||||||||
\(399\) | −0.237895 | −0.0119097 | ||||||||
\(400\) | −36.9482 | −1.84741 | ||||||||
\(401\) | −11.5538 | −0.576972 | −0.288486 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288486 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(402\) | 1.38553 | 0.0691041 | ||||||||
\(403\) | −0.129276 | −0.00643967 | ||||||||
\(404\) | −0.378981 | −0.0188550 | ||||||||
\(405\) | 35.7732 | 1.77759 | ||||||||
\(406\) | 0.392767 | 0.0194927 | ||||||||
\(407\) | 4.40751 | 0.218472 | ||||||||
\(408\) | −0.667696 | −0.0330559 | ||||||||
\(409\) | 27.1171 | 1.34085 | 0.670426 | − | 0.741976i | \(-0.266111\pi\) | ||||
0.670426 | + | 0.741976i | \(0.266111\pi\) | |||||||
\(410\) | −12.9969 | −0.641873 | ||||||||
\(411\) | −2.13075 | −0.105102 | ||||||||
\(412\) | −0.836133 | −0.0411933 | ||||||||
\(413\) | −0.888499 | −0.0437202 | ||||||||
\(414\) | 20.3062 | 0.997995 | ||||||||
\(415\) | 2.53942 | 0.124655 | ||||||||
\(416\) | −0.618582 | −0.0303285 | ||||||||
\(417\) | −0.412951 | −0.0202223 | ||||||||
\(418\) | −6.87304 | −0.336172 | ||||||||
\(419\) | −17.8829 | −0.873636 | −0.436818 | − | 0.899550i | \(-0.643895\pi\) | ||||
−0.436818 | + | 0.899550i | \(0.643895\pi\) | |||||||
\(420\) | −0.0768766 | −0.00375119 | ||||||||
\(421\) | 6.20436 | 0.302382 | 0.151191 | − | 0.988505i | \(-0.451689\pi\) | ||||
0.151191 | + | 0.988505i | \(0.451689\pi\) | |||||||
\(422\) | −8.39436 | −0.408631 | ||||||||
\(423\) | −3.06387 | −0.148971 | ||||||||
\(424\) | −5.98018 | −0.290423 | ||||||||
\(425\) | 12.4283 | 0.602861 | ||||||||
\(426\) | −1.37591 | −0.0666633 | ||||||||
\(427\) | −0.0322160 | −0.00155904 | ||||||||
\(428\) | −2.66608 | −0.128870 | ||||||||
\(429\) | 0.0576705 | 0.00278436 | ||||||||
\(430\) | 5.24130 | 0.252758 | ||||||||
\(431\) | 24.1398 | 1.16277 | 0.581387 | − | 0.813627i | \(-0.302510\pi\) | ||||
0.581387 | + | 0.813627i | \(0.302510\pi\) | |||||||
\(432\) | −3.88251 | −0.186797 | ||||||||
\(433\) | −19.4029 | −0.932442 | −0.466221 | − | 0.884668i | \(-0.654385\pi\) | ||||
−0.466221 | + | 0.884668i | \(0.654385\pi\) | |||||||
\(434\) | −0.122299 | −0.00587053 | ||||||||
\(435\) | −1.44697 | −0.0693768 | ||||||||
\(436\) | 2.08959 | 0.100073 | ||||||||
\(437\) | −29.9958 | −1.43489 | ||||||||
\(438\) | 4.37469 | 0.209031 | ||||||||
\(439\) | 9.20578 | 0.439368 | 0.219684 | − | 0.975571i | \(-0.429497\pi\) | ||||
0.219684 | + | 0.975571i | \(0.429497\pi\) | |||||||
\(440\) | −12.7036 | −0.605622 | ||||||||
\(441\) | 20.5472 | 0.978438 | ||||||||
\(442\) | −0.329979 | −0.0156955 | ||||||||
\(443\) | 12.3157 | 0.585138 | 0.292569 | − | 0.956244i | \(-0.405490\pi\) | ||||
0.292569 | + | 0.956244i | \(0.405490\pi\) | |||||||
\(444\) | −0.409817 | −0.0194491 | ||||||||
\(445\) | −69.9789 | −3.31732 | ||||||||
\(446\) | −5.22403 | −0.247365 | ||||||||
\(447\) | 4.93200 | 0.233275 | ||||||||
\(448\) | −1.76276 | −0.0832824 | ||||||||
\(449\) | 21.5655 | 1.01774 | 0.508869 | − | 0.860844i | \(-0.330064\pi\) | ||||
0.508869 | + | 0.860844i | \(0.330064\pi\) | |||||||
\(450\) | 46.0593 | 2.17126 | ||||||||
\(451\) | −2.47972 | −0.116765 | ||||||||
\(452\) | −5.56391 | −0.261704 | ||||||||
\(453\) | −4.39538 | −0.206513 | ||||||||
\(454\) | 23.5528 | 1.10539 | ||||||||
\(455\) | −0.217307 | −0.0101875 | ||||||||
\(456\) | 3.65525 | 0.171173 | ||||||||
\(457\) | 0.729361 | 0.0341181 | 0.0170590 | − | 0.999854i | \(-0.494570\pi\) | ||||
0.0170590 | + | 0.999854i | \(0.494570\pi\) | |||||||
\(458\) | 8.81181 | 0.411749 | ||||||||
\(459\) | 1.30596 | 0.0609571 | ||||||||
\(460\) | −9.69323 | −0.451949 | ||||||||
\(461\) | −28.7517 | −1.33910 | −0.669549 | − | 0.742768i | \(-0.733513\pi\) | ||||
−0.669549 | + | 0.742768i | \(0.733513\pi\) | |||||||
\(462\) | 0.0545581 | 0.00253827 | ||||||||
\(463\) | 30.2490 | 1.40579 | 0.702894 | − | 0.711294i | \(-0.251891\pi\) | ||||
0.702894 | + | 0.711294i | \(0.251891\pi\) | |||||||
\(464\) | −4.69608 | −0.218010 | ||||||||
\(465\) | 0.450553 | 0.0208939 | ||||||||
\(466\) | 17.9480 | 0.831427 | ||||||||
\(467\) | −19.5618 | −0.905211 | −0.452606 | − | 0.891711i | \(-0.649505\pi\) | ||||
−0.452606 | + | 0.891711i | \(0.649505\pi\) | |||||||
\(468\) | 0.328768 | 0.0151973 | ||||||||
\(469\) | −0.996088 | −0.0459951 | ||||||||
\(470\) | −5.44019 | −0.250937 | ||||||||
\(471\) | −4.72600 | −0.217763 | ||||||||
\(472\) | 13.6517 | 0.628372 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 1.89236 | 0.0869189 | ||||||||
\(475\) | −68.0376 | −3.12178 | ||||||||
\(476\) | 0.0839245 | 0.00384667 | ||||||||
\(477\) | 5.80107 | 0.265613 | ||||||||
\(478\) | 21.4570 | 0.981419 | ||||||||
\(479\) | −12.0797 | −0.551933 | −0.275967 | − | 0.961167i | \(-0.588998\pi\) | ||||
−0.275967 | + | 0.961167i | \(0.588998\pi\) | |||||||
\(480\) | 2.15589 | 0.0984025 | ||||||||
\(481\) | −1.15843 | −0.0528197 | ||||||||
\(482\) | 14.1306 | 0.643629 | ||||||||
\(483\) | 0.238106 | 0.0108342 | ||||||||
\(484\) | −0.423759 | −0.0192618 | ||||||||
\(485\) | −70.3375 | −3.19386 | ||||||||
\(486\) | 7.27943 | 0.330202 | ||||||||
\(487\) | 24.9364 | 1.12997 | 0.564987 | − | 0.825100i | \(-0.308881\pi\) | ||||
0.564987 | + | 0.825100i | \(0.308881\pi\) | |||||||
\(488\) | 0.494996 | 0.0224074 | ||||||||
\(489\) | −0.639015 | −0.0288973 | ||||||||
\(490\) | 36.4835 | 1.64816 | ||||||||
\(491\) | −12.8485 | −0.579844 | −0.289922 | − | 0.957050i | \(-0.593629\pi\) | ||||
−0.289922 | + | 0.957050i | \(0.593629\pi\) | |||||||
\(492\) | 0.230568 | 0.0103948 | ||||||||
\(493\) | 1.57962 | 0.0711427 | ||||||||
\(494\) | 1.80645 | 0.0812758 | ||||||||
\(495\) | 12.3232 | 0.553885 | ||||||||
\(496\) | 1.46225 | 0.0656571 | ||||||||
\(497\) | 0.989173 | 0.0443705 | ||||||||
\(498\) | 0.167570 | 0.00750899 | ||||||||
\(499\) | −5.85117 | −0.261934 | −0.130967 | − | 0.991387i | \(-0.541808\pi\) | ||||
−0.130967 | + | 0.991387i | \(0.541808\pi\) | |||||||
\(500\) | −13.1412 | −0.587692 | ||||||||
\(501\) | −5.18874 | −0.231816 | ||||||||
\(502\) | 22.8847 | 1.02139 | ||||||||
\(503\) | 18.8977 | 0.842608 | 0.421304 | − | 0.906919i | \(-0.361572\pi\) | ||||
0.421304 | + | 0.906919i | \(0.361572\pi\) | |||||||
\(504\) | 1.77896 | 0.0792411 | ||||||||
\(505\) | 3.73358 | 0.166142 | ||||||||
\(506\) | 6.87913 | 0.305815 | ||||||||
\(507\) | 2.83731 | 0.126010 | ||||||||
\(508\) | −6.23623 | −0.276688 | ||||||||
\(509\) | 33.7919 | 1.49780 | 0.748899 | − | 0.662684i | \(-0.230583\pi\) | ||||
0.748899 | + | 0.662684i | \(0.230583\pi\) | |||||||
\(510\) | 1.15005 | 0.0509251 | ||||||||
\(511\) | −3.14505 | −0.139129 | ||||||||
\(512\) | 25.0899 | 1.10883 | ||||||||
\(513\) | −7.14938 | −0.315653 | ||||||||
\(514\) | −26.4016 | −1.16452 | ||||||||
\(515\) | 8.23729 | 0.362978 | ||||||||
\(516\) | −0.0929815 | −0.00409328 | ||||||||
\(517\) | −1.03795 | −0.0456489 | ||||||||
\(518\) | −1.09591 | −0.0481515 | ||||||||
\(519\) | −0.875733 | −0.0384404 | ||||||||
\(520\) | 3.33890 | 0.146421 | ||||||||
\(521\) | 23.6466 | 1.03598 | 0.517989 | − | 0.855388i | \(-0.326681\pi\) | ||||
0.517989 | + | 0.855388i | \(0.326681\pi\) | |||||||
\(522\) | 5.85410 | 0.256227 | ||||||||
\(523\) | 9.70761 | 0.424484 | 0.212242 | − | 0.977217i | \(-0.431923\pi\) | ||||
0.212242 | + | 0.977217i | \(0.431923\pi\) | |||||||
\(524\) | −8.16392 | −0.356642 | ||||||||
\(525\) | 0.540082 | 0.0235711 | ||||||||
\(526\) | −3.56618 | −0.155493 | ||||||||
\(527\) | −0.491859 | −0.0214257 | ||||||||
\(528\) | −0.652319 | −0.0283885 | ||||||||
\(529\) | 7.02234 | 0.305319 | ||||||||
\(530\) | 10.3004 | 0.447419 | ||||||||
\(531\) | −13.2429 | −0.574691 | ||||||||
\(532\) | −0.459438 | −0.0199192 | ||||||||
\(533\) | 0.651745 | 0.0282302 | ||||||||
\(534\) | −4.61774 | −0.199829 | ||||||||
\(535\) | 26.2652 | 1.13554 | ||||||||
\(536\) | 15.3048 | 0.661068 | ||||||||
\(537\) | 2.09661 | 0.0904754 | ||||||||
\(538\) | 17.0658 | 0.735759 | ||||||||
\(539\) | 6.96078 | 0.299822 | ||||||||
\(540\) | −2.31034 | −0.0994213 | ||||||||
\(541\) | −9.46586 | −0.406969 | −0.203485 | − | 0.979078i | \(-0.565227\pi\) | ||||
−0.203485 | + | 0.979078i | \(0.565227\pi\) | |||||||
\(542\) | −13.1448 | −0.564616 | ||||||||
\(543\) | 0.250247 | 0.0107391 | ||||||||
\(544\) | −2.35354 | −0.100907 | ||||||||
\(545\) | −20.5859 | −0.881803 | ||||||||
\(546\) | −0.0143395 | −0.000613676 0 | ||||||||
\(547\) | 16.8704 | 0.721327 | 0.360663 | − | 0.932696i | \(-0.382550\pi\) | ||||
0.360663 | + | 0.932696i | \(0.382550\pi\) | |||||||
\(548\) | −4.11504 | −0.175786 | ||||||||
\(549\) | −0.480171 | −0.0204932 | ||||||||
\(550\) | 15.6035 | 0.665336 | ||||||||
\(551\) | −8.64752 | −0.368397 | ||||||||
\(552\) | −3.65848 | −0.155715 | ||||||||
\(553\) | −1.36046 | −0.0578524 | ||||||||
\(554\) | −16.6138 | −0.705852 | ||||||||
\(555\) | 4.03737 | 0.171377 | ||||||||
\(556\) | −0.797515 | −0.0338222 | ||||||||
\(557\) | 29.1365 | 1.23455 | 0.617277 | − | 0.786746i | \(-0.288236\pi\) | ||||
0.617277 | + | 0.786746i | \(0.288236\pi\) | |||||||
\(558\) | −1.82283 | −0.0771667 | ||||||||
\(559\) | −0.262830 | −0.0111165 | ||||||||
\(560\) | 2.45799 | 0.103869 | ||||||||
\(561\) | 0.219421 | 0.00926396 | ||||||||
\(562\) | 9.82881 | 0.414603 | ||||||||
\(563\) | 22.9194 | 0.965936 | 0.482968 | − | 0.875638i | \(-0.339559\pi\) | ||||
0.482968 | + | 0.875638i | \(0.339559\pi\) | |||||||
\(564\) | 0.0965100 | 0.00406380 | ||||||||
\(565\) | 54.8136 | 2.30603 | ||||||||
\(566\) | −35.9373 | −1.51056 | ||||||||
\(567\) | −1.69707 | −0.0712704 | ||||||||
\(568\) | −15.1986 | −0.637718 | ||||||||
\(569\) | 28.3524 | 1.18860 | 0.594298 | − | 0.804245i | \(-0.297430\pi\) | ||||
0.594298 | + | 0.804245i | \(0.297430\pi\) | |||||||
\(570\) | −6.29585 | −0.263704 | ||||||||
\(571\) | −12.3064 | −0.515009 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(572\) | 0.111377 | 0.00465689 | ||||||||
\(573\) | −3.78085 | −0.157947 | ||||||||
\(574\) | 0.616572 | 0.0257352 | ||||||||
\(575\) | 68.0979 | 2.83988 | ||||||||
\(576\) | −26.2734 | −1.09473 | ||||||||
\(577\) | 1.38978 | 0.0578574 | 0.0289287 | − | 0.999581i | \(-0.490790\pi\) | ||||
0.0289287 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(578\) | −1.25548 | −0.0522213 | ||||||||
\(579\) | 0.724780 | 0.0301208 | ||||||||
\(580\) | −2.79447 | −0.116034 | ||||||||
\(581\) | −0.120469 | −0.00499791 | ||||||||
\(582\) | −4.64140 | −0.192392 | ||||||||
\(583\) | 1.96523 | 0.0813915 | ||||||||
\(584\) | 48.3235 | 1.99964 | ||||||||
\(585\) | −3.23890 | −0.133912 | ||||||||
\(586\) | −6.57439 | −0.271586 | ||||||||
\(587\) | −0.186409 | −0.00769394 | −0.00384697 | − | 0.999993i | \(-0.501225\pi\) | ||||
−0.00384697 | + | 0.999993i | \(0.501225\pi\) | |||||||
\(588\) | −0.647224 | −0.0266911 | ||||||||
\(589\) | 2.69264 | 0.110948 | ||||||||
\(590\) | −23.5140 | −0.968054 | ||||||||
\(591\) | −1.90690 | −0.0784393 | ||||||||
\(592\) | 13.1031 | 0.538535 | ||||||||
\(593\) | 26.3400 | 1.08165 | 0.540826 | − | 0.841134i | \(-0.318112\pi\) | ||||
0.540826 | + | 0.841134i | \(0.318112\pi\) | |||||||
\(594\) | 1.63961 | 0.0672742 | ||||||||
\(595\) | −0.826794 | −0.0338953 | ||||||||
\(596\) | 9.52497 | 0.390158 | ||||||||
\(597\) | −0.695755 | −0.0284753 | ||||||||
\(598\) | −1.80804 | −0.0739365 | ||||||||
\(599\) | 40.5886 | 1.65840 | 0.829202 | − | 0.558949i | \(-0.188795\pi\) | ||||
0.829202 | + | 0.558949i | \(0.188795\pi\) | |||||||
\(600\) | −8.29832 | −0.338777 | ||||||||
\(601\) | 1.05716 | 0.0431225 | 0.0215612 | − | 0.999768i | \(-0.493136\pi\) | ||||
0.0215612 | + | 0.999768i | \(0.493136\pi\) | |||||||
\(602\) | −0.248646 | −0.0101341 | ||||||||
\(603\) | −14.8464 | −0.604594 | ||||||||
\(604\) | −8.48861 | −0.345397 | ||||||||
\(605\) | 4.17472 | 0.169727 | ||||||||
\(606\) | 0.246370 | 0.0100081 | ||||||||
\(607\) | 24.8145 | 1.00719 | 0.503594 | − | 0.863940i | \(-0.332011\pi\) | ||||
0.503594 | + | 0.863940i | \(0.332011\pi\) | |||||||
\(608\) | 12.8843 | 0.522526 | ||||||||
\(609\) | 0.0686439 | 0.00278159 | ||||||||
\(610\) | −0.852589 | −0.0345203 | ||||||||
\(611\) | 0.272804 | 0.0110365 | ||||||||
\(612\) | 1.25087 | 0.0505636 | ||||||||
\(613\) | −41.2735 | −1.66702 | −0.833511 | − | 0.552504i | \(-0.813673\pi\) | ||||
−0.833511 | + | 0.552504i | \(0.813673\pi\) | |||||||
\(614\) | −17.4096 | −0.702594 | ||||||||
\(615\) | −2.27147 | −0.0915946 | ||||||||
\(616\) | 0.602658 | 0.0242818 | ||||||||
\(617\) | 23.9969 | 0.966079 | 0.483040 | − | 0.875599i | \(-0.339533\pi\) | ||||
0.483040 | + | 0.875599i | \(0.339533\pi\) | |||||||
\(618\) | 0.543558 | 0.0218651 | ||||||||
\(619\) | 23.9276 | 0.961733 | 0.480867 | − | 0.876794i | \(-0.340322\pi\) | ||||
0.480867 | + | 0.876794i | \(0.340322\pi\) | |||||||
\(620\) | 0.870135 | 0.0349455 | ||||||||
\(621\) | 7.15571 | 0.287149 | ||||||||
\(622\) | 27.1506 | 1.08864 | ||||||||
\(623\) | 3.31979 | 0.133004 | ||||||||
\(624\) | 0.171449 | 0.00686346 | ||||||||
\(625\) | 67.3209 | 2.69284 | ||||||||
\(626\) | −29.7494 | −1.18903 | ||||||||
\(627\) | −1.20120 | −0.0479714 | ||||||||
\(628\) | −9.12714 | −0.364212 | ||||||||
\(629\) | −4.40751 | −0.175739 | ||||||||
\(630\) | −3.06411 | −0.122077 | ||||||||
\(631\) | −2.18475 | −0.0869733 | −0.0434867 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434867 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(632\) | 20.9033 | 0.831489 | ||||||||
\(633\) | −1.46708 | −0.0583113 | ||||||||
\(634\) | −35.1408 | −1.39562 | ||||||||
\(635\) | 61.4371 | 2.43806 | ||||||||
\(636\) | −0.182730 | −0.00724572 | ||||||||
\(637\) | −1.82950 | −0.0724876 | ||||||||
\(638\) | 1.98319 | 0.0785154 | ||||||||
\(639\) | 14.7434 | 0.583239 | ||||||||
\(640\) | −27.0002 | −1.06728 | ||||||||
\(641\) | −8.17441 | −0.322870 | −0.161435 | − | 0.986883i | \(-0.551612\pi\) | ||||
−0.161435 | + | 0.986883i | \(0.551612\pi\) | |||||||
\(642\) | 1.73318 | 0.0684031 | ||||||||
\(643\) | −8.45652 | −0.333493 | −0.166746 | − | 0.986000i | \(-0.553326\pi\) | ||||
−0.166746 | + | 0.986000i | \(0.553326\pi\) | |||||||
\(644\) | 0.459845 | 0.0181204 | ||||||||
\(645\) | 0.916021 | 0.0360683 | ||||||||
\(646\) | 6.87304 | 0.270416 | ||||||||
\(647\) | −20.3019 | −0.798150 | −0.399075 | − | 0.916918i | \(-0.630669\pi\) | ||||
−0.399075 | + | 0.916918i | \(0.630669\pi\) | |||||||
\(648\) | 26.0754 | 1.02434 | ||||||||
\(649\) | −4.48629 | −0.176102 | ||||||||
\(650\) | −4.10108 | −0.160858 | ||||||||
\(651\) | −0.0213742 | −0.000837719 0 | ||||||||
\(652\) | −1.23410 | −0.0483313 | ||||||||
\(653\) | −20.4317 | −0.799555 | −0.399778 | − | 0.916612i | \(-0.630913\pi\) | ||||
−0.399778 | + | 0.916612i | \(0.630913\pi\) | |||||||
\(654\) | −1.35841 | −0.0531182 | ||||||||
\(655\) | 80.4280 | 3.14258 | ||||||||
\(656\) | −7.37198 | −0.287827 | ||||||||
\(657\) | −46.8762 | −1.82881 | ||||||||
\(658\) | 0.258082 | 0.0100611 | ||||||||
\(659\) | 18.0598 | 0.703511 | 0.351755 | − | 0.936092i | \(-0.385585\pi\) | ||||
0.351755 | + | 0.936092i | \(0.385585\pi\) | |||||||
\(660\) | −0.388172 | −0.0151096 | ||||||||
\(661\) | 8.33527 | 0.324204 | 0.162102 | − | 0.986774i | \(-0.448173\pi\) | ||||
0.162102 | + | 0.986774i | \(0.448173\pi\) | |||||||
\(662\) | −25.8550 | −1.00488 | ||||||||
\(663\) | −0.0576705 | −0.00223974 | ||||||||
\(664\) | 1.85100 | 0.0718329 | ||||||||
\(665\) | 4.52622 | 0.175519 | ||||||||
\(666\) | −16.3343 | −0.632940 | ||||||||
\(667\) | 8.65518 | 0.335130 | ||||||||
\(668\) | −10.0208 | −0.387717 | ||||||||
\(669\) | −0.913003 | −0.0352987 | ||||||||
\(670\) | −26.3613 | −1.01842 | ||||||||
\(671\) | −0.162668 | −0.00627971 | ||||||||
\(672\) | −0.102275 | −0.00394535 | ||||||||
\(673\) | 14.5473 | 0.560758 | 0.280379 | − | 0.959889i | \(-0.409540\pi\) | ||||
0.280379 | + | 0.959889i | \(0.409540\pi\) | |||||||
\(674\) | 13.8583 | 0.533801 | ||||||||
\(675\) | 16.2309 | 0.624726 | ||||||||
\(676\) | 5.47959 | 0.210753 | ||||||||
\(677\) | −38.9940 | −1.49866 | −0.749331 | − | 0.662195i | \(-0.769625\pi\) | ||||
−0.749331 | + | 0.662195i | \(0.769625\pi\) | |||||||
\(678\) | 3.61702 | 0.138911 | ||||||||
\(679\) | 3.33680 | 0.128054 | ||||||||
\(680\) | 12.7036 | 0.487162 | ||||||||
\(681\) | 4.11633 | 0.157738 | ||||||||
\(682\) | −0.617522 | −0.0236461 | ||||||||
\(683\) | −5.40974 | −0.206998 | −0.103499 | − | 0.994630i | \(-0.533004\pi\) | ||||
−0.103499 | + | 0.994630i | \(0.533004\pi\) | |||||||
\(684\) | −6.84781 | −0.261832 | ||||||||
\(685\) | 40.5399 | 1.54895 | ||||||||
\(686\) | −3.47129 | −0.132535 | ||||||||
\(687\) | 1.54004 | 0.0587562 | ||||||||
\(688\) | 2.97291 | 0.113341 | ||||||||
\(689\) | −0.516522 | −0.0196779 | ||||||||
\(690\) | 6.30143 | 0.239891 | ||||||||
\(691\) | 16.8797 | 0.642132 | 0.321066 | − | 0.947057i | \(-0.395959\pi\) | ||||
0.321066 | + | 0.947057i | \(0.395959\pi\) | |||||||
\(692\) | −1.69127 | −0.0642924 | ||||||||
\(693\) | −0.584608 | −0.0222074 | ||||||||
\(694\) | −12.5835 | −0.477664 | ||||||||
\(695\) | 7.85683 | 0.298027 | ||||||||
\(696\) | −1.05471 | −0.0399786 | ||||||||
\(697\) | 2.47972 | 0.0939260 | ||||||||
\(698\) | 20.5608 | 0.778239 | ||||||||
\(699\) | 3.13678 | 0.118644 | ||||||||
\(700\) | 1.04304 | 0.0394231 | ||||||||
\(701\) | 33.0451 | 1.24809 | 0.624047 | − | 0.781387i | \(-0.285487\pi\) | ||||
0.624047 | + | 0.781387i | \(0.285487\pi\) | |||||||
\(702\) | −0.430940 | −0.0162648 | ||||||||
\(703\) | 24.1285 | 0.910025 | ||||||||
\(704\) | −8.90065 | −0.335456 | ||||||||
\(705\) | −0.950782 | −0.0358085 | ||||||||
\(706\) | 32.1489 | 1.20994 | ||||||||
\(707\) | −0.177120 | −0.00666130 | ||||||||
\(708\) | 0.417142 | 0.0156771 | ||||||||
\(709\) | 45.6191 | 1.71326 | 0.856631 | − | 0.515929i | \(-0.172553\pi\) | ||||
0.856631 | + | 0.515929i | \(0.172553\pi\) | |||||||
\(710\) | 26.1783 | 0.982453 | ||||||||
\(711\) | −20.2772 | −0.760456 | ||||||||
\(712\) | −51.0083 | −1.91162 | ||||||||
\(713\) | −2.69503 | −0.100930 | ||||||||
\(714\) | −0.0545581 | −0.00204179 | ||||||||
\(715\) | −1.09724 | −0.0410346 | ||||||||
\(716\) | 4.04910 | 0.151322 | ||||||||
\(717\) | 3.75003 | 0.140048 | ||||||||
\(718\) | 24.4635 | 0.912970 | ||||||||
\(719\) | 35.9360 | 1.34019 | 0.670094 | − | 0.742277i | \(-0.266254\pi\) | ||||
0.670094 | + | 0.742277i | \(0.266254\pi\) | |||||||
\(720\) | 36.6357 | 1.36533 | ||||||||
\(721\) | −0.390775 | −0.0145532 | ||||||||
\(722\) | −13.7717 | −0.512530 | ||||||||
\(723\) | 2.46960 | 0.0918453 | ||||||||
\(724\) | 0.483293 | 0.0179614 | ||||||||
\(725\) | 19.6320 | 0.729115 | ||||||||
\(726\) | 0.275480 | 0.0102240 | ||||||||
\(727\) | −36.2870 | −1.34581 | −0.672905 | − | 0.739729i | \(-0.734954\pi\) | ||||
−0.672905 | + | 0.739729i | \(0.734954\pi\) | |||||||
\(728\) | −0.158397 | −0.00587058 | ||||||||
\(729\) | −24.4348 | −0.904993 | ||||||||
\(730\) | −83.2331 | −3.08060 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 0.0151251 | 0.000559039 0 | ||||||||
\(733\) | 24.6054 | 0.908821 | 0.454410 | − | 0.890792i | \(-0.349850\pi\) | ||||
0.454410 | + | 0.890792i | \(0.349850\pi\) | |||||||
\(734\) | −39.8628 | −1.47136 | ||||||||
\(735\) | 6.37622 | 0.235190 | ||||||||
\(736\) | −12.8957 | −0.475341 | ||||||||
\(737\) | −5.02953 | −0.185265 | ||||||||
\(738\) | 9.18985 | 0.338283 | ||||||||
\(739\) | −27.7395 | −1.02041 | −0.510207 | − | 0.860052i | \(-0.670431\pi\) | ||||
−0.510207 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(740\) | 7.79721 | 0.286631 | ||||||||
\(741\) | 0.315712 | 0.0115980 | ||||||||
\(742\) | −0.488647 | −0.0179388 | ||||||||
\(743\) | 35.3944 | 1.29849 | 0.649247 | − | 0.760577i | \(-0.275084\pi\) | ||||
0.649247 | + | 0.760577i | \(0.275084\pi\) | |||||||
\(744\) | 0.328412 | 0.0120402 | ||||||||
\(745\) | −93.8366 | −3.43791 | ||||||||
\(746\) | 5.65269 | 0.206960 | ||||||||
\(747\) | −1.79557 | −0.0656963 | ||||||||
\(748\) | 0.423759 | 0.0154942 | ||||||||
\(749\) | −1.24602 | −0.0455285 | ||||||||
\(750\) | 8.54290 | 0.311943 | ||||||||
\(751\) | 8.13716 | 0.296929 | 0.148465 | − | 0.988918i | \(-0.452567\pi\) | ||||
0.148465 | + | 0.988918i | \(0.452567\pi\) | |||||||
\(752\) | −3.08573 | −0.112525 | ||||||||
\(753\) | 3.99956 | 0.145752 | ||||||||
\(754\) | −0.521243 | −0.0189826 | ||||||||
\(755\) | 83.6268 | 3.04349 | ||||||||
\(756\) | 0.109602 | 0.00398619 | ||||||||
\(757\) | −10.2325 | −0.371906 | −0.185953 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185953 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(758\) | 39.8653 | 1.44797 | ||||||||
\(759\) | 1.20227 | 0.0436395 | ||||||||
\(760\) | −69.5450 | −2.52266 | ||||||||
\(761\) | 30.3022 | 1.09845 | 0.549227 | − | 0.835673i | \(-0.314922\pi\) | ||||
0.549227 | + | 0.835673i | \(0.314922\pi\) | |||||||
\(762\) | 4.05408 | 0.146864 | ||||||||
\(763\) | 0.976591 | 0.0353550 | ||||||||
\(764\) | −7.30180 | −0.264170 | ||||||||
\(765\) | −12.3232 | −0.445545 | ||||||||
\(766\) | −0.407744 | −0.0147324 | ||||||||
\(767\) | 1.17913 | 0.0425760 | ||||||||
\(768\) | 2.12430 | 0.0766541 | ||||||||
\(769\) | 3.84778 | 0.138755 | 0.0693773 | − | 0.997590i | \(-0.477899\pi\) | ||||
0.0693773 | + | 0.997590i | \(0.477899\pi\) | |||||||
\(770\) | −1.03803 | −0.0374079 | ||||||||
\(771\) | −4.61420 | −0.166176 | ||||||||
\(772\) | 1.39974 | 0.0503777 | ||||||||
\(773\) | 5.66585 | 0.203787 | 0.101893 | − | 0.994795i | \(-0.467510\pi\) | ||||
0.101893 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(774\) | −3.70601 | −0.133210 | ||||||||
\(775\) | −6.11297 | −0.219584 | ||||||||
\(776\) | −51.2696 | −1.84047 | ||||||||
\(777\) | −0.191532 | −0.00687117 | ||||||||
\(778\) | 44.2291 | 1.58569 | ||||||||
\(779\) | −13.5750 | −0.486375 | ||||||||
\(780\) | 0.102023 | 0.00365302 | ||||||||
\(781\) | 4.99462 | 0.178721 | ||||||||
\(782\) | −6.87913 | −0.245997 | ||||||||
\(783\) | 2.06293 | 0.0737230 | ||||||||
\(784\) | 20.6938 | 0.739063 | ||||||||
\(785\) | 89.9173 | 3.20929 | ||||||||
\(786\) | 5.30725 | 0.189303 | ||||||||
\(787\) | 9.40645 | 0.335304 | 0.167652 | − | 0.985846i | \(-0.446382\pi\) | ||||
0.167652 | + | 0.985846i | \(0.446382\pi\) | |||||||
\(788\) | −3.68272 | −0.131191 | ||||||||
\(789\) | −0.623262 | −0.0221887 | ||||||||
\(790\) | −36.0042 | −1.28097 | ||||||||
\(791\) | −2.60035 | −0.0924577 | ||||||||
\(792\) | 8.98247 | 0.319178 | ||||||||
\(793\) | 0.0427540 | 0.00151824 | ||||||||
\(794\) | 1.24860 | 0.0443111 | ||||||||
\(795\) | 1.80019 | 0.0638462 | ||||||||
\(796\) | −1.34368 | −0.0476256 | ||||||||
\(797\) | −43.9783 | −1.55779 | −0.778895 | − | 0.627154i | \(-0.784220\pi\) | ||||
−0.778895 | + | 0.627154i | \(0.784220\pi\) | |||||||
\(798\) | 0.298674 | 0.0105729 | ||||||||
\(799\) | 1.03795 | 0.0367200 | ||||||||
\(800\) | −29.2505 | −1.03416 | ||||||||
\(801\) | 49.4806 | 1.74831 | ||||||||
\(802\) | 14.5057 | 0.512213 | ||||||||
\(803\) | −15.8803 | −0.560402 | ||||||||
\(804\) | 0.467654 | 0.0164929 | ||||||||
\(805\) | −4.53023 | −0.159669 | ||||||||
\(806\) | 0.162303 | 0.00571689 | ||||||||
\(807\) | 2.98259 | 0.104992 | ||||||||
\(808\) | 2.72144 | 0.0957400 | ||||||||
\(809\) | −14.1277 | −0.496704 | −0.248352 | − | 0.968670i | \(-0.579889\pi\) | ||||
−0.248352 | + | 0.968670i | \(0.579889\pi\) | |||||||
\(810\) | −44.9127 | −1.57807 | ||||||||
\(811\) | −42.2820 | −1.48472 | −0.742360 | − | 0.670001i | \(-0.766294\pi\) | ||||
−0.742360 | + | 0.670001i | \(0.766294\pi\) | |||||||
\(812\) | 0.132569 | 0.00465227 | ||||||||
\(813\) | −2.29731 | −0.0805702 | ||||||||
\(814\) | −5.53356 | −0.193951 | ||||||||
\(815\) | 12.1580 | 0.425875 | ||||||||
\(816\) | 0.652319 | 0.0228357 | ||||||||
\(817\) | 5.47442 | 0.191526 | ||||||||
\(818\) | −34.0451 | −1.19036 | ||||||||
\(819\) | 0.153653 | 0.00536907 | ||||||||
\(820\) | −4.38680 | −0.153194 | ||||||||
\(821\) | 25.3616 | 0.885128 | 0.442564 | − | 0.896737i | \(-0.354069\pi\) | ||||
0.442564 | + | 0.896737i | \(0.354069\pi\) | |||||||
\(822\) | 2.67513 | 0.0933058 | ||||||||
\(823\) | 7.98785 | 0.278439 | 0.139219 | − | 0.990262i | \(-0.455541\pi\) | ||||
0.139219 | + | 0.990262i | \(0.455541\pi\) | |||||||
\(824\) | 6.00423 | 0.209167 | ||||||||
\(825\) | 2.72703 | 0.0949429 | ||||||||
\(826\) | 1.11550 | 0.0388131 | ||||||||
\(827\) | −33.2617 | −1.15662 | −0.578311 | − | 0.815816i | \(-0.696288\pi\) | ||||
−0.578311 | + | 0.815816i | \(0.696288\pi\) | |||||||
\(828\) | 6.85387 | 0.238188 | ||||||||
\(829\) | 28.0611 | 0.974602 | 0.487301 | − | 0.873234i | \(-0.337981\pi\) | ||||
0.487301 | + | 0.873234i | \(0.337981\pi\) | |||||||
\(830\) | −3.18820 | −0.110664 | ||||||||
\(831\) | −2.90359 | −0.100724 | ||||||||
\(832\) | 2.33936 | 0.0811028 | ||||||||
\(833\) | −6.96078 | −0.241177 | ||||||||
\(834\) | 0.518453 | 0.0179526 | ||||||||
\(835\) | 98.7214 | 3.41639 | ||||||||
\(836\) | −2.31983 | −0.0802331 | ||||||||
\(837\) | −0.642349 | −0.0222028 | ||||||||
\(838\) | 22.4517 | 0.775581 | ||||||||
\(839\) | 37.4342 | 1.29237 | 0.646187 | − | 0.763179i | \(-0.276363\pi\) | ||||
0.646187 | + | 0.763179i | \(0.276363\pi\) | |||||||
\(840\) | 0.552047 | 0.0190474 | ||||||||
\(841\) | −26.5048 | −0.913958 | ||||||||
\(842\) | −7.78948 | −0.268443 | ||||||||
\(843\) | 1.71778 | 0.0591635 | ||||||||
\(844\) | −2.83332 | −0.0975268 | ||||||||
\(845\) | −53.9830 | −1.85707 | ||||||||
\(846\) | 3.84664 | 0.132250 | ||||||||
\(847\) | −0.198048 | −0.00680501 | ||||||||
\(848\) | 5.84245 | 0.200631 | ||||||||
\(849\) | −6.28076 | −0.215555 | ||||||||
\(850\) | −15.6035 | −0.535196 | ||||||||
\(851\) | −24.1499 | −0.827848 | ||||||||
\(852\) | −0.464407 | −0.0159103 | ||||||||
\(853\) | 28.2181 | 0.966170 | 0.483085 | − | 0.875573i | \(-0.339516\pi\) | ||||
0.483085 | + | 0.875573i | \(0.339516\pi\) | |||||||
\(854\) | 0.0404467 | 0.00138406 | ||||||||
\(855\) | 67.4621 | 2.30716 | ||||||||
\(856\) | 19.1450 | 0.654361 | ||||||||
\(857\) | −7.20776 | −0.246213 | −0.123106 | − | 0.992393i | \(-0.539286\pi\) | ||||
−0.123106 | + | 0.992393i | \(0.539286\pi\) | |||||||
\(858\) | −0.0724044 | −0.00247185 | ||||||||
\(859\) | −22.9052 | −0.781514 | −0.390757 | − | 0.920494i | \(-0.627787\pi\) | ||||
−0.390757 | + | 0.920494i | \(0.627787\pi\) | |||||||
\(860\) | 1.76907 | 0.0603249 | ||||||||
\(861\) | 0.107758 | 0.00367239 | ||||||||
\(862\) | −30.3072 | −1.03227 | ||||||||
\(863\) | −22.4308 | −0.763552 | −0.381776 | − | 0.924255i | \(-0.624687\pi\) | ||||
−0.381776 | + | 0.924255i | \(0.624687\pi\) | |||||||
\(864\) | −3.07363 | −0.104567 | ||||||||
\(865\) | 16.6618 | 0.566517 | ||||||||
\(866\) | 24.3600 | 0.827786 | ||||||||
\(867\) | −0.219421 | −0.00745192 | ||||||||
\(868\) | −0.0412790 | −0.00140110 | ||||||||
\(869\) | −6.86933 | −0.233026 | ||||||||
\(870\) | 1.81665 | 0.0615901 | ||||||||
\(871\) | 1.32191 | 0.0447913 | ||||||||
\(872\) | −15.0053 | −0.508142 | ||||||||
\(873\) | 49.7341 | 1.68324 | ||||||||
\(874\) | 37.6592 | 1.27384 | ||||||||
\(875\) | −6.14167 | −0.207626 | ||||||||
\(876\) | 1.47657 | 0.0498887 | ||||||||
\(877\) | 26.0520 | 0.879713 | 0.439856 | − | 0.898068i | \(-0.355029\pi\) | ||||
0.439856 | + | 0.898068i | \(0.355029\pi\) | |||||||
\(878\) | −11.5577 | −0.390054 | ||||||||
\(879\) | −1.14901 | −0.0387550 | ||||||||
\(880\) | 12.4111 | 0.418377 | ||||||||
\(881\) | −32.9724 | −1.11087 | −0.555434 | − | 0.831561i | \(-0.687448\pi\) | ||||
−0.555434 | + | 0.831561i | \(0.687448\pi\) | |||||||
\(882\) | −25.7967 | −0.868620 | ||||||||
\(883\) | 31.3018 | 1.05339 | 0.526694 | − | 0.850055i | \(-0.323431\pi\) | ||||
0.526694 | + | 0.850055i | \(0.323431\pi\) | |||||||
\(884\) | −0.111377 | −0.00374600 | ||||||||
\(885\) | −4.10953 | −0.138140 | ||||||||
\(886\) | −15.4622 | −0.519463 | ||||||||
\(887\) | −7.60261 | −0.255271 | −0.127635 | − | 0.991821i | \(-0.540739\pi\) | ||||
−0.127635 | + | 0.991821i | \(0.540739\pi\) | |||||||
\(888\) | 2.94288 | 0.0987565 | ||||||||
\(889\) | −2.91456 | −0.0977513 | ||||||||
\(890\) | 87.8575 | 2.94499 | ||||||||
\(891\) | −8.56901 | −0.287073 | ||||||||
\(892\) | −1.76324 | −0.0590378 | ||||||||
\(893\) | −5.68216 | −0.190146 | ||||||||
\(894\) | −6.19205 | −0.207093 | ||||||||
\(895\) | −39.8903 | −1.33338 | ||||||||
\(896\) | 1.28089 | 0.0427914 | ||||||||
\(897\) | −0.315992 | −0.0105507 | ||||||||
\(898\) | −27.0751 | −0.903509 | ||||||||
\(899\) | −0.776952 | −0.0259128 | ||||||||
\(900\) | 15.5462 | 0.518207 | ||||||||
\(901\) | −1.96523 | −0.0654713 | ||||||||
\(902\) | 3.11325 | 0.103660 | ||||||||
\(903\) | −0.0434558 | −0.00144612 | ||||||||
\(904\) | 39.9542 | 1.32886 | ||||||||
\(905\) | −4.76123 | −0.158268 | ||||||||
\(906\) | 5.51833 | 0.183334 | ||||||||
\(907\) | 39.5886 | 1.31452 | 0.657259 | − | 0.753664i | \(-0.271716\pi\) | ||||
0.657259 | + | 0.753664i | \(0.271716\pi\) | |||||||
\(908\) | 7.94970 | 0.263820 | ||||||||
\(909\) | −2.63994 | −0.0875611 | ||||||||
\(910\) | 0.272825 | 0.00904407 | ||||||||
\(911\) | 25.4149 | 0.842034 | 0.421017 | − | 0.907053i | \(-0.361673\pi\) | ||||
0.421017 | + | 0.907053i | \(0.361673\pi\) | |||||||
\(912\) | −3.57107 | −0.118250 | ||||||||
\(913\) | −0.608284 | −0.0201313 | ||||||||
\(914\) | −0.915702 | −0.0302887 | ||||||||
\(915\) | −0.149007 | −0.00492602 | ||||||||
\(916\) | 2.97422 | 0.0982708 | ||||||||
\(917\) | −3.81549 | −0.125999 | ||||||||
\(918\) | −1.63961 | −0.0541153 | ||||||||
\(919\) | −50.7219 | −1.67316 | −0.836580 | − | 0.547845i | \(-0.815448\pi\) | ||||
−0.836580 | + | 0.547845i | \(0.815448\pi\) | |||||||
\(920\) | 69.6066 | 2.29486 | ||||||||
\(921\) | −3.04267 | −0.100260 | ||||||||
\(922\) | 36.0973 | 1.18880 | ||||||||
\(923\) | −1.31274 | −0.0432093 | ||||||||
\(924\) | 0.0184148 | 0.000605802 0 | ||||||||
\(925\) | −54.7778 | −1.80108 | ||||||||
\(926\) | −37.9771 | −1.24800 | ||||||||
\(927\) | −5.82441 | −0.191299 | ||||||||
\(928\) | −3.71771 | −0.122040 | ||||||||
\(929\) | −4.82556 | −0.158322 | −0.0791608 | − | 0.996862i | \(-0.525224\pi\) | ||||
−0.0791608 | + | 0.996862i | \(0.525224\pi\) | |||||||
\(930\) | −0.565663 | −0.0185488 | ||||||||
\(931\) | 38.1062 | 1.24888 | ||||||||
\(932\) | 6.05793 | 0.198434 | ||||||||
\(933\) | 4.74511 | 0.155348 | ||||||||
\(934\) | 24.5595 | 0.803612 | ||||||||
\(935\) | −4.17472 | −0.136528 | ||||||||
\(936\) | −2.36087 | −0.0771673 | ||||||||
\(937\) | −19.6040 | −0.640435 | −0.320218 | − | 0.947344i | \(-0.603756\pi\) | ||||
−0.320218 | + | 0.947344i | \(0.603756\pi\) | |||||||
\(938\) | 1.25057 | 0.0408327 | ||||||||
\(939\) | −5.19930 | −0.169673 | ||||||||
\(940\) | −1.83621 | −0.0598905 | ||||||||
\(941\) | −25.6887 | −0.837427 | −0.418714 | − | 0.908118i | \(-0.637519\pi\) | ||||
−0.418714 | + | 0.908118i | \(0.637519\pi\) | |||||||
\(942\) | 5.93342 | 0.193321 | ||||||||
\(943\) | 13.5870 | 0.442454 | ||||||||
\(944\) | −13.3373 | −0.434093 | ||||||||
\(945\) | −1.07976 | −0.0351246 | ||||||||
\(946\) | −1.25548 | −0.0408193 | ||||||||
\(947\) | 9.84383 | 0.319882 | 0.159941 | − | 0.987127i | \(-0.448870\pi\) | ||||
0.159941 | + | 0.987127i | \(0.448870\pi\) | |||||||
\(948\) | 0.638720 | 0.0207447 | ||||||||
\(949\) | 4.17381 | 0.135488 | ||||||||
\(950\) | 85.4202 | 2.77140 | ||||||||
\(951\) | −6.14155 | −0.199153 | ||||||||
\(952\) | −0.602658 | −0.0195323 | ||||||||
\(953\) | 50.3340 | 1.63048 | 0.815239 | − | 0.579125i | \(-0.196606\pi\) | ||||
0.815239 | + | 0.579125i | \(0.196606\pi\) | |||||||
\(954\) | −7.28316 | −0.235801 | ||||||||
\(955\) | 71.9348 | 2.32775 | ||||||||
\(956\) | 7.24229 | 0.234232 | ||||||||
\(957\) | 0.346603 | 0.0112041 | ||||||||
\(958\) | 15.1658 | 0.489985 | ||||||||
\(959\) | −1.92320 | −0.0621035 | ||||||||
\(960\) | −8.15319 | −0.263143 | ||||||||
\(961\) | −30.7581 | −0.992196 | ||||||||
\(962\) | 1.45439 | 0.0468913 | ||||||||
\(963\) | −18.5716 | −0.598461 | ||||||||
\(964\) | 4.76943 | 0.153613 | ||||||||
\(965\) | −13.7897 | −0.443907 | ||||||||
\(966\) | −0.298938 | −0.00961819 | ||||||||
\(967\) | 38.3721 | 1.23396 | 0.616981 | − | 0.786978i | \(-0.288356\pi\) | ||||
0.616981 | + | 0.786978i | \(0.288356\pi\) | |||||||
\(968\) | 3.04299 | 0.0978055 | ||||||||
\(969\) | 1.20120 | 0.0385882 | ||||||||
\(970\) | 88.3076 | 2.83539 | ||||||||
\(971\) | −55.0151 | −1.76552 | −0.882759 | − | 0.469827i | \(-0.844316\pi\) | ||||
−0.882759 | + | 0.469827i | \(0.844316\pi\) | |||||||
\(972\) | 2.45700 | 0.0788082 | ||||||||
\(973\) | −0.372727 | −0.0119491 | ||||||||
\(974\) | −31.3072 | −1.00315 | ||||||||
\(975\) | −0.716745 | −0.0229542 | ||||||||
\(976\) | −0.483596 | −0.0154795 | ||||||||
\(977\) | −4.72353 | −0.151119 | −0.0755596 | − | 0.997141i | \(-0.524074\pi\) | ||||
−0.0755596 | + | 0.997141i | \(0.524074\pi\) | |||||||
\(978\) | 0.802274 | 0.0256539 | ||||||||
\(979\) | 16.7625 | 0.535733 | ||||||||
\(980\) | 12.3141 | 0.393360 | ||||||||
\(981\) | 14.5559 | 0.464733 | ||||||||
\(982\) | 16.1311 | 0.514763 | ||||||||
\(983\) | −11.4263 | −0.364444 | −0.182222 | − | 0.983257i | \(-0.558329\pi\) | ||||
−0.182222 | + | 0.983257i | \(0.558329\pi\) | |||||||
\(984\) | −1.65570 | −0.0527817 | ||||||||
\(985\) | 36.2808 | 1.15600 | ||||||||
\(986\) | −1.98319 | −0.0631577 | ||||||||
\(987\) | 0.0451049 | 0.00143571 | ||||||||
\(988\) | 0.609722 | 0.0193979 | ||||||||
\(989\) | −5.47926 | −0.174230 | ||||||||
\(990\) | −15.4715 | −0.491718 | ||||||||
\(991\) | −28.7124 | −0.912081 | −0.456040 | − | 0.889959i | \(-0.650733\pi\) | ||||
−0.456040 | + | 0.889959i | \(0.650733\pi\) | |||||||
\(992\) | 1.15761 | 0.0367541 | ||||||||
\(993\) | −4.51868 | −0.143396 | ||||||||
\(994\) | −1.24189 | −0.0393904 | ||||||||
\(995\) | 13.2375 | 0.419657 | ||||||||
\(996\) | 0.0565592 | 0.00179215 | ||||||||
\(997\) | 0.0920907 | 0.00291654 | 0.00145827 | − | 0.999999i | \(-0.499536\pi\) | ||||
0.00145827 | + | 0.999999i | \(0.499536\pi\) | |||||||
\(998\) | 7.34605 | 0.232535 | ||||||||
\(999\) | −5.75604 | −0.182113 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.f.1.18 | ✓ | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.f.1.18 | ✓ | 66 | 1.1 | even | 1 | trivial |