Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55291 | −1.80518 | −0.902591 | − | 0.430500i | \(-0.858337\pi\) | ||||
−0.902591 | + | 0.430500i | \(0.858337\pi\) | |||||||
\(3\) | −0.169380 | −0.0977917 | −0.0488958 | − | 0.998804i | \(-0.515570\pi\) | ||||
−0.0488958 | + | 0.998804i | \(0.515570\pi\) | |||||||
\(4\) | 4.51736 | 2.25868 | ||||||||
\(5\) | −0.762748 | −0.341111 | −0.170556 | − | 0.985348i | \(-0.554556\pi\) | ||||
−0.170556 | + | 0.985348i | \(0.554556\pi\) | |||||||
\(6\) | 0.432413 | 0.176532 | ||||||||
\(7\) | 0.998481 | 0.377390 | 0.188695 | − | 0.982036i | \(-0.439574\pi\) | ||||
0.188695 | + | 0.982036i | \(0.439574\pi\) | |||||||
\(8\) | −6.42660 | −2.27215 | ||||||||
\(9\) | −2.97131 | −0.990437 | ||||||||
\(10\) | 1.94723 | 0.615768 | ||||||||
\(11\) | 3.25596 | 0.981708 | 0.490854 | − | 0.871242i | \(-0.336685\pi\) | ||||
0.490854 | + | 0.871242i | \(0.336685\pi\) | |||||||
\(12\) | −0.765151 | −0.220880 | ||||||||
\(13\) | −2.38564 | −0.661657 | −0.330829 | − | 0.943691i | \(-0.607328\pi\) | ||||
−0.330829 | + | 0.943691i | \(0.607328\pi\) | |||||||
\(14\) | −2.54904 | −0.681258 | ||||||||
\(15\) | 0.129194 | 0.0333578 | ||||||||
\(16\) | 7.37183 | 1.84296 | ||||||||
\(17\) | −5.61636 | −1.36217 | −0.681083 | − | 0.732206i | \(-0.738491\pi\) | ||||
−0.681083 | + | 0.732206i | \(0.738491\pi\) | |||||||
\(18\) | 7.58549 | 1.78792 | ||||||||
\(19\) | −0.236108 | −0.0541670 | −0.0270835 | − | 0.999633i | \(-0.508622\pi\) | ||||
−0.0270835 | + | 0.999633i | \(0.508622\pi\) | |||||||
\(20\) | −3.44561 | −0.770462 | ||||||||
\(21\) | −0.169123 | −0.0369056 | ||||||||
\(22\) | −8.31217 | −1.77216 | ||||||||
\(23\) | 0.0343603 | 0.00716463 | 0.00358231 | − | 0.999994i | \(-0.498860\pi\) | ||||
0.00358231 | + | 0.999994i | \(0.498860\pi\) | |||||||
\(24\) | 1.08854 | 0.222197 | ||||||||
\(25\) | −4.41822 | −0.883643 | ||||||||
\(26\) | 6.09033 | 1.19441 | ||||||||
\(27\) | 1.01142 | 0.194648 | ||||||||
\(28\) | 4.51050 | 0.852404 | ||||||||
\(29\) | 4.27471 | 0.793793 | 0.396896 | − | 0.917863i | \(-0.370087\pi\) | ||||
0.396896 | + | 0.917863i | \(0.370087\pi\) | |||||||
\(30\) | −0.329822 | −0.0602170 | ||||||||
\(31\) | 1.74002 | 0.312517 | 0.156258 | − | 0.987716i | \(-0.450057\pi\) | ||||
0.156258 | + | 0.987716i | \(0.450057\pi\) | |||||||
\(32\) | −5.96642 | −1.05472 | ||||||||
\(33\) | −0.551494 | −0.0960028 | ||||||||
\(34\) | 14.3381 | 2.45896 | ||||||||
\(35\) | −0.761590 | −0.128732 | ||||||||
\(36\) | −13.4225 | −2.23708 | ||||||||
\(37\) | −0.632150 | −0.103925 | −0.0519624 | − | 0.998649i | \(-0.516548\pi\) | ||||
−0.0519624 | + | 0.998649i | \(0.516548\pi\) | |||||||
\(38\) | 0.602764 | 0.0977812 | ||||||||
\(39\) | 0.404080 | 0.0647046 | ||||||||
\(40\) | 4.90188 | 0.775055 | ||||||||
\(41\) | 3.96974 | 0.619969 | 0.309984 | − | 0.950742i | \(-0.399676\pi\) | ||||
0.309984 | + | 0.950742i | \(0.399676\pi\) | |||||||
\(42\) | 0.431756 | 0.0666214 | ||||||||
\(43\) | 3.03857 | 0.463377 | 0.231689 | − | 0.972790i | \(-0.425575\pi\) | ||||
0.231689 | + | 0.972790i | \(0.425575\pi\) | |||||||
\(44\) | 14.7083 | 2.21736 | ||||||||
\(45\) | 2.26636 | 0.337849 | ||||||||
\(46\) | −0.0877189 | −0.0129335 | ||||||||
\(47\) | 0.324569 | 0.0473432 | 0.0236716 | − | 0.999720i | \(-0.492464\pi\) | ||||
0.0236716 | + | 0.999720i | \(0.492464\pi\) | |||||||
\(48\) | −1.24864 | −0.180226 | ||||||||
\(49\) | −6.00304 | −0.857576 | ||||||||
\(50\) | 11.2793 | 1.59514 | ||||||||
\(51\) | 0.951299 | 0.133209 | ||||||||
\(52\) | −10.7768 | −1.49447 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −2.58207 | −0.351375 | ||||||||
\(55\) | −2.48347 | −0.334872 | ||||||||
\(56\) | −6.41684 | −0.857486 | ||||||||
\(57\) | 0.0399921 | 0.00529708 | ||||||||
\(58\) | −10.9129 | −1.43294 | ||||||||
\(59\) | 13.5090 | 1.75872 | 0.879361 | − | 0.476156i | \(-0.157970\pi\) | ||||
0.879361 | + | 0.476156i | \(0.157970\pi\) | |||||||
\(60\) | 0.583618 | 0.0753447 | ||||||||
\(61\) | 9.22106 | 1.18064 | 0.590318 | − | 0.807171i | \(-0.299002\pi\) | ||||
0.590318 | + | 0.807171i | \(0.299002\pi\) | |||||||
\(62\) | −4.44212 | −0.564150 | ||||||||
\(63\) | −2.96680 | −0.373781 | ||||||||
\(64\) | 0.488101 | 0.0610127 | ||||||||
\(65\) | 1.81964 | 0.225699 | ||||||||
\(66\) | 1.40792 | 0.173302 | ||||||||
\(67\) | −8.81790 | −1.07728 | −0.538639 | − | 0.842537i | \(-0.681061\pi\) | ||||
−0.538639 | + | 0.842537i | \(0.681061\pi\) | |||||||
\(68\) | −25.3711 | −3.07670 | ||||||||
\(69\) | −0.00581996 | −0.000700641 0 | ||||||||
\(70\) | 1.94427 | 0.232385 | ||||||||
\(71\) | 14.2107 | 1.68650 | 0.843252 | − | 0.537519i | \(-0.180638\pi\) | ||||
0.843252 | + | 0.537519i | \(0.180638\pi\) | |||||||
\(72\) | 19.0954 | 2.25042 | ||||||||
\(73\) | 7.81582 | 0.914773 | 0.457386 | − | 0.889268i | \(-0.348786\pi\) | ||||
0.457386 | + | 0.889268i | \(0.348786\pi\) | |||||||
\(74\) | 1.61382 | 0.187603 | ||||||||
\(75\) | 0.748358 | 0.0864129 | ||||||||
\(76\) | −1.06659 | −0.122346 | ||||||||
\(77\) | 3.25101 | 0.370487 | ||||||||
\(78\) | −1.03158 | −0.116803 | ||||||||
\(79\) | −0.258786 | −0.0291157 | −0.0145579 | − | 0.999894i | \(-0.504634\pi\) | ||||
−0.0145579 | + | 0.999894i | \(0.504634\pi\) | |||||||
\(80\) | −5.62285 | −0.628653 | ||||||||
\(81\) | 8.74262 | 0.971402 | ||||||||
\(82\) | −10.1344 | −1.11916 | ||||||||
\(83\) | −7.55717 | −0.829507 | −0.414754 | − | 0.909934i | \(-0.636132\pi\) | ||||
−0.414754 | + | 0.909934i | \(0.636132\pi\) | |||||||
\(84\) | −0.763989 | −0.0833580 | ||||||||
\(85\) | 4.28387 | 0.464651 | ||||||||
\(86\) | −7.75720 | −0.836480 | ||||||||
\(87\) | −0.724050 | −0.0776263 | ||||||||
\(88\) | −20.9247 | −2.23058 | ||||||||
\(89\) | 9.59998 | 1.01760 | 0.508798 | − | 0.860886i | \(-0.330090\pi\) | ||||
0.508798 | + | 0.860886i | \(0.330090\pi\) | |||||||
\(90\) | −5.78582 | −0.609879 | ||||||||
\(91\) | −2.38202 | −0.249703 | ||||||||
\(92\) | 0.155218 | 0.0161826 | ||||||||
\(93\) | −0.294725 | −0.0305615 | ||||||||
\(94\) | −0.828595 | −0.0854631 | ||||||||
\(95\) | 0.180091 | 0.0184770 | ||||||||
\(96\) | 1.01059 | 0.103143 | ||||||||
\(97\) | 9.21304 | 0.935442 | 0.467721 | − | 0.883876i | \(-0.345075\pi\) | ||||
0.467721 | + | 0.883876i | \(0.345075\pi\) | |||||||
\(98\) | 15.3252 | 1.54808 | ||||||||
\(99\) | −9.67446 | −0.972319 | ||||||||
\(100\) | −19.9587 | −1.99587 | ||||||||
\(101\) | −6.01080 | −0.598097 | −0.299048 | − | 0.954238i | \(-0.596669\pi\) | ||||
−0.299048 | + | 0.954238i | \(0.596669\pi\) | |||||||
\(102\) | −2.42858 | −0.240466 | ||||||||
\(103\) | −1.75012 | −0.172445 | −0.0862225 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862225 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(104\) | 15.3316 | 1.50338 | ||||||||
\(105\) | 0.128998 | 0.0125889 | ||||||||
\(106\) | 2.55291 | 0.247961 | ||||||||
\(107\) | 7.05450 | 0.681984 | 0.340992 | − | 0.940066i | \(-0.389237\pi\) | ||||
0.340992 | + | 0.940066i | \(0.389237\pi\) | |||||||
\(108\) | 4.56895 | 0.439648 | ||||||||
\(109\) | −15.2490 | −1.46059 | −0.730296 | − | 0.683131i | \(-0.760618\pi\) | ||||
−0.730296 | + | 0.683131i | \(0.760618\pi\) | |||||||
\(110\) | 6.34009 | 0.604504 | ||||||||
\(111\) | 0.107074 | 0.0101630 | ||||||||
\(112\) | 7.36063 | 0.695514 | ||||||||
\(113\) | −12.5740 | −1.18286 | −0.591431 | − | 0.806355i | \(-0.701437\pi\) | ||||
−0.591431 | + | 0.806355i | \(0.701437\pi\) | |||||||
\(114\) | −0.102096 | −0.00956219 | ||||||||
\(115\) | −0.0262083 | −0.00244394 | ||||||||
\(116\) | 19.3104 | 1.79292 | ||||||||
\(117\) | 7.08847 | 0.655330 | ||||||||
\(118\) | −34.4873 | −3.17481 | ||||||||
\(119\) | −5.60783 | −0.514069 | ||||||||
\(120\) | −0.830281 | −0.0757939 | ||||||||
\(121\) | −0.398752 | −0.0362502 | ||||||||
\(122\) | −23.5406 | −2.13126 | ||||||||
\(123\) | −0.672395 | −0.0606278 | ||||||||
\(124\) | 7.86030 | 0.705876 | ||||||||
\(125\) | 7.18373 | 0.642532 | ||||||||
\(126\) | 7.57397 | 0.674743 | ||||||||
\(127\) | −6.02956 | −0.535037 | −0.267518 | − | 0.963553i | \(-0.586204\pi\) | ||||
−0.267518 | + | 0.963553i | \(0.586204\pi\) | |||||||
\(128\) | 10.6868 | 0.944586 | ||||||||
\(129\) | −0.514673 | −0.0453144 | ||||||||
\(130\) | −4.64539 | −0.407427 | ||||||||
\(131\) | −19.5158 | −1.70510 | −0.852552 | − | 0.522642i | \(-0.824946\pi\) | ||||
−0.852552 | + | 0.522642i | \(0.824946\pi\) | |||||||
\(132\) | −2.49130 | −0.216840 | ||||||||
\(133\) | −0.235750 | −0.0204421 | ||||||||
\(134\) | 22.5113 | 1.94468 | ||||||||
\(135\) | −0.771460 | −0.0663967 | ||||||||
\(136\) | 36.0941 | 3.09504 | ||||||||
\(137\) | −0.456732 | −0.0390213 | −0.0195106 | − | 0.999810i | \(-0.506211\pi\) | ||||
−0.0195106 | + | 0.999810i | \(0.506211\pi\) | |||||||
\(138\) | 0.0148578 | 0.00126478 | ||||||||
\(139\) | 13.5613 | 1.15025 | 0.575126 | − | 0.818065i | \(-0.304953\pi\) | ||||
0.575126 | + | 0.818065i | \(0.304953\pi\) | |||||||
\(140\) | −3.44038 | −0.290765 | ||||||||
\(141\) | −0.0549755 | −0.00462977 | ||||||||
\(142\) | −36.2788 | −3.04445 | ||||||||
\(143\) | −7.76754 | −0.649554 | ||||||||
\(144\) | −21.9040 | −1.82533 | ||||||||
\(145\) | −3.26052 | −0.270772 | ||||||||
\(146\) | −19.9531 | −1.65133 | ||||||||
\(147\) | 1.01679 | 0.0838638 | ||||||||
\(148\) | −2.85565 | −0.234733 | ||||||||
\(149\) | 7.22946 | 0.592260 | 0.296130 | − | 0.955148i | \(-0.404304\pi\) | ||||
0.296130 | + | 0.955148i | \(0.404304\pi\) | |||||||
\(150\) | −1.91049 | −0.155991 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 1.51737 | 0.123075 | ||||||||
\(153\) | 16.6879 | 1.34914 | ||||||||
\(154\) | −8.29955 | −0.668796 | ||||||||
\(155\) | −1.32720 | −0.106603 | ||||||||
\(156\) | 1.82537 | 0.146147 | ||||||||
\(157\) | 0.772562 | 0.0616572 | 0.0308286 | − | 0.999525i | \(-0.490185\pi\) | ||||
0.0308286 | + | 0.999525i | \(0.490185\pi\) | |||||||
\(158\) | 0.660658 | 0.0525592 | ||||||||
\(159\) | 0.169380 | 0.0134327 | ||||||||
\(160\) | 4.55088 | 0.359779 | ||||||||
\(161\) | 0.0343082 | 0.00270386 | ||||||||
\(162\) | −22.3191 | −1.75356 | ||||||||
\(163\) | −1.65366 | −0.129525 | −0.0647624 | − | 0.997901i | \(-0.520629\pi\) | ||||
−0.0647624 | + | 0.997901i | \(0.520629\pi\) | |||||||
\(164\) | 17.9327 | 1.40031 | ||||||||
\(165\) | 0.420651 | 0.0327477 | ||||||||
\(166\) | 19.2928 | 1.49741 | ||||||||
\(167\) | −0.0974749 | −0.00754284 | −0.00377142 | − | 0.999993i | \(-0.501200\pi\) | ||||
−0.00377142 | + | 0.999993i | \(0.501200\pi\) | |||||||
\(168\) | 1.08689 | 0.0838550 | ||||||||
\(169\) | −7.30873 | −0.562210 | ||||||||
\(170\) | −10.9363 | −0.838779 | ||||||||
\(171\) | 0.701551 | 0.0536490 | ||||||||
\(172\) | 13.7263 | 1.04662 | ||||||||
\(173\) | 15.7605 | 1.19825 | 0.599125 | − | 0.800656i | \(-0.295515\pi\) | ||||
0.599125 | + | 0.800656i | \(0.295515\pi\) | |||||||
\(174\) | 1.84844 | 0.140130 | ||||||||
\(175\) | −4.41150 | −0.333478 | ||||||||
\(176\) | 24.0023 | 1.80924 | ||||||||
\(177\) | −2.28816 | −0.171988 | ||||||||
\(178\) | −24.5079 | −1.83695 | ||||||||
\(179\) | 23.8386 | 1.78178 | 0.890892 | − | 0.454215i | \(-0.150080\pi\) | ||||
0.890892 | + | 0.454215i | \(0.150080\pi\) | |||||||
\(180\) | 10.2380 | 0.763094 | ||||||||
\(181\) | −0.399625 | −0.0297039 | −0.0148520 | − | 0.999890i | \(-0.504728\pi\) | ||||
−0.0148520 | + | 0.999890i | \(0.504728\pi\) | |||||||
\(182\) | 6.08108 | 0.450759 | ||||||||
\(183\) | −1.56186 | −0.115456 | ||||||||
\(184\) | −0.220820 | −0.0162791 | ||||||||
\(185\) | 0.482171 | 0.0354499 | ||||||||
\(186\) | 0.752407 | 0.0551691 | ||||||||
\(187\) | −18.2866 | −1.33725 | ||||||||
\(188\) | 1.46619 | 0.106933 | ||||||||
\(189\) | 1.00989 | 0.0734583 | ||||||||
\(190\) | −0.459757 | −0.0333543 | ||||||||
\(191\) | −6.94831 | −0.502762 | −0.251381 | − | 0.967888i | \(-0.580885\pi\) | ||||
−0.251381 | + | 0.967888i | \(0.580885\pi\) | |||||||
\(192\) | −0.0826747 | −0.00596653 | ||||||||
\(193\) | −19.1235 | −1.37654 | −0.688268 | − | 0.725456i | \(-0.741629\pi\) | ||||
−0.688268 | + | 0.725456i | \(0.741629\pi\) | |||||||
\(194\) | −23.5201 | −1.68864 | ||||||||
\(195\) | −0.308211 | −0.0220715 | ||||||||
\(196\) | −27.1179 | −1.93699 | ||||||||
\(197\) | 8.89670 | 0.633864 | 0.316932 | − | 0.948448i | \(-0.397347\pi\) | ||||
0.316932 | + | 0.948448i | \(0.397347\pi\) | |||||||
\(198\) | 24.6980 | 1.75521 | ||||||||
\(199\) | −14.6032 | −1.03519 | −0.517597 | − | 0.855624i | \(-0.673173\pi\) | ||||
−0.517597 | + | 0.855624i | \(0.673173\pi\) | |||||||
\(200\) | 28.3941 | 2.00777 | ||||||||
\(201\) | 1.49358 | 0.105349 | ||||||||
\(202\) | 15.3450 | 1.07967 | ||||||||
\(203\) | 4.26821 | 0.299570 | ||||||||
\(204\) | 4.29736 | 0.300876 | ||||||||
\(205\) | −3.02791 | −0.211478 | ||||||||
\(206\) | 4.46791 | 0.311294 | ||||||||
\(207\) | −0.102095 | −0.00709611 | ||||||||
\(208\) | −17.5865 | −1.21941 | ||||||||
\(209\) | −0.768759 | −0.0531761 | ||||||||
\(210\) | −0.329321 | −0.0227253 | ||||||||
\(211\) | −20.8058 | −1.43233 | −0.716165 | − | 0.697931i | \(-0.754104\pi\) | ||||
−0.716165 | + | 0.697931i | \(0.754104\pi\) | |||||||
\(212\) | −4.51736 | −0.310254 | ||||||||
\(213\) | −2.40702 | −0.164926 | ||||||||
\(214\) | −18.0095 | −1.23111 | ||||||||
\(215\) | −2.31766 | −0.158063 | ||||||||
\(216\) | −6.50000 | −0.442269 | ||||||||
\(217\) | 1.73738 | 0.117941 | ||||||||
\(218\) | 38.9294 | 2.63663 | ||||||||
\(219\) | −1.32384 | −0.0894571 | ||||||||
\(220\) | −11.2188 | −0.756368 | ||||||||
\(221\) | 13.3986 | 0.901288 | ||||||||
\(222\) | −0.273350 | −0.0183460 | ||||||||
\(223\) | −23.7859 | −1.59282 | −0.796411 | − | 0.604756i | \(-0.793271\pi\) | ||||
−0.796411 | + | 0.604756i | \(0.793271\pi\) | |||||||
\(224\) | −5.95736 | −0.398043 | ||||||||
\(225\) | 13.1279 | 0.875193 | ||||||||
\(226\) | 32.1003 | 2.13528 | ||||||||
\(227\) | 22.8458 | 1.51633 | 0.758165 | − | 0.652063i | \(-0.226096\pi\) | ||||
0.758165 | + | 0.652063i | \(0.226096\pi\) | |||||||
\(228\) | 0.180659 | 0.0119644 | ||||||||
\(229\) | 6.02333 | 0.398033 | 0.199017 | − | 0.979996i | \(-0.436225\pi\) | ||||
0.199017 | + | 0.979996i | \(0.436225\pi\) | |||||||
\(230\) | 0.0669075 | 0.00441175 | ||||||||
\(231\) | −0.550657 | −0.0362305 | ||||||||
\(232\) | −27.4718 | −1.80361 | ||||||||
\(233\) | −27.0992 | −1.77533 | −0.887665 | − | 0.460490i | \(-0.847674\pi\) | ||||
−0.887665 | + | 0.460490i | \(0.847674\pi\) | |||||||
\(234\) | −18.0963 | −1.18299 | ||||||||
\(235\) | −0.247564 | −0.0161493 | ||||||||
\(236\) | 61.0250 | 3.97239 | ||||||||
\(237\) | 0.0438332 | 0.00284727 | ||||||||
\(238\) | 14.3163 | 0.927988 | ||||||||
\(239\) | −26.7586 | −1.73087 | −0.865434 | − | 0.501023i | \(-0.832957\pi\) | ||||
−0.865434 | + | 0.501023i | \(0.832957\pi\) | |||||||
\(240\) | 0.952399 | 0.0614771 | ||||||||
\(241\) | 27.5376 | 1.77385 | 0.886925 | − | 0.461913i | \(-0.152837\pi\) | ||||
0.886925 | + | 0.461913i | \(0.152837\pi\) | |||||||
\(242\) | 1.01798 | 0.0654381 | ||||||||
\(243\) | −4.51509 | −0.289643 | ||||||||
\(244\) | 41.6548 | 2.66668 | ||||||||
\(245\) | 4.57880 | 0.292529 | ||||||||
\(246\) | 1.71656 | 0.109444 | ||||||||
\(247\) | 0.563270 | 0.0358400 | ||||||||
\(248\) | −11.1824 | −0.710084 | ||||||||
\(249\) | 1.28003 | 0.0811189 | ||||||||
\(250\) | −18.3394 | −1.15989 | ||||||||
\(251\) | −26.9056 | −1.69827 | −0.849133 | − | 0.528179i | \(-0.822875\pi\) | ||||
−0.849133 | + | 0.528179i | \(0.822875\pi\) | |||||||
\(252\) | −13.4021 | −0.844253 | ||||||||
\(253\) | 0.111876 | 0.00703357 | ||||||||
\(254\) | 15.3929 | 0.965838 | ||||||||
\(255\) | −0.725602 | −0.0454390 | ||||||||
\(256\) | −28.2586 | −1.76616 | ||||||||
\(257\) | 4.90814 | 0.306161 | 0.153081 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153081 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(258\) | 1.31392 | 0.0818008 | ||||||||
\(259\) | −0.631190 | −0.0392202 | ||||||||
\(260\) | 8.21998 | 0.509782 | ||||||||
\(261\) | −12.7015 | −0.786202 | ||||||||
\(262\) | 49.8222 | 3.07802 | ||||||||
\(263\) | −17.0341 | −1.05037 | −0.525185 | − | 0.850988i | \(-0.676004\pi\) | ||||
−0.525185 | + | 0.850988i | \(0.676004\pi\) | |||||||
\(264\) | 3.54423 | 0.218132 | ||||||||
\(265\) | 0.762748 | 0.0468553 | ||||||||
\(266\) | 0.601849 | 0.0369017 | ||||||||
\(267\) | −1.62605 | −0.0995124 | ||||||||
\(268\) | −39.8336 | −2.43323 | ||||||||
\(269\) | −19.9660 | −1.21735 | −0.608674 | − | 0.793420i | \(-0.708298\pi\) | ||||
−0.608674 | + | 0.793420i | \(0.708298\pi\) | |||||||
\(270\) | 1.96947 | 0.119858 | ||||||||
\(271\) | −0.484274 | −0.0294176 | −0.0147088 | − | 0.999892i | \(-0.504682\pi\) | ||||
−0.0147088 | + | 0.999892i | \(0.504682\pi\) | |||||||
\(272\) | −41.4028 | −2.51041 | ||||||||
\(273\) | 0.403466 | 0.0244189 | ||||||||
\(274\) | 1.16600 | 0.0704405 | ||||||||
\(275\) | −14.3855 | −0.867479 | ||||||||
\(276\) | −0.0262909 | −0.00158252 | ||||||||
\(277\) | −9.62834 | −0.578511 | −0.289255 | − | 0.957252i | \(-0.593408\pi\) | ||||
−0.289255 | + | 0.957252i | \(0.593408\pi\) | |||||||
\(278\) | −34.6207 | −2.07641 | ||||||||
\(279\) | −5.17014 | −0.309528 | ||||||||
\(280\) | 4.89443 | 0.292498 | ||||||||
\(281\) | −2.67286 | −0.159449 | −0.0797246 | − | 0.996817i | \(-0.525404\pi\) | ||||
−0.0797246 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(282\) | 0.140348 | 0.00835758 | ||||||||
\(283\) | −9.10043 | −0.540964 | −0.270482 | − | 0.962725i | \(-0.587183\pi\) | ||||
−0.270482 | + | 0.962725i | \(0.587183\pi\) | |||||||
\(284\) | 64.1950 | 3.80927 | ||||||||
\(285\) | −0.0305039 | −0.00180689 | ||||||||
\(286\) | 19.8298 | 1.17256 | ||||||||
\(287\) | 3.96371 | 0.233970 | ||||||||
\(288\) | 17.7281 | 1.04464 | ||||||||
\(289\) | 14.5435 | 0.855499 | ||||||||
\(290\) | 8.32383 | 0.488792 | ||||||||
\(291\) | −1.56051 | −0.0914784 | ||||||||
\(292\) | 35.3069 | 2.06618 | ||||||||
\(293\) | 14.2652 | 0.833381 | 0.416691 | − | 0.909048i | \(-0.363190\pi\) | ||||
0.416691 | + | 0.909048i | \(0.363190\pi\) | |||||||
\(294\) | −2.59579 | −0.151389 | ||||||||
\(295\) | −10.3040 | −0.599920 | ||||||||
\(296\) | 4.06257 | 0.236132 | ||||||||
\(297\) | 3.29314 | 0.191088 | ||||||||
\(298\) | −18.4562 | −1.06914 | ||||||||
\(299\) | −0.0819714 | −0.00474053 | ||||||||
\(300\) | 3.38060 | 0.195179 | ||||||||
\(301\) | 3.03395 | 0.174874 | ||||||||
\(302\) | 2.55291 | 0.146904 | ||||||||
\(303\) | 1.01811 | 0.0584889 | ||||||||
\(304\) | −1.74055 | −0.0998274 | ||||||||
\(305\) | −7.03335 | −0.402728 | ||||||||
\(306\) | −42.6029 | −2.43544 | ||||||||
\(307\) | 10.1713 | 0.580506 | 0.290253 | − | 0.956950i | \(-0.406261\pi\) | ||||
0.290253 | + | 0.956950i | \(0.406261\pi\) | |||||||
\(308\) | 14.6860 | 0.836812 | ||||||||
\(309\) | 0.296436 | 0.0168637 | ||||||||
\(310\) | 3.38822 | 0.192438 | ||||||||
\(311\) | −6.47695 | −0.367274 | −0.183637 | − | 0.982994i | \(-0.558787\pi\) | ||||
−0.183637 | + | 0.982994i | \(0.558787\pi\) | |||||||
\(312\) | −2.59686 | −0.147018 | ||||||||
\(313\) | −34.7056 | −1.96168 | −0.980838 | − | 0.194827i | \(-0.937585\pi\) | ||||
−0.980838 | + | 0.194827i | \(0.937585\pi\) | |||||||
\(314\) | −1.97228 | −0.111302 | ||||||||
\(315\) | 2.26292 | 0.127501 | ||||||||
\(316\) | −1.16903 | −0.0657631 | ||||||||
\(317\) | 18.8186 | 1.05696 | 0.528478 | − | 0.848947i | \(-0.322763\pi\) | ||||
0.528478 | + | 0.848947i | \(0.322763\pi\) | |||||||
\(318\) | −0.432413 | −0.0242485 | ||||||||
\(319\) | 13.9183 | 0.779273 | ||||||||
\(320\) | −0.372298 | −0.0208121 | ||||||||
\(321\) | −1.19489 | −0.0666924 | ||||||||
\(322\) | −0.0875857 | −0.00488096 | ||||||||
\(323\) | 1.32607 | 0.0737845 | ||||||||
\(324\) | 39.4936 | 2.19409 | ||||||||
\(325\) | 10.5403 | 0.584669 | ||||||||
\(326\) | 4.22165 | 0.233816 | ||||||||
\(327\) | 2.58288 | 0.142834 | ||||||||
\(328\) | −25.5119 | −1.40866 | ||||||||
\(329\) | 0.324076 | 0.0178669 | ||||||||
\(330\) | −1.07389 | −0.0591155 | ||||||||
\(331\) | −14.5066 | −0.797355 | −0.398678 | − | 0.917091i | \(-0.630531\pi\) | ||||
−0.398678 | + | 0.917091i | \(0.630531\pi\) | |||||||
\(332\) | −34.1385 | −1.87359 | ||||||||
\(333\) | 1.87831 | 0.102931 | ||||||||
\(334\) | 0.248845 | 0.0136162 | ||||||||
\(335\) | 6.72584 | 0.367472 | ||||||||
\(336\) | −1.24674 | −0.0680155 | ||||||||
\(337\) | −25.1291 | −1.36887 | −0.684435 | − | 0.729074i | \(-0.739951\pi\) | ||||
−0.684435 | + | 0.729074i | \(0.739951\pi\) | |||||||
\(338\) | 18.6585 | 1.01489 | ||||||||
\(339\) | 2.12979 | 0.115674 | ||||||||
\(340\) | 19.3518 | 1.04950 | ||||||||
\(341\) | 5.66543 | 0.306800 | ||||||||
\(342\) | −1.79100 | −0.0968461 | ||||||||
\(343\) | −12.9833 | −0.701032 | ||||||||
\(344\) | −19.5277 | −1.05286 | ||||||||
\(345\) | 0.00443916 | 0.000238997 0 | ||||||||
\(346\) | −40.2352 | −2.16306 | ||||||||
\(347\) | 12.1097 | 0.650085 | 0.325042 | − | 0.945699i | \(-0.394621\pi\) | ||||
0.325042 | + | 0.945699i | \(0.394621\pi\) | |||||||
\(348\) | −3.27080 | −0.175333 | ||||||||
\(349\) | −9.60542 | −0.514167 | −0.257083 | − | 0.966389i | \(-0.582761\pi\) | ||||
−0.257083 | + | 0.966389i | \(0.582761\pi\) | |||||||
\(350\) | 11.2622 | 0.601989 | ||||||||
\(351\) | −2.41289 | −0.128790 | ||||||||
\(352\) | −19.4264 | −1.03543 | ||||||||
\(353\) | −9.19399 | −0.489347 | −0.244673 | − | 0.969606i | \(-0.578681\pi\) | ||||
−0.244673 | + | 0.969606i | \(0.578681\pi\) | |||||||
\(354\) | 5.84146 | 0.310470 | ||||||||
\(355\) | −10.8392 | −0.575286 | ||||||||
\(356\) | 43.3666 | 2.29842 | ||||||||
\(357\) | 0.949855 | 0.0502716 | ||||||||
\(358\) | −60.8580 | −3.21644 | ||||||||
\(359\) | 25.6514 | 1.35383 | 0.676915 | − | 0.736061i | \(-0.263316\pi\) | ||||
0.676915 | + | 0.736061i | \(0.263316\pi\) | |||||||
\(360\) | −14.5650 | −0.767643 | ||||||||
\(361\) | −18.9443 | −0.997066 | ||||||||
\(362\) | 1.02021 | 0.0536209 | ||||||||
\(363\) | 0.0675406 | 0.00354496 | ||||||||
\(364\) | −10.7604 | −0.564000 | ||||||||
\(365\) | −5.96150 | −0.312039 | ||||||||
\(366\) | 3.98730 | 0.208420 | ||||||||
\(367\) | 20.9507 | 1.09362 | 0.546809 | − | 0.837257i | \(-0.315842\pi\) | ||||
0.546809 | + | 0.837257i | \(0.315842\pi\) | |||||||
\(368\) | 0.253298 | 0.0132041 | ||||||||
\(369\) | −11.7953 | −0.614040 | ||||||||
\(370\) | −1.23094 | −0.0639936 | ||||||||
\(371\) | −0.998481 | −0.0518386 | ||||||||
\(372\) | −1.33138 | −0.0690288 | ||||||||
\(373\) | 6.23367 | 0.322767 | 0.161384 | − | 0.986892i | \(-0.448404\pi\) | ||||
0.161384 | + | 0.986892i | \(0.448404\pi\) | |||||||
\(374\) | 46.6841 | 2.41398 | ||||||||
\(375\) | −1.21678 | −0.0628343 | ||||||||
\(376\) | −2.08587 | −0.107571 | ||||||||
\(377\) | −10.1979 | −0.525219 | ||||||||
\(378\) | −2.57815 | −0.132606 | ||||||||
\(379\) | −5.01634 | −0.257672 | −0.128836 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128836 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(380\) | 0.813537 | 0.0417336 | ||||||||
\(381\) | 1.02129 | 0.0523221 | ||||||||
\(382\) | 17.7384 | 0.907577 | ||||||||
\(383\) | −17.2339 | −0.880611 | −0.440306 | − | 0.897848i | \(-0.645130\pi\) | ||||
−0.440306 | + | 0.897848i | \(0.645130\pi\) | |||||||
\(384\) | −1.81013 | −0.0923726 | ||||||||
\(385\) | −2.47970 | −0.126377 | ||||||||
\(386\) | 48.8205 | 2.48490 | ||||||||
\(387\) | −9.02853 | −0.458946 | ||||||||
\(388\) | 41.6186 | 2.11286 | ||||||||
\(389\) | 7.33855 | 0.372079 | 0.186040 | − | 0.982542i | \(-0.440435\pi\) | ||||
0.186040 | + | 0.982542i | \(0.440435\pi\) | |||||||
\(390\) | 0.786836 | 0.0398430 | ||||||||
\(391\) | −0.192980 | −0.00975942 | ||||||||
\(392\) | 38.5791 | 1.94854 | ||||||||
\(393\) | 3.30559 | 0.166745 | ||||||||
\(394\) | −22.7125 | −1.14424 | ||||||||
\(395\) | 0.197389 | 0.00993171 | ||||||||
\(396\) | −43.7030 | −2.19616 | ||||||||
\(397\) | 37.4051 | 1.87731 | 0.938653 | − | 0.344862i | \(-0.112074\pi\) | ||||
0.938653 | + | 0.344862i | \(0.112074\pi\) | |||||||
\(398\) | 37.2807 | 1.86871 | ||||||||
\(399\) | 0.0399313 | 0.00199907 | ||||||||
\(400\) | −32.5703 | −1.62852 | ||||||||
\(401\) | 38.6015 | 1.92767 | 0.963835 | − | 0.266501i | \(-0.0858676\pi\) | ||||
0.963835 | + | 0.266501i | \(0.0858676\pi\) | |||||||
\(402\) | −3.81297 | −0.190174 | ||||||||
\(403\) | −4.15106 | −0.206779 | ||||||||
\(404\) | −27.1529 | −1.35091 | ||||||||
\(405\) | −6.66842 | −0.331356 | ||||||||
\(406\) | −10.8964 | −0.540778 | ||||||||
\(407\) | −2.05825 | −0.102024 | ||||||||
\(408\) | −6.11362 | −0.302669 | ||||||||
\(409\) | 23.7642 | 1.17506 | 0.587532 | − | 0.809201i | \(-0.300100\pi\) | ||||
0.587532 | + | 0.809201i | \(0.300100\pi\) | |||||||
\(410\) | 7.72999 | 0.381757 | ||||||||
\(411\) | 0.0773614 | 0.00381595 | ||||||||
\(412\) | −7.90594 | −0.389498 | ||||||||
\(413\) | 13.4885 | 0.663725 | ||||||||
\(414\) | 0.260640 | 0.0128098 | ||||||||
\(415\) | 5.76422 | 0.282954 | ||||||||
\(416\) | 14.2337 | 0.697866 | ||||||||
\(417\) | −2.29701 | −0.112485 | ||||||||
\(418\) | 1.96257 | 0.0959926 | ||||||||
\(419\) | 17.9562 | 0.877220 | 0.438610 | − | 0.898678i | \(-0.355471\pi\) | ||||
0.438610 | + | 0.898678i | \(0.355471\pi\) | |||||||
\(420\) | 0.582731 | 0.0284344 | ||||||||
\(421\) | 1.08410 | 0.0528359 | 0.0264180 | − | 0.999651i | \(-0.491590\pi\) | ||||
0.0264180 | + | 0.999651i | \(0.491590\pi\) | |||||||
\(422\) | 53.1153 | 2.58561 | ||||||||
\(423\) | −0.964394 | −0.0468905 | ||||||||
\(424\) | 6.42660 | 0.312103 | ||||||||
\(425\) | 24.8143 | 1.20367 | ||||||||
\(426\) | 6.14490 | 0.297721 | ||||||||
\(427\) | 9.20705 | 0.445561 | ||||||||
\(428\) | 31.8677 | 1.54038 | ||||||||
\(429\) | 1.31567 | 0.0635210 | ||||||||
\(430\) | 5.91679 | 0.285333 | ||||||||
\(431\) | −9.53990 | −0.459521 | −0.229761 | − | 0.973247i | \(-0.573794\pi\) | ||||
−0.229761 | + | 0.973247i | \(0.573794\pi\) | |||||||
\(432\) | 7.45602 | 0.358728 | ||||||||
\(433\) | 27.7840 | 1.33521 | 0.667607 | − | 0.744514i | \(-0.267319\pi\) | ||||
0.667607 | + | 0.744514i | \(0.267319\pi\) | |||||||
\(434\) | −4.43537 | −0.212905 | ||||||||
\(435\) | 0.552268 | 0.0264792 | ||||||||
\(436\) | −68.8854 | −3.29901 | ||||||||
\(437\) | −0.00811277 | −0.000388086 0 | ||||||||
\(438\) | 3.37966 | 0.161486 | ||||||||
\(439\) | 23.5155 | 1.12233 | 0.561166 | − | 0.827703i | \(-0.310353\pi\) | ||||
0.561166 | + | 0.827703i | \(0.310353\pi\) | |||||||
\(440\) | 15.9603 | 0.760877 | ||||||||
\(441\) | 17.8369 | 0.849375 | ||||||||
\(442\) | −34.2055 | −1.62699 | ||||||||
\(443\) | 4.86448 | 0.231118 | 0.115559 | − | 0.993301i | \(-0.463134\pi\) | ||||
0.115559 | + | 0.993301i | \(0.463134\pi\) | |||||||
\(444\) | 0.483690 | 0.0229549 | ||||||||
\(445\) | −7.32237 | −0.347114 | ||||||||
\(446\) | 60.7233 | 2.87533 | ||||||||
\(447\) | −1.22453 | −0.0579181 | ||||||||
\(448\) | 0.487360 | 0.0230256 | ||||||||
\(449\) | 27.7489 | 1.30955 | 0.654776 | − | 0.755823i | \(-0.272763\pi\) | ||||
0.654776 | + | 0.755823i | \(0.272763\pi\) | |||||||
\(450\) | −33.5143 | −1.57988 | ||||||||
\(451\) | 12.9253 | 0.608628 | ||||||||
\(452\) | −56.8013 | −2.67171 | ||||||||
\(453\) | 0.169380 | 0.00795817 | ||||||||
\(454\) | −58.3233 | −2.73725 | ||||||||
\(455\) | 1.81688 | 0.0851766 | ||||||||
\(456\) | −0.257013 | −0.0120357 | ||||||||
\(457\) | −13.7244 | −0.642001 | −0.321001 | − | 0.947079i | \(-0.604019\pi\) | ||||
−0.321001 | + | 0.947079i | \(0.604019\pi\) | |||||||
\(458\) | −15.3770 | −0.718522 | ||||||||
\(459\) | −5.68050 | −0.265143 | ||||||||
\(460\) | −0.118392 | −0.00552007 | ||||||||
\(461\) | 12.9906 | 0.605031 | 0.302516 | − | 0.953144i | \(-0.402174\pi\) | ||||
0.302516 | + | 0.953144i | \(0.402174\pi\) | |||||||
\(462\) | 1.40578 | 0.0654027 | ||||||||
\(463\) | 18.0506 | 0.838881 | 0.419440 | − | 0.907783i | \(-0.362226\pi\) | ||||
0.419440 | + | 0.907783i | \(0.362226\pi\) | |||||||
\(464\) | 31.5124 | 1.46293 | ||||||||
\(465\) | 0.224801 | 0.0104249 | ||||||||
\(466\) | 69.1820 | 3.20479 | ||||||||
\(467\) | −20.6379 | −0.955009 | −0.477504 | − | 0.878629i | \(-0.658459\pi\) | ||||
−0.477504 | + | 0.878629i | \(0.658459\pi\) | |||||||
\(468\) | 32.0212 | 1.48018 | ||||||||
\(469\) | −8.80451 | −0.406554 | ||||||||
\(470\) | 0.632010 | 0.0291524 | ||||||||
\(471\) | −0.130857 | −0.00602956 | ||||||||
\(472\) | −86.8169 | −3.99607 | ||||||||
\(473\) | 9.89345 | 0.454901 | ||||||||
\(474\) | −0.111902 | −0.00513985 | ||||||||
\(475\) | 1.04318 | 0.0478643 | ||||||||
\(476\) | −25.3326 | −1.16112 | ||||||||
\(477\) | 2.97131 | 0.136047 | ||||||||
\(478\) | 68.3123 | 3.12453 | ||||||||
\(479\) | 8.19536 | 0.374456 | 0.187228 | − | 0.982317i | \(-0.440050\pi\) | ||||
0.187228 | + | 0.982317i | \(0.440050\pi\) | |||||||
\(480\) | −0.770828 | −0.0351833 | ||||||||
\(481\) | 1.50808 | 0.0687626 | ||||||||
\(482\) | −70.3010 | −3.20212 | ||||||||
\(483\) | −0.00581112 | −0.000264415 0 | ||||||||
\(484\) | −1.80131 | −0.0818775 | ||||||||
\(485\) | −7.02723 | −0.319090 | ||||||||
\(486\) | 11.5266 | 0.522858 | ||||||||
\(487\) | −2.73244 | −0.123819 | −0.0619093 | − | 0.998082i | \(-0.519719\pi\) | ||||
−0.0619093 | + | 0.998082i | \(0.519719\pi\) | |||||||
\(488\) | −59.2601 | −2.68258 | ||||||||
\(489\) | 0.280097 | 0.0126664 | ||||||||
\(490\) | −11.6893 | −0.528068 | ||||||||
\(491\) | −21.5899 | −0.974339 | −0.487169 | − | 0.873308i | \(-0.661971\pi\) | ||||
−0.487169 | + | 0.873308i | \(0.661971\pi\) | |||||||
\(492\) | −3.03745 | −0.136939 | ||||||||
\(493\) | −24.0083 | −1.08128 | ||||||||
\(494\) | −1.43798 | −0.0646977 | ||||||||
\(495\) | 7.37917 | 0.331669 | ||||||||
\(496\) | 12.8271 | 0.575955 | ||||||||
\(497\) | 14.1892 | 0.636470 | ||||||||
\(498\) | −3.26782 | −0.146434 | ||||||||
\(499\) | −20.7945 | −0.930888 | −0.465444 | − | 0.885077i | \(-0.654105\pi\) | ||||
−0.465444 | + | 0.885077i | \(0.654105\pi\) | |||||||
\(500\) | 32.4515 | 1.45127 | ||||||||
\(501\) | 0.0165103 | 0.000737626 0 | ||||||||
\(502\) | 68.6876 | 3.06568 | ||||||||
\(503\) | −25.0163 | −1.11542 | −0.557710 | − | 0.830036i | \(-0.688320\pi\) | ||||
−0.557710 | + | 0.830036i | \(0.688320\pi\) | |||||||
\(504\) | 19.0664 | 0.849286 | ||||||||
\(505\) | 4.58473 | 0.204018 | ||||||||
\(506\) | −0.285609 | −0.0126969 | ||||||||
\(507\) | 1.23795 | 0.0549794 | ||||||||
\(508\) | −27.2377 | −1.20848 | ||||||||
\(509\) | −16.6451 | −0.737783 | −0.368891 | − | 0.929472i | \(-0.620263\pi\) | ||||
−0.368891 | + | 0.929472i | \(0.620263\pi\) | |||||||
\(510\) | 1.85240 | 0.0820256 | ||||||||
\(511\) | 7.80395 | 0.345226 | ||||||||
\(512\) | 50.7681 | 2.24366 | ||||||||
\(513\) | −0.238805 | −0.0105435 | ||||||||
\(514\) | −12.5301 | −0.552677 | ||||||||
\(515\) | 1.33490 | 0.0588229 | ||||||||
\(516\) | −2.32496 | −0.102351 | ||||||||
\(517\) | 1.05678 | 0.0464772 | ||||||||
\(518\) | 1.61137 | 0.0707996 | ||||||||
\(519\) | −2.66952 | −0.117179 | ||||||||
\(520\) | −11.6941 | −0.512821 | ||||||||
\(521\) | 25.4052 | 1.11302 | 0.556511 | − | 0.830841i | \(-0.312140\pi\) | ||||
0.556511 | + | 0.830841i | \(0.312140\pi\) | |||||||
\(522\) | 32.4258 | 1.41924 | ||||||||
\(523\) | −37.7426 | −1.65037 | −0.825185 | − | 0.564862i | \(-0.808929\pi\) | ||||
−0.825185 | + | 0.564862i | \(0.808929\pi\) | |||||||
\(524\) | −88.1600 | −3.85129 | ||||||||
\(525\) | 0.747221 | 0.0326114 | ||||||||
\(526\) | 43.4867 | 1.89611 | ||||||||
\(527\) | −9.77258 | −0.425700 | ||||||||
\(528\) | −4.06552 | −0.176929 | ||||||||
\(529\) | −22.9988 | −0.999949 | ||||||||
\(530\) | −1.94723 | −0.0845822 | ||||||||
\(531\) | −40.1394 | −1.74190 | ||||||||
\(532\) | −1.06497 | −0.0461722 | ||||||||
\(533\) | −9.47036 | −0.410207 | ||||||||
\(534\) | 4.15115 | 0.179638 | ||||||||
\(535\) | −5.38081 | −0.232633 | ||||||||
\(536\) | 56.6691 | 2.44773 | ||||||||
\(537\) | −4.03779 | −0.174244 | ||||||||
\(538\) | 50.9715 | 2.19754 | ||||||||
\(539\) | −19.5456 | −0.841889 | ||||||||
\(540\) | −3.48496 | −0.149969 | ||||||||
\(541\) | 35.7933 | 1.53887 | 0.769437 | − | 0.638723i | \(-0.220537\pi\) | ||||
0.769437 | + | 0.638723i | \(0.220537\pi\) | |||||||
\(542\) | 1.23631 | 0.0531041 | ||||||||
\(543\) | 0.0676886 | 0.00290479 | ||||||||
\(544\) | 33.5096 | 1.43671 | ||||||||
\(545\) | 11.6312 | 0.498225 | ||||||||
\(546\) | −1.03001 | −0.0440805 | ||||||||
\(547\) | 14.8935 | 0.636800 | 0.318400 | − | 0.947956i | \(-0.396854\pi\) | ||||
0.318400 | + | 0.947956i | \(0.396854\pi\) | |||||||
\(548\) | −2.06322 | −0.0881366 | ||||||||
\(549\) | −27.3986 | −1.16934 | ||||||||
\(550\) | 36.7250 | 1.56596 | ||||||||
\(551\) | −1.00929 | −0.0429974 | ||||||||
\(552\) | 0.0374026 | 0.00159196 | ||||||||
\(553\) | −0.258393 | −0.0109880 | ||||||||
\(554\) | 24.5803 | 1.04432 | ||||||||
\(555\) | −0.0816702 | −0.00346671 | ||||||||
\(556\) | 61.2612 | 2.59805 | ||||||||
\(557\) | −20.3983 | −0.864304 | −0.432152 | − | 0.901801i | \(-0.642246\pi\) | ||||
−0.432152 | + | 0.901801i | \(0.642246\pi\) | |||||||
\(558\) | 13.1989 | 0.558755 | ||||||||
\(559\) | −7.24893 | −0.306597 | ||||||||
\(560\) | −5.61431 | −0.237248 | ||||||||
\(561\) | 3.09739 | 0.130772 | ||||||||
\(562\) | 6.82357 | 0.287835 | ||||||||
\(563\) | 3.22812 | 0.136049 | 0.0680246 | − | 0.997684i | \(-0.478330\pi\) | ||||
0.0680246 | + | 0.997684i | \(0.478330\pi\) | |||||||
\(564\) | −0.248344 | −0.0104572 | ||||||||
\(565\) | 9.59080 | 0.403488 | ||||||||
\(566\) | 23.2326 | 0.976539 | ||||||||
\(567\) | 8.72934 | 0.366598 | ||||||||
\(568\) | −91.3267 | −3.83198 | ||||||||
\(569\) | −25.7502 | −1.07950 | −0.539752 | − | 0.841824i | \(-0.681482\pi\) | ||||
−0.539752 | + | 0.841824i | \(0.681482\pi\) | |||||||
\(570\) | 0.0778737 | 0.00326177 | ||||||||
\(571\) | 4.35595 | 0.182291 | 0.0911454 | − | 0.995838i | \(-0.470947\pi\) | ||||
0.0911454 | + | 0.995838i | \(0.470947\pi\) | |||||||
\(572\) | −35.0888 | −1.46713 | ||||||||
\(573\) | 1.17691 | 0.0491659 | ||||||||
\(574\) | −10.1190 | −0.422359 | ||||||||
\(575\) | −0.151811 | −0.00633097 | ||||||||
\(576\) | −1.45030 | −0.0604292 | ||||||||
\(577\) | 38.1063 | 1.58639 | 0.793193 | − | 0.608970i | \(-0.208417\pi\) | ||||
0.793193 | + | 0.608970i | \(0.208417\pi\) | |||||||
\(578\) | −37.1282 | −1.54433 | ||||||||
\(579\) | 3.23913 | 0.134614 | ||||||||
\(580\) | −14.7290 | −0.611587 | ||||||||
\(581\) | −7.54569 | −0.313048 | ||||||||
\(582\) | 3.98383 | 0.165135 | ||||||||
\(583\) | −3.25596 | −0.134848 | ||||||||
\(584\) | −50.2292 | −2.07850 | ||||||||
\(585\) | −5.40672 | −0.223540 | ||||||||
\(586\) | −36.4178 | −1.50440 | ||||||||
\(587\) | −45.8227 | −1.89131 | −0.945653 | − | 0.325177i | \(-0.894576\pi\) | ||||
−0.945653 | + | 0.325177i | \(0.894576\pi\) | |||||||
\(588\) | 4.59323 | 0.189422 | ||||||||
\(589\) | −0.410834 | −0.0169281 | ||||||||
\(590\) | 26.3051 | 1.08296 | ||||||||
\(591\) | −1.50692 | −0.0619866 | ||||||||
\(592\) | −4.66010 | −0.191529 | ||||||||
\(593\) | 3.16572 | 0.130001 | 0.0650003 | − | 0.997885i | \(-0.479295\pi\) | ||||
0.0650003 | + | 0.997885i | \(0.479295\pi\) | |||||||
\(594\) | −8.40710 | −0.344948 | ||||||||
\(595\) | 4.27736 | 0.175355 | ||||||||
\(596\) | 32.6581 | 1.33773 | ||||||||
\(597\) | 2.47349 | 0.101233 | ||||||||
\(598\) | 0.209266 | 0.00855751 | ||||||||
\(599\) | −2.11033 | −0.0862257 | −0.0431128 | − | 0.999070i | \(-0.513727\pi\) | ||||
−0.0431128 | + | 0.999070i | \(0.513727\pi\) | |||||||
\(600\) | −4.80940 | −0.196343 | ||||||||
\(601\) | −40.9755 | −1.67142 | −0.835712 | − | 0.549168i | \(-0.814945\pi\) | ||||
−0.835712 | + | 0.549168i | \(0.814945\pi\) | |||||||
\(602\) | −7.74542 | −0.315680 | ||||||||
\(603\) | 26.2007 | 1.06698 | ||||||||
\(604\) | −4.51736 | −0.183809 | ||||||||
\(605\) | 0.304147 | 0.0123653 | ||||||||
\(606\) | −2.59914 | −0.105583 | ||||||||
\(607\) | −36.3526 | −1.47551 | −0.737753 | − | 0.675070i | \(-0.764113\pi\) | ||||
−0.737753 | + | 0.675070i | \(0.764113\pi\) | |||||||
\(608\) | 1.40872 | 0.0571312 | ||||||||
\(609\) | −0.722951 | −0.0292954 | ||||||||
\(610\) | 17.9555 | 0.726998 | ||||||||
\(611\) | −0.774304 | −0.0313250 | ||||||||
\(612\) | 75.3855 | 3.04728 | ||||||||
\(613\) | −37.1747 | −1.50147 | −0.750735 | − | 0.660603i | \(-0.770301\pi\) | ||||
−0.750735 | + | 0.660603i | \(0.770301\pi\) | |||||||
\(614\) | −25.9664 | −1.04792 | ||||||||
\(615\) | 0.512868 | 0.0206808 | ||||||||
\(616\) | −20.8929 | −0.841801 | ||||||||
\(617\) | 24.6099 | 0.990756 | 0.495378 | − | 0.868677i | \(-0.335030\pi\) | ||||
0.495378 | + | 0.868677i | \(0.335030\pi\) | |||||||
\(618\) | −0.756776 | −0.0304420 | ||||||||
\(619\) | 29.5641 | 1.18828 | 0.594140 | − | 0.804362i | \(-0.297493\pi\) | ||||
0.594140 | + | 0.804362i | \(0.297493\pi\) | |||||||
\(620\) | −5.99543 | −0.240782 | ||||||||
\(621\) | 0.0347528 | 0.00139458 | ||||||||
\(622\) | 16.5351 | 0.662996 | ||||||||
\(623\) | 9.58540 | 0.384031 | ||||||||
\(624\) | 2.97881 | 0.119248 | ||||||||
\(625\) | 16.6117 | 0.664468 | ||||||||
\(626\) | 88.6003 | 3.54118 | ||||||||
\(627\) | 0.130212 | 0.00520018 | ||||||||
\(628\) | 3.48994 | 0.139264 | ||||||||
\(629\) | 3.55038 | 0.141563 | ||||||||
\(630\) | −5.77704 | −0.230163 | ||||||||
\(631\) | −30.8086 | −1.22647 | −0.613236 | − | 0.789900i | \(-0.710132\pi\) | ||||
−0.613236 | + | 0.789900i | \(0.710132\pi\) | |||||||
\(632\) | 1.66312 | 0.0661552 | ||||||||
\(633\) | 3.52409 | 0.140070 | ||||||||
\(634\) | −48.0421 | −1.90800 | ||||||||
\(635\) | 4.59903 | 0.182507 | ||||||||
\(636\) | 0.765151 | 0.0303402 | ||||||||
\(637\) | 14.3211 | 0.567422 | ||||||||
\(638\) | −35.5321 | −1.40673 | ||||||||
\(639\) | −42.2245 | −1.67038 | ||||||||
\(640\) | −8.15131 | −0.322209 | ||||||||
\(641\) | −23.5705 | −0.930978 | −0.465489 | − | 0.885054i | \(-0.654122\pi\) | ||||
−0.465489 | + | 0.885054i | \(0.654122\pi\) | |||||||
\(642\) | 3.05045 | 0.120392 | ||||||||
\(643\) | −31.9327 | −1.25930 | −0.629651 | − | 0.776878i | \(-0.716802\pi\) | ||||
−0.629651 | + | 0.776878i | \(0.716802\pi\) | |||||||
\(644\) | 0.154982 | 0.00610716 | ||||||||
\(645\) | 0.392566 | 0.0154573 | ||||||||
\(646\) | −3.38534 | −0.133194 | ||||||||
\(647\) | 34.0811 | 1.33987 | 0.669934 | − | 0.742421i | \(-0.266323\pi\) | ||||
0.669934 | + | 0.742421i | \(0.266323\pi\) | |||||||
\(648\) | −56.1853 | −2.20717 | ||||||||
\(649\) | 43.9847 | 1.72655 | ||||||||
\(650\) | −26.9084 | −1.05543 | ||||||||
\(651\) | −0.294277 | −0.0115336 | ||||||||
\(652\) | −7.47019 | −0.292555 | ||||||||
\(653\) | 45.6180 | 1.78517 | 0.892584 | − | 0.450881i | \(-0.148890\pi\) | ||||
0.892584 | + | 0.450881i | \(0.148890\pi\) | |||||||
\(654\) | −6.59387 | −0.257841 | ||||||||
\(655\) | 14.8857 | 0.581631 | ||||||||
\(656\) | 29.2642 | 1.14258 | ||||||||
\(657\) | −23.2232 | −0.906024 | ||||||||
\(658\) | −0.827337 | −0.0322530 | ||||||||
\(659\) | −17.7410 | −0.691090 | −0.345545 | − | 0.938402i | \(-0.612306\pi\) | ||||
−0.345545 | + | 0.938402i | \(0.612306\pi\) | |||||||
\(660\) | 1.90023 | 0.0739665 | ||||||||
\(661\) | −36.0502 | −1.40219 | −0.701095 | − | 0.713068i | \(-0.747305\pi\) | ||||
−0.701095 | + | 0.713068i | \(0.747305\pi\) | |||||||
\(662\) | 37.0341 | 1.43937 | ||||||||
\(663\) | −2.26946 | −0.0881384 | ||||||||
\(664\) | 48.5669 | 1.88476 | ||||||||
\(665\) | 0.179818 | 0.00697304 | ||||||||
\(666\) | −4.79517 | −0.185809 | ||||||||
\(667\) | 0.146880 | 0.00568723 | ||||||||
\(668\) | −0.440329 | −0.0170369 | ||||||||
\(669\) | 4.02886 | 0.155765 | ||||||||
\(670\) | −17.1705 | −0.663353 | ||||||||
\(671\) | 30.0234 | 1.15904 | ||||||||
\(672\) | 1.00906 | 0.0389253 | ||||||||
\(673\) | −17.0259 | −0.656300 | −0.328150 | − | 0.944626i | \(-0.606425\pi\) | ||||
−0.328150 | + | 0.944626i | \(0.606425\pi\) | |||||||
\(674\) | 64.1525 | 2.47106 | ||||||||
\(675\) | −4.46868 | −0.171999 | ||||||||
\(676\) | −33.0161 | −1.26985 | ||||||||
\(677\) | 0.925431 | 0.0355672 | 0.0177836 | − | 0.999842i | \(-0.494339\pi\) | ||||
0.0177836 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(678\) | −5.43716 | −0.208813 | ||||||||
\(679\) | 9.19904 | 0.353027 | ||||||||
\(680\) | −27.5307 | −1.05575 | ||||||||
\(681\) | −3.86963 | −0.148284 | ||||||||
\(682\) | −14.4633 | −0.553830 | ||||||||
\(683\) | −39.6444 | −1.51695 | −0.758476 | − | 0.651701i | \(-0.774056\pi\) | ||||
−0.758476 | + | 0.651701i | \(0.774056\pi\) | |||||||
\(684\) | 3.16916 | 0.121176 | ||||||||
\(685\) | 0.348372 | 0.0133106 | ||||||||
\(686\) | 33.1452 | 1.26549 | ||||||||
\(687\) | −1.02023 | −0.0389243 | ||||||||
\(688\) | 22.3998 | 0.853984 | ||||||||
\(689\) | 2.38564 | 0.0908856 | ||||||||
\(690\) | −0.0113328 | −0.000431432 0 | ||||||||
\(691\) | 13.4582 | 0.511974 | 0.255987 | − | 0.966680i | \(-0.417600\pi\) | ||||
0.255987 | + | 0.966680i | \(0.417600\pi\) | |||||||
\(692\) | 71.1959 | 2.70646 | ||||||||
\(693\) | −9.65976 | −0.366944 | ||||||||
\(694\) | −30.9151 | −1.17352 | ||||||||
\(695\) | −10.3438 | −0.392364 | ||||||||
\(696\) | 4.65318 | 0.176378 | ||||||||
\(697\) | −22.2955 | −0.844501 | ||||||||
\(698\) | 24.5218 | 0.928164 | ||||||||
\(699\) | 4.59007 | 0.173612 | ||||||||
\(700\) | −19.9284 | −0.753221 | ||||||||
\(701\) | 26.1009 | 0.985817 | 0.492908 | − | 0.870081i | \(-0.335934\pi\) | ||||
0.492908 | + | 0.870081i | \(0.335934\pi\) | |||||||
\(702\) | 6.15989 | 0.232490 | ||||||||
\(703\) | 0.149256 | 0.00562929 | ||||||||
\(704\) | 1.58924 | 0.0598966 | ||||||||
\(705\) | 0.0419325 | 0.00157927 | ||||||||
\(706\) | 23.4715 | 0.883360 | ||||||||
\(707\) | −6.00167 | −0.225716 | ||||||||
\(708\) | −10.3364 | −0.388467 | ||||||||
\(709\) | −43.6199 | −1.63818 | −0.819090 | − | 0.573664i | \(-0.805521\pi\) | ||||
−0.819090 | + | 0.573664i | \(0.805521\pi\) | |||||||
\(710\) | 27.6716 | 1.03850 | ||||||||
\(711\) | 0.768934 | 0.0288373 | ||||||||
\(712\) | −61.6953 | −2.31213 | ||||||||
\(713\) | 0.0597877 | 0.00223907 | ||||||||
\(714\) | −2.42490 | −0.0907494 | ||||||||
\(715\) | 5.92467 | 0.221570 | ||||||||
\(716\) | 107.688 | 4.02448 | ||||||||
\(717\) | 4.53237 | 0.169264 | ||||||||
\(718\) | −65.4859 | −2.44391 | ||||||||
\(719\) | 15.3015 | 0.570650 | 0.285325 | − | 0.958431i | \(-0.407899\pi\) | ||||
0.285325 | + | 0.958431i | \(0.407899\pi\) | |||||||
\(720\) | 16.7072 | 0.622642 | ||||||||
\(721\) | −1.74747 | −0.0650791 | ||||||||
\(722\) | 48.3630 | 1.79989 | ||||||||
\(723\) | −4.66432 | −0.173468 | ||||||||
\(724\) | −1.80525 | −0.0670916 | ||||||||
\(725\) | −18.8866 | −0.701430 | ||||||||
\(726\) | −0.172425 | −0.00639930 | ||||||||
\(727\) | −7.21452 | −0.267572 | −0.133786 | − | 0.991010i | \(-0.542713\pi\) | ||||
−0.133786 | + | 0.991010i | \(0.542713\pi\) | |||||||
\(728\) | 15.3083 | 0.567362 | ||||||||
\(729\) | −25.4631 | −0.943077 | ||||||||
\(730\) | 15.2192 | 0.563288 | ||||||||
\(731\) | −17.0657 | −0.631197 | ||||||||
\(732\) | −7.05550 | −0.260779 | ||||||||
\(733\) | −13.9927 | −0.516831 | −0.258416 | − | 0.966034i | \(-0.583200\pi\) | ||||
−0.258416 | + | 0.966034i | \(0.583200\pi\) | |||||||
\(734\) | −53.4853 | −1.97418 | ||||||||
\(735\) | −0.775558 | −0.0286069 | ||||||||
\(736\) | −0.205008 | −0.00755671 | ||||||||
\(737\) | −28.7107 | −1.05757 | ||||||||
\(738\) | 30.1124 | 1.10845 | ||||||||
\(739\) | 38.4809 | 1.41554 | 0.707772 | − | 0.706441i | \(-0.249701\pi\) | ||||
0.707772 | + | 0.706441i | \(0.249701\pi\) | |||||||
\(740\) | 2.17814 | 0.0800701 | ||||||||
\(741\) | −0.0954067 | −0.00350485 | ||||||||
\(742\) | 2.54904 | 0.0935780 | ||||||||
\(743\) | −22.4613 | −0.824027 | −0.412013 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412013 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(744\) | 1.89408 | 0.0694403 | ||||||||
\(745\) | −5.51426 | −0.202027 | ||||||||
\(746\) | −15.9140 | −0.582653 | ||||||||
\(747\) | 22.4547 | 0.821574 | ||||||||
\(748\) | −82.6072 | −3.02042 | ||||||||
\(749\) | 7.04379 | 0.257374 | ||||||||
\(750\) | 3.10633 | 0.113427 | ||||||||
\(751\) | 8.93870 | 0.326178 | 0.163089 | − | 0.986611i | \(-0.447854\pi\) | ||||
0.163089 | + | 0.986611i | \(0.447854\pi\) | |||||||
\(752\) | 2.39266 | 0.0872515 | ||||||||
\(753\) | 4.55727 | 0.166076 | ||||||||
\(754\) | 26.0344 | 0.948115 | ||||||||
\(755\) | 0.762748 | 0.0277593 | ||||||||
\(756\) | 4.56202 | 0.165919 | ||||||||
\(757\) | −12.5755 | −0.457066 | −0.228533 | − | 0.973536i | \(-0.573393\pi\) | ||||
−0.228533 | + | 0.973536i | \(0.573393\pi\) | |||||||
\(758\) | 12.8063 | 0.465145 | ||||||||
\(759\) | −0.0189495 | −0.000687824 0 | ||||||||
\(760\) | −1.15737 | −0.0419824 | ||||||||
\(761\) | −52.1364 | −1.88994 | −0.944971 | − | 0.327153i | \(-0.893911\pi\) | ||||
−0.944971 | + | 0.327153i | \(0.893911\pi\) | |||||||
\(762\) | −2.60726 | −0.0944509 | ||||||||
\(763\) | −15.2259 | −0.551214 | ||||||||
\(764\) | −31.3880 | −1.13558 | ||||||||
\(765\) | −12.7287 | −0.460207 | ||||||||
\(766\) | 43.9966 | 1.58966 | ||||||||
\(767\) | −32.2276 | −1.16367 | ||||||||
\(768\) | 4.78644 | 0.172716 | ||||||||
\(769\) | −15.3059 | −0.551944 | −0.275972 | − | 0.961166i | \(-0.589000\pi\) | ||||
−0.275972 | + | 0.961166i | \(0.589000\pi\) | |||||||
\(770\) | 6.33046 | 0.228134 | ||||||||
\(771\) | −0.831342 | −0.0299400 | ||||||||
\(772\) | −86.3875 | −3.10916 | ||||||||
\(773\) | −5.57430 | −0.200494 | −0.100247 | − | 0.994963i | \(-0.531963\pi\) | ||||
−0.100247 | + | 0.994963i | \(0.531963\pi\) | |||||||
\(774\) | 23.0490 | 0.828481 | ||||||||
\(775\) | −7.68779 | −0.276153 | ||||||||
\(776\) | −59.2085 | −2.12546 | ||||||||
\(777\) | 0.106911 | 0.00383541 | ||||||||
\(778\) | −18.7347 | −0.671670 | ||||||||
\(779\) | −0.937289 | −0.0335818 | ||||||||
\(780\) | −1.39230 | −0.0498524 | ||||||||
\(781\) | 46.2695 | 1.65565 | ||||||||
\(782\) | 0.492661 | 0.0176175 | ||||||||
\(783\) | 4.32353 | 0.154510 | ||||||||
\(784\) | −44.2533 | −1.58048 | ||||||||
\(785\) | −0.589270 | −0.0210320 | ||||||||
\(786\) | −8.43888 | −0.301005 | ||||||||
\(787\) | −5.10825 | −0.182089 | −0.0910447 | − | 0.995847i | \(-0.529021\pi\) | ||||
−0.0910447 | + | 0.995847i | \(0.529021\pi\) | |||||||
\(788\) | 40.1896 | 1.43170 | ||||||||
\(789\) | 2.88524 | 0.102717 | ||||||||
\(790\) | −0.503916 | −0.0179285 | ||||||||
\(791\) | −12.5549 | −0.446401 | ||||||||
\(792\) | 62.1739 | 2.20925 | ||||||||
\(793\) | −21.9981 | −0.781176 | ||||||||
\(794\) | −95.4919 | −3.38888 | ||||||||
\(795\) | −0.129194 | −0.00458205 | ||||||||
\(796\) | −65.9680 | −2.33817 | ||||||||
\(797\) | −46.8567 | −1.65975 | −0.829874 | − | 0.557950i | \(-0.811588\pi\) | ||||
−0.829874 | + | 0.557950i | \(0.811588\pi\) | |||||||
\(798\) | −0.101941 | −0.00360868 | ||||||||
\(799\) | −1.82289 | −0.0644894 | ||||||||
\(800\) | 26.3609 | 0.932000 | ||||||||
\(801\) | −28.5245 | −1.00786 | ||||||||
\(802\) | −98.5464 | −3.47979 | ||||||||
\(803\) | 25.4480 | 0.898039 | ||||||||
\(804\) | 6.74703 | 0.237949 | ||||||||
\(805\) | −0.0261685 | −0.000922318 0 | ||||||||
\(806\) | 10.5973 | 0.373274 | ||||||||
\(807\) | 3.38184 | 0.119047 | ||||||||
\(808\) | 38.6290 | 1.35896 | ||||||||
\(809\) | −22.9741 | −0.807728 | −0.403864 | − | 0.914819i | \(-0.632333\pi\) | ||||
−0.403864 | + | 0.914819i | \(0.632333\pi\) | |||||||
\(810\) | 17.0239 | 0.598158 | ||||||||
\(811\) | −18.0720 | −0.634595 | −0.317297 | − | 0.948326i | \(-0.602775\pi\) | ||||
−0.317297 | + | 0.948326i | \(0.602775\pi\) | |||||||
\(812\) | 19.2811 | 0.676633 | ||||||||
\(813\) | 0.0820265 | 0.00287679 | ||||||||
\(814\) | 5.25454 | 0.184171 | ||||||||
\(815\) | 1.26133 | 0.0441824 | ||||||||
\(816\) | 7.01281 | 0.245498 | ||||||||
\(817\) | −0.717432 | −0.0250998 | ||||||||
\(818\) | −60.6679 | −2.12120 | ||||||||
\(819\) | 7.07771 | 0.247315 | ||||||||
\(820\) | −13.6782 | −0.477662 | ||||||||
\(821\) | 34.7123 | 1.21147 | 0.605733 | − | 0.795668i | \(-0.292880\pi\) | ||||
0.605733 | + | 0.795668i | \(0.292880\pi\) | |||||||
\(822\) | −0.197497 | −0.00688849 | ||||||||
\(823\) | 56.0970 | 1.95542 | 0.977710 | − | 0.209961i | \(-0.0673336\pi\) | ||||
0.977710 | + | 0.209961i | \(0.0673336\pi\) | |||||||
\(824\) | 11.2474 | 0.391820 | ||||||||
\(825\) | 2.43662 | 0.0848322 | ||||||||
\(826\) | −34.4349 | −1.19814 | ||||||||
\(827\) | −12.6496 | −0.439868 | −0.219934 | − | 0.975515i | \(-0.570584\pi\) | ||||
−0.219934 | + | 0.975515i | \(0.570584\pi\) | |||||||
\(828\) | −0.461201 | −0.0160278 | ||||||||
\(829\) | −8.61089 | −0.299069 | −0.149534 | − | 0.988757i | \(-0.547777\pi\) | ||||
−0.149534 | + | 0.988757i | \(0.547777\pi\) | |||||||
\(830\) | −14.7155 | −0.510784 | ||||||||
\(831\) | 1.63085 | 0.0565735 | ||||||||
\(832\) | −1.16443 | −0.0403695 | ||||||||
\(833\) | 33.7152 | 1.16816 | ||||||||
\(834\) | 5.86406 | 0.203056 | ||||||||
\(835\) | 0.0743488 | 0.00257295 | ||||||||
\(836\) | −3.47276 | −0.120108 | ||||||||
\(837\) | 1.75989 | 0.0608308 | ||||||||
\(838\) | −45.8407 | −1.58354 | ||||||||
\(839\) | −51.8300 | −1.78937 | −0.894685 | − | 0.446698i | \(-0.852600\pi\) | ||||
−0.894685 | + | 0.446698i | \(0.852600\pi\) | |||||||
\(840\) | −0.829020 | −0.0286039 | ||||||||
\(841\) | −10.7269 | −0.369893 | ||||||||
\(842\) | −2.76762 | −0.0953784 | ||||||||
\(843\) | 0.452729 | 0.0155928 | ||||||||
\(844\) | −93.9872 | −3.23517 | ||||||||
\(845\) | 5.57472 | 0.191776 | ||||||||
\(846\) | 2.46201 | 0.0846458 | ||||||||
\(847\) | −0.398146 | −0.0136805 | ||||||||
\(848\) | −7.37183 | −0.253150 | ||||||||
\(849\) | 1.54143 | 0.0529018 | ||||||||
\(850\) | −63.3487 | −2.17284 | ||||||||
\(851\) | −0.0217209 | −0.000744582 0 | ||||||||
\(852\) | −10.8734 | −0.372515 | ||||||||
\(853\) | 11.4215 | 0.391063 | 0.195532 | − | 0.980697i | \(-0.437357\pi\) | ||||
0.195532 | + | 0.980697i | \(0.437357\pi\) | |||||||
\(854\) | −23.5048 | −0.804318 | ||||||||
\(855\) | −0.535107 | −0.0183003 | ||||||||
\(856\) | −45.3365 | −1.54957 | ||||||||
\(857\) | −19.8844 | −0.679239 | −0.339619 | − | 0.940563i | \(-0.610298\pi\) | ||||
−0.339619 | + | 0.940563i | \(0.610298\pi\) | |||||||
\(858\) | −3.35878 | −0.114667 | ||||||||
\(859\) | −46.8552 | −1.59868 | −0.799340 | − | 0.600879i | \(-0.794817\pi\) | ||||
−0.799340 | + | 0.600879i | \(0.794817\pi\) | |||||||
\(860\) | −10.4697 | −0.357014 | ||||||||
\(861\) | −0.671373 | −0.0228803 | ||||||||
\(862\) | 24.3545 | 0.829519 | ||||||||
\(863\) | −8.43346 | −0.287078 | −0.143539 | − | 0.989645i | \(-0.545848\pi\) | ||||
−0.143539 | + | 0.989645i | \(0.545848\pi\) | |||||||
\(864\) | −6.03457 | −0.205300 | ||||||||
\(865\) | −12.0213 | −0.408737 | ||||||||
\(866\) | −70.9301 | −2.41030 | ||||||||
\(867\) | −2.46338 | −0.0836606 | ||||||||
\(868\) | 7.84836 | 0.266391 | ||||||||
\(869\) | −0.842596 | −0.0285831 | ||||||||
\(870\) | −1.40989 | −0.0477998 | ||||||||
\(871\) | 21.0363 | 0.712789 | ||||||||
\(872\) | 97.9994 | 3.31868 | ||||||||
\(873\) | −27.3748 | −0.926496 | ||||||||
\(874\) | 0.0207112 | 0.000700566 0 | ||||||||
\(875\) | 7.17282 | 0.242485 | ||||||||
\(876\) | −5.98028 | −0.202055 | ||||||||
\(877\) | 43.4804 | 1.46823 | 0.734114 | − | 0.679026i | \(-0.237598\pi\) | ||||
0.734114 | + | 0.679026i | \(0.237598\pi\) | |||||||
\(878\) | −60.0330 | −2.02601 | ||||||||
\(879\) | −2.41624 | −0.0814977 | ||||||||
\(880\) | −18.3077 | −0.617154 | ||||||||
\(881\) | −52.9936 | −1.78540 | −0.892699 | − | 0.450653i | \(-0.851191\pi\) | ||||
−0.892699 | + | 0.450653i | \(0.851191\pi\) | |||||||
\(882\) | −45.5360 | −1.53328 | ||||||||
\(883\) | 3.90506 | 0.131416 | 0.0657079 | − | 0.997839i | \(-0.479069\pi\) | ||||
0.0657079 | + | 0.997839i | \(0.479069\pi\) | |||||||
\(884\) | 60.5263 | 2.03572 | ||||||||
\(885\) | 1.74529 | 0.0586672 | ||||||||
\(886\) | −12.4186 | −0.417211 | ||||||||
\(887\) | −47.0119 | −1.57851 | −0.789253 | − | 0.614068i | \(-0.789532\pi\) | ||||
−0.789253 | + | 0.614068i | \(0.789532\pi\) | |||||||
\(888\) | −0.688119 | −0.0230918 | ||||||||
\(889\) | −6.02040 | −0.201918 | ||||||||
\(890\) | 18.6934 | 0.626603 | ||||||||
\(891\) | 28.4656 | 0.953633 | ||||||||
\(892\) | −107.450 | −3.59768 | ||||||||
\(893\) | −0.0766334 | −0.00256444 | ||||||||
\(894\) | 3.12611 | 0.104553 | ||||||||
\(895\) | −18.1829 | −0.607787 | ||||||||
\(896\) | 10.6705 | 0.356478 | ||||||||
\(897\) | 0.0138843 | 0.000463584 0 | ||||||||
\(898\) | −70.8405 | −2.36398 | ||||||||
\(899\) | 7.43808 | 0.248074 | ||||||||
\(900\) | 59.3034 | 1.97678 | ||||||||
\(901\) | 5.61636 | 0.187108 | ||||||||
\(902\) | −32.9971 | −1.09868 | ||||||||
\(903\) | −0.513891 | −0.0171012 | ||||||||
\(904\) | 80.8081 | 2.68764 | ||||||||
\(905\) | 0.304813 | 0.0101323 | ||||||||
\(906\) | −0.432413 | −0.0143659 | ||||||||
\(907\) | 9.01943 | 0.299485 | 0.149743 | − | 0.988725i | \(-0.452155\pi\) | ||||
0.149743 | + | 0.988725i | \(0.452155\pi\) | |||||||
\(908\) | 103.203 | 3.42490 | ||||||||
\(909\) | 17.8599 | 0.592377 | ||||||||
\(910\) | −4.63833 | −0.153759 | ||||||||
\(911\) | −42.2466 | −1.39969 | −0.699846 | − | 0.714293i | \(-0.746748\pi\) | ||||
−0.699846 | + | 0.714293i | \(0.746748\pi\) | |||||||
\(912\) | 0.294815 | 0.00976229 | ||||||||
\(913\) | −24.6058 | −0.814334 | ||||||||
\(914\) | 35.0372 | 1.15893 | ||||||||
\(915\) | 1.19131 | 0.0393835 | ||||||||
\(916\) | 27.2096 | 0.899030 | ||||||||
\(917\) | −19.4862 | −0.643490 | ||||||||
\(918\) | 14.5018 | 0.478632 | ||||||||
\(919\) | 60.3277 | 1.99003 | 0.995014 | − | 0.0997377i | \(-0.0318004\pi\) | ||||
0.995014 | + | 0.0997377i | \(0.0318004\pi\) | |||||||
\(920\) | 0.168430 | 0.00555298 | ||||||||
\(921\) | −1.72281 | −0.0567686 | ||||||||
\(922\) | −33.1638 | −1.09219 | ||||||||
\(923\) | −33.9017 | −1.11589 | ||||||||
\(924\) | −2.48751 | −0.0818332 | ||||||||
\(925\) | 2.79297 | 0.0918324 | ||||||||
\(926\) | −46.0815 | −1.51433 | ||||||||
\(927\) | 5.20016 | 0.170796 | ||||||||
\(928\) | −25.5047 | −0.837233 | ||||||||
\(929\) | −16.8834 | −0.553927 | −0.276963 | − | 0.960880i | \(-0.589328\pi\) | ||||
−0.276963 | + | 0.960880i | \(0.589328\pi\) | |||||||
\(930\) | −0.573897 | −0.0188188 | ||||||||
\(931\) | 1.41737 | 0.0464523 | ||||||||
\(932\) | −122.417 | −4.00990 | ||||||||
\(933\) | 1.09707 | 0.0359163 | ||||||||
\(934\) | 52.6868 | 1.72396 | ||||||||
\(935\) | 13.9481 | 0.456151 | ||||||||
\(936\) | −45.5548 | −1.48901 | ||||||||
\(937\) | −36.3703 | −1.18817 | −0.594083 | − | 0.804404i | \(-0.702485\pi\) | ||||
−0.594083 | + | 0.804404i | \(0.702485\pi\) | |||||||
\(938\) | 22.4771 | 0.733905 | ||||||||
\(939\) | 5.87843 | 0.191835 | ||||||||
\(940\) | −1.11834 | −0.0364761 | ||||||||
\(941\) | 55.5612 | 1.81124 | 0.905622 | − | 0.424086i | \(-0.139404\pi\) | ||||
0.905622 | + | 0.424086i | \(0.139404\pi\) | |||||||
\(942\) | 0.334066 | 0.0108844 | ||||||||
\(943\) | 0.136402 | 0.00444185 | ||||||||
\(944\) | 99.5860 | 3.24125 | ||||||||
\(945\) | −0.770288 | −0.0250575 | ||||||||
\(946\) | −25.2571 | −0.821179 | ||||||||
\(947\) | 8.40232 | 0.273039 | 0.136519 | − | 0.990637i | \(-0.456408\pi\) | ||||
0.136519 | + | 0.990637i | \(0.456408\pi\) | |||||||
\(948\) | 0.198011 | 0.00643108 | ||||||||
\(949\) | −18.6457 | −0.605266 | ||||||||
\(950\) | −2.66314 | −0.0864037 | ||||||||
\(951\) | −3.18749 | −0.103361 | ||||||||
\(952\) | 36.0393 | 1.16804 | ||||||||
\(953\) | −32.9371 | −1.06694 | −0.533469 | − | 0.845819i | \(-0.679112\pi\) | ||||
−0.533469 | + | 0.845819i | \(0.679112\pi\) | |||||||
\(954\) | −7.58549 | −0.245589 | ||||||||
\(955\) | 5.29981 | 0.171498 | ||||||||
\(956\) | −120.878 | −3.90948 | ||||||||
\(957\) | −2.35748 | −0.0762064 | ||||||||
\(958\) | −20.9220 | −0.675960 | ||||||||
\(959\) | −0.456039 | −0.0147263 | ||||||||
\(960\) | 0.0630600 | 0.00203525 | ||||||||
\(961\) | −27.9723 | −0.902333 | ||||||||
\(962\) | −3.85000 | −0.124129 | ||||||||
\(963\) | −20.9611 | −0.675462 | ||||||||
\(964\) | 124.397 | 4.00656 | ||||||||
\(965\) | 14.5864 | 0.469552 | ||||||||
\(966\) | 0.0148353 | 0.000477317 0 | ||||||||
\(967\) | −24.6122 | −0.791476 | −0.395738 | − | 0.918364i | \(-0.629511\pi\) | ||||
−0.395738 | + | 0.918364i | \(0.629511\pi\) | |||||||
\(968\) | 2.56262 | 0.0823657 | ||||||||
\(969\) | −0.224610 | −0.00721551 | ||||||||
\(970\) | 17.9399 | 0.576015 | ||||||||
\(971\) | 52.6849 | 1.69074 | 0.845369 | − | 0.534182i | \(-0.179380\pi\) | ||||
0.845369 | + | 0.534182i | \(0.179380\pi\) | |||||||
\(972\) | −20.3963 | −0.654211 | ||||||||
\(973\) | 13.5407 | 0.434094 | ||||||||
\(974\) | 6.97567 | 0.223515 | ||||||||
\(975\) | −1.78531 | −0.0571757 | ||||||||
\(976\) | 67.9760 | 2.17586 | ||||||||
\(977\) | −22.6088 | −0.723320 | −0.361660 | − | 0.932310i | \(-0.617790\pi\) | ||||
−0.361660 | + | 0.932310i | \(0.617790\pi\) | |||||||
\(978\) | −0.715064 | −0.0228652 | ||||||||
\(979\) | 31.2571 | 0.998982 | ||||||||
\(980\) | 20.6841 | 0.660730 | ||||||||
\(981\) | 45.3096 | 1.44662 | ||||||||
\(982\) | 55.1171 | 1.75886 | ||||||||
\(983\) | −4.22584 | −0.134783 | −0.0673917 | − | 0.997727i | \(-0.521468\pi\) | ||||
−0.0673917 | + | 0.997727i | \(0.521468\pi\) | |||||||
\(984\) | 4.32121 | 0.137755 | ||||||||
\(985\) | −6.78594 | −0.216218 | ||||||||
\(986\) | 61.2910 | 1.95190 | ||||||||
\(987\) | −0.0548920 | −0.00174723 | ||||||||
\(988\) | 2.54449 | 0.0809511 | ||||||||
\(989\) | 0.104406 | 0.00331993 | ||||||||
\(990\) | −18.8384 | −0.598723 | ||||||||
\(991\) | −43.9999 | −1.39770 | −0.698851 | − | 0.715267i | \(-0.746305\pi\) | ||||
−0.698851 | + | 0.715267i | \(0.746305\pi\) | |||||||
\(992\) | −10.3817 | −0.329619 | ||||||||
\(993\) | 2.45713 | 0.0779747 | ||||||||
\(994\) | −36.2237 | −1.14894 | ||||||||
\(995\) | 11.1386 | 0.353117 | ||||||||
\(996\) | 5.78238 | 0.183222 | ||||||||
\(997\) | −15.2447 | −0.482805 | −0.241402 | − | 0.970425i | \(-0.577607\pi\) | ||||
−0.241402 | + | 0.970425i | \(0.577607\pi\) | |||||||
\(998\) | 53.0864 | 1.68042 | ||||||||
\(999\) | −0.639370 | −0.0202288 |
(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 | 8003.2.a.b.1.8 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.8 | ✓ | 153 | 1.1 | even | 1 | trivial |