Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.43 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37316 | 1.67808 | 0.839040 | − | 0.544070i | \(-0.183117\pi\) | ||||
0.839040 | + | 0.544070i | \(0.183117\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.63190 | 1.81595 | ||||||||
\(5\) | −3.39062 | −1.51633 | −0.758166 | − | 0.652061i | \(-0.773904\pi\) | ||||
−0.758166 | + | 0.652061i | \(0.773904\pi\) | |||||||
\(6\) | −2.37316 | −0.968840 | ||||||||
\(7\) | −2.72468 | −1.02983 | −0.514916 | − | 0.857240i | \(-0.672177\pi\) | ||||
−0.514916 | + | 0.857240i | \(0.672177\pi\) | |||||||
\(8\) | 3.87278 | 1.36923 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.04650 | −2.54453 | ||||||||
\(11\) | 0.191904 | 0.0578612 | 0.0289306 | − | 0.999581i | \(-0.490790\pi\) | ||||
0.0289306 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(12\) | −3.63190 | −1.04844 | ||||||||
\(13\) | 3.63167 | 1.00724 | 0.503622 | − | 0.863924i | \(-0.332000\pi\) | ||||
0.503622 | + | 0.863924i | \(0.332000\pi\) | |||||||
\(14\) | −6.46611 | −1.72814 | ||||||||
\(15\) | 3.39062 | 0.875455 | ||||||||
\(16\) | 1.92692 | 0.481731 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 2.37316 | 0.559360 | ||||||||
\(19\) | 6.06019 | 1.39030 | 0.695152 | − | 0.718863i | \(-0.255337\pi\) | ||||
0.695152 | + | 0.718863i | \(0.255337\pi\) | |||||||
\(20\) | −12.3144 | −2.75359 | ||||||||
\(21\) | 2.72468 | 0.594574 | ||||||||
\(22\) | 0.455420 | 0.0970958 | ||||||||
\(23\) | 7.64992 | 1.59512 | 0.797559 | − | 0.603241i | \(-0.206124\pi\) | ||||
0.797559 | + | 0.603241i | \(0.206124\pi\) | |||||||
\(24\) | −3.87278 | −0.790527 | ||||||||
\(25\) | 6.49632 | 1.29926 | ||||||||
\(26\) | 8.61855 | 1.69024 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −9.89578 | −1.87013 | ||||||||
\(29\) | −5.48562 | −1.01865 | −0.509327 | − | 0.860573i | \(-0.670106\pi\) | ||||
−0.509327 | + | 0.860573i | \(0.670106\pi\) | |||||||
\(30\) | 8.04650 | 1.46908 | ||||||||
\(31\) | −6.85276 | −1.23079 | −0.615396 | − | 0.788218i | \(-0.711004\pi\) | ||||
−0.615396 | + | 0.788218i | \(0.711004\pi\) | |||||||
\(32\) | −3.17265 | −0.560851 | ||||||||
\(33\) | −0.191904 | −0.0334062 | ||||||||
\(34\) | −2.37316 | −0.406994 | ||||||||
\(35\) | 9.23837 | 1.56157 | ||||||||
\(36\) | 3.63190 | 0.605317 | ||||||||
\(37\) | 2.95555 | 0.485889 | 0.242945 | − | 0.970040i | \(-0.421887\pi\) | ||||
0.242945 | + | 0.970040i | \(0.421887\pi\) | |||||||
\(38\) | 14.3818 | 2.33304 | ||||||||
\(39\) | −3.63167 | −0.581533 | ||||||||
\(40\) | −13.1311 | −2.07621 | ||||||||
\(41\) | 5.70226 | 0.890544 | 0.445272 | − | 0.895395i | \(-0.353107\pi\) | ||||
0.445272 | + | 0.895395i | \(0.353107\pi\) | |||||||
\(42\) | 6.46611 | 0.997743 | ||||||||
\(43\) | −1.32018 | −0.201326 | −0.100663 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100663 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(44\) | 0.696977 | 0.105073 | ||||||||
\(45\) | −3.39062 | −0.505444 | ||||||||
\(46\) | 18.1545 | 2.67674 | ||||||||
\(47\) | 2.64382 | 0.385640 | 0.192820 | − | 0.981234i | \(-0.438237\pi\) | ||||
0.192820 | + | 0.981234i | \(0.438237\pi\) | |||||||
\(48\) | −1.92692 | −0.278127 | ||||||||
\(49\) | 0.423888 | 0.0605554 | ||||||||
\(50\) | 15.4168 | 2.18027 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 13.1899 | 1.82911 | ||||||||
\(53\) | −5.38691 | −0.739949 | −0.369975 | − | 0.929042i | \(-0.620634\pi\) | ||||
−0.369975 | + | 0.929042i | \(0.620634\pi\) | |||||||
\(54\) | −2.37316 | −0.322947 | ||||||||
\(55\) | −0.650674 | −0.0877369 | ||||||||
\(56\) | −10.5521 | −1.41008 | ||||||||
\(57\) | −6.06019 | −0.802692 | ||||||||
\(58\) | −13.0183 | −1.70938 | ||||||||
\(59\) | −7.04781 | −0.917547 | −0.458773 | − | 0.888553i | \(-0.651711\pi\) | ||||
−0.458773 | + | 0.888553i | \(0.651711\pi\) | |||||||
\(60\) | 12.3144 | 1.58978 | ||||||||
\(61\) | −1.28646 | −0.164715 | −0.0823573 | − | 0.996603i | \(-0.526245\pi\) | ||||
−0.0823573 | + | 0.996603i | \(0.526245\pi\) | |||||||
\(62\) | −16.2627 | −2.06537 | ||||||||
\(63\) | −2.72468 | −0.343278 | ||||||||
\(64\) | −11.3831 | −1.42288 | ||||||||
\(65\) | −12.3136 | −1.52732 | ||||||||
\(66\) | −0.455420 | −0.0560583 | ||||||||
\(67\) | −8.81575 | −1.07702 | −0.538508 | − | 0.842621i | \(-0.681012\pi\) | ||||
−0.538508 | + | 0.842621i | \(0.681012\pi\) | |||||||
\(68\) | −3.63190 | −0.440433 | ||||||||
\(69\) | −7.64992 | −0.920942 | ||||||||
\(70\) | 21.9242 | 2.62044 | ||||||||
\(71\) | −6.29632 | −0.747235 | −0.373618 | − | 0.927583i | \(-0.621883\pi\) | ||||
−0.373618 | + | 0.927583i | \(0.621883\pi\) | |||||||
\(72\) | 3.87278 | 0.456411 | ||||||||
\(73\) | −7.91126 | −0.925943 | −0.462971 | − | 0.886373i | \(-0.653217\pi\) | ||||
−0.462971 | + | 0.886373i | \(0.653217\pi\) | |||||||
\(74\) | 7.01400 | 0.815361 | ||||||||
\(75\) | −6.49632 | −0.750131 | ||||||||
\(76\) | 22.0100 | 2.52472 | ||||||||
\(77\) | −0.522877 | −0.0595874 | ||||||||
\(78\) | −8.61855 | −0.975859 | ||||||||
\(79\) | −5.71367 | −0.642838 | −0.321419 | − | 0.946937i | \(-0.604160\pi\) | ||||
−0.321419 | + | 0.946937i | \(0.604160\pi\) | |||||||
\(80\) | −6.53347 | −0.730464 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.5324 | 1.49440 | ||||||||
\(83\) | −0.273284 | −0.0299968 | −0.0149984 | − | 0.999888i | \(-0.504774\pi\) | ||||
−0.0149984 | + | 0.999888i | \(0.504774\pi\) | |||||||
\(84\) | 9.89578 | 1.07972 | ||||||||
\(85\) | 3.39062 | 0.367765 | ||||||||
\(86\) | −3.13301 | −0.337841 | ||||||||
\(87\) | 5.48562 | 0.588121 | ||||||||
\(88\) | 0.743201 | 0.0792255 | ||||||||
\(89\) | 8.77053 | 0.929674 | 0.464837 | − | 0.885396i | \(-0.346113\pi\) | ||||
0.464837 | + | 0.885396i | \(0.346113\pi\) | |||||||
\(90\) | −8.04650 | −0.848176 | ||||||||
\(91\) | −9.89515 | −1.03729 | ||||||||
\(92\) | 27.7838 | 2.89666 | ||||||||
\(93\) | 6.85276 | 0.710599 | ||||||||
\(94\) | 6.27421 | 0.647135 | ||||||||
\(95\) | −20.5478 | −2.10816 | ||||||||
\(96\) | 3.17265 | 0.323807 | ||||||||
\(97\) | 3.56633 | 0.362106 | 0.181053 | − | 0.983473i | \(-0.442049\pi\) | ||||
0.181053 | + | 0.983473i | \(0.442049\pi\) | |||||||
\(98\) | 1.00595 | 0.101617 | ||||||||
\(99\) | 0.191904 | 0.0192871 | ||||||||
\(100\) | 23.5940 | 2.35940 | ||||||||
\(101\) | 0.332282 | 0.0330633 | 0.0165317 | − | 0.999863i | \(-0.494738\pi\) | ||||
0.0165317 | + | 0.999863i | \(0.494738\pi\) | |||||||
\(102\) | 2.37316 | 0.234978 | ||||||||
\(103\) | 7.78283 | 0.766865 | 0.383433 | − | 0.923569i | \(-0.374742\pi\) | ||||
0.383433 | + | 0.923569i | \(0.374742\pi\) | |||||||
\(104\) | 14.0647 | 1.37915 | ||||||||
\(105\) | −9.23837 | −0.901572 | ||||||||
\(106\) | −12.7840 | −1.24169 | ||||||||
\(107\) | 8.27010 | 0.799501 | 0.399750 | − | 0.916624i | \(-0.369097\pi\) | ||||
0.399750 | + | 0.916624i | \(0.369097\pi\) | |||||||
\(108\) | −3.63190 | −0.349480 | ||||||||
\(109\) | −16.7955 | −1.60872 | −0.804361 | − | 0.594142i | \(-0.797492\pi\) | ||||
−0.804361 | + | 0.594142i | \(0.797492\pi\) | |||||||
\(110\) | −1.54416 | −0.147229 | ||||||||
\(111\) | −2.95555 | −0.280528 | ||||||||
\(112\) | −5.25025 | −0.496102 | ||||||||
\(113\) | −12.1634 | −1.14423 | −0.572117 | − | 0.820172i | \(-0.693878\pi\) | ||||
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(114\) | −14.3818 | −1.34698 | ||||||||
\(115\) | −25.9380 | −2.41873 | ||||||||
\(116\) | −19.9233 | −1.84983 | ||||||||
\(117\) | 3.63167 | 0.335748 | ||||||||
\(118\) | −16.7256 | −1.53972 | ||||||||
\(119\) | 2.72468 | 0.249771 | ||||||||
\(120\) | 13.1311 | 1.19870 | ||||||||
\(121\) | −10.9632 | −0.996652 | ||||||||
\(122\) | −3.05298 | −0.276404 | ||||||||
\(123\) | −5.70226 | −0.514156 | ||||||||
\(124\) | −24.8886 | −2.23506 | ||||||||
\(125\) | −5.07346 | −0.453784 | ||||||||
\(126\) | −6.46611 | −0.576047 | ||||||||
\(127\) | −5.12275 | −0.454571 | −0.227285 | − | 0.973828i | \(-0.572985\pi\) | ||||
−0.227285 | + | 0.973828i | \(0.572985\pi\) | |||||||
\(128\) | −20.6686 | −1.82686 | ||||||||
\(129\) | 1.32018 | 0.116236 | ||||||||
\(130\) | −29.2223 | −2.56296 | ||||||||
\(131\) | −8.14562 | −0.711686 | −0.355843 | − | 0.934546i | \(-0.615806\pi\) | ||||
−0.355843 | + | 0.934546i | \(0.615806\pi\) | |||||||
\(132\) | −0.696977 | −0.0606641 | ||||||||
\(133\) | −16.5121 | −1.43178 | ||||||||
\(134\) | −20.9212 | −1.80732 | ||||||||
\(135\) | 3.39062 | 0.291818 | ||||||||
\(136\) | −3.87278 | −0.332088 | ||||||||
\(137\) | −1.37856 | −0.117778 | −0.0588892 | − | 0.998265i | \(-0.518756\pi\) | ||||
−0.0588892 | + | 0.998265i | \(0.518756\pi\) | |||||||
\(138\) | −18.1545 | −1.54541 | ||||||||
\(139\) | −10.5415 | −0.894118 | −0.447059 | − | 0.894504i | \(-0.647529\pi\) | ||||
−0.447059 | + | 0.894504i | \(0.647529\pi\) | |||||||
\(140\) | 33.5529 | 2.83573 | ||||||||
\(141\) | −2.64382 | −0.222649 | ||||||||
\(142\) | −14.9422 | −1.25392 | ||||||||
\(143\) | 0.696933 | 0.0582804 | ||||||||
\(144\) | 1.92692 | 0.160577 | ||||||||
\(145\) | 18.5997 | 1.54462 | ||||||||
\(146\) | −18.7747 | −1.55381 | ||||||||
\(147\) | −0.423888 | −0.0349617 | ||||||||
\(148\) | 10.7343 | 0.882352 | ||||||||
\(149\) | −4.28942 | −0.351403 | −0.175701 | − | 0.984444i | \(-0.556219\pi\) | ||||
−0.175701 | + | 0.984444i | \(0.556219\pi\) | |||||||
\(150\) | −15.4168 | −1.25878 | ||||||||
\(151\) | −2.93543 | −0.238882 | −0.119441 | − | 0.992841i | \(-0.538110\pi\) | ||||
−0.119441 | + | 0.992841i | \(0.538110\pi\) | |||||||
\(152\) | 23.4698 | 1.90365 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −1.24087 | −0.0999924 | ||||||||
\(155\) | 23.2351 | 1.86629 | ||||||||
\(156\) | −13.1899 | −1.05604 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −13.5595 | −1.07873 | ||||||||
\(159\) | 5.38691 | 0.427210 | ||||||||
\(160\) | 10.7573 | 0.850436 | ||||||||
\(161\) | −20.8436 | −1.64271 | ||||||||
\(162\) | 2.37316 | 0.186453 | ||||||||
\(163\) | −3.34783 | −0.262222 | −0.131111 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131111 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(164\) | 20.7101 | 1.61718 | ||||||||
\(165\) | 0.650674 | 0.0506549 | ||||||||
\(166\) | −0.648547 | −0.0503370 | ||||||||
\(167\) | 0.761191 | 0.0589027 | 0.0294514 | − | 0.999566i | \(-0.490624\pi\) | ||||
0.0294514 | + | 0.999566i | \(0.490624\pi\) | |||||||
\(168\) | 10.5521 | 0.814111 | ||||||||
\(169\) | 0.189051 | 0.0145424 | ||||||||
\(170\) | 8.04650 | 0.617139 | ||||||||
\(171\) | 6.06019 | 0.463434 | ||||||||
\(172\) | −4.79478 | −0.365598 | ||||||||
\(173\) | 14.2672 | 1.08471 | 0.542357 | − | 0.840148i | \(-0.317532\pi\) | ||||
0.542357 | + | 0.840148i | \(0.317532\pi\) | |||||||
\(174\) | 13.0183 | 0.986913 | ||||||||
\(175\) | −17.7004 | −1.33803 | ||||||||
\(176\) | 0.369784 | 0.0278735 | ||||||||
\(177\) | 7.04781 | 0.529746 | ||||||||
\(178\) | 20.8139 | 1.56007 | ||||||||
\(179\) | 9.48174 | 0.708698 | 0.354349 | − | 0.935113i | \(-0.384702\pi\) | ||||
0.354349 | + | 0.935113i | \(0.384702\pi\) | |||||||
\(180\) | −12.3144 | −0.917863 | ||||||||
\(181\) | −10.5384 | −0.783312 | −0.391656 | − | 0.920112i | \(-0.628098\pi\) | ||||
−0.391656 | + | 0.920112i | \(0.628098\pi\) | |||||||
\(182\) | −23.4828 | −1.74066 | ||||||||
\(183\) | 1.28646 | 0.0950980 | ||||||||
\(184\) | 29.6264 | 2.18409 | ||||||||
\(185\) | −10.0212 | −0.736770 | ||||||||
\(186\) | 16.2627 | 1.19244 | ||||||||
\(187\) | −0.191904 | −0.0140334 | ||||||||
\(188\) | 9.60209 | 0.700304 | ||||||||
\(189\) | 2.72468 | 0.198191 | ||||||||
\(190\) | −48.7633 | −3.53766 | ||||||||
\(191\) | −14.1219 | −1.02183 | −0.510914 | − | 0.859632i | \(-0.670693\pi\) | ||||
−0.510914 | + | 0.859632i | \(0.670693\pi\) | |||||||
\(192\) | 11.3831 | 0.821502 | ||||||||
\(193\) | −19.2420 | −1.38507 | −0.692534 | − | 0.721385i | \(-0.743506\pi\) | ||||
−0.692534 | + | 0.721385i | \(0.743506\pi\) | |||||||
\(194\) | 8.46349 | 0.607643 | ||||||||
\(195\) | 12.3136 | 0.881798 | ||||||||
\(196\) | 1.53952 | 0.109966 | ||||||||
\(197\) | 23.4939 | 1.67387 | 0.836934 | − | 0.547303i | \(-0.184346\pi\) | ||||
0.836934 | + | 0.547303i | \(0.184346\pi\) | |||||||
\(198\) | 0.455420 | 0.0323653 | ||||||||
\(199\) | −12.3584 | −0.876062 | −0.438031 | − | 0.898960i | \(-0.644324\pi\) | ||||
−0.438031 | + | 0.898960i | \(0.644324\pi\) | |||||||
\(200\) | 25.1588 | 1.77900 | ||||||||
\(201\) | 8.81575 | 0.621815 | ||||||||
\(202\) | 0.788560 | 0.0554829 | ||||||||
\(203\) | 14.9466 | 1.04904 | ||||||||
\(204\) | 3.63190 | 0.254284 | ||||||||
\(205\) | −19.3342 | −1.35036 | ||||||||
\(206\) | 18.4699 | 1.28686 | ||||||||
\(207\) | 7.64992 | 0.531706 | ||||||||
\(208\) | 6.99796 | 0.485221 | ||||||||
\(209\) | 1.16298 | 0.0804447 | ||||||||
\(210\) | −21.9242 | −1.51291 | ||||||||
\(211\) | −14.4101 | −0.992033 | −0.496017 | − | 0.868313i | \(-0.665205\pi\) | ||||
−0.496017 | + | 0.868313i | \(0.665205\pi\) | |||||||
\(212\) | −19.5648 | −1.34371 | ||||||||
\(213\) | 6.29632 | 0.431417 | ||||||||
\(214\) | 19.6263 | 1.34163 | ||||||||
\(215\) | 4.47624 | 0.305277 | ||||||||
\(216\) | −3.87278 | −0.263509 | ||||||||
\(217\) | 18.6716 | 1.26751 | ||||||||
\(218\) | −39.8586 | −2.69956 | ||||||||
\(219\) | 7.91126 | 0.534593 | ||||||||
\(220\) | −2.36319 | −0.159326 | ||||||||
\(221\) | −3.63167 | −0.244293 | ||||||||
\(222\) | −7.01400 | −0.470749 | ||||||||
\(223\) | 19.8049 | 1.32623 | 0.663116 | − | 0.748517i | \(-0.269234\pi\) | ||||
0.663116 | + | 0.748517i | \(0.269234\pi\) | |||||||
\(224\) | 8.64446 | 0.577582 | ||||||||
\(225\) | 6.49632 | 0.433088 | ||||||||
\(226\) | −28.8657 | −1.92012 | ||||||||
\(227\) | −18.6053 | −1.23487 | −0.617437 | − | 0.786620i | \(-0.711829\pi\) | ||||
−0.617437 | + | 0.786620i | \(0.711829\pi\) | |||||||
\(228\) | −22.0100 | −1.45765 | ||||||||
\(229\) | 22.3431 | 1.47647 | 0.738236 | − | 0.674543i | \(-0.235659\pi\) | ||||
0.738236 | + | 0.674543i | \(0.235659\pi\) | |||||||
\(230\) | −61.5551 | −4.05882 | ||||||||
\(231\) | 0.522877 | 0.0344028 | ||||||||
\(232\) | −21.2446 | −1.39478 | ||||||||
\(233\) | 5.62788 | 0.368695 | 0.184347 | − | 0.982861i | \(-0.440983\pi\) | ||||
0.184347 | + | 0.982861i | \(0.440983\pi\) | |||||||
\(234\) | 8.61855 | 0.563413 | ||||||||
\(235\) | −8.96418 | −0.584759 | ||||||||
\(236\) | −25.5970 | −1.66622 | ||||||||
\(237\) | 5.71367 | 0.371143 | ||||||||
\(238\) | 6.46611 | 0.419136 | ||||||||
\(239\) | 5.73694 | 0.371092 | 0.185546 | − | 0.982636i | \(-0.440595\pi\) | ||||
0.185546 | + | 0.982636i | \(0.440595\pi\) | |||||||
\(240\) | 6.53347 | 0.421734 | ||||||||
\(241\) | −13.9510 | −0.898664 | −0.449332 | − | 0.893365i | \(-0.648338\pi\) | ||||
−0.449332 | + | 0.893365i | \(0.648338\pi\) | |||||||
\(242\) | −26.0174 | −1.67246 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.67231 | −0.299114 | ||||||||
\(245\) | −1.43724 | −0.0918221 | ||||||||
\(246\) | −13.5324 | −0.862794 | ||||||||
\(247\) | 22.0086 | 1.40038 | ||||||||
\(248\) | −26.5392 | −1.68524 | ||||||||
\(249\) | 0.273284 | 0.0173187 | ||||||||
\(250\) | −12.0402 | −0.761487 | ||||||||
\(251\) | 25.4006 | 1.60327 | 0.801636 | − | 0.597813i | \(-0.203963\pi\) | ||||
0.801636 | + | 0.597813i | \(0.203963\pi\) | |||||||
\(252\) | −9.89578 | −0.623376 | ||||||||
\(253\) | 1.46805 | 0.0922955 | ||||||||
\(254\) | −12.1571 | −0.762806 | ||||||||
\(255\) | −3.39062 | −0.212329 | ||||||||
\(256\) | −26.2838 | −1.64274 | ||||||||
\(257\) | −28.5674 | −1.78198 | −0.890991 | − | 0.454021i | \(-0.849989\pi\) | ||||
−0.890991 | + | 0.454021i | \(0.849989\pi\) | |||||||
\(258\) | 3.13301 | 0.195053 | ||||||||
\(259\) | −8.05293 | −0.500385 | ||||||||
\(260\) | −44.7219 | −2.77354 | ||||||||
\(261\) | −5.48562 | −0.339552 | ||||||||
\(262\) | −19.3309 | −1.19427 | ||||||||
\(263\) | −5.67725 | −0.350074 | −0.175037 | − | 0.984562i | \(-0.556005\pi\) | ||||
−0.175037 | + | 0.984562i | \(0.556005\pi\) | |||||||
\(264\) | −0.743201 | −0.0457409 | ||||||||
\(265\) | 18.2650 | 1.12201 | ||||||||
\(266\) | −39.1859 | −2.40264 | ||||||||
\(267\) | −8.77053 | −0.536748 | ||||||||
\(268\) | −32.0180 | −1.95581 | ||||||||
\(269\) | 17.9223 | 1.09274 | 0.546369 | − | 0.837544i | \(-0.316009\pi\) | ||||
0.546369 | + | 0.837544i | \(0.316009\pi\) | |||||||
\(270\) | 8.04650 | 0.489695 | ||||||||
\(271\) | −21.3728 | −1.29831 | −0.649154 | − | 0.760657i | \(-0.724877\pi\) | ||||
−0.649154 | + | 0.760657i | \(0.724877\pi\) | |||||||
\(272\) | −1.92692 | −0.116837 | ||||||||
\(273\) | 9.89515 | 0.598882 | ||||||||
\(274\) | −3.27155 | −0.197641 | ||||||||
\(275\) | 1.24667 | 0.0751770 | ||||||||
\(276\) | −27.7838 | −1.67239 | ||||||||
\(277\) | 21.9877 | 1.32111 | 0.660555 | − | 0.750778i | \(-0.270321\pi\) | ||||
0.660555 | + | 0.750778i | \(0.270321\pi\) | |||||||
\(278\) | −25.0167 | −1.50040 | ||||||||
\(279\) | −6.85276 | −0.410264 | ||||||||
\(280\) | 35.7781 | 2.13815 | ||||||||
\(281\) | −6.01868 | −0.359044 | −0.179522 | − | 0.983754i | \(-0.557455\pi\) | ||||
−0.179522 | + | 0.983754i | \(0.557455\pi\) | |||||||
\(282\) | −6.27421 | −0.373624 | ||||||||
\(283\) | −25.6402 | −1.52415 | −0.762076 | − | 0.647488i | \(-0.775820\pi\) | ||||
−0.762076 | + | 0.647488i | \(0.775820\pi\) | |||||||
\(284\) | −22.8676 | −1.35694 | ||||||||
\(285\) | 20.5478 | 1.21715 | ||||||||
\(286\) | 1.65394 | 0.0977992 | ||||||||
\(287\) | −15.5368 | −0.917111 | ||||||||
\(288\) | −3.17265 | −0.186950 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 44.1401 | 2.59199 | ||||||||
\(291\) | −3.56633 | −0.209062 | ||||||||
\(292\) | −28.7329 | −1.68147 | ||||||||
\(293\) | −15.7560 | −0.920474 | −0.460237 | − | 0.887796i | \(-0.652236\pi\) | ||||
−0.460237 | + | 0.887796i | \(0.652236\pi\) | |||||||
\(294\) | −1.00595 | −0.0586684 | ||||||||
\(295\) | 23.8965 | 1.39131 | ||||||||
\(296\) | 11.4462 | 0.665296 | ||||||||
\(297\) | −0.191904 | −0.0111354 | ||||||||
\(298\) | −10.1795 | −0.589682 | ||||||||
\(299\) | 27.7820 | 1.60667 | ||||||||
\(300\) | −23.5940 | −1.36220 | ||||||||
\(301\) | 3.59708 | 0.207332 | ||||||||
\(302\) | −6.96625 | −0.400863 | ||||||||
\(303\) | −0.332282 | −0.0190891 | ||||||||
\(304\) | 11.6775 | 0.669752 | ||||||||
\(305\) | 4.36191 | 0.249762 | ||||||||
\(306\) | −2.37316 | −0.135665 | ||||||||
\(307\) | 15.5196 | 0.885748 | 0.442874 | − | 0.896584i | \(-0.353959\pi\) | ||||
0.442874 | + | 0.896584i | \(0.353959\pi\) | |||||||
\(308\) | −1.89904 | −0.108208 | ||||||||
\(309\) | −7.78283 | −0.442750 | ||||||||
\(310\) | 55.1408 | 3.13179 | ||||||||
\(311\) | 1.09937 | 0.0623396 | 0.0311698 | − | 0.999514i | \(-0.490077\pi\) | ||||
0.0311698 | + | 0.999514i | \(0.490077\pi\) | |||||||
\(312\) | −14.0647 | −0.796255 | ||||||||
\(313\) | 19.2900 | 1.09034 | 0.545168 | − | 0.838327i | \(-0.316466\pi\) | ||||
0.545168 | + | 0.838327i | \(0.316466\pi\) | |||||||
\(314\) | −2.37316 | −0.133925 | ||||||||
\(315\) | 9.23837 | 0.520523 | ||||||||
\(316\) | −20.7515 | −1.16736 | ||||||||
\(317\) | −14.9672 | −0.840642 | −0.420321 | − | 0.907376i | \(-0.638082\pi\) | ||||
−0.420321 | + | 0.907376i | \(0.638082\pi\) | |||||||
\(318\) | 12.7840 | 0.716892 | ||||||||
\(319\) | −1.05271 | −0.0589406 | ||||||||
\(320\) | 38.5957 | 2.15756 | ||||||||
\(321\) | −8.27010 | −0.461592 | ||||||||
\(322\) | −49.4652 | −2.75659 | ||||||||
\(323\) | −6.06019 | −0.337198 | ||||||||
\(324\) | 3.63190 | 0.201772 | ||||||||
\(325\) | 23.5925 | 1.30868 | ||||||||
\(326\) | −7.94494 | −0.440030 | ||||||||
\(327\) | 16.7955 | 0.928796 | ||||||||
\(328\) | 22.0836 | 1.21936 | ||||||||
\(329\) | −7.20355 | −0.397145 | ||||||||
\(330\) | 1.54416 | 0.0850030 | ||||||||
\(331\) | −7.89985 | −0.434215 | −0.217108 | − | 0.976148i | \(-0.569662\pi\) | ||||
−0.217108 | + | 0.976148i | \(0.569662\pi\) | |||||||
\(332\) | −0.992540 | −0.0544727 | ||||||||
\(333\) | 2.95555 | 0.161963 | ||||||||
\(334\) | 1.80643 | 0.0988435 | ||||||||
\(335\) | 29.8909 | 1.63311 | ||||||||
\(336\) | 5.25025 | 0.286425 | ||||||||
\(337\) | 16.1420 | 0.879308 | 0.439654 | − | 0.898167i | \(-0.355101\pi\) | ||||
0.439654 | + | 0.898167i | \(0.355101\pi\) | |||||||
\(338\) | 0.448649 | 0.0244033 | ||||||||
\(339\) | 12.1634 | 0.660624 | ||||||||
\(340\) | 12.3144 | 0.667843 | ||||||||
\(341\) | −1.31507 | −0.0712152 | ||||||||
\(342\) | 14.3818 | 0.777680 | ||||||||
\(343\) | 17.9178 | 0.967471 | ||||||||
\(344\) | −5.11277 | −0.275662 | ||||||||
\(345\) | 25.9380 | 1.39645 | ||||||||
\(346\) | 33.8584 | 1.82024 | ||||||||
\(347\) | −30.2270 | −1.62267 | −0.811335 | − | 0.584581i | \(-0.801259\pi\) | ||||
−0.811335 | + | 0.584581i | \(0.801259\pi\) | |||||||
\(348\) | 19.9233 | 1.06800 | ||||||||
\(349\) | −16.4799 | −0.882147 | −0.441073 | − | 0.897471i | \(-0.645402\pi\) | ||||
−0.441073 | + | 0.897471i | \(0.645402\pi\) | |||||||
\(350\) | −42.0060 | −2.24531 | ||||||||
\(351\) | −3.63167 | −0.193844 | ||||||||
\(352\) | −0.608844 | −0.0324515 | ||||||||
\(353\) | −4.56441 | −0.242939 | −0.121470 | − | 0.992595i | \(-0.538761\pi\) | ||||
−0.121470 | + | 0.992595i | \(0.538761\pi\) | |||||||
\(354\) | 16.7256 | 0.888956 | ||||||||
\(355\) | 21.3484 | 1.13306 | ||||||||
\(356\) | 31.8537 | 1.68824 | ||||||||
\(357\) | −2.72468 | −0.144205 | ||||||||
\(358\) | 22.5017 | 1.18925 | ||||||||
\(359\) | −3.05799 | −0.161395 | −0.0806974 | − | 0.996739i | \(-0.525715\pi\) | ||||
−0.0806974 | + | 0.996739i | \(0.525715\pi\) | |||||||
\(360\) | −13.1311 | −0.692071 | ||||||||
\(361\) | 17.7259 | 0.932943 | ||||||||
\(362\) | −25.0093 | −1.31446 | ||||||||
\(363\) | 10.9632 | 0.575417 | ||||||||
\(364\) | −35.9383 | −1.88368 | ||||||||
\(365\) | 26.8241 | 1.40404 | ||||||||
\(366\) | 3.05298 | 0.159582 | ||||||||
\(367\) | 2.71249 | 0.141591 | 0.0707953 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707953 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(368\) | 14.7408 | 0.768418 | ||||||||
\(369\) | 5.70226 | 0.296848 | ||||||||
\(370\) | −23.7818 | −1.23636 | ||||||||
\(371\) | 14.6776 | 0.762024 | ||||||||
\(372\) | 24.8886 | 1.29041 | ||||||||
\(373\) | −5.55810 | −0.287787 | −0.143894 | − | 0.989593i | \(-0.545962\pi\) | ||||
−0.143894 | + | 0.989593i | \(0.545962\pi\) | |||||||
\(374\) | −0.455420 | −0.0235492 | ||||||||
\(375\) | 5.07346 | 0.261993 | ||||||||
\(376\) | 10.2389 | 0.528031 | ||||||||
\(377\) | −19.9220 | −1.02603 | ||||||||
\(378\) | 6.46611 | 0.332581 | ||||||||
\(379\) | −2.69896 | −0.138636 | −0.0693181 | − | 0.997595i | \(-0.522082\pi\) | ||||
−0.0693181 | + | 0.997595i | \(0.522082\pi\) | |||||||
\(380\) | −74.6277 | −3.82832 | ||||||||
\(381\) | 5.12275 | 0.262447 | ||||||||
\(382\) | −33.5137 | −1.71471 | ||||||||
\(383\) | −3.35029 | −0.171192 | −0.0855958 | − | 0.996330i | \(-0.527279\pi\) | ||||
−0.0855958 | + | 0.996330i | \(0.527279\pi\) | |||||||
\(384\) | 20.6686 | 1.05474 | ||||||||
\(385\) | 1.77288 | 0.0903543 | ||||||||
\(386\) | −45.6644 | −2.32426 | ||||||||
\(387\) | −1.32018 | −0.0671087 | ||||||||
\(388\) | 12.9526 | 0.657568 | ||||||||
\(389\) | −5.22188 | −0.264760 | −0.132380 | − | 0.991199i | \(-0.542262\pi\) | ||||
−0.132380 | + | 0.991199i | \(0.542262\pi\) | |||||||
\(390\) | 29.2223 | 1.47973 | ||||||||
\(391\) | −7.64992 | −0.386873 | ||||||||
\(392\) | 1.64162 | 0.0829144 | ||||||||
\(393\) | 8.14562 | 0.410892 | ||||||||
\(394\) | 55.7548 | 2.80889 | ||||||||
\(395\) | 19.3729 | 0.974756 | ||||||||
\(396\) | 0.696977 | 0.0350244 | ||||||||
\(397\) | −26.9283 | −1.35149 | −0.675746 | − | 0.737134i | \(-0.736178\pi\) | ||||
−0.675746 | + | 0.737134i | \(0.736178\pi\) | |||||||
\(398\) | −29.3285 | −1.47010 | ||||||||
\(399\) | 16.5121 | 0.826638 | ||||||||
\(400\) | 12.5179 | 0.625896 | ||||||||
\(401\) | −3.13136 | −0.156373 | −0.0781864 | − | 0.996939i | \(-0.524913\pi\) | ||||
−0.0781864 | + | 0.996939i | \(0.524913\pi\) | |||||||
\(402\) | 20.9212 | 1.04346 | ||||||||
\(403\) | −24.8870 | −1.23971 | ||||||||
\(404\) | 1.20682 | 0.0600414 | ||||||||
\(405\) | −3.39062 | −0.168481 | ||||||||
\(406\) | 35.4707 | 1.76038 | ||||||||
\(407\) | 0.567182 | 0.0281142 | ||||||||
\(408\) | 3.87278 | 0.191731 | ||||||||
\(409\) | 25.0095 | 1.23664 | 0.618321 | − | 0.785926i | \(-0.287813\pi\) | ||||
0.618321 | + | 0.785926i | \(0.287813\pi\) | |||||||
\(410\) | −45.8833 | −2.26601 | ||||||||
\(411\) | 1.37856 | 0.0679994 | ||||||||
\(412\) | 28.2665 | 1.39259 | ||||||||
\(413\) | 19.2030 | 0.944920 | ||||||||
\(414\) | 18.1545 | 0.892245 | ||||||||
\(415\) | 0.926602 | 0.0454851 | ||||||||
\(416\) | −11.5220 | −0.564914 | ||||||||
\(417\) | 10.5415 | 0.516219 | ||||||||
\(418\) | 2.75993 | 0.134993 | ||||||||
\(419\) | −18.6931 | −0.913215 | −0.456608 | − | 0.889668i | \(-0.650936\pi\) | ||||
−0.456608 | + | 0.889668i | \(0.650936\pi\) | |||||||
\(420\) | −33.5529 | −1.63721 | ||||||||
\(421\) | 13.5966 | 0.662657 | 0.331328 | − | 0.943516i | \(-0.392503\pi\) | ||||
0.331328 | + | 0.943516i | \(0.392503\pi\) | |||||||
\(422\) | −34.1976 | −1.66471 | ||||||||
\(423\) | 2.64382 | 0.128547 | ||||||||
\(424\) | −20.8623 | −1.01316 | ||||||||
\(425\) | −6.49632 | −0.315118 | ||||||||
\(426\) | 14.9422 | 0.723952 | ||||||||
\(427\) | 3.50520 | 0.169628 | ||||||||
\(428\) | 30.0362 | 1.45186 | ||||||||
\(429\) | −0.696933 | −0.0336482 | ||||||||
\(430\) | 10.6229 | 0.512280 | ||||||||
\(431\) | 0.429543 | 0.0206904 | 0.0103452 | − | 0.999946i | \(-0.496707\pi\) | ||||
0.0103452 | + | 0.999946i | \(0.496707\pi\) | |||||||
\(432\) | −1.92692 | −0.0927092 | ||||||||
\(433\) | −40.7644 | −1.95901 | −0.979506 | − | 0.201417i | \(-0.935445\pi\) | ||||
−0.979506 | + | 0.201417i | \(0.935445\pi\) | |||||||
\(434\) | 44.3108 | 2.12698 | ||||||||
\(435\) | −18.5997 | −0.891786 | ||||||||
\(436\) | −60.9998 | −2.92136 | ||||||||
\(437\) | 46.3600 | 2.21770 | ||||||||
\(438\) | 18.7747 | 0.897090 | ||||||||
\(439\) | −12.4056 | −0.592085 | −0.296043 | − | 0.955175i | \(-0.595667\pi\) | ||||
−0.296043 | + | 0.955175i | \(0.595667\pi\) | |||||||
\(440\) | −2.51992 | −0.120132 | ||||||||
\(441\) | 0.423888 | 0.0201851 | ||||||||
\(442\) | −8.61855 | −0.409943 | ||||||||
\(443\) | −13.1699 | −0.625722 | −0.312861 | − | 0.949799i | \(-0.601287\pi\) | ||||
−0.312861 | + | 0.949799i | \(0.601287\pi\) | |||||||
\(444\) | −10.7343 | −0.509426 | ||||||||
\(445\) | −29.7376 | −1.40970 | ||||||||
\(446\) | 47.0002 | 2.22552 | ||||||||
\(447\) | 4.28942 | 0.202883 | ||||||||
\(448\) | 31.0152 | 1.46533 | ||||||||
\(449\) | 18.5882 | 0.877231 | 0.438615 | − | 0.898675i | \(-0.355469\pi\) | ||||
0.438615 | + | 0.898675i | \(0.355469\pi\) | |||||||
\(450\) | 15.4168 | 0.726757 | ||||||||
\(451\) | 1.09429 | 0.0515279 | ||||||||
\(452\) | −44.1762 | −2.07788 | ||||||||
\(453\) | 2.93543 | 0.137918 | ||||||||
\(454\) | −44.1533 | −2.07222 | ||||||||
\(455\) | 33.5507 | 1.57288 | ||||||||
\(456\) | −23.4698 | −1.09907 | ||||||||
\(457\) | −2.93771 | −0.137420 | −0.0687102 | − | 0.997637i | \(-0.521888\pi\) | ||||
−0.0687102 | + | 0.997637i | \(0.521888\pi\) | |||||||
\(458\) | 53.0238 | 2.47764 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −94.2043 | −4.39230 | ||||||||
\(461\) | 32.0428 | 1.49238 | 0.746190 | − | 0.665733i | \(-0.231881\pi\) | ||||
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(462\) | 1.24087 | 0.0577306 | ||||||||
\(463\) | −26.9135 | −1.25078 | −0.625388 | − | 0.780314i | \(-0.715059\pi\) | ||||
−0.625388 | + | 0.780314i | \(0.715059\pi\) | |||||||
\(464\) | −10.5704 | −0.490717 | ||||||||
\(465\) | −23.2351 | −1.07750 | ||||||||
\(466\) | 13.3559 | 0.618700 | ||||||||
\(467\) | 42.7441 | 1.97796 | 0.988981 | − | 0.148039i | \(-0.0472962\pi\) | ||||
0.988981 | + | 0.148039i | \(0.0472962\pi\) | |||||||
\(468\) | 13.1899 | 0.609703 | ||||||||
\(469\) | 24.0201 | 1.10915 | ||||||||
\(470\) | −21.2735 | −0.981272 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −27.2946 | −1.25634 | ||||||||
\(473\) | −0.253348 | −0.0116490 | ||||||||
\(474\) | 13.5595 | 0.622807 | ||||||||
\(475\) | 39.3690 | 1.80637 | ||||||||
\(476\) | 9.89578 | 0.453572 | ||||||||
\(477\) | −5.38691 | −0.246650 | ||||||||
\(478\) | 13.6147 | 0.622722 | ||||||||
\(479\) | 23.5351 | 1.07535 | 0.537673 | − | 0.843153i | \(-0.319303\pi\) | ||||
0.537673 | + | 0.843153i | \(0.319303\pi\) | |||||||
\(480\) | −10.7573 | −0.490999 | ||||||||
\(481\) | 10.7336 | 0.489410 | ||||||||
\(482\) | −33.1080 | −1.50803 | ||||||||
\(483\) | 20.8436 | 0.948416 | ||||||||
\(484\) | −39.8172 | −1.80987 | ||||||||
\(485\) | −12.0921 | −0.549073 | ||||||||
\(486\) | −2.37316 | −0.107649 | ||||||||
\(487\) | 12.3847 | 0.561204 | 0.280602 | − | 0.959824i | \(-0.409466\pi\) | ||||
0.280602 | + | 0.959824i | \(0.409466\pi\) | |||||||
\(488\) | −4.98218 | −0.225533 | ||||||||
\(489\) | 3.34783 | 0.151394 | ||||||||
\(490\) | −3.41081 | −0.154085 | ||||||||
\(491\) | 26.6924 | 1.20461 | 0.602306 | − | 0.798266i | \(-0.294249\pi\) | ||||
0.602306 | + | 0.798266i | \(0.294249\pi\) | |||||||
\(492\) | −20.7101 | −0.933682 | ||||||||
\(493\) | 5.48562 | 0.247060 | ||||||||
\(494\) | 52.2301 | 2.34994 | ||||||||
\(495\) | −0.650674 | −0.0292456 | ||||||||
\(496\) | −13.2048 | −0.592911 | ||||||||
\(497\) | 17.1555 | 0.769527 | ||||||||
\(498\) | 0.648547 | 0.0290621 | ||||||||
\(499\) | −42.6461 | −1.90910 | −0.954551 | − | 0.298048i | \(-0.903664\pi\) | ||||
−0.954551 | + | 0.298048i | \(0.903664\pi\) | |||||||
\(500\) | −18.4263 | −0.824051 | ||||||||
\(501\) | −0.761191 | −0.0340075 | ||||||||
\(502\) | 60.2798 | 2.69042 | ||||||||
\(503\) | 28.7603 | 1.28236 | 0.641178 | − | 0.767392i | \(-0.278446\pi\) | ||||
0.641178 | + | 0.767392i | \(0.278446\pi\) | |||||||
\(504\) | −10.5521 | −0.470027 | ||||||||
\(505\) | −1.12664 | −0.0501350 | ||||||||
\(506\) | 3.48392 | 0.154879 | ||||||||
\(507\) | −0.189051 | −0.00839604 | ||||||||
\(508\) | −18.6053 | −0.825479 | ||||||||
\(509\) | 29.6347 | 1.31353 | 0.656767 | − | 0.754094i | \(-0.271924\pi\) | ||||
0.656767 | + | 0.754094i | \(0.271924\pi\) | |||||||
\(510\) | −8.04650 | −0.356305 | ||||||||
\(511\) | 21.5557 | 0.953566 | ||||||||
\(512\) | −21.0385 | −0.929781 | ||||||||
\(513\) | −6.06019 | −0.267564 | ||||||||
\(514\) | −67.7950 | −2.99031 | ||||||||
\(515\) | −26.3886 | −1.16282 | ||||||||
\(516\) | 4.79478 | 0.211078 | ||||||||
\(517\) | 0.507359 | 0.0223136 | ||||||||
\(518\) | −19.1109 | −0.839686 | ||||||||
\(519\) | −14.2672 | −0.626260 | ||||||||
\(520\) | −47.6880 | −2.09126 | ||||||||
\(521\) | −31.3579 | −1.37382 | −0.686908 | − | 0.726745i | \(-0.741032\pi\) | ||||
−0.686908 | + | 0.726745i | \(0.741032\pi\) | |||||||
\(522\) | −13.0183 | −0.569795 | ||||||||
\(523\) | 1.96648 | 0.0859881 | 0.0429941 | − | 0.999075i | \(-0.486310\pi\) | ||||
0.0429941 | + | 0.999075i | \(0.486310\pi\) | |||||||
\(524\) | −29.5841 | −1.29239 | ||||||||
\(525\) | 17.7004 | 0.772509 | ||||||||
\(526\) | −13.4730 | −0.587453 | ||||||||
\(527\) | 6.85276 | 0.298511 | ||||||||
\(528\) | −0.369784 | −0.0160928 | ||||||||
\(529\) | 35.5213 | 1.54440 | ||||||||
\(530\) | 43.3458 | 1.88282 | ||||||||
\(531\) | −7.04781 | −0.305849 | ||||||||
\(532\) | −59.9703 | −2.60004 | ||||||||
\(533\) | 20.7087 | 0.896995 | ||||||||
\(534\) | −20.8139 | −0.900705 | ||||||||
\(535\) | −28.0408 | −1.21231 | ||||||||
\(536\) | −34.1414 | −1.47469 | ||||||||
\(537\) | −9.48174 | −0.409167 | ||||||||
\(538\) | 42.5324 | 1.83370 | ||||||||
\(539\) | 0.0813457 | 0.00350381 | ||||||||
\(540\) | 12.3144 | 0.529928 | ||||||||
\(541\) | 40.3332 | 1.73406 | 0.867029 | − | 0.498258i | \(-0.166027\pi\) | ||||
0.867029 | + | 0.498258i | \(0.166027\pi\) | |||||||
\(542\) | −50.7212 | −2.17866 | ||||||||
\(543\) | 10.5384 | 0.452245 | ||||||||
\(544\) | 3.17265 | 0.136026 | ||||||||
\(545\) | 56.9473 | 2.43936 | ||||||||
\(546\) | 23.4828 | 1.00497 | ||||||||
\(547\) | 10.0861 | 0.431249 | 0.215624 | − | 0.976476i | \(-0.430821\pi\) | ||||
0.215624 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(548\) | −5.00680 | −0.213880 | ||||||||
\(549\) | −1.28646 | −0.0549048 | ||||||||
\(550\) | 2.95855 | 0.126153 | ||||||||
\(551\) | −33.2439 | −1.41624 | ||||||||
\(552\) | −29.6264 | −1.26098 | ||||||||
\(553\) | 15.5679 | 0.662015 | ||||||||
\(554\) | 52.1803 | 2.21693 | ||||||||
\(555\) | 10.0212 | 0.425374 | ||||||||
\(556\) | −38.2857 | −1.62368 | ||||||||
\(557\) | −42.4211 | −1.79744 | −0.898720 | − | 0.438524i | \(-0.855502\pi\) | ||||
−0.898720 | + | 0.438524i | \(0.855502\pi\) | |||||||
\(558\) | −16.2627 | −0.688456 | ||||||||
\(559\) | −4.79447 | −0.202785 | ||||||||
\(560\) | 17.8016 | 0.752256 | ||||||||
\(561\) | 0.191904 | 0.00810219 | ||||||||
\(562\) | −14.2833 | −0.602505 | ||||||||
\(563\) | 2.14959 | 0.0905945 | 0.0452972 | − | 0.998974i | \(-0.485577\pi\) | ||||
0.0452972 | + | 0.998974i | \(0.485577\pi\) | |||||||
\(564\) | −9.60209 | −0.404321 | ||||||||
\(565\) | 41.2414 | 1.73504 | ||||||||
\(566\) | −60.8484 | −2.55765 | ||||||||
\(567\) | −2.72468 | −0.114426 | ||||||||
\(568\) | −24.3842 | −1.02314 | ||||||||
\(569\) | 14.5936 | 0.611796 | 0.305898 | − | 0.952064i | \(-0.401043\pi\) | ||||
0.305898 | + | 0.952064i | \(0.401043\pi\) | |||||||
\(570\) | 48.7633 | 2.04247 | ||||||||
\(571\) | −12.6971 | −0.531358 | −0.265679 | − | 0.964062i | \(-0.585596\pi\) | ||||
−0.265679 | + | 0.964062i | \(0.585596\pi\) | |||||||
\(572\) | 2.53119 | 0.105835 | ||||||||
\(573\) | 14.1219 | 0.589953 | ||||||||
\(574\) | −36.8715 | −1.53899 | ||||||||
\(575\) | 49.6963 | 2.07248 | ||||||||
\(576\) | −11.3831 | −0.474294 | ||||||||
\(577\) | −43.6114 | −1.81557 | −0.907784 | − | 0.419439i | \(-0.862227\pi\) | ||||
−0.907784 | + | 0.419439i | \(0.862227\pi\) | |||||||
\(578\) | 2.37316 | 0.0987106 | ||||||||
\(579\) | 19.2420 | 0.799670 | ||||||||
\(580\) | 67.5523 | 2.80496 | ||||||||
\(581\) | 0.744611 | 0.0308917 | ||||||||
\(582\) | −8.46349 | −0.350823 | ||||||||
\(583\) | −1.03377 | −0.0428144 | ||||||||
\(584\) | −30.6385 | −1.26783 | ||||||||
\(585\) | −12.3136 | −0.509106 | ||||||||
\(586\) | −37.3915 | −1.54463 | ||||||||
\(587\) | 33.8700 | 1.39797 | 0.698983 | − | 0.715138i | \(-0.253636\pi\) | ||||
0.698983 | + | 0.715138i | \(0.253636\pi\) | |||||||
\(588\) | −1.53952 | −0.0634887 | ||||||||
\(589\) | −41.5291 | −1.71118 | ||||||||
\(590\) | 56.7102 | 2.33472 | ||||||||
\(591\) | −23.4939 | −0.966409 | ||||||||
\(592\) | 5.69512 | 0.234068 | ||||||||
\(593\) | −32.0023 | −1.31418 | −0.657088 | − | 0.753814i | \(-0.728212\pi\) | ||||
−0.657088 | + | 0.753814i | \(0.728212\pi\) | |||||||
\(594\) | −0.455420 | −0.0186861 | ||||||||
\(595\) | −9.23837 | −0.378736 | ||||||||
\(596\) | −15.5788 | −0.638131 | ||||||||
\(597\) | 12.3584 | 0.505795 | ||||||||
\(598\) | 65.9312 | 2.69613 | ||||||||
\(599\) | 6.87403 | 0.280865 | 0.140433 | − | 0.990090i | \(-0.455151\pi\) | ||||
0.140433 | + | 0.990090i | \(0.455151\pi\) | |||||||
\(600\) | −25.1588 | −1.02710 | ||||||||
\(601\) | 30.4331 | 1.24139 | 0.620696 | − | 0.784051i | \(-0.286850\pi\) | ||||
0.620696 | + | 0.784051i | \(0.286850\pi\) | |||||||
\(602\) | 8.53645 | 0.347920 | ||||||||
\(603\) | −8.81575 | −0.359005 | ||||||||
\(604\) | −10.6612 | −0.433798 | ||||||||
\(605\) | 37.1720 | 1.51126 | ||||||||
\(606\) | −0.788560 | −0.0320330 | ||||||||
\(607\) | −1.57393 | −0.0638838 | −0.0319419 | − | 0.999490i | \(-0.510169\pi\) | ||||
−0.0319419 | + | 0.999490i | \(0.510169\pi\) | |||||||
\(608\) | −19.2269 | −0.779752 | ||||||||
\(609\) | −14.9466 | −0.605666 | ||||||||
\(610\) | 10.3515 | 0.419121 | ||||||||
\(611\) | 9.60147 | 0.388434 | ||||||||
\(612\) | −3.63190 | −0.146811 | ||||||||
\(613\) | −25.6767 | −1.03707 | −0.518536 | − | 0.855056i | \(-0.673523\pi\) | ||||
−0.518536 | + | 0.855056i | \(0.673523\pi\) | |||||||
\(614\) | 36.8305 | 1.48636 | ||||||||
\(615\) | 19.3342 | 0.779631 | ||||||||
\(616\) | −2.02499 | −0.0815891 | ||||||||
\(617\) | 14.7843 | 0.595194 | 0.297597 | − | 0.954692i | \(-0.403815\pi\) | ||||
0.297597 | + | 0.954692i | \(0.403815\pi\) | |||||||
\(618\) | −18.4699 | −0.742969 | ||||||||
\(619\) | −8.67475 | −0.348668 | −0.174334 | − | 0.984687i | \(-0.555777\pi\) | ||||
−0.174334 | + | 0.984687i | \(0.555777\pi\) | |||||||
\(620\) | 84.3878 | 3.38910 | ||||||||
\(621\) | −7.64992 | −0.306981 | ||||||||
\(622\) | 2.60898 | 0.104611 | ||||||||
\(623\) | −23.8969 | −0.957409 | ||||||||
\(624\) | −6.99796 | −0.280142 | ||||||||
\(625\) | −15.2794 | −0.611176 | ||||||||
\(626\) | 45.7783 | 1.82967 | ||||||||
\(627\) | −1.16298 | −0.0464447 | ||||||||
\(628\) | −3.63190 | −0.144929 | ||||||||
\(629\) | −2.95555 | −0.117846 | ||||||||
\(630\) | 21.9242 | 0.873479 | ||||||||
\(631\) | −0.279777 | −0.0111377 | −0.00556887 | − | 0.999984i | \(-0.501773\pi\) | ||||
−0.00556887 | + | 0.999984i | \(0.501773\pi\) | |||||||
\(632\) | −22.1278 | −0.880195 | ||||||||
\(633\) | 14.4101 | 0.572751 | ||||||||
\(634\) | −35.5196 | −1.41066 | ||||||||
\(635\) | 17.3693 | 0.689280 | ||||||||
\(636\) | 19.5648 | 0.775793 | ||||||||
\(637\) | 1.53942 | 0.0609941 | ||||||||
\(638\) | −2.49826 | −0.0989071 | ||||||||
\(639\) | −6.29632 | −0.249078 | ||||||||
\(640\) | 70.0793 | 2.77013 | ||||||||
\(641\) | −47.1913 | −1.86395 | −0.931973 | − | 0.362529i | \(-0.881913\pi\) | ||||
−0.931973 | + | 0.362529i | \(0.881913\pi\) | |||||||
\(642\) | −19.6263 | −0.774588 | ||||||||
\(643\) | 24.2565 | 0.956581 | 0.478291 | − | 0.878202i | \(-0.341257\pi\) | ||||
0.478291 | + | 0.878202i | \(0.341257\pi\) | |||||||
\(644\) | −75.7019 | −2.98307 | ||||||||
\(645\) | −4.47624 | −0.176252 | ||||||||
\(646\) | −14.3818 | −0.565845 | ||||||||
\(647\) | 12.2686 | 0.482330 | 0.241165 | − | 0.970484i | \(-0.422471\pi\) | ||||
0.241165 | + | 0.970484i | \(0.422471\pi\) | |||||||
\(648\) | 3.87278 | 0.152137 | ||||||||
\(649\) | −1.35250 | −0.0530904 | ||||||||
\(650\) | 55.9889 | 2.19607 | ||||||||
\(651\) | −18.6716 | −0.731798 | ||||||||
\(652\) | −12.1590 | −0.476183 | ||||||||
\(653\) | −4.55672 | −0.178318 | −0.0891591 | − | 0.996017i | \(-0.528418\pi\) | ||||
−0.0891591 | + | 0.996017i | \(0.528418\pi\) | |||||||
\(654\) | 39.8586 | 1.55859 | ||||||||
\(655\) | 27.6187 | 1.07915 | ||||||||
\(656\) | 10.9878 | 0.429002 | ||||||||
\(657\) | −7.91126 | −0.308648 | ||||||||
\(658\) | −17.0952 | −0.666441 | ||||||||
\(659\) | 11.8468 | 0.461485 | 0.230743 | − | 0.973015i | \(-0.425884\pi\) | ||||
0.230743 | + | 0.973015i | \(0.425884\pi\) | |||||||
\(660\) | 2.36319 | 0.0919869 | ||||||||
\(661\) | −8.54857 | −0.332501 | −0.166251 | − | 0.986084i | \(-0.553166\pi\) | ||||
−0.166251 | + | 0.986084i | \(0.553166\pi\) | |||||||
\(662\) | −18.7476 | −0.728648 | ||||||||
\(663\) | 3.63167 | 0.141043 | ||||||||
\(664\) | −1.05837 | −0.0410726 | ||||||||
\(665\) | 55.9863 | 2.17105 | ||||||||
\(666\) | 7.01400 | 0.271787 | ||||||||
\(667\) | −41.9646 | −1.62487 | ||||||||
\(668\) | 2.76457 | 0.106965 | ||||||||
\(669\) | −19.8049 | −0.765701 | ||||||||
\(670\) | 70.9360 | 2.74050 | ||||||||
\(671\) | −0.246877 | −0.00953058 | ||||||||
\(672\) | −8.64446 | −0.333467 | ||||||||
\(673\) | −22.0835 | −0.851255 | −0.425628 | − | 0.904898i | \(-0.639947\pi\) | ||||
−0.425628 | + | 0.904898i | \(0.639947\pi\) | |||||||
\(674\) | 38.3075 | 1.47555 | ||||||||
\(675\) | −6.49632 | −0.250044 | ||||||||
\(676\) | 0.686615 | 0.0264083 | ||||||||
\(677\) | 4.49547 | 0.172775 | 0.0863874 | − | 0.996262i | \(-0.472468\pi\) | ||||
0.0863874 | + | 0.996262i | \(0.472468\pi\) | |||||||
\(678\) | 28.8657 | 1.10858 | ||||||||
\(679\) | −9.71712 | −0.372909 | ||||||||
\(680\) | 13.1311 | 0.503556 | ||||||||
\(681\) | 18.6053 | 0.712955 | ||||||||
\(682\) | −3.12088 | −0.119505 | ||||||||
\(683\) | 20.7049 | 0.792251 | 0.396125 | − | 0.918196i | \(-0.370355\pi\) | ||||
0.396125 | + | 0.918196i | \(0.370355\pi\) | |||||||
\(684\) | 22.0100 | 0.841575 | ||||||||
\(685\) | 4.67418 | 0.178591 | ||||||||
\(686\) | 42.5219 | 1.62349 | ||||||||
\(687\) | −22.3431 | −0.852441 | ||||||||
\(688\) | −2.54389 | −0.0969850 | ||||||||
\(689\) | −19.5635 | −0.745310 | ||||||||
\(690\) | 61.5551 | 2.34336 | ||||||||
\(691\) | 21.2809 | 0.809563 | 0.404781 | − | 0.914413i | \(-0.367348\pi\) | ||||
0.404781 | + | 0.914413i | \(0.367348\pi\) | |||||||
\(692\) | 51.8170 | 1.96979 | ||||||||
\(693\) | −0.522877 | −0.0198625 | ||||||||
\(694\) | −71.7336 | −2.72297 | ||||||||
\(695\) | 35.7422 | 1.35578 | ||||||||
\(696\) | 21.2446 | 0.805274 | ||||||||
\(697\) | −5.70226 | −0.215989 | ||||||||
\(698\) | −39.1094 | −1.48031 | ||||||||
\(699\) | −5.62788 | −0.212866 | ||||||||
\(700\) | −64.2862 | −2.42979 | ||||||||
\(701\) | −30.1948 | −1.14044 | −0.570220 | − | 0.821492i | \(-0.693142\pi\) | ||||
−0.570220 | + | 0.821492i | \(0.693142\pi\) | |||||||
\(702\) | −8.61855 | −0.325286 | ||||||||
\(703\) | 17.9112 | 0.675534 | ||||||||
\(704\) | −2.18446 | −0.0823298 | ||||||||
\(705\) | 8.96418 | 0.337611 | ||||||||
\(706\) | −10.8321 | −0.407671 | ||||||||
\(707\) | −0.905363 | −0.0340497 | ||||||||
\(708\) | 25.5970 | 0.961993 | ||||||||
\(709\) | 21.2486 | 0.798006 | 0.399003 | − | 0.916950i | \(-0.369356\pi\) | ||||
0.399003 | + | 0.916950i | \(0.369356\pi\) | |||||||
\(710\) | 50.6633 | 1.90136 | ||||||||
\(711\) | −5.71367 | −0.214279 | ||||||||
\(712\) | 33.9663 | 1.27294 | ||||||||
\(713\) | −52.4231 | −1.96326 | ||||||||
\(714\) | −6.46611 | −0.241988 | ||||||||
\(715\) | −2.36304 | −0.0883725 | ||||||||
\(716\) | 34.4368 | 1.28696 | ||||||||
\(717\) | −5.73694 | −0.214250 | ||||||||
\(718\) | −7.25712 | −0.270833 | ||||||||
\(719\) | 39.6830 | 1.47993 | 0.739964 | − | 0.672647i | \(-0.234843\pi\) | ||||
0.739964 | + | 0.672647i | \(0.234843\pi\) | |||||||
\(720\) | −6.53347 | −0.243488 | ||||||||
\(721\) | −21.2057 | −0.789743 | ||||||||
\(722\) | 42.0665 | 1.56555 | ||||||||
\(723\) | 13.9510 | 0.518844 | ||||||||
\(724\) | −38.2744 | −1.42246 | ||||||||
\(725\) | −35.6364 | −1.32350 | ||||||||
\(726\) | 26.0174 | 0.965596 | ||||||||
\(727\) | −13.7912 | −0.511486 | −0.255743 | − | 0.966745i | \(-0.582320\pi\) | ||||
−0.255743 | + | 0.966745i | \(0.582320\pi\) | |||||||
\(728\) | −38.3217 | −1.42030 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 63.6580 | 2.35609 | ||||||||
\(731\) | 1.32018 | 0.0488287 | ||||||||
\(732\) | 4.67231 | 0.172693 | ||||||||
\(733\) | 15.2325 | 0.562624 | 0.281312 | − | 0.959616i | \(-0.409230\pi\) | ||||
0.281312 | + | 0.959616i | \(0.409230\pi\) | |||||||
\(734\) | 6.43717 | 0.237600 | ||||||||
\(735\) | 1.43724 | 0.0530135 | ||||||||
\(736\) | −24.2705 | −0.894623 | ||||||||
\(737\) | −1.69178 | −0.0623174 | ||||||||
\(738\) | 13.5324 | 0.498134 | ||||||||
\(739\) | −5.74760 | −0.211429 | −0.105714 | − | 0.994397i | \(-0.533713\pi\) | ||||
−0.105714 | + | 0.994397i | \(0.533713\pi\) | |||||||
\(740\) | −36.3959 | −1.33794 | ||||||||
\(741\) | −22.0086 | −0.808507 | ||||||||
\(742\) | 34.8324 | 1.27874 | ||||||||
\(743\) | 35.4555 | 1.30074 | 0.650369 | − | 0.759619i | \(-0.274614\pi\) | ||||
0.650369 | + | 0.759619i | \(0.274614\pi\) | |||||||
\(744\) | 26.5392 | 0.972975 | ||||||||
\(745\) | 14.5438 | 0.532844 | ||||||||
\(746\) | −13.1903 | −0.482930 | ||||||||
\(747\) | −0.273284 | −0.00999893 | ||||||||
\(748\) | −0.696977 | −0.0254840 | ||||||||
\(749\) | −22.5334 | −0.823352 | ||||||||
\(750\) | 12.0402 | 0.439645 | ||||||||
\(751\) | −25.8075 | −0.941730 | −0.470865 | − | 0.882205i | \(-0.656058\pi\) | ||||
−0.470865 | + | 0.882205i | \(0.656058\pi\) | |||||||
\(752\) | 5.09443 | 0.185775 | ||||||||
\(753\) | −25.4006 | −0.925649 | ||||||||
\(754\) | −47.2781 | −1.72177 | ||||||||
\(755\) | 9.95293 | 0.362224 | ||||||||
\(756\) | 9.89578 | 0.359906 | ||||||||
\(757\) | −24.2778 | −0.882391 | −0.441195 | − | 0.897411i | \(-0.645445\pi\) | ||||
−0.441195 | + | 0.897411i | \(0.645445\pi\) | |||||||
\(758\) | −6.40507 | −0.232643 | ||||||||
\(759\) | −1.46805 | −0.0532868 | ||||||||
\(760\) | −79.5771 | −2.88657 | ||||||||
\(761\) | −8.93062 | −0.323735 | −0.161867 | − | 0.986813i | \(-0.551752\pi\) | ||||
−0.161867 | + | 0.986813i | \(0.551752\pi\) | |||||||
\(762\) | 12.1571 | 0.440406 | ||||||||
\(763\) | 45.7625 | 1.65671 | ||||||||
\(764\) | −51.2896 | −1.85559 | ||||||||
\(765\) | 3.39062 | 0.122588 | ||||||||
\(766\) | −7.95077 | −0.287273 | ||||||||
\(767\) | −25.5953 | −0.924194 | ||||||||
\(768\) | 26.2838 | 0.948434 | ||||||||
\(769\) | 26.4051 | 0.952193 | 0.476097 | − | 0.879393i | \(-0.342051\pi\) | ||||
0.476097 | + | 0.879393i | \(0.342051\pi\) | |||||||
\(770\) | 4.20733 | 0.151622 | ||||||||
\(771\) | 28.5674 | 1.02883 | ||||||||
\(772\) | −69.8851 | −2.51522 | ||||||||
\(773\) | −47.6233 | −1.71289 | −0.856445 | − | 0.516238i | \(-0.827332\pi\) | ||||
−0.856445 | + | 0.516238i | \(0.827332\pi\) | |||||||
\(774\) | −3.13301 | −0.112614 | ||||||||
\(775\) | −44.5178 | −1.59913 | ||||||||
\(776\) | 13.8116 | 0.495808 | ||||||||
\(777\) | 8.05293 | 0.288897 | ||||||||
\(778\) | −12.3924 | −0.444288 | ||||||||
\(779\) | 34.5568 | 1.23813 | ||||||||
\(780\) | 44.7219 | 1.60130 | ||||||||
\(781\) | −1.20829 | −0.0432360 | ||||||||
\(782\) | −18.1545 | −0.649204 | ||||||||
\(783\) | 5.48562 | 0.196040 | ||||||||
\(784\) | 0.816799 | 0.0291714 | ||||||||
\(785\) | 3.39062 | 0.121017 | ||||||||
\(786\) | 19.3309 | 0.689510 | ||||||||
\(787\) | 2.91188 | 0.103797 | 0.0518987 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518987 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(788\) | 85.3275 | 3.03967 | ||||||||
\(789\) | 5.67725 | 0.202116 | ||||||||
\(790\) | 45.9750 | 1.63572 | ||||||||
\(791\) | 33.1413 | 1.17837 | ||||||||
\(792\) | 0.743201 | 0.0264085 | ||||||||
\(793\) | −4.67201 | −0.165908 | ||||||||
\(794\) | −63.9052 | −2.26791 | ||||||||
\(795\) | −18.2650 | −0.647792 | ||||||||
\(796\) | −44.8845 | −1.59089 | ||||||||
\(797\) | 16.2468 | 0.575492 | 0.287746 | − | 0.957707i | \(-0.407094\pi\) | ||||
0.287746 | + | 0.957707i | \(0.407094\pi\) | |||||||
\(798\) | 39.1859 | 1.38717 | ||||||||
\(799\) | −2.64382 | −0.0935315 | ||||||||
\(800\) | −20.6106 | −0.728693 | ||||||||
\(801\) | 8.77053 | 0.309891 | ||||||||
\(802\) | −7.43124 | −0.262406 | ||||||||
\(803\) | −1.51820 | −0.0535762 | ||||||||
\(804\) | 32.0180 | 1.12919 | ||||||||
\(805\) | 70.6728 | 2.49089 | ||||||||
\(806\) | −59.0609 | −2.08033 | ||||||||
\(807\) | −17.9223 | −0.630893 | ||||||||
\(808\) | 1.28685 | 0.0452714 | ||||||||
\(809\) | −25.7473 | −0.905226 | −0.452613 | − | 0.891707i | \(-0.649508\pi\) | ||||
−0.452613 | + | 0.891707i | \(0.649508\pi\) | |||||||
\(810\) | −8.04650 | −0.282725 | ||||||||
\(811\) | −32.3623 | −1.13639 | −0.568197 | − | 0.822892i | \(-0.692359\pi\) | ||||
−0.568197 | + | 0.822892i | \(0.692359\pi\) | |||||||
\(812\) | 54.2845 | 1.90501 | ||||||||
\(813\) | 21.3728 | 0.749578 | ||||||||
\(814\) | 1.34602 | 0.0471778 | ||||||||
\(815\) | 11.3512 | 0.397616 | ||||||||
\(816\) | 1.92692 | 0.0674558 | ||||||||
\(817\) | −8.00056 | −0.279904 | ||||||||
\(818\) | 59.3517 | 2.07518 | ||||||||
\(819\) | −9.89515 | −0.345765 | ||||||||
\(820\) | −70.2200 | −2.45219 | ||||||||
\(821\) | −4.63571 | −0.161787 | −0.0808936 | − | 0.996723i | \(-0.525777\pi\) | ||||
−0.0808936 | + | 0.996723i | \(0.525777\pi\) | |||||||
\(822\) | 3.27155 | 0.114108 | ||||||||
\(823\) | 23.5333 | 0.820318 | 0.410159 | − | 0.912014i | \(-0.365473\pi\) | ||||
0.410159 | + | 0.912014i | \(0.365473\pi\) | |||||||
\(824\) | 30.1412 | 1.05002 | ||||||||
\(825\) | −1.24667 | −0.0434035 | ||||||||
\(826\) | 45.5719 | 1.58565 | ||||||||
\(827\) | −5.60101 | −0.194766 | −0.0973831 | − | 0.995247i | \(-0.531047\pi\) | ||||
−0.0973831 | + | 0.995247i | \(0.531047\pi\) | |||||||
\(828\) | 27.7838 | 0.965553 | ||||||||
\(829\) | −4.83821 | −0.168038 | −0.0840189 | − | 0.996464i | \(-0.526776\pi\) | ||||
−0.0840189 | + | 0.996464i | \(0.526776\pi\) | |||||||
\(830\) | 2.19898 | 0.0763276 | ||||||||
\(831\) | −21.9877 | −0.762743 | ||||||||
\(832\) | −41.3396 | −1.43319 | ||||||||
\(833\) | −0.423888 | −0.0146868 | ||||||||
\(834\) | 25.0167 | 0.866257 | ||||||||
\(835\) | −2.58091 | −0.0893162 | ||||||||
\(836\) | 4.22381 | 0.146084 | ||||||||
\(837\) | 6.85276 | 0.236866 | ||||||||
\(838\) | −44.3617 | −1.53245 | ||||||||
\(839\) | 13.5095 | 0.466401 | 0.233201 | − | 0.972429i | \(-0.425080\pi\) | ||||
0.233201 | + | 0.972429i | \(0.425080\pi\) | |||||||
\(840\) | −35.7781 | −1.23446 | ||||||||
\(841\) | 1.09206 | 0.0376574 | ||||||||
\(842\) | 32.2669 | 1.11199 | ||||||||
\(843\) | 6.01868 | 0.207294 | ||||||||
\(844\) | −52.3362 | −1.80149 | ||||||||
\(845\) | −0.641000 | −0.0220511 | ||||||||
\(846\) | 6.27421 | 0.215712 | ||||||||
\(847\) | 29.8712 | 1.02638 | ||||||||
\(848\) | −10.3802 | −0.356456 | ||||||||
\(849\) | 25.6402 | 0.879969 | ||||||||
\(850\) | −15.4168 | −0.528793 | ||||||||
\(851\) | 22.6097 | 0.775051 | ||||||||
\(852\) | 22.8676 | 0.783432 | ||||||||
\(853\) | −3.82277 | −0.130889 | −0.0654445 | − | 0.997856i | \(-0.520847\pi\) | ||||
−0.0654445 | + | 0.997856i | \(0.520847\pi\) | |||||||
\(854\) | 8.31841 | 0.284650 | ||||||||
\(855\) | −20.5478 | −0.702721 | ||||||||
\(856\) | 32.0283 | 1.09470 | ||||||||
\(857\) | −48.3635 | −1.65207 | −0.826033 | − | 0.563622i | \(-0.809408\pi\) | ||||
−0.826033 | + | 0.563622i | \(0.809408\pi\) | |||||||
\(858\) | −1.65394 | −0.0564644 | ||||||||
\(859\) | 1.02138 | 0.0348490 | 0.0174245 | − | 0.999848i | \(-0.494453\pi\) | ||||
0.0174245 | + | 0.999848i | \(0.494453\pi\) | |||||||
\(860\) | 16.2573 | 0.554369 | ||||||||
\(861\) | 15.5368 | 0.529494 | ||||||||
\(862\) | 1.01938 | 0.0347201 | ||||||||
\(863\) | −52.8846 | −1.80021 | −0.900106 | − | 0.435671i | \(-0.856511\pi\) | ||||
−0.900106 | + | 0.435671i | \(0.856511\pi\) | |||||||
\(864\) | 3.17265 | 0.107936 | ||||||||
\(865\) | −48.3746 | −1.64479 | ||||||||
\(866\) | −96.7405 | −3.28738 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 67.8135 | 2.30174 | ||||||||
\(869\) | −1.09648 | −0.0371954 | ||||||||
\(870\) | −44.1401 | −1.49649 | ||||||||
\(871\) | −32.0159 | −1.08482 | ||||||||
\(872\) | −65.0454 | −2.20271 | ||||||||
\(873\) | 3.56633 | 0.120702 | ||||||||
\(874\) | 110.020 | 3.72148 | ||||||||
\(875\) | 13.8236 | 0.467322 | ||||||||
\(876\) | 28.7329 | 0.970796 | ||||||||
\(877\) | −17.3570 | −0.586104 | −0.293052 | − | 0.956097i | \(-0.594671\pi\) | ||||
−0.293052 | + | 0.956097i | \(0.594671\pi\) | |||||||
\(878\) | −29.4404 | −0.993567 | ||||||||
\(879\) | 15.7560 | 0.531436 | ||||||||
\(880\) | −1.25380 | −0.0422656 | ||||||||
\(881\) | 34.9333 | 1.17693 | 0.588467 | − | 0.808522i | \(-0.299732\pi\) | ||||
0.588467 | + | 0.808522i | \(0.299732\pi\) | |||||||
\(882\) | 1.00595 | 0.0338722 | ||||||||
\(883\) | −51.6710 | −1.73887 | −0.869434 | − | 0.494049i | \(-0.835516\pi\) | ||||
−0.869434 | + | 0.494049i | \(0.835516\pi\) | |||||||
\(884\) | −13.1899 | −0.443624 | ||||||||
\(885\) | −23.8965 | −0.803271 | ||||||||
\(886\) | −31.2544 | −1.05001 | ||||||||
\(887\) | 53.1390 | 1.78423 | 0.892117 | − | 0.451804i | \(-0.149219\pi\) | ||||
0.892117 | + | 0.451804i | \(0.149219\pi\) | |||||||
\(888\) | −11.4462 | −0.384109 | ||||||||
\(889\) | 13.9579 | 0.468132 | ||||||||
\(890\) | −70.5721 | −2.36558 | ||||||||
\(891\) | 0.191904 | 0.00642903 | ||||||||
\(892\) | 71.9294 | 2.40837 | ||||||||
\(893\) | 16.0220 | 0.536157 | ||||||||
\(894\) | 10.1795 | 0.340453 | ||||||||
\(895\) | −32.1490 | −1.07462 | ||||||||
\(896\) | 56.3153 | 1.88136 | ||||||||
\(897\) | −27.7820 | −0.927614 | ||||||||
\(898\) | 44.1128 | 1.47206 | ||||||||
\(899\) | 37.5917 | 1.25375 | ||||||||
\(900\) | 23.5940 | 0.786468 | ||||||||
\(901\) | 5.38691 | 0.179464 | ||||||||
\(902\) | 2.59692 | 0.0864680 | ||||||||
\(903\) | −3.59708 | −0.119703 | ||||||||
\(904\) | −47.1061 | −1.56672 | ||||||||
\(905\) | 35.7317 | 1.18776 | ||||||||
\(906\) | 6.96625 | 0.231438 | ||||||||
\(907\) | −48.3648 | −1.60593 | −0.802964 | − | 0.596028i | \(-0.796745\pi\) | ||||
−0.802964 | + | 0.596028i | \(0.796745\pi\) | |||||||
\(908\) | −67.5725 | −2.24247 | ||||||||
\(909\) | 0.332282 | 0.0110211 | ||||||||
\(910\) | 79.6214 | 2.63942 | ||||||||
\(911\) | 38.1072 | 1.26255 | 0.631273 | − | 0.775560i | \(-0.282533\pi\) | ||||
0.631273 | + | 0.775560i | \(0.282533\pi\) | |||||||
\(912\) | −11.6775 | −0.386682 | ||||||||
\(913\) | −0.0524442 | −0.00173565 | ||||||||
\(914\) | −6.97167 | −0.230602 | ||||||||
\(915\) | −4.36191 | −0.144200 | ||||||||
\(916\) | 81.1479 | 2.68120 | ||||||||
\(917\) | 22.1942 | 0.732918 | ||||||||
\(918\) | 2.37316 | 0.0783261 | ||||||||
\(919\) | 20.8793 | 0.688745 | 0.344373 | − | 0.938833i | \(-0.388092\pi\) | ||||
0.344373 | + | 0.938833i | \(0.388092\pi\) | |||||||
\(920\) | −100.452 | −3.31181 | ||||||||
\(921\) | −15.5196 | −0.511387 | ||||||||
\(922\) | 76.0427 | 2.50433 | ||||||||
\(923\) | −22.8662 | −0.752649 | ||||||||
\(924\) | 1.89904 | 0.0624738 | ||||||||
\(925\) | 19.2002 | 0.631299 | ||||||||
\(926\) | −63.8701 | −2.09890 | ||||||||
\(927\) | 7.78283 | 0.255622 | ||||||||
\(928\) | 17.4040 | 0.571313 | ||||||||
\(929\) | −19.2764 | −0.632439 | −0.316220 | − | 0.948686i | \(-0.602414\pi\) | ||||
−0.316220 | + | 0.948686i | \(0.602414\pi\) | |||||||
\(930\) | −55.1408 | −1.80814 | ||||||||
\(931\) | 2.56884 | 0.0841903 | ||||||||
\(932\) | 20.4399 | 0.669533 | ||||||||
\(933\) | −1.09937 | −0.0359918 | ||||||||
\(934\) | 101.439 | 3.31918 | ||||||||
\(935\) | 0.650674 | 0.0212793 | ||||||||
\(936\) | 14.0647 | 0.459718 | ||||||||
\(937\) | 43.6237 | 1.42512 | 0.712562 | − | 0.701609i | \(-0.247535\pi\) | ||||
0.712562 | + | 0.701609i | \(0.247535\pi\) | |||||||
\(938\) | 57.0036 | 1.86124 | ||||||||
\(939\) | −19.2900 | −0.629506 | ||||||||
\(940\) | −32.5570 | −1.06189 | ||||||||
\(941\) | −38.6703 | −1.26062 | −0.630308 | − | 0.776345i | \(-0.717071\pi\) | ||||
−0.630308 | + | 0.776345i | \(0.717071\pi\) | |||||||
\(942\) | 2.37316 | 0.0773218 | ||||||||
\(943\) | 43.6218 | 1.42052 | ||||||||
\(944\) | −13.5806 | −0.442011 | ||||||||
\(945\) | −9.23837 | −0.300524 | ||||||||
\(946\) | −0.601237 | −0.0195479 | ||||||||
\(947\) | 5.94121 | 0.193063 | 0.0965317 | − | 0.995330i | \(-0.469225\pi\) | ||||
0.0965317 | + | 0.995330i | \(0.469225\pi\) | |||||||
\(948\) | 20.7515 | 0.673977 | ||||||||
\(949\) | −28.7311 | −0.932651 | ||||||||
\(950\) | 93.4290 | 3.03124 | ||||||||
\(951\) | 14.9672 | 0.485345 | ||||||||
\(952\) | 10.5521 | 0.341995 | ||||||||
\(953\) | −26.0723 | −0.844565 | −0.422282 | − | 0.906464i | \(-0.638771\pi\) | ||||
−0.422282 | + | 0.906464i | \(0.638771\pi\) | |||||||
\(954\) | −12.7840 | −0.413898 | ||||||||
\(955\) | 47.8822 | 1.54943 | ||||||||
\(956\) | 20.8360 | 0.673885 | ||||||||
\(957\) | 1.05271 | 0.0340294 | ||||||||
\(958\) | 55.8527 | 1.80452 | ||||||||
\(959\) | 3.75614 | 0.121292 | ||||||||
\(960\) | −38.5957 | −1.24567 | ||||||||
\(961\) | 15.9604 | 0.514851 | ||||||||
\(962\) | 25.4726 | 0.821269 | ||||||||
\(963\) | 8.27010 | 0.266500 | ||||||||
\(964\) | −50.6687 | −1.63193 | ||||||||
\(965\) | 65.2423 | 2.10022 | ||||||||
\(966\) | 49.4652 | 1.59152 | ||||||||
\(967\) | 21.1321 | 0.679563 | 0.339781 | − | 0.940504i | \(-0.389647\pi\) | ||||
0.339781 | + | 0.940504i | \(0.389647\pi\) | |||||||
\(968\) | −42.4579 | −1.36465 | ||||||||
\(969\) | 6.06019 | 0.194681 | ||||||||
\(970\) | −28.6965 | −0.921389 | ||||||||
\(971\) | −59.3368 | −1.90421 | −0.952104 | − | 0.305774i | \(-0.901085\pi\) | ||||
−0.952104 | + | 0.305774i | \(0.901085\pi\) | |||||||
\(972\) | −3.63190 | −0.116493 | ||||||||
\(973\) | 28.7222 | 0.920792 | ||||||||
\(974\) | 29.3909 | 0.941746 | ||||||||
\(975\) | −23.5925 | −0.755565 | ||||||||
\(976\) | −2.47891 | −0.0793481 | ||||||||
\(977\) | 0.848607 | 0.0271494 | 0.0135747 | − | 0.999908i | \(-0.495679\pi\) | ||||
0.0135747 | + | 0.999908i | \(0.495679\pi\) | |||||||
\(978\) | 7.94494 | 0.254051 | ||||||||
\(979\) | 1.68310 | 0.0537921 | ||||||||
\(980\) | −5.21993 | −0.166745 | ||||||||
\(981\) | −16.7955 | −0.536240 | ||||||||
\(982\) | 63.3454 | 2.02143 | ||||||||
\(983\) | −15.2561 | −0.486595 | −0.243298 | − | 0.969952i | \(-0.578229\pi\) | ||||
−0.243298 | + | 0.969952i | \(0.578229\pi\) | |||||||
\(984\) | −22.0836 | −0.703999 | ||||||||
\(985\) | −79.6588 | −2.53814 | ||||||||
\(986\) | 13.0183 | 0.414587 | ||||||||
\(987\) | 7.20355 | 0.229292 | ||||||||
\(988\) | 79.9333 | 2.54302 | ||||||||
\(989\) | −10.0993 | −0.321139 | ||||||||
\(990\) | −1.54416 | −0.0490765 | ||||||||
\(991\) | 26.9241 | 0.855271 | 0.427636 | − | 0.903951i | \(-0.359347\pi\) | ||||
0.427636 | + | 0.903951i | \(0.359347\pi\) | |||||||
\(992\) | 21.7414 | 0.690291 | ||||||||
\(993\) | 7.89985 | 0.250694 | ||||||||
\(994\) | 40.7127 | 1.29133 | ||||||||
\(995\) | 41.9026 | 1.32840 | ||||||||
\(996\) | 0.992540 | 0.0314498 | ||||||||
\(997\) | 42.4673 | 1.34495 | 0.672476 | − | 0.740119i | \(-0.265231\pi\) | ||||
0.672476 | + | 0.740119i | \(0.265231\pi\) | |||||||
\(998\) | −101.206 | −3.20363 | ||||||||
\(999\) | −2.95555 | −0.0935095 |
(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 | 8007.2.a.f.1.43 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.43 | ✓ | 48 | 1.1 | even | 1 | trivial |