Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.50067\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50067 | 1.06114 | 0.530569 | − | 0.847642i | \(-0.321978\pi\) | ||||
0.530569 | + | 0.847642i | \(0.321978\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.252024 | 0.126012 | ||||||||
\(5\) | −0.569898 | −0.254866 | −0.127433 | − | 0.991847i | \(-0.540674\pi\) | ||||
−0.127433 | + | 0.991847i | \(0.540674\pi\) | |||||||
\(6\) | −1.50067 | −0.612648 | ||||||||
\(7\) | −3.97554 | −1.50261 | −0.751306 | − | 0.659954i | \(-0.770576\pi\) | ||||
−0.751306 | + | 0.659954i | \(0.770576\pi\) | |||||||
\(8\) | −2.62314 | −0.927421 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.855232 | −0.270448 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.252024 | −0.0727532 | ||||||||
\(13\) | −3.48724 | −0.967186 | −0.483593 | − | 0.875293i | \(-0.660669\pi\) | ||||
−0.483593 | + | 0.875293i | \(0.660669\pi\) | |||||||
\(14\) | −5.96599 | −1.59448 | ||||||||
\(15\) | 0.569898 | 0.147147 | ||||||||
\(16\) | −4.44053 | −1.11013 | ||||||||
\(17\) | 7.75664 | 1.88126 | 0.940631 | − | 0.339430i | \(-0.110234\pi\) | ||||
0.940631 | + | 0.339430i | \(0.110234\pi\) | |||||||
\(18\) | 1.50067 | 0.353712 | ||||||||
\(19\) | 1.56002 | 0.357894 | 0.178947 | − | 0.983859i | \(-0.442731\pi\) | ||||
0.178947 | + | 0.983859i | \(0.442731\pi\) | |||||||
\(20\) | −0.143628 | −0.0321162 | ||||||||
\(21\) | 3.97554 | 0.867533 | ||||||||
\(22\) | 1.50067 | 0.319945 | ||||||||
\(23\) | 4.91362 | 1.02456 | 0.512280 | − | 0.858819i | \(-0.328801\pi\) | ||||
0.512280 | + | 0.858819i | \(0.328801\pi\) | |||||||
\(24\) | 2.62314 | 0.535447 | ||||||||
\(25\) | −4.67522 | −0.935043 | ||||||||
\(26\) | −5.23321 | −1.02632 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00193 | −0.189347 | ||||||||
\(29\) | 6.29679 | 1.16928 | 0.584642 | − | 0.811291i | \(-0.301235\pi\) | ||||
0.584642 | + | 0.811291i | \(0.301235\pi\) | |||||||
\(30\) | 0.855232 | 0.156143 | ||||||||
\(31\) | 2.87665 | 0.516662 | 0.258331 | − | 0.966056i | \(-0.416828\pi\) | ||||
0.258331 | + | 0.966056i | \(0.416828\pi\) | |||||||
\(32\) | −1.41751 | −0.250583 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 11.6402 | 1.99628 | ||||||||
\(35\) | 2.26565 | 0.382965 | ||||||||
\(36\) | 0.252024 | 0.0420041 | ||||||||
\(37\) | −9.34414 | −1.53617 | −0.768083 | − | 0.640350i | \(-0.778789\pi\) | ||||
−0.768083 | + | 0.640350i | \(0.778789\pi\) | |||||||
\(38\) | 2.34109 | 0.379775 | ||||||||
\(39\) | 3.48724 | 0.558405 | ||||||||
\(40\) | 1.49492 | 0.236368 | ||||||||
\(41\) | 1.58419 | 0.247409 | 0.123704 | − | 0.992319i | \(-0.460523\pi\) | ||||
0.123704 | + | 0.992319i | \(0.460523\pi\) | |||||||
\(42\) | 5.96599 | 0.920572 | ||||||||
\(43\) | 5.31329 | 0.810269 | 0.405134 | − | 0.914257i | \(-0.367225\pi\) | ||||
0.405134 | + | 0.914257i | \(0.367225\pi\) | |||||||
\(44\) | 0.252024 | 0.0379941 | ||||||||
\(45\) | −0.569898 | −0.0849554 | ||||||||
\(46\) | 7.37374 | 1.08720 | ||||||||
\(47\) | 3.46571 | 0.505526 | 0.252763 | − | 0.967528i | \(-0.418661\pi\) | ||||
0.252763 | + | 0.967528i | \(0.418661\pi\) | |||||||
\(48\) | 4.44053 | 0.640936 | ||||||||
\(49\) | 8.80489 | 1.25784 | ||||||||
\(50\) | −7.01598 | −0.992209 | ||||||||
\(51\) | −7.75664 | −1.08615 | ||||||||
\(52\) | −0.878869 | −0.121877 | ||||||||
\(53\) | 10.8254 | 1.48699 | 0.743493 | − | 0.668744i | \(-0.233168\pi\) | ||||
0.743493 | + | 0.668744i | \(0.233168\pi\) | |||||||
\(54\) | −1.50067 | −0.204216 | ||||||||
\(55\) | −0.569898 | −0.0768451 | ||||||||
\(56\) | 10.4284 | 1.39355 | ||||||||
\(57\) | −1.56002 | −0.206630 | ||||||||
\(58\) | 9.44943 | 1.24077 | ||||||||
\(59\) | 0.418492 | 0.0544831 | 0.0272415 | − | 0.999629i | \(-0.491328\pi\) | ||||
0.0272415 | + | 0.999629i | \(0.491328\pi\) | |||||||
\(60\) | 0.143628 | 0.0185423 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 4.31692 | 0.548249 | ||||||||
\(63\) | −3.97554 | −0.500871 | ||||||||
\(64\) | 6.75385 | 0.844231 | ||||||||
\(65\) | 1.98737 | 0.246503 | ||||||||
\(66\) | −1.50067 | −0.184720 | ||||||||
\(67\) | 9.84375 | 1.20260 | 0.601302 | − | 0.799022i | \(-0.294649\pi\) | ||||
0.601302 | + | 0.799022i | \(0.294649\pi\) | |||||||
\(68\) | 1.95486 | 0.237062 | ||||||||
\(69\) | −4.91362 | −0.591530 | ||||||||
\(70\) | 3.40001 | 0.406378 | ||||||||
\(71\) | 9.93167 | 1.17867 | 0.589336 | − | 0.807888i | \(-0.299389\pi\) | ||||
0.589336 | + | 0.807888i | \(0.299389\pi\) | |||||||
\(72\) | −2.62314 | −0.309140 | ||||||||
\(73\) | 7.11859 | 0.833168 | 0.416584 | − | 0.909097i | \(-0.363227\pi\) | ||||
0.416584 | + | 0.909097i | \(0.363227\pi\) | |||||||
\(74\) | −14.0225 | −1.63008 | ||||||||
\(75\) | 4.67522 | 0.539847 | ||||||||
\(76\) | 0.393164 | 0.0450990 | ||||||||
\(77\) | −3.97554 | −0.453054 | ||||||||
\(78\) | 5.23321 | 0.592545 | ||||||||
\(79\) | −13.1270 | −1.47690 | −0.738450 | − | 0.674308i | \(-0.764442\pi\) | ||||
−0.738450 | + | 0.674308i | \(0.764442\pi\) | |||||||
\(80\) | 2.53065 | 0.282935 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.37735 | 0.262535 | ||||||||
\(83\) | 4.04331 | 0.443811 | 0.221906 | − | 0.975068i | \(-0.428772\pi\) | ||||
0.221906 | + | 0.975068i | \(0.428772\pi\) | |||||||
\(84\) | 1.00193 | 0.109320 | ||||||||
\(85\) | −4.42050 | −0.479470 | ||||||||
\(86\) | 7.97351 | 0.859806 | ||||||||
\(87\) | −6.29679 | −0.675086 | ||||||||
\(88\) | −2.62314 | −0.279628 | ||||||||
\(89\) | −13.4410 | −1.42474 | −0.712371 | − | 0.701803i | \(-0.752379\pi\) | ||||
−0.712371 | + | 0.701803i | \(0.752379\pi\) | |||||||
\(90\) | −0.855232 | −0.0901493 | ||||||||
\(91\) | 13.8636 | 1.45331 | ||||||||
\(92\) | 1.23835 | 0.129107 | ||||||||
\(93\) | −2.87665 | −0.298295 | ||||||||
\(94\) | 5.20090 | 0.536432 | ||||||||
\(95\) | −0.889055 | −0.0912151 | ||||||||
\(96\) | 1.41751 | 0.144674 | ||||||||
\(97\) | −1.77923 | −0.180653 | −0.0903267 | − | 0.995912i | \(-0.528791\pi\) | ||||
−0.0903267 | + | 0.995912i | \(0.528791\pi\) | |||||||
\(98\) | 13.2133 | 1.33474 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.17827 | −0.117827 | ||||||||
\(101\) | −18.9035 | −1.88096 | −0.940482 | − | 0.339844i | \(-0.889626\pi\) | ||||
−0.940482 | + | 0.339844i | \(0.889626\pi\) | |||||||
\(102\) | −11.6402 | −1.15255 | ||||||||
\(103\) | 2.41802 | 0.238254 | 0.119127 | − | 0.992879i | \(-0.461990\pi\) | ||||
0.119127 | + | 0.992879i | \(0.461990\pi\) | |||||||
\(104\) | 9.14753 | 0.896989 | ||||||||
\(105\) | −2.26565 | −0.221105 | ||||||||
\(106\) | 16.2454 | 1.57790 | ||||||||
\(107\) | 10.7538 | 1.03961 | 0.519806 | − | 0.854285i | \(-0.326004\pi\) | ||||
0.519806 | + | 0.854285i | \(0.326004\pi\) | |||||||
\(108\) | −0.252024 | −0.0242511 | ||||||||
\(109\) | −14.6227 | −1.40060 | −0.700298 | − | 0.713851i | \(-0.746950\pi\) | ||||
−0.700298 | + | 0.713851i | \(0.746950\pi\) | |||||||
\(110\) | −0.855232 | −0.0815432 | ||||||||
\(111\) | 9.34414 | 0.886906 | ||||||||
\(112\) | 17.6535 | 1.66810 | ||||||||
\(113\) | −8.88757 | −0.836072 | −0.418036 | − | 0.908430i | \(-0.637281\pi\) | ||||
−0.418036 | + | 0.908430i | \(0.637281\pi\) | |||||||
\(114\) | −2.34109 | −0.219263 | ||||||||
\(115\) | −2.80026 | −0.261126 | ||||||||
\(116\) | 1.58694 | 0.147344 | ||||||||
\(117\) | −3.48724 | −0.322395 | ||||||||
\(118\) | 0.628021 | 0.0578140 | ||||||||
\(119\) | −30.8368 | −2.82681 | ||||||||
\(120\) | −1.49492 | −0.136467 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.50067 | −0.135865 | ||||||||
\(123\) | −1.58419 | −0.142842 | ||||||||
\(124\) | 0.724986 | 0.0651057 | ||||||||
\(125\) | 5.51389 | 0.493177 | ||||||||
\(126\) | −5.96599 | −0.531492 | ||||||||
\(127\) | −16.2612 | −1.44295 | −0.721473 | − | 0.692443i | \(-0.756535\pi\) | ||||
−0.721473 | + | 0.692443i | \(0.756535\pi\) | |||||||
\(128\) | 12.9703 | 1.14643 | ||||||||
\(129\) | −5.31329 | −0.467809 | ||||||||
\(130\) | 2.98240 | 0.261574 | ||||||||
\(131\) | 16.7549 | 1.46389 | 0.731943 | − | 0.681366i | \(-0.238614\pi\) | ||||
0.731943 | + | 0.681366i | \(0.238614\pi\) | |||||||
\(132\) | −0.252024 | −0.0219359 | ||||||||
\(133\) | −6.20193 | −0.537776 | ||||||||
\(134\) | 14.7723 | 1.27613 | ||||||||
\(135\) | 0.569898 | 0.0490490 | ||||||||
\(136\) | −20.3468 | −1.74472 | ||||||||
\(137\) | 21.7052 | 1.85440 | 0.927198 | − | 0.374571i | \(-0.122210\pi\) | ||||
0.927198 | + | 0.374571i | \(0.122210\pi\) | |||||||
\(138\) | −7.37374 | −0.627694 | ||||||||
\(139\) | 9.86673 | 0.836885 | 0.418442 | − | 0.908243i | \(-0.362576\pi\) | ||||
0.418442 | + | 0.908243i | \(0.362576\pi\) | |||||||
\(140\) | 0.570999 | 0.0482582 | ||||||||
\(141\) | −3.46571 | −0.291865 | ||||||||
\(142\) | 14.9042 | 1.25073 | ||||||||
\(143\) | −3.48724 | −0.291618 | ||||||||
\(144\) | −4.44053 | −0.370044 | ||||||||
\(145\) | −3.58853 | −0.298011 | ||||||||
\(146\) | 10.6827 | 0.884106 | ||||||||
\(147\) | −8.80489 | −0.726215 | ||||||||
\(148\) | −2.35495 | −0.193576 | ||||||||
\(149\) | 16.9431 | 1.38803 | 0.694017 | − | 0.719959i | \(-0.255839\pi\) | ||||
0.694017 | + | 0.719959i | \(0.255839\pi\) | |||||||
\(150\) | 7.01598 | 0.572852 | ||||||||
\(151\) | 16.5384 | 1.34587 | 0.672937 | − | 0.739700i | \(-0.265032\pi\) | ||||
0.672937 | + | 0.739700i | \(0.265032\pi\) | |||||||
\(152\) | −4.09217 | −0.331918 | ||||||||
\(153\) | 7.75664 | 0.627088 | ||||||||
\(154\) | −5.96599 | −0.480753 | ||||||||
\(155\) | −1.63940 | −0.131680 | ||||||||
\(156\) | 0.878869 | 0.0703659 | ||||||||
\(157\) | 17.8806 | 1.42703 | 0.713515 | − | 0.700640i | \(-0.247102\pi\) | ||||
0.713515 | + | 0.700640i | \(0.247102\pi\) | |||||||
\(158\) | −19.6993 | −1.56719 | ||||||||
\(159\) | −10.8254 | −0.858511 | ||||||||
\(160\) | 0.807836 | 0.0638650 | ||||||||
\(161\) | −19.5343 | −1.53952 | ||||||||
\(162\) | 1.50067 | 0.117904 | ||||||||
\(163\) | −0.855017 | −0.0669701 | −0.0334851 | − | 0.999439i | \(-0.510661\pi\) | ||||
−0.0334851 | + | 0.999439i | \(0.510661\pi\) | |||||||
\(164\) | 0.399254 | 0.0311765 | ||||||||
\(165\) | 0.569898 | 0.0443665 | ||||||||
\(166\) | 6.06770 | 0.470945 | ||||||||
\(167\) | 13.4101 | 1.03770 | 0.518852 | − | 0.854864i | \(-0.326360\pi\) | ||||
0.518852 | + | 0.854864i | \(0.326360\pi\) | |||||||
\(168\) | −10.4284 | −0.804568 | ||||||||
\(169\) | −0.839160 | −0.0645508 | ||||||||
\(170\) | −6.63373 | −0.508784 | ||||||||
\(171\) | 1.56002 | 0.119298 | ||||||||
\(172\) | 1.33908 | 0.102104 | ||||||||
\(173\) | −9.03817 | −0.687160 | −0.343580 | − | 0.939123i | \(-0.611640\pi\) | ||||
−0.343580 | + | 0.939123i | \(0.611640\pi\) | |||||||
\(174\) | −9.44943 | −0.716359 | ||||||||
\(175\) | 18.5865 | 1.40501 | ||||||||
\(176\) | −4.44053 | −0.334718 | ||||||||
\(177\) | −0.418492 | −0.0314558 | ||||||||
\(178\) | −20.1706 | −1.51185 | ||||||||
\(179\) | −26.1042 | −1.95112 | −0.975559 | − | 0.219736i | \(-0.929480\pi\) | ||||
−0.975559 | + | 0.219736i | \(0.929480\pi\) | |||||||
\(180\) | −0.143628 | −0.0107054 | ||||||||
\(181\) | 3.16435 | 0.235204 | 0.117602 | − | 0.993061i | \(-0.462479\pi\) | ||||
0.117602 | + | 0.993061i | \(0.462479\pi\) | |||||||
\(182\) | 20.8048 | 1.54216 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −12.8891 | −0.950198 | ||||||||
\(185\) | 5.32521 | 0.391517 | ||||||||
\(186\) | −4.31692 | −0.316532 | ||||||||
\(187\) | 7.75664 | 0.567222 | ||||||||
\(188\) | 0.873443 | 0.0637024 | ||||||||
\(189\) | 3.97554 | 0.289178 | ||||||||
\(190\) | −1.33418 | −0.0967917 | ||||||||
\(191\) | −0.339788 | −0.0245862 | −0.0122931 | − | 0.999924i | \(-0.503913\pi\) | ||||
−0.0122931 | + | 0.999924i | \(0.503913\pi\) | |||||||
\(192\) | −6.75385 | −0.487417 | ||||||||
\(193\) | −10.9988 | −0.791714 | −0.395857 | − | 0.918312i | \(-0.629552\pi\) | ||||
−0.395857 | + | 0.918312i | \(0.629552\pi\) | |||||||
\(194\) | −2.67005 | −0.191698 | ||||||||
\(195\) | −1.98737 | −0.142319 | ||||||||
\(196\) | 2.21905 | 0.158503 | ||||||||
\(197\) | 13.6647 | 0.973571 | 0.486786 | − | 0.873522i | \(-0.338169\pi\) | ||||
0.486786 | + | 0.873522i | \(0.338169\pi\) | |||||||
\(198\) | 1.50067 | 0.106648 | ||||||||
\(199\) | −5.05352 | −0.358235 | −0.179117 | − | 0.983828i | \(-0.557324\pi\) | ||||
−0.179117 | + | 0.983828i | \(0.557324\pi\) | |||||||
\(200\) | 12.2638 | 0.867179 | ||||||||
\(201\) | −9.84375 | −0.694324 | ||||||||
\(202\) | −28.3679 | −1.99596 | ||||||||
\(203\) | −25.0331 | −1.75698 | ||||||||
\(204\) | −1.95486 | −0.136868 | ||||||||
\(205\) | −0.902827 | −0.0630561 | ||||||||
\(206\) | 3.62865 | 0.252820 | ||||||||
\(207\) | 4.91362 | 0.341520 | ||||||||
\(208\) | 15.4852 | 1.07371 | ||||||||
\(209\) | 1.56002 | 0.107909 | ||||||||
\(210\) | −3.40001 | −0.234623 | ||||||||
\(211\) | 0.418379 | 0.0288024 | 0.0144012 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0144012 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(212\) | 2.72827 | 0.187378 | ||||||||
\(213\) | −9.93167 | −0.680507 | ||||||||
\(214\) | 16.1380 | 1.10317 | ||||||||
\(215\) | −3.02803 | −0.206510 | ||||||||
\(216\) | 2.62314 | 0.178482 | ||||||||
\(217\) | −11.4362 | −0.776342 | ||||||||
\(218\) | −21.9438 | −1.48622 | ||||||||
\(219\) | −7.11859 | −0.481030 | ||||||||
\(220\) | −0.143628 | −0.00968341 | ||||||||
\(221\) | −27.0493 | −1.81953 | ||||||||
\(222\) | 14.0225 | 0.941129 | ||||||||
\(223\) | 8.46953 | 0.567162 | 0.283581 | − | 0.958948i | \(-0.408478\pi\) | ||||
0.283581 | + | 0.958948i | \(0.408478\pi\) | |||||||
\(224\) | 5.63536 | 0.376528 | ||||||||
\(225\) | −4.67522 | −0.311681 | ||||||||
\(226\) | −13.3373 | −0.887187 | ||||||||
\(227\) | −1.28958 | −0.0855927 | −0.0427963 | − | 0.999084i | \(-0.513627\pi\) | ||||
−0.0427963 | + | 0.999084i | \(0.513627\pi\) | |||||||
\(228\) | −0.393164 | −0.0260379 | ||||||||
\(229\) | 18.0318 | 1.19157 | 0.595787 | − | 0.803143i | \(-0.296840\pi\) | ||||
0.595787 | + | 0.803143i | \(0.296840\pi\) | |||||||
\(230\) | −4.20228 | −0.277090 | ||||||||
\(231\) | 3.97554 | 0.261571 | ||||||||
\(232\) | −16.5174 | −1.08442 | ||||||||
\(233\) | 15.1799 | 0.994470 | 0.497235 | − | 0.867616i | \(-0.334349\pi\) | ||||
0.497235 | + | 0.867616i | \(0.334349\pi\) | |||||||
\(234\) | −5.23321 | −0.342106 | ||||||||
\(235\) | −1.97510 | −0.128841 | ||||||||
\(236\) | 0.105470 | 0.00686553 | ||||||||
\(237\) | 13.1270 | 0.852689 | ||||||||
\(238\) | −46.2760 | −2.99963 | ||||||||
\(239\) | 5.61796 | 0.363396 | 0.181698 | − | 0.983354i | \(-0.441841\pi\) | ||||
0.181698 | + | 0.983354i | \(0.441841\pi\) | |||||||
\(240\) | −2.53065 | −0.163353 | ||||||||
\(241\) | −9.85967 | −0.635117 | −0.317559 | − | 0.948239i | \(-0.602863\pi\) | ||||
−0.317559 | + | 0.948239i | \(0.602863\pi\) | |||||||
\(242\) | 1.50067 | 0.0964670 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.252024 | −0.0161342 | ||||||||
\(245\) | −5.01789 | −0.320581 | ||||||||
\(246\) | −2.37735 | −0.151574 | ||||||||
\(247\) | −5.44018 | −0.346150 | ||||||||
\(248\) | −7.54587 | −0.479163 | ||||||||
\(249\) | −4.04331 | −0.256235 | ||||||||
\(250\) | 8.27455 | 0.523329 | ||||||||
\(251\) | 31.0856 | 1.96210 | 0.981052 | − | 0.193743i | \(-0.0620629\pi\) | ||||
0.981052 | + | 0.193743i | \(0.0620629\pi\) | |||||||
\(252\) | −1.00193 | −0.0631158 | ||||||||
\(253\) | 4.91362 | 0.308916 | ||||||||
\(254\) | −24.4027 | −1.53116 | ||||||||
\(255\) | 4.42050 | 0.276822 | ||||||||
\(256\) | 5.95657 | 0.372286 | ||||||||
\(257\) | −10.0493 | −0.626855 | −0.313428 | − | 0.949612i | \(-0.601477\pi\) | ||||
−0.313428 | + | 0.949612i | \(0.601477\pi\) | |||||||
\(258\) | −7.97351 | −0.496409 | ||||||||
\(259\) | 37.1480 | 2.30826 | ||||||||
\(260\) | 0.500866 | 0.0310624 | ||||||||
\(261\) | 6.29679 | 0.389761 | ||||||||
\(262\) | 25.1437 | 1.55338 | ||||||||
\(263\) | 19.8284 | 1.22267 | 0.611337 | − | 0.791370i | \(-0.290632\pi\) | ||||
0.611337 | + | 0.791370i | \(0.290632\pi\) | |||||||
\(264\) | 2.62314 | 0.161443 | ||||||||
\(265\) | −6.16938 | −0.378982 | ||||||||
\(266\) | −9.30708 | −0.570654 | ||||||||
\(267\) | 13.4410 | 0.822576 | ||||||||
\(268\) | 2.48086 | 0.151543 | ||||||||
\(269\) | −11.7548 | −0.716702 | −0.358351 | − | 0.933587i | \(-0.616661\pi\) | ||||
−0.358351 | + | 0.933587i | \(0.616661\pi\) | |||||||
\(270\) | 0.855232 | 0.0520477 | ||||||||
\(271\) | −19.0082 | −1.15467 | −0.577334 | − | 0.816508i | \(-0.695907\pi\) | ||||
−0.577334 | + | 0.816508i | \(0.695907\pi\) | |||||||
\(272\) | −34.4436 | −2.08845 | ||||||||
\(273\) | −13.8636 | −0.839066 | ||||||||
\(274\) | 32.5724 | 1.96777 | ||||||||
\(275\) | −4.67522 | −0.281926 | ||||||||
\(276\) | −1.23835 | −0.0745399 | ||||||||
\(277\) | −27.7437 | −1.66695 | −0.833477 | − | 0.552553i | \(-0.813654\pi\) | ||||
−0.833477 | + | 0.552553i | \(0.813654\pi\) | |||||||
\(278\) | 14.8067 | 0.888050 | ||||||||
\(279\) | 2.87665 | 0.172221 | ||||||||
\(280\) | −5.94313 | −0.355170 | ||||||||
\(281\) | −26.9692 | −1.60885 | −0.804424 | − | 0.594056i | \(-0.797526\pi\) | ||||
−0.804424 | + | 0.594056i | \(0.797526\pi\) | |||||||
\(282\) | −5.20090 | −0.309709 | ||||||||
\(283\) | 30.2378 | 1.79745 | 0.898725 | − | 0.438513i | \(-0.144495\pi\) | ||||
0.898725 | + | 0.438513i | \(0.144495\pi\) | |||||||
\(284\) | 2.50302 | 0.148527 | ||||||||
\(285\) | 0.889055 | 0.0526631 | ||||||||
\(286\) | −5.23321 | −0.309446 | ||||||||
\(287\) | −6.29800 | −0.371759 | ||||||||
\(288\) | −1.41751 | −0.0835275 | ||||||||
\(289\) | 43.1655 | 2.53915 | ||||||||
\(290\) | −5.38521 | −0.316230 | ||||||||
\(291\) | 1.77923 | 0.104300 | ||||||||
\(292\) | 1.79406 | 0.104989 | ||||||||
\(293\) | 6.99534 | 0.408672 | 0.204336 | − | 0.978901i | \(-0.434496\pi\) | ||||
0.204336 | + | 0.978901i | \(0.434496\pi\) | |||||||
\(294\) | −13.2133 | −0.770614 | ||||||||
\(295\) | −0.238498 | −0.0138859 | ||||||||
\(296\) | 24.5110 | 1.42467 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 25.4261 | 1.47289 | ||||||||
\(299\) | −17.1350 | −0.990940 | ||||||||
\(300\) | 1.17827 | 0.0680273 | ||||||||
\(301\) | −21.1232 | −1.21752 | ||||||||
\(302\) | 24.8187 | 1.42816 | ||||||||
\(303\) | 18.9035 | 1.08597 | ||||||||
\(304\) | −6.92734 | −0.397310 | ||||||||
\(305\) | 0.569898 | 0.0326323 | ||||||||
\(306\) | 11.6402 | 0.665426 | ||||||||
\(307\) | 7.80207 | 0.445288 | 0.222644 | − | 0.974900i | \(-0.428531\pi\) | ||||
0.222644 | + | 0.974900i | \(0.428531\pi\) | |||||||
\(308\) | −1.00193 | −0.0570904 | ||||||||
\(309\) | −2.41802 | −0.137556 | ||||||||
\(310\) | −2.46020 | −0.139730 | ||||||||
\(311\) | −1.36849 | −0.0775998 | −0.0387999 | − | 0.999247i | \(-0.512353\pi\) | ||||
−0.0387999 | + | 0.999247i | \(0.512353\pi\) | |||||||
\(312\) | −9.14753 | −0.517877 | ||||||||
\(313\) | −5.14485 | −0.290804 | −0.145402 | − | 0.989373i | \(-0.546448\pi\) | ||||
−0.145402 | + | 0.989373i | \(0.546448\pi\) | |||||||
\(314\) | 26.8330 | 1.51427 | ||||||||
\(315\) | 2.26565 | 0.127655 | ||||||||
\(316\) | −3.30832 | −0.186107 | ||||||||
\(317\) | 30.3916 | 1.70696 | 0.853482 | − | 0.521122i | \(-0.174486\pi\) | ||||
0.853482 | + | 0.521122i | \(0.174486\pi\) | |||||||
\(318\) | −16.2454 | −0.910998 | ||||||||
\(319\) | 6.29679 | 0.352552 | ||||||||
\(320\) | −3.84900 | −0.215166 | ||||||||
\(321\) | −10.7538 | −0.600220 | ||||||||
\(322\) | −29.3146 | −1.63364 | ||||||||
\(323\) | 12.1006 | 0.673293 | ||||||||
\(324\) | 0.252024 | 0.0140014 | ||||||||
\(325\) | 16.3036 | 0.904361 | ||||||||
\(326\) | −1.28310 | −0.0710645 | ||||||||
\(327\) | 14.6227 | 0.808634 | ||||||||
\(328\) | −4.15555 | −0.229452 | ||||||||
\(329\) | −13.7781 | −0.759609 | ||||||||
\(330\) | 0.855232 | 0.0470790 | ||||||||
\(331\) | 17.3933 | 0.956024 | 0.478012 | − | 0.878353i | \(-0.341357\pi\) | ||||
0.478012 | + | 0.878353i | \(0.341357\pi\) | |||||||
\(332\) | 1.01901 | 0.0559256 | ||||||||
\(333\) | −9.34414 | −0.512056 | ||||||||
\(334\) | 20.1242 | 1.10115 | ||||||||
\(335\) | −5.60993 | −0.306503 | ||||||||
\(336\) | −17.6535 | −0.963077 | ||||||||
\(337\) | 3.38221 | 0.184241 | 0.0921203 | − | 0.995748i | \(-0.470636\pi\) | ||||
0.0921203 | + | 0.995748i | \(0.470636\pi\) | |||||||
\(338\) | −1.25931 | −0.0684972 | ||||||||
\(339\) | 8.88757 | 0.482706 | ||||||||
\(340\) | −1.11407 | −0.0604191 | ||||||||
\(341\) | 2.87665 | 0.155779 | ||||||||
\(342\) | 2.34109 | 0.126592 | ||||||||
\(343\) | −7.17541 | −0.387436 | ||||||||
\(344\) | −13.9375 | −0.751460 | ||||||||
\(345\) | 2.80026 | 0.150761 | ||||||||
\(346\) | −13.5634 | −0.729171 | ||||||||
\(347\) | 22.0213 | 1.18217 | 0.591084 | − | 0.806610i | \(-0.298700\pi\) | ||||
0.591084 | + | 0.806610i | \(0.298700\pi\) | |||||||
\(348\) | −1.58694 | −0.0850691 | ||||||||
\(349\) | −6.15318 | −0.329372 | −0.164686 | − | 0.986346i | \(-0.552661\pi\) | ||||
−0.164686 | + | 0.986346i | \(0.552661\pi\) | |||||||
\(350\) | 27.8923 | 1.49090 | ||||||||
\(351\) | 3.48724 | 0.186135 | ||||||||
\(352\) | −1.41751 | −0.0755535 | ||||||||
\(353\) | −2.81549 | −0.149853 | −0.0749267 | − | 0.997189i | \(-0.523872\pi\) | ||||
−0.0749267 | + | 0.997189i | \(0.523872\pi\) | |||||||
\(354\) | −0.628021 | −0.0333789 | ||||||||
\(355\) | −5.66004 | −0.300404 | ||||||||
\(356\) | −3.38746 | −0.179535 | ||||||||
\(357\) | 30.8368 | 1.63206 | ||||||||
\(358\) | −39.1739 | −2.07040 | ||||||||
\(359\) | −19.3450 | −1.02099 | −0.510494 | − | 0.859881i | \(-0.670537\pi\) | ||||
−0.510494 | + | 0.859881i | \(0.670537\pi\) | |||||||
\(360\) | 1.49492 | 0.0787894 | ||||||||
\(361\) | −16.5663 | −0.871912 | ||||||||
\(362\) | 4.74865 | 0.249584 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 3.49398 | 0.183134 | ||||||||
\(365\) | −4.05687 | −0.212346 | ||||||||
\(366\) | 1.50067 | 0.0784415 | ||||||||
\(367\) | 9.48578 | 0.495154 | 0.247577 | − | 0.968868i | \(-0.420366\pi\) | ||||
0.247577 | + | 0.968868i | \(0.420366\pi\) | |||||||
\(368\) | −21.8191 | −1.13740 | ||||||||
\(369\) | 1.58419 | 0.0824696 | ||||||||
\(370\) | 7.99140 | 0.415453 | ||||||||
\(371\) | −43.0368 | −2.23436 | ||||||||
\(372\) | −0.724986 | −0.0375888 | ||||||||
\(373\) | −28.1396 | −1.45701 | −0.728507 | − | 0.685038i | \(-0.759785\pi\) | ||||
−0.728507 | + | 0.685038i | \(0.759785\pi\) | |||||||
\(374\) | 11.6402 | 0.601900 | ||||||||
\(375\) | −5.51389 | −0.284736 | ||||||||
\(376\) | −9.09105 | −0.468835 | ||||||||
\(377\) | −21.9584 | −1.13092 | ||||||||
\(378\) | 5.96599 | 0.306857 | ||||||||
\(379\) | −28.6718 | −1.47277 | −0.736386 | − | 0.676561i | \(-0.763469\pi\) | ||||
−0.736386 | + | 0.676561i | \(0.763469\pi\) | |||||||
\(380\) | −0.224063 | −0.0114942 | ||||||||
\(381\) | 16.2612 | 0.833085 | ||||||||
\(382\) | −0.509911 | −0.0260893 | ||||||||
\(383\) | −35.9467 | −1.83679 | −0.918395 | − | 0.395666i | \(-0.870514\pi\) | ||||
−0.918395 | + | 0.395666i | \(0.870514\pi\) | |||||||
\(384\) | −12.9703 | −0.661890 | ||||||||
\(385\) | 2.26565 | 0.115468 | ||||||||
\(386\) | −16.5057 | −0.840118 | ||||||||
\(387\) | 5.31329 | 0.270090 | ||||||||
\(388\) | −0.448409 | −0.0227645 | ||||||||
\(389\) | −36.5774 | −1.85455 | −0.927274 | − | 0.374383i | \(-0.877855\pi\) | ||||
−0.927274 | + | 0.374383i | \(0.877855\pi\) | |||||||
\(390\) | −2.98240 | −0.151020 | ||||||||
\(391\) | 38.1132 | 1.92747 | ||||||||
\(392\) | −23.0965 | −1.16655 | ||||||||
\(393\) | −16.7549 | −0.845175 | ||||||||
\(394\) | 20.5063 | 1.03309 | ||||||||
\(395\) | 7.48104 | 0.376412 | ||||||||
\(396\) | 0.252024 | 0.0126647 | ||||||||
\(397\) | 17.4290 | 0.874738 | 0.437369 | − | 0.899282i | \(-0.355910\pi\) | ||||
0.437369 | + | 0.899282i | \(0.355910\pi\) | |||||||
\(398\) | −7.58370 | −0.380136 | ||||||||
\(399\) | 6.20193 | 0.310485 | ||||||||
\(400\) | 20.7604 | 1.03802 | ||||||||
\(401\) | −28.3816 | −1.41731 | −0.708655 | − | 0.705556i | \(-0.750697\pi\) | ||||
−0.708655 | + | 0.705556i | \(0.750697\pi\) | |||||||
\(402\) | −14.7723 | −0.736773 | ||||||||
\(403\) | −10.0316 | −0.499708 | ||||||||
\(404\) | −4.76413 | −0.237024 | ||||||||
\(405\) | −0.569898 | −0.0283185 | ||||||||
\(406\) | −37.5665 | −1.86440 | ||||||||
\(407\) | −9.34414 | −0.463172 | ||||||||
\(408\) | 20.3468 | 1.00732 | ||||||||
\(409\) | 27.6614 | 1.36777 | 0.683883 | − | 0.729592i | \(-0.260290\pi\) | ||||
0.683883 | + | 0.729592i | \(0.260290\pi\) | |||||||
\(410\) | −1.35485 | −0.0669112 | ||||||||
\(411\) | −21.7052 | −1.07064 | ||||||||
\(412\) | 0.609399 | 0.0300229 | ||||||||
\(413\) | −1.66373 | −0.0818669 | ||||||||
\(414\) | 7.37374 | 0.362399 | ||||||||
\(415\) | −2.30428 | −0.113113 | ||||||||
\(416\) | 4.94319 | 0.242360 | ||||||||
\(417\) | −9.86673 | −0.483176 | ||||||||
\(418\) | 2.34109 | 0.114506 | ||||||||
\(419\) | −1.14196 | −0.0557883 | −0.0278942 | − | 0.999611i | \(-0.508880\pi\) | ||||
−0.0278942 | + | 0.999611i | \(0.508880\pi\) | |||||||
\(420\) | −0.570999 | −0.0278619 | ||||||||
\(421\) | 5.24502 | 0.255627 | 0.127813 | − | 0.991798i | \(-0.459204\pi\) | ||||
0.127813 | + | 0.991798i | \(0.459204\pi\) | |||||||
\(422\) | 0.627850 | 0.0305633 | ||||||||
\(423\) | 3.46571 | 0.168509 | ||||||||
\(424\) | −28.3966 | −1.37906 | ||||||||
\(425\) | −36.2640 | −1.75906 | ||||||||
\(426\) | −14.9042 | −0.722111 | ||||||||
\(427\) | 3.97554 | 0.192390 | ||||||||
\(428\) | 2.71022 | 0.131004 | ||||||||
\(429\) | 3.48724 | 0.168366 | ||||||||
\(430\) | −4.54409 | −0.219136 | ||||||||
\(431\) | 39.7537 | 1.91487 | 0.957434 | − | 0.288651i | \(-0.0932068\pi\) | ||||
0.957434 | + | 0.288651i | \(0.0932068\pi\) | |||||||
\(432\) | 4.44053 | 0.213645 | ||||||||
\(433\) | −22.4352 | −1.07817 | −0.539084 | − | 0.842252i | \(-0.681229\pi\) | ||||
−0.539084 | + | 0.842252i | \(0.681229\pi\) | |||||||
\(434\) | −17.1621 | −0.823806 | ||||||||
\(435\) | 3.58853 | 0.172057 | ||||||||
\(436\) | −3.68526 | −0.176492 | ||||||||
\(437\) | 7.66536 | 0.366684 | ||||||||
\(438\) | −10.6827 | −0.510439 | ||||||||
\(439\) | −5.46960 | −0.261050 | −0.130525 | − | 0.991445i | \(-0.541666\pi\) | ||||
−0.130525 | + | 0.991445i | \(0.541666\pi\) | |||||||
\(440\) | 1.49492 | 0.0712677 | ||||||||
\(441\) | 8.80489 | 0.419280 | ||||||||
\(442\) | −40.5922 | −1.93077 | ||||||||
\(443\) | −4.21494 | −0.200258 | −0.100129 | − | 0.994974i | \(-0.531926\pi\) | ||||
−0.100129 | + | 0.994974i | \(0.531926\pi\) | |||||||
\(444\) | 2.35495 | 0.111761 | ||||||||
\(445\) | 7.66000 | 0.363119 | ||||||||
\(446\) | 12.7100 | 0.601837 | ||||||||
\(447\) | −16.9431 | −0.801381 | ||||||||
\(448\) | −26.8502 | −1.26855 | ||||||||
\(449\) | 23.8577 | 1.12592 | 0.562958 | − | 0.826485i | \(-0.309663\pi\) | ||||
0.562958 | + | 0.826485i | \(0.309663\pi\) | |||||||
\(450\) | −7.01598 | −0.330736 | ||||||||
\(451\) | 1.58419 | 0.0745966 | ||||||||
\(452\) | −2.23988 | −0.105355 | ||||||||
\(453\) | −16.5384 | −0.777041 | ||||||||
\(454\) | −1.93525 | −0.0908256 | ||||||||
\(455\) | −7.90087 | −0.370398 | ||||||||
\(456\) | 4.09217 | 0.191633 | ||||||||
\(457\) | 35.7911 | 1.67424 | 0.837119 | − | 0.547021i | \(-0.184238\pi\) | ||||
0.837119 | + | 0.547021i | \(0.184238\pi\) | |||||||
\(458\) | 27.0598 | 1.26442 | ||||||||
\(459\) | −7.75664 | −0.362049 | ||||||||
\(460\) | −0.705734 | −0.0329050 | ||||||||
\(461\) | 33.0708 | 1.54026 | 0.770131 | − | 0.637886i | \(-0.220191\pi\) | ||||
0.770131 | + | 0.637886i | \(0.220191\pi\) | |||||||
\(462\) | 5.96599 | 0.277563 | ||||||||
\(463\) | −30.1684 | −1.40205 | −0.701023 | − | 0.713139i | \(-0.747273\pi\) | ||||
−0.701023 | + | 0.713139i | \(0.747273\pi\) | |||||||
\(464\) | −27.9611 | −1.29806 | ||||||||
\(465\) | 1.63940 | 0.0760253 | ||||||||
\(466\) | 22.7801 | 1.05527 | ||||||||
\(467\) | 13.3041 | 0.615642 | 0.307821 | − | 0.951444i | \(-0.400400\pi\) | ||||
0.307821 | + | 0.951444i | \(0.400400\pi\) | |||||||
\(468\) | −0.878869 | −0.0406257 | ||||||||
\(469\) | −39.1342 | −1.80705 | ||||||||
\(470\) | −2.96399 | −0.136718 | ||||||||
\(471\) | −17.8806 | −0.823896 | ||||||||
\(472\) | −1.09777 | −0.0505287 | ||||||||
\(473\) | 5.31329 | 0.244305 | ||||||||
\(474\) | 19.6993 | 0.904820 | ||||||||
\(475\) | −7.29345 | −0.334646 | ||||||||
\(476\) | −7.77163 | −0.356212 | ||||||||
\(477\) | 10.8254 | 0.495662 | ||||||||
\(478\) | 8.43073 | 0.385613 | ||||||||
\(479\) | 36.2381 | 1.65576 | 0.827881 | − | 0.560904i | \(-0.189546\pi\) | ||||
0.827881 | + | 0.560904i | \(0.189546\pi\) | |||||||
\(480\) | −0.807836 | −0.0368725 | ||||||||
\(481\) | 32.5852 | 1.48576 | ||||||||
\(482\) | −14.7962 | −0.673947 | ||||||||
\(483\) | 19.5343 | 0.888839 | ||||||||
\(484\) | 0.252024 | 0.0114557 | ||||||||
\(485\) | 1.01398 | 0.0460425 | ||||||||
\(486\) | −1.50067 | −0.0680720 | ||||||||
\(487\) | 4.94148 | 0.223920 | 0.111960 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111960 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(488\) | 2.62314 | 0.118744 | ||||||||
\(489\) | 0.855017 | 0.0386652 | ||||||||
\(490\) | −7.53022 | −0.340181 | ||||||||
\(491\) | −14.0150 | −0.632489 | −0.316245 | − | 0.948678i | \(-0.602422\pi\) | ||||
−0.316245 | + | 0.948678i | \(0.602422\pi\) | |||||||
\(492\) | −0.399254 | −0.0179998 | ||||||||
\(493\) | 48.8419 | 2.19973 | ||||||||
\(494\) | −8.16394 | −0.367313 | ||||||||
\(495\) | −0.569898 | −0.0256150 | ||||||||
\(496\) | −12.7739 | −0.573563 | ||||||||
\(497\) | −39.4837 | −1.77109 | ||||||||
\(498\) | −6.06770 | −0.271900 | ||||||||
\(499\) | 15.0317 | 0.672913 | 0.336456 | − | 0.941699i | \(-0.390772\pi\) | ||||
0.336456 | + | 0.941699i | \(0.390772\pi\) | |||||||
\(500\) | 1.38963 | 0.0621463 | ||||||||
\(501\) | −13.4101 | −0.599118 | ||||||||
\(502\) | 46.6493 | 2.08206 | ||||||||
\(503\) | −4.69369 | −0.209281 | −0.104641 | − | 0.994510i | \(-0.533369\pi\) | ||||
−0.104641 | + | 0.994510i | \(0.533369\pi\) | |||||||
\(504\) | 10.4284 | 0.464518 | ||||||||
\(505\) | 10.7730 | 0.479394 | ||||||||
\(506\) | 7.37374 | 0.327803 | ||||||||
\(507\) | 0.839160 | 0.0372684 | ||||||||
\(508\) | −4.09821 | −0.181829 | ||||||||
\(509\) | 2.29316 | 0.101643 | 0.0508214 | − | 0.998708i | \(-0.483816\pi\) | ||||
0.0508214 | + | 0.998708i | \(0.483816\pi\) | |||||||
\(510\) | 6.63373 | 0.293746 | ||||||||
\(511\) | −28.3002 | −1.25193 | ||||||||
\(512\) | −17.0018 | −0.751381 | ||||||||
\(513\) | −1.56002 | −0.0688767 | ||||||||
\(514\) | −15.0807 | −0.665179 | ||||||||
\(515\) | −1.37802 | −0.0607229 | ||||||||
\(516\) | −1.33908 | −0.0589496 | ||||||||
\(517\) | 3.46571 | 0.152422 | ||||||||
\(518\) | 55.7470 | 2.44938 | ||||||||
\(519\) | 9.03817 | 0.396732 | ||||||||
\(520\) | −5.21316 | −0.228612 | ||||||||
\(521\) | 6.53621 | 0.286356 | 0.143178 | − | 0.989697i | \(-0.454268\pi\) | ||||
0.143178 | + | 0.989697i | \(0.454268\pi\) | |||||||
\(522\) | 9.44943 | 0.413590 | ||||||||
\(523\) | 28.4759 | 1.24516 | 0.622582 | − | 0.782554i | \(-0.286084\pi\) | ||||
0.622582 | + | 0.782554i | \(0.286084\pi\) | |||||||
\(524\) | 4.22265 | 0.184467 | ||||||||
\(525\) | −18.5865 | −0.811181 | ||||||||
\(526\) | 29.7560 | 1.29742 | ||||||||
\(527\) | 22.3132 | 0.971977 | ||||||||
\(528\) | 4.44053 | 0.193249 | ||||||||
\(529\) | 1.14362 | 0.0497224 | ||||||||
\(530\) | −9.25824 | −0.402152 | ||||||||
\(531\) | 0.418492 | 0.0181610 | ||||||||
\(532\) | −1.56304 | −0.0677663 | ||||||||
\(533\) | −5.52445 | −0.239290 | ||||||||
\(534\) | 20.1706 | 0.872866 | ||||||||
\(535\) | −6.12858 | −0.264962 | ||||||||
\(536\) | −25.8215 | −1.11532 | ||||||||
\(537\) | 26.1042 | 1.12648 | ||||||||
\(538\) | −17.6401 | −0.760519 | ||||||||
\(539\) | 8.80489 | 0.379253 | ||||||||
\(540\) | 0.143628 | 0.00618077 | ||||||||
\(541\) | −22.4670 | −0.965931 | −0.482965 | − | 0.875640i | \(-0.660440\pi\) | ||||
−0.482965 | + | 0.875640i | \(0.660440\pi\) | |||||||
\(542\) | −28.5252 | −1.22526 | ||||||||
\(543\) | −3.16435 | −0.135795 | ||||||||
\(544\) | −10.9951 | −0.471412 | ||||||||
\(545\) | 8.33342 | 0.356965 | ||||||||
\(546\) | −20.8048 | −0.890364 | ||||||||
\(547\) | −21.9796 | −0.939779 | −0.469889 | − | 0.882725i | \(-0.655706\pi\) | ||||
−0.469889 | + | 0.882725i | \(0.655706\pi\) | |||||||
\(548\) | 5.47023 | 0.233677 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −7.01598 | −0.299162 | ||||||||
\(551\) | 9.82314 | 0.418480 | ||||||||
\(552\) | 12.8891 | 0.548597 | ||||||||
\(553\) | 52.1868 | 2.21921 | ||||||||
\(554\) | −41.6342 | −1.76887 | ||||||||
\(555\) | −5.32521 | −0.226042 | ||||||||
\(556\) | 2.48665 | 0.105458 | ||||||||
\(557\) | −0.280608 | −0.0118897 | −0.00594487 | − | 0.999982i | \(-0.501892\pi\) | ||||
−0.00594487 | + | 0.999982i | \(0.501892\pi\) | |||||||
\(558\) | 4.31692 | 0.182750 | ||||||||
\(559\) | −18.5287 | −0.783681 | ||||||||
\(560\) | −10.0607 | −0.425142 | ||||||||
\(561\) | −7.75664 | −0.327486 | ||||||||
\(562\) | −40.4720 | −1.70721 | ||||||||
\(563\) | 5.01496 | 0.211355 | 0.105678 | − | 0.994400i | \(-0.466299\pi\) | ||||
0.105678 | + | 0.994400i | \(0.466299\pi\) | |||||||
\(564\) | −0.873443 | −0.0367786 | ||||||||
\(565\) | 5.06501 | 0.213087 | ||||||||
\(566\) | 45.3771 | 1.90734 | ||||||||
\(567\) | −3.97554 | −0.166957 | ||||||||
\(568\) | −26.0522 | −1.09313 | ||||||||
\(569\) | −0.592920 | −0.0248565 | −0.0124282 | − | 0.999923i | \(-0.503956\pi\) | ||||
−0.0124282 | + | 0.999923i | \(0.503956\pi\) | |||||||
\(570\) | 1.33418 | 0.0558827 | ||||||||
\(571\) | 0.318940 | 0.0133472 | 0.00667360 | − | 0.999978i | \(-0.497876\pi\) | ||||
0.00667360 | + | 0.999978i | \(0.497876\pi\) | |||||||
\(572\) | −0.878869 | −0.0367474 | ||||||||
\(573\) | 0.339788 | 0.0141948 | ||||||||
\(574\) | −9.45125 | −0.394488 | ||||||||
\(575\) | −22.9722 | −0.958008 | ||||||||
\(576\) | 6.75385 | 0.281410 | ||||||||
\(577\) | 36.7863 | 1.53143 | 0.765716 | − | 0.643179i | \(-0.222385\pi\) | ||||
0.765716 | + | 0.643179i | \(0.222385\pi\) | |||||||
\(578\) | 64.7774 | 2.69439 | ||||||||
\(579\) | 10.9988 | 0.457097 | ||||||||
\(580\) | −0.904396 | −0.0375530 | ||||||||
\(581\) | −16.0743 | −0.666876 | ||||||||
\(582\) | 2.67005 | 0.110677 | ||||||||
\(583\) | 10.8254 | 0.448343 | ||||||||
\(584\) | −18.6731 | −0.772698 | ||||||||
\(585\) | 1.98737 | 0.0821677 | ||||||||
\(586\) | 10.4977 | 0.433657 | ||||||||
\(587\) | 35.9317 | 1.48306 | 0.741530 | − | 0.670920i | \(-0.234101\pi\) | ||||
0.741530 | + | 0.670920i | \(0.234101\pi\) | |||||||
\(588\) | −2.21905 | −0.0915119 | ||||||||
\(589\) | 4.48765 | 0.184910 | ||||||||
\(590\) | −0.357908 | −0.0147348 | ||||||||
\(591\) | −13.6647 | −0.562092 | ||||||||
\(592\) | 41.4929 | 1.70535 | ||||||||
\(593\) | 5.63179 | 0.231270 | 0.115635 | − | 0.993292i | \(-0.463110\pi\) | ||||
0.115635 | + | 0.993292i | \(0.463110\pi\) | |||||||
\(594\) | −1.50067 | −0.0615734 | ||||||||
\(595\) | 17.5739 | 0.720458 | ||||||||
\(596\) | 4.27008 | 0.174909 | ||||||||
\(597\) | 5.05352 | 0.206827 | ||||||||
\(598\) | −25.7140 | −1.05152 | ||||||||
\(599\) | −25.5479 | −1.04386 | −0.521929 | − | 0.852989i | \(-0.674787\pi\) | ||||
−0.521929 | + | 0.852989i | \(0.674787\pi\) | |||||||
\(600\) | −12.2638 | −0.500666 | ||||||||
\(601\) | 39.1627 | 1.59748 | 0.798741 | − | 0.601675i | \(-0.205500\pi\) | ||||
0.798741 | + | 0.601675i | \(0.205500\pi\) | |||||||
\(602\) | −31.6990 | −1.29195 | ||||||||
\(603\) | 9.84375 | 0.400868 | ||||||||
\(604\) | 4.16807 | 0.169597 | ||||||||
\(605\) | −0.569898 | −0.0231697 | ||||||||
\(606\) | 28.3679 | 1.15237 | ||||||||
\(607\) | 8.19398 | 0.332583 | 0.166292 | − | 0.986077i | \(-0.446821\pi\) | ||||
0.166292 | + | 0.986077i | \(0.446821\pi\) | |||||||
\(608\) | −2.21135 | −0.0896820 | ||||||||
\(609\) | 25.0331 | 1.01439 | ||||||||
\(610\) | 0.855232 | 0.0346273 | ||||||||
\(611\) | −12.0858 | −0.488938 | ||||||||
\(612\) | 1.95486 | 0.0790207 | ||||||||
\(613\) | 29.6138 | 1.19609 | 0.598046 | − | 0.801462i | \(-0.295944\pi\) | ||||
0.598046 | + | 0.801462i | \(0.295944\pi\) | |||||||
\(614\) | 11.7084 | 0.472511 | ||||||||
\(615\) | 0.902827 | 0.0364055 | ||||||||
\(616\) | 10.4284 | 0.420172 | ||||||||
\(617\) | 24.1413 | 0.971894 | 0.485947 | − | 0.873988i | \(-0.338475\pi\) | ||||
0.485947 | + | 0.873988i | \(0.338475\pi\) | |||||||
\(618\) | −3.62865 | −0.145966 | ||||||||
\(619\) | −15.2803 | −0.614168 | −0.307084 | − | 0.951682i | \(-0.599353\pi\) | ||||
−0.307084 | + | 0.951682i | \(0.599353\pi\) | |||||||
\(620\) | −0.413168 | −0.0165932 | ||||||||
\(621\) | −4.91362 | −0.197177 | ||||||||
\(622\) | −2.05365 | −0.0823440 | ||||||||
\(623\) | 53.4352 | 2.14084 | ||||||||
\(624\) | −15.4852 | −0.619904 | ||||||||
\(625\) | 20.2337 | 0.809349 | ||||||||
\(626\) | −7.72075 | −0.308583 | ||||||||
\(627\) | −1.56002 | −0.0623014 | ||||||||
\(628\) | 4.50635 | 0.179823 | ||||||||
\(629\) | −72.4791 | −2.88993 | ||||||||
\(630\) | 3.40001 | 0.135459 | ||||||||
\(631\) | −25.2273 | −1.00428 | −0.502142 | − | 0.864785i | \(-0.667454\pi\) | ||||
−0.502142 | + | 0.864785i | \(0.667454\pi\) | |||||||
\(632\) | 34.4339 | 1.36971 | ||||||||
\(633\) | −0.418379 | −0.0166291 | ||||||||
\(634\) | 45.6080 | 1.81132 | ||||||||
\(635\) | 9.26722 | 0.367758 | ||||||||
\(636\) | −2.72827 | −0.108183 | ||||||||
\(637\) | −30.7048 | −1.21657 | ||||||||
\(638\) | 9.44943 | 0.374106 | ||||||||
\(639\) | 9.93167 | 0.392891 | ||||||||
\(640\) | −7.39177 | −0.292186 | ||||||||
\(641\) | −11.1758 | −0.441417 | −0.220709 | − | 0.975340i | \(-0.570837\pi\) | ||||
−0.220709 | + | 0.975340i | \(0.570837\pi\) | |||||||
\(642\) | −16.1380 | −0.636916 | ||||||||
\(643\) | 33.0083 | 1.30172 | 0.650861 | − | 0.759197i | \(-0.274408\pi\) | ||||
0.650861 | + | 0.759197i | \(0.274408\pi\) | |||||||
\(644\) | −4.92311 | −0.193998 | ||||||||
\(645\) | 3.02803 | 0.119229 | ||||||||
\(646\) | 18.1590 | 0.714456 | ||||||||
\(647\) | −10.2919 | −0.404616 | −0.202308 | − | 0.979322i | \(-0.564844\pi\) | ||||
−0.202308 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(648\) | −2.62314 | −0.103047 | ||||||||
\(649\) | 0.418492 | 0.0164273 | ||||||||
\(650\) | 24.4664 | 0.959651 | ||||||||
\(651\) | 11.4362 | 0.448221 | ||||||||
\(652\) | −0.215485 | −0.00843905 | ||||||||
\(653\) | −8.56890 | −0.335327 | −0.167664 | − | 0.985844i | \(-0.553622\pi\) | ||||
−0.167664 | + | 0.985844i | \(0.553622\pi\) | |||||||
\(654\) | 21.9438 | 0.858072 | ||||||||
\(655\) | −9.54861 | −0.373095 | ||||||||
\(656\) | −7.03464 | −0.274657 | ||||||||
\(657\) | 7.11859 | 0.277723 | ||||||||
\(658\) | −20.6764 | −0.806049 | ||||||||
\(659\) | 0.185337 | 0.00721972 | 0.00360986 | − | 0.999993i | \(-0.498851\pi\) | ||||
0.00360986 | + | 0.999993i | \(0.498851\pi\) | |||||||
\(660\) | 0.143628 | 0.00559072 | ||||||||
\(661\) | 6.58896 | 0.256281 | 0.128141 | − | 0.991756i | \(-0.459099\pi\) | ||||
0.128141 | + | 0.991756i | \(0.459099\pi\) | |||||||
\(662\) | 26.1017 | 1.01447 | ||||||||
\(663\) | 27.0493 | 1.05051 | ||||||||
\(664\) | −10.6062 | −0.411600 | ||||||||
\(665\) | 3.53447 | 0.137061 | ||||||||
\(666\) | −14.0225 | −0.543361 | ||||||||
\(667\) | 30.9400 | 1.19800 | ||||||||
\(668\) | 3.37967 | 0.130763 | ||||||||
\(669\) | −8.46953 | −0.327451 | ||||||||
\(670\) | −8.41868 | −0.325242 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −5.63536 | −0.217389 | ||||||||
\(673\) | 32.8732 | 1.26717 | 0.633584 | − | 0.773674i | \(-0.281583\pi\) | ||||
0.633584 | + | 0.773674i | \(0.281583\pi\) | |||||||
\(674\) | 5.07559 | 0.195505 | ||||||||
\(675\) | 4.67522 | 0.179949 | ||||||||
\(676\) | −0.211489 | −0.00813418 | ||||||||
\(677\) | −49.0282 | −1.88431 | −0.942154 | − | 0.335181i | \(-0.891203\pi\) | ||||
−0.942154 | + | 0.335181i | \(0.891203\pi\) | |||||||
\(678\) | 13.3373 | 0.512218 | ||||||||
\(679\) | 7.07339 | 0.271452 | ||||||||
\(680\) | 11.5956 | 0.444671 | ||||||||
\(681\) | 1.28958 | 0.0494170 | ||||||||
\(682\) | 4.31692 | 0.165303 | ||||||||
\(683\) | −24.9821 | −0.955912 | −0.477956 | − | 0.878384i | \(-0.658622\pi\) | ||||
−0.477956 | + | 0.878384i | \(0.658622\pi\) | |||||||
\(684\) | 0.393164 | 0.0150330 | ||||||||
\(685\) | −12.3697 | −0.472623 | ||||||||
\(686\) | −10.7680 | −0.411122 | ||||||||
\(687\) | −18.0318 | −0.687955 | ||||||||
\(688\) | −23.5938 | −0.899506 | ||||||||
\(689\) | −37.7508 | −1.43819 | ||||||||
\(690\) | 4.20228 | 0.159978 | ||||||||
\(691\) | 8.91705 | 0.339221 | 0.169610 | − | 0.985511i | \(-0.445749\pi\) | ||||
0.169610 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(692\) | −2.27784 | −0.0865905 | ||||||||
\(693\) | −3.97554 | −0.151018 | ||||||||
\(694\) | 33.0469 | 1.25444 | ||||||||
\(695\) | −5.62303 | −0.213294 | ||||||||
\(696\) | 16.5174 | 0.626089 | ||||||||
\(697\) | 12.2880 | 0.465441 | ||||||||
\(698\) | −9.23392 | −0.349509 | ||||||||
\(699\) | −15.1799 | −0.574158 | ||||||||
\(700\) | 4.68425 | 0.177048 | ||||||||
\(701\) | −19.3770 | −0.731861 | −0.365930 | − | 0.930642i | \(-0.619249\pi\) | ||||
−0.365930 | + | 0.930642i | \(0.619249\pi\) | |||||||
\(702\) | 5.23321 | 0.197515 | ||||||||
\(703\) | −14.5771 | −0.549785 | ||||||||
\(704\) | 6.75385 | 0.254545 | ||||||||
\(705\) | 1.97510 | 0.0743866 | ||||||||
\(706\) | −4.22513 | −0.159015 | ||||||||
\(707\) | 75.1514 | 2.82636 | ||||||||
\(708\) | −0.105470 | −0.00396382 | ||||||||
\(709\) | −31.7098 | −1.19089 | −0.595444 | − | 0.803397i | \(-0.703024\pi\) | ||||
−0.595444 | + | 0.803397i | \(0.703024\pi\) | |||||||
\(710\) | −8.49388 | −0.318770 | ||||||||
\(711\) | −13.1270 | −0.492300 | ||||||||
\(712\) | 35.2577 | 1.32134 | ||||||||
\(713\) | 14.1348 | 0.529351 | ||||||||
\(714\) | 46.2760 | 1.73184 | ||||||||
\(715\) | 1.98737 | 0.0743235 | ||||||||
\(716\) | −6.57889 | −0.245865 | ||||||||
\(717\) | −5.61796 | −0.209807 | ||||||||
\(718\) | −29.0305 | −1.08341 | ||||||||
\(719\) | −29.9033 | −1.11521 | −0.557603 | − | 0.830108i | \(-0.688279\pi\) | ||||
−0.557603 | + | 0.830108i | \(0.688279\pi\) | |||||||
\(720\) | 2.53065 | 0.0943118 | ||||||||
\(721\) | −9.61291 | −0.358003 | ||||||||
\(722\) | −24.8607 | −0.925218 | ||||||||
\(723\) | 9.85967 | 0.366685 | ||||||||
\(724\) | 0.797492 | 0.0296386 | ||||||||
\(725\) | −29.4388 | −1.09333 | ||||||||
\(726\) | −1.50067 | −0.0556953 | ||||||||
\(727\) | −11.3206 | −0.419859 | −0.209930 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209930 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(728\) | −36.3663 | −1.34783 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.08805 | −0.225329 | ||||||||
\(731\) | 41.2133 | 1.52433 | ||||||||
\(732\) | 0.252024 | 0.00931509 | ||||||||
\(733\) | 46.5548 | 1.71954 | 0.859771 | − | 0.510680i | \(-0.170606\pi\) | ||||
0.859771 | + | 0.510680i | \(0.170606\pi\) | |||||||
\(734\) | 14.2351 | 0.525426 | ||||||||
\(735\) | 5.01789 | 0.185088 | ||||||||
\(736\) | −6.96509 | −0.256737 | ||||||||
\(737\) | 9.84375 | 0.362599 | ||||||||
\(738\) | 2.37735 | 0.0875116 | ||||||||
\(739\) | 3.40428 | 0.125229 | 0.0626143 | − | 0.998038i | \(-0.480056\pi\) | ||||
0.0626143 | + | 0.998038i | \(0.480056\pi\) | |||||||
\(740\) | 1.34208 | 0.0493359 | ||||||||
\(741\) | 5.44018 | 0.199850 | ||||||||
\(742\) | −64.5843 | −2.37096 | ||||||||
\(743\) | 3.46368 | 0.127070 | 0.0635350 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635350 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(744\) | 7.54587 | 0.276645 | ||||||||
\(745\) | −9.65585 | −0.353763 | ||||||||
\(746\) | −42.2284 | −1.54609 | ||||||||
\(747\) | 4.04331 | 0.147937 | ||||||||
\(748\) | 1.95486 | 0.0714769 | ||||||||
\(749\) | −42.7522 | −1.56213 | ||||||||
\(750\) | −8.27455 | −0.302144 | ||||||||
\(751\) | −1.89930 | −0.0693065 | −0.0346532 | − | 0.999399i | \(-0.511033\pi\) | ||||
−0.0346532 | + | 0.999399i | \(0.511033\pi\) | |||||||
\(752\) | −15.3896 | −0.561201 | ||||||||
\(753\) | −31.0856 | −1.13282 | ||||||||
\(754\) | −32.9524 | −1.20006 | ||||||||
\(755\) | −9.42519 | −0.343018 | ||||||||
\(756\) | 1.00193 | 0.0364399 | ||||||||
\(757\) | 8.67210 | 0.315193 | 0.157596 | − | 0.987504i | \(-0.449626\pi\) | ||||
0.157596 | + | 0.987504i | \(0.449626\pi\) | |||||||
\(758\) | −43.0271 | −1.56281 | ||||||||
\(759\) | −4.91362 | −0.178353 | ||||||||
\(760\) | 2.33212 | 0.0845948 | ||||||||
\(761\) | 37.5110 | 1.35977 | 0.679887 | − | 0.733317i | \(-0.262029\pi\) | ||||
0.679887 | + | 0.733317i | \(0.262029\pi\) | |||||||
\(762\) | 24.4027 | 0.884018 | ||||||||
\(763\) | 58.1329 | 2.10455 | ||||||||
\(764\) | −0.0856348 | −0.00309816 | ||||||||
\(765\) | −4.42050 | −0.159823 | ||||||||
\(766\) | −53.9443 | −1.94909 | ||||||||
\(767\) | −1.45938 | −0.0526953 | ||||||||
\(768\) | −5.95657 | −0.214939 | ||||||||
\(769\) | −30.1552 | −1.08743 | −0.543713 | − | 0.839271i | \(-0.682982\pi\) | ||||
−0.543713 | + | 0.839271i | \(0.682982\pi\) | |||||||
\(770\) | 3.40001 | 0.122528 | ||||||||
\(771\) | 10.0493 | 0.361915 | ||||||||
\(772\) | −2.77198 | −0.0997656 | ||||||||
\(773\) | −23.2997 | −0.838031 | −0.419015 | − | 0.907979i | \(-0.637625\pi\) | ||||
−0.419015 | + | 0.907979i | \(0.637625\pi\) | |||||||
\(774\) | 7.97351 | 0.286602 | ||||||||
\(775\) | −13.4490 | −0.483101 | ||||||||
\(776\) | 4.66717 | 0.167542 | ||||||||
\(777\) | −37.1480 | −1.33268 | ||||||||
\(778\) | −54.8908 | −1.96793 | ||||||||
\(779\) | 2.47137 | 0.0885461 | ||||||||
\(780\) | −0.500866 | −0.0179339 | ||||||||
\(781\) | 9.93167 | 0.355383 | ||||||||
\(782\) | 57.1955 | 2.04531 | ||||||||
\(783\) | −6.29679 | −0.225029 | ||||||||
\(784\) | −39.0984 | −1.39637 | ||||||||
\(785\) | −10.1901 | −0.363702 | ||||||||
\(786\) | −25.1437 | −0.896847 | ||||||||
\(787\) | 51.3754 | 1.83134 | 0.915668 | − | 0.401936i | \(-0.131663\pi\) | ||||
0.915668 | + | 0.401936i | \(0.131663\pi\) | |||||||
\(788\) | 3.44384 | 0.122682 | ||||||||
\(789\) | −19.8284 | −0.705911 | ||||||||
\(790\) | 11.2266 | 0.399425 | ||||||||
\(791\) | 35.3329 | 1.25629 | ||||||||
\(792\) | −2.62314 | −0.0932093 | ||||||||
\(793\) | 3.48724 | 0.123836 | ||||||||
\(794\) | 26.1553 | 0.928217 | ||||||||
\(795\) | 6.16938 | 0.218806 | ||||||||
\(796\) | −1.27361 | −0.0451419 | ||||||||
\(797\) | 17.7177 | 0.627593 | 0.313796 | − | 0.949490i | \(-0.398399\pi\) | ||||
0.313796 | + | 0.949490i | \(0.398399\pi\) | |||||||
\(798\) | 9.30708 | 0.329467 | ||||||||
\(799\) | 26.8823 | 0.951027 | ||||||||
\(800\) | 6.62716 | 0.234305 | ||||||||
\(801\) | −13.4410 | −0.474914 | ||||||||
\(802\) | −42.5915 | −1.50396 | ||||||||
\(803\) | 7.11859 | 0.251210 | ||||||||
\(804\) | −2.48086 | −0.0874933 | ||||||||
\(805\) | 11.1325 | 0.392370 | ||||||||
\(806\) | −15.0541 | −0.530259 | ||||||||
\(807\) | 11.7548 | 0.413788 | ||||||||
\(808\) | 49.5864 | 1.74445 | ||||||||
\(809\) | 16.0592 | 0.564612 | 0.282306 | − | 0.959324i | \(-0.408901\pi\) | ||||
0.282306 | + | 0.959324i | \(0.408901\pi\) | |||||||
\(810\) | −0.855232 | −0.0300498 | ||||||||
\(811\) | −12.0185 | −0.422028 | −0.211014 | − | 0.977483i | \(-0.567677\pi\) | ||||
−0.211014 | + | 0.977483i | \(0.567677\pi\) | |||||||
\(812\) | −6.30895 | −0.221401 | ||||||||
\(813\) | 19.0082 | 0.666648 | ||||||||
\(814\) | −14.0225 | −0.491489 | ||||||||
\(815\) | 0.487273 | 0.0170684 | ||||||||
\(816\) | 34.4436 | 1.20577 | ||||||||
\(817\) | 8.28885 | 0.289990 | ||||||||
\(818\) | 41.5107 | 1.45139 | ||||||||
\(819\) | 13.8636 | 0.484435 | ||||||||
\(820\) | −0.227534 | −0.00794584 | ||||||||
\(821\) | −12.6542 | −0.441636 | −0.220818 | − | 0.975315i | \(-0.570873\pi\) | ||||
−0.220818 | + | 0.975315i | \(0.570873\pi\) | |||||||
\(822\) | −32.5724 | −1.13609 | ||||||||
\(823\) | −0.0537888 | −0.00187496 | −0.000937480 | − | 1.00000i | \(-0.500298\pi\) | ||||
−0.000937480 | 1.00000i | \(0.500298\pi\) | ||||||||
\(824\) | −6.34280 | −0.220962 | ||||||||
\(825\) | 4.67522 | 0.162770 | ||||||||
\(826\) | −2.49672 | −0.0868720 | ||||||||
\(827\) | −31.9496 | −1.11100 | −0.555498 | − | 0.831518i | \(-0.687472\pi\) | ||||
−0.555498 | + | 0.831518i | \(0.687472\pi\) | |||||||
\(828\) | 1.23835 | 0.0430357 | ||||||||
\(829\) | 35.7815 | 1.24274 | 0.621372 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621372 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(830\) | −3.45797 | −0.120028 | ||||||||
\(831\) | 27.7437 | 0.962417 | ||||||||
\(832\) | −23.5523 | −0.816528 | ||||||||
\(833\) | 68.2964 | 2.36633 | ||||||||
\(834\) | −14.8067 | −0.512716 | ||||||||
\(835\) | −7.64238 | −0.264476 | ||||||||
\(836\) | 0.393164 | 0.0135979 | ||||||||
\(837\) | −2.87665 | −0.0994316 | ||||||||
\(838\) | −1.71371 | −0.0591990 | ||||||||
\(839\) | 6.85181 | 0.236551 | 0.118275 | − | 0.992981i | \(-0.462263\pi\) | ||||
0.118275 | + | 0.992981i | \(0.462263\pi\) | |||||||
\(840\) | 5.94313 | 0.205057 | ||||||||
\(841\) | 10.6495 | 0.367224 | ||||||||
\(842\) | 7.87107 | 0.271255 | ||||||||
\(843\) | 26.9692 | 0.928869 | ||||||||
\(844\) | 0.105442 | 0.00362945 | ||||||||
\(845\) | 0.478236 | 0.0164518 | ||||||||
\(846\) | 5.20090 | 0.178811 | ||||||||
\(847\) | −3.97554 | −0.136601 | ||||||||
\(848\) | −48.0706 | −1.65075 | ||||||||
\(849\) | −30.2378 | −1.03776 | ||||||||
\(850\) | −54.4204 | −1.86661 | ||||||||
\(851\) | −45.9135 | −1.57389 | ||||||||
\(852\) | −2.50302 | −0.0857521 | ||||||||
\(853\) | −42.9971 | −1.47219 | −0.736096 | − | 0.676877i | \(-0.763333\pi\) | ||||
−0.736096 | + | 0.676877i | \(0.763333\pi\) | |||||||
\(854\) | 5.96599 | 0.204152 | ||||||||
\(855\) | −0.889055 | −0.0304050 | ||||||||
\(856\) | −28.2088 | −0.964157 | ||||||||
\(857\) | −3.32058 | −0.113429 | −0.0567145 | − | 0.998390i | \(-0.518062\pi\) | ||||
−0.0567145 | + | 0.998390i | \(0.518062\pi\) | |||||||
\(858\) | 5.23321 | 0.178659 | ||||||||
\(859\) | 46.4438 | 1.58464 | 0.792321 | − | 0.610105i | \(-0.208873\pi\) | ||||
0.792321 | + | 0.610105i | \(0.208873\pi\) | |||||||
\(860\) | −0.763138 | −0.0260228 | ||||||||
\(861\) | 6.29800 | 0.214635 | ||||||||
\(862\) | 59.6574 | 2.03194 | ||||||||
\(863\) | 11.1536 | 0.379672 | 0.189836 | − | 0.981816i | \(-0.439204\pi\) | ||||
0.189836 | + | 0.981816i | \(0.439204\pi\) | |||||||
\(864\) | 1.41751 | 0.0482246 | ||||||||
\(865\) | 5.15084 | 0.175134 | ||||||||
\(866\) | −33.6679 | −1.14408 | ||||||||
\(867\) | −43.1655 | −1.46598 | ||||||||
\(868\) | −2.88221 | −0.0978286 | ||||||||
\(869\) | −13.1270 | −0.445302 | ||||||||
\(870\) | 5.38521 | 0.182576 | ||||||||
\(871\) | −34.3275 | −1.16314 | ||||||||
\(872\) | 38.3573 | 1.29894 | ||||||||
\(873\) | −1.77923 | −0.0602178 | ||||||||
\(874\) | 11.5032 | 0.389102 | ||||||||
\(875\) | −21.9207 | −0.741054 | ||||||||
\(876\) | −1.79406 | −0.0606156 | ||||||||
\(877\) | −29.0494 | −0.980929 | −0.490464 | − | 0.871461i | \(-0.663173\pi\) | ||||
−0.490464 | + | 0.871461i | \(0.663173\pi\) | |||||||
\(878\) | −8.20810 | −0.277010 | ||||||||
\(879\) | −6.99534 | −0.235947 | ||||||||
\(880\) | 2.53065 | 0.0853082 | ||||||||
\(881\) | −21.4381 | −0.722269 | −0.361134 | − | 0.932514i | \(-0.617610\pi\) | ||||
−0.361134 | + | 0.932514i | \(0.617610\pi\) | |||||||
\(882\) | 13.2133 | 0.444914 | ||||||||
\(883\) | −35.2149 | −1.18508 | −0.592538 | − | 0.805542i | \(-0.701874\pi\) | ||||
−0.592538 | + | 0.805542i | \(0.701874\pi\) | |||||||
\(884\) | −6.81708 | −0.229283 | ||||||||
\(885\) | 0.238498 | 0.00801703 | ||||||||
\(886\) | −6.32525 | −0.212501 | ||||||||
\(887\) | 41.4951 | 1.39327 | 0.696635 | − | 0.717426i | \(-0.254680\pi\) | ||||
0.696635 | + | 0.717426i | \(0.254680\pi\) | |||||||
\(888\) | −24.5110 | −0.822535 | ||||||||
\(889\) | 64.6469 | 2.16819 | ||||||||
\(890\) | 11.4952 | 0.385319 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 2.13453 | 0.0714693 | ||||||||
\(893\) | 5.40659 | 0.180925 | ||||||||
\(894\) | −25.4261 | −0.850376 | ||||||||
\(895\) | 14.8767 | 0.497274 | ||||||||
\(896\) | −51.5641 | −1.72263 | ||||||||
\(897\) | 17.1350 | 0.572119 | ||||||||
\(898\) | 35.8027 | 1.19475 | ||||||||
\(899\) | 18.1137 | 0.604124 | ||||||||
\(900\) | −1.17827 | −0.0392756 | ||||||||
\(901\) | 83.9689 | 2.79741 | ||||||||
\(902\) | 2.37735 | 0.0791572 | ||||||||
\(903\) | 21.1232 | 0.702935 | ||||||||
\(904\) | 23.3134 | 0.775391 | ||||||||
\(905\) | −1.80336 | −0.0599456 | ||||||||
\(906\) | −24.8187 | −0.824547 | ||||||||
\(907\) | −21.7745 | −0.723009 | −0.361505 | − | 0.932370i | \(-0.617737\pi\) | ||||
−0.361505 | + | 0.932370i | \(0.617737\pi\) | |||||||
\(908\) | −0.325007 | −0.0107857 | ||||||||
\(909\) | −18.9035 | −0.626988 | ||||||||
\(910\) | −11.8566 | −0.393044 | ||||||||
\(911\) | 26.9675 | 0.893472 | 0.446736 | − | 0.894666i | \(-0.352586\pi\) | ||||
0.446736 | + | 0.894666i | \(0.352586\pi\) | |||||||
\(912\) | 6.92734 | 0.229387 | ||||||||
\(913\) | 4.04331 | 0.133814 | ||||||||
\(914\) | 53.7108 | 1.77660 | ||||||||
\(915\) | −0.569898 | −0.0188403 | ||||||||
\(916\) | 4.54445 | 0.150153 | ||||||||
\(917\) | −66.6099 | −2.19965 | ||||||||
\(918\) | −11.6402 | −0.384184 | ||||||||
\(919\) | 25.4015 | 0.837917 | 0.418958 | − | 0.908005i | \(-0.362395\pi\) | ||||
0.418958 | + | 0.908005i | \(0.362395\pi\) | |||||||
\(920\) | 7.34548 | 0.242173 | ||||||||
\(921\) | −7.80207 | −0.257087 | ||||||||
\(922\) | 49.6285 | 1.63443 | ||||||||
\(923\) | −34.6341 | −1.14000 | ||||||||
\(924\) | 1.00193 | 0.0329611 | ||||||||
\(925\) | 43.6859 | 1.43638 | ||||||||
\(926\) | −45.2730 | −1.48776 | ||||||||
\(927\) | 2.41802 | 0.0794181 | ||||||||
\(928\) | −8.92575 | −0.293002 | ||||||||
\(929\) | −29.0759 | −0.953949 | −0.476975 | − | 0.878917i | \(-0.658267\pi\) | ||||
−0.476975 | + | 0.878917i | \(0.658267\pi\) | |||||||
\(930\) | 2.46020 | 0.0806733 | ||||||||
\(931\) | 13.7358 | 0.450174 | ||||||||
\(932\) | 3.82571 | 0.125315 | ||||||||
\(933\) | 1.36849 | 0.0448022 | ||||||||
\(934\) | 19.9652 | 0.653280 | ||||||||
\(935\) | −4.42050 | −0.144566 | ||||||||
\(936\) | 9.14753 | 0.298996 | ||||||||
\(937\) | −21.2285 | −0.693506 | −0.346753 | − | 0.937957i | \(-0.612716\pi\) | ||||
−0.346753 | + | 0.937957i | \(0.612716\pi\) | |||||||
\(938\) | −58.7277 | −1.91753 | ||||||||
\(939\) | 5.14485 | 0.167896 | ||||||||
\(940\) | −0.497774 | −0.0162356 | ||||||||
\(941\) | 53.6582 | 1.74921 | 0.874604 | − | 0.484839i | \(-0.161122\pi\) | ||||
0.874604 | + | 0.484839i | \(0.161122\pi\) | |||||||
\(942\) | −26.8330 | −0.874266 | ||||||||
\(943\) | 7.78410 | 0.253485 | ||||||||
\(944\) | −1.85833 | −0.0604835 | ||||||||
\(945\) | −2.26565 | −0.0737016 | ||||||||
\(946\) | 7.97351 | 0.259241 | ||||||||
\(947\) | 42.9691 | 1.39631 | 0.698154 | − | 0.715947i | \(-0.254005\pi\) | ||||
0.698154 | + | 0.715947i | \(0.254005\pi\) | |||||||
\(948\) | 3.30832 | 0.107449 | ||||||||
\(949\) | −24.8242 | −0.805829 | ||||||||
\(950\) | −10.9451 | −0.355106 | ||||||||
\(951\) | −30.3916 | −0.985516 | ||||||||
\(952\) | 80.8894 | 2.62164 | ||||||||
\(953\) | 20.7043 | 0.670678 | 0.335339 | − | 0.942098i | \(-0.391149\pi\) | ||||
0.335339 | + | 0.942098i | \(0.391149\pi\) | |||||||
\(954\) | 16.2454 | 0.525965 | ||||||||
\(955\) | 0.193644 | 0.00626619 | ||||||||
\(956\) | 1.41586 | 0.0457923 | ||||||||
\(957\) | −6.29679 | −0.203546 | ||||||||
\(958\) | 54.3816 | 1.75699 | ||||||||
\(959\) | −86.2896 | −2.78644 | ||||||||
\(960\) | 3.84900 | 0.124226 | ||||||||
\(961\) | −22.7249 | −0.733060 | ||||||||
\(962\) | 48.8998 | 1.57659 | ||||||||
\(963\) | 10.7538 | 0.346537 | ||||||||
\(964\) | −2.48488 | −0.0800325 | ||||||||
\(965\) | 6.26822 | 0.201781 | ||||||||
\(966\) | 29.3146 | 0.943181 | ||||||||
\(967\) | −28.9634 | −0.931401 | −0.465701 | − | 0.884942i | \(-0.654198\pi\) | ||||
−0.465701 | + | 0.884942i | \(0.654198\pi\) | |||||||
\(968\) | −2.62314 | −0.0843110 | ||||||||
\(969\) | −12.1006 | −0.388726 | ||||||||
\(970\) | 1.52165 | 0.0488574 | ||||||||
\(971\) | 41.1027 | 1.31905 | 0.659524 | − | 0.751684i | \(-0.270758\pi\) | ||||
0.659524 | + | 0.751684i | \(0.270758\pi\) | |||||||
\(972\) | −0.252024 | −0.00808368 | ||||||||
\(973\) | −39.2255 | −1.25751 | ||||||||
\(974\) | 7.41556 | 0.237610 | ||||||||
\(975\) | −16.3036 | −0.522133 | ||||||||
\(976\) | 4.44053 | 0.142138 | ||||||||
\(977\) | 0.544347 | 0.0174152 | 0.00870761 | − | 0.999962i | \(-0.497228\pi\) | ||||
0.00870761 | + | 0.999962i | \(0.497228\pi\) | |||||||
\(978\) | 1.28310 | 0.0410291 | ||||||||
\(979\) | −13.4410 | −0.429576 | ||||||||
\(980\) | −1.26463 | −0.0403971 | ||||||||
\(981\) | −14.6227 | −0.466865 | ||||||||
\(982\) | −21.0320 | −0.671158 | ||||||||
\(983\) | 19.5398 | 0.623224 | 0.311612 | − | 0.950209i | \(-0.399131\pi\) | ||||
0.311612 | + | 0.950209i | \(0.399131\pi\) | |||||||
\(984\) | 4.15555 | 0.132474 | ||||||||
\(985\) | −7.78750 | −0.248130 | ||||||||
\(986\) | 73.2958 | 2.33422 | ||||||||
\(987\) | 13.7781 | 0.438560 | ||||||||
\(988\) | −1.37106 | −0.0436191 | ||||||||
\(989\) | 26.1074 | 0.830169 | ||||||||
\(990\) | −0.855232 | −0.0271811 | ||||||||
\(991\) | −45.5206 | −1.44601 | −0.723004 | − | 0.690843i | \(-0.757239\pi\) | ||||
−0.723004 | + | 0.690843i | \(0.757239\pi\) | |||||||
\(992\) | −4.07768 | −0.129466 | ||||||||
\(993\) | −17.3933 | −0.551961 | ||||||||
\(994\) | −59.2522 | −1.87937 | ||||||||
\(995\) | 2.87999 | 0.0913020 | ||||||||
\(996\) | −1.01901 | −0.0322887 | ||||||||
\(997\) | 8.42755 | 0.266903 | 0.133452 | − | 0.991055i | \(-0.457394\pi\) | ||||
0.133452 | + | 0.991055i | \(0.457394\pi\) | |||||||
\(998\) | 22.5577 | 0.714052 | ||||||||
\(999\) | 9.34414 | 0.295635 |
(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 | 2013.2.a.e.1.9 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.5 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.9 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.5 | 13 | 3.2 | odd | 2 |