Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.62622704.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 5x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.52648\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52648 | 1.07939 | 0.539694 | − | 0.841862i | \(-0.318540\pi\) | ||||
0.539694 | + | 0.841862i | \(0.318540\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.330154 | 0.165077 | ||||||||
\(5\) | −0.362203 | −0.161982 | −0.0809909 | − | 0.996715i | \(-0.525808\pi\) | ||||
−0.0809909 | + | 0.996715i | \(0.525808\pi\) | |||||||
\(6\) | −1.52648 | −0.623185 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.54899 | −0.901205 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.552896 | −0.174841 | ||||||||
\(11\) | −1.14818 | −0.346189 | −0.173095 | − | 0.984905i | \(-0.555377\pi\) | ||||
−0.173095 | + | 0.984905i | \(0.555377\pi\) | |||||||
\(12\) | −0.330154 | −0.0953071 | ||||||||
\(13\) | 3.55853 | 0.986959 | 0.493480 | − | 0.869757i | \(-0.335725\pi\) | ||||
0.493480 | + | 0.869757i | \(0.335725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.362203 | 0.0935203 | ||||||||
\(16\) | −4.55131 | −1.13783 | ||||||||
\(17\) | 4.81035 | 1.16668 | 0.583340 | − | 0.812228i | \(-0.301745\pi\) | ||||
0.583340 | + | 0.812228i | \(0.301745\pi\) | |||||||
\(18\) | 1.52648 | 0.359796 | ||||||||
\(19\) | −4.61068 | −1.05776 | −0.528882 | − | 0.848696i | \(-0.677388\pi\) | ||||
−0.528882 | + | 0.848696i | \(0.677388\pi\) | |||||||
\(20\) | −0.119582 | −0.0267395 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.75268 | −0.373672 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.54899 | 0.520311 | ||||||||
\(25\) | −4.86881 | −0.973762 | ||||||||
\(26\) | 5.43204 | 1.06531 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.29122 | 0.239773 | 0.119887 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119887 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(30\) | 0.552896 | 0.100945 | ||||||||
\(31\) | 9.28398 | 1.66745 | 0.833726 | − | 0.552178i | \(-0.186203\pi\) | ||||
0.833726 | + | 0.552178i | \(0.186203\pi\) | |||||||
\(32\) | −1.84951 | −0.326950 | ||||||||
\(33\) | 1.14818 | 0.199872 | ||||||||
\(34\) | 7.34292 | 1.25930 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.330154 | 0.0550256 | ||||||||
\(37\) | −9.08983 | −1.49436 | −0.747180 | − | 0.664622i | \(-0.768593\pi\) | ||||
−0.747180 | + | 0.664622i | \(0.768593\pi\) | |||||||
\(38\) | −7.03813 | −1.14174 | ||||||||
\(39\) | −3.55853 | −0.569821 | ||||||||
\(40\) | 0.923252 | 0.145979 | ||||||||
\(41\) | 6.09893 | 0.952493 | 0.476247 | − | 0.879312i | \(-0.341997\pi\) | ||||
0.476247 | + | 0.879312i | \(0.341997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.31350 | 0.962800 | 0.481400 | − | 0.876501i | \(-0.340128\pi\) | ||||
0.481400 | + | 0.876501i | \(0.340128\pi\) | |||||||
\(44\) | −0.379076 | −0.0571478 | ||||||||
\(45\) | −0.362203 | −0.0539940 | ||||||||
\(46\) | −1.52648 | −0.225068 | ||||||||
\(47\) | 0.0368774 | 0.00537912 | 0.00268956 | − | 0.999996i | \(-0.499144\pi\) | ||||
0.00268956 | + | 0.999996i | \(0.499144\pi\) | |||||||
\(48\) | 4.55131 | 0.656924 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.43216 | −1.05107 | ||||||||
\(51\) | −4.81035 | −0.673583 | ||||||||
\(52\) | 1.17486 | 0.162924 | ||||||||
\(53\) | 8.82952 | 1.21283 | 0.606414 | − | 0.795149i | \(-0.292607\pi\) | ||||
0.606414 | + | 0.795149i | \(0.292607\pi\) | |||||||
\(54\) | −1.52648 | −0.207728 | ||||||||
\(55\) | 0.415874 | 0.0560764 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.61068 | 0.610700 | ||||||||
\(58\) | 1.97102 | 0.258808 | ||||||||
\(59\) | 3.94636 | 0.513772 | 0.256886 | − | 0.966442i | \(-0.417304\pi\) | ||||
0.256886 | + | 0.966442i | \(0.417304\pi\) | |||||||
\(60\) | 0.119582 | 0.0154380 | ||||||||
\(61\) | −2.77141 | −0.354843 | −0.177422 | − | 0.984135i | \(-0.556776\pi\) | ||||
−0.177422 | + | 0.984135i | \(0.556776\pi\) | |||||||
\(62\) | 14.1718 | 1.79983 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.27937 | 0.784921 | ||||||||
\(65\) | −1.28891 | −0.159870 | ||||||||
\(66\) | 1.75268 | 0.215740 | ||||||||
\(67\) | 11.7895 | 1.44032 | 0.720161 | − | 0.693807i | \(-0.244068\pi\) | ||||
0.720161 | + | 0.693807i | \(0.244068\pi\) | |||||||
\(68\) | 1.58815 | 0.192592 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.56084 | −1.13466 | −0.567332 | − | 0.823489i | \(-0.692024\pi\) | ||||
−0.567332 | + | 0.823489i | \(0.692024\pi\) | |||||||
\(72\) | −2.54899 | −0.300402 | ||||||||
\(73\) | −0.157279 | −0.0184081 | −0.00920405 | − | 0.999958i | \(-0.502930\pi\) | ||||
−0.00920405 | + | 0.999958i | \(0.502930\pi\) | |||||||
\(74\) | −13.8755 | −1.61299 | ||||||||
\(75\) | 4.86881 | 0.562202 | ||||||||
\(76\) | −1.52223 | −0.174612 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.43204 | −0.615058 | ||||||||
\(79\) | 8.32568 | 0.936712 | 0.468356 | − | 0.883540i | \(-0.344847\pi\) | ||||
0.468356 | + | 0.883540i | \(0.344847\pi\) | |||||||
\(80\) | 1.64849 | 0.184307 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.30993 | 1.02811 | ||||||||
\(83\) | 16.3582 | 1.79554 | 0.897772 | − | 0.440460i | \(-0.145185\pi\) | ||||
0.897772 | + | 0.440460i | \(0.145185\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.74232 | −0.188981 | ||||||||
\(86\) | 9.63746 | 1.03923 | ||||||||
\(87\) | −1.29122 | −0.138433 | ||||||||
\(88\) | 2.92670 | 0.311988 | ||||||||
\(89\) | 1.02159 | 0.108289 | 0.0541444 | − | 0.998533i | \(-0.482757\pi\) | ||||
0.0541444 | + | 0.998533i | \(0.482757\pi\) | |||||||
\(90\) | −0.552896 | −0.0582804 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.330154 | −0.0344209 | ||||||||
\(93\) | −9.28398 | −0.962704 | ||||||||
\(94\) | 0.0562928 | 0.00580616 | ||||||||
\(95\) | 1.67000 | 0.171338 | ||||||||
\(96\) | 1.84951 | 0.188765 | ||||||||
\(97\) | 7.41172 | 0.752546 | 0.376273 | − | 0.926509i | \(-0.377205\pi\) | ||||
0.376273 | + | 0.926509i | \(0.377205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.14818 | −0.115396 | ||||||||
\(100\) | −1.60746 | −0.160746 | ||||||||
\(101\) | −0.484421 | −0.0482017 | −0.0241009 | − | 0.999710i | \(-0.507672\pi\) | ||||
−0.0241009 | + | 0.999710i | \(0.507672\pi\) | |||||||
\(102\) | −7.34292 | −0.727057 | ||||||||
\(103\) | 15.3646 | 1.51392 | 0.756961 | − | 0.653460i | \(-0.226683\pi\) | ||||
0.756961 | + | 0.653460i | \(0.226683\pi\) | |||||||
\(104\) | −9.07068 | −0.889453 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4781 | 1.30911 | ||||||||
\(107\) | 7.81576 | 0.755578 | 0.377789 | − | 0.925892i | \(-0.376684\pi\) | ||||
0.377789 | + | 0.925892i | \(0.376684\pi\) | |||||||
\(108\) | −0.330154 | −0.0317690 | ||||||||
\(109\) | −5.14991 | −0.493272 | −0.246636 | − | 0.969108i | \(-0.579325\pi\) | ||||
−0.246636 | + | 0.969108i | \(0.579325\pi\) | |||||||
\(110\) | 0.634825 | 0.0605281 | ||||||||
\(111\) | 9.08983 | 0.862769 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.04584 | −0.850961 | −0.425480 | − | 0.904968i | \(-0.639895\pi\) | ||||
−0.425480 | + | 0.904968i | \(0.639895\pi\) | |||||||
\(114\) | 7.03813 | 0.659182 | ||||||||
\(115\) | 0.362203 | 0.0337756 | ||||||||
\(116\) | 0.426300 | 0.0395810 | ||||||||
\(117\) | 3.55853 | 0.328986 | ||||||||
\(118\) | 6.02405 | 0.554559 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.923252 | −0.0842810 | ||||||||
\(121\) | −9.68168 | −0.880153 | ||||||||
\(122\) | −4.23052 | −0.383013 | ||||||||
\(123\) | −6.09893 | −0.549922 | ||||||||
\(124\) | 3.06514 | 0.275258 | ||||||||
\(125\) | 3.57451 | 0.319714 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3531 | 1.36237 | 0.681186 | − | 0.732111i | \(-0.261465\pi\) | ||||
0.681186 | + | 0.732111i | \(0.261465\pi\) | |||||||
\(128\) | 13.2844 | 1.17418 | ||||||||
\(129\) | −6.31350 | −0.555873 | ||||||||
\(130\) | −1.96750 | −0.172561 | ||||||||
\(131\) | −11.3557 | −0.992151 | −0.496075 | − | 0.868280i | \(-0.665226\pi\) | ||||
−0.496075 | + | 0.868280i | \(0.665226\pi\) | |||||||
\(132\) | 0.379076 | 0.0329943 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.9966 | 1.55467 | ||||||||
\(135\) | 0.362203 | 0.0311734 | ||||||||
\(136\) | −12.2615 | −1.05142 | ||||||||
\(137\) | −9.72371 | −0.830753 | −0.415376 | − | 0.909650i | \(-0.636350\pi\) | ||||
−0.415376 | + | 0.909650i | \(0.636350\pi\) | |||||||
\(138\) | 1.52648 | 0.129943 | ||||||||
\(139\) | 18.5445 | 1.57293 | 0.786463 | − | 0.617638i | \(-0.211910\pi\) | ||||
0.786463 | + | 0.617638i | \(0.211910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0368774 | −0.00310564 | ||||||||
\(142\) | −14.5945 | −1.22474 | ||||||||
\(143\) | −4.08584 | −0.341675 | ||||||||
\(144\) | −4.55131 | −0.379275 | ||||||||
\(145\) | −0.467682 | −0.0388389 | ||||||||
\(146\) | −0.240084 | −0.0198695 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00104 | −0.246684 | ||||||||
\(149\) | 15.5066 | 1.27035 | 0.635175 | − | 0.772368i | \(-0.280928\pi\) | ||||
0.635175 | + | 0.772368i | \(0.280928\pi\) | |||||||
\(150\) | 7.43216 | 0.606833 | ||||||||
\(151\) | 17.6314 | 1.43482 | 0.717411 | − | 0.696651i | \(-0.245327\pi\) | ||||
0.717411 | + | 0.696651i | \(0.245327\pi\) | |||||||
\(152\) | 11.7526 | 0.953262 | ||||||||
\(153\) | 4.81035 | 0.388894 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.36268 | −0.270097 | ||||||||
\(156\) | −1.17486 | −0.0940643 | ||||||||
\(157\) | 6.37508 | 0.508786 | 0.254393 | − | 0.967101i | \(-0.418124\pi\) | ||||
0.254393 | + | 0.967101i | \(0.418124\pi\) | |||||||
\(158\) | 12.7090 | 1.01107 | ||||||||
\(159\) | −8.82952 | −0.700227 | ||||||||
\(160\) | 0.669897 | 0.0529600 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.52648 | 0.119932 | ||||||||
\(163\) | 14.3869 | 1.12687 | 0.563435 | − | 0.826160i | \(-0.309480\pi\) | ||||
0.563435 | + | 0.826160i | \(0.309480\pi\) | |||||||
\(164\) | 2.01359 | 0.157235 | ||||||||
\(165\) | −0.415874 | −0.0323757 | ||||||||
\(166\) | 24.9705 | 1.93809 | ||||||||
\(167\) | 2.05019 | 0.158649 | 0.0793243 | − | 0.996849i | \(-0.474724\pi\) | ||||
0.0793243 | + | 0.996849i | \(0.474724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.336843 | −0.0259110 | ||||||||
\(170\) | −2.65962 | −0.203984 | ||||||||
\(171\) | −4.61068 | −0.352588 | ||||||||
\(172\) | 2.08443 | 0.158936 | ||||||||
\(173\) | −18.8742 | −1.43498 | −0.717490 | − | 0.696569i | \(-0.754709\pi\) | ||||
−0.717490 | + | 0.696569i | \(0.754709\pi\) | |||||||
\(174\) | −1.97102 | −0.149423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.22572 | 0.393903 | ||||||||
\(177\) | −3.94636 | −0.296626 | ||||||||
\(178\) | 1.55945 | 0.116886 | ||||||||
\(179\) | 15.4735 | 1.15655 | 0.578274 | − | 0.815843i | \(-0.303727\pi\) | ||||
0.578274 | + | 0.815843i | \(0.303727\pi\) | |||||||
\(180\) | −0.119582 | −0.00891315 | ||||||||
\(181\) | 18.0888 | 1.34453 | 0.672266 | − | 0.740310i | \(-0.265321\pi\) | ||||
0.672266 | + | 0.740310i | \(0.265321\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.77141 | 0.204869 | ||||||||
\(184\) | 2.54899 | 0.187914 | ||||||||
\(185\) | 3.29236 | 0.242059 | ||||||||
\(186\) | −14.1718 | −1.03913 | ||||||||
\(187\) | −5.52314 | −0.403892 | ||||||||
\(188\) | 0.0121752 | 0.000887968 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.54923 | 0.184941 | ||||||||
\(191\) | −11.3386 | −0.820436 | −0.410218 | − | 0.911988i | \(-0.634547\pi\) | ||||
−0.410218 | + | 0.911988i | \(0.634547\pi\) | |||||||
\(192\) | −6.27937 | −0.453174 | ||||||||
\(193\) | −9.25207 | −0.665979 | −0.332989 | − | 0.942931i | \(-0.608057\pi\) | ||||
−0.332989 | + | 0.942931i | \(0.608057\pi\) | |||||||
\(194\) | 11.3139 | 0.812289 | ||||||||
\(195\) | 1.28891 | 0.0923007 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.7108 | −1.19059 | −0.595296 | − | 0.803506i | \(-0.702965\pi\) | ||||
−0.595296 | + | 0.803506i | \(0.702965\pi\) | |||||||
\(198\) | −1.75268 | −0.124557 | ||||||||
\(199\) | −13.4796 | −0.955546 | −0.477773 | − | 0.878483i | \(-0.658556\pi\) | ||||
−0.477773 | + | 0.878483i | \(0.658556\pi\) | |||||||
\(200\) | 12.4106 | 0.877559 | ||||||||
\(201\) | −11.7895 | −0.831570 | ||||||||
\(202\) | −0.739461 | −0.0520283 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.58815 | −0.111193 | ||||||||
\(205\) | −2.20905 | −0.154287 | ||||||||
\(206\) | 23.4539 | 1.63411 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −16.1960 | −1.12299 | ||||||||
\(209\) | 5.29389 | 0.366186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.29341 | 0.157885 | 0.0789426 | − | 0.996879i | \(-0.474846\pi\) | ||||
0.0789426 | + | 0.996879i | \(0.474846\pi\) | |||||||
\(212\) | 2.91510 | 0.200210 | ||||||||
\(213\) | 9.56084 | 0.655098 | ||||||||
\(214\) | 11.9306 | 0.815561 | ||||||||
\(215\) | −2.28677 | −0.155956 | ||||||||
\(216\) | 2.54899 | 0.173437 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.86126 | −0.532432 | ||||||||
\(219\) | 0.157279 | 0.0106279 | ||||||||
\(220\) | 0.137302 | 0.00925691 | ||||||||
\(221\) | 17.1178 | 1.15147 | ||||||||
\(222\) | 13.8755 | 0.931262 | ||||||||
\(223\) | −19.3317 | −1.29454 | −0.647272 | − | 0.762259i | \(-0.724090\pi\) | ||||
−0.647272 | + | 0.762259i | \(0.724090\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.86881 | −0.324587 | ||||||||
\(226\) | −13.8083 | −0.918516 | ||||||||
\(227\) | −4.17014 | −0.276782 | −0.138391 | − | 0.990378i | \(-0.544193\pi\) | ||||
−0.138391 | + | 0.990378i | \(0.544193\pi\) | |||||||
\(228\) | 1.52223 | 0.100812 | ||||||||
\(229\) | −20.4191 | −1.34933 | −0.674667 | − | 0.738123i | \(-0.735713\pi\) | ||||
−0.674667 | + | 0.738123i | \(0.735713\pi\) | |||||||
\(230\) | 0.552896 | 0.0364569 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.29131 | −0.216085 | ||||||||
\(233\) | −6.36384 | −0.416909 | −0.208455 | − | 0.978032i | \(-0.566843\pi\) | ||||
−0.208455 | + | 0.978032i | \(0.566843\pi\) | |||||||
\(234\) | 5.43204 | 0.355104 | ||||||||
\(235\) | −0.0133571 | −0.000871320 0 | ||||||||
\(236\) | 1.30290 | 0.0848118 | ||||||||
\(237\) | −8.32568 | −0.540811 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.437573 | −0.0283043 | −0.0141521 | − | 0.999900i | \(-0.504505\pi\) | ||||
−0.0141521 | + | 0.999900i | \(0.504505\pi\) | |||||||
\(240\) | −1.64849 | −0.106410 | ||||||||
\(241\) | −21.3225 | −1.37350 | −0.686750 | − | 0.726893i | \(-0.740963\pi\) | ||||
−0.686750 | + | 0.726893i | \(0.740963\pi\) | |||||||
\(242\) | −14.7789 | −0.950026 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.914992 | −0.0585764 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.30993 | −0.593579 | ||||||||
\(247\) | −16.4073 | −1.04397 | ||||||||
\(248\) | −23.6648 | −1.50272 | ||||||||
\(249\) | −16.3582 | −1.03666 | ||||||||
\(250\) | 5.45643 | 0.345095 | ||||||||
\(251\) | 19.2965 | 1.21798 | 0.608992 | − | 0.793176i | \(-0.291574\pi\) | ||||
0.608992 | + | 0.793176i | \(0.291574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.14818 | 0.0721855 | ||||||||
\(254\) | 23.4363 | 1.47053 | ||||||||
\(255\) | 1.74232 | 0.109108 | ||||||||
\(256\) | 7.71965 | 0.482478 | ||||||||
\(257\) | 31.7543 | 1.98078 | 0.990389 | − | 0.138307i | \(-0.0441661\pi\) | ||||
0.990389 | + | 0.138307i | \(0.0441661\pi\) | |||||||
\(258\) | −9.63746 | −0.600002 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.425538 | −0.0263908 | ||||||||
\(261\) | 1.29122 | 0.0799244 | ||||||||
\(262\) | −17.3343 | −1.07091 | ||||||||
\(263\) | −12.5428 | −0.773421 | −0.386711 | − | 0.922201i | \(-0.626389\pi\) | ||||
−0.386711 | + | 0.922201i | \(0.626389\pi\) | |||||||
\(264\) | −2.92670 | −0.180126 | ||||||||
\(265\) | −3.19808 | −0.196456 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.02159 | −0.0625206 | ||||||||
\(268\) | 3.89236 | 0.237764 | ||||||||
\(269\) | −8.77914 | −0.535273 | −0.267637 | − | 0.963520i | \(-0.586243\pi\) | ||||
−0.267637 | + | 0.963520i | \(0.586243\pi\) | |||||||
\(270\) | 0.552896 | 0.0336482 | ||||||||
\(271\) | 19.1142 | 1.16110 | 0.580552 | − | 0.814223i | \(-0.302837\pi\) | ||||
0.580552 | + | 0.814223i | \(0.302837\pi\) | |||||||
\(272\) | −21.8934 | −1.32748 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.8431 | −0.896704 | ||||||||
\(275\) | 5.59027 | 0.337106 | ||||||||
\(276\) | 0.330154 | 0.0198729 | ||||||||
\(277\) | −0.388387 | −0.0233359 | −0.0116680 | − | 0.999932i | \(-0.503714\pi\) | ||||
−0.0116680 | + | 0.999932i | \(0.503714\pi\) | |||||||
\(278\) | 28.3079 | 1.69780 | ||||||||
\(279\) | 9.28398 | 0.555817 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.6703 | −1.05412 | −0.527062 | − | 0.849827i | \(-0.676706\pi\) | ||||
−0.527062 | + | 0.849827i | \(0.676706\pi\) | |||||||
\(282\) | −0.0562928 | −0.00335219 | ||||||||
\(283\) | 11.7855 | 0.700576 | 0.350288 | − | 0.936642i | \(-0.386084\pi\) | ||||
0.350288 | + | 0.936642i | \(0.386084\pi\) | |||||||
\(284\) | −3.15655 | −0.187307 | ||||||||
\(285\) | −1.67000 | −0.0989223 | ||||||||
\(286\) | −6.23696 | −0.368799 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.84951 | −0.108983 | ||||||||
\(289\) | 6.13945 | 0.361144 | ||||||||
\(290\) | −0.713910 | −0.0419222 | ||||||||
\(291\) | −7.41172 | −0.434483 | ||||||||
\(292\) | −0.0519262 | −0.00303875 | ||||||||
\(293\) | −6.25525 | −0.365436 | −0.182718 | − | 0.983165i | \(-0.558490\pi\) | ||||
−0.182718 | + | 0.983165i | \(0.558490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.42938 | −0.0832217 | ||||||||
\(296\) | 23.1699 | 1.34672 | ||||||||
\(297\) | 1.14818 | 0.0666242 | ||||||||
\(298\) | 23.6706 | 1.37120 | ||||||||
\(299\) | −3.55853 | −0.205795 | ||||||||
\(300\) | 1.60746 | 0.0928065 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 26.9140 | 1.54873 | ||||||||
\(303\) | 0.484421 | 0.0278293 | ||||||||
\(304\) | 20.9846 | 1.20355 | ||||||||
\(305\) | 1.00381 | 0.0574781 | ||||||||
\(306\) | 7.34292 | 0.419767 | ||||||||
\(307\) | −22.6051 | −1.29014 | −0.645072 | − | 0.764122i | \(-0.723172\pi\) | ||||
−0.645072 | + | 0.764122i | \(0.723172\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3646 | −0.874063 | ||||||||
\(310\) | −5.13308 | −0.291539 | ||||||||
\(311\) | −18.2540 | −1.03509 | −0.517546 | − | 0.855656i | \(-0.673154\pi\) | ||||
−0.517546 | + | 0.855656i | \(0.673154\pi\) | |||||||
\(312\) | 9.07068 | 0.513526 | ||||||||
\(313\) | −3.19524 | −0.180606 | −0.0903029 | − | 0.995914i | \(-0.528784\pi\) | ||||
−0.0903029 | + | 0.995914i | \(0.528784\pi\) | |||||||
\(314\) | 9.73145 | 0.549178 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.74875 | 0.154629 | ||||||||
\(317\) | 28.0472 | 1.57529 | 0.787645 | − | 0.616130i | \(-0.211300\pi\) | ||||
0.787645 | + | 0.616130i | \(0.211300\pi\) | |||||||
\(318\) | −13.4781 | −0.755816 | ||||||||
\(319\) | −1.48255 | −0.0830069 | ||||||||
\(320\) | −2.27440 | −0.127143 | ||||||||
\(321\) | −7.81576 | −0.436233 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.1790 | −1.23407 | ||||||||
\(324\) | 0.330154 | 0.0183419 | ||||||||
\(325\) | −17.3258 | −0.961063 | ||||||||
\(326\) | 21.9614 | 1.21633 | ||||||||
\(327\) | 5.14991 | 0.284791 | ||||||||
\(328\) | −15.5461 | −0.858392 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.634825 | −0.0349459 | ||||||||
\(331\) | −22.1074 | −1.21513 | −0.607567 | − | 0.794269i | \(-0.707854\pi\) | ||||
−0.607567 | + | 0.794269i | \(0.707854\pi\) | |||||||
\(332\) | 5.40072 | 0.296403 | ||||||||
\(333\) | −9.08983 | −0.498120 | ||||||||
\(334\) | 3.12959 | 0.171243 | ||||||||
\(335\) | −4.27020 | −0.233306 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.18599 | 0.336972 | 0.168486 | − | 0.985704i | \(-0.446112\pi\) | ||||
0.168486 | + | 0.985704i | \(0.446112\pi\) | |||||||
\(338\) | −0.514186 | −0.0279680 | ||||||||
\(339\) | 9.04584 | 0.491302 | ||||||||
\(340\) | −0.575233 | −0.0311964 | ||||||||
\(341\) | −10.6597 | −0.577254 | ||||||||
\(342\) | −7.03813 | −0.380579 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −16.0931 | −0.867681 | ||||||||
\(345\) | −0.362203 | −0.0195003 | ||||||||
\(346\) | −28.8112 | −1.54890 | ||||||||
\(347\) | 30.6463 | 1.64518 | 0.822591 | − | 0.568634i | \(-0.192528\pi\) | ||||
0.822591 | + | 0.568634i | \(0.192528\pi\) | |||||||
\(348\) | −0.426300 | −0.0228521 | ||||||||
\(349\) | 14.4898 | 0.775623 | 0.387812 | − | 0.921739i | \(-0.373231\pi\) | ||||
0.387812 | + | 0.921739i | \(0.373231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.55853 | −0.189940 | ||||||||
\(352\) | 2.12357 | 0.113187 | ||||||||
\(353\) | −19.2273 | −1.02337 | −0.511683 | − | 0.859174i | \(-0.670978\pi\) | ||||
−0.511683 | + | 0.859174i | \(0.670978\pi\) | |||||||
\(354\) | −6.02405 | −0.320175 | ||||||||
\(355\) | 3.46296 | 0.183795 | ||||||||
\(356\) | 0.337283 | 0.0178760 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.6201 | 1.24836 | ||||||||
\(359\) | −9.38911 | −0.495538 | −0.247769 | − | 0.968819i | \(-0.579697\pi\) | ||||
−0.247769 | + | 0.968819i | \(0.579697\pi\) | |||||||
\(360\) | 0.923252 | 0.0486597 | ||||||||
\(361\) | 2.25839 | 0.118863 | ||||||||
\(362\) | 27.6123 | 1.45127 | ||||||||
\(363\) | 9.68168 | 0.508157 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0569668 | 0.00298178 | ||||||||
\(366\) | 4.23052 | 0.221133 | ||||||||
\(367\) | 11.5737 | 0.604142 | 0.302071 | − | 0.953285i | \(-0.402322\pi\) | ||||
0.302071 | + | 0.953285i | \(0.402322\pi\) | |||||||
\(368\) | 4.55131 | 0.237253 | ||||||||
\(369\) | 6.09893 | 0.317498 | ||||||||
\(370\) | 5.02574 | 0.261276 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.06514 | −0.158920 | ||||||||
\(373\) | 3.71521 | 0.192366 | 0.0961830 | − | 0.995364i | \(-0.469337\pi\) | ||||
0.0961830 | + | 0.995364i | \(0.469337\pi\) | |||||||
\(374\) | −8.43099 | −0.435956 | ||||||||
\(375\) | −3.57451 | −0.184587 | ||||||||
\(376\) | −0.0940003 | −0.00484769 | ||||||||
\(377\) | 4.59484 | 0.236646 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6927 | 0.754715 | 0.377358 | − | 0.926068i | \(-0.376833\pi\) | ||||
0.377358 | + | 0.926068i | \(0.376833\pi\) | |||||||
\(380\) | 0.551357 | 0.0282840 | ||||||||
\(381\) | −15.3531 | −0.786565 | ||||||||
\(382\) | −17.3083 | −0.885568 | ||||||||
\(383\) | −5.25211 | −0.268370 | −0.134185 | − | 0.990956i | \(-0.542842\pi\) | ||||
−0.134185 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(384\) | −13.2844 | −0.677915 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.1231 | −0.718849 | ||||||||
\(387\) | 6.31350 | 0.320933 | ||||||||
\(388\) | 2.44701 | 0.124228 | ||||||||
\(389\) | −16.2374 | −0.823268 | −0.411634 | − | 0.911349i | \(-0.635042\pi\) | ||||
−0.411634 | + | 0.911349i | \(0.635042\pi\) | |||||||
\(390\) | 1.96750 | 0.0996282 | ||||||||
\(391\) | −4.81035 | −0.243270 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.3557 | 0.572818 | ||||||||
\(394\) | −25.5087 | −1.28511 | ||||||||
\(395\) | −3.01558 | −0.151730 | ||||||||
\(396\) | −0.379076 | −0.0190493 | ||||||||
\(397\) | −8.53398 | −0.428308 | −0.214154 | − | 0.976800i | \(-0.568699\pi\) | ||||
−0.214154 | + | 0.976800i | \(0.568699\pi\) | |||||||
\(398\) | −20.5764 | −1.03140 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.1594 | 1.10797 | ||||||||
\(401\) | −4.19425 | −0.209451 | −0.104725 | − | 0.994501i | \(-0.533396\pi\) | ||||
−0.104725 | + | 0.994501i | \(0.533396\pi\) | |||||||
\(402\) | −17.9966 | −0.897586 | ||||||||
\(403\) | 33.0373 | 1.64571 | ||||||||
\(404\) | −0.159933 | −0.00795698 | ||||||||
\(405\) | −0.362203 | −0.0179980 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4368 | 0.517331 | ||||||||
\(408\) | 12.2615 | 0.607037 | ||||||||
\(409\) | 17.6741 | 0.873929 | 0.436965 | − | 0.899479i | \(-0.356054\pi\) | ||||
0.436965 | + | 0.899479i | \(0.356054\pi\) | |||||||
\(410\) | −3.37208 | −0.166535 | ||||||||
\(411\) | 9.72371 | 0.479635 | ||||||||
\(412\) | 5.07269 | 0.249913 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.52648 | −0.0750226 | ||||||||
\(415\) | −5.92498 | −0.290846 | ||||||||
\(416\) | −6.58154 | −0.322686 | ||||||||
\(417\) | −18.5445 | −0.908129 | ||||||||
\(418\) | 8.08104 | 0.395257 | ||||||||
\(419\) | 17.1268 | 0.836699 | 0.418350 | − | 0.908286i | \(-0.362609\pi\) | ||||
0.418350 | + | 0.908286i | \(0.362609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8574 | 1.60137 | 0.800685 | − | 0.599086i | \(-0.204469\pi\) | ||||
0.800685 | + | 0.599086i | \(0.204469\pi\) | |||||||
\(422\) | 3.50086 | 0.170419 | ||||||||
\(423\) | 0.0368774 | 0.00179304 | ||||||||
\(424\) | −22.5064 | −1.09301 | ||||||||
\(425\) | −23.4207 | −1.13607 | ||||||||
\(426\) | 14.5945 | 0.707104 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.58040 | 0.124728 | ||||||||
\(429\) | 4.08584 | 0.197266 | ||||||||
\(430\) | −3.49071 | −0.168337 | ||||||||
\(431\) | −18.6306 | −0.897405 | −0.448702 | − | 0.893681i | \(-0.648114\pi\) | ||||
−0.448702 | + | 0.893681i | \(0.648114\pi\) | |||||||
\(432\) | 4.55131 | 0.218975 | ||||||||
\(433\) | 18.2241 | 0.875794 | 0.437897 | − | 0.899025i | \(-0.355723\pi\) | ||||
0.437897 | + | 0.899025i | \(0.355723\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.467682 | 0.0224237 | ||||||||
\(436\) | −1.70026 | −0.0814278 | ||||||||
\(437\) | 4.61068 | 0.220559 | ||||||||
\(438\) | 0.240084 | 0.0114716 | ||||||||
\(439\) | 22.4033 | 1.06925 | 0.534626 | − | 0.845089i | \(-0.320452\pi\) | ||||
0.534626 | + | 0.845089i | \(0.320452\pi\) | |||||||
\(440\) | −1.06006 | −0.0505364 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.1300 | 1.24288 | ||||||||
\(443\) | −19.0957 | −0.907263 | −0.453632 | − | 0.891189i | \(-0.649872\pi\) | ||||
−0.453632 | + | 0.891189i | \(0.649872\pi\) | |||||||
\(444\) | 3.00104 | 0.142423 | ||||||||
\(445\) | −0.370024 | −0.0175408 | ||||||||
\(446\) | −29.5095 | −1.39731 | ||||||||
\(447\) | −15.5066 | −0.733437 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4684 | −1.06035 | −0.530174 | − | 0.847889i | \(-0.677873\pi\) | ||||
−0.530174 | + | 0.847889i | \(0.677873\pi\) | |||||||
\(450\) | −7.43216 | −0.350355 | ||||||||
\(451\) | −7.00267 | −0.329743 | ||||||||
\(452\) | −2.98652 | −0.140474 | ||||||||
\(453\) | −17.6314 | −0.828394 | ||||||||
\(454\) | −6.36565 | −0.298755 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.7526 | −0.550366 | ||||||||
\(457\) | −11.5263 | −0.539177 | −0.269588 | − | 0.962976i | \(-0.586888\pi\) | ||||
−0.269588 | + | 0.962976i | \(0.586888\pi\) | |||||||
\(458\) | −31.1695 | −1.45645 | ||||||||
\(459\) | −4.81035 | −0.224528 | ||||||||
\(460\) | 0.119582 | 0.00557556 | ||||||||
\(461\) | −28.3690 | −1.32128 | −0.660638 | − | 0.750705i | \(-0.729714\pi\) | ||||
−0.660638 | + | 0.750705i | \(0.729714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.83032 | −0.224484 | −0.112242 | − | 0.993681i | \(-0.535803\pi\) | ||||
−0.112242 | + | 0.993681i | \(0.535803\pi\) | |||||||
\(464\) | −5.87673 | −0.272820 | ||||||||
\(465\) | 3.36268 | 0.155941 | ||||||||
\(466\) | −9.71430 | −0.450006 | ||||||||
\(467\) | 2.02413 | 0.0936656 | 0.0468328 | − | 0.998903i | \(-0.485087\pi\) | ||||
0.0468328 | + | 0.998903i | \(0.485087\pi\) | |||||||
\(468\) | 1.17486 | 0.0543080 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.0203894 | −0.000940492 0 | ||||||||
\(471\) | −6.37508 | −0.293748 | ||||||||
\(472\) | −10.0592 | −0.463014 | ||||||||
\(473\) | −7.24904 | −0.333311 | ||||||||
\(474\) | −12.7090 | −0.583744 | ||||||||
\(475\) | 22.4485 | 1.03001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.82952 | 0.404276 | ||||||||
\(478\) | −0.667949 | −0.0305513 | ||||||||
\(479\) | 37.4692 | 1.71201 | 0.856007 | − | 0.516964i | \(-0.172938\pi\) | ||||
0.856007 | + | 0.516964i | \(0.172938\pi\) | |||||||
\(480\) | −0.669897 | −0.0305765 | ||||||||
\(481\) | −32.3465 | −1.47487 | ||||||||
\(482\) | −32.5484 | −1.48254 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.19644 | −0.145293 | ||||||||
\(485\) | −2.68454 | −0.121899 | ||||||||
\(486\) | −1.52648 | −0.0692427 | ||||||||
\(487\) | 24.5261 | 1.11138 | 0.555691 | − | 0.831389i | \(-0.312454\pi\) | ||||
0.555691 | + | 0.831389i | \(0.312454\pi\) | |||||||
\(488\) | 7.06431 | 0.319786 | ||||||||
\(489\) | −14.3869 | −0.650599 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.79882 | 0.0811798 | 0.0405899 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405899 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(492\) | −2.01359 | −0.0907794 | ||||||||
\(493\) | 6.21121 | 0.279739 | ||||||||
\(494\) | −25.0454 | −1.12685 | ||||||||
\(495\) | 0.415874 | 0.0186921 | ||||||||
\(496\) | −42.2542 | −1.89727 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −24.9705 | −1.11896 | ||||||||
\(499\) | 7.21026 | 0.322776 | 0.161388 | − | 0.986891i | \(-0.448403\pi\) | ||||
0.161388 | + | 0.986891i | \(0.448403\pi\) | |||||||
\(500\) | 1.18014 | 0.0527773 | ||||||||
\(501\) | −2.05019 | −0.0915958 | ||||||||
\(502\) | 29.4558 | 1.31468 | ||||||||
\(503\) | −33.8658 | −1.51000 | −0.755000 | − | 0.655725i | \(-0.772363\pi\) | ||||
−0.755000 | + | 0.655725i | \(0.772363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.175459 | 0.00780780 | ||||||||
\(506\) | 1.75268 | 0.0779161 | ||||||||
\(507\) | 0.336843 | 0.0149597 | ||||||||
\(508\) | 5.06890 | 0.224896 | ||||||||
\(509\) | 23.4274 | 1.03840 | 0.519200 | − | 0.854653i | \(-0.326230\pi\) | ||||
0.519200 | + | 0.854653i | \(0.326230\pi\) | |||||||
\(510\) | 2.65962 | 0.117770 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.7848 | −0.653403 | ||||||||
\(513\) | 4.61068 | 0.203567 | ||||||||
\(514\) | 48.4724 | 2.13803 | ||||||||
\(515\) | −5.56511 | −0.245228 | ||||||||
\(516\) | −2.08443 | −0.0917617 | ||||||||
\(517\) | −0.0423419 | −0.00186219 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8742 | 0.828486 | ||||||||
\(520\) | 3.28542 | 0.144075 | ||||||||
\(521\) | −7.31051 | −0.320279 | −0.160140 | − | 0.987094i | \(-0.551194\pi\) | ||||
−0.160140 | + | 0.987094i | \(0.551194\pi\) | |||||||
\(522\) | 1.97102 | 0.0862694 | ||||||||
\(523\) | −26.4075 | −1.15472 | −0.577360 | − | 0.816490i | \(-0.695917\pi\) | ||||
−0.577360 | + | 0.816490i | \(0.695917\pi\) | |||||||
\(524\) | −3.74912 | −0.163781 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1464 | −0.834821 | ||||||||
\(527\) | 44.6592 | 1.94538 | ||||||||
\(528\) | −5.22572 | −0.227420 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.88181 | −0.212052 | ||||||||
\(531\) | 3.94636 | 0.171257 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.7033 | 0.940072 | ||||||||
\(534\) | −1.55945 | −0.0674839 | ||||||||
\(535\) | −2.83089 | −0.122390 | ||||||||
\(536\) | −30.0515 | −1.29803 | ||||||||
\(537\) | −15.4735 | −0.667733 | ||||||||
\(538\) | −13.4012 | −0.577767 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.119582 | 0.00514601 | ||||||||
\(541\) | 30.9483 | 1.33057 | 0.665286 | − | 0.746589i | \(-0.268310\pi\) | ||||
0.665286 | + | 0.746589i | \(0.268310\pi\) | |||||||
\(542\) | 29.1775 | 1.25328 | ||||||||
\(543\) | −18.0888 | −0.776265 | ||||||||
\(544\) | −8.89678 | −0.381446 | ||||||||
\(545\) | 1.86531 | 0.0799012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3008 | −0.654215 | −0.327108 | − | 0.944987i | \(-0.606074\pi\) | ||||
−0.327108 | + | 0.944987i | \(0.606074\pi\) | |||||||
\(548\) | −3.21032 | −0.137138 | ||||||||
\(549\) | −2.77141 | −0.118281 | ||||||||
\(550\) | 8.53346 | 0.363868 | ||||||||
\(551\) | −5.95340 | −0.253623 | ||||||||
\(552\) | −2.54899 | −0.108492 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.592866 | −0.0251885 | ||||||||
\(555\) | −3.29236 | −0.139753 | ||||||||
\(556\) | 6.12254 | 0.259653 | ||||||||
\(557\) | 22.9275 | 0.971471 | 0.485735 | − | 0.874106i | \(-0.338552\pi\) | ||||
0.485735 | + | 0.874106i | \(0.338552\pi\) | |||||||
\(558\) | 14.1718 | 0.599942 | ||||||||
\(559\) | 22.4668 | 0.950245 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.52314 | 0.233187 | ||||||||
\(562\) | −26.9735 | −1.13781 | ||||||||
\(563\) | 20.6641 | 0.870887 | 0.435444 | − | 0.900216i | \(-0.356592\pi\) | ||||
0.435444 | + | 0.900216i | \(0.356592\pi\) | |||||||
\(564\) | −0.0121752 | −0.000512669 0 | ||||||||
\(565\) | 3.27643 | 0.137840 | ||||||||
\(566\) | 17.9904 | 0.756193 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.3705 | 1.02256 | ||||||||
\(569\) | −13.1030 | −0.549305 | −0.274653 | − | 0.961544i | \(-0.588563\pi\) | ||||
−0.274653 | + | 0.961544i | \(0.588563\pi\) | |||||||
\(570\) | −2.54923 | −0.106775 | ||||||||
\(571\) | 3.84337 | 0.160840 | 0.0804200 | − | 0.996761i | \(-0.474374\pi\) | ||||
0.0804200 | + | 0.996761i | \(0.474374\pi\) | |||||||
\(572\) | −1.34895 | −0.0564026 | ||||||||
\(573\) | 11.3386 | 0.473679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.86881 | 0.203043 | ||||||||
\(576\) | 6.27937 | 0.261640 | ||||||||
\(577\) | −0.416558 | −0.0173415 | −0.00867077 | − | 0.999962i | \(-0.502760\pi\) | ||||
−0.00867077 | + | 0.999962i | \(0.502760\pi\) | |||||||
\(578\) | 9.37177 | 0.389814 | ||||||||
\(579\) | 9.25207 | 0.384503 | ||||||||
\(580\) | −0.154407 | −0.00641140 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.3139 | −0.468975 | ||||||||
\(583\) | −10.1379 | −0.419868 | ||||||||
\(584\) | 0.400903 | 0.0165895 | ||||||||
\(585\) | −1.28891 | −0.0532899 | ||||||||
\(586\) | −9.54855 | −0.394447 | ||||||||
\(587\) | 14.5968 | 0.602474 | 0.301237 | − | 0.953549i | \(-0.402600\pi\) | ||||
0.301237 | + | 0.953549i | \(0.402600\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.8055 | −1.76377 | ||||||||
\(590\) | −2.18193 | −0.0898285 | ||||||||
\(591\) | 16.7108 | 0.687389 | ||||||||
\(592\) | 41.3706 | 1.70032 | ||||||||
\(593\) | −14.8949 | −0.611658 | −0.305829 | − | 0.952086i | \(-0.598934\pi\) | ||||
−0.305829 | + | 0.952086i | \(0.598934\pi\) | |||||||
\(594\) | 1.75268 | 0.0719133 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.11956 | 0.209705 | ||||||||
\(597\) | 13.4796 | 0.551685 | ||||||||
\(598\) | −5.43204 | −0.222133 | ||||||||
\(599\) | −26.7160 | −1.09159 | −0.545794 | − | 0.837920i | \(-0.683772\pi\) | ||||
−0.545794 | + | 0.837920i | \(0.683772\pi\) | |||||||
\(600\) | −12.4106 | −0.506659 | ||||||||
\(601\) | −1.43227 | −0.0584234 | −0.0292117 | − | 0.999573i | \(-0.509300\pi\) | ||||
−0.0292117 | + | 0.999573i | \(0.509300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7895 | 0.480107 | ||||||||
\(604\) | 5.82106 | 0.236856 | ||||||||
\(605\) | 3.50673 | 0.142569 | ||||||||
\(606\) | 0.739461 | 0.0300386 | ||||||||
\(607\) | 10.1424 | 0.411665 | 0.205833 | − | 0.978587i | \(-0.434010\pi\) | ||||
0.205833 | + | 0.978587i | \(0.434010\pi\) | |||||||
\(608\) | 8.52749 | 0.345836 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.53230 | 0.0620412 | ||||||||
\(611\) | 0.131229 | 0.00530897 | ||||||||
\(612\) | 1.58815 | 0.0641973 | ||||||||
\(613\) | 19.7885 | 0.799250 | 0.399625 | − | 0.916679i | \(-0.369140\pi\) | ||||
0.399625 | + | 0.916679i | \(0.369140\pi\) | |||||||
\(614\) | −34.5064 | −1.39256 | ||||||||
\(615\) | 2.20905 | 0.0890775 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.9335 | 0.601201 | 0.300601 | − | 0.953750i | \(-0.402813\pi\) | ||||
0.300601 | + | 0.953750i | \(0.402813\pi\) | |||||||
\(618\) | −23.4539 | −0.943453 | ||||||||
\(619\) | −13.6719 | −0.549521 | −0.274761 | − | 0.961513i | \(-0.588599\pi\) | ||||
−0.274761 | + | 0.961513i | \(0.588599\pi\) | |||||||
\(620\) | −1.11020 | −0.0445868 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −27.8645 | −1.11726 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 16.1960 | 0.648358 | ||||||||
\(625\) | 23.0494 | 0.921974 | ||||||||
\(626\) | −4.87748 | −0.194943 | ||||||||
\(627\) | −5.29389 | −0.211418 | ||||||||
\(628\) | 2.10475 | 0.0839888 | ||||||||
\(629\) | −43.7253 | −1.74344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7959 | −0.509397 | −0.254698 | − | 0.967021i | \(-0.581976\pi\) | ||||
−0.254698 | + | 0.967021i | \(0.581976\pi\) | |||||||
\(632\) | −21.2221 | −0.844170 | ||||||||
\(633\) | −2.29341 | −0.0911550 | ||||||||
\(634\) | 42.8136 | 1.70035 | ||||||||
\(635\) | −5.56095 | −0.220680 | ||||||||
\(636\) | −2.91510 | −0.115591 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.26309 | −0.0895966 | ||||||||
\(639\) | −9.56084 | −0.378221 | ||||||||
\(640\) | −4.81163 | −0.190196 | ||||||||
\(641\) | −36.4415 | −1.43935 | −0.719677 | − | 0.694309i | \(-0.755710\pi\) | ||||
−0.719677 | + | 0.694309i | \(0.755710\pi\) | |||||||
\(642\) | −11.9306 | −0.470865 | ||||||||
\(643\) | −46.2850 | −1.82530 | −0.912652 | − | 0.408738i | \(-0.865969\pi\) | ||||
−0.912652 | + | 0.408738i | \(0.865969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.28677 | 0.0900414 | ||||||||
\(646\) | −33.8559 | −1.33204 | ||||||||
\(647\) | 2.48710 | 0.0977779 | 0.0488890 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488890 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(648\) | −2.54899 | −0.100134 | ||||||||
\(649\) | −4.53113 | −0.177862 | ||||||||
\(650\) | −26.4476 | −1.03736 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.74989 | 0.186020 | ||||||||
\(653\) | −32.5227 | −1.27271 | −0.636356 | − | 0.771396i | \(-0.719559\pi\) | ||||
−0.636356 | + | 0.771396i | \(0.719559\pi\) | |||||||
\(654\) | 7.86126 | 0.307400 | ||||||||
\(655\) | 4.11306 | 0.160710 | ||||||||
\(656\) | −27.7581 | −1.08377 | ||||||||
\(657\) | −0.157279 | −0.00613603 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.6593 | −0.999545 | −0.499773 | − | 0.866157i | \(-0.666583\pi\) | ||||
−0.499773 | + | 0.866157i | \(0.666583\pi\) | |||||||
\(660\) | −0.137302 | −0.00534448 | ||||||||
\(661\) | −15.8031 | −0.614671 | −0.307335 | − | 0.951601i | \(-0.599437\pi\) | ||||
−0.307335 | + | 0.951601i | \(0.599437\pi\) | |||||||
\(662\) | −33.7466 | −1.31160 | ||||||||
\(663\) | −17.1178 | −0.664800 | ||||||||
\(664\) | −41.6969 | −1.61815 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.8755 | −0.537664 | ||||||||
\(667\) | −1.29122 | −0.0499962 | ||||||||
\(668\) | 0.676878 | 0.0261892 | ||||||||
\(669\) | 19.3317 | 0.747405 | ||||||||
\(670\) | −6.51840 | −0.251828 | ||||||||
\(671\) | 3.18208 | 0.122843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4301 | 1.09590 | 0.547950 | − | 0.836511i | \(-0.315409\pi\) | ||||
0.547950 | + | 0.836511i | \(0.315409\pi\) | |||||||
\(674\) | 9.44281 | 0.363724 | ||||||||
\(675\) | 4.86881 | 0.187401 | ||||||||
\(676\) | −0.111210 | −0.00427731 | ||||||||
\(677\) | 32.7622 | 1.25915 | 0.629577 | − | 0.776938i | \(-0.283228\pi\) | ||||
0.629577 | + | 0.776938i | \(0.283228\pi\) | |||||||
\(678\) | 13.8083 | 0.530306 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.44116 | 0.170311 | ||||||||
\(681\) | 4.17014 | 0.159800 | ||||||||
\(682\) | −16.2718 | −0.623081 | ||||||||
\(683\) | −10.1105 | −0.386868 | −0.193434 | − | 0.981113i | \(-0.561963\pi\) | ||||
−0.193434 | + | 0.981113i | \(0.561963\pi\) | |||||||
\(684\) | −1.52223 | −0.0582041 | ||||||||
\(685\) | 3.52195 | 0.134567 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.4191 | 0.779038 | ||||||||
\(688\) | −28.7347 | −1.09550 | ||||||||
\(689\) | 31.4201 | 1.19701 | ||||||||
\(690\) | −0.552896 | −0.0210484 | ||||||||
\(691\) | −51.3417 | −1.95313 | −0.976565 | − | 0.215223i | \(-0.930952\pi\) | ||||
−0.976565 | + | 0.215223i | \(0.930952\pi\) | |||||||
\(692\) | −6.23139 | −0.236882 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.7811 | 1.77579 | ||||||||
\(695\) | −6.71687 | −0.254785 | ||||||||
\(696\) | 3.29131 | 0.124757 | ||||||||
\(697\) | 29.3380 | 1.11126 | ||||||||
\(698\) | 22.1185 | 0.837198 | ||||||||
\(699\) | 6.36384 | 0.240703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7533 | −0.406145 | −0.203073 | − | 0.979164i | \(-0.565093\pi\) | ||||
−0.203073 | + | 0.979164i | \(0.565093\pi\) | |||||||
\(702\) | −5.43204 | −0.205019 | ||||||||
\(703\) | 41.9103 | 1.58068 | ||||||||
\(704\) | −7.20984 | −0.271731 | ||||||||
\(705\) | 0.0133571 | 0.000503057 0 | ||||||||
\(706\) | −29.3502 | −1.10461 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.30290 | −0.0489661 | ||||||||
\(709\) | 15.5488 | 0.583949 | 0.291975 | − | 0.956426i | \(-0.405688\pi\) | ||||
0.291975 | + | 0.956426i | \(0.405688\pi\) | |||||||
\(710\) | 5.28615 | 0.198386 | ||||||||
\(711\) | 8.32568 | 0.312237 | ||||||||
\(712\) | −2.60404 | −0.0975905 | ||||||||
\(713\) | −9.28398 | −0.347688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.47990 | 0.0553451 | ||||||||
\(716\) | 5.10865 | 0.190919 | ||||||||
\(717\) | 0.437573 | 0.0163415 | ||||||||
\(718\) | −14.3323 | −0.534878 | ||||||||
\(719\) | −27.1655 | −1.01310 | −0.506552 | − | 0.862209i | \(-0.669080\pi\) | ||||
−0.506552 | + | 0.862209i | \(0.669080\pi\) | |||||||
\(720\) | 1.64849 | 0.0614358 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.44740 | 0.128299 | ||||||||
\(723\) | 21.3225 | 0.792991 | ||||||||
\(724\) | 5.97209 | 0.221951 | ||||||||
\(725\) | −6.28669 | −0.233482 | ||||||||
\(726\) | 14.7789 | 0.548498 | ||||||||
\(727\) | 14.8781 | 0.551798 | 0.275899 | − | 0.961187i | \(-0.411024\pi\) | ||||
0.275899 | + | 0.961187i | \(0.411024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.0869589 | 0.00321849 | ||||||||
\(731\) | 30.3701 | 1.12328 | ||||||||
\(732\) | 0.914992 | 0.0338191 | ||||||||
\(733\) | −17.4530 | −0.644642 | −0.322321 | − | 0.946630i | \(-0.604463\pi\) | ||||
−0.322321 | + | 0.946630i | \(0.604463\pi\) | |||||||
\(734\) | 17.6671 | 0.652103 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.84951 | 0.0681738 | ||||||||
\(737\) | −13.5365 | −0.498624 | ||||||||
\(738\) | 9.30993 | 0.342703 | ||||||||
\(739\) | −8.59955 | −0.316340 | −0.158170 | − | 0.987412i | \(-0.550559\pi\) | ||||
−0.158170 | + | 0.987412i | \(0.550559\pi\) | |||||||
\(740\) | 1.08699 | 0.0399584 | ||||||||
\(741\) | 16.4073 | 0.602736 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.61075 | 0.0957790 | 0.0478895 | − | 0.998853i | \(-0.484750\pi\) | ||||
0.0478895 | + | 0.998853i | \(0.484750\pi\) | |||||||
\(744\) | 23.6648 | 0.867594 | ||||||||
\(745\) | −5.61653 | −0.205774 | ||||||||
\(746\) | 5.67120 | 0.207638 | ||||||||
\(747\) | 16.3582 | 0.598515 | ||||||||
\(748\) | −1.82349 | −0.0666733 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.45643 | −0.199241 | ||||||||
\(751\) | 23.1435 | 0.844517 | 0.422259 | − | 0.906475i | \(-0.361237\pi\) | ||||
0.422259 | + | 0.906475i | \(0.361237\pi\) | |||||||
\(752\) | −0.167840 | −0.00612051 | ||||||||
\(753\) | −19.2965 | −0.703204 | ||||||||
\(754\) | 7.01395 | 0.255433 | ||||||||
\(755\) | −6.38613 | −0.232415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.5217 | 1.90893 | 0.954466 | − | 0.298319i | \(-0.0964259\pi\) | ||||
0.954466 | + | 0.298319i | \(0.0964259\pi\) | |||||||
\(758\) | 22.4282 | 0.814630 | ||||||||
\(759\) | −1.14818 | −0.0416763 | ||||||||
\(760\) | −4.25682 | −0.154411 | ||||||||
\(761\) | −50.5578 | −1.83272 | −0.916359 | − | 0.400358i | \(-0.868886\pi\) | ||||
−0.916359 | + | 0.400358i | \(0.868886\pi\) | |||||||
\(762\) | −23.4363 | −0.849009 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.74350 | −0.135435 | ||||||||
\(765\) | −1.74232 | −0.0629937 | ||||||||
\(766\) | −8.01726 | −0.289676 | ||||||||
\(767\) | 14.0432 | 0.507072 | ||||||||
\(768\) | −7.71965 | −0.278559 | ||||||||
\(769\) | 31.1463 | 1.12316 | 0.561581 | − | 0.827421i | \(-0.310193\pi\) | ||||
0.561581 | + | 0.827421i | \(0.310193\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.7543 | −1.14360 | ||||||||
\(772\) | −3.05461 | −0.109938 | ||||||||
\(773\) | 10.3788 | 0.373301 | 0.186650 | − | 0.982426i | \(-0.440237\pi\) | ||||
0.186650 | + | 0.982426i | \(0.440237\pi\) | |||||||
\(774\) | 9.63746 | 0.346411 | ||||||||
\(775\) | −45.2019 | −1.62370 | ||||||||
\(776\) | −18.8924 | −0.678199 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.7861 | −0.888625 | ||||||||
\(779\) | −28.1202 | −1.00751 | ||||||||
\(780\) | 0.425538 | 0.0152367 | ||||||||
\(781\) | 10.9776 | 0.392808 | ||||||||
\(782\) | −7.34292 | −0.262582 | ||||||||
\(783\) | −1.29122 | −0.0461444 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.30907 | −0.0824142 | ||||||||
\(786\) | 17.3343 | 0.618293 | ||||||||
\(787\) | 32.7493 | 1.16739 | 0.583694 | − | 0.811974i | \(-0.301607\pi\) | ||||
0.583694 | + | 0.811974i | \(0.301607\pi\) | |||||||
\(788\) | −5.51712 | −0.196539 | ||||||||
\(789\) | 12.5428 | 0.446535 | ||||||||
\(790\) | −4.60324 | −0.163776 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.92670 | 0.103996 | ||||||||
\(793\) | −9.86216 | −0.350216 | ||||||||
\(794\) | −13.0270 | −0.462310 | ||||||||
\(795\) | 3.19808 | 0.113424 | ||||||||
\(796\) | −4.45035 | −0.157738 | ||||||||
\(797\) | 46.9165 | 1.66187 | 0.830934 | − | 0.556371i | \(-0.187806\pi\) | ||||
0.830934 | + | 0.556371i | \(0.187806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.177393 | 0.00627572 | ||||||||
\(800\) | 9.00490 | 0.318371 | ||||||||
\(801\) | 1.02159 | 0.0360963 | ||||||||
\(802\) | −6.40245 | −0.226078 | ||||||||
\(803\) | 0.180584 | 0.00637269 | ||||||||
\(804\) | −3.89236 | −0.137273 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.4310 | 1.77636 | ||||||||
\(807\) | 8.77914 | 0.309040 | ||||||||
\(808\) | 1.23479 | 0.0434396 | ||||||||
\(809\) | −22.2380 | −0.781846 | −0.390923 | − | 0.920423i | \(-0.627844\pi\) | ||||
−0.390923 | + | 0.920423i | \(0.627844\pi\) | |||||||
\(810\) | −0.552896 | −0.0194268 | ||||||||
\(811\) | −10.3032 | −0.361794 | −0.180897 | − | 0.983502i | \(-0.557900\pi\) | ||||
−0.180897 | + | 0.983502i | \(0.557900\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.1142 | −0.670363 | ||||||||
\(814\) | 15.9316 | 0.558401 | ||||||||
\(815\) | −5.21098 | −0.182533 | ||||||||
\(816\) | 21.8934 | 0.766421 | ||||||||
\(817\) | −29.1096 | −1.01841 | ||||||||
\(818\) | 26.9793 | 0.943308 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.729326 | −0.0254692 | ||||||||
\(821\) | −8.13312 | −0.283848 | −0.141924 | − | 0.989878i | \(-0.545329\pi\) | ||||
−0.141924 | + | 0.989878i | \(0.545329\pi\) | |||||||
\(822\) | 14.8431 | 0.517712 | ||||||||
\(823\) | −31.4034 | −1.09465 | −0.547326 | − | 0.836919i | \(-0.684354\pi\) | ||||
−0.547326 | + | 0.836919i | \(0.684354\pi\) | |||||||
\(824\) | −39.1643 | −1.36435 | ||||||||
\(825\) | −5.59027 | −0.194628 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.1633 | −0.840240 | −0.420120 | − | 0.907468i | \(-0.638012\pi\) | ||||
−0.420120 | + | 0.907468i | \(0.638012\pi\) | |||||||
\(828\) | −0.330154 | −0.0114736 | ||||||||
\(829\) | 41.3530 | 1.43625 | 0.718124 | − | 0.695915i | \(-0.245001\pi\) | ||||
0.718124 | + | 0.695915i | \(0.245001\pi\) | |||||||
\(830\) | −9.04439 | −0.313935 | ||||||||
\(831\) | 0.388387 | 0.0134730 | ||||||||
\(832\) | 22.3453 | 0.774685 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −28.3079 | −0.980223 | ||||||||
\(835\) | −0.742585 | −0.0256982 | ||||||||
\(836\) | 1.74780 | 0.0604489 | ||||||||
\(837\) | −9.28398 | −0.320901 | ||||||||
\(838\) | 26.1438 | 0.903123 | ||||||||
\(839\) | 33.7897 | 1.16655 | 0.583275 | − | 0.812275i | \(-0.301771\pi\) | ||||
0.583275 | + | 0.812275i | \(0.301771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3328 | −0.942509 | ||||||||
\(842\) | 50.1562 | 1.72850 | ||||||||
\(843\) | 17.6703 | 0.608599 | ||||||||
\(844\) | 0.757179 | 0.0260632 | ||||||||
\(845\) | 0.122005 | 0.00419711 | ||||||||
\(846\) | 0.0562928 | 0.00193539 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −40.1859 | −1.37999 | ||||||||
\(849\) | −11.7855 | −0.404478 | ||||||||
\(850\) | −35.7513 | −1.22626 | ||||||||
\(851\) | 9.08983 | 0.311596 | ||||||||
\(852\) | 3.15655 | 0.108142 | ||||||||
\(853\) | 13.6538 | 0.467496 | 0.233748 | − | 0.972297i | \(-0.424901\pi\) | ||||
0.233748 | + | 0.972297i | \(0.424901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.67000 | 0.0571128 | ||||||||
\(856\) | −19.9223 | −0.680931 | ||||||||
\(857\) | 43.3590 | 1.48111 | 0.740557 | − | 0.671993i | \(-0.234562\pi\) | ||||
0.740557 | + | 0.671993i | \(0.234562\pi\) | |||||||
\(858\) | 6.23696 | 0.212926 | ||||||||
\(859\) | 17.3944 | 0.593488 | 0.296744 | − | 0.954957i | \(-0.404099\pi\) | ||||
0.296744 | + | 0.954957i | \(0.404099\pi\) | |||||||
\(860\) | −0.754984 | −0.0257448 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.4393 | −0.968647 | ||||||||
\(863\) | −44.3182 | −1.50861 | −0.754305 | − | 0.656524i | \(-0.772026\pi\) | ||||
−0.754305 | + | 0.656524i | \(0.772026\pi\) | |||||||
\(864\) | 1.84951 | 0.0629215 | ||||||||
\(865\) | 6.83629 | 0.232441 | ||||||||
\(866\) | 27.8188 | 0.945321 | ||||||||
\(867\) | −6.13945 | −0.208507 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.55937 | −0.324280 | ||||||||
\(870\) | 0.713910 | 0.0242038 | ||||||||
\(871\) | 41.9535 | 1.42154 | ||||||||
\(872\) | 13.1271 | 0.444540 | ||||||||
\(873\) | 7.41172 | 0.250849 | ||||||||
\(874\) | 7.03813 | 0.238068 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0519262 | 0.00175442 | ||||||||
\(877\) | 15.1032 | 0.509999 | 0.254999 | − | 0.966941i | \(-0.417925\pi\) | ||||
0.254999 | + | 0.966941i | \(0.417925\pi\) | |||||||
\(878\) | 34.1983 | 1.15414 | ||||||||
\(879\) | 6.25525 | 0.210984 | ||||||||
\(880\) | −1.89277 | −0.0638052 | ||||||||
\(881\) | 28.8598 | 0.972312 | 0.486156 | − | 0.873872i | \(-0.338399\pi\) | ||||
0.486156 | + | 0.873872i | \(0.338399\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3145 | −0.952860 | −0.476430 | − | 0.879212i | \(-0.658069\pi\) | ||||
−0.476430 | + | 0.879212i | \(0.658069\pi\) | |||||||
\(884\) | 5.65150 | 0.190080 | ||||||||
\(885\) | 1.42938 | 0.0480481 | ||||||||
\(886\) | −29.1493 | −0.979289 | ||||||||
\(887\) | 6.73068 | 0.225994 | 0.112997 | − | 0.993595i | \(-0.463955\pi\) | ||||
0.112997 | + | 0.993595i | \(0.463955\pi\) | |||||||
\(888\) | −23.1699 | −0.777532 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.564836 | −0.0189333 | ||||||||
\(891\) | −1.14818 | −0.0384655 | ||||||||
\(892\) | −6.38242 | −0.213699 | ||||||||
\(893\) | −0.170030 | −0.00568984 | ||||||||
\(894\) | −23.6706 | −0.791662 | ||||||||
\(895\) | −5.60456 | −0.187340 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.55853 | 0.118816 | ||||||||
\(898\) | −34.2976 | −1.14453 | ||||||||
\(899\) | 11.9876 | 0.399810 | ||||||||
\(900\) | −1.60746 | −0.0535818 | ||||||||
\(901\) | 42.4731 | 1.41498 | ||||||||
\(902\) | −10.6895 | −0.355920 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.0578 | 0.766890 | ||||||||
\(905\) | −6.55182 | −0.217790 | ||||||||
\(906\) | −26.9140 | −0.894158 | ||||||||
\(907\) | 39.9950 | 1.32801 | 0.664007 | − | 0.747726i | \(-0.268855\pi\) | ||||
0.664007 | + | 0.747726i | \(0.268855\pi\) | |||||||
\(908\) | −1.37679 | −0.0456903 | ||||||||
\(909\) | −0.484421 | −0.0160672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.3937 | 1.43770 | 0.718849 | − | 0.695167i | \(-0.244669\pi\) | ||||
0.718849 | + | 0.695167i | \(0.244669\pi\) | |||||||
\(912\) | −20.9846 | −0.694870 | ||||||||
\(913\) | −18.7821 | −0.621598 | ||||||||
\(914\) | −17.5947 | −0.581981 | ||||||||
\(915\) | −1.00381 | −0.0331850 | ||||||||
\(916\) | −6.74145 | −0.222744 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.34292 | −0.242352 | ||||||||
\(919\) | −13.4176 | −0.442607 | −0.221304 | − | 0.975205i | \(-0.571031\pi\) | ||||
−0.221304 | + | 0.975205i | \(0.571031\pi\) | |||||||
\(920\) | −0.923252 | −0.0304387 | ||||||||
\(921\) | 22.6051 | 0.744865 | ||||||||
\(922\) | −43.3048 | −1.42617 | ||||||||
\(923\) | −34.0226 | −1.11987 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.2567 | 1.45515 | ||||||||
\(926\) | −7.37341 | −0.242305 | ||||||||
\(927\) | 15.3646 | 0.504641 | ||||||||
\(928\) | −2.38812 | −0.0783938 | ||||||||
\(929\) | −44.7540 | −1.46833 | −0.734166 | − | 0.678970i | \(-0.762427\pi\) | ||||
−0.734166 | + | 0.678970i | \(0.762427\pi\) | |||||||
\(930\) | 5.13308 | 0.168320 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.10105 | −0.0688220 | ||||||||
\(933\) | 18.2540 | 0.597610 | ||||||||
\(934\) | 3.08980 | 0.101101 | ||||||||
\(935\) | 2.00050 | 0.0654233 | ||||||||
\(936\) | −9.07068 | −0.296484 | ||||||||
\(937\) | −11.0734 | −0.361753 | −0.180877 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180877 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.19524 | 0.104273 | ||||||||
\(940\) | −0.00440989 | −0.000143835 0 | ||||||||
\(941\) | −18.2486 | −0.594887 | −0.297443 | − | 0.954739i | \(-0.596134\pi\) | ||||
−0.297443 | + | 0.954739i | \(0.596134\pi\) | |||||||
\(942\) | −9.73145 | −0.317068 | ||||||||
\(943\) | −6.09893 | −0.198609 | ||||||||
\(944\) | −17.9611 | −0.584583 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.0655 | −0.359772 | ||||||||
\(947\) | −29.1174 | −0.946187 | −0.473093 | − | 0.881012i | \(-0.656863\pi\) | ||||
−0.473093 | + | 0.881012i | \(0.656863\pi\) | |||||||
\(948\) | −2.74875 | −0.0892753 | ||||||||
\(949\) | −0.559682 | −0.0181680 | ||||||||
\(950\) | 34.2673 | 1.11178 | ||||||||
\(951\) | −28.0472 | −0.909494 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.1747 | −0.880274 | −0.440137 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440137 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(954\) | 13.4781 | 0.436370 | ||||||||
\(955\) | 4.10689 | 0.132896 | ||||||||
\(956\) | −0.144466 | −0.00467238 | ||||||||
\(957\) | 1.48255 | 0.0479241 | ||||||||
\(958\) | 57.1962 | 1.84793 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.27440 | 0.0734060 | ||||||||
\(961\) | 55.1923 | 1.78040 | ||||||||
\(962\) | −49.3764 | −1.59196 | ||||||||
\(963\) | 7.81576 | 0.251859 | ||||||||
\(964\) | −7.03969 | −0.226733 | ||||||||
\(965\) | 3.35112 | 0.107877 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.0093 | −1.44740 | −0.723701 | − | 0.690113i | \(-0.757561\pi\) | ||||
−0.723701 | + | 0.690113i | \(0.757561\pi\) | |||||||
\(968\) | 24.6786 | 0.793199 | ||||||||
\(969\) | 22.1790 | 0.712492 | ||||||||
\(970\) | −4.09791 | −0.131576 | ||||||||
\(971\) | 54.0959 | 1.73602 | 0.868011 | − | 0.496545i | \(-0.165398\pi\) | ||||
0.868011 | + | 0.496545i | \(0.165398\pi\) | |||||||
\(972\) | −0.330154 | −0.0105897 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37.4386 | 1.19961 | ||||||||
\(975\) | 17.3258 | 0.554870 | ||||||||
\(976\) | 12.6135 | 0.403750 | ||||||||
\(977\) | −14.0548 | −0.449654 | −0.224827 | − | 0.974399i | \(-0.572182\pi\) | ||||
−0.224827 | + | 0.974399i | \(0.572182\pi\) | |||||||
\(978\) | −21.9614 | −0.702248 | ||||||||
\(979\) | −1.17297 | −0.0374884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.14991 | −0.164424 | ||||||||
\(982\) | 2.74588 | 0.0876245 | ||||||||
\(983\) | −25.9120 | −0.826465 | −0.413232 | − | 0.910626i | \(-0.635600\pi\) | ||||
−0.413232 | + | 0.910626i | \(0.635600\pi\) | |||||||
\(984\) | 15.5461 | 0.495593 | ||||||||
\(985\) | 6.05268 | 0.192854 | ||||||||
\(986\) | 9.48131 | 0.301946 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.41692 | −0.172335 | ||||||||
\(989\) | −6.31350 | −0.200758 | ||||||||
\(990\) | 0.634825 | 0.0201760 | ||||||||
\(991\) | −12.2782 | −0.390028 | −0.195014 | − | 0.980800i | \(-0.562475\pi\) | ||||
−0.195014 | + | 0.980800i | \(0.562475\pi\) | |||||||
\(992\) | −17.1708 | −0.545173 | ||||||||
\(993\) | 22.1074 | 0.701557 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.88236 | 0.154781 | ||||||||
\(996\) | −5.40072 | −0.171128 | ||||||||
\(997\) | 8.82008 | 0.279335 | 0.139667 | − | 0.990198i | \(-0.455397\pi\) | ||||
0.139667 | + | 0.990198i | \(0.455397\pi\) | |||||||
\(998\) | 11.0064 | 0.348400 | ||||||||
\(999\) | 9.08983 | 0.287590 |
(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 | 3381.2.a.ba.1.5 | ✓ | 6 | |
7.6 | odd | 2 | 3381.2.a.bb.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3381.2.a.ba.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
3381.2.a.bb.1.5 | yes | 6 | 7.6 | odd | 2 |