Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3696,2,Mod(1,3696)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3696, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3696.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3696.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: | \(29.5127085871\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3696.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410 | 0.894427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.46410 | −1.25355 | −0.626775 | − | 0.779200i | \(-0.715626\pi\) | ||||
−0.626775 | + | 0.779200i | \(0.715626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92820 | −1.44463 | −0.722315 | − | 0.691564i | \(-0.756922\pi\) | ||||
−0.722315 | + | 0.691564i | \(0.756922\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.46410 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410 | 0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.92820 | −0.810192 | −0.405096 | − | 0.914274i | \(-0.632762\pi\) | ||||
−0.405096 | + | 0.914274i | \(0.632762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9282 | 1.66654 | 0.833268 | − | 0.552870i | \(-0.186467\pi\) | ||||
0.833268 | + | 0.552870i | \(0.186467\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.46410 | −0.516398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.46410 | −1.38048 | −0.690241 | − | 0.723580i | \(-0.742495\pi\) | ||||
−0.690241 | + | 0.723580i | \(0.742495\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.46410 | −0.485071 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.928203 | −0.127499 | −0.0637493 | − | 0.997966i | \(-0.520306\pi\) | ||||
−0.0637493 | + | 0.997966i | \(0.520306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46410 | 0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.46410 | 0.723738 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.92820 | −0.859338 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9282 | −1.82377 | −0.911885 | − | 0.410445i | \(-0.865373\pi\) | ||||
−0.911885 | + | 0.410445i | \(0.865373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820 | 0.834058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.535898 | −0.0627222 | −0.0313611 | − | 0.999508i | \(-0.509984\pi\) | ||||
−0.0313611 | + | 0.999508i | \(0.509984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.00000 | −0.808290 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9282 | 1.22952 | 0.614759 | − | 0.788715i | \(-0.289253\pi\) | ||||
0.614759 | + | 0.788715i | \(0.289253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.39230 | −0.482118 | −0.241059 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241059 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | −1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.46410 | 0.566601 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.9282 | 1.94199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.8564 | −1.97579 | −0.987893 | − | 0.155136i | \(-0.950418\pi\) | ||||
−0.987893 | + | 0.155136i | \(0.950418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4641 | 1.32666 | 0.663329 | − | 0.748328i | \(-0.269143\pi\) | ||||
0.663329 | + | 0.748328i | \(0.269143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46410 | −0.338062 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | 0.669775 | 0.334887 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334887 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8564 | 1.51877 | 0.759384 | − | 0.650643i | \(-0.225500\pi\) | ||||
0.759384 | + | 0.650643i | \(0.225500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.92820 | 0.467764 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.85641 | 0.739069 | 0.369534 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369534 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.0000 | 2.23801 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.46410 | −0.312348 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9282 | 0.969721 | 0.484861 | − | 0.874591i | \(-0.338870\pi\) | ||||
0.484861 | + | 0.874591i | \(0.338870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9282 | −0.962175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.39230 | 0.383757 | 0.191879 | − | 0.981419i | \(-0.438542\pi\) | ||||
0.191879 | + | 0.981419i | \(0.438542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.46410 | 0.473798 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.46410 | 0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.85641 | 0.671218 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4641 | 1.14201 | 0.571005 | − | 0.820947i | \(-0.306554\pi\) | ||||
0.571005 | + | 0.820947i | \(0.306554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.46410 | 0.797021 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.7846 | 1.72607 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410 | 0.280056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9282 | 1.52035 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.39230 | −0.190927 | −0.0954634 | − | 0.995433i | \(-0.530433\pi\) | ||||
−0.0954634 | + | 0.995433i | \(0.530433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.928203 | 0.0736113 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.46410 | −0.269680 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.46410 | −0.417850 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.928203 | −0.0705700 | −0.0352850 | − | 0.999377i | \(-0.511234\pi\) | ||||
−0.0352850 | + | 0.999377i | \(0.511234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.00000 | −0.529150 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.92820 | 0.520756 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7846 | 1.55351 | 0.776757 | − | 0.629800i | \(-0.216863\pi\) | ||||
0.776757 | + | 0.629800i | \(0.216863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.39230 | 0.475136 | 0.237568 | − | 0.971371i | \(-0.423650\pi\) | ||||
0.237568 | + | 0.971371i | \(0.423650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.0718 | 1.25514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | −0.253320 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.7846 | −1.50392 | −0.751961 | − | 0.659208i | \(-0.770892\pi\) | ||||
−0.751961 | + | 0.659208i | \(0.770892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.0000 | 1.87152 | 0.935760 | − | 0.352636i | \(-0.114715\pi\) | ||||
0.935760 | + | 0.352636i | \(0.114715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.92820 | 0.496139 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.392305 | −0.0278098 | −0.0139049 | − | 0.999903i | \(-0.504426\pi\) | ||||
−0.0139049 | + | 0.999903i | \(0.504426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.9282 | 1.05295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.00000 | 0.421117 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | −0.838116 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.92820 | −0.481543 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.46410 | 0.377960 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7846 | −1.15550 | −0.577750 | − | 0.816214i | \(-0.696069\pi\) | ||||
−0.577750 | + | 0.816214i | \(0.696069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −37.8564 | −2.58179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.46410 | 0.370927 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.535898 | 0.0362127 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.92820 | 0.466041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.39230 | 0.561990 | 0.280995 | − | 0.959709i | \(-0.409336\pi\) | ||||
0.280995 | + | 0.959709i | \(0.409336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.39230 | 0.291528 | 0.145764 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145764 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3205 | −1.40890 | −0.704449 | − | 0.709754i | \(-0.748806\pi\) | ||||
−0.704449 | + | 0.709754i | \(0.748806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.85641 | −0.514690 | −0.257345 | − | 0.966320i | \(-0.582848\pi\) | ||||
−0.257345 | + | 0.966320i | \(0.582848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7846 | 2.13863 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9282 | −0.709863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.60770 | 0.618886 | 0.309443 | − | 0.950918i | \(-0.399857\pi\) | ||||
0.309443 | + | 0.950918i | \(0.399857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.46410 | −0.221313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9282 | −0.695345 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.39230 | 0.278351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.9282 | −1.95217 | −0.976085 | − | 0.217387i | \(-0.930247\pi\) | ||||
−0.976085 | + | 0.217387i | \(0.930247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.92820 | 0.435572 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.0000 | 0.751469 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9282 | 0.806439 | 0.403220 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403220 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.92820 | 0.306224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.07180 | 0.312740 | 0.156370 | − | 0.987699i | \(-0.450021\pi\) | ||||
0.156370 | + | 0.987699i | \(0.450021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.21539 | 0.197520 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.928203 | 0.0568051 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.2487 | 1.47847 | 0.739235 | − | 0.673448i | \(-0.235187\pi\) | ||||
0.739235 | + | 0.673448i | \(0.235187\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.7846 | 1.50556 | 0.752779 | − | 0.658273i | \(-0.228713\pi\) | ||||
0.752779 | + | 0.658273i | \(0.228713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.00000 | −0.422116 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8564 | −0.712382 | −0.356191 | − | 0.934413i | \(-0.615925\pi\) | ||||
−0.356191 | + | 0.934413i | \(0.615925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.46410 | −0.327127 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.85641 | −0.468674 | −0.234337 | − | 0.972155i | \(-0.575292\pi\) | ||||
−0.234337 | + | 0.972155i | \(0.575292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4641 | 0.800358 | 0.400179 | − | 0.916437i | \(-0.368948\pi\) | ||||
0.400179 | + | 0.916437i | \(0.368948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.9282 | −1.12121 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.46410 | −0.204479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.00000 | −0.117242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.9282 | −1.45632 | −0.728161 | − | 0.685407i | \(-0.759625\pi\) | ||||
−0.728161 | + | 0.685407i | \(0.759625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.8564 | −0.801337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9282 | −0.629891 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.8564 | 1.14072 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.92820 | −0.396708 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5359 | −0.601315 | −0.300658 | − | 0.953732i | \(-0.597206\pi\) | ||||
−0.300658 | + | 0.953732i | \(0.597206\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.4641 | −0.765946 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.3923 | −1.60998 | −0.804990 | − | 0.593288i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593288i | \(0.797829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9282 | −0.956839 | −0.478419 | − | 0.878132i | \(-0.658790\pi\) | ||||
−0.478419 | + | 0.878132i | \(0.658790\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.46410 | 0.195180 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.9282 | 0.726120 | 0.363060 | − | 0.931766i | \(-0.381732\pi\) | ||||
0.363060 | + | 0.931766i | \(0.381732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.92820 | −0.386695 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.9282 | −1.05319 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000 | 0.776580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.8564 | −0.876861 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.46410 | 0.521773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.07180 | 0.498631 | 0.249316 | − | 0.968422i | \(-0.419794\pi\) | ||||
0.249316 | + | 0.968422i | \(0.419794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.92820 | −0.270064 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 51.7128 | 2.82537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9282 | 1.14003 | 0.570016 | − | 0.821634i | \(-0.306937\pi\) | ||||
0.570016 | + | 0.821634i | \(0.306937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.85641 | −0.426701 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.46410 | 0.295898 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.0000 | −1.29212 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | 1.11578 | 0.557888 | − | 0.829916i | \(-0.311612\pi\) | ||||
0.557888 | + | 0.829916i | \(0.311612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.7846 | 0.577287 | 0.288643 | − | 0.957437i | \(-0.406796\pi\) | ||||
0.288643 | + | 0.957437i | \(0.406796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −41.5692 | −2.20627 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.46410 | 0.183340 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.07180 | 0.267679 | 0.133840 | − | 0.991003i | \(-0.457269\pi\) | ||||
0.133840 | + | 0.991003i | \(0.457269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8564 | 0.571390 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.85641 | 0.0971688 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.3205 | −1.00852 | −0.504261 | − | 0.863551i | \(-0.668235\pi\) | ||||
−0.504261 | + | 0.863551i | \(0.668235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.46410 | 0.180334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.928203 | 0.0481899 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.7128 | 1.53847 | 0.769236 | − | 0.638965i | \(-0.220637\pi\) | ||||
0.769236 | + | 0.638965i | \(0.220637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.92820 | 0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.8564 | 0.917222 | 0.458611 | − | 0.888637i | \(-0.348347\pi\) | ||||
0.458611 | + | 0.888637i | \(0.348347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9282 | −0.559869 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5359 | −0.742750 | −0.371375 | − | 0.928483i | \(-0.621114\pi\) | ||||
−0.371375 | + | 0.928483i | \(0.621114\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.46410 | −0.176547 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9282 | 0.555512 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.39230 | −0.221562 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −37.8564 | −1.90476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.39230 | −0.120066 | −0.0600332 | − | 0.998196i | \(-0.519121\pi\) | ||||
−0.0600332 | + | 0.998196i | \(0.519121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.46410 | −0.273547 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.14359 | 0.206921 | 0.103461 | − | 0.994634i | \(-0.467008\pi\) | ||||
0.103461 | + | 0.994634i | \(0.467008\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9282 | −0.544373 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.46410 | −0.172133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.92820 | 0.244282 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.32051 | −0.460869 | −0.230435 | − | 0.973088i | \(-0.574015\pi\) | ||||
−0.230435 | + | 0.973088i | \(0.574015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.85641 | −0.387528 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.92820 | 0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.2154 | 0.746894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.4641 | −0.659340 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.7128 | −1.83801 | −0.919005 | − | 0.394246i | \(-0.871006\pi\) | ||||
−0.919005 | + | 0.394246i | \(0.871006\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.46410 | −0.460160 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.2487 | 1.17624 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.9282 | 0.911739 | 0.455870 | − | 0.890047i | \(-0.349328\pi\) | ||||
0.455870 | + | 0.890047i | \(0.349328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.7846 | −0.996546 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.8564 | 1.81092 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7846 | 1.18290 | 0.591452 | − | 0.806340i | \(-0.298555\pi\) | ||||
0.591452 | + | 0.806340i | \(0.298555\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7846 | 0.987507 | 0.493753 | − | 0.869602i | \(-0.335625\pi\) | ||||
0.493753 | + | 0.869602i | \(0.335625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.21539 | 0.152424 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8564 | −0.937082 | −0.468541 | − | 0.883442i | \(-0.655220\pi\) | ||||
−0.468541 | + | 0.883442i | \(0.655220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.46410 | −0.163118 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0000 | −0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.92820 | 0.324799 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8564 | 0.741731 | 0.370866 | − | 0.928687i | \(-0.379061\pi\) | ||||
0.370866 | + | 0.928687i | \(0.379061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.46410 | −0.161690 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.9282 | −0.877774 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.7128 | 0.727102 | 0.363551 | − | 0.931574i | \(-0.381564\pi\) | ||||
0.363551 | + | 0.931574i | \(0.381564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.9282 | 0.689320 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.39230 | 0.110232 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.9282 | −0.502479 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.2487 | −1.75497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.928203 | −0.0424995 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.8564 | 0.633115 | 0.316558 | − | 0.948573i | \(-0.397473\pi\) | ||||
0.316558 | + | 0.948573i | \(0.397473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.85641 | −0.449413 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.92820 | −0.315244 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.92820 | −0.314594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.7846 | −1.84813 | −0.924064 | − | 0.382239i | \(-0.875153\pi\) | ||||
−0.924064 | + | 0.382239i | \(0.875153\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.85641 | 0.0837785 | 0.0418892 | − | 0.999122i | \(-0.486662\pi\) | ||||
0.0418892 | + | 0.999122i | \(0.486662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.7846 | −0.936092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.46410 | 0.155700 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.07180 | 0.406109 | 0.203055 | − | 0.979167i | \(-0.434913\pi\) | ||||
0.203055 | + | 0.979167i | \(0.434913\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.9282 | 0.845650 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9282 | −0.843967 | −0.421983 | − | 0.906604i | \(-0.638666\pi\) | ||||
−0.421983 | + | 0.906604i | \(0.638666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 68.7846 | 3.06087 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.3205 | −1.83150 | −0.915750 | − | 0.401749i | \(-0.868402\pi\) | ||||
−0.915750 | + | 0.401749i | \(0.868402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.535898 | 0.0237067 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.46410 | 0.241246 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −46.6410 | −2.05525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.46410 | 0.416231 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.928203 | 0.0407436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.9282 | 1.61785 | 0.808927 | − | 0.587909i | \(-0.200049\pi\) | ||||
0.808927 | + | 0.587909i | \(0.200049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3923 | −1.06660 | −0.533301 | − | 0.845926i | \(-0.679048\pi\) | ||||
−0.533301 | + | 0.845926i | \(0.679048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.00000 | 0.305505 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.9282 | −0.824525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.92820 | −0.300658 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.92820 | 0.300094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0000 | −1.03761 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.7846 | −0.896922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7128 | −1.10548 | −0.552740 | − | 0.833354i | \(-0.686418\pi\) | ||||
−0.552740 | + | 0.833354i | \(0.686418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.39230 | −0.274320 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −54.9282 | −2.35287 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.7846 | 1.39667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9282 | −0.464714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.0718 | −0.724657 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.7128 | 0.920001 | 0.460001 | − | 0.887919i | \(-0.347849\pi\) | ||||
0.460001 | + | 0.887919i | \(0.347849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8564 | 0.924427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.46410 | 0.146254 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2487 | 0.769091 | 0.384546 | − | 0.923106i | \(-0.374358\pi\) | ||||
0.384546 | + | 0.923106i | \(0.374358\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.2154 | −1.14496 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.8564 | −1.33549 | −0.667745 | − | 0.744390i | \(-0.732740\pi\) | ||||
−0.667745 | + | 0.744390i | \(0.732740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7846 | 0.868290 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.4974 | −2.02248 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.7846 | −1.28158 | −0.640790 | − | 0.767716i | \(-0.721393\pi\) | ||||
−0.640790 | + | 0.767716i | \(0.721393\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.0000 | −1.08052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.39230 | 0.182224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.928203 | 0.0384422 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.92820 | −0.286446 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7846 | 0.857873 | 0.428936 | − | 0.903335i | \(-0.358888\pi\) | ||||
0.428936 | + | 0.903335i | \(0.358888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.8564 | 1.23021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | −0.740421 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5359 | −0.843308 | −0.421654 | − | 0.906757i | \(-0.638550\pi\) | ||||
−0.421654 | + | 0.906757i | \(0.638550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.392305 | 0.0160560 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.85641 | −0.0758507 | −0.0379254 | − | 0.999281i | \(-0.512075\pi\) | ||||
−0.0379254 | + | 0.999281i | \(0.512075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.3923 | 0.750238 | 0.375119 | − | 0.926977i | \(-0.377602\pi\) | ||||
0.375119 | + | 0.926977i | \(0.377602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.9282 | −0.607923 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.46410 | −0.140836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.7128 | 0.800118 | 0.400059 | − | 0.916489i | \(-0.368990\pi\) | ||||
0.400059 | + | 0.916489i | \(0.368990\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.00000 | −0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.9282 | −0.765753 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0000 | −0.888572 | −0.444286 | − | 0.895885i | \(-0.646543\pi\) | ||||
−0.444286 | + | 0.895885i | \(0.646543\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | 0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.8564 | −0.799389 | −0.399694 | − | 0.916648i | \(-0.630884\pi\) | ||||
−0.399694 | + | 0.916648i | \(0.630884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.7128 | 1.27465 | 0.637323 | − | 0.770597i | \(-0.280042\pi\) | ||||
0.637323 | + | 0.770597i | \(0.280042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.92820 | 0.278019 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.928203 | 0.0371877 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.46410 | −0.218215 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.0718 | −0.680697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.784610 | 0.0312348 | 0.0156174 | − | 0.999878i | \(-0.495029\pi\) | ||||
0.0156174 | + | 0.999878i | \(0.495029\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.7846 | 0.667128 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.8564 | −1.50229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.8564 | 1.25825 | 0.629126 | − | 0.777303i | \(-0.283413\pi\) | ||||
0.629126 | + | 0.777303i | \(0.283413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.9282 | −0.588711 | −0.294355 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294355 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.8564 | 1.49059 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.679492 | −0.0267136 | −0.0133568 | − | 0.999911i | \(-0.504252\pi\) | ||||
−0.0133568 | + | 0.999911i | \(0.504252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.92820 | 0.271956 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.46410 | −0.214155 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.7128 | −1.31928 | −0.659642 | − | 0.751580i | \(-0.729292\pi\) | ||||
−0.659642 | + | 0.751580i | \(0.729292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.2154 | −0.594514 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.535898 | −0.0209074 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0718 | 0.665023 | 0.332511 | − | 0.943099i | \(-0.392104\pi\) | ||||
0.332511 | + | 0.943099i | \(0.392104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.2487 | 1.72108 | 0.860538 | − | 0.509387i | \(-0.170128\pi\) | ||||
0.860538 | + | 0.509387i | \(0.170128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.92820 | −0.269069 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.9282 | −0.734004 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.5692 | 1.60957 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.39230 | −0.324465 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9282 | 0.806723 | 0.403361 | − | 0.915041i | \(-0.367842\pi\) | ||||
0.403361 | + | 0.915041i | \(0.367842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.00000 | −0.269430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.78461 | 0.107021 | 0.0535106 | − | 0.998567i | \(-0.482959\pi\) | ||||
0.0535106 | + | 0.998567i | \(0.482959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | −0.0767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.39230 | −0.168313 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.21539 | −0.123033 | −0.0615167 | − | 0.998106i | \(-0.519594\pi\) | ||||
−0.0615167 | + | 0.998106i | \(0.519594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.2154 | −1.03985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.3205 | 0.813428 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.85641 | −0.0707235 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.0718 | 1.25811 | 0.629055 | − | 0.777361i | \(-0.283442\pi\) | ||||
0.629055 | + | 0.777361i | \(0.283442\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.6410 | −1.76919 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000 | 0.454532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.85641 | 0.297157 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.7128 | 1.72655 | 0.863275 | − | 0.504735i | \(-0.168410\pi\) | ||||
0.863275 | + | 0.504735i | \(0.168410\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.9282 | 1.01562 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.7846 | −1.23474 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.8564 | 0.746777 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.7846 | 1.75703 | 0.878516 | − | 0.477712i | \(-0.158534\pi\) | ||||
0.878516 | + | 0.477712i | \(0.158534\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.9282 | 0.409840 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.8564 | 1.41773 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.92820 | 0.259100 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0000 | −0.896296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.1769 | 1.38646 | 0.693232 | − | 0.720714i | \(-0.256186\pi\) | ||||
0.693232 | + | 0.720714i | \(0.256186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4641 | −0.501429 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.60770 | −0.357314 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.0000 | −1.55984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.1769 | −1.23046 | −0.615232 | − | 0.788346i | \(-0.710938\pi\) | ||||
−0.615232 | + | 0.788346i | \(0.710938\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.8564 | 1.40017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1436 | 0.448534 | 0.224267 | − | 0.974528i | \(-0.428001\pi\) | ||||
0.224267 | + | 0.974528i | \(0.428001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.46410 | 0.127775 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.9282 | 0.549887 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | −0.294285 | −0.147142 | − | 0.989115i | \(-0.547008\pi\) | ||||
−0.147142 | + | 0.989115i | \(0.547008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9282 | 0.401458 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.5692 | 1.52503 | 0.762513 | − | 0.646972i | \(-0.223965\pi\) | ||||
0.762513 | + | 0.646972i | \(0.223965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7846 | 0.761489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.39230 | −0.160706 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.92820 | −0.253151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.7846 | 0.904403 | 0.452202 | − | 0.891916i | \(-0.350639\pi\) | ||||
0.452202 | + | 0.891916i | \(0.350639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.9282 | 1.12709 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55.4256 | −2.01715 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.7846 | 0.828121 | 0.414060 | − | 0.910249i | \(-0.364110\pi\) | ||||
0.414060 | + | 0.910249i | \(0.364110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.92820 | −0.251478 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6077 | −0.928278 | −0.464139 | − | 0.885762i | \(-0.653636\pi\) | ||||
−0.464139 | + | 0.885762i | \(0.653636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.8564 | −0.574040 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0000 | −0.433861 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.8564 | −0.500326 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.5359 | 1.02903 | 0.514515 | − | 0.857481i | \(-0.327972\pi\) | ||||
0.514515 | + | 0.857481i | \(0.327972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.9282 | −0.465598 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.5359 | −1.17023 | −0.585117 | − | 0.810949i | \(-0.698952\pi\) | ||||
−0.585117 | + | 0.810949i | \(0.698952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.2487 | −1.37393 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.92820 | −0.176798 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.9282 | −0.678173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.28719 | 0.295782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.1769 | −1.18263 | −0.591315 | − | 0.806441i | \(-0.701391\pi\) | ||||
−0.591315 | + | 0.806441i | \(0.701391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.07180 | −0.180561 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.85641 | −0.279342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.21539 | −0.114038 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.5359 | −1.15248 | −0.576240 | − | 0.817280i | \(-0.695481\pi\) | ||||
−0.576240 | + | 0.817280i | \(0.695481\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.7846 | −1.15984 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.928203 | −0.0327964 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.535898 | 0.0189114 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0000 | −0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.2487 | −0.853595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0718 | 0.389264 | 0.194632 | − | 0.980876i | \(-0.437649\pi\) | ||||
0.194632 | + | 0.980876i | \(0.437649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.1769 | 0.603163 | 0.301582 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301582 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.7846 | −0.869234 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.8564 | −0.485369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −59.7128 | −2.08909 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.00000 | −0.209401 | −0.104701 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104701 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.7846 | −1.42166 | −0.710831 | − | 0.703363i | \(-0.751681\pi\) | ||||
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.00000 | 0.243709 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.2487 | 1.53682 | 0.768411 | − | 0.639957i | \(-0.221048\pi\) | ||||
0.768411 | + | 0.639957i | \(0.221048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.8564 | 0.411294 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 65.5692 | 2.26912 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.46410 | 0.188867 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.4641 | 1.15531 | 0.577655 | − | 0.816281i | \(-0.303968\pi\) | ||||
0.577655 | + | 0.816281i | \(0.303968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.85641 | 0.270589 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.1769 | 1.07252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.4641 | −0.462087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.1436 | 1.17043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.7128 | −1.70213 | −0.851067 | − | 0.525057i | \(-0.824044\pi\) | ||||
−0.851067 | + | 0.525057i | \(0.824044\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.9282 | 0.647331 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.32051 | −0.181745 | −0.0908725 | − | 0.995863i | \(-0.528966\pi\) | ||||
−0.0908725 | + | 0.995863i | \(0.528966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.7846 | −1.80099 | −0.900494 | − | 0.434869i | \(-0.856795\pi\) | ||||
−0.900494 | + | 0.434869i | \(0.856795\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.46410 | 0.118056 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.7846 | −1.52449 | −0.762243 | − | 0.647291i | \(-0.775902\pi\) | ||||
−0.762243 | + | 0.647291i | \(0.775902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.21539 | 0.109327 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.00000 | 0.169809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.9282 | −0.370714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.8564 | −1.01165 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820 | 0.234216 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.0000 | −1.55331 | −0.776655 | − | 0.629926i | \(-0.783085\pi\) | ||||
−0.776655 | + | 0.629926i | \(0.783085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.9282 | 0.840807 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.8564 | 1.40858 | 0.704290 | − | 0.709912i | \(-0.251265\pi\) | ||||
0.704290 | + | 0.709912i | \(0.251265\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.0000 | −0.806751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1436 | −0.340589 | −0.170294 | − | 0.985393i | \(-0.554472\pi\) | ||||
−0.170294 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9282 | −0.366520 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.7128 | 1.73050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −72.0000 | −2.40669 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.8564 | 0.462652 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.7846 | 1.09343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.21539 | −0.107120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.9282 | 0.363668 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.1436 | −0.736078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.9282 | −0.495683 | −0.247841 | − | 0.968801i | \(-0.579721\pi\) | ||||
−0.247841 | + | 0.968801i | \(0.579721\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.8564 | −0.658595 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.4974 | 1.60679 | 0.803396 | − | 0.595446i | \(-0.203024\pi\) | ||||
0.803396 | + | 0.595446i | \(0.203024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.39230 | 0.145364 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.92820 | 0.229039 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.39230 | −0.145047 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.8564 | −0.720976 | −0.360488 | − | 0.932764i | \(-0.617390\pi\) | ||||
−0.360488 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.5359 | 0.347170 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.4974 | −1.13427 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.4641 | 0.442219 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.6410 | 1.33339 | 0.666694 | − | 0.745331i | \(-0.267709\pi\) | ||||
0.666694 | + | 0.745331i | \(0.267709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.46410 | −0.179079 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.3923 | 0.929522 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | 0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.3923 | −0.470176 | −0.235088 | − | 0.971974i | \(-0.575538\pi\) | ||||
−0.235088 | + | 0.971974i | \(0.575538\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9282 | 0.552431 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0718 | −0.360930 | −0.180465 | − | 0.983581i | \(-0.557760\pi\) | ||||
−0.180465 | + | 0.983581i | \(0.557760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | −0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.46410 | −0.112687 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.8564 | −1.62012 | −0.810058 | − | 0.586350i | \(-0.800564\pi\) | ||||
−0.810058 | + | 0.586350i | \(0.800564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07180 | −0.0347920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.9282 | −0.419226 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.7846 | −0.867639 | −0.433819 | − | 0.901000i | \(-0.642834\pi\) | ||||
−0.433819 | + | 0.901000i | \(0.642834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 72.0000 | 2.32987 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.00000 | −0.193952 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.85641 | −0.253697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.92820 | 0.223258 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −90.0666 | −2.89935 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9282 | 0.608061 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7128 | 0.504248 | 0.252124 | − | 0.967695i | \(-0.418871\pi\) | ||||
0.252124 | + | 0.967695i | \(0.418871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.4641 | −0.431639 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0000 | −0.448359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.5692 | −1.52187 | −0.760937 | − | 0.648826i | \(-0.775260\pi\) | ||||
−0.760937 | + | 0.648826i | \(0.775260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.928203 | 0.0296655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.8564 | 0.506256 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.3205 | −0.743809 | −0.371904 | − | 0.928271i | \(-0.621295\pi\) | ||||
−0.371904 | + | 0.928271i | \(0.621295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −62.3538 | −1.98676 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.46410 | −0.301246 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −75.7128 | −2.40753 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.14359 | 0.0680935 | 0.0340467 | − | 0.999420i | \(-0.489160\pi\) | ||||
0.0340467 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.07180 | −0.287885 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.35898 | 0.0430827 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6410 | 0.780389 | 0.390194 | − | 0.920732i | \(-0.372408\pi\) | ||||
0.390194 | + | 0.920732i | \(0.372408\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.92820 | 0.155921 |
(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 | 3696.2.a.bc.1.1 | 2 | ||
4.3 | odd | 2 | 462.2.a.h.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 1386.2.a.p.1.2 | 2 | |||
28.27 | even | 2 | 3234.2.a.x.1.2 | 2 | |||
44.43 | even | 2 | 5082.2.a.bu.1.1 | 2 | |||
84.83 | odd | 2 | 9702.2.a.dd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.a.h.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
1386.2.a.p.1.2 | 2 | 12.11 | even | 2 | |||
3234.2.a.x.1.2 | 2 | 28.27 | even | 2 | |||
3696.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5082.2.a.bu.1.1 | 2 | 44.43 | even | 2 | |||
9702.2.a.dd.1.1 | 2 | 84.83 | odd | 2 |