Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.69230\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.393270 | 0.118575 | 0.0592877 | − | 0.998241i | \(-0.481117\pi\) | ||||
0.0592877 | + | 0.998241i | \(0.481117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.21302 | 1.50688 | 0.753440 | − | 0.657517i | \(-0.228393\pi\) | ||||
0.753440 | + | 0.657517i | \(0.228393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.34271 | −1.68453 | −0.842266 | − | 0.539062i | \(-0.818779\pi\) | ||||
−0.842266 | + | 0.539062i | \(0.818779\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.44383 | 0.301060 | 0.150530 | − | 0.988605i | \(-0.451902\pi\) | ||||
0.150530 | + | 0.988605i | \(0.451902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65685 | 0.297580 | 0.148790 | − | 0.988869i | \(-0.452462\pi\) | ||||
0.148790 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.393270 | 0.0684595 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.78654 | −1.11570 | −0.557850 | − | 0.829942i | \(-0.688374\pi\) | ||||
−0.557850 | + | 0.829942i | \(0.688374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77786 | 0.590003 | 0.295002 | − | 0.955497i | \(-0.404680\pi\) | ||||
0.295002 | + | 0.955497i | \(0.404680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.51428 | 0.383424 | 0.191712 | − | 0.981451i | \(-0.438596\pi\) | ||||
0.191712 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00868 | −0.438860 | −0.219430 | − | 0.975628i | \(-0.570420\pi\) | ||||
−0.219430 | + | 0.975628i | \(0.570420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.21302 | 0.869997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.55573 | 1.31258 | 0.656290 | − | 0.754509i | \(-0.272125\pi\) | ||||
0.656290 | + | 0.754509i | \(0.272125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.34271 | −0.972565 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.393270 | 0.0511994 | 0.0255997 | − | 0.999672i | \(-0.491850\pi\) | ||||
0.0255997 | + | 0.999672i | \(0.491850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0414 | 1.41371 | 0.706856 | − | 0.707357i | \(-0.250113\pi\) | ||||
0.706856 | + | 0.707357i | \(0.250113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5557 | −1.90043 | −0.950217 | − | 0.311588i | \(-0.899139\pi\) | ||||
−0.950217 | + | 0.311588i | \(0.899139\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.44383 | 0.173817 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.56440 | 0.779051 | 0.389526 | − | 0.921016i | \(-0.372639\pi\) | ||||
0.389526 | + | 0.921016i | \(0.372639\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.6150 | −1.59351 | −0.796756 | − | 0.604302i | \(-0.793452\pi\) | ||||
−0.796756 | + | 0.604302i | \(0.793452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.11233 | −0.126762 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.9403 | −1.68092 | −0.840459 | − | 0.541875i | \(-0.817714\pi\) | ||||
−0.840459 | + | 0.541875i | \(0.817714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.4633 | −1.80708 | −0.903540 | − | 0.428504i | \(-0.859041\pi\) | ||||
−0.903540 | + | 0.428504i | \(0.859041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.828427 | −0.0888167 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.67674 | −1.02573 | −0.512866 | − | 0.858469i | \(-0.671416\pi\) | ||||
−0.512866 | + | 0.858469i | \(0.671416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.65685 | 0.171808 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0418875 | −0.00425303 | −0.00212652 | − | 0.999998i | \(-0.500677\pi\) | ||||
−0.00212652 | + | 0.999998i | \(0.500677\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.393270 | 0.0395251 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1421 | 1.20819 | 0.604094 | − | 0.796913i | \(-0.293535\pi\) | ||||
0.604094 | + | 0.796913i | \(0.293535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0173504 | 0.00170958 | 0.000854792 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000854792 | 1.00000i | \(0.499728\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.10113 | −0.203123 | −0.101562 | − | 0.994829i | \(-0.532384\pi\) | ||||
−0.101562 | + | 0.994829i | \(0.532384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.21302 | 0.595100 | 0.297550 | − | 0.954706i | \(-0.403831\pi\) | ||||
0.297550 | + | 0.954706i | \(0.403831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.78654 | −0.644150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.42648 | −0.134192 | −0.0670961 | − | 0.997747i | \(-0.521373\pi\) | ||||
−0.0670961 | + | 0.997747i | \(0.521373\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.5731 | −1.61092 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8453 | −0.985940 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.77786 | 0.340639 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.50307 | −0.133376 | −0.0666880 | − | 0.997774i | \(-0.521243\pi\) | ||||
−0.0666880 | + | 0.997774i | \(0.521243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.51428 | 0.221370 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.85699 | 0.336987 | 0.168493 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168493 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.7683 | 1.80084 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.5644 | −1.41519 | −0.707596 | − | 0.706617i | \(-0.750220\pi\) | ||||
−0.707596 | + | 0.706617i | \(0.750220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6854 | 0.906325 | 0.453163 | − | 0.891428i | \(-0.350296\pi\) | ||||
0.453163 | + | 0.891428i | \(0.350296\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00868 | −0.253376 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.393270 | −0.0328869 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.05012 | 0.331799 | 0.165900 | − | 0.986143i | \(-0.446947\pi\) | ||||
0.165900 | + | 0.986143i | \(0.446947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.02856 | 0.409218 | 0.204609 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204609 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.21302 | 0.502293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.4961 | −1.95500 | −0.977499 | − | 0.210940i | \(-0.932347\pi\) | ||||
−0.977499 | + | 0.210940i | \(0.932347\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.55573 | 0.757819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.08378 | −0.321847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.3137 | −1.19946 | −0.599731 | − | 0.800202i | \(-0.704726\pi\) | ||||
−0.599731 | + | 0.800202i | \(0.704726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.7770 | 1.22086 | 0.610430 | − | 0.792070i | \(-0.290997\pi\) | ||||
0.610430 | + | 0.792070i | \(0.290997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.34271 | −0.561511 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.9706 | 1.13819 | 0.569095 | − | 0.822272i | \(-0.307294\pi\) | ||||
0.569095 | + | 0.822272i | \(0.307294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.393270 | 0.0295600 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.84578 | −0.362190 | −0.181095 | − | 0.983466i | \(-0.557964\pi\) | ||||
−0.181095 | + | 0.983466i | \(0.557964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.99912 | −0.594570 | −0.297285 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297285 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0414 | 0.816207 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.44339 | 0.178679 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.4260 | −1.47798 | −0.738988 | − | 0.673718i | \(-0.764696\pi\) | ||||
−0.738988 | + | 0.673718i | \(0.764696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.0237 | −1.72926 | −0.864630 | − | 0.502408i | \(-0.832447\pi\) | ||||
−0.864630 | + | 0.502408i | \(0.832447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.80642 | 0.342444 | 0.171222 | − | 0.985233i | \(-0.445229\pi\) | ||||
0.171222 | + | 0.985233i | \(0.445229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9403 | −1.05909 | −0.529546 | − | 0.848281i | \(-0.677638\pi\) | ||||
−0.529546 | + | 0.848281i | \(0.677638\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.5557 | −1.09722 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.34315 | 0.164457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.44383 | 0.100353 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.88767 | −0.199744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.82799 | −0.125844 | −0.0629220 | − | 0.998018i | \(-0.520042\pi\) | ||||
−0.0629220 | + | 0.998018i | \(0.520042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.56440 | 0.449786 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.68629 | −0.318126 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.6150 | −0.920014 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.21302 | −0.417933 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.07045 | 0.473472 | 0.236736 | − | 0.971574i | \(-0.423922\pi\) | ||||
0.236736 | + | 0.971574i | \(0.423922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.43560 | −0.360773 | −0.180387 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180387 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.8147 | 1.63980 | 0.819899 | − | 0.572508i | \(-0.194029\pi\) | ||||
0.819899 | + | 0.572508i | \(0.194029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.11233 | −0.0731863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.4256 | −1.53466 | −0.767331 | − | 0.641251i | \(-0.778416\pi\) | ||||
−0.767331 | + | 0.641251i | \(0.778416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.9403 | −0.970478 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.7779 | −1.40869 | −0.704346 | − | 0.709856i | \(-0.748760\pi\) | ||||
−0.704346 | + | 0.709856i | \(0.748760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2126 | −0.979929 | −0.489964 | − | 0.871742i | \(-0.662990\pi\) | ||||
−0.489964 | + | 0.871742i | \(0.662990\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.34271 | 0.467205 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.4633 | −1.04332 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.9399 | −1.13236 | −0.566178 | − | 0.824283i | \(-0.691578\pi\) | ||||
−0.566178 | + | 0.824283i | \(0.691578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.567816 | 0.0356983 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.88810 | −0.242533 | −0.121267 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121267 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.1952 | 1.19273 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.828427 | −0.0512784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.296797 | 0.0183013 | 0.00915064 | − | 0.999958i | \(-0.497087\pi\) | ||||
0.00915064 | + | 0.999958i | \(0.497087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.67674 | −0.592207 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.25447 | −0.0764864 | −0.0382432 | − | 0.999268i | \(-0.512176\pi\) | ||||
−0.0382432 | + | 0.999268i | \(0.512176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.81510 | 0.596225 | 0.298112 | − | 0.954531i | \(-0.403643\pi\) | ||||
0.298112 | + | 0.954531i | \(0.403643\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843 | 0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.35603 | 0.261729 | 0.130864 | − | 0.991400i | \(-0.458225\pi\) | ||||
0.130864 | + | 0.991400i | \(0.458225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.65685 | 0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.45207 | 0.205933 | 0.102967 | − | 0.994685i | \(-0.467167\pi\) | ||||
0.102967 | + | 0.994685i | \(0.467167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.25937 | −0.134306 | −0.0671528 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671528 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6854 | −0.630740 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6016 | 1.27068 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0418875 | −0.00245549 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5358 | −1.14130 | −0.570648 | − | 0.821195i | \(-0.693308\pi\) | ||||
−0.570648 | + | 0.821195i | \(0.693308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.393270 | 0.0228198 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.44383 | −0.0834990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.11146 | −0.409898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1421 | 0.697547 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.8142 | 1.58744 | 0.793721 | − | 0.608282i | \(-0.208141\pi\) | ||||
0.793721 | + | 0.608282i | \(0.208141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0173504 | 0.000987028 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.10113 | 0.119144 | 0.0595719 | − | 0.998224i | \(-0.481026\pi\) | ||||
0.0595719 | + | 0.998224i | \(0.481026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.64397 | −0.545109 | −0.272555 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272555 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1201 | 0.905397 | 0.452698 | − | 0.891664i | \(-0.350461\pi\) | ||||
0.452698 | + | 0.891664i | \(0.350461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.325795 | −0.0182410 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.10113 | −0.117273 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −45.6204 | −2.53839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.21302 | 0.343581 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.50982 | 0.469161 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9537 | 0.766962 | 0.383481 | − | 0.923549i | \(-0.374725\pi\) | ||||
0.383481 | + | 0.923549i | \(0.374725\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.78654 | −0.371900 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.66974 | −0.526744 | −0.263372 | − | 0.964694i | \(-0.584835\pi\) | ||||
−0.263372 | + | 0.964694i | \(0.584835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.42648 | −0.0774759 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.651591 | 0.0352856 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2014 | −0.547638 | −0.273819 | − | 0.961781i | \(-0.588287\pi\) | ||||
−0.273819 | + | 0.961781i | \(0.588287\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.7402 | 1.53843 | 0.769214 | − | 0.638992i | \(-0.220648\pi\) | ||||
0.769214 | + | 0.638992i | \(0.220648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9067 | −1.11275 | −0.556375 | − | 0.830931i | \(-0.687808\pi\) | ||||
−0.556375 | + | 0.830931i | \(0.687808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.5731 | −0.930066 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.3162 | 1.01947 | 0.509736 | − | 0.860331i | \(-0.329743\pi\) | ||||
0.509736 | + | 0.860331i | \(0.329743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.9153 | 1.83765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8453 | −0.569233 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −37.6957 | −1.96770 | −0.983851 | − | 0.178990i | \(-0.942717\pi\) | ||||
−0.983851 | + | 0.178990i | \(0.942717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.77786 | 0.196668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.0277 | −1.40321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.4607 | −1.16297 | −0.581487 | − | 0.813556i | \(-0.697529\pi\) | ||||
−0.581487 | + | 0.813556i | \(0.697529\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.828427 | 0.0426662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3133 | −1.24889 | −0.624444 | − | 0.781069i | \(-0.714675\pi\) | ||||
−0.624444 | + | 0.781069i | \(0.714675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50307 | −0.0770046 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.2498 | −1.90338 | −0.951688 | − | 0.307065i | \(-0.900653\pi\) | ||||
−0.951688 | + | 0.307065i | \(0.900653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.51428 | 0.127808 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.467931 | −0.0237250 | −0.0118625 | − | 0.999930i | \(-0.503776\pi\) | ||||
−0.0118625 | + | 0.999930i | \(0.503776\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.97056 | 0.453661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.85699 | 0.194559 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.5263 | −1.73282 | −0.866412 | − | 0.499329i | \(-0.833580\pi\) | ||||
−0.866412 | + | 0.499329i | \(0.833580\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.7683 | 1.03972 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.8781 | 1.59192 | 0.795958 | − | 0.605351i | \(-0.206967\pi\) | ||||
0.795958 | + | 0.605351i | \(0.206967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.65685 | −0.0825338 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.66894 | −0.132294 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.01735 | −0.396432 | −0.198216 | − | 0.980158i | \(-0.563515\pi\) | ||||
−0.198216 | + | 0.980158i | \(0.563515\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.5644 | −0.817062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.11233 | −0.0547344 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.6854 | 0.523267 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.40151 | 0.410440 | 0.205220 | − | 0.978716i | \(-0.434209\pi\) | ||||
0.205220 | + | 0.978716i | \(0.434209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7514 | −0.572728 | −0.286364 | − | 0.958121i | \(-0.592447\pi\) | ||||
−0.286364 | + | 0.958121i | \(0.592447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00868 | −0.146287 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.2299 | −1.51132 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.393270 | −0.0189872 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.5818 | −0.991388 | −0.495694 | − | 0.868497i | \(-0.665086\pi\) | ||||
−0.495694 | + | 0.868497i | \(0.665086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.12522 | 0.246303 | 0.123151 | − | 0.992388i | \(-0.460700\pi\) | ||||
0.123151 | + | 0.992388i | \(0.460700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.6016 | −0.507145 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.8868 | −0.615053 | −0.307526 | − | 0.951540i | \(-0.599501\pi\) | ||||
−0.307526 | + | 0.951540i | \(0.599501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.1279 | 1.66898 | 0.834489 | − | 0.551024i | \(-0.185763\pi\) | ||||
0.834489 | + | 0.551024i | \(0.185763\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.05012 | 0.191564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.2213 | 0.859914 | 0.429957 | − | 0.902849i | \(-0.358529\pi\) | ||||
0.429957 | + | 0.902849i | \(0.358529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.48572 | 0.0699598 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.02856 | 0.236262 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.4118 | 1.09516 | 0.547580 | − | 0.836753i | \(-0.315549\pi\) | ||||
0.547580 | + | 0.836753i | \(0.315549\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.21302 | 0.289999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.2913 | −0.665611 | −0.332805 | − | 0.942996i | \(-0.607995\pi\) | ||||
−0.332805 | + | 0.942996i | \(0.607995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.7152 | 1.10214 | 0.551070 | − | 0.834459i | \(-0.314220\pi\) | ||||
0.551070 | + | 0.834459i | \(0.314220\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.8989 | −1.01336 | −0.506680 | − | 0.862134i | \(-0.669127\pi\) | ||||
−0.506680 | + | 0.862134i | \(0.669127\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.9982 | 2.03165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.4961 | −1.12872 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.988790 | 0.0454646 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.55573 | 0.437527 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0916 | −0.780934 | −0.390467 | − | 0.920617i | \(-0.627686\pi\) | ||||
−0.390467 | + | 0.920617i | \(0.627686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.78654 | 0.309440 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.08378 | −0.185818 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.87434 | −0.0849343 | −0.0424672 | − | 0.999098i | \(-0.513522\pi\) | ||||
−0.0424672 | + | 0.999098i | \(0.513522\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.3137 | −0.692510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7704 | −0.486063 | −0.243031 | − | 0.970018i | \(-0.578142\pi\) | ||||
−0.243031 | + | 0.970018i | \(0.578142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.14704 | −0.231811 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.5669 | −0.832841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.5259 | 1.50082 | 0.750412 | − | 0.660971i | \(-0.229855\pi\) | ||||
0.750412 | + | 0.660971i | \(0.229855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.7770 | 0.704864 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.58473 | 0.338186 | 0.169093 | − | 0.985600i | \(-0.445916\pi\) | ||||
0.169093 | + | 0.985600i | \(0.445916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.0145 | 1.68497 | 0.842483 | − | 0.538724i | \(-0.181093\pi\) | ||||
0.842483 | + | 0.538724i | \(0.181093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.5089 | 1.70354 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.34271 | −0.324188 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.18322 | −0.0520380 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.9706 | 0.657135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2420 | −0.799197 | −0.399599 | − | 0.916690i | \(-0.630851\pi\) | ||||
−0.399599 | + | 0.916690i | \(0.630851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1720 | −0.444791 | −0.222396 | − | 0.974957i | \(-0.571388\pi\) | ||||
−0.222396 | + | 0.974957i | \(0.571388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2941 | 0.448417 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9153 | −0.909363 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.393270 | 0.0170665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.77786 | −0.163637 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.84578 | −0.209111 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.393270 | 0.0169393 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.98923 | 0.0855236 | 0.0427618 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427618 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.99912 | −0.343275 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.31817 | −0.0563609 | −0.0281804 | − | 0.999603i | \(-0.508971\pi\) | ||||
−0.0281804 | + | 0.999603i | \(0.508971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.0414 | 0.471238 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.08290 | 0.259140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.2576 | 1.79698 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0804 | −0.511861 | −0.255931 | − | 0.966695i | \(-0.582382\pi\) | ||||
−0.255931 | + | 0.966695i | \(0.582382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.51428 | −0.106343 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.44339 | 0.103160 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9930 | 0.969039 | 0.484519 | − | 0.874781i | \(-0.338995\pi\) | ||||
0.484519 | + | 0.874781i | \(0.338995\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.0370 | 1.21729 | 0.608647 | − | 0.793441i | \(-0.291713\pi\) | ||||
0.608647 | + | 0.793441i | \(0.291713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.56950 | 0.233076 | 0.116538 | − | 0.993186i | \(-0.462820\pi\) | ||||
0.116538 | + | 0.993186i | \(0.462820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.4260 | −0.853310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.2822 | 0.844357 | 0.422179 | − | 0.906513i | \(-0.361266\pi\) | ||||
0.422179 | + | 0.906513i | \(0.361266\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.0237 | −0.998389 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 46.5652 | 1.93185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.75798 | 0.155640 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.82377 | −0.364196 | −0.182098 | − | 0.983280i | \(-0.558289\pi\) | ||||
−0.182098 | + | 0.983280i | \(0.558289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.1658 | −0.501283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.80642 | 0.197710 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.2213 | −0.419737 | −0.209868 | − | 0.977730i | \(-0.567304\pi\) | ||||
−0.209868 | + | 0.977730i | \(0.567304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.9403 | −0.611467 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.4925 | −0.755582 | −0.377791 | − | 0.925891i | \(-0.623316\pi\) | ||||
−0.377791 | + | 0.925891i | \(0.623316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0129 | 1.06109 | 0.530544 | − | 0.847657i | \(-0.321988\pi\) | ||||
0.530544 | + | 0.847657i | \(0.321988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.5557 | −0.633478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.1227 | −0.979109 | −0.489554 | − | 0.871973i | \(-0.662841\pi\) | ||||
−0.489554 | + | 0.871973i | \(0.662841\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.34315 | 0.0949491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00868 | 0.121718 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2056 | −1.38155 | −0.690775 | − | 0.723070i | \(-0.742730\pi\) | ||||
−0.690775 | + | 0.723070i | \(0.742730\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.3622 | 0.497682 | 0.248841 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248841 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.6685 | −0.468997 | −0.234498 | − | 0.972117i | \(-0.575345\pi\) | ||||
−0.234498 | + | 0.972117i | \(0.575345\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.44383 | 0.0579390 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.3700 | 1.09655 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.88767 | −0.115322 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.1649 | −1.68123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.79775 | 0.151186 | 0.0755930 | − | 0.997139i | \(-0.475915\pi\) | ||||
0.0755930 | + | 0.997139i | \(0.475915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.82799 | −0.0726560 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.56440 | 0.259684 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.91008 | −0.272932 | −0.136466 | − | 0.990645i | \(-0.543574\pi\) | ||||
−0.136466 | + | 0.990645i | \(0.543574\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.50139 | 0.0986452 | 0.0493226 | − | 0.998783i | \(-0.484294\pi\) | ||||
0.0493226 | + | 0.998783i | \(0.484294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.3124 | 1.19170 | 0.595852 | − | 0.803095i | \(-0.296815\pi\) | ||||
0.595852 | + | 0.803095i | \(0.296815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.154661 | 0.00607098 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.68629 | −0.183670 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.4537 | 1.30915 | 0.654573 | − | 0.755999i | \(-0.272849\pi\) | ||||
0.654573 | + | 0.755999i | \(0.272849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.6150 | −0.531170 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.2942 | −1.21905 | −0.609525 | − | 0.792767i | \(-0.708640\pi\) | ||||
−0.609525 | + | 0.792767i | \(0.708640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1119 | 1.56017 | 0.780086 | − | 0.625672i | \(-0.215175\pi\) | ||||
0.780086 | + | 0.625672i | \(0.215175\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.21302 | −0.241294 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.19611 | −0.0463136 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.07045 | 0.273359 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.34227 | 0.167631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.99386 | −0.192499 | −0.0962496 | − | 0.995357i | \(-0.530685\pi\) | ||||
−0.0962496 | + | 0.995357i | \(0.530685\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.0174 | 0.615597 | 0.307798 | − | 0.951452i | \(-0.400408\pi\) | ||||
0.307798 | + | 0.951452i | \(0.400408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.118476 | 0.00454668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.43560 | −0.208292 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.5400 | 1.35990 | 0.679951 | − | 0.733258i | \(-0.262001\pi\) | ||||
0.679951 | + | 0.733258i | \(0.262001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.8147 | 0.946738 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.55573 | −0.364044 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0393 | 0.496040 | 0.248020 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248020 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.11233 | −0.0422541 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.4720 | 0.889064 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.4256 | −0.886038 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.502632 | −0.0189841 | −0.00949207 | − | 0.999955i | \(-0.503021\pi\) | ||||
−0.00949207 | + | 0.999955i | \(0.503021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.8316 | 1.87943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.3431 | −1.29161 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0712 | 1.58002 | 0.790009 | − | 0.613095i | \(-0.210076\pi\) | ||||
0.790009 | + | 0.613095i | \(0.210076\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.9403 | −0.560306 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.39222 | 0.0895893 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.7779 | −0.813309 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.7848 | 1.22267 | 0.611333 | − | 0.791373i | \(-0.290634\pi\) | ||||
0.611333 | + | 0.791373i | \(0.290634\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0490743 | −0.00182762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.2126 | −0.565762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.5246 | 1.83677 | 0.918383 | − | 0.395692i | \(-0.129495\pi\) | ||||
0.918383 | + | 0.395692i | \(0.129495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.6213 | 0.577774 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.11848 | 0.0782477 | 0.0391238 | − | 0.999234i | \(-0.487543\pi\) | ||||
0.0391238 | + | 0.999234i | \(0.487543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.11760 | −0.225345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.7014 | −1.75473 | −0.877363 | − | 0.479827i | \(-0.840699\pi\) | ||||
−0.877363 | + | 0.479827i | \(0.840699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.34271 | 0.269741 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.8055 | −1.20352 | −0.601759 | − | 0.798677i | \(-0.705533\pi\) | ||||
−0.601759 | + | 0.798677i | \(0.705533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.4633 | −0.602360 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.94288 | 0.217148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.852087 | −0.0310931 | −0.0155465 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155465 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.9399 | −0.653766 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.68454 | 0.242954 | 0.121477 | − | 0.992594i | \(-0.461237\pi\) | ||||
0.121477 | + | 0.992594i | \(0.461237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.567816 | 0.0206104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.92578 | −0.106059 | −0.0530297 | − | 0.998593i | \(-0.516888\pi\) | ||||
−0.0530297 | + | 0.998593i | \(0.516888\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.5731 | −0.636188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.393270 | −0.0142001 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6274 | −0.455356 | −0.227678 | − | 0.973736i | \(-0.573113\pi\) | ||||
−0.227678 | + | 0.973736i | \(0.573113\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.88810 | −0.140027 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.9454 | −0.573517 | −0.286758 | − | 0.958003i | \(-0.592578\pi\) | ||||
−0.286758 | + | 0.958003i | \(0.592578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.1952 | 0.688625 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.7398 | −0.993880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.58158 | 0.0923763 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.828427 | −0.0296056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.5825 | −1.73178 | −0.865890 | − | 0.500234i | \(-0.833247\pi\) | ||||
−0.865890 | + | 0.500234i | \(0.833247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.296797 | 0.0105662 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.03470 | 0.143457 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0414 | −0.392093 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.8971 | −0.704792 | −0.352396 | − | 0.935851i | \(-0.614633\pi\) | ||||
−0.352396 | + | 0.935851i | \(0.614633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.6930 | −0.661310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.67674 | −0.341911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.35436 | −0.188951 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.25447 | −0.0441595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.5487 | −0.441189 | −0.220595 | − | 0.975366i | \(-0.570800\pi\) | ||||
−0.220595 | + | 0.975366i | \(0.570800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.9149 | 1.08557 | 0.542785 | − | 0.839872i | \(-0.317370\pi\) | ||||
0.542785 | + | 0.839872i | \(0.317370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.81510 | 0.344231 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.4616 | −0.645890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.82843 | 0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.9308 | −1.04459 | −0.522296 | − | 0.852765i | \(-0.674924\pi\) | ||||
−0.522296 | + | 0.852765i | \(0.674924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1831 | 0.564109 | 0.282055 | − | 0.959398i | \(-0.408984\pi\) | ||||
0.282055 | + | 0.959398i | \(0.408984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.2022 | −1.88479 | −0.942397 | − | 0.334497i | \(-0.891434\pi\) | ||||
−0.942397 | + | 0.334497i | \(0.891434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.2929 | −1.46889 | −0.734447 | − | 0.678666i | \(-0.762558\pi\) | ||||
−0.734447 | + | 0.678666i | \(0.762558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.35603 | 0.151109 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.21302 | 0.215268 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.65685 | 0.0572693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.7873 | 1.27004 | 0.635020 | − | 0.772496i | \(-0.280992\pi\) | ||||
0.635020 | + | 0.772496i | \(0.280992\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.45207 | 0.118896 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.6753 | 1.05401 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.25937 | −0.0775414 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.79863 | −0.335893 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4148 | 0.527794 | 0.263897 | − | 0.964551i | \(-0.414992\pi\) | ||||
0.263897 | + | 0.964551i | \(0.414992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0628221 | −0.00214596 | −0.00107298 | − | 0.999999i | \(-0.500342\pi\) | ||||
−0.00107298 | + | 0.999999i | \(0.500342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.6577 | 0.977787 | 0.488893 | − | 0.872344i | \(-0.337401\pi\) | ||||
0.488893 | + | 0.872344i | \(0.337401\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.6854 | −0.364158 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.96189 | 0.202945 | 0.101473 | − | 0.994838i | \(-0.467645\pi\) | ||||
0.101473 | + | 0.994838i | \(0.467645\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.6016 | 0.733630 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.87558 | −0.199315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5557 | 0.527086 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.0418875 | −0.00141768 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.70276 | 0.226336 | 0.113168 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113168 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.5358 | −0.658928 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8624 | 1.34300 | 0.671500 | − | 0.741005i | \(-0.265651\pi\) | ||||
0.671500 | + | 0.741005i | \(0.265651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.7131 | −0.730704 | −0.365352 | − | 0.930869i | \(-0.619051\pi\) | ||||
−0.365352 | + | 0.930869i | \(0.619051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.3757 | −1.72503 | −0.862513 | − | 0.506035i | \(-0.831111\pi\) | ||||
−0.862513 | + | 0.506035i | \(0.831111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.25133 | 0.142585 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.393270 | 0.0131750 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.0918 | 0.739275 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.44383 | −0.0482082 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.37258 | −0.0457782 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.3700 | 1.97790 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.11146 | −0.236654 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.3966 | 0.710463 | 0.355231 | − | 0.934778i | \(-0.384402\pi\) | ||||
0.355231 | + | 0.934778i | \(0.384402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.1421 | 0.402729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.0044 | −1.68985 | −0.844925 | − | 0.534884i | \(-0.820355\pi\) | ||||
−0.844925 | + | 0.534884i | \(0.820355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.47451 | −0.214275 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.9092 | −0.360254 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.3664 | 0.374942 | 0.187471 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187471 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.8142 | 0.916510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.56440 | −0.216070 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0173504 | 0.000569861 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.9344 | 1.57268 | 0.786338 | − | 0.617797i | \(-0.211975\pi\) | ||||
0.786338 | + | 0.617797i | \(0.211975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.34271 | −0.240648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.10113 | 0.0687878 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3266 | 0.762047 | 0.381023 | − | 0.924565i | \(-0.375572\pi\) | ||||
0.381023 | + | 0.924565i | \(0.375572\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.64397 | −0.314719 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.6316 | −1.29195 | −0.645977 | − | 0.763357i | \(-0.723550\pi\) | ||||
−0.645977 | + | 0.763357i | \(0.723550\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.45460 | 0.177626 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7770 | 0.642666 | 0.321333 | − | 0.946966i | \(-0.395869\pi\) | ||||
0.321333 | + | 0.946966i | \(0.395869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6150 | 0.441961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1201 | 0.522731 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2847 | 1.46692 | 0.733458 | − | 0.679735i | \(-0.237905\pi\) | ||||
0.733458 | + | 0.679735i | \(0.237905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.325795 | −0.0105315 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.8512 | 1.51290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2548 | −0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.10113 | −0.0677078 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3903 | −0.430603 | −0.215301 | − | 0.976548i | \(-0.569073\pi\) | ||||
−0.215301 | + | 0.976548i | \(0.569073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45.6204 | −1.46554 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.6150 | −1.27130 | −0.635652 | − | 0.771975i | \(-0.719269\pi\) | ||||
−0.635652 | + | 0.771975i | \(0.719269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.2229 | −0.968902 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.2100 | 0.614584 | 0.307292 | − | 0.951615i | \(-0.400577\pi\) | ||||
0.307292 | + | 0.951615i | \(0.400577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.80557 | −0.121627 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.21302 | 0.198367 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.3960 | 1.03327 | 0.516636 | − | 0.856205i | \(-0.327184\pi\) | ||||
0.516636 | + | 0.856205i | \(0.327184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.50982 | 0.270871 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.63020 | 0.115434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5107 | 0.333883 | 0.166942 | − | 0.985967i | \(-0.446611\pi\) | ||||
0.166942 | + | 0.985967i | \(0.446611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.9537 | 0.442806 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.0753 | −1.30087 | −0.650433 | − | 0.759563i | \(-0.725413\pi\) | ||||
−0.650433 | + | 0.759563i | \(0.725413\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.78654 | −0.214717 |
(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 | 7800.2.a.bw.1.2 | 4 | ||
5.2 | odd | 4 | 1560.2.l.e.1249.2 | ✓ | 8 | ||
5.3 | odd | 4 | 1560.2.l.e.1249.6 | yes | 8 | ||
5.4 | even | 2 | 7800.2.a.bv.1.4 | 4 | |||
15.2 | even | 4 | 4680.2.l.f.2809.5 | 8 | |||
15.8 | even | 4 | 4680.2.l.f.2809.6 | 8 | |||
20.3 | even | 4 | 3120.2.l.o.1249.2 | 8 | |||
20.7 | even | 4 | 3120.2.l.o.1249.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.e.1249.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1560.2.l.e.1249.6 | yes | 8 | 5.3 | odd | 4 | ||
3120.2.l.o.1249.2 | 8 | 20.3 | even | 4 | |||
3120.2.l.o.1249.6 | 8 | 20.7 | even | 4 | |||
4680.2.l.f.2809.5 | 8 | 15.2 | even | 4 | |||
4680.2.l.f.2809.6 | 8 | 15.8 | even | 4 | |||
7800.2.a.bv.1.4 | 4 | 5.4 | even | 2 | |||
7800.2.a.bw.1.2 | 4 | 1.1 | even | 1 | trivial |