Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.12311 | −1.18042 | −0.590211 | − | 0.807249i | \(-0.700956\pi\) | ||||
−0.590211 | + | 0.807249i | \(0.700956\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56155 | 0.987797 | 0.493899 | − | 0.869520i | \(-0.335571\pi\) | ||||
0.493899 | + | 0.869520i | \(0.335571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.12311 | 1.24254 | 0.621268 | − | 0.783598i | \(-0.286618\pi\) | ||||
0.621268 | + | 0.783598i | \(0.286618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.87689 | 1.06423 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.43845 | −0.824199 | −0.412099 | − | 0.911139i | \(-0.635204\pi\) | ||||
−0.412099 | + | 0.911139i | \(0.635204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.56155 | 0.998884 | 0.499442 | − | 0.866347i | \(-0.333538\pi\) | ||||
0.499442 | + | 0.866347i | \(0.333538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.24621 | 1.08733 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.12311 | −0.527901 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.56155 | −0.890561 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.56155 | −0.556221 | −0.278111 | − | 0.960549i | \(-0.589708\pi\) | ||||
−0.278111 | + | 0.960549i | \(0.589708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.876894 | −0.133725 | −0.0668626 | − | 0.997762i | \(-0.521299\pi\) | ||||
−0.0668626 | + | 0.997762i | \(0.521299\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.68466 | 1.26679 | 0.633394 | − | 0.773830i | \(-0.281661\pi\) | ||||
0.633394 | + | 0.773830i | \(0.281661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.75379 | 0.393398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | −1.12022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2462 | 1.68215 | 0.841073 | − | 0.540921i | \(-0.181924\pi\) | ||||
0.841073 | + | 0.540921i | \(0.181924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.24621 | −0.827331 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2462 | 1.33394 | 0.666972 | − | 0.745083i | \(-0.267590\pi\) | ||||
0.666972 | + | 0.745083i | \(0.267590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.87689 | 0.368349 | 0.184174 | − | 0.982894i | \(-0.441039\pi\) | ||||
0.184174 | + | 0.982894i | \(0.441039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.75379 | 0.220957 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56155 | 0.441756 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2462 | −1.25177 | −0.625887 | − | 0.779914i | \(-0.715263\pi\) | ||||
−0.625887 | + | 0.779914i | \(0.715263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.56155 | −0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.68466 | −1.03068 | −0.515340 | − | 0.856986i | \(-0.672334\pi\) | ||||
−0.515340 | + | 0.856986i | \(0.672334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4384 | 1.45581 | 0.727905 | − | 0.685678i | \(-0.240494\pi\) | ||||
0.727905 | + | 0.685678i | \(0.240494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.4924 | 1.42364 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.24621 | 0.702754 | 0.351377 | − | 0.936234i | \(-0.385714\pi\) | ||||
0.351377 | + | 0.936234i | \(0.385714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.12311 | 0.555679 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.93087 | 0.743067 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.1231 | −1.16602 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.68466 | −0.900557 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.246211 | 0.0249990 | 0.0124995 | − | 0.999922i | \(-0.496021\pi\) | ||||
0.0124995 | + | 0.999922i | \(0.496021\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.24621 | 0.225753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2462 | −1.61656 | −0.808279 | − | 0.588799i | \(-0.799601\pi\) | ||||
−0.808279 | + | 0.588799i | \(0.799601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.87689 | 0.475936 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.24621 | −0.789844 | −0.394922 | − | 0.918715i | \(-0.629228\pi\) | ||||
−0.394922 | + | 0.918715i | \(0.629228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.75379 | −0.166462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.75379 | 0.353127 | 0.176563 | − | 0.984289i | \(-0.443502\pi\) | ||||
0.176563 | + | 0.984289i | \(0.443502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.0000 | −1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.56155 | 0.501468 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.80776 | 0.337884 | 0.168942 | − | 0.985626i | \(-0.445965\pi\) | ||||
0.168942 | + | 0.985626i | \(0.445965\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.36932 | 0.120562 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9309 | −1.65400 | −0.826999 | − | 0.562204i | \(-0.809954\pi\) | ||||
−0.826999 | + | 0.562204i | \(0.809954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.4924 | −1.08323 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.87689 | 0.587533 | 0.293766 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293766 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6847 | 1.07590 | 0.537949 | − | 0.842977i | \(-0.319199\pi\) | ||||
0.537949 | + | 0.842977i | \(0.319199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5616 | −1.14209 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.2462 | −1.19133 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.43845 | −0.368593 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.30019 | −0.354673 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2462 | 1.00325 | 0.501624 | − | 0.865086i | \(-0.332736\pi\) | ||||
0.501624 | + | 0.865086i | \(0.332736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.80776 | 0.309871 | 0.154936 | − | 0.987925i | \(-0.450483\pi\) | ||||
0.154936 | + | 0.987925i | \(0.450483\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.87689 | −0.232583 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.56155 | 0.446715 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.1231 | −1.51656 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.12311 | −0.246135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6847 | −0.993539 | −0.496770 | − | 0.867882i | \(-0.665481\pi\) | ||||
−0.496770 | + | 0.867882i | \(0.665481\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.24621 | 0.486267 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.24621 | −0.171772 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.4924 | −1.71007 | −0.855034 | − | 0.518573i | \(-0.826464\pi\) | ||||
−0.855034 | + | 0.518573i | \(0.826464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12311 | −0.236085 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.0000 | −1.20263 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.68466 | 0.350148 | 0.175074 | − | 0.984555i | \(-0.443984\pi\) | ||||
0.175074 | + | 0.984555i | \(0.443984\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.12311 | −0.380797 | −0.190399 | − | 0.981707i | \(-0.560978\pi\) | ||||
−0.190399 | + | 0.981707i | \(0.560978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.49242 | −0.332089 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.12311 | 0.0825724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.4924 | −1.49855 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.3693 | −1.26343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1231 | −0.804840 | −0.402420 | − | 0.915455i | \(-0.631831\pi\) | ||||
−0.402420 | + | 0.915455i | \(0.631831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4384 | 1.47119 | 0.735596 | − | 0.677421i | \(-0.236902\pi\) | ||||
0.735596 | + | 0.677421i | \(0.236902\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.56155 | −0.398271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5616 | −1.10871 | −0.554357 | − | 0.832279i | \(-0.687036\pi\) | ||||
−0.554357 | + | 0.832279i | \(0.687036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.8617 | 0.972903 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.56155 | −0.248750 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.561553 | −0.0390306 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.24621 | 0.154636 | 0.0773178 | − | 0.997006i | \(-0.475364\pi\) | ||||
0.0773178 | + | 0.997006i | \(0.475364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.5616 | 0.929222 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.876894 | −0.0598037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.3693 | −1.17911 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.4233 | −1.31250 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.2462 | 1.22737 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.4924 | 0.836554 | 0.418277 | − | 0.908319i | \(-0.362634\pi\) | ||||
0.418277 | + | 0.908319i | \(0.362634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.876894 | 0.0582015 | 0.0291008 | − | 0.999576i | \(-0.490736\pi\) | ||||
0.0291008 | + | 0.999576i | \(0.490736\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2462 | −1.07358 | −0.536790 | − | 0.843716i | \(-0.680363\pi\) | ||||
−0.536790 | + | 0.843716i | \(0.680363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.5076 | −1.28350 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.43845 | −0.552821 | −0.276411 | − | 0.961040i | \(-0.589145\pi\) | ||||
−0.276411 | + | 0.961040i | \(0.589145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.68466 | 0.566525 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.75379 | −0.633577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8078 | 0.763781 | 0.381890 | − | 0.924208i | \(-0.375273\pi\) | ||||
0.381890 | + | 0.924208i | \(0.375273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4924 | 0.933539 | 0.466769 | − | 0.884379i | \(-0.345418\pi\) | ||||
0.466769 | + | 0.884379i | \(0.345418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.75379 | 0.175933 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2462 | 0.906465 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.7386 | −1.18751 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2462 | −0.646735 | −0.323368 | − | 0.946273i | \(-0.604815\pi\) | ||||
−0.323368 | + | 0.946273i | \(0.604815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.0540 | 1.74996 | 0.874979 | − | 0.484160i | \(-0.160875\pi\) | ||||
0.874979 | + | 0.484160i | \(0.160875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50758 | −0.217950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.49242 | 0.154277 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.2462 | 0.752279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.6155 | −0.955655 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.3002 | 1.84743 | 0.923717 | − | 0.383074i | \(-0.125135\pi\) | ||||
0.923717 | + | 0.383074i | \(0.125135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2462 | 0.865396 | 0.432698 | − | 0.901539i | \(-0.357562\pi\) | ||||
0.432698 | + | 0.901539i | \(0.357562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.3693 | 1.05124 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5616 | −0.935003 | −0.467502 | − | 0.883992i | \(-0.654846\pi\) | ||||
−0.467502 | + | 0.883992i | \(0.654846\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.12311 | −0.186975 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.49242 | −0.148685 | −0.0743427 | − | 0.997233i | \(-0.523686\pi\) | ||||
−0.0743427 | + | 0.997233i | \(0.523686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.1231 | 1.85008 | 0.925038 | − | 0.379874i | \(-0.124033\pi\) | ||||
0.925038 | + | 0.379874i | \(0.124033\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.24621 | −0.369994 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1231 | 0.656576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.24621 | 0.543895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.384472 | −0.0225381 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.1231 | −1.23403 | −0.617013 | − | 0.786953i | \(-0.711657\pi\) | ||||
−0.617013 | + | 0.786953i | \(0.711657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2462 | 0.596557 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.2462 | −1.29086 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.56155 | 0.205970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.73863 | 0.157852 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.3693 | 1.45743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.87689 | 0.164730 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.2462 | −1.26554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.9309 | −0.846652 | −0.423326 | − | 0.905977i | \(-0.639137\pi\) | ||||
−0.423326 | + | 0.905977i | \(0.639137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.87689 | 0.388705 | 0.194353 | − | 0.980932i | \(-0.437739\pi\) | ||||
0.194353 | + | 0.980932i | \(0.437739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.75379 | 0.0988148 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.7386 | −1.61412 | −0.807061 | − | 0.590468i | \(-0.798943\pi\) | ||||
−0.807061 | + | 0.590468i | \(0.798943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.7538 | 0.994021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.7386 | 1.04589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.4924 | 1.14023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.56155 | 0.197559 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.8769 | 0.712094 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.1231 | −1.49535 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.43845 | 0.353889 | 0.176945 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176945 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.630683 | −0.0345612 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2462 | −0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.2462 | 1.75656 | 0.878282 | − | 0.478144i | \(-0.158690\pi\) | ||||
0.878282 | + | 0.478144i | \(0.158690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.86174 | −0.318366 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.2462 | −1.20470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2614 | 0.716046 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.56155 | −0.0840712 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4924 | 0.885360 | 0.442680 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442680 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8078 | 0.953228 | 0.476614 | − | 0.879113i | \(-0.341864\pi\) | ||||
0.476614 | + | 0.879113i | \(0.341864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.8078 | 1.05726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1922 | 0.755377 | 0.377688 | − | 0.925933i | \(-0.376719\pi\) | ||||
0.377688 | + | 0.925933i | \(0.376719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.68466 | −0.460934 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.9848 | 1.32234 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.2462 | −1.59633 | −0.798167 | − | 0.602436i | \(-0.794197\pi\) | ||||
−0.798167 | + | 0.602436i | \(0.794197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.80776 | −0.409801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.4384 | 0.651058 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4924 | −0.652099 | −0.326050 | − | 0.945353i | \(-0.605718\pi\) | ||||
−0.326050 | + | 0.945353i | \(0.605718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −38.2462 | −1.98564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7386 | 1.28092 | 0.640459 | − | 0.767992i | \(-0.278744\pi\) | ||||
0.640459 | + | 0.767992i | \(0.278744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.8078 | −0.814141 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.24621 | 0.115380 | 0.0576901 | − | 0.998335i | \(-0.481626\pi\) | ||||
0.0576901 | + | 0.998335i | \(0.481626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.94602 | −0.304624 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.61553 | −0.389135 | −0.194568 | − | 0.980889i | \(-0.562330\pi\) | ||||
−0.194568 | + | 0.980889i | \(0.562330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4924 | 0.636673 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.492423 | 0.0250312 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.6155 | −1.70437 | −0.852187 | − | 0.523237i | \(-0.824724\pi\) | ||||
−0.852187 | + | 0.523237i | \(0.824724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.12311 | 0.259087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.5616 | 1.49118 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.24621 | 0.314281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.9309 | −1.25124 | −0.625622 | − | 0.780126i | \(-0.715155\pi\) | ||||
−0.625622 | + | 0.780126i | \(0.715155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.5076 | 0.976600 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.7386 | 1.03564 | 0.517819 | − | 0.855490i | \(-0.326744\pi\) | ||||
0.517819 | + | 0.855490i | \(0.326744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8078 | 0.986695 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.49242 | −0.222681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.6847 | −0.726110 | −0.363055 | − | 0.931768i | \(-0.618266\pi\) | ||||
−0.363055 | + | 0.931768i | \(0.618266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7386 | −0.529698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.0000 | −1.57462 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.8078 | −0.969990 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.876894 | −0.0428391 | −0.0214195 | − | 0.999771i | \(-0.506819\pi\) | ||||
−0.0214195 | + | 0.999771i | \(0.506819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.49242 | −0.316421 | −0.158211 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158211 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.87689 | −0.237123 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.12311 | 0.248507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.98485 | −0.434807 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.2462 | 1.07406 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.61553 | 0.366827 | 0.183414 | − | 0.983036i | \(-0.441285\pi\) | ||||
0.183414 | + | 0.983036i | \(0.441285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7386 | −1.18886 | −0.594431 | − | 0.804146i | \(-0.702623\pi\) | ||||
−0.594431 | + | 0.804146i | \(0.702623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.93087 | 0.332310 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3002 | −1.54160 | −0.770802 | − | 0.637075i | \(-0.780144\pi\) | ||||
−0.770802 | + | 0.637075i | \(0.780144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.54640 | −0.0736380 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.31534 | −0.157517 | −0.0787583 | − | 0.996894i | \(-0.525096\pi\) | ||||
−0.0787583 | + | 0.996894i | \(0.525096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.1231 | −0.904492 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.7386 | −1.54503 | −0.772516 | − | 0.634996i | \(-0.781002\pi\) | ||||
−0.772516 | + | 0.634996i | \(0.781002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.2462 | 0.670828 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.94602 | −0.279369 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.1231 | −0.521459 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.12311 | −0.426761 | −0.213380 | − | 0.976969i | \(-0.568447\pi\) | ||||
−0.213380 | + | 0.976969i | \(0.568447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.4924 | 1.32991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5616 | 1.28367 | 0.641835 | − | 0.766843i | \(-0.278174\pi\) | ||||
0.641835 | + | 0.766843i | \(0.278174\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.24621 | −0.290286 | −0.145143 | − | 0.989411i | \(-0.546364\pi\) | ||||
−0.145143 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.68466 | −0.402741 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6307 | 0.491929 | 0.245965 | − | 0.969279i | \(-0.420895\pi\) | ||||
0.245965 | + | 0.969279i | \(0.420895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.12311 | 0.143905 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.50758 | 0.161279 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.87689 | −0.314871 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.87689 | 0.221906 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.246211 | 0.0111799 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0540 | 1.54313 | 0.771566 | − | 0.636149i | \(-0.219474\pi\) | ||||
0.771566 | + | 0.636149i | \(0.219474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8078 | 0.895738 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.43845 | 0.290563 | 0.145282 | − | 0.989390i | \(-0.453591\pi\) | ||||
0.145282 | + | 0.989390i | \(0.453591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.7386 | −1.02410 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.24621 | 0.100960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.1231 | 1.21664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.0540 | 1.70353 | 0.851765 | − | 0.523924i | \(-0.175532\pi\) | ||||
0.851765 | + | 0.523924i | \(0.175532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4924 | 0.558120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6155 | −0.696262 | −0.348131 | − | 0.937446i | \(-0.613184\pi\) | ||||
−0.348131 | + | 0.937446i | \(0.613184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.2462 | −0.722947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.492423 | 0.0218693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.43845 | −0.196731 | −0.0983654 | − | 0.995150i | \(-0.531361\pi\) | ||||
−0.0983654 | + | 0.995150i | \(0.531361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.8466 | −1.71847 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.2462 | 0.982194 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2462 | 0.627763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.7386 | −1.52780 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.1231 | 1.54173 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.8617 | 1.74637 | 0.873187 | − | 0.487385i | \(-0.162049\pi\) | ||||
0.873187 | + | 0.487385i | \(0.162049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.8617 | 1.48067 | 0.740335 | − | 0.672238i | \(-0.234667\pi\) | ||||
0.740335 | + | 0.672238i | \(0.234667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.87689 | 0.212845 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.4924 | 1.24115 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.75379 | −0.249693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6847 | −0.549434 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | −0.518805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.31534 | −0.315680 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0152 | −0.474456 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3153 | 0.916418 | 0.458209 | − | 0.888844i | \(-0.348491\pi\) | ||||
0.458209 | + | 0.888844i | \(0.348491\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.00000 | 0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.24621 | −0.353229 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0540 | 1.62707 | 0.813535 | − | 0.581516i | \(-0.197540\pi\) | ||||
0.813535 | + | 0.581516i | \(0.197540\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.61553 | −0.0689491 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.7538 | −0.756337 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.5076 | −0.829547 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.75379 | −0.0744442 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2462 | −1.02734 | −0.513672 | − | 0.857986i | \(-0.671715\pi\) | ||||
−0.513672 | + | 0.857986i | \(0.671715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.12311 | −0.132093 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.0000 | 1.35104 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.2311 | 1.82197 | 0.910986 | − | 0.412438i | \(-0.135322\pi\) | ||||
0.910986 | + | 0.412438i | \(0.135322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.75379 | 0.157923 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.8617 | 0.918107 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.7386 | 1.20479 | 0.602393 | − | 0.798200i | \(-0.294214\pi\) | ||||
0.602393 | + | 0.798200i | \(0.294214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3693 | 0.725614 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.4233 | 1.22491 | 0.612454 | − | 0.790506i | \(-0.290183\pi\) | ||||
0.612454 | + | 0.790506i | \(0.290183\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.9157 | −1.32637 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.4773 | −1.55482 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −48.9848 | −2.02874 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.17708 | 0.378779 | 0.189389 | − | 0.981902i | \(-0.439349\pi\) | ||||
0.189389 | + | 0.981902i | \(0.439349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.2462 | 0.916639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.3002 | 0.999576 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.9848 | −1.60092 | −0.800458 | − | 0.599389i | \(-0.795410\pi\) | ||||
−0.800458 | + | 0.599389i | \(0.795410\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0000 | −0.655936 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.4773 | −1.53384 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1771 | −1.10858 | −0.554288 | − | 0.832325i | \(-0.687009\pi\) | ||||
−0.554288 | + | 0.832325i | \(0.687009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.75379 | 0.234312 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.6458 | −0.877134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9309 | 1.25133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.12311 | −0.206920 | −0.103460 | − | 0.994634i | \(-0.532991\pi\) | ||||
−0.103460 | + | 0.994634i | \(0.532991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.56155 | 0.224263 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.61553 | −0.226073 | −0.113036 | − | 0.993591i | \(-0.536058\pi\) | ||||
−0.113036 | + | 0.993591i | \(0.536058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.9848 | 1.48655 | 0.743273 | − | 0.668988i | \(-0.233272\pi\) | ||||
0.743273 | + | 0.668988i | \(0.233272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56155 | 0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.2311 | −1.25125 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.9848 | 0.997799 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.75379 | 0.229419 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.63068 | −0.263963 | −0.131982 | − | 0.991252i | \(-0.542134\pi\) | ||||
−0.131982 | + | 0.991252i | \(0.542134\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.50758 | −0.139414 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.80776 | 0.151107 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.80776 | 0.388598 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.87689 | 0.192927 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.2462 | 1.58963 | 0.794815 | − | 0.606852i | \(-0.207568\pi\) | ||||
0.794815 | + | 0.606852i | \(0.207568\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.3542 | −1.82803 | −0.914015 | − | 0.405681i | \(-0.867034\pi\) | ||||
−0.914015 | + | 0.405681i | \(0.867034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.36932 | 0.0539168 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.56155 | −0.218647 | −0.109324 | − | 0.994006i | \(-0.534868\pi\) | ||||
−0.109324 | + | 0.994006i | \(0.534868\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.9848 | −1.60880 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.1231 | 1.06304 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 50.7926 | 1.98767 | 0.993834 | − | 0.110876i | \(-0.0353658\pi\) | ||||
0.993834 | + | 0.110876i | \(0.0353658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9309 | −0.739690 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.98485 | −0.272505 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.24621 | −0.0875000 | −0.0437500 | − | 0.999043i | \(-0.513930\pi\) | ||||
−0.0437500 | + | 0.999043i | \(0.513930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4924 | −0.874854 | −0.437427 | − | 0.899254i | \(-0.644110\pi\) | ||||
−0.437427 | + | 0.899254i | \(0.644110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.4924 | −1.10655 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.4924 | −0.484435 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.43845 | −0.171857 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.5076 | −0.754207 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.5076 | −0.444245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.438447 | −0.0169009 | −0.00845045 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00845045 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.7386 | −1.10452 | −0.552258 | − | 0.833673i | \(-0.686234\pi\) | ||||
−0.552258 | + | 0.833673i | \(0.686234\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.768944 | −0.0295094 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.36932 | −0.0524723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.4384 | −0.552472 | −0.276236 | − | 0.961090i | \(-0.589087\pi\) | ||||
−0.276236 | + | 0.961090i | \(0.589087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.87689 | 0.262753 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.3693 | 0.967900 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.6155 | 1.66162 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.2462 | −0.389784 | −0.194892 | − | 0.980825i | \(-0.562436\pi\) | ||||
−0.194892 | + | 0.980825i | \(0.562436\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.01515 | −0.266484 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.6847 | 0.481157 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.2462 | −0.691125 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.1771 | 0.498403 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.9848 | −1.01920 | −0.509602 | − | 0.860410i | \(-0.670207\pi\) | ||||
−0.509602 | + | 0.860410i | \(0.670207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.49242 | 0.169435 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.5616 | −0.510758 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.7386 | 1.90822 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.73863 | 0.328186 | 0.164093 | − | 0.986445i | \(-0.447530\pi\) | ||||
0.164093 | + | 0.986445i | \(0.447530\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.50758 | −0.131544 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.56155 | 0.208282 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.2462 | −0.532778 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.4384 | −0.688596 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7386 | −0.400483 | −0.200242 | − | 0.979747i | \(-0.564173\pi\) | ||||
−0.200242 | + | 0.979747i | \(0.564173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.4924 | −1.65698 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.6307 | −0.841644 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.43845 | −0.164840 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.8769 | 1.07098 | 0.535492 | − | 0.844540i | \(-0.320126\pi\) | ||||
0.535492 | + | 0.844540i | \(0.320126\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.49242 | −0.166158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.87689 | 0.106261 | 0.0531303 | − | 0.998588i | \(-0.483080\pi\) | ||||
0.0531303 | + | 0.998588i | \(0.483080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.30019 | −0.158615 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.9848 | 1.50970 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.5464 | −1.56509 | −0.782547 | − | 0.622591i | \(-0.786080\pi\) | ||||
−0.782547 | + | 0.622591i | \(0.786080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.2462 | −0.817235 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.2462 | −1.10963 | −0.554813 | − | 0.831975i | \(-0.687210\pi\) | ||||
−0.554813 | + | 0.831975i | \(0.687210\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2462 | 0.448666 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.73863 | −0.246554 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.4773 | 1.36939 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.38447 | 0.305954 | 0.152977 | − | 0.988230i | \(-0.451114\pi\) | ||||
0.152977 | + | 0.988230i | \(0.451114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.0000 | 0.583072 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.80776 | 0.138579 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.1231 | 1.20388 | 0.601940 | − | 0.798541i | \(-0.294395\pi\) | ||||
0.601940 | + | 0.798541i | \(0.294395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.24621 | 0.226723 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3002 | 1.53338 | 0.766690 | − | 0.642017i | \(-0.221902\pi\) | ||||
0.766690 | + | 0.642017i | \(0.221902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.7538 | 0.932350 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.87689 | −0.104014 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.4924 | 1.31767 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50758 | 0.198608 | 0.0993042 | − | 0.995057i | \(-0.468338\pi\) | ||||
0.0993042 | + | 0.995057i | \(0.468338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.8078 | −1.57770 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2462 | 0.440466 | 0.220233 | − | 0.975447i | \(-0.429318\pi\) | ||||
0.220233 | + | 0.975447i | \(0.429318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.56155 | 0.199777 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.47727 | 0.196496 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.2462 | −0.510423 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.7386 | 1.24305 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.6847 | −0.882158 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7538 | −1.06061 | −0.530304 | − | 0.847808i | \(-0.677922\pi\) | ||||
−0.530304 | + | 0.847808i | \(0.677922\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.4924 | 0.444742 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.7235 | −0.416839 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.2462 | 0.363854 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.1231 | −0.678227 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.8769 | 0.668654 | 0.334327 | − | 0.942457i | \(-0.391491\pi\) | ||||
0.334327 | + | 0.942457i | \(0.391491\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.4924 | 1.57403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.61553 | −0.198415 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −49.7538 | −1.75577 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.12311 | −0.110075 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.3153 | −1.66558 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.4924 | 0.790791 | 0.395396 | − | 0.918511i | \(-0.370607\pi\) | ||||
0.395396 | + | 0.918511i | \(0.370607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6847 | −0.726337 | −0.363168 | − | 0.931724i | \(-0.618305\pi\) | ||||
−0.363168 | + | 0.931724i | \(0.618305\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.2462 | −0.780209 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.6847 | −0.444324 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50758 | −0.122715 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.24621 | 0.218260 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.2462 | −1.68380 | −0.841902 | − | 0.539630i | \(-0.818564\pi\) | ||||
−0.841902 | + | 0.539630i | \(0.818564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.5616 | −0.751588 | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.24621 | 0.217465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.5076 | 0.608063 | 0.304032 | − | 0.952662i | \(-0.401667\pi\) | ||||
0.304032 | + | 0.952662i | \(0.401667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.3002 | 0.842964 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.1080 | 0.488812 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.9309 | 1.06913 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.6155 | −1.09149 | −0.545745 | − | 0.837952i | \(-0.683753\pi\) | ||||
−0.545745 | + | 0.837952i | \(0.683753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.30019 | −0.320696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.89205 | 0.134049 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.315342 | −0.0108481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.6155 | −0.536556 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48.6004 | −1.66796 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.12311 | 0.0384996 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.9848 | −1.47177 | −0.735887 | − | 0.677105i | \(-0.763234\pi\) | ||||
−0.735887 | + | 0.677105i | \(0.763234\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.24621 | −0.0768188 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.1771 | −0.381802 | −0.190901 | − | 0.981609i | \(-0.561141\pi\) | ||||
−0.190901 | + | 0.981609i | \(0.561141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.4233 | −0.799192 | −0.399596 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399596 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.3693 | −0.591945 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.4233 | −1.47815 | −0.739073 | − | 0.673625i | \(-0.764736\pi\) | ||||
−0.739073 | + | 0.673625i | \(0.764736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.4924 | −0.764765 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4384 | −0.490355 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.9848 | −0.847553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.4924 | −1.23650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.138261 | −0.00467941 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.12311 | −0.105580 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.73863 | 0.295083 | 0.147541 | − | 0.989056i | \(-0.452864\pi\) | ||||
0.147541 | + | 0.989056i | \(0.452864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.9848 | 1.11255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.1080 | −1.68818 | −0.844090 | − | 0.536202i | \(-0.819859\pi\) | ||||
−0.844090 | + | 0.536202i | \(0.819859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.50758 | −0.252650 | −0.126325 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126325 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0000 | −0.537834 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.5616 | −1.26119 | −0.630597 | − | 0.776111i | \(-0.717190\pi\) | ||||
−0.630597 | + | 0.776111i | \(0.717190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8920 | −0.398847 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.0000 | 0.938035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.7386 | 1.16248 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.68466 | 0.156591 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.56155 | −0.185695 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.6847 | −0.823279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.7386 | 2.09013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.27652 | −0.142314 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.12311 | −0.170298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.12311 | 0.302594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.4924 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433647\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433647\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0000 | −1.58857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.49242 | −0.148515 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.1231 | 1.95242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8617 | 0.721152 | 0.360576 | − | 0.932730i | \(-0.382580\pi\) | ||||
0.360576 | + | 0.932730i | \(0.382580\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.7386 | −0.617459 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.9309 | −1.01810 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12311 | 0.0369275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0540 | −0.789185 | −0.394593 | − | 0.918856i | \(-0.629114\pi\) | ||||
−0.394593 | + | 0.918856i | \(0.629114\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0152 | 0.361007 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.3153 | 0.763310 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.4924 | −0.670174 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6307 | 0.543301 | 0.271650 | − | 0.962396i | \(-0.412431\pi\) | ||||
0.271650 | + | 0.962396i | \(0.412431\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7386 | −0.350442 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.6004 | 1.51913 | 0.759564 | − | 0.650432i | \(-0.225412\pi\) | ||||
0.759564 | + | 0.650432i | \(0.225412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.56155 | −0.115980 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.3693 | −0.565024 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.8078 | −1.81351 | −0.906754 | − | 0.421659i | \(-0.861448\pi\) | ||||
−0.906754 | + | 0.421659i | \(0.861448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.3002 | 1.43804 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.8769 | 1.45523 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.4924 | 1.50604 | 0.753019 | − | 0.657999i | \(-0.228597\pi\) | ||||
0.753019 | + | 0.657999i | \(0.228597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.1231 | −0.359935 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.7235 | −0.896173 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.4773 | −0.693537 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0691303 | −0.00223001 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.73863 | 0.217149 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.4384 | 0.657937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.1771 | −1.45280 | −0.726398 | − | 0.687274i | \(-0.758807\pi\) | ||||
−0.726398 | + | 0.687274i | \(0.758807\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.0000 | −1.02799 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.3693 | −0.685774 | −0.342887 | − | 0.939377i | \(-0.611405\pi\) | ||||
−0.342887 | + | 0.939377i | \(0.611405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.6155 | −1.27002 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.56155 | −0.178112 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.1080 | −0.835267 | −0.417634 | − | 0.908615i | \(-0.637140\pi\) | ||||
−0.417634 | + | 0.908615i | \(0.637140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.0000 | −1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.63068 | 0.147846 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.8769 | 0.921030 | 0.460515 | − | 0.887652i | \(-0.347665\pi\) | ||||
0.460515 | + | 0.887652i | \(0.347665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.5616 | −0.495832 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.3542 | 1.34815 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.876894 | −0.0278836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4924 | 0.650963 | 0.325482 | − | 0.945548i | \(-0.394474\pi\) | ||||
0.325482 | + | 0.945548i | \(0.394474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0540 | −0.319053 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | 0.760851 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.738634 | 0.0233928 | 0.0116964 | − | 0.999932i | \(-0.496277\pi\) | ||||
0.0116964 | + | 0.999932i | \(0.496277\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.24621 | 0.197621 |
(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 | 920.2.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 8280.2.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | 1840.2.a.k.1.2 | 2 | |||
5.2 | odd | 4 | 4600.2.e.m.4049.3 | 4 | |||
5.3 | odd | 4 | 4600.2.e.m.4049.2 | 4 | |||
5.4 | even | 2 | 4600.2.a.r.1.2 | 2 | |||
8.3 | odd | 2 | 7360.2.a.bm.1.1 | 2 | |||
8.5 | even | 2 | 7360.2.a.bj.1.2 | 2 | |||
20.19 | odd | 2 | 9200.2.a.bx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1840.2.a.k.1.2 | 2 | 4.3 | odd | 2 | |||
4600.2.a.r.1.2 | 2 | 5.4 | even | 2 | |||
4600.2.e.m.4049.2 | 4 | 5.3 | odd | 4 | |||
4600.2.e.m.4049.3 | 4 | 5.2 | odd | 4 | |||
7360.2.a.bj.1.2 | 2 | 8.5 | even | 2 | |||
7360.2.a.bm.1.1 | 2 | 8.3 | odd | 2 | |||
8280.2.a.bb.1.1 | 2 | 3.2 | odd | 2 | |||
9200.2.a.bx.1.1 | 2 | 20.19 | odd | 2 |