Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9702,2,Mod(1,9702)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9702, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9702.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9702.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: | \(77.4708600410\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.41883\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9702.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.41883 | −1.97616 | −0.988081 | − | 0.153935i | \(-0.950805\pi\) | ||||
−0.988081 | + | 0.153935i | \(0.950805\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.41883 | 1.39736 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.37683 | −0.576467 | −0.288233 | − | 0.957560i | \(-0.593068\pi\) | ||||
−0.288233 | + | 0.957560i | \(0.593068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.68842 | −0.846181 | −0.423090 | − | 0.906087i | \(-0.639055\pi\) | ||||
−0.423090 | + | 0.906087i | \(0.639055\pi\) | |||||||
\(20\) | −4.41883 | −0.988081 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −4.73042 | −0.986360 | −0.493180 | − | 0.869927i | \(-0.664166\pi\) | ||||
−0.493180 | + | 0.869927i | \(0.664166\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.5261 | 2.90522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.52608 | 1.21186 | 0.605932 | − | 0.795517i | \(-0.292801\pi\) | ||||
0.605932 | + | 0.795517i | \(0.292801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37683 | −0.606497 | −0.303249 | − | 0.952911i | \(-0.598071\pi\) | ||||
−0.303249 | + | 0.952911i | \(0.598071\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.37683 | 0.407624 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.68842 | 1.26397 | 0.631984 | − | 0.774981i | \(-0.282241\pi\) | ||||
0.631984 | + | 0.774981i | \(0.282241\pi\) | |||||||
\(38\) | 3.68842 | 0.598340 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.41883 | 0.698679 | ||||||||
\(41\) | −12.1492 | −1.89739 | −0.948697 | − | 0.316187i | \(-0.897597\pi\) | ||||
−0.948697 | + | 0.316187i | \(0.897597\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.06525 | 0.467446 | 0.233723 | − | 0.972303i | \(-0.424909\pi\) | ||||
0.233723 | + | 0.972303i | \(0.424909\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.73042 | 0.697462 | ||||||||
\(47\) | 4.10725 | 0.599104 | 0.299552 | − | 0.954080i | \(-0.403163\pi\) | ||||
0.299552 | + | 0.954080i | \(0.403163\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.5261 | −2.05430 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.41883 | −0.595835 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.52608 | −0.856917 | ||||||||
\(59\) | 12.5261 | 1.63076 | 0.815379 | − | 0.578928i | \(-0.196529\pi\) | ||||
0.815379 | + | 0.578928i | \(0.196529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.79567 | 0.485985 | 0.242993 | − | 0.970028i | \(-0.421871\pi\) | ||||
0.242993 | + | 0.970028i | \(0.421871\pi\) | |||||||
\(62\) | 3.37683 | 0.428858 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1492 | 1.23993 | 0.619964 | − | 0.784630i | \(-0.287147\pi\) | ||||
0.619964 | + | 0.784630i | \(0.287147\pi\) | |||||||
\(68\) | −2.37683 | −0.288233 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.934749 | −0.110934 | −0.0554672 | − | 0.998461i | \(-0.517665\pi\) | ||||
−0.0554672 | + | 0.998461i | \(0.517665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.46083 | −0.873224 | −0.436612 | − | 0.899650i | \(-0.643822\pi\) | ||||
−0.436612 | + | 0.899650i | \(0.643822\pi\) | |||||||
\(74\) | −7.68842 | −0.893760 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.68842 | −0.423090 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.418833 | −0.0471224 | −0.0235612 | − | 0.999722i | \(-0.507500\pi\) | ||||
−0.0235612 | + | 0.999722i | \(0.507500\pi\) | |||||||
\(80\) | −4.41883 | −0.494041 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.1492 | 1.34166 | ||||||||
\(83\) | 2.14925 | 0.235911 | 0.117955 | − | 0.993019i | \(-0.462366\pi\) | ||||
0.117955 | + | 0.993019i | \(0.462366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5028 | 1.13919 | ||||||||
\(86\) | −3.06525 | −0.330534 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 12.8377 | 1.36079 | 0.680395 | − | 0.732846i | \(-0.261808\pi\) | ||||
0.680395 | + | 0.732846i | \(0.261808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.73042 | −0.493180 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.10725 | −0.423630 | ||||||||
\(95\) | 16.2985 | 1.67219 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.5261 | 1.45261 | ||||||||
\(101\) | 15.3637 | 1.52875 | 0.764375 | − | 0.644772i | \(-0.223048\pi\) | ||||
0.764375 | + | 0.644772i | \(0.223048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.62317 | −0.258468 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | −10.9029 | −1.05402 | −0.527012 | − | 0.849858i | \(-0.676688\pi\) | ||||
−0.527012 | + | 0.849858i | \(0.676688\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7957 | −1.12982 | −0.564910 | − | 0.825153i | \(-0.691089\pi\) | ||||
−0.564910 | + | 0.825153i | \(0.691089\pi\) | |||||||
\(110\) | 4.41883 | 0.421319 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.37683 | −0.505810 | −0.252905 | − | 0.967491i | \(-0.581386\pi\) | ||||
−0.252905 | + | 0.967491i | \(0.581386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.9029 | 1.94921 | ||||||||
\(116\) | 6.52608 | 0.605932 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.5261 | −1.15312 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.79567 | −0.343643 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.37683 | −0.303249 | ||||||||
\(125\) | −42.0942 | −3.76502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.730416 | 0.0648139 | 0.0324070 | − | 0.999475i | \(-0.489683\pi\) | ||||
0.0324070 | + | 0.999475i | \(0.489683\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.37683 | −0.644517 | −0.322258 | − | 0.946652i | \(-0.604442\pi\) | ||||
−0.322258 | + | 0.946652i | \(0.604442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.1492 | −0.876762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.37683 | 0.203812 | ||||||||
\(137\) | 8.83767 | 0.755053 | 0.377526 | − | 0.925999i | \(-0.376775\pi\) | ||||
0.377526 | + | 0.925999i | \(0.376775\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.47392 | 0.125016 | 0.0625080 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625080 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.934749 | 0.0784424 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.8377 | −2.39484 | ||||||||
\(146\) | 7.46083 | 0.617463 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.68842 | 0.631984 | ||||||||
\(149\) | 9.36375 | 0.767108 | 0.383554 | − | 0.923518i | \(-0.374700\pi\) | ||||
0.383554 | + | 0.923518i | \(0.374700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5681 | −1.10415 | −0.552077 | − | 0.833793i | \(-0.686165\pi\) | ||||
−0.552077 | + | 0.833793i | \(0.686165\pi\) | |||||||
\(152\) | 3.68842 | 0.299170 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.9217 | 1.19854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.7406 | −1.49566 | −0.747831 | − | 0.663890i | \(-0.768904\pi\) | ||||
−0.747831 | + | 0.663890i | \(0.768904\pi\) | |||||||
\(158\) | 0.418833 | 0.0333205 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.41883 | 0.349339 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7724 | 1.47037 | 0.735185 | − | 0.677867i | \(-0.237096\pi\) | ||||
0.735185 | + | 0.677867i | \(0.237096\pi\) | |||||||
\(164\) | −12.1492 | −0.948697 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.14925 | −0.166814 | ||||||||
\(167\) | 23.8898 | 1.84865 | 0.924325 | − | 0.381606i | \(-0.124629\pi\) | ||||
0.924325 | + | 0.381606i | \(0.124629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −10.5028 | −0.805530 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.06525 | 0.233723 | ||||||||
\(173\) | −11.3768 | −0.864965 | −0.432482 | − | 0.901642i | \(-0.642362\pi\) | ||||
−0.432482 | + | 0.901642i | \(0.642362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.8377 | −0.962224 | ||||||||
\(179\) | −24.6101 | −1.83944 | −0.919722 | − | 0.392571i | \(-0.871586\pi\) | ||||
−0.919722 | + | 0.392571i | \(0.871586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4608 | 1.29785 | 0.648927 | − | 0.760851i | \(-0.275218\pi\) | ||||
0.648927 | + | 0.760851i | \(0.275218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.73042 | 0.348731 | ||||||||
\(185\) | −33.9738 | −2.49781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.37683 | −0.173811 | ||||||||
\(188\) | 4.10725 | 0.299552 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.2985 | −1.18242 | ||||||||
\(191\) | 16.8377 | 1.21833 | 0.609165 | − | 0.793043i | \(-0.291505\pi\) | ||||
0.609165 | + | 0.793043i | \(0.291505\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.46083 | 0.393079 | 0.196540 | − | 0.980496i | \(-0.437030\pi\) | ||||
0.196540 | + | 0.980496i | \(0.437030\pi\) | |||||||
\(194\) | −7.00000 | −0.502571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.68842 | 0.690271 | 0.345136 | − | 0.938553i | \(-0.387833\pi\) | ||||
0.345136 | + | 0.938553i | \(0.387833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2985 | 1.43892 | 0.719461 | − | 0.694533i | \(-0.244389\pi\) | ||||
0.719461 | + | 0.694533i | \(0.244389\pi\) | |||||||
\(200\) | −14.5261 | −1.02715 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.3637 | −1.08099 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 53.6855 | 3.74956 | ||||||||
\(206\) | 2.62317 | 0.182765 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.68842 | −0.255133 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5130 | 1.54986 | 0.774929 | − | 0.632048i | \(-0.217785\pi\) | ||||
0.774929 | + | 0.632048i | \(0.217785\pi\) | |||||||
\(212\) | −8.00000 | −0.549442 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.9029 | 0.745308 | ||||||||
\(215\) | −13.5448 | −0.923750 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.7957 | 0.798903 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.41883 | −0.297918 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.46083 | −0.499614 | −0.249807 | − | 0.968296i | \(-0.580367\pi\) | ||||
−0.249807 | + | 0.968296i | \(0.580367\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.37683 | 0.357662 | ||||||||
\(227\) | 2.77241 | 0.184012 | 0.0920058 | − | 0.995758i | \(-0.470672\pi\) | ||||
0.0920058 | + | 0.995758i | \(0.470672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.53917 | −0.167793 | −0.0838965 | − | 0.996474i | \(-0.526737\pi\) | ||||
−0.0838965 | + | 0.996474i | \(0.526737\pi\) | |||||||
\(230\) | −20.9029 | −1.37830 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.52608 | −0.428458 | ||||||||
\(233\) | 24.0522 | 1.57571 | 0.787855 | − | 0.615861i | \(-0.211192\pi\) | ||||
0.787855 | + | 0.615861i | \(0.211192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.1492 | −1.18393 | ||||||||
\(236\) | 12.5261 | 0.815379 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.59133 | −0.491042 | −0.245521 | − | 0.969391i | \(-0.578959\pi\) | ||||
−0.245521 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2985 | 1.04988 | 0.524939 | − | 0.851140i | \(-0.324088\pi\) | ||||
0.524939 | + | 0.851140i | \(0.324088\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.79567 | 0.242993 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.37683 | 0.214429 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 42.0942 | 2.66227 | ||||||||
\(251\) | 8.61008 | 0.543463 | 0.271732 | − | 0.962373i | \(-0.412404\pi\) | ||||
0.271732 | + | 0.962373i | \(0.412404\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.73042 | −0.297399 | ||||||||
\(254\) | −0.730416 | −0.0458304 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.837665 | −0.0522521 | −0.0261261 | − | 0.999659i | \(-0.508317\pi\) | ||||
−0.0261261 | + | 0.999659i | \(0.508317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.37683 | 0.455742 | ||||||||
\(263\) | −10.8377 | −0.668279 | −0.334140 | − | 0.942524i | \(-0.608446\pi\) | ||||
−0.334140 | + | 0.942524i | \(0.608446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.3507 | 2.17157 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.1492 | 0.619964 | ||||||||
\(269\) | −17.8797 | −1.09014 | −0.545071 | − | 0.838390i | \(-0.683497\pi\) | ||||
−0.545071 | + | 0.838390i | \(0.683497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.83767 | −0.536850 | −0.268425 | − | 0.963301i | \(-0.586503\pi\) | ||||
−0.268425 | + | 0.963301i | \(0.586503\pi\) | |||||||
\(272\) | −2.37683 | −0.144117 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.83767 | −0.533903 | ||||||||
\(275\) | 14.5261 | 0.875956 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | −1.47392 | −0.0883997 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9217 | 0.949807 | 0.474903 | − | 0.880038i | \(-0.342483\pi\) | ||||
0.474903 | + | 0.880038i | \(0.342483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0840 | −1.07498 | −0.537491 | − | 0.843269i | \(-0.680628\pi\) | ||||
−0.537491 | + | 0.843269i | \(0.680628\pi\) | |||||||
\(284\) | −0.934749 | −0.0554672 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.3507 | −0.667686 | ||||||||
\(290\) | 28.8377 | 1.69341 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.46083 | −0.436612 | ||||||||
\(293\) | −25.1492 | −1.46923 | −0.734617 | − | 0.678482i | \(-0.762638\pi\) | ||||
−0.734617 | + | 0.678482i | \(0.762638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −55.3507 | −3.22264 | ||||||||
\(296\) | −7.68842 | −0.446880 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.36375 | −0.542427 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.5681 | 0.780755 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.68842 | −0.211545 | ||||||||
\(305\) | −16.7724 | −0.960386 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.86950 | −0.220844 | −0.110422 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110422 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.9217 | −0.847494 | ||||||||
\(311\) | 13.5681 | 0.769375 | 0.384688 | − | 0.923047i | \(-0.374309\pi\) | ||||
0.384688 | + | 0.923047i | \(0.374309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.52608 | 0.142783 | 0.0713913 | − | 0.997448i | \(-0.477256\pi\) | ||||
0.0713913 | + | 0.997448i | \(0.477256\pi\) | |||||||
\(314\) | 18.7406 | 1.05759 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.418833 | −0.0235612 | ||||||||
\(317\) | 20.0102 | 1.12388 | 0.561941 | − | 0.827177i | \(-0.310055\pi\) | ||||
0.561941 | + | 0.827177i | \(0.310055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.52608 | 0.365390 | ||||||||
\(320\) | −4.41883 | −0.247020 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.76675 | 0.487795 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.7724 | −1.03971 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.1492 | 0.670830 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.1492 | −0.887643 | −0.443821 | − | 0.896115i | \(-0.646378\pi\) | ||||
−0.443821 | + | 0.896115i | \(0.646378\pi\) | |||||||
\(332\) | 2.14925 | 0.117955 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.8898 | −1.30719 | ||||||||
\(335\) | −44.8478 | −2.45030 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1362 | 1.26031 | 0.630154 | − | 0.776471i | \(-0.282992\pi\) | ||||
0.630154 | + | 0.776471i | \(0.282992\pi\) | |||||||
\(338\) | 13.0000 | 0.707107 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.5028 | 0.569596 | ||||||||
\(341\) | −3.37683 | −0.182866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.06525 | −0.165267 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.3768 | 0.611622 | ||||||||
\(347\) | −15.6566 | −0.840489 | −0.420245 | − | 0.907411i | \(-0.638056\pi\) | ||||
−0.420245 | + | 0.907411i | \(0.638056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0102 | −1.07112 | −0.535560 | − | 0.844497i | \(-0.679899\pi\) | ||||
−0.535560 | + | 0.844497i | \(0.679899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −7.46083 | −0.397100 | −0.198550 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198550 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.13050 | 0.219224 | ||||||||
\(356\) | 12.8377 | 0.680395 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.6101 | 1.30068 | ||||||||
\(359\) | 11.2463 | 0.593559 | 0.296779 | − | 0.954946i | \(-0.404087\pi\) | ||||
0.296779 | + | 0.954946i | \(0.404087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.39558 | −0.283978 | ||||||||
\(362\) | −17.4608 | −0.917721 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9682 | 1.72563 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.91600 | −0.308813 | −0.154406 | − | 0.988007i | \(-0.549347\pi\) | ||||
−0.154406 | + | 0.988007i | \(0.549347\pi\) | |||||||
\(368\) | −4.73042 | −0.246590 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 33.9738 | 1.76622 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1260 | −1.19742 | −0.598709 | − | 0.800966i | \(-0.704320\pi\) | ||||
−0.598709 | + | 0.800966i | \(0.704320\pi\) | |||||||
\(374\) | 2.37683 | 0.122903 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.10725 | −0.211815 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.77241 | −0.347876 | −0.173938 | − | 0.984757i | \(-0.555649\pi\) | ||||
−0.173938 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(380\) | 16.2985 | 0.836095 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.8377 | −0.861490 | ||||||||
\(383\) | −25.3637 | −1.29603 | −0.648013 | − | 0.761629i | \(-0.724400\pi\) | ||||
−0.648013 | + | 0.761629i | \(0.724400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.46083 | −0.277949 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.00000 | 0.355371 | ||||||||
\(389\) | −25.2565 | −1.28056 | −0.640278 | − | 0.768144i | \(-0.721181\pi\) | ||||
−0.640278 | + | 0.768144i | \(0.721181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2434 | 0.568604 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.68842 | −0.488095 | ||||||||
\(395\) | 1.85075 | 0.0931214 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4739 | −0.676237 | −0.338118 | − | 0.941104i | \(-0.609790\pi\) | ||||
−0.338118 | + | 0.941104i | \(0.609790\pi\) | |||||||
\(398\) | −20.2985 | −1.01747 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.5261 | 0.726304 | ||||||||
\(401\) | −33.8898 | −1.69238 | −0.846189 | − | 0.532883i | \(-0.821108\pi\) | ||||
−0.846189 | + | 0.532883i | \(0.821108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.3637 | 0.764375 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.68842 | 0.381101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.21450 | −0.208394 | −0.104197 | − | 0.994557i | \(-0.533227\pi\) | ||||
−0.104197 | + | 0.994557i | \(0.533227\pi\) | |||||||
\(410\) | −53.6855 | −2.65134 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.62317 | −0.129234 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.49717 | −0.466198 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.68842 | 0.180406 | ||||||||
\(419\) | 22.3116 | 1.08999 | 0.544996 | − | 0.838439i | \(-0.316531\pi\) | ||||
0.544996 | + | 0.838439i | \(0.316531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3116 | 0.892452 | 0.446226 | − | 0.894920i | \(-0.352768\pi\) | ||||
0.446226 | + | 0.894920i | \(0.352768\pi\) | |||||||
\(422\) | −22.5130 | −1.09592 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.00000 | 0.388514 | ||||||||
\(425\) | −34.5261 | −1.67476 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.9029 | −0.527012 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.5448 | 0.653190 | ||||||||
\(431\) | 28.8377 | 1.38906 | 0.694531 | − | 0.719463i | \(-0.255612\pi\) | ||||
0.694531 | + | 0.719463i | \(0.255612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.62317 | 0.366346 | 0.183173 | − | 0.983081i | \(-0.441363\pi\) | ||||
0.183173 | + | 0.983081i | \(0.441363\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7957 | −0.564910 | ||||||||
\(437\) | 17.4477 | 0.834639 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.3739 | −1.59285 | −0.796425 | − | 0.604737i | \(-0.793278\pi\) | ||||
−0.796425 | + | 0.604737i | \(0.793278\pi\) | |||||||
\(440\) | 4.41883 | 0.210660 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.85075 | 0.230466 | 0.115233 | − | 0.993338i | \(-0.463239\pi\) | ||||
0.115233 | + | 0.993338i | \(0.463239\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −56.7275 | −2.68914 | ||||||||
\(446\) | 7.46083 | 0.353281 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3450 | −0.676982 | −0.338491 | − | 0.940970i | \(-0.609917\pi\) | ||||
−0.338491 | + | 0.940970i | \(0.609917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1492 | −0.572086 | ||||||||
\(452\) | −5.37683 | −0.252905 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.77241 | −0.130116 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.1827 | −1.17800 | −0.588998 | − | 0.808135i | \(-0.700477\pi\) | ||||
−0.588998 | + | 0.808135i | \(0.700477\pi\) | |||||||
\(458\) | 2.53917 | 0.118648 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.9029 | 0.974603 | ||||||||
\(461\) | −13.0187 | −0.606344 | −0.303172 | − | 0.952936i | \(-0.598046\pi\) | ||||
−0.303172 | + | 0.952936i | \(0.598046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.2145 | −0.660604 | −0.330302 | − | 0.943875i | \(-0.607151\pi\) | ||||
−0.330302 | + | 0.943875i | \(0.607151\pi\) | |||||||
\(464\) | 6.52608 | 0.302966 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0522 | −1.11420 | ||||||||
\(467\) | 2.39558 | 0.110854 | 0.0554271 | − | 0.998463i | \(-0.482348\pi\) | ||||
0.0554271 | + | 0.998463i | \(0.482348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.1492 | 0.837162 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.5261 | −0.576560 | ||||||||
\(473\) | 3.06525 | 0.140940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −53.5782 | −2.45834 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.59133 | 0.347219 | ||||||||
\(479\) | −10.8377 | −0.495186 | −0.247593 | − | 0.968864i | \(-0.579640\pi\) | ||||
−0.247593 | + | 0.968864i | \(0.579640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.2985 | −0.742376 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −30.9318 | −1.40454 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6435 | −1.56985 | −0.784923 | − | 0.619593i | \(-0.787298\pi\) | ||||
−0.784923 | + | 0.619593i | \(0.787298\pi\) | |||||||
\(488\) | −3.79567 | −0.171822 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.1492 | −1.72165 | −0.860826 | − | 0.508900i | \(-0.830052\pi\) | ||||
−0.860826 | + | 0.508900i | \(0.830052\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.5114 | −0.698599 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.37683 | −0.151624 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.623166 | −0.0278968 | −0.0139484 | − | 0.999903i | \(-0.504440\pi\) | ||||
−0.0139484 | + | 0.999903i | \(0.504440\pi\) | |||||||
\(500\) | −42.0942 | −1.88251 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.61008 | −0.384287 | ||||||||
\(503\) | −31.1362 | −1.38829 | −0.694146 | − | 0.719834i | \(-0.744218\pi\) | ||||
−0.694146 | + | 0.719834i | \(0.744218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −67.8898 | −3.02106 | ||||||||
\(506\) | 4.73042 | 0.210293 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.730416 | 0.0324070 | ||||||||
\(509\) | 42.1043 | 1.86624 | 0.933121 | − | 0.359563i | \(-0.117074\pi\) | ||||
0.933121 | + | 0.359563i | \(0.117074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.837665 | 0.0369478 | ||||||||
\(515\) | 11.5913 | 0.510775 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.10725 | 0.180637 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.2667 | −1.10483 | −0.552417 | − | 0.833568i | \(-0.686294\pi\) | ||||
−0.552417 | + | 0.833568i | \(0.686294\pi\) | |||||||
\(524\) | −7.37683 | −0.322258 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8377 | 0.472545 | ||||||||
\(527\) | 8.02617 | 0.349626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.623166 | −0.0270942 | ||||||||
\(530\) | −35.3507 | −1.53553 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.1782 | 2.08292 | ||||||||
\(536\) | −10.1492 | −0.438381 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.8797 | 0.770847 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.41883 | −0.189980 | −0.0949902 | − | 0.995478i | \(-0.530282\pi\) | ||||
−0.0949902 | + | 0.995478i | \(0.530282\pi\) | |||||||
\(542\) | 8.83767 | 0.379610 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.37683 | 0.101906 | ||||||||
\(545\) | 52.1231 | 2.23271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.6622 | −1.18275 | −0.591376 | − | 0.806396i | \(-0.701415\pi\) | ||||
−0.591376 | + | 0.806396i | \(0.701415\pi\) | |||||||
\(548\) | 8.83767 | 0.377526 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.5261 | −0.619394 | ||||||||
\(551\) | −24.0709 | −1.02546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.47392 | 0.0625080 | ||||||||
\(557\) | 7.98691 | 0.338416 | 0.169208 | − | 0.985580i | \(-0.445879\pi\) | ||||
0.169208 | + | 0.985580i | \(0.445879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.9217 | −0.671615 | ||||||||
\(563\) | 27.3507 | 1.15269 | 0.576346 | − | 0.817205i | \(-0.304478\pi\) | ||||
0.576346 | + | 0.817205i | \(0.304478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.7593 | 0.999562 | ||||||||
\(566\) | 18.0840 | 0.760127 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.934749 | 0.0392212 | ||||||||
\(569\) | 29.4477 | 1.23451 | 0.617257 | − | 0.786762i | \(-0.288244\pi\) | ||||
0.617257 | + | 0.786762i | \(0.288244\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5261 | −0.607898 | −0.303949 | − | 0.952688i | \(-0.598305\pi\) | ||||
−0.303949 | + | 0.952688i | \(0.598305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −68.7144 | −2.86559 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.3956 | 0.557665 | 0.278833 | − | 0.960340i | \(-0.410053\pi\) | ||||
0.278833 | + | 0.960340i | \(0.410053\pi\) | |||||||
\(578\) | 11.3507 | 0.472125 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −28.8377 | −1.19742 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 7.46083 | 0.308731 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.1492 | 1.03891 | ||||||||
\(587\) | 11.2928 | 0.466105 | 0.233053 | − | 0.972464i | \(-0.425129\pi\) | ||||
0.233053 | + | 0.972464i | \(0.425129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4552 | 0.513206 | ||||||||
\(590\) | 55.3507 | 2.27875 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.68842 | 0.315992 | ||||||||
\(593\) | 19.5782 | 0.803982 | 0.401991 | − | 0.915644i | \(-0.368318\pi\) | ||||
0.401991 | + | 0.915644i | \(0.368318\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.36375 | 0.383554 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9318 | −0.446662 | −0.223331 | − | 0.974743i | \(-0.571693\pi\) | ||||
−0.223331 | + | 0.974743i | \(0.571693\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2202 | −1.68141 | −0.840703 | − | 0.541497i | \(-0.817858\pi\) | ||||
−0.840703 | + | 0.541497i | \(0.817858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.5681 | −0.552077 | ||||||||
\(605\) | −4.41883 | −0.179651 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.3405 | −1.27207 | −0.636036 | − | 0.771660i | \(-0.719427\pi\) | ||||
−0.636036 | + | 0.771660i | \(0.719427\pi\) | |||||||
\(608\) | 3.68842 | 0.149585 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.7724 | 0.679095 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0885 | 0.690198 | 0.345099 | − | 0.938566i | \(-0.387845\pi\) | ||||
0.345099 | + | 0.938566i | \(0.387845\pi\) | |||||||
\(614\) | 3.86950 | 0.156160 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.96817 | 0.280528 | 0.140264 | − | 0.990114i | \(-0.455205\pi\) | ||||
0.140264 | + | 0.990114i | \(0.455205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0187473 | −0.000753517 0 | −0.000376759 | − | 1.00000i | \(-0.500120\pi\) | ||||
−0.000376759 | 1.00000i | \(0.500120\pi\) | ||||||||
\(620\) | 14.9217 | 0.599268 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.5681 | −0.544030 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 113.377 | 4.53507 | ||||||||
\(626\) | −2.52608 | −0.100963 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.7406 | −0.747831 | ||||||||
\(629\) | −18.2741 | −0.728636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.78550 | −0.230317 | −0.115159 | − | 0.993347i | \(-0.536738\pi\) | ||||
−0.115159 | + | 0.993347i | \(0.536738\pi\) | |||||||
\(632\) | 0.418833 | 0.0166603 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.0102 | −0.794705 | ||||||||
\(635\) | −3.22759 | −0.128083 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.52608 | −0.258370 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.41883 | 0.174670 | ||||||||
\(641\) | −15.3768 | −0.607348 | −0.303674 | − | 0.952776i | \(-0.598213\pi\) | ||||
−0.303674 | + | 0.952776i | \(0.598213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.8058 | −1.41204 | −0.706022 | − | 0.708190i | \(-0.749512\pi\) | ||||
−0.706022 | + | 0.708190i | \(0.749512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.76675 | −0.344923 | ||||||||
\(647\) | −9.25650 | −0.363910 | −0.181955 | − | 0.983307i | \(-0.558243\pi\) | ||||
−0.181955 | + | 0.983307i | \(0.558243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.5261 | 0.491692 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.7724 | 0.735185 | ||||||||
\(653\) | −24.8478 | −0.972371 | −0.486185 | − | 0.873856i | \(-0.661612\pi\) | ||||
−0.486185 | + | 0.873856i | \(0.661612\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.5970 | 1.27367 | ||||||||
\(656\) | −12.1492 | −0.474348 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.60442 | 0.257272 | 0.128636 | − | 0.991692i | \(-0.458940\pi\) | ||||
0.128636 | + | 0.991692i | \(0.458940\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2332 | −0.514714 | −0.257357 | − | 0.966316i | \(-0.582852\pi\) | ||||
−0.257357 | + | 0.966316i | \(0.582852\pi\) | |||||||
\(662\) | 16.1492 | 0.627658 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.14925 | −0.0834070 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.8711 | −1.19533 | ||||||||
\(668\) | 23.8898 | 0.924325 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 44.8478 | 1.73262 | ||||||||
\(671\) | 3.79567 | 0.146530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.130501 | 0.00503045 | 0.00251523 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251523 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(674\) | −23.1362 | −0.891172 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −28.1174 | −1.08064 | −0.540320 | − | 0.841460i | \(-0.681697\pi\) | ||||
−0.540320 | + | 0.841460i | \(0.681697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10.5028 | −0.402765 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.37683 | 0.129306 | ||||||||
\(683\) | −15.9029 | −0.608508 | −0.304254 | − | 0.952591i | \(-0.598407\pi\) | ||||
−0.304254 | + | 0.952591i | \(0.598407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.0522 | −1.49211 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.06525 | 0.116862 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.9813 | −0.607956 | −0.303978 | − | 0.952679i | \(-0.598315\pi\) | ||||
−0.303978 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(692\) | −11.3768 | −0.432482 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6566 | 0.594316 | ||||||||
\(695\) | −6.51300 | −0.247052 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.8767 | 1.09378 | ||||||||
\(698\) | 20.0102 | 0.757396 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9869 | −0.528278 | −0.264139 | − | 0.964485i | \(-0.585088\pi\) | ||||
−0.264139 | + | 0.964485i | \(0.585088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.3581 | −1.06955 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.46083 | 0.280792 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.64191 | 0.286998 | 0.143499 | − | 0.989650i | \(-0.454165\pi\) | ||||
0.143499 | + | 0.989650i | \(0.454165\pi\) | |||||||
\(710\) | −4.13050 | −0.155015 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.8377 | −0.481112 | ||||||||
\(713\) | 15.9738 | 0.598225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.6101 | −0.919722 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.2463 | −0.419709 | ||||||||
\(719\) | 19.4376 | 0.724899 | 0.362450 | − | 0.932003i | \(-0.381940\pi\) | ||||
0.362450 | + | 0.932003i | \(0.381940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.39558 | 0.200803 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.4608 | 0.648927 | ||||||||
\(725\) | 94.7984 | 3.52072 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.9217 | −1.66605 | −0.833026 | − | 0.553234i | \(-0.813394\pi\) | ||||
−0.833026 | + | 0.553234i | \(0.813394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.9682 | −1.22021 | ||||||||
\(731\) | −7.28559 | −0.269467 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.0420 | 0.924947 | 0.462474 | − | 0.886633i | \(-0.346962\pi\) | ||||
0.462474 | + | 0.886633i | \(0.346962\pi\) | |||||||
\(734\) | 5.91600 | 0.218364 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.73042 | 0.174365 | ||||||||
\(737\) | 10.1492 | 0.373852 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.62317 | −0.243637 | −0.121819 | − | 0.992552i | \(-0.538873\pi\) | ||||
−0.121819 | + | 0.992552i | \(0.538873\pi\) | |||||||
\(740\) | −33.9738 | −1.24890 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.3972 | 1.44534 | 0.722671 | − | 0.691192i | \(-0.242914\pi\) | ||||
0.722671 | + | 0.691192i | \(0.242914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41.3768 | −1.51593 | ||||||||
\(746\) | 23.1260 | 0.846703 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.37683 | −0.0869056 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7072 | −0.390710 | −0.195355 | − | 0.980733i | \(-0.562586\pi\) | ||||
−0.195355 | + | 0.980733i | \(0.562586\pi\) | |||||||
\(752\) | 4.10725 | 0.149776 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.9551 | 2.18199 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.2797 | −0.628043 | −0.314022 | − | 0.949416i | \(-0.601676\pi\) | ||||
−0.314022 | + | 0.949416i | \(0.601676\pi\) | |||||||
\(758\) | 6.77241 | 0.245985 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.2985 | −0.591209 | ||||||||
\(761\) | 32.7087 | 1.18569 | 0.592846 | − | 0.805316i | \(-0.298004\pi\) | ||||
0.592846 | + | 0.805316i | \(0.298004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.8377 | 0.609165 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.3637 | 0.916429 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.2145 | 0.440466 | 0.220233 | − | 0.975447i | \(-0.429318\pi\) | ||||
0.220233 | + | 0.975447i | \(0.429318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.46083 | 0.196540 | ||||||||
\(773\) | −0.204334 | −0.00734937 | −0.00367468 | − | 0.999993i | \(-0.501170\pi\) | ||||
−0.00367468 | + | 0.999993i | \(0.501170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.0522 | −1.76201 | ||||||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.2565 | 0.905489 | ||||||||
\(779\) | 44.8115 | 1.60554 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.934749 | −0.0334480 | ||||||||
\(782\) | −11.2434 | −0.402064 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 82.8115 | 2.95567 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5579 | 0.911041 | 0.455521 | − | 0.890225i | \(-0.349453\pi\) | ||||
0.455521 | + | 0.890225i | \(0.349453\pi\) | |||||||
\(788\) | 9.68842 | 0.345136 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.85075 | −0.0658468 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.4739 | 0.478171 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.2985 | 0.719461 | ||||||||
\(797\) | −30.0477 | −1.06434 | −0.532171 | − | 0.846637i | \(-0.678624\pi\) | ||||
−0.532171 | + | 0.846637i | \(0.678624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.76225 | −0.345364 | ||||||||
\(800\) | −14.5261 | −0.513575 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.8898 | 1.19669 | ||||||||
\(803\) | −7.46083 | −0.263287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.3637 | −0.540495 | ||||||||
\(809\) | −2.34342 | −0.0823901 | −0.0411951 | − | 0.999151i | \(-0.513117\pi\) | ||||
−0.0411951 | + | 0.999151i | \(0.513117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8695 | −0.416794 | −0.208397 | − | 0.978044i | \(-0.566825\pi\) | ||||
−0.208397 | + | 0.978044i | \(0.566825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.68842 | −0.269479 | ||||||||
\(815\) | −82.9522 | −2.90569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.3059 | −0.395544 | ||||||||
\(818\) | 4.21450 | 0.147357 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 53.6855 | 1.87478 | ||||||||
\(821\) | 37.4812 | 1.30810 | 0.654051 | − | 0.756451i | \(-0.273068\pi\) | ||||
0.654051 | + | 0.756451i | \(0.273068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.29284 | 0.0450654 | 0.0225327 | − | 0.999746i | \(-0.492827\pi\) | ||||
0.0225327 | + | 0.999746i | \(0.492827\pi\) | |||||||
\(824\) | 2.62317 | 0.0913823 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.3319 | −1.50680 | −0.753399 | − | 0.657563i | \(-0.771587\pi\) | ||||
−0.753399 | + | 0.657563i | \(0.771587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.1174 | 1.39334 | 0.696668 | − | 0.717394i | \(-0.254665\pi\) | ||||
0.696668 | + | 0.717394i | \(0.254665\pi\) | |||||||
\(830\) | 9.49717 | 0.329652 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −105.565 | −3.65323 | ||||||||
\(836\) | −3.68842 | −0.127567 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.3116 | −0.770741 | ||||||||
\(839\) | −54.6912 | −1.88815 | −0.944074 | − | 0.329733i | \(-0.893041\pi\) | ||||
−0.944074 | + | 0.329733i | \(0.893041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5897 | 0.468612 | ||||||||
\(842\) | −18.3116 | −0.631059 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.5130 | 0.774929 | ||||||||
\(845\) | 57.4448 | 1.97616 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.00000 | −0.274721 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.5261 | 1.18423 | ||||||||
\(851\) | −36.3694 | −1.24673 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.8275 | −0.713120 | −0.356560 | − | 0.934272i | \(-0.616050\pi\) | ||||
−0.356560 | + | 0.934272i | \(0.616050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.9029 | 0.372654 | ||||||||
\(857\) | 36.8433 | 1.25854 | 0.629272 | − | 0.777185i | \(-0.283353\pi\) | ||||
0.629272 | + | 0.777185i | \(0.283353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.5782 | 1.31627 | 0.658136 | − | 0.752899i | \(-0.271345\pi\) | ||||
0.658136 | + | 0.752899i | \(0.271345\pi\) | |||||||
\(860\) | −13.5448 | −0.461875 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.8377 | −0.982215 | ||||||||
\(863\) | 17.2565 | 0.587418 | 0.293709 | − | 0.955895i | \(-0.405110\pi\) | ||||
0.293709 | + | 0.955895i | \(0.405110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.2723 | 1.70931 | ||||||||
\(866\) | −7.62317 | −0.259046 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.418833 | −0.0142079 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 11.7957 | 0.399452 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.4477 | −0.590179 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.250837 | 0.00847016 | 0.00423508 | − | 0.999991i | \(-0.498652\pi\) | ||||
0.00423508 | + | 0.999991i | \(0.498652\pi\) | |||||||
\(878\) | 33.3739 | 1.12632 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.41883 | −0.148959 | ||||||||
\(881\) | −16.2985 | −0.549110 | −0.274555 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274555 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9551 | −1.14268 | −0.571340 | − | 0.820714i | \(-0.693576\pi\) | ||||
−0.571340 | + | 0.820714i | \(0.693576\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.85075 | −0.162964 | ||||||||
\(887\) | −19.4608 | −0.653431 | −0.326715 | − | 0.945123i | \(-0.605942\pi\) | ||||
−0.326715 | + | 0.945123i | \(0.605942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 56.7275 | 1.90151 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.46083 | −0.249807 | ||||||||
\(893\) | −15.1492 | −0.506950 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 108.748 | 3.63504 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.3450 | 0.478699 | ||||||||
\(899\) | −22.0375 | −0.734992 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.0147 | 0.633470 | ||||||||
\(902\) | 12.1492 | 0.404526 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.37683 | 0.178831 | ||||||||
\(905\) | −77.1565 | −2.56477 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.772415 | 0.0256476 | 0.0128238 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128238 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(908\) | 2.77241 | 0.0920058 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.94491 | 0.296358 | 0.148179 | − | 0.988961i | \(-0.452659\pi\) | ||||
0.148179 | + | 0.988961i | \(0.452659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.14925 | 0.0711297 | ||||||||
\(914\) | 25.1827 | 0.832969 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.53917 | −0.0838965 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.8812 | 1.94231 | 0.971157 | − | 0.238443i | \(-0.0766369\pi\) | ||||
0.971157 | + | 0.238443i | \(0.0766369\pi\) | |||||||
\(920\) | −20.9029 | −0.689149 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.0187 | 0.428750 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 111.683 | 3.67210 | ||||||||
\(926\) | 14.2145 | 0.467117 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.52608 | −0.214229 | ||||||||
\(929\) | 22.5392 | 0.739486 | 0.369743 | − | 0.929134i | \(-0.379446\pi\) | ||||
0.369743 | + | 0.929134i | \(0.379446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24.0522 | 0.787855 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.39558 | −0.0783858 | ||||||||
\(935\) | 10.5028 | 0.343479 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.9478 | −0.422987 | −0.211494 | − | 0.977379i | \(-0.567833\pi\) | ||||
−0.211494 | + | 0.977379i | \(0.567833\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.1492 | −0.591963 | ||||||||
\(941\) | −48.8246 | −1.59164 | −0.795818 | − | 0.605536i | \(-0.792959\pi\) | ||||
−0.795818 | + | 0.605536i | \(0.792959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.4710 | 1.87151 | ||||||||
\(944\) | 12.5261 | 0.407689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.06525 | −0.0996599 | ||||||||
\(947\) | 31.1231 | 1.01136 | 0.505682 | − | 0.862720i | \(-0.331241\pi\) | ||||
0.505682 | + | 0.862720i | \(0.331241\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 53.5782 | 1.73831 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.2797 | −0.527353 | −0.263676 | − | 0.964611i | \(-0.584935\pi\) | ||||
−0.263676 | + | 0.964611i | \(0.584935\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −74.4028 | −2.40762 | ||||||||
\(956\) | −7.59133 | −0.245521 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.8377 | 0.350149 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5970 | −0.632161 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.2985 | 0.524939 | ||||||||
\(965\) | −24.1305 | −0.776788 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.91308 | 0.125836 | 0.0629181 | − | 0.998019i | \(-0.479959\pi\) | ||||
0.0629181 | + | 0.998019i | \(0.479959\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.9318 | 0.993161 | ||||||||
\(971\) | −39.3132 | −1.26162 | −0.630810 | − | 0.775938i | \(-0.717277\pi\) | ||||
−0.630810 | + | 0.775938i | \(0.717277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.6435 | 1.11005 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.79567 | 0.121496 | ||||||||
\(977\) | 23.3507 | 0.747054 | 0.373527 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373527 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8377 | 0.410294 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 38.1492 | 1.21739 | ||||||||
\(983\) | 4.51592 | 0.144035 | 0.0720177 | − | 0.997403i | \(-0.477056\pi\) | ||||
0.0720177 | + | 0.997403i | \(0.477056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.8115 | −1.36409 | ||||||||
\(986\) | 15.5114 | 0.493984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.4999 | −0.461070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.9273 | 1.90365 | 0.951827 | − | 0.306635i | \(-0.0992032\pi\) | ||||
0.951827 | + | 0.306635i | \(0.0992032\pi\) | |||||||
\(992\) | 3.37683 | 0.107215 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −89.6957 | −2.84354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.5073 | −0.681144 | −0.340572 | − | 0.940218i | \(-0.610621\pi\) | ||||
−0.340572 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(998\) | 0.623166 | 0.0197260 | ||||||||
\(999\) | 0 | 0 |
(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 | 9702.2.a.dv.1.1 | 3 | ||
3.2 | odd | 2 | 3234.2.a.bf.1.3 | 3 | |||
7.2 | even | 3 | 1386.2.k.v.991.3 | 6 | |||
7.4 | even | 3 | 1386.2.k.v.793.3 | 6 | |||
7.6 | odd | 2 | 9702.2.a.dw.1.3 | 3 | |||
21.2 | odd | 6 | 462.2.i.g.67.1 | ✓ | 6 | ||
21.11 | odd | 6 | 462.2.i.g.331.1 | yes | 6 | ||
21.20 | even | 2 | 3234.2.a.bh.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.g.67.1 | ✓ | 6 | 21.2 | odd | 6 | ||
462.2.i.g.331.1 | yes | 6 | 21.11 | odd | 6 | ||
1386.2.k.v.793.3 | 6 | 7.4 | even | 3 | |||
1386.2.k.v.991.3 | 6 | 7.2 | even | 3 | |||
3234.2.a.bf.1.3 | 3 | 3.2 | odd | 2 | |||
3234.2.a.bh.1.1 | 3 | 21.20 | even | 2 | |||
9702.2.a.dv.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9702.2.a.dw.1.3 | 3 | 7.6 | odd | 2 |