Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.791953.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 7x^{2} + 9x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4600) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.21042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | 2.21042 | 1.27618 | 0.638092 | − | 0.769960i | \(-0.279724\pi\) | ||||
0.638092 | + | 0.769960i | \(0.279724\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.22487 | −0.840920 | −0.420460 | − | 0.907311i | \(-0.638131\pi\) | ||||
−0.420460 | + | 0.907311i | \(0.638131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.88594 | 0.628648 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.57300 | 0.474276 | 0.237138 | − | 0.971476i | \(-0.423791\pi\) | ||||
0.237138 | + | 0.971476i | \(0.423791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.96189 | −1.09883 | −0.549416 | − | 0.835549i | \(-0.685150\pi\) | ||||
−0.549416 | + | 0.835549i | \(0.685150\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.294907 | −0.0715256 | −0.0357628 | − | 0.999360i | \(-0.511386\pi\) | ||||
−0.0357628 | + | 0.999360i | \(0.511386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.76572 | 1.78158 | 0.890789 | − | 0.454418i | \(-0.150153\pi\) | ||||
0.890789 | + | 0.454418i | \(0.150153\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.91788 | −1.07317 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.46253 | −0.473914 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.29233 | −1.72554 | −0.862771 | − | 0.505595i | \(-0.831273\pi\) | ||||
−0.862771 | + | 0.505595i | \(0.831273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.18913 | −1.65042 | −0.825208 | − | 0.564829i | \(-0.808942\pi\) | ||||
−0.825208 | + | 0.564829i | \(0.808942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.47698 | 0.605264 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5425 | 1.73318 | 0.866588 | − | 0.499024i | \(-0.166308\pi\) | ||||
0.866588 | + | 0.499024i | \(0.166308\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.75744 | −1.40231 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.34251 | −0.365839 | −0.182920 | − | 0.983128i | \(-0.558555\pi\) | ||||
−0.182920 | + | 0.983128i | \(0.558555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.67460 | 1.01787 | 0.508933 | − | 0.860806i | \(-0.330040\pi\) | ||||
0.508933 | + | 0.860806i | \(0.330040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.38007 | −0.201304 | −0.100652 | − | 0.994922i | \(-0.532093\pi\) | ||||
−0.100652 | + | 0.994922i | \(0.532093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.04998 | −0.292854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.651868 | −0.0912798 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0395 | 1.51640 | 0.758199 | − | 0.652023i | \(-0.226080\pi\) | ||||
0.758199 | + | 0.652023i | \(0.226080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.1655 | 2.27362 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.09378 | 0.663154 | 0.331577 | − | 0.943428i | \(-0.392419\pi\) | ||||
0.331577 | + | 0.943428i | \(0.392419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.91788 | −1.14182 | −0.570909 | − | 0.821014i | \(-0.693409\pi\) | ||||
−0.570909 | + | 0.821014i | \(0.693409\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.19597 | −0.528642 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.12002 | −0.136832 | −0.0684160 | − | 0.997657i | \(-0.521795\pi\) | ||||
−0.0684160 | + | 0.997657i | \(0.521795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.21042 | −0.266103 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.60168 | −0.902154 | −0.451077 | − | 0.892485i | \(-0.648960\pi\) | ||||
−0.451077 | + | 0.892485i | \(0.648960\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8549 | −1.50455 | −0.752276 | − | 0.658848i | \(-0.771044\pi\) | ||||
−0.752276 | + | 0.658848i | \(0.771044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.49971 | −0.398828 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0211 | −1.23997 | −0.619984 | − | 0.784614i | \(-0.712861\pi\) | ||||
−0.619984 | + | 0.784614i | \(0.712861\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1010 | −1.23345 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.5257 | −1.48464 | −0.742318 | − | 0.670048i | \(-0.766274\pi\) | ||||
−0.742318 | + | 0.670048i | \(0.766274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.5399 | −2.20211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3475 | 1.52084 | 0.760418 | − | 0.649434i | \(-0.224994\pi\) | ||||
0.760418 | + | 0.649434i | \(0.224994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.81468 | 0.924030 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.3118 | −2.10624 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.199218 | 0.0202275 | 0.0101137 | − | 0.999949i | \(-0.496781\pi\) | ||||
0.0101137 | + | 0.999949i | \(0.496781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.96658 | 0.298153 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.07595 | −0.604580 | −0.302290 | − | 0.953216i | \(-0.597751\pi\) | ||||
−0.302290 | + | 0.953216i | \(0.597751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9423 | −1.17671 | −0.588353 | − | 0.808604i | \(-0.700223\pi\) | ||||
−0.588353 | + | 0.808604i | \(0.700223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.99058 | 0.772479 | 0.386239 | − | 0.922399i | \(-0.373774\pi\) | ||||
0.386239 | + | 0.922399i | \(0.373774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.36170 | −0.417775 | −0.208888 | − | 0.977940i | \(-0.566984\pi\) | ||||
−0.208888 | + | 0.977940i | \(0.566984\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.3033 | 2.21185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9156 | −1.21500 | −0.607501 | − | 0.794319i | \(-0.707828\pi\) | ||||
−0.607501 | + | 0.794319i | \(0.707828\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.47191 | −0.690778 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.656129 | 0.0601473 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.52568 | −0.775062 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.17793 | −0.466878 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3759 | 1.45313 | 0.726565 | − | 0.687098i | \(-0.241116\pi\) | ||||
0.726565 | + | 0.687098i | \(0.241116\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.7536 | 1.29899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.62242 | −0.840715 | −0.420357 | − | 0.907359i | \(-0.638095\pi\) | ||||
−0.420357 | + | 0.907359i | \(0.638095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.2777 | −1.49816 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.78721 | 0.579871 | 0.289935 | − | 0.957046i | \(-0.406366\pi\) | ||||
0.289935 | + | 0.957046i | \(0.406366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.55788 | −0.556232 | −0.278116 | − | 0.960547i | \(-0.589710\pi\) | ||||
−0.278116 | + | 0.960547i | \(0.589710\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.05053 | −0.256901 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.23205 | −0.521150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.53130 | −0.373735 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8647 | −1.13584 | −0.567918 | − | 0.823085i | \(-0.692251\pi\) | ||||
−0.567918 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.42205 | −0.197104 | −0.0985520 | − | 0.995132i | \(-0.531421\pi\) | ||||
−0.0985520 | + | 0.995132i | \(0.531421\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.556179 | −0.0449644 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2638 | 1.61723 | 0.808613 | − | 0.588341i | \(-0.200219\pi\) | ||||
0.808613 | + | 0.588341i | \(0.200219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.4020 | 1.93520 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.22487 | 0.175344 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.91982 | −0.542002 | −0.271001 | − | 0.962579i | \(-0.587355\pi\) | ||||
−0.271001 | + | 0.962579i | \(0.587355\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.8296 | −1.45708 | −0.728539 | − | 0.685005i | \(-0.759800\pi\) | ||||
−0.728539 | + | 0.685005i | \(0.759800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.69661 | 0.207431 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6457 | 1.11998 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.2017 | 1.76399 | 0.881997 | − | 0.471255i | \(-0.156199\pi\) | ||||
0.881997 | + | 0.471255i | \(0.156199\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.2594 | 0.846307 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7011 | 0.799837 | 0.399918 | − | 0.916551i | \(-0.369038\pi\) | ||||
0.399918 | + | 0.916551i | \(0.369038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.27484 | −0.540735 | −0.270367 | − | 0.962757i | \(-0.587145\pi\) | ||||
−0.270367 | + | 0.962757i | \(0.587145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.7122 | −1.45717 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.463888 | −0.0339229 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.47880 | 0.398524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.74624 | 0.271068 | 0.135534 | − | 0.990773i | \(-0.456725\pi\) | ||||
0.135534 | + | 0.990773i | \(0.456725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8470 | 0.852763 | 0.426381 | − | 0.904543i | \(-0.359788\pi\) | ||||
0.426381 | + | 0.904543i | \(0.359788\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0064 | −0.712924 | −0.356462 | − | 0.934310i | \(-0.616017\pi\) | ||||
−0.356462 | + | 0.934310i | \(0.616017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.19597 | −0.439221 | −0.219610 | − | 0.975588i | \(-0.570479\pi\) | ||||
−0.219610 | + | 0.975588i | \(0.570479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.47571 | −0.174623 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.6742 | 1.45104 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.88594 | −0.131082 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2154 | 0.844960 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.825746 | 0.0568467 | 0.0284234 | − | 0.999596i | \(-0.490951\pi\) | ||||
0.0284234 | + | 0.999596i | \(0.490951\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.8029 | −1.15132 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.4446 | 1.38787 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.4147 | −1.92009 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16839 | 0.0785946 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.2911 | −1.22486 | −0.612430 | − | 0.790525i | \(-0.709808\pi\) | ||||
−0.612430 | + | 0.790525i | \(0.709808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5556 | −1.43069 | −0.715347 | − | 0.698769i | \(-0.753732\pi\) | ||||
−0.715347 | + | 0.698769i | \(0.753732\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.65960 | 0.638324 | 0.319162 | − | 0.947700i | \(-0.396599\pi\) | ||||
0.319162 | + | 0.947700i | \(0.396599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.73581 | −0.508979 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.879774 | 0.0576359 | 0.0288179 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288179 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.3612 | −1.58243 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.3240 | −1.44402 | −0.722010 | − | 0.691883i | \(-0.756782\pi\) | ||||
−0.722010 | + | 0.691883i | \(0.756782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.43761 | −0.479098 | −0.239549 | − | 0.970884i | \(-0.577000\pi\) | ||||
−0.239549 | + | 0.970884i | \(0.577000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.1504 | −1.10020 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.7669 | −1.95765 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.8974 | −1.89467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.4221 | −1.35215 | −0.676074 | − | 0.736833i | \(-0.736320\pi\) | ||||
−0.676074 | + | 0.736833i | \(0.736320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.57300 | −0.0988935 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9788 | −0.684838 | −0.342419 | − | 0.939547i | \(-0.611246\pi\) | ||||
−0.342419 | + | 0.939547i | \(0.611246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.4556 | −1.45746 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.5248 | −1.08476 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3268 | −0.698440 | −0.349220 | − | 0.937041i | \(-0.613553\pi\) | ||||
−0.349220 | + | 0.937041i | \(0.613553\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 31.7141 | 1.94087 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.1010 | 1.89626 | 0.948130 | − | 0.317883i | \(-0.102972\pi\) | ||||
0.948130 | + | 0.317883i | \(0.102972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.1151 | −1.76862 | −0.884308 | − | 0.466905i | \(-0.845369\pi\) | ||||
−0.884308 | + | 0.466905i | \(0.845369\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.4841 | 1.17923 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.6829 | 1.36288 | 0.681441 | − | 0.731873i | \(-0.261354\pi\) | ||||
0.681441 | + | 0.731873i | \(0.261354\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.3302 | −1.03753 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2531 | 0.671305 | 0.335653 | − | 0.941986i | \(-0.391043\pi\) | ||||
0.335653 | + | 0.941986i | \(0.391043\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.419014 | 0.0249078 | 0.0124539 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124539 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.21177 | 0.307641 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9130 | −0.994884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.440354 | 0.0258140 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.06844 | −0.0624190 | −0.0312095 | − | 0.999513i | \(-0.509936\pi\) | ||||
−0.0312095 | + | 0.999513i | \(0.509936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.87355 | −0.224766 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.96189 | 0.229122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8501 | −0.855944 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.4304 | −0.771555 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3991 | 1.27838 | 0.639191 | − | 0.769048i | \(-0.279269\pi\) | ||||
0.639191 | + | 0.769048i | \(0.279269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.3974 | −1.50169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.9717 | 1.13249 | 0.566245 | − | 0.824237i | \(-0.308396\pi\) | ||||
0.566245 | + | 0.824237i | \(0.308396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.1975 | −0.802488 | −0.401244 | − | 0.915971i | \(-0.631422\pi\) | ||||
−0.401244 | + | 0.915971i | \(0.631422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.48205 | 0.420234 | 0.210117 | − | 0.977676i | \(-0.432616\pi\) | ||||
0.210117 | + | 0.977676i | \(0.432616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.6168 | −0.818384 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6625 | 0.985826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.29017 | −0.127428 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.64118 | −0.533158 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.07047 | 0.169280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.56494 | −0.360842 | −0.180421 | − | 0.983590i | \(-0.557746\pi\) | ||||
−0.180421 | + | 0.983590i | \(0.557746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.8826 | 1.08956 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2484 | −0.939583 | −0.469791 | − | 0.882777i | \(-0.655671\pi\) | ||||
−0.469791 | + | 0.882777i | \(0.655671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.5490 | −1.55057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4545 | −0.782753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1350 | 1.08719 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.18016 | 0.224403 | 0.112201 | − | 0.993685i | \(-0.464210\pi\) | ||||
0.112201 | + | 0.993685i | \(0.464210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.6150 | 0.621736 | 0.310868 | − | 0.950453i | \(-0.399380\pi\) | ||||
0.310868 | + | 0.950453i | \(0.399380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.75628 | 0.520752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8241 | −0.842233 | −0.421117 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421117 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.45032 | 0.0767590 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.25850 | 0.330311 | 0.165156 | − | 0.986268i | \(-0.447187\pi\) | ||||
0.165156 | + | 0.986268i | \(0.447187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.3064 | 2.17402 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.8453 | −0.989122 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.01500 | −0.261781 | −0.130890 | − | 0.991397i | \(-0.541784\pi\) | ||||
−0.130890 | + | 0.991397i | \(0.541784\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.41785 | −0.229984 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.5615 | −1.27517 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1804 | 1.04490 | 0.522450 | − | 0.852670i | \(-0.325018\pi\) | ||||
0.522450 | + | 0.852670i | \(0.325018\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.8152 | 1.89608 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9860 | −0.564314 | −0.282157 | − | 0.959368i | \(-0.591050\pi\) | ||||
−0.282157 | + | 0.959368i | \(0.591050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.1977 | 1.85446 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.9968 | −1.22618 | −0.613088 | − | 0.790014i | \(-0.710073\pi\) | ||||
−0.613088 | + | 0.790014i | \(0.710073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5879 | 0.639879 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.3913 | 0.983180 | 0.491590 | − | 0.870827i | \(-0.336416\pi\) | ||||
0.491590 | + | 0.870827i | \(0.336416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.294907 | 0.0149141 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.2696 | −1.07291 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0550 | 0.504644 | 0.252322 | − | 0.967643i | \(-0.418806\pi\) | ||||
0.252322 | + | 0.967643i | \(0.418806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −38.1909 | −1.91193 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6178 | −0.829854 | −0.414927 | − | 0.909855i | \(-0.636193\pi\) | ||||
−0.414927 | + | 0.909855i | \(0.636193\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.4064 | 1.81353 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.5833 | 0.822005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.92642 | 0.391936 | 0.195968 | − | 0.980610i | \(-0.437215\pi\) | ||||
0.195968 | + | 0.980610i | \(0.437215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.0026 | 0.740022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3330 | −0.557659 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.4956 | −0.709855 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.4944 | −1.97828 | −0.989141 | − | 0.146967i | \(-0.953049\pi\) | ||||
−0.989141 | + | 0.146967i | \(0.953049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.67870 | 0.374237 | 0.187118 | − | 0.982337i | \(-0.440085\pi\) | ||||
0.187118 | + | 0.982337i | \(0.440085\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.60273 | −0.126549 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.8411 | 0.960177 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.7754 | −0.665084 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.1674 | 1.74212 | 0.871061 | − | 0.491175i | \(-0.163433\pi\) | ||||
0.871061 | + | 0.491175i | \(0.163433\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.42856 | 0.453108 | 0.226554 | − | 0.973999i | \(-0.427254\pi\) | ||||
0.226554 | + | 0.973999i | \(0.427254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.76572 | −0.371485 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.4443 | −1.16666 | −0.583332 | − | 0.812234i | \(-0.698251\pi\) | ||||
−0.583332 | + | 0.812234i | \(0.698251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.86614 | −0.184102 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.5786 | −1.69039 | −0.845195 | − | 0.534458i | \(-0.820516\pi\) | ||||
−0.845195 | + | 0.534458i | \(0.820516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.6467 | −1.44954 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.660651 | −0.0311780 | −0.0155890 | − | 0.999878i | \(-0.504962\pi\) | ||||
−0.0155890 | + | 0.999878i | \(0.504962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.68476 | −0.173509 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.35375 | −0.251541 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.62187 | 0.403314 | 0.201657 | − | 0.979456i | \(-0.435367\pi\) | ||||
0.201657 | + | 0.979456i | \(0.435367\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.726219 | 0.0338970 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.54580 | −0.258294 | −0.129147 | − | 0.991625i | \(-0.541224\pi\) | ||||
−0.129147 | + | 0.991625i | \(0.541224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.15748 | 0.286162 | 0.143081 | − | 0.989711i | \(-0.454299\pi\) | ||||
0.143081 | + | 0.989711i | \(0.454299\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.93879 | 0.135991 | 0.0679954 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679954 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.49189 | 0.115065 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.7914 | 2.06388 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.4991 | 0.482750 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.8200 | 0.953280 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.4939 | −0.616550 | −0.308275 | − | 0.951297i | \(-0.599752\pi\) | ||||
−0.308275 | + | 0.951297i | \(0.599752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.7683 | −1.90447 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.91788 | 0.223771 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.28554 | −0.148882 | −0.0744410 | − | 0.997225i | \(-0.523717\pi\) | ||||
−0.0744410 | + | 0.997225i | \(0.523717\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.2957 | −0.691695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2119 | −1.09267 | −0.546335 | − | 0.837567i | \(-0.683977\pi\) | ||||
−0.546335 | + | 0.837567i | \(0.683977\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.74038 | 0.123420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.9127 | 0.758639 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.5956 | 1.68301 | 0.841506 | − | 0.540248i | \(-0.181669\pi\) | ||||
0.841506 | + | 0.540248i | \(0.181669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.6212 | −1.85950 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0448 | 0.492464 | 0.246232 | − | 0.969211i | \(-0.420807\pi\) | ||||
0.246232 | + | 0.969211i | \(0.420807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.96062 | 0.264720 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.4409 | −1.39359 | −0.696796 | − | 0.717269i | \(-0.745392\pi\) | ||||
−0.696796 | + | 0.717269i | \(0.745392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.6004 | 1.26521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.1233 | −0.844315 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.17084 | −0.0954735 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 51.2855 | 2.25118 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.3591 | 1.54911 | 0.774555 | − | 0.632506i | \(-0.217974\pi\) | ||||
0.774555 | + | 0.632506i | \(0.217974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.8119 | 1.82830 | 0.914152 | − | 0.405371i | \(-0.132858\pi\) | ||||
0.914152 | + | 0.405371i | \(0.132858\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.70994 | 0.118047 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.60658 | 0.416890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.28079 | 0.401996 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.6539 | 1.02074 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.22460 | −0.138894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.43188 | 0.0615612 | 0.0307806 | − | 0.999526i | \(-0.490201\pi\) | ||||
0.0307806 | + | 0.999526i | \(0.490201\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.0804 | −0.690077 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.8700 | 1.91850 | 0.959251 | − | 0.282555i | \(-0.0911821\pi\) | ||||
0.959251 | + | 0.282555i | \(0.0911821\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.8186 | −0.717801 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −72.1616 | −3.07419 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.5204 | 1.04271 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3106 | 0.945329 | 0.472665 | − | 0.881242i | \(-0.343292\pi\) | ||||
0.472665 | + | 0.881242i | \(0.343292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.4440 | −1.11846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.02539 | −0.0432919 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.41928 | −0.0598153 | −0.0299077 | − | 0.999553i | \(-0.509521\pi\) | ||||
−0.0299077 | + | 0.999553i | \(0.509521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.6983 | 1.03723 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.4950 | −0.901116 | −0.450558 | − | 0.892747i | \(-0.648775\pi\) | ||||
−0.450558 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.0272 | −1.71694 | −0.858468 | − | 0.512868i | \(-0.828583\pi\) | ||||
−0.858468 | + | 0.512868i | \(0.828583\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.28075 | 0.345933 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1477 | −1.54648 | −0.773239 | − | 0.634114i | \(-0.781365\pi\) | ||||
−0.773239 | + | 0.634114i | \(0.781365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.1867 | 1.08828 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0928 | 1.24846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.3652 | 0.719192 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.1838 | 0.502881 | 0.251440 | − | 0.967873i | \(-0.419096\pi\) | ||||
0.251440 | + | 0.967873i | \(0.419096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −71.3602 | −2.94034 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.1183 | −0.909823 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.1421 | −1.64844 | −0.824220 | − | 0.566270i | \(-0.808386\pi\) | ||||
−0.824220 | + | 0.566270i | \(0.808386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.6957 | −0.560527 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.4377 | 0.671624 | 0.335812 | − | 0.941929i | \(-0.390989\pi\) | ||||
0.335812 | + | 0.941929i | \(0.390989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.98809 | −0.203469 | −0.101734 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101734 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.11229 | −0.0860191 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.09352 | −0.0443846 | −0.0221923 | − | 0.999754i | \(-0.507065\pi\) | ||||
−0.0221923 | + | 0.999754i | \(0.507065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.6986 | 1.85180 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.46768 | 0.221199 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.4617 | 0.664880 | 0.332440 | − | 0.943124i | \(-0.392128\pi\) | ||||
0.332440 | + | 0.943124i | \(0.392128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9090 | 0.962540 | 0.481270 | − | 0.876572i | \(-0.340176\pi\) | ||||
0.481270 | + | 0.876572i | \(0.340176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.7498 | 1.07517 | 0.537583 | − | 0.843211i | \(-0.319337\pi\) | ||||
0.537583 | + | 0.843211i | \(0.319337\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.46253 | 0.0988179 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.9213 | −1.27890 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.0012 | 1.07833 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.10906 | −0.123966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.317634 | −0.0126448 | −0.00632241 | − | 0.999980i | \(-0.502012\pi\) | ||||
−0.00632241 | + | 0.999980i | \(0.502012\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.82524 | 0.0725469 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.12179 | 0.321797 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.3363 | −0.567137 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.9895 | 0.789539 | 0.394769 | − | 0.918780i | \(-0.370825\pi\) | ||||
0.394769 | + | 0.918780i | \(0.370825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0837 | 0.792023 | 0.396011 | − | 0.918246i | \(-0.370394\pi\) | ||||
0.396011 | + | 0.918246i | \(0.370394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.0801 | −0.868060 | −0.434030 | − | 0.900898i | \(-0.642909\pi\) | ||||
−0.434030 | + | 0.900898i | \(0.642909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.01250 | 0.314518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.1910 | 1.77118 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.2385 | 1.30072 | 0.650362 | − | 0.759625i | \(-0.274617\pi\) | ||||
0.650362 | + | 0.759625i | \(0.274617\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.2436 | −0.945833 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.3023 | −0.674002 | −0.337001 | − | 0.941504i | \(-0.609413\pi\) | ||||
−0.337001 | + | 0.941504i | \(0.609413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9521 | −1.12611 | −0.563053 | − | 0.826421i | \(-0.690373\pi\) | ||||
−0.563053 | + | 0.826421i | \(0.690373\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.58263 | 0.100301 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.29233 | 0.359800 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.4309 | −1.56315 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0278 | −0.541537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.7860 | −0.415771 | −0.207885 | − | 0.978153i | \(-0.566658\pi\) | ||||
−0.207885 | + | 0.978153i | \(0.566658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.1146 | 0.619336 | 0.309668 | − | 0.950845i | \(-0.399782\pi\) | ||||
0.309668 | + | 0.950845i | \(0.399782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.443232 | −0.0170097 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.6468 | −1.82583 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1106 | 0.463399 | 0.231699 | − | 0.972787i | \(-0.425571\pi\) | ||||
0.231699 | + | 0.972787i | \(0.425571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.3517 | 0.814620 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.7375 | −1.66627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.1463 | 1.14682 | 0.573410 | − | 0.819269i | \(-0.305620\pi\) | ||||
0.573410 | + | 0.819269i | \(0.305620\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.60025 | −0.250723 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.690824 | 0.0261668 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.94467 | 0.0735540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8464 | 0.560741 | 0.280371 | − | 0.959892i | \(-0.409543\pi\) | ||||
0.280371 | + | 0.959892i | \(0.409543\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.8701 | 3.08779 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.5182 | 0.508403 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.0163 | 1.39018 | 0.695088 | − | 0.718924i | \(-0.255365\pi\) | ||||
0.695088 | + | 0.718924i | \(0.255365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.7851 | −0.779503 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.18913 | 0.344136 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.3454 | −1.84284 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.63459 | −0.284722 | −0.142361 | − | 0.989815i | \(-0.545469\pi\) | ||||
−0.142361 | + | 0.989815i | \(0.545469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.5699 | 0.989515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.4402 | −0.611418 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1278 | −1.08029 | −0.540146 | − | 0.841571i | \(-0.681631\pi\) | ||||
−0.540146 | + | 0.841571i | \(0.681631\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.60629 | −0.170603 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.96839 | −0.0728034 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.30466 | 0.269804 | 0.134902 | − | 0.990859i | \(-0.456928\pi\) | ||||
0.134902 | + | 0.990859i | \(0.456928\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.76178 | −0.0648962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5109 | 0.386649 | 0.193324 | − | 0.981135i | \(-0.438073\pi\) | ||||
0.193324 | + | 0.981135i | \(0.438073\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −68.0078 | −2.49833 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.4448 | 0.419869 | 0.209934 | − | 0.977715i | \(-0.432675\pi\) | ||||
0.209934 | + | 0.977715i | \(0.432675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.5087 | −0.933313 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.7780 | −0.649593 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.62069 | 0.278083 | 0.139041 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139041 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −47.3517 | −1.72559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.3725 | −1.50371 | −0.751855 | − | 0.659329i | \(-0.770841\pi\) | ||||
−0.751855 | + | 0.659329i | \(0.770841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.47698 | −0.126206 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5358 | 0.454421 | 0.227211 | − | 0.973846i | \(-0.427039\pi\) | ||||
0.227211 | + | 0.973846i | \(0.427039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.70420 | 0.351315 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.1810 | −0.728694 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0182 | −0.902180 | −0.451090 | − | 0.892479i | \(-0.648965\pi\) | ||||
−0.451090 | + | 0.892479i | \(0.648965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.2677 | −0.873980 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.1948 | 1.33781 | 0.668903 | − | 0.743350i | \(-0.266764\pi\) | ||||
0.668903 | + | 0.743350i | \(0.266764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −51.8467 | −1.85999 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.1913 | −0.651771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9574 | −0.427870 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.8826 | 0.817759 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.64645 | −0.272567 | −0.136283 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136283 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.0369 | −0.891338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.7356 | 1.02172 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.3317 | 1.25467 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.38544 | 0.0844966 | 0.0422483 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422483 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.406992 | 0.0143984 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.0586 | 0.956070 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.2207 | −0.713573 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 68.7461 | 2.41998 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.4937 | 0.544730 | 0.272365 | − | 0.962194i | \(-0.412194\pi\) | ||||
0.272365 | + | 0.962194i | \(0.412194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.3850 | −1.94483 | −0.972415 | − | 0.233259i | \(-0.925061\pi\) | ||||
−0.972415 | + | 0.233259i | \(0.925061\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −64.3565 | −2.25708 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.8330 | 1.81341 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.6240 | 0.580889 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.7241 | −1.35148 | −0.675740 | − | 0.737140i | \(-0.736176\pi\) | ||||
−0.675740 | + | 0.737140i | \(0.736176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.237837 | −0.00829047 | −0.00414524 | − | 0.999991i | \(-0.501319\pi\) | ||||
−0.00414524 | + | 0.999991i | \(0.501319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.5821 | −0.611391 | −0.305695 | − | 0.952129i | \(-0.598889\pi\) | ||||
−0.305695 | + | 0.952129i | \(0.598889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5607 | 0.714103 | 0.357051 | − | 0.934085i | \(-0.383782\pi\) | ||||
0.357051 | + | 0.934085i | \(0.383782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.1386 | 1.73929 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.604553 | 0.0209465 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.6285 | 0.782156 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1584 | 0.523325 | 0.261663 | − | 0.965159i | \(-0.415729\pi\) | ||||
0.261663 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.3474 | 1.97750 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.8741 | 0.856709 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9685 | 0.651765 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.926197 | 0.0317870 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5425 | −0.361392 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.7788 | −0.642973 | −0.321486 | − | 0.946914i | \(-0.604182\pi\) | ||||
−0.321486 | + | 0.946914i | \(0.604182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.4670 | 1.00657 | 0.503286 | − | 0.864120i | \(-0.332124\pi\) | ||||
0.503286 | + | 0.864120i | \(0.332124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.7562 | 1.73178 | 0.865889 | − | 0.500236i | \(-0.166753\pi\) | ||||
0.865889 | + | 0.500236i | \(0.166753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.5202 | 0.392607 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5166 | 0.664351 | 0.332176 | − | 0.943218i | \(-0.392217\pi\) | ||||
0.332176 | + | 0.943218i | \(0.392217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.3848 | −1.26966 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.3361 | −0.588088 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.43739 | 0.150355 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.375713 | 0.0127160 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.68909 | 0.225874 | 0.112937 | − | 0.993602i | \(-0.463974\pi\) | ||||
0.112937 | + | 0.993602i | \(0.463974\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.36170 | −0.0796582 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.1211 | 1.58755 | 0.793775 | − | 0.608212i | \(-0.208113\pi\) | ||||
0.793775 | + | 0.608212i | \(0.208113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.5934 | −1.36608 | −0.683038 | − | 0.730383i | \(-0.739342\pi\) | ||||
−0.683038 | + | 0.730383i | \(0.739342\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.89101 | −0.332108 | −0.166054 | − | 0.986117i | \(-0.553103\pi\) | ||||
−0.166054 | + | 0.986117i | \(0.553103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.4343 | −1.22197 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.4619 | −0.584996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.7172 | −0.358638 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.75744 | 0.292402 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 85.3884 | 2.84786 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.25564 | −0.108461 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.8249 | −1.09234 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.3250 | 1.40538 | 0.702689 | − | 0.711497i | \(-0.251983\pi\) | ||||
0.702689 | + | 0.711497i | \(0.251983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.4589 | −0.380068 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.48129 | −0.181603 | −0.0908016 | − | 0.995869i | \(-0.528943\pi\) | ||||
−0.0908016 | + | 0.995869i | \(0.528943\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.2759 | −0.704128 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.4086 | 0.706974 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.6386 | −0.548856 | −0.274428 | − | 0.961608i | \(-0.588488\pi\) | ||||
−0.274428 | + | 0.961608i | \(0.588488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49.5113 | 1.63145 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.1171 | 0.991315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.5224 | −0.739733 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.2326 | −0.991900 | −0.495950 | − | 0.868351i | \(-0.665180\pi\) | ||||
−0.495950 | + | 0.868351i | \(0.665180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.9195 | −0.521741 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.1457 | 1.44527 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.8718 | 0.910532 | 0.455266 | − | 0.890356i | \(-0.349544\pi\) | ||||
0.455266 | + | 0.890356i | \(0.349544\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.3823 | −1.02412 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.8768 | 0.876159 | 0.438079 | − | 0.898936i | \(-0.355659\pi\) | ||||
0.438079 | + | 0.898936i | \(0.355659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.34251 | 0.0762827 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.1773 | 0.753161 | 0.376581 | − | 0.926384i | \(-0.377100\pi\) | ||||
0.376581 | + | 0.926384i | \(0.377100\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.9297 | 1.65325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.5384 | 0.536296 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.21870 | −0.136657 | −0.0683285 | − | 0.997663i | \(-0.521767\pi\) | ||||
−0.0683285 | + | 0.997663i | \(0.521767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −32.3092 | −1.04441 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.1006 | −0.487625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.4401 | 1.72387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0698 | 0.485617 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8055 | −0.572588 | −0.286294 | − | 0.958142i | \(-0.592423\pi\) | ||||
−0.286294 | + | 0.958142i | \(0.592423\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.06223 | −0.162622 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.9741 | −0.576815 | −0.288408 | − | 0.957508i | \(-0.593126\pi\) | ||||
−0.288408 | + | 0.957508i | \(0.593126\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.5904 | 0.467747 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.6275 | 1.87566 | 0.937829 | − | 0.347097i | \(-0.112833\pi\) | ||||
0.937829 | + | 0.347097i | \(0.112833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5686 | 0.721297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.22592 | −0.262633 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.84103 | −0.250090 | −0.125045 | − | 0.992151i | \(-0.539908\pi\) | ||||
−0.125045 | + | 0.992151i | \(0.539908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.78701 | 0.216033 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.67460 | −0.212240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.1872 | 1.05423 | 0.527114 | − | 0.849795i | \(-0.323274\pi\) | ||||
0.527114 | + | 0.849795i | \(0.323274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.5112 | −0.460500 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.8220 | −1.92625 | −0.963127 | − | 0.269049i | \(-0.913291\pi\) | ||||
−0.963127 | + | 0.269049i | \(0.913291\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.9612 | −0.821377 |
(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 | 9200.2.a.cs.1.5 | 5 | ||
4.3 | odd | 2 | 4600.2.a.bg.1.1 | yes | 5 | ||
5.4 | even | 2 | 9200.2.a.cw.1.1 | 5 | |||
20.3 | even | 4 | 4600.2.e.v.4049.2 | 10 | |||
20.7 | even | 4 | 4600.2.e.v.4049.9 | 10 | |||
20.19 | odd | 2 | 4600.2.a.bc.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.5 | ✓ | 5 | 20.19 | odd | 2 | ||
4600.2.a.bg.1.1 | yes | 5 | 4.3 | odd | 2 | ||
4600.2.e.v.4049.2 | 10 | 20.3 | even | 4 | |||
4600.2.e.v.4049.9 | 10 | 20.7 | even | 4 | |||
9200.2.a.cs.1.5 | 5 | 1.1 | even | 1 | trivial | ||
9200.2.a.cw.1.1 | 5 | 5.4 | even | 2 |