Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 103x^{6} + 239x^{4} + 197x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.9 | ||
Root | \(-1.45894i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.v.4049.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.21042i | 1.27618i | 0.769960 | + | 0.638092i | \(0.220276\pi\) | ||||
−0.769960 | + | 0.638092i | \(0.779724\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.22487i | 0.840920i | 0.907311 | + | 0.420460i | \(0.138131\pi\) | ||||
−0.907311 | + | 0.420460i | \(0.861869\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.88594 | −0.628648 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.57300 | −0.474276 | −0.237138 | − | 0.971476i | \(-0.576209\pi\) | ||||
−0.237138 | + | 0.971476i | \(0.576209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.96189i | 1.09883i | 0.835549 | + | 0.549416i | \(0.185150\pi\) | ||||
−0.835549 | + | 0.549416i | \(0.814850\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 0.294907i | − 0.0715256i | −0.999360 | − | 0.0357628i | \(-0.988614\pi\) | ||||
0.999360 | − | 0.0357628i | \(-0.0113861\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.46253i | 0.473914i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.29233 | 1.72554 | 0.862771 | − | 0.505595i | \(-0.168727\pi\) | ||||
0.862771 | + | 0.505595i | \(0.168727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.18913 | 1.65042 | 0.825208 | − | 0.564829i | \(-0.191058\pi\) | ||||
0.825208 | + | 0.564829i | \(0.191058\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 3.47698i | − 0.605264i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5425i | 1.73318i | 0.499024 | + | 0.866588i | \(0.333692\pi\) | ||||
−0.499024 | + | 0.866588i | \(0.666308\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 6.67460i | 1.01787i | 0.860806 | + | 0.508933i | \(0.169960\pi\) | ||||
−0.860806 | + | 0.508933i | \(0.830040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.38007i | 0.201304i | 0.994922 | + | 0.100652i | \(0.0320928\pi\) | ||||
−0.994922 | + | 0.100652i | \(0.967907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.04998 | 0.292854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.651868 | 0.0912798 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.0395i | − 1.51640i | −0.652023 | − | 0.758199i | \(-0.726080\pi\) | ||||
0.652023 | − | 0.758199i | \(-0.273920\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.1655i | 2.27362i | ||||||||
\(58\) | 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 | ||||||||
\(63\) | − 4.19597i | − 0.528642i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.12002i | 0.136832i | 0.997657 | + | 0.0684160i | \(0.0217945\pi\) | ||||
−0.997657 | + | 0.0684160i | \(0.978205\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.21042 | 0.266103 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.60168 | 0.902154 | 0.451077 | − | 0.892485i | \(-0.351040\pi\) | ||||
0.451077 | + | 0.892485i | \(0.351040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.8549i | 1.50455i | 0.658848 | + | 0.752276i | \(0.271044\pi\) | ||||
−0.658848 | + | 0.752276i | \(0.728956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.49971i | − 0.398828i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | − 13.5257i | − 1.48464i | −0.670048 | − | 0.742318i | \(-0.733726\pi\) | ||||
0.670048 | − | 0.742318i | \(-0.266274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.5399i | 2.20211i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3475 | −1.52084 | −0.760418 | − | 0.649434i | \(-0.775006\pi\) | ||||
−0.760418 | + | 0.649434i | \(0.775006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.81468 | −0.924030 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.3118i | 2.10624i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.199218i | 0.0202275i | 0.999949 | + | 0.0101137i | \(0.00321936\pi\) | ||||
−0.999949 | + | 0.0101137i | \(0.996781\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | − 11.9423i | − 1.17671i | −0.808604 | − | 0.588353i | \(-0.799777\pi\) | ||||
0.808604 | − | 0.588353i | \(-0.200223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.99058i | − 0.772479i | −0.922399 | − | 0.386239i | \(-0.873774\pi\) | ||||
0.922399 | − | 0.386239i | \(-0.126226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.36170 | 0.417775 | 0.208888 | − | 0.977940i | \(-0.433016\pi\) | ||||
0.208888 | + | 0.977940i | \(0.433016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.3033 | −2.21185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9156i | 1.21500i | 0.794319 | + | 0.607501i | \(0.207828\pi\) | ||||
−0.794319 | + | 0.607501i | \(0.792172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 7.47191i | − 0.690778i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.656129 | 0.0601473 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.52568 | −0.775062 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.17793i | − 0.466878i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.3759i | − 1.45313i | −0.687098 | − | 0.726565i | \(-0.741116\pi\) | ||||
0.687098 | − | 0.726565i | \(-0.258884\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.7536 | −1.29899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.62242 | 0.840715 | 0.420357 | − | 0.907359i | \(-0.361905\pi\) | ||||
0.420357 | + | 0.907359i | \(0.361905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.2777i | 1.49816i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.78721i | 0.579871i | 0.957046 | + | 0.289935i | \(0.0936338\pi\) | ||||
−0.957046 | + | 0.289935i | \(0.906366\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | − 6.23205i | − 0.521150i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.53130i | 0.373735i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.8647 | 1.13584 | 0.567918 | − | 0.823085i | \(-0.307749\pi\) | ||||
0.567918 | + | 0.823085i | \(0.307749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.42205 | 0.197104 | 0.0985520 | − | 0.995132i | \(-0.468579\pi\) | ||||
0.0985520 | + | 0.995132i | \(0.468579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.556179i | 0.0449644i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2638i | 1.61723i | 0.588341 | + | 0.808613i | \(0.299781\pi\) | ||||
−0.588341 | + | 0.808613i | \(0.700219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.4020 | 1.93520 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.22487 | 0.175344 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.91982i | − 0.542002i | −0.962579 | − | 0.271001i | \(-0.912645\pi\) | ||||
0.962579 | − | 0.271001i | \(-0.0873547\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.8296i | 1.45708i | 0.685005 | + | 0.728539i | \(0.259800\pi\) | ||||
−0.685005 | + | 0.728539i | \(0.740200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.69661 | −0.207431 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6457 | −1.11998 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 23.2017i | − 1.76399i | −0.471255 | − | 0.881997i | \(-0.656199\pi\) | ||||
0.471255 | − | 0.881997i | \(-0.343801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.2594i | 0.846307i | ||||||||
\(178\) | 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 | ||||||||
\(183\) | − 19.7122i | − 1.45717i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.463888i | 0.0339229i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.47880 | −0.398524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.74624 | −0.271068 | −0.135534 | − | 0.990773i | \(-0.543275\pi\) | ||||
−0.135534 | + | 0.990773i | \(0.543275\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 11.8470i | − 0.852763i | −0.904543 | − | 0.426381i | \(-0.859788\pi\) | ||||
0.904543 | − | 0.426381i | \(-0.140212\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 10.0064i | − 0.712924i | −0.934310 | − | 0.356462i | \(-0.883983\pi\) | ||||
0.934310 | − | 0.356462i | \(-0.116017\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 20.6742i | 1.45104i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.88594i | 0.131082i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.2154 | −0.844960 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.825746 | −0.0568467 | −0.0284234 | − | 0.999596i | \(-0.509049\pi\) | ||||
−0.0284234 | + | 0.999596i | \(0.509049\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.8029i | 1.15132i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.4446i | 1.38787i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.4147 | −1.92009 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16839 | 0.0785946 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 18.2911i | − 1.22486i | −0.790525 | − | 0.612430i | \(-0.790192\pi\) | ||||
0.790525 | − | 0.612430i | \(-0.209808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.5556i | 1.43069i | 0.698769 | + | 0.715347i | \(0.253732\pi\) | ||||
−0.698769 | + | 0.715347i | \(0.746268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.65960 | −0.638324 | −0.319162 | − | 0.947700i | \(-0.603401\pi\) | ||||
−0.319162 | + | 0.947700i | \(0.603401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.73581 | 0.508979 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 0.879774i | − 0.0576359i | −0.999585 | − | 0.0288179i | \(-0.990826\pi\) | ||||
0.999585 | − | 0.0288179i | \(-0.00917431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 24.3612i | − 1.58243i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − 17.1504i | − 1.10020i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.7669i | 1.95765i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.8974 | 1.89467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4221 | 1.35215 | 0.676074 | − | 0.736833i | \(-0.263680\pi\) | ||||
0.676074 | + | 0.736833i | \(0.263680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.57300i | 0.0988935i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 10.9788i | − 0.684838i | −0.939547 | − | 0.342419i | \(-0.888754\pi\) | ||||
0.939547 | − | 0.342419i | \(-0.111246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.4556 | −1.45746 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.5248 | −1.08476 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 11.3268i | − 0.698440i | −0.937041 | − | 0.349220i | \(-0.886447\pi\) | ||||
0.937041 | − | 0.349220i | \(-0.113553\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 31.7141i | − 1.94087i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.1010 | −1.89626 | −0.948130 | − | 0.317883i | \(-0.897028\pi\) | ||||
−0.948130 | + | 0.317883i | \(0.897028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1151 | 1.76862 | 0.884308 | − | 0.466905i | \(-0.154631\pi\) | ||||
0.884308 | + | 0.466905i | \(0.154631\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 19.4841i | − 1.17923i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.6829i | 1.36288i | 0.731873 | + | 0.681441i | \(0.238646\pi\) | ||||
−0.731873 | + | 0.681441i | \(0.761354\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 0.419014i | 0.0249078i | 0.999922 | + | 0.0124539i | \(0.00396431\pi\) | ||||
−0.999922 | + | 0.0124539i | \(0.996036\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 5.21177i | − 0.307641i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9130 | 0.994884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.440354 | −0.0258140 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.06844i | 0.0624190i | 0.999513 | + | 0.0312095i | \(0.00993591\pi\) | ||||
−0.999513 | + | 0.0312095i | \(0.990064\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 3.87355i | − 0.224766i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.96189 | 0.229122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8501 | −0.855944 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 13.4304i | − 0.771555i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 22.3991i | − 1.27838i | −0.769048 | − | 0.639191i | \(-0.779269\pi\) | ||||
0.769048 | − | 0.639191i | \(-0.220731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.3974 | 1.50169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9717 | −1.13249 | −0.566245 | − | 0.824237i | \(-0.691604\pi\) | ||||
−0.566245 | + | 0.824237i | \(0.691604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1975i | 0.802488i | 0.915971 | + | 0.401244i | \(0.131422\pi\) | ||||
−0.915971 | + | 0.401244i | \(0.868578\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.48205i | 0.420234i | 0.977676 | + | 0.210117i | \(0.0673844\pi\) | ||||
−0.977676 | + | 0.210117i | \(0.932616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.6168 | −0.818384 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6625 | 0.985826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.29017i | − 0.127428i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.64118i | 0.533158i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.07047 | −0.169280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.56494 | 0.360842 | 0.180421 | − | 0.983590i | \(-0.442254\pi\) | ||||
0.180421 | + | 0.983590i | \(0.442254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 19.8826i | − 1.08956i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 17.2484i | − 0.939583i | −0.882777 | − | 0.469791i | \(-0.844329\pi\) | ||||
0.882777 | − | 0.469791i | \(-0.155671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.5490 | −1.55057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4545 | −0.782753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1350i | 1.08719i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.18016i | − 0.224403i | −0.993685 | − | 0.112201i | \(-0.964210\pi\) | ||||
0.993685 | − | 0.112201i | \(-0.0357902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.6150 | −0.621736 | −0.310868 | − | 0.950453i | \(-0.600620\pi\) | ||||
−0.310868 | + | 0.950453i | \(0.600620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.75628 | −0.520752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8241i | 0.842233i | 0.907006 | + | 0.421117i | \(0.138362\pi\) | ||||
−0.907006 | + | 0.421117i | \(0.861638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.45032i | 0.0767590i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | − 18.8453i | − 0.989122i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.01500i | 0.261781i | 0.991397 | + | 0.130890i | \(0.0417836\pi\) | ||||
−0.991397 | + | 0.130890i | \(0.958216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.41785 | 0.229984 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.5615 | 1.27517 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.1804i | − 1.04490i | −0.852670 | − | 0.522450i | \(-0.825018\pi\) | ||||
0.852670 | − | 0.522450i | \(-0.174982\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.8152i | 1.89608i | ||||||||
\(378\) | 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 | ||||||||
\(383\) | − 23.9968i | − 1.22618i | −0.790014 | − | 0.613088i | \(-0.789927\pi\) | ||||
0.790014 | − | 0.613088i | \(-0.210073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 12.5879i | − 0.639879i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.3913 | −0.983180 | −0.491590 | − | 0.870827i | \(-0.663584\pi\) | ||||
−0.491590 | + | 0.870827i | \(0.663584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.294907 | −0.0149141 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.2696i | 1.07291i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0550i | 0.504644i | 0.967643 | + | 0.252322i | \(0.0811942\pi\) | ||||
−0.967643 | + | 0.252322i | \(0.918806\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 36.4064i | 1.81353i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 16.5833i | − 0.822005i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.92642 | −0.391936 | −0.195968 | − | 0.980610i | \(-0.562785\pi\) | ||||
−0.195968 | + | 0.980610i | \(0.562785\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.0026 | −0.740022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3330i | 0.557659i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 14.4956i | − 0.709855i | ||||||||
\(418\) | 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 | ||||||||
\(423\) | − 2.60273i | − 0.126549i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 19.8411i | − 0.960177i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.7754 | 0.665084 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1674 | −1.74212 | −0.871061 | − | 0.491175i | \(-0.836567\pi\) | ||||
−0.871061 | + | 0.491175i | \(0.836567\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 9.42856i | − 0.453108i | −0.973999 | − | 0.226554i | \(-0.927254\pi\) | ||||
0.973999 | − | 0.226554i | \(-0.0727459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.76572i | − 0.371485i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 35.5786i | − 1.69039i | −0.534458 | − | 0.845195i | \(-0.679484\pi\) | ||||
0.534458 | − | 0.845195i | \(-0.320516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.6467i | 1.44954i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.660651 | 0.0311780 | 0.0155890 | − | 0.999878i | \(-0.495038\pi\) | ||||
0.0155890 | + | 0.999878i | \(0.495038\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.68476 | 0.173509 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.35375i | 0.251541i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.62187i | 0.403314i | 0.979456 | + | 0.201657i | \(0.0646326\pi\) | ||||
−0.979456 | + | 0.201657i | \(0.935367\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 6.15748i | 0.286162i | 0.989711 | + | 0.143081i | \(0.0457010\pi\) | ||||
−0.989711 | + | 0.143081i | \(0.954299\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2.93879i | − 0.135991i | −0.997686 | − | 0.0679954i | \(-0.978340\pi\) | ||||
0.997686 | − | 0.0679954i | \(-0.0216603\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.49189 | −0.115065 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.7914 | −2.06388 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 10.4991i | − 0.482750i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.8200i | 0.953280i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 4.91788i | 0.223771i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.28554i | 0.148882i | 0.997225 | + | 0.0744410i | \(0.0237173\pi\) | ||||
−0.997225 | + | 0.0744410i | \(0.976283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.2957 | 0.691695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2119 | 1.09267 | 0.546335 | − | 0.837567i | \(-0.316023\pi\) | ||||
0.546335 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.74038i | − 0.123420i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.9127i | 0.758639i | ||||||||
\(498\) | 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 | ||||||||
\(503\) | 11.0448i | 0.492464i | 0.969211 | + | 0.246232i | \(0.0791925\pi\) | ||||
−0.969211 | + | 0.246232i | \(0.920807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 5.96062i | − 0.264720i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.4409 | 1.39359 | 0.696796 | − | 0.717269i | \(-0.254608\pi\) | ||||
0.696796 | + | 0.717269i | \(0.254608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.6004 | −1.26521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.1233i | 0.844315i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.17084i | − 0.0954735i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 41.8119i | 1.82830i | 0.405371 | + | 0.914152i | \(0.367142\pi\) | ||||
−0.405371 | + | 0.914152i | \(0.632858\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.70994i | − 0.118047i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.60658 | −0.416890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.28079i | − 0.401996i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.6539i | 1.02074i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − 16.0804i | − 0.690077i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 44.8700i | − 1.91850i | −0.282555 | − | 0.959251i | \(-0.591182\pi\) | ||||
0.282555 | − | 0.959251i | \(-0.408818\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.8186 | 0.717801 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 72.1616 | 3.07419 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 24.5204i | − 1.04271i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3106i | 0.945329i | 0.881242 | + | 0.472665i | \(0.156708\pi\) | ||||
−0.881242 | + | 0.472665i | \(0.843292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.4440 | −1.11846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.02539 | −0.0432919 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.41928i | − 0.0598153i | −0.999553 | − | 0.0299077i | \(-0.990479\pi\) | ||||
0.999553 | − | 0.0299077i | \(-0.00952132\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 24.6983i | − 1.03723i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.4950 | 0.901116 | 0.450558 | − | 0.892747i | \(-0.351225\pi\) | ||||
0.450558 | + | 0.892747i | \(0.351225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.0272 | 1.71694 | 0.858468 | − | 0.512868i | \(-0.171417\pi\) | ||||
0.858468 | + | 0.512868i | \(0.171417\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8.28075i | − 0.345933i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 37.1477i | − 1.54648i | −0.634114 | − | 0.773239i | \(-0.718635\pi\) | ||||
0.634114 | − | 0.773239i | \(-0.281365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.1867 | 1.08828 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0928 | 1.24846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.3652i | 0.719192i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 12.1838i | − 0.502881i | −0.967873 | − | 0.251440i | \(-0.919096\pi\) | ||||
0.967873 | − | 0.251440i | \(-0.0809043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 71.3602 | 2.94034 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.1183 | 0.909823 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.1421i | 1.64844i | 0.566270 | + | 0.824220i | \(0.308386\pi\) | ||||
−0.566270 | + | 0.824220i | \(0.691614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 13.6957i | − 0.560527i | ||||||||
\(598\) | 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 | ||||||||
\(603\) | − 2.11229i | − 0.0860191i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.09352i | 0.0443846i | 0.999754 | + | 0.0221923i | \(0.00706461\pi\) | ||||
−0.999754 | + | 0.0221923i | \(0.992935\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −45.6986 | −1.85180 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.46768 | −0.221199 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 16.4617i | − 0.664880i | −0.943124 | − | 0.332440i | \(-0.892128\pi\) | ||||
0.943124 | − | 0.332440i | \(-0.107872\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9090i | 0.962540i | 0.876572 | + | 0.481270i | \(0.159824\pi\) | ||||
−0.876572 | + | 0.481270i | \(0.840176\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | − 31.9213i | − 1.27890i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 27.0012i | − 1.07833i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.10906 | 0.123966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.317634 | 0.0126448 | 0.00632241 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00632241 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 1.82524i | − 0.0725469i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.12179i | 0.321797i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 20.0837i | 0.792023i | 0.918246 | + | 0.396011i | \(0.129606\pi\) | ||||
−0.918246 | + | 0.396011i | \(0.870394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0801i | 0.868060i | 0.900898 | + | 0.434030i | \(0.142909\pi\) | ||||
−0.900898 | + | 0.434030i | \(0.857091\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.01250 | −0.314518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.1910 | −1.77118 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 33.2385i | − 1.30072i | −0.759625 | − | 0.650362i | \(-0.774617\pi\) | ||||
0.759625 | − | 0.650362i | \(-0.225383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 24.2436i | − 0.945833i | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 2.58263i | 0.100301i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.29233i | − 0.359800i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.4309 | 1.56315 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0278 | 0.541537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.7860i | 0.415771i | 0.978153 | + | 0.207885i | \(0.0666581\pi\) | ||||
−0.978153 | + | 0.207885i | \(0.933342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.1146i | 0.619336i | 0.950845 | + | 0.309668i | \(0.100218\pi\) | ||||
−0.950845 | + | 0.309668i | \(0.899782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.443232 | −0.0170097 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.6468 | −1.82583 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1106i | 0.463399i | 0.972787 | + | 0.231699i | \(0.0744286\pi\) | ||||
−0.972787 | + | 0.231699i | \(0.925571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 21.3517i | − 0.814620i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.7375 | 1.66627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.1463 | −1.14682 | −0.573410 | − | 0.819269i | \(-0.694380\pi\) | ||||
−0.573410 | + | 0.819269i | \(0.694380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.60025i | 0.250723i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.690824i | 0.0261668i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 81.8701i | 3.08779i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 13.5182i | − 0.508403i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0163 | −1.39018 | −0.695088 | − | 0.718924i | \(-0.744635\pi\) | ||||
−0.695088 | + | 0.718924i | \(0.744635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.7851 | 0.779503 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 9.18913i | − 0.344136i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 49.3454i | − 1.84284i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | − 16.4402i | − 0.611418i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1278i | 1.08029i | 0.841571 | + | 0.540146i | \(0.181631\pi\) | ||||
−0.841571 | + | 0.540146i | \(0.818369\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.60629 | 0.170603 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.96839 | 0.0728034 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.30466i | − 0.269804i | −0.990859 | − | 0.134902i | \(-0.956928\pi\) | ||||
0.990859 | − | 0.134902i | \(-0.0430719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.76178i | − 0.0648962i | ||||||||
\(738\) | 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 | ||||||||
\(743\) | 11.4448i | 0.419869i | 0.977715 | + | 0.209934i | \(0.0673250\pi\) | ||||
−0.977715 | + | 0.209934i | \(0.932675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.5087i | 0.933313i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.7780 | 0.649593 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.62069 | −0.278083 | −0.139041 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139041 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 47.3517i | 1.72559i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 41.3725i | − 1.50371i | −0.659329 | − | 0.751855i | \(-0.729159\pi\) | ||||
0.659329 | − | 0.751855i | \(-0.270841\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 9.70420i | 0.351315i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.1810i | 0.728694i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0182 | 0.902180 | 0.451090 | − | 0.892479i | \(-0.351035\pi\) | ||||
0.451090 | + | 0.892479i | \(0.351035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.2677 | 0.873980 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 37.1948i | − 1.33781i | −0.743350 | − | 0.668903i | \(-0.766764\pi\) | ||||
0.743350 | − | 0.668903i | \(-0.233236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 51.8467i | − 1.85999i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.1913 | −0.651771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9574 | −0.427870 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.8826i | 0.817759i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.64645i | 0.272567i | 0.990670 | + | 0.136283i | \(0.0435157\pi\) | ||||
−0.990670 | + | 0.136283i | \(0.956484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.0369 | 0.891338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.7356 | −1.02172 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 35.3317i | − 1.25467i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.38544i | 0.0844966i | 0.999107 | + | 0.0422483i | \(0.0134521\pi\) | ||||
−0.999107 | + | 0.0422483i | \(0.986548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.406992 | 0.0143984 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.0586 | 0.956070 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 20.2207i | − 0.713573i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 68.7461i | − 2.41998i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.4937 | −0.544730 | −0.272365 | − | 0.962194i | \(-0.587806\pi\) | ||||
−0.272365 | + | 0.962194i | \(0.587806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.3850 | 1.94483 | 0.972415 | − | 0.233259i | \(-0.0749389\pi\) | ||||
0.972415 | + | 0.233259i | \(0.0749389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.3565i | 2.25708i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.8330i | 1.81341i | ||||||||
\(818\) | 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 | ||||||||
\(823\) | − 0.237837i | − 0.00829047i | −0.999991 | − | 0.00414524i | \(-0.998681\pi\) | ||||
0.999991 | − | 0.00414524i | \(-0.00131947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5821i | 0.611391i | 0.952129 | + | 0.305695i | \(0.0988889\pi\) | ||||
−0.952129 | + | 0.305695i | \(0.901111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5607 | −0.714103 | −0.357051 | − | 0.934085i | \(-0.616218\pi\) | ||||
−0.357051 | + | 0.934085i | \(0.616218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.1386 | −1.73929 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.604553i | − 0.0209465i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.6285i | 0.782156i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 24.8741i | 0.856709i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 18.9685i | − 0.651765i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.926197 | −0.0317870 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5425 | 0.361392 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.7788i | 0.642973i | 0.946914 | + | 0.321486i | \(0.104182\pi\) | ||||
−0.946914 | + | 0.321486i | \(0.895818\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.4670i | 1.00657i | 0.864120 | + | 0.503286i | \(0.167876\pi\) | ||||
−0.864120 | + | 0.503286i | \(0.832124\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | 19.5166i | 0.664351i | 0.943218 | + | 0.332176i | \(0.107783\pi\) | ||||
−0.943218 | + | 0.332176i | \(0.892217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.3848i | 1.26966i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.3361 | 0.588088 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.43739 | −0.150355 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 0.375713i | − 0.0127160i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.68909i | 0.225874i | 0.993602 | + | 0.112937i | \(0.0360259\pi\) | ||||
−0.993602 | + | 0.112937i | \(0.963974\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 40.5934i | − 1.36608i | −0.730383 | − | 0.683038i | \(-0.760658\pi\) | ||||
0.730383 | − | 0.683038i | \(-0.239342\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.89101i | 0.332108i | 0.986117 | + | 0.166054i | \(0.0531025\pi\) | ||||
−0.986117 | + | 0.166054i | \(0.946897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.4343 | 1.22197 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.4619 | 0.584996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.7172i | 0.358638i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.75744i | 0.292402i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 85.3884 | 2.84786 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.25564 | −0.108461 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 32.8249i | − 1.09234i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.3250i | − 1.40538i | −0.711497 | − | 0.702689i | \(-0.751983\pi\) | ||||
0.711497 | − | 0.702689i | \(-0.248017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.4589 | 0.380068 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.48129 | 0.181603 | 0.0908016 | − | 0.995869i | \(-0.471057\pi\) | ||||
0.0908016 | + | 0.995869i | \(0.471057\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.2759i | 0.704128i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.4086i | 0.706974i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 30.1171i | 0.991315i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.5224i | 0.739733i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.2326 | 0.991900 | 0.495950 | − | 0.868351i | \(-0.334820\pi\) | ||||
0.495950 | + | 0.868351i | \(0.334820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.9195 | 0.521741 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 44.1457i | − 1.44527i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.8718i | 0.910532i | 0.890356 | + | 0.455266i | \(0.150456\pi\) | ||||
−0.890356 | + | 0.455266i | \(0.849544\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 2.34251i | 0.0762827i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23.1773i | − 0.753161i | −0.926384 | − | 0.376581i | \(-0.877100\pi\) | ||||
0.926384 | − | 0.376581i | \(-0.122900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.9297 | −1.65325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.5384 | −0.536296 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.21870i | 0.136657i | 0.997663 | + | 0.0683285i | \(0.0217666\pi\) | ||||
−0.997663 | + | 0.0683285i | \(0.978233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 32.3092i | − 1.04441i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.1006 | −0.487625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.4401 | 1.72387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0698i | 0.485617i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8055i | 0.572588i | 0.958142 | + | 0.286294i | \(0.0924233\pi\) | ||||
−0.958142 | + | 0.286294i | \(0.907577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.06223 | 0.162622 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.9741 | 0.576815 | 0.288408 | − | 0.957508i | \(-0.406874\pi\) | ||||
0.288408 | + | 0.957508i | \(0.406874\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 14.5904i | − 0.467747i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.6275i | 1.87566i | 0.347097 | + | 0.937829i | \(0.387167\pi\) | ||||
−0.347097 | + | 0.937829i | \(0.612833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5686 | 0.721297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.22592 | −0.262633 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 7.84103i | − 0.250090i | −0.992151 | − | 0.125045i | \(-0.960092\pi\) | ||||
0.992151 | − | 0.125045i | \(-0.0399075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6.78701i | − 0.216033i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.67460 | 0.212240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.1872 | −1.05423 | −0.527114 | − | 0.849795i | \(-0.676726\pi\) | ||||
−0.527114 | + | 0.849795i | \(0.676726\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.5112i | 0.460500i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 60.8220i | − 1.92625i | −0.269049 | − | 0.963127i | \(-0.586709\pi\) | ||||
0.269049 | − | 0.963127i | \(-0.413291\pi\) | |||||||
\(998\) | 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 | 4600.2.e.v.4049.9 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bc.1.5 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bg.1.1 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.v.4049.2 | 10 | ||
20.3 | even | 4 | 9200.2.a.cs.1.5 | 5 | |||
20.7 | even | 4 | 9200.2.a.cw.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.5 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bg.1.1 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.v.4049.2 | 10 | 5.4 | even | 2 | inner | ||
4600.2.e.v.4049.9 | 10 | 1.1 | even | 1 | trivial | ||
9200.2.a.cs.1.5 | 5 | 20.3 | even | 4 | |||
9200.2.a.cw.1.1 | 5 | 20.7 | even | 4 |