Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(643,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.643");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.e (of order \(4\), degree \(2\), 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: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.12877254853348294656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 26x^{12} + 12x^{10} + 35x^{8} + 180x^{6} + 686x^{4} + 632x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.2 | ||
Root | \(1.90419 + 1.19709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1057 |
Dual form | 1150.2.e.f.643.2 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | 2.39417 | − | 2.39417i | 0.904911 | − | 0.904911i | −0.0909447 | − | 0.995856i | \(-0.528989\pi\) |
0.995856 | + | 0.0909447i | \(0.0289886\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.14655i | 0.647210i | 0.946192 | + | 0.323605i | \(0.104895\pi\) | ||||
−0.946192 | + | 0.323605i | \(0.895105\pi\) | |||||||
\(12\) | −1.22474 | − | 1.22474i | −0.353553 | − | 0.353553i | ||||
\(13\) | −0.896575 | + | 0.896575i | −0.248665 | + | 0.248665i | −0.820423 | − | 0.571757i | \(-0.806262\pi\) |
0.571757 | + | 0.820423i | \(0.306262\pi\) | |||||||
\(14\) | −3.38587 | −0.904911 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.91201 | − | 3.91201i | 0.948803 | − | 0.948803i | −0.0499492 | − | 0.998752i | \(-0.515906\pi\) |
0.998752 | + | 0.0499492i | \(0.0159059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.14655 | 0.492453 | 0.246227 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246227 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.86450i | 1.27974i | ||||||||
\(22\) | 1.51784 | − | 1.51784i | 0.323605 | − | 0.323605i | ||||
\(23\) | −1.27671 | − | 4.62277i | −0.266212 | − | 0.963915i | ||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.26795 | 0.248665 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | 2.39417 | + | 2.39417i | 0.452456 | + | 0.452456i | ||||
\(29\) | 1.46410i | 0.271877i | 0.990717 | + | 0.135938i | \(0.0434049\pi\) | ||||
−0.990717 | + | 0.135938i | \(0.956595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26795 | 0.227730 | 0.113865 | − | 0.993496i | \(-0.463677\pi\) | ||||
0.113865 | + | 0.993496i | \(0.463677\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −2.62898 | − | 2.62898i | −0.457647 | − | 0.457647i | ||||
\(34\) | −5.53242 | −0.948803 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.75265 | + | 1.75265i | −0.288135 | + | 0.288135i | −0.836342 | − | 0.548208i | \(-0.815310\pi\) |
0.548208 | + | 0.836342i | \(0.315310\pi\) | |||||||
\(38\) | −1.51784 | − | 1.51784i | −0.246227 | − | 0.246227i | ||||
\(39\) | − | 2.19615i | − | 0.351666i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92820 | 0.301135 | 0.150567 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150567 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(42\) | 4.14682 | − | 4.14682i | 0.639869 | − | 0.639869i | ||||
\(43\) | 6.54099 | + | 6.54099i | 0.997492 | + | 0.997492i | 0.999997 | − | 0.00250455i | \(-0.000797223\pi\) |
−0.00250455 | + | 0.999997i | \(0.500797\pi\) | |||||||
\(44\) | −2.14655 | −0.323605 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.36603 | + | 4.17156i | −0.348851 | + | 0.615063i | ||||
\(47\) | −0.896575 | − | 0.896575i | −0.130779 | − | 0.130779i | 0.638687 | − | 0.769466i | \(-0.279478\pi\) |
−0.769466 | + | 0.638687i | \(0.779478\pi\) | |||||||
\(48\) | 1.22474 | − | 1.22474i | 0.176777 | − | 0.176777i | ||||
\(49\) | − | 4.46410i | − | 0.637729i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.58244i | 1.34181i | ||||||||
\(52\) | −0.896575 | − | 0.896575i | −0.124333 | − | 0.124333i | ||||
\(53\) | −1.11114 | − | 1.11114i | −0.152627 | − | 0.152627i | 0.626663 | − | 0.779290i | \(-0.284420\pi\) |
−0.779290 | + | 0.626663i | \(0.784420\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.38587i | − | 0.452456i | ||||||
\(57\) | −2.62898 | + | 2.62898i | −0.348217 | + | 0.348217i | ||||
\(58\) | 1.03528 | − | 1.03528i | 0.135938 | − | 0.135938i | ||||
\(59\) | − | 7.46410i | − | 0.971743i | −0.874030 | − | 0.485872i | \(-0.838502\pi\) | ||
0.874030 | − | 0.485872i | \(-0.161498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.86450i | 0.750872i | 0.926848 | + | 0.375436i | \(0.122507\pi\) | ||||
−0.926848 | + | 0.375436i | \(0.877493\pi\) | |||||||
\(62\) | −0.896575 | − | 0.896575i | −0.113865 | − | 0.113865i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.71794i | 0.457647i | ||||||||
\(67\) | 0.876327 | − | 0.876327i | 0.107060 | − | 0.107060i | −0.651547 | − | 0.758608i | \(-0.725880\pi\) |
0.758608 | + | 0.651547i | \(0.225880\pi\) | |||||||
\(68\) | 3.91201 | + | 3.91201i | 0.474401 | + | 0.474401i | ||||
\(69\) | 7.22536 | + | 4.09808i | 0.869831 | + | 0.493350i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9282 | 1.77165 | 0.885826 | − | 0.464018i | \(-0.153593\pi\) | ||||
0.885826 | + | 0.464018i | \(0.153593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.91688 | − | 7.91688i | 0.926600 | − | 0.926600i | −0.0708844 | − | 0.997485i | \(-0.522582\pi\) |
0.997485 | + | 0.0708844i | \(0.0225821\pi\) | |||||||
\(74\) | 2.47863 | 0.288135 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.14655i | 0.246227i | ||||||||
\(77\) | 5.13922 | + | 5.13922i | 0.585668 | + | 0.585668i | ||||
\(78\) | −1.55291 | + | 1.55291i | −0.175833 | + | 0.175833i | ||||
\(79\) | 16.0221 | 1.80263 | 0.901313 | − | 0.433167i | \(-0.142604\pi\) | ||||
0.901313 | + | 0.433167i | \(0.142604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −1.36345 | − | 1.36345i | −0.150567 | − | 0.150567i | ||||
\(83\) | 10.9226 | + | 10.9226i | 1.19891 | + | 1.19891i | 0.974492 | + | 0.224422i | \(0.0720495\pi\) |
0.224422 | + | 0.974492i | \(0.427950\pi\) | |||||||
\(84\) | −5.86450 | −0.639869 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 9.25036i | − | 0.997492i | ||||||
\(87\) | −1.79315 | − | 1.79315i | −0.192246 | − | 0.192246i | ||||
\(88\) | 1.51784 | + | 1.51784i | 0.161803 | + | 0.161803i | ||||
\(89\) | 9.58244 | 1.01574 | 0.507868 | − | 0.861435i | \(-0.330434\pi\) | ||||
0.507868 | + | 0.861435i | \(0.330434\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.29311i | 0.450040i | ||||||||
\(92\) | 4.62277 | − | 1.27671i | 0.481957 | − | 0.133106i | ||||
\(93\) | −1.55291 | + | 1.55291i | −0.161030 | + | 0.161030i | ||||
\(94\) | 1.26795i | 0.130779i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.73205 | −0.176777 | ||||||||
\(97\) | −6.54099 | + | 6.54099i | −0.664137 | + | 0.664137i | −0.956353 | − | 0.292215i | \(-0.905608\pi\) |
0.292215 | + | 0.956353i | \(0.405608\pi\) | |||||||
\(98\) | −3.15660 | + | 3.15660i | −0.318864 | + | 0.318864i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.12436 | −0.708900 | −0.354450 | − | 0.935075i | \(-0.615332\pi\) | ||||
−0.354450 | + | 0.935075i | \(0.615332\pi\) | |||||||
\(102\) | 6.77581 | − | 6.77581i | 0.670905 | − | 0.670905i | ||||
\(103\) | 13.7235 | + | 13.7235i | 1.35222 | + | 1.35222i | 0.883177 | + | 0.469040i | \(0.155400\pi\) |
0.469040 | + | 0.883177i | \(0.344600\pi\) | |||||||
\(104\) | 1.26795i | 0.124333i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.57139i | 0.152627i | ||||||||
\(107\) | 3.91201 | − | 3.91201i | 0.378189 | − | 0.378189i | −0.492260 | − | 0.870448i | \(-0.663829\pi\) |
0.870448 | + | 0.492260i | \(0.163829\pi\) | |||||||
\(108\) | 3.67423 | − | 3.67423i | 0.353553 | − | 0.353553i | ||||
\(109\) | 4.29311 | 0.411205 | 0.205603 | − | 0.978636i | \(-0.434085\pi\) | ||||
0.205603 | + | 0.978636i | \(0.434085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.29311i | − | 0.407484i | ||||||
\(112\) | −2.39417 | + | 2.39417i | −0.226228 | + | 0.226228i | ||||
\(113\) | −8.70035 | − | 8.70035i | −0.818460 | − | 0.818460i | 0.167424 | − | 0.985885i | \(-0.446455\pi\) |
−0.985885 | + | 0.167424i | \(0.946455\pi\) | |||||||
\(114\) | 3.71794 | 0.348217 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.46410 | −0.135938 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.27792 | + | 5.27792i | −0.485872 | + | 0.485872i | ||||
\(119\) | − | 18.7321i | − | 1.71716i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.39230 | 0.581119 | ||||||||
\(122\) | 4.14682 | − | 4.14682i | 0.375436 | − | 0.375436i | ||||
\(123\) | −2.36156 | + | 2.36156i | −0.212934 | + | 0.212934i | ||||
\(124\) | 1.26795i | 0.113865i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.55291 | + | 1.55291i | 0.137799 | + | 0.137799i | 0.772641 | − | 0.634843i | \(-0.218935\pi\) |
−0.634843 | + | 0.772641i | \(0.718935\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −16.0221 | −1.41067 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.0000 | −1.22319 | −0.611593 | − | 0.791173i | \(-0.709471\pi\) | ||||
−0.611593 | + | 0.791173i | \(0.709471\pi\) | |||||||
\(132\) | 2.62898 | − | 2.62898i | 0.228823 | − | 0.228823i | ||||
\(133\) | 5.13922 | − | 5.13922i | 0.445627 | − | 0.445627i | ||||
\(134\) | −1.23931 | −0.107060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.53242i | − | 0.474401i | ||||||
\(137\) | −3.91201 | + | 3.91201i | −0.334226 | + | 0.334226i | −0.854189 | − | 0.519963i | \(-0.825946\pi\) |
0.519963 | + | 0.854189i | \(0.325946\pi\) | |||||||
\(138\) | −2.21132 | − | 8.00688i | −0.188240 | − | 0.681591i | ||||
\(139\) | 2.07180i | 0.175728i | 0.996133 | + | 0.0878638i | \(0.0280040\pi\) | ||||
−0.996133 | + | 0.0878638i | \(0.971996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.19615 | 0.184949 | ||||||||
\(142\) | −10.5558 | − | 10.5558i | −0.885826 | − | 0.885826i | ||||
\(143\) | −1.92455 | − | 1.92455i | −0.160939 | − | 0.160939i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.1962 | −0.926600 | ||||||||
\(147\) | 5.46739 | + | 5.46739i | 0.450942 | + | 0.450942i | ||||
\(148\) | −1.75265 | − | 1.75265i | −0.144067 | − | 0.144067i | ||||
\(149\) | 1.57139 | 0.128733 | 0.0643665 | − | 0.997926i | \(-0.479497\pi\) | ||||
0.0643665 | + | 0.997926i | \(0.479497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.19615 | −0.666993 | −0.333497 | − | 0.942751i | \(-0.608229\pi\) | ||||
−0.333497 | + | 0.942751i | \(0.608229\pi\) | |||||||
\(152\) | 1.51784 | − | 1.51784i | 0.123113 | − | 0.123113i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 7.26795i | − | 0.585668i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.19615 | 0.175833 | ||||||||
\(157\) | −10.0463 | + | 10.0463i | −0.801782 | + | 0.801782i | −0.983374 | − | 0.181592i | \(-0.941875\pi\) |
0.181592 | + | 0.983374i | \(0.441875\pi\) | |||||||
\(158\) | −11.3293 | − | 11.3293i | −0.901313 | − | 0.901313i | ||||
\(159\) | 2.72172 | 0.215847 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.1244 | − | 8.01105i | −1.11316 | − | 0.631359i | ||||
\(162\) | −6.36396 | − | 6.36396i | −0.500000 | − | 0.500000i | ||||
\(163\) | 13.9527 | − | 13.9527i | 1.09286 | − | 1.09286i | 0.0976349 | − | 0.995222i | \(-0.468872\pi\) |
0.995222 | − | 0.0976349i | \(-0.0311277\pi\) | |||||||
\(164\) | 1.92820i | 0.150567i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 15.4469i | − | 1.19891i | ||||||
\(167\) | −14.2808 | − | 14.2808i | −1.10508 | − | 1.10508i | −0.993787 | − | 0.111297i | \(-0.964499\pi\) |
−0.111297 | − | 0.993787i | \(-0.535501\pi\) | |||||||
\(168\) | 4.14682 | + | 4.14682i | 0.319934 | + | 0.319934i | ||||
\(169\) | 11.3923i | 0.876331i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.54099 | + | 6.54099i | −0.498746 | + | 0.498746i | ||||
\(173\) | −3.58630 | + | 3.58630i | −0.272661 | + | 0.272661i | −0.830171 | − | 0.557509i | \(-0.811757\pi\) |
0.557509 | + | 0.830171i | \(0.311757\pi\) | |||||||
\(174\) | 2.53590i | 0.192246i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.14655i | − | 0.161803i | ||||||
\(177\) | 9.14162 | + | 9.14162i | 0.687126 | + | 0.687126i | ||||
\(178\) | −6.77581 | − | 6.77581i | −0.507868 | − | 0.507868i | ||||
\(179\) | 1.00000i | 0.0747435i | 0.999301 | + | 0.0373718i | \(0.0118986\pi\) | ||||
−0.999301 | + | 0.0373718i | \(0.988101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.43588i | − | 0.552705i | −0.961056 | − | 0.276352i | \(-0.910874\pi\) | ||
0.961056 | − | 0.276352i | \(-0.0891257\pi\) | |||||||
\(182\) | 3.03569 | − | 3.03569i | 0.225020 | − | 0.225020i | ||||
\(183\) | −7.18251 | − | 7.18251i | −0.530946 | − | 0.530946i | ||||
\(184\) | −4.17156 | − | 2.36603i | −0.307532 | − | 0.174426i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.19615 | 0.161030 | ||||||||
\(187\) | 8.39735 | + | 8.39735i | 0.614075 | + | 0.614075i | ||||
\(188\) | 0.896575 | − | 0.896575i | 0.0653895 | − | 0.0653895i | ||||
\(189\) | −17.5935 | −1.27974 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.5935i | − | 1.27302i | −0.771268 | − | 0.636510i | \(-0.780377\pi\) | ||
0.771268 | − | 0.636510i | \(-0.219623\pi\) | |||||||
\(192\) | 1.22474 | + | 1.22474i | 0.0883883 | + | 0.0883883i | ||||
\(193\) | −11.0227 | + | 11.0227i | −0.793432 | + | 0.793432i | −0.982050 | − | 0.188619i | \(-0.939599\pi\) |
0.188619 | + | 0.982050i | \(0.439599\pi\) | |||||||
\(194\) | 9.25036 | 0.664137 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.46410 | 0.318864 | ||||||||
\(197\) | 16.7303 | + | 16.7303i | 1.19199 | + | 1.19199i | 0.976509 | + | 0.215478i | \(0.0691308\pi\) |
0.215478 | + | 0.976509i | \(0.430869\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.57139 | −0.111393 | −0.0556963 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556963 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.14655i | 0.151406i | ||||||||
\(202\) | 5.03768 | + | 5.03768i | 0.354450 | + | 0.354450i | ||||
\(203\) | 3.50531 | + | 3.50531i | 0.246024 | + | 0.246024i | ||||
\(204\) | −9.58244 | −0.670905 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 19.4080i | − | 1.35222i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.896575 | − | 0.896575i | 0.0621663 | − | 0.0621663i | ||||
\(209\) | 4.60770i | 0.318721i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.46410 | −0.445007 | −0.222504 | − | 0.974932i | \(-0.571423\pi\) | ||||
−0.222504 | + | 0.974932i | \(0.571423\pi\) | |||||||
\(212\) | 1.11114 | − | 1.11114i | 0.0763133 | − | 0.0763133i | ||||
\(213\) | −18.2832 | + | 18.2832i | −1.25275 | + | 1.25275i | ||||
\(214\) | −5.53242 | −0.378189 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | 3.03569 | − | 3.03569i | 0.206076 | − | 0.206076i | ||||
\(218\) | −3.03569 | − | 3.03569i | −0.205603 | − | 0.205603i | ||||
\(219\) | 19.3923i | 1.31041i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.01483i | 0.471869i | ||||||||
\(222\) | −3.03569 | + | 3.03569i | −0.203742 | + | 0.203742i | ||||
\(223\) | 11.5911 | − | 11.5911i | 0.776198 | − | 0.776198i | −0.202984 | − | 0.979182i | \(-0.565064\pi\) |
0.979182 | + | 0.202984i | \(0.0650639\pi\) | |||||||
\(224\) | 3.38587 | 0.226228 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3042i | 0.818460i | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | −2.62898 | − | 2.62898i | −0.174109 | − | 0.174109i | ||||
\(229\) | 10.1576 | 0.671233 | 0.335617 | − | 0.941999i | \(-0.391055\pi\) | ||||
0.335617 | + | 0.941999i | \(0.391055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5885 | −0.828260 | ||||||||
\(232\) | 1.03528 | + | 1.03528i | 0.0679692 | + | 0.0679692i | ||||
\(233\) | −18.2832 | + | 18.2832i | −1.19777 | + | 1.19777i | −0.222944 | + | 0.974831i | \(0.571567\pi\) |
−0.974831 | + | 0.222944i | \(0.928433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.46410 | 0.485872 | ||||||||
\(237\) | −19.6230 | + | 19.6230i | −1.27465 | + | 1.27465i | ||||
\(238\) | −13.2456 | + | 13.2456i | −0.858582 | + | 0.858582i | ||||
\(239\) | − | 3.26795i | − | 0.211386i | −0.994399 | − | 0.105693i | \(-0.966294\pi\) | ||
0.994399 | − | 0.105693i | \(-0.0337061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.58244i | − | 0.617259i | −0.951182 | − | 0.308629i | \(-0.900130\pi\) | ||
0.951182 | − | 0.308629i | \(-0.0998703\pi\) | |||||||
\(242\) | −4.52004 | − | 4.52004i | −0.290559 | − | 0.290559i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.86450 | −0.375436 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.33975 | 0.212934 | ||||||||
\(247\) | −1.92455 | + | 1.92455i | −0.122456 | + | 0.122456i | ||||
\(248\) | 0.896575 | − | 0.896575i | 0.0569326 | − | 0.0569326i | ||||
\(249\) | −26.7549 | −1.69552 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.8755i | − | 0.875817i | −0.899020 | − | 0.437908i | \(-0.855719\pi\) | ||
0.899020 | − | 0.437908i | \(-0.144281\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.92303 | − | 2.74052i | 0.623856 | − | 0.172295i | ||||
\(254\) | − | 2.19615i | − | 0.137799i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.5211 | − | 14.5211i | −0.905800 | − | 0.905800i | 0.0901303 | − | 0.995930i | \(-0.471272\pi\) |
−0.995930 | + | 0.0901303i | \(0.971272\pi\) | |||||||
\(258\) | 11.3293 | + | 11.3293i | 0.705334 | + | 0.705334i | ||||
\(259\) | 8.39230i | 0.521472i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.89949 | + | 9.89949i | 0.611593 | + | 0.611593i | ||||
\(263\) | −15.4762 | − | 15.4762i | −0.954301 | − | 0.954301i | 0.0446996 | − | 0.999000i | \(-0.485767\pi\) |
−0.999000 | + | 0.0446996i | \(0.985767\pi\) | |||||||
\(264\) | −3.71794 | −0.228823 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.26795 | −0.445627 | ||||||||
\(267\) | −11.7360 | + | 11.7360i | −0.718234 | + | 0.718234i | ||||
\(268\) | 0.876327 | + | 0.876327i | 0.0535302 | + | 0.0535302i | ||||
\(269\) | 4.33975i | 0.264599i | 0.991210 | + | 0.132299i | \(0.0422361\pi\) | ||||
−0.991210 | + | 0.132299i | \(0.957764\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7846 | 1.14108 | 0.570542 | − | 0.821269i | \(-0.306733\pi\) | ||||
0.570542 | + | 0.821269i | \(0.306733\pi\) | |||||||
\(272\) | −3.91201 | + | 3.91201i | −0.237201 | + | 0.237201i | ||||
\(273\) | −5.25796 | − | 5.25796i | −0.318226 | − | 0.318226i | ||||
\(274\) | 5.53242 | 0.334226 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.09808 | + | 7.22536i | −0.246675 | + | 0.434915i | ||||
\(277\) | 1.31268 | + | 1.31268i | 0.0788712 | + | 0.0788712i | 0.745442 | − | 0.666571i | \(-0.232239\pi\) |
−0.666571 | + | 0.745442i | \(0.732239\pi\) | |||||||
\(278\) | 1.46498 | − | 1.46498i | 0.0878638 | − | 0.0878638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0221i | 0.955798i | 0.878415 | + | 0.477899i | \(0.158602\pi\) | ||||
−0.878415 | + | 0.477899i | \(0.841398\pi\) | |||||||
\(282\) | −1.55291 | − | 1.55291i | −0.0924747 | − | 0.0924747i | ||||
\(283\) | 9.63960 | + | 9.63960i | 0.573015 | + | 0.573015i | 0.932970 | − | 0.359955i | \(-0.117208\pi\) |
−0.359955 | + | 0.932970i | \(0.617208\pi\) | |||||||
\(284\) | 14.9282i | 0.885826i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72172i | 0.160939i | ||||||||
\(287\) | 4.61645 | − | 4.61645i | 0.272500 | − | 0.272500i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.6077i | − | 0.800453i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 16.0221i | − | 0.939232i | ||||||
\(292\) | 7.91688 | + | 7.91688i | 0.463300 | + | 0.463300i | ||||
\(293\) | −18.9815 | − | 18.9815i | −1.10891 | − | 1.10891i | −0.993294 | − | 0.115615i | \(-0.963116\pi\) |
−0.115615 | − | 0.993294i | \(-0.536884\pi\) | |||||||
\(294\) | − | 7.73205i | − | 0.450942i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.47863i | 0.144067i | ||||||||
\(297\) | 7.88694 | − | 7.88694i | 0.457647 | − | 0.457647i | ||||
\(298\) | −1.11114 | − | 1.11114i | −0.0643665 | − | 0.0643665i | ||||
\(299\) | 5.28933 | + | 3.00000i | 0.305890 | + | 0.173494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.3205 | 1.80528 | ||||||||
\(302\) | 5.79555 | + | 5.79555i | 0.333497 | + | 0.333497i | ||||
\(303\) | 8.72552 | − | 8.72552i | 0.501268 | − | 0.501268i | ||||
\(304\) | −2.14655 | −0.123113 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.3011 | + | 21.3011i | 1.21572 | + | 1.21572i | 0.969116 | + | 0.246604i | \(0.0793146\pi\) |
0.246604 | + | 0.969116i | \(0.420685\pi\) | |||||||
\(308\) | −5.13922 | + | 5.13922i | −0.292834 | + | 0.292834i | ||||
\(309\) | −33.6156 | −1.91232 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7846 | 0.611539 | 0.305770 | − | 0.952106i | \(-0.401086\pi\) | ||||
0.305770 | + | 0.952106i | \(0.401086\pi\) | |||||||
\(312\) | −1.55291 | − | 1.55291i | −0.0879165 | − | 0.0879165i | ||||
\(313\) | −14.8346 | − | 14.8346i | −0.838504 | − | 0.838504i | 0.150158 | − | 0.988662i | \(-0.452022\pi\) |
−0.988662 | + | 0.150158i | \(0.952022\pi\) | |||||||
\(314\) | 14.2076 | 0.801782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0221i | 0.901313i | ||||||||
\(317\) | −21.3891 | − | 21.3891i | −1.20133 | − | 1.20133i | −0.973762 | − | 0.227567i | \(-0.926923\pi\) |
−0.227567 | − | 0.973762i | \(-0.573077\pi\) | |||||||
\(318\) | −1.92455 | − | 1.92455i | −0.107923 | − | 0.107923i | ||||
\(319\) | −3.14277 | −0.175962 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.58244i | 0.534839i | ||||||||
\(322\) | 4.32276 | + | 15.6521i | 0.240898 | + | 0.872257i | ||||
\(323\) | 8.39735 | − | 8.39735i | 0.467241 | − | 0.467241i | ||||
\(324\) | 9.00000i | 0.500000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.7321 | −1.09286 | ||||||||
\(327\) | −5.25796 | + | 5.25796i | −0.290766 | + | 0.290766i | ||||
\(328\) | 1.36345 | − | 1.36345i | 0.0752837 | − | 0.0752837i | ||||
\(329\) | −4.29311 | −0.236687 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.7846 | −1.19739 | −0.598695 | − | 0.800977i | \(-0.704314\pi\) | ||||
−0.598695 | + | 0.800977i | \(0.704314\pi\) | |||||||
\(332\) | −10.9226 | + | 10.9226i | −0.599457 | + | 0.599457i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.1962i | 1.10508i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 5.86450i | − | 0.319934i | ||||||
\(337\) | −18.2770 | + | 18.2770i | −0.995613 | + | 0.995613i | −0.999990 | − | 0.00437692i | \(-0.998607\pi\) |
0.00437692 | + | 0.999990i | \(0.498607\pi\) | |||||||
\(338\) | 8.05558 | − | 8.05558i | 0.438166 | − | 0.438166i | ||||
\(339\) | 21.3114 | 1.15748 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.72172i | 0.147389i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.07137 | + | 6.07137i | 0.327823 | + | 0.327823i | ||||
\(344\) | 9.25036 | 0.498746 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.07180 | 0.272661 | ||||||||
\(347\) | −8.39735 | − | 8.39735i | −0.450793 | − | 0.450793i | 0.444824 | − | 0.895618i | \(-0.353266\pi\) |
−0.895618 | + | 0.444824i | \(0.853266\pi\) | |||||||
\(348\) | 1.79315 | − | 1.79315i | 0.0961230 | − | 0.0961230i | ||||
\(349\) | − | 30.7846i | − | 1.64786i | −0.566690 | − | 0.823931i | \(-0.691776\pi\) | ||
0.566690 | − | 0.823931i | \(-0.308224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.58846 | 0.351666 | ||||||||
\(352\) | −1.51784 | + | 1.51784i | −0.0809013 | + | 0.0809013i | ||||
\(353\) | −19.4201 | + | 19.4201i | −1.03363 | + | 1.03363i | −0.0342104 | + | 0.999415i | \(0.510892\pi\) |
−0.999415 | + | 0.0342104i | \(0.989108\pi\) | |||||||
\(354\) | − | 12.9282i | − | 0.687126i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.58244i | 0.507868i | ||||||||
\(357\) | 22.9420 | + | 22.9420i | 1.21422 | + | 1.21422i | ||||
\(358\) | 0.707107 | − | 0.707107i | 0.0373718 | − | 0.0373718i | ||||
\(359\) | 17.5935 | 0.928549 | 0.464274 | − | 0.885691i | \(-0.346315\pi\) | ||||
0.464274 | + | 0.885691i | \(0.346315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3923 | −0.757490 | ||||||||
\(362\) | −5.25796 | + | 5.25796i | −0.276352 | + | 0.276352i | ||||
\(363\) | −7.82894 | + | 7.82894i | −0.410913 | + | 0.410913i | ||||
\(364\) | −4.29311 | −0.225020 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.1576i | 0.530946i | ||||||||
\(367\) | 15.9458 | − | 15.9458i | 0.832363 | − | 0.832363i | −0.155477 | − | 0.987840i | \(-0.549691\pi\) |
0.987840 | + | 0.155477i | \(0.0496913\pi\) | |||||||
\(368\) | 1.27671 | + | 4.62277i | 0.0665529 | + | 0.240979i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.32051 | −0.276227 | ||||||||
\(372\) | −1.55291 | − | 1.55291i | −0.0805149 | − | 0.0805149i | ||||
\(373\) | −4.61645 | − | 4.61645i | −0.239031 | − | 0.239031i | 0.577418 | − | 0.816449i | \(-0.304060\pi\) |
−0.816449 | + | 0.577418i | \(0.804060\pi\) | |||||||
\(374\) | − | 11.8756i | − | 0.614075i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.26795 | −0.0653895 | ||||||||
\(377\) | −1.31268 | − | 1.31268i | −0.0676063 | − | 0.0676063i | ||||
\(378\) | 12.4405 | + | 12.4405i | 0.639869 | + | 0.639869i | ||||
\(379\) | −5.28933 | −0.271695 | −0.135847 | − | 0.990730i | \(-0.543376\pi\) | ||||
−0.135847 | + | 0.990730i | \(0.543376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.80385 | −0.194877 | ||||||||
\(382\) | −12.4405 | + | 12.4405i | −0.636510 | + | 0.636510i | ||||
\(383\) | −6.54099 | − | 6.54099i | −0.334229 | − | 0.334229i | 0.519961 | − | 0.854190i | \(-0.325947\pi\) |
−0.854190 | + | 0.519961i | \(0.825947\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.5885 | 0.793432 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.54099 | − | 6.54099i | −0.332069 | − | 0.332069i | ||||
\(389\) | 29.3225 | 1.48671 | 0.743354 | − | 0.668898i | \(-0.233234\pi\) | ||||
0.743354 | + | 0.668898i | \(0.233234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.0788 | − | 13.0899i | −1.16715 | − | 0.661982i | ||||
\(392\) | −3.15660 | − | 3.15660i | −0.159432 | − | 0.159432i | ||||
\(393\) | 17.1464 | − | 17.1464i | 0.864923 | − | 0.864923i | ||||
\(394\) | − | 23.6603i | − | 1.19199i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3843 | − | 13.3843i | −0.671737 | − | 0.671737i | 0.286379 | − | 0.958116i | \(-0.407548\pi\) |
−0.958116 | + | 0.286379i | \(0.907548\pi\) | |||||||
\(398\) | 1.11114 | + | 1.11114i | 0.0556963 | + | 0.0556963i | ||||
\(399\) | 12.5885i | 0.630211i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6.43966i | − | 0.321581i | −0.986989 | − | 0.160791i | \(-0.948596\pi\) | ||
0.986989 | − | 0.160791i | \(-0.0514044\pi\) | |||||||
\(402\) | 1.51784 | − | 1.51784i | 0.0757031 | − | 0.0757031i | ||||
\(403\) | −1.13681 | + | 1.13681i | −0.0566286 | + | 0.0566286i | ||||
\(404\) | − | 7.12436i | − | 0.354450i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 4.95725i | − | 0.246024i | ||||||
\(407\) | −3.76217 | − | 3.76217i | −0.186484 | − | 0.186484i | ||||
\(408\) | 6.77581 | + | 6.77581i | 0.335452 | + | 0.335452i | ||||
\(409\) | 12.4641i | 0.616310i | 0.951336 | + | 0.308155i | \(0.0997116\pi\) | ||||
−0.951336 | + | 0.308155i | \(0.900288\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 9.58244i | − | 0.472667i | ||||||
\(412\) | −13.7235 | + | 13.7235i | −0.676109 | + | 0.676109i | ||||
\(413\) | −17.8703 | − | 17.8703i | −0.879341 | − | 0.879341i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.26795 | −0.0621663 | ||||||||
\(417\) | −2.53742 | − | 2.53742i | −0.124258 | − | 0.124258i | ||||
\(418\) | 3.25813 | − | 3.25813i | 0.159360 | − | 0.159360i | ||||
\(419\) | −10.7328 | −0.524330 | −0.262165 | − | 0.965023i | \(-0.584437\pi\) | ||||
−0.262165 | + | 0.965023i | \(0.584437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.7584i | 1.79149i | 0.444565 | + | 0.895746i | \(0.353358\pi\) | ||||
−0.444565 | + | 0.895746i | \(0.646642\pi\) | |||||||
\(422\) | 4.57081 | + | 4.57081i | 0.222504 | + | 0.222504i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.57139 | −0.0763133 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 25.8564 | 1.25275 | ||||||||
\(427\) | 14.0406 | + | 14.0406i | 0.679472 | + | 0.679472i | ||||
\(428\) | 3.91201 | + | 3.91201i | 0.189094 | + | 0.189094i | ||||
\(429\) | 4.71416 | 0.227602 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.72172i | − | 0.131101i | −0.997849 | − | 0.0655504i | \(-0.979120\pi\) | ||
0.997849 | − | 0.0655504i | \(-0.0208803\pi\) | |||||||
\(432\) | 3.67423 | + | 3.67423i | 0.176777 | + | 0.176777i | ||||
\(433\) | 13.4887 | + | 13.4887i | 0.648225 | + | 0.648225i | 0.952564 | − | 0.304339i | \(-0.0984354\pi\) |
−0.304339 | + | 0.952564i | \(0.598435\pi\) | |||||||
\(434\) | −4.29311 | −0.206076 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.29311i | 0.205603i | ||||||||
\(437\) | −2.74052 | − | 9.92303i | −0.131097 | − | 0.474683i | ||||
\(438\) | 13.7124 | − | 13.7124i | 0.655205 | − | 0.655205i | ||||
\(439\) | − | 34.9808i | − | 1.66954i | −0.550598 | − | 0.834770i | \(-0.685600\pi\) | ||
0.550598 | − | 0.834770i | \(-0.314400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.96023 | − | 4.96023i | 0.235934 | − | 0.235934i | ||||
\(443\) | −12.8159 | + | 12.8159i | −0.608900 | + | 0.608900i | −0.942658 | − | 0.333759i | \(-0.891683\pi\) |
0.333759 | + | 0.942658i | \(0.391683\pi\) | |||||||
\(444\) | 4.29311 | 0.203742 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.3923 | −0.776198 | ||||||||
\(447\) | −1.92455 | + | 1.92455i | −0.0910280 | + | 0.0910280i | ||||
\(448\) | −2.39417 | − | 2.39417i | −0.113114 | − | 0.113114i | ||||
\(449\) | 18.8564i | 0.889889i | 0.895558 | + | 0.444944i | \(0.146777\pi\) | ||||
−0.895558 | + | 0.444944i | \(0.853223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.13899i | 0.194898i | ||||||||
\(452\) | 8.70035 | − | 8.70035i | 0.409230 | − | 0.409230i | ||||
\(453\) | 10.0382 | − | 10.0382i | 0.471636 | − | 0.471636i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.71794i | 0.174109i | ||||||||
\(457\) | 20.4993 | − | 20.4993i | 0.958917 | − | 0.958917i | −0.0402715 | − | 0.999189i | \(-0.512822\pi\) |
0.999189 | + | 0.0402715i | \(0.0128223\pi\) | |||||||
\(458\) | −7.18251 | − | 7.18251i | −0.335617 | − | 0.335617i | ||||
\(459\) | −28.7473 | −1.34181 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.3923 | −0.949764 | −0.474882 | − | 0.880049i | \(-0.657509\pi\) | ||||
−0.474882 | + | 0.880049i | \(0.657509\pi\) | |||||||
\(462\) | 8.90138 | + | 8.90138i | 0.414130 | + | 0.414130i | ||||
\(463\) | −28.9778 | + | 28.9778i | −1.34671 | + | 1.34671i | −0.457504 | + | 0.889208i | \(0.651256\pi\) |
−0.889208 | + | 0.457504i | \(0.848744\pi\) | |||||||
\(464\) | − | 1.46410i | − | 0.0679692i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.8564 | 1.19777 | ||||||||
\(467\) | 20.4364 | − | 20.4364i | 0.945684 | − | 0.945684i | −0.0529155 | − | 0.998599i | \(-0.516851\pi\) |
0.998599 | + | 0.0529155i | \(0.0168514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.19615i | − | 0.193760i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 24.6083i | − | 1.13389i | ||||||
\(472\) | −5.27792 | − | 5.27792i | −0.242936 | − | 0.242936i | ||||
\(473\) | −14.0406 | + | 14.0406i | −0.645587 | + | 0.645587i | ||||
\(474\) | 27.7511 | 1.27465 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.7321 | 0.858582 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.31079 | + | 2.31079i | −0.105693 | + | 0.105693i | ||||
\(479\) | 37.9087 | 1.73209 | 0.866046 | − | 0.499964i | \(-0.166653\pi\) | ||||
0.866046 | + | 0.499964i | \(0.166653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.14277i | − | 0.143298i | ||||||
\(482\) | −6.77581 | + | 6.77581i | −0.308629 | + | 0.308629i | ||||
\(483\) | 27.1102 | − | 7.48724i | 1.23356 | − | 0.340681i | ||||
\(484\) | 6.39230i | 0.290559i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5211 | − | 14.5211i | −0.658013 | − | 0.658013i | 0.296897 | − | 0.954910i | \(-0.404048\pi\) |
−0.954910 | + | 0.296897i | \(0.904048\pi\) | |||||||
\(488\) | 4.14682 | + | 4.14682i | 0.187718 | + | 0.187718i | ||||
\(489\) | 34.1769i | 1.54553i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.4641 | 0.517368 | 0.258684 | − | 0.965962i | \(-0.416711\pi\) | ||||
0.258684 | + | 0.965962i | \(0.416711\pi\) | |||||||
\(492\) | −2.36156 | − | 2.36156i | −0.106467 | − | 0.106467i | ||||
\(493\) | 5.72758 | + | 5.72758i | 0.257957 | + | 0.257957i | ||||
\(494\) | 2.72172 | 0.122456 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.26795 | −0.0569326 | ||||||||
\(497\) | 35.7407 | − | 35.7407i | 1.60319 | − | 1.60319i | ||||
\(498\) | 18.9186 | + | 18.9186i | 0.847761 | + | 0.847761i | ||||
\(499\) | 22.0000i | 0.984855i | 0.870353 | + | 0.492428i | \(0.163890\pi\) | ||||
−0.870353 | + | 0.492428i | \(0.836110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.9808 | 1.56283 | ||||||||
\(502\) | −9.81149 | + | 9.81149i | −0.437908 | + | 0.437908i | ||||
\(503\) | 8.29365 | + | 8.29365i | 0.369796 | + | 0.369796i | 0.867403 | − | 0.497607i | \(-0.165788\pi\) |
−0.497607 | + | 0.867403i | \(0.665788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.95448 | − | 5.07880i | −0.398075 | − | 0.225780i | ||||
\(507\) | −13.9527 | − | 13.9527i | −0.619660 | − | 0.619660i | ||||
\(508\) | −1.55291 | + | 1.55291i | −0.0688994 | + | 0.0688994i | ||||
\(509\) | − | 11.8038i | − | 0.523196i | −0.965177 | − | 0.261598i | \(-0.915750\pi\) | ||
0.965177 | − | 0.261598i | \(-0.0842495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 37.9087i | − | 1.67698i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −7.88694 | − | 7.88694i | −0.348217 | − | 0.348217i | ||||
\(514\) | 20.5359i | 0.905800i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 16.0221i | − | 0.705334i | ||||||
\(517\) | 1.92455 | − | 1.92455i | 0.0846415 | − | 0.0846415i | ||||
\(518\) | 5.93426 | − | 5.93426i | 0.260736 | − | 0.260736i | ||||
\(519\) | − | 8.78461i | − | 0.385602i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4839i | 1.68601i | 0.537907 | + | 0.843004i | \(0.319215\pi\) | ||||
−0.537907 | + | 0.843004i | \(0.680785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.7930 | + | 28.7930i | 1.25903 | + | 1.25903i | 0.951558 | + | 0.307471i | \(0.0994826\pi\) |
0.307471 | + | 0.951558i | \(0.400517\pi\) | |||||||
\(524\) | − | 14.0000i | − | 0.611593i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.8866i | 0.954301i | ||||||||
\(527\) | 4.96023 | − | 4.96023i | 0.216071 | − | 0.216071i | ||||
\(528\) | 2.62898 | + | 2.62898i | 0.114412 | + | 0.114412i | ||||
\(529\) | −19.7400 | + | 11.8038i | −0.858263 | + | 0.513211i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.13922 | + | 5.13922i | 0.222813 | + | 0.222813i | ||||
\(533\) | −1.72878 | + | 1.72878i | −0.0748818 | + | 0.0748818i | ||||
\(534\) | 16.5973 | 0.718234 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 1.23931i | − | 0.0535302i | ||||||
\(537\) | −1.22474 | − | 1.22474i | −0.0528516 | − | 0.0528516i | ||||
\(538\) | 3.06866 | − | 3.06866i | 0.132299 | − | 0.132299i | ||||
\(539\) | 9.58244 | 0.412745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.39230 | 0.188840 | 0.0944200 | − | 0.995532i | \(-0.469900\pi\) | ||||
0.0944200 | + | 0.995532i | \(0.469900\pi\) | |||||||
\(542\) | −13.2827 | − | 13.2827i | −0.570542 | − | 0.570542i | ||||
\(543\) | 9.10706 | + | 9.10706i | 0.390821 | + | 0.390821i | ||||
\(544\) | 5.53242 | 0.237201 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.43588i | 0.318226i | ||||||||
\(547\) | −26.8565 | − | 26.8565i | −1.14830 | − | 1.14830i | −0.986887 | − | 0.161412i | \(-0.948395\pi\) |
−0.161412 | − | 0.986887i | \(-0.551605\pi\) | |||||||
\(548\) | −3.91201 | − | 3.91201i | −0.167113 | − | 0.167113i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.14277i | 0.133887i | ||||||||
\(552\) | 8.00688 | − | 2.21132i | 0.340795 | − | 0.0941201i | ||||
\(553\) | 38.3596 | − | 38.3596i | 1.63122 | − | 1.63122i | ||||
\(554\) | − | 1.85641i | − | 0.0788712i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.07180 | −0.0878638 | ||||||||
\(557\) | 24.2394 | − | 24.2394i | 1.02706 | − | 1.02706i | 0.0274340 | − | 0.999624i | \(-0.491266\pi\) |
0.999624 | − | 0.0274340i | \(-0.00873361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7290 | −0.496083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.5692 | −0.868433 | ||||||||
\(562\) | 11.3293 | − | 11.3293i | 0.477899 | − | 0.477899i | ||||
\(563\) | −15.6481 | − | 15.6481i | −0.659487 | − | 0.659487i | 0.295772 | − | 0.955259i | \(-0.404423\pi\) |
−0.955259 | + | 0.295772i | \(0.904423\pi\) | |||||||
\(564\) | 2.19615i | 0.0924747i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 13.6325i | − | 0.573015i | ||||||
\(567\) | 21.5475 | − | 21.5475i | 0.904911 | − | 0.904911i | ||||
\(568\) | 10.5558 | − | 10.5558i | 0.442913 | − | 0.442913i | ||||
\(569\) | −37.3335 | −1.56510 | −0.782551 | − | 0.622586i | \(-0.786082\pi\) | ||||
−0.782551 | + | 0.622586i | \(0.786082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.6083i | − | 1.02983i | −0.857242 | − | 0.514913i | \(-0.827824\pi\) | ||
0.857242 | − | 0.514913i | \(-0.172176\pi\) | |||||||
\(572\) | 1.92455 | − | 1.92455i | 0.0804694 | − | 0.0804694i | ||||
\(573\) | 21.5475 | + | 21.5475i | 0.900161 | + | 0.900161i | ||||
\(574\) | −6.52864 | −0.272500 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.4022 | − | 16.4022i | −0.682831 | − | 0.682831i | 0.277806 | − | 0.960637i | \(-0.410393\pi\) |
−0.960637 | + | 0.277806i | \(0.910393\pi\) | |||||||
\(578\) | −9.62209 | + | 9.62209i | −0.400226 | + | 0.400226i | ||||
\(579\) | − | 27.0000i | − | 1.12208i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.3013 | 2.16982 | ||||||||
\(582\) | −11.3293 | + | 11.3293i | −0.469616 | + | 0.469616i | ||||
\(583\) | 2.38512 | − | 2.38512i | 0.0987815 | − | 0.0987815i | ||||
\(584\) | − | 11.1962i | − | 0.463300i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.8438i | 1.10891i | ||||||||
\(587\) | 20.8207 | + | 20.8207i | 0.859361 | + | 0.859361i | 0.991263 | − | 0.131902i | \(-0.0421084\pi\) |
−0.131902 | + | 0.991263i | \(0.542108\pi\) | |||||||
\(588\) | −5.46739 | + | 5.46739i | −0.225471 | + | 0.225471i | ||||
\(589\) | 2.72172 | 0.112147 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.9808 | −1.68572 | ||||||||
\(592\) | 1.75265 | − | 1.75265i | 0.0720336 | − | 0.0720336i | ||||
\(593\) | 2.53742 | − | 2.53742i | 0.104199 | − | 0.104199i | −0.653085 | − | 0.757285i | \(-0.726526\pi\) |
0.757285 | + | 0.653085i | \(0.226526\pi\) | |||||||
\(594\) | −11.1538 | −0.457647 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.57139i | 0.0643665i | ||||||||
\(597\) | 1.92455 | − | 1.92455i | 0.0787665 | − | 0.0787665i | ||||
\(598\) | −1.61880 | − | 5.86144i | −0.0661976 | − | 0.239692i | ||||
\(599\) | − | 4.19615i | − | 0.171450i | −0.996319 | − | 0.0857251i | \(-0.972679\pi\) | ||
0.996319 | − | 0.0857251i | \(-0.0273207\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6077 | −0.514279 | −0.257139 | − | 0.966374i | \(-0.582780\pi\) | ||||
−0.257139 | + | 0.966374i | \(0.582780\pi\) | |||||||
\(602\) | −22.1469 | − | 22.1469i | −0.902642 | − | 0.902642i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 8.19615i | − | 0.333497i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.3397 | −0.501268 | ||||||||
\(607\) | −13.8004 | − | 13.8004i | −0.560139 | − | 0.560139i | 0.369208 | − | 0.929347i | \(-0.379629\pi\) |
−0.929347 | + | 0.369208i | \(0.879629\pi\) | |||||||
\(608\) | 1.51784 | + | 1.51784i | 0.0615567 | + | 0.0615567i | ||||
\(609\) | −8.58622 | −0.347931 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.60770 | 0.0650404 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.89948 | + | 5.89948i | 0.238278 | + | 0.238278i | 0.816137 | − | 0.577859i | \(-0.196112\pi\) |
−0.577859 | + | 0.816137i | \(0.696112\pi\) | |||||||
\(614\) | − | 30.1244i | − | 1.21572i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.26795 | 0.292834 | ||||||||
\(617\) | 30.9523 | − | 30.9523i | 1.24609 | − | 1.24609i | 0.288663 | − | 0.957431i | \(-0.406789\pi\) |
0.957431 | − | 0.288663i | \(-0.0932106\pi\) | |||||||
\(618\) | 23.7698 | + | 23.7698i | 0.956162 | + | 0.956162i | ||||
\(619\) | −33.1945 | −1.33420 | −0.667100 | − | 0.744968i | \(-0.732465\pi\) | ||||
−0.667100 | + | 0.744968i | \(0.732465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.2942 | + | 21.6761i | −0.493350 | + | 0.869831i | ||||
\(622\) | −7.62587 | − | 7.62587i | −0.305770 | − | 0.305770i | ||||
\(623\) | 22.9420 | − | 22.9420i | 0.919151 | − | 0.919151i | ||||
\(624\) | 2.19615i | 0.0879165i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.9794i | 0.838504i | ||||||||
\(627\) | −5.64325 | − | 5.64325i | −0.225370 | − | 0.225370i | ||||
\(628\) | −10.0463 | − | 10.0463i | −0.400891 | − | 0.400891i | ||||
\(629\) | 13.7128i | 0.546766i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.6229i | 1.69679i | 0.529364 | + | 0.848395i | \(0.322430\pi\) | ||||
−0.529364 | + | 0.848395i | \(0.677570\pi\) | |||||||
\(632\) | 11.3293 | − | 11.3293i | 0.450657 | − | 0.450657i | ||||
\(633\) | 7.91688 | − | 7.91688i | 0.314668 | − | 0.314668i | ||||
\(634\) | 30.2487i | 1.20133i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.72172i | 0.107923i | ||||||||
\(637\) | 4.00240 | + | 4.00240i | 0.158581 | + | 0.158581i | ||||
\(638\) | 2.22228 | + | 2.22228i | 0.0879808 | + | 0.0879808i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.44344i | − | 0.215003i | −0.994205 | − | 0.107502i | \(-0.965715\pi\) | ||
0.994205 | − | 0.107502i | \(-0.0342851\pi\) | |||||||
\(642\) | 6.77581 | − | 6.77581i | 0.267420 | − | 0.267420i | ||||
\(643\) | 29.6693 | + | 29.6693i | 1.17004 | + | 1.17004i | 0.982199 | + | 0.187843i | \(0.0601498\pi\) |
0.187843 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(644\) | 8.01105 | − | 14.1244i | 0.315680 | − | 0.556578i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.8756 | −0.467241 | ||||||||
\(647\) | −6.69213 | − | 6.69213i | −0.263095 | − | 0.263095i | 0.563215 | − | 0.826310i | \(-0.309564\pi\) |
−0.826310 | + | 0.563215i | \(0.809564\pi\) | |||||||
\(648\) | 6.36396 | − | 6.36396i | 0.250000 | − | 0.250000i | ||||
\(649\) | 16.0221 | 0.628922 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.43588i | 0.291435i | ||||||||
\(652\) | 13.9527 | + | 13.9527i | 0.546429 | + | 0.546429i | ||||
\(653\) | 9.62209 | − | 9.62209i | 0.376542 | − | 0.376542i | −0.493311 | − | 0.869853i | \(-0.664214\pi\) |
0.869853 | + | 0.493311i | \(0.164214\pi\) | |||||||
\(654\) | 7.43588 | 0.290766 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.92820 | −0.0752837 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.03569 | + | 3.03569i | 0.118343 | + | 0.118343i | ||||
\(659\) | −28.7473 | −1.11984 | −0.559918 | − | 0.828548i | \(-0.689167\pi\) | ||||
−0.559918 | + | 0.828548i | \(0.689167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 23.4580i | − | 0.912410i | −0.889875 | − | 0.456205i | \(-0.849208\pi\) | ||
0.889875 | − | 0.456205i | \(-0.150792\pi\) | |||||||
\(662\) | 15.4040 | + | 15.4040i | 0.598695 | + | 0.598695i | ||||
\(663\) | −8.59138 | − | 8.59138i | −0.333661 | − | 0.333661i | ||||
\(664\) | 15.4469 | 0.599457 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.76821 | − | 1.86923i | 0.262066 | − | 0.0723768i | ||||
\(668\) | 14.2808 | − | 14.2808i | 0.552542 | − | 0.552542i | ||||
\(669\) | 28.3923i | 1.09771i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.5885 | −0.485972 | ||||||||
\(672\) | −4.14682 | + | 4.14682i | −0.159967 | + | 0.159967i | ||||
\(673\) | −26.1122 | + | 26.1122i | −1.00655 | + | 1.00655i | −0.00657228 | + | 0.999978i | \(0.502092\pi\) |
−0.999978 | + | 0.00657228i | \(0.997908\pi\) | |||||||
\(674\) | 25.8476 | 0.995613 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.3923 | −0.438166 | ||||||||
\(677\) | −6.36910 | + | 6.36910i | −0.244784 | + | 0.244784i | −0.818826 | − | 0.574042i | \(-0.805375\pi\) |
0.574042 | + | 0.818826i | \(0.305375\pi\) | |||||||
\(678\) | −15.0695 | − | 15.0695i | −0.578739 | − | 0.578739i | ||||
\(679\) | 31.3205i | 1.20197i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.92455 | − | 1.92455i | 0.0736947 | − | 0.0736947i | ||||
\(683\) | 10.3664 | − | 10.3664i | 0.396658 | − | 0.396658i | −0.480395 | − | 0.877052i | \(-0.659507\pi\) |
0.877052 | + | 0.480395i | \(0.159507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 8.58622i | − | 0.327823i | ||||||
\(687\) | −12.4405 | + | 12.4405i | −0.474634 | + | 0.474634i | ||||
\(688\) | −6.54099 | − | 6.54099i | −0.249373 | − | 0.249373i | ||||
\(689\) | 1.99244 | 0.0759059 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.1769 | −1.52840 | −0.764201 | − | 0.644978i | \(-0.776866\pi\) | ||||
−0.764201 | + | 0.644978i | \(0.776866\pi\) | |||||||
\(692\) | −3.58630 | − | 3.58630i | −0.136331 | − | 0.136331i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.8756i | 0.450793i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.53590 | −0.0961230 | ||||||||
\(697\) | 7.54316 | − | 7.54316i | 0.285717 | − | 0.285717i | ||||
\(698\) | −21.7680 | + | 21.7680i | −0.823931 | + | 0.823931i | ||||
\(699\) | − | 44.7846i | − | 1.69391i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.7732i | 1.65329i | 0.562723 | + | 0.826645i | \(0.309754\pi\) | ||||
−0.562723 | + | 0.826645i | \(0.690246\pi\) | |||||||
\(702\) | −4.65874 | − | 4.65874i | −0.175833 | − | 0.175833i | ||||
\(703\) | −3.76217 | + | 3.76217i | −0.141893 | + | 0.141893i | ||||
\(704\) | 2.14655 | 0.0809013 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.4641 | 1.03363 | ||||||||
\(707\) | −17.0569 | + | 17.0569i | −0.641491 | + | 0.641491i | ||||
\(708\) | −9.14162 | + | 9.14162i | −0.343563 | + | 0.343563i | ||||
\(709\) | 17.1724 | 0.644924 | 0.322462 | − | 0.946582i | \(-0.395489\pi\) | ||||
0.322462 | + | 0.946582i | \(0.395489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.77581 | − | 6.77581i | 0.253934 | − | 0.253934i | ||||
\(713\) | −1.61880 | − | 5.86144i | −0.0606245 | − | 0.219513i | ||||
\(714\) | − | 32.4449i | − | 1.21422i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.00000 | −0.0373718 | ||||||||
\(717\) | 4.00240 | + | 4.00240i | 0.149473 | + | 0.149473i | ||||
\(718\) | −12.4405 | − | 12.4405i | −0.464274 | − | 0.464274i | ||||
\(719\) | − | 9.26795i | − | 0.345636i | −0.984954 | − | 0.172818i | \(-0.944713\pi\) | ||
0.984954 | − | 0.172818i | \(-0.0552873\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.7128 | 2.44727 | ||||||||
\(722\) | 10.1769 | + | 10.1769i | 0.378745 | + | 0.378745i | ||||
\(723\) | 11.7360 | + | 11.7360i | 0.436468 | + | 0.436468i | ||||
\(724\) | 7.43588 | 0.276352 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.0718 | 0.410913 | ||||||||
\(727\) | −17.8703 | + | 17.8703i | −0.662774 | + | 0.662774i | −0.956033 | − | 0.293259i | \(-0.905260\pi\) |
0.293259 | + | 0.956033i | \(0.405260\pi\) | |||||||
\(728\) | 3.03569 | + | 3.03569i | 0.112510 | + | 0.112510i | ||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.1769 | 1.89285 | ||||||||
\(732\) | 7.18251 | − | 7.18251i | 0.265473 | − | 0.265473i | ||||
\(733\) | 2.86379 | + | 2.86379i | 0.105777 | + | 0.105777i | 0.758014 | − | 0.652238i | \(-0.226170\pi\) |
−0.652238 | + | 0.758014i | \(0.726170\pi\) | |||||||
\(734\) | −22.5507 | −0.832363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.36603 | − | 4.17156i | 0.0872129 | − | 0.153766i | ||||
\(737\) | 1.88108 | + | 1.88108i | 0.0692906 | + | 0.0692906i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.85641i | 0.289003i | 0.989505 | + | 0.144501i | \(0.0461578\pi\) | ||||
−0.989505 | + | 0.144501i | \(0.953842\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.71416i | − | 0.173179i | ||||||
\(742\) | 3.76217 | + | 3.76217i | 0.138114 | + | 0.138114i | ||||
\(743\) | −22.1890 | − | 22.1890i | −0.814037 | − | 0.814037i | 0.171199 | − | 0.985236i | \(-0.445236\pi\) |
−0.985236 | + | 0.171199i | \(0.945236\pi\) | |||||||
\(744\) | 2.19615i | 0.0805149i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.52864i | 0.239031i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.39735 | + | 8.39735i | −0.307037 | + | 0.307037i | ||||
\(749\) | − | 18.7321i | − | 0.684454i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.9014i | − | 1.05463i | −0.849671 | − | 0.527314i | \(-0.823199\pi\) | ||
0.849671 | − | 0.527314i | \(-0.176801\pi\) | |||||||
\(752\) | 0.896575 | + | 0.896575i | 0.0326947 | + | 0.0326947i | ||||
\(753\) | 16.9940 | + | 16.9940i | 0.619296 | + | 0.619296i | ||||
\(754\) | 1.85641i | 0.0676063i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 17.5935i | − | 0.639869i | ||||||
\(757\) | −28.3863 | + | 28.3863i | −1.03172 | + | 1.03172i | −0.0322357 | + | 0.999480i | \(0.510263\pi\) |
−0.999480 | + | 0.0322357i | \(0.989737\pi\) | |||||||
\(758\) | 3.74012 | + | 3.74012i | 0.135847 | + | 0.135847i | ||||
\(759\) | −8.79674 | + | 15.5096i | −0.319302 | + | 0.562964i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.8564 | 0.901044 | 0.450522 | − | 0.892765i | \(-0.351238\pi\) | ||||
0.450522 | + | 0.892765i | \(0.351238\pi\) | |||||||
\(762\) | 2.68973 | + | 2.68973i | 0.0974385 | + | 0.0974385i | ||||
\(763\) | 10.2784 | − | 10.2784i | 0.372104 | − | 0.372104i | ||||
\(764\) | 17.5935 | 0.636510 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.25036i | 0.334229i | ||||||||
\(767\) | 6.69213 | + | 6.69213i | 0.241639 | + | 0.241639i | ||||
\(768\) | −1.22474 | + | 1.22474i | −0.0441942 | + | 0.0441942i | ||||
\(769\) | −18.1687 | −0.655178 | −0.327589 | − | 0.944820i | \(-0.606236\pi\) | ||||
−0.327589 | + | 0.944820i | \(0.606236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.5692 | 1.28099 | ||||||||
\(772\) | −11.0227 | − | 11.0227i | −0.396716 | − | 0.396716i | ||||
\(773\) | −15.6481 | − | 15.6481i | −0.562821 | − | 0.562821i | 0.367287 | − | 0.930108i | \(-0.380287\pi\) |
−0.930108 | + | 0.367287i | \(0.880287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.25036i | 0.332069i | ||||||||
\(777\) | −10.2784 | − | 10.2784i | −0.368737 | − | 0.368737i | ||||
\(778\) | −20.7341 | − | 20.7341i | −0.743354 | − | 0.743354i | ||||
\(779\) | 4.13899 | 0.148295 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0442i | 1.14663i | ||||||||
\(782\) | 7.06328 | + | 25.5751i | 0.252582 | + | 0.914565i | ||||
\(783\) | 5.37945 | − | 5.37945i | 0.192246 | − | 0.192246i | ||||
\(784\) | 4.46410i | 0.159432i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −24.2487 | −0.864923 | ||||||||
\(787\) | −4.78834 | + | 4.78834i | −0.170686 | + | 0.170686i | −0.787281 | − | 0.616595i | \(-0.788512\pi\) |
0.616595 | + | 0.787281i | \(0.288512\pi\) | |||||||
\(788\) | −16.7303 | + | 16.7303i | −0.595993 | + | 0.595993i | ||||
\(789\) | 37.9087 | 1.34959 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.6603 | −1.48127 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.25796 | − | 5.25796i | −0.186716 | − | 0.186716i | ||||
\(794\) | 18.9282i | 0.671737i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 1.57139i | − | 0.0556963i | ||||||
\(797\) | −6.54099 | + | 6.54099i | −0.231694 | + | 0.231694i | −0.813399 | − | 0.581706i | \(-0.802386\pi\) |
0.581706 | + | 0.813399i | \(0.302386\pi\) | |||||||
\(798\) | 8.90138 | − | 8.90138i | 0.315106 | − | 0.315106i | ||||
\(799\) | −7.01483 | −0.248167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.55353 | + | 4.55353i | −0.160791 | + | 0.160791i | ||||
\(803\) | 16.9940 | + | 16.9940i | 0.599705 | + | 0.599705i | ||||
\(804\) | −2.14655 | −0.0757031 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.60770 | 0.0566286 | ||||||||
\(807\) | −5.31508 | − | 5.31508i | −0.187100 | − | 0.187100i | ||||
\(808\) | −5.03768 | + | 5.03768i | −0.177225 | + | 0.177225i | ||||
\(809\) | − | 29.8564i | − | 1.04970i | −0.851196 | − | 0.524848i | \(-0.824122\pi\) | ||
0.851196 | − | 0.524848i | \(-0.175878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.2154 | −0.464055 | −0.232028 | − | 0.972709i | \(-0.574536\pi\) | ||||
−0.232028 | + | 0.972709i | \(0.574536\pi\) | |||||||
\(812\) | −3.50531 | + | 3.50531i | −0.123012 | + | 0.123012i | ||||
\(813\) | −23.0064 | + | 23.0064i | −0.806868 | + | 0.806868i | ||||
\(814\) | 5.32051i | 0.186484i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 9.58244i | − | 0.335452i | ||||||
\(817\) | 14.0406 | + | 14.0406i | 0.491218 | + | 0.491218i | ||||
\(818\) | 8.81345 | − | 8.81345i | 0.308155 | − | 0.308155i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.41154 | 0.119064 | 0.0595318 | − | 0.998226i | \(-0.481039\pi\) | ||||
0.0595318 | + | 0.998226i | \(0.481039\pi\) | |||||||
\(822\) | −6.77581 | + | 6.77581i | −0.236333 | + | 0.236333i | ||||
\(823\) | −10.2141 | + | 10.2141i | −0.356040 | + | 0.356040i | −0.862351 | − | 0.506311i | \(-0.831009\pi\) |
0.506311 | + | 0.862351i | \(0.331009\pi\) | |||||||
\(824\) | 19.4080 | 0.676109 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.2725i | 0.879341i | ||||||||
\(827\) | −24.4742 | + | 24.4742i | −0.851053 | + | 0.851053i | −0.990263 | − | 0.139210i | \(-0.955544\pi\) |
0.139210 | + | 0.990263i | \(0.455544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.6410i | − | 1.20313i | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||
0.798823 | − | 0.601566i | \(-0.205456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.21539 | −0.111541 | ||||||||
\(832\) | 0.896575 | + | 0.896575i | 0.0310832 | + | 0.0310832i | ||||
\(833\) | −17.4636 | − | 17.4636i | −0.605079 | − | 0.605079i | ||||
\(834\) | 3.58846i | 0.124258i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.60770 | −0.159360 | ||||||||
\(837\) | −4.65874 | − | 4.65874i | −0.161030 | − | 0.161030i | ||||
\(838\) | 7.58922 | + | 7.58922i | 0.262165 | + | 0.262165i | ||||
\(839\) | 33.6156 | 1.16054 | 0.580269 | − | 0.814425i | \(-0.302947\pi\) | ||||
0.580269 | + | 0.814425i | \(0.302947\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8564 | 0.926083 | ||||||||
\(842\) | 25.9921 | − | 25.9921i | 0.895746 | − | 0.895746i | ||||
\(843\) | −19.6230 | − | 19.6230i | −0.675851 | − | 0.675851i | ||||
\(844\) | − | 6.46410i | − | 0.222504i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3043 | − | 15.3043i | 0.525861 | − | 0.525861i | ||||
\(848\) | 1.11114 | + | 1.11114i | 0.0381566 | + | 0.0381566i | ||||
\(849\) | −23.6121 | −0.810365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.3397 | + | 5.86450i | 0.354442 | + | 0.201032i | ||||
\(852\) | −18.2832 | − | 18.2832i | −0.626373 | − | 0.626373i | ||||
\(853\) | 25.2156 | − | 25.2156i | 0.863366 | − | 0.863366i | −0.128361 | − | 0.991727i | \(-0.540972\pi\) |
0.991727 | + | 0.128361i | \(0.0409718\pi\) | |||||||
\(854\) | − | 19.8564i | − | 0.679472i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 5.53242i | − | 0.189094i | ||||||
\(857\) | 2.36156 | + | 2.36156i | 0.0806693 | + | 0.0806693i | 0.746290 | − | 0.665621i | \(-0.231833\pi\) |
−0.665621 | + | 0.746290i | \(0.731833\pi\) | |||||||
\(858\) | −3.33341 | − | 3.33341i | −0.113801 | − | 0.113801i | ||||
\(859\) | 9.39230i | 0.320461i | 0.987080 | + | 0.160231i | \(0.0512238\pi\) | ||||
−0.987080 | + | 0.160231i | \(0.948776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.3079i | 0.385374i | ||||||||
\(862\) | −1.92455 | + | 1.92455i | −0.0655504 | + | 0.0655504i | ||||
\(863\) | −33.9411 | + | 33.9411i | −1.15537 | + | 1.15537i | −0.169910 | + | 0.985460i | \(0.554348\pi\) |
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(864\) | − | 5.19615i | − | 0.176777i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 19.0759i | − | 0.648225i | ||||||
\(867\) | 16.6660 | + | 16.6660i | 0.566006 | + | 0.566006i | ||||
\(868\) | 3.03569 | + | 3.03569i | 0.103038 | + | 0.103038i | ||||
\(869\) | 34.3923i | 1.16668i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.57139i | 0.0532444i | ||||||||
\(872\) | 3.03569 | − | 3.03569i | 0.102801 | − | 0.102801i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.07880 | + | 8.95448i | −0.171793 | + | 0.302890i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.3923 | −0.655205 | ||||||||
\(877\) | 2.68973 | + | 2.68973i | 0.0908256 | + | 0.0908256i | 0.751060 | − | 0.660234i | \(-0.229543\pi\) |
−0.660234 | + | 0.751060i | \(0.729543\pi\) | |||||||
\(878\) | −24.7351 | + | 24.7351i | −0.834770 | + | 0.834770i | ||||
\(879\) | 46.4949 | 1.56823 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.1870i | − | 1.18548i | −0.805394 | − | 0.592740i | \(-0.798046\pi\) | ||
0.805394 | − | 0.592740i | \(-0.201954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.4118 | − | 32.4118i | 1.09074 | − | 1.09074i | 0.0952938 | − | 0.995449i | \(-0.469621\pi\) |
0.995449 | − | 0.0952938i | \(-0.0303791\pi\) | |||||||
\(884\) | −7.01483 | −0.235934 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.1244 | 0.608900 | ||||||||
\(887\) | 28.0812 | + | 28.0812i | 0.942874 | + | 0.942874i | 0.998454 | − | 0.0555799i | \(-0.0177007\pi\) |
−0.0555799 | + | 0.998454i | \(0.517701\pi\) | |||||||
\(888\) | −3.03569 | − | 3.03569i | −0.101871 | − | 0.101871i | ||||
\(889\) | 7.43588 | 0.249391 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.3190i | 0.647210i | ||||||||
\(892\) | 11.5911 | + | 11.5911i | 0.388099 | + | 0.388099i | ||||
\(893\) | −1.92455 | − | 1.92455i | −0.0644025 | − | 0.0644025i | ||||
\(894\) | 2.72172 | 0.0910280 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.38587i | 0.113114i | ||||||||
\(897\) | −10.1523 | + | 2.80384i | −0.338976 | + | 0.0936176i | ||||
\(898\) | 13.3335 | − | 13.3335i | 0.444944 | − | 0.444944i | ||||
\(899\) | 1.85641i | 0.0619146i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.69358 | −0.289625 | ||||||||
\(902\) | 2.92671 | − | 2.92671i | 0.0974488 | − | 0.0974488i | ||||
\(903\) | −38.3596 | + | 38.3596i | −1.27653 | + | 1.27653i | ||||
\(904\) | −12.3042 | −0.409230 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.1962 | −0.471636 | ||||||||
\(907\) | −13.4258 | + | 13.4258i | −0.445796 | + | 0.445796i | −0.893954 | − | 0.448159i | \(-0.852080\pi\) |
0.448159 | + | 0.893954i | \(0.352080\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.01483i | 0.232412i | 0.993225 | + | 0.116206i | \(0.0370732\pi\) | ||||
−0.993225 | + | 0.116206i | \(0.962927\pi\) | |||||||
\(912\) | 2.62898 | − | 2.62898i | 0.0870543 | − | 0.0870543i | ||||
\(913\) | −23.4460 | + | 23.4460i | −0.775950 | + | 0.775950i | ||||
\(914\) | −28.9904 | −0.958917 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.1576i | 0.335617i | ||||||||
\(917\) | −33.5184 | + | 33.5184i | −1.10687 | + | 1.10687i | ||||
\(918\) | 20.3274 | + | 20.3274i | 0.670905 | + | 0.670905i | ||||
\(919\) | −26.1797 | −0.863589 | −0.431794 | − | 0.901972i | \(-0.642119\pi\) | ||||
−0.431794 | + | 0.901972i | \(0.642119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.1769 | −1.71929 | ||||||||
\(922\) | 14.4195 | + | 14.4195i | 0.474882 | + | 0.474882i | ||||
\(923\) | −13.3843 | + | 13.3843i | −0.440548 | + | 0.440548i | ||||
\(924\) | − | 12.5885i | − | 0.414130i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 40.9808 | 1.34671 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.03528 | + | 1.03528i | −0.0339846 | + | 0.0339846i | ||||
\(929\) | − | 28.1051i | − | 0.922099i | −0.887374 | − | 0.461050i | \(-0.847473\pi\) | ||
0.887374 | − | 0.461050i | \(-0.152527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.58244i | − | 0.314052i | ||||||
\(932\) | −18.2832 | − | 18.2832i | −0.598887 | − | 0.598887i | ||||
\(933\) | −13.2084 | + | 13.2084i | −0.432423 | + | 0.432423i | ||||
\(934\) | −28.9014 | −0.945684 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0760 | − | 30.0760i | 0.982540 | − | 0.982540i | −0.0173104 | − | 0.999850i | \(-0.505510\pi\) |
0.999850 | + | 0.0173104i | \(0.00551033\pi\) | |||||||
\(938\) | −2.96713 | + | 2.96713i | −0.0968802 | + | 0.0968802i | ||||
\(939\) | 36.3373 | 1.18582 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3152i | 0.662257i | 0.943586 | + | 0.331128i | \(0.107429\pi\) | ||||
−0.943586 | + | 0.331128i | \(0.892571\pi\) | |||||||
\(942\) | −17.4007 | + | 17.4007i | −0.566946 | + | 0.566946i | ||||
\(943\) | −2.46175 | − | 8.91364i | −0.0801656 | − | 0.290268i | ||||
\(944\) | 7.46410i | 0.242936i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.8564 | 0.645587 | ||||||||
\(947\) | 1.79315 | + | 1.79315i | 0.0582696 | + | 0.0582696i | 0.735641 | − | 0.677372i | \(-0.236881\pi\) |
−0.677372 | + | 0.735641i | \(0.736881\pi\) | |||||||
\(948\) | −19.6230 | − | 19.6230i | −0.637325 | − | 0.637325i | ||||
\(949\) | 14.1962i | 0.460827i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.3923 | 1.69894 | ||||||||
\(952\) | −13.2456 | − | 13.2456i | −0.429291 | − | 0.429291i | ||||
\(953\) | 2.62898 | + | 2.62898i | 0.0851611 | + | 0.0851611i | 0.748404 | − | 0.663243i | \(-0.230820\pi\) |
−0.663243 | + | 0.748404i | \(0.730820\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.26795 | 0.105693 | ||||||||
\(957\) | 3.84910 | − | 3.84910i | 0.124424 | − | 0.124424i | ||||
\(958\) | −26.8055 | − | 26.8055i | −0.866046 | − | 0.866046i | ||||
\(959\) | 18.7321i | 0.604889i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3923 | −0.948139 | ||||||||
\(962\) | −2.22228 | + | 2.22228i | −0.0716491 | + | 0.0716491i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.58244 | 0.308629 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −24.4641 | − | 13.8755i | −0.787120 | − | 0.446438i | ||||
\(967\) | 14.6969 | + | 14.6969i | 0.472622 | + | 0.472622i | 0.902762 | − | 0.430140i | \(-0.141536\pi\) |
−0.430140 | + | 0.902762i | \(0.641536\pi\) | |||||||
\(968\) | 4.52004 | − | 4.52004i | 0.145280 | − | 0.145280i | ||||
\(969\) | 20.5692i | 0.660779i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3335i | 1.19809i | 0.800715 | + | 0.599045i | \(0.204453\pi\) | ||||
−0.800715 | + | 0.599045i | \(0.795547\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.96023 | + | 4.96023i | 0.159018 | + | 0.159018i | ||||
\(974\) | 20.5359i | 0.658013i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 5.86450i | − | 0.187718i | ||||||
\(977\) | −18.2770 | + | 18.2770i | −0.584734 | + | 0.584734i | −0.936201 | − | 0.351466i | \(-0.885683\pi\) |
0.351466 | + | 0.936201i | \(0.385683\pi\) | |||||||
\(978\) | 24.1667 | − | 24.1667i | 0.772767 | − | 0.772767i | ||||
\(979\) | 20.5692i | 0.657395i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.10634 | − | 8.10634i | −0.258684 | − | 0.258684i | ||||
\(983\) | −22.1890 | − | 22.1890i | −0.707721 | − | 0.707721i | 0.258335 | − | 0.966055i | \(-0.416826\pi\) |
−0.966055 | + | 0.258335i | \(0.916826\pi\) | |||||||
\(984\) | 3.33975i | 0.106467i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 8.10003i | − | 0.257957i | ||||||
\(987\) | 5.25796 | − | 5.25796i | 0.167363 | − | 0.167363i | ||||
\(988\) | −1.92455 | − | 1.92455i | −0.0612280 | − | 0.0612280i | ||||
\(989\) | 21.8866 | − | 38.5885i | 0.695953 | − | 1.22704i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1051 | −0.829256 | −0.414628 | − | 0.909991i | \(-0.636088\pi\) | ||||
−0.414628 | + | 0.909991i | \(0.636088\pi\) | |||||||
\(992\) | 0.896575 | + | 0.896575i | 0.0284663 | + | 0.0284663i | ||||
\(993\) | 26.6806 | − | 26.6806i | 0.846683 | − | 0.846683i | ||||
\(994\) | −50.5449 | −1.60319 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 26.7549i | − | 0.847761i | ||||||
\(997\) | 6.27603 | + | 6.27603i | 0.198764 | + | 0.198764i | 0.799470 | − | 0.600706i | \(-0.205114\pi\) |
−0.600706 | + | 0.799470i | \(0.705114\pi\) | |||||||
\(998\) | 15.5563 | − | 15.5563i | 0.492428 | − | 0.492428i | ||||
\(999\) | 12.8793 | 0.407484 |
(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 | 1150.2.e.f.1057.2 | yes | 16 | |
5.2 | odd | 4 | inner | 1150.2.e.f.643.8 | yes | 16 | |
5.3 | odd | 4 | inner | 1150.2.e.f.643.1 | ✓ | 16 | |
5.4 | even | 2 | inner | 1150.2.e.f.1057.7 | yes | 16 | |
23.22 | odd | 2 | inner | 1150.2.e.f.1057.1 | yes | 16 | |
115.22 | even | 4 | inner | 1150.2.e.f.643.7 | yes | 16 | |
115.68 | even | 4 | inner | 1150.2.e.f.643.2 | yes | 16 | |
115.114 | odd | 2 | inner | 1150.2.e.f.1057.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.2.e.f.643.1 | ✓ | 16 | 5.3 | odd | 4 | inner | |
1150.2.e.f.643.2 | yes | 16 | 115.68 | even | 4 | inner | |
1150.2.e.f.643.7 | yes | 16 | 115.22 | even | 4 | inner | |
1150.2.e.f.643.8 | yes | 16 | 5.2 | odd | 4 | inner | |
1150.2.e.f.1057.1 | yes | 16 | 23.22 | odd | 2 | inner | |
1150.2.e.f.1057.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1150.2.e.f.1057.7 | yes | 16 | 5.4 | even | 2 | inner | |
1150.2.e.f.1057.8 | yes | 16 | 115.114 | odd | 2 | inner |