Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,2,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (of order \(2\), degree \(1\), 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: | \(0.550967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8869743.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{3} + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 68.2 | ||
Root | \(-1.07255 - 0.921756i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.2.c.a.68.5 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.84351i | − | 1.30356i | −0.758408 | − | 0.651780i | \(-0.774023\pi\) | ||
0.758408 | − | 0.651780i | \(-0.225977\pi\) | |||||||
\(3\) | −1.37328 | − | 1.05550i | −0.792866 | − | 0.609396i | ||||
\(4\) | −1.39853 | −0.699267 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −1.94584 | + | 2.53166i | −0.794384 | + | 1.03355i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | − | 1.10881i | − | 0.392023i | ||||||
\(9\) | 0.771819 | + | 2.89902i | 0.257273 | + | 0.966339i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.92059 | + | 1.47616i | 0.554425 | + | 0.426131i | ||||
\(13\) | 7.03677 | 1.95165 | 0.975825 | − | 0.218554i | \(-0.0701339\pi\) | ||||
0.975825 | + | 0.218554i | \(0.0701339\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.84117 | −1.21029 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 5.34437 | − | 1.42286i | 1.25968 | − | 0.335370i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79583i | 1.00000i | ||||||||
\(24\) | −1.17035 | + | 1.52271i | −0.238897 | + | 0.310822i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | − | 12.9724i | − | 2.54409i | ||||||
\(27\) | 2.00000 | − | 4.79583i | 0.384900 | − | 0.922958i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.0201i | 1.86068i | 0.366702 | + | 0.930339i | \(0.380487\pi\) | ||||
−0.366702 | + | 0.930339i | \(0.619513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.83384 | −1.04779 | −0.523895 | − | 0.851783i | \(-0.675521\pi\) | ||||
−0.523895 | + | 0.851783i | \(0.675521\pi\) | |||||||
\(32\) | 6.70714i | 1.18567i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.07941 | − | 4.05437i | −0.179902 | − | 0.675729i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.66349 | − | 7.42735i | −1.54740 | − | 1.18933i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.64601i | − | 0.413237i | −0.978422 | − | 0.206618i | \(-0.933754\pi\) | ||
0.978422 | − | 0.206618i | \(-0.0662459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.84117 | 1.30356 | ||||||||
\(47\) | − | 13.7071i | − | 1.99938i | −0.0248485 | − | 0.999691i | \(-0.507910\pi\) | ||
0.0248485 | − | 0.999691i | \(-0.492090\pi\) | |||||||
\(48\) | 6.64830 | + | 5.10988i | 0.959600 | + | 0.737548i | ||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 9.21756i | 1.30356i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.84117 | −1.36472 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −8.84117 | − | 3.68702i | −1.20313 | − | 0.501740i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.4721 | 2.42550 | ||||||||
\(59\) | 9.59166i | 1.24873i | 0.781133 | + | 0.624364i | \(0.214642\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 10.7548i | 1.36586i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.68234 | 0.335293 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.06202 | − | 6.58604i | 0.609396 | − | 0.792866i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.04102i | − | 0.123546i | −0.998090 | − | 0.0617729i | \(-0.980325\pi\) | ||
0.998090 | − | 0.0617729i | \(-0.0196755\pi\) | |||||||
\(72\) | 3.21445 | − | 0.855799i | 0.378827 | − | 0.100857i | ||||
\(73\) | −9.44264 | −1.10518 | −0.552588 | − | 0.833454i | \(-0.686360\pi\) | ||||
−0.552588 | + | 0.833454i | \(0.686360\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.86642 | + | 5.27752i | 0.792866 | + | 0.609396i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.6924 | + | 17.8148i | −1.55036 | + | 2.01712i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.80859 | + | 4.47503i | −0.867621 | + | 0.497225i | ||||
\(82\) | −4.87794 | −0.538679 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.5762 | − | 13.7604i | 1.13389 | − | 1.47527i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 6.70714i | − | 0.699267i | ||||||
\(93\) | 8.01152 | + | 6.15765i | 0.830756 | + | 0.638519i | ||||
\(94\) | −25.2692 | −2.60631 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.07941 | − | 9.21080i | 0.722540 | − | 0.940074i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 12.9046i | − | 1.30356i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.99267 | 0.699267 | ||||||||
\(101\) | − | 19.1833i | − | 1.90881i | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||
0.298511 | − | 0.954406i | \(-0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | − | 7.80244i | − | 0.765092i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −2.79707 | + | 6.70714i | −0.269148 | + | 0.645394i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 14.0134i | − | 1.30111i | ||||||
\(117\) | 5.43111 | + | 20.3997i | 0.502107 | + | 1.88595i | ||||
\(118\) | 17.6823 | 1.62779 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.79287 | + | 3.63372i | −0.251825 | + | 0.327641i | ||||
\(124\) | 8.15883 | 0.732685 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.3133 | −1.97998 | −0.989990 | − | 0.141134i | \(-0.954925\pi\) | ||||
−0.989990 | + | 0.141134i | \(0.954925\pi\) | |||||||
\(128\) | 8.46935i | 0.748591i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.0811i | 1.84187i | 0.389721 | + | 0.920933i | \(0.372572\pi\) | ||||
−0.389721 | + | 0.920933i | \(0.627428\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −12.1414 | − | 9.33190i | −1.03355 | − | 0.794384i | ||||
\(139\) | 19.9074 | 1.68852 | 0.844261 | − | 0.535932i | \(-0.180040\pi\) | ||||
0.844261 | + | 0.535932i | \(0.180040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.4679 | + | 18.8237i | −1.21842 | + | 1.58524i | ||||
\(142\) | −1.91912 | −0.161049 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.73651 | − | 14.0346i | −0.311375 | − | 1.16955i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.4076i | 1.44066i | ||||||||
\(147\) | −9.61299 | − | 7.38853i | −0.792866 | − | 0.609396i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 9.72918 | − | 12.6583i | 0.794384 | − | 1.03355i | ||||
\(151\) | 10.6456 | 0.866324 | 0.433162 | − | 0.901316i | \(-0.357398\pi\) | ||||
0.433162 | + | 0.901316i | \(0.357398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.5147 | + | 10.3874i | 1.08204 | + | 0.831658i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.24977 | + | 14.3952i | 0.648163 | + | 1.13100i | ||||
\(163\) | 3.42798 | 0.268500 | 0.134250 | − | 0.990947i | \(-0.457137\pi\) | ||||
0.134250 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(164\) | 3.70053i | 0.288963i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.59166i | 0.742225i | 0.928588 | + | 0.371113i | \(0.121024\pi\) | ||||
−0.928588 | + | 0.371113i | \(0.878976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.5162 | 2.80894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 19.1833i | − | 1.45848i | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||
0.684257 | − | 0.729241i | \(-0.260127\pi\) | |||||||
\(174\) | −25.3674 | − | 19.4974i | −1.92310 | − | 1.47809i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.1240 | − | 13.1721i | 0.760970 | − | 0.990074i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.41506i | 0.628971i | 0.949262 | + | 0.314486i | \(0.101832\pi\) | ||||
−0.949262 | + | 0.314486i | \(0.898168\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.31766 | 0.392023 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.3517 | − | 14.7693i | 0.832347 | − | 1.08294i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 19.1698i | 1.39810i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −3.68362 | − | 2.83122i | −0.265842 | − | 0.204326i | ||||
\(193\) | −18.7045 | −1.34638 | −0.673188 | − | 0.739471i | \(-0.735076\pi\) | ||||
−0.673188 | + | 0.739471i | \(0.735076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.78974 | −0.699267 | ||||||||
\(197\) | − | 24.7681i | − | 1.76466i | −0.470634 | − | 0.882329i | \(-0.655975\pi\) | ||
0.470634 | − | 0.882329i | \(-0.344025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 5.54404i | 0.392023i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −35.3647 | −2.48825 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.9032 | + | 3.70151i | −0.966339 | + | 0.257273i | ||||
\(208\) | −34.0662 | −2.36207 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.09880 | + | 1.42961i | −0.0752884 | + | 0.0979553i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.31766 | − | 2.21762i | −0.361821 | − | 0.150890i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9674 | + | 9.96675i | 0.876257 | + | 0.673490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.85909 | − | 14.4951i | −0.257273 | − | 0.966339i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.1103 | 0.729428 | ||||||||
\(233\) | 22.6861i | 1.48622i | 0.669171 | + | 0.743108i | \(0.266649\pi\) | ||||
−0.669171 | + | 0.743108i | \(0.733351\pi\) | |||||||
\(234\) | 37.6071 | − | 10.0123i | 2.45845 | − | 0.654526i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 13.4143i | − | 0.873195i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.3731i | − | 1.70594i | −0.521963 | − | 0.852968i | \(-0.674800\pi\) | ||
0.521963 | − | 0.852968i | \(-0.325200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 20.2786i | 1.30356i | ||||||||
\(243\) | 15.4468 | + | 2.09652i | 0.990915 | + | 0.134492i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.69880 | + | 5.14869i | 0.427100 | + | 0.328269i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.46861i | 0.410757i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 41.1347i | 2.58102i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9780 | 1.31113 | ||||||||
\(257\) | − | 12.1021i | − | 0.754907i | −0.926028 | − | 0.377454i | \(-0.876800\pi\) | ||
0.926028 | − | 0.377454i | \(-0.123200\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.0483 | + | 7.73366i | −1.79804 | + | 0.478702i | ||||
\(262\) | 38.8633 | 2.40098 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.3121i | − | 0.933593i | −0.884365 | − | 0.466797i | \(-0.845408\pi\) | ||
0.884365 | − | 0.466797i | \(-0.154592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.07941 | + | 9.21080i | −0.426131 | + | 0.554425i | ||||
\(277\) | −2.22505 | −0.133690 | −0.0668451 | − | 0.997763i | \(-0.521293\pi\) | ||||
−0.0668451 | + | 0.997763i | \(0.521293\pi\) | |||||||
\(278\) | − | 36.6995i | − | 2.20109i | ||||||
\(279\) | −4.50267 | − | 16.9124i | −0.269568 | − | 1.01252i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 34.7017 | + | 26.6717i | 2.06646 | + | 1.58828i | ||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 1.45590i | 0.0863916i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −19.4441 | + | 5.17669i | −1.14575 | + | 0.305039i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.2059 | 0.772814 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −13.6208 | + | 17.7217i | −0.794384 | + | 1.03355i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.7472i | 1.95165i | ||||||||
\(300\) | −9.60293 | − | 7.38080i | −0.554425 | − | 0.426131i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 19.6252i | − | 1.12930i | ||||||
\(303\) | −20.2481 | + | 26.3442i | −1.16322 | + | 1.51343i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.6250i | 0.659196i | 0.944121 | + | 0.329598i | \(0.106913\pi\) | ||||
−0.944121 | + | 0.329598i | \(0.893087\pi\) | |||||||
\(312\) | −8.23551 | + | 10.7150i | −0.466244 | + | 0.606615i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.1833i | − | 1.07744i | −0.842484 | − | 0.538721i | \(-0.818908\pi\) | ||
0.842484 | − | 0.538721i | \(-0.181092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 10.9206 | − | 6.25848i | 0.606699 | − | 0.347693i | ||||
\(325\) | −35.1839 | −1.95165 | ||||||||
\(326\) | − | 6.31952i | − | 0.350006i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.93392 | −0.161998 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36.3868 | 2.00000 | 1.00000 | 0.000796384i | \(-0.000253497\pi\) | |||||
1.00000 | 0.000796384i | \(0.000253497\pi\) | ||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.6823 | 0.967535 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | − | 67.3180i | − | 3.66162i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −35.3647 | −1.90122 | ||||||||
\(347\) | 9.59166i | 0.514907i | 0.966291 | + | 0.257454i | \(0.0828835\pi\) | ||||
−0.966291 | + | 0.257454i | \(0.917117\pi\) | |||||||
\(348\) | −14.7912 | + | 19.2444i | −0.792892 | + | 1.03161i | ||||
\(349\) | −25.9220 | −1.38758 | −0.693788 | − | 0.720180i | \(-0.744059\pi\) | ||||
−0.693788 | + | 0.720180i | \(0.744059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0735 | − | 33.7472i | 0.751190 | − | 1.80129i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 37.4342i | − | 1.99242i | −0.0869714 | − | 0.996211i | \(-0.527719\pi\) | ||
0.0869714 | − | 0.996211i | \(-0.472281\pi\) | |||||||
\(354\) | −24.2829 | − | 18.6638i | −1.29062 | − | 0.991970i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.5133 | 0.819901 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.1061 | + | 11.6106i | 0.792866 | + | 0.609396i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | − | 23.2174i | − | 1.21029i | ||||||
\(369\) | 7.67082 | − | 2.04224i | 0.399327 | − | 0.106315i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.2044 | − | 8.61169i | −0.580921 | − | 0.446495i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.1985 | −0.783804 | ||||||||
\(377\) | 70.5088i | 3.63139i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.6424 | + | 23.5517i | 1.56986 | + | 1.20659i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 8.93944 | − | 11.6308i | 0.456189 | − | 0.593533i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 34.4819i | 1.75508i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 7.76166i | − | 0.392023i | ||||||
\(393\) | 22.2512 | − | 28.9504i | 1.12243 | − | 1.46035i | ||||
\(394\) | −45.6604 | −2.30034 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2986 | 0.818003 | 0.409002 | − | 0.912534i | \(-0.365877\pi\) | ||||
0.409002 | + | 0.912534i | \(0.365877\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.2059 | 1.21029 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.0514 | −2.04492 | ||||||||
\(404\) | 26.8285i | 1.33477i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.7780 | 1.62077 | 0.810384 | − | 0.585899i | \(-0.199258\pi\) | ||||
0.810384 | + | 0.585899i | \(0.199258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.82378 | + | 25.6307i | 0.335370 | + | 1.25968i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 47.1966i | 2.31400i | ||||||||
\(417\) | −27.3385 | − | 21.0123i | −1.33877 | − | 1.02898i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 7.37405i | 0.358963i | ||||||||
\(423\) | 39.7370 | − | 10.5794i | 1.93208 | − | 0.514387i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.63550 | + | 2.02565i | 0.127691 | + | 0.0981429i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −9.68234 | + | 23.2174i | −0.465842 | + | 1.11705i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 18.3738 | − | 23.9056i | 0.877935 | − | 1.14225i | ||||
\(439\) | −38.7927 | −1.85147 | −0.925736 | − | 0.378170i | \(-0.876554\pi\) | ||||
−0.925736 | + | 0.378170i | \(0.876554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.40273 | + | 20.2931i | 0.257273 | + | 0.966339i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.25100i | − | 0.201971i | −0.994888 | − | 0.100985i | \(-0.967800\pi\) | ||
0.994888 | − | 0.100985i | \(-0.0321996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 14.7481i | − | 0.698342i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.3667i | 1.81063i | 0.424736 | + | 0.905317i | \(0.360367\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | −26.7218 | + | 7.11428i | −1.25968 | + | 0.335370i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.6194 | − | 11.2364i | −0.686879 | − | 0.527934i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4761i | 0.907094i | 0.891232 | + | 0.453547i | \(0.149842\pi\) | ||||
−0.891232 | + | 0.453547i | \(0.850158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | − | 48.5088i | − | 2.25196i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 41.8221 | 1.93737 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | −7.59560 | − | 28.5297i | −0.351107 | − | 1.31879i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.6353 | 0.489530 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −48.6192 | −2.22379 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.3839 | 0.699267 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.86496 | − | 28.4764i | 0.175318 | − | 1.29172i | ||||
\(487\) | 27.1250 | 1.22915 | 0.614575 | − | 0.788858i | \(-0.289328\pi\) | ||||
0.614575 | + | 0.788858i | \(0.289328\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.70759 | − | 3.61825i | −0.212885 | − | 0.163623i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 35.8292i | − | 1.61695i | −0.588531 | − | 0.808475i | \(-0.700293\pi\) | ||
0.588531 | − | 0.808475i | \(-0.299707\pi\) | |||||||
\(492\) | 3.90593 | − | 5.08188i | 0.176093 | − | 0.229109i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.2426 | 1.26813 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5751 | −1.41349 | −0.706747 | − | 0.707466i | \(-0.749838\pi\) | ||||
−0.706747 | + | 0.707466i | \(0.749838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1240 | − | 13.1721i | 0.452309 | − | 0.588485i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −50.1471 | − | 38.5430i | −2.22711 | − | 1.71176i | ||||
\(508\) | 31.2059 | 1.38454 | ||||||||
\(509\) | 44.8082i | 1.98609i | 0.117732 | + | 0.993045i | \(0.462438\pi\) | ||||
−0.117732 | + | 0.993045i | \(0.537562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 21.7345i | − | 0.960539i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.3103 | −0.984067 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.2481 | + | 26.3442i | −0.888793 | + | 1.15638i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 14.2571 | + | 53.5509i | 0.624016 | + | 2.34386i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | − | 29.4827i | − | 1.28796i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.8064 | + | 7.40302i | −1.20669 | + | 0.321264i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 18.6194i | − | 0.806494i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.88214 | − | 11.5563i | 0.383293 | − | 0.498690i | ||||
\(538\) | −28.2280 | −1.21699 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.9956 | 1.71954 | 0.859772 | − | 0.510677i | \(-0.170605\pi\) | ||||
0.859772 | + | 0.510677i | \(0.170605\pi\) | |||||||
\(542\) | 29.4962i | 1.26697i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0957 | −0.645444 | −0.322722 | − | 0.946494i | \(-0.604598\pi\) | ||||
−0.322722 | + | 0.946494i | \(0.604598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −7.30266 | − | 5.61282i | −0.310822 | − | 0.238897i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.10190i | 0.174273i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.8412 | −1.18073 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | −31.1782 | + | 8.30072i | −1.31988 | + | 0.351397i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 20.2338 | − | 26.3256i | 0.851998 | − | 1.10851i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.15429 | −0.0484328 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 23.9792i | − | 1.00000i | ||||||
\(576\) | 2.07028 | + | 7.77615i | 0.0862617 | + | 0.324006i | ||||
\(577\) | 14.2544 | 0.593417 | 0.296708 | − | 0.954968i | \(-0.404111\pi\) | ||||
0.296708 | + | 0.954968i | \(0.404111\pi\) | |||||||
\(578\) | 31.3397i | 1.30356i | ||||||||
\(579\) | 25.6865 | + | 19.7426i | 1.06750 | + | 0.820476i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.4701i | 0.433255i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 23.1632i | − | 0.956046i | −0.878347 | − | 0.478023i | \(-0.841354\pi\) | ||
0.878347 | − | 0.478023i | \(-0.158646\pi\) | |||||||
\(588\) | 13.4441 | + | 10.3331i | 0.554425 | + | 0.426131i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.1429 | + | 34.0137i | −1.07538 | + | 1.39914i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.3667i | 1.57553i | 0.615976 | + | 0.787765i | \(0.288762\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 62.2133 | 2.54409 | ||||||||
\(599\) | 9.59166i | 0.391905i | 0.980613 | + | 0.195952i | \(0.0627798\pi\) | ||||
−0.980613 | + | 0.195952i | \(0.937220\pi\) | |||||||
\(600\) | 5.85177 | − | 7.61355i | 0.238897 | − | 0.310822i | ||||
\(601\) | −0.180813 | −0.00737552 | −0.00368776 | − | 0.999993i | \(-0.501174\pi\) | ||||
−0.00368776 | + | 0.999993i | \(0.501174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.8882 | −0.605792 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 48.5658 | + | 37.3276i | 1.97285 | + | 1.51633i | ||||
\(607\) | −40.0000 | −1.62355 | −0.811775 | − | 0.583970i | \(-0.801498\pi\) | ||||
−0.811775 | + | 0.583970i | \(0.801498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 96.4536i | − | 3.90209i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | − | 36.8702i | − | 1.48796i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.0000 | + | 9.59166i | 0.922958 | + | 0.384900i | ||||
\(622\) | 21.4309 | 0.859301 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 46.7826 | + | 35.9571i | 1.87280 | + | 1.43943i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.49314 | + | 4.22202i | 0.218333 | + | 0.167810i | ||||
\(634\) | −35.3647 | −1.40451 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 49.2574 | 1.95165 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.01792 | − | 0.803476i | 0.119387 | − | 0.0317850i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 39.0392i | − | 1.53479i | −0.641175 | − | 0.767395i | \(-0.721553\pi\) | ||
0.641175 | − | 0.767395i | \(-0.278447\pi\) | |||||||
\(648\) | 4.96195 | + | 8.65823i | 0.194924 | + | 0.340128i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 64.8619i | 2.54409i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.79415 | −0.187753 | ||||||||
\(653\) | 35.3522i | 1.38344i | 0.722167 | + | 0.691719i | \(0.243146\pi\) | ||||
−0.722167 | + | 0.691719i | \(0.756854\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.8098i | 0.500137i | ||||||||
\(657\) | −7.28800 | − | 27.3744i | −0.284332 | − | 1.06798i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | − | 67.0795i | − | 2.60712i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.0545 | −1.86068 | ||||||||
\(668\) | − | 13.4143i | − | 0.519014i | ||||||
\(669\) | −10.9863 | − | 8.44404i | −0.424754 | − | 0.326465i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −51.6633 | −1.99147 | −0.995737 | − | 0.0922433i | \(-0.970596\pi\) | ||||
−0.995737 | + | 0.0922433i | \(0.970596\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.0000 | + | 23.9792i | −0.384900 | + | 0.922958i | ||||
\(676\) | −51.0691 | −1.96420 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.4132i | 1.77595i | 0.459889 | + | 0.887977i | \(0.347889\pi\) | ||||
−0.459889 | + | 0.887977i | \(0.652111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | 26.8285i | 1.01987i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.6823 | 0.671212 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −15.2576 | − | 11.7270i | −0.578339 | − | 0.444511i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 47.7876i | 1.80879i | ||||||||
\(699\) | 23.9453 | − | 31.1545i | 0.905695 | − | 1.17837i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −62.2133 | − | 25.9447i | −2.34809 | − | 0.979221i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −69.0104 | −2.59724 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.1588 | + | 18.4216i | −0.532121 | + | 0.692326i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.9781i | − | 1.04779i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 11.7688i | − | 0.439819i | ||||||
\(717\) | −27.8370 | + | 36.2178i | −1.03959 | + | 1.35258i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 47.9583i | − | 1.78854i | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||
0.447524 | − | 0.894272i | \(-0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 35.0267i | − | 1.30356i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 50.1003i | − | 1.86068i | ||||||
\(726\) | 21.4042 | − | 27.8483i | 0.794384 | − | 1.03355i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.0000 | − | 19.1833i | −0.703704 | − | 0.710494i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.1663 | −1.18567 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.76489 | − | 14.1412i | −0.138587 | − | 0.520546i | ||||
\(739\) | 52.8662 | 1.94471 | 0.972357 | − | 0.233497i | \(-0.0750170\pi\) | ||||
0.972357 | + | 0.233497i | \(0.0750170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 6.82766 | − | 8.88325i | 0.250314 | − | 0.325676i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 66.3583i | 2.41984i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 129.984 | 4.73373 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.81007i | 0.246865i | 0.992353 | + | 0.123432i | \(0.0393902\pi\) | ||||
−0.992353 | + | 0.123432i | \(0.960610\pi\) | |||||||
\(762\) | 43.4179 | − | 56.4897i | 1.57287 | − | 2.04641i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 67.4944i | 2.43708i | ||||||||
\(768\) | −28.8088 | − | 22.1424i | −1.03955 | − | 0.798995i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7738 | + | 16.6196i | −0.460038 | + | 0.598540i | ||||
\(772\) | 26.1588 | 0.941477 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.1692 | 1.04779 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48.0545 | + | 20.0401i | 1.71733 | + | 0.716175i | ||||
\(784\) | −33.8882 | −1.21029 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −53.3703 | − | 41.0204i | −1.90366 | − | 1.46315i | ||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 34.6391i | 1.23397i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 30.0466i | − | 1.06632i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 33.5357i | − | 1.18567i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 75.6788i | 2.66567i | ||||||||
\(807\) | −16.1620 | + | 21.0278i | −0.568928 | + | 0.740214i | ||||
\(808\) | −21.2706 | −0.748298 | ||||||||
\(809\) | 38.3667i | 1.34890i | 0.738321 | + | 0.674450i | \(0.235619\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38374 | 0.0485898 | 0.0242949 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242949 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9725 | + | 16.8881i | 0.770611 | + | 0.592291i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 60.4266i | − | 2.11277i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 19.1833i | − | 0.669503i | −0.942306 | − | 0.334751i | \(-0.891348\pi\) | ||
0.942306 | − | 0.334751i | \(-0.108652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.6486 | 1.59121 | 0.795605 | − | 0.605815i | \(-0.207153\pi\) | ||||
0.795605 | + | 0.605815i | \(0.207153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 19.4441 | − | 5.17669i | 0.675729 | − | 0.179902i | ||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.05562 | + | 2.34855i | 0.105998 | + | 0.0814703i | ||||
\(832\) | 18.8750 | 0.654374 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −38.7365 | + | 50.3988i | −1.34134 | + | 1.74517i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.6677 | + | 27.9781i | −0.403294 | + | 0.967066i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −71.4015 | −2.46212 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.59414 | 0.192558 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19.5032 | − | 73.2557i | −0.670534 | − | 2.51858i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.53671 | − | 1.99936i | 0.0526467 | − | 0.0684969i | ||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.4743i | 1.96328i | 0.190730 | + | 0.981642i | \(0.438914\pi\) | ||||
−0.190730 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.5308 | −1.00758 | −0.503790 | − | 0.863826i | \(-0.668061\pi\) | ||||
−0.503790 | + | 0.863826i | \(0.668061\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.8693i | 1.90181i | 0.309477 | + | 0.950907i | \(0.399846\pi\) | ||||
−0.309477 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(864\) | 32.1663 | + | 13.4143i | 1.09432 | + | 0.456363i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.3458 | + | 17.9436i | 0.792866 | + | 0.609396i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.1354 | − | 13.9388i | −0.612738 | − | 0.470950i | ||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 71.5147i | 2.41350i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 37.4106 | − | 9.95999i | 1.25968 | − | 0.335370i | ||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.83676 | −0.263281 | ||||||||
\(887\) | 30.5372i | 1.02534i | 0.858586 | + | 0.512669i | \(0.171343\pi\) | ||||
−0.858586 | + | 0.512669i | \(0.828657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.1883 | −0.374611 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35.6203 | − | 46.3445i | 1.18933 | − | 1.54740i | ||||
\(898\) | 70.7294 | 2.36027 | ||||||||
\(899\) | − | 58.4554i | − | 1.94960i | ||||||
\(900\) | 5.39707 | + | 20.2719i | 0.179902 | + | 0.675729i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20.7145 | + | 26.9510i | −0.688194 | + | 0.895387i | ||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 55.6128 | − | 14.8060i | 1.84456 | − | 0.491086i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.4657 | − | 21.1101i | −0.905025 | − | 0.695601i | ||||
\(922\) | 35.9045 | 1.18245 | ||||||||
\(923\) | − | 7.32539i | − | 0.241118i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 58.9924i | − | 1.93861i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −67.2059 | −2.20614 | ||||||||
\(929\) | − | 46.8903i | − | 1.53842i | −0.638996 | − | 0.769210i | \(-0.720650\pi\) | ||
0.638996 | − | 0.769210i | \(-0.279350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 31.7273i | − | 1.03926i | ||||||
\(933\) | 12.2703 | − | 15.9645i | 0.401711 | − | 0.522654i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 22.6194 | − | 6.02206i | 0.739338 | − | 0.196837i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6898 | 0.413237 | ||||||||
\(944\) | − | 46.4349i | − | 1.51133i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 61.1613i | − | 1.98748i | −0.111734 | − | 0.993738i | \(-0.535641\pi\) | ||
0.111734 | − | 0.993738i | \(-0.464359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66.4457 | −2.15692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.2481 | + | 26.3442i | −0.656589 | + | 0.854268i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.8837i | 1.19291i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03372 | 0.0978619 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.2721 | −1.77743 | −0.888715 | − | 0.458460i | \(-0.848401\pi\) | ||||
−0.888715 | + | 0.458460i | \(0.848401\pi\) | |||||||
\(968\) | 12.1969i | 0.392023i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −21.6029 | − | 2.93206i | −0.692914 | − | 0.0940458i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 50.0052i | − | 1.60227i | ||||||
\(975\) | 48.3174 | + | 37.1367i | 1.54740 | + | 1.18933i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | −6.67029 | + | 8.67850i | −0.213292 | + | 0.277508i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −66.0516 | −2.10779 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 4.02910 | + | 3.09676i | 0.128443 | + | 0.0987212i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.0000 | 1.77890 | 0.889449 | − | 0.457034i | \(-0.151088\pi\) | ||||
0.889449 | + | 0.457034i | \(0.151088\pi\) | |||||||
\(992\) | − | 39.1284i | − | 1.24233i | ||||||
\(993\) | −49.9694 | − | 38.4064i | −1.58573 | − | 1.21879i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000 | 0.823428 | 0.411714 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411714 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(998\) | 58.2090i | 1.84257i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 69.2.c.a.68.2 | ✓ | 6 | |
3.2 | odd | 2 | inner | 69.2.c.a.68.5 | yes | 6 | |
4.3 | odd | 2 | 1104.2.m.a.689.6 | 6 | |||
12.11 | even | 2 | 1104.2.m.a.689.5 | 6 | |||
23.22 | odd | 2 | CM | 69.2.c.a.68.2 | ✓ | 6 | |
69.68 | even | 2 | inner | 69.2.c.a.68.5 | yes | 6 | |
92.91 | even | 2 | 1104.2.m.a.689.6 | 6 | |||
276.275 | odd | 2 | 1104.2.m.a.689.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.2.c.a.68.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
69.2.c.a.68.2 | ✓ | 6 | 23.22 | odd | 2 | CM | |
69.2.c.a.68.5 | yes | 6 | 3.2 | odd | 2 | inner | |
69.2.c.a.68.5 | yes | 6 | 69.68 | even | 2 | inner | |
1104.2.m.a.689.5 | 6 | 12.11 | even | 2 | |||
1104.2.m.a.689.5 | 6 | 276.275 | odd | 2 | |||
1104.2.m.a.689.6 | 6 | 4.3 | odd | 2 | |||
1104.2.m.a.689.6 | 6 | 92.91 | even | 2 |