Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1471,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.i (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32x^{14} + 400x^{12} - 2398x^{10} + 7128x^{8} - 9200x^{6} + 4705x^{4} + 2696x^{2} + 784 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.15 | ||
Root | \(2.25010 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1471 |
Dual form | 1840.2.i.a.1471.2 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.11612i | 1.79909i | 0.436824 | + | 0.899547i | \(0.356103\pi\) | ||||
−0.436824 | + | 0.899547i | \(0.643897\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.38407 | −0.523130 | −0.261565 | − | 0.965186i | \(-0.584239\pi\) | ||||
−0.261565 | + | 0.965186i | \(0.584239\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.71022 | −2.23674 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.13521 | 1.54832 | 0.774162 | − | 0.632987i | \(-0.218171\pi\) | ||||
0.774162 | + | 0.632987i | \(0.218171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.71022 | 1.58373 | 0.791865 | − | 0.610696i | \(-0.209110\pi\) | ||||
0.791865 | + | 0.610696i | \(0.209110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.11612 | 0.804579 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.71022i | − | 1.14240i | −0.820812 | − | 0.571198i | \(-0.806479\pi\) | ||
0.820812 | − | 0.571198i | \(-0.193521\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.44538 | 1.93750 | 0.968752 | − | 0.248033i | \(-0.0797840\pi\) | ||||
0.968752 | + | 0.248033i | \(0.0797840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.31294i | − | 0.941160i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.287039 | − | 4.78723i | 0.0598518 | − | 0.998207i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 11.5615i | − | 2.22501i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.10750 | −0.762744 | −0.381372 | − | 0.924422i | \(-0.624548\pi\) | ||||
−0.381372 | + | 0.924422i | \(0.624548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.74538i | − | 1.21151i | −0.795652 | − | 0.605753i | \(-0.792872\pi\) | ||
0.795652 | − | 0.605753i | \(-0.207128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.0020i | 2.78558i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.38407i | 0.233951i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.81577i | − | 0.298511i | −0.988799 | − | 0.149256i | \(-0.952312\pi\) | ||
0.988799 | − | 0.149256i | \(-0.0476877\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.7937i | 2.84928i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.20739 | 0.657084 | 0.328542 | − | 0.944489i | \(-0.393443\pi\) | ||||
0.328542 | + | 0.944489i | \(0.393443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.76814 | 0.422138 | 0.211069 | − | 0.977471i | \(-0.432306\pi\) | ||||
0.211069 | + | 0.977471i | \(0.432306\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.71022i | 1.00030i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.44501i | 0.210777i | 0.994431 | + | 0.105388i | \(0.0336085\pi\) | ||||
−0.994431 | + | 0.105388i | \(0.966391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.08434 | −0.726335 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.6776 | 2.05528 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.60467i | − | 1.31930i | −0.751572 | − | 0.659651i | \(-0.770704\pi\) | ||
0.751572 | − | 0.659651i | \(-0.229296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.13521i | − | 0.692432i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26.3168i | 3.48575i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.9895i | 1.82128i | 0.413201 | + | 0.910640i | \(0.364411\pi\) | ||||
−0.413201 | + | 0.910640i | \(0.635589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.90012i | 0.755432i | 0.925921 | + | 0.377716i | \(0.123291\pi\) | ||||
−0.925921 | + | 0.377716i | \(0.876709\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.28743 | 1.17011 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.71022i | − | 0.708266i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4154 | 1.63896 | 0.819478 | − | 0.573111i | \(-0.194263\pi\) | ||||
0.819478 | + | 0.573111i | \(0.194263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.9176 | + | 0.894449i | 1.79587 | + | 0.107679i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.94519i | 0.468208i | 0.972212 | + | 0.234104i | \(0.0752155\pi\) | ||||
−0.972212 | + | 0.234104i | \(0.924784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.12871 | −0.366188 | −0.183094 | − | 0.983095i | \(-0.558611\pi\) | ||||
−0.183094 | + | 0.983095i | \(0.558611\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 3.11612i | − | 0.359819i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.10750 | −0.809975 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.45259 | 1.06350 | 0.531750 | − | 0.846902i | \(-0.321535\pi\) | ||||
0.531750 | + | 0.846902i | \(0.321535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.8964 | 1.76627 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4154 | −1.47254 | −0.736268 | − | 0.676690i | \(-0.763414\pi\) | ||||
−0.736268 | + | 0.676690i | \(0.763414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.71022 | −0.510895 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 12.7995i | − | 1.37225i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4204i | 1.42256i | 0.702907 | + | 0.711282i | \(0.251885\pi\) | ||||
−0.702907 | + | 0.711282i | \(0.748115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.90336 | −0.828497 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.0194 | 2.17961 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.44538i | − | 0.866478i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.26857i | 0.433408i | 0.976237 | + | 0.216704i | \(0.0695306\pi\) | ||||
−0.976237 | + | 0.216704i | \(0.930469\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34.4584 | −3.46320 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.18990 | 0.118399 | 0.0591995 | − | 0.998246i | \(-0.481145\pi\) | ||||
0.0591995 | + | 0.998246i | \(0.481145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7555 | −1.15831 | −0.579154 | − | 0.815218i | \(-0.696617\pi\) | ||||
−0.579154 | + | 0.815218i | \(0.696617\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.31294 | −0.420900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.2936 | −1.28514 | −0.642568 | − | 0.766228i | \(-0.722131\pi\) | ||||
−0.642568 | + | 0.766228i | \(0.722131\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.58151i | 0.438829i | 0.975632 | + | 0.219415i | \(0.0704147\pi\) | ||||
−0.975632 | + | 0.219415i | \(0.929585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.65817 | 0.537049 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.6103i | − | 0.998137i | −0.866563 | − | 0.499068i | \(-0.833676\pi\) | ||
0.866563 | − | 0.499068i | \(-0.166324\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.78723 | − | 0.287039i | −0.446412 | − | 0.0267665i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38.3168 | −3.54239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.51928i | 0.597622i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3704 | 1.39731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.1107i | 1.18216i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.71505i | − | 0.240922i | −0.992718 | − | 0.120461i | \(-0.961563\pi\) | ||
0.992718 | − | 0.120461i | \(-0.0384372\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.62588i | 0.759466i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.78723i | 0.418263i | 0.977888 | + | 0.209131i | \(0.0670636\pi\) | ||||
−0.977888 | + | 0.209131i | \(0.932936\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6890 | −1.01357 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.5615 | −0.995056 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.58718i | − | 0.648216i | −0.946020 | − | 0.324108i | \(-0.894936\pi\) | ||
0.946020 | − | 0.324108i | \(-0.105064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.88598i | − | 0.159967i | −0.996796 | − | 0.0799835i | \(-0.974513\pi\) | ||
0.996796 | − | 0.0799835i | \(-0.0254868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50283 | −0.379207 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.3232 | 2.45213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.10750i | 0.341110i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 15.8434i | − | 1.30675i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.83326i | − | 0.477880i | −0.971034 | − | 0.238940i | \(-0.923200\pi\) | ||
0.971034 | − | 0.238940i | \(-0.0767999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.3109i | − | 1.57150i | −0.618544 | − | 0.785751i | \(-0.712277\pi\) | ||
0.618544 | − | 0.785751i | \(-0.287723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.6066i | 2.55524i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.74538 | −0.541802 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.6103i | − | 1.32565i | −0.748775 | − | 0.662825i | \(-0.769357\pi\) | ||
0.748775 | − | 0.662825i | \(-0.230643\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.9293 | 2.37355 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.397283 | + | 6.62588i | −0.0313103 | + | 0.522192i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5867i | 1.53415i | 0.641556 | + | 0.767076i | \(0.278289\pi\) | ||||
−0.641556 | + | 0.767076i | \(0.721711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.0020 | 1.24575 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.51036i | 0.735934i | 0.929839 | + | 0.367967i | \(0.119946\pi\) | ||||
−0.929839 | + | 0.367967i | \(0.880054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.6066 | 1.50820 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −56.6704 | −4.33369 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.3206 | 1.01274 | 0.506372 | − | 0.862315i | \(-0.330986\pi\) | ||||
0.506372 | + | 0.862315i | \(0.330986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38407 | 0.104626 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −43.5930 | −3.27665 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.749054i | − | 0.0559869i | −0.999608 | − | 0.0279935i | \(-0.991088\pi\) | ||
0.999608 | − | 0.0279935i | \(-0.00891176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7965i | 1.54579i | 0.634532 | + | 0.772897i | \(0.281193\pi\) | ||||
−0.634532 | + | 0.772897i | \(0.718807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.3855 | −1.35909 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.81577 | −0.133498 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 24.1880i | − | 1.76880i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.0020i | 1.16397i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1108 | 1.09338 | 0.546688 | − | 0.837336i | \(-0.315888\pi\) | ||||
0.546688 | + | 0.837336i | \(0.315888\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9233 | −0.858256 | −0.429128 | − | 0.903244i | \(-0.641179\pi\) | ||||
−0.429128 | + | 0.903244i | \(0.641179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.7937 | 1.27424 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.59705 | −0.683762 | −0.341881 | − | 0.939743i | \(-0.611064\pi\) | ||||
−0.341881 | + | 0.939743i | \(0.611064\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.64626 | 0.187589 | 0.0937944 | − | 0.995592i | \(-0.470100\pi\) | ||||
0.0937944 | + | 0.995592i | \(0.470100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.8041i | 2.94864i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.68508 | 0.399014 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.20739i | − | 0.293857i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.92610 | + | 32.1234i | −0.133873 | + | 2.23273i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 43.3688 | 2.99988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.29317i | 0.295554i | 0.989021 | + | 0.147777i | \(0.0472117\pi\) | ||||
−0.989021 | + | 0.147777i | \(0.952788\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.2937 | −0.842349 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.76814i | − | 0.188786i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.33610i | 0.633776i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 9.74944i | − | 0.658806i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 26.8964i | − | 1.80925i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.89002i | 0.193530i | 0.995307 | + | 0.0967651i | \(0.0308496\pi\) | ||||
−0.995307 | + | 0.0967651i | \(0.969150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.71022 | 0.447348 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7345 | 0.911593 | 0.455796 | − | 0.890084i | \(-0.349355\pi\) | ||||
0.455796 | + | 0.890084i | \(0.349355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.2150i | − | 1.20368i | −0.798616 | − | 0.601841i | \(-0.794434\pi\) | ||
0.798616 | − | 0.601841i | \(-0.205566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 22.1479i | − | 1.45722i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.0806 | −1.44655 | −0.723275 | − | 0.690560i | \(-0.757364\pi\) | ||||
−0.723275 | + | 0.690560i | \(0.757364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.44501 | 0.0942622 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.4554i | 1.91334i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.69231i | 0.562259i | 0.959670 | + | 0.281129i | \(0.0907090\pi\) | ||||
−0.959670 | + | 0.281129i | \(0.909291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 12.7832i | − | 0.823440i | −0.911310 | − | 0.411720i | \(-0.864928\pi\) | ||
0.911310 | − | 0.411720i | \(-0.135072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8506i | 0.952668i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.08434i | 0.324827i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 48.2250 | 3.06848 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 41.8041i | − | 2.64923i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7736 | 1.18498 | 0.592489 | − | 0.805579i | \(-0.298145\pi\) | ||||
0.592489 | + | 0.805579i | \(0.298145\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.47401 | − | 24.5835i | 0.0926701 | − | 1.54555i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 14.6776i | − | 0.919149i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.9233 | 1.11802 | 0.559012 | − | 0.829160i | \(-0.311181\pi\) | ||||
0.559012 | + | 0.829160i | \(0.311181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.51316i | 0.156160i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.5623 | 1.70606 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.8046 | −0.666241 | −0.333120 | − | 0.942884i | \(-0.608102\pi\) | ||||
−0.333120 | + | 0.942884i | \(0.608102\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.60467 | −0.590010 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −41.8197 | −2.55933 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8964 | −1.09116 | −0.545581 | − | 0.838058i | \(-0.683691\pi\) | ||||
−0.545581 | + | 0.838058i | \(0.683691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4808i | 1.42636i | 0.700982 | + | 0.713179i | \(0.252745\pi\) | ||||
−0.700982 | + | 0.713179i | \(0.747255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 24.6278i | − | 1.49054i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.13521 | −0.309665 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.28607 | −0.0772722 | −0.0386361 | − | 0.999253i | \(-0.512301\pi\) | ||||
−0.0386361 | + | 0.999253i | \(0.512301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 45.2630i | 2.70983i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.6298i | − | 0.872740i | −0.899767 | − | 0.436370i | \(-0.856264\pi\) | ||
0.899767 | − | 0.436370i | \(-0.143736\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.80314 | 0.285517 | 0.142758 | − | 0.989758i | \(-0.454403\pi\) | ||||
0.142758 | + | 0.989758i | \(0.454403\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26.3168 | 1.55888 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.82333 | −0.343740 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.18618 | −0.305070 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3014 | −0.779742 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.80444i | − | 0.572781i | −0.958113 | − | 0.286391i | \(-0.907544\pi\) | ||
0.958113 | − | 0.286391i | \(-0.0924555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.9895 | 0.814501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 59.3708i | − | 3.44504i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63906 | − | 27.3362i | 0.0947891 | − | 1.58089i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.83131 | −0.220833 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.70786i | 0.213011i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.90012 | 0.337840 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8813i | 0.735172i | 0.929990 | + | 0.367586i | \(0.119816\pi\) | ||||
−0.929990 | + | 0.367586i | \(0.880184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 36.6317i | − | 2.08391i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.813161i | − | 0.0461102i | −0.999734 | − | 0.0230551i | \(-0.992661\pi\) | ||
0.999734 | − | 0.0230551i | \(-0.00733931\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0695i | 1.07787i | 0.842347 | + | 0.538935i | \(0.181173\pi\) | ||||
−0.842347 | + | 0.538935i | \(0.818827\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 9.28743i | − | 0.523287i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.62783 | −0.484587 | −0.242294 | − | 0.970203i | \(-0.577900\pi\) | ||||
−0.242294 | + | 0.970203i | \(0.577900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.0929 | −1.18098 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 41.4243i | − | 2.31208i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 39.7796i | − | 2.21340i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.71022 | −0.316746 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2766 | −0.789495 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.00000i | − | 0.110264i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8226i | 0.869690i | 0.900505 | + | 0.434845i | \(0.143197\pi\) | ||||
−0.900505 | + | 0.434845i | \(0.856803\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.1842i | 0.667692i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 13.4154i | − | 0.732963i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.25371i | − | 0.395135i | −0.980289 | − | 0.197567i | \(-0.936696\pi\) | ||
0.980289 | − | 0.197567i | \(-0.0633041\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.0631 | 1.79574 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 34.6390i | − | 1.87581i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7256 | 0.903098 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.894449 | − | 14.9176i | 0.0481555 | − | 0.803137i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.65960i | 0.411189i | 0.978637 | + | 0.205594i | \(0.0659128\pi\) | ||||
−0.978637 | + | 0.205594i | \(0.934087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.5223 | −1.41971 | −0.709853 | − | 0.704350i | \(-0.751238\pi\) | ||||
−0.709853 | + | 0.704350i | \(0.751238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 66.0187i | − | 3.52382i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.7008 | −1.26147 | −0.630734 | − | 0.775999i | \(-0.717246\pi\) | ||||
−0.630734 | + | 0.775999i | \(0.717246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.94519 | 0.209389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.3149 | −1.07518 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.0768 | −1.11239 | −0.556195 | − | 0.831052i | \(-0.687739\pi\) | ||||
−0.556195 | + | 0.831052i | \(0.687739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.3245 | 2.75392 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 47.8961i | 2.51389i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.12871i | 0.163764i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.79123 | 0.0935016 | 0.0467508 | − | 0.998907i | \(-0.485113\pi\) | ||||
0.0467508 | + | 0.998907i | \(0.485113\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.2325 | −1.46973 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.2936i | 0.690167i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.80023i | 0.0932125i | 0.998913 | + | 0.0466063i | \(0.0148406\pi\) | ||||
−0.998913 | + | 0.0466063i | \(0.985159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.11612 | −0.160916 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.4548 | −1.20798 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6838 | 1.16519 | 0.582594 | − | 0.812763i | \(-0.302038\pi\) | ||||
0.582594 | + | 0.812763i | \(0.302038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.46042 | 0.433441 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.1003 | 1.48695 | 0.743477 | − | 0.668761i | \(-0.233175\pi\) | ||||
0.743477 | + | 0.668761i | \(0.233175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.10750i | 0.362232i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.5749 | −0.944213 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3612i | 0.728142i | 0.931371 | + | 0.364071i | \(0.118613\pi\) | ||||
−0.931371 | + | 0.364071i | \(0.881387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.5489 | − | 1.35202i | −1.14035 | − | 0.0683745i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.9176 | −0.752494 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 9.45259i | − | 0.475611i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.9047 | 1.90238 | 0.951191 | − | 0.308603i | \(-0.0998613\pi\) | ||||
0.951191 | + | 0.308603i | \(0.0998613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 36.4244i | − | 1.82350i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.0577i | 0.702006i | 0.936374 | + | 0.351003i | \(0.114159\pi\) | ||||
−0.936374 | + | 0.351003i | \(0.885841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 38.5176i | − | 1.91870i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 15.8964i | − | 0.789899i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.32437i | − | 0.462192i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1519 | 0.699765 | 0.349882 | − | 0.936794i | \(-0.386222\pi\) | ||||
0.349882 | + | 0.936794i | \(0.386222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.6426 | 1.16620 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 19.3625i | − | 0.952766i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4154i | 0.658538i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.87696 | 0.287796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.307866 | −0.0150402 | −0.00752012 | − | 0.999972i | \(-0.502394\pi\) | ||||
−0.00752012 | + | 0.999972i | \(0.502394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.99805i | 0.194853i | 0.995243 | + | 0.0974264i | \(0.0310611\pi\) | ||||
−0.995243 | + | 0.0974264i | \(0.968939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 9.69635i | − | 0.471453i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.71022i | 0.228479i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.16619i | − | 0.395189i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 91.3747i | 4.41161i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.76849 | −0.374195 | −0.187098 | − | 0.982341i | \(-0.559908\pi\) | ||||
−0.187098 | + | 0.982341i | \(0.559908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.86580i | − | 0.426063i | −0.977045 | − | 0.213032i | \(-0.931666\pi\) | ||
0.977045 | − | 0.213032i | \(-0.0683337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.7995 | −0.613688 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.42416 | − | 40.4300i | 0.115963 | − | 1.93403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9290i | 1.09434i | 0.837022 | + | 0.547170i | \(0.184295\pi\) | ||||
−0.837022 | + | 0.547170i | \(0.815705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 34.1171 | 1.62462 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.94225i | 0.0922790i | 0.998935 | + | 0.0461395i | \(0.0146919\pi\) | ||||
−0.998935 | + | 0.0461395i | \(0.985308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4204 | 0.636190 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.1772 | 0.859750 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.2788 | −1.71210 | −0.856052 | − | 0.516890i | \(-0.827090\pi\) | ||||
−0.856052 | + | 0.516890i | \(0.827090\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.6058 | 1.01738 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.1752 | 2.82728 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.90336i | 0.370515i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1881i | 0.850805i | 0.905004 | + | 0.425403i | \(0.139867\pi\) | ||||
−0.905004 | + | 0.425403i | \(0.860133\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −54.4572 | −2.54185 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.9176 | −1.16053 | −0.580264 | − | 0.814428i | \(-0.697051\pi\) | ||||
−0.580264 | + | 0.814428i | \(0.697051\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.76432i | 0.0819949i | 0.999159 | + | 0.0409975i | \(0.0130536\pi\) | ||||
−0.999159 | + | 0.0409975i | \(0.986946\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 21.0194i | − | 0.974753i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.4533 | −0.576268 | −0.288134 | − | 0.957590i | \(-0.593035\pi\) | ||||
−0.288134 | + | 0.957590i | \(0.593035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.5679 | −0.857387 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 51.7599 | 2.38497 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.2150 | 0.653607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.44538 | −0.387501 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 64.4495i | 2.95094i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.2674 | −1.24588 | −0.622939 | − | 0.782270i | \(-0.714062\pi\) | ||||
−0.622939 | + | 0.782270i | \(0.714062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10.3685i | − | 0.472761i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.6470 | − | 1.23798i | −0.939473 | − | 0.0563301i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.26857 | 0.193826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.2566i | 1.68826i | 0.536139 | + | 0.844130i | \(0.319882\pi\) | ||||
−0.536139 | + | 0.844130i | \(0.680118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −61.0347 | −2.76008 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3504i | 0.467109i | 0.972344 | + | 0.233554i | \(0.0750357\pi\) | ||||
−0.972344 | + | 0.233554i | \(0.924964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3473i | 0.871356i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34.4584i | 1.54879i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.46042i | − | 0.244933i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0430i | 1.03155i | 0.856725 | + | 0.515773i | \(0.172495\pi\) | ||||
−0.856725 | + | 0.515773i | \(0.827505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.6354 | −1.32401 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.12594 | 0.139379 | 0.0696893 | − | 0.997569i | \(-0.477799\pi\) | ||||
0.0696893 | + | 0.997569i | \(0.477799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.18990i | − | 0.0529497i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 61.0966i | 2.71340i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.11738 | −0.226824 | −0.113412 | − | 0.993548i | \(-0.536178\pi\) | ||||
−0.113412 | + | 0.993548i | \(0.536178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.33036 | 0.191564 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 97.6413i | − | 4.31097i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.7555i | 0.518011i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.42044i | 0.326351i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.5085i | 1.82202i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.43178i | 0.325592i | 0.986660 | + | 0.162796i | \(0.0520512\pi\) | ||||
−0.986660 | + | 0.162796i | \(0.947949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.89037 | −0.345022 | −0.172511 | − | 0.985008i | \(-0.555188\pi\) | ||||
−0.172511 | + | 0.985008i | \(0.555188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.31294i | 0.188232i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.7723 | −1.38402 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8352 | − | 2.74825i | −0.992836 | − | 0.119489i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 93.8727i | − | 4.07373i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0251 | 1.04064 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2936i | 0.574730i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.33414 | 0.100726 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.1092 | −1.12460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.7528 | 1.32217 | 0.661084 | − | 0.750312i | \(-0.270097\pi\) | ||||
0.661084 | + | 0.750312i | \(0.270097\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −64.8045 | −2.78103 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.58151 | 0.196250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.8904i | − | 0.593912i | −0.954891 | − | 0.296956i | \(-0.904029\pi\) | ||
0.954891 | − | 0.296956i | \(-0.0959715\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 39.5911i | − | 1.68971i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.6894 | −1.47782 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.0831 | −0.556348 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 5.65817i | − | 0.240176i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.97489i | 0.380278i | 0.981757 | + | 0.190139i | \(0.0608939\pi\) | ||||
−0.981757 | + | 0.190139i | \(0.939106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8067 | 0.668553 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 75.3727 | 3.18224 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3356 | 0.772752 | 0.386376 | − | 0.922341i | \(-0.373727\pi\) | ||||
0.386376 | + | 0.922341i | \(0.373727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.6103 | −0.446380 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0018 | −0.923987 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 28.8448i | − | 1.20924i | −0.796515 | − | 0.604618i | \(-0.793326\pi\) | ||
0.796515 | − | 0.604618i | \(-0.206674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.1139 | −1.17653 | −0.588265 | − | 0.808668i | \(-0.700189\pi\) | ||||
−0.588265 | + | 0.808668i | \(0.700189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47.0870i | 1.96709i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.287039 | + | 4.78723i | −0.0119704 | + | 0.199641i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.4661 | −0.643862 | −0.321931 | − | 0.946763i | \(-0.604332\pi\) | ||||
−0.321931 | + | 0.946763i | \(0.604332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 37.1544i | − | 1.54408i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.5679 | 0.770327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 49.3220i | − | 2.04271i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 38.3168i | 1.58421i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.8769i | 0.737860i | 0.929457 | + | 0.368930i | \(0.120276\pi\) | ||||
−0.929457 | + | 0.368930i | \(0.879724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 56.9673i | − | 2.34730i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 29.9056i | − | 1.23015i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.2557 | −0.626475 | −0.313237 | − | 0.949675i | \(-0.601414\pi\) | ||||
−0.313237 | + | 0.949675i | \(0.601414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.51928 | 0.267265 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.24609i | 0.337490i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.7916i | − | 1.05382i | −0.849922 | − | 0.526908i | \(-0.823351\pi\) | ||
0.849922 | − | 0.526908i | \(-0.176649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.09422 | 0.0854249 | 0.0427124 | − | 0.999087i | \(-0.486400\pi\) | ||||
0.0427124 | + | 0.999087i | \(0.486400\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −90.0205 | −3.66592 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 15.3704i | − | 0.624896i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.0509i | 1.01678i | 0.861126 | + | 0.508392i | \(0.169760\pi\) | ||||
−0.861126 | + | 0.508392i | \(0.830240\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.7154i | 0.717865i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.25134i | 0.333813i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3741i | 1.18641i | 0.805052 | + | 0.593205i | \(0.202138\pi\) | ||||
−0.805052 | + | 0.593205i | \(0.797862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.1107 | 0.528676 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.8308i | − | 1.03991i | −0.854194 | − | 0.519955i | \(-0.825949\pi\) | ||
0.854194 | − | 0.519955i | \(-0.174051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.51718 | −0.0609805 | −0.0304903 | − | 0.999535i | \(-0.509707\pi\) | ||||
−0.0304903 | + | 0.999535i | \(0.509707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −55.3476 | − | 3.31861i | −2.22102 | − | 0.133171i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 18.5749i | − | 0.744186i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 135.143i | 5.39708i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.55269 | −0.341018 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9588 | 0.515881 | 0.257940 | − | 0.966161i | \(-0.416956\pi\) | ||||
0.257940 | + | 0.966161i | \(0.416956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.3780 | −0.531729 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.71505 | −0.107743 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.0327 | −1.15032 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 26.4731i | − | 1.04726i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 30.2500i | − | 1.19480i | −0.801942 | − | 0.597401i | \(-0.796200\pi\) | ||
0.801942 | − | 0.597401i | \(-0.203800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.2977 | −0.761028 | −0.380514 | − | 0.924775i | \(-0.624253\pi\) | ||||
−0.380514 | + | 0.924775i | \(0.624253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.62588 | 0.339644 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.1803i | − | 1.30445i | −0.758024 | − | 0.652226i | \(-0.773835\pi\) | ||
0.758024 | − | 0.652226i | \(-0.226165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 71.8391i | 2.81993i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.0924 | −1.14022 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.28978 | −0.246138 | −0.123069 | − | 0.992398i | \(-0.539274\pi\) | ||||
−0.123069 | + | 0.992398i | \(0.539274\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.78723 | 0.187053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.9943 | 0.819067 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.3430 | −0.675586 | −0.337793 | − | 0.941220i | \(-0.609680\pi\) | ||||
−0.337793 | + | 0.941220i | \(0.609680\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.4036i | − | 0.482445i | −0.970470 | − | 0.241222i | \(-0.922452\pi\) | ||
0.970470 | − | 0.241222i | \(-0.0775483\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 83.8125 | 3.25501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.6890i | 0.453281i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.17901 | + | 19.6636i | −0.0456516 | + | 0.761377i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.00567 | −0.348179 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.2984i | 1.16965i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.656283 | −0.0252978 | −0.0126489 | − | 0.999920i | \(-0.504026\pi\) | ||||
−0.0126489 | + | 0.999920i | \(0.504026\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.5615i | 0.445002i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.8214i | − | 0.569634i | −0.958582 | − | 0.284817i | \(-0.908067\pi\) | ||
0.958582 | − | 0.284817i | \(-0.0919329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.90801i | − | 0.226729i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.7985i | 1.64004i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.47598i | − | 0.171269i | −0.996327 | − | 0.0856344i | \(-0.972708\pi\) | ||
0.996327 | − | 0.0856344i | \(-0.0272917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.58718 | −0.289891 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 56.7602 | 2.16554 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 54.8448i | − | 2.08942i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.46410i | − | 0.131781i | −0.997827 | − | 0.0658903i | \(-0.979011\pi\) | ||
0.997827 | − | 0.0658903i | \(-0.0209887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 47.6929 | 1.81170 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.88598 | −0.0715394 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.8177i | − | 0.750650i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 68.8060i | − | 2.60248i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.24980i | − | 0.349360i | −0.984625 | − | 0.174680i | \(-0.944111\pi\) | ||
0.984625 | − | 0.174680i | \(-0.0558891\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 15.3349i | − | 0.578366i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.50283i | 0.169587i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.64690 | −0.0619381 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.6073i | 1.29970i | 0.760061 | + | 0.649852i | \(0.225169\pi\) | ||||
−0.760061 | + | 0.649852i | \(0.774831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −63.4290 | −2.37877 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.2917 | − | 1.93619i | −1.20933 | − | 0.0725109i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 29.3232i | − | 1.09663i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.0863 | −1.01156 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 31.5572i | − | 1.17688i | −0.808540 | − | 0.588442i | \(-0.799742\pi\) | ||
0.808540 | − | 0.588442i | \(-0.200258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.2705 | 0.605946 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.8341 | 1.48145 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.10750 | 0.152549 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.15799 | −0.117123 | −0.0585617 | − | 0.998284i | \(-0.518651\pi\) | ||||
−0.0585617 | + | 0.998284i | \(0.518651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.41282 | 0.0523267 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 13.0386i | − | 0.482249i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.8349i | 1.47134i | 0.677342 | + | 0.735668i | \(0.263132\pi\) | ||||
−0.677342 | + | 0.735668i | \(0.736868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.8434 | −0.584394 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 68.8911 | 2.53764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.7912i | − | 0.764815i | −0.923994 | − | 0.382408i | \(-0.875095\pi\) | ||
0.923994 | − | 0.382408i | \(-0.124905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 150.275i | 5.52049i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.6592 | −1.52833 | −0.764163 | − | 0.645023i | \(-0.776848\pi\) | ||||
−0.764163 | + | 0.645023i | \(0.776848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.83326 | −0.213714 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 90.0205 | 3.29368 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3992 | 0.672293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.1430 | 1.02695 | 0.513476 | − | 0.858104i | \(-0.328357\pi\) | ||||
0.513476 | + | 0.858104i | \(0.328357\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58.5008i | 2.13189i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.3109 | −0.702797 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.01554i | − | 0.0732560i | −0.999329 | − | 0.0366280i | \(-0.988338\pi\) | ||
0.999329 | − | 0.0366280i | \(-0.0116617\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 76.6051 | + | 4.59319i | 2.78059 | + | 0.166722i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.4316 | 0.958145 | 0.479072 | − | 0.877775i | \(-0.340973\pi\) | ||||
0.479072 | + | 0.877775i | \(0.340973\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 6.34114i | − | 0.229565i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.6066 | 1.14274 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 79.8832i | 2.88442i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.5778i | 1.35509i | 0.735481 | + | 0.677545i | \(0.236956\pi\) | ||||
−0.735481 | + | 0.677545i | \(0.763044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.8511i | 2.01143i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.0096i | − | 1.40308i | −0.712632 | − | 0.701538i | \(-0.752497\pi\) | ||
0.712632 | − | 0.701538i | \(-0.247503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.74538i | 0.242301i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.83131 | −0.280947 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.5330 | 1.27310 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.2594i | 0.724937i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 47.4889i | 1.69712i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.6103 | −0.592848 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.2081 | −1.29068 | −0.645340 | − | 0.763895i | \(-0.723284\pi\) | ||||
−0.645340 | + | 0.763895i | \(0.723284\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 33.6685i | − | 1.19863i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6855i | 0.522155i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.6910i | 1.19640i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 29.9293i | − | 1.06148i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.3643i | 0.508808i | 0.967098 | + | 0.254404i | \(0.0818793\pi\) | ||||
−0.967098 | + | 0.254404i | \(0.918121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.80632 | 0.240790 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 90.0541i | − | 3.18191i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.0666 | −0.566978 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.62588 | + | 0.397283i | 0.233531 | + | 0.0140024i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 55.7674i | − | 1.96311i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.70455 | 0.341194 | 0.170597 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170597 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 32.5534i | − | 1.14310i | −0.820566 | − | 0.571552i | \(-0.806342\pi\) | ||
0.820566 | − | 0.571552i | \(-0.193658\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −73.1691 | −2.56615 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.5867 | 0.686094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.3780 | 0.817894 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 53.0333 | 1.85313 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.5524 | 1.69449 | 0.847245 | − | 0.531202i | \(-0.178260\pi\) | ||||
0.847245 | + | 0.531202i | \(0.178260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 36.8269i | − | 1.28370i | −0.766828 | − | 0.641852i | \(-0.778166\pi\) | ||
0.766828 | − | 0.641852i | \(-0.221834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 16.0020i | − | 0.557117i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.1227 | 1.01270 | 0.506348 | − | 0.862329i | \(-0.330995\pi\) | ||||
0.506348 | + | 0.862329i | \(0.330995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.2305 | −0.980487 | −0.490244 | − | 0.871585i | \(-0.663092\pi\) | ||||
−0.490244 | + | 0.871585i | \(0.663092\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 4.00754i | − | 0.139020i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.9484i | 0.829762i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.51036 | 0.329120 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −77.9868 | −2.69562 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.8228 | 0.856978 | 0.428489 | − | 0.903547i | \(-0.359046\pi\) | ||||
0.428489 | + | 0.903547i | \(0.359046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1284 | −0.418221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45.5882 | 1.57014 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 19.6066i | − | 0.674488i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.2738 | −0.730975 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.9672i | 0.513672i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.69252 | − | 0.521198i | −0.297976 | − | 0.0178664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.8333 | 1.50082 | 0.750411 | − | 0.660971i | \(-0.229856\pi\) | ||||
0.750411 | + | 0.660971i | \(0.229856\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.6704i | 1.93809i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.8328 | −1.12155 | −0.560773 | − | 0.827969i | \(-0.689496\pi\) | ||||
−0.560773 | + | 0.827969i | \(0.689496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.2489i | − | 0.827363i | −0.910422 | − | 0.413681i | \(-0.864243\pi\) | ||
0.910422 | − | 0.413681i | \(-0.135757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 18.1462i | − | 0.618421i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.3698i | 0.557234i | 0.960402 | + | 0.278617i | \(0.0898760\pi\) | ||||
−0.960402 | + | 0.278617i | \(0.910124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 13.3206i | − | 0.452913i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.1608i | − | 0.548849i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.5411 | 1.64664 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.6051 | 2.59566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 28.6431i | − | 0.969421i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.38407i | − | 0.0467902i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.32056 | −0.0445921 | −0.0222960 | − | 0.999751i | \(-0.507098\pi\) | ||||
−0.0222960 | + | 0.999751i | \(0.507098\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.5518 | 1.03049 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.188433i | 0.00634848i | 0.999995 | + | 0.00317424i | \(0.00101039\pi\) | ||||
−0.999995 | + | 0.00317424i | \(0.998990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11.4152i | − | 0.384152i | −0.981380 | − | 0.192076i | \(-0.938478\pi\) | ||
0.981380 | − | 0.192076i | \(-0.0615220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.5930i | 1.46536i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 7.34694i | − | 0.246686i | −0.992364 | − | 0.123343i | \(-0.960638\pi\) | ||
0.992364 | − | 0.123343i | \(-0.0393615\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.75782i | 0.126033i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 81.6314 | 2.73476 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2037i | 0.408380i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.749054 | −0.0250381 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 85.1828 | + | 5.10750i | 2.84417 | + | 0.170535i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.7067i | 0.924070i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.2401 | −1.50717 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 11.9388i | − | 0.397299i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7965 | 0.691300 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.8008 | −1.62040 | −0.810202 | − | 0.586150i | \(-0.800643\pi\) | ||||
−0.810202 | + | 0.586150i | \(0.800643\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.98446 | −0.264828 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.6250 | −0.981519 | −0.490760 | − | 0.871295i | \(-0.663281\pi\) | ||||
−0.490760 | + | 0.871295i | \(0.663281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −68.8911 | −2.27996 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.3855i | 0.607805i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.62588i | − | 0.218806i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.2691 | −1.26238 | −0.631190 | − | 0.775628i | \(-0.717433\pi\) | ||||
−0.631190 | + | 0.775628i | \(0.717433\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −40.1396 | −1.32264 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.5279i | 0.741514i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.81577i | 0.0597022i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 78.8823 | 2.59084 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.5223 | 0.410843 | 0.205421 | − | 0.978674i | \(-0.434144\pi\) | ||||
0.205421 | + | 0.978674i | \(0.434144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.9392 | −1.40728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.53391 | 0.0829565 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.1880 | −0.791032 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.4928i | 0.604133i | 0.953287 | + | 0.302066i | \(0.0976764\pi\) | ||||
−0.953287 | + | 0.302066i | \(0.902324\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −59.4228 | −1.93919 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 16.2725i | − | 0.530468i | −0.964184 | − | 0.265234i | \(-0.914551\pi\) | ||
0.964184 | − | 0.265234i | \(-0.0854492\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.20769 | − | 20.1417i | 0.0393276 | − | 0.655906i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.0020 | 0.520544 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.0330i | 1.07343i | 0.843764 | + | 0.536715i | \(0.180335\pi\) | ||||
−0.843764 | + | 0.536715i | \(0.819665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.8656 | −0.579943 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 26.8854i | − | 0.871818i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 19.1558i | − | 0.620516i | −0.950652 | − | 0.310258i | \(-0.899584\pi\) | ||
0.950652 | − | 0.310258i | \(-0.100416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 15.1108i | − | 0.488973i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 65.7281i | − | 2.12469i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5012i | 0.339101i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5002 | −0.467749 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 89.2027 | 2.87452 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.9233i | 0.383824i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.05093i | 0.194585i | 0.995256 | + | 0.0972925i | \(0.0310182\pi\) | ||||
−0.995256 | + | 0.0972925i | \(0.968982\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 123.958 | 3.98211 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.6158 | −0.854141 | −0.427071 | − | 0.904218i | \(-0.640454\pi\) | ||||
−0.427071 | + | 0.904218i | \(0.640454\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.61034i | 0.0836836i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 17.7937i | − | 0.569856i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.69535i | 0.310182i | 0.987900 | + | 0.155091i | \(0.0495671\pi\) | ||||
−0.987900 | + | 0.155091i | \(0.950433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.9168i | 2.20259i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 30.7430i | − | 0.981547i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.4218 | −1.25736 | −0.628680 | − | 0.777664i | \(-0.716405\pi\) | ||||
−0.628680 | + | 0.777664i | \(0.716405\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.59705i | 0.305787i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.23225 | 0.198375 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.794566 | − | 13.2518i | 0.0252657 | − | 0.421381i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.3661i | 1.47287i | 0.676509 | + | 0.736434i | \(0.263492\pi\) | ||||
−0.676509 | + | 0.736434i | \(0.736508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −49.3052 | −1.56465 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.64626i | − | 0.0838922i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4724 | 0.901731 | 0.450865 | − | 0.892592i | \(-0.351115\pi\) | ||||
0.450865 | + | 0.892592i | \(0.351115\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.9931 | −0.664191 |
(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 | 1840.2.i.a.1471.15 | yes | 16 | |
4.3 | odd | 2 | inner | 1840.2.i.a.1471.1 | ✓ | 16 | |
23.22 | odd | 2 | inner | 1840.2.i.a.1471.16 | yes | 16 | |
92.91 | even | 2 | inner | 1840.2.i.a.1471.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.i.a.1471.1 | ✓ | 16 | 4.3 | odd | 2 | inner | |
1840.2.i.a.1471.2 | yes | 16 | 92.91 | even | 2 | inner | |
1840.2.i.a.1471.15 | yes | 16 | 1.1 | even | 1 | trivial | |
1840.2.i.a.1471.16 | yes | 16 | 23.22 | odd | 2 | inner |