Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1025,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2736.1025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 37x^{4} + 22x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.6 | ||
Root | \(0.626815i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1025 |
Dual form | 2736.2.f.h.1025.3 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.32945i | 1.04176i | 0.853630 | + | 0.520880i | \(0.174396\pi\) | ||||
−0.853630 | + | 0.520880i | \(0.825604\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.34658 | −1.64285 | −0.821427 | − | 0.570314i | \(-0.806822\pi\) | ||||
−0.821427 | + | 0.570314i | \(0.806822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.264508i | 0.0797522i | 0.999205 | + | 0.0398761i | \(0.0126963\pi\) | ||||
−0.999205 | + | 0.0398761i | \(0.987304\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.38147i | − | 1.76990i | −0.465685 | − | 0.884950i | \(-0.654192\pi\) | ||
0.465685 | − | 0.884950i | \(-0.345808\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.56392i | − | 0.621842i | −0.950436 | − | 0.310921i | \(-0.899363\pi\) | ||
0.950436 | − | 0.310921i | \(-0.100637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.62593 | + | 3.47915i | −0.602429 | + | 0.798172i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.66784i | 0.556284i | 0.960540 | + | 0.278142i | \(0.0897186\pi\) | ||||
−0.960540 | + | 0.278142i | \(0.910281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.426319 | −0.0852637 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.92026 | 1.65645 | 0.828226 | − | 0.560395i | \(-0.189351\pi\) | ||||
0.828226 | + | 0.560395i | \(0.189351\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.78265i | − | 0.320173i | −0.987103 | − | 0.160086i | \(-0.948823\pi\) | ||
0.987103 | − | 0.160086i | \(-0.0511773\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 10.1251i | − | 1.71146i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.08409i | 0.507022i | 0.967332 | + | 0.253511i | \(0.0815854\pi\) | ||||
−0.967332 | + | 0.253511i | \(0.918415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.44131 | −1.16214 | −0.581068 | − | 0.813855i | \(-0.697365\pi\) | ||||
−0.581068 | + | 0.813855i | \(0.697365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.05225 | 0.770461 | 0.385230 | − | 0.922820i | \(-0.374122\pi\) | ||||
0.385230 | + | 0.922820i | \(0.374122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.45728i | − | 1.08776i | −0.839164 | − | 0.543878i | \(-0.816955\pi\) | ||
0.839164 | − | 0.543878i | \(-0.183045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.8928 | 1.69897 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.10450 | 0.563796 | 0.281898 | − | 0.959444i | \(-0.409036\pi\) | ||||
0.281898 | + | 0.959444i | \(0.409036\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.616157 | −0.0830826 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.36157 | 1.08858 | 0.544292 | − | 0.838896i | \(-0.316798\pi\) | ||||
0.544292 | + | 0.838896i | \(0.316798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.45108 | −1.08205 | −0.541025 | − | 0.841007i | \(-0.681963\pi\) | ||||
−0.541025 | + | 0.841007i | \(0.681963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.8653 | 1.84381 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.35948i | − | 0.288256i | −0.989559 | − | 0.144128i | \(-0.953962\pi\) | ||
0.989559 | − | 0.144128i | \(-0.0460378\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.02476 | −0.596329 | −0.298165 | − | 0.954514i | \(-0.596374\pi\) | ||||
−0.298165 | + | 0.954514i | \(0.596374\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9973 | 1.75530 | 0.877649 | − | 0.479304i | \(-0.159111\pi\) | ||||
0.877649 | + | 0.479304i | \(0.159111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.14971i | − | 0.131021i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.23369i | 0.701345i | 0.936498 | + | 0.350672i | \(0.114047\pi\) | ||||
−0.936498 | + | 0.350672i | \(0.885953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.0076i | − | 1.75706i | −0.477683 | − | 0.878532i | \(-0.658523\pi\) | ||
0.477683 | − | 0.878532i | \(-0.341477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.97251 | 0.647810 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.25707 | 0.875248 | 0.437624 | − | 0.899158i | \(-0.355820\pi\) | ||||
0.437624 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.7376i | 2.90769i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.10450 | − | 6.11696i | −0.831504 | − | 0.627587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.1224i | 1.53545i | 0.640780 | + | 0.767724i | \(0.278611\pi\) | ||||
−0.640780 | + | 0.767724i | \(0.721389\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.837379i | − | 0.0833223i | −0.999132 | − | 0.0416611i | \(-0.986735\pi\) | ||
0.999132 | − | 0.0416611i | \(-0.0132650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8470i | 1.56145i | 0.624872 | + | 0.780727i | \(0.285151\pi\) | ||||
−0.624872 | + | 0.780727i | \(0.714849\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.8653 | 1.82378 | 0.911888 | − | 0.410439i | \(-0.134625\pi\) | ||||
0.911888 | + | 0.410439i | \(0.134625\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.724614i | − | 0.0694054i | −0.999398 | − | 0.0347027i | \(-0.988952\pi\) | ||
0.999398 | − | 0.0347027i | \(-0.0110484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.73603 | 0.915889 | 0.457944 | − | 0.888981i | \(-0.348586\pi\) | ||||
0.457944 | + | 0.888981i | \(0.348586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.21460 | −0.579514 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.1443i | 1.02159i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9300 | 0.993640 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6541i | 0.952936i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.724614i | 0.0642991i | 0.999483 | + | 0.0321495i | \(0.0102353\pi\) | ||||
−0.999483 | + | 0.0321495i | \(0.989765\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.38771i | 0.820208i | 0.912039 | + | 0.410104i | \(0.134508\pi\) | ||||
−0.912039 | + | 0.410104i | \(0.865492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4138 | − | 15.1224i | 0.989703 | − | 1.31128i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.814718i | 0.0696061i | 0.999394 | + | 0.0348030i | \(0.0110804\pi\) | ||||
−0.999394 | + | 0.0348030i | \(0.988920\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.82554 | 0.154840 | 0.0774201 | − | 0.996999i | \(-0.475332\pi\) | ||||
0.0774201 | + | 0.996999i | \(0.475332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.68795 | 0.141153 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.7793i | 1.72562i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.8339i | − | 0.969470i | −0.874661 | − | 0.484735i | \(-0.838916\pi\) | ||
0.874661 | − | 0.484735i | \(-0.161084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.5080i | − | 1.58754i | −0.608221 | − | 0.793768i | \(-0.708117\pi\) | ||
0.608221 | − | 0.793768i | \(-0.291883\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.15258 | 0.333543 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.97524 | 0.237450 | 0.118725 | − | 0.992927i | \(-0.462119\pi\) | ||||
0.118725 | + | 0.992927i | \(0.462119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.5960i | − | 0.913893i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4292 | 1.13018 | 0.565091 | − | 0.825029i | \(-0.308841\pi\) | ||||
0.565091 | + | 0.825029i | \(0.308841\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2021 | 1.40852 | 0.704260 | − | 0.709942i | \(-0.251279\pi\) | ||||
0.704260 | + | 0.709942i | \(0.251279\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.7231 | −2.13255 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2818 | −1.31391 | −0.656957 | − | 0.753928i | \(-0.728157\pi\) | ||||
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.85303 | 0.140076 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.66319 | 0.647517 | 0.323759 | − | 0.946140i | \(-0.395053\pi\) | ||||
0.323759 | + | 0.946140i | \(0.395053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0424i | 0.746446i | 0.927742 | + | 0.373223i | \(0.121747\pi\) | ||||
−0.927742 | + | 0.373223i | \(0.878253\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.18423 | −0.528195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.678177 | 0.0495932 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.0581i | − | 0.800139i | −0.916485 | − | 0.400070i | \(-0.868986\pi\) | ||
0.916485 | − | 0.400070i | \(-0.131014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.05803i | − | 0.0761588i | −0.999275 | − | 0.0380794i | \(-0.987876\pi\) | ||
0.999275 | − | 0.0380794i | \(-0.0121240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.7506i | − | 1.69216i | −0.533056 | − | 0.846080i | \(-0.678956\pi\) | ||
0.533056 | − | 0.846080i | \(-0.321044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.05225 | 0.0745919 | 0.0372959 | − | 0.999304i | \(-0.488126\pi\) | ||||
0.0372959 | + | 0.999304i | \(0.488126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −38.7727 | −2.72131 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 17.3341i | − | 1.21067i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.920263 | − | 0.694579i | −0.0636559 | − | 0.0480450i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 13.9687i | − | 0.961648i | −0.876817 | − | 0.480824i | \(-0.840338\pi\) | ||
0.876817 | − | 0.480824i | \(-0.159662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7689i | 0.802635i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.74842i | 0.525997i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3616 | −1.10060 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.9926i | − | 1.40577i | −0.711306 | − | 0.702883i | \(-0.751896\pi\) | ||
0.711306 | − | 0.702883i | \(-0.248104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.79101 | −0.251618 | −0.125809 | − | 0.992054i | \(-0.540153\pi\) | ||||
−0.125809 | + | 0.992054i | \(0.540153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.7758 | −1.76939 | −0.884697 | − | 0.466167i | \(-0.845634\pi\) | ||||
−0.884697 | + | 0.466167i | \(0.845634\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.18450i | − | 0.339648i | −0.985474 | − | 0.169824i | \(-0.945680\pi\) | ||
0.985474 | − | 0.169824i | \(-0.0543199\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.3713 | 1.13318 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.30565i | − | 0.343194i | −0.985167 | − | 0.171597i | \(-0.945107\pi\) | ||
0.985167 | − | 0.171597i | \(-0.0548927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.147779i | − | 0.00951929i | −0.999989 | − | 0.00475965i | \(-0.998485\pi\) | ||
0.999989 | − | 0.00475965i | \(-0.00151505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.7036i | 1.76992i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.2021 | + | 16.7573i | 1.41269 | + | 1.06624i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8783i | 1.31783i | 0.752218 | + | 0.658914i | \(0.228984\pi\) | ||||
−0.752218 | + | 0.658914i | \(0.771016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.705666 | −0.0443648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.6434 | 1.84910 | 0.924552 | − | 0.381055i | \(-0.124439\pi\) | ||||
0.924552 | + | 0.381055i | \(0.124439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.4053i | − | 0.832963i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 17.1696i | − | 1.05872i | −0.848397 | − | 0.529361i | \(-0.822432\pi\) | ||
0.848397 | − | 0.529361i | \(-0.177568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.56120i | 0.587340i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.2397 | −0.746271 | −0.373135 | − | 0.927777i | \(-0.621717\pi\) | ||||
−0.373135 | + | 0.927777i | \(0.621717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.79101 | 0.230287 | 0.115144 | − | 0.993349i | \(-0.463267\pi\) | ||||
0.115144 | + | 0.993349i | \(0.463267\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.112765i | − | 0.00679997i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.56847 | −0.0942400 | −0.0471200 | − | 0.998889i | \(-0.515004\pi\) | ||||
−0.0471200 | + | 0.998889i | \(0.515004\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6082 | 1.11007 | 0.555036 | − | 0.831826i | \(-0.312704\pi\) | ||||
0.555036 | + | 0.831826i | \(0.312704\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.7754 | −1.76996 | −0.884981 | − | 0.465626i | \(-0.845829\pi\) | ||||
−0.884981 | + | 0.465626i | \(0.845829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.3442 | 1.90922 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4263 | 0.613313 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.9871 | 0.641874 | 0.320937 | − | 0.947101i | \(-0.396002\pi\) | ||||
0.320937 | + | 0.947101i | \(0.396002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.4778i | 1.13404i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.0248 | 0.984567 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.9600 | −1.26575 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 19.6863i | − | 1.12724i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.0186i | − | 1.31374i | −0.754003 | − | 0.656871i | \(-0.771880\pi\) | ||
0.754003 | − | 0.656871i | \(-0.228120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.862537i | − | 0.0489100i | −0.999701 | − | 0.0244550i | \(-0.992215\pi\) | ||
0.999701 | − | 0.0244550i | \(-0.00778505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.84053 | −0.104033 | −0.0520164 | − | 0.998646i | \(-0.516565\pi\) | ||||
−0.0520164 | + | 0.998646i | \(0.516565\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.10450 | −0.455194 | −0.227597 | − | 0.973755i | \(-0.573087\pi\) | ||||
−0.227597 | + | 0.973755i | \(0.573087\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.35948i | 0.132106i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.92026 | + | 6.73267i | 0.496337 | + | 0.374616i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.72054i | 0.150908i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.4137i | 1.78702i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.6315i | − | 1.13401i | −0.823715 | − | 0.567005i | \(-0.808102\pi\) | ||
0.823715 | − | 0.567005i | \(-0.191898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.49628 | 0.300294 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7648i | 0.858761i | 0.903124 | + | 0.429380i | \(0.141268\pi\) | ||||
−0.903124 | + | 0.429380i | \(0.858732\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.471524 | 0.0255345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.2668 | −1.14830 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.5373i | − | 0.673038i | −0.941677 | − | 0.336519i | \(-0.890750\pi\) | ||
0.941677 | − | 0.336519i | \(-0.109250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8507 | −0.634353 | −0.317176 | − | 0.948367i | \(-0.602735\pi\) | ||||
−0.317176 | + | 0.948367i | \(0.602735\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 34.7830i | − | 1.85131i | −0.378364 | − | 0.925657i | \(-0.623513\pi\) | ||
0.378364 | − | 0.925657i | \(-0.376487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.7049i | − | 0.621232i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.3698i | 1.23341i | 0.787194 | + | 0.616706i | \(0.211533\pi\) | ||||
−0.787194 | + | 0.616706i | \(0.788467\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.20899 | − | 18.2720i | −0.274157 | − | 0.961685i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.9353i | 1.82860i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5141 | 0.653233 | 0.326617 | − | 0.945157i | \(-0.394091\pi\) | ||||
0.326617 | + | 0.945157i | \(0.394091\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.8405 | −0.926234 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.9926i | 1.08695i | 0.839424 | + | 0.543477i | \(0.182892\pi\) | ||||
−0.839424 | + | 0.543477i | \(0.817108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 56.9244i | − | 2.93175i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7335i | 1.52731i | 0.645626 | + | 0.763654i | \(0.276596\pi\) | ||||
−0.645626 | + | 0.763654i | \(0.723404\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.4111 | 1.14515 | 0.572577 | − | 0.819851i | \(-0.305944\pi\) | ||||
0.572577 | + | 0.819851i | \(0.305944\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.67818 | 0.136493 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 17.9064i | − | 0.907892i | −0.891029 | − | 0.453946i | \(-0.850016\pi\) | ||
0.891029 | − | 0.453946i | \(-0.149984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.84014 | 0.345921 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.5210 | −0.730633 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.57929 | −0.330205 | −0.165102 | − | 0.986276i | \(-0.552795\pi\) | ||||
−0.165102 | + | 0.986276i | \(0.552795\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.4413 | −0.571352 | −0.285676 | − | 0.958326i | \(-0.592218\pi\) | ||||
−0.285676 | + | 0.958326i | \(0.592218\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3759 | −0.566674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.815768 | −0.0404361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1265i | 0.649063i | 0.945875 | + | 0.324532i | \(0.105207\pi\) | ||||
−0.945875 | + | 0.324532i | \(0.894793\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.3442 | −1.78838 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.2889 | 1.83044 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.6098i | 0.567177i | 0.958946 | + | 0.283588i | \(0.0915249\pi\) | ||||
−0.958946 | + | 0.283588i | \(0.908475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 31.7074i | − | 1.54533i | −0.634817 | − | 0.772663i | \(-0.718924\pi\) | ||
0.634817 | − | 0.772663i | \(-0.281076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.09305i | 0.0530205i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.7333 | 1.77765 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.5953 | 1.23288 | 0.616442 | − | 0.787401i | \(-0.288574\pi\) | ||||
0.616442 | + | 0.787401i | \(0.288574\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.0286i | − | 0.866399i | −0.901298 | − | 0.433199i | \(-0.857385\pi\) | ||
0.901298 | − | 0.433199i | \(-0.142615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.28183 | − | 7.00557i | −0.444010 | − | 0.335122i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.0442i | − | 0.622566i | −0.950317 | − | 0.311283i | \(-0.899241\pi\) | ||
0.950317 | − | 0.311283i | \(-0.100759\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8655i | 1.37144i | 0.727864 | + | 0.685721i | \(0.240513\pi\) | ||||
−0.727864 | + | 0.685721i | \(0.759487\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.2344i | 0.911798i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.466064 | 0.0219949 | 0.0109975 | − | 0.999940i | \(-0.496499\pi\) | ||||
0.0109975 | + | 0.999940i | \(0.496499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.96828i | − | 0.0926829i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −64.6132 | −3.02911 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.78828 | −0.130430 | −0.0652151 | − | 0.997871i | \(-0.520773\pi\) | ||||
−0.0652151 | + | 0.997871i | \(0.520773\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.3276i | 1.50564i | 0.658224 | + | 0.752822i | \(0.271308\pi\) | ||||
−0.658224 | + | 0.752822i | \(0.728692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.36573 | 0.342315 | 0.171157 | − | 0.985244i | \(-0.445249\pi\) | ||||
0.171157 | + | 0.985244i | \(0.445249\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.9622i | 1.75668i | 0.478035 | + | 0.878341i | \(0.341349\pi\) | ||||
−0.478035 | + | 0.878341i | \(0.658651\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.2557i | 0.473563i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.33636i | 0.0614459i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.11948 | − | 1.48323i | 0.0513654 | − | 0.0680551i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.21862i | − | 0.0556800i | −0.999612 | − | 0.0278400i | \(-0.991137\pi\) | ||
0.999612 | − | 0.0278400i | \(-0.00886289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.6811 | 0.897379 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.2269 | −1.59957 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.4581i | − | 1.38019i | −0.723719 | − | 0.690094i | \(-0.757569\pi\) | ||
0.723719 | − | 0.690094i | \(-0.242431\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 27.8583i | − | 1.25723i | −0.777718 | − | 0.628613i | \(-0.783623\pi\) | ||
0.777718 | − | 0.628613i | \(-0.216377\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 22.8708i | − | 1.03005i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.8405 | 0.979682 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.9050 | −1.24920 | −0.624600 | − | 0.780945i | \(-0.714738\pi\) | ||||
−0.624600 | + | 0.780945i | \(0.714738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 29.6931i | − | 1.32395i | −0.749527 | − | 0.661974i | \(-0.769719\pi\) | ||
0.749527 | − | 0.661974i | \(-0.230281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.95063 | 0.0868018 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1471 | −0.715708 | −0.357854 | − | 0.933777i | \(-0.616492\pi\) | ||||
−0.357854 | + | 0.933777i | \(0.616492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −65.1869 | −2.88370 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.9148 | −1.62666 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.97251 | 0.0867509 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.5156 | −1.68740 | −0.843699 | − | 0.536816i | \(-0.819627\pi\) | ||||
−0.843699 | + | 0.536816i | \(0.819627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.75068i | − | 0.120279i | −0.998190 | − | 0.0601394i | \(-0.980845\pi\) | ||
0.998190 | − | 0.0601394i | \(-0.0191545\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.57056 | −0.199097 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.8826 | 0.690548 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.4865i | 2.05687i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.9457i | 1.89994i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.14573i | 0.135496i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7883 | 0.635798 | 0.317899 | − | 0.948125i | \(-0.397023\pi\) | ||||
0.317899 | + | 0.948125i | \(0.397023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.68795 | 0.0723038 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.20355i | 0.265245i | 0.991167 | + | 0.132622i | \(0.0423397\pi\) | ||||
−0.991167 | + | 0.132622i | \(0.957660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.4240 | + | 31.0349i | −0.997895 | + | 1.32213i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 27.0952i | − | 1.15221i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.92419i | 0.378130i | 0.981965 | + | 0.189065i | \(0.0605457\pi\) | ||||
−0.981965 | + | 0.189065i | \(0.939454\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 32.2408i | − | 1.36364i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.6805 | 0.703000 | 0.351500 | − | 0.936188i | \(-0.385672\pi\) | ||||
0.351500 | + | 0.936188i | \(0.385672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.6796i | 0.954136i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.1293 | 1.05347 | 0.526737 | − | 0.850029i | \(-0.323415\pi\) | ||||
0.526737 | + | 0.850029i | \(0.323415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.51415 | −0.356306 | −0.178153 | − | 0.984003i | \(-0.557012\pi\) | ||||
−0.178153 | + | 0.984003i | \(0.557012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.13735i | − | 0.0474308i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.6037 | −0.857741 | −0.428871 | − | 0.903366i | \(-0.641088\pi\) | ||||
−0.428871 | + | 0.903366i | \(0.641088\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 69.5784i | 2.88660i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.08567i | 0.0449639i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 28.9223i | − | 1.19375i | −0.802334 | − | 0.596875i | \(-0.796409\pi\) | ||
0.802334 | − | 0.596875i | \(-0.203591\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.20210 | + | 4.68110i | 0.255553 | + | 0.192881i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0022i | 1.06778i | 0.845553 | + | 0.533891i | \(0.179271\pi\) | ||||
−0.845553 | + | 0.533891i | \(0.820729\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.9600 | −1.06426 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.3690 | −1.19998 | −0.599992 | − | 0.800006i | \(-0.704830\pi\) | ||||
−0.599992 | + | 0.800006i | \(0.704830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.8731i | − | 0.729059i | −0.931192 | − | 0.364529i | \(-0.881230\pi\) | ||
0.931192 | − | 0.364529i | \(-0.118770\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.4609i | 1.03513i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.9876i | 1.70422i | 0.523359 | + | 0.852112i | \(0.324679\pi\) | ||||
−0.523359 | + | 0.852112i | \(0.675321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −47.5884 | −1.92522 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6480 | −0.470457 | −0.235228 | − | 0.971940i | \(-0.575584\pi\) | ||||
−0.235228 | + | 0.971940i | \(0.575584\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5817i | 0.466263i | 0.972445 | + | 0.233131i | \(0.0748972\pi\) | ||||
−0.972445 | + | 0.233131i | \(0.925103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6486 | 0.508391 | 0.254195 | − | 0.967153i | \(-0.418189\pi\) | ||||
0.254195 | + | 0.967153i | \(0.418189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.8900 | −1.43790 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.9498 | −1.07799 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.90737 | 0.315287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.3644 | −0.611649 | −0.305824 | − | 0.952088i | \(-0.598932\pi\) | ||||
−0.305824 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.68795 | −0.0669842 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 75.8934i | − | 3.00700i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.6330 | 0.617465 | 0.308733 | − | 0.951149i | \(-0.400095\pi\) | ||||
0.308733 | + | 0.951149i | \(0.400095\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.62881 | −0.261415 | −0.130707 | − | 0.991421i | \(-0.541725\pi\) | ||||
−0.130707 | + | 0.991421i | \(0.541725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.0200i | 1.33746i | 0.743504 | + | 0.668732i | \(0.233163\pi\) | ||||
−0.743504 | + | 0.668732i | \(0.766837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.21170i | 0.0868169i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 37.5888i | − | 1.47096i | −0.677545 | − | 0.735482i | \(-0.736956\pi\) | ||
0.677545 | − | 0.735482i | \(-0.263044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.8682 | −0.854460 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.37889 | 0.326395 | 0.163198 | − | 0.986593i | \(-0.447819\pi\) | ||||
0.163198 | + | 0.986593i | \(0.447819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.1281i | − | 1.21074i | −0.795943 | − | 0.605371i | \(-0.793025\pi\) | ||
0.795943 | − | 0.605371i | \(-0.206975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.2269 | + | 26.5879i | 1.36604 | + | 1.03103i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.7979i | 0.921457i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.23538i | − | 0.0862958i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3650i | 1.17048i | 0.810859 | + | 0.585242i | \(0.199000\pi\) | ||||
−0.810859 | + | 0.585242i | \(0.801000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.8955 | −0.918379 | −0.459189 | − | 0.888338i | \(-0.651860\pi\) | ||||
−0.459189 | + | 0.888338i | \(0.651860\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 65.7308i | − | 2.52252i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.7306 | 0.678441 | 0.339221 | − | 0.940707i | \(-0.389837\pi\) | ||||
0.339221 | + | 0.940707i | \(0.389837\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.89784 | −0.0725128 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 26.1927i | − | 0.997863i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.7957 | −1.13348 | −0.566741 | − | 0.823896i | \(-0.691796\pi\) | ||||
−0.566741 | + | 0.823896i | \(0.691796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.25250i | 0.161306i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0789i | 0.722665i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.13657i | 0.269544i | 0.990877 | + | 0.134772i | \(0.0430303\pi\) | ||||
−0.990877 | + | 0.134772i | \(0.956970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7300 | − | 8.09861i | −0.404691 | − | 0.305445i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.63974i | 0.136886i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5562 | 0.434003 | 0.217002 | − | 0.976171i | \(-0.430372\pi\) | ||||
0.217002 | + | 0.976171i | \(0.430372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.75582 | 0.178107 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.93199i | 0.147048i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.2870i | 0.570108i | 0.958512 | + | 0.285054i | \(0.0920115\pi\) | ||||
−0.958512 | + | 0.285054i | \(0.907989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 68.8804i | − | 2.56524i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.80287 | −0.141235 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.5664 | 0.503150 | 0.251575 | − | 0.967838i | \(-0.419052\pi\) | ||||
0.251575 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 12.9536i | − | 0.479105i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.16691 | −0.190844 | −0.0954220 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954220 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.624101 | 0.0229891 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.57290 | 0.168217 | 0.0841084 | − | 0.996457i | \(-0.473196\pi\) | ||||
0.0841084 | + | 0.996457i | \(0.473196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.589451 | −0.0216249 | −0.0108124 | − | 0.999942i | \(-0.503442\pi\) | ||||
−0.0108124 | + | 0.999942i | \(0.503442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.5664 | 1.00995 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −81.9995 | −2.99620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7704i | 0.429508i | 0.976668 | + | 0.214754i | \(0.0688950\pi\) | ||||
−0.976668 | + | 0.214754i | \(0.931105\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.4427 | 1.65383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.0526 | 0.656134 | 0.328067 | − | 0.944654i | \(-0.393603\pi\) | ||||
0.328067 | + | 0.944654i | \(0.393603\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.87400i | − | 0.285432i | −0.989764 | − | 0.142716i | \(-0.954416\pi\) | ||
0.989764 | − | 0.142716i | \(-0.0455836\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.14959i | 0.114023i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 53.3591i | − | 1.92668i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.8805 | 0.428422 | 0.214211 | − | 0.976787i | \(-0.431282\pi\) | ||||
0.214211 | + | 0.976787i | \(0.431282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.9381 | −0.573255 | −0.286627 | − | 0.958042i | \(-0.592534\pi\) | ||||
−0.286627 | + | 0.958042i | \(0.592534\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.759975i | 0.0272991i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.5403 | − | 25.8894i | 0.700105 | − | 0.927585i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.32909i | − | 0.0475585i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.93066i | 0.247366i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.4321i | − | 1.01349i | −0.862095 | − | 0.506747i | \(-0.830848\pi\) | ||
0.862095 | − | 0.506747i | \(-0.169152\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.3185 | −1.50467 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.9303i | 1.91512i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.7246 | 1.65507 | 0.827535 | − | 0.561415i | \(-0.189743\pi\) | ||||
0.827535 | + | 0.561415i | \(0.189743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.1199 | −0.676413 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.96690i | 0.139989i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.0123 | 0.952057 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4026i | 0.576684i | 0.957528 | + | 0.288342i | \(0.0931039\pi\) | ||||
−0.957528 | + | 0.288342i | \(0.906896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.3863i | − | 0.610514i | −0.952270 | − | 0.305257i | \(-0.901258\pi\) | ||
0.952270 | − | 0.305257i | \(-0.0987424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.6120i | 1.17738i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2668 | + | 17.5775i | −0.464148 | + | 0.614960i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 33.4165i | − | 1.16625i | −0.812384 | − | 0.583123i | \(-0.801831\pi\) | ||
0.812384 | − | 0.583123i | \(-0.198169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7134 | 0.966027 | 0.483014 | − | 0.875613i | \(-0.339542\pi\) | ||||
0.483014 | + | 0.875613i | \(0.339542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.87218 | −0.308516 | −0.154258 | − | 0.988031i | \(-0.549299\pi\) | ||||
−0.154258 | + | 0.988031i | \(0.549299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.3606i | − | 1.08920i | −0.838696 | − | 0.544600i | \(-0.816681\pi\) | ||
0.838696 | − | 0.544600i | \(-0.183319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 30.4921i | − | 1.05649i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.4008i | 1.46734i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.8510 | −0.685331 | −0.342666 | − | 0.939457i | \(-0.611330\pi\) | ||||
−0.342666 | + | 0.939457i | \(0.611330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.5711 | 1.74383 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 64.5796i | − | 2.22160i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.5083 | −1.63240 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.22788 | −0.282048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.0570 | −1.81664 | −0.908318 | − | 0.418281i | \(-0.862633\pi\) | ||||
−0.908318 | + | 0.418281i | \(0.862633\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.0297 | 1.33323 | 0.666615 | − | 0.745402i | \(-0.267743\pi\) | ||||
0.666615 | + | 0.745402i | \(0.267743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.5861 | 1.62362 | 0.811808 | − | 0.583924i | \(-0.198484\pi\) | ||||
0.811808 | + | 0.583924i | \(0.198484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.0179 | 1.32818 | 0.664092 | − | 0.747651i | \(-0.268818\pi\) | ||||
0.664092 | + | 0.747651i | \(0.268818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 40.2571i | − | 1.36878i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.64886 | −0.0559338 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0570 | −0.510185 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 46.3091i | − | 1.56553i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.1150i | 1.35459i | 0.735714 | + | 0.677293i | \(0.236847\pi\) | ||||
−0.735714 | + | 0.677293i | \(0.763153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0749i | 0.710033i | 0.934860 | + | 0.355016i | \(0.115525\pi\) | ||||
−0.934860 | + | 0.355016i | \(0.884475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.887168 | −0.0298556 | −0.0149278 | − | 0.999889i | \(-0.504752\pi\) | ||||
−0.0149278 | + | 0.999889i | \(0.504752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.4185 | 1.86077 | 0.930386 | − | 0.366582i | \(-0.119472\pi\) | ||||
0.930386 | + | 0.366582i | \(0.119472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.14959i | − | 0.105634i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.9450 | + | 19.5823i | 0.868217 | + | 0.655297i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.1804i | 0.674558i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 15.9017i | − | 0.530350i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.5236i | − | 0.350592i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3932 | −0.777617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7439i | 0.688790i | 0.938825 | + | 0.344395i | \(0.111916\pi\) | ||||
−0.938825 | + | 0.344395i | \(0.888084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.17380 | −0.171416 | −0.0857079 | − | 0.996320i | \(-0.527315\pi\) | ||||
−0.0857079 | + | 0.996320i | \(0.527315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.23414 | 0.140130 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 40.8044i | − | 1.34748i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.7050 | −1.34274 | −0.671368 | − | 0.741125i | \(-0.734293\pi\) | ||||
−0.671368 | + | 0.741125i | \(0.734293\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.0653i | 1.05544i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.31481i | − | 0.0432306i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.5496i | 1.75691i | 0.477829 | + | 0.878453i | \(0.341424\pi\) | ||||
−0.477829 | + | 0.878453i | \(0.658576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.2296 | + | 41.3768i | −1.02351 | + | 1.35607i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.57978i | 0.0516642i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.5060 | −1.74796 | −0.873982 | − | 0.485959i | \(-0.838470\pi\) | ||||
−0.873982 | + | 0.485959i | \(0.838470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.6751 | 1.58676 | 0.793381 | − | 0.608726i | \(-0.208319\pi\) | ||||
0.793381 | + | 0.608726i | \(0.208319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19.8522i | − | 0.646478i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 26.4888i | − | 0.860771i | −0.902645 | − | 0.430386i | \(-0.858378\pi\) | ||
0.902645 | − | 0.430386i | \(-0.141622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 95.7046i | − | 3.10670i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0545 | 1.29749 | 0.648746 | − | 0.761005i | \(-0.275294\pi\) | ||||
0.648746 | + | 0.761005i | \(0.275294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.7593 | 0.833553 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 3.54124i | − | 0.114353i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.8222 | 0.897489 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.46463 | 0.0793392 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.6629 | 0.632318 | 0.316159 | − | 0.948706i | \(-0.397607\pi\) | ||||
0.316159 | + | 0.948706i | \(0.397607\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.1590 | −1.03203 | −0.516015 | − | 0.856579i | \(-0.672585\pi\) | ||||
−0.516015 | + | 0.856579i | \(0.672585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.93486 | −0.254380 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.05498 | −0.0657446 | −0.0328723 | − | 0.999460i | \(-0.510465\pi\) | ||||
−0.0328723 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.18406i | 0.0698029i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.3789 | 0.777566 | 0.388783 | − | 0.921329i | \(-0.372896\pi\) | ||||
0.388783 | + | 0.921329i | \(0.372896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.3257 | 1.76282 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.4786i | 0.428595i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4835i | 0.491849i | 0.969289 | + | 0.245924i | \(0.0790915\pi\) | ||||
−0.969289 | + | 0.245924i | \(0.920909\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.45115i | 0.0777068i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6405 | 0.717033 | 0.358516 | − | 0.933523i | \(-0.383283\pi\) | ||||
0.358516 | + | 0.933523i | \(0.383283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2736.2.f.h.1025.6 | 8 | ||
3.2 | odd | 2 | 2736.2.f.g.1025.3 | 8 | |||
4.3 | odd | 2 | 1368.2.f.d.1025.6 | yes | 8 | ||
12.11 | even | 2 | 1368.2.f.c.1025.3 | ✓ | 8 | ||
19.18 | odd | 2 | 2736.2.f.g.1025.6 | 8 | |||
57.56 | even | 2 | inner | 2736.2.f.h.1025.3 | 8 | ||
76.75 | even | 2 | 1368.2.f.c.1025.6 | yes | 8 | ||
228.227 | odd | 2 | 1368.2.f.d.1025.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.f.c.1025.3 | ✓ | 8 | 12.11 | even | 2 | ||
1368.2.f.c.1025.6 | yes | 8 | 76.75 | even | 2 | ||
1368.2.f.d.1025.3 | yes | 8 | 228.227 | odd | 2 | ||
1368.2.f.d.1025.6 | yes | 8 | 4.3 | odd | 2 | ||
2736.2.f.g.1025.3 | 8 | 3.2 | odd | 2 | |||
2736.2.f.g.1025.6 | 8 | 19.18 | odd | 2 | |||
2736.2.f.h.1025.3 | 8 | 57.56 | even | 2 | inner | ||
2736.2.f.h.1025.6 | 8 | 1.1 | even | 1 | trivial |