Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 559.3 | ||
Root | \(0.403374 - 1.68443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.559 |
Dual form | 2736.2.bm.o.1855.3 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.66044 | − | 2.87597i | 0.742572 | − | 1.28617i | −0.208748 | − | 0.977969i | \(-0.566939\pi\) |
0.951320 | − | 0.308204i | \(-0.0997278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.71781i | − | 1.02724i | −0.858019 | − | 0.513618i | \(-0.828305\pi\) | ||
0.858019 | − | 0.513618i | \(-0.171695\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.985762i | 0.297218i | 0.988896 | + | 0.148609i | \(0.0474796\pi\) | ||||
−0.988896 | + | 0.148609i | \(0.952520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.33502 | − | 2.50283i | 1.20232 | − | 0.694159i | 0.241248 | − | 0.970463i | \(-0.422443\pi\) |
0.961070 | + | 0.276304i | \(0.0891098\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.51414 | − | 4.35461i | 0.609768 | − | 1.05615i | −0.381511 | − | 0.924364i | \(-0.624596\pi\) |
0.991278 | − | 0.131784i | \(-0.0420706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.193252 | − | 4.35461i | 0.0443351 | − | 0.999017i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.68872 | + | 2.12968i | −0.769150 | + | 0.444069i | −0.832571 | − | 0.553918i | \(-0.813132\pi\) |
0.0634210 | + | 0.997987i | \(0.479799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.01414 | − | 5.22064i | −0.602827 | − | 1.04413i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.83502 | + | 3.36885i | −1.08354 | + | 0.625580i | −0.931848 | − | 0.362848i | \(-0.881804\pi\) |
−0.151688 | + | 0.988428i | \(0.548471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32088 | 0.416843 | 0.208422 | − | 0.978039i | \(-0.433167\pi\) | ||||
0.208422 | + | 0.978039i | \(0.433167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.81635 | − | 4.51277i | −1.32120 | − | 0.762797i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.27925i | − | 1.36110i | −0.732701 | − | 0.680550i | \(-0.761741\pi\) | ||
0.732701 | − | 0.680550i | \(-0.238259\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.96265 | + | 5.75194i | 1.55591 | + | 0.898302i | 0.997642 | + | 0.0686385i | \(0.0218655\pi\) |
0.558263 | + | 0.829664i | \(0.311468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.48133 | + | 5.47405i | 1.44589 | + | 0.834784i | 0.998233 | − | 0.0594217i | \(-0.0189257\pi\) |
0.447656 | + | 0.894206i | \(0.352259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.41478 | + | 3.70357i | −0.935692 | + | 0.540222i | −0.888607 | − | 0.458669i | \(-0.848326\pi\) |
−0.0470845 | + | 0.998891i | \(0.514993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.386505 | −0.0552150 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.14631 | + | 2.97122i | −0.706899 | + | 0.408129i | −0.809912 | − | 0.586551i | \(-0.800485\pi\) |
0.103013 | + | 0.994680i | \(0.467152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.83502 | + | 1.63680i | 0.382274 | + | 0.220706i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.66044 | − | 2.87597i | 0.216171 | − | 0.374419i | −0.737463 | − | 0.675387i | \(-0.763976\pi\) |
0.953634 | + | 0.300968i | \(0.0973097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.62763 | + | 6.28324i | 0.464471 | + | 0.804487i | 0.999177 | − | 0.0405508i | \(-0.0129113\pi\) |
−0.534707 | + | 0.845038i | \(0.679578\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 16.6232i | − | 2.06185i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.67458 | − | 11.5607i | −0.815430 | − | 1.41237i | −0.909019 | − | 0.416755i | \(-0.863167\pi\) |
0.0935894 | − | 0.995611i | \(-0.470166\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19325 | + | 3.79882i | −0.260291 | + | 0.450838i | −0.966319 | − | 0.257346i | \(-0.917152\pi\) |
0.706028 | + | 0.708184i | \(0.250485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.52827 | + | 4.37910i | −0.295912 | + | 0.512535i | −0.975197 | − | 0.221340i | \(-0.928957\pi\) |
0.679285 | + | 0.733875i | \(0.262290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.67912 | 0.305314 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.48133 | + | 9.49394i | −0.616697 | + | 1.06815i | 0.373387 | + | 0.927676i | \(0.378196\pi\) |
−0.990084 | + | 0.140476i | \(0.955137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.70923i | 0.955962i | 0.878370 | + | 0.477981i | \(0.158631\pi\) | ||||
−0.878370 | + | 0.477981i | \(0.841369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.34916 | − | 14.4612i | −0.905593 | − | 1.56853i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.10896 | − | 3.52701i | 0.647548 | − | 0.373862i | −0.139968 | − | 0.990156i | \(-0.544700\pi\) |
0.787516 | + | 0.616294i | \(0.211367\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.80221 | − | 11.7818i | −0.713065 | − | 1.23507i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.2029 | − | 7.78637i | −1.25199 | − | 0.798865i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.12763 | − | 4.11514i | −0.723701 | − | 0.417829i | 0.0924121 | − | 0.995721i | \(-0.470542\pi\) |
−0.816113 | + | 0.577892i | \(0.803876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.83502 | − | 4.91040i | −0.282095 | − | 0.488603i | 0.689805 | − | 0.723995i | \(-0.257696\pi\) |
−0.971901 | + | 0.235392i | \(0.924363\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1222 | −0.997367 | −0.498683 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498683 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.971726 | −0.0939403 | −0.0469702 | − | 0.998896i | \(-0.514957\pi\) | ||||
−0.0469702 | + | 0.998896i | \(0.514957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.579757 | − | 0.334723i | −0.0555307 | − | 0.0320607i | 0.471978 | − | 0.881611i | \(-0.343540\pi\) |
−0.527508 | + | 0.849550i | \(0.676874\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.39291i | − | 0.789539i | −0.918780 | − | 0.394769i | \(-0.870825\pi\) | ||
0.918780 | − | 0.394769i | \(-0.129175\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1449i | 1.31901i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.8350 | − | 6.83295i | −1.08491 | − | 0.626376i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0283 | 0.911661 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.41478 | −0.305427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.70739 | + | 6.42139i | 0.328978 | + | 0.569806i | 0.982309 | − | 0.187266i | \(-0.0599626\pi\) |
−0.653332 | + | 0.757072i | \(0.726629\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5424 | + | 9.55077i | 1.44532 | + | 0.834454i | 0.998197 | − | 0.0600198i | \(-0.0191164\pi\) |
0.447120 | + | 0.894474i | \(0.352450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.8350 | − | 0.525224i | −1.02623 | − | 0.0455427i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5424 | − | 18.2600i | −0.900699 | − | 1.56006i | −0.826589 | − | 0.562806i | \(-0.809722\pi\) |
−0.0741101 | − | 0.997250i | \(-0.523612\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8588 | − | 6.26931i | 0.921028 | − | 0.531756i | 0.0370651 | − | 0.999313i | \(-0.488199\pi\) |
0.883963 | + | 0.467557i | \(0.154866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.46719 | + | 4.27330i | 0.206317 | + | 0.357351i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.3751i | 1.85815i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.04695 | + | 5.27747i | −0.249616 | + | 0.432347i | −0.963419 | − | 0.267999i | \(-0.913638\pi\) |
0.713804 | + | 0.700346i | \(0.246971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6983 | −1.03337 | −0.516687 | − | 0.856174i | \(-0.672835\pi\) | ||||
−0.516687 | + | 0.856174i | \(0.672835\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.85369 | − | 6.67479i | 0.309536 | − | 0.536132i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.43438 | + | 14.6088i | −0.673137 | + | 1.16591i | 0.303873 | + | 0.952713i | \(0.401720\pi\) |
−0.977010 | + | 0.213195i | \(0.931613\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.78807 | + | 10.0252i | 0.456164 | + | 0.790100i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1932i | 1.26835i | 0.773189 | + | 0.634175i | \(0.218660\pi\) | ||||
−0.773189 | + | 0.634175i | \(0.781340\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.68872 | − | 11.5852i | −0.517588 | − | 0.896489i | −0.999791 | − | 0.0204298i | \(-0.993497\pi\) |
0.482203 | − | 0.876060i | \(-0.339837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.02827 | − | 10.4413i | 0.463713 | − | 0.803175i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9572 | − | 6.32614i | −0.833060 | − | 0.480967i | 0.0218394 | − | 0.999761i | \(-0.493048\pi\) |
−0.854899 | + | 0.518794i | \(0.826381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.1887 | + | 8.19186i | −1.07257 | + | 0.619246i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.735663 | −0.0549861 | −0.0274930 | − | 0.999622i | \(-0.508752\pi\) | ||||
−0.0274930 | + | 0.999622i | \(0.508752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.42024 | − | 3.12938i | 0.402883 | − | 0.232605i | −0.284844 | − | 0.958574i | \(-0.591942\pi\) |
0.687727 | + | 0.725969i | \(0.258608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.8109 | − | 13.7472i | −1.75061 | − | 1.01072i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.29261 | + | 2.47834i | 0.313907 | + | 0.181234i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.84571i | − | 0.133551i | −0.997768 | − | 0.0667754i | \(-0.978729\pi\) | ||
0.997768 | − | 0.0667754i | \(-0.0212711\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.92024 | − | 2.26335i | −0.282185 | − | 0.162920i | 0.352227 | − | 0.935915i | \(-0.385424\pi\) |
−0.634412 | + | 0.772995i | \(0.718758\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6892 | 0.975318 | 0.487659 | − | 0.873034i | \(-0.337851\pi\) | ||||
0.487659 | + | 0.873034i | \(0.337851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.10389 | − | 1.21468i | 0.149141 | − | 0.0861067i | −0.423572 | − | 0.905862i | \(-0.639224\pi\) |
0.572714 | + | 0.819756i | \(0.305891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.15591 | + | 15.8585i | 0.642619 | + | 1.11305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.0848 | − | 19.1015i | 2.31074 | − | 1.33411i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.29261 | + | 0.190501i | 0.296926 | + | 0.0131772i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.77394 | − | 11.7328i | 0.466337 | − | 0.807720i | −0.532924 | − | 0.846163i | \(-0.678907\pi\) |
0.999261 | + | 0.0384438i | \(0.0122401\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.4864 | − | 18.1787i | 2.14735 | − | 1.23978i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.30773i | − | 0.428197i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.1698i | − | 1.69310i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.80221 | − | 13.5138i | 0.522475 | − | 0.904953i | −0.477183 | − | 0.878804i | \(-0.658342\pi\) |
0.999658 | − | 0.0261490i | \(-0.00832443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.2926 | −1.08138 | −0.540689 | − | 0.841222i | \(-0.681837\pi\) | ||||
−0.540689 | + | 0.841222i | \(0.681837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3118 | 0.747506 | 0.373753 | − | 0.927528i | \(-0.378071\pi\) | ||||
0.373753 | + | 0.927528i | \(0.378071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7977 | − | 22.1662i | 0.838404 | − | 1.45216i | −0.0528253 | − | 0.998604i | \(-0.516823\pi\) |
0.891229 | − | 0.453554i | \(-0.149844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.5983i | 1.60462i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.47834i | − | 0.160310i | −0.996782 | − | 0.0801552i | \(-0.974458\pi\) | ||
0.996782 | − | 0.0801552i | \(-0.0255416\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9148 | + | 8.03370i | −0.896330 | + | 0.517496i | −0.876008 | − | 0.482297i | \(-0.839803\pi\) |
−0.0203221 | + | 0.999793i | \(0.506469\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.641769 | + | 1.11158i | −0.0410011 | + | 0.0710160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0611 | − | 19.3610i | −0.640171 | − | 1.23191i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.45213 | − | 1.41574i | 0.154777 | − | 0.0893604i | −0.420611 | − | 0.907241i | \(-0.638184\pi\) |
0.575388 | + | 0.817881i | \(0.304851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.09936 | − | 3.63620i | −0.131986 | − | 0.228606i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.23113 | − | 1.28814i | 0.139174 | − | 0.0803521i | −0.428796 | − | 0.903401i | \(-0.641062\pi\) |
0.567970 | + | 0.823049i | \(0.307729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.5015 | −1.39817 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.7977 | + | 14.3169i | 1.52909 | + | 0.882821i | 0.999400 | + | 0.0346292i | \(0.0110250\pi\) |
0.529690 | + | 0.848191i | \(0.322308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.7342i | 1.21226i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.2685 | + | 11.1247i | 1.17482 | + | 0.678282i | 0.954810 | − | 0.297215i | \(-0.0960580\pi\) |
0.220009 | + | 0.975498i | \(0.429391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.67004 | − | 1.54155i | −0.162194 | − | 0.0936425i | 0.416706 | − | 0.909041i | \(-0.363184\pi\) |
−0.578900 | + | 0.815399i | \(0.696518\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.14631 | − | 2.97122i | 0.310334 | − | 0.179171i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.25526 | 0.255674 | 0.127837 | − | 0.991795i | \(-0.459197\pi\) | ||||
0.127837 | + | 0.991795i | \(0.459197\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2366 | + | 7.64215i | −0.789629 | + | 0.455892i | −0.839832 | − | 0.542847i | \(-0.817346\pi\) |
0.0502030 | + | 0.998739i | \(0.484013\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.3027 | − | 14.0312i | −1.44465 | − | 0.834068i | −0.446493 | − | 0.894787i | \(-0.647327\pi\) |
−0.998155 | + | 0.0607193i | \(0.980661\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.6327 | − | 27.0766i | 0.922769 | − | 1.59828i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.14177 | − | 7.17375i | −0.243633 | − | 0.421986i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.11158i | 0.0649390i | 0.999473 | + | 0.0324695i | \(0.0103372\pi\) | ||||
−0.999473 | + | 0.0324695i | \(0.989663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.51414 | − | 9.55077i | −0.321045 | − | 0.556067i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.6604 | + | 18.4644i | −0.616509 | + | 1.06783i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.8774 | − | 25.7685i | 0.857521 | − | 1.48527i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.0939 | 1.37961 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4485 | + | 21.5615i | −0.710474 | + | 1.23058i | 0.254205 | + | 0.967150i | \(0.418186\pi\) |
−0.964679 | + | 0.263427i | \(0.915147\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.06236i | − | 0.513879i | −0.966427 | − | 0.256940i | \(-0.917286\pi\) | ||
0.966427 | − | 0.256940i | \(-0.0827141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.19325 | + | 5.53088i | 0.180493 | + | 0.312624i | 0.942049 | − | 0.335476i | \(-0.108897\pi\) |
−0.761555 | + | 0.648100i | \(0.775564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.39611 | + | 1.38339i | −0.134579 | + | 0.0776990i | −0.565778 | − | 0.824558i | \(-0.691424\pi\) |
0.431199 | + | 0.902257i | \(0.358091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.32088 | − | 5.75194i | −0.185934 | − | 0.322047i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.4768 | − | 11.7896i | −1.02808 | − | 0.655993i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.1327 | − | 15.0877i | −1.44958 | − | 0.836916i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0656 | + | 17.4342i | 0.554936 | + | 0.961177i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.6610 | 1.52038 | 0.760192 | − | 0.649698i | \(-0.225105\pi\) | ||||
0.760192 | + | 0.649698i | \(0.225105\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −44.3310 | −2.42206 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9202 | + | 9.19156i | 0.867231 | + | 0.500696i | 0.866427 | − | 0.499304i | \(-0.166411\pi\) |
0.000803838 | 1.00000i | \(0.499744\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.28784i | 0.123893i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.9742i | − | 0.970518i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.73153 | − | 2.73175i | −0.254002 | − | 0.146648i | 0.367594 | − | 0.929987i | \(-0.380182\pi\) |
−0.621595 | + | 0.783339i | \(0.713515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.6700 | 1.21350 | 0.606750 | − | 0.794893i | \(-0.292473\pi\) | ||||
0.606750 | + | 0.794893i | \(0.292473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.03735 | −0.108437 | −0.0542185 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542185 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.28354 | + | 12.6155i | 0.386570 | + | 0.669559i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.7175 | − | 17.7348i | −1.62121 | − | 0.936005i | −0.986597 | − | 0.163174i | \(-0.947827\pi\) |
−0.634611 | − | 0.772832i | \(-0.718840\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9253 | − | 1.68308i | −0.996069 | − | 0.0885831i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.39611 | + | 14.5425i | 0.439472 | + | 0.761188i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.44398 | − | 0.833682i | 0.0753752 | − | 0.0435179i | −0.461839 | − | 0.886964i | \(-0.652810\pi\) |
0.537214 | + | 0.843446i | \(0.319477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.07522 | + | 13.9867i | 0.419245 | + | 0.726153i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.5110i | 0.906686i | 0.891336 | + | 0.453343i | \(0.149769\pi\) | ||||
−0.891336 | + | 0.453343i | \(0.850231\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.8633 | + | 29.2081i | −0.868504 | + | 1.50429i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4905 | 1.15526 | 0.577630 | − | 0.816298i | \(-0.303978\pi\) | ||||
0.577630 | + | 0.816298i | \(0.303978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.1746 | + | 17.6229i | −0.519897 | + | 0.900488i | 0.479836 | + | 0.877358i | \(0.340696\pi\) |
−0.999732 | + | 0.0231292i | \(0.992637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.44852 | − | 7.70506i | 0.226717 | − | 0.392686i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7881 | − | 20.4175i | −0.597679 | − | 1.03521i | −0.993163 | − | 0.116738i | \(-0.962756\pi\) |
0.395484 | − | 0.918473i | \(-0.370577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.4172i | 1.08312i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.2029 | + | 31.5283i | 0.915885 | + | 1.58636i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3633 | + | 28.3421i | −0.821250 | + | 1.42245i | 0.0835014 | + | 0.996508i | \(0.473390\pi\) |
−0.904752 | + | 0.425939i | \(0.859944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.3533 | + | 9.44158i | 0.816645 | + | 0.471490i | 0.849258 | − | 0.527978i | \(-0.177050\pi\) |
−0.0326134 | + | 0.999468i | \(0.510383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0611 | − | 5.80877i | 0.501178 | − | 0.289355i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.16137 | 0.404544 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6646 | − | 9.04395i | 0.774564 | − | 0.447194i | −0.0599366 | − | 0.998202i | \(-0.519090\pi\) |
0.834500 | + | 0.551008i | \(0.185757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.81635 | − | 4.51277i | −0.384617 | − | 0.222059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.0475 | + | 14.4612i | 1.22953 | + | 0.709871i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.353130i | 0.0172515i | 0.999963 | + | 0.00862577i | \(0.00274570\pi\) | ||||
−0.999963 | + | 0.00862577i | \(0.997254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.7977 | + | 14.3169i | 1.20856 | + | 0.697765i | 0.962446 | − | 0.271474i | \(-0.0875112\pi\) |
0.246119 | + | 0.969240i | \(0.420845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.3118 | −1.47034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0767 | − | 9.85922i | 0.826398 | − | 0.477121i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.41478 | + | 11.1107i | 0.308989 | + | 0.535185i | 0.978141 | − | 0.207940i | \(-0.0666760\pi\) |
−0.669152 | + | 0.743125i | \(0.733343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0525 | + | 11.5773i | −0.963664 | + | 0.556371i | −0.897299 | − | 0.441424i | \(-0.854473\pi\) |
−0.0663649 | + | 0.997795i | \(0.521140\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.56108 | + | 16.4745i | 0.409532 | + | 0.788082i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0894 | − | 22.6714i | 0.624721 | − | 1.08205i | −0.363874 | − | 0.931448i | \(-0.618546\pi\) |
0.988595 | − | 0.150600i | \(-0.0481206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.2871 | − | 9.98074i | 0.821337 | − | 0.474199i | −0.0295402 | − | 0.999564i | \(-0.509404\pi\) |
0.850877 | + | 0.525364i | \(0.176071\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 23.4256i | − | 1.11048i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.3224i | 1.43100i | 0.698613 | + | 0.715500i | \(0.253801\pi\) | ||||
−0.698613 | + | 0.715500i | \(0.746199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.67004 | + | 9.82080i | −0.266992 | + | 0.462444i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45.1787 | −2.11801 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5569 | −0.680945 | −0.340473 | − | 0.940254i | \(-0.610587\pi\) | ||||
−0.340473 | + | 0.940254i | \(0.610587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.5147 | + | 32.0683i | −0.862314 | + | 1.49357i | 0.00737587 | + | 0.999973i | \(0.497652\pi\) |
−0.869690 | + | 0.493599i | \(0.835681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.4283i | − | 1.83239i | −0.400735 | − | 0.916194i | \(-0.631245\pi\) | ||
0.400735 | − | 0.916194i | \(-0.368755\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.16620i | 0.285338i | 0.989770 | + | 0.142669i | \(0.0455684\pi\) | ||||
−0.989770 | + | 0.142669i | \(0.954432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.4198 | + | 18.1403i | −1.45083 | + | 0.837639i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.39611 | + | 9.34633i | −0.248113 | + | 0.429745i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.3163 | + | 12.1165i | −1.06983 | + | 0.555943i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.6382 | − | 17.1116i | 1.35420 | − | 0.781849i | 0.365367 | − | 0.930864i | \(-0.380943\pi\) |
0.988835 | + | 0.149015i | \(0.0476101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7215 | − | 35.8907i | −0.944820 | − | 1.63648i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.6700 | + | 13.6659i | −1.07480 | + | 0.620537i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0565 | 0.818220 | 0.409110 | − | 0.912485i | \(-0.365839\pi\) | ||||
0.409110 | + | 0.912485i | \(0.365839\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2871 | + | 8.24869i | 0.644770 | + | 0.372258i | 0.786450 | − | 0.617654i | \(-0.211917\pi\) |
−0.141680 | + | 0.989913i | \(0.545250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.8790i | 1.52583i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3245 | + | 5.96085i | 0.463117 | + | 0.267381i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0237 | + | 16.7569i | 1.29928 | + | 0.750140i | 0.980280 | − | 0.197614i | \(-0.0633193\pi\) |
0.319001 | + | 0.947754i | \(0.396653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.62723 | − | 2.67153i | 0.206318 | − | 0.119118i | −0.393281 | − | 0.919418i | \(-0.628660\pi\) |
0.599599 | + | 0.800301i | \(0.295327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8296 | −0.837904 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.7074 | + | 13.1101i | −1.00649 | + | 0.581096i | −0.910161 | − | 0.414254i | \(-0.864042\pi\) |
−0.0963261 | + | 0.995350i | \(0.530709\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9016 | + | 6.87137i | 0.526494 | + | 0.303972i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.8073 | + | 29.1111i | −0.740617 | + | 1.28279i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.65084 | − | 6.32344i | −0.160564 | − | 0.278105i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.6197i | − | 1.29766i | −0.760933 | − | 0.648830i | \(-0.775259\pi\) | ||
0.760933 | − | 0.648830i | \(-0.224741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.70285 | + | 6.41353i | 0.161914 | + | 0.280444i | 0.935555 | − | 0.353180i | \(-0.114900\pi\) |
−0.773641 | + | 0.633624i | \(0.781566\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.83502 | − | 10.1066i | 0.254178 | − | 0.440248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.42892 | + | 4.20701i | −0.105605 | + | 0.182913i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 57.5844 | 2.49426 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.61350 | + | 2.79466i | −0.0697575 | + | 0.120823i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.381002i | − | 0.0164109i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.30128 | + | 12.6462i | 0.313907 | + | 0.543702i | 0.979204 | − | 0.202876i | \(-0.0650288\pi\) |
−0.665298 | + | 0.746578i | \(0.731695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.92531 | + | 1.11158i | −0.0824711 | + | 0.0476147i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.8022 | − | 36.0305i | −0.889438 | − | 1.54055i | −0.840541 | − | 0.541749i | \(-0.817762\pi\) |
−0.0488977 | − | 0.998804i | \(-0.515571\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5424 | + | 26.0603i | 0.576926 | + | 1.11021i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.8027 | + | 14.8972i | 1.09724 | + | 0.633494i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.2125 | + | 38.4731i | 0.941172 | + | 1.63016i | 0.763240 | + | 0.646115i | \(0.223607\pi\) |
0.177931 | + | 0.984043i | \(0.443059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.8023 | 2.31789 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.2545 | 1.65438 | 0.827189 | − | 0.561923i | \(-0.189938\pi\) | ||||
0.827189 | + | 0.561923i | \(0.189938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.1378 | − | 13.9359i | −1.01548 | − | 0.586290i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.2761i | 1.14347i | 0.820438 | + | 0.571736i | \(0.193730\pi\) | ||||
−0.820438 | + | 0.571736i | \(0.806270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.07155i | − | 0.0448429i | −0.999749 | − | 0.0224214i | \(-0.992862\pi\) | ||
0.999749 | − | 0.0224214i | \(-0.00713757\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.2366 | + | 12.8383i | 0.927330 | + | 0.535394i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6135 | 0.733259 | 0.366630 | − | 0.930367i | \(-0.380512\pi\) | ||||
0.366630 | + | 0.930367i | \(0.380512\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.6700 | 0.981999 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.92892 | − | 5.07303i | −0.121303 | − | 0.210103i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.2366 | + | 11.1063i | 0.793979 | + | 0.458404i | 0.841361 | − | 0.540473i | \(-0.181755\pi\) |
−0.0473824 | + | 0.998877i | \(0.515088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.448517 | − | 10.1066i | 0.0184808 | − | 0.416433i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.10896 | + | 10.5810i | 0.250865 | + | 0.434511i | 0.963764 | − | 0.266756i | \(-0.0859517\pi\) |
−0.712899 | + | 0.701266i | \(0.752618\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.3027 | + | 22.6914i | −1.61126 | + | 0.930259i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4955 | − | 23.3748i | −0.551410 | − | 0.955070i | −0.998173 | − | 0.0604175i | \(-0.980757\pi\) |
0.446763 | − | 0.894652i | \(-0.352577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.4514i | 0.997392i | 0.866777 | + | 0.498696i | \(0.166188\pi\) | ||||
−0.866777 | + | 0.498696i | \(0.833812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.6514 | − | 28.8410i | 0.676974 | − | 1.17255i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.7175 | −0.556777 | −0.278388 | − | 0.960469i | \(-0.589800\pi\) | ||||
−0.278388 | + | 0.960469i | \(0.589800\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.5388 | + | 32.1101i | −0.750000 | + | 1.29904i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6646 | + | 35.7921i | −0.834634 | + | 1.44563i | 0.0596932 | + | 0.998217i | \(0.480988\pi\) |
−0.894328 | + | 0.447413i | \(0.852346\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.9157 | − | 22.3707i | −0.519967 | − | 0.900609i | −0.999731 | − | 0.0232112i | \(-0.992611\pi\) |
0.479764 | − | 0.877398i | \(-0.340722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.1873i | 1.53488i | 0.641121 | + | 0.767440i | \(0.278470\pi\) | ||||
−0.641121 | + | 0.767440i | \(0.721530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.58575 | − | 16.6030i | −0.384045 | − | 0.665185i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.40064 | − | 16.2824i | 0.376026 | − | 0.651296i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.0529 | − | 20.8152i | −1.43752 | − | 0.829955i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.6090 | + | 13.0533i | −0.900048 | + | 0.519643i | −0.877216 | − | 0.480096i | \(-0.840602\pi\) |
−0.0228325 | + | 0.999739i | \(0.507268\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.6236 | 0.977159 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.67551 | + | 0.967354i | −0.0663860 | + | 0.0383280i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.4249 | + | 6.59617i | 0.451257 | + | 0.260533i | 0.708361 | − | 0.705851i | \(-0.249435\pi\) |
−0.257104 | + | 0.966384i | \(0.582768\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.2790 | + | 16.3269i | 1.11521 | + | 0.643870i | 0.940175 | − | 0.340692i | \(-0.110661\pi\) |
0.175040 | + | 0.984561i | \(0.443995\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 23.5235i | − | 0.924805i | −0.886670 | − | 0.462403i | \(-0.846988\pi\) | ||
0.886670 | − | 0.462403i | \(-0.153012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.83502 | + | 1.63680i | 0.111284 | + | 0.0642500i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −49.5953 | −1.94082 | −0.970408 | − | 0.241471i | \(-0.922370\pi\) | ||||
−0.970408 | + | 0.241471i | \(0.922370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.9354 | − | 31.7170i | 2.14651 | − | 1.23929i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.49546 | − | 12.9825i | −0.291982 | − | 0.505727i | 0.682296 | − | 0.731076i | \(-0.260981\pi\) |
−0.974278 | + | 0.225348i | \(0.927648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5953 | + | 11.3134i | −0.762171 | + | 0.440040i | −0.830075 | − | 0.557652i | \(-0.811702\pi\) |
0.0679038 | + | 0.997692i | \(0.478369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.1619 | + | 33.1651i | −0.820623 | + | 1.28609i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.3492 | − | 24.8535i | 0.555602 | − | 0.962330i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.19378 | + | 3.57598i | −0.239108 | + | 0.138049i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.1398i | − | 1.00762i | −0.863815 | − | 0.503808i | \(-0.831932\pi\) | ||
0.863815 | − | 0.503808i | \(-0.168068\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.42199i | − | 0.169951i | −0.996383 | − | 0.0849755i | \(-0.972919\pi\) | ||
0.996383 | − | 0.0849755i | \(-0.0270812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.1842 | + | 19.3716i | −0.429209 | + | 0.743413i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.2361 | −0.697784 | −0.348892 | − | 0.937163i | \(-0.613442\pi\) | ||||
−0.348892 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −70.0203 | −2.67534 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.8729 | + | 25.7606i | −0.566612 | + | 0.981401i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.05341i | − | 0.344408i | −0.985061 | − | 0.172204i | \(-0.944911\pi\) | ||
0.985061 | − | 0.172204i | \(-0.0550888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 41.6393i | − | 1.57947i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.0950 | − | 28.9223i | 1.89748 | − | 1.09551i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6514 | − | 18.4487i | 0.402297 | − | 0.696798i | −0.591706 | − | 0.806154i | \(-0.701545\pi\) |
0.994003 | + | 0.109356i | \(0.0348787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.0529 | − | 1.59999i | −1.35976 | − | 0.0603446i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.3455 | + | 7.70506i | −0.501911 | + | 0.289778i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50546 | − | 4.33959i | −0.0940947 | − | 0.162977i | 0.815136 | − | 0.579270i | \(-0.196662\pi\) |
−0.909230 | + | 0.416293i | \(0.863329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.56108 | + | 4.94274i | −0.320615 | + | 0.185107i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.3865 | 0.612821 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.2366 | + | 16.3024i | 1.05305 | + | 0.607977i | 0.923501 | − | 0.383596i | \(-0.125315\pi\) |
0.129546 | + | 0.991573i | \(0.458648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5102i | 1.02453i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.1751 | + | 20.3084i | 1.30637 | + | 0.754233i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.8113 | − | 9.12865i | −0.586408 | − | 0.338563i | 0.177268 | − | 0.984163i | \(-0.443274\pi\) |
−0.763676 | + | 0.645600i | \(0.776607\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.6747 | − | 27.5250i | 1.76331 | − | 1.01805i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.0275 | 1.70006 | 0.850032 | − | 0.526731i | \(-0.176583\pi\) | ||||
0.850032 | + | 0.526731i | \(0.176583\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3961 | − | 6.57954i | 0.419781 | − | 0.242361i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.5607 | + | 14.7575i | 0.940265 | + | 0.542862i | 0.890043 | − | 0.455876i | \(-0.150674\pi\) |
0.0502216 | + | 0.998738i | \(0.484007\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.18365 | − | 12.4424i | 0.263543 | − | 0.456469i | −0.703638 | − | 0.710558i | \(-0.748442\pi\) |
0.967181 | + | 0.254089i | \(0.0817757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.1186 | + | 17.5259i | 0.370715 | + | 0.642098i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.64097i | 0.0964989i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.90157 | − | 8.48977i | −0.178861 | − | 0.309796i | 0.762630 | − | 0.646835i | \(-0.223908\pi\) |
−0.941491 | + | 0.337039i | \(0.890575\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.0848 | + | 36.5200i | −0.767355 | + | 1.32910i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5620 | − | 21.7580i | 0.456574 | − | 0.790810i | −0.542203 | − | 0.840247i | \(-0.682410\pi\) |
0.998777 | + | 0.0494379i | \(0.0157430\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.8778 | 0.901821 | 0.450910 | − | 0.892569i | \(-0.351099\pi\) | ||||
0.450910 | + | 0.892569i | \(0.351099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.909714 | + | 1.57567i | −0.0329339 | + | 0.0570431i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 16.6232i | − | 0.600229i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.36876 | + | 16.2272i | 0.337846 | + | 0.585167i | 0.984027 | − | 0.178017i | \(-0.0569683\pi\) |
−0.646181 | + | 0.763184i | \(0.723635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.9627 | − | 10.9481i | 0.682039 | − | 0.393776i | −0.118584 | − | 0.992944i | \(-0.537835\pi\) |
0.800623 | + | 0.599169i | \(0.204502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.99546 | − | 12.1165i | −0.251284 | − | 0.435237i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.9728 | − | 42.2719i | 0.966400 | − | 1.51455i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.74474 | − | 2.16202i | −0.133997 | − | 0.0773633i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.0096 | + | 48.5141i | 0.999706 | + | 1.73154i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.9336 | −1.53042 | −0.765208 | − | 0.643783i | \(-0.777364\pi\) | ||||
−0.765208 | + | 0.643783i | \(0.777364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.8104 | −0.811043 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.4517 | + | 18.1587i | 1.11688 | + | 0.644833i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.30208i | 0.0461219i | 0.999734 | + | 0.0230610i | \(0.00734119\pi\) | ||||
−0.999734 | + | 0.0230610i | \(0.992659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.2452i | 1.31764i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.31675 | − | 2.49228i | −0.152335 | − | 0.0879505i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.4431 | 1.35494 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.3593 | −1.10253 | −0.551267 | − | 0.834329i | \(-0.685855\pi\) | ||||
−0.551267 | + | 0.834329i | \(0.685855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0373465 | + | 0.0646860i | 0.00131141 | + | 0.00227143i | 0.866680 | − | 0.498864i | \(-0.166249\pi\) |
−0.865369 | + | 0.501135i | \(0.832916\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.5712 | + | 26.8879i | 1.63132 | + | 0.941842i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.6696 | − | 40.2296i | 0.898067 | − | 1.40746i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8350 | + | 20.4989i | 0.413045 | + | 0.715415i | 0.995221 | − | 0.0976477i | \(-0.0311318\pi\) |
−0.582176 | + | 0.813063i | \(0.697799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.2070 | + | 16.8627i | −1.01809 | + | 0.587795i | −0.913551 | − | 0.406725i | \(-0.866671\pi\) |
−0.104541 | + | 0.994521i | \(0.533337\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.5990 | − | 20.0900i | −0.403335 | − | 0.698597i | 0.590791 | − | 0.806825i | \(-0.298816\pi\) |
−0.994126 | + | 0.108228i | \(0.965483\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6537i | 0.474214i | 0.971484 | + | 0.237107i | \(0.0761992\pi\) | ||||
−0.971484 | + | 0.237107i | \(0.923801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.971726 | + | 1.68308i | −0.0336683 | + | 0.0583152i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.4249 | −1.53739 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.48639 | − | 12.9668i | 0.258459 | − | 0.447664i | −0.707370 | − | 0.706843i | \(-0.750119\pi\) |
0.965829 | + | 0.259179i | \(0.0834520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.19832 | − | 14.1999i | 0.282701 | − | 0.489652i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.0192 | − | 34.6743i | −0.688681 | − | 1.19283i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.2550i | − | 0.936492i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.6322 | + | 30.5398i | 0.604423 | + | 1.04689i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4909 | + | 19.9029i | −0.393442 | + | 0.681461i | −0.992901 | − | 0.118944i | \(-0.962049\pi\) |
0.599459 | + | 0.800405i | \(0.295382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.45213 | − | 1.41574i | −0.0837630 | − | 0.0483606i | 0.457533 | − | 0.889192i | \(-0.348733\pi\) |
−0.541296 | + | 0.840832i | \(0.682066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.42839 | − | 3.71143i | 0.219334 | − | 0.126632i | −0.386308 | − | 0.922370i | \(-0.626250\pi\) |
0.605642 | + | 0.795737i | \(0.292916\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.96080 | 0.100787 | 0.0503934 | − | 0.998729i | \(-0.483952\pi\) | ||||
0.0503934 | + | 0.998729i | \(0.483952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.3876 | + | 21.0084i | −1.23721 | + | 0.714306i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.35876 | − | 5.40328i | −0.317474 | − | 0.183294i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.8689 | − | 33.4106i | −1.96081 | − | 1.13208i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.28073i | 0.313746i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.3133 | + | 27.8937i | 1.63142 | + | 0.941903i | 0.983655 | + | 0.180065i | \(0.0576309\pi\) |
0.647768 | + | 0.761837i | \(0.275702\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.9627 | −1.54852 | −0.774261 | − | 0.632867i | \(-0.781878\pi\) | ||||
−0.774261 | + | 0.632867i | \(0.781878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.73659 | + | 1.57997i | −0.0920936 | + | 0.0531703i | −0.545340 | − | 0.838215i | \(-0.683599\pi\) |
0.453246 | + | 0.891386i | \(0.350266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.7453 | − | 29.0036i | −0.562251 | − | 0.973847i | −0.997300 | − | 0.0734403i | \(-0.976602\pi\) |
0.435049 | − | 0.900407i | \(-0.356731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.4521 | − | 10.0760i | 0.585325 | − | 0.337938i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.8880 | + | 28.6496i | 0.498207 | + | 0.958722i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.22153 | + | 2.11575i | −0.0408311 | + | 0.0707216i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.5424 | + | 7.81871i | −0.451665 | + | 0.260769i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.8802i | 0.995455i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 20.7846i | − | 0.690904i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.37743 | − | 16.2422i | 0.311373 | − | 0.539313i | −0.667287 | − | 0.744800i | \(-0.732545\pi\) |
0.978660 | + | 0.205487i | \(0.0658780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.4540 | −1.00899 | −0.504493 | − | 0.863416i | \(-0.668320\pi\) | ||||
−0.504493 | + | 0.863416i | \(0.668320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.58522 | −0.284129 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.9572 | − | 44.9592i | 0.857182 | − | 1.48468i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.8834i | − | 0.787841i | −0.919144 | − | 0.393921i | \(-0.871118\pi\) | ||
0.919144 | − | 0.393921i | \(-0.128882\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.9573i | 0.722734i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.2230 | + | 24.9548i | −1.42116 | + | 0.820509i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2457 | − | 17.7460i | 0.336149 | − | 0.582228i | −0.647556 | − | 0.762018i | \(-0.724209\pi\) |
0.983705 | + | 0.179791i | \(0.0575420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0746930 | + | 1.68308i | −0.00244796 | + | 0.0551607i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.2553 | − | 8.23028i | 0.466197 | − | 0.269159i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.68418 | + | 9.84529i | 0.185694 | + | 0.321632i | 0.943810 | − | 0.330488i | \(-0.107213\pi\) |
−0.758116 | + | 0.652120i | \(0.773880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.51053 | − | 2.60415i | 0.147039 | − | 0.0848930i | −0.424676 | − | 0.905346i | \(-0.639612\pi\) |
0.571715 | + | 0.820453i | \(0.306278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −48.9992 | −1.59563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.5525 | + | 29.7639i | 1.67523 | + | 0.967196i | 0.964632 | + | 0.263600i | \(0.0849099\pi\) |
0.710600 | + | 0.703596i | \(0.248423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.3113i | 0.821640i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.6988 | − | 18.8787i | −1.05922 | − | 0.611541i | −0.134003 | − | 0.990981i | \(-0.542783\pi\) |
−0.925216 | + | 0.379440i | \(0.876117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.30820 | − | 3.06469i | −0.171769 | − | 0.0991711i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.6272 | + | 28.6523i | −1.60255 | + | 0.925231i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6135 | −0.826242 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.0187 | + | 7.51633i | −0.419086 | + | 0.241959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.7366 | + | 20.6325i | 1.14921 | + | 0.663497i | 0.948695 | − | 0.316193i | \(-0.102405\pi\) |
0.200516 | + | 0.979690i | \(0.435738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.3209 | − | 52.5173i | 0.973043 | − | 1.68536i | 0.286797 | − | 0.957991i | \(-0.407409\pi\) |
0.686246 | − | 0.727370i | \(-0.259257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0388 | − | 29.5121i | −0.546239 | − | 0.946114i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20.5016i | − | 0.655903i | −0.944695 | − | 0.327951i | \(-0.893642\pi\) | ||
0.944695 | − | 0.327951i | \(-0.106358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.47679 | + | 6.02198i | 0.111119 | + | 0.192463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.36237 | − | 7.55584i | 0.139138 | − | 0.240994i | −0.788033 | − | 0.615633i | \(-0.788900\pi\) |
0.927171 | + | 0.374640i | \(0.122234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.7302 | − | 39.3699i | 0.724244 | − | 1.25443i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.6319 | −1.48281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6227 | + | 35.7196i | −0.655102 | + | 1.13467i | 0.326767 | + | 0.945105i | \(0.394041\pi\) |
−0.981868 | + | 0.189564i | \(0.939293\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.06765i | − | 0.255762i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.46265 | − | 2.53339i | −0.0463227 | − | 0.0802333i | 0.841934 | − | 0.539580i | \(-0.181417\pi\) |
−0.888257 | + | 0.459347i | \(0.848084\pi\) | |||||||
\(998\) | 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.bm.o.559.3 | 6 | ||
3.2 | odd | 2 | 912.2.bb.f.559.1 | yes | 6 | ||
4.3 | odd | 2 | 2736.2.bm.n.559.3 | 6 | |||
12.11 | even | 2 | 912.2.bb.e.559.1 | yes | 6 | ||
19.12 | odd | 6 | 2736.2.bm.n.1855.3 | 6 | |||
57.50 | even | 6 | 912.2.bb.e.31.1 | ✓ | 6 | ||
76.31 | even | 6 | inner | 2736.2.bm.o.1855.3 | 6 | ||
228.107 | odd | 6 | 912.2.bb.f.31.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.bb.e.31.1 | ✓ | 6 | 57.50 | even | 6 | ||
912.2.bb.e.559.1 | yes | 6 | 12.11 | even | 2 | ||
912.2.bb.f.31.1 | yes | 6 | 228.107 | odd | 6 | ||
912.2.bb.f.559.1 | yes | 6 | 3.2 | odd | 2 | ||
2736.2.bm.n.559.3 | 6 | 4.3 | odd | 2 | |||
2736.2.bm.n.1855.3 | 6 | 19.12 | odd | 6 | |||
2736.2.bm.o.559.3 | 6 | 1.1 | even | 1 | trivial | ||
2736.2.bm.o.1855.3 | 6 | 76.31 | even | 6 | inner |