Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (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: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.6 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.c.2591.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −1.45856 | − | 0.842100i | −0.652288 | − | 0.376599i | 0.137044 | − | 0.990565i | \(-0.456240\pi\) |
−0.789332 | + | 0.613966i | \(0.789573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.172239i | − | 0.0651001i | −0.999470 | − | 0.0325501i | \(-0.989637\pi\) | ||
0.999470 | − | 0.0325501i | \(-0.0103628\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.01814 | 0.608492 | 0.304246 | − | 0.952593i | \(-0.401595\pi\) | ||||
0.304246 | + | 0.952593i | \(0.401595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.109175 | − | 0.189097i | −0.0302798 | − | 0.0524461i | 0.850488 | − | 0.525994i | \(-0.176306\pi\) |
−0.880768 | + | 0.473548i | \(0.842973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.01452 | + | 2.89514i | 1.21620 | + | 0.702174i | 0.964103 | − | 0.265528i | \(-0.0855462\pi\) |
0.252098 | + | 0.967702i | \(0.418880\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.23503 | + | 2.92140i | 0.742167 | + | 0.670215i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.27652 | − | 7.40715i | −0.891717 | − | 1.54450i | −0.837816 | − | 0.545952i | \(-0.816168\pi\) |
−0.0539000 | − | 0.998546i | \(-0.517165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.08173 | − | 1.87362i | −0.216347 | − | 0.374724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.957321 | − | 0.552710i | 0.177770 | − | 0.102636i | −0.408474 | − | 0.912770i | \(-0.633939\pi\) |
0.586245 | + | 0.810134i | \(0.300606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.93488i | 1.60475i | 0.596819 | + | 0.802376i | \(0.296431\pi\) | ||||
−0.596819 | + | 0.802376i | \(0.703569\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.145042 | + | 0.251221i | −0.0245166 | + | 0.0424640i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.80687 | −1.11904 | −0.559521 | − | 0.828816i | \(-0.689015\pi\) | ||||
−0.559521 | + | 0.828816i | \(0.689015\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.97185 | − | 3.44785i | −0.932646 | − | 0.538463i | −0.0449983 | − | 0.998987i | \(-0.514328\pi\) |
−0.887647 | + | 0.460524i | \(0.847662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.91085 | + | 2.83528i | 0.748897 | + | 0.432376i | 0.825295 | − | 0.564702i | \(-0.191009\pi\) |
−0.0763983 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.15411 | + | 1.99898i | 0.168345 | + | 0.291581i | 0.937838 | − | 0.347073i | \(-0.112825\pi\) |
−0.769493 | + | 0.638655i | \(0.779491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.97033 | 0.995762 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.55596 | + | 2.05304i | −0.488449 | + | 0.282006i | −0.723931 | − | 0.689872i | \(-0.757667\pi\) |
0.235482 | + | 0.971879i | \(0.424333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.94358 | − | 1.69948i | −0.396912 | − | 0.229157i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.14055 | − | 8.90369i | 0.669243 | − | 1.15916i | −0.308874 | − | 0.951103i | \(-0.599952\pi\) |
0.978116 | − | 0.208059i | \(-0.0667147\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.39443 | + | 9.34342i | 0.690686 | + | 1.19630i | 0.971614 | + | 0.236574i | \(0.0760245\pi\) |
−0.280928 | + | 0.959729i | \(0.590642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.367746i | 0.0456133i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6245 | − | 6.13404i | 1.29798 | − | 0.749392i | 0.317929 | − | 0.948115i | \(-0.397013\pi\) |
0.980056 | + | 0.198723i | \(0.0636794\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.30373 | − | 12.6504i | 0.866794 | − | 1.50133i | 0.00153867 | − | 0.999999i | \(-0.499510\pi\) |
0.865255 | − | 0.501332i | \(-0.167156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.47256 | + | 4.28260i | −0.289391 | + | 0.501240i | −0.973665 | − | 0.227985i | \(-0.926786\pi\) |
0.684273 | + | 0.729226i | \(0.260119\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.347602i | − | 0.0396129i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.20917 | + | 3.00752i | 0.586078 | + | 0.338372i | 0.763545 | − | 0.645755i | \(-0.223457\pi\) |
−0.177467 | + | 0.984127i | \(0.556790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.8767 | 1.52317 | 0.761584 | − | 0.648066i | \(-0.224422\pi\) | ||||
0.761584 | + | 0.648066i | \(0.224422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.87599 | − | 8.44547i | −0.528876 | − | 0.916039i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.701447 | − | 0.404980i | 0.0743532 | − | 0.0429278i | −0.462362 | − | 0.886691i | \(-0.652998\pi\) |
0.536716 | + | 0.843763i | \(0.319665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0325699 | + | 0.0188042i | −0.00341425 | + | 0.00197122i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.25838 | − | 6.98526i | −0.231705 | − | 0.716672i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.990995 | + | 1.71645i | −0.100620 | + | 0.174279i | −0.911940 | − | 0.410323i | \(-0.865416\pi\) |
0.811320 | + | 0.584602i | \(0.198749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.6486 | − | 6.14795i | 1.05957 | − | 0.611744i | 0.134258 | − | 0.990946i | \(-0.457135\pi\) |
0.925314 | + | 0.379203i | \(0.123802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.2681i | − | 1.20881i | −0.796678 | − | 0.604404i | \(-0.793411\pi\) | ||
0.796678 | − | 0.604404i | \(-0.206589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.30553 | 0.319558 | 0.159779 | − | 0.987153i | \(-0.448922\pi\) | ||||
0.159779 | + | 0.987153i | \(0.448922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.27625 | − | 14.3349i | 0.792721 | − | 1.37303i | −0.131556 | − | 0.991309i | \(-0.541997\pi\) |
0.924276 | − | 0.381724i | \(-0.124669\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.44267i | − | 0.512004i | −0.966676 | − | 0.256002i | \(-0.917595\pi\) | ||
0.966676 | − | 0.256002i | \(-0.0824053\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4050i | 1.34328i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.498655 | − | 0.863695i | 0.0457116 | − | 0.0791748i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.92711 | −0.629737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0647i | 1.07910i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4187 | − | 8.90200i | 1.36819 | − | 0.789925i | 0.377493 | − | 0.926013i | \(-0.376786\pi\) |
0.990697 | + | 0.136088i | \(0.0434530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.39893 | − | 12.8153i | 0.646448 | − | 1.11968i | −0.337517 | − | 0.941319i | \(-0.609587\pi\) |
0.983965 | − | 0.178361i | \(-0.0570795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.503178 | − | 0.557198i | 0.0436310 | − | 0.0483152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.27194 | + | 5.35315i | −0.792155 | + | 0.457351i | −0.840721 | − | 0.541469i | \(-0.817868\pi\) |
0.0485657 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.43914 | − | 1.40824i | 0.206885 | − | 0.119445i | −0.392978 | − | 0.919548i | \(-0.628555\pi\) |
0.599863 | + | 0.800103i | \(0.295222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.220331 | − | 0.381625i | −0.0184250 | − | 0.0319131i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.86175 | −0.154610 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.18752 | + | 4.72707i | 0.670748 | + | 0.387256i | 0.796360 | − | 0.604823i | \(-0.206756\pi\) |
−0.125612 | + | 0.992079i | \(0.540089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.56225i | 0.696786i | 0.937349 | + | 0.348393i | \(0.113272\pi\) | ||||
−0.937349 | + | 0.348393i | \(0.886728\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.52406 | − | 13.0321i | 0.604347 | − | 1.04676i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.59434 | + | 6.22558i | −0.286860 | + | 0.496856i | −0.973058 | − | 0.230558i | \(-0.925945\pi\) |
0.686199 | + | 0.727414i | \(0.259278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.27580 | + | 0.736583i | −0.100547 | + | 0.0580508i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1222i | 1.18446i | 0.805770 | + | 0.592229i | \(0.201752\pi\) | ||||
−0.805770 | + | 0.592229i | \(0.798248\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.50773 | − | 2.61146i | −0.116671 | − | 0.202081i | 0.801775 | − | 0.597626i | \(-0.203889\pi\) |
−0.918447 | + | 0.395545i | \(0.870556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.47616 | − | 11.2170i | 0.498166 | − | 0.862849i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.1827 | − | 7.61104i | −1.00226 | − | 0.578657i | −0.0933459 | − | 0.995634i | \(-0.529756\pi\) |
−0.908917 | + | 0.416977i | \(0.863090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.322710 | + | 0.186317i | −0.0243946 | + | 0.0140842i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5866 | 1.01551 | 0.507756 | − | 0.861501i | \(-0.330475\pi\) | ||||
0.507756 | + | 0.861501i | \(0.330475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.64864 | + | 14.9799i | 0.642848 | + | 1.11345i | 0.984794 | + | 0.173726i | \(0.0555807\pi\) |
−0.341946 | + | 0.939720i | \(0.611086\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.92822 | + | 5.73206i | 0.729938 | + | 0.421430i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1200 | + | 5.84279i | 0.740049 | + | 0.427267i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5893 | −0.910932 | −0.455466 | − | 0.890253i | \(-0.650527\pi\) | ||||
−0.455466 | + | 0.890253i | \(0.650527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.29786 | + | 12.6403i | −0.525311 | + | 0.909866i | 0.474254 | + | 0.880388i | \(0.342718\pi\) |
−0.999565 | + | 0.0294780i | \(0.990615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.6636i | − | 0.902247i | −0.892461 | − | 0.451124i | \(-0.851023\pi\) | ||
0.892461 | − | 0.451124i | \(-0.148977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.38255 | − | 4.26232i | 0.523335 | − | 0.302148i | −0.214963 | − | 0.976622i | \(-0.568963\pi\) |
0.738298 | + | 0.674474i | \(0.235630\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0951980 | − | 0.164888i | −0.00668159 | − | 0.0115729i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.80687 | + | 10.0578i | 0.405569 | + | 0.702466i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.52875 | + | 5.89579i | 0.451603 | + | 0.407820i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.73783 | − | 4.46744i | −0.532694 | − | 0.307551i | 0.209419 | − | 0.977826i | \(-0.432843\pi\) |
−0.742113 | + | 0.670275i | \(0.766176\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.77518 | − | 8.27085i | −0.325664 | − | 0.564067i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.53893 | 0.104470 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.26431i | − | 0.0850467i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.20595 | − | 1.27361i | −0.147721 | − | 0.0852870i | 0.424317 | − | 0.905513i | \(-0.360514\pi\) |
−0.572039 | + | 0.820226i | \(0.693847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.290085 | −0.0192536 | −0.00962679 | − | 0.999954i | \(-0.503064\pi\) | ||||
−0.00962679 | + | 0.999954i | \(0.503064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.65505 | 0.307614 | 0.153807 | − | 0.988101i | \(-0.450847\pi\) | ||||
0.153807 | + | 0.988101i | \(0.450847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.69124 | − | 5.59524i | −0.634894 | − | 0.366556i | 0.147751 | − | 0.989025i | \(-0.452797\pi\) |
−0.782645 | + | 0.622468i | \(0.786130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.88751i | − | 0.253593i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.74889 | 0.177811 | 0.0889054 | − | 0.996040i | \(-0.471663\pi\) | ||||
0.0889054 | + | 0.996040i | \(0.471663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3305 | − | 24.8212i | −0.923111 | − | 1.59888i | −0.794571 | − | 0.607171i | \(-0.792304\pi\) |
−0.128540 | − | 0.991704i | \(-0.541029\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.1667 | − | 5.86972i | −0.649524 | − | 0.375003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.199242 | − | 0.930680i | 0.0126775 | − | 0.0592178i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.07433 | + | 10.5211i | 0.383408 | + | 0.664083i | 0.991547 | − | 0.129748i | \(-0.0414168\pi\) |
−0.608139 | + | 0.793831i | \(0.708084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.63062 | − | 14.9487i | −0.542603 | − | 0.939815i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.83271 | − | 1.05811i | 0.114321 | − | 0.0660033i | −0.441749 | − | 0.897139i | \(-0.645642\pi\) |
0.556070 | + | 0.831135i | \(0.312309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.17241i | 0.0728497i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.59382 | − | 13.1529i | 0.468255 | − | 0.811041i | −0.531087 | − | 0.847317i | \(-0.678216\pi\) |
0.999342 | + | 0.0362761i | \(0.0115496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.91545 | 0.424813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.07559 | − | 0.620993i | −0.0655800 | − | 0.0378626i | 0.466851 | − | 0.884336i | \(-0.345388\pi\) |
−0.532431 | + | 0.846473i | \(0.678722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.93201 | + | 1.11545i | 0.117361 | + | 0.0677585i | 0.557531 | − | 0.830156i | \(-0.311749\pi\) |
−0.440170 | + | 0.897914i | \(0.645082\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.18309 | − | 3.78123i | −0.131645 | − | 0.228017i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6434 | −1.00000 | −0.500002 | − | 0.866024i | \(-0.666668\pi\) | ||||
−0.500002 | + | 0.866024i | \(0.666668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4047 | − | 8.31658i | 0.859314 | − | 0.496125i | −0.00446838 | − | 0.999990i | \(-0.501422\pi\) |
0.863783 | + | 0.503865i | \(0.168089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.7174 | + | 11.9612i | 1.23152 | + | 0.711020i | 0.967347 | − | 0.253455i | \(-0.0815670\pi\) |
0.264175 | + | 0.964475i | \(0.414900\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.593853 | + | 1.02858i | −0.0350540 | + | 0.0607153i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.26364 | + | 14.3130i | 0.486096 | + | 0.841944i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.6769i | 1.61690i | 0.588565 | + | 0.808450i | \(0.299693\pi\) | ||||
−0.588565 | + | 0.808450i | \(0.700307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.9956 | + | 8.65772i | −0.873078 | + | 0.504072i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.933782 | + | 1.61736i | −0.0540020 | + | 0.0935342i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.488345 | − | 0.845838i | 0.0281477 | − | 0.0487533i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 18.1706i | − | 1.04045i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.10845 | − | 5.25876i | −0.519846 | − | 0.300133i | 0.217025 | − | 0.976166i | \(-0.430365\pi\) |
−0.736872 | + | 0.676032i | \(0.763698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.4262 | −1.72531 | −0.862655 | − | 0.505793i | \(-0.831200\pi\) | ||||
−0.862655 | + | 0.505793i | \(0.831200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.83955 | + | 13.5785i | 0.443117 | + | 0.767502i | 0.997919 | − | 0.0644810i | \(-0.0205392\pi\) |
−0.554802 | + | 0.831983i | \(0.687206\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.875384 | + | 0.505403i | −0.0491665 | + | 0.0283863i | −0.524382 | − | 0.851483i | \(-0.675704\pi\) |
0.475215 | + | 0.879870i | \(0.342370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.93201 | − | 1.11545i | 0.108172 | − | 0.0624530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.76431 | + | 24.0153i | 0.432017 | + | 1.33625i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.236197 | + | 0.409106i | −0.0131019 | + | 0.0226931i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.344302 | − | 0.198783i | 0.0189820 | − | 0.0109593i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1733i | 1.60351i | 0.597654 | + | 0.801754i | \(0.296099\pi\) | ||||
−0.597654 | + | 0.801754i | \(0.703901\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.6619 | −1.12888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.90025 | − | 13.6836i | 0.430354 | − | 0.745396i | −0.566549 | − | 0.824028i | \(-0.691722\pi\) |
0.996904 | + | 0.0786323i | \(0.0250553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0318i | 0.976479i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.40623i | − | 0.129924i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.06526 | − | 8.77329i | 0.271917 | − | 0.470975i | −0.697435 | − | 0.716648i | \(-0.745676\pi\) |
0.969353 | + | 0.245673i | \(0.0790089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6980 | −0.893821 | −0.446910 | − | 0.894579i | \(-0.647476\pi\) | ||||
−0.446910 | + | 0.894579i | \(0.647476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.5505i | 1.35991i | 0.733252 | + | 0.679957i | \(0.238001\pi\) | ||||
−0.733252 | + | 0.679957i | \(0.761999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.3059 | + | 12.3010i | −1.13080 | + | 0.652867i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.7027 | + | 25.4658i | −0.775977 | + | 1.34403i | 0.158267 | + | 0.987396i | \(0.449409\pi\) |
−0.934244 | + | 0.356635i | \(0.883924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.93087 | + | 18.9016i | 0.101625 | + | 0.994823i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.21275 | − | 4.16429i | 0.377533 | − | 0.217969i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.27753 | + | 4.77904i | −0.432084 | + | 0.249464i | −0.700234 | − | 0.713913i | \(-0.746921\pi\) |
0.268150 | + | 0.963377i | \(0.413588\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.353612 | + | 0.612475i | 0.0183586 | + | 0.0317981i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7961 | 1.07678 | 0.538390 | − | 0.842696i | \(-0.319033\pi\) | ||||
0.538390 | + | 0.842696i | \(0.319033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.209032 | − | 0.120685i | −0.0107657 | − | 0.00621557i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.16095i | 0.162367i | 0.996699 | + | 0.0811836i | \(0.0258700\pi\) | ||||
−0.996699 | + | 0.0811836i | \(0.974130\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0608 | + | 17.4258i | −0.514081 | + | 0.890415i | 0.485785 | + | 0.874078i | \(0.338534\pi\) |
−0.999867 | + | 0.0163367i | \(0.994800\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.292716 | + | 0.506999i | −0.0149182 | + | 0.0258390i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.05815 | + | 0.610921i | −0.0536501 | + | 0.0309749i | −0.526585 | − | 0.850122i | \(-0.676528\pi\) |
0.472935 | + | 0.881097i | \(0.343195\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 49.5245i | − | 2.50456i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.06526 | − | 8.77329i | −0.254861 | − | 0.441432i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.20352 | + | 5.54866i | −0.160780 | + | 0.278479i | −0.935149 | − | 0.354256i | \(-0.884734\pi\) |
0.774369 | + | 0.632735i | \(0.218068\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.3130 | − | 9.99568i | −0.864571 | − | 0.499160i | 0.000969118 | − | 1.00000i | \(-0.499692\pi\) |
−0.865540 | + | 0.500839i | \(0.833025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.68956 | − | 0.975469i | 0.0841630 | − | 0.0485916i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.7372 | −0.680928 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.32392 | + | 2.29310i | 0.0654638 | + | 0.113387i | 0.896900 | − | 0.442234i | \(-0.145814\pi\) |
−0.831436 | + | 0.555621i | \(0.812481\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.53356 | − | 0.885402i | −0.0754616 | − | 0.0435678i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.2400 | − | 11.6856i | −0.993544 | − | 0.573623i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.6528 | 1.69290 | 0.846451 | − | 0.532467i | \(-0.178735\pi\) | ||||
0.846451 | + | 0.532467i | \(0.178735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5521 | − | 25.2049i | 0.709224 | − | 1.22841i | −0.255921 | − | 0.966698i | \(-0.582379\pi\) |
0.965145 | − | 0.261715i | \(-0.0842880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 12.5271i | − | 0.607652i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.60930 | − | 0.929129i | 0.0778794 | − | 0.0449637i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.38079 | + | 9.31980i | 0.259184 | + | 0.448919i | 0.966023 | − | 0.258454i | \(-0.0832132\pi\) |
−0.706840 | + | 0.707374i | \(0.749880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1284 | − | 31.3993i | −0.871195 | − | 1.50895i | −0.860761 | − | 0.509009i | \(-0.830012\pi\) |
−0.0104340 | − | 0.999946i | \(-0.503321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.80455 | − | 36.4558i | 0.373342 | − | 1.74392i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.2247 | + | 11.0994i | 0.917545 | + | 0.529745i | 0.882851 | − | 0.469653i | \(-0.155621\pi\) |
0.0346940 | + | 0.999398i | \(0.488954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.13148 | + | 7.15593i | 0.196293 | + | 0.339989i | 0.947323 | − | 0.320278i | \(-0.103776\pi\) |
−0.751031 | + | 0.660267i | \(0.770443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.36414 | −0.0646663 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.27444i | − | 0.296109i | −0.988979 | − | 0.148055i | \(-0.952699\pi\) | ||
0.988979 | − | 0.148055i | \(-0.0473012\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0520 | − | 6.95824i | −0.567508 | − | 0.327651i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0633402 | 0.00296943 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5021 | 0.538044 | 0.269022 | − | 0.963134i | \(-0.413300\pi\) | ||||
0.269022 | + | 0.963134i | \(0.413300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.75865 | + | 2.74741i | 0.221632 | + | 0.127960i | 0.606706 | − | 0.794926i | \(-0.292491\pi\) |
−0.385073 | + | 0.922886i | \(0.625824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.3399i | − | 1.08470i | −0.840153 | − | 0.542349i | \(-0.817535\pi\) | ||
0.840153 | − | 0.542349i | \(-0.182465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.61376 | −0.259774 | −0.129887 | − | 0.991529i | \(-0.541461\pi\) | ||||
−0.129887 | + | 0.991529i | \(0.541461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.05652 | − | 1.82994i | −0.0487855 | − | 0.0844989i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.91078 | + | 5.72199i | 0.455698 | + | 0.263097i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.97414 | − | 9.22139i | 0.0905797 | − | 0.423107i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.41707 | + | 16.3108i | 0.430277 | + | 0.745262i | 0.996897 | − | 0.0787176i | \(-0.0250825\pi\) |
−0.566620 | + | 0.823979i | \(0.691749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.743142 | + | 1.28716i | 0.0338844 | + | 0.0586894i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.89085 | − | 1.66903i | 0.131267 | − | 0.0757869i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 43.4061i | − | 1.96692i | −0.181135 | − | 0.983458i | \(-0.557977\pi\) | ||
0.181135 | − | 0.983458i | \(-0.442023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.30373 | + | 12.6504i | −0.329613 | + | 0.570906i | −0.982435 | − | 0.186605i | \(-0.940252\pi\) |
0.652822 | + | 0.757511i | \(0.273585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.40068 | 0.288272 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.17890 | − | 1.25799i | −0.0977368 | − | 0.0564284i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.2166 | − | 16.2908i | −1.26315 | − | 0.729278i | −0.289464 | − | 0.957189i | \(-0.593477\pi\) |
−0.973682 | + | 0.227911i | \(0.926811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.94108 | − | 6.82616i | −0.175724 | − | 0.304363i | 0.764687 | − | 0.644401i | \(-0.222893\pi\) |
−0.940412 | + | 0.340038i | \(0.889560\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.7088 | −0.921528 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.1464 | + | 7.59006i | −0.582703 | + | 0.336424i | −0.762207 | − | 0.647334i | \(-0.775884\pi\) |
0.179504 | + | 0.983757i | \(0.442551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.737629 | + | 0.425870i | 0.0326308 | + | 0.0188394i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.3309 | + | 17.8937i | −0.455236 | + | 0.788492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.32916 | + | 4.03423i | 0.102436 | + | 0.177425i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.8859i | 1.13408i | 0.823689 | + | 0.567041i | \(0.191912\pi\) | ||||
−0.823689 | + | 0.567041i | \(0.808088\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0962 | + | 7.56108i | −0.572655 | + | 0.330623i | −0.758209 | − | 0.652011i | \(-0.773925\pi\) |
0.185554 | + | 0.982634i | \(0.440592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.8677 | + | 44.8042i | −1.12681 | + | 1.95170i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.0773 | + | 43.4351i | −1.09032 | + | 1.88848i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.50568i | 0.0652182i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.82132 | − | 2.78359i | −0.208444 | − | 0.120345i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.0671 | 0.605914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.47033 | + | 4.27874i | 0.106208 | + | 0.183958i | 0.914231 | − | 0.405193i | \(-0.132796\pi\) |
−0.808023 | + | 0.589151i | \(0.799462\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.1428 | + | 13.9389i | −1.03416 | + | 0.597075i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.7483 | + | 20.6393i | −1.52849 | + | 0.882472i | −0.529060 | + | 0.848584i | \(0.677455\pi\) |
−0.999426 | + | 0.0338872i | \(0.989211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.71165 | + | 1.00868i | 0.200723 | + | 0.0429713i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.518011 | − | 0.897221i | 0.0220281 | − | 0.0381537i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.7555 | − | 16.6020i | 1.21841 | − | 0.703449i | 0.253831 | − | 0.967249i | \(-0.418309\pi\) |
0.964577 | + | 0.263800i | \(0.0849759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.23817i | − | 0.0523690i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.6020 | 0.868272 | 0.434136 | − | 0.900847i | \(-0.357054\pi\) | ||||
0.434136 | + | 0.900847i | \(0.357054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.58328 | + | 7.93847i | −0.192820 | + | 0.333974i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.2258i | 1.47674i | 0.674394 | + | 0.738371i | \(0.264405\pi\) | ||||
−0.674394 | + | 0.738371i | \(0.735595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.7468i | − | 1.45411i | −0.686580 | − | 0.727054i | \(-0.740889\pi\) | ||
0.686580 | − | 0.727054i | \(-0.259111\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.25212 | + | 16.0251i | −0.385840 | + | 0.668295i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.4671 | 0.643904 | 0.321952 | − | 0.946756i | \(-0.395661\pi\) | ||||
0.321952 | + | 0.946756i | \(0.395661\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.39011i | − | 0.0991584i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.17644 | + | 4.14332i | −0.297218 | + | 0.171599i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.1741 | + | 21.0862i | −0.502479 | + | 0.870320i | 0.497517 | + | 0.867454i | \(0.334245\pi\) |
−0.999996 | + | 0.00286514i | \(0.999088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.1023 | + | 28.9046i | −1.07553 | + | 1.19099i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.5771 | − | 17.0763i | 1.21459 | − | 0.701241i | 0.250831 | − | 0.968031i | \(-0.419296\pi\) |
0.963755 | + | 0.266790i | \(0.0859630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.45464 | + | 0.839835i | −0.0596343 | + | 0.0344299i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.64190 | − | 8.04000i | −0.189663 | − | 0.328505i | 0.755475 | − | 0.655177i | \(-0.227406\pi\) |
−0.945138 | + | 0.326672i | \(0.894073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.17512 | 0.374261 | 0.187131 | − | 0.982335i | \(-0.440081\pi\) | ||||
0.187131 | + | 0.982335i | \(0.440081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.1036 | + | 5.83332i | 0.410770 | + | 0.237158i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.2294i | − | 1.02403i | −0.858976 | − | 0.512016i | \(-0.828899\pi\) | ||
0.858976 | − | 0.512016i | \(-0.171101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.252001 | − | 0.436479i | 0.0101949 | − | 0.0176581i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.71776 | − | 9.90345i | 0.230938 | − | 0.399997i | −0.727146 | − | 0.686483i | \(-0.759154\pi\) |
0.958084 | + | 0.286486i | \(0.0924871\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5273 | + | 16.4703i | −1.14847 | + | 0.663067i | −0.948513 | − | 0.316738i | \(-0.897412\pi\) |
−0.199953 | + | 0.979805i | \(0.564079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.8796i | 1.52251i | 0.648453 | + | 0.761255i | \(0.275416\pi\) | ||||
−0.648453 | + | 0.761255i | \(0.724584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0697533 | − | 0.120816i | −0.00279461 | − | 0.00484040i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.75103 | − | 8.22903i | 0.190041 | − | 0.329161i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.1332 | − | 19.7068i | −1.36098 | − | 0.785762i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7897 | − | 12.5803i | 0.867434 | − | 0.500813i | 0.000939347 | − | 1.00000i | \(-0.499701\pi\) |
0.866495 | + | 0.499186i | \(0.166368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.9855 | −1.18994 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.760989 | − | 1.31807i | −0.0301515 | − | 0.0522239i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.1330 | − | 19.1294i | −1.30868 | − | 0.755565i | −0.326801 | − | 0.945093i | \(-0.605971\pi\) |
−0.981875 | + | 0.189528i | \(0.939304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.504443 | + | 0.291240i | 0.0198933 | + | 0.0114854i | 0.509914 | − | 0.860226i | \(-0.329677\pi\) |
−0.490020 | + | 0.871711i | \(0.663011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.7409 | −1.79826 | −0.899129 | − | 0.437683i | \(-0.855799\pi\) | ||||
−0.899129 | + | 0.437683i | \(0.855799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.3744 | − | 17.9689i | 0.407229 | − | 0.705341i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 23.7797i | − | 0.930570i | −0.885161 | − | 0.465285i | \(-0.845952\pi\) | ||
0.885161 | − | 0.465285i | \(-0.154048\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.5836 | + | 12.4613i | −0.843340 | + | 0.486903i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.85047 | + | 8.40125i | 0.188947 | + | 0.327266i | 0.944900 | − | 0.327360i | \(-0.106159\pi\) |
−0.755952 | + | 0.654627i | \(0.772826\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.80687 | − | 6.59368i | −0.148070 | − | 0.256465i | 0.782444 | − | 0.622721i | \(-0.213973\pi\) |
−0.930514 | + | 0.366256i | \(0.880639\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.20313 | + | 0.388981i | −0.0466554 | + | 0.0150840i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.18801 | − | 4.72735i | −0.317041 | − | 0.183044i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8867 | + | 18.8563i | 0.420277 | + | 0.727941i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.8822 | 1.65299 | 0.826493 | − | 0.562946i | \(-0.190332\pi\) | ||||
0.826493 | + | 0.562946i | \(0.190332\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.8674i | 1.30163i | 0.759236 | + | 0.650815i | \(0.225573\pi\) | ||||
−0.759236 | + | 0.650815i | \(0.774427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.295640 | + | 0.170688i | 0.0113456 | + | 0.00655039i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.32361 | −0.356758 | −0.178379 | − | 0.983962i | \(-0.557085\pi\) | ||||
−0.178379 | + | 0.983962i | \(0.557085\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0316 | 0.688951 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.776447 | + | 0.448282i | 0.0295803 | + | 0.0170782i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.2936i | 1.79913i | 0.436784 | + | 0.899566i | \(0.356117\pi\) | ||||
−0.436784 | + | 0.899566i | \(0.643883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.74351 | −0.179931 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.9640 | − | 34.5786i | −0.756190 | − | 1.30976i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.3169 | + | 8.84321i | 0.578511 | + | 0.334004i | 0.760541 | − | 0.649289i | \(-0.224934\pi\) |
−0.182030 | + | 0.983293i | \(0.558267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.0204 | − | 19.8856i | −0.830516 | − | 0.749998i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.05891 | − | 1.83409i | −0.0398246 | − | 0.0689782i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.212948 | − | 0.368836i | −0.00799742 | − | 0.0138519i | 0.861999 | − | 0.506910i | \(-0.169212\pi\) |
−0.869996 | + | 0.493058i | \(0.835879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 66.1820 | − | 38.2102i | 2.47854 | − | 1.43098i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.742164i | 0.0277554i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.08340 | + | 12.2688i | −0.264166 | + | 0.457550i | −0.967345 | − | 0.253464i | \(-0.918430\pi\) |
0.703179 | + | 0.711013i | \(0.251763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.11304 | −0.0786936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.07113 | − | 1.19577i | −0.0769200 | − | 0.0444098i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.79442 | − | 1.61336i | −0.103639 | − | 0.0598361i | 0.447285 | − | 0.894392i | \(-0.352391\pi\) |
−0.550924 | + | 0.834556i | \(0.685724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.4170 | + | 28.4351i | 0.607206 | + | 1.05171i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9587 | −1.03268 | −0.516339 | − | 0.856384i | \(-0.672705\pi\) | ||||
−0.516339 | + | 0.856384i | \(0.672705\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.4417 | − | 12.3793i | 0.789814 | − | 0.455999i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.4433 | − | 12.9576i | −0.825590 | − | 0.476655i | 0.0267502 | − | 0.999642i | \(-0.491484\pi\) |
−0.852340 | + | 0.522987i | \(0.824817\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9220 | + | 36.2380i | −0.767555 | + | 1.32944i | 0.171330 | + | 0.985214i | \(0.445194\pi\) |
−0.938885 | + | 0.344231i | \(0.888140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.96133 | − | 13.7894i | −0.291681 | − | 0.505205i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 0.569341i | − | 0.0208033i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0270700 | + | 0.0156289i | −0.000987799 | + | 0.000570306i | −0.500494 | − | 0.865740i | \(-0.666848\pi\) |
0.499506 | + | 0.866310i | \(0.333515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.21027 | − | 12.4886i | 0.262409 | − | 0.454505i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6270 | + | 23.6027i | −0.495283 | + | 0.857855i | −0.999985 | − | 0.00543871i | \(-0.998269\pi\) |
0.504703 | + | 0.863293i | \(0.331602\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.4135i | − | 0.486237i | −0.969997 | − | 0.243119i | \(-0.921830\pi\) | ||
0.969997 | − | 0.243119i | \(-0.0781704\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.46902 | − | 1.42549i | −0.0893846 | − | 0.0516062i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.24489 | −0.0810581 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.88817 | − | 10.1986i | −0.212333 | − | 0.367772i | 0.740111 | − | 0.672484i | \(-0.234773\pi\) |
−0.952444 | + | 0.304713i | \(0.901439\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.4951 | + | 17.0290i | −1.06087 | + | 0.612492i | −0.925672 | − | 0.378327i | \(-0.876499\pi\) |
−0.135195 | + | 0.990819i | \(0.543166\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.7406 | − | 9.66517i | 0.601339 | − | 0.347183i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.24659 | − | 28.6000i | −0.331293 | − | 1.02470i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7400 | − | 25.5304i | 0.527437 | − | 0.913548i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4851 | − | 6.05359i | 0.374230 | − | 0.216062i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.5159i | − | 1.15907i | −0.814948 | − | 0.579533i | \(-0.803235\pi\) | ||
0.814948 | − | 0.579533i | \(-0.196765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.937439 | −0.0333315 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.17788 | − | 2.04014i | 0.0418276 | − | 0.0724476i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.8868i | 0.456474i | 0.973606 | + | 0.228237i | \(0.0732962\pi\) | ||||
−0.973606 | + | 0.228237i | \(0.926704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.3653i | 0.472829i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.98997 | + | 8.64289i | −0.176092 | + | 0.305001i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.48111 | 0.0874475 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.2442i | 0.782063i | 0.920377 | + | 0.391031i | \(0.127882\pi\) | ||||
−0.920377 | + | 0.391031i | \(0.872118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.1859 | − | 6.45816i | 0.392789 | − | 0.226777i | −0.290579 | − | 0.956851i | \(-0.593848\pi\) |
0.683368 | + | 0.730074i | \(0.260515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.7344 | − | 22.0566i | 0.446065 | − | 0.772608i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.60377 | + | 23.5187i | 0.266022 | + | 0.822817i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.7950 | + | 6.23249i | −0.376748 | + | 0.217515i | −0.676402 | − | 0.736532i | \(-0.736462\pi\) |
0.299655 | + | 0.954048i | \(0.403129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.13742 | + | 4.12079i | −0.248795 | + | 0.143642i | −0.619212 | − | 0.785224i | \(-0.712548\pi\) |
0.370417 | + | 0.928865i | \(0.379215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.902111 | − | 1.56250i | −0.0313695 | − | 0.0543335i | 0.849914 | − | 0.526921i | \(-0.176654\pi\) |
−0.881284 | + | 0.472587i | \(0.843320\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.8057 | 0.548954 | 0.274477 | − | 0.961594i | \(-0.411495\pi\) | ||||
0.274477 | + | 0.961594i | \(0.411495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.9529 | + | 20.1801i | 1.21105 | + | 0.699198i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.07862i | 0.175753i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.00727 | + | 8.67284i | −0.172870 | + | 0.299420i | −0.939422 | − | 0.342762i | \(-0.888637\pi\) |
0.766552 | + | 0.642182i | \(0.221971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.8890 | + | 24.0565i | −0.478932 | + | 0.829534i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.8917 | + | 10.9072i | −0.649896 | + | 0.375218i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.19312i | 0.0409960i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.1097 | + | 50.4195i | 0.997868 | + | 1.72836i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.2794 | + | 17.8045i | −0.351961 | + | 0.609614i | −0.986593 | − | 0.163200i | \(-0.947818\pi\) |
0.634632 | + | 0.772814i | \(0.281152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.3464 | − | 23.8714i | −1.41237 | − | 0.815430i | −0.416755 | − | 0.909019i | \(-0.636833\pi\) |
−0.995611 | + | 0.0935891i | \(0.970166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.0965 | + | 10.4480i | −0.617446 | + | 0.356483i | −0.775874 | − | 0.630888i | \(-0.782691\pi\) |
0.158428 | + | 0.987371i | \(0.449357\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.49946 | −0.323366 | −0.161683 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161683 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.8185 | + | 22.2023i | 0.435843 | + | 0.754902i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.5128 | + | 6.06959i | 0.356624 | + | 0.205897i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.31986 | − | 1.33937i | −0.0786054 | − | 0.0453828i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.07801 | 0.0702496 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0799 | − | 27.8513i | 0.542981 | − | 0.940470i | −0.455750 | − | 0.890108i | \(-0.650629\pi\) |
0.998731 | − | 0.0503626i | \(-0.0160377\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.5821i | 1.06403i | 0.846736 | + | 0.532014i | \(0.178565\pi\) | ||||
−0.846736 | + | 0.532014i | \(0.821435\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7492 | + | 6.20608i | −0.361741 | + | 0.208851i | −0.669844 | − | 0.742502i | \(-0.733639\pi\) |
0.308103 | + | 0.951353i | \(0.400306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.8795 | − | 41.3605i | −0.801795 | − | 1.38875i | −0.918434 | − | 0.395575i | \(-0.870545\pi\) |
0.116638 | − | 0.993174i | \(-0.462788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.53327 | − | 2.65570i | −0.0514242 | − | 0.0890693i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.10623 | + | 9.83839i | −0.0704822 | + | 0.329229i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8169 | − | 11.4413i | −0.662407 | − | 0.382441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.93839 | + | 8.55355i | 0.164705 | + | 0.285277i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.7753 | −0.792070 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 29.1321i | − | 0.968383i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0023 | + | 21.3633i | 1.22864 | + | 0.709356i | 0.966746 | − | 0.255740i | \(-0.0823191\pi\) |
0.261895 | + | 0.965096i | \(0.415652\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.3000 | −0.771964 | −0.385982 | − | 0.922506i | \(-0.626137\pi\) | ||||
−0.385982 | + | 0.922506i | \(0.626137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.0052 | 0.926836 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.20730 | − | 1.27438i | −0.0728913 | − | 0.0420838i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2297i | 0.469395i | 0.972069 | + | 0.234697i | \(0.0754099\pi\) | ||||
−0.972069 | + | 0.234697i | \(0.924590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.18955 | −0.104985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.36322 | + | 12.7535i | 0.242101 | + | 0.419332i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.0463 | − | 25.4301i | −1.44511 | − | 0.834336i | −0.446928 | − | 0.894570i | \(-0.647482\pi\) |
−0.998184 | + | 0.0602338i | \(0.980815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5493 | + | 20.3631i | 0.739022 | + | 0.667374i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.84044 | − | 17.0441i | −0.321817 | − | 0.557403i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.13439 | + | 8.89303i | 0.167733 | + | 0.290523i | 0.937623 | − | 0.347655i | \(-0.113022\pi\) |
−0.769889 | + | 0.638177i | \(0.779689\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.13944 | − | 4.12196i | 0.232739 | − | 0.134372i | −0.379096 | − | 0.925357i | \(-0.623765\pi\) |
0.611835 | + | 0.790985i | \(0.290432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.9792i | 1.92063i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4715 | + | 26.7974i | −0.502756 | + | 0.870799i | 0.497239 | + | 0.867614i | \(0.334347\pi\) |
−0.999995 | + | 0.00318534i | \(0.998986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07977 | 0.0350508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.3702 | − | 19.8436i | −1.11336 | − | 0.642798i | −0.173662 | − | 0.984805i | \(-0.555560\pi\) |
−0.939697 | + | 0.342007i | \(0.888893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.3623 | + | 10.6015i | 0.594190 | + | 0.343056i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.922020 | + | 1.59699i | 0.0297736 | + | 0.0515694i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.8321 | −1.57523 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.2887 | − | 12.2911i | 0.685309 | − | 0.395663i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.2876 | − | 18.0639i | −1.00614 | − | 0.580896i | −0.0960818 | − | 0.995373i | \(-0.530631\pi\) |
−0.910060 | + | 0.414477i | \(0.863964\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.7154 | − | 48.0044i | 0.889428 | − | 1.54053i | 0.0488755 | − | 0.998805i | \(-0.484436\pi\) |
0.840553 | − | 0.541730i | \(-0.182230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.242553 | − | 0.420114i | −0.00777589 | − | 0.0134682i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.3001i | 1.70522i | 0.522546 | + | 0.852611i | \(0.324982\pi\) | ||||
−0.522546 | + | 0.852611i | \(0.675018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.41562 | − | 0.817308i | 0.0452434 | − | 0.0261213i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.5159 | − | 37.2666i | 0.686250 | − | 1.18862i | −0.286792 | − | 0.957993i | \(-0.592589\pi\) |
0.973042 | − | 0.230628i | \(-0.0740779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.6641 | + | 18.4707i | −0.339785 | + | 0.588525i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 48.5005i | − | 1.54223i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.57619 | − | 2.64206i | −0.145367 | − | 0.0839279i | 0.425552 | − | 0.904934i | \(-0.360080\pi\) |
−0.570920 | + | 0.821006i | \(0.693413\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3572 | −0.455154 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.36964 | − | 11.0325i | −0.201728 | − | 0.349404i | 0.747357 | − | 0.664423i | \(-0.231322\pi\) |
−0.949085 | + | 0.315019i | \(0.897989\pi\) | |||||||
\(998\) | 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.cg.c.1151.6 | yes | 32 | |
3.2 | odd | 2 | inner | 2736.2.cg.c.1151.12 | yes | 32 | |
4.3 | odd | 2 | inner | 2736.2.cg.c.1151.5 | ✓ | 32 | |
12.11 | even | 2 | inner | 2736.2.cg.c.1151.11 | yes | 32 | |
19.7 | even | 3 | inner | 2736.2.cg.c.2591.12 | yes | 32 | |
57.26 | odd | 6 | inner | 2736.2.cg.c.2591.6 | yes | 32 | |
76.7 | odd | 6 | inner | 2736.2.cg.c.2591.11 | yes | 32 | |
228.83 | even | 6 | inner | 2736.2.cg.c.2591.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.c.1151.5 | ✓ | 32 | 4.3 | odd | 2 | inner | |
2736.2.cg.c.1151.6 | yes | 32 | 1.1 | even | 1 | trivial | |
2736.2.cg.c.1151.11 | yes | 32 | 12.11 | even | 2 | inner | |
2736.2.cg.c.1151.12 | yes | 32 | 3.2 | odd | 2 | inner | |
2736.2.cg.c.2591.5 | yes | 32 | 228.83 | even | 6 | inner | |
2736.2.cg.c.2591.6 | yes | 32 | 57.26 | odd | 6 | inner | |
2736.2.cg.c.2591.11 | yes | 32 | 76.7 | odd | 6 | inner | |
2736.2.cg.c.2591.12 | yes | 32 | 19.7 | even | 3 | inner |