Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.1 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.f.3025.24 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.46300i | − 1.54870i | −0.632757 | − | 0.774351i | \(-0.718077\pi\) | ||||
0.632757 | − | 0.774351i | \(-0.281923\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.31902i | − 1.00072i | −0.865817 | − | 0.500361i | \(-0.833201\pi\) | ||||
0.865817 | − | 0.500361i | \(-0.166799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.10840i | − 0.862116i | −0.902324 | − | 0.431058i | \(-0.858140\pi\) | ||||
0.902324 | − | 0.431058i | \(-0.141860\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40277 | −0.340221 | −0.170110 | − | 0.985425i | \(-0.554412\pi\) | ||||
−0.170110 | + | 0.985425i | \(0.554412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.80674i | 1.10274i | 0.834260 | + | 0.551371i | \(0.185895\pi\) | ||||
−0.834260 | + | 0.551371i | \(0.814105\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.79960 | −1.83484 | −0.917421 | − | 0.397917i | \(-0.869733\pi\) | ||||
−0.917421 | + | 0.397917i | \(0.869733\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.99238 | −1.39848 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.87397i | 1.83355i | 0.399404 | + | 0.916775i | \(0.369217\pi\) | ||||
−0.399404 | + | 0.916775i | \(0.630783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.83557 | 1.40731 | 0.703655 | − | 0.710541i | \(-0.251550\pi\) | ||||
0.703655 | + | 0.710541i | \(0.251550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46300i | 0.585354i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.42317i | − 0.891564i | −0.895142 | − | 0.445782i | \(-0.852926\pi\) | ||||
0.895142 | − | 0.445782i | \(-0.147074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.5710 | −1.80708 | −0.903542 | − | 0.428499i | \(-0.859043\pi\) | ||||
−0.903542 | + | 0.428499i | \(0.859043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.03957i | 1.07352i | 0.843733 | + | 0.536762i | \(0.180353\pi\) | ||||
−0.843733 | + | 0.536762i | \(0.819647\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.2916 | −1.64704 | −0.823522 | − | 0.567284i | \(-0.807994\pi\) | ||||
−0.823522 | + | 0.567284i | \(0.807994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.51655i | − 0.895117i | −0.894255 | − | 0.447559i | \(-0.852294\pi\) | ||||
0.894255 | − | 0.447559i | \(-0.147706\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.4938 | −1.54982 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 3.89654i | − 0.507287i | −0.967298 | − | 0.253643i | \(-0.918371\pi\) | ||||
0.967298 | − | 0.253643i | \(-0.0816290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.42334i | 1.20653i | 0.797539 | + | 0.603267i | \(0.206135\pi\) | ||||
−0.797539 | + | 0.603267i | \(0.793865\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7644 | −1.33516 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.909712i | − 0.111139i | −0.998455 | − | 0.0555695i | \(-0.982303\pi\) | ||||
0.998455 | − | 0.0555695i | \(-0.0176974\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.42314 | 0.762286 | 0.381143 | − | 0.924516i | \(-0.375531\pi\) | ||||
0.381143 | + | 0.924516i | \(0.375531\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.56257 | 0.182884 | 0.0914422 | − | 0.995810i | \(-0.470852\pi\) | ||||
0.0914422 | + | 0.995810i | \(0.470852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.31902i | 0.378238i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1619 | 1.25582 | 0.627908 | − | 0.778288i | \(-0.283912\pi\) | ||||
0.627908 | + | 0.778288i | \(0.283912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.370241i | − 0.0406392i | −0.999794 | − | 0.0203196i | \(-0.993532\pi\) | ||||
0.999794 | − | 0.0203196i | \(-0.00646837\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.85778i | 0.526900i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.85047 | 0.514149 | 0.257075 | − | 0.966392i | \(-0.417241\pi\) | ||||
0.257075 | + | 0.966392i | \(0.417241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10840i | 0.325849i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.6457 | 1.70782 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.63283 | 0.165789 | 0.0828946 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828946 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1650i | 1.30997i | 0.755643 | + | 0.654983i | \(0.227324\pi\) | ||||
−0.755643 | + | 0.654983i | \(0.772676\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.6983 | −1.54680 | −0.773399 | − | 0.633920i | \(-0.781445\pi\) | ||||
−0.773399 | + | 0.633920i | \(0.781445\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.37257i | − 0.906081i | −0.891490 | − | 0.453040i | \(-0.850339\pi\) | ||||
0.891490 | − | 0.453040i | \(-0.149661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.31490i | 0.700640i | 0.936630 | + | 0.350320i | \(0.113927\pi\) | ||||
−0.936630 | + | 0.350320i | \(0.886073\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9153 | 1.02683 | 0.513414 | − | 0.858141i | \(-0.328380\pi\) | ||||
0.513414 | + | 0.858141i | \(0.328380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.4730i | 2.84162i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.40277 | 0.128591 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0159016 | −0.00144560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.89962i | 0.617121i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.37545 | −0.299523 | −0.149761 | − | 0.988722i | \(-0.547851\pi\) | ||||
−0.149761 | + | 0.988722i | \(0.547851\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.15460i | − 0.625100i | −0.949901 | − | 0.312550i | \(-0.898817\pi\) | ||||
0.949901 | − | 0.312550i | \(-0.101183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.80674i | − 0.416797i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.22854 | 0.361269 | 0.180634 | − | 0.983550i | \(-0.442185\pi\) | ||||
0.180634 | + | 0.983550i | \(0.442185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31473i | 0.281152i | 0.990070 | + | 0.140576i | \(0.0448954\pi\) | ||||
−0.990070 | + | 0.140576i | \(0.955105\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3169 | −0.862739 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.1936 | 2.83962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.08433i | 0.580371i | 0.956970 | + | 0.290185i | \(0.0937169\pi\) | ||||
−0.956970 | + | 0.290185i | \(0.906283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.252443 | −0.0205436 | −0.0102718 | − | 0.999947i | \(-0.503270\pi\) | ||||
−0.0102718 | + | 0.999947i | \(0.503270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 27.1346i | − 2.17950i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.11021i | − 0.248222i | −0.992268 | − | 0.124111i | \(-0.960392\pi\) | ||||
0.992268 | − | 0.124111i | \(-0.0396078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.79960 | 0.693505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18.5595i | − 1.45369i | −0.686800 | − | 0.726847i | \(-0.740985\pi\) | ||||
0.686800 | − | 0.726847i | \(-0.259015\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.3221 | 1.10828 | 0.554140 | − | 0.832424i | \(-0.313047\pi\) | ||||
0.554140 | + | 0.832424i | \(0.313047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.33782 | 0.256755 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.40183i | − 0.106579i | −0.998579 | − | 0.0532896i | \(-0.983029\pi\) | ||||
0.998579 | − | 0.0532896i | \(-0.0169707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.99238 | 0.528574 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.46849i | 0.259247i | 0.991563 | + | 0.129624i | \(0.0413769\pi\) | ||||
−0.991563 | + | 0.129624i | \(0.958623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.3992i | 1.44193i | 0.692972 | + | 0.720965i | \(0.256301\pi\) | ||||
−0.692972 | + | 0.720965i | \(0.743699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.7805 | −1.38077 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.65581i | 0.340466i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.4610 | −1.69758 | −0.848790 | − | 0.528729i | \(-0.822669\pi\) | ||||
−0.848790 | + | 0.528729i | \(0.822669\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.5374 | −1.11840 | −0.559202 | − | 0.829031i | \(-0.688893\pi\) | ||||
−0.559202 | + | 0.829031i | \(0.688893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8278i | 1.05643i | 0.849109 | + | 0.528217i | \(0.177139\pi\) | ||||
−0.849109 | + | 0.528217i | \(0.822861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2095 | −0.936397 | −0.468199 | − | 0.883623i | \(-0.655097\pi\) | ||||
−0.468199 | + | 0.883623i | \(0.655097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.87397i | − 0.693017i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.0703i | 2.79863i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.9537 | 1.10354 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3790i | 0.852206i | 0.904675 | + | 0.426103i | \(0.140114\pi\) | ||||
−0.904675 | + | 0.426103i | \(0.859886\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.3781 | 1.66257 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.83557 | −0.531913 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.36036i | 0.293310i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.91170 | −0.194982 | −0.0974910 | − | 0.995236i | \(-0.531082\pi\) | ||||
−0.0974910 | + | 0.995236i | \(0.531082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.3550i | − 0.753658i | −0.926283 | − | 0.376829i | \(-0.877014\pi\) | ||||
0.926283 | − | 0.376829i | \(-0.122986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 17.4776i | − 1.15495i | −0.816407 | − | 0.577477i | \(-0.804037\pi\) | ||||
0.816407 | − | 0.577477i | \(-0.195963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.98827 | 0.130256 | 0.0651279 | − | 0.997877i | \(-0.479254\pi\) | ||||
0.0651279 | + | 0.997877i | \(0.479254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.1027i | 2.55078i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3430 | 1.38056 | 0.690282 | − | 0.723540i | \(-0.257486\pi\) | ||||
0.690282 | + | 0.723540i | \(0.257486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3714 | −0.861330 | −0.430665 | − | 0.902512i | \(-0.641721\pi\) | ||||
−0.430665 | + | 0.902512i | \(0.641721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.46300i | − 0.221243i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.9413 | 0.950691 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.92814i | 0.121703i | 0.998147 | + | 0.0608514i | \(0.0193816\pi\) | ||||
−0.998147 | + | 0.0608514i | \(0.980618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.2060i | 1.83617i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.22415 | −0.325873 | −0.162937 | − | 0.986637i | \(-0.552097\pi\) | ||||
−0.162937 | + | 0.986637i | \(0.552097\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.42317i | 0.336980i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.69624 | 0.289583 | 0.144791 | − | 0.989462i | \(-0.453749\pi\) | ||||
0.144791 | + | 0.989462i | \(0.453749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5668 | −1.38627 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.9906i | 1.64565i | 0.568297 | + | 0.822824i | \(0.307603\pi\) | ||||
−0.568297 | + | 0.822824i | \(0.692397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.75175 | −0.167157 | −0.0835784 | − | 0.996501i | \(-0.526635\pi\) | ||||
−0.0835784 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.2079i | 1.39949i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0526i | 0.724173i | 0.932145 | + | 0.362086i | \(0.117935\pi\) | ||||
−0.932145 | + | 0.362086i | \(0.882065\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.74449 | −0.402342 | −0.201171 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201171 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.53083i | − 0.507105i | −0.967322 | − | 0.253552i | \(-0.918401\pi\) | ||||
0.967322 | − | 0.253552i | \(-0.0815991\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5710 | 0.683014 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0322 | −0.884250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2926i | 0.659718i | 0.944030 | + | 0.329859i | \(0.107001\pi\) | ||||
−0.944030 | + | 0.329859i | \(0.892999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4937 | −0.785636 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.3527i | 1.58185i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.03957i | − 0.405754i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.6330 | 1.86856 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.15810i | − 0.522680i | −0.965247 | − | 0.261340i | \(-0.915836\pi\) | ||||
0.965247 | − | 0.261340i | \(-0.0841644\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0122 | −0.567741 | −0.283870 | − | 0.958863i | \(-0.591619\pi\) | ||||
−0.283870 | + | 0.958863i | \(0.591619\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3334 | −0.584076 | −0.292038 | − | 0.956407i | \(-0.594333\pi\) | ||||
−0.292038 | + | 0.956407i | \(0.594333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 34.9339i | − 1.96208i | −0.193794 | − | 0.981042i | \(-0.562079\pi\) | ||||
0.193794 | − | 0.981042i | \(-0.437921\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.7719 | 1.83487 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.74273i | − 0.375175i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.7352i | 1.20565i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.2916 | 0.622524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.71488i | 0.479013i | 0.970895 | + | 0.239507i | \(0.0769857\pi\) | ||||
−0.970895 | + | 0.239507i | \(0.923014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.15034 | −0.172121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.63703 | −0.470489 | −0.235244 | − | 0.971936i | \(-0.575589\pi\) | ||||
−0.235244 | + | 0.971936i | \(0.575589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 26.0064i | − 1.40833i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.2190i | 1.51488i | 0.652907 | + | 0.757438i | \(0.273549\pi\) | ||||
−0.652907 | + | 0.757438i | \(0.726451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 13.6266i | − 0.729416i | −0.931122 | − | 0.364708i | \(-0.881169\pi\) | ||||
0.931122 | − | 0.364708i | \(-0.118831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.4282 | −1.72598 | −0.862990 | − | 0.505220i | \(-0.831411\pi\) | ||||
−0.862990 | + | 0.505220i | \(0.831411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 22.2433i | − 1.18055i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.9995 | 0.686087 | 0.343044 | − | 0.939319i | \(-0.388542\pi\) | ||||
0.343044 | + | 0.939319i | \(0.388542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.10474 | −0.216039 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.41117i | − 0.283233i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.55576 | 0.394408 | 0.197204 | − | 0.980363i | \(-0.436814\pi\) | ||||
0.197204 | + | 0.980363i | \(0.436814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.51655i | 0.338323i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6651i | 1.79489i | 0.441124 | + | 0.897446i | \(0.354580\pi\) | ||||
−0.441124 | + | 0.897446i | \(0.645420\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.6923 | 1.58073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.308373i | 0.0158401i | 0.999969 | + | 0.00792004i | \(0.00252105\pi\) | ||||
−0.999969 | + | 0.00792004i | \(0.997479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.36024 | −0.222798 | −0.111399 | − | 0.993776i | \(-0.535533\pi\) | ||||
−0.111399 | + | 0.993776i | \(0.535533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.4938 | 0.585777 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.33391i | − 0.0676317i | −0.999428 | − | 0.0338159i | \(-0.989234\pi\) | ||||
0.999428 | − | 0.0338159i | \(-0.0107660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3438 | 0.624251 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 38.6538i | − 1.94488i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6.92952i | − 0.347783i | −0.984765 | − | 0.173891i | \(-0.944366\pi\) | ||||
0.984765 | − | 0.173891i | \(-0.0556342\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.9669 | −1.19685 | −0.598426 | − | 0.801178i | \(-0.704207\pi\) | ||||
−0.598426 | + | 0.801178i | \(0.704207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 24.3561i | − 1.21327i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.9996 | −0.892208 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6936 | 1.07268 | 0.536340 | − | 0.844002i | \(-0.319807\pi\) | ||||
0.536340 | + | 0.844002i | \(0.319807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.89654i | 0.191736i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.28214 | −0.0629380 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 27.5910i | − 1.34791i | −0.738772 | − | 0.673955i | \(-0.764594\pi\) | ||||
0.738772 | − | 0.673955i | \(-0.235406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.3335i | 1.86826i | 0.356929 | + | 0.934131i | \(0.383824\pi\) | ||||
−0.356929 | + | 0.934131i | \(0.616176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.80867 | 0.475790 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 9.42334i | − 0.456027i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.22510 | −0.107179 | −0.0535896 | − | 0.998563i | \(-0.517066\pi\) | ||||
−0.0535896 | + | 0.998563i | \(0.517066\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2235 | 1.35633 | 0.678167 | − | 0.734908i | \(-0.262775\pi\) | ||||
0.678167 | + | 0.734908i | \(0.262775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 42.2974i | − 2.02336i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.63936 | 0.269152 | 0.134576 | − | 0.990903i | \(-0.457033\pi\) | ||||
0.134576 | + | 0.990903i | \(0.457033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.81672i | 0.276361i | 0.990407 | + | 0.138180i | \(0.0441254\pi\) | ||||
−0.990407 | + | 0.138180i | \(0.955875\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 16.7972i | − 0.796264i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.66921 | −0.0787748 | −0.0393874 | − | 0.999224i | \(-0.512541\pi\) | ||||
−0.0393874 | + | 0.999224i | \(0.512541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.4043i | 1.80839i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7644 | 0.504643 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4606 | −0.769994 | −0.384997 | − | 0.922918i | \(-0.625797\pi\) | ||||
−0.384997 | + | 0.922918i | \(0.625797\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 22.7915i | − 1.06151i | −0.847527 | − | 0.530753i | \(-0.821909\pi\) | ||||
0.847527 | − | 0.530753i | \(-0.178091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3165 | 0.758293 | 0.379146 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379146 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.3073i | 1.54128i | 0.637271 | + | 0.770639i | \(0.280063\pi\) | ||||
−0.637271 | + | 0.770639i | \(0.719937\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.909712i | 0.0420066i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.3645 | 1.07430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 33.6105i | − 1.54216i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.5717 | −1.30547 | −0.652737 | − | 0.757584i | \(-0.726379\pi\) | ||||
−0.652737 | + | 0.757584i | \(0.726379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.8574 | −0.768632 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 5.65451i | − 0.256758i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.0149 | −1.76793 | −0.883967 | − | 0.467550i | \(-0.845137\pi\) | ||||
−0.883967 | + | 0.467550i | \(0.845137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5799i | 0.567722i | 0.958866 | + | 0.283861i | \(0.0916153\pi\) | ||||
−0.958866 | + | 0.283861i | \(0.908385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 13.8509i | − 0.623811i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.42314 | −0.288117 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3054i | 0.774697i | 0.921933 | + | 0.387349i | \(0.126609\pi\) | ||||
−0.921933 | + | 0.387349i | \(0.873391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.1289 | −0.808326 | −0.404163 | − | 0.914687i | \(-0.632437\pi\) | ||||
−0.404163 | + | 0.914687i | \(0.632437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.5904 | 2.02875 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.3445i | 0.768780i | 0.923171 | + | 0.384390i | \(0.125588\pi\) | ||||
−0.923171 | + | 0.384390i | \(0.874412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.56257 | −0.0691238 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 54.3632i | 2.39553i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.4770i | 1.64823i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.7507 | −0.733861 | −0.366930 | − | 0.930248i | \(-0.619591\pi\) | ||||
−0.366930 | + | 0.930248i | \(0.619591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8692i | 0.912545i | 0.889840 | + | 0.456273i | \(0.150816\pi\) | ||||
−0.889840 | + | 0.456273i | \(0.849184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.9915 | −0.478796 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.4329 | 2.36665 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.9673i | 1.55792i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.4572 | −1.40325 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.31902i | − 0.142960i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 37.7498i | − 1.62299i | −0.584359 | − | 0.811495i | \(-0.698654\pi\) | ||||
0.584359 | − | 0.811495i | \(-0.301346\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.3315 | 1.08508 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4520i | 1.47306i | 0.676404 | + | 0.736531i | \(0.263537\pi\) | ||||
−0.676404 | + | 0.736531i | \(0.736463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −47.4616 | −2.02193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1619 | −0.474653 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 27.7136i | − 1.17426i | −0.809491 | − | 0.587132i | \(-0.800257\pi\) | ||||
0.809491 | − | 0.587132i | \(-0.199743\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8818 | 0.925503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.570384i | 0.0240388i | 0.999928 | + | 0.0120194i | \(0.00382599\pi\) | ||||
−0.999928 | + | 0.0120194i | \(0.996174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 37.7998i | − 1.59025i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4090 | −0.771745 | −0.385872 | − | 0.922552i | \(-0.626099\pi\) | ||||
−0.385872 | + | 0.922552i | \(0.626099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.3534i | 1.81428i | 0.420824 | + | 0.907142i | \(0.361741\pi\) | ||||
−0.420824 | + | 0.907142i | \(0.638259\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 61.5301 | 2.56598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.6209 | −1.64944 | −0.824720 | − | 0.565541i | \(-0.808667\pi\) | ||||
−0.824720 | + | 0.565541i | \(0.808667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.370241i | 0.0153602i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.6286 | −0.895764 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 13.4388i | − 0.554677i | −0.960772 | − | 0.277338i | \(-0.910548\pi\) | ||||
0.960772 | − | 0.277338i | \(-0.0894523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.6636i | 1.55190i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.3157 | −0.916395 | −0.458198 | − | 0.888850i | \(-0.651505\pi\) | ||||
−0.458198 | + | 0.888850i | \(0.651505\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.85778i | − 0.199150i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.2622 | −0.582740 | −0.291370 | − | 0.956610i | \(-0.594111\pi\) | ||||
−0.291370 | + | 0.956610i | \(0.594111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.40215 | −0.0979858 | −0.0489929 | − | 0.998799i | \(-0.515601\pi\) | ||||
−0.0489929 | + | 0.998799i | \(0.515601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0550671i | 0.00223880i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0506 | 0.407940 | 0.203970 | − | 0.978977i | \(-0.434615\pi\) | ||||
0.203970 | + | 0.978977i | \(0.434615\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.0988i | 1.41994i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.57394i | 0.103961i | 0.998648 | + | 0.0519803i | \(0.0165533\pi\) | ||||
−0.998648 | + | 0.0519803i | \(0.983447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.3495 | 1.46337 | 0.731687 | − | 0.681640i | \(-0.238733\pi\) | ||||
0.731687 | + | 0.681640i | \(0.238733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 16.6498i | − 0.669211i | −0.942358 | − | 0.334606i | \(-0.891397\pi\) | ||||
0.942358 | − | 0.334606i | \(-0.108603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.85047 | −0.194330 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0685 | −0.442740 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.60744i | 0.303328i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7898 | −0.588773 | −0.294387 | − | 0.955686i | \(-0.595115\pi\) | ||||
−0.294387 | + | 0.955686i | \(0.595115\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.6892i | 0.463871i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.10840i | − 0.123159i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.8085 | −1.29586 | −0.647928 | − | 0.761701i | \(-0.724364\pi\) | ||||
−0.647928 | + | 0.761701i | \(0.724364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.3479i | 0.605263i | 0.953108 | + | 0.302631i | \(0.0978651\pi\) | ||||
−0.953108 | + | 0.302631i | \(0.902135\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.19107 | −0.243396 | −0.121698 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121698 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9327 | −0.507653 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.4848i | 0.684234i | 0.939657 | + | 0.342117i | \(0.111144\pi\) | ||||
−0.939657 | + | 0.342117i | \(0.888856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.7764 | −0.968093 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 13.8987i | − 0.541416i | −0.962661 | − | 0.270708i | \(-0.912742\pi\) | ||||
0.962661 | − | 0.270708i | \(-0.0872578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.69978i | 0.0661137i | 0.999453 | + | 0.0330568i | \(0.0105242\pi\) | ||||
−0.999453 | + | 0.0330568i | \(0.989476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.6457 | −0.645494 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 86.8869i | − 3.36428i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.2762 | 1.20741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7847 | −0.878284 | −0.439142 | − | 0.898418i | \(-0.644718\pi\) | ||||
−0.439142 | + | 0.898418i | \(0.644718\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 34.2963i | − 1.31811i | −0.752093 | − | 0.659057i | \(-0.770956\pi\) | ||||
0.752093 | − | 0.659057i | \(-0.229044\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.63283 | −0.0626624 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 10.5590i | − 0.404029i | −0.979383 | − | 0.202014i | \(-0.935251\pi\) | ||||
0.979383 | − | 0.202014i | \(-0.0647487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 14.6434i | − 0.559497i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.2561 | −0.771695 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.3879i | 0.547342i | 0.961823 | + | 0.273671i | \(0.0882380\pi\) | ||||
−0.961823 | + | 0.273671i | \(0.911762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.4789 | 0.435421 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.2314 | 0.614807 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 17.8913i | − 0.675746i | −0.941192 | − | 0.337873i | \(-0.890292\pi\) | ||||
0.941192 | − | 0.337873i | \(-0.109708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0678 | 0.983165 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 13.1650i | − 0.495121i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 22.0614i | − 0.828535i | −0.910155 | − | 0.414267i | \(-0.864038\pi\) | ||||
0.910155 | − | 0.414267i | \(-0.135962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −68.9499 | −2.58219 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7273i | 1.33613i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.8888 | −0.592552 | −0.296276 | − | 0.955102i | \(-0.595745\pi\) | ||||
−0.296276 | + | 0.955102i | \(0.595745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.6983 | 0.584634 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 69.0425i | − 2.56418i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.2510 | 0.973595 | 0.486798 | − | 0.873515i | \(-0.338165\pi\) | ||||
0.486798 | + | 0.873515i | \(0.338165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 9.87487i | − 0.365235i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 23.1441i | − 0.854848i | −0.904051 | − | 0.427424i | \(-0.859421\pi\) | ||||
0.904051 | − | 0.427424i | \(-0.140579\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.01935 | −0.111219 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2767i | 0.414819i | 0.978254 | + | 0.207409i | \(0.0665032\pi\) | ||||
−0.978254 | + | 0.207409i | \(0.933497\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.16580 | −0.189515 | −0.0947575 | − | 0.995500i | \(-0.530208\pi\) | ||||
−0.0947575 | + | 0.995500i | \(0.530208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.5330 | 0.898821 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.37257i | 0.342466i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.7670 | −1.30516 | −0.652578 | − | 0.757722i | \(-0.726313\pi\) | ||||
−0.652578 | + | 0.757722i | \(0.726313\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.874212i | 0.0318158i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 31.6174i | − 1.14916i | −0.818450 | − | 0.574578i | \(-0.805166\pi\) | ||||
0.818450 | − | 0.574578i | \(-0.194834\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.7856 | −0.463477 | −0.231738 | − | 0.972778i | \(-0.574441\pi\) | ||||
−0.231738 | + | 0.972778i | \(0.574441\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.31490i | − 0.264817i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.1120 | −0.437340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.55622 | 0.236423 | 0.118212 | − | 0.992988i | \(-0.462284\pi\) | ||||
0.118212 | + | 0.992988i | \(0.462284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.7250i | 0.997197i | 0.866833 | + | 0.498599i | \(0.166152\pi\) | ||||
−0.866833 | + | 0.498599i | \(0.833848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −54.7893 | −1.96809 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 55.6187i | − 1.99275i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 21.3185i | − 0.762837i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.7707 | −0.384421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.9751i | 0.925911i | 0.886382 | + | 0.462955i | \(0.153211\pi\) | ||||
−0.886382 | + | 0.462955i | \(0.846789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9153 | −0.388105 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.2915 | 1.04017 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.5049i | 1.61187i | 0.592006 | + | 0.805934i | \(0.298336\pi\) | ||||
−0.592006 | + | 0.805934i | \(0.701664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.8394 | 0.560358 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5.18619i | − 0.183017i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 30.4730i | − 1.07403i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8396 | 0.732682 | 0.366341 | − | 0.930481i | \(-0.380610\pi\) | ||||
0.366341 | + | 0.930481i | \(0.380610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 52.1223i | − 1.83026i | −0.403158 | − | 0.915130i | \(-0.632088\pi\) | ||||
0.403158 | − | 0.915130i | \(-0.367912\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64.2716 | −2.25134 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.8374 | −1.18382 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9160i | 0.485673i | 0.970067 | + | 0.242837i | \(0.0780779\pi\) | ||||
−0.970067 | + | 0.242837i | \(0.921922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.31771 | −0.0459323 | −0.0229662 | − | 0.999736i | \(-0.507311\pi\) | ||||
−0.0229662 | + | 0.999736i | \(0.507311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.9111i | 0.761925i | 0.924591 | + | 0.380962i | \(0.124407\pi\) | ||||
−0.924591 | + | 0.380962i | \(0.875593\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.0419i | 1.14759i | 0.818999 | + | 0.573795i | \(0.194530\pi\) | ||||
−0.818999 | + | 0.573795i | \(0.805470\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.40277 | −0.0486029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 49.5976i | − 1.71639i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.2548 | −0.561177 | −0.280589 | − | 0.959828i | \(-0.590530\pi\) | ||||
−0.280589 | + | 0.959828i | \(0.590530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −68.4952 | −2.36190 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 11.5589i | − 0.397638i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0159016 | 0.000546384 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.7217i | 1.63588i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 43.5342i | − 1.49058i | −0.666738 | − | 0.745292i | \(-0.732310\pi\) | ||||
0.666738 | − | 0.745292i | \(-0.267690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.968943 | −0.0330985 | −0.0165492 | − | 0.999863i | \(-0.505268\pi\) | ||||
−0.0165492 | + | 0.999863i | \(0.505268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9386i | 0.407341i | 0.979040 | + | 0.203670i | \(0.0652871\pi\) | ||||
−0.979040 | + | 0.203670i | \(0.934713\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.95989 | 0.270958 | 0.135479 | − | 0.990780i | \(-0.456743\pi\) | ||||
0.135479 | + | 0.990780i | \(0.456743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.85455 | −0.165059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 37.0467i | − 1.25672i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82775 | −0.0958148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.89962i | − 0.233250i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3998i | 0.891459i | 0.895168 | + | 0.445730i | \(0.147056\pi\) | ||||
−0.895168 | + | 0.445730i | \(0.852944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4550 | 1.09344 | 0.546718 | − | 0.837317i | \(-0.315877\pi\) | ||||
0.546718 | + | 0.837317i | \(0.315877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.46140i | − 0.116486i | −0.998302 | − | 0.0582428i | \(-0.981450\pi\) | ||||
0.998302 | − | 0.0582428i | \(-0.0185497\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.9279 | −0.568385 | −0.284192 | − | 0.958767i | \(-0.591725\pi\) | ||||
−0.284192 | + | 0.958767i | \(0.591725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.37545 | 0.113209 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 54.2756i | − 1.81626i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0114 | 0.401497 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 77.3682i | 2.58037i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.14120i | 0.304537i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.1794 | 2.23312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1236i | 0.967034i | 0.875335 | + | 0.483517i | \(0.160641\pi\) | ||||
−0.875335 | + | 0.483517i | \(0.839359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.85198 | −0.227016 | −0.113508 | − | 0.993537i | \(-0.536209\pi\) | ||||
−0.113508 | + | 0.993537i | \(0.536209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.22884 | −0.0406685 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.15460i | 0.236266i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.3468 | 1.23196 | 0.615979 | − | 0.787763i | \(-0.288761\pi\) | ||||
0.615979 | + | 0.787763i | \(0.288761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 19.9657i | − 0.657179i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.9209i | 1.24683i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.8771 | −1.27552 | −0.637758 | − | 0.770236i | \(-0.720138\pi\) | ||||
−0.637758 | + | 0.770236i | \(0.720138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.80674i | 0.157534i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.1231 | 0.527281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.3583 | −0.403727 | −0.201863 | − | 0.979414i | \(-0.564700\pi\) | ||||
−0.201863 | + | 0.979414i | \(0.564700\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.1798i | 1.30982i | 0.755705 | + | 0.654912i | \(0.227294\pi\) | ||||
−0.755705 | + | 0.654912i | \(0.772706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 101.820 | 3.31572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.7512i | 0.479351i | 0.970853 | + | 0.239676i | \(0.0770411\pi\) | ||||
−0.970853 | + | 0.239676i | \(0.922959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.85708i | − 0.157668i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.2336 | 1.17372 | 0.586861 | − | 0.809687i | \(-0.300363\pi\) | ||||
0.586861 | + | 0.809687i | \(0.300363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.2456i | 2.62905i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.22854 | −0.136547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3962 | 0.980523 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53.8060i | 1.73208i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.6101 | 1.04867 | 0.524335 | − | 0.851512i | \(-0.324314\pi\) | ||||
0.524335 | + | 0.851512i | \(0.324314\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 37.3897i | − 1.19989i | −0.800040 | − | 0.599947i | \(-0.795188\pi\) | ||||
0.800040 | − | 0.599947i | \(-0.204812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.31473i | − 0.106265i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.76353 | 0.120406 | 0.0602029 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602029 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 16.0988i | − 0.514521i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.8112 | 1.17410 | 0.587048 | − | 0.809552i | \(-0.300290\pi\) | ||||
0.587048 | + | 0.809552i | \(0.300290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.3485 | 1.63610 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 61.9454i | − 1.96975i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.0994 | 1.68676 | 0.843379 | − | 0.537319i | \(-0.180563\pi\) | ||||
0.843379 | + | 0.537319i | \(0.180563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45.7445i | 1.45020i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.5497i | − 0.935847i | −0.883769 | − | 0.467923i | \(-0.845002\pi\) | ||||
0.883769 | − | 0.467923i | \(-0.154998\pi\) | |||||||
\(998\) | 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 | 6048.2.c.f.3025.1 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.f.3025.23 | 24 | ||
4.3 | odd | 2 | 1512.2.c.g.757.23 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.g.757.24 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.f.3025.24 | 24 | ||
12.11 | even | 2 | 1512.2.c.g.757.2 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.f.3025.2 | 24 | ||
24.11 | even | 2 | 1512.2.c.g.757.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.1 | ✓ | 24 | 24.11 | even | 2 | ||
1512.2.c.g.757.2 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.g.757.23 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.g.757.24 | yes | 24 | 8.3 | odd | 2 | ||
6048.2.c.f.3025.1 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.f.3025.2 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.f.3025.23 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.f.3025.24 | 24 | 8.5 | even | 2 | inner |