Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1855.2 | ||
Root | \(1.71903 - 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1855 |
Dual form | 2736.2.bm.o.559.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.675970 | + | 1.17081i | 0.302303 | + | 0.523604i | 0.976657 | − | 0.214804i | \(-0.0689113\pi\) |
−0.674354 | + | 0.738408i | \(0.735578\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.45735i | − | 0.550826i | −0.961326 | − | 0.275413i | \(-0.911185\pi\) | ||
0.961326 | − | 0.275413i | \(-0.0888145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.18940i | 0.961640i | 0.876819 | + | 0.480820i | \(0.159661\pi\) | ||||
−0.876819 | + | 0.480820i | \(0.840339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.23419 | − | 1.28991i | −0.619653 | − | 0.357757i | 0.157081 | − | 0.987586i | \(-0.449792\pi\) |
−0.776734 | + | 0.629829i | \(0.783125\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.08613 | − | 3.61328i | −0.505961 | − | 0.876350i | −0.999976 | − | 0.00689678i | \(-0.997805\pi\) |
0.494015 | − | 0.869453i | \(-0.335529\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.43807 | − | 3.61328i | −0.559331 | − | 0.828944i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.49629 | + | 3.75064i | 1.35457 | + | 0.782062i | 0.988886 | − | 0.148677i | \(-0.0475016\pi\) |
0.365685 | + | 0.930739i | \(0.380835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.58613 | − | 2.74726i | 0.317226 | − | 0.549452i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.734191 | + | 0.423885i | 0.136336 | + | 0.0787135i | 0.566617 | − | 0.823982i | \(-0.308252\pi\) |
−0.430281 | + | 0.902695i | \(0.641585\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.351939 | 0.0632101 | 0.0316051 | − | 0.999500i | \(-0.489938\pi\) | ||||
0.0316051 | + | 0.999500i | \(0.489938\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.70628 | − | 0.985122i | 0.288414 | − | 0.166516i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.89169i | − | 1.13299i | −0.824066 | − | 0.566494i | \(-0.808300\pi\) | ||
0.824066 | − | 0.566494i | \(-0.191700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.05582 | − | 2.34163i | 0.633412 | − | 0.365701i | −0.148660 | − | 0.988888i | \(-0.547496\pi\) |
0.782072 | + | 0.623188i | \(0.214163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.52791 | − | 3.76889i | 0.995497 | − | 0.574750i | 0.0885840 | − | 0.996069i | \(-0.471766\pi\) |
0.906913 | + | 0.421318i | \(0.138433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.04840 | + | 4.64675i | 1.17398 | + | 0.677797i | 0.954614 | − | 0.297845i | \(-0.0962679\pi\) |
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.87614 | 0.696591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.76210 | − | 5.05880i | −1.20357 | − | 0.694880i | −0.242220 | − | 0.970221i | \(-0.577876\pi\) |
−0.961346 | + | 0.275342i | \(0.911209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.73419 | + | 2.15594i | −0.503518 | + | 0.290706i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.675970 | + | 1.17081i | 0.0880037 | + | 0.152427i | 0.906667 | − | 0.421847i | \(-0.138618\pi\) |
−0.818663 | + | 0.574274i | \(0.805285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29001 | − | 7.43051i | 0.549279 | − | 0.951380i | −0.449045 | − | 0.893509i | \(-0.648236\pi\) |
0.998324 | − | 0.0578704i | \(-0.0184310\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.48776i | − | 0.432604i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.08984 | + | 1.88766i | −0.133145 | + | 0.230614i | −0.924887 | − | 0.380241i | \(-0.875841\pi\) |
0.791742 | + | 0.610855i | \(0.209174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.438069 | + | 0.758758i | 0.0519893 | + | 0.0900481i | 0.890849 | − | 0.454300i | \(-0.150111\pi\) |
−0.838860 | + | 0.544348i | \(0.816777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.67226 | + | 11.5567i | 0.780929 | + | 1.35261i | 0.931401 | + | 0.363994i | \(0.118587\pi\) |
−0.150472 | + | 0.988614i | \(0.548079\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.64806 | 0.529696 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.52791 | − | 4.37847i | −0.284412 | − | 0.492616i | 0.688054 | − | 0.725659i | \(-0.258465\pi\) |
−0.972466 | + | 0.233043i | \(0.925132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.22657i | 0.793219i | 0.917987 | + | 0.396609i | \(0.129813\pi\) | ||||
−0.917987 | + | 0.396609i | \(0.870187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82032 | − | 4.88494i | 0.305907 | − | 0.529846i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.81792 | + | 2.20428i | 0.404698 | + | 0.233653i | 0.688509 | − | 0.725228i | \(-0.258265\pi\) |
−0.283811 | + | 0.958880i | \(0.591599\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.87985 | + | 3.25599i | −0.197062 | + | 0.341321i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.58242 | − | 5.29699i | 0.264951 | − | 0.543460i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.79001 | + | 4.49756i | −0.790956 | + | 0.456658i | −0.840299 | − | 0.542123i | \(-0.817620\pi\) |
0.0493433 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.73419 | − | 6.46781i | 0.371566 | − | 0.643571i | −0.618241 | − | 0.785989i | \(-0.712154\pi\) |
0.989807 | + | 0.142418i | \(0.0454877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5726 | 1.14028 | 0.570141 | − | 0.821547i | \(-0.306889\pi\) | ||||
0.570141 | + | 0.821547i | \(0.306889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1723 | −0.983390 | −0.491695 | − | 0.870768i | \(-0.663622\pi\) | ||||
−0.491695 | + | 0.870768i | \(0.663622\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.31421 | − | 4.22286i | 0.700574 | − | 0.404477i | −0.106987 | − | 0.994260i | \(-0.534120\pi\) |
0.807561 | + | 0.589784i | \(0.200787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.4829i | − | 1.17429i | −0.809481 | − | 0.587146i | \(-0.800252\pi\) | ||
0.809481 | − | 0.587146i | \(-0.199748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1413i | 0.945678i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.26581 | + | 3.04022i | −0.482716 | + | 0.278696i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.827740 | 0.0752491 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0484 | 0.988199 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.52420 | + | 6.10409i | −0.312722 | + | 0.541651i | −0.978951 | − | 0.204097i | \(-0.934574\pi\) |
0.666229 | + | 0.745748i | \(0.267908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.74161 | − | 1.58287i | 0.239536 | − | 0.138296i | −0.375428 | − | 0.926852i | \(-0.622504\pi\) |
0.614963 | + | 0.788556i | \(0.289171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.26581 | + | 3.55311i | −0.456604 | + | 0.308094i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.25839 | − | 5.64370i | 0.278383 | − | 0.482174i | −0.692600 | − | 0.721322i | \(-0.743535\pi\) |
0.970983 | + | 0.239148i | \(0.0768682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4647 | − | 7.19648i | −1.05724 | − | 0.610398i | −0.132572 | − | 0.991173i | \(-0.542324\pi\) |
−0.924667 | + | 0.380776i | \(0.875657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.11404 | − | 7.12572i | 0.344033 | − | 0.595883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.14613i | 0.0951813i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.20017 | + | 5.54286i | 0.262168 | + | 0.454088i | 0.966818 | − | 0.255467i | \(-0.0822292\pi\) |
−0.704650 | + | 0.709555i | \(0.748896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.64064 | 0.784544 | 0.392272 | − | 0.919849i | \(-0.371689\pi\) | ||||
0.392272 | + | 0.919849i | \(0.371689\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.237900 | + | 0.412055i | 0.0191086 | + | 0.0330971i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.7281 | − | 20.3136i | −0.936003 | − | 1.62120i | −0.772836 | − | 0.634605i | \(-0.781163\pi\) |
−0.163166 | − | 0.986599i | \(-0.552171\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.46598 | − | 9.46735i | 0.430779 | − | 0.746132i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.15289i | 0.246953i | 0.992347 | + | 0.123477i | \(0.0394044\pi\) | ||||
−0.992347 | + | 0.123477i | \(0.960596\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.49629 | − | 6.05575i | 0.270551 | − | 0.468608i | −0.698452 | − | 0.715657i | \(-0.746127\pi\) |
0.969003 | + | 0.247049i | \(0.0794608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.17226 | − | 5.49452i | −0.244020 | − | 0.422655i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3068 | − | 9.99208i | 1.31581 | − | 0.759684i | 0.332759 | − | 0.943012i | \(-0.392020\pi\) |
0.983052 | + | 0.183328i | \(0.0586871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00371 | − | 2.31154i | −0.302652 | − | 0.174736i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.6965 | 1.17321 | 0.586604 | − | 0.809874i | \(-0.300464\pi\) | ||||
0.586604 | + | 0.809874i | \(0.300464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3142 | + | 7.68696i | 0.989637 | + | 0.571367i | 0.905166 | − | 0.425059i | \(-0.139746\pi\) |
0.0844714 | + | 0.996426i | \(0.473080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.06889 | − | 4.65858i | 0.593237 | − | 0.342505i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.5242 | − | 6.65350i | 0.842733 | − | 0.486552i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.85914i | − | 0.279238i | −0.990205 | − | 0.139619i | \(-0.955412\pi\) | ||
0.990205 | − | 0.139619i | \(-0.0445878\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8142 | + | 6.82094i | −0.850405 | + | 0.490982i | −0.860788 | − | 0.508964i | \(-0.830028\pi\) |
0.0103823 | + | 0.999946i | \(0.496695\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.7571 | −1.69262 | −0.846311 | − | 0.532689i | \(-0.821182\pi\) | ||||
−0.846311 | + | 0.532689i | \(0.821182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5205 | + | 11.2702i | 1.38377 | + | 0.798920i | 0.992604 | − | 0.121399i | \(-0.0387381\pi\) |
0.391167 | + | 0.920320i | \(0.372071\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.617748 | − | 1.06997i | 0.0433574 | − | 0.0750973i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.48322 | + | 3.16574i | 0.382965 | + | 0.221105i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.5242 | − | 7.77597i | 0.797146 | − | 0.537875i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0521 | + | 19.1428i | 0.760859 | + | 1.31785i | 0.942409 | + | 0.334464i | \(0.108555\pi\) |
−0.181550 | + | 0.983382i | \(0.558111\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.82534 | + | 5.09531i | 0.601883 | + | 0.347497i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.512898i | − | 0.0348178i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.7637i | 0.724044i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.87985 | + | 4.98804i | 0.192849 | + | 0.334024i | 0.946193 | − | 0.323602i | \(-0.104894\pi\) |
−0.753344 | + | 0.657626i | \(0.771561\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.5242 | −1.56136 | −0.780678 | − | 0.624934i | \(-0.785126\pi\) | ||||
−0.780678 | + | 0.624934i | \(0.785126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.76450 | −0.380929 | −0.190465 | − | 0.981694i | \(-0.560999\pi\) | ||||
−0.190465 | + | 0.981694i | \(0.560999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.321627 | + | 0.557074i | 0.0210705 | + | 0.0364951i | 0.876368 | − | 0.481641i | \(-0.159959\pi\) |
−0.855298 | + | 0.518137i | \(0.826626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.5642i | 0.819600i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.65350i | 0.430379i | 0.976572 | + | 0.215190i | \(0.0690369\pi\) | ||||
−0.976572 | + | 0.215190i | \(0.930963\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.548399 | + | 0.316618i | 0.0353255 | + | 0.0203952i | 0.517559 | − | 0.855648i | \(-0.326841\pi\) |
−0.482233 | + | 0.876043i | \(0.660174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.29612 | + | 5.70905i | 0.210581 | + | 0.364738i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.786299 | + | 11.2177i | 0.0500310 | + | 0.713762i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.10422 | − | 3.52427i | −0.385295 | − | 0.222450i | 0.294825 | − | 0.955551i | \(-0.404739\pi\) |
−0.680119 | + | 0.733101i | \(0.738072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9623 | + | 20.7193i | −0.752061 | + | 1.30261i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.7547 | − | 12.5601i | −1.35702 | − | 0.783476i | −0.367799 | − | 0.929905i | \(-0.619888\pi\) |
−0.989221 | + | 0.146430i | \(0.953222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0436 | −0.624078 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3216 | − | 7.11389i | 0.759784 | − | 0.438662i | −0.0694342 | − | 0.997587i | \(-0.522119\pi\) |
0.829218 | + | 0.558925i | \(0.188786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 13.6784i | − | 0.840256i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.18950 | − | 0.686759i | 0.0725252 | − | 0.0418724i | −0.463299 | − | 0.886202i | \(-0.653334\pi\) |
0.535824 | + | 0.844330i | \(0.320001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4684 | − | 6.04392i | 0.635909 | − | 0.367142i | −0.147128 | − | 0.989117i | \(-0.547003\pi\) |
0.783037 | + | 0.621975i | \(0.213670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.76210 | + | 5.05880i | 0.528374 | + | 0.305057i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.58002 | 0.335271 | 0.167635 | − | 0.985849i | \(-0.446387\pi\) | ||||
0.167635 | + | 0.985849i | \(0.446387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6079 | − | 6.70184i | −0.692471 | − | 0.399798i | 0.112066 | − | 0.993701i | \(-0.464253\pi\) |
−0.804537 | + | 0.593903i | \(0.797586\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.88095 | − | 4.55007i | 0.468474 | − | 0.270473i | −0.247127 | − | 0.968983i | \(-0.579486\pi\) |
0.715601 | + | 0.698510i | \(0.246153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.41256 | − | 5.91073i | −0.201437 | − | 0.348900i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.203878 | + | 0.353128i | −0.0119928 | + | 0.0207722i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.70905i | 0.333526i | 0.985997 | + | 0.166763i | \(0.0533315\pi\) | ||||
−0.985997 | + | 0.166763i | \(0.946668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.913870 | + | 1.58287i | −0.0532076 | + | 0.0921582i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.67597 | − | 16.7593i | −0.559576 | − | 0.969214i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.49258 | − | 9.51343i | −0.316587 | − | 0.548345i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.5997 | 0.664195 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1419 | − | 19.2984i | −0.635905 | − | 1.10142i | −0.986323 | − | 0.164826i | \(-0.947294\pi\) |
0.350418 | − | 0.936593i | \(-0.386039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.9286i | − | 1.18675i | −0.804925 | − | 0.593376i | \(-0.797795\pi\) | ||
0.804925 | − | 0.593376i | \(-0.202205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.561931 | − | 0.973292i | 0.0317622 | − | 0.0550137i | −0.849707 | − | 0.527255i | \(-0.823221\pi\) |
0.881470 | + | 0.472241i | \(0.156555\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0205 | + | 8.67208i | 0.843635 | + | 0.487073i | 0.858498 | − | 0.512817i | \(-0.171398\pi\) |
−0.0148633 | + | 0.999890i | \(0.504731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.35194 | + | 2.34163i | −0.0756941 | + | 0.131106i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.96969 | + | 16.3472i | −0.443445 | + | 0.909583i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.08744 | + | 4.09193i | −0.393140 | + | 0.226980i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.77192 | − | 11.7293i | 0.373348 | − | 0.646658i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.584825 | −0.0321449 | −0.0160724 | − | 0.999871i | \(-0.505116\pi\) | ||||
−0.0160724 | + | 0.999871i | \(0.505116\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.94679 | −0.161001 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8142 | − | 13.7491i | 1.29724 | − | 0.748963i | 0.317316 | − | 0.948320i | \(-0.397219\pi\) |
0.979927 | + | 0.199357i | \(0.0638852\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.12247i | 0.0607854i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.3077i | − | 0.934526i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.8105 | + | 13.1696i | −1.22453 | + | 0.706984i | −0.965881 | − | 0.258987i | \(-0.916611\pi\) |
−0.258651 | + | 0.965971i | \(0.583278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.53162 | 0.510216 | 0.255108 | − | 0.966913i | \(-0.417889\pi\) | ||||
0.255108 | + | 0.966913i | \(0.417889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.94418 | −0.422826 | −0.211413 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211413 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.592243 | + | 1.02580i | −0.0314330 | + | 0.0544436i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.9293 | − | 9.19681i | 0.840719 | − | 0.485389i | −0.0167898 | − | 0.999859i | \(-0.505345\pi\) |
0.857508 | + | 0.514470i | \(0.172011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.11164 | + | 17.6189i | −0.374297 | + | 0.927309i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.02049 | + | 15.6239i | −0.472154 | + | 0.817795i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.41627 | − | 4.28179i | −0.387126 | − | 0.223507i | 0.293788 | − | 0.955871i | \(-0.405084\pi\) |
−0.680914 | + | 0.732363i | \(0.738417\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.37243 | + | 12.7694i | −0.382757 | + | 0.662955i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 25.0965i | − | 1.29945i | −0.760171 | − | 0.649723i | \(-0.774885\pi\) | ||
0.760171 | − | 0.649723i | \(-0.225115\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.09355 | − | 1.89408i | −0.0563206 | − | 0.0975502i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.6816 | −1.78148 | −0.890738 | − | 0.454518i | \(-0.849812\pi\) | ||||
−0.890738 | + | 0.454518i | \(0.849812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.58984 | − | 7.94984i | −0.234530 | − | 0.406218i | 0.724606 | − | 0.689163i | \(-0.242022\pi\) |
−0.959136 | + | 0.282946i | \(0.908688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.14195 | + | 5.44201i | 0.160128 | + | 0.277351i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.4660 | + | 19.8597i | −0.581348 | + | 1.00692i | 0.413972 | + | 0.910290i | \(0.364141\pi\) |
−0.995320 | + | 0.0966348i | \(0.969192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 31.2973i | − | 1.58277i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.41758 | − | 5.91942i | 0.171957 | − | 0.297838i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.593549 | − | 1.02806i | −0.0297894 | − | 0.0515967i | 0.850746 | − | 0.525576i | \(-0.176150\pi\) |
−0.880536 | + | 0.473980i | \(0.842817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3273 | + | 16.9321i | −1.46453 | + | 0.845549i | −0.999216 | − | 0.0395939i | \(-0.987394\pi\) |
−0.465319 | + | 0.885143i | \(0.654060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.786299 | − | 0.453970i | −0.0391684 | − | 0.0226139i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.9804 | 1.08953 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.8310 | − | 11.4494i | −0.980579 | − | 0.566138i | −0.0781343 | − | 0.996943i | \(-0.524896\pi\) |
−0.902445 | + | 0.430805i | \(0.858230\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.70628 | − | 0.985122i | 0.0839607 | − | 0.0484747i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.46096 | + | 4.88494i | −0.415332 | + | 0.239792i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7020i | 0.669389i | 0.942327 | + | 0.334694i | \(0.108633\pi\) | ||||
−0.942327 | + | 0.334694i | \(0.891367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3216 | − | 7.11389i | 0.600519 | − | 0.346710i | −0.168727 | − | 0.985663i | \(-0.553965\pi\) |
0.769246 | + | 0.638953i | \(0.220632\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.2355 | −0.642016 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8288 | − | 6.25203i | −0.524044 | − | 0.302557i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.04840 | + | 13.9402i | −0.387678 | + | 0.671478i | −0.992137 | − | 0.125159i | \(-0.960056\pi\) |
0.604459 | + | 0.796636i | \(0.293389\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.1635 | + | 19.1470i | 1.59374 | + | 0.920145i | 0.992658 | + | 0.120956i | \(0.0385960\pi\) |
0.601080 | + | 0.799189i | \(0.294737\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.28630 | − | 32.6172i | −0.109369 | − | 1.56029i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.95856 | − | 12.0526i | −0.332114 | − | 0.575238i | 0.650812 | − | 0.759239i | \(-0.274429\pi\) |
−0.982926 | + | 0.184001i | \(0.941095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.16159 | + | 1.24800i | 0.102700 | + | 0.0592941i | 0.550470 | − | 0.834855i | \(-0.314448\pi\) |
−0.447770 | + | 0.894149i | \(0.647782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.96009i | 0.282536i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.4766i | 1.86302i | 0.363721 | + | 0.931508i | \(0.381506\pi\) | ||||
−0.363721 | + | 0.931508i | \(0.618494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.46838 | + | 12.9356i | 0.351672 | + | 0.609114i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.08288 | −0.238289 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.2207 | −1.78789 | −0.893944 | − | 0.448180i | \(-0.852072\pi\) | ||||
−0.893944 | + | 0.448180i | \(0.852072\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3469 | + | 23.1176i | 0.621628 | + | 1.07669i | 0.989183 | + | 0.146690i | \(0.0468619\pi\) |
−0.367554 | + | 0.930002i | \(0.619805\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.96877i | − | 0.230918i | −0.993312 | − | 0.115459i | \(-0.963166\pi\) | ||
0.993312 | − | 0.115459i | \(-0.0368339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.1757i | 1.11872i | 0.828926 | + | 0.559359i | \(0.188953\pi\) | ||||
−0.828926 | + | 0.559359i | \(0.811047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.75097 | + | 1.58827i | 0.127028 | + | 0.0733397i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0205 | + | 20.8201i | 0.552703 | + | 0.957309i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.7937 | + | 0.966868i | −0.632899 | + | 0.0443629i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.9500 | + | 19.0237i | 1.50553 | + | 0.869216i | 0.999979 | + | 0.00641641i | \(0.00204242\pi\) |
0.505546 | + | 0.862799i | \(0.331291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.88967 | + | 15.3974i | −0.405334 | + | 0.702059i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5316 | − | 6.08043i | −0.478216 | − | 0.276098i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.344521 | −0.0156117 | −0.00780586 | − | 0.999970i | \(-0.502485\pi\) | ||||
−0.00780586 | + | 0.999970i | \(0.502485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.838408 | + | 0.484055i | −0.0378368 | + | 0.0218451i | −0.518799 | − | 0.854896i | \(-0.673621\pi\) |
0.480962 | + | 0.876741i | \(0.340287\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.53712i | − | 0.159304i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.10577 | − | 0.638419i | 0.0496008 | − | 0.0286370i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2695 | − | 7.08381i | 0.549259 | − | 0.317115i | −0.199564 | − | 0.979885i | \(-0.563953\pi\) |
0.748823 | + | 0.662770i | \(0.230619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.7752 | − | 21.2322i | −1.63972 | − | 0.946695i | −0.980928 | − | 0.194374i | \(-0.937733\pi\) |
−0.658796 | − | 0.752321i | \(-0.728934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0968 | 0.449302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.4758 | − | 8.93496i | −0.685953 | − | 0.396035i | 0.116141 | − | 0.993233i | \(-0.462947\pi\) |
−0.802094 | + | 0.597198i | \(0.796281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.8421 | − | 9.72380i | 0.745051 | − | 0.430156i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.82272 | + | 13.5494i | 0.344710 | + | 0.597056i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.8203 | + | 25.6695i | −0.651797 | + | 1.12895i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0384i | 0.483601i | 0.970326 | + | 0.241800i | \(0.0777379\pi\) | ||||
−0.970326 | + | 0.241800i | \(0.922262\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.0824 | + | 19.1953i | −0.484600 | + | 0.839353i | −0.999843 | − | 0.0176915i | \(-0.994368\pi\) |
0.515243 | + | 0.857044i | \(0.327702\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.734191 | − | 1.27166i | −0.0319819 | − | 0.0553942i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.6345 | + | 28.8119i | 0.723240 | + | 1.25269i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0820 | −0.523328 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.87614 | − | 11.9098i | −0.297281 | − | 0.514906i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5519i | 0.669870i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4245 | + | 21.5199i | −0.534173 | + | 0.925214i | 0.465030 | + | 0.885295i | \(0.346043\pi\) |
−0.999203 | + | 0.0399193i | \(0.987290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.88836 | + | 5.70905i | 0.423571 | + | 0.244549i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.8798 | + | 27.5047i | −0.678973 | + | 1.17602i | 0.296317 | + | 0.955090i | \(0.404241\pi\) |
−0.975290 | + | 0.220927i | \(0.929092\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.258391 | − | 3.68630i | −0.0110078 | − | 0.157042i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.38095 | + | 3.68404i | −0.271345 | + | 0.156661i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.72677 | + | 8.18701i | −0.200280 | + | 0.346895i | −0.948619 | − | 0.316422i | \(-0.897518\pi\) |
0.748339 | + | 0.663317i | \(0.230852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.4461 | −0.822484 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.5503 | −1.83543 | −0.917714 | − | 0.397242i | \(-0.869968\pi\) | ||||
−0.917714 | + | 0.397242i | \(0.869968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6151 | − | 8.43805i | 0.614863 | − | 0.354992i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.3471i | 1.94297i | 0.237097 | + | 0.971486i | \(0.423804\pi\) | ||||
−0.237097 | + | 0.971486i | \(0.576196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.0346i | − | 1.59170i | −0.605495 | − | 0.795849i | \(-0.707025\pi\) | ||
0.605495 | − | 0.795849i | \(-0.292975\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.6079 | − | 11.8980i | 0.859410 | − | 0.496181i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.8761 | 0.952346 | 0.476173 | − | 0.879352i | \(-0.342024\pi\) | ||||
0.476173 | + | 0.879352i | \(0.342024\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5316 | 0.436925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.1345 | − | 27.9458i | 0.668224 | − | 1.15740i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.6079 | − | 10.1659i | 0.726757 | − | 0.419593i | −0.0904777 | − | 0.995898i | \(-0.528839\pi\) |
0.817235 | + | 0.576305i | \(0.195506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.858052 | − | 1.27166i | −0.0353554 | − | 0.0523977i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.81792 | − | 6.61283i | 0.156783 | − | 0.271556i | −0.776924 | − | 0.629595i | \(-0.783221\pi\) |
0.933707 | + | 0.358038i | \(0.116554\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.11905 | − | 4.11019i | −0.291853 | − | 0.168501i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.94178 | + | 10.2915i | −0.242774 | + | 0.420498i | −0.961504 | − | 0.274792i | \(-0.911391\pi\) |
0.718729 | + | 0.695290i | \(0.244724\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.0962i | − | 1.43161i | −0.698303 | − | 0.715803i | \(-0.746061\pi\) | ||
0.698303 | − | 0.715803i | \(-0.253939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.559527 | + | 0.969129i | 0.0227480 | + | 0.0394007i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9293 | 1.33656 | 0.668280 | − | 0.743909i | \(-0.267031\pi\) | ||||
0.668280 | + | 0.743909i | \(0.267031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.9878 | − | 20.7634i | −0.484973 | − | 0.839999i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.8310 | + | 25.6880i | 0.599018 | + | 1.03753i | 0.992966 | + | 0.118397i | \(0.0377756\pi\) |
−0.393948 | + | 0.919133i | \(0.628891\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2560 | + | 22.9600i | −0.533666 | + | 0.924337i | 0.465561 | + | 0.885016i | \(0.345853\pi\) |
−0.999227 | + | 0.0393206i | \(0.987481\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8510i | 0.797878i | 0.916977 | + | 0.398939i | \(0.130621\pi\) | ||||
−0.916977 | + | 0.398939i | \(0.869379\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.21240 | − | 5.56403i | 0.128702 | − | 0.222918i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.462269 | − | 0.800673i | −0.0184908 | − | 0.0320269i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.9016 | + | 14.3770i | −0.992894 | + | 0.573247i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.3179 | − | 11.7306i | −0.808844 | − | 0.466986i | 0.0377106 | − | 0.999289i | \(-0.487994\pi\) |
−0.846554 | + | 0.532303i | \(0.821327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.52901 | −0.378147 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.8942 | − | 6.28978i | −0.431645 | − | 0.249210i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.4535 | + | 24.5106i | −1.67681 | + | 0.968109i | −0.713143 | + | 0.701019i | \(0.752729\pi\) |
−0.963672 | + | 0.267090i | \(0.913938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8495 | − | 7.41868i | 0.506736 | − | 0.292564i | −0.224755 | − | 0.974415i | \(-0.572158\pi\) |
0.731491 | + | 0.681851i | \(0.238825\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.8135i | − | 1.01484i | −0.861700 | − | 0.507418i | \(-0.830600\pi\) | ||
0.861700 | − | 0.507418i | \(-0.169400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.73419 | + | 2.15594i | −0.146580 | + | 0.0846279i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.6433 | −0.964365 | −0.482183 | − | 0.876071i | \(-0.660156\pi\) | ||||
−0.482183 | + | 0.876071i | \(0.660156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.70649 | + | 2.13994i | 0.144825 | + | 0.0836145i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0582214 | − | 0.100842i | 0.00226798 | − | 0.00392826i | −0.864889 | − | 0.501963i | \(-0.832611\pi\) |
0.867157 | + | 0.498035i | \(0.165945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.35675 | + | 3.09272i | 0.208353 | + | 0.120293i | 0.600546 | − | 0.799590i | \(-0.294950\pi\) |
−0.392193 | + | 0.919883i | \(0.628283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.71956 | − | 3.76348i | −0.299352 | − | 0.145942i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.17968 | + | 5.50737i | 0.123118 | + | 0.213246i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.6989 | + | 13.6825i | 0.914884 | + | 0.528209i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.6082i | − | 0.717292i | −0.933474 | − | 0.358646i | \(-0.883239\pi\) | ||
0.933474 | − | 0.358646i | \(-0.116761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 28.9793i | − | 1.11376i | −0.830591 | − | 0.556882i | \(-0.811997\pi\) | ||
0.830591 | − | 0.556882i | \(-0.188003\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.55451 | + | 11.3527i | 0.251539 | + | 0.435678i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.8687 | −1.67859 | −0.839295 | − | 0.543676i | \(-0.817032\pi\) | ||||
−0.839295 | + | 0.543676i | \(0.817032\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.81029 | 0.336624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.0508 | + | 22.6047i | 0.497196 | + | 0.861169i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2837i | 1.03792i | 0.854798 | + | 0.518961i | \(0.173681\pi\) | ||||
−0.854798 | + | 0.518961i | \(0.826319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19.4584i | − | 0.738100i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9219 | − | 9.76988i | −0.640964 | − | 0.370061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.44047 | − | 9.42318i | −0.205484 | − | 0.355908i | 0.744803 | − | 0.667284i | \(-0.232543\pi\) |
−0.950287 | + | 0.311376i | \(0.899210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.9016 | + | 16.8024i | −0.939183 | + | 0.633716i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.42584 | − | 5.44201i | −0.354495 | − | 0.204668i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.8626 | + | 43.0633i | −0.933735 | + | 1.61728i | −0.156860 | + | 0.987621i | \(0.550137\pi\) |
−0.776875 | + | 0.629655i | \(0.783196\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.28630 | + | 1.32000i | 0.0856226 | + | 0.0494342i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1239 | 0.416009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.6079 | − | 15.3621i | 0.992308 | − | 0.572909i | 0.0863447 | − | 0.996265i | \(-0.472481\pi\) |
0.905963 | + | 0.423356i | \(0.139148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.8653i | − | 0.628096i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.32905 | − | 1.34467i | 0.0864986 | − | 0.0499400i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9963 | + | 15.0090i | −0.964149 | + | 0.556652i | −0.897448 | − | 0.441121i | \(-0.854581\pi\) |
−0.0667015 | + | 0.997773i | \(0.521248\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.2361 | − | 15.7248i | −1.00736 | − | 0.581602i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.3026 | −1.74716 | −0.873581 | − | 0.486679i | \(-0.838208\pi\) | ||||
−0.873581 | + | 0.486679i | \(0.838208\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.02049 | − | 3.47593i | −0.221768 | − | 0.128038i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.3515 | + | 15.7914i | −1.00614 | + | 0.580895i | −0.910059 | − | 0.414478i | \(-0.863964\pi\) |
−0.0960811 | + | 0.995374i | \(0.530631\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.7063 | + | 28.9361i | 0.612894 | + | 1.06156i | 0.990750 | + | 0.135699i | \(0.0433281\pi\) |
−0.377856 | + | 0.925864i | \(0.623339\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.32643 | + | 7.49360i | −0.158508 | + | 0.274544i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.8245i | 0.541676i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.84212 | + | 17.0470i | −0.359144 | + | 0.622056i | −0.987818 | − | 0.155613i | \(-0.950265\pi\) |
0.628674 | + | 0.777669i | \(0.283598\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.51678 | + | 11.2874i | 0.237170 | + | 0.410790i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.5181 | + | 28.6102i | 0.600360 | + | 1.03985i | 0.992766 | + | 0.120062i | \(0.0383094\pi\) |
−0.392406 | + | 0.919792i | \(0.628357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.5726 | 1.68826 | 0.844128 | − | 0.536142i | \(-0.180119\pi\) | ||||
0.844128 | + | 0.536142i | \(0.180119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.15417 | − | 10.6593i | −0.222796 | − | 0.385894i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.48776i | − | 0.125936i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9562 | − | 27.6369i | 0.575394 | − | 0.996611i | −0.420605 | − | 0.907244i | \(-0.638182\pi\) |
0.995999 | − | 0.0893673i | \(-0.0284845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0558 | + | 7.53778i | 0.469585 | + | 0.271115i | 0.716066 | − | 0.698033i | \(-0.245941\pi\) |
−0.246481 | + | 0.969148i | \(0.579274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.558221 | − | 0.966868i | 0.0200519 | − | 0.0347309i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.3493 | − | 8.94577i | −0.657433 | − | 0.320515i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.41998 | + | 1.39718i | −0.0865938 | + | 0.0499949i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8556 | − | 27.4628i | 0.565912 | − | 0.980189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.9023 | 1.35107 | 0.675535 | − | 0.737328i | \(-0.263913\pi\) | ||||
0.675535 | + | 0.737328i | \(0.263913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.1919 | −0.646830 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.1694 | + | 11.0675i | −0.680725 | + | 0.393017i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.06692i | − | 0.0732142i | −0.999330 | − | 0.0366071i | \(-0.988345\pi\) | ||
0.999330 | − | 0.0366071i | \(-0.0116550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 38.7749i | − | 1.37176i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.8589 | + | 21.2805i | −1.30072 | + | 0.750972i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.7793 | 0.520903 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.2255 | 0.675931 | 0.337966 | − | 0.941158i | \(-0.390261\pi\) | ||||
0.337966 | + | 0.941158i | \(0.390261\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.94418 | − | 10.2956i | 0.208728 | − | 0.361528i | −0.742586 | − | 0.669751i | \(-0.766401\pi\) |
0.951314 | + | 0.308223i | \(0.0997342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.69145 | + | 2.13126i | −0.129306 | + | 0.0746547i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.5336 | − | 14.3984i | −1.03325 | − | 0.503735i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.26581 | − | 9.12065i | 0.183778 | − | 0.318313i | −0.759386 | − | 0.650640i | \(-0.774501\pi\) |
0.943164 | + | 0.332327i | \(0.107834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0894 | + | 11.5986i | 0.700272 | + | 0.404302i | 0.807449 | − | 0.589938i | \(-0.200848\pi\) |
−0.107177 | + | 0.994240i | \(0.534181\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.6029 | − | 35.6853i | 0.716433 | − | 1.24090i | −0.245971 | − | 0.969277i | \(-0.579107\pi\) |
0.962404 | − | 0.271622i | \(-0.0875600\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.00889i | − | 0.104503i | −0.998634 | − | 0.0522515i | \(-0.983360\pi\) | ||
0.998634 | − | 0.0522515i | \(-0.0166398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.1723 | − | 17.6189i | −0.352448 | − | 0.610458i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.45355 | 0.327153 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.1747 | − | 26.2833i | −0.523888 | − | 0.907400i | −0.999613 | − | 0.0278063i | \(-0.991148\pi\) |
0.475726 | − | 0.879594i | \(-0.342185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1406 | − | 24.4923i | −0.487608 | − | 0.844562i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.28870 | − | 7.42825i | 0.147536 | − | 0.255540i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.20630i | − | 0.0414491i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.8482 | − | 44.7704i | 0.886066 | − | 1.53471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.61644 | + | 6.26386i | 0.123825 | + | 0.214471i | 0.921273 | − | 0.388917i | \(-0.127151\pi\) |
−0.797448 | + | 0.603387i | \(0.793817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.10422 | − | 3.52427i | 0.208516 | − | 0.120387i | −0.392105 | − | 0.919920i | \(-0.628253\pi\) |
0.600622 | + | 0.799533i | \(0.294920\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.6263 | + | 8.44448i | 0.499042 | + | 0.288122i | 0.728318 | − | 0.685240i | \(-0.240303\pi\) |
−0.229276 | + | 0.973361i | \(0.573636\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.5530 | −1.10812 | −0.554058 | − | 0.832478i | \(-0.686921\pi\) | ||||
−0.554058 | + | 0.832478i | \(0.686921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3977 | + | 13.5087i | 0.795547 | + | 0.459309i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9647 | − | 8.06251i | 0.473719 | − | 0.273502i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.86982 | − | 2.81159i | 0.165008 | − | 0.0952671i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 16.1014i | − | 0.544325i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.7791 | − | 10.8421i | 0.634125 | − | 0.366112i | −0.148223 | − | 0.988954i | \(-0.547355\pi\) |
0.782348 | + | 0.622842i | \(0.214022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.0558 | −1.34951 | −0.674757 | − | 0.738040i | \(-0.735752\pi\) | ||||
−0.674757 | + | 0.738040i | \(0.735752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.10793 | − | 0.639661i | −0.0372847 | − | 0.0215263i | 0.481242 | − | 0.876588i | \(-0.340186\pi\) |
−0.518526 | + | 0.855062i | \(0.673519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8408 | − | 20.5089i | 0.397576 | − | 0.688621i | −0.595851 | − | 0.803095i | \(-0.703185\pi\) |
0.993426 | + | 0.114474i | \(0.0365183\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.89578 | + | 5.13598i | 0.298355 | + | 0.172255i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.83255 | − | 40.4102i | −0.0947876 | − | 1.35228i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.6103 | + | 18.3776i | 0.354664 | + | 0.614296i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.258391 | + | 0.149182i | 0.00861781 | + | 0.00497549i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.2133i | 1.40633i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7846i | 0.690904i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.9926 | − | 19.0397i | −0.365003 | − | 0.632203i | 0.623774 | − | 0.781605i | \(-0.285599\pi\) |
−0.988777 | + | 0.149402i | \(0.952265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.5046 | −1.70642 | −0.853211 | − | 0.521566i | \(-0.825348\pi\) | ||||
−0.853211 | + | 0.521566i | \(0.825348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.0484 | −0.762791 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.30679 | − | 3.99548i | −0.0761769 | − | 0.131942i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.8792i | 1.15056i | 0.817957 | + | 0.575279i | \(0.195107\pi\) | ||||
−0.817957 | + | 0.575279i | \(0.804893\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.26028i | − | 0.0743981i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.9333 | − | 10.9311i | −0.622522 | − | 0.359413i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.7244 | + | 41.0918i | 0.778371 | + | 1.34818i | 0.932880 | + | 0.360187i | \(0.117287\pi\) |
−0.154509 | + | 0.987991i | \(0.549379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8884 | − | 17.6189i | −0.389625 | − | 0.577435i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.5800 | + | 8.99513i | 0.509521 | + | 0.294172i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0545 | + | 20.8790i | −0.393804 | + | 0.682088i | −0.992948 | − | 0.118553i | \(-0.962174\pi\) |
0.599144 | + | 0.800641i | \(0.295508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.16003 | + | 4.13385i | 0.233410 | + | 0.134760i | 0.612144 | − | 0.790746i | \(-0.290307\pi\) |
−0.378734 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.1304 | 1.14400 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.66354 | + | 0.960443i | −0.0540577 | + | 0.0312102i | −0.526785 | − | 0.849998i | \(-0.676603\pi\) |
0.472728 | + | 0.881209i | \(0.343269\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 34.4265i | − | 1.11753i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.9014 | − | 9.75805i | 0.547491 | − | 0.316094i | −0.200618 | − | 0.979669i | \(-0.564295\pi\) |
0.748110 | + | 0.663575i | \(0.230962\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.51834 | − | 2.60866i | 0.146210 | − | 0.0844144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.22483 | − | 4.74861i | −0.265594 | − | 0.153341i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8761 | −0.996004 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.9721 | − | 9.22149i | −0.514160 | − | 0.296850i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.1079 | − | 19.6922i | 1.09684 | − | 0.633259i | 0.161449 | − | 0.986881i | \(-0.448383\pi\) |
0.935388 | + | 0.353622i | \(0.115050\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.3519 | + | 49.1070i | 0.909857 | + | 1.57592i | 0.814261 | + | 0.580498i | \(0.197142\pi\) |
0.0955956 | + | 0.995420i | \(0.469524\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.4878 | + | 18.1654i | −0.336223 | + | 0.582355i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26.5410i | − | 0.849121i | −0.905400 | − | 0.424561i | \(-0.860429\pi\) | ||
0.905400 | − | 0.424561i | \(-0.139571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.03031 | + | 12.1769i | −0.224690 | + | 0.389174i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.2108 | − | 45.3985i | −0.835996 | − | 1.44799i | −0.893217 | − | 0.449626i | \(-0.851557\pi\) |
0.0572211 | − | 0.998362i | \(-0.481776\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0591 | − | 27.8151i | −0.511684 | − | 0.886263i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.5429 | 1.79796 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.3334 | + | 49.0749i | 0.900040 | + | 1.55891i | 0.827440 | + | 0.561554i | \(0.189796\pi\) |
0.0725996 | + | 0.997361i | \(0.476870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.4731i | 0.966064i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.44418 | − | 7.69755i | 0.140749 | − | 0.243784i | −0.787030 | − | 0.616915i | \(-0.788382\pi\) |
0.927779 | + | 0.373131i | \(0.121716\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.bm.o.1855.2 | 6 | ||
3.2 | odd | 2 | 912.2.bb.f.31.2 | yes | 6 | ||
4.3 | odd | 2 | 2736.2.bm.n.1855.2 | 6 | |||
12.11 | even | 2 | 912.2.bb.e.31.2 | ✓ | 6 | ||
19.8 | odd | 6 | 2736.2.bm.n.559.2 | 6 | |||
57.8 | even | 6 | 912.2.bb.e.559.2 | yes | 6 | ||
76.27 | even | 6 | inner | 2736.2.bm.o.559.2 | 6 | ||
228.179 | odd | 6 | 912.2.bb.f.559.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.bb.e.31.2 | ✓ | 6 | 12.11 | even | 2 | ||
912.2.bb.e.559.2 | yes | 6 | 57.8 | even | 6 | ||
912.2.bb.f.31.2 | yes | 6 | 3.2 | odd | 2 | ||
912.2.bb.f.559.2 | yes | 6 | 228.179 | odd | 6 | ||
2736.2.bm.n.559.2 | 6 | 19.8 | odd | 6 | |||
2736.2.bm.n.1855.2 | 6 | 4.3 | odd | 2 | |||
2736.2.bm.o.559.2 | 6 | 76.27 | even | 6 | inner | ||
2736.2.bm.o.1855.2 | 6 | 1.1 | even | 1 | trivial |