Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(961,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1110.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.h (of order \(2\), degree \(1\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{73})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 37x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(3.77200i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.d.961.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.77200i | 1.04617i | 0.852282 | + | 0.523083i | \(0.175218\pi\) | ||||
−0.852282 | + | 0.523083i | \(0.824782\pi\) | |||||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000i | 0.242536i | 0.992620 | + | 0.121268i | \(0.0386960\pi\) | ||||
−0.992620 | + | 0.121268i | \(0.961304\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | − | 7.77200i | − | 1.78302i | −0.453001 | − | 0.891510i | \(-0.649647\pi\) | ||
0.453001 | − | 0.891510i | \(-0.350353\pi\) | |||||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | − | 7.77200i | − | 1.62057i | −0.586033 | − | 0.810287i | \(-0.699311\pi\) | ||
0.586033 | − | 0.810287i | \(-0.300689\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.77200 | 0.739750 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | − | 0.772002i | − | 0.143357i | −0.997428 | − | 0.0716786i | \(-0.977164\pi\) | ||
0.997428 | − | 0.0716786i | \(-0.0228356\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − | 0.772002i | − | 0.138656i | −0.997594 | − | 0.0693278i | \(-0.977915\pi\) | ||
0.997594 | − | 0.0693278i | \(-0.0220854\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | − | 1.00000i | − | 0.169031i | ||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.77200 | − | 3.77200i | 0.784512 | − | 0.620113i | ||||
\(38\) | −7.77200 | −1.26079 | ||||||||
\(39\) | − | 3.77200i | − | 0.604004i | ||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −0.772002 | −0.120566 | −0.0602832 | − | 0.998181i | \(-0.519200\pi\) | ||||
−0.0602832 | + | 0.998181i | \(0.519200\pi\) | |||||||
\(42\) | − | 1.00000i | − | 0.154303i | ||||||
\(43\) | 1.22800i | 0.187268i | 0.995607 | + | 0.0936340i | \(0.0298483\pi\) | ||||
−0.995607 | + | 0.0936340i | \(0.970152\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | −7.77200 | −1.14592 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | − | 1.00000i | − | 0.140028i | ||||||
\(52\) | − | 3.77200i | − | 0.523083i | ||||||
\(53\) | −10.5440 | −1.44833 | −0.724165 | − | 0.689627i | \(-0.757775\pi\) | ||||
−0.724165 | + | 0.689627i | \(0.757775\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | − | 1.00000i | − | 0.134840i | ||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 7.77200i | 1.02943i | ||||||||
\(58\) | −0.772002 | −0.101369 | ||||||||
\(59\) | − | 7.54400i | − | 0.982146i | −0.871119 | − | 0.491073i | \(-0.836605\pi\) | ||
0.871119 | − | 0.491073i | \(-0.163395\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | − | 12.7720i | − | 1.63529i | −0.575725 | − | 0.817644i | \(-0.695280\pi\) | ||
0.575725 | − | 0.817644i | \(-0.304720\pi\) | |||||||
\(62\) | −0.772002 | −0.0980443 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.77200 | −0.467859 | ||||||||
\(66\) | − | 1.00000i | − | 0.123091i | ||||||
\(67\) | 9.54400 | 1.16599 | 0.582993 | − | 0.812477i | \(-0.301882\pi\) | ||||
0.582993 | + | 0.812477i | \(0.301882\pi\) | |||||||
\(68\) | − | 1.00000i | − | 0.121268i | ||||||
\(69\) | 7.77200i | 0.935639i | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 0.227998 | 0.0266852 | 0.0133426 | − | 0.999911i | \(-0.495753\pi\) | ||||
0.0133426 | + | 0.999911i | \(0.495753\pi\) | |||||||
\(74\) | −3.77200 | − | 4.77200i | −0.438486 | − | 0.554734i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 7.77200i | 0.891510i | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −3.77200 | −0.427095 | ||||||||
\(79\) | − | 11.5440i | − | 1.29880i | −0.760446 | − | 0.649401i | \(-0.775020\pi\) | ||
0.760446 | − | 0.649401i | \(-0.224980\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.772002i | 0.0852533i | ||||||||
\(83\) | −1.77200 | −0.194502 | −0.0972512 | − | 0.995260i | \(-0.531005\pi\) | ||||
−0.0972512 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | 1.22800 | 0.132418 | ||||||||
\(87\) | 0.772002i | 0.0827673i | ||||||||
\(88\) | − | 1.00000i | − | 0.106600i | ||||||
\(89\) | − | 17.3160i | − | 1.83549i | −0.397167 | − | 0.917746i | \(-0.630007\pi\) | ||
0.397167 | − | 0.917746i | \(-0.369993\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | − | 3.77200i | − | 0.395413i | ||||||
\(92\) | 7.77200i | 0.810287i | ||||||||
\(93\) | 0.772002i | 0.0800529i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.77200 | 0.797391 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − | 10.7720i | − | 1.09373i | −0.837220 | − | 0.546866i | \(-0.815821\pi\) | ||
0.837220 | − | 0.546866i | \(-0.184179\pi\) | |||||||
\(98\) | 6.00000i | 0.606092i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.5440 | −1.14867 | −0.574336 | − | 0.818620i | \(-0.694740\pi\) | ||||
−0.574336 | + | 0.818620i | \(0.694740\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | 17.5440i | 1.72866i | 0.502923 | + | 0.864331i | \(0.332258\pi\) | ||||
−0.502923 | + | 0.864331i | \(0.667742\pi\) | |||||||
\(104\) | −3.77200 | −0.369875 | ||||||||
\(105\) | 1.00000i | 0.0975900i | ||||||||
\(106\) | 10.5440i | 1.02412i | ||||||||
\(107\) | −7.77200 | −0.751348 | −0.375674 | − | 0.926752i | \(-0.622589\pi\) | ||||
−0.375674 | + | 0.926752i | \(0.622589\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −4.77200 | + | 3.77200i | −0.452938 | + | 0.358023i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 14.3160i | 1.34674i | 0.739307 | + | 0.673368i | \(0.235153\pi\) | ||||
−0.739307 | + | 0.673368i | \(0.764847\pi\) | |||||||
\(114\) | 7.77200 | 0.727915 | ||||||||
\(115\) | 7.77200 | 0.724743 | ||||||||
\(116\) | 0.772002i | 0.0716786i | ||||||||
\(117\) | 3.77200i | 0.348722i | ||||||||
\(118\) | −7.54400 | −0.694482 | ||||||||
\(119\) | − | 1.00000i | − | 0.0916698i | ||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −12.7720 | −1.15632 | ||||||||
\(123\) | 0.772002 | 0.0696091 | ||||||||
\(124\) | 0.772002i | 0.0693278i | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.00000i | 0.0890871i | ||||||||
\(127\) | 13.3160 | 1.18160 | 0.590802 | − | 0.806816i | \(-0.298811\pi\) | ||||
0.590802 | + | 0.806816i | \(0.298811\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | − | 1.22800i | − | 0.108119i | ||||||
\(130\) | 3.77200i | 0.330826i | ||||||||
\(131\) | 0.455996i | 0.0398406i | 0.999802 | + | 0.0199203i | \(0.00634124\pi\) | ||||
−0.999802 | + | 0.0199203i | \(0.993659\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 7.77200i | 0.673918i | ||||||||
\(134\) | − | 9.54400i | − | 0.824476i | ||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −19.0880 | −1.63080 | −0.815399 | − | 0.578899i | \(-0.803483\pi\) | ||||
−0.815399 | + | 0.578899i | \(0.803483\pi\) | |||||||
\(138\) | 7.77200 | 0.661597 | ||||||||
\(139\) | 20.3160 | 1.72318 | 0.861591 | − | 0.507604i | \(-0.169469\pi\) | ||||
0.861591 | + | 0.507604i | \(0.169469\pi\) | |||||||
\(140\) | 1.00000i | 0.0845154i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | − | 3.77200i | − | 0.315431i | ||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.772002 | 0.0641113 | ||||||||
\(146\) | − | 0.227998i | − | 0.0188693i | ||||||
\(147\) | 6.00000 | 0.494872 | ||||||||
\(148\) | −4.77200 | + | 3.77200i | −0.392256 | + | 0.310057i | ||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | − | 1.00000i | − | 0.0816497i | ||||||
\(151\) | 8.22800 | 0.669585 | 0.334792 | − | 0.942292i | \(-0.391334\pi\) | ||||
0.334792 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(152\) | 7.77200 | 0.630393 | ||||||||
\(153\) | 1.00000i | 0.0808452i | ||||||||
\(154\) | − | 1.00000i | − | 0.0805823i | ||||||
\(155\) | 0.772002 | 0.0620087 | ||||||||
\(156\) | 3.77200i | 0.302002i | ||||||||
\(157\) | 17.8600 | 1.42538 | 0.712692 | − | 0.701477i | \(-0.247476\pi\) | ||||
0.712692 | + | 0.701477i | \(0.247476\pi\) | |||||||
\(158\) | −11.5440 | −0.918392 | ||||||||
\(159\) | 10.5440 | 0.836194 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 7.77200i | 0.612520i | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 3.45600i | − | 0.270695i | −0.990798 | − | 0.135347i | \(-0.956785\pi\) | ||
0.990798 | − | 0.135347i | \(-0.0432150\pi\) | |||||||
\(164\) | 0.772002 | 0.0602832 | ||||||||
\(165\) | 1.00000i | 0.0778499i | ||||||||
\(166\) | 1.77200i | 0.137534i | ||||||||
\(167\) | − | 11.3160i | − | 0.875659i | −0.899058 | − | 0.437829i | \(-0.855747\pi\) | ||
0.899058 | − | 0.437829i | \(-0.144253\pi\) | |||||||
\(168\) | 1.00000i | 0.0771517i | ||||||||
\(169\) | −1.22800 | −0.0944614 | ||||||||
\(170\) | 1.00000i | 0.0766965i | ||||||||
\(171\) | − | 7.77200i | − | 0.594340i | ||||||
\(172\) | − | 1.22800i | − | 0.0936340i | ||||||
\(173\) | 15.0000 | 1.14043 | 0.570214 | − | 0.821496i | \(-0.306860\pi\) | ||||
0.570214 | + | 0.821496i | \(0.306860\pi\) | |||||||
\(174\) | 0.772002 | 0.0585253 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 7.54400i | 0.567042i | ||||||||
\(178\) | −17.3160 | −1.29789 | ||||||||
\(179\) | − | 9.54400i | − | 0.713352i | −0.934228 | − | 0.356676i | \(-0.883910\pi\) | ||
0.934228 | − | 0.356676i | \(-0.116090\pi\) | |||||||
\(180\) | − | 1.00000i | − | 0.0745356i | ||||||
\(181\) | 23.5440 | 1.75001 | 0.875006 | − | 0.484112i | \(-0.160857\pi\) | ||||
0.875006 | + | 0.484112i | \(0.160857\pi\) | |||||||
\(182\) | −3.77200 | −0.279599 | ||||||||
\(183\) | 12.7720i | 0.944134i | ||||||||
\(184\) | 7.77200 | 0.572960 | ||||||||
\(185\) | 3.77200 | + | 4.77200i | 0.277323 | + | 0.350845i | ||||
\(186\) | 0.772002 | 0.0566059 | ||||||||
\(187\) | − | 1.00000i | − | 0.0731272i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | − | 7.77200i | − | 0.563840i | ||||||
\(191\) | 12.5440i | 0.907652i | 0.891090 | + | 0.453826i | \(0.149941\pi\) | ||||
−0.891090 | + | 0.453826i | \(0.850059\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − | 6.45600i | − | 0.464713i | −0.972631 | − | 0.232356i | \(-0.925356\pi\) | ||
0.972631 | − | 0.232356i | \(-0.0746436\pi\) | |||||||
\(194\) | −10.7720 | −0.773385 | ||||||||
\(195\) | 3.77200 | 0.270119 | ||||||||
\(196\) | 6.00000 | 0.428571 | ||||||||
\(197\) | 11.7720 | 0.838720 | 0.419360 | − | 0.907820i | \(-0.362254\pi\) | ||||
0.419360 | + | 0.907820i | \(0.362254\pi\) | |||||||
\(198\) | 1.00000i | 0.0710669i | ||||||||
\(199\) | − | 7.54400i | − | 0.534780i | −0.963588 | − | 0.267390i | \(-0.913839\pi\) | ||
0.963588 | − | 0.267390i | \(-0.0861612\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −9.54400 | −0.673182 | ||||||||
\(202\) | 11.5440i | 0.812233i | ||||||||
\(203\) | 0.772002i | 0.0541839i | ||||||||
\(204\) | 1.00000i | 0.0700140i | ||||||||
\(205\) | − | 0.772002i | − | 0.0539189i | ||||||
\(206\) | 17.5440 | 1.22235 | ||||||||
\(207\) | − | 7.77200i | − | 0.540191i | ||||||
\(208\) | 3.77200i | 0.261541i | ||||||||
\(209\) | 7.77200i | 0.537601i | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | −11.2280 | −0.772967 | −0.386484 | − | 0.922296i | \(-0.626310\pi\) | ||||
−0.386484 | + | 0.922296i | \(0.626310\pi\) | |||||||
\(212\) | 10.5440 | 0.724165 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 7.77200i | 0.531283i | ||||||||
\(215\) | −1.22800 | −0.0837488 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0.772002i | 0.0524069i | ||||||||
\(218\) | 7.00000 | 0.474100 | ||||||||
\(219\) | −0.227998 | −0.0154067 | ||||||||
\(220\) | 1.00000i | 0.0674200i | ||||||||
\(221\) | −3.77200 | −0.253732 | ||||||||
\(222\) | 3.77200 | + | 4.77200i | 0.253160 | + | 0.320276i | ||||
\(223\) | −17.2280 | −1.15367 | −0.576836 | − | 0.816860i | \(-0.695713\pi\) | ||||
−0.576836 | + | 0.816860i | \(0.695713\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 14.3160 | 0.952287 | ||||||||
\(227\) | 6.77200i | 0.449474i | 0.974420 | + | 0.224737i | \(0.0721522\pi\) | ||||
−0.974420 | + | 0.224737i | \(0.927848\pi\) | |||||||
\(228\) | − | 7.77200i | − | 0.514713i | ||||||
\(229\) | 13.5440 | 0.895013 | 0.447506 | − | 0.894281i | \(-0.352312\pi\) | ||||
0.447506 | + | 0.894281i | \(0.352312\pi\) | |||||||
\(230\) | − | 7.77200i | − | 0.512471i | ||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0.772002 | 0.0506844 | ||||||||
\(233\) | −12.0000 | −0.786146 | −0.393073 | − | 0.919507i | \(-0.628588\pi\) | ||||
−0.393073 | + | 0.919507i | \(0.628588\pi\) | |||||||
\(234\) | 3.77200 | 0.246583 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.54400i | 0.491073i | ||||||||
\(237\) | 11.5440i | 0.749864i | ||||||||
\(238\) | −1.00000 | −0.0648204 | ||||||||
\(239\) | − | 5.22800i | − | 0.338171i | −0.985601 | − | 0.169086i | \(-0.945919\pi\) | ||
0.985601 | − | 0.169086i | \(-0.0540814\pi\) | |||||||
\(240\) | − | 1.00000i | − | 0.0645497i | ||||||
\(241\) | 16.0000i | 1.03065i | 0.856995 | + | 0.515325i | \(0.172329\pi\) | ||||
−0.856995 | + | 0.515325i | \(0.827671\pi\) | |||||||
\(242\) | 10.0000i | 0.642824i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.7720i | 0.817644i | ||||||||
\(245\) | − | 6.00000i | − | 0.383326i | ||||||
\(246\) | − | 0.772002i | − | 0.0492210i | ||||||
\(247\) | 29.3160 | 1.86533 | ||||||||
\(248\) | 0.772002 | 0.0490222 | ||||||||
\(249\) | 1.77200 | 0.112296 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | − | 27.0880i | − | 1.70978i | −0.518809 | − | 0.854890i | \(-0.673625\pi\) | ||
0.518809 | − | 0.854890i | \(-0.326375\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 7.77200i | 0.488622i | ||||||||
\(254\) | − | 13.3160i | − | 0.835521i | ||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.22800i | − | 0.263735i | −0.991267 | − | 0.131868i | \(-0.957903\pi\) | ||
0.991267 | − | 0.131868i | \(-0.0420974\pi\) | |||||||
\(258\) | −1.22800 | −0.0764518 | ||||||||
\(259\) | −4.77200 | + | 3.77200i | −0.296518 | + | 0.234381i | ||||
\(260\) | 3.77200 | 0.233930 | ||||||||
\(261\) | − | 0.772002i | − | 0.0477857i | ||||||
\(262\) | 0.455996 | 0.0281715 | ||||||||
\(263\) | 5.22800 | 0.322372 | 0.161186 | − | 0.986924i | \(-0.448468\pi\) | ||||
0.161186 | + | 0.986924i | \(0.448468\pi\) | |||||||
\(264\) | 1.00000i | 0.0615457i | ||||||||
\(265\) | − | 10.5440i | − | 0.647713i | ||||||
\(266\) | 7.77200 | 0.476532 | ||||||||
\(267\) | 17.3160i | 1.05972i | ||||||||
\(268\) | −9.54400 | −0.582993 | ||||||||
\(269\) | 9.31601 | 0.568007 | 0.284003 | − | 0.958823i | \(-0.408337\pi\) | ||||
0.284003 | + | 0.958823i | \(0.408337\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −23.0880 | −1.40250 | −0.701248 | − | 0.712917i | \(-0.747374\pi\) | ||||
−0.701248 | + | 0.712917i | \(0.747374\pi\) | |||||||
\(272\) | 1.00000i | 0.0606339i | ||||||||
\(273\) | 3.77200i | 0.228292i | ||||||||
\(274\) | 19.0880i | 1.15315i | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | − | 7.77200i | − | 0.467820i | ||||||
\(277\) | 6.22800i | 0.374204i | 0.982340 | + | 0.187102i | \(0.0599095\pi\) | ||||
−0.982340 | + | 0.187102i | \(0.940090\pi\) | |||||||
\(278\) | − | 20.3160i | − | 1.21847i | ||||||
\(279\) | − | 0.772002i | − | 0.0462185i | ||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 3.77200i | 0.225019i | 0.993651 | + | 0.112509i | \(0.0358888\pi\) | ||||
−0.993651 | + | 0.112509i | \(0.964111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.22800i | − | 0.132441i | −0.997805 | − | 0.0662204i | \(-0.978906\pi\) | ||
0.997805 | − | 0.0662204i | \(-0.0210940\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | −7.77200 | −0.460374 | ||||||||
\(286\) | −3.77200 | −0.223043 | ||||||||
\(287\) | 0.772002 | 0.0455698 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 16.0000 | 0.941176 | ||||||||
\(290\) | − | 0.772002i | − | 0.0453335i | ||||||
\(291\) | 10.7720i | 0.631466i | ||||||||
\(292\) | −0.227998 | −0.0133426 | ||||||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | − | 6.00000i | − | 0.349927i | ||||||
\(295\) | 7.54400 | 0.439229 | ||||||||
\(296\) | 3.77200 | + | 4.77200i | 0.219243 | + | 0.277367i | ||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 29.3160 | 1.69539 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − | 1.22800i | − | 0.0707806i | ||||||
\(302\) | − | 8.22800i | − | 0.473468i | ||||||
\(303\) | 11.5440 | 0.663186 | ||||||||
\(304\) | − | 7.77200i | − | 0.445755i | ||||||
\(305\) | 12.7720 | 0.731323 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | − | 17.5440i | − | 0.998044i | ||||||
\(310\) | − | 0.772002i | − | 0.0438468i | ||||||
\(311\) | − | 6.77200i | − | 0.384005i | −0.981394 | − | 0.192002i | \(-0.938502\pi\) | ||
0.981394 | − | 0.192002i | \(-0.0614982\pi\) | |||||||
\(312\) | 3.77200 | 0.213548 | ||||||||
\(313\) | 17.0880i | 0.965871i | 0.875656 | + | 0.482936i | \(0.160429\pi\) | ||||
−0.875656 | + | 0.482936i | \(0.839571\pi\) | |||||||
\(314\) | − | 17.8600i | − | 1.00790i | ||||||
\(315\) | − | 1.00000i | − | 0.0563436i | ||||||
\(316\) | 11.5440i | 0.649401i | ||||||||
\(317\) | −33.4040 | −1.87616 | −0.938078 | − | 0.346424i | \(-0.887396\pi\) | ||||
−0.938078 | + | 0.346424i | \(0.887396\pi\) | |||||||
\(318\) | − | 10.5440i | − | 0.591278i | ||||||
\(319\) | 0.772002i | 0.0432238i | ||||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 7.77200 | 0.433791 | ||||||||
\(322\) | 7.77200 | 0.433117 | ||||||||
\(323\) | 7.77200 | 0.432446 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 3.77200i | − | 0.209233i | ||||||
\(326\) | −3.45600 | −0.191410 | ||||||||
\(327\) | − | 7.00000i | − | 0.387101i | ||||||
\(328\) | − | 0.772002i | − | 0.0426267i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | − | 17.5440i | − | 0.964306i | −0.876087 | − | 0.482153i | \(-0.839855\pi\) | ||
0.876087 | − | 0.482153i | \(-0.160145\pi\) | |||||||
\(332\) | 1.77200 | 0.0972512 | ||||||||
\(333\) | 4.77200 | − | 3.77200i | 0.261504 | − | 0.206704i | ||||
\(334\) | −11.3160 | −0.619184 | ||||||||
\(335\) | 9.54400i | 0.521445i | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −1.31601 | −0.0716874 | −0.0358437 | − | 0.999357i | \(-0.511412\pi\) | ||||
−0.0358437 | + | 0.999357i | \(0.511412\pi\) | |||||||
\(338\) | 1.22800i | 0.0667943i | ||||||||
\(339\) | − | 14.3160i | − | 0.777539i | ||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | 0.772002i | 0.0418062i | ||||||||
\(342\) | −7.77200 | −0.420262 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −1.22800 | −0.0662092 | ||||||||
\(345\) | −7.77200 | −0.418431 | ||||||||
\(346\) | − | 15.0000i | − | 0.806405i | ||||||
\(347\) | 23.5440i | 1.26391i | 0.775006 | + | 0.631954i | \(0.217747\pi\) | ||||
−0.775006 | + | 0.631954i | \(0.782253\pi\) | |||||||
\(348\) | − | 0.772002i | − | 0.0413836i | ||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | − | 1.00000i | − | 0.0534522i | ||||||
\(351\) | − | 3.77200i | − | 0.201335i | ||||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | 36.7720i | 1.95718i | 0.205828 | + | 0.978588i | \(0.434011\pi\) | ||||
−0.205828 | + | 0.978588i | \(0.565989\pi\) | |||||||
\(354\) | 7.54400 | 0.400959 | ||||||||
\(355\) | − | 6.00000i | − | 0.318447i | ||||||
\(356\) | 17.3160i | 0.917746i | ||||||||
\(357\) | 1.00000i | 0.0529256i | ||||||||
\(358\) | −9.54400 | −0.504416 | ||||||||
\(359\) | −4.45600 | −0.235178 | −0.117589 | − | 0.993062i | \(-0.537517\pi\) | ||||
−0.117589 | + | 0.993062i | \(0.537517\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −41.4040 | −2.17916 | ||||||||
\(362\) | − | 23.5440i | − | 1.23745i | ||||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | 3.77200i | 0.197707i | ||||||||
\(365\) | 0.227998i | 0.0119340i | ||||||||
\(366\) | 12.7720 | 0.667603 | ||||||||
\(367\) | −16.0880 | −0.839787 | −0.419894 | − | 0.907573i | \(-0.637933\pi\) | ||||
−0.419894 | + | 0.907573i | \(0.637933\pi\) | |||||||
\(368\) | − | 7.77200i | − | 0.405144i | ||||||
\(369\) | −0.772002 | −0.0401888 | ||||||||
\(370\) | 4.77200 | − | 3.77200i | 0.248085 | − | 0.196097i | ||||
\(371\) | 10.5440 | 0.547417 | ||||||||
\(372\) | − | 0.772002i | − | 0.0400264i | ||||||
\(373\) | 21.5440 | 1.11551 | 0.557753 | − | 0.830007i | \(-0.311664\pi\) | ||||
0.557753 | + | 0.830007i | \(0.311664\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.91199 | 0.149975 | ||||||||
\(378\) | − | 1.00000i | − | 0.0514344i | ||||||
\(379\) | −23.5440 | −1.20937 | −0.604687 | − | 0.796463i | \(-0.706702\pi\) | ||||
−0.604687 | + | 0.796463i | \(0.706702\pi\) | |||||||
\(380\) | −7.77200 | −0.398695 | ||||||||
\(381\) | −13.3160 | −0.682200 | ||||||||
\(382\) | 12.5440 | 0.641807 | ||||||||
\(383\) | − | 15.3160i | − | 0.782611i | −0.920261 | − | 0.391306i | \(-0.872024\pi\) | ||
0.920261 | − | 0.391306i | \(-0.127976\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 1.00000i | 0.0509647i | ||||||||
\(386\) | −6.45600 | −0.328602 | ||||||||
\(387\) | 1.22800i | 0.0624227i | ||||||||
\(388\) | 10.7720i | 0.546866i | ||||||||
\(389\) | 6.77200i | 0.343354i | 0.985153 | + | 0.171677i | \(0.0549186\pi\) | ||||
−0.985153 | + | 0.171677i | \(0.945081\pi\) | |||||||
\(390\) | − | 3.77200i | − | 0.191003i | ||||||
\(391\) | 7.77200 | 0.393047 | ||||||||
\(392\) | − | 6.00000i | − | 0.303046i | ||||||
\(393\) | − | 0.455996i | − | 0.0230020i | ||||||
\(394\) | − | 11.7720i | − | 0.593065i | ||||||
\(395\) | 11.5440 | 0.580842 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 1.54400 | 0.0774913 | 0.0387457 | − | 0.999249i | \(-0.487664\pi\) | ||||
0.0387457 | + | 0.999249i | \(0.487664\pi\) | |||||||
\(398\) | −7.54400 | −0.378147 | ||||||||
\(399\) | − | 7.77200i | − | 0.389087i | ||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 23.3160i | 1.16435i | 0.813065 | + | 0.582173i | \(0.197797\pi\) | ||||
−0.813065 | + | 0.582173i | \(0.802203\pi\) | |||||||
\(402\) | 9.54400i | 0.476012i | ||||||||
\(403\) | 2.91199 | 0.145057 | ||||||||
\(404\) | 11.5440 | 0.574336 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0.772002 | 0.0383138 | ||||||||
\(407\) | −4.77200 | + | 3.77200i | −0.236539 | + | 0.186971i | ||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 4.00000i | 0.197787i | 0.995098 | + | 0.0988936i | \(0.0315304\pi\) | ||||
−0.995098 | + | 0.0988936i | \(0.968470\pi\) | |||||||
\(410\) | −0.772002 | −0.0381265 | ||||||||
\(411\) | 19.0880 | 0.941542 | ||||||||
\(412\) | − | 17.5440i | − | 0.864331i | ||||||
\(413\) | 7.54400i | 0.371216i | ||||||||
\(414\) | −7.77200 | −0.381973 | ||||||||
\(415\) | − | 1.77200i | − | 0.0869842i | ||||||
\(416\) | 3.77200 | 0.184938 | ||||||||
\(417\) | −20.3160 | −0.994879 | ||||||||
\(418\) | 7.77200 | 0.380141 | ||||||||
\(419\) | 12.8600 | 0.628253 | 0.314126 | − | 0.949381i | \(-0.398288\pi\) | ||||
0.314126 | + | 0.949381i | \(0.398288\pi\) | |||||||
\(420\) | − | 1.00000i | − | 0.0487950i | ||||||
\(421\) | − | 6.00000i | − | 0.292422i | −0.989253 | − | 0.146211i | \(-0.953292\pi\) | ||
0.989253 | − | 0.146211i | \(-0.0467079\pi\) | |||||||
\(422\) | 11.2280i | 0.546570i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 10.5440i | − | 0.512062i | ||||||
\(425\) | − | 1.00000i | − | 0.0485071i | ||||||
\(426\) | − | 6.00000i | − | 0.290701i | ||||||
\(427\) | 12.7720i | 0.618080i | ||||||||
\(428\) | 7.77200 | 0.375674 | ||||||||
\(429\) | 3.77200i | 0.182114i | ||||||||
\(430\) | 1.22800i | 0.0592193i | ||||||||
\(431\) | 10.0880i | 0.485922i | 0.970036 | + | 0.242961i | \(0.0781187\pi\) | ||||
−0.970036 | + | 0.242961i | \(0.921881\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.77200 | −0.373499 | −0.186749 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186749 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(434\) | 0.772002 | 0.0370573 | ||||||||
\(435\) | −0.772002 | −0.0370147 | ||||||||
\(436\) | − | 7.00000i | − | 0.335239i | ||||||
\(437\) | −60.4040 | −2.88952 | ||||||||
\(438\) | 0.227998i | 0.0108942i | ||||||||
\(439\) | 20.7720i | 0.991394i | 0.868496 | + | 0.495697i | \(0.165087\pi\) | ||||
−0.868496 | + | 0.495697i | \(0.834913\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 3.77200i | 0.179416i | ||||||||
\(443\) | −20.0000 | −0.950229 | −0.475114 | − | 0.879924i | \(-0.657593\pi\) | ||||
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(444\) | 4.77200 | − | 3.77200i | 0.226469 | − | 0.179011i | ||||
\(445\) | 17.3160 | 0.820857 | ||||||||
\(446\) | 17.2280i | 0.815769i | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | − | 2.00000i | − | 0.0943858i | −0.998886 | − | 0.0471929i | \(-0.984972\pi\) | ||
0.998886 | − | 0.0471929i | \(-0.0150276\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 0.772002 | 0.0363521 | ||||||||
\(452\) | − | 14.3160i | − | 0.673368i | ||||||
\(453\) | −8.22800 | −0.386585 | ||||||||
\(454\) | 6.77200 | 0.317826 | ||||||||
\(455\) | 3.77200 | 0.176834 | ||||||||
\(456\) | −7.77200 | −0.363957 | ||||||||
\(457\) | − | 34.3160i | − | 1.60524i | −0.596494 | − | 0.802618i | \(-0.703440\pi\) | ||
0.596494 | − | 0.802618i | \(-0.296560\pi\) | |||||||
\(458\) | − | 13.5440i | − | 0.632870i | ||||||
\(459\) | − | 1.00000i | − | 0.0466760i | ||||||
\(460\) | −7.77200 | −0.362371 | ||||||||
\(461\) | − | 21.2280i | − | 0.988686i | −0.869267 | − | 0.494343i | \(-0.835409\pi\) | ||
0.869267 | − | 0.494343i | \(-0.164591\pi\) | |||||||
\(462\) | 1.00000i | 0.0465242i | ||||||||
\(463\) | 30.6320i | 1.42359i | 0.702387 | + | 0.711795i | \(0.252118\pi\) | ||||
−0.702387 | + | 0.711795i | \(0.747882\pi\) | |||||||
\(464\) | − | 0.772002i | − | 0.0358393i | ||||||
\(465\) | −0.772002 | −0.0358007 | ||||||||
\(466\) | 12.0000i | 0.555889i | ||||||||
\(467\) | 4.31601i | 0.199721i | 0.995001 | + | 0.0998605i | \(0.0318396\pi\) | ||||
−0.995001 | + | 0.0998605i | \(0.968160\pi\) | |||||||
\(468\) | − | 3.77200i | − | 0.174361i | ||||||
\(469\) | −9.54400 | −0.440701 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8600 | −0.822946 | ||||||||
\(472\) | 7.54400 | 0.347241 | ||||||||
\(473\) | − | 1.22800i | − | 0.0564634i | ||||||
\(474\) | 11.5440 | 0.530234 | ||||||||
\(475\) | 7.77200i | 0.356604i | ||||||||
\(476\) | 1.00000i | 0.0458349i | ||||||||
\(477\) | −10.5440 | −0.482777 | ||||||||
\(478\) | −5.22800 | −0.239123 | ||||||||
\(479\) | 10.2280i | 0.467329i | 0.972317 | + | 0.233665i | \(0.0750718\pi\) | ||||
−0.972317 | + | 0.233665i | \(0.924928\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 14.2280 | + | 18.0000i | 0.648741 | + | 0.820729i | ||||
\(482\) | 16.0000 | 0.728780 | ||||||||
\(483\) | − | 7.77200i | − | 0.353638i | ||||||
\(484\) | 10.0000 | 0.454545 | ||||||||
\(485\) | 10.7720 | 0.489131 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − | 15.0880i | − | 0.683703i | −0.939754 | − | 0.341851i | \(-0.888946\pi\) | ||
0.939754 | − | 0.341851i | \(-0.111054\pi\) | |||||||
\(488\) | 12.7720 | 0.578161 | ||||||||
\(489\) | 3.45600i | 0.156286i | ||||||||
\(490\) | −6.00000 | −0.271052 | ||||||||
\(491\) | 30.2280 | 1.36417 | 0.682085 | − | 0.731273i | \(-0.261073\pi\) | ||||
0.682085 | + | 0.731273i | \(0.261073\pi\) | |||||||
\(492\) | −0.772002 | −0.0348045 | ||||||||
\(493\) | 0.772002 | 0.0347692 | ||||||||
\(494\) | − | 29.3160i | − | 1.31899i | ||||||
\(495\) | − | 1.00000i | − | 0.0449467i | ||||||
\(496\) | − | 0.772002i | − | 0.0346639i | ||||||
\(497\) | 6.00000 | 0.269137 | ||||||||
\(498\) | − | 1.77200i | − | 0.0794053i | ||||||
\(499\) | − | 4.68399i | − | 0.209684i | −0.994489 | − | 0.104842i | \(-0.966566\pi\) | ||
0.994489 | − | 0.104842i | \(-0.0334337\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 11.3160i | 0.505562i | ||||||||
\(502\) | −27.0880 | −1.20900 | ||||||||
\(503\) | 3.08801i | 0.137687i | 0.997627 | + | 0.0688437i | \(0.0219310\pi\) | ||||
−0.997627 | + | 0.0688437i | \(0.978069\pi\) | |||||||
\(504\) | − | 1.00000i | − | 0.0445435i | ||||||
\(505\) | − | 11.5440i | − | 0.513701i | ||||||
\(506\) | 7.77200 | 0.345508 | ||||||||
\(507\) | 1.22800 | 0.0545373 | ||||||||
\(508\) | −13.3160 | −0.590802 | ||||||||
\(509\) | 25.3160 | 1.12211 | 0.561056 | − | 0.827778i | \(-0.310395\pi\) | ||||
0.561056 | + | 0.827778i | \(0.310395\pi\) | |||||||
\(510\) | − | 1.00000i | − | 0.0442807i | ||||||
\(511\) | −0.227998 | −0.0100860 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 7.77200i | 0.343142i | ||||||||
\(514\) | −4.22800 | −0.186489 | ||||||||
\(515\) | −17.5440 | −0.773081 | ||||||||
\(516\) | 1.22800i | 0.0540596i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.77200 | + | 4.77200i | 0.165732 | + | 0.209670i | ||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | − | 3.77200i | − | 0.165413i | ||||||
\(521\) | −17.4040 | −0.762484 | −0.381242 | − | 0.924475i | \(-0.624503\pi\) | ||||
−0.381242 | + | 0.924475i | \(0.624503\pi\) | |||||||
\(522\) | −0.772002 | −0.0337896 | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | − | 0.455996i | − | 0.0199203i | ||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | − | 5.22800i | − | 0.227952i | ||||||
\(527\) | 0.772002 | 0.0336289 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −37.4040 | −1.62626 | ||||||||
\(530\) | −10.5440 | −0.458002 | ||||||||
\(531\) | − | 7.54400i | − | 0.327382i | ||||||
\(532\) | − | 7.77200i | − | 0.336959i | ||||||
\(533\) | − | 2.91199i | − | 0.126132i | ||||||
\(534\) | 17.3160 | 0.749337 | ||||||||
\(535\) | − | 7.77200i | − | 0.336013i | ||||||
\(536\) | 9.54400i | 0.412238i | ||||||||
\(537\) | 9.54400i | 0.411854i | ||||||||
\(538\) | − | 9.31601i | − | 0.401642i | ||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 11.7720i | 0.506118i | 0.967451 | + | 0.253059i | \(0.0814367\pi\) | ||||
−0.967451 | + | 0.253059i | \(0.918563\pi\) | |||||||
\(542\) | 23.0880i | 0.991715i | ||||||||
\(543\) | −23.5440 | −1.01037 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −7.00000 | −0.299847 | ||||||||
\(546\) | 3.77200 | 0.161427 | ||||||||
\(547\) | − | 14.5440i | − | 0.621857i | −0.950433 | − | 0.310928i | \(-0.899360\pi\) | ||
0.950433 | − | 0.310928i | \(-0.100640\pi\) | |||||||
\(548\) | 19.0880 | 0.815399 | ||||||||
\(549\) | − | 12.7720i | − | 0.545096i | ||||||
\(550\) | − | 1.00000i | − | 0.0426401i | ||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | −7.77200 | −0.330798 | ||||||||
\(553\) | 11.5440i | 0.490901i | ||||||||
\(554\) | 6.22800 | 0.264602 | ||||||||
\(555\) | −3.77200 | − | 4.77200i | −0.160113 | − | 0.202560i | ||||
\(556\) | −20.3160 | −0.861591 | ||||||||
\(557\) | 16.4560i | 0.697263i | 0.937260 | + | 0.348631i | \(0.113354\pi\) | ||||
−0.937260 | + | 0.348631i | \(0.886646\pi\) | |||||||
\(558\) | −0.772002 | −0.0326814 | ||||||||
\(559\) | −4.63201 | −0.195913 | ||||||||
\(560\) | − | 1.00000i | − | 0.0422577i | ||||||
\(561\) | 1.00000i | 0.0422200i | ||||||||
\(562\) | 3.77200 | 0.159112 | ||||||||
\(563\) | − | 42.9480i | − | 1.81004i | −0.425366 | − | 0.905022i | \(-0.639855\pi\) | ||
0.425366 | − | 0.905022i | \(-0.360145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3160 | −0.602279 | ||||||||
\(566\) | −2.22800 | −0.0936497 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 5.31601i | 0.222859i | 0.993772 | + | 0.111429i | \(0.0355429\pi\) | ||||
−0.993772 | + | 0.111429i | \(0.964457\pi\) | |||||||
\(570\) | 7.77200i | 0.325533i | ||||||||
\(571\) | −40.9480 | −1.71362 | −0.856811 | − | 0.515631i | \(-0.827557\pi\) | ||||
−0.856811 | + | 0.515631i | \(0.827557\pi\) | |||||||
\(572\) | 3.77200i | 0.157715i | ||||||||
\(573\) | − | 12.5440i | − | 0.524033i | ||||||
\(574\) | − | 0.772002i | − | 0.0322227i | ||||||
\(575\) | 7.77200i | 0.324115i | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 22.4560i | 0.934855i | 0.884031 | + | 0.467428i | \(0.154819\pi\) | ||||
−0.884031 | + | 0.467428i | \(0.845181\pi\) | |||||||
\(578\) | − | 16.0000i | − | 0.665512i | ||||||
\(579\) | 6.45600i | 0.268302i | ||||||||
\(580\) | −0.772002 | −0.0320556 | ||||||||
\(581\) | 1.77200 | 0.0735150 | ||||||||
\(582\) | 10.7720 | 0.446514 | ||||||||
\(583\) | 10.5440 | 0.436688 | ||||||||
\(584\) | 0.227998i | 0.00943463i | ||||||||
\(585\) | −3.77200 | −0.155953 | ||||||||
\(586\) | 9.00000i | 0.371787i | ||||||||
\(587\) | − | 11.8600i | − | 0.489515i | −0.969584 | − | 0.244757i | \(-0.921292\pi\) | ||
0.969584 | − | 0.244757i | \(-0.0787083\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | − | 7.54400i | − | 0.310582i | ||||||
\(591\) | −11.7720 | −0.484235 | ||||||||
\(592\) | 4.77200 | − | 3.77200i | 0.196128 | − | 0.155028i | ||||
\(593\) | −11.5440 | −0.474055 | −0.237028 | − | 0.971503i | \(-0.576173\pi\) | ||||
−0.237028 | + | 0.971503i | \(0.576173\pi\) | |||||||
\(594\) | − | 1.00000i | − | 0.0410305i | ||||||
\(595\) | 1.00000 | 0.0409960 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 7.54400i | 0.308756i | ||||||||
\(598\) | − | 29.3160i | − | 1.19882i | ||||||
\(599\) | −21.0880 | −0.861633 | −0.430816 | − | 0.902440i | \(-0.641774\pi\) | ||||
−0.430816 | + | 0.902440i | \(0.641774\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −30.5440 | −1.24592 | −0.622958 | − | 0.782255i | \(-0.714069\pi\) | ||||
−0.622958 | + | 0.782255i | \(0.714069\pi\) | |||||||
\(602\) | −1.22800 | −0.0500495 | ||||||||
\(603\) | 9.54400 | 0.388662 | ||||||||
\(604\) | −8.22800 | −0.334792 | ||||||||
\(605\) | − | 10.0000i | − | 0.406558i | ||||||
\(606\) | − | 11.5440i | − | 0.468943i | ||||||
\(607\) | − | 24.0000i | − | 0.974130i | −0.873366 | − | 0.487065i | \(-0.838067\pi\) | ||
0.873366 | − | 0.487065i | \(-0.161933\pi\) | |||||||
\(608\) | −7.77200 | −0.315196 | ||||||||
\(609\) | − | 0.772002i | − | 0.0312831i | ||||||
\(610\) | − | 12.7720i | − | 0.517123i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 1.00000i | − | 0.0404226i | ||||||
\(613\) | 13.8600 | 0.559801 | 0.279900 | − | 0.960029i | \(-0.409699\pi\) | ||||
0.279900 | + | 0.960029i | \(0.409699\pi\) | |||||||
\(614\) | 28.0000i | 1.12999i | ||||||||
\(615\) | 0.772002i | 0.0311301i | ||||||||
\(616\) | 1.00000i | 0.0402911i | ||||||||
\(617\) | 16.4560 | 0.662493 | 0.331247 | − | 0.943544i | \(-0.392531\pi\) | ||||
0.331247 | + | 0.943544i | \(0.392531\pi\) | |||||||
\(618\) | −17.5440 | −0.705723 | ||||||||
\(619\) | 5.22800 | 0.210131 | 0.105065 | − | 0.994465i | \(-0.466495\pi\) | ||||
0.105065 | + | 0.994465i | \(0.466495\pi\) | |||||||
\(620\) | −0.772002 | −0.0310043 | ||||||||
\(621\) | 7.77200i | 0.311880i | ||||||||
\(622\) | −6.77200 | −0.271533 | ||||||||
\(623\) | 17.3160i | 0.693751i | ||||||||
\(624\) | − | 3.77200i | − | 0.151001i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.0880 | 0.682974 | ||||||||
\(627\) | − | 7.77200i | − | 0.310384i | ||||||
\(628\) | −17.8600 | −0.712692 | ||||||||
\(629\) | 3.77200 | + | 4.77200i | 0.150400 | + | 0.190272i | ||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | − | 4.31601i | − | 0.171817i | −0.996303 | − | 0.0859087i | \(-0.972621\pi\) | ||
0.996303 | − | 0.0859087i | \(-0.0273793\pi\) | |||||||
\(632\) | 11.5440 | 0.459196 | ||||||||
\(633\) | 11.2280 | 0.446273 | ||||||||
\(634\) | 33.4040i | 1.32664i | ||||||||
\(635\) | 13.3160i | 0.528430i | ||||||||
\(636\) | −10.5440 | −0.418097 | ||||||||
\(637\) | − | 22.6320i | − | 0.896713i | ||||||
\(638\) | 0.772002 | 0.0305638 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −33.8600 | −1.33739 | −0.668695 | − | 0.743537i | \(-0.733147\pi\) | ||||
−0.668695 | + | 0.743537i | \(0.733147\pi\) | |||||||
\(642\) | − | 7.77200i | − | 0.306736i | ||||||
\(643\) | 13.0000i | 0.512670i | 0.966588 | + | 0.256335i | \(0.0825150\pi\) | ||||
−0.966588 | + | 0.256335i | \(0.917485\pi\) | |||||||
\(644\) | − | 7.77200i | − | 0.306260i | ||||||
\(645\) | 1.22800 | 0.0483524 | ||||||||
\(646\) | − | 7.77200i | − | 0.305785i | ||||||
\(647\) | − | 23.3160i | − | 0.916647i | −0.888786 | − | 0.458323i | \(-0.848450\pi\) | ||
0.888786 | − | 0.458323i | \(-0.151550\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 7.54400i | 0.296128i | ||||||||
\(650\) | −3.77200 | −0.147950 | ||||||||
\(651\) | − | 0.772002i | − | 0.0302571i | ||||||
\(652\) | 3.45600i | 0.135347i | ||||||||
\(653\) | 17.0880i | 0.668705i | 0.942448 | + | 0.334353i | \(0.108518\pi\) | ||||
−0.942448 | + | 0.334353i | \(0.891482\pi\) | |||||||
\(654\) | −7.00000 | −0.273722 | ||||||||
\(655\) | −0.455996 | −0.0178172 | ||||||||
\(656\) | −0.772002 | −0.0301416 | ||||||||
\(657\) | 0.227998 | 0.00889505 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.0880 | 0.743563 | 0.371782 | − | 0.928320i | \(-0.378747\pi\) | ||||
0.371782 | + | 0.928320i | \(0.378747\pi\) | |||||||
\(660\) | − | 1.00000i | − | 0.0389249i | ||||||
\(661\) | − | 32.0880i | − | 1.24808i | −0.781393 | − | 0.624039i | \(-0.785490\pi\) | ||
0.781393 | − | 0.624039i | \(-0.214510\pi\) | |||||||
\(662\) | −17.5440 | −0.681867 | ||||||||
\(663\) | 3.77200 | 0.146492 | ||||||||
\(664\) | − | 1.77200i | − | 0.0687670i | ||||||
\(665\) | −7.77200 | −0.301385 | ||||||||
\(666\) | −3.77200 | − | 4.77200i | −0.146162 | − | 0.184911i | ||||
\(667\) | −6.00000 | −0.232321 | ||||||||
\(668\) | 11.3160i | 0.437829i | ||||||||
\(669\) | 17.2280 | 0.666073 | ||||||||
\(670\) | 9.54400 | 0.368717 | ||||||||
\(671\) | 12.7720i | 0.493058i | ||||||||
\(672\) | − | 1.00000i | − | 0.0385758i | ||||||
\(673\) | 16.6840 | 0.643121 | 0.321560 | − | 0.946889i | \(-0.395793\pi\) | ||||
0.321560 | + | 0.946889i | \(0.395793\pi\) | |||||||
\(674\) | 1.31601i | 0.0506906i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 1.22800 | 0.0472307 | ||||||||
\(677\) | −27.7720 | −1.06736 | −0.533682 | − | 0.845685i | \(-0.679192\pi\) | ||||
−0.533682 | + | 0.845685i | \(0.679192\pi\) | |||||||
\(678\) | −14.3160 | −0.549803 | ||||||||
\(679\) | 10.7720i | 0.413391i | ||||||||
\(680\) | − | 1.00000i | − | 0.0383482i | ||||||
\(681\) | − | 6.77200i | − | 0.259504i | ||||||
\(682\) | 0.772002 | 0.0295615 | ||||||||
\(683\) | 11.6840i | 0.447076i | 0.974695 | + | 0.223538i | \(0.0717606\pi\) | ||||
−0.974695 | + | 0.223538i | \(0.928239\pi\) | |||||||
\(684\) | 7.77200i | 0.297170i | ||||||||
\(685\) | − | 19.0880i | − | 0.729315i | ||||||
\(686\) | − | 13.0000i | − | 0.496342i | ||||||
\(687\) | −13.5440 | −0.516736 | ||||||||
\(688\) | 1.22800i | 0.0468170i | ||||||||
\(689\) | − | 39.7720i | − | 1.51519i | ||||||
\(690\) | 7.77200i | 0.295875i | ||||||||
\(691\) | 15.2280 | 0.579300 | 0.289650 | − | 0.957133i | \(-0.406461\pi\) | ||||
0.289650 | + | 0.957133i | \(0.406461\pi\) | |||||||
\(692\) | −15.0000 | −0.570214 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 23.5440 | 0.893718 | ||||||||
\(695\) | 20.3160i | 0.770630i | ||||||||
\(696\) | −0.772002 | −0.0292627 | ||||||||
\(697\) | − | 0.772002i | − | 0.0292417i | ||||||
\(698\) | 6.00000i | 0.227103i | ||||||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 45.5440i | 1.72017i | 0.510148 | + | 0.860087i | \(0.329591\pi\) | ||||
−0.510148 | + | 0.860087i | \(0.670409\pi\) | |||||||
\(702\) | −3.77200 | −0.142365 | ||||||||
\(703\) | −29.3160 | − | 37.0880i | −1.10567 | − | 1.39880i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.7720 | 1.38393 | ||||||||
\(707\) | 11.5440 | 0.434157 | ||||||||
\(708\) | − | 7.54400i | − | 0.283521i | ||||||
\(709\) | 18.5440i | 0.696435i | 0.937414 | + | 0.348217i | \(0.113213\pi\) | ||||
−0.937414 | + | 0.348217i | \(0.886787\pi\) | |||||||
\(710\) | −6.00000 | −0.225176 | ||||||||
\(711\) | − | 11.5440i | − | 0.432934i | ||||||
\(712\) | 17.3160 | 0.648945 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 1.00000 | 0.0374241 | ||||||||
\(715\) | 3.77200 | 0.141065 | ||||||||
\(716\) | 9.54400i | 0.356676i | ||||||||
\(717\) | 5.22800i | 0.195243i | ||||||||
\(718\) | 4.45600i | 0.166296i | ||||||||
\(719\) | −12.0000 | −0.447524 | −0.223762 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − | 17.5440i | − | 0.653373i | ||||||
\(722\) | 41.4040i | 1.54090i | ||||||||
\(723\) | − | 16.0000i | − | 0.595046i | ||||||
\(724\) | −23.5440 | −0.875006 | ||||||||
\(725\) | 0.772002i | 0.0286714i | ||||||||
\(726\) | − | 10.0000i | − | 0.371135i | ||||||
\(727\) | − | 52.1760i | − | 1.93510i | −0.252677 | − | 0.967551i | \(-0.581311\pi\) | ||
0.252677 | − | 0.967551i | \(-0.418689\pi\) | |||||||
\(728\) | 3.77200 | 0.139800 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.227998 | 0.00843859 | ||||||||
\(731\) | −1.22800 | −0.0454192 | ||||||||
\(732\) | − | 12.7720i | − | 0.472067i | ||||||
\(733\) | −13.6840 | −0.505430 | −0.252715 | − | 0.967541i | \(-0.581323\pi\) | ||||
−0.252715 | + | 0.967541i | \(0.581323\pi\) | |||||||
\(734\) | 16.0880i | 0.593819i | ||||||||
\(735\) | 6.00000i | 0.221313i | ||||||||
\(736\) | −7.77200 | −0.286480 | ||||||||
\(737\) | −9.54400 | −0.351558 | ||||||||
\(738\) | 0.772002i | 0.0284178i | ||||||||
\(739\) | −49.8600 | −1.83413 | −0.917065 | − | 0.398738i | \(-0.869448\pi\) | ||||
−0.917065 | + | 0.398738i | \(0.869448\pi\) | |||||||
\(740\) | −3.77200 | − | 4.77200i | −0.138662 | − | 0.175422i | ||||
\(741\) | −29.3160 | −1.07695 | ||||||||
\(742\) | − | 10.5440i | − | 0.387083i | ||||||
\(743\) | 31.8600 | 1.16883 | 0.584415 | − | 0.811455i | \(-0.301324\pi\) | ||||
0.584415 | + | 0.811455i | \(0.301324\pi\) | |||||||
\(744\) | −0.772002 | −0.0283030 | ||||||||
\(745\) | − | 6.00000i | − | 0.219823i | ||||||
\(746\) | − | 21.5440i | − | 0.788782i | ||||||
\(747\) | −1.77200 | −0.0648342 | ||||||||
\(748\) | 1.00000i | 0.0365636i | ||||||||
\(749\) | 7.77200 | 0.283983 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 16.6320 | 0.606911 | 0.303455 | − | 0.952846i | \(-0.401860\pi\) | ||||
0.303455 | + | 0.952846i | \(0.401860\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.0880i | 0.987142i | ||||||||
\(754\) | − | 2.91199i | − | 0.106049i | ||||||
\(755\) | 8.22800i | 0.299448i | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | − | 47.4920i | − | 1.72613i | −0.505096 | − | 0.863063i | \(-0.668543\pi\) | ||
0.505096 | − | 0.863063i | \(-0.331457\pi\) | |||||||
\(758\) | 23.5440i | 0.855157i | ||||||||
\(759\) | − | 7.77200i | − | 0.282106i | ||||||
\(760\) | 7.77200i | 0.281920i | ||||||||
\(761\) | 40.4920 | 1.46783 | 0.733917 | − | 0.679239i | \(-0.237690\pi\) | ||||
0.733917 | + | 0.679239i | \(0.237690\pi\) | |||||||
\(762\) | 13.3160i | 0.482388i | ||||||||
\(763\) | − | 7.00000i | − | 0.253417i | ||||||
\(764\) | − | 12.5440i | − | 0.453826i | ||||||
\(765\) | −1.00000 | −0.0361551 | ||||||||
\(766\) | −15.3160 | −0.553390 | ||||||||
\(767\) | 28.4560 | 1.02749 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 7.54400i | 0.272044i | 0.990706 | + | 0.136022i | \(0.0434317\pi\) | ||||
−0.990706 | + | 0.136022i | \(0.956568\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | 4.22800i | 0.152268i | ||||||||
\(772\) | 6.45600i | 0.232356i | ||||||||
\(773\) | 33.6320 | 1.20966 | 0.604830 | − | 0.796355i | \(-0.293241\pi\) | ||||
0.604830 | + | 0.796355i | \(0.293241\pi\) | |||||||
\(774\) | 1.22800 | 0.0441395 | ||||||||
\(775\) | 0.772002i | 0.0277311i | ||||||||
\(776\) | 10.7720 | 0.386692 | ||||||||
\(777\) | 4.77200 | − | 3.77200i | 0.171195 | − | 0.135320i | ||||
\(778\) | 6.77200 | 0.242788 | ||||||||
\(779\) | 6.00000i | 0.214972i | ||||||||
\(780\) | −3.77200 | −0.135059 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | − | 7.77200i | − | 0.277926i | ||||||
\(783\) | 0.772002i | 0.0275891i | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | 17.8600i | 0.637451i | ||||||||
\(786\) | −0.455996 | −0.0162648 | ||||||||
\(787\) | 48.1760 | 1.71729 | 0.858645 | − | 0.512571i | \(-0.171307\pi\) | ||||
0.858645 | + | 0.512571i | \(0.171307\pi\) | |||||||
\(788\) | −11.7720 | −0.419360 | ||||||||
\(789\) | −5.22800 | −0.186122 | ||||||||
\(790\) | − | 11.5440i | − | 0.410717i | ||||||
\(791\) | − | 14.3160i | − | 0.509019i | ||||||
\(792\) | − | 1.00000i | − | 0.0355335i | ||||||
\(793\) | 48.1760 | 1.71078 | ||||||||
\(794\) | − | 1.54400i | − | 0.0547946i | ||||||
\(795\) | 10.5440i | 0.373957i | ||||||||
\(796\) | 7.54400i | 0.267390i | ||||||||
\(797\) | − | 27.0880i | − | 0.959506i | −0.877403 | − | 0.479753i | \(-0.840726\pi\) | ||
0.877403 | − | 0.479753i | \(-0.159274\pi\) | |||||||
\(798\) | −7.77200 | −0.275126 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − | 17.3160i | − | 0.611831i | ||||||
\(802\) | 23.3160 | 0.823317 | ||||||||
\(803\) | −0.227998 | −0.00804588 | ||||||||
\(804\) | 9.54400 | 0.336591 | ||||||||
\(805\) | −7.77200 | −0.273927 | ||||||||
\(806\) | − | 2.91199i | − | 0.102571i | ||||||
\(807\) | −9.31601 | −0.327939 | ||||||||
\(808\) | − | 11.5440i | − | 0.406117i | ||||||
\(809\) | 47.3160i | 1.66354i | 0.555119 | + | 0.831771i | \(0.312673\pi\) | ||||
−0.555119 | + | 0.831771i | \(0.687327\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 4.45600 | 0.156471 | 0.0782356 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782356 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(812\) | − | 0.772002i | − | 0.0270920i | ||||||
\(813\) | 23.0880 | 0.809732 | ||||||||
\(814\) | 3.77200 | + | 4.77200i | 0.132209 | + | 0.167259i | ||||
\(815\) | 3.45600 | 0.121058 | ||||||||
\(816\) | − | 1.00000i | − | 0.0350070i | ||||||
\(817\) | 9.54400 | 0.333902 | ||||||||
\(818\) | 4.00000 | 0.139857 | ||||||||
\(819\) | − | 3.77200i | − | 0.131804i | ||||||
\(820\) | 0.772002i | 0.0269595i | ||||||||
\(821\) | 39.9480 | 1.39420 | 0.697098 | − | 0.716976i | \(-0.254474\pi\) | ||||
0.697098 | + | 0.716976i | \(0.254474\pi\) | |||||||
\(822\) | − | 19.0880i | − | 0.665771i | ||||||
\(823\) | −36.8600 | −1.28486 | −0.642430 | − | 0.766345i | \(-0.722073\pi\) | ||||
−0.642430 | + | 0.766345i | \(0.722073\pi\) | |||||||
\(824\) | −17.5440 | −0.611174 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 7.54400 | 0.262489 | ||||||||
\(827\) | − | 21.6840i | − | 0.754026i | −0.926208 | − | 0.377013i | \(-0.876951\pi\) | ||
0.926208 | − | 0.377013i | \(-0.123049\pi\) | |||||||
\(828\) | 7.77200i | 0.270096i | ||||||||
\(829\) | − | 47.0000i | − | 1.63238i | −0.577785 | − | 0.816189i | \(-0.696083\pi\) | ||
0.577785 | − | 0.816189i | \(-0.303917\pi\) | |||||||
\(830\) | −1.77200 | −0.0615071 | ||||||||
\(831\) | − | 6.22800i | − | 0.216047i | ||||||
\(832\) | − | 3.77200i | − | 0.130771i | ||||||
\(833\) | − | 6.00000i | − | 0.207888i | ||||||
\(834\) | 20.3160i | 0.703486i | ||||||||
\(835\) | 11.3160 | 0.391607 | ||||||||
\(836\) | − | 7.77200i | − | 0.268800i | ||||||
\(837\) | 0.772002i | 0.0266843i | ||||||||
\(838\) | − | 12.8600i | − | 0.444242i | ||||||
\(839\) | 14.4560 | 0.499076 | 0.249538 | − | 0.968365i | \(-0.419721\pi\) | ||||
0.249538 | + | 0.968365i | \(0.419721\pi\) | |||||||
\(840\) | −1.00000 | −0.0345033 | ||||||||
\(841\) | 28.4040 | 0.979449 | ||||||||
\(842\) | −6.00000 | −0.206774 | ||||||||
\(843\) | − | 3.77200i | − | 0.129915i | ||||||
\(844\) | 11.2280 | 0.386484 | ||||||||
\(845\) | − | 1.22800i | − | 0.0422444i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | −10.5440 | −0.362083 | ||||||||
\(849\) | 2.22800i | 0.0764647i | ||||||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | −29.3160 | − | 37.0880i | −1.00494 | − | 1.27136i | ||||
\(852\) | −6.00000 | −0.205557 | ||||||||
\(853\) | − | 38.8600i | − | 1.33054i | −0.746602 | − | 0.665271i | \(-0.768316\pi\) | ||
0.746602 | − | 0.665271i | \(-0.231684\pi\) | |||||||
\(854\) | 12.7720 | 0.437049 | ||||||||
\(855\) | 7.77200 | 0.265797 | ||||||||
\(856\) | − | 7.77200i | − | 0.265642i | ||||||
\(857\) | 15.0000i | 0.512390i | 0.966625 | + | 0.256195i | \(0.0824690\pi\) | ||||
−0.966625 | + | 0.256195i | \(0.917531\pi\) | |||||||
\(858\) | 3.77200 | 0.128774 | ||||||||
\(859\) | 7.77200i | 0.265177i | 0.991171 | + | 0.132589i | \(0.0423289\pi\) | ||||
−0.991171 | + | 0.132589i | \(0.957671\pi\) | |||||||
\(860\) | 1.22800 | 0.0418744 | ||||||||
\(861\) | −0.772002 | −0.0263098 | ||||||||
\(862\) | 10.0880 | 0.343599 | ||||||||
\(863\) | 32.3160 | 1.10005 | 0.550025 | − | 0.835148i | \(-0.314618\pi\) | ||||
0.550025 | + | 0.835148i | \(0.314618\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 15.0000i | 0.510015i | ||||||||
\(866\) | 7.77200i | 0.264103i | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | − | 0.772002i | − | 0.0262035i | ||||||
\(869\) | 11.5440i | 0.391604i | ||||||||
\(870\) | 0.772002i | 0.0261733i | ||||||||
\(871\) | 36.0000i | 1.21981i | ||||||||
\(872\) | −7.00000 | −0.237050 | ||||||||
\(873\) | − | 10.7720i | − | 0.364577i | ||||||
\(874\) | 60.4040i | 2.04320i | ||||||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 0.227998 | 0.00770334 | ||||||||
\(877\) | −9.22800 | −0.311607 | −0.155804 | − | 0.987788i | \(-0.549797\pi\) | ||||
−0.155804 | + | 0.987788i | \(0.549797\pi\) | |||||||
\(878\) | 20.7720 | 0.701021 | ||||||||
\(879\) | 9.00000 | 0.303562 | ||||||||
\(880\) | − | 1.00000i | − | 0.0337100i | ||||||
\(881\) | −40.7720 | −1.37364 | −0.686822 | − | 0.726826i | \(-0.740995\pi\) | ||||
−0.686822 | + | 0.726826i | \(0.740995\pi\) | |||||||
\(882\) | 6.00000i | 0.202031i | ||||||||
\(883\) | − | 1.91199i | − | 0.0643437i | −0.999482 | − | 0.0321718i | \(-0.989758\pi\) | ||
0.999482 | − | 0.0321718i | \(-0.0102424\pi\) | |||||||
\(884\) | 3.77200 | 0.126866 | ||||||||
\(885\) | −7.54400 | −0.253589 | ||||||||
\(886\) | 20.0000i | 0.671913i | ||||||||
\(887\) | −27.6840 | −0.929538 | −0.464769 | − | 0.885432i | \(-0.653863\pi\) | ||||
−0.464769 | + | 0.885432i | \(0.653863\pi\) | |||||||
\(888\) | −3.77200 | − | 4.77200i | −0.126580 | − | 0.160138i | ||||
\(889\) | −13.3160 | −0.446604 | ||||||||
\(890\) | − | 17.3160i | − | 0.580434i | ||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 17.2280 | 0.576836 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 6.00000i | − | 0.200670i | ||||||
\(895\) | 9.54400 | 0.319021 | ||||||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | −29.3160 | −0.978833 | ||||||||
\(898\) | −2.00000 | −0.0667409 | ||||||||
\(899\) | −0.595987 | −0.0198773 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | − | 10.5440i | − | 0.351272i | ||||||
\(902\) | − | 0.772002i | − | 0.0257049i | ||||||
\(903\) | 1.22800i | 0.0408652i | ||||||||
\(904\) | −14.3160 | −0.476143 | ||||||||
\(905\) | 23.5440i | 0.782629i | ||||||||
\(906\) | 8.22800i | 0.273357i | ||||||||
\(907\) | 30.2280i | 1.00370i | 0.864953 | + | 0.501852i | \(0.167348\pi\) | ||||
−0.864953 | + | 0.501852i | \(0.832652\pi\) | |||||||
\(908\) | − | 6.77200i | − | 0.224737i | ||||||
\(909\) | −11.5440 | −0.382890 | ||||||||
\(910\) | − | 3.77200i | − | 0.125041i | ||||||
\(911\) | − | 24.0000i | − | 0.795155i | −0.917568 | − | 0.397578i | \(-0.869851\pi\) | ||
0.917568 | − | 0.397578i | \(-0.130149\pi\) | |||||||
\(912\) | 7.77200i | 0.257357i | ||||||||
\(913\) | 1.77200 | 0.0586447 | ||||||||
\(914\) | −34.3160 | −1.13507 | ||||||||
\(915\) | −12.7720 | −0.422229 | ||||||||
\(916\) | −13.5440 | −0.447506 | ||||||||
\(917\) | − | 0.455996i | − | 0.0150583i | ||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 32.0000i | 1.05558i | 0.849374 | + | 0.527791i | \(0.176980\pi\) | ||||
−0.849374 | + | 0.527791i | \(0.823020\pi\) | |||||||
\(920\) | 7.77200i | 0.256235i | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | −21.2280 | −0.699107 | ||||||||
\(923\) | − | 22.6320i | − | 0.744942i | ||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | −4.77200 | + | 3.77200i | −0.156902 | + | 0.124023i | ||||
\(926\) | 30.6320 | 1.00663 | ||||||||
\(927\) | 17.5440i | 0.576221i | ||||||||
\(928\) | −0.772002 | −0.0253422 | ||||||||
\(929\) | 29.2280 | 0.958940 | 0.479470 | − | 0.877558i | \(-0.340829\pi\) | ||||
0.479470 | + | 0.877558i | \(0.340829\pi\) | |||||||
\(930\) | 0.772002i | 0.0253149i | ||||||||
\(931\) | 46.6320i | 1.52830i | ||||||||
\(932\) | 12.0000 | 0.393073 | ||||||||
\(933\) | 6.77200i | 0.221705i | ||||||||
\(934\) | 4.31601 | 0.141224 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | −3.77200 | −0.123292 | ||||||||
\(937\) | −24.4560 | −0.798943 | −0.399471 | − | 0.916746i | \(-0.630806\pi\) | ||||
−0.399471 | + | 0.916746i | \(0.630806\pi\) | |||||||
\(938\) | 9.54400i | 0.311623i | ||||||||
\(939\) | − | 17.0880i | − | 0.557646i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.6320 | 1.52016 | 0.760080 | − | 0.649829i | \(-0.225160\pi\) | ||||
0.760080 | + | 0.649829i | \(0.225160\pi\) | |||||||
\(942\) | 17.8600i | 0.581911i | ||||||||
\(943\) | 6.00000i | 0.195387i | ||||||||
\(944\) | − | 7.54400i | − | 0.245536i | ||||||
\(945\) | 1.00000i | 0.0325300i | ||||||||
\(946\) | −1.22800 | −0.0399257 | ||||||||
\(947\) | 5.86001i | 0.190425i | 0.995457 | + | 0.0952124i | \(0.0303530\pi\) | ||||
−0.995457 | + | 0.0952124i | \(0.969647\pi\) | |||||||
\(948\) | − | 11.5440i | − | 0.374932i | ||||||
\(949\) | 0.860009i | 0.0279171i | ||||||||
\(950\) | 7.77200 | 0.252157 | ||||||||
\(951\) | 33.4040 | 1.08320 | ||||||||
\(952\) | 1.00000 | 0.0324102 | ||||||||
\(953\) | 25.5440 | 0.827451 | 0.413726 | − | 0.910402i | \(-0.364227\pi\) | ||||
0.413726 | + | 0.910402i | \(0.364227\pi\) | |||||||
\(954\) | 10.5440i | 0.341375i | ||||||||
\(955\) | −12.5440 | −0.405914 | ||||||||
\(956\) | 5.22800i | 0.169086i | ||||||||
\(957\) | − | 0.772002i | − | 0.0249553i | ||||||
\(958\) | 10.2280 | 0.330452 | ||||||||
\(959\) | 19.0880 | 0.616384 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 30.4040 | 0.980775 | ||||||||
\(962\) | 18.0000 | − | 14.2280i | 0.580343 | − | 0.458729i | ||||
\(963\) | −7.77200 | −0.250449 | ||||||||
\(964\) | − | 16.0000i | − | 0.515325i | ||||||
\(965\) | 6.45600 | 0.207826 | ||||||||
\(966\) | −7.77200 | −0.250060 | ||||||||
\(967\) | 24.6320i | 0.792112i | 0.918226 | + | 0.396056i | \(0.129621\pi\) | ||||
−0.918226 | + | 0.396056i | \(0.870379\pi\) | |||||||
\(968\) | − | 10.0000i | − | 0.321412i | ||||||
\(969\) | −7.77200 | −0.249673 | ||||||||
\(970\) | − | 10.7720i | − | 0.345868i | ||||||
\(971\) | −33.8600 | −1.08662 | −0.543310 | − | 0.839532i | \(-0.682829\pi\) | ||||
−0.543310 | + | 0.839532i | \(0.682829\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −20.3160 | −0.651301 | ||||||||
\(974\) | −15.0880 | −0.483451 | ||||||||
\(975\) | 3.77200i | 0.120801i | ||||||||
\(976\) | − | 12.7720i | − | 0.408822i | ||||||
\(977\) | − | 33.0000i | − | 1.05576i | −0.849318 | − | 0.527882i | \(-0.822986\pi\) | ||
0.849318 | − | 0.527882i | \(-0.177014\pi\) | |||||||
\(978\) | 3.45600 | 0.110511 | ||||||||
\(979\) | 17.3160i | 0.553422i | ||||||||
\(980\) | 6.00000i | 0.191663i | ||||||||
\(981\) | 7.00000i | 0.223493i | ||||||||
\(982\) | − | 30.2280i | − | 0.964614i | ||||||
\(983\) | −27.4040 | −0.874052 | −0.437026 | − | 0.899449i | \(-0.643968\pi\) | ||||
−0.437026 | + | 0.899449i | \(0.643968\pi\) | |||||||
\(984\) | 0.772002i | 0.0246105i | ||||||||
\(985\) | 11.7720i | 0.375087i | ||||||||
\(986\) | − | 0.772002i | − | 0.0245855i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.3160 | −0.932666 | ||||||||
\(989\) | 9.54400 | 0.303482 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | − | 8.13999i | − | 0.258575i | −0.991607 | − | 0.129288i | \(-0.958731\pi\) | ||
0.991607 | − | 0.129288i | \(-0.0412691\pi\) | |||||||
\(992\) | −0.772002 | −0.0245111 | ||||||||
\(993\) | 17.5440i | 0.556742i | ||||||||
\(994\) | − | 6.00000i | − | 0.190308i | ||||||
\(995\) | 7.54400 | 0.239161 | ||||||||
\(996\) | −1.77200 | −0.0561480 | ||||||||
\(997\) | − | 52.4040i | − | 1.65965i | −0.558022 | − | 0.829826i | \(-0.688440\pi\) | ||
0.558022 | − | 0.829826i | \(-0.311560\pi\) | |||||||
\(998\) | −4.68399 | −0.148269 | ||||||||
\(999\) | −4.77200 | + | 3.77200i | −0.150979 | + | 0.119341i |
(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 | 1110.2.h.d.961.2 | ✓ | 4 | |
3.2 | odd | 2 | 3330.2.h.j.2071.4 | 4 | |||
37.36 | even | 2 | inner | 1110.2.h.d.961.3 | yes | 4 | |
111.110 | odd | 2 | 3330.2.h.j.2071.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.d.961.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1110.2.h.d.961.3 | yes | 4 | 37.36 | even | 2 | inner | |
3330.2.h.j.2071.1 | 4 | 111.110 | odd | 2 | |||
3330.2.h.j.2071.4 | 4 | 3.2 | odd | 2 |