Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.116319195136.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 77x^{4} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.3 | ||
Root | \(-2.09428 - 2.09428i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.d.1791.4 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.477491 | −0.275680 | −0.137840 | − | 0.990455i | \(-0.544016\pi\) | ||||
−0.137840 | + | 0.990455i | \(0.544016\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.09428 | + | 1.61679i | −0.791563 | + | 0.611088i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.77200 | −0.924001 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.66605i | − | 1.40687i | −0.710761 | − | 0.703433i | \(-0.751649\pi\) | ||
0.710761 | − | 0.703433i | \(-0.248351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.77200i | 1.04617i | 0.852282 | + | 0.523083i | \(0.175218\pi\) | ||||
−0.852282 | + | 0.523083i | \(0.824782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.477491i | 0.123288i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.77200i | 0.914845i | 0.889250 | + | 0.457422i | \(0.151227\pi\) | ||||
−0.889250 | + | 0.457422i | \(0.848773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.42213 | 1.70275 | 0.851377 | − | 0.524555i | \(-0.175768\pi\) | ||||
0.851377 | + | 0.524555i | \(0.175768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 0.772002i | 0.218218 | − | 0.168465i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.23357i | 0.674247i | 0.941460 | + | 0.337123i | \(0.109454\pi\) | ||||
−0.941460 | + | 0.337123i | \(0.890546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.75608 | 0.530408 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.77200 | −0.700443 | −0.350222 | − | 0.936667i | \(-0.613894\pi\) | ||||
−0.350222 | + | 0.936667i | \(0.613894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.954983 | 0.171520 | 0.0857600 | − | 0.996316i | \(-0.472668\pi\) | ||||
0.0857600 | + | 0.996316i | \(0.472668\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.22800i | 0.387845i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61679 | + | 2.09428i | 0.273287 | + | 0.353998i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.54400 | −0.911429 | −0.455714 | − | 0.890126i | \(-0.650616\pi\) | ||||
−0.455714 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.80110i | − | 0.288407i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.5657i | − | 1.91625i | −0.286356 | − | 0.958123i | \(-0.592444\pi\) | ||
0.286356 | − | 0.958123i | \(-0.407556\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.77200i | 0.413226i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.89962 | 1.15228 | 0.576139 | − | 0.817352i | \(-0.304559\pi\) | ||||
0.576139 | + | 0.817352i | \(0.304559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.77200 | − | 6.77200i | 0.253143 | − | 0.967429i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.80110i | − | 0.252204i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.66605 | −0.629170 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.54400 | −0.469415 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.33210 | 1.21494 | 0.607468 | − | 0.794344i | \(-0.292185\pi\) | ||||
0.607468 | + | 0.794344i | \(0.292185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.5440i | − | 1.73413i | −0.498193 | − | 0.867066i | \(-0.666003\pi\) | ||
0.498193 | − | 0.867066i | \(-0.333997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.80534 | − | 4.48174i | 0.731404 | − | 0.564646i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.77200 | 0.467859 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.09852i | − | 0.745053i | −0.928022 | − | 0.372527i | \(-0.878492\pi\) | ||
0.928022 | − | 0.372527i | \(-0.121508\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.54400i | − | 0.185876i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.33210i | − | 1.10752i | −0.832678 | − | 0.553758i | \(-0.813193\pi\) | ||
0.832678 | − | 0.553758i | \(-0.186807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.477491 | 0.0551360 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.54400 | + | 9.77200i | 0.859719 | + | 1.11362i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.1332i | − | 1.25258i | −0.779589 | − | 0.626291i | \(-0.784572\pi\) | ||
0.779589 | − | 0.626291i | \(-0.215428\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | 0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5657 | −1.37926 | −0.689631 | − | 0.724161i | \(-0.742227\pi\) | ||||
−0.689631 | + | 0.724161i | \(0.742227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.77200 | 0.409131 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.80110 | 0.193098 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.09852 | − | 7.89962i | −0.639299 | − | 0.828105i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.455996 | −0.0472846 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 7.42213i | − | 0.761494i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.22800i | − | 0.835427i | −0.908579 | − | 0.417713i | \(-0.862832\pi\) | ||
0.908579 | − | 0.417713i | \(-0.137168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.9343i | 1.29995i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.54400i | 0.750656i | 0.926892 | + | 0.375328i | \(0.122470\pi\) | ||||
−0.926892 | + | 0.375328i | \(0.877530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.85460 | 0.872470 | 0.436235 | − | 0.899833i | \(-0.356312\pi\) | ||||
0.436235 | + | 0.899833i | \(0.356312\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.772002 | − | 1.00000i | −0.0753397 | − | 0.0975900i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.09852i | 0.589566i | 0.955564 | + | 0.294783i | \(0.0952474\pi\) | ||||
−0.955564 | + | 0.294783i | \(0.904753\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.77200 | 0.169727 | 0.0848635 | − | 0.996393i | \(-0.472955\pi\) | ||||
0.0848635 | + | 0.996393i | \(0.472955\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.64721 | 0.251262 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.54400 | 0.145248 | 0.0726238 | − | 0.997359i | \(-0.476863\pi\) | ||||
0.0726238 | + | 0.997359i | \(0.476863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.23357 | 0.301532 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 10.4560i | − | 0.966657i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.09852 | − | 7.89962i | −0.559051 | − | 0.724157i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7720 | −0.979273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.86495i | 0.258324i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.09852i | − | 0.541156i | −0.962698 | − | 0.270578i | \(-0.912785\pi\) | ||
0.962698 | − | 0.270578i | \(-0.0872149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000i | 0.528271i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.46715 | −0.565037 | −0.282519 | − | 0.959262i | \(-0.591170\pi\) | ||||
−0.282519 | + | 0.959262i | \(0.591170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.5440 | + | 12.0000i | −1.34784 | + | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.75608i | − | 0.237206i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5440 | 1.15714 | 0.578571 | − | 0.815632i | \(-0.303611\pi\) | ||||
0.578571 | + | 0.815632i | \(0.303611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.8443 | 1.25907 | 0.629537 | − | 0.776971i | \(-0.283245\pi\) | ||||
0.629537 | + | 0.776971i | \(0.283245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.77200 | −0.317660 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.6003 | 1.47181 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.77200i | 0.313248i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.846116 | + | 3.23357i | −0.0697865 | + | 0.266701i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.54400 | 0.618029 | 0.309014 | − | 0.951057i | \(-0.400001\pi\) | ||||
0.309014 | + | 0.951057i | \(0.400001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.66605i | 0.379718i | 0.981811 | + | 0.189859i | \(0.0608030\pi\) | ||||
−0.981811 | + | 0.189859i | \(0.939197\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.4560i | − | 0.845317i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.954983i | − | 0.0767061i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.00000i | − | 0.478852i | −0.970915 | − | 0.239426i | \(-0.923041\pi\) | ||
0.970915 | − | 0.239426i | \(-0.0769593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.86495 | −0.227205 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.22800 | − | 6.77200i | −0.412024 | − | 0.533709i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.70072i | − | 0.759819i | −0.925024 | − | 0.379910i | \(-0.875955\pi\) | ||
0.925024 | − | 0.379910i | \(-0.124045\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.22800 | 0.173449 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0967 | 1.55513 | 0.777563 | − | 0.628805i | \(-0.216455\pi\) | ||||
0.777563 | + | 0.628805i | \(0.216455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.22800 | −0.0944614 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.5742 | −1.57335 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 23.3160i | − | 1.77268i | −0.463032 | − | 0.886342i | \(-0.653239\pi\) | ||
0.463032 | − | 0.886342i | \(-0.346761\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.09428 | − | 1.61679i | 0.158313 | − | 0.122218i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.45600 | −0.334933 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.7992i | 1.18089i | 0.807078 | + | 0.590445i | \(0.201048\pi\) | ||||
−0.807078 | + | 0.590445i | \(0.798952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.54400i | 0.560741i | 0.959892 | + | 0.280371i | \(0.0904574\pi\) | ||||
−0.959892 | + | 0.280371i | \(0.909543\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.46715i | 0.478065i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.54400i | 0.407603i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.6003 | 1.28706 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.77200 | + | 4.45600i | −0.419851 | + | 0.324126i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.26825i | − | 0.598269i | −0.954211 | − | 0.299135i | \(-0.903302\pi\) | ||
0.954211 | − | 0.299135i | \(-0.0966980\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5440 | −1.55077 | −0.775386 | − | 0.631488i | \(-0.782445\pi\) | ||||
−0.775386 | + | 0.631488i | \(0.782445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.80110 | −0.128979 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.42213 | −0.526141 | −0.263070 | − | 0.964777i | \(-0.584735\pi\) | ||||
−0.263070 | + | 0.964777i | \(0.584735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.91199i | 0.205396i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.89962 | − | 6.09852i | 0.554445 | − | 0.428032i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 8.96347i | − | 0.623004i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 34.6320i | − | 2.39555i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.6003i | − | 1.21166i | −0.795595 | − | 0.605829i | \(-0.792842\pi\) | ||
0.795595 | − | 0.605829i | \(-0.207158\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.45600i | 0.305320i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.5657 | −0.856972 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | + | 1.54400i | −0.135769 | + | 0.104814i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.86495i | − | 0.193595i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2280 | −0.957079 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.98966 | −0.401097 | −0.200548 | − | 0.979684i | \(-0.564272\pi\) | ||||
−0.200548 | + | 0.979684i | \(0.564272\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.77200 | 0.184800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7646 | 0.714470 | 0.357235 | − | 0.934015i | \(-0.383720\pi\) | ||||
0.357235 | + | 0.934015i | \(0.383720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.45600i | − | 0.294461i | −0.989102 | − | 0.147230i | \(-0.952964\pi\) | ||
0.989102 | − | 0.147230i | \(-0.0470358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.60220 | − | 4.66605i | −0.237007 | − | 0.307003i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5440 | 1.67344 | 0.836722 | − | 0.547628i | \(-0.184469\pi\) | ||||
0.836722 | + | 0.547628i | \(0.184469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.89962i | − | 0.515314i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.31601i | 0.345312i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.80110i | 0.116503i | 0.998302 | + | 0.0582517i | \(0.0185526\pi\) | ||||
−0.998302 | + | 0.0582517i | \(0.981447\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.5440i | 1.64543i | 0.568451 | + | 0.822717i | \(0.307543\pi\) | ||||
−0.568451 | + | 0.822717i | \(0.692457\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.6107 | −0.744826 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.77200 | − | 1.77200i | −0.432647 | − | 0.113209i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.9963i | 1.78136i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1970 | 0.769871 | 0.384935 | − | 0.922944i | \(-0.374224\pi\) | ||||
0.384935 | + | 0.922944i | \(0.374224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0880 | 0.948575 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.80110 | −0.112789 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.0880i | 1.31543i | 0.753265 | + | 0.657717i | \(0.228478\pi\) | ||||
−0.753265 | + | 0.657717i | \(0.771522\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6107 | − | 8.96347i | 0.721453 | − | 0.556963i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.4560 | 0.647210 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.0328i | 1.17361i | 0.809727 | + | 0.586807i | \(0.199615\pi\) | ||||
−0.809727 | + | 0.586807i | \(0.800385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.00000i | − | 0.368577i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.72990i | − | 0.350664i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.54400i | − | 0.0941396i | −0.998892 | − | 0.0470698i | \(-0.985012\pi\) | ||
0.998892 | − | 0.0470698i | \(-0.0149883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.37711 | −0.508873 | −0.254437 | − | 0.967089i | \(-0.581890\pi\) | ||||
−0.254437 | + | 0.967089i | \(0.581890\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.91199 | + | 3.77200i | 0.176242 | + | 0.228292i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.66605i | 0.281373i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.45600 | −0.147567 | −0.0737833 | − | 0.997274i | \(-0.523507\pi\) | ||||
−0.0737833 | + | 0.997274i | \(0.523507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.64721 | −0.158485 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.31601 | −0.317126 | −0.158563 | − | 0.987349i | \(-0.550686\pi\) | ||||
−0.158563 | + | 0.987349i | \(0.550686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4568 | 0.740480 | 0.370240 | − | 0.928936i | \(-0.379275\pi\) | ||||
0.370240 | + | 0.928936i | \(0.379275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.54400i | 0.209929i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.70072 | + | 12.5657i | 0.572615 | + | 0.741728i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.77200 | 0.163059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.92880i | 0.230310i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.3160i | − | 0.661088i | −0.943791 | − | 0.330544i | \(-0.892768\pi\) | ||
0.943791 | − | 0.330544i | \(-0.107232\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.33210i | − | 0.543336i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 12.8600i | − | 0.746213i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.1970 | −0.705373 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3160 | + | 26.3160i | 1.17100 | + | 1.51683i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.60220i | − | 0.206941i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.5440 | −0.775527 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.12471 | 0.178336 | 0.0891682 | − | 0.996017i | \(-0.471579\pi\) | ||||
0.0891682 | + | 0.996017i | \(0.471579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.22800 | −0.240522 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.7335 | −1.62933 | −0.814665 | − | 0.579932i | \(-0.803079\pi\) | ||||
−0.814665 | + | 0.579932i | \(0.803079\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.77200i | − | 0.213206i | −0.994302 | − | 0.106603i | \(-0.966003\pi\) | ||
0.994302 | − | 0.106603i | \(-0.0339974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.48174 | − | 5.80534i | −0.252517 | − | 0.327094i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.08801 | 0.510433 | 0.255217 | − | 0.966884i | \(-0.417853\pi\) | ||||
0.255217 | + | 0.966884i | \(0.417853\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6003i | 0.985430i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.91199i | − | 0.162532i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.9963i | 1.55776i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.77200i | − | 0.209233i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.846116 | −0.0467903 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.5440 | + | 12.7720i | −0.912100 | + | 0.704143i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 22.2664i | − | 1.22387i | −0.790908 | − | 0.611936i | \(-0.790391\pi\) | ||
0.790908 | − | 0.611936i | \(-0.209609\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.3680 | 0.842161 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.09852 | −0.333198 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5440 | 1.17358 | 0.586788 | − | 0.809740i | \(-0.300392\pi\) | ||||
0.586788 | + | 0.809740i | \(0.300392\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.737249 | −0.0400419 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.45600i | − | 0.241306i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.23782 | + | 17.0474i | 0.390805 | + | 0.920473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.54400 | −0.0831264 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.23357i | − | 0.173587i | −0.996226 | − | 0.0867937i | \(-0.972338\pi\) | ||
0.996226 | − | 0.0867937i | \(-0.0276621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.5440i | − | 1.04617i | −0.852282 | − | 0.523083i | \(-0.824782\pi\) | ||
0.852282 | − | 0.523083i | \(-0.175218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3959i | 0.554895i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.86001i | − | 0.365121i | −0.983195 | − | 0.182561i | \(-0.941561\pi\) | ||
0.983195 | − | 0.182561i | \(-0.0584386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.33210 | −0.495296 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.91199 | + | 3.77200i | 0.154119 | + | 0.199636i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7992i | 0.833852i | 0.908940 | + | 0.416926i | \(0.136893\pi\) | ||||
−0.908940 | + | 0.416926i | \(0.863107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.0880 | 1.89937 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.14354 | 0.269966 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.38746 | −0.124624 | −0.0623121 | − | 0.998057i | \(-0.519847\pi\) | ||||
−0.0623121 | + | 0.998057i | \(0.519847\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.6320i | 0.865828i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.5657 | + | 9.70072i | −0.652377 | + | 0.503636i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.5440 | −1.11551 | −0.557753 | − | 0.830007i | \(-0.688336\pi\) | ||||
−0.557753 | + | 0.830007i | \(0.688336\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 0.477491i | − | 0.0246576i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 14.2280i | − | 0.732779i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.7992i | − | 0.811553i | −0.913972 | − | 0.405776i | \(-0.867001\pi\) | ||
0.913972 | − | 0.405776i | \(-0.132999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.91199i | 0.149186i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.0328 | −0.972531 | −0.486266 | − | 0.873811i | \(-0.661641\pi\) | ||||
−0.486266 | + | 0.873811i | \(0.661641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.77200 | − | 7.54400i | 0.498027 | − | 0.384478i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.8321i | 1.77061i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.31601 | −0.269532 | −0.134766 | − | 0.990877i | \(-0.543028\pi\) | ||||
−0.134766 | + | 0.990877i | \(0.543028\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1970 | −0.616831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.08801 | 0.155769 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.1332 | −0.560172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.22800i | 0.412951i | 0.978452 | + | 0.206476i | \(0.0661994\pi\) | ||||
−0.978452 | + | 0.206476i | \(0.933801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.42213 | − | 5.72990i | 0.371571 | − | 0.286854i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.7720 | −0.787616 | −0.393808 | − | 0.919193i | \(-0.628843\pi\) | ||||
−0.393808 | + | 0.919193i | \(0.628843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.60220i | 0.179438i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 7.00000i | − | 0.347833i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.8686i | 1.28226i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.91199i | 0.143989i | 0.997405 | + | 0.0719944i | \(0.0229364\pi\) | ||||
−0.997405 | + | 0.0719944i | \(0.977064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.46715 | −0.319001 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.5440 | + | 15.0880i | −0.961698 | + | 0.742432i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.5657i | 0.616824i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.08801 | −0.347101 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.2664 | −1.08778 | −0.543892 | − | 0.839155i | \(-0.683050\pi\) | ||||
−0.543892 | + | 0.839155i | \(0.683050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.8600 | −1.40655 | −0.703275 | − | 0.710918i | \(-0.748280\pi\) | ||||
−0.703275 | + | 0.710918i | \(0.748280\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.8978 | −1.06471 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.77200i | − | 0.182969i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.8978 | + | 28.3649i | 1.05971 | + | 1.37267i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.40401 | −0.405750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.8667i | − | 1.92031i | −0.279463 | − | 0.960156i | \(-0.590157\pi\) | ||
0.279463 | − | 0.960156i | \(-0.409843\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.08801i | − | 0.436742i | −0.975866 | − | 0.218371i | \(-0.929926\pi\) | ||
0.975866 | − | 0.218371i | \(-0.0700743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 1.80110i | − | 0.0863561i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.0000i | 1.14808i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.90997 | 0.0911577 | 0.0455789 | − | 0.998961i | \(-0.485487\pi\) | ||||
0.0455789 | + | 0.998961i | \(0.485487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.91199 | + | 18.7720i | −0.233904 | + | 0.893905i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0328i | 0.904276i | 0.891948 | + | 0.452138i | \(0.149339\pi\) | ||||
−0.891948 | + | 0.452138i | \(0.850661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.60220 | −0.170378 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.8600 | −0.606901 | −0.303451 | − | 0.952847i | \(-0.598139\pi\) | ||||
−0.303451 | + | 0.952847i | \(0.598139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.9963 | −1.31829 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.22800i | − | 0.104680i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.89962 | + | 6.09852i | −0.370340 | + | 0.285903i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.1760 | −1.87935 | −0.939677 | − | 0.342062i | \(-0.888875\pi\) | ||||
−0.939677 | + | 0.342062i | \(0.888875\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.3959i | 0.485241i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 27.0880i | − | 1.26161i | −0.775940 | − | 0.630807i | \(-0.782724\pi\) | ||
0.775940 | − | 0.630807i | \(-0.217276\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.3649i | − | 1.31823i | −0.752043 | − | 0.659115i | \(-0.770931\pi\) | ||
0.752043 | − | 0.659115i | \(-0.229069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.455996i | 0.0211463i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.3011 | −1.26334 | −0.631671 | − | 0.775236i | \(-0.717631\pi\) | ||||
−0.631671 | + | 0.775236i | \(0.717631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.86001 | + | 12.7720i | 0.455293 | + | 0.589756i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.86495i | 0.132010i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −58.6320 | −2.69590 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.42213 | −0.340551 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.6320 | −0.761527 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.3284 | 1.70558 | 0.852789 | − | 0.522256i | \(-0.174910\pi\) | ||||
0.852789 | + | 0.522256i | \(0.174910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 20.9120i | − | 0.953505i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.49632 | + | 3.23357i | 0.113587 | + | 0.147133i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.22800 | −0.373614 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.70072i | − | 0.439582i | −0.975547 | − | 0.219791i | \(-0.929463\pi\) | ||
0.975547 | − | 0.219791i | \(-0.0705375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.63201i | 0.209467i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.26825i | 0.373141i | 0.982442 | + | 0.186570i | \(0.0597372\pi\) | ||||
−0.982442 | + | 0.186570i | \(0.940263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.2280i | − | 0.640797i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.9343 | 0.581353 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.0880 | + | 19.5440i | 0.676790 | + | 0.876668i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8631i | 0.754896i | 0.926031 | + | 0.377448i | \(0.123198\pi\) | ||||
−0.926031 | + | 0.377448i | \(0.876802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.59599 | −0.428717 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.43247 | −0.0638709 | −0.0319354 | − | 0.999490i | \(-0.510167\pi\) | ||||
−0.0319354 | + | 0.999490i | \(0.510167\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.54400 | 0.335704 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.586359 | 0.0260411 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.0880i | 0.668764i | 0.942438 | + | 0.334382i | \(0.108528\pi\) | ||||
−0.942438 | + | 0.334382i | \(0.891472\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.70072 | − | 12.5657i | −0.429135 | − | 0.555872i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.4560 | 0.903154 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.85460i | − | 0.390180i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 36.8600i | − | 1.62110i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1332i | 0.488693i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.45600i | − | 0.195221i | −0.995225 | − | 0.0976104i | \(-0.968880\pi\) | ||
0.995225 | − | 0.0976104i | \(-0.0311199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.6727 | 1.16631 | 0.583157 | − | 0.812359i | \(-0.301817\pi\) | ||||
0.583157 | + | 0.812359i | \(0.301817\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | + | 0.772002i | −0.0436436 | + | 0.0336929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.60220i | 0.156914i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5440 | 0.545391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.8686 | −1.12260 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.6320 | 0.980301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.09852 | 0.263662 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 7.54400i | − | 0.325548i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.5985 | − | 8.26825i | −1.36104 | − | 0.356139i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.7720 | 1.02204 | 0.511019 | − | 0.859569i | \(-0.329268\pi\) | ||||
0.511019 | + | 0.859569i | \(0.329268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 3.60220i | − | 0.154585i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.77200i | − | 0.0759042i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.3649i | 1.21280i | 0.795161 | + | 0.606398i | \(0.207386\pi\) | ||||
−0.795161 | + | 0.606398i | \(0.792614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.5440i | 1.60234i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.9963 | −1.19268 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000 | + | 23.3160i | 0.765438 | + | 0.991497i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 2.64721i | − | 0.112368i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.5440 | −1.59079 | −0.795395 | − | 0.606091i | \(-0.792737\pi\) | ||||
−0.795395 | + | 0.606091i | \(0.792737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.3977 | 2.00471 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.40401 | −0.354818 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0328 | −0.802138 | −0.401069 | − | 0.916048i | \(-0.631361\pi\) | ||||
−0.401069 | + | 0.916048i | \(0.631361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.54400i | − | 0.0649567i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.6599 | + | 11.3175i | −0.615660 | + | 0.475291i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.6320 | 1.45185 | 0.725925 | − | 0.687774i | \(-0.241412\pi\) | ||||
0.725925 | + | 0.687774i | \(0.241412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.33210i | − | 0.390536i | −0.980750 | − | 0.195268i | \(-0.937442\pi\) | ||
0.980750 | − | 0.195268i | \(-0.0625577\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.94802i | 0.164931i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.23357i | − | 0.134849i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.8600i | 1.78429i | 0.451754 | + | 0.892143i | \(0.350799\pi\) | ||||
−0.451754 | + | 0.892143i | \(0.649201\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2871 | 0.427516 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.3160 | − | 20.3160i | 1.09177 | − | 0.842850i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.9963i | − | 1.15949i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.4560 | −0.432302 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.5657 | 0.518641 | 0.259320 | − | 0.965791i | \(-0.416501\pi\) | ||||
0.259320 | + | 0.965791i | \(0.416501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.08801 | 0.292056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.86495 | −0.117848 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 30.8600i | − | 1.26727i | −0.773633 | − | 0.633634i | \(-0.781562\pi\) | ||
0.773633 | − | 0.633634i | \(-0.218438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.89962 | + | 6.09852i | −0.323853 | + | 0.250015i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.54400 | 0.145046 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.1295i | 1.59879i | 0.600808 | + | 0.799394i | \(0.294846\pi\) | ||||
−0.600808 | + | 0.799394i | \(0.705154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.1760i | − | 0.986160i | −0.869984 | − | 0.493080i | \(-0.835871\pi\) | ||
0.869984 | − | 0.493080i | \(-0.164129\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.9051i | 0.688430i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.7720i | 0.437944i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7439 | 0.923146 | 0.461573 | − | 0.887102i | \(-0.347285\pi\) | ||||
0.461573 | + | 0.887102i | \(0.347285\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.77200 | + | 2.91199i | −0.152849 | + | 0.118000i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.7974i | 1.20547i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.0000 | 1.37325 | 0.686624 | − | 0.727013i | \(-0.259092\pi\) | ||||
0.686624 | + | 0.727013i | \(0.259092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.86495 | 0.115526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.54400 | 0.0621593 | 0.0310796 | − | 0.999517i | \(-0.490105\pi\) | ||||
0.0310796 | + | 0.999517i | \(0.490105\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.90997 | 0.0767680 | 0.0383840 | − | 0.999263i | \(-0.487779\pi\) | ||||
0.0383840 | + | 0.999263i | \(0.487779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.91199i | 0.357626i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.4014 | − | 25.1313i | −0.777302 | − | 1.00687i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.5365i | 0.660404i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 20.9120i | − | 0.833816i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13.9981i | − | 0.557257i | −0.960399 | − | 0.278629i | \(-0.910120\pi\) | ||
0.960399 | − | 0.278629i | \(-0.0898799\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.40401i | 0.334030i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.09852 | −0.242012 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.5440 | + | 6.68399i | 1.01209 | + | 0.264829i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.8686i | 1.02335i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.6320 | 1.84185 | 0.920927 | − | 0.389735i | \(-0.127434\pi\) | ||||
0.920927 | + | 0.389735i | \(0.127434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4568 | 0.491248 | 0.245624 | − | 0.969365i | \(-0.421007\pi\) | ||||
0.245624 | + | 0.969365i | \(0.421007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.2299 | 1.22777 | 0.613886 | − | 0.789395i | \(-0.289605\pi\) | ||||
0.613886 | + | 0.789395i | \(0.289605\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 43.5440i | − | 1.70925i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.954983 | − | 0.737249i | 0.0374287 | − | 0.0288951i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.0880 | −1.29483 | −0.647417 | − | 0.762136i | \(-0.724151\pi\) | ||||
−0.647417 | + | 0.762136i | \(0.724151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.46715i | 0.252692i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 16.6320i | − | 0.648877i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.92880i | 0.153044i | 0.997068 | + | 0.0765221i | \(0.0243816\pi\) | ||||
−0.997068 | + | 0.0765221i | \(0.975618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.54400i | 0.0600548i | 0.999549 | + | 0.0300274i | \(0.00955945\pi\) | ||||
−0.999549 | + | 0.0300274i | \(0.990441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.79375 | 0.263847 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | + | 15.5440i | 0.465340 | + | 0.602771i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12.1970i | − | 0.472271i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.86001 | 0.110574 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.1970 | −2.43969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.4560 | −0.711426 | −0.355713 | − | 0.934595i | \(-0.615762\pi\) | ||||
−0.355713 | + | 0.934595i | \(0.615762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.75608 | −0.106082 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.22800i | 0.316228i | 0.987421 | + | 0.158114i | \(0.0505413\pi\) | ||||
−0.987421 | + | 0.158114i | \(0.949459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3029 | + | 17.2317i | 0.510519 | + | 0.661293i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.13999 | −0.196965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.6350i | 0.866105i | 0.901369 | + | 0.433052i | \(0.142563\pi\) | ||||
−0.901369 | + | 0.433052i | \(0.857437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 13.5440i | − | 0.517490i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.12770i | 0.0811768i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.6320i | 0.862211i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.2871 | −0.391339 | −0.195669 | − | 0.980670i | \(-0.562688\pi\) | ||||
−0.195669 | + | 0.980670i | \(0.562688\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.9120 | − | 27.0880i | −0.794381 | − | 1.02899i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 14.8443i | − | 0.563075i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.6320 | 0.857249 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1970 | −0.461335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.8600 | −0.485716 | −0.242858 | − | 0.970062i | \(-0.578085\pi\) | ||||
−0.242858 | + | 0.970062i | \(0.578085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.1483 | −1.55194 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.77200i | 0.142062i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.1970 | − | 15.7992i | −0.458717 | − | 0.594192i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.3160 | 1.47654 | 0.738272 | − | 0.674503i | \(-0.235642\pi\) | ||||
0.738272 | + | 0.674503i | \(0.235642\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.8612i | 1.15739i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.08801i | 0.115647i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 17.6003i | − | 0.658215i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.860009i | − | 0.0321176i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.5985 | 1.17842 | 0.589212 | − | 0.807978i | \(-0.299438\pi\) | ||||
0.589212 | + | 0.807978i | \(0.299438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.5440 | + | 14.3160i | −0.690615 | + | 0.533156i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 12.1970i | − | 0.453613i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.77200 | 0.140089 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00849 | −0.297018 | −0.148509 | − | 0.988911i | \(-0.547447\pi\) | ||||
−0.148509 | + | 0.988911i | \(0.547447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.4560 | −0.572444 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.3977 | 1.75307 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.7720i | 1.46901i | 0.678602 | + | 0.734506i | \(0.262586\pi\) | ||||
−0.678602 | + | 0.734506i | \(0.737414\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.23357 | + | 0.846116i | 0.119272 | + | 0.0312095i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.4560 | −1.04819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.40330i | 0.198763i | 0.995049 | + | 0.0993817i | \(0.0316865\pi\) | ||||
−0.995049 | + | 0.0993817i | \(0.968314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 13.3680i | − | 0.491085i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.1642i | 1.62023i | 0.586274 | + | 0.810113i | \(0.300594\pi\) | ||||
−0.586274 | + | 0.810113i | \(0.699406\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.54400i | − | 0.276391i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.8321 | 1.27444 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.86001 | − | 12.7720i | −0.360277 | − | 0.466679i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 32.6623i | − | 1.19187i | −0.803034 | − | 0.595933i | \(-0.796782\pi\) | ||
0.803034 | − | 0.595933i | \(-0.203218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.82399 | −0.212238 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.66605 | 0.169815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.54400 | 0.201500 | 0.100750 | − | 0.994912i | \(-0.467876\pi\) | ||||
0.100750 | + | 0.994912i | \(0.467876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.20440 | −0.261503 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.71106 | + | 2.86495i | −0.134350 | + | 0.103718i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4560 | −0.378037 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.2007i | 1.27102i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.6320i | 0.816131i | 0.912953 | + | 0.408066i | \(0.133797\pi\) | ||||
−0.912953 | + | 0.408066i | \(0.866203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10.0693i | − | 0.362639i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 51.7720i | 1.86211i | 0.364880 | + | 0.931055i | \(0.381110\pi\) | ||||
−0.364880 | + | 0.931055i | \(0.618890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.954983 | −0.0343040 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.54400 | + | 4.27998i | −0.198890 | + | 0.153543i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 44.5328i | − | 1.59555i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.5440 | −1.55813 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.3959 | −0.371521 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.5431 | 1.37391 | 0.686957 | − | 0.726698i | \(-0.258946\pi\) | ||||
0.686957 | + | 0.726698i | \(0.258946\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 9.08801i | − | 0.323542i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.23357 | + | 2.49632i | −0.114973 | + | 0.0887591i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.0880 | 1.81419 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.86495i | 0.101609i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 27.7720i | − | 0.983735i | −0.870670 | − | 0.491867i | \(-0.836314\pi\) | ||
0.870670 | − | 0.491867i | \(-0.163686\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.7974i | 1.05416i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 33.2640i | − | 1.17533i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.9963 | 0.987968 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.77200 | + | 5.22800i | −0.238682 | + | 0.184263i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.737249i | 0.0259524i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.3160 | −0.397850 | −0.198925 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198925 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.6155 | −1.67200 | −0.836002 | − | 0.548726i | \(-0.815113\pi\) | ||||
−0.836002 | + | 0.548726i | \(0.815113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000 | 0.140286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.70072 | −0.339801 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 93.2640i | − | 3.26290i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.9051 | + | 21.8978i | 0.590713 | + | 0.765170i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.3160 | 1.44194 | 0.720969 | − | 0.692967i | \(-0.243697\pi\) | ||||
0.720969 | + | 0.692967i | \(0.243697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.5000i | − | 0.888873i | −0.895810 | − | 0.444436i | \(-0.853404\pi\) | ||
0.895810 | − | 0.444436i | \(-0.146596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.22800i | − | 0.0775689i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.23357i | − | 0.112442i | −0.998418 | − | 0.0562212i | \(-0.982095\pi\) | ||
0.998418 | − | 0.0562212i | \(-0.0179052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 14.9120i | − | 0.517915i | −0.965889 | − | 0.258957i | \(-0.916621\pi\) | ||
0.965889 | − | 0.258957i | \(-0.0833789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.17272 | 0.0406811 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.5440 | + | 6.68399i | 0.885047 | + | 0.231587i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20.0967i | − | 0.695474i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.63201 | 0.0909756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.5985 | −1.09090 | −0.545450 | − | 0.838143i | \(-0.683641\pi\) | ||||
−0.545450 | + | 0.838143i | \(0.683641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7720 | −0.509379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.53835 | 0.0874253 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.22800i | 0.0422444i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.5596 | − | 17.4160i | 0.775156 | − | 0.598422i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.94802 | −0.204135 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 17.9269i | − | 0.614528i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 48.1760i | − | 1.64952i | −0.565486 | − | 0.824758i | \(-0.691311\pi\) | ||
0.565486 | − | 0.824758i | \(-0.308689\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.5742i | 0.703621i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 6.00000i | − | 0.204956i | −0.994735 | − | 0.102478i | \(-0.967323\pi\) | ||
0.994735 | − | 0.102478i | \(-0.0326771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.2383 | −1.33880 | −0.669398 | − | 0.742904i | \(-0.733448\pi\) | ||||
−0.669398 | + | 0.742904i | \(0.733448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.63201 | − | 6.00000i | −0.157859 | − | 0.204479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6970i | 1.28322i | 0.767031 | + | 0.641611i | \(0.221733\pi\) | ||||
−0.767031 | + | 0.641611i | \(0.778267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.3160 | −0.792768 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.32361 | −0.0449521 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.9480 | −1.76222 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0036 | 0.779449 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.8080i | 0.771935i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.61679 | − | 2.09428i | −0.0546574 | − | 0.0707995i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0880 | −0.982232 | −0.491116 | − | 0.871094i | \(-0.663411\pi\) | ||||
−0.491116 | + | 0.871094i | \(0.663411\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.40330i | 0.182249i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.6320i | 0.560347i | 0.959949 | + | 0.280173i | \(0.0903919\pi\) | ||||
−0.959949 | + | 0.280173i | \(0.909608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.8321i | − | 1.17219i | −0.810242 | − | 0.586096i | \(-0.800664\pi\) | ||
0.810242 | − | 0.586096i | \(-0.199336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.45600i | 0.149787i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.7701 | −0.663814 | −0.331907 | − | 0.943312i | \(-0.607692\pi\) | ||||
−0.331907 | + | 0.943312i | \(0.607692\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.86001 | + | 12.7720i | 0.330694 | + | 0.428359i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 32.6623i | − | 1.09423i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58.6320 | 1.96205 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.7992 | 0.528110 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.82399 | 0.194457 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.60220 | −0.120140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.6320i | 0.753982i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.70072 | − | 12.5657i | −0.322820 | − | 0.418159i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.54400 | 0.250771 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 15.4306i | − | 0.512365i | −0.966628 | − | 0.256183i | \(-0.917535\pi\) | ||
0.966628 | − | 0.256183i | \(-0.0824648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 20.9120i | − | 0.693607i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.2007i | − | 1.16625i | −0.812382 | − | 0.583125i | \(-0.801830\pi\) | ||
0.812382 | − | 0.583125i | \(-0.198170\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58.6320i | 1.94044i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.46715 | 0.213797 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.5440 | − | 10.4560i | 0.447262 | − | 0.345287i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 48.4616i | − | 1.59860i | −0.600932 | − | 0.799300i | \(-0.705204\pi\) | ||
0.600932 | − | 0.799300i | \(-0.294796\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.49202 | −0.0491638 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.2007 | 1.15864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.54400 | 0.182286 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.5450 | −0.806163 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33.0880i | − | 1.08558i | −0.839868 | − | 0.542791i | \(-0.817368\pi\) | ||
0.839868 | − | 0.542791i | \(-0.182632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1520 | − | 50.2627i | 0.431040 | − | 1.64729i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.7200 | 0.449173 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 17.6003i | − | 0.575593i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7720i | 0.907272i | 0.891187 | + | 0.453636i | \(0.149873\pi\) | ||||
−0.891187 | + | 0.453636i | \(0.850127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.80110i | 0.0587766i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.1760i | 1.37490i | 0.726232 | + | 0.687449i | \(0.241270\pi\) | ||||
−0.726232 | + | 0.687449i | \(0.758730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.4014 | 0.631798 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.45600 | + | 5.77200i | 0.144954 | + | 0.187763i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 6.83577i | − | 0.222133i | −0.993813 | − | 0.111066i | \(-0.964573\pi\) | ||
0.993813 | − | 0.111066i | \(-0.0354266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.6320 | −0.734666 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.33945 | −0.140716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.26825 | −0.267554 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 8.40401i | − | 0.271663i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.3649 | + | 21.8978i | −0.915951 | + | 0.707116i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0880 | −0.970581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 16.9051i | − | 0.544760i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.5440i | 0.693526i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.4269i | − | 1.39652i | −0.715847 | − | 0.698258i | \(-0.753959\pi\) | ||
0.715847 | − | 0.698258i | \(-0.246041\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 13.3680i | − | 0.429442i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5291 | 0.690903 | 0.345451 | − | 0.938437i | \(-0.387726\pi\) | ||||
0.345451 | + | 0.938437i | \(0.387726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.0880 | + | 24.0000i | −0.996636 | + | 0.769405i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.80110i | 0.0576813i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.91199 | 0.0931629 | 0.0465814 | − | 0.998914i | \(-0.485167\pi\) | ||||
0.0465814 | + | 0.998914i | \(0.485167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55.9926 | 1.78953 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.91199 | −0.156828 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.7646 | 0.343336 | 0.171668 | − | 0.985155i | \(-0.445084\pi\) | ||||
0.171668 | + | 0.985155i | \(0.445084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.00000i | − | 0.191176i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.89962 | − | 6.09852i | 0.251448 | − | 0.194118i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.6320 | 1.29202 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.0620i | − | 0.478460i | −0.970963 | − | 0.239230i | \(-0.923105\pi\) | ||
0.970963 | − | 0.239230i | \(-0.0768950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.6320i | 0.337397i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.42213i | 0.235297i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.4040i | 0.836223i | 0.908396 | + | 0.418112i | \(0.137308\pi\) | ||||
−0.908396 | + | 0.418112i | \(0.862692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.2797 | −0.483429 |
(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 | 2240.2.k.d.1791.3 | 8 | ||
4.3 | odd | 2 | inner | 2240.2.k.d.1791.5 | 8 | ||
7.6 | odd | 2 | inner | 2240.2.k.d.1791.6 | 8 | ||
8.3 | odd | 2 | 560.2.k.b.111.4 | yes | 8 | ||
8.5 | even | 2 | 560.2.k.b.111.6 | yes | 8 | ||
24.5 | odd | 2 | 5040.2.d.d.4591.1 | 8 | |||
24.11 | even | 2 | 5040.2.d.d.4591.4 | 8 | |||
28.27 | even | 2 | inner | 2240.2.k.d.1791.4 | 8 | ||
40.3 | even | 4 | 2800.2.e.g.2799.3 | 8 | |||
40.13 | odd | 4 | 2800.2.e.g.2799.6 | 8 | |||
40.19 | odd | 2 | 2800.2.k.m.2351.6 | 8 | |||
40.27 | even | 4 | 2800.2.e.h.2799.6 | 8 | |||
40.29 | even | 2 | 2800.2.k.m.2351.3 | 8 | |||
40.37 | odd | 4 | 2800.2.e.h.2799.3 | 8 | |||
56.13 | odd | 2 | 560.2.k.b.111.3 | ✓ | 8 | ||
56.27 | even | 2 | 560.2.k.b.111.5 | yes | 8 | ||
168.83 | odd | 2 | 5040.2.d.d.4591.5 | 8 | |||
168.125 | even | 2 | 5040.2.d.d.4591.8 | 8 | |||
280.13 | even | 4 | 2800.2.e.h.2799.4 | 8 | |||
280.27 | odd | 4 | 2800.2.e.g.2799.4 | 8 | |||
280.69 | odd | 2 | 2800.2.k.m.2351.5 | 8 | |||
280.83 | odd | 4 | 2800.2.e.h.2799.5 | 8 | |||
280.139 | even | 2 | 2800.2.k.m.2351.4 | 8 | |||
280.237 | even | 4 | 2800.2.e.g.2799.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.k.b.111.3 | ✓ | 8 | 56.13 | odd | 2 | ||
560.2.k.b.111.4 | yes | 8 | 8.3 | odd | 2 | ||
560.2.k.b.111.5 | yes | 8 | 56.27 | even | 2 | ||
560.2.k.b.111.6 | yes | 8 | 8.5 | even | 2 | ||
2240.2.k.d.1791.3 | 8 | 1.1 | even | 1 | trivial | ||
2240.2.k.d.1791.4 | 8 | 28.27 | even | 2 | inner | ||
2240.2.k.d.1791.5 | 8 | 4.3 | odd | 2 | inner | ||
2240.2.k.d.1791.6 | 8 | 7.6 | odd | 2 | inner | ||
2800.2.e.g.2799.3 | 8 | 40.3 | even | 4 | |||
2800.2.e.g.2799.4 | 8 | 280.27 | odd | 4 | |||
2800.2.e.g.2799.5 | 8 | 280.237 | even | 4 | |||
2800.2.e.g.2799.6 | 8 | 40.13 | odd | 4 | |||
2800.2.e.h.2799.3 | 8 | 40.37 | odd | 4 | |||
2800.2.e.h.2799.4 | 8 | 280.13 | even | 4 | |||
2800.2.e.h.2799.5 | 8 | 280.83 | odd | 4 | |||
2800.2.e.h.2799.6 | 8 | 40.27 | even | 4 | |||
2800.2.k.m.2351.3 | 8 | 40.29 | even | 2 | |||
2800.2.k.m.2351.4 | 8 | 280.139 | even | 2 | |||
2800.2.k.m.2351.5 | 8 | 280.69 | odd | 2 | |||
2800.2.k.m.2351.6 | 8 | 40.19 | odd | 2 | |||
5040.2.d.d.4591.1 | 8 | 24.5 | odd | 2 | |||
5040.2.d.d.4591.4 | 8 | 24.11 | even | 2 | |||
5040.2.d.d.4591.5 | 8 | 168.83 | odd | 2 | |||
5040.2.d.d.4591.8 | 8 | 168.125 | even | 2 |