Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1009,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.t (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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.5 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1009 |
Dual form | 1680.2.t.k.1009.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.311108 | + | 2.21432i | 0.139132 | + | 0.990274i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.42864i | − | 1.78298i | −0.453037 | − | 0.891492i | \(-0.649659\pi\) | ||
0.453037 | − | 0.891492i | \(-0.350341\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.21432 | + | 0.311108i | −0.571735 | + | 0.0803277i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.42864i | − | 1.07410i | −0.843550 | − | 0.537051i | \(-0.819538\pi\) | ||
0.843550 | − | 0.537051i | \(-0.180462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.42864 | −0.557168 | −0.278584 | − | 0.960412i | \(-0.589865\pi\) | ||||
−0.278584 | + | 0.960412i | \(0.589865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.37778i | − | 0.287288i | −0.989629 | − | 0.143644i | \(-0.954118\pi\) | ||
0.989629 | − | 0.143644i | \(-0.0458820\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80642 | + | 1.37778i | −0.961285 | + | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.755569 | −0.140306 | −0.0701528 | − | 0.997536i | \(-0.522349\pi\) | ||||
−0.0701528 | + | 0.997536i | \(0.522349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.18421 | −0.931111 | −0.465556 | − | 0.885019i | \(-0.654145\pi\) | ||||
−0.465556 | + | 0.885019i | \(0.654145\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.00000i | − | 0.348155i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.21432 | − | 0.311108i | 0.374288 | − | 0.0525868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.61285i | − | 1.25154i | −0.780006 | − | 0.625772i | \(-0.784784\pi\) | ||
0.780006 | − | 0.625772i | \(-0.215216\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.42864 | 1.02941 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.23506 | −1.28610 | −0.643050 | − | 0.765824i | \(-0.722331\pi\) | ||||
−0.643050 | + | 0.765824i | \(0.722331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.1017i | − | 1.54050i | −0.637744 | − | 0.770248i | \(-0.720132\pi\) | ||
0.637744 | − | 0.770248i | \(-0.279868\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.311108 | − | 2.21432i | −0.0463772 | − | 0.330091i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.75557i | 0.401941i | 0.979597 | + | 0.200971i | \(0.0644095\pi\) | ||||
−0.979597 | + | 0.200971i | \(0.935590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.42864 | 0.620134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.18421i | 1.26155i | 0.775967 | + | 0.630774i | \(0.217263\pi\) | ||||
−0.775967 | + | 0.630774i | \(0.782737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.622216 | − | 4.42864i | −0.0838995 | − | 0.597158i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.42864i | − | 0.321681i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1017 | 1.83589 | 0.917943 | − | 0.396712i | \(-0.129849\pi\) | ||||
0.917943 | + | 0.396712i | \(0.129849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.85728 | 0.877985 | 0.438992 | − | 0.898491i | \(-0.355336\pi\) | ||||
0.438992 | + | 0.898491i | \(0.355336\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.2351 | − | 2.00000i | 1.76564 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.75557i | 0.336646i | 0.985732 | + | 0.168323i | \(0.0538352\pi\) | ||||
−0.985732 | + | 0.168323i | \(0.946165\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.37778 | 0.165866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.57136i | − | 0.183914i | −0.995763 | − | 0.0919569i | \(-0.970688\pi\) | ||
0.995763 | − | 0.0919569i | \(-0.0293122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.37778 | − | 4.80642i | −0.159093 | − | 0.554998i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.85728 | −0.546487 | −0.273243 | − | 0.961945i | \(-0.588096\pi\) | ||||
−0.273243 | + | 0.961945i | \(0.588096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.6128i | − | 1.27468i | −0.770585 | − | 0.637338i | \(-0.780036\pi\) | ||
0.770585 | − | 0.637338i | \(-0.219964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.80642 | − | 1.37778i | 1.06366 | − | 0.149442i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.755569i | − | 0.0810055i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.62222 | −0.489954 | −0.244977 | − | 0.969529i | \(-0.578780\pi\) | ||||
−0.244977 | + | 0.969529i | \(0.578780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.42864 | −0.673905 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.18421i | − | 0.537577i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.755569 | − | 5.37778i | −0.0775197 | − | 0.551749i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9398i | 1.21230i | 0.795350 | + | 0.606150i | \(0.207287\pi\) | ||||
−0.795350 | + | 0.606150i | \(0.792713\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.47949 | 0.147215 | 0.0736076 | − | 0.997287i | \(-0.476549\pi\) | ||||
0.0736076 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.85728i | 0.872734i | 0.899769 | + | 0.436367i | \(0.143735\pi\) | ||||
−0.899769 | + | 0.436367i | \(0.856265\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.311108 | + | 2.21432i | 0.0303610 | + | 0.216095i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.76494i | 0.170623i | 0.996354 | + | 0.0853114i | \(0.0271885\pi\) | ||||
−0.996354 | + | 0.0853114i | \(0.972811\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.61285 | −0.537613 | −0.268807 | − | 0.963194i | \(-0.586629\pi\) | ||||
−0.268807 | + | 0.963194i | \(0.586629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.61285 | 0.722580 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.2859i | − | 1.06169i | −0.847469 | − | 0.530845i | \(-0.821875\pi\) | ||
0.847469 | − | 0.530845i | \(-0.178125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.05086 | − | 0.428639i | 0.284494 | − | 0.0399708i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.42864i | 0.594328i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.42864 | −0.405973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.23506i | − | 0.742531i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.54617 | − | 10.2143i | −0.406622 | − | 0.913597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.8573i | − | 1.14090i | −0.821333 | − | 0.570450i | \(-0.806769\pi\) | ||
0.821333 | − | 0.570450i | \(-0.193231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1017 | 0.889406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.10171 | 0.183627 | 0.0918136 | − | 0.995776i | \(-0.470734\pi\) | ||||
0.0918136 | + | 0.995776i | \(0.470734\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.42864i | 0.210590i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.21432 | − | 0.311108i | 0.190578 | − | 0.0267759i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.9398i | − | 1.36183i | −0.732364 | − | 0.680914i | \(-0.761583\pi\) | ||
0.732364 | − | 0.680914i | \(-0.238417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6731 | 0.990097 | 0.495048 | − | 0.868865i | \(-0.335150\pi\) | ||||
0.495048 | + | 0.868865i | \(0.335150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.75557 | −0.232061 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.8573i | 1.07518i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.235063 | − | 1.67307i | −0.0195209 | − | 0.138941i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.2257 | 1.73888 | 0.869438 | − | 0.494041i | \(-0.164481\pi\) | ||||
0.869438 | + | 0.494041i | \(0.164481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8573 | −1.37183 | −0.685913 | − | 0.727684i | \(-0.740597\pi\) | ||||
−0.685913 | + | 0.727684i | \(0.740597\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.42864i | 0.358034i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.61285 | − | 11.4795i | −0.129547 | − | 0.922055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4286i | 0.832296i | 0.909297 | + | 0.416148i | \(0.136620\pi\) | ||||
−0.909297 | + | 0.416148i | \(0.863380\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.18421 | −0.728355 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.37778 | −0.108585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.8573i | − | 1.63367i | −0.576873 | − | 0.816834i | \(-0.695727\pi\) | ||
0.576873 | − | 0.816834i | \(-0.304273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.42864 | − | 0.622216i | 0.344769 | − | 0.0484394i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3461i | 1.18752i | 0.804642 | + | 0.593760i | \(0.202357\pi\) | ||||
−0.804642 | + | 0.593760i | \(0.797643\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.3274 | −2.17903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.42864 | 0.185723 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.06022i | 0.156636i | 0.996928 | + | 0.0783179i | \(0.0249549\pi\) | ||||
−0.996928 | + | 0.0783179i | \(0.975045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.37778 | + | 4.80642i | 0.104151 | + | 0.363331i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.1017i | 1.05995i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1017 | −0.899513 | −0.449757 | − | 0.893151i | \(-0.648489\pi\) | ||||
−0.449757 | + | 0.893151i | \(0.648489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.85728i | 0.506905i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.8573 | − | 2.36842i | 1.23937 | − | 0.174129i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.85728i | 0.647708i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.488863 | −0.0353729 | −0.0176864 | − | 0.999844i | \(-0.505630\pi\) | ||||
−0.0176864 | + | 0.999844i | \(0.505630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 22.9590i | − | 1.65262i | −0.563212 | − | 0.826312i | \(-0.690435\pi\) | ||
0.563212 | − | 0.826312i | \(-0.309565\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.00000 | + | 14.2351i | 0.143223 | + | 1.01939i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.18421i | 0.0843713i | 0.999110 | + | 0.0421857i | \(0.0134321\pi\) | ||||
−0.999110 | + | 0.0421857i | \(0.986568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.79706 | 0.623607 | 0.311803 | − | 0.950147i | \(-0.399067\pi\) | ||||
0.311803 | + | 0.950147i | \(0.399067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.75557 | −0.194363 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.755569i | 0.0530305i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.56199 | − | 18.2351i | −0.178937 | − | 1.27359i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.37778i | 0.0957626i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.85728 | 0.335985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.2257 | −1.59892 | −0.799461 | − | 0.600717i | \(-0.794882\pi\) | ||||
−0.799461 | + | 0.600717i | \(0.794882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2.00000i | − | 0.137038i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.3684 | − | 3.14272i | 1.52551 | − | 0.214332i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.18421i | 0.351927i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.57136 | 0.106183 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.4701 | −1.91511 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.2257i | 1.01959i | 0.860297 | + | 0.509794i | \(0.170278\pi\) | ||||
−0.860297 | + | 0.509794i | \(0.829722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.80642 | − | 1.37778i | 0.320428 | − | 0.0918523i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.3684i | − | 0.953665i | −0.878994 | − | 0.476833i | \(-0.841785\pi\) | ||
0.878994 | − | 0.476833i | \(-0.158215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.61285 | 0.370907 | 0.185454 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185454 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.2859i | 1.52551i | 0.646687 | + | 0.762756i | \(0.276154\pi\) | ||||
−0.646687 | + | 0.762756i | \(0.723846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.10171 | + | 0.857279i | −0.398032 | + | 0.0559227i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.85728i | − | 0.315514i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.48886 | −0.549099 | −0.274549 | − | 0.961573i | \(-0.588529\pi\) | ||||
−0.274549 | + | 0.961573i | \(0.588529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.24443 | −0.466655 | −0.233327 | − | 0.972398i | \(-0.574961\pi\) | ||||
−0.233327 | + | 0.972398i | \(0.574961\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.311108 | − | 2.21432i | −0.0198759 | − | 0.141468i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.6128i | 0.993422i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.6128 | 0.735934 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.6128 | −1.74291 | −0.871454 | − | 0.490478i | \(-0.836822\pi\) | ||||
−0.871454 | + | 0.490478i | \(0.836822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.75557i | 0.173241i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.37778 | + | 9.80642i | 0.0862802 | + | 0.614102i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.428639i | 0.0267378i | 0.999911 | + | 0.0133689i | \(0.00425558\pi\) | ||||
−0.999911 | + | 0.0133689i | \(0.995744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.61285 | −0.473039 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.755569 | 0.0467685 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.37778i | 0.578259i | 0.957290 | + | 0.289129i | \(0.0933658\pi\) | ||||
−0.957290 | + | 0.289129i | \(0.906634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.3368 | + | 2.85728i | −1.24928 | + | 0.175521i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.62222i | − | 0.282875i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.74620 | −0.106468 | −0.0532339 | − | 0.998582i | \(-0.516953\pi\) | ||||
−0.0532339 | + | 0.998582i | \(0.516953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.69535 | 0.163731 | 0.0818653 | − | 0.996643i | \(-0.473912\pi\) | ||||
0.0818653 | + | 0.996643i | \(0.473912\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.42864i | − | 0.389079i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.61285 | − | 2.75557i | 0.579677 | − | 0.166167i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12399i | 0.307870i | 0.988081 | + | 0.153935i | \(0.0491947\pi\) | ||||
−0.988081 | + | 0.153935i | \(0.950805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.18421 | 0.310370 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.9813 | 1.43060 | 0.715301 | − | 0.698816i | \(-0.246290\pi\) | ||||
0.715301 | + | 0.698816i | \(0.246290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.36842i | − | 0.140788i | −0.997519 | − | 0.0703939i | \(-0.977574\pi\) | ||
0.997519 | − | 0.0703939i | \(-0.0224256\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.37778 | − | 0.755569i | 0.318552 | − | 0.0447560i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.23506i | 0.486100i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.61285 | −0.153697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.9398 | −0.699922 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.42864i | 0.492406i | 0.969218 | + | 0.246203i | \(0.0791831\pi\) | ||||
−0.969218 | + | 0.246203i | \(0.920817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.38715 | + | 31.2257i | 0.255430 | + | 1.81803i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000i | 0.116052i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.85728 | −0.512230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1017 | −0.582253 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.47949i | 0.0849947i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.13335 | + | 15.1842i | 0.122155 | + | 0.869445i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.5718i | − | 1.28824i | −0.764923 | − | 0.644121i | \(-0.777223\pi\) | ||
0.764923 | − | 0.644121i | \(-0.222777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.85728 | −0.503873 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0830 | 1.36562 | 0.682810 | − | 0.730596i | \(-0.260758\pi\) | ||||
0.682810 | + | 0.730596i | \(0.260758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.65433i | 0.545695i | 0.962057 | + | 0.272848i | \(0.0879655\pi\) | ||||
−0.962057 | + | 0.272848i | \(0.912035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.21432 | + | 0.311108i | −0.124763 | + | 0.0175289i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.04149i | 0.339324i | 0.985502 | + | 0.169662i | \(0.0542676\pi\) | ||||
−0.985502 | + | 0.169662i | \(0.945732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.51114 | 0.0846075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.76494 | −0.0985092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.7556i | 0.598456i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.85728 | + | 30.8988i | 0.491313 | + | 1.71396i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5.61285i | − | 0.310391i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.75557 | 0.151919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5111 | −0.742639 | −0.371320 | − | 0.928505i | \(-0.621095\pi\) | ||||
−0.371320 | + | 0.928505i | \(0.621095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.61285i | 0.417181i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.10171 | + | 0.857279i | −0.333372 | + | 0.0468382i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.4889i | − | 0.571365i | −0.958324 | − | 0.285682i | \(-0.907780\pi\) | ||
0.958324 | − | 0.285682i | \(-0.0922202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2859 | 0.612967 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3684 | 0.561481 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.428639 | + | 3.05086i | 0.0230772 | + | 0.164253i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 16.7239i | − | 0.897787i | −0.893585 | − | 0.448894i | \(-0.851818\pi\) | ||
0.893585 | − | 0.448894i | \(-0.148182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.3684 | 0.876181 | 0.438091 | − | 0.898931i | \(-0.355655\pi\) | ||||
0.438091 | + | 0.898931i | \(0.355655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.42864 | −0.343135 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.549086i | 0.0292249i | 0.999893 | + | 0.0146124i | \(0.00465145\pi\) | ||||
−0.999893 | + | 0.0146124i | \(0.995349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.622216 | − | 4.42864i | −0.0330238 | − | 0.235048i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 4.42864i | − | 0.234388i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.285442 | −0.0150651 | −0.00753253 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753253 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1017 | −0.689564 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.47949 | − | 0.488863i | 0.182125 | − | 0.0255882i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71456i | 0.0894992i | 0.998998 | + | 0.0447496i | \(0.0142490\pi\) | ||||
−0.998998 | + | 0.0447496i | \(0.985751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.23506 | 0.428700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.18421 | 0.476820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0000i | 0.828449i | 0.910175 | + | 0.414224i | \(0.135947\pi\) | ||||
−0.910175 | + | 0.414224i | \(0.864053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2143 | − | 4.54617i | 0.527465 | − | 0.234763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.85728i | 0.250163i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.85728 | −0.249502 | −0.124751 | − | 0.992188i | \(-0.539813\pi\) | ||||
−0.124751 | + | 0.992188i | \(0.539813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.8573 | 0.658698 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.38715i | 0.428563i | 0.976772 | + | 0.214282i | \(0.0687411\pi\) | ||||
−0.976772 | + | 0.214282i | \(0.931259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.42864 | + | 0.622216i | −0.225704 | + | 0.0317110i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.1017i | 0.513499i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.95899 | −0.454239 | −0.227119 | − | 0.973867i | \(-0.572931\pi\) | ||||
−0.227119 | + | 0.973867i | \(0.572931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.10171 | −0.308577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.10171i | 0.106017i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.51114 | − | 10.7556i | −0.0760336 | − | 0.541171i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.54909i | 0.127935i | 0.997952 | + | 0.0639675i | \(0.0203754\pi\) | ||||
−0.997952 | + | 0.0639675i | \(0.979625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.42864 | −0.121584 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.958989 | 0.0478896 | 0.0239448 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239448 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.3274i | 1.66016i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.311108 | + | 2.21432i | 0.0154591 | + | 0.110030i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.2257i | 0.754710i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.9813 | 1.58137 | 0.790686 | − | 0.612222i | \(-0.209724\pi\) | ||||
0.790686 | + | 0.612222i | \(0.209724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9398 | 0.786251 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 14.1017i | − | 0.693900i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.7146 | − | 3.61285i | 1.26228 | − | 0.177348i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.6731i | 0.571633i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.470127 | −0.0229672 | −0.0114836 | − | 0.999934i | \(-0.503655\pi\) | ||||
−0.0114836 | + | 0.999934i | \(0.503655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6128 | −1.63819 | −0.819095 | − | 0.573658i | \(-0.805524\pi\) | ||||
−0.819095 | + | 0.573658i | \(0.805524\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.75557i | − | 0.133980i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.10171 | + | 21.2859i | 0.295976 | + | 1.03252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.85728i | − | 0.331847i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.8573 | −0.620755 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.7146 | −0.564270 | −0.282135 | − | 0.959375i | \(-0.591043\pi\) | ||||
−0.282135 | + | 0.959375i | \(0.591043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.0602231i | − | 0.00289414i | −0.999999 | − | 0.00144707i | \(-0.999539\pi\) | ||
0.999999 | − | 0.00144707i | \(-0.000460616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.67307 | − | 0.235063i | 0.0802176 | − | 0.0112704i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.34614i | 0.160068i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.4286 | −1.07046 | −0.535230 | − | 0.844706i | \(-0.679775\pi\) | ||||
−0.535230 | + | 0.844706i | \(0.679775\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.9496i | 1.13788i | 0.822379 | + | 0.568940i | \(0.192647\pi\) | ||||
−0.822379 | + | 0.568940i | \(0.807353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.43801 | − | 10.2351i | −0.0681681 | − | 0.485189i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.2257i | 1.00394i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.4291 | −1.38885 | −0.694423 | − | 0.719567i | \(-0.744340\pi\) | ||||
−0.694423 | + | 0.719567i | \(0.744340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.4701 | 0.775548 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 16.8573i | − | 0.792024i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | − | 14.2351i | −0.0937614 | − | 0.667350i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.14272i | 0.147010i | 0.997295 | + | 0.0735051i | \(0.0234185\pi\) | ||||
−0.997295 | + | 0.0735051i | \(0.976581\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.42864 | −0.206711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.37778 | −0.157319 | −0.0786596 | − | 0.996902i | \(-0.525064\pi\) | ||||
−0.0786596 | + | 0.996902i | \(0.525064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.8573i | − | 0.969320i | −0.874703 | − | 0.484660i | \(-0.838943\pi\) | ||
0.874703 | − | 0.484660i | \(-0.161057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.4795 | − | 1.61285i | 0.532349 | − | 0.0747940i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 14.3684i | − | 0.664891i | −0.943122 | − | 0.332446i | \(-0.892126\pi\) | ||
0.943122 | − | 0.332446i | \(-0.107874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.75557 | 0.127240 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4286 | −0.480526 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.2034i | 0.928954i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.6731 | − | 3.34614i | 0.535597 | − | 0.153532i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.18421i | − | 0.420516i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.36842 | 0.290980 | 0.145490 | − | 0.989360i | \(-0.453524\pi\) | ||||
0.145490 | + | 0.989360i | \(0.453524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.9403 | −2.23148 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.37778i | − | 0.0626914i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.4385 | + | 3.71456i | −1.20051 | + | 0.168669i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3274i | 0.785180i | 0.919714 | + | 0.392590i | \(0.128421\pi\) | ||||
−0.919714 | + | 0.392590i | \(0.871579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.8573 | 0.943199 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.00000 | −0.0902587 | −0.0451294 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451294 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.34614i | 0.150703i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.622216 | + | 4.42864i | 0.0279665 | + | 0.199053i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.00000i | 0.0897123i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.3461 | 1.04512 | 0.522558 | − | 0.852603i | \(-0.324978\pi\) | ||||
0.522558 | + | 0.852603i | \(0.324978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3461 | −0.685615 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 0.387152i | − | 0.0172623i | −0.999963 | − | 0.00863113i | \(-0.997253\pi\) | ||
0.999963 | − | 0.00863113i | \(-0.00274741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.460282 | + | 3.27607i | 0.0204823 | + | 0.145783i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 28.3274i | − | 1.25806i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.9496 | 1.32749 | 0.663747 | − | 0.747957i | \(-0.268965\pi\) | ||||
0.663747 | + | 0.747957i | \(0.268965\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.57136 | −0.0695129 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.42864i | 0.107227i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.6128 | + | 2.75557i | −0.864245 | + | 0.121425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.51114i | − | 0.242380i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.06022 | −0.0904338 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.5205 | −0.811398 | −0.405699 | − | 0.914007i | \(-0.632972\pi\) | ||||
−0.405699 | + | 0.914007i | \(0.632972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.80642 | + | 1.37778i | −0.209770 | + | 0.0601314i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.9590i | 1.00011i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1017 | 0.917466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.1017 | −0.611962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.9403i | 2.29310i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.90813 | + | 0.549086i | −0.168963 | + | 0.0237390i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0000i | 0.431532i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5906 | 0.627298 | 0.313649 | − | 0.949539i | \(-0.398449\pi\) | ||||
0.313649 | + | 0.949539i | \(0.398449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 12.1017i | − | 0.519334i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.74620 | − | 12.4286i | −0.0747990 | − | 0.532384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.7556i | − | 0.801930i | −0.916093 | − | 0.400965i | \(-0.868675\pi\) | ||
0.916093 | − | 0.400965i | \(-0.131325\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.85728 | −0.292662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.83500 | 0.0781738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.85728i | 0.206553i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.36842 | + | 16.8573i | 0.100534 | + | 0.715552i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 31.8765i | − | 1.35065i | −0.737520 | − | 0.675325i | \(-0.764003\pi\) | ||
0.737520 | − | 0.675325i | \(-0.235997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −64.9403 | −2.74668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.85728 | −0.373955 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.01874i | 0.0850796i | 0.999095 | + | 0.0425398i | \(0.0135449\pi\) | ||||
−0.999095 | + | 0.0425398i | \(0.986455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.9906 | − | 3.51114i | 1.05136 | − | 0.147715i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.9590 | 1.21402 | 0.607012 | − | 0.794693i | \(-0.292368\pi\) | ||||
0.607012 | + | 0.794693i | \(0.292368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.97773 | −0.375706 | −0.187853 | − | 0.982197i | \(-0.560153\pi\) | ||||
−0.187853 | + | 0.982197i | \(0.560153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.488863i | − | 0.0204225i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.89829 | + | 6.62222i | 0.0791642 | + | 0.276165i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 28.6766i | − | 1.19382i | −0.802307 | − | 0.596911i | \(-0.796394\pi\) | ||
0.802307 | − | 0.596911i | \(-0.203606\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.9590 | 0.954143 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6128 | −0.481782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.3684i | − | 0.760742i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.2351 | + | 2.00000i | −0.588547 | + | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.2070i | 1.86589i | 0.360018 | + | 0.932945i | \(0.382771\pi\) | ||||
−0.360018 | + | 0.932945i | \(0.617229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.5906 | 0.518786 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18421 | −0.0487118 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.2636i | − | 0.749998i | −0.927025 | − | 0.374999i | \(-0.877643\pi\) | ||
0.927025 | − | 0.374999i | \(-0.122357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37778 | − | 9.80642i | −0.0564837 | − | 0.402024i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.79706i | 0.360040i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7368 | −0.929002 | −0.464501 | − | 0.885573i | \(-0.653766\pi\) | ||||
−0.464501 | + | 0.885573i | \(0.653766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.488863 | 0.0199411 | 0.00997056 | − | 0.999950i | \(-0.496826\pi\) | ||||
0.00997056 | + | 0.999950i | \(0.496826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.75557i | − | 0.112215i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.17775 | − | 15.5002i | −0.0885383 | − | 0.630174i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.2034i | 0.820032i | 0.912078 | + | 0.410016i | \(0.134477\pi\) | ||||
−0.912078 | + | 0.410016i | \(0.865523\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.755569 | −0.0306172 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.7146 | 0.716654 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 10.3684i | − | 0.418776i | −0.977833 | − | 0.209388i | \(-0.932853\pi\) | ||
0.977833 | − | 0.209388i | \(-0.0671472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.2351 | − | 2.56199i | 0.735309 | − | 0.103310i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.2859i | − | 1.58159i | −0.612080 | − | 0.790796i | \(-0.709667\pi\) | ||
0.612080 | − | 0.790796i | \(-0.290333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.8988 | 1.72425 | 0.862123 | − | 0.506698i | \(-0.169134\pi\) | ||||
0.862123 | + | 0.506698i | \(0.169134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.37778 | −0.0552886 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.62222i | 0.185185i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.85728i | 0.193981i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.7146 | −1.34429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.3461 | −0.610920 | −0.305460 | − | 0.952205i | \(-0.598810\pi\) | ||||
−0.305460 | + | 0.952205i | \(0.598810\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 23.2257i | − | 0.923139i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.4701 | − | 4.00000i | 1.12980 | − | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.42864i | 0.254712i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.6735 | 1.21153 | 0.605766 | − | 0.795643i | \(-0.292867\pi\) | ||||
0.605766 | + | 0.795643i | \(0.292867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 49.0607i | − | 1.93477i | −0.253320 | − | 0.967383i | \(-0.581523\pi\) | ||
0.253320 | − | 0.967383i | \(-0.418477\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.14272 | + | 22.3684i | 0.123745 | + | 0.880756i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3461i | 0.603319i | 0.953416 | + | 0.301660i | \(0.0975406\pi\) | ||||
−0.953416 | + | 0.301660i | \(0.902459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.2034 | −1.10708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.18421 | −0.203185 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4697i | 0.761906i | 0.924594 | + | 0.380953i | \(0.124404\pi\) | ||||
−0.924594 | + | 0.380953i | \(0.875596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.653858 | + | 4.65386i | 0.0255484 | + | 0.181841i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.57136i | 0.0613046i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9403 | 1.20526 | 0.602631 | − | 0.798020i | \(-0.294119\pi\) | ||||
0.602631 | + | 0.798020i | \(0.294119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.7975 | 1.85911 | 0.929554 | − | 0.368685i | \(-0.120192\pi\) | ||||
0.929554 | + | 0.368685i | \(0.120192\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 28.4701i | − | 1.10569i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.37778 | + | 0.755569i | −0.208542 | + | 0.0292997i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.04101i | 0.0403081i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.2257 | −0.588659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.7146 | −0.529445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 27.8163i | − | 1.07224i | −0.844142 | − | 0.536119i | \(-0.819890\pi\) | ||
0.844142 | − | 0.536119i | \(-0.180110\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.37778 | + | 4.80642i | 0.0530309 | + | 0.184999i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 19.0005i | − | 0.730248i | −0.930959 | − | 0.365124i | \(-0.881027\pi\) | ||
0.930959 | − | 0.365124i | \(-0.118973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9398 | 0.458207 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3684 | 0.550599 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.52051i | 0.172972i | 0.996253 | + | 0.0864862i | \(0.0275638\pi\) | ||||
−0.996253 | + | 0.0864862i | \(0.972436\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.2958 | − | 4.95899i | 1.34858 | − | 0.189473i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.61285i | 0.214143i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.0420 | 2.24932 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18421 | 0.0450494 | 0.0225247 | − | 0.999746i | \(-0.492830\pi\) | ||||
0.0225247 | + | 0.999746i | \(0.492830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 2.00000i | − | 0.0759737i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.63158 | + | 25.8479i | 0.137754 | + | 0.980467i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.4701i | 1.38140i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2859 | −0.880754 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6735 | −1.00745 | −0.503723 | − | 0.863865i | \(-0.668037\pi\) | ||||
−0.503723 | + | 0.863865i | \(0.668037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.4889i | 0.697321i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.857279 | − | 6.10171i | −0.0322870 | − | 0.229804i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.47949i | − | 0.0556421i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.2034 | 0.683644 | 0.341822 | − | 0.939765i | \(-0.388956\pi\) | ||||
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.85728 | 0.182162 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.14272i | 0.267497i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.4701 | + | 4.00000i | −1.06472 | + | 0.149592i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.48886i | − | 0.317022i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.85728 | 0.181146 | 0.0905730 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905730 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.85728 | 0.329862 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.24443i | − | 0.269423i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.63158 | − | 1.04101i | 0.134874 | − | 0.0386622i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.0607i | − | 0.781098i | −0.920582 | − | 0.390549i | \(-0.872285\pi\) | ||
0.920582 | − | 0.390549i | \(-0.127715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.7368 | −1.65465 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 9.45091i | − | 0.349077i | −0.984650 | − | 0.174539i | \(-0.944157\pi\) | ||
0.984650 | − | 0.174539i | \(-0.0558434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.21432 | − | 0.311108i | 0.0816764 | − | 0.0114754i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.51114i | − | 0.203005i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.20342 | −0.301768 | −0.150884 | − | 0.988551i | \(-0.548212\pi\) | ||||
−0.150884 | + | 0.988551i | \(0.548212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.6128 | −0.573552 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.33677i | 0.305847i | 0.988238 | + | 0.152923i | \(0.0488687\pi\) | ||||
−0.988238 | + | 0.152923i | \(0.951131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.60348 | + | 47.0005i | 0.241933 | + | 1.72196i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6128i | 0.424892i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.76494 | 0.0644894 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.9180 | 0.945760 | 0.472880 | − | 0.881127i | \(-0.343214\pi\) | ||||
0.472880 | + | 0.881127i | \(0.343214\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 27.6128i | − | 1.00627i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.24443 | − | 37.3274i | −0.190864 | − | 1.35848i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.94025i | 0.324939i | 0.986714 | + | 0.162470i | \(0.0519459\pi\) | ||||
−0.986714 | + | 0.162470i | \(0.948054\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.75557 | −0.100021 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.825636 | −0.0299293 | −0.0149646 | − | 0.999888i | \(-0.504764\pi\) | ||||
−0.0149646 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.61285i | 0.203199i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.80642 | + | 1.37778i | −0.354552 | + | 0.0498139i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 90.6548i | − | 3.27336i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.2257 | −0.765418 | −0.382709 | − | 0.923869i | \(-0.625009\pi\) | ||||
−0.382709 | + | 0.923869i | \(0.625009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.428639 | −0.0154371 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 29.4893i | − | 1.06066i | −0.847792 | − | 0.530329i | \(-0.822068\pi\) | ||
0.847792 | − | 0.530329i | \(-0.177932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.9175 | − | 7.14272i | 0.895063 | − | 0.256574i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.61285i | − | 0.273109i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.755569i | 0.0270018i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.0923 | + | 3.24443i | −0.824201 | + | 0.115799i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.4514i | 1.22806i | 0.789283 | + | 0.614030i | \(0.210453\pi\) | ||||
−0.789283 | + | 0.614030i | \(0.789547\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.37778 | −0.333858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2859 | −0.401281 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 44.0830i | − | 1.56543i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.85728 | − | 20.3368i | −0.101337 | − | 0.721271i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.9175i | 0.670092i | 0.942202 | + | 0.335046i | \(0.108752\pi\) | ||||
−0.942202 | + | 0.335046i | \(0.891248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2034 | 0.431726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.62222 | 0.163318 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.14272i | 0.110904i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.428639 | − | 3.05086i | −0.0151076 | − | 0.107529i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.74620i | − | 0.0614692i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.2257 | −0.746256 | −0.373128 | − | 0.927780i | \(-0.621715\pi\) | ||||
−0.373128 | + | 0.927780i | \(0.621715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.5081 | 0.755251 | 0.377625 | − | 0.925958i | \(-0.376741\pi\) | ||||
0.377625 | + | 0.925958i | \(0.376741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.69535i | 0.0945299i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.1847 | − | 6.48886i | 1.61778 | − | 0.227295i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.5334i | 0.858315i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.42864 | 0.224635 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.2034 | −1.61251 | −0.806255 | − | 0.591568i | \(-0.798509\pi\) | ||||
−0.806255 | + | 0.591568i | \(0.798509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 17.8350i | − | 0.621689i | −0.950461 | − | 0.310845i | \(-0.899388\pi\) | ||
0.950461 | − | 0.310845i | \(-0.100612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.75557 | + | 9.61285i | 0.0959366 | + | 0.334676i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 35.2128i | − | 1.22447i | −0.790676 | − | 0.612234i | \(-0.790271\pi\) | ||
0.790676 | − | 0.612234i | \(-0.209729\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3872 | −0.499686 | −0.249843 | − | 0.968286i | \(-0.580379\pi\) | ||||
−0.249843 | + | 0.968286i | \(0.580379\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.12399 | −0.177749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.42864i | 0.153443i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.9813 | + | 4.77430i | −1.17597 | + | 0.165222i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.18421i | 0.179192i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.51114 | 0.0521703 | 0.0260851 | − | 0.999660i | \(-0.491696\pi\) | ||||
0.0260851 | + | 0.999660i | \(0.491696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4291 | −0.980314 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.9813i | 0.825959i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.81288 | − | 62.7259i | −0.303172 | − | 2.15784i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000i | 0.240523i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.36842 | 0.0812838 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.4889 | −0.359554 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4064i | 0.527504i | 0.964591 | + | 0.263752i | \(0.0849600\pi\) | ||||
−0.964591 | + | 0.263752i | \(0.915040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.755569 | + | 5.37778i | 0.0258399 | + | 0.183916i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.8578i | 0.678328i | 0.940727 | + | 0.339164i | \(0.110144\pi\) | ||||
−0.940727 | + | 0.339164i | \(0.889856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.42864 | 0.0828641 | 0.0414321 | − | 0.999141i | \(-0.486808\pi\) | ||||
0.0414321 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.23506 | −0.280650 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 39.2958i | − | 1.33764i | −0.743423 | − | 0.668822i | \(-0.766799\pi\) | ||
0.743423 | − | 0.668822i | \(-0.233201\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.56199 | + | 0.640951i | −0.155112 | + | 0.0217930i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.61285i | − | 0.0887370i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.71456 | 0.329544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7146 | 0.600235 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 11.9398i | − | 0.404100i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.2143 | + | 4.54617i | −0.345307 | + | 0.153689i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 56.2864i | − | 1.90066i | −0.311249 | − | 0.950328i | \(-0.600747\pi\) | ||
0.311249 | − | 0.950328i | \(-0.399253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.42864 | −0.284291 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.33677 | −0.0787279 | −0.0393640 | − | 0.999225i | \(-0.512533\pi\) | ||||
−0.0393640 | + | 0.999225i | \(0.512533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.7146i | 1.13459i | 0.823516 | + | 0.567293i | \(0.192009\pi\) | ||||
−0.823516 | + | 0.567293i | \(0.807991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.2257 | + | 4.38715i | −1.04964 | + | 0.147473i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 47.8992i | − | 1.60830i | −0.594427 | − | 0.804150i | \(-0.702621\pi\) | ||
0.594427 | − | 0.804150i | \(-0.297379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.8573 | −0.431219 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.69228i | − | 0.223949i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.11108 | + | 22.1432i | 0.103992 | + | 0.740165i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 8.85728i | − | 0.295736i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.91703 | 0.130640 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.6735 | 1.35503 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 10.1017i | − | 0.336164i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.76494 | − | 26.7971i | −0.125151 | − | 0.890764i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.7591i | − | 0.788908i | −0.918916 | − | 0.394454i | \(-0.870934\pi\) | ||
0.918916 | − | 0.394454i | \(-0.129066\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.47949 | −0.0490717 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.9403 | −0.760045 | −0.380022 | − | 0.924977i | \(-0.624084\pi\) | ||||
−0.380022 | + | 0.924977i | \(0.624084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.2257i | 0.768658i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.1842 | + | 2.13335i | −0.501974 | + | 0.0705265i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.10171i | − | 0.0694046i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9777 | 0.560043 | 0.280022 | − | 0.959994i | \(-0.409658\pi\) | ||||
0.280022 | + | 0.959994i | \(0.409658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.5718 | 0.743767 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.8573i | 0.423202i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4889 | + | 36.5906i | 0.344872 | + | 1.20309i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 8.85728i | − | 0.290911i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.3403 | −1.29071 | −0.645357 | − | 0.763881i | \(-0.723291\pi\) | ||||
−0.645357 | + | 0.763881i | \(0.723291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.42864 | 0.0795954 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.0830i | 0.788441i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.6128 | + | 2.75557i | −0.641409 | + | 0.0901167i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.7748i | − | 0.580677i | −0.956924 | − | 0.290338i | \(-0.906232\pi\) | ||
0.956924 | − | 0.290338i | \(-0.0937679\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.65433 | −0.315057 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5812 | 1.15991 | 0.579957 | − | 0.814647i | \(-0.303069\pi\) | ||||
0.579957 | + | 0.814647i | \(0.303069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3461i | 0.369481i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.311108 | − | 2.21432i | −0.0101203 | − | 0.0720318i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.5018i | − | 0.991174i | −0.868558 | − | 0.495587i | \(-0.834953\pi\) | ||
0.868558 | − | 0.495587i | \(-0.165047\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.1017 | −0.327915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.04149 | −0.195909 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.1655i | 1.65741i | 0.559684 | + | 0.828706i | \(0.310923\pi\) | ||||
−0.559684 | + | 0.828706i | \(0.689077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.152089 | − | 1.08250i | −0.00492148 | − | 0.0350288i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.51114i | 0.0488481i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.9398 | −0.514722 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.12399 | −0.133032 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.76494i | − | 0.0568743i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.8385 | − | 7.14272i | 1.63655 | − | 0.229932i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.8992i | − | 1.54034i | −0.637841 | − | 0.770168i | \(-0.720172\pi\) | ||
0.637841 | − | 0.770168i | \(-0.279828\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.7556 | −0.345519 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.6735 | −1.30528 | −0.652638 | − | 0.757670i | \(-0.726338\pi\) | ||||
−0.652638 | + | 0.757670i | \(0.726338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.6731i | − | 0.374221i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.8988 | + | 8.85728i | −0.989552 | + | 0.283660i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27.4893i | − | 0.879462i | −0.898130 | − | 0.439731i | \(-0.855074\pi\) | ||
0.898130 | − | 0.439731i | \(-0.144926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.24443 | 0.295453 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.61285 | 0.179204 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.62222 | + | 0.368416i | −0.0835507 | + | 0.0117387i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.75557i | 0.0877107i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.9180 | −0.442566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.6923 | 1.10204 | 0.551018 | − | 0.834493i | \(-0.314239\pi\) | ||||
0.551018 | + | 0.834493i | \(0.314239\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.5111i | − | 0.428763i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.73683 | + | 19.4795i | 0.0867634 | + | 0.617541i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 28.6766i | − | 0.908197i | −0.890951 | − | 0.454099i | \(-0.849961\pi\) | ||
0.890951 | − | 0.454099i | \(-0.150039\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.61285 | −0.240860 |
(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 | 1680.2.t.k.1009.5 | 6 | ||
3.2 | odd | 2 | 5040.2.t.v.1009.3 | 6 | |||
4.3 | odd | 2 | 105.2.d.b.64.5 | yes | 6 | ||
5.2 | odd | 4 | 8400.2.a.dj.1.1 | 3 | |||
5.3 | odd | 4 | 8400.2.a.dg.1.3 | 3 | |||
5.4 | even | 2 | inner | 1680.2.t.k.1009.2 | 6 | ||
12.11 | even | 2 | 315.2.d.e.64.2 | 6 | |||
15.14 | odd | 2 | 5040.2.t.v.1009.4 | 6 | |||
20.3 | even | 4 | 525.2.a.j.1.3 | 3 | |||
20.7 | even | 4 | 525.2.a.k.1.1 | 3 | |||
20.19 | odd | 2 | 105.2.d.b.64.2 | ✓ | 6 | ||
28.3 | even | 6 | 735.2.q.f.79.2 | 12 | |||
28.11 | odd | 6 | 735.2.q.e.79.2 | 12 | |||
28.19 | even | 6 | 735.2.q.f.214.5 | 12 | |||
28.23 | odd | 6 | 735.2.q.e.214.5 | 12 | |||
28.27 | even | 2 | 735.2.d.b.589.5 | 6 | |||
60.23 | odd | 4 | 1575.2.a.x.1.1 | 3 | |||
60.47 | odd | 4 | 1575.2.a.w.1.3 | 3 | |||
60.59 | even | 2 | 315.2.d.e.64.5 | 6 | |||
84.83 | odd | 2 | 2205.2.d.l.1324.2 | 6 | |||
140.19 | even | 6 | 735.2.q.f.214.2 | 12 | |||
140.27 | odd | 4 | 3675.2.a.bj.1.1 | 3 | |||
140.39 | odd | 6 | 735.2.q.e.79.5 | 12 | |||
140.59 | even | 6 | 735.2.q.f.79.5 | 12 | |||
140.79 | odd | 6 | 735.2.q.e.214.2 | 12 | |||
140.83 | odd | 4 | 3675.2.a.bi.1.3 | 3 | |||
140.139 | even | 2 | 735.2.d.b.589.2 | 6 | |||
420.419 | odd | 2 | 2205.2.d.l.1324.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.2 | ✓ | 6 | 20.19 | odd | 2 | ||
105.2.d.b.64.5 | yes | 6 | 4.3 | odd | 2 | ||
315.2.d.e.64.2 | 6 | 12.11 | even | 2 | |||
315.2.d.e.64.5 | 6 | 60.59 | even | 2 | |||
525.2.a.j.1.3 | 3 | 20.3 | even | 4 | |||
525.2.a.k.1.1 | 3 | 20.7 | even | 4 | |||
735.2.d.b.589.2 | 6 | 140.139 | even | 2 | |||
735.2.d.b.589.5 | 6 | 28.27 | even | 2 | |||
735.2.q.e.79.2 | 12 | 28.11 | odd | 6 | |||
735.2.q.e.79.5 | 12 | 140.39 | odd | 6 | |||
735.2.q.e.214.2 | 12 | 140.79 | odd | 6 | |||
735.2.q.e.214.5 | 12 | 28.23 | odd | 6 | |||
735.2.q.f.79.2 | 12 | 28.3 | even | 6 | |||
735.2.q.f.79.5 | 12 | 140.59 | even | 6 | |||
735.2.q.f.214.2 | 12 | 140.19 | even | 6 | |||
735.2.q.f.214.5 | 12 | 28.19 | even | 6 | |||
1575.2.a.w.1.3 | 3 | 60.47 | odd | 4 | |||
1575.2.a.x.1.1 | 3 | 60.23 | odd | 4 | |||
1680.2.t.k.1009.2 | 6 | 5.4 | even | 2 | inner | ||
1680.2.t.k.1009.5 | 6 | 1.1 | even | 1 | trivial | ||
2205.2.d.l.1324.2 | 6 | 84.83 | odd | 2 | |||
2205.2.d.l.1324.5 | 6 | 420.419 | odd | 2 | |||
3675.2.a.bi.1.3 | 3 | 140.83 | odd | 4 | |||
3675.2.a.bj.1.1 | 3 | 140.27 | odd | 4 | |||
5040.2.t.v.1009.3 | 6 | 3.2 | odd | 2 | |||
5040.2.t.v.1009.4 | 6 | 15.14 | odd | 2 | |||
8400.2.a.dg.1.3 | 3 | 5.3 | odd | 4 | |||
8400.2.a.dj.1.1 | 3 | 5.2 | odd | 4 |