Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(2239,2240)]
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, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.2239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.e (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: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2239.3 | ||
Root | \(1.00781 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.2239 |
Dual form | 2240.2.e.e.2239.8 |
$q$-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 | ||||||||
\(3\) | − | 1.41421i | − | 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | − | 1.87083i | 0.547723 | − | 0.836660i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 1.00000 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | 0.679366 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.64575 | − | 1.73205i | −0.683130 | − | 0.447214i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.48074 | −1.48678 | −0.743392 | − | 0.668856i | \(-0.766784\pi\) | ||||
−0.743392 | + | 0.668856i | \(0.766784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.74166i | − | 0.816497i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 4.58258i | −0.400000 | − | 0.916515i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.65685i | − | 1.08866i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.89898 | −0.852803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.24037 | − | 4.94975i | 0.547723 | − | 0.836660i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.16515i | − | 1.50674i | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||
0.657596 | − | 0.753371i | \(-0.271573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.46410i | − | 0.554700i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.48331i | 1.16870i | 0.811503 | + | 0.584349i | \(0.198650\pi\) | ||||
−0.811503 | + | 0.584349i | \(0.801350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.29150 | 0.806947 | 0.403473 | − | 0.914991i | \(-0.367803\pi\) | ||||
0.403473 | + | 0.914991i | \(0.367803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.22474 | − | 1.87083i | 0.182574 | − | 0.278887i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.82843i | − | 0.412568i | −0.978492 | − | 0.206284i | \(-0.933863\pi\) | ||
0.978492 | − | 0.206284i | \(-0.0661372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.92820i | 0.970143i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.16515i | 1.25893i | 0.777029 | + | 0.629465i | \(0.216726\pi\) | ||||
−0.777029 | + | 0.629465i | \(0.783274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.48074 | − | 4.24264i | −0.873863 | − | 0.572078i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.16515i | 1.21395i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.48074 | −0.843721 | −0.421860 | − | 0.906661i | \(-0.638623\pi\) | ||||
−0.421860 | + | 0.906661i | \(0.638623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2250i | 1.43721i | 0.695418 | + | 0.718605i | \(0.255219\pi\) | ||||
−0.695418 | + | 0.718605i | \(0.744781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.64575 | 0.333333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 4.58258i | 0.372104 | − | 0.568399i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.29150 | −0.646460 | −0.323230 | − | 0.946320i | \(-0.604769\pi\) | ||||
−0.323230 | + | 0.946320i | \(0.604769\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796 | 1.14676 | 0.573382 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573382 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.48074 | + | 2.82843i | −0.748331 | + | 0.326599i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 9.16515i | − | 1.04447i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.92820i | 0.779484i | 0.920924 | + | 0.389742i | \(0.127436\pi\) | ||||
−0.920924 | + | 0.389742i | \(0.872564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.89949i | − | 1.08661i | −0.839535 | − | 0.543305i | \(-0.817173\pi\) | ||
0.839535 | − | 0.543305i | \(-0.182827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | + | 9.16515i | −0.650791 | + | 0.994100i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.48528i | − | 0.909718i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.48331i | − | 0.793230i | −0.917985 | − | 0.396615i | \(-0.870185\pi\) | ||
0.917985 | − | 0.396615i | \(-0.129815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.48074 | 0.679366 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.93725 | + | 12.1244i | −0.814345 | + | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6969 | 1.49225 | 0.746124 | − | 0.665807i | \(-0.231913\pi\) | ||||
0.746124 | + | 0.665807i | \(0.231913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.74166i | 0.372309i | 0.982521 | + | 0.186154i | \(0.0596025\pi\) | ||||
−0.982521 | + | 0.186154i | \(0.940398\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.9706i | − | 1.67216i | −0.548608 | − | 0.836080i | \(-0.684842\pi\) | ||
0.548608 | − | 0.836080i | \(-0.315158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.00000 | − | 4.58258i | −0.683130 | − | 0.447214i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.8745 | −1.53465 | −0.767323 | − | 0.641260i | \(-0.778412\pi\) | ||||
−0.767323 | + | 0.641260i | \(0.778412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.9615 | −1.23025 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.16515i | − | 0.862185i | −0.902308 | − | 0.431092i | \(-0.858128\pi\) | ||
0.902308 | − | 0.431092i | \(-0.141872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.44949 | 0.226455 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.9615 | −1.18818 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5830 | 0.954237 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0227 | − | 1.87083i | −0.985901 | − | 0.167332i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5830 | 0.939090 | 0.469545 | − | 0.882909i | \(-0.344418\pi\) | ||||
0.469545 | + | 0.882909i | \(0.344418\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.48331i | − | 0.658869i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4422 | −1.69867 | −0.849337 | − | 0.527850i | \(-0.822998\pi\) | ||||
−0.849337 | + | 0.527850i | \(0.822998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.1464 | −1.48678 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.5830 | − | 6.92820i | −0.910840 | − | 0.596285i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3303i | 1.56606i | 0.621982 | + | 0.783032i | \(0.286328\pi\) | ||||
−0.621982 | + | 0.783032i | \(0.713672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4422 | 1.64907 | 0.824534 | − | 0.565813i | \(-0.191437\pi\) | ||||
0.824534 | + | 0.565813i | \(0.191437\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.48528i | − | 0.709575i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.34847 | − | 11.2250i | 0.610257 | − | 0.932183i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 9.89949i | − | 0.816497i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.89898 | −0.396059 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.34847 | −0.586472 | −0.293236 | − | 0.956040i | \(-0.594732\pi\) | ||||
−0.293236 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.9615 | 1.02791 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.29150 | 0.414462 | 0.207231 | − | 0.978292i | \(-0.433555\pi\) | ||||
0.207231 | + | 0.978292i | \(0.433555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | + | 9.16515i | −0.467099 | + | 0.713506i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.65685i | − | 0.437741i | −0.975754 | − | 0.218870i | \(-0.929763\pi\) | ||
0.975754 | − | 0.218870i | \(-0.0702371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.48074 | −0.495595 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.34847 | 0.558694 | 0.279347 | − | 0.960190i | \(-0.409882\pi\) | ||||
0.279347 | + | 0.960190i | \(0.409882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.29150 | − | 12.1244i | −0.400000 | − | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.16515i | 0.688895i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.2487i | 1.81243i | 0.422813 | + | 0.906217i | \(0.361043\pi\) | ||||
−0.422813 | + | 0.906217i | \(0.638957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2250i | 0.834346i | 0.908827 | + | 0.417173i | \(0.136979\pi\) | ||||
−0.908827 | + | 0.417173i | \(0.863021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.8745 | 1.17348 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.1464 | − | 11.2250i | −1.26063 | − | 0.825276i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9706i | 1.24101i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 14.9666i | − | 1.08866i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.92820i | 0.501307i | 0.968077 | + | 0.250654i | \(0.0806455\pi\) | ||||
−0.968077 | + | 0.250654i | \(0.919354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.16515i | 0.659722i | 0.944030 | + | 0.329861i | \(0.107002\pi\) | ||||
−0.944030 | + | 0.329861i | \(0.892998\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.48074 | − | 4.24264i | −0.464095 | − | 0.303822i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.16515i | − | 0.652990i | −0.945199 | − | 0.326495i | \(-0.894132\pi\) | ||
0.945199 | − | 0.326495i | \(-0.105868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9615 | −0.918815 | −0.459408 | − | 0.888226i | \(-0.651938\pi\) | ||||
−0.459408 | + | 0.888226i | \(0.651938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.48331i | 0.527832i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.8745 | 1.11417 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0000 | + | 9.16515i | 0.977802 | + | 0.640122i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.4499i | 1.55290i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.3923i | − | 0.715436i | −0.933830 | − | 0.357718i | \(-0.883555\pi\) | ||
0.933830 | − | 0.357718i | \(-0.116445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.48074 | − | 9.89949i | 0.441983 | − | 0.675140i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 13.8564i | − | 0.936329i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4558i | 1.70465i | 0.523013 | + | 0.852325i | \(0.324808\pi\) | ||||
−0.523013 | + | 0.852325i | \(0.675192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | − | 4.58258i | −0.133333 | − | 0.305505i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18.3848i | − | 1.22024i | −0.792309 | − | 0.610120i | \(-0.791121\pi\) | ||
0.792309 | − | 0.610120i | \(-0.208879\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2250i | 0.741767i | 0.928679 | + | 0.370884i | \(0.120945\pi\) | ||||
−0.928679 | + | 0.370884i | \(0.879055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.9615 | −0.852803 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.3303i | − | 1.20086i | −0.799678 | − | 0.600429i | \(-0.794996\pi\) | ||
0.799678 | − | 0.600429i | \(-0.205004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.29150 | − | 3.46410i | −0.345180 | − | 0.225973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.79796 | 0.636446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 9.89949i | − | 0.635053i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.57321 | − | 13.0958i | 0.547723 | − | 0.836660i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.8745 | −1.01007 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.0000 | −0.887214 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.48074 | 0.409061 | 0.204530 | − | 0.978860i | \(-0.434433\pi\) | ||||
0.204530 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9615 | + | 8.48528i | 0.811679 | + | 0.531369i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6969 | −0.916770 | −0.458385 | − | 0.888754i | \(-0.651572\pi\) | ||||
−0.458385 | + | 0.888754i | \(0.651572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 24.2487i | − | 1.50674i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8745 | 0.978864 | 0.489432 | − | 0.872041i | \(-0.337204\pi\) | ||||
0.489432 | + | 0.872041i | \(0.337204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.1464 | + | 11.2250i | 1.05330 | + | 0.689545i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.5830 | −0.647669 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.7083i | − | 1.14066i | −0.821414 | − | 0.570332i | \(-0.806814\pi\) | ||
0.821414 | − | 0.570332i | \(-0.193186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9230 | 1.57471 | 0.787354 | − | 0.616501i | \(-0.211450\pi\) | ||||
0.787354 | + | 0.616501i | \(0.211450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 9.16515i | − | 0.554700i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.8745 | + | 6.92820i | −0.957269 | + | 0.417786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.16515i | − | 0.550681i | −0.961347 | − | 0.275340i | \(-0.911209\pi\) | ||
0.961347 | − | 0.275340i | \(-0.0887905\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.2132i | 1.26099i | 0.776192 | + | 0.630497i | \(0.217149\pi\) | ||||
−0.776192 | + | 0.630497i | \(0.782851\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.1464 | + | 11.2250i | 1.01567 | + | 0.664910i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.7990i | 1.16870i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 20.7846i | − | 1.21842i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.8434 | 1.86031 | 0.930155 | − | 0.367168i | \(-0.119673\pi\) | ||||
0.930155 | + | 0.367168i | \(0.119673\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.93725 | + | 12.1244i | −0.462125 | + | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.5959 | −1.13707 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.0000 | 0.806947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.29150 | 0.303989 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.0000 | + | 13.7477i | 1.20246 | + | 0.787193i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.24264i | 0.242140i | 0.992644 | + | 0.121070i | \(0.0386326\pi\) | ||||
−0.992644 | + | 0.121070i | \(0.961367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.0000 | −1.36531 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9615 | 0.734978 | 0.367489 | − | 0.930028i | \(-0.380218\pi\) | ||||
0.367489 | + | 0.930028i | \(0.380218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.79796 | −0.553813 | −0.276907 | − | 0.960897i | \(-0.589309\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.24037 | − | 4.94975i | 0.182574 | − | 0.278887i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.16515i | 0.514766i | 0.966309 | + | 0.257383i | \(0.0828602\pi\) | ||||
−0.966309 | + | 0.257383i | \(0.917140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 20.7846i | − | 1.16371i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.4499i | 1.25303i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.7490 | 1.76656 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.89898 | − | 11.2250i | −0.271746 | − | 0.622649i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.82843i | − | 0.156412i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.48331i | − | 0.412568i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2487i | 1.33283i | 0.745581 | + | 0.666415i | \(0.232172\pi\) | ||||
−0.745581 | + | 0.666415i | \(0.767828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 9.16515i | − | 0.502247i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.48074 | + | 9.89949i | −0.354081 | + | 0.540867i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.16515i | − | 0.499258i | −0.968342 | − | 0.249629i | \(-0.919691\pi\) | ||
0.968342 | − | 0.249629i | \(-0.0803086\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.9615 | −0.703971 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.8745 | −0.852188 | −0.426094 | − | 0.904679i | \(-0.640111\pi\) | ||||
−0.426094 | + | 0.904679i | \(0.640111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2250i | 0.600859i | 0.953804 | + | 0.300429i | \(0.0971300\pi\) | ||||
−0.953804 | + | 0.300429i | \(0.902870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 13.8564i | − | 0.739600i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.89898 | 0.260746 | 0.130373 | − | 0.991465i | \(-0.458382\pi\) | ||||
0.130373 | + | 0.991465i | \(0.458382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.3303i | 0.970143i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.2487i | 1.27980i | 0.768459 | + | 0.639899i | \(0.221024\pi\) | ||||
−0.768459 | + | 0.639899i | \(0.778976\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.0000 | 1.21053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41421i | 0.0742270i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | − | 18.3303i | 0.628109 | − | 0.959452i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528i | 0.442928i | 0.975169 | + | 0.221464i | \(0.0710835\pi\) | ||||
−0.975169 | + | 0.221464i | \(0.928916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.48331i | 0.389566i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2487i | 1.25893i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.16515i | − | 0.474554i | −0.971442 | − | 0.237277i | \(-0.923745\pi\) | ||
0.971442 | − | 0.237277i | \(-0.0762548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.64575 | + | 15.5885i | −0.136626 | + | 0.804984i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2487i | 1.24557i | 0.782392 | + | 0.622786i | \(0.213999\pi\) | ||||
−0.782392 | + | 0.622786i | \(0.786001\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 14.9666i | − | 0.766764i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.7990i | 1.01168i | 0.862627 | + | 0.505841i | \(0.168818\pi\) | ||||
−0.862627 | + | 0.505841i | \(0.831182\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.1464 | − | 11.2250i | −0.873863 | − | 0.572078i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.29150 | 0.268982 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.0000 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.4955i | 1.38696i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9615 | + | 8.48528i | 0.652163 | + | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.34847 | −0.368809 | −0.184405 | − | 0.982850i | \(-0.559036\pi\) | ||||
−0.184405 | + | 0.982850i | \(0.559036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.2487i | 1.21395i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0000 | −1.19850 | −0.599251 | − | 0.800561i | \(-0.704535\pi\) | ||||
−0.599251 | + | 0.800561i | \(0.704535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.12372 | + | 9.35414i | −0.304290 | + | 0.464811i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.7490 | −1.57374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.4499i | − | 1.11008i | −0.831824 | − | 0.555039i | \(-0.812703\pi\) | ||
0.831824 | − | 0.555039i | \(-0.187297\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.9230 | 1.27869 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.1464 | −0.843721 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.5203 | − | 12.1244i | −0.909124 | − | 0.595161i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 27.4955i | − | 1.34646i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.48074 | −0.316605 | −0.158302 | − | 0.987391i | \(-0.550602\pi\) | ||||
−0.158302 | + | 0.987391i | \(0.550602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.82843i | − | 0.137523i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.79796 | + | 22.4499i | 0.475271 | + | 1.08898i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.6985i | 1.43721i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | −0.579365 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.46410i | 0.166860i | 0.996514 | + | 0.0834300i | \(0.0265875\pi\) | ||||
−0.996514 | + | 0.0834300i | \(0.973413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.89898 | 0.235430 | 0.117715 | − | 0.993047i | \(-0.462443\pi\) | ||||
0.117715 | + | 0.993047i | \(0.462443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.8745 | − | 10.3923i | −0.761124 | − | 0.498273i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9615 | 0.618618 | 0.309309 | − | 0.950962i | \(-0.399902\pi\) | ||||
0.309309 | + | 0.950962i | \(0.399902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.8745 | 0.754221 | 0.377110 | − | 0.926168i | \(-0.376918\pi\) | ||||
0.377110 | + | 0.926168i | \(0.376918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | − | 9.16515i | −0.663664 | − | 0.434470i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.48528i | 0.401340i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.9230 | 1.22066 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.89898 | −0.230174 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.93725 | − | 12.1244i | 0.372104 | − | 0.568399i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.4955i | − | 1.28618i | −0.765789 | − | 0.643092i | \(-0.777651\pi\) | ||
0.765789 | − | 0.643092i | \(-0.222349\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.7128i | 1.29352i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.7083i | 0.871332i | 0.900108 | + | 0.435666i | \(0.143487\pi\) | ||||
−0.900108 | + | 0.435666i | \(0.856513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4575 | 1.22958 | 0.614792 | − | 0.788689i | \(-0.289240\pi\) | ||||
0.614792 | + | 0.788689i | \(0.289240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.07107i | 0.327210i | 0.986526 | + | 0.163605i | \(0.0523123\pi\) | ||||
−0.986526 | + | 0.163605i | \(0.947688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3923i | 0.478852i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 18.3303i | − | 0.842828i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9615 | + | 29.6985i | 0.594714 | + | 1.36266i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.16515i | 0.419643i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.9230 | 1.18445 | 0.592225 | − | 0.805772i | \(-0.298250\pi\) | ||||
0.592225 | + | 0.805772i | \(0.298250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 22.4499i | − | 1.02363i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.0000 | − | 27.4955i | 0.817338 | − | 1.24850i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.1660 | −0.959123 | −0.479562 | − | 0.877508i | \(-0.659204\pi\) | ||||
−0.479562 | + | 0.877508i | \(0.659204\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.48331i | − | 0.338407i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.3923i | − | 0.468998i | −0.972116 | − | 0.234499i | \(-0.924655\pi\) | ||
0.972116 | − | 0.234499i | \(-0.0753450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.3939 | −1.32383 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.48074 | − | 4.24264i | −0.291288 | − | 0.190693i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.3205i | − | 0.775372i | −0.921791 | − | 0.387686i | \(-0.873274\pi\) | ||
0.921791 | − | 0.387686i | \(-0.126726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.65685i | − | 0.252227i | −0.992016 | − | 0.126113i | \(-0.959750\pi\) | ||
0.992016 | − | 0.126113i | \(-0.0402503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.00000 | + | 4.58258i | 0.311496 | + | 0.203922i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.89949i | 0.439652i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.74166i | 0.165846i | 0.996556 | + | 0.0829230i | \(0.0264256\pi\) | ||||
−0.996556 | + | 0.0829230i | \(0.973574\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.9230 | 1.14676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.6606i | 1.61861i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31.7490 | − | 20.7846i | −1.39903 | − | 0.915879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.79796 | −0.430914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.3923i | − | 0.456172i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 37.4166i | − | 1.63925i | −0.572900 | − | 0.819625i | \(-0.694182\pi\) | ||
0.572900 | − | 0.819625i | \(-0.305818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.6985i | 1.29862i | 0.760522 | + | 0.649312i | \(0.224943\pi\) | ||||
−0.760522 | + | 0.649312i | \(0.775057\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.1464 | + | 7.48331i | −0.748331 | + | 0.326599i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.48074 | −0.281240 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.3303i | 0.793974i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.4422 | + | 29.6985i | −0.840561 | + | 1.28398i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.2929 | 1.47985 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 24.2487i | − | 1.04447i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.0000 | −1.63375 | −0.816874 | − | 0.576816i | \(-0.804295\pi\) | ||||
−0.816874 | + | 0.576816i | \(0.804295\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8745 | 0.681240 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.44949 | − | 3.74166i | 0.104925 | − | 0.160275i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4575 | 1.13124 | 0.565621 | − | 0.824665i | \(-0.308637\pi\) | ||||
0.565621 | + | 0.824665i | \(0.308637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.2250i | 0.479070i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.8844 | −1.65653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.3303i | 0.779484i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.8745 | + | 24.2487i | −0.673835 | + | 1.02930i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.4955i | 1.16502i | 0.812824 | + | 0.582510i | \(0.197929\pi\) | ||||
−0.812824 | + | 0.582510i | \(0.802071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9615 | 0.548212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.89949i | 0.417214i | 0.978000 | + | 0.208607i | \(0.0668929\pi\) | ||||
−0.978000 | + | 0.208607i | \(0.933107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.1464 | − | 11.2250i | −0.721356 | − | 0.472238i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.2288 | −0.555556 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.0000 | 1.50920 | 0.754599 | − | 0.656186i | \(-0.227831\pi\) | ||||
0.754599 | + | 0.656186i | \(0.227831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.2487i | − | 1.01478i | −0.861717 | − | 0.507388i | \(-0.830611\pi\) | ||
0.861717 | − | 0.507388i | \(-0.169389\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.79796 | 0.409316 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.89898 | 0.203947 | 0.101974 | − | 0.994787i | \(-0.467484\pi\) | ||||
0.101974 | + | 0.994787i | \(0.467484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9615 | 0.538661 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 26.1916i | − | 1.08661i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.7490 | 1.31491 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | − | 4.58258i | 0.124035 | − | 0.189466i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.89949i | 0.408596i | 0.978909 | + | 0.204298i | \(0.0654911\pi\) | ||||
−0.978909 | + | 0.204298i | \(0.934509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9615 | −0.533164 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.4949 | 1.00588 | 0.502942 | − | 0.864320i | \(-0.332251\pi\) | ||||
0.502942 | + | 0.864320i | \(0.332251\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.8745 | + | 24.2487i | −0.650791 | + | 0.994100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.3303i | 0.750209i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.7128i | − | 1.13231i | −0.824297 | − | 0.566157i | \(-0.808429\pi\) | ||
0.824297 | − | 0.566157i | \(-0.191571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.4499i | 0.915752i | 0.889016 | + | 0.457876i | \(0.151390\pi\) | ||||
−0.889016 | + | 0.457876i | \(0.848610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.29150 | −0.215487 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.22474 | + | 1.87083i | −0.0497930 | + | 0.0760600i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.4264i | 1.72203i | 0.508576 | + | 0.861017i | \(0.330172\pi\) | ||||
−0.508576 | + | 0.861017i | \(0.669828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 22.4499i | − | 0.909718i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6.92820i | − | 0.280285i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27.4955i | − | 1.11053i | −0.831673 | − | 0.555265i | \(-0.812617\pi\) | ||
0.831673 | − | 0.555265i | \(-0.187383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.9615 | − | 19.7990i | 0.522657 | − | 0.798372i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 27.4955i | − | 1.10693i | −0.832874 | − | 0.553463i | \(-0.813306\pi\) | ||
0.832874 | − | 0.553463i | \(-0.186694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.3652 | 1.82338 | 0.911690 | − | 0.410878i | \(-0.134778\pi\) | ||||
0.911690 | + | 0.410878i | \(0.134778\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 19.7990i | − | 0.793230i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0000 | + | 18.3303i | −0.680000 | + | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.7490 | 1.26793 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.8999i | 1.79028i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8564i | 0.551615i | 0.961213 | + | 0.275807i | \(0.0889452\pi\) | ||||
−0.961213 | + | 0.275807i | \(0.911055\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6969 | −0.584151 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9615 | − | 19.7990i | 0.514361 | − | 0.785699i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.1464 | 0.679366 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.24264i | 0.167313i | 0.996495 | + | 0.0836567i | \(0.0266599\pi\) | ||||
−0.996495 | + | 0.0836567i | \(0.973340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.0000 | − | 9.16515i | −0.551249 | − | 0.360877i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 39.5980i | − | 1.55676i | −0.627795 | − | 0.778379i | \(-0.716042\pi\) | ||
0.627795 | − | 0.778379i | \(-0.283958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.4499i | 0.881237i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4955i | 1.07598i | 0.842951 | + | 0.537990i | \(0.180816\pi\) | ||||
−0.842951 | + | 0.537990i | \(0.819184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.8118 | + | 36.3731i | −0.930403 | + | 1.42121i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.79796 | 0.382255 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.3923i | − | 0.404827i | −0.979300 | − | 0.202413i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202413i | \(-0.0648785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.6749i | − | 1.30980i | −0.755714 | − | 0.654901i | \(-0.772710\pi\) | ||
0.755714 | − | 0.654901i | \(-0.227290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.9706i | 0.659082i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.0000 | + | 32.0780i | −0.814345 | + | 1.24393i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.0000 | 1.39184 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.8844 | 1.50112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9230 | + | 11.3137i | −0.997775 | + | 0.435465i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.34847 | 0.282425 | 0.141212 | − | 0.989979i | \(-0.454900\pi\) | ||||
0.141212 | + | 0.989979i | \(0.454900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.8844 | 1.49225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0000 | −0.996322 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.6235 | 1.82226 | 0.911132 | − | 0.412115i | \(-0.135210\pi\) | ||||
0.911132 | + | 0.412115i | \(0.135210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.2929 | + | 22.4499i | 1.31026 | + | 0.857768i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.8745 | 0.605650 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.4499i | 0.855275i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.48074 | 0.246539 | 0.123269 | − | 0.992373i | \(-0.460662\pi\) | ||||
0.123269 | + | 0.992373i | \(0.460662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 9.16515i | − | 0.348155i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.8118 | − | 36.3731i | 0.903232 | − | 1.37971i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 36.6606i | − | 1.38862i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.9230 | −0.980497 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.3970i | 2.24020i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.89898 | + | 7.48331i | −0.184506 | + | 0.281838i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.89949i | 0.372309i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.92820i | 0.259828i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.8745 | − | 10.3923i | −0.593673 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.6969 | −0.548867 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.8459 | −1.93353 | −0.966763 | − | 0.255673i | \(-0.917703\pi\) | ||||
−0.966763 | + | 0.255673i | \(0.917703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 44.8999i | − | 1.67216i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | − | 27.4955i | −0.445669 | − | 1.02116i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.9230 | −0.958795 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.9444 | 0.995214 | 0.497607 | − | 0.867403i | \(-0.334212\pi\) | ||||
0.497607 | + | 0.867403i | \(0.334212\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.5203 | − | 12.1244i | −0.683130 | − | 0.447214i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.3303i | 0.675205i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.9615i | 1.91144i | 0.294285 | + | 0.955718i | \(0.404919\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.4499i | 0.824719i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.34847 | + | 11.2250i | −0.269227 | + | 0.411251i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 9.89949i | − | 0.362204i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.0000 | −1.53465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.1769i | − | 1.13766i | −0.822455 | − | 0.568831i | \(-0.807396\pi\) | ||
0.822455 | − | 0.568831i | \(-0.192604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9.16515i | − | 0.333997i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.48074 | − | 4.24264i | −0.235858 | − | 0.154406i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.8258i | 1.66557i | 0.553600 | + | 0.832783i | \(0.313254\pi\) | ||||
−0.553600 | + | 0.832783i | \(0.686746\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.4166i | 1.35635i | 0.734901 | + | 0.678175i | \(0.237229\pi\) | ||||
−0.734901 | + | 0.678175i | \(0.762771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.29150 | 0.191565 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | + | 9.16515i | −0.216930 | + | 0.331367i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.8745 | −0.573195 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.8999i | 1.61913i | 0.587029 | + | 0.809566i | \(0.300297\pi\) | ||||
−0.587029 | + | 0.809566i | \(0.699703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.7846i | 0.748539i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2474 | −0.440510 | −0.220255 | − | 0.975442i | \(-0.570689\pi\) | ||||
−0.220255 | + | 0.975442i | \(0.570689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34.2929 | −1.23025 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 48.4974i | − | 1.73760i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 33.9411i | − | 1.21296i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.00000 | + | 13.7477i | −0.321224 | + | 0.490677i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.1838i | − | 1.36110i | −0.732700 | − | 0.680552i | \(-0.761740\pi\) | ||
0.732700 | − | 0.680552i | \(-0.238260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 22.4499i | − | 0.799239i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24.2487i | − | 0.862185i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.4955i | 0.976392i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.8745 | − | 24.2487i | 0.563011 | − | 0.860013i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.7423 | 1.30148 | 0.650740 | − | 0.759300i | \(-0.274459\pi\) | ||||
0.650740 | + | 0.759300i | \(0.274459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8564i | 0.490204i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.48331i | − | 0.264410i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 33.9411i | − | 1.19776i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.4575 | −0.931349 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0000 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.48074 | −0.227570 | −0.113785 | − | 0.993505i | \(-0.536297\pi\) | ||||
−0.113785 | + | 0.993505i | \(0.536297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 36.6606i | − | 1.28574i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.48074 | − | 9.89949i | 0.227010 | − | 0.346764i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.2929 | −1.19976 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.48074 | 0.226455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4575 | 0.922251 | 0.461125 | − | 0.887335i | \(-0.347446\pi\) | ||||
0.461125 | + | 0.887335i | \(0.347446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.79796 | + | 22.4499i | 0.341121 | + | 0.781607i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.6235 | −1.65603 | −0.828016 | − | 0.560704i | \(-0.810530\pi\) | ||||
−0.828016 | + | 0.560704i | \(0.810530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 56.1249i | − | 1.94930i | −0.223742 | − | 0.974648i | \(-0.571827\pi\) | ||
0.223742 | − | 0.974648i | \(-0.428173\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.9615 | −0.449629 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.2929 | −1.18818 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5830 | − | 6.92820i | −0.366240 | − | 0.239760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9615 | −0.447480 | −0.223740 | − | 0.974649i | \(-0.571827\pi\) | ||||
−0.223740 | + | 0.974649i | \(0.571827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 8.48528i | − | 0.292249i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.57321 | + | 13.0958i | −0.294928 | + | 0.450509i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.64575 | −0.0909091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.0000 | 1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0454 | 0.754820 | 0.377410 | − | 0.926046i | \(-0.376815\pi\) | ||||
0.377410 | + | 0.926046i | \(0.376815\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.93725 | + | 12.1244i | −0.271448 | + | 0.414644i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.79796 | −0.334692 | −0.167346 | − | 0.985898i | \(-0.553520\pi\) | ||||
−0.167346 | + | 0.985898i | \(0.553520\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.48074 | 0.221120 | 0.110560 | − | 0.993869i | \(-0.464736\pi\) | ||||
0.110560 | + | 0.993869i | \(0.464736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.0000 | 0.954237 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.8745 | 0.540375 | 0.270187 | − | 0.962808i | \(-0.412914\pi\) | ||||
0.270187 | + | 0.962808i | \(0.412914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 13.7477i | 0.306009 | − | 0.467437i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 9.89949i | − | 0.336204i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9615 | −0.439183 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.6969 | 0.497416 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.1633 | − | 4.94975i | −0.985901 | − | 0.167332i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.16515i | 0.309485i | 0.987955 | + | 0.154743i | \(0.0494548\pi\) | ||||
−0.987955 | + | 0.154743i | \(0.950545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 45.0333i | − | 1.51894i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.9333i | − | 1.00848i | −0.863564 | − | 0.504239i | \(-0.831773\pi\) | ||
0.863564 | − | 0.504239i | \(-0.168227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.29150 | −0.178073 | −0.0890366 | − | 0.996028i | \(-0.528379\pi\) | ||||
−0.0890366 | + | 0.996028i | \(0.528379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.1464 | + | 11.2250i | 0.576371 | + | 0.377323i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.5980i | 1.32957i | 0.747035 | + | 0.664785i | \(0.231477\pi\) | ||||
−0.747035 | + | 0.664785i | \(0.768523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.0000 | 0.939090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.3205i | 0.580259i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.3303i | 0.613400i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.3652 | + | 29.6985i | 1.51639 | + | 0.992711i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 44.8999i | − | 1.49583i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 19.7990i | − | 0.658869i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0000 | + | 13.7477i | 0.698064 | + | 0.456990i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.29150 | −0.175701 | −0.0878507 | − | 0.996134i | \(-0.528000\pi\) | ||||
−0.0878507 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.74166i | 0.124103i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2487i | 0.803396i | 0.915772 | + | 0.401698i | \(0.131580\pi\) | ||||
−0.915772 | + | 0.401698i | \(0.868420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.2929 | −1.13493 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.4422 | − | 29.6985i | 0.642740 | − | 0.981802i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −51.4393 | −1.69867 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.4256i | 1.82832i | 0.405351 | + | 0.914161i | \(0.367149\pi\) | ||||
−0.405351 | + | 0.914161i | \(0.632851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | 0.197707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.0000 | + | 18.3303i | −1.38095 | + | 0.602697i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 16.9706i | − | 0.557386i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.9666i | 0.491039i | 0.969392 | + | 0.245520i | \(0.0789586\pi\) | ||||
−0.969392 | + | 0.245520i | \(0.921041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.3652 | −1.48678 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 18.3303i | − | 0.600107i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.7490 | + | 20.7846i | 1.03830 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.5959 | −0.640171 | −0.320085 | − | 0.947389i | \(-0.603712\pi\) | ||||
−0.320085 | + | 0.947389i | \(0.603712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8564i | 0.452187i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.1916i | − | 0.853822i | −0.904294 | − | 0.426911i | \(-0.859602\pi\) | ||
0.904294 | − | 0.426911i | \(-0.140398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −28.0000 | − | 18.3303i | −0.910840 | − | 0.596285i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.8745 | 0.515852 | 0.257926 | − | 0.966165i | \(-0.416961\pi\) | ||||
0.257926 | + | 0.966165i | \(0.416961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.9615 | 0.420305 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 54.9909i | − | 1.78133i | −0.454660 | − | 0.890665i | \(-0.650239\pi\) | ||
0.454660 | − | 0.890665i | \(-0.349761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.9615 | + | 8.48528i | 0.419424 | + | 0.274577i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.3939 | −0.950169 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.4974i | 1.56606i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.8745 | −0.511549 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.1464 | + | 11.2250i | 0.551963 | + | 0.361345i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.3320 | −1.36131 | −0.680653 | − | 0.732606i | \(-0.738304\pi\) | ||||
−0.680653 | + | 0.732606i | \(0.738304\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 44.8999i | − | 1.44239i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.48074 | 0.207977 | 0.103988 | − | 0.994579i | \(-0.466840\pi\) | ||||
0.103988 | + | 0.994579i | \(0.466840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 51.4393 | 1.64907 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.8745 | + | 6.92820i | −0.508391 | + | 0.221880i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.6606i | 1.17288i | 0.809994 | + | 0.586438i | \(0.199470\pi\) | ||||
−0.809994 | + | 0.586438i | \(0.800530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.9230 | −0.828501 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 11.3137i | − | 0.360851i | −0.983589 | − | 0.180426i | \(-0.942252\pi\) | ||
0.983589 | − | 0.180426i | \(-0.0577475\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.1464 | − | 11.2250i | −0.546331 | − | 0.357657i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.5830 | −0.336861 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.4974i | 1.54057i | 0.637699 | + | 0.770286i | \(0.279886\pi\) | ||||
−0.637699 | + | 0.770286i | \(0.720114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.2929 | 1.08825 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.8745 | + | 24.2487i | −0.503256 | + | 0.768736i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0454 | 0.698185 | 0.349093 | − | 0.937088i | \(-0.386490\pi\) | ||||
0.349093 | + | 0.937088i | \(0.386490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.8459 | −1.64033 |
(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.e.e.2239.3 | 8 | ||
4.3 | odd | 2 | inner | 2240.2.e.e.2239.7 | 8 | ||
5.4 | even | 2 | inner | 2240.2.e.e.2239.5 | 8 | ||
7.6 | odd | 2 | inner | 2240.2.e.e.2239.6 | 8 | ||
8.3 | odd | 2 | 560.2.e.d.559.2 | yes | 8 | ||
8.5 | even | 2 | 560.2.e.d.559.6 | yes | 8 | ||
20.19 | odd | 2 | inner | 2240.2.e.e.2239.1 | 8 | ||
28.27 | even | 2 | inner | 2240.2.e.e.2239.2 | 8 | ||
35.34 | odd | 2 | inner | 2240.2.e.e.2239.4 | 8 | ||
40.3 | even | 4 | 2800.2.k.k.2351.7 | 8 | |||
40.13 | odd | 4 | 2800.2.k.k.2351.2 | 8 | |||
40.19 | odd | 2 | 560.2.e.d.559.8 | yes | 8 | ||
40.27 | even | 4 | 2800.2.k.k.2351.1 | 8 | |||
40.29 | even | 2 | 560.2.e.d.559.4 | yes | 8 | ||
40.37 | odd | 4 | 2800.2.k.k.2351.8 | 8 | |||
56.13 | odd | 2 | 560.2.e.d.559.3 | yes | 8 | ||
56.27 | even | 2 | 560.2.e.d.559.7 | yes | 8 | ||
140.139 | even | 2 | inner | 2240.2.e.e.2239.8 | 8 | ||
280.13 | even | 4 | 2800.2.k.k.2351.6 | 8 | |||
280.27 | odd | 4 | 2800.2.k.k.2351.5 | 8 | |||
280.69 | odd | 2 | 560.2.e.d.559.5 | yes | 8 | ||
280.83 | odd | 4 | 2800.2.k.k.2351.3 | 8 | |||
280.139 | even | 2 | 560.2.e.d.559.1 | ✓ | 8 | ||
280.237 | even | 4 | 2800.2.k.k.2351.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.e.d.559.1 | ✓ | 8 | 280.139 | even | 2 | ||
560.2.e.d.559.2 | yes | 8 | 8.3 | odd | 2 | ||
560.2.e.d.559.3 | yes | 8 | 56.13 | odd | 2 | ||
560.2.e.d.559.4 | yes | 8 | 40.29 | even | 2 | ||
560.2.e.d.559.5 | yes | 8 | 280.69 | odd | 2 | ||
560.2.e.d.559.6 | yes | 8 | 8.5 | even | 2 | ||
560.2.e.d.559.7 | yes | 8 | 56.27 | even | 2 | ||
560.2.e.d.559.8 | yes | 8 | 40.19 | odd | 2 | ||
2240.2.e.e.2239.1 | 8 | 20.19 | odd | 2 | inner | ||
2240.2.e.e.2239.2 | 8 | 28.27 | even | 2 | inner | ||
2240.2.e.e.2239.3 | 8 | 1.1 | even | 1 | trivial | ||
2240.2.e.e.2239.4 | 8 | 35.34 | odd | 2 | inner | ||
2240.2.e.e.2239.5 | 8 | 5.4 | even | 2 | inner | ||
2240.2.e.e.2239.6 | 8 | 7.6 | odd | 2 | inner | ||
2240.2.e.e.2239.7 | 8 | 4.3 | odd | 2 | inner | ||
2240.2.e.e.2239.8 | 8 | 140.139 | even | 2 | inner | ||
2800.2.k.k.2351.1 | 8 | 40.27 | even | 4 | |||
2800.2.k.k.2351.2 | 8 | 40.13 | odd | 4 | |||
2800.2.k.k.2351.3 | 8 | 280.83 | odd | 4 | |||
2800.2.k.k.2351.4 | 8 | 280.237 | even | 4 | |||
2800.2.k.k.2351.5 | 8 | 280.27 | odd | 4 | |||
2800.2.k.k.2351.6 | 8 | 280.13 | even | 4 | |||
2800.2.k.k.2351.7 | 8 | 40.3 | even | 4 | |||
2800.2.k.k.2351.8 | 8 | 40.37 | odd | 4 |