Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1121,2240)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3534400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.2 | ||
Root | \(0.627553 - 1.14620i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1121 |
Dual form | 2240.2.b.f.1121.5 |
$q$-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 | ||||||||
\(3\) | − 2.29240i | − 1.32352i | −0.749716 | − | 0.661759i | \(-0.769810\pi\) | ||||
0.749716 | − | 0.661759i | \(-0.230190\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.25511 | −0.751702 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.744895i | − 0.224594i | −0.993675 | − | 0.112297i | \(-0.964179\pi\) | ||||
0.993675 | − | 0.112297i | \(-0.0358208\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.83991i | 1.06500i | 0.846430 | + | 0.532499i | \(0.178747\pi\) | ||||
−0.846430 | + | 0.532499i | \(0.821253\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.29240 | −0.591896 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.38741 | 1.79171 | 0.895856 | − | 0.444345i | \(-0.146564\pi\) | ||||
0.895856 | + | 0.444345i | \(0.146564\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.58480i | − 1.05183i | −0.850538 | − | 0.525913i | \(-0.823724\pi\) | ||||
0.850538 | − | 0.525913i | \(-0.176276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.29240i | − 0.500243i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51021 | −0.523415 | −0.261707 | − | 0.965147i | \(-0.584286\pi\) | ||||
−0.261707 | + | 0.965147i | \(0.584286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.70760i | − 0.328627i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.80261i | − 0.891823i | −0.895077 | − | 0.445911i | \(-0.852880\pi\) | ||||
0.895077 | − | 0.445911i | \(-0.147120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.09501 | 0.555881 | 0.277940 | − | 0.960598i | \(-0.410348\pi\) | ||||
0.277940 | + | 0.960598i | \(0.410348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.70760 | −0.297255 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.00000i | − 0.169031i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 11.6798i | − 1.92015i | −0.279743 | − | 0.960075i | \(-0.590249\pi\) | ||||
0.279743 | − | 0.960075i | \(-0.409751\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.80261 | 1.40955 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41520 | −0.221017 | −0.110508 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110508 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.00000i | − 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.25511i | 0.336171i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.83991 | −0.268378 | −0.134189 | − | 0.990956i | \(-0.542843\pi\) | ||||
−0.134189 | + | 0.990956i | \(0.542843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 16.9349i | − 2.37136i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0950i | 1.52402i | 0.647567 | + | 0.762009i | \(0.275787\pi\) | ||||
−0.647567 | + | 0.762009i | \(0.724213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.744895 | −0.100442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.5102 | −1.39211 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 11.0950i | − 1.44445i | −0.691659 | − | 0.722224i | \(-0.743120\pi\) | ||||
0.691659 | − | 0.722224i | \(-0.256880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.51021i | 1.08962i | 0.838559 | + | 0.544810i | \(0.183398\pi\) | ||||
−0.838559 | + | 0.544810i | \(0.816602\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.25511 | −0.284117 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.83991 | 0.476282 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.5848i | − 1.29314i | −0.762855 | − | 0.646570i | \(-0.776203\pi\) | ||||
0.762855 | − | 0.646570i | \(-0.223797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.75441i | 0.692749i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.41520 | −0.405309 | −0.202655 | − | 0.979250i | \(-0.564957\pi\) | ||||
−0.202655 | + | 0.979250i | \(0.564957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.51021 | −0.996045 | −0.498022 | − | 0.867164i | \(-0.665940\pi\) | ||||
−0.498022 | + | 0.867164i | \(0.665940\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.29240i | 0.264704i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.744895i | − 0.0848887i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.36699 | 0.941360 | 0.470680 | − | 0.882304i | \(-0.344009\pi\) | ||||
0.470680 | + | 0.882304i | \(0.344009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6798 | −1.18665 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.58480i | − 0.503248i | −0.967825 | − | 0.251624i | \(-0.919035\pi\) | ||||
0.967825 | − | 0.251624i | \(-0.0809645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 7.38741i | − 0.801278i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.0095 | −1.18034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.48979 | −0.793916 | −0.396958 | − | 0.917837i | \(-0.629934\pi\) | ||||
−0.396958 | + | 0.917837i | \(0.629934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.83991i | 0.402532i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.09501i | − 0.735719i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.58480 | −0.470391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.38741 | −0.343940 | −0.171970 | − | 0.985102i | \(-0.555013\pi\) | ||||
−0.171970 | + | 0.985102i | \(0.555013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.67982i | 0.168828i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1696i | 1.11142i | 0.831377 | + | 0.555709i | \(0.187553\pi\) | ||||
−0.831377 | + | 0.555709i | \(0.812447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8399 | 1.36369 | 0.681843 | − | 0.731498i | \(-0.261179\pi\) | ||||
0.681843 | + | 0.731498i | \(0.261179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.29240 | −0.223715 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.19003i | 0.791760i | 0.918302 | + | 0.395880i | \(0.129560\pi\) | ||||
−0.918302 | + | 0.395880i | \(0.870440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3670i | 1.18454i | 0.805738 | + | 0.592272i | \(0.201769\pi\) | ||||
−0.805738 | + | 0.592272i | \(0.798231\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.7748 | −2.54135 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.07459 | −0.383305 | −0.191653 | − | 0.981463i | \(-0.561385\pi\) | ||||
−0.191653 | + | 0.981463i | \(0.561385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.51021i | 0.234078i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 8.65940i | − 0.800561i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.38741 | 0.677203 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4451 | 0.949557 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.24420i | 0.292520i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.09501 | 0.629581 | 0.314790 | − | 0.949161i | \(-0.398066\pi\) | ||||
0.314790 | + | 0.949161i | \(0.398066\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.58480 | −0.403669 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.67982i | 0.321507i | 0.986995 | + | 0.160754i | \(0.0513924\pi\) | ||||
−0.986995 | + | 0.160754i | \(0.948608\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.58480i | − 0.397553i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.70760 | −0.146967 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.48979 | −0.298153 | −0.149076 | − | 0.988826i | \(-0.547630\pi\) | ||||
−0.149076 | + | 0.988826i | \(0.547630\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6798i | 0.990669i | 0.868702 | + | 0.495335i | \(0.164955\pi\) | ||||
−0.868702 | + | 0.495335i | \(0.835045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.21781i | 0.355204i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.86033 | 0.239193 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.80261 | −0.398835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.29240i | − 0.189074i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.19003i | 0.507107i | 0.967321 | + | 0.253553i | \(0.0815993\pi\) | ||||
−0.967321 | + | 0.253553i | \(0.918401\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.97222 | −0.811528 | −0.405764 | − | 0.913978i | \(-0.632994\pi\) | ||||
−0.405764 | + | 0.913978i | \(0.632994\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.6594 | −1.34683 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.09501i | − 0.248597i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 23.1696i | − 1.84914i | −0.381017 | − | 0.924568i | \(-0.624426\pi\) | ||||
0.381017 | − | 0.924568i | \(-0.375574\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.4342 | 2.01707 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.51021 | −0.197832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.07459i | − 0.319147i | −0.987186 | − | 0.159573i | \(-0.948988\pi\) | ||||
0.987186 | − | 0.159573i | \(-0.0510119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.70760i | 0.132936i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.1791 | −1.87104 | −0.935518 | − | 0.353278i | \(-0.885067\pi\) | ||||
−0.935518 | + | 0.353278i | \(0.885067\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.74489 | −0.134223 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3392i | 0.790659i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.0299i | − 1.06668i | −0.845902 | − | 0.533338i | \(-0.820937\pi\) | ||||
0.845902 | − | 0.533338i | \(-0.179063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.4342 | −1.91175 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 5.67982i | − 0.424529i | −0.977212 | − | 0.212265i | \(-0.931916\pi\) | ||||
0.977212 | − | 0.212265i | \(-0.0680839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.56438i | 0.413597i | 0.978384 | + | 0.206799i | \(0.0663045\pi\) | ||||
−0.978384 | + | 0.206799i | \(0.933695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.5088 | 1.44213 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.6798 | −0.858717 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.50285i | − 0.402408i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.70760i | − 0.124210i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5570 | 1.05331 | 0.526655 | − | 0.850079i | \(-0.323446\pi\) | ||||
0.526655 | + | 0.850079i | \(0.323446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.8494 | 1.93266 | 0.966332 | − | 0.257299i | \(-0.0828325\pi\) | ||||
0.966332 | + | 0.257299i | \(0.0828325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 8.80261i | − 0.630368i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 23.2442i | − 1.65608i | −0.560669 | − | 0.828040i | \(-0.689456\pi\) | ||||
0.560669 | − | 0.828040i | \(-0.310544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1154 | −0.858840 | −0.429420 | − | 0.903105i | \(-0.641282\pi\) | ||||
−0.429420 | + | 0.903105i | \(0.641282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.2646 | −1.71149 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.80261i | − 0.337077i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.41520i | 0.0988416i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.66079 | 0.393452 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.41520 | −0.236234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.08550i | 0.143572i | 0.997420 | + | 0.0717858i | \(0.0228698\pi\) | ||||
−0.997420 | + | 0.0717858i | \(0.977130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.82900i | 0.536434i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00000 | −0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.09501 | 0.210103 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.5088i | 1.31828i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.3670i | 1.90817i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.1791 | −1.61915 | −0.809577 | − | 0.587014i | \(-0.800303\pi\) | ||||
−0.809577 | + | 0.587014i | \(0.800303\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.25511 | 0.150340 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 23.8976i | − 1.58614i | −0.609130 | − | 0.793071i | \(-0.708481\pi\) | ||||
0.609130 | − | 0.793071i | \(-0.291519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7748i | 1.10851i | 0.832346 | + | 0.554256i | \(0.186997\pi\) | ||||
−0.832346 | + | 0.554256i | \(0.813003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.70760 | −0.112352 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.8698 | −1.56377 | −0.781883 | − | 0.623426i | \(-0.785740\pi\) | ||||
−0.781883 | + | 0.623426i | \(0.785740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.83991i | 0.120022i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 19.1805i | − 1.24591i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.19739 | 0.465560 | 0.232780 | − | 0.972529i | \(-0.425218\pi\) | ||||
0.232780 | + | 0.972529i | \(0.425218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.83039 | 0.311153 | 0.155577 | − | 0.987824i | \(-0.450276\pi\) | ||||
0.155577 | + | 0.987824i | \(0.450276\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.3596i | 1.24192i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.00000i | − 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.6052 | 1.12019 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.5102 | −0.666057 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 11.6798i | − 0.737223i | −0.929583 | − | 0.368612i | \(-0.879833\pi\) | ||||
0.929583 | − | 0.368612i | \(-0.120167\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.86984i | 0.117556i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.9349 | −1.06051 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.6594 | 0.789671 | 0.394836 | − | 0.918752i | \(-0.370802\pi\) | ||||
0.394836 | + | 0.918752i | \(0.370802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 11.6798i | − 0.725748i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8304i | 0.670385i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5848 | 1.26931 | 0.634657 | − | 0.772794i | \(-0.281142\pi\) | ||||
0.634657 | + | 0.772794i | \(0.281142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0950 | 0.681561 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.1696i | 1.05076i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 8.07459i | − 0.492317i | −0.969230 | − | 0.246158i | \(-0.920832\pi\) | ||||
0.969230 | − | 0.246158i | \(-0.0791683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.16961 | 0.0710485 | 0.0355243 | − | 0.999369i | \(-0.488690\pi\) | ||||
0.0355243 | + | 0.999369i | \(0.488690\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.80261 | 0.532758 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.744895i | 0.0449189i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.51021i | 0.391161i | 0.980688 | + | 0.195580i | \(0.0626590\pi\) | ||||
−0.980688 | + | 0.195580i | \(0.937341\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.97958 | −0.417857 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.08550 | −0.124410 | −0.0622052 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622052 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.5028i | 1.75376i | 0.480707 | + | 0.876881i | \(0.340380\pi\) | ||||
−0.480707 | + | 0.876881i | \(0.659620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.5102i | 0.622571i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.41520 | −0.0835364 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.5739 | 2.21023 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.76532i | 0.455211i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.32970i | 0.0776818i | 0.999245 | + | 0.0388409i | \(0.0123666\pi\) | ||||
−0.999245 | + | 0.0388409i | \(0.987633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0950 | −0.645977 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.27198 | −0.0738079 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 9.63898i | − 0.557436i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.00000i | − 0.115278i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.6052 | 1.47098 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.51021 | 0.487293 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8976i | 0.907325i | 0.891173 | + | 0.453663i | \(0.149883\pi\) | ||||
−0.891173 | + | 0.453663i | \(0.850117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 31.7266i | − 1.80486i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.6798 | −1.79640 | −0.898199 | − | 0.439590i | \(-0.855124\pi\) | ||||
−0.898199 | + | 0.439590i | \(0.855124\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1418 | 1.42110 | 0.710550 | − | 0.703647i | \(-0.248446\pi\) | ||||
0.710550 | + | 0.703647i | \(0.248446\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.25511i | 0.127061i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 12.7340i | − 0.715212i | −0.933873 | − | 0.357606i | \(-0.883593\pi\) | ||||
0.933873 | − | 0.357606i | \(-0.116407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.57744 | −0.200298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.7748 | 1.04791 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 33.8698i | − 1.88457i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.83991i | − 0.213000i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.3501 | 1.56777 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.83991 | −0.101437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 17.0394i | − 0.936573i | −0.883577 | − | 0.468286i | \(-0.844872\pi\) | ||||
0.883577 | − | 0.468286i | \(-0.155128\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.3392i | 1.44338i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.5848 | −0.578310 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0746 | 0.875639 | 0.437819 | − | 0.899063i | \(-0.355751\pi\) | ||||
0.437819 | + | 0.899063i | \(0.355751\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.34060i | 0.507312i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.30546i | − 0.124848i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.75441 | 0.309807 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.945827i | 0.0507747i | 0.999678 | + | 0.0253873i | \(0.00808191\pi\) | ||||
−0.999678 | + | 0.0253873i | \(0.991918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.5292i | 1.42008i | 0.704163 | + | 0.710039i | \(0.251323\pi\) | ||||
−0.704163 | + | 0.710039i | \(0.748677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.55702 | 0.349988 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9314 | 0.741492 | 0.370746 | − | 0.928734i | \(-0.379102\pi\) | ||||
0.370746 | + | 0.928734i | \(0.379102\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.41520i | 0.181260i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 16.9349i | − 0.896291i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.9444 | 1.47485 | 0.737425 | − | 0.675429i | \(-0.236041\pi\) | ||||
0.737425 | + | 0.675429i | \(0.236041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.02042 | −0.106338 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 23.9444i | − 1.25676i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.51021i | 0.445445i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00951 | 0.365894 | 0.182947 | − | 0.983123i | \(-0.441436\pi\) | ||||
0.182947 | + | 0.983123i | \(0.441436\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.19142 | 0.166139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.0950i | 0.576024i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.83039i | 0.146552i | 0.997312 | + | 0.0732761i | \(0.0233454\pi\) | ||||
−0.997312 | + | 0.0732761i | \(0.976655\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.29240 | 0.118379 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.4416 | 0.949790 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 10.8494i | − 0.557297i | −0.960393 | − | 0.278649i | \(-0.910113\pi\) | ||||
0.960393 | − | 0.278649i | \(-0.0898865\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 16.2646i | − 0.833262i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.5497 | −1.91870 | −0.959349 | − | 0.282222i | \(-0.908928\pi\) | ||||
−0.959349 | + | 0.282222i | \(0.908928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.744895 | −0.0379634 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.51021i | 0.229267i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 9.38741i | − 0.475961i | −0.971270 | − | 0.237980i | \(-0.923515\pi\) | ||||
0.971270 | − | 0.237980i | \(-0.0764854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.5440 | −0.937809 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.43562 | 0.425521 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 8.36699i | − 0.420989i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.3705i | − 0.771425i | −0.922619 | − | 0.385713i | \(-0.873956\pi\) | ||||
0.922619 | − | 0.385713i | \(-0.126044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.5102 | −0.526169 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.7653 | 0.687407 | 0.343704 | − | 0.939078i | \(-0.388318\pi\) | ||||
0.343704 | + | 0.939078i | \(0.388318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8846i | 0.592012i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.6798i | 0.530684i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.70024 | −0.431255 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0745931 | −0.00368839 | −0.00184420 | − | 0.999998i | \(-0.500587\pi\) | ||||
−0.00184420 | + | 0.999998i | \(0.500587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000i | 0.394611i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.0950i | − 0.545950i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.58480 | −0.225059 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.7748 | 1.31117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0746i | 1.07841i | 0.842173 | + | 0.539207i | \(0.181276\pi\) | ||||
−0.842173 | + | 0.539207i | \(0.818724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.38741i | 0.262567i | 0.991345 | + | 0.131283i | \(0.0419097\pi\) | ||||
−0.991345 | + | 0.131283i | \(0.958090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.14919 | 0.201740 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.38741 | −0.358342 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.51021i | 0.411838i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 6.55702i | − 0.316576i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.9167 | 1.44103 | 0.720517 | − | 0.693437i | \(-0.243904\pi\) | ||||
0.720517 | + | 0.693437i | \(0.243904\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.15058 | 0.247521 | 0.123760 | − | 0.992312i | \(-0.460505\pi\) | ||||
0.123760 | + | 0.992312i | \(0.460505\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.0095i | 0.527866i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.5088i | 0.550541i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4152 | 0.735727 | 0.367864 | − | 0.929880i | \(-0.380089\pi\) | ||||
0.367864 | + | 0.929880i | \(0.380089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.25511 | −0.107386 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 25.5088i | − 1.21196i | −0.795480 | − | 0.605980i | \(-0.792781\pi\) | ||||
0.795480 | − | 0.605980i | \(-0.207219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.48979i | 0.355050i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.1900 | 0.671165 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.0841 | 1.08941 | 0.544703 | − | 0.838629i | \(-0.316642\pi\) | ||||
0.544703 | + | 0.838629i | \(0.316642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.05417i | 0.0496391i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.8603i | 1.07407i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.83991 | 0.180018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.774830 | 0.0362450 | 0.0181225 | − | 0.999836i | \(-0.494231\pi\) | ||||
0.0181225 | + | 0.999836i | \(0.494231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 12.6147i | − 0.588806i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.0599i | 1.58633i | 0.609009 | + | 0.793163i | \(0.291567\pi\) | ||||
−0.609009 | + | 0.793163i | \(0.708433\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1492 | −0.564621 | −0.282310 | − | 0.959323i | \(-0.591101\pi\) | ||||
−0.282310 | + | 0.959323i | \(0.591101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.09501 | −0.329023 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8772i | 0.873533i | 0.899575 | + | 0.436766i | \(0.143876\pi\) | ||||
−0.899575 | + | 0.436766i | \(0.856124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10.5848i | − 0.488761i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.1140 | −2.44737 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.48979 | −0.0685006 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.58480i | 0.210365i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 25.0204i | − 1.14561i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.56438 | −0.162861 | −0.0814304 | − | 0.996679i | \(-0.525949\pi\) | ||||
−0.0814304 | + | 0.996679i | \(0.525949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.8494 | 2.04496 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.75441i | 0.261835i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.38741i | 0.153815i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.6594 | 1.38931 | 0.694655 | − | 0.719343i | \(-0.255557\pi\) | ||||
0.694655 | + | 0.719343i | \(0.255557\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.34060 | −0.422397 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.44513i | 0.426253i | 0.977025 | + | 0.213126i | \(0.0683646\pi\) | ||||
−0.977025 | + | 0.213126i | \(0.931635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 35.4789i | − 1.59789i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.67982 | 0.0755021 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.41520 | −0.153193 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.2537i | 1.62294i | 0.584395 | + | 0.811470i | \(0.301332\pi\) | ||||
−0.584395 | + | 0.811470i | \(0.698668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 55.4283i | 2.47635i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6703 | −0.743292 | −0.371646 | − | 0.928375i | \(-0.621206\pi\) | ||||
−0.371646 | + | 0.928375i | \(0.621206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1696 | 0.497041 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.00000i | 0.177646i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.07459i | 0.180603i | 0.995914 | + | 0.0903016i | \(0.0287831\pi\) | ||||
−0.995914 | + | 0.0903016i | \(0.971217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.51021 | −0.376470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.82900 | −0.345659 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 13.8399i | − 0.609859i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.37054i | 0.0602762i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.1622 | −1.41177 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.4546 | 1.07138 | 0.535689 | − | 0.844416i | \(-0.320052\pi\) | ||||
0.535689 | + | 0.844416i | \(0.320052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.584803i | − 0.0255717i | −0.999918 | − | 0.0127858i | \(-0.995930\pi\) | ||||
0.999918 | − | 0.0127858i | \(-0.00406997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.29240i | 0.100049i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.8641 | 0.995978 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6988 | −0.726037 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.0204i | 1.08579i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.43423i | − 0.235382i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.19003 | 0.354086 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.0204 | −0.561873 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.744895i | − 0.0320849i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.44298i | 0.0620385i | 0.999519 | + | 0.0310193i | \(0.00987532\pi\) | ||||
−0.999519 | + | 0.0310193i | \(0.990125\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.7558 | 0.547404 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.3670 | 0.529744 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5102i | 1.04798i | 0.851724 | + | 0.523990i | \(0.175557\pi\) | ||||
−0.851724 | + | 0.523990i | \(0.824443\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 19.1914i | − 0.819070i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.0190 | −0.938042 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.36699 | 0.355801 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.7748i | 1.13653i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.1492i | 0.684263i | 0.939652 | + | 0.342131i | \(0.111149\pi\) | ||||
−0.939652 | + | 0.342131i | \(0.888851\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.67982 | 0.324822 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.6147 | −0.532595 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.7544i | 1.42258i | 0.702899 | + | 0.711289i | \(0.251888\pi\) | ||||
−0.702899 | + | 0.711289i | \(0.748112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.07459i | 0.171419i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.6798 | −0.448510 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.5088 | 1.40476 | 0.702381 | − | 0.711801i | \(-0.252120\pi\) | ||||
0.702381 | + | 0.711801i | \(0.252120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6798i | 0.907272i | 0.891187 | + | 0.453636i | \(0.149873\pi\) | ||||
−0.891187 | + | 0.453636i | \(0.850127\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 33.3705i | − 1.39407i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.51021 | 0.104683 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.9722 | 1.66407 | 0.832033 | − | 0.554727i | \(-0.187177\pi\) | ||||
0.832033 | + | 0.554727i | \(0.187177\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 61.5497i | − 2.55792i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.58480i | − 0.190210i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.26462 | 0.342286 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.65940 | −0.358022 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 41.6052i | − 1.71723i | −0.512620 | − | 0.858616i | \(-0.671325\pi\) | ||||
0.512620 | − | 0.858616i | \(-0.328675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 14.1900i | − 0.584690i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −53.2850 | −2.19185 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.80261 | −0.115089 | −0.0575447 | − | 0.998343i | \(-0.518327\pi\) | ||||
−0.0575447 | + | 0.998343i | \(0.518327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7.38741i | − 0.302854i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.7734i | 1.13669i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.8026 | 1.66715 | 0.833575 | − | 0.552407i | \(-0.186290\pi\) | ||||
0.833575 | + | 0.552407i | \(0.186290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.8143 | −1.62406 | −0.812029 | − | 0.583617i | \(-0.801637\pi\) | ||||
−0.812029 | + | 0.583617i | \(0.801637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.8698i | 0.972055i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 10.4451i | − 0.424655i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.3093 | 0.580796 | 0.290398 | − | 0.956906i | \(-0.406212\pi\) | ||||
0.290398 | + | 0.956906i | \(0.406212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.0095 | −0.446128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 7.06508i | − 0.285822i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 18.1345i | − 0.732444i | −0.930528 | − | 0.366222i | \(-0.880651\pi\) | ||||
0.930528 | − | 0.366222i | \(-0.119349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.24420 | 0.130819 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.6038 | −1.47361 | −0.736807 | − | 0.676103i | \(-0.763668\pi\) | ||||
−0.736807 | + | 0.676103i | \(0.763668\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 38.3991i | − 1.54339i | −0.635993 | − | 0.771695i | \(-0.719409\pi\) | ||||
0.635993 | − | 0.771695i | \(-0.280591\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.28643i | 0.172009i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.48979 | −0.300072 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.82900i | 0.312660i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 86.2836i | − 3.44035i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1974 | −1.24195 | −0.620974 | − | 0.783831i | \(-0.713263\pi\) | ||||
−0.620974 | + | 0.783831i | \(0.713263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.78080 | 0.190020 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 7.09501i | − 0.281557i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.83991i | 0.152143i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.70163 | 0.304672 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.339213 | 0.0133981 | 0.00669905 | − | 0.999978i | \(-0.497868\pi\) | ||||
0.00669905 | + | 0.999978i | \(0.497868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.8216i | 1.37323i | 0.727021 | + | 0.686616i | \(0.240904\pi\) | ||||
−0.727021 | + | 0.686616i | \(0.759096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.58480i | 0.180526i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.5497 | 1.63349 | 0.816743 | − | 0.577002i | \(-0.195777\pi\) | ||||
0.816743 | + | 0.577002i | \(0.195777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.26462 | −0.324415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 7.09501i | − 0.278075i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 16.7340i | − 0.654852i | −0.944877 | − | 0.327426i | \(-0.893819\pi\) | ||||
0.944877 | − | 0.327426i | \(-0.106181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.67982 | 0.143782 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.1914 | 0.748729 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.1440i | 1.83647i | 0.396038 | + | 0.918234i | \(0.370385\pi\) | ||||
−0.396038 | + | 0.918234i | \(0.629615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.8698i | 1.08401i | 0.840375 | + | 0.542006i | \(0.182335\pi\) | ||||
−0.840375 | + | 0.542006i | \(0.817665\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 65.0285 | 2.52550 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.58480 | −0.177791 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0556i | 0.466793i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.4283i | 2.14298i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.33921 | 0.244723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.3406 | 0.745525 | 0.372763 | − | 0.927927i | \(-0.378411\pi\) | ||||
0.372763 | + | 0.927927i | \(0.378411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.70760i | 0.0657255i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.6893i | 1.10262i | 0.834300 | + | 0.551310i | \(0.185872\pi\) | ||||
−0.834300 | + | 0.551310i | \(0.814128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.38741 | −0.129997 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54.7830 | −2.09929 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.6798i | 0.523444i | 0.965143 | + | 0.261722i | \(0.0842903\pi\) | ||||
−0.965143 | + | 0.261722i | \(0.915710\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.48979i | 0.133338i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.4546 | 1.46714 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.6038 | −1.62308 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1492i | 0.462177i | 0.972933 | + | 0.231088i | \(0.0742287\pi\) | ||||
−0.972933 | + | 0.231088i | \(0.925771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.67982i | 0.0638109i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.6798 | 0.443041 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.4546 | −0.395998 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 54.7193i | 2.06967i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.5162i | 0.623808i | 0.950114 | + | 0.311904i | \(0.100967\pi\) | ||||
−0.950114 | + | 0.311904i | \(0.899033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53.5497 | −2.01966 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.21781 | 0.158852 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.1696i | 0.420076i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 14.8435i | − 0.557458i | −0.960370 | − | 0.278729i | \(-0.910087\pi\) | ||||
0.960370 | − | 0.278729i | \(-0.0899130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.8685 | −0.707622 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.76913 | −0.290956 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.86033i | − 0.106970i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 16.4993i | − 0.616178i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.9240 | −0.407397 | −0.203699 | − | 0.979034i | \(-0.565296\pi\) | ||||
−0.203699 | + | 0.979034i | \(0.565296\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8399 | 0.515425 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 11.0732i | − 0.411817i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.80261i | 0.178365i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.12877 | 0.116040 | 0.0580198 | − | 0.998315i | \(-0.481521\pi\) | ||||
0.0580198 | + | 0.998315i | \(0.481521\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.3406 | 0.457059 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 14.7748i | − 0.546467i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3705i | 0.567724i | 0.958865 | + | 0.283862i | \(0.0916157\pi\) | ||||
−0.958865 | + | 0.283862i | \(0.908384\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.29240 | −0.0845565 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.88457 | −0.290432 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.8252i | 1.83285i | 0.400208 | + | 0.916425i | \(0.368938\pi\) | ||||
−0.400208 | + | 0.916425i | \(0.631062\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 40.3582i | − 1.48260i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2238 | −0.521820 | −0.260910 | − | 0.965363i | \(-0.584023\pi\) | ||||
−0.260910 | + | 0.965363i | \(0.584023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.19003 | 0.226785 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3392i | 0.378292i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.19003i | 0.299257i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9314 | 0.581344 | 0.290672 | − | 0.956823i | \(-0.406121\pi\) | ||||
0.290672 | + | 0.956823i | \(0.406121\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.7748 | −0.975729 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.97222i | 0.362926i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5088i | 0.418295i | 0.977884 | + | 0.209148i | \(0.0670689\pi\) | ||||
−0.977884 | + | 0.209148i | \(0.932931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.28643 | 0.155588 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.3801 | 1.39128 | 0.695638 | − | 0.718393i | \(-0.255122\pi\) | ||||
0.695638 | + | 0.718393i | \(0.255122\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3670i | 0.447715i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.6594i | 0.602322i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.6038 | 1.53834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.7939 | 1.11045 | 0.555227 | − | 0.831699i | \(-0.312631\pi\) | ||||
0.555227 | + | 0.831699i | \(0.312631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 29.0204i | − 1.04514i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.1805i | 0.761810i | 0.924614 | + | 0.380905i | \(0.124388\pi\) | ||||
−0.924614 | + | 0.380905i | \(0.875612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.09501 | −0.111176 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.7748 | −0.960542 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.48840i | 0.232471i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.54396i | 0.0910302i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.20093 | −0.293077 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.1696 | −0.826959 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2368i | 1.22041i | 0.792243 | + | 0.610206i | \(0.208913\pi\) | ||||
−0.792243 | + | 0.610206i | \(0.791087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 47.1886i | − 1.67996i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.07459 | −0.144876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.6784 | −1.16044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 25.4342i | − 0.902059i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 10.9905i | − 0.389303i | −0.980872 | − | 0.194651i | \(-0.937642\pi\) | ||||
0.980872 | − | 0.194651i | \(-0.0623576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.5922 | −0.480856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.8903 | 0.596788 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.33921i | 0.223706i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.51021i | 0.0884733i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5102 | −0.651590 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5549 | −0.511722 | −0.255861 | − | 0.966714i | \(-0.582359\pi\) | ||||
−0.255861 | + | 0.966714i | \(0.582359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5.63898i | − 0.198011i | −0.995087 | − | 0.0990056i | \(-0.968434\pi\) | ||||
0.995087 | − | 0.0990056i | \(-0.0315662\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.68121i | − 0.0940341i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.07459 | −0.142727 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.16961 | −0.320804 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 8.65940i | − 0.302584i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.3114i | 1.26728i | 0.773629 | + | 0.633639i | \(0.218439\pi\) | ||||
−0.773629 | + | 0.633639i | \(0.781561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0746 | 0.630041 | 0.315020 | − | 0.949085i | \(-0.397989\pi\) | ||||
0.315020 | + | 0.949085i | \(0.397989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.70760 | 0.0594509 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 29.6243i | − 1.03014i | −0.857149 | − | 0.515068i | \(-0.827767\pi\) | ||||
0.857149 | − | 0.515068i | \(-0.172233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 40.2836i | − 1.39911i | −0.714579 | − | 0.699554i | \(-0.753382\pi\) | ||||
0.714579 | − | 0.699554i | \(-0.246618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9240 | 0.517708 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.38741 | 0.255959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.1791i | 0.836753i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 5.28504i | − 0.182678i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.1549 | −1.62797 | −0.813984 | − | 0.580888i | \(-0.802706\pi\) | ||||
−0.813984 | + | 0.580888i | \(0.802706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.93492 | 0.204652 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.78080i | 0.164660i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.74489i | 0.0600262i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.4451 | 0.358899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 67.6324 | 2.32114 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.3188i | 1.00504i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 46.6784i | − 1.59824i | −0.601172 | − | 0.799119i | \(-0.705299\pi\) | ||||
0.601172 | − | 0.799119i | \(-0.294701\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.3392 | 0.353594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.0190 | −0.547200 | −0.273600 | − | 0.961844i | \(-0.588214\pi\) | ||||
−0.273600 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.4209i | 1.31090i | 0.755237 | + | 0.655452i | \(0.227522\pi\) | ||||
−0.755237 | + | 0.655452i | \(0.772478\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.24420i | 0.110562i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.8143 | −1.55954 | −0.779768 | − | 0.626068i | \(-0.784663\pi\) | ||||
−0.779768 | + | 0.626068i | \(0.784663\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0299 | −0.477032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 86.1345i | − 2.92528i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.23253i | − 0.211424i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.6447 | 1.37719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.63898 | 0.258540 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.9240i | 0.503948i | 0.967734 | + | 0.251974i | \(0.0810798\pi\) | ||||
−0.967734 | + | 0.251974i | \(0.918920\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.04820 | 0.102813 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.0190 | −1.48304 | −0.741519 | − | 0.670931i | \(-0.765894\pi\) | ||||
−0.741519 | + | 0.670931i | \(0.765894\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 36.8903i | − 1.24146i | −0.784026 | − | 0.620728i | \(-0.786837\pi\) | ||||
0.784026 | − | 0.620728i | \(-0.213163\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.4342i | 0.854962i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.5497 | 1.39510 | 0.697551 | − | 0.716536i | \(-0.254273\pi\) | ||||
0.697551 | + | 0.716536i | \(0.254273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.09501 | 0.237959 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.95534i | 0.266514i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.43562i | 0.282287i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.67982 | −0.189855 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.0964 | −0.737777 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 14.8641i | − 0.495747i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 81.9635i | 2.73060i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.58480 | −0.152573 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.56438 | 0.184966 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 6.90499i | − 0.229276i | −0.993407 | − | 0.114638i | \(-0.963429\pi\) | ||||
0.993407 | − | 0.114638i | \(-0.0365709\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 25.1886i | − 0.835454i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.1140 | −1.22964 | −0.614822 | − | 0.788666i | \(-0.710772\pi\) | ||||
−0.614822 | + | 0.788666i | \(0.710772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.41520 | −0.113027 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 19.5088i | − 0.644942i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.67982i | 0.121518i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.9167 | −1.77855 | −0.889273 | − | 0.457376i | \(-0.848789\pi\) | ||||
−0.889273 | + | 0.457376i | \(0.848789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.4437 | 1.20086 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 13.1140i | − 0.431654i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6798i | 0.384030i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.2104 | −1.02509 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.3041 | −1.74885 | −0.874425 | − | 0.485161i | \(-0.838761\pi\) | ||||
−0.874425 | + | 0.485161i | \(0.838761\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.58480i | − 0.150261i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 72.6229i | 2.37757i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.50285 | −0.179962 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.9518 | 1.27250 | 0.636250 | − | 0.771483i | \(-0.280485\pi\) | ||||
0.636250 | + | 0.771483i | \(0.280485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 57.6352i | − 1.88085i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 33.1886i | − 1.08192i | −0.841049 | − | 0.540959i | \(-0.818061\pi\) | ||||
0.841049 | − | 0.540959i | \(-0.181939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.55244 | 0.115683 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.70760 | −0.0555482 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 22.8157i | − 0.741410i | −0.928751 | − | 0.370705i | \(-0.879116\pi\) | ||||
0.928751 | − | 0.370705i | \(-0.120884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 32.6784i | − 1.06079i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.1914 | −0.946597 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.4356 | −0.467616 | −0.233808 | − | 0.972283i | \(-0.575119\pi\) | ||||
−0.233808 | + | 0.972283i | \(0.575119\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14.5570i | − 0.471054i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.20093i | 0.265098i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.48979 | −0.112691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4209 | −0.690997 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 18.4694i | − 0.595167i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 26.8494i | − 0.864313i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.7544 | −1.21410 | −0.607050 | − | 0.794664i | \(-0.707647\pi\) | ||||
−0.607050 | + | 0.794664i | \(0.707647\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −77.6433 | −2.49426 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 32.1154i | − 1.03063i | −0.857000 | − | 0.515317i | \(-0.827674\pi\) | ||||
0.857000 | − | 0.515317i | \(-0.172326\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6798i | 0.374438i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.80261 | −0.281909 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.04084 | −0.257249 | −0.128625 | − | 0.991693i | \(-0.541056\pi\) | ||||
−0.128625 | + | 0.991693i | \(0.541056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.57911i | 0.178309i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 27.8889i | − 0.890423i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.16009 | −0.0688962 | −0.0344481 | − | 0.999406i | \(-0.510967\pi\) | ||||
−0.0344481 | + | 0.999406i | \(0.510967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2442 | −0.740622 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.21781i | 0.134254i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.02042i | 0.159640i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.1140 | 1.43309 | 0.716547 | − | 0.697538i | \(-0.245721\pi\) | ||||
0.716547 | + | 0.697538i | \(0.245721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.0613 | −1.23957 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.1154i | 0.384085i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 22.6703i | − 0.717976i | −0.933342 | − | 0.358988i | \(-0.883122\pi\) | ||||
0.933342 | − | 0.358988i | \(-0.116878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.9444 | −0.631014 |
(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.b.f.1121.2 | yes | 6 | |
4.3 | odd | 2 | 2240.2.b.e.1121.5 | yes | 6 | ||
8.3 | odd | 2 | 2240.2.b.e.1121.2 | ✓ | 6 | ||
8.5 | even | 2 | inner | 2240.2.b.f.1121.5 | yes | 6 | |
16.3 | odd | 4 | 8960.2.a.bk.1.1 | 3 | |||
16.5 | even | 4 | 8960.2.a.bn.1.1 | 3 | |||
16.11 | odd | 4 | 8960.2.a.bq.1.3 | 3 | |||
16.13 | even | 4 | 8960.2.a.bh.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.b.e.1121.2 | ✓ | 6 | 8.3 | odd | 2 | ||
2240.2.b.e.1121.5 | yes | 6 | 4.3 | odd | 2 | ||
2240.2.b.f.1121.2 | yes | 6 | 1.1 | even | 1 | trivial | |
2240.2.b.f.1121.5 | yes | 6 | 8.5 | even | 2 | inner | |
8960.2.a.bh.1.3 | 3 | 16.13 | even | 4 | |||
8960.2.a.bk.1.1 | 3 | 16.3 | odd | 4 | |||
8960.2.a.bn.1.1 | 3 | 16.5 | even | 4 | |||
8960.2.a.bq.1.3 | 3 | 16.11 | odd | 4 |