Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.7 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.e.881.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | 1.53225i | 0.461991i | 0.972955 | + | 0.230995i | \(0.0741982\pi\) | ||||
−0.972955 | + | 0.230995i | \(0.925802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.48236i | − 0.411133i | −0.978643 | − | 0.205567i | \(-0.934096\pi\) | ||||
0.978643 | − | 0.205567i | \(-0.0659037\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.42883 | −0.589077 | −0.294538 | − | 0.955640i | \(-0.595166\pi\) | ||||
−0.294538 | + | 0.955640i | \(0.595166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.86370i | 1.11581i | 0.829905 | + | 0.557905i | \(0.188395\pi\) | ||||
−0.829905 | + | 0.557905i | \(0.811605\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.53225 | −0.326677 | ||||||||
\(23\) | 0.267949i | 0.0558713i | 0.999610 | + | 0.0279356i | \(0.00889335\pi\) | ||||
−0.999610 | + | 0.0279356i | \(0.991107\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.48236 | 0.290715 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.898979i | 0.166936i | 0.996510 | + | 0.0834681i | \(0.0265997\pi\) | ||||
−0.996510 | + | 0.0834681i | \(0.973400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427i | 0.148790i | 0.997229 | + | 0.0743950i | \(0.0237025\pi\) | ||||
−0.997229 | + | 0.0743950i | \(0.976297\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 2.42883i | − 0.416540i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.48236 | −0.901295 | −0.450647 | − | 0.892702i | \(-0.648807\pi\) | ||||
−0.450647 | + | 0.892702i | \(0.648807\pi\) | |||||||
\(38\) | −4.86370 | −0.788997 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 1.00000i | − 0.158114i | ||||||||
\(41\) | −8.76028 | −1.36813 | −0.684063 | − | 0.729423i | \(-0.739789\pi\) | ||||
−0.684063 | + | 0.729423i | \(0.739789\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86370 | 0.284212 | 0.142106 | − | 0.989851i | \(-0.454613\pi\) | ||||
0.142106 | + | 0.989851i | \(0.454613\pi\) | |||||||
\(44\) | − 1.53225i | − 0.230995i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.267949 | −0.0395070 | ||||||||
\(47\) | 7.45946 | 1.08807 | 0.544037 | − | 0.839061i | \(-0.316895\pi\) | ||||
0.544037 | + | 0.839061i | \(0.316895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.48236i | 0.205567i | ||||||||
\(53\) | − 3.47015i | − 0.476662i | −0.971184 | − | 0.238331i | \(-0.923400\pi\) | ||||
0.971184 | − | 0.238331i | \(-0.0766004\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.53225i | 0.206609i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.898979 | −0.118042 | ||||||||
\(59\) | −6.25674 | −0.814558 | −0.407279 | − | 0.913304i | \(-0.633522\pi\) | ||||
−0.407279 | + | 0.913304i | \(0.633522\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.62158i | 0.847806i | 0.905708 | + | 0.423903i | \(0.139340\pi\) | ||||
−0.905708 | + | 0.423903i | \(0.860660\pi\) | |||||||
\(62\) | −0.828427 | −0.105210 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 1.48236i | − 0.183864i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0340 | 1.95887 | 0.979434 | − | 0.201763i | \(-0.0646671\pi\) | ||||
0.979434 | + | 0.201763i | \(0.0646671\pi\) | |||||||
\(68\) | 2.42883 | 0.294538 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7627i | 1.51465i | 0.653037 | + | 0.757326i | \(0.273495\pi\) | ||||
−0.653037 | + | 0.757326i | \(0.726505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.343146i | − 0.0401622i | −0.999798 | − | 0.0200811i | \(-0.993608\pi\) | ||||
0.999798 | − | 0.0200811i | \(-0.00639244\pi\) | |||||||
\(74\) | − 5.48236i | − 0.637312i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 4.86370i | − 0.557905i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4488 | −1.17558 | −0.587789 | − | 0.809014i | \(-0.700001\pi\) | ||||
−0.587789 | + | 0.809014i | \(0.700001\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 8.76028i | − 0.967411i | ||||||||
\(83\) | −5.45001 | −0.598216 | −0.299108 | − | 0.954219i | \(-0.596689\pi\) | ||||
−0.299108 | + | 0.954219i | \(0.596689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.42883 | −0.263443 | ||||||||
\(86\) | 1.86370i | 0.200968i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.53225 | 0.163338 | ||||||||
\(89\) | −15.9700 | −1.69282 | −0.846411 | − | 0.532531i | \(-0.821241\pi\) | ||||
−0.846411 | + | 0.532531i | \(0.821241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 0.267949i | − 0.0279356i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.45946i | 0.769384i | ||||||||
\(95\) | 4.86370i | 0.499005i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9481i | 1.51775i | 0.651234 | + | 0.758877i | \(0.274252\pi\) | ||||
−0.651234 | + | 0.758877i | \(0.725748\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 2.73545 | 0.272188 | 0.136094 | − | 0.990696i | \(-0.456545\pi\) | ||||
0.136094 | + | 0.990696i | \(0.456545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.17690i | − 0.608628i | −0.952572 | − | 0.304314i | \(-0.901573\pi\) | ||||
0.952572 | − | 0.304314i | \(-0.0984272\pi\) | |||||||
\(104\) | −1.48236 | −0.145358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.47015 | 0.337051 | ||||||||
\(107\) | 4.56993i | 0.441792i | 0.975297 | + | 0.220896i | \(0.0708981\pi\) | ||||
−0.975297 | + | 0.220896i | \(0.929102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.95867 | −0.570737 | −0.285369 | − | 0.958418i | \(-0.592116\pi\) | ||||
−0.285369 | + | 0.958418i | \(0.592116\pi\) | |||||||
\(110\) | −1.53225 | −0.146094 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.8977i | 1.87182i | 0.352237 | + | 0.935911i | \(0.385421\pi\) | ||||
−0.352237 | + | 0.935911i | \(0.614579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.267949i | 0.0249864i | ||||||||
\(116\) | − 0.898979i | − 0.0834681i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 6.25674i | − 0.575979i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.65221 | 0.786565 | ||||||||
\(122\) | −6.62158 | −0.599490 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 0.828427i | − 0.0743950i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.2025 | −1.88142 | −0.940708 | − | 0.339219i | \(-0.889837\pi\) | ||||
−0.940708 | + | 0.339219i | \(0.889837\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.48236 | 0.130012 | ||||||||
\(131\) | −7.46170 | −0.651932 | −0.325966 | − | 0.945382i | \(-0.605689\pi\) | ||||
−0.325966 | + | 0.945382i | \(0.605689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.0340i | 1.38513i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.42883i | 0.208270i | ||||||||
\(137\) | 0.621578i | 0.0531050i | 0.999647 | + | 0.0265525i | \(0.00845292\pi\) | ||||
−0.999647 | + | 0.0265525i | \(0.991547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 18.5334i | − 1.57198i | −0.618237 | − | 0.785992i | \(-0.712153\pi\) | ||||
0.618237 | − | 0.785992i | \(-0.287847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.7627 | −1.07102 | ||||||||
\(143\) | 2.27135 | 0.189940 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.898979i | 0.0746562i | ||||||||
\(146\) | 0.343146 | 0.0283989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.48236 | 0.450647 | ||||||||
\(149\) | 13.9834i | 1.14557i | 0.819707 | + | 0.572783i | \(0.194136\pi\) | ||||
−0.819707 | + | 0.572783i | \(0.805864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.6768 | 1.60127 | 0.800637 | − | 0.599149i | \(-0.204494\pi\) | ||||
0.800637 | + | 0.599149i | \(0.204494\pi\) | |||||||
\(152\) | 4.86370 | 0.394498 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.828427i | 0.0665409i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.06010i | 0.723075i | 0.932358 | + | 0.361538i | \(0.117748\pi\) | ||||
−0.932358 | + | 0.361538i | \(0.882252\pi\) | |||||||
\(158\) | − 10.4488i | − 0.831259i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8204 | 0.925844 | 0.462922 | − | 0.886399i | \(-0.346801\pi\) | ||||
0.462922 | + | 0.886399i | \(0.346801\pi\) | |||||||
\(164\) | 8.76028 | 0.684063 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 5.45001i | − 0.423002i | ||||||||
\(167\) | −15.7778 | −1.22092 | −0.610462 | − | 0.792046i | \(-0.709016\pi\) | ||||
−0.610462 | + | 0.792046i | \(0.709016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8026 | 0.830969 | ||||||||
\(170\) | − 2.42883i | − 0.186282i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.86370 | −0.142106 | ||||||||
\(173\) | −20.2221 | −1.53746 | −0.768730 | − | 0.639573i | \(-0.779111\pi\) | ||||
−0.768730 | + | 0.639573i | \(0.779111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.53225i | 0.115498i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 15.9700i | − 1.19701i | ||||||||
\(179\) | − 6.86662i | − 0.513235i | −0.966513 | − | 0.256618i | \(-0.917392\pi\) | ||||
0.966513 | − | 0.256618i | \(-0.0826081\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 16.3066i | − 1.21206i | −0.795441 | − | 0.606031i | \(-0.792761\pi\) | ||||
0.795441 | − | 0.606031i | \(-0.207239\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.267949 | 0.0197535 | ||||||||
\(185\) | −5.48236 | −0.403071 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.72157i | − 0.272148i | ||||||||
\(188\) | −7.45946 | −0.544037 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.86370 | −0.352850 | ||||||||
\(191\) | 17.1623i | 1.24182i | 0.783882 | + | 0.620910i | \(0.213237\pi\) | ||||
−0.783882 | + | 0.620910i | \(0.786763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.05521 | 0.651808 | 0.325904 | − | 0.945403i | \(-0.394331\pi\) | ||||
0.325904 | + | 0.945403i | \(0.394331\pi\) | |||||||
\(194\) | −14.9481 | −1.07321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.7379i | 1.54876i | 0.632720 | + | 0.774380i | \(0.281938\pi\) | ||||
−0.632720 | + | 0.774380i | \(0.718062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.32656i | 0.590254i | 0.955458 | + | 0.295127i | \(0.0953620\pi\) | ||||
−0.955458 | + | 0.295127i | \(0.904638\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.73545i | 0.192466i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.76028 | −0.611844 | ||||||||
\(206\) | 6.17690 | 0.430365 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1.48236i | − 0.102783i | ||||||||
\(209\) | −7.45241 | −0.515494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9330 | −1.37225 | −0.686123 | − | 0.727486i | \(-0.740689\pi\) | ||||
−0.686123 | + | 0.727486i | \(0.740689\pi\) | |||||||
\(212\) | 3.47015i | 0.238331i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.56993 | −0.312394 | ||||||||
\(215\) | 1.86370 | 0.127104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 5.95867i | − 0.403572i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 1.53225i | − 0.103304i | ||||||||
\(221\) | 3.60040i | 0.242189i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.16604i | − 0.479873i | −0.970789 | − | 0.239937i | \(-0.922873\pi\) | ||||
0.970789 | − | 0.239937i | \(-0.0771267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.8977 | −1.32358 | ||||||||
\(227\) | −15.8544 | −1.05229 | −0.526147 | − | 0.850393i | \(-0.676364\pi\) | ||||
−0.526147 | + | 0.850393i | \(0.676364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.2175i | 1.86466i | 0.361603 | + | 0.932332i | \(0.382230\pi\) | ||||
−0.361603 | + | 0.932332i | \(0.617770\pi\) | |||||||
\(230\) | −0.267949 | −0.0176680 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.898979 | 0.0590209 | ||||||||
\(233\) | 24.2973i | 1.59177i | 0.605447 | + | 0.795886i | \(0.292994\pi\) | ||||
−0.605447 | + | 0.795886i | \(0.707006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.45946 | 0.486601 | ||||||||
\(236\) | 6.25674 | 0.407279 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 19.9081i | − 1.28774i | −0.765133 | − | 0.643872i | \(-0.777327\pi\) | ||||
0.765133 | − | 0.643872i | \(-0.222673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 20.5254i | − 1.32216i | −0.750318 | − | 0.661078i | \(-0.770099\pi\) | ||||
0.750318 | − | 0.661078i | \(-0.229901\pi\) | |||||||
\(242\) | 8.65221i | 0.556185i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 6.62158i | − 0.423903i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.20977 | 0.458747 | ||||||||
\(248\) | 0.828427 | 0.0526052 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −5.86787 | −0.370376 | −0.185188 | − | 0.982703i | \(-0.559289\pi\) | ||||
−0.185188 | + | 0.982703i | \(0.559289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.410565 | −0.0258120 | ||||||||
\(254\) | − 21.2025i | − 1.33036i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.66166 | 0.477921 | 0.238961 | − | 0.971029i | \(-0.423193\pi\) | ||||
0.238961 | + | 0.971029i | \(0.423193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.48236i | 0.0919322i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 7.46170i | − 0.460985i | ||||||||
\(263\) | 8.46286i | 0.521842i | 0.965360 | + | 0.260921i | \(0.0840262\pi\) | ||||
−0.965360 | + | 0.260921i | \(0.915974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 3.47015i | − 0.213170i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.0340 | −0.979434 | ||||||||
\(269\) | −17.0431 | −1.03914 | −0.519568 | − | 0.854429i | \(-0.673907\pi\) | ||||
−0.519568 | + | 0.854429i | \(0.673907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 10.5359i | − 0.640010i | −0.947416 | − | 0.320005i | \(-0.896315\pi\) | ||||
0.947416 | − | 0.320005i | \(-0.103685\pi\) | |||||||
\(272\) | −2.42883 | −0.147269 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.621578 | −0.0375509 | ||||||||
\(275\) | 1.53225i | 0.0923981i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.09122 | −0.486154 | −0.243077 | − | 0.970007i | \(-0.578157\pi\) | ||||
−0.243077 | + | 0.970007i | \(0.578157\pi\) | |||||||
\(278\) | 18.5334 | 1.11156 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 11.1684i | − 0.666253i | −0.942882 | − | 0.333127i | \(-0.891896\pi\) | ||||
0.942882 | − | 0.333127i | \(-0.108104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.21592i | 0.428942i | 0.976730 | + | 0.214471i | \(0.0688028\pi\) | ||||
−0.976730 | + | 0.214471i | \(0.931197\pi\) | |||||||
\(284\) | − 12.7627i | − 0.757326i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.27135i | 0.134308i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1008 | −0.652989 | ||||||||
\(290\) | −0.898979 | −0.0527899 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.343146i | 0.0200811i | ||||||||
\(293\) | −18.2573 | −1.06660 | −0.533300 | − | 0.845926i | \(-0.679048\pi\) | ||||
−0.533300 | + | 0.845926i | \(0.679048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.25674 | −0.364281 | ||||||||
\(296\) | 5.48236i | 0.318656i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.9834 | −0.810037 | ||||||||
\(299\) | 0.397198 | 0.0229705 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.6768i | 1.13227i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.86370i | 0.278953i | ||||||||
\(305\) | 6.62158i | 0.379150i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.42078i | − 0.195234i | −0.995224 | − | 0.0976172i | \(-0.968878\pi\) | ||||
0.995224 | − | 0.0976172i | \(-0.0311221\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.828427 | −0.0470515 | ||||||||
\(311\) | −5.69089 | −0.322701 | −0.161350 | − | 0.986897i | \(-0.551585\pi\) | ||||
−0.161350 | + | 0.986897i | \(0.551585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 13.3467i | − 0.754401i | −0.926132 | − | 0.377200i | \(-0.876887\pi\) | ||||
0.926132 | − | 0.377200i | \(-0.123113\pi\) | |||||||
\(314\) | −9.06010 | −0.511291 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4488 | 0.587789 | ||||||||
\(317\) | 12.5266i | 0.703565i | 0.936082 | + | 0.351782i | \(0.114424\pi\) | ||||
−0.936082 | + | 0.351782i | \(0.885576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.37746 | −0.0771230 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 11.8131i | − 0.657298i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.48236i | − 0.0822266i | ||||||||
\(326\) | 11.8204i | 0.654670i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.76028i | 0.483705i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.28183 | −0.0704559 | −0.0352279 | − | 0.999379i | \(-0.511216\pi\) | ||||
−0.0352279 | + | 0.999379i | \(0.511216\pi\) | |||||||
\(332\) | 5.45001 | 0.299108 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 15.7778i | − 0.863323i | ||||||||
\(335\) | 16.0340 | 0.876033 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.1058 | −0.713920 | −0.356960 | − | 0.934120i | \(-0.616187\pi\) | ||||
−0.356960 | + | 0.934120i | \(0.616187\pi\) | |||||||
\(338\) | 10.8026i | 0.587584i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.42883 | 0.131722 | ||||||||
\(341\) | −1.26936 | −0.0687396 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 1.86370i | − 0.100484i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 20.2221i | − 1.08715i | ||||||||
\(347\) | 14.2852i | 0.766871i | 0.923568 | + | 0.383436i | \(0.125259\pi\) | ||||
−0.923568 | + | 0.383436i | \(0.874741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 13.2713i | − 0.710399i | −0.934791 | − | 0.355200i | \(-0.884413\pi\) | ||||
0.934791 | − | 0.355200i | \(-0.115587\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.53225 | −0.0816692 | ||||||||
\(353\) | 32.6463 | 1.73759 | 0.868794 | − | 0.495173i | \(-0.164895\pi\) | ||||
0.868794 | + | 0.495173i | \(0.164895\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.7627i | 0.677373i | ||||||||
\(356\) | 15.9700 | 0.846411 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.86662 | 0.362912 | ||||||||
\(359\) | − 6.24337i | − 0.329512i | −0.986334 | − | 0.164756i | \(-0.947316\pi\) | ||||
0.986334 | − | 0.164756i | \(-0.0526837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.65561 | −0.245032 | ||||||||
\(362\) | 16.3066 | 0.857057 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.343146i | − 0.0179611i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 12.5892i | − 0.657152i | −0.944478 | − | 0.328576i | \(-0.893431\pi\) | ||||
0.944478 | − | 0.328576i | \(-0.106569\pi\) | |||||||
\(368\) | 0.267949i | 0.0139678i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 5.48236i | − 0.285014i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.9583 | 1.86185 | 0.930924 | − | 0.365212i | \(-0.119004\pi\) | ||||
0.930924 | + | 0.365212i | \(0.119004\pi\) | |||||||
\(374\) | 3.72157 | 0.192438 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 7.45946i | − 0.384692i | ||||||||
\(377\) | 1.33261 | 0.0686331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.5899 | −0.595331 | −0.297666 | − | 0.954670i | \(-0.596208\pi\) | ||||
−0.297666 | + | 0.954670i | \(0.596208\pi\) | |||||||
\(380\) | − 4.86370i | − 0.249503i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.1623 | −0.878099 | ||||||||
\(383\) | 4.46750 | 0.228279 | 0.114139 | − | 0.993465i | \(-0.463589\pi\) | ||||
0.114139 | + | 0.993465i | \(0.463589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.05521i | 0.460898i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 14.9481i | − 0.758877i | ||||||||
\(389\) | − 12.9554i | − 0.656867i | −0.944527 | − | 0.328433i | \(-0.893479\pi\) | ||||
0.944527 | − | 0.328433i | \(-0.106521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 0.650802i | − 0.0329125i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.7379 | −1.09514 | ||||||||
\(395\) | −10.4488 | −0.525734 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.27991i | 0.465745i | 0.972507 | + | 0.232873i | \(0.0748125\pi\) | ||||
−0.972507 | + | 0.232873i | \(0.925187\pi\) | |||||||
\(398\) | −8.32656 | −0.417373 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.43927i | 0.371500i | 0.982597 | + | 0.185750i | \(0.0594714\pi\) | ||||
−0.982597 | + | 0.185750i | \(0.940529\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.22803 | 0.0611725 | ||||||||
\(404\) | −2.73545 | −0.136094 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 8.40035i | − 0.416390i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0096i | 0.791625i | 0.918331 | + | 0.395812i | \(0.129537\pi\) | ||||
−0.918331 | + | 0.395812i | \(0.870463\pi\) | |||||||
\(410\) | − 8.76028i | − 0.432639i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.17690i | 0.304314i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.45001 | −0.267530 | ||||||||
\(416\) | 1.48236 | 0.0726788 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 7.45241i | − 0.364509i | ||||||||
\(419\) | −28.4419 | −1.38948 | −0.694738 | − | 0.719263i | \(-0.744480\pi\) | ||||
−0.694738 | + | 0.719263i | \(0.744480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8345 | 0.869199 | 0.434600 | − | 0.900624i | \(-0.356890\pi\) | ||||
0.434600 | + | 0.900624i | \(0.356890\pi\) | |||||||
\(422\) | − 19.9330i | − 0.970324i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.47015 | −0.168526 | ||||||||
\(425\) | −2.42883 | −0.117815 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 4.56993i | − 0.220896i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.86370i | 0.0898758i | ||||||||
\(431\) | − 30.8927i | − 1.48805i | −0.668152 | − | 0.744025i | \(-0.732914\pi\) | ||||
0.668152 | − | 0.744025i | \(-0.267086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2207i | 0.731462i | 0.930721 | + | 0.365731i | \(0.119181\pi\) | ||||
−0.930721 | + | 0.365731i | \(0.880819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.95867 | 0.285369 | ||||||||
\(437\) | −1.30323 | −0.0623417 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3246i | 0.683674i | 0.939759 | + | 0.341837i | \(0.111049\pi\) | ||||
−0.939759 | + | 0.341837i | \(0.888951\pi\) | |||||||
\(440\) | 1.53225 | 0.0730472 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.60040 | −0.171253 | ||||||||
\(443\) | 5.15748i | 0.245039i | 0.992466 | + | 0.122520i | \(0.0390974\pi\) | ||||
−0.992466 | + | 0.122520i | \(0.960903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.9700 | −0.757053 | ||||||||
\(446\) | 7.16604 | 0.339322 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 19.9377i | − 0.940918i | −0.882422 | − | 0.470459i | \(-0.844088\pi\) | ||||
0.882422 | − | 0.470459i | \(-0.155912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 13.4229i | − 0.632061i | ||||||||
\(452\) | − 19.8977i | − 0.935911i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 15.8544i | − 0.744085i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3399 | 0.530459 | 0.265229 | − | 0.964185i | \(-0.414552\pi\) | ||||
0.265229 | + | 0.964185i | \(0.414552\pi\) | |||||||
\(458\) | −28.2175 | −1.31852 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 0.267949i | − 0.0124932i | ||||||||
\(461\) | −2.01890 | −0.0940298 | −0.0470149 | − | 0.998894i | \(-0.514971\pi\) | ||||
−0.0470149 | + | 0.998894i | \(0.514971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.2844 | −1.26801 | −0.634007 | − | 0.773327i | \(-0.718591\pi\) | ||||
−0.634007 | + | 0.773327i | \(0.718591\pi\) | |||||||
\(464\) | 0.898979i | 0.0417341i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2973 | −1.12555 | ||||||||
\(467\) | −0.692130 | −0.0320280 | −0.0160140 | − | 0.999872i | \(-0.505098\pi\) | ||||
−0.0160140 | + | 0.999872i | \(0.505098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.45946i | 0.344079i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.25674i | 0.287990i | ||||||||
\(473\) | 2.85566i | 0.131303i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.86370i | 0.223162i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.9081 | 0.910573 | ||||||||
\(479\) | −15.9081 | −0.726858 | −0.363429 | − | 0.931622i | \(-0.618394\pi\) | ||||
−0.363429 | + | 0.931622i | \(0.618394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.12684i | 0.370552i | ||||||||
\(482\) | 20.5254 | 0.934905 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.65221 | −0.393282 | ||||||||
\(485\) | 14.9481i | 0.678760i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.7498 | −1.30278 | −0.651390 | − | 0.758743i | \(-0.725814\pi\) | ||||
−0.651390 | + | 0.758743i | \(0.725814\pi\) | |||||||
\(488\) | 6.62158 | 0.299745 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.45753i | 0.246295i | 0.992388 | + | 0.123148i | \(0.0392988\pi\) | ||||
−0.992388 | + | 0.123148i | \(0.960701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.18346i | − 0.0983383i | ||||||||
\(494\) | 7.20977i | 0.324383i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.828427i | 0.0371975i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.86296 | −0.396760 | −0.198380 | − | 0.980125i | \(-0.563568\pi\) | ||||
−0.198380 | + | 0.980125i | \(0.563568\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 5.86787i | − 0.261896i | ||||||||
\(503\) | 9.36536 | 0.417581 | 0.208790 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208790 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.73545 | 0.121726 | ||||||||
\(506\) | − 0.410565i | − 0.0182518i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.2025 | 0.940708 | ||||||||
\(509\) | −35.0328 | −1.55280 | −0.776400 | − | 0.630240i | \(-0.782957\pi\) | ||||
−0.776400 | + | 0.630240i | \(0.782957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.66166i | 0.337941i | ||||||||
\(515\) | − 6.17690i | − 0.272187i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4298i | 0.502680i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.48236 | −0.0650059 | ||||||||
\(521\) | 19.9961 | 0.876047 | 0.438023 | − | 0.898964i | \(-0.355679\pi\) | ||||
0.438023 | + | 0.898964i | \(0.355679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 33.5029i | − 1.46498i | −0.680777 | − | 0.732491i | \(-0.738358\pi\) | ||||
0.680777 | − | 0.732491i | \(-0.261642\pi\) | |||||||
\(524\) | 7.46170 | 0.325966 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.46286 | −0.368998 | ||||||||
\(527\) | − 2.01210i | − 0.0876487i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9282 | 0.996878 | ||||||||
\(530\) | 3.47015 | 0.150734 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.9859i | 0.562482i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.56993i | 0.197575i | ||||||||
\(536\) | − 16.0340i | − 0.692565i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 17.0431i | − 0.734781i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7532 | 1.62314 | 0.811568 | − | 0.584258i | \(-0.198614\pi\) | ||||
0.811568 | + | 0.584258i | \(0.198614\pi\) | |||||||
\(542\) | 10.5359 | 0.452556 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 2.42883i | − 0.104135i | ||||||||
\(545\) | −5.95867 | −0.255241 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.07130 | 0.216833 | 0.108417 | − | 0.994106i | \(-0.465422\pi\) | ||||
0.108417 | + | 0.994106i | \(0.465422\pi\) | |||||||
\(548\) | − 0.621578i | − 0.0265525i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.53225 | −0.0653354 | ||||||||
\(551\) | −4.37237 | −0.186269 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 8.09122i | − 0.343763i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.5334i | 0.785992i | ||||||||
\(557\) | − 34.3556i | − 1.45569i | −0.685740 | − | 0.727846i | \(-0.740522\pi\) | ||||
0.685740 | − | 0.727846i | \(-0.259478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 2.76268i | − 0.116849i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.1684 | 0.471112 | ||||||||
\(563\) | 47.0586 | 1.98328 | 0.991641 | − | 0.129028i | \(-0.0411857\pi\) | ||||
0.991641 | + | 0.129028i | \(0.0411857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.8977i | 0.837104i | ||||||||
\(566\) | −7.21592 | −0.303308 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.7627 | 0.535510 | ||||||||
\(569\) | − 44.1869i | − 1.85241i | −0.377019 | − | 0.926206i | \(-0.623051\pi\) | ||||
0.377019 | − | 0.926206i | \(-0.376949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.1608 | 1.72253 | 0.861263 | − | 0.508159i | \(-0.169674\pi\) | ||||
0.861263 | + | 0.508159i | \(0.169674\pi\) | |||||||
\(572\) | −2.27135 | −0.0949699 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.267949i | 0.0111743i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 14.1212i | − 0.587872i | −0.955825 | − | 0.293936i | \(-0.905035\pi\) | ||||
0.955825 | − | 0.293936i | \(-0.0949653\pi\) | |||||||
\(578\) | − 11.1008i | − 0.461733i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 0.898979i | − 0.0373281i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.31714 | 0.220214 | ||||||||
\(584\) | −0.343146 | −0.0141995 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 18.2573i | − 0.754200i | ||||||||
\(587\) | 37.7819 | 1.55942 | 0.779712 | − | 0.626138i | \(-0.215365\pi\) | ||||
0.779712 | + | 0.626138i | \(0.215365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.02922 | −0.166021 | ||||||||
\(590\) | − 6.25674i | − 0.257586i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.48236 | −0.225324 | ||||||||
\(593\) | 26.1961 | 1.07575 | 0.537873 | − | 0.843026i | \(-0.319228\pi\) | ||||
0.537873 | + | 0.843026i | \(0.319228\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 13.9834i | − 0.572783i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.397198i | 0.0162426i | ||||||||
\(599\) | 4.80023i | 0.196132i | 0.995180 | + | 0.0980661i | \(0.0312657\pi\) | ||||
−0.995180 | + | 0.0980661i | \(0.968734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.3722i | 1.52444i | 0.647317 | + | 0.762221i | \(0.275891\pi\) | ||||
−0.647317 | + | 0.762221i | \(0.724109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.6768 | −0.800637 | ||||||||
\(605\) | 8.65221 | 0.351762 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2390i | 1.51148i | 0.654869 | + | 0.755742i | \(0.272724\pi\) | ||||
−0.654869 | + | 0.755742i | \(0.727276\pi\) | |||||||
\(608\) | −4.86370 | −0.197249 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.62158 | −0.268100 | ||||||||
\(611\) | − 11.0576i | − 0.447343i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.85954 | −0.398223 | −0.199112 | − | 0.979977i | \(-0.563806\pi\) | ||||
−0.199112 | + | 0.979977i | \(0.563806\pi\) | |||||||
\(614\) | 3.42078 | 0.138052 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3545i | 1.26229i | 0.775666 | + | 0.631143i | \(0.217414\pi\) | ||||
−0.775666 | + | 0.631143i | \(0.782586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2355i | 0.612366i | 0.951973 | + | 0.306183i | \(0.0990519\pi\) | ||||
−0.951973 | + | 0.306183i | \(0.900948\pi\) | |||||||
\(620\) | − 0.828427i | − 0.0332704i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 5.69089i | − 0.228184i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.3467 | 0.533442 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 9.06010i | − 0.361538i | ||||||||
\(629\) | 13.3157 | 0.530932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00406 | −0.0399710 | −0.0199855 | − | 0.999800i | \(-0.506362\pi\) | ||||
−0.0199855 | + | 0.999800i | \(0.506362\pi\) | |||||||
\(632\) | 10.4488i | 0.415629i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.5266 | −0.497495 | ||||||||
\(635\) | −21.2025 | −0.841394 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 1.37746i | − 0.0545342i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 1.00000i | − 0.0395285i | ||||||||
\(641\) | 23.4045i | 0.924423i | 0.886770 | + | 0.462211i | \(0.152944\pi\) | ||||
−0.886770 | + | 0.462211i | \(0.847056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.4475i | 1.31904i | 0.751686 | + | 0.659521i | \(0.229241\pi\) | ||||
−0.751686 | + | 0.659521i | \(0.770759\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.8131 | 0.464780 | ||||||||
\(647\) | 16.5708 | 0.651465 | 0.325733 | − | 0.945462i | \(-0.394389\pi\) | ||||
0.325733 | + | 0.945462i | \(0.394389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 9.58689i | − 0.376318i | ||||||||
\(650\) | 1.48236 | 0.0581430 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.8204 | −0.462922 | ||||||||
\(653\) | 6.02906i | 0.235935i | 0.993017 | + | 0.117968i | \(0.0376379\pi\) | ||||
−0.993017 | + | 0.117968i | \(0.962362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.46170 | −0.291553 | ||||||||
\(656\) | −8.76028 | −0.342031 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 36.3672i | − 1.41666i | −0.705880 | − | 0.708332i | \(-0.749448\pi\) | ||||
0.705880 | − | 0.708332i | \(-0.250552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.4349i | 0.444765i | 0.974959 | + | 0.222383i | \(0.0713834\pi\) | ||||
−0.974959 | + | 0.222383i | \(0.928617\pi\) | |||||||
\(662\) | − 1.28183i | − 0.0498198i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.45001i | 0.211501i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.240881 | −0.00932694 | ||||||||
\(668\) | 15.7778 | 0.610462 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.0340i | 0.619449i | ||||||||
\(671\) | −10.1459 | −0.391679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8070 | 0.416581 | 0.208290 | − | 0.978067i | \(-0.433210\pi\) | ||||
0.208290 | + | 0.978067i | \(0.433210\pi\) | |||||||
\(674\) | − 13.1058i | − 0.504818i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8026 | −0.415485 | ||||||||
\(677\) | −14.0456 | −0.539816 | −0.269908 | − | 0.962886i | \(-0.586993\pi\) | ||||
−0.269908 | + | 0.962886i | \(0.586993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.42883i | 0.0931412i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 1.26936i | − 0.0486062i | ||||||||
\(683\) | 36.4770i | 1.39575i | 0.716217 | + | 0.697877i | \(0.245872\pi\) | ||||
−0.716217 | + | 0.697877i | \(0.754128\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.621578i | 0.0237493i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.86370 | 0.0710530 | ||||||||
\(689\) | −5.14402 | −0.195972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 23.7673i | − 0.904150i | −0.891980 | − | 0.452075i | \(-0.850684\pi\) | ||||
0.891980 | − | 0.452075i | \(-0.149316\pi\) | |||||||
\(692\) | 20.2221 | 0.768730 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.2852 | −0.542260 | ||||||||
\(695\) | − 18.5334i | − 0.703012i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2772 | 0.805931 | ||||||||
\(698\) | 13.2713 | 0.502328 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.74502i | 0.0659086i | 0.999457 | + | 0.0329543i | \(0.0104916\pi\) | ||||
−0.999457 | + | 0.0329543i | \(0.989508\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 26.6646i | − 1.00567i | ||||||||
\(704\) | − 1.53225i | − 0.0577488i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.6463i | 1.22866i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.1232 | −0.455298 | −0.227649 | − | 0.973743i | \(-0.573104\pi\) | ||||
−0.227649 | + | 0.973743i | \(0.573104\pi\) | |||||||
\(710\) | −12.7627 | −0.478975 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.9700i | 0.598503i | ||||||||
\(713\) | −0.221976 | −0.00831308 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.27135 | 0.0849436 | ||||||||
\(716\) | 6.86662i | 0.256618i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.24337 | 0.233000 | ||||||||
\(719\) | 1.78635 | 0.0666197 | 0.0333098 | − | 0.999445i | \(-0.489395\pi\) | ||||
0.0333098 | + | 0.999445i | \(0.489395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 4.65561i | − 0.173264i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.3066i | 0.606031i | ||||||||
\(725\) | 0.898979i | 0.0333873i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 29.8785i | − 1.10813i | −0.832472 | − | 0.554066i | \(-0.813075\pi\) | ||||
0.832472 | − | 0.554066i | \(-0.186925\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.343146 | 0.0127004 | ||||||||
\(731\) | −4.52661 | −0.167423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13.7911i | − 0.509385i | −0.967022 | − | 0.254692i | \(-0.918026\pi\) | ||||
0.967022 | − | 0.254692i | \(-0.0819742\pi\) | |||||||
\(734\) | 12.5892 | 0.464677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.267949 | −0.00987674 | ||||||||
\(737\) | 24.5681i | 0.904979i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.36698 | 0.270999 | 0.135499 | − | 0.990777i | \(-0.456736\pi\) | ||||
0.135499 | + | 0.990777i | \(0.456736\pi\) | |||||||
\(740\) | 5.48236 | 0.201536 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 11.0774i | − 0.406389i | −0.979138 | − | 0.203194i | \(-0.934868\pi\) | ||||
0.979138 | − | 0.203194i | \(-0.0651323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.9834i | 0.512313i | ||||||||
\(746\) | 35.9583i | 1.31653i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.72157i | 0.136074i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3757 | 0.889483 | 0.444741 | − | 0.895659i | \(-0.353296\pi\) | ||||
0.444741 | + | 0.895659i | \(0.353296\pi\) | |||||||
\(752\) | 7.45946 | 0.272018 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.33261i | 0.0485309i | ||||||||
\(755\) | 19.6768 | 0.716112 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6761 | 0.715139 | 0.357569 | − | 0.933887i | \(-0.383606\pi\) | ||||
0.357569 | + | 0.933887i | \(0.383606\pi\) | |||||||
\(758\) | − 11.5899i | − 0.420963i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.86370 | 0.176425 | ||||||||
\(761\) | 49.8337 | 1.80647 | 0.903234 | − | 0.429147i | \(-0.141186\pi\) | ||||
0.903234 | + | 0.429147i | \(0.141186\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 17.1623i | − 0.620910i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.46750i | 0.161417i | ||||||||
\(767\) | 9.27475i | 0.334892i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0584i | 1.12000i | 0.828494 | + | 0.559998i | \(0.189198\pi\) | ||||
−0.828494 | + | 0.559998i | \(0.810802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.05521 | −0.325904 | ||||||||
\(773\) | 3.97049 | 0.142809 | 0.0714043 | − | 0.997447i | \(-0.477252\pi\) | ||||
0.0714043 | + | 0.997447i | \(0.477252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.828427i | 0.0297580i | ||||||||
\(776\) | 14.9481 | 0.536607 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.9554 | 0.464475 | ||||||||
\(779\) | − 42.6074i | − 1.52657i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.5556 | −0.699755 | ||||||||
\(782\) | 0.650802 | 0.0232726 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.06010i | 0.323369i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 44.8026i | − 1.59704i | −0.601969 | − | 0.798519i | \(-0.705617\pi\) | ||||
0.601969 | − | 0.798519i | \(-0.294383\pi\) | |||||||
\(788\) | − 21.7379i | − 0.774380i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 10.4488i | − 0.371750i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.81558 | 0.348561 | ||||||||
\(794\) | −9.27991 | −0.329332 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 8.32656i | − 0.295127i | ||||||||
\(797\) | 38.4813 | 1.36308 | 0.681539 | − | 0.731781i | \(-0.261311\pi\) | ||||
0.681539 | + | 0.731781i | \(0.261311\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.1177 | −0.640959 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.43927 | −0.262690 | ||||||||
\(803\) | 0.525785 | 0.0185546 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.22803i | 0.0432555i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 2.73545i | − 0.0962328i | ||||||||
\(809\) | 17.3550i | 0.610168i | 0.952326 | + | 0.305084i | \(0.0986845\pi\) | ||||
−0.952326 | + | 0.305084i | \(0.901316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 32.7270i | − 1.14920i | −0.818434 | − | 0.574601i | \(-0.805157\pi\) | ||||
0.818434 | − | 0.574601i | \(-0.194843\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.40035 | 0.294432 | ||||||||
\(815\) | 11.8204 | 0.414050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.06450i | 0.317127i | ||||||||
\(818\) | −16.0096 | −0.559763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.76028 | 0.305922 | ||||||||
\(821\) | − 17.7932i | − 0.620985i | −0.950576 | − | 0.310493i | \(-0.899506\pi\) | ||||
0.950576 | − | 0.310493i | \(-0.100494\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.82165 | 0.342361 | 0.171181 | − | 0.985240i | \(-0.445242\pi\) | ||||
0.171181 | + | 0.985240i | \(0.445242\pi\) | |||||||
\(824\) | −6.17690 | −0.215182 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 7.78482i | − 0.270705i | −0.990798 | − | 0.135352i | \(-0.956783\pi\) | ||||
0.990798 | − | 0.135352i | \(-0.0432167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.1283i | 0.525426i | 0.964874 | + | 0.262713i | \(0.0846172\pi\) | ||||
−0.964874 | + | 0.262713i | \(0.915383\pi\) | |||||||
\(830\) | − 5.45001i | − 0.189172i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.48236i | 0.0513917i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.7778 | −0.546014 | ||||||||
\(836\) | 7.45241 | 0.257747 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 28.4419i | − 0.982508i | ||||||||
\(839\) | 25.2077 | 0.870265 | 0.435133 | − | 0.900366i | \(-0.356701\pi\) | ||||
0.435133 | + | 0.900366i | \(0.356701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1918 | 0.972132 | ||||||||
\(842\) | 17.8345i | 0.614617i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.9330 | 0.686123 | ||||||||
\(845\) | 10.8026 | 0.371621 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 3.47015i | − 0.119166i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 2.42883i | − 0.0833080i | ||||||||
\(851\) | − 1.46899i | − 0.0503565i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3020i | 0.797846i | 0.916984 | + | 0.398923i | \(0.130616\pi\) | ||||
−0.916984 | + | 0.398923i | \(0.869384\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.56993 | 0.156197 | ||||||||
\(857\) | −26.6060 | −0.908842 | −0.454421 | − | 0.890787i | \(-0.650154\pi\) | ||||
−0.454421 | + | 0.890787i | \(0.650154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.5854i | 1.93067i | 0.261017 | + | 0.965334i | \(0.415942\pi\) | ||||
−0.261017 | + | 0.965334i | \(0.584058\pi\) | |||||||
\(860\) | −1.86370 | −0.0635518 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.8927 | 1.05221 | ||||||||
\(863\) | 34.0566i | 1.15930i | 0.814865 | + | 0.579650i | \(0.196811\pi\) | ||||
−0.814865 | + | 0.579650i | \(0.803189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.2221 | −0.687573 | ||||||||
\(866\) | −15.2207 | −0.517222 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 16.0101i | − 0.543106i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 23.7682i | − 0.805356i | ||||||||
\(872\) | 5.95867i | 0.201786i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 1.30323i | − 0.0440823i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1382 | 0.815089 | 0.407545 | − | 0.913185i | \(-0.366385\pi\) | ||||
0.407545 | + | 0.913185i | \(0.366385\pi\) | |||||||
\(878\) | −14.3246 | −0.483431 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.53225i | 0.0516521i | ||||||||
\(881\) | −37.2609 | −1.25535 | −0.627676 | − | 0.778475i | \(-0.715994\pi\) | ||||
−0.627676 | + | 0.778475i | \(0.715994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.5544 | 1.63398 | 0.816992 | − | 0.576648i | \(-0.195640\pi\) | ||||
0.816992 | + | 0.576648i | \(0.195640\pi\) | |||||||
\(884\) | − 3.60040i | − 0.121094i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.15748 | −0.173269 | ||||||||
\(887\) | 17.4709 | 0.586615 | 0.293308 | − | 0.956018i | \(-0.405244\pi\) | ||||
0.293308 | + | 0.956018i | \(0.405244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 15.9700i | − 0.535317i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.16604i | 0.239937i | ||||||||
\(893\) | 36.2806i | 1.21408i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 6.86662i | − 0.229526i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.9377 | 0.665329 | ||||||||
\(899\) | −0.744739 | −0.0248384 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.42840i | 0.280791i | ||||||||
\(902\) | 13.4229 | 0.446935 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.8977 | 0.661789 | ||||||||
\(905\) | − 16.3066i | − 0.542051i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.4520 | −0.712302 | −0.356151 | − | 0.934428i | \(-0.615911\pi\) | ||||
−0.356151 | + | 0.934428i | \(0.615911\pi\) | |||||||
\(908\) | 15.8544 | 0.526147 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 42.2281i | − 1.39908i | −0.714593 | − | 0.699540i | \(-0.753388\pi\) | ||||
0.714593 | − | 0.699540i | \(-0.246612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 8.35077i | − 0.276370i | ||||||||
\(914\) | 11.3399i | 0.375091i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 28.2175i | − 0.932332i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.1631 | −1.85265 | −0.926325 | − | 0.376726i | \(-0.877050\pi\) | ||||
−0.926325 | + | 0.376726i | \(0.877050\pi\) | |||||||
\(920\) | 0.267949 | 0.00883402 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 2.01890i | − 0.0664891i | ||||||||
\(923\) | 18.9189 | 0.622724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.48236 | −0.180259 | ||||||||
\(926\) | − 27.2844i | − 0.896621i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.898979 | −0.0295104 | ||||||||
\(929\) | −18.5388 | −0.608239 | −0.304120 | − | 0.952634i | \(-0.598362\pi\) | ||||
−0.304120 | + | 0.952634i | \(0.598362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 24.2973i | − 0.795886i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 0.692130i | − 0.0226472i | ||||||||
\(935\) | − 3.72157i | − 0.121708i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.5337i | 1.29151i | 0.763545 | + | 0.645755i | \(0.223457\pi\) | ||||
−0.763545 | + | 0.645755i | \(0.776543\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.45946 | −0.243301 | ||||||||
\(941\) | −50.4949 | −1.64609 | −0.823043 | − | 0.567979i | \(-0.807726\pi\) | ||||
−0.823043 | + | 0.567979i | \(0.807726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.34731i | − 0.0764389i | ||||||||
\(944\) | −6.25674 | −0.203639 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.85566 | −0.0928455 | ||||||||
\(947\) | − 39.1628i | − 1.27262i | −0.771433 | − | 0.636310i | \(-0.780460\pi\) | ||||
0.771433 | − | 0.636310i | \(-0.219540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.508666 | −0.0165120 | ||||||||
\(950\) | −4.86370 | −0.157799 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 52.9933i | − 1.71662i | −0.513130 | − | 0.858311i | \(-0.671514\pi\) | ||||
0.513130 | − | 0.858311i | \(-0.328486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.1623i | 0.555358i | ||||||||
\(956\) | 19.9081i | 0.643872i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 15.9081i | − 0.513966i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3137 | 0.977862 | ||||||||
\(962\) | −8.12684 | −0.262020 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.5254i | 0.661078i | ||||||||
\(965\) | 9.05521 | 0.291498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6208 | 0.984700 | 0.492350 | − | 0.870397i | \(-0.336138\pi\) | ||||
0.492350 | + | 0.870397i | \(0.336138\pi\) | |||||||
\(968\) | − 8.65221i | − 0.278093i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.9481 | −0.479956 | ||||||||
\(971\) | −12.0710 | −0.387376 | −0.193688 | − | 0.981063i | \(-0.562045\pi\) | ||||
−0.193688 | + | 0.981063i | \(0.562045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 28.7498i | − 0.921205i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.62158i | 0.211952i | ||||||||
\(977\) | 11.2328i | 0.359370i | 0.983724 | + | 0.179685i | \(0.0575079\pi\) | ||||
−0.983724 | + | 0.179685i | \(0.942492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 24.4701i | − 0.782068i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.45753 | −0.174157 | ||||||||
\(983\) | 22.7921 | 0.726954 | 0.363477 | − | 0.931603i | \(-0.381590\pi\) | ||||
0.363477 | + | 0.931603i | \(0.381590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.7379i | 0.692627i | ||||||||
\(986\) | 2.18346 | 0.0695357 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.20977 | −0.229373 | ||||||||
\(989\) | 0.499378i | 0.0158793i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.82113 | −0.280212 | −0.140106 | − | 0.990136i | \(-0.544744\pi\) | ||||
−0.140106 | + | 0.990136i | \(0.544744\pi\) | |||||||
\(992\) | −0.828427 | −0.0263026 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.32656i | 0.263970i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.4763i | 1.47192i | 0.677026 | + | 0.735960i | \(0.263269\pi\) | ||||
−0.677026 | + | 0.735960i | \(0.736731\pi\) | |||||||
\(998\) | − 8.86296i | − 0.280552i | ||||||||
\(999\) | 0 | 0 |
(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 | 4410.2.b.e.881.7 | 8 | ||
3.2 | odd | 2 | 4410.2.b.b.881.2 | 8 | |||
7.2 | even | 3 | 630.2.be.a.521.4 | yes | 8 | ||
7.3 | odd | 6 | 630.2.be.b.341.2 | yes | 8 | ||
7.6 | odd | 2 | 4410.2.b.b.881.7 | 8 | |||
21.2 | odd | 6 | 630.2.be.b.521.2 | yes | 8 | ||
21.17 | even | 6 | 630.2.be.a.341.4 | ✓ | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.e.881.2 | 8 | ||
35.2 | odd | 12 | 3150.2.bp.d.899.3 | 8 | |||
35.3 | even | 12 | 3150.2.bp.c.1349.3 | 8 | |||
35.9 | even | 6 | 3150.2.bf.b.1151.1 | 8 | |||
35.17 | even | 12 | 3150.2.bp.f.1349.2 | 8 | |||
35.23 | odd | 12 | 3150.2.bp.a.899.2 | 8 | |||
35.24 | odd | 6 | 3150.2.bf.c.1601.3 | 8 | |||
105.2 | even | 12 | 3150.2.bp.c.899.3 | 8 | |||
105.17 | odd | 12 | 3150.2.bp.a.1349.2 | 8 | |||
105.23 | even | 12 | 3150.2.bp.f.899.2 | 8 | |||
105.38 | odd | 12 | 3150.2.bp.d.1349.3 | 8 | |||
105.44 | odd | 6 | 3150.2.bf.c.1151.3 | 8 | |||
105.59 | even | 6 | 3150.2.bf.b.1601.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.4 | ✓ | 8 | 21.17 | even | 6 | ||
630.2.be.a.521.4 | yes | 8 | 7.2 | even | 3 | ||
630.2.be.b.341.2 | yes | 8 | 7.3 | odd | 6 | ||
630.2.be.b.521.2 | yes | 8 | 21.2 | odd | 6 | ||
3150.2.bf.b.1151.1 | 8 | 35.9 | even | 6 | |||
3150.2.bf.b.1601.1 | 8 | 105.59 | even | 6 | |||
3150.2.bf.c.1151.3 | 8 | 105.44 | odd | 6 | |||
3150.2.bf.c.1601.3 | 8 | 35.24 | odd | 6 | |||
3150.2.bp.a.899.2 | 8 | 35.23 | odd | 12 | |||
3150.2.bp.a.1349.2 | 8 | 105.17 | odd | 12 | |||
3150.2.bp.c.899.3 | 8 | 105.2 | even | 12 | |||
3150.2.bp.c.1349.3 | 8 | 35.3 | even | 12 | |||
3150.2.bp.d.899.3 | 8 | 35.2 | odd | 12 | |||
3150.2.bp.d.1349.3 | 8 | 105.38 | odd | 12 | |||
3150.2.bp.f.899.2 | 8 | 105.23 | even | 12 | |||
3150.2.bp.f.1349.2 | 8 | 35.17 | even | 12 | |||
4410.2.b.b.881.2 | 8 | 3.2 | odd | 2 | |||
4410.2.b.b.881.7 | 8 | 7.6 | odd | 2 | |||
4410.2.b.e.881.2 | 8 | 21.20 | even | 2 | inner | ||
4410.2.b.e.881.7 | 8 | 1.1 | even | 1 | trivial |