Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1567,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, 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("1764.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.1 | ||
Root | \(-0.895644 - 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1567 |
Dual form | 1764.2.b.b.1567.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 1.32288i | −0.353553 | − | 0.935414i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.50000 | + | 1.32288i | −0.750000 | + | 0.661438i | ||||
\(5\) | − | 1.73205i | − | 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.50000 | + | 1.32288i | 0.883883 | + | 0.467707i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.29129 | + | 0.866025i | −0.724569 | + | 0.273861i | ||||
\(11\) | 2.64575i | 0.797724i | 0.917011 | + | 0.398862i | \(0.130595\pi\) | ||||
−0.917011 | + | 0.398862i | \(0.869405\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 3.96863i | 0.125000 | − | 0.992157i | ||||
\(17\) | 6.92820i | 1.68034i | 0.542326 | + | 0.840168i | \(0.317544\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 2.29129 | + | 2.59808i | 0.512348 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.50000 | − | 1.32288i | 0.746203 | − | 0.282038i | ||||
\(23\) | 5.29150i | 1.10335i | 0.834058 | + | 0.551677i | \(0.186012\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | −4.58258 | + | 1.73205i | −0.898717 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58258 | −0.823055 | −0.411527 | − | 0.911397i | \(-0.635005\pi\) | ||||
−0.411527 | + | 0.911397i | \(0.635005\pi\) | |||||||
\(32\) | −5.50000 | + | 1.32288i | −0.972272 | + | 0.233854i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.16515 | − | 3.46410i | 1.57181 | − | 0.594089i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.29129 | − | 4.33013i | 0.362284 | − | 0.684653i | ||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5830i | 1.61389i | 0.590624 | + | 0.806947i | \(0.298881\pi\) | ||||
−0.590624 | + | 0.806947i | \(0.701119\pi\) | |||||||
\(44\) | −3.50000 | − | 3.96863i | −0.527645 | − | 0.598293i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.00000 | − | 2.64575i | 1.03209 | − | 0.390095i | ||||
\(47\) | 9.16515 | 1.33687 | 0.668437 | − | 0.743768i | \(-0.266963\pi\) | ||||
0.668437 | + | 0.743768i | \(0.266963\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | − | 2.64575i | −0.141421 | − | 0.374166i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.58258 | + | 5.19615i | 0.635489 | + | 0.720577i | ||||
\(53\) | −7.00000 | −0.961524 | −0.480762 | − | 0.876851i | \(-0.659640\pi\) | ||||
−0.480762 | + | 0.876851i | \(0.659640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.58258 | 0.617914 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | + | 6.61438i | 0.328266 | + | 0.868510i | ||||
\(59\) | 13.7477 | 1.78980 | 0.894901 | − | 0.446265i | \(-0.147246\pi\) | ||||
0.894901 | + | 0.446265i | \(0.147246\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.3923i | − | 1.33060i | −0.746577 | − | 0.665299i | \(-0.768304\pi\) | ||
0.746577 | − | 0.665299i | \(-0.231696\pi\) | |||||||
\(62\) | 2.29129 | + | 6.06218i | 0.290994 | + | 0.769897i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.50000 | + | 6.61438i | 0.562500 | + | 0.826797i | ||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | −9.16515 | − | 10.3923i | −1.11144 | − | 1.26025i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.29150i | 0.627986i | 0.949425 | + | 0.313993i | \(0.101667\pi\) | ||||
−0.949425 | + | 0.313993i | \(0.898333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.93725i | 0.893011i | 0.894781 | + | 0.446505i | \(0.147332\pi\) | ||||
−0.894781 | + | 0.446505i | \(0.852668\pi\) | |||||||
\(80\) | −6.87386 | − | 0.866025i | −0.768521 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.58258 | − | 1.73205i | 0.506061 | − | 0.191273i | ||||
\(83\) | −4.58258 | −0.503003 | −0.251502 | − | 0.967857i | \(-0.580924\pi\) | ||||
−0.251502 | + | 0.967857i | \(0.580924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 14.0000 | − | 5.29150i | 1.50966 | − | 0.570597i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.50000 | + | 6.61438i | −0.373101 | + | 0.705095i | ||||
\(89\) | 10.3923i | 1.10158i | 0.834643 | + | 0.550791i | \(0.185674\pi\) | ||||
−0.834643 | + | 0.550791i | \(0.814326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.00000 | − | 7.93725i | −0.729800 | − | 0.827516i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.58258 | − | 12.1244i | −0.472657 | − | 1.25053i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.66025i | − | 0.879316i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) | ||
0.898165 | − | 0.439658i | \(-0.144900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 2.64575i | −0.300000 | + | 0.264575i | ||||
\(101\) | − | 6.92820i | − | 0.689382i | −0.938716 | − | 0.344691i | \(-0.887984\pi\) | ||
0.938716 | − | 0.344691i | \(-0.112016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3303 | 1.80614 | 0.903069 | − | 0.429495i | \(-0.141308\pi\) | ||||
0.903069 | + | 0.429495i | \(0.141308\pi\) | |||||||
\(104\) | 4.58258 | − | 8.66025i | 0.449359 | − | 0.849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.50000 | + | 9.26013i | 0.339950 | + | 0.899423i | ||||
\(107\) | 18.5203i | 1.79042i | 0.445644 | + | 0.895211i | \(0.352975\pi\) | ||||
−0.445644 | + | 0.895211i | \(0.647025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | −2.29129 | − | 6.06218i | −0.218466 | − | 0.578006i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.16515 | 0.854655 | ||||||||
\(116\) | 7.50000 | − | 6.61438i | 0.696358 | − | 0.614130i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.87386 | − | 18.1865i | −0.632790 | − | 1.67421i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.00000 | 0.363636 | ||||||||
\(122\) | −13.7477 | + | 5.19615i | −1.24466 | + | 0.470438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.87386 | − | 6.06218i | 0.617291 | − | 0.544400i | ||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.93725i | − | 0.704317i | −0.935940 | − | 0.352159i | \(-0.885448\pi\) | ||
0.935940 | − | 0.352159i | \(-0.114552\pi\) | |||||||
\(128\) | 6.50000 | − | 9.26013i | 0.574524 | − | 0.818488i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.00000 | + | 7.93725i | 0.263117 | + | 0.696143i | ||||
\(131\) | 13.7477 | 1.20114 | 0.600572 | − | 0.799570i | \(-0.294939\pi\) | ||||
0.600572 | + | 0.799570i | \(0.294939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.16515 | + | 17.3205i | −0.785905 | + | 1.48522i | ||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.16515 | 0.777378 | 0.388689 | − | 0.921369i | \(-0.372928\pi\) | ||||
0.388689 | + | 0.921369i | \(0.372928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.00000 | − | 2.64575i | 0.587427 | − | 0.222027i | ||||
\(143\) | 9.16515 | 0.766428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.66025i | 0.719195i | ||||||||
\(146\) | 9.16515 | − | 3.46410i | 0.758513 | − | 0.286691i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2288i | 1.07654i | 0.842772 | + | 0.538270i | \(0.180922\pi\) | ||||
−0.842772 | + | 0.538270i | \(0.819078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.93725i | 0.637536i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.92820i | − | 0.552931i | −0.961024 | − | 0.276465i | \(-0.910837\pi\) | ||
0.961024 | − | 0.276465i | \(-0.0891631\pi\) | |||||||
\(158\) | 10.5000 | − | 3.96863i | 0.835335 | − | 0.315727i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.29129 | + | 9.52628i | 0.181142 | + | 0.753119i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.8745i | − | 1.24339i | −0.783260 | − | 0.621694i | \(-0.786445\pi\) | ||
0.783260 | − | 0.621694i | \(-0.213555\pi\) | |||||||
\(164\) | −4.58258 | − | 5.19615i | −0.357839 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.29129 | + | 6.06218i | 0.177838 | + | 0.470516i | ||||
\(167\) | −18.3303 | −1.41844 | −0.709221 | − | 0.704987i | \(-0.750953\pi\) | ||||
−0.709221 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −6.00000 | − | 15.8745i | −0.460179 | − | 1.21752i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.0000 | − | 15.8745i | −1.06749 | − | 1.21042i | ||||
\(173\) | 13.8564i | 1.05348i | 0.850026 | + | 0.526742i | \(0.176586\pi\) | ||||
−0.850026 | + | 0.526742i | \(0.823414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.5000 | + | 1.32288i | 0.791467 | + | 0.0997155i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.7477 | − | 5.19615i | 1.03044 | − | 0.389468i | ||||
\(179\) | 5.29150i | 0.395505i | 0.980252 | + | 0.197753i | \(0.0633643\pi\) | ||||
−0.980252 | + | 0.197753i | \(0.936636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.00000 | + | 13.2288i | −0.516047 | + | 0.975237i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.3303 | −1.34044 | ||||||||
\(188\) | −13.7477 | + | 12.1244i | −1.00266 | + | 0.884260i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5830i | 0.765759i | 0.923798 | + | 0.382880i | \(0.125068\pi\) | ||||
−0.923798 | + | 0.382880i | \(0.874932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.00000 | 0.215945 | 0.107972 | − | 0.994154i | \(-0.465564\pi\) | ||||
0.107972 | + | 0.994154i | \(0.465564\pi\) | |||||||
\(194\) | −11.4564 | + | 4.33013i | −0.822524 | + | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0000 | −0.997459 | −0.498729 | − | 0.866758i | \(-0.666200\pi\) | ||||
−0.498729 | + | 0.866758i | \(0.666200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3303 | −1.29940 | −0.649700 | − | 0.760190i | \(-0.725106\pi\) | ||||
−0.649700 | + | 0.760190i | \(0.725106\pi\) | |||||||
\(200\) | 5.00000 | + | 2.64575i | 0.353553 | + | 0.187083i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.16515 | + | 3.46410i | −0.644858 | + | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | −9.16515 | − | 24.2487i | −0.638566 | − | 1.68949i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.7477 | − | 1.73205i | −0.953233 | − | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.29150i | 0.364282i | 0.983272 | + | 0.182141i | \(0.0583027\pi\) | ||||
−0.983272 | + | 0.182141i | \(0.941697\pi\) | |||||||
\(212\) | 10.5000 | − | 9.26013i | 0.721143 | − | 0.635988i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.5000 | − | 9.26013i | 1.67479 | − | 0.633009i | ||||
\(215\) | 18.3303 | 1.25012 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.87386 | + | 6.06218i | −0.463436 | + | 0.408712i | ||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.58258 | 0.306872 | 0.153436 | − | 0.988159i | \(-0.450966\pi\) | ||||
0.153436 | + | 0.988159i | \(0.450966\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.00000 | − | 18.5203i | −0.465633 | − | 1.23195i | ||||
\(227\) | −4.58258 | −0.304156 | −0.152078 | − | 0.988368i | \(-0.548597\pi\) | ||||
−0.152078 | + | 0.988368i | \(0.548597\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3923i | − | 0.686743i | −0.939200 | − | 0.343371i | \(-0.888431\pi\) | ||
0.939200 | − | 0.343371i | \(-0.111569\pi\) | |||||||
\(230\) | −4.58258 | − | 12.1244i | −0.302166 | − | 0.799456i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.5000 | − | 6.61438i | −0.820665 | − | 0.434255i | ||||
\(233\) | 20.0000 | 1.31024 | 0.655122 | − | 0.755523i | \(-0.272617\pi\) | ||||
0.655122 | + | 0.755523i | \(0.272617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 15.8745i | − | 1.03554i | ||||||
\(236\) | −20.6216 | + | 18.1865i | −1.34235 | + | 1.18384i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.29150i | − | 0.342279i | −0.985247 | − | 0.171139i | \(-0.945255\pi\) | ||
0.985247 | − | 0.171139i | \(-0.0547449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.19615i | 0.334714i | 0.985896 | + | 0.167357i | \(0.0535232\pi\) | ||||
−0.985896 | + | 0.167357i | \(0.946477\pi\) | |||||||
\(242\) | −2.00000 | − | 5.29150i | −0.128565 | − | 0.340151i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.7477 | + | 15.5885i | 0.880108 | + | 0.997949i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.4564 | − | 6.06218i | −0.727485 | − | 0.384949i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.0390 | + | 6.06218i | −1.01440 | + | 0.383406i | ||||
\(251\) | 4.58258 | 0.289250 | 0.144625 | − | 0.989487i | \(-0.453802\pi\) | ||||
0.144625 | + | 0.989487i | \(0.453802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0000 | −0.880172 | ||||||||
\(254\) | −10.5000 | + | 3.96863i | −0.658829 | + | 0.249014i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | − | 3.96863i | −0.968750 | − | 0.248039i | ||||
\(257\) | − | 10.3923i | − | 0.648254i | −0.946014 | − | 0.324127i | \(-0.894929\pi\) | ||
0.946014 | − | 0.324127i | \(-0.105071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.00000 | − | 7.93725i | 0.558156 | − | 0.492248i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.87386 | − | 18.1865i | −0.424669 | − | 1.12357i | ||||
\(263\) | − | 10.5830i | − | 0.652576i | −0.945270 | − | 0.326288i | \(-0.894202\pi\) | ||
0.945270 | − | 0.326288i | \(-0.105798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1244i | 0.744793i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.0526i | 1.16166i | 0.814027 | + | 0.580828i | \(0.197271\pi\) | ||||
−0.814027 | + | 0.580828i | \(0.802729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.7477 | −0.835115 | −0.417557 | − | 0.908651i | \(-0.637114\pi\) | ||||
−0.417557 | + | 0.908651i | \(0.637114\pi\) | |||||||
\(272\) | 27.4955 | + | 3.46410i | 1.66716 | + | 0.210042i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | − | 5.29150i | −0.120824 | − | 0.319671i | ||||
\(275\) | 5.29150i | 0.319090i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | −0.240337 | −0.120168 | − | 0.992754i | \(-0.538343\pi\) | ||||
−0.120168 | + | 0.992754i | \(0.538343\pi\) | |||||||
\(278\) | −4.58258 | − | 12.1244i | −0.274845 | − | 0.727171i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.0000 | −0.954480 | −0.477240 | − | 0.878773i | \(-0.658363\pi\) | ||||
−0.477240 | + | 0.878773i | \(0.658363\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3303 | 1.08962 | 0.544812 | − | 0.838558i | \(-0.316601\pi\) | ||||
0.544812 | + | 0.838558i | \(0.316601\pi\) | |||||||
\(284\) | −7.00000 | − | 7.93725i | −0.415374 | − | 0.470989i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.58258 | − | 12.1244i | −0.270973 | − | 0.716928i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0000 | −1.82353 | ||||||||
\(290\) | 11.4564 | − | 4.33013i | 0.672745 | − | 0.254274i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.16515 | − | 10.3923i | −0.536350 | − | 0.608164i | ||||
\(293\) | − | 15.5885i | − | 0.910687i | −0.890316 | − | 0.455344i | \(-0.849516\pi\) | ||
0.890316 | − | 0.455344i | \(-0.150484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 23.8118i | − | 1.38637i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.00000 | + | 18.5203i | 0.405499 | + | 1.07285i | ||||
\(299\) | 18.3303 | 1.06007 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.5000 | − | 6.61438i | 1.00701 | − | 0.380615i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.0000 | −1.03068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.4955 | −1.56925 | −0.784624 | − | 0.619972i | \(-0.787144\pi\) | ||||
−0.784624 | + | 0.619972i | \(0.787144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.5000 | − | 3.96863i | 0.596360 | − | 0.225403i | ||||
\(311\) | 9.16515 | 0.519708 | 0.259854 | − | 0.965648i | \(-0.416326\pi\) | ||||
0.259854 | + | 0.965648i | \(0.416326\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.5167i | 1.27272i | 0.771393 | + | 0.636358i | \(0.219560\pi\) | ||||
−0.771393 | + | 0.636358i | \(0.780440\pi\) | |||||||
\(314\) | −9.16515 | + | 3.46410i | −0.517219 | + | 0.195491i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5000 | − | 11.9059i | −0.590671 | − | 0.669758i | ||||
\(317\) | −7.00000 | −0.393159 | −0.196580 | − | 0.980488i | \(-0.562983\pi\) | ||||
−0.196580 | + | 0.980488i | \(0.562983\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 13.2288i | − | 0.740668i | ||||||
\(320\) | 11.4564 | − | 7.79423i | 0.640434 | − | 0.435711i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.92820i | − | 0.384308i | ||||||
\(326\) | −21.0000 | + | 7.93725i | −1.16308 | + | 0.439604i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.58258 | + | 8.66025i | −0.253030 | + | 0.478183i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5830i | 0.581695i | 0.956769 | + | 0.290847i | \(0.0939372\pi\) | ||||
−0.956769 | + | 0.290847i | \(0.906063\pi\) | |||||||
\(332\) | 6.87386 | − | 6.06218i | 0.377252 | − | 0.332705i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.16515 | + | 24.2487i | 0.501495 | + | 1.32683i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0000 | −1.14394 | −0.571971 | − | 0.820274i | \(-0.693821\pi\) | ||||
−0.571971 | + | 0.820274i | \(0.693821\pi\) | |||||||
\(338\) | −0.500000 | − | 1.32288i | −0.0271964 | − | 0.0719549i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −18.0000 | + | 15.8745i | −0.976187 | + | 0.860916i | ||||
\(341\) | − | 12.1244i | − | 0.656571i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −14.0000 | + | 26.4575i | −0.754829 | + | 1.42649i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.3303 | − | 6.92820i | 0.985443 | − | 0.372463i | ||||
\(347\) | 5.29150i | 0.284063i | 0.989862 | + | 0.142031i | \(0.0453634\pi\) | ||||
−0.989862 | + | 0.142031i | \(0.954637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7846i | 1.11257i | 0.830990 | + | 0.556287i | \(0.187775\pi\) | ||||
−0.830990 | + | 0.556287i | \(0.812225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.50000 | − | 14.5516i | −0.186551 | − | 0.775605i | ||||
\(353\) | − | 6.92820i | − | 0.368751i | −0.982856 | − | 0.184376i | \(-0.940974\pi\) | ||
0.982856 | − | 0.184376i | \(-0.0590263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.16515 | 0.486436 | ||||||||
\(356\) | −13.7477 | − | 15.5885i | −0.728628 | − | 0.826187i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.00000 | − | 2.64575i | 0.369961 | − | 0.139832i | ||||
\(359\) | 10.5830i | 0.558550i | 0.960211 | + | 0.279275i | \(0.0900940\pi\) | ||||
−0.960211 | + | 0.279275i | \(0.909906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 4.58258 | − | 1.73205i | 0.240855 | − | 0.0910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.58258 | 0.239209 | 0.119604 | − | 0.992822i | \(-0.461837\pi\) | ||||
0.119604 | + | 0.992822i | \(0.461837\pi\) | |||||||
\(368\) | 21.0000 | + | 2.64575i | 1.09470 | + | 0.137919i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.0000 | 1.76045 | 0.880227 | − | 0.474554i | \(-0.157390\pi\) | ||||
0.880227 | + | 0.474554i | \(0.157390\pi\) | |||||||
\(374\) | 9.16515 | + | 24.2487i | 0.473919 | + | 1.25387i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.9129 | + | 12.1244i | 1.18164 | + | 0.625266i | ||||
\(377\) | 17.3205i | 0.892052i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.29150i | 0.271806i | 0.990722 | + | 0.135903i | \(0.0433936\pi\) | ||||
−0.990722 | + | 0.135903i | \(0.956606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.0000 | − | 5.29150i | 0.716302 | − | 0.270737i | ||||
\(383\) | −27.4955 | −1.40495 | −0.702476 | − | 0.711707i | \(-0.747922\pi\) | ||||
−0.702476 | + | 0.711707i | \(0.747922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | − | 3.96863i | −0.0763480 | − | 0.201998i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.4564 | + | 12.9904i | 0.581613 | + | 0.659487i | ||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.6606 | −1.85401 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.00000 | + | 18.5203i | 0.352655 | + | 0.933037i | ||||
\(395\) | 13.7477 | 0.691723 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.8564i | 0.695433i | 0.937600 | + | 0.347717i | \(0.113043\pi\) | ||||
−0.937600 | + | 0.347717i | \(0.886957\pi\) | |||||||
\(398\) | 9.16515 | + | 24.2487i | 0.459408 | + | 1.21548i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | − | 7.93725i | 0.0500000 | − | 0.396863i | ||||
\(401\) | −8.00000 | −0.399501 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.8745i | 0.790766i | ||||||||
\(404\) | 9.16515 | + | 10.3923i | 0.455983 | + | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.19615i | − | 0.256933i | −0.991714 | − | 0.128467i | \(-0.958994\pi\) | ||
0.991714 | − | 0.128467i | \(-0.0410055\pi\) | |||||||
\(410\) | −3.00000 | − | 7.93725i | −0.148159 | − | 0.391993i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27.4955 | + | 24.2487i | −1.35460 | + | 1.19465i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.93725i | 0.389624i | ||||||||
\(416\) | 4.58258 | + | 19.0526i | 0.224679 | + | 0.934129i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 7.00000 | − | 2.64575i | 0.340755 | − | 0.128793i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.5000 | − | 9.26013i | −0.849875 | − | 0.449712i | ||||
\(425\) | 13.8564i | 0.672134i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −24.5000 | − | 27.7804i | −1.18425 | − | 1.34282i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.16515 | − | 24.2487i | −0.441983 | − | 1.16938i | ||||
\(431\) | 26.4575i | 1.27441i | 0.770693 | + | 0.637207i | \(0.219910\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.7846i | − | 0.998845i | −0.866359 | − | 0.499422i | \(-0.833546\pi\) | ||
0.866359 | − | 0.499422i | \(-0.166454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.58258 | 0.218714 | 0.109357 | − | 0.994003i | \(-0.465121\pi\) | ||||
0.109357 | + | 0.994003i | \(0.465121\pi\) | |||||||
\(440\) | 11.4564 | + | 6.06218i | 0.546164 | + | 0.289003i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | − | 31.7490i | −0.570782 | − | 1.51015i | ||||
\(443\) | − | 18.5203i | − | 0.879924i | −0.898016 | − | 0.439962i | \(-0.854992\pi\) | ||
0.898016 | − | 0.439962i | \(-0.145008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | −2.29129 | − | 6.06218i | −0.108496 | − | 0.287052i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.16515 | −0.431570 | ||||||||
\(452\) | −21.0000 | + | 18.5203i | −0.987757 | + | 0.871120i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.29129 | + | 6.06218i | 0.107535 | + | 0.284512i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.0000 | −1.26301 | −0.631503 | − | 0.775373i | \(-0.717562\pi\) | ||||
−0.631503 | + | 0.775373i | \(0.717562\pi\) | |||||||
\(458\) | −13.7477 | + | 5.19615i | −0.642389 | + | 0.242800i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.7477 | + | 12.1244i | −0.640991 | + | 0.565301i | ||||
\(461\) | 27.7128i | 1.29071i | 0.763881 | + | 0.645357i | \(0.223291\pi\) | ||||
−0.763881 | + | 0.645357i | \(0.776709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8745i | 0.737751i | 0.929479 | + | 0.368875i | \(0.120257\pi\) | ||||
−0.929479 | + | 0.368875i | \(0.879743\pi\) | |||||||
\(464\) | −2.50000 | + | 19.8431i | −0.116060 | + | 0.921194i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | − | 26.4575i | −0.463241 | − | 1.22562i | ||||
\(467\) | −36.6606 | −1.69645 | −0.848225 | − | 0.529636i | \(-0.822329\pi\) | ||||
−0.848225 | + | 0.529636i | \(0.822329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −21.0000 | + | 7.93725i | −0.968658 | + | 0.366118i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.3693 | + | 18.1865i | 1.58198 | + | 0.837103i | ||||
\(473\) | −28.0000 | −1.28744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.00000 | + | 2.64575i | −0.320173 | + | 0.121014i | ||||
\(479\) | −18.3303 | −0.837533 | −0.418766 | − | 0.908094i | \(-0.637537\pi\) | ||||
−0.418766 | + | 0.908094i | \(0.637537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.87386 | − | 2.59808i | 0.313096 | − | 0.118339i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.00000 | + | 5.29150i | −0.272727 | + | 0.240523i | ||||
\(485\) | −15.0000 | −0.681115 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.64575i | 0.119890i | 0.998202 | + | 0.0599452i | \(0.0190926\pi\) | ||||
−0.998202 | + | 0.0599452i | \(0.980907\pi\) | |||||||
\(488\) | 13.7477 | − | 25.9808i | 0.622330 | − | 1.17609i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.64575i | 0.119401i | 0.998216 | + | 0.0597005i | \(0.0190146\pi\) | ||||
−0.998216 | + | 0.0597005i | \(0.980985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 34.6410i | − | 1.56015i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.29129 | + | 18.1865i | −0.102882 | + | 0.816599i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.29150i | 0.236880i | 0.992961 | + | 0.118440i | \(0.0377894\pi\) | ||||
−0.992961 | + | 0.118440i | \(0.962211\pi\) | |||||||
\(500\) | 16.0390 | + | 18.1865i | 0.717287 | + | 0.813327i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.29129 | − | 6.06218i | −0.102265 | − | 0.270568i | ||||
\(503\) | 36.6606 | 1.63462 | 0.817308 | − | 0.576201i | \(-0.195466\pi\) | ||||
0.817308 | + | 0.576201i | \(0.195466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 7.00000 | + | 18.5203i | 0.311188 | + | 0.823326i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.5000 | + | 11.9059i | 0.465862 | + | 0.528238i | ||||
\(509\) | 1.73205i | 0.0767718i | 0.999263 | + | 0.0383859i | \(0.0122216\pi\) | ||||
−0.999263 | + | 0.0383859i | \(0.987778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.50000 | + | 22.4889i | 0.110485 | + | 0.993878i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.7477 | + | 5.19615i | −0.606386 | + | 0.229192i | ||||
\(515\) | − | 31.7490i | − | 1.39903i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.2487i | 1.06646i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.0000 | − | 7.93725i | −0.657794 | − | 0.348072i | ||||
\(521\) | − | 6.92820i | − | 0.303530i | −0.988417 | − | 0.151765i | \(-0.951504\pi\) | ||
0.988417 | − | 0.151765i | \(-0.0484957\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.4955 | −1.20229 | −0.601146 | − | 0.799139i | \(-0.705289\pi\) | ||||
−0.601146 | + | 0.799139i | \(0.705289\pi\) | |||||||
\(524\) | −20.6216 | + | 18.1865i | −0.900858 | + | 0.794482i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0000 | + | 5.29150i | −0.610429 | + | 0.230720i | ||||
\(527\) | − | 31.7490i | − | 1.38301i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.00000 | −0.217391 | ||||||||
\(530\) | 16.0390 | − | 6.06218i | 0.696690 | − | 0.263324i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0780 | 1.38685 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.2042 | − | 9.52628i | 1.08663 | − | 0.410707i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 6.87386 | + | 18.1865i | 0.295258 | + | 0.781179i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.16515 | − | 38.1051i | −0.392953 | − | 1.63374i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.7490i | − | 1.35749i | −0.734374 | − | 0.678745i | \(-0.762524\pi\) | ||
0.734374 | − | 0.678745i | \(-0.237476\pi\) | |||||||
\(548\) | −6.00000 | + | 5.29150i | −0.256307 | + | 0.226042i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.00000 | − | 2.64575i | 0.298481 | − | 0.112815i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.00000 | + | 5.29150i | 0.0849719 | + | 0.224814i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.7477 | + | 12.1244i | −0.583033 | + | 0.514187i | ||||
\(557\) | 7.00000 | 0.296600 | 0.148300 | − | 0.988942i | \(-0.452620\pi\) | ||||
0.148300 | + | 0.988942i | \(0.452620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.6606 | 1.55058 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00000 | + | 21.1660i | 0.337460 | + | 0.892834i | ||||
\(563\) | −22.9129 | −0.965663 | −0.482831 | − | 0.875713i | \(-0.660392\pi\) | ||||
−0.482831 | + | 0.875713i | \(0.660392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 24.2487i | − | 1.02015i | ||||||
\(566\) | −9.16515 | − | 24.2487i | −0.385240 | − | 1.01925i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.00000 | + | 13.2288i | −0.293713 | + | 0.555066i | ||||
\(569\) | 8.00000 | 0.335377 | 0.167689 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167689 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.8745i | − | 0.664327i | −0.943222 | − | 0.332164i | \(-0.892221\pi\) | ||
0.943222 | − | 0.332164i | \(-0.107779\pi\) | |||||||
\(572\) | −13.7477 | + | 12.1244i | −0.574821 | + | 0.506945i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.5830i | 0.441342i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.3013i | 1.80266i | 0.433138 | + | 0.901328i | \(0.357406\pi\) | ||||
−0.433138 | + | 0.901328i | \(0.642594\pi\) | |||||||
\(578\) | 15.5000 | + | 41.0091i | 0.644715 | + | 1.70576i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.4564 | − | 12.9904i | −0.475703 | − | 0.539396i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.5203i | − | 0.767031i | ||||||
\(584\) | −9.16515 | + | 17.3205i | −0.379257 | + | 0.716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.6216 | + | 7.79423i | −0.851870 | + | 0.321977i | ||||
\(587\) | −22.9129 | −0.945716 | −0.472858 | − | 0.881139i | \(-0.656778\pi\) | ||||
−0.472858 | + | 0.881139i | \(0.656778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −31.5000 | + | 11.9059i | −1.29683 | + | 0.490157i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10.3923i | − | 0.426761i | −0.976969 | − | 0.213380i | \(-0.931553\pi\) | ||
0.976969 | − | 0.213380i | \(-0.0684474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.0000 | − | 18.5203i | 0.860194 | − | 0.758619i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.16515 | − | 24.2487i | −0.374791 | − | 0.991604i | ||||
\(599\) | 10.5830i | 0.432410i | 0.976348 | + | 0.216205i | \(0.0693679\pi\) | ||||
−0.976348 | + | 0.216205i | \(0.930632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.66025i | 0.353259i | 0.984277 | + | 0.176630i | \(0.0565195\pi\) | ||||
−0.984277 | + | 0.176630i | \(0.943481\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.5000 | − | 19.8431i | −0.712065 | − | 0.807406i | ||||
\(605\) | − | 6.92820i | − | 0.281672i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.7477 | −0.558003 | −0.279002 | − | 0.960291i | \(-0.590003\pi\) | ||||
−0.279002 | + | 0.960291i | \(0.590003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.00000 | + | 23.8118i | 0.364399 | + | 0.964110i | ||||
\(611\) | − | 31.7490i | − | 1.28443i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 13.7477 | + | 36.3731i | 0.554813 | + | 1.46790i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.4955 | −1.10514 | −0.552568 | − | 0.833468i | \(-0.686352\pi\) | ||||
−0.552568 | + | 0.833468i | \(0.686352\pi\) | |||||||
\(620\) | −10.5000 | − | 11.9059i | −0.421690 | − | 0.478152i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.58258 | − | 12.1244i | −0.183745 | − | 0.486142i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 29.7867 | − | 11.2583i | 1.19052 | − | 0.449973i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.16515 | + | 10.3923i | 0.365729 | + | 0.414698i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.93725i | − | 0.315977i | −0.987441 | − | 0.157989i | \(-0.949499\pi\) | ||
0.987441 | − | 0.157989i | \(-0.0505009\pi\) | |||||||
\(632\) | −10.5000 | + | 19.8431i | −0.417668 | + | 0.789318i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.50000 | + | 9.26013i | 0.139003 | + | 0.367767i | ||||
\(635\) | −13.7477 | −0.545562 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −17.5000 | + | 6.61438i | −0.692832 | + | 0.261866i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.0390 | − | 11.2583i | −0.633998 | − | 0.445025i | ||||
\(641\) | 38.0000 | 1.50091 | 0.750455 | − | 0.660922i | \(-0.229834\pi\) | ||||
0.750455 | + | 0.660922i | \(0.229834\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3303 | 0.722877 | 0.361438 | − | 0.932396i | \(-0.382286\pi\) | ||||
0.361438 | + | 0.932396i | \(0.382286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.16515 | 0.360319 | 0.180160 | − | 0.983637i | \(-0.442339\pi\) | ||||
0.180160 | + | 0.983637i | \(0.442339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.3731i | 1.42777i | ||||||||
\(650\) | −9.16515 | + | 3.46410i | −0.359487 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.0000 | + | 23.8118i | 0.822423 | + | 0.932541i | ||||
\(653\) | 43.0000 | 1.68272 | 0.841360 | − | 0.540475i | \(-0.181755\pi\) | ||||
0.841360 | + | 0.540475i | \(0.181755\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 23.8118i | − | 0.930403i | ||||||
\(656\) | 13.7477 | + | 1.73205i | 0.536759 | + | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.4575i | − | 1.03064i | −0.856998 | − | 0.515319i | \(-0.827673\pi\) | ||
0.856998 | − | 0.515319i | \(-0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.92820i | − | 0.269476i | −0.990881 | − | 0.134738i | \(-0.956981\pi\) | ||
0.990881 | − | 0.134738i | \(-0.0430193\pi\) | |||||||
\(662\) | 14.0000 | − | 5.29150i | 0.544125 | − | 0.205660i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.4564 | − | 6.06218i | −0.444596 | − | 0.235258i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 26.4575i | − | 1.02444i | ||||||
\(668\) | 27.4955 | − | 24.2487i | 1.06383 | − | 0.938211i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.4955 | 1.06145 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0000 | 0.809491 | 0.404745 | − | 0.914429i | \(-0.367360\pi\) | ||||
0.404745 | + | 0.914429i | \(0.367360\pi\) | |||||||
\(674\) | 10.5000 | + | 27.7804i | 0.404445 | + | 1.07006i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | + | 1.32288i | −0.0576923 | + | 0.0508798i | ||||
\(677\) | − | 22.5167i | − | 0.865386i | −0.901541 | − | 0.432693i | \(-0.857563\pi\) | ||
0.901541 | − | 0.432693i | \(-0.142437\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 30.0000 | + | 15.8745i | 1.15045 | + | 0.608760i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.0390 | + | 6.06218i | −0.614166 | + | 0.232133i | ||||
\(683\) | 2.64575i | 0.101237i | 0.998718 | + | 0.0506184i | \(0.0161192\pi\) | ||||
−0.998718 | + | 0.0506184i | \(0.983881\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.92820i | − | 0.264713i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 42.0000 | + | 5.29150i | 1.60123 | + | 0.201737i | ||||
\(689\) | 24.2487i | 0.923802i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.8258 | 1.74329 | 0.871647 | − | 0.490134i | \(-0.163052\pi\) | ||||
0.871647 | + | 0.490134i | \(0.163052\pi\) | |||||||
\(692\) | −18.3303 | − | 20.7846i | −0.696814 | − | 0.790112i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.00000 | − | 2.64575i | 0.265716 | − | 0.100431i | ||||
\(695\) | − | 15.8745i | − | 0.602154i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | −0.909065 | ||||||||
\(698\) | 27.4955 | − | 10.3923i | 1.04072 | − | 0.393355i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.0000 | −0.868698 | −0.434349 | − | 0.900745i | \(-0.643022\pi\) | ||||
−0.434349 | + | 0.900745i | \(0.643022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −17.5000 | + | 11.9059i | −0.659556 | + | 0.448720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.16515 | + | 3.46410i | −0.344935 | + | 0.130373i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0000 | 1.57734 | 0.788672 | − | 0.614815i | \(-0.210769\pi\) | ||||
0.788672 | + | 0.614815i | \(0.210769\pi\) | |||||||
\(710\) | −4.58258 | − | 12.1244i | −0.171981 | − | 0.455019i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.7477 | + | 25.9808i | −0.515218 | + | 0.973670i | ||||
\(713\) | − | 24.2487i | − | 0.908121i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 15.8745i | − | 0.593673i | ||||||
\(716\) | −7.00000 | − | 7.93725i | −0.261602 | − | 0.296629i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.0000 | − | 5.29150i | 0.522475 | − | 0.197477i | ||||
\(719\) | −27.4955 | −1.02541 | −0.512704 | − | 0.858566i | \(-0.671356\pi\) | ||||
−0.512704 | + | 0.858566i | \(0.671356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.50000 | + | 25.1346i | 0.353553 | + | 0.935414i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.58258 | − | 5.19615i | −0.170310 | − | 0.193113i | ||||
\(725\) | −10.0000 | −0.371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7477 | −0.509875 | −0.254937 | − | 0.966958i | \(-0.582055\pi\) | ||||
−0.254937 | + | 0.966958i | \(0.582055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | − | 15.8745i | −0.222070 | − | 0.587542i | ||||
\(731\) | −73.3212 | −2.71188 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.6410i | − | 1.27950i | −0.768585 | − | 0.639748i | \(-0.779039\pi\) | ||
0.768585 | − | 0.639748i | \(-0.220961\pi\) | |||||||
\(734\) | −2.29129 | − | 6.06218i | −0.0845730 | − | 0.223759i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | − | 29.1033i | −0.258023 | − | 1.07276i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.6235i | 1.75186i | 0.482439 | + | 0.875930i | \(0.339751\pi\) | ||||
−0.482439 | + | 0.875930i | \(0.660249\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.1660i | − | 0.776506i | −0.921553 | − | 0.388253i | \(-0.873079\pi\) | ||
0.921553 | − | 0.388253i | \(-0.126921\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.2487i | 0.888404i | ||||||||
\(746\) | −17.0000 | − | 44.9778i | −0.622414 | − | 1.64675i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27.4955 | − | 24.2487i | 1.00533 | − | 0.886621i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 13.2288i | − | 0.482724i | −0.970435 | − | 0.241362i | \(-0.922406\pi\) | ||
0.970435 | − | 0.241362i | \(-0.0775941\pi\) | |||||||
\(752\) | 4.58258 | − | 36.3731i | 0.167109 | − | 1.32639i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.9129 | − | 8.66025i | 0.834438 | − | 0.315388i | ||||
\(755\) | 22.9129 | 0.833885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 7.00000 | − | 2.64575i | 0.254251 | − | 0.0960980i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 38.1051i | − | 1.38131i | −0.723185 | − | 0.690655i | \(-0.757322\pi\) | ||
0.723185 | − | 0.690655i | \(-0.242678\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.0000 | − | 15.8745i | −0.506502 | − | 0.574320i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.7477 | + | 36.3731i | 0.496726 | + | 1.31421i | ||||
\(767\) | − | 47.6235i | − | 1.71959i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.9090i | − | 1.18673i | −0.804934 | − | 0.593364i | \(-0.797800\pi\) | ||
0.804934 | − | 0.593364i | \(-0.202200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.50000 | + | 3.96863i | −0.161959 | + | 0.142834i | ||||
\(773\) | − | 41.5692i | − | 1.49514i | −0.664183 | − | 0.747570i | \(-0.731220\pi\) | ||
0.664183 | − | 0.747570i | \(-0.268780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.16515 | −0.329222 | ||||||||
\(776\) | 11.4564 | − | 21.6506i | 0.411262 | − | 0.777213i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.00000 | + | 13.2288i | 0.179259 | + | 0.474274i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | −0.500959 | ||||||||
\(782\) | 18.3303 | + | 48.4974i | 0.655490 | + | 1.73426i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.4955 | −0.980107 | −0.490054 | − | 0.871692i | \(-0.663023\pi\) | ||||
−0.490054 | + | 0.871692i | \(0.663023\pi\) | |||||||
\(788\) | 21.0000 | − | 18.5203i | 0.748094 | − | 0.659757i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.87386 | − | 18.1865i | −0.244561 | − | 0.647048i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | −1.27840 | ||||||||
\(794\) | 18.3303 | − | 6.92820i | 0.650518 | − | 0.245873i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.4955 | − | 24.2487i | 0.974551 | − | 0.859473i | ||||
\(797\) | − | 15.5885i | − | 0.552171i | −0.961133 | − | 0.276086i | \(-0.910963\pi\) | ||
0.961133 | − | 0.276086i | \(-0.0890374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 63.4980i | 2.24640i | ||||||||
\(800\) | −11.0000 | + | 2.64575i | −0.388909 | + | 0.0935414i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.00000 | + | 10.5830i | 0.141245 | + | 0.373699i | ||||
\(803\) | −18.3303 | −0.646862 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.0000 | − | 7.93725i | 0.739693 | − | 0.279578i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.16515 | − | 17.3205i | 0.322429 | − | 0.609333i | ||||
\(809\) | 28.0000 | 0.984428 | 0.492214 | − | 0.870474i | \(-0.336188\pi\) | ||||
0.492214 | + | 0.870474i | \(0.336188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.6606 | 1.28733 | 0.643664 | − | 0.765308i | \(-0.277413\pi\) | ||||
0.643664 | + | 0.765308i | \(0.277413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.4955 | −0.963124 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.87386 | + | 2.59808i | −0.240339 | + | 0.0908396i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | + | 7.93725i | −0.314294 | + | 0.277181i | ||||
\(821\) | 49.0000 | 1.71011 | 0.855056 | − | 0.518536i | \(-0.173523\pi\) | ||||
0.855056 | + | 0.518536i | \(0.173523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.6235i | 1.66005i | 0.557725 | + | 0.830026i | \(0.311674\pi\) | ||||
−0.557725 | + | 0.830026i | \(0.688326\pi\) | |||||||
\(824\) | 45.8258 | + | 24.2487i | 1.59642 | + | 0.844744i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.3948i | − | 1.19602i | −0.801487 | − | 0.598012i | \(-0.795958\pi\) | ||
0.801487 | − | 0.598012i | \(-0.204042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.92820i | − | 0.240626i | −0.992736 | − | 0.120313i | \(-0.961610\pi\) | ||
0.992736 | − | 0.120313i | \(-0.0383899\pi\) | |||||||
\(830\) | 10.5000 | − | 3.96863i | 0.364460 | − | 0.137753i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.9129 | − | 15.5885i | 0.794361 | − | 0.540433i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.7490i | 1.09872i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.6606 | −1.26566 | −0.632832 | − | 0.774289i | \(-0.718108\pi\) | ||||
−0.632832 | + | 0.774289i | \(0.718108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 1.00000 | + | 2.64575i | 0.0344623 | + | 0.0911786i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.00000 | − | 7.93725i | −0.240950 | − | 0.273212i | ||||
\(845\) | − | 1.73205i | − | 0.0595844i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.50000 | + | 27.7804i | −0.120190 | + | 0.953982i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.3303 | − | 6.92820i | 0.628724 | − | 0.237635i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.7128i | − | 0.948869i | −0.880291 | − | 0.474434i | \(-0.842653\pi\) | ||
0.880291 | − | 0.474434i | \(-0.157347\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.5000 | + | 46.3006i | −0.837393 | + | 1.58252i | ||||
\(857\) | − | 31.1769i | − | 1.06498i | −0.846435 | − | 0.532492i | \(-0.821256\pi\) | ||
0.846435 | − | 0.532492i | \(-0.178744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.6606 | 1.25084 | 0.625422 | − | 0.780287i | \(-0.284927\pi\) | ||||
0.625422 | + | 0.780287i | \(0.284927\pi\) | |||||||
\(860\) | −27.4955 | + | 24.2487i | −0.937587 | + | 0.826874i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.0000 | − | 13.2288i | 1.19210 | − | 0.450573i | ||||
\(863\) | − | 26.4575i | − | 0.900624i | −0.892871 | − | 0.450312i | \(-0.851313\pi\) | ||
0.892871 | − | 0.450312i | \(-0.148687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | −27.4955 | + | 10.3923i | −0.934334 | + | 0.353145i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.0000 | −0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.0000 | 0.945493 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(878\) | −2.29129 | − | 6.06218i | −0.0773272 | − | 0.204589i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.29129 | − | 18.1865i | 0.0772393 | − | 0.613068i | ||||
\(881\) | 27.7128i | 0.933668i | 0.884345 | + | 0.466834i | \(0.154606\pi\) | ||||
−0.884345 | + | 0.466834i | \(0.845394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.29150i | − | 0.178073i | −0.996028 | − | 0.0890366i | \(-0.971621\pi\) | ||
0.996028 | − | 0.0890366i | \(-0.0283788\pi\) | |||||||
\(884\) | −36.0000 | + | 31.7490i | −1.21081 | + | 1.06783i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.5000 | + | 9.26013i | −0.823094 | + | 0.311100i | ||||
\(887\) | −27.4955 | −0.923207 | −0.461603 | − | 0.887086i | \(-0.652726\pi\) | ||||
−0.461603 | + | 0.887086i | \(0.652726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.00000 | − | 23.8118i | −0.301681 | − | 0.798172i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.87386 | + | 6.06218i | −0.230154 | + | 0.202977i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.16515 | 0.306357 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.00000 | − | 18.5203i | −0.233593 | − | 0.618029i | ||||
\(899\) | 22.9129 | 0.764187 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 48.4974i | − | 1.61568i | ||||||
\(902\) | 4.58258 | + | 12.1244i | 0.152583 | + | 0.403697i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.0000 | + | 18.5203i | 1.16408 | + | 0.615975i | ||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 37.0405i | − | 1.22991i | −0.788562 | − | 0.614955i | \(-0.789174\pi\) | ||
0.788562 | − | 0.614955i | \(-0.210826\pi\) | |||||||
\(908\) | 6.87386 | − | 6.06218i | 0.228117 | − | 0.201180i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.29150i | 0.175315i | 0.996151 | + | 0.0876577i | \(0.0279382\pi\) | ||||
−0.996151 | + | 0.0876577i | \(0.972062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.1244i | − | 0.401258i | ||||||
\(914\) | 13.5000 | + | 35.7176i | 0.446540 | + | 1.18143i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.7477 | + | 15.5885i | 0.454238 | + | 0.515057i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.29150i | − | 0.174551i | −0.996184 | − | 0.0872753i | \(-0.972184\pi\) | ||
0.996184 | − | 0.0872753i | \(-0.0278160\pi\) | |||||||
\(920\) | 22.9129 | + | 12.1244i | 0.755415 | + | 0.399728i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.6606 | − | 13.8564i | 1.20735 | − | 0.456336i | ||||
\(923\) | 18.3303 | 0.603349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.0000 | − | 7.93725i | 0.690103 | − | 0.260834i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 27.5000 | − | 6.61438i | 0.902732 | − | 0.217128i | ||||
\(929\) | 34.6410i | 1.13653i | 0.822844 | + | 0.568267i | \(0.192386\pi\) | ||||
−0.822844 | + | 0.568267i | \(0.807614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.0000 | + | 26.4575i | −0.982683 | + | 0.866645i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.3303 | + | 48.4974i | 0.599786 | + | 1.58688i | ||||
\(935\) | 31.7490i | 1.03830i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.5885i | − | 0.509253i | −0.967040 | − | 0.254626i | \(-0.918048\pi\) | ||
0.967040 | − | 0.254626i | \(-0.0819525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.0000 | + | 23.8118i | 0.684944 | + | 0.776654i | ||||
\(941\) | − | 5.19615i | − | 0.169390i | −0.996407 | − | 0.0846949i | \(-0.973008\pi\) | ||
0.996407 | − | 0.0846949i | \(-0.0269915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.3303 | −0.596917 | ||||||||
\(944\) | 6.87386 | − | 54.5596i | 0.223725 | − | 1.77576i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.0000 | + | 37.0405i | 0.455179 | + | 1.20429i | ||||
\(947\) | − | 37.0405i | − | 1.20366i | −0.798626 | − | 0.601828i | \(-0.794439\pi\) | ||
0.798626 | − | 0.601828i | \(-0.205561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0000 | 0.907009 | 0.453504 | − | 0.891254i | \(-0.350174\pi\) | ||||
0.453504 | + | 0.891254i | \(0.350174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.3303 | 0.593155 | ||||||||
\(956\) | 7.00000 | + | 7.93725i | 0.226396 | + | 0.256709i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.16515 | + | 24.2487i | 0.296113 | + | 0.783440i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0000 | −0.322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.87386 | − | 7.79423i | −0.221392 | − | 0.251035i | ||||
\(965\) | − | 5.19615i | − | 0.167270i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.6863i | 1.27622i | 0.769943 | + | 0.638112i | \(0.220284\pi\) | ||||
−0.769943 | + | 0.638112i | \(0.779716\pi\) | |||||||
\(968\) | 10.0000 | + | 5.29150i | 0.321412 | + | 0.170075i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.50000 | + | 19.8431i | 0.240810 | + | 0.637125i | ||||
\(971\) | −4.58258 | −0.147062 | −0.0735309 | − | 0.997293i | \(-0.523427\pi\) | ||||
−0.0735309 | + | 0.997293i | \(0.523427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.50000 | − | 1.32288i | 0.112147 | − | 0.0423877i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.2432 | − | 5.19615i | −1.32016 | − | 0.166325i | ||||
\(977\) | 32.0000 | 1.02377 | 0.511885 | − | 0.859054i | \(-0.328947\pi\) | ||||
0.511885 | + | 0.859054i | \(0.328947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.4955 | −0.878759 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.50000 | − | 1.32288i | 0.111689 | − | 0.0422147i | ||||
\(983\) | −45.8258 | −1.46161 | −0.730807 | − | 0.682584i | \(-0.760856\pi\) | ||||
−0.730807 | + | 0.682584i | \(0.760856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2487i | 0.772628i | ||||||||
\(986\) | −45.8258 | + | 17.3205i | −1.45939 | + | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.0000 | −1.78070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 50.2693i | − | 1.59686i | −0.602090 | − | 0.798428i | \(-0.705665\pi\) | ||
0.602090 | − | 0.798428i | \(-0.294335\pi\) | |||||||
\(992\) | 25.2042 | − | 6.06218i | 0.800233 | − | 0.192474i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.7490i | 1.00651i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 6.92820i | − | 0.219418i | −0.993964 | − | 0.109709i | \(-0.965008\pi\) | ||
0.993964 | − | 0.109709i | \(-0.0349920\pi\) | |||||||
\(998\) | 7.00000 | − | 2.64575i | 0.221581 | − | 0.0837498i | ||||
\(999\) | 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 | 1764.2.b.b.1567.1 | 4 | ||
3.2 | odd | 2 | 1764.2.b.h.1567.4 | 4 | |||
4.3 | odd | 2 | inner | 1764.2.b.b.1567.3 | 4 | ||
7.2 | even | 3 | 252.2.bf.d.199.1 | yes | 4 | ||
7.3 | odd | 6 | 252.2.bf.d.19.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 1764.2.b.b.1567.2 | 4 | ||
12.11 | even | 2 | 1764.2.b.h.1567.2 | 4 | |||
21.2 | odd | 6 | 252.2.bf.a.199.2 | yes | 4 | ||
21.17 | even | 6 | 252.2.bf.a.19.1 | ✓ | 4 | ||
21.20 | even | 2 | 1764.2.b.h.1567.3 | 4 | |||
28.3 | even | 6 | 252.2.bf.d.19.1 | yes | 4 | ||
28.23 | odd | 6 | 252.2.bf.d.199.2 | yes | 4 | ||
28.27 | even | 2 | inner | 1764.2.b.b.1567.4 | 4 | ||
84.23 | even | 6 | 252.2.bf.a.199.1 | yes | 4 | ||
84.59 | odd | 6 | 252.2.bf.a.19.2 | yes | 4 | ||
84.83 | odd | 2 | 1764.2.b.h.1567.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.bf.a.19.1 | ✓ | 4 | 21.17 | even | 6 | ||
252.2.bf.a.19.2 | yes | 4 | 84.59 | odd | 6 | ||
252.2.bf.a.199.1 | yes | 4 | 84.23 | even | 6 | ||
252.2.bf.a.199.2 | yes | 4 | 21.2 | odd | 6 | ||
252.2.bf.d.19.1 | yes | 4 | 28.3 | even | 6 | ||
252.2.bf.d.19.2 | yes | 4 | 7.3 | odd | 6 | ||
252.2.bf.d.199.1 | yes | 4 | 7.2 | even | 3 | ||
252.2.bf.d.199.2 | yes | 4 | 28.23 | odd | 6 | ||
1764.2.b.b.1567.1 | 4 | 1.1 | even | 1 | trivial | ||
1764.2.b.b.1567.2 | 4 | 7.6 | odd | 2 | inner | ||
1764.2.b.b.1567.3 | 4 | 4.3 | odd | 2 | inner | ||
1764.2.b.b.1567.4 | 4 | 28.27 | even | 2 | inner | ||
1764.2.b.h.1567.1 | 4 | 84.83 | odd | 2 | |||
1764.2.b.h.1567.2 | 4 | 12.11 | even | 2 | |||
1764.2.b.h.1567.3 | 4 | 21.20 | even | 2 | |||
1764.2.b.h.1567.4 | 4 | 3.2 | odd | 2 |