Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(11,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 8, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bw (of order \(12\), degree \(4\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.11 |
Dual form | 273.2.bw.a.149.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 1.73205 | 1.00000 | ||||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 2.50000i | −0.327327 | + | 0.944911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.866025 | − | 0.500000i | ||||
\(13\) | −3.46410 | + | 1.00000i | −0.960769 | + | 0.277350i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.83013 | − | 3.83013i | −0.878691 | − | 0.878691i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | + | 4.33013i | −0.327327 | + | 0.944911i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.33013 | − | 2.50000i | −0.866025 | − | 0.500000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 1.00000 | + | 5.19615i | 0.188982 | + | 0.981981i | ||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.13397 | + | 0.303848i | −0.203668 | + | 0.0545726i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
0.155543 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.19615 | − | 3.00000i | 0.866025 | − | 0.500000i | ||||
\(37\) | 1.06218 | + | 3.96410i | 0.174621 | + | 0.651694i | 0.996616 | + | 0.0821995i | \(0.0261945\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | + | 1.73205i | −0.960769 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000 | + | 5.19615i | 1.37249 | + | 0.792406i | 0.991241 | − | 0.132068i | \(-0.0421616\pi\) |
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(48\) | 3.46410 | − | 6.00000i | 0.500000 | − | 0.866025i | ||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.00000 | + | 5.19615i | −0.693375 | + | 0.720577i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.63397 | − | 6.63397i | −0.878691 | − | 0.878691i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.5885 | −1.99590 | −0.997949 | − | 0.0640184i | \(-0.979608\pi\) | ||||
−0.997949 | + | 0.0640184i | \(0.979608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.59808 | + | 7.50000i | −0.327327 | + | 0.944911i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.5622 | − | 11.5622i | −1.41254 | − | 1.41254i | −0.740613 | − | 0.671932i | \(-0.765465\pi\) |
−0.671932 | − | 0.740613i | \(-0.734535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.36603 | + | 16.2942i | 0.511005 | + | 1.90710i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.50000 | − | 4.33013i | −0.866025 | − | 0.500000i | ||||
\(76\) | −10.4641 | − | 2.80385i | −1.20031 | − | 0.321623i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.06218 | + | 10.5000i | 0.682048 | + | 1.18134i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) |
−0.292306 | + | 0.956325i | \(0.594423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 1.73205 | + | 9.00000i | 0.188982 | + | 0.981981i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.500000 | − | 9.52628i | 0.0524142 | − | 0.998625i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.96410 | + | 0.526279i | −0.203668 | + | 0.0545726i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.42820 | − | 2.52628i | 0.957289 | − | 0.256505i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
0.703452 | + | 0.710742i | \(0.251641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | + | 1.73205i | −0.295599 | + | 0.170664i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
0.344865 | + | 0.938652i | \(0.387925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.866025 | − | 0.500000i | ||||
\(109\) | 15.5622 | − | 4.16987i | 1.49059 | − | 0.399401i | 0.580651 | − | 0.814152i | \(-0.302798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.83975 | + | 6.86603i | 0.174621 | + | 0.651694i | ||||
\(112\) | 6.92820 | + | 8.00000i | 0.654654 | + | 0.755929i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.3923 | + | 3.00000i | −0.960769 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.0000i | − | 1.00000i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.66025 | + | 1.66025i | −0.149095 | + | 0.149095i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3205 | − | 10.0000i | 1.53695 | − | 0.887357i | 0.537931 | − | 0.842989i | \(-0.319206\pi\) |
0.999015 | − | 0.0443678i | \(-0.0141274\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.5885 | + | 9.00000i | 1.37249 | + | 0.792406i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.8923 | − | 6.25833i | 1.11790 | − | 0.542666i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | − | 6.06218i | 0.296866 | − | 0.514187i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.975417 | + | 0.220366i | \(0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | − | 10.3923i | 0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.52628 | − | 7.50000i | −0.785714 | − | 0.618590i | ||||
\(148\) | 5.80385 | + | 5.80385i | 0.477073 | + | 0.477073i | ||||
\(149\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.70577 | + | 13.8301i | 0.301571 | + | 1.12548i | 0.935857 | + | 0.352381i | \(0.114628\pi\) |
−0.634285 | + | 0.773099i | \(0.718706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.66025 | + | 9.00000i | −0.693375 | + | 0.720577i | ||||
\(157\) | −12.5000 | + | 21.6506i | −0.997609 | + | 1.72791i | −0.438948 | + | 0.898513i | \(0.644649\pi\) |
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0263 | − | 18.0263i | 1.41193 | − | 1.41193i | 0.665771 | − | 0.746156i | \(-0.268103\pi\) |
0.746156 | − | 0.665771i | \(-0.231897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | − | 6.92820i | 0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.4904 | − | 11.4904i | −0.878691 | − | 0.878691i | ||||
\(172\) | 20.7846 | 1.58481 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | − | 8.66025i | 0.755929 | − | 0.654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0526i | 1.41617i | 0.706129 | + | 0.708083i | \(0.250440\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.0000 | −1.99590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | + | 12.9904i | −0.327327 | + | 0.944911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | − | 13.8564i | − | 1.00000i | ||||||
\(193\) | −14.8564 | + | 14.8564i | −1.06939 | + | 1.06939i | −0.0719816 | + | 0.997406i | \(0.522932\pi\) |
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.8564 | − | 2.00000i | −0.989743 | − | 0.142857i | ||||
\(197\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.52628 | − | 5.50000i | 0.675300 | − | 0.389885i | −0.122782 | − | 0.992434i | \(-0.539182\pi\) |
0.798082 | + | 0.602549i | \(0.205848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.0263 | − | 20.0263i | −1.41254 | − | 1.41254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.46410 | + | 14.0000i | −0.240192 | + | 0.970725i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.866025 | + | 1.50000i | 0.0596196 | + | 0.103264i | 0.894295 | − | 0.447478i | \(-0.147678\pi\) |
−0.834675 | + | 0.550743i | \(0.814345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.222432 | − | 3.09808i | 0.0150997 | − | 0.210311i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.56218 | + | 28.2224i | 0.511005 | + | 1.90710i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.02628 | − | 26.2224i | 0.470514 | − | 1.75598i | −0.167412 | − | 0.985887i | \(-0.553541\pi\) |
0.637927 | − | 0.770097i | \(-0.279792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.9904 | − | 7.50000i | −0.866025 | − | 0.500000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(228\) | −18.1244 | − | 4.85641i | −1.20031 | − | 0.321623i | ||||
\(229\) | 25.7224 | + | 6.89230i | 1.69979 | + | 0.455456i | 0.972886 | − | 0.231287i | \(-0.0742935\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.5000 | + | 18.1865i | 0.682048 | + | 1.18134i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4904 | − | 7.63397i | −1.83523 | − | 0.491748i | −0.836784 | − | 0.547533i | \(-0.815567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 1.00000 | ||||||||
\(244\) | −27.0000 | + | 15.5885i | −1.72850 | + | 0.997949i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.0981 | + | 9.43782i | 1.08792 | + | 0.600514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | 3.00000 | + | 15.5885i | 0.188982 | + | 0.981981i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8301 | − | 0.777568i | −0.672951 | − | 0.0483157i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −31.5885 | − | 8.46410i | −1.92957 | − | 0.517027i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.20577 | − | 23.1603i | −0.376974 | − | 1.40689i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.473466 | − | 0.880812i | \(-0.343003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.866025 | − | 16.5000i | 0.0524142 | − | 0.998625i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.5000 | + | 16.4545i | −1.71240 | + | 0.988654i | −0.781094 | + | 0.624413i | \(0.785338\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.40192 | + | 0.911543i | −0.203668 | + | 0.0545726i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 32.0000i | − | 1.90220i | −0.308879 | − | 0.951101i | \(-0.599954\pi\) | ||
0.308879 | − | 0.951101i | \(-0.400046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.3301 | − | 4.37564i | 0.957289 | − | 0.256505i | ||||
\(292\) | 23.8564 | + | 23.8564i | 1.39609 | + | 1.39609i | ||||
\(293\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −17.3205 | −1.00000 | ||||||||
\(301\) | −20.7846 | + | 18.0000i | −1.19800 | + | 1.03750i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.9282 | + | 5.60770i | −1.20031 | + | 0.321623i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3660 | − | 18.3660i | 1.04820 | − | 1.04820i | 0.0494267 | − | 0.998778i | \(-0.484261\pi\) |
0.998778 | − | 0.0494267i | \(-0.0157394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.19615 | + | 3.00000i | −0.295599 | + | 0.170664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8564 | + | 24.0000i | 0.783210 | + | 1.35656i | 0.930062 | + | 0.367402i | \(0.119753\pi\) |
−0.146852 | + | 0.989158i | \(0.546914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.0000 | + | 12.1244i | 1.18134 | + | 0.682048i | ||||
\(317\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 15.5885 | − | 9.00000i | 0.866025 | − | 0.500000i | ||||
\(325\) | 17.5000 | + | 4.33013i | 0.970725 | + | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.9545 | − | 7.22243i | 1.49059 | − | 0.399401i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6603 | − | 24.6603i | −1.35545 | − | 1.35545i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
−0.476011 | − | 0.879440i | \(-0.657918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.18653 | + | 11.8923i | 0.174621 | + | 0.651694i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.0000 | + | 13.8564i | 0.654654 | + | 0.755929i | ||||
\(337\) | 34.0000i | 1.85210i | 0.377403 | + | 0.926049i | \(0.376817\pi\) | ||||
−0.377403 | + | 0.926049i | \(0.623183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7224 | − | 5.82051i | −1.16278 | − | 0.311565i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
−0.788074 | + | 0.615581i | \(0.788921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | + | 5.19615i | −0.960769 | + | 0.277350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3397i | 0.544197i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 19.0526i | − | 1.00000i | ||||||
\(364\) | −8.66025 | − | 17.0000i | −0.453921 | − | 0.891042i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | 0.208798 | 0.104399 | − | 0.994535i | \(-0.466708\pi\) | ||||
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.87564 | + | 2.87564i | −0.149095 | + | 0.149095i | ||||
\(373\) | −36.3731 | −1.88333 | −0.941663 | − | 0.336557i | \(-0.890737\pi\) | ||||
−0.941663 | + | 0.336557i | \(0.890737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.99038 | + | 33.5526i | −0.461805 | + | 1.72348i | 0.205466 | + | 0.978664i | \(0.434129\pi\) |
−0.667271 | + | 0.744815i | \(0.732538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.0000 | − | 17.3205i | 1.53695 | − | 0.887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.0000 | + | 15.5885i | 1.37249 | + | 0.792406i | ||||
\(388\) | 13.8038 | − | 13.8038i | 0.700784 | − | 0.700784i | ||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3923 | − | 27.3923i | 1.37478 | − | 1.37478i | 0.521575 | − | 0.853206i | \(-0.325345\pi\) |
0.853206 | − | 0.521575i | \(-0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.3301 | − | 10.8397i | 1.11790 | − | 0.542666i | ||||
\(400\) | −17.3205 | + | 10.0000i | −0.866025 | + | 0.500000i | ||||
\(401\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.62436 | − | 2.18653i | 0.180542 | − | 0.108919i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.41858 | + | 16.4904i | −0.218485 | + | 0.815397i | 0.766426 | + | 0.642333i | \(0.222033\pi\) |
−0.984911 | + | 0.173064i | \(0.944633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.46410 | + | 6.00000i | −0.170664 | + | 0.295599i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.06218 | − | 10.5000i | 0.296866 | − | 0.514187i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.68653 | − | 8.68653i | −0.423356 | − | 0.423356i | 0.463002 | − | 0.886357i | \(-0.346772\pi\) |
−0.886357 | + | 0.463002i | \(0.846772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.5000 | − | 38.9711i | 0.653311 | − | 1.88595i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(432\) | 10.3923 | − | 18.0000i | 0.500000 | − | 0.866025i | ||||
\(433\) | 30.3109 | + | 17.5000i | 1.45665 | + | 0.840996i | 0.998845 | − | 0.0480569i | \(-0.0153029\pi\) |
0.457804 | + | 0.889053i | \(0.348636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.7846 | − | 22.7846i | 1.09118 | − | 1.09118i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.50000 | + | 4.33013i | 0.357955 | + | 0.206666i | 0.668184 | − | 0.743996i | \(-0.267072\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.5000 | − | 12.9904i | −0.785714 | − | 0.618590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 10.0526 | + | 10.0526i | 0.477073 | + | 0.477073i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.0000 | + | 6.92820i | 0.944911 | + | 0.327327i | ||||
\(449\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.41858 | + | 23.9545i | 0.301571 | + | 1.12548i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.7224 | + | 5.28461i | −0.922576 | + | 0.247204i | −0.688686 | − | 0.725059i | \(-0.741812\pi\) |
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.05256 | + | 9.05256i | −0.420708 | + | 0.420708i | −0.885448 | − | 0.464739i | \(-0.846148\pi\) |
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | −15.0000 | + | 15.5885i | −0.693375 | + | 0.720577i | ||||
\(469\) | 38.9186 | − | 18.8923i | 1.79709 | − | 0.872366i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.6506 | + | 37.5000i | −0.997609 | + | 1.72791i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.00962 | + | 26.1603i | 0.321623 | + | 1.20031i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.64359 | − | 12.6699i | −0.348518 | − | 0.577696i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | − | 19.0526i | −0.500000 | − | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.7679 | + | 40.1865i | −0.487942 | + | 1.82103i | 0.0784867 | + | 0.996915i | \(0.474991\pi\) |
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.2224 | − | 31.2224i | 1.41193 | − | 1.41193i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.21539 | + | 4.53590i | −0.0545726 | + | 0.203668i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.91154 | + | 22.0622i | −0.264637 | + | 0.987639i | 0.697835 | + | 0.716258i | \(0.254147\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0526 | − | 12.0000i | 0.846154 | − | 0.532939i | ||||
\(508\) | 20.0000 | − | 34.6410i | 0.887357 | − | 1.53695i | ||||
\(509\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.5167 | − | 3.19615i | −1.96930 | − | 0.141389i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.9019 | − | 19.9019i | −0.878691 | − | 0.878691i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 36.0000 | 1.58481 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.5000 | + | 37.2391i | −0.940129 | + | 1.62835i | −0.174908 | + | 0.984585i | \(0.555963\pi\) |
−0.765222 | + | 0.643767i | \(0.777371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.3205 | − | 15.0000i | 0.755929 | − | 0.654654i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.0718 | − | 23.7321i | 0.696801 | − | 1.02891i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.1506 | − | 9.68653i | −1.55424 | − | 0.416457i | −0.623404 | − | 0.781900i | \(-0.714251\pi\) |
−0.930834 | + | 0.365444i | \(0.880917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.0000i | 1.41617i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | −0.0213785 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.7654 | −1.99590 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.5000 | + | 6.06218i | −1.33952 | + | 0.257790i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 14.0000i | − | 0.593732i | ||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.3731 | − | 9.00000i | −1.53842 | − | 0.380659i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.79423 | + | 22.5000i | −0.327327 | + | 0.944911i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.7032 | − | 23.5000i | −1.70338 | − | 0.983444i | −0.942293 | − | 0.334790i | \(-0.891335\pi\) |
−0.761083 | − | 0.648655i | \(-0.775332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 24.0000i | − | 1.00000i | ||||||
\(577\) | −39.4545 | + | 10.5718i | −1.64251 | + | 0.440110i | −0.957503 | − | 0.288425i | \(-0.906868\pi\) |
−0.685009 | + | 0.728535i | \(0.740202\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.7321 | + | 25.7321i | −1.06939 | + | 1.06939i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(588\) | −24.0000 | − | 3.46410i | −0.989743 | − | 0.142857i | ||||
\(589\) | 5.50704 | + | 3.17949i | 0.226914 | + | 0.131009i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.8564 | + | 4.24871i | 0.651694 | + | 0.174621i | ||||
\(593\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.5000 | − | 9.52628i | 0.675300 | − | 0.389885i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.6506 | − | 37.5000i | −0.883148 | − | 1.52966i | −0.847822 | − | 0.530281i | \(-0.822086\pi\) |
−0.0353259 | − | 0.999376i | \(-0.511247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34.6865 | − | 34.6865i | −1.41254 | − | 1.41254i | ||||
\(604\) | 20.2487 | + | 20.2487i | 0.823908 | + | 0.823908i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.0000 | −1.17707 | −0.588537 | − | 0.808470i | \(-0.700296\pi\) | ||||
−0.588537 | + | 0.808470i | \(0.700296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.2942 | + | 31.2942i | 1.26396 | + | 1.26396i | 0.949156 | + | 0.314806i | \(0.101939\pi\) |
0.314806 | + | 0.949156i | \(0.398061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8301 | − | 47.8827i | −0.515686 | − | 1.92457i | −0.341644 | − | 0.939829i | \(-0.610984\pi\) |
−0.174042 | − | 0.984738i | \(-0.555683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | + | 24.2487i | −0.240192 | + | 0.970725i | ||||
\(625\) | 12.5000 | + | 21.6506i | 0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 50.0000i | 1.99522i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.11474 | + | 11.6244i | 0.123996 | + | 0.462758i | 0.999802 | − | 0.0199047i | \(-0.00633628\pi\) |
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.50000 | + | 2.59808i | 0.0596196 | + | 0.103264i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.3827 | + | 9.50000i | 0.926456 | + | 0.376404i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.02628 | + | 1.61474i | −0.237653 | + | 0.0636790i | −0.375680 | − | 0.926750i | \(-0.622591\pi\) |
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.385263 | − | 5.36603i | 0.0150997 | − | 0.210311i | ||||
\(652\) | 13.1962 | − | 49.2487i | 0.516801 | − | 1.92873i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0981 | + | 48.8827i | 0.511005 | + | 1.90710i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7058 | + | 16.7058i | −0.649779 | + | 0.649779i | −0.952940 | − | 0.303160i | \(-0.901958\pi\) |
0.303160 | + | 0.952940i | \(0.401958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.1699 | − | 45.4186i | 0.470514 | − | 1.75598i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000 | − | 6.92820i | 0.462566 | − | 0.267063i | −0.250557 | − | 0.968102i | \(-0.580614\pi\) |
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.5000 | − | 12.9904i | −0.866025 | − | 0.500000i | ||||
\(676\) | 12.1244 | − | 23.0000i | 0.466321 | − | 0.884615i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.84936 | + | 25.7583i | −0.0709721 | + | 0.988514i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(684\) | −31.3923 | − | 8.41154i | −1.20031 | − | 0.321623i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44.5526 | + | 11.9378i | 1.69979 | + | 0.455456i | ||||
\(688\) | 36.0000 | − | 20.7846i | 1.37249 | − | 0.792406i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0263 | − | 8.04552i | 1.14225 | − | 0.306066i | 0.362397 | − | 0.932024i | \(-0.381959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.66025 | − | 25.0000i | 0.327327 | − | 0.944911i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1147 | − | 19.2513i | 0.419200 | − | 0.726076i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.15064 | − | 6.15064i | 0.230992 | − | 0.230992i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.813107 | + | 0.582115i | \(0.197775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.1865 | + | 31.5000i | 0.682048 | + | 1.18134i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.73205 | − | 9.00000i | −0.0645049 | − | 0.335178i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −49.3468 | − | 13.2224i | −1.83523 | − | 0.491748i | ||||
\(724\) | 19.0526 | + | 33.0000i | 0.708083 | + | 1.22644i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.0000i | 1.81731i | 0.417548 | + | 0.908655i | \(0.362889\pi\) | ||||
−0.417548 | + | 0.908655i | \(0.637111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −46.7654 | + | 27.0000i | −1.72850 | + | 0.997949i | ||||
\(733\) | 8.54552 | − | 31.8923i | 0.315636 | − | 1.17797i | −0.607760 | − | 0.794121i | \(-0.707932\pi\) |
0.923396 | − | 0.383849i | \(-0.125402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.4186 | − | 38.4186i | 1.41325 | − | 1.41325i | 0.680534 | − | 0.732717i | \(-0.261748\pi\) |
0.732717 | − | 0.680534i | \(-0.238252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.6147 | + | 16.3468i | 1.08792 | + | 0.600514i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.5000 | + | 26.8468i | 1.69681 | + | 0.979653i | 0.948753 | + | 0.316017i | \(0.102346\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.19615 | + | 27.0000i | 0.188982 | + | 0.981981i | ||||
\(757\) | −24.2487 | − | 42.0000i | −0.881334 | − | 1.52652i | −0.849858 | − | 0.527011i | \(-0.823312\pi\) |
−0.0314762 | − | 0.999505i | \(-0.510021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.05256 | + | 42.5167i | −0.110510 | + | 1.53921i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13.8564 | − | 24.0000i | −0.500000 | − | 0.866025i | ||||
\(769\) | 3.21281 | − | 11.9904i | 0.115857 | − | 0.432384i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.999350 | + | 0.0360609i | \(0.0114810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.8756 | + | 40.5885i | −0.391423 | + | 1.46081i | ||||
\(773\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.66987 | + | 1.51924i | 0.203668 | + | 0.0545726i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.7583 | − | 1.34679i | −0.672951 | − | 0.0483157i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.0000 | + | 10.3923i | −0.928571 | + | 0.371154i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.1147 | + | 14.2321i | 1.89334 | + | 0.507318i | 0.998092 | + | 0.0617409i | \(0.0196653\pi\) |
0.895244 | + | 0.445577i | \(0.147001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.0000 | − | 15.5885i | 1.91760 | − | 0.553562i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0000 | − | 19.0526i | 0.389885 | − | 0.675300i | ||||
\(797\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −54.7128 | − | 14.6603i | −1.92957 | − | 0.517027i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.15064 | − | 3.15064i | −0.110634 | − | 0.110634i | 0.649623 | − | 0.760257i | \(-0.274927\pi\) |
−0.760257 | + | 0.649623i | \(0.774927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.7487 | − | 40.1147i | −0.376974 | − | 1.40689i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5692 | − | 54.3731i | −0.509712 | − | 1.90227i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.50000 | − | 28.5788i | 0.0524142 | − | 0.998625i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0000 | + | 12.1244i | −0.732014 | + | 0.422628i | −0.819159 | − | 0.573567i | \(-0.805559\pi\) |
0.0871445 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0000i | 1.59765i | 0.601566 | + | 0.798823i | \(0.294544\pi\) | ||||
−0.601566 | + | 0.798823i | \(0.705456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49.3634 | + | 28.5000i | −1.71240 | + | 0.988654i | ||||
\(832\) | 8.00000 | + | 27.7128i | 0.277350 | + | 0.960769i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.89230 | + | 1.57884i | −0.203668 | + | 0.0545726i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.00000 | + | 1.73205i | 0.103264 | + | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.5000 | + | 9.52628i | 0.944911 | + | 0.327327i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 55.4256i | − | 1.90220i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.8827 | − | 40.8827i | 1.39980 | − | 1.39980i | 0.599189 | − | 0.800608i | \(-0.295490\pi\) |
0.800608 | − | 0.599189i | \(-0.204510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.9186 | − | 34.5000i | −0.679613 | − | 1.17712i | −0.975097 | − | 0.221777i | \(-0.928814\pi\) |
0.295484 | − | 0.955348i | \(-0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7224 | − | 25.5000i | 0.500000 | − | 0.866025i | ||||
\(868\) | −2.71281 | − | 5.58846i | −0.0920789 | − | 0.189685i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.6147 | + | 28.4904i | 1.74890 | + | 0.965360i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.2846 | − | 7.57884i | 0.957289 | − | 0.256505i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 41.3205 | + | 41.3205i | 1.39609 | + | 1.39609i | ||||
\(877\) | 7.24871 | + | 7.24871i | 0.244772 | + | 0.244772i | 0.818821 | − | 0.574049i | \(-0.194628\pi\) |
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0000 | + | 51.9615i | 0.335389 | + | 1.74273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.0526 | − | 52.4449i | −0.470514 | − | 1.75598i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −30.0000 | −1.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.0000 | + | 31.1769i | −1.19800 | + | 1.03750i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 19.0000i | − | 0.630885i | −0.948945 | − | 0.315442i | \(-0.897847\pi\) | ||
0.948945 | − | 0.315442i | \(-0.102153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −36.2487 | + | 9.71281i | −1.20031 | + | 0.321623i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 51.4449 | − | 13.7846i | 1.69979 | − | 0.455456i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.4449 | 0.971296 | 0.485648 | − | 0.874154i | \(-0.338584\pi\) | ||||
0.485648 | + | 0.874154i | \(0.338584\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.8109 | − | 31.8109i | 1.04820 | − | 1.04820i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.31089 | − | 19.8205i | 0.174621 | − | 0.651694i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.00000 | + | 5.19615i | −0.295599 | + | 0.170664i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.48076 | + | 37.6506i | 0.146851 | + | 1.23395i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.19615 | −0.169751 | −0.0848755 | − | 0.996392i | \(-0.527049\pi\) | ||||
−0.0848755 | + | 0.996392i | \(0.527049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | + | 41.5692i | 0.783210 | + | 1.35656i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(948\) | 36.3731 | + | 21.0000i | 1.18134 | + | 0.682048i | ||||
\(949\) | −31.4186 | − | 52.0788i | −1.01989 | − | 1.69055i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6532 | + | 14.8109i | −0.827523 | + | 0.477771i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −56.9808 | + | 15.2679i | −1.83523 | + | 0.491748i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.88269 | + | 2.88269i | 0.0927009 | + | 0.0927009i | 0.751936 | − | 0.659236i | \(-0.229120\pi\) |
−0.659236 | + | 0.751936i | \(0.729120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 27.0000 | − | 15.5885i | 0.866025 | − | 0.500000i | ||||
\(973\) | 12.1244 | + | 14.0000i | 0.388689 | + | 0.448819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.3109 | + | 7.50000i | 0.970725 | + | 0.240192i | ||||
\(976\) | −31.1769 | + | 54.0000i | −0.997949 | + | 1.72850i | ||||
\(977\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.6865 | − | 12.5096i | 1.49059 | − | 0.399401i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39.0526 | − | 0.751289i | 1.24243 | − | 0.0239017i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.0000 | −1.93773 | −0.968864 | − | 0.247592i | \(-0.920361\pi\) | ||||
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.7128 | − | 42.7128i | −1.35545 | − | 1.35545i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.00000 | − | 8.66025i | −0.158352 | − | 0.274273i | 0.775923 | − | 0.630828i | \(-0.217285\pi\) |
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.51924 | + | 20.5981i | 0.174621 | + | 0.651694i |
(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 | 273.2.bw.a.11.1 | yes | 4 | |
3.2 | odd | 2 | CM | 273.2.bw.a.11.1 | yes | 4 | |
7.2 | even | 3 | 273.2.bv.a.128.1 | yes | 4 | ||
13.6 | odd | 12 | 273.2.bv.a.32.1 | ✓ | 4 | ||
21.2 | odd | 6 | 273.2.bv.a.128.1 | yes | 4 | ||
39.32 | even | 12 | 273.2.bv.a.32.1 | ✓ | 4 | ||
91.58 | odd | 12 | inner | 273.2.bw.a.149.1 | yes | 4 | |
273.149 | even | 12 | inner | 273.2.bw.a.149.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bv.a.32.1 | ✓ | 4 | 13.6 | odd | 12 | ||
273.2.bv.a.32.1 | ✓ | 4 | 39.32 | even | 12 | ||
273.2.bv.a.128.1 | yes | 4 | 7.2 | even | 3 | ||
273.2.bv.a.128.1 | yes | 4 | 21.2 | odd | 6 | ||
273.2.bw.a.11.1 | yes | 4 | 1.1 | even | 1 | trivial | |
273.2.bw.a.11.1 | yes | 4 | 3.2 | odd | 2 | CM | |
273.2.bw.a.149.1 | yes | 4 | 91.58 | odd | 12 | inner | |
273.2.bw.a.149.1 | yes | 4 | 273.149 | even | 12 | inner |