Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), degree \(2\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.i.865.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 1.73205i | 0.447214 | − | 0.774597i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
0.998203 | + | 0.0599153i | \(0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 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 | ||||||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | − | 5.19615i | 0.169031 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | − | 1.73205i | 0.145865 | − | 0.252646i | −0.783830 | − | 0.620975i | \(-0.786737\pi\) |
0.929695 | + | 0.368329i | \(0.120070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.00000 | − | 8.66025i | −0.686803 | − | 1.18958i | −0.972867 | − | 0.231367i | \(-0.925680\pi\) |
0.286064 | − | 0.958211i | \(-0.407653\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | − | 10.3923i | 0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | + | 5.19615i | 0.366508 | + | 0.634811i | 0.989017 | − | 0.147802i | \(-0.0472198\pi\) |
−0.622509 | + | 0.782613i | \(0.713886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.50000 | + | 9.52628i | 0.643726 | + | 1.11497i | 0.984594 | + | 0.174855i | \(0.0559458\pi\) |
−0.340868 | + | 0.940111i | \(0.610721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | + | 5.19615i | 0.683763 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0000 | −1.64646 | −0.823232 | − | 0.567705i | \(-0.807831\pi\) | ||||
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.00000 | − | 8.66025i | 0.529999 | − | 0.917985i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
0.999388 | − | 0.0349934i | \(-0.0111410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0000 | − | 5.19615i | 1.57243 | − | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | + | 6.92820i | 0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | − | 13.8564i | −0.766261 | − | 1.32720i | −0.939577 | − | 0.342337i | \(-0.888782\pi\) |
0.173316 | − | 0.984866i | \(-0.444552\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 6.92820i | 0.373002 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00000 | + | 6.92820i | 0.733359 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.50000 | + | 11.2583i | −0.567908 | + | 0.983645i | 0.428865 | + | 0.903369i | \(0.358914\pi\) |
−0.996773 | + | 0.0802763i | \(0.974420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 10.3923i | −0.173422 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.00000 | − | 13.8564i | −0.683486 | − | 1.18383i | −0.973910 | − | 0.226935i | \(-0.927130\pi\) |
0.290424 | − | 0.956898i | \(-0.406204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00000 | + | 15.5885i | 0.752618 | + | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | + | 8.66025i | −0.415227 | + | 0.719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.50000 | + | 4.33013i | −0.204808 | + | 0.354738i | −0.950072 | − | 0.312032i | \(-0.898990\pi\) |
0.745264 | + | 0.666770i | \(0.232324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50000 | − | 16.4545i | −0.773099 | − | 1.33905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.162758 | − | 0.986666i | \(-0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.0000 | −1.12451 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 15.5885i | 0.718278 | + | 1.24409i | 0.961681 | + | 0.274169i | \(0.0884028\pi\) |
−0.243403 | + | 0.969925i | \(0.578264\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | + | 10.3923i | −0.157622 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | − | 12.1244i | 0.548282 | − | 0.949653i | −0.450110 | − | 0.892973i | \(-0.648615\pi\) |
0.998392 | − | 0.0566798i | \(-0.0180514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.50000 | − | 9.52628i | 0.418157 | − | 0.724270i | −0.577597 | − | 0.816322i | \(-0.696009\pi\) |
0.995754 | + | 0.0920525i | \(0.0293428\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.500000 | − | 0.866025i | −0.0373718 | − | 0.0647298i | 0.846735 | − | 0.532016i | \(-0.178565\pi\) |
−0.884106 | + | 0.467286i | \(0.845232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 10.3923i | −0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.00000 | − | 8.66025i | 0.361787 | − | 0.626634i | −0.626468 | − | 0.779447i | \(-0.715500\pi\) |
0.988255 | + | 0.152813i | \(0.0488333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5000 | − | 18.1865i | −0.755807 | − | 1.30910i | −0.944972 | − | 0.327150i | \(-0.893912\pi\) |
0.189166 | − | 0.981945i | \(-0.439422\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | + | 6.06218i | 0.248108 | + | 0.429736i | 0.963001 | − | 0.269498i | \(-0.0868577\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.5000 | + | 4.33013i | −0.877328 | + | 0.303915i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | − | 13.8564i | 0.545595 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.0000 | − | 12.1244i | −0.950382 | − | 0.823055i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | + | 20.7846i | 0.807207 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.0000 | −1.40626 | −0.703132 | − | 0.711059i | \(-0.748216\pi\) | ||||
−0.703132 | + | 0.711059i | \(0.748216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.50000 | − | 11.2583i | −0.431420 | − | 0.747242i | 0.565576 | − | 0.824696i | \(-0.308654\pi\) |
−0.996996 | + | 0.0774548i | \(0.975321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.00000 | + | 8.66025i | −0.327561 | + | 0.567352i | −0.982027 | − | 0.188739i | \(-0.939560\pi\) |
0.654466 | + | 0.756091i | \(0.272893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | − | 3.46410i | −0.130466 | − | 0.225973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | − | 13.8564i | −0.127775 | − | 0.885253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | + | 20.7846i | −0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.0000 | −0.820553 | −0.410276 | − | 0.911961i | \(-0.634568\pi\) | ||||
−0.410276 | + | 0.911961i | \(0.634568\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.0000 | −1.22859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5000 | − | 23.3827i | −0.823110 | − | 1.42567i | −0.903356 | − | 0.428892i | \(-0.858904\pi\) |
0.0802460 | − | 0.996775i | \(-0.474429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | − | 6.92820i | −0.237775 | − | 0.411839i | 0.722300 | − | 0.691580i | \(-0.243085\pi\) |
−0.960076 | + | 0.279741i | \(0.909752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.00000 | − | 1.73205i | 0.295141 | − | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.0000 | 1.04800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | − | 6.92820i | 1.15278 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.00000 | − | 13.8564i | −0.458079 | − | 0.793416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | + | 15.5885i | 0.510343 | + | 0.883940i | 0.999928 | + | 0.0119847i | \(0.00381495\pi\) |
−0.489585 | + | 0.871956i | \(0.662852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0000 | + | 22.5167i | −0.734803 | + | 1.27272i | 0.220006 | + | 0.975499i | \(0.429392\pi\) |
−0.954810 | + | 0.297218i | \(0.903941\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5000 | + | 23.3827i | −0.758236 | + | 1.31330i | 0.185514 | + | 0.982642i | \(0.440605\pi\) |
−0.943750 | + | 0.330661i | \(0.892728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.50000 | − | 12.9904i | −0.419919 | − | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | + | 5.19615i | 0.166410 | + | 0.288231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00000 | − | 5.19615i | 0.0551318 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | + | 27.7128i | −0.879440 | + | 1.52323i | −0.0274825 | + | 0.999622i | \(0.508749\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0000 | 1.57973 | 0.789865 | − | 0.613280i | \(-0.210150\pi\) | ||||
0.789865 | + | 0.613280i | \(0.210150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5000 | − | 18.1865i | 0.568607 | − | 0.984856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.50000 | + | 2.59808i | 0.0805242 | + | 0.139472i | 0.903475 | − | 0.428640i | \(-0.141007\pi\) |
−0.822951 | + | 0.568112i | \(0.807674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00000 | −0.214115 | −0.107058 | − | 0.994253i | \(-0.534143\pi\) | ||||
−0.107058 | + | 0.994253i | \(0.534143\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.00000 | + | 5.19615i | 0.159674 | + | 0.276563i | 0.934751 | − | 0.355303i | \(-0.115622\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | + | 20.7846i | −0.636894 | + | 1.10313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000 | − | 20.7846i | 0.633336 | − | 1.09697i | −0.353529 | − | 0.935423i | \(-0.615019\pi\) |
0.986865 | − | 0.161546i | \(-0.0516481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.0000 | 1.15153 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | − | 17.3205i | −0.521996 | − | 0.904123i | −0.999673 | − | 0.0255875i | \(-0.991854\pi\) |
0.477677 | − | 0.878536i | \(-0.341479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.0000 | − | 17.3205i | −1.03835 | − | 0.899236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | − | 3.46410i | 0.103556 | − | 0.179364i | −0.809591 | − | 0.586994i | \(-0.800311\pi\) |
0.913147 | + | 0.407630i | \(0.133645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.0000 | −1.54508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.00000 | −0.308199 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | + | 31.1769i | −0.919757 | + | 1.59307i | −0.119974 | + | 0.992777i | \(0.538281\pi\) |
−0.799783 | + | 0.600289i | \(0.795052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0000 | − | 5.19615i | 0.764471 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.50000 | + | 16.4545i | 0.481669 | + | 0.834275i | 0.999779 | − | 0.0210389i | \(-0.00669738\pi\) |
−0.518110 | + | 0.855314i | \(0.673364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.00000 | + | 1.73205i | 0.0503155 | + | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | + | 19.0526i | −0.552074 | + | 0.956221i | 0.446051 | + | 0.895008i | \(0.352830\pi\) |
−0.998125 | + | 0.0612128i | \(0.980503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.0000 | − | 36.3731i | −1.04608 | − | 1.81187i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | − | 5.19615i | −0.148340 | − | 0.256933i | 0.782274 | − | 0.622935i | \(-0.214060\pi\) |
−0.930614 | + | 0.366002i | \(0.880726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.0000 | + | 15.5885i | 0.885722 | + | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | + | 25.9808i | −0.736321 | + | 1.27535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | + | 3.46410i | −0.0970143 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00000 | − | 20.7846i | 0.193574 | − | 1.00584i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00000 | + | 15.5885i | 0.433515 | + | 0.750870i | 0.997173 | − | 0.0751385i | \(-0.0239399\pi\) |
−0.563658 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0000 | −1.10531 | −0.552655 | − | 0.833410i | \(-0.686385\pi\) | ||||
−0.552655 | + | 0.833410i | \(0.686385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | − | 13.8564i | −0.382692 | − | 0.662842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.50000 | + | 12.9904i | −0.357955 | + | 0.619997i | −0.987619 | − | 0.156871i | \(-0.949859\pi\) |
0.629664 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5000 | − | 25.1147i | 0.688916 | − | 1.19324i | −0.283273 | − | 0.959039i | \(-0.591420\pi\) |
0.972189 | − | 0.234198i | \(-0.0752464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | − | 17.3205i | −0.474045 | − | 0.821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | − | 31.1769i | 0.281284 | − | 1.46160i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | + | 19.0526i | −0.514558 | + | 0.891241i | 0.485299 | + | 0.874348i | \(0.338711\pi\) |
−0.999857 | + | 0.0168929i | \(0.994623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0000 | 0.978068 | 0.489034 | − | 0.872265i | \(-0.337349\pi\) | ||||
0.489034 | + | 0.872265i | \(0.337349\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.50000 | + | 12.9904i | −0.347059 | + | 0.601123i | −0.985726 | − | 0.168360i | \(-0.946153\pi\) |
0.638667 | + | 0.769483i | \(0.279486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | + | 10.3923i | 0.554109 | + | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | + | 20.7846i | 0.551761 | + | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.00000 | − | 1.73205i | −0.0456912 | − | 0.0791394i | 0.842275 | − | 0.539048i | \(-0.181216\pi\) |
−0.887967 | + | 0.459908i | \(0.847882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.50000 | − | 6.06218i | −0.158600 | − | 0.274703i | 0.775764 | − | 0.631023i | \(-0.217365\pi\) |
−0.934364 | + | 0.356320i | \(0.884031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | − | 17.3205i | −0.450377 | − | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.0000 | + | 10.3923i | −1.34568 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | − | 6.92820i | 0.179065 | − | 0.310149i | −0.762496 | − | 0.646993i | \(-0.776026\pi\) |
0.941560 | + | 0.336844i | \(0.109360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.0000 | 0.624229 | 0.312115 | − | 0.950044i | \(-0.398963\pi\) | ||||
0.312115 | + | 0.950044i | \(0.398963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.0000 | −1.33498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.5000 | + | 33.7750i | −0.864322 | + | 1.49705i | 0.00339621 | + | 0.999994i | \(0.498919\pi\) |
−0.867719 | + | 0.497056i | \(0.834414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.0000 | + | 19.0526i | 0.973223 | + | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | + | 20.7846i | 0.525730 | + | 0.910590i | 0.999551 | + | 0.0299693i | \(0.00954094\pi\) |
−0.473821 | + | 0.880621i | \(0.657126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.00000 | + | 1.73205i | −0.0437269 | + | 0.0757373i | −0.887061 | − | 0.461653i | \(-0.847256\pi\) |
0.843334 | + | 0.537390i | \(0.180590\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0000 | − | 24.2487i | 0.609850 | − | 1.05629i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | + | 20.7846i | 0.518805 | + | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.5000 | + | 7.79423i | 0.839924 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | + | 8.66025i | −0.214967 | + | 0.372333i | −0.953262 | − | 0.302144i | \(-0.902298\pi\) |
0.738296 | + | 0.674477i | \(0.235631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.0000 | −1.37073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0000 | 0.940652 | 0.470326 | − | 0.882493i | \(-0.344136\pi\) | ||||
0.470326 | + | 0.882493i | \(0.344136\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0000 | − | 17.3205i | 0.426014 | − | 0.737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.50000 | + | 6.06218i | 0.148300 | + | 0.256863i | 0.930599 | − | 0.366040i | \(-0.119287\pi\) |
−0.782299 | + | 0.622903i | \(0.785953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.0000 | − | 17.3205i | −0.421450 | − | 0.729972i | 0.574632 | − | 0.818412i | \(-0.305145\pi\) |
−0.996082 | + | 0.0884397i | \(0.971812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0000 | − | 20.7846i | 0.504844 | − | 0.874415i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0000 | + | 31.1769i | −0.754599 | + | 1.30700i | 0.190974 | + | 0.981595i | \(0.438835\pi\) |
−0.945573 | + | 0.325409i | \(0.894498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50000 | − | 2.59808i | −0.0624458 | − | 0.108159i | 0.833112 | − | 0.553104i | \(-0.186557\pi\) |
−0.895558 | + | 0.444945i | \(0.853223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.5000 | + | 12.9904i | −1.55576 | + | 0.538932i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | − | 25.9808i | 0.621237 | − | 1.07601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.0000 | 0.825488 | 0.412744 | − | 0.910847i | \(-0.364570\pi\) | ||||
0.412744 | + | 0.910847i | \(0.364570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | 1.15372 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | + | 10.3923i | −0.246390 | + | 0.426761i | −0.962522 | − | 0.271205i | \(-0.912578\pi\) |
0.716131 | + | 0.697966i | \(0.245911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0000 | − | 6.92820i | 0.819920 | − | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.00000 | − | 12.1244i | −0.286012 | − | 0.495388i | 0.686842 | − | 0.726807i | \(-0.258996\pi\) |
−0.972854 | + | 0.231419i | \(0.925663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00000 | − | 3.46410i | −0.0813116 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.50000 | + | 16.4545i | −0.385593 | + | 0.667867i | −0.991851 | − | 0.127401i | \(-0.959336\pi\) |
0.606258 | + | 0.795268i | \(0.292670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | − | 10.3923i | 0.242734 | − | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.0000 | − | 29.4449i | −0.686624 | − | 1.18927i | −0.972924 | − | 0.231127i | \(-0.925759\pi\) |
0.286300 | − | 0.958140i | \(-0.407575\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0000 | + | 31.1769i | 0.723481 | + | 1.25311i | 0.959596 | + | 0.281381i | \(0.0907924\pi\) |
−0.236115 | + | 0.971725i | \(0.575874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.00000 | − | 25.9808i | 0.200321 | − | 1.04090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.0000 | 1.63218 | 0.816092 | − | 0.577922i | \(-0.196136\pi\) | ||||
0.816092 | + | 0.577922i | \(0.196136\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | − | 13.8564i | 0.317470 | − | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.0000 | − | 25.9808i | 1.30751 | − | 1.02940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.0000 | − | 32.9090i | −0.750455 | − | 1.29983i | −0.947602 | − | 0.319452i | \(-0.896501\pi\) |
0.197148 | − | 0.980374i | \(-0.436832\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | + | 15.5885i | 0.353827 | + | 0.612845i | 0.986916 | − | 0.161233i | \(-0.0515470\pi\) |
−0.633090 | + | 0.774078i | \(0.718214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5000 | + | 23.3827i | −0.529921 | + | 0.917851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00000 | − | 12.1244i | 0.273931 | − | 0.474463i | −0.695934 | − | 0.718106i | \(-0.745009\pi\) |
0.969865 | + | 0.243643i | \(0.0783426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.0000 | + | 22.5167i | 0.507952 | + | 0.879799i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.0000 | −0.895953 | −0.447976 | − | 0.894045i | \(-0.647855\pi\) | ||||
−0.447976 | + | 0.894045i | \(0.647855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0000 | + | 39.8372i | 0.894596 | + | 1.54949i | 0.834303 | + | 0.551306i | \(0.185870\pi\) |
0.0602929 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000 | + | 13.8564i | 0.620453 | + | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | − | 17.3205i | 0.387202 | − | 0.670653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.50000 | − | 2.59808i | 0.0576497 | − | 0.0998522i | −0.835760 | − | 0.549095i | \(-0.814973\pi\) |
0.893410 | + | 0.449242i | \(0.148306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.5000 | + | 4.33013i | −0.479706 | + | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5000 | − | 38.9711i | −0.860939 | − | 1.49119i | −0.871024 | − | 0.491240i | \(-0.836544\pi\) |
0.0100856 | − | 0.999949i | \(-0.496790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.0000 | −1.22266 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.0000 | − | 51.9615i | −1.14291 | − | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | − | 13.8564i | 0.304334 | − | 0.527123i | −0.672779 | − | 0.739844i | \(-0.734899\pi\) |
0.977113 | + | 0.212721i | \(0.0682327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | + | 6.92820i | 0.151511 | + | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.0000 | −1.73740 | −0.868698 | − | 0.495342i | \(-0.835043\pi\) | ||||
−0.868698 | + | 0.495342i | \(0.835043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.0000 | − | 25.9808i | −1.12827 | − | 0.977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.0000 | + | 34.6410i | −0.751116 | + | 1.30097i | 0.196167 | + | 0.980571i | \(0.437151\pi\) |
−0.947282 | + | 0.320400i | \(0.896183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.0000 | 1.04861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | 1.34632 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0000 | − | 36.3731i | 0.783168 | − | 1.35649i | −0.146920 | − | 0.989148i | \(-0.546936\pi\) |
0.930087 | − | 0.367338i | \(-0.119731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.50000 | − | 4.33013i | −0.0928477 | − | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.0000 | −1.48352 | −0.741759 | − | 0.670667i | \(-0.766008\pi\) | ||||
−0.741759 | + | 0.670667i | \(0.766008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | + | 27.7128i | 0.591781 | + | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0000 | − | 17.3205i | 0.369358 | − | 0.639748i | −0.620107 | − | 0.784517i | \(-0.712911\pi\) |
0.989465 | + | 0.144770i | \(0.0462441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.00000 | + | 15.5885i | −0.331519 | + | 0.574208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.00000 | + | 12.1244i | 0.257499 | + | 0.446002i | 0.965571 | − | 0.260138i | \(-0.0837682\pi\) |
−0.708072 | + | 0.706140i | \(0.750435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.0000 | 1.24734 | 0.623670 | − | 0.781688i | \(-0.285641\pi\) | ||||
0.623670 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | + | 8.66025i | 0.183186 | + | 0.317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 31.1769i | −0.219235 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.0000 | −1.38296 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.0000 | 1.67190 | 0.835949 | − | 0.548807i | \(-0.184918\pi\) | ||||
0.835949 | + | 0.548807i | \(0.184918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0000 | + | 41.5692i | −0.869999 | + | 1.50688i | −0.00800331 | + | 0.999968i | \(0.502548\pi\) |
−0.861996 | + | 0.506915i | \(0.830786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.0000 | − | 27.7128i | −1.15848 | − | 1.00327i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.0000 | + | 46.7654i | 0.974913 | + | 1.68860i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0000 | 0.901523 | 0.450762 | − | 0.892644i | \(-0.351152\pi\) | ||||
0.450762 | + | 0.892644i | \(0.351152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0000 | + | 19.0526i | 0.395643 | + | 0.685273i | 0.993183 | − | 0.116566i | \(-0.0371886\pi\) |
−0.597540 | + | 0.801839i | \(0.703855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.50000 | − | 6.06218i | 0.125724 | − | 0.217760i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.00000 | + | 6.92820i | −0.143315 | + | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.0000 | 1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.00000 | + | 12.1244i | 0.249523 | + | 0.432187i | 0.963394 | − | 0.268091i | \(-0.0863928\pi\) |
−0.713871 | + | 0.700278i | \(0.753059\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.0000 | − | 10.3923i | 1.06668 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | − | 41.5692i | 0.852265 | − | 1.47617i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.00000 | −0.106265 | −0.0531327 | − | 0.998587i | \(-0.516921\pi\) | ||||
−0.0531327 | + | 0.998587i | \(0.516921\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.5000 | + | 28.5788i | −0.582272 | + | 1.00853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | + | 13.8564i | 0.563926 | + | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.00000 | + | 5.19615i | 0.105474 | + | 0.182687i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.00000 | 0.210688 | 0.105344 | − | 0.994436i | \(-0.466406\pi\) | ||||
0.105344 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.0000 | − | 24.2487i | −0.490399 | − | 0.849395i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | + | 27.7128i | −0.559769 | + | 0.969549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | + | 23.3827i | −0.471153 | + | 0.816061i | −0.999456 | − | 0.0329950i | \(-0.989495\pi\) |
0.528302 | + | 0.849056i | \(0.322829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.50000 | − | 14.7224i | −0.296291 | − | 0.513192i | 0.678993 | − | 0.734145i | \(-0.262417\pi\) |
−0.975284 | + | 0.220953i | \(0.929083\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0000 | −1.56480 | −0.782402 | − | 0.622774i | \(-0.786006\pi\) | ||||
−0.782402 | + | 0.622774i | \(0.786006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0000 | + | 29.4449i | 0.590434 | + | 1.02266i | 0.994174 | + | 0.107788i | \(0.0343769\pi\) |
−0.403739 | + | 0.914874i | \(0.632290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.0000 | + | 10.3923i | 0.900847 | + | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 31.1769i | 0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.0000 | − | 39.8372i | 0.791224 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | − | 5.19615i | 0.0343604 | − | 0.178542i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | + | 13.8564i | −0.272956 | + | 0.472774i | −0.969618 | − | 0.244626i | \(-0.921335\pi\) |
0.696661 | + | 0.717400i | \(0.254668\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.00000 | − | 12.1244i | 0.238283 | − | 0.412718i | −0.721939 | − | 0.691957i | \(-0.756749\pi\) |
0.960222 | + | 0.279239i | \(0.0900822\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0000 | − | 19.0526i | −0.374011 | − | 0.647806i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00000 | −0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0000 | + | 31.1769i | 0.609907 | + | 1.05639i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.0000 | − | 10.3923i | 1.01419 | − | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0000 | 0.336527 | 0.168263 | − | 0.985742i | \(-0.446184\pi\) | ||||
0.168263 | + | 0.985742i | \(0.446184\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.00000 | − | 15.5885i | 0.302190 | − | 0.523409i | −0.674441 | − | 0.738328i | \(-0.735615\pi\) |
0.976632 | + | 0.214919i | \(0.0689488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | − | 6.92820i | 0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.00000 | + | 6.92820i | 0.133855 | + | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.00000 | −0.0668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.5000 | + | 30.3109i | 0.583658 | + | 1.01092i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0000 | − | 34.6410i | 0.666297 | − | 1.15406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.0000 | + | 27.7128i | −0.531858 | + | 0.921205i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.0000 | 1.45779 | 0.728893 | − | 0.684628i | \(-0.240035\pi\) | ||||
0.728893 | + | 0.684628i | \(0.240035\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.5000 | − | 38.9711i | −0.744641 | − | 1.28976i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.50000 | + | 33.7750i | −0.214649 | + | 1.11535i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.500000 | + | 0.866025i | −0.0164935 | + | 0.0285675i | −0.874154 | − | 0.485648i | \(-0.838584\pi\) |
0.857661 | + | 0.514216i | \(0.171917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −72.0000 | −2.36991 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.00000 | − | 3.46410i | 0.0656179 | − | 0.113653i | −0.831350 | − | 0.555749i | \(-0.812431\pi\) |
0.896968 | + | 0.442096i | \(0.145765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | + | 27.7128i | 0.131095 | + | 0.908251i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | + | 20.7846i | 0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5000 | − | 28.5788i | −0.537885 | − | 0.931644i | −0.999018 | − | 0.0443125i | \(-0.985890\pi\) |
0.461133 | − | 0.887331i | \(-0.347443\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.00000 | + | 6.92820i | −0.130258 | + | 0.225613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.50000 | − | 6.06218i | 0.113735 | − | 0.196994i | −0.803539 | − | 0.595253i | \(-0.797052\pi\) |
0.917273 | + | 0.398258i | \(0.130385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.0000 | + | 57.1577i | 1.07123 | + | 1.85542i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0000 | − | 17.3205i | −0.323592 | − | 0.560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.0000 | − | 27.7128i | −1.03333 | − | 0.894893i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.0000 | −1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0000 | − | 45.0333i | 0.834380 | − | 1.44519i | −0.0601548 | − | 0.998189i | \(-0.519159\pi\) |
0.894534 | − | 0.446999i | \(-0.147507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.0000 | − | 46.7654i | −0.863807 | − | 1.49616i | −0.868227 | − | 0.496167i | \(-0.834741\pi\) |
0.00442082 | − | 0.999990i | \(-0.498593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | − | 5.19615i | 0.0955879 | − | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | + | 27.7128i | −0.508770 | + | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0000 | − | 41.5692i | −0.762385 | − | 1.32049i | −0.941618 | − | 0.336683i | \(-0.890695\pi\) |
0.179233 | − | 0.983807i | \(-0.442638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0000 | 0.443830 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0000 | − | 39.8372i | −0.728417 | − | 1.26166i | −0.957552 | − | 0.288261i | \(-0.906923\pi\) |
0.229135 | − | 0.973395i | \(-0.426410\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1512.2.s.i.1297.1 | yes | 2 | |
3.2 | odd | 2 | 1512.2.s.e.1297.1 | yes | 2 | ||
7.4 | even | 3 | inner | 1512.2.s.i.865.1 | yes | 2 | |
21.11 | odd | 6 | 1512.2.s.e.865.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.e.865.1 | ✓ | 2 | 21.11 | odd | 6 | ||
1512.2.s.e.1297.1 | yes | 2 | 3.2 | odd | 2 | ||
1512.2.s.i.865.1 | yes | 2 | 7.4 | even | 3 | inner | |
1512.2.s.i.1297.1 | yes | 2 | 1.1 | even | 1 | trivial |