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.e.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 | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 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 | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 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 | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | 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 | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 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 | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 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 | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 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 | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 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 | \(0.0743197\pi\) |
−0.286064 | + | 0.958211i | \(0.592347\pi\) | |||||||
\(54\) | 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 | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 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 | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 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 | \(-0.192169\pi\) | ||||
0.823232 | + | 0.567705i | \(0.192169\pi\) | |||||||
\(84\) | 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 | \(0.344474\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | 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 | \(0.101494\pi\) |
−0.203317 | + | 0.979113i | \(0.565172\pi\) | |||||||
\(102\) | 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 | \(-0.636370\pi\) |
0.995474 | − | 0.0950377i | \(-0.0302972\pi\) | |||||||
\(108\) | 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 | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 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 | \(-0.641086\pi\) |
0.996773 | − | 0.0802763i | \(-0.0255803\pi\) | |||||||
\(132\) | 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 | \(0.0728704\pi\) |
−0.290424 | + | 0.956898i | \(0.593796\pi\) | |||||||
\(138\) | 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 | −0.745264 | − | 0.666770i | \(-0.767676\pi\) |
0.950072 | + | 0.312032i | \(0.101010\pi\) | |||||||
\(150\) | 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 | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 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 | −0.995754 | − | 0.0920525i | \(-0.970657\pi\) |
0.577597 | + | 0.816322i | \(0.303991\pi\) | |||||||
\(174\) | 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 | 0.884106 | − | 0.467286i | \(-0.154768\pi\) |
−0.846735 | + | 0.532016i | \(0.821435\pi\) | |||||||
\(180\) | 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 | −0.988255 | − | 0.152813i | \(-0.951167\pi\) |
0.626468 | + | 0.779447i | \(0.284500\pi\) | |||||||
\(192\) | 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 | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 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 | 0.996996 | − | 0.0774548i | \(-0.0246793\pi\) |
−0.565576 | + | 0.824696i | \(0.691346\pi\) | |||||||
\(228\) | 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 | −0.654466 | − | 0.756091i | \(-0.727107\pi\) |
0.982027 | + | 0.188739i | \(0.0604400\pi\) | |||||||
\(234\) | 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 | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 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 | \(-0.365432\pi\) | ||||
0.410276 | + | 0.911961i | \(0.365432\pi\) | |||||||
\(252\) | 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 | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 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 | \(0.141096\pi\) |
−0.0802460 | + | 0.996775i | \(0.525571\pi\) | |||||||
\(270\) | 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 | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 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 | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 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 | \(-0.996185\pi\) |
0.489585 | − | 0.871956i | \(-0.337148\pi\) | |||||||
\(312\) | 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 | \(-0.559395\pi\) |
0.943750 | − | 0.330661i | \(-0.107272\pi\) | |||||||
\(318\) | 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 | 0.822951 | − | 0.568112i | \(-0.192326\pi\) |
−0.903475 | + | 0.428640i | \(0.858993\pi\) | |||||||
\(348\) | 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 | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 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 | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 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 | \(-0.461719\pi\) |
0.799783 | − | 0.600289i | \(-0.204948\pi\) | |||||||
\(384\) | 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 | 0.518110 | − | 0.855314i | \(-0.326636\pi\) |
−0.999779 | + | 0.0210389i | \(0.993303\pi\) | |||||||
\(390\) | 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 | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 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 | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 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 | 0.563658 | − | 0.826008i | \(-0.309393\pi\) |
−0.997173 | + | 0.0751385i | \(0.976060\pi\) | |||||||
\(432\) | 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 | \(0.408580\pi\) |
−0.972189 | + | 0.234198i | \(0.924754\pi\) | |||||||
\(444\) | 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 | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 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 | \(-0.662651\pi\) | ||||
−0.489034 | + | 0.872265i | \(0.662651\pi\) | |||||||
\(462\) | 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 | −0.638667 | − | 0.769483i | \(-0.720514\pi\) |
0.985726 | + | 0.168360i | \(0.0538472\pi\) | |||||||
\(468\) | 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 | 0.887967 | − | 0.459908i | \(-0.152118\pi\) |
−0.842275 | + | 0.539048i | \(0.818784\pi\) | |||||||
\(480\) | 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 | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | 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 | \(-0.601037\pi\) | ||||
−0.312115 | + | 0.950044i | \(0.601037\pi\) | |||||||
\(504\) | 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 | \(-0.501081\pi\) |
0.867719 | − | 0.497056i | \(-0.165586\pi\) | |||||||
\(510\) | 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 | \(-0.990459\pi\) |
0.473821 | − | 0.880621i | \(-0.342874\pi\) | |||||||
\(522\) | 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 | 0.782299 | − | 0.622903i | \(-0.214047\pi\) |
−0.930599 | + | 0.366040i | \(0.880713\pi\) | |||||||
\(558\) | 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 | 0.996082 | − | 0.0884397i | \(-0.0281881\pi\) |
−0.574632 | + | 0.818412i | \(0.694855\pi\) | |||||||
\(564\) | 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 | \(-0.561165\pi\) |
0.945573 | − | 0.325409i | \(-0.105502\pi\) | |||||||
\(570\) | 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 | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | 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 | −0.716131 | − | 0.697966i | \(-0.754089\pi\) |
0.962522 | + | 0.271205i | \(0.0874221\pi\) | |||||||
\(594\) | 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 | 0.972854 | − | 0.231419i | \(-0.0743369\pi\) |
−0.686842 | + | 0.726807i | \(0.741004\pi\) | |||||||
\(600\) | 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 | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 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 | \(0.103499\pi\) |
−0.197148 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(642\) | 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 | 0.633090 | − | 0.774078i | \(-0.281786\pi\) |
−0.986916 | + | 0.161233i | \(0.948453\pi\) | |||||||
\(648\) | 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 | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | 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 | \(-0.352145\pi\) | ||||
0.447976 | + | 0.894045i | \(0.352145\pi\) | |||||||
\(660\) | 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 | −0.893410 | − | 0.449242i | \(-0.851694\pi\) |
0.835760 | + | 0.549095i | \(0.185027\pi\) | |||||||
\(678\) | 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 | \(0.163456\pi\) |
−0.0100856 | + | 0.999949i | \(0.503210\pi\) | |||||||
\(684\) | 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 | \(-0.164957\pi\) | ||||
0.868698 | + | 0.495342i | \(0.164957\pi\) | |||||||
\(702\) | 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 | \(0.453064\pi\) |
−0.930087 | + | 0.367338i | \(0.880269\pi\) | |||||||
\(720\) | 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 | \(-0.714359\pi\) | ||||
−0.623670 | + | 0.781688i | \(0.714359\pi\) | |||||||
\(744\) | 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 | \(-0.497452\pi\) |
0.861996 | − | 0.506915i | \(-0.169214\pi\) | |||||||
\(762\) | 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 | 0.597540 | − | 0.801839i | \(-0.296145\pi\) |
−0.993183 | + | 0.116566i | \(0.962811\pi\) | |||||||
\(774\) | 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 | \(-0.483079\pi\) | ||||
0.0531327 | + | 0.998587i | \(0.483079\pi\) | |||||||
\(798\) | 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 | 0.808458 | − | 0.588555i | \(-0.200303\pi\) |
−0.913932 | + | 0.405868i | \(0.866969\pi\) | |||||||
\(810\) | 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 | −0.528302 | − | 0.849056i | \(-0.677171\pi\) |
0.999456 | + | 0.0329950i | \(0.0105045\pi\) | |||||||
\(822\) | 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 | \(-0.213994\pi\) | ||||
0.782402 | + | 0.622774i | \(0.213994\pi\) | |||||||
\(828\) | 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 | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 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 | 0.670366 | − | 0.742030i | \(-0.266137\pi\) |
−0.977800 | + | 0.209539i | \(0.932804\pi\) | |||||||
\(858\) | 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 | −0.960222 | − | 0.279239i | \(-0.909918\pi\) |
0.721939 | + | 0.691957i | \(0.243251\pi\) | |||||||
\(864\) | 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 | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 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 | −0.976632 | − | 0.214919i | \(-0.931051\pi\) |
0.674441 | + | 0.738328i | \(0.264385\pi\) | |||||||
\(888\) | 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 | \(-0.759965\pi\) | ||||
−0.728893 | + | 0.684628i | \(0.759965\pi\) | |||||||
\(912\) | 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 | −0.896968 | − | 0.442096i | \(-0.854235\pi\) |
0.831350 | + | 0.555749i | \(0.187569\pi\) | |||||||
\(930\) | 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 | \(0.0141097\pi\) |
−0.461133 | + | 0.887331i | \(0.652557\pi\) | |||||||
\(942\) | 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 | −0.917273 | − | 0.398258i | \(-0.869615\pi\) |
0.803539 | + | 0.595253i | \(0.202948\pi\) | |||||||
\(948\) | 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 | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 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 | \(0.480841\pi\) |
−0.894534 | + | 0.446999i | \(0.852493\pi\) | |||||||
\(972\) | 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 | \(0.165259\pi\) |
−0.00442082 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(978\) | 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 | \(-0.972015\pi\) |
0.422027 | − | 0.906583i | \(-0.361319\pi\) | |||||||
\(984\) | 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.e.1297.1 | yes | 2 | |
3.2 | odd | 2 | 1512.2.s.i.1297.1 | yes | 2 | ||
7.4 | even | 3 | inner | 1512.2.s.e.865.1 | ✓ | 2 | |
21.11 | odd | 6 | 1512.2.s.i.865.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.e.865.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
1512.2.s.e.1297.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1512.2.s.i.865.1 | yes | 2 | 21.11 | odd | 6 | ||
1512.2.s.i.1297.1 | yes | 2 | 3.2 | odd | 2 |