Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(215,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.i (of order \(6\), degree \(2\), not 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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.2 | ||
Root | \(1.93649 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.215 |
Dual form | 567.2.i.c.269.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607i | 1.58114i | 0.612372 | + | 0.790569i | \(0.290215\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.87298 | + | 2.23607i | 1.16775 | + | 0.674200i | 0.953149 | − | 0.302502i | \(-0.0978220\pi\) |
0.214600 | + | 0.976702i | \(0.431155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 0.866025i | −0.416025 | − | 0.240192i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −1.93649 | + | 5.59017i | −0.517549 | + | 1.49404i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.87298 | + | 6.70820i | 0.939336 | + | 1.62698i | 0.766712 | + | 0.641991i | \(0.221891\pi\) |
0.172624 | + | 0.984988i | \(0.444775\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 1.73205i | −0.688247 | − | 0.397360i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.00000 | + | 8.66025i | −1.06600 | + | 1.84637i | ||||
\(23\) | −3.87298 | + | 2.23607i | −0.807573 | + | 0.466252i | −0.846112 | − | 0.533005i | \(-0.821063\pi\) |
0.0385394 | + | 0.999257i | \(0.487729\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 1.93649 | − | 3.35410i | 0.379777 | − | 0.657794i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.50000 | − | 2.59808i | −1.41737 | − | 0.490990i | ||||
\(29\) | −3.87298 | + | 2.23607i | −0.719195 | + | 0.415227i | −0.814456 | − | 0.580225i | \(-0.802965\pi\) |
0.0952614 | + | 0.995452i | \(0.469631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | − | 6.70820i | − | 1.18585i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.0000 | + | 8.66025i | −2.57248 | + | 1.48522i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50000 | + | 4.33013i | −0.410997 | + | 0.711868i | −0.994999 | − | 0.0998840i | \(-0.968153\pi\) |
0.584002 | + | 0.811752i | \(0.301486\pi\) | |||||||
\(38\) | 3.87298 | − | 6.70820i | 0.628281 | − | 1.08821i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.87298 | − | 6.70820i | 0.604858 | − | 1.04765i | −0.387215 | − | 0.921989i | \(-0.626563\pi\) |
0.992074 | − | 0.125656i | \(-0.0401036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | + | 6.06218i | 0.533745 | + | 0.924473i | 0.999223 | + | 0.0394140i | \(0.0125491\pi\) |
−0.465478 | + | 0.885059i | \(0.654118\pi\) | |||||||
\(44\) | −11.6190 | − | 6.70820i | −1.75162 | − | 1.01130i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | − | 8.66025i | −0.737210 | − | 1.27688i | ||||
\(47\) | −7.74597 | −1.12987 | −0.564933 | − | 0.825137i | \(-0.691098\pi\) | ||||
−0.564933 | + | 0.825137i | \(0.691098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 9.68246 | + | 5.59017i | 1.36931 | + | 0.790569i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.50000 | + | 2.59808i | 0.624038 | + | 0.360288i | ||||
\(53\) | −3.87298 | + | 2.23607i | −0.531995 | + | 0.307148i | −0.741829 | − | 0.670590i | \(-0.766041\pi\) |
0.209833 | + | 0.977737i | \(0.432708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.93649 | − | 5.59017i | 0.258775 | − | 0.747018i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | − | 8.66025i | −0.656532 | − | 1.13715i | ||||
\(59\) | 7.74597 | 1.00844 | 0.504219 | − | 0.863576i | \(-0.331780\pi\) | ||||
0.504219 | + | 0.863576i | \(0.331780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.66025i | − | 1.10883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) | ||
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 3.87298 | 0.491869 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | −0.0610847 | − | 0.998133i | \(-0.519456\pi\) | ||||
−0.0610847 | + | 0.998133i | \(0.519456\pi\) | |||||||
\(68\) | −11.6190 | − | 20.1246i | −1.40900 | − | 2.44047i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427i | 1.06149i | 0.847532 | + | 0.530745i | \(0.178088\pi\) | ||||
−0.847532 | + | 0.530745i | \(0.821912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | − | 3.46410i | 0.702247 | − | 0.405442i | −0.105937 | − | 0.994373i | \(-0.533784\pi\) |
0.808184 | + | 0.588930i | \(0.200451\pi\) | |||||||
\(74\) | −9.68246 | − | 5.59017i | −1.12556 | − | 0.649844i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.00000 | + | 5.19615i | 1.03237 | + | 0.596040i | ||||
\(77\) | 7.74597 | + | 8.94427i | 0.882735 | + | 1.01929i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.0000 | + | 8.66025i | 1.65647 | + | 0.956365i | ||||
\(83\) | −3.87298 | − | 6.70820i | −0.425115 | − | 0.736321i | 0.571316 | − | 0.820730i | \(-0.306433\pi\) |
−0.996431 | + | 0.0844091i | \(0.973100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −13.5554 | + | 7.82624i | −1.46172 | + | 0.843925i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.00000 | − | 8.66025i | 0.533002 | − | 0.923186i | ||||
\(89\) | 7.74597 | − | 13.4164i | 0.821071 | − | 1.42214i | −0.0838147 | − | 0.996481i | \(-0.526710\pi\) |
0.904886 | − | 0.425655i | \(-0.139956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | − | 3.46410i | −0.314485 | − | 0.363137i | ||||
\(92\) | 11.6190 | − | 6.70820i | 1.21136 | − | 0.699379i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 17.3205i | − | 1.78647i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.50000 | + | 0.866025i | −0.152302 | + | 0.0879316i | −0.574214 | − | 0.818705i | \(-0.694692\pi\) |
0.421912 | + | 0.906637i | \(0.361359\pi\) | |||||||
\(98\) | −9.68246 | + | 12.2984i | −0.978076 | + | 1.24232i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.50000 | + | 12.9904i | −0.750000 | + | 1.29904i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50000 | − | 2.59808i | 0.443398 | − | 0.255996i | −0.261640 | − | 0.965166i | \(-0.584263\pi\) |
0.705038 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(104\) | −1.93649 | + | 3.35410i | −0.189889 | + | 0.328897i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.00000 | − | 8.66025i | −0.485643 | − | 0.841158i | ||||
\(107\) | 3.87298 | + | 2.23607i | 0.374415 | + | 0.216169i | 0.675386 | − | 0.737465i | \(-0.263977\pi\) |
−0.300970 | + | 0.953634i | \(0.597310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | −7.74597 | − | 4.47214i | −0.728679 | − | 0.420703i | 0.0892596 | − | 0.996008i | \(-0.471550\pi\) |
−0.817939 | + | 0.575305i | \(0.804883\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.6190 | − | 6.70820i | 1.07879 | − | 0.622841i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.3205i | 1.59448i | ||||||||
\(119\) | 3.87298 | + | 20.1246i | 0.355036 | + | 1.84482i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.50000 | + | 7.79423i | 0.409091 | + | 0.708566i | ||||
\(122\) | 19.3649 | 1.75322 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.19615i | 0.466628i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 15.6525i | 1.38350i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 6.92820i | −0.520266 | − | 0.600751i | ||||
\(134\) | − | 2.23607i | − | 0.193167i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0000 | − | 8.66025i | 1.28624 | − | 0.742611i | ||||
\(137\) | 3.87298 | + | 2.23607i | 0.330891 | + | 0.191040i | 0.656237 | − | 0.754555i | \(-0.272147\pi\) |
−0.325345 | + | 0.945595i | \(0.605481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.50000 | + | 4.33013i | 0.636142 | + | 0.367277i | 0.783127 | − | 0.621862i | \(-0.213624\pi\) |
−0.146985 | + | 0.989139i | \(0.546957\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.0000 | −1.67836 | ||||||||
\(143\) | −3.87298 | − | 6.70820i | −0.323875 | − | 0.560968i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.74597 | + | 13.4164i | 0.641061 | + | 1.11035i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.50000 | − | 12.9904i | 0.616496 | − | 1.06780i | ||||
\(149\) | −15.4919 | + | 8.94427i | −1.26915 | + | 0.732743i | −0.974827 | − | 0.222963i | \(-0.928427\pi\) |
−0.294322 | + | 0.955706i | \(0.595094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.50000 | − | 11.2583i | 0.528962 | − | 0.916190i | −0.470467 | − | 0.882418i | \(-0.655915\pi\) |
0.999430 | − | 0.0337724i | \(-0.0107521\pi\) | |||||||
\(152\) | −3.87298 | + | 6.70820i | −0.314140 | + | 0.544107i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20.0000 | + | 17.3205i | −1.61165 | + | 1.39573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8564i | 1.10586i | 0.833227 | + | 0.552931i | \(0.186491\pi\) | ||||
−0.833227 | + | 0.552931i | \(0.813509\pi\) | |||||||
\(158\) | 24.5967i | 1.95681i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.6190 | + | 2.23607i | −0.915702 | + | 0.176227i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.50000 | − | 11.2583i | 0.509119 | − | 0.881820i | −0.490825 | − | 0.871258i | \(-0.663305\pi\) |
0.999944 | − | 0.0105623i | \(-0.00336213\pi\) | |||||||
\(164\) | −11.6190 | + | 20.1246i | −0.907288 | + | 1.57147i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0000 | − | 8.66025i | 1.16423 | − | 0.672166i | ||||
\(167\) | 3.87298 | − | 6.70820i | 0.299700 | − | 0.519096i | −0.676367 | − | 0.736565i | \(-0.736447\pi\) |
0.976067 | + | 0.217468i | \(0.0697799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | − | 8.66025i | −0.384615 | − | 0.666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.5000 | − | 18.1865i | −0.800617 | − | 1.38671i | ||||
\(173\) | 15.4919 | 1.17783 | 0.588915 | − | 0.808195i | \(-0.299555\pi\) | ||||
0.588915 | + | 0.808195i | \(0.299555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | − | 8.66025i | 0.755929 | − | 0.654654i | ||||
\(176\) | −3.87298 | − | 2.23607i | −0.291937 | − | 0.168550i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.0000 | + | 17.3205i | 2.24860 | + | 1.29823i | ||||
\(179\) | 7.74597 | − | 4.47214i | 0.578961 | − | 0.334263i | −0.181760 | − | 0.983343i | \(-0.558179\pi\) |
0.760720 | + | 0.649080i | \(0.224846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 7.74597 | − | 6.70820i | 0.574169 | − | 0.497245i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.00000 | + | 8.66025i | 0.368605 | + | 0.638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.6410i | 2.53320i | ||||||||
\(188\) | 23.2379 | 1.69480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.8885i | − | 1.29437i | −0.762333 | − | 0.647185i | \(-0.775946\pi\) | ||
0.762333 | − | 0.647185i | \(-0.224054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | −1.93649 | − | 3.35410i | −0.139032 | − | 0.240810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.5000 | − | 12.9904i | −1.17857 | − | 0.927884i | ||||
\(197\) | 8.94427i | 0.637253i | 0.947880 | + | 0.318626i | \(0.103222\pi\) | ||||
−0.947880 | + | 0.318626i | \(0.896778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5000 | − | 11.2583i | 1.38232 | − | 0.798082i | 0.389885 | − | 0.920864i | \(-0.372515\pi\) |
0.992434 | + | 0.122782i | \(0.0391815\pi\) | |||||||
\(200\) | −9.68246 | − | 5.59017i | −0.684653 | − | 0.395285i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.6190 | + | 2.23607i | −0.815490 | + | 0.156941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.80948 | + | 10.0623i | 0.404765 | + | 0.701074i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.50000 | + | 0.866025i | 0.104006 | + | 0.0600481i | ||||
\(209\) | −7.74597 | − | 13.4164i | −0.535800 | − | 0.928032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.50000 | − | 16.4545i | 0.654007 | − | 1.13277i | −0.328135 | − | 0.944631i | \(-0.606420\pi\) |
0.982142 | − | 0.188142i | \(-0.0602466\pi\) | |||||||
\(212\) | 11.6190 | − | 6.70820i | 0.797993 | − | 0.460721i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.00000 | + | 8.66025i | −0.341793 | + | 0.592003i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50000 | − | 4.33013i | 0.101827 | − | 0.293948i | ||||
\(218\) | −1.93649 | + | 1.11803i | −0.131156 | + | 0.0757228i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.4164i | − | 0.902485i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.0000 | − | 12.1244i | 1.40626 | − | 0.811907i | 0.411239 | − | 0.911528i | \(-0.365096\pi\) |
0.995025 | + | 0.0996209i | \(0.0317630\pi\) | |||||||
\(224\) | 5.80948 | − | 16.7705i | 0.388162 | − | 1.12053i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0000 | − | 17.3205i | 0.665190 | − | 1.15214i | ||||
\(227\) | 11.6190 | − | 20.1246i | 0.771177 | − | 1.33572i | −0.165742 | − | 0.986169i | \(-0.553002\pi\) |
0.936918 | − | 0.349548i | \(-0.113665\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.5000 | + | 12.9904i | −1.48684 | + | 0.858429i | −0.999888 | − | 0.0149989i | \(-0.995226\pi\) |
−0.486954 | + | 0.873427i | \(0.661892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00000 | + | 8.66025i | 0.328266 | + | 0.568574i | ||||
\(233\) | −7.74597 | − | 4.47214i | −0.507455 | − | 0.292979i | 0.224332 | − | 0.974513i | \(-0.427980\pi\) |
−0.731787 | + | 0.681533i | \(0.761313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −23.2379 | −1.51266 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −45.0000 | + | 8.66025i | −2.91692 | + | 0.561361i | ||||
\(239\) | −7.74597 | − | 4.47214i | −0.501045 | − | 0.289278i | 0.228100 | − | 0.973638i | \(-0.426749\pi\) |
−0.729145 | + | 0.684359i | \(0.760082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5000 | − | 7.79423i | −0.869611 | − | 0.502070i | −0.00239235 | − | 0.999997i | \(-0.500762\pi\) |
−0.867219 | + | 0.497927i | \(0.834095\pi\) | |||||||
\(242\) | −17.4284 | + | 10.0623i | −1.12034 | + | 0.646830i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 25.9808i | 1.66325i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | + | 5.19615i | 0.190885 | + | 0.330623i | ||||
\(248\) | −3.87298 | −0.245935 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.2379 | −1.46676 | −0.733382 | − | 0.679817i | \(-0.762059\pi\) | ||||
−0.733382 | + | 0.679817i | \(0.762059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | − | 2.23607i | − | 0.140303i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | 11.6190 | + | 20.1246i | 0.724770 | + | 1.25534i | 0.959069 | + | 0.283174i | \(0.0913874\pi\) |
−0.234298 | + | 0.972165i | \(0.575279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0000 | + | 8.66025i | −0.621370 | + | 0.538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.87298 | + | 2.23607i | 0.238818 | + | 0.137882i | 0.614634 | − | 0.788813i | \(-0.289304\pi\) |
−0.375815 | + | 0.926695i | \(0.622637\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.4919 | − | 13.4164i | 0.949871 | − | 0.822613i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.00000 | 0.183254 | ||||||||
\(269\) | −7.74597 | − | 13.4164i | −0.472280 | − | 0.818013i | 0.527217 | − | 0.849731i | \(-0.323236\pi\) |
−0.999497 | + | 0.0317179i | \(0.989902\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50000 | + | 0.866025i | 0.0911185 | + | 0.0526073i | 0.544867 | − | 0.838523i | \(-0.316580\pi\) |
−0.453748 | + | 0.891130i | \(0.649914\pi\) | |||||||
\(272\) | −3.87298 | − | 6.70820i | −0.234834 | − | 0.406745i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.00000 | + | 8.66025i | −0.302061 | + | 0.523185i | ||||
\(275\) | 19.3649 | − | 11.1803i | 1.16775 | − | 0.674200i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.50000 | + | 4.33013i | −0.150210 | + | 0.260172i | −0.931305 | − | 0.364241i | \(-0.881328\pi\) |
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −9.68246 | + | 16.7705i | −0.580715 | + | 1.00583i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4919 | + | 8.94427i | −0.924171 | + | 0.533571i | −0.884963 | − | 0.465661i | \(-0.845817\pi\) |
−0.0392078 | + | 0.999231i | \(0.512483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.1244i | − | 0.720718i | −0.932814 | − | 0.360359i | \(-0.882654\pi\) | ||
0.932814 | − | 0.360359i | \(-0.117346\pi\) | |||||||
\(284\) | − | 26.8328i | − | 1.59223i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0000 | − | 8.66025i | 0.886969 | − | 0.512092i | ||||
\(287\) | 15.4919 | − | 13.4164i | 0.914460 | − | 0.791946i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.5000 | + | 37.2391i | −1.26471 | + | 2.19053i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.0000 | + | 10.3923i | −1.05337 | + | 0.608164i | ||||
\(293\) | 3.87298 | − | 6.70820i | 0.226262 | − | 0.391897i | −0.730435 | − | 0.682982i | \(-0.760683\pi\) |
0.956697 | + | 0.291084i | \(0.0940161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.68246 | + | 5.59017i | 0.562781 | + | 0.324922i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.0000 | − | 34.6410i | −1.15857 | − | 2.00670i | ||||
\(299\) | 7.74597 | 0.447961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.50000 | + | 18.1865i | 0.201737 | + | 1.04825i | ||||
\(302\) | 25.1744 | + | 14.5344i | 1.44862 | + | 0.836363i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | + | 1.73205i | 0.172062 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.19615i | − | 0.296560i | −0.988945 | − | 0.148280i | \(-0.952626\pi\) | ||
0.988945 | − | 0.148280i | \(-0.0473737\pi\) | |||||||
\(308\) | −23.2379 | − | 26.8328i | −1.32410 | − | 1.52894i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4919 | −0.878467 | −0.439233 | − | 0.898373i | \(-0.644750\pi\) | ||||
−0.439233 | + | 0.898373i | \(0.644750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.8564i | − | 0.783210i | −0.920133 | − | 0.391605i | \(-0.871920\pi\) | ||
0.920133 | − | 0.391605i | \(-0.128080\pi\) | |||||||
\(314\) | −30.9839 | −1.74852 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33.0000 | −1.85640 | ||||||||
\(317\) | − | 4.47214i | − | 0.251180i | −0.992082 | − | 0.125590i | \(-0.959918\pi\) | ||
0.992082 | − | 0.125590i | \(-0.0400824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.0000 | −1.11979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.00000 | − | 25.9808i | −0.278639 | − | 1.44785i | ||||
\(323\) | − | 26.8328i | − | 1.49302i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.50000 | + | 4.33013i | −0.416025 | + | 0.240192i | ||||
\(326\) | 25.1744 | + | 14.5344i | 1.39428 | + | 0.804988i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.0000 | − | 8.66025i | −0.828236 | − | 0.478183i | ||||
\(329\) | −19.3649 | − | 6.70820i | −1.06762 | − | 0.369835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 11.6190 | + | 20.1246i | 0.637673 | + | 1.10448i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.0000 | + | 8.66025i | 0.820763 | + | 0.473868i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | − | 8.66025i | 0.272367 | − | 0.471754i | −0.697100 | − | 0.716974i | \(-0.745527\pi\) |
0.969468 | + | 0.245220i | \(0.0788601\pi\) | |||||||
\(338\) | 19.3649 | − | 11.1803i | 1.05331 | − | 0.608130i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.87298 | − | 6.70820i | 0.209734 | − | 0.363270i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 13.5554 | − | 7.82624i | 0.730860 | − | 0.421962i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.6410i | 1.86231i | ||||||||
\(347\) | 8.94427i | 0.480154i | 0.970754 | + | 0.240077i | \(0.0771726\pi\) | ||||
−0.970754 | + | 0.240077i | \(0.922827\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.5000 | + | 11.2583i | −1.04381 | + | 0.602645i | −0.920910 | − | 0.389774i | \(-0.872553\pi\) |
−0.122901 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(350\) | 19.3649 | + | 22.3607i | 1.03510 | + | 1.19523i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0000 | − | 25.9808i | 0.799503 | − | 1.38478i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −23.2379 | + | 40.2492i | −1.23161 | + | 2.13320i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000 | + | 17.3205i | 0.528516 | + | 0.915417i | ||||
\(359\) | 3.87298 | + | 2.23607i | 0.204408 | + | 0.118015i | 0.598710 | − | 0.800966i | \(-0.295680\pi\) |
−0.394302 | + | 0.918981i | \(0.629014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | − | 6.06218i | −0.184211 | − | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.00000 | + | 10.3923i | 0.471728 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.00000 | + | 5.19615i | 0.469796 | + | 0.271237i | 0.716154 | − | 0.697942i | \(-0.245901\pi\) |
−0.246358 | + | 0.969179i | \(0.579234\pi\) | |||||||
\(368\) | 3.87298 | − | 2.23607i | 0.201893 | − | 0.116563i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6190 | + | 2.23607i | −0.603226 | + | 0.116091i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | − | 1.73205i | −0.0517780 | − | 0.0896822i | 0.838975 | − | 0.544170i | \(-0.183156\pi\) |
−0.890753 | + | 0.454488i | \(0.849822\pi\) | |||||||
\(374\) | −77.4597 | −4.00534 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.3205i | 0.893237i | ||||||||
\(377\) | 7.74597 | 0.398938 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0000 | 0.873231 | 0.436616 | − | 0.899648i | \(-0.356177\pi\) | ||||
0.436616 | + | 0.899648i | \(0.356177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 40.0000 | 2.04658 | ||||||||
\(383\) | 11.6190 | + | 20.1246i | 0.593701 | + | 1.02832i | 0.993729 | + | 0.111817i | \(0.0356670\pi\) |
−0.400028 | + | 0.916503i | \(0.631000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 15.6525i | − | 0.796690i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.50000 | − | 2.59808i | 0.228453 | − | 0.131897i | ||||
\(389\) | −7.74597 | − | 4.47214i | −0.392736 | − | 0.226746i | 0.290609 | − | 0.956842i | \(-0.406142\pi\) |
−0.683345 | + | 0.730096i | \(0.739475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.0000 | − | 17.3205i | −1.51717 | − | 0.875936i | ||||
\(392\) | 9.68246 | − | 12.2984i | 0.489038 | − | 0.621162i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.0000 | −1.00759 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5000 | − | 14.7224i | −1.27981 | − | 0.738898i | −0.302995 | − | 0.952992i | \(-0.597987\pi\) |
−0.976813 | + | 0.214094i | \(0.931320\pi\) | |||||||
\(398\) | 25.1744 | + | 43.6033i | 1.26188 | + | 2.18564i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.50000 | + | 4.33013i | −0.125000 | + | 0.216506i | ||||
\(401\) | 19.3649 | − | 11.1803i | 0.967038 | − | 0.558320i | 0.0687059 | − | 0.997637i | \(-0.478113\pi\) |
0.898332 | + | 0.439317i | \(0.144780\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50000 | + | 2.59808i | −0.0747203 | + | 0.129419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.00000 | − | 25.9808i | −0.248146 | − | 1.28940i | ||||
\(407\) | −19.3649 | + | 11.1803i | −0.959883 | + | 0.554189i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.5167i | − | 1.11338i | −0.830721 | − | 0.556689i | \(-0.812072\pi\) | ||
0.830721 | − | 0.556689i | \(-0.187928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.5000 | + | 7.79423i | −0.665097 | + | 0.383994i | ||||
\(413\) | 19.3649 | + | 6.70820i | 0.952885 | + | 0.330089i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.80948 | + | 10.0623i | −0.284833 | + | 0.493345i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.0000 | − | 17.3205i | 1.46735 | − | 0.847174i | ||||
\(419\) | −7.74597 | + | 13.4164i | −0.378415 | + | 0.655434i | −0.990832 | − | 0.135101i | \(-0.956864\pi\) |
0.612417 | + | 0.790535i | \(0.290198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | + | 29.4449i | 0.828529 | + | 1.43505i | 0.899192 | + | 0.437555i | \(0.144155\pi\) |
−0.0706626 | + | 0.997500i | \(0.522511\pi\) | |||||||
\(422\) | 36.7933 | + | 21.2426i | 1.79107 | + | 1.03408i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.00000 | + | 8.66025i | 0.242821 | + | 0.420579i | ||||
\(425\) | 38.7298 | 1.87867 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.50000 | − | 21.6506i | 0.362950 | − | 1.04775i | ||||
\(428\) | −11.6190 | − | 6.70820i | −0.561623 | − | 0.324253i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.1109 | + | 15.6525i | −1.30589 | + | 0.753953i | −0.981407 | − | 0.191940i | \(-0.938522\pi\) |
−0.324479 | + | 0.945893i | \(0.605189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5885i | 0.749133i | 0.927200 | + | 0.374567i | \(0.122209\pi\) | ||||
−0.927200 | + | 0.374567i | \(0.877791\pi\) | |||||||
\(434\) | 9.68246 | + | 3.35410i | 0.464773 | + | 0.161002i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.50000 | − | 2.59808i | −0.0718370 | − | 0.124425i | ||||
\(437\) | 15.4919 | 0.741080 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.46410i | − | 0.165333i | −0.996577 | − | 0.0826663i | \(-0.973656\pi\) | ||
0.996577 | − | 0.0826663i | \(-0.0263436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | 35.7771i | 1.69982i | 0.526927 | + | 0.849910i | \(0.323344\pi\) | ||||
−0.526927 | + | 0.849910i | \(0.676656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.1109 | + | 46.9574i | 1.28374 | + | 2.22350i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 32.5000 | + | 11.2583i | 1.53548 | + | 0.531906i | ||||
\(449\) | 8.94427i | 0.422106i | 0.977475 | + | 0.211053i | \(0.0676893\pi\) | ||||
−0.977475 | + | 0.211053i | \(0.932311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.0000 | − | 17.3205i | 1.41264 | − | 0.815591i | ||||
\(452\) | 23.2379 | + | 13.4164i | 1.09302 | + | 0.631055i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 45.0000 | + | 25.9808i | 2.11195 | + | 1.21934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | 0.514558 | 0.257279 | − | 0.966337i | \(-0.417174\pi\) | ||||
0.257279 | + | 0.966337i | \(0.417174\pi\) | |||||||
\(458\) | −29.0474 | − | 50.3115i | −1.35729 | − | 2.35090i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.87298 | − | 6.70820i | −0.180383 | − | 0.312432i | 0.761628 | − | 0.648014i | \(-0.224400\pi\) |
−0.942011 | + | 0.335582i | \(0.891067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | + | 6.92820i | −0.185896 | + | 0.321981i | −0.943878 | − | 0.330294i | \(-0.892852\pi\) |
0.757982 | + | 0.652275i | \(0.226185\pi\) | |||||||
\(464\) | 3.87298 | − | 2.23607i | 0.179799 | − | 0.103807i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0000 | − | 17.3205i | 0.463241 | − | 0.802357i | ||||
\(467\) | −15.4919 | + | 26.8328i | −0.716881 | + | 1.24167i | 0.245348 | + | 0.969435i | \(0.421098\pi\) |
−0.962229 | + | 0.272240i | \(0.912236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.50000 | − | 0.866025i | −0.115439 | − | 0.0399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 17.3205i | − | 0.797241i | ||||||
\(473\) | 31.3050i | 1.43940i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | + | 8.66025i | −0.688247 | + | 0.397360i | ||||
\(476\) | −11.6190 | − | 60.3738i | −0.532554 | − | 2.76723i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.0000 | − | 17.3205i | 0.457389 | − | 0.792222i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50000 | − | 4.33013i | 0.341971 | − | 0.197437i | ||||
\(482\) | 17.4284 | − | 30.1869i | 0.793843 | − | 1.37498i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.5000 | − | 23.3827i | −0.613636 | − | 1.06285i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | + | 34.6410i | 0.906287 | + | 1.56973i | 0.819181 | + | 0.573535i | \(0.194428\pi\) |
0.0871056 | + | 0.996199i | \(0.472238\pi\) | |||||||
\(488\) | −19.3649 | −0.876609 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3649 | − | 11.1803i | −0.873926 | − | 0.504562i | −0.00527540 | − | 0.999986i | \(-0.501679\pi\) |
−0.868651 | + | 0.495424i | \(0.835013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.0000 | − | 17.3205i | −1.35113 | − | 0.780076i | ||||
\(494\) | −11.6190 | + | 6.70820i | −0.522761 | + | 0.301816i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −7.74597 | + | 22.3607i | −0.347454 | + | 1.00301i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | + | 26.8468i | 0.693875 | + | 1.20183i | 0.970558 | + | 0.240866i | \(0.0774314\pi\) |
−0.276683 | + | 0.960961i | \(0.589235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 51.9615i | − | 2.31916i | ||||||
\(503\) | 23.2379 | 1.03613 | 0.518063 | − | 0.855342i | \(-0.326653\pi\) | ||||
0.518063 | + | 0.855342i | \(0.326653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 44.7214i | − | 1.98811i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.00000 | 0.133103 | ||||||||
\(509\) | −11.6190 | − | 20.1246i | −0.515001 | − | 0.892008i | −0.999848 | − | 0.0174091i | \(-0.994458\pi\) |
0.484848 | − | 0.874599i | \(-0.338875\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | − | 3.46410i | 0.796273 | − | 0.153243i | ||||
\(512\) | 11.1803i | 0.494106i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −45.0000 | + | 25.9808i | −1.98486 | + | 1.14596i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.0000 | − | 17.3205i | −1.31940 | − | 0.761755i | ||||
\(518\) | −19.3649 | − | 22.3607i | −0.850846 | − | 0.982472i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.87298 | + | 6.70820i | 0.169678 | + | 0.293892i | 0.938307 | − | 0.345804i | \(-0.112394\pi\) |
−0.768628 | + | 0.639696i | \(0.779060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5000 | − | 9.52628i | −0.721495 | − | 0.416555i | 0.0938079 | − | 0.995590i | \(-0.470096\pi\) |
−0.815303 | + | 0.579035i | \(0.803429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.00000 | + | 8.66025i | −0.218010 | + | 0.377605i | ||||
\(527\) | 11.6190 | − | 6.70820i | 0.506129 | − | 0.292214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.50000 | + | 2.59808i | −0.0652174 | + | 0.112960i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.0000 | + | 20.7846i | 0.780399 | + | 0.901127i | ||||
\(533\) | −11.6190 | + | 6.70820i | −0.503273 | + | 0.290565i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.23607i | 0.0965834i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.0000 | − | 17.3205i | 1.29339 | − | 0.746740i | ||||
\(539\) | 11.6190 | + | 29.0689i | 0.500464 | + | 1.25209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | + | 12.1244i | −0.300954 | + | 0.521267i | −0.976352 | − | 0.216186i | \(-0.930638\pi\) |
0.675399 | + | 0.737453i | \(0.263972\pi\) | |||||||
\(542\) | −1.93649 | + | 3.35410i | −0.0831794 | + | 0.144071i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 45.0000 | − | 25.9808i | 1.92936 | − | 1.11392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.50000 | − | 9.52628i | −0.235163 | − | 0.407314i | 0.724157 | − | 0.689635i | \(-0.242229\pi\) |
−0.959320 | + | 0.282321i | \(0.908896\pi\) | |||||||
\(548\) | −11.6190 | − | 6.70820i | −0.496337 | − | 0.286560i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.0000 | + | 43.3013i | 1.06600 | + | 1.84637i | ||||
\(551\) | 15.4919 | 0.659979 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.5000 | + | 9.52628i | 1.16942 | + | 0.405099i | ||||
\(554\) | −9.68246 | − | 5.59017i | −0.411368 | − | 0.237504i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.5000 | − | 12.9904i | −0.954213 | − | 0.550915i | ||||
\(557\) | 30.9839 | − | 17.8885i | 1.31283 | − | 0.757962i | 0.330265 | − | 0.943888i | \(-0.392862\pi\) |
0.982564 | + | 0.185926i | \(0.0595286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.1244i | − | 0.512806i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0000 | − | 34.6410i | −0.843649 | − | 1.46124i | ||||
\(563\) | 7.74597 | 0.326454 | 0.163227 | − | 0.986589i | \(-0.447810\pi\) | ||||
0.163227 | + | 0.986589i | \(0.447810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.1109 | 1.13956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0000 | 0.839181 | ||||||||
\(569\) | − | 17.8885i | − | 0.749927i | −0.927040 | − | 0.374963i | \(-0.877655\pi\) | ||
0.927040 | − | 0.374963i | \(-0.122345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 11.6190 | + | 20.1246i | 0.485813 | + | 0.841452i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 30.0000 | + | 34.6410i | 1.25218 | + | 1.44589i | ||||
\(575\) | 22.3607i | 0.932505i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.5000 | + | 19.9186i | −1.43625 | + | 0.829222i | −0.997587 | − | 0.0694283i | \(-0.977883\pi\) |
−0.438667 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(578\) | −83.2691 | − | 48.0755i | −3.46354 | − | 1.99968i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.87298 | − | 20.1246i | −0.160678 | − | 0.834910i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.0000 | −0.828315 | ||||||||
\(584\) | −7.74597 | − | 13.4164i | −0.320530 | − | 0.555175i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0000 | + | 8.66025i | 0.619644 | + | 0.357752i | ||||
\(587\) | −15.4919 | − | 26.8328i | −0.639421 | − | 1.10751i | −0.985560 | − | 0.169326i | \(-0.945841\pi\) |
0.346140 | − | 0.938183i | \(-0.387492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | + | 5.19615i | −0.123613 | + | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50000 | − | 4.33013i | 0.102749 | − | 0.177967i | ||||
\(593\) | −15.4919 | + | 26.8328i | −0.636177 | + | 1.10189i | 0.350087 | + | 0.936717i | \(0.386152\pi\) |
−0.986264 | + | 0.165174i | \(0.947181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 46.4758 | − | 26.8328i | 1.90372 | − | 1.09911i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.3205i | 0.708288i | ||||||||
\(599\) | 8.94427i | 0.365453i | 0.983164 | + | 0.182727i | \(0.0584923\pi\) | ||||
−0.983164 | + | 0.182727i | \(0.941508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.5000 | + | 21.6506i | −1.52966 | + | 0.883148i | −0.530281 | + | 0.847822i | \(0.677914\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | −40.6663 | + | 7.82624i | −1.65744 | + | 0.318974i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.5000 | + | 33.7750i | −0.793444 | + | 1.37428i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.0000 | + | 15.5885i | −1.09590 | + | 0.632716i | −0.935140 | − | 0.354278i | \(-0.884727\pi\) |
−0.160756 | + | 0.986994i | \(0.551393\pi\) | |||||||
\(608\) | −11.6190 | + | 20.1246i | −0.471211 | + | 0.816161i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.6190 | + | 6.70820i | 0.470052 | + | 0.271385i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5000 | − | 19.9186i | −0.464481 | − | 0.804504i | 0.534697 | − | 0.845044i | \(-0.320426\pi\) |
−0.999178 | + | 0.0405396i | \(0.987092\pi\) | |||||||
\(614\) | 11.6190 | 0.468903 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.0000 | − | 17.3205i | 0.805823 | − | 0.697863i | ||||
\(617\) | −19.3649 | − | 11.1803i | −0.779602 | − | 0.450104i | 0.0566871 | − | 0.998392i | \(-0.481946\pi\) |
−0.836289 | + | 0.548288i | \(0.815280\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.50000 | − | 2.59808i | −0.180870 | − | 0.104425i | 0.406831 | − | 0.913503i | \(-0.366634\pi\) |
−0.587701 | + | 0.809078i | \(0.699967\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 34.6410i | − | 1.38898i | ||||||
\(623\) | 30.9839 | − | 26.8328i | 1.24134 | − | 1.07503i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 30.9839 | 1.23836 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 41.5692i | − | 1.65879i | ||||||
\(629\) | −38.7298 | −1.54426 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | − | 24.5967i | − | 0.978406i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | 0.397151 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.50000 | − | 11.2583i | −0.178296 | − | 0.446071i | ||||
\(638\) | − | 44.7214i | − | 1.77054i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.87298 | + | 2.23607i | 0.152974 | + | 0.0883194i | 0.574533 | − | 0.818481i | \(-0.305184\pi\) |
−0.421559 | + | 0.906801i | \(0.638517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5000 | + | 9.52628i | 0.650696 | + | 0.375680i | 0.788723 | − | 0.614749i | \(-0.210743\pi\) |
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 34.8569 | − | 6.70820i | 1.37355 | − | 0.264340i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 60.0000 | 2.36067 | ||||||||
\(647\) | −7.74597 | − | 13.4164i | −0.304525 | − | 0.527453i | 0.672630 | − | 0.739979i | \(-0.265165\pi\) |
−0.977156 | + | 0.212525i | \(0.931831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.0000 | + | 17.3205i | 1.17760 | + | 0.679889i | ||||
\(650\) | −9.68246 | − | 16.7705i | −0.379777 | − | 0.657794i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.5000 | + | 33.7750i | −0.763679 | + | 1.32273i | ||||
\(653\) | 19.3649 | − | 11.1803i | 0.757808 | − | 0.437521i | −0.0707003 | − | 0.997498i | \(-0.522523\pi\) |
0.828508 | + | 0.559977i | \(0.189190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.87298 | + | 6.70820i | −0.151215 | + | 0.261911i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.0000 | − | 43.3013i | 0.584761 | − | 1.68806i | ||||
\(659\) | −15.4919 | + | 8.94427i | −0.603480 | + | 0.348419i | −0.770409 | − | 0.637549i | \(-0.779948\pi\) |
0.166929 | + | 0.985969i | \(0.446615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 27.7128i | − | 1.07790i | −0.842337 | − | 0.538952i | \(-0.818821\pi\) | ||
0.842337 | − | 0.538952i | \(-0.181179\pi\) | |||||||
\(662\) | − | 8.94427i | − | 0.347629i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0000 | + | 8.66025i | −0.582113 | + | 0.336083i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | − | 17.3205i | 0.387202 | − | 0.670653i | ||||
\(668\) | −11.6190 | + | 20.1246i | −0.449551 | + | 0.778645i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3649 | − | 33.5410i | 0.747574 | − | 1.29484i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | − | 1.73205i | −0.0385472 | − | 0.0667657i | 0.846108 | − | 0.533011i | \(-0.178940\pi\) |
−0.884655 | + | 0.466246i | \(0.845606\pi\) | |||||||
\(674\) | 19.3649 | + | 11.1803i | 0.745909 | + | 0.430651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0000 | + | 25.9808i | 0.576923 | + | 0.999260i | ||||
\(677\) | −30.9839 | −1.19081 | −0.595403 | − | 0.803427i | \(-0.703008\pi\) | ||||
−0.595403 | + | 0.803427i | \(0.703008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50000 | + | 0.866025i | −0.172694 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.0000 | + | 8.66025i | 0.574380 | + | 0.331618i | ||||
\(683\) | 30.9839 | − | 17.8885i | 1.18556 | − | 0.684486i | 0.228269 | − | 0.973598i | \(-0.426693\pi\) |
0.957295 | + | 0.289112i | \(0.0933600\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34.8569 | + | 22.3607i | −1.33084 | + | 0.853735i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | 7.74597 | 0.295098 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.9090i | 1.25192i | 0.779857 | + | 0.625958i | \(0.215292\pi\) | ||||
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | −46.4758 | −1.76674 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 60.0000 | 2.27266 | ||||||||
\(698\) | −25.1744 | − | 43.6033i | −0.952865 | − | 1.65041i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −30.0000 | + | 25.9808i | −1.13389 | + | 0.981981i | ||||
\(701\) | 8.94427i | 0.337820i | 0.985631 | + | 0.168910i | \(0.0540248\pi\) | ||||
−0.985631 | + | 0.168910i | \(0.945975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0000 | − | 8.66025i | 0.565736 | − | 0.326628i | ||||
\(704\) | 50.3488 | + | 29.0689i | 1.89759 | + | 1.09557i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0000 | 0.413114 | 0.206557 | − | 0.978435i | \(-0.433774\pi\) | ||||
0.206557 | + | 0.978435i | \(0.433774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30.0000 | − | 17.3205i | −1.12430 | − | 0.649113i | ||||
\(713\) | 3.87298 | + | 6.70820i | 0.145044 | + | 0.251224i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.2379 | + | 13.4164i | −0.868441 | + | 0.501395i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.00000 | + | 8.66025i | −0.186598 | + | 0.323198i | ||||
\(719\) | 7.74597 | − | 13.4164i | 0.288876 | − | 0.500348i | −0.684666 | − | 0.728857i | \(-0.740052\pi\) |
0.973542 | + | 0.228509i | \(0.0733852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.5000 | − | 2.59808i | 0.502766 | − | 0.0967574i | ||||
\(722\) | 13.5554 | − | 7.82624i | 0.504481 | − | 0.291262i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.3607i | 0.830455i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5000 | − | 9.52628i | 0.611951 | − | 0.353310i | −0.161778 | − | 0.986827i | \(-0.551723\pi\) |
0.773729 | + | 0.633517i | \(0.218389\pi\) | |||||||
\(728\) | −7.74597 | + | 6.70820i | −0.287085 | + | 0.248623i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.1109 | + | 46.9574i | −1.00273 | + | 1.73678i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.5000 | + | 18.1865i | −1.16348 | + | 0.671735i | −0.952135 | − | 0.305677i | \(-0.901117\pi\) |
−0.211344 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(734\) | −11.6190 | + | 20.1246i | −0.428863 | + | 0.742813i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.0000 | + | 25.9808i | 0.552907 | + | 0.957664i | ||||
\(737\) | −3.87298 | − | 2.23607i | −0.142663 | − | 0.0823666i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.5000 | − | 19.9186i | −0.423034 | − | 0.732717i | 0.573200 | − | 0.819415i | \(-0.305702\pi\) |
−0.996235 | + | 0.0866983i | \(0.972368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.00000 | − | 25.9808i | −0.183556 | − | 0.953784i | ||||
\(743\) | 27.1109 | + | 15.6525i | 0.994602 | + | 0.574234i | 0.906647 | − | 0.421891i | \(-0.138633\pi\) |
0.0879552 | + | 0.996124i | \(0.471967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.87298 | − | 2.23607i | 0.141800 | − | 0.0818683i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 103.923i | − | 3.79980i | ||||||
\(749\) | 7.74597 | + | 8.94427i | 0.283031 | + | 0.326817i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 7.74597 | 0.282466 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.3205i | 0.630776i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0000 | −0.908640 | −0.454320 | − | 0.890838i | \(-0.650118\pi\) | ||||
−0.454320 | + | 0.890838i | \(0.650118\pi\) | |||||||
\(758\) | 38.0132i | 1.38070i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.500000 | + | 2.59808i | 0.0181012 | + | 0.0940567i | ||||
\(764\) | 53.6656i | 1.94155i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −45.0000 | + | 25.9808i | −1.62592 | + | 0.938723i | ||||
\(767\) | −11.6190 | − | 6.70820i | −0.419536 | − | 0.242219i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | + | 17.3205i | 1.08183 | + | 0.624593i | 0.931389 | − | 0.364026i | \(-0.118598\pi\) |
0.150439 | + | 0.988619i | \(0.451931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.0000 | 0.755807 | ||||||||
\(773\) | 15.4919 | + | 26.8328i | 0.557206 | + | 0.965109i | 0.997728 | + | 0.0673675i | \(0.0214600\pi\) |
−0.440522 | + | 0.897742i | \(0.645207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.50000 | − | 4.33013i | −0.269408 | − | 0.155543i | ||||
\(776\) | 1.93649 | + | 3.35410i | 0.0695160 | + | 0.120405i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0000 | − | 17.3205i | 0.358517 | − | 0.620970i | ||||
\(779\) | −23.2379 | + | 13.4164i | −0.832584 | + | 0.480693i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0000 | + | 34.6410i | −0.715656 | + | 1.23955i | ||||
\(782\) | 38.7298 | − | 67.0820i | 1.38498 | − | 2.39885i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0526i | 0.679150i | 0.940579 | + | 0.339575i | \(0.110283\pi\) | ||||
−0.940579 | + | 0.339575i | \(0.889717\pi\) | |||||||
\(788\) | − | 26.8328i | − | 0.955879i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.4919 | − | 17.8885i | −0.550830 | − | 0.636043i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.50000 | + | 12.9904i | −0.266333 | + | 0.461302i | ||||
\(794\) | 32.9204 | − | 57.0197i | 1.16830 | − | 2.02355i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −58.5000 | + | 33.7750i | −2.07348 | + | 1.19712i | ||||
\(797\) | −19.3649 | + | 33.5410i | −0.685941 | + | 1.18808i | 0.287200 | + | 0.957871i | \(0.407276\pi\) |
−0.973140 | + | 0.230213i | \(0.926058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.0000 | − | 51.9615i | −1.06132 | − | 1.83827i | ||||
\(800\) | −29.0474 | − | 16.7705i | −1.02698 | − | 0.592927i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.0000 | + | 43.3013i | 0.882781 | + | 1.52902i | ||||
\(803\) | 30.9839 | 1.09340 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.80948 | − | 3.35410i | −0.204630 | − | 0.118143i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.87298 | + | 2.23607i | −0.136167 | + | 0.0786160i | −0.566536 | − | 0.824037i | \(-0.691717\pi\) |
0.430369 | + | 0.902653i | \(0.358383\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | 34.8569 | − | 6.70820i | 1.22324 | − | 0.235412i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.0000 | − | 43.3013i | −0.876250 | − | 1.51771i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.2487i | − | 0.848355i | ||||||
\(818\) | 50.3488 | 1.76040 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3607i | 0.780393i | 0.920732 | + | 0.390197i | \(0.127593\pi\) | ||||
−0.920732 | + | 0.390197i | \(0.872407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.0000 | −1.49889 | −0.749443 | − | 0.662069i | \(-0.769679\pi\) | ||||
−0.749443 | + | 0.662069i | \(0.769679\pi\) | |||||||
\(824\) | −5.80948 | − | 10.0623i | −0.202383 | − | 0.350537i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.0000 | + | 43.3013i | −0.521917 | + | 1.50664i | ||||
\(827\) | 8.94427i | 0.311023i | 0.987834 | + | 0.155511i | \(0.0497025\pi\) | ||||
−0.987834 | + | 0.155511i | \(0.950297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0000 | + | 6.92820i | −0.416777 | + | 0.240626i | −0.693698 | − | 0.720266i | \(-0.744020\pi\) |
0.276920 | + | 0.960893i | \(0.410686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19.5000 | − | 11.2583i | −0.676041 | − | 0.390312i | ||||
\(833\) | −7.74597 | + | 53.6656i | −0.268382 | + | 1.85940i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 23.2379 | + | 40.2492i | 0.803700 | + | 1.39205i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.0000 | − | 17.3205i | −1.03633 | − | 0.598327i | ||||
\(839\) | −3.87298 | − | 6.70820i | −0.133710 | − | 0.231593i | 0.791394 | − | 0.611307i | \(-0.209356\pi\) |
−0.925104 | + | 0.379714i | \(0.876022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.50000 | + | 7.79423i | −0.155172 | + | 0.268767i | ||||
\(842\) | −65.8407 | + | 38.0132i | −2.26902 | + | 1.31002i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.5000 | + | 49.3634i | −0.981010 | + | 1.69916i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.50000 | + | 23.3827i | 0.154622 | + | 0.803439i | ||||
\(848\) | 3.87298 | − | 2.23607i | 0.132999 | − | 0.0767869i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 86.6025i | 2.97044i | ||||||||
\(851\) | − | 22.3607i | − | 0.766514i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0000 | − | 6.92820i | 0.410872 | − | 0.237217i | −0.280292 | − | 0.959915i | \(-0.590431\pi\) |
0.691164 | + | 0.722698i | \(0.257098\pi\) | |||||||
\(854\) | 48.4123 | + | 16.7705i | 1.65663 | + | 0.573875i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.00000 | − | 8.66025i | 0.170896 | − | 0.296001i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.50000 | + | 2.59808i | −0.153538 | + | 0.0886452i | −0.574801 | − | 0.818293i | \(-0.694920\pi\) |
0.421263 | + | 0.906939i | \(0.361587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −35.0000 | − | 60.6218i | −1.19210 | − | 2.06479i | ||||
\(863\) | −30.9839 | − | 17.8885i | −1.05470 | − | 0.608933i | −0.130741 | − | 0.991417i | \(-0.541736\pi\) |
−0.923962 | + | 0.382483i | \(0.875069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −34.8569 | −1.18448 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.50000 | + | 12.9904i | −0.152740 | + | 0.440922i | ||||
\(869\) | 42.6028 | + | 24.5967i | 1.44520 | + | 0.834388i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50000 | + | 0.866025i | 0.0508256 | + | 0.0293442i | ||||
\(872\) | 1.93649 | − | 1.11803i | 0.0655779 | − | 0.0378614i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34.6410i | 1.17175i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.5000 | + | 21.6506i | 0.422095 | + | 0.731090i | 0.996144 | − | 0.0877308i | \(-0.0279615\pi\) |
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | 7.74597 | 0.261414 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.2379 | 0.782905 | 0.391452 | − | 0.920198i | \(-0.371973\pi\) | ||||
0.391452 | + | 0.920198i | \(0.371973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 40.2492i | 1.35373i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −80.0000 | −2.68765 | ||||||||
\(887\) | −11.6190 | − | 20.1246i | −0.390126 | − | 0.675718i | 0.602340 | − | 0.798240i | \(-0.294235\pi\) |
−0.992466 | + | 0.122522i | \(0.960902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50000 | − | 0.866025i | −0.0838473 | − | 0.0290456i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −63.0000 | + | 36.3731i | −2.10940 | + | 1.21786i | ||||
\(893\) | 23.2379 | + | 13.4164i | 0.777627 | + | 0.448963i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.5554 | + | 39.1312i | −0.452856 | + | 1.30728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.0000 | −0.667409 | ||||||||
\(899\) | 3.87298 | + | 6.70820i | 0.129171 | + | 0.223731i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.0000 | − | 17.3205i | −0.999445 | − | 0.577030i | ||||
\(902\) | 38.7298 | + | 67.0820i | 1.28956 | + | 2.23359i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.0000 | + | 17.3205i | −0.332595 | + | 0.576072i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.50000 | + | 4.33013i | −0.0830111 | + | 0.143780i | −0.904542 | − | 0.426385i | \(-0.859787\pi\) |
0.821531 | + | 0.570164i | \(0.193120\pi\) | |||||||
\(908\) | −34.8569 | + | 60.3738i | −1.15677 | + | 2.00358i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87298 | + | 2.23607i | −0.128318 | + | 0.0740842i | −0.562785 | − | 0.826603i | \(-0.690270\pi\) |
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 34.6410i | − | 1.14645i | ||||||
\(914\) | 24.5967i | 0.813588i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 67.5000 | − | 38.9711i | 2.23026 | − | 1.28764i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.50000 | − | 11.2583i | 0.214415 | − | 0.371378i | −0.738676 | − | 0.674060i | \(-0.764549\pi\) |
0.953092 | + | 0.302682i | \(0.0978821\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.0000 | − | 8.66025i | 0.493999 | − | 0.285210i | ||||
\(923\) | 7.74597 | − | 13.4164i | 0.254962 | − | 0.441606i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5000 | + | 21.6506i | 0.410997 | + | 0.711868i | ||||
\(926\) | −15.4919 | − | 8.94427i | −0.509097 | − | 0.293927i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.0000 | + | 25.9808i | 0.492399 | + | 0.852860i | ||||
\(929\) | −30.9839 | −1.01655 | −0.508274 | − | 0.861196i | \(-0.669716\pi\) | ||||
−0.508274 | + | 0.861196i | \(0.669716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | − | 22.5167i | −0.294963 | − | 0.737954i | ||||
\(932\) | 23.2379 | + | 13.4164i | 0.761183 | + | 0.439469i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −60.0000 | − | 34.6410i | −1.96326 | − | 1.13349i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 46.7654i | − | 1.52776i | −0.645359 | − | 0.763879i | \(-0.723292\pi\) | ||
0.645359 | − | 0.763879i | \(-0.276708\pi\) | |||||||
\(938\) | 1.93649 | − | 5.59017i | 0.0632287 | − | 0.182526i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.7298 | −1.26256 | −0.631278 | − | 0.775556i | \(-0.717469\pi\) | ||||
−0.631278 | + | 0.775556i | \(0.717469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.6410i | 1.12807i | ||||||||
\(944\) | −7.74597 | −0.252110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −70.0000 | −2.27590 | ||||||||
\(947\) | − | 4.47214i | − | 0.145325i | −0.997357 | − | 0.0726624i | \(-0.976850\pi\) | ||
0.997357 | − | 0.0726624i | \(-0.0231496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | −19.3649 | − | 33.5410i | −0.628281 | − | 1.08821i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 45.0000 | − | 8.66025i | 1.45846 | − | 0.280680i | ||||
\(953\) | − | 58.1378i | − | 1.88327i | −0.336640 | − | 0.941634i | \(-0.609290\pi\) | ||
0.336640 | − | 0.941634i | \(-0.390710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23.2379 | + | 13.4164i | 0.751567 | + | 0.433918i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.74597 | + | 8.94427i | 0.250130 | + | 0.288826i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 9.68246 | + | 16.7705i | 0.312175 | + | 0.540703i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40.5000 | + | 23.3827i | 1.30442 | + | 0.753106i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5000 | − | 21.6506i | 0.401973 | − | 0.696237i | −0.591991 | − | 0.805945i | \(-0.701658\pi\) |
0.993964 | + | 0.109707i | \(0.0349913\pi\) | |||||||
\(968\) | 17.4284 | − | 10.0623i | 0.560171 | − | 0.323415i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.9839 | − | 53.6656i | 0.994320 | − | 1.72221i | 0.404984 | − | 0.914324i | \(-0.367277\pi\) |
0.589336 | − | 0.807888i | \(-0.299390\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0000 | + | 17.3205i | 0.480878 | + | 0.555270i | ||||
\(974\) | −77.4597 | + | 44.7214i | −2.48197 | + | 1.43296i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.66025i | 0.277208i | ||||||||
\(977\) | − | 58.1378i | − | 1.85999i | −0.367570 | − | 0.929996i | \(-0.619810\pi\) | ||
0.367570 | − | 0.929996i | \(-0.380190\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60.0000 | − | 34.6410i | 1.91761 | − | 1.10713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.0000 | − | 43.3013i | 0.797782 | − | 1.38180i | ||||
\(983\) | 23.2379 | − | 40.2492i | 0.741174 | − | 1.28375i | −0.210787 | − | 0.977532i | \(-0.567603\pi\) |
0.951961 | − | 0.306219i | \(-0.0990639\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38.7298 | − | 67.0820i | 1.23341 | − | 2.13633i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.00000 | − | 15.5885i | −0.286328 | − | 0.495935i | ||||
\(989\) | −27.1109 | − | 15.6525i | −0.862076 | − | 0.497720i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5000 | + | 42.4352i | 0.778268 | + | 1.34800i | 0.932939 | + | 0.360034i | \(0.117235\pi\) |
−0.154671 | + | 0.987966i | \(0.549432\pi\) | |||||||
\(992\) | −11.6190 | −0.368902 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −50.0000 | − | 17.3205i | −1.58590 | − | 0.549373i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.5000 | + | 23.3827i | 1.28265 | + | 0.740537i | 0.977332 | − | 0.211714i | \(-0.0679045\pi\) |
0.305316 | + | 0.952251i | \(0.401238\pi\) | |||||||
\(998\) | −60.0312 | + | 34.6591i | −1.90026 | + | 1.09711i | ||||
\(999\) | 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 | 567.2.i.c.215.2 | 4 | ||
3.2 | odd | 2 | inner | 567.2.i.c.215.1 | 4 | ||
7.3 | odd | 6 | 567.2.s.e.458.1 | 4 | |||
9.2 | odd | 6 | 567.2.s.e.26.1 | 4 | |||
9.4 | even | 3 | 189.2.p.c.26.1 | ✓ | 4 | ||
9.5 | odd | 6 | 189.2.p.c.26.2 | yes | 4 | ||
9.7 | even | 3 | 567.2.s.e.26.2 | 4 | |||
21.17 | even | 6 | 567.2.s.e.458.2 | 4 | |||
63.5 | even | 6 | 1323.2.c.b.1322.1 | 4 | |||
63.23 | odd | 6 | 1323.2.c.b.1322.2 | 4 | |||
63.31 | odd | 6 | 189.2.p.c.80.2 | yes | 4 | ||
63.38 | even | 6 | inner | 567.2.i.c.269.1 | 4 | ||
63.40 | odd | 6 | 1323.2.c.b.1322.3 | 4 | |||
63.52 | odd | 6 | inner | 567.2.i.c.269.2 | 4 | ||
63.58 | even | 3 | 1323.2.c.b.1322.4 | 4 | |||
63.59 | even | 6 | 189.2.p.c.80.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.c.26.1 | ✓ | 4 | 9.4 | even | 3 | ||
189.2.p.c.26.2 | yes | 4 | 9.5 | odd | 6 | ||
189.2.p.c.80.1 | yes | 4 | 63.59 | even | 6 | ||
189.2.p.c.80.2 | yes | 4 | 63.31 | odd | 6 | ||
567.2.i.c.215.1 | 4 | 3.2 | odd | 2 | inner | ||
567.2.i.c.215.2 | 4 | 1.1 | even | 1 | trivial | ||
567.2.i.c.269.1 | 4 | 63.38 | even | 6 | inner | ||
567.2.i.c.269.2 | 4 | 63.52 | odd | 6 | inner | ||
567.2.s.e.26.1 | 4 | 9.2 | odd | 6 | |||
567.2.s.e.26.2 | 4 | 9.7 | even | 3 | |||
567.2.s.e.458.1 | 4 | 7.3 | odd | 6 | |||
567.2.s.e.458.2 | 4 | 21.17 | even | 6 | |||
1323.2.c.b.1322.1 | 4 | 63.5 | even | 6 | |||
1323.2.c.b.1322.2 | 4 | 63.23 | odd | 6 | |||
1323.2.c.b.1322.3 | 4 | 63.40 | odd | 6 | |||
1323.2.c.b.1322.4 | 4 | 63.58 | even | 3 |