Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(26,567)]
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([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.s (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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Root | \(1.93649 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.26 |
Dual form | 567.2.s.e.458.2 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93649 | − | 1.11803i | 1.36931 | − | 0.790569i | 0.378467 | − | 0.925615i | \(-0.376451\pi\) |
0.990839 | + | 0.135045i | \(0.0431180\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 2.59808i | 0.750000 | − | 1.29904i | ||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.47214i | − | 1.34840i | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||
0.738549 | − | 0.674200i | \(-0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50000 | − | 0.866025i | 0.416025 | − | 0.240192i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −3.87298 | − | 4.47214i | −1.03510 | − | 1.19523i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 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 | ||||
\(23\) | − | 4.47214i | − | 0.932505i | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||
0.884652 | − | 0.466252i | \(-0.154396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 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 | \(-0.197035\pi\) |
−0.0952614 | + | 0.995452i | \(0.530369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 0.866025i | 0.269408 | + | 0.155543i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 5.80948 | + | 3.35410i | 1.02698 | + | 0.592927i | ||||
\(33\) | 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 | \(0.301486\pi\) | |||||||
\(38\) | −7.74597 | −1.25656 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.87298 | + | 6.70820i | 0.604858 | + | 1.04765i | 0.992074 | + | 0.125656i | \(0.0401036\pi\) |
−0.387215 | + | 0.921989i | \(0.626563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | − | 6.06218i | 0.533745 | − | 0.924473i | −0.465478 | − | 0.885059i | \(-0.654118\pi\) |
0.999223 | − | 0.0394140i | \(-0.0125491\pi\) | |||||||
\(44\) | −11.6190 | − | 6.70820i | −1.75162 | − | 1.01130i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | − | 8.66025i | −0.737210 | − | 1.27688i | ||||
\(47\) | 3.87298 | + | 6.70820i | 0.564933 | + | 0.978492i | 0.997056 | + | 0.0766776i | \(0.0244312\pi\) |
−0.432123 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | −9.68246 | + | 5.59017i | −1.36931 | + | 0.790569i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 5.19615i | − | 0.720577i | ||||||
\(53\) | −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 | ||||||||
\(56\) | −5.80948 | + | 1.11803i | −0.776324 | + | 0.149404i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.0000 | 1.31306 | ||||||||
\(59\) | −3.87298 | + | 6.70820i | −0.504219 | + | 0.873334i | 0.495769 | + | 0.868455i | \(0.334886\pi\) |
−0.999988 | + | 0.00487911i | \(0.998447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.50000 | + | 4.33013i | −0.960277 | + | 0.554416i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 3.87298 | 0.491869 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.500000 | − | 0.866025i | 0.0610847 | − | 0.105802i | −0.833866 | − | 0.551967i | \(-0.813877\pi\) |
0.894951 | + | 0.446165i | \(0.147211\pi\) | |||||||
\(68\) | 23.2379 | 2.81801 | ||||||||
\(69\) | 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 | \(0.200451\pi\) | |||||||
\(74\) | 11.1803i | 1.29969i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.00000 | + | 5.19615i | −1.03237 | + | 0.596040i | ||||
\(77\) | −11.6190 | + | 2.23607i | −1.32410 | + | 0.254824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | − | 9.52628i | −0.618798 | − | 1.07179i | −0.989705 | − | 0.143120i | \(-0.954286\pi\) |
0.370907 | − | 0.928670i | \(-0.379047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.0000 | + | 8.66025i | 1.65647 | + | 0.956365i | ||||
\(83\) | −3.87298 | + | 6.70820i | −0.425115 | + | 0.736321i | −0.996431 | − | 0.0844091i | \(-0.973100\pi\) |
0.571316 | + | 0.820730i | \(0.306433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 15.6525i | − | 1.68785i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.0000 | −1.06600 | ||||||||
\(89\) | 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 | ||||||||
\(94\) | 15.0000 | + | 8.66025i | 1.54713 | + | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50000 | + | 0.866025i | 0.152302 | + | 0.0879316i | 0.574214 | − | 0.818705i | \(-0.305308\pi\) |
−0.421912 | + | 0.906637i | \(0.638641\pi\) | |||||||
\(98\) | −9.68246 | + | 12.2984i | −0.978076 | + | 1.24232i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.50000 | + | 12.9904i | −0.750000 | + | 1.29904i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.19615i | 0.511992i | 0.966678 | + | 0.255996i | \(0.0824034\pi\) | ||||
−0.966678 | + | 0.255996i | \(0.917597\pi\) | |||||||
\(104\) | −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 | ||||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | 7.74597 | − | 4.47214i | 0.728679 | − | 0.420703i | −0.0892596 | − | 0.996008i | \(-0.528450\pi\) |
0.817939 | + | 0.575305i | \(0.195117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.6190 | − | 6.70820i | 1.07879 | − | 0.622841i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.3205i | 1.59448i | ||||||||
\(119\) | 15.4919 | − | 13.4164i | 1.42014 | − | 1.22988i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | −9.68246 | + | 16.7705i | −0.876609 | + | 1.51833i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.50000 | − | 2.59808i | 0.404112 | − | 0.233314i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 13.5554 | − | 7.82624i | 1.19814 | − | 0.691748i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 8.66025i | −0.260133 | + | 0.750939i | ||||
\(134\) | − | 2.23607i | − | 0.193167i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0000 | − | 8.66025i | 1.28624 | − | 0.742611i | ||||
\(137\) | − | 4.47214i | − | 0.382080i | −0.981582 | − | 0.191040i | \(-0.938814\pi\) | ||
0.981582 | − | 0.191040i | \(-0.0611861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.50000 | + | 4.33013i | −0.636142 | + | 0.367277i | −0.783127 | − | 0.621862i | \(-0.786376\pi\) |
0.146985 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.0000 | + | 17.3205i | 0.839181 | + | 1.45350i | ||||
\(143\) | −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 | ||||
\(149\) | − | 17.8885i | − | 1.46549i | −0.680505 | − | 0.732743i | \(-0.738240\pi\) | ||
0.680505 | − | 0.732743i | \(-0.261760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0000 | −1.05792 | −0.528962 | − | 0.848645i | \(-0.677419\pi\) | ||||
−0.528962 | + | 0.848645i | \(0.677419\pi\) | |||||||
\(152\) | −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 | ||||||||
\(157\) | −12.0000 | − | 6.92820i | −0.957704 | − | 0.552931i | −0.0622385 | − | 0.998061i | \(-0.519824\pi\) |
−0.895466 | + | 0.445130i | \(0.853157\pi\) | |||||||
\(158\) | −21.3014 | − | 12.2984i | −1.69465 | − | 0.978406i | ||||
\(159\) | 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 | \(-0.00336213\pi\) | |||||||
\(164\) | 23.2379 | 1.81458 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.3205i | 1.34433i | ||||||||
\(167\) | 3.87298 | + | 6.70820i | 0.299700 | + | 0.519096i | 0.976067 | − | 0.217468i | \(-0.0697799\pi\) |
−0.676367 | + | 0.736565i | \(0.736447\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −7.74597 | − | 13.4164i | −0.588915 | − | 1.02003i | −0.994375 | − | 0.105918i | \(-0.966222\pi\) |
0.405460 | − | 0.914113i | \(-0.367111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | + | 12.9904i | 0.188982 | + | 0.981981i | ||||
\(176\) | 3.87298 | − | 2.23607i | 0.291937 | − | 0.168550i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 34.6410i | − | 2.59645i | ||||||
\(179\) | 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 | \(\pi\) | |||||||||
\(182\) | −9.68246 | − | 3.35410i | −0.717712 | − | 0.248623i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0000 | −0.737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.0000 | − | 17.3205i | 2.19382 | − | 1.26660i | ||||
\(188\) | 23.2379 | 1.69480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.4919 | + | 8.94427i | −1.12096 | + | 0.647185i | −0.941645 | − | 0.336607i | \(-0.890720\pi\) |
−0.179312 | + | 0.983792i | \(0.557387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | 3.87298 | 0.278064 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | + | 20.7846i | −0.214286 | + | 1.48461i | ||||
\(197\) | 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 | \(0.0391815\pi\) | |||||||
\(200\) | 11.1803i | 0.790569i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.87298 | − | 11.1803i | 0.271830 | − | 0.784706i | ||||
\(204\) | 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 | 0.982142 | + | 0.188142i | \(0.0602466\pi\) |
−0.328135 | + | 0.944631i | \(0.606420\pi\) | |||||||
\(212\) | 13.4164i | 0.921443i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.0000 | 0.683586 | ||||||||
\(215\) | 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 | ||||||||
\(221\) | 11.6190 | + | 6.70820i | 0.781575 | + | 0.451243i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.0000 | − | 12.1244i | −1.40626 | − | 0.811907i | −0.411239 | − | 0.911528i | \(-0.634904\pi\) |
−0.995025 | + | 0.0996209i | \(0.968237\pi\) | |||||||
\(224\) | 5.80948 | − | 16.7705i | 0.388162 | − | 1.12053i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0000 | − | 17.3205i | 0.665190 | − | 1.15214i | ||||
\(227\) | −23.2379 | −1.54235 | −0.771177 | − | 0.636621i | \(-0.780332\pi\) | ||||
−0.771177 | + | 0.636621i | \(0.780332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.9808i | − | 1.71686i | −0.512933 | − | 0.858429i | \(-0.671441\pi\) | ||
0.512933 | − | 0.858429i | \(-0.328559\pi\) | |||||||
\(230\) | 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 | ||||||||
\(236\) | 11.6190 | + | 20.1246i | 0.756329 | + | 1.31000i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.0000 | − | 43.3013i | 0.972306 | − | 2.80680i | ||||
\(239\) | 7.74597 | − | 4.47214i | 0.501045 | − | 0.289278i | −0.228100 | − | 0.973638i | \(-0.573251\pi\) |
0.729145 | + | 0.684359i | \(0.239918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5885i | 1.00414i | 0.864827 | + | 0.502070i | \(0.167428\pi\) | ||||
−0.864827 | + | 0.502070i | \(0.832572\pi\) | |||||||
\(242\) | −17.4284 | + | 10.0623i | −1.12034 | + | 0.646830i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 25.9808i | 1.66325i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 1.93649 | − | 3.35410i | 0.122967 | − | 0.212986i | ||||
\(249\) | 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 | ||||||||
\(254\) | −1.93649 | + | 1.11803i | −0.121506 | + | 0.0701517i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.50000 | − | 7.79423i | 0.281250 | − | 0.487139i | ||||
\(257\) | −23.2379 | −1.44954 | −0.724770 | − | 0.688991i | \(-0.758054\pi\) | ||||
−0.724770 | + | 0.688991i | \(0.758054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5000 | + | 4.33013i | 0.776712 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.47214i | − | 0.275764i | −0.990449 | − | 0.137882i | \(-0.955971\pi\) | ||
0.990449 | − | 0.137882i | \(-0.0440294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.87298 | + | 20.1246i | 0.237468 | + | 1.23392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | −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 | ||||
\(275\) | 22.3607i | 1.34840i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | −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 | \(-0.154183\pi\) |
0.0392078 | + | 0.999231i | \(0.487517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5000 | + | 6.06218i | 0.624160 | + | 0.360359i | 0.778487 | − | 0.627661i | \(-0.215988\pi\) |
−0.154327 | + | 0.988020i | \(0.549321\pi\) | |||||||
\(284\) | 23.2379 | + | 13.4164i | 1.37892 | + | 0.796117i | ||||
\(285\) | 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 | ||||||||
\(292\) | − | 20.7846i | − | 1.21633i | ||||||
\(293\) | 3.87298 | + | 6.70820i | 0.226262 | + | 0.391897i | 0.956697 | − | 0.291084i | \(-0.0940161\pi\) |
−0.730435 | + | 0.682982i | \(0.760683\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | −3.87298 | − | 6.70820i | −0.223980 | − | 0.387945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.5000 | − | 6.06218i | −1.00868 | − | 0.349418i | ||||
\(302\) | −25.1744 | + | 14.5344i | −1.44862 | + | 0.836363i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 3.46410i | − | 0.198680i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.19615i | − | 0.296560i | −0.988945 | − | 0.148280i | \(-0.952626\pi\) | ||
0.988945 | − | 0.148280i | \(-0.0473737\pi\) | |||||||
\(308\) | −11.6190 | + | 33.5410i | −0.662051 | + | 1.91118i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.74597 | − | 13.4164i | 0.439233 | − | 0.760775i | −0.558397 | − | 0.829574i | \(-0.688583\pi\) |
0.997631 | + | 0.0687991i | \(0.0219168\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | + | 6.92820i | −0.678280 | + | 0.391605i | −0.799207 | − | 0.601056i | \(-0.794747\pi\) |
0.120927 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(314\) | −30.9839 | −1.74852 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33.0000 | −1.85640 | ||||||||
\(317\) | −3.87298 | + | 2.23607i | −0.217528 | + | 0.125590i | −0.604805 | − | 0.796373i | \(-0.706749\pi\) |
0.387277 | + | 0.921963i | \(0.373416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | − | 17.3205i | 0.559893 | − | 0.969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.0000 | + | 17.3205i | −1.11456 | + | 0.965234i | ||||
\(323\) | − | 26.8328i | − | 1.49302i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.50000 | + | 4.33013i | −0.416025 | + | 0.240192i | ||||
\(326\) | − | 29.0689i | − | 1.60998i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.0000 | − | 8.66025i | 0.828236 | − | 0.478183i | ||||
\(329\) | 15.4919 | − | 13.4164i | 0.854098 | − | 0.739671i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 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 | 0.969468 | − | 0.245220i | \(-0.0788601\pi\) |
−0.697100 | + | 0.716974i | \(0.745527\pi\) | |||||||
\(338\) | 22.3607i | 1.21626i | ||||||||
\(339\) | 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 | ||||||||
\(346\) | −30.0000 | − | 17.3205i | −1.61281 | − | 0.931156i | ||||
\(347\) | −7.74597 | − | 4.47214i | −0.415825 | − | 0.240077i | 0.277464 | − | 0.960736i | \(-0.410506\pi\) |
−0.693290 | + | 0.720659i | \(0.743839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5000 | + | 11.2583i | 1.04381 | + | 0.602645i | 0.920910 | − | 0.389774i | \(-0.127447\pi\) |
0.122901 | + | 0.992419i | \(0.460780\pi\) | |||||||
\(350\) | 19.3649 | + | 22.3607i | 1.03510 | + | 1.19523i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0000 | − | 25.9808i | 0.799503 | − | 1.38478i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 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 | ||||||||
\(364\) | −13.5000 | + | 2.59808i | −0.707592 | + | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.3923i | − | 0.542474i | −0.962513 | − | 0.271237i | \(-0.912567\pi\) | ||
0.962513 | − | 0.271237i | \(-0.0874327\pi\) | |||||||
\(368\) | 3.87298 | − | 2.23607i | 0.201893 | − | 0.116563i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.74597 | + | 8.94427i | 0.402151 | + | 0.464363i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | 38.7298 | − | 67.0820i | 2.00267 | − | 3.46873i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.0000 | − | 8.66025i | 0.773566 | − | 0.446619i | ||||
\(377\) | 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 | ||||||||
\(382\) | −20.0000 | + | 34.6410i | −1.02329 | + | 1.77239i | ||||
\(383\) | −23.2379 | −1.18740 | −0.593701 | − | 0.804686i | \(-0.702334\pi\) | ||||
−0.593701 | + | 0.804686i | \(0.702334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 15.6525i | − | 0.796690i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.50000 | − | 2.59808i | 0.228453 | − | 0.131897i | ||||
\(389\) | 8.94427i | 0.453493i | 0.973954 | + | 0.226746i | \(0.0728088\pi\) | ||||
−0.973954 | + | 0.226746i | \(0.927191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.0000 | − | 17.3205i | 1.51717 | − | 0.875936i | ||||
\(392\) | 5.80948 | + | 14.5344i | 0.293423 | + | 0.734100i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0000 | + | 17.3205i | 0.503793 | + | 0.872595i | ||||
\(395\) | 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 | ||||
\(401\) | 22.3607i | 1.11664i | 0.829626 | + | 0.558320i | \(0.188554\pi\) | ||||
−0.829626 | + | 0.558320i | \(0.811446\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | 0.149441 | ||||||||
\(404\) | 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 | ||||||||
\(409\) | 19.5000 | + | 11.2583i | 0.964213 | + | 0.556689i | 0.897467 | − | 0.441081i | \(-0.145405\pi\) |
0.0667458 | + | 0.997770i | \(0.478738\pi\) | |||||||
\(410\) | 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 | ||||||||
\(416\) | 11.6190 | 0.569666 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.6410i | 1.69435i | ||||||||
\(419\) | −7.74597 | − | 13.4164i | −0.378415 | − | 0.655434i | 0.612417 | − | 0.790535i | \(-0.290198\pi\) |
−0.990832 | + | 0.135101i | \(0.956864\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | − | 29.4449i | 0.828529 | − | 1.43505i | −0.0706626 | − | 0.997500i | \(-0.522511\pi\) |
0.899192 | − | 0.437555i | \(-0.144155\pi\) | |||||||
\(422\) | 36.7933 | + | 21.2426i | 1.79107 | + | 1.03408i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.00000 | + | 8.66025i | 0.242821 | + | 0.420579i | ||||
\(425\) | −19.3649 | − | 33.5410i | −0.939336 | − | 1.62698i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.0000 | + | 17.3205i | 0.725901 | + | 0.838198i | ||||
\(428\) | 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 | \(0.877791\pi\) | |||||||
\(434\) | −1.93649 | − | 10.0623i | −0.0929546 | − | 0.483006i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.00000 | 0.143674 | ||||||||
\(437\) | −7.74597 | + | 13.4164i | −0.370540 | + | 0.641794i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.00000 | + | 1.73205i | −0.143182 | + | 0.0826663i | −0.569880 | − | 0.821728i | \(-0.693010\pi\) |
0.426698 | + | 0.904394i | \(0.359677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | 30.9839 | − | 17.8885i | 1.47209 | − | 0.849910i | 0.472580 | − | 0.881288i | \(-0.343323\pi\) |
0.999508 | + | 0.0313772i | \(0.00998932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −54.2218 | −2.56748 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.50000 | − | 33.7750i | −0.307096 | − | 1.59572i | ||||
\(449\) | 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 | ||||
\(452\) | − | 26.8328i | − | 1.26211i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −45.0000 | + | 25.9808i | −2.11195 | + | 1.21934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | − | 9.52628i | −0.257279 | − | 0.445621i | 0.708233 | − | 0.705979i | \(-0.249493\pi\) |
−0.965512 | + | 0.260358i | \(0.916159\pi\) | |||||||
\(458\) | −29.0474 | − | 50.3115i | −1.35729 | − | 2.35090i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.87298 | + | 6.70820i | −0.180383 | + | 0.312432i | −0.942011 | − | 0.335582i | \(-0.891067\pi\) |
0.761628 | + | 0.648014i | \(0.224400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | − | 6.92820i | −0.185896 | − | 0.321981i | 0.757982 | − | 0.652275i | \(-0.226185\pi\) |
−0.943878 | + | 0.330294i | \(0.892852\pi\) | |||||||
\(464\) | 4.47214i | 0.207614i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.0000 | −0.926482 | ||||||||
\(467\) | −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 | ||||||||
\(472\) | 15.0000 | + | 8.66025i | 0.690431 | + | 0.398621i | ||||
\(473\) | −27.1109 | − | 15.6525i | −1.24656 | − | 0.719702i | ||||
\(474\) | 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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.66025i | 0.394874i | ||||||||
\(482\) | 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 | \(0.472238\pi\) | |||||||
\(488\) | 9.68246 | + | 16.7705i | 0.438304 | + | 0.759165i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3649 | − | 11.1803i | 0.873926 | − | 0.504562i | 0.00527540 | − | 0.999986i | \(-0.498321\pi\) |
0.868651 | + | 0.495424i | \(0.164987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.6410i | 1.56015i | ||||||||
\(494\) | −11.6190 | + | 6.70820i | −0.522761 | + | 0.301816i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | 23.2379 | − | 4.47214i | 1.04236 | − | 0.200603i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.0000 | −1.38775 | −0.693875 | − | 0.720095i | \(-0.744098\pi\) | ||||
−0.693875 | + | 0.720095i | \(0.744098\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −45.0000 | + | 25.9808i | −2.00845 | + | 1.15958i | ||||
\(503\) | 23.2379 | 1.03613 | 0.518063 | − | 0.855342i | \(-0.326653\pi\) | ||||
0.518063 | + | 0.855342i | \(0.326653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −38.7298 | + | 22.3607i | −1.72175 | + | 0.994053i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.50000 | + | 2.59808i | −0.0665517 | + | 0.115271i | ||||
\(509\) | 23.2379 | 1.03000 | 0.515001 | − | 0.857190i | \(-0.327792\pi\) | ||||
0.515001 | + | 0.857190i | \(0.327792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 13.8564i | −0.530849 | − | 0.612971i | ||||
\(512\) | 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 | ||||
\(518\) | 29.0474 | − | 5.59017i | 1.27627 | − | 0.245618i | ||||
\(519\) | 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 | ||||
\(527\) | 13.4164i | 0.584428i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 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 | ||||||||
\(536\) | −1.93649 | − | 1.11803i | −0.0836437 | − | 0.0482917i | ||||
\(537\) | 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 | \(0.263972\pi\) | |||||||
\(542\) | 3.87298 | 0.166359 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 51.9615i | 2.22783i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.50000 | + | 9.52628i | −0.235163 | + | 0.407314i | −0.959320 | − | 0.282321i | \(-0.908896\pi\) |
0.724157 | + | 0.689635i | \(0.242229\pi\) | |||||||
\(548\) | −11.6190 | − | 6.70820i | −0.496337 | − | 0.286560i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.0000 | + | 43.3013i | 1.06600 | + | 1.84637i | ||||
\(551\) | −7.74597 | − | 13.4164i | −0.329989 | − | 0.571558i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.0000 | + | 19.0526i | −0.935535 | + | 0.810197i | ||||
\(554\) | 9.68246 | − | 5.59017i | 0.411368 | − | 0.237504i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.9808i | 1.10183i | ||||||||
\(557\) | 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 | ||||||||
\(562\) | 40.0000 | 1.68730 | ||||||||
\(563\) | −3.87298 | + | 6.70820i | −0.163227 | + | 0.282717i | −0.936024 | − | 0.351936i | \(-0.885524\pi\) |
0.772797 | + | 0.634653i | \(0.218857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.1109 | 1.13956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0000 | 0.839181 | ||||||||
\(569\) | −15.4919 | + | 8.94427i | −0.649456 | + | 0.374963i | −0.788248 | − | 0.615358i | \(-0.789011\pi\) |
0.138792 | + | 0.990322i | \(0.455678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | − | 13.8564i | 0.334790 | − | 0.579873i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | −23.2379 | −0.971625 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.0000 | − | 43.3013i | 0.626088 | − | 1.80736i | ||||
\(575\) | 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 | \(0.644549\pi\) | |||||||
\(578\) | 96.1509i | 3.99935i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.3649 | + | 6.70820i | 0.803392 | + | 0.278303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0000 | + | 17.3205i | 0.414158 | + | 0.717342i | ||||
\(584\) | −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 | 0.346140 | + | 0.938183i | \(0.387492\pi\) |
−0.985560 | + | 0.169326i | \(0.945841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | − | 5.19615i | −0.123613 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.00000 | −0.205499 | ||||||||
\(593\) | −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 | ||||||||
\(598\) | −15.0000 | − | 8.66025i | −0.613396 | − | 0.354144i | ||||
\(599\) | −7.74597 | − | 4.47214i | −0.316492 | − | 0.182727i | 0.333336 | − | 0.942808i | \(-0.391826\pi\) |
−0.649828 | + | 0.760082i | \(0.725159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.5000 | + | 21.6506i | 1.52966 | + | 0.883148i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) |
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | −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 | ||||||||
\(607\) | − | 31.1769i | − | 1.26543i | −0.774384 | − | 0.632716i | \(-0.781940\pi\) | ||
0.774384 | − | 0.632716i | \(-0.218060\pi\) | |||||||
\(608\) | −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 | \(0.987092\pi\) | |||||||
\(614\) | −5.80948 | − | 10.0623i | −0.234451 | − | 0.406082i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.00000 | + | 25.9808i | 0.201456 | + | 1.04679i | ||||
\(617\) | 19.3649 | − | 11.1803i | 0.779602 | − | 0.450104i | −0.0566871 | − | 0.998392i | \(-0.518054\pi\) |
0.836289 | + | 0.548288i | \(0.184720\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.19615i | 0.208851i | 0.994533 | + | 0.104425i | \(0.0333004\pi\) | ||||
−0.994533 | + | 0.104425i | \(0.966700\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 34.6410i | − | 1.38898i | ||||||
\(623\) | −38.7298 | − | 13.4164i | −1.55168 | − | 0.537517i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −15.4919 | + | 26.8328i | −0.619182 | + | 1.07246i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.0000 | + | 20.7846i | −1.43656 | + | 0.829396i | ||||
\(629\) | −38.7298 | −1.54426 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | −21.3014 | + | 12.2984i | −0.847325 | + | 0.489203i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.00000 | + | 8.66025i | −0.198575 | + | 0.343943i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.50000 | + | 9.52628i | −0.297161 | + | 0.377445i | ||||
\(638\) | − | 44.7214i | − | 1.77054i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.47214i | − | 0.176639i | −0.996092 | − | 0.0883194i | \(-0.971850\pi\) | ||
0.996092 | − | 0.0883194i | \(-0.0281496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5000 | + | 9.52628i | −0.650696 | + | 0.375680i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | −11.6190 | + | 33.5410i | −0.457851 | + | 1.32170i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.0000 | − | 51.9615i | −1.18033 | − | 2.04440i | ||||
\(647\) | −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 | ||||
\(653\) | 22.3607i | 0.875041i | 0.899208 | + | 0.437521i | \(0.144143\pi\) | ||||
−0.899208 | + | 0.437521i | \(0.855857\pi\) | |||||||
\(654\) | 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 | \(-0.220052\pi\) |
−0.166929 | + | 0.985969i | \(0.553385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0000 | + | 13.8564i | 0.933492 | + | 0.538952i | 0.887914 | − | 0.460009i | \(-0.152154\pi\) |
0.0455776 | + | 0.998961i | \(0.485487\pi\) | |||||||
\(662\) | 7.74597 | + | 4.47214i | 0.301056 | + | 0.173814i | ||||
\(663\) | 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 | ||||
\(668\) | 23.2379 | 0.899101 | ||||||||
\(669\) | 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 | −0.884655 | − | 0.466246i | \(-0.845606\pi\) |
0.846108 | + | 0.533011i | \(0.178940\pi\) | |||||||
\(674\) | 19.3649 | + | 11.1803i | 0.745909 | + | 0.430651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0000 | + | 25.9808i | 0.576923 | + | 0.999260i | ||||
\(677\) | 15.4919 | + | 26.8328i | 0.595403 | + | 1.03127i | 0.993490 | + | 0.113921i | \(0.0363411\pi\) |
−0.398086 | + | 0.917348i | \(0.630326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.50000 | − | 4.33013i | 0.0575647 | − | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 17.3205i | − | 0.663237i | ||||||
\(683\) | 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 | ||||||||
\(686\) | 36.7933 | + | 19.0066i | 1.40478 | + | 0.725675i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.00000 | 0.266872 | ||||||||
\(689\) | −3.87298 | + | 6.70820i | −0.147549 | + | 0.255562i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5000 | − | 16.4545i | 1.08419 | − | 0.625958i | 0.152167 | − | 0.988355i | \(-0.451375\pi\) |
0.932024 | + | 0.362397i | \(0.118041\pi\) | |||||||
\(692\) | −46.4758 | −1.76674 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.0000 | + | 51.9615i | −1.13633 | + | 1.96818i | ||||
\(698\) | 50.3488 | 1.90573 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 37.5000 | + | 12.9904i | 1.41737 | + | 0.490990i | ||||
\(701\) | 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 | ||||
\(704\) | − | 58.1378i | − | 2.19115i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.50000 | − | 9.52628i | −0.206557 | − | 0.357767i | 0.744071 | − | 0.668101i | \(-0.232892\pi\) |
−0.950628 | + | 0.310334i | \(0.899559\pi\) | |||||||
\(710\) | 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 | ||||||||
\(716\) | − | 26.8328i | − | 1.00279i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.0000 | 0.373197 | ||||||||
\(719\) | 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 | ||||||||
\(725\) | −19.3649 | − | 11.1803i | −0.719195 | − | 0.415227i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.5000 | − | 9.52628i | −0.611951 | − | 0.353310i | 0.161778 | − | 0.986827i | \(-0.448277\pi\) |
−0.773729 | + | 0.633517i | \(0.781611\pi\) | |||||||
\(728\) | −7.74597 | + | 6.70820i | −0.287085 | + | 0.248623i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.2218 | 2.00546 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 36.3731i | − | 1.34347i | −0.740792 | − | 0.671735i | \(-0.765549\pi\) | ||
0.740792 | − | 0.671735i | \(-0.234451\pi\) | |||||||
\(734\) | −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 | ||||||||
\(742\) | 25.0000 | + | 8.66025i | 0.917779 | + | 0.317928i | ||||
\(743\) | −27.1109 | + | 15.6525i | −0.994602 | + | 0.574234i | −0.906647 | − | 0.421891i | \(-0.861367\pi\) |
−0.0879552 | + | 0.996124i | \(0.528033\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.87298 | − | 2.23607i | 0.141800 | − | 0.0818683i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 103.923i | − | 3.79980i | ||||||
\(749\) | 3.87298 | − | 11.1803i | 0.141516 | − | 0.408521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | −3.87298 | + | 6.70820i | −0.141233 | + | 0.244623i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.0000 | − | 8.66025i | 0.546268 | − | 0.315388i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0000 | −0.908640 | −0.454320 | − | 0.890838i | \(-0.650118\pi\) | ||||
−0.454320 | + | 0.890838i | \(0.650118\pi\) | |||||||
\(758\) | 32.9204 | − | 19.0066i | 1.19572 | − | 0.690350i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00000 | − | 1.73205i | 0.0724049 | − | 0.0627044i | ||||
\(764\) | 53.6656i | 1.94155i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −45.0000 | + | 25.9808i | −1.62592 | + | 0.938723i | ||||
\(767\) | 13.4164i | 0.484438i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | + | 17.3205i | −1.08183 | + | 0.624593i | −0.931389 | − | 0.364026i | \(-0.881402\pi\) |
−0.150439 | + | 0.988619i | \(0.548069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.5000 | − | 18.1865i | −0.377903 | − | 0.654548i | ||||
\(773\) | 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 | ||||
\(779\) | − | 26.8328i | − | 0.961385i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.0000 | 1.43131 | ||||||||
\(782\) | 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 | ||||||||
\(787\) | −16.5000 | − | 9.52628i | −0.588161 | − | 0.339575i | 0.176209 | − | 0.984353i | \(-0.443617\pi\) |
−0.764370 | + | 0.644778i | \(0.776950\pi\) | |||||||
\(788\) | 23.2379 | + | 13.4164i | 0.827816 | + | 0.477940i | ||||
\(789\) | 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 | ||||
\(794\) | −65.8407 | −2.33660 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 67.5500i | − | 2.39425i | ||||||
\(797\) | −19.3649 | − | 33.5410i | −0.685941 | − | 1.18808i | −0.973140 | − | 0.230213i | \(-0.926058\pi\) |
0.287200 | − | 0.957871i | \(-0.407276\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | −15.4919 | − | 26.8328i | −0.546698 | − | 0.946910i | ||||
\(804\) | 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 | \(-0.0584065\pi\) | |||||||
\(812\) | −23.2379 | − | 26.8328i | −0.815490 | − | 0.941647i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 50.0000 | 1.75250 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.0000 | + | 12.1244i | −0.734697 | + | 0.424178i | ||||
\(818\) | 50.3488 | 1.76040 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3649 | − | 11.1803i | 0.675840 | − | 0.390197i | −0.122446 | − | 0.992475i | \(-0.539074\pi\) |
0.798286 | + | 0.602279i | \(0.205740\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5000 | − | 37.2391i | 0.749443 | − | 1.29807i | −0.198647 | − | 0.980071i | \(-0.563655\pi\) |
0.948090 | − | 0.318002i | \(-0.103012\pi\) | |||||||
\(824\) | 11.6190 | 0.404765 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 45.0000 | − | 8.66025i | 1.56575 | − | 0.301329i | ||||
\(827\) | 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 | ||||
\(833\) | −42.6028 | − | 33.5410i | −1.47610 | − | 1.16213i | ||||
\(834\) | 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 | −0.925104 | − | 0.379714i | \(-0.876022\pi\) |
0.791394 | + | 0.611307i | \(0.209356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.50000 | − | 7.79423i | −0.155172 | − | 0.268767i | ||||
\(842\) | − | 76.0263i | − | 2.62004i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 57.0000 | 1.96202 | ||||||||
\(845\) | 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 | ||||||||
\(850\) | −75.0000 | − | 43.3013i | −2.57248 | − | 1.48522i | ||||
\(851\) | 19.3649 | + | 11.1803i | 0.663821 | + | 0.383257i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0000 | − | 6.92820i | −0.410872 | − | 0.237217i | 0.280292 | − | 0.959915i | \(-0.409569\pi\) |
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(854\) | 48.4123 | + | 16.7705i | 1.65663 | + | 0.573875i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.00000 | − | 8.66025i | 0.170896 | − | 0.296001i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.19615i | − | 0.177290i | −0.996063 | − | 0.0886452i | \(-0.971746\pi\) | ||
0.996063 | − | 0.0886452i | \(-0.0282537\pi\) | |||||||
\(860\) | 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 | ||||||||
\(866\) | 17.4284 | + | 30.1869i | 0.592242 | + | 1.02579i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.00000 | − | 10.3923i | −0.305480 | − | 0.352738i | ||||
\(869\) | −42.6028 | + | 24.5967i | −1.44520 | + | 0.834388i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.73205i | − | 0.0586883i | ||||||
\(872\) | 1.93649 | − | 1.11803i | 0.0655779 | − | 0.0378614i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34.6410i | 1.17175i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.0000 | −0.844190 | −0.422095 | − | 0.906552i | \(-0.638705\pi\) | ||||
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(878\) | −3.87298 | + | 6.70820i | −0.130707 | + | 0.226391i | ||||
\(879\) | 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 | \(0.457022\pi\) | |||||||
\(884\) | 34.8569 | − | 20.1246i | 1.17236 | − | 0.676864i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.0000 | − | 69.2820i | 1.34383 | − | 2.32758i | ||||
\(887\) | 23.2379 | 0.780252 | 0.390126 | − | 0.920761i | \(-0.372431\pi\) | ||||
0.390126 | + | 0.920761i | \(0.372431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.500000 | + | 2.59808i | 0.0167695 | + | 0.0871367i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −63.0000 | + | 36.3731i | −2.10940 | + | 1.21786i | ||||
\(893\) | − | 26.8328i | − | 0.897926i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −27.1109 | − | 31.3050i | −0.905711 | − | 1.04583i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0000 | + | 17.3205i | 0.333704 | + | 0.577993i | ||||
\(899\) | 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 | ||||||||
\(907\) | 5.00000 | 0.166022 | 0.0830111 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830111 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(908\) | −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 | \(-0.309730\pi\) |
−0.434467 | + | 0.900688i | \(0.643063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.0000 | + | 17.3205i | 0.992855 | + | 0.573225i | ||||
\(914\) | −21.3014 | − | 12.2984i | −0.704588 | − | 0.406794i | ||||
\(915\) | 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 | ||||||||
\(922\) | 17.3205i | 0.570421i | ||||||||
\(923\) | 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 | ||||
\(929\) | 15.4919 | + | 26.8328i | 0.508274 | + | 0.880356i | 0.999954 | + | 0.00958031i | \(0.00304955\pi\) |
−0.491680 | + | 0.870776i | \(0.663617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0000 | + | 3.46410i | 0.786568 | + | 0.113531i | ||||
\(932\) | −23.2379 | + | 13.4164i | −0.761183 | + | 0.439469i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 69.2820i | 2.26698i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 46.7654i | − | 1.52776i | −0.645359 | − | 0.763879i | \(-0.723292\pi\) | ||
0.645359 | − | 0.763879i | \(-0.276708\pi\) | |||||||
\(938\) | −5.80948 | + | 1.11803i | −0.189686 | + | 0.0365051i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.3649 | − | 33.5410i | 0.631278 | − | 1.09341i | −0.356012 | − | 0.934481i | \(-0.615864\pi\) |
0.987291 | − | 0.158925i | \(-0.0508027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0000 | − | 17.3205i | 0.976934 | − | 0.564033i | ||||
\(944\) | −7.74597 | −0.252110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −70.0000 | −2.27590 | ||||||||
\(947\) | −3.87298 | + | 2.23607i | −0.125855 | + | 0.0726624i | −0.561606 | − | 0.827405i | \(-0.689816\pi\) |
0.435751 | + | 0.900067i | \(0.356483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | − | 10.3923i | 0.194768 | − | 0.337348i | ||||
\(950\) | 38.7298 | 1.25656 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −30.0000 | − | 34.6410i | −0.972306 | − | 1.12272i | ||||
\(953\) | − | 58.1378i | − | 1.88327i | −0.336640 | − | 0.941634i | \(-0.609290\pi\) | ||
0.336640 | − | 0.941634i | \(-0.390710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 26.8328i | − | 0.867835i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6190 | + | 2.23607i | −0.375195 | + | 0.0722064i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 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 | 0.993964 | − | 0.109707i | \(-0.0349913\pi\) |
−0.591991 | + | 0.805945i | \(0.701658\pi\) | |||||||
\(968\) | 20.1246i | 0.646830i | ||||||||
\(969\) | 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 | ||||||||
\(976\) | −7.50000 | − | 4.33013i | −0.240069 | − | 0.138604i | ||||
\(977\) | 50.3488 | + | 29.0689i | 1.61080 | + | 0.929996i | 0.989185 | + | 0.146673i | \(0.0468566\pi\) |
0.621615 | + | 0.783323i | \(0.286477\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | −46.4758 | −1.48235 | −0.741174 | − | 0.671313i | \(-0.765731\pi\) | ||||
−0.741174 | + | 0.671313i | \(0.765731\pi\) | |||||||
\(984\) | 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 | \(0.549432\pi\) | |||||||
\(992\) | 5.80948 | + | 10.0623i | 0.184451 | + | 0.319479i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 40.0000 | − | 34.6410i | 1.26872 | − | 1.09875i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 46.7654i | − | 1.48107i | −0.672015 | − | 0.740537i | \(-0.734571\pi\) | ||
0.672015 | − | 0.740537i | \(-0.265429\pi\) | |||||||
\(998\) | −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.s.e.26.2 | 4 | ||
3.2 | odd | 2 | inner | 567.2.s.e.26.1 | 4 | ||
7.3 | odd | 6 | 567.2.i.c.269.2 | 4 | |||
9.2 | odd | 6 | 189.2.p.c.26.2 | yes | 4 | ||
9.4 | even | 3 | 567.2.i.c.215.2 | 4 | |||
9.5 | odd | 6 | 567.2.i.c.215.1 | 4 | |||
9.7 | even | 3 | 189.2.p.c.26.1 | ✓ | 4 | ||
21.17 | even | 6 | 567.2.i.c.269.1 | 4 | |||
63.2 | odd | 6 | 1323.2.c.b.1322.2 | 4 | |||
63.16 | even | 3 | 1323.2.c.b.1322.4 | 4 | |||
63.31 | odd | 6 | inner | 567.2.s.e.458.1 | 4 | ||
63.38 | even | 6 | 189.2.p.c.80.1 | yes | 4 | ||
63.47 | even | 6 | 1323.2.c.b.1322.1 | 4 | |||
63.52 | odd | 6 | 189.2.p.c.80.2 | yes | 4 | ||
63.59 | even | 6 | inner | 567.2.s.e.458.2 | 4 | ||
63.61 | odd | 6 | 1323.2.c.b.1322.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.c.26.1 | ✓ | 4 | 9.7 | even | 3 | ||
189.2.p.c.26.2 | yes | 4 | 9.2 | odd | 6 | ||
189.2.p.c.80.1 | yes | 4 | 63.38 | even | 6 | ||
189.2.p.c.80.2 | yes | 4 | 63.52 | odd | 6 | ||
567.2.i.c.215.1 | 4 | 9.5 | odd | 6 | |||
567.2.i.c.215.2 | 4 | 9.4 | even | 3 | |||
567.2.i.c.269.1 | 4 | 21.17 | even | 6 | |||
567.2.i.c.269.2 | 4 | 7.3 | odd | 6 | |||
567.2.s.e.26.1 | 4 | 3.2 | odd | 2 | inner | ||
567.2.s.e.26.2 | 4 | 1.1 | even | 1 | trivial | ||
567.2.s.e.458.1 | 4 | 63.31 | odd | 6 | inner | ||
567.2.s.e.458.2 | 4 | 63.59 | even | 6 | inner | ||
1323.2.c.b.1322.1 | 4 | 63.47 | even | 6 | |||
1323.2.c.b.1322.2 | 4 | 63.2 | odd | 6 | |||
1323.2.c.b.1322.3 | 4 | 63.61 | odd | 6 | |||
1323.2.c.b.1322.4 | 4 | 63.16 | even | 3 |