Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(26,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.50917259820\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.1 | ||
Root | \(-1.93649 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.80 |
Dual form | 189.2.p.c.26.1 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | −0.990839 | − | 0.135045i | \(-0.956882\pi\) |
−0.378467 | + | 0.925615i | \(0.623549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 2.59808i | 0.750000 | − | 1.29904i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.87298 | − | 2.23607i | −1.16775 | − | 0.674200i | −0.214600 | − | 0.976702i | \(-0.568845\pi\) |
−0.953149 | + | 0.302502i | \(0.902178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.73205i | − | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) | ||
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 5.80948 | + | 1.11803i | 1.55265 | + | 0.298807i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 3.87298 | − | 6.70820i | 0.939336 | − | 1.62698i | 0.172624 | − | 0.984988i | \(-0.444775\pi\) |
0.766712 | − | 0.641991i | \(-0.221891\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.0000 | 2.13201 | ||||||||
\(23\) | 3.87298 | − | 2.23607i | 0.807573 | − | 0.466252i | −0.0385394 | − | 0.999257i | \(-0.512271\pi\) |
0.846112 | + | 0.533005i | \(0.178937\pi\) | |||||||
\(24\) | 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 | ||||
\(29\) | 4.47214i | 0.830455i | 0.909718 | + | 0.415227i | \(0.136298\pi\) | ||||
−0.909718 | + | 0.415227i | \(0.863702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −5.80948 | − | 3.35410i | −1.02698 | − | 0.592927i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.3205i | 2.97044i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50000 | − | 4.33013i | −0.410997 | − | 0.711868i | 0.584002 | − | 0.811752i | \(-0.301486\pi\) |
−0.994999 | + | 0.0998840i | \(0.968153\pi\) | |||||||
\(38\) | 3.87298 | − | 6.70820i | 0.628281 | − | 1.08821i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.74597 | −1.20972 | −0.604858 | − | 0.796333i | \(-0.706770\pi\) | ||||
−0.604858 | + | 0.796333i | \(0.706770\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.00000 | −1.06749 | −0.533745 | − | 0.845645i | \(-0.679216\pi\) | ||||
−0.533745 | + | 0.845645i | \(0.679216\pi\) | |||||||
\(44\) | −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 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 11.1803i | 1.58114i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.50000 | − | 2.59808i | −0.624038 | − | 0.360288i | ||||
\(53\) | −3.87298 | − | 2.23607i | −0.531995 | − | 0.307148i | 0.209833 | − | 0.977737i | \(-0.432708\pi\) |
−0.741829 | + | 0.670590i | \(0.766041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.87298 | − | 4.47214i | 0.517549 | − | 0.597614i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | − | 8.66025i | −0.656532 | − | 1.13715i | ||||
\(59\) | −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 | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 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 | \(0.147211\pi\) | |||||||
\(68\) | −11.6190 | − | 20.1246i | −1.40900 | − | 2.44047i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.94427i | − | 1.06149i | −0.847532 | − | 0.530745i | \(-0.821912\pi\) | ||
0.847532 | − | 0.530745i | \(-0.178088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | + | 3.46410i | 0.702247 | + | 0.405442i | 0.808184 | − | 0.588930i | \(-0.200451\pi\) |
−0.105937 | + | 0.994373i | \(0.533784\pi\) | |||||||
\(74\) | 9.68246 | + | 5.59017i | 1.12556 | + | 0.649844i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3923i | 1.19208i | ||||||||
\(77\) | 3.87298 | + | 11.1803i | 0.441367 | + | 1.27412i | ||||
\(78\) | 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 | ||||
\(83\) | 7.74597 | 0.850230 | 0.425115 | − | 0.905139i | \(-0.360234\pi\) | ||||
0.425115 | + | 0.905139i | \(0.360234\pi\) | |||||||
\(84\) | 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 | 0.904886 | + | 0.425655i | \(0.139956\pi\) |
−0.0838147 | + | 0.996481i | \(0.526710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 3.46410i | −0.314485 | + | 0.363137i | ||||
\(92\) | − | 13.4164i | − | 1.39876i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.0000 | − | 8.66025i | −1.54713 | − | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.73205i | 0.175863i | 0.996127 | + | 0.0879316i | \(0.0280257\pi\) | ||||
−0.996127 | + | 0.0879316i | \(0.971974\pi\) | |||||||
\(98\) | −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 | −0.705038 | − | 0.709170i | \(-0.749070\pi\) |
0.261640 | + | 0.965166i | \(0.415737\pi\) | |||||||
\(104\) | 3.87298 | 0.379777 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | 3.87298 | − | 2.23607i | 0.374415 | − | 0.216169i | −0.300970 | − | 0.953634i | \(-0.597310\pi\) |
0.675386 | + | 0.737465i | \(0.263977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | − | 0.866025i | 0.0478913 | − | 0.0829502i | −0.841086 | − | 0.540901i | \(-0.818083\pi\) |
0.888977 | + | 0.457951i | \(0.151417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | − | 8.94427i | − | 0.841406i | −0.907198 | − | 0.420703i | \(-0.861783\pi\) | ||
0.907198 | − | 0.420703i | \(-0.138217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.6190 | + | 6.70820i | 1.07879 | + | 0.622841i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 17.3205i | − | 1.59448i | ||||||
\(119\) | −19.3649 | + | 6.70820i | −1.77518 | + | 0.614940i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.50000 | + | 7.79423i | 0.409091 | + | 0.708566i | ||||
\(122\) | −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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.00000 | + | 1.73205i | 0.780399 | + | 0.150188i | ||||
\(134\) | 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 | 0.325345 | − | 0.945595i | \(-0.394519\pi\) |
−0.656237 | + | 0.754555i | \(0.727853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.66025i | 0.734553i | 0.930112 | + | 0.367277i | \(0.119710\pi\) | ||||
−0.930112 | + | 0.367277i | \(0.880290\pi\) | |||||||
\(140\) | 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 | ||||||||
\(146\) | −15.4919 | −1.28212 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.0000 | −1.23299 | ||||||||
\(149\) | 15.4919 | − | 8.94427i | 1.26915 | − | 0.732743i | 0.294322 | − | 0.955706i | \(-0.404906\pi\) |
0.974827 | + | 0.222963i | \(0.0715729\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | 12.0000 | + | 6.92820i | 0.957704 | + | 0.552931i | 0.895466 | − | 0.445130i | \(-0.146843\pi\) |
0.0622385 | + | 0.998061i | \(0.480176\pi\) | |||||||
\(158\) | 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 | 0.999944 | + | 0.0105623i | \(0.00336213\pi\) |
−0.490825 | + | 0.871258i | \(0.663305\pi\) | |||||||
\(164\) | −11.6190 | + | 20.1246i | −0.907288 | + | 1.57147i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0000 | + | 8.66025i | −1.16423 | + | 0.672166i | ||||
\(167\) | −7.74597 | −0.599401 | −0.299700 | − | 0.954033i | \(-0.596887\pi\) | ||||
−0.299700 | + | 0.954033i | \(0.596887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0000 | 0.769231 | ||||||||
\(170\) | 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 | ||||||||
\(175\) | −12.5000 | + | 4.33013i | −0.944911 | + | 0.327327i | ||||
\(176\) | − | 4.47214i | − | 0.337100i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −30.0000 | − | 17.3205i | −2.24860 | − | 1.29823i | ||||
\(179\) | 7.74597 | + | 4.47214i | 0.578961 | + | 0.334263i | 0.760720 | − | 0.649080i | \(-0.224846\pi\) |
−0.181760 | + | 0.983343i | \(0.558179\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 1.93649 | − | 10.0623i | 0.143542 | − | 0.745868i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.00000 | + | 8.66025i | 0.368605 | + | 0.638442i | ||||
\(185\) | 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 | 0.179312 | − | 0.983792i | \(-0.442613\pi\) |
0.941645 | + | 0.336607i | \(0.109280\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | −1.93649 | − | 3.35410i | −0.139032 | − | 0.240810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.5000 | + | 7.79423i | 1.39286 | + | 0.556731i | ||||
\(197\) | − | 8.94427i | − | 0.637253i | −0.947880 | − | 0.318626i | \(-0.896778\pi\) | ||
0.947880 | − | 0.318626i | \(-0.103222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5000 | + | 11.2583i | 1.38232 | + | 0.798082i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | 9.68246 | + | 5.59017i | 0.684653 | + | 0.395285i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.74597 | − | 8.94427i | 0.543660 | − | 0.627765i | ||||
\(204\) | 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 | ||||
\(209\) | 15.4919 | 1.07160 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0000 | −1.30801 | −0.654007 | − | 0.756489i | \(-0.726913\pi\) | ||||
−0.654007 | + | 0.756489i | \(0.726913\pi\) | |||||||
\(212\) | −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 | ||||
\(218\) | 2.23607i | 0.151446i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.6190 | − | 6.70820i | −0.781575 | − | 0.451243i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.2487i | − | 1.62381i | −0.583787 | − | 0.811907i | \(-0.698430\pi\) | ||
0.583787 | − | 0.811907i | \(-0.301570\pi\) | |||||||
\(224\) | 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 | 0.486954 | − | 0.873427i | \(-0.338108\pi\) |
0.999888 | + | 0.0149989i | \(0.00477447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0000 | −0.656532 | ||||||||
\(233\) | −7.74597 | + | 4.47214i | −0.507455 | + | 0.292979i | −0.731787 | − | 0.681533i | \(-0.761313\pi\) |
0.224332 | + | 0.974513i | \(0.427980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.6190 | + | 20.1246i | 0.756329 | + | 1.31000i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 30.0000 | − | 34.6410i | 1.94461 | − | 2.24544i | ||||
\(239\) | − | 8.94427i | − | 0.578557i | −0.957245 | − | 0.289278i | \(-0.906585\pi\) | ||
0.957245 | − | 0.289278i | \(-0.0934153\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5000 | + | 7.79423i | 0.869611 | + | 0.502070i | 0.867219 | − | 0.497927i | \(-0.165905\pi\) |
0.00239235 | + | 0.999997i | \(0.499238\pi\) | |||||||
\(242\) | −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 | ||||
\(248\) | 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 | ||||
\(257\) | 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 | ||||||||
\(259\) | −2.50000 | + | 12.9904i | −0.155342 | + | 0.807183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.87298 | − | 2.23607i | −0.238818 | − | 0.137882i | 0.375815 | − | 0.926695i | \(-0.377363\pi\) |
−0.614634 | + | 0.788813i | \(0.710696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19.3649 | + | 6.70820i | −1.18734 | + | 0.411306i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | −7.74597 | + | 13.4164i | −0.472280 | + | 0.818013i | −0.999497 | − | 0.0317179i | \(-0.989902\pi\) |
0.527217 | + | 0.849731i | \(0.323236\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50000 | − | 0.866025i | 0.0911185 | − | 0.0526073i | −0.453748 | − | 0.891130i | \(-0.649914\pi\) |
0.544867 | + | 0.838523i | \(0.316580\pi\) | |||||||
\(272\) | 7.74597 | 0.469668 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | −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 | ||||||||
\(281\) | 17.8885i | 1.06714i | 0.845756 | + | 0.533571i | \(0.179150\pi\) | ||||
−0.845756 | + | 0.533571i | \(0.820850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5000 | − | 6.06218i | −0.624160 | − | 0.360359i | 0.154327 | − | 0.988020i | \(-0.450679\pi\) |
−0.778487 | + | 0.627661i | \(0.784012\pi\) | |||||||
\(284\) | −23.2379 | − | 13.4164i | −1.37892 | − | 0.796117i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 17.3205i | − | 1.02418i | ||||||
\(287\) | 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 | ||||
\(293\) | −7.74597 | −0.452524 | −0.226262 | − | 0.974066i | \(-0.572651\pi\) | ||||
−0.226262 | + | 0.974066i | \(0.572651\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 14.0000 | + | 12.1244i | 0.806947 | + | 0.698836i | ||||
\(302\) | 29.0689i | 1.67273i | ||||||||
\(303\) | 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 | \(0.0473737\pi\) | ||||
−0.988945 | + | 0.148280i | \(0.952626\pi\) | |||||||
\(308\) | 34.8569 | + | 6.70820i | 1.98615 | + | 0.382235i | ||||
\(309\) | 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 | −0.120927 | − | 0.992661i | \(-0.538587\pi\) |
0.799207 | + | 0.601056i | \(0.205253\pi\) | |||||||
\(314\) | −30.9839 | −1.74852 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33.0000 | −1.85640 | ||||||||
\(317\) | 3.87298 | − | 2.23607i | 0.217528 | − | 0.125590i | −0.387277 | − | 0.921963i | \(-0.626584\pi\) |
0.604805 | + | 0.796373i | \(0.293251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | − | 17.3205i | 0.559893 | − | 0.969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.0000 | − | 8.66025i | 1.39320 | − | 0.482617i | ||||
\(323\) | 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 | ||||||||
\(328\) | − | 17.3205i | − | 0.956365i | ||||||
\(329\) | 3.87298 | − | 20.1246i | 0.213524 | − | 1.10951i | ||||
\(330\) | 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 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | −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 | ||||
\(344\) | − | 15.6525i | − | 0.843925i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.0000 | + | 17.3205i | 1.61281 | + | 0.931156i | ||||
\(347\) | 7.74597 | + | 4.47214i | 0.415825 | + | 0.240077i | 0.693290 | − | 0.720659i | \(-0.256161\pi\) |
−0.277464 | + | 0.960736i | \(0.589494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.5167i | 1.20529i | 0.798010 | + | 0.602645i | \(0.205886\pi\) | ||||
−0.798010 | + | 0.602645i | \(0.794114\pi\) | |||||||
\(350\) | 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 | ||||||||
\(356\) | 46.4758 | 2.46321 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | −1.05703 | ||||||||
\(359\) | 3.87298 | − | 2.23607i | 0.204408 | − | 0.118015i | −0.394302 | − | 0.918981i | \(-0.629014\pi\) |
0.598710 | + | 0.800966i | \(0.295680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.50000 | + | 12.9904i | 0.235864 | + | 0.680881i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.00000 | − | 5.19615i | −0.469796 | − | 0.271237i | 0.246358 | − | 0.969179i | \(-0.420766\pi\) |
−0.716154 | + | 0.697942i | \(0.754099\pi\) | |||||||
\(368\) | 3.87298 | + | 2.23607i | 0.201893 | + | 0.116563i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.87298 | + | 11.1803i | 0.201075 | + | 0.580454i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | − | 1.73205i | −0.0517780 | − | 0.0896822i | 0.838975 | − | 0.544170i | \(-0.183156\pi\) |
−0.890753 | + | 0.454488i | \(0.849822\pi\) | |||||||
\(374\) | 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 | ||||
\(383\) | 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 | 0.683345 | − | 0.730096i | \(-0.260525\pi\) |
−0.290609 | + | 0.956842i | \(0.593858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 34.6410i | − | 1.75187i | ||||||
\(392\) | −15.4919 | + | 2.23607i | −0.782461 | + | 0.112938i | ||||
\(393\) | 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 | −0.976813 | − | 0.214094i | \(-0.931320\pi\) |
−0.302995 | + | 0.952992i | \(0.597987\pi\) | |||||||
\(398\) | −50.3488 | −2.52376 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | −19.3649 | + | 11.1803i | −0.967038 | + | 0.558320i | −0.898332 | − | 0.439317i | \(-0.855220\pi\) |
−0.0687059 | + | 0.997637i | \(0.521887\pi\) | |||||||
\(402\) | 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 | ||||
\(407\) | 22.3607i | 1.10838i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5000 | − | 11.2583i | −0.964213 | − | 0.556689i | −0.0667458 | − | 0.997770i | \(-0.521262\pi\) |
−0.897467 | + | 0.441081i | \(0.854595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.5885i | 0.767988i | ||||||||
\(413\) | 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 | ||||
\(419\) | 15.4919 | 0.756830 | 0.378415 | − | 0.925636i | \(-0.376469\pi\) | ||||
0.378415 | + | 0.925636i | \(0.376469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −22.5000 | − | 4.33013i | −1.08885 | − | 0.209550i | ||||
\(428\) | − | 13.4164i | − | 0.648507i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.1109 | − | 15.6525i | −1.30589 | − | 0.753953i | −0.324479 | − | 0.945893i | \(-0.605189\pi\) |
−0.981407 | + | 0.191940i | \(0.938522\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.5885i | − | 0.749133i | −0.927200 | − | 0.374567i | \(-0.877791\pi\) | ||
0.927200 | − | 0.374567i | \(-0.122209\pi\) | |||||||
\(434\) | −7.74597 | − | 6.70820i | −0.371818 | − | 0.322004i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.50000 | − | 2.59808i | −0.0718370 | − | 0.124425i | ||||
\(437\) | −7.74597 | + | 13.4164i | −0.370540 | + | 0.641794i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00000 | − | 1.73205i | 0.143182 | − | 0.0826663i | −0.426698 | − | 0.904394i | \(-0.640323\pi\) |
0.569880 | + | 0.821728i | \(0.306990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | −30.9839 | + | 17.8885i | −1.47209 | + | 0.849910i | −0.999508 | − | 0.0313772i | \(-0.990011\pi\) |
−0.472580 | + | 0.881288i | \(0.656677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.1109 | + | 46.9574i | 1.28374 | + | 2.22350i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −26.0000 | − | 22.5167i | −1.22838 | − | 1.06381i | ||||
\(449\) | − | 8.94427i | − | 0.422106i | −0.977475 | − | 0.211053i | \(-0.932311\pi\) | ||
0.977475 | − | 0.211053i | \(-0.0676893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.0000 | + | 17.3205i | 1.41264 | + | 0.815591i | ||||
\(452\) | −23.2379 | − | 13.4164i | −1.09302 | − | 0.631055i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 51.9615i | 2.43868i | ||||||||
\(455\) | 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 | ||||||||
\(461\) | 7.74597 | 0.360766 | 0.180383 | − | 0.983596i | \(-0.442266\pi\) | ||||
0.180383 | + | 0.983596i | \(0.442266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −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 | −0.962229 | − | 0.272240i | \(-0.912236\pi\) |
0.245348 | − | 0.969435i | \(-0.421098\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 17.3205i | 0.794719i | ||||||||
\(476\) | −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 | ||||
\(482\) | −34.8569 | −1.58769 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.0000 | 1.22727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | − | 34.6410i | 0.906287 | − | 1.56973i | 0.0871056 | − | 0.996199i | \(-0.472238\pi\) |
0.819181 | − | 0.573535i | \(-0.194428\pi\) | |||||||
\(488\) | 9.68246 | + | 16.7705i | 0.438304 | + | 0.759165i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.3607i | − | 1.00912i | −0.863376 | − | 0.504562i | \(-0.831654\pi\) | ||
0.863376 | − | 0.504562i | \(-0.168346\pi\) | |||||||
\(492\) | 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 | ||||||
\(497\) | −15.4919 | + | 17.8885i | −0.694908 | + | 0.802411i | ||||
\(498\) | 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 | ||||||||
\(502\) | 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 | ||||
\(509\) | −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 | ||||||||
\(511\) | −6.00000 | − | 17.3205i | −0.265424 | − | 0.766214i | ||||
\(512\) | − | 11.1803i | − | 0.494106i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −45.0000 | − | 25.9808i | −1.98486 | − | 1.14596i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 34.6410i | − | 1.52351i | ||||||
\(518\) | −9.68246 | − | 27.9508i | −0.425423 | − | 1.22809i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.87298 | − | 6.70820i | 0.169678 | − | 0.293892i | −0.768628 | − | 0.639696i | \(-0.779060\pi\) |
0.938307 | + | 0.345804i | \(0.112394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5000 | + | 9.52628i | −0.721495 | + | 0.416555i | −0.815303 | − | 0.579035i | \(-0.803429\pi\) |
0.0938079 | + | 0.995590i | \(0.470096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | 0.436021 | ||||||||
\(527\) | −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 | ||||
\(533\) | 13.4164i | 0.581129i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.93649 | + | 1.11803i | 0.0836437 | + | 0.0482917i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 34.6410i | − | 1.49348i | ||||||
\(539\) | 11.6190 | − | 29.0689i | 0.500464 | − | 1.25209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | − | 12.1244i | −0.300954 | − | 0.521267i | 0.675399 | − | 0.737453i | \(-0.263972\pi\) |
−0.976352 | + | 0.216186i | \(0.930638\pi\) | |||||||
\(542\) | −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 | ||||||||
\(547\) | 11.0000 | 0.470326 | 0.235163 | − | 0.971956i | \(-0.424438\pi\) | ||||
0.235163 | + | 0.971956i | \(0.424438\pi\) | |||||||
\(548\) | −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 | ||||||||
\(553\) | −5.50000 | + | 28.5788i | −0.233884 | + | 1.21530i | ||||
\(554\) | − | 11.1803i | − | 0.475007i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.5000 | + | 12.9904i | 0.954213 | + | 0.550915i | ||||
\(557\) | 30.9839 | + | 17.8885i | 1.31283 | + | 0.757962i | 0.982564 | − | 0.185926i | \(-0.0595286\pi\) |
0.330265 | + | 0.943888i | \(0.392862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1244i | 0.512806i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0000 | − | 34.6410i | −0.843649 | − | 1.46124i | ||||
\(563\) | −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 | −0.138792 | − | 0.990322i | \(-0.544322\pi\) |
0.788248 | + | 0.615358i | \(0.210989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | − | 13.8564i | 0.334790 | − | 0.579873i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 11.6190 | + | 20.1246i | 0.485813 | + | 0.841452i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −45.0000 | − | 8.66025i | −1.87826 | − | 0.361472i | ||||
\(575\) | − | 22.3607i | − | 0.932505i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.5000 | − | 19.9186i | −1.43625 | − | 0.829222i | −0.438667 | − | 0.898650i | \(-0.644549\pi\) |
−0.997587 | + | 0.0694283i | \(0.977883\pi\) | |||||||
\(578\) | 83.2691 | + | 48.0755i | 3.46354 | + | 1.99968i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4919 | − | 13.4164i | −0.642714 | − | 0.556606i | ||||
\(582\) | 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 | ||||
\(587\) | 30.9839 | 1.27884 | 0.639421 | − | 0.768857i | \(-0.279174\pi\) | ||||
0.639421 | + | 0.768857i | \(0.279174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50000 | − | 4.33013i | 0.102749 | − | 0.177967i | ||||
\(593\) | −15.4919 | − | 26.8328i | −0.636177 | − | 1.10189i | −0.986264 | − | 0.165174i | \(-0.947181\pi\) |
0.350087 | − | 0.936717i | \(-0.386152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 53.6656i | − | 2.19823i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.0000 | + | 8.66025i | 0.613396 | + | 0.354144i | ||||
\(599\) | 7.74597 | + | 4.47214i | 0.316492 | + | 0.182727i | 0.649828 | − | 0.760082i | \(-0.274841\pi\) |
−0.333336 | + | 0.942808i | \(0.608174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.3013i | 1.76630i | 0.469095 | + | 0.883148i | \(0.344580\pi\) | ||||
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | −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 | 0.160756 | − | 0.986994i | \(-0.448607\pi\) |
0.935140 | + | 0.354278i | \(0.115273\pi\) | |||||||
\(608\) | 23.2379 | 0.942421 | ||||||||
\(609\) | 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 | −0.999178 | − | 0.0405396i | \(-0.987092\pi\) |
0.534697 | + | 0.845044i | \(0.320426\pi\) | |||||||
\(614\) | −5.80948 | − | 10.0623i | −0.234451 | − | 0.406082i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.0000 | + | 8.66025i | −1.00728 | + | 0.348932i | ||||
\(617\) | − | 22.3607i | − | 0.900207i | −0.892976 | − | 0.450104i | \(-0.851387\pi\) | ||
0.892976 | − | 0.450104i | \(-0.148613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.50000 | + | 2.59808i | 0.180870 | + | 0.104425i | 0.587701 | − | 0.809078i | \(-0.300033\pi\) |
−0.406831 | + | 0.913503i | \(0.633366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.6410i | 1.38898i | ||||||||
\(623\) | 7.74597 | − | 40.2492i | 0.310336 | − | 1.61255i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −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 | ||||||||
\(637\) | 12.0000 | − | 1.73205i | 0.475457 | − | 0.0686264i | ||||
\(638\) | 44.7214i | 1.77054i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.87298 | − | 2.23607i | −0.152974 | − | 0.0883194i | 0.421559 | − | 0.906801i | \(-0.361483\pi\) |
−0.574533 | + | 0.818481i | \(0.694816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0526i | 0.751360i | 0.926750 | + | 0.375680i | \(0.122591\pi\) | ||||
−0.926750 | + | 0.375680i | \(0.877409\pi\) | |||||||
\(644\) | −23.2379 | + | 26.8328i | −0.915702 | + | 1.05736i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.0000 | − | 51.9615i | −1.18033 | − | 2.04440i | ||||
\(647\) | −7.74597 | + | 13.4164i | −0.304525 | + | 0.527453i | −0.977156 | − | 0.212525i | \(-0.931831\pi\) |
0.672630 | + | 0.739979i | \(0.265165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.0000 | − | 17.3205i | 1.17760 | − | 0.679889i | ||||
\(650\) | 19.3649 | 0.759555 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39.0000 | 1.52736 | ||||||||
\(653\) | −19.3649 | + | 11.1803i | −0.757808 | + | 0.437521i | −0.828508 | − | 0.559977i | \(-0.810810\pi\) |
0.0707003 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(654\) | 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 | ||||
\(659\) | 17.8885i | 0.696839i | 0.937339 | + | 0.348419i | \(0.113281\pi\) | ||||
−0.937339 | + | 0.348419i | \(0.886719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0000 | − | 13.8564i | −0.933492 | − | 0.538952i | −0.0455776 | − | 0.998961i | \(-0.514513\pi\) |
−0.887914 | + | 0.460009i | \(0.847846\pi\) | |||||||
\(662\) | −7.74597 | − | 4.47214i | −0.301056 | − | 0.173814i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.3205i | 0.672166i | ||||||||
\(665\) | 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 | ||||||||
\(671\) | −38.7298 | −1.49515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 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 | ||||||||
\(679\) | 3.00000 | − | 3.46410i | 0.115129 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.0000 | − | 8.66025i | −0.574380 | − | 0.331618i | ||||
\(683\) | 30.9839 | + | 17.8885i | 1.18556 | + | 0.684486i | 0.957295 | − | 0.289112i | \(-0.0933600\pi\) |
0.228269 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.93649 | + | 41.3673i | −0.0739356 | + | 1.57941i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | −3.87298 | + | 6.70820i | −0.147549 | + | 0.255562i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5000 | + | 16.4545i | −1.08419 | + | 0.625958i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | −25.1744 | − | 43.6033i | −0.952865 | − | 1.65041i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.50000 | + | 38.9711i | −0.283473 | + | 1.47297i | ||||
\(701\) | − | 8.94427i | − | 0.337820i | −0.985631 | − | 0.168910i | \(-0.945975\pi\) | ||
0.985631 | − | 0.168910i | \(-0.0540248\pi\) | |||||||
\(702\) | 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 | ||||||||
\(709\) | −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 | ||||
\(713\) | −7.74597 | −0.290089 | ||||||||
\(714\) | 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 | 0.973542 | − | 0.228509i | \(-0.0733852\pi\) |
−0.684666 | + | 0.728857i | \(0.740052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.5000 | + | 2.59808i | 0.502766 | + | 0.0967574i | ||||
\(722\) | − | 15.6525i | − | 0.582525i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.3649 | + | 11.1803i | 0.719195 | + | 0.415227i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.0526i | − | 0.706620i | −0.935506 | − | 0.353310i | \(-0.885056\pi\) | ||
0.935506 | − | 0.353310i | \(-0.114944\pi\) | |||||||
\(728\) | −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 | 0.211344 | − | 0.977412i | \(-0.432216\pi\) |
0.952135 | + | 0.305677i | \(0.0988827\pi\) | |||||||
\(734\) | 23.2379 | 0.857727 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.0000 | −1.10581 | ||||||||
\(737\) | −3.87298 | + | 2.23607i | −0.142663 | + | 0.0823666i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.5000 | + | 19.9186i | −0.423034 | + | 0.732717i | −0.996235 | − | 0.0866983i | \(-0.972368\pi\) |
0.573200 | + | 0.819415i | \(0.305702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.0000 | − | 17.3205i | −0.734223 | − | 0.635856i | ||||
\(743\) | 31.3050i | 1.14847i | 0.818691 | + | 0.574234i | \(0.194700\pi\) | ||||
−0.818691 | + | 0.574234i | \(0.805300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.87298 | + | 2.23607i | 0.141800 | + | 0.0818683i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 103.923i | 3.79980i | ||||||||
\(749\) | −11.6190 | − | 2.23607i | −0.424547 | − | 0.0817041i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | −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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.50000 | + | 0.866025i | −0.0905061 | + | 0.0313522i | ||||
\(764\) | − | 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 | ||||||||
\(769\) | 34.6410i | 1.24919i | 0.780950 | + | 0.624593i | \(0.214735\pi\) | ||||
−0.780950 | + | 0.624593i | \(0.785265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.5000 | − | 18.1865i | −0.377903 | − | 0.654548i | ||||
\(773\) | 15.4919 | − | 26.8328i | 0.557206 | − | 0.965109i | −0.440522 | − | 0.897742i | \(-0.645207\pi\) |
0.997728 | − | 0.0673675i | \(-0.0214600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.50000 | + | 4.33013i | −0.269408 | + | 0.155543i | ||||
\(776\) | −3.87298 | −0.139032 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.0000 | −0.717035 | ||||||||
\(779\) | 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 | ||||||||
\(787\) | 16.5000 | + | 9.52628i | 0.588161 | + | 0.339575i | 0.764370 | − | 0.644778i | \(-0.223050\pi\) |
−0.176209 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(788\) | −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 | ||||
\(794\) | 32.9204 | − | 57.0197i | 1.16830 | − | 2.02355i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 58.5000 | − | 33.7750i | 2.07348 | − | 1.19712i | ||||
\(797\) | 38.7298 | 1.37188 | 0.685941 | − | 0.727658i | \(-0.259391\pi\) | ||||
0.685941 | + | 0.727658i | \(0.259391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.0000 | 2.12265 | ||||||||
\(800\) | −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 | ||||||||
\(806\) | − | 6.70820i | − | 0.236286i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.87298 | − | 2.23607i | −0.136167 | − | 0.0786160i | 0.430369 | − | 0.902653i | \(-0.358383\pi\) |
−0.566536 | + | 0.824037i | \(0.691717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3923i | 0.364923i | 0.983213 | + | 0.182462i | \(0.0584065\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | −11.6190 | − | 33.5410i | −0.407745 | − | 1.17706i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.0000 | − | 43.3013i | −0.876250 | − | 1.51771i | ||||
\(815\) | 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 | −0.798286 | − | 0.602279i | \(-0.794260\pi\) |
0.122446 | + | 0.992475i | \(0.460926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5000 | − | 37.2391i | 0.749443 | − | 1.29807i | −0.198647 | − | 0.980071i | \(-0.563655\pi\) |
0.948090 | − | 0.318002i | \(-0.103012\pi\) | |||||||
\(824\) | −5.80948 | − | 10.0623i | −0.202383 | − | 0.350537i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | + | 34.6410i | −1.04383 | + | 1.20532i | ||||
\(827\) | − | 8.94427i | − | 0.311023i | −0.987834 | − | 0.155511i | \(-0.950297\pi\) | ||
0.987834 | − | 0.155511i | \(-0.0497025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0000 | − | 6.92820i | −0.416777 | − | 0.240626i | 0.276920 | − | 0.960893i | \(-0.410686\pi\) |
−0.693698 | + | 0.720266i | \(0.744020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 22.5167i | − | 0.780625i | ||||||
\(833\) | 50.3488 | + | 20.1246i | 1.74448 | + | 0.697276i | ||||
\(834\) | 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 | ||||
\(839\) | 7.74597 | 0.267420 | 0.133710 | − | 0.991020i | \(-0.457311\pi\) | ||||
0.133710 | + | 0.991020i | \(0.457311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 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 | ||||
\(848\) | − | 4.47214i | − | 0.153574i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 75.0000 | + | 43.3013i | 2.57248 | + | 1.48522i | ||||
\(851\) | −19.3649 | − | 11.1803i | −0.663821 | − | 0.383257i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.8564i | − | 0.474434i | −0.971457 | − | 0.237217i | \(-0.923765\pi\) | ||
0.971457 | − | 0.237217i | \(-0.0762353\pi\) | |||||||
\(854\) | 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 | −0.421263 | − | 0.906939i | \(-0.638413\pi\) |
0.574801 | + | 0.818293i | \(0.305080\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 70.0000 | 2.38421 | ||||||||
\(863\) | −30.9839 | + | 17.8885i | −1.05470 | + | 0.608933i | −0.923962 | − | 0.382483i | \(-0.875069\pi\) |
−0.130741 | + | 0.991417i | \(0.541736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.4284 | + | 30.1869i | 0.592242 | + | 1.02579i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.5000 | + | 2.59808i | 0.458220 | + | 0.0881845i | ||||
\(869\) | 49.1935i | 1.66878i | ||||||||
\(870\) | 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 | \(0.694628\pi\) | |||||||
\(878\) | −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 | ||||
\(887\) | −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 | ||||||||
\(889\) | 2.00000 | + | 1.73205i | 0.0670778 | + | 0.0580911i | ||||
\(890\) | 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 | ||||||||
\(896\) | 40.6663 | + | 7.82624i | 1.35857 | + | 0.261456i | ||||
\(897\) | 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 | ||||
\(902\) | −77.4597 | −2.57912 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.0000 | 0.665190 | ||||||||
\(905\) | 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 | ||||||||
\(911\) | 4.47214i | 0.148168i | 0.997252 | + | 0.0740842i | \(0.0236034\pi\) | ||||
−0.997252 | + | 0.0740842i | \(0.976397\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0000 | − | 17.3205i | −0.992855 | − | 0.573225i | ||||
\(914\) | 21.3014 | + | 12.2984i | 0.704588 | + | 0.406794i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 77.9423i | − | 2.57529i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.50000 | + | 11.2583i | 0.214415 | + | 0.371378i | 0.953092 | − | 0.302682i | \(-0.0978821\pi\) |
−0.738676 | + | 0.674060i | \(0.764549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.0000 | + | 8.66025i | −0.493999 | + | 0.285210i | ||||
\(923\) | −15.4919 | −0.509923 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.0000 | −0.821995 | ||||||||
\(926\) | −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 | ||||||||
\(931\) | −15.0000 | − | 19.0526i | −0.491605 | − | 0.624422i | ||||
\(932\) | 26.8328i | 0.878938i | ||||||||
\(933\) | 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 | \(0.276708\pi\) | ||||
−0.645359 | + | 0.763879i | \(0.723292\pi\) | |||||||
\(938\) | 3.87298 | − | 4.47214i | 0.126457 | − | 0.146020i | ||||
\(939\) | 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 | −0.435751 | − | 0.900067i | \(-0.643517\pi\) |
0.561606 | + | 0.827405i | \(0.310184\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | − | 10.3923i | 0.194768 | − | 0.337348i | ||||
\(950\) | −19.3649 | − | 33.5410i | −0.628281 | − | 1.08821i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.0000 | − | 43.3013i | −0.486153 | − | 1.40340i | ||||
\(953\) | 58.1378i | 1.88327i | 0.336640 | + | 0.941634i | \(0.390710\pi\) | ||||
−0.336640 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.2379 | − | 13.4164i | −0.751567 | − | 0.433918i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.87298 | + | 11.1803i | 0.125065 | + | 0.361032i | ||||
\(960\) | 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 | ||||||||
\(967\) | −25.0000 | −0.803946 | −0.401973 | − | 0.915652i | \(-0.631675\pi\) | ||||
−0.401973 | + | 0.915652i | \(0.631675\pi\) | |||||||
\(968\) | −17.4284 | + | 10.0623i | −0.560171 | + | 0.323415i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.9839 | + | 53.6656i | 0.994320 | + | 1.72221i | 0.589336 | + | 0.807888i | \(0.299390\pi\) |
0.404984 | + | 0.914324i | \(0.367277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0000 | − | 17.3205i | 0.480878 | − | 0.555270i | ||||
\(974\) | 89.4427i | 2.86593i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.50000 | + | 4.33013i | 0.240069 | + | 0.138604i | ||||
\(977\) | −50.3488 | − | 29.0689i | −1.61080 | − | 0.929996i | −0.989185 | − | 0.146673i | \(-0.953143\pi\) |
−0.621615 | − | 0.783323i | \(-0.713523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 69.2820i | − | 2.21426i | ||||||
\(980\) | 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 | ||||||||
\(986\) | −77.4597 | −2.46682 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.0000 | 0.572656 | ||||||||
\(989\) | −27.1109 | + | 15.6525i | −0.862076 | + | 0.497720i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5000 | − | 42.4352i | 0.778268 | − | 1.34800i | −0.154671 | − | 0.987966i | \(-0.549432\pi\) |
0.932939 | − | 0.360034i | \(-0.117235\pi\) | |||||||
\(992\) | 5.80948 | + | 10.0623i | 0.184451 | + | 0.319479i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.0000 | − | 51.9615i | 0.317181 | − | 1.64812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.5000 | − | 23.3827i | −1.28265 | − | 0.740537i | −0.305316 | − | 0.952251i | \(-0.598762\pi\) |
−0.977332 | + | 0.211714i | \(0.932095\pi\) | |||||||
\(998\) | −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 | 189.2.p.c.80.1 | yes | 4 | |
3.2 | odd | 2 | inner | 189.2.p.c.80.2 | yes | 4 | |
7.3 | odd | 6 | 1323.2.c.b.1322.2 | 4 | |||
7.4 | even | 3 | 1323.2.c.b.1322.1 | 4 | |||
7.5 | odd | 6 | inner | 189.2.p.c.26.2 | yes | 4 | |
9.2 | odd | 6 | 567.2.s.e.458.1 | 4 | |||
9.4 | even | 3 | 567.2.i.c.269.1 | 4 | |||
9.5 | odd | 6 | 567.2.i.c.269.2 | 4 | |||
9.7 | even | 3 | 567.2.s.e.458.2 | 4 | |||
21.5 | even | 6 | inner | 189.2.p.c.26.1 | ✓ | 4 | |
21.11 | odd | 6 | 1323.2.c.b.1322.3 | 4 | |||
21.17 | even | 6 | 1323.2.c.b.1322.4 | 4 | |||
63.5 | even | 6 | 567.2.s.e.26.2 | 4 | |||
63.40 | odd | 6 | 567.2.s.e.26.1 | 4 | |||
63.47 | even | 6 | 567.2.i.c.215.2 | 4 | |||
63.61 | odd | 6 | 567.2.i.c.215.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.c.26.1 | ✓ | 4 | 21.5 | even | 6 | inner | |
189.2.p.c.26.2 | yes | 4 | 7.5 | odd | 6 | inner | |
189.2.p.c.80.1 | yes | 4 | 1.1 | even | 1 | trivial | |
189.2.p.c.80.2 | yes | 4 | 3.2 | odd | 2 | inner | |
567.2.i.c.215.1 | 4 | 63.61 | odd | 6 | |||
567.2.i.c.215.2 | 4 | 63.47 | even | 6 | |||
567.2.i.c.269.1 | 4 | 9.4 | even | 3 | |||
567.2.i.c.269.2 | 4 | 9.5 | odd | 6 | |||
567.2.s.e.26.1 | 4 | 63.40 | odd | 6 | |||
567.2.s.e.26.2 | 4 | 63.5 | even | 6 | |||
567.2.s.e.458.1 | 4 | 9.2 | odd | 6 | |||
567.2.s.e.458.2 | 4 | 9.7 | even | 3 | |||
1323.2.c.b.1322.1 | 4 | 7.4 | even | 3 | |||
1323.2.c.b.1322.2 | 4 | 7.3 | odd | 6 | |||
1323.2.c.b.1322.3 | 4 | 21.11 | odd | 6 | |||
1323.2.c.b.1322.4 | 4 | 21.17 | even | 6 |