Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(31,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bf (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 943.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.943 |
Dual form | 1008.2.bf.b.31.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50000 | − | 0.866025i | 0.416025 | − | 0.240192i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | − | 0.866025i | 0.363803 | − | 0.210042i | −0.306944 | − | 0.951727i | \(-0.599307\pi\) |
0.670748 | + | 0.741685i | \(0.265973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | + | 0.866025i | −0.0898027 | + | 0.155543i | −0.907428 | − | 0.420208i | \(-0.861957\pi\) |
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | 1.04447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.50000 | − | 2.59808i | −0.240192 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 0.866025i | 0.234261 | − | 0.135250i | −0.378275 | − | 0.925693i | \(-0.623483\pi\) |
0.612536 | + | 0.790443i | \(0.290149\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.50000 | − | 0.866025i | −0.228748 | − | 0.132068i | 0.381246 | − | 0.924473i | \(-0.375495\pi\) |
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.50000 | + | 7.79423i | 0.656392 | + | 1.13691i | 0.981543 | + | 0.191243i | \(0.0612518\pi\) |
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | − | 2.59808i | −0.210042 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50000 | + | 4.33013i | 0.993399 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.50000 | − | 12.9904i | 0.976417 | − | 1.69120i | 0.301239 | − | 0.953549i | \(-0.402600\pi\) |
0.675178 | − | 0.737655i | \(-0.264067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.50000 | − | 0.866025i | 0.192055 | − | 0.110883i | −0.400889 | − | 0.916127i | \(-0.631299\pi\) |
0.592944 | + | 0.805243i | \(0.297965\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | − | 5.19615i | 0.755929 | − | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.5000 | − | 7.79423i | −1.64929 | − | 0.952217i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
−0.671932 | − | 0.740613i | \(-0.734535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923i | 1.23334i | 0.787222 | + | 0.616670i | \(0.211519\pi\) | ||||
−0.787222 | + | 0.616670i | \(0.788481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | − | 0.866025i | 0.175562 | − | 0.101361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | − | 6.92820i | −0.683763 | − | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | − | 0.866025i | 0.168763 | − | 0.0974355i | −0.413239 | − | 0.910622i | \(-0.635603\pi\) |
0.582003 | + | 0.813187i | \(0.302269\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.50000 | + | 2.59808i | 0.482451 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50000 | + | 0.866025i | 0.159000 | + | 0.0917985i | 0.577389 | − | 0.816469i | \(-0.304072\pi\) |
−0.418389 | + | 0.908268i | \(0.637405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50000 | + | 4.33013i | −0.157243 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | + | 0.866025i | 0.155543 | + | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 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 | \(0.638641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 10.3923i | − | 1.04447i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564i | 1.37876i | 0.724398 | + | 0.689382i | \(0.242118\pi\) | ||||
−0.724398 | + | 0.689382i | \(0.757882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50000 | − | 0.866025i | −0.145010 | − | 0.0837218i | 0.425739 | − | 0.904846i | \(-0.360014\pi\) |
−0.570750 | + | 0.821124i | \(0.693347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50000 | − | 9.52628i | −0.526804 | − | 0.912452i | −0.999512 | − | 0.0312328i | \(-0.990057\pi\) |
0.472708 | − | 0.881219i | \(-0.343277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5000 | + | 6.06218i | 0.996616 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.50000 | + | 2.59808i | −0.416025 | + | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | + | 4.33013i | −0.137505 | + | 0.396942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.50000 | − | 2.59808i | −0.135250 | − | 0.234261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3923i | 0.922168i | 0.887357 | + | 0.461084i | \(0.152539\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50000 | + | 2.59808i | −0.132068 | + | 0.228748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | − | 12.9904i | −0.216777 | − | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.5000 | − | 7.79423i | 1.13691 | − | 0.656392i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0000 | − | 1.73205i | −0.989743 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.3205i | − | 1.40952i | −0.709444 | − | 0.704761i | \(-0.751054\pi\) | ||
0.709444 | − | 0.704761i | \(-0.248946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.50000 | + | 2.59808i | −0.363803 | + | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5000 | − | 6.06218i | −0.837991 | − | 0.483814i | 0.0185897 | − | 0.999827i | \(-0.494082\pi\) |
−0.856581 | + | 0.516013i | \(0.827416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.5000 | − | 7.79423i | 1.07062 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | − | 6.92820i | −0.472866 | − | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5000 | − | 7.79423i | −1.05740 | − | 0.610491i | −0.132689 | − | 0.991158i | \(-0.542361\pi\) |
−0.924712 | + | 0.380667i | \(0.875695\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5000 | + | 18.1865i | 0.812514 | + | 1.40732i | 0.911099 | + | 0.412188i | \(0.135235\pi\) |
−0.0985846 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.50000 | − | 12.9904i | 0.573539 | − | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.5000 | + | 9.52628i | −1.25447 | + | 0.724270i | −0.971994 | − | 0.235004i | \(-0.924490\pi\) |
−0.282477 | + | 0.959274i | \(0.591156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | + | 8.66025i | −0.755929 | + | 0.654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.5000 | − | 12.9904i | −1.69120 | − | 0.976417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | + | 6.06218i | −0.784807 | + | 0.453108i | −0.838131 | − | 0.545469i | \(-0.816352\pi\) |
0.0533243 | + | 0.998577i | \(0.483018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.8564i | − | 1.02994i | −0.857209 | − | 0.514969i | \(-0.827803\pi\) | ||
0.857209 | − | 0.514969i | \(-0.172197\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.50000 | − | 2.59808i | −0.110883 | − | 0.192055i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | − | 10.3923i | −0.654654 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | − | 0.866025i | 0.108536 | − | 0.0626634i | −0.444749 | − | 0.895655i | \(-0.646707\pi\) |
0.553285 | + | 0.832992i | \(0.313374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.50000 | − | 14.7224i | 0.611843 | − | 1.05974i | −0.379086 | − | 0.925361i | \(-0.623762\pi\) |
0.990930 | − | 0.134382i | \(-0.0429051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.500000 | + | 0.866025i | 0.0354441 | + | 0.0613909i | 0.883203 | − | 0.468990i | \(-0.155382\pi\) |
−0.847759 | + | 0.530381i | \(0.822049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5000 | + | 23.3827i | −0.952217 | + | 1.64929i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.50000 | − | 7.79423i | −0.105279 | − | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 10.3923i | − | 0.722315i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0000 | − | 8.66025i | −1.03757 | − | 0.599042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5000 | + | 6.06218i | −0.722850 | + | 0.417338i | −0.815801 | − | 0.578333i | \(-0.803703\pi\) |
0.0929509 | + | 0.995671i | \(0.470370\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | 1.23334 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.500000 | − | 2.59808i | −0.0339422 | − | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.50000 | − | 2.59808i | −0.101361 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.50000 | − | 2.59808i | 0.100901 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.50000 | + | 4.33013i | −0.167412 | + | 0.289967i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | −1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8564i | 0.915657i | 0.889041 | + | 0.457829i | \(0.151373\pi\) | ||||
−0.889041 | + | 0.457829i | \(0.848627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | + | 10.3923i | −0.789542 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | − | 18.1865i | 0.687878 | − | 1.19144i | −0.284645 | − | 0.958633i | \(-0.591876\pi\) |
0.972523 | − | 0.232806i | \(-0.0747909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.50000 | − | 2.59808i | −0.0974355 | − | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5000 | − | 11.2583i | 1.26135 | − | 0.728241i | 0.288014 | − | 0.957626i | \(-0.407005\pi\) |
0.973336 | + | 0.229385i | \(0.0736716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.7846i | 1.33885i | 0.742878 | + | 0.669427i | \(0.233460\pi\) | ||||
−0.742878 | + | 0.669427i | \(0.766540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.66025i | 0.551039i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5000 | + | 7.79423i | 0.855528 | + | 0.493939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 27.7128i | − | 1.72868i | −0.502910 | − | 0.864339i | \(-0.667737\pi\) | ||
0.502910 | − | 0.864339i | \(-0.332263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50000 | − | 18.1865i | −0.217479 | − | 1.13006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | − | 7.79423i | 0.278543 | − | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 31.1769i | − | 1.92245i | −0.275764 | − | 0.961225i | \(-0.588931\pi\) | ||
0.275764 | − | 0.961225i | \(-0.411069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.50000 | − | 2.59808i | 0.0917985 | − | 0.159000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.5000 | − | 11.2583i | 1.18894 | − | 0.686433i | 0.230871 | − | 0.972984i | \(-0.425842\pi\) |
0.958065 | + | 0.286552i | \(0.0925091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.500000 | + | 0.866025i | −0.0303728 | + | 0.0526073i | −0.880812 | − | 0.473466i | \(-0.843003\pi\) |
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.50000 | + | 2.59808i | 0.453921 | + | 0.157243i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.3205i | 1.04447i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | −0.841178 | −0.420589 | − | 0.907251i | \(-0.638177\pi\) | ||||
−0.420589 | + | 0.907251i | \(0.638177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50000 | − | 2.59808i | 0.0898027 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.50000 | + | 12.9904i | −0.447412 | + | 0.774941i | −0.998217 | − | 0.0596933i | \(-0.980988\pi\) |
0.550804 | + | 0.834634i | \(0.314321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5000 | − | 26.8468i | 0.921379 | − | 1.59588i | 0.124096 | − | 0.992270i | \(-0.460397\pi\) |
0.797283 | − | 0.603606i | \(-0.206270\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.50000 | + | 4.33013i | −0.0885422 | + | 0.255599i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | + | 12.1244i | −0.411765 | + | 0.713197i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.50000 | − | 2.59808i | 0.0879316 | − | 0.152302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.5000 | + | 12.9904i | −1.31446 | + | 0.758906i | −0.982832 | − | 0.184503i | \(-0.940933\pi\) |
−0.331632 | + | 0.943409i | \(0.607599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.0000 | −1.04447 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.50000 | − | 0.866025i | 0.259376 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.0000 | 1.37876 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8564i | 0.788263i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.50000 | − | 2.59808i | 0.0850572 | − | 0.147323i | −0.820358 | − | 0.571850i | \(-0.806226\pi\) |
0.905416 | + | 0.424526i | \(0.139559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5000 | − | 14.7224i | 1.44135 | − | 0.832161i | 0.443406 | − | 0.896321i | \(-0.353770\pi\) |
0.997940 | + | 0.0641600i | \(0.0204368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5000 | + | 18.1865i | 0.589739 | + | 1.02146i | 0.994266 | + | 0.106932i | \(0.0341026\pi\) |
−0.404528 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | − | 5.19615i | −0.503903 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.50000 | + | 2.59808i | −0.0837218 | + | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.66025i | 0.481869i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.50000 | − | 4.33013i | 0.416025 | − | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.5000 | + | 9.52628i | −0.912452 | + | 0.526804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5000 | − | 7.79423i | −1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.50000 | + | 2.59808i | −0.247342 | + | 0.142803i | −0.618547 | − | 0.785748i | \(-0.712278\pi\) |
0.371204 | + | 0.928551i | \(0.378945\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.5000 | − | 18.1865i | 0.575396 | − | 0.996616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.50000 | − | 9.52628i | −0.299604 | − | 0.518930i | 0.676441 | − | 0.736497i | \(-0.263521\pi\) |
−0.976045 | + | 0.217567i | \(0.930188\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5000 | − | 7.79423i | 0.733219 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | − | 1.73205i | −0.162459 | − | 0.0937958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5000 | − | 11.2583i | −1.04681 | − | 0.604379i | −0.125059 | − | 0.992149i | \(-0.539912\pi\) |
−0.921756 | + | 0.387770i | \(0.873245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.5000 | − | 12.9904i | −1.20440 | − | 0.695359i | −0.242867 | − | 0.970059i | \(-0.578088\pi\) |
−0.961530 | + | 0.274700i | \(0.911421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.50000 | + | 7.79423i | 0.240192 | + | 0.416025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7846i | 1.10625i | 0.833097 | + | 0.553127i | \(0.186565\pi\) | ||||
−0.833097 | + | 0.553127i | \(0.813435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.50000 | + | 2.59808i | 0.396942 | + | 0.137505i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5000 | + | 6.06218i | 0.554169 | + | 0.319950i | 0.750802 | − | 0.660528i | \(-0.229667\pi\) |
−0.196633 | + | 0.980477i | \(0.563001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.73205i | 0.0909091i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.50000 | + | 2.59808i | −0.234261 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.5000 | − | 7.79423i | −1.16814 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.19615i | 0.267615i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.2487i | − | 1.24557i | −0.782392 | − | 0.622786i | \(-0.786001\pi\) | ||
0.782392 | − | 0.622786i | \(-0.213999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.50000 | + | 2.59808i | 0.228748 | + | 0.132068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00000 | + | 5.19615i | 0.151717 | + | 0.262781i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.7846i | − | 1.04844i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5000 | + | 7.79423i | 0.677546 | + | 0.391181i | 0.798930 | − | 0.601424i | \(-0.205400\pi\) |
−0.121384 | + | 0.992606i | \(0.538733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.5000 | + | 4.33013i | −1.12641 | + | 0.216777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.73205i | 0.0862796i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.0000 | − | 12.1244i | −1.04093 | − | 0.600982i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.5000 | + | 14.7224i | 1.26089 | + | 0.727977i | 0.973247 | − | 0.229759i | \(-0.0737939\pi\) |
0.287646 | + | 0.957737i | \(0.407127\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.1769i | 1.53784i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.50000 | + | 38.9711i | 0.369051 | + | 1.91764i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.50000 | − | 4.33013i | 0.367277 | − | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.50000 | − | 12.9904i | −0.366399 | − | 0.634622i | 0.622601 | − | 0.782540i | \(-0.286076\pi\) |
−0.989000 | + | 0.147918i | \(0.952743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.50000 | − | 4.33013i | 0.121843 | − | 0.211037i | −0.798652 | − | 0.601793i | \(-0.794453\pi\) |
0.920494 | + | 0.390756i | \(0.127786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.5000 | − | 23.3827i | −0.656392 | − | 1.13691i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.50000 | − | 4.33013i | 0.363803 | − | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.50000 | + | 4.33013i | −0.0725901 | + | 0.209550i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.00000 | − | 5.19615i | 0.434524 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.5000 | + | 12.9904i | −1.08379 | + | 0.625725i | −0.931915 | − | 0.362676i | \(-0.881863\pi\) |
−0.151871 | + | 0.988400i | \(0.548530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8564i | 0.665896i | 0.942945 | + | 0.332948i | \(0.108043\pi\) | ||||
−0.942945 | + | 0.332948i | \(0.891957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.0000 | − | 8.66025i | −0.717547 | − | 0.414276i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5000 | + | 21.6506i | 0.596592 | + | 1.03333i | 0.993320 | + | 0.115392i | \(0.0368124\pi\) |
−0.396728 | + | 0.917936i | \(0.629854\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5000 | + | 12.9904i | −1.06901 | + | 0.617192i | −0.927910 | − | 0.372804i | \(-0.878396\pi\) |
−0.141097 | + | 0.989996i | \(0.545063\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.3923i | 0.491539i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.0000 | −1.40952 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.50000 | + | 7.79423i | 0.210042 | + | 0.363803i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5000 | + | 11.2583i | 0.908206 | + | 0.524353i | 0.879853 | − | 0.475245i | \(-0.157641\pi\) |
0.0283522 | + | 0.999598i | \(0.490974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.5000 | − | 18.1865i | 1.46393 | − | 0.845200i | 0.464739 | − | 0.885448i | \(-0.346148\pi\) |
0.999190 | + | 0.0402476i | \(0.0128147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.50000 | − | 12.9904i | 0.347059 | − | 0.601123i | −0.638667 | − | 0.769483i | \(-0.720514\pi\) |
0.985726 | + | 0.168360i | \(0.0538472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.5000 | − | 7.79423i | 1.87012 | − | 0.359904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5000 | + | 18.1865i | −0.483814 | + | 0.837991i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.5000 | + | 21.6506i | −0.573539 | + | 0.993399i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.5000 | − | 23.3827i | −0.618123 | − | 1.07062i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1244i | 0.552823i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0000 | + | 10.3923i | −0.546019 | + | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5000 | − | 7.79423i | 0.611743 | − | 0.353190i | −0.161904 | − | 0.986807i | \(-0.551764\pi\) |
0.773647 | + | 0.633616i | \(0.218430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.5000 | + | 23.3827i | −0.610491 | + | 1.05740i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50000 | − | 4.33013i | 0.338470 | − | 0.195416i | −0.321125 | − | 0.947037i | \(-0.604061\pi\) |
0.659595 | + | 0.751621i | \(0.270728\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.19615i | 0.234023i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.0000 | − | 20.7846i | −0.807410 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.46410i | 0.155074i | 0.996989 | + | 0.0775372i | \(0.0247057\pi\) | ||||
−0.996989 | + | 0.0775372i | \(0.975294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.5000 | − | 18.1865i | 1.40732 | − | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.0000 | + | 8.66025i | 0.666173 | + | 0.384615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 34.6410i | − | 1.53544i | −0.640788 | − | 0.767718i | \(-0.721392\pi\) | ||
0.640788 | − | 0.767718i | \(-0.278608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50000 | + | 4.33013i | −0.0663561 | + | 0.191554i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.5000 | − | 12.9904i | −0.993399 | − | 0.573539i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0000 | + | 15.5885i | −1.18746 | + | 0.685580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.5000 | + | 28.5788i | 0.724270 | + | 1.25447i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5000 | − | 11.2583i | 0.854311 | − | 0.493236i | −0.00779240 | − | 0.999970i | \(-0.502480\pi\) |
0.862103 | + | 0.506733i | \(0.169147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.50000 | + | 11.2583i | −0.284225 | + | 0.492292i | −0.972421 | − | 0.233233i | \(-0.925070\pi\) |
0.688196 | + | 0.725525i | \(0.258403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.0000 | + | 17.3205i | 0.654654 | + | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.73205i | 0.0754493i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.5000 | + | 38.9711i | −0.976417 | + | 1.69120i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.50000 | − | 2.59808i | 0.0649722 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.5000 | + | 18.1865i | 0.453108 | + | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.0000 | + | 3.46410i | 1.03375 | + | 0.149209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.5000 | + | 37.2391i | −0.924357 | + | 1.60103i | −0.131765 | + | 0.991281i | \(0.542065\pi\) |
−0.792592 | + | 0.609753i | \(0.791269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.0000 | −1.02994 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.50000 | − | 4.33013i | −0.320677 | − | 0.185143i | 0.331017 | − | 0.943625i | \(-0.392608\pi\) |
−0.651694 | + | 0.758482i | \(0.725941\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.50000 | + | 2.59808i | −0.192055 | + | 0.110883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.50000 | − | 12.9904i | −0.319511 | − | 0.553409i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.50000 | + | 4.33013i | −0.0637865 | + | 0.184136i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5000 | + | 28.5788i | 0.699127 | + | 1.21092i | 0.968769 | + | 0.247964i | \(0.0797613\pi\) |
−0.269642 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | − | 5.19615i | 0.379980 | − | 0.219382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5000 | + | 18.1865i | −0.442522 | + | 0.766471i | −0.997876 | − | 0.0651433i | \(-0.979250\pi\) |
0.555354 | + | 0.831614i | \(0.312583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0000 | + | 15.5885i | −0.755929 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | \(-0.186696\pi\) |
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5000 | + | 19.9186i | 1.44378 | + | 0.833567i | 0.998099 | − | 0.0616252i | \(-0.0196283\pi\) |
0.445681 | + | 0.895192i | \(0.352962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.50000 | − | 2.59808i | −0.0626634 | − | 0.108536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.3205i | 0.722315i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5000 | + | 12.9904i | −0.936687 | + | 0.540797i | −0.888920 | − | 0.458062i | \(-0.848544\pi\) |
−0.0477669 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.5000 | − | 14.7224i | −1.05974 | − | 0.611843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.50000 | − | 23.3827i | −0.186691 | − | 0.970077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0000 | + | 15.5885i | −1.11823 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5000 | − | 23.3827i | 0.557205 | − | 0.965107i | −0.440524 | − | 0.897741i | \(-0.645207\pi\) |
0.997728 | − | 0.0673658i | \(-0.0214594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.50000 | − | 4.33013i | −0.103011 | − | 0.178420i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 10.3923i | − | 0.427482i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.50000 | + | 4.33013i | 0.307988 | + | 0.177817i | 0.646026 | − | 0.763316i | \(-0.276430\pi\) |
−0.338038 | + | 0.941133i | \(0.609763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.50000 | − | 0.866025i | 0.0613909 | − | 0.0354441i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5000 | − | 18.1865i | −1.28706 | − | 0.743082i | −0.308927 | − | 0.951086i | \(-0.599970\pi\) |
−0.978128 | + | 0.208004i | \(0.933303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.5000 | + | 18.1865i | 1.28491 | + | 0.741844i | 0.977742 | − | 0.209811i | \(-0.0672847\pi\) |
0.307170 | + | 0.951655i | \(0.400618\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.5000 | + | 23.3827i | 1.64929 | + | 0.952217i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.5000 | + | 2.59808i | −0.547048 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5000 | + | 7.79423i | 0.546152 | + | 0.315321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.5000 | − | 30.3109i | −0.706818 | − | 1.22425i | −0.966031 | − | 0.258425i | \(-0.916796\pi\) |
0.259213 | − | 0.965820i | \(-0.416537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5000 | − | 23.3827i | −0.543490 | − | 0.941351i | −0.998700 | − | 0.0509678i | \(-0.983769\pi\) |
0.455211 | − | 0.890384i | \(-0.349564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000 | 1.12542 | 0.562708 | − | 0.826656i | \(-0.309760\pi\) | ||||
0.562708 | + | 0.826656i | \(0.309760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | −0.722315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.50000 | + | 0.866025i | −0.180289 | + | 0.0346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.0000 | + | 25.9808i | −0.599042 | + | 1.03757i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.1244i | 0.483430i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.1769i | − | 1.24113i | −0.784154 | − | 0.620567i | \(-0.786903\pi\) | ||
0.784154 | − | 0.620567i | \(-0.213097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5000 | + | 18.1865i | 0.417338 | + | 0.722850i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.50000 | − | 11.2583i | −0.178296 | − | 0.446071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 31.1769i | − | 1.23334i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.00000 | 0.236986 | 0.118493 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118493 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.50000 | + | 11.2583i | 0.256335 | + | 0.443985i | 0.965257 | − | 0.261301i | \(-0.0841516\pi\) |
−0.708922 | + | 0.705287i | \(0.750818\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.50000 | − | 12.9904i | −0.294855 | − | 0.510705i | 0.680096 | − | 0.733123i | \(-0.261938\pi\) |
−0.974951 | + | 0.222419i | \(0.928605\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.0000 | + | 25.9808i | 1.76640 | + | 1.01983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.50000 | + | 0.866025i | −0.176369 | + | 0.0339422i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0000 | 1.17399 | 0.586995 | − | 0.809590i | \(-0.300311\pi\) | ||||
0.586995 | + | 0.809590i | \(0.300311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.50000 | + | 2.59808i | −0.175562 | + | 0.101361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5000 | − | 11.2583i | −0.759612 | − | 0.438562i | 0.0695443 | − | 0.997579i | \(-0.477845\pi\) |
−0.829156 | + | 0.559017i | \(0.811179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.50000 | + | 4.33013i | 0.291716 | + | 0.168422i | 0.638716 | − | 0.769443i | \(-0.279466\pi\) |
−0.346999 | + | 0.937865i | \(0.612799\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.50000 | − | 2.59808i | −0.174766 | − | 0.100901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | − | 5.19615i | −0.348481 | − | 0.201196i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.50000 | + | 4.33013i | 0.289967 | + | 0.167412i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.00000 | + | 5.19615i | 0.115814 | + | 0.200595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.50000 | + | 6.06218i | −0.134915 | + | 0.233680i | −0.925565 | − | 0.378589i | \(-0.876409\pi\) |
0.790650 | + | 0.612268i | \(0.209743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9808i | 1.00000i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.50000 | − | 0.866025i | 0.0576497 | − | 0.0332841i | −0.470898 | − | 0.882188i | \(-0.656070\pi\) |
0.528548 | + | 0.848904i | \(0.322737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50000 | + | 0.866025i | −0.172694 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 20.7846i | − | 0.796468i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.5000 | − | 21.6506i | 1.43490 | − | 0.828439i | 0.437409 | − | 0.899263i | \(-0.355896\pi\) |
0.997489 | + | 0.0708242i | \(0.0225629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0000 | 0.915657 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5000 | + | 7.79423i | 0.514309 | + | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.50000 | + | 4.33013i | 0.0951045 | + | 0.164726i | 0.909652 | − | 0.415371i | \(-0.136348\pi\) |
−0.814548 | + | 0.580097i | \(0.803015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0000 | + | 20.7846i | 0.683763 | + | 0.789542i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50000 | − | 2.59808i | 0.0568166 | − | 0.0984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.5000 | − | 18.1865i | −1.19144 | − | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.5000 | − | 30.3109i | −0.660025 | − | 1.14320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.0000 | − | 27.7128i | −0.902613 | − | 1.04225i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5000 | + | 32.0429i | 0.694782 | + | 1.20340i | 0.970254 | + | 0.242089i | \(0.0778325\pi\) |
−0.275472 | + | 0.961309i | \(0.588834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.50000 | + | 2.59808i | −0.168763 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00000 | − | 1.73205i | −0.112351 | − | 0.0648658i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.5000 | − | 33.7750i | −0.728241 | − | 1.26135i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.5000 | − | 23.3827i | 0.503465 | − | 0.872027i | −0.496527 | − | 0.868021i | \(-0.665392\pi\) |
0.999992 | − | 0.00400572i | \(-0.00127506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | − | 13.8564i | 0.595871 | − | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.0000 | 1.33885 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.50000 | + | 12.9904i | −0.278543 | + | 0.482451i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5000 | − | 30.3109i | 0.649039 | − | 1.12417i | −0.334314 | − | 0.942462i | \(-0.608504\pi\) |
0.983353 | − | 0.181707i | \(-0.0581622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | −0.110959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7846i | 0.767697i | 0.923396 | + | 0.383849i | \(0.125402\pi\) | ||||
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.0000 | − | 46.7654i | 0.994558 | − | 1.72262i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.5000 | − | 7.79423i | 0.496606 | − | 0.286715i | −0.230705 | − | 0.973024i | \(-0.574103\pi\) |
0.727311 | + | 0.686308i | \(0.240770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0000 | 0.551039 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5000 | + | 6.06218i | −0.385208 | + | 0.222400i | −0.680082 | − | 0.733136i | \(-0.738056\pi\) |
0.294874 | + | 0.955536i | \(0.404722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5000 | − | 23.3827i | 0.493939 | − | 0.855528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.50000 | − | 0.866025i | 0.164426 | − | 0.0316439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 17.3205i | − | 0.632034i | −0.948753 | − | 0.316017i | \(-0.897654\pi\) | ||
0.948753 | − | 0.316017i | \(-0.102346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846i | 0.754434i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.4974i | − | 1.75803i | −0.476794 | − | 0.879015i | \(-0.658201\pi\) | ||
0.476794 | − | 0.879015i | \(-0.341799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5000 | + | 9.52628i | 0.995567 | + | 0.344874i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 25.9808i | − | 0.938111i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.50000 | + | 2.59808i | −0.162274 | + | 0.0936890i | −0.578938 | − | 0.815372i | \(-0.696533\pi\) |
0.416664 | + | 0.909061i | \(0.363199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.0000 | −1.72868 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.5000 | + | 16.4545i | −1.02507 | + | 0.591827i | −0.915570 | − | 0.402160i | \(-0.868260\pi\) |
−0.109504 | + | 0.993986i | \(0.534926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.50000 | + | 4.33013i | −0.0898027 | + | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.5000 | + | 6.06218i | −1.13006 | + | 0.217479i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.66025i | 0.310286i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.5000 | − | 7.79423i | −0.482451 | − | 0.278543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.50000 | + | 11.2583i | −0.231700 | + | 0.401316i | −0.958308 | − | 0.285736i | \(-0.907762\pi\) |
0.726609 | + | 0.687052i | \(0.241095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.0000 | −1.92245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.5000 | − | 7.79423i | −0.800008 | − | 0.277131i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.50000 | − | 2.59808i | 0.0532666 | − | 0.0922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.5000 | + | 16.4545i | −1.00952 | + | 0.582848i | −0.911052 | − | 0.412292i | \(-0.864728\pi\) |
−0.0984702 | + | 0.995140i | \(0.531395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5000 | + | 7.79423i | 0.477596 | + | 0.275740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.50000 | − | 2.59808i | −0.159000 | − | 0.0917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00000 | + | 5.19615i | 0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.5000 | − | 33.7750i | −0.686433 | − | 1.18894i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.50000 | + | 7.79423i | 0.158212 | + | 0.274030i | 0.934224 | − | 0.356687i | \(-0.116094\pi\) |
−0.776012 | + | 0.630718i | \(0.782761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.50000 | + | 0.866025i | 0.0526073 | + | 0.0303728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.50000 | − | 4.33013i | 0.262392 | − | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.50000 | − | 12.9904i | 0.157243 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5000 | + | 28.5788i | 0.575854 | + | 0.997408i | 0.995948 | + | 0.0899279i | \(0.0286637\pi\) |
−0.420094 | + | 0.907480i | \(0.638003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5000 | + | 6.06218i | 0.366007 | + | 0.211314i | 0.671713 | − | 0.740812i | \(-0.265559\pi\) |
−0.305706 | + | 0.952126i | \(0.598892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.0000 | 1.04447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.5000 | − | 7.79423i | 0.468874 | − | 0.270705i | −0.246894 | − | 0.969042i | \(-0.579410\pi\) |
0.715768 | + | 0.698338i | \(0.246077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.2487i | 0.841178i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.50000 | − | 11.2583i | −0.155916 | − | 0.390078i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.50000 | − | 2.59808i | −0.155543 | − | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.5000 | − | 23.3827i | 0.466072 | − | 0.807260i | −0.533177 | − | 0.846003i | \(-0.679002\pi\) |
0.999249 | + | 0.0387435i | \(0.0123355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.5000 | + | 12.9904i | 0.774941 | + | 0.447412i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | − | 1.73205i | 0.0687208 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46.5000 | − | 26.8468i | −1.59588 | − | 0.921379i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0000 | − | 12.1244i | −0.719871 | − | 0.415618i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.5000 | − | 26.8468i | −1.59213 | − | 0.919216i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
−0.599189 | − | 0.800608i | \(-0.704510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.92820i | 0.236663i | 0.992974 | + | 0.118331i | \(0.0377545\pi\) | ||||
−0.992974 | + | 0.118331i | \(0.962245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.50000 | + | 2.59808i | 0.255599 | + | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5000 | + | 12.9904i | 0.765909 | + | 0.442198i | 0.831413 | − | 0.555655i | \(-0.187532\pi\) |
−0.0655043 | + | 0.997852i | \(0.520866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.0000 | + | 12.1244i | 0.713197 | + | 0.411765i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | + | 5.19615i | 0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.0000 | −0.914860 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.50000 | − | 2.59808i | −0.152302 | − | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.0000 | −1.55331 | −0.776655 | − | 0.629926i | \(-0.783085\pi\) | ||||
−0.776655 | + | 0.629926i | \(0.783085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5000 | + | 38.9711i | 0.758906 | + | 1.31446i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.7846i | − | 0.700251i | −0.936703 | − | 0.350126i | \(-0.886139\pi\) | ||
0.936703 | − | 0.350126i | \(-0.113861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1769i | 1.04919i | 0.851353 | + | 0.524593i | \(0.175783\pi\) | ||||
−0.851353 | + | 0.524593i | \(0.824217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | − | 20.7846i | −0.603701 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.1769i | 1.04447i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.0000 | −1.50587 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.00000 | − | 5.19615i | 0.300501 | − | 0.173494i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.50000 | − | 2.59808i | −0.0500278 | − | 0.0866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | + | 7.79423i | 0.449750 | + | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.50000 | − | 7.79423i | −0.0499169 | − | 0.259376i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.1051i | − | 1.26526i | −0.774454 | − | 0.632630i | \(-0.781975\pi\) | ||
0.774454 | − | 0.632630i | \(-0.218025\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 41.5692i | − | 1.37876i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.5000 | − | 28.5788i | −1.64001 | − | 0.946859i | −0.980828 | − | 0.194874i | \(-0.937570\pi\) |
−0.659180 | − | 0.751985i | \(-0.729096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.0000 | − | 15.5885i | −0.893570 | − | 0.515903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.0000 | + | 20.7846i | −0.792550 | + | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.5000 | − | 11.2583i | −0.643246 | − | 0.371378i | 0.142618 | − | 0.989778i | \(-0.454448\pi\) |
−0.785864 | + | 0.618400i | \(0.787781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 13.8564i | − | 0.456584i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.00000 | + | 15.5885i | 0.296239 | + | 0.513100i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.5000 | + | 30.3109i | −0.575396 | + | 0.996616i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.0000 | 0.788263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.50000 | − | 4.33013i | 0.246067 | − | 0.142067i | −0.371895 | − | 0.928275i | \(-0.621292\pi\) |
0.617962 | + | 0.786208i | \(0.287959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.5000 | + | 21.6506i | 0.901276 | + | 0.709571i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.50000 | − | 2.59808i | −0.147323 | − | 0.0850572i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 48.4974i | − | 1.58434i | −0.610299 | − | 0.792171i | \(-0.708951\pi\) | ||
0.610299 | − | 0.792171i | \(-0.291049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.5000 | − | 44.1673i | −0.832161 | − | 1.44135i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.5000 | + | 14.7224i | 0.831276 | + | 0.479938i | 0.854289 | − | 0.519798i | \(-0.173993\pi\) |
−0.0230132 | + | 0.999735i | \(0.507326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.00000 | + | 5.19615i | 0.0976934 | + | 0.169210i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.50000 | + | 2.59808i | −0.146230 | + | 0.0844261i | −0.571330 | − | 0.820720i | \(-0.693572\pi\) |
0.425100 | + | 0.905147i | \(0.360239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50000 | − | 2.59808i | 0.0486921 | − | 0.0843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.5000 | − | 18.1865i | 1.02146 | − | 0.589739i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.00000 | + | 15.5885i | −0.290929 | + | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.0000 | − | 31.1769i | 1.16250 | − | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.50000 | + | 2.59808i | 0.145010 | + | 0.0837218i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5000 | − | 7.79423i | 0.434131 | − | 0.250645i | −0.266974 | − | 0.963704i | \(-0.586024\pi\) |
0.701105 | + | 0.713058i | \(0.252690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.0000 | 0.481869 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | − | 12.9904i | 0.240686 | − | 0.416881i | −0.720224 | − | 0.693742i | \(-0.755961\pi\) |
0.960910 | + | 0.276861i | \(0.0892941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5000 | − | 4.33013i | −0.400732 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.50000 | − | 12.9904i | −0.240192 | − | 0.416025i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.5000 | + | 44.1673i | −0.815817 | + | 1.41304i | 0.0929223 | + | 0.995673i | \(0.470379\pi\) |
−0.908740 | + | 0.417364i | \(0.862954\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00000 | + | 5.19615i | −0.0958804 | + | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.5000 | + | 28.5788i | 0.526804 | + | 0.912452i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.0000 | −0.382741 | −0.191370 | − | 0.981518i | \(-0.561293\pi\) | ||||
−0.191370 | + | 0.981518i | \(0.561293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.5000 | + | 38.9711i | −0.429710 | + | 1.24047i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.00000 | − | 5.19615i | 0.0953945 | − | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.5000 | − | 18.1865i | 1.00063 | − | 0.577714i | 0.0921957 | − | 0.995741i | \(-0.470611\pi\) |
0.908435 | + | 0.418027i | \(0.137278\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.50000 | + | 7.79423i | 0.142803 | + | 0.247342i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 55.4256i | − | 1.75535i | −0.479259 | − | 0.877674i | \(-0.659094\pi\) | ||
0.479259 | − | 0.877674i | \(-0.340906\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.5000 | − | 18.1865i | −0.996616 | − | 0.575396i |
(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 | 1008.2.bf.b.943.1 | yes | 2 | |
3.2 | odd | 2 | 3024.2.bf.b.2287.1 | 2 | |||
4.3 | odd | 2 | 1008.2.bf.c.943.1 | yes | 2 | ||
7.3 | odd | 6 | 1008.2.cz.d.367.1 | yes | 2 | ||
9.4 | even | 3 | 1008.2.cz.a.607.1 | yes | 2 | ||
9.5 | odd | 6 | 3024.2.cz.a.1279.1 | 2 | |||
12.11 | even | 2 | 3024.2.bf.c.2287.1 | 2 | |||
21.17 | even | 6 | 3024.2.cz.b.2719.1 | 2 | |||
28.3 | even | 6 | 1008.2.cz.a.367.1 | yes | 2 | ||
36.23 | even | 6 | 3024.2.cz.b.1279.1 | 2 | |||
36.31 | odd | 6 | 1008.2.cz.d.607.1 | yes | 2 | ||
63.31 | odd | 6 | 1008.2.bf.c.31.1 | yes | 2 | ||
63.59 | even | 6 | 3024.2.bf.c.1711.1 | 2 | |||
84.59 | odd | 6 | 3024.2.cz.a.2719.1 | 2 | |||
252.31 | even | 6 | inner | 1008.2.bf.b.31.1 | ✓ | 2 | |
252.59 | odd | 6 | 3024.2.bf.b.1711.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.b.31.1 | ✓ | 2 | 252.31 | even | 6 | inner | |
1008.2.bf.b.943.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1008.2.bf.c.31.1 | yes | 2 | 63.31 | odd | 6 | ||
1008.2.bf.c.943.1 | yes | 2 | 4.3 | odd | 2 | ||
1008.2.cz.a.367.1 | yes | 2 | 28.3 | even | 6 | ||
1008.2.cz.a.607.1 | yes | 2 | 9.4 | even | 3 | ||
1008.2.cz.d.367.1 | yes | 2 | 7.3 | odd | 6 | ||
1008.2.cz.d.607.1 | yes | 2 | 36.31 | odd | 6 | ||
3024.2.bf.b.1711.1 | 2 | 252.59 | odd | 6 | |||
3024.2.bf.b.2287.1 | 2 | 3.2 | odd | 2 | |||
3024.2.bf.c.1711.1 | 2 | 63.59 | even | 6 | |||
3024.2.bf.c.2287.1 | 2 | 12.11 | even | 2 | |||
3024.2.cz.a.1279.1 | 2 | 9.5 | odd | 6 | |||
3024.2.cz.a.2719.1 | 2 | 84.59 | odd | 6 | |||
3024.2.cz.b.1279.1 | 2 | 36.23 | even | 6 | |||
3024.2.cz.b.2719.1 | 2 | 21.17 | even | 6 |