Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(367,1008)]
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, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cz (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: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 367.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.367 |
Dual form | 1008.2.cz.a.607.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | + | 1.73205i | −0.904534 | + | 0.522233i | −0.878668 | − | 0.477432i | \(-0.841568\pi\) |
−0.0258656 | + | 0.999665i | \(0.508234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 0.866025i | −0.416025 | + | 0.240192i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 0.866025i | 0.363803 | + | 0.210042i | 0.670748 | − | 0.741685i | \(-0.265973\pi\) |
−0.306944 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | − | 4.33013i | −0.327327 | − | 0.944911i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 1.73205i | 0.625543 | + | 0.361158i | 0.779024 | − | 0.626994i | \(-0.215715\pi\) |
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.50000 | − | 4.33013i | −0.500000 | − | 0.866025i | ||||
\(26\) | 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 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | − | 5.19615i | 0.522233 | − | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | − | 2.59808i | 0.240192 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 0.866025i | −0.234261 | + | 0.135250i | −0.612536 | − | 0.790443i | \(-0.709851\pi\) |
0.378275 | + | 0.925693i | \(0.376517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50000 | + | 0.866025i | 0.228748 | + | 0.132068i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00000 | −1.31278 | −0.656392 | − | 0.754420i | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50000 | + | 4.33013i | 0.993399 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.0000 | −1.95283 | −0.976417 | − | 0.215894i | \(-0.930733\pi\) | ||||
−0.976417 | + | 0.215894i | \(0.930733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.73205i | − | 0.221766i | −0.993833 | − | 0.110883i | \(-0.964632\pi\) | ||
0.993833 | − | 0.110883i | \(-0.0353679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | + | 5.19615i | 0.755929 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 15.5885i | − | 1.90443i | −0.305424 | − | 0.952217i | \(-0.598798\pi\) | ||
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3923i | − | 1.23334i | −0.787222 | − | 0.616670i | \(-0.788481\pi\) | ||
0.787222 | − | 0.616670i | \(-0.211519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | + | 0.866025i | 0.175562 | + | 0.101361i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.50000 | + | 4.33013i | 0.866025 | + | 0.500000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00000 | − | 8.66025i | −0.341882 | − | 0.986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.73205i | − | 0.194871i | −0.995242 | − | 0.0974355i | \(-0.968936\pi\) | ||
0.995242 | − | 0.0974355i | \(-0.0310640\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 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 | ||||||||
\(87\) | − | 5.19615i | − | 0.557086i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50000 | − | 0.866025i | 0.159000 | − | 0.0917985i | −0.418389 | − | 0.908268i | \(-0.637405\pi\) |
0.577389 | + | 0.816469i | \(0.304072\pi\) | |||||||
\(90\) | 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 | 0.421912 | − | 0.906637i | \(-0.361359\pi\) |
−0.574214 | + | 0.818705i | \(0.694692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | + | 6.92820i | −1.19404 | + | 0.689382i | −0.959221 | − | 0.282656i | \(-0.908784\pi\) |
−0.234823 | + | 0.972038i | \(0.575451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | − | 6.92820i | 0.394132 | − | 0.682656i | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50000 | + | 0.866025i | −0.145010 | + | 0.0837218i | −0.570750 | − | 0.821124i | \(-0.693347\pi\) |
0.425739 | + | 0.904846i | \(0.360014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | 5.19615i | 0.480384i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 3.46410i | −0.275010 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 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 | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.00000 | −0.264135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5000 | − | 4.33013i | 1.08389 | − | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 15.5885i | 0.768922 | + | 1.33181i | 0.938148 | + | 0.346235i | \(0.112540\pi\) |
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(138\) | 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 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0000 | − | 8.66025i | 1.22068 | − | 0.704761i | 0.255619 | − | 0.966778i | \(-0.417721\pi\) |
0.965064 | + | 0.262016i | \(0.0843873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50000 | − | 2.59808i | 0.363803 | − | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.1244i | − | 0.967629i | −0.875171 | − | 0.483814i | \(-0.839251\pi\) | ||
0.875171 | − | 0.483814i | \(-0.160749\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.5885i | 1.23625i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | + | 6.92820i | −0.472866 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5000 | + | 7.79423i | −1.05740 | + | 0.610491i | −0.924712 | − | 0.380667i | \(-0.875695\pi\) |
−0.132689 | + | 0.991158i | \(0.542361\pi\) | |||||||
\(164\) | 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 | ||||||||
\(171\) | −15.0000 | −1.14708 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0526i | 1.44854i | 0.689517 | + | 0.724270i | \(0.257823\pi\) | ||||
−0.689517 | + | 0.724270i | \(0.742177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5000 | − | 4.33013i | 0.944911 | − | 0.327327i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.5000 | − | 12.9904i | 1.69120 | − | 0.976417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | − | 6.06218i | −0.784807 | − | 0.453108i | 0.0533243 | − | 0.998577i | \(-0.483018\pi\) |
−0.838131 | + | 0.545469i | \(0.816352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.50000 | + | 2.59808i | 0.110883 | + | 0.192055i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | −0.438763 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.5000 | − | 2.59808i | −0.981981 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.73205i | − | 0.125327i | −0.998035 | − | 0.0626634i | \(-0.980041\pi\) | ||
0.998035 | − | 0.0626634i | \(-0.0199595\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.0000 | −1.22369 | −0.611843 | − | 0.790979i | \(-0.709572\pi\) | ||||
−0.611843 | + | 0.790979i | \(0.709572\pi\) | |||||||
\(194\) | 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 | −0.847759 | − | 0.530381i | \(-0.822049\pi\) |
0.883203 | + | 0.468990i | \(0.155382\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.5000 | + | 23.3827i | 0.952217 | + | 1.64929i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | − | 5.19615i | −0.421117 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | − | 5.19615i | 0.625543 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0000 | + | 8.66025i | 1.03757 | + | 0.599042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5000 | − | 6.06218i | 0.722850 | − | 0.417338i | −0.0929509 | − | 0.995671i | \(-0.529630\pi\) |
0.815801 | + | 0.578333i | \(0.196297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.00000 | + | 15.5885i | 0.616670 | + | 1.06810i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.500000 | + | 2.59808i | −0.0339422 | + | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00000 | −0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | + | 6.92820i | 0.792982 | + | 0.457829i | 0.841011 | − | 0.541017i | \(-0.181961\pi\) |
−0.0480291 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | + | 10.3923i | 0.789542 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | + | 18.1865i | 0.687878 | + | 1.19144i | 0.972523 | + | 0.232806i | \(0.0747909\pi\) |
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(234\) | 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 | −0.973336 | − | 0.229385i | \(-0.926328\pi\) |
−0.288014 | + | 0.957626i | \(0.592995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | + | 10.3923i | −1.15948 | + | 0.669427i | −0.951180 | − | 0.308637i | \(-0.900127\pi\) |
−0.208302 | + | 0.978065i | \(0.566794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.50000 | + | 4.33013i | 0.477214 | + | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.5885i | − | 0.987878i | ||||||
\(250\) | 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 | ||||||||
\(257\) | −24.0000 | − | 13.8564i | −1.49708 | − | 0.864339i | −0.497085 | − | 0.867702i | \(-0.665596\pi\) |
−0.999994 | + | 0.00336324i | \(0.998929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.5000 | − | 6.06218i | 1.08740 | − | 0.376685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | + | 7.79423i | 0.278543 | + | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.0000 | − | 15.5885i | 1.66489 | − | 0.961225i | 0.694564 | − | 0.719431i | \(-0.255597\pi\) |
0.970328 | − | 0.241794i | \(-0.0777359\pi\) | |||||||
\(264\) | 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 | 0.958065 | − | 0.286552i | \(-0.0925091\pi\) |
0.230871 | + | 0.972984i | \(0.425842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.500000 | − | 0.866025i | −0.0303728 | − | 0.0526073i | 0.850439 | − | 0.526073i | \(-0.176336\pi\) |
−0.880812 | + | 0.473466i | \(0.843003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | + | 5.19615i | 0.363137 | + | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.0000 | + | 8.66025i | 0.904534 | + | 0.522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | + | 12.1244i | 0.420589 | + | 0.728482i | 0.995997 | − | 0.0893846i | \(-0.0284900\pi\) |
−0.575408 | + | 0.817867i | \(0.695157\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −31.0000 | −1.84276 | −0.921379 | − | 0.388664i | \(-0.872937\pi\) | ||||
−0.921379 | + | 0.388664i | \(0.872937\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | 3.00000 | 0.175863 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.5000 | − | 12.9904i | 1.31446 | − | 0.758906i | 0.331632 | − | 0.943409i | \(-0.392401\pi\) |
0.982832 | + | 0.184503i | \(0.0590674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.00000 | − | 15.5885i | −0.522233 | − | 0.904534i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | + | 3.46410i | −0.172917 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | − | 20.7846i | 0.689382 | − | 1.19404i | ||||
\(304\) | 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 | ||||||||
\(311\) | −3.00000 | −0.170114 | −0.0850572 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850572 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 29.4449i | − | 1.66432i | −0.554534 | − | 0.832161i | \(-0.687103\pi\) | ||
0.554534 | − | 0.832161i | \(-0.312897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.0000 | −1.17948 | −0.589739 | − | 0.807594i | \(-0.700769\pi\) | ||||
−0.589739 | + | 0.807594i | \(0.700769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.3923i | − | 0.581857i | ||||||
\(320\) | 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 | ||||||||
\(327\) | − | 19.0526i | − | 1.05361i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | − | 23.3827i | 0.248093 | − | 1.28913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.19615i | 0.285606i | 0.989751 | + | 0.142803i | \(0.0456116\pi\) | ||||
−0.989751 | + | 0.142803i | \(0.954388\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.0000 | −1.15079 | ||||||||
\(334\) | 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 | ||||||||
\(347\) | − | 22.5167i | − | 1.20876i | −0.796697 | − | 0.604379i | \(-0.793421\pi\) | ||
0.796697 | − | 0.604379i | \(-0.206579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.5000 | + | 12.9904i | 1.20440 | + | 0.695359i | 0.961530 | − | 0.274700i | \(-0.0885786\pi\) |
0.242867 | + | 0.970059i | \(0.421912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.50000 | − | 7.79423i | −0.240192 | − | 0.416025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | + | 10.3923i | −0.958043 | + | 0.553127i | −0.895570 | − | 0.444920i | \(-0.853232\pi\) |
−0.0624731 | + | 0.998047i | \(0.519899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.50000 | − | 7.79423i | 0.0793884 | − | 0.412514i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5000 | − | 6.06218i | 0.554169 | − | 0.319950i | −0.196633 | − | 0.980477i | \(-0.563001\pi\) |
0.750802 | + | 0.660528i | \(0.229667\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.19615i | 0.270501i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0000 | + | 15.5885i | 0.934513 | + | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 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 | \(0.213999\pi\) | ||||
−0.782392 | + | 0.622786i | \(0.786001\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.00000 | + | 15.5885i | 0.461084 | + | 0.798621i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0000 | + | 20.7846i | −0.613171 | + | 1.06204i | 0.377531 | + | 0.925997i | \(0.376773\pi\) |
−0.990702 | + | 0.136047i | \(0.956560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.50000 | − | 2.59808i | 0.228748 | − | 0.132068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.00000 | − | 15.5885i | −0.456318 | − | 0.790366i | 0.542445 | − | 0.840091i | \(-0.317499\pi\) |
−0.998763 | + | 0.0497253i | \(0.984165\pi\) | |||||||
\(390\) | 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 | −0.121384 | − | 0.992606i | \(-0.538733\pi\) |
0.798930 | + | 0.601424i | \(0.205400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.0000 | + | 17.3205i | −0.750939 | + | 0.867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | + | 25.9808i | −0.749064 | + | 1.29742i | 0.199207 | + | 0.979957i | \(0.436163\pi\) |
−0.948272 | + | 0.317460i | \(0.897170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50000 | + | 0.866025i | −0.0747203 | + | 0.0431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0000 | + | 12.1244i | 1.04093 | + | 0.600982i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4449i | 1.45595i | 0.685601 | + | 0.727977i | \(0.259539\pi\) | ||||
−0.685601 | + | 0.727977i | \(0.740461\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.0000 | − | 15.5885i | −1.33181 | − | 0.768922i | ||||
\(412\) | 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 | ||||||||
\(425\) | − | 8.66025i | − | 0.420084i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.50000 | + | 0.866025i | 0.217770 | + | 0.0419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.3923i | 0.501745i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.5000 | − | 12.9904i | −1.08379 | − | 0.625725i | −0.151871 | − | 0.988400i | \(-0.548530\pi\) |
−0.931915 | + | 0.362676i | \(0.881863\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.8564i | − | 0.665896i | −0.942945 | − | 0.332948i | \(-0.891957\pi\) | ||
0.942945 | − | 0.332948i | \(-0.108043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 17.3205i | − | 0.828552i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0000 | −1.19318 | −0.596592 | − | 0.802544i | \(-0.703479\pi\) | ||||
−0.596592 | + | 0.802544i | \(0.703479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.5000 | + | 12.9904i | −0.785714 | + | 0.618590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.9808i | 1.23438i | 0.786813 | + | 0.617192i | \(0.211730\pi\) | ||||
−0.786813 | + | 0.617192i | \(0.788270\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | −15.0000 | + | 25.9808i | −0.704761 | + | 1.22068i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.50000 | + | 7.79423i | −0.210042 | + | 0.363803i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.5000 | − | 11.2583i | −0.908206 | − | 0.524353i | −0.0283522 | − | 0.999598i | \(-0.509026\pi\) |
−0.879853 | + | 0.475245i | \(0.842359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.5000 | + | 18.1865i | −1.46393 | + | 0.845200i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.50000 | + | 12.9904i | 0.347059 | + | 0.601123i | 0.985726 | − | 0.168360i | \(-0.0538472\pi\) |
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | + | 6.06218i | 0.478759 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.00000 | − | 15.5885i | 0.136505 | − | 0.709299i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5000 | + | 7.79423i | 0.611743 | + | 0.353190i | 0.773647 | − | 0.633616i | \(-0.218430\pi\) |
−0.161904 | + | 0.986807i | \(0.551764\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.5000 | − | 23.3827i | 0.610491 | − | 1.05740i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | + | 4.33013i | −0.338470 | + | 0.195416i | −0.659595 | − | 0.751621i | \(-0.729272\pi\) |
0.321125 | + | 0.947037i | \(0.395939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.50000 | + | 2.59808i | −0.202670 | + | 0.117011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.0000 | + | 5.19615i | 1.21112 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.00000 | + | 1.73205i | 0.134298 | + | 0.0775372i | 0.565644 | − | 0.824650i | \(-0.308628\pi\) |
−0.431346 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | − | 17.3205i | − | 0.769231i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.0000 | − | 17.3205i | −1.32973 | − | 0.767718i | −0.344469 | − | 0.938798i | \(-0.611941\pi\) |
−0.985257 | + | 0.171080i | \(0.945274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | + | 3.46410i | −0.132712 | + | 0.153243i | ||||
\(512\) | 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 | 0.862103 | − | 0.506733i | \(-0.169147\pi\) |
−0.00779240 | + | 0.999970i | \(0.502480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.50000 | − | 11.2583i | −0.284225 | − | 0.492292i | 0.688196 | − | 0.725525i | \(-0.258403\pi\) |
−0.972421 | + | 0.233233i | \(0.925070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.0000 | + | 17.3205i | −0.654654 | + | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.50000 | + | 0.866025i | 0.0653410 | + | 0.0377247i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.50000 | − | 9.52628i | −0.239130 | − | 0.414186i | ||||
\(530\) | 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 | ||||||||
\(537\) | 21.0000 | 0.906217 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.0000 | − | 3.46410i | 1.03375 | − | 0.149209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.5000 | − | 37.2391i | −0.924357 | − | 1.60103i | −0.792592 | − | 0.609753i | \(-0.791269\pi\) |
−0.131765 | − | 0.991281i | \(-0.542065\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | − | 20.7846i | −0.514969 | − | 0.891953i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.50000 | + | 4.33013i | 0.320677 | + | 0.185143i | 0.651694 | − | 0.758482i | \(-0.274059\pi\) |
−0.331017 | + | 0.943625i | \(0.607392\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.50000 | − | 2.59808i | −0.192055 | − | 0.110883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | 0.639021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.50000 | + | 0.866025i | 0.191359 | + | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5000 | − | 28.5788i | 0.699127 | − | 1.21092i | −0.269642 | − | 0.962961i | \(-0.586905\pi\) |
0.968769 | − | 0.247964i | \(-0.0797613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | − | 5.19615i | 0.379980 | − | 0.219382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.0000 | 0.885044 | 0.442522 | − | 0.896758i | \(-0.354084\pi\) | ||||
0.442522 | + | 0.896758i | \(0.354084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.5000 | − | 7.79423i | 0.944911 | − | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | 0.125767 | 0.0628833 | − | 0.998021i | \(-0.479970\pi\) | ||||
0.0628833 | + | 0.998021i | \(0.479970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.8372i | 1.66713i | 0.552419 | + | 0.833567i | \(0.313705\pi\) | ||||
−0.552419 | + | 0.833567i | \(0.686295\pi\) | |||||||
\(572\) | 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 | −0.0477669 | − | 0.998859i | \(-0.515210\pi\) |
−0.888920 | + | 0.458062i | \(0.848544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.5000 | − | 14.7224i | 1.05974 | − | 0.611843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | − | 15.5885i | −0.746766 | − | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.1769i | 1.29122i | ||||||||
\(584\) | 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 | ||||||||
\(591\) | −9.00000 | + | 5.19615i | −0.370211 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.50000 | − | 4.33013i | 0.307988 | − | 0.177817i | −0.338038 | − | 0.941133i | \(-0.609763\pi\) |
0.646026 | + | 0.763316i | \(0.276430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.73205i | 0.0708881i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.3731i | − | 1.48616i | −0.669201 | − | 0.743082i | \(-0.733363\pi\) | ||
0.669201 | − | 0.743082i | \(-0.266637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.5000 | − | 18.1865i | −1.28491 | − | 0.741844i | −0.307170 | − | 0.951655i | \(-0.599382\pi\) |
−0.977742 | + | 0.209811i | \(0.932715\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −40.5000 | − | 23.3827i | −1.64929 | − | 0.952217i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | + | 27.7128i | −0.649420 | + | 1.12483i | 0.333842 | + | 0.942629i | \(0.391655\pi\) |
−0.983262 | + | 0.182199i | \(0.941678\pi\) | |||||||
\(608\) | 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 | 0.259213 | + | 0.965820i | \(0.416537\pi\) |
−0.966031 | + | 0.258425i | \(0.916796\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −14.0000 | − | 24.2487i | −0.562708 | − | 0.974638i | −0.997259 | − | 0.0739910i | \(-0.976426\pi\) |
0.434551 | − | 0.900647i | \(-0.356907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.00000 | + | 15.5885i | −0.361158 | + | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.50000 | + | 4.33013i | 0.0600962 | + | 0.173483i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.0000 | −1.19808 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.1244i | − | 0.483430i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1769i | 1.24113i | 0.784154 | + | 0.620567i | \(0.213097\pi\) | ||||
−0.784154 | + | 0.620567i | \(0.786903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.5000 | + | 18.1865i | −0.417338 | + | 0.722850i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | − | 1.73205i | 0.475457 | − | 0.0686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.0000 | − | 15.5885i | −1.06810 | − | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.00000 | − | 5.19615i | −0.118493 | − | 0.205236i | 0.800678 | − | 0.599095i | \(-0.204473\pi\) |
−0.919171 | + | 0.393860i | \(0.871140\pi\) | |||||||
\(642\) | 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 | −0.974951 | − | 0.222419i | \(-0.928605\pi\) |
0.680096 | + | 0.733123i | \(0.261938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.0000 | − | 25.9808i | 1.76640 | − | 1.01983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.50000 | − | 4.33013i | −0.0587896 | − | 0.169711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0000 | + | 25.9808i | −0.586995 | + | 1.01671i | 0.407628 | + | 0.913148i | \(0.366356\pi\) |
−0.994623 | + | 0.103558i | \(0.966977\pi\) | |||||||
\(654\) | 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 | 0.829156 | − | 0.559017i | \(-0.188821\pi\) |
−0.0695443 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.66025i | 0.336845i | 0.985715 | + | 0.168422i | \(0.0538673\pi\) | ||||
−0.985715 | + | 0.168422i | \(0.946133\pi\) | |||||||
\(662\) | 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 | ||||||||
\(669\) | − | 8.66025i | − | 0.334825i | ||||||
\(670\) | 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 | ||||||||
\(675\) | 22.5000 | − | 12.9904i | 0.866025 | − | 0.500000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.73205i | − | 0.0665681i | −0.999446 | − | 0.0332841i | \(-0.989403\pi\) | ||
0.999446 | − | 0.0332841i | \(-0.0105966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.00000 | − | 3.46410i | 0.115129 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | + | 10.3923i | 0.689761 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.5000 | + | 21.6506i | 1.43490 | + | 0.828439i | 0.997489 | − | 0.0708242i | \(-0.0225629\pi\) |
0.437409 | + | 0.899263i | \(0.355896\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.0000 | −0.915657 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.5885i | 0.593873i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.00000 | −0.190209 | −0.0951045 | − | 0.995467i | \(-0.530319\pi\) | ||||
−0.0951045 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.0000 | − | 5.19615i | −1.02565 | − | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.00000 | −0.113633 | ||||||||
\(698\) | 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 | ||||||||
\(707\) | −12.0000 | − | 34.6410i | −0.451306 | − | 1.30281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0000 | −1.38956 | −0.694782 | − | 0.719220i | \(-0.744499\pi\) | ||||
−0.694782 | + | 0.719220i | \(0.744499\pi\) | |||||||
\(710\) | 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 | 0.999992 | + | 0.00400572i | \(0.00127506\pi\) |
−0.496527 | + | 0.868021i | \(0.665392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | + | 13.8564i | 0.595871 | + | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.0000 | − | 31.1769i | 0.669427 | − | 1.15948i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0000 | 0.557086 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0000 | + | 10.3923i | 0.664845 | + | 0.383849i | 0.794121 | − | 0.607760i | \(-0.207932\pi\) |
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | 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 | 0.727311 | − | 0.686308i | \(-0.240770\pi\) |
−0.230705 | + | 0.973024i | \(0.574103\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.0000 | −0.551039 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5000 | − | 6.06218i | 0.385208 | − | 0.222400i | −0.294874 | − | 0.955536i | \(-0.595278\pi\) |
0.680082 | + | 0.733136i | \(0.261944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5000 | + | 23.3827i | 0.493939 | + | 0.855528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.50000 | − | 4.33013i | −0.0548088 | − | 0.158219i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0000 | − | 8.66025i | −0.547358 | − | 0.316017i | 0.200698 | − | 0.979653i | \(-0.435679\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 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 | ||||||||
\(759\) | 18.0000 | − | 10.3923i | 0.653359 | − | 0.377217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | − | 24.2487i | −1.52250 | − | 0.879015i | −0.999646 | − | 0.0265919i | \(-0.991535\pi\) |
−0.522852 | − | 0.852423i | \(-0.675132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.0000 | − | 19.0526i | −0.796453 | − | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.5000 | − | 12.9904i | 0.812428 | − | 0.469055i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.50000 | − | 2.59808i | 0.162274 | − | 0.0936890i | −0.416664 | − | 0.909061i | \(-0.636801\pi\) |
0.578938 | + | 0.815372i | \(0.303467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.0000 | 1.72868 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.5000 | − | 16.4545i | −1.02507 | − | 0.591827i | −0.109504 | − | 0.993986i | \(-0.534926\pi\) |
−0.915570 | + | 0.402160i | \(0.868260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.50000 | − | 4.33013i | −0.0898027 | − | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.0000 | + | 24.2487i | −0.753371 | + | 0.869918i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.50000 | + | 4.33013i | 0.268715 | + | 0.155143i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.5000 | − | 7.79423i | −0.482451 | − | 0.278543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0000 | 0.463400 | 0.231700 | − | 0.972787i | \(-0.425571\pi\) | ||||
0.231700 | + | 0.972787i | \(0.425571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.0000 | + | 46.7654i | −0.961225 | + | 1.66489i | ||||
\(790\) | 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 | 0.0984702 | − | 0.995140i | \(-0.468605\pi\) |
0.911052 | + | 0.412292i | \(0.135272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.5000 | − | 7.79423i | −0.477596 | − | 0.275740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.19615i | − | 0.183597i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | −0.211735 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −39.0000 | −1.37287 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.50000 | − | 7.79423i | 0.158212 | − | 0.274030i | −0.776012 | − | 0.630718i | \(-0.782761\pi\) |
0.934224 | + | 0.356687i | \(0.116094\pi\) | |||||||
\(810\) | 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 | ||||||||
\(817\) | − | 8.66025i | − | 0.302984i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.5000 | − | 2.59808i | −0.471728 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.0000 | −1.15171 | −0.575854 | − | 0.817553i | \(-0.695330\pi\) | ||||
−0.575854 | + | 0.817553i | \(0.695330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.1244i | 0.422628i | 0.977418 | + | 0.211314i | \(0.0677743\pi\) | ||||
−0.977418 | + | 0.211314i | \(0.932226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.0000 | −1.04447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.3205i | − | 0.602293i | −0.953578 | − | 0.301147i | \(-0.902631\pi\) | ||
0.953578 | − | 0.301147i | \(-0.0973693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.5000 | + | 7.79423i | 0.468874 | + | 0.270705i | 0.715768 | − | 0.698338i | \(-0.246077\pi\) |
−0.246894 | + | 0.969042i | \(0.579410\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0000 | − | 12.1244i | −0.728482 | − | 0.420589i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.50000 | − | 9.52628i | −0.259860 | − | 0.330066i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.19615i | 0.179605i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − | 25.9808i | − | 0.894825i | ||||||
\(844\) | 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 | ||||||||
\(851\) | − | 24.2487i | − | 0.831235i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.5000 | + | 26.8468i | 1.59213 | + | 0.919216i | 0.992941 | + | 0.118609i | \(0.0378434\pi\) |
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00000 | + | 3.46410i | −0.204956 | + | 0.118331i | −0.598965 | − | 0.800775i | \(-0.704421\pi\) |
0.394009 | + | 0.919107i | \(0.371088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | + | 5.19615i | 0.204479 | + | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5000 | − | 12.9904i | 0.765909 | − | 0.442198i | −0.0655043 | − | 0.997852i | \(-0.520866\pi\) |
0.831413 | + | 0.555655i | \(0.187532\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 13.5000 | + | 23.3827i | 0.457430 | + | 0.792292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.50000 | + | 2.59808i | −0.152302 | + | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | − | 39.8372i | 0.776655 | − | 1.34521i | −0.157205 | − | 0.987566i | \(-0.550248\pi\) |
0.933860 | − | 0.357640i | \(-0.116418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.5000 | + | 38.9711i | −0.758906 | + | 1.31446i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7846i | 0.700251i | 0.936703 | + | 0.350126i | \(0.113861\pi\) | ||||
−0.936703 | + | 0.350126i | \(0.886139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31.1769i | − | 1.04919i | −0.851353 | − | 0.524593i | \(-0.824217\pi\) | ||
0.851353 | − | 0.524593i | \(-0.175783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | − | 10.3923i | 0.201460 | − | 0.348939i | −0.747539 | − | 0.664218i | \(-0.768765\pi\) |
0.948999 | + | 0.315279i | \(0.102098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.0000 | + | 5.19615i | 0.905551 | + | 0.174273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | + | 15.5885i | 0.904534 | + | 0.522233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.5000 | + | 38.9711i | 0.752934 | + | 1.30412i | ||||
\(894\) | 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 | ||||||||
\(907\) | 33.0000 | − | 19.0526i | 1.09575 | − | 0.632630i | 0.160646 | − | 0.987012i | \(-0.448642\pi\) |
0.935101 | + | 0.354382i | \(0.115309\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.5692i | 1.37876i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.5000 | + | 28.5788i | 1.64001 | + | 0.946859i | 0.980828 | + | 0.194874i | \(0.0624297\pi\) |
0.659180 | + | 0.751985i | \(0.270904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.1769i | − | 1.03181i | ||||||
\(914\) | 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 | −0.785864 | − | 0.618400i | \(-0.787781\pi\) |
0.142618 | + | 0.989778i | \(0.454448\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | + | 6.92820i | −0.395413 | + | 0.228292i | ||||
\(922\) | 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 | ||||||||
\(927\) | −12.0000 | − | 20.7846i | −0.394132 | − | 0.682656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.66025i | − | 0.284134i | −0.989857 | − | 0.142067i | \(-0.954625\pi\) | ||
0.989857 | − | 0.142067i | \(-0.0453748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | + | 34.6410i | 0.163868 | + | 1.13531i | ||||
\(932\) | 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 | \(0.291049\pi\) | ||||
−0.610299 | + | 0.792171i | \(0.708951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5000 | + | 44.1673i | 0.832161 | + | 1.44135i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.4449i | 0.959875i | 0.877303 | + | 0.479938i | \(0.159341\pi\) | ||||
−0.877303 | + | 0.479938i | \(0.840659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | −0.195387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.19615i | 0.168852i | 0.996430 | + | 0.0844261i | \(0.0269057\pi\) | ||||
−0.996430 | + | 0.0844261i | \(0.973094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.00000 | −0.0973841 | ||||||||
\(950\) | 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 | ||||||||
\(959\) | −45.0000 | + | 15.5885i | −1.45313 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.19615i | 0.167444i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5000 | + | 7.79423i | −0.434131 | + | 0.250645i | −0.701105 | − | 0.713058i | \(-0.747310\pi\) |
0.266974 | + | 0.963704i | \(0.413976\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.50000 | + | 12.9904i | 0.240935 | + | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | + | 12.9904i | 0.240686 | + | 0.416881i | 0.960910 | − | 0.276861i | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5000 | + | 4.33013i | −0.400732 | + | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.0000 | −0.480384 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.0000 | 1.63163 | 0.815817 | − | 0.578310i | \(-0.196287\pi\) | ||||
0.815817 | + | 0.578310i | \(0.196287\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 6.00000 | + | 10.3923i | 0.191370 | + | 0.331463i | 0.945705 | − | 0.325027i | \(-0.105374\pi\) |
−0.754334 | + | 0.656490i | \(0.772040\pi\) | |||||||
\(984\) | 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 | 0.908435 | − | 0.418027i | \(-0.137278\pi\) |
0.0921957 | + | 0.995741i | \(0.470611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.50000 | − | 7.79423i | −0.142803 | − | 0.247342i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.0000 | − | 27.7128i | 1.52018 | − | 0.877674i | 0.520458 | − | 0.853887i | \(-0.325761\pi\) |
0.999717 | − | 0.0237864i | \(-0.00757217\pi\) | |||||||
\(998\) | 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.cz.a.367.1 | yes | 2 | |
3.2 | odd | 2 | 3024.2.cz.a.2719.1 | 2 | |||
4.3 | odd | 2 | 1008.2.cz.d.367.1 | yes | 2 | ||
7.5 | odd | 6 | 1008.2.bf.c.943.1 | yes | 2 | ||
9.4 | even | 3 | 1008.2.bf.b.31.1 | ✓ | 2 | ||
9.5 | odd | 6 | 3024.2.bf.b.1711.1 | 2 | |||
12.11 | even | 2 | 3024.2.cz.b.2719.1 | 2 | |||
21.5 | even | 6 | 3024.2.bf.c.2287.1 | 2 | |||
28.19 | even | 6 | 1008.2.bf.b.943.1 | yes | 2 | ||
36.23 | even | 6 | 3024.2.bf.c.1711.1 | 2 | |||
36.31 | odd | 6 | 1008.2.bf.c.31.1 | yes | 2 | ||
63.5 | even | 6 | 3024.2.cz.b.1279.1 | 2 | |||
63.40 | odd | 6 | 1008.2.cz.d.607.1 | yes | 2 | ||
84.47 | odd | 6 | 3024.2.bf.b.2287.1 | 2 | |||
252.103 | even | 6 | inner | 1008.2.cz.a.607.1 | yes | 2 | |
252.131 | odd | 6 | 3024.2.cz.a.1279.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.b.31.1 | ✓ | 2 | 9.4 | even | 3 | ||
1008.2.bf.b.943.1 | yes | 2 | 28.19 | even | 6 | ||
1008.2.bf.c.31.1 | yes | 2 | 36.31 | odd | 6 | ||
1008.2.bf.c.943.1 | yes | 2 | 7.5 | odd | 6 | ||
1008.2.cz.a.367.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1008.2.cz.a.607.1 | yes | 2 | 252.103 | even | 6 | inner | |
1008.2.cz.d.367.1 | yes | 2 | 4.3 | odd | 2 | ||
1008.2.cz.d.607.1 | yes | 2 | 63.40 | odd | 6 | ||
3024.2.bf.b.1711.1 | 2 | 9.5 | odd | 6 | |||
3024.2.bf.b.2287.1 | 2 | 84.47 | odd | 6 | |||
3024.2.bf.c.1711.1 | 2 | 36.23 | even | 6 | |||
3024.2.bf.c.2287.1 | 2 | 21.5 | even | 6 | |||
3024.2.cz.a.1279.1 | 2 | 252.131 | odd | 6 | |||
3024.2.cz.a.2719.1 | 2 | 3.2 | odd | 2 | |||
3024.2.cz.b.1279.1 | 2 | 63.5 | even | 6 | |||
3024.2.cz.b.2719.1 | 2 | 12.11 | even | 2 |