Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(64,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.d (of order \(2\), degree \(1\), 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: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.64 |
Dual form | 65.2.d.a.64.1 |
$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 2.00000i | 1.15470i | 0.816497 | + | 0.577350i | \(0.195913\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | − | 2.00000i | − | 0.816497i | ||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.00000 | − | 2.00000i | 0.316228 | − | 0.632456i | ||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | − | 2.00000i | − | 0.577350i | ||||||
\(13\) | 3.00000 | − | 2.00000i | 0.832050 | − | 0.554700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | − | 2.00000i | −1.03280 | − | 0.516398i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 1.00000 | − | 2.00000i | 0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 6.00000i | 1.22474i | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | −3.00000 | + | 2.00000i | −0.588348 | + | 0.392232i | ||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 4.00000 | + | 2.00000i | 0.730297 | + | 0.365148i | ||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | 4.00000 | + | 6.00000i | 0.640513 | + | 0.960769i | ||||
\(40\) | −3.00000 | + | 6.00000i | −0.474342 | + | 0.948683i | ||||
\(41\) | − | 8.00000i | − | 1.24939i | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||
0.780869 | − | 0.624695i | \(-0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.00000i | − | 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | − | 2.00000i | − | 0.301511i | ||||||
\(45\) | 1.00000 | − | 2.00000i | 0.149071 | − | 0.298142i | ||||
\(46\) | − | 6.00000i | − | 0.884652i | ||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | − | 2.00000i | − | 0.288675i | ||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 3.00000 | + | 4.00000i | 0.424264 | + | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | + | 2.00000i | −0.416025 | + | 0.277350i | ||||
\(53\) | − | 12.0000i | − | 1.64833i | −0.566352 | − | 0.824163i | \(-0.691646\pi\) | ||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | − | 4.00000i | − | 0.544331i | ||||||
\(55\) | −4.00000 | − | 2.00000i | −0.539360 | − | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0000 | 1.58944 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 2.00000i | 0.260378i | 0.991489 | + | 0.130189i | \(0.0415584\pi\) | ||||
−0.991489 | + | 0.130189i | \(0.958442\pi\) | |||||||
\(60\) | 4.00000 | + | 2.00000i | 0.516398 | + | 0.258199i | ||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | − | 6.00000i | − | 0.762001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 1.00000 | + | 8.00000i | 0.124035 | + | 0.992278i | ||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.0000 | −1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.00000i | − | 0.237356i | −0.992933 | − | 0.118678i | \(-0.962134\pi\) | ||
0.992933 | − | 0.118678i | \(-0.0378657\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | 8.00000 | − | 6.00000i | 0.923760 | − | 0.692820i | ||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | − | 6.00000i | −0.452911 | − | 0.679366i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.00000 | − | 2.00000i | 0.111803 | − | 0.223607i | ||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 8.00000i | 0.883452i | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.00000i | 0.646997i | ||||||||
\(87\) | 12.0000i | 1.28654i | ||||||||
\(88\) | 6.00000i | 0.639602i | ||||||||
\(89\) | − | 8.00000i | − | 0.847998i | −0.905663 | − | 0.423999i | \(-0.860626\pi\) | ||
0.905663 | − | 0.423999i | \(-0.139374\pi\) | |||||||
\(90\) | −1.00000 | + | 2.00000i | −0.105409 | + | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | −12.0000 | −1.24434 | ||||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 12.0000 | + | 6.00000i | 1.23117 | + | 0.615587i | ||||
\(96\) | − | 10.0000i | − | 1.02062i | ||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 9.00000 | − | 6.00000i | 0.882523 | − | 0.588348i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000i | 1.16554i | ||||||||
\(107\) | − | 6.00000i | − | 0.580042i | −0.957020 | − | 0.290021i | \(-0.906338\pi\) | ||
0.957020 | − | 0.290021i | \(-0.0936623\pi\) | |||||||
\(108\) | − | 4.00000i | − | 0.384900i | ||||||
\(109\) | 12.0000i | 1.14939i | 0.818367 | + | 0.574696i | \(0.194880\pi\) | ||||
−0.818367 | + | 0.574696i | \(0.805120\pi\) | |||||||
\(110\) | 4.00000 | + | 2.00000i | 0.381385 | + | 0.190693i | ||||
\(111\) | 12.0000i | 1.13899i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | −12.0000 | −1.12390 | ||||||||
\(115\) | −12.0000 | − | 6.00000i | −1.11901 | − | 0.559503i | ||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | −3.00000 | + | 2.00000i | −0.277350 | + | 0.184900i | ||||
\(118\) | − | 2.00000i | − | 0.184115i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.0000 | − | 6.00000i | −1.09545 | − | 0.547723i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 16.0000 | 1.44267 | ||||||||
\(124\) | − | 6.00000i | − | 0.538816i | ||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | −1.00000 | − | 8.00000i | −0.0877058 | − | 0.701646i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | −8.00000 | − | 4.00000i | −0.688530 | − | 0.344265i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 12.0000 | 1.02151 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 16.0000i | − | 1.34744i | ||||||
\(142\) | 2.00000i | 0.167836i | ||||||||
\(143\) | 4.00000 | + | 6.00000i | 0.334497 | + | 0.501745i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.00000 | + | 12.0000i | −0.498273 | + | 0.996546i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | − | 14.0000i | − | 1.15470i | ||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 20.0000i | 1.63846i | 0.573462 | + | 0.819232i | \(0.305600\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | −8.00000 | + | 6.00000i | −0.653197 | + | 0.489898i | ||||
\(151\) | − | 18.0000i | − | 1.46482i | −0.680864 | − | 0.732410i | \(-0.738396\pi\) | ||
0.680864 | − | 0.732410i | \(-0.261604\pi\) | |||||||
\(152\) | − | 18.0000i | − | 1.45999i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | − | 6.00000i | −0.963863 | − | 0.481932i | ||||
\(156\) | −4.00000 | − | 6.00000i | −0.320256 | − | 0.480384i | ||||
\(157\) | 12.0000i | 0.957704i | 0.877896 | + | 0.478852i | \(0.158947\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.0000 | 1.90332 | ||||||||
\(160\) | 5.00000 | − | 10.0000i | 0.395285 | − | 0.790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 8.00000i | 0.624695i | ||||||||
\(165\) | 4.00000 | − | 8.00000i | 0.311400 | − | 0.622799i | ||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | − | 12.0000i | 0.384615 | − | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000i | 0.458831i | ||||||||
\(172\) | 6.00000i | 0.457496i | ||||||||
\(173\) | 12.0000i | 0.912343i | 0.889892 | + | 0.456172i | \(0.150780\pi\) | ||||
−0.889892 | + | 0.456172i | \(0.849220\pi\) | |||||||
\(174\) | − | 12.0000i | − | 0.909718i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.00000i | − | 0.150756i | ||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 8.00000i | 0.599625i | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | −1.00000 | + | 2.00000i | −0.0745356 | + | 0.149071i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000i | 0.887066i | ||||||||
\(184\) | 18.0000i | 1.32698i | ||||||||
\(185\) | −6.00000 | + | 12.0000i | −0.441129 | + | 0.882258i | ||||
\(186\) | 12.0000 | 0.879883 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | − | 6.00000i | −0.870572 | − | 0.435286i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 14.0000i | 1.01036i | ||||||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | −16.0000 | + | 2.00000i | −1.14578 | + | 0.143223i | ||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 2.00000i | 0.142134i | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | −9.00000 | − | 12.0000i | −0.636396 | − | 0.848528i | ||||
\(201\) | 24.0000i | 1.69283i | ||||||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0000 | + | 8.00000i | 1.11749 | + | 0.558744i | ||||
\(206\) | − | 6.00000i | − | 0.418040i | ||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | −3.00000 | + | 2.00000i | −0.208013 | + | 0.138675i | ||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 12.0000i | 0.824163i | ||||||||
\(213\) | 4.00000 | 0.274075 | ||||||||
\(214\) | 6.00000i | 0.410152i | ||||||||
\(215\) | 12.0000 | + | 6.00000i | 0.818393 | + | 0.409197i | ||||
\(216\) | 12.0000i | 0.816497i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 12.0000i | − | 0.812743i | ||||||
\(219\) | − | 12.0000i | − | 0.810885i | ||||||
\(220\) | 4.00000 | + | 2.00000i | 0.269680 | + | 0.134840i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 12.0000i | − | 0.805387i | ||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | + | 4.00000i | 0.200000 | + | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | −12.0000 | −0.794719 | ||||||||
\(229\) | − | 12.0000i | − | 0.792982i | −0.918039 | − | 0.396491i | \(-0.870228\pi\) | ||
0.918039 | − | 0.396491i | \(-0.129772\pi\) | |||||||
\(230\) | 12.0000 | + | 6.00000i | 0.791257 | + | 0.395628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0000 | 1.18176 | ||||||||
\(233\) | − | 24.0000i | − | 1.57229i | −0.618041 | − | 0.786146i | \(-0.712073\pi\) | ||
0.618041 | − | 0.786146i | \(-0.287927\pi\) | |||||||
\(234\) | 3.00000 | − | 2.00000i | 0.196116 | − | 0.130744i | ||||
\(235\) | 8.00000 | − | 16.0000i | 0.521862 | − | 1.04372i | ||||
\(236\) | − | 2.00000i | − | 0.130189i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.0000i | − | 0.646846i | −0.946254 | − | 0.323423i | \(-0.895166\pi\) | ||
0.946254 | − | 0.323423i | \(-0.104834\pi\) | |||||||
\(240\) | 4.00000 | + | 2.00000i | 0.258199 | + | 0.129099i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | − | 10.0000i | − | 0.641500i | ||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 7.00000 | − | 14.0000i | 0.447214 | − | 0.894427i | ||||
\(246\) | −16.0000 | −1.02012 | ||||||||
\(247\) | −12.0000 | − | 18.0000i | −0.763542 | − | 1.14531i | ||||
\(248\) | 18.0000i | 1.14300i | ||||||||
\(249\) | − | 8.00000i | − | 0.506979i | ||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 2.00000i | 0.125491i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | −12.0000 | −0.747087 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.00000 | − | 8.00000i | −0.0620174 | − | 0.496139i | ||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 12.0000 | 0.741362 | ||||||||
\(263\) | 6.00000i | 0.369976i | 0.982741 | + | 0.184988i | \(0.0592246\pi\) | ||||
−0.982741 | + | 0.184988i | \(0.940775\pi\) | |||||||
\(264\) | −12.0000 | −0.738549 | ||||||||
\(265\) | 24.0000 | + | 12.0000i | 1.47431 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0000 | 0.979184 | ||||||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 8.00000 | + | 4.00000i | 0.486864 | + | 0.243432i | ||||
\(271\) | 6.00000i | 0.364474i | 0.983255 | + | 0.182237i | \(0.0583338\pi\) | ||||
−0.983255 | + | 0.182237i | \(0.941666\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 8.00000 | − | 6.00000i | 0.482418 | − | 0.361814i | ||||
\(276\) | 12.0000 | 0.722315 | ||||||||
\(277\) | − | 12.0000i | − | 0.721010i | −0.932757 | − | 0.360505i | \(-0.882604\pi\) | ||
0.932757 | − | 0.360505i | \(-0.117396\pi\) | |||||||
\(278\) | 4.00000 | 0.239904 | ||||||||
\(279\) | − | 6.00000i | − | 0.359211i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000i | 0.477240i | 0.971113 | + | 0.238620i | \(0.0766950\pi\) | ||||
−0.971113 | + | 0.238620i | \(0.923305\pi\) | |||||||
\(282\) | 16.0000i | 0.952786i | ||||||||
\(283\) | − | 22.0000i | − | 1.30776i | −0.756596 | − | 0.653882i | \(-0.773139\pi\) | ||
0.756596 | − | 0.653882i | \(-0.226861\pi\) | |||||||
\(284\) | 2.00000i | 0.118678i | ||||||||
\(285\) | −12.0000 | + | 24.0000i | −0.710819 | + | 1.42164i | ||||
\(286\) | −4.00000 | − | 6.00000i | −0.236525 | − | 0.354787i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 6.00000 | − | 12.0000i | 0.352332 | − | 0.704664i | ||||
\(291\) | − | 12.0000i | − | 0.703452i | ||||||
\(292\) | 6.00000 | 0.351123 | ||||||||
\(293\) | −26.0000 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(294\) | 14.0000i | 0.816497i | ||||||||
\(295\) | −4.00000 | − | 2.00000i | −0.232889 | − | 0.116445i | ||||
\(296\) | 18.0000 | 1.04623 | ||||||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | − | 20.0000i | − | 1.15857i | ||||||
\(299\) | 12.0000 | + | 18.0000i | 0.693978 | + | 1.04097i | ||||
\(300\) | −8.00000 | + | 6.00000i | −0.461880 | + | 0.346410i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.0000i | 1.03578i | ||||||||
\(303\) | 12.0000i | 0.689382i | ||||||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | −6.00000 | + | 12.0000i | −0.343559 | + | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | −0.682656 | ||||||||
\(310\) | 12.0000 | + | 6.00000i | 0.681554 | + | 0.340777i | ||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 12.0000 | + | 18.0000i | 0.679366 | + | 1.01905i | ||||
\(313\) | 8.00000i | 0.452187i | 0.974106 | + | 0.226093i | \(0.0725954\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(314\) | − | 12.0000i | − | 0.677199i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | −0.112331 | −0.0561656 | − | 0.998421i | \(-0.517887\pi\) | ||||
−0.0561656 | + | 0.998421i | \(0.517887\pi\) | |||||||
\(318\) | −24.0000 | −1.34585 | ||||||||
\(319\) | 12.0000i | 0.671871i | ||||||||
\(320\) | −7.00000 | + | 14.0000i | −0.391312 | + | 0.782624i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 11.0000 | 0.611111 | ||||||||
\(325\) | −17.0000 | − | 6.00000i | −0.942990 | − | 0.332820i | ||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | −24.0000 | −1.32720 | ||||||||
\(328\) | − | 24.0000i | − | 1.32518i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.00000 | + | 8.00000i | −0.220193 | + | 0.440386i | ||||
\(331\) | − | 30.0000i | − | 1.64895i | −0.565899 | − | 0.824475i | \(-0.691471\pi\) | ||
0.565899 | − | 0.824475i | \(-0.308529\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | 16.0000 | 0.875481 | ||||||||
\(335\) | −12.0000 | + | 24.0000i | −0.655630 | + | 1.31126i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0000i | 1.74315i | 0.490261 | + | 0.871576i | \(0.336901\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | −5.00000 | + | 12.0000i | −0.271964 | + | 0.652714i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 18.0000i | − | 0.970495i | ||||||
\(345\) | 12.0000 | − | 24.0000i | 0.646058 | − | 1.29212i | ||||
\(346\) | − | 12.0000i | − | 0.645124i | ||||||
\(347\) | − | 6.00000i | − | 0.322097i | −0.986947 | − | 0.161048i | \(-0.948512\pi\) | ||
0.986947 | − | 0.161048i | \(-0.0514875\pi\) | |||||||
\(348\) | − | 12.0000i | − | 0.643268i | ||||||
\(349\) | 12.0000i | 0.642345i | 0.947021 | + | 0.321173i | \(0.104077\pi\) | ||||
−0.947021 | + | 0.321173i | \(0.895923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000 | + | 12.0000i | 0.427008 | + | 0.640513i | ||||
\(352\) | − | 10.0000i | − | 0.533002i | ||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 4.00000 | 0.212598 | ||||||||
\(355\) | 4.00000 | + | 2.00000i | 0.212298 | + | 0.106149i | ||||
\(356\) | 8.00000i | 0.423999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | − | 2.00000i | − | 0.105556i | −0.998606 | − | 0.0527780i | \(-0.983192\pi\) | ||
0.998606 | − | 0.0527780i | \(-0.0168076\pi\) | |||||||
\(360\) | 3.00000 | − | 6.00000i | 0.158114 | − | 0.316228i | ||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 2.00000 | 0.105118 | ||||||||
\(363\) | 14.0000i | 0.734809i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | − | 12.0000i | 0.314054 | − | 0.628109i | ||||
\(366\) | − | 12.0000i | − | 0.627250i | ||||||
\(367\) | − | 18.0000i | − | 0.939592i | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||
0.882775 | − | 0.469796i | \(-0.155673\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 8.00000i | 0.416463i | ||||||||
\(370\) | 6.00000 | − | 12.0000i | 0.311925 | − | 0.623850i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.0000 | 0.622171 | ||||||||
\(373\) | 4.00000i | 0.207112i | 0.994624 | + | 0.103556i | \(0.0330221\pi\) | ||||
−0.994624 | + | 0.103556i | \(0.966978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.00000 | + | 22.0000i | 0.206559 | + | 1.13608i | ||||
\(376\) | −24.0000 | −1.23771 | ||||||||
\(377\) | 18.0000 | − | 12.0000i | 0.927047 | − | 0.618031i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(380\) | −12.0000 | − | 6.00000i | −0.615587 | − | 0.307794i | ||||
\(381\) | 4.00000 | 0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 6.00000i | 0.306186i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | 6.00000i | 0.304997i | ||||||||
\(388\) | 6.00000 | 0.304604 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 16.0000 | − | 2.00000i | 0.810191 | − | 0.101274i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −21.0000 | −1.06066 | ||||||||
\(393\) | − | 24.0000i | − | 1.21064i | ||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000i | 0.100504i | ||||||||
\(397\) | −18.0000 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(398\) | 24.0000 | 1.20301 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 16.0000i | 0.799002i | 0.916733 | + | 0.399501i | \(0.130817\pi\) | ||||
−0.916733 | + | 0.399501i | \(0.869183\pi\) | |||||||
\(402\) | − | 24.0000i | − | 1.19701i | ||||||
\(403\) | 12.0000 | + | 18.0000i | 0.597763 | + | 0.896644i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 11.0000 | − | 22.0000i | 0.546594 | − | 1.09319i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 24.0000i | − | 1.18672i | −0.804936 | − | 0.593362i | \(-0.797800\pi\) | ||
0.804936 | − | 0.593362i | \(-0.202200\pi\) | |||||||
\(410\) | −16.0000 | − | 8.00000i | −0.790184 | − | 0.395092i | ||||
\(411\) | 4.00000i | 0.197305i | ||||||||
\(412\) | − | 6.00000i | − | 0.295599i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000i | 0.294884i | ||||||||
\(415\) | 4.00000 | − | 8.00000i | 0.196352 | − | 0.392705i | ||||
\(416\) | −15.0000 | + | 10.0000i | −0.735436 | + | 0.490290i | ||||
\(417\) | − | 8.00000i | − | 0.391762i | ||||||
\(418\) | −12.0000 | −0.586939 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.0000i | 1.75453i | 0.480004 | + | 0.877266i | \(0.340635\pi\) | ||||
−0.480004 | + | 0.877266i | \(0.659365\pi\) | |||||||
\(422\) | 12.0000 | 0.584151 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | − | 36.0000i | − | 1.74831i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.00000 | −0.193801 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | −12.0000 | + | 8.00000i | −0.579365 | + | 0.386244i | ||||
\(430\) | −12.0000 | − | 6.00000i | −0.578691 | − | 0.289346i | ||||
\(431\) | − | 10.0000i | − | 0.481683i | −0.970564 | − | 0.240842i | \(-0.922577\pi\) | ||
0.970564 | − | 0.240842i | \(-0.0774234\pi\) | |||||||
\(432\) | − | 4.00000i | − | 0.192450i | ||||||
\(433\) | 16.0000i | 0.768911i | 0.923144 | + | 0.384455i | \(0.125611\pi\) | ||||
−0.923144 | + | 0.384455i | \(0.874389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.0000 | − | 12.0000i | −1.15071 | − | 0.575356i | ||||
\(436\) | − | 12.0000i | − | 0.574696i | ||||||
\(437\) | 36.0000 | 1.72211 | ||||||||
\(438\) | 12.0000i | 0.573382i | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | −12.0000 | − | 6.00000i | −0.572078 | − | 0.286039i | ||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6.00000i | − | 0.285069i | −0.989790 | − | 0.142534i | \(-0.954475\pi\) | ||
0.989790 | − | 0.142534i | \(-0.0455251\pi\) | |||||||
\(444\) | − | 12.0000i | − | 0.569495i | ||||||
\(445\) | 16.0000 | + | 8.00000i | 0.758473 | + | 0.379236i | ||||
\(446\) | −24.0000 | −1.13643 | ||||||||
\(447\) | −40.0000 | −1.89194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.0000i | − | 0.755087i | −0.925992 | − | 0.377543i | \(-0.876769\pi\) | ||
0.925992 | − | 0.377543i | \(-0.123231\pi\) | |||||||
\(450\) | −3.00000 | − | 4.00000i | −0.141421 | − | 0.188562i | ||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 36.0000 | 1.69143 | ||||||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 36.0000 | 1.68585 | ||||||||
\(457\) | −30.0000 | −1.40334 | −0.701670 | − | 0.712502i | \(-0.747562\pi\) | ||||
−0.701670 | + | 0.712502i | \(0.747562\pi\) | |||||||
\(458\) | 12.0000i | 0.560723i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0000 | + | 6.00000i | 0.559503 | + | 0.279751i | ||||
\(461\) | − | 4.00000i | − | 0.186299i | −0.995652 | − | 0.0931493i | \(-0.970307\pi\) | ||
0.995652 | − | 0.0931493i | \(-0.0296934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 12.0000 | − | 24.0000i | 0.556487 | − | 1.11297i | ||||
\(466\) | 24.0000i | 1.11178i | ||||||||
\(467\) | 18.0000i | 0.832941i | 0.909149 | + | 0.416470i | \(0.136733\pi\) | ||||
−0.909149 | + | 0.416470i | \(0.863267\pi\) | |||||||
\(468\) | 3.00000 | − | 2.00000i | 0.138675 | − | 0.0924500i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.00000 | + | 16.0000i | −0.369012 | + | 0.738025i | ||||
\(471\) | −24.0000 | −1.10586 | ||||||||
\(472\) | 6.00000i | 0.276172i | ||||||||
\(473\) | 12.0000 | 0.551761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.0000 | + | 18.0000i | −1.10120 | + | 0.825897i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000i | 0.549442i | ||||||||
\(478\) | 10.0000i | 0.457389i | ||||||||
\(479\) | 22.0000i | 1.00521i | 0.864517 | + | 0.502603i | \(0.167624\pi\) | ||||
−0.864517 | + | 0.502603i | \(0.832376\pi\) | |||||||
\(480\) | 20.0000 | + | 10.0000i | 0.912871 | + | 0.456435i | ||||
\(481\) | 18.0000 | − | 12.0000i | 0.820729 | − | 0.547153i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 6.00000 | − | 12.0000i | 0.272446 | − | 0.544892i | ||||
\(486\) | 10.0000i | 0.453609i | ||||||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 18.0000 | 0.814822 | ||||||||
\(489\) | 24.0000i | 1.08532i | ||||||||
\(490\) | −7.00000 | + | 14.0000i | −0.316228 | + | 0.632456i | ||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −16.0000 | −0.721336 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 12.0000 | + | 18.0000i | 0.539906 | + | 0.809858i | ||||
\(495\) | 4.00000 | + | 2.00000i | 0.179787 | + | 0.0898933i | ||||
\(496\) | − | 6.00000i | − | 0.269408i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.00000i | 0.358489i | ||||||||
\(499\) | − | 6.00000i | − | 0.268597i | −0.990941 | − | 0.134298i | \(-0.957122\pi\) | ||
0.990941 | − | 0.134298i | \(-0.0428781\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | − | 32.0000i | − | 1.42965i | ||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 6.00000i | 0.267527i | 0.991013 | + | 0.133763i | \(0.0427062\pi\) | ||||
−0.991013 | + | 0.133763i | \(0.957294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | + | 12.0000i | −0.266996 | + | 0.533993i | ||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | 24.0000 | + | 10.0000i | 1.06588 | + | 0.444116i | ||||
\(508\) | 2.00000i | 0.0887357i | ||||||||
\(509\) | − | 20.0000i | − | 0.886484i | −0.896402 | − | 0.443242i | \(-0.853828\pi\) | ||
0.896402 | − | 0.443242i | \(-0.146172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 24.0000 | 1.05963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | − | 6.00000i | −0.528783 | − | 0.264392i | ||||
\(516\) | −12.0000 | −0.528271 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 3.00000 | + | 24.0000i | 0.131559 | + | 1.05247i | ||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 6.00000 | 0.262613 | ||||||||
\(523\) | 42.0000i | 1.83653i | 0.395964 | + | 0.918266i | \(0.370410\pi\) | ||||
−0.395964 | + | 0.918266i | \(0.629590\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 6.00000i | − | 0.261612i | ||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −24.0000 | − | 12.0000i | −1.04249 | − | 0.521247i | ||||
\(531\) | − | 2.00000i | − | 0.0867926i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.0000 | − | 24.0000i | −0.693037 | − | 1.03956i | ||||
\(534\) | −16.0000 | −0.692388 | ||||||||
\(535\) | 12.0000 | + | 6.00000i | 0.518805 | + | 0.259403i | ||||
\(536\) | 36.0000 | 1.55496 | ||||||||
\(537\) | − | 24.0000i | − | 1.03568i | ||||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | − | 14.0000i | − | 0.603023i | ||||||
\(540\) | 8.00000 | + | 4.00000i | 0.344265 | + | 0.172133i | ||||
\(541\) | 12.0000i | 0.515920i | 0.966156 | + | 0.257960i | \(0.0830503\pi\) | ||||
−0.966156 | + | 0.257960i | \(0.916950\pi\) | |||||||
\(542\) | − | 6.00000i | − | 0.257722i | ||||||
\(543\) | − | 4.00000i | − | 0.171656i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.0000 | − | 12.0000i | −1.02805 | − | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.0000i | 0.769624i | 0.922995 | + | 0.384812i | \(0.125734\pi\) | ||||
−0.922995 | + | 0.384812i | \(0.874266\pi\) | |||||||
\(548\) | −2.00000 | −0.0854358 | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | −8.00000 | + | 6.00000i | −0.341121 | + | 0.255841i | ||||
\(551\) | − | 36.0000i | − | 1.53365i | ||||||
\(552\) | −36.0000 | −1.53226 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.0000i | 0.509831i | ||||||||
\(555\) | −24.0000 | − | 12.0000i | −1.01874 | − | 0.509372i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 14.0000 | 0.593199 | 0.296600 | − | 0.955002i | \(-0.404147\pi\) | ||||
0.296600 | + | 0.955002i | \(0.404147\pi\) | |||||||
\(558\) | 6.00000i | 0.254000i | ||||||||
\(559\) | −12.0000 | − | 18.0000i | −0.507546 | − | 0.761319i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 8.00000i | − | 0.337460i | ||||||
\(563\) | − | 30.0000i | − | 1.26435i | −0.774826 | − | 0.632175i | \(-0.782163\pi\) | ||
0.774826 | − | 0.632175i | \(-0.217837\pi\) | |||||||
\(564\) | 16.0000i | 0.673722i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.0000i | 0.924729i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 12.0000 | − | 24.0000i | 0.502625 | − | 1.00525i | ||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | −4.00000 | − | 6.00000i | −0.167248 | − | 0.250873i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | − | 18.0000i | 1.00087 | − | 0.750652i | ||||
\(576\) | −7.00000 | −0.291667 | ||||||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | −17.0000 | −0.707107 | ||||||||
\(579\) | − | 12.0000i | − | 0.498703i | ||||||
\(580\) | 6.00000 | − | 12.0000i | 0.249136 | − | 0.498273i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.0000i | 0.497416i | ||||||||
\(583\) | 24.0000 | 0.993978 | ||||||||
\(584\) | −18.0000 | −0.744845 | ||||||||
\(585\) | −1.00000 | − | 8.00000i | −0.0413449 | − | 0.330759i | ||||
\(586\) | 26.0000 | 1.07405 | ||||||||
\(587\) | 20.0000 | 0.825488 | 0.412744 | − | 0.910847i | \(-0.364570\pi\) | ||||
0.412744 | + | 0.910847i | \(0.364570\pi\) | |||||||
\(588\) | 14.0000i | 0.577350i | ||||||||
\(589\) | 36.0000 | 1.48335 | ||||||||
\(590\) | 4.00000 | + | 2.00000i | 0.164677 | + | 0.0823387i | ||||
\(591\) | − | 4.00000i | − | 0.164538i | ||||||
\(592\) | −6.00000 | −0.246598 | ||||||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 8.00000 | 0.328244 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 20.0000i | − | 0.819232i | ||||||
\(597\) | − | 48.0000i | − | 1.96451i | ||||||
\(598\) | −12.0000 | − | 18.0000i | −0.490716 | − | 0.736075i | ||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 24.0000 | − | 18.0000i | 0.979796 | − | 0.734847i | ||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 18.0000i | 0.732410i | ||||||||
\(605\) | −7.00000 | + | 14.0000i | −0.284590 | + | 0.569181i | ||||
\(606\) | − | 12.0000i | − | 0.487467i | ||||||
\(607\) | − | 18.0000i | − | 0.730597i | −0.930890 | − | 0.365299i | \(-0.880967\pi\) | ||
0.930890 | − | 0.365299i | \(-0.119033\pi\) | |||||||
\(608\) | 30.0000i | 1.21666i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | − | 12.0000i | 0.242933 | − | 0.485866i | ||||
\(611\) | −24.0000 | + | 16.0000i | −0.970936 | + | 0.647291i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | −12.0000 | −0.484281 | ||||||||
\(615\) | −16.0000 | + | 32.0000i | −0.645182 | + | 1.29036i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | 12.0000 | 0.482711 | ||||||||
\(619\) | 18.0000i | 0.723481i | 0.932279 | + | 0.361741i | \(0.117817\pi\) | ||||
−0.932279 | + | 0.361741i | \(0.882183\pi\) | |||||||
\(620\) | 12.0000 | + | 6.00000i | 0.481932 | + | 0.240966i | ||||
\(621\) | −24.0000 | −0.963087 | ||||||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | − | 6.00000i | −0.160128 | − | 0.240192i | ||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | − | 8.00000i | − | 0.319744i | ||||||
\(627\) | 24.0000i | 0.958468i | ||||||||
\(628\) | − | 12.0000i | − | 0.478852i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0000i | 1.19428i | 0.802137 | + | 0.597141i | \(0.203697\pi\) | ||||
−0.802137 | + | 0.597141i | \(0.796303\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 24.0000i | − | 0.953914i | ||||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | 4.00000 | + | 2.00000i | 0.158735 | + | 0.0793676i | ||||
\(636\) | −24.0000 | −0.951662 | ||||||||
\(637\) | −21.0000 | + | 14.0000i | −0.832050 | + | 0.554700i | ||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | 2.00000i | 0.0791188i | ||||||||
\(640\) | −3.00000 | + | 6.00000i | −0.118585 | + | 0.237171i | ||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | −12.0000 | −0.473602 | ||||||||
\(643\) | −36.0000 | −1.41970 | −0.709851 | − | 0.704352i | \(-0.751238\pi\) | ||||
−0.709851 | + | 0.704352i | \(0.751238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | + | 24.0000i | −0.472500 | + | 0.944999i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | −33.0000 | −1.29636 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 17.0000 | + | 6.00000i | 0.666795 | + | 0.235339i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | − | 36.0000i | − | 1.40879i | −0.709809 | − | 0.704394i | \(-0.751219\pi\) | ||
0.709809 | − | 0.704394i | \(-0.248781\pi\) | |||||||
\(654\) | 24.0000 | 0.938474 | ||||||||
\(655\) | 12.0000 | − | 24.0000i | 0.468879 | − | 0.937758i | ||||
\(656\) | 8.00000i | 0.312348i | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | −4.00000 | + | 8.00000i | −0.155700 | + | 0.311400i | ||||
\(661\) | − | 12.0000i | − | 0.466746i | −0.972387 | − | 0.233373i | \(-0.925024\pi\) | ||
0.972387 | − | 0.233373i | \(-0.0749763\pi\) | |||||||
\(662\) | 30.0000i | 1.16598i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | 36.0000i | 1.39393i | ||||||||
\(668\) | 16.0000 | 0.619059 | ||||||||
\(669\) | 48.0000i | 1.85579i | ||||||||
\(670\) | 12.0000 | − | 24.0000i | 0.463600 | − | 0.927201i | ||||
\(671\) | 12.0000i | 0.463255i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.0000i | 1.85026i | 0.379646 | + | 0.925132i | \(0.376046\pi\) | ||||
−0.379646 | + | 0.925132i | \(0.623954\pi\) | |||||||
\(674\) | − | 32.0000i | − | 1.23259i | ||||||
\(675\) | 16.0000 | − | 12.0000i | 0.615840 | − | 0.461880i | ||||
\(676\) | −5.00000 | + | 12.0000i | −0.192308 | + | 0.461538i | ||||
\(677\) | 36.0000i | 1.38359i | 0.722093 | + | 0.691796i | \(0.243180\pi\) | ||||
−0.722093 | + | 0.691796i | \(0.756820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 8.00000i | − | 0.306561i | ||||||
\(682\) | 12.0000 | 0.459504 | ||||||||
\(683\) | −44.0000 | −1.68361 | −0.841807 | − | 0.539779i | \(-0.818508\pi\) | ||||
−0.841807 | + | 0.539779i | \(0.818508\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | −2.00000 | + | 4.00000i | −0.0764161 | + | 0.152832i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0000 | 0.915657 | ||||||||
\(688\) | 6.00000i | 0.228748i | ||||||||
\(689\) | −24.0000 | − | 36.0000i | −0.914327 | − | 1.37149i | ||||
\(690\) | −12.0000 | + | 24.0000i | −0.456832 | + | 0.913664i | ||||
\(691\) | 42.0000i | 1.59776i | 0.601494 | + | 0.798878i | \(0.294573\pi\) | ||||
−0.601494 | + | 0.798878i | \(0.705427\pi\) | |||||||
\(692\) | − | 12.0000i | − | 0.456172i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000i | 0.227757i | ||||||||
\(695\) | 4.00000 | − | 8.00000i | 0.151729 | − | 0.303457i | ||||
\(696\) | 36.0000i | 1.36458i | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 12.0000i | − | 0.454207i | ||||||
\(699\) | 48.0000 | 1.81553 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | −8.00000 | − | 12.0000i | −0.301941 | − | 0.452911i | ||||
\(703\) | − | 36.0000i | − | 1.35777i | ||||||
\(704\) | 14.0000i | 0.527645i | ||||||||
\(705\) | 32.0000 | + | 16.0000i | 1.20519 | + | 0.602595i | ||||
\(706\) | 14.0000 | 0.526897 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.00000 | 0.150329 | ||||||||
\(709\) | − | 12.0000i | − | 0.450669i | −0.974281 | − | 0.225335i | \(-0.927652\pi\) | ||
0.974281 | − | 0.225335i | \(-0.0723476\pi\) | |||||||
\(710\) | −4.00000 | − | 2.00000i | −0.150117 | − | 0.0750587i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 24.0000i | − | 0.899438i | ||||||
\(713\) | −36.0000 | −1.34821 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | + | 2.00000i | −0.598366 | + | 0.0747958i | ||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | 20.0000 | 0.746914 | ||||||||
\(718\) | 2.00000i | 0.0746393i | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −1.00000 | + | 2.00000i | −0.0372678 | + | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.00000 | 0.0743294 | ||||||||
\(725\) | −18.0000 | − | 24.0000i | −0.668503 | − | 0.891338i | ||||
\(726\) | − | 14.0000i | − | 0.519589i | ||||||
\(727\) | − | 26.0000i | − | 0.964287i | −0.876092 | − | 0.482143i | \(-0.839858\pi\) | ||
0.876092 | − | 0.482143i | \(-0.160142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | −6.00000 | + | 12.0000i | −0.222070 | + | 0.444140i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 12.0000i | − | 0.443533i | ||||||
\(733\) | −42.0000 | −1.55131 | −0.775653 | − | 0.631160i | \(-0.782579\pi\) | ||||
−0.775653 | + | 0.631160i | \(0.782579\pi\) | |||||||
\(734\) | 18.0000i | 0.664392i | ||||||||
\(735\) | 28.0000 | + | 14.0000i | 1.03280 | + | 0.516398i | ||||
\(736\) | − | 30.0000i | − | 1.10581i | ||||||
\(737\) | 24.0000i | 0.884051i | ||||||||
\(738\) | − | 8.00000i | − | 0.294484i | ||||||
\(739\) | − | 6.00000i | − | 0.220714i | −0.993892 | − | 0.110357i | \(-0.964801\pi\) | ||
0.993892 | − | 0.110357i | \(-0.0351994\pi\) | |||||||
\(740\) | 6.00000 | − | 12.0000i | 0.220564 | − | 0.441129i | ||||
\(741\) | 36.0000 | − | 24.0000i | 1.32249 | − | 0.881662i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | −36.0000 | −1.31982 | ||||||||
\(745\) | −40.0000 | − | 20.0000i | −1.46549 | − | 0.732743i | ||||
\(746\) | − | 4.00000i | − | 0.146450i | ||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.00000 | − | 22.0000i | −0.146059 | − | 0.803326i | ||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 24.0000i | 0.874609i | ||||||||
\(754\) | −18.0000 | + | 12.0000i | −0.655521 | + | 0.437014i | ||||
\(755\) | 36.0000 | + | 18.0000i | 1.31017 | + | 0.655087i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0000i | 0.726912i | 0.931611 | + | 0.363456i | \(0.118403\pi\) | ||||
−0.931611 | + | 0.363456i | \(0.881597\pi\) | |||||||
\(758\) | − | 18.0000i | − | 0.653789i | ||||||
\(759\) | − | 24.0000i | − | 0.871145i | ||||||
\(760\) | 36.0000 | + | 18.0000i | 1.30586 | + | 0.652929i | ||||
\(761\) | − | 40.0000i | − | 1.45000i | −0.688749 | − | 0.724999i | \(-0.741840\pi\) | ||
0.688749 | − | 0.724999i | \(-0.258160\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.00000 | −0.289052 | ||||||||
\(767\) | 4.00000 | + | 6.00000i | 0.144432 | + | 0.216647i | ||||
\(768\) | − | 34.0000i | − | 1.22687i | ||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.00000 | 0.215945 | ||||||||
\(773\) | 38.0000 | 1.36677 | 0.683383 | − | 0.730061i | \(-0.260508\pi\) | ||||
0.683383 | + | 0.730061i | \(0.260508\pi\) | |||||||
\(774\) | − | 6.00000i | − | 0.215666i | ||||||
\(775\) | 24.0000 | − | 18.0000i | 0.862105 | − | 0.646579i | ||||
\(776\) | −18.0000 | −0.646162 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | −48.0000 | −1.71978 | ||||||||
\(780\) | 16.0000 | − | 2.00000i | 0.572892 | − | 0.0716115i | ||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.0000i | 0.857690i | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −24.0000 | − | 12.0000i | −0.856597 | − | 0.428298i | ||||
\(786\) | 24.0000i | 0.856052i | ||||||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | 2.00000 | 0.0712470 | ||||||||
\(789\) | −12.0000 | −0.427211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 6.00000i | − | 0.213201i | ||||||
\(793\) | 18.0000 | − | 12.0000i | 0.639199 | − | 0.426132i | ||||
\(794\) | 18.0000 | 0.638796 | ||||||||
\(795\) | −24.0000 | + | 48.0000i | −0.851192 | + | 1.70238i | ||||
\(796\) | 24.0000 | 0.850657 | ||||||||
\(797\) | 12.0000i | 0.425062i | 0.977154 | + | 0.212531i | \(0.0681706\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 15.0000 | + | 20.0000i | 0.530330 | + | 0.707107i | ||||
\(801\) | 8.00000i | 0.282666i | ||||||||
\(802\) | − | 16.0000i | − | 0.564980i | ||||||
\(803\) | − | 12.0000i | − | 0.423471i | ||||||
\(804\) | − | 24.0000i | − | 0.846415i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | − | 18.0000i | −0.422682 | − | 0.634023i | ||||
\(807\) | − | 36.0000i | − | 1.26726i | ||||||
\(808\) | 18.0000 | 0.633238 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | −11.0000 | + | 22.0000i | −0.386501 | + | 0.773001i | ||||
\(811\) | − | 30.0000i | − | 1.05344i | −0.850038 | − | 0.526721i | \(-0.823421\pi\) | ||
0.850038 | − | 0.526721i | \(-0.176579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | − | 12.0000i | − | 0.420600i | ||||||
\(815\) | −12.0000 | + | 24.0000i | −0.420342 | + | 0.840683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 24.0000i | 0.839140i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.0000 | − | 8.00000i | −0.558744 | − | 0.279372i | ||||
\(821\) | 20.0000i | 0.698005i | 0.937122 | + | 0.349002i | \(0.113479\pi\) | ||||
−0.937122 | + | 0.349002i | \(0.886521\pi\) | |||||||
\(822\) | − | 4.00000i | − | 0.139516i | ||||||
\(823\) | − | 42.0000i | − | 1.46403i | −0.681290 | − | 0.732014i | \(-0.738581\pi\) | ||
0.681290 | − | 0.732014i | \(-0.261419\pi\) | |||||||
\(824\) | 18.0000i | 0.627060i | ||||||||
\(825\) | 12.0000 | + | 16.0000i | 0.417786 | + | 0.557048i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.00000 | 0.139094 | 0.0695468 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695468 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(828\) | 6.00000i | 0.208514i | ||||||||
\(829\) | 6.00000 | 0.208389 | 0.104194 | − | 0.994557i | \(-0.466774\pi\) | ||||
0.104194 | + | 0.994557i | \(0.466774\pi\) | |||||||
\(830\) | −4.00000 | + | 8.00000i | −0.138842 | + | 0.277684i | ||||
\(831\) | 24.0000 | 0.832551 | ||||||||
\(832\) | 21.0000 | − | 14.0000i | 0.728044 | − | 0.485363i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.00000i | 0.277017i | ||||||||
\(835\) | 16.0000 | − | 32.0000i | 0.553703 | − | 1.10741i | ||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | −24.0000 | −0.829561 | ||||||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | 46.0000i | 1.58810i | 0.607855 | + | 0.794048i | \(0.292030\pi\) | ||||
−0.607855 | + | 0.794048i | \(0.707970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | − | 36.0000i | − | 1.24064i | ||||||
\(843\) | −16.0000 | −0.551069 | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 19.0000 | + | 22.0000i | 0.653620 | + | 0.756823i | ||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.0000i | 0.412082i | ||||||||
\(849\) | 44.0000 | 1.51008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000i | 1.23406i | ||||||||
\(852\) | −4.00000 | −0.137038 | ||||||||
\(853\) | 54.0000 | 1.84892 | 0.924462 | − | 0.381273i | \(-0.124514\pi\) | ||||
0.924462 | + | 0.381273i | \(0.124514\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | − | 6.00000i | −0.410391 | − | 0.205196i | ||||
\(856\) | − | 18.0000i | − | 0.615227i | ||||||
\(857\) | 24.0000i | 0.819824i | 0.912125 | + | 0.409912i | \(0.134441\pi\) | ||||
−0.912125 | + | 0.409912i | \(0.865559\pi\) | |||||||
\(858\) | 12.0000 | − | 8.00000i | 0.409673 | − | 0.273115i | ||||
\(859\) | −36.0000 | −1.22830 | −0.614152 | − | 0.789188i | \(-0.710502\pi\) | ||||
−0.614152 | + | 0.789188i | \(0.710502\pi\) | |||||||
\(860\) | −12.0000 | − | 6.00000i | −0.409197 | − | 0.204598i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.0000i | 0.340601i | ||||||||
\(863\) | −8.00000 | −0.272323 | −0.136162 | − | 0.990687i | \(-0.543477\pi\) | ||||
−0.136162 | + | 0.990687i | \(0.543477\pi\) | |||||||
\(864\) | − | 20.0000i | − | 0.680414i | ||||||
\(865\) | −24.0000 | − | 12.0000i | −0.816024 | − | 0.408012i | ||||
\(866\) | − | 16.0000i | − | 0.543702i | ||||||
\(867\) | 34.0000i | 1.15470i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 24.0000 | + | 12.0000i | 0.813676 | + | 0.406838i | ||||
\(871\) | 36.0000 | − | 24.0000i | 1.21981 | − | 0.813209i | ||||
\(872\) | 36.0000i | 1.21911i | ||||||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | −36.0000 | −1.21772 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000i | 0.405442i | ||||||||
\(877\) | 6.00000 | 0.202606 | 0.101303 | − | 0.994856i | \(-0.467699\pi\) | ||||
0.101303 | + | 0.994856i | \(0.467699\pi\) | |||||||
\(878\) | −8.00000 | −0.269987 | ||||||||
\(879\) | − | 52.0000i | − | 1.75392i | ||||||
\(880\) | 4.00000 | + | 2.00000i | 0.134840 | + | 0.0674200i | ||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | −7.00000 | −0.235702 | ||||||||
\(883\) | 2.00000i | 0.0673054i | 0.999434 | + | 0.0336527i | \(0.0107140\pi\) | ||||
−0.999434 | + | 0.0336527i | \(0.989286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | − | 8.00000i | 0.134459 | − | 0.268917i | ||||
\(886\) | 6.00000i | 0.201574i | ||||||||
\(887\) | − | 42.0000i | − | 1.41022i | −0.709097 | − | 0.705111i | \(-0.750897\pi\) | ||
0.709097 | − | 0.705111i | \(-0.249103\pi\) | |||||||
\(888\) | 36.0000i | 1.20808i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.0000 | − | 8.00000i | −0.536321 | − | 0.268161i | ||||
\(891\) | − | 22.0000i | − | 0.737028i | ||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | 48.0000i | 1.60626i | ||||||||
\(894\) | 40.0000 | 1.33780 | ||||||||
\(895\) | 12.0000 | − | 24.0000i | 0.401116 | − | 0.802232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | + | 24.0000i | −1.20201 | + | 0.801337i | ||||
\(898\) | 16.0000i | 0.533927i | ||||||||
\(899\) | 36.0000i | 1.20067i | ||||||||
\(900\) | −3.00000 | − | 4.00000i | −0.100000 | − | 0.133333i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −16.0000 | −0.532742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.00000 | − | 4.00000i | 0.0664822 | − | 0.132964i | ||||
\(906\) | −36.0000 | −1.19602 | ||||||||
\(907\) | 10.0000i | 0.332045i | 0.986122 | + | 0.166022i | \(0.0530924\pi\) | ||||
−0.986122 | + | 0.166022i | \(0.946908\pi\) | |||||||
\(908\) | 4.00000 | 0.132745 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | −12.0000 | −0.397360 | ||||||||
\(913\) | − | 8.00000i | − | 0.264761i | ||||||
\(914\) | 30.0000 | 0.992312 | ||||||||
\(915\) | −24.0000 | − | 12.0000i | −0.793416 | − | 0.396708i | ||||
\(916\) | 12.0000i | 0.396491i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | −36.0000 | − | 18.0000i | −1.18688 | − | 0.593442i | ||||
\(921\) | 24.0000i | 0.790827i | ||||||||
\(922\) | 4.00000i | 0.131733i | ||||||||
\(923\) | −4.00000 | − | 6.00000i | −0.131662 | − | 0.197492i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0000 | − | 24.0000i | −0.591836 | − | 0.789115i | ||||
\(926\) | 24.0000 | 0.788689 | ||||||||
\(927\) | − | 6.00000i | − | 0.197066i | ||||||
\(928\) | −30.0000 | −0.984798 | ||||||||
\(929\) | 16.0000i | 0.524943i | 0.964940 | + | 0.262471i | \(0.0845376\pi\) | ||||
−0.964940 | + | 0.262471i | \(0.915462\pi\) | |||||||
\(930\) | −12.0000 | + | 24.0000i | −0.393496 | + | 0.786991i | ||||
\(931\) | 42.0000i | 1.37649i | ||||||||
\(932\) | 24.0000i | 0.786146i | ||||||||
\(933\) | 48.0000i | 1.57145i | ||||||||
\(934\) | − | 18.0000i | − | 0.588978i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.00000 | + | 6.00000i | −0.294174 | + | 0.196116i | ||||
\(937\) | − | 56.0000i | − | 1.82944i | −0.404088 | − | 0.914720i | \(-0.632411\pi\) | ||
0.404088 | − | 0.914720i | \(-0.367589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | −8.00000 | + | 16.0000i | −0.260931 | + | 0.521862i | ||||
\(941\) | 28.0000i | 0.912774i | 0.889781 | + | 0.456387i | \(0.150857\pi\) | ||||
−0.889781 | + | 0.456387i | \(0.849143\pi\) | |||||||
\(942\) | 24.0000 | 0.781962 | ||||||||
\(943\) | 48.0000 | 1.56310 | ||||||||
\(944\) | − | 2.00000i | − | 0.0650945i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 28.0000 | 0.909878 | 0.454939 | − | 0.890523i | \(-0.349661\pi\) | ||||
0.454939 | + | 0.890523i | \(0.349661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | + | 12.0000i | −0.584305 | + | 0.389536i | ||||
\(950\) | 24.0000 | − | 18.0000i | 0.778663 | − | 0.583997i | ||||
\(951\) | − | 4.00000i | − | 0.129709i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | − | 12.0000i | − | 0.388514i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.0000i | 0.323423i | ||||||||
\(957\) | −24.0000 | −0.775810 | ||||||||
\(958\) | − | 22.0000i | − | 0.710788i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −28.0000 | − | 14.0000i | −0.903696 | − | 0.451848i | ||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | −18.0000 | + | 12.0000i | −0.580343 | + | 0.386896i | ||||
\(963\) | 6.00000i | 0.193347i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.00000 | − | 12.0000i | 0.193147 | − | 0.386294i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 21.0000 | 0.674966 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.00000 | + | 12.0000i | −0.192648 | + | 0.385297i | ||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 10.0000i | 0.320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | − | 34.0000i | 0.384308 | − | 1.08887i | ||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | 34.0000 | 1.08776 | 0.543878 | − | 0.839164i | \(-0.316955\pi\) | ||||
0.543878 | + | 0.839164i | \(0.316955\pi\) | |||||||
\(978\) | − | 24.0000i | − | 0.767435i | ||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | −7.00000 | + | 14.0000i | −0.223607 | + | 0.447214i | ||||
\(981\) | − | 12.0000i | − | 0.383131i | ||||||
\(982\) | −12.0000 | −0.382935 | ||||||||
\(983\) | 16.0000 | 0.510321 | 0.255160 | − | 0.966899i | \(-0.417872\pi\) | ||||
0.255160 | + | 0.966899i | \(0.417872\pi\) | |||||||
\(984\) | 48.0000 | 1.53018 | ||||||||
\(985\) | 2.00000 | − | 4.00000i | 0.0637253 | − | 0.127451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000 | + | 18.0000i | 0.381771 | + | 0.572656i | ||||
\(989\) | 36.0000 | 1.14473 | ||||||||
\(990\) | −4.00000 | − | 2.00000i | −0.127128 | − | 0.0635642i | ||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | − | 30.0000i | − | 0.952501i | ||||||
\(993\) | 60.0000 | 1.90404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | − | 48.0000i | 0.760851 | − | 1.52170i | ||||
\(996\) | 8.00000i | 0.253490i | ||||||||
\(997\) | − | 60.0000i | − | 1.90022i | −0.311916 | − | 0.950110i | \(-0.600971\pi\) | ||
0.311916 | − | 0.950110i | \(-0.399029\pi\) | |||||||
\(998\) | 6.00000i | 0.189927i | ||||||||
\(999\) | 24.0000i | 0.759326i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))