Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(469,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.e (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: | \(9.34249703649\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 469.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.469 |
Dual form | 1170.2.e.c.469.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 2.00000i | 0.316228 | + | 0.632456i | ||||
\(11\) | 6.00000 | 1.80907 | 0.904534 | − | 0.426401i | \(-0.140219\pi\) | ||||
0.904534 | + | 0.426401i | \(0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 2.00000 | − | 1.00000i | 0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | −10.0000 | −1.85695 | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 4.00000 | + | 8.00000i | 0.676123 | + | 1.35225i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.00000i | − | 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | − | 2.00000i | −0.158114 | − | 0.316228i | ||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | + | 6.00000i | −1.61808 | + | 0.809040i | ||||
\(56\) | 4.00000 | 0.534522 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.0000i | 1.31306i | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.00000 | + | 2.00000i | 0.124035 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | − | 4.00000i | − | 0.485071i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.00000 | − | 4.00000i | 0.956183 | − | 0.478091i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | − | 24.0000i | − | 2.73505i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −2.00000 | + | 1.00000i | −0.223607 | + | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.0000i | 1.10432i | ||||||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 8.00000i | −0.433861 | − | 0.867722i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000i | 0.639602i | ||||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 4.00000 | − | 2.00000i | 0.410391 | − | 0.205196i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0000i | 1.42148i | 0.703452 | + | 0.710742i | \(0.251641\pi\) | ||||
−0.703452 | + | 0.710742i | \(0.748359\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 6.00000 | + | 12.0000i | 0.572078 | + | 1.14416i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 4.00000i | − | 0.377964i | ||||||
\(113\) | − | 4.00000i | − | 0.376288i | −0.982141 | − | 0.188144i | \(-0.939753\pi\) | ||
0.982141 | − | 0.188144i | \(-0.0602472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | + | 12.0000i | 0.559503 | + | 1.11901i | ||||
\(116\) | 10.0000 | 0.928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 16.0000 | 1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | 6.00000i | 0.543214i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.0000i | − | 0.887357i | −0.896186 | − | 0.443678i | \(-0.853673\pi\) | ||
0.896186 | − | 0.443678i | \(-0.146327\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 1.00000i | 0.175412 | − | 0.0877058i | ||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | 14.0000i | 1.19610i | 0.801459 | + | 0.598050i | \(0.204058\pi\) | ||||
−0.801459 | + | 0.598050i | \(0.795942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | −4.00000 | − | 8.00000i | −0.338062 | − | 0.676123i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.00000i | − | 0.501745i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.0000 | − | 10.0000i | 1.66091 | − | 0.830455i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000i | 0.493197i | ||||||||
\(149\) | 16.0000 | 1.31077 | 0.655386 | − | 0.755295i | \(-0.272506\pi\) | ||||
0.655386 | + | 0.755295i | \(0.272506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | − | 2.00000i | − | 0.162221i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.0000 | −1.93398 | ||||||||
\(155\) | −8.00000 | + | 4.00000i | −0.642575 | + | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000i | 0.478852i | 0.970915 | + | 0.239426i | \(0.0769593\pi\) | ||||
−0.970915 | + | 0.239426i | \(0.923041\pi\) | |||||||
\(158\) | − | 8.00000i | − | 0.636446i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | + | 2.00000i | 0.0790569 | + | 0.158114i | ||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 10.0000 | 0.780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 16.0000i | 1.23812i | 0.785345 | + | 0.619059i | \(0.212486\pi\) | ||||
−0.785345 | + | 0.619059i | \(0.787514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −8.00000 | + | 4.00000i | −0.613572 | + | 0.306786i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.0000i | − | 1.67263i | −0.548250 | − | 0.836315i | \(-0.684706\pi\) | ||
0.548250 | − | 0.836315i | \(-0.315294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.0000 | − | 12.0000i | −1.20949 | − | 0.907115i | ||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 14.0000i | − | 1.04934i | ||||||
\(179\) | −24.0000 | −1.79384 | −0.896922 | − | 0.442189i | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442189i | \(0.854202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 6.00000 | + | 12.0000i | 0.441129 | + | 0.882258i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0000i | 1.75505i | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.00000 | − | 4.00000i | −0.145095 | − | 0.290191i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000i | 0.143963i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) | ||||
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 14.0000 | 1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | 40.0000i | 2.80745i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | − | 10.0000i | 1.39686 | − | 0.698430i | ||||
\(206\) | 2.00000 | 0.139347 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.00000i | − | 0.0693375i | ||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.0000i | − | 1.08615i | ||||||
\(218\) | 4.00000i | 0.270914i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.0000 | − | 6.00000i | 0.809040 | − | 0.404520i | ||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.00000 | −0.266076 | ||||||||
\(227\) | 4.00000i | 0.265489i | 0.991150 | + | 0.132745i | \(0.0423790\pi\) | ||||
−0.991150 | + | 0.132745i | \(0.957621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | −0.528655 | −0.264327 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264327 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(230\) | 12.0000 | − | 6.00000i | 0.791257 | − | 0.395628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 10.0000i | − | 0.656532i | ||||||
\(233\) | − | 12.0000i | − | 0.786146i | −0.919507 | − | 0.393073i | \(-0.871412\pi\) | ||
0.919507 | − | 0.393073i | \(-0.128588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | + | 16.0000i | 0.521862 | + | 1.04372i | ||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 16.0000i | − | 1.03713i | ||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 18.0000 | − | 9.00000i | 1.14998 | − | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000i | 0.127257i | ||||||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.0000 | + | 2.00000i | 0.695701 | + | 0.126491i | ||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 36.0000i | − | 2.26330i | ||||||
\(254\) | −10.0000 | −0.627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 28.0000i | − | 1.74659i | −0.487190 | − | 0.873296i | \(-0.661978\pi\) | ||
0.487190 | − | 0.873296i | \(-0.338022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.0000 | −1.49129 | ||||||||
\(260\) | −1.00000 | − | 2.00000i | −0.0620174 | − | 0.124035i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 8.00000i | − | 0.494242i | ||||||
\(263\) | − | 10.0000i | − | 0.616626i | −0.951285 | − | 0.308313i | \(-0.900236\pi\) | ||
0.951285 | − | 0.308313i | \(-0.0997645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | + | 12.0000i | 0.368577 | + | 0.737154i | ||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0000 | 0.845771 | ||||||||
\(275\) | 18.0000 | − | 24.0000i | 1.08544 | − | 1.44725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.0000i | − | 0.841178i | −0.907251 | − | 0.420589i | \(-0.861823\pi\) | ||
0.907251 | − | 0.420589i | \(-0.138177\pi\) | |||||||
\(278\) | 16.0000i | 0.959616i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.00000 | + | 4.00000i | −0.478091 | + | 0.239046i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000i | 0.713326i | 0.934233 | + | 0.356663i | \(0.116086\pi\) | ||||
−0.934233 | + | 0.356663i | \(0.883914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 40.0000i | 2.36113i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −10.0000 | − | 20.0000i | −0.587220 | − | 1.17444i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000i | 0.117041i | ||||||||
\(293\) | 18.0000i | 1.05157i | 0.850617 | + | 0.525786i | \(0.176229\pi\) | ||||
−0.850617 | + | 0.525786i | \(0.823771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | − | 6.00000i | 0.698667 | − | 0.349334i | ||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 16.0000i | − | 0.926855i | ||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 16.0000i | − | 0.920697i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 12.0000 | − | 6.00000i | 0.687118 | − | 0.343559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 24.0000i | 1.36753i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | + | 8.00000i | 0.227185 | + | 0.454369i | ||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00000i | 0.452187i | 0.974106 | + | 0.226093i | \(0.0725954\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(314\) | 6.00000 | 0.338600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 2.00000i | − | 0.112331i | −0.998421 | − | 0.0561656i | \(-0.982113\pi\) | ||
0.998421 | − | 0.0561656i | \(-0.0178875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −60.0000 | −3.35936 | ||||||||
\(320\) | 2.00000 | − | 1.00000i | 0.111803 | − | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.0000i | 1.33747i | ||||||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | − | 3.00000i | −0.221880 | − | 0.166410i | ||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 10.0000i | − | 0.552158i | ||||||
\(329\) | −32.0000 | −1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | 4.00000i | 0.219529i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.0000 | 0.875481 | ||||||||
\(335\) | 12.0000 | + | 24.0000i | 0.655630 | + | 1.31126i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000i | 0.871576i | 0.900049 | + | 0.435788i | \(0.143530\pi\) | ||||
−0.900049 | + | 0.435788i | \(0.856470\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | + | 8.00000i | 0.216930 | + | 0.433861i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.0000 | −1.18273 | ||||||||
\(347\) | − | 16.0000i | − | 0.858925i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000 | 0.214115 | 0.107058 | − | 0.994253i | \(-0.465857\pi\) | ||||
0.107058 | + | 0.994253i | \(0.465857\pi\) | |||||||
\(350\) | −12.0000 | + | 16.0000i | −0.641427 | + | 0.855236i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 6.00000i | − | 0.319801i | ||||||
\(353\) | − | 26.0000i | − | 1.38384i | −0.721974 | − | 0.691920i | \(-0.756765\pi\) | ||
0.721974 | − | 0.691920i | \(-0.243235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.0000i | 1.26844i | ||||||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | − | 6.00000i | − | 0.315353i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 2.00000 | + | 4.00000i | 0.104685 | + | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.0000i | − | 0.939592i | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||
0.882775 | − | 0.469796i | \(-0.155673\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.0000 | − | 6.00000i | 0.623850 | − | 0.311925i | ||||
\(371\) | −24.0000 | −1.24602 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0000i | 0.932005i | 0.884783 | + | 0.466002i | \(0.154306\pi\) | ||||
−0.884783 | + | 0.466002i | \(0.845694\pi\) | |||||||
\(374\) | 24.0000 | 1.24101 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 10.0000i | 0.515026i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | −4.00000 | + | 2.00000i | −0.205196 | + | 0.102598i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.0000i | 1.02195i | 0.859595 | + | 0.510976i | \(0.170716\pi\) | ||||
−0.859595 | + | 0.510976i | \(0.829284\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.0000 | + | 48.0000i | 1.22315 | + | 2.44631i | ||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 14.0000i | − | 0.710742i | ||||||
\(389\) | 30.0000 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | − | 9.00000i | − | 0.454569i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −16.0000 | + | 8.00000i | −0.805047 | + | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.0000i | − | 0.501886i | −0.968002 | − | 0.250943i | \(-0.919259\pi\) | ||
0.968002 | − | 0.250943i | \(-0.0807406\pi\) | |||||||
\(398\) | − | 8.00000i | − | 0.401004i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 10.0000 | 0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.0000 | 1.98517 | ||||||||
\(407\) | − | 36.0000i | − | 1.78445i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.0000 | 1.68119 | 0.840596 | − | 0.541663i | \(-0.182205\pi\) | ||||
0.840596 | + | 0.541663i | \(0.182205\pi\) | |||||||
\(410\) | −10.0000 | − | 20.0000i | −0.493865 | − | 0.987730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.00000i | − | 0.0985329i | ||||||
\(413\) | 24.0000i | 1.18096i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | + | 8.00000i | 0.196352 | + | 0.392705i | ||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.0000i | 0.586939i | ||||||||
\(419\) | 8.00000 | 0.390826 | 0.195413 | − | 0.980721i | \(-0.437395\pi\) | ||||
0.195413 | + | 0.980721i | \(0.437395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | 0.194948 | 0.0974740 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974740 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(422\) | − | 4.00000i | − | 0.194717i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 16.0000 | + | 12.0000i | 0.776114 | + | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0000i | 1.16144i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | −16.0000 | −0.768025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | 12.0000i | 0.574038i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | −6.00000 | − | 12.0000i | −0.286039 | − | 0.572078i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 4.00000i | − | 0.190261i | ||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.0000 | + | 14.0000i | −1.32733 | + | 0.663664i | ||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00000i | 0.188982i | ||||||||
\(449\) | 38.0000 | 1.79333 | 0.896665 | − | 0.442709i | \(-0.145982\pi\) | ||||
0.896665 | + | 0.442709i | \(0.145982\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −60.0000 | −2.82529 | ||||||||
\(452\) | 4.00000i | 0.188144i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 8.00000 | − | 4.00000i | 0.375046 | − | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0000i | 0.654892i | 0.944870 | + | 0.327446i | \(0.106188\pi\) | ||||
−0.944870 | + | 0.327446i | \(0.893812\pi\) | |||||||
\(458\) | 8.00000i | 0.373815i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.00000 | − | 12.0000i | −0.279751 | − | 0.559503i | ||||
\(461\) | 4.00000 | 0.186299 | 0.0931493 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931493 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | −10.0000 | −0.464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | −0.555889 | ||||||||
\(467\) | − | 8.00000i | − | 0.370196i | −0.982720 | − | 0.185098i | \(-0.940740\pi\) | ||
0.982720 | − | 0.185098i | \(-0.0592602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48.0000 | −2.21643 | ||||||||
\(470\) | 16.0000 | − | 8.00000i | 0.738025 | − | 0.369012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.00000i | − | 0.276172i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 8.00000i | −0.275299 | + | 0.367065i | ||||
\(476\) | −16.0000 | −0.733359 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.00000i | 0.182956i | ||||||||
\(479\) | −20.0000 | −0.913823 | −0.456912 | − | 0.889512i | \(-0.651044\pi\) | ||||
−0.456912 | + | 0.889512i | \(0.651044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | −0.273576 | ||||||||
\(482\) | − | 18.0000i | − | 0.819878i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.0000 | −1.13636 | ||||||||
\(485\) | −14.0000 | − | 28.0000i | −0.635707 | − | 1.27141i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | − | 6.00000i | − | 0.271607i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.00000 | − | 18.0000i | −0.406579 | − | 0.813157i | ||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 40.0000i | − | 1.80151i | ||||||
\(494\) | 2.00000 | 0.0899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0000 | 0.805791 | 0.402895 | − | 0.915246i | \(-0.368004\pi\) | ||||
0.402895 | + | 0.915246i | \(0.368004\pi\) | |||||||
\(500\) | 2.00000 | − | 11.0000i | 0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 20.0000i | − | 0.892644i | ||||||
\(503\) | − | 14.0000i | − | 0.624229i | −0.950044 | − | 0.312115i | \(-0.898963\pi\) | ||
0.950044 | − | 0.312115i | \(-0.101037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0000 | − | 10.0000i | 0.889988 | − | 0.444994i | ||||
\(506\) | −36.0000 | −1.60040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0000i | 0.443678i | ||||||||
\(509\) | 16.0000 | 0.709188 | 0.354594 | − | 0.935020i | \(-0.384619\pi\) | ||||
0.354594 | + | 0.935020i | \(0.384619\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.0000 | −1.23503 | ||||||||
\(515\) | −2.00000 | − | 4.00000i | −0.0881305 | − | 0.176261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 48.0000i | − | 2.11104i | ||||||
\(518\) | 24.0000i | 1.05450i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.00000 | + | 1.00000i | −0.0877058 | + | 0.0438529i | ||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0000i | − | 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | −8.00000 | −0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0000 | −0.436021 | ||||||||
\(527\) | 16.0000i | 0.696971i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 12.0000 | − | 6.00000i | 0.521247 | − | 0.260623i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 8.00000i | − | 0.346844i | ||||||
\(533\) | 10.0000i | 0.433148i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.0000i | − | 0.431131i | ||||||
\(539\) | −54.0000 | −2.32594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0000 | −1.37579 | −0.687894 | − | 0.725811i | \(-0.741464\pi\) | ||||
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(542\) | 8.00000i | 0.343629i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 8.00000 | − | 4.00000i | 0.342682 | − | 0.171341i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0000i | 1.53925i | 0.638497 | + | 0.769624i | \(0.279557\pi\) | ||||
−0.638497 | + | 0.769624i | \(0.720443\pi\) | |||||||
\(548\) | − | 14.0000i | − | 0.598050i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.0000 | − | 18.0000i | −1.02336 | − | 0.767523i | ||||
\(551\) | 20.0000 | 0.852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 32.0000i | − | 1.36078i | ||||||
\(554\) | −14.0000 | −0.594803 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | 18.0000i | 0.762684i | 0.924434 | + | 0.381342i | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.00000 | + | 8.00000i | 0.169031 | + | 0.338062i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 18.0000i | − | 0.759284i | ||||||
\(563\) | 24.0000i | 1.01148i | 0.862686 | + | 0.505740i | \(0.168780\pi\) | ||||
−0.862686 | + | 0.505740i | \(0.831220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | + | 8.00000i | 0.168281 | + | 0.336563i | ||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.0000 | −1.76073 | −0.880366 | − | 0.474295i | \(-0.842703\pi\) | ||||
−0.880366 | + | 0.474295i | \(0.842703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 6.00000i | 0.250873i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 40.0000 | 1.66957 | ||||||||
\(575\) | −24.0000 | − | 18.0000i | −1.00087 | − | 0.750652i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.0000 | + | 10.0000i | −0.830455 | + | 0.415227i | ||||
\(581\) | −16.0000 | −0.663792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 36.0000i | − | 1.49097i | ||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | 0.743573 | ||||||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | −6.00000 | − | 12.0000i | −0.247016 | − | 0.494032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 6.00000i | − | 0.246598i | ||||||
\(593\) | 14.0000i | 0.574911i | 0.957794 | + | 0.287456i | \(0.0928094\pi\) | ||||
−0.957794 | + | 0.287456i | \(0.907191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.0000 | + | 16.0000i | −1.31187 | + | 0.655936i | ||||
\(596\) | −16.0000 | −0.655386 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.00000i | 0.245358i | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | −50.0000 | + | 25.0000i | −2.03279 | + | 1.01639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.0000i | 1.70473i | 0.522949 | + | 0.852364i | \(0.324832\pi\) | ||||
−0.522949 | + | 0.852364i | \(0.675168\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | − | 12.0000i | −0.242933 | − | 0.485866i | ||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0000i | 1.53481i | 0.641165 | + | 0.767403i | \(0.278451\pi\) | ||||
−0.641165 | + | 0.767403i | \(0.721549\pi\) | |||||||
\(614\) | −4.00000 | −0.161427 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000 | 0.966988 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | 0.884255 | 0.442127 | − | 0.896952i | \(-0.354224\pi\) | ||||
0.442127 | + | 0.896952i | \(0.354224\pi\) | |||||||
\(620\) | 8.00000 | − | 4.00000i | 0.321288 | − | 0.160644i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8.00000i | − | 0.320771i | ||||||
\(623\) | − | 56.0000i | − | 2.24359i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 8.00000 | 0.319744 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 6.00000i | − | 0.239426i | ||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 8.00000i | 0.318223i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.00000 | −0.0794301 | ||||||||
\(635\) | 10.0000 | + | 20.0000i | 0.396838 | + | 0.793676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.00000i | 0.356593i | ||||||||
\(638\) | 60.0000i | 2.37542i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | − | 2.00000i | −0.0395285 | − | 0.0790569i | ||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 24.0000 | 0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | −0.314756 | ||||||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | −3.00000 | + | 4.00000i | −0.117670 | + | 0.156893i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 4.00000i | − | 0.156652i | ||||||
\(653\) | − | 10.0000i | − | 0.391330i | −0.980671 | − | 0.195665i | \(-0.937313\pi\) | ||
0.980671 | − | 0.195665i | \(-0.0626866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | + | 8.00000i | −0.625172 | + | 0.312586i | ||||
\(656\) | −10.0000 | −0.390434 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.0000i | 1.24749i | ||||||||
\(659\) | −32.0000 | −1.24654 | −0.623272 | − | 0.782006i | \(-0.714197\pi\) | ||||
−0.623272 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.0000 | −1.24466 | −0.622328 | − | 0.782757i | \(-0.713813\pi\) | ||||
−0.622328 | + | 0.782757i | \(0.713813\pi\) | |||||||
\(662\) | − | 2.00000i | − | 0.0777322i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | −8.00000 | − | 16.0000i | −0.310227 | − | 0.620453i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 60.0000i | 2.32321i | ||||||||
\(668\) | − | 16.0000i | − | 0.619059i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.0000 | − | 12.0000i | 0.927201 | − | 0.463600i | ||||
\(671\) | −36.0000 | −1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 44.0000i | − | 1.69608i | −0.529936 | − | 0.848038i | \(-0.677784\pi\) | ||
0.529936 | − | 0.848038i | \(-0.322216\pi\) | |||||||
\(674\) | 16.0000 | 0.616297 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − | 6.00000i | − | 0.230599i | −0.993331 | − | 0.115299i | \(-0.963217\pi\) | ||
0.993331 | − | 0.115299i | \(-0.0367827\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 56.0000 | 2.14908 | ||||||||
\(680\) | 8.00000 | − | 4.00000i | 0.306786 | − | 0.153393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 24.0000i | − | 0.919007i | ||||||
\(683\) | − | 20.0000i | − | 0.765279i | −0.923898 | − | 0.382639i | \(-0.875015\pi\) | ||
0.923898 | − | 0.382639i | \(-0.124985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0000 | − | 28.0000i | −0.534913 | − | 1.06983i | ||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0000 | 0.684752 | 0.342376 | − | 0.939563i | \(-0.388768\pi\) | ||||
0.342376 | + | 0.939563i | \(0.388768\pi\) | |||||||
\(692\) | 22.0000i | 0.836315i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | 32.0000 | − | 16.0000i | 1.21383 | − | 0.606915i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 40.0000i | − | 1.51511i | ||||||
\(698\) | − | 4.00000i | − | 0.151402i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.0000 | + | 12.0000i | 0.604743 | + | 0.453557i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000i | 0.452589i | ||||||||
\(704\) | −6.00000 | −0.226134 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | 40.0000i | 1.50435i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000 | 0.300446 | 0.150223 | − | 0.988652i | \(-0.452001\pi\) | ||||
0.150223 | + | 0.988652i | \(0.452001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0000i | 0.524672i | ||||||||
\(713\) | − | 24.0000i | − | 0.898807i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 12.0000i | 0.224387 | + | 0.448775i | ||||
\(716\) | 24.0000 | 0.896922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.0000i | 0.746393i | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.00000 | −0.222988 | ||||||||
\(725\) | −30.0000 | + | 40.0000i | −1.11417 | + | 1.48556i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.0000i | 1.40934i | 0.709534 | + | 0.704671i | \(0.248905\pi\) | ||||
−0.709534 | + | 0.704671i | \(0.751095\pi\) | |||||||
\(728\) | − | 4.00000i | − | 0.148250i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.00000 | − | 2.00000i | 0.148047 | − | 0.0740233i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0000i | 0.664845i | 0.943131 | + | 0.332423i | \(0.107866\pi\) | ||||
−0.943131 | + | 0.332423i | \(0.892134\pi\) | |||||||
\(734\) | −18.0000 | −0.664392 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | − | 72.0000i | − | 2.65215i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000 | 0.0735712 | 0.0367856 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367856 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(740\) | −6.00000 | − | 12.0000i | −0.220564 | − | 0.441129i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.0000i | 0.881068i | ||||||||
\(743\) | − | 36.0000i | − | 1.32071i | −0.750953 | − | 0.660356i | \(-0.770405\pi\) | ||
0.750953 | − | 0.660356i | \(-0.229595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.0000 | + | 16.0000i | −1.17239 | + | 0.586195i | ||||
\(746\) | 18.0000 | 0.659027 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.0000 | −1.75154 | −0.875772 | − | 0.482724i | \(-0.839647\pi\) | ||||
−0.875772 | + | 0.482724i | \(0.839647\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.0000 | 0.364179 | ||||||||
\(755\) | −32.0000 | + | 16.0000i | −1.16460 | + | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.0000i | − | 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | 10.0000i | 0.363216i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00000 | + | 4.00000i | 0.0725476 | + | 0.145095i | ||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000i | 0.579239i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.0000 | 0.722629 | ||||||||
\(767\) | 6.00000i | 0.216647i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 48.0000 | − | 24.0000i | 1.72980 | − | 0.864900i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 2.00000i | − | 0.0719816i | ||||||
\(773\) | − | 18.0000i | − | 0.647415i | −0.946157 | − | 0.323708i | \(-0.895071\pi\) | ||
0.946157 | − | 0.323708i | \(-0.104929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0000 | − | 16.0000i | 0.431053 | − | 0.574737i | ||||
\(776\) | −14.0000 | −0.502571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 30.0000i | − | 1.07555i | ||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 24.0000i | − | 0.858238i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | −6.00000 | − | 12.0000i | −0.214149 | − | 0.428298i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.0000i | − | 0.427754i | −0.976861 | − | 0.213877i | \(-0.931391\pi\) | ||
0.976861 | − | 0.213877i | \(-0.0686091\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.00000 | + | 16.0000i | 0.284627 | + | 0.569254i | ||||
\(791\) | −16.0000 | −0.568895 | ||||||||
\(792\) | 0 |