Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,1,Mod(13,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(128))
chi = DirichletCharacter(H, H._module([0, 111, 64]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.cd (of order \(128\), degree \(64\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Coefficient field: | \(\Q(\zeta_{128})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{64} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{128}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{128} - \cdots)\) |
Embedding invariants
Embedding label | 1413.1 | ||
Root | \(-0.970031 + 0.242980i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1413 |
Dual form | 3584.1.cd.a.1357.1 |
$q$-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 \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{33}{128}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.336890 | − | 0.941544i | −0.336890 | − | 0.941544i | ||||
\(3\) | 0 | 0 | −0.997290 | − | 0.0735646i | \(-0.976562\pi\) | ||||
0.997290 | + | 0.0735646i | \(0.0234375\pi\) | |||||||
\(4\) | −0.773010 | + | 0.634393i | −0.773010 | + | 0.634393i | ||||
\(5\) | 0 | 0 | −0.689541 | − | 0.724247i | \(-0.742188\pi\) | ||||
0.689541 | + | 0.724247i | \(0.257812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.970031 | + | 0.242980i | 0.970031 | + | 0.242980i | ||||
\(8\) | 0.857729 | + | 0.514103i | 0.857729 | + | 0.514103i | ||||
\(9\) | 0.989177 | + | 0.146730i | 0.989177 | + | 0.146730i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.88072 | + | 0.520464i | −1.88072 | + | 0.520464i | −0.881921 | + | 0.471397i | \(0.843750\pi\) |
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.359895 | − | 0.932993i | \(-0.382812\pi\) | ||||
−0.359895 | + | 0.932993i | \(0.617188\pi\) | |||||||
\(14\) | −0.0980171 | − | 0.995185i | −0.0980171 | − | 0.995185i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(17\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(18\) | −0.195090 | − | 0.980785i | −0.195090 | − | 0.980785i | ||||
\(19\) | 0 | 0 | 0.975702 | − | 0.219101i | \(-0.0703125\pi\) | ||||
−0.975702 | + | 0.219101i | \(0.929688\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.12363 | + | 1.59544i | 1.12363 | + | 1.59544i | ||||
\(23\) | 0.541185 | − | 1.51251i | 0.541185 | − | 1.51251i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0490677 | + | 0.998795i | −0.0490677 | + | 0.998795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.903989 | + | 0.427555i | −0.903989 | + | 0.427555i | ||||
\(29\) | 1.23009 | − | 1.57622i | 1.23009 | − | 1.57622i | 0.595699 | − | 0.803208i | \(-0.296875\pi\) |
0.634393 | − | 0.773010i | \(-0.281250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(32\) | −0.989177 | + | 0.146730i | −0.989177 | + | 0.146730i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.857729 | + | 0.514103i | −0.857729 | + | 0.514103i | ||||
\(37\) | 0.329538 | + | 1.89917i | 0.329538 | + | 1.89917i | 0.427555 | + | 0.903989i | \(0.359375\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.0490677 | − | 0.998795i | \(-0.515625\pi\) | ||||
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.159911 | + | 0.185381i | −0.159911 | + | 0.185381i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(44\) | 1.12363 | − | 1.59544i | 1.12363 | − | 1.59544i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.60642 | −1.60642 | ||||||||
\(47\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.881921 | + | 0.471397i | 0.881921 | + | 0.471397i | ||||
\(50\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.553230 | + | 0.708899i | 0.553230 | + | 0.708899i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.89848 | − | 0.627175i | −1.89848 | − | 0.627175i | ||||
\(59\) | 0 | 0 | 0.932993 | − | 0.359895i | \(-0.117188\pi\) | ||||
−0.932993 | + | 0.359895i | \(0.882812\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.313682 | − | 0.949528i | \(-0.601562\pi\) | ||||
0.313682 | + | 0.949528i | \(0.398438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(64\) | 0.471397 | + | 0.881921i | 0.471397 | + | 0.881921i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.680899 | − | 1.35271i | 0.680899 | − | 1.35271i | −0.242980 | − | 0.970031i | \(-0.578125\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.53724 | + | 1.14010i | 1.53724 | + | 1.14010i | 0.941544 | + | 0.336890i | \(0.109375\pi\) |
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(72\) | 0.773010 | + | 0.634393i | 0.773010 | + | 0.634393i | ||||
\(73\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(74\) | 1.67714 | − | 0.950087i | 1.67714 | − | 0.950087i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.95082 | + | 0.0478899i | −1.95082 | + | 0.0478899i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.389887 | + | 1.28528i | 0.389887 | + | 1.28528i | 0.903989 | + | 0.427555i | \(0.140625\pi\) |
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.956940 | + | 0.290285i | 0.956940 | + | 0.290285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.170962 | − | 0.985278i | \(-0.445312\pi\) | ||||
−0.170962 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.228417 | + | 0.0881100i | 0.228417 | + | 0.0881100i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.88072 | − | 0.520464i | −1.88072 | − | 0.520464i | ||||
\(89\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.541185 | + | 1.51251i | 0.541185 | + | 1.51251i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(98\) | 0.146730 | − | 0.989177i | 0.146730 | − | 0.989177i | ||||
\(99\) | −1.93673 | + | 0.238873i | −1.93673 | + | 0.238873i | ||||
\(100\) | −0.595699 | − | 0.803208i | −0.595699 | − | 0.803208i | ||||
\(101\) | 0 | 0 | 0.844854 | − | 0.534998i | \(-0.179688\pi\) | ||||
−0.844854 | + | 0.534998i | \(0.820312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.481082 | − | 0.759711i | 0.481082 | − | 0.759711i | ||||
\(107\) | 0.282070 | + | 0.560376i | 0.282070 | + | 0.560376i | 0.989177 | − | 0.146730i | \(-0.0468750\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.05424 | + | 1.66483i | −1.05424 | + | 1.66483i | −0.382683 | + | 0.923880i | \(0.625000\pi\) |
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.427555 | − | 0.903989i | 0.427555 | − | 0.903989i | ||||
\(113\) | 0.483620 | + | 0.0476324i | 0.483620 | + | 0.0476324i | 0.336890 | − | 0.941544i | \(-0.390625\pi\) |
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0490677 | + | 1.99880i | 0.0490677 | + | 1.99880i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.40848 | − | 1.44359i | 2.40848 | − | 1.44359i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0490677 | − | 0.998795i | 0.0490677 | − | 0.998795i | ||||
\(127\) | −1.40740 | − | 1.40740i | −1.40740 | − | 1.40740i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
−0.634393 | − | 0.773010i | \(-0.718750\pi\) | |||||||
\(128\) | 0.671559 | − | 0.740951i | 0.671559 | − | 0.740951i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.653173 | − | 0.757209i | \(-0.726562\pi\) | ||||
0.653173 | + | 0.757209i | \(0.273438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.50303 | − | 0.185381i | −1.50303 | − | 0.185381i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0788231 | − | 0.0584592i | 0.0788231 | − | 0.0584592i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.870087 | − | 0.492898i | \(-0.835938\pi\) | ||||
0.870087 | + | 0.492898i | \(0.164062\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.555570 | − | 1.83147i | 0.555570 | − | 1.83147i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.336890 | − | 0.941544i | 0.336890 | − | 0.941544i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.45956 | − | 1.25902i | −1.45956 | − | 1.25902i | ||||
\(149\) | 0.131419 | − | 0.0661509i | 0.131419 | − | 0.0661509i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.609090 | + | 0.288078i | −0.609090 | + | 0.288078i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.702301 | + | 1.82065i | 0.702301 | + | 1.82065i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.122411 | − | 0.992480i | \(-0.539062\pi\) | ||||
0.122411 | + | 0.992480i | \(0.460938\pi\) | |||||||
\(158\) | 1.07880 | − | 0.800094i | 1.07880 | − | 0.800094i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.892476 | − | 1.33569i | 0.892476 | − | 1.33569i | ||||
\(162\) | −0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | ||||
\(163\) | −0.191977 | + | 0.693716i | −0.191977 | + | 0.693716i | 0.803208 | + | 0.595699i | \(0.203125\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.740951 | − | 0.671559i | −0.740951 | − | 0.671559i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.00600822 | − | 0.244748i | 0.00600822 | − | 0.244748i | ||||
\(173\) | 0 | 0 | −0.985278 | − | 0.170962i | \(-0.945312\pi\) | ||||
0.985278 | + | 0.170962i | \(0.0546875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.290285 | + | 0.956940i | −0.290285 | + | 0.956940i | ||||
\(176\) | 0.143554 | + | 1.94612i | 0.143554 | + | 1.94612i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0427060 | − | 1.73965i | −0.0427060 | − | 1.73965i | −0.514103 | − | 0.857729i | \(-0.671875\pi\) |
0.471397 | − | 0.881921i | \(-0.343750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.992480 | − | 0.122411i | \(-0.960938\pi\) | ||||
0.992480 | + | 0.122411i | \(0.0390625\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.24178 | − | 1.01910i | 1.24178 | − | 1.01910i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.327237 | − | 0.790019i | −0.327237 | − | 0.790019i | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) |
0.671559 | − | 0.740951i | \(-0.265625\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.757083 | − | 1.82776i | 0.757083 | − | 1.82776i | 0.242980 | − | 0.970031i | \(-0.421875\pi\) |
0.514103 | − | 0.857729i | \(-0.328125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(197\) | −0.567444 | − | 1.47104i | −0.567444 | − | 1.47104i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) |
0.290285 | − | 0.956940i | \(-0.406250\pi\) | |||||||
\(198\) | 0.877373 | + | 1.74304i | 0.877373 | + | 1.74304i | ||||
\(199\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(200\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.57622 | − | 1.23009i | 1.57622 | − | 1.23009i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.757259 | − | 1.41673i | 0.757259 | − | 1.41673i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12752 | − | 0.794086i | 1.12752 | − | 0.794086i | 0.146730 | − | 0.989177i | \(-0.453125\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(212\) | −0.877373 | − | 0.197021i | −0.877373 | − | 0.197021i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.432593 | − | 0.454366i | 0.432593 | − | 0.454366i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.92267 | + | 0.431751i | 1.92267 | + | 0.431751i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(224\) | −0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | ||||
\(225\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(226\) | −0.118079 | − | 0.471397i | −0.118079 | − | 0.471397i | ||||
\(227\) | 0 | 0 | −0.788346 | − | 0.615232i | \(-0.789062\pi\) | ||||
0.788346 | + | 0.615232i | \(0.210938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.219101 | − | 0.975702i | \(-0.429688\pi\) | ||||
−0.219101 | + | 0.975702i | \(0.570312\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.86542 | − | 0.719573i | 1.86542 | − | 0.719573i | ||||
\(233\) | −1.39528 | − | 0.499238i | −1.39528 | − | 0.499238i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.980785 | + | 1.19509i | −0.980785 | + | 1.19509i | 1.00000i | \(0.5\pi\) | ||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(242\) | −2.17060 | − | 1.78136i | −2.17060 | − | 1.78136i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.724247 | − | 0.689541i | \(-0.242188\pi\) | ||||
−0.724247 | + | 0.689541i | \(0.757812\pi\) | |||||||
\(252\) | −0.956940 | + | 0.290285i | −0.956940 | + | 0.290285i | ||||
\(253\) | −0.230608 | + | 3.12627i | −0.230608 | + | 3.12627i | ||||
\(254\) | −0.850993 | + | 1.79927i | −0.850993 | + | 1.79927i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.141800 | + | 1.92233i | −0.141800 | + | 1.92233i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.44806 | − | 1.37867i | 1.44806 | − | 1.37867i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.404061 | + | 1.61310i | −0.404061 | + | 1.61310i | 0.336890 | + | 0.941544i | \(0.390625\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.331811 | + | 1.47762i | 0.331811 | + | 1.47762i | ||||
\(269\) | 0 | 0 | −0.932993 | − | 0.359895i | \(-0.882812\pi\) | ||||
0.932993 | + | 0.359895i | \(0.117188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0815966 | − | 0.0545211i | −0.0815966 | − | 0.0545211i | ||||
\(275\) | −0.427555 | − | 1.90399i | −0.427555 | − | 1.90399i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.361241 | − | 1.09349i | 0.361241 | − | 1.09349i | −0.595699 | − | 0.803208i | \(-0.703125\pi\) |
0.956940 | − | 0.290285i | \(-0.0937500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.88082 | − | 0.0923988i | −1.88082 | − | 0.0923988i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.219101 | − | 0.975702i | \(-0.429688\pi\) | ||||
−0.219101 | + | 0.975702i | \(0.570312\pi\) | |||||||
\(284\) | −1.91158 | + | 0.0939097i | −1.91158 | + | 0.0939097i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −1.00000 | ||||||||
\(289\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.985278 | − | 0.170962i | \(-0.0546875\pi\) | ||||
−0.985278 | + | 0.170962i | \(0.945312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.693716 | + | 1.79839i | −0.693716 | + | 1.79839i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.106558 | − | 0.101451i | −0.106558 | − | 0.101451i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.200162 | + | 0.140970i | −0.200162 | + | 0.140970i | ||||
\(302\) | 0.476434 | + | 0.476434i | 0.476434 | + | 0.476434i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.689541 | − | 0.724247i | \(-0.257812\pi\) | ||||
−0.689541 | + | 0.724247i | \(0.742188\pi\) | |||||||
\(308\) | 1.47762 | − | 1.27460i | 1.47762 | − | 1.27460i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.11676 | − | 0.746196i | −1.11676 | − | 0.746196i | ||||
\(317\) | 1.77181 | − | 0.585326i | 1.77181 | − | 0.585326i | 0.773010 | − | 0.634393i | \(-0.218750\pi\) |
0.998795 | + | 0.0490677i | \(0.0156250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.49309 | + | 3.60464i | −1.49309 | + | 3.60464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.55827 | − | 0.390327i | −1.55827 | − | 0.390327i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.717840 | − | 0.0529510i | 0.717840 | − | 0.0529510i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.81467 | − | 0.223818i | −1.81467 | − | 0.223818i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0473045 | + | 1.92697i | 0.0473045 | + | 1.92697i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.497971 | + | 1.64159i | −0.497971 | + | 1.64159i | 0.242980 | + | 0.970031i | \(0.421875\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(338\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.740951 | + | 0.671559i | 0.740951 | + | 0.671559i | ||||
\(344\) | −0.232465 | + | 0.0767960i | −0.232465 | + | 0.0767960i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.662638 | − | 0.466683i | −0.662638 | − | 0.466683i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.266713 | − | 0.963776i | \(-0.414062\pi\) | ||||
−0.266713 | + | 0.963776i | \(0.585938\pi\) | |||||||
\(350\) | 0.998795 | − | 0.0490677i | 0.998795 | − | 0.0490677i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.78399 | − | 0.790790i | 1.78399 | − | 0.790790i | ||||
\(353\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.62357 | + | 0.626280i | −1.62357 | + | 0.626280i | ||||
\(359\) | −1.15203 | − | 1.27107i | −1.15203 | − | 1.27107i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
−0.195090 | − | 0.980785i | \(-0.562500\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.903989 | − | 0.427555i | 0.903989 | − | 0.427555i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(368\) | −1.37787 | − | 0.825862i | −1.37787 | − | 0.825862i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.364402 | + | 0.822078i | 0.364402 | + | 0.822078i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.930989 | + | 0.527399i | 0.930989 | + | 0.527399i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.78591 | − | 0.0438416i | −1.78591 | − | 0.0438416i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.633595 | + | 0.574257i | −0.633595 | + | 0.574257i | ||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.97597 | − | 0.0970732i | −1.97597 | − | 0.0970732i | ||||
\(387\) | −0.185381 | + | 0.159911i | −0.185381 | + | 0.159911i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0487133 | + | 1.98436i | −0.0487133 | + | 1.98436i | 0.0980171 | + | 0.995185i | \(0.468750\pi\) |
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.514103 | + | 0.857729i | 0.514103 | + | 0.857729i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.19389 | + | 1.02985i | −1.19389 | + | 1.02985i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.34557 | − | 1.41330i | 1.34557 | − | 1.41330i | ||||
\(397\) | 0 | 0 | 0.914210 | − | 0.405241i | \(-0.132812\pi\) | ||||
−0.914210 | + | 0.405241i | \(0.867188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.970031 | + | 0.242980i | 0.970031 | + | 0.242980i | ||||
\(401\) | −0.100782 | − | 1.02325i | −0.100782 | − | 1.02325i | −0.903989 | − | 0.427555i | \(-0.859375\pi\) |
0.803208 | − | 0.595699i | \(-0.203125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.68920 | − | 1.06967i | −1.68920 | − | 1.06967i | ||||
\(407\) | −1.60822 | − | 3.40030i | −1.60822 | − | 3.40030i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.58903 | − | 0.235710i | −1.58903 | − | 0.235710i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.963776 | − | 0.266713i | \(-0.914062\pi\) | ||||
0.963776 | + | 0.266713i | \(0.0859375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.414461 | + | 0.588489i | −0.414461 | + | 0.588489i | −0.970031 | − | 0.242980i | \(-0.921875\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(422\) | −1.12752 | − | 0.794086i | −1.12752 | − | 0.794086i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.110074 | + | 0.892460i | 0.110074 | + | 0.892460i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.573542 | − | 0.254234i | −0.573542 | − | 0.254234i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.373380 | − | 0.113263i | −0.373380 | − | 0.113263i | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.241217 | − | 1.95574i | −0.241217 | − | 1.95574i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.803208 | + | 0.595699i | 0.803208 | + | 0.595699i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.216166 | + | 0.487663i | −0.216166 | + | 0.487663i | −0.989177 | − | 0.146730i | \(-0.953125\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.242980 | + | 0.970031i | 0.242980 | + | 0.970031i | ||||
\(449\) | −0.871028 | − | 0.360791i | −0.871028 | − | 0.360791i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(450\) | 0.989177 | − | 0.146730i | 0.989177 | − | 0.146730i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.404061 | + | 0.269985i | −0.404061 | + | 0.269985i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.32607 | − | 0.794814i | −1.32607 | − | 0.794814i | −0.336890 | − | 0.941544i | \(-0.609375\pi\) |
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.724247 | − | 0.689541i | \(-0.757812\pi\) | ||||
0.724247 | + | 0.689541i | \(0.242188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.906796 | + | 0.484693i | 0.906796 | + | 0.484693i | 0.857729 | − | 0.514103i | \(-0.171875\pi\) |
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(464\) | −1.30595 | − | 1.51396i | −1.30595 | − | 1.51396i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.48190i | 1.48190i | ||||||||
\(467\) | 0 | 0 | −0.575808 | − | 0.817585i | \(-0.695312\pi\) | ||||
0.575808 | + | 0.817585i | \(0.304688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.989177 | − | 1.14673i | 0.989177 | − | 1.14673i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.204262 | − | 0.431877i | 0.204262 | − | 0.431877i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.443225 | + | 0.782402i | 0.443225 | + | 0.782402i | ||||
\(478\) | 1.45565 | + | 0.520839i | 1.45565 | + | 0.520839i | ||||
\(479\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.945979 | + | 2.64384i | −0.945979 | + | 2.64384i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.00481527 | + | 0.0980171i | −0.00481527 | + | 0.0980171i | 0.995185 | + | 0.0980171i | \(0.0312500\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.139703 | − | 0.0461517i | −0.139703 | − | 0.0461517i | 0.242980 | − | 0.970031i | \(-0.421875\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.21415 | + | 1.47945i | 1.21415 | + | 1.47945i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.717840 | − | 1.86093i | 0.717840 | − | 1.86093i | 0.290285 | − | 0.956940i | \(-0.406250\pi\) |
0.427555 | − | 0.903989i | \(-0.359375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.989177 | − | 0.146730i | \(-0.953125\pi\) | ||||
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(504\) | 0.595699 | + | 0.803208i | 0.595699 | + | 0.803208i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.02121 | − | 0.836082i | 3.02121 | − | 0.836082i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.98079 | + | 0.195090i | 1.98079 | + | 0.195090i | ||||
\(509\) | 0 | 0 | −0.997290 | − | 0.0735646i | \(-0.976562\pi\) | ||||
0.997290 | + | 0.0735646i | \(0.0234375\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.0490677 | + | 0.998795i | −0.0490677 | + | 0.998795i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.85773 | − | 0.514103i | 1.85773 | − | 0.514103i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.989177 | − | 0.146730i | \(-0.953125\pi\) | ||||
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(522\) | −1.78591 | − | 0.898952i | −1.78591 | − | 0.898952i | ||||
\(523\) | 0 | 0 | 0.963776 | − | 0.266713i | \(-0.0859375\pi\) | ||||
−0.963776 | + | 0.266713i | \(0.914062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.65493 | − | 0.162997i | 1.65493 | − | 0.162997i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.22180 | − | 1.00270i | −1.22180 | − | 1.00270i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.27946 | − | 0.810210i | 1.27946 | − | 0.810210i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.90399 | − | 0.427555i | −1.90399 | − | 0.427555i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.16836 | + | 1.49711i | −1.16836 | + | 1.49711i | −0.336890 | + | 0.941544i | \(0.609375\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.713960 | + | 1.26032i | 0.713960 | + | 1.26032i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(548\) | −0.0238449 | + | 0.0951944i | −0.0238449 | + | 0.0951944i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.64865 | + | 1.04400i | −1.64865 | + | 1.04400i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0659037 | + | 1.34150i | 0.0659037 | + | 1.34150i | ||||
\(554\) | −1.15127 | + | 0.0282621i | −1.15127 | + | 0.0282621i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.941544 | + | 1.33689i | 0.941544 | + | 1.33689i | 0.941544 | + | 0.336890i | \(0.109375\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.546632 | + | 1.80200i | 0.546632 | + | 1.80200i | ||||
\(563\) | 0 | 0 | −0.724247 | − | 0.689541i | \(-0.757812\pi\) | ||||
0.724247 | + | 0.689541i | \(0.242188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.857729 | + | 0.514103i | 0.857729 | + | 0.514103i | ||||
\(568\) | 0.732410 | + | 1.76820i | 0.732410 | + | 1.76820i | ||||
\(569\) | 1.96883 | − | 0.292048i | 1.96883 | − | 0.292048i | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) |
0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0457936 | − | 0.0176645i | 0.0457936 | − | 0.0176645i | −0.336890 | − | 0.941544i | \(-0.609375\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.48413 | + | 0.614748i | 1.48413 | + | 0.614748i | ||||
\(576\) | 0.336890 | + | 0.941544i | 0.336890 | + | 0.941544i | ||||
\(577\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(578\) | 0.857729 | − | 0.514103i | 0.857729 | − | 0.514103i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.40943 | − | 1.04530i | −1.40943 | − | 1.04530i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.122411 | − | 0.992480i | \(-0.460938\pi\) | ||||
−0.122411 | + | 0.992480i | \(0.539062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.92697 | + | 0.0473045i | 1.92697 | + | 0.0473045i | ||||
\(593\) | 0 | 0 | −0.956940 | − | 0.290285i | \(-0.906250\pi\) | ||||
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0596228 | + | 0.134507i | −0.0596228 | + | 0.134507i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.746196 | + | 0.823301i | −0.746196 | + | 0.823301i | −0.989177 | − | 0.146730i | \(-0.953125\pi\) |
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(602\) | 0.200162 | + | 0.140970i | 0.200162 | + | 0.140970i | ||||
\(603\) | 0.872014 | − | 1.23816i | 0.872014 | − | 1.23816i | ||||
\(604\) | 0.288078 | − | 0.609090i | 0.288078 | − | 0.609090i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.684739 | − | 0.433606i | 0.684739 | − | 0.433606i | −0.146730 | − | 0.989177i | \(-0.546875\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.69789 | − | 0.961844i | −1.69789 | − | 0.961844i | ||||
\(617\) | −0.542476 | − | 1.14697i | −0.542476 | − | 1.14697i | −0.970031 | − | 0.242980i | \(-0.921875\pi\) |
0.427555 | − | 0.903989i | \(-0.359375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.449611 | − | 0.893224i | \(-0.648438\pi\) | ||||
0.449611 | + | 0.893224i | \(0.351562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.561621 | − | 0.757259i | −0.561621 | − | 0.757259i | 0.427555 | − | 0.903989i | \(-0.359375\pi\) |
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(632\) | −0.326351 | + | 1.30287i | −0.326351 | + | 1.30287i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.14801 | − | 1.47104i | −1.14801 | − | 1.47104i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.89693 | + | 0.191444i | 3.89693 | + | 0.191444i | ||||
\(639\) | 1.35332 | + | 1.35332i | 1.35332 | + | 1.35332i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.207508 | + | 0.207508i | −0.207508 | + | 0.207508i | −0.803208 | − | 0.595699i | \(-0.796875\pi\) |
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.653173 | − | 0.757209i | \(-0.726562\pi\) | ||||
0.653173 | + | 0.757209i | \(0.273438\pi\) | |||||||
\(644\) | 0.157456 | + | 1.59868i | 0.157456 | + | 1.59868i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(648\) | 0.671559 | + | 0.740951i | 0.671559 | + | 0.740951i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.291689 | − | 0.658039i | −0.291689 | − | 0.658039i | ||||
\(653\) | −0.684739 | − | 1.54475i | −0.684739 | − | 1.54475i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.146730 | − | 0.989177i | \(-0.453125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.288876 | − | 0.182928i | −0.288876 | − | 0.182928i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.893224 | − | 0.449611i | \(-0.148438\pi\) | ||||
−0.893224 | + | 0.449611i | \(0.851562\pi\) | |||||||
\(662\) | 0.400609 | + | 1.78399i | 0.400609 | + | 1.78399i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.79839 | − | 0.693716i | 1.79839 | − | 0.693716i | ||||
\(667\) | −1.71834 | − | 2.71355i | −1.71834 | − | 2.71355i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.979938 | − | 1.46658i | 0.979938 | − | 1.46658i | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(674\) | 1.71339 | − | 0.0841735i | 1.71339 | − | 0.0841735i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.998795 | + | 0.0490677i | 0.998795 | + | 0.0490677i | ||||
\(677\) | 0 | 0 | −0.817585 | − | 0.575808i | \(-0.804688\pi\) | ||||
0.817585 | + | 0.575808i | \(0.195312\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.983125 | + | 0.0725197i | −0.983125 | + | 0.0725197i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.150622 | + | 0.193004i | 0.150622 | + | 0.193004i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.0245412 | − | 0.999699i | \(-0.507812\pi\) | ||||
0.0245412 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.93673 | − | 0.238873i | −1.93673 | − | 0.238873i | ||||
\(694\) | −0.216166 | + | 0.781124i | −0.216166 | + | 0.781124i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(701\) | −1.09908 | − | 0.553230i | −1.09908 | − | 0.553230i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.34557 | − | 1.41330i | −1.34557 | − | 1.41330i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.608117 | − | 1.57648i | −0.608117 | − | 1.57648i | −0.803208 | − | 0.595699i | \(-0.796875\pi\) |
0.195090 | − | 0.980785i | \(-0.437500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.197076 | + | 1.32858i | 0.197076 | + | 1.32858i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.13663 | + | 1.31768i | 1.13663 | + | 1.31768i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.808661 | + | 1.51290i | −0.808661 | + | 1.51290i | ||||
\(719\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.51396 | + | 1.30595i | 1.51396 | + | 1.30595i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | ||||
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.903989 | + | 0.427555i | 0.903989 | + | 0.427555i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.870087 | − | 0.492898i | \(-0.164062\pi\) | ||||
−0.870087 | + | 0.492898i | \(0.835938\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.313396 | + | 1.57555i | −0.313396 | + | 1.57555i | ||||
\(737\) | −0.576539 | + | 2.89846i | −0.576539 | + | 2.89846i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.907873 | + | 0.708511i | 0.907873 | + | 0.708511i | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) |
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.651259 | − | 0.620050i | 0.651259 | − | 0.620050i | ||||
\(743\) | −1.80580 | − | 0.0887133i | −1.80580 | − | 0.0887133i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.182928 | − | 1.05424i | 0.182928 | − | 1.05424i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.137456 | + | 0.612120i | 0.137456 | + | 0.612120i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.598102 | + | 0.728789i | −0.598102 | + | 0.728789i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.167326 | − | 0.604638i | −0.167326 | − | 0.604638i | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(758\) | 0.560376 | + | 1.69628i | 0.560376 | + | 1.69628i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.242980 | − | 0.970031i | \(-0.421875\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.42717 | + | 1.35878i | −1.42717 | + | 1.35878i | ||||
\(764\) | 0.754140 | + | 0.403096i | 0.754140 | + | 0.403096i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.574286 | + | 1.89317i | 0.574286 | + | 1.89317i | ||||
\(773\) | 0 | 0 | 0.724247 | − | 0.689541i | \(-0.242188\pi\) | ||||
−0.724247 | + | 0.689541i | \(0.757812\pi\) | |||||||
\(774\) | 0.213016 | + | 0.120672i | 0.213016 | + | 0.120672i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.88477 | − | 0.622645i | 1.88477 | − | 0.622645i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.48450 | − | 1.34412i | −3.48450 | − | 1.34412i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.219101 | − | 0.975702i | \(-0.570312\pi\) | ||||
0.219101 | + | 0.975702i | \(0.429688\pi\) | |||||||
\(788\) | 1.37186 | + | 0.777149i | 1.37186 | + | 0.777149i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.457553 | + | 0.163715i | 0.457553 | + | 0.163715i | ||||
\(792\) | −1.78399 | − | 0.790790i | −1.78399 | − | 0.790790i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.788346 | − | 0.615232i | \(-0.789062\pi\) | ||||
0.788346 | + | 0.615232i | \(0.210938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.0980171 | − | 0.995185i | −0.0980171 | − | 0.995185i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.929487 | + | 0.439614i | −0.929487 | + | 0.439614i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.26726 | + | 0.0622564i | −1.26726 | + | 0.0622564i | −0.671559 | − | 0.740951i | \(-0.734375\pi\) |
−0.595699 | + | 0.803208i | \(0.703125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.757209 | − | 0.653173i | \(-0.773438\pi\) | ||||
0.757209 | + | 0.653173i | \(0.226562\pi\) | |||||||
\(812\) | −0.438071 | + | 1.95082i | −0.438071 | + | 1.95082i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.65974 | + | 2.65974i | −2.65974 | + | 2.65974i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.638941 | + | 0.498635i | −0.638941 | + | 0.498635i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.571240 | − | 0.953057i | 0.571240 | − | 0.953057i | −0.427555 | − | 0.903989i | \(-0.640625\pi\) |
0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.442838 | − | 1.14801i | −0.442838 | − | 1.14801i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
0.514103 | − | 0.857729i | \(-0.328125\pi\) | |||||||
\(828\) | 0.313396 | + | 1.57555i | 0.313396 | + | 1.57555i | ||||
\(829\) | 0 | 0 | 0.949528 | − | 0.313682i | \(-0.101562\pi\) | ||||
−0.949528 | + | 0.313682i | \(0.898438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.595699 | − | 0.803208i | \(-0.296875\pi\) | ||||
−0.595699 | + | 0.803208i | \(0.703125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.728355 | − | 2.90776i | −0.728355 | − | 2.90776i | ||||
\(842\) | 0.693716 | + | 0.191977i | 0.693716 | + | 0.191977i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.367819 | + | 1.32913i | −0.367819 | + | 1.32913i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.68707 | − | 0.815113i | 2.68707 | − | 0.815113i | ||||
\(848\) | 0.803208 | − | 0.404301i | 0.803208 | − | 0.404301i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.05086 | + | 0.529375i | 3.05086 | + | 0.529375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.997290 | − | 0.0735646i | \(-0.0234375\pi\) | ||||
−0.997290 | + | 0.0735646i | \(0.976562\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0461517 | + | 0.625664i | −0.0461517 | + | 0.625664i | ||||
\(857\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.817585 | − | 0.575808i | \(-0.804688\pi\) | ||||
0.817585 | + | 0.575808i | \(0.195312\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0191453 | + | 0.389711i | 0.0191453 | + | 0.389711i | ||||
\(863\) | −1.04619 | + | 1.56573i | −1.04619 | + | 1.56573i | −0.242980 | + | 0.970031i | \(0.578125\pi\) |
−0.803208 | + | 0.595699i | \(0.796875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.40221 | − | 2.21433i | −1.40221 | − | 2.21433i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.76015 | + | 0.885984i | −1.76015 | + | 0.885984i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.03956 | − | 0.658295i | −1.03956 | − | 0.658295i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(882\) | 0.290285 | − | 0.956940i | 0.290285 | − | 0.956940i | ||||
\(883\) | 0.756174 | + | 1.70590i | 0.756174 | + | 1.70590i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.531980 | + | 0.0392412i | 0.531980 | + | 0.0392412i | ||||
\(887\) | 0 | 0 | 0.803208 | − | 0.595699i | \(-0.203125\pi\) | ||||
−0.803208 | + | 0.595699i | \(0.796875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.02325 | − | 1.70720i | −1.02325 | − | 1.70720i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.95082 | − | 0.0478899i | −1.95082 | − | 0.0478899i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0462607 | + | 0.941658i | −0.0462607 | + | 0.941658i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.390327 | + | 0.289486i | 0.390327 | + | 0.289486i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.971283 | − | 1.71455i | 0.971283 | − | 1.71455i | 0.336890 | − | 0.941544i | \(-0.390625\pi\) |
0.634393 | − | 0.773010i | \(-0.281250\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.26268 | + | 0.124363i | 1.26268 | + | 0.124363i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.301614 | + | 1.51631i | −0.301614 | + | 1.51631i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0838155 | + | 0.177213i | 0.0838155 | + | 0.177213i | 0.941544 | − | 0.336890i | \(-0.109375\pi\) |
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.91306 | + | 0.235953i | −1.91306 | + | 0.235953i | ||||
\(926\) | 0.150869 | − | 1.01708i | 0.150869 | − | 1.01708i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.985499 | + | 1.73965i | −0.985499 | + | 1.73965i | ||||
\(929\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.39528 | − | 0.499238i | 1.39528 | − | 0.499238i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.671559 | − | 0.740951i | \(-0.265625\pi\) | ||||
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(938\) | −1.41294 | − | 0.545031i | −1.41294 | − | 0.545031i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.170962 | − | 0.985278i | \(-0.445312\pi\) | ||||
−0.170962 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.475445 | − | 0.0468272i | −0.475445 | − | 0.0468272i | ||||
\(947\) | −1.15127 | + | 0.0282621i | −1.15127 | + | 0.0282621i | −0.595699 | − | 0.803208i | \(-0.703125\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.686831 | − | 0.509389i | −0.686831 | − | 0.509389i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(954\) | 0.587348 | − | 0.680899i | 0.587348 | − | 0.680899i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.54602i | − | 1.54602i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0906652 | − | 0.0375548i | 0.0906652 | − | 0.0375548i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.196792 | + | 0.595699i | 0.196792 | + | 0.595699i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.86271 | − | 0.276306i | 1.86271 | − | 0.276306i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(968\) | 2.80798 | 2.80798 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.615232 | − | 0.788346i | \(-0.710938\pi\) | ||||
0.615232 | + | 0.788346i | \(0.289062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.0939097 | − | 0.0284872i | 0.0939097 | − | 0.0284872i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.273678 | − | 0.512016i | −0.273678 | − | 0.512016i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.28711 | + | 1.49212i | −1.28711 | + | 1.49212i | ||||
\(982\) | 0.00361073 | + | 0.147085i | 0.00361073 | + | 0.147085i | ||||
\(983\) | 0 | 0 | −0.0490677 | − | 0.998795i | \(-0.515625\pi\) | ||||
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.193849 | + | 0.342192i | 0.193849 | + | 0.342192i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00845 | + | 0.200593i | −1.00845 | + | 0.200593i | −0.671559 | − | 0.740951i | \(-0.734375\pi\) |
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.983931 | − | 1.64159i | 0.983931 | − | 1.64159i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.975702 | − | 0.219101i | \(-0.929688\pi\) | ||||
0.975702 | + | 0.219101i | \(0.0703125\pi\) | |||||||
\(998\) | −1.99398 | − | 0.0489495i | −1.99398 | − | 0.0489495i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3584.1.cd.a.1413.1 | yes | 64 | |
7.6 | odd | 2 | CM | 3584.1.cd.a.1413.1 | yes | 64 | |
512.333 | even | 128 | inner | 3584.1.cd.a.1357.1 | ✓ | 64 | |
3584.1357 | odd | 128 | inner | 3584.1.cd.a.1357.1 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.1.cd.a.1357.1 | ✓ | 64 | 512.333 | even | 128 | inner | |
3584.1.cd.a.1357.1 | ✓ | 64 | 3584.1357 | odd | 128 | inner | |
3584.1.cd.a.1413.1 | yes | 64 | 1.1 | even | 1 | trivial | |
3584.1.cd.a.1413.1 | yes | 64 | 7.6 | odd | 2 | CM |