Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.1 | ||
Root | \(1.35489 + 0.405301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.c.3599.1 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | − | 1.41421i | −0.632456 | − | 0.632456i | 0.316228 | − | 0.948683i | \(-0.397584\pi\) |
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.89918 | + | 1.89918i | −0.572624 | + | 0.572624i | −0.932861 | − | 0.360237i | \(-0.882696\pi\) |
0.360237 | + | 0.932861i | \(0.382696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.853635 | + | 0.853635i | 0.236756 | + | 0.236756i | 0.815505 | − | 0.578750i | \(-0.196459\pi\) |
−0.578750 | + | 0.815505i | \(0.696459\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.59114i | − | 0.628443i | −0.949350 | − | 0.314222i | \(-0.898256\pi\) | ||
0.949350 | − | 0.314222i | \(-0.101744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.206992i | − | 0.0431608i | −0.999767 | − | 0.0215804i | \(-0.993130\pi\) | ||
0.999767 | − | 0.0215804i | \(-0.00686979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.10640 | + | 3.10640i | −0.576844 | + | 0.576844i | −0.934032 | − | 0.357188i | \(-0.883735\pi\) |
0.357188 | + | 0.934032i | \(0.383735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.70727i | − | 0.306635i | −0.988177 | − | 0.153317i | \(-0.951004\pi\) | ||
0.988177 | − | 0.153317i | \(-0.0489957\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | − | 1.41421i | −0.239046 | − | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.00000i | −0.164399 | + | 0.164399i | −0.784512 | − | 0.620113i | \(-0.787087\pi\) |
0.620113 | + | 0.784512i | \(0.287087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0764 | −1.72985 | −0.864923 | − | 0.501904i | \(-0.832633\pi\) | ||||
−0.864923 | + | 0.501904i | \(0.832633\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.12494 | + | 7.12494i | 1.08654 | + | 1.08654i | 0.995882 | + | 0.0906618i | \(0.0288982\pi\) |
0.0906618 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.24241 | 0.472954 | 0.236477 | − | 0.971637i | \(-0.424007\pi\) | ||||
0.236477 | + | 0.971637i | \(0.424007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.722255 | − | 0.722255i | −0.0992094 | − | 0.0992094i | 0.655760 | − | 0.754969i | \(-0.272348\pi\) |
−0.754969 | + | 0.655760i | \(0.772348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.37169 | 0.724319 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.00558 | + | 5.00558i | −0.651671 | + | 0.651671i | −0.953395 | − | 0.301724i | \(-0.902438\pi\) |
0.301724 | + | 0.953395i | \(0.402438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.14637 | − | 3.14637i | −0.402851 | − | 0.402851i | 0.476386 | − | 0.879236i | \(-0.341947\pi\) |
−0.879236 | + | 0.476386i | \(0.841947\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.41444i | − | 0.299475i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.14637 | + | 4.14637i | −0.506559 | + | 0.506559i | −0.913469 | − | 0.406909i | \(-0.866606\pi\) |
0.406909 | + | 0.913469i | \(0.366606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.0762i | − | 1.19582i | −0.801562 | − | 0.597912i | \(-0.795997\pi\) | ||
0.801562 | − | 0.597912i | \(-0.204003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.66442i | − | 0.662971i | −0.943460 | − | 0.331485i | \(-0.892450\pi\) | ||
0.943460 | − | 0.331485i | \(-0.107550\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.89918 | + | 1.89918i | −0.216432 | + | 0.216432i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.41454i | 0.384166i | 0.981379 | + | 0.192083i | \(0.0615242\pi\) | ||||
−0.981379 | + | 0.192083i | \(0.938476\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.27806 | + | 7.27806i | 0.798871 | + | 0.798871i | 0.982918 | − | 0.184047i | \(-0.0589198\pi\) |
−0.184047 | + | 0.982918i | \(0.558920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.66442 | + | 3.66442i | −0.397463 | + | 0.397463i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.1473 | −1.81761 | −0.908803 | − | 0.417226i | \(-0.863002\pi\) | ||||
−0.908803 | + | 0.417226i | \(0.863002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.853635 | + | 0.853635i | 0.0894852 | + | 0.0894852i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5426 | −1.67965 | −0.839824 | − | 0.542859i | \(-0.817342\pi\) | ||||
−0.839824 | + | 0.542859i | \(0.817342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.206992 | + | 0.206992i | 0.0205965 | + | 0.0205965i | 0.717330 | − | 0.696734i | \(-0.245364\pi\) |
−0.696734 | + | 0.717330i | \(0.745364\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.95715 | 0.586976 | 0.293488 | − | 0.955963i | \(-0.405184\pi\) | ||||
0.293488 | + | 0.955963i | \(0.405184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.10617 | + | 2.10617i | −0.203611 | + | 0.203611i | −0.801545 | − | 0.597934i | \(-0.795988\pi\) |
0.597934 | + | 0.801545i | \(0.295988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.00000i | 0.0957826 | + | 0.0957826i | 0.753374 | − | 0.657592i | \(-0.228425\pi\) |
−0.657592 | + | 0.753374i | \(0.728425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.79859i | 0.451413i | 0.974195 | + | 0.225707i | \(0.0724691\pi\) | ||||
−0.974195 | + | 0.225707i | \(0.927531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.292731 | + | 0.292731i | −0.0272973 | + | 0.0272973i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.59114i | − | 0.237529i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.78623i | 0.344203i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.48528 | + | 8.48528i | −0.758947 | + | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0790i | 1.51551i | 0.652538 | + | 0.757756i | \(0.273704\pi\) | ||||
−0.652538 | + | 0.757756i | \(0.726296\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.62121 | + | 1.62121i | 0.141645 | + | 0.141645i | 0.774374 | − | 0.632728i | \(-0.218065\pi\) |
−0.632728 | + | 0.774374i | \(0.718065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.6377 | −1.33602 | −0.668010 | − | 0.744152i | \(-0.732854\pi\) | ||||
−0.668010 | + | 0.744152i | \(0.732854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.58546 | − | 2.58546i | −0.219296 | − | 0.219296i | 0.588906 | − | 0.808202i | \(-0.299559\pi\) |
−0.808202 | + | 0.588906i | \(0.799559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.24241 | −0.271144 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.78623 | 0.729657 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.31920 | + | 9.31920i | 0.763459 | + | 0.763459i | 0.976946 | − | 0.213487i | \(-0.0684821\pi\) |
−0.213487 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0361 | 1.22362 | 0.611811 | − | 0.791004i | \(-0.290441\pi\) | ||||
0.611811 | + | 0.791004i | \(0.290441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.41444 | + | 2.41444i | −0.193933 | + | 0.193933i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.81079 | + | 8.81079i | 0.703177 | + | 0.703177i | 0.965091 | − | 0.261914i | \(-0.0843536\pi\) |
−0.261914 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.206992i | − | 0.0163133i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.1825 | + | 15.1825i | −1.18918 | + | 1.18918i | −0.211890 | + | 0.977293i | \(0.567962\pi\) |
−0.977293 | + | 0.211890i | \(0.932038\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00046i | 0.154800i | 0.997000 | + | 0.0774001i | \(0.0246619\pi\) | ||||
−0.997000 | + | 0.0774001i | \(0.975338\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.5426i | − | 0.887894i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.27271 | − | 3.27271i | 0.248819 | − | 0.248819i | −0.571667 | − | 0.820486i | \(-0.693703\pi\) |
0.820486 | + | 0.571667i | \(0.193703\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.3898 | − | 14.3898i | −1.07555 | − | 1.07555i | −0.996903 | − | 0.0786423i | \(-0.974942\pi\) |
−0.0786423 | − | 0.996903i | \(-0.525058\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2253 | + | 10.2253i | −0.760043 | + | 0.760043i | −0.976330 | − | 0.216287i | \(-0.930605\pi\) |
0.216287 | + | 0.976330i | \(0.430605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.82843 | 0.207950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.92104 | + | 4.92104i | 0.359862 | + | 0.359862i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.51000 | −0.253974 | −0.126987 | − | 0.991904i | \(-0.540531\pi\) | ||||
−0.126987 | + | 0.991904i | \(0.540531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5612 | + | 10.5612i | 0.752451 | + | 0.752451i | 0.974936 | − | 0.222485i | \(-0.0714168\pi\) |
−0.222485 | + | 0.974936i | \(0.571417\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.921039 | 0.0652907 | 0.0326453 | − | 0.999467i | \(-0.489607\pi\) | ||||
0.0326453 | + | 0.999467i | \(0.489607\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.10640 | + | 3.10640i | −0.218027 | + | 0.218027i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.6644 | + | 15.6644i | 1.09405 | + | 1.09405i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8322 | + | 14.8322i | −1.02109 | + | 1.02109i | −0.0213188 | + | 0.999773i | \(0.506787\pi\) |
−0.999773 | + | 0.0213188i | \(0.993213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 20.1524i | − | 1.37438i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.70727i | − | 0.115897i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.21189 | − | 2.21189i | 0.148788 | − | 0.148788i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4078i | 1.76840i | 0.467111 | + | 0.884199i | \(0.345295\pi\) | ||||
−0.467111 | + | 0.884199i | \(0.654705\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.38392 | + | 1.38392i | 0.0918538 | + | 0.0918538i | 0.751541 | − | 0.659687i | \(-0.229311\pi\) |
−0.659687 | + | 0.751541i | \(0.729311\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.77467 | − | 1.77467i | 0.117274 | − | 0.117274i | −0.646035 | − | 0.763308i | \(-0.723574\pi\) |
0.763308 | + | 0.646035i | \(0.223574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.5864 | 0.955588 | 0.477794 | − | 0.878472i | \(-0.341437\pi\) | ||||
0.477794 | + | 0.878472i | \(0.341437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.58546 | − | 4.58546i | −0.299123 | − | 0.299123i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.9866 | −1.87499 | −0.937494 | − | 0.348001i | \(-0.886861\pi\) | ||||
−0.937494 | + | 0.348001i | \(0.886861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3717 | 0.732515 | 0.366258 | − | 0.930514i | \(-0.380639\pi\) | ||||
0.366258 | + | 0.930514i | \(0.380639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.41421 | − | 1.41421i | −0.0903508 | − | 0.0903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.8091 | + | 11.8091i | −0.745382 | + | 0.745382i | −0.973608 | − | 0.228227i | \(-0.926707\pi\) |
0.228227 | + | 0.973608i | \(0.426707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.393115 | + | 0.393115i | 0.0247149 | + | 0.0247149i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.0871i | 1.19062i | 0.803495 | + | 0.595311i | \(0.202971\pi\) | ||||
−0.803495 | + | 0.595311i | \(0.797029\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | + | 1.00000i | −0.0621370 | + | 0.0621370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.2589i | 1.06423i | 0.846672 | + | 0.532116i | \(0.178603\pi\) | ||||
−0.846672 | + | 0.532116i | \(0.821397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.04285i | 0.125491i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.66221 | − | 9.66221i | 0.589115 | − | 0.589115i | −0.348277 | − | 0.937392i | \(-0.613233\pi\) |
0.937392 | + | 0.348277i | \(0.113233\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9572i | 0.847837i | 0.905700 | + | 0.423918i | \(0.139346\pi\) | ||||
−0.905700 | + | 0.423918i | \(0.860654\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.89918 | + | 1.89918i | 0.114525 | + | 0.114525i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2713 | + | 14.2713i | −0.857480 | + | 0.857480i | −0.991041 | − | 0.133561i | \(-0.957359\pi\) |
0.133561 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.9510 | −1.48845 | −0.744225 | − | 0.667929i | \(-0.767181\pi\) | ||||
−0.744225 | + | 0.667929i | \(0.767181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.0361 | − | 23.0361i | −1.36935 | − | 1.36935i | −0.861360 | − | 0.507995i | \(-0.830387\pi\) |
−0.507995 | − | 0.861360i | \(-0.669613\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0764 | −0.653820 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2860 | 0.605059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5314 | − | 19.5314i | −1.14104 | − | 1.14104i | −0.988261 | − | 0.152776i | \(-0.951179\pi\) |
−0.152776 | − | 0.988261i | \(-0.548821\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1579 | 0.824306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.176696 | − | 0.176696i | 0.0102186 | − | 0.0102186i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.12494 | + | 7.12494i | 0.410675 | + | 0.410675i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.89927i | 0.509570i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7434 | − | 14.7434i | 0.841449 | − | 0.841449i | −0.147598 | − | 0.989047i | \(-0.547154\pi\) |
0.989047 | + | 0.147598i | \(0.0471542\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.76875i | − | 0.383821i | −0.981412 | − | 0.191910i | \(-0.938532\pi\) | ||
0.981412 | − | 0.191910i | \(-0.0614683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.0361i | − | 1.52817i | −0.645115 | − | 0.764086i | \(-0.723190\pi\) | ||
0.645115 | − | 0.764086i | \(-0.276810\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.93460 | − | 4.93460i | 0.277155 | − | 0.277155i | −0.554817 | − | 0.831972i | \(-0.687212\pi\) |
0.831972 | + | 0.554817i | \(0.187212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.7992i | − | 0.660630i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.853635 | − | 0.853635i | 0.0473511 | − | 0.0473511i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.24241 | 0.178760 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.4538 | − | 18.4538i | −1.01431 | − | 1.01431i | −0.999896 | − | 0.0144159i | \(-0.995411\pi\) |
−0.0144159 | − | 0.999896i | \(-0.504589\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.7277 | 0.640752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.15792 | 0.444390 | 0.222195 | − | 0.975002i | \(-0.428678\pi\) | ||||
0.222195 | + | 0.975002i | \(0.428678\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.24241 | + | 3.24241i | 0.175586 | + | 0.175586i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.0166 | + | 21.0166i | −1.12823 | + | 1.12823i | −0.137765 | + | 0.990465i | \(0.543992\pi\) |
−0.990465 | + | 0.137765i | \(0.956008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4752 | + | 20.4752i | 1.09601 | + | 1.09601i | 0.994872 | + | 0.101141i | \(0.0322493\pi\) |
0.101141 | + | 0.994872i | \(0.467751\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.6731i | − | 0.993871i | −0.867787 | − | 0.496935i | \(-0.834459\pi\) | ||
0.867787 | − | 0.496935i | \(-0.165541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2499 | + | 14.2499i | −0.756305 | + | 0.756305i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.31889i | − | 0.0696083i | −0.999394 | − | 0.0348042i | \(-0.988919\pi\) | ||
0.999394 | − | 0.0348042i | \(-0.0110807\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000i | 1.00000i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.01070 | + | 8.01070i | −0.419299 | + | 0.419299i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.6644i | − | 1.44407i | −0.691856 | − | 0.722036i | \(-0.743207\pi\) | ||
0.691856 | − | 0.722036i | \(-0.256793\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.722255 | − | 0.722255i | −0.0374976 | − | 0.0374976i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6430 | + | 21.6430i | −1.12063 | + | 1.12063i | −0.128986 | + | 0.991646i | \(0.541172\pi\) |
−0.991646 | + | 0.128986i | \(0.958828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.30346 | −0.273142 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.582326 | + | 0.582326i | 0.0299121 | + | 0.0299121i | 0.721905 | − | 0.691993i | \(-0.243267\pi\) |
−0.691993 | + | 0.721905i | \(0.743267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.8396 | −0.656072 | −0.328036 | − | 0.944665i | \(-0.606387\pi\) | ||||
−0.328036 | + | 0.944665i | \(0.606387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.37169 | 0.273767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.8334 | − | 11.8334i | −0.599977 | − | 0.599977i | 0.340329 | − | 0.940306i | \(-0.389462\pi\) |
−0.940306 | + | 0.340329i | \(0.889462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.536345 | −0.0271241 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.82889 | − | 4.82889i | 0.242968 | − | 0.242968i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.8898 | − | 19.8898i | −0.998238 | − | 0.998238i | 0.00176051 | − | 0.999998i | \(-0.499440\pi\) |
−0.999998 | + | 0.00176051i | \(0.999440\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.44474i | 0.122084i | 0.998135 | + | 0.0610422i | \(0.0194424\pi\) | ||||
−0.998135 | + | 0.0610422i | \(0.980558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.45738 | − | 1.45738i | 0.0725975 | − | 0.0725975i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.79836i | − | 0.188278i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.1151i | − | 1.09352i | −0.837289 | − | 0.546760i | \(-0.815861\pi\) | ||
0.837289 | − | 0.546760i | \(-0.184139\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.00558 | + | 5.00558i | −0.246309 | + | 0.246309i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.5855i | − | 1.01050i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0163 | + | 13.0163i | 0.635887 | + | 0.635887i | 0.949538 | − | 0.313651i | \(-0.101552\pi\) |
−0.313651 | + | 0.949538i | \(0.601552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.64300 | + | 7.64300i | −0.372497 | + | 0.372497i | −0.868386 | − | 0.495889i | \(-0.834842\pi\) |
0.495889 | + | 0.868386i | \(0.334842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.59114 | −0.125689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.14637 | − | 3.14637i | −0.152263 | − | 0.152263i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.83332 | 0.232813 | 0.116406 | − | 0.993202i | \(-0.462862\pi\) | ||||
0.116406 | + | 0.993202i | \(0.462862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.03612 | −0.145906 | −0.0729532 | − | 0.997335i | \(-0.523242\pi\) | ||||
−0.0729532 | + | 0.997335i | \(0.523242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.6577 | 1.27230 | 0.636151 | − | 0.771564i | \(-0.280525\pi\) | ||||
0.636151 | + | 0.771564i | \(0.280525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.45513 | − | 2.45513i | 0.116647 | − | 0.116647i | −0.646374 | − | 0.763021i | \(-0.723715\pi\) |
0.763021 | + | 0.646374i | \(0.223715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.2499 | + | 24.2499i | 1.14955 | + | 1.14955i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.41421i | − | 0.0667409i | −0.999443 | − | 0.0333704i | \(-0.989376\pi\) | ||
0.999443 | − | 0.0333704i | \(-0.0106241\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0361 | − | 21.0361i | 0.990552 | − | 0.990552i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.41444i | − | 0.113191i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.78623i | − | 0.223890i | −0.993714 | − | 0.111945i | \(-0.964292\pi\) | ||
0.993714 | − | 0.111945i | \(-0.0357081\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5258 | − | 14.5258i | 0.676535 | − | 0.676535i | −0.282679 | − | 0.959214i | \(-0.591223\pi\) |
0.959214 | + | 0.282679i | \(0.0912233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.17092i | − | 0.0544174i | −0.999630 | − | 0.0272087i | \(-0.991338\pi\) | ||
0.999630 | − | 0.0272087i | \(-0.00866187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.38392 | − | 1.38392i | −0.0640400 | − | 0.0640400i | 0.674361 | − | 0.738401i | \(-0.264419\pi\) |
−0.738401 | + | 0.674361i | \(0.764419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.14637 | + | 4.14637i | −0.191461 | + | 0.191461i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.0631 | −1.24436 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.4969 | 0.936527 | 0.468264 | − | 0.883589i | \(-0.344880\pi\) | ||||
0.468264 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70727 | −0.0778448 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.3948 | + | 23.3948i | 1.06230 | + | 1.06230i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7073 | 1.07428 | 0.537139 | − | 0.843493i | \(-0.319505\pi\) | ||||
0.537139 | + | 0.843493i | \(0.319505\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.07121 | + | 1.07121i | −0.0483431 | + | 0.0483431i | −0.730865 | − | 0.682522i | \(-0.760883\pi\) |
0.682522 | + | 0.730865i | \(0.260883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.04912 | + | 8.04912i | 0.362514 | + | 0.362514i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 10.0762i | − | 0.451979i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.53948 | + | 6.53948i | −0.292747 | + | 0.292747i | −0.838165 | − | 0.545417i | \(-0.816371\pi\) |
0.545417 | + | 0.838165i | \(0.316371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.6270i | − | 0.919711i | −0.887994 | − | 0.459855i | \(-0.847901\pi\) | ||
0.887994 | − | 0.459855i | \(-0.152099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.585462i | − | 0.0260527i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.11679 | − | 3.11679i | 0.138149 | − | 0.138149i | −0.634650 | − | 0.772800i | \(-0.718856\pi\) |
0.772800 | + | 0.634650i | \(0.218856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.66442i | − | 0.250579i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.42469 | − | 8.42469i | −0.371236 | − | 0.371236i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.15792 | + | 6.15792i | −0.270825 | + | 0.270825i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.5729 | 1.29561 | 0.647805 | − | 0.761806i | \(-0.275687\pi\) | ||||
0.647805 | + | 0.761806i | \(0.275687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.46365 | + | 3.46365i | 0.151455 | + | 0.151455i | 0.778768 | − | 0.627313i | \(-0.215845\pi\) |
−0.627313 | + | 0.778768i | \(0.715845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.42377 | −0.192702 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9572 | 0.998137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.45521 | − | 9.45521i | −0.409551 | − | 0.409551i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.95715 | 0.257550 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.89918 | + | 1.89918i | −0.0818035 | + | 0.0818035i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8438 | − | 21.8438i | −0.939137 | − | 0.939137i | 0.0591142 | − | 0.998251i | \(-0.481172\pi\) |
−0.998251 | + | 0.0591142i | \(0.981172\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.82843i | − | 0.121157i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.89648 | − | 1.89648i | 0.0810876 | − | 0.0810876i | −0.665400 | − | 0.746487i | \(-0.731739\pi\) |
0.746487 | + | 0.665400i | \(0.231739\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.41454i | 0.145201i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.2695 | − | 31.2695i | 1.32493 | − | 1.32493i | 0.415201 | − | 0.909730i | \(-0.363711\pi\) |
0.909730 | − | 0.415201i | \(-0.136289\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1642i | 0.514491i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.2288 | + | 31.2288i | 1.31614 | + | 1.31614i | 0.916807 | + | 0.399330i | \(0.130757\pi\) |
0.399330 | + | 0.916807i | \(0.369243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.78623 | − | 6.78623i | 0.285499 | − | 0.285499i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.94055 | 0.207119 | 0.103559 | − | 0.994623i | \(-0.466977\pi\) | ||||
0.103559 | + | 0.994623i | \(0.466977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.1396 | − | 25.1396i | −1.05206 | − | 1.05206i | −0.998568 | − | 0.0534928i | \(-0.982965\pi\) |
−0.0534928 | − | 0.998568i | \(-0.517035\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.206992 | −0.00863217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.1579 | −1.50527 | −0.752637 | − | 0.658436i | \(-0.771218\pi\) | ||||
−0.752637 | + | 0.658436i | \(0.771218\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.27806 | + | 7.27806i | 0.301945 | + | 0.301945i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.74338 | 0.113619 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.8091 | + | 11.8091i | −0.487412 | + | 0.487412i | −0.907489 | − | 0.420076i | \(-0.862003\pi\) |
0.420076 | + | 0.907489i | \(0.362003\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.3603i | − | 0.466514i | −0.972415 | − | 0.233257i | \(-0.925062\pi\) | ||
0.972415 | − | 0.233257i | \(-0.0749383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.66442 | + | 3.66442i | −0.150227 | + | 0.150227i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.8449i | 0.688266i | 0.938921 | + | 0.344133i | \(0.111827\pi\) | ||||
−0.938921 | + | 0.344133i | \(0.888173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.0722i | − | 0.655600i | −0.944747 | − | 0.327800i | \(-0.893693\pi\) | ||
0.944747 | − | 0.327800i | \(-0.106307\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.35454 | − | 5.35454i | 0.217693 | − | 0.217693i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.99327i | − | 0.283848i | −0.989878 | − | 0.141924i | \(-0.954671\pi\) | ||
0.989878 | − | 0.141924i | \(-0.0453289\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.76783 | + | 2.76783i | 0.111975 | + | 0.111975i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.97858 | − | 5.97858i | 0.241472 | − | 0.241472i | −0.575987 | − | 0.817459i | \(-0.695382\pi\) |
0.817459 | + | 0.575987i | \(0.195382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.59695 | 0.346100 | 0.173050 | − | 0.984913i | \(-0.444638\pi\) | ||||
0.173050 | + | 0.984913i | \(0.444638\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.70727 | − | 9.70727i | −0.390168 | − | 0.390168i | 0.484579 | − | 0.874747i | \(-0.338973\pi\) |
−0.874747 | + | 0.484579i | \(0.838973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.1473 | −0.686990 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.59114 | + | 2.59114i | 0.103315 | + | 0.103315i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4935 | −0.815833 | −0.407917 | − | 0.913019i | \(-0.633745\pi\) | ||||
−0.407917 | + | 0.913019i | \(0.633745\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.1533 | − | 24.1533i | 0.958494 | − | 0.958494i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.853635 | + | 0.853635i | 0.0338222 | + | 0.0338222i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.04054i | − | 0.238587i | −0.992859 | − | 0.119294i | \(-0.961937\pi\) | ||
0.992859 | − | 0.119294i | \(-0.0380630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.12181 | + | 7.12181i | −0.280857 | + | 0.280857i | −0.833451 | − | 0.552594i | \(-0.813638\pi\) |
0.552594 | + | 0.833451i | \(0.313638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.6676i | − | 0.537327i | −0.963234 | − | 0.268664i | \(-0.913418\pi\) | ||
0.963234 | − | 0.268664i | \(-0.0865820\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.0130i | − | 0.746326i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.2893 | − | 24.2893i | 0.950514 | − | 0.950514i | −0.0483179 | − | 0.998832i | \(-0.515386\pi\) |
0.998832 | + | 0.0483179i | \(0.0153861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.58546i | − | 0.179169i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.4301 | + | 19.4301i | 0.756890 | + | 0.756890i | 0.975755 | − | 0.218865i | \(-0.0702354\pi\) |
−0.218865 | + | 0.975755i | \(0.570235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.34713 | + | 7.34713i | −0.285770 | + | 0.285770i | −0.835405 | − | 0.549635i | \(-0.814767\pi\) |
0.549635 | + | 0.835405i | \(0.314767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.643000 | + | 0.643000i | 0.0248971 | + | 0.0248971i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9510 | 0.461364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.15792 | 0.0831818 | 0.0415909 | − | 0.999135i | \(-0.486757\pi\) | ||||
0.0415909 | + | 0.999135i | \(0.486757\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3053 | + | 29.3053i | 1.12629 | + | 1.12629i | 0.990775 | + | 0.135519i | \(0.0432700\pi\) |
0.135519 | + | 0.990775i | \(0.456730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.5426 | −0.634847 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.312705 | + | 0.312705i | −0.0119653 | + | 0.0119653i | −0.713064 | − | 0.701099i | \(-0.752693\pi\) |
0.701099 | + | 0.713064i | \(0.252693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.1151 | + | 22.1151i | 0.844974 | + | 0.844974i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.23308i | − | 0.0469767i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9572 | + | 11.9572i | −0.454872 | + | 0.454872i | −0.896968 | − | 0.442096i | \(-0.854235\pi\) |
0.442096 | + | 0.896968i | \(0.354235\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.31279i | 0.277390i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.7005i | 1.08711i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.8557 | + | 31.8557i | −1.20317 | + | 1.20317i | −0.229979 | + | 0.973196i | \(0.573866\pi\) |
−0.973196 | + | 0.229979i | \(0.926134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.206992 | + | 0.206992i | 0.00778474 | + | 0.00778474i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3717 | − | 16.3717i | 0.614852 | − | 0.614852i | −0.329355 | − | 0.944206i | \(-0.606831\pi\) |
0.944206 | + | 0.329355i | \(0.106831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.353391 | −0.0132346 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.58546 | + | 4.58546i | 0.171487 | + | 0.171487i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.0036 | 1.67835 | 0.839175 | − | 0.543861i | \(-0.183038\pi\) | ||||
0.839175 | + | 0.543861i | \(0.183038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.95715 | 0.221856 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.10640 | + | 3.10640i | 0.115369 | + | 0.115369i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.6283 | 1.13594 | 0.567971 | − | 0.823049i | \(-0.307729\pi\) | ||||
0.567971 | + | 0.823049i | \(0.307729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4617 | − | 18.4617i | 0.682831 | − | 0.682831i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.3534 | − | 23.3534i | −0.862578 | − | 0.862578i | 0.129059 | − | 0.991637i | \(-0.458804\pi\) |
−0.991637 | + | 0.129059i | \(0.958804\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 15.7494i | − | 0.580136i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.93260 | + | 8.93260i | −0.328591 | + | 0.328591i | −0.852050 | − | 0.523460i | \(-0.824641\pi\) |
0.523460 | + | 0.852050i | \(0.324641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.5823i | − | 0.681717i | −0.940115 | − | 0.340858i | \(-0.889282\pi\) | ||
0.940115 | − | 0.340858i | \(-0.110718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 26.3587i | − | 0.965708i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.10617 | + | 2.10617i | −0.0769579 | + | 0.0769579i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.9865i | − | 1.67807i | −0.544075 | − | 0.839036i | \(-0.683119\pi\) | ||
0.544075 | − | 0.839036i | \(-0.316881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.2643 | − | 21.2643i | −0.773886 | − | 0.773886i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.6283 | + | 17.6283i | −0.640712 | + | 0.640712i | −0.950730 | − | 0.310019i | \(-0.899665\pi\) |
0.310019 | + | 0.950730i | \(0.399665\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.3291 | −0.736928 | −0.368464 | − | 0.929642i | \(-0.620116\pi\) | ||||
−0.368464 | + | 0.929642i | \(0.620116\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | + | 1.00000i | 0.0362024 | + | 0.0362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.54587 | −0.308574 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.5359 | −1.85843 | −0.929216 | − | 0.369538i | \(-0.879516\pi\) | ||||
−0.929216 | + | 0.369538i | \(0.879516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.6027 | + | 27.6027i | 0.992800 | + | 0.992800i | 0.999974 | − | 0.00717408i | \(-0.00228360\pi\) |
−0.00717408 | + | 0.999974i | \(0.502284\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.70727 | −0.0613269 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.1365 | + | 19.1365i | 0.684758 | + | 0.684758i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 24.9207i | − | 0.889457i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1709 | − | 15.1709i | 0.540785 | − | 0.540785i | −0.382974 | − | 0.923759i | \(-0.625100\pi\) |
0.923759 | + | 0.382974i | \(0.125100\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.79859i | 0.170618i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.37169i | − | 0.190754i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.27225 | + | 1.27225i | −0.0450654 | + | 0.0450654i | −0.729280 | − | 0.684215i | \(-0.760145\pi\) |
0.684215 | + | 0.729280i | \(0.260145\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.40154i | − | 0.297225i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.7578 | + | 10.7578i | 0.379633 | + | 0.379633i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.292731 | + | 0.292731i | −0.0103174 | + | 0.0103174i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.95963 | 0.279846 | 0.139923 | − | 0.990162i | \(-0.455315\pi\) | ||||
0.139923 | + | 0.990162i | \(0.455315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.5426 | − | 14.5426i | −0.510660 | − | 0.510660i | 0.404068 | − | 0.914729i | \(-0.367596\pi\) |
−0.914729 | + | 0.404068i | \(0.867596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42.9425 | 1.50421 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.76257 | + | 5.76257i | 0.201115 | + | 0.201115i | 0.800478 | − | 0.599363i | \(-0.204579\pi\) |
−0.599363 | + | 0.800478i | \(0.704579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.6644 | −1.59176 | −0.795881 | − | 0.605453i | \(-0.792992\pi\) | ||||
−0.795881 | + | 0.605453i | \(0.792992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2894 | + | 11.2894i | −0.392570 | + | 0.392570i | −0.875602 | − | 0.483033i | \(-0.839535\pi\) |
0.483033 | + | 0.875602i | \(0.339535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.2614 | − | 21.2614i | −0.738440 | − | 0.738440i | 0.233836 | − | 0.972276i | \(-0.424872\pi\) |
−0.972276 | + | 0.233836i | \(0.924872\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.59114i | − | 0.0897776i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.82908 | − | 2.82908i | 0.0979042 | − | 0.0979042i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.7277i | 0.404885i | 0.979294 | + | 0.202442i | \(0.0648879\pi\) | ||||
−0.979294 | + | 0.202442i | \(0.935112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.70054i | 0.334501i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.3237 | + | 16.3237i | −0.561553 | + | 0.561553i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.78623i | 0.130096i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.206992 | + | 0.206992i | 0.00709560 | + | 0.00709560i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0968 | − | 38.0968i | 1.30441 | − | 1.30441i | 0.379021 | − | 0.925388i | \(-0.376261\pi\) |
0.925388 | − | 0.379021i | \(-0.123739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.9379 | 1.43257 | 0.716285 | − | 0.697808i | \(-0.245841\pi\) | ||||
0.716285 | + | 0.697808i | \(0.245841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2070 | + | 10.2070i | 0.348260 | + | 0.348260i | 0.859461 | − | 0.511201i | \(-0.170799\pi\) |
−0.511201 | + | 0.859461i | \(0.670799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.7636 | 0.570639 | 0.285319 | − | 0.958433i | \(-0.407900\pi\) | ||||
0.285319 | + | 0.958433i | \(0.407900\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.25662 | −0.314734 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.48482 | − | 6.48482i | −0.219983 | − | 0.219983i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.07896 | −0.239861 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.48528 | + | 8.48528i | −0.286855 | + | 0.286855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.7648 | − | 28.7648i | −0.971319 | − | 0.971319i | 0.0282815 | − | 0.999600i | \(-0.490997\pi\) |
−0.999600 | + | 0.0282815i | \(0.990997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.0581i | 1.28221i | 0.767453 | + | 0.641106i | \(0.221524\pi\) | ||||
−0.767453 | + | 0.641106i | \(0.778476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.3257 | + | 23.3257i | −0.784973 | + | 0.784973i | −0.980665 | − | 0.195693i | \(-0.937305\pi\) |
0.195693 | + | 0.980665i | \(0.437305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.2726i | 0.546382i | 0.961960 | + | 0.273191i | \(0.0880791\pi\) | ||||
−0.961960 | + | 0.273191i | \(0.911921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.0790i | 0.572810i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.7005i | 1.36047i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.30346 | + | 5.30346i | 0.176880 | + | 0.176880i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.87146 | + | 1.87146i | −0.0623475 | + | 0.0623475i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.9216 | 0.961386 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.16779 | + | 5.16779i | 0.171594 | + | 0.171594i | 0.787679 | − | 0.616086i | \(-0.211282\pi\) |
−0.616086 | + | 0.787679i | \(0.711282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.8030 | 0.589839 | 0.294919 | − | 0.955522i | \(-0.404707\pi\) | ||||
0.294919 | + | 0.955522i | \(0.404707\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.6447 | −0.914906 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.62121 | + | 1.62121i | 0.0535369 | + | 0.0535369i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.6577 | −0.483513 | −0.241756 | − | 0.970337i | \(-0.577723\pi\) | ||||
−0.241756 | + | 0.970337i | \(0.577723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.60138 | − | 8.60138i | 0.283118 | − | 0.283118i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | + | 1.00000i | 0.0328798 | + | 0.0328798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 13.4909i | − | 0.442621i | −0.975203 | − | 0.221310i | \(-0.928967\pi\) | ||
0.975203 | − | 0.221310i | \(-0.0710334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 13.9188i | − | 0.455193i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.8291i | − | 0.549782i | −0.961475 | − | 0.274891i | \(-0.911358\pi\) | ||
0.961475 | − | 0.274891i | \(-0.0886418\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.2355 | − | 41.2355i | 1.34424 | − | 1.34424i | 0.452450 | − | 0.891790i | \(-0.350550\pi\) |
0.891790 | − | 0.452450i | \(-0.149450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.29273i | 0.0746616i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.93414 | − | 2.93414i | −0.0953467 | − | 0.0953467i | 0.657824 | − | 0.753171i | \(-0.271477\pi\) |
−0.753171 | + | 0.657824i | \(0.771477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83535 | − | 4.83535i | 0.156962 | − | 0.156962i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.6582 | −0.798757 | −0.399378 | − | 0.916786i | \(-0.630774\pi\) | ||||
−0.399378 | + | 0.916786i | \(0.630774\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.96388 | + | 4.96388i | 0.160628 | + | 0.160628i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.6377 | −0.504968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0852 | 0.905975 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.82843 | + | 2.82843i | 0.0910503 | + | 0.0910503i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.9143 | 0.897664 | 0.448832 | − | 0.893616i | \(-0.351840\pi\) | ||||
0.448832 | + | 0.893616i | \(0.351840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.9813 | − | 24.9813i | 0.801687 | − | 0.801687i | −0.181672 | − | 0.983359i | \(-0.558151\pi\) |
0.983359 | + | 0.181672i | \(0.0581510\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.58546 | − | 2.58546i | −0.0828861 | − | 0.0828861i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.5279i | 1.26461i | 0.774720 | + | 0.632304i | \(0.217891\pi\) | ||||
−0.774720 | + | 0.632304i | \(0.782109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.5657 | − | 32.5657i | 1.04081 | − | 1.04081i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 48.6600i | − | 1.55201i | −0.630725 | − | 0.776006i | \(-0.717242\pi\) | ||
0.630725 | − | 0.776006i | \(-0.282758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 29.8715i | − | 0.951784i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.47481 | − | 1.47481i | 0.0468961 | − | 0.0468961i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.2070i | 1.15015i | 0.818099 | + | 0.575077i | \(0.195028\pi\) | ||||
−0.818099 | + | 0.575077i | \(0.804972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.30255 | − | 1.30255i | −0.0412935 | − | 0.0412935i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.9326 | − | 35.9326i | 1.13800 | − | 1.13800i | 0.149188 | − | 0.988809i | \(-0.452334\pi\) |
0.988809 | − | 0.149188i | \(-0.0476659\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4032.2.v.c.1583.1 | 12 | ||
3.2 | odd | 2 | inner | 4032.2.v.c.1583.6 | 12 | ||
4.3 | odd | 2 | 1008.2.v.c.323.1 | ✓ | 12 | ||
12.11 | even | 2 | 1008.2.v.c.323.6 | yes | 12 | ||
16.5 | even | 4 | 1008.2.v.c.827.6 | yes | 12 | ||
16.11 | odd | 4 | inner | 4032.2.v.c.3599.6 | 12 | ||
48.5 | odd | 4 | 1008.2.v.c.827.1 | yes | 12 | ||
48.11 | even | 4 | inner | 4032.2.v.c.3599.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.c.323.1 | ✓ | 12 | 4.3 | odd | 2 | ||
1008.2.v.c.323.6 | yes | 12 | 12.11 | even | 2 | ||
1008.2.v.c.827.1 | yes | 12 | 48.5 | odd | 4 | ||
1008.2.v.c.827.6 | yes | 12 | 16.5 | even | 4 | ||
4032.2.v.c.1583.1 | 12 | 1.1 | even | 1 | trivial | ||
4032.2.v.c.1583.6 | 12 | 3.2 | odd | 2 | inner | ||
4032.2.v.c.3599.1 | 12 | 48.11 | even | 4 | inner | ||
4032.2.v.c.3599.6 | 12 | 16.11 | odd | 4 | inner |