Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(223,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.j (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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 223.3 | ||
Root | \(-0.944649 + 1.05244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.223 |
Dual form | 896.2.j.g.671.3 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.28999 | − | 1.28999i | −0.744774 | − | 0.744774i | 0.228719 | − | 0.973493i | \(-0.426546\pi\) |
−0.973493 | + | 0.228719i | \(0.926546\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.599312 | + | 0.599312i | 0.268021 | + | 0.268021i | 0.828302 | − | 0.560282i | \(-0.189307\pi\) |
−0.560282 | + | 0.828302i | \(0.689307\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.152445 | + | 2.64136i | 0.0576187 | + | 0.998339i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.328129i | 0.109376i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | − | 2.00000i | −0.603023 | − | 0.603023i | 0.338091 | − | 0.941113i | \(-0.390219\pi\) |
−0.941113 | + | 0.338091i | \(0.890219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00197 | + | 1.00197i | −0.277897 | + | 0.277897i | −0.832269 | − | 0.554372i | \(-0.812959\pi\) |
0.554372 | + | 0.832269i | \(0.312959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.54621i | − | 0.399229i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.48134i | 1.57195i | 0.618255 | + | 0.785977i | \(0.287840\pi\) | ||||
−0.618255 | + | 0.785977i | \(0.712160\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.93134 | − | 3.93134i | −0.901912 | − | 0.901912i | 0.0936897 | − | 0.995601i | \(-0.470134\pi\) |
−0.995601 | + | 0.0936897i | \(0.970134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.21066 | − | 3.60396i | 0.700624 | − | 0.786449i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.40731 | −0.918988 | −0.459494 | − | 0.888181i | \(-0.651969\pi\) | ||||
−0.459494 | + | 0.888181i | \(0.651969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.28165i | − | 0.856330i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.44668 | + | 3.44668i | −0.663313 | + | 0.663313i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.241319 | − | 0.241319i | −0.0448119 | − | 0.0448119i | 0.684346 | − | 0.729158i | \(-0.260088\pi\) |
−0.729158 | + | 0.684346i | \(0.760088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.38529 | −0.608017 | −0.304008 | − | 0.952669i | \(-0.598325\pi\) | ||||
−0.304008 | + | 0.952669i | \(0.598325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.15994i | 0.898231i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.49163 | + | 1.67436i | −0.252132 | + | 0.283018i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.73544 | + | 2.73544i | −0.449704 | + | 0.449704i | −0.895256 | − | 0.445552i | \(-0.853007\pi\) |
0.445552 | + | 0.895256i | \(0.353007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.58506 | 0.413941 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.88941 | 0.763597 | 0.381799 | − | 0.924246i | \(-0.375305\pi\) | ||||
0.381799 | + | 0.924246i | \(0.375305\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.40731 | + | 4.40731i | 0.672109 | + | 0.672109i | 0.958202 | − | 0.286093i | \(-0.0923566\pi\) |
−0.286093 | + | 0.958202i | \(0.592357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.196652 | + | 0.196652i | −0.0293151 | + | 0.0293151i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.45461 | −1.37910 | −0.689548 | − | 0.724240i | \(-0.742191\pi\) | ||||
−0.689548 | + | 0.724240i | \(0.742191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95352 | + | 0.805321i | −0.993360 | + | 0.115046i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.36083 | − | 8.36083i | 1.17075 | − | 1.17075i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.21808 | + | 3.21808i | −0.442037 | + | 0.442037i | −0.892696 | − | 0.450659i | \(-0.851189\pi\) |
0.450659 | + | 0.892696i | \(0.351189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.39725i | − | 0.323245i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.1428i | 1.34344i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.35137 | − | 1.35137i | 0.175933 | − | 0.175933i | −0.613647 | − | 0.789580i | \(-0.710298\pi\) |
0.789580 | + | 0.613647i | \(0.210298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.84334 | + | 9.84334i | −1.26031 | + | 1.26031i | −0.309369 | + | 0.950942i | \(0.600118\pi\) |
−0.950942 | + | 0.309369i | \(0.899882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.866705 | + | 0.0500215i | −0.109195 | + | 0.00630211i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.20099 | −0.148964 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.71220 | + | 8.71220i | −1.06436 | + | 1.06436i | −0.0665840 | + | 0.997781i | \(0.521210\pi\) |
−0.997781 | + | 0.0665840i | \(0.978790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.68537 | + | 5.68537i | 0.684438 | + | 0.684438i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2855 | 1.45802 | 0.729011 | − | 0.684502i | \(-0.239980\pi\) | ||||
0.729011 | + | 0.684502i | \(0.239980\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.805321 | −0.0942557 | −0.0471279 | − | 0.998889i | \(-0.515007\pi\) | ||||
−0.0471279 | + | 0.998889i | \(0.515007\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.52327 | + | 5.52327i | −0.637772 | + | 0.637772i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.97782 | − | 5.58760i | 0.567276 | − | 0.636766i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7681i | 1.21151i | 0.795651 | + | 0.605756i | \(0.207129\pi\) | ||||
−0.795651 | + | 0.605756i | \(0.792871\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.87672 | 1.09741 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.76738 | + | 5.76738i | 0.633052 | + | 0.633052i | 0.948832 | − | 0.315780i | \(-0.102266\pi\) |
−0.315780 | + | 0.948832i | \(0.602266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.88434 | + | 3.88434i | −0.421316 | + | 0.421316i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.622597i | 0.0667494i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3281 | −1.41278 | −0.706389 | − | 0.707824i | \(-0.749677\pi\) | ||||
−0.706389 | + | 0.707824i | \(0.749677\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.79931 | − | 2.49382i | −0.293448 | − | 0.261423i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.36698 | + | 4.36698i | 0.452835 | + | 0.452835i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.71220i | − | 0.483462i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.8360i | − | 1.10022i | −0.835091 | − | 0.550112i | \(-0.814585\pi\) | ||
0.835091 | − | 0.550112i | \(-0.185415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.656257 | − | 0.656257i | 0.0659564 | − | 0.0659564i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.47936 | + | 5.47936i | 0.545217 | + | 0.545217i | 0.925054 | − | 0.379837i | \(-0.124020\pi\) |
−0.379837 | + | 0.925054i | \(0.624020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.5535i | − | 1.13840i | −0.822200 | − | 0.569199i | \(-0.807254\pi\) | ||
0.822200 | − | 0.569199i | \(-0.192746\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.08409 | − | 0.235711i | 0.398566 | − | 0.0230031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.86110 | + | 4.86110i | 0.469941 | + | 0.469941i | 0.901895 | − | 0.431955i | \(-0.142176\pi\) |
−0.431955 | + | 0.901895i | \(0.642176\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0792 | − | 10.0792i | −0.965411 | − | 0.965411i | 0.0340107 | − | 0.999421i | \(-0.489172\pi\) |
−0.999421 | + | 0.0340107i | \(0.989172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.05736 | 0.669855 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.05034 | −0.286952 | −0.143476 | − | 0.989654i | \(-0.545828\pi\) | ||||
−0.143476 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.64136 | − | 2.64136i | −0.246308 | − | 0.246308i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.328776 | − | 0.328776i | −0.0303954 | − | 0.0303954i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.1195 | + | 0.988045i | −1.56934 | + | 0.0905739i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.00000i | − | 0.272727i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.30727 | − | 6.30727i | −0.568707 | − | 0.568707i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.56261 | − | 5.56261i | 0.497535 | − | 0.497535i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.01709i | − | 0.800137i | −0.916485 | − | 0.400069i | \(-0.868986\pi\) | ||
0.916485 | − | 0.400069i | \(-0.131014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 11.3707i | − | 1.00114i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.484665 | − | 0.484665i | −0.0423454 | − | 0.0423454i | 0.685617 | − | 0.727962i | \(-0.259532\pi\) |
−0.727962 | + | 0.685617i | \(0.759532\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.78476 | − | 10.9834i | 0.848446 | − | 0.952380i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.13127 | −0.355563 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.1466i | − | 1.46493i | −0.680803 | − | 0.732467i | \(-0.738369\pi\) | ||
0.680803 | − | 0.732467i | \(-0.261631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.13391 | − | 7.13391i | 0.605090 | − | 0.605090i | −0.336568 | − | 0.941659i | \(-0.609266\pi\) |
0.941659 | + | 0.336568i | \(0.109266\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1963 | + | 12.1963i | 1.02712 | + | 1.02712i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00789 | 0.335157 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.289251i | − | 0.0240210i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.0088 | + | 7.93109i | 0.825512 | + | 0.654146i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.85110 | − | 8.85110i | 0.725110 | − | 0.725110i | −0.244531 | − | 0.969641i | \(-0.578634\pi\) |
0.969641 | + | 0.244531i | \(0.0786341\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.73930 | −0.548436 | −0.274218 | − | 0.961668i | \(-0.588419\pi\) | ||||
−0.274218 | + | 0.961668i | \(0.588419\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.12671 | −0.171935 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.02885 | − | 2.02885i | −0.162961 | − | 0.162961i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.08606 | + | 5.08606i | −0.405912 | + | 0.405912i | −0.880310 | − | 0.474398i | \(-0.842666\pi\) |
0.474398 | + | 0.880310i | \(0.342666\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.30256 | 0.658436 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.671871 | − | 11.6413i | −0.0529509 | − | 0.917461i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.30489 | − | 6.30489i | 0.493837 | − | 0.493837i | −0.415676 | − | 0.909513i | \(-0.636455\pi\) |
0.909513 | + | 0.415676i | \(0.136455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.09242 | + | 3.09242i | −0.240744 | + | 0.240744i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.3480i | 1.26504i | 0.774543 | + | 0.632522i | \(0.217980\pi\) | ||||
−0.774543 | + | 0.632522i | \(0.782020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9921i | 0.845546i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.28999 | − | 1.28999i | 0.0986477 | − | 0.0986477i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.4446 | − | 11.4446i | 0.870119 | − | 0.870119i | −0.122366 | − | 0.992485i | \(-0.539048\pi\) |
0.992485 | + | 0.122366i | \(0.0390482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.3094 | − | 0.652715i | 0.854907 | − | 0.0493406i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.48650 | −0.262061 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.84347 | + | 8.84347i | −0.660992 | + | 0.660992i | −0.955614 | − | 0.294622i | \(-0.904806\pi\) |
0.294622 | + | 0.955614i | \(0.404806\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5233 | − | 17.5233i | −1.30250 | − | 1.30250i | −0.926703 | − | 0.375794i | \(-0.877370\pi\) |
−0.375794 | − | 0.926703i | \(-0.622630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.3956 | 1.87729 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.27877 | −0.241060 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9627 | − | 12.9627i | 0.947924 | − | 0.947924i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.62933 | − | 8.57847i | −0.700431 | − | 0.623992i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.50974i | − | 0.326313i | −0.986600 | − | 0.163157i | \(-0.947832\pi\) | ||
0.986600 | − | 0.163157i | \(-0.0521676\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9227 | 1.00217 | 0.501087 | − | 0.865397i | \(-0.332934\pi\) | ||||
0.501087 | + | 0.865397i | \(0.332934\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.54926 | + | 1.54926i | 0.110945 | + | 0.110945i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1598 | + | 10.1598i | −0.723859 | + | 0.723859i | −0.969389 | − | 0.245530i | \(-0.921038\pi\) |
0.245530 | + | 0.969389i | \(0.421038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.91320i | − | 0.702728i | −0.936239 | − | 0.351364i | \(-0.885718\pi\) | ||
0.936239 | − | 0.351364i | \(-0.114282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.4772 | 1.58542 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.600623 | − | 0.674198i | 0.0421554 | − | 0.0473194i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.93028 | + | 2.93028i | 0.204660 | + | 0.204660i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.44617i | − | 0.100515i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.7254i | 1.08775i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.53445 | − | 6.53445i | 0.449850 | − | 0.449850i | −0.445454 | − | 0.895305i | \(-0.646958\pi\) |
0.895305 | + | 0.445454i | \(0.146958\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.8481 | − | 15.8481i | −1.08590 | − | 1.08590i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.28271i | 0.360278i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.516070 | − | 8.94176i | −0.0350331 | − | 0.607007i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.03885 | + | 1.03885i | 0.0701992 | + | 0.0701992i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.49412 | − | 6.49412i | −0.436842 | − | 0.436842i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.27448 | 0.152311 | 0.0761553 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761553 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.40493 | 0.0936622 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.90856 | + | 8.90856i | 0.591282 | + | 0.591282i | 0.937978 | − | 0.346696i | \(-0.112696\pi\) |
−0.346696 | + | 0.937978i | \(0.612696\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.03915 | − | 6.03915i | −0.399078 | − | 0.399078i | 0.478830 | − | 0.877908i | \(-0.341061\pi\) |
−0.877908 | + | 0.478830i | \(0.841061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.6293 | + | 0.786606i | −0.896739 | + | 0.0517549i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.1926i | 1.71593i | 0.513707 | + | 0.857966i | \(0.328272\pi\) | ||||
−0.513707 | + | 0.857966i | \(0.671728\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.66626 | − | 5.66626i | −0.369626 | − | 0.369626i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8908 | − | 13.8908i | 0.902302 | − | 0.902302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.6122i | 1.33329i | 0.745375 | + | 0.666645i | \(0.232270\pi\) | ||||
−0.745375 | + | 0.666645i | \(0.767730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.710410i | − | 0.0457615i | −0.999738 | − | 0.0228808i | \(-0.992716\pi\) | ||
0.999738 | − | 0.0228808i | \(-0.00728381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.40080 | − | 2.40080i | −0.154011 | − | 0.154011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.64997 | − | 3.68469i | −0.297076 | − | 0.235406i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.87820 | 0.501278 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.8797i | − | 0.942961i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.98077 | − | 4.98077i | 0.314383 | − | 0.314383i | −0.532222 | − | 0.846605i | \(-0.678643\pi\) |
0.846605 | + | 0.532222i | \(0.178643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.81463 | + | 8.81463i | 0.554171 | + | 0.554171i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.0215 | 0.627571 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.21080i | − | 0.387419i | −0.981059 | − | 0.193710i | \(-0.937948\pi\) | ||
0.981059 | − | 0.193710i | \(-0.0620519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.64228 | − | 6.80827i | −0.474868 | − | 0.423045i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0791838 | − | 0.0791838i | 0.00490136 | − | 0.00490136i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.783397 | −0.0483063 | −0.0241532 | − | 0.999708i | \(-0.507689\pi\) | ||||
−0.0241532 | + | 0.999708i | \(0.507689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.85727 | −0.236950 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.1931 | + | 17.1931i | 1.05220 | + | 1.05220i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.3540 | − | 12.3540i | 0.753237 | − | 0.753237i | −0.221845 | − | 0.975082i | \(-0.571208\pi\) |
0.975082 | + | 0.221845i | \(0.0712079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.43477 | 0.390884 | 0.195442 | − | 0.980715i | \(-0.437386\pi\) | ||||
0.195442 | + | 0.980715i | \(0.437386\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.394079 | + | 6.82807i | 0.0238507 | + | 0.413254i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.56330 | + | 8.56330i | −0.516386 | + | 0.516386i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.22956 | − | 5.22956i | 0.314214 | − | 0.314214i | −0.532326 | − | 0.846540i | \(-0.678682\pi\) |
0.846540 | + | 0.532326i | \(0.178682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.11081i | − | 0.0665026i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8611i | 0.886539i | 0.896388 | + | 0.443270i | \(0.146182\pi\) | ||||
−0.896388 | + | 0.443270i | \(0.853818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.28739 | + | 8.28739i | −0.492634 | + | 0.492634i | −0.909135 | − | 0.416501i | \(-0.863256\pi\) |
0.416501 | + | 0.909135i | \(0.363256\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.07868 | + | 6.07868i | −0.360070 | + | 0.360070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.745364 | + | 12.9147i | 0.0439975 | + | 0.762329i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.0077 | −1.47104 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.9782 | + | 13.9782i | −0.819419 | + | 0.819419i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.11929 | + | 8.11929i | 0.474334 | + | 0.474334i | 0.903314 | − | 0.428980i | \(-0.141127\pi\) |
−0.428980 | + | 0.903314i | \(0.641127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.61978 | 0.0943075 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.7867 | 0.799986 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.41601 | − | 4.41601i | 0.255384 | − | 0.255384i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9694 | + | 12.3132i | −0.632266 | + | 0.709718i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 14.1366i | − | 0.812127i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.7985 | −0.675578 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.2527 | − | 14.2527i | −0.813442 | − | 0.813442i | 0.171706 | − | 0.985148i | \(-0.445072\pi\) |
−0.985148 | + | 0.171706i | \(0.945072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.9038 | + | 14.9038i | −0.847848 | + | 0.847848i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7171i | 0.721123i | 0.932735 | + | 0.360561i | \(0.117415\pi\) | ||||
−0.932735 | + | 0.360561i | \(0.882585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.7983 | −1.40168 | −0.700841 | − | 0.713317i | \(-0.747192\pi\) | ||||
−0.700841 | + | 0.713317i | \(0.747192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.549405 | − | 0.489448i | −0.0309555 | − | 0.0275773i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.43818 | + | 1.43818i | 0.0807761 | + | 0.0807761i | 0.746340 | − | 0.665564i | \(-0.231809\pi\) |
−0.665564 | + | 0.746340i | \(0.731809\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.965278i | 0.0540452i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 12.5415i | − | 0.699999i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4803 | − | 25.4803i | 1.41776 | − | 1.41776i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.29010 | + | 4.29010i | 0.237972 | + | 0.237972i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.0040i | 1.43803i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.44131 | − | 24.9730i | −0.0794617 | − | 1.37681i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.03647 | + | 1.03647i | 0.0569697 | + | 0.0569697i | 0.735018 | − | 0.678048i | \(-0.237174\pi\) |
−0.678048 | + | 0.735018i | \(0.737174\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.897577 | − | 0.897577i | −0.0491869 | − | 0.0491869i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.4427 | −0.570543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9109 | 0.921195 | 0.460598 | − | 0.887609i | \(-0.347635\pi\) | ||||
0.460598 | + | 0.887609i | \(0.347635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.93489 | + | 3.93489i | 0.213714 | + | 0.213714i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.77059 | + | 6.77059i | 0.366648 | + | 0.366648i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.18717 | − | 18.2440i | −0.172091 | − | 0.985081i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.81463i | 0.366887i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.32198 | − | 1.32198i | −0.0709676 | − | 0.0709676i | 0.670732 | − | 0.741700i | \(-0.265980\pi\) |
−0.741700 | + | 0.670732i | \(0.765980\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2528 | + | 17.2528i | −0.923520 | + | 0.923520i | −0.997276 | − | 0.0737567i | \(-0.976501\pi\) |
0.0737567 | + | 0.997276i | \(0.476501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6.90695i | − | 0.368666i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.98951i | − | 0.159116i | −0.996830 | − | 0.0795579i | \(-0.974649\pi\) | ||
0.996830 | − | 0.0795579i | \(-0.0253509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.36285 | + | 7.36285i | 0.390780 | + | 0.390780i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.3585 | + | 20.8094i | 1.23626 | + | 1.10135i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.62687 | 0.508087 | 0.254043 | − | 0.967193i | \(-0.418239\pi\) | ||||
0.254043 | + | 0.967193i | \(0.418239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9109i | 0.626889i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.86996 | + | 3.86996i | −0.203120 | + | 0.203120i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.482639 | − | 0.482639i | −0.0252625 | − | 0.0252625i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.38157 | −0.385315 | −0.192657 | − | 0.981266i | \(-0.561711\pi\) | ||||
−0.192657 | + | 0.981266i | \(0.561711\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.60436i | 0.0835194i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.99067 | − | 8.00952i | −0.466773 | − | 0.415833i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.46142 | + | 2.46142i | −0.127447 | + | 0.127447i | −0.767953 | − | 0.640506i | \(-0.778725\pi\) |
0.640506 | + | 0.767953i | \(0.278725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.3514 | −0.741101 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.483591 | 0.0249062 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4803 | + | 11.4803i | 0.589706 | + | 0.589706i | 0.937552 | − | 0.347846i | \(-0.113087\pi\) |
−0.347846 | + | 0.937552i | \(0.613087\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.6319 | + | 11.6319i | −0.595921 | + | 0.595921i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.164009 | 0.00838045 | 0.00419023 | − | 0.999991i | \(-0.498666\pi\) | ||||
0.00419023 | + | 0.999991i | \(0.498666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.33199 | − | 0.365448i | 0.322708 | − | 0.0186249i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.44617 | + | 1.44617i | −0.0735127 | + | 0.0735127i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.5501 | − | 15.5501i | 0.788420 | − | 0.788420i | −0.192815 | − | 0.981235i | \(-0.561762\pi\) |
0.981235 | + | 0.192815i | \(0.0617619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 28.5653i | − | 1.44461i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.25042i | 0.0630755i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.45348 | + | 6.45348i | −0.324710 | + | 0.324710i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2821 | − | 18.2821i | 0.917550 | − | 0.917550i | −0.0793007 | − | 0.996851i | \(-0.525269\pi\) |
0.996851 | + | 0.0793007i | \(0.0252687\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −26.7906 | + | 1.54621i | −1.34121 | + | 0.0774073i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.7378 | 0.785909 | 0.392955 | − | 0.919558i | \(-0.371453\pi\) | ||||
0.392955 | + | 0.919558i | \(0.371453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.39197 | − | 3.39197i | 0.168966 | − | 0.168966i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.91924 | + | 5.91924i | 0.294129 | + | 0.294129i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9418 | 0.542363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.8252 | −1.37587 | −0.687935 | − | 0.725773i | \(-0.741482\pi\) | ||||
−0.687935 | + | 0.725773i | \(0.741482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.1189 | + | 22.1189i | −1.09104 | + | 1.09104i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.77546 | + | 3.36344i | 0.185778 | + | 0.165504i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.91292i | 0.339342i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.4053 | −0.901311 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.380613 | − | 0.380613i | −0.0185942 | − | 0.0185942i | 0.697749 | − | 0.716343i | \(-0.254185\pi\) |
−0.716343 | + | 0.697749i | \(0.754185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.48089 | + | 5.48089i | −0.267122 | + | 0.267122i | −0.827940 | − | 0.560817i | \(-0.810487\pi\) |
0.560817 | + | 0.827940i | \(0.310487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.10233i | − | 0.150840i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.7508 | 1.34611 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.5003 | − | 24.4992i | −1.33083 | − | 1.18560i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.17012 | − | 5.17012i | −0.249616 | − | 0.249616i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.4850i | − | 0.890392i | −0.895433 | − | 0.445196i | \(-0.853134\pi\) | ||
0.895433 | − | 0.445196i | \(-0.146866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.9347i | 1.48663i | 0.668944 | + | 0.743313i | \(0.266746\pi\) | ||||
−0.668944 | + | 0.743313i | \(0.733254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.373130 | + | 0.373130i | −0.0178902 | + | 0.0178902i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.3267 | + | 17.3267i | 0.828846 | + | 0.828846i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.0317i | − | 0.956059i | −0.878344 | − | 0.478029i | \(-0.841351\pi\) | ||
0.878344 | − | 0.478029i | \(-0.158649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.264249 | − | 2.28165i | −0.0125833 | − | 0.108650i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.426694 | − | 0.426694i | −0.0202729 | − | 0.0202729i | 0.696898 | − | 0.717171i | \(-0.254563\pi\) |
−0.717171 | + | 0.696898i | \(0.754563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.98770 | − | 7.98770i | −0.378653 | − | 0.378653i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.8356 | −1.08009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1266 | 0.619483 | 0.309741 | − | 0.950821i | \(-0.399758\pi\) | ||||
0.309741 | + | 0.950821i | \(0.399758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.77882 | − | 9.77882i | −0.460467 | − | 0.460467i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.69360 | + | 8.69360i | 0.408461 | + | 0.408461i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.183084 | − | 3.17224i | −0.00858313 | − | 0.148717i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.6449i | − | 0.731836i | −0.930647 | − | 0.365918i | \(-0.880755\pi\) | ||
0.930647 | − | 0.365918i | \(-0.119245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.3391 | − | 22.3391i | −1.04270 | − | 1.04270i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.3593 | + | 28.3593i | −1.32082 | + | 1.32082i | −0.407712 | + | 0.913111i | \(0.633673\pi\) |
−0.913111 | + | 0.407712i | \(0.866327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.1195i | − | 0.609716i | −0.952398 | − | 0.304858i | \(-0.901391\pi\) | ||
0.952398 | − | 0.304858i | \(-0.0986089\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.23437i | 0.242738i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.4475 | + | 28.4475i | 1.31639 | + | 1.31639i | 0.916610 | + | 0.399782i | \(0.130914\pi\) |
0.399782 | + | 0.916610i | \(0.369086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.3402 | − | 21.6839i | −1.12392 | − | 1.00127i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1219 | 0.604625 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 17.6293i | − | 0.810594i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.8326 | + | 16.8326i | −0.772334 | + | 0.772334i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.05594 | − | 1.05594i | −0.0483484 | − | 0.0483484i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.5612 | −1.53345 | −0.766725 | − | 0.641975i | \(-0.778115\pi\) | ||||
−0.766725 | + | 0.641975i | \(0.778115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.48168i | − | 0.249943i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.1504 | + | 15.8838i | −0.643865 | + | 0.722738i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.49412 | − | 6.49412i | 0.294883 | − | 0.294883i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.4268 | −0.789683 | −0.394841 | − | 0.918749i | \(-0.629200\pi\) | ||||
−0.394841 | + | 0.918749i | \(0.629200\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2664 | −0.735594 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.00947 | − | 4.00947i | −0.180945 | − | 0.180945i | 0.610823 | − | 0.791767i | \(-0.290839\pi\) |
−0.791767 | + | 0.610823i | \(0.790839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.56407 | − | 1.56407i | 0.0704423 | − | 0.0704423i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.786606 | 0.0353553 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.87286 | + | 32.4504i | 0.0840093 | + | 1.45560i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.2319 | + | 16.2319i | −0.726642 | + | 0.726642i | −0.969949 | − | 0.243308i | \(-0.921768\pi\) |
0.243308 | + | 0.969949i | \(0.421768\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.0886 | − | 21.0886i | 0.942171 | − | 0.942171i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.85332i | − | 0.0826356i | −0.999146 | − | 0.0413178i | \(-0.986844\pi\) | ||
0.999146 | − | 0.0413178i | \(-0.0131556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.56770i | 0.292259i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.1797 | − | 14.1797i | 0.629741 | − | 0.629741i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.64044 | + | 7.64044i | −0.338656 | + | 0.338656i | −0.855861 | − | 0.517205i | \(-0.826972\pi\) |
0.517205 | + | 0.855861i | \(0.326972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.122767 | − | 2.12714i | −0.00543089 | − | 0.0940991i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.1001 | 1.19650 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.92413 | − | 6.92413i | 0.305114 | − | 0.305114i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.9092 | + | 18.9092i | 0.831627 | + | 0.831627i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.5268 | −1.29608 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9055 | 1.48543 | 0.742713 | − | 0.669610i | \(-0.233539\pi\) | ||||
0.742713 | + | 0.669610i | \(0.233539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.20989 | − | 1.20989i | 0.0529047 | − | 0.0529047i | −0.680159 | − | 0.733064i | \(-0.738089\pi\) |
0.733064 | + | 0.680159i | \(0.238089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.4309 | − | 13.7469i | −0.673460 | − | 0.599965i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 21.9412i | − | 0.955775i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.57560 | −0.155461 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.443423 | + | 0.443423i | 0.0192429 | + | 0.0192429i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.89905 | + | 4.89905i | −0.212202 | + | 0.212202i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.82664i | 0.251907i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.8159 | 0.984579 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5177 | + | 12.2964i | 0.668394 | + | 0.529643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.39969 | + | 2.39969i | 0.103171 | + | 0.103171i | 0.756808 | − | 0.653637i | \(-0.226758\pi\) |
−0.653637 | + | 0.756808i | \(0.726758\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.2096i | 1.94013i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 12.0812i | − | 0.517500i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2048 | − | 14.2048i | 0.607355 | − | 0.607355i | −0.334899 | − | 0.942254i | \(-0.608702\pi\) |
0.942254 | + | 0.334899i | \(0.108702\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.22988 | − | 3.22988i | −0.137848 | − | 0.137848i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.89742i | 0.0808327i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.4425 | + | 1.64155i | −1.20950 | + | 0.0698057i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.22956 | + | 4.22956i | 0.179535 | + | 0.179535i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.9862 | + | 21.9862i | 0.931586 | + | 0.931586i | 0.997805 | − | 0.0662188i | \(-0.0210935\pi\) |
−0.0662188 | + | 0.997805i | \(0.521094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.83201 | −0.373554 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.4433 | −1.41198 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.2913 | − | 19.2913i | −0.813030 | − | 0.813030i | 0.172057 | − | 0.985087i | \(-0.444959\pi\) |
−0.985087 | + | 0.172057i | \(0.944959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.82810 | − | 1.82810i | −0.0769089 | − | 0.0769089i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.50565 | + | 26.0879i | 0.0632315 | + | 1.09559i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.17452i | 0.384616i | 0.981335 | + | 0.192308i | \(0.0615973\pi\) | ||||
−0.981335 | + | 0.192308i | \(0.938403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.7388 | + | 29.7388i | 1.24453 | + | 1.24453i | 0.958102 | + | 0.286426i | \(0.0924672\pi\) |
0.286426 | + | 0.958102i | \(0.407533\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.81750 | + | 5.81750i | −0.243029 | + | 0.243029i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.8706i | 0.786957i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.4855i | 1.06097i | 0.847693 | + | 0.530487i | \(0.177991\pi\) | ||||
−0.847693 | + | 0.530487i | \(0.822009\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.9600 | − | 17.9600i | −0.746394 | − | 0.746394i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.3545 | + | 16.1129i | −0.595525 | + | 0.668476i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.8723 | 0.533117 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.394079i | − | 0.0162932i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.3219 | + | 18.3219i | −0.756227 | + | 0.756227i | −0.975634 | − | 0.219406i | \(-0.929588\pi\) |
0.219406 | + | 0.975634i | \(0.429588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.3087 | + | 13.3087i | 0.548377 | + | 0.548377i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.2121 | 1.07822 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.4985i | − | 0.636449i | −0.948015 | − | 0.318225i | \(-0.896913\pi\) | ||
0.948015 | − | 0.318225i | \(-0.103087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.8521 | − | 9.66779i | −0.444892 | − | 0.396341i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.7879 | + | 12.7879i | −0.523374 | + | 0.523374i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4750 | −0.550574 | −0.275287 | − | 0.961362i | \(-0.588773\pi\) | ||||
−0.275287 | + | 0.961362i | \(0.588773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.365448 | 0.0149069 | 0.00745346 | − | 0.999972i | \(-0.497627\pi\) | ||||
0.00745346 | + | 0.999972i | \(0.497627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.85872 | − | 2.85872i | −0.116416 | − | 0.116416i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.79794 | − | 1.79794i | 0.0730965 | − | 0.0730965i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.31485 | −0.256312 | −0.128156 | − | 0.991754i | \(-0.540906\pi\) | ||||
−0.128156 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.64450 | + | 0.0949116i | −0.0666385 | + | 0.00384601i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.47326 | − | 9.47326i | 0.383247 | − | 0.383247i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.02472 | + | 7.02472i | −0.283726 | + | 0.283726i | −0.834593 | − | 0.550867i | \(-0.814297\pi\) |
0.550867 | + | 0.834593i | \(0.314297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.56005i | − | 0.304850i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.7832i | 1.36006i | 0.733184 | + | 0.680031i | \(0.238034\pi\) | ||||
−0.733184 | + | 0.680031i | \(0.761966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0472 | − | 19.0472i | 0.765570 | − | 0.765570i | −0.211753 | − | 0.977323i | \(-0.567917\pi\) |
0.977323 | + | 0.211753i | \(0.0679173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.1906 | − | 15.1906i | 0.609577 | − | 0.609577i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.03180 | − | 35.2043i | −0.0814024 | − | 1.41043i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.7408 | −0.589631 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.2855 | − | 20.2855i | 0.810125 | − | 0.810125i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.7293 | − | 17.7293i | −0.706914 | − | 0.706914i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.5097 | 1.29419 | 0.647096 | − | 0.762408i | \(-0.275983\pi\) | ||||
0.647096 | + | 0.762408i | \(0.275983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.8587 | −0.670073 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.40405 | − | 5.40405i | 0.214453 | − | 0.214453i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.16033 | − | 7.77415i | 0.244081 | − | 0.308023i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.03123i | 0.159473i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5907 | −0.615794 | −0.307897 | − | 0.951420i | \(-0.599625\pi\) | ||||
−0.307897 | + | 0.951420i | \(0.599625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.1182 | − | 12.1182i | −0.477896 | − | 0.477896i | 0.426562 | − | 0.904458i | \(-0.359725\pi\) |
−0.904458 | + | 0.426562i | \(0.859725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.81463 | − | 6.81463i | 0.268326 | − | 0.268326i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.1478i | 0.949350i | 0.880161 | + | 0.474675i | \(0.157434\pi\) | ||||
−0.880161 | + | 0.474675i | \(0.842566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.40548 | −0.212184 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.8690 | + | 12.2005i | −0.425991 | + | 0.478174i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.71220 | − | 7.71220i | −0.301802 | − | 0.301802i | 0.539917 | − | 0.841718i | \(-0.318456\pi\) |
−0.841718 | + | 0.539917i | \(0.818456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.580931i | − | 0.0226989i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.264249i | − | 0.0103093i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7175 | + | 20.7175i | −0.807041 | + | 0.807041i | −0.984185 | − | 0.177144i | \(-0.943314\pi\) |
0.177144 | + | 0.984185i | \(0.443314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.243222 | − | 0.243222i | −0.00946024 | − | 0.00946024i | 0.702361 | − | 0.711821i | \(-0.252129\pi\) |
−0.711821 | + | 0.702361i | \(0.752129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.7547i | 0.650697i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4466 | − | 0.718350i | 0.482659 | − | 0.0278564i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.06357 | + | 1.06357i | 0.0411816 | + | 0.0411816i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.93405 | − | 2.93405i | −0.113437 | − | 0.113437i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.3734 | 1.51999 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4244 | −0.594567 | −0.297284 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297284 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.7575 | + | 14.7575i | 0.568015 | + | 0.568015i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3926 | − | 13.3926i | −0.514721 | − | 0.514721i | 0.401248 | − | 0.915969i | \(-0.368576\pi\) |
−0.915969 | + | 0.401248i | \(0.868576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.6216 | − | 1.65188i | 1.09840 | − | 0.0633935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 22.9838i | − | 0.880743i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.23131 | + | 6.23131i | 0.238435 | + | 0.238435i | 0.816202 | − | 0.577767i | \(-0.196076\pi\) |
−0.577767 | + | 0.816202i | \(0.696076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.2762 | − | 10.2762i | 0.392632 | − | 0.392632i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.5808i | 0.594446i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6.44886i | − | 0.245682i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.85947 | − | 6.85947i | −0.260947 | − | 0.260947i | 0.564492 | − | 0.825439i | \(-0.309072\pi\) |
−0.825439 | + | 0.564492i | \(0.809072\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.83345 | + | 1.63337i | 0.0696471 | + | 0.0620465i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.55088 | 0.324353 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.6899i | 1.20034i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.7880 | − | 33.7880i | 1.27798 | − | 1.27798i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.666263 | − | 0.666263i | −0.0251644 | − | 0.0251644i | 0.694413 | − | 0.719577i | \(-0.255664\pi\) |
−0.719577 | + | 0.694413i | \(0.755664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.5079 | 0.811186 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.6188i | 0.550576i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6376 | + | 15.3082i | −0.512897 | + | 0.575726i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.0551 | + | 29.0551i | −1.09119 | + | 1.09119i | −0.0957864 | + | 0.995402i | \(0.530537\pi\) |
−0.995402 | + | 0.0957864i | \(0.969463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.53334 | −0.132511 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.9200 | 0.558760 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.40198 | + | 2.40198i | 0.0898289 | + | 0.0898289i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.5894 | − | 26.5894i | 0.992999 | − | 0.992999i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.2867 | 1.16680 | 0.583399 | − | 0.812186i | \(-0.301722\pi\) | ||||
0.583399 | + | 0.812186i | \(0.301722\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.5168 | − | 1.76126i | 1.13651 | − | 0.0655929i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.916419 | + | 0.916419i | −0.0340820 | + | 0.0340820i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.03325 | + | 1.03325i | −0.0383738 | + | 0.0383738i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8730i | 0.848313i | 0.905589 | + | 0.424157i | \(0.139429\pi\) | ||||
−0.905589 | + | 0.424157i | \(0.860571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 23.4362i | − | 0.868006i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.5653 | + | 28.5653i | −1.05652 | + | 1.05652i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.2886 | + | 13.2886i | −0.490825 | + | 0.490825i | −0.908566 | − | 0.417741i | \(-0.862822\pi\) |
0.417741 | + | 0.908566i | \(0.362822\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.24519 | + | 10.7516i | 0.0459297 | + | 0.396579i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.8488 | 1.28367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.3244 | − | 19.3244i | 0.710858 | − | 0.710858i | −0.255857 | − | 0.966715i | \(-0.582358\pi\) |
0.966715 | + | 0.255857i | \(0.0823575\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1628 | − | 10.1628i | −0.373338 | − | 0.373338i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.76335 | −0.0646911 | −0.0323455 | − | 0.999477i | \(-0.510298\pi\) | ||||
−0.0323455 | + | 0.999477i | \(0.510298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.6091 | 0.388689 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.89244 | + | 1.89244i | −0.0692408 | + | 0.0692408i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0989 | + | 13.5810i | −0.442083 | + | 0.496237i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.6805i | 1.63042i | 0.579169 | + | 0.815208i | \(0.303377\pi\) | ||||
−0.579169 | + | 0.815208i | \(0.696623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.8503 | −0.468289 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.03894 | − | 4.03894i | −0.146992 | − | 0.146992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.5033 | − | 36.5033i | 1.32674 | − | 1.32674i | 0.418535 | − | 0.908201i | \(-0.362544\pi\) |
0.908201 | − | 0.418535i | \(-0.137456\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 22.7415i | − | 0.825464i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.3290 | −1.49817 | −0.749087 | − | 0.662471i | \(-0.769508\pi\) | ||||
−0.749087 | + | 0.662471i | \(0.769508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.0862 | − | 28.1592i | 0.908181 | − | 1.01943i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.27456 | − | 1.27456i | −0.0460820 | − | 0.0460820i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.70807i | 0.0977828i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11.7612i | − | 0.424120i | −0.977257 | − | 0.212060i | \(-0.931983\pi\) | ||
0.977257 | − | 0.212060i | \(-0.0680171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.01185 | + | 8.01185i | −0.288540 | + | 0.288540i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.8247 | − | 22.8247i | −0.820949 | − | 0.820949i | 0.165296 | − | 0.986244i | \(-0.447142\pi\) |
−0.986244 | + | 0.165296i | \(0.947142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.4946i | 0.520663i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.07586 | + | 18.6410i | 0.0385962 | + | 0.668742i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.2219 | − | 19.2219i | −0.688697 | − | 0.688697i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.5710 | − | 24.5710i | −0.879220 | − | 0.879220i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.66350 | 0.0594486 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.09628 | −0.217585 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.2460 | + | 28.2460i | 1.00686 | + | 1.00686i | 0.999976 | + | 0.00688641i | \(0.00219203\pi\) |
0.00688641 | + | 0.999976i | \(0.497808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.01057 | + | 1.01057i | 0.0359773 | + | 0.0359773i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.465008 | − | 8.05702i | −0.0165338 | − | 0.286475i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 19.7255i | − | 0.700474i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.97582 | + | 4.97582i | 0.176474 | + | 0.176474i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.7459 | − | 34.7459i | 1.23076 | − | 1.23076i | 0.267092 | − | 0.963671i | \(-0.413937\pi\) |
0.963671 | − | 0.267092i | \(-0.0860628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 61.2785i | − | 2.16788i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 4.37334i | − | 0.154524i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.61064 | + | 1.61064i | 0.0568383 | + | 0.0568383i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.57410 | − | 7.37942i | 0.231707 | − | 0.260090i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.8730 | −1.12198 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.316372i | 0.0111231i | 0.999985 | + | 0.00556153i | \(0.00177030\pi\) | ||||
−0.999985 | + | 0.00556153i | \(0.998230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0273 | − | 16.0273i | 0.562795 | − | 0.562795i | −0.367305 | − | 0.930100i | \(-0.619720\pi\) |
0.930100 | + | 0.367305i | \(0.119720\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.30076 | − | 8.30076i | −0.291120 | − | 0.291120i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.55719 | 0.264717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 34.6533i | − | 1.21237i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.818294 | − | 0.918535i | 0.0285935 | − | 0.0320962i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.9318 | + | 20.9318i | −0.730523 | + | 0.730523i | −0.970723 | − | 0.240200i | \(-0.922787\pi\) |
0.240200 | + | 0.970723i | \(0.422787\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.9383 | −1.53159 | −0.765796 | − | 0.643084i | \(-0.777655\pi\) | ||||
−0.765796 | + | 0.643084i | \(0.777655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22.0931 | 0.769182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.6799 | − | 31.6799i | −1.10162 | − | 1.10162i | −0.994216 | − | 0.107401i | \(-0.965747\pi\) |
−0.107401 | − | 0.994216i | \(-0.534253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.78620 | + | 8.78620i | −0.305157 | + | 0.305157i | −0.843028 | − | 0.537870i | \(-0.819229\pi\) |
0.537870 | + | 0.843028i | \(0.319229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4921 | −0.468037 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.21956 | − | 45.0681i | −0.180847 | − | 1.56152i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.79753 | + | 9.79753i | −0.339058 | + | 0.339058i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.6680 | − | 11.6680i | 0.403306 | − | 0.403306i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 15.1931i | − | 0.524523i | −0.964997 | − | 0.262261i | \(-0.915532\pi\) | ||
0.964997 | − | 0.262261i | \(-0.0844682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.8835i | − | 0.995984i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.1706 | − | 19.1706i | 0.660271 | − | 0.660271i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.58770 | + | 6.58770i | −0.226624 | + | 0.226624i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.92407 | − | 0.457334i | 0.272274 | − | 0.0157142i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.3812 | 0.733802 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0559 | − | 12.0559i | 0.413272 | − | 0.413272i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.19631 | − | 1.19631i | −0.0409610 | − | 0.0409610i | 0.686330 | − | 0.727291i | \(-0.259221\pi\) |
−0.727291 | + | 0.686330i | \(0.759221\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.54621 | 0.0528792 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.4253 | 0.663555 | 0.331778 | − | 0.943358i | \(-0.392352\pi\) | ||||
0.331778 | + | 0.943358i | \(0.392352\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.38850 | − | 4.38850i | 0.149734 | − | 0.149734i | −0.628265 | − | 0.777999i | \(-0.716235\pi\) |
0.777999 | + | 0.628265i | \(0.216235\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.6982 | − | 17.6213i | 0.534994 | − | 0.600531i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 25.3161i | − | 0.861770i | −0.902407 | − | 0.430885i | \(-0.858201\pi\) | ||
0.902407 | − | 0.430885i | \(-0.141799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7178 | 0.466420 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.2596 | + | 32.2596i | 1.09559 | + | 1.09559i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.5363 | − | 21.5363i | 0.730569 | − | 0.730569i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 17.4588i | − | 0.591568i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.55559 | 0.120338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.5408 | + | 13.8448i | 0.525375 | + | 0.468041i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5883 | + | 14.5883i | 0.492612 | + | 0.492612i | 0.909128 | − | 0.416517i | \(-0.136749\pi\) |
−0.416517 | + | 0.909128i | \(0.636749\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 20.9476i | − | 0.706543i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12.5228i | − | 0.421904i | −0.977496 | − | 0.210952i | \(-0.932344\pi\) | ||
0.977496 | − | 0.210952i | \(-0.0676563\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9459 | + | 26.9459i | −0.906802 | + | 0.906802i | −0.996013 | − | 0.0892111i | \(-0.971565\pi\) |
0.0892111 | + | 0.996013i | \(0.471565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.08950 | − | 2.08950i | −0.0702378 | − | 0.0702378i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 19.2631i | − | 0.646790i | −0.946264 | − | 0.323395i | \(-0.895176\pi\) | ||
0.946264 | − | 0.323395i | \(-0.104824\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.8173 | − | 1.37461i | 0.798808 | − | 0.0461029i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.7534 | − | 19.7534i | −0.661765 | − | 0.661765i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.1693 | + | 37.1693i | 1.24382 | + | 1.24382i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.6000 | −0.354319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3932 | −0.380407 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.816937 | + | 0.816937i | 0.0272464 | + | 0.0272464i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.8575 | − | 20.8575i | −0.694863 | − | 0.694863i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.0342 | − | 1.73341i | 0.999475 | − | 0.0576843i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 21.0039i | − | 0.698192i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.21072 | + | 3.21072i | 0.106610 | + | 0.106610i | 0.758400 | − | 0.651790i | \(-0.225981\pi\) |
−0.651790 | + | 0.758400i | \(0.725981\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.79794 | + | 1.79794i | −0.0596338 | + | 0.0596338i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.2409i | 1.49890i | 0.662063 | + | 0.749448i | \(0.269681\pi\) | ||||
−0.662063 | + | 0.749448i | \(0.730319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.0695i | − | 0.763489i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.2199 | + | 15.2199i | 0.503153 | + | 0.503153i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.20629 | − | 1.35406i | 0.0398351 | − | 0.0447149i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.91404 | 0.0961253 | 0.0480626 | − | 0.998844i | \(-0.484695\pi\) | ||||
0.0480626 | + | 0.998844i | \(0.484695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.7715i | 1.21166i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.3097 | + | 12.3097i | −0.405180 | + | 0.405180i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.7122 | + | 11.7122i | 0.385095 | + | 0.385095i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.79102 | 0.124514 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.3476i | 0.930054i | 0.885296 | + | 0.465027i | \(0.153955\pi\) | ||||
−0.885296 | + | 0.465027i | \(0.846045\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.5027 | + | 24.1707i | 0.999684 | + | 0.792162i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.4049 | − | 16.4049i | 0.537073 | − | 0.537073i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.5374 | 0.508126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.1147 | −0.461108 | −0.230554 | − | 0.973060i | \(-0.574054\pi\) | ||||
−0.230554 | + | 0.973060i | \(0.574054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.9895 | + | 31.9895i | 1.04394 | + | 1.04394i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.1476 | + | 20.1476i | −0.656793 | + | 0.656793i | −0.954620 | − | 0.297827i | \(-0.903738\pi\) |
0.297827 | + | 0.954620i | \(0.403738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.5492 | −0.701737 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.629790 | − | 10.9122i | −0.0204871 | − | 0.354972i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.4197 | − | 20.4197i | 0.663552 | − | 0.663552i | −0.292663 | − | 0.956216i | \(-0.594542\pi\) |
0.956216 | + | 0.292663i | \(0.0945415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.806910 | − | 0.806910i | 0.0261934 | − | 0.0261934i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.71046i | − | 0.120320i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.38196i | − | 0.239125i | −0.992827 | − | 0.119563i | \(-0.961851\pi\) | ||
0.992827 | − | 0.119563i | \(-0.0381492\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.70274 | − | 2.70274i | 0.0874586 | − | 0.0874586i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.24519 | − | 1.24519i | 0.0402514 | − | 0.0402514i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.2903 | − | 2.61391i | 1.46250 | − | 0.0844075i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5398 | −0.630316 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.59507 | + | 1.59507i | −0.0514003 | + | 0.0514003i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.34402 | + | 8.34402i | 0.268603 | + | 0.268603i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.4068 | −1.52450 | −0.762250 | − | 0.647283i | \(-0.775905\pi\) | ||||
−0.762250 | + | 0.647283i | \(0.775905\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −65.7386 | −2.11183 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3328 | − | 14.3328i | 0.459960 | − | 0.459960i | −0.438682 | − | 0.898642i | \(-0.644555\pi\) |
0.898642 | + | 0.438682i | \(0.144555\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.9307 | + | 17.7557i | 0.638950 | + | 0.569221i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 11.0683i | − | 0.354470i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.59453 | −0.210978 | −0.105489 | − | 0.994420i | \(-0.533641\pi\) | ||||
−0.105489 | + | 0.994420i | \(0.533641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.6562 | + | 26.6562i | 0.851937 | + | 0.851937i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.30727 | − | 3.30727i | 0.105593 | − | 0.105593i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 37.5317i | − | 1.19707i | −0.801095 | − | 0.598537i | \(-0.795749\pi\) | ||
0.801095 | − | 0.598537i | \(-0.204251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1778 | −0.388018 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.3556 | + | 34.0741i | −0.966228 | + | 1.08459i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.4244 | − | 19.4244i | −0.617660 | − | 0.617660i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.8074i | 0.375076i | 0.982257 | + | 0.187538i | \(0.0600508\pi\) | ||||
−0.982257 | + | 0.187538i | \(0.939949\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.67407i | − | 0.0848591i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.94110 | − | 5.94110i | 0.188346 | − | 0.188346i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9885 | + | 16.9885i | 0.538032 | + | 0.538032i | 0.922950 | − | 0.384919i | \(-0.125771\pi\) |
−0.384919 | + | 0.922950i | \(0.625771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 18.8564i | − | 0.596589i |
(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 | 896.2.j.g.223.3 | 16 | ||
4.3 | odd | 2 | 896.2.j.h.223.6 | 16 | |||
7.6 | odd | 2 | inner | 896.2.j.g.223.6 | 16 | ||
8.3 | odd | 2 | 112.2.j.d.83.3 | yes | 16 | ||
8.5 | even | 2 | 448.2.j.d.111.6 | 16 | |||
16.3 | odd | 4 | 448.2.j.d.335.3 | 16 | |||
16.5 | even | 4 | 896.2.j.h.671.3 | 16 | |||
16.11 | odd | 4 | inner | 896.2.j.g.671.6 | 16 | ||
16.13 | even | 4 | 112.2.j.d.27.4 | yes | 16 | ||
28.27 | even | 2 | 896.2.j.h.223.3 | 16 | |||
56.3 | even | 6 | 784.2.w.e.19.4 | 32 | |||
56.11 | odd | 6 | 784.2.w.e.19.3 | 32 | |||
56.13 | odd | 2 | 448.2.j.d.111.3 | 16 | |||
56.19 | even | 6 | 784.2.w.e.227.7 | 32 | |||
56.27 | even | 2 | 112.2.j.d.83.4 | yes | 16 | ||
56.51 | odd | 6 | 784.2.w.e.227.8 | 32 | |||
112.13 | odd | 4 | 112.2.j.d.27.3 | ✓ | 16 | ||
112.27 | even | 4 | inner | 896.2.j.g.671.3 | 16 | ||
112.45 | odd | 12 | 784.2.w.e.411.8 | 32 | |||
112.61 | odd | 12 | 784.2.w.e.619.3 | 32 | |||
112.69 | odd | 4 | 896.2.j.h.671.6 | 16 | |||
112.83 | even | 4 | 448.2.j.d.335.6 | 16 | |||
112.93 | even | 12 | 784.2.w.e.619.4 | 32 | |||
112.109 | even | 12 | 784.2.w.e.411.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.3 | ✓ | 16 | 112.13 | odd | 4 | ||
112.2.j.d.27.4 | yes | 16 | 16.13 | even | 4 | ||
112.2.j.d.83.3 | yes | 16 | 8.3 | odd | 2 | ||
112.2.j.d.83.4 | yes | 16 | 56.27 | even | 2 | ||
448.2.j.d.111.3 | 16 | 56.13 | odd | 2 | |||
448.2.j.d.111.6 | 16 | 8.5 | even | 2 | |||
448.2.j.d.335.3 | 16 | 16.3 | odd | 4 | |||
448.2.j.d.335.6 | 16 | 112.83 | even | 4 | |||
784.2.w.e.19.3 | 32 | 56.11 | odd | 6 | |||
784.2.w.e.19.4 | 32 | 56.3 | even | 6 | |||
784.2.w.e.227.7 | 32 | 56.19 | even | 6 | |||
784.2.w.e.227.8 | 32 | 56.51 | odd | 6 | |||
784.2.w.e.411.7 | 32 | 112.109 | even | 12 | |||
784.2.w.e.411.8 | 32 | 112.45 | odd | 12 | |||
784.2.w.e.619.3 | 32 | 112.61 | odd | 12 | |||
784.2.w.e.619.4 | 32 | 112.93 | even | 12 | |||
896.2.j.g.223.3 | 16 | 1.1 | even | 1 | trivial | ||
896.2.j.g.223.6 | 16 | 7.6 | odd | 2 | inner | ||
896.2.j.g.671.3 | 16 | 112.27 | even | 4 | inner | ||
896.2.j.g.671.6 | 16 | 16.11 | odd | 4 | inner | ||
896.2.j.h.223.3 | 16 | 28.27 | even | 2 | |||
896.2.j.h.223.6 | 16 | 4.3 | odd | 2 | |||
896.2.j.h.671.3 | 16 | 16.5 | even | 4 | |||
896.2.j.h.671.6 | 16 | 112.69 | odd | 4 |