Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 227.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.227 |
Dual form | 784.2.w.d.411.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.258819 | + | 0.965926i | ||||
\(3\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | −0.896575 | + | 3.34607i | −0.400961 | + | 1.49641i | 0.410425 | + | 0.911894i | \(0.365380\pi\) |
−0.811386 | + | 0.584511i | \(0.801286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.866025 | + | 0.500000i | ||||
\(10\) | −4.24264 | − | 2.44949i | −1.34164 | − | 0.774597i | ||||
\(11\) | −1.36603 | + | 0.366025i | −0.411872 | + | 0.110361i | −0.458804 | − | 0.888537i | \(-0.651722\pi\) |
0.0469323 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | + | 2.44949i | −0.679366 | + | 0.679366i | −0.959857 | − | 0.280491i | \(-0.909503\pi\) |
0.280491 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 4.24264 | + | 2.44949i | 1.02899 | + | 0.594089i | 0.916696 | − | 0.399586i | \(-0.130846\pi\) |
0.112296 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(18\) | −1.09808 | − | 4.09808i | −0.258819 | − | 0.965926i | ||||
\(19\) | 1.79315 | − | 6.69213i | 0.411377 | − | 1.53528i | −0.380606 | − | 0.924737i | \(-0.624285\pi\) |
0.791983 | − | 0.610543i | \(-0.209049\pi\) | |||||||
\(20\) | 4.89898 | − | 4.89898i | 1.09545 | − | 1.09545i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.06218 | − | 3.50000i | −1.21244 | − | 0.700000i | ||||
\(26\) | −2.44949 | − | 4.24264i | −0.480384 | − | 0.832050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 3.00000i | −0.557086 | − | 0.557086i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.44949 | + | 4.24264i | −0.439941 | + | 0.762001i | −0.997684 | − | 0.0680129i | \(-0.978334\pi\) |
0.557743 | + | 0.830014i | \(0.311667\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.965926 | + | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.89898 | + | 4.89898i | −0.840168 | + | 0.840168i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −6.83013 | − | 1.83013i | −1.12287 | − | 0.300871i | −0.350823 | − | 0.936442i | \(-0.614098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 8.48528 | + | 4.89898i | 1.37649 | + | 0.794719i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.89898 | + | 8.48528i | 0.774597 | + | 1.34164i | ||||
\(41\) | 4.89898 | 0.765092 | 0.382546 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382546 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 5.00000i | −0.762493 | − | 0.762493i | 0.214280 | − | 0.976772i | \(-0.431260\pi\) |
−0.976772 | + | 0.214280i | \(0.931260\pi\) | |||||||
\(44\) | 2.73205 | + | 0.732051i | 0.411872 | + | 0.110361i | ||||
\(45\) | −2.68973 | − | 10.0382i | −0.400961 | − | 1.49641i | ||||
\(46\) | 5.46410 | − | 1.46410i | 0.805638 | − | 0.215870i | ||||
\(47\) | 2.44949 | + | 4.24264i | 0.357295 | + | 0.618853i | 0.987508 | − | 0.157569i | \(-0.0503658\pi\) |
−0.630213 | + | 0.776422i | \(0.717032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.00000 | − | 7.00000i | 0.989949 | − | 0.989949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.69213 | − | 1.79315i | 0.928032 | − | 0.248665i | ||||
\(53\) | −0.366025 | − | 1.36603i | −0.0502775 | − | 0.187638i | 0.936220 | − | 0.351414i | \(-0.114299\pi\) |
−0.986498 | + | 0.163776i | \(0.947632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.89898i | − | 0.660578i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.19615 | − | 3.00000i | 0.682288 | − | 0.393919i | ||||
\(59\) | −1.79315 | − | 6.69213i | −0.233448 | − | 0.871241i | −0.978842 | − | 0.204617i | \(-0.934405\pi\) |
0.745394 | − | 0.666624i | \(-0.232261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.34607 | − | 0.896575i | −0.428420 | − | 0.114795i | 0.0381645 | − | 0.999271i | \(-0.487849\pi\) |
−0.466584 | + | 0.884477i | \(0.654516\pi\) | |||||||
\(62\) | −4.89898 | − | 4.89898i | −0.622171 | − | 0.622171i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −6.00000 | − | 10.3923i | −0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.83013 | + | 6.83013i | 0.223586 | + | 0.834433i | 0.982966 | + | 0.183786i | \(0.0588354\pi\) |
−0.759381 | + | 0.650647i | \(0.774498\pi\) | |||||||
\(68\) | −4.89898 | − | 8.48528i | −0.594089 | − | 1.02899i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −2.19615 | + | 8.19615i | −0.258819 | + | 0.965926i | ||||
\(73\) | −4.89898 | + | 8.48528i | −0.573382 | + | 0.993127i | 0.422833 | + | 0.906208i | \(0.361036\pi\) |
−0.996215 | + | 0.0869195i | \(0.972298\pi\) | |||||||
\(74\) | 5.00000 | − | 8.66025i | 0.581238 | − | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.79796 | + | 9.79796i | −1.12390 | + | 1.12390i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46410 | − | 2.00000i | 0.389742 | − | 0.225018i | −0.292306 | − | 0.956325i | \(-0.594423\pi\) |
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | −13.3843 | + | 3.58630i | −1.49641 | + | 0.400961i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −1.79315 | + | 6.69213i | −0.198020 | + | 0.739022i | ||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | + | 12.0000i | −1.30158 | + | 1.30158i | ||||
\(86\) | 8.66025 | − | 5.00000i | 0.933859 | − | 0.539164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 14.6969 | 1.54919 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.69213 | + | 1.79315i | −0.690241 | + | 0.184949i | ||||
\(95\) | 20.7846 | + | 12.0000i | 2.13246 | + | 1.23117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | − | 3.00000i | 0.301511 | − | 0.301511i | ||||
\(100\) | 7.00000 | + | 12.1244i | 0.700000 | + | 1.21244i | ||||
\(101\) | −3.34607 | + | 0.896575i | −0.332946 | + | 0.0892126i | −0.421419 | − | 0.906866i | \(-0.638468\pi\) |
0.0884733 | + | 0.996079i | \(0.471801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.48528 | + | 4.89898i | −0.836080 | + | 0.482711i | −0.855930 | − | 0.517092i | \(-0.827014\pi\) |
0.0198501 | + | 0.999803i | \(0.493681\pi\) | |||||||
\(104\) | 9.79796i | 0.960769i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 1.09808 | − | 4.09808i | 0.106155 | − | 0.396176i | −0.892319 | − | 0.451406i | \(-0.850923\pi\) |
0.998474 | + | 0.0552301i | \(0.0175892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.56218 | + | 2.56218i | −0.915891 | + | 0.245412i | −0.685828 | − | 0.727764i | \(-0.740560\pi\) |
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(110\) | 6.69213 | + | 1.79315i | 0.638070 | + | 0.170970i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.3843 | − | 3.58630i | 1.24809 | − | 0.334424i | ||||
\(116\) | 2.19615 | + | 8.19615i | 0.203908 | + | 0.760994i | ||||
\(117\) | 2.68973 | − | 10.0382i | 0.248665 | − | 0.928032i | ||||
\(118\) | 9.79796 | 0.901975 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.79423 | + | 4.50000i | −0.708566 | + | 0.409091i | ||||
\(122\) | 2.44949 | − | 4.24264i | 0.221766 | − | 0.384111i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.48528 | − | 4.89898i | 0.762001 | − | 0.439941i | ||||
\(125\) | 4.89898 | − | 4.89898i | 0.438178 | − | 0.438178i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.965926 | + | 0.258819i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 16.3923 | − | 4.39230i | 1.43770 | − | 0.385231i | ||||
\(131\) | −3.58630 | + | 13.3843i | −0.313337 | + | 1.16939i | 0.612192 | + | 0.790710i | \(0.290288\pi\) |
−0.925528 | + | 0.378679i | \(0.876379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.3843 | − | 3.58630i | 1.14769 | − | 0.307523i | ||||
\(137\) | −6.92820 | − | 4.00000i | −0.591916 | − | 0.341743i | 0.173939 | − | 0.984757i | \(-0.444351\pi\) |
−0.765855 | + | 0.643013i | \(0.777684\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.89898 | + | 4.89898i | −0.415526 | + | 0.415526i | −0.883658 | − | 0.468132i | \(-0.844927\pi\) |
0.468132 | + | 0.883658i | \(0.344927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.732051 | + | 2.73205i | −0.0614323 | + | 0.229269i | ||||
\(143\) | 2.44949 | − | 4.24264i | 0.204837 | − | 0.354787i | ||||
\(144\) | −10.3923 | − | 6.00000i | −0.866025 | − | 0.500000i | ||||
\(145\) | 12.7279 | − | 7.34847i | 1.05700 | − | 0.610257i | ||||
\(146\) | −9.79796 | − | 9.79796i | −0.810885 | − | 0.810885i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0000 | + | 10.0000i | 0.821995 | + | 0.821995i | ||||
\(149\) | −4.09808 | − | 1.09808i | −0.335727 | − | 0.0899579i | 0.0870170 | − | 0.996207i | \(-0.472267\pi\) |
−0.422744 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | −9.79796 | − | 16.9706i | −0.794719 | − | 1.37649i | ||||
\(153\) | −14.6969 | −1.18818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | − | 12.0000i | −0.963863 | − | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.48288 | + | 16.7303i | 0.357773 | + | 1.33523i | 0.876959 | + | 0.480565i | \(0.159568\pi\) |
−0.519187 | + | 0.854661i | \(0.673765\pi\) | |||||||
\(158\) | 1.46410 | + | 5.46410i | 0.116478 | + | 0.434701i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 19.5959i | − | 1.54919i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.707107 | + | 0.707107i | ||||
\(163\) | 1.36603 | + | 0.366025i | 0.106995 | + | 0.0286693i | 0.311919 | − | 0.950109i | \(-0.399028\pi\) |
−0.204924 | + | 0.978778i | \(0.565695\pi\) | |||||||
\(164\) | −8.48528 | − | 4.89898i | −0.662589 | − | 0.382546i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5959i | 1.51638i | 0.652035 | + | 0.758189i | \(0.273915\pi\) | ||||
−0.652035 | + | 0.758189i | \(0.726085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | −12.0000 | − | 20.7846i | −0.920358 | − | 1.59411i | ||||
\(171\) | 5.37945 | + | 20.0764i | 0.411377 | + | 1.53528i | ||||
\(172\) | 3.66025 | + | 13.6603i | 0.279092 | + | 1.04158i | ||||
\(173\) | 3.34607 | + | 0.896575i | 0.254397 | + | 0.0681654i | 0.383763 | − | 0.923431i | \(-0.374628\pi\) |
−0.129367 | + | 0.991597i | \(0.541294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | − | 4.00000i | −0.301511 | − | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.09808 | + | 4.09808i | 0.0820741 | + | 0.306305i | 0.994744 | − | 0.102393i | \(-0.0326498\pi\) |
−0.912670 | + | 0.408697i | \(0.865983\pi\) | |||||||
\(180\) | −5.37945 | + | 20.0764i | −0.400961 | + | 1.49641i | ||||
\(181\) | 2.44949 | + | 2.44949i | 0.182069 | + | 0.182069i | 0.792257 | − | 0.610188i | \(-0.208906\pi\) |
−0.610188 | + | 0.792257i | \(0.708906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.9282 | − | 2.92820i | −0.805638 | − | 0.215870i | ||||
\(185\) | 12.2474 | − | 21.2132i | 0.900450 | − | 1.55963i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.69213 | − | 1.79315i | −0.489377 | − | 0.131128i | ||||
\(188\) | − | 9.79796i | − | 0.714590i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.0000 | + | 24.0000i | −1.74114 | + | 1.74114i | ||||
\(191\) | 17.3205 | − | 10.0000i | 1.25327 | − | 0.723575i | 0.281511 | − | 0.959558i | \(-0.409164\pi\) |
0.971757 | + | 0.235983i | \(0.0758311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | − | 13.8564i | 0.575853 | − | 0.997406i | −0.420096 | − | 0.907480i | \(-0.638004\pi\) |
0.995948 | − | 0.0899262i | \(-0.0286631\pi\) | |||||||
\(194\) | 6.69213 | + | 1.79315i | 0.480467 | + | 0.128741i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0000 | + | 15.0000i | −1.06871 | + | 1.06871i | −0.0712470 | + | 0.997459i | \(0.522698\pi\) |
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 3.00000 | + | 5.19615i | 0.213201 | + | 0.369274i | ||||
\(199\) | −8.48528 | − | 4.89898i | −0.601506 | − | 0.347279i | 0.168128 | − | 0.985765i | \(-0.446228\pi\) |
−0.769634 | + | 0.638486i | \(0.779561\pi\) | |||||||
\(200\) | −19.1244 | + | 5.12436i | −1.35230 | + | 0.362347i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.89898i | − | 0.344691i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.39230 | + | 16.3923i | −0.306772 | + | 1.14489i | ||||
\(206\) | −3.58630 | − | 13.3843i | −0.249869 | − | 0.932526i | ||||
\(207\) | 10.3923 | + | 6.00000i | 0.722315 | + | 0.417029i | ||||
\(208\) | −13.3843 | − | 3.58630i | −0.928032 | − | 0.248665i | ||||
\(209\) | 9.79796i | 0.677739i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | − | 1.00000i | 0.0688428 | − | 0.0688428i | −0.671847 | − | 0.740690i | \(-0.734499\pi\) |
0.740690 | + | 0.671847i | \(0.234499\pi\) | |||||||
\(212\) | −0.732051 | + | 2.73205i | −0.0502775 | + | 0.187638i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.19615 | + | 3.00000i | 0.355202 | + | 0.205076i | ||||
\(215\) | 21.2132 | − | 12.2474i | 1.44673 | − | 0.835269i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.89898 | + | 8.48528i | −0.330289 | + | 0.572078i | ||||
\(221\) | −16.3923 | + | 4.39230i | −1.10267 | + | 0.295458i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.79796 | 0.656120 | 0.328060 | − | 0.944657i | \(-0.393605\pi\) | ||||
0.328060 | + | 0.944657i | \(0.393605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.0000 | 1.40000 | ||||||||
\(226\) | −1.46410 | + | 5.46410i | −0.0973906 | + | 0.363467i | ||||
\(227\) | −26.7685 | + | 7.17260i | −1.77669 | + | 0.476062i | −0.989974 | − | 0.141253i | \(-0.954887\pi\) |
−0.786716 | + | 0.617316i | \(0.788220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.68973 | + | 10.0382i | −0.177742 | + | 0.663343i | 0.818326 | + | 0.574754i | \(0.194902\pi\) |
−0.996068 | + | 0.0885886i | \(0.971764\pi\) | |||||||
\(230\) | 19.5959i | 1.29212i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | −0.787839 | ||||||||
\(233\) | −3.46410 | + | 2.00000i | −0.226941 | + | 0.131024i | −0.609160 | − | 0.793047i | \(-0.708493\pi\) |
0.382219 | + | 0.924072i | \(0.375160\pi\) | |||||||
\(234\) | 12.7279 | + | 7.34847i | 0.832050 | + | 0.480384i | ||||
\(235\) | −16.3923 | + | 4.39230i | −1.06932 | + | 0.286522i | ||||
\(236\) | −3.58630 | + | 13.3843i | −0.233448 | + | 0.871241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0000i | 0.905585i | 0.891616 | + | 0.452792i | \(0.149572\pi\) | ||||
−0.891616 | + | 0.452792i | \(0.850428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2132 | − | 12.2474i | −1.36646 | − | 0.788928i | −0.375988 | − | 0.926624i | \(-0.622697\pi\) |
−0.990474 | + | 0.137697i | \(0.956030\pi\) | |||||||
\(242\) | −3.29423 | − | 12.2942i | −0.211761 | − | 0.790303i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.89898 | + | 4.89898i | 0.313625 | + | 0.313625i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | 3.58630 | + | 13.3843i | 0.227730 | + | 0.849901i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.89898 | + | 8.48528i | 0.309839 | + | 0.536656i | ||||
\(251\) | 14.6969 | − | 14.6969i | 0.927663 | − | 0.927663i | −0.0698920 | − | 0.997555i | \(-0.522265\pi\) |
0.997555 | + | 0.0698920i | \(0.0222655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | + | 4.00000i | 0.251478 | + | 0.251478i | ||||
\(254\) | −24.5885 | − | 6.58846i | −1.54282 | − | 0.413397i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −25.4558 | + | 14.6969i | −1.58789 | + | 0.916770i | −0.594238 | + | 0.804289i | \(0.702546\pi\) |
−0.993654 | + | 0.112481i | \(0.964120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 24.0000i | 1.48842i | ||||||||
\(261\) | 12.2942 | + | 3.29423i | 0.760994 | + | 0.203908i | ||||
\(262\) | −16.9706 | − | 9.79796i | −1.04844 | − | 0.605320i | ||||
\(263\) | 13.0000 | − | 22.5167i | 0.801614 | − | 1.38844i | −0.116939 | − | 0.993139i | \(-0.537308\pi\) |
0.918553 | − | 0.395298i | \(-0.129359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.89898 | 0.300942 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.66025 | − | 13.6603i | 0.223586 | − | 0.834433i | ||||
\(269\) | 2.68973 | + | 10.0382i | 0.163996 | + | 0.612040i | 0.998166 | + | 0.0605332i | \(0.0192801\pi\) |
−0.834171 | + | 0.551506i | \(0.814053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.6969 | − | 25.4558i | −0.892775 | − | 1.54633i | −0.836534 | − | 0.547915i | \(-0.815422\pi\) |
−0.0562416 | − | 0.998417i | \(-0.517912\pi\) | |||||||
\(272\) | 19.5959i | 1.18818i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | − | 8.00000i | 0.483298 | − | 0.483298i | ||||
\(275\) | 9.56218 | + | 2.56218i | 0.576621 | + | 0.154505i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.83013 | + | 6.83013i | 0.109962 | + | 0.410383i | 0.998861 | − | 0.0477206i | \(-0.0151957\pi\) |
−0.888899 | + | 0.458103i | \(0.848529\pi\) | |||||||
\(278\) | −4.89898 | − | 8.48528i | −0.293821 | − | 0.508913i | ||||
\(279\) | − | 14.6969i | − | 0.879883i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.0000i | − | 1.19310i | −0.802576 | − | 0.596550i | \(-0.796538\pi\) | ||
0.802576 | − | 0.596550i | \(-0.203462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.37945 | − | 20.0764i | −0.319775 | − | 1.19342i | −0.919461 | − | 0.393182i | \(-0.871374\pi\) |
0.599685 | − | 0.800236i | \(-0.295292\pi\) | |||||||
\(284\) | −3.46410 | − | 2.00000i | −0.205557 | − | 0.118678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.89898 | + | 4.89898i | 0.289683 | + | 0.289683i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.0000 | − | 12.0000i | 0.707107 | − | 0.707107i | ||||
\(289\) | 3.50000 | + | 6.06218i | 0.205882 | + | 0.356599i | ||||
\(290\) | 5.37945 | + | 20.0764i | 0.315892 | + | 1.17893i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.9706 | − | 9.79796i | 0.993127 | − | 0.573382i | ||||
\(293\) | −12.2474 | − | 12.2474i | −0.715504 | − | 0.715504i | 0.252177 | − | 0.967681i | \(-0.418853\pi\) |
−0.967681 | + | 0.252177i | \(0.918853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | −17.3205 | + | 10.0000i | −1.00673 | + | 0.581238i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | 13.3843 | + | 3.58630i | 0.774032 | + | 0.207401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.0000 | − | 12.0000i | −0.690522 | − | 0.690522i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.7685 | − | 7.17260i | 1.53528 | − | 0.411377i | ||||
\(305\) | 6.00000 | − | 10.3923i | 0.343559 | − | 0.595062i | ||||
\(306\) | 5.37945 | − | 20.0764i | 0.307523 | − | 1.14769i | ||||
\(307\) | −4.89898 | − | 4.89898i | −0.279600 | − | 0.279600i | 0.553350 | − | 0.832949i | \(-0.313349\pi\) |
−0.832949 | + | 0.553350i | \(0.813349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.7846 | − | 12.0000i | 1.18049 | − | 0.681554i | ||||
\(311\) | 21.2132 | + | 12.2474i | 1.20289 | + | 0.694489i | 0.961197 | − | 0.275864i | \(-0.0889638\pi\) |
0.241694 | + | 0.970353i | \(0.422297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.34847 | + | 12.7279i | 0.415360 | + | 0.719425i | 0.995466 | − | 0.0951162i | \(-0.0303223\pi\) |
−0.580106 | + | 0.814541i | \(0.696989\pi\) | |||||||
\(314\) | −24.4949 | −1.38233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 4.75833 | − | 17.7583i | 0.267254 | − | 0.997407i | −0.693602 | − | 0.720359i | \(-0.743977\pi\) |
0.960856 | − | 0.277048i | \(-0.0893562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.19615 | + | 3.00000i | 0.290929 | + | 0.167968i | ||||
\(320\) | 26.7685 | + | 7.17260i | 1.49641 | + | 0.400961i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | − | 24.0000i | 1.33540 | − | 1.33540i | ||||
\(324\) | −15.5885 | + | 9.00000i | −0.866025 | + | 0.500000i | ||||
\(325\) | 23.4225 | − | 6.27603i | 1.29924 | − | 0.348131i | ||||
\(326\) | −1.00000 | + | 1.73205i | −0.0553849 | + | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.79796 | − | 9.79796i | 0.541002 | − | 0.541002i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.95448 | + | 25.9545i | −0.382253 | + | 1.42659i | 0.460199 | + | 0.887816i | \(0.347778\pi\) |
−0.842452 | + | 0.538772i | \(0.818889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.4904 | − | 5.49038i | 1.12287 | − | 0.300871i | ||||
\(334\) | −26.7685 | − | 7.17260i | −1.46471 | − | 0.392467i | ||||
\(335\) | −24.4949 | −1.33830 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | −1.36603 | − | 0.366025i | −0.0743020 | − | 0.0199092i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 32.7846 | − | 8.78461i | 1.77800 | − | 0.476412i | ||||
\(341\) | 1.79315 | − | 6.69213i | 0.0971046 | − | 0.362399i | ||||
\(342\) | −29.3939 | −1.58944 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.44949 | + | 4.24264i | −0.131685 | + | 0.228086i | ||||
\(347\) | −4.09808 | + | 1.09808i | −0.219996 | + | 0.0589478i | −0.367133 | − | 0.930168i | \(-0.619661\pi\) |
0.147137 | + | 0.989116i | \(0.452994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.34847 | − | 7.34847i | 0.393355 | − | 0.393355i | −0.482527 | − | 0.875881i | \(-0.660281\pi\) |
0.875881 | + | 0.482527i | \(0.160281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.92820 | − | 4.00000i | 0.369274 | − | 0.213201i | ||||
\(353\) | 8.48528 | + | 4.89898i | 0.451626 | + | 0.260746i | 0.708517 | − | 0.705694i | \(-0.249365\pi\) |
−0.256891 | + | 0.966440i | \(0.582698\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.79315 | + | 6.69213i | −0.0951706 | + | 0.355181i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | −10.0000 | − | 17.3205i | −0.527780 | − | 0.914141i | −0.999476 | − | 0.0323801i | \(-0.989691\pi\) |
0.471696 | − | 0.881761i | \(-0.343642\pi\) | |||||||
\(360\) | −25.4558 | − | 14.6969i | −1.34164 | − | 0.774597i | ||||
\(361\) | −25.1147 | − | 14.5000i | −1.32183 | − | 0.763158i | ||||
\(362\) | −4.24264 | + | 2.44949i | −0.222988 | + | 0.128742i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.0000 | − | 24.0000i | −1.25622 | − | 1.25622i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6969 | − | 25.4558i | 0.767174 | − | 1.32878i | −0.171916 | − | 0.985112i | \(-0.554996\pi\) |
0.939090 | − | 0.343673i | \(-0.111671\pi\) | |||||||
\(368\) | 8.00000 | − | 13.8564i | 0.417029 | − | 0.722315i | ||||
\(369\) | −12.7279 | + | 7.34847i | −0.662589 | + | 0.382546i | ||||
\(370\) | 24.4949 | + | 24.4949i | 1.27343 | + | 1.27343i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0263 | + | 4.02628i | 0.778031 | + | 0.208473i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
0.152115 | + | 0.988363i | \(0.451392\pi\) | |||||||
\(374\) | 4.89898 | − | 8.48528i | 0.253320 | − | 0.438763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.3843 | + | 3.58630i | 0.690241 | + | 0.184949i | ||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | − | 23.0000i | −1.18143 | − | 1.18143i | −0.979374 | − | 0.202057i | \(-0.935237\pi\) |
−0.202057 | − | 0.979374i | \(-0.564763\pi\) | |||||||
\(380\) | −24.0000 | − | 41.5692i | −1.23117 | − | 2.13246i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.32051 | + | 27.3205i | 0.374550 | + | 1.39784i | ||||
\(383\) | 7.34847 | + | 12.7279i | 0.375489 | + | 0.650366i | 0.990400 | − | 0.138230i | \(-0.0441414\pi\) |
−0.614911 | + | 0.788597i | \(0.710808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | + | 16.0000i | 0.814379 | + | 0.814379i | ||||
\(387\) | 20.4904 | + | 5.49038i | 1.04158 | + | 0.279092i | ||||
\(388\) | −4.89898 | + | 8.48528i | −0.248708 | + | 0.430775i | ||||
\(389\) | 4.75833 | + | 17.7583i | 0.241257 | + | 0.900383i | 0.975228 | + | 0.221202i | \(0.0709981\pi\) |
−0.733971 | + | 0.679181i | \(0.762335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5959i | − | 0.991008i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | − | 25.9808i | −0.755689 | − | 1.30889i | ||||
\(395\) | 3.58630 | + | 13.3843i | 0.180446 | + | 0.673435i | ||||
\(396\) | −8.19615 | + | 2.19615i | −0.411872 | + | 0.110361i | ||||
\(397\) | 16.7303 | + | 4.48288i | 0.839671 | + | 0.224989i | 0.652928 | − | 0.757420i | \(-0.273540\pi\) |
0.186743 | + | 0.982409i | \(0.440207\pi\) | |||||||
\(398\) | 9.79796 | − | 9.79796i | 0.491127 | − | 0.491127i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 28.0000i | − | 1.40000i | ||||||
\(401\) | 4.00000 | + | 6.92820i | 0.199750 | + | 0.345978i | 0.948447 | − | 0.316934i | \(-0.102654\pi\) |
−0.748697 | + | 0.662912i | \(0.769320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.39230 | − | 16.3923i | −0.218796 | − | 0.816559i | ||||
\(404\) | 6.69213 | + | 1.79315i | 0.332946 | + | 0.0892126i | ||||
\(405\) | 22.0454 | + | 22.0454i | 1.09545 | + | 1.09545i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000 | 0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.2474 | + | 21.2132i | −0.605597 | + | 1.04893i | 0.386359 | + | 0.922348i | \(0.373732\pi\) |
−0.991957 | + | 0.126577i | \(0.959601\pi\) | |||||||
\(410\) | −20.7846 | − | 12.0000i | −1.02648 | − | 0.592638i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.5959 | 0.965422 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0000 | + | 12.0000i | −0.589768 | + | 0.589768i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.79796 | − | 16.9706i | 0.480384 | − | 0.832050i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.3843 | − | 3.58630i | −0.654646 | − | 0.175412i | ||||
\(419\) | 4.89898 | + | 4.89898i | 0.239331 | + | 0.239331i | 0.816573 | − | 0.577242i | \(-0.195871\pi\) |
−0.577242 | + | 0.816573i | \(0.695871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 11.0000i | 0.536107 | − | 0.536107i | −0.386276 | − | 0.922383i | \(-0.626239\pi\) |
0.922383 | + | 0.386276i | \(0.126239\pi\) | |||||||
\(422\) | 1.00000 | + | 1.73205i | 0.0486792 | + | 0.0843149i | ||||
\(423\) | −12.7279 | − | 7.34847i | −0.618853 | − | 0.357295i | ||||
\(424\) | −3.46410 | − | 2.00000i | −0.168232 | − | 0.0971286i | ||||
\(425\) | −17.1464 | − | 29.6985i | −0.831724 | − | 1.44059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.00000 | + | 6.00000i | −0.290021 | + | 0.290021i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.96575 | + | 33.4607i | 0.432367 | + | 1.61362i | ||||
\(431\) | −8.66025 | − | 5.00000i | −0.417150 | − | 0.240842i | 0.276707 | − | 0.960954i | \(-0.410757\pi\) |
−0.693857 | + | 0.720113i | \(0.744090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6969i | 0.706290i | 0.935569 | + | 0.353145i | \(0.114888\pi\) | ||||
−0.935569 | + | 0.353145i | \(0.885112\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.1244 | + | 5.12436i | 0.915891 | + | 0.245412i | ||||
\(437\) | −26.7685 | + | 7.17260i | −1.28051 | + | 0.343112i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.7279 | + | 7.34847i | −0.607471 | + | 0.350723i | −0.771975 | − | 0.635653i | \(-0.780731\pi\) |
0.164504 | + | 0.986376i | \(0.447398\pi\) | |||||||
\(440\) | −9.79796 | − | 9.79796i | −0.467099 | − | 0.467099i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 24.0000i | − | 1.14156i | ||||||
\(443\) | 1.83013 | − | 6.83013i | 0.0869520 | − | 0.324509i | −0.908725 | − | 0.417396i | \(-0.862943\pi\) |
0.995677 | + | 0.0928868i | \(0.0296095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.58630 | + | 13.3843i | −0.169816 | + | 0.633763i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | −7.68653 | + | 28.6865i | −0.362347 | + | 1.35230i | ||||
\(451\) | −6.69213 | + | 1.79315i | −0.315120 | + | 0.0844362i | ||||
\(452\) | −6.92820 | − | 4.00000i | −0.325875 | − | 0.188144i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 39.1918i | − | 1.83936i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5885 | − | 9.00000i | 0.729197 | − | 0.421002i | −0.0889312 | − | 0.996038i | \(-0.528345\pi\) |
0.818128 | + | 0.575036i | \(0.195012\pi\) | |||||||
\(458\) | −12.7279 | − | 7.34847i | −0.594737 | − | 0.343371i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −26.7685 | − | 7.17260i | −1.24809 | − | 0.334424i | ||||
\(461\) | −22.0454 | + | 22.0454i | −1.02676 | + | 1.02676i | −0.0271249 | + | 0.999632i | \(0.508635\pi\) |
−0.999632 | + | 0.0271249i | \(0.991365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | 4.39230 | − | 16.3923i | 0.203908 | − | 0.760994i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.46410 | − | 5.46410i | −0.0678232 | − | 0.253120i | ||||
\(467\) | 7.17260 | − | 26.7685i | 0.331909 | − | 1.23870i | −0.575274 | − | 0.817961i | \(-0.695104\pi\) |
0.907182 | − | 0.420738i | \(-0.138229\pi\) | |||||||
\(468\) | −14.6969 | + | 14.6969i | −0.679366 | + | 0.679366i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 24.0000i | − | 1.10704i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.9706 | − | 9.79796i | −0.781133 | − | 0.450988i | ||||
\(473\) | 8.66025 | + | 5.00000i | 0.398199 | + | 0.229900i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.2929 | + | 34.2929i | −1.57346 | + | 1.57346i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | + | 3.00000i | 0.137361 | + | 0.137361i | ||||
\(478\) | −19.1244 | − | 5.12436i | −0.874728 | − | 0.234383i | ||||
\(479\) | −12.2474 | + | 21.2132i | −0.559600 | + | 0.969256i | 0.437929 | + | 0.899009i | \(0.355712\pi\) |
−0.997530 | + | 0.0702467i | \(0.977621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.2132 | − | 12.2474i | 0.967239 | − | 0.558436i | ||||
\(482\) | 24.4949 | − | 24.4949i | 1.11571 | − | 1.11571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0000 | 0.818182 | ||||||||
\(485\) | 16.3923 | + | 4.39230i | 0.744336 | + | 0.199444i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | − | 10.3923i | 0.271886 | − | 0.470920i | −0.697459 | − | 0.716625i | \(-0.745686\pi\) |
0.969345 | + | 0.245705i | \(0.0790193\pi\) | |||||||
\(488\) | −8.48528 | + | 4.89898i | −0.384111 | + | 0.221766i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0000 | + | 11.0000i | 0.496423 | + | 0.496423i | 0.910323 | − | 0.413900i | \(-0.135834\pi\) |
−0.413900 | + | 0.910323i | \(0.635834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.37945 | − | 20.0764i | −0.242278 | − | 0.904195i | ||||
\(494\) | −32.7846 | + | 8.78461i | −1.47505 | + | 0.395238i | ||||
\(495\) | 7.34847 | + | 12.7279i | 0.330289 | + | 0.572078i | ||||
\(496\) | −19.5959 | −0.879883 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.4186 | − | 8.41858i | −1.40649 | − | 0.376868i | −0.525818 | − | 0.850597i | \(-0.676241\pi\) |
−0.880671 | + | 0.473729i | \(0.842908\pi\) | |||||||
\(500\) | −13.3843 | + | 3.58630i | −0.598562 | + | 0.160384i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.6969 | + | 25.4558i | 0.655956 | + | 1.13615i | ||||
\(503\) | 14.6969i | 0.655304i | 0.944798 | + | 0.327652i | \(0.106257\pi\) | ||||
−0.944798 | + | 0.327652i | \(0.893743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.0000i | − | 0.533993i | ||||||
\(506\) | −6.92820 | + | 4.00000i | −0.307996 | + | 0.177822i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.0000 | − | 31.1769i | 0.798621 | − | 1.38325i | ||||
\(509\) | −10.0382 | − | 2.68973i | −0.444935 | − | 0.119220i | 0.0293934 | − | 0.999568i | \(-0.490642\pi\) |
−0.474329 | + | 0.880348i | \(0.657309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.7589 | − | 40.1528i | −0.474555 | − | 1.77106i | ||||
\(515\) | −8.78461 | − | 32.7846i | −0.387096 | − | 1.44466i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.89898 | − | 4.89898i | −0.215457 | − | 0.215457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.7846 | − | 8.78461i | −1.43770 | − | 0.385231i | ||||
\(521\) | −2.44949 | + | 4.24264i | −0.107314 | + | 0.185873i | −0.914681 | − | 0.404176i | \(-0.867558\pi\) |
0.807367 | + | 0.590049i | \(0.200892\pi\) | |||||||
\(522\) | −9.00000 | + | 15.5885i | −0.393919 | + | 0.682288i | ||||
\(523\) | 20.0764 | + | 5.37945i | 0.877879 | + | 0.235227i | 0.669492 | − | 0.742819i | \(-0.266512\pi\) |
0.208387 | + | 0.978046i | \(0.433179\pi\) | |||||||
\(524\) | 19.5959 | − | 19.5959i | 0.856052 | − | 0.856052i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.0000 | + | 26.0000i | 1.13365 | + | 1.13365i | ||||
\(527\) | −20.7846 | + | 12.0000i | −0.905392 | + | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −1.79315 | + | 6.69213i | −0.0778895 | + | 0.290688i | ||||
\(531\) | 14.6969 | + | 14.6969i | 0.637793 | + | 0.637793i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | + | 12.0000i | −0.519778 | + | 0.519778i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7279 | + | 7.34847i | 0.550276 | + | 0.317702i | ||||
\(536\) | 17.3205 | + | 10.0000i | 0.748132 | + | 0.431934i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.6969 | −0.633630 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6147 | + | 39.6147i | −0.456363 | + | 1.70317i | 0.227686 | + | 0.973735i | \(0.426884\pi\) |
−0.684049 | + | 0.729436i | \(0.739783\pi\) | |||||||
\(542\) | 40.1528 | − | 10.7589i | 1.72471 | − | 0.462135i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −26.7685 | − | 7.17260i | −1.14769 | − | 0.307523i | ||||
\(545\) | − | 34.2929i | − | 1.46894i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | + | 5.00000i | −0.213785 | + | 0.213785i | −0.805873 | − | 0.592088i | \(-0.798304\pi\) |
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(548\) | 8.00000 | + | 13.8564i | 0.341743 | + | 0.591916i | ||||
\(549\) | 10.0382 | − | 2.68973i | 0.428420 | − | 0.114795i | ||||
\(550\) | −7.00000 | + | 12.1244i | −0.298481 | + | 0.516984i | ||||
\(551\) | −25.4558 | + | 14.6969i | −1.08446 | + | 0.626111i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.3843 | − | 3.58630i | 0.567619 | − | 0.152093i | ||||
\(557\) | −4.09808 | + | 1.09808i | −0.173641 | + | 0.0465270i | −0.344592 | − | 0.938753i | \(-0.611983\pi\) |
0.170951 | + | 0.985280i | \(0.445316\pi\) | |||||||
\(558\) | 20.0764 | + | 5.37945i | 0.849901 | + | 0.227730i | ||||
\(559\) | 24.4949 | 1.03602 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.3205 | + | 7.32051i | 1.15245 | + | 0.308797i | ||||
\(563\) | 33.4607 | − | 8.96575i | 1.41020 | − | 0.377862i | 0.528202 | − | 0.849118i | \(-0.322866\pi\) |
0.881996 | + | 0.471257i | \(0.156200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.58630 | + | 13.3843i | −0.150877 | + | 0.563080i | ||||
\(566\) | 29.3939 | 1.23552 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.00000 | − | 4.00000i | 0.167836 | − | 0.167836i | ||||
\(569\) | 12.1244 | − | 7.00000i | 0.508279 | − | 0.293455i | −0.223847 | − | 0.974624i | \(-0.571861\pi\) |
0.732126 | + | 0.681169i | \(0.238528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.3468 | + | 11.3468i | −1.77216 | + | 0.474848i | −0.989118 | − | 0.147123i | \(-0.952999\pi\) |
−0.783040 | + | 0.621972i | \(0.786332\pi\) | |||||||
\(572\) | −8.48528 | + | 4.89898i | −0.354787 | + | 0.204837i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0000i | 1.16768i | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.500000 | + | 0.866025i | ||||
\(577\) | 25.4558 | + | 14.6969i | 1.05974 | + | 0.611842i | 0.925361 | − | 0.379088i | \(-0.123762\pi\) |
0.134380 | + | 0.990930i | \(0.457096\pi\) | |||||||
\(578\) | −9.56218 | + | 2.56218i | −0.397734 | + | 0.106573i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −29.3939 | −1.22051 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00000 | + | 1.73205i | 0.0414158 | + | 0.0717342i | ||||
\(584\) | 7.17260 | + | 26.7685i | 0.296804 | + | 1.10769i | ||||
\(585\) | 31.1769 | + | 18.0000i | 1.28901 | + | 0.744208i | ||||
\(586\) | 21.2132 | − | 12.2474i | 0.876309 | − | 0.505937i | ||||
\(587\) | 24.4949 | − | 24.4949i | 1.01101 | − | 1.01101i | 0.0110739 | − | 0.999939i | \(-0.496475\pi\) |
0.999939 | − | 0.0110739i | \(-0.00352501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | + | 24.0000i | 0.988903 | + | 0.988903i | ||||
\(590\) | −8.78461 | + | 32.7846i | −0.361657 | + | 1.34972i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.32051 | − | 27.3205i | −0.300871 | − | 1.12287i | ||||
\(593\) | 33.9411 | − | 19.5959i | 1.39379 | − | 0.804708i | 0.400062 | − | 0.916488i | \(-0.368989\pi\) |
0.993733 | + | 0.111780i | \(0.0356552\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | + | 6.00000i | 0.245770 | + | 0.245770i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.79796 | + | 16.9706i | −0.400668 | + | 0.693978i | ||||
\(599\) | −5.00000 | + | 8.66025i | −0.204294 | + | 0.353848i | −0.949908 | − | 0.312531i | \(-0.898823\pi\) |
0.745613 | + | 0.666379i | \(0.232157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.5959 | −0.799334 | −0.399667 | − | 0.916660i | \(-0.630874\pi\) | ||||
−0.399667 | + | 0.916660i | \(0.630874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.0000 | − | 15.0000i | −0.610847 | − | 0.610847i | ||||
\(604\) | 20.7846 | − | 12.0000i | 0.845714 | − | 0.488273i | ||||
\(605\) | −8.06918 | − | 30.1146i | −0.328059 | − | 1.22433i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.6969 | + | 25.4558i | 0.596530 | + | 1.03322i | 0.993329 | + | 0.115315i | \(0.0367878\pi\) |
−0.396799 | + | 0.917906i | \(0.629879\pi\) | |||||||
\(608\) | 39.1918i | 1.58944i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | + | 12.0000i | 0.485866 | + | 0.485866i | ||||
\(611\) | −16.3923 | − | 4.39230i | −0.663162 | − | 0.177694i | ||||
\(612\) | 25.4558 | + | 14.6969i | 1.02899 | + | 0.594089i | ||||
\(613\) | 6.95448 | + | 25.9545i | 0.280889 | + | 1.04829i | 0.951791 | + | 0.306746i | \(0.0992402\pi\) |
−0.670902 | + | 0.741546i | \(0.734093\pi\) | |||||||
\(614\) | 8.48528 | − | 4.89898i | 0.342438 | − | 0.197707i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.79315 | − | 6.69213i | −0.0720728 | − | 0.268979i | 0.920481 | − | 0.390788i | \(-0.127797\pi\) |
−0.992554 | + | 0.121808i | \(0.961131\pi\) | |||||||
\(620\) | 8.78461 | + | 32.7846i | 0.352798 | + | 1.31666i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.4949 | + | 24.4949i | −0.982156 | + | 0.982156i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | −20.0764 | + | 5.37945i | −0.802414 | + | 0.215006i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.96575 | − | 33.4607i | 0.357773 | − | 1.33523i | ||||
\(629\) | −24.4949 | − | 24.4949i | −0.976676 | − | 0.976676i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | 2.92820 | − | 10.9282i | 0.116478 | − | 0.434701i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.5167 | + | 13.0000i | 0.894251 | + | 0.516296i | ||||
\(635\) | −60.2292 | − | 16.1384i | −2.39012 | − | 0.640431i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.00000 | + | 6.00000i | −0.237542 | + | 0.237542i | ||||
\(639\) | −5.19615 | + | 3.00000i | −0.205557 | + | 0.118678i | ||||
\(640\) | −19.5959 | + | 33.9411i | −0.774597 | + | 1.34164i | ||||
\(641\) | −16.0000 | + | 27.7128i | −0.631962 | + | 1.09459i | 0.355188 | + | 0.934795i | \(0.384417\pi\) |
−0.987150 | + | 0.159795i | \(0.948917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | + | 41.5692i | 0.944267 | + | 1.63552i | ||||
\(647\) | −16.9706 | − | 9.79796i | −0.667182 | − | 0.385198i | 0.127826 | − | 0.991797i | \(-0.459200\pi\) |
−0.795008 | + | 0.606599i | \(0.792533\pi\) | |||||||
\(648\) | −6.58846 | − | 24.5885i | −0.258819 | − | 0.965926i | ||||
\(649\) | 4.89898 | + | 8.48528i | 0.192302 | + | 0.333076i | ||||
\(650\) | 34.2929i | 1.34508i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | − | 2.00000i | −0.0783260 | − | 0.0783260i | ||||
\(653\) | 5.49038 | − | 20.4904i | 0.214855 | − | 0.801851i | −0.771362 | − | 0.636396i | \(-0.780424\pi\) |
0.986217 | − | 0.165454i | \(-0.0529090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.5692 | − | 24.0000i | −1.62424 | − | 0.937758i | ||||
\(656\) | 9.79796 | + | 16.9706i | 0.382546 | + | 0.662589i | ||||
\(657\) | − | 29.3939i | − | 1.14676i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.0000 | + | 27.0000i | −1.05177 | + | 1.05177i | −0.0531861 | + | 0.998585i | \(0.516938\pi\) |
−0.998585 | + | 0.0531861i | \(0.983062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.34607 | + | 0.896575i | −0.130147 | + | 0.0348727i | −0.323304 | − | 0.946295i | \(-0.604794\pi\) |
0.193158 | + | 0.981168i | \(0.438127\pi\) | |||||||
\(662\) | −32.9090 | − | 19.0000i | −1.27904 | − | 0.738456i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.0000i | 1.16248i | ||||||||
\(667\) | −4.39230 | + | 16.3923i | −0.170071 | + | 0.634713i | ||||
\(668\) | 19.5959 | − | 33.9411i | 0.758189 | − | 1.31322i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.96575 | − | 33.4607i | 0.346377 | − | 1.29270i | ||||
\(671\) | 4.89898 | 0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00000 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(674\) | −10.2487 | + | 38.2487i | −0.394766 | + | 1.47329i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | − | 1.73205i | 0.0384615 | − | 0.0666173i | ||||
\(677\) | 2.68973 | − | 10.0382i | 0.103375 | − | 0.385799i | −0.894781 | − | 0.446505i | \(-0.852668\pi\) |
0.998156 | + | 0.0607058i | \(0.0193352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 48.0000i | 1.84072i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.48528 | + | 4.89898i | 0.324918 | + | 0.187592i | ||||
\(683\) | 34.1506 | − | 9.15064i | 1.30674 | − | 0.350139i | 0.462744 | − | 0.886492i | \(-0.346865\pi\) |
0.843994 | + | 0.536353i | \(0.180198\pi\) | |||||||
\(684\) | 10.7589 | − | 40.1528i | 0.411377 | − | 1.53528i | ||||
\(685\) | 19.5959 | − | 19.5959i | 0.748722 | − | 0.748722i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.32051 | − | 27.3205i | 0.279092 | − | 1.04158i | ||||
\(689\) | 4.24264 | + | 2.44949i | 0.161632 | + | 0.0933181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.58630 | + | 13.3843i | −0.136429 | + | 0.509161i | 0.863559 | + | 0.504249i | \(0.168230\pi\) |
−0.999988 | + | 0.00491275i | \(0.998436\pi\) | |||||||
\(692\) | −4.89898 | − | 4.89898i | −0.186231 | − | 0.186231i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.00000i | − | 0.227757i | ||||||
\(695\) | −12.0000 | − | 20.7846i | −0.455186 | − | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.7846 | + | 12.0000i | 0.787273 | + | 0.454532i | ||||
\(698\) | 7.34847 | + | 12.7279i | 0.278144 | + | 0.481759i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0000 | − | 29.0000i | −1.09531 | − | 1.09531i | −0.994951 | − | 0.100364i | \(-0.967999\pi\) |
−0.100364 | − | 0.994951i | \(-0.532001\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4949 | + | 42.4264i | −0.923843 | + | 1.60014i | ||||
\(704\) | 2.92820 | + | 10.9282i | 0.110361 | + | 0.411872i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.79796 | + | 9.79796i | −0.368751 | + | 0.368751i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.4186 | − | 8.41858i | −1.17995 | − | 0.316167i | −0.385043 | − | 0.922899i | \(-0.625813\pi\) |
−0.794906 | + | 0.606732i | \(0.792480\pi\) | |||||||
\(710\) | −8.48528 | − | 4.89898i | −0.318447 | − | 0.183855i | ||||
\(711\) | −6.00000 | + | 10.3923i | −0.225018 | + | 0.389742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5959 | 0.733873 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | + | 12.0000i | 0.448775 | + | 0.448775i | ||||
\(716\) | 2.19615 | − | 8.19615i | 0.0820741 | − | 0.306305i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.3205 | − | 7.32051i | 1.01959 | − | 0.273199i | ||||
\(719\) | −12.2474 | − | 21.2132i | −0.456753 | − | 0.791119i | 0.542034 | − | 0.840356i | \(-0.317654\pi\) |
−0.998787 | + | 0.0492373i | \(0.984321\pi\) | |||||||
\(720\) | 29.3939 | − | 29.3939i | 1.09545 | − | 1.09545i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 29.0000 | − | 29.0000i | 1.07927 | − | 1.07927i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.79315 | − | 6.69213i | −0.0666419 | − | 0.248711i | ||||
\(725\) | 7.68653 | + | 28.6865i | 0.285471 | + | 1.06539i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5959i | 0.726772i | 0.931639 | + | 0.363386i | \(0.118379\pi\) | ||||
−0.931639 | + | 0.363386i | \(0.881621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 41.5692 | − | 24.0000i | 1.53855 | − | 0.888280i | ||||
\(731\) | −8.96575 | − | 33.4607i | −0.331610 | − | 1.23759i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.1146 | − | 8.06918i | −1.11231 | − | 0.298042i | −0.344541 | − | 0.938771i | \(-0.611965\pi\) |
−0.767767 | + | 0.640729i | \(0.778632\pi\) | |||||||
\(734\) | 29.3939 | + | 29.3939i | 1.08495 | + | 1.08495i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | + | 16.0000i | 0.589768 | + | 0.589768i | ||||
\(737\) | −5.00000 | − | 8.66025i | −0.184177 | − | 0.319005i | ||||
\(738\) | −5.37945 | − | 20.0764i | −0.198020 | − | 0.739022i | ||||
\(739\) | −6.22243 | − | 23.2224i | −0.228896 | − | 0.854251i | −0.980806 | − | 0.194986i | \(-0.937534\pi\) |
0.751910 | − | 0.659265i | \(-0.229133\pi\) | |||||||
\(740\) | −42.4264 | + | 24.4949i | −1.55963 | + | 0.900450i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.00000 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.34847 | − | 12.7279i | 0.269227 | − | 0.466315i | ||||
\(746\) | −11.0000 | + | 19.0526i | −0.402739 | + | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.79796 | + | 9.79796i | 0.358249 | + | 0.358249i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.66025 | + | 5.00000i | −0.316017 | + | 0.182453i | −0.649616 | − | 0.760263i | \(-0.725070\pi\) |
0.333599 | + | 0.942715i | \(0.391737\pi\) | |||||||
\(752\) | −9.79796 | + | 16.9706i | −0.357295 | + | 0.618853i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.37945 | + | 20.0764i | −0.195908 | + | 0.731139i | ||||
\(755\) | −29.3939 | − | 29.3939i | −1.06975 | − | 1.06975i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.00000 | + | 5.00000i | −0.181728 | + | 0.181728i | −0.792108 | − | 0.610380i | \(-0.791017\pi\) |
0.610380 | + | 0.792108i | \(0.291017\pi\) | |||||||
\(758\) | 39.8372 | − | 23.0000i | 1.44695 | − | 0.835398i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 65.5692 | − | 17.5692i | 2.37845 | − | 0.637303i | ||||
\(761\) | 22.0454 | + | 38.1838i | 0.799145 | + | 1.38416i | 0.920173 | + | 0.391511i | \(0.128048\pi\) |
−0.121028 | + | 0.992649i | \(0.538619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −40.0000 | −1.44715 | ||||||||
\(765\) | 13.1769 | − | 49.1769i | 0.476412 | − | 1.77800i | ||||
\(766\) | −20.0764 | + | 5.37945i | −0.725390 | + | 0.194368i | ||||
\(767\) | 20.7846 | + | 12.0000i | 0.750489 | + | 0.433295i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.2929i | 1.23663i | 0.785930 | + | 0.618316i | \(0.212185\pi\) | ||||
−0.785930 | + | 0.618316i | \(0.787815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.7128 | + | 16.0000i | −0.997406 | + | 0.575853i | ||||
\(773\) | −16.7303 | + | 4.48288i | −0.601748 | + | 0.161238i | −0.546817 | − | 0.837252i | \(-0.684161\pi\) |
−0.0549312 | + | 0.998490i | \(0.517494\pi\) | |||||||
\(774\) | −15.0000 | + | 25.9808i | −0.539164 | + | 0.933859i | ||||
\(775\) | 29.6985 | − | 17.1464i | 1.06680 | − | 0.615918i | ||||
\(776\) | −9.79796 | − | 9.79796i | −0.351726 | − | 0.351726i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | 8.78461 | − | 32.7846i | 0.314741 | − | 1.17463i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.73205 | + | 0.732051i | −0.0977605 | + | 0.0261948i | ||||
\(782\) | 26.7685 | + | 7.17260i | 0.957240 | + | 0.256492i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.0000 | −2.14149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.69213 | − | 1.79315i | 0.238549 | − | 0.0639189i | −0.137564 | − | 0.990493i | \(-0.543927\pi\) |
0.376113 | + | 0.926574i | \(0.377261\pi\) | |||||||
\(788\) | 40.9808 | − | 10.9808i | 1.45988 | − | 0.391173i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.5959 | −0.697191 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 12.0000i | − | 0.426401i | ||||||
\(793\) | 10.3923 | − | 6.00000i | 0.369042 | − | 0.213066i | ||||
\(794\) | −12.2474 | + | 21.2132i | −0.434646 | + | 0.752828i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.79796 | + | 16.9706i | 0.347279 | + | 0.601506i | ||||
\(797\) | −12.2474 | + | 12.2474i | −0.433827 | + | 0.433827i | −0.889928 | − | 0.456101i | \(-0.849246\pi\) |
0.456101 | + | 0.889928i | \(0.349246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000i | 0.849059i | ||||||||
\(800\) | 38.2487 | + | 10.2487i | 1.35230 | + | 0.362347i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.9282 | + | 2.92820i | −0.385888 | + | 0.103398i | ||||
\(803\) | 3.58630 | − | 13.3843i | 0.126558 | − | 0.472320i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.89898 | + | 8.48528i | −0.172345 | + | 0.298511i | ||||
\(809\) | 39.8372 | + | 23.0000i | 1.40060 | + | 0.808637i | 0.994454 | − | 0.105171i | \(-0.0335391\pi\) |
0.406146 | + | 0.913808i | \(0.366872\pi\) | |||||||
\(810\) | −38.1838 | + | 22.0454i | −1.34164 | + | 0.774597i | ||||
\(811\) | 14.6969 | − | 14.6969i | 0.516079 | − | 0.516079i | −0.400303 | − | 0.916383i | \(-0.631095\pi\) |
0.916383 | + | 0.400303i | \(0.131095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.66025 | + | 13.6603i | −0.128292 | + | 0.478792i | ||||
\(815\) | −2.44949 | + | 4.24264i | −0.0858019 | + | 0.148613i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.4264 | + | 24.4949i | −1.48431 | + | 0.856968i | ||||
\(818\) | −24.4949 | − | 24.4949i | −0.856444 | − | 0.856444i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0000 | − | 24.0000i | 0.838116 | − | 0.838116i | ||||
\(821\) | 25.9545 | + | 6.95448i | 0.905818 | + | 0.242713i | 0.681513 | − | 0.731806i | \(-0.261322\pi\) |
0.224305 | + | 0.974519i | \(0.427989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00000 | − | 5.19615i | 0.104573 | − | 0.181126i | −0.808990 | − | 0.587822i | \(-0.799986\pi\) |
0.913564 | + | 0.406695i | \(0.133319\pi\) | |||||||
\(824\) | −7.17260 | + | 26.7685i | −0.249869 | + | 0.932526i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0000 | + | 33.0000i | 1.14752 | + | 1.14752i | 0.987038 | + | 0.160484i | \(0.0513055\pi\) |
0.160484 | + | 0.987038i | \(0.448695\pi\) | |||||||
\(828\) | −12.0000 | − | 20.7846i | −0.417029 | − | 0.722315i | ||||
\(829\) | 2.68973 | + | 10.0382i | 0.0934181 | + | 0.348641i | 0.996775 | − | 0.0802489i | \(-0.0255715\pi\) |
−0.903357 | + | 0.428890i | \(0.858905\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.5959 | + | 19.5959i | 0.679366 | + | 0.679366i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.5692 | − | 17.5692i | −2.26912 | − | 0.608008i | ||||
\(836\) | 9.79796 | − | 16.9706i | 0.338869 | − | 0.586939i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.48528 | + | 4.89898i | −0.293119 | + | 0.169232i | ||||
\(839\) | 9.79796i | 0.338263i | 0.985593 | + | 0.169132i | \(0.0540963\pi\) | ||||
−0.985593 | + | 0.169132i | \(0.945904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | 11.0000 | + | 19.0526i | 0.379085 | + | 0.656595i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.73205 | + | 0.732051i | −0.0940411 | + | 0.0251982i | ||||
\(845\) | −3.34607 | − | 0.896575i | −0.115108 | − | 0.0308431i | ||||
\(846\) | 14.6969 | − | 14.6969i | 0.505291 | − | 0.505291i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | − | 4.00000i | 0.137361 | − | 0.137361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 46.8449 | − | 12.5521i | 1.60677 | − | 0.430532i | ||||
\(851\) | 7.32051 | + | 27.3205i | 0.250944 | + | 0.936535i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2474 | + | 12.2474i | 0.419345 | + | 0.419345i | 0.884978 | − | 0.465633i | \(-0.154173\pi\) |
−0.465633 | + | 0.884978i | \(0.654173\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −72.0000 | −2.46235 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | 2.44949 | − | 4.24264i | 0.0836730 | − | 0.144926i | −0.821152 | − | 0.570710i | \(-0.806668\pi\) |
0.904825 | + | 0.425784i | \(0.140002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1528 | + | 10.7589i | 1.37000 | + | 0.367089i | 0.867477 | − | 0.497477i | \(-0.165740\pi\) |
0.502518 | + | 0.864567i | \(0.332407\pi\) | |||||||
\(860\) | −48.9898 | −1.67054 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.0000 | − | 10.0000i | 0.340601 | − | 0.340601i | ||||
\(863\) | −3.46410 | + | 2.00000i | −0.117919 | + | 0.0680808i | −0.557800 | − | 0.829976i | \(-0.688354\pi\) |
0.439880 | + | 0.898056i | \(0.355021\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | + | 10.3923i | −0.204006 | + | 0.353349i | ||||
\(866\) | −20.0764 | − | 5.37945i | −0.682224 | − | 0.182801i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.00000 | + | 4.00000i | −0.135691 | + | 0.135691i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.2132 | − | 12.2474i | −0.718782 | − | 0.414989i | ||||
\(872\) | −14.0000 | + | 24.2487i | −0.474100 | + | 0.821165i | ||||
\(873\) | 7.34847 | + | 12.7279i | 0.248708 | + | 0.430775i | ||||
\(874\) | − | 39.1918i | − | 1.32568i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.75833 | − | 17.7583i | 0.160677 | − | 0.599656i | −0.837875 | − | 0.545863i | \(-0.816202\pi\) |
0.998552 | − | 0.0537936i | \(-0.0171313\pi\) | |||||||
\(878\) | −5.37945 | − | 20.0764i | −0.181548 | − | 0.677545i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.9706 | − | 9.79796i | 0.572078 | − | 0.330289i | ||||
\(881\) | 48.9898i | 1.65051i | 0.564762 | + | 0.825254i | \(0.308968\pi\) | ||||
−0.564762 | + | 0.825254i | \(0.691032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.0000 | + | 31.0000i | −1.04323 | + | 1.04323i | −0.0442108 | + | 0.999022i | \(0.514077\pi\) |
−0.999022 | + | 0.0442108i | \(0.985923\pi\) | |||||||
\(884\) | 32.7846 | + | 8.78461i | 1.10267 | + | 0.295458i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.66025 | + | 5.00000i | 0.290947 | + | 0.167978i | ||||
\(887\) | 16.9706 | − | 9.79796i | 0.569816 | − | 0.328983i | −0.187260 | − | 0.982310i | \(-0.559961\pi\) |
0.757076 | + | 0.653327i | \(0.226627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.29423 | + | 12.2942i | −0.110361 | + | 0.411872i | ||||
\(892\) | −16.9706 | − | 9.79796i | −0.568216 | − | 0.328060i | ||||
\(893\) | 32.7846 | − | 8.78461i | 1.09710 | − | 0.293966i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6969 | −0.491264 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.66025 | + | 13.6603i | −0.122144 | + | 0.455849i | ||||
\(899\) | 20.0764 | − | 5.37945i | 0.669585 | − | 0.179415i | ||||
\(900\) | −36.3731 | − | 21.0000i | −1.21244 | − | 0.700000i | ||||
\(901\) | 1.79315 | − | 6.69213i | 0.0597385 | − | 0.222947i | ||||
\(902\) | − | 9.79796i | − | 0.326236i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | − | 8.00000i | 0.266076 | − | 0.266076i | ||||
\(905\) | −10.3923 | + | 6.00000i | −0.345452 | + | 0.199447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.56218 | − | 2.56218i | 0.317507 | − | 0.0850757i | −0.0965460 | − | 0.995329i | \(-0.530780\pi\) |
0.414053 | + | 0.910253i | \(0.364113\pi\) | |||||||
\(908\) | 53.5370 | + | 14.3452i | 1.77669 | + | 0.476062i | ||||
\(909\) | 7.34847 | − | 7.34847i | 0.243733 | − | 0.243733i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.0000i | − | 1.65657i | −0.560304 | − | 0.828287i | \(-0.689316\pi\) | ||
0.560304 | − | 0.828287i | \(-0.310684\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.58846 | + | 24.5885i | 0.217927 | + | 0.813314i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.6969 | − | 14.6969i | 0.485601 | − | 0.485601i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.00000 | + | 8.66025i | 0.164935 | + | 0.285675i | 0.936632 | − | 0.350315i | \(-0.113925\pi\) |
−0.771697 | + | 0.635990i | \(0.780592\pi\) | |||||||
\(920\) | 19.5959 | − | 33.9411i | 0.646058 | − | 1.11901i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.0454 | − | 38.1838i | −0.726027 | − | 1.25752i | ||||
\(923\) | −4.89898 | + | 4.89898i | −0.161252 | + | 0.161252i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.0000 | + | 35.0000i | 1.15079 | + | 1.15079i | ||||
\(926\) | 5.46410 | + | 1.46410i | 0.179562 | + | 0.0481134i | ||||
\(927\) | 14.6969 | − | 25.4558i | 0.482711 | − | 0.836080i | ||||
\(928\) | 20.7846 | + | 12.0000i | 0.682288 | + | 0.393919i | ||||
\(929\) | 29.6985 | − | 17.1464i | 0.974376 | − | 0.562556i | 0.0738083 | − | 0.997272i | \(-0.476485\pi\) |
0.900567 | + | 0.434716i | \(0.143151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.00000 | 0.262049 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.9411 | + | 19.5959i | 1.11059 | + | 0.641198i | ||||
\(935\) | 12.0000 | − | 20.7846i | 0.392442 | − | 0.679729i | ||||
\(936\) | −14.6969 | − | 25.4558i | −0.480384 | − | 0.832050i | ||||
\(937\) | −29.3939 | −0.960256 | −0.480128 | − | 0.877198i | \(-0.659410\pi\) | ||||
−0.480128 | + | 0.877198i | \(0.659410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 32.7846 | + | 8.78461i | 1.06932 | + | 0.286522i | ||||
\(941\) | 9.86233 | + | 36.8067i | 0.321503 | + | 1.19986i | 0.917781 | + | 0.397087i | \(0.129979\pi\) |
−0.596278 | + | 0.802778i | \(0.703354\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.79796 | − | 16.9706i | −0.319065 | − | 0.552638i | ||||
\(944\) | 19.5959 | − | 19.5959i | 0.637793 | − | 0.637793i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | + | 10.0000i | −0.325128 | + | 0.325128i | ||||
\(947\) | 20.4904 | + | 5.49038i | 0.665848 | + | 0.178413i | 0.575884 | − | 0.817532i | \(-0.304658\pi\) |
0.0899642 | + | 0.995945i | \(0.471325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.78461 | − | 32.7846i | −0.285160 | − | 1.06423i | ||||
\(950\) | −34.2929 | − | 59.3970i | −1.11261 | − | 1.92709i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.0000i | 0.518291i | 0.965838 | + | 0.259145i | \(0.0834409\pi\) | ||||
−0.965838 | + | 0.259145i | \(0.916559\pi\) | |||||||
\(954\) | −5.19615 | + | 3.00000i | −0.168232 | + | 0.0971286i | ||||
\(955\) | 17.9315 | + | 66.9213i | 0.580250 | + | 2.16552i | ||||
\(956\) | 14.0000 | − | 24.2487i | 0.452792 | − | 0.784259i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.4949 | − | 24.4949i | −0.791394 | − | 0.791394i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.50000 | + | 6.06218i | 0.112903 | + | 0.195554i | ||||
\(962\) | 8.96575 | + | 33.4607i | 0.289068 | + | 1.07881i | ||||
\(963\) | 3.29423 | + | 12.2942i | 0.106155 | + | 0.396176i | ||||
\(964\) | 24.4949 | + | 42.4264i | 0.788928 | + | 1.36646i | ||||
\(965\) | 39.1918 | + | 39.1918i | 1.26163 | + | 1.26163i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0000 | 0.900419 | 0.450210 | − | 0.892923i | \(-0.351349\pi\) | ||||
0.450210 | + | 0.892923i | \(0.351349\pi\) | |||||||
\(968\) | −6.58846 | + | 24.5885i | −0.211761 | + | 0.790303i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.0000 | + | 20.7846i | −0.385297 | + | 0.667354i | ||||
\(971\) | 13.3843 | + | 3.58630i | 0.429521 | + | 0.115090i | 0.467101 | − | 0.884204i | \(-0.345298\pi\) |
−0.0375801 | + | 0.999294i | \(0.511965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.0000 | + | 12.0000i | 0.384505 | + | 0.384505i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.58630 | − | 13.3843i | −0.114795 | − | 0.428420i | ||||
\(977\) | −19.0000 | + | 32.9090i | −0.607864 | + | 1.05285i | 0.383728 | + | 0.923446i | \(0.374640\pi\) |
−0.991592 | + | 0.129405i | \(0.958693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.0000 | − | 21.0000i | 0.670478 | − | 0.670478i | ||||
\(982\) | −19.0526 | + | 11.0000i | −0.607992 | + | 0.351024i | ||||
\(983\) | 8.48528 | + | 4.89898i | 0.270638 | + | 0.156253i | 0.629178 | − | 0.777261i | \(-0.283392\pi\) |
−0.358539 | + | 0.933515i | \(0.616725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.7423 | − | 63.6396i | −1.17071 | − | 2.02773i | ||||
\(986\) | 29.3939 | 0.936092 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 48.0000i | − | 1.52708i | ||||||
\(989\) | −7.32051 | + | 27.3205i | −0.232779 | + | 0.868742i | ||||
\(990\) | −20.0764 | + | 5.37945i | −0.638070 | + | 0.170970i | ||||
\(991\) | −51.9615 | − | 30.0000i | −1.65061 | − | 0.952981i | −0.976820 | − | 0.214060i | \(-0.931331\pi\) |
−0.673792 | − | 0.738921i | \(-0.735336\pi\) | |||||||
\(992\) | 7.17260 | − | 26.7685i | 0.227730 | − | 0.849901i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | − | 24.0000i | 0.760851 | − | 0.760851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0382 | + | 2.68973i | −0.317913 | + | 0.0851845i | −0.414247 | − | 0.910165i | \(-0.635955\pi\) |
0.0963340 | + | 0.995349i | \(0.469288\pi\) | |||||||
\(998\) | 23.0000 | − | 39.8372i | 0.728052 | − | 1.26102i | ||||
\(999\) | 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 | 784.2.w.d.227.1 | 8 | ||
7.2 | even | 3 | inner | 784.2.w.d.19.2 | 8 | ||
7.3 | odd | 6 | 112.2.j.a.83.2 | yes | 4 | ||
7.4 | even | 3 | 112.2.j.a.83.1 | yes | 4 | ||
7.5 | odd | 6 | inner | 784.2.w.d.19.1 | 8 | ||
7.6 | odd | 2 | inner | 784.2.w.d.227.2 | 8 | ||
16.11 | odd | 4 | inner | 784.2.w.d.619.1 | 8 | ||
28.3 | even | 6 | 448.2.j.b.111.2 | 4 | |||
28.11 | odd | 6 | 448.2.j.b.111.1 | 4 | |||
56.3 | even | 6 | 896.2.j.e.223.1 | 4 | |||
56.11 | odd | 6 | 896.2.j.e.223.2 | 4 | |||
56.45 | odd | 6 | 896.2.j.b.223.1 | 4 | |||
56.53 | even | 6 | 896.2.j.b.223.2 | 4 | |||
112.3 | even | 12 | 896.2.j.b.671.2 | 4 | |||
112.11 | odd | 12 | 112.2.j.a.27.2 | yes | 4 | ||
112.27 | even | 4 | inner | 784.2.w.d.619.2 | 8 | ||
112.45 | odd | 12 | 896.2.j.e.671.2 | 4 | |||
112.53 | even | 12 | 448.2.j.b.335.2 | 4 | |||
112.59 | even | 12 | 112.2.j.a.27.1 | ✓ | 4 | ||
112.67 | odd | 12 | 896.2.j.b.671.1 | 4 | |||
112.75 | even | 12 | inner | 784.2.w.d.411.1 | 8 | ||
112.101 | odd | 12 | 448.2.j.b.335.1 | 4 | |||
112.107 | odd | 12 | inner | 784.2.w.d.411.2 | 8 | ||
112.109 | even | 12 | 896.2.j.e.671.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.a.27.1 | ✓ | 4 | 112.59 | even | 12 | ||
112.2.j.a.27.2 | yes | 4 | 112.11 | odd | 12 | ||
112.2.j.a.83.1 | yes | 4 | 7.4 | even | 3 | ||
112.2.j.a.83.2 | yes | 4 | 7.3 | odd | 6 | ||
448.2.j.b.111.1 | 4 | 28.11 | odd | 6 | |||
448.2.j.b.111.2 | 4 | 28.3 | even | 6 | |||
448.2.j.b.335.1 | 4 | 112.101 | odd | 12 | |||
448.2.j.b.335.2 | 4 | 112.53 | even | 12 | |||
784.2.w.d.19.1 | 8 | 7.5 | odd | 6 | inner | ||
784.2.w.d.19.2 | 8 | 7.2 | even | 3 | inner | ||
784.2.w.d.227.1 | 8 | 1.1 | even | 1 | trivial | ||
784.2.w.d.227.2 | 8 | 7.6 | odd | 2 | inner | ||
784.2.w.d.411.1 | 8 | 112.75 | even | 12 | inner | ||
784.2.w.d.411.2 | 8 | 112.107 | odd | 12 | inner | ||
784.2.w.d.619.1 | 8 | 16.11 | odd | 4 | inner | ||
784.2.w.d.619.2 | 8 | 112.27 | even | 4 | inner | ||
896.2.j.b.223.1 | 4 | 56.45 | odd | 6 | |||
896.2.j.b.223.2 | 4 | 56.53 | even | 6 | |||
896.2.j.b.671.1 | 4 | 112.67 | odd | 12 | |||
896.2.j.b.671.2 | 4 | 112.3 | even | 12 | |||
896.2.j.e.223.1 | 4 | 56.3 | even | 6 | |||
896.2.j.e.223.2 | 4 | 56.11 | odd | 6 | |||
896.2.j.e.671.1 | 4 | 112.109 | even | 12 | |||
896.2.j.e.671.2 | 4 | 112.45 | odd | 12 |