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 | 619.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.619 |
Dual form | 784.2.w.d.19.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −3.34607 | − | 0.896575i | −1.49641 | − | 0.400961i | −0.584511 | − | 0.811386i | \(-0.698714\pi\) |
−0.911894 | + | 0.410425i | \(0.865380\pi\) | |||||||
\(6\) | 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 | ||||
\(11\) | 0.366025 | + | 1.36603i | 0.110361 | + | 0.411872i | 0.998898 | − | 0.0469323i | \(-0.0149445\pi\) |
−0.888537 | + | 0.458804i | \(0.848278\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | + | 2.44949i | 0.679366 | + | 0.679366i | 0.959857 | − | 0.280491i | \(-0.0904971\pi\) |
−0.280491 | + | 0.959857i | \(0.590497\pi\) | |||||||
\(14\) | 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 | \(0.464180\pi\) | |||||||
\(18\) | 4.09808 | − | 1.09808i | 0.965926 | − | 0.258819i | ||||
\(19\) | 6.69213 | + | 1.79315i | 1.53528 | + | 0.411377i | 0.924737 | − | 0.380606i | \(-0.124285\pi\) |
0.610543 | + | 0.791983i | \(0.290951\pi\) | |||||||
\(20\) | −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 | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.44949 | − | 4.24264i | 0.439941 | − | 0.762001i | −0.557743 | − | 0.830014i | \(-0.688333\pi\) |
0.997684 | + | 0.0680129i | \(0.0216659\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.89898 | + | 4.89898i | 0.840168 | + | 0.840168i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 1.83013 | − | 6.83013i | 0.300871 | − | 1.12287i | −0.635571 | − | 0.772043i | \(-0.719235\pi\) |
0.936442 | − | 0.350823i | \(-0.114098\pi\) | |||||||
\(38\) | 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 | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | + | 5.00000i | −0.762493 | + | 0.762493i | −0.976772 | − | 0.214280i | \(-0.931260\pi\) |
0.214280 | + | 0.976772i | \(0.431260\pi\) | |||||||
\(44\) | −0.732051 | + | 2.73205i | −0.110361 | + | 0.411872i | ||||
\(45\) | −10.0382 | + | 2.68973i | −1.49641 | + | 0.400961i | ||||
\(46\) | −1.46410 | − | 5.46410i | −0.215870 | − | 0.805638i | ||||
\(47\) | −2.44949 | − | 4.24264i | −0.357295 | − | 0.618853i | 0.630213 | − | 0.776422i | \(-0.282968\pi\) |
−0.987508 | + | 0.157569i | \(0.949634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.00000 | + | 7.00000i | 0.989949 | + | 0.989949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.79315 | + | 6.69213i | 0.248665 | + | 0.928032i | ||||
\(53\) | 1.36603 | − | 0.366025i | 0.187638 | − | 0.0502775i | −0.163776 | − | 0.986498i | \(-0.552368\pi\) |
0.351414 | + | 0.936220i | \(0.385701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.89898i | − | 0.660578i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | −6.69213 | + | 1.79315i | −0.871241 | + | 0.233448i | −0.666624 | − | 0.745394i | \(-0.732261\pi\) |
−0.204617 | + | 0.978842i | \(0.565595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.896575 | + | 3.34607i | −0.114795 | + | 0.428420i | −0.999271 | − | 0.0381645i | \(-0.987849\pi\) |
0.884477 | + | 0.466584i | \(0.154516\pi\) | |||||||
\(62\) | 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 | ||||||||
\(67\) | −6.83013 | + | 1.83013i | −0.834433 | + | 0.223586i | −0.650647 | − | 0.759381i | \(-0.725502\pi\) |
−0.183786 | + | 0.982966i | \(0.558835\pi\) | |||||||
\(68\) | 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 | \(0.462134\pi\) | |||||||
\(72\) | 8.19615 | + | 2.19615i | 0.965926 | + | 0.258819i | ||||
\(73\) | 4.89898 | − | 8.48528i | 0.573382 | − | 0.993127i | −0.422833 | − | 0.906208i | \(-0.638964\pi\) |
0.996215 | − | 0.0869195i | \(-0.0277023\pi\) | |||||||
\(74\) | 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 | −0.682048 | − | 0.731307i | \(-0.738911\pi\) |
0.292306 | + | 0.956325i | \(0.405577\pi\) | |||||||
\(80\) | −3.58630 | − | 13.3843i | −0.400961 | − | 1.49641i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −6.69213 | − | 1.79315i | −0.739022 | − | 0.198020i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 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 | ||||||||
\(94\) | −1.79315 | − | 6.69213i | −0.184949 | − | 0.690241i | ||||
\(95\) | −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 | ||||
\(101\) | −0.896575 | − | 3.34607i | −0.0892126 | − | 0.332946i | 0.906866 | − | 0.421419i | \(-0.138468\pi\) |
−0.996079 | + | 0.0884733i | \(0.971801\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | −4.09808 | − | 1.09808i | −0.396176 | − | 0.106155i | 0.0552301 | − | 0.998474i | \(-0.482411\pi\) |
−0.451406 | + | 0.892319i | \(0.649077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.56218 | + | 9.56218i | 0.245412 | + | 0.915891i | 0.973176 | + | 0.230063i | \(0.0738931\pi\) |
−0.727764 | + | 0.685828i | \(0.759440\pi\) | |||||||
\(110\) | 1.79315 | − | 6.69213i | 0.170970 | − | 0.638070i | ||||
\(111\) | 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 | ||||||||
\(115\) | 3.58630 | + | 13.3843i | 0.334424 | + | 1.24809i | ||||
\(116\) | −8.19615 | + | 2.19615i | −0.760994 | + | 0.203908i | ||||
\(117\) | 10.0382 | + | 2.68973i | 0.928032 | + | 0.248665i | ||||
\(118\) | −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 | \(-0.705563\pi\) | ||
0.601834 | − | 0.798621i | \(-0.294437\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.39230 | − | 16.3923i | −0.385231 | − | 1.43770i | ||||
\(131\) | −13.3843 | − | 3.58630i | −1.16939 | − | 0.313337i | −0.378679 | − | 0.925528i | \(-0.623621\pi\) |
−0.790710 | + | 0.612192i | \(0.790288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.58630 | + | 13.3843i | 0.307523 | + | 1.14769i | ||||
\(137\) | 6.92820 | + | 4.00000i | 0.591916 | + | 0.341743i | 0.765855 | − | 0.643013i | \(-0.222316\pi\) |
−0.173939 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.89898 | + | 4.89898i | 0.415526 | + | 0.415526i | 0.883658 | − | 0.468132i | \(-0.155073\pi\) |
−0.468132 | + | 0.883658i | \(0.655073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.73205 | + | 0.732051i | 0.229269 | + | 0.0614323i | ||||
\(143\) | −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 | ||||
\(149\) | 1.09808 | − | 4.09808i | 0.0899579 | − | 0.335727i | −0.906249 | − | 0.422744i | \(-0.861067\pi\) |
0.996207 | + | 0.0870170i | \(0.0277334\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | 16.7303 | − | 4.48288i | 1.33523 | − | 0.357773i | 0.480565 | − | 0.876959i | \(-0.340432\pi\) |
0.854661 | + | 0.519187i | \(0.173765\pi\) | |||||||
\(158\) | −5.46410 | + | 1.46410i | −0.434701 | + | 0.116478i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 19.5959i | − | 1.54919i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.707107 | − | 0.707107i | ||||
\(163\) | −0.366025 | + | 1.36603i | −0.0286693 | + | 0.106995i | −0.978778 | − | 0.204924i | \(-0.934305\pi\) |
0.950109 | + | 0.311919i | \(0.100972\pi\) | |||||||
\(164\) | −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 | ||||
\(171\) | 20.0764 | − | 5.37945i | 1.53528 | − | 0.411377i | ||||
\(172\) | −13.6603 | + | 3.66025i | −1.04158 | + | 0.279092i | ||||
\(173\) | 0.896575 | − | 3.34607i | 0.0681654 | − | 0.254397i | −0.923431 | − | 0.383763i | \(-0.874628\pi\) |
0.991597 | + | 0.129367i | \(0.0412945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | + | 4.00000i | −0.301511 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.09808 | + | 1.09808i | −0.306305 | + | 0.0820741i | −0.408697 | − | 0.912670i | \(-0.634017\pi\) |
0.102393 | + | 0.994744i | \(0.467350\pi\) | |||||||
\(180\) | −20.0764 | − | 5.37945i | −1.49641 | − | 0.400961i | ||||
\(181\) | −2.44949 | + | 2.44949i | −0.182069 | + | 0.182069i | −0.792257 | − | 0.610188i | \(-0.791094\pi\) |
0.610188 | + | 0.792257i | \(0.291094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.92820 | − | 10.9282i | 0.215870 | − | 0.805638i | ||||
\(185\) | −12.2474 | + | 21.2132i | −0.900450 | + | 1.55963i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.79315 | + | 6.69213i | −0.131128 | + | 0.489377i | ||||
\(188\) | − | 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 | −0.971757 | − | 0.235983i | \(-0.924169\pi\) |
−0.281511 | + | 0.959558i | \(0.590836\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | − | 13.8564i | 0.575853 | − | 0.997406i | −0.420096 | − | 0.907480i | \(-0.638004\pi\) |
0.995948 | − | 0.0899262i | \(-0.0286631\pi\) | |||||||
\(194\) | 1.79315 | − | 6.69213i | 0.128741 | − | 0.480467i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0000 | − | 15.0000i | −1.06871 | − | 1.06871i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) |
−0.0712470 | − | 0.997459i | \(-0.522698\pi\) | |||||||
\(198\) | 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 | \(0.779561\pi\) | |||||||
\(200\) | 5.12436 | + | 19.1244i | 0.362347 | + | 1.35230i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.89898i | − | 0.344691i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.3923 | + | 4.39230i | 1.14489 | + | 0.306772i | ||||
\(206\) | −13.3843 | + | 3.58630i | −0.932526 | + | 0.249869i | ||||
\(207\) | −10.3923 | − | 6.00000i | −0.722315 | − | 0.417029i | ||||
\(208\) | −3.58630 | + | 13.3843i | −0.248665 | + | 0.928032i | ||||
\(209\) | 9.79796i | 0.677739i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | + | 1.00000i | 0.0688428 | + | 0.0688428i | 0.740690 | − | 0.671847i | \(-0.234499\pi\) |
−0.671847 | + | 0.740690i | \(0.734499\pi\) | |||||||
\(212\) | 2.73205 | + | 0.732051i | 0.187638 | + | 0.0502775i | ||||
\(213\) | 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 | ||||
\(221\) | 4.39230 | + | 16.3923i | 0.295458 | + | 1.10267i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.79796 | −0.656120 | −0.328060 | − | 0.944657i | \(-0.606395\pi\) | ||||
−0.328060 | + | 0.944657i | \(0.606395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.0000 | 1.40000 | ||||||||
\(226\) | 5.46410 | + | 1.46410i | 0.363467 | + | 0.0973906i | ||||
\(227\) | −7.17260 | − | 26.7685i | −0.476062 | − | 1.77669i | −0.617316 | − | 0.786716i | \(-0.711780\pi\) |
0.141253 | − | 0.989974i | \(-0.454887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0382 | − | 2.68973i | −0.663343 | − | 0.177742i | −0.0885886 | − | 0.996068i | \(-0.528236\pi\) |
−0.574754 | + | 0.818326i | \(0.694902\pi\) | |||||||
\(230\) | 19.5959i | 1.29212i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | −0.787839 | ||||||||
\(233\) | 3.46410 | − | 2.00000i | 0.226941 | − | 0.131024i | −0.382219 | − | 0.924072i | \(-0.624840\pi\) |
0.609160 | + | 0.793047i | \(0.291507\pi\) | |||||||
\(234\) | 12.7279 | + | 7.34847i | 0.832050 | + | 0.480384i | ||||
\(235\) | 4.39230 | + | 16.3923i | 0.286522 | + | 1.06932i | ||||
\(236\) | −13.3843 | − | 3.58630i | −0.871241 | − | 0.233448i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 14.0000i | − | 0.905585i | −0.891616 | − | 0.452792i | \(-0.850428\pi\) | ||
0.891616 | − | 0.452792i | \(-0.149572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2132 | − | 12.2474i | −1.36646 | − | 0.788928i | −0.375988 | − | 0.926624i | \(-0.622697\pi\) |
−0.990474 | + | 0.137697i | \(0.956030\pi\) | |||||||
\(242\) | 12.2942 | − | 3.29423i | 0.790303 | − | 0.211761i | ||||
\(243\) | 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 | ||||
\(248\) | 13.3843 | − | 3.58630i | 0.849901 | − | 0.227730i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.89898 | − | 8.48528i | −0.309839 | − | 0.536656i | ||||
\(251\) | −14.6969 | − | 14.6969i | −0.927663 | − | 0.927663i | 0.0698920 | − | 0.997555i | \(-0.477735\pi\) |
−0.997555 | + | 0.0698920i | \(0.977735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | − | 4.00000i | 0.251478 | − | 0.251478i | ||||
\(254\) | 6.58846 | − | 24.5885i | 0.413397 | − | 1.54282i | ||||
\(255\) | 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 | ||||||
\(261\) | −3.29423 | + | 12.2942i | −0.203908 | + | 0.760994i | ||||
\(262\) | −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 | ||||||||
\(268\) | −13.6603 | − | 3.66025i | −0.834433 | − | 0.223586i | ||||
\(269\) | 10.0382 | − | 2.68973i | 0.612040 | − | 0.163996i | 0.0605332 | − | 0.998166i | \(-0.480720\pi\) |
0.551506 | + | 0.834171i | \(0.314053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6969 | + | 25.4558i | 0.892775 | + | 1.54633i | 0.836534 | + | 0.547915i | \(0.184578\pi\) |
0.0562416 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(272\) | 19.5959i | 1.18818i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | + | 8.00000i | 0.483298 | + | 0.483298i | ||||
\(275\) | −2.56218 | + | 9.56218i | −0.154505 | + | 0.576621i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.83013 | + | 1.83013i | −0.410383 | + | 0.109962i | −0.458103 | − | 0.888899i | \(-0.651471\pi\) |
0.0477206 | + | 0.998861i | \(0.484804\pi\) | |||||||
\(278\) | 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 | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0764 | + | 5.37945i | −1.19342 | + | 0.319775i | −0.800236 | − | 0.599685i | \(-0.795292\pi\) |
−0.393182 | + | 0.919461i | \(0.628626\pi\) | |||||||
\(284\) | 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 | ||||
\(290\) | 20.0764 | − | 5.37945i | 1.17893 | − | 0.315892i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.9706 | − | 9.79796i | 0.993127 | − | 0.573382i | ||||
\(293\) | 12.2474 | − | 12.2474i | 0.715504 | − | 0.715504i | −0.252177 | − | 0.967681i | \(-0.581147\pi\) |
0.967681 | + | 0.252177i | \(0.0811467\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | 3.58630 | − | 13.3843i | 0.207401 | − | 0.774032i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.0000 | + | 12.0000i | −0.690522 | + | 0.690522i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.17260 | + | 26.7685i | 0.411377 | + | 1.53528i | ||||
\(305\) | 6.00000 | − | 10.3923i | 0.343559 | − | 0.595062i | ||||
\(306\) | 20.0764 | + | 5.37945i | 1.14769 | + | 0.307523i | ||||
\(307\) | 4.89898 | − | 4.89898i | 0.279600 | − | 0.279600i | −0.553350 | − | 0.832949i | \(-0.686651\pi\) |
0.832949 | + | 0.553350i | \(0.186651\pi\) | |||||||
\(308\) | 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 | 0.580106 | − | 0.814541i | \(-0.303011\pi\) |
−0.995466 | + | 0.0951162i | \(0.969678\pi\) | |||||||
\(314\) | 24.4949 | 1.38233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −17.7583 | − | 4.75833i | −0.997407 | − | 0.267254i | −0.277048 | − | 0.960856i | \(-0.589356\pi\) |
−0.720359 | + | 0.693602i | \(0.756023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.19615 | − | 3.00000i | −0.290929 | − | 0.167968i | ||||
\(320\) | 7.17260 | − | 26.7685i | 0.400961 | − | 1.49641i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | + | 24.0000i | 1.33540 | + | 1.33540i | ||||
\(324\) | 15.5885 | − | 9.00000i | 0.866025 | − | 0.500000i | ||||
\(325\) | 6.27603 | + | 23.4225i | 0.348131 | + | 1.29924i | ||||
\(326\) | −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 | ||||||||
\(331\) | 25.9545 | + | 6.95448i | 1.42659 | + | 0.382253i | 0.887816 | − | 0.460199i | \(-0.152222\pi\) |
0.538772 | + | 0.842452i | \(0.318889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.49038 | − | 20.4904i | −0.300871 | − | 1.12287i | ||||
\(334\) | −7.17260 | + | 26.7685i | −0.392467 | + | 1.46471i | ||||
\(335\) | 24.4949 | 1.33830 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 0.366025 | − | 1.36603i | 0.0199092 | − | 0.0743020i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.78461 | − | 32.7846i | −0.476412 | − | 1.77800i | ||||
\(341\) | 6.69213 | + | 1.79315i | 0.362399 | + | 0.0971046i | ||||
\(342\) | 29.3939 | 1.58944 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.44949 | − | 4.24264i | 0.131685 | − | 0.228086i | ||||
\(347\) | 1.09808 | + | 4.09808i | 0.0589478 | + | 0.219996i | 0.989116 | − | 0.147137i | \(-0.0470059\pi\) |
−0.930168 | + | 0.367133i | \(0.880339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.34847 | − | 7.34847i | −0.393355 | − | 0.393355i | 0.482527 | − | 0.875881i | \(-0.339719\pi\) |
−0.875881 | + | 0.482527i | \(0.839719\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −6.69213 | − | 1.79315i | −0.355181 | − | 0.0951706i | ||||
\(356\) | 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 | \(0.445004\pi\) |
−0.939090 | + | 0.343673i | \(0.888329\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | −4.02628 | + | 15.0263i | −0.208473 | + | 0.778031i | 0.779890 | + | 0.625917i | \(0.215275\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | −4.89898 | + | 8.48528i | −0.253320 | + | 0.438763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.58630 | − | 13.3843i | 0.184949 | − | 0.690241i | ||||
\(377\) | −14.6969 | −0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | + | 23.0000i | −1.18143 | + | 1.18143i | −0.202057 | + | 0.979374i | \(0.564763\pi\) |
−0.979374 | + | 0.202057i | \(0.935237\pi\) | |||||||
\(380\) | −24.0000 | − | 41.5692i | −1.23117 | − | 2.13246i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27.3205 | + | 7.32051i | −1.39784 | + | 0.374550i | ||||
\(383\) | −7.34847 | − | 12.7279i | −0.375489 | − | 0.650366i | 0.614911 | − | 0.788597i | \(-0.289192\pi\) |
−0.990400 | + | 0.138230i | \(0.955859\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | − | 16.0000i | 0.814379 | − | 0.814379i | ||||
\(387\) | −5.49038 | + | 20.4904i | −0.279092 | + | 1.04158i | ||||
\(388\) | 4.89898 | − | 8.48528i | 0.248708 | − | 0.430775i | ||||
\(389\) | −17.7583 | + | 4.75833i | −0.900383 | + | 0.241257i | −0.679181 | − | 0.733971i | \(-0.737665\pi\) |
−0.221202 | + | 0.975228i | \(0.570998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5959i | − | 0.991008i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | − | 25.9808i | −0.755689 | − | 1.30889i | ||||
\(395\) | 13.3843 | − | 3.58630i | 0.673435 | − | 0.180446i | ||||
\(396\) | 2.19615 | + | 8.19615i | 0.110361 | + | 0.411872i | ||||
\(397\) | 4.48288 | − | 16.7303i | 0.224989 | − | 0.839671i | −0.757420 | − | 0.652928i | \(-0.773540\pi\) |
0.982409 | − | 0.186743i | \(-0.0597931\pi\) | |||||||
\(398\) | −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 | ||||||||
\(403\) | 16.3923 | − | 4.39230i | 0.816559 | − | 0.218796i | ||||
\(404\) | 1.79315 | − | 6.69213i | 0.0892126 | − | 0.332946i | ||||
\(405\) | −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 | \(-0.626268\pi\) |
0.991957 | − | 0.126577i | \(-0.0403991\pi\) | |||||||
\(410\) | 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 | ||||||||
\(418\) | −3.58630 | + | 13.3843i | −0.175412 | + | 0.654646i | ||||
\(419\) | −4.89898 | + | 4.89898i | −0.239331 | + | 0.239331i | −0.816573 | − | 0.577242i | \(-0.804129\pi\) |
0.577242 | + | 0.816573i | \(0.304129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | + | 11.0000i | 0.536107 | + | 0.536107i | 0.922383 | − | 0.386276i | \(-0.126239\pi\) |
−0.386276 | + | 0.922383i | \(0.626239\pi\) | |||||||
\(422\) | 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 | ||||||||
\(430\) | 33.4607 | − | 8.96575i | 1.61362 | − | 0.432367i | ||||
\(431\) | 8.66025 | + | 5.00000i | 0.417150 | + | 0.240842i | 0.693857 | − | 0.720113i | \(-0.255910\pi\) |
−0.276707 | + | 0.960954i | \(0.589243\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | −5.12436 | + | 19.1244i | −0.245412 | + | 0.915891i | ||||
\(437\) | −7.17260 | − | 26.7685i | −0.343112 | − | 1.28051i | ||||
\(438\) | 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 | ||||||||
\(443\) | −6.83013 | − | 1.83013i | −0.324509 | − | 0.0869520i | 0.0928868 | − | 0.995677i | \(-0.470391\pi\) |
−0.417396 | + | 0.908725i | \(0.637057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.3843 | − | 3.58630i | −0.633763 | − | 0.169816i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 28.6865 | + | 7.68653i | 1.35230 | + | 0.362347i | ||||
\(451\) | −1.79315 | − | 6.69213i | −0.0844362 | − | 0.315120i | ||||
\(452\) | 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 | −0.818128 | − | 0.575036i | \(-0.804988\pi\) |
0.0889312 | + | 0.996038i | \(0.471655\pi\) | |||||||
\(458\) | −12.7279 | − | 7.34847i | −0.594737 | − | 0.343371i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.17260 | + | 26.7685i | −0.334424 | + | 1.24809i | ||||
\(461\) | 22.0454 | + | 22.0454i | 1.02676 | + | 1.02676i | 0.999632 | + | 0.0271249i | \(0.00863520\pi\) |
0.0271249 | + | 0.999632i | \(0.491365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | −16.3923 | − | 4.39230i | −0.760994 | − | 0.203908i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.46410 | − | 1.46410i | 0.253120 | − | 0.0678232i | ||||
\(467\) | 26.7685 | + | 7.17260i | 1.23870 | + | 0.331909i | 0.817961 | − | 0.575274i | \(-0.195104\pi\) |
0.420738 | + | 0.907182i | \(0.361771\pi\) | |||||||
\(468\) | 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 | ||||
\(478\) | 5.12436 | − | 19.1244i | 0.234383 | − | 0.874728i | ||||
\(479\) | 12.2474 | − | 21.2132i | 0.559600 | − | 0.969256i | −0.437929 | − | 0.899009i | \(-0.644288\pi\) |
0.997530 | − | 0.0702467i | \(-0.0223786\pi\) | |||||||
\(480\) | 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 | ||||||||
\(485\) | −4.39230 | + | 16.3923i | −0.199444 | + | 0.744336i | ||||
\(486\) | 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 | −0.413900 | − | 0.910323i | \(-0.635834\pi\) |
0.910323 | + | 0.413900i | \(0.135834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0764 | + | 5.37945i | −0.904195 | + | 0.242278i | ||||
\(494\) | 8.78461 | + | 32.7846i | 0.395238 | + | 1.47505i | ||||
\(495\) | −7.34847 | − | 12.7279i | −0.330289 | − | 0.572078i | ||||
\(496\) | 19.5959 | 0.879883 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.41858 | − | 31.4186i | 0.376868 | − | 1.40649i | −0.473729 | − | 0.880671i | \(-0.657092\pi\) |
0.850597 | − | 0.525818i | \(-0.176241\pi\) | |||||||
\(500\) | −3.58630 | − | 13.3843i | −0.160384 | − | 0.598562i | ||||
\(501\) | 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 | ||||
\(509\) | −2.68973 | + | 10.0382i | −0.119220 | + | 0.444935i | −0.999568 | − | 0.0293934i | \(-0.990642\pi\) |
0.880348 | + | 0.474329i | \(0.157309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −40.1528 | + | 10.7589i | −1.77106 | + | 0.474555i | ||||
\(515\) | 32.7846 | − | 8.78461i | 1.44466 | − | 0.387096i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.89898 | − | 4.89898i | 0.215457 | − | 0.215457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.78461 | − | 32.7846i | 0.385231 | − | 1.43770i | ||||
\(521\) | 2.44949 | − | 4.24264i | 0.107314 | − | 0.185873i | −0.807367 | − | 0.590049i | \(-0.799108\pi\) |
0.914681 | + | 0.404176i | \(0.132442\pi\) | |||||||
\(522\) | −9.00000 | + | 15.5885i | −0.393919 | + | 0.682288i | ||||
\(523\) | 5.37945 | − | 20.0764i | 0.235227 | − | 0.877879i | −0.742819 | − | 0.669492i | \(-0.766512\pi\) |
0.978046 | − | 0.208387i | \(-0.0668215\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | −6.69213 | − | 1.79315i | −0.290688 | − | 0.0778895i | ||||
\(531\) | −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 | ||||||||
\(541\) | 39.6147 | + | 10.6147i | 1.70317 | + | 0.456363i | 0.973735 | − | 0.227686i | \(-0.0731160\pi\) |
0.729436 | + | 0.684049i | \(0.239783\pi\) | |||||||
\(542\) | 10.7589 | + | 40.1528i | 0.462135 | + | 1.72471i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.17260 | + | 26.7685i | −0.307523 | + | 1.14769i | ||||
\(545\) | − | 34.2929i | − | 1.46894i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | − | 5.00000i | −0.213785 | − | 0.213785i | 0.592088 | − | 0.805873i | \(-0.298304\pi\) |
−0.805873 | + | 0.592088i | \(0.798304\pi\) | |||||||
\(548\) | 8.00000 | + | 13.8564i | 0.341743 | + | 0.591916i | ||||
\(549\) | 2.68973 | + | 10.0382i | 0.114795 | + | 0.428420i | ||||
\(550\) | −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 | ||||||||
\(556\) | 3.58630 | + | 13.3843i | 0.152093 | + | 0.567619i | ||||
\(557\) | 1.09808 | + | 4.09808i | 0.0465270 | + | 0.173641i | 0.985280 | − | 0.170951i | \(-0.0546839\pi\) |
−0.938753 | + | 0.344592i | \(0.888017\pi\) | |||||||
\(558\) | 5.37945 | − | 20.0764i | 0.227730 | − | 0.849901i | ||||
\(559\) | −24.4949 | −1.03602 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.32051 | + | 27.3205i | −0.308797 | + | 1.15245i | ||||
\(563\) | 8.96575 | + | 33.4607i | 0.377862 | + | 1.41020i | 0.849118 | + | 0.528202i | \(0.177134\pi\) |
−0.471257 | + | 0.881996i | \(0.656200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3843 | − | 3.58630i | −0.563080 | − | 0.150877i | ||||
\(566\) | −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 | −0.732126 | − | 0.681169i | \(-0.761472\pi\) |
0.223847 | + | 0.974624i | \(0.428139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3468 | + | 42.3468i | 0.474848 | + | 1.77216i | 0.621972 | + | 0.783040i | \(0.286332\pi\) |
−0.147123 | + | 0.989118i | \(0.547001\pi\) | |||||||
\(572\) | −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 | \(0.457096\pi\) | |||||||
\(578\) | 2.56218 | + | 9.56218i | 0.106573 | + | 0.397734i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 29.3939 | 1.22051 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00000 | + | 1.73205i | 0.0414158 | + | 0.0717342i | ||||
\(584\) | 26.7685 | − | 7.17260i | 1.10769 | − | 0.296804i | ||||
\(585\) | −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 | −0.999939 | − | 0.0110739i | \(-0.996475\pi\) |
−0.0110739 | − | 0.999939i | \(-0.503525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | − | 24.0000i | 0.988903 | − | 0.988903i | ||||
\(590\) | 32.7846 | + | 8.78461i | 1.34972 | + | 0.361657i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.3205 | − | 7.32051i | 1.12287 | − | 0.300871i | ||||
\(593\) | 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 | \(-0.369126\pi\) | ||||
0.399667 | + | 0.916660i | \(0.369126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.0000 | + | 15.0000i | −0.610847 | + | 0.610847i | ||||
\(604\) | −20.7846 | + | 12.0000i | −0.845714 | + | 0.488273i | ||||
\(605\) | −30.1146 | + | 8.06918i | −1.22433 | + | 0.328059i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.6969 | − | 25.4558i | −0.596530 | − | 1.03322i | −0.993329 | − | 0.115315i | \(-0.963212\pi\) |
0.396799 | − | 0.917906i | \(-0.370121\pi\) | |||||||
\(608\) | 39.1918i | 1.58944i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | − | 12.0000i | 0.485866 | − | 0.485866i | ||||
\(611\) | 4.39230 | − | 16.3923i | 0.177694 | − | 0.663162i | ||||
\(612\) | 25.4558 | + | 14.6969i | 1.02899 | + | 0.594089i | ||||
\(613\) | −25.9545 | + | 6.95448i | −1.04829 | + | 0.280889i | −0.741546 | − | 0.670902i | \(-0.765907\pi\) |
−0.306746 | + | 0.951791i | \(0.599240\pi\) | |||||||
\(614\) | 8.48528 | − | 4.89898i | 0.342438 | − | 0.197707i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.69213 | + | 1.79315i | −0.268979 | + | 0.0720728i | −0.390788 | − | 0.920481i | \(-0.627797\pi\) |
0.121808 | + | 0.992554i | \(0.461131\pi\) | |||||||
\(620\) | −32.7846 | + | 8.78461i | −1.31666 | + | 0.352798i | ||||
\(621\) | 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 | ||||
\(626\) | −5.37945 | − | 20.0764i | −0.215006 | − | 0.802414i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 33.4607 | + | 8.96575i | 1.33523 | + | 0.357773i | ||||
\(629\) | 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 | \(0.616638\pi\) | |||||||
\(632\) | −10.9282 | − | 2.92820i | −0.434701 | − | 0.116478i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.5167 | − | 13.0000i | −0.894251 | − | 0.516296i | ||||
\(635\) | −16.1384 | + | 60.2292i | −0.640431 | + | 2.39012i | ||||
\(636\) | 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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 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 | \(0.792533\pi\) | |||||||
\(648\) | 24.5885 | − | 6.58846i | 0.965926 | − | 0.258819i | ||||
\(649\) | −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 | ||||
\(653\) | −20.4904 | − | 5.49038i | −0.801851 | − | 0.214855i | −0.165454 | − | 0.986217i | \(-0.552909\pi\) |
−0.636396 | + | 0.771362i | \(0.719576\pi\) | |||||||
\(654\) | 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 | −0.998585 | − | 0.0531861i | \(-0.983062\pi\) |
−0.0531861 | − | 0.998585i | \(-0.516938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.896575 | − | 3.34607i | −0.0348727 | − | 0.130147i | 0.946295 | − | 0.323304i | \(-0.104794\pi\) |
−0.981168 | + | 0.193158i | \(0.938127\pi\) | |||||||
\(662\) | 32.9090 | + | 19.0000i | 1.27904 | + | 0.738456i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 30.0000i | − | 1.16248i | ||||||
\(667\) | 16.3923 | + | 4.39230i | 0.634713 | + | 0.170071i | ||||
\(668\) | −19.5959 | + | 33.9411i | −0.758189 | + | 1.31322i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 33.4607 | + | 8.96575i | 1.29270 | + | 0.346377i | ||||
\(671\) | −4.89898 | −0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00000 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(674\) | 38.2487 | + | 10.2487i | 1.47329 | + | 0.394766i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | − | 1.73205i | 0.0384615 | − | 0.0666173i | ||||
\(677\) | 10.0382 | + | 2.68973i | 0.385799 | + | 0.103375i | 0.446505 | − | 0.894781i | \(-0.352668\pi\) |
−0.0607058 | + | 0.998156i | \(0.519335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 48.0000i | − | 1.84072i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.48528 | + | 4.89898i | 0.324918 | + | 0.187592i | ||||
\(683\) | −9.15064 | − | 34.1506i | −0.350139 | − | 1.30674i | −0.886492 | − | 0.462744i | \(-0.846865\pi\) |
0.536353 | − | 0.843994i | \(-0.319802\pi\) | |||||||
\(684\) | 40.1528 | + | 10.7589i | 1.53528 | + | 0.411377i | ||||
\(685\) | −19.5959 | − | 19.5959i | −0.748722 | − | 0.748722i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.3205 | − | 7.32051i | −1.04158 | − | 0.279092i | ||||
\(689\) | 4.24264 | + | 2.44949i | 0.161632 | + | 0.0933181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.3843 | − | 3.58630i | −0.509161 | − | 0.136429i | −0.00491275 | − | 0.999988i | \(-0.501564\pi\) |
−0.504249 | + | 0.863559i | \(0.668230\pi\) | |||||||
\(692\) | 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 | −0.100364 | + | 0.994951i | \(0.532001\pi\) |
−0.994951 | + | 0.100364i | \(0.967999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.4949 | − | 42.4264i | 0.923843 | − | 1.60014i | ||||
\(704\) | −10.9282 | + | 2.92820i | −0.411872 | + | 0.110361i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.79796 | + | 9.79796i | 0.368751 | + | 0.368751i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.41858 | − | 31.4186i | 0.316167 | − | 1.17995i | −0.606732 | − | 0.794906i | \(-0.707520\pi\) |
0.922899 | − | 0.385043i | \(-0.125813\pi\) | |||||||
\(710\) | −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 | ||||
\(716\) | −8.19615 | − | 2.19615i | −0.306305 | − | 0.0820741i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.32051 | − | 27.3205i | −0.273199 | − | 1.01959i | ||||
\(719\) | 12.2474 | + | 21.2132i | 0.456753 | + | 0.791119i | 0.998787 | − | 0.0492373i | \(-0.0156791\pi\) |
−0.542034 | + | 0.840356i | \(0.682346\pi\) | |||||||
\(720\) | −29.3939 | − | 29.3939i | −1.09545 | − | 1.09545i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 29.0000 | + | 29.0000i | 1.07927 | + | 1.07927i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.69213 | + | 1.79315i | −0.248711 | + | 0.0666419i | ||||
\(725\) | −28.6865 | + | 7.68653i | −1.06539 | + | 0.285471i | ||||
\(726\) | 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 | ||||
\(731\) | −33.4607 | + | 8.96575i | −1.23759 | + | 0.331610i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.06918 | + | 30.1146i | −0.298042 | + | 1.11231i | 0.640729 | + | 0.767767i | \(0.278632\pi\) |
−0.938771 | + | 0.344541i | \(0.888035\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | −20.0764 | + | 5.37945i | −0.739022 | + | 0.198020i | ||||
\(739\) | 23.2224 | − | 6.22243i | 0.854251 | − | 0.228896i | 0.194986 | − | 0.980806i | \(-0.437534\pi\) |
0.659265 | + | 0.751910i | \(0.270867\pi\) | |||||||
\(740\) | −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 | −0.333599 | − | 0.942715i | \(-0.608263\pi\) |
0.649616 | + | 0.760263i | \(0.274930\pi\) | |||||||
\(752\) | 9.79796 | − | 16.9706i | 0.357295 | − | 0.618853i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.0764 | − | 5.37945i | −0.731139 | − | 0.195908i | ||||
\(755\) | 29.3939 | − | 29.3939i | 1.06975 | − | 1.06975i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.00000 | − | 5.00000i | −0.181728 | − | 0.181728i | 0.610380 | − | 0.792108i | \(-0.291017\pi\) |
−0.792108 | + | 0.610380i | \(0.791017\pi\) | |||||||
\(758\) | −39.8372 | + | 23.0000i | −1.44695 | + | 0.835398i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.5692 | − | 65.5692i | −0.637303 | − | 2.37845i | ||||
\(761\) | −22.0454 | − | 38.1838i | −0.799145 | − | 1.38416i | −0.920173 | − | 0.391511i | \(-0.871952\pi\) |
0.121028 | − | 0.992649i | \(-0.461381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −40.0000 | −1.44715 | ||||||||
\(765\) | −49.1769 | − | 13.1769i | −1.77800 | − | 0.476412i | ||||
\(766\) | −5.37945 | − | 20.0764i | −0.194368 | − | 0.725390i | ||||
\(767\) | −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 | ||||
\(773\) | −4.48288 | − | 16.7303i | −0.161238 | − | 0.601748i | −0.998490 | − | 0.0549312i | \(-0.982506\pi\) |
0.837252 | − | 0.546817i | \(-0.184161\pi\) | |||||||
\(774\) | −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 | ||||||||
\(779\) | −32.7846 | − | 8.78461i | −1.17463 | − | 0.314741i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.732051 | + | 2.73205i | 0.0261948 | + | 0.0977605i | ||||
\(782\) | 7.17260 | − | 26.7685i | 0.256492 | − | 0.957240i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.0000 | −2.14149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.79315 | + | 6.69213i | 0.0639189 | + | 0.238549i | 0.990493 | − | 0.137564i | \(-0.0439272\pi\) |
−0.926574 | + | 0.376113i | \(0.877261\pi\) | |||||||
\(788\) | −10.9808 | − | 40.9808i | −0.391173 | − | 1.45988i | ||||
\(789\) | 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 | \(-0.150754\pi\) |
−0.456101 | + | 0.889928i | \(0.650754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.0000i | − | 0.849059i | ||||||
\(800\) | −10.2487 | + | 38.2487i | −0.362347 | + | 1.35230i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.92820 | + | 10.9282i | 0.103398 | + | 0.385888i | ||||
\(803\) | 13.3843 | + | 3.58630i | 0.472320 | + | 0.126558i | ||||
\(804\) | 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 | −0.406146 | − | 0.913808i | \(-0.633128\pi\) |
−0.994454 | + | 0.105171i | \(0.966461\pi\) | |||||||
\(810\) | −38.1838 | + | 22.0454i | −1.34164 | + | 0.774597i | ||||
\(811\) | −14.6969 | − | 14.6969i | −0.516079 | − | 0.516079i | 0.400303 | − | 0.916383i | \(-0.368905\pi\) |
−0.916383 | + | 0.400303i | \(0.868905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.6603 | + | 3.66025i | 0.478792 | + | 0.128292i | ||||
\(815\) | 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 | ||||
\(821\) | −6.95448 | + | 25.9545i | −0.242713 | + | 0.905818i | 0.731806 | + | 0.681513i | \(0.238678\pi\) |
−0.974519 | + | 0.224305i | \(0.927989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00000 | − | 5.19615i | 0.104573 | − | 0.181126i | −0.808990 | − | 0.587822i | \(-0.799986\pi\) |
0.913564 | + | 0.406695i | \(0.133319\pi\) | |||||||
\(824\) | −26.7685 | − | 7.17260i | −0.932526 | − | 0.249869i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0000 | − | 33.0000i | 1.14752 | − | 1.14752i | 0.160484 | − | 0.987038i | \(-0.448695\pi\) |
0.987038 | − | 0.160484i | \(-0.0513055\pi\) | |||||||
\(828\) | −12.0000 | − | 20.7846i | −0.417029 | − | 0.722315i | ||||
\(829\) | 10.0382 | − | 2.68973i | 0.348641 | − | 0.0934181i | −0.0802489 | − | 0.996775i | \(-0.525572\pi\) |
0.428890 | + | 0.903357i | \(0.358905\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19.5959 | + | 19.5959i | −0.679366 | + | 0.679366i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.5692 | − | 65.5692i | 0.608008 | − | 2.26912i | ||||
\(836\) | −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 | ||||||||
\(844\) | 0.732051 | + | 2.73205i | 0.0251982 | + | 0.0940411i | ||||
\(845\) | −0.896575 | + | 3.34607i | −0.0308431 | + | 0.115108i | ||||
\(846\) | −14.6969 | − | 14.6969i | −0.505291 | − | 0.505291i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | + | 4.00000i | 0.137361 | + | 0.137361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.5521 | + | 46.8449i | 0.430532 | + | 1.60677i | ||||
\(851\) | −27.3205 | + | 7.32051i | −0.936535 | + | 0.250944i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2474 | + | 12.2474i | −0.419345 | + | 0.419345i | −0.884978 | − | 0.465633i | \(-0.845827\pi\) |
0.465633 | + | 0.884978i | \(0.345827\pi\) | |||||||
\(854\) | 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 | −0.904825 | − | 0.425784i | \(-0.859998\pi\) |
0.821152 | + | 0.570710i | \(0.193332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7589 | − | 40.1528i | 0.367089 | − | 1.37000i | −0.497477 | − | 0.867477i | \(-0.665740\pi\) |
0.864567 | − | 0.502518i | \(-0.167593\pi\) | |||||||
\(860\) | 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 | −0.439880 | − | 0.898056i | \(-0.644979\pi\) |
0.557800 | + | 0.829976i | \(0.311646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | + | 10.3923i | −0.204006 | + | 0.353349i | ||||
\(866\) | −5.37945 | + | 20.0764i | −0.182801 | + | 0.682224i | ||||
\(867\) | 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 | ||||||||
\(877\) | −17.7583 | − | 4.75833i | −0.599656 | − | 0.160677i | −0.0537936 | − | 0.998552i | \(-0.517131\pi\) |
−0.545863 | + | 0.837875i | \(0.683798\pi\) | |||||||
\(878\) | −20.0764 | + | 5.37945i | −0.677545 | + | 0.181548i | ||||
\(879\) | 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 | −0.999022 | − | 0.0442108i | \(-0.985923\pi\) |
−0.0442108 | − | 0.999022i | \(-0.514077\pi\) | |||||||
\(884\) | −8.78461 | + | 32.7846i | −0.295458 | + | 1.10267i | ||||
\(885\) | 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 | ||||||||
\(891\) | 12.2942 | + | 3.29423i | 0.411872 | + | 0.110361i | ||||
\(892\) | −16.9706 | − | 9.79796i | −0.568216 | − | 0.328060i | ||||
\(893\) | −8.78461 | − | 32.7846i | −0.293966 | − | 1.09710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6969 | 0.491264 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.6603 | + | 3.66025i | 0.455849 | + | 0.122144i | ||||
\(899\) | 5.37945 | + | 20.0764i | 0.179415 | + | 0.669585i | ||||
\(900\) | 36.3731 | + | 21.0000i | 1.21244 | + | 0.700000i | ||||
\(901\) | 6.69213 | + | 1.79315i | 0.222947 | + | 0.0597385i | ||||
\(902\) | − | 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 | ||||||||
\(907\) | −2.56218 | − | 9.56218i | −0.0850757 | − | 0.317507i | 0.910253 | − | 0.414053i | \(-0.135887\pi\) |
−0.995329 | + | 0.0965460i | \(0.969220\pi\) | |||||||
\(908\) | 14.3452 | − | 53.5370i | 0.476062 | − | 1.77669i | ||||
\(909\) | −7.34847 | − | 7.34847i | −0.243733 | − | 0.243733i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.0000i | 1.65657i | 0.560304 | + | 0.828287i | \(0.310684\pi\) | ||||
−0.560304 | + | 0.828287i | \(0.689316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.5885 | + | 6.58846i | −0.813314 | + | 0.217927i | ||||
\(915\) | 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 | ||||
\(926\) | −1.46410 | + | 5.46410i | −0.0481134 | + | 0.179562i | ||||
\(927\) | −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 | \(-0.340590\pi\) | ||||
0.480128 | + | 0.877198i | \(0.340590\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.78461 | + | 32.7846i | −0.286522 | + | 1.06932i | ||||
\(941\) | 36.8067 | − | 9.86233i | 1.19986 | − | 0.321503i | 0.397087 | − | 0.917781i | \(-0.370021\pi\) |
0.802778 | + | 0.596278i | \(0.203354\pi\) | |||||||
\(942\) | 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 | ||||
\(947\) | −5.49038 | + | 20.4904i | −0.178413 | + | 0.665848i | 0.817532 | + | 0.575884i | \(0.195342\pi\) |
−0.995945 | + | 0.0899642i | \(0.971325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.7846 | − | 8.78461i | 1.06423 | − | 0.285160i | ||||
\(950\) | 34.2929 | + | 59.3970i | 1.11261 | + | 1.92709i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | 5.19615 | − | 3.00000i | 0.168232 | − | 0.0971286i | ||||
\(955\) | 66.9213 | − | 17.9315i | 2.16552 | − | 0.580250i | ||||
\(956\) | 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 | ||||
\(962\) | 33.4607 | − | 8.96575i | 1.07881 | − | 0.289068i | ||||
\(963\) | −12.2942 | + | 3.29423i | −0.396176 | + | 0.106155i | ||||
\(964\) | −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 | \(0.351349\pi\) | |||||||
\(968\) | 24.5885 | + | 6.58846i | 0.790303 | + | 0.211761i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.0000 | + | 20.7846i | −0.385297 | + | 0.667354i | ||||
\(971\) | 3.58630 | − | 13.3843i | 0.115090 | − | 0.429521i | −0.884204 | − | 0.467101i | \(-0.845298\pi\) |
0.999294 | + | 0.0375801i | \(0.0119649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.0000 | − | 12.0000i | 0.384505 | − | 0.384505i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.3843 | + | 3.58630i | −0.428420 | + | 0.114795i | ||||
\(977\) | −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 | ||||||||
\(989\) | 27.3205 | + | 7.32051i | 0.868742 | + | 0.232779i | ||||
\(990\) | −5.37945 | − | 20.0764i | −0.170970 | − | 0.638070i | ||||
\(991\) | 51.9615 | + | 30.0000i | 1.65061 | + | 0.952981i | 0.976820 | + | 0.214060i | \(0.0686688\pi\) |
0.673792 | + | 0.738921i | \(0.264664\pi\) | |||||||
\(992\) | 26.7685 | + | 7.17260i | 0.849901 | + | 0.227730i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | + | 24.0000i | 0.760851 | + | 0.760851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.68973 | − | 10.0382i | −0.0851845 | − | 0.317913i | 0.910165 | − | 0.414247i | \(-0.135955\pi\) |
−0.995349 | + | 0.0963340i | \(0.969288\pi\) | |||||||
\(998\) | 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.619.1 | 8 | ||
7.2 | even | 3 | inner | 784.2.w.d.411.2 | 8 | ||
7.3 | odd | 6 | 112.2.j.a.27.1 | ✓ | 4 | ||
7.4 | even | 3 | 112.2.j.a.27.2 | yes | 4 | ||
7.5 | odd | 6 | inner | 784.2.w.d.411.1 | 8 | ||
7.6 | odd | 2 | inner | 784.2.w.d.619.2 | 8 | ||
16.3 | odd | 4 | inner | 784.2.w.d.227.1 | 8 | ||
28.3 | even | 6 | 448.2.j.b.335.1 | 4 | |||
28.11 | odd | 6 | 448.2.j.b.335.2 | 4 | |||
56.3 | even | 6 | 896.2.j.e.671.2 | 4 | |||
56.11 | odd | 6 | 896.2.j.e.671.1 | 4 | |||
56.45 | odd | 6 | 896.2.j.b.671.2 | 4 | |||
56.53 | even | 6 | 896.2.j.b.671.1 | 4 | |||
112.3 | even | 12 | 112.2.j.a.83.2 | yes | 4 | ||
112.11 | odd | 12 | 896.2.j.b.223.2 | 4 | |||
112.19 | even | 12 | inner | 784.2.w.d.19.1 | 8 | ||
112.45 | odd | 12 | 448.2.j.b.111.2 | 4 | |||
112.51 | odd | 12 | inner | 784.2.w.d.19.2 | 8 | ||
112.53 | even | 12 | 896.2.j.e.223.2 | 4 | |||
112.59 | even | 12 | 896.2.j.b.223.1 | 4 | |||
112.67 | odd | 12 | 112.2.j.a.83.1 | yes | 4 | ||
112.83 | even | 4 | inner | 784.2.w.d.227.2 | 8 | ||
112.101 | odd | 12 | 896.2.j.e.223.1 | 4 | |||
112.109 | even | 12 | 448.2.j.b.111.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.a.27.1 | ✓ | 4 | 7.3 | odd | 6 | ||
112.2.j.a.27.2 | yes | 4 | 7.4 | even | 3 | ||
112.2.j.a.83.1 | yes | 4 | 112.67 | odd | 12 | ||
112.2.j.a.83.2 | yes | 4 | 112.3 | even | 12 | ||
448.2.j.b.111.1 | 4 | 112.109 | even | 12 | |||
448.2.j.b.111.2 | 4 | 112.45 | odd | 12 | |||
448.2.j.b.335.1 | 4 | 28.3 | even | 6 | |||
448.2.j.b.335.2 | 4 | 28.11 | odd | 6 | |||
784.2.w.d.19.1 | 8 | 112.19 | even | 12 | inner | ||
784.2.w.d.19.2 | 8 | 112.51 | odd | 12 | inner | ||
784.2.w.d.227.1 | 8 | 16.3 | odd | 4 | inner | ||
784.2.w.d.227.2 | 8 | 112.83 | even | 4 | inner | ||
784.2.w.d.411.1 | 8 | 7.5 | odd | 6 | inner | ||
784.2.w.d.411.2 | 8 | 7.2 | even | 3 | inner | ||
784.2.w.d.619.1 | 8 | 1.1 | even | 1 | trivial | ||
784.2.w.d.619.2 | 8 | 7.6 | odd | 2 | inner | ||
896.2.j.b.223.1 | 4 | 112.59 | even | 12 | |||
896.2.j.b.223.2 | 4 | 112.11 | odd | 12 | |||
896.2.j.b.671.1 | 4 | 56.53 | even | 6 | |||
896.2.j.b.671.2 | 4 | 56.45 | odd | 6 | |||
896.2.j.e.223.1 | 4 | 112.101 | odd | 12 | |||
896.2.j.e.223.2 | 4 | 112.53 | even | 12 | |||
896.2.j.e.671.1 | 4 | 56.11 | odd | 6 | |||
896.2.j.e.671.2 | 4 | 56.3 | even | 6 |