Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(109,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.109 |
Dual form | 567.2.g.e.541.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | −0.633316 | − | 0.773893i | \(-0.718307\pi\) |
0.986869 | + | 0.161521i | \(0.0516399\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 4.00000 | 1.78885 | 0.894427 | − | 0.447214i | \(-0.147584\pi\) | ||||
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 3.46410i | 0.632456 | − | 1.09545i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | −0.926995 | − | 0.375073i | \(-0.877618\pi\) |
0.788320 | + | 0.615265i | \(0.210951\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 2.00000 | + | 3.46410i | 0.447214 | + | 0.774597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | + | 1.73205i | −0.213201 | + | 0.369274i | ||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.0000 | 2.20000 | ||||||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | 1.00000 | + | 1.73205i | 0.185695 | + | 0.321634i | 0.943811 | − | 0.330487i | \(-0.107213\pi\) |
−0.758115 | + | 0.652121i | \(0.773880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 2.50000 | + | 4.33013i | 0.441942 | + | 0.765466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | + | 5.19615i | 0.514496 | + | 0.891133i | ||||
\(35\) | 2.00000 | − | 10.3923i | 0.338062 | − | 1.75662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.0000 | 1.89737 | ||||||||
\(41\) | −1.00000 | + | 1.73205i | −0.156174 | + | 0.270501i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) |
0.777312 | + | 0.629115i | \(0.216583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 5.50000 | − | 9.52628i | 0.777817 | − | 1.34722i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 1.50000 | − | 7.79423i | 0.200446 | − | 1.04155i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | −3.00000 | −0.381000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50000 | − | 6.06218i | −0.427593 | − | 0.740613i | 0.569066 | − | 0.822292i | \(-0.307305\pi\) |
−0.996659 | + | 0.0816792i | \(0.973972\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.00000 | − | 6.92820i | −0.956183 | − | 0.828079i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | − | 5.19615i | 0.351123 | − | 0.608164i | −0.635323 | − | 0.772246i | \(-0.719133\pi\) |
0.986447 | + | 0.164083i | \(0.0524664\pi\) | |||||||
\(74\) | −3.00000 | −0.348743 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | −1.00000 | + | 5.19615i | −0.113961 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 2.00000 | − | 3.46410i | 0.223607 | − | 0.387298i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.00000 | + | 1.73205i | 0.110432 | + | 0.191273i | ||||
\(83\) | 3.00000 | + | 5.19615i | 0.329293 | + | 0.570352i | 0.982372 | − | 0.186938i | \(-0.0598564\pi\) |
−0.653079 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | + | 20.7846i | −1.30158 | + | 2.25441i | ||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.00000 | −0.639602 | ||||||||
\(89\) | −2.00000 | − | 3.46410i | −0.212000 | − | 0.367194i | 0.740341 | − | 0.672232i | \(-0.234664\pi\) |
−0.952340 | + | 0.305038i | \(0.901331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | −3.00000 | − | 5.19615i | −0.312772 | − | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | −8.00000 | − | 13.8564i | −0.820783 | − | 1.42164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.50000 | − | 7.79423i | −0.456906 | − | 0.791384i | 0.541890 | − | 0.840450i | \(-0.317709\pi\) |
−0.998796 | + | 0.0490655i | \(0.984376\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.50000 | + | 9.52628i | 0.550000 | + | 0.952628i | ||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0000 | 1.67506 | 0.837530 | − | 0.546392i | \(-0.183999\pi\) | ||||
0.837530 | + | 0.546392i | \(0.183999\pi\) | |||||||
\(104\) | −1.50000 | + | 2.59808i | −0.147087 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 1.00000 | + | 1.73205i | 0.0966736 | + | 0.167444i | 0.910306 | − | 0.413936i | \(-0.135846\pi\) |
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | + | 7.79423i | −0.431022 | + | 0.746552i | −0.996962 | − | 0.0778949i | \(-0.975180\pi\) |
0.565940 | + | 0.824447i | \(0.308513\pi\) | |||||||
\(110\) | −4.00000 | + | 6.92820i | −0.381385 | + | 0.660578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | −8.00000 | + | 13.8564i | −0.752577 | + | 1.30350i | 0.193993 | + | 0.981003i | \(0.437856\pi\) |
−0.946570 | + | 0.322498i | \(0.895477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.0000 | −2.23801 | ||||||||
\(116\) | −1.00000 | + | 1.73205i | −0.0928477 | + | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 12.0000 | + | 10.3923i | 1.10004 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −2.50000 | − | 4.33013i | −0.226339 | − | 0.392031i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50000 | − | 2.59808i | 0.134704 | − | 0.233314i | ||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | −0.798621 | −0.399310 | − | 0.916816i | \(-0.630750\pi\) | ||||
−0.399310 | + | 0.916816i | \(0.630750\pi\) | |||||||
\(128\) | −1.50000 | + | 2.59808i | −0.132583 | + | 0.229640i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.0000 | + | 3.46410i | −0.867110 | + | 0.300376i | ||||
\(134\) | −7.00000 | −0.604708 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.00000 | + | 15.5885i | −0.771744 | + | 1.33670i | ||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50000 | + | 7.79423i | −0.381685 | + | 0.661098i | −0.991303 | − | 0.131597i | \(-0.957989\pi\) |
0.609618 | + | 0.792695i | \(0.291323\pi\) | |||||||
\(140\) | 10.0000 | − | 3.46410i | 0.845154 | − | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | − | 1.73205i | 0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | + | 6.92820i | 0.332182 | + | 0.575356i | ||||
\(146\) | −3.00000 | − | 5.19615i | −0.248282 | − | 0.430037i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.50000 | − | 2.59808i | 0.123299 | − | 0.213561i | ||||
\(149\) | 24.0000 | 1.96616 | 0.983078 | − | 0.183186i | \(-0.0586410\pi\) | ||||
0.983078 | + | 0.183186i | \(0.0586410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | 0.406894 | 0.203447 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203447 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(152\) | −6.00000 | − | 10.3923i | −0.486664 | − | 0.842927i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000 | + | 3.46410i | 0.322329 | + | 0.279145i | ||||
\(155\) | −6.00000 | − | 10.3923i | −0.481932 | − | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | − | 8.66025i | −0.399043 | − | 0.691164i | 0.594565 | − | 0.804048i | \(-0.297324\pi\) |
−0.993608 | + | 0.112884i | \(0.963991\pi\) | |||||||
\(158\) | 5.50000 | + | 9.52628i | 0.437557 | + | 0.757870i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.0000 | + | 17.3205i | 0.790569 | + | 1.36931i | ||||
\(161\) | −3.00000 | + | 15.5885i | −0.236433 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.50000 | − | 16.4545i | −0.744097 | − | 1.28881i | −0.950615 | − | 0.310372i | \(-0.899546\pi\) |
0.206518 | − | 0.978443i | \(-0.433787\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 7.00000 | − | 12.1244i | 0.541676 | − | 0.938211i | −0.457132 | − | 0.889399i | \(-0.651123\pi\) |
0.998808 | − | 0.0488118i | \(-0.0155435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 12.0000 | + | 20.7846i | 0.920358 | + | 1.59411i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.500000 | + | 0.866025i | −0.0381246 | + | 0.0660338i | ||||
\(173\) | 8.00000 | − | 13.8564i | 0.608229 | − | 1.05348i | −0.383304 | − | 0.923622i | \(-0.625214\pi\) |
0.991532 | − | 0.129861i | \(-0.0414530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.50000 | − | 28.5788i | 0.415761 | − | 2.16036i | ||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.00000 | −0.299813 | ||||||||
\(179\) | 2.00000 | − | 3.46410i | 0.149487 | − | 0.258919i | −0.781551 | − | 0.623841i | \(-0.785571\pi\) |
0.931038 | + | 0.364922i | \(0.118904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 2.50000 | − | 0.866025i | 0.185312 | − | 0.0641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.0000 | −1.32698 | ||||||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.0000 | −1.16076 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5000 | + | 21.6506i | 0.899770 | + | 1.55845i | 0.827788 | + | 0.561041i | \(0.189599\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | −9.00000 | −0.646162 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | −20.0000 | −1.42494 | −0.712470 | − | 0.701702i | \(-0.752424\pi\) | ||||
−0.712470 | + | 0.701702i | \(0.752424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.50000 | − | 7.79423i | 0.318997 | − | 0.552518i | −0.661282 | − | 0.750137i | \(-0.729987\pi\) |
0.980279 | + | 0.197619i | \(0.0633208\pi\) | |||||||
\(200\) | 33.0000 | 2.33345 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.00000 | − | 6.92820i | 0.281439 | − | 0.487467i | ||||
\(203\) | 5.00000 | − | 1.73205i | 0.350931 | − | 0.121566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 6.92820i | −0.279372 | + | 0.483887i | ||||
\(206\) | 8.50000 | − | 14.7224i | 0.592223 | − | 1.02576i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | 4.00000 | + | 6.92820i | 0.276686 | + | 0.479234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | − | 4.33013i | 0.172107 | − | 0.298098i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) |
0.939156 | + | 0.343490i | \(0.111609\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 2.00000 | + | 3.46410i | 0.136399 | + | 0.236250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.50000 | + | 2.59808i | −0.509133 | + | 0.176369i | ||||
\(218\) | 4.50000 | + | 7.79423i | 0.304778 | + | 0.527892i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | − | 6.92820i | −0.269680 | − | 0.467099i | ||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | − | 13.8564i | −0.535720 | − | 0.927894i | −0.999128 | − | 0.0417488i | \(-0.986707\pi\) |
0.463409 | − | 0.886145i | \(-0.346626\pi\) | |||||||
\(224\) | 12.5000 | − | 4.33013i | 0.835191 | − | 0.289319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.00000 | + | 13.8564i | 0.532152 | + | 0.921714i | ||||
\(227\) | −18.0000 | −1.19470 | −0.597351 | − | 0.801980i | \(-0.703780\pi\) | ||||
−0.597351 | + | 0.801980i | \(0.703780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | −0.462573 | −0.231287 | − | 0.972886i | \(-0.574293\pi\) | ||||
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | −12.0000 | + | 20.7846i | −0.791257 | + | 1.37050i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | + | 5.19615i | 0.196960 | + | 0.341144i | ||||
\(233\) | −12.0000 | − | 20.7846i | −0.786146 | − | 1.36165i | −0.928312 | − | 0.371802i | \(-0.878740\pi\) |
0.142166 | − | 0.989843i | \(-0.454593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | − | 20.7846i | 0.782794 | − | 1.35584i | ||||
\(236\) | −3.00000 | + | 5.19615i | −0.195283 | + | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.0000 | − | 5.19615i | 0.972306 | − | 0.336817i | ||||
\(239\) | −6.00000 | + | 10.3923i | −0.388108 | + | 0.672222i | −0.992195 | − | 0.124696i | \(-0.960204\pi\) |
0.604087 | + | 0.796918i | \(0.293538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0000 | 1.09507 | 0.547533 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | −3.50000 | + | 6.06218i | −0.224989 | + | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.00000 | 0.320092 | ||||||||
\(245\) | −26.0000 | − | 10.3923i | −1.66108 | − | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | −4.50000 | − | 7.79423i | −0.285750 | − | 0.494934i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | − | 20.7846i | 0.758947 | − | 1.31453i | ||||
\(251\) | −26.0000 | −1.64111 | −0.820553 | − | 0.571571i | \(-0.806334\pi\) | ||||
−0.820553 | + | 0.571571i | \(0.806334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | −4.50000 | + | 7.79423i | −0.282355 | + | 0.489053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | −10.0000 | −0.623783 | −0.311891 | − | 0.950118i | \(-0.600963\pi\) | ||||
−0.311891 | + | 0.950118i | \(0.600963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.50000 | + | 2.59808i | −0.466027 | + | 0.161437i | ||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.00000 | − | 3.46410i | 0.123560 | − | 0.214013i | ||||
\(263\) | −2.00000 | −0.123325 | −0.0616626 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616626 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | + | 20.7846i | −0.737154 | + | 1.27679i | ||||
\(266\) | −2.00000 | + | 10.3923i | −0.122628 | + | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.50000 | − | 6.06218i | 0.213797 | − | 0.370306i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.50000 | + | 9.52628i | 0.334101 | + | 0.578680i | 0.983312 | − | 0.181928i | \(-0.0582339\pi\) |
−0.649211 | + | 0.760609i | \(0.724901\pi\) | |||||||
\(272\) | 3.00000 | + | 5.19615i | 0.181902 | + | 0.315063i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.00000 | + | 15.5885i | −0.543710 | + | 0.941733i | ||||
\(275\) | −22.0000 | −1.32665 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | 0.781094 | 0.390547 | − | 0.920583i | \(-0.372286\pi\) | ||||
0.390547 | + | 0.920583i | \(0.372286\pi\) | |||||||
\(278\) | 4.50000 | + | 7.79423i | 0.269892 | + | 0.467467i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.00000 | − | 31.1769i | 0.358569 | − | 1.86318i | ||||
\(281\) | 8.00000 | + | 13.8564i | 0.477240 | + | 0.826604i | 0.999660 | − | 0.0260845i | \(-0.00830391\pi\) |
−0.522420 | + | 0.852688i | \(0.674971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.50000 | + | 4.33013i | 0.148610 | + | 0.257399i | 0.930714 | − | 0.365748i | \(-0.119187\pi\) |
−0.782104 | + | 0.623148i | \(0.785854\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.00000 | − | 1.73205i | −0.0591312 | − | 0.102418i | ||||
\(287\) | 4.00000 | + | 3.46410i | 0.236113 | + | 0.204479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 8.00000 | 0.469776 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | 0.351123 | ||||||||
\(293\) | 11.0000 | − | 19.0526i | 0.642627 | − | 1.11306i | −0.342217 | − | 0.939621i | \(-0.611178\pi\) |
0.984844 | − | 0.173442i | \(-0.0554888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | + | 20.7846i | 0.698667 | + | 1.21013i | ||||
\(296\) | −4.50000 | − | 7.79423i | −0.261557 | − | 0.453030i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0000 | − | 20.7846i | 0.695141 | − | 1.20402i | ||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.50000 | − | 0.866025i | 0.144098 | − | 0.0499169i | ||||
\(302\) | 2.50000 | − | 4.33013i | 0.143859 | − | 0.249171i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 10.0000 | − | 17.3205i | 0.572598 | − | 0.991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0000 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247149\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247149\pi\) | |||||||
\(308\) | −5.00000 | + | 1.73205i | −0.284901 | + | 0.0986928i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.0000 | −0.681554 | ||||||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0000 | − | 19.0526i | 0.621757 | − | 1.07691i | −0.367402 | − | 0.930062i | \(-0.619753\pi\) |
0.989158 | − | 0.146852i | \(-0.0469141\pi\) | |||||||
\(314\) | −10.0000 | −0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.0000 | −0.618798 | ||||||||
\(317\) | 15.0000 | − | 25.9808i | 0.842484 | − | 1.45922i | −0.0453045 | − | 0.998973i | \(-0.514426\pi\) |
0.887788 | − | 0.460252i | \(-0.152241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | − | 3.46410i | −0.111979 | − | 0.193952i | ||||
\(320\) | 28.0000 | 1.56525 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.0000 | + | 10.3923i | 0.668734 | + | 0.579141i | ||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.50000 | + | 9.52628i | −0.305085 | + | 0.528423i | ||||
\(326\) | −19.0000 | −1.05231 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | −12.0000 | − | 10.3923i | −0.661581 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.00000 | − | 12.1244i | −0.383023 | − | 0.663415i | ||||
\(335\) | −14.0000 | − | 24.2487i | −0.764902 | − | 1.32485i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | + | 8.66025i | −0.272367 | + | 0.471754i | −0.969468 | − | 0.245220i | \(-0.921140\pi\) |
0.697100 | + | 0.716974i | \(0.254473\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.0000 | −1.30158 | ||||||||
\(341\) | 3.00000 | + | 5.19615i | 0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 1.50000 | + | 2.59808i | 0.0808746 | + | 0.140079i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.00000 | − | 13.8564i | −0.430083 | − | 0.744925i | ||||
\(347\) | 8.00000 | + | 13.8564i | 0.429463 | + | 0.743851i | 0.996826 | − | 0.0796169i | \(-0.0253697\pi\) |
−0.567363 | + | 0.823468i | \(0.692036\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50000 | + | 4.33013i | 0.133822 | + | 0.231786i | 0.925147 | − | 0.379610i | \(-0.123942\pi\) |
−0.791325 | + | 0.611396i | \(0.790608\pi\) | |||||||
\(350\) | −22.0000 | − | 19.0526i | −1.17595 | − | 1.01840i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.00000 | − | 8.66025i | −0.266501 | − | 0.461593i | ||||
\(353\) | 28.0000 | 1.49029 | 0.745145 | − | 0.666903i | \(-0.232380\pi\) | ||||
0.745145 | + | 0.666903i | \(0.232380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000 | − | 3.46410i | 0.106000 | − | 0.183597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | − | 3.46410i | −0.105703 | − | 0.183083i | ||||
\(359\) | 11.0000 | + | 19.0526i | 0.580558 | + | 1.00556i | 0.995413 | + | 0.0956683i | \(0.0304988\pi\) |
−0.414855 | + | 0.909887i | \(0.636168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | −1.00000 | + | 1.73205i | −0.0525588 | + | 0.0910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.500000 | + | 2.59808i | −0.0262071 | + | 0.136176i | ||||
\(365\) | 12.0000 | − | 20.7846i | 0.628109 | − | 1.08792i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0000 | 0.626395 | 0.313197 | − | 0.949688i | \(-0.398600\pi\) | ||||
0.313197 | + | 0.949688i | \(0.398600\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.0000 | −0.623850 | ||||||||
\(371\) | 12.0000 | + | 10.3923i | 0.623009 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0000 | 1.34623 | 0.673114 | − | 0.739538i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739538i | \(0.264956\pi\) | |||||||
\(374\) | −6.00000 | − | 10.3923i | −0.310253 | − | 0.537373i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.00000 | − | 15.5885i | 0.464140 | − | 0.803913i | ||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.00000 | −0.462299 | −0.231149 | − | 0.972918i | \(-0.574249\pi\) | ||||
−0.231149 | + | 0.972918i | \(0.574249\pi\) | |||||||
\(380\) | 8.00000 | − | 13.8564i | 0.410391 | − | 0.710819i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.00000 | + | 3.46410i | 0.102329 | + | 0.177239i | ||||
\(383\) | 18.0000 | 0.919757 | 0.459879 | − | 0.887982i | \(-0.347893\pi\) | ||||
0.459879 | + | 0.887982i | \(0.347893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | + | 20.7846i | −0.203859 | + | 1.05928i | ||||
\(386\) | 25.0000 | 1.27247 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.50000 | − | 7.79423i | 0.228453 | − | 0.395692i | ||||
\(389\) | 12.0000 | 0.608424 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | − | 31.1769i | 0.910299 | − | 1.57668i | ||||
\(392\) | −19.5000 | − | 7.79423i | −0.984899 | − | 0.393668i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0000 | + | 17.3205i | −0.503793 | + | 0.872595i | ||||
\(395\) | −22.0000 | + | 38.1051i | −1.10694 | + | 1.91728i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5000 | + | 28.5788i | 0.828111 | + | 1.43433i | 0.899518 | + | 0.436884i | \(0.143918\pi\) |
−0.0714068 | + | 0.997447i | \(0.522749\pi\) | |||||||
\(398\) | −4.50000 | − | 7.79423i | −0.225565 | − | 0.390689i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.50000 | − | 9.52628i | 0.275000 | − | 0.476314i | ||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | 0.149441 | ||||||||
\(404\) | 4.00000 | + | 6.92820i | 0.199007 | + | 0.344691i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.00000 | − | 5.19615i | 0.0496292 | − | 0.257881i | ||||
\(407\) | 3.00000 | + | 5.19615i | 0.148704 | + | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | − | 4.33013i | −0.123617 | − | 0.214111i | 0.797574 | − | 0.603220i | \(-0.206116\pi\) |
−0.921192 | + | 0.389109i | \(0.872783\pi\) | |||||||
\(410\) | 4.00000 | + | 6.92820i | 0.197546 | + | 0.342160i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.50000 | + | 14.7224i | 0.418765 | + | 0.725322i | ||||
\(413\) | 15.0000 | − | 5.19615i | 0.738102 | − | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | + | 20.7846i | 0.589057 | + | 1.02028i | ||||
\(416\) | −5.00000 | −0.245145 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000 | 0.391293 | ||||||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | −2.50000 | − | 4.33013i | −0.121698 | − | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.00000 | + | 15.5885i | −0.437079 | + | 0.757042i | ||||
\(425\) | −33.0000 | + | 57.1577i | −1.60074 | + | 2.77255i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0000 | − | 8.66025i | −0.483934 | − | 0.419099i | ||||
\(428\) | −1.00000 | + | 1.73205i | −0.0483368 | + | 0.0837218i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | 9.00000 | − | 15.5885i | 0.433515 | − | 0.750870i | −0.563658 | − | 0.826008i | \(-0.690607\pi\) |
0.997173 | + | 0.0751385i | \(0.0239399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.0000 | −0.816968 | −0.408484 | − | 0.912766i | \(-0.633942\pi\) | ||||
−0.408484 | + | 0.912766i | \(0.633942\pi\) | |||||||
\(434\) | −1.50000 | + | 7.79423i | −0.0720023 | + | 0.374135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.00000 | −0.431022 | ||||||||
\(437\) | 12.0000 | + | 20.7846i | 0.574038 | + | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | + | 20.7846i | −0.572729 | + | 0.991995i | 0.423556 | + | 0.905870i | \(0.360782\pi\) |
−0.996284 | + | 0.0861252i | \(0.972552\pi\) | |||||||
\(440\) | −24.0000 | −1.14416 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | −12.0000 | + | 20.7846i | −0.570137 | + | 0.987507i | 0.426414 | + | 0.904528i | \(0.359777\pi\) |
−0.996551 | + | 0.0829786i | \(0.973557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | − | 13.8564i | −0.379236 | − | 0.656857i | ||||
\(446\) | −16.0000 | −0.757622 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.50000 | − | 18.1865i | 0.165359 | − | 0.859233i | ||||
\(449\) | 36.0000 | 1.69895 | 0.849473 | − | 0.527633i | \(-0.176920\pi\) | ||||
0.849473 | + | 0.527633i | \(0.176920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | − | 3.46410i | 0.0941763 | − | 0.163118i | ||||
\(452\) | −16.0000 | −0.752577 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.00000 | + | 15.5885i | −0.422391 | + | 0.731603i | ||||
\(455\) | 8.00000 | + | 6.92820i | 0.375046 | + | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.50000 | + | 11.2583i | −0.304057 | + | 0.526642i | −0.977051 | − | 0.213006i | \(-0.931675\pi\) |
0.672994 | + | 0.739648i | \(0.265008\pi\) | |||||||
\(458\) | −3.50000 | + | 6.06218i | −0.163544 | + | 0.283267i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | − | 20.7846i | −0.559503 | − | 0.969087i | ||||
\(461\) | −1.00000 | − | 1.73205i | −0.0465746 | − | 0.0806696i | 0.841798 | − | 0.539792i | \(-0.181497\pi\) |
−0.888373 | + | 0.459123i | \(0.848164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | − | 27.7128i | 0.743583 | − | 1.28792i | −0.207271 | − | 0.978284i | \(-0.566458\pi\) |
0.950854 | − | 0.309640i | \(-0.100209\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0000 | −1.11178 | ||||||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5000 | + | 6.06218i | −0.808075 | + | 0.279925i | ||||
\(470\) | −12.0000 | − | 20.7846i | −0.553519 | − | 0.958723i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.00000 | + | 15.5885i | 0.414259 | + | 0.717517i | ||||
\(473\) | −1.00000 | − | 1.73205i | −0.0459800 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.0000 | − | 38.1051i | −1.00943 | − | 1.74838i | ||||
\(476\) | −3.00000 | + | 15.5885i | −0.137505 | + | 0.714496i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.00000 | + | 10.3923i | 0.274434 | + | 0.475333i | ||||
\(479\) | −16.0000 | −0.731059 | −0.365529 | − | 0.930800i | \(-0.619112\pi\) | ||||
−0.365529 | + | 0.930800i | \(0.619112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.00000 | 0.136788 | ||||||||
\(482\) | 8.50000 | − | 14.7224i | 0.387164 | − | 0.670588i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.50000 | − | 6.06218i | −0.159091 | − | 0.275554i | ||||
\(485\) | −18.0000 | − | 31.1769i | −0.817338 | − | 1.41567i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | + | 13.8564i | −0.362515 | + | 0.627894i | −0.988374 | − | 0.152042i | \(-0.951415\pi\) |
0.625859 | + | 0.779936i | \(0.284748\pi\) | |||||||
\(488\) | 7.50000 | − | 12.9904i | 0.339509 | − | 0.588047i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22.0000 | + | 17.3205i | −0.993859 | + | 0.782461i | ||||
\(491\) | 17.0000 | − | 29.4449i | 0.767199 | − | 1.32883i | −0.171877 | − | 0.985118i | \(-0.554983\pi\) |
0.939076 | − | 0.343710i | \(-0.111684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 2.00000 | − | 3.46410i | 0.0899843 | − | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.0000 | −0.761025 | −0.380512 | − | 0.924776i | \(-0.624252\pi\) | ||||
−0.380512 | + | 0.924776i | \(0.624252\pi\) | |||||||
\(500\) | 12.0000 | + | 20.7846i | 0.536656 | + | 0.929516i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.0000 | + | 22.5167i | −0.580218 | + | 1.00497i | ||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.0000 | 1.42398 | ||||||||
\(506\) | 6.00000 | − | 10.3923i | 0.266733 | − | 0.461994i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.50000 | − | 7.79423i | −0.199655 | − | 0.345813i | ||||
\(509\) | −22.0000 | −0.975133 | −0.487566 | − | 0.873086i | \(-0.662115\pi\) | ||||
−0.487566 | + | 0.873086i | \(0.662115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 10.3923i | −0.530849 | − | 0.459728i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.00000 | + | 8.66025i | −0.220541 | + | 0.381987i | ||||
\(515\) | 68.0000 | 2.99644 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | + | 10.3923i | −0.263880 | + | 0.457053i | ||||
\(518\) | −1.50000 | + | 7.79423i | −0.0659062 | + | 0.342459i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | + | 10.3923i | −0.263117 | + | 0.455733i | ||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.50000 | + | 14.7224i | 0.371679 | + | 0.643767i | 0.989824 | − | 0.142297i | \(-0.0454489\pi\) |
−0.618145 | + | 0.786064i | \(0.712116\pi\) | |||||||
\(524\) | 2.00000 | + | 3.46410i | 0.0873704 | + | 0.151330i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.00000 | + | 1.73205i | −0.0436021 | + | 0.0755210i | ||||
\(527\) | 18.0000 | 0.784092 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 12.0000 | + | 20.7846i | 0.521247 | + | 0.902826i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.00000 | − | 6.92820i | −0.346844 | − | 0.300376i | ||||
\(533\) | −1.00000 | − | 1.73205i | −0.0433148 | − | 0.0750234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | + | 6.92820i | 0.172935 | + | 0.299532i | ||||
\(536\) | −10.5000 | − | 18.1865i | −0.453531 | − | 0.785539i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.0000 | + | 5.19615i | 0.559950 | + | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 11.0000 | 0.472490 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.0000 | −1.28624 | ||||||||
\(545\) | −18.0000 | + | 31.1769i | −0.771035 | + | 1.33547i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5000 | − | 37.2391i | −0.919274 | − | 1.59223i | −0.800521 | − | 0.599305i | \(-0.795444\pi\) |
−0.118753 | − | 0.992924i | \(-0.537890\pi\) | |||||||
\(548\) | −9.00000 | − | 15.5885i | −0.384461 | − | 0.665906i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.0000 | + | 19.0526i | −0.469042 | + | 0.812404i | ||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0000 | + | 19.0526i | 0.935535 | + | 0.810197i | ||||
\(554\) | 6.50000 | − | 11.2583i | 0.276159 | − | 0.478321i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.00000 | −0.381685 | ||||||||
\(557\) | −14.0000 | + | 24.2487i | −0.593199 | + | 1.02745i | 0.400599 | + | 0.916253i | \(0.368802\pi\) |
−0.993798 | + | 0.111198i | \(0.964531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | −8.00000 | − | 6.92820i | −0.338062 | − | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.0000 | 0.674919 | ||||||||
\(563\) | −5.00000 | − | 8.66025i | −0.210725 | − | 0.364986i | 0.741217 | − | 0.671266i | \(-0.234249\pi\) |
−0.951942 | + | 0.306280i | \(0.900916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.0000 | + | 55.4256i | −1.34625 | + | 2.33177i | ||||
\(566\) | 5.00000 | 0.210166 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0000 | − | 27.7128i | 0.670755 | − | 1.16178i | −0.306935 | − | 0.951730i | \(-0.599304\pi\) |
0.977690 | − | 0.210051i | \(-0.0673631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 2.00000 | 0.0836242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.00000 | − | 1.73205i | 0.208696 | − | 0.0722944i | ||||
\(575\) | −66.0000 | −2.75239 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | − | 14.7224i | 0.353860 | − | 0.612903i | −0.633062 | − | 0.774101i | \(-0.718202\pi\) |
0.986922 | + | 0.161198i | \(0.0515357\pi\) | |||||||
\(578\) | −19.0000 | −0.790296 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.00000 | + | 6.92820i | −0.166091 | + | 0.287678i | ||||
\(581\) | 15.0000 | − | 5.19615i | 0.622305 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | 9.00000 | − | 15.5885i | 0.372423 | − | 0.645055i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.0000 | − | 19.0526i | −0.454406 | − | 0.787054i | ||||
\(587\) | −14.0000 | − | 24.2487i | −0.577842 | − | 1.00085i | −0.995726 | − | 0.0923513i | \(-0.970562\pi\) |
0.417885 | − | 0.908500i | \(-0.362772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | + | 10.3923i | −0.247226 | + | 0.428207i | ||||
\(590\) | 24.0000 | 0.988064 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | −0.123299 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.0000 | + | 41.5692i | 1.96781 | + | 1.70417i | ||||
\(596\) | 12.0000 | + | 20.7846i | 0.491539 | + | 0.851371i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5000 | + | 28.5788i | 0.673049 | + | 1.16576i | 0.977035 | + | 0.213079i | \(0.0683491\pi\) |
−0.303986 | + | 0.952676i | \(0.598318\pi\) | |||||||
\(602\) | 0.500000 | − | 2.59808i | 0.0203785 | − | 0.105890i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.50000 | + | 4.33013i | 0.101724 | + | 0.176190i | ||||
\(605\) | −28.0000 | −1.13836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 10.0000 | − | 17.3205i | 0.405554 | − | 0.702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0000 | − | 17.3205i | −0.404888 | − | 0.701287i | ||||
\(611\) | 3.00000 | + | 5.19615i | 0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.50000 | + | 6.06218i | −0.141364 | + | 0.244849i | −0.928010 | − | 0.372554i | \(-0.878482\pi\) |
0.786647 | + | 0.617403i | \(0.211815\pi\) | |||||||
\(614\) | 12.5000 | − | 21.6506i | 0.504459 | − | 0.873749i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | + | 15.5885i | −0.120873 | + | 0.628077i | ||||
\(617\) | −9.00000 | + | 15.5885i | −0.362326 | + | 0.627568i | −0.988343 | − | 0.152242i | \(-0.951351\pi\) |
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.0000 | −1.64793 | −0.823965 | − | 0.566641i | \(-0.808243\pi\) | ||||
−0.823965 | + | 0.566641i | \(0.808243\pi\) | |||||||
\(620\) | 6.00000 | − | 10.3923i | 0.240966 | − | 0.417365i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | −10.0000 | + | 3.46410i | −0.400642 | + | 0.138786i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 41.0000 | 1.64000 | ||||||||
\(626\) | −11.0000 | − | 19.0526i | −0.439648 | − | 0.761493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.00000 | − | 8.66025i | 0.199522 | − | 0.345582i | ||||
\(629\) | 18.0000 | 0.717707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | −16.5000 | + | 28.5788i | −0.656335 | + | 1.13681i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.0000 | − | 25.9808i | −0.595726 | − | 1.03183i | ||||
\(635\) | −36.0000 | −1.42862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.50000 | − | 4.33013i | 0.217918 | − | 0.171566i | ||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.00000 | + | 10.3923i | −0.237171 | + | 0.410792i | ||||
\(641\) | −6.00000 | −0.236986 | −0.118493 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118493 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5000 | − | 21.6506i | 0.492952 | − | 0.853818i | −0.507015 | − | 0.861937i | \(-0.669251\pi\) |
0.999967 | + | 0.00811944i | \(0.00258453\pi\) | |||||||
\(644\) | −15.0000 | + | 5.19615i | −0.591083 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | − | 20.7846i | 0.472134 | − | 0.817760i | ||||
\(647\) | 14.0000 | − | 24.2487i | 0.550397 | − | 0.953315i | −0.447849 | − | 0.894109i | \(-0.647810\pi\) |
0.998246 | − | 0.0592060i | \(-0.0188569\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | − | 10.3923i | −0.235521 | − | 0.407934i | ||||
\(650\) | 5.50000 | + | 9.52628i | 0.215728 | + | 0.373651i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.50000 | − | 16.4545i | 0.372049 | − | 0.644407i | ||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0000 | 0.625172 | ||||||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.0000 | + | 5.19615i | −0.584761 | + | 0.202567i | ||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | −14.0000 | − | 24.2487i | −0.544125 | − | 0.942453i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | + | 15.5885i | 0.349268 | + | 0.604949i | ||||
\(665\) | −40.0000 | + | 13.8564i | −1.55113 | + | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.00000 | − | 10.3923i | −0.232321 | − | 0.402392i | ||||
\(668\) | 14.0000 | 0.541676 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.0000 | −1.08173 | ||||||||
\(671\) | −5.00000 | + | 8.66025i | −0.193023 | + | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0000 | − | 19.0526i | −0.424019 | − | 0.734422i | 0.572309 | − | 0.820038i | \(-0.306048\pi\) |
−0.996328 | + | 0.0856156i | \(0.972714\pi\) | |||||||
\(674\) | 5.00000 | + | 8.66025i | 0.192593 | + | 0.333581i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 6.00000 | − | 10.3923i | 0.230599 | − | 0.399409i | −0.727386 | − | 0.686229i | \(-0.759265\pi\) |
0.957984 | + | 0.286820i | \(0.0925982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.5000 | + | 7.79423i | −0.863471 | + | 0.299115i | ||||
\(680\) | −36.0000 | + | 62.3538i | −1.38054 | + | 2.39116i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −72.0000 | −2.75098 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5000 | + | 35.5070i | −0.779857 | + | 1.35075i | 0.152167 | + | 0.988355i | \(0.451375\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 16.0000 | 0.608229 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000 | 0.607352 | ||||||||
\(695\) | −18.0000 | + | 31.1769i | −0.682779 | + | 1.18261i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | − | 10.3923i | −0.227266 | − | 0.393637i | ||||
\(698\) | 5.00000 | 0.189253 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 27.5000 | − | 9.52628i | 1.03940 | − | 0.360060i | ||||
\(701\) | −24.0000 | −0.906467 | −0.453234 | − | 0.891392i | \(-0.649730\pi\) | ||||
−0.453234 | + | 0.891392i | \(0.649730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 10.3923i | −0.226294 | + | 0.391953i | ||||
\(704\) | −14.0000 | −0.527645 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.0000 | − | 24.2487i | 0.526897 | − | 0.912612i | ||||
\(707\) | 4.00000 | − | 20.7846i | 0.150435 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5000 | + | 18.1865i | −0.394336 | + | 0.683010i | −0.993016 | − | 0.117978i | \(-0.962359\pi\) |
0.598680 | + | 0.800988i | \(0.295692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.00000 | − | 10.3923i | −0.224860 | − | 0.389468i | ||||
\(713\) | 9.00000 | + | 15.5885i | 0.337053 | + | 0.583792i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | − | 6.92820i | 0.149592 | − | 0.259100i | ||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.0000 | 0.821033 | ||||||||
\(719\) | −24.0000 | − | 41.5692i | −0.895049 | − | 1.55027i | −0.833744 | − | 0.552151i | \(-0.813807\pi\) |
−0.0613050 | − | 0.998119i | \(-0.519526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.50000 | − | 44.1673i | 0.316557 | − | 1.64488i | ||||
\(722\) | −1.50000 | − | 2.59808i | −0.0558242 | − | 0.0966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 11.0000 | + | 19.0526i | 0.408530 | + | 0.707594i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5000 | − | 35.5070i | −0.760303 | − | 1.31688i | −0.942694 | − | 0.333657i | \(-0.891717\pi\) |
0.182392 | − | 0.983226i | \(-0.441616\pi\) | |||||||
\(728\) | 6.00000 | + | 5.19615i | 0.222375 | + | 0.192582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.0000 | − | 20.7846i | −0.444140 | − | 0.769273i | ||||
\(731\) | −6.00000 | −0.221918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.0000 | 0.775653 | 0.387826 | − | 0.921732i | \(-0.373226\pi\) | ||||
0.387826 | + | 0.921732i | \(0.373226\pi\) | |||||||
\(734\) | 6.00000 | − | 10.3923i | 0.221464 | − | 0.383587i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.0000 | − | 25.9808i | −0.552907 | − | 0.957664i | ||||
\(737\) | 7.00000 | + | 12.1244i | 0.257848 | + | 0.446606i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.50000 | − | 7.79423i | 0.165535 | − | 0.286715i | −0.771310 | − | 0.636460i | \(-0.780398\pi\) |
0.936845 | + | 0.349744i | \(0.113732\pi\) | |||||||
\(740\) | 6.00000 | − | 10.3923i | 0.220564 | − | 0.382029i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0000 | − | 5.19615i | 0.550667 | − | 0.190757i | ||||
\(743\) | −21.0000 | + | 36.3731i | −0.770415 | + | 1.33440i | 0.166920 | + | 0.985970i | \(0.446618\pi\) |
−0.937336 | + | 0.348428i | \(0.886716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 96.0000 | 3.51717 | ||||||||
\(746\) | 13.0000 | − | 22.5167i | 0.475964 | − | 0.824394i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | 5.00000 | − | 1.73205i | 0.182696 | − | 0.0632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | −3.00000 | − | 5.19615i | −0.109399 | − | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.00000 | + | 1.73205i | −0.0364179 | + | 0.0630776i | ||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0000 | 0.617876 | 0.308938 | − | 0.951082i | \(-0.400027\pi\) | ||||
0.308938 | + | 0.951082i | \(0.400027\pi\) | |||||||
\(758\) | −4.50000 | + | 7.79423i | −0.163447 | + | 0.283099i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.0000 | − | 41.5692i | −0.870572 | − | 1.50787i | ||||
\(761\) | 48.0000 | 1.74000 | 0.869999 | − | 0.493053i | \(-0.164119\pi\) | ||||
0.869999 | + | 0.493053i | \(0.164119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0000 | + | 15.5885i | 0.651644 | + | 0.564340i | ||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.00000 | − | 15.5885i | 0.325183 | − | 0.563234i | ||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | − | 8.66025i | 0.180305 | − | 0.312297i | −0.761680 | − | 0.647954i | \(-0.775625\pi\) |
0.941984 | + | 0.335657i | \(0.108958\pi\) | |||||||
\(770\) | 16.0000 | + | 13.8564i | 0.576600 | + | 0.499350i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.5000 | + | 21.6506i | −0.449885 | + | 0.779223i | ||||
\(773\) | 8.00000 | − | 13.8564i | 0.287740 | − | 0.498380i | −0.685530 | − | 0.728044i | \(-0.740429\pi\) |
0.973270 | + | 0.229664i | \(0.0737628\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.5000 | − | 28.5788i | −0.592697 | − | 1.02658i | ||||
\(776\) | −13.5000 | − | 23.3827i | −0.484622 | − | 0.839390i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | − | 10.3923i | 0.215110 | − | 0.372582i | ||||
\(779\) | 8.00000 | 0.286630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | − | 31.1769i | −0.643679 | − | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.50000 | + | 4.33013i | −0.196429 | + | 0.154647i | ||||
\(785\) | −20.0000 | − | 34.6410i | −0.713831 | − | 1.23639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.5000 | + | 40.7032i | 0.837685 | + | 1.45091i | 0.891826 | + | 0.452379i | \(0.149425\pi\) |
−0.0541413 | + | 0.998533i | \(0.517242\pi\) | |||||||
\(788\) | −10.0000 | − | 17.3205i | −0.356235 | − | 0.617018i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.0000 | + | 38.1051i | 0.782725 | + | 1.35572i | ||||
\(791\) | 32.0000 | + | 27.7128i | 1.13779 | + | 0.985354i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.50000 | + | 4.33013i | 0.0887776 | + | 0.153767i | ||||
\(794\) | 33.0000 | 1.17113 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.00000 | 0.318997 | ||||||||
\(797\) | 7.00000 | − | 12.1244i | 0.247953 | − | 0.429467i | −0.715005 | − | 0.699119i | \(-0.753576\pi\) |
0.962958 | + | 0.269653i | \(0.0869089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | + | 31.1769i | 0.636794 | + | 1.10296i | ||||
\(800\) | 27.5000 | + | 47.6314i | 0.972272 | + | 1.68402i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.0000 | + | 25.9808i | −0.529668 | + | 0.917413i | ||||
\(803\) | −6.00000 | + | 10.3923i | −0.211735 | + | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | + | 62.3538i | −0.422944 | + | 2.19768i | ||||
\(806\) | 1.50000 | − | 2.59808i | 0.0528352 | − | 0.0915133i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.0000 | 0.844317 | ||||||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | 4.00000 | + | 3.46410i | 0.140372 | + | 0.121566i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | −38.0000 | − | 65.8179i | −1.33108 | − | 2.30550i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | −5.00000 | −0.174821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.00000 | −0.279372 | ||||||||
\(821\) | 11.0000 | − | 19.0526i | 0.383903 | − | 0.664939i | −0.607714 | − | 0.794156i | \(-0.707913\pi\) |
0.991616 | + | 0.129217i | \(0.0412465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.5000 | − | 38.9711i | −0.784301 | − | 1.35845i | −0.929416 | − | 0.369034i | \(-0.879689\pi\) |
0.145115 | − | 0.989415i | \(-0.453645\pi\) | |||||||
\(824\) | 51.0000 | 1.77667 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00000 | − | 15.5885i | 0.104383 | − | 0.542392i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.00000 | − | 8.66025i | 0.173657 | − | 0.300783i | −0.766039 | − | 0.642795i | \(-0.777775\pi\) |
0.939696 | + | 0.342012i | \(0.111108\pi\) | |||||||
\(830\) | 24.0000 | 0.833052 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.50000 | + | 6.06218i | −0.121341 | + | 0.210168i | ||||
\(833\) | 33.0000 | − | 25.9808i | 1.14338 | − | 0.900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.0000 | − | 48.4974i | 0.968980 | − | 1.67832i | ||||
\(836\) | −4.00000 | + | 6.92820i | −0.138343 | + | 0.239617i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.00000 | + | 10.3923i | 0.207267 | + | 0.358996i | ||||
\(839\) | 13.0000 | + | 22.5167i | 0.448810 | + | 0.777361i | 0.998309 | − | 0.0581329i | \(-0.0185147\pi\) |
−0.549499 | + | 0.835494i | \(0.685181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.00000 | 0.172107 | ||||||||
\(845\) | 24.0000 | + | 41.5692i | 0.825625 | + | 1.43002i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.50000 | + | 18.1865i | −0.120261 | + | 0.624897i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 33.0000 | + | 57.1577i | 1.13189 | + | 1.96049i | ||||
\(851\) | 9.00000 | + | 15.5885i | 0.308516 | + | 0.534365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.0000 | − | 22.5167i | −0.445112 | − | 0.770956i | 0.552948 | − | 0.833215i | \(-0.313503\pi\) |
−0.998060 | + | 0.0622597i | \(0.980169\pi\) | |||||||
\(854\) | −12.5000 | + | 4.33013i | −0.427741 | + | 0.148174i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | 16.0000 | 0.546550 | 0.273275 | − | 0.961936i | \(-0.411893\pi\) | ||||
0.273275 | + | 0.961936i | \(0.411893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0000 | −0.852989 | −0.426494 | − | 0.904490i | \(-0.640252\pi\) | ||||
−0.426494 | + | 0.904490i | \(0.640252\pi\) | |||||||
\(860\) | −2.00000 | + | 3.46410i | −0.0681994 | + | 0.118125i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.00000 | − | 15.5885i | −0.306541 | − | 0.530945i | ||||
\(863\) | 18.0000 | + | 31.1769i | 0.612727 | + | 1.06127i | 0.990779 | + | 0.135490i | \(0.0432609\pi\) |
−0.378052 | + | 0.925785i | \(0.623406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.0000 | − | 55.4256i | 1.08803 | − | 1.88453i | ||||
\(866\) | −8.50000 | + | 14.7224i | −0.288842 | + | 0.500289i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.00000 | − | 5.19615i | −0.203653 | − | 0.176369i | ||||
\(869\) | 11.0000 | − | 19.0526i | 0.373149 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | 0.237186 | ||||||||
\(872\) | −13.5000 | + | 23.3827i | −0.457168 | + | 0.791838i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 12.0000 | − | 62.3538i | 0.405674 | − | 2.10794i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.00000 | 0.236373 | 0.118187 | − | 0.992991i | \(-0.462292\pi\) | ||||
0.118187 | + | 0.992991i | \(0.462292\pi\) | |||||||
\(878\) | 12.0000 | + | 20.7846i | 0.404980 | + | 0.701447i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.00000 | + | 6.92820i | −0.134840 | + | 0.233550i | ||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | + | 20.7846i | 0.403148 | + | 0.698273i | ||||
\(887\) | −22.0000 | −0.738688 | −0.369344 | − | 0.929293i | \(-0.620418\pi\) | ||||
−0.369344 | + | 0.929293i | \(0.620418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.50000 | + | 23.3827i | −0.150925 | + | 0.784230i | ||||
\(890\) | −16.0000 | −0.536321 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | −24.0000 | −0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | − | 13.8564i | 0.267411 | − | 0.463169i | ||||
\(896\) | 6.00000 | + | 5.19615i | 0.200446 | + | 0.173591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | − | 31.1769i | 0.600668 | − | 1.04039i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | −2.00000 | − | 3.46410i | −0.0665927 | − | 0.115342i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.0000 | + | 41.5692i | −0.798228 | + | 1.38257i | ||||
\(905\) | −8.00000 | −0.265929 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0000 | −0.431658 | −0.215829 | − | 0.976431i | \(-0.569245\pi\) | ||||
−0.215829 | + | 0.976431i | \(0.569245\pi\) | |||||||
\(908\) | −9.00000 | − | 15.5885i | −0.298675 | − | 0.517321i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.0000 | − | 3.46410i | 0.331497 | − | 0.114834i | ||||
\(911\) | −9.00000 | − | 15.5885i | −0.298183 | − | 0.516469i | 0.677537 | − | 0.735489i | \(-0.263047\pi\) |
−0.975720 | + | 0.219020i | \(0.929714\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00000 | − | 10.3923i | −0.198571 | − | 0.343935i | ||||
\(914\) | 6.50000 | + | 11.2583i | 0.215001 | + | 0.372392i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.50000 | − | 6.06218i | −0.115643 | − | 0.200300i | ||||
\(917\) | 2.00000 | − | 10.3923i | 0.0660458 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.5000 | − | 25.1147i | −0.478311 | − | 0.828459i | 0.521380 | − | 0.853325i | \(-0.325417\pi\) |
−0.999691 | + | 0.0248659i | \(0.992084\pi\) | |||||||
\(920\) | −72.0000 | −2.37377 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.00000 | −0.0658665 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.5000 | − | 28.5788i | −0.542517 | − | 0.939666i | ||||
\(926\) | −16.0000 | − | 27.7128i | −0.525793 | − | 0.910700i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.00000 | + | 8.66025i | −0.164133 | + | 0.284287i | ||||
\(929\) | 2.00000 | − | 3.46410i | 0.0656179 | − | 0.113653i | −0.831350 | − | 0.555749i | \(-0.812431\pi\) |
0.896968 | + | 0.442096i | \(0.145765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | + | 27.7128i | 0.131095 | + | 0.908251i | ||||
\(932\) | 12.0000 | − | 20.7846i | 0.393073 | − | 0.680823i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.0000 | − | 41.5692i | 0.784884 | − | 1.35946i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0000 | −0.686040 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(938\) | −3.50000 | + | 18.1865i | −0.114279 | + | 0.593811i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.0000 | 0.782794 | ||||||||
\(941\) | 23.0000 | + | 39.8372i | 0.749779 | + | 1.29865i | 0.947929 | + | 0.318483i | \(0.103173\pi\) |
−0.198150 | + | 0.980172i | \(0.563493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | − | 10.3923i | 0.195387 | − | 0.338420i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00000 | −0.0650256 | ||||||||
\(947\) | −13.0000 | + | 22.5167i | −0.422443 | + | 0.731693i | −0.996178 | − | 0.0873481i | \(-0.972161\pi\) |
0.573735 | + | 0.819041i | \(0.305494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00000 | + | 5.19615i | 0.0973841 | + | 0.168674i | ||||
\(950\) | −44.0000 | −1.42755 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36.0000 | + | 31.1769i | 1.16677 | + | 1.01045i | ||||
\(953\) | 14.0000 | 0.453504 | 0.226752 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226752 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | + | 13.8564i | −0.258874 | + | 0.448383i | ||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.00000 | + | 13.8564i | −0.258468 | + | 0.447680i | ||||
\(959\) | −9.00000 | + | 46.7654i | −0.290625 | + | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 1.50000 | − | 2.59808i | 0.0483619 | − | 0.0837653i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.50000 | + | 14.7224i | 0.273767 | + | 0.474178i | ||||
\(965\) | 50.0000 | + | 86.6025i | 1.60956 | + | 2.78783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.50000 | − | 14.7224i | 0.273342 | − | 0.473441i | −0.696374 | − | 0.717679i | \(-0.745204\pi\) |
0.969715 | + | 0.244238i | \(0.0785377\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.0000 | −1.15589 | ||||||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0000 | + | 15.5885i | 0.577054 | + | 0.499743i | ||||
\(974\) | 8.00000 | + | 13.8564i | 0.256337 | + | 0.443988i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.50000 | − | 4.33013i | −0.0800230 | − | 0.138604i | ||||
\(977\) | 3.00000 | + | 5.19615i | 0.0959785 | + | 0.166240i | 0.910017 | − | 0.414572i | \(-0.136069\pi\) |
−0.814038 | + | 0.580812i | \(0.802735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | + | 6.92820i | 0.127841 | + | 0.221426i | ||||
\(980\) | −4.00000 | − | 27.7128i | −0.127775 | − | 0.885253i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.0000 | − | 29.4449i | −0.542492 | − | 0.939623i | ||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −80.0000 | −2.54901 | ||||||||
\(986\) | −6.00000 | + | 10.3923i | −0.191079 | + | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.00000 | + | 3.46410i | 0.0636285 | + | 0.110208i | ||||
\(989\) | −3.00000 | − | 5.19615i | −0.0953945 | − | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5000 | − | 47.6314i | 0.873566 | − | 1.51306i | 0.0152841 | − | 0.999883i | \(-0.495135\pi\) |
0.858282 | − | 0.513178i | \(-0.171532\pi\) | |||||||
\(992\) | 7.50000 | − | 12.9904i | 0.238125 | − | 0.412445i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0000 | − | 31.1769i | 0.570638 | − | 0.988375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0000 | −0.918439 | −0.459220 | − | 0.888323i | \(-0.651871\pi\) | ||||
−0.459220 | + | 0.888323i | \(0.651871\pi\) | |||||||
\(998\) | −8.50000 | + | 14.7224i | −0.269063 | + | 0.466030i | ||||
\(999\) | 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 | 567.2.g.e.109.1 | 2 | ||
3.2 | odd | 2 | 567.2.g.b.109.1 | 2 | |||
7.2 | even | 3 | 567.2.h.b.352.1 | 2 | |||
9.2 | odd | 6 | 567.2.h.e.298.1 | 2 | |||
9.4 | even | 3 | 189.2.e.c.109.1 | yes | 2 | ||
9.5 | odd | 6 | 189.2.e.a.109.1 | ✓ | 2 | ||
9.7 | even | 3 | 567.2.h.b.298.1 | 2 | |||
21.2 | odd | 6 | 567.2.h.e.352.1 | 2 | |||
63.2 | odd | 6 | 567.2.g.b.541.1 | 2 | |||
63.4 | even | 3 | 1323.2.a.g.1.1 | 1 | |||
63.16 | even | 3 | inner | 567.2.g.e.541.1 | 2 | ||
63.23 | odd | 6 | 189.2.e.a.163.1 | yes | 2 | ||
63.31 | odd | 6 | 1323.2.a.d.1.1 | 1 | |||
63.32 | odd | 6 | 1323.2.a.m.1.1 | 1 | |||
63.58 | even | 3 | 189.2.e.c.163.1 | yes | 2 | ||
63.59 | even | 6 | 1323.2.a.p.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.a.109.1 | ✓ | 2 | 9.5 | odd | 6 | ||
189.2.e.a.163.1 | yes | 2 | 63.23 | odd | 6 | ||
189.2.e.c.109.1 | yes | 2 | 9.4 | even | 3 | ||
189.2.e.c.163.1 | yes | 2 | 63.58 | even | 3 | ||
567.2.g.b.109.1 | 2 | 3.2 | odd | 2 | |||
567.2.g.b.541.1 | 2 | 63.2 | odd | 6 | |||
567.2.g.e.109.1 | 2 | 1.1 | even | 1 | trivial | ||
567.2.g.e.541.1 | 2 | 63.16 | even | 3 | inner | ||
567.2.h.b.298.1 | 2 | 9.7 | even | 3 | |||
567.2.h.b.352.1 | 2 | 7.2 | even | 3 | |||
567.2.h.e.298.1 | 2 | 9.2 | odd | 6 | |||
567.2.h.e.352.1 | 2 | 21.2 | odd | 6 | |||
1323.2.a.d.1.1 | 1 | 63.31 | odd | 6 | |||
1323.2.a.g.1.1 | 1 | 63.4 | even | 3 | |||
1323.2.a.m.1.1 | 1 | 63.32 | odd | 6 | |||
1323.2.a.p.1.1 | 1 | 63.59 | even | 6 |