Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(89,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.k (of order \(6\), degree \(2\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.353 |
Dual form | 462.2.k.f.89.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 1.70711 | + | 0.292893i | 0.985599 | + | 0.169102i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.241181 | + | 0.417738i | 0.107859 | + | 0.186818i | 0.914903 | − | 0.403674i | \(-0.132267\pi\) |
−0.807043 | + | 0.590492i | \(0.798934\pi\) | |||||||
\(6\) | −1.62484 | + | 0.599900i | −0.663340 | + | 0.244908i | ||||
\(7\) | 1.48356 | + | 2.19067i | 0.560734 | + | 0.827996i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | −0.417738 | − | 0.241181i | −0.132100 | − | 0.0762681i | ||||
\(11\) | −0.866025 | − | 0.500000i | −0.261116 | − | 0.150756i | ||||
\(12\) | 1.10721 | − | 1.33195i | 0.319623 | − | 0.384501i | ||||
\(13\) | 0.550510i | 0.152684i | 0.997082 | + | 0.0763420i | \(0.0243241\pi\) | ||||
−0.997082 | + | 0.0763420i | \(0.975676\pi\) | |||||||
\(14\) | −2.38014 | − | 1.15539i | −0.636119 | − | 0.308792i | ||||
\(15\) | 0.289369 | + | 0.783763i | 0.0747148 | + | 0.202367i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.926868 | + | 1.60538i | −0.224798 | + | 0.389362i | −0.956259 | − | 0.292521i | \(-0.905506\pi\) |
0.731460 | + | 0.681884i | \(0.238839\pi\) | |||||||
\(18\) | −2.94949 | + | 0.548188i | −0.695201 | + | 0.129209i | ||||
\(19\) | −0.334273 | + | 0.192993i | −0.0766876 | + | 0.0442756i | −0.537853 | − | 0.843038i | \(-0.680765\pi\) |
0.461166 | + | 0.887314i | \(0.347431\pi\) | |||||||
\(20\) | 0.482362 | 0.107859 | ||||||||
\(21\) | 1.89097 | + | 4.17423i | 0.412643 | + | 0.910893i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 0.216237 | − | 0.124844i | 0.0450885 | − | 0.0260319i | −0.477286 | − | 0.878748i | \(-0.658380\pi\) |
0.522375 | + | 0.852716i | \(0.325046\pi\) | |||||||
\(24\) | −0.292893 | + | 1.70711i | −0.0597866 | + | 0.348462i | ||||
\(25\) | 2.38366 | − | 4.12863i | 0.476733 | − | 0.825725i | ||||
\(26\) | −0.275255 | − | 0.476756i | −0.0539820 | − | 0.0934995i | ||||
\(27\) | 4.53553 | + | 2.53553i | 0.872864 | + | 0.487964i | ||||
\(28\) | 2.63896 | − | 0.189469i | 0.498716 | − | 0.0358062i | ||||
\(29\) | 4.48477i | 0.832800i | 0.909181 | + | 0.416400i | \(0.136708\pi\) | ||||
−0.909181 | + | 0.416400i | \(0.863292\pi\) | |||||||
\(30\) | −0.642483 | − | 0.534074i | −0.117301 | − | 0.0975082i | ||||
\(31\) | 1.08018 | + | 0.623642i | 0.194006 | + | 0.112009i | 0.593857 | − | 0.804571i | \(-0.297605\pi\) |
−0.399851 | + | 0.916580i | \(0.630938\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.33195 | − | 1.10721i | −0.231863 | − | 0.192740i | ||||
\(34\) | − | 1.85374i | − | 0.317913i | ||||||
\(35\) | −0.557318 | + | 1.14809i | −0.0942040 | + | 0.194062i | ||||
\(36\) | 2.28024 | − | 1.94949i | 0.380040 | − | 0.324915i | ||||
\(37\) | −2.72853 | − | 4.72595i | −0.448567 | − | 0.776941i | 0.549726 | − | 0.835345i | \(-0.314732\pi\) |
−0.998293 | + | 0.0584042i | \(0.981399\pi\) | |||||||
\(38\) | 0.192993 | − | 0.334273i | 0.0313076 | − | 0.0542263i | ||||
\(39\) | −0.161241 | + | 0.939780i | −0.0258192 | + | 0.150485i | ||||
\(40\) | −0.417738 | + | 0.241181i | −0.0660501 | + | 0.0381341i | ||||
\(41\) | 5.67387 | 0.886110 | 0.443055 | − | 0.896495i | \(-0.353895\pi\) | ||||
0.443055 | + | 0.896495i | \(0.353895\pi\) | |||||||
\(42\) | −3.72474 | − | 2.66951i | −0.574741 | − | 0.411914i | ||||
\(43\) | −0.682163 | −0.104029 | −0.0520144 | − | 0.998646i | \(-0.516564\pi\) | ||||
−0.0520144 | + | 0.998646i | \(0.516564\pi\) | |||||||
\(44\) | −0.866025 | + | 0.500000i | −0.130558 | + | 0.0753778i | ||||
\(45\) | 0.264425 | + | 1.42272i | 0.0394182 | + | 0.212087i | ||||
\(46\) | −0.124844 | + | 0.216237i | −0.0184073 | + | 0.0318824i | ||||
\(47\) | −4.41421 | − | 7.64564i | −0.643879 | − | 1.11523i | −0.984559 | − | 0.175052i | \(-0.943991\pi\) |
0.340680 | − | 0.940179i | \(-0.389343\pi\) | |||||||
\(48\) | −0.599900 | − | 1.62484i | −0.0865882 | − | 0.234526i | ||||
\(49\) | −2.59808 | + | 6.50000i | −0.371154 | + | 0.928571i | ||||
\(50\) | 4.76733i | 0.674202i | ||||||||
\(51\) | −2.05247 | + | 2.46909i | −0.287403 | + | 0.345741i | ||||
\(52\) | 0.476756 | + | 0.275255i | 0.0661141 | + | 0.0381710i | ||||
\(53\) | 6.54441 | + | 3.77841i | 0.898943 | + | 0.519005i | 0.876857 | − | 0.480751i | \(-0.159636\pi\) |
0.0220861 | + | 0.999756i | \(0.492969\pi\) | |||||||
\(54\) | −5.19565 | + | 0.0719302i | −0.707039 | + | 0.00978846i | ||||
\(55\) | − | 0.482362i | − | 0.0650417i | ||||||
\(56\) | −2.19067 | + | 1.48356i | −0.292741 | + | 0.198250i | ||||
\(57\) | −0.627167 | + | 0.231553i | −0.0830702 | + | 0.0306699i | ||||
\(58\) | −2.24238 | − | 3.88392i | −0.294439 | − | 0.509984i | ||||
\(59\) | −1.82465 | + | 3.16038i | −0.237549 | + | 0.411446i | −0.960010 | − | 0.279965i | \(-0.909677\pi\) |
0.722462 | + | 0.691411i | \(0.243011\pi\) | |||||||
\(60\) | 0.823443 | + | 0.141281i | 0.106306 | + | 0.0182392i | ||||
\(61\) | −7.63593 | + | 4.40861i | −0.977681 | + | 0.564464i | −0.901569 | − | 0.432635i | \(-0.857584\pi\) |
−0.0761117 | + | 0.997099i | \(0.524251\pi\) | |||||||
\(62\) | −1.24728 | −0.158405 | ||||||||
\(63\) | 2.00548 | + | 7.67972i | 0.252667 | + | 0.967553i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.229969 | + | 0.132773i | −0.0285241 | + | 0.0164684i | ||||
\(66\) | 1.70711 | + | 0.292893i | 0.210130 | + | 0.0360527i | ||||
\(67\) | 4.35690 | − | 7.54636i | 0.532279 | − | 0.921935i | −0.467010 | − | 0.884252i | \(-0.654669\pi\) |
0.999290 | − | 0.0376832i | \(-0.0119978\pi\) | |||||||
\(68\) | 0.926868 | + | 1.60538i | 0.112399 | + | 0.194681i | ||||
\(69\) | 0.405706 | − | 0.149788i | 0.0488412 | − | 0.0180324i | ||||
\(70\) | −0.0913925 | − | 1.27293i | −0.0109235 | − | 0.152145i | ||||
\(71\) | 5.76028i | 0.683619i | 0.939769 | + | 0.341810i | \(0.111040\pi\) | ||||
−0.939769 | + | 0.341810i | \(0.888960\pi\) | |||||||
\(72\) | −1.00000 | + | 2.82843i | −0.117851 | + | 0.333333i | ||||
\(73\) | −1.94534 | − | 1.12314i | −0.227685 | − | 0.131454i | 0.381819 | − | 0.924237i | \(-0.375298\pi\) |
−0.609504 | + | 0.792783i | \(0.708631\pi\) | |||||||
\(74\) | 4.72595 | + | 2.72853i | 0.549380 | + | 0.317185i | ||||
\(75\) | 5.27841 | − | 6.34985i | 0.609499 | − | 0.733217i | ||||
\(76\) | 0.385986i | 0.0442756i | ||||||||
\(77\) | −0.189469 | − | 2.63896i | −0.0215920 | − | 0.300737i | ||||
\(78\) | −0.330251 | − | 0.894494i | −0.0373936 | − | 0.101281i | ||||
\(79\) | −6.71587 | − | 11.6322i | −0.755595 | − | 1.30873i | −0.945078 | − | 0.326844i | \(-0.894015\pi\) |
0.189483 | − | 0.981884i | \(-0.439319\pi\) | |||||||
\(80\) | 0.241181 | − | 0.417738i | 0.0269649 | − | 0.0467045i | ||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | −4.91372 | + | 2.83694i | −0.542629 | + | 0.313287i | ||||
\(83\) | 6.48941 | 0.712305 | 0.356153 | − | 0.934428i | \(-0.384088\pi\) | ||||
0.356153 | + | 0.934428i | \(0.384088\pi\) | |||||||
\(84\) | 4.56048 | + | 0.449490i | 0.497589 | + | 0.0490434i | ||||
\(85\) | −0.894171 | −0.0969865 | ||||||||
\(86\) | 0.590770 | − | 0.341081i | 0.0637044 | − | 0.0367798i | ||||
\(87\) | −1.31356 | + | 7.65597i | −0.140828 | + | 0.820807i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −5.64394 | − | 9.77559i | −0.598257 | − | 1.03621i | −0.993078 | − | 0.117453i | \(-0.962527\pi\) |
0.394822 | − | 0.918758i | \(-0.370806\pi\) | |||||||
\(90\) | −0.940360 | − | 1.09990i | −0.0991226 | − | 0.115940i | ||||
\(91\) | −1.20599 | + | 0.816717i | −0.126422 | + | 0.0856152i | ||||
\(92\) | − | 0.249689i | − | 0.0260319i | ||||||
\(93\) | 1.66132 | + | 1.38100i | 0.172271 | + | 0.143203i | ||||
\(94\) | 7.64564 | + | 4.41421i | 0.788588 | + | 0.455291i | ||||
\(95\) | −0.161241 | − | 0.0930924i | −0.0165429 | − | 0.00955108i | ||||
\(96\) | 1.33195 | + | 1.10721i | 0.135942 | + | 0.113004i | ||||
\(97\) | − | 16.8389i | − | 1.70973i | −0.518849 | − | 0.854866i | \(-0.673639\pi\) | ||
0.518849 | − | 0.854866i | \(-0.326361\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | −1.94949 | − | 2.28024i | −0.195931 | − | 0.229173i | ||||
\(100\) | −2.38366 | − | 4.12863i | −0.238366 | − | 0.412863i | ||||
\(101\) | 0.855693 | − | 1.48210i | 0.0851447 | − | 0.147475i | −0.820308 | − | 0.571922i | \(-0.806198\pi\) |
0.905453 | + | 0.424447i | \(0.139531\pi\) | |||||||
\(102\) | 0.542947 | − | 3.16452i | 0.0537597 | − | 0.313335i | ||||
\(103\) | 0.170088 | − | 0.0982005i | 0.0167593 | − | 0.00967599i | −0.491597 | − | 0.870823i | \(-0.663587\pi\) |
0.508356 | + | 0.861147i | \(0.330253\pi\) | |||||||
\(104\) | −0.550510 | −0.0539820 | ||||||||
\(105\) | −1.28767 | + | 1.79668i | −0.125664 | + | 0.175338i | ||||
\(106\) | −7.55683 | −0.733984 | ||||||||
\(107\) | −8.08991 | + | 4.67071i | −0.782081 | + | 0.451535i | −0.837167 | − | 0.546947i | \(-0.815790\pi\) |
0.0550863 | + | 0.998482i | \(0.482457\pi\) | |||||||
\(108\) | 4.46360 | − | 2.66012i | 0.429510 | − | 0.255970i | ||||
\(109\) | 3.15161 | − | 5.45875i | 0.301870 | − | 0.522854i | −0.674690 | − | 0.738101i | \(-0.735723\pi\) |
0.976559 | + | 0.215248i | \(0.0690559\pi\) | |||||||
\(110\) | 0.241181 | + | 0.417738i | 0.0229957 | + | 0.0398297i | ||||
\(111\) | −3.27369 | − | 8.86686i | −0.310725 | − | 0.841605i | ||||
\(112\) | 1.15539 | − | 2.38014i | 0.109175 | − | 0.224902i | ||||
\(113\) | − | 19.8084i | − | 1.86342i | −0.363201 | − | 0.931711i | \(-0.618316\pi\) | ||
0.363201 | − | 0.931711i | \(-0.381684\pi\) | |||||||
\(114\) | 0.427366 | − | 0.514114i | 0.0400265 | − | 0.0481512i | ||||
\(115\) | 0.104304 | + | 0.0602202i | 0.00972644 | + | 0.00561556i | ||||
\(116\) | 3.88392 | + | 2.24238i | 0.360613 | + | 0.208200i | ||||
\(117\) | −0.550510 | + | 1.55708i | −0.0508947 | + | 0.143952i | ||||
\(118\) | − | 3.64929i | − | 0.335944i | ||||||
\(119\) | −4.89193 | + | 0.351225i | −0.448443 | + | 0.0321967i | ||||
\(120\) | −0.783763 | + | 0.289369i | −0.0715475 | + | 0.0264157i | ||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 4.40861 | − | 7.63593i | 0.399137 | − | 0.691325i | ||||
\(123\) | 9.68590 | + | 1.66184i | 0.873348 | + | 0.149843i | ||||
\(124\) | 1.08018 | − | 0.623642i | 0.0970031 | − | 0.0560047i | ||||
\(125\) | 4.71139 | 0.421399 | ||||||||
\(126\) | −5.57666 | − | 5.64809i | −0.496808 | − | 0.503172i | ||||
\(127\) | −21.1440 | −1.87623 | −0.938114 | − | 0.346326i | \(-0.887429\pi\) | ||||
−0.938114 | + | 0.346326i | \(0.887429\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −1.16452 | − | 0.199801i | −0.102531 | − | 0.0175915i | ||||
\(130\) | 0.132773 | − | 0.229969i | 0.0116449 | − | 0.0201696i | ||||
\(131\) | −8.17009 | − | 14.1510i | −0.713824 | − | 1.23638i | −0.963411 | − | 0.268027i | \(-0.913628\pi\) |
0.249587 | − | 0.968352i | \(-0.419705\pi\) | |||||||
\(132\) | −1.62484 | + | 0.599900i | −0.141425 | + | 0.0522146i | ||||
\(133\) | −0.918700 | − | 0.445966i | −0.0796614 | − | 0.0386701i | ||||
\(134\) | 8.71379i | 0.752757i | ||||||||
\(135\) | 0.0346964 | + | 2.50619i | 0.00298619 | + | 0.215698i | ||||
\(136\) | −1.60538 | − | 0.926868i | −0.137660 | − | 0.0794783i | ||||
\(137\) | −9.95875 | − | 5.74969i | −0.850834 | − | 0.491229i | 0.0100984 | − | 0.999949i | \(-0.496786\pi\) |
−0.860932 | + | 0.508720i | \(0.830119\pi\) | |||||||
\(138\) | −0.276457 | + | 0.332573i | −0.0235336 | + | 0.0283105i | ||||
\(139\) | 3.37945i | 0.286641i | 0.989676 | + | 0.143321i | \(0.0457780\pi\) | ||||
−0.989676 | + | 0.143321i | \(0.954222\pi\) | |||||||
\(140\) | 0.715615 | + | 1.05670i | 0.0604805 | + | 0.0893071i | ||||
\(141\) | −5.29618 | − | 14.3448i | −0.446019 | − | 1.20805i | ||||
\(142\) | −2.88014 | − | 4.98855i | −0.241696 | − | 0.418630i | ||||
\(143\) | 0.275255 | − | 0.476756i | 0.0230180 | − | 0.0398683i | ||||
\(144\) | −0.548188 | − | 2.94949i | −0.0456823 | − | 0.245791i | ||||
\(145\) | −1.87346 | + | 1.08164i | −0.155582 | + | 0.0898253i | ||||
\(146\) | 2.24629 | 0.185904 | ||||||||
\(147\) | −6.33900 | + | 10.3352i | −0.522832 | + | 0.852436i | ||||
\(148\) | −5.45705 | −0.448567 | ||||||||
\(149\) | 14.3154 | − | 8.26500i | 1.17276 | − | 0.677096i | 0.218434 | − | 0.975852i | \(-0.429905\pi\) |
0.954330 | + | 0.298756i | \(0.0965717\pi\) | |||||||
\(150\) | −1.39632 | + | 8.13834i | −0.114009 | + | 0.664492i | ||||
\(151\) | −0.0763986 | + | 0.132326i | −0.00621723 | + | 0.0107686i | −0.869117 | − | 0.494606i | \(-0.835312\pi\) |
0.862900 | + | 0.505375i | \(0.168646\pi\) | |||||||
\(152\) | −0.192993 | − | 0.334273i | −0.0156538 | − | 0.0271131i | ||||
\(153\) | −4.22696 | + | 3.61384i | −0.341729 | + | 0.292162i | ||||
\(154\) | 1.48356 | + | 2.19067i | 0.119549 | + | 0.176529i | ||||
\(155\) | 0.601643i | 0.0483251i | ||||||||
\(156\) | 0.733253 | + | 0.609528i | 0.0587072 | + | 0.0488013i | ||||
\(157\) | 9.11357 | + | 5.26172i | 0.727342 | + | 0.419931i | 0.817449 | − | 0.576001i | \(-0.195388\pi\) |
−0.0901071 | + | 0.995932i | \(0.528721\pi\) | |||||||
\(158\) | 11.6322 | + | 6.71587i | 0.925411 | + | 0.534286i | ||||
\(159\) | 10.0653 | + | 8.36697i | 0.798232 | + | 0.663544i | ||||
\(160\) | 0.482362i | 0.0381341i | ||||||||
\(161\) | 0.594294 | + | 0.288489i | 0.0468370 | + | 0.0227361i | ||||
\(162\) | −8.89060 | − | 1.39898i | −0.698512 | − | 0.109914i | ||||
\(163\) | −4.34228 | − | 7.52106i | −0.340114 | − | 0.589095i | 0.644340 | − | 0.764739i | \(-0.277132\pi\) |
−0.984454 | + | 0.175645i | \(0.943799\pi\) | |||||||
\(164\) | 2.83694 | − | 4.91372i | 0.221527 | − | 0.383697i | ||||
\(165\) | 0.141281 | − | 0.823443i | 0.0109987 | − | 0.0641050i | ||||
\(166\) | −5.61999 | + | 3.24471i | −0.436196 | + | 0.251838i | ||||
\(167\) | 2.01096 | 0.155613 | 0.0778065 | − | 0.996968i | \(-0.475208\pi\) | ||||
0.0778065 | + | 0.996968i | \(0.475208\pi\) | |||||||
\(168\) | −4.17423 | + | 1.89097i | −0.322049 | + | 0.145891i | ||||
\(169\) | 12.6969 | 0.976688 | ||||||||
\(170\) | 0.774375 | − | 0.447086i | 0.0593919 | − | 0.0342899i | ||||
\(171\) | −1.13846 | + | 0.211593i | −0.0870603 | + | 0.0161809i | ||||
\(172\) | −0.341081 | + | 0.590770i | −0.0260072 | + | 0.0450458i | ||||
\(173\) | 6.58140 | + | 11.3993i | 0.500375 | + | 0.866674i | 1.00000 | 0.000432574i | \(0.000137693\pi\) | |
−0.499625 | + | 0.866242i | \(0.666529\pi\) | |||||||
\(174\) | −2.69041 | − | 7.28705i | −0.203960 | − | 0.552430i | ||||
\(175\) | 12.5808 | − | 0.903259i | 0.951017 | − | 0.0682800i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | −4.04052 | + | 4.86068i | −0.303704 | + | 0.365351i | ||||
\(178\) | 9.77559 | + | 5.64394i | 0.732712 | + | 0.423031i | ||||
\(179\) | −11.4624 | − | 6.61780i | −0.856737 | − | 0.494637i | 0.00618127 | − | 0.999981i | \(-0.498032\pi\) |
−0.862918 | + | 0.505344i | \(0.831366\pi\) | |||||||
\(180\) | 1.36433 | + | 0.482362i | 0.101691 | + | 0.0359531i | ||||
\(181\) | 25.8936i | 1.92466i | 0.271890 | + | 0.962328i | \(0.412351\pi\) | ||||
−0.271890 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(182\) | 0.636057 | − | 1.31029i | 0.0471476 | − | 0.0971252i | ||||
\(183\) | −14.3266 | + | 5.28945i | −1.05905 | + | 0.391007i | ||||
\(184\) | 0.124844 | + | 0.216237i | 0.00920365 | + | 0.0159412i | ||||
\(185\) | 1.31614 | − | 2.27962i | 0.0967643 | − | 0.167601i | ||||
\(186\) | −2.12925 | − | 0.365321i | −0.156124 | − | 0.0267867i | ||||
\(187\) | 1.60538 | − | 0.926868i | 0.117397 | − | 0.0677793i | ||||
\(188\) | −8.82843 | −0.643879 | ||||||||
\(189\) | 1.17423 | + | 13.6975i | 0.0854130 | + | 0.996346i | ||||
\(190\) | 0.186185 | 0.0135073 | ||||||||
\(191\) | −15.1791 | + | 8.76368i | −1.09832 | + | 0.634118i | −0.935780 | − | 0.352584i | \(-0.885303\pi\) |
−0.162544 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(192\) | −1.70711 | − | 0.292893i | −0.123200 | − | 0.0211377i | ||||
\(193\) | 3.68204 | − | 6.37748i | 0.265039 | − | 0.459061i | −0.702535 | − | 0.711649i | \(-0.747949\pi\) |
0.967574 | + | 0.252588i | \(0.0812819\pi\) | |||||||
\(194\) | 8.41946 | + | 14.5829i | 0.604482 | + | 1.04699i | ||||
\(195\) | −0.431470 | + | 0.159301i | −0.0308982 | + | 0.0114078i | ||||
\(196\) | 4.33013 | + | 5.50000i | 0.309295 | + | 0.392857i | ||||
\(197\) | − | 19.2932i | − | 1.37458i | −0.726381 | − | 0.687292i | \(-0.758799\pi\) | ||
0.726381 | − | 0.687292i | \(-0.241201\pi\) | |||||||
\(198\) | 2.82843 | + | 1.00000i | 0.201008 | + | 0.0710669i | ||||
\(199\) | 17.4020 | + | 10.0471i | 1.23360 | + | 0.712218i | 0.967778 | − | 0.251805i | \(-0.0810242\pi\) |
0.265819 | + | 0.964023i | \(0.414358\pi\) | |||||||
\(200\) | 4.12863 | + | 2.38366i | 0.291938 | + | 0.168550i | ||||
\(201\) | 9.64796 | − | 11.6063i | 0.680515 | − | 0.818648i | ||||
\(202\) | 1.71139i | 0.120413i | ||||||||
\(203\) | −9.82465 | + | 6.65344i | −0.689555 | + | 0.466980i | ||||
\(204\) | 1.11206 | + | 3.01203i | 0.0778595 | + | 0.210884i | ||||
\(205\) | 1.36843 | + | 2.37019i | 0.0955753 | + | 0.165541i | ||||
\(206\) | −0.0982005 | + | 0.170088i | −0.00684196 | + | 0.0118506i | ||||
\(207\) | 0.736455 | − | 0.136876i | 0.0511872 | − | 0.00951357i | ||||
\(208\) | 0.476756 | − | 0.275255i | 0.0330571 | − | 0.0190855i | ||||
\(209\) | 0.385986 | 0.0266992 | ||||||||
\(210\) | 0.216817 | − | 2.19980i | 0.0149618 | − | 0.151801i | ||||
\(211\) | −4.98514 | −0.343191 | −0.171596 | − | 0.985167i | \(-0.554892\pi\) | ||||
−0.171596 | + | 0.985167i | \(0.554892\pi\) | |||||||
\(212\) | 6.54441 | − | 3.77841i | 0.449472 | − | 0.259503i | ||||
\(213\) | −1.68715 | + | 9.83341i | −0.115601 | + | 0.673774i | ||||
\(214\) | 4.67071 | − | 8.08991i | 0.319283 | − | 0.553015i | ||||
\(215\) | −0.164525 | − | 0.284965i | −0.0112205 | − | 0.0194345i | ||||
\(216\) | −2.53553 | + | 4.53553i | −0.172521 | + | 0.308604i | ||||
\(217\) | 0.236321 | + | 3.29153i | 0.0160425 | + | 0.223444i | ||||
\(218\) | 6.30323i | 0.426908i | ||||||||
\(219\) | −2.99195 | − | 2.48711i | −0.202177 | − | 0.168063i | ||||
\(220\) | −0.417738 | − | 0.241181i | −0.0281639 | − | 0.0162604i | ||||
\(221\) | −0.883779 | − | 0.510250i | −0.0594494 | − | 0.0343231i | ||||
\(222\) | 7.26853 | + | 6.04208i | 0.487832 | + | 0.405518i | ||||
\(223\) | 13.2416i | 0.886726i | 0.896342 | + | 0.443363i | \(0.146215\pi\) | ||||
−0.896342 | + | 0.443363i | \(0.853785\pi\) | |||||||
\(224\) | 0.189469 | + | 2.63896i | 0.0126594 | + | 0.176323i | ||||
\(225\) | 10.8706 | − | 9.29386i | 0.724710 | − | 0.619590i | ||||
\(226\) | 9.90422 | + | 17.1546i | 0.658819 | + | 1.14111i | ||||
\(227\) | −13.8591 | + | 24.0046i | −0.919858 | + | 1.59324i | −0.120229 | + | 0.992746i | \(0.538363\pi\) |
−0.799629 | + | 0.600495i | \(0.794970\pi\) | |||||||
\(228\) | −0.113053 | + | 0.658919i | −0.00748709 | + | 0.0436380i | ||||
\(229\) | 7.21733 | − | 4.16693i | 0.476935 | − | 0.275358i | −0.242203 | − | 0.970225i | \(-0.577870\pi\) |
0.719138 | + | 0.694867i | \(0.244537\pi\) | |||||||
\(230\) | −0.120440 | −0.00794161 | ||||||||
\(231\) | 0.449490 | − | 4.56048i | 0.0295743 | − | 0.300057i | ||||
\(232\) | −4.48477 | −0.294439 | ||||||||
\(233\) | 7.01267 | − | 4.04877i | 0.459415 | − | 0.265244i | −0.252383 | − | 0.967627i | \(-0.581214\pi\) |
0.711798 | + | 0.702384i | \(0.247881\pi\) | |||||||
\(234\) | −0.301783 | − | 1.62372i | −0.0197282 | − | 0.106146i | ||||
\(235\) | 2.12925 | − | 3.68797i | 0.138897 | − | 0.240576i | ||||
\(236\) | 1.82465 | + | 3.16038i | 0.118774 | + | 0.205723i | ||||
\(237\) | −8.05771 | − | 21.8245i | −0.523404 | − | 1.41765i | ||||
\(238\) | 4.06092 | − | 2.75014i | 0.263231 | − | 0.178265i | ||||
\(239\) | 23.6386i | 1.52905i | 0.644592 | + | 0.764527i | \(0.277027\pi\) | ||||
−0.644592 | + | 0.764527i | \(0.722973\pi\) | |||||||
\(240\) | 0.534074 | − | 0.642483i | 0.0344743 | − | 0.0414721i | ||||
\(241\) | 14.7528 | + | 8.51751i | 0.950309 | + | 0.548661i | 0.893177 | − | 0.449705i | \(-0.148471\pi\) |
0.0571323 | + | 0.998367i | \(0.481804\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | 10.2929 | + | 11.7071i | 0.660289 | + | 0.751011i | ||||
\(244\) | 8.81722i | 0.564464i | ||||||||
\(245\) | −3.34190 | + | 0.482362i | −0.213506 | + | 0.0308170i | ||||
\(246\) | −9.21916 | + | 3.40376i | −0.587792 | + | 0.217016i | ||||
\(247\) | −0.106245 | − | 0.184021i | −0.00676018 | − | 0.0117090i | ||||
\(248\) | −0.623642 | + | 1.08018i | −0.0396013 | + | 0.0685915i | ||||
\(249\) | 11.0781 | + | 1.90070i | 0.702047 | + | 0.120452i | ||||
\(250\) | −4.08018 | + | 2.35569i | −0.258053 | + | 0.148987i | ||||
\(251\) | −12.6075 | −0.795777 | −0.397889 | − | 0.917434i | \(-0.630257\pi\) | ||||
−0.397889 | + | 0.917434i | \(0.630257\pi\) | |||||||
\(252\) | 7.65357 | + | 2.10306i | 0.482130 | + | 0.132480i | ||||
\(253\) | −0.249689 | −0.0156978 | ||||||||
\(254\) | 18.3113 | − | 10.5720i | 1.14895 | − | 0.663347i | ||||
\(255\) | −1.52645 | − | 0.261897i | −0.0955898 | − | 0.0164006i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.204527 | − | 0.354251i | −0.0127580 | − | 0.0220976i | 0.859576 | − | 0.511008i | \(-0.170728\pi\) |
−0.872334 | + | 0.488911i | \(0.837394\pi\) | |||||||
\(258\) | 1.10841 | − | 0.409230i | 0.0690065 | − | 0.0254775i | ||||
\(259\) | 6.30505 | − | 12.9885i | 0.391777 | − | 0.807069i | ||||
\(260\) | 0.265545i | 0.0164684i | ||||||||
\(261\) | −4.48477 | + | 12.6848i | −0.277600 | + | 0.785171i | ||||
\(262\) | 14.1510 | + | 8.17009i | 0.874252 | + | 0.504750i | ||||
\(263\) | −12.6093 | − | 7.28000i | −0.777524 | − | 0.448904i | 0.0580278 | − | 0.998315i | \(-0.481519\pi\) |
−0.835552 | + | 0.549411i | \(0.814852\pi\) | |||||||
\(264\) | 1.10721 | − | 1.33195i | 0.0681438 | − | 0.0819759i | ||||
\(265\) | 3.64513i | 0.223918i | ||||||||
\(266\) | 1.01860 | − | 0.0731322i | 0.0624544 | − | 0.00448402i | ||||
\(267\) | −6.77161 | − | 18.3411i | −0.414416 | − | 1.12245i | ||||
\(268\) | −4.35690 | − | 7.54636i | −0.266140 | − | 0.460968i | ||||
\(269\) | −12.3960 | + | 21.4704i | −0.755795 | + | 1.30907i | 0.189184 | + | 0.981942i | \(0.439416\pi\) |
−0.944978 | + | 0.327133i | \(0.893918\pi\) | |||||||
\(270\) | −1.28314 | − | 2.15307i | −0.0780895 | − | 0.131032i | ||||
\(271\) | −24.6174 | + | 14.2128i | −1.49540 | + | 0.863369i | −0.999986 | − | 0.00528874i | \(-0.998317\pi\) |
−0.495413 | + | 0.868658i | \(0.664983\pi\) | |||||||
\(272\) | 1.85374 | 0.112399 | ||||||||
\(273\) | −2.29796 | + | 1.04100i | −0.139079 | + | 0.0630041i | ||||
\(274\) | 11.4994 | 0.694703 | ||||||||
\(275\) | −4.12863 | + | 2.38366i | −0.248966 | + | 0.143740i | ||||
\(276\) | 0.0731322 | − | 0.426246i | 0.00440204 | − | 0.0256570i | ||||
\(277\) | −1.73179 | + | 2.99955i | −0.104053 | + | 0.180226i | −0.913351 | − | 0.407173i | \(-0.866515\pi\) |
0.809298 | + | 0.587399i | \(0.199848\pi\) | |||||||
\(278\) | −1.68973 | − | 2.92669i | −0.101343 | − | 0.175531i | ||||
\(279\) | 2.43157 | + | 2.84411i | 0.145574 | + | 0.170272i | ||||
\(280\) | −1.14809 | − | 0.557318i | −0.0686114 | − | 0.0333061i | ||||
\(281\) | − | 20.5607i | − | 1.22655i | −0.789869 | − | 0.613276i | \(-0.789852\pi\) | ||
0.789869 | − | 0.613276i | \(-0.210148\pi\) | |||||||
\(282\) | 11.7590 | + | 9.77489i | 0.700240 | + | 0.582086i | ||||
\(283\) | 6.42343 | + | 3.70857i | 0.381833 | + | 0.220451i | 0.678615 | − | 0.734494i | \(-0.262580\pi\) |
−0.296782 | + | 0.954945i | \(0.595914\pi\) | |||||||
\(284\) | 4.98855 | + | 2.88014i | 0.296016 | + | 0.170905i | ||||
\(285\) | −0.247989 | − | 0.206145i | −0.0146896 | − | 0.0122110i | ||||
\(286\) | 0.550510i | 0.0325524i | ||||||||
\(287\) | 8.41755 | + | 12.4296i | 0.496872 | + | 0.733695i | ||||
\(288\) | 1.94949 | + | 2.28024i | 0.114875 | + | 0.134364i | ||||
\(289\) | 6.78183 | + | 11.7465i | 0.398931 | + | 0.690969i | ||||
\(290\) | 1.08164 | − | 1.87346i | 0.0635161 | − | 0.110013i | ||||
\(291\) | 4.93200 | − | 28.7458i | 0.289119 | − | 1.68511i | ||||
\(292\) | −1.94534 | + | 1.12314i | −0.113843 | + | 0.0657271i | ||||
\(293\) | 33.1199 | 1.93488 | 0.967442 | − | 0.253093i | \(-0.0814479\pi\) | ||||
0.967442 | + | 0.253093i | \(0.0814479\pi\) | |||||||
\(294\) | 0.322117 | − | 12.1201i | 0.0187862 | − | 0.706857i | ||||
\(295\) | −1.76028 | −0.102487 | ||||||||
\(296\) | 4.72595 | − | 2.72853i | 0.274690 | − | 0.158592i | ||||
\(297\) | −2.66012 | − | 4.46360i | −0.154356 | − | 0.259005i | ||||
\(298\) | −8.26500 | + | 14.3154i | −0.478779 | + | 0.829269i | ||||
\(299\) | 0.0687281 | + | 0.119041i | 0.00397465 | + | 0.00688430i | ||||
\(300\) | −2.85992 | − | 7.74616i | −0.165118 | − | 0.447225i | ||||
\(301\) | −1.01203 | − | 1.49439i | −0.0583326 | − | 0.0861354i | ||||
\(302\) | − | 0.152797i | − | 0.00879249i | ||||||
\(303\) | 1.89486 | − | 2.27948i | 0.108857 | − | 0.130953i | ||||
\(304\) | 0.334273 | + | 0.192993i | 0.0191719 | + | 0.0110689i | ||||
\(305\) | −3.68328 | − | 2.12654i | −0.210904 | − | 0.121766i | ||||
\(306\) | 1.85374 | − | 5.24316i | 0.105971 | − | 0.299731i | ||||
\(307\) | 11.6047i | 0.662317i | 0.943575 | + | 0.331158i | \(0.107439\pi\) | ||||
−0.943575 | + | 0.331158i | \(0.892561\pi\) | |||||||
\(308\) | −2.38014 | − | 1.15539i | −0.135621 | − | 0.0658347i | ||||
\(309\) | 0.319121 | − | 0.117821i | 0.0181542 | − | 0.00670261i | ||||
\(310\) | −0.300821 | − | 0.521038i | −0.0170855 | − | 0.0295930i | ||||
\(311\) | 1.12484 | − | 1.94829i | 0.0637841 | − | 0.110477i | −0.832370 | − | 0.554220i | \(-0.813016\pi\) |
0.896154 | + | 0.443743i | \(0.146350\pi\) | |||||||
\(312\) | −0.939780 | − | 0.161241i | −0.0532046 | − | 0.00912846i | ||||
\(313\) | −8.92899 | + | 5.15515i | −0.504696 | + | 0.291387i | −0.730651 | − | 0.682751i | \(-0.760783\pi\) |
0.225955 | + | 0.974138i | \(0.427450\pi\) | |||||||
\(314\) | −10.5234 | −0.593872 | ||||||||
\(315\) | −2.72442 | + | 2.68997i | −0.153504 | + | 0.151562i | ||||
\(316\) | −13.4317 | −0.755595 | ||||||||
\(317\) | −13.7259 | + | 7.92463i | −0.770921 | + | 0.445091i | −0.833203 | − | 0.552967i | \(-0.813495\pi\) |
0.0622821 | + | 0.998059i | \(0.480162\pi\) | |||||||
\(318\) | −12.9003 | − | 2.21334i | −0.723414 | − | 0.124118i | ||||
\(319\) | 2.24238 | − | 3.88392i | 0.125549 | − | 0.217458i | ||||
\(320\) | −0.241181 | − | 0.417738i | −0.0134824 | − | 0.0233522i | ||||
\(321\) | −15.1784 | + | 5.60392i | −0.847173 | + | 0.312780i | ||||
\(322\) | −0.658919 | + | 0.0473082i | −0.0367201 | + | 0.00263638i | ||||
\(323\) | − | 0.715515i | − | 0.0398123i | ||||||
\(324\) | 8.39898 | − | 3.23375i | 0.466610 | − | 0.179653i | ||||
\(325\) | 2.27285 | + | 1.31223i | 0.126075 | + | 0.0727895i | ||||
\(326\) | 7.52106 | + | 4.34228i | 0.416553 | + | 0.240497i | ||||
\(327\) | 6.97897 | − | 8.39559i | 0.385938 | − | 0.464277i | ||||
\(328\) | 5.67387i | 0.313287i | ||||||||
\(329\) | 10.2003 | − | 21.0129i | 0.562362 | − | 1.15848i | ||||
\(330\) | 0.289369 | + | 0.783763i | 0.0159292 | + | 0.0431447i | ||||
\(331\) | −3.37516 | − | 5.84594i | −0.185515 | − | 0.321322i | 0.758235 | − | 0.651982i | \(-0.226062\pi\) |
−0.943750 | + | 0.330660i | \(0.892729\pi\) | |||||||
\(332\) | 3.24471 | − | 5.61999i | 0.178076 | − | 0.308437i | ||||
\(333\) | −2.99149 | − | 16.0955i | −0.163933 | − | 0.882029i | ||||
\(334\) | −1.74155 | + | 1.00548i | −0.0952931 | + | 0.0550175i | ||||
\(335\) | 4.20320 | 0.229645 | ||||||||
\(336\) | 2.66951 | − | 3.72474i | 0.145634 | − | 0.203201i | ||||
\(337\) | 1.02093 | 0.0556137 | 0.0278068 | − | 0.999613i | \(-0.491148\pi\) | ||||
0.0278068 | + | 0.999613i | \(0.491148\pi\) | |||||||
\(338\) | −10.9959 | + | 6.34847i | −0.598097 | + | 0.345311i | ||||
\(339\) | 5.80176 | − | 33.8151i | 0.315108 | − | 1.83659i | ||||
\(340\) | −0.447086 | + | 0.774375i | −0.0242466 | + | 0.0419964i | ||||
\(341\) | −0.623642 | − | 1.08018i | −0.0337721 | − | 0.0584950i | ||||
\(342\) | 0.880139 | − | 0.752475i | 0.0475925 | − | 0.0406892i | ||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | − | 0.682163i | − | 0.0367798i | ||||||
\(345\) | 0.160421 | + | 0.133352i | 0.00863676 | + | 0.00717945i | ||||
\(346\) | −11.3993 | − | 6.58140i | −0.612831 | − | 0.353818i | ||||
\(347\) | −24.6613 | − | 14.2382i | −1.32389 | − | 0.764349i | −0.339544 | − | 0.940590i | \(-0.610273\pi\) |
−0.984347 | + | 0.176242i | \(0.943606\pi\) | |||||||
\(348\) | 5.97349 | + | 4.96556i | 0.320213 | + | 0.266182i | ||||
\(349\) | − | 12.9437i | − | 0.692861i | −0.938076 | − | 0.346430i | \(-0.887394\pi\) | ||
0.938076 | − | 0.346430i | \(-0.112606\pi\) | |||||||
\(350\) | −10.4436 | + | 7.07263i | −0.558236 | + | 0.378048i | ||||
\(351\) | −1.39584 | + | 2.49686i | −0.0745043 | + | 0.133272i | ||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 8.66631 | − | 15.0105i | 0.461261 | − | 0.798927i | −0.537763 | − | 0.843096i | \(-0.680731\pi\) |
0.999024 | + | 0.0441686i | \(0.0140639\pi\) | |||||||
\(354\) | 1.06885 | − | 6.22973i | 0.0568089 | − | 0.331106i | ||||
\(355\) | −2.40629 | + | 1.38927i | −0.127712 | + | 0.0737348i | ||||
\(356\) | −11.2879 | −0.598257 | ||||||||
\(357\) | −8.45392 | − | 0.833235i | −0.447429 | − | 0.0440995i | ||||
\(358\) | 13.2356 | 0.699523 | ||||||||
\(359\) | 6.33088 | − | 3.65514i | 0.334131 | − | 0.192911i | −0.323543 | − | 0.946214i | \(-0.604874\pi\) |
0.657674 | + | 0.753303i | \(0.271541\pi\) | |||||||
\(360\) | −1.42272 | + | 0.264425i | −0.0749840 | + | 0.0139364i | ||||
\(361\) | −9.42551 | + | 16.3255i | −0.496079 | + | 0.859235i | ||||
\(362\) | −12.9468 | − | 22.4245i | −0.680469 | − | 1.17861i | ||||
\(363\) | 0.599900 | + | 1.62484i | 0.0314866 | + | 0.0852822i | ||||
\(364\) | 0.104304 | + | 1.45277i | 0.00546704 | + | 0.0761460i | ||||
\(365\) | − | 1.08352i | − | 0.0567143i | ||||||
\(366\) | 9.76248 | − | 11.7441i | 0.510293 | − | 0.613874i | ||||
\(367\) | 8.47438 | + | 4.89269i | 0.442359 | + | 0.255396i | 0.704598 | − | 0.709607i | \(-0.251127\pi\) |
−0.262239 | + | 0.965003i | \(0.584461\pi\) | |||||||
\(368\) | −0.216237 | − | 0.124844i | −0.0112721 | − | 0.00650797i | ||||
\(369\) | 16.0481 | + | 5.67387i | 0.835432 | + | 0.295370i | ||||
\(370\) | 2.63227i | 0.136845i | ||||||||
\(371\) | 1.43178 | + | 19.9422i | 0.0743344 | + | 1.03535i | ||||
\(372\) | 2.02664 | − | 0.748247i | 0.105077 | − | 0.0387948i | ||||
\(373\) | −14.0289 | − | 24.2988i | −0.726391 | − | 1.25815i | −0.958399 | − | 0.285432i | \(-0.907863\pi\) |
0.232008 | − | 0.972714i | \(-0.425470\pi\) | |||||||
\(374\) | −0.926868 | + | 1.60538i | −0.0479272 | + | 0.0830123i | ||||
\(375\) | 8.04284 | + | 1.37993i | 0.415330 | + | 0.0712594i | ||||
\(376\) | 7.64564 | − | 4.41421i | 0.394294 | − | 0.227646i | ||||
\(377\) | −2.46891 | −0.127155 | ||||||||
\(378\) | −7.86566 | − | 11.2753i | −0.404566 | − | 0.579937i | ||||
\(379\) | 29.2641 | 1.50320 | 0.751598 | − | 0.659622i | \(-0.229284\pi\) | ||||
0.751598 | + | 0.659622i | \(0.229284\pi\) | |||||||
\(380\) | −0.161241 | + | 0.0930924i | −0.00827147 | + | 0.00477554i | ||||
\(381\) | −36.0951 | − | 6.19294i | −1.84921 | − | 0.317274i | ||||
\(382\) | 8.76368 | − | 15.1791i | 0.448389 | − | 0.776632i | ||||
\(383\) | 4.89376 | + | 8.47623i | 0.250059 | + | 0.433115i | 0.963542 | − | 0.267558i | \(-0.0862166\pi\) |
−0.713483 | + | 0.700673i | \(0.752883\pi\) | |||||||
\(384\) | 1.62484 | − | 0.599900i | 0.0829175 | − | 0.0306135i | ||||
\(385\) | 1.05670 | − | 0.715615i | 0.0538542 | − | 0.0364711i | ||||
\(386\) | 7.36408i | 0.374822i | ||||||||
\(387\) | −1.92945 | − | 0.682163i | −0.0980793 | − | 0.0346763i | ||||
\(388\) | −14.5829 | − | 8.41946i | −0.740336 | − | 0.427433i | ||||
\(389\) | 32.1589 | + | 18.5669i | 1.63052 | + | 0.941380i | 0.983933 | + | 0.178539i | \(0.0571370\pi\) |
0.646586 | + | 0.762841i | \(0.276196\pi\) | |||||||
\(390\) | 0.294013 | − | 0.353693i | 0.0148879 | − | 0.0179100i | ||||
\(391\) | 0.462857i | 0.0234077i | ||||||||
\(392\) | −6.50000 | − | 2.59808i | −0.328300 | − | 0.131223i | ||||
\(393\) | −9.80248 | − | 26.5502i | −0.494470 | − | 1.33928i | ||||
\(394\) | 9.64660 | + | 16.7084i | 0.485989 | + | 0.841757i | ||||
\(395\) | 3.23948 | − | 5.61095i | 0.162996 | − | 0.282317i | ||||
\(396\) | −2.94949 | + | 0.548188i | −0.148217 | + | 0.0275475i | ||||
\(397\) | −31.3992 | + | 18.1283i | −1.57588 | + | 0.909835i | −0.580456 | + | 0.814292i | \(0.697126\pi\) |
−0.995425 | + | 0.0955439i | \(0.969541\pi\) | |||||||
\(398\) | −20.0941 | −1.00723 | ||||||||
\(399\) | −1.43770 | − | 1.03039i | −0.0719749 | − | 0.0515841i | ||||
\(400\) | −4.76733 | −0.238366 | ||||||||
\(401\) | 23.6204 | − | 13.6373i | 1.17955 | − | 0.681013i | 0.223638 | − | 0.974672i | \(-0.428207\pi\) |
0.955910 | + | 0.293660i | \(0.0948732\pi\) | |||||||
\(402\) | −2.55221 | + | 14.8754i | −0.127293 | + | 0.741916i | ||||
\(403\) | −0.343322 | + | 0.594650i | −0.0171021 | + | 0.0296216i | ||||
\(404\) | −0.855693 | − | 1.48210i | −0.0425723 | − | 0.0737374i | ||||
\(405\) | −0.674814 | + | 4.28849i | −0.0335318 | + | 0.213097i | ||||
\(406\) | 5.18167 | − | 10.6744i | 0.257162 | − | 0.529760i | ||||
\(407\) | 5.45705i | 0.270496i | ||||||||
\(408\) | −2.46909 | − | 2.05247i | −0.122238 | − | 0.101612i | ||||
\(409\) | 10.8109 | + | 6.24170i | 0.534566 | + | 0.308632i | 0.742874 | − | 0.669431i | \(-0.233462\pi\) |
−0.208308 | + | 0.978063i | \(0.566796\pi\) | |||||||
\(410\) | −2.37019 | − | 1.36843i | −0.117055 | − | 0.0675819i | ||||
\(411\) | −15.3166 | − | 12.7322i | −0.755513 | − | 0.628032i | ||||
\(412\) | − | 0.196401i | − | 0.00967599i | ||||||
\(413\) | −9.63033 | + | 0.691426i | −0.473877 | + | 0.0340229i | ||||
\(414\) | −0.569350 | + | 0.486766i | −0.0279820 | + | 0.0239232i | ||||
\(415\) | 1.56512 | + | 2.71087i | 0.0768288 | + | 0.133071i | ||||
\(416\) | −0.275255 | + | 0.476756i | −0.0134955 | + | 0.0233749i | ||||
\(417\) | −0.989819 | + | 5.76909i | −0.0484716 | + | 0.282513i | ||||
\(418\) | −0.334273 | + | 0.192993i | −0.0163498 | + | 0.00943959i | ||||
\(419\) | 14.3077 | 0.698975 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(420\) | 0.912132 | + | 2.01349i | 0.0445075 | + | 0.0982483i | ||||
\(421\) | 15.2015 | 0.740875 | 0.370437 | − | 0.928857i | \(-0.379208\pi\) | ||||
0.370437 | + | 0.928857i | \(0.379208\pi\) | |||||||
\(422\) | 4.31726 | − | 2.49257i | 0.210161 | − | 0.121336i | ||||
\(423\) | −4.83964 | − | 26.0394i | −0.235311 | − | 1.26608i | ||||
\(424\) | −3.77841 | + | 6.54441i | −0.183496 | + | 0.317824i | ||||
\(425\) | 4.41868 | + | 7.65338i | 0.214338 | + | 0.371244i | ||||
\(426\) | −3.45559 | − | 9.35956i | −0.167424 | − | 0.453472i | ||||
\(427\) | −20.9862 | − | 10.1874i | −1.01559 | − | 0.493001i | ||||
\(428\) | 9.34142i | 0.451535i | ||||||||
\(429\) | 0.609528 | − | 0.733253i | 0.0294283 | − | 0.0354018i | ||||
\(430\) | 0.284965 | + | 0.164525i | 0.0137422 | + | 0.00793408i | ||||
\(431\) | −1.44564 | − | 0.834638i | −0.0696338 | − | 0.0402031i | 0.464779 | − | 0.885427i | \(-0.346134\pi\) |
−0.534413 | + | 0.845224i | \(0.679467\pi\) | |||||||
\(432\) | −0.0719302 | − | 5.19565i | −0.00346074 | − | 0.249976i | ||||
\(433\) | 10.5393i | 0.506486i | 0.967403 | + | 0.253243i | \(0.0814973\pi\) | ||||
−0.967403 | + | 0.253243i | \(0.918503\pi\) | |||||||
\(434\) | −1.85043 | − | 2.73239i | −0.0888233 | − | 0.131159i | ||||
\(435\) | −3.51499 | + | 1.29775i | −0.168531 | + | 0.0622225i | ||||
\(436\) | −3.15161 | − | 5.45875i | −0.150935 | − | 0.261427i | ||||
\(437\) | −0.0481882 | + | 0.0834643i | −0.00230515 | + | 0.00399264i | ||||
\(438\) | 3.83466 | + | 0.657923i | 0.183227 | + | 0.0314368i | ||||
\(439\) | 19.4237 | − | 11.2143i | 0.927041 | − | 0.535227i | 0.0411662 | − | 0.999152i | \(-0.486893\pi\) |
0.885874 | + | 0.463925i | \(0.153559\pi\) | |||||||
\(440\) | 0.482362 | 0.0229957 | ||||||||
\(441\) | −13.8485 | + | 15.7867i | −0.659451 | + | 0.751748i | ||||
\(442\) | 1.02050 | 0.0485403 | ||||||||
\(443\) | −5.36156 | + | 3.09550i | −0.254735 | + | 0.147071i | −0.621931 | − | 0.783072i | \(-0.713651\pi\) |
0.367195 | + | 0.930144i | \(0.380318\pi\) | |||||||
\(444\) | −9.31577 | − | 1.59833i | −0.442107 | − | 0.0758536i | ||||
\(445\) | 2.72242 | − | 4.71537i | 0.129055 | − | 0.223530i | ||||
\(446\) | −6.62082 | − | 11.4676i | −0.313505 | − | 0.543007i | ||||
\(447\) | 26.8587 | − | 9.91636i | 1.27037 | − | 0.469028i | ||||
\(448\) | −1.48356 | − | 2.19067i | −0.0700918 | − | 0.103499i | ||||
\(449\) | − | 1.55464i | − | 0.0733680i | −0.999327 | − | 0.0366840i | \(-0.988321\pi\) | ||
0.999327 | − | 0.0366840i | \(-0.0116795\pi\) | |||||||
\(450\) | −4.76733 | + | 13.4840i | −0.224734 | + | 0.635644i | ||||
\(451\) | −4.91372 | − | 2.83694i | −0.231378 | − | 0.133586i | ||||
\(452\) | −17.1546 | − | 9.90422i | −0.806885 | − | 0.465855i | ||||
\(453\) | −0.169178 | + | 0.203518i | −0.00794867 | + | 0.00956213i | ||||
\(454\) | − | 27.7181i | − | 1.30088i | ||||||
\(455\) | −0.632035 | − | 0.306809i | −0.0296302 | − | 0.0143834i | ||||
\(456\) | −0.231553 | − | 0.627167i | −0.0108435 | − | 0.0293698i | ||||
\(457\) | −8.17556 | − | 14.1605i | −0.382437 | − | 0.662400i | 0.608973 | − | 0.793191i | \(-0.291582\pi\) |
−0.991410 | + | 0.130791i | \(0.958248\pi\) | |||||||
\(458\) | −4.16693 | + | 7.21733i | −0.194708 | + | 0.337244i | ||||
\(459\) | −8.27434 | + | 4.93116i | −0.386213 | + | 0.230167i | ||||
\(460\) | 0.104304 | − | 0.0602202i | 0.00486322 | − | 0.00280778i | ||||
\(461\) | 20.2754 | 0.944321 | 0.472160 | − | 0.881513i | \(-0.343474\pi\) | ||||
0.472160 | + | 0.881513i | \(0.343474\pi\) | |||||||
\(462\) | 1.89097 | + | 4.17423i | 0.0879759 | + | 0.194203i | ||||
\(463\) | 5.63443 | 0.261854 | 0.130927 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130927 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(464\) | 3.88392 | − | 2.24238i | 0.180307 | − | 0.104100i | ||||
\(465\) | −0.176217 | + | 1.02707i | −0.00817187 | + | 0.0476292i | ||||
\(466\) | −4.04877 | + | 7.01267i | −0.187556 | + | 0.324856i | ||||
\(467\) | 18.8229 | + | 32.6022i | 0.871020 | + | 1.50865i | 0.860943 | + | 0.508702i | \(0.169874\pi\) |
0.0100773 | + | 0.999949i | \(0.496792\pi\) | |||||||
\(468\) | 1.07321 | + | 1.25529i | 0.0496093 | + | 0.0580260i | ||||
\(469\) | 22.9953 | − | 1.65099i | 1.06183 | − | 0.0762357i | ||||
\(470\) | 4.25850i | 0.196430i | ||||||||
\(471\) | 14.0167 | + | 11.6516i | 0.645856 | + | 0.536878i | ||||
\(472\) | −3.16038 | − | 1.82465i | −0.145468 | − | 0.0839861i | ||||
\(473\) | 0.590770 | + | 0.341081i | 0.0271636 | + | 0.0156829i | ||||
\(474\) | 17.8904 | + | 14.8717i | 0.821735 | + | 0.683080i | ||||
\(475\) | 1.84012i | 0.0844305i | ||||||||
\(476\) | −2.14180 | + | 4.41215i | −0.0981691 | + | 0.202231i | ||||
\(477\) | 14.7320 | + | 17.2314i | 0.674530 | + | 0.788971i | ||||
\(478\) | −11.8193 | − | 20.4716i | −0.540602 | − | 0.936350i | ||||
\(479\) | 8.08725 | − | 14.0075i | 0.369516 | − | 0.640020i | −0.619974 | − | 0.784622i | \(-0.712857\pi\) |
0.989490 | + | 0.144602i | \(0.0461903\pi\) | |||||||
\(480\) | −0.141281 | + | 0.823443i | −0.00644854 | + | 0.0375849i | ||||
\(481\) | 2.60168 | − | 1.50208i | 0.118626 | − | 0.0684890i | ||||
\(482\) | −17.0350 | −0.775924 | ||||||||
\(483\) | 0.930027 | + | 0.666547i | 0.0423177 | + | 0.0303289i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.03425 | − | 4.06122i | 0.319409 | − | 0.184411i | ||||
\(486\) | −14.7675 | − | 4.99221i | −0.669866 | − | 0.226451i | ||||
\(487\) | −10.8869 | + | 18.8567i | −0.493335 | + | 0.854481i | −0.999971 | − | 0.00767942i | \(-0.997556\pi\) |
0.506636 | + | 0.862160i | \(0.330889\pi\) | |||||||
\(488\) | −4.40861 | − | 7.63593i | −0.199568 | − | 0.345662i | ||||
\(489\) | −5.20988 | − | 14.1111i | −0.235599 | − | 0.638125i | ||||
\(490\) | 2.65299 | − | 2.08869i | 0.119850 | − | 0.0943573i | ||||
\(491\) | 14.3125i | 0.645912i | 0.946414 | + | 0.322956i | \(0.104677\pi\) | ||||
−0.946414 | + | 0.322956i | \(0.895323\pi\) | |||||||
\(492\) | 6.28215 | − | 7.55732i | 0.283221 | − | 0.340710i | ||||
\(493\) | −7.19976 | − | 4.15679i | −0.324261 | − | 0.187212i | ||||
\(494\) | 0.184021 | + | 0.106245i | 0.00827949 | + | 0.00478017i | ||||
\(495\) | 0.482362 | − | 1.36433i | 0.0216806 | − | 0.0613219i | ||||
\(496\) | − | 1.24728i | − | 0.0560047i | ||||||
\(497\) | −12.6189 | + | 8.54574i | −0.566034 | + | 0.383329i | ||||
\(498\) | −10.5443 | + | 3.89300i | −0.472501 | + | 0.174449i | ||||
\(499\) | −4.02874 | − | 6.97799i | −0.180351 | − | 0.312378i | 0.761649 | − | 0.647990i | \(-0.224390\pi\) |
−0.942000 | + | 0.335612i | \(0.891057\pi\) | |||||||
\(500\) | 2.35569 | − | 4.08018i | 0.105350 | − | 0.182471i | ||||
\(501\) | 3.43293 | + | 0.588998i | 0.153372 | + | 0.0263145i | ||||
\(502\) | 10.9184 | − | 6.30374i | 0.487312 | − | 0.281350i | ||||
\(503\) | 20.9014 | 0.931947 | 0.465973 | − | 0.884799i | \(-0.345704\pi\) | ||||
0.465973 | + | 0.884799i | \(0.345704\pi\) | |||||||
\(504\) | −7.67972 | + | 2.00548i | −0.342082 | + | 0.0893313i | ||||
\(505\) | 0.825508 | 0.0367346 | ||||||||
\(506\) | 0.216237 | − | 0.124844i | 0.00961290 | − | 0.00555001i | ||||
\(507\) | 21.6750 | + | 3.71885i | 0.962622 | + | 0.165160i | ||||
\(508\) | −10.5720 | + | 18.3113i | −0.469057 | + | 0.812431i | ||||
\(509\) | 20.0442 | + | 34.7175i | 0.888442 | + | 1.53883i | 0.841717 | + | 0.539920i | \(0.181545\pi\) |
0.0467259 | + | 0.998908i | \(0.485121\pi\) | |||||||
\(510\) | 1.45289 | − | 0.536414i | 0.0643350 | − | 0.0237528i | ||||
\(511\) | −0.425601 | − | 5.92786i | −0.0188275 | − | 0.262233i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.00545 | + | 0.0277640i | −0.0885427 | + | 0.00122581i | ||||
\(514\) | 0.354251 | + | 0.204527i | 0.0156253 | + | 0.00902130i | ||||
\(515\) | 0.0820441 | + | 0.0473682i | 0.00361530 | + | 0.00208729i | ||||
\(516\) | −0.755295 | + | 0.908608i | −0.0332500 | + | 0.0399992i | ||||
\(517\) | 8.82843i | 0.388274i | ||||||||
\(518\) | 1.03394 | + | 14.4009i | 0.0454287 | + | 0.632741i | ||||
\(519\) | 7.89637 | + | 21.3875i | 0.346612 | + | 0.938807i | ||||
\(520\) | −0.132773 | − | 0.229969i | −0.00582246 | − | 0.0100848i | ||||
\(521\) | −2.01266 | + | 3.48604i | −0.0881764 | + | 0.152726i | −0.906740 | − | 0.421689i | \(-0.861437\pi\) |
0.818564 | + | 0.574415i | \(0.194771\pi\) | |||||||
\(522\) | −2.45850 | − | 13.2278i | −0.107605 | − | 0.578964i | ||||
\(523\) | −22.8435 | + | 13.1887i | −0.998876 | + | 0.576701i | −0.907915 | − | 0.419153i | \(-0.862327\pi\) |
−0.0909602 | + | 0.995855i | \(0.528994\pi\) | |||||||
\(524\) | −16.3402 | −0.713824 | ||||||||
\(525\) | 21.7413 | + | 2.14286i | 0.948868 | + | 0.0935223i | ||||
\(526\) | 14.5600 | 0.634846 | ||||||||
\(527\) | −2.00237 | + | 1.15607i | −0.0872246 | + | 0.0503591i | ||||
\(528\) | −0.292893 | + | 1.70711i | −0.0127465 | + | 0.0742923i | ||||
\(529\) | −11.4688 | + | 19.8646i | −0.498645 | + | 0.863678i | ||||
\(530\) | −1.82256 | − | 3.15677i | −0.0791671 | − | 0.137121i | ||||
\(531\) | −8.32125 | + | 7.11425i | −0.361112 | + | 0.308732i | ||||
\(532\) | −0.845567 | + | 0.572634i | −0.0366600 | + | 0.0248268i | ||||
\(533\) | 3.12352i | 0.135295i | ||||||||
\(534\) | 15.0349 | + | 12.4980i | 0.650624 | + | 0.540842i | ||||
\(535\) | −3.90226 | − | 2.25297i | −0.168710 | − | 0.0974045i | ||||
\(536\) | 7.54636 | + | 4.35690i | 0.325953 | + | 0.188189i | ||||
\(537\) | −17.6292 | − | 14.6545i | −0.760755 | − | 0.632390i | ||||
\(538\) | − | 24.7919i | − | 1.06885i | ||||||
\(539\) | 5.50000 | − | 4.33013i | 0.236902 | − | 0.186512i | ||||
\(540\) | 2.18777 | + | 1.22304i | 0.0941466 | + | 0.0526315i | ||||
\(541\) | −9.66000 | − | 16.7316i | −0.415316 | − | 0.719348i | 0.580146 | − | 0.814513i | \(-0.302996\pi\) |
−0.995462 | + | 0.0951647i | \(0.969662\pi\) | |||||||
\(542\) | 14.2128 | − | 24.6174i | 0.610494 | − | 1.05741i | ||||
\(543\) | −7.58406 | + | 44.2032i | −0.325463 | + | 1.89694i | ||||
\(544\) | −1.60538 | + | 0.926868i | −0.0688302 | + | 0.0397391i | ||||
\(545\) | 3.04044 | 0.130238 | ||||||||
\(546\) | 1.46959 | − | 2.05051i | 0.0628927 | − | 0.0877537i | ||||
\(547\) | 6.96837 | 0.297946 | 0.148973 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148973 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(548\) | −9.95875 | + | 5.74969i | −0.425417 | + | 0.245615i | ||||
\(549\) | −26.0063 | + | 4.83349i | −1.10992 | + | 0.206288i | ||||
\(550\) | 2.38366 | − | 4.12863i | 0.101640 | − | 0.176045i | ||||
\(551\) | −0.865528 | − | 1.49914i | −0.0368727 | − | 0.0638654i | ||||
\(552\) | 0.149788 | + | 0.405706i | 0.00637542 | + | 0.0172680i | ||||
\(553\) | 15.5190 | − | 31.9694i | 0.659933 | − | 1.35948i | ||||
\(554\) | − | 3.46359i | − | 0.147154i | ||||||
\(555\) | 2.91447 | − | 3.50606i | 0.123712 | − | 0.148824i | ||||
\(556\) | 2.92669 | + | 1.68973i | 0.124119 | + | 0.0716604i | ||||
\(557\) | −12.4468 | − | 7.18616i | −0.527388 | − | 0.304487i | 0.212564 | − | 0.977147i | \(-0.431818\pi\) |
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(558\) | −3.52785 | − | 1.24728i | −0.149346 | − | 0.0528018i | ||||
\(559\) | − | 0.375538i | − | 0.0158835i | ||||||
\(560\) | 1.27293 | − | 0.0913925i | 0.0537912 | − | 0.00386204i | ||||
\(561\) | 3.01203 | − | 1.11206i | 0.127168 | − | 0.0469511i | ||||
\(562\) | 10.2804 | + | 17.8061i | 0.433651 | + | 0.751106i | ||||
\(563\) | 15.5721 | − | 26.9717i | 0.656286 | − | 1.13672i | −0.325284 | − | 0.945616i | \(-0.605460\pi\) |
0.981570 | − | 0.191104i | \(-0.0612066\pi\) | |||||||
\(564\) | −15.0711 | − | 2.58579i | −0.634606 | − | 0.108881i | ||||
\(565\) | 8.27473 | − | 4.77742i | 0.348121 | − | 0.200988i | ||||
\(566\) | −7.41713 | −0.311765 | ||||||||
\(567\) | −2.00736 | + | 23.7270i | −0.0843011 | + | 0.996440i | ||||
\(568\) | −5.76028 | −0.241696 | ||||||||
\(569\) | −26.5762 | + | 15.3438i | −1.11413 | + | 0.643244i | −0.939896 | − | 0.341461i | \(-0.889078\pi\) |
−0.174234 | + | 0.984704i | \(0.555745\pi\) | |||||||
\(570\) | 0.317837 | + | 0.0545323i | 0.0133127 | + | 0.00228410i | ||||
\(571\) | 7.29934 | − | 12.6428i | 0.305468 | − | 0.529086i | −0.671898 | − | 0.740644i | \(-0.734521\pi\) |
0.977365 | + | 0.211558i | \(0.0678539\pi\) | |||||||
\(572\) | −0.275255 | − | 0.476756i | −0.0115090 | − | 0.0199342i | ||||
\(573\) | −28.4792 | + | 10.5147i | −1.18974 | + | 0.439257i | ||||
\(574\) | −13.5046 | − | 6.55556i | −0.563671 | − | 0.273624i | ||||
\(575\) | − | 1.19035i | − | 0.0496410i | ||||||
\(576\) | −2.82843 | − | 1.00000i | −0.117851 | − | 0.0416667i | ||||
\(577\) | −23.3520 | − | 13.4823i | −0.972154 | − | 0.561274i | −0.0722621 | − | 0.997386i | \(-0.523022\pi\) |
−0.899892 | + | 0.436112i | \(0.856355\pi\) | |||||||
\(578\) | −11.7465 | − | 6.78183i | −0.488589 | − | 0.282087i | ||||
\(579\) | 8.15355 | − | 9.80859i | 0.338850 | − | 0.407631i | ||||
\(580\) | 2.16328i | 0.0898253i | ||||||||
\(581\) | 9.62745 | + | 14.2162i | 0.399414 | + | 0.589786i | ||||
\(582\) | 10.1017 | + | 27.3606i | 0.418728 | + | 1.13413i | ||||
\(583\) | −3.77841 | − | 6.54441i | −0.156486 | − | 0.271042i | ||||
\(584\) | 1.12314 | − | 1.94534i | 0.0464761 | − | 0.0804989i | ||||
\(585\) | −0.783223 | + | 0.145569i | −0.0323823 | + | 0.00601853i | ||||
\(586\) | −28.6827 | + | 16.5599i | −1.18487 | + | 0.684085i | ||||
\(587\) | 4.39307 | 0.181321 | 0.0906607 | − | 0.995882i | \(-0.471102\pi\) | ||||
0.0906607 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(588\) | 5.78108 | + | 10.6574i | 0.238408 | + | 0.439502i | ||||
\(589\) | −0.481434 | −0.0198371 | ||||||||
\(590\) | 1.52445 | − | 0.880139i | 0.0627605 | − | 0.0362348i | ||||
\(591\) | 5.65085 | − | 32.9356i | 0.232445 | − | 1.35479i | ||||
\(592\) | −2.72853 | + | 4.72595i | −0.112142 | + | 0.194235i | ||||
\(593\) | −20.1436 | − | 34.8897i | −0.827197 | − | 1.43275i | −0.900229 | − | 0.435417i | \(-0.856601\pi\) |
0.0730318 | − | 0.997330i | \(-0.476733\pi\) | |||||||
\(594\) | 4.53553 | + | 2.53553i | 0.186095 | + | 0.104034i | ||||
\(595\) | −1.32656 | − | 1.95884i | −0.0543837 | − | 0.0803044i | ||||
\(596\) | − | 16.5300i | − | 0.677096i | ||||||
\(597\) | 26.7644 | + | 22.2484i | 1.09539 | + | 0.910565i | ||||
\(598\) | −0.119041 | − | 0.0687281i | −0.00486793 | − | 0.00281050i | ||||
\(599\) | −24.9757 | − | 14.4197i | −1.02048 | − | 0.589173i | −0.106236 | − | 0.994341i | \(-0.533880\pi\) |
−0.914242 | + | 0.405167i | \(0.867213\pi\) | |||||||
\(600\) | 6.34985 | + | 5.27841i | 0.259231 | + | 0.215490i | ||||
\(601\) | − | 24.5161i | − | 1.00003i | −0.866015 | − | 0.500017i | \(-0.833327\pi\) | ||
0.866015 | − | 0.500017i | \(-0.166673\pi\) | |||||||
\(602\) | 1.62364 | + | 0.788167i | 0.0661747 | + | 0.0321233i | ||||
\(603\) | 19.8695 | − | 16.9874i | 0.809150 | − | 0.691782i | ||||
\(604\) | 0.0763986 | + | 0.132326i | 0.00310861 | + | 0.00538428i | ||||
\(605\) | −0.241181 | + | 0.417738i | −0.00980540 | + | 0.0169835i | ||||
\(606\) | −0.501254 | + | 2.92152i | −0.0203620 | + | 0.118679i | ||||
\(607\) | −7.37857 | + | 4.26002i | −0.299487 | + | 0.172909i | −0.642212 | − | 0.766527i | \(-0.721983\pi\) |
0.342725 | + | 0.939436i | \(0.388650\pi\) | |||||||
\(608\) | −0.385986 | −0.0156538 | ||||||||
\(609\) | −18.7205 | + | 8.48056i | −0.758592 | + | 0.343649i | ||||
\(610\) | 4.25309 | 0.172203 | ||||||||
\(611\) | 4.20900 | − | 2.43007i | 0.170278 | − | 0.0983101i | ||||
\(612\) | 1.01620 | + | 5.46757i | 0.0410773 | + | 0.221014i | ||||
\(613\) | −22.8423 | + | 39.5640i | −0.922592 | + | 1.59798i | −0.127204 | + | 0.991877i | \(0.540600\pi\) |
−0.795388 | + | 0.606100i | \(0.792733\pi\) | |||||||
\(614\) | −5.80236 | − | 10.0500i | −0.234164 | − | 0.405584i | ||||
\(615\) | 1.64184 | + | 4.44697i | 0.0662055 | + | 0.179319i | ||||
\(616\) | 2.63896 | − | 0.189469i | 0.106327 | − | 0.00763391i | ||||
\(617\) | − | 20.7786i | − | 0.836513i | −0.908329 | − | 0.418257i | \(-0.862641\pi\) | ||
0.908329 | − | 0.418257i | \(-0.137359\pi\) | |||||||
\(618\) | −0.217456 | + | 0.261597i | −0.00874738 | + | 0.0105230i | ||||
\(619\) | 17.3550 | + | 10.0199i | 0.697558 | + | 0.402735i | 0.806437 | − | 0.591320i | \(-0.201393\pi\) |
−0.108879 | + | 0.994055i | \(0.534726\pi\) | |||||||
\(620\) | 0.521038 | + | 0.300821i | 0.0209254 | + | 0.0120813i | ||||
\(621\) | 1.29730 | − | 0.0179602i | 0.0520587 | − | 0.000720717i | ||||
\(622\) | 2.24969i | 0.0902043i | ||||||||
\(623\) | 13.0420 | − | 26.8667i | 0.522515 | − | 1.07639i | ||||
\(624\) | 0.894494 | − | 0.330251i | 0.0358084 | − | 0.0132206i | ||||
\(625\) | −10.7820 | − | 18.6750i | −0.431281 | − | 0.747000i | ||||
\(626\) | 5.15515 | − | 8.92899i | 0.206041 | − | 0.356874i | ||||
\(627\) | 0.658919 | + | 0.113053i | 0.0263147 | + | 0.00451488i | ||||
\(628\) | 9.11357 | − | 5.26172i | 0.363671 | − | 0.209966i | ||||
\(629\) | 10.1159 | 0.403349 | ||||||||
\(630\) | 1.01444 | − | 3.69179i | 0.0404161 | − | 0.147084i | ||||
\(631\) | 6.16436 | 0.245399 | 0.122700 | − | 0.992444i | \(-0.460845\pi\) | ||||
0.122700 | + | 0.992444i | \(0.460845\pi\) | |||||||
\(632\) | 11.6322 | − | 6.71587i | 0.462705 | − | 0.267143i | ||||
\(633\) | −8.51017 | − | 1.46011i | −0.338249 | − | 0.0580343i | ||||
\(634\) | 7.92463 | − | 13.7259i | 0.314727 | − | 0.545123i | ||||
\(635\) | −5.09954 | − | 8.83266i | −0.202369 | − | 0.350513i | ||||
\(636\) | 12.2787 | − | 4.53335i | 0.486881 | − | 0.179759i | ||||
\(637\) | −3.57832 | − | 1.43027i | −0.141778 | − | 0.0566693i | ||||
\(638\) | 4.48477i | 0.177554i | ||||||||
\(639\) | −5.76028 | + | 16.2925i | −0.227873 | + | 0.644522i | ||||
\(640\) | 0.417738 | + | 0.241181i | 0.0165125 | + | 0.00953351i | ||||
\(641\) | 21.4440 | + | 12.3807i | 0.846988 | + | 0.489009i | 0.859634 | − | 0.510911i | \(-0.170692\pi\) |
−0.0126451 | + | 0.999920i | \(0.504025\pi\) | |||||||
\(642\) | 10.3429 | − | 12.4423i | 0.408201 | − | 0.491059i | ||||
\(643\) | 32.9650i | 1.30001i | 0.759929 | + | 0.650006i | \(0.225234\pi\) | ||||
−0.759929 | + | 0.650006i | \(0.774766\pi\) | |||||||
\(644\) | 0.546986 | − | 0.370429i | 0.0215543 | − | 0.0145970i | ||||
\(645\) | −0.197397 | − | 0.534654i | −0.00777249 | − | 0.0210520i | ||||
\(646\) | 0.357758 | + | 0.619654i | 0.0140758 | + | 0.0243800i | ||||
\(647\) | −6.74037 | + | 11.6747i | −0.264991 | + | 0.458978i | −0.967561 | − | 0.252636i | \(-0.918702\pi\) |
0.702570 | + | 0.711615i | \(0.252036\pi\) | |||||||
\(648\) | −5.65685 | + | 7.00000i | −0.222222 | + | 0.274986i | ||||
\(649\) | 3.16038 | − | 1.82465i | 0.124056 | − | 0.0716236i | ||||
\(650\) | −2.62446 | −0.102940 | ||||||||
\(651\) | −0.560642 | + | 5.68822i | −0.0219733 | + | 0.222939i | ||||
\(652\) | −8.68457 | −0.340114 | ||||||||
\(653\) | −12.6035 | + | 7.27663i | −0.493213 | + | 0.284757i | −0.725906 | − | 0.687793i | \(-0.758579\pi\) |
0.232693 | + | 0.972550i | \(0.425246\pi\) | |||||||
\(654\) | −1.84617 | + | 10.7603i | −0.0721910 | + | 0.420760i | ||||
\(655\) | 3.94094 | − | 6.82591i | 0.153985 | − | 0.266710i | ||||
\(656\) | −2.83694 | − | 4.91372i | −0.110764 | − | 0.191848i | ||||
\(657\) | −4.37912 | − | 5.12208i | −0.170846 | − | 0.199831i | ||||
\(658\) | 1.67271 | + | 23.2979i | 0.0652090 | + | 0.908245i | ||||
\(659\) | 30.1076i | 1.17283i | 0.810012 | + | 0.586413i | \(0.199460\pi\) | ||||
−0.810012 | + | 0.586413i | \(0.800540\pi\) | |||||||
\(660\) | −0.642483 | − | 0.534074i | −0.0250086 | − | 0.0207888i | ||||
\(661\) | −30.8753 | − | 17.8258i | −1.20091 | − | 0.693345i | −0.240152 | − | 0.970735i | \(-0.577197\pi\) |
−0.960757 | + | 0.277390i | \(0.910530\pi\) | |||||||
\(662\) | 5.84594 | + | 3.37516i | 0.227209 | + | 0.131179i | ||||
\(663\) | −1.35926 | − | 1.12990i | −0.0527892 | − | 0.0438819i | ||||
\(664\) | 6.48941i | 0.251838i | ||||||||
\(665\) | −0.0352762 | − | 0.491334i | −0.00136795 | − | 0.0190531i | ||||
\(666\) | 10.6385 | + | 12.4434i | 0.412232 | + | 0.482171i | ||||
\(667\) | 0.559898 | + | 0.969772i | 0.0216793 | + | 0.0375497i | ||||
\(668\) | 1.00548 | − | 1.74155i | 0.0389033 | − | 0.0673824i | ||||
\(669\) | −3.87839 | + | 22.6049i | −0.149947 | + | 0.873956i | ||||
\(670\) | −3.64008 | + | 2.10160i | −0.140629 | + | 0.0811919i | ||||
\(671\) | 8.81722 | 0.340385 | ||||||||
\(672\) | −0.449490 | + | 4.56048i | −0.0173394 | + | 0.175924i | ||||
\(673\) | 47.2677 | 1.82203 | 0.911017 | − | 0.412369i | \(-0.135298\pi\) | ||||
0.911017 | + | 0.412369i | \(0.135298\pi\) | |||||||
\(674\) | −0.884152 | + | 0.510466i | −0.0340563 | + | 0.0196624i | ||||
\(675\) | 21.2795 | − | 12.6817i | 0.819047 | − | 0.488118i | ||||
\(676\) | 6.34847 | − | 10.9959i | 0.244172 | − | 0.422918i | ||||
\(677\) | 16.9764 | + | 29.4040i | 0.652456 | + | 1.13009i | 0.982525 | + | 0.186130i | \(0.0595945\pi\) |
−0.330069 | + | 0.943957i | \(0.607072\pi\) | |||||||
\(678\) | 11.8831 | + | 32.1856i | 0.456367 | + | 1.23608i | ||||
\(679\) | 36.8885 | − | 24.9816i | 1.41565 | − | 0.958706i | ||||
\(680\) | − | 0.894171i | − | 0.0342899i | ||||||
\(681\) | −30.6897 | + | 36.9192i | −1.17603 | + | 1.41475i | ||||
\(682\) | 1.08018 | + | 0.623642i | 0.0413622 | + | 0.0238805i | ||||
\(683\) | −30.2293 | − | 17.4529i | −1.15669 | − | 0.667817i | −0.206184 | − | 0.978513i | \(-0.566104\pi\) |
−0.950509 | + | 0.310696i | \(0.899438\pi\) | |||||||
\(684\) | −0.385986 | + | 1.09173i | −0.0147585 | + | 0.0417434i | ||||
\(685\) | − | 5.54686i | − | 0.211935i | ||||||
\(686\) | 13.6938 | − | 12.4691i | 0.522834 | − | 0.476073i | ||||
\(687\) | 13.5412 | − | 4.99948i | 0.516630 | − | 0.190742i | ||||
\(688\) | 0.341081 | + | 0.590770i | 0.0130036 | + | 0.0225229i | ||||
\(689\) | −2.08006 | + | 3.60276i | −0.0792438 | + | 0.137254i | ||||
\(690\) | −0.205605 | − | 0.0352762i | −0.00782724 | − | 0.00134294i | ||||
\(691\) | 8.04299 | − | 4.64362i | 0.305970 | − | 0.176652i | −0.339152 | − | 0.940732i | \(-0.610140\pi\) |
0.645122 | + | 0.764080i | \(0.276807\pi\) | |||||||
\(692\) | 13.1628 | 0.500375 | ||||||||
\(693\) | 2.10306 | − | 7.65357i | 0.0798886 | − | 0.290735i | ||||
\(694\) | 28.4765 | 1.08095 | ||||||||
\(695\) | −1.41172 | + | 0.815060i | −0.0535498 | + | 0.0309170i | ||||
\(696\) | −7.65597 | − | 1.31356i | −0.290199 | − | 0.0497903i | ||||
\(697\) | −5.25893 | + | 9.10873i | −0.199196 | + | 0.345018i | ||||
\(698\) | 6.47185 | + | 11.2096i | 0.244963 | + | 0.424289i | ||||
\(699\) | 13.1572 | − | 4.85772i | 0.497652 | − | 0.183736i | ||||
\(700\) | 5.50814 | − | 11.3469i | 0.208188 | − | 0.428873i | ||||
\(701\) | 32.9715i | 1.24531i | 0.782495 | + | 0.622657i | \(0.213947\pi\) | ||||
−0.782495 | + | 0.622657i | \(0.786053\pi\) | |||||||
\(702\) | −0.0395983 | − | 2.86026i | −0.00149454 | − | 0.107954i | ||||
\(703\) | 1.82415 | + | 1.05317i | 0.0687990 | + | 0.0397211i | ||||
\(704\) | 0.866025 | + | 0.500000i | 0.0326396 | + | 0.0188445i | ||||
\(705\) | 4.71503 | − | 5.67211i | 0.177578 | − | 0.213624i | ||||
\(706\) | 17.3326i | 0.652321i | ||||||||
\(707\) | 4.51628 | − | 0.324254i | 0.169852 | − | 0.0121948i | ||||
\(708\) | 2.18921 | + | 5.92953i | 0.0822756 | + | 0.222845i | ||||
\(709\) | 8.32304 | + | 14.4159i | 0.312578 | + | 0.541401i | 0.978920 | − | 0.204245i | \(-0.0654740\pi\) |
−0.666342 | + | 0.745647i | \(0.732141\pi\) | |||||||
\(710\) | 1.38927 | − | 2.40629i | 0.0521384 | − | 0.0903063i | ||||
\(711\) | −7.36312 | − | 39.6168i | −0.276139 | − | 1.48575i | ||||
\(712\) | 9.77559 | − | 5.64394i | 0.366356 | − | 0.211516i | ||||
\(713\) | 0.311433 | 0.0116633 | ||||||||
\(714\) | 7.73793 | − | 3.50536i | 0.289585 | − | 0.131185i | ||||
\(715\) | 0.265545 | 0.00993083 | ||||||||
\(716\) | −11.4624 | + | 6.61780i | −0.428368 | + | 0.247319i | ||||
\(717\) | −6.92358 | + | 40.3536i | −0.258566 | + | 1.50703i | ||||
\(718\) | −3.65514 | + | 6.33088i | −0.136408 | + | 0.236266i | ||||
\(719\) | −21.6348 | − | 37.4725i | −0.806841 | − | 1.39749i | −0.915041 | − | 0.403360i | \(-0.867842\pi\) |
0.108201 | − | 0.994129i | \(-0.465491\pi\) | |||||||
\(720\) | 1.09990 | − | 0.940360i | 0.0409909 | − | 0.0350451i | ||||
\(721\) | 0.467462 | + | 0.226921i | 0.0174092 | + | 0.00845097i | ||||
\(722\) | − | 18.8510i | − | 0.701562i | ||||||
\(723\) | 22.6898 | + | 18.8613i | 0.843844 | + | 0.701459i | ||||
\(724\) | 22.4245 | + | 12.9468i | 0.833401 | + | 0.481164i | ||||
\(725\) | 18.5159 | + | 10.6902i | 0.687664 | + | 0.397023i | ||||
\(726\) | −1.33195 | − | 1.10721i | −0.0494333 | − | 0.0410923i | ||||
\(727\) | − | 41.7432i | − | 1.54817i | −0.633082 | − | 0.774085i | \(-0.718210\pi\) | ||
0.633082 | − | 0.774085i | \(-0.281790\pi\) | |||||||
\(728\) | −0.816717 | − | 1.20599i | −0.0302696 | − | 0.0446968i | ||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 0.541762 | + | 0.938360i | 0.0200515 | + | 0.0347302i | ||||
\(731\) | 0.632275 | − | 1.09513i | 0.0233855 | − | 0.0405049i | ||||
\(732\) | −2.58250 | + | 15.0519i | −0.0954520 | + | 0.556335i | ||||
\(733\) | 2.60675 | − | 1.50501i | 0.0962826 | − | 0.0555888i | −0.451086 | − | 0.892481i | \(-0.648963\pi\) |
0.547368 | + | 0.836892i | \(0.315630\pi\) | |||||||
\(734\) | −9.78537 | −0.361185 | ||||||||
\(735\) | −5.84626 | − | 0.155377i | −0.215643 | − | 0.00573117i | ||||
\(736\) | 0.249689 | 0.00920365 | ||||||||
\(737\) | −7.54636 | + | 4.35690i | −0.277974 | + | 0.160488i | ||||
\(738\) | −16.7350 | + | 3.11035i | −0.616025 | + | 0.114494i | ||||
\(739\) | −5.43041 | + | 9.40575i | −0.199761 | + | 0.345996i | −0.948451 | − | 0.316924i | \(-0.897350\pi\) |
0.748690 | + | 0.662920i | \(0.230683\pi\) | |||||||
\(740\) | −1.31614 | − | 2.27962i | −0.0483822 | − | 0.0838004i | ||||
\(741\) | −0.127472 | − | 0.345262i | −0.00468281 | − | 0.0126835i | ||||
\(742\) | −11.2110 | − | 16.5545i | −0.411570 | − | 0.607736i | ||||
\(743\) | − | 32.1359i | − | 1.17895i | −0.807786 | − | 0.589476i | \(-0.799334\pi\) | ||
0.807786 | − | 0.589476i | \(-0.200666\pi\) | |||||||
\(744\) | −1.38100 | + | 1.66132i | −0.0506300 | + | 0.0609070i | ||||
\(745\) | 6.90521 | + | 3.98672i | 0.252987 | + | 0.146062i | ||||
\(746\) | 24.2988 | + | 14.0289i | 0.889644 | + | 0.513636i | ||||
\(747\) | 18.3548 | + | 6.48941i | 0.671568 | + | 0.237435i | ||||
\(748\) | − | 1.85374i | − | 0.0677793i | ||||||
\(749\) | −22.2339 | − | 10.7930i | −0.812408 | − | 0.394369i | ||||
\(750\) | −7.65527 | + | 2.82636i | −0.279531 | + | 0.103204i | ||||
\(751\) | 14.4715 | + | 25.0654i | 0.528072 | + | 0.914648i | 0.999464 | + | 0.0327241i | \(0.0104183\pi\) |
−0.471392 | + | 0.881924i | \(0.656248\pi\) | |||||||
\(752\) | −4.41421 | + | 7.64564i | −0.160970 | + | 0.278808i | ||||
\(753\) | −21.5223 | − | 3.69265i | −0.784317 | − | 0.134567i | ||||
\(754\) | 2.13814 | − | 1.23445i | 0.0778664 | − | 0.0449562i | ||||
\(755\) | −0.0737035 | −0.00268235 | ||||||||
\(756\) | 12.4495 | + | 5.83183i | 0.452784 | + | 0.212101i | ||||
\(757\) | 11.8099 | 0.429239 | 0.214619 | − | 0.976698i | \(-0.431149\pi\) | ||||
0.214619 | + | 0.976698i | \(0.431149\pi\) | |||||||
\(758\) | −25.3434 | + | 14.6320i | −0.920515 | + | 0.531460i | ||||
\(759\) | −0.426246 | − | 0.0731322i | −0.0154717 | − | 0.00265453i | ||||
\(760\) | 0.0930924 | − | 0.161241i | 0.00337682 | − | 0.00584882i | ||||
\(761\) | −2.72848 | − | 4.72586i | −0.0989071 | − | 0.171312i | 0.812325 | − | 0.583204i | \(-0.198201\pi\) |
−0.911233 | + | 0.411892i | \(0.864868\pi\) | |||||||
\(762\) | 34.3558 | − | 12.6843i | 1.24458 | − | 0.459504i | ||||
\(763\) | 16.6339 | − | 1.19426i | 0.602189 | − | 0.0432353i | ||||
\(764\) | 17.5274i | 0.634118i | ||||||||
\(765\) | −2.52910 | − | 0.894171i | −0.0914398 | − | 0.0323288i | ||||
\(766\) | −8.47623 | − | 4.89376i | −0.306259 | − | 0.176819i | ||||
\(767\) | −1.73982 | − | 1.00449i | −0.0628213 | − | 0.0362699i | ||||
\(768\) | −1.10721 | + | 1.33195i | −0.0399529 | + | 0.0480627i | ||||
\(769\) | 20.7871i | 0.749602i | 0.927105 | + | 0.374801i | \(0.122289\pi\) | ||||
−0.927105 | + | 0.374801i | \(0.877711\pi\) | |||||||
\(770\) | −0.557318 | + | 1.14809i | −0.0200844 | + | 0.0413742i | ||||
\(771\) | −0.245392 | − | 0.664649i | −0.00883756 | − | 0.0239367i | ||||
\(772\) | −3.68204 | − | 6.37748i | −0.132519 | − | 0.229530i | ||||
\(773\) | −23.4534 | + | 40.6225i | −0.843560 | + | 1.46109i | 0.0433053 | + | 0.999062i | \(0.486211\pi\) |
−0.886866 | + | 0.462027i | \(0.847122\pi\) | |||||||
\(774\) | 2.01203 | − | 0.373954i | 0.0723210 | − | 0.0134415i | ||||
\(775\) | 5.14957 | − | 2.97311i | 0.184978 | − | 0.106797i | ||||
\(776\) | 16.8389 | 0.604482 | ||||||||
\(777\) | 14.5677 | − | 20.3261i | 0.522612 | − | 0.729196i | ||||
\(778\) | −37.1338 | −1.33131 | ||||||||
\(779\) | −1.89662 | + | 1.09502i | −0.0679536 | + | 0.0392330i | ||||
\(780\) | −0.0777764 | + | 0.453314i | −0.00278484 | + | 0.0162312i | ||||
\(781\) | 2.88014 | − | 4.98855i | 0.103059 | − | 0.178504i | ||||
\(782\) | −0.231429 | − | 0.400846i | −0.00827587 | − | 0.0143342i | ||||
\(783\) | −11.3713 | + | 20.3408i | −0.406376 | + | 0.726921i | ||||
\(784\) | 6.92820 | − | 1.00000i | 0.247436 | − | 0.0357143i | ||||
\(785\) | 5.07611i | 0.181174i | ||||||||
\(786\) | 21.7643 | + | 18.0919i | 0.776308 | + | 0.645318i | ||||
\(787\) | −22.6920 | − | 13.1012i | −0.808881 | − | 0.467008i | 0.0376861 | − | 0.999290i | \(-0.488001\pi\) |
−0.846567 | + | 0.532282i | \(0.821335\pi\) | |||||||
\(788\) | −16.7084 | − | 9.64660i | −0.595212 | − | 0.343646i | ||||
\(789\) | −19.3932 | − | 16.1209i | −0.690416 | − | 0.573920i | ||||
\(790\) | 6.47896i | 0.230511i | ||||||||
\(791\) | 43.3938 | − | 29.3871i | 1.54290 | − | 1.04488i | ||||
\(792\) | 2.28024 | − | 1.94949i | 0.0810248 | − | 0.0692721i | ||||
\(793\) | −2.42698 | − | 4.20366i | −0.0861847 | − | 0.149276i | ||||
\(794\) | 18.1283 | − | 31.3992i | 0.643351 | − | 1.11432i | ||||
\(795\) | −1.06763 | + | 6.22262i | −0.0378650 | + | 0.220694i | ||||
\(796\) | 17.4020 | − | 10.0471i | 0.616799 | − | 0.356109i | ||||
\(797\) | −5.14751 | −0.182334 | −0.0911671 | − | 0.995836i | \(-0.529060\pi\) | ||||
−0.0911671 | + | 0.995836i | \(0.529060\pi\) | |||||||
\(798\) | 1.76028 | + | 0.173497i | 0.0623132 | + | 0.00614171i | ||||
\(799\) | 16.3656 | 0.578972 | ||||||||
\(800\) | 4.12863 | − | 2.38366i | 0.145969 | − | 0.0842752i | ||||
\(801\) | −6.18788 | − | 33.2935i | −0.218638 | − | 1.17637i | ||||
\(802\) | −13.6373 | + | 23.6204i | −0.481549 | + | 0.834067i | ||||
\(803\) | 1.12314 | + | 1.94534i | 0.0396349 | + | 0.0686497i | ||||
\(804\) | −5.22741 | − | 14.1586i | −0.184356 | − | 0.499334i | ||||
\(805\) | 0.0228197 | + | 0.317837i | 0.000804288 | + | 0.0112023i | ||||
\(806\) | − | 0.686643i | − | 0.0241860i | ||||||
\(807\) | −27.4498 | + | 33.0216i | −0.966277 | + | 1.16242i | ||||
\(808\) | 1.48210 | + | 0.855693i | 0.0521402 | + | 0.0301032i | ||||
\(809\) | 6.76716 | + | 3.90702i | 0.237921 | + | 0.137364i | 0.614221 | − | 0.789134i | \(-0.289470\pi\) |
−0.376300 | + | 0.926498i | \(0.622804\pi\) | |||||||
\(810\) | −1.55984 | − | 4.05135i | −0.0548071 | − | 0.142350i | ||||
\(811\) | − | 9.92215i | − | 0.348414i | −0.984709 | − | 0.174207i | \(-0.944264\pi\) | ||
0.984709 | − | 0.174207i | \(-0.0557362\pi\) | |||||||
\(812\) | 0.849723 | + | 11.8351i | 0.0298194 | + | 0.415331i | ||||
\(813\) | −46.1873 | + | 17.0526i | −1.61986 | + | 0.598060i | ||||
\(814\) | −2.72853 | − | 4.72595i | −0.0956348 | − | 0.165644i | ||||
\(815\) | 2.09455 | − | 3.62787i | 0.0733690 | − | 0.127079i | ||||
\(816\) | 3.16452 | + | 0.542947i | 0.110781 | + | 0.0190069i | ||||
\(817\) | 0.228029 | − | 0.131652i | 0.00797772 | − | 0.00460594i | ||||
\(818\) | −12.4834 | −0.436472 | ||||||||
\(819\) | −4.22776 | + | 1.10404i | −0.147730 | + | 0.0385782i | ||||
\(820\) | 2.73686 | 0.0955753 | ||||||||
\(821\) | −16.6405 | + | 9.60741i | −0.580758 | + | 0.335301i | −0.761435 | − | 0.648242i | \(-0.775505\pi\) |
0.180676 | + | 0.983543i | \(0.442171\pi\) | |||||||
\(822\) | 19.6307 | + | 3.36809i | 0.684698 | + | 0.117476i | ||||
\(823\) | −9.79913 | + | 16.9726i | −0.341576 | + | 0.591627i | −0.984726 | − | 0.174113i | \(-0.944294\pi\) |
0.643149 | + | 0.765741i | \(0.277627\pi\) | |||||||
\(824\) | 0.0982005 | + | 0.170088i | 0.00342098 | + | 0.00592531i | ||||
\(825\) | −7.74616 | + | 2.85992i | −0.269687 | + | 0.0995697i | ||||
\(826\) | 7.99439 | − | 5.41396i | 0.278161 | − | 0.188376i | ||||
\(827\) | 3.35552i | 0.116683i | 0.998297 | + | 0.0583414i | \(0.0185812\pi\) | ||||
−0.998297 | + | 0.0583414i | \(0.981419\pi\) | |||||||
\(828\) | 0.249689 | − | 0.706227i | 0.00867729 | − | 0.0245431i | ||||
\(829\) | −33.3865 | − | 19.2757i | −1.15956 | − | 0.669474i | −0.208363 | − | 0.978051i | \(-0.566814\pi\) |
−0.951199 | + | 0.308578i | \(0.900147\pi\) | |||||||
\(830\) | −2.71087 | − | 1.56512i | −0.0940957 | − | 0.0543262i | ||||
\(831\) | −3.83490 | + | 4.61333i | −0.133031 | + | 0.160035i | ||||
\(832\) | − | 0.550510i | − | 0.0190855i | ||||||
\(833\) | −8.02691 | − | 10.1955i | −0.278116 | − | 0.353255i | ||||
\(834\) | −2.02734 | − | 5.49109i | −0.0702009 | − | 0.190141i | ||||
\(835\) | 0.485006 | + | 0.840055i | 0.0167843 | + | 0.0290713i | ||||
\(836\) | 0.192993 | − | 0.334273i | 0.00667480 | − | 0.0115611i | ||||
\(837\) | 3.31793 | + | 5.56739i | 0.114684 | + | 0.192437i | ||||
\(838\) | −12.3908 | + | 7.15383i | −0.428033 | + | 0.247125i | ||||
\(839\) | −33.3680 | −1.15199 | −0.575996 | − | 0.817452i | \(-0.695386\pi\) | ||||
−0.575996 | + | 0.817452i | \(0.695386\pi\) | |||||||
\(840\) | −1.79668 | − | 1.28767i | −0.0619912 | − | 0.0444288i | ||||
\(841\) | 8.88687 | 0.306444 | ||||||||
\(842\) | −13.1649 | + | 7.60074i | −0.453691 | + | 0.261939i | ||||
\(843\) | 6.02210 | − | 35.0994i | 0.207412 | − | 1.20889i | ||||
\(844\) | −2.49257 | + | 4.31726i | −0.0857978 | + | 0.148606i | ||||
\(845\) | 3.06226 | + | 5.30399i | 0.105345 | + | 0.182463i | ||||
\(846\) | 17.2109 | + | 20.1309i | 0.591724 | + | 0.692115i | ||||
\(847\) | −1.15539 | + | 2.38014i | −0.0396998 | + | 0.0817826i | ||||
\(848\) | − | 7.55683i | − | 0.259503i | ||||||
\(849\) | 9.87926 | + | 8.21230i | 0.339055 | + | 0.281845i | ||||
\(850\) | −7.65338 | − | 4.41868i | −0.262509 | − | 0.151560i | ||||
\(851\) | −1.18002 | − | 0.681283i | −0.0404504 | − | 0.0233541i | ||||
\(852\) | 7.67241 | + | 6.37782i | 0.262852 | + | 0.218500i | ||||
\(853\) | 7.56740i | 0.259103i | 0.991573 | + | 0.129551i | \(0.0413537\pi\) | ||||
−0.991573 | + | 0.129551i | \(0.958646\pi\) | |||||||
\(854\) | 23.2683 | − | 1.67059i | 0.796224 | − | 0.0571663i | ||||
\(855\) | −0.362965 | − | 0.424546i | −0.0124131 | − | 0.0145192i | ||||
\(856\) | −4.67071 | − | 8.08991i | −0.159642 | − | 0.276507i | ||||
\(857\) | −22.1795 | + | 38.4160i | −0.757636 | + | 1.31226i | 0.186416 | + | 0.982471i | \(0.440313\pi\) |
−0.944053 | + | 0.329794i | \(0.893021\pi\) | |||||||
\(858\) | −0.161241 | + | 0.939780i | −0.00550467 | + | 0.0320836i | ||||
\(859\) | 15.3094 | − | 8.83889i | 0.522350 | − | 0.301579i | −0.215545 | − | 0.976494i | \(-0.569153\pi\) |
0.737896 | + | 0.674915i | \(0.235820\pi\) | |||||||
\(860\) | −0.329049 | −0.0112205 | ||||||||
\(861\) | 10.7291 | + | 23.6841i | 0.365647 | + | 0.807151i | ||||
\(862\) | 1.66928 | 0.0568558 | ||||||||
\(863\) | 27.0927 | − | 15.6420i | 0.922248 | − | 0.532460i | 0.0378962 | − | 0.999282i | \(-0.487934\pi\) |
0.884351 | + | 0.466822i | \(0.154601\pi\) | |||||||
\(864\) | 2.66012 | + | 4.46360i | 0.0904991 | + | 0.151855i | ||||
\(865\) | −3.17462 | + | 5.49860i | −0.107940 | + | 0.186958i | ||||
\(866\) | −5.26965 | − | 9.12730i | −0.179070 | − | 0.310158i | ||||
\(867\) | 8.13685 | + | 22.0388i | 0.276342 | + | 0.748478i | ||||
\(868\) | 2.96871 | + | 1.44111i | 0.100765 | + | 0.0489143i | ||||
\(869\) | 13.4317i | 0.455641i | ||||||||
\(870\) | 2.39520 | − | 2.88138i | 0.0812048 | − | 0.0976881i | ||||
\(871\) | 4.15435 | + | 2.39852i | 0.140765 | + | 0.0812706i | ||||
\(872\) | 5.45875 | + | 3.15161i | 0.184857 | + | 0.106727i | ||||
\(873\) | 16.8389 | − | 47.6276i | 0.569911 | − | 1.61195i | ||||
\(874\) | − | 0.0963763i | − | 0.00325998i | ||||||
\(875\) | 6.98964 | + | 10.3211i | 0.236293 | + | 0.348917i | ||||
\(876\) | −3.64987 | + | 1.34755i | −0.123318 | + | 0.0455295i | ||||
\(877\) | 6.71183 | + | 11.6252i | 0.226642 | + | 0.392556i | 0.956811 | − | 0.290711i | \(-0.0938918\pi\) |
−0.730168 | + | 0.683267i | \(0.760558\pi\) | |||||||
\(878\) | −11.2143 | + | 19.4237i | −0.378463 | + | 0.655517i | ||||
\(879\) | 56.5392 | + | 9.70059i | 1.90702 | + | 0.327193i | ||||
\(880\) | −0.417738 | + | 0.241181i | −0.0140819 | + | 0.00813021i | ||||
\(881\) | −17.4395 | −0.587551 | −0.293775 | − | 0.955874i | \(-0.594912\pi\) | ||||
−0.293775 | + | 0.955874i | \(0.594912\pi\) | |||||||
\(882\) | 4.09978 | − | 20.5959i | 0.138047 | − | 0.693501i | ||||
\(883\) | −46.0054 | −1.54820 | −0.774102 | − | 0.633061i | \(-0.781798\pi\) | ||||
−0.774102 | + | 0.633061i | \(0.781798\pi\) | |||||||
\(884\) | −0.883779 | + | 0.510250i | −0.0297247 | + | 0.0171616i | ||||
\(885\) | −3.00498 | − | 0.515574i | −0.101011 | − | 0.0173308i | ||||
\(886\) | 3.09550 | − | 5.36156i | 0.103995 | − | 0.180125i | ||||
\(887\) | −16.2645 | − | 28.1710i | −0.546109 | − | 0.945888i | −0.998536 | − | 0.0540868i | \(-0.982775\pi\) |
0.452428 | − | 0.891801i | \(-0.350558\pi\) | |||||||
\(888\) | 8.86686 | − | 3.27369i | 0.297552 | − | 0.109858i | ||||
\(889\) | −31.3685 | − | 46.3196i | −1.05207 | − | 1.55351i | ||||
\(890\) | 5.44485i | 0.182512i | ||||||||
\(891\) | −3.23375 | − | 8.39898i | −0.108335 | − | 0.281376i | ||||
\(892\) | 11.4676 | + | 6.62082i | 0.383964 | + | 0.221682i | ||||
\(893\) | 2.95111 | + | 1.70382i | 0.0987551 | + | 0.0570163i | ||||
\(894\) | −18.3021 | + | 22.0172i | −0.612115 | + | 0.736364i | ||||
\(895\) | − | 6.38435i | − | 0.213405i | ||||||
\(896\) | 2.38014 | + | 1.15539i | 0.0795149 | + | 0.0385990i | ||||
\(897\) | 0.0824601 | + | 0.223345i | 0.00275326 | + | 0.00745728i | ||||
\(898\) | 0.777320 | + | 1.34636i | 0.0259395 | + | 0.0449285i | ||||
\(899\) | −2.79689 | + | 4.84436i | −0.0932815 | + | 0.161568i | ||||
\(900\) | −2.61339 | − | 14.0612i | −0.0871131 | − | 0.468706i | ||||
\(901\) | −12.1316 | + | 7.00418i | −0.404162 | + | 0.233343i | ||||
\(902\) | 5.67387 | 0.188919 | ||||||||
\(903\) | −1.28995 | − | 2.84751i | −0.0429268 | − | 0.0947591i | ||||
\(904\) | 19.8084 | 0.658819 | ||||||||
\(905\) | −10.8167 | + | 6.24504i | −0.359560 | + | 0.207592i | ||||
\(906\) | 0.0447532 | − | 0.260841i | 0.00148683 | − | 0.00866586i | ||||
\(907\) | 1.11719 | − | 1.93503i | 0.0370957 | − | 0.0642517i | −0.846881 | − | 0.531782i | \(-0.821523\pi\) |
0.883977 | + | 0.467530i | \(0.154856\pi\) | |||||||
\(908\) | 13.8591 | + | 24.0046i | 0.459929 | + | 0.796620i | ||||
\(909\) | 3.90237 | − | 3.33633i | 0.129433 | − | 0.110659i | ||||
\(910\) | 0.700763 | − | 0.0503125i | 0.0232301 | − | 0.00166784i | ||||
\(911\) | 30.4938i | 1.01030i | 0.863030 | + | 0.505152i | \(0.168564\pi\) | ||||
−0.863030 | + | 0.505152i | \(0.831436\pi\) | |||||||
\(912\) | 0.514114 | + | 0.427366i | 0.0170240 | + | 0.0141515i | ||||
\(913\) | −5.61999 | − | 3.24471i | −0.185995 | − | 0.107384i | ||||
\(914\) | 14.1605 | + | 8.17556i | 0.468387 | + | 0.270424i | ||||
\(915\) | −5.66491 | − | 4.70905i | −0.187276 | − | 0.155676i | ||||
\(916\) | − | 8.33386i | − | 0.275358i | ||||||
\(917\) | 18.8794 | − | 38.8919i | 0.623451 | − | 1.28432i | ||||
\(918\) | 4.70021 | − | 8.40768i | 0.155130 | − | 0.277495i | ||||
\(919\) | 1.57169 | + | 2.72225i | 0.0518453 | + | 0.0897986i | 0.890783 | − | 0.454428i | \(-0.150156\pi\) |
−0.838938 | + | 0.544227i | \(0.816823\pi\) | |||||||
\(920\) | −0.0602202 | + | 0.104304i | −0.00198540 | + | 0.00343882i | ||||
\(921\) | −3.39895 | + | 19.8105i | −0.111999 | + | 0.652778i | ||||
\(922\) | −17.5590 | + | 10.1377i | −0.578276 | + | 0.333868i | ||||
\(923\) | −3.17109 | −0.104378 | ||||||||
\(924\) | −3.72474 | − | 2.66951i | −0.122535 | − | 0.0878204i | ||||
\(925\) | −26.0156 | −0.855386 | ||||||||
\(926\) | −4.87956 | + | 2.81722i | −0.160352 | + | 0.0925794i | ||||
\(927\) | 0.579283 | − | 0.107665i | 0.0190261 | − | 0.00353617i | ||||
\(928\) | −2.24238 | + | 3.88392i | −0.0736098 | + | 0.127496i | ||||
\(929\) | 23.0663 | + | 39.9519i | 0.756779 | + | 1.31078i | 0.944485 | + | 0.328555i | \(0.106562\pi\) |
−0.187706 | + | 0.982225i | \(0.560105\pi\) | |||||||
\(930\) | −0.360926 | − | 0.977576i | −0.0118352 | − | 0.0320560i | ||||
\(931\) | −0.385986 | − | 2.67419i | −0.0126502 | − | 0.0876429i | ||||
\(932\) | − | 8.09754i | − | 0.265244i | ||||||
\(933\) | 2.49087 | − | 2.99648i | 0.0815474 | − | 0.0981002i | ||||
\(934\) | −32.6022 | − | 18.8229i | −1.06678 | − | 0.615904i | ||||
\(935\) | 0.774375 | + | 0.447086i | 0.0253248 | + | 0.0146213i | ||||
\(936\) | −1.55708 | − | 0.550510i | −0.0508947 | − | 0.0179940i | ||||
\(937\) | − | 29.7606i | − | 0.972236i | −0.873893 | − | 0.486118i | \(-0.838413\pi\) | ||
0.873893 | − | 0.486118i | \(-0.161587\pi\) | |||||||
\(938\) | −19.0890 | + | 12.9275i | −0.623279 | + | 0.422097i | ||||
\(939\) | −16.7526 | + | 6.18516i | −0.546702 | + | 0.201845i | ||||
\(940\) | −2.12925 | − | 3.68797i | −0.0694484 | − | 0.120288i | ||||
\(941\) | −3.16738 | + | 5.48605i | −0.103253 | + | 0.178840i | −0.913023 | − | 0.407907i | \(-0.866259\pi\) |
0.809770 | + | 0.586748i | \(0.199592\pi\) | |||||||
\(942\) | −17.9646 | − | 3.08224i | −0.585320 | − | 0.100425i | ||||
\(943\) | 1.22690 | − | 0.708351i | 0.0399534 | − | 0.0230671i | ||||
\(944\) | 3.64929 | 0.118774 | ||||||||
\(945\) | −5.43875 | + | 3.79410i | −0.176923 | + | 0.123422i | ||||
\(946\) | −0.682163 | −0.0221790 | ||||||||
\(947\) | 38.3205 | − | 22.1244i | 1.24525 | − | 0.718945i | 0.275091 | − | 0.961418i | \(-0.411292\pi\) |
0.970158 | + | 0.242473i | \(0.0779587\pi\) | |||||||
\(948\) | −22.9294 | − | 3.93407i | −0.744713 | − | 0.127773i | ||||
\(949\) | 0.618303 | − | 1.07093i | 0.0200710 | − | 0.0347639i | ||||
\(950\) | −0.920060 | − | 1.59359i | −0.0298507 | − | 0.0517029i | ||||
\(951\) | −25.7526 | + | 9.50797i | −0.835084 | + | 0.308317i | ||||
\(952\) | −0.351225 | − | 4.89193i | −0.0113833 | − | 0.158548i | ||||
\(953\) | − | 49.7571i | − | 1.61179i | −0.592059 | − | 0.805895i | \(-0.701685\pi\) | ||
0.592059 | − | 0.805895i | \(-0.298315\pi\) | |||||||
\(954\) | −21.3739 | − | 7.55683i | −0.692007 | − | 0.244661i | ||||
\(955\) | −7.32184 | − | 4.22726i | −0.236929 | − | 0.136791i | ||||
\(956\) | 20.4716 | + | 11.8193i | 0.662100 | + | 0.382263i | ||||
\(957\) | 4.96556 | − | 5.97349i | 0.160514 | − | 0.193095i | ||||
\(958\) | 16.1745i | 0.522574i | ||||||||
\(959\) | −2.17877 | − | 30.3464i | −0.0703562 | − | 0.979936i | ||||
\(960\) | −0.289369 | − | 0.783763i | −0.00933935 | − | 0.0252958i | ||||
\(961\) | −14.7221 | − | 25.4995i | −0.474908 | − | 0.822564i | ||||
\(962\) | −1.50208 | + | 2.60168i | −0.0484291 | + | 0.0838816i | ||||
\(963\) | −27.5524 | + | 5.12086i | −0.887865 | + | 0.165017i | ||||
\(964\) | 14.7528 | − | 8.51751i | 0.475155 | − | 0.274331i | ||||
\(965\) | 3.55215 | 0.114348 | ||||||||
\(966\) | −1.13870 | − | 0.112233i | −0.0366371 | − | 0.00361102i | ||||
\(967\) | −31.3556 | −1.00833 | −0.504164 | − | 0.863608i | \(-0.668199\pi\) | ||||
−0.504164 | + | 0.863608i | \(0.668199\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | 0.209570 | − | 1.22146i | 0.00673234 | − | 0.0392390i | ||||
\(970\) | −4.06122 | + | 7.03425i | −0.130398 | + | 0.225856i | ||||
\(971\) | 26.2882 | + | 45.5325i | 0.843628 | + | 1.46121i | 0.886807 | + | 0.462139i | \(0.152918\pi\) |
−0.0431796 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(972\) | 15.2851 | − | 3.06035i | 0.490270 | − | 0.0981609i | ||||
\(973\) | −7.40327 | + | 5.01363i | −0.237338 | + | 0.160730i | ||||
\(974\) | − | 21.7739i | − | 0.697681i | ||||||
\(975\) | 3.49566 | + | 2.90582i | 0.111951 | + | 0.0930608i | ||||
\(976\) | 7.63593 | + | 4.40861i | 0.244420 | + | 0.141116i | ||||
\(977\) | 27.9026 | + | 16.1096i | 0.892682 | + | 0.515390i | 0.874819 | − | 0.484450i | \(-0.160980\pi\) |
0.0178633 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(978\) | 11.5674 | + | 9.61561i | 0.369885 | + | 0.307473i | ||||
\(979\) | 11.2879i | 0.360762i | ||||||||
\(980\) | −1.25321 | + | 3.13535i | −0.0400324 | + | 0.100155i | ||||
\(981\) | 14.3729 | − | 12.2881i | 0.458890 | − | 0.392328i | ||||
\(982\) | −7.15623 | − | 12.3950i | −0.228365 | − | 0.395539i | ||||
\(983\) | 9.07712 | − | 15.7220i | 0.289515 | − | 0.501455i | −0.684179 | − | 0.729314i | \(-0.739839\pi\) |
0.973694 | + | 0.227859i | \(0.0731726\pi\) | |||||||
\(984\) | −1.66184 | + | 9.68590i | −0.0529775 | + | 0.308775i | ||||
\(985\) | 8.05950 | − | 4.65315i | 0.256797 | − | 0.148262i | ||||
\(986\) | 8.31357 | 0.264758 | ||||||||
\(987\) | 23.5676 | − | 32.8836i | 0.750164 | − | 1.04670i | ||||
\(988\) | −0.212489 | −0.00676018 | ||||||||
\(989\) | −0.147509 | + | 0.0851642i | −0.00469051 | + | 0.00270807i | ||||
\(990\) | 0.264425 | + | 1.42272i | 0.00840398 | + | 0.0452171i | ||||
\(991\) | 24.0610 | − | 41.6748i | 0.764321 | − | 1.32384i | −0.176283 | − | 0.984339i | \(-0.556408\pi\) |
0.940605 | − | 0.339504i | \(-0.110259\pi\) | |||||||
\(992\) | 0.623642 | + | 1.08018i | 0.0198007 | + | 0.0342958i | ||||
\(993\) | −4.04951 | − | 10.9682i | −0.128507 | − | 0.348065i | ||||
\(994\) | 6.65539 | − | 13.7103i | 0.211096 | − | 0.434863i | ||||
\(995\) | 9.69265i | 0.307278i | ||||||||
\(996\) | 7.18512 | − | 8.64358i | 0.227669 | − | 0.273882i | ||||
\(997\) | −5.51486 | − | 3.18400i | −0.174657 | − | 0.100838i | 0.410123 | − | 0.912030i | \(-0.365486\pi\) |
−0.584780 | + | 0.811192i | \(0.698819\pi\) | |||||||
\(998\) | 6.97799 | + | 4.02874i | 0.220884 | + | 0.127528i | ||||
\(999\) | −0.392527 | − | 28.3530i | −0.0124190 | − | 0.897048i |
(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 | 462.2.k.f.353.2 | yes | 8 | |
3.2 | odd | 2 | 462.2.k.e.353.3 | yes | 8 | ||
7.5 | odd | 6 | 462.2.k.e.89.3 | ✓ | 8 | ||
21.5 | even | 6 | inner | 462.2.k.f.89.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.k.e.89.3 | ✓ | 8 | 7.5 | odd | 6 | ||
462.2.k.e.353.3 | yes | 8 | 3.2 | odd | 2 | ||
462.2.k.f.89.2 | yes | 8 | 21.5 | even | 6 | inner | |
462.2.k.f.353.2 | yes | 8 | 1.1 | even | 1 | trivial |