Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(109,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, 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("1134.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.h (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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.109 |
Dual form | 1134.2.h.t.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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.64575 | −0.736002 | −0.368001 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32288 | − | 2.29129i | −0.500000 | − | 0.866025i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.822876 | + | 1.42526i | −0.260216 | + | 0.450708i | ||||
\(11\) | 1.64575 | 0.496213 | 0.248106 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248106 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.322876 | + | 0.559237i | −0.0895496 | + | 0.155104i | −0.907321 | − | 0.420439i | \(-0.861876\pi\) |
0.817771 | + | 0.575543i | \(0.195209\pi\) | |||||||
\(14\) | −2.64575 | −0.707107 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.822876 | + | 1.42526i | −0.199577 | + | 0.345677i | −0.948391 | − | 0.317103i | \(-0.897290\pi\) |
0.748815 | + | 0.662780i | \(0.230623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0.822876 | + | 1.42526i | 0.184001 | + | 0.318698i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.822876 | − | 1.42526i | 0.175438 | − | 0.303867i | ||||
\(23\) | −9.29150 | −1.93741 | −0.968706 | − | 0.248211i | \(-0.920158\pi\) | ||||
−0.968706 | + | 0.248211i | \(0.920158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | 0.322876 | + | 0.559237i | 0.0633211 | + | 0.109675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.32288 | + | 2.29129i | −0.250000 | + | 0.433013i | ||||
\(29\) | 3.82288 | + | 6.62141i | 0.709890 | + | 1.22957i | 0.964898 | + | 0.262627i | \(0.0845888\pi\) |
−0.255007 | + | 0.966939i | \(0.582078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.322876 | − | 0.559237i | −0.0579902 | − | 0.100442i | 0.835573 | − | 0.549380i | \(-0.185136\pi\) |
−0.893563 | + | 0.448938i | \(0.851803\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.822876 | + | 1.42526i | 0.141122 | + | 0.244430i | ||||
\(35\) | 2.17712 | + | 3.77089i | 0.368001 | + | 0.637397i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.96863 | − | 3.40976i | −0.323640 | − | 0.560561i | 0.657596 | − | 0.753371i | \(-0.271573\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.64575 | 0.260216 | ||||||||
\(41\) | −2.46863 | + | 4.27579i | −0.385535 | + | 0.667766i | −0.991843 | − | 0.127464i | \(-0.959316\pi\) |
0.606308 | + | 0.795230i | \(0.292650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | −0.822876 | − | 1.42526i | −0.124053 | − | 0.214866i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.64575 | + | 8.04668i | −0.684979 | + | 1.18642i | ||||
\(47\) | −5.46863 | + | 9.47194i | −0.797681 | + | 1.38162i | 0.123441 | + | 0.992352i | \(0.460607\pi\) |
−0.921123 | + | 0.389273i | \(0.872726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | −1.14575 | + | 1.98450i | −0.162034 | + | 0.280651i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.645751 | 0.0895496 | ||||||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.70850 | −0.365214 | ||||||||
\(56\) | 1.32288 | + | 2.29129i | 0.176777 | + | 0.306186i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.64575 | 1.00394 | ||||||||
\(59\) | 6.82288 | + | 11.8176i | 0.888263 | + | 1.53852i | 0.841928 | + | 0.539590i | \(0.181421\pi\) |
0.0463350 | + | 0.998926i | \(0.485246\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.32288 | + | 10.9515i | −0.809561 | + | 1.40220i | 0.103607 | + | 0.994618i | \(0.466962\pi\) |
−0.913168 | + | 0.407583i | \(0.866372\pi\) | |||||||
\(62\) | −0.645751 | −0.0820105 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.531373 | − | 0.920365i | 0.0659087 | − | 0.114157i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.14575 | − | 7.18065i | −0.506484 | − | 0.877256i | −0.999972 | − | 0.00750349i | \(-0.997612\pi\) |
0.493488 | − | 0.869753i | \(-0.335722\pi\) | |||||||
\(68\) | 1.64575 | 0.199577 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.35425 | 0.520432 | ||||||||
\(71\) | −10.3542 | −1.22882 | −0.614412 | − | 0.788986i | \(-0.710607\pi\) | ||||
−0.614412 | + | 0.788986i | \(0.710607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.29150 | − | 9.16515i | 0.619324 | − | 1.07270i | −0.370286 | − | 0.928918i | \(-0.620740\pi\) |
0.989609 | − | 0.143782i | \(-0.0459264\pi\) | |||||||
\(74\) | −3.93725 | −0.457696 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −2.17712 | − | 3.77089i | −0.248106 | − | 0.429733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.61438 | − | 13.1885i | 0.856684 | − | 1.48382i | −0.0183890 | − | 0.999831i | \(-0.505854\pi\) |
0.875073 | − | 0.483990i | \(-0.160813\pi\) | |||||||
\(80\) | 0.822876 | − | 1.42526i | 0.0920003 | − | 0.159349i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.46863 | + | 4.27579i | 0.272614 | + | 0.472182i | ||||
\(83\) | −1.35425 | − | 2.34563i | −0.148648 | − | 0.257466i | 0.782080 | − | 0.623178i | \(-0.214159\pi\) |
−0.930728 | + | 0.365712i | \(0.880826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.35425 | − | 2.34563i | 0.146889 | − | 0.254419i | ||||
\(86\) | −5.00000 | −0.539164 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.64575 | −0.175438 | ||||||||
\(89\) | −5.46863 | − | 9.47194i | −0.579673 | − | 1.00402i | −0.995517 | − | 0.0945873i | \(-0.969847\pi\) |
0.415843 | − | 0.909436i | \(-0.363486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.70850 | 0.179099 | ||||||||
\(92\) | 4.64575 | + | 8.04668i | 0.484353 | + | 0.838924i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.46863 | + | 9.47194i | 0.564046 | + | 0.976956i | ||||
\(95\) | 1.64575 | + | 2.85052i | 0.168851 | + | 0.292458i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.79150 | + | 6.56708i | 0.384969 | + | 0.666785i | 0.991765 | − | 0.128072i | \(-0.0408789\pi\) |
−0.606796 | + | 0.794858i | \(0.707546\pi\) | |||||||
\(98\) | 3.50000 | + | 6.06218i | 0.353553 | + | 0.612372i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.14575 | + | 1.98450i | 0.114575 | + | 0.198450i | ||||
\(101\) | −13.6458 | −1.35780 | −0.678902 | − | 0.734229i | \(-0.737544\pi\) | ||||
−0.678902 | + | 0.734229i | \(0.737544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9373 | −1.17621 | −0.588106 | − | 0.808784i | \(-0.700126\pi\) | ||||
−0.588106 | + | 0.808784i | \(0.700126\pi\) | |||||||
\(104\) | 0.322876 | − | 0.559237i | 0.0316606 | − | 0.0548377i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.32288 | − | 7.48744i | 0.414056 | − | 0.717167i | −0.581272 | − | 0.813709i | \(-0.697445\pi\) |
0.995329 | + | 0.0965423i | \(0.0307783\pi\) | |||||||
\(110\) | −1.35425 | + | 2.34563i | −0.129123 | + | 0.223647i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.64575 | 0.250000 | ||||||||
\(113\) | 3.82288 | − | 6.62141i | 0.359626 | − | 0.622890i | −0.628272 | − | 0.777993i | \(-0.716238\pi\) |
0.987898 | + | 0.155103i | \(0.0495710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.2915 | 1.42594 | ||||||||
\(116\) | 3.82288 | − | 6.62141i | 0.354945 | − | 0.614783i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.6458 | 1.25619 | ||||||||
\(119\) | 4.35425 | 0.399153 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.29150 | −0.753773 | ||||||||
\(122\) | 6.32288 | + | 10.9515i | 0.572446 | + | 0.991506i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.322876 | + | 0.559237i | −0.0289951 | + | 0.0502210i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.64575 | 0.589715 | 0.294858 | − | 0.955541i | \(-0.404728\pi\) | ||||
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.531373 | − | 0.920365i | −0.0466045 | − | 0.0807214i | ||||
\(131\) | −6.58301 | −0.575160 | −0.287580 | − | 0.957757i | \(-0.592851\pi\) | ||||
−0.287580 | + | 0.957757i | \(0.592851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.64575 | + | 4.58258i | −0.229416 | + | 0.397360i | ||||
\(134\) | −8.29150 | −0.716277 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.822876 | − | 1.42526i | 0.0705610 | − | 0.122215i | ||||
\(137\) | 9.29150 | 0.793827 | 0.396913 | − | 0.917856i | \(-0.370081\pi\) | ||||
0.396913 | + | 0.917856i | \(0.370081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.79150 | − | 16.9594i | 0.830504 | − | 1.43848i | −0.0671344 | − | 0.997744i | \(-0.521386\pi\) |
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(140\) | 2.17712 | − | 3.77089i | 0.184001 | − | 0.318698i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.17712 | + | 8.96704i | −0.434455 | + | 0.752497i | ||||
\(143\) | −0.531373 | + | 0.920365i | −0.0444356 | + | 0.0769648i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.29150 | − | 10.8972i | −0.522481 | − | 0.904963i | ||||
\(146\) | −5.29150 | − | 9.16515i | −0.437928 | − | 0.758513i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.96863 | + | 3.40976i | −0.161820 | + | 0.280281i | ||||
\(149\) | −7.06275 | −0.578603 | −0.289301 | − | 0.957238i | \(-0.593423\pi\) | ||||
−0.289301 | + | 0.957238i | \(0.593423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.22876 | 0.588268 | 0.294134 | − | 0.955764i | \(-0.404969\pi\) | ||||
0.294134 | + | 0.955764i | \(0.404969\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.35425 | −0.350875 | ||||||||
\(155\) | 0.531373 | + | 0.920365i | 0.0426809 | + | 0.0739255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | −7.61438 | − | 13.1885i | −0.605767 | − | 1.04922i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.822876 | − | 1.42526i | −0.0650540 | − | 0.112677i | ||||
\(161\) | 12.2915 | + | 21.2895i | 0.968706 | + | 1.67785i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | + | 0.866025i | 0.0391630 | + | 0.0678323i | 0.884943 | − | 0.465700i | \(-0.154198\pi\) |
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(164\) | 4.93725 | 0.385535 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.70850 | −0.210220 | ||||||||
\(167\) | 6.29150 | − | 10.8972i | 0.486851 | − | 0.843251i | −0.513035 | − | 0.858368i | \(-0.671479\pi\) |
0.999886 | + | 0.0151171i | \(0.00481210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.29150 | + | 10.8972i | 0.483962 | + | 0.838246i | ||||
\(170\) | −1.35425 | − | 2.34563i | −0.103866 | − | 0.179901i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.50000 | + | 4.33013i | −0.190623 | + | 0.330169i | ||||
\(173\) | 3.29150 | − | 5.70105i | 0.250248 | − | 0.433443i | −0.713346 | − | 0.700812i | \(-0.752821\pi\) |
0.963594 | + | 0.267369i | \(0.0861544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.03137 | + | 5.25049i | 0.229150 | + | 0.396900i | ||||
\(176\) | −0.822876 | + | 1.42526i | −0.0620266 | + | 0.107433i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.9373 | −0.819782 | ||||||||
\(179\) | 0.531373 | − | 0.920365i | 0.0397167 | − | 0.0687913i | −0.845484 | − | 0.534001i | \(-0.820688\pi\) |
0.885200 | + | 0.465210i | \(0.154021\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2915 | −0.987950 | −0.493975 | − | 0.869476i | \(-0.664457\pi\) | ||||
−0.493975 | + | 0.869476i | \(0.664457\pi\) | |||||||
\(182\) | 0.854249 | − | 1.47960i | 0.0633211 | − | 0.109675i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.29150 | 0.684979 | ||||||||
\(185\) | 3.23987 | + | 5.61162i | 0.238200 | + | 0.412575i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.35425 | + | 2.34563i | −0.0990325 | + | 0.171529i | ||||
\(188\) | 10.9373 | 0.797681 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.29150 | 0.238791 | ||||||||
\(191\) | 13.4059 | − | 23.2197i | 0.970015 | − | 1.68012i | 0.274526 | − | 0.961580i | \(-0.411479\pi\) |
0.695489 | − | 0.718537i | \(-0.255188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | + | 6.06218i | 0.251936 | + | 0.436365i | 0.964059 | − | 0.265689i | \(-0.0855996\pi\) |
−0.712123 | + | 0.702055i | \(0.752266\pi\) | |||||||
\(194\) | 7.58301 | 0.544428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | −15.2915 | −1.08947 | −0.544737 | − | 0.838607i | \(-0.683371\pi\) | ||||
−0.544737 | + | 0.838607i | \(0.683371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9686 | + | 18.9982i | −0.777545 | + | 1.34675i | 0.155807 | + | 0.987787i | \(0.450202\pi\) |
−0.933353 | + | 0.358961i | \(0.883131\pi\) | |||||||
\(200\) | 2.29150 | 0.162034 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.82288 | + | 11.8176i | −0.480056 | + | 0.831481i | ||||
\(203\) | 10.1144 | − | 17.5186i | 0.709890 | − | 1.22957i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.06275 | − | 7.03688i | 0.283754 | − | 0.491477i | ||||
\(206\) | −5.96863 | + | 10.3380i | −0.415854 | + | 0.720280i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.322876 | − | 0.559237i | −0.0223874 | − | 0.0387761i | ||||
\(209\) | −1.64575 | − | 2.85052i | −0.113839 | − | 0.197175i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.43725 | − | 14.6138i | 0.580845 | − | 1.00605i | −0.414535 | − | 0.910033i | \(-0.636056\pi\) |
0.995380 | − | 0.0960188i | \(-0.0306109\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | −0.410152 | ||||||||
\(215\) | 4.11438 | + | 7.12631i | 0.280598 | + | 0.486010i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.854249 | + | 1.47960i | −0.0579902 | + | 0.100442i | ||||
\(218\) | −4.32288 | − | 7.48744i | −0.292782 | − | 0.507113i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.35425 | + | 2.34563i | 0.0913034 | + | 0.158142i | ||||
\(221\) | −0.531373 | − | 0.920365i | −0.0357440 | − | 0.0619105i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.93725 | − | 15.4798i | −0.598483 | − | 1.03660i | −0.993045 | − | 0.117733i | \(-0.962437\pi\) |
0.394562 | − | 0.918869i | \(-0.370896\pi\) | |||||||
\(224\) | 1.32288 | − | 2.29129i | 0.0883883 | − | 0.153093i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.82288 | − | 6.62141i | −0.254294 | − | 0.440450i | ||||
\(227\) | −6.00000 | −0.398234 | −0.199117 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199117 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.6458 | −0.967818 | −0.483909 | − | 0.875118i | \(-0.660784\pi\) | ||||
−0.483909 | + | 0.875118i | \(0.660784\pi\) | |||||||
\(230\) | 7.64575 | − | 13.2428i | 0.504146 | − | 0.873206i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.82288 | − | 6.62141i | −0.250984 | − | 0.434717i | ||||
\(233\) | −4.35425 | − | 7.54178i | −0.285256 | − | 0.494078i | 0.687415 | − | 0.726265i | \(-0.258745\pi\) |
−0.972671 | + | 0.232186i | \(0.925412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | − | 15.5885i | 0.587095 | − | 1.01688i | ||||
\(236\) | 6.82288 | − | 11.8176i | 0.444131 | − | 0.769258i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.17712 | − | 3.77089i | 0.141122 | − | 0.244430i | ||||
\(239\) | 2.46863 | − | 4.27579i | 0.159682 | − | 0.276578i | −0.775072 | − | 0.631873i | \(-0.782286\pi\) |
0.934754 | + | 0.355295i | \(0.115620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | 0.322078 | 0.161039 | − | 0.986948i | \(-0.448515\pi\) | ||||
0.161039 | + | 0.986948i | \(0.448515\pi\) | |||||||
\(242\) | −4.14575 | + | 7.18065i | −0.266499 | + | 0.461590i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6458 | 0.809561 | ||||||||
\(245\) | 5.76013 | − | 9.97684i | 0.368001 | − | 0.637397i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.29150 | 0.0821763 | ||||||||
\(248\) | 0.322876 | + | 0.559237i | 0.0205026 | + | 0.0355116i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | − | 10.3923i | 0.379473 | − | 0.657267i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.2915 | −0.961369 | ||||||||
\(254\) | 3.32288 | − | 5.75539i | 0.208496 | − | 0.361125i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.8745 | 0.990225 | 0.495112 | − | 0.868829i | \(-0.335127\pi\) | ||||
0.495112 | + | 0.868829i | \(0.335127\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.20850 | + | 9.02138i | −0.323640 | + | 0.560561i | ||||
\(260\) | −1.06275 | −0.0659087 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.29150 | + | 5.70105i | −0.203350 | + | 0.352212i | ||||
\(263\) | −10.9373 | −0.674420 | −0.337210 | − | 0.941429i | \(-0.609483\pi\) | ||||
−0.337210 | + | 0.941429i | \(0.609483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.93725 | + | 8.55157i | −0.303293 | + | 0.525319i | ||||
\(266\) | 2.64575 | + | 4.58258i | 0.162221 | + | 0.280976i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.14575 | + | 7.18065i | −0.253242 | + | 0.438628i | ||||
\(269\) | −13.6458 | + | 23.6351i | −0.831996 | + | 1.44106i | 0.0644567 | + | 0.997921i | \(0.479469\pi\) |
−0.896453 | + | 0.443139i | \(0.853865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6144 | + | 18.3846i | 0.644778 | + | 1.11679i | 0.984353 | + | 0.176209i | \(0.0563833\pi\) |
−0.339575 | + | 0.940579i | \(0.610283\pi\) | |||||||
\(272\) | −0.822876 | − | 1.42526i | −0.0498942 | − | 0.0864192i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.64575 | − | 8.04668i | 0.280660 | − | 0.486118i | ||||
\(275\) | −3.77124 | −0.227415 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.9373 | −1.07775 | −0.538873 | − | 0.842387i | \(-0.681150\pi\) | ||||
−0.538873 | + | 0.842387i | \(0.681150\pi\) | |||||||
\(278\) | −9.79150 | − | 16.9594i | −0.587255 | − | 1.01716i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.17712 | − | 3.77089i | −0.130108 | − | 0.225354i | ||||
\(281\) | −8.76013 | − | 15.1730i | −0.522586 | − | 0.905145i | −0.999655 | − | 0.0262789i | \(-0.991634\pi\) |
0.477069 | − | 0.878866i | \(-0.341699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.14575 | − | 7.18065i | −0.246439 | − | 0.426845i | 0.716096 | − | 0.698002i | \(-0.245927\pi\) |
−0.962535 | + | 0.271156i | \(0.912594\pi\) | |||||||
\(284\) | 5.17712 | + | 8.96704i | 0.307206 | + | 0.532096i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.531373 | + | 0.920365i | 0.0314207 | + | 0.0544223i | ||||
\(287\) | 13.0627 | 0.771070 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.14575 | + | 12.3768i | 0.420338 | + | 0.728047i | ||||
\(290\) | −12.5830 | −0.738900 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.5830 | −0.619324 | ||||||||
\(293\) | 11.4686 | − | 19.8642i | 0.670004 | − | 1.16048i | −0.307898 | − | 0.951419i | \(-0.599626\pi\) |
0.977902 | − | 0.209062i | \(-0.0670411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2288 | − | 19.4488i | −0.653763 | − | 1.13235i | ||||
\(296\) | 1.96863 | + | 3.40976i | 0.114424 | + | 0.198188i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.53137 | + | 6.11652i | −0.204567 | + | 0.354320i | ||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.61438 | + | 11.4564i | −0.381246 | + | 0.660338i | ||||
\(302\) | 3.61438 | − | 6.26029i | 0.207984 | − | 0.360239i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 10.4059 | − | 18.0235i | 0.595839 | − | 1.03202i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5830 | −0.775223 | −0.387612 | − | 0.921823i | \(-0.626700\pi\) | ||||
−0.387612 | + | 0.921823i | \(0.626700\pi\) | |||||||
\(308\) | −2.17712 | + | 3.77089i | −0.124053 | + | 0.214866i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.06275 | 0.0603599 | ||||||||
\(311\) | 11.7601 | + | 20.3691i | 0.666856 | + | 1.15503i | 0.978779 | + | 0.204921i | \(0.0656936\pi\) |
−0.311923 | + | 0.950107i | \(0.600973\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6458 | + | 20.1710i | −0.658257 | + | 1.14013i | 0.322810 | + | 0.946464i | \(0.395373\pi\) |
−0.981067 | + | 0.193670i | \(0.937961\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.2288 | −0.856684 | ||||||||
\(317\) | −10.4059 | + | 18.0235i | −0.584452 | + | 1.01230i | 0.410491 | + | 0.911865i | \(0.365357\pi\) |
−0.994943 | + | 0.100437i | \(0.967976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.29150 | + | 10.8972i | 0.352257 | + | 0.610126i | ||||
\(320\) | −1.64575 | −0.0920003 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.5830 | 1.36996 | ||||||||
\(323\) | 3.29150 | 0.183144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.739870 | − | 1.28149i | 0.0410406 | − | 0.0710844i | ||||
\(326\) | 1.00000 | 0.0553849 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.46863 | − | 4.27579i | 0.136307 | − | 0.236091i | ||||
\(329\) | 28.9373 | 1.59536 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0627461 | − | 0.108679i | 0.00344884 | − | 0.00597356i | −0.864296 | − | 0.502984i | \(-0.832236\pi\) |
0.867745 | + | 0.497010i | \(0.165569\pi\) | |||||||
\(332\) | −1.35425 | + | 2.34563i | −0.0743241 | + | 0.128733i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.29150 | − | 10.8972i | −0.344256 | − | 0.596268i | ||||
\(335\) | 6.82288 | + | 11.8176i | 0.372774 | + | 0.645663i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70850 | − | 8.15536i | 0.256488 | − | 0.444251i | −0.708810 | − | 0.705399i | \(-0.750768\pi\) |
0.965299 | + | 0.261148i | \(0.0841012\pi\) | |||||||
\(338\) | 12.5830 | 0.684425 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.70850 | −0.146889 | ||||||||
\(341\) | −0.531373 | − | 0.920365i | −0.0287755 | − | 0.0498406i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 2.50000 | + | 4.33013i | 0.134791 | + | 0.233465i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.29150 | − | 5.70105i | −0.176952 | − | 0.306490i | ||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.6144 | − | 21.8487i | −0.675232 | − | 1.16954i | −0.976401 | − | 0.215966i | \(-0.930710\pi\) |
0.301169 | − | 0.953571i | \(-0.402623\pi\) | |||||||
\(350\) | 6.06275 | 0.324067 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.822876 | + | 1.42526i | 0.0438594 | + | 0.0759667i | ||||
\(353\) | 12.0000 | 0.638696 | 0.319348 | − | 0.947638i | \(-0.396536\pi\) | ||||
0.319348 | + | 0.947638i | \(0.396536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.0405 | 0.904417 | ||||||||
\(356\) | −5.46863 | + | 9.47194i | −0.289837 | + | 0.502012i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.531373 | − | 0.920365i | −0.0280839 | − | 0.0486428i | ||||
\(359\) | −15.5830 | − | 26.9906i | −0.822440 | − | 1.42451i | −0.903860 | − | 0.427827i | \(-0.859279\pi\) |
0.0814209 | − | 0.996680i | \(-0.474054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −6.64575 | + | 11.5108i | −0.349293 | + | 0.604993i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.854249 | − | 1.47960i | −0.0447748 | − | 0.0775522i | ||||
\(365\) | −8.70850 | + | 15.0836i | −0.455824 | + | 0.789510i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.87451 | −0.0978485 | −0.0489243 | − | 0.998802i | \(-0.515579\pi\) | ||||
−0.0489243 | + | 0.998802i | \(0.515579\pi\) | |||||||
\(368\) | 4.64575 | − | 8.04668i | 0.242177 | − | 0.419462i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.47974 | 0.336866 | ||||||||
\(371\) | −15.8745 | −0.824163 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5830 | −0.858635 | −0.429318 | − | 0.903154i | \(-0.641246\pi\) | ||||
−0.429318 | + | 0.903154i | \(0.641246\pi\) | |||||||
\(374\) | 1.35425 | + | 2.34563i | 0.0700265 | + | 0.121290i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.46863 | − | 9.47194i | 0.282023 | − | 0.488478i | ||||
\(377\) | −4.93725 | −0.254282 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.41699 | 0.226886 | 0.113443 | − | 0.993545i | \(-0.463812\pi\) | ||||
0.113443 | + | 0.993545i | \(0.463812\pi\) | |||||||
\(380\) | 1.64575 | − | 2.85052i | 0.0844253 | − | 0.146229i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.4059 | − | 23.2197i | −0.685905 | − | 1.18802i | ||||
\(383\) | 0.583005 | 0.0297902 | 0.0148951 | − | 0.999889i | \(-0.495259\pi\) | ||||
0.0148951 | + | 0.999889i | \(0.495259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.58301 | + | 6.20595i | 0.182607 | + | 0.316284i | ||||
\(386\) | 7.00000 | 0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.79150 | − | 6.56708i | 0.192484 | − | 0.333393i | ||||
\(389\) | −8.70850 | −0.441538 | −0.220769 | − | 0.975326i | \(-0.570857\pi\) | ||||
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.64575 | − | 13.2428i | 0.386662 | − | 0.669719i | ||||
\(392\) | 3.50000 | − | 6.06218i | 0.176777 | − | 0.306186i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.64575 | + | 13.2428i | −0.385187 | + | 0.667164i | ||||
\(395\) | −12.5314 | + | 21.7050i | −0.630522 | + | 1.09210i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.67712 | + | 9.83307i | 0.284927 | + | 0.493508i | 0.972591 | − | 0.232521i | \(-0.0746974\pi\) |
−0.687665 | + | 0.726028i | \(0.741364\pi\) | |||||||
\(398\) | 10.9686 | + | 18.9982i | 0.549808 | + | 0.952295i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.14575 | − | 1.98450i | 0.0572876 | − | 0.0992250i | ||||
\(401\) | −26.8118 | −1.33892 | −0.669458 | − | 0.742850i | \(-0.733473\pi\) | ||||
−0.669458 | + | 0.742850i | \(0.733473\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.416995 | 0.0207720 | ||||||||
\(404\) | 6.82288 | + | 11.8176i | 0.339451 | + | 0.587946i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1144 | − | 17.5186i | −0.501968 | − | 0.869434i | ||||
\(407\) | −3.23987 | − | 5.61162i | −0.160594 | − | 0.278158i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.43725 | + | 14.6138i | 0.417195 | + | 0.722604i | 0.995656 | − | 0.0931066i | \(-0.0296798\pi\) |
−0.578461 | + | 0.815710i | \(0.696346\pi\) | |||||||
\(410\) | −4.06275 | − | 7.03688i | −0.200645 | − | 0.347527i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.96863 | + | 10.3380i | 0.294053 | + | 0.509315i | ||||
\(413\) | 18.0516 | − | 31.2663i | 0.888263 | − | 1.53852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.22876 | + | 3.86032i | 0.109405 | + | 0.189496i | ||||
\(416\) | −0.645751 | −0.0316606 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.29150 | −0.160993 | ||||||||
\(419\) | 6.53137 | − | 11.3127i | 0.319078 | − | 0.552660i | −0.661218 | − | 0.750194i | \(-0.729960\pi\) |
0.980296 | + | 0.197534i | \(0.0632933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6458 | + | 21.9031i | 0.616316 | + | 1.06749i | 0.990152 | + | 0.139996i | \(0.0447090\pi\) |
−0.373836 | + | 0.927495i | \(0.621958\pi\) | |||||||
\(422\) | −8.43725 | − | 14.6138i | −0.410719 | − | 0.711386i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 1.88562 | − | 3.26599i | 0.0914661 | − | 0.158424i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.4575 | 1.61912 | ||||||||
\(428\) | −3.00000 | + | 5.19615i | −0.145010 | + | 0.251166i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.22876 | 0.396826 | ||||||||
\(431\) | −4.40588 | + | 7.63121i | −0.212224 | + | 0.367582i | −0.952410 | − | 0.304819i | \(-0.901404\pi\) |
0.740186 | + | 0.672402i | \(0.234737\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 0.854249 | + | 1.47960i | 0.0410052 | + | 0.0710232i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.64575 | −0.414056 | ||||||||
\(437\) | 9.29150 | + | 16.0934i | 0.444473 | + | 0.769850i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.58301 | − | 14.8662i | 0.409644 | − | 0.709525i | −0.585205 | − | 0.810885i | \(-0.698986\pi\) |
0.994850 | + | 0.101360i | \(0.0323194\pi\) | |||||||
\(440\) | 2.70850 | 0.129123 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.06275 | −0.0505497 | ||||||||
\(443\) | −4.35425 | + | 7.54178i | −0.206877 | + | 0.358321i | −0.950729 | − | 0.310023i | \(-0.899663\pi\) |
0.743852 | + | 0.668344i | \(0.232997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | −17.8745 | −0.846382 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.32288 | − | 2.29129i | −0.0625000 | − | 0.108253i | ||||
\(449\) | −7.64575 | −0.360825 | −0.180413 | − | 0.983591i | \(-0.557743\pi\) | ||||
−0.180413 | + | 0.983591i | \(0.557743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.06275 | + | 7.03688i | −0.191307 | + | 0.331354i | ||||
\(452\) | −7.64575 | −0.359626 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.00000 | + | 5.19615i | −0.140797 | + | 0.243868i | ||||
\(455\) | −2.81176 | −0.131817 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.14575 | + | 1.98450i | −0.0535960 | + | 0.0928310i | −0.891579 | − | 0.452866i | \(-0.850402\pi\) |
0.837983 | + | 0.545697i | \(0.183735\pi\) | |||||||
\(458\) | −7.32288 | + | 12.6836i | −0.342176 | + | 0.592665i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.64575 | − | 13.2428i | −0.356485 | − | 0.617450i | ||||
\(461\) | −1.11438 | − | 1.93016i | −0.0519018 | − | 0.0898965i | 0.838907 | − | 0.544274i | \(-0.183195\pi\) |
−0.890809 | + | 0.454378i | \(0.849862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6458 | + | 25.3672i | −0.680646 | + | 1.17891i | 0.294138 | + | 0.955763i | \(0.404967\pi\) |
−0.974784 | + | 0.223150i | \(0.928366\pi\) | |||||||
\(464\) | −7.64575 | −0.354945 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.70850 | −0.403413 | ||||||||
\(467\) | −13.1144 | − | 22.7148i | −0.606861 | − | 1.05111i | −0.991754 | − | 0.128153i | \(-0.959095\pi\) |
0.384893 | − | 0.922961i | \(-0.374238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.9686 | + | 18.9982i | −0.506484 | + | 0.877256i | ||||
\(470\) | −9.00000 | − | 15.5885i | −0.415139 | − | 0.719042i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.82288 | − | 11.8176i | −0.314048 | − | 0.543948i | ||||
\(473\) | −4.11438 | − | 7.12631i | −0.189179 | − | 0.327668i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.29150 | + | 3.96900i | 0.105141 | + | 0.182110i | ||||
\(476\) | −2.17712 | − | 3.77089i | −0.0997883 | − | 0.172838i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.46863 | − | 4.27579i | −0.112912 | − | 0.195570i | ||||
\(479\) | 1.64575 | 0.0751963 | 0.0375981 | − | 0.999293i | \(-0.488029\pi\) | ||||
0.0375981 | + | 0.999293i | \(0.488029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.54249 | 0.115927 | ||||||||
\(482\) | 2.50000 | − | 4.33013i | 0.113872 | − | 0.197232i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.14575 | + | 7.18065i | 0.188443 | + | 0.326393i | ||||
\(485\) | −6.23987 | − | 10.8078i | −0.283338 | − | 0.490756i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.93725 | − | 6.81952i | 0.178414 | − | 0.309022i | −0.762923 | − | 0.646489i | \(-0.776237\pi\) |
0.941337 | + | 0.337467i | \(0.109570\pi\) | |||||||
\(488\) | 6.32288 | − | 10.9515i | 0.286223 | − | 0.495753i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.76013 | − | 9.97684i | −0.260216 | − | 0.450708i | ||||
\(491\) | −18.8745 | + | 32.6916i | −0.851795 | + | 1.47535i | 0.0277925 | + | 0.999614i | \(0.491152\pi\) |
−0.879587 | + | 0.475738i | \(0.842181\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.5830 | −0.566710 | ||||||||
\(494\) | 0.645751 | − | 1.11847i | 0.0290537 | − | 0.0503225i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.645751 | 0.0289951 | ||||||||
\(497\) | 13.6974 | + | 23.7246i | 0.614412 | + | 1.06419i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.1660 | 1.61901 | 0.809506 | − | 0.587111i | \(-0.199735\pi\) | ||||
0.809506 | + | 0.587111i | \(0.199735\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | − | 15.5885i | 0.401690 | − | 0.695747i | ||||
\(503\) | 27.8745 | 1.24286 | 0.621431 | − | 0.783469i | \(-0.286551\pi\) | ||||
0.621431 | + | 0.783469i | \(0.286551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.4575 | 0.999346 | ||||||||
\(506\) | −7.64575 | + | 13.2428i | −0.339895 | + | 0.588716i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.32288 | − | 5.75539i | −0.147429 | − | 0.255354i | ||||
\(509\) | −39.8745 | −1.76741 | −0.883703 | − | 0.468048i | \(-0.844958\pi\) | ||||
−0.883703 | + | 0.468048i | \(0.844958\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | −1.23865 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.93725 | − | 13.7477i | 0.350097 | − | 0.606386i | ||||
\(515\) | 19.6458 | 0.865695 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00000 | + | 15.5885i | −0.395820 | + | 0.685580i | ||||
\(518\) | 5.20850 | + | 9.02138i | 0.228848 | + | 0.396377i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.531373 | + | 0.920365i | −0.0233022 | + | 0.0403607i | ||||
\(521\) | −19.9373 | + | 34.5323i | −0.873467 | + | 1.51289i | −0.0150801 | + | 0.999886i | \(0.504800\pi\) |
−0.858387 | + | 0.513003i | \(0.828533\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | + | 0.866025i | 0.0218635 | + | 0.0378686i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(524\) | 3.29150 | + | 5.70105i | 0.143790 | + | 0.249052i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.46863 | + | 9.47194i | −0.238443 | + | 0.412996i | ||||
\(527\) | 1.06275 | 0.0462939 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 63.3320 | 2.75357 | ||||||||
\(530\) | 4.93725 | + | 8.55157i | 0.214461 | + | 0.371457i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.29150 | 0.229416 | ||||||||
\(533\) | −1.59412 | − | 2.76110i | −0.0690490 | − | 0.119596i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.93725 | + | 8.55157i | 0.213456 | + | 0.369717i | ||||
\(536\) | 4.14575 | + | 7.18065i | 0.179069 | + | 0.310157i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.6458 | + | 23.6351i | 0.588310 | + | 1.01898i | ||||
\(539\) | −5.76013 | + | 9.97684i | −0.248106 | + | 0.429733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5830 | + | 35.6508i | 0.884933 | + | 1.53275i | 0.845791 | + | 0.533514i | \(0.179129\pi\) |
0.0391415 | + | 0.999234i | \(0.487538\pi\) | |||||||
\(542\) | 21.2288 | 0.911853 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.64575 | −0.0705610 | ||||||||
\(545\) | −7.11438 | + | 12.3225i | −0.304746 | + | 0.527836i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.85425 | − | 6.67575i | −0.164796 | − | 0.285435i | 0.771787 | − | 0.635881i | \(-0.219363\pi\) |
−0.936583 | + | 0.350447i | \(0.886030\pi\) | |||||||
\(548\) | −4.64575 | − | 8.04668i | −0.198457 | − | 0.343737i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.88562 | + | 3.26599i | −0.0804032 | + | 0.139262i | ||||
\(551\) | 7.64575 | − | 13.2428i | 0.325720 | − | 0.564164i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.2915 | −1.71337 | ||||||||
\(554\) | −8.96863 | + | 15.5341i | −0.381040 | + | 0.659981i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.5830 | −0.830504 | ||||||||
\(557\) | −16.1144 | + | 27.9109i | −0.682788 | + | 1.18262i | 0.291338 | + | 0.956620i | \(0.405899\pi\) |
−0.974126 | + | 0.226004i | \(0.927434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.22876 | 0.136562 | ||||||||
\(560\) | −4.35425 | −0.184001 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.5203 | −0.739048 | ||||||||
\(563\) | −17.2288 | − | 29.8411i | −0.726106 | − | 1.25765i | −0.958517 | − | 0.285034i | \(-0.907995\pi\) |
0.232412 | − | 0.972617i | \(-0.425338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.29150 | + | 10.8972i | −0.264686 | + | 0.458449i | ||||
\(566\) | −8.29150 | −0.348518 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.3542 | 0.434455 | ||||||||
\(569\) | −0.531373 | + | 0.920365i | −0.0222763 | + | 0.0385837i | −0.876949 | − | 0.480584i | \(-0.840425\pi\) |
0.854672 | + | 0.519168i | \(0.173758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.645751 | + | 1.11847i | 0.0270239 | + | 0.0468067i | 0.879221 | − | 0.476414i | \(-0.158064\pi\) |
−0.852197 | + | 0.523221i | \(0.824730\pi\) | |||||||
\(572\) | 1.06275 | 0.0444356 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.53137 | − | 11.3127i | 0.272614 | − | 0.472182i | ||||
\(575\) | 21.2915 | 0.887917 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8542 | − | 18.8001i | 0.451868 | − | 0.782659i | −0.546634 | − | 0.837372i | \(-0.684091\pi\) |
0.998502 | + | 0.0547129i | \(0.0174244\pi\) | |||||||
\(578\) | 14.2915 | 0.594448 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.29150 | + | 10.8972i | −0.261240 | + | 0.452482i | ||||
\(581\) | −3.58301 | + | 6.20595i | −0.148648 | + | 0.257466i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.93725 | − | 8.55157i | 0.204480 | − | 0.354170i | ||||
\(584\) | −5.29150 | + | 9.16515i | −0.218964 | + | 0.379257i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.4686 | − | 19.8642i | −0.473765 | − | 0.820584i | ||||
\(587\) | 19.1144 | + | 33.1071i | 0.788935 | + | 1.36648i | 0.926620 | + | 0.375999i | \(0.122700\pi\) |
−0.137685 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.645751 | + | 1.11847i | −0.0266077 | + | 0.0460859i | ||||
\(590\) | −22.4575 | −0.924561 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.93725 | 0.161820 | ||||||||
\(593\) | 12.5314 | + | 21.7050i | 0.514602 | + | 0.891316i | 0.999856 | + | 0.0169436i | \(0.00539357\pi\) |
−0.485255 | + | 0.874373i | \(0.661273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.16601 | −0.293778 | ||||||||
\(596\) | 3.53137 | + | 6.11652i | 0.144651 | + | 0.250542i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | −10.9373 | − | 18.9439i | −0.446884 | − | 0.774026i | 0.551297 | − | 0.834309i | \(-0.314133\pi\) |
−0.998181 | + | 0.0602830i | \(0.980800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.43725 | + | 4.22145i | 0.0994177 | + | 0.172196i | 0.911444 | − | 0.411425i | \(-0.134969\pi\) |
−0.812026 | + | 0.583621i | \(0.801635\pi\) | |||||||
\(602\) | 6.61438 | + | 11.4564i | 0.269582 | + | 0.466930i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.61438 | − | 6.26029i | −0.147067 | − | 0.254727i | ||||
\(605\) | 13.6458 | 0.554779 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.5830 | 1.07897 | 0.539485 | − | 0.841995i | \(-0.318619\pi\) | ||||
0.539485 | + | 0.841995i | \(0.318619\pi\) | |||||||
\(608\) | 1.00000 | − | 1.73205i | 0.0405554 | − | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.4059 | − | 18.0235i | −0.421322 | − | 0.729751i | ||||
\(611\) | −3.53137 | − | 6.11652i | −0.142864 | − | 0.247448i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.1974 | + | 22.8585i | −0.533037 | + | 0.923248i | 0.466218 | + | 0.884670i | \(0.345616\pi\) |
−0.999256 | + | 0.0385780i | \(0.987717\pi\) | |||||||
\(614\) | −6.79150 | + | 11.7632i | −0.274083 | + | 0.474725i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.17712 | + | 3.77089i | 0.0877188 | + | 0.151933i | ||||
\(617\) | −17.7601 | + | 30.7614i | −0.714996 | + | 1.23841i | 0.247965 | + | 0.968769i | \(0.420238\pi\) |
−0.962961 | + | 0.269640i | \(0.913095\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.29150 | 0.0921033 | 0.0460516 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460516 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(620\) | 0.531373 | − | 0.920365i | 0.0213405 | − | 0.0369628i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.5203 | 0.943076 | ||||||||
\(623\) | −14.4686 | + | 25.0604i | −0.579673 | + | 1.00402i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | 11.6458 | + | 20.1710i | 0.465458 | + | 0.806197i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | 6.47974 | 0.258364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9373 | 0.873308 | 0.436654 | − | 0.899629i | \(-0.356163\pi\) | ||||
0.436654 | + | 0.899629i | \(0.356163\pi\) | |||||||
\(632\) | −7.61438 | + | 13.1885i | −0.302884 | + | 0.524610i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.4059 | + | 18.0235i | 0.413270 | + | 0.715805i | ||||
\(635\) | −10.9373 | −0.434032 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.26013 | − | 3.91466i | −0.0895496 | − | 0.155104i | ||||
\(638\) | 12.5830 | 0.498166 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.822876 | + | 1.42526i | −0.0325270 | + | 0.0563384i | ||||
\(641\) | −8.22876 | −0.325016 | −0.162508 | − | 0.986707i | \(-0.551958\pi\) | ||||
−0.162508 | + | 0.986707i | \(0.551958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4373 | − | 30.2022i | 0.687658 | − | 1.19106i | −0.284935 | − | 0.958547i | \(-0.591972\pi\) |
0.972593 | − | 0.232512i | \(-0.0746945\pi\) | |||||||
\(644\) | 12.2915 | − | 21.2895i | 0.484353 | − | 0.838924i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64575 | − | 2.85052i | 0.0647512 | − | 0.112152i | ||||
\(647\) | −10.9373 | + | 18.9439i | −0.429988 | + | 0.744761i | −0.996872 | − | 0.0790370i | \(-0.974815\pi\) |
0.566884 | + | 0.823798i | \(0.308149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2288 | + | 19.4488i | 0.440767 | + | 0.763431i | ||||
\(650\) | −0.739870 | − | 1.28149i | −0.0290201 | − | 0.0502643i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.500000 | − | 0.866025i | 0.0195815 | − | 0.0339162i | ||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8340 | 0.423319 | ||||||||
\(656\) | −2.46863 | − | 4.27579i | −0.0963837 | − | 0.166941i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.4686 | − | 25.0604i | 0.564046 | − | 0.976956i | ||||
\(659\) | 1.11438 | + | 1.93016i | 0.0434100 | + | 0.0751884i | 0.886914 | − | 0.461934i | \(-0.152844\pi\) |
−0.843504 | + | 0.537123i | \(0.819511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5830 | − | 33.9188i | −0.761691 | − | 1.31929i | −0.941979 | − | 0.335673i | \(-0.891036\pi\) |
0.180288 | − | 0.983614i | \(-0.442297\pi\) | |||||||
\(662\) | −0.0627461 | − | 0.108679i | −0.00243870 | − | 0.00422394i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.35425 | + | 2.34563i | 0.0525550 | + | 0.0910280i | ||||
\(665\) | 4.35425 | − | 7.54178i | 0.168851 | − | 0.292458i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.5203 | − | 61.5229i | −1.37535 | − | 2.38218i | ||||
\(668\) | −12.5830 | −0.486851 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.6458 | 0.527181 | ||||||||
\(671\) | −10.4059 | + | 18.0235i | −0.401715 | + | 0.695790i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8745 | + | 41.3519i | 0.920295 | + | 1.59400i | 0.798959 | + | 0.601386i | \(0.205384\pi\) |
0.121336 | + | 0.992612i | \(0.461282\pi\) | |||||||
\(674\) | −4.70850 | − | 8.15536i | −0.181365 | − | 0.314133i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.29150 | − | 10.8972i | 0.241981 | − | 0.419123i | ||||
\(677\) | −7.06275 | + | 12.2330i | −0.271443 | + | 0.470154i | −0.969232 | − | 0.246150i | \(-0.920834\pi\) |
0.697788 | + | 0.716304i | \(0.254168\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0314 | − | 17.3748i | 0.384969 | − | 0.666785i | ||||
\(680\) | −1.35425 | + | 2.34563i | −0.0519331 | + | 0.0899507i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.06275 | −0.0406947 | ||||||||
\(683\) | 10.4059 | − | 18.0235i | 0.398170 | − | 0.689651i | −0.595330 | − | 0.803481i | \(-0.702979\pi\) |
0.993500 | + | 0.113831i | \(0.0363121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.2915 | −0.584258 | ||||||||
\(686\) | 9.26013 | − | 16.0390i | 0.353553 | − | 0.612372i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.00000 | 0.190623 | ||||||||
\(689\) | 1.93725 | + | 3.35542i | 0.0738035 | + | 0.127831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3745 | + | 21.4333i | −0.470748 | + | 0.815360i | −0.999440 | − | 0.0334536i | \(-0.989349\pi\) |
0.528692 | + | 0.848814i | \(0.322683\pi\) | |||||||
\(692\) | −6.58301 | −0.250248 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −16.1144 | + | 27.9109i | −0.611253 | + | 1.05872i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.06275 | − | 7.03688i | −0.153887 | − | 0.266541i | ||||
\(698\) | −25.2288 | −0.954923 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.03137 | − | 5.25049i | 0.114575 | − | 0.198450i | ||||
\(701\) | 5.41699 | 0.204597 | 0.102299 | − | 0.994754i | \(-0.467380\pi\) | ||||
0.102299 | + | 0.994754i | \(0.467380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.93725 | + | 6.81952i | −0.148496 | + | 0.257203i | ||||
\(704\) | 1.64575 | 0.0620266 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | − | 10.3923i | 0.225813 | − | 0.391120i | ||||
\(707\) | 18.0516 | + | 31.2663i | 0.678902 | + | 1.17589i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.90588 | − | 8.49723i | 0.184244 | − | 0.319120i | −0.759077 | − | 0.651000i | \(-0.774350\pi\) |
0.943322 | + | 0.331880i | \(0.107683\pi\) | |||||||
\(710\) | 8.52026 | − | 14.7575i | 0.319760 | − | 0.553840i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.46863 | + | 9.47194i | 0.204945 | + | 0.354976i | ||||
\(713\) | 3.00000 | + | 5.19615i | 0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.874508 | − | 1.51469i | 0.0327047 | − | 0.0566463i | ||||
\(716\) | −1.06275 | −0.0397167 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.1660 | −1.16311 | ||||||||
\(719\) | 3.53137 | + | 6.11652i | 0.131698 | + | 0.228108i | 0.924331 | − | 0.381591i | \(-0.124624\pi\) |
−0.792633 | + | 0.609699i | \(0.791290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.7915 | + | 27.3517i | 0.588106 | + | 1.01863i | ||||
\(722\) | −7.50000 | − | 12.9904i | −0.279121 | − | 0.483452i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.64575 | + | 11.5108i | 0.246987 | + | 0.427795i | ||||
\(725\) | −8.76013 | − | 15.1730i | −0.325343 | − | 0.563511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.6144 | − | 21.8487i | −0.467841 | − | 0.810325i | 0.531483 | − | 0.847069i | \(-0.321635\pi\) |
−0.999325 | + | 0.0367437i | \(0.988301\pi\) | |||||||
\(728\) | −1.70850 | −0.0633211 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.70850 | + | 15.0836i | 0.322316 | + | 0.558268i | ||||
\(731\) | 8.22876 | 0.304352 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.77124 | 0.323973 | 0.161987 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161987 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(734\) | −0.937254 | + | 1.62337i | −0.0345947 | + | 0.0599197i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.64575 | − | 8.04668i | −0.171245 | − | 0.296604i | ||||
\(737\) | −6.82288 | − | 11.8176i | −0.251324 | − | 0.435306i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7288 | + | 18.5828i | −0.394664 | + | 0.683578i | −0.993058 | − | 0.117624i | \(-0.962472\pi\) |
0.598395 | + | 0.801202i | \(0.295806\pi\) | |||||||
\(740\) | 3.23987 | − | 5.61162i | 0.119100 | − | 0.206287i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.93725 | + | 13.7477i | −0.291386 | + | 0.504695i | ||||
\(743\) | −6.53137 | + | 11.3127i | −0.239613 | + | 0.415022i | −0.960603 | − | 0.277923i | \(-0.910354\pi\) |
0.720990 | + | 0.692945i | \(0.243687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.6235 | 0.425853 | ||||||||
\(746\) | −8.29150 | + | 14.3613i | −0.303573 | + | 0.525805i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.70850 | 0.0990325 | ||||||||
\(749\) | −7.93725 | + | 13.7477i | −0.290021 | + | 0.502331i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.457513 | 0.0166949 | 0.00834745 | − | 0.999965i | \(-0.497343\pi\) | ||||
0.00834745 | + | 0.999965i | \(0.497343\pi\) | |||||||
\(752\) | −5.46863 | − | 9.47194i | −0.199420 | − | 0.345406i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.46863 | + | 4.27579i | −0.0899021 | + | 0.155715i | ||||
\(755\) | −11.8967 | −0.432967 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.9778 | −1.48936 | −0.744681 | − | 0.667420i | \(-0.767398\pi\) | ||||
−0.744681 | + | 0.667420i | \(0.767398\pi\) | |||||||
\(758\) | 2.20850 | − | 3.82523i | 0.0802162 | − | 0.138939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.64575 | − | 2.85052i | −0.0596977 | − | 0.103399i | ||||
\(761\) | 18.5830 | 0.673633 | 0.336817 | − | 0.941570i | \(-0.390650\pi\) | ||||
0.336817 | + | 0.941570i | \(0.390650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.8745 | −0.828113 | ||||||||
\(764\) | −26.8118 | −0.970015 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.291503 | − | 0.504897i | 0.0105324 | − | 0.0182427i | ||||
\(767\) | −8.81176 | −0.318174 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.70850 | + | 16.8156i | −0.350097 | + | 0.606386i | −0.986266 | − | 0.165163i | \(-0.947185\pi\) |
0.636169 | + | 0.771550i | \(0.280518\pi\) | |||||||
\(770\) | 7.16601 | 0.258245 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | − | 6.06218i | 0.125968 | − | 0.218183i | ||||
\(773\) | 19.1660 | − | 33.1965i | 0.689353 | − | 1.19400i | −0.282694 | − | 0.959210i | \(-0.591228\pi\) |
0.972047 | − | 0.234785i | \(-0.0754386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.739870 | + | 1.28149i | 0.0265769 | + | 0.0460326i | ||||
\(776\) | −3.79150 | − | 6.56708i | −0.136107 | − | 0.235744i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.35425 | + | 7.54178i | −0.156107 | + | 0.270386i | ||||
\(779\) | 9.87451 | 0.353791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0405 | −0.609758 | ||||||||
\(782\) | −7.64575 | − | 13.2428i | −0.273412 | − | 0.473563i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.50000 | − | 6.06218i | −0.125000 | − | 0.216506i | ||||
\(785\) | −3.29150 | − | 5.70105i | −0.117479 | − | 0.203479i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1458 | + | 19.3050i | 0.397303 | + | 0.688149i | 0.993392 | − | 0.114769i | \(-0.0366128\pi\) |
−0.596089 | + | 0.802918i | \(0.703279\pi\) | |||||||
\(788\) | 7.64575 | + | 13.2428i | 0.272369 | + | 0.471756i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.5314 | + | 21.7050i | 0.445846 | + | 0.772228i | ||||
\(791\) | −20.2288 | −0.719252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.08301 | − | 7.07197i | −0.144992 | − | 0.251133i | ||||
\(794\) | 11.3542 | 0.402947 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.9373 | 0.777545 | ||||||||
\(797\) | 16.4059 | − | 28.4158i | 0.581126 | − | 1.00654i | −0.414220 | − | 0.910177i | \(-0.635946\pi\) |
0.995346 | − | 0.0963632i | \(-0.0307210\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | − | 15.5885i | −0.318397 | − | 0.551480i | ||||
\(800\) | −1.14575 | − | 1.98450i | −0.0405084 | − | 0.0701627i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.4059 | + | 23.2197i | −0.473378 | + | 0.819915i | ||||
\(803\) | 8.70850 | − | 15.0836i | 0.307316 | − | 0.532287i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.2288 | − | 35.0372i | −0.712970 | − | 1.23490i | ||||
\(806\) | 0.208497 | − | 0.361128i | 0.00734401 | − | 0.0127202i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.6458 | 0.480056 | ||||||||
\(809\) | 18.2915 | − | 31.6818i | 0.643095 | − | 1.11387i | −0.341643 | − | 0.939830i | \(-0.610983\pi\) |
0.984738 | − | 0.174043i | \(-0.0556833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7085 | −0.656944 | −0.328472 | − | 0.944514i | \(-0.606534\pi\) | ||||
−0.328472 | + | 0.944514i | \(0.606534\pi\) | |||||||
\(812\) | −20.2288 | −0.709890 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.47974 | −0.227115 | ||||||||
\(815\) | −0.822876 | − | 1.42526i | −0.0288241 | − | 0.0499248i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00000 | + | 8.66025i | −0.174928 | + | 0.302984i | ||||
\(818\) | 16.8745 | 0.590003 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.12549 | −0.283754 | ||||||||
\(821\) | −0.291503 | + | 0.504897i | −0.0101735 | + | 0.0176210i | −0.871067 | − | 0.491164i | \(-0.836572\pi\) |
0.860894 | + | 0.508785i | \(0.169905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5516 | − | 20.0080i | −0.402665 | − | 0.697436i | 0.591382 | − | 0.806392i | \(-0.298583\pi\) |
−0.994047 | + | 0.108956i | \(0.965249\pi\) | |||||||
\(824\) | 11.9373 | 0.415854 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0516 | − | 31.2663i | −0.628097 | − | 1.08790i | ||||
\(827\) | −19.7490 | −0.686741 | −0.343370 | − | 0.939200i | \(-0.611569\pi\) | ||||
−0.343370 | + | 0.939200i | \(0.611569\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35425 | − | 16.2020i | 0.324886 | − | 0.562720i | −0.656603 | − | 0.754236i | \(-0.728007\pi\) |
0.981489 | + | 0.191517i | \(0.0613406\pi\) | |||||||
\(830\) | 4.45751 | 0.154723 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.322876 | + | 0.559237i | −0.0111937 | + | 0.0193881i | ||||
\(833\) | −5.76013 | − | 9.97684i | −0.199577 | − | 0.345677i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.3542 | + | 17.9341i | −0.358324 | + | 0.620635i | ||||
\(836\) | −1.64575 | + | 2.85052i | −0.0569195 | + | 0.0985875i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.53137 | − | 11.3127i | −0.225623 | − | 0.390790i | ||||
\(839\) | −19.3542 | − | 33.5225i | −0.668183 | − | 1.15733i | −0.978412 | − | 0.206665i | \(-0.933739\pi\) |
0.310229 | − | 0.950662i | \(-0.399594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7288 | + | 25.5110i | −0.507888 | + | 0.879688i | ||||
\(842\) | 25.2915 | 0.871603 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.8745 | −0.580845 | ||||||||
\(845\) | −10.3542 | − | 17.9341i | −0.356197 | − | 0.616951i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9686 | + | 18.9982i | 0.376886 | + | 0.652787i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.88562 | − | 3.26599i | −0.0646763 | − | 0.112023i | ||||
\(851\) | 18.2915 | + | 31.6818i | 0.627025 | + | 1.08604i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.06275 | − | 13.9651i | −0.276063 | − | 0.478155i | 0.694340 | − | 0.719647i | \(-0.255697\pi\) |
−0.970403 | + | 0.241492i | \(0.922363\pi\) | |||||||
\(854\) | 16.7288 | − | 28.9751i | 0.572446 | − | 0.991506i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | −20.8118 | −0.710916 | −0.355458 | − | 0.934692i | \(-0.615675\pi\) | ||||
−0.355458 | + | 0.934692i | \(0.615675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.00000 | −0.238837 | −0.119418 | − | 0.992844i | \(-0.538103\pi\) | ||||
−0.119418 | + | 0.992844i | \(0.538103\pi\) | |||||||
\(860\) | 4.11438 | − | 7.12631i | 0.140299 | − | 0.243005i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.40588 | + | 7.63121i | 0.150065 | + | 0.259920i | ||||
\(863\) | −6.58301 | − | 11.4021i | −0.224088 | − | 0.388132i | 0.731957 | − | 0.681350i | \(-0.238607\pi\) |
−0.956045 | + | 0.293218i | \(0.905274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.41699 | + | 9.38251i | −0.184183 | + | 0.319015i | ||||
\(866\) | −9.50000 | + | 16.4545i | −0.322823 | + | 0.559146i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.70850 | 0.0579902 | ||||||||
\(869\) | 12.5314 | − | 21.7050i | 0.425098 | − | 0.736291i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.35425 | 0.181422 | ||||||||
\(872\) | −4.32288 | + | 7.48744i | −0.146391 | + | 0.253557i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.5830 | 0.628580 | ||||||||
\(875\) | −15.8745 | − | 27.4955i | −0.536656 | − | 0.929516i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.3542 | 0.721082 | 0.360541 | − | 0.932743i | \(-0.382592\pi\) | ||||
0.360541 | + | 0.932743i | \(0.382592\pi\) | |||||||
\(878\) | −8.58301 | − | 14.8662i | −0.289662 | − | 0.501710i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.35425 | − | 2.34563i | 0.0456517 | − | 0.0790711i | ||||
\(881\) | −27.8745 | −0.939116 | −0.469558 | − | 0.882902i | \(-0.655587\pi\) | ||||
−0.469558 | + | 0.882902i | \(0.655587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8745 | 0.399609 | 0.199805 | − | 0.979836i | \(-0.435969\pi\) | ||||
0.199805 | + | 0.979836i | \(0.435969\pi\) | |||||||
\(884\) | −0.531373 | + | 0.920365i | −0.0178720 | + | 0.0309552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.35425 | + | 7.54178i | 0.146284 | + | 0.253371i | ||||
\(887\) | 15.8745 | 0.533014 | 0.266507 | − | 0.963833i | \(-0.414130\pi\) | ||||
0.266507 | + | 0.963833i | \(0.414130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.79150 | − | 15.2273i | −0.294858 | − | 0.510708i | ||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.93725 | + | 15.4798i | −0.299241 | + | 0.518301i | ||||
\(893\) | 21.8745 | 0.732002 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.874508 | + | 1.51469i | −0.0292316 | + | 0.0506306i | ||||
\(896\) | −2.64575 | −0.0883883 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.82288 | + | 6.62141i | −0.127571 | + | 0.220959i | ||||
\(899\) | 2.46863 | − | 4.27579i | 0.0823333 | − | 0.142605i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.93725 | + | 8.55157i | 0.164484 | + | 0.284894i | ||||
\(902\) | 4.06275 | + | 7.03688i | 0.135275 | + | 0.234303i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.82288 | + | 6.62141i | −0.127147 | + | 0.220225i | ||||
\(905\) | 21.8745 | 0.727133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.7085 | 0.853637 | 0.426818 | − | 0.904337i | \(-0.359634\pi\) | ||||
0.426818 | + | 0.904337i | \(0.359634\pi\) | |||||||
\(908\) | 3.00000 | + | 5.19615i | 0.0995585 | + | 0.172440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.40588 | + | 2.43506i | −0.0466045 | + | 0.0807214i | ||||
\(911\) | 6.53137 | + | 11.3127i | 0.216394 | + | 0.374805i | 0.953703 | − | 0.300750i | \(-0.0972371\pi\) |
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.22876 | − | 3.86032i | −0.0737611 | − | 0.127758i | ||||
\(914\) | 1.14575 | + | 1.98450i | 0.0378981 | + | 0.0656414i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.32288 | + | 12.6836i | 0.241955 | + | 0.419078i | ||||
\(917\) | 8.70850 | + | 15.0836i | 0.287580 | + | 0.498103i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.6144 | − | 47.8295i | −0.910914 | − | 1.57775i | −0.812775 | − | 0.582577i | \(-0.802044\pi\) |
−0.0981388 | − | 0.995173i | \(-0.531289\pi\) | |||||||
\(920\) | −15.2915 | −0.504146 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.22876 | −0.0734002 | ||||||||
\(923\) | 3.34313 | − | 5.79048i | 0.110041 | − | 0.190596i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.51111 | + | 7.81348i | 0.148325 | + | 0.256906i | ||||
\(926\) | 14.6458 | + | 25.3672i | 0.481289 | + | 0.833617i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.82288 | + | 6.62141i | −0.125492 | + | 0.217359i | ||||
\(929\) | −0.531373 | + | 0.920365i | −0.0174338 | + | 0.0301962i | −0.874611 | − | 0.484826i | \(-0.838883\pi\) |
0.857177 | + | 0.515022i | \(0.172216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0000 | 0.458831 | ||||||||
\(932\) | −4.35425 | + | 7.54178i | −0.142628 | + | 0.247039i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.2288 | −0.858231 | ||||||||
\(935\) | 2.22876 | − | 3.86032i | 0.0728881 | − | 0.126246i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.7490 | 0.612504 | 0.306252 | − | 0.951951i | \(-0.400925\pi\) | ||||
0.306252 | + | 0.951951i | \(0.400925\pi\) | |||||||
\(938\) | 10.9686 | + | 18.9982i | 0.358138 | + | 0.620314i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0000 | −0.587095 | ||||||||
\(941\) | 7.69738 | + | 13.3323i | 0.250928 | + | 0.434619i | 0.963781 | − | 0.266693i | \(-0.0859311\pi\) |
−0.712854 | + | 0.701313i | \(0.752598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.9373 | − | 39.7285i | 0.746940 | − | 1.29374i | ||||
\(944\) | −13.6458 | −0.444131 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.22876 | −0.267540 | ||||||||
\(947\) | 23.7601 | − | 41.1538i | 0.772100 | − | 1.33732i | −0.164309 | − | 0.986409i | \(-0.552540\pi\) |
0.936410 | − | 0.350908i | \(-0.114127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.41699 | + | 5.91841i | 0.110920 | + | 0.192120i | ||||
\(950\) | 4.58301 | 0.148692 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.35425 | −0.141122 | ||||||||
\(953\) | 32.3320 | 1.04734 | 0.523668 | − | 0.851922i | \(-0.324563\pi\) | ||||
0.523668 | + | 0.851922i | \(0.324563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.0627 | + | 38.2138i | −0.713934 | + | 1.23657i | ||||
\(956\) | −4.93725 | −0.159682 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.822876 | − | 1.42526i | 0.0265859 | − | 0.0460481i | ||||
\(959\) | −12.2915 | − | 21.2895i | −0.396913 | − | 0.687474i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2915 | − | 26.4857i | 0.493274 | − | 0.854376i | ||||
\(962\) | 1.27124 | − | 2.20186i | 0.0409865 | − | 0.0709908i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.50000 | − | 4.33013i | −0.0805196 | − | 0.139464i | ||||
\(965\) | −5.76013 | − | 9.97684i | −0.185425 | − | 0.321166i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.9686 | + | 44.9790i | −0.835095 | + | 1.44643i | 0.0588585 | + | 0.998266i | \(0.481254\pi\) |
−0.893953 | + | 0.448160i | \(0.852079\pi\) | |||||||
\(968\) | 8.29150 | 0.266499 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.4797 | −0.400700 | ||||||||
\(971\) | 10.9373 | + | 18.9439i | 0.350993 | + | 0.607938i | 0.986424 | − | 0.164220i | \(-0.0525107\pi\) |
−0.635431 | + | 0.772158i | \(0.719177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.8118 | −1.66101 | ||||||||
\(974\) | −3.93725 | − | 6.81952i | −0.126158 | − | 0.218512i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.32288 | − | 10.9515i | −0.202390 | − | 0.350550i | ||||
\(977\) | −10.0627 | − | 17.4292i | −0.321936 | − | 0.557609i | 0.658952 | − | 0.752185i | \(-0.271000\pi\) |
−0.980887 | + | 0.194576i | \(0.937667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | − | 15.5885i | −0.287641 | − | 0.498209i | ||||
\(980\) | −11.5203 | −0.368001 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.8745 | + | 32.6916i | 0.602310 | + | 1.04323i | ||||
\(983\) | 26.8118 | 0.855162 | 0.427581 | − | 0.903977i | \(-0.359366\pi\) | ||||
0.427581 | + | 0.903977i | \(0.359366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.1660 | 0.801856 | ||||||||
\(986\) | −6.29150 | + | 10.8972i | −0.200362 | + | 0.347038i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.645751 | − | 1.11847i | −0.0205441 | − | 0.0355834i | ||||
\(989\) | 23.2288 | + | 40.2334i | 0.738631 | + | 1.27935i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.9686 | − | 36.3187i | 0.666090 | − | 1.15370i | −0.312898 | − | 0.949787i | \(-0.601300\pi\) |
0.978988 | − | 0.203916i | \(-0.0653668\pi\) | |||||||
\(992\) | 0.322876 | − | 0.559237i | 0.0102513 | − | 0.0177558i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27.3948 | 0.868909 | ||||||||
\(995\) | 18.0516 | − | 31.2663i | 0.572275 | − | 0.991210i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.6863 | −1.76360 | −0.881801 | − | 0.471622i | \(-0.843669\pi\) | ||||
−0.881801 | + | 0.471622i | \(0.843669\pi\) | |||||||
\(998\) | 18.0830 | − | 31.3207i | 0.572408 | − | 0.991439i | ||||
\(999\) | 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 | 1134.2.h.t.109.1 | 4 | ||
3.2 | odd | 2 | 1134.2.h.q.109.2 | 4 | |||
7.2 | even | 3 | 1134.2.e.q.919.2 | 4 | |||
9.2 | odd | 6 | 1134.2.e.t.865.1 | 4 | |||
9.4 | even | 3 | 378.2.g.h.109.2 | yes | 4 | ||
9.5 | odd | 6 | 378.2.g.g.109.1 | ✓ | 4 | ||
9.7 | even | 3 | 1134.2.e.q.865.2 | 4 | |||
21.2 | odd | 6 | 1134.2.e.t.919.1 | 4 | |||
63.2 | odd | 6 | 1134.2.h.q.541.2 | 4 | |||
63.4 | even | 3 | 2646.2.a.bi.1.1 | 2 | |||
63.16 | even | 3 | inner | 1134.2.h.t.541.1 | 4 | ||
63.23 | odd | 6 | 378.2.g.g.163.1 | yes | 4 | ||
63.31 | odd | 6 | 2646.2.a.bf.1.2 | 2 | |||
63.32 | odd | 6 | 2646.2.a.bl.1.2 | 2 | |||
63.58 | even | 3 | 378.2.g.h.163.2 | yes | 4 | ||
63.59 | even | 6 | 2646.2.a.bo.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.g.109.1 | ✓ | 4 | 9.5 | odd | 6 | ||
378.2.g.g.163.1 | yes | 4 | 63.23 | odd | 6 | ||
378.2.g.h.109.2 | yes | 4 | 9.4 | even | 3 | ||
378.2.g.h.163.2 | yes | 4 | 63.58 | even | 3 | ||
1134.2.e.q.865.2 | 4 | 9.7 | even | 3 | |||
1134.2.e.q.919.2 | 4 | 7.2 | even | 3 | |||
1134.2.e.t.865.1 | 4 | 9.2 | odd | 6 | |||
1134.2.e.t.919.1 | 4 | 21.2 | odd | 6 | |||
1134.2.h.q.109.2 | 4 | 3.2 | odd | 2 | |||
1134.2.h.q.541.2 | 4 | 63.2 | odd | 6 | |||
1134.2.h.t.109.1 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.h.t.541.1 | 4 | 63.16 | even | 3 | inner | ||
2646.2.a.bf.1.2 | 2 | 63.31 | odd | 6 | |||
2646.2.a.bi.1.1 | 2 | 63.4 | even | 3 | |||
2646.2.a.bl.1.2 | 2 | 63.32 | odd | 6 | |||
2646.2.a.bo.1.1 | 2 | 63.59 | even | 6 |