Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), 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: | \(3.01834519640\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.109 |
Dual form | 378.2.g.g.163.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(5\) | −0.822876 | − | 1.42526i | −0.368001 | − | 0.637397i | 0.621252 | − | 0.783611i | \(-0.286624\pi\) |
−0.989253 | + | 0.146214i | \(0.953291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 1.00000 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.822876 | + | 1.42526i | −0.260216 | + | 0.450708i | ||||
\(11\) | 0.822876 | − | 1.42526i | 0.248106 | − | 0.429733i | −0.714894 | − | 0.699233i | \(-0.753525\pi\) |
0.963000 | + | 0.269500i | \(0.0868584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.645751 | 0.179099 | 0.0895496 | − | 0.995982i | \(-0.471457\pi\) | ||||
0.0895496 | + | 0.995982i | \(0.471457\pi\) | |||||||
\(14\) | −1.32288 | − | 2.29129i | −0.353553 | − | 0.612372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.822876 | − | 1.42526i | 0.199577 | − | 0.345677i | −0.748815 | − | 0.662780i | \(-0.769377\pi\) |
0.948391 | + | 0.317103i | \(0.102710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 1.64575 | 0.368001 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.64575 | −0.350875 | ||||||||
\(23\) | −4.64575 | − | 8.04668i | −0.968706 | − | 1.67785i | −0.699310 | − | 0.714819i | \(-0.746509\pi\) |
−0.269396 | − | 0.963029i | \(-0.586824\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14575 | − | 1.98450i | 0.229150 | − | 0.396900i | ||||
\(26\) | −0.322876 | − | 0.559237i | −0.0633211 | − | 0.109675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.32288 | + | 2.29129i | −0.250000 | + | 0.433013i | ||||
\(29\) | 7.64575 | 1.41978 | 0.709890 | − | 0.704312i | \(-0.248745\pi\) | ||||
0.709890 | + | 0.704312i | \(0.248745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.322876 | + | 0.559237i | −0.0579902 | + | 0.100442i | −0.893563 | − | 0.448938i | \(-0.851803\pi\) |
0.835573 | + | 0.549380i | \(0.185136\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.64575 | −0.282244 | ||||||||
\(35\) | −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 | \(0.938240\pi\) | |||||||
\(38\) | −1.00000 | + | 1.73205i | −0.162221 | + | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.822876 | − | 1.42526i | −0.130108 | − | 0.225354i | ||||
\(41\) | −4.93725 | −0.771070 | −0.385535 | − | 0.922693i | \(-0.625983\pi\) | ||||
−0.385535 | + | 0.922693i | \(0.625983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 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 | 0.921123 | + | 0.389273i | \(0.127274\pi\) |
−0.123441 | + | 0.992352i | \(0.539393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −2.29150 | −0.324067 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.322876 | + | 0.559237i | −0.0447748 | + | 0.0775522i | ||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.70850 | −0.365214 | ||||||||
\(56\) | 2.64575 | 0.353553 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.82288 | − | 6.62141i | −0.501968 | − | 0.869434i | ||||
\(59\) | −6.82288 | + | 11.8176i | −0.888263 | + | 1.53852i | −0.0463350 | + | 0.998926i | \(0.514754\pi\) |
−0.841928 | + | 0.539590i | \(0.818579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.32288 | − | 10.9515i | −0.809561 | − | 1.40220i | −0.913168 | − | 0.407583i | \(-0.866372\pi\) |
0.103607 | − | 0.994618i | \(-0.466962\pi\) | |||||||
\(62\) | 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 | 0.493488 | + | 0.869753i | \(0.335722\pi\) |
−0.999972 | + | 0.00750349i | \(0.997612\pi\) | |||||||
\(68\) | 0.822876 | + | 1.42526i | 0.0997883 | + | 0.172838i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.17712 | + | 3.77089i | −0.260216 | + | 0.450708i | ||||
\(71\) | 10.3542 | 1.22882 | 0.614412 | − | 0.788986i | \(-0.289393\pi\) | ||||
0.614412 | + | 0.788986i | \(0.289393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.29150 | − | 9.16515i | 0.619324 | − | 1.07270i | −0.370286 | − | 0.928918i | \(-0.620740\pi\) |
0.989609 | − | 0.143782i | \(-0.0459264\pi\) | |||||||
\(74\) | −1.96863 | + | 3.40976i | −0.228848 | + | 0.396377i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 2.17712 | − | 3.77089i | 0.248106 | − | 0.429733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.61438 | + | 13.1885i | 0.856684 | + | 1.48382i | 0.875073 | + | 0.483990i | \(0.160813\pi\) |
−0.0183890 | + | 0.999831i | \(0.505854\pi\) | |||||||
\(80\) | −0.822876 | + | 1.42526i | −0.0920003 | + | 0.159349i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.46863 | + | 4.27579i | 0.272614 | + | 0.472182i | ||||
\(83\) | −2.70850 | −0.297296 | −0.148648 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148648 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.70850 | −0.293778 | ||||||||
\(86\) | −2.50000 | − | 4.33013i | −0.269582 | − | 0.466930i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.822876 | − | 1.42526i | 0.0877188 | − | 0.151933i | ||||
\(89\) | 5.46863 | + | 9.47194i | 0.579673 | + | 1.00402i | 0.995517 | + | 0.0945873i | \(0.0301532\pi\) |
−0.415843 | + | 0.909436i | \(0.636514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.70850 | 0.179099 | ||||||||
\(92\) | 9.29150 | 0.968706 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.46863 | − | 9.47194i | 0.564046 | − | 0.976956i | ||||
\(95\) | −1.64575 | + | 2.85052i | −0.168851 | + | 0.292458i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.58301 | −0.769938 | −0.384969 | − | 0.922930i | \(-0.625788\pi\) | ||||
−0.384969 | + | 0.922930i | \(0.625788\pi\) | |||||||
\(98\) | −3.50000 | − | 6.06218i | −0.353553 | − | 0.612372i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.14575 | + | 1.98450i | 0.114575 | + | 0.198450i | ||||
\(101\) | −6.82288 | + | 11.8176i | −0.678902 | + | 1.17589i | 0.296411 | + | 0.955061i | \(0.404210\pi\) |
−0.975312 | + | 0.220831i | \(0.929123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.96863 | + | 10.3380i | 0.588106 | + | 1.01863i | 0.994480 | + | 0.104923i | \(0.0334597\pi\) |
−0.406374 | + | 0.913707i | \(0.633207\pi\) | |||||||
\(104\) | 0.645751 | 0.0633211 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | 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 | ||||||||
\(112\) | −1.32288 | − | 2.29129i | −0.125000 | − | 0.216506i | ||||
\(113\) | 7.64575 | 0.719252 | 0.359626 | − | 0.933097i | \(-0.382904\pi\) | ||||
0.359626 | + | 0.933097i | \(0.382904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.64575 | + | 13.2428i | −0.712970 | + | 1.23490i | ||||
\(116\) | −3.82288 | + | 6.62141i | −0.354945 | + | 0.614783i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.6458 | 1.25619 | ||||||||
\(119\) | 2.17712 | − | 3.77089i | 0.199577 | − | 0.345677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.14575 | + | 7.18065i | 0.376886 | + | 0.652787i | ||||
\(122\) | −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 | ||||
\(131\) | −3.29150 | − | 5.70105i | −0.287580 | − | 0.498103i | 0.685652 | − | 0.727930i | \(-0.259517\pi\) |
−0.973232 | + | 0.229827i | \(0.926184\pi\) | |||||||
\(132\) | 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 | ||||
\(137\) | 4.64575 | − | 8.04668i | 0.396913 | − | 0.687474i | −0.596430 | − | 0.802665i | \(-0.703415\pi\) |
0.993343 | + | 0.115191i | \(0.0367480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.5830 | −1.66101 | −0.830504 | − | 0.557012i | \(-0.811948\pi\) | ||||
−0.830504 | + | 0.557012i | \(0.811948\pi\) | |||||||
\(140\) | 4.35425 | 0.368001 | ||||||||
\(141\) | 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 | ||||
\(146\) | −10.5830 | −0.875856 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.93725 | 0.323640 | ||||||||
\(149\) | −3.53137 | − | 6.11652i | −0.289301 | − | 0.501085i | 0.684342 | − | 0.729161i | \(-0.260090\pi\) |
−0.973643 | + | 0.228077i | \(0.926756\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.61438 | + | 6.26029i | −0.294134 | + | 0.509455i | −0.974783 | − | 0.223155i | \(-0.928365\pi\) |
0.680649 | + | 0.732610i | \(0.261698\pi\) | |||||||
\(152\) | −1.00000 | − | 1.73205i | −0.0811107 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.35425 | −0.350875 | ||||||||
\(155\) | 1.06275 | 0.0853618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | − | 3.46410i | 0.159617 | − | 0.276465i | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(158\) | 7.61438 | − | 13.1885i | 0.605767 | − | 1.04922i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.64575 | 0.130108 | ||||||||
\(161\) | −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 | \(0.820864\pi\) | |||||||
\(164\) | 2.46863 | − | 4.27579i | 0.192767 | − | 0.333883i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.35425 | + | 2.34563i | 0.105110 | + | 0.182056i | ||||
\(167\) | 12.5830 | 0.973702 | 0.486851 | − | 0.873485i | \(-0.338145\pi\) | ||||
0.486851 | + | 0.873485i | \(0.338145\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5830 | −0.967923 | ||||||||
\(170\) | 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 | \(-0.247179\pi\) |
−0.963594 | + | 0.267369i | \(0.913846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.03137 | − | 5.25049i | 0.229150 | − | 0.396900i | ||||
\(176\) | −1.64575 | −0.124053 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.46863 | − | 9.47194i | 0.409891 | − | 0.709952i | ||||
\(179\) | −0.531373 | + | 0.920365i | −0.0397167 | + | 0.0687913i | −0.885200 | − | 0.465210i | \(-0.845979\pi\) |
0.845484 | + | 0.534001i | \(0.179312\pi\) | |||||||
\(180\) | 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 | ||||||||
\(184\) | −4.64575 | − | 8.04668i | −0.342489 | − | 0.593209i | ||||
\(185\) | −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 | −0.695489 | − | 0.718537i | \(-0.744812\pi\) |
−0.274526 | − | 0.961580i | \(-0.588521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | 3.79150 | + | 6.56708i | 0.272214 | + | 0.471489i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.50000 | + | 6.06218i | −0.250000 | + | 0.433013i | ||||
\(197\) | 15.2915 | 1.08947 | 0.544737 | − | 0.838607i | \(-0.316629\pi\) | ||||
0.544737 | + | 0.838607i | \(0.316629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9686 | + | 18.9982i | −0.777545 | + | 1.34675i | 0.155807 | + | 0.987787i | \(0.450202\pi\) |
−0.933353 | + | 0.358961i | \(0.883131\pi\) | |||||||
\(200\) | 1.14575 | − | 1.98450i | 0.0810169 | − | 0.140325i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.6458 | 0.960112 | ||||||||
\(203\) | 20.2288 | 1.41978 | ||||||||
\(204\) | 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 | ||||
\(209\) | −3.29150 | −0.227678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8745 | −1.16169 | −0.580845 | − | 0.814015i | \(-0.697278\pi\) | ||||
−0.580845 | + | 0.814015i | \(0.697278\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −4.11438 | − | 7.12631i | −0.280598 | − | 0.486010i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.854249 | + | 1.47960i | −0.0579902 | + | 0.100442i | ||||
\(218\) | −8.64575 | −0.585564 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.35425 | − | 2.34563i | 0.0913034 | − | 0.158142i | ||||
\(221\) | 0.531373 | − | 0.920365i | 0.0357440 | − | 0.0619105i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8745 | 1.19697 | 0.598483 | − | 0.801136i | \(-0.295770\pi\) | ||||
0.598483 | + | 0.801136i | \(0.295770\pi\) | |||||||
\(224\) | −1.32288 | + | 2.29129i | −0.0883883 | + | 0.153093i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.82288 | − | 6.62141i | −0.254294 | − | 0.440450i | ||||
\(227\) | −3.00000 | + | 5.19615i | −0.199117 | + | 0.344881i | −0.948242 | − | 0.317547i | \(-0.897141\pi\) |
0.749125 | + | 0.662428i | \(0.230474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.32288 | + | 12.6836i | 0.483909 | + | 0.838155i | 0.999829 | − | 0.0184814i | \(-0.00588315\pi\) |
−0.515920 | + | 0.856637i | \(0.672550\pi\) | |||||||
\(230\) | 15.2915 | 1.00829 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.64575 | 0.501968 | ||||||||
\(233\) | 4.35425 | + | 7.54178i | 0.285256 | + | 0.494078i | 0.972671 | − | 0.232186i | \(-0.0745879\pi\) |
−0.687415 | + | 0.726265i | \(0.741255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | − | 15.5885i | 0.587095 | − | 1.01688i | ||||
\(236\) | −6.82288 | − | 11.8176i | −0.444131 | − | 0.769258i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.35425 | −0.282244 | ||||||||
\(239\) | 4.93725 | 0.319364 | 0.159682 | − | 0.987168i | \(-0.448953\pi\) | ||||
0.159682 | + | 0.987168i | \(0.448953\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | 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 | ||||||||
\(247\) | −0.645751 | − | 1.11847i | −0.0410882 | − | 0.0711668i | ||||
\(248\) | −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 | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 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 | ||||
\(257\) | 7.93725 | + | 13.7477i | 0.495112 | + | 0.857560i | 0.999984 | − | 0.00563467i | \(-0.00179358\pi\) |
−0.504872 | + | 0.863194i | \(0.668460\pi\) | |||||||
\(258\) | 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 | ||||
\(263\) | −5.46863 | + | 9.47194i | −0.337210 | + | 0.584065i | −0.983907 | − | 0.178682i | \(-0.942817\pi\) |
0.646697 | + | 0.762747i | \(0.276150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.87451 | 0.606586 | ||||||||
\(266\) | −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 | \(-0.520531\pi\) |
0.896453 | − | 0.443139i | \(-0.146135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6144 | + | 18.3846i | 0.644778 | + | 1.11679i | 0.984353 | + | 0.176209i | \(0.0563833\pi\) |
−0.339575 | + | 0.940579i | \(0.610283\pi\) | |||||||
\(272\) | −1.64575 | −0.0997883 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.29150 | −0.561320 | ||||||||
\(275\) | −1.88562 | − | 3.26599i | −0.113707 | − | 0.196947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.96863 | − | 15.5341i | 0.538873 | − | 0.933355i | −0.460093 | − | 0.887871i | \(-0.652184\pi\) |
0.998965 | − | 0.0454837i | \(-0.0144829\pi\) | |||||||
\(278\) | 9.79150 | + | 16.9594i | 0.587255 | + | 1.01716i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.17712 | − | 3.77089i | −0.130108 | − | 0.225354i | ||||
\(281\) | −17.5203 | −1.04517 | −0.522586 | − | 0.852587i | \(-0.675032\pi\) | ||||
−0.522586 | + | 0.852587i | \(0.675032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.14575 | + | 7.18065i | −0.246439 | + | 0.426845i | −0.962535 | − | 0.271156i | \(-0.912594\pi\) |
0.716096 | + | 0.698002i | \(0.245927\pi\) | |||||||
\(284\) | −5.17712 | + | 8.96704i | −0.307206 | + | 0.532096i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.06275 | −0.0628415 | ||||||||
\(287\) | −13.0627 | −0.771070 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.14575 | + | 12.3768i | 0.420338 | + | 0.728047i | ||||
\(290\) | −6.29150 | + | 10.8972i | −0.369450 | + | 0.639906i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.29150 | + | 9.16515i | 0.309662 | + | 0.536350i | ||||
\(293\) | 22.9373 | 1.34001 | 0.670004 | − | 0.742357i | \(-0.266292\pi\) | ||||
0.670004 | + | 0.742357i | \(0.266292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.4575 | 1.30753 | ||||||||
\(296\) | −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 | ||||||||
\(301\) | 13.2288 | 0.762493 | ||||||||
\(302\) | 7.22876 | 0.415968 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | −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 | ||||||||
\(310\) | −0.531373 | − | 0.920365i | −0.0301800 | − | 0.0522732i | ||||
\(311\) | −11.7601 | + | 20.3691i | −0.666856 | + | 1.15503i | 0.311923 | + | 0.950107i | \(0.399027\pi\) |
−0.978779 | + | 0.204921i | \(0.934306\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6458 | − | 20.1710i | −0.658257 | − | 1.14013i | −0.981067 | − | 0.193670i | \(-0.937961\pi\) |
0.322810 | − | 0.946464i | \(-0.395373\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.2288 | −0.856684 | ||||||||
\(317\) | 10.4059 | + | 18.0235i | 0.584452 | + | 1.01230i | 0.994943 | + | 0.100437i | \(0.0320240\pi\) |
−0.410491 | + | 0.911865i | \(0.634643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.29150 | − | 10.8972i | 0.352257 | − | 0.610126i | ||||
\(320\) | −0.822876 | − | 1.42526i | −0.0460001 | − | 0.0796746i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.2915 | + | 21.2895i | −0.684979 | + | 1.18642i | ||||
\(323\) | −3.29150 | −0.183144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.739870 | − | 1.28149i | 0.0410406 | − | 0.0710844i | ||||
\(326\) | 0.500000 | − | 0.866025i | 0.0276924 | − | 0.0479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.93725 | −0.272614 | ||||||||
\(329\) | 14.4686 | + | 25.0604i | 0.797681 | + | 1.38162i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0627461 | + | 0.108679i | 0.00344884 | + | 0.00597356i | 0.867745 | − | 0.497010i | \(-0.165569\pi\) |
−0.864296 | + | 0.502984i | \(0.832236\pi\) | |||||||
\(332\) | 1.35425 | − | 2.34563i | 0.0743241 | − | 0.128733i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.29150 | − | 10.8972i | −0.344256 | − | 0.596268i | ||||
\(335\) | 13.6458 | 0.745547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.41699 | −0.512976 | −0.256488 | − | 0.966547i | \(-0.582565\pi\) | ||||
−0.256488 | + | 0.966547i | \(0.582565\pi\) | |||||||
\(338\) | 6.29150 | + | 10.8972i | 0.342213 | + | 0.592730i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.35425 | − | 2.34563i | 0.0734444 | − | 0.127210i | ||||
\(341\) | 0.531373 | + | 0.920365i | 0.0287755 | + | 0.0498406i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 5.00000 | 0.269582 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.29150 | + | 5.70105i | −0.176952 | + | 0.306490i | ||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.2288 | 1.35046 | 0.675232 | − | 0.737605i | \(-0.264043\pi\) | ||||
0.675232 | + | 0.737605i | \(0.264043\pi\) | |||||||
\(350\) | −6.06275 | −0.324067 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.822876 | + | 1.42526i | 0.0438594 | + | 0.0759667i | ||||
\(353\) | 6.00000 | − | 10.3923i | 0.319348 | − | 0.553127i | −0.661004 | − | 0.750382i | \(-0.729870\pi\) |
0.980352 | + | 0.197256i | \(0.0632029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.52026 | − | 14.7575i | −0.452208 | − | 0.783248i | ||||
\(356\) | −10.9373 | −0.579673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.06275 | 0.0561679 | ||||||||
\(359\) | 15.5830 | + | 26.9906i | 0.822440 | + | 1.42451i | 0.903860 | + | 0.427827i | \(0.140721\pi\) |
−0.0814209 | + | 0.996680i | \(0.525946\pi\) | |||||||
\(360\) | 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 | ||||
\(365\) | −17.4170 | −0.911647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.937254 | − | 1.62337i | 0.0489243 | − | 0.0847393i | −0.840526 | − | 0.541771i | \(-0.817754\pi\) |
0.889450 | + | 0.457032i | \(0.151087\pi\) | |||||||
\(368\) | −4.64575 | + | 8.04668i | −0.242177 | + | 0.419462i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.47974 | 0.336866 | ||||||||
\(371\) | −7.93725 | + | 13.7477i | −0.412082 | + | 0.713746i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.29150 | + | 14.3613i | 0.429318 | + | 0.743600i | 0.996813 | − | 0.0797767i | \(-0.0254207\pi\) |
−0.567495 | + | 0.823377i | \(0.692087\pi\) | |||||||
\(374\) | −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 | ||||
\(383\) | 0.291503 | + | 0.504897i | 0.0148951 | + | 0.0257990i | 0.873377 | − | 0.487045i | \(-0.161925\pi\) |
−0.858482 | + | 0.512844i | \(0.828592\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.16601 | −0.365214 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.79150 | − | 6.56708i | 0.192484 | − | 0.333393i | ||||
\(389\) | −4.35425 | + | 7.54178i | −0.220769 | + | 0.382383i | −0.955042 | − | 0.296471i | \(-0.904190\pi\) |
0.734273 | + | 0.678855i | \(0.237523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.2915 | −0.773325 | ||||||||
\(392\) | 7.00000 | 0.353553 | ||||||||
\(393\) | 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 | \(0.741364\pi\) | |||||||
\(398\) | 21.9373 | 1.09962 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.29150 | −0.114575 | ||||||||
\(401\) | −13.4059 | − | 23.2197i | −0.669458 | − | 1.15953i | −0.978056 | − | 0.208342i | \(-0.933193\pi\) |
0.308598 | − | 0.951192i | \(-0.400140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.208497 | + | 0.361128i | −0.0103860 | + | 0.0179891i | ||||
\(404\) | −6.82288 | − | 11.8176i | −0.339451 | − | 0.587946i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1144 | − | 17.5186i | −0.501968 | − | 0.869434i | ||||
\(407\) | −6.47974 | −0.321189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.43725 | − | 14.6138i | 0.417195 | − | 0.722604i | −0.578461 | − | 0.815710i | \(-0.696346\pi\) |
0.995656 | + | 0.0931066i | \(0.0296798\pi\) | |||||||
\(410\) | 4.06275 | − | 7.03688i | 0.200645 | − | 0.347527i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.9373 | −0.588106 | ||||||||
\(413\) | −18.0516 | + | 31.2663i | −0.888263 | + | 1.53852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.22876 | + | 3.86032i | 0.109405 | + | 0.189496i | ||||
\(416\) | −0.322876 | + | 0.559237i | −0.0158303 | + | 0.0274189i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.64575 | + | 2.85052i | 0.0804963 | + | 0.139424i | ||||
\(419\) | 13.0627 | 0.638157 | 0.319078 | − | 0.947728i | \(-0.396627\pi\) | ||||
0.319078 | + | 0.947728i | \(0.396627\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2915 | −1.23263 | −0.616316 | − | 0.787499i | \(-0.711376\pi\) | ||||
−0.616316 | + | 0.787499i | \(0.711376\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −16.7288 | − | 28.9751i | −0.809561 | − | 1.40220i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.11438 | + | 7.12631i | −0.198413 | + | 0.343661i | ||||
\(431\) | 4.40588 | − | 7.63121i | 0.212224 | − | 0.367582i | −0.740186 | − | 0.672402i | \(-0.765263\pi\) |
0.952410 | + | 0.304819i | \(0.0985961\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 1.70850 | 0.0820105 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.32288 | + | 7.48744i | 0.207028 | + | 0.358583i | ||||
\(437\) | −9.29150 | + | 16.0934i | −0.444473 | + | 0.769850i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.58301 | + | 14.8662i | 0.409644 | + | 0.709525i | 0.994850 | − | 0.101360i | \(-0.0323194\pi\) |
−0.585205 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(440\) | −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 | \(-0.100337\pi\) |
−0.743852 | + | 0.668344i | \(0.767003\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | −8.93725 | − | 15.4798i | −0.423191 | − | 0.732989i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.64575 | 0.125000 | ||||||||
\(449\) | 7.64575 | 0.360825 | 0.180413 | − | 0.983591i | \(-0.442257\pi\) | ||||
0.180413 | + | 0.983591i | \(0.442257\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.06275 | + | 7.03688i | −0.191307 | + | 0.331354i | ||||
\(452\) | −3.82288 | + | 6.62141i | −0.179813 | + | 0.311445i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | −1.40588 | − | 2.43506i | −0.0659087 | − | 0.114157i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.14575 | − | 1.98450i | −0.0535960 | − | 0.0928310i | 0.837983 | − | 0.545697i | \(-0.183735\pi\) |
−0.891579 | + | 0.452866i | \(0.850402\pi\) | |||||||
\(458\) | 7.32288 | − | 12.6836i | 0.342176 | − | 0.592665i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.64575 | − | 13.2428i | −0.356485 | − | 0.617450i | ||||
\(461\) | −2.22876 | −0.103804 | −0.0519018 | − | 0.998652i | \(-0.516528\pi\) | ||||
−0.0519018 | + | 0.998652i | \(0.516528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2915 | 1.36129 | 0.680646 | − | 0.732613i | \(-0.261699\pi\) | ||||
0.680646 | + | 0.732613i | \(0.261699\pi\) | |||||||
\(464\) | −3.82288 | − | 6.62141i | −0.177473 | − | 0.307391i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.35425 | − | 7.54178i | 0.201707 | − | 0.349366i | ||||
\(467\) | 13.1144 | + | 22.7148i | 0.606861 | + | 1.05111i | 0.991754 | + | 0.128153i | \(0.0409049\pi\) |
−0.384893 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.9686 | + | 18.9982i | −0.506484 | + | 0.877256i | ||||
\(470\) | −18.0000 | −0.830278 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.82288 | + | 11.8176i | −0.314048 | + | 0.543948i | ||||
\(473\) | 4.11438 | − | 7.12631i | 0.189179 | − | 0.327668i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.58301 | −0.210283 | ||||||||
\(476\) | 2.17712 | + | 3.77089i | 0.0997883 | + | 0.172838i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.46863 | − | 4.27579i | −0.112912 | − | 0.195570i | ||||
\(479\) | 0.822876 | − | 1.42526i | 0.0375981 | − | 0.0651219i | −0.846614 | − | 0.532207i | \(-0.821363\pi\) |
0.884212 | + | 0.467086i | \(0.154696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27124 | − | 2.20186i | −0.0579637 | − | 0.100396i | ||||
\(482\) | 5.00000 | 0.227744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.29150 | −0.376886 | ||||||||
\(485\) | 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 | ||||
\(491\) | −37.7490 | −1.70359 | −0.851795 | − | 0.523876i | \(-0.824486\pi\) | ||||
−0.851795 | + | 0.523876i | \(0.824486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.29150 | − | 10.8972i | 0.283355 | − | 0.490785i | ||||
\(494\) | −0.645751 | + | 1.11847i | −0.0290537 | + | 0.0503225i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.645751 | 0.0289951 | ||||||||
\(497\) | 27.3948 | 1.22882 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0830 | − | 31.3207i | −0.809506 | − | 1.40211i | −0.913206 | − | 0.407498i | \(-0.866401\pi\) |
0.103700 | − | 0.994609i | \(-0.466932\pi\) | |||||||
\(500\) | 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 | \(-0.713449\pi\) | ||||
−0.621431 | + | 0.783469i | \(0.713449\pi\) | |||||||
\(504\) | 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 | ||||
\(509\) | −19.9373 | − | 34.5323i | −0.883703 | − | 1.53062i | −0.847193 | − | 0.531286i | \(-0.821709\pi\) |
−0.0365105 | − | 0.999333i | \(-0.511624\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | − | 24.2487i | 0.619324 | − | 1.07270i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.93725 | − | 13.7477i | 0.350097 | − | 0.606386i | ||||
\(515\) | 9.82288 | − | 17.0137i | 0.432848 | − | 0.749714i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | −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 | \(-0.495200\pi\) |
0.858387 | − | 0.513003i | \(-0.171467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | + | 0.866025i | 0.0218635 | + | 0.0378686i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(524\) | 6.58301 | 0.287580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9373 | 0.476887 | ||||||||
\(527\) | 0.531373 | + | 0.920365i | 0.0231470 | + | 0.0400917i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.6660 | + | 54.8471i | −1.37678 | + | 2.38466i | ||||
\(530\) | −4.93725 | − | 8.55157i | −0.214461 | − | 0.371457i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.29150 | 0.229416 | ||||||||
\(533\) | −3.18824 | −0.138098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.93725 | − | 8.55157i | 0.213456 | − | 0.369717i | ||||
\(536\) | −4.14575 | + | 7.18065i | −0.179069 | + | 0.310157i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.2915 | −1.17662 | ||||||||
\(539\) | 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 | \(0.487538\pi\) | |||||||
\(542\) | 10.6144 | − | 18.3846i | 0.455927 | − | 0.789688i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.822876 | + | 1.42526i | 0.0352805 | + | 0.0611076i | ||||
\(545\) | −14.2288 | −0.609493 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.70850 | 0.329592 | 0.164796 | − | 0.986328i | \(-0.447303\pi\) | ||||
0.164796 | + | 0.986328i | \(0.447303\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 20.1458 | + | 34.8935i | 0.856684 | + | 1.48382i | ||||
\(554\) | −17.9373 | −0.762081 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.79150 | − | 16.9594i | 0.415252 | − | 0.719238i | ||||
\(557\) | 16.1144 | − | 27.9109i | 0.682788 | − | 1.18262i | −0.291338 | − | 0.956620i | \(-0.594101\pi\) |
0.974126 | − | 0.226004i | \(-0.0725661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.22876 | 0.136562 | ||||||||
\(560\) | −2.17712 | + | 3.77089i | −0.0920003 | + | 0.159349i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.76013 | + | 15.1730i | 0.369524 | + | 0.640034i | ||||
\(563\) | 17.2288 | − | 29.8411i | 0.726106 | − | 1.25765i | −0.232412 | − | 0.972617i | \(-0.574662\pi\) |
0.958517 | − | 0.285034i | \(-0.0920050\pi\) | |||||||
\(564\) | 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 | \(-0.159575\pi\) |
−0.854672 | + | 0.519168i | \(0.826242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.645751 | − | 1.11847i | 0.0270239 | − | 0.0468067i | −0.852197 | − | 0.523221i | \(-0.824730\pi\) |
0.879221 | + | 0.476414i | \(0.158064\pi\) | |||||||
\(572\) | 0.531373 | + | 0.920365i | 0.0222178 | + | 0.0384824i | ||||
\(573\) | 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 | \(0.0174244\pi\) | |||||||
\(578\) | 7.14575 | − | 12.3768i | 0.297224 | − | 0.514807i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.5830 | 0.522481 | ||||||||
\(581\) | −7.16601 | −0.297296 | ||||||||
\(582\) | 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 | ||||
\(587\) | 38.2288 | 1.57787 | 0.788935 | − | 0.614477i | \(-0.210633\pi\) | ||||
0.788935 | + | 0.614477i | \(0.210633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29150 | 0.0532154 | ||||||||
\(590\) | −11.2288 | − | 19.4488i | −0.462281 | − | 0.800693i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.96863 | + | 3.40976i | −0.0809101 | + | 0.140140i | ||||
\(593\) | −12.5314 | − | 21.7050i | −0.514602 | − | 0.891316i | −0.999856 | − | 0.0169436i | \(-0.994606\pi\) |
0.485255 | − | 0.874373i | \(-0.338727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.16601 | −0.293778 | ||||||||
\(596\) | 7.06275 | 0.289301 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | + | 5.19615i | −0.122679 | + | 0.212486i | ||||
\(599\) | 10.9373 | − | 18.9439i | 0.446884 | − | 0.774026i | −0.551297 | − | 0.834309i | \(-0.685867\pi\) |
0.998181 | + | 0.0602830i | \(0.0192003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.87451 | −0.198835 | −0.0994177 | − | 0.995046i | \(-0.531698\pi\) | ||||
−0.0994177 | + | 0.995046i | \(0.531698\pi\) | |||||||
\(602\) | −6.61438 | − | 11.4564i | −0.269582 | − | 0.466930i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.61438 | − | 6.26029i | −0.147067 | − | 0.254727i | ||||
\(605\) | 6.82288 | − | 11.8176i | 0.277389 | − | 0.480452i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.2915 | − | 23.0216i | −0.539485 | − | 0.934416i | −0.998932 | − | 0.0462106i | \(-0.985285\pi\) |
0.459446 | − | 0.888206i | \(-0.348048\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.8118 | 0.842644 | ||||||||
\(611\) | 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 | ||||
\(617\) | −35.5203 | −1.42999 | −0.714996 | − | 0.699129i | \(-0.753571\pi\) | ||||
−0.714996 | + | 0.699129i | \(0.753571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.14575 | + | 1.98450i | −0.0460516 | + | 0.0797638i | −0.888132 | − | 0.459588i | \(-0.847997\pi\) |
0.842081 | + | 0.539351i | \(0.181331\pi\) | |||||||
\(620\) | −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 | ||||||||
\(625\) | 4.14575 | + | 7.18065i | 0.165830 | + | 0.287226i | ||||
\(626\) | −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 | ||||
\(635\) | −5.46863 | − | 9.47194i | −0.217016 | − | 0.375882i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.52026 | 0.179099 | ||||||||
\(638\) | −12.5830 | −0.498166 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.822876 | + | 1.42526i | −0.0325270 | + | 0.0563384i | ||||
\(641\) | −4.11438 | + | 7.12631i | −0.162508 | + | 0.281472i | −0.935768 | − | 0.352617i | \(-0.885292\pi\) |
0.773259 | + | 0.634090i | \(0.218625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.8745 | −1.37532 | −0.687658 | − | 0.726035i | \(-0.741361\pi\) | ||||
−0.687658 | + | 0.726035i | \(0.741361\pi\) | |||||||
\(644\) | 24.5830 | 0.968706 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64575 | + | 2.85052i | 0.0647512 | + | 0.112152i | ||||
\(647\) | 10.9373 | − | 18.9439i | 0.429988 | − | 0.744761i | −0.566884 | − | 0.823798i | \(-0.691851\pi\) |
0.996872 | + | 0.0790370i | \(0.0251845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2288 | + | 19.4488i | 0.440767 | + | 0.763431i | ||||
\(650\) | −1.47974 | −0.0580402 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | −0.0391630 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.41699 | + | 9.38251i | −0.211659 | + | 0.366605i | ||||
\(656\) | 2.46863 | + | 4.27579i | 0.0963837 | + | 0.166941i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.4686 | − | 25.0604i | 0.564046 | − | 0.976956i | ||||
\(659\) | 2.22876 | 0.0868200 | 0.0434100 | − | 0.999057i | \(-0.486178\pi\) | ||||
0.0434100 | + | 0.999057i | \(0.486178\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5830 | + | 33.9188i | −0.761691 | + | 1.31929i | 0.180288 | + | 0.983614i | \(0.442297\pi\) |
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(662\) | 0.0627461 | − | 0.108679i | 0.00243870 | − | 0.00422394i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.70850 | −0.105110 | ||||||||
\(665\) | −4.35425 | + | 7.54178i | −0.168851 | + | 0.292458i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.5203 | − | 61.5229i | −1.37535 | − | 2.38218i | ||||
\(668\) | −6.29150 | + | 10.8972i | −0.243426 | + | 0.421625i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.82288 | − | 11.8176i | −0.263591 | − | 0.456552i | ||||
\(671\) | −20.8118 | −0.803429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.7490 | −1.84059 | −0.920295 | − | 0.391226i | \(-0.872051\pi\) | ||||
−0.920295 | + | 0.391226i | \(0.872051\pi\) | |||||||
\(674\) | 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 | \(-0.0791657\pi\) |
−0.697788 | + | 0.716304i | \(0.745832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0627 | −0.769938 | ||||||||
\(680\) | −2.70850 | −0.103866 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.531373 | − | 0.920365i | 0.0203473 | − | 0.0352426i | ||||
\(683\) | −10.4059 | + | 18.0235i | −0.398170 | + | 0.689651i | −0.993500 | − | 0.113831i | \(-0.963688\pi\) |
0.595330 | + | 0.803481i | \(0.297021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.2915 | −0.584258 | ||||||||
\(686\) | −9.26013 | − | 16.0390i | −0.353553 | − | 0.612372i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.50000 | − | 4.33013i | −0.0953116 | − | 0.165085i | ||||
\(689\) | −1.93725 | + | 3.35542i | −0.0738035 | + | 0.127831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3745 | − | 21.4333i | −0.470748 | − | 0.815360i | 0.528692 | − | 0.848814i | \(-0.322683\pi\) |
−0.999440 | + | 0.0334536i | \(0.989349\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | −12.6144 | − | 21.8487i | −0.477461 | − | 0.826987i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.03137 | + | 5.25049i | 0.114575 | + | 0.198450i | ||||
\(701\) | −5.41699 | −0.204597 | −0.102299 | − | 0.994754i | \(-0.532620\pi\) | ||||
−0.102299 | + | 0.994754i | \(0.532620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.93725 | + | 6.81952i | −0.148496 | + | 0.257203i | ||||
\(704\) | 0.822876 | − | 1.42526i | 0.0310133 | − | 0.0537166i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | −18.0516 | + | 31.2663i | −0.678902 | + | 1.17589i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.90588 | + | 8.49723i | 0.184244 | + | 0.319120i | 0.943322 | − | 0.331880i | \(-0.107683\pi\) |
−0.759077 | + | 0.651000i | \(0.774350\pi\) | |||||||
\(710\) | −8.52026 | + | 14.7575i | −0.319760 | + | 0.553840i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.46863 | + | 9.47194i | 0.204945 | + | 0.354976i | ||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.74902 | −0.0654095 | ||||||||
\(716\) | −0.531373 | − | 0.920365i | −0.0198583 | − | 0.0343957i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.5830 | − | 26.9906i | 0.581553 | − | 1.00728i | ||||
\(719\) | −3.53137 | − | 6.11652i | −0.131698 | − | 0.228108i | 0.792633 | − | 0.609699i | \(-0.208710\pi\) |
−0.924331 | + | 0.381591i | \(0.875376\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.7915 | + | 27.3517i | 0.588106 | + | 1.01863i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.64575 | − | 11.5108i | 0.246987 | − | 0.427795i | ||||
\(725\) | 8.76013 | − | 15.1730i | 0.325343 | − | 0.563511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2288 | 0.935683 | 0.467841 | − | 0.883812i | \(-0.345032\pi\) | ||||
0.467841 | + | 0.883812i | \(0.345032\pi\) | |||||||
\(728\) | 1.70850 | 0.0633211 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.70850 | + | 15.0836i | 0.322316 | + | 0.558268i | ||||
\(731\) | 4.11438 | − | 7.12631i | 0.152176 | − | 0.263576i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.38562 | − | 7.59612i | −0.161987 | − | 0.280569i | 0.773594 | − | 0.633681i | \(-0.218457\pi\) |
−0.935581 | + | 0.353112i | \(0.885123\pi\) | |||||||
\(734\) | −1.87451 | −0.0691893 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.29150 | 0.342489 | ||||||||
\(737\) | 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 | ||||||||
\(742\) | 15.8745 | 0.582772 | ||||||||
\(743\) | −13.0627 | −0.479226 | −0.239613 | − | 0.970869i | \(-0.577021\pi\) | ||||
−0.239613 | + | 0.970869i | \(0.577021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.81176 | + | 10.0663i | −0.212926 | + | 0.368799i | ||||
\(746\) | 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 | ||||||||
\(751\) | −0.228757 | − | 0.396218i | −0.00834745 | − | 0.0144582i | 0.861822 | − | 0.507212i | \(-0.169324\pi\) |
−0.870169 | + | 0.492753i | \(0.835990\pi\) | |||||||
\(752\) | 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 | ||||
\(761\) | 9.29150 | + | 16.0934i | 0.336817 | + | 0.583384i | 0.983832 | − | 0.179093i | \(-0.0573164\pi\) |
−0.647015 | + | 0.762477i | \(0.723983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4373 | − | 19.8099i | 0.414056 | − | 0.717167i | ||||
\(764\) | 26.8118 | 0.970015 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.291503 | − | 0.504897i | 0.0105324 | − | 0.0182427i | ||||
\(767\) | −4.40588 | + | 7.63121i | −0.159087 | + | 0.275547i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4170 | 0.700195 | 0.350097 | − | 0.936713i | \(-0.386148\pi\) | ||||
0.350097 | + | 0.936713i | \(0.386148\pi\) | |||||||
\(770\) | 3.58301 | + | 6.20595i | 0.129123 | + | 0.223647i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | + | 6.06218i | 0.125968 | + | 0.218183i | ||||
\(773\) | −19.1660 | + | 33.1965i | −0.689353 | + | 1.19400i | 0.282694 | + | 0.959210i | \(0.408772\pi\) |
−0.972047 | + | 0.234785i | \(0.924561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.739870 | + | 1.28149i | 0.0265769 | + | 0.0460326i | ||||
\(776\) | −7.58301 | −0.272214 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.70850 | 0.312215 | ||||||||
\(779\) | 4.93725 | + | 8.55157i | 0.176895 | + | 0.306392i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.52026 | − | 14.7575i | 0.304879 | − | 0.528066i | ||||
\(782\) | 7.64575 | + | 13.2428i | 0.273412 | + | 0.473563i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.50000 | − | 6.06218i | −0.125000 | − | 0.216506i | ||||
\(785\) | −6.58301 | −0.234958 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1458 | − | 19.3050i | 0.397303 | − | 0.688149i | −0.596089 | − | 0.802918i | \(-0.703279\pi\) |
0.993392 | + | 0.114769i | \(0.0366128\pi\) | |||||||
\(788\) | −7.64575 | + | 13.2428i | −0.272369 | + | 0.471756i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.0627 | −0.891692 | ||||||||
\(791\) | 20.2288 | 0.719252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.08301 | − | 7.07197i | −0.144992 | − | 0.251133i | ||||
\(794\) | 5.67712 | − | 9.83307i | 0.201474 | − | 0.348963i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.9686 | − | 18.9982i | −0.388773 | − | 0.673374i | ||||
\(797\) | 32.8118 | 1.16225 | 0.581126 | − | 0.813814i | \(-0.302612\pi\) | ||||
0.581126 | + | 0.813814i | \(0.302612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 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 | ||||
\(806\) | 0.416995 | 0.0146880 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.82288 | + | 11.8176i | −0.240028 | + | 0.415741i | ||||
\(809\) | −18.2915 | + | 31.6818i | −0.643095 | + | 1.11387i | 0.341643 | + | 0.939830i | \(0.389017\pi\) |
−0.984738 | + | 0.174043i | \(0.944317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7085 | −0.656944 | −0.328472 | − | 0.944514i | \(-0.606534\pi\) | ||||
−0.328472 | + | 0.944514i | \(0.606534\pi\) | |||||||
\(812\) | −10.1144 | + | 17.5186i | −0.354945 | + | 0.614783i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.23987 | + | 5.61162i | 0.113557 | + | 0.196687i | ||||
\(815\) | 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 | \(-0.163428\pi\) |
−0.860894 | + | 0.508785i | \(0.830095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5516 | + | 20.0080i | −0.402665 | + | 0.697436i | −0.994047 | − | 0.108956i | \(-0.965249\pi\) |
0.591382 | + | 0.806392i | \(0.298583\pi\) | |||||||
\(824\) | 5.96863 | + | 10.3380i | 0.207927 | + | 0.360140i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.1033 | 1.25619 | ||||||||
\(827\) | 19.7490 | 0.686741 | 0.343370 | − | 0.939200i | \(-0.388431\pi\) | ||||
0.343370 | + | 0.939200i | \(0.388431\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35425 | − | 16.2020i | 0.324886 | − | 0.562720i | −0.656603 | − | 0.754236i | \(-0.728007\pi\) |
0.981489 | + | 0.191517i | \(0.0613406\pi\) | |||||||
\(830\) | 2.22876 | − | 3.86032i | 0.0773613 | − | 0.133994i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.645751 | 0.0223874 | ||||||||
\(833\) | 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 | ||||
\(839\) | −38.7085 | −1.33637 | −0.668183 | − | 0.743997i | \(-0.732928\pi\) | ||||
−0.668183 | + | 0.743997i | \(0.732928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.4575 | 1.01578 | ||||||||
\(842\) | 12.6458 | + | 21.9031i | 0.435801 | + | 0.754830i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.43725 | − | 14.6138i | 0.290422 | − | 0.503026i | ||||
\(845\) | 10.3542 | + | 17.9341i | 0.356197 | + | 0.616951i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9686 | + | 18.9982i | 0.376886 | + | 0.652787i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.88562 | + | 3.26599i | −0.0646763 | + | 0.112023i | ||||
\(851\) | −18.2915 | + | 31.6818i | −0.627025 | + | 1.08604i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.1255 | 0.552126 | 0.276063 | − | 0.961139i | \(-0.410970\pi\) | ||||
0.276063 | + | 0.961139i | \(0.410970\pi\) | |||||||
\(854\) | −16.7288 | + | 28.9751i | −0.572446 | + | 0.991506i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | −10.4059 | + | 18.0235i | −0.355458 | + | 0.615672i | −0.987196 | − | 0.159510i | \(-0.949008\pi\) |
0.631738 | + | 0.775182i | \(0.282342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50000 | + | 6.06218i | 0.119418 | + | 0.206839i | 0.919537 | − | 0.393003i | \(-0.128564\pi\) |
−0.800119 | + | 0.599841i | \(0.795230\pi\) | |||||||
\(860\) | 8.22876 | 0.280598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.81176 | −0.300130 | ||||||||
\(863\) | 6.58301 | + | 11.4021i | 0.224088 | + | 0.388132i | 0.956045 | − | 0.293218i | \(-0.0947263\pi\) |
−0.731957 | + | 0.681350i | \(0.761393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.41699 | + | 9.38251i | −0.184183 | + | 0.319015i | ||||
\(866\) | 9.50000 | + | 16.4545i | 0.322823 | + | 0.559146i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.854249 | − | 1.47960i | −0.0289951 | − | 0.0502210i | ||||
\(869\) | 25.0627 | 0.850195 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.67712 | + | 4.63692i | −0.0907109 | + | 0.157116i | ||||
\(872\) | 4.32288 | − | 7.48744i | 0.146391 | − | 0.253557i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.5830 | 0.628580 | ||||||||
\(875\) | −31.7490 | −1.07331 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.6771 | − | 18.4933i | −0.360541 | − | 0.624475i | 0.627509 | − | 0.778609i | \(-0.284075\pi\) |
−0.988050 | + | 0.154134i | \(0.950741\pi\) | |||||||
\(878\) | 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 | \(-0.344413\pi\) | ||||
0.469558 | + | 0.882902i | \(0.344413\pi\) | |||||||
\(882\) | 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 | ||||
\(887\) | 7.93725 | + | 13.7477i | 0.266507 | + | 0.461603i | 0.967957 | − | 0.251115i | \(-0.0807972\pi\) |
−0.701450 | + | 0.712718i | \(0.747464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.5830 | 0.589715 | ||||||||
\(890\) | −18.0000 | −0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.93725 | + | 15.4798i | −0.299241 | + | 0.518301i | ||||
\(893\) | 10.9373 | − | 18.9439i | 0.366001 | − | 0.633933i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.74902 | 0.0584631 | ||||||||
\(896\) | −1.32288 | − | 2.29129i | −0.0441942 | − | 0.0765466i | ||||
\(897\) | 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 | ||||
\(902\) | 8.12549 | 0.270549 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.64575 | 0.254294 | ||||||||
\(905\) | 10.9373 | + | 18.9439i | 0.363567 | + | 0.629716i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.8542 | + | 22.2642i | −0.426818 | + | 0.739271i | −0.996588 | − | 0.0825332i | \(-0.973699\pi\) |
0.569770 | + | 0.821804i | \(0.307032\pi\) | |||||||
\(908\) | −3.00000 | − | 5.19615i | −0.0995585 | − | 0.172440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.40588 | + | 2.43506i | −0.0466045 | + | 0.0807214i | ||||
\(911\) | 13.0627 | 0.432788 | 0.216394 | − | 0.976306i | \(-0.430570\pi\) | ||||
0.216394 | + | 0.976306i | \(0.430570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.22876 | + | 3.86032i | −0.0737611 | + | 0.127758i | ||||
\(914\) | −1.14575 | + | 1.98450i | −0.0378981 | + | 0.0656414i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.6458 | −0.483909 | ||||||||
\(917\) | −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 | \(-0.531289\pi\) | |||||||
\(920\) | −7.64575 | + | 13.2428i | −0.252073 | + | 0.436603i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.11438 | + | 1.93016i | 0.0367001 | + | 0.0635664i | ||||
\(923\) | 6.68627 | 0.220081 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.02223 | −0.296649 | ||||||||
\(926\) | −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 | \(-0.161117\pi\) |
−0.857177 | + | 0.515022i | \(0.827784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | − | 12.1244i | −0.229416 | − | 0.397360i | ||||
\(932\) | −8.70850 | −0.285256 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.1144 | − | 22.7148i | 0.429116 | − | 0.743250i | ||||
\(935\) | −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 | \(0.400925\pi\) | |||||||
\(938\) | 21.9373 | 0.716277 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.00000 | + | 15.5885i | 0.293548 | + | 0.508439i | ||||
\(941\) | −7.69738 | + | 13.3323i | −0.250928 | + | 0.434619i | −0.963781 | − | 0.266693i | \(-0.914069\pi\) |
0.712854 | + | 0.701313i | \(0.247402\pi\) | |||||||
\(942\) | 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 | −0.936410 | − | 0.350908i | \(-0.885873\pi\) |
0.164309 | − | 0.986409i | \(-0.447460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.41699 | − | 5.91841i | 0.110920 | − | 0.192120i | ||||
\(950\) | 2.29150 | + | 3.96900i | 0.0743462 | + | 0.128771i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.17712 | − | 3.77089i | 0.0705610 | − | 0.122215i | ||||
\(953\) | −32.3320 | −1.04734 | −0.523668 | − | 0.851922i | \(-0.675437\pi\) | ||||
−0.523668 | + | 0.851922i | \(0.675437\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.0627 | + | 38.2138i | −0.713934 | + | 1.23657i | ||||
\(956\) | −2.46863 | + | 4.27579i | −0.0798411 | + | 0.138289i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.64575 | −0.0531718 | ||||||||
\(959\) | 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 | ||||
\(965\) | −11.5203 | −0.370850 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.9373 | 1.67019 | 0.835095 | − | 0.550106i | \(-0.185413\pi\) | ||||
0.835095 | + | 0.550106i | \(0.185413\pi\) | |||||||
\(968\) | 4.14575 | + | 7.18065i | 0.133249 | + | 0.230795i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.23987 | − | 10.8078i | 0.200350 | − | 0.347017i | ||||
\(971\) | −10.9373 | − | 18.9439i | −0.350993 | − | 0.607938i | 0.635431 | − | 0.772158i | \(-0.280823\pi\) |
−0.986424 | + | 0.164220i | \(0.947489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.8118 | −1.66101 | ||||||||
\(974\) | −7.87451 | −0.252316 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.32288 | + | 10.9515i | −0.202390 | + | 0.350550i | ||||
\(977\) | 10.0627 | − | 17.4292i | 0.321936 | − | 0.557609i | −0.658952 | − | 0.752185i | \(-0.729000\pi\) |
0.980887 | + | 0.194576i | \(0.0623332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 11.5203 | 0.368001 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.8745 | + | 32.6916i | 0.602310 | + | 1.04323i | ||||
\(983\) | 13.4059 | − | 23.2197i | 0.427581 | − | 0.740592i | −0.569076 | − | 0.822285i | \(-0.692699\pi\) |
0.996658 | + | 0.0816923i | \(0.0260325\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.5830 | − | 21.7944i | −0.400928 | − | 0.694427i | ||||
\(986\) | −12.5830 | −0.400725 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.29150 | 0.0410882 | ||||||||
\(989\) | −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 | ||||||||
\(994\) | −13.6974 | − | 23.7246i | −0.434455 | − | 0.752497i | ||||
\(995\) | 36.1033 | 1.14455 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.8431 | − | 48.2257i | 0.881801 | − | 1.52732i | 0.0324640 | − | 0.999473i | \(-0.489665\pi\) |
0.849337 | − | 0.527851i | \(-0.177002\pi\) | |||||||
\(998\) | −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 | 378.2.g.g.109.1 | ✓ | 4 | |
3.2 | odd | 2 | 378.2.g.h.109.2 | yes | 4 | ||
7.2 | even | 3 | inner | 378.2.g.g.163.1 | yes | 4 | |
7.3 | odd | 6 | 2646.2.a.bo.1.1 | 2 | |||
7.4 | even | 3 | 2646.2.a.bl.1.2 | 2 | |||
9.2 | odd | 6 | 1134.2.h.t.109.1 | 4 | |||
9.4 | even | 3 | 1134.2.e.t.865.1 | 4 | |||
9.5 | odd | 6 | 1134.2.e.q.865.2 | 4 | |||
9.7 | even | 3 | 1134.2.h.q.109.2 | 4 | |||
21.2 | odd | 6 | 378.2.g.h.163.2 | yes | 4 | ||
21.11 | odd | 6 | 2646.2.a.bi.1.1 | 2 | |||
21.17 | even | 6 | 2646.2.a.bf.1.2 | 2 | |||
63.2 | odd | 6 | 1134.2.e.q.919.2 | 4 | |||
63.16 | even | 3 | 1134.2.e.t.919.1 | 4 | |||
63.23 | odd | 6 | 1134.2.h.t.541.1 | 4 | |||
63.58 | even | 3 | 1134.2.h.q.541.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.g.109.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
378.2.g.g.163.1 | yes | 4 | 7.2 | even | 3 | inner | |
378.2.g.h.109.2 | yes | 4 | 3.2 | odd | 2 | ||
378.2.g.h.163.2 | yes | 4 | 21.2 | odd | 6 | ||
1134.2.e.q.865.2 | 4 | 9.5 | odd | 6 | |||
1134.2.e.q.919.2 | 4 | 63.2 | odd | 6 | |||
1134.2.e.t.865.1 | 4 | 9.4 | even | 3 | |||
1134.2.e.t.919.1 | 4 | 63.16 | even | 3 | |||
1134.2.h.q.109.2 | 4 | 9.7 | even | 3 | |||
1134.2.h.q.541.2 | 4 | 63.58 | even | 3 | |||
1134.2.h.t.109.1 | 4 | 9.2 | odd | 6 | |||
1134.2.h.t.541.1 | 4 | 63.23 | odd | 6 | |||
2646.2.a.bf.1.2 | 2 | 21.17 | even | 6 | |||
2646.2.a.bi.1.1 | 2 | 21.11 | odd | 6 | |||
2646.2.a.bl.1.2 | 2 | 7.4 | even | 3 | |||
2646.2.a.bo.1.1 | 2 | 7.3 | odd | 6 |