Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [440,2,Mod(81,440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(440, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("440.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.y (of order \(5\), degree \(4\), 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: | \(3.51341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 201.3 | ||
Root | \(-2.19470 - 1.59454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 440.201 |
Dual form | 440.2.y.c.81.3 |
$q$-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 \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(221\) | \(321\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.529284 | + | 1.62897i | 0.305582 | + | 0.940486i | 0.979459 | + | 0.201642i | \(0.0646279\pi\) |
−0.673877 | + | 0.738844i | \(0.735372\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14492 | − | 3.52372i | 0.432741 | − | 1.33184i | −0.462643 | − | 0.886545i | \(-0.653099\pi\) |
0.895384 | − | 0.445295i | \(-0.146901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0536500 | − | 0.0389790i | 0.0178833 | − | 0.0129930i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.68927 | + | 1.94109i | 0.810845 | + | 0.585261i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.952617 | − | 0.692117i | 0.264208 | − | 0.191959i | −0.447792 | − | 0.894138i | \(-0.647789\pi\) |
0.712000 | + | 0.702179i | \(0.247789\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.529284 | + | 1.62897i | −0.136661 | + | 0.420598i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.36891 | + | 3.17420i | 1.05962 | + | 0.769856i | 0.974017 | − | 0.226473i | \(-0.0727196\pi\) |
0.0855991 | + | 0.996330i | \(0.472720\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.18895 | − | 3.65921i | −0.272764 | − | 0.839480i | −0.989802 | − | 0.142447i | \(-0.954503\pi\) |
0.717039 | − | 0.697033i | \(-0.245497\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.34602 | 1.38481 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.68237 | −1.81040 | −0.905200 | − | 0.424986i | \(-0.860279\pi\) | ||||
−0.905200 | + | 0.424986i | \(0.860279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.24895 | + | 3.08704i | 0.817710 | + | 0.594101i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.12479 | + | 6.53944i | −0.394564 | + | 1.21434i | 0.534736 | + | 0.845019i | \(0.320411\pi\) |
−0.929301 | + | 0.369324i | \(0.879589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.08327 | + | 5.14630i | −1.27219 | + | 0.924302i | −0.999288 | − | 0.0377385i | \(-0.987985\pi\) |
−0.272905 | + | 0.962041i | \(0.587985\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73859 | + | 5.40813i | −0.302650 | + | 0.941434i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.99745 | − | 2.17778i | 0.506662 | − | 0.368111i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.696735 | − | 2.14433i | 0.114543 | − | 0.352526i | −0.877309 | − | 0.479926i | \(-0.840663\pi\) |
0.991851 | + | 0.127401i | \(0.0406634\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.63164 | + | 1.18546i | 0.261272 | + | 0.189825i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.493602 | + | 1.51915i | 0.0770877 | + | 0.237251i | 0.982173 | − | 0.187978i | \(-0.0601934\pi\) |
−0.905086 | + | 0.425229i | \(0.860193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.11979 | 0.628262 | 0.314131 | − | 0.949380i | \(-0.398287\pi\) | ||||
0.314131 | + | 0.949380i | \(0.398287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0663151 | 0.00988567 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.91833 | − | 12.0594i | −0.571547 | − | 1.75904i | −0.647648 | − | 0.761940i | \(-0.724247\pi\) |
0.0761009 | − | 0.997100i | \(-0.475753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.44260 | − | 3.95428i | −0.777514 | − | 0.564897i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.85828 | + | 8.79688i | −0.400239 | + | 1.23181i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0152 | − | 7.27650i | 1.37570 | − | 0.999504i | 0.378432 | − | 0.925629i | \(-0.376464\pi\) |
0.997268 | − | 0.0738747i | \(-0.0235365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.03472 | + | 3.15109i | 0.139521 | + | 0.424893i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.33145 | − | 3.87353i | 0.706168 | − | 0.513061i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.121753 | + | 0.374716i | −0.0158508 | + | 0.0487838i | −0.958669 | − | 0.284523i | \(-0.908165\pi\) |
0.942818 | + | 0.333307i | \(0.108165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.45692 | − | 1.05851i | −0.186539 | − | 0.135529i | 0.490596 | − | 0.871387i | \(-0.336779\pi\) |
−0.677136 | + | 0.735858i | \(0.736779\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0759258 | − | 0.233676i | −0.00956575 | − | 0.0294404i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17750 | 0.146051 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.3809 | −1.75691 | −0.878455 | − | 0.477826i | \(-0.841425\pi\) | ||||
−0.878455 | + | 0.477826i | \(0.841425\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.59544 | − | 14.1433i | −0.553227 | − | 1.70266i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.54603 | + | 4.02943i | 0.658192 | + | 0.478205i | 0.866052 | − | 0.499954i | \(-0.166650\pi\) |
−0.207860 | + | 0.978159i | \(0.566650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.10719 | − | 9.56296i | 0.363670 | − | 1.11926i | −0.587140 | − | 0.809485i | \(-0.699746\pi\) |
0.950810 | − | 0.309775i | \(-0.100254\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.38568 | + | 1.00676i | −0.160005 | + | 0.116250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.91887 | − | 7.25381i | 1.13036 | − | 0.826649i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.901110 | − | 0.654695i | 0.101383 | − | 0.0736589i | −0.535939 | − | 0.844257i | \(-0.680042\pi\) |
0.637322 | + | 0.770598i | \(0.280042\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.71832 | + | 8.36612i | −0.302035 | + | 0.929569i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.0140132 | − | 0.0101812i | −0.00153814 | − | 0.00111753i | 0.587016 | − | 0.809575i | \(-0.300303\pi\) |
−0.588554 | + | 0.808458i | \(0.700303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.66878 | + | 5.13596i | 0.181004 | + | 0.557073i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.7772 | −1.26265 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.49434 | −0.900399 | −0.450199 | − | 0.892928i | \(-0.648647\pi\) | ||||
−0.450199 | + | 0.892928i | \(0.648647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.34815 | − | 4.14917i | −0.141324 | − | 0.434951i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.1322 | − | 8.81458i | −1.25805 | − | 0.914029i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.18895 | − | 3.65921i | 0.121984 | − | 0.375427i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.50719 | + | 6.18083i | −0.863774 | + | 0.627569i | −0.928909 | − | 0.370308i | \(-0.879252\pi\) |
0.0651351 | + | 0.997876i | \(0.479252\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.219941 | 0.000685401i | 0.0221049 | 6.88853e-5i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.80762 | + | 4.21949i | −0.577880 | + | 0.419855i | −0.837959 | − | 0.545733i | \(-0.816251\pi\) |
0.260079 | + | 0.965587i | \(0.416251\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.15886 | + | 3.56662i | −0.114186 | + | 0.351429i | −0.991776 | − | 0.127982i | \(-0.959150\pi\) |
0.877590 | + | 0.479412i | \(0.159150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.13404 | + | 3.73010i | 0.501031 | + | 0.364020i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.96265 | − | 6.04042i | −0.189737 | − | 0.583950i | 0.810261 | − | 0.586069i | \(-0.199325\pi\) |
−0.999998 | + | 0.00211949i | \(0.999325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.32407 | 0.126823 | 0.0634115 | − | 0.997987i | \(-0.479802\pi\) | ||||
0.0634115 | + | 0.997987i | \(0.479802\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.86182 | 0.366548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.64758 | + | 5.07074i | 0.154992 | + | 0.477015i | 0.998160 | − | 0.0606344i | \(-0.0193124\pi\) |
−0.843168 | + | 0.537649i | \(0.819312\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.02419 | − | 5.10337i | −0.655009 | − | 0.475892i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0241299 | − | 0.0742642i | 0.00223081 | − | 0.00686572i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.1870 | − | 11.7606i | 1.48386 | − | 1.07809i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.46432 | + | 10.4402i | 0.314938 | + | 0.949112i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.21339 | + | 1.60813i | −0.199575 | + | 0.145000i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8445 | − | 8.60553i | −1.05103 | − | 0.763617i | −0.0786209 | − | 0.996905i | \(-0.525052\pi\) |
−0.972408 | + | 0.233288i | \(0.925052\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.18054 | + | 6.71101i | 0.191986 | + | 0.590871i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.93922 | 0.518912 | 0.259456 | − | 0.965755i | \(-0.416457\pi\) | ||||
0.259456 | + | 0.965755i | \(0.416457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.2553 | −1.23609 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.62295 | + | 4.99493i | 0.139682 | + | 0.429896i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.9490 | − | 8.68146i | −1.02087 | − | 0.741707i | −0.0544107 | − | 0.998519i | \(-0.517328\pi\) |
−0.966461 | + | 0.256812i | \(0.917328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.399410 | − | 1.22926i | 0.0338775 | − | 0.104264i | −0.932688 | − | 0.360684i | \(-0.882543\pi\) |
0.966565 | + | 0.256420i | \(0.0825431\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.5704 | − | 12.7657i | 1.47970 | − | 1.07506i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.90530 | − | 0.0121701i | 0.326578 | − | 0.00101771i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.56278 | + | 4.04160i | −0.461964 | + | 0.335636i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.56072 | − | 10.9588i | 0.293683 | − | 0.903864i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.3404 | − | 14.0516i | −1.58443 | − | 1.15115i | −0.911390 | − | 0.411543i | \(-0.864990\pi\) |
−0.673036 | − | 0.739610i | \(-0.735010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.55881 | + | 7.87521i | 0.208233 | + | 0.640875i | 0.999565 | + | 0.0294888i | \(0.00938793\pi\) |
−0.791332 | + | 0.611387i | \(0.790612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.358119 | 0.0289522 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.75541 | −0.703251 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.46115 | − | 7.57463i | −0.196421 | − | 0.604521i | −0.999957 | − | 0.00926547i | \(-0.997051\pi\) |
0.803536 | − | 0.595256i | \(-0.202949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.1541 | + | 12.4632i | 1.36041 | + | 0.988395i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.94066 | + | 30.5942i | −0.783434 | + | 2.41116i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.30709 | − | 2.40274i | 0.259031 | − | 0.188197i | −0.450689 | − | 0.892681i | \(-0.648822\pi\) |
0.709720 | + | 0.704484i | \(0.248822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.58537 | + | 3.35335i | −0.356970 | + | 0.261058i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.22174 | − | 2.34073i | 0.249306 | − | 0.181131i | −0.456113 | − | 0.889922i | \(-0.650759\pi\) |
0.705419 | + | 0.708790i | \(0.250759\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.58877 | + | 11.0451i | −0.276059 | + | 0.849622i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.206420 | − | 0.149973i | −0.0157853 | − | 0.0114687i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.45640 | + | 16.7931i | 0.414843 | + | 1.27675i | 0.912392 | + | 0.409319i | \(0.134234\pi\) |
−0.497549 | + | 0.867436i | \(0.665766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.70505 | 0.280076 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.674842 | −0.0507243 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.69018 | + | 11.3572i | 0.275817 | + | 0.848877i | 0.989002 | + | 0.147902i | \(0.0472519\pi\) |
−0.713185 | + | 0.700976i | \(0.752748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.834670 | + | 0.606423i | 0.0620405 | + | 0.0450751i | 0.618373 | − | 0.785885i | \(-0.287792\pi\) |
−0.556333 | + | 0.830960i | \(0.687792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.953162 | − | 2.93353i | 0.0704598 | − | 0.216853i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.82408 | − | 1.32527i | 0.134109 | − | 0.0974357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.58776 | + | 17.0167i | 0.408617 | + | 1.24439i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.7426 | − | 11.4376i | 1.14510 | − | 0.831967i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.87606 | − | 18.0846i | 0.425176 | − | 1.30856i | −0.477649 | − | 0.878551i | \(-0.658511\pi\) |
0.902825 | − | 0.430008i | \(-0.141489\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.37576 | − | 3.17918i | −0.314974 | − | 0.228842i | 0.419054 | − | 0.907961i | \(-0.362362\pi\) |
−0.734028 | + | 0.679119i | \(0.762362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.623232 | + | 1.91811i | 0.0446306 | + | 0.137359i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.07618 | 0.290416 | 0.145208 | − | 0.989401i | \(-0.453615\pi\) | ||||
0.145208 | + | 0.989401i | \(0.453615\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0711 | −0.855700 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.61160 | − | 23.4261i | −0.536881 | − | 1.65235i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.6104 | + | 14.9743i | 1.44657 | + | 1.05099i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.493602 | + | 1.51915i | −0.0344746 | + | 0.106102i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.465810 | + | 0.338431i | −0.0323760 | + | 0.0235225i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.90546 | − | 12.1485i | 0.270146 | − | 0.840326i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.53429 | − | 5.47398i | 0.518682 | − | 0.376844i | −0.297425 | − | 0.954745i | \(-0.596128\pi\) |
0.816107 | + | 0.577901i | \(0.196128\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.62839 | + | 11.1670i | −0.248613 | + | 0.765152i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.33298 | + | 2.42155i | 0.227307 | + | 0.165148i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0243 | + | 30.8516i | 0.680492 | + | 2.09434i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.2224 | 1.16378 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.35881 | 0.427740 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.46586 | − | 4.51147i | −0.0981616 | − | 0.302110i | 0.889903 | − | 0.456150i | \(-0.150772\pi\) |
−0.988065 | + | 0.154039i | \(0.950772\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0536500 | + | 0.0389790i | 0.00357667 | + | 0.00259860i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.08627 | − | 3.34318i | 0.0720980 | − | 0.221895i | −0.908514 | − | 0.417855i | \(-0.862782\pi\) |
0.980612 | + | 0.195960i | \(0.0627822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.38320 | − | 5.36421i | 0.487895 | − | 0.354477i | −0.316479 | − | 0.948600i | \(-0.602501\pi\) |
0.804374 | + | 0.594123i | \(0.202501\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.0661 | + | 12.3182i | 1.12287 | + | 0.810478i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.4142 | − | 12.6522i | 1.14084 | − | 0.828870i | 0.153606 | − | 0.988132i | \(-0.450911\pi\) |
0.987236 | + | 0.159262i | \(0.0509114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.91833 | − | 12.0594i | 0.255603 | − | 0.786667i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.54342 | + | 1.12136i | 0.100256 | + | 0.0728403i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.49419 | + | 10.7540i | 0.226020 | + | 0.695619i | 0.998186 | + | 0.0601983i | \(0.0191733\pi\) |
−0.772166 | + | 0.635421i | \(0.780827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.1144 | −1.68218 | −0.841089 | − | 0.540897i | \(-0.818085\pi\) | ||||
−0.841089 | + | 0.540897i | \(0.818085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.689039 | 0.0442019 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.07889 | − | 6.39816i | −0.132815 | − | 0.408764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.66521 | − | 2.66293i | −0.233212 | − | 0.169438i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.00916785 | − | 0.0282158i | 0.000580989 | − | 0.00178810i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00802 | − | 2.18545i | 0.189865 | − | 0.137945i | −0.488792 | − | 0.872400i | \(-0.662562\pi\) |
0.678657 | + | 0.734456i | \(0.262562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.3492 | − | 16.8533i | −1.46795 | − | 1.05956i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.48307 | + | 5.43677i | −0.468608 | + | 0.340464i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.19179 | + | 6.74564i | −0.136720 | + | 0.420781i | −0.995854 | − | 0.0909703i | \(-0.971003\pi\) |
0.859133 | + | 0.511752i | \(0.171003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.75830 | − | 4.91019i | −0.419940 | − | 0.305104i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.140906 | + | 0.433664i | 0.00872185 | + | 0.0268431i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3578 | 1.44030 | 0.720151 | − | 0.693817i | \(-0.244073\pi\) | ||||
0.720151 | + | 0.693817i | \(0.244073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.3795 | 0.760468 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.49592 | − | 13.8370i | −0.275146 | − | 0.846813i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.8194 | + | 10.0404i | 0.842585 | + | 0.612174i | 0.923092 | − | 0.384580i | \(-0.125654\pi\) |
−0.0805064 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.47767 | + | 26.0916i | −0.514982 | + | 1.58495i | 0.268334 | + | 0.963326i | \(0.413527\pi\) |
−0.783315 | + | 0.621624i | \(0.786473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.04532 | − | 4.39218i | 0.365880 | − | 0.265827i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.01506 | + | 3.15748i | −0.0612103 | + | 0.190403i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5985 | − | 14.2391i | 1.17756 | − | 0.855546i | 0.185664 | − | 0.982613i | \(-0.440556\pi\) |
0.991894 | + | 0.127067i | \(0.0405565\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.179420 | + | 0.552198i | −0.0107416 | + | 0.0330592i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8855 | + | 10.0884i | 0.828338 | + | 0.601823i | 0.919089 | − | 0.394051i | \(-0.128927\pi\) |
−0.0907503 | + | 0.995874i | \(0.528927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.43047 | + | 4.40252i | 0.0850324 | + | 0.261703i | 0.984528 | − | 0.175227i | \(-0.0560659\pi\) |
−0.899496 | + | 0.436930i | \(0.856066\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.59004 | 0.390360 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.91819 | 0.349340 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.75855 | + | 11.5676i | 0.221091 | + | 0.680449i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5711 | − | 10.5865i | −0.854174 | − | 0.620594i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.71701 | + | 17.5951i | −0.333991 | + | 1.02792i | 0.633226 | + | 0.773967i | \(0.281730\pi\) |
−0.967217 | + | 0.253952i | \(0.918270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.318752 | + | 0.231587i | −0.0185585 | + | 0.0134835i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.43432 | + | 16.5495i | 0.315331 | + | 0.960298i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.27098 | + | 6.00922i | −0.478323 | + | 0.347522i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.71685 | − | 14.5170i | 0.271874 | − | 0.836744i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.94730 | − | 7.22714i | −0.571458 | − | 0.415188i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.556493 | − | 1.71271i | −0.0318647 | − | 0.0980695i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.2021 | −1.55250 | −0.776252 | − | 0.630422i | \(-0.782882\pi\) | ||||
−0.776252 | + | 0.630422i | \(0.782882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.42328 | −0.365408 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.96884 | + | 30.6809i | 0.565281 | + | 1.73976i | 0.667115 | + | 0.744955i | \(0.267529\pi\) |
−0.101834 | + | 0.994801i | \(0.532471\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.235220 | + | 0.170898i | 0.0132954 | + | 0.00965970i | 0.594413 | − | 0.804160i | \(-0.297384\pi\) |
−0.581118 | + | 0.813820i | \(0.697384\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0759258 | − | 0.233676i | 0.00427793 | − | 0.0131661i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4735 | + | 13.4218i | −1.03758 | + | 0.753844i | −0.969811 | − | 0.243857i | \(-0.921587\pi\) |
−0.0677665 | + | 0.997701i | \(0.521587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.4078 | + | 13.4619i | −1.03064 | + | 0.753721i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.80087 | − | 6.39420i | 0.491216 | − | 0.356890i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42065 | − | 19.7607i | 0.357254 | − | 1.09952i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.952617 | + | 0.692117i | 0.0528417 | + | 0.0383917i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.700810 | + | 2.15687i | 0.0387549 | + | 0.119275i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −46.9800 | −2.59009 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5262 | −0.798433 | −0.399217 | − | 0.916857i | \(-0.630718\pi\) | ||||
−0.399217 | + | 0.916857i | \(0.630718\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0462040 | − | 0.142201i | −0.00253197 | − | 0.00779259i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.6344 | − | 8.45289i | −0.635656 | − | 0.461831i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.33684 | − | 13.3474i | 0.236243 | − | 0.727081i | −0.760711 | − | 0.649090i | \(-0.775150\pi\) |
0.996954 | − | 0.0779903i | \(-0.0248503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.38804 | + | 5.36773i | −0.401263 | + | 0.291535i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.0383 | + | 0.0904916i | −1.57251 | + | 0.00490040i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.817029 | − | 0.593607i | 0.0441154 | − | 0.0320517i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.59544 | − | 14.1433i | 0.247410 | − | 0.761451i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.0640 | + | 16.0304i | 1.18446 | + | 0.860558i | 0.992667 | − | 0.120878i | \(-0.0385711\pi\) |
0.191789 | + | 0.981436i | \(0.438571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.69815 | − | 23.6925i | −0.412073 | − | 1.26823i | −0.914843 | − | 0.403809i | \(-0.867686\pi\) |
0.502771 | − | 0.864420i | \(-0.332314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.18421 | 0.330089 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2916 | −1.18646 | −0.593232 | − | 0.805031i | \(-0.702148\pi\) | ||||
−0.593232 | + | 0.805031i | \(0.702148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.11839 | + | 6.51975i | 0.112433 | + | 0.346032i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.7252 | + | 20.1435i | 1.46737 | + | 1.06611i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.577219 | − | 1.77650i | 0.0304645 | − | 0.0937599i | −0.934668 | − | 0.355521i | \(-0.884303\pi\) |
0.965133 | + | 0.261761i | \(0.0843033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.39510 | − | 2.46669i | 0.178690 | − | 0.129826i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.1732 | + | 11.1691i | −0.796387 | + | 0.586227i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.13474 | − | 5.91023i | 0.425792 | − | 0.309356i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.796316 | − | 2.45081i | 0.0415674 | − | 0.127931i | −0.928119 | − | 0.372283i | \(-0.878575\pi\) |
0.969687 | + | 0.244352i | \(0.0785751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0856968 | + | 0.0622623i | 0.00446120 | + | 0.00324125i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.1736 | − | 43.6219i | −0.735858 | − | 2.26474i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.12031 | 0.368675 | 0.184338 | − | 0.982863i | \(-0.440986\pi\) | ||||
0.184338 | + | 0.982863i | \(0.440986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.71280 | −0.0884486 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.50194 | + | 7.70018i | 0.128857 | + | 0.396580i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0912 | + | 16.7768i | 1.18612 | + | 0.861765i | 0.992849 | − | 0.119381i | \(-0.0380909\pi\) |
0.193269 | + | 0.981146i | \(0.438091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.74904 | − | 23.8491i | 0.396995 | − | 1.22183i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.54866 | − | 5.48442i | 0.385718 | − | 0.280241i | −0.377980 | − | 0.925814i | \(-0.623381\pi\) |
0.763699 | + | 0.645573i | \(0.223381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.2882 | − | 0.0382936i | 0.626265 | − | 0.00195162i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.221027 | − | 0.160585i | 0.0112354 | − | 0.00816301i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.137494 | − | 0.423163i | 0.00697123 | − | 0.0214552i | −0.947510 | − | 0.319725i | \(-0.896409\pi\) |
0.954482 | + | 0.298270i | \(0.0964095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.9325 | − | 27.5596i | −1.91833 | − | 1.39375i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.14354 | + | 9.67481i | 0.158570 | + | 0.488030i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.11383 | 0.0560431 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66941 | 0.0837850 | 0.0418925 | − | 0.999122i | \(-0.486661\pi\) | ||||
0.0418925 | + | 0.999122i | \(0.486661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.54510 | − | 23.2214i | −0.377727 | − | 1.16252i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.3906 | − | 19.9004i | −1.36782 | − | 0.993780i | −0.997904 | − | 0.0647154i | \(-0.979386\pi\) |
−0.369917 | − | 0.929065i | \(-0.620614\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.18581 | + | 9.80490i | −0.158696 | + | 0.488417i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.11665 | + | 5.17055i | −0.353629 | + | 0.256926i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.03605 | − | 4.41425i | 0.299196 | − | 0.218806i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5651 | − | 12.7618i | 0.868539 | − | 0.631031i | −0.0616554 | − | 0.998097i | \(-0.519638\pi\) |
0.930195 | + | 0.367067i | \(0.119638\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.81741 | − | 24.0595i | 0.385605 | − | 1.18677i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.18099 | + | 0.858043i | 0.0581129 | + | 0.0422215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.00535255 | − | 0.0164735i | −0.000262746 | − | 0.000808651i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.21382 | 0.108411 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.5502 | −1.29706 | −0.648532 | − | 0.761187i | \(-0.724617\pi\) | ||||
−0.648532 | + | 0.761187i | \(0.724617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.23989 | − | 9.97137i | −0.157903 | − | 0.485975i | 0.840541 | − | 0.541749i | \(-0.182237\pi\) |
−0.998443 | + | 0.0557736i | \(0.982237\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.680281 | − | 0.494253i | −0.0330764 | − | 0.0240314i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.66878 | + | 5.13596i | −0.0809475 | + | 0.249131i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.39796 | + | 3.92185i | −0.261226 | + | 0.189792i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.08684 | + | 6.35518i | 0.100754 | + | 0.306831i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.37855 | + | 3.18120i | −0.210907 | + | 0.153233i | −0.688224 | − | 0.725498i | \(-0.741609\pi\) |
0.477317 | + | 0.878731i | \(0.341609\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.80625 | − | 8.63676i | 0.134860 | − | 0.415056i | −0.860708 | − | 0.509099i | \(-0.829979\pi\) |
0.995568 | + | 0.0940422i | \(0.0299789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.52793 | − | 6.92245i | −0.456829 | − | 0.331906i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.3229 | + | 31.7706i | 0.493811 | + | 1.51980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3683 | 0.828945 | 0.414473 | − | 0.910062i | \(-0.363966\pi\) | ||||
0.414473 | + | 0.910062i | \(0.363966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.446130 | −0.0212443 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.22224 | − | 12.9947i | −0.200604 | − | 0.617397i | −0.999865 | − | 0.0164128i | \(-0.994775\pi\) |
0.799261 | − | 0.600984i | \(-0.205225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.87207 | − | 4.99285i | −0.325767 | − | 0.236684i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.6531 | − | 38.9422i | 0.598471 | − | 1.84190i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.1532 | − | 8.82983i | 0.573546 | − | 0.416706i | −0.262846 | − | 0.964838i | \(-0.584661\pi\) |
0.836392 | + | 0.548132i | \(0.184661\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.62138 | + | 5.04353i | −0.0763479 | + | 0.237490i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.4741 | + | 8.33645i | −0.539102 | + | 0.391681i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.34815 | − | 4.14917i | 0.0632021 | − | 0.194516i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.12304 | + | 1.54248i | 0.0993115 | + | 0.0721540i | 0.636333 | − | 0.771415i | \(-0.280451\pi\) |
−0.537021 | + | 0.843569i | \(0.680451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.76438 | + | 26.9740i | 0.409086 | + | 1.25904i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.2715 | 1.82906 | 0.914529 | − | 0.404521i | \(-0.132562\pi\) | ||||
0.914529 | + | 0.404521i | \(0.132562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.26421 | −0.151701 | −0.0758505 | − | 0.997119i | \(-0.524167\pi\) | ||||
−0.0758505 | + | 0.997119i | \(0.524167\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.63410 | − | 14.2623i | −0.214901 | − | 0.661398i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3484 | + | 14.7840i | 0.941613 | + | 0.684122i | 0.948809 | − | 0.315852i | \(-0.102290\pi\) |
−0.00719505 | + | 0.999974i | \(0.502290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4651 | + | 50.6743i | −0.760286 | + | 2.33992i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0362 | − | 8.01827i | 0.508521 | − | 0.369462i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0792 | + | 7.99689i | 0.509423 | + | 0.367697i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.11271 | − | 2.26152i | 0.142821 | − | 0.103765i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.253687 | − | 0.780769i | 0.0116155 | − | 0.0357490i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.1885 | − | 17.5740i | −1.10520 | − | 0.802977i | −0.123301 | − | 0.992369i | \(-0.539348\pi\) |
−0.981901 | + | 0.189393i | \(0.939348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.820405 | − | 2.52495i | −0.0374072 | − | 0.115128i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −55.0985 | −2.50707 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5155 | −0.477483 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.66165 | + | 29.7355i | 0.437811 | + | 1.34744i | 0.890178 | + | 0.455612i | \(0.150580\pi\) |
−0.452367 | + | 0.891832i | \(0.649420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.66438 | + | 4.11541i | 0.256152 | + | 0.186105i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.52081 | − | 7.75827i | 0.113763 | − | 0.350126i | −0.877924 | − | 0.478800i | \(-0.841072\pi\) |
0.991687 | + | 0.128674i | \(0.0410721\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.0405 | + | 21.8257i | −1.35296 | + | 0.982980i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.178339 | + | 0.128724i | 0.00801574 | + | 0.00578570i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.5483 | − | 14.9292i | 0.921719 | − | 0.669668i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.63513 | − | 8.11010i | 0.117965 | − | 0.363058i | −0.874589 | − | 0.484865i | \(-0.838869\pi\) |
0.992554 | + | 0.121807i | \(0.0388689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.51820 | + | 4.00921i | 0.246535 | + | 0.179118i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.04027 | + | 9.35700i | 0.135559 | + | 0.417208i | 0.995677 | − | 0.0928880i | \(-0.0296099\pi\) |
−0.860117 | + | 0.510096i | \(0.829610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.17862 | −0.319444 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.8916 | −0.883417 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.151062 | − | 0.464920i | −0.00669569 | − | 0.0206072i | 0.947653 | − | 0.319302i | \(-0.103449\pi\) |
−0.954349 | + | 0.298695i | \(0.903449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.1397 | − | 21.8977i | −1.33330 | − | 0.968699i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.24435 | − | 19.2181i | 0.275695 | − | 0.848501i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.03395 | + | 2.20429i | −0.133692 | + | 0.0971327i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.8709 | − | 40.0367i | 0.566062 | − | 1.76081i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.4674 | + | 17.7766i | −1.07400 | + | 0.780308i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.44666 | − | 10.6077i | 0.151001 | − | 0.464734i | −0.846733 | − | 0.532019i | \(-0.821434\pi\) |
0.997734 | + | 0.0672849i | \(0.0214337\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.72056 | − | 1.97660i | −0.118962 | − | 0.0864307i | 0.526714 | − | 0.850043i | \(-0.323424\pi\) |
−0.645675 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.96103 | + | 6.03542i | 0.0855862 | + | 0.263407i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.2816 | −2.05962 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.3836 | 2.27755 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.00807403 | + | 0.0248493i | 0.000350383 | + | 0.00107837i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.52164 | + | 1.10554i | 0.0659097 | + | 0.0478862i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.96265 | − | 6.04042i | 0.0848529 | − | 0.261150i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.5474 | + | 12.0224i | −0.714072 | + | 0.518804i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.96099 | − | 21.1987i | −0.299831 | − | 0.913093i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.13323 | + | 1.54988i | −0.0917145 | + | 0.0666345i | −0.632697 | − | 0.774399i | \(-0.718052\pi\) |
0.540983 | + | 0.841034i | \(0.318052\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.546067 | + | 1.68062i | −0.0234340 | + | 0.0721224i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.07120 | + | 0.778270i | 0.0458850 | + | 0.0333374i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8276 | + | 36.4018i | 0.505714 | + | 1.55643i | 0.799567 | + | 0.600577i | \(0.205062\pi\) |
−0.293854 | + | 0.955850i | \(0.594938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.119424 | −0.00509687 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.4555 | 1.12704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.27526 | − | 3.92483i | −0.0542294 | − | 0.166901i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.12428 | + | 2.26992i | 0.132618 | + | 0.0963528i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.59589 | + | 17.2224i | −0.237105 | + | 0.729736i | 0.759730 | + | 0.650239i | \(0.225331\pi\) |
−0.996835 | + | 0.0794966i | \(0.974669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.92458 | − | 2.85137i | 0.165992 | − | 0.120600i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.7622 | + | 18.1090i | −1.04546 | + | 0.764562i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.88702 | + | 2.09754i | −0.121673 | + | 0.0884008i | −0.646958 | − | 0.762526i | \(-0.723959\pi\) |
0.525284 | + | 0.850927i | \(0.323959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.64758 | + | 5.07074i | −0.0693143 | + | 0.213328i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.3676 | + | 19.1571i | 1.10733 | + | 0.804525i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.4766 | − | 38.3990i | −0.523046 | − | 1.60977i | −0.768147 | − | 0.640274i | \(-0.778821\pi\) |
0.245100 | − | 0.969498i | \(-0.421179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.3873 | 1.52276 | 0.761381 | − | 0.648305i | \(-0.224522\pi\) | ||||
0.761381 | + | 0.648305i | \(0.224522\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.5694 | 1.36061 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.68300 | − | 8.25743i | −0.111889 | − | 0.344359i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.20076 | + | 0.872400i | 0.0499881 | + | 0.0363185i | 0.612499 | − | 0.790472i | \(-0.290164\pi\) |
−0.562511 | + | 0.826790i | \(0.690164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.86276 | − | 8.81067i | 0.118972 | − | 0.366159i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0519195 | + | 0.0377217i | −0.00215399 | + | 0.00156496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.0580 | − | 0.127949i | 1.70045 | − | 0.00529909i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0631729 | − | 0.0458978i | 0.00261188 | − | 0.00189764i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.1618 | + | 37.4300i | −0.501969 | + | 1.54490i | 0.303837 | + | 0.952724i | \(0.401732\pi\) |
−0.805806 | + | 0.592179i | \(0.798268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.2530 | + | 19.8005i | 1.12294 | + | 0.815865i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.15746 | + | 6.63998i | 0.0887460 | + | 0.273132i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.2990 | 1.12104 | 0.560518 | − | 0.828142i | \(-0.310602\pi\) | ||||
0.560518 | + | 0.828142i | \(0.310602\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0083 | 0.820260 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.38907 | − | 19.6635i | −0.261487 | − | 0.804774i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.0954 | − | 12.4205i | −0.698499 | − | 0.507490i | 0.180944 | − | 0.983493i | \(-0.442085\pi\) |
−0.879443 | + | 0.476004i | \(0.842085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.884593 | + | 2.72250i | −0.0360833 | + | 0.111053i | −0.967476 | − | 0.252963i | \(-0.918595\pi\) |
0.931393 | + | 0.364016i | \(0.118595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.771537 | + | 0.560554i | −0.0314194 | + | 0.0228275i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.33392 | + | 10.4826i | −0.135543 | + | 0.426178i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8840 | + | 18.8058i | −1.05060 | + | 0.763305i | −0.972326 | − | 0.233627i | \(-0.924941\pi\) |
−0.0782733 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.4840 | + | 41.4994i | −0.546398 | + | 1.68164i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0792 | − | 8.77602i | −0.488670 | − | 0.355040i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0013 | − | 33.8584i | −0.444337 | − | 1.36753i | −0.883209 | − | 0.468979i | \(-0.844622\pi\) |
0.438873 | − | 0.898549i | \(-0.355378\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.73591 | −0.110322 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.9894 | −1.48914 | −0.744568 | − | 0.667546i | \(-0.767345\pi\) | ||||
−0.744568 | + | 0.667546i | \(0.767345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.5038 | + | 32.3274i | 0.422184 | + | 1.29935i | 0.905665 | + | 0.423995i | \(0.139372\pi\) |
−0.483480 | + | 0.875355i | \(0.660628\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −36.8909 | − | 26.8028i | −1.48038 | − | 1.07556i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.72538 | + | 29.9317i | −0.389639 | + | 1.19919i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.8566 | − | 0.0681114i | 0.872867 | − | 0.00272011i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.85050 | − | 7.15681i | 0.392765 | − | 0.285361i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.891987 | − | 2.74525i | 0.0355094 | − | 0.109287i | −0.931731 | − | 0.363150i | \(-0.881701\pi\) |
0.967240 | + | 0.253863i | \(0.0817013\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.9047 | + | 9.37584i | 0.512917 | + | 0.372656i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.52419 | − | 13.9240i | −0.179537 | − | 0.552558i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.92154 | −0.313863 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.454608 | 0.0179840 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.59179 | + | 11.0544i | 0.141867 | + | 0.436623i | 0.996595 | − | 0.0824541i | \(-0.0262758\pi\) |
−0.854728 | + | 0.519077i | \(0.826276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9133 | + | 15.9210i | 0.864178 | + | 0.627862i | 0.929018 | − | 0.370033i | \(-0.120654\pi\) |
−0.0648403 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.18054 | + | 6.71101i | −0.0858586 | + | 0.264246i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.34353 | + | 0.976135i | −0.0528198 | + | 0.0383758i | −0.613882 | − | 0.789398i | \(-0.710393\pi\) |
0.561062 | + | 0.827774i | \(0.310393\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.05478 | + | 0.771378i | −0.0414039 | + | 0.0302792i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44.9506 | + | 32.6585i | −1.76175 | + | 1.27999i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.4505 | + | 38.3186i | −0.487224 | + | 1.49952i | 0.341510 | + | 0.939878i | \(0.389062\pi\) |
−0.828734 | + | 0.559643i | \(0.810938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.80493 | + | 3.49099i | 0.187744 | + | 0.136404i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.206054 | − | 0.634169i | −0.00803893 | − | 0.0247413i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.7115 | 1.31321 | 0.656607 | − | 0.754233i | \(-0.271991\pi\) | ||||
0.656607 | + | 0.754233i | \(0.271991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.4279 | 1.65026 | 0.825128 | − | 0.564946i | \(-0.191103\pi\) | ||||
0.825128 | + | 0.564946i | \(0.191103\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.36562 | + | 10.3583i | 0.130710 | + | 0.402284i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.5328 | − | 8.37904i | −0.447221 | − | 0.324925i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.4482 | − | 56.7779i | 0.714319 | − | 2.19845i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.57319 | − | 4.77570i | 0.254134 | − | 0.184639i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.86337 | − | 5.67464i | −0.0719347 | − | 0.219067i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.8456 | − | 22.4107i | 1.18901 | − | 0.863868i | 0.195853 | − | 0.980633i | \(-0.437253\pi\) |
0.993160 | + | 0.116765i | \(0.0372525\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.62295 | + | 4.99493i | −0.0624675 | + | 0.192255i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.71587 | + | 7.05899i | 0.373411 | + | 0.271299i | 0.758624 | − | 0.651529i | \(-0.225872\pi\) |
−0.385213 | + | 0.922828i | \(0.625872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0394 | + | 37.0535i | 0.462030 | + | 1.42198i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.02089 | 0.230721 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.6564 | 1.44088 | 0.720441 | − | 0.693516i | \(-0.243939\pi\) | ||||
0.720441 | + | 0.693516i | \(0.243939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.56411 | − | 14.0469i | −0.174386 | − | 0.536704i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6459 | + | 9.18782i | 0.482473 | + | 0.350537i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.50450 | − | 13.8634i | 0.171608 | − | 0.528155i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.03817 | − | 5.84007i | 0.305786 | − | 0.222167i | −0.424300 | − | 0.905522i | \(-0.639480\pi\) |
0.730086 | + | 0.683355i | \(0.239480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.249401 | − | 0.775795i | 0.00947396 | − | 0.0294700i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.04567 | − | 0.759722i | 0.0396644 | − | 0.0288179i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.66558 | + | 8.20382i | −0.100966 | + | 0.310742i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.8270 | + | 21.6706i | 1.12816 | + | 0.819658i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.11652 | + | 9.59166i | 0.117709 | + | 0.362272i | 0.992502 | − | 0.122225i | \(-0.0390028\pi\) |
−0.874793 | + | 0.484497i | \(0.839003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.67494 | −0.327181 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.7183 | 0.817957 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.21898 | + | 25.2954i | 0.309106 | + | 0.951332i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.22013 | − | 3.06611i | −0.158490 | − | 0.115150i | 0.505713 | − | 0.862702i | \(-0.331229\pi\) |
−0.664204 | + | 0.747552i | \(0.731229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0228252 | − | 0.0702488i | 0.000856013 | − | 0.00263454i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 61.4996 | − | 44.6821i | 2.30318 | − | 1.67336i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.16661 | + | 2.28563i | 0.118425 | + | 0.0854779i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.6685 | + | 11.3839i | −0.585152 | + | 0.425138i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.44416 | + | 7.52235i | −0.0911518 | + | 0.280536i | −0.986232 | − | 0.165369i | \(-0.947118\pi\) |
0.895080 | + | 0.445906i | \(0.147118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2409 | + | 8.16702i | 0.418634 | + | 0.304156i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.8220 | − | 42.5396i | −0.514044 | − | 1.58206i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.87597 | −0.255367 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.2281 | 0.379338 | 0.189669 | − | 0.981848i | \(-0.439258\pi\) | ||||
0.189669 | + | 0.981848i | \(0.439258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.51965 | + | 26.2208i | 0.315542 | + | 0.971140i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.9990 | + | 13.0770i | 0.665716 | + | 0.483671i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.74873 | + | 14.6151i | −0.175398 | + | 0.539821i | −0.999651 | − | 0.0264009i | \(-0.991595\pi\) |
0.824253 | + | 0.566222i | \(0.191595\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.32209 | − | 6.77289i | 0.343850 | − | 0.249822i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.6742 | − | 27.9147i | −1.42458 | − | 1.02825i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.8200 | − | 16.5797i | 0.839449 | − | 0.609895i | −0.0827676 | − | 0.996569i | \(-0.526376\pi\) |
0.922217 | + | 0.386673i | \(0.126376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.39790 | − | 7.37997i | 0.0880890 | − | 0.271110i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.6824 | − | 25.9248i | −1.30906 | − | 0.951089i | −1.00000 | 4.66582e-5i | \(-0.999985\pi\) | |
−0.309061 | − | 0.951042i | \(-0.600015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.38737 | − | 22.7360i | −0.270652 | − | 0.832982i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.00114866 | −4.20272e−5 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.5318 | −0.859834 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.3439 | − | 41.0682i | −0.486924 | − | 1.49860i | −0.829174 | − | 0.558990i | \(-0.811189\pi\) |
0.342250 | − | 0.939609i | \(-0.388811\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.15214 | + | 3.74325i | 0.187754 | + | 0.136411i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.55881 | + | 7.87521i | −0.0931246 | + | 0.286608i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5978 | + | 11.3325i | −0.566913 | + | 0.411886i | −0.833982 | − | 0.551791i | \(-0.813945\pi\) |
0.267070 | + | 0.963677i | \(0.413945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.0951 | − | 46.9554i | 0.547918 | − | 1.70437i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.2423 | + | 20.5193i | −1.02378 | + | 0.743823i | −0.967055 | − | 0.254567i | \(-0.918067\pi\) |
−0.0567289 | + | 0.998390i | \(0.518067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.51596 | − | 4.66565i | 0.0548815 | − | 0.168908i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.289725 | + | 0.210497i | 0.0104750 | + | 0.00761055i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.143364 | + | 0.441228i | 0.00517656 | + | 0.0159318i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.7367 | 0.387177 | 0.193588 | − | 0.981083i | \(-0.437987\pi\) | ||||
0.193588 | + | 0.981083i | \(0.437987\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.1485 | −0.437518 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.77736 | + | 30.0916i | 0.351667 | + | 1.08232i | 0.957917 | + | 0.287046i | \(0.0926733\pi\) |
−0.606249 | + | 0.795275i | \(0.707327\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.08327 | − | 5.14630i | −0.254439 | − | 0.184860i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.42149 | − | 13.6080i | 0.158620 | − | 0.488183i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.97202 | − | 3.61239i | 0.178141 | − | 0.129427i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.09327 | + | 21.6016i | 0.253817 | + | 0.772964i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.2156 | + | 21.2264i | −1.04408 | + | 0.758570i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.46115 | − | 7.57463i | 0.0878421 | − | 0.270350i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6566 | − | 9.19553i | −0.451158 | − | 0.327785i | 0.338895 | − | 0.940824i | \(-0.389947\pi\) |
−0.790053 | + | 0.613039i | \(0.789947\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.3629 | + | 38.0491i | 0.440131 | + | 1.35458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.7542 | 0.702379 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.12050 | −0.0753011 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.55229 | + | 20.1659i | 0.232386 | + | 0.715209i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.02872 | + | 2.92704i | 0.142705 | + | 0.103681i | 0.656847 | − | 0.754024i | \(-0.271890\pi\) |
−0.514142 | + | 0.857705i | \(0.671890\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1600 | − | 65.1239i | 0.748588 | − | 2.30392i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.455722 | + | 0.331101i | −0.0161021 | + | 0.0116989i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.9187 | − | 19.6860i | 0.949939 | − | 0.694704i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.0250 | + | 18.9083i | −0.917261 | + | 0.666429i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.04110 | + | 27.8257i | −0.318262 | + | 0.979510i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.9907 | − | 18.1568i | −0.878627 | − | 0.638360i | 0.0542612 | − | 0.998527i | \(-0.482720\pi\) |
−0.932888 | + | 0.360167i | \(0.882720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38422 | + | 4.26019i | 0.0486066 | + | 0.149596i | 0.972414 | − | 0.233262i | \(-0.0749400\pi\) |
−0.923807 | + | 0.382858i | \(0.874940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.9895 | −1.64799 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.08778 | 0.143189 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.89822 | − | 15.0752i | −0.171367 | − | 0.527413i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.234059 | − | 0.170054i | −0.00817868 | − | 0.00594216i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.85678 | − | 11.8699i | 0.134603 | − | 0.414264i | −0.860925 | − | 0.508731i | \(-0.830115\pi\) |
0.995528 | + | 0.0944672i | \(0.0301147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3519 | + | 9.70071i | −0.465417 | + | 0.338146i | −0.795653 | − | 0.605753i | \(-0.792872\pi\) |
0.330235 | + | 0.943899i | \(0.392872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.68069 | + | 0.0177027i | −0.197776 | + | 0.000616328i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.5649 | − | 26.5660i | 1.27149 | − | 0.923789i | 0.272225 | − | 0.962233i | \(-0.412240\pi\) |
0.999261 | + | 0.0384447i | \(0.0122404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.51891 | + | 10.8301i | −0.122217 | + | 0.376144i | −0.993384 | − | 0.114842i | \(-0.963364\pi\) |
0.871167 | + | 0.490987i | \(0.163364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.5683 | + | 24.3888i | 1.16447 | + | 0.846037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.2266 | − | 34.5518i | −0.388977 | − | 1.19715i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.98229 | 0.137813 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −45.9833 | −1.58941 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.36023 | − | 13.4194i | −0.150532 | − | 0.463289i | 0.847149 | − | 0.531355i | \(-0.178317\pi\) |
−0.997681 | + | 0.0680663i | \(0.978317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7880 | − | 10.7441i | −0.509932 | − | 0.370487i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.08432 | + | 27.9587i | −0.312881 | + | 0.962948i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.39552 | + | 6.82624i | −0.323216 | + | 0.234830i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.7548 | − | 0.254010i | 1.40035 | − | 0.00872789i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.41445 | + | 4.66037i | −0.220143 | + | 0.159944i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.04931 | + | 18.6179i | −0.207368 | + | 0.638212i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9736 | + | 12.3320i | 0.581165 | + | 0.422241i | 0.839144 | − | 0.543909i | \(-0.183056\pi\) |
−0.257979 | + | 0.966151i | \(0.583056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0788453 | − | 0.242661i | −0.00269645 | − | 0.00829883i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.0649 | 0.856201 | 0.428101 | − | 0.903731i | \(-0.359183\pi\) | ||||
0.428101 | + | 0.903731i | \(0.359183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.0496 | −1.29823 | −0.649117 | − | 0.760689i | \(-0.724861\pi\) | ||||
−0.649117 | + | 0.760689i | \(0.724861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.13241 | + | 9.64055i | 0.106752 | + | 0.328549i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.94855 | + | 5.04842i | 0.236531 | + | 0.171850i | 0.699737 | − | 0.714401i | \(-0.253301\pi\) |
−0.463205 | + | 0.886251i | \(0.653301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.45640 | + | 16.7931i | −0.185523 | + | 0.570982i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8540 | + | 12.2451i | −0.572391 | + | 0.415866i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.69415 | − | 0.0115120i | 0.125315 | − | 0.000390519i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.6995 | + | 9.95328i | −0.464190 | + | 0.337254i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.215488 | + | 0.663204i | −0.00729316 | + | 0.0224461i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.99745 | + | 2.17778i | 0.101332 | + | 0.0736223i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.26516 | − | 10.0491i | −0.110257 | − | 0.339335i | 0.880671 | − | 0.473727i | \(-0.157092\pi\) |
−0.990928 | + | 0.134392i | \(0.957092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.6879 | −1.06881 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.5069 | −1.19626 | −0.598129 | − | 0.801400i | \(-0.704089\pi\) | ||||
−0.598129 | + | 0.801400i | \(0.704089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5115 | − | 32.3511i | −0.353740 | − | 1.08870i | −0.956736 | − | 0.290957i | \(-0.906026\pi\) |
0.602996 | − | 0.797744i | \(-0.293974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.545959 | − | 0.396662i | −0.0183522 | − | 0.0133337i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.08945 | + | 9.50834i | −0.103733 | + | 0.319259i | −0.989431 | − | 0.145004i | \(-0.953681\pi\) |
0.885698 | + | 0.464263i | \(0.153681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.8845 | + | 31.8839i | −1.47184 | + | 1.06935i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.5497 | + | 17.2222i | −0.788944 | + | 0.576966i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.4691 | + | 28.6760i | −1.32078 | + | 0.959605i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.69018 | + | 11.3572i | −0.123349 | + | 0.379629i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.1665 | − | 10.2926i | −0.473007 | − | 0.343659i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.6034 | − | 57.2554i | −0.620459 | − | 1.90958i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.8528 | 2.22719 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.1442 | 0.870026 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.318815 | + | 0.981213i | 0.0105978 | + | 0.0326166i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.6476 | − | 8.46245i | −0.386751 | − | 0.280991i | 0.377372 | − | 0.926062i | \(-0.376828\pi\) |
−0.764123 | + | 0.645071i | \(0.776828\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.147108 | + | 0.452751i | −0.00487926 | + | 0.0150168i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.0870 | − | 9.50830i | 0.433593 | − | 0.315024i | −0.349491 | − | 0.936940i | \(-0.613645\pi\) |
0.783084 | + | 0.621916i | \(0.213645\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0179226 | − | 0.0545807i | −0.000593151 | − | 0.00180636i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.49541 | − | 1.81302i | 0.0824957 | − | 0.0599366i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.79996 | − | 20.9281i | 0.224555 | − | 0.691108i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7072 | + | 10.6854i | 0.485144 | + | 0.352478i | 0.803314 | − | 0.595556i | \(-0.203068\pi\) |
−0.318170 | + | 0.948034i | \(0.603068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.3976 | − | 44.3114i | −0.474418 | − | 1.46011i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.07207 | 0.265696 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.25468 | 0.0741335 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0768502 | + | 0.236521i | 0.00252409 | + | 0.00776836i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6811 | + | 14.2992i | 0.645717 | + | 0.469141i | 0.861810 | − | 0.507232i | \(-0.169331\pi\) |
−0.216092 | + | 0.976373i | \(0.569331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.99857 | + | 24.6171i | −0.262143 | + | 0.806792i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44.7020 | + | 32.4779i | −1.46348 | + | 1.06328i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.48159 | + | 17.0512i | −0.179267 | + | 0.557635i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.5700 | + | 14.2184i | −0.639323 | + | 0.464495i | −0.859617 | − | 0.510938i | \(-0.829298\pi\) |
0.220295 | + | 0.975433i | \(0.429298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.153889 | + | 0.473620i | −0.00502196 | + | 0.0154560i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.95329 | + | 3.59878i | 0.161473 | + | 0.117317i | 0.665587 | − | 0.746320i | \(-0.268181\pi\) |
−0.504115 | + | 0.863637i | \(0.668181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.28564 | − | 13.1898i | −0.139559 | − | 0.429520i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19.4589 | 0.632998 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.4758 | 0.990330 | 0.495165 | − | 0.868799i | \(-0.335108\pi\) | ||||
0.495165 | + | 0.868799i | \(0.335108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.65872 | − | 11.2604i | −0.118767 | − | 0.365527i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.6415 | − | 22.9889i | −1.02605 | − | 0.745466i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.80261 | − | 11.7032i | 0.123179 | − | 0.379105i | −0.870386 | − | 0.492370i | \(-0.836131\pi\) |
0.993565 | + | 0.113265i | \(0.0361309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.3837 | − | 11.1769i | 0.497805 | − | 0.361677i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.6720 | − | 22.8606i | −1.02381 | − | 0.738977i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.2717 | + | 32.1653i | −1.42961 | + | 1.03867i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1088 | − | 43.4225i | 0.455123 | − | 1.40073i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.340746 | − | 0.247567i | −0.0109804 | − | 0.00797772i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.67139 | − | 5.14402i | −0.0538040 | − | 0.165592i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5927 | 0.726532 | 0.363266 | − | 0.931685i | \(-0.381662\pi\) | ||||
0.363266 | + | 0.931685i | \(0.381662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.5880 | 1.14325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3663 | + | 41.1374i | 0.428946 | + | 1.32016i | 0.899164 | + | 0.437611i | \(0.144175\pi\) |
−0.470218 | + | 0.882550i | \(0.655825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.87426 | − | 2.81481i | −0.124203 | − | 0.0902387i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.623232 | + | 1.91811i | −0.0199594 | + | 0.0614287i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.1952 | + | 8.86033i | −0.390159 | + | 0.283467i | −0.765521 | − | 0.643411i | \(-0.777518\pi\) |
0.375362 | + | 0.926878i | \(0.377518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.8436 | − | 16.4883i | −0.730084 | − | 0.526969i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0710365 | − | 0.0516110i | 0.00226802 | − | 0.00164781i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9536 | + | 39.8672i | −0.413157 | + | 1.27157i | 0.500732 | + | 0.865602i | \(0.333064\pi\) |
−0.913889 | + | 0.405964i | \(0.866936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.29770 | + | 2.39592i | 0.105073 | + | 0.0763403i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.8658 | − | 76.5290i | −0.791486 | − | 2.43594i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.7695 | −1.13740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5068 | 0.937314 | 0.468657 | − | 0.883380i | \(-0.344738\pi\) | ||||
0.468657 | + | 0.883380i | \(0.344738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.68850 | − | 23.6628i | −0.243987 | − | 0.750916i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.76576 | − | 7.09524i | −0.309595 | − | 0.224934i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0230 | − | 46.2361i | 0.475784 | − | 1.46431i | −0.369113 | − | 0.929384i | \(-0.620339\pi\) |
0.844897 | − | 0.534929i | \(-0.179661\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.58002 | − | 6.96029i | 0.303098 | − | 0.220214i |
(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 | 440.2.y.c.201.3 | yes | 12 | |
4.3 | odd | 2 | 880.2.bo.i.641.1 | 12 | |||
11.2 | odd | 10 | 4840.2.a.ba.1.6 | 6 | |||
11.4 | even | 5 | inner | 440.2.y.c.81.3 | ✓ | 12 | |
11.9 | even | 5 | 4840.2.a.bb.1.6 | 6 | |||
44.15 | odd | 10 | 880.2.bo.i.81.1 | 12 | |||
44.31 | odd | 10 | 9680.2.a.dc.1.1 | 6 | |||
44.35 | even | 10 | 9680.2.a.dd.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.c.81.3 | ✓ | 12 | 11.4 | even | 5 | inner | |
440.2.y.c.201.3 | yes | 12 | 1.1 | even | 1 | trivial | |
880.2.bo.i.81.1 | 12 | 44.15 | odd | 10 | |||
880.2.bo.i.641.1 | 12 | 4.3 | odd | 2 | |||
4840.2.a.ba.1.6 | 6 | 11.2 | odd | 10 | |||
4840.2.a.bb.1.6 | 6 | 11.9 | even | 5 | |||
9680.2.a.dc.1.1 | 6 | 44.31 | odd | 10 | |||
9680.2.a.dd.1.1 | 6 | 44.35 | even | 10 |