Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [456,2,Mod(65,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 456 = 2^{3} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 456.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.64117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 456.65 |
Dual form | 456.2.bf.a.449.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.68614 | − | 0.396143i | 0.973494 | − | 0.228714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18614 | − | 1.26217i | −0.977672 | − | 0.564459i | −0.0761054 | − | 0.997100i | \(-0.524249\pi\) |
−0.901566 | + | 0.432641i | \(0.857582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.37228 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.68614 | − | 1.33591i | 0.895380 | − | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.87228 | − | 1.65831i | 0.796628 | − | 0.459933i | −0.0456630 | − | 0.998957i | \(-0.514540\pi\) |
0.842291 | + | 0.539024i | \(0.181207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.18614 | − | 1.26217i | −1.08086 | − | 0.325891i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.18614 | − | 1.26217i | −0.530217 | − | 0.306121i | 0.210888 | − | 0.977510i | \(-0.432365\pi\) |
−0.741105 | + | 0.671389i | \(0.765698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.68614 | − | 1.33591i | 1.24082 | − | 0.291519i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.93070 | − | 4.57879i | 1.65367 | − | 0.954744i | 0.678119 | − | 0.734952i | \(-0.262795\pi\) |
0.975547 | − | 0.219793i | \(-0.0705381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.686141 | + | 1.18843i | 0.137228 | + | 0.237686i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | − | 3.31662i | 0.769800 | − | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.186141 | + | 0.322405i | 0.0345655 | + | 0.0598691i | 0.882791 | − | 0.469767i | \(-0.155662\pi\) |
−0.848225 | + | 0.529636i | \(0.822329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.72049i | − | 1.38664i | −0.720629 | − | 0.693320i | \(-0.756147\pi\) | ||
0.720629 | − | 0.693320i | \(-0.243853\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.37228 | + | 5.84096i | 0.238884 | + | 1.01678i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.37228 | − | 4.25639i | −1.24614 | − | 0.719461i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1846i | 1.83874i | 0.393399 | + | 0.919368i | \(0.371299\pi\) | ||||
−0.393399 | + | 0.919368i | \(0.628701\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.18614 | − | 3.93398i | 0.670319 | − | 0.629942i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.18614 | + | 5.51856i | −0.497592 | + | 0.861854i | −0.999996 | − | 0.00277878i | \(-0.999115\pi\) |
0.502405 | + | 0.864633i | \(0.332449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.87228 | + | 10.1711i | −0.895515 | + | 1.55108i | −0.0623480 | + | 0.998054i | \(0.519859\pi\) |
−0.833167 | + | 0.553022i | \(0.813474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.55842 | − | 0.469882i | −1.12674 | − | 0.0700459i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.813859 | + | 0.469882i | −0.118714 | + | 0.0685393i | −0.558181 | − | 0.829719i | \(-0.688501\pi\) |
0.439467 | + | 0.898259i | \(0.355167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.18614 | − | 1.26217i | −0.586177 | − | 0.176739i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.81386 | + | 4.87375i | 0.386513 | + | 0.669461i | 0.991978 | − | 0.126412i | \(-0.0403460\pi\) |
−0.605465 | + | 0.795872i | \(0.707013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37228 | − | 7.57301i | 0.589558 | − | 1.02114i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.43070 | − | 1.33591i | −0.984221 | − | 0.176945i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.813859 | + | 1.40965i | −0.105955 | + | 0.183520i | −0.914128 | − | 0.405425i | \(-0.867123\pi\) |
0.808173 | + | 0.588946i | \(0.200457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.05842 | − | 4.50506i | 1.14125 | − | 0.567584i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.37228 | −1.03845 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.24456 | + | 0.718549i | −0.152048 | + | 0.0877847i | −0.574094 | − | 0.818790i | \(-0.694645\pi\) |
0.422046 | + | 0.906574i | \(0.361312\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.5584 | − | 10.8622i | 1.39147 | − | 1.30765i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.18614 | + | 10.7147i | −0.734160 | + | 1.27160i | 0.220931 | + | 0.975289i | \(0.429090\pi\) |
−0.955091 | + | 0.296313i | \(0.904243\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.87228 | + | 4.97494i | −0.336175 | + | 0.582272i | −0.983710 | − | 0.179764i | \(-0.942467\pi\) |
0.647535 | + | 0.762036i | \(0.275800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.62772 | + | 1.73205i | 0.187953 | + | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6819i | 1.33128i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9891 | − | 7.49927i | −1.46139 | − | 0.843734i | −0.462315 | − | 0.886716i | \(-0.652981\pi\) |
−0.999076 | + | 0.0429815i | \(0.986314\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.18614 | + | 5.51856i | 0.345585 | + | 0.598572i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.441578 | + | 0.469882i | 0.0473421 | + | 0.0503766i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.813859 | + | 1.40965i | 0.0862689 | + | 0.149422i | 0.905931 | − | 0.423425i | \(-0.139172\pi\) |
−0.819662 | + | 0.572847i | \(0.805839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.68614 | − | 5.59230i | 1.01538 | − | 0.586232i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.05842 | − | 13.0178i | −0.317144 | − | 1.34989i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.55842 | + | 8.83518i | 0.672880 | + | 0.906471i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.44158 | + | 1.40965i | 0.247905 | + | 0.143128i | 0.618804 | − | 0.785545i | \(-0.287617\pi\) |
−0.370900 | + | 0.928673i | \(0.620951\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.62772 | + | 9.30506i | 0.465103 | + | 0.935194i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.18614 | + | 1.26217i | −0.217529 | + | 0.125590i | −0.604806 | − | 0.796373i | \(-0.706749\pi\) |
0.387277 | + | 0.921964i | \(0.373416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.30506i | − | 0.916855i | −0.888732 | − | 0.458428i | \(-0.848413\pi\) | ||
0.888732 | − | 0.458428i | \(-0.151587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.1168 | − | 4.25639i | −1.37766 | − | 0.415381i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.25544 | 0.508062 | 0.254031 | − | 0.967196i | \(-0.418243\pi\) | ||||
0.254031 | + | 0.967196i | \(0.418243\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.55842 | − | 2.05446i | −0.340835 | − | 0.196781i | 0.319806 | − | 0.947483i | \(-0.396382\pi\) |
−0.660641 | + | 0.750702i | \(0.729716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.43070 | + | 18.8588i | 0.420544 | + | 1.79000i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.25544 | −0.306246 | −0.153123 | − | 0.988207i | \(-0.548933\pi\) | ||||
−0.153123 | + | 0.988207i | \(0.548933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.1168 | −2.15566 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.50000 | − | 8.29156i | 0.508475 | − | 0.766555i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.37228 | − | 4.25639i | −0.675816 | − | 0.390183i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.18614 | + | 10.5672i | −0.287285 | + | 0.952815i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.15759i | 0.819080i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.30298 | − | 1.90698i | 0.293092 | − | 0.169217i | −0.346243 | − | 0.938145i | \(-0.612543\pi\) |
0.639336 | + | 0.768928i | \(0.279209\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.87228 | + | 19.4762i | −0.517026 | + | 1.71478i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3030 | − | 8.83518i | −1.33703 | − | 0.771933i | −0.350662 | − | 0.936502i | \(-0.614044\pi\) |
−0.986366 | + | 0.164569i | \(0.947377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.4891 | − | 5.84096i | −1.16966 | − | 0.506476i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.9307 | + | 2.20193i | −1.11290 | + | 0.189512i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.1861 | + | 8.19037i | −1.21200 | + | 0.699751i | −0.963195 | − | 0.268802i | \(-0.913372\pi\) |
−0.248808 | + | 0.968553i | \(0.580039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.24456 | + | 5.61975i | 0.275200 | + | 0.476661i | 0.970186 | − | 0.242363i | \(-0.0779225\pi\) |
−0.694985 | + | 0.719024i | \(0.744589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.18614 | + | 1.11469i | −0.0998911 | + | 0.0938740i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.74456 | + | 9.94987i | 0.480384 | + | 0.832050i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.939764i | − | 0.0780431i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.37228 | − | 1.73205i | 0.608056 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.55842 | + | 3.78651i | 0.537287 | + | 0.310203i | 0.743979 | − | 0.668203i | \(-0.232936\pi\) |
−0.206692 | + | 0.978406i | \(0.566270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.294954i | − | 0.0240030i | −0.999928 | − | 0.0120015i | \(-0.996180\pi\) | ||
0.999928 | − | 0.0120015i | \(-0.00382029\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.55842 | − | 0.469882i | −0.611062 | − | 0.0379877i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.74456 | + | 16.8781i | −0.782702 | + | 1.35568i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.24456 | − | 2.15565i | 0.0993269 | − | 0.172039i | −0.812079 | − | 0.583547i | \(-0.801664\pi\) |
0.911406 | + | 0.411508i | \(0.134998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.67527 | + | 7.10313i | 0.529383 | + | 0.563315i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.7446 | − | 15.4410i | 2.10777 | − | 1.21692i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3723 | 1.20405 | 0.602025 | − | 0.798477i | \(-0.294361\pi\) | ||||
0.602025 | + | 0.798477i | \(0.294361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.37228 | − | 14.5012i | 0.340382 | − | 1.12892i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.441578 | − | 0.764836i | −0.0341703 | − | 0.0591848i | 0.848434 | − | 0.529300i | \(-0.177546\pi\) |
−0.882605 | + | 0.470116i | \(0.844212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | + | 1.73205i | −0.0769231 | + | 0.133235i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.0584 | + | 0.691097i | −0.998602 | + | 0.0528495i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.93070 | − | 12.0043i | 0.526932 | − | 0.912672i | −0.472576 | − | 0.881290i | \(-0.656676\pi\) |
0.999507 | − | 0.0313823i | \(-0.00999094\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.31386 | + | 4.00772i | 0.174911 | + | 0.302955i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.813859 | + | 2.69927i | −0.0611734 | + | 0.202889i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.48913 | −0.111302 | −0.0556512 | − | 0.998450i | \(-0.517723\pi\) | ||||
−0.0556512 | + | 0.998450i | \(0.517723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.3030 | + | 10.5672i | −1.36045 | + | 0.785456i | −0.989684 | − | 0.143270i | \(-0.954238\pi\) |
−0.370766 | + | 0.928726i | \(0.620905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.18614 | + | 1.26217i | 0.0876820 | + | 0.0933022i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.1168 | − | 24.4511i | 1.03789 | − | 1.79768i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.37228 | − | 7.57301i | 0.319733 | − | 0.553794i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.4891 | − | 11.1846i | 0.981189 | − | 0.813559i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.63325i | − | 0.479965i | −0.970777 | − | 0.239983i | \(-0.922858\pi\) | ||
0.970777 | − | 0.239983i | \(-0.0771417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5000 | + | 7.79423i | 0.971751 | + | 0.561041i | 0.899770 | − | 0.436365i | \(-0.143734\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.1168 | + | 3.31662i | −1.01093 | + | 0.237508i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.3639i | − | 1.66461i | −0.554321 | − | 0.832303i | \(-0.687022\pi\) | ||
0.554321 | − | 0.832303i | \(-0.312978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.24456 | + | 2.15565i | 0.0882247 | + | 0.152810i | 0.906761 | − | 0.421645i | \(-0.138547\pi\) |
−0.818536 | + | 0.574455i | \(0.805214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.81386 | + | 1.70460i | −0.127940 | + | 0.120233i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.627719 | + | 1.08724i | 0.0440572 | + | 0.0763093i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9307 | − | 8.04290i | 0.972963 | − | 0.561740i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.1861 | − | 22.8940i | 1.05551 | − | 1.59124i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | − | 13.8564i | 0.415029 | − | 0.958468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.98913 | + | 5.76722i | 0.687680 | + | 0.397032i | 0.802742 | − | 0.596326i | \(-0.203373\pi\) |
−0.115062 | + | 0.993358i | \(0.536707\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.18614 | + | 20.5171i | −0.423867 | + | 1.40581i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.6753 | − | 14.8236i | 1.75104 | − | 1.01096i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 26.0357i | − | 1.76742i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.87228 | + | 9.52628i | −0.194091 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.37228 | −0.563181 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7337 | + | 10.8159i | 1.25450 | + | 0.724286i | 0.972000 | − | 0.234981i | \(-0.0755028\pi\) |
0.282501 | + | 0.959267i | \(0.408836\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.43070 | + | 2.27567i | 0.228714 | + | 0.151711i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.7446 | −1.24412 | −0.622060 | − | 0.782969i | \(-0.713704\pi\) | ||||
−0.622060 | + | 0.782969i | \(0.713704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.88316 | −0.256606 | −0.128303 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128303 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.62772 | + | 19.6974i | 0.304482 | + | 1.29599i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.5584 | + | 7.25061i | 0.822730 | + | 0.475003i | 0.851357 | − | 0.524587i | \(-0.175780\pi\) |
−0.0286273 | + | 0.999590i | \(0.509114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.37228 | 0.154751 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.8723 | − | 7.49927i | −1.61563 | − | 0.487130i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6168 | − | 10.1711i | 1.13480 | − | 0.655177i | 0.189663 | − | 0.981849i | \(-0.439261\pi\) |
0.945138 | + | 0.326672i | \(0.105927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.31386 | − | 14.2525i | 0.405034 | − | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.55842 | − | 5.51856i | −0.610665 | − | 0.352568i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.3614 | + | 1.65831i | −0.913794 | + | 0.105516i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.37228 | − | 5.84096i | −0.0869648 | − | 0.370156i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9307 | − | 11.5070i | 1.25801 | − | 0.726315i | 0.285327 | − | 0.958430i | \(-0.407898\pi\) |
0.972688 | + | 0.232115i | \(0.0745646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8614 | + | 27.4728i | 0.997198 | + | 1.72720i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.55842 | + | 8.04290i | 0.473327 | + | 0.503666i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.55842 | + | 16.5557i | 0.596238 | + | 1.03271i | 0.993371 | + | 0.114953i | \(0.0366719\pi\) |
−0.397133 | + | 0.917761i | \(0.629995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.7176i | 2.34366i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.930703 | + | 0.617359i | 0.0576091 | + | 0.0382135i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9307 | + | 6.31084i | 0.674016 | + | 0.389143i | 0.797597 | − | 0.603191i | \(-0.206104\pi\) |
−0.123581 | + | 0.992335i | \(0.539438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 14.2063i | − | 0.872684i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.93070 | + | 2.05446i | 0.118157 | + | 0.125731i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.93070 | + | 13.7364i | −0.483544 | + | 0.837522i | −0.999821 | − | 0.0188992i | \(-0.993984\pi\) |
0.516278 | + | 0.856421i | \(0.327317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.93070 | − | 17.2005i | 0.603247 | − | 1.04485i | −0.389079 | − | 0.921205i | \(-0.627207\pi\) |
0.992326 | − | 0.123650i | \(-0.0394601\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.1168 | − | 13.2665i | 0.854390 | − | 0.802925i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.11684 | + | 2.37686i | −0.248255 | + | 0.143330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.4891 | −1.17099 | −0.585494 | − | 0.810677i | \(-0.699099\pi\) | ||||
−0.585494 | + | 0.810677i | \(0.699099\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.3139 | − | 20.7383i | −0.617475 | − | 1.24157i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.30298 | − | 12.6491i | −0.435660 | − | 0.754584i | 0.561690 | − | 0.827348i | \(-0.310151\pi\) |
−0.997349 | + | 0.0727635i | \(0.976818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0692967 | + | 0.120025i | −0.00411926 | + | 0.00713477i | −0.868078 | − | 0.496428i | \(-0.834645\pi\) |
0.863958 | + | 0.503563i | \(0.167978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.5584 | + | 12.2993i | 0.862366 | + | 0.728547i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7446 | + | 18.6101i | −0.634231 | + | 1.09852i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.31386 | − | 9.20387i | −0.312580 | − | 0.541404i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.67527 | + | 1.40965i | 0.274069 | + | 0.0826349i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.7446 | −1.21191 | −0.605955 | − | 0.795499i | \(-0.707209\pi\) | ||||
−0.605955 | + | 0.795499i | \(0.707209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.55842 | − | 2.05446i | 0.207179 | − | 0.119615i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.4891 | + | 13.8564i | 0.666667 | + | 0.804030i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1861 | − | 26.3032i | 0.878237 | − | 1.52115i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8030 | + | 34.2998i | −1.14143 | + | 1.97701i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.18614 | + | 2.99422i | −0.183039 | + | 0.172013i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.52434i | − | 0.144543i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.7921 | − | 15.4684i | −1.52911 | − | 0.882830i | −0.999400 | − | 0.0346493i | \(-0.988969\pi\) |
−0.529707 | − | 0.848181i | \(-0.677698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.68614 | − | 15.6896i | −0.209697 | − | 0.892553i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.9051i | − | 1.07201i | −0.844215 | − | 0.536004i | \(-0.819933\pi\) | ||
0.844215 | − | 0.536004i | \(-0.180067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.67527 | + | 16.7581i | 0.546878 | + | 0.947221i | 0.998486 | + | 0.0550045i | \(0.0175173\pi\) |
−0.451608 | + | 0.892217i | \(0.649149\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.4891 | − | 1.58457i | −1.43615 | − | 0.0892806i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.81386 | − | 13.5340i | −0.438870 | − | 0.760145i | 0.558733 | − | 0.829348i | \(-0.311288\pi\) |
−0.997603 | + | 0.0692026i | \(0.977954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.11684 | + | 0.644810i | −0.0625313 | + | 0.0361024i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.86141 | − | 2.08191i | 0.494595 | − | 0.116201i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.55842 | + | 8.83518i | 0.364920 | + | 0.491603i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.94158 | + | 2.27567i | 0.218639 | + | 0.126232i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.81386 | − | 2.05446i | −0.376807 | − | 0.113612i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.74456 | + | 1.58457i | −0.151313 | + | 0.0873604i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.96677i | 0.163068i | 0.996671 | + | 0.0815342i | \(0.0259820\pi\) | ||||
−0.996671 | + | 0.0815342i | \(0.974018\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.9416 | + | 30.0434i | 0.818793 | + | 1.64637i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.62772 | 0.198203 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7337 | − | 14.2800i | −1.34733 | − | 0.777881i | −0.359459 | − | 0.933161i | \(-0.617039\pi\) |
−0.987871 | + | 0.155280i | \(0.950372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.48913 | + | 1.28962i | −0.298128 | + | 0.0700426i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.7446 | 1.44830 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.86141 | −0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −38.9783 | + | 9.15759i | −2.09852 | + | 0.493028i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0475 | − | 13.8839i | −1.29094 | − | 0.745325i | −0.312119 | − | 0.950043i | \(-0.601039\pi\) |
−0.978821 | + | 0.204718i | \(0.934372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.60597 | 0.514196 | 0.257098 | − | 0.966385i | \(-0.417234\pi\) | ||||
0.257098 | + | 0.966385i | \(0.417234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.98913 | − | 16.1595i | 0.319676 | − | 0.862532i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.0920i | 0.590369i | 0.955440 | + | 0.295184i | \(0.0953810\pi\) | ||||
−0.955440 | + | 0.295184i | \(0.904619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0475 | − | 15.6159i | 1.43553 | − | 0.828806i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.1168 | − | 4.25639i | −0.747143 | − | 0.225272i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3030 | + | 10.5672i | 0.965995 | + | 0.557717i | 0.898013 | − | 0.439969i | \(-0.145011\pi\) |
0.0679818 | + | 0.997687i | \(0.478344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.68614 | + | 0.396143i | −0.0884994 | + | 0.0207921i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.5584 | − | 7.25061i | 0.657338 | − | 0.379514i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.61684 | − | 13.1928i | −0.397596 | − | 0.688657i | 0.595833 | − | 0.803109i | \(-0.296822\pi\) |
−0.993429 | + | 0.114452i | \(0.963489\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.18614 | + | 19.0800i | −0.0617480 | + | 0.993266i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.48913 | + | 16.4356i | 0.492651 | + | 0.853296i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.92820i | − | 0.358729i | −0.983783 | − | 0.179364i | \(-0.942596\pi\) | ||
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.62772 | + | 15.4410i | 0.187335 | + | 0.797369i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.06930 | + | 0.617359i | 0.0550716 | + | 0.0317956i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4742i | 0.640757i | 0.947290 | + | 0.320379i | \(0.103810\pi\) | ||||
−0.947290 | + | 0.320379i | \(0.896190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.81386 | − | 4.52389i | 0.246621 | − | 0.231766i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.3030 | − | 26.5055i | 0.781946 | − | 1.35437i | −0.148861 | − | 0.988858i | \(-0.547561\pi\) |
0.930807 | − | 0.365512i | \(-0.119106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7446 | − | 25.5383i | 0.751452 | − | 1.30155i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.18614 | + | 35.1658i | −0.111128 | + | 1.78758i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.1644 | − | 12.7966i | 1.12378 | − | 0.648814i | 0.181416 | − | 0.983406i | \(-0.441932\pi\) |
0.942363 | + | 0.334592i | \(0.108599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.1168 | −1.16907 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.3030 | − | 8.83518i | −1.47814 | − | 0.445676i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.9307 | + | 32.7889i | 0.952507 | + | 1.64979i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.6168 | − | 21.8530i | 0.633221 | − | 1.09677i | −0.353668 | − | 0.935371i | \(-0.615066\pi\) |
0.986889 | − | 0.161400i | \(-0.0516010\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.0584 | − | 4.50506i | −1.25449 | − | 0.225535i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6753 | + | 28.8824i | −0.832723 | + | 1.44232i | 0.0631479 | + | 0.998004i | \(0.479886\pi\) |
−0.895871 | + | 0.444314i | \(0.853447\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8030 | − | 22.1754i | −0.637762 | − | 1.10464i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.9307 | + | 8.83518i | −1.04006 | + | 0.439024i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.7446 | −1.92050 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7921 | + | 6.80818i | −0.583082 | + | 0.336643i | −0.762357 | − | 0.647156i | \(-0.775958\pi\) |
0.179275 | + | 0.983799i | \(0.442625\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.6753 | + | 19.4299i | −1.01984 | + | 0.958405i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.74456 | + | 4.75372i | −0.135051 | + | 0.233915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.37228 | + | 7.57301i | −0.214627 | + | 0.371745i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.69702 | + | 8.19037i | 0.376924 | + | 0.401084i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9822i | 0.536516i | 0.963347 | + | 0.268258i | \(0.0864480\pi\) | ||||
−0.963347 | + | 0.268258i | \(0.913552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7921 | − | 10.2723i | −0.867134 | − | 0.500640i | −0.000739475 | − | 1.00000i | \(-0.500235\pi\) |
−0.866395 | + | 0.499359i | \(0.833569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.55842 | + | 2.34941i | −0.0757731 | + | 0.114232i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.46410i | − | 0.168034i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.68614 | + | 2.92048i | 0.0815981 | + | 0.141332i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.6277 | + | 14.5012i | 0.657952 | + | 0.700125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.06930 | + | 7.04823i | 0.196011 | + | 0.339501i | 0.947232 | − | 0.320550i | \(-0.103868\pi\) |
−0.751220 | + | 0.660051i | \(0.770534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.7337 | + | 17.7441i | −1.47697 | + | 0.852727i | −0.999662 | − | 0.0260105i | \(-0.991720\pi\) |
−0.477305 | + | 0.878738i | \(0.658386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.372281 | − | 1.58457i | −0.0178495 | − | 0.0759745i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −39.6535 | + | 4.57879i | −1.89688 | + | 0.219033i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.50000 | + | 2.59808i | 0.214773 | + | 0.123999i | 0.603528 | − | 0.797342i | \(-0.293761\pi\) |
−0.388755 | + | 0.921341i | \(0.627095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7446 | − | 5.84096i | 0.559265 | − | 0.278141i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.5367 | − | 13.5889i | 1.11826 | − | 0.645628i | 0.177305 | − | 0.984156i | \(-0.443262\pi\) |
0.940956 | + | 0.338528i | \(0.109929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4.10891i | − | 0.194781i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.5584 | + | 3.78651i | 0.593993 | + | 0.179096i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4674 | 1.43784 | 0.718922 | − | 0.695091i | \(-0.244636\pi\) | ||||
0.718922 | + | 0.695091i | \(0.244636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1168 | − | 11.0371i | −0.900177 | − | 0.519717i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.116844 | − | 0.497333i | −0.00548981 | − | 0.0233668i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28.2337 | −1.32362 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.6277 | 1.43270 | 0.716352 | − | 0.697739i | \(-0.245810\pi\) | ||||
0.716352 | + | 0.697739i | \(0.245810\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.9307 | + | 2.20193i | −0.603554 | + | 0.102777i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.9307 | + | 14.9711i | 1.20771 | + | 0.697274i | 0.962259 | − | 0.272135i | \(-0.0877296\pi\) |
0.245454 | + | 0.969408i | \(0.421063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3723 | 1.08620 | 0.543101 | − | 0.839667i | \(-0.317250\pi\) | ||||
0.543101 | + | 0.839667i | \(0.317250\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.74456 | + | 32.3191i | −0.451893 | + | 1.49876i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 42.2689i | − | 1.95597i | −0.208668 | − | 0.977986i | \(-0.566913\pi\) | ||
0.208668 | − | 0.977986i | \(-0.433087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.19702 | + | 2.42315i | −0.193800 | + | 0.111891i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.24456 | − | 4.12775i | 0.0573464 | − | 0.190197i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.2337 | − | 20.3422i | −1.62005 | − | 0.935334i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.686141 | − | 5.94215i | −0.0314823 | − | 0.272645i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.0693 | + | 9.33252i | 0.644189 | + | 0.427307i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9307 | + | 13.2390i | −1.04773 | + | 0.604908i | −0.922013 | − | 0.387159i | \(-0.873457\pi\) |
−0.125717 | + | 0.992066i | \(0.540123\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.5475 | + | 32.1253i | 0.845695 | + | 1.46479i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.9783 | − | 36.6303i | 1.77357 | − | 1.66674i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.55842 | − | 6.16337i | −0.161580 | − | 0.279864i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5615i | 0.614528i | 0.951624 | + | 0.307264i | \(0.0994135\pi\) | ||||
−0.951624 | + | 0.307264i | \(0.900587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.9198 | − | 6.08963i | 1.17214 | − | 0.275383i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.67527 | + | 4.43132i | 0.346380 | + | 0.199983i | 0.663090 | − | 0.748540i | \(-0.269245\pi\) |
−0.316710 | + | 0.948522i | \(0.602578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.939764i | − | 0.0423248i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.62772 | − | 26.1831i | 0.0731605 | − | 1.17684i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.8614 | + | 36.1330i | −0.935762 | + | 1.62079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.12772 | − | 10.6135i | 0.274314 | − | 0.475126i | −0.695648 | − | 0.718383i | \(-0.744882\pi\) |
0.969962 | + | 0.243257i | \(0.0782158\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.04755 | − | 1.11469i | −0.0468010 | − | 0.0498008i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.8139 | − | 19.5224i | 1.50769 | − | 0.870463i | 0.507725 | − | 0.861519i | \(-0.330486\pi\) |
0.999960 | − | 0.00894369i | \(-0.00284690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.37228 | 0.283563 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | + | 3.31662i | −0.0444116 | + | 0.147296i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.55842 | + | 6.16337i | 0.157724 | + | 0.273186i | 0.934048 | − | 0.357148i | \(-0.116251\pi\) |
−0.776323 | + | 0.630335i | \(0.782918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.68614 | + | 16.7769i | −0.428490 | + | 0.742166i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.7446 | + | 6.33830i | −0.960046 | + | 0.279843i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7446 | + | 20.3422i | −0.517527 | + | 0.896384i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.62772 | − | 2.81929i | −0.0715870 | − | 0.123992i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.93070 | − | 22.9865i | 0.304224 | − | 1.00900i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.24456 | + | 0.718549i | −0.0544209 | + | 0.0314199i | −0.526964 | − | 0.849888i | \(-0.676670\pi\) |
0.472543 | + | 0.881308i | \(0.343336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.48913 | + | 5.84096i | 0.239565 | + | 0.254921i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.74456 | + | 16.8781i | −0.424480 | + | 0.735221i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.4307 | − | 52.7075i | 1.32307 | − | 2.29163i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.302985 | + | 4.87375i | −0.0131484 | + | 0.211503i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.1345i | 0.915435i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.4891 | − | 6.63325i | −0.496718 | − | 0.286780i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.51087 | + | 0.589907i | −0.108352 | + | 0.0254564i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.1460i | 0.652386i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9891 | − | 25.9619i | −0.644433 | − | 1.11619i | −0.984432 | − | 0.175765i | \(-0.943760\pi\) |
0.339999 | − | 0.940426i | \(-0.389573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.6753 | + | 25.0684i | −1.14475 | + | 1.07579i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.18614 | + | 8.98266i | 0.222150 | + | 0.384775i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.3832 | + | 10.6135i | −0.786007 | + | 0.453801i | −0.838555 | − | 0.544817i | \(-0.816599\pi\) |
0.0525479 | + | 0.998618i | \(0.483266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.50000 | + | 1.65831i | 0.106697 | + | 0.0707750i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.186141 | − | 1.61203i | −0.00792986 | − | 0.0686746i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.8030 | − | 25.2897i | −1.86269 | − | 1.07543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.1168 | − | 46.8203i | 0.599227 | − | 1.98741i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0693 | − | 7.54556i | 0.553764 | − | 0.319716i | −0.196875 | − | 0.980429i | \(-0.563079\pi\) |
0.750639 | + | 0.660713i | \(0.229746\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.9523i | 1.64751i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.37228 | − | 14.5012i | 0.184598 | − | 0.612242i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.7228 | 0.578348 | 0.289174 | − | 0.957277i | \(-0.406619\pi\) | ||||
0.289174 | + | 0.957277i | \(0.406619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.11684 | + | 4.10891i | 0.299408 | + | 0.172863i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.3139 | − | 24.2024i | 0.769110 | − | 1.01641i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.2554 | −1.14261 | −0.571304 | − | 0.820739i | \(-0.693562\pi\) | ||||
−0.571304 | + | 0.820739i | \(0.693562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3723 | 0.643310 | 0.321655 | − | 0.946857i | \(-0.395761\pi\) | ||||
0.321655 | + | 0.946857i | \(0.395761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.62772 | − | 11.1846i | −0.109775 | − | 0.467243i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8832 | + | 6.28339i | 0.453859 | + | 0.262036i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.51087 | −0.187790 | −0.0938951 | − | 0.995582i | \(-0.529932\pi\) | ||||
−0.0938951 | + | 0.995582i | \(0.529932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.8505 | + | 7.79423i | 1.07431 | + | 0.323917i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.6819i | − | 0.484648i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.8832 | + | 9.74749i | −0.699229 | + | 0.403700i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.4891 | + | 11.1846i | −0.929811 | + | 0.462426i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.1861 | − | 23.7788i | −1.69993 | − | 0.981457i | −0.945807 | − | 0.324728i | \(-0.894727\pi\) |
−0.754127 | − | 0.656729i | \(-0.771940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.3723 | + | 30.8820i | −0.550995 | + | 1.27247i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.25544 | − | 39.3947i | −0.380718 | − | 1.62048i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.0475 | + | 15.6159i | −1.11071 | + | 0.641269i | −0.939013 | − | 0.343881i | \(-0.888258\pi\) |
−0.171697 | + | 0.985150i | \(0.554925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.7446 | + | 18.6101i | 0.440484 | + | 0.762941i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.95245 | + | 3.14170i | 0.120836 | + | 0.128581i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.55842 | − | 14.8236i | −0.349688 | − | 0.605677i | 0.636506 | − | 0.771272i | \(-0.280379\pi\) |
−0.986194 | + | 0.165595i | \(0.947046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2766i | 0.908682i | 0.890828 | + | 0.454341i | \(0.150125\pi\) | ||||
−0.890828 | + | 0.454341i | \(0.849875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.38316 | + | 3.59274i | −0.0970496 | + | 0.146308i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.18614 | + | 1.26217i | 0.0888793 | + | 0.0513145i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 0.792287i | − | 0.0321579i | −0.999871 | − | 0.0160790i | \(-0.994882\pi\) | ||
0.999871 | − | 0.0160790i | \(-0.00511832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.48913 | + | 1.58457i | 0.0603424 | + | 0.0642102i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.55842 | + | 2.69927i | −0.0630470 | + | 0.109201i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5584 | + | 21.7518i | −0.507230 | + | 0.878548i | 0.492735 | + | 0.870179i | \(0.335997\pi\) |
−0.999965 | + | 0.00836857i | \(0.997336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.3030 | − | 19.0800i | 0.818695 | − | 0.769380i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.5584 | − | 7.25061i | 0.505583 | − | 0.291898i | −0.225433 | − | 0.974259i | \(-0.572380\pi\) |
0.731016 | + | 0.682360i | \(0.239046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.13859 | 0.126151 | 0.0630754 | − | 0.998009i | \(-0.479909\pi\) | ||||
0.0630754 | + | 0.998009i | \(0.479909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.5367 | − | 44.6183i | 0.663594 | − | 1.79047i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.74456 | + | 4.75372i | 0.109959 | + | 0.190454i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.9891 | − | 25.9619i | 0.599565 | − | 1.03848i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.62772 | − | 25.7407i | 0.184813 | − | 1.02798i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1168 | − | 24.4511i | 0.562875 | − | 0.974929i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6168 | + | 21.8530i | 0.502269 | + | 0.869955i | 0.999997 | + | 0.00262157i | \(0.000834473\pi\) |
−0.497728 | + | 0.867333i | \(0.665832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.1277 | + | 5.76722i | 0.760259 | + | 0.229227i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.62772 | −0.382064 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.5584 | − | 7.25061i | 0.497583 | − | 0.287280i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.30298 | + | 37.0453i | −0.0911047 | + | 1.46549i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.1861 | + | 22.8391i | −0.520821 | + | 0.902089i | 0.478886 | + | 0.877877i | \(0.341041\pi\) |
−0.999707 | + | 0.0242115i | \(0.992292\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.50000 | − | 2.59808i | 0.0591542 | − | 0.102458i | −0.834932 | − | 0.550353i | \(-0.814493\pi\) |
0.894086 | + | 0.447895i | \(0.147826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.4198 | − | 35.1658i | 1.47340 | − | 1.38465i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.9104i | 0.704131i | 0.935975 | + | 0.352066i | \(0.114521\pi\) | ||||
−0.935975 | + | 0.352066i | \(0.885479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.88316 | − | 2.81929i | −0.191681 | − | 0.110667i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3139 | − | 43.8998i | −0.404232 | − | 1.72057i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.17448i | 0.0850940i | 0.999094 | + | 0.0425470i | \(0.0135472\pi\) | ||||
−0.999094 | + | 0.0425470i | \(0.986453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3030 | + | 38.6299i | 0.871450 | + | 1.50940i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.06930 | + | 17.2005i | −0.0417172 | + | 0.671055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0475 | − | 20.8670i | −0.469306 | − | 0.812862i | 0.530078 | − | 0.847949i | \(-0.322162\pi\) |
−0.999384 | + | 0.0350871i | \(0.988829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3030 | + | 14.0313i | −0.945277 | + | 0.545756i | −0.891610 | − | 0.452803i | \(-0.850424\pi\) |
−0.0536661 | + | 0.998559i | \(0.517091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1168 | + | 3.31662i | −0.548253 | + | 0.128807i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.1168 | + | 29.7947i | 0.857654 | + | 1.15539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.95245 | + | 1.70460i | 0.114319 | + | 0.0660024i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.8723 | + | 10.8159i | 1.38690 | + | 0.418167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | + | 1.73205i | −0.115814 | + | 0.0668651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.08191i | 0.0802516i | 0.999195 | + | 0.0401258i | \(0.0127759\pi\) | ||||
−0.999195 | + | 0.0401258i | \(0.987224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.68614 | + | 2.47805i | 0.257350 | + | 0.0953802i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.2554 | −0.586314 | −0.293157 | − | 0.956064i | \(-0.594706\pi\) | ||||
−0.293157 | + | 0.956064i | \(0.594706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.23369 | + | 4.75372i | 0.315980 | + | 0.182431i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.6060 | + | 7.42554i | −1.21114 | + | 0.284547i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.74456 | 0.258074 | 0.129037 | − | 0.991640i | \(-0.458811\pi\) | ||||
0.129037 | + | 0.991640i | \(0.458811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.3505 | 1.57992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.54755 | + | 1.53829i | −0.249805 | + | 0.0586893i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.1644 | + | 9.33252i | 0.615814 | + | 0.355541i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.9565 | 1.90043 | 0.950217 | − | 0.311588i | \(-0.100861\pi\) | ||||
0.950217 | + | 0.311588i | \(0.100861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.6060 | + | 31.3793i | 0.592822 | + | 1.19200i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 16.3807i | − | 0.621357i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.9307 | − | 8.04290i | 0.527663 | − | 0.304646i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0475 | + | 7.25061i | 0.909562 | + | 0.274243i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.44158 | − | 3.14170i | −0.205526 | − | 0.118660i | 0.393705 | − | 0.919237i | \(-0.371193\pi\) |
−0.599230 | + | 0.800577i | \(0.704527\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3723 | − | 44.7384i | 0.730639 | − | 1.68734i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | − | 0.939764i | 0.150649 | − | 0.0353936i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.37228 | + | 4.25639i | −0.277263 | + | 0.160078i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2446 | + | 19.4762i | 0.422298 | + | 0.731442i | 0.996164 | − | 0.0875073i | \(-0.0278901\pi\) |
−0.573865 | + | 0.818950i | \(0.694557\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.9090 | − | 2.79184i | −1.68422 | − | 0.104702i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.3505 | − | 61.2289i | −1.32389 | − | 2.29304i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 29.0024i | − | 1.08463i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.11684 | − | 17.5229i | −0.153746 | − | 0.654404i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.813859 | + | 0.469882i | 0.0303518 | + | 0.0175236i | 0.515099 | − | 0.857131i | \(-0.327755\pi\) |
−0.484747 | + | 0.874654i | \(0.661088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 31.3793i | − | 1.16863i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.6753 | − | 24.1287i | 0.954873 | − | 0.897355i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.255437 | + | 0.442430i | −0.00948671 | + | 0.0164315i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.1277 | + | 19.2738i | −0.412704 | + | 0.714825i | −0.995184 | − | 0.0980202i | \(-0.968749\pi\) |
0.582480 | + | 0.812845i | \(0.302082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.6753 | − | 14.8236i | 0.949634 | − | 0.548271i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9783 | 0.774849 | 0.387425 | − | 0.921901i | \(-0.373365\pi\) | ||||
0.387425 | + | 0.921901i | \(0.373365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.3030 | − | 5.51856i | −0.675116 | − | 0.203555i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.48913 | − | 4.31129i | −0.0916881 | − | 0.158808i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.75544 | + | 6.50461i | −0.138146 | + | 0.239276i | −0.926795 | − | 0.375568i | \(-0.877448\pi\) |
0.788649 | + | 0.614844i | \(0.210781\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.5584 | + | 8.48533i | −0.865440 | + | 0.311716i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.18614 | + | 14.1788i | −0.300320 | + | 0.520170i | −0.976208 | − | 0.216834i | \(-0.930427\pi\) |
0.675888 | + | 0.737004i | \(0.263760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.55842 | − | 16.5557i | −0.350193 | − | 0.606553i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.62772 | − | 9.30506i | −0.169319 | − | 0.340454i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.7228 | 0.647578 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.01087 | − | 1.16098i | 0.0733779 | − | 0.0423647i | −0.462862 | − | 0.886430i | \(-0.653178\pi\) |
0.536240 | + | 0.844066i | \(0.319844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.0475 | − | 27.2978i | 1.05855 | − | 0.994788i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.372281 | + | 0.644810i | −0.0135487 | + | 0.0234670i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.12772 | − | 12.3456i | 0.259061 | − | 0.448707i | −0.706929 | − | 0.707284i | \(-0.749920\pi\) |
0.965991 | + | 0.258577i | \(0.0832535\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.6277 | + | 40.0395i | 1.36580 | + | 1.45334i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.6048i | − | 0.710673i | −0.934738 | − | 0.355337i | \(-0.884366\pi\) | ||
0.934738 | − | 0.355337i | \(-0.115634\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.0000 | − | 6.92820i | −0.434429 | − | 0.250818i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.9307 | + | 10.5672i | 0.575976 | + | 0.382059i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.39853i | 0.194930i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.8723 | + | 27.4916i | 0.572369 | + | 0.991372i | 0.996322 | + | 0.0856881i | \(0.0273089\pi\) |
−0.423953 | + | 0.905684i | \(0.639358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.6753 | + | 24.1287i | 0.816630 | + | 0.868973i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8139 | + | 32.5866i | 0.676687 | + | 1.17206i | 0.975973 | + | 0.217893i | \(0.0699185\pi\) |
−0.299285 | + | 0.954164i | \(0.596748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.17527 | − | 5.29734i | 0.329585 | − | 0.190286i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.9416 | + | 63.5972i | 0.536026 | + | 2.28154i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.3030 | − | 16.5557i | 0.799087 | − | 0.593169i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.1168 | − | 21.4294i | −1.32815 | − | 0.766805i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.81386 | + | 0.672262i | 0.0648220 | + | 0.0240247i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.44158 | + | 3.14170i | −0.194218 | + | 0.112132i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.37686i | − | 0.0847259i | −0.999102 | − | 0.0423630i | \(-0.986511\pi\) | ||
0.999102 | − | 0.0423630i | \(-0.0134886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.9307 | + | 6.31084i | 0.745153 | + | 0.224672i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9783 | −0.390342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.87228 | + | 1.65831i | 0.101998 | + | 0.0588884i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.62772 | − | 23.9538i | −0.199595 | − | 0.849552i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.5109 | −0.868220 | −0.434110 | − | 0.900860i | \(-0.642937\pi\) | ||||
−0.434110 | + | 0.900860i | \(0.642937\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.37228 | 0.0839253 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.06930 | + | 2.69927i | 0.143782 | + | 0.0953739i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.2337 | − | 9.94987i | −0.608164 | − | 0.351123i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −77.9565 | −2.74761 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.93070 | + | 26.3032i | −0.279174 | + | 0.925915i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.58457i | 0.0557107i | 0.999612 | + | 0.0278553i | \(0.00886777\pi\) | ||||
−0.999612 | + | 0.0278553i | \(0.991132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.67527 | + | 0.967215i | −0.0588265 | + | 0.0339635i | −0.529125 | − | 0.848544i | \(-0.677480\pi\) |
0.470298 | + | 0.882508i | \(0.344146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.93070 | − | 32.9364i | 0.348285 | − | 1.15513i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.6060 | − | 19.4024i | −1.17717 | − | 0.679637i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.1060 | − | 30.5133i | 1.43812 | − | 1.06752i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.5475 | − | 27.9615i | 0.648104 | − | 0.977053i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.9090 | + | 9.18504i | −0.555226 | + | 0.320560i | −0.751227 | − | 0.660044i | \(-0.770538\pi\) |
0.196001 | + | 0.980604i | \(0.437204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.9307 | − | 31.0569i | −0.625025 | − | 1.08258i | −0.988536 | − | 0.150985i | \(-0.951755\pi\) |
0.363511 | − | 0.931590i | \(-0.381578\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | + | 5.63858i | −0.208893 | + | 0.196310i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9307 | + | 29.3248i | 0.588738 | + | 1.01972i | 0.994398 | + | 0.105700i | \(0.0337084\pi\) |
−0.405660 | + | 0.914024i | \(0.632958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.25106i | − | 0.182377i | −0.995834 | − | 0.0911883i | \(-0.970933\pi\) | ||
0.995834 | − | 0.0911883i | \(-0.0290665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.8614 | + | 7.72049i | −1.13995 | + | 0.267821i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.55842 | − | 5.51856i | −0.331180 | − | 0.191207i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.22938i | 0.0771510i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.6060 | − | 30.8820i | −0.885072 | − | 1.06744i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.18614 | + | 7.25061i | −0.144522 | + | 0.250319i | −0.929194 | − | 0.369591i | \(-0.879498\pi\) |
0.784673 | + | 0.619910i | \(0.212831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4307 | − | 24.9947i | 0.497610 | − | 0.861887i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.3247 | − | 18.4352i | −0.596696 | − | 0.634942i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.37228 | − | 2.52434i | 0.150411 | − | 0.0868399i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.37228 | −0.115873 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0692967 | + | 0.229831i | −0.00237826 | + | 0.00788778i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.2119 | + | 88.7017i | 1.75552 | + | 3.04065i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.872281 | + | 1.51084i | −0.0298663 | + | 0.0517300i | −0.880572 | − | 0.473912i | \(-0.842841\pi\) |
0.850706 | + | 0.525642i | \(0.176175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.4198 | + | 14.9711i | 1.00614 | + | 0.512001i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.18614 | + | 8.98266i | −0.177155 | + | 0.306842i | −0.940905 | − | 0.338671i | \(-0.890023\pi\) |
0.763750 | + | 0.645512i | \(0.223356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6168 | + | 35.7094i | 0.703438 | + | 1.21839i | 0.967252 | + | 0.253816i | \(0.0816859\pi\) |
−0.263815 | + | 0.964573i | \(0.584981\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7446 | + | 35.6357i | −0.366174 | + | 1.21446i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.4891 | −1.13998 | −0.569992 | − | 0.821651i | \(-0.693054\pi\) | ||||
−0.569992 | + | 0.821651i | \(0.693054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.3030 | + | 17.4954i | −1.03033 | + | 0.594863i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.6060 | − | 13.4140i | −0.428121 | − | 0.455563i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9783 | − | 44.9956i | 0.881252 | − | 1.52637i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.38316 | + | 4.12775i | −0.0807502 | + | 0.139863i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.44158 | + | 0.524785i | 0.285704 | + | 0.0177613i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.8820i | 1.04400i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3614 | − | 6.55951i | −0.383647 | − | 0.221499i | 0.295757 | − | 0.955263i | \(-0.404428\pi\) |
−0.679404 | + | 0.733764i | \(0.737762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −34.9783 | + | 8.21782i | −1.17979 | + | 0.277180i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.4410i | − | 0.520220i | −0.965579 | − | 0.260110i | \(-0.916241\pi\) | ||
0.965579 | − | 0.260110i | \(-0.0837588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.12772 | − | 7.14942i | −0.138909 | − | 0.240597i | 0.788175 | − | 0.615451i | \(-0.211026\pi\) |
−0.927084 | + | 0.374854i | \(0.877693\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.18614 | − | 4.87375i | 0.174330 | − | 0.163829i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3030 | + | 31.7017i | 0.614554 | + | 1.06444i | 0.990463 | + | 0.137782i | \(0.0439974\pi\) |
−0.375908 | + | 0.926657i | \(0.622669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.1386 | − | 6.43087i | 0.373576 | − | 0.215684i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.8614 | + | 18.8125i | 0.832888 | + | 0.630243i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.06930 | − | 0.469882i | 0.136174 | − | 0.0157240i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.25544 | + | 1.87953i | 0.108817 | + | 0.0628257i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.1861 | − | 50.3667i | 0.507050 | − | 1.68170i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.48913 | − | 1.43710i | 0.0830170 | − | 0.0479299i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.2063i | − | 0.473279i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.8030 | + | 65.6791i | −0.659002 | + | 2.18566i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53.3505 | 1.77343 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4416 | + | 10.0699i | 0.579138 | + | 0.334366i | 0.760791 | − | 0.648997i | \(-0.224811\pi\) |
−0.181653 | + | 0.983363i | \(0.558145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.18614 | + | 6.31084i | −0.138846 | + | 0.209317i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.4891 | −0.446915 | −0.223457 | − | 0.974714i | \(-0.571734\pi\) | ||||
−0.223457 | + | 0.974714i | \(0.571734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.00000 | − | 4.25639i | −0.0330590 | − | 0.140712i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −51.6060 | − | 29.7947i | −1.70418 | − | 0.983908i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.86141 | −0.292311 | −0.146155 | − | 0.989262i | \(-0.546690\pi\) | ||||
−0.146155 | + | 0.989262i | \(0.546690\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.3030 | − | 15.4684i | −1.69049 | − | 0.509702i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.0342i | 1.35066i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.2921 | + | 7.67420i | −0.437042 | + | 0.252326i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4307 | − | 24.9947i | −0.408278 | − | 0.820934i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.1861 | − | 11.6545i | −0.662286 | − | 0.382371i | 0.130862 | − | 0.991401i | \(-0.458226\pi\) |
−0.793147 | + | 0.609030i | \(0.791559\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.4891 | − | 7.57301i | −0.573183 | − | 0.248195i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.48913 | − | 31.8766i | −0.245183 | − | 1.04359i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.1168 | + | 11.0371i | −0.625188 | + | 0.360952i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.9891 | − | 29.4260i | −0.555011 | − | 0.961306i | −0.997903 | − | 0.0647316i | \(-0.979381\pi\) |
0.442892 | − | 0.896575i | \(-0.353952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.9525 | + | 24.4236i | 0.749025 | + | 0.797035i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.69702 | − | 13.3316i | −0.250916 | − | 0.434598i | 0.712863 | − | 0.701304i | \(-0.247398\pi\) |
−0.963778 | + | 0.266705i | \(0.914065\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.3547i | 1.90029i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −43.6060 | + | 7.42554i | −1.41850 | + | 0.241553i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.81386 | − | 2.20193i | −0.123934 | − | 0.0715532i | 0.436752 | − | 0.899582i | \(-0.356129\pi\) |
−0.560685 | + | 0.828029i | \(0.689462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.0526i | 0.618472i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.5367 | − | 19.7248i | −0.601093 | − | 0.639621i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.69702 | − | 8.13547i | 0.152151 | − | 0.263534i | −0.779867 | − | 0.625945i | \(-0.784713\pi\) |
0.932018 | + | 0.362412i | \(0.118047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.37228 | + | 14.5012i | −0.270921 | + | 0.469248i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.62772 | + | 1.52967i | −0.0526167 | + | 0.0494472i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −47.8397 | + | 27.6202i | −1.54482 | + | 0.891904i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6060 | −0.922773 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.1168 | − | 7.02078i | 0.454909 | − | 0.226241i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.6753 | − | 34.0786i | −0.633369 | − | 1.09703i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.87228 | + | 6.70699i | −0.124524 | + | 0.215682i | −0.921547 | − | 0.388267i | \(-0.873074\pi\) |
0.797023 | + | 0.603949i | \(0.206407\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5584 | + | 12.2993i | 0.467684 | + | 0.395110i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.9307 | − | 24.1287i | 0.447058 | − | 0.774326i | −0.551135 | − | 0.834416i | \(-0.685805\pi\) |
0.998193 | + | 0.0600894i | \(0.0191386\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.9416 | + | 18.9514i | 0.350771 | + | 0.607553i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.54755 | + | 2.27567i | 0.241715 | + | 0.0728798i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.2119 | 1.19052 | 0.595258 | − | 0.803535i | \(-0.297050\pi\) | ||||
0.595258 | + | 0.803535i | \(0.297050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.88316 | + | 2.81929i | −0.156066 | + | 0.0901049i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.3030 | − | 0.764836i | −0.392804 | − | 0.0244193i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9307 | + | 22.3966i | −0.412425 | + | 0.714342i | −0.995154 | − | 0.0983248i | \(-0.968652\pi\) |
0.582729 | + | 0.812667i | \(0.301985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.4891 | + | 51.0767i | −0.939602 | + | 1.62744i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.00000 | + | 3.75906i | −0.127321 | + | 0.119652i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 107.552i | 3.41995i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.12772 | + | 5.26989i | 0.289952 | + | 0.167404i | 0.637920 | − | 0.770103i | \(-0.279795\pi\) |
−0.347968 | + | 0.937506i | \(0.613128\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.17527 | + | 5.00239i | 0.0372959 | + | 0.158746i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6.28339i | − | 0.199197i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2446 | − | 31.6005i | −0.577811 | − | 1.00080i | −0.995730 | − | 0.0923138i | \(-0.970574\pi\) |
0.417919 | − | 0.908484i | \(-0.362760\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37.0951 | + | 44.7384i | 1.17364 | + | 1.41546i |
(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 | 456.2.bf.a.65.2 | ✓ | 4 | |
3.2 | odd | 2 | 456.2.bf.b.65.2 | yes | 4 | ||
4.3 | odd | 2 | 912.2.bn.j.65.1 | 4 | |||
12.11 | even | 2 | 912.2.bn.i.65.1 | 4 | |||
19.12 | odd | 6 | 456.2.bf.b.449.1 | yes | 4 | ||
57.50 | even | 6 | inner | 456.2.bf.a.449.2 | yes | 4 | |
76.31 | even | 6 | 912.2.bn.i.449.2 | 4 | |||
228.107 | odd | 6 | 912.2.bn.j.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.bf.a.65.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
456.2.bf.a.449.2 | yes | 4 | 57.50 | even | 6 | inner | |
456.2.bf.b.65.2 | yes | 4 | 3.2 | odd | 2 | ||
456.2.bf.b.449.1 | yes | 4 | 19.12 | odd | 6 | ||
912.2.bn.i.65.1 | 4 | 12.11 | even | 2 | |||
912.2.bn.i.449.2 | 4 | 76.31 | even | 6 | |||
912.2.bn.j.65.1 | 4 | 4.3 | odd | 2 | |||
912.2.bn.j.449.1 | 4 | 228.107 | odd | 6 |