LMFDB - Embedded newform 1232.2.be.b.1167.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(815,1232)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1232.815");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.be (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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1167.10
Character	$\chi$	$=$	1232.1167
Dual form			1232.2.be.b.815.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.534042 + 0.924987i) q^{3} +(-2.90816 - 1.67903i) q^{5} +(0.00296709 + 2.64575i) q^{7} +(0.929599 - 1.61011i) q^{9} +O(q^{10})$	\(q+(0.534042 + 0.924987i) q^{3} +(-2.90816 - 1.67903i) q^{5} +(0.00296709 + 2.64575i) q^{7} +(0.929599 - 1.61011i) q^{9} +(-0.866025 + 0.500000i) q^{11} +0.179479i q^{13} -3.58668i q^{15} +(6.57865 - 3.79818i) q^{17} +(-1.36632 + 2.36654i) q^{19} +(-2.44570 + 1.41569i) q^{21} +(1.92258 + 1.11000i) q^{23} +(3.13826 + 5.43563i) q^{25} +5.19003 q^{27} -2.27278 q^{29} +(4.95243 + 8.57787i) q^{31} +(-0.924987 - 0.534042i) q^{33} +(4.43366 - 7.69924i) q^{35} +(-3.44854 + 5.97305i) q^{37} +(-0.166016 + 0.0958494i) q^{39} +8.27425i q^{41} +1.24901i q^{43} +(-5.40684 + 3.12164i) q^{45} +(2.31266 - 4.00564i) q^{47} +(-6.99998 + 0.0157004i) q^{49} +(7.02654 + 4.05678i) q^{51} +(4.21100 + 7.29366i) q^{53} +3.35805 q^{55} -2.91869 q^{57} +(3.85081 + 6.66981i) q^{59} +(4.31253 + 2.48984i) q^{61} +(4.26271 + 2.45471i) q^{63} +(0.301350 - 0.521954i) q^{65} +(4.07575 - 2.35313i) q^{67} +2.37115i q^{69} -6.96826i q^{71} +(12.6036 - 7.27671i) q^{73} +(-3.35192 + 5.80570i) q^{75} +(-1.32544 - 2.28980i) q^{77} +(-3.00092 - 1.73258i) q^{79} +(-0.0171051 - 0.0296269i) q^{81} +14.4143 q^{83} -25.5090 q^{85} +(-1.21376 - 2.10230i) q^{87} +(6.60674 + 3.81440i) q^{89} +(-0.474857 + 0.000532531i) q^{91} +(-5.28961 + 9.16188i) q^{93} +(7.94697 - 4.58818i) q^{95} -11.9139i q^{97} +1.85920i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9	$ 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9} + 18 q^{17} - 14 q^{19} - 2 q^{21} + 12 q^{23} + 14 q^{25} + 16 q^{27} + 16 q^{29} - 10 q^{31} - 6 q^{35} - 4 q^{37} - 42 q^{39} - 42 q^{45} - 6 q^{47} - 4 q^{49} + 24 q^{51} - 2 q^{53} - 48 q^{57} + 12 q^{59} - 12 q^{61} + 26 q^{63} + 6 q^{65} + 48 q^{67} + 6 q^{73} + 14 q^{75} + 2 q^{77} - 48 q^{79} - 22 q^{81} + 84 q^{83} + 16 q^{85} - 18 q^{87} + 6 q^{89} + 18 q^{91} + 28 q^{93} + 36 q^{95}+O(q^{100}) $ 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9 + 18 * q^17 - 14 * q^19 - 2 * q^21 + 12 * q^23 + 14 * q^25 + 16 * q^27 + 16 * q^29 - 10 * q^31 - 6 * q^35 - 4 * q^37 - 42 * q^39 - 42 * q^45 - 6 * q^47 - 4 * q^49 + 24 * q^51 - 2 * q^53 - 48 * q^57 + 12 * q^59 - 12 * q^61 + 26 * q^63 + 6 * q^65 + 48 * q^67 + 6 * q^73 + 14 * q^75 + 2 * q^77 - 48 * q^79 - 22 * q^81 + 84 * q^83 + 16 * q^85 - 18 * q^87 + 6 * q^89 + 18 * q^91 + 28 * q^93 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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
$2$		0			0
$3$	0.534042	+	0.924987i	0.308329	+	0.534042i	0.977997	−	0.208619i	$-0.0668969\pi$
$3$	0.534042	+	0.924987i	0.308329	+	0.534042i	−0.669668	+	0.742661i	$0.733564\pi$
$4$		0			0
$5$	−2.90816	−	1.67903i	−1.30057	−	0.750884i	−0.320067	−	0.947395i	$-0.603705\pi$
$5$	−2.90816	−	1.67903i	−1.30057	−	0.750884i	−0.980502	+	0.196511i	$0.937039\pi$
$6$		0			0
$7$	0.00296709	+	2.64575i	0.00112145	+	0.999999i
$7$	0.00296709	+	2.64575i	0.00112145	+	0.999999i
$8$		0			0
$9$	0.929599	−	1.61011i	0.309866	−	0.536704i
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$		0			0
$13$			0.179479i			0.0497786i	0.999690	+	0.0248893i	$0.00792332\pi$
$13$			0.179479i			0.0497786i	−0.999690	+	0.0248893i	$0.992077\pi$
$14$		0			0
$15$		−	3.58668i		−	0.926077i
$16$		0			0
$17$	6.57865	−	3.79818i	1.59556	−	0.921195i	0.603227	−	0.797570i	$-0.293881\pi$
$17$	6.57865	−	3.79818i	1.59556	−	0.921195i	0.992329	−	0.123625i	$-0.0394519\pi$
$18$		0			0
$19$	−1.36632	+	2.36654i	−0.313456	+	0.542921i	−0.979108	−	0.203341i	$-0.934820\pi$
$19$	−1.36632	+	2.36654i	−0.313456	+	0.542921i	0.665652	+	0.746262i	$0.268153\pi$
$20$		0			0
$21$	−2.44570	+	1.41569i	−0.533696	+	0.308928i
$22$		0			0
$23$	1.92258	+	1.11000i	0.400886	+	0.231452i	0.686866	−	0.726784i	$-0.258986\pi$
$23$	1.92258	+	1.11000i	0.400886	+	0.231452i	−0.285980	+	0.958236i	$0.592319\pi$
$24$		0			0
$25$	3.13826	+	5.43563i	0.627652	+	1.08713i
$26$		0			0
$27$	5.19003			0.998821
$28$		0			0
$29$	−2.27278			−0.422045			−0.211023	−	0.977481i	$-0.567679\pi$
$29$	−2.27278			−0.422045			−0.211023	+	0.977481i	$0.567679\pi$
$30$		0			0
$31$	4.95243	+	8.57787i	0.889483	+	1.54063i	0.840487	+	0.541832i	$0.182269\pi$
$31$	4.95243	+	8.57787i	0.889483	+	1.54063i	0.0489963	+	0.998799i	$0.484398\pi$
$32$		0			0
$33$	−0.924987	−	0.534042i	−0.161020	−	0.0929647i
$34$		0			0
$35$	4.43366	−	7.69924i	0.749425	−	1.30141i
$36$		0			0
$37$	−3.44854	+	5.97305i	−0.566937	+	0.981964i	0.429930	+	0.902862i	$0.358538\pi$
$37$	−3.44854	+	5.97305i	−0.566937	+	0.981964i	−0.996867	+	0.0791011i	$0.974795\pi$
$38$		0			0
$39$	−0.166016	+	0.0958494i	−0.0265838	+	0.0153482i
$40$		0			0
$41$			8.27425i			1.29222i	0.763244	+	0.646110i	$0.223605\pi$
$41$			8.27425i			1.29222i	−0.763244	+	0.646110i	$0.776395\pi$
$42$		0			0
$43$			1.24901i			0.190473i	0.995455	+	0.0952363i	$0.0303607\pi$
$43$			1.24901i			0.190473i	−0.995455	+	0.0952363i	$0.969639\pi$
$44$		0			0
$45$	−5.40684	+	3.12164i	−0.806005	+	0.465347i
$46$		0			0
$47$	2.31266	−	4.00564i	0.337335	−	0.584282i	−0.646595	−	0.762833i	$-0.723808\pi$
$47$	2.31266	−	4.00564i	0.337335	−	0.584282i	0.983931	+	0.178551i	$0.0571410\pi$
$48$		0			0
$49$	−6.99998	+	0.0157004i	−0.999997	+	0.00224291i
$50$		0			0
$51$	7.02654	+	4.05678i	0.983913	+	0.568062i
$52$		0			0
$53$	4.21100	+	7.29366i	0.578425	+	1.00186i	0.995660	+	0.0930629i	$0.0296658\pi$
$53$	4.21100	+	7.29366i	0.578425	+	1.00186i	−0.417235	+	0.908799i	$0.637001\pi$
$54$		0			0
$55$	3.35805			0.452800
$56$		0			0
$57$	−2.91869			−0.386590
$58$		0			0
$59$	3.85081	+	6.66981i	0.501333	+	0.868335i	0.999999	+	0.00154033i	$0.000490302\pi$
$59$	3.85081	+	6.66981i	0.501333	+	0.868335i	−0.498665	+	0.866795i	$0.666176\pi$
$60$		0			0
$61$	4.31253	+	2.48984i	0.552163	+	0.318792i	0.749994	−	0.661445i	$-0.230056\pi$
$61$	4.31253	+	2.48984i	0.552163	+	0.318792i	−0.197831	+	0.980236i	$0.563390\pi$
$62$		0			0
$63$	4.26271	+	2.45471i	0.537051	+	0.309264i
$64$		0			0
$65$	0.301350	−	0.521954i	0.0373779	−	0.0647404i
$66$		0			0
$67$	4.07575	−	2.35313i	0.497932	−	0.287481i	−0.229927	−	0.973208i	$-0.573849\pi$
$67$	4.07575	−	2.35313i	0.497932	−	0.287481i	0.727859	+	0.685727i	$0.240516\pi$
$68$		0			0
$69$			2.37115i			0.285453i
$70$		0			0
$71$		−	6.96826i		−	0.826980i	−0.910509	−	0.413490i	$-0.864310\pi$
$71$		−	6.96826i		−	0.826980i	0.910509	−	0.413490i	$-0.135690\pi$
$72$		0			0
$73$	12.6036	−	7.27671i	1.47514	−	0.851675i	0.475537	−	0.879696i	$-0.342254\pi$
$73$	12.6036	−	7.27671i	1.47514	−	0.851675i	0.999607	+	0.0280209i	$0.00892051\pi$
$74$		0			0
$75$	−3.35192	+	5.80570i	−0.387047	+	0.670385i
$76$		0			0
$77$	−1.32544	−	2.28980i	−0.151048	−	0.260947i
$78$		0			0
$79$	−3.00092	−	1.73258i	−0.337630	−	0.194931i	0.321593	−	0.946878i	$-0.395782\pi$
$79$	−3.00092	−	1.73258i	−0.337630	−	0.194931i	−0.659224	+	0.751947i	$0.729115\pi$
$80$		0			0
$81$	−0.0171051	−	0.0296269i	−0.00190056	−	0.00329187i
$82$		0			0
$83$	14.4143			1.58217			0.791087	−	0.611704i	$-0.209516\pi$
$83$	14.4143			1.58217			0.791087	+	0.611704i	$0.209516\pi$
$84$		0			0
$85$	−25.5090			−2.76684
$86$		0			0
$87$	−1.21376	−	2.10230i	−0.130129	−	0.225390i
$88$		0			0
$89$	6.60674	+	3.81440i	0.700313	+	0.404326i	0.807464	−	0.589917i	$-0.200839\pi$
$89$	6.60674	+	3.81440i	0.700313	+	0.404326i	−0.107151	+	0.994243i	$0.534173\pi$
$90$		0			0
$91$	−0.474857		0.000532531i	−0.0497785		5.58244e-5i
$92$		0			0
$93$	−5.28961	+	9.16188i	−0.548507	+	0.950042i
$94$		0			0
$95$	7.94697	−	4.58818i	0.815342	−	0.470738i
$96$		0			0
$97$		−	11.9139i		−	1.20968i	−0.796348	−	0.604839i	$-0.793238\pi$
$97$		−	11.9139i		−	1.20968i	0.796348	−	0.604839i	$-0.206762\pi$
$98$		0			0
$99$			1.85920i			0.186856i
$100$		0			0
$101$	4.23862	−	2.44717i	0.421758	−	0.243502i	−0.274071	−	0.961709i	$-0.588370\pi$
$101$	4.23862	−	2.44717i	0.421758	−	0.243502i	0.695829	+	0.718207i	$0.255037\pi$
$102$		0			0
$103$	−9.06505	+	15.7011i	−0.893205	+	1.54708i	−0.0571955	+	0.998363i	$0.518216\pi$
$103$	−9.06505	+	15.7011i	−0.893205	+	1.54708i	−0.836010	+	0.548714i	$0.815118\pi$
$104$		0			0
$105$	9.48946	−	0.0106420i	0.926076	−	0.00103855i
$106$		0			0
$107$	−8.31054	−	4.79809i	−0.803410	−	0.463849i	0.0412520	−	0.999149i	$-0.486865\pi$
$107$	−8.31054	−	4.79809i	−0.803410	−	0.463849i	−0.844662	+	0.535300i	$0.820199\pi$
$108$		0			0
$109$	0.759547	+	1.31557i	0.0727514	+	0.126009i	0.900106	−	0.435670i	$-0.143489\pi$
$109$	0.759547	+	1.31557i	0.0727514	+	0.126009i	−0.827355	+	0.561680i	$0.810155\pi$
$110$		0			0
$111$	−7.36666			−0.699213
$112$		0			0
$113$	−16.9194			−1.59165			−0.795823	−	0.605529i	$-0.792962\pi$
$113$	−16.9194			−1.59165			−0.795823	+	0.605529i	$0.792962\pi$
$114$		0			0
$115$	−3.72745	−	6.45613i	−0.347586	−	0.602037i
$116$		0			0
$117$	0.288982	+	0.166844i	0.0267164	+	0.0154247i
$118$		0			0
$119$	10.0686	+	17.3942i	0.922983	+	1.59452i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−7.65358	+	4.41879i	−0.690100	+	0.398429i
$124$		0			0
$125$		−	4.28663i		−	0.383408i
$126$		0			0
$127$			1.54042i			0.136690i	0.997662	+	0.0683451i	$0.0217719\pi$
$127$			1.54042i			0.136690i	−0.997662	+	0.0683451i	$0.978228\pi$
$128$		0			0
$129$	−1.15532	+	0.667025i	−0.101720	+	0.0587283i
$130$		0			0
$131$	5.21343	−	9.02993i	0.455500	−	0.788949i	−0.543217	−	0.839592i	$-0.682794\pi$
$131$	5.21343	−	9.02993i	0.455500	−	0.788949i	0.998717	+	0.0506434i	$0.0161272\pi$
$132$		0			0
$133$	−6.26533	−	3.60793i	−0.543273	−	0.312847i
$134$		0			0
$135$	−15.0934	−	8.71420i	−1.29904	−	0.749999i
$136$		0			0
$137$	9.21956	+	15.9687i	0.787680	+	1.36430i	0.927385	+	0.374108i	$0.122051\pi$
$137$	9.21956	+	15.9687i	0.787680	+	1.36430i	−0.139705	+	0.990193i	$0.544615\pi$
$138$		0			0
$139$	−15.3107			−1.29863			−0.649317	−	0.760518i	$-0.724945\pi$
$139$	−15.3107			−1.29863			−0.649317	+	0.760518i	$0.724945\pi$
$140$		0			0
$141$	4.94022			0.416041
$142$		0			0
$143$	−0.0897396	−	0.155434i	−0.00750440	−	0.0129980i
$144$		0			0
$145$	6.60961	+	3.81606i	0.548899	+	0.316907i
$146$		0			0
$147$	−3.75281	−	6.46651i	−0.309526	−	0.533349i
$148$		0			0
$149$	7.17304	−	12.4241i	0.587638	−	1.01782i	−0.406902	−	0.913472i	$-0.633391\pi$
$149$	7.17304	−	12.4241i	0.587638	−	1.01782i	0.994541	−	0.104348i	$-0.0332755\pi$
$150$		0			0
$151$	−0.278769	+	0.160947i	−0.0226859	+	0.0130977i	−0.511300	−	0.859402i	$-0.670836\pi$
$151$	−0.278769	+	0.160947i	−0.0226859	+	0.0130977i	0.488614	+	0.872500i	$0.337503\pi$
$152$		0			0
$153$		−	14.1231i		−	1.14179i
$154$		0			0
$155$		−	33.2611i		−	2.67159i
$156$		0			0
$157$	−7.38299	+	4.26257i	−0.589227	+	0.340190i	−0.764792	−	0.644278i	$-0.777158\pi$
$157$	−7.38299	+	4.26257i	−0.589227	+	0.340190i	0.175565	+	0.984468i	$0.443825\pi$
$158$		0			0
$159$	−4.49770	+	7.79024i	−0.356691	+	0.617806i
$160$		0			0
$161$	−2.93108	+	5.08996i	−0.231002	+	0.401145i
$162$		0			0
$163$	−4.71692	−	2.72332i	−0.369458	−	0.213307i	0.303764	−	0.952747i	$-0.401757\pi$
$163$	−4.71692	−	2.72332i	−0.369458	−	0.213307i	−0.673222	+	0.739441i	$0.735090\pi$
$164$		0			0
$165$	1.79334	+	3.10616i	0.139611	+	0.241814i
$166$		0			0
$167$	11.8817			0.919430			0.459715	−	0.888066i	$-0.347952\pi$
$167$	11.8817			0.919430			0.459715	+	0.888066i	$0.347952\pi$
$168$		0			0
$169$	12.9678			0.997522
$170$		0			0
$171$	2.54026	+	4.39987i	0.194259	+	0.336466i
$172$		0			0
$173$	−15.0436	−	8.68540i	−1.14374	−	0.660339i	−0.196386	−	0.980527i	$-0.562921\pi$
$173$	−15.0436	−	8.68540i	−1.14374	−	0.660339i	−0.947354	+	0.320188i	$0.896254\pi$
$174$		0			0
$175$	−14.3720	+	8.31918i	−1.08642	+	0.628871i
$176$		0			0
$177$	−4.11299	+	7.12391i	−0.309151	+	0.535466i
$178$		0			0
$179$	−1.70927	+	0.986849i	−0.127757	+	0.0737605i	−0.562516	−	0.826786i	$-0.690167\pi$
$179$	−1.70927	+	0.986849i	−0.127757	+	0.0737605i	0.434759	+	0.900547i	$0.356833\pi$
$180$		0			0
$181$		−	11.8085i		−	0.877718i	−0.898556	−	0.438859i	$-0.855383\pi$
$181$		−	11.8085i		−	0.877718i	0.898556	−	0.438859i	$-0.144617\pi$
$182$		0			0
$183$			5.31872i			0.393171i
$184$		0			0
$185$	20.0578	−	11.5804i	1.47468	−	0.851407i
$186$		0			0
$187$	−3.79818	+	6.57865i	−0.277751	+	0.481078i
$188$		0			0
$189$	0.0153993	+	13.7315i	0.00112013	+	0.998821i
$190$		0			0
$191$	−1.93037	−	1.11450i	−0.139676	−	0.0806422i	0.428533	−	0.903526i	$-0.359030\pi$
$191$	−1.93037	−	1.11450i	−0.139676	−	0.0806422i	−0.568210	+	0.822884i	$0.692364\pi$
$192$		0			0
$193$	−4.28887	−	7.42854i	−0.308720	−	0.534718i	0.669363	−	0.742936i	$-0.266567\pi$
$193$	−4.28887	−	7.42854i	−0.308720	−	0.534718i	−0.978083	+	0.208218i	$0.933234\pi$
$194$		0			0
$195$	0.643735			0.0460988
$196$		0			0
$197$	−12.4040			−0.883746			−0.441873	−	0.897078i	$-0.645686\pi$
$197$	−12.4040			−0.883746			−0.441873	+	0.897078i	$0.645686\pi$
$198$		0			0
$199$	−0.339672	−	0.588329i	−0.0240787	−	0.0417056i	0.853735	−	0.520708i	$-0.174332\pi$
$199$	−0.339672	−	0.588329i	−0.0240787	−	0.0417056i	−0.877814	+	0.479002i	$0.840999\pi$
$200$		0			0
$201$	4.35324	+	2.51334i	0.307054	+	0.177278i
$202$		0			0
$203$	−0.00674355	−	6.01321i	−0.000473304	−	0.422045i
$204$		0			0
$205$	13.8927	−	24.0628i	0.970307	−	1.68062i
$206$		0			0
$207$	3.57446	−	2.06371i	0.248442	−	0.143438i
$208$		0			0
$209$		−	2.73264i		−	0.189021i
$210$		0			0
$211$			20.6903i			1.42438i	0.701988	+	0.712189i	$0.252296\pi$
$211$			20.6903i			1.42438i	−0.701988	+	0.712189i	$0.747704\pi$
$212$		0			0
$213$	6.44555	−	3.72134i	0.441642	−	0.254982i
$214$		0			0
$215$	2.09713	−	3.63233i	0.143023	−	0.247723i
$216$		0			0
$217$	−22.6802	+	13.1284i	−1.53963	+	0.891211i
$218$		0			0
$219$	13.4617	+	7.77214i	0.909660	+	0.525192i
$220$		0			0
$221$	0.681695	+	1.18073i	0.0458558	+	0.0794245i
$222$		0			0
$223$	20.8545			1.39652			0.698261	−	0.715844i	$-0.253958\pi$
$223$	20.8545			1.39652			0.698261	+	0.715844i	$0.253958\pi$
$224$		0			0
$225$	11.6693			0.777953
$226$		0			0
$227$	9.19749	+	15.9305i	0.610459	+	1.05735i	0.991163	+	0.132649i	$0.0423483\pi$
$227$	9.19749	+	15.9305i	0.610459	+	1.05735i	−0.380704	+	0.924697i	$0.624318\pi$
$228$		0			0
$229$	7.36734	+	4.25353i	0.486847	+	0.281081i	0.723266	−	0.690570i	$-0.242640\pi$
$229$	7.36734	+	4.25353i	0.486847	+	0.281081i	−0.236418	+	0.971651i	$0.575974\pi$
$230$		0			0
$231$	1.41020	−	2.44887i	0.0927841	−	0.161124i
$232$		0			0
$233$	−1.68040	+	2.91055i	−0.110087	+	0.190676i	−0.915805	−	0.401623i	$-0.868446\pi$
$233$	−1.68040	+	2.91055i	−0.110087	+	0.190676i	0.805718	+	0.592299i	$0.201780\pi$
$234$		0			0
$235$	−13.4511	+	7.76602i	−0.877456	+	0.506599i
$236$		0			0
$237$		−	3.70109i		−	0.240412i
$238$		0			0
$239$		−	30.2077i		−	1.95397i	−0.213300	−	0.976987i	$-0.568421\pi$
$239$		−	30.2077i		−	1.95397i	0.213300	−	0.976987i	$-0.431579\pi$
$240$		0			0
$241$	−14.6188	+	8.44014i	−0.941677	+	0.543677i	−0.890486	−	0.455012i	$-0.849635\pi$
$241$	−14.6188	+	8.44014i	−0.941677	+	0.543677i	−0.0511912	+	0.998689i	$0.516302\pi$
$242$		0			0
$243$	7.80331	−	13.5157i	0.500583	−	0.867035i
$244$		0			0
$245$	20.3834	+	11.7075i	1.30225	+	0.747965i
$246$		0			0
$247$	−0.424745	−	0.245226i	−0.0270259	−	0.0156034i
$248$		0			0
$249$	7.69783	+	13.3330i	0.487830	+	0.844947i
$250$		0			0
$251$	−0.634873			−0.0400728			−0.0200364	−	0.999799i	$-0.506378\pi$
$251$	−0.634873			−0.0400728			−0.0200364	+	0.999799i	$0.506378\pi$
$252$		0			0
$253$	−2.22001			−0.139571
$254$		0			0
$255$	−13.6229	−	23.5955i	−0.853097	−	1.47761i
$256$		0			0
$257$	12.4115	+	7.16575i	0.774205	+	0.446987i	0.834373	−	0.551201i	$-0.185830\pi$
$257$	12.4115	+	7.16575i	0.774205	+	0.446987i	−0.0601676	+	0.998188i	$0.519164\pi$
$258$		0			0
$259$	−15.8134	−	9.10626i	−0.982599	−	0.565835i
$260$		0			0
$261$	−2.11278	+	3.65944i	−0.130778	+	0.226513i
$262$		0			0
$263$	−16.4344	+	9.48839i	−1.01339	+	0.585079i	−0.912182	−	0.409786i	$-0.865603\pi$
$263$	−16.4344	+	9.48839i	−1.01339	+	0.585079i	−0.101205	+	0.994866i	$0.532270\pi$
$264$		0			0
$265$		−	28.2815i		−	1.73732i
$266$		0			0
$267$			8.14820i			0.498662i
$268$		0			0
$269$	12.3172	−	7.11132i	0.750991	−	0.433585i	−0.0750606	−	0.997179i	$-0.523915\pi$
$269$	12.3172	−	7.11132i	0.750991	−	0.433585i	0.826052	+	0.563594i	$0.190582\pi$
$270$		0			0
$271$	−8.09940	+	14.0286i	−0.492003	+	0.852175i	−0.999958	−	0.00920939i	$-0.997069\pi$
$271$	−8.09940	+	14.0286i	−0.492003	+	0.852175i	0.507954	+	0.861384i	$0.330402\pi$
$272$		0			0
$273$	−0.254086	−	0.438952i	−0.0153780	−	0.0265666i
$274$		0			0
$275$	−5.43563	−	3.13826i	−0.327781	−	0.189244i
$276$		0			0
$277$	−14.9102	−	25.8253i	−0.895869	−	1.55169i	−0.832726	−	0.553686i	$-0.813221\pi$
$277$	−14.9102	−	25.8253i	−0.895869	−	1.55169i	−0.0631434	−	0.998004i	$-0.520113\pi$
$278$		0			0
$279$	18.4151			1.10248
$280$		0			0
$281$	9.34991			0.557769			0.278884	−	0.960325i	$-0.410035\pi$
$281$	9.34991			0.557769			0.278884	+	0.960325i	$0.410035\pi$
$282$		0			0
$283$	−3.68931	−	6.39007i	−0.219307	−	0.379850i	0.735289	−	0.677753i	$-0.237046\pi$
$283$	−3.68931	−	6.39007i	−0.219307	−	0.379850i	−0.954596	+	0.297903i	$0.903713\pi$
$284$		0			0
$285$	8.48802	+	4.90056i	0.502787	+	0.290284i
$286$		0			0
$287$	−21.8916	+	0.0245504i	−1.29222	+	0.00144917i
$288$		0			0
$289$	20.3524	−	35.2514i	1.19720	−	2.07361i
$290$		0			0
$291$	11.0202	−	6.36254i	0.646018	−	0.372979i
$292$		0			0
$293$		−	1.23684i		−	0.0722571i	−0.999347	−	0.0361286i	$-0.988497\pi$
$293$		−	1.23684i		−	0.0722571i	0.999347	−	0.0361286i	$-0.0115026\pi$
$294$		0			0
$295$		−	25.8625i		−	1.50577i
$296$		0			0
$297$	−4.49470	+	2.59501i	−0.260809	+	0.150578i
$298$		0			0
$299$	−0.199222	+	0.345063i	−0.0115213	+	0.0199555i
$300$		0			0
$301$	−3.30458	+	0.00370593i	−0.190473	+	0.000213606i
$302$		0			0
$303$	4.52720	+	2.61378i	0.260081	+	0.150158i
$304$		0			0
$305$	−8.36102	−	14.4817i	−0.478751	−	0.829221i
$306$		0			0
$307$	−23.5296			−1.34291			−0.671453	−	0.741048i	$-0.734329\pi$
$307$	−23.5296			−1.34291			−0.671453	+	0.741048i	$0.734329\pi$
$308$		0			0
$309$	−19.3644			−1.10161
$310$		0			0
$311$	−3.11429	−	5.39411i	−0.176595	−	0.305872i	0.764117	−	0.645078i	$-0.223175\pi$
$311$	−3.11429	−	5.39411i	−0.176595	−	0.305872i	−0.940712	+	0.339206i	$0.889842\pi$
$312$		0			0
$313$	0.668987	+	0.386240i	0.0378134	+	0.0218316i	0.518788	−	0.854903i	$-0.326384\pi$
$313$	0.668987	+	0.386240i	0.0378134	+	0.0218316i	−0.480974	+	0.876735i	$0.659717\pi$
$314$		0			0
$315$	−8.27513	−	14.2959i	−0.466251	−	0.805482i
$316$		0			0
$317$	10.1380	−	17.5595i	0.569406	−	0.986240i	−0.427219	−	0.904148i	$-0.640507\pi$
$317$	10.1380	−	17.5595i	0.569406	−	0.986240i	0.996625	−	0.0820915i	$-0.0261600\pi$
$318$		0			0
$319$	1.96829	−	1.13639i	0.110203	−	0.0636257i
$320$		0			0
$321$		−	10.2495i		−	0.572073i
$322$		0			0
$323$			20.7582i			1.15502i
$324$		0			0
$325$	−0.975582	+	0.563253i	−0.0541156	+	0.0312436i
$326$		0			0
$327$	−0.811259	+	1.40514i	−0.0448627	+	0.0777046i
$328$		0			0
$329$	10.6048	+	6.10682i	0.584660	+	0.336680i
$330$		0			0
$331$	17.9281	+	10.3508i	0.985418	+	0.568931i	0.903902	−	0.427741i	$-0.140690\pi$
$331$	17.9281	+	10.3508i	0.985418	+	0.568931i	0.0815166	+	0.996672i	$0.474024\pi$
$332$		0			0
$333$	6.41152	+	11.1051i	0.351349	+	0.608555i
$334$		0			0
$335$	−15.8039			−0.863459
$336$		0			0
$337$	5.08713			0.277114			0.138557	−	0.990354i	$-0.455754\pi$
$337$	5.08713			0.277114			0.138557	+	0.990354i	$0.455754\pi$
$338$		0			0
$339$	−9.03569	−	15.6503i	−0.490751	−	0.850006i
$340$		0			0
$341$	−8.57787	−	4.95243i	−0.464518	−	0.268189i
$342$		0			0
$343$	−0.0623088	−	18.5202i	−0.00336436	−	0.999994i
$344$		0			0
$345$	3.98123	−	6.89568i	0.214342	−	0.371251i
$346$		0			0
$347$	−20.7294	+	11.9681i	−1.11281	+	0.642483i	−0.939557	−	0.342393i	$-0.888763\pi$
$347$	−20.7294	+	11.9681i	−1.11281	+	0.642483i	−0.173257	+	0.984877i	$0.555429\pi$
$348$		0			0
$349$			2.01896i			0.108073i	0.998539	+	0.0540363i	$0.0172087\pi$
$349$			2.01896i			0.108073i	−0.998539	+	0.0540363i	$0.982791\pi$
$350$		0			0
$351$			0.931502i			0.0497199i
$352$		0			0
$353$	−28.4872	+	16.4471i	−1.51622	+	0.875390i	−0.516401	+	0.856347i	$0.672728\pi$
$353$	−28.4872	+	16.4471i	−1.51622	+	0.875390i	−0.999819	+	0.0190426i	$0.993938\pi$
$354$		0			0
$355$	−11.6999	+	20.2648i	−0.620966	+	1.07554i
$356$		0			0
$357$	−10.7124	+	18.6025i	−0.566958	+	0.984549i
$358$		0			0
$359$	−10.8260	−	6.25037i	−0.571372	−	0.329882i	0.186325	−	0.982488i	$-0.440342\pi$
$359$	−10.8260	−	6.25037i	−0.571372	−	0.329882i	−0.757697	+	0.652606i	$0.773676\pi$
$360$		0			0
$361$	5.76633	+	9.98757i	0.303491	+	0.525662i
$362$		0			0
$363$	1.06808			0.0560598
$364$		0			0
$365$	−48.8712			−2.55803
$366$		0			0
$367$	1.55792	+	2.69840i	0.0813229	+	0.140855i	0.903818	−	0.427916i	$-0.140752\pi$
$367$	1.55792	+	2.69840i	0.0813229	+	0.140855i	−0.822496	+	0.568772i	$0.807419\pi$
$368$		0			0
$369$	13.3225	+	7.69173i	0.693540	+	0.400416i
$370$		0			0
$371$	−19.2847	+	11.1629i	−1.00121	+	0.579548i
$372$		0			0
$373$	−7.06815	+	12.2424i	−0.365975	+	0.633888i	−0.988932	−	0.148369i	$-0.952598\pi$
$373$	−7.06815	+	12.2424i	−0.365975	+	0.633888i	0.622957	+	0.782256i	$0.285931\pi$
$374$		0			0
$375$	3.96508	−	2.28924i	0.204756	−	0.118216i
$376$		0			0
$377$		−	0.407917i		−	0.0210088i
$378$		0			0
$379$		−	30.2451i		−	1.55359i	−0.629756	−	0.776793i	$-0.716845\pi$
$379$		−	30.2451i		−	1.55359i	0.629756	−	0.776793i	$-0.283155\pi$
$380$		0			0
$381$	−1.42487	+	0.822649i	−0.0729983	+	0.0421456i
$382$		0			0
$383$	−16.5189	+	28.6115i	−0.844074	+	1.46198i	0.0423487	+	0.999103i	$0.486516\pi$
$383$	−16.5189	+	28.6115i	−0.844074	+	1.46198i	−0.886423	+	0.462876i	$0.846817\pi$
$384$		0			0
$385$	0.00996364	+	8.88457i	0.000507794	+	0.452800i
$386$		0			0
$387$	2.01105	+	1.16108i	0.102227	+	0.0590211i
$388$		0			0
$389$	−3.93960	−	6.82359i	−0.199746	−	0.345970i	0.748700	−	0.662909i	$-0.230678\pi$
$389$	−3.93960	−	6.82359i	−0.199746	−	0.345970i	−0.948446	+	0.316939i	$0.897345\pi$
$390$		0			0
$391$	16.8640			0.852848
$392$		0			0
$393$	11.1368			0.561776
$394$		0			0
$395$	5.81811	+	10.0773i	0.292741	+	0.507042i
$396$		0			0
$397$	−6.51118	−	3.75923i	−0.326787	−	0.188670i	0.327627	−	0.944807i	$-0.393751\pi$
$397$	−6.51118	−	3.75923i	−0.326787	−	0.188670i	−0.654414	+	0.756137i	$0.727084\pi$
$398$		0			0
$399$	−0.00866002	−	7.72213i	−0.000433543	−	0.386590i
$400$		0			0
$401$	3.44356	−	5.96442i	0.171963	−	0.297849i	−0.767143	−	0.641476i	$-0.778322\pi$
$401$	3.44356	−	5.96442i	0.171963	−	0.297849i	0.939106	+	0.343627i	$0.111656\pi$
$402$		0			0
$403$	−1.53955	+	0.888859i	−0.0766904	+	0.0442772i
$404$		0			0
$405$			0.114880i			0.00570841i
$406$		0			0
$407$		−	6.89708i		−	0.341876i
$408$		0			0
$409$	−8.98182	+	5.18566i	−0.444122	+	0.256414i	−0.705345	−	0.708864i	$-0.749208\pi$
$409$	−8.98182	+	5.18566i	−0.444122	+	0.256414i	0.261222	+	0.965279i	$0.415874\pi$
$410$		0			0
$411$	−9.84725	+	17.0559i	−0.485729	+	0.841308i
$412$		0			0
$413$	−17.6352	+	10.2081i	−0.867772	+	0.502307i
$414$		0			0
$415$	−41.9190	−	24.2020i	−2.05772	−	1.18803i
$416$		0			0
$417$	−8.17653	−	14.1622i	−0.400406	−	0.693524i
$418$		0			0
$419$	−9.95876			−0.486517			−0.243259	−	0.969961i	$-0.578216\pi$
$419$	−9.95876			−0.486517			−0.243259	+	0.969961i	$0.578216\pi$
$420$		0			0
$421$	22.8742			1.11482			0.557410	−	0.830237i	$-0.311795\pi$
$421$	22.8742			1.11482			0.557410	+	0.830237i	$0.311795\pi$
$422$		0			0
$423$	−4.29968	−	7.44727i	−0.209058	−	0.362099i
$424$		0			0
$425$	41.2910	+	23.8394i	2.00291	+	1.15638i
$426$		0			0
$427$	−6.57470	+	11.4173i	−0.318172	+	0.552520i
$428$		0			0
$429$	0.0958494	−	0.166016i	0.00462765	−	0.00801533i
$430$		0			0
$431$	13.2808	−	7.66767i	0.639713	−	0.369339i	−0.144791	−	0.989462i	$-0.546251\pi$
$431$	13.2808	−	7.66767i	0.639713	−	0.369339i	0.784504	+	0.620124i	$0.212918\pi$
$432$		0			0
$433$		−	29.8741i		−	1.43566i	−0.696221	−	0.717828i	$-0.745137\pi$
$433$		−	29.8741i		−	1.43566i	0.696221	−	0.717828i	$-0.254863\pi$
$434$		0			0
$435$			8.15175i			0.390846i
$436$		0			0
$437$	−5.25373	+	3.03324i	−0.251320	+	0.145100i
$438$		0			0
$439$	7.42192	−	12.8551i	0.354229	−	0.613542i	−0.632757	−	0.774351i	$-0.718077\pi$
$439$	7.42192	−	12.8551i	0.354229	−	0.613542i	0.986986	+	0.160808i	$0.0514100\pi$
$440$		0			0
$441$	−6.48190	+	11.2854i	−0.308662	+	0.537398i
$442$		0			0
$443$	12.3684	+	7.14088i	0.587639	+	0.339274i	0.764163	−	0.645023i	$-0.223152\pi$
$443$	12.3684	+	7.14088i	0.587639	+	0.339274i	−0.176524	+	0.984296i	$0.556485\pi$
$444$		0			0
$445$	−12.8090	−	22.1858i	−0.607203	−	1.05171i
$446$		0			0
$447$	15.3228			0.724744
$448$		0			0
$449$	−12.6244			−0.595782			−0.297891	−	0.954600i	$-0.596283\pi$
$449$	−12.6244			−0.595782			−0.297891	+	0.954600i	$0.596283\pi$
$450$		0			0
$451$	−4.13713	−	7.16571i	−0.194810	−	0.337420i
$452$		0			0
$453$	−0.297748	−	0.171905i	−0.0139894	−	0.00807681i
$454$		0			0
$455$	1.38185	+	0.795749i	0.0647823	+	0.0373053i
$456$		0			0
$457$	−17.8540	+	30.9240i	−0.835175	+	1.44657i	0.0587126	+	0.998275i	$0.481300\pi$
$457$	−17.8540	+	30.9240i	−0.835175	+	1.44657i	−0.893888	+	0.448291i	$0.852033\pi$
$458$		0			0
$459$	34.1434	−	19.7127i	1.59368	−	0.920109i
$460$		0			0
$461$		−	19.2323i		−	0.895740i	−0.894099	−	0.447870i	$-0.852183\pi$
$461$		−	19.2323i		−	0.895740i	0.894099	−	0.447870i	$-0.147817\pi$
$462$		0			0
$463$			29.7105i			1.38076i	0.723445	+	0.690382i	$0.242558\pi$
$463$			29.7105i			1.38076i	−0.723445	+	0.690382i	$0.757442\pi$
$464$		0			0
$465$	30.7661	−	17.7628i	1.42674	−	0.823730i
$466$		0			0
$467$	4.70903	−	8.15627i	0.217908	−	0.377427i	−0.736260	−	0.676698i	$-0.763410\pi$
$467$	4.70903	−	8.15627i	0.217908	−	0.377427i	0.954168	+	0.299271i	$0.0967435\pi$
$468$		0			0
$469$	6.23790	+	10.7764i	0.288039	+	0.497609i
$470$		0			0
$471$	−7.88565	−	4.55278i	−0.363351	−	0.209781i
$472$		0			0
$473$	−0.624507	−	1.08168i	−0.0287148	−	0.0497356i
$474$		0			0
$475$	−17.1515			−0.786965
$476$		0			0
$477$	15.6582			0.716938
$478$		0			0
$479$	−9.29360	−	16.0970i	−0.424635	−	0.735490i	0.571751	−	0.820427i	$-0.306264\pi$
$479$	−9.29360	−	16.0970i	−0.424635	−	0.735490i	−0.996386	+	0.0849373i	$0.972931\pi$
$480$		0			0
$481$	−1.07204	−	0.618942i	−0.0488807	−	0.0282213i
$482$		0			0
$483$	−6.27347	+	0.00703542i	−0.285453	+	0.000320123i
$484$		0			0
$485$	−20.0038	+	34.6476i	−0.908327	+	1.57327i
$486$		0			0
$487$	−11.6874	+	6.74773i	−0.529607	+	0.305769i	−0.740856	−	0.671663i	$-0.765580\pi$
$487$	−11.6874	+	6.74773i	−0.529607	+	0.305769i	0.211249	+	0.977432i	$0.432247\pi$
$488$		0			0
$489$		−	5.81746i		−	0.263074i
$490$		0			0
$491$			7.06836i			0.318990i	0.987199	+	0.159495i	$0.0509867\pi$
$491$			7.06836i			0.318990i	−0.987199	+	0.159495i	$0.949013\pi$
$492$		0			0
$493$	−14.9518	+	8.63244i	−0.673397	+	0.388786i
$494$		0			0
$495$	3.12164	−	5.40684i	0.140307	−	0.243020i
$496$		0			0
$497$	18.4363	−	0.0206755i	0.826980	−	0.000927421i
$498$		0			0
$499$	26.1557	+	15.1010i	1.17089	+	0.676014i	0.953890	−	0.300158i	$-0.0970393\pi$
$499$	26.1557	+	15.1010i	1.17089	+	0.676014i	0.217001	+	0.976171i	$0.430373\pi$
$500$		0			0
$501$	6.34530	+	10.9904i	0.283487	+	0.491014i
$502$		0			0
$503$	42.6303			1.90079			0.950395	−	0.311046i	$-0.100679\pi$
$503$	42.6303			1.90079			0.950395	+	0.311046i	$0.100679\pi$
$504$		0			0
$505$	−16.4354			−0.731368
$506$		0			0
$507$	6.92534	+	11.9950i	0.307565	+	0.532718i
$508$		0			0
$509$	23.4574	+	13.5431i	1.03973	+	0.600288i	0.919757	−	0.392489i	$-0.128386\pi$
$509$	23.4574	+	13.5431i	1.03973	+	0.600288i	0.119972	+	0.992777i	$0.461719\pi$
$510$		0			0
$511$	19.2898	+	33.3245i	0.853329	+	1.47419i
$512$		0			0
$513$	−7.09125	+	12.2824i	−0.313086	+	0.542282i
$514$		0			0
$515$	52.7252	−	30.4409i	2.32335	−	1.34139i
$516$		0			0
$517$			4.62531i			0.203421i
$518$		0			0
$519$		−	18.5535i		−	0.814407i
$520$		0			0
$521$	32.0235	−	18.4888i	1.40298	−	0.810008i	0.408278	−	0.912857i	$-0.366129\pi$
$521$	32.0235	−	18.4888i	1.40298	−	0.810008i	0.994697	+	0.102849i	$0.0327959\pi$
$522$		0			0
$523$	11.9201	−	20.6463i	0.521231	−	0.902798i	−0.478464	−	0.878107i	$-0.658806\pi$
$523$	11.9201	−	20.6463i	0.521231	−	0.902798i	0.999695	−	0.0246910i	$-0.00786020\pi$
$524$		0			0
$525$	−15.3704	−	8.85113i	−0.670818	−	0.386295i
$526$		0			0
$527$	65.1606	+	37.6205i	2.83844	+	1.63877i
$528$		0			0
$529$	−9.03579	−	15.6504i	−0.392860	−	0.680454i
$530$		0			0
$531$	14.3189			0.621385
$532$		0			0
$533$	−1.48506			−0.0643249
$534$		0			0
$535$	16.1123	+	27.9072i	0.696593	+	1.20654i
$536$		0			0
$537$	−1.82565	−	1.05404i	−0.0787824	−	0.0454850i
$538$		0			0
$539$	6.05431	−	3.51359i	0.260778	−	0.151341i
$540$		0			0
$541$	−8.40240	+	14.5534i	−0.361248	+	0.625699i	−0.988166	−	0.153385i	$-0.950982\pi$
$541$	−8.40240	+	14.5534i	−0.361248	+	0.625699i	0.626919	+	0.779085i	$0.284316\pi$
$542$		0			0
$543$	10.9227	−	6.30623i	0.468738	−	0.270626i
$544$		0			0
$545$		−	5.10120i		−	0.218511i
$546$		0			0
$547$			4.42960i			0.189396i	0.995506	+	0.0946979i	$0.0301885\pi$
$547$			4.42960i			0.189396i	−0.995506	+	0.0946979i	$0.969811\pi$
$548$		0			0
$549$	8.01785	−	4.62911i	0.342194	−	0.197566i
$550$		0			0
$551$	3.10535	−	5.37863i	0.132293	−	0.229137i
$552$		0			0
$553$	4.57508	−	7.94483i	0.194552	−	0.337849i
$554$		0			0
$555$	21.4234	+	12.3688i	0.909374	+	0.525027i
$556$		0			0
$557$	−16.0814	−	27.8538i	−0.681392	−	1.18021i	−0.974556	−	0.224143i	$-0.928042\pi$
$557$	−16.0814	−	27.8538i	−0.681392	−	1.18021i	0.293164	−	0.956062i	$-0.405292\pi$
$558$		0			0
$559$	−0.224172			−0.00948146
$560$		0			0
$561$	−8.11355			−0.342554
$562$		0			0
$563$	20.6441	+	35.7567i	0.870046	+	1.50696i	0.861948	+	0.506997i	$0.169245\pi$
$563$	20.6441	+	35.7567i	0.870046	+	1.50696i	0.00809888	+	0.999967i	$0.497422\pi$
$564$		0			0
$565$	49.2044	+	28.4082i	2.07005	+	1.19514i
$566$		0			0
$567$	0.0783345	−	0.0453437i	0.00328974	−	0.00190425i
$568$		0			0
$569$	0.930686	−	1.61199i	0.0390164	−	0.0675783i	−0.845858	−	0.533408i	$-0.820911\pi$
$569$	0.930686	−	1.61199i	0.0390164	−	0.0675783i	0.884874	+	0.465830i	$0.154244\pi$
$570$		0			0
$571$	−37.3707	+	21.5760i	−1.56391	+	0.902926i	−0.567059	+	0.823677i	$0.691919\pi$
$571$	−37.3707	+	21.5760i	−1.56391	+	0.902926i	−0.996855	+	0.0792494i	$0.974748\pi$
$572$		0			0
$573$		−	2.38075i		−	0.0994574i
$574$		0			0
$575$			13.9339i			0.581084i
$576$		0			0
$577$	5.58590	−	3.22502i	0.232544	−	0.134259i	−0.379201	−	0.925314i	$-0.623801\pi$
$577$	5.58590	−	3.22502i	0.232544	−	0.134259i	0.611745	+	0.791055i	$0.290468\pi$
$578$		0			0
$579$	4.58087	−	7.93430i	0.190374	−	0.329738i
$580$		0			0
$581$	0.0427685	+	38.1366i	0.00177434	+	1.58217i
$582$		0			0
$583$	−7.29366	−	4.21100i	−0.302073	−	0.174402i
$584$		0			0
$585$	−0.560270	−	0.970416i	−0.0231643	−	0.0401218i
$586$		0			0
$587$	−19.3428			−0.798365			−0.399182	−	0.916872i	$-0.630706\pi$
$587$	−19.3428			−0.798365			−0.399182	+	0.916872i	$0.630706\pi$
$588$		0			0
$589$	−27.0665			−1.11526
$590$		0			0
$591$	−6.62424	−	11.4735i	−0.272485	−	0.471957i
$592$		0			0
$593$	−1.02316	−	0.590725i	−0.0420163	−	0.0242582i	0.478845	−	0.877900i	$-0.341056\pi$
$593$	−1.02316	−	0.590725i	−0.0420163	−	0.0242582i	−0.520861	+	0.853641i	$0.674389\pi$
$594$		0			0
$595$	−0.0756875	−	67.4904i	−0.00310288	−	2.76684i
$596$		0			0
$597$	0.362798	−	0.628385i	0.0148483	−	0.0257181i
$598$		0			0
$599$	−28.5984	+	16.5113i	−1.16850	+	0.674632i	−0.953326	−	0.301944i	$-0.902365\pi$
$599$	−28.5984	+	16.5113i	−1.16850	+	0.674632i	−0.215172	+	0.976576i	$0.569031\pi$
$600$		0			0
$601$			2.60986i			0.106458i	0.998582	+	0.0532292i	$0.0169514\pi$
$601$			2.60986i			0.106458i	−0.998582	+	0.0532292i	$0.983049\pi$
$602$		0			0
$603$		−	8.74988i		−	0.356323i
$604$		0			0
$605$	−2.90816	+	1.67903i	−0.118233	+	0.0682621i
$606$		0			0
$607$	10.3068	−	17.8520i	0.418342	−	0.724589i	−0.577431	−	0.816439i	$-0.695945\pi$
$607$	10.3068	−	17.8520i	0.418342	−	0.724589i	0.995773	+	0.0918503i	$0.0292781\pi$
$608$		0			0
$609$	5.55855	−	3.21755i	0.225244	−	0.130382i
$610$		0			0
$611$	0.718928	+	0.415074i	0.0290847	+	0.0167921i
$612$		0			0
$613$	12.2557	+	21.2275i	0.495003	+	0.857371i	0.999983	−	0.00576020i	$-0.00183354\pi$
$613$	12.2557	+	21.2275i	0.495003	+	0.857371i	−0.504980	+	0.863131i	$0.668500\pi$
$614$		0			0
$615$	29.6771			1.19670
$616$		0			0
$617$	−31.6673			−1.27488			−0.637439	−	0.770500i	$-0.720006\pi$
$617$	−31.6673			−1.27488			−0.637439	+	0.770500i	$0.720006\pi$
$618$		0			0
$619$	18.0220	+	31.2151i	0.724366	+	1.25464i	0.959234	+	0.282612i	$0.0912009\pi$
$619$	18.0220	+	31.2151i	0.724366	+	1.25464i	−0.234868	+	0.972027i	$0.575466\pi$
$620$		0			0
$621$	9.97825	+	5.76095i	0.400413	+	0.231179i
$622$		0			0
$623$	−10.0724	+	17.4911i	−0.403540	+	0.700766i
$624$		0			0
$625$	8.49394	−	14.7119i	0.339758	−	0.588478i
$626$		0			0
$627$	2.52766	−	1.45935i	0.100945	−	0.0582807i
$628$		0			0
$629$			52.3928i			2.08904i
$630$		0			0
$631$			29.1758i			1.16147i	0.814092	+	0.580736i	$0.197235\pi$
$631$			29.1758i			1.16147i	−0.814092	+	0.580736i	$0.802765\pi$
$632$		0			0
$633$	−19.1382	+	11.0495i	−0.760677	+	0.439177i
$634$		0			0
$635$	2.58641	−	4.47979i	0.102638	−	0.177775i
$636$		0			0
$637$	−0.00281789	−	1.25635i	−0.000111649	−	0.0497785i
$638$		0			0
$639$	−11.2197	−	6.47769i	−0.443844	−	0.256253i
$640$		0			0
$641$	5.61868	+	9.73184i	0.221924	+	0.384384i	0.955392	−	0.295340i	$-0.0954328\pi$
$641$	5.61868	+	9.73184i	0.221924	+	0.384384i	−0.733468	+	0.679724i	$0.762100\pi$
$642$		0			0
$643$	25.4296			1.00285			0.501423	−	0.865202i	$-0.332810\pi$
$643$	25.4296			1.00285			0.501423	+	0.865202i	$0.332810\pi$
$644$		0			0
$645$	4.47981			0.176392
$646$		0			0
$647$	−4.99573	−	8.65286i	−0.196402	−	0.340179i	0.750957	−	0.660351i	$-0.229593\pi$
$647$	−4.99573	−	8.65286i	−0.196402	−	0.340179i	−0.947359	+	0.320172i	$0.896259\pi$
$648$		0			0
$649$	−6.66981	−	3.85081i	−0.261813	−	0.151158i
$650$		0			0
$651$	−24.2557	−	13.9678i	−0.950657	−	0.547442i
$652$		0			0
$653$	17.7969	−	30.8252i	0.696448	−	1.20628i	−0.273243	−	0.961945i	$-0.588096\pi$
$653$	17.7969	−	30.8252i	0.696448	−	1.20628i	0.969690	−	0.244338i	$-0.0785705\pi$
$654$		0			0
$655$	−30.3230	+	17.5070i	−1.18482	+	0.684055i
$656$		0			0
$657$		−	27.0577i		−	1.05562i
$658$		0			0
$659$		−	21.8126i		−	0.849697i	−0.905264	−	0.424849i	$-0.860327\pi$
$659$		−	21.8126i		−	0.849697i	0.905264	−	0.424849i	$-0.139673\pi$
$660$		0			0
$661$	−5.94261	+	3.43097i	−0.231141	+	0.133449i	−0.611098	−	0.791555i	$-0.709272\pi$
$661$	−5.94261	+	3.43097i	−0.231141	+	0.133449i	0.379958	+	0.925004i	$0.375939\pi$
$662$		0			0
$663$	−0.728107	+	1.26112i	−0.0282773	+	0.0489778i
$664$		0			0
$665$	12.1628	+	21.0121i	0.471652	+	0.814813i
$666$		0			0
$667$	−4.36961	−	2.52280i	−0.169192	−	0.0976830i
$668$		0			0
$669$	11.1372	+	19.2902i	0.430588	+	0.745800i
$670$		0			0
$671$	−4.97968			−0.192239
$672$		0			0
$673$	−34.0984			−1.31440			−0.657198	−	0.753718i	$-0.728258\pi$
$673$	−34.0984			−1.31440			−0.657198	+	0.753718i	$0.728258\pi$
$674$		0			0
$675$	16.2877	+	28.2111i	0.626912	+	1.08584i
$676$		0			0
$677$	16.5216	+	9.53873i	0.634975	+	0.366603i	0.782676	−	0.622429i	$-0.213854\pi$
$677$	16.5216	+	9.53873i	0.634975	+	0.366603i	−0.147701	+	0.989032i	$0.547187\pi$
$678$		0			0
$679$	31.5213	−	0.0353497i	1.20968	−	0.00135660i
$680$		0			0
$681$	−9.82369	+	17.0151i	−0.376444	+	0.652021i
$682$		0			0
$683$	14.1063	−	8.14427i	0.539762	−	0.311632i	−0.205220	−	0.978716i	$-0.565791\pi$
$683$	14.1063	−	8.14427i	0.539762	−	0.311632i	0.744983	+	0.667084i	$0.232458\pi$
$684$		0			0
$685$		−	61.9195i		−	2.36582i
$686$		0			0
$687$			9.08626i			0.346662i
$688$		0			0
$689$	−1.30906	+	0.755786i	−0.0498712	+	0.0287932i
$690$		0			0
$691$	−17.3937	+	30.1267i	−0.661686	+	1.14607i	0.318486	+	0.947927i	$0.396825\pi$
$691$	−17.3937	+	30.1267i	−0.661686	+	1.14607i	−0.980172	+	0.198146i	$0.936508\pi$
$692$		0			0
$693$	−4.91897	+	0.00551641i	−0.186856	+	0.000209551i
$694$		0			0
$695$	44.5258	+	25.7070i	1.68896	+	0.975122i
$696$		0			0
$697$	31.4271	+	54.4334i	1.19039	+	2.06181i
$698$		0			0
$699$	−3.58962			−0.135772
$700$		0			0
$701$	−35.7012			−1.34842			−0.674209	−	0.738541i	$-0.735515\pi$
$701$	−35.7012			−1.34842			−0.674209	+	0.738541i	$0.735515\pi$
$702$		0			0
$703$	−9.42364	−	16.3222i	−0.355419	−	0.615604i
$704$		0			0
$705$	−14.3669	−	8.29476i	−0.541090	−	0.312399i
$706$		0			0
$707$	6.48717	+	11.2071i	0.243975	+	0.421485i
$708$		0			0
$709$	23.6785	−	41.0123i	0.889263	−	1.54025i	0.0485149	−	0.998822i	$-0.484551\pi$
$709$	23.6785	−	41.0123i	0.889263	−	1.54025i	0.840748	−	0.541426i	$-0.182116\pi$
$710$		0			0
$711$	−5.57931	+	3.22122i	−0.209241	+	0.120805i
$712$		0			0
$713$			21.9889i			0.823489i
$714$		0			0
$715$			0.602701i			0.0225397i
$716$		0			0
$717$	27.9417	−	16.1322i	1.04350	−	0.602467i
$718$		0			0
$719$	17.6699	−	30.6052i	0.658976	−	1.14138i	−0.321905	−	0.946772i	$-0.604323\pi$
$719$	17.6699	−	30.6052i	0.658976	−	1.14138i	0.980881	−	0.194608i	$-0.0623435\pi$
$720$		0			0
$721$	−41.5681	−	23.9373i	−1.54808	−	0.891470i
$722$		0			0
$723$	−15.6140	−	9.01478i	−0.580693	−	0.335263i
$724$		0			0
$725$	−7.13259	−	12.3540i	−0.264898	−	0.458816i
$726$		0			0
$727$	−13.2478			−0.491334			−0.245667	−	0.969354i	$-0.579007\pi$
$727$	−13.2478			−0.491334			−0.245667	+	0.969354i	$0.579007\pi$
$728$		0			0
$729$	16.5665			0.613576
$730$		0			0
$731$	4.74398	+	8.21681i	0.175462	+	0.303910i
$732$		0			0
$733$	−23.6315	−	13.6436i	−0.872849	−	0.503940i	−0.00455505	−	0.999990i	$-0.501450\pi$
$733$	−23.6315	−	13.6436i	−0.872849	−	0.503940i	−0.868294	+	0.496050i	$0.834783\pi$
$734$		0			0
$735$	0.0563122	+	25.1067i	0.00207711	+	0.926075i
$736$		0			0
$737$	−2.35313	+	4.07575i	−0.0866788	+	0.150132i
$738$		0			0
$739$	−41.6816	+	24.0649i	−1.53328	+	0.885240i	−0.534074	+	0.845438i	$0.679339\pi$
$739$	−41.6816	+	24.0649i	−1.53328	+	0.885240i	−0.999208	+	0.0398023i	$0.987327\pi$
$740$		0			0
$741$		−	0.523845i		−	0.0192439i
$742$		0			0
$743$			11.5095i			0.422243i	0.977460	+	0.211121i	$0.0677115\pi$
$743$			11.5095i			0.422243i	−0.977460	+	0.211121i	$0.932288\pi$
$744$		0			0
$745$	−41.7207	+	24.0875i	−1.52853	+	0.882496i
$746$		0			0
$747$	13.3995	−	23.2086i	0.490262	−	0.849159i
$748$		0			0
$749$	12.6699	−	22.0018i	0.462948	−	0.803930i
$750$		0			0
$751$	18.2343	+	10.5276i	0.665379	+	0.384157i	0.794323	−	0.607495i	$-0.207826\pi$
$751$	18.2343	+	10.5276i	0.665379	+	0.384157i	−0.128945	+	0.991652i	$0.541159\pi$
$752$		0			0
$753$	−0.339049	−	0.587249i	−0.0123556	−	0.0214006i
$754$		0			0
$755$	1.08094			0.0393394
$756$		0			0
$757$	42.7442			1.55356			0.776782	−	0.629770i	$-0.216851\pi$
$757$	42.7442			1.55356			0.776782	+	0.629770i	$0.216851\pi$
$758$		0			0
$759$	−1.18558	−	2.05348i	−0.0430337	−	0.0745365i
$760$		0			0
$761$	−18.6168	−	10.7484i	−0.674858	−	0.389629i	0.123057	−	0.992400i	$-0.460730\pi$
$761$	−18.6168	−	10.7484i	−0.674858	−	0.389629i	−0.797915	+	0.602770i	$0.794064\pi$
$762$		0			0
$763$	−3.47843	+	2.01347i	−0.125927	+	0.0728927i
$764$		0			0
$765$	−23.7131	+	41.0724i	−0.857350	+	1.48497i
$766$		0			0
$767$	−1.19709	+	0.691141i	−0.0432245	+	0.0249557i
$768$		0			0
$769$			52.6301i			1.89789i	0.315440	+	0.948946i	$0.397848\pi$
$769$			52.6301i			1.89789i	−0.315440	+	0.948946i	$0.602152\pi$
$770$		0			0
$771$			15.3072i			0.551277i
$772$		0			0
$773$	−3.12787	+	1.80588i	−0.112502	+	0.0649529i	−0.555195	−	0.831720i	$-0.687356\pi$
$773$	−3.12787	+	1.80588i	−0.112502	+	0.0649529i	0.442693	+	0.896673i	$0.354023\pi$
$774$		0			0
$775$	−31.0841	+	53.8392i	−1.11657	+	1.93396i
$776$		0			0
$777$	−0.0218575	−	19.4903i	−0.000784135	−	0.699212i
$778$		0			0
$779$	−19.5813	−	11.3053i	−0.701574	−	0.405054i
$780$		0			0
$781$	3.48413	+	6.03469i	0.124672	+	0.215938i
$782$		0			0
$783$	−11.7958			−0.421548
$784$		0			0
$785$	28.6279			1.02177
$786$		0			0
$787$	2.86547	+	4.96315i	0.102143	+	0.176917i	0.912567	−	0.408926i	$-0.134097\pi$
$787$	2.86547	+	4.96315i	0.102143	+	0.176917i	−0.810424	+	0.585843i	$0.800763\pi$
$788$		0			0
$789$	−17.5533	−	10.1344i	−0.624913	−	0.360794i
$790$		0			0
$791$	−0.0502015	−	44.7646i	−0.00178496	−	1.59165i
$792$		0			0
$793$	−0.446875	+	0.774010i	−0.0158690	+	0.0274859i
$794$		0			0
$795$	26.1600	−	15.1035i	0.927801	−	0.535666i
$796$		0			0
$797$			32.9773i			1.16812i	0.811712	+	0.584058i	$0.198536\pi$
$797$			32.9773i			1.16812i	−0.811712	+	0.584058i	$0.801464\pi$
$798$		0			0
$799$		−	35.1355i		−	1.24301i
$800$		0			0
$801$	12.2832	−	7.09173i	0.434007	−	0.250574i
$802$		0			0
$803$	−7.27671	+	12.6036i	−0.256790	+	0.444773i
$804$		0			0
$805$	17.0702	−	9.88105i	0.601647	−	0.348261i
$806$		0			0
$807$	13.1558	+	7.59549i	0.463105	+	0.267374i
$808$		0			0
$809$	−6.27518	−	10.8689i	−0.220623	−	0.382131i	0.734374	−	0.678745i	$-0.237476\pi$
$809$	−6.27518	−	10.8689i	−0.220623	−	0.382131i	−0.954997	+	0.296614i	$0.904143\pi$
$810$		0			0
$811$	10.6804			0.375039			0.187520	−	0.982261i	$-0.439955\pi$
$811$	10.6804			0.375039			0.187520	+	0.982261i	$0.439955\pi$
$812$		0			0
$813$	−17.3017			−0.606796
$814$		0			0
$815$	9.14504	+	15.8397i	0.320337	+	0.554839i
$816$		0			0
$817$	−2.95584	−	1.70655i	−0.103412	−	0.0597048i
$818$		0			0
$819$	−0.440569	+	0.765068i	−0.0153947	+	0.0267337i
$820$		0			0
$821$	11.2111	−	19.4181i	0.391269	−	0.677698i	−0.601348	−	0.798987i	$-0.705370\pi$
$821$	11.2111	−	19.4181i	0.391269	−	0.677698i	0.992617	+	0.121289i	$0.0387029\pi$
$822$		0			0
$823$	−41.4551	+	23.9341i	−1.44503	+	0.834290i	−0.998179	−	0.0603172i	$-0.980789\pi$
$823$	−41.4551	+	23.9341i	−1.44503	+	0.834290i	−0.446853	+	0.894607i	$0.647455\pi$
$824$		0			0
$825$		−	6.70385i		−	0.233398i
$826$		0			0
$827$		−	44.2694i		−	1.53940i	−0.638407	−	0.769699i	$-0.720406\pi$
$827$		−	44.2694i		−	1.53940i	0.638407	−	0.769699i	$-0.279594\pi$
$828$		0			0
$829$	14.1933	−	8.19449i	0.492953	−	0.284606i	−0.232846	−	0.972514i	$-0.574804\pi$
$829$	14.1933	−	8.19449i	0.492953	−	0.284606i	0.725799	+	0.687907i	$0.241470\pi$
$830$		0			0
$831$	15.9254	−	27.5835i	0.552445	−	0.956863i
$832$		0			0
$833$	−45.9908	+	26.6905i	−1.59349	+	0.924771i
$834$		0			0
$835$	−34.5538	−	19.9496i	−1.19578	−	0.690385i
$836$		0			0
$837$	25.7033	+	44.5194i	0.888435	+	1.53881i
$838$		0			0
$839$	−21.7160			−0.749720			−0.374860	−	0.927081i	$-0.622309\pi$
$839$	−21.7160			−0.749720			−0.374860	+	0.927081i	$0.622309\pi$
$840$		0			0
$841$	−23.8345			−0.821878
$842$		0			0
$843$	4.99324	+	8.64855i	0.171976	+	0.297872i
$844$		0			0
$845$	−37.7124	−	21.7733i	−1.29735	−	0.749023i
$846$		0			0
$847$	2.29277	+	1.32031i	0.0787805	+	0.0453662i
$848$		0			0
$849$	3.94049	−	6.82513i	0.135237	−	0.234238i
$850$		0			0
$851$	−13.2602	+	7.65578i	−0.454554	+	0.262437i
$852$		0			0
$853$		−	37.8764i		−	1.29686i	−0.761273	−	0.648431i	$-0.775425\pi$
$853$		−	37.8764i		−	1.29686i	0.761273	−	0.648431i	$-0.224575\pi$
$854$		0			0
$855$		−	17.0607i		−	0.583463i
$856$		0			0
$857$	34.9828	−	20.1973i	1.19499	−	0.689927i	0.235555	−	0.971861i	$-0.424309\pi$
$857$	34.9828	−	20.1973i	1.19499	−	0.689927i	0.959434	+	0.281934i	$0.0909758\pi$
$858$		0			0
$859$	13.8236	−	23.9432i	0.471656	−	0.816931i	−0.527819	−	0.849357i	$-0.676990\pi$
$859$	13.8236	−	23.9432i	0.471656	−	0.816931i	0.999474	+	0.0324257i	$0.0103232\pi$
$860$		0			0
$861$	−11.7137	−	20.2363i	−0.399203	−	0.689653i
$862$		0			0
$863$	−4.01295	−	2.31688i	−0.136602	−	0.0788675i	0.430141	−	0.902762i	$-0.358464\pi$
$863$	−4.01295	−	2.31688i	−0.136602	−	0.0788675i	−0.566744	+	0.823894i	$0.691797\pi$
$864$		0			0
$865$	29.1660	+	50.5171i	0.991675	+	1.71763i
$866$		0			0
$867$	43.4761			1.47653
$868$		0			0
$869$	3.46517			0.117548
$870$		0			0
$871$	0.422339	+	0.731512i	0.0143104	+	0.0247863i
$872$		0			0
$873$	−19.1828	−	11.0752i	−0.649239	−	0.374838i
$874$		0			0
$875$	11.3413	−	0.0127188i	0.383407	−	0.000429974i
$876$		0			0
$877$	11.8754	−	20.5689i	0.401005	−	0.694561i	−0.592843	−	0.805318i	$-0.701994\pi$
$877$	11.8754	−	20.5689i	0.401005	−	0.694561i	0.993847	+	0.110758i	$0.0353277\pi$
$878$		0			0
$879$	1.14406	−	0.660526i	0.0385883	−	0.0222790i
$880$		0			0
$881$		−	17.2281i		−	0.580429i	−0.956962	−	0.290215i	$-0.906273\pi$
$881$		−	17.2281i		−	0.580429i	0.956962	−	0.290215i	$-0.0937267\pi$
$882$		0			0
$883$			2.73586i			0.0920691i	0.998940	+	0.0460345i	$0.0146584\pi$
$883$			2.73586i			0.0920691i	−0.998940	+	0.0460345i	$0.985342\pi$
$884$		0			0
$885$	23.9225	−	13.8116i	0.804145	−	0.464273i
$886$		0			0
$887$	8.67547	−	15.0264i	0.291294	−	0.504536i	−0.682822	−	0.730585i	$-0.739248\pi$
$887$	8.67547	−	15.0264i	0.291294	−	0.504536i	0.974116	+	0.226049i	$0.0725810\pi$
$888$		0			0
$889$	−4.07557	+	0.00457057i	−0.136690	+	0.000153292i
$890$		0			0
$891$	0.0296269	+	0.0171051i	0.000992537	+	0.000573042i
$892$		0			0
$893$	6.31966	+	10.9460i	0.211480	+	0.366293i
$894$		0			0
$895$	6.62778			0.221542
$896$		0			0
$897$	−0.425572			−0.0142094
$898$		0			0
$899$	−11.2558	−	19.4956i	−0.375402	−	0.650216i
$900$		0			0
$901$	55.4053	+	31.9883i	1.84582	+	1.06568i
$902$		0			0
$903$	−1.76821	−	3.05471i	−0.0588423	−	0.101654i
$904$		0			0
$905$	−19.8268	+	34.3410i	−0.659064	+	1.14153i
$906$		0			0
$907$	32.5977	−	18.8203i	1.08239	−	0.624918i	0.150850	−	0.988557i	$-0.451799\pi$
$907$	32.5977	−	18.8203i	1.08239	−	0.624918i	0.931540	+	0.363638i	$0.118466\pi$
$908$		0			0
$909$		−	9.09954i		−	0.301813i
$910$		0			0
$911$		−	6.12808i		−	0.203032i	−0.994834	−	0.101516i	$-0.967631\pi$
$911$		−	6.12808i		−	0.203032i	0.994834	−	0.101516i	$-0.0323694\pi$
$912$		0			0
$913$	−12.4831	+	7.20714i	−0.413132	+	0.238522i
$914$		0			0
$915$	8.93027	−	15.4677i	0.295226	−	0.511346i
$916$		0			0
$917$	23.9064	+	13.7667i	0.789459	+	0.454615i
$918$		0			0
$919$	22.1538	+	12.7905i	0.730787	+	0.421920i	0.818710	−	0.574207i	$-0.194690\pi$
$919$	22.1538	+	12.7905i	0.730787	+	0.421920i	−0.0879230	+	0.996127i	$0.528023\pi$
$920$		0			0
$921$	−12.5658	−	21.7646i	−0.414057	−	0.717167i
$922$		0			0
$923$	1.25066			0.0411659
$924$		0			0
$925$	−43.2897			−1.42336
$926$		0			0
$927$	16.8537	+	29.1915i	0.553549	+	0.958774i
$928$		0			0
$929$	−26.6709	−	15.3985i	−0.875045	−	0.505207i	−0.00602346	−	0.999982i	$-0.501917\pi$
$929$	−26.6709	−	15.3985i	−0.875045	−	0.505207i	−0.869021	+	0.494774i	$0.835251\pi$
$930$		0			0
$931$	9.52708	−	16.5872i	0.312237	−	0.543623i
$932$		0			0
$933$	3.32632	−	5.76136i	0.108899	−	0.188618i
$934$		0			0
$935$	22.0914	−	12.7545i	0.722467	−	0.417117i
$936$		0			0
$937$			3.26443i			0.106644i	0.998577	+	0.0533222i	$0.0169810\pi$
$937$			3.26443i			0.106644i	−0.998577	+	0.0533222i	$0.983019\pi$
$938$		0			0
$939$			0.825073i			0.0269252i
$940$		0			0
$941$	28.2694	−	16.3214i	0.921557	−	0.532061i	0.0374253	−	0.999299i	$-0.488084\pi$
$941$	28.2694	−	16.3214i	0.921557	−	0.532061i	0.884131	+	0.467238i	$0.154751\pi$
$942$		0			0
$943$	−9.18444	+	15.9079i	−0.299087	+	0.518033i
$944$		0			0
$945$	23.0108	−	39.9593i	0.748541	−	1.29988i
$946$		0			0
$947$	−35.4482	−	20.4660i	−1.15191	−	0.665056i	−0.202559	−	0.979270i	$-0.564926\pi$
$947$	−35.4482	−	20.4660i	−1.15191	−	0.665056i	−0.949352	+	0.314214i	$0.898259\pi$
$948$		0			0
$949$	1.30602	+	2.26209i	0.0423952	+	0.0734306i
$950$		0			0
$951$	21.6564			0.702257
$952$		0			0
$953$	−15.6672			−0.507509			−0.253755	−	0.967269i	$-0.581666\pi$
$953$	−15.6672			−0.507509			−0.253755	+	0.967269i	$0.581666\pi$
$954$		0			0
$955$	3.74254	+	6.48227i	0.121106	+	0.209761i
$956$		0			0
$957$	2.10230	+	1.21376i	0.0679576	+	0.0392353i
$958$		0			0
$959$	−42.2219	+	24.4400i	−1.36342	+	0.789209i
$960$		0			0
$961$	−33.5532	+	58.1159i	−1.08236	+	1.87471i
$962$		0			0
$963$	−15.4509	+	8.92060i	−0.497900	+	0.287462i
$964$		0			0
$965$			28.8045i			0.927250i
$966$		0			0
$967$		−	13.6688i		−	0.439560i	−0.975549	−	0.219780i	$-0.929466\pi$
$967$		−	13.6688i		−	0.439560i	0.975549	−	0.219780i	$-0.0705339\pi$
$968$		0			0
$969$	−19.2010	+	11.0857i	−0.616826	+	0.356125i
$970$		0			0
$971$	−14.6299	+	25.3398i	−0.469497	+	0.813193i	−0.999392	−	0.0348707i	$-0.988898\pi$
$971$	−14.6299	+	25.3398i	−0.469497	+	0.813193i	0.529895	+	0.848063i	$0.322231\pi$
$972$		0			0
$973$	−0.0454281	−	40.5082i	−0.00145636	−	1.29863i
$974$		0			0
$975$	−1.04200	−	0.601601i	−0.0333708	−	0.0192666i
$976$		0			0
$977$	−3.63732	−	6.30002i	−0.116368	−	0.201555i	0.801958	−	0.597381i	$-0.203792\pi$
$977$	−3.63732	−	6.30002i	−0.116368	−	0.201555i	−0.918326	+	0.395825i	$0.870459\pi$
$978$		0			0
$979$	−7.62881			−0.243818
$980$		0			0
$981$	2.82430			0.0901728
$982$		0			0
$983$	−13.6878	−	23.7079i	−0.436572	−	0.756165i	0.560851	−	0.827917i	$-0.310474\pi$
$983$	−13.6878	−	23.7079i	−0.436572	−	0.756165i	−0.997422	+	0.0717523i	$0.977141\pi$
$984$		0			0
$985$	36.0727	+	20.8266i	1.14937	+	0.663591i
$986$		0			0
$987$	0.0146581	+	13.0706i	0.000466571	+	0.416041i
$988$		0			0
$989$	−1.38641	+	2.40133i	−0.0440852	+	0.0763578i
$990$		0			0
$991$	−31.2061	+	18.0168i	−0.991293	+	0.572323i	−0.905661	−	0.424003i	$-0.860624\pi$
$991$	−31.2061	+	18.0168i	−0.991293	+	0.572323i	−0.0856325	+	0.996327i	$0.527291\pi$
$992$		0			0
$993$			22.1110i			0.701672i
$994$		0			0
$995$			2.28127i			0.0723213i
$996$		0			0
$997$	1.47489	−	0.851531i	0.0467104	−	0.0269683i	−0.476463	−	0.879195i	$-0.658081\pi$
$997$	1.47489	−	0.851531i	0.0467104	−	0.0269683i	0.523173	+	0.852226i	$0.324748\pi$
$998$		0			0
$999$	−17.8980	+	31.0003i	−0.566269	+	0.980806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.be.b.1167.10	yes	28
4.3	odd	2		1232.2.be.c.1167.5	yes	28
7.3	odd	6		1232.2.be.c.815.5	yes	28
28.3	even	6	inner	1232.2.be.b.815.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.be.b.815.10	✓	28	28.3	even	6	inner
1232.2.be.b.1167.10	yes	28	1.1	even	1	trivial
1232.2.be.c.815.5	yes	28	7.3	odd	6
1232.2.be.c.1167.5	yes	28	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.534042 + 0.924987i) q^{3} +(-2.90816 - 1.67903i) q^{5} +(0.00296709 + 2.64575i) q^{7} +(0.929599 - 1.61011i) q^{9} +O(q^{10})\)	\(q+(0.534042 + 0.924987i) q^{3} +(-2.90816 - 1.67903i) q^{5} +(0.00296709 + 2.64575i) q^{7} +(0.929599 - 1.61011i) q^{9} +(-0.866025 + 0.500000i) q^{11} +0.179479i q^{13} -3.58668i q^{15} +(6.57865 - 3.79818i) q^{17} +(-1.36632 + 2.36654i) q^{19} +(-2.44570 + 1.41569i) q^{21} +(1.92258 + 1.11000i) q^{23} +(3.13826 + 5.43563i) q^{25} +5.19003 q^{27} -2.27278 q^{29} +(4.95243 + 8.57787i) q^{31} +(-0.924987 - 0.534042i) q^{33} +(4.43366 - 7.69924i) q^{35} +(-3.44854 + 5.97305i) q^{37} +(-0.166016 + 0.0958494i) q^{39} +8.27425i q^{41} +1.24901i q^{43} +(-5.40684 + 3.12164i) q^{45} +(2.31266 - 4.00564i) q^{47} +(-6.99998 + 0.0157004i) q^{49} +(7.02654 + 4.05678i) q^{51} +(4.21100 + 7.29366i) q^{53} +3.35805 q^{55} -2.91869 q^{57} +(3.85081 + 6.66981i) q^{59} +(4.31253 + 2.48984i) q^{61} +(4.26271 + 2.45471i) q^{63} +(0.301350 - 0.521954i) q^{65} +(4.07575 - 2.35313i) q^{67} +2.37115i q^{69} -6.96826i q^{71} +(12.6036 - 7.27671i) q^{73} +(-3.35192 + 5.80570i) q^{75} +(-1.32544 - 2.28980i) q^{77} +(-3.00092 - 1.73258i) q^{79} +(-0.0171051 - 0.0296269i) q^{81} +14.4143 q^{83} -25.5090 q^{85} +(-1.21376 - 2.10230i) q^{87} +(6.60674 + 3.81440i) q^{89} +(-0.474857 + 0.000532531i) q^{91} +(-5.28961 + 9.16188i) q^{93} +(7.94697 - 4.58818i) q^{95} -11.9139i q^{97} +1.85920i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9	\( 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9} + 18 q^{17} - 14 q^{19} - 2 q^{21} + 12 q^{23} + 14 q^{25} + 16 q^{27} + 16 q^{29} - 10 q^{31} - 6 q^{35} - 4 q^{37} - 42 q^{39} - 42 q^{45} - 6 q^{47} - 4 q^{49} + 24 q^{51} - 2 q^{53} - 48 q^{57} + 12 q^{59} - 12 q^{61} + 26 q^{63} + 6 q^{65} + 48 q^{67} + 6 q^{73} + 14 q^{75} + 2 q^{77} - 48 q^{79} - 22 q^{81} + 84 q^{83} + 16 q^{85} - 18 q^{87} + 6 q^{89} + 18 q^{91} + 28 q^{93} + 36 q^{95}+O(q^{100}) \) 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9 + 18 * q^17 - 14 * q^19 - 2 * q^21 + 12 * q^23 + 14 * q^25 + 16 * q^27 + 16 * q^29 - 10 * q^31 - 6 * q^35 - 4 * q^37 - 42 * q^39 - 42 * q^45 - 6 * q^47 - 4 * q^49 + 24 * q^51 - 2 * q^53 - 48 * q^57 + 12 * q^59 - 12 * q^61 + 26 * q^63 + 6 * q^65 + 48 * q^67 + 6 * q^73 + 14 * q^75 + 2 * q^77 - 48 * q^79 - 22 * q^81 + 84 * q^83 + 16 * q^85 - 18 * q^87 + 6 * q^89 + 18 * q^91 + 28 * q^93 + 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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