LMFDB - Embedded newform 1232.2.bi.b.527.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(527,1232)]

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, 2, 3]))

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

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

chi := DirichletCharacter("1232.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bi (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.8
Character	$\chi$	$=$	1232.527
Dual form			1232.2.bi.b.879.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.497216 + 0.287068i) q^{3} +(0.0931719 - 0.161379i) q^{5} +(-1.17817 - 2.36895i) q^{7} +(-1.33518 + 2.31261i) q^{9} +O(q^{10})$	\(q+(-0.497216 + 0.287068i) q^{3} +(0.0931719 - 0.161379i) q^{5} +(-1.17817 - 2.36895i) q^{7} +(-1.33518 + 2.31261i) q^{9} +(0.691567 + 3.24372i) q^{11} -2.60748i q^{13} +0.106987i q^{15} +(2.71814 - 1.56932i) q^{17} +(-1.90321 + 3.29645i) q^{19} +(1.26585 + 0.839665i) q^{21} +(-6.10413 - 3.52422i) q^{23} +(2.48264 + 4.30006i) q^{25} -3.25556i q^{27} +2.51768i q^{29} +(-7.39137 + 4.26741i) q^{31} +(-1.27503 - 1.41430i) q^{33} +(-0.492070 - 0.0305882i) q^{35} +(-1.18007 + 2.04394i) q^{37} +(0.748523 + 1.29648i) q^{39} +9.66118i q^{41} +2.06895 q^{43} +(0.248803 + 0.430940i) q^{45} +(-4.65352 - 2.68671i) q^{47} +(-4.22383 + 5.58205i) q^{49} +(-0.901001 + 1.56058i) q^{51} +(3.47173 + 6.01321i) q^{53} +(0.587902 + 0.190620i) q^{55} -2.18540i q^{57} +(0.586493 - 0.338612i) q^{59} +(-6.14860 - 3.54990i) q^{61} +(7.05152 + 0.438339i) q^{63} +(-0.420791 - 0.242944i) q^{65} +(-10.1223 + 5.84414i) q^{67} +4.04677 q^{69} +5.20158i q^{71} +(8.45446 - 4.88118i) q^{73} +(-2.46882 - 1.42537i) q^{75} +(6.86943 - 5.45994i) q^{77} +(-5.83616 + 10.1085i) q^{79} +(-3.07099 - 5.31910i) q^{81} -0.452209 q^{83} -0.584865i q^{85} +(-0.722745 - 1.25183i) q^{87} +(-6.54754 + 11.3407i) q^{89} +(-6.17698 + 3.07205i) q^{91} +(2.45007 - 4.24365i) q^{93} +(0.354651 + 0.614273i) q^{95} -8.54347 q^{97} +(-8.42482 - 2.73164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 12 * q^9	$ 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) $ 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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
$3$	−0.497216	+	0.287068i	−0.287068	+	0.165739i	−0.636619	−	0.771179i	$-0.719667\pi$
$3$	−0.497216	+	0.287068i	−0.287068	+	0.165739i	0.349551	+	0.936917i	$0.386334\pi$
$4$		0			0
$5$	0.0931719	−	0.161379i	0.0416678	−	0.0721707i	−0.844439	−	0.535651i	$-0.820066\pi$
$5$	0.0931719	−	0.161379i	0.0416678	−	0.0721707i	0.886107	+	0.463480i	$0.153400\pi$
$6$		0			0
$7$	−1.17817	−	2.36895i	−0.445306	−	0.895378i
$7$	−1.17817	−	2.36895i	−0.445306	−	0.895378i
$8$		0			0
$9$	−1.33518	+	2.31261i	−0.445061	+	0.770869i
$10$		0			0
$11$	0.691567	+	3.24372i	0.208515	+	0.978019i
$11$	0.691567	+	3.24372i	0.208515	+	0.978019i
$12$		0			0
$13$		−	2.60748i		−	0.723184i	−0.932336	−	0.361592i	$-0.882233\pi$
$13$		−	2.60748i		−	0.723184i	0.932336	−	0.361592i	$-0.117767\pi$
$14$		0			0
$15$			0.106987i			0.0276238i
$16$		0			0
$17$	2.71814	−	1.56932i	0.659245	−	0.380615i	−0.132744	−	0.991150i	$-0.542379\pi$
$17$	2.71814	−	1.56932i	0.659245	−	0.380615i	0.791989	+	0.610535i	$0.209046\pi$
$18$		0			0
$19$	−1.90321	+	3.29645i	−0.436626	+	0.756258i	−0.997427	−	0.0716929i	$-0.977160\pi$
$19$	−1.90321	+	3.29645i	−0.436626	+	0.756258i	0.560801	+	0.827950i	$0.310493\pi$
$20$		0			0
$21$	1.26585	+	0.839665i	0.276232	+	0.183230i
$22$		0			0
$23$	−6.10413	−	3.52422i	−1.27280	−	0.734851i	−0.297286	−	0.954788i	$-0.596081\pi$
$23$	−6.10413	−	3.52422i	−1.27280	−	0.734851i	−0.975514	+	0.219937i	$0.929415\pi$
$24$		0			0
$25$	2.48264	+	4.30006i	0.496528	+	0.860011i
$26$		0			0
$27$		−	3.25556i		−	0.626533i
$28$		0			0
$29$			2.51768i			0.467522i	0.972294	+	0.233761i	$0.0751033\pi$
$29$			2.51768i			0.467522i	−0.972294	+	0.233761i	$0.924897\pi$
$30$		0			0
$31$	−7.39137	+	4.26741i	−1.32753	+	0.766449i	−0.984917	−	0.173028i	$-0.944645\pi$
$31$	−7.39137	+	4.26741i	−1.32753	+	0.766449i	−0.342612	+	0.939477i	$0.611312\pi$
$32$		0			0
$33$	−1.27503	−	1.41430i	−0.221954	−	0.246199i
$34$		0			0
$35$	−0.492070	−	0.0305882i	−0.0831750	−	0.00517036i
$36$		0			0
$37$	−1.18007	+	2.04394i	−0.194003	+	0.336022i	−0.946573	−	0.322489i	$-0.895480\pi$
$37$	−1.18007	+	2.04394i	−0.194003	+	0.336022i	0.752571	+	0.658512i	$0.228814\pi$
$38$		0			0
$39$	0.748523	+	1.29648i	0.119860	+	0.207603i
$40$		0			0
$41$			9.66118i			1.50882i	0.656402	+	0.754411i	$0.272077\pi$
$41$			9.66118i			1.50882i	−0.656402	+	0.754411i	$0.727923\pi$
$42$		0			0
$43$	2.06895			0.315512			0.157756	−	0.987478i	$-0.449574\pi$
$43$	2.06895			0.315512			0.157756	+	0.987478i	$0.449574\pi$
$44$		0			0
$45$	0.248803	+	0.430940i	0.0370894	+	0.0642408i
$46$		0			0
$47$	−4.65352	−	2.68671i	−0.678786	−	0.391897i	0.120611	−	0.992700i	$-0.461515\pi$
$47$	−4.65352	−	2.68671i	−0.678786	−	0.391897i	−0.799398	+	0.600802i	$0.794848\pi$
$48$		0			0
$49$	−4.22383	+	5.58205i	−0.603405	+	0.797435i
$50$		0			0
$51$	−0.901001	+	1.56058i	−0.126165	+	0.218525i
$52$		0			0
$53$	3.47173	+	6.01321i	0.476878	+	0.825978i	0.999649	−	0.0264959i	$-0.00843488\pi$
$53$	3.47173	+	6.01321i	0.476878	+	0.825978i	−0.522771	+	0.852473i	$0.675102\pi$
$54$		0			0
$55$	0.587902	+	0.190620i	0.0792727	+	0.0257032i
$56$		0			0
$57$		−	2.18540i		−	0.289463i
$58$		0			0
$59$	0.586493	−	0.338612i	0.0763549	−	0.0440835i	−0.461336	−	0.887225i	$-0.652630\pi$
$59$	0.586493	−	0.338612i	0.0763549	−	0.0440835i	0.537691	+	0.843142i	$0.319297\pi$
$60$		0			0
$61$	−6.14860	−	3.54990i	−0.787248	−	0.454518i	0.0517449	−	0.998660i	$-0.483522\pi$
$61$	−6.14860	−	3.54990i	−0.787248	−	0.454518i	−0.838993	+	0.544143i	$0.816855\pi$
$62$		0			0
$63$	7.05152	+	0.438339i	0.888408	+	0.0552256i
$64$		0			0
$65$	−0.420791	−	0.242944i	−0.0521927	−	0.0301335i
$66$		0			0
$67$	−10.1223	+	5.84414i	−1.23664	+	0.713975i	−0.968406	−	0.249379i	$-0.919774\pi$
$67$	−10.1223	+	5.84414i	−1.23664	+	0.713975i	−0.268235	+	0.963354i	$0.586440\pi$
$68$		0			0
$69$	4.04677			0.487173
$70$		0			0
$71$			5.20158i			0.617315i	0.951173	+	0.308657i	$0.0998796\pi$
$71$			5.20158i			0.617315i	−0.951173	+	0.308657i	$0.900120\pi$
$72$		0			0
$73$	8.45446	−	4.88118i	0.989520	−	0.571299i	0.0843890	−	0.996433i	$-0.473106\pi$
$73$	8.45446	−	4.88118i	0.989520	−	0.571299i	0.905131	+	0.425133i	$0.139773\pi$
$74$		0			0
$75$	−2.46882	−	1.42537i	−0.285074	−	0.164588i
$76$		0			0
$77$	6.86943	−	5.45994i	0.782844	−	0.622218i
$78$		0			0
$79$	−5.83616	+	10.1085i	−0.656619	+	1.13730i	0.324866	+	0.945760i	$0.394681\pi$
$79$	−5.83616	+	10.1085i	−0.656619	+	1.13730i	−0.981485	+	0.191538i	$0.938653\pi$
$80$		0			0
$81$	−3.07099	−	5.31910i	−0.341221	−	0.591011i
$82$		0			0
$83$	−0.452209			−0.0496364			−0.0248182	−	0.999692i	$-0.507901\pi$
$83$	−0.452209			−0.0496364			−0.0248182	+	0.999692i	$0.507901\pi$
$84$		0			0
$85$		−	0.584865i		−	0.0634375i
$86$		0			0
$87$	−0.722745	−	1.25183i	−0.0774864	−	0.134210i
$88$		0			0
$89$	−6.54754	+	11.3407i	−0.694038	+	1.20211i	0.276467	+	0.961024i	$0.410837\pi$
$89$	−6.54754	+	11.3407i	−0.694038	+	1.20211i	−0.970504	+	0.241085i	$0.922497\pi$
$90$		0			0
$91$	−6.17698	+	3.07205i	−0.647523	+	0.322038i
$92$		0			0
$93$	2.45007	−	4.24365i	0.254061	−	0.440046i
$94$		0			0
$95$	0.354651	+	0.614273i	0.0363864	+	0.0630231i
$96$		0			0
$97$	−8.54347			−0.867458			−0.433729	−	0.901043i	$-0.642802\pi$
$97$	−8.54347			−0.867458			−0.433729	+	0.901043i	$0.642802\pi$
$98$		0			0
$99$	−8.42482	−	2.73164i	−0.846727	−	0.274541i
$100$		0			0
$101$	12.5610	−	7.25211i	1.24987	−	0.721612i	0.278786	−	0.960353i	$-0.410068\pi$
$101$	12.5610	−	7.25211i	1.24987	−	0.721612i	0.971083	+	0.238741i	$0.0767347\pi$
$102$		0			0
$103$	3.15969	+	1.82425i	0.311333	+	0.179748i	0.647523	−	0.762046i	$-0.275805\pi$
$103$	3.15969	+	1.82425i	0.311333	+	0.179748i	−0.336190	+	0.941794i	$0.609138\pi$
$104$		0			0
$105$	0.253446	−	0.126048i	0.0247338	−	0.0123011i
$106$		0			0
$107$	5.79101	−	10.0303i	0.559838	−	0.969668i	−0.437671	−	0.899135i	$-0.644197\pi$
$107$	5.79101	−	10.0303i	0.559838	−	0.969668i	0.997509	−	0.0705333i	$-0.0224701\pi$
$108$		0			0
$109$	−6.89061	+	3.97830i	−0.660001	+	0.381052i	−0.792277	−	0.610161i	$-0.791105\pi$
$109$	−6.89061	+	3.97830i	−0.660001	+	0.381052i	0.132276	+	0.991213i	$0.457771\pi$
$110$		0			0
$111$		−	1.35504i		−	0.128615i
$112$		0			0
$113$	−8.82673			−0.830349			−0.415175	−	0.909742i	$-0.636280\pi$
$113$	−8.82673			−0.830349			−0.415175	+	0.909742i	$0.636280\pi$
$114$		0			0
$115$	−1.13747	+	0.656718i	−0.106069	+	0.0612392i
$116$		0			0
$117$	6.03007	+	3.48146i	0.557480	+	0.321861i
$118$		0			0
$119$	−6.92006	−	4.59020i	−0.634360	−	0.420783i
$120$		0			0
$121$	−10.0435	+	4.48650i	−0.913043	+	0.407864i
$122$		0			0
$123$	−2.77341	−	4.80369i	−0.250070	−	0.433134i
$124$		0			0
$125$	1.85697			0.166092
$126$		0			0
$127$	−13.6087			−1.20758			−0.603788	−	0.797145i	$-0.706343\pi$
$127$	−13.6087			−1.20758			−0.603788	+	0.797145i	$0.706343\pi$
$128$		0			0
$129$	−1.02871	+	0.593929i	−0.0905733	+	0.0522925i
$130$		0			0
$131$	−2.49859	+	4.32769i	−0.218303	+	0.378112i	−0.954289	−	0.298885i	$-0.903385\pi$
$131$	−2.49859	+	4.32769i	−0.218303	+	0.378112i	0.735986	+	0.676996i	$0.236719\pi$
$132$		0			0
$133$	10.0514	+	0.624821i	0.871569	+	0.0541788i
$134$		0			0
$135$	−0.525378	−	0.303327i	−0.0452173	−	0.0261062i
$136$		0			0
$137$	−2.62376	−	4.54449i	−0.224163	−	0.388262i	0.731905	−	0.681407i	$-0.238631\pi$
$137$	−2.62376	−	4.54449i	−0.224163	−	0.388262i	−0.956068	+	0.293145i	$0.905298\pi$
$138$		0			0
$139$	17.8009			1.50985			0.754926	−	0.655810i	$-0.227673\pi$
$139$	17.8009			1.50985			0.754926	+	0.655810i	$0.227673\pi$
$140$		0			0
$141$	3.08508			0.259810
$142$		0			0
$143$	8.45793	−	1.80325i	0.707288	−	0.150795i
$144$		0			0
$145$	0.406300	+	0.234577i	0.0337413	+	0.0194806i
$146$		0			0
$147$	0.497732	−	3.98801i	0.0410522	−	0.328925i
$148$		0			0
$149$	−19.0024	−	10.9710i	−1.55674	−	0.898781i	−0.997566	−	0.0697278i	$-0.977787\pi$
$149$	−19.0024	−	10.9710i	−1.55674	−	0.898781i	−0.559169	−	0.829054i	$-0.688880\pi$
$150$		0			0
$151$	6.95448	+	12.0455i	0.565948	+	0.980250i	0.996961	+	0.0779043i	$0.0248229\pi$
$151$	6.95448	+	12.0455i	0.565948	+	0.980250i	−0.431013	+	0.902346i	$0.641844\pi$
$152$		0			0
$153$			8.38131i			0.677589i
$154$		0			0
$155$			1.59041i			0.127745i
$156$		0			0
$157$	−3.84987	−	6.66817i	−0.307253	−	0.532178i	0.670507	−	0.741903i	$-0.266076\pi$
$157$	−3.84987	−	6.66817i	−0.307253	−	0.532178i	−0.977760	+	0.209725i	$0.932743\pi$
$158$		0			0
$159$	−3.45240	−	1.99324i	−0.273793	−	0.158074i
$160$		0			0
$161$	−1.15700	+	18.6125i	−0.0911843	+	1.46687i
$162$		0			0
$163$	5.08717	+	2.93708i	0.398458	+	0.230050i	0.685819	−	0.727773i	$-0.259444\pi$
$163$	5.08717	+	2.93708i	0.398458	+	0.230050i	−0.287360	+	0.957823i	$0.592778\pi$
$164$		0			0
$165$	−0.347035	+	0.0739885i	−0.0270166	+	0.00575999i
$166$		0			0
$167$	1.09739			0.0849190			0.0424595	−	0.999098i	$-0.486481\pi$
$167$	1.09739			0.0849190			0.0424595	+	0.999098i	$0.486481\pi$
$168$		0			0
$169$	6.20106			0.477005
$170$		0			0
$171$	−5.08226	−	8.80274i	−0.388650	−	0.673162i
$172$		0			0
$173$	8.77946	+	5.06882i	0.667490	+	0.385375i	0.795125	−	0.606446i	$-0.207405\pi$
$173$	8.77946	+	5.06882i	0.667490	+	0.385375i	−0.127635	+	0.991821i	$0.540739\pi$
$174$		0			0
$175$	7.26164	−	10.9474i	0.548928	−	0.827548i
$176$		0			0
$177$	−0.194409	+	0.336727i	−0.0146127	+	0.0253099i
$178$		0			0
$179$	16.5795	−	9.57216i	1.23921	−	0.715457i	0.270275	−	0.962783i	$-0.412885\pi$
$179$	16.5795	−	9.57216i	1.23921	−	0.715457i	0.968932	+	0.247326i	$0.0795520\pi$
$180$		0			0
$181$	25.6825			1.90897			0.954483	−	0.298265i	$-0.0964080\pi$
$181$	25.6825			1.90897			0.954483	+	0.298265i	$0.0964080\pi$
$182$		0			0
$183$	4.07625			0.301325
$184$		0			0
$185$	0.219899	+	0.380876i	0.0161673	+	0.0280026i
$186$		0			0
$187$	6.97020	+	7.73159i	0.509712	+	0.565390i
$188$		0			0
$189$	−7.71226	+	3.83560i	−0.560984	+	0.278999i
$190$		0			0
$191$	11.5743	+	6.68242i	0.837486	+	0.483523i	0.856409	−	0.516298i	$-0.172690\pi$
$191$	11.5743	+	6.68242i	0.837486	+	0.483523i	−0.0189230	+	0.999821i	$0.506024\pi$
$192$		0			0
$193$	−3.92447	+	2.26580i	−0.282490	+	0.163096i	−0.634550	−	0.772882i	$-0.718815\pi$
$193$	−3.92447	+	2.26580i	−0.282490	+	0.163096i	0.352060	+	0.935977i	$0.385481\pi$
$194$		0			0
$195$	0.278965			0.0199771
$196$		0			0
$197$		−	11.6601i		−	0.830746i	−0.909651	−	0.415373i	$-0.863651\pi$
$197$		−	11.6601i		−	0.830746i	0.909651	−	0.415373i	$-0.136349\pi$
$198$		0			0
$199$	1.22294	−	0.706063i	0.0866917	−	0.0500514i	−0.456027	−	0.889966i	$-0.650728\pi$
$199$	1.22294	−	0.706063i	0.0866917	−	0.0500514i	0.542719	+	0.839914i	$0.317395\pi$
$200$		0			0
$201$	3.35533	−	5.81160i	0.236667	−	0.409918i
$202$		0			0
$203$	5.96426	−	2.96625i	0.418609	−	0.208190i
$204$		0			0
$205$	1.55911	+	0.900151i	0.108893	+	0.0628692i
$206$		0			0
$207$	16.3003	−	9.41098i	1.13295	−	0.654108i
$208$		0			0
$209$	−12.0090	−	3.89376i	−0.830677	−	0.269337i
$210$		0			0
$211$	0.00586402			0.000403696			0.000201848	−	1.00000i	$-0.499936\pi$
$211$	0.00586402			0.000403696			0.000201848		1.00000i	$0.499936\pi$
$212$		0			0
$213$	−1.49321	−	2.58631i	−0.102313	−	0.177211i
$214$		0			0
$215$	0.192768	−	0.333884i	0.0131467	−	0.0227707i
$216$		0			0
$217$	18.8176	+	12.4820i	1.27742	+	0.847336i
$218$		0			0
$219$	−2.80246	+	4.85401i	−0.189373	+	0.328003i
$220$		0			0
$221$	−4.09196	−	7.08748i	−0.275255	−	0.476755i
$222$		0			0
$223$			21.6723i			1.45128i	0.688072	+	0.725642i	$0.258457\pi$
$223$			21.6723i			1.45128i	−0.688072	+	0.725642i	$0.741543\pi$
$224$		0			0
$225$	−13.2591			−0.883941
$226$		0			0
$227$	−7.89341	−	13.6718i	−0.523904	−	0.907428i	−0.999613	−	0.0278253i	$-0.991142\pi$
$227$	−7.89341	−	13.6718i	−0.523904	−	0.907428i	0.475709	−	0.879603i	$-0.342192\pi$
$228$		0			0
$229$	10.0953	−	17.4855i	0.667114	−	1.15548i	−0.311594	−	0.950215i	$-0.600863\pi$
$229$	10.0953	−	17.4855i	0.667114	−	1.15548i	0.978708	−	0.205260i	$-0.0658039\pi$
$230$		0			0
$231$	−1.84822	+	4.68676i	−0.121604	+	0.308366i
$232$		0			0
$233$	−20.5706	−	11.8765i	−1.34763	−	0.778053i	−0.359714	−	0.933063i	$-0.617126\pi$
$233$	−20.5706	−	11.8765i	−1.34763	−	0.778053i	−0.987913	+	0.155010i	$0.950459\pi$
$234$		0			0
$235$	−0.867156	+	0.500653i	−0.0565670	+	0.0326590i
$236$		0			0
$237$		−	6.70149i		−	0.435309i
$238$		0			0
$239$	−7.78208			−0.503381			−0.251691	−	0.967808i	$-0.580987\pi$
$239$	−7.78208			−0.503381			−0.251691	+	0.967808i	$0.580987\pi$
$240$		0			0
$241$	13.4860	−	7.78614i	0.868709	−	0.501550i	0.00179024	−	0.999998i	$-0.499430\pi$
$241$	13.4860	−	7.78614i	0.868709	−	0.501550i	0.866919	+	0.498449i	$0.166097\pi$
$242$		0			0
$243$	11.5121	+	6.64650i	0.738500	+	0.426373i
$244$		0			0
$245$	0.507280	+	1.20173i	0.0324089	+	0.0767755i
$246$		0			0
$247$	8.59542	+	4.96257i	0.546913	+	0.315761i
$248$		0			0
$249$	0.224846	−	0.129815i	0.0142490	−	0.00822667i
$250$		0			0
$251$			0.786340i			0.0496333i	0.999692	+	0.0248167i	$0.00790020\pi$
$251$			0.786340i			0.0496333i	−0.999692	+	0.0248167i	$0.992100\pi$
$252$		0			0
$253$	7.21018	−	22.2374i	0.453300	−	1.39805i
$254$		0			0
$255$	0.167896	+	0.290804i	0.0105141	+	0.0182109i
$256$		0			0
$257$	1.04980	−	1.81831i	0.0654849	−	0.113423i	−0.831424	−	0.555638i	$-0.812474\pi$
$257$	1.04980	−	1.81831i	0.0654849	−	0.113423i	0.896909	+	0.442215i	$0.145807\pi$
$258$		0			0
$259$	6.23232	+	0.387416i	0.387258	+	0.0240729i
$260$		0			0
$261$	−5.82240	−	3.36157i	−0.360398	−	0.208076i
$262$		0			0
$263$	−11.2950	−	19.5635i	−0.696479	−	1.20634i	−0.969680	−	0.244380i	$-0.921416\pi$
$263$	−11.2950	−	19.5635i	−0.696479	−	1.20634i	0.273200	−	0.961957i	$-0.411918\pi$
$264$		0			0
$265$	1.29387			0.0794818
$266$		0			0
$267$		−	7.51835i		−	0.460115i
$268$		0			0
$269$	−10.6026	−	18.3643i	−0.646452	−	1.11969i	−0.983964	−	0.178367i	$-0.942919\pi$
$269$	−10.6026	−	18.3643i	−0.646452	−	1.11969i	0.337512	−	0.941321i	$-0.390415\pi$
$270$		0			0
$271$	12.5827	−	21.7939i	0.764346	−	1.32389i	−0.176246	−	0.984346i	$-0.556395\pi$
$271$	12.5827	−	21.7939i	0.764346	−	1.32389i	0.940592	−	0.339540i	$-0.110271\pi$
$272$		0			0
$273$	2.18941	−	3.30068i	0.132509	−	0.199766i
$274$		0			0
$275$	−12.2313	+	11.0268i	−0.737574	+	0.664939i
$276$		0			0
$277$	−8.05157	+	4.64858i	−0.483772	+	0.279306i	−0.721987	−	0.691907i	$-0.756771\pi$
$277$	−8.05157	+	4.64858i	−0.483772	+	0.279306i	0.238215	+	0.971212i	$0.423438\pi$
$278$		0			0
$279$		−	22.7911i		−	1.36447i
$280$		0			0
$281$		−	22.2571i		−	1.32775i	−0.747844	−	0.663875i	$-0.768911\pi$
$281$		−	22.2571i		−	1.32775i	0.747844	−	0.663875i	$-0.231089\pi$
$282$		0			0
$283$	−6.97259	−	12.0769i	−0.414478	−	0.717897i	0.580896	−	0.813978i	$-0.302702\pi$
$283$	−6.97259	−	12.0769i	−0.414478	−	0.717897i	−0.995373	+	0.0960815i	$0.969369\pi$
$284$		0			0
$285$	−0.352676	−	0.203618i	−0.0208907	−	0.0120613i
$286$		0			0
$287$	22.8868	−	11.3825i	1.35097	−	0.671888i
$288$		0			0
$289$	−3.57449	+	6.19120i	−0.210264	+	0.364188i
$290$		0			0
$291$	4.24795	−	2.45256i	0.249019	−	0.143771i
$292$		0			0
$293$			32.8832i			1.92106i	0.278181	+	0.960529i	$0.410269\pi$
$293$			32.8832i			1.92106i	−0.278181	+	0.960529i	$0.589731\pi$
$294$		0			0
$295$		−	0.126197i		−	0.00734745i
$296$		0			0
$297$	10.5601	−	2.25144i	0.612761	−	0.130642i
$298$		0			0
$299$	−9.18933	+	15.9164i	−0.531433	+	0.920469i
$300$		0			0
$301$	−2.43757	−	4.90123i	−0.140499	−	0.282502i
$302$		0			0
$303$	−4.16370	+	7.21174i	−0.239198	+	0.414303i
$304$		0			0
$305$	−1.14575	+	0.661502i	−0.0656057	+	0.0378775i
$306$		0			0
$307$	18.7701			1.07126			0.535632	−	0.844451i	$-0.320073\pi$
$307$	18.7701			1.07126			0.535632	+	0.844451i	$0.320073\pi$
$308$		0			0
$309$	−2.09473			−0.119165
$310$		0			0
$311$	13.2206	−	7.63290i	0.749670	−	0.432822i	−0.0759046	−	0.997115i	$-0.524184\pi$
$311$	13.2206	−	7.63290i	0.749670	−	0.432822i	0.825575	+	0.564293i	$0.190851\pi$
$312$		0			0
$313$	−9.10934	+	15.7778i	−0.514890	+	0.891816i	0.484960	+	0.874536i	$0.338834\pi$
$313$	−9.10934	+	15.7778i	−0.514890	+	0.891816i	−0.999851	+	0.0172802i	$0.994499\pi$
$314$		0			0
$315$	0.727742	−	1.09712i	0.0410036	−	0.0618159i
$316$		0			0
$317$	4.49416	−	7.78412i	0.252417	−	0.437200i	−0.711773	−	0.702409i	$-0.752108\pi$
$317$	4.49416	−	7.78412i	0.252417	−	0.437200i	0.964191	+	0.265209i	$0.0854411\pi$
$318$		0			0
$319$	−8.16666	+	1.74115i	−0.457245	+	0.0974854i
$320$		0			0
$321$			6.64965i			0.371148i
$322$		0			0
$323$			11.9469i			0.664745i
$324$		0			0
$325$	11.2123	−	6.47342i	0.621946	−	0.359081i
$326$		0			0
$327$	2.28408	−	3.95615i	0.126310	−	0.218775i
$328$		0			0
$329$	−0.882045	+	14.1894i	−0.0486287	+	0.782285i
$330$		0			0
$331$	13.9100	+	8.03095i	0.764564	+	0.441421i	0.830932	−	0.556374i	$-0.187808\pi$
$331$	13.9100	+	8.03095i	0.764564	+	0.441421i	−0.0663683	+	0.997795i	$0.521141\pi$
$332$		0			0
$333$	−3.15123	−	5.45808i	−0.172686	−	0.299101i
$334$		0			0
$335$			2.17804i			0.118999i
$336$		0			0
$337$			32.7156i			1.78213i	0.453875	+	0.891065i	$0.350041\pi$
$337$			32.7156i			1.78213i	−0.453875	+	0.891065i	$0.649959\pi$
$338$		0			0
$339$	4.38879	−	2.53387i	0.238367	−	0.137621i
$340$		0			0
$341$	−18.9539	−	21.0243i	−1.02641	−	1.13853i
$342$		0			0
$343$	18.2000	+	3.42945i	0.982706	+	0.185173i
$344$		0			0
$345$	0.377045	−	0.653061i	0.0202994	−	0.0351596i
$346$		0			0
$347$	4.01242	+	6.94972i	0.215398	+	0.373081i	0.953396	−	0.301723i	$-0.0975617\pi$
$347$	4.01242	+	6.94972i	0.215398	+	0.373081i	−0.737997	+	0.674803i	$0.764228\pi$
$348$		0			0
$349$			25.8972i			1.38625i	0.720819	+	0.693124i	$0.243766\pi$
$349$			25.8972i			1.38625i	−0.720819	+	0.693124i	$0.756234\pi$
$350$		0			0
$351$	−8.48880			−0.453099
$352$		0			0
$353$	−11.3705	−	19.6942i	−0.605188	−	1.04822i	−0.992022	−	0.126067i	$-0.959765\pi$
$353$	−11.3705	−	19.6942i	−0.605188	−	1.04822i	0.386833	−	0.922150i	$-0.373569\pi$
$354$		0			0
$355$	0.839424	+	0.484642i	0.0445520	+	0.0257221i
$356$		0			0
$357$	4.75846	+	0.295798i	0.251845	+	0.0156553i
$358$		0			0
$359$	1.82279	−	3.15717i	0.0962033	−	0.166629i	−0.813907	−	0.580995i	$-0.802663\pi$
$359$	1.82279	−	3.15717i	0.0962033	−	0.166629i	0.910110	+	0.414366i	$0.135997\pi$
$360$		0			0
$361$	2.25561	+	3.90683i	0.118716	+	0.205623i
$362$		0			0
$363$	3.70584	−	5.11392i	0.194506	−	0.268411i
$364$		0			0
$365$		−	1.81916i		−	0.0952191i
$366$		0			0
$367$	−15.9970	+	9.23588i	−0.835038	+	0.482109i	−0.855574	−	0.517680i	$-0.826796\pi$
$367$	−15.9970	+	9.23588i	−0.835038	+	0.482109i	0.0205367	+	0.999789i	$0.493463\pi$
$368$		0			0
$369$	−22.3425	−	12.8994i	−1.16310	−	0.671518i
$370$		0			0
$371$	10.1547	−	15.3089i	0.527206	−	0.794800i
$372$		0			0
$373$	−4.74646	−	2.74037i	−0.245762	−	0.141891i	0.372060	−	0.928209i	$-0.378652\pi$
$373$	−4.74646	−	2.74037i	−0.245762	−	0.141891i	−0.617822	+	0.786318i	$0.711985\pi$
$374$		0			0
$375$	−0.923314	+	0.533076i	−0.0476798	+	0.0275279i
$376$		0			0
$377$	6.56479			0.338104
$378$		0			0
$379$			6.06482i			0.311529i	0.987794	+	0.155764i	$0.0497841\pi$
$379$			6.06482i			0.311529i	−0.987794	+	0.155764i	$0.950216\pi$
$380$		0			0
$381$	6.76646	−	3.90662i	0.346656	−	0.200142i
$382$		0			0
$383$	14.8608	+	8.57986i	0.759349	+	0.438410i	0.829062	−	0.559157i	$-0.188875\pi$
$383$	14.8608	+	8.57986i	0.759349	+	0.438410i	−0.0697130	+	0.997567i	$0.522208\pi$
$384$		0			0
$385$	−0.241080	−	1.61729i	−0.0122865	−	0.0824248i
$386$		0			0
$387$	−2.76243	+	4.78467i	−0.140422	+	0.243218i
$388$		0			0
$389$	10.0390	+	17.3881i	0.509000	+	0.881614i	0.999946	+	0.0104236i	$0.00331801\pi$
$389$	10.0390	+	17.3881i	0.509000	+	0.881614i	−0.490946	+	0.871190i	$0.663349\pi$
$390$		0			0
$391$	−22.1225			−1.11878
$392$		0			0
$393$		−	2.86906i		−	0.144725i
$394$		0			0
$395$	1.08753	+	1.88366i	0.0547197	+	0.0947773i
$396$		0			0
$397$	7.66954	−	13.2840i	0.384923	−	0.666706i	−0.606836	−	0.794827i	$-0.707561\pi$
$397$	7.66954	−	13.2840i	0.384923	−	0.666706i	0.991759	+	0.128121i	$0.0408947\pi$
$398$		0			0
$399$	−5.17709	+	2.57477i	−0.259179	+	0.128900i
$400$		0			0
$401$	−3.31035	+	5.73369i	−0.165311	+	0.286327i	−0.936766	−	0.349957i	$-0.886196\pi$
$401$	−3.31035	+	5.73369i	−0.165311	+	0.286327i	0.771455	+	0.636284i	$0.219529\pi$
$402$		0			0
$403$	11.1272	+	19.2728i	0.554284	+	0.960047i
$404$		0			0
$405$	−1.14452			−0.0568716
$406$		0			0
$407$	−7.44608	−	2.41430i	−0.369089	−	0.119672i
$408$		0			0
$409$	12.8038	−	7.39230i	0.633109	−	0.365526i	−0.148846	−	0.988860i	$-0.547556\pi$
$409$	12.8038	−	7.39230i	0.633109	−	0.365526i	0.781955	+	0.623335i	$0.214222\pi$
$410$		0			0
$411$	2.60915	+	1.50640i	0.128700	+	0.0743050i
$412$		0			0
$413$	−1.49314	−	0.990429i	−0.0734727	−	0.0487358i
$414$		0			0
$415$	−0.0421332	+	0.0729768i	−0.00206824	+	0.00358229i
$416$		0			0
$417$	−8.85089	+	5.11006i	−0.433430	+	0.250241i
$418$		0			0
$419$		−	31.9024i		−	1.55853i	−0.626693	−	0.779266i	$-0.715592\pi$
$419$		−	31.9024i		−	1.55853i	0.626693	−	0.779266i	$-0.284408\pi$
$420$		0			0
$421$	8.55288			0.416842			0.208421	−	0.978039i	$-0.433168\pi$
$421$	8.55288			0.416842			0.208421	+	0.978039i	$0.433168\pi$
$422$		0			0
$423$	12.4266	−	7.17452i	0.604203	−	0.348837i
$424$		0			0
$425$	13.4963	+	7.79209i	0.654667	+	0.377972i
$426$		0			0
$427$	−1.16543	+	18.7481i	−0.0563990	+	0.907284i
$428$		0			0
$429$	−3.68777	+	3.32460i	−0.178047	+	0.160513i
$430$		0			0
$431$	9.50279	+	16.4593i	0.457733	+	0.792817i	0.998841	−	0.0481363i	$-0.0153282\pi$
$431$	9.50279	+	16.4593i	0.457733	+	0.792817i	−0.541108	+	0.840953i	$0.681995\pi$
$432$		0			0
$433$	1.87501			0.0901070			0.0450535	−	0.998985i	$-0.485654\pi$
$433$	1.87501			0.0901070			0.0450535	+	0.998985i	$0.485654\pi$
$434$		0			0
$435$	−0.269358			−0.0129147
$436$		0			0
$437$	23.2349	−	13.4147i	1.11147	−	0.641710i
$438$		0			0
$439$	4.18025	−	7.24040i	0.199512	−	0.345565i	−0.748858	−	0.662730i	$-0.769398\pi$
$439$	4.18025	−	7.24040i	0.199512	−	0.345565i	0.948370	+	0.317165i	$0.102731\pi$
$440$		0			0
$441$	−7.26948	−	17.2211i	−0.346166	−	0.820054i
$442$		0			0
$443$	10.0958	+	5.82881i	0.479666	+	0.276935i	0.720277	−	0.693686i	$-0.244015\pi$
$443$	10.0958	+	5.82881i	0.479666	+	0.276935i	−0.240611	+	0.970622i	$0.577348\pi$
$444$		0			0
$445$	1.22009	+	2.11326i	0.0578380	+	0.100178i
$446$		0			0
$447$	12.5977			0.595851
$448$		0			0
$449$	−28.6168			−1.35051			−0.675255	−	0.737584i	$-0.735966\pi$
$449$	−28.6168			−1.35051			−0.675255	+	0.737584i	$0.735966\pi$
$450$		0			0
$451$	−31.3382	+	6.68135i	−1.47566	+	0.314613i
$452$		0			0
$453$	−6.91576	−	3.99281i	−0.324931	−	0.187599i
$454$		0			0
$455$	−0.0797581	+	1.28306i	−0.00373912	+	0.0601508i
$456$		0			0
$457$	−36.7574	−	21.2219i	−1.71944	−	0.992720i	−0.919944	−	0.392049i	$-0.871766\pi$
$457$	−36.7574	−	21.2219i	−1.71944	−	0.992720i	−0.799497	−	0.600671i	$-0.794900\pi$
$458$		0			0
$459$	−5.10901	−	8.84906i	−0.238468	−	0.413039i
$460$		0			0
$461$			8.85226i			0.412291i	0.978521	+	0.206145i	$0.0660920\pi$
$461$			8.85226i			0.412291i	−0.978521	+	0.206145i	$0.933908\pi$
$462$		0			0
$463$			23.6360i			1.09846i	0.835672	+	0.549229i	$0.185079\pi$
$463$			23.6360i			1.09846i	−0.835672	+	0.549229i	$0.814921\pi$
$464$		0			0
$465$	−0.456556	−	0.790778i	−0.0211723	−	0.0366714i
$466$		0			0
$467$	−22.0163	−	12.7111i	−1.01879	−	0.588201i	−0.105040	−	0.994468i	$-0.533497\pi$
$467$	−22.0163	−	12.7111i	−1.01879	−	0.588201i	−0.913754	+	0.406267i	$0.866830\pi$
$468$		0			0
$469$	25.7703	+	17.0939i	1.18996	+	0.789324i
$470$		0			0
$471$	3.82843	+	2.21035i	0.176405	+	0.101847i
$472$		0			0
$473$	1.43082	+	6.71110i	0.0657890	+	0.308577i
$474$		0			0
$475$	−18.8999			−0.867186
$476$		0			0
$477$	−18.5416			−0.848961
$478$		0			0
$479$	−10.5313	−	18.2407i	−0.481186	−	0.833439i	0.518581	−	0.855029i	$-0.326460\pi$
$479$	−10.5313	−	18.2407i	−0.481186	−	0.833439i	−0.999767	+	0.0215900i	$0.993127\pi$
$480$		0			0
$481$	5.32954	+	3.07701i	0.243006	+	0.140300i
$482$		0			0
$483$	−4.76778	−	9.58658i	−0.216941	−	0.436204i
$484$		0			0
$485$	−0.796012	+	1.37873i	−0.0361450	+	0.0626050i
$486$		0			0
$487$	−9.87295	+	5.70015i	−0.447386	+	0.258298i	−0.706726	−	0.707488i	$-0.749828\pi$
$487$	−9.87295	+	5.70015i	−0.447386	+	0.258298i	0.259340	+	0.965786i	$0.416495\pi$
$488$		0			0
$489$	−3.37257			−0.152513
$490$		0			0
$491$	19.6069			0.884846			0.442423	−	0.896807i	$-0.354119\pi$
$491$	19.6069			0.884846			0.442423	+	0.896807i	$0.354119\pi$
$492$		0			0
$493$	3.95104	+	6.84340i	0.177946	+	0.308211i
$494$		0			0
$495$	−1.22579	+	1.10507i	−0.0550950	+	0.0496693i
$496$		0			0
$497$	12.3223	−	6.12835i	0.552730	−	0.274894i
$498$		0			0
$499$	−32.5338	−	18.7834i	−1.45641	−	0.840860i	−0.457580	−	0.889168i	$-0.651284\pi$
$499$	−32.5338	−	18.7834i	−1.45641	−	0.840860i	−0.998832	+	0.0483081i	$0.984617\pi$
$500$		0			0
$501$	−0.545642	+	0.315027i	−0.0243775	+	0.0140744i
$502$		0			0
$503$	25.8868			1.15423			0.577117	−	0.816661i	$-0.304178\pi$
$503$	25.8868			1.15423			0.577117	+	0.816661i	$0.304178\pi$
$504$		0			0
$505$		−	2.70277i		−	0.120272i
$506$		0			0
$507$	−3.08327	+	1.78013i	−0.136933	+	0.0790582i
$508$		0			0
$509$	−15.4883	+	26.8265i	−0.686505	+	1.18906i	0.286456	+	0.958093i	$0.407523\pi$
$509$	−15.4883	+	26.8265i	−0.686505	+	1.18906i	−0.972961	+	0.230968i	$0.925811\pi$
$510$		0			0
$511$	−21.5241	−	14.2773i	−0.952168	−	0.631591i
$512$		0			0
$513$	10.7318	+	6.19600i	0.473820	+	0.273560i
$514$		0			0
$515$	0.588789	−	0.339937i	0.0259451	−	0.0149794i
$516$		0			0
$517$	5.49673	−	16.9528i	0.241746	−	0.745583i
$518$		0			0
$519$	−5.82038			−0.255486
$520$		0			0
$521$	1.34695	+	2.33299i	0.0590111	+	0.102210i	0.894022	−	0.448024i	$-0.147872\pi$
$521$	1.34695	+	2.33299i	0.0590111	+	0.102210i	−0.835011	+	0.550234i	$0.814539\pi$
$522$		0			0
$523$	−16.7489	+	29.0100i	−0.732380	+	1.26852i	0.223483	+	0.974708i	$0.428257\pi$
$523$	−16.7489	+	29.0100i	−0.732380	+	1.26852i	−0.955863	+	0.293812i	$0.905076\pi$
$524$		0			0
$525$	−0.467948	+	7.52782i	−0.0204229	+	0.328541i
$526$		0			0
$527$	−13.3938	+	23.1988i	−0.583444	+	1.01056i
$528$		0			0
$529$	13.3403	+	23.1061i	0.580013	+	1.00461i
$530$		0			0
$531$			1.80844i			0.0784795i
$532$		0			0
$533$	25.1913			1.09116
$534$		0			0
$535$	−1.07912	−	1.86909i	−0.0466544	−	0.0808078i
$536$		0			0
$537$	−5.49572	+	9.51886i	−0.237158	+	0.410769i
$538$		0			0
$539$	−21.0277	−	9.84058i	−0.905726	−	0.423864i
$540$		0			0
$541$	−23.9581	−	13.8322i	−1.03004	−	0.594694i	−0.113044	−	0.993590i	$-0.536060\pi$
$541$	−23.9581	−	13.8322i	−1.03004	−	0.594694i	−0.916996	+	0.398896i	$0.869393\pi$
$542$		0			0
$543$	−12.7698	+	7.37262i	−0.548003	+	0.316390i
$544$		0			0
$545$			1.48266i			0.0635103i
$546$		0			0
$547$	25.1532			1.07547			0.537736	−	0.843113i	$-0.319280\pi$
$547$	25.1532			1.07547			0.537736	+	0.843113i	$0.319280\pi$
$548$		0			0
$549$	16.4190	−	9.47953i	0.700747	−	0.404577i
$550$		0			0
$551$	−8.29941	−	4.79167i	−0.353567	−	0.204132i
$552$		0			0
$553$	30.8225	+	1.91600i	1.31071	+	0.0814768i
$554$		0			0
$555$	−0.218675	−	0.126252i	−0.00928223	−	0.00535910i
$556$		0			0
$557$	−9.78963	+	5.65204i	−0.414800	+	0.239485i	−0.692850	−	0.721082i	$-0.743645\pi$
$557$	−9.78963	+	5.65204i	−0.414800	+	0.239485i	0.278050	+	0.960567i	$0.410312\pi$
$558$		0			0
$559$		−	5.39474i		−	0.228173i
$560$		0			0
$561$	−5.68519	−	1.84335i	−0.240029	−	0.0778263i
$562$		0			0
$563$	−19.9103	−	34.4856i	−0.839118	−	1.45339i	−0.890633	−	0.454723i	$-0.849738\pi$
$563$	−19.9103	−	34.4856i	−0.839118	−	1.45339i	0.0515152	−	0.998672i	$-0.483595\pi$
$564$		0			0
$565$	−0.822404	+	1.42445i	−0.0345988	+	0.0599269i
$566$		0			0
$567$	−8.98254	+	13.5418i	−0.377231	+	0.568703i
$568$		0			0
$569$	29.7686	+	17.1869i	1.24797	+	0.720513i	0.970703	−	0.240281i	$-0.0772397\pi$
$569$	29.7686	+	17.1869i	1.24797	+	0.720513i	0.277262	+	0.960794i	$0.410573\pi$
$570$		0			0
$571$	12.4196	+	21.5114i	0.519745	+	0.900225i	0.999737	+	0.0229521i	$0.00730652\pi$
$571$	12.4196	+	21.5114i	0.519745	+	0.900225i	−0.479991	+	0.877273i	$0.659360\pi$
$572$		0			0
$573$	−7.67323			−0.320554
$574$		0			0
$575$		−	34.9975i		−	1.45950i
$576$		0			0
$577$	5.10104	+	8.83525i	0.212359	+	0.367816i	0.952452	−	0.304688i	$-0.0985521\pi$
$577$	5.10104	+	8.83525i	0.212359	+	0.367816i	−0.740093	+	0.672504i	$0.765219\pi$
$578$		0			0
$579$	1.30087	−	2.25318i	0.0540625	−	0.0936390i
$580$		0			0
$581$	0.532779	+	1.07126i	0.0221034	+	0.0444434i
$582$		0			0
$583$	−17.1042	+	15.4199i	−0.708385	+	0.638625i
$584$		0			0
$585$	1.12367	−	0.648749i	0.0464579	−	0.0268225i
$586$		0			0
$587$			14.6889i			0.606278i	0.952946	+	0.303139i	$0.0980346\pi$
$587$			14.6889i			0.606278i	−0.952946	+	0.303139i	$0.901965\pi$
$588$		0			0
$589$		−	32.4870i		−	1.33860i
$590$		0			0
$591$	3.34723	+	5.79758i	0.137687	+	0.238480i
$592$		0			0
$593$	−3.72534	−	2.15083i	−0.152981	−	0.0883238i	0.421555	−	0.906803i	$-0.361484\pi$
$593$	−3.72534	−	2.15083i	−0.152981	−	0.0883238i	−0.574537	+	0.818479i	$0.694818\pi$
$594$		0			0
$595$	−1.38552	+	0.689070i	−0.0568006	+	0.0282491i
$596$		0			0
$597$	−0.405376	+	0.702131i	−0.0165909	+	0.0287363i
$598$		0			0
$599$	−11.4541	+	6.61300i	−0.468000	+	0.270200i	−0.715402	−	0.698713i	$-0.753756\pi$
$599$	−11.4541	+	6.61300i	−0.468000	+	0.270200i	0.247402	+	0.968913i	$0.420423\pi$
$600$		0			0
$601$			16.5070i			0.673335i	0.941624	+	0.336667i	$0.109300\pi$
$601$			16.5070i			0.673335i	−0.941624	+	0.336667i	$0.890700\pi$
$602$		0			0
$603$		−	31.2120i		−	1.27105i
$604$		0			0
$605$	−0.211744	+	2.03882i	−0.00860863	+	0.0828897i
$606$		0			0
$607$	−1.90155	+	3.29359i	−0.0771816	+	0.133683i	−0.902033	−	0.431667i	$-0.857925\pi$
$607$	−1.90155	+	3.29359i	−0.0771816	+	0.133683i	0.824851	+	0.565350i	$0.191259\pi$
$608$		0			0
$609$	−2.11401	+	3.18702i	−0.0856639	+	0.129144i
$610$		0			0
$611$	−7.00554	+	12.1340i	−0.283414	+	0.490887i
$612$		0			0
$613$	−7.33108	+	4.23260i	−0.296100	+	0.170953i	−0.640689	−	0.767800i	$-0.721351\pi$
$613$	−7.33108	+	4.23260i	−0.296100	+	0.170953i	0.344590	+	0.938753i	$0.388018\pi$
$614$		0			0
$615$	−1.03362			−0.0416795
$616$		0			0
$617$	23.0627			0.928470			0.464235	−	0.885712i	$-0.346329\pi$
$617$	23.0627			0.928470			0.464235	+	0.885712i	$0.346329\pi$
$618$		0			0
$619$	−30.7653	+	17.7623i	−1.23656	+	0.713928i	−0.968389	−	0.249443i	$-0.919752\pi$
$619$	−30.7653	+	17.7623i	−1.23656	+	0.713928i	−0.268171	+	0.963371i	$0.586419\pi$
$620$		0			0
$621$	−11.4733	+	19.8724i	−0.460409	+	0.797451i
$622$		0			0
$623$	34.5796	+	2.14955i	1.38540	+	0.0861199i
$624$		0			0
$625$	−12.2402	+	21.2006i	−0.489607	+	0.848024i
$626$		0			0
$627$	7.08882	−	1.51135i	0.283100	−	0.0603575i
$628$		0			0
$629$			7.40762i			0.295361i
$630$		0			0
$631$			11.8052i			0.469959i	0.972000	+	0.234980i	$0.0755024\pi$
$631$			11.8052i			0.469959i	−0.972000	+	0.234980i	$0.924498\pi$
$632$		0			0
$633$	−0.00291569	+	0.00168337i	−0.000115888	+	6.69080e-5i
$634$		0			0
$635$	−1.26795	+	2.19615i	−0.0503170	+	0.0871516i
$636$		0			0
$637$	14.5551	+	11.0135i	0.576692	+	0.436373i
$638$		0			0
$639$	−12.0292	−	6.94507i	−0.475869	−	0.274743i
$640$		0			0
$641$	−24.1410	−	41.8135i	−0.953514	−	1.65153i	−0.737734	−	0.675092i	$-0.764104\pi$
$641$	−24.1410	−	41.8135i	−0.953514	−	1.65153i	−0.215780	−	0.976442i	$-0.569229\pi$
$642$		0			0
$643$			46.8888i			1.84911i	0.381046	+	0.924556i	$0.375564\pi$
$643$			46.8888i			1.84911i	−0.381046	+	0.924556i	$0.624436\pi$
$644$		0			0
$645$			0.221350i			0.00871565i
$646$		0			0
$647$	−27.1526	+	15.6766i	−1.06748	+	0.616310i	−0.927492	−	0.373843i	$-0.878040\pi$
$647$	−27.1526	+	15.6766i	−1.06748	+	0.616310i	−0.139988	+	0.990153i	$0.544707\pi$
$648$		0			0
$649$	1.50396	+	1.66825i	0.0590357	+	0.0654844i
$650$		0			0
$651$	−12.9396	−	0.804356i	−0.507142	−	0.0315252i
$652$		0			0
$653$	−10.6910	+	18.5174i	−0.418371	+	0.724640i	−0.995776	−	0.0918181i	$-0.970732\pi$
$653$	−10.6910	+	18.5174i	−0.418371	+	0.724640i	0.577405	+	0.816458i	$0.304065\pi$
$654$		0			0
$655$	0.465597	+	0.806438i	0.0181924	+	0.0315101i
$656$		0			0
$657$			26.0691i			1.01705i
$658$		0			0
$659$	26.9096			1.04825			0.524125	−	0.851642i	$-0.324393\pi$
$659$	26.9096			1.04825			0.524125	+	0.851642i	$0.324393\pi$
$660$		0			0
$661$	13.4338	+	23.2681i	0.522515	+	0.905023i	0.999657	+	0.0261966i	$0.00833960\pi$
$661$	13.4338	+	23.2681i	0.522515	+	0.905023i	−0.477141	+	0.878826i	$0.658327\pi$
$662$		0			0
$663$	4.06917	+	2.34934i	0.158034	+	0.0912407i
$664$		0			0
$665$	1.03734	−	1.56387i	0.0402264	−	0.0606442i
$666$		0			0
$667$	8.87287	−	15.3683i	0.343559	−	0.595061i
$668$		0			0
$669$	−6.22142	−	10.7758i	−0.240534	−	0.416617i
$670$		0			0
$671$	7.26271	−	22.3994i	0.280374	−	0.864717i
$672$		0			0
$673$		−	38.4307i		−	1.48140i	−0.671838	−	0.740698i	$-0.734495\pi$
$673$		−	38.4307i		−	1.48140i	0.671838	−	0.740698i	$-0.265505\pi$
$674$		0			0
$675$	13.9991	−	8.08238i	0.538825	−	0.311091i
$676$		0			0
$677$	−9.57488	−	5.52806i	−0.367992	−	0.212461i	0.304589	−	0.952484i	$-0.401481\pi$
$677$	−9.57488	−	5.52806i	−0.367992	−	0.212461i	−0.672581	+	0.740023i	$0.734814\pi$
$678$		0			0
$679$	10.0657	+	20.2390i	0.386284	+	0.776703i
$680$		0			0
$681$	7.84946	+	4.53189i	0.300792	+	0.173662i
$682$		0			0
$683$	−12.2473	+	7.07100i	−0.468631	+	0.270564i	−0.715666	−	0.698442i	$-0.753877\pi$
$683$	−12.2473	+	7.07100i	−0.468631	+	0.270564i	0.247035	+	0.969006i	$0.420544\pi$
$684$		0			0
$685$	−0.977844			−0.0373615
$686$		0			0
$687$			11.5921i			0.442266i
$688$		0			0
$689$	15.6793	−	9.05245i	0.597334	−	0.344871i
$690$		0			0
$691$	3.93592	+	2.27241i	0.149729	+	0.0864464i	0.572993	−	0.819560i	$-0.305782\pi$
$691$	3.93592	+	2.27241i	0.149729	+	0.0864464i	−0.423264	+	0.906007i	$0.639116\pi$
$692$		0			0
$693$	3.45475	+	23.1763i	0.131235	+	0.880395i
$694$		0			0
$695$	1.65854	−	2.87268i	0.0629121	−	0.108967i
$696$		0			0
$697$	15.1614	+	26.2604i	0.574281	+	0.994683i
$698$		0			0
$699$	13.6374			0.515814
$700$		0			0
$701$			30.5692i			1.15458i	0.816538	+	0.577292i	$0.195890\pi$
$701$			30.5692i			1.15458i	−0.816538	+	0.577292i	$0.804110\pi$
$702$		0			0
$703$	−4.49184	−	7.78009i	−0.169413	−	0.293432i
$704$		0			0
$705$	0.287443	−	0.497865i	0.0108257	−	0.0187507i
$706$		0			0
$707$	−31.9789	−	21.2122i	−1.20269	−	0.797767i
$708$		0			0
$709$	1.93918	−	3.35875i	0.0728273	−	0.126141i	−0.827312	−	0.561743i	$-0.810131\pi$
$709$	1.93918	−	3.35875i	0.0728273	−	0.126141i	0.900139	+	0.435602i	$0.143464\pi$
$710$		0			0
$711$	−15.5847	−	26.9935i	−0.584472	−	1.01233i
$712$		0			0
$713$	60.1572			2.25290
$714$		0			0
$715$	0.497037	−	1.53294i	0.0185881	−	0.0573287i
$716$		0			0
$717$	3.86938	−	2.23399i	0.144505	−	0.0834297i
$718$		0			0
$719$	−25.5379	−	14.7443i	−0.952403	−	0.549870i	−0.0585762	−	0.998283i	$-0.518656\pi$
$719$	−25.5379	−	14.7443i	−0.952403	−	0.549870i	−0.893826	+	0.448413i	$0.851989\pi$
$720$		0			0
$721$	0.598898	−	9.63441i	0.0223041	−	0.358804i
$722$		0			0
$723$	−4.47030	+	7.74279i	−0.166252	+	0.287958i
$724$		0			0
$725$	−10.8262	+	6.25049i	−0.402074	+	0.232137i
$726$		0			0
$727$			18.3277i			0.679736i	0.940473	+	0.339868i	$0.110382\pi$
$727$			18.3277i			0.679736i	−0.940473	+	0.339868i	$0.889618\pi$
$728$		0			0
$729$	10.7939			0.399775
$730$		0			0
$731$	5.62369	−	3.24684i	0.208000	−	0.120089i
$732$		0			0
$733$	29.3935	+	16.9703i	1.08567	+	0.626814i	0.932421	−	0.361373i	$-0.117692\pi$
$733$	29.3935	+	16.9703i	1.08567	+	0.626814i	0.153252	+	0.988187i	$0.451025\pi$
$734$		0			0
$735$	−0.597204	−	0.451894i	−0.0220282	−	0.0166684i
$736$		0			0
$737$	−25.9570	−	28.7924i	−0.956140	−	1.06058i
$738$		0			0
$739$	−3.10016	−	5.36963i	−0.114041	−	0.197525i	0.803355	−	0.595501i	$-0.203046\pi$
$739$	−3.10016	−	5.36963i	−0.114041	−	0.197525i	−0.917396	+	0.397976i	$0.869713\pi$
$740$		0			0
$741$	−5.69837			−0.209335
$742$		0			0
$743$	−45.7175			−1.67721			−0.838607	−	0.544737i	$-0.816629\pi$
$743$	−45.7175			−1.67721			−0.838607	+	0.544737i	$0.816629\pi$
$744$		0			0
$745$	−3.54098	+	2.04438i	−0.129731	+	0.0749004i
$746$		0			0
$747$	0.603782	−	1.04578i	0.0220912	−	0.0382632i
$748$		0			0
$749$	−30.5841	−	1.90118i	−1.11752	−	0.0694677i
$750$		0			0
$751$	8.51990	+	4.91897i	0.310896	+	0.179496i	0.647327	−	0.762212i	$-0.275887\pi$
$751$	8.51990	+	4.91897i	0.310896	+	0.179496i	−0.336432	+	0.941708i	$0.609220\pi$
$752$		0			0
$753$	−0.225733	−	0.390981i	−0.00822617	−	0.0142481i
$754$		0			0
$755$	2.59185			0.0943271
$756$		0			0
$757$	−19.3219			−0.702265			−0.351133	−	0.936326i	$-0.614203\pi$
$757$	−19.3219			−0.702265			−0.351133	+	0.936326i	$0.614203\pi$
$758$		0			0
$759$	2.79861	+	13.1266i	0.101583	+	0.476465i
$760$		0			0
$761$	−29.5911	−	17.0844i	−1.07267	−	0.619309i	−0.143764	−	0.989612i	$-0.545921\pi$
$761$	−29.5911	−	17.0844i	−1.07267	−	0.619309i	−0.928911	+	0.370303i	$0.879254\pi$
$762$		0			0
$763$	17.5427	+	11.6364i	0.635088	+	0.421266i
$764$		0			0
$765$	1.35256	+	0.780903i	0.0489020	+	0.0282336i
$766$		0			0
$767$	−0.882923	−	1.52927i	−0.0318805	−	0.0552186i
$768$		0			0
$769$			0.367144i			0.0132395i	0.999978	+	0.00661977i	$0.00210715\pi$
$769$			0.367144i			0.0132395i	−0.999978	+	0.00661977i	$0.997893\pi$
$770$		0			0
$771$			1.20546i			0.0434135i
$772$		0			0
$773$	9.33216	+	16.1638i	0.335655	+	0.581371i	0.983610	−	0.180307i	$-0.0577092\pi$
$773$	9.33216	+	16.1638i	0.335655	+	0.581371i	−0.647956	+	0.761678i	$0.724376\pi$
$774$		0			0
$775$	−36.7002	−	21.1889i	−1.31831	−	0.761126i
$776$		0			0
$777$	−3.21003	+	1.59647i	−0.115159	+	0.0572730i
$778$		0			0
$779$	−31.8476	−	18.3872i	−1.14106	−	0.658790i
$780$		0			0
$781$	−16.8725	+	3.59725i	−0.603745	+	0.128720i
$782$		0			0
$783$	8.19646			0.292918
$784$		0			0
$785$	−1.43480			−0.0512102
$786$		0			0
$787$	10.1248	+	17.5367i	0.360911	+	0.625117i	0.988111	−	0.153742i	$-0.0491324\pi$
$787$	10.1248	+	17.5367i	0.360911	+	0.625117i	−0.627200	+	0.778858i	$0.715799\pi$
$788$		0			0
$789$	11.2321	+	6.48486i	0.399873	+	0.230867i
$790$		0			0
$791$	10.3994	+	20.9101i	0.369760	+	0.743477i
$792$		0			0
$793$	−9.25627	+	16.0323i	−0.328700	+	0.569325i
$794$		0			0
$795$	−0.643333	+	0.371429i	−0.0228167	+	0.0131732i
$796$		0			0
$797$	−35.5650			−1.25978			−0.629889	−	0.776685i	$-0.716900\pi$
$797$	−35.5650			−1.25978			−0.629889	+	0.776685i	$0.716900\pi$
$798$		0			0
$799$	−16.8652			−0.596649
$800$		0			0
$801$	−17.4843	−	30.2838i	−0.617779	−	1.07002i
$802$		0			0
$803$	21.6800	+	24.0483i	0.765072	+	0.848644i
$804$		0			0
$805$	2.89586	+	1.92088i	0.102066	+	0.0677021i
$806$		0			0
$807$	10.5436	+	6.08734i	0.371151	+	0.214284i
$808$		0			0
$809$	26.8927	−	15.5265i	0.945495	−	0.545882i	0.0538167	−	0.998551i	$-0.482861\pi$
$809$	26.8927	−	15.5265i	0.945495	−	0.545882i	0.891679	+	0.452669i	$0.149528\pi$
$810$		0			0
$811$	−6.44773			−0.226410			−0.113205	−	0.993572i	$-0.536112\pi$
$811$	−6.44773			−0.226410			−0.113205	+	0.993572i	$0.536112\pi$
$812$		0			0
$813$			14.4484i			0.506727i
$814$		0			0
$815$	0.947964	−	0.547307i	0.0332057	−	0.0191713i
$816$		0			0
$817$	−3.93764	+	6.82019i	−0.137760	+	0.238608i
$818$		0			0
$819$	1.14296	−	18.3867i	0.0399383	−	0.642482i
$820$		0			0
$821$	31.0684	+	17.9373i	1.08429	+	0.626017i	0.932052	−	0.362326i	$-0.118017\pi$
$821$	31.0684	+	17.9373i	1.08429	+	0.626017i	0.152243	+	0.988343i	$0.451351\pi$
$822$		0			0
$823$	0.691903	−	0.399471i	0.0241182	−	0.0139247i	−0.487892	−	0.872904i	$-0.662234\pi$
$823$	0.691903	−	0.399471i	0.0241182	−	0.0139247i	0.512011	+	0.858979i	$0.328901\pi$
$824$		0			0
$825$	2.91616	−	8.99389i	0.101528	−	0.313127i
$826$		0			0
$827$	−20.9504			−0.728516			−0.364258	−	0.931298i	$-0.618677\pi$
$827$	−20.9504			−0.728516			−0.364258	+	0.931298i	$0.618677\pi$
$828$		0			0
$829$	−17.5190	−	30.3438i	−0.608459	−	1.05388i	−0.991494	−	0.130149i	$-0.958455\pi$
$829$	−17.5190	−	30.3438i	−0.608459	−	1.05388i	0.383035	−	0.923734i	$-0.374879\pi$
$830$		0			0
$831$	2.66891	−	4.62269i	0.0925836	−	0.160359i
$832$		0			0
$833$	−2.72096	+	21.8013i	−0.0942756	+	0.755370i
$834$		0			0
$835$	0.102246	−	0.177096i	0.00353838	−	0.00612866i
$836$		0			0
$837$	13.8928	+	24.0630i	0.480206	+	0.831740i
$838$		0			0
$839$		−	4.29711i		−	0.148353i	−0.997245	−	0.0741763i	$-0.976367\pi$
$839$		−	4.29711i		−	0.148353i	0.997245	−	0.0741763i	$-0.0236328\pi$
$840$		0			0
$841$	22.6613			0.781424
$842$		0			0
$843$	6.38931	+	11.0666i	0.220059	+	0.381154i
$844$		0			0
$845$	0.577765	−	1.00072i	0.0198757	−	0.0344258i
$846$		0			0
$847$	22.4612	+	18.5066i	0.771776	+	0.635894i
$848$		0			0
$849$	6.93377	+	4.00322i	0.237966	+	0.137390i
$850$		0			0
$851$	14.4066	−	8.31767i	0.493853	−	0.285126i
$852$		0			0
$853$		−	43.8425i		−	1.50114i	−0.660793	−	0.750569i	$-0.729780\pi$
$853$		−	43.8425i		−	1.50114i	0.660793	−	0.750569i	$-0.270220\pi$
$854$		0			0
$855$	−1.89410			−0.0647767
$856$		0			0
$857$	−15.9796	+	9.22581i	−0.545852	+	0.315148i	−0.747447	−	0.664321i	$-0.768721\pi$
$857$	−15.9796	+	9.22581i	−0.545852	+	0.315148i	0.201595	+	0.979469i	$0.435387\pi$
$858$		0			0
$859$	−43.1062	−	24.8874i	−1.47077	−	0.849147i	−0.471305	−	0.881970i	$-0.656217\pi$
$859$	−43.1062	−	24.8874i	−1.47077	−	0.849147i	−0.999461	+	0.0328232i	$0.989550\pi$
$860$		0			0
$861$	−8.11215	+	12.2296i	−0.276461	+	0.416785i
$862$		0			0
$863$	22.9567	+	13.2541i	0.781456	+	0.451174i	0.836946	−	0.547285i	$-0.184339\pi$
$863$	22.9567	+	13.2541i	0.781456	+	0.451174i	−0.0554901	+	0.998459i	$0.517672\pi$
$864$		0			0
$865$	1.63600	−	0.944544i	0.0556256	−	0.0321155i
$866$		0			0
$867$		−	4.10448i		−	0.139396i
$868$		0			0
$869$	−36.8253	−	11.9402i	−1.24921	−	0.405042i
$870$		0			0
$871$	15.2384	+	26.3938i	0.516335	+	0.894319i
$872$		0			0
$873$	11.4071	−	19.7577i	0.386072	−	0.668696i
$874$		0			0
$875$	−2.18782	−	4.39906i	−0.0739619	−	0.148715i
$876$		0			0
$877$	−21.0080	−	12.1289i	−0.709388	−	0.409565i	0.101446	−	0.994841i	$-0.467653\pi$
$877$	−21.0080	−	12.1289i	−0.709388	−	0.409565i	−0.810834	+	0.585276i	$0.800986\pi$
$878$		0			0
$879$	−9.43971	−	16.3501i	−0.318394	−	0.551474i
$880$		0			0
$881$	−2.09655			−0.0706345			−0.0353172	−	0.999376i	$-0.511244\pi$
$881$	−2.09655			−0.0706345			−0.0353172	+	0.999376i	$0.511244\pi$
$882$		0			0
$883$			18.9937i			0.639189i	0.947554	+	0.319595i	$0.103547\pi$
$883$			18.9937i			0.639189i	−0.947554	+	0.319595i	$0.896453\pi$
$884$		0			0
$885$	0.0362270	+	0.0627469i	0.00121776	+	0.00210922i
$886$		0			0
$887$	0.530422	−	0.918719i	0.0178098	−	0.0308476i	−0.856983	−	0.515344i	$-0.827664\pi$
$887$	0.530422	−	0.918719i	0.0178098	−	0.0308476i	0.874793	+	0.484497i	$0.160997\pi$
$888$		0			0
$889$	16.0334	+	32.2383i	0.537741	+	1.08124i
$890$		0			0
$891$	15.1299	−	13.6399i	0.506871	−	0.456955i
$892$		0			0
$893$	17.7132	−	10.2267i	0.592751	−	0.342225i
$894$		0			0
$895$		−	3.56743i		−	0.119246i
$896$		0			0
$897$		−	10.5518i		−	0.352316i
$898$		0			0
$899$	−10.7440	−	18.6091i	−0.358331	−	0.620648i
$900$		0			0
$901$	18.8733	+	10.8965i	0.628759	+	0.363014i
$902$		0			0
$903$	2.61899	+	1.73722i	0.0871544	+	0.0578112i
$904$		0			0
$905$	2.39289	−	4.14461i	0.0795423	−	0.137771i
$906$		0			0
$907$	16.3493	−	9.43928i	0.542870	−	0.313426i	−0.203371	−	0.979102i	$-0.565190\pi$
$907$	16.3493	−	9.43928i	0.542870	−	0.313426i	0.746241	+	0.665676i	$0.231857\pi$
$908$		0			0
$909$			38.7316i			1.28465i
$910$		0			0
$911$			10.1699i			0.336945i	0.985706	+	0.168473i	$0.0538835\pi$
$911$			10.1699i			0.336945i	−0.985706	+	0.168473i	$0.946117\pi$
$912$		0			0
$913$	−0.312733	−	1.46684i	−0.0103500	−	0.0485453i
$914$		0			0
$915$	0.379792	−	0.657819i	0.0125555	−	0.0217468i
$916$		0			0
$917$	13.1958	+	0.820285i	0.435765	+	0.0270882i
$918$		0			0
$919$	−10.1303	+	17.5461i	−0.334167	+	0.578794i	−0.983324	−	0.181860i	$-0.941788\pi$
$919$	−10.1303	+	17.5461i	−0.334167	+	0.578794i	0.649158	+	0.760654i	$0.275122\pi$
$920$		0			0
$921$	−9.33278	+	5.38828i	−0.307525	+	0.177550i
$922$		0			0
$923$	13.5630			0.446432
$924$		0			0
$925$	−11.7188			−0.385310
$926$		0			0
$927$	−8.43753	+	4.87141i	−0.277125	+	0.159998i
$928$		0			0
$929$	13.9000	−	24.0755i	0.456043	−	0.789890i	−0.542704	−	0.839924i	$-0.682600\pi$
$929$	13.9000	−	24.0755i	0.456043	−	0.789890i	0.998748	+	0.0500338i	$0.0159329\pi$
$930$		0			0
$931$	−10.3621	−	24.5474i	−0.339604	−	0.804510i
$932$		0			0
$933$	−4.38232	+	7.59040i	−0.143471	+	0.248499i
$934$		0			0
$935$	1.89714	−	0.404474i	0.0620431	−	0.0132277i
$936$		0			0
$937$		−	40.6166i		−	1.32689i	−0.748226	−	0.663444i	$-0.769094\pi$
$937$		−	40.6166i		−	1.32689i	0.748226	−	0.663444i	$-0.230906\pi$
$938$		0			0
$939$		−	10.4600i		−	0.341349i
$940$		0			0
$941$	7.43741	−	4.29399i	0.242453	−	0.139980i	−0.373851	−	0.927489i	$-0.621963\pi$
$941$	7.43741	−	4.29399i	0.242453	−	0.139980i	0.616304	+	0.787509i	$0.288629\pi$
$942$		0			0
$943$	34.0481	−	58.9731i	1.10876	−	1.92043i
$944$		0			0
$945$	−0.0995819	+	1.60196i	−0.00323940	+	0.0521119i
$946$		0			0
$947$	27.1655	+	15.6840i	0.882759	+	0.509661i	0.871567	−	0.490276i	$-0.163104\pi$
$947$	27.1655	+	15.6840i	0.882759	+	0.509661i	0.0111919	+	0.999937i	$0.496437\pi$
$948$		0			0
$949$	−12.7276	−	22.0448i	−0.413155	−	0.715605i
$950$		0			0
$951$			5.16052i			0.167341i
$952$		0			0
$953$		−	3.87560i		−	0.125543i	−0.998028	−	0.0627715i	$-0.980006\pi$
$953$		−	3.87560i		−	0.125543i	0.998028	−	0.0627715i	$-0.0199939\pi$
$954$		0			0
$955$	2.15680	−	1.24523i	0.0697923	−	0.0402946i
$956$		0			0
$957$	3.56077	−	3.21011i	0.115103	−	0.103768i
$958$		0			0
$959$	−7.67442	+	11.5697i	−0.247820	+	0.373606i
$960$		0			0
$961$	20.9215	−	36.2372i	0.674888	−	1.16894i
$962$		0			0
$963$	15.4641	+	26.7847i	0.498325	+	0.863124i
$964$		0			0
$965$			0.844434i			0.0271833i
$966$		0			0
$967$	−16.3554			−0.525954			−0.262977	−	0.964802i	$-0.584704\pi$
$967$	−16.3554			−0.525954			−0.262977	+	0.964802i	$0.584704\pi$
$968$		0			0
$969$	−3.42958	−	5.94021i	−0.110174	−	0.190827i
$970$		0			0
$971$	40.4299	+	23.3422i	1.29746	+	0.749087i	0.979964	−	0.199174i	$-0.0638260\pi$
$971$	40.4299	+	23.3422i	1.29746	+	0.749087i	0.317492	+	0.948261i	$0.397159\pi$
$972$		0			0
$973$	−20.9725	−	42.1694i	−0.672346	−	1.35189i
$974$		0			0
$975$	−3.71662	+	6.43738i	−0.119027	+	0.206161i
$976$		0			0
$977$	−3.19939	−	5.54151i	−0.102358	−	0.177288i	0.810298	−	0.586018i	$-0.199305\pi$
$977$	−3.19939	−	5.54151i	−0.102358	−	0.177288i	−0.912656	+	0.408730i	$0.865972\pi$
$978$		0			0
$979$	−41.3140	−	13.3956i	−1.32040	−	0.428124i
$980$		0			0
$981$		−	21.2470i		−	0.678366i
$982$		0			0
$983$	20.1910	−	11.6573i	0.643994	−	0.371810i	−0.142157	−	0.989844i	$-0.545404\pi$
$983$	20.1910	−	11.6573i	0.643994	−	0.371810i	0.786152	+	0.618034i	$0.212071\pi$
$984$		0			0
$985$	−1.88169	−	1.08639i	−0.0599555	−	0.0346153i
$986$		0			0
$987$	−3.63474	−	7.30839i	−0.115695	−	0.232629i
$988$		0			0
$989$	−12.6291	−	7.29144i	−0.401583	−	0.231854i
$990$		0			0
$991$	−17.2629	+	9.96676i	−0.548375	+	0.316605i	−0.748466	−	0.663173i	$-0.769209\pi$
$991$	−17.2629	+	9.96676i	−0.548375	+	0.316605i	0.200091	+	0.979777i	$0.435876\pi$
$992$		0			0
$993$	−9.22171			−0.292642
$994$		0			0
$995$		−	0.263141i		−	0.00834213i
$996$		0			0
$997$	−23.2684	+	13.4340i	−0.736919	+	0.425460i	−0.820948	−	0.571003i	$-0.806554\pi$
$997$	−23.2684	+	13.4340i	−0.736919	+	0.425460i	0.0840291	+	0.996463i	$0.473221\pi$
$998$		0			0
$999$	6.65418	+	3.84179i	0.210529	+	0.121549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bi.b.527.8	yes	32
4.3	odd	2		1232.2.bi.a.527.9	✓	32
7.4	even	3		1232.2.bi.a.879.10	yes	32
11.10	odd	2	inner	1232.2.bi.b.527.7	yes	32
28.11	odd	6	inner	1232.2.bi.b.879.7	yes	32
44.43	even	2		1232.2.bi.a.527.10	yes	32
77.32	odd	6		1232.2.bi.a.879.9	yes	32
308.263	even	6	inner	1232.2.bi.b.879.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.bi.a.527.9	✓	32	4.3	odd	2
1232.2.bi.a.527.10	yes	32	44.43	even	2
1232.2.bi.a.879.9	yes	32	77.32	odd	6
1232.2.bi.a.879.10	yes	32	7.4	even	3
1232.2.bi.b.527.7	yes	32	11.10	odd	2	inner
1232.2.bi.b.527.8	yes	32	1.1	even	1	trivial
1232.2.bi.b.879.7	yes	32	28.11	odd	6	inner
1232.2.bi.b.879.8	yes	32	308.263	even	6	inner

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.497216 + 0.287068i) q^{3} +(0.0931719 - 0.161379i) q^{5} +(-1.17817 - 2.36895i) q^{7} +(-1.33518 + 2.31261i) q^{9} +O(q^{10})\)	\(q+(-0.497216 + 0.287068i) q^{3} +(0.0931719 - 0.161379i) q^{5} +(-1.17817 - 2.36895i) q^{7} +(-1.33518 + 2.31261i) q^{9} +(0.691567 + 3.24372i) q^{11} -2.60748i q^{13} +0.106987i q^{15} +(2.71814 - 1.56932i) q^{17} +(-1.90321 + 3.29645i) q^{19} +(1.26585 + 0.839665i) q^{21} +(-6.10413 - 3.52422i) q^{23} +(2.48264 + 4.30006i) q^{25} -3.25556i q^{27} +2.51768i q^{29} +(-7.39137 + 4.26741i) q^{31} +(-1.27503 - 1.41430i) q^{33} +(-0.492070 - 0.0305882i) q^{35} +(-1.18007 + 2.04394i) q^{37} +(0.748523 + 1.29648i) q^{39} +9.66118i q^{41} +2.06895 q^{43} +(0.248803 + 0.430940i) q^{45} +(-4.65352 - 2.68671i) q^{47} +(-4.22383 + 5.58205i) q^{49} +(-0.901001 + 1.56058i) q^{51} +(3.47173 + 6.01321i) q^{53} +(0.587902 + 0.190620i) q^{55} -2.18540i q^{57} +(0.586493 - 0.338612i) q^{59} +(-6.14860 - 3.54990i) q^{61} +(7.05152 + 0.438339i) q^{63} +(-0.420791 - 0.242944i) q^{65} +(-10.1223 + 5.84414i) q^{67} +4.04677 q^{69} +5.20158i q^{71} +(8.45446 - 4.88118i) q^{73} +(-2.46882 - 1.42537i) q^{75} +(6.86943 - 5.45994i) q^{77} +(-5.83616 + 10.1085i) q^{79} +(-3.07099 - 5.31910i) q^{81} -0.452209 q^{83} -0.584865i q^{85} +(-0.722745 - 1.25183i) q^{87} +(-6.54754 + 11.3407i) q^{89} +(-6.17698 + 3.07205i) q^{91} +(2.45007 - 4.24365i) q^{93} +(0.354651 + 0.614273i) q^{95} -8.54347 q^{97} +(-8.42482 - 2.73164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 12 * q^9	\( 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) \) 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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