LMFDB - Embedded newform 640.2.x.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(81,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("640.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.x (of order $8$, degree $4$, not 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	640.81
Dual form			640.2.x.a.561.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.06141 - 1.26808i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(1.47530 - 1.47530i) q^{7} +(5.64289 + 5.64289i) q^{9} +O(q^{10})$	\(q+(-3.06141 - 1.26808i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(1.47530 - 1.47530i) q^{7} +(5.64289 + 5.64289i) q^{9} +(2.52526 - 1.04600i) q^{11} +(1.19553 - 2.88627i) q^{13} +3.31365i q^{15} -4.57348i q^{17} +(-0.489776 + 1.18242i) q^{19} +(-6.38730 + 2.64571i) q^{21} +(3.31089 + 3.31089i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-6.31534 - 15.2466i) q^{27} +(-2.16451 - 0.896568i) q^{29} -4.27786 q^{31} -9.05725 q^{33} +(-1.92758 - 0.798428i) q^{35} +(-1.55074 - 3.74382i) q^{37} +(-7.32004 + 7.32004i) q^{39} +(-6.61864 - 6.61864i) q^{41} +(-5.87081 + 2.43177i) q^{43} +(3.05391 - 7.37279i) q^{45} -8.98123i q^{47} +2.64697i q^{49} +(-5.79952 + 14.0013i) q^{51} +(-3.90461 + 1.61734i) q^{53} +(-1.93275 - 1.93275i) q^{55} +(2.99881 - 2.99881i) q^{57} +(-2.12040 - 5.11911i) q^{59} +(11.7259 + 4.85704i) q^{61} +16.6499 q^{63} -3.12408 q^{65} +(3.86407 + 1.60055i) q^{67} +(-5.93753 - 14.3345i) q^{69} +(10.4976 - 10.4976i) q^{71} +(1.94166 + 1.94166i) q^{73} +(3.06141 - 1.26808i) q^{75} +(2.18236 - 5.26868i) q^{77} -4.93294i q^{79} +30.7437i q^{81} +(-3.10823 + 7.50393i) q^{83} +(-4.22534 + 1.75019i) q^{85} +(5.48953 + 5.48953i) q^{87} +(-3.83531 + 3.83531i) q^{89} +(-2.49435 - 6.02190i) q^{91} +(13.0963 + 5.42466i) q^{93} +1.27985 q^{95} -17.5723 q^{97} +(20.1522 + 8.34731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) $ 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	−3.06141	−	1.26808i	−1.76751	−	0.732125i	−0.995310	−	0.0967407i	$-0.969158\pi$
$3$	−3.06141	−	1.26808i	−1.76751	−	0.732125i	−0.772196	−	0.635384i	$-0.780842\pi$
$4$		0			0
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$6$		0			0
$7$	1.47530	−	1.47530i	0.557612	−	0.557612i	−0.371015	−	0.928627i	$-0.620990\pi$
$7$	1.47530	−	1.47530i	0.557612	−	0.557612i	0.928627	+	0.371015i	$0.120990\pi$
$8$		0			0
$9$	5.64289	+	5.64289i	1.88096	+	1.88096i
$10$		0			0
$11$	2.52526	−	1.04600i	0.761394	−	0.315380i	0.0320127	−	0.999487i	$-0.489808\pi$
$11$	2.52526	−	1.04600i	0.761394	−	0.315380i	0.729381	+	0.684108i	$0.239808\pi$
$12$		0			0
$13$	1.19553	−	2.88627i	0.331581	−	0.800508i	−0.666886	−	0.745160i	$-0.732373\pi$
$13$	1.19553	−	2.88627i	0.331581	−	0.800508i	0.998467	−	0.0553483i	$-0.0176269\pi$
$14$		0			0
$15$			3.31365i			0.855580i
$16$		0			0
$17$		−	4.57348i		−	1.10923i	−0.832107	−	0.554616i	$-0.812865\pi$
$17$		−	4.57348i		−	1.10923i	0.832107	−	0.554616i	$-0.187135\pi$
$18$		0			0
$19$	−0.489776	+	1.18242i	−0.112362	+	0.271267i	−0.970050	−	0.242904i	$-0.921900\pi$
$19$	−0.489776	+	1.18242i	−0.112362	+	0.271267i	0.857688	+	0.514170i	$0.171900\pi$
$20$		0			0
$21$	−6.38730	+	2.64571i	−1.39382	+	0.577341i
$22$		0			0
$23$	3.31089	+	3.31089i	0.690368	+	0.690368i	0.962313	−	0.271945i	$-0.0876667\pi$
$23$	3.31089	+	3.31089i	0.690368	+	0.690368i	−0.271945	+	0.962313i	$0.587667\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	−6.31534	−	15.2466i	−1.21539	−	2.93421i
$28$		0			0
$29$	−2.16451	−	0.896568i	−0.401939	−	0.166489i	0.172550	−	0.985001i	$-0.444799\pi$
$29$	−2.16451	−	0.896568i	−0.401939	−	0.166489i	−0.574489	+	0.818512i	$0.694799\pi$
$30$		0			0
$31$	−4.27786			−0.768327			−0.384163	−	0.923265i	$-0.625510\pi$
$31$	−4.27786			−0.768327			−0.384163	+	0.923265i	$0.625510\pi$
$32$		0			0
$33$	−9.05725			−1.57666
$34$		0			0
$35$	−1.92758	−	0.798428i	−0.325820	−	0.134959i
$36$		0			0
$37$	−1.55074	−	3.74382i	−0.254940	−	0.615479i	0.743650	−	0.668569i	$-0.233093\pi$
$37$	−1.55074	−	3.74382i	−0.254940	−	0.615479i	−0.998590	+	0.0530899i	$0.983093\pi$
$38$		0			0
$39$	−7.32004	+	7.32004i	−1.17214	+	1.17214i
$40$		0			0
$41$	−6.61864	−	6.61864i	−1.03366	−	1.03366i	−0.999413	−	0.0342449i	$-0.989097\pi$
$41$	−6.61864	−	6.61864i	−1.03366	−	1.03366i	−0.0342449	−	0.999413i	$-0.510903\pi$
$42$		0			0
$43$	−5.87081	+	2.43177i	−0.895290	+	0.370841i	−0.782407	−	0.622767i	$-0.786008\pi$
$43$	−5.87081	+	2.43177i	−0.895290	+	0.370841i	−0.112883	+	0.993608i	$0.536008\pi$
$44$		0			0
$45$	3.05391	−	7.37279i	0.455250	−	1.09907i
$46$		0			0
$47$		−	8.98123i		−	1.31005i	−0.755608	−	0.655024i	$-0.772659\pi$
$47$		−	8.98123i		−	1.31005i	0.755608	−	0.655024i	$-0.227341\pi$
$48$		0			0
$49$			2.64697i			0.378138i
$50$		0			0
$51$	−5.79952	+	14.0013i	−0.812096	+	1.96057i
$52$		0			0
$53$	−3.90461	+	1.61734i	−0.536340	+	0.222159i	−0.634378	−	0.773023i	$-0.718744\pi$
$53$	−3.90461	+	1.61734i	−0.536340	+	0.222159i	0.0980374	+	0.995183i	$0.468744\pi$
$54$		0			0
$55$	−1.93275	−	1.93275i	−0.260612	−	0.260612i
$56$		0			0
$57$	2.99881	−	2.99881i	0.397202	−	0.397202i
$58$		0			0
$59$	−2.12040	−	5.11911i	−0.276053	−	0.666451i	0.723666	−	0.690150i	$-0.242456\pi$
$59$	−2.12040	−	5.11911i	−0.276053	−	0.666451i	−0.999719	+	0.0236991i	$0.992456\pi$
$60$		0			0
$61$	11.7259	+	4.85704i	1.50135	+	0.621880i	0.973752	−	0.227614i	$-0.0730923\pi$
$61$	11.7259	+	4.85704i	1.50135	+	0.621880i	0.527599	+	0.849493i	$0.323092\pi$
$62$		0			0
$63$	16.6499			2.09769
$64$		0			0
$65$	−3.12408			−0.387494
$66$		0			0
$67$	3.86407	+	1.60055i	0.472071	+	0.195538i	0.606019	−	0.795450i	$-0.292765\pi$
$67$	3.86407	+	1.60055i	0.472071	+	0.195538i	−0.133948	+	0.990988i	$0.542765\pi$
$68$		0			0
$69$	−5.93753	−	14.3345i	−0.714794	−	1.72567i
$70$		0			0
$71$	10.4976	−	10.4976i	1.24584	−	1.24584i	0.288298	−	0.957541i	$-0.406911\pi$
$71$	10.4976	−	10.4976i	1.24584	−	1.24584i	0.957541	−	0.288298i	$-0.0930893\pi$
$72$		0			0
$73$	1.94166	+	1.94166i	0.227254	+	0.227254i	0.811545	−	0.584290i	$-0.198627\pi$
$73$	1.94166	+	1.94166i	0.227254	+	0.227254i	−0.584290	+	0.811545i	$0.698627\pi$
$74$		0			0
$75$	3.06141	−	1.26808i	0.353501	−	0.146425i
$76$		0			0
$77$	2.18236	−	5.26868i	0.248703	−	0.600421i
$78$		0			0
$79$		−	4.93294i		−	0.554999i	−0.960726	−	0.277499i	$-0.910494\pi$
$79$		−	4.93294i		−	0.554999i	0.960726	−	0.277499i	$-0.0895057\pi$
$80$		0			0
$81$			30.7437i			3.41596i
$82$		0			0
$83$	−3.10823	+	7.50393i	−0.341172	+	0.823663i	0.656425	+	0.754391i	$0.272068\pi$
$83$	−3.10823	+	7.50393i	−0.341172	+	0.823663i	−0.997598	+	0.0692720i	$0.977932\pi$
$84$		0			0
$85$	−4.22534	+	1.75019i	−0.458303	+	0.189835i
$86$		0			0
$87$	5.48953	+	5.48953i	0.588539	+	0.588539i
$88$		0			0
$89$	−3.83531	+	3.83531i	−0.406542	+	0.406542i	−0.880531	−	0.473989i	$-0.842814\pi$
$89$	−3.83531	+	3.83531i	−0.406542	+	0.406542i	0.473989	+	0.880531i	$0.342814\pi$
$90$		0			0
$91$	−2.49435	−	6.02190i	−0.261479	−	0.631267i
$92$		0			0
$93$	13.0963	+	5.42466i	1.35802	+	0.562511i
$94$		0			0
$95$	1.27985			0.131309
$96$		0			0
$97$	−17.5723			−1.78420			−0.892099	−	0.451840i	$-0.850768\pi$
$97$	−17.5723			−1.78420			−0.892099	+	0.451840i	$0.850768\pi$
$98$		0			0
$99$	20.1522	+	8.34731i	2.02537	+	0.838936i
$100$		0			0
$101$	0.497712	+	1.20158i	0.0495242	+	0.119562i	0.946706	−	0.322100i	$-0.104389\pi$
$101$	0.497712	+	1.20158i	0.0495242	+	0.119562i	−0.897181	+	0.441662i	$0.854389\pi$
$102$		0			0
$103$	−0.375339	+	0.375339i	−0.0369833	+	0.0369833i	−0.725357	−	0.688373i	$-0.758325\pi$
$103$	−0.375339	+	0.375339i	−0.0369833	+	0.0369833i	0.688373	+	0.725357i	$0.258325\pi$
$104$		0			0
$105$	4.88863	+	4.88863i	0.477081	+	0.477081i
$106$		0			0
$107$	0.211809	−	0.0877341i	0.0204763	−	0.00848157i	−0.372422	−	0.928064i	$-0.621473\pi$
$107$	0.211809	−	0.0877341i	0.0204763	−	0.00848157i	0.392898	+	0.919582i	$0.371473\pi$
$108$		0			0
$109$	−1.30838	+	3.15871i	−0.125320	+	0.302550i	−0.974071	−	0.226244i	$-0.927355\pi$
$109$	−1.30838	+	3.15871i	−0.125320	+	0.302550i	0.848751	+	0.528793i	$0.177355\pi$
$110$		0			0
$111$			13.4278i			1.27451i
$112$		0			0
$113$		−	14.0527i		−	1.32197i	−0.750399	−	0.660985i	$-0.770139\pi$
$113$		−	14.0527i		−	1.32197i	0.750399	−	0.660985i	$-0.229861\pi$
$114$		0			0
$115$	1.79184	−	4.32589i	0.167090	−	0.403391i
$116$		0			0
$117$	23.0332	−	9.54066i	2.12942	−	0.882034i
$118$		0			0
$119$	−6.74726	−	6.74726i	−0.618521	−	0.618521i
$120$		0			0
$121$	−2.49536	+	2.49536i	−0.226851	+	0.226851i
$122$		0			0
$123$	11.8694	+	28.6553i	1.07023	+	2.58376i
$124$		0			0
$125$	0.923880	+	0.382683i	0.0826343	+	0.0342282i
$126$		0			0
$127$	5.66042			0.502281			0.251140	−	0.967951i	$-0.419194\pi$
$127$	5.66042			0.502281			0.251140	+	0.967951i	$0.419194\pi$
$128$		0			0
$129$	21.0566			1.85393
$130$		0			0
$131$	−11.5314	−	4.77645i	−1.00750	−	0.417320i	−0.182958	−	0.983121i	$-0.558567\pi$
$131$	−11.5314	−	4.77645i	−1.00750	−	0.417320i	−0.824542	+	0.565801i	$0.808567\pi$
$132$		0			0
$133$	1.02186	+	2.46700i	0.0886069	+	0.213916i
$134$		0			0
$135$	−11.6692	+	11.6692i	−1.00433	+	1.00433i
$136$		0			0
$137$	−4.84493	−	4.84493i	−0.413930	−	0.413930i	0.469175	−	0.883105i	$-0.344551\pi$
$137$	−4.84493	−	4.84493i	−0.413930	−	0.413930i	−0.883105	+	0.469175i	$0.844551\pi$
$138$		0			0
$139$	7.25419	−	3.00479i	0.615293	−	0.254863i	−0.0531970	−	0.998584i	$-0.516941\pi$
$139$	7.25419	−	3.00479i	0.615293	−	0.254863i	0.668490	+	0.743721i	$0.266941\pi$
$140$		0			0
$141$	−11.3889	+	27.4952i	−0.959118	+	2.31552i
$142$		0			0
$143$		−	8.53911i		−	0.714076i
$144$		0			0
$145$			2.34285i			0.194563i
$146$		0			0
$147$	3.35656	−	8.10345i	0.276844	−	0.668361i
$148$		0			0
$149$	2.97619	−	1.23278i	0.243819	−	0.100993i	−0.257428	−	0.966298i	$-0.582875\pi$
$149$	2.97619	−	1.23278i	0.243819	−	0.100993i	0.501247	+	0.865304i	$0.332875\pi$
$150$		0			0
$151$	4.31859	+	4.31859i	0.351442	+	0.351442i	0.860646	−	0.509204i	$-0.170060\pi$
$151$	4.31859	+	4.31859i	0.351442	+	0.351442i	−0.509204	+	0.860646i	$0.670060\pi$
$152$		0			0
$153$	25.8076	−	25.8076i	2.08642	−	2.08642i
$154$		0			0
$155$	1.63707	+	3.95223i	0.131492	+	0.317451i
$156$		0			0
$157$	12.6563	+	5.24240i	1.01008	+	0.418389i	0.825484	−	0.564425i	$-0.190902\pi$
$157$	12.6563	+	5.24240i	1.01008	+	0.418389i	0.184597	+	0.982814i	$0.440902\pi$
$158$		0			0
$159$	14.0045			1.11063
$160$		0			0
$161$	9.76913			0.769915
$162$		0			0
$163$	−15.0565	−	6.23659i	−1.17931	−	0.488488i	−0.295053	−	0.955481i	$-0.595337\pi$
$163$	−15.0565	−	6.23659i	−1.17931	−	0.488488i	−0.884261	+	0.466993i	$0.845337\pi$
$164$		0			0
$165$	3.46606	+	8.36781i	0.269832	+	0.651433i
$166$		0			0
$167$	−1.78435	+	1.78435i	−0.138077	+	0.138077i	−0.772767	−	0.634690i	$-0.781128\pi$
$167$	−1.78435	+	1.78435i	−0.138077	+	0.138077i	0.634690	+	0.772767i	$0.281128\pi$
$168$		0			0
$169$	2.29111	+	2.29111i	0.176239	+	0.176239i
$170$		0			0
$171$	−9.43604	+	3.90854i	−0.721592	+	0.298893i
$172$		0			0
$173$	2.50637	−	6.05091i	0.190556	−	0.460042i	−0.799509	−	0.600654i	$-0.794907\pi$
$173$	2.50637	−	6.05091i	0.190556	−	0.460042i	0.990065	+	0.140612i	$0.0449070\pi$
$174$		0			0
$175$			2.08639i			0.157716i
$176$		0			0
$177$			18.3605i			1.38006i
$178$		0			0
$179$	−0.0970802	+	0.234372i	−0.00725611	+	0.0175178i	−0.927466	−	0.373907i	$-0.878018\pi$
$179$	−0.0970802	+	0.234372i	−0.00725611	+	0.0175178i	0.920210	+	0.391425i	$0.128018\pi$
$180$		0			0
$181$	19.1612	−	7.93681i	1.42424	−	0.589939i	0.468316	−	0.883561i	$-0.344861\pi$
$181$	19.1612	−	7.93681i	1.42424	−	0.589939i	0.955922	+	0.293622i	$0.0948608\pi$
$182$		0			0
$183$	−29.7388	−	29.7388i	−2.19835	−	2.19835i
$184$		0			0
$185$	−2.86539	+	2.86539i	−0.210668	+	0.210668i
$186$		0			0
$187$	−4.78384	−	11.5492i	−0.349829	−	0.844562i
$188$		0			0
$189$	−31.8104	−	13.1763i	−2.31386	−	0.958434i
$190$		0			0
$191$	−0.530731			−0.0384024			−0.0192012	−	0.999816i	$-0.506112\pi$
$191$	−0.530731			−0.0384024			−0.0192012	+	0.999816i	$0.506112\pi$
$192$		0			0
$193$	−4.06405			−0.292537			−0.146268	−	0.989245i	$-0.546726\pi$
$193$	−4.06405			−0.292537			−0.146268	+	0.989245i	$0.546726\pi$
$194$		0			0
$195$	9.56409	+	3.96158i	0.684899	+	0.283694i
$196$		0			0
$197$	−4.01470	−	9.69235i	−0.286036	−	0.690551i	0.713917	−	0.700230i	$-0.246919\pi$
$197$	−4.01470	−	9.69235i	−0.286036	−	0.690551i	−0.999953	+	0.00967864i	$0.996919\pi$
$198$		0			0
$199$	−4.73554	+	4.73554i	−0.335693	+	0.335693i	−0.854744	−	0.519050i	$-0.826286\pi$
$199$	−4.73554	+	4.73554i	−0.335693	+	0.335693i	0.519050	+	0.854744i	$0.326286\pi$
$200$		0			0
$201$	−9.79988	−	9.79988i	−0.691230	−	0.691230i
$202$		0			0
$203$	−4.51601	+	1.87059i	−0.316962	+	0.131290i
$204$		0			0
$205$	−3.58198	+	8.64767i	−0.250177	+	0.603980i
$206$		0			0
$207$			37.3660i			2.59711i
$208$		0			0
$209$			3.49823i			0.241977i
$210$		0			0
$211$	−2.77266	+	6.69379i	−0.190878	+	0.460820i	−0.990126	−	0.140182i	$-0.955231\pi$
$211$	−2.77266	+	6.69379i	−0.190878	+	0.460820i	0.799248	+	0.601001i	$0.205231\pi$
$212$		0			0
$213$	−45.4493	+	18.8257i	−3.11414	+	1.28992i
$214$		0			0
$215$	4.49332	+	4.49332i	0.306442	+	0.306442i
$216$		0			0
$217$	−6.31114	+	6.31114i	−0.428428	+	0.428428i
$218$		0			0
$219$	−3.48205	−	8.40640i	−0.235295	−	0.568052i
$220$		0			0
$221$	−13.2003	−	5.46775i	−0.887949	−	0.367801i
$222$		0			0
$223$	10.9003			0.729937			0.364968	−	0.931020i	$-0.381080\pi$
$223$	10.9003			0.729937			0.364968	+	0.931020i	$0.381080\pi$
$224$		0			0
$225$	−7.98025			−0.532017
$226$		0			0
$227$	1.64679	+	0.682122i	0.109301	+	0.0452740i	0.436664	−	0.899625i	$-0.356160\pi$
$227$	1.64679	+	0.682122i	0.109301	+	0.0452740i	−0.327363	+	0.944899i	$0.606160\pi$
$228$		0			0
$229$	4.35081	+	10.5038i	0.287509	+	0.694109i	0.999971	−	0.00760199i	$-0.00241981\pi$
$229$	4.35081	+	10.5038i	0.287509	+	0.694109i	−0.712462	+	0.701711i	$0.752420\pi$
$230$		0			0
$231$	−13.3622	+	13.3622i	−0.879167	+	0.879167i
$232$		0			0
$233$	0.792166	+	0.792166i	0.0518965	+	0.0518965i	0.732579	−	0.680682i	$-0.238317\pi$
$233$	0.792166	+	0.792166i	0.0518965	+	0.0518965i	−0.680682	+	0.732579i	$0.738317\pi$
$234$		0			0
$235$	−8.29758	+	3.43697i	−0.541274	+	0.224203i
$236$		0			0
$237$	−6.25535	+	15.1017i	−0.406328	+	0.980964i
$238$		0			0
$239$		−	28.9574i		−	1.87310i	−0.350532	−	0.936551i	$-0.613999\pi$
$239$		−	28.9574i		−	1.87310i	0.350532	−	0.936551i	$-0.386001\pi$
$240$		0			0
$241$		−	23.6539i		−	1.52368i	−0.647763	−	0.761842i	$-0.724295\pi$
$241$		−	23.6539i		−	1.52368i	0.647763	−	0.761842i	$-0.275705\pi$
$242$		0			0
$243$	20.0393	−	48.3792i	1.28552	−	3.10352i
$244$		0			0
$245$	2.44548	−	1.01295i	0.156236	−	0.0647150i
$246$		0			0
$247$	2.82726	+	2.82726i	0.179894	+	0.179894i
$248$		0			0
$249$	19.0311	−	19.0311i	1.20605	−	1.20605i
$250$		0			0
$251$	−2.00619	−	4.84337i	−0.126630	−	0.305711i	0.847832	−	0.530265i	$-0.177907\pi$
$251$	−2.00619	−	4.84337i	−0.126630	−	0.305711i	−0.974462	+	0.224554i	$0.927907\pi$
$252$		0			0
$253$	11.8240	+	4.89767i	0.743370	+	0.307914i
$254$		0			0
$255$	15.1549			0.949036
$256$		0			0
$257$	29.6462			1.84928			0.924641	−	0.380840i	$-0.124365\pi$
$257$	29.6462			1.84928			0.924641	+	0.380840i	$0.124365\pi$
$258$		0			0
$259$	−7.81107	−	3.23545i	−0.485356	−	0.201041i
$260$		0			0
$261$	−7.15484	−	17.2733i	−0.442874	−	1.06919i
$262$		0			0
$263$	−15.9146	+	15.9146i	−0.981335	+	0.981335i	−0.999829	−	0.0184942i	$-0.994113\pi$
$263$	−15.9146	+	15.9146i	−0.981335	+	0.981335i	0.0184942	+	0.999829i	$0.494113\pi$
$264$		0			0
$265$	2.98846	+	2.98846i	0.183580	+	0.183580i
$266$		0			0
$267$	16.6049	−	6.87799i	1.01621	−	0.420926i
$268$		0			0
$269$	0.718268	−	1.73405i	0.0437936	−	0.105727i	−0.900469	−	0.434920i	$-0.856777\pi$
$269$	0.718268	−	1.73405i	0.0437936	−	0.105727i	0.944263	+	0.329193i	$0.106777\pi$
$270$		0			0
$271$		−	3.84074i		−	0.233308i	−0.993173	−	0.116654i	$-0.962783\pi$
$271$		−	3.84074i		−	0.233308i	0.993173	−	0.116654i	$-0.0372169\pi$
$272$		0			0
$273$			21.5985i			1.30720i
$274$		0			0
$275$	−1.04600	+	2.52526i	−0.0630759	+	0.152279i
$276$		0			0
$277$	−10.1799	+	4.21664i	−0.611649	+	0.253353i	−0.666933	−	0.745117i	$-0.732393\pi$
$277$	−10.1799	+	4.21664i	−0.611649	+	0.253353i	0.0552844	+	0.998471i	$0.482393\pi$
$278$		0			0
$279$	−24.1395	−	24.1395i	−1.44519	−	1.44519i
$280$		0			0
$281$	12.0113	−	12.0113i	0.716534	−	0.716534i	−0.251360	−	0.967894i	$-0.580878\pi$
$281$	12.0113	−	12.0113i	0.716534	−	0.716534i	0.967894	+	0.251360i	$0.0808777\pi$
$282$		0			0
$283$	4.08381	+	9.85918i	0.242757	+	0.586067i	0.997555	−	0.0698904i	$-0.0222649\pi$
$283$	4.08381	+	9.85918i	0.242757	+	0.586067i	−0.754798	+	0.655958i	$0.772265\pi$
$284$		0			0
$285$	−3.91813	−	1.62294i	−0.232090	−	0.0961349i
$286$		0			0
$287$	−19.5290			−1.15276
$288$		0			0
$289$	−3.91670			−0.230394
$290$		0			0
$291$	53.7960	+	22.2831i	3.15358	+	1.30626i
$292$		0			0
$293$	1.77297	+	4.28032i	0.103578	+	0.250059i	0.967169	−	0.254133i	$-0.0817902\pi$
$293$	1.77297	+	4.28032i	0.103578	+	0.250059i	−0.863591	+	0.504192i	$0.831790\pi$
$294$		0			0
$295$	−3.91800	+	3.91800i	−0.228115	+	0.228115i
$296$		0			0
$297$	−31.8957	−	31.8957i	−1.85078	−	1.85078i
$298$		0			0
$299$	13.5144	−	5.59785i	0.781559	−	0.323732i
$300$		0			0
$301$	−5.07363	+	12.2488i	−0.292439	+	0.706010i
$302$		0			0
$303$		−	4.30968i		−	0.247585i
$304$		0			0
$305$		−	12.6920i		−	0.726745i
$306$		0			0
$307$	−2.14655	+	5.18223i	−0.122510	+	0.295765i	−0.973222	−	0.229866i	$-0.926171\pi$
$307$	−2.14655	+	5.18223i	−0.122510	+	0.295765i	0.850712	+	0.525632i	$0.176171\pi$
$308$		0			0
$309$	1.62503	−	0.673108i	0.0924445	−	0.0382918i
$310$		0			0
$311$	20.5492	+	20.5492i	1.16524	+	1.16524i	0.983313	+	0.181923i	$0.0582321\pi$
$311$	20.5492	+	20.5492i	1.16524	+	1.16524i	0.181923	+	0.983313i	$0.441768\pi$
$312$		0			0
$313$	−9.00747	+	9.00747i	−0.509133	+	0.509133i	−0.914260	−	0.405128i	$-0.867227\pi$
$313$	−9.00747	+	9.00747i	−0.509133	+	0.509133i	0.405128	+	0.914260i	$0.367227\pi$
$314$		0			0
$315$	−6.37165	−	15.3825i	−0.359002	−	0.866708i
$316$		0			0
$317$	25.0786	+	10.3879i	1.40856	+	0.583443i	0.951958	−	0.306229i	$-0.0990674\pi$
$317$	25.0786	+	10.3879i	1.40856	+	0.583443i	0.456599	+	0.889673i	$0.349067\pi$
$318$		0			0
$319$	−6.40374			−0.358541
$320$		0			0
$321$	−0.759687			−0.0424016
$322$		0			0
$323$	5.40779	+	2.23998i	0.300897	+	0.124636i
$324$		0			0
$325$	1.19553	+	2.88627i	0.0663163	+	0.160102i
$326$		0			0
$327$	8.01098	−	8.01098i	0.443008	−	0.443008i
$328$		0			0
$329$	−13.2500	−	13.2500i	−0.730498	−	0.730498i
$330$		0			0
$331$	2.03806	−	0.844194i	0.112022	−	0.0464011i	−0.325968	−	0.945381i	$-0.605690\pi$
$331$	2.03806	−	0.844194i	0.112022	−	0.0464011i	0.437991	+	0.898980i	$0.355690\pi$
$332$		0			0
$333$	12.3753	−	29.8766i	0.678162	−	1.63723i
$334$		0			0
$335$		−	4.18244i		−	0.228511i
$336$		0			0
$337$			6.27046i			0.341574i	0.985308	+	0.170787i	$0.0546309\pi$
$337$			6.27046i			0.341574i	−0.985308	+	0.170787i	$0.945369\pi$
$338$		0			0
$339$	−17.8199	+	43.0212i	−0.967847	+	2.33659i
$340$		0			0
$341$	−10.8027	+	4.47463i	−0.584999	+	0.242315i
$342$		0			0
$343$	14.2322	+	14.2322i	0.768466	+	0.768466i
$344$		0			0
$345$	−10.9711	+	10.9711i	−0.590665	+	0.590665i
$346$		0			0
$347$	9.33707	+	22.5417i	0.501240	+	1.21010i	0.948809	+	0.315851i	$0.102290\pi$
$347$	9.33707	+	22.5417i	0.501240	+	1.21010i	−0.447568	+	0.894250i	$0.647710\pi$
$348$		0			0
$349$	−2.98730	−	1.23738i	−0.159907	−	0.0662355i	0.301294	−	0.953531i	$-0.402581\pi$
$349$	−2.98730	−	1.23738i	−0.159907	−	0.0662355i	−0.461201	+	0.887296i	$0.652581\pi$
$350$		0			0
$351$	−51.5560			−2.75186
$352$		0			0
$353$	−16.1662			−0.860439			−0.430220	−	0.902724i	$-0.641564\pi$
$353$	−16.1662			−0.860439			−0.430220	+	0.902724i	$0.641564\pi$
$354$		0			0
$355$	−13.7158	−	5.68127i	−0.727959	−	0.301531i
$356$		0			0
$357$	12.1001	+	29.2122i	0.640404	+	1.54607i
$358$		0			0
$359$	25.7023	−	25.7023i	1.35651	−	1.35651i	0.478340	−	0.878175i	$-0.341239\pi$
$359$	25.7023	−	25.7023i	1.35651	−	1.35651i	0.878175	−	0.478340i	$-0.158761\pi$
$360$		0			0
$361$	12.2768	+	12.2768i	0.646146	+	0.646146i
$362$		0			0
$363$	10.8036	−	4.47501i	0.567043	−	0.234877i
$364$		0			0
$365$	1.05082	−	2.53690i	0.0550024	−	0.132788i
$366$		0			0
$367$		−	2.16361i		−	0.112940i	−0.998404	−	0.0564699i	$-0.982016\pi$
$367$		−	2.16361i		−	0.112940i	0.998404	−	0.0564699i	$-0.0179845\pi$
$368$		0			0
$369$		−	74.6965i		−	3.88855i
$370$		0			0
$371$	−3.37442	+	8.14656i	−0.175191	+	0.422948i
$372$		0			0
$373$	7.48006	−	3.09834i	0.387303	−	0.160426i	−0.180531	−	0.983569i	$-0.557782\pi$
$373$	7.48006	−	3.09834i	0.387303	−	0.160426i	0.567834	+	0.823143i	$0.307782\pi$
$374$		0			0
$375$	−2.34310	−	2.34310i	−0.120997	−	0.120997i
$376$		0			0
$377$	−5.17548	+	5.17548i	−0.266551	+	0.266551i
$378$		0			0
$379$	−1.71515	−	4.14074i	−0.0881013	−	0.212695i	0.873688	−	0.486487i	$-0.161722\pi$
$379$	−1.71515	−	4.14074i	−0.0881013	−	0.212695i	−0.961789	+	0.273792i	$0.911722\pi$
$380$		0			0
$381$	−17.3289	−	7.17785i	−0.887784	−	0.367732i
$382$		0			0
$383$	−33.4265			−1.70801			−0.854006	−	0.520263i	$-0.825834\pi$
$383$	−33.4265			−1.70801			−0.854006	+	0.520263i	$0.825834\pi$
$384$		0			0
$385$	−5.70277			−0.290640
$386$		0			0
$387$	−46.8505	−	19.4061i	−2.38155	−	0.986469i
$388$		0			0
$389$	3.77153	+	9.10527i	0.191224	+	0.461656i	0.990191	−	0.139719i	$-0.0446200\pi$
$389$	3.77153	+	9.10527i	0.191224	+	0.461656i	−0.798967	+	0.601375i	$0.794620\pi$
$390$		0			0
$391$	15.1423	−	15.1423i	0.765778	−	0.765778i
$392$		0			0
$393$	29.2453	+	29.2453i	1.47523	+	1.47523i
$394$		0			0
$395$	−4.55744	+	1.88775i	−0.229310	+	0.0949832i
$396$		0			0
$397$	10.6895	−	25.8068i	0.536491	−	1.29520i	−0.390666	−	0.920533i	$-0.627755\pi$
$397$	10.6895	−	25.8068i	0.536491	−	1.29520i	0.927157	−	0.374672i	$-0.122245\pi$
$398$		0			0
$399$		−	8.84830i		−	0.442969i
$400$		0			0
$401$		−	13.6670i		−	0.682498i	−0.939973	−	0.341249i	$-0.889150\pi$
$401$		−	13.6670i		−	0.682498i	0.939973	−	0.341249i	$-0.110850\pi$
$402$		0			0
$403$	−5.11433	+	12.3471i	−0.254763	+	0.615052i
$404$		0			0
$405$	28.4034	−	11.7651i	1.41138	−	0.584612i
$406$		0			0
$407$	−7.83203	−	7.83203i	−0.388219	−	0.388219i
$408$		0			0
$409$	−24.8408	+	24.8408i	−1.22830	+	1.22830i	−0.263690	+	0.964607i	$0.584940\pi$
$409$	−24.8408	+	24.8408i	−1.22830	+	1.22830i	−0.964607	+	0.263690i	$0.915060\pi$
$410$		0			0
$411$	8.68857	+	20.9761i	0.428575	+	1.03467i
$412$		0			0
$413$	−10.6805	−	4.42400i	−0.525552	−	0.217691i
$414$		0			0
$415$	8.12219			0.398703
$416$		0			0
$417$	−26.0184			−1.27412
$418$		0			0
$419$	23.9649	+	9.92661i	1.17076	+	0.484946i	0.881445	−	0.472286i	$-0.156571\pi$
$419$	23.9649	+	9.92661i	1.17076	+	0.484946i	0.289319	+	0.957233i	$0.406571\pi$
$420$		0			0
$421$	−4.51118	−	10.8909i	−0.219861	−	0.530792i	0.775009	−	0.631950i	$-0.217745\pi$
$421$	−4.51118	−	10.8909i	−0.219861	−	0.530792i	−0.994870	+	0.101158i	$0.967745\pi$
$422$		0			0
$423$	50.6801	−	50.6801i	2.46415	−	2.46415i
$424$		0			0
$425$	3.23394	+	3.23394i	0.156869	+	0.156869i
$426$		0			0
$427$	24.4649	−	10.1337i	1.18394	−	0.490403i
$428$		0			0
$429$	−10.8282	+	26.1417i	−0.522793	+	1.26213i
$430$		0			0
$431$		−	28.4989i		−	1.37274i	−0.727251	−	0.686372i	$-0.759202\pi$
$431$		−	28.4989i		−	1.37274i	0.727251	−	0.686372i	$-0.240798\pi$
$432$		0			0
$433$			16.9020i			0.812257i	0.913816	+	0.406128i	$0.133121\pi$
$433$			16.9020i			0.812257i	−0.913816	+	0.406128i	$0.866879\pi$
$434$		0			0
$435$	2.97091	−	7.17241i	0.142444	−	0.343891i
$436$		0			0
$437$	−5.53647	+	2.29328i	−0.264845	+	0.109703i
$438$		0			0
$439$	27.0558	+	27.0558i	1.29130	+	1.29130i	0.933980	+	0.357324i	$0.116311\pi$
$439$	27.0558	+	27.0558i	1.29130	+	1.29130i	0.357324	+	0.933980i	$0.383689\pi$
$440$		0			0
$441$	−14.9365	+	14.9365i	−0.711264	+	0.711264i
$442$		0			0
$443$	0.361235	+	0.872098i	0.0171628	+	0.0414346i	0.932229	−	0.361870i	$-0.117862\pi$
$443$	0.361235	+	0.872098i	0.0171628	+	0.0414346i	−0.915066	+	0.403305i	$0.867862\pi$
$444$		0			0
$445$	5.01108	+	2.07566i	0.237548	+	0.0983955i
$446$		0			0
$447$	−10.6746			−0.504891
$448$		0			0
$449$	5.90078			0.278475			0.139237	−	0.990259i	$-0.455535\pi$
$449$	5.90078			0.278475			0.139237	+	0.990259i	$0.455535\pi$
$450$		0			0
$451$	−23.6368	−	9.79070i	−1.11302	−	0.461026i
$452$		0			0
$453$	−7.74467	−	18.6973i	−0.363876	−	0.878475i
$454$		0			0
$455$	−4.60896	+	4.60896i	−0.216072	+	0.216072i
$456$		0			0
$457$	4.53279	+	4.53279i	0.212035	+	0.212035i	0.805131	−	0.593096i	$-0.202095\pi$
$457$	4.53279	+	4.53279i	0.212035	+	0.212035i	−0.593096	+	0.805131i	$0.702095\pi$
$458$		0			0
$459$	−69.7299	+	28.8831i	−3.25472	+	1.34815i
$460$		0			0
$461$	6.66348	−	16.0871i	0.310349	−	0.749249i	−0.689343	−	0.724435i	$-0.742101\pi$
$461$	6.66348	−	16.0871i	0.310349	−	0.749249i	0.999692	−	0.0248137i	$-0.00789927\pi$
$462$		0			0
$463$			27.2988i			1.26868i	0.773052	+	0.634342i	$0.218729\pi$
$463$			27.2988i			1.26868i	−0.773052	+	0.634342i	$0.781271\pi$
$464$		0			0
$465$		−	14.1753i		−	0.657365i
$466$		0			0
$467$	8.90983	−	21.5102i	0.412298	−	0.995375i	−0.572222	−	0.820099i	$-0.693918\pi$
$467$	8.90983	−	21.5102i	0.412298	−	0.995375i	0.984519	−	0.175276i	$-0.0560818\pi$
$468$		0			0
$469$	8.06197	−	3.33938i	0.372267	−	0.154198i
$470$		0			0
$471$	−32.0983	−	32.0983i	−1.47901	−	1.47901i
$472$		0			0
$473$	−12.2817	+	12.2817i	−0.564712	+	0.564712i
$474$		0			0
$475$	−0.489776	−	1.18242i	−0.0224725	−	0.0542533i
$476$		0			0
$477$	−31.1598	−	12.9068i	−1.42671	−	0.590962i
$478$		0			0
$479$	−12.3228			−0.563044			−0.281522	−	0.959555i	$-0.590839\pi$
$479$	−12.3228			−0.563044			−0.281522	+	0.959555i	$0.590839\pi$
$480$		0			0
$481$	−12.6596			−0.577230
$482$		0			0
$483$	−29.9073	−	12.3880i	−1.36083	−	0.563674i
$484$		0			0
$485$	6.72463	+	16.2347i	0.305350	+	0.737180i
$486$		0			0
$487$	−16.1714	+	16.1714i	−0.732797	+	0.732797i	−0.971173	−	0.238376i	$-0.923385\pi$
$487$	−16.1714	+	16.1714i	−0.732797	+	0.732797i	0.238376	+	0.971173i	$0.423385\pi$
$488$		0			0
$489$	38.1855	+	38.1855i	1.72681	+	1.72681i
$490$		0			0
$491$	7.15565	−	2.96397i	0.322930	−	0.133762i	−0.215329	−	0.976542i	$-0.569082\pi$
$491$	7.15565	−	2.96397i	0.322930	−	0.133762i	0.538259	+	0.842780i	$0.319082\pi$
$492$		0			0
$493$	−4.10044	+	9.89933i	−0.184674	+	0.445843i
$494$		0			0
$495$		−	21.8126i		−	0.980402i
$496$		0			0
$497$		−	30.9743i		−	1.38939i
$498$		0			0
$499$	−12.4657	+	30.0948i	−0.558040	+	1.34723i	0.353275	+	0.935519i	$0.385068\pi$
$499$	−12.4657	+	30.0948i	−0.558040	+	1.34723i	−0.911315	+	0.411709i	$0.864932\pi$
$500$		0			0
$501$	7.72532	−	3.19993i	0.345142	−	0.142962i
$502$		0			0
$503$	6.04193	+	6.04193i	0.269396	+	0.269396i	0.828857	−	0.559461i	$-0.188992\pi$
$503$	6.04193	+	6.04193i	0.269396	+	0.269396i	−0.559461	+	0.828857i	$0.688992\pi$
$504$		0			0
$505$	0.919652	−	0.919652i	0.0409240	−	0.0409240i
$506$		0			0
$507$	−4.10873	−	9.91934i	−0.182475	−	0.440533i
$508$		0			0
$509$	10.5215	+	4.35817i	0.466359	+	0.193172i	0.603474	−	0.797383i	$-0.293783\pi$
$509$	10.5215	+	4.35817i	0.466359	+	0.193172i	−0.137114	+	0.990555i	$0.543783\pi$
$510$		0			0
$511$	5.72908			0.253440
$512$		0			0
$513$	21.1210			0.932517
$514$		0			0
$515$	0.490404	+	0.203132i	0.0216098	+	0.00895107i
$516$		0			0
$517$	−9.39433	−	22.6799i	−0.413162	−	0.997462i
$518$		0			0
$519$	−15.3460	+	15.3460i	−0.673616	+	0.673616i
$520$		0			0
$521$	3.70345	+	3.70345i	0.162251	+	0.162251i	0.783563	−	0.621312i	$-0.213400\pi$
$521$	3.70345	+	3.70345i	0.162251	+	0.162251i	−0.621312	+	0.783563i	$0.713400\pi$
$522$		0			0
$523$	29.2716	−	12.1247i	1.27996	−	0.530176i	0.363980	−	0.931407i	$-0.381418\pi$
$523$	29.2716	−	12.1247i	1.27996	−	0.530176i	0.915977	+	0.401231i	$0.131418\pi$
$524$		0			0
$525$	2.64571	−	6.38730i	0.115468	−	0.278765i
$526$		0			0
$527$			19.5647i			0.852252i
$528$		0			0
$529$		−	1.07601i		−	0.0467832i
$530$		0			0
$531$	16.9214	−	40.8518i	0.734324	−	1.77282i
$532$		0			0
$533$	−27.0160	+	11.1904i	−1.17019	+	0.484710i
$534$		0			0
$535$	−0.162111	−	0.162111i	−0.00700869	−	0.00700869i
$536$		0			0
$537$	0.594404	−	0.594404i	0.0256504	−	0.0256504i
$538$		0			0
$539$	2.76872	+	6.68427i	0.119257	+	0.287912i
$540$		0			0
$541$	39.0693	+	16.1831i	1.67972	+	0.695764i	0.999313	−	0.0370683i	$-0.0118019\pi$
$541$	39.0693	+	16.1831i	1.67972	+	0.695764i	0.680410	+	0.732832i	$0.261802\pi$
$542$		0			0
$543$	−68.7247			−2.94926
$544$		0			0
$545$	3.41897			0.146452
$546$		0			0
$547$	24.3324	+	10.0788i	1.04038	+	0.430938i	0.836447	−	0.548047i	$-0.184629\pi$
$547$	24.3324	+	10.0788i	1.04038	+	0.430938i	0.203930	+	0.978986i	$0.434629\pi$
$548$		0			0
$549$	38.7604	+	93.5758i	1.65425	+	3.99372i
$550$		0			0
$551$	2.12025	−	2.12025i	0.0903256	−	0.0903256i
$552$		0			0
$553$	−7.27757	−	7.27757i	−0.309474	−	0.309474i
$554$		0			0
$555$	12.4057	−	5.13860i	0.526592	−	0.218121i
$556$		0			0
$557$	14.3980	−	34.7599i	0.610063	−	1.47282i	−0.252867	−	0.967501i	$-0.581374\pi$
$557$	14.3980	−	34.7599i	0.610063	−	1.47282i	0.862931	−	0.505322i	$-0.168626\pi$
$558$		0			0
$559$			19.8520i			0.839651i
$560$		0			0
$561$			41.4231i			1.74889i
$562$		0			0
$563$	12.7387	−	30.7541i	0.536874	−	1.29613i	−0.390020	−	0.920806i	$-0.627532\pi$
$563$	12.7387	−	30.7541i	0.536874	−	1.29613i	0.926894	−	0.375323i	$-0.122468\pi$
$564$		0			0
$565$	−12.9830	+	5.37775i	−0.546200	+	0.226243i
$566$		0			0
$567$	45.3562	+	45.3562i	1.90478	+	1.90478i
$568$		0			0
$569$	−2.83900	+	2.83900i	−0.119017	+	0.119017i	−0.764107	−	0.645090i	$-0.776820\pi$
$569$	−2.83900	+	2.83900i	−0.119017	+	0.119017i	0.645090	+	0.764107i	$0.276820\pi$
$570$		0			0
$571$	−5.19688	−	12.5464i	−0.217483	−	0.525050i	0.777054	−	0.629434i	$-0.216713\pi$
$571$	−5.19688	−	12.5464i	−0.217483	−	0.525050i	−0.994537	+	0.104384i	$0.966713\pi$
$572$		0			0
$573$	1.62479	+	0.673008i	0.0678764	+	0.0281153i
$574$		0			0
$575$	−4.68231			−0.195266
$576$		0			0
$577$	−7.59777			−0.316299			−0.158150	−	0.987415i	$-0.550553\pi$
$577$	−7.59777			−0.316299			−0.158150	+	0.987415i	$0.550553\pi$
$578$		0			0
$579$	12.4417	+	5.15353i	0.517060	+	0.214173i
$580$		0			0
$581$	6.48498	+	15.6561i	0.269042	+	0.649526i
$582$		0			0
$583$	−8.16842	+	8.16842i	−0.338301	+	0.338301i
$584$		0			0
$585$	−17.6288	−	17.6288i	−0.728863	−	0.728863i
$586$		0			0
$587$	−38.0128	+	15.7454i	−1.56896	+	0.649883i	−0.986616	−	0.163062i	$-0.947863\pi$
$587$	−38.0128	+	15.7454i	−1.56896	+	0.649883i	−0.582341	+	0.812945i	$0.697863\pi$
$588$		0			0
$589$	2.09519	−	5.05825i	0.0863310	−	0.208421i
$590$		0			0
$591$			34.7632i			1.42997i
$592$		0			0
$593$			20.6204i			0.846779i	0.905948	+	0.423390i	$0.139160\pi$
$593$			20.6204i			0.846779i	−0.905948	+	0.423390i	$0.860840\pi$
$594$		0			0
$595$	−3.65159	+	8.81572i	−0.149701	+	0.361409i
$596$		0			0
$597$	20.5024	−	8.49239i	0.839109	−	0.347570i
$598$		0			0
$599$	21.4760	+	21.4760i	0.877486	+	0.877486i	0.993274	−	0.115788i	$-0.0369393\pi$
$599$	21.4760	+	21.4760i	0.877486	+	0.877486i	−0.115788	+	0.993274i	$0.536939\pi$
$600$		0			0
$601$	23.9957	−	23.9957i	0.978804	−	0.978804i	−0.0209761	−	0.999780i	$-0.506677\pi$
$601$	23.9957	−	23.9957i	0.978804	−	0.978804i	0.999780	+	0.0209761i	$0.00667740\pi$
$602$		0			0
$603$	12.7728	+	30.8362i	0.520148	+	1.25575i
$604$		0			0
$605$	3.26034	+	1.35048i	0.132552	+	0.0549048i
$606$		0			0
$607$	32.5602			1.32158			0.660789	−	0.750572i	$-0.270222\pi$
$607$	32.5602			1.32158			0.660789	+	0.750572i	$0.270222\pi$
$608$		0			0
$609$	16.1974			0.656353
$610$		0			0
$611$	−25.9223	−	10.7374i	−1.04870	−	0.434387i
$612$		0			0
$613$	−12.2037	−	29.4624i	−0.492904	−	1.18997i	−0.953236	−	0.302228i	$-0.902270\pi$
$613$	−12.2037	−	29.4624i	−0.492904	−	1.18997i	0.460332	−	0.887747i	$-0.347730\pi$
$614$		0			0
$615$	21.9318	−	21.9318i	0.884377	−	0.884377i
$616$		0			0
$617$	26.9916	+	26.9916i	1.08664	+	1.08664i	0.995872	+	0.0907675i	$0.0289320\pi$
$617$	26.9916	+	26.9916i	1.08664	+	1.08664i	0.0907675	+	0.995872i	$0.471068\pi$
$618$		0			0
$619$	−6.82301	+	2.82618i	−0.274240	+	0.113594i	−0.515565	−	0.856850i	$-0.672418\pi$
$619$	−6.82301	+	2.82618i	−0.274240	+	0.113594i	0.241325	+	0.970444i	$0.422418\pi$
$620$		0			0
$621$	29.5704	−	71.3892i	1.18662	−	2.86475i
$622$		0			0
$623$			11.3165i			0.453386i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	4.43602	−	10.7095i	0.177158	−	0.427697i
$628$		0			0
$629$	−17.1223	+	7.09227i	−0.682709	+	0.282787i
$630$		0			0
$631$	32.2859	+	32.2859i	1.28528	+	1.28528i	0.937619	+	0.347663i	$0.113025\pi$
$631$	32.2859	+	32.2859i	1.28528	+	1.28528i	0.347663	+	0.937619i	$0.386975\pi$
$632$		0			0
$633$	16.9765	−	16.9765i	0.674755	−	0.674755i
$634$		0			0
$635$	−2.16615	−	5.22954i	−0.0859609	−	0.207528i
$636$		0			0
$637$	7.63987	+	3.16454i	0.302703	+	0.125384i
$638$		0			0
$639$	118.474			4.68675
$640$		0			0
$641$	42.0351			1.66029			0.830143	−	0.557550i	$-0.188259\pi$
$641$	42.0351			1.66029			0.830143	+	0.557550i	$0.188259\pi$
$642$		0			0
$643$	18.7880	+	7.78224i	0.740926	+	0.306902i	0.721033	−	0.692901i	$-0.243668\pi$
$643$	18.7880	+	7.78224i	0.740926	+	0.306902i	0.0198927	+	0.999802i	$0.493668\pi$
$644$		0			0
$645$	−8.05802	−	19.4538i	−0.317284	−	0.765992i
$646$		0			0
$647$	1.93936	−	1.93936i	0.0762441	−	0.0762441i	−0.667956	−	0.744200i	$-0.732831\pi$
$647$	1.93936	−	1.93936i	0.0762441	−	0.0762441i	0.744200	+	0.667956i	$0.232831\pi$
$648$		0			0
$649$	−10.7091	−	10.7091i	−0.420370	−	0.420370i
$650$		0			0
$651$	27.3240	−	11.3180i	1.07091	−	0.443586i
$652$		0			0
$653$	−17.0389	+	41.1356i	−0.666785	+	1.60976i	0.120172	+	0.992753i	$0.461655\pi$
$653$	−17.0389	+	41.1356i	−0.666785	+	1.60976i	−0.786957	+	0.617008i	$0.788345\pi$
$654$		0			0
$655$			12.4815i			0.487691i
$656$		0			0
$657$			21.9132i			0.854914i
$658$		0			0
$659$	5.13071	−	12.3866i	0.199864	−	0.482515i	−0.791891	−	0.610663i	$-0.790903\pi$
$659$	5.13071	−	12.3866i	0.199864	−	0.482515i	0.991755	+	0.128148i	$0.0409032\pi$
$660$		0			0
$661$	−19.4037	+	8.03726i	−0.754715	+	0.312613i	−0.726664	−	0.686993i	$-0.758930\pi$
$661$	−19.4037	+	8.03726i	−0.754715	+	0.312613i	−0.0280514	+	0.999606i	$0.508930\pi$
$662$		0			0
$663$	33.4780	+	33.4780i	1.30018	+	1.30018i
$664$		0			0
$665$	1.88816	−	1.88816i	0.0732197	−	0.0732197i
$666$		0			0
$667$	−4.19801	−	10.1349i	−0.162547	−	0.392424i
$668$		0			0
$669$	−33.3702	−	13.8224i	−1.29017	−	0.534405i
$670$		0			0
$671$	34.6914			1.33925
$672$		0			0
$673$	40.0043			1.54205			0.771026	−	0.636804i	$-0.219744\pi$
$673$	40.0043			1.54205			0.771026	+	0.636804i	$0.219744\pi$
$674$		0			0
$675$	15.2466	+	6.31534i	0.586842	+	0.243078i
$676$		0			0
$677$	−10.3188	−	24.9119i	−0.396585	−	0.957441i	−0.988470	−	0.151418i	$-0.951616\pi$
$677$	−10.3188	−	24.9119i	−0.396585	−	0.957441i	0.591885	−	0.806022i	$-0.298384\pi$
$678$		0			0
$679$	−25.9245	+	25.9245i	−0.994890	+	0.994890i
$680$		0			0
$681$	−4.17651	−	4.17651i	−0.160044	−	0.160044i
$682$		0			0
$683$	7.35740	−	3.04753i	0.281523	−	0.116611i	−0.237454	−	0.971399i	$-0.576313\pi$
$683$	7.35740	−	3.04753i	0.281523	−	0.116611i	0.518977	+	0.854788i	$0.326313\pi$
$684$		0			0
$685$	−2.62206	+	6.33020i	−0.100184	+	0.241865i
$686$		0			0
$687$		−	37.6735i		−	1.43733i
$688$		0			0
$689$			13.2034i			0.503009i
$690$		0			0
$691$	15.7665	−	38.0637i	0.599785	−	1.44801i	−0.274015	−	0.961725i	$-0.588352\pi$
$691$	15.7665	−	38.0637i	0.599785	−	1.44801i	0.873800	−	0.486285i	$-0.161648\pi$
$692$		0			0
$693$	42.0454	−	17.4158i	1.59717	−	0.661570i
$694$		0			0
$695$	−5.55212	−	5.55212i	−0.210604	−	0.210604i
$696$		0			0
$697$	−30.2702	+	30.2702i	−1.14657	+	1.14657i
$698$		0			0
$699$	−1.42062	−	3.42967i	−0.0537327	−	0.129722i
$700$		0			0
$701$	−34.7510	−	14.3943i	−1.31253	−	0.543667i	−0.386907	−	0.922119i	$-0.626457\pi$
$701$	−34.7510	−	14.3943i	−1.31253	−	0.543667i	−0.925621	+	0.378452i	$0.876457\pi$
$702$		0			0
$703$	5.18629			0.195605
$704$		0			0
$705$	29.7606			1.12085
$706$		0			0
$707$	2.50698	+	1.03842i	0.0942845	+	0.0390539i
$708$		0			0
$709$	−17.0450	−	41.1502i	−0.640137	−	1.54543i	−0.826494	−	0.562946i	$-0.809668\pi$
$709$	−17.0450	−	41.1502i	−0.640137	−	1.54543i	0.186356	−	0.982482i	$-0.440332\pi$
$710$		0			0
$711$	27.8360	−	27.8360i	1.04393	−	1.04393i
$712$		0			0
$713$	−14.1635	−	14.1635i	−0.530429	−	0.530429i
$714$		0			0
$715$	−7.88911	+	3.26777i	−0.295036	+	0.122208i
$716$		0			0
$717$	−36.7203	+	88.6506i	−1.37134	+	3.31072i
$718$		0			0
$719$		−	28.8010i		−	1.07410i	−0.843551	−	0.537048i	$-0.819539\pi$
$719$		−	28.8010i		−	1.07410i	0.843551	−	0.537048i	$-0.180461\pi$
$720$		0			0
$721$			1.10748i			0.0412446i
$722$		0			0
$723$	−29.9950	+	72.4144i	−1.11553	+	2.69312i
$724$		0			0
$725$	2.16451	−	0.896568i	0.0803878	−	0.0332977i
$726$		0			0
$727$	−21.6039	−	21.6039i	−0.801246	−	0.801246i	0.182045	−	0.983290i	$-0.441728\pi$
$727$	−21.6039	−	21.6039i	−0.801246	−	0.801246i	−0.983290	+	0.182045i	$0.941728\pi$
$728$		0			0
$729$	−57.4799	+	57.4799i	−2.12889	+	2.12889i
$730$		0			0
$731$	11.1216	+	26.8500i	0.411349	+	0.993084i
$732$		0			0
$733$	−23.6540	−	9.79783i	−0.873682	−	0.361891i	−0.0996388	−	0.995024i	$-0.531769\pi$
$733$	−23.6540	−	9.79783i	−0.873682	−	0.361891i	−0.774043	+	0.633133i	$0.781769\pi$
$734$		0			0
$735$	−8.77111			−0.323527
$736$		0			0
$737$	11.4319			0.421101
$738$		0			0
$739$	−21.5114	−	8.91033i	−0.791311	−	0.327772i	−0.0498403	−	0.998757i	$-0.515871\pi$
$739$	−21.5114	−	8.91033i	−0.791311	−	0.327772i	−0.741470	+	0.670986i	$0.765871\pi$
$740$		0			0
$741$	−5.07021	−	12.2406i	−0.186259	−	0.449668i
$742$		0			0
$743$	−2.00383	+	2.00383i	−0.0735133	+	0.0735133i	−0.742907	−	0.669394i	$-0.766554\pi$
$743$	−2.00383	+	2.00383i	−0.0735133	+	0.0735133i	0.669394	+	0.742907i	$0.266554\pi$
$744$		0			0
$745$	−2.27788	−	2.27788i	−0.0834549	−	0.0834549i
$746$		0			0
$747$	−59.8832	+	24.8044i	−2.19101	+	0.907547i
$748$		0			0
$749$	0.183048	−	0.441916i	0.00668842	−	0.0161473i
$750$		0			0
$751$			20.6825i			0.754716i	0.926067	+	0.377358i	$0.123167\pi$
$751$			20.6825i			0.754716i	−0.926067	+	0.377358i	$0.876833\pi$
$752$		0			0
$753$			17.3715i			0.633054i
$754$		0			0
$755$	2.33721	−	5.64251i	0.0850596	−	0.205352i
$756$		0			0
$757$	27.9158	−	11.5631i	1.01462	−	0.420269i	0.187481	−	0.982268i	$-0.439968\pi$
$757$	27.9158	−	11.5631i	1.01462	−	0.420269i	0.827137	+	0.562000i	$0.189968\pi$
$758$		0			0
$759$	−29.9876	−	29.9876i	−1.08848	−	1.08848i
$760$		0			0
$761$	−9.32439	+	9.32439i	−0.338009	+	0.338009i	−0.855617	−	0.517609i	$-0.826822\pi$
$761$	−9.32439	+	9.32439i	−0.338009	+	0.338009i	0.517609	+	0.855617i	$0.326822\pi$
$762$		0			0
$763$	2.72980	+	6.59031i	0.0988253	+	0.238585i
$764$		0			0
$765$	−33.7193	−	13.9670i	−1.21912	−	0.504978i
$766$		0			0
$767$	−17.3102			−0.625034
$768$		0			0
$769$	−39.0551			−1.40836			−0.704181	−	0.710021i	$-0.748686\pi$
$769$	−39.0551			−1.40836			−0.704181	+	0.710021i	$0.748686\pi$
$770$		0			0
$771$	−90.7593	−	37.5937i	−3.26862	−	1.35391i
$772$		0			0
$773$	18.0571	+	43.5936i	0.649467	+	1.56795i	0.813543	+	0.581505i	$0.197536\pi$
$773$	18.0571	+	43.5936i	0.649467	+	1.56795i	−0.164075	+	0.986448i	$0.552464\pi$
$774$		0			0
$775$	3.02491	−	3.02491i	0.108658	−	0.108658i
$776$		0			0
$777$	19.8101	+	19.8101i	0.710683	+	0.710683i
$778$		0			0
$779$	11.0677	−	4.58439i	0.396541	−	0.164253i
$780$		0			0
$781$	15.5287	−	37.4897i	0.555661	−	1.34149i
$782$		0			0
$783$			38.6635i			1.38172i
$784$		0			0
$785$		−	13.6991i		−	0.488940i
$786$		0			0
$787$	3.51905	−	8.49574i	0.125441	−	0.302841i	−0.848666	−	0.528929i	$-0.822594\pi$
$787$	3.51905	−	8.49574i	0.125441	−	0.302841i	0.974107	+	0.226088i	$0.0725938\pi$
$788$		0			0
$789$	68.9020	−	28.5401i	2.45297	−	1.01606i
$790$		0			0
$791$	−20.7320	−	20.7320i	−0.737146	−	0.737146i
$792$		0			0
$793$	28.0375	−	28.0375i	0.995640	−	0.995640i
$794$		0			0
$795$	−5.35931	−	12.9385i	−0.190075	−	0.458882i
$796$		0			0
$797$	−21.8462	−	9.04899i	−0.773832	−	0.320532i	−0.0394086	−	0.999223i	$-0.512547\pi$
$797$	−21.8462	−	9.04899i	−0.773832	−	0.320532i	−0.734424	+	0.678691i	$0.762547\pi$
$798$		0			0
$799$	−41.0755			−1.45315
$800$		0			0
$801$	−43.2845			−1.52938
$802$		0			0
$803$	6.93417	+	2.87223i	0.244701	+	0.101359i
$804$		0			0
$805$	−3.73848	−	9.02550i	−0.131764	−	0.318107i
$806$		0			0
$807$	−4.39783	+	4.39783i	−0.154811	+	0.154811i
$808$		0			0
$809$	25.1351	+	25.1351i	0.883704	+	0.883704i	0.993909	−	0.110205i	$-0.0351508\pi$
$809$	25.1351	+	25.1351i	0.883704	+	0.883704i	−0.110205	+	0.993909i	$0.535151\pi$
$810$		0			0
$811$	6.52290	−	2.70187i	0.229050	−	0.0948756i	−0.265207	−	0.964192i	$-0.585440\pi$
$811$	6.52290	−	2.70187i	0.229050	−	0.0948756i	0.494257	+	0.869316i	$0.335440\pi$
$812$		0			0
$813$	−4.87035	+	11.7581i	−0.170811	+	0.412374i
$814$		0			0
$815$			16.2970i			0.570859i
$816$		0			0
$817$		−	8.13281i		−	0.284531i
$818$		0			0
$819$	19.9056	−	48.0563i	0.695557	−	1.67922i
$820$		0			0
$821$	−22.0871	+	9.14877i	−0.770845	+	0.319294i	−0.733215	−	0.679997i	$-0.761981\pi$
$821$	−22.0871	+	9.14877i	−0.770845	+	0.319294i	−0.0376302	+	0.999292i	$0.511981\pi$
$822$		0			0
$823$	−22.8283	−	22.8283i	−0.795744	−	0.795744i	0.186677	−	0.982421i	$-0.440228\pi$
$823$	−22.8283	−	22.8283i	−0.795744	−	0.795744i	−0.982421	+	0.186677i	$0.940228\pi$
$824$		0			0
$825$	6.40444	−	6.40444i	0.222974	−	0.222974i
$826$		0			0
$827$	8.71493	+	21.0397i	0.303048	+	0.731622i	0.999896	+	0.0144036i	$0.00458496\pi$
$827$	8.71493	+	21.0397i	0.303048	+	0.731622i	−0.696849	+	0.717218i	$0.745415\pi$
$828$		0			0
$829$	−42.4750	−	17.5937i	−1.47522	−	0.611056i	−0.507176	−	0.861842i	$-0.669311\pi$
$829$	−42.4750	−	17.5937i	−1.47522	−	0.611056i	−0.968042	+	0.250787i	$0.919311\pi$
$830$		0			0
$831$	36.5118			1.26658
$832$		0			0
$833$	12.1058			0.419443
$834$		0			0
$835$	2.33137	+	0.965683i	0.0806802	+	0.0334189i
$836$		0			0
$837$	27.0162	+	65.2228i	0.933816	+	2.25443i
$838$		0			0
$839$	−6.48396	+	6.48396i	−0.223851	+	0.223851i	−0.810118	−	0.586267i	$-0.800597\pi$
$839$	−6.48396	+	6.48396i	−0.223851	+	0.223851i	0.586267	+	0.810118i	$0.300597\pi$
$840$		0			0
$841$	−16.6248	−	16.6248i	−0.573270	−	0.573270i
$842$		0			0
$843$	−52.0028	+	21.5403i	−1.79107	+	0.741886i
$844$		0			0
$845$	1.23994	−	2.99348i	0.0426553	−	0.102979i
$846$		0			0
$847$			7.36282i			0.252990i
$848$		0			0
$849$		−	35.3616i		−	1.21361i
$850$		0			0
$851$	7.26103	−	17.5297i	0.248905	−	0.600910i
$852$		0			0
$853$	48.1414	−	19.9408i	1.64833	−	0.682761i	0.651233	−	0.758878i	$-0.274252\pi$
$853$	48.1414	−	19.9408i	1.64833	−	0.682761i	0.997099	+	0.0761168i	$0.0242522\pi$
$854$		0			0
$855$	7.22203	+	7.22203i	0.246988	+	0.246988i
$856$		0			0
$857$	−19.0666	+	19.0666i	−0.651301	+	0.651301i	−0.953306	−	0.302005i	$-0.902344\pi$
$857$	−19.0666	+	19.0666i	−0.651301	+	0.651301i	0.302005	+	0.953306i	$0.402344\pi$
$858$		0			0
$859$	−13.0225	−	31.4392i	−0.444323	−	1.07269i	−0.974416	−	0.224751i	$-0.927843\pi$
$859$	−13.0225	−	31.4392i	−0.444323	−	1.07269i	0.530093	−	0.847939i	$-0.322157\pi$
$860$		0			0
$861$	59.7863	+	24.7643i	2.03751	+	0.843965i
$862$		0			0
$863$	−36.9753			−1.25866			−0.629328	−	0.777140i	$-0.716670\pi$
$863$	−36.9753			−1.25866			−0.629328	+	0.777140i	$0.716670\pi$
$864$		0			0
$865$	−6.54945			−0.222688
$866$		0			0
$867$	11.9906	+	4.96668i	0.407223	+	0.168677i
$868$		0			0
$869$	−5.15983	−	12.4569i	−0.175035	−	0.422573i
$870$		0			0
$871$	9.23925	−	9.23925i	0.313060	−	0.313060i
$872$		0			0
$873$	−99.1586	−	99.1586i	−3.35601	−	3.35601i
$874$		0			0
$875$	1.92758	−	0.798428i	0.0651639	−	0.0269918i
$876$		0			0
$877$	2.46912	−	5.96098i	0.0833762	−	0.201288i	−0.876693	−	0.481050i	$-0.840256\pi$
$877$	2.46912	−	5.96098i	0.0833762	−	0.201288i	0.960069	+	0.279762i	$0.0902555\pi$
$878$		0			0
$879$		−	15.3521i		−	0.517813i
$880$		0			0
$881$		−	0.524770i		−	0.0176800i	−0.999961	−	0.00883998i	$-0.997186\pi$
$881$		−	0.524770i		−	0.0176800i	0.999961	−	0.00883998i	$-0.00281389\pi$
$882$		0			0
$883$	5.83067	−	14.0765i	0.196218	−	0.473712i	−0.794893	−	0.606749i	$-0.792473\pi$
$883$	5.83067	−	14.0765i	0.196218	−	0.473712i	0.991111	+	0.133038i	$0.0424731\pi$
$884$		0			0
$885$	16.9629	−	7.02627i	0.570202	−	0.236185i
$886$		0			0
$887$	−19.7246	−	19.7246i	−0.662287	−	0.662287i	0.293632	−	0.955919i	$-0.405136\pi$
$887$	−19.7246	−	19.7246i	−0.662287	−	0.662287i	−0.955919	+	0.293632i	$0.905136\pi$
$888$		0			0
$889$	8.35082	−	8.35082i	0.280078	−	0.280078i
$890$		0			0
$891$	32.1577	+	77.6356i	1.07732	+	2.60089i
$892$		0			0
$893$	10.6196	+	4.39879i	0.355372	+	0.147200i
$894$		0			0
$895$	0.253683			0.00847968
$896$		0			0
$897$	−48.4717			−1.61842
$898$		0			0
$899$	9.25947	+	3.83540i	0.308821	+	0.127918i
$900$		0			0
$901$	7.39689	+	17.8577i	0.246426	+	0.594925i
$902$		0			0
$903$	31.0649	−	31.0649i	1.03377	−	1.03377i
$904$		0			0
$905$	−14.6653	−	14.6653i	−0.487492	−	0.487492i
$906$		0			0
$907$	36.7507	−	15.2226i	1.22029	−	0.505459i	0.322786	−	0.946472i	$-0.395381\pi$
$907$	36.7507	−	15.2226i	1.22029	−	0.505459i	0.897501	+	0.441013i	$0.145381\pi$
$908$		0			0
$909$	−3.97187	+	9.58894i	−0.131739	+	0.318045i
$910$		0			0
$911$		−	7.60256i		−	0.251884i	−0.992038	−	0.125942i	$-0.959805\pi$
$911$		−	7.60256i		−	0.251884i	0.992038	−	0.125942i	$-0.0401953\pi$
$912$		0			0
$913$			22.2005i			0.734730i
$914$		0			0
$915$	−16.0945	+	38.8556i	−0.532068	+	1.28453i
$916$		0			0
$917$	−24.0590	+	9.96555i	−0.794497	+	0.329091i
$918$		0			0
$919$	−29.6127	−	29.6127i	−0.976832	−	0.976832i	0.0229057	−	0.999738i	$-0.492708\pi$
$919$	−29.6127	−	29.6127i	−0.976832	−	0.976832i	−0.999738	+	0.0229057i	$0.992708\pi$
$920$		0			0
$921$	13.1429	−	13.1429i	0.433075	−	0.433075i
$922$		0			0
$923$	−17.7488	−	42.8493i	−0.584207	−	1.41040i
$924$		0			0
$925$	3.74382	+	1.55074i	0.123096	+	0.0509880i
$926$		0			0
$927$	−4.23600			−0.139128
$928$		0			0
$929$	34.4092			1.12893			0.564465	−	0.825457i	$-0.309083\pi$
$929$	34.4092			1.12893			0.564465	+	0.825457i	$0.309083\pi$
$930$		0			0
$931$	−3.12984	−	1.29642i	−0.102576	−	0.0424885i
$932$		0			0
$933$	−36.8515	−	88.9673i	−1.20646	−	2.91266i
$934$		0			0
$935$	−8.83938	+	8.83938i	−0.289079	+	0.289079i
$936$		0			0
$937$	28.2238	+	28.2238i	0.922030	+	0.922030i	0.997173	−	0.0751430i	$-0.0239413\pi$
$937$	28.2238	+	28.2238i	0.922030	+	0.922030i	−0.0751430	+	0.997173i	$0.523941\pi$
$938$		0			0
$939$	38.9977	−	16.1534i	1.27264	−	0.527146i
$940$		0			0
$941$	−13.3194	+	32.1558i	−0.434199	+	1.04825i	0.543720	+	0.839267i	$0.317015\pi$
$941$	−13.3194	+	32.1558i	−0.434199	+	1.04825i	−0.977919	+	0.208983i	$0.932985\pi$
$942$		0			0
$943$		−	43.8272i		−	1.42721i
$944$		0			0
$945$			34.4313i			1.12005i
$946$		0			0
$947$	3.93030	−	9.48859i	0.127718	−	0.308338i	−0.847067	−	0.531487i	$-0.821634\pi$
$947$	3.93030	−	9.48859i	0.127718	−	0.308338i	0.974784	+	0.223149i	$0.0716336\pi$
$948$		0			0
$949$	7.92549	−	3.28285i	0.257272	−	0.106566i
$950$		0			0
$951$	−63.6033	−	63.6033i	−2.06248	−	2.06248i
$952$		0			0
$953$	−37.4848	+	37.4848i	−1.21425	+	1.21425i	−0.244639	+	0.969614i	$0.578669\pi$
$953$	−37.4848	+	37.4848i	−1.21425	+	1.21425i	−0.969614	+	0.244639i	$0.921331\pi$
$954$		0			0
$955$	0.203102	+	0.490332i	0.00657223	+	0.0158668i
$956$		0			0
$957$	19.6045	+	8.12044i	0.633723	+	0.262497i
$958$		0			0
$959$	−14.2955			−0.461625
$960$		0			0
$961$	−12.6999			−0.409674
$962$		0			0
$963$	1.69029	+	0.700140i	0.0544687	+	0.0225617i
$964$		0			0
$965$	1.55524	+	3.75469i	0.0500651	+	0.120868i
$966$		0			0
$967$	−15.9858	+	15.9858i	−0.514070	+	0.514070i	−0.915771	−	0.401701i	$-0.868419\pi$
$967$	−15.9858	+	15.9858i	−0.514070	+	0.514070i	0.401701	+	0.915771i	$0.368419\pi$
$968$		0			0
$969$	−13.7150	−	13.7150i	−0.440589	−	0.440589i
$970$		0			0
$971$	−46.7311	+	19.3566i	−1.49967	+	0.621184i	−0.973396	−	0.229130i	$-0.926412\pi$
$971$	−46.7311	+	19.3566i	−1.49967	+	0.621184i	−0.526276	+	0.850314i	$0.676412\pi$
$972$		0			0
$973$	6.26916	−	15.1351i	0.200980	−	0.485209i
$974$		0			0
$975$		−	10.3521i		−	0.331532i
$976$		0			0
$977$			13.5700i			0.434144i	0.976156	+	0.217072i	$0.0696506\pi$
$977$			13.5700i			0.434144i	−0.976156	+	0.217072i	$0.930349\pi$
$978$		0			0
$979$	−5.67343	+	13.6969i	−0.181324	+	0.437754i
$980$		0			0
$981$	−25.2073	+	10.4412i	−0.804808	+	0.333362i
$982$		0			0
$983$	30.4791	+	30.4791i	0.972134	+	0.972134i	0.999622	−	0.0274882i	$-0.00875087\pi$
$983$	30.4791	+	30.4791i	0.972134	+	0.972134i	−0.0274882	+	0.999622i	$0.508751\pi$
$984$		0			0
$985$	−7.41820	+	7.41820i	−0.236364	+	0.236364i
$986$		0			0
$987$	23.7617	+	57.3659i	0.756344	+	1.82598i
$988$		0			0
$989$	−27.4889	−	11.3863i	−0.874097	−	0.362063i
$990$		0			0
$991$	−4.79075			−0.152183			−0.0760916	−	0.997101i	$-0.524244\pi$
$991$	−4.79075			−0.152183			−0.0760916	+	0.997101i	$0.524244\pi$
$992$		0			0
$993$	−7.30986			−0.231971
$994$		0			0
$995$	6.18728	+	2.56285i	0.196150	+	0.0812479i
$996$		0			0
$997$	13.7912	+	33.2948i	0.436770	+	1.05446i	0.977057	+	0.212976i	$0.0683157\pi$
$997$	13.7912	+	33.2948i	0.436770	+	1.05446i	−0.540287	+	0.841481i	$0.681684\pi$
$998$		0			0
$999$	−47.2870	+	47.2870i	−1.49609	+	1.49609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.x.a.81.1		64
4.3	odd	2		160.2.x.a.61.8	yes	64
20.3	even	4		800.2.ba.e.349.14		64
20.7	even	4		800.2.ba.g.349.3		64
20.19	odd	2		800.2.y.c.701.9		64
32.11	odd	8		160.2.x.a.21.8	✓	64
32.21	even	8	inner	640.2.x.a.561.1		64
160.43	even	8		800.2.ba.g.149.3		64
160.107	even	8		800.2.ba.e.149.14		64
160.139	odd	8		800.2.y.c.501.9		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.x.a.21.8	✓	64	32.11	odd	8
160.2.x.a.61.8	yes	64	4.3	odd	2
640.2.x.a.81.1		64	1.1	even	1	trivial
640.2.x.a.561.1		64	32.21	even	8	inner
800.2.y.c.501.9		64	160.139	odd	8
800.2.y.c.701.9		64	20.19	odd	2
800.2.ba.e.149.14		64	160.107	even	8
800.2.ba.e.349.14		64	20.3	even	4
800.2.ba.g.149.3		64	160.43	even	8
800.2.ba.g.349.3		64	20.7	even	4

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.06141 - 1.26808i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(1.47530 - 1.47530i) q^{7} +(5.64289 + 5.64289i) q^{9} +O(q^{10})\)	\(q+(-3.06141 - 1.26808i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(1.47530 - 1.47530i) q^{7} +(5.64289 + 5.64289i) q^{9} +(2.52526 - 1.04600i) q^{11} +(1.19553 - 2.88627i) q^{13} +3.31365i q^{15} -4.57348i q^{17} +(-0.489776 + 1.18242i) q^{19} +(-6.38730 + 2.64571i) q^{21} +(3.31089 + 3.31089i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-6.31534 - 15.2466i) q^{27} +(-2.16451 - 0.896568i) q^{29} -4.27786 q^{31} -9.05725 q^{33} +(-1.92758 - 0.798428i) q^{35} +(-1.55074 - 3.74382i) q^{37} +(-7.32004 + 7.32004i) q^{39} +(-6.61864 - 6.61864i) q^{41} +(-5.87081 + 2.43177i) q^{43} +(3.05391 - 7.37279i) q^{45} -8.98123i q^{47} +2.64697i q^{49} +(-5.79952 + 14.0013i) q^{51} +(-3.90461 + 1.61734i) q^{53} +(-1.93275 - 1.93275i) q^{55} +(2.99881 - 2.99881i) q^{57} +(-2.12040 - 5.11911i) q^{59} +(11.7259 + 4.85704i) q^{61} +16.6499 q^{63} -3.12408 q^{65} +(3.86407 + 1.60055i) q^{67} +(-5.93753 - 14.3345i) q^{69} +(10.4976 - 10.4976i) q^{71} +(1.94166 + 1.94166i) q^{73} +(3.06141 - 1.26808i) q^{75} +(2.18236 - 5.26868i) q^{77} -4.93294i q^{79} +30.7437i q^{81} +(-3.10823 + 7.50393i) q^{83} +(-4.22534 + 1.75019i) q^{85} +(5.48953 + 5.48953i) q^{87} +(-3.83531 + 3.83531i) q^{89} +(-2.49435 - 6.02190i) q^{91} +(13.0963 + 5.42466i) q^{93} +1.27985 q^{95} -17.5723 q^{97} +(20.1522 + 8.34731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) \) 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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