LMFDB - Embedded newform 832.2.w.i.257.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [832,2,Mod(257,832)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("832.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(832, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,0,0,0,6,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.1
Root			$0.560908 + 1.63871i$ of defining polynomial
Character	$\chi$	$=$	832.257
Dual form			832.2.w.i.641.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13871 - 1.97231i) q^{3} +1.12182i q^{5} +(2.26053 + 1.30512i) q^{7} +(-1.09334 + 1.89372i) q^{9} +(2.26053 - 1.30512i) q^{11} +(-3.30591 + 1.43909i) q^{13} +(2.21257 - 1.27743i) q^{15} +(-2.77743 + 4.81064i) q^{17} +(6.88024 + 3.97231i) q^{19} -5.94462i q^{21} +(1.13871 + 1.97231i) q^{23} +3.74153 q^{25} -1.85229 q^{27} +(3.89924 + 6.75369i) q^{29} -8.26259i q^{31} +(-5.14819 - 2.97231i) q^{33} +(-1.46410 + 2.53590i) q^{35} +(-3.11971 + 1.80117i) q^{37} +(6.60282 + 4.88156i) q^{39} +(4.96410 - 2.86603i) q^{41} +(2.01690 - 3.49337i) q^{43} +(-2.12440 - 1.22652i) q^{45} -2.66562i q^{47} +(-0.0933372 - 0.161665i) q^{49} +12.6508 q^{51} +9.54002 q^{53} +(1.46410 + 2.53590i) q^{55} -18.0933i q^{57} +(3.31749 + 1.91535i) q^{59} +(3.84229 - 6.65503i) q^{61} +(-4.94304 + 2.85387i) q^{63} +(-1.61440 - 3.70862i) q^{65} +(-1.52690 + 0.881557i) q^{67} +(2.59334 - 4.49179i) q^{69} +(-0.880242 - 0.508208i) q^{71} +0.323330i q^{73} +(-4.26053 - 7.37945i) q^{75} +6.81333 q^{77} +2.66877 q^{79} +(5.38924 + 9.33444i) q^{81} -2.77953i q^{83} +(-5.39666 - 3.11576i) q^{85} +(8.88024 - 15.3810i) q^{87} +(-9.99531 + 5.77080i) q^{89} +(-9.35128 - 1.06149i) q^{91} +(-16.2964 + 9.40872i) q^{93} +(-4.45620 + 7.71837i) q^{95} +(13.5553 + 7.82618i) q^{97} +5.70773i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{19} - 2 q^{23} - 20 q^{25} - 28 q^{27} + 8 q^{29} + 6 q^{33} + 16 q^{35} + 24 q^{37} + 14 q^{39} + 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49}+ \cdots + 30 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^19 - 2 * q^23 - 20 * q^25 - 28 * q^27 + 8 * q^29 + 6 * q^33 + 16 * q^35 + 24 * q^37 + 14 * q^39 + 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 - 20 * q^53 - 16 * q^55 + 18 * q^59 + 4 * q^61 - 36 * q^63 + 14 * q^65 - 42 * q^67 + 18 * q^69 + 54 * q^71 - 22 * q^75 + 60 * q^77 - 16 * q^79 - 20 * q^81 - 6 * q^85 + 10 * q^87 - 18 * q^89 - 46 * q^91 - 36 * q^93 - 16 * q^95 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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
$3$	−1.13871	−	1.97231i	−0.657437	−	1.13871i	−0.981277	−	0.192602i	$-0.938307\pi$
$3$	−1.13871	−	1.97231i	−0.657437	−	1.13871i	0.323840	−	0.946112i	$-0.395026\pi$
$4$		0			0
$5$			1.12182i			0.501691i	0.968027	+	0.250846i	$0.0807087\pi$
$5$			1.12182i			0.501691i	−0.968027	+	0.250846i	$0.919291\pi$
$6$		0			0
$7$	2.26053	+	1.30512i	0.854400	+	0.493288i	0.862133	−	0.506682i	$-0.169128\pi$
$7$	2.26053	+	1.30512i	0.854400	+	0.493288i	−0.00773308	+	0.999970i	$0.502462\pi$
$8$		0			0
$9$	−1.09334	+	1.89372i	−0.364446	+	0.631239i
$10$		0			0
$11$	2.26053	−	1.30512i	0.681575	−	0.393508i	−0.118873	−	0.992909i	$-0.537928\pi$
$11$	2.26053	−	1.30512i	0.681575	−	0.393508i	0.800448	+	0.599402i	$0.204595\pi$
$12$		0			0
$13$	−3.30591	+	1.43909i	−0.916893	+	0.399132i
$13$	−3.30591	+	1.43909i	−0.916893	+	0.399132i
$14$		0			0
$15$	2.21257	−	1.27743i	0.571283	−	0.329830i
$16$		0			0
$17$	−2.77743	+	4.81064i	−0.673625	+	1.16675i	0.303244	+	0.952913i	$0.401930\pi$
$17$	−2.77743	+	4.81064i	−0.673625	+	1.16675i	−0.976869	+	0.213840i	$0.931403\pi$
$18$		0			0
$19$	6.88024	+	3.97231i	1.57844	+	0.911310i	0.995078	+	0.0990951i	$0.0315948\pi$
$19$	6.88024	+	3.97231i	1.57844	+	0.911310i	0.583358	+	0.812215i	$0.301739\pi$
$20$		0			0
$21$		−	5.94462i		−	1.29722i
$22$		0			0
$23$	1.13871	+	1.97231i	0.237438	+	0.411255i	0.959978	−	0.280074i	$-0.0903589\pi$
$23$	1.13871	+	1.97231i	0.237438	+	0.411255i	−0.722540	+	0.691329i	$0.757026\pi$
$24$		0			0
$25$	3.74153			0.748306
$26$		0			0
$27$	−1.85229			−0.356473
$28$		0			0
$29$	3.89924	+	6.75369i	0.724071	+	1.25413i	0.959355	+	0.282202i	$0.0910647\pi$
$29$	3.89924	+	6.75369i	0.724071	+	1.25413i	−0.235284	+	0.971927i	$0.575602\pi$
$30$		0			0
$31$		−	8.26259i		−	1.48400i	−0.670397	−	0.742002i	$-0.733876\pi$
$31$		−	8.26259i		−	1.48400i	0.670397	−	0.742002i	$-0.266124\pi$
$32$		0			0
$33$	−5.14819	−	2.97231i	−0.896185	−	0.517413i
$34$		0			0
$35$	−1.46410	+	2.53590i	−0.247478	+	0.428645i
$36$		0			0
$37$	−3.11971	+	1.80117i	−0.512878	+	0.296110i	−0.734016	−	0.679132i	$-0.762356\pi$
$37$	−3.11971	+	1.80117i	−0.512878	+	0.296110i	0.221138	+	0.975243i	$0.429023\pi$
$38$		0			0
$39$	6.60282	+	4.88156i	1.05730	+	0.781675i
$40$		0			0
$41$	4.96410	−	2.86603i	0.775262	−	0.447598i	−0.0594862	−	0.998229i	$-0.518946\pi$
$41$	4.96410	−	2.86603i	0.775262	−	0.447598i	0.834749	+	0.550631i	$0.185613\pi$
$42$		0			0
$43$	2.01690	−	3.49337i	0.307574	−	0.532734i	−0.670257	−	0.742129i	$-0.733816\pi$
$43$	2.01690	−	3.49337i	0.307574	−	0.532734i	0.977831	+	0.209395i	$0.0671495\pi$
$44$		0			0
$45$	−2.12440	−	1.22652i	−0.316687	−	0.182839i
$46$		0			0
$47$		−	2.66562i		−	0.388820i	−0.980920	−	0.194410i	$-0.937721\pi$
$47$		−	2.66562i		−	0.388820i	0.980920	−	0.194410i	$-0.0622792\pi$
$48$		0			0
$49$	−0.0933372	−	0.161665i	−0.0133339	−	0.0230950i
$50$		0			0
$51$	12.6508			1.77146
$52$		0			0
$53$	9.54002			1.31042			0.655211	−	0.755446i	$-0.272580\pi$
$53$	9.54002			1.31042			0.655211	+	0.755446i	$0.272580\pi$
$54$		0			0
$55$	1.46410	+	2.53590i	0.197419	+	0.341940i
$56$		0			0
$57$		−	18.0933i		−	2.39652i
$58$		0			0
$59$	3.31749	+	1.91535i	0.431900	+	0.249358i	0.700156	−	0.713990i	$-0.253114\pi$
$59$	3.31749	+	1.91535i	0.431900	+	0.249358i	−0.268256	+	0.963348i	$0.586447\pi$
$60$		0			0
$61$	3.84229	−	6.65503i	0.491954	−	0.852090i	−0.508003	−	0.861355i	$-0.669616\pi$
$61$	3.84229	−	6.65503i	0.491954	−	0.852090i	0.999957	+	0.00926564i	$0.00294939\pi$
$62$		0			0
$63$	−4.94304	+	2.85387i	−0.622765	+	0.359553i
$64$		0			0
$65$	−1.61440	−	3.70862i	−0.200241	−	0.459997i
$66$		0			0
$67$	−1.52690	+	0.881557i	−0.186541	+	0.107699i	−0.590362	−	0.807139i	$-0.701015\pi$
$67$	−1.52690	+	0.881557i	−0.186541	+	0.107699i	0.403821	+	0.914838i	$0.367682\pi$
$68$		0			0
$69$	2.59334	−	4.49179i	0.312201	−	0.540748i
$70$		0			0
$71$	−0.880242	−	0.508208i	−0.104466	−	0.0603132i	0.446857	−	0.894605i	$-0.352543\pi$
$71$	−0.880242	−	0.508208i	−0.104466	−	0.0603132i	−0.551323	+	0.834292i	$0.685877\pi$
$72$		0			0
$73$			0.323330i			0.0378429i	0.999821	+	0.0189214i	$0.00602324\pi$
$73$			0.323330i			0.0378429i	−0.999821	+	0.0189214i	$0.993977\pi$
$74$		0			0
$75$	−4.26053	−	7.37945i	−0.491964	−	0.852106i
$76$		0			0
$77$	6.81333			0.776451
$78$		0			0
$79$	2.66877			0.300260			0.150130	−	0.988666i	$-0.452031\pi$
$79$	2.66877			0.300260			0.150130	+	0.988666i	$0.452031\pi$
$80$		0			0
$81$	5.38924	+	9.33444i	0.598804	+	1.03716i
$82$		0			0
$83$		−	2.77953i		−	0.305093i	−0.988296	−	0.152547i	$-0.951253\pi$
$83$		−	2.77953i		−	0.305093i	0.988296	−	0.152547i	$-0.0487474\pi$
$84$		0			0
$85$	−5.39666	−	3.11576i	−0.585350	−	0.337952i
$86$		0			0
$87$	8.88024	−	15.3810i	0.952062	−	1.64902i
$88$		0			0
$89$	−9.99531	+	5.77080i	−1.05950	+	0.611703i	−0.925294	−	0.379250i	$-0.876182\pi$
$89$	−9.99531	+	5.77080i	−1.05950	+	0.611703i	−0.134207	+	0.990953i	$0.542849\pi$
$90$		0			0
$91$	−9.35128	−	1.06149i	−0.980281	−	0.111274i
$92$		0			0
$93$	−16.2964	+	9.40872i	−1.68986	+	0.975639i
$94$		0			0
$95$	−4.45620	+	7.71837i	−0.457197	+	0.791888i
$96$		0			0
$97$	13.5553	+	7.82618i	1.37634	+	0.794628i	0.991716	−	0.128447i	$-0.0409993\pi$
$97$	13.5553	+	7.82618i	1.37634	+	0.794628i	0.384619	+	0.923075i	$0.374333\pi$
$98$		0			0
$99$			5.70773i			0.573649i
$100$		0			0
$101$	−8.17667	−	14.1624i	−0.813609	−	1.40921i	−0.910322	−	0.413900i	$-0.864166\pi$
$101$	−8.17667	−	14.1624i	−0.813609	−	1.40921i	0.0967132	−	0.995312i	$-0.469167\pi$
$102$		0			0
$103$	−2.24363			−0.221072			−0.110536	−	0.993872i	$-0.535257\pi$
$103$	−2.24363			−0.221072			−0.110536	+	0.993872i	$0.535257\pi$
$104$		0			0
$105$	6.66877			0.650805
$106$		0			0
$107$	5.41614	+	9.38103i	0.523598	+	0.906898i	0.999623	+	0.0274665i	$0.00874397\pi$
$107$	5.41614	+	9.38103i	0.523598	+	0.906898i	−0.476025	+	0.879432i	$0.657923\pi$
$108$		0			0
$109$			2.92820i			0.280471i	0.990118	+	0.140236i	$0.0447860\pi$
$109$			2.92820i			0.280471i	−0.990118	+	0.140236i	$0.955214\pi$
$110$		0			0
$111$	7.10492	+	4.10203i	0.674369	+	0.389347i
$112$		0			0
$113$	−5.02106	+	8.69673i	−0.472342	+	0.818120i	−0.999499	−	0.0316481i	$-0.989924\pi$
$113$	−5.02106	+	8.69673i	−0.472342	+	0.818120i	0.527158	+	0.849768i	$0.323258\pi$
$114$		0			0
$115$	−2.21257	+	1.27743i	−0.206323	+	0.119121i
$116$		0			0
$117$	0.889239	−	7.83386i	0.0822102	−	0.724240i
$118$		0			0
$119$	−12.5569	+	7.24974i	−1.15109	+	0.664582i
$120$		0			0
$121$	−2.09334	+	3.62577i	−0.190303	+	0.329615i
$122$		0			0
$123$	−11.3054	−	6.52716i	−1.01937	−	0.588535i
$124$		0			0
$125$			9.80639i			0.877110i
$126$		0			0
$127$	−0.195671	−	0.338912i	−0.0173630	−	0.0300736i	0.857213	−	0.514961i	$-0.172194\pi$
$127$	−0.195671	−	0.338912i	−0.0173630	−	0.0300736i	−0.874576	+	0.484888i	$0.838860\pi$
$128$		0			0
$129$	−9.18667			−0.808842
$130$		0			0
$131$	−19.3533			−1.69091			−0.845455	−	0.534047i	$-0.820670\pi$
$131$	−19.3533			−1.69091			−0.845455	+	0.534047i	$0.820670\pi$
$132$		0			0
$133$	10.3687	+	17.9590i	0.899077	+	1.55725i
$134$		0			0
$135$		−	2.07793i		−	0.178840i
$136$		0			0
$137$	3.44304	+	1.98784i	0.294159	+	0.169833i	0.639816	−	0.768528i	$-0.279011\pi$
$137$	3.44304	+	1.98784i	0.294159	+	0.169833i	−0.345657	+	0.938361i	$0.612344\pi$
$138$		0			0
$139$	9.48100	−	16.4216i	0.804168	−	1.39286i	−0.112684	−	0.993631i	$-0.535945\pi$
$139$	9.48100	−	16.4216i	0.804168	−	1.39286i	0.916851	−	0.399229i	$-0.130722\pi$
$140$		0			0
$141$	−5.25742	+	3.03537i	−0.442755	+	0.255624i
$142$		0			0
$143$	−5.59491	+	7.56771i	−0.467870	+	0.632843i
$144$		0			0
$145$	−7.57639	+	4.37423i	−0.629185	+	0.363260i
$146$		0			0
$147$	−0.212569	+	0.368180i	−0.0175324	+	0.0303670i
$148$		0			0
$149$	1.27259	+	0.734731i	0.104255	+	0.0601915i	0.551221	−	0.834359i	$-0.314162\pi$
$149$	1.27259	+	0.734731i	0.104255	+	0.0601915i	−0.446966	+	0.894551i	$0.647496\pi$
$150$		0			0
$151$			5.59382i			0.455218i	0.973753	+	0.227609i	$0.0730909\pi$
$151$			5.59382i			0.455218i	−0.973753	+	0.227609i	$0.926909\pi$
$152$		0			0
$153$	−6.07333	−	10.5193i	−0.491000	−	0.850436i
$154$		0			0
$155$	9.26910			0.744512
$156$		0			0
$157$	−0.430307			−0.0343422			−0.0171711	−	0.999853i	$-0.505466\pi$
$157$	−0.430307			−0.0343422			−0.0171711	+	0.999853i	$0.505466\pi$
$158$		0			0
$159$	−10.8633	−	18.8159i	−0.861519	−	1.49220i
$160$		0			0
$161$			5.94462i			0.468502i
$162$		0			0
$163$	−3.18873	−	1.84102i	−0.249761	−	0.144199i	0.369894	−	0.929074i	$-0.379394\pi$
$163$	−3.18873	−	1.84102i	−0.249761	−	0.144199i	−0.619655	+	0.784875i	$0.712727\pi$
$164$		0			0
$165$	3.33438	−	5.77532i	0.259582	−	0.449608i
$166$		0			0
$167$	−14.2605	+	8.23332i	−1.10351	+	0.637113i	−0.937141	−	0.348950i	$-0.886538\pi$
$167$	−14.2605	+	8.23332i	−1.10351	+	0.637113i	−0.166371	+	0.986063i	$0.553205\pi$
$168$		0			0
$169$	8.85803	−	9.51501i	0.681387	−	0.731924i
$170$		0			0
$171$	−15.0449	+	8.68615i	−1.15051	+	0.664246i
$172$		0			0
$173$	−11.8897	+	20.5936i	−0.903959	+	1.56570i	−0.0816498	+	0.996661i	$0.526019\pi$
$173$	−11.8897	+	20.5936i	−0.903959	+	1.56570i	−0.822309	+	0.569041i	$0.807314\pi$
$174$		0			0
$175$	8.45784	+	4.88313i	0.639352	+	0.369130i
$176$		0			0
$177$		−	8.72415i		−	0.655747i
$178$		0			0
$179$	2.53796	+	4.39587i	0.189696	+	0.328563i	0.945149	−	0.326640i	$-0.105916\pi$
$179$	2.53796	+	4.39587i	0.189696	+	0.328563i	−0.755453	+	0.655203i	$0.772583\pi$
$180$		0			0
$181$	9.16667			0.681353			0.340676	−	0.940181i	$-0.389344\pi$
$181$	9.16667			0.681353			0.340676	+	0.940181i	$0.389344\pi$
$182$		0			0
$183$	−17.5011			−1.29371
$184$		0			0
$185$	−2.02058	−	3.49974i	−0.148556	−	0.257306i
$186$		0			0
$187$			14.4995i			1.06031i
$188$		0			0
$189$	−4.18716	−	2.41746i	−0.304571	−	0.175844i
$190$		0			0
$191$	−8.49205	+	14.7087i	−0.614463	+	1.06428i	0.376015	+	0.926614i	$0.377294\pi$
$191$	−8.49205	+	14.7087i	−0.614463	+	1.06428i	−0.990478	+	0.137668i	$0.956039\pi$
$192$		0			0
$193$	−17.7426	+	10.2437i	−1.27714	+	0.737356i	−0.976321	−	0.216325i	$-0.930593\pi$
$193$	−17.7426	+	10.2437i	−1.27714	+	0.737356i	−0.300817	+	0.953682i	$0.597260\pi$
$194$		0			0
$195$	−5.47621	+	7.40714i	−0.392159	+	0.530437i
$196$		0			0
$197$	13.4594	−	7.77080i	0.958944	−	0.553646i	0.0630958	−	0.998007i	$-0.479903\pi$
$197$	13.4594	−	7.77080i	0.958944	−	0.553646i	0.895848	+	0.444361i	$0.146569\pi$
$198$		0			0
$199$	9.67873	−	16.7640i	0.686107	−	1.18837i	−0.286981	−	0.957936i	$-0.592652\pi$
$199$	9.67873	−	16.7640i	0.686107	−	1.18837i	0.973088	−	0.230436i	$-0.0740151\pi$
$200$		0			0
$201$	3.47741	+	2.00768i	0.245277	+	0.141611i
$202$		0			0
$203$			20.3559i			1.42870i
$204$		0			0
$205$	3.21515	+	5.56881i	0.224556	+	0.388942i
$206$		0			0
$207$	−4.97999			−0.346133
$208$		0			0
$209$	20.7373			1.43443
$210$		0			0
$211$	−9.93720	−	17.2117i	−0.684105	−	1.18490i	−0.973717	−	0.227761i	$-0.926860\pi$
$211$	−9.93720	−	17.2117i	−0.684105	−	1.18490i	0.289612	−	0.957144i	$-0.406474\pi$
$212$		0			0
$213$			2.31481i			0.158608i
$214$		0			0
$215$	3.91892	+	2.26259i	0.267268	+	0.154307i
$216$		0			0
$217$	10.7836	−	18.6778i	0.732042	−	1.26793i
$218$		0			0
$219$	0.637706	−	0.368180i	0.0430922	−	0.0248793i
$220$		0			0
$221$	2.25895	−	19.9005i	0.151954	−	1.33865i
$222$		0			0
$223$	14.9613	−	8.63792i	1.00188	−	0.578438i	0.0930791	−	0.995659i	$-0.470329\pi$
$223$	14.9613	−	8.63792i	1.00188	−	0.578438i	0.908805	+	0.417220i	$0.136996\pi$
$224$		0			0
$225$	−4.09075	+	7.08539i	−0.272717	+	0.472359i
$226$		0			0
$227$	−6.97616	−	4.02769i	−0.463024	−	0.267327i	0.250291	−	0.968171i	$-0.419474\pi$
$227$	−6.97616	−	4.02769i	−0.463024	−	0.267327i	−0.713315	+	0.700844i	$0.752807\pi$
$228$		0			0
$229$		−	10.9282i		−	0.722156i	−0.932536	−	0.361078i	$-0.882409\pi$
$229$		−	10.9282i		−	0.722156i	0.932536	−	0.361078i	$-0.117591\pi$
$230$		0			0
$231$	−7.75843	−	13.4380i	−0.510467	−	0.884155i
$232$		0			0
$233$	4.66877			0.305861			0.152931	−	0.988237i	$-0.451129\pi$
$233$	4.66877			0.305861			0.152931	+	0.988237i	$0.451129\pi$
$234$		0			0
$235$	2.99033			0.195068
$236$		0			0
$237$	−3.03896	−	5.26364i	−0.197402	−	0.341910i
$238$		0			0
$239$		−	17.4862i		−	1.13109i	−0.824718	−	0.565545i	$-0.808666\pi$
$239$		−	17.4862i		−	1.13109i	0.824718	−	0.565545i	$-0.191334\pi$
$240$		0			0
$241$	−12.2184	−	7.05428i	−0.787054	−	0.454406i	0.0518703	−	0.998654i	$-0.483482\pi$
$241$	−12.2184	−	7.05428i	−0.787054	−	0.454406i	−0.838924	+	0.544248i	$0.816815\pi$
$242$		0			0
$243$	9.49516	−	16.4461i	0.609115	−	1.05502i
$244$		0			0
$245$	0.181358	−	0.104707i	0.0115865	−	0.00668950i
$246$		0			0
$247$	−28.4620	−	3.23078i	−1.81099	−	0.205570i
$248$		0			0
$249$	−5.48210	+	3.16509i	−0.347414	+	0.200579i
$250$		0			0
$251$	−9.28642	+	16.0846i	−0.586154	+	1.01525i	0.408577	+	0.912724i	$0.366025\pi$
$251$	−9.28642	+	16.0846i	−0.586154	+	1.01525i	−0.994731	+	0.102524i	$0.967308\pi$
$252$		0			0
$253$	5.14819	+	2.97231i	0.323664	+	0.186868i
$254$		0			0
$255$			14.1918i			0.888728i
$256$		0			0
$257$	−2.16562	−	3.75096i	−0.135087	−	0.233978i	0.790543	−	0.612406i	$-0.209798\pi$
$257$	−2.16562	−	3.75096i	−0.135087	−	0.233978i	−0.925631	+	0.378428i	$0.876465\pi$
$258$		0			0
$259$	−9.40294			−0.584270
$260$		0			0
$261$	−17.0528			−1.05554
$262$		0			0
$263$	−2.11282	−	3.65951i	−0.130282	−	0.225655i	0.793503	−	0.608566i	$-0.208255\pi$
$263$	−2.11282	−	3.65951i	−0.130282	−	0.225655i	−0.923785	+	0.382911i	$0.874922\pi$
$264$		0			0
$265$			10.7021i			0.657427i
$266$		0			0
$267$	22.7636	+	13.1426i	1.39311	+	0.804312i
$268$		0			0
$269$	−4.11440	+	7.12634i	−0.250859	+	0.434501i	−0.963763	−	0.266761i	$-0.914046\pi$
$269$	−4.11440	+	7.12634i	−0.250859	+	0.434501i	0.712903	+	0.701262i	$0.247380\pi$
$270$		0			0
$271$	−6.68567	+	3.85997i	−0.406125	+	0.234477i	−0.689124	−	0.724644i	$-0.742004\pi$
$271$	−6.68567	+	3.85997i	−0.406125	+	0.234477i	0.282998	+	0.959120i	$0.408671\pi$
$272$		0			0
$273$	8.55485	+	19.6524i	0.517763	+	1.18941i
$274$		0			0
$275$	8.45784	−	4.88313i	0.510027	−	0.294464i
$276$		0			0
$277$	4.75153	−	8.22990i	0.285492	−	0.494487i	−0.687236	−	0.726434i	$-0.741176\pi$
$277$	4.75153	−	8.22990i	0.285492	−	0.494487i	0.972728	+	0.231947i	$0.0745097\pi$
$278$		0			0
$279$	15.6470	+	9.03380i	0.936761	+	0.540839i
$280$		0			0
$281$		−	23.0300i		−	1.37386i	−0.726726	−	0.686928i	$-0.758959\pi$
$281$		−	23.0300i		−	1.37386i	0.726726	−	0.686928i	$-0.241041\pi$
$282$		0			0
$283$	−6.68567	−	11.5799i	−0.397422	−	0.688355i	0.595985	−	0.802995i	$-0.296762\pi$
$283$	−6.68567	−	11.5799i	−0.397422	−	0.688355i	−0.993407	+	0.114641i	$0.963428\pi$
$284$		0			0
$285$	20.2973			1.20231
$286$		0			0
$287$	14.9620			0.883179
$288$		0			0
$289$	−6.92820	−	12.0000i	−0.407541	−	0.705882i
$290$		0			0
$291$		−	35.6471i		−	2.08967i
$292$		0			0
$293$	−15.0659	−	8.69831i	−0.880160	−	0.508161i	−0.00944872	−	0.999955i	$-0.503008\pi$
$293$	−15.0659	−	8.69831i	−0.880160	−	0.508161i	−0.870711	+	0.491795i	$0.836341\pi$
$294$		0			0
$295$	−2.14867	+	3.72161i	−0.125101	+	0.216681i
$296$		0			0
$297$	−4.18716	+	2.41746i	−0.242963	+	0.140275i
$298$		0			0
$299$	−6.60282	−	4.88156i	−0.381851	−	0.282308i
$300$		0			0
$301$	9.11851	−	5.26458i	0.525582	−	0.303445i
$302$		0			0
$303$	−18.6218	+	32.2539i	−1.06979	+	1.85294i
$304$		0			0
$305$	7.46572	+	4.31034i	0.427486	+	0.246809i
$306$		0			0
$307$		−	4.00315i		−	0.228472i	−0.993454	−	0.114236i	$-0.963558\pi$
$307$		−	4.00315i		−	0.228472i	0.993454	−	0.114236i	$-0.0364420\pi$
$308$		0			0
$309$	2.55485	+	4.42514i	0.145341	+	0.251737i
$310$		0			0
$311$	28.4630			1.61399			0.806996	−	0.590557i	$-0.201092\pi$
$311$	28.4630			1.61399			0.806996	+	0.590557i	$0.201092\pi$
$312$		0			0
$313$	−3.55906			−0.201170			−0.100585	−	0.994928i	$-0.532071\pi$
$313$	−3.55906			−0.201170			−0.100585	+	0.994928i	$0.532071\pi$
$314$		0			0
$315$	−3.20151	−	5.54518i	−0.180385	−	0.312436i
$316$		0			0
$317$		−	1.38125i		−	0.0775787i	−0.999247	−	0.0387894i	$-0.987650\pi$
$317$		−	1.38125i		−	0.0775787i	0.999247	−	0.0387894i	$-0.0123501\pi$
$318$		0			0
$319$	17.6287	+	10.1779i	0.987018	+	0.569855i
$320$		0			0
$321$	12.3349	−	21.3646i	0.688465	−	1.19246i
$322$		0			0
$323$	−38.2187	+	22.0656i	−2.12655	+	1.22776i
$324$		0			0
$325$	−12.3691	+	5.38440i	−0.686117	+	0.298673i
$326$		0			0
$327$	5.77532	−	3.33438i	0.319376	−	0.184392i
$328$		0			0
$329$	3.47894	−	6.02570i	0.191800	−	0.332208i
$330$		0			0
$331$	8.16461	+	4.71384i	0.448767	+	0.259096i	0.707310	−	0.706904i	$-0.249909\pi$
$331$	8.16461	+	4.71384i	0.448767	+	0.259096i	−0.258542	+	0.966000i	$0.583242\pi$
$332$		0			0
$333$		−	7.87713i		−	0.431664i
$334$		0			0
$335$	−0.988945	−	1.71290i	−0.0540318	−	0.0935859i
$336$		0			0
$337$	1.21215			0.0660298			0.0330149	−	0.999455i	$-0.489489\pi$
$337$	1.21215			0.0660298			0.0330149	+	0.999455i	$0.489489\pi$
$338$		0			0
$339$	22.8702			1.24214
$340$		0			0
$341$	−10.7836	−	18.6778i	−0.583967	−	1.01146i
$342$		0			0
$343$		−	18.7589i		−	1.01289i
$344$		0			0
$345$	5.03896	+	2.90925i	0.271289	+	0.156629i
$346$		0			0
$347$	7.13871	−	12.3646i	0.383226	−	0.663767i	−0.608295	−	0.793711i	$-0.708146\pi$
$347$	7.13871	−	12.3646i	0.383226	−	0.663767i	0.991521	+	0.129944i	$0.0414796\pi$
$348$		0			0
$349$	−20.2862	+	11.7123i	−1.08590	+	0.626943i	−0.932481	−	0.361219i	$-0.882361\pi$
$349$	−20.2862	+	11.7123i	−1.08590	+	0.626943i	−0.153416	+	0.988162i	$0.549027\pi$
$350$		0			0
$351$	6.12350	−	2.66562i	0.326848	−	0.142280i
$352$		0			0
$353$	7.02421	−	4.05543i	0.373861	−	0.215849i	−0.301283	−	0.953535i	$-0.597415\pi$
$353$	7.02421	−	4.05543i	0.373861	−	0.215849i	0.675144	+	0.737686i	$0.264081\pi$
$354$		0			0
$355$	0.570116	−	0.987470i	0.0302586	−	0.0524095i
$356$		0			0
$357$	28.5975	+	16.5107i	1.51354	+	0.873841i
$358$		0			0
$359$			26.3302i			1.38965i	0.719177	+	0.694827i	$0.244519\pi$
$359$			26.3302i			1.38965i	−0.719177	+	0.694827i	$0.755481\pi$
$360$		0			0
$361$	22.0585	+	38.2064i	1.16097	+	2.01086i
$362$		0			0
$363$	9.53485			0.500450
$364$		0			0
$365$	−0.362716			−0.0189854
$366$		0			0
$367$	−5.04279	−	8.73437i	−0.263232	−	0.455930i	0.703867	−	0.710332i	$-0.251455\pi$
$367$	−5.04279	−	8.73437i	−0.263232	−	0.455930i	−0.967099	+	0.254401i	$0.918122\pi$
$368$		0			0
$369$			12.5341i			0.652501i
$370$		0			0
$371$	21.5655	+	12.4508i	1.11962	+	0.646415i
$372$		0			0
$373$	0.305425	−	0.529011i	0.0158143	−	0.0273912i	−0.858010	−	0.513633i	$-0.828299\pi$
$373$	0.305425	−	0.529011i	0.0158143	−	0.0273912i	0.873824	+	0.486242i	$0.161633\pi$
$374$		0			0
$375$	19.3412	−	11.1667i	0.998777	−	0.576644i
$376$		0			0
$377$	−22.6097	−	16.7157i	−1.16446	−	0.860902i
$378$		0			0
$379$	3.12291	−	1.80301i	0.160413	−	0.0926146i	−0.417644	−	0.908611i	$-0.637144\pi$
$379$	3.12291	−	1.80301i	0.160413	−	0.0926146i	0.578058	+	0.815996i	$0.303811\pi$
$380$		0			0
$381$	−0.445627	+	0.771848i	−0.0228302	+	0.0395430i
$382$		0			0
$383$	10.3744	+	5.98969i	0.530109	+	0.306059i	0.741061	−	0.671438i	$-0.234323\pi$
$383$	10.3744	+	5.98969i	0.530109	+	0.306059i	−0.210952	+	0.977497i	$0.567656\pi$
$384$		0			0
$385$			7.64330i			0.389539i
$386$		0			0
$387$	4.41030	+	7.63886i	0.224188	+	0.388305i
$388$		0			0
$389$	−10.1245			−0.513335			−0.256667	−	0.966500i	$-0.582625\pi$
$389$	−10.1245			−0.513335			−0.256667	+	0.966500i	$0.582625\pi$
$390$		0			0
$391$	−12.6508			−0.639777
$392$		0			0
$393$	22.0379	+	38.1708i	1.11167	+	1.92546i
$394$		0			0
$395$			2.99387i			0.150638i
$396$		0			0
$397$	9.98985	+	5.76764i	0.501376	+	0.289470i	0.729282	−	0.684214i	$-0.239854\pi$
$397$	9.98985	+	5.76764i	0.501376	+	0.289470i	−0.227906	+	0.973683i	$0.573188\pi$
$398$		0			0
$399$	23.6139	−	40.9004i	1.18217	−	2.04758i
$400$		0			0
$401$	4.40408	−	2.54270i	0.219929	−	0.126976i	−0.385988	−	0.922504i	$-0.626139\pi$
$401$	4.40408	−	2.54270i	0.219929	−	0.126976i	0.605917	+	0.795528i	$0.292806\pi$
$402$		0			0
$403$	11.8906	+	27.3153i	0.592314	+	1.36067i
$404$		0			0
$405$	−10.4715	+	6.04573i	−0.520334	+	0.300415i
$406$		0			0
$407$	−4.70147	+	8.14318i	−0.233043	+	0.403643i
$408$		0			0
$409$	−33.6287	−	19.4155i	−1.66283	−	0.960036i	−0.971354	−	0.237636i	$-0.923627\pi$
$409$	−33.6287	−	19.4155i	−1.66283	−	0.960036i	−0.691476	−	0.722399i	$-0.743039\pi$
$410$		0			0
$411$		−	9.05433i		−	0.446617i
$412$		0			0
$413$	4.99952	+	8.65942i	0.246010	+	0.426102i
$414$		0			0
$415$	3.11812			0.153063
$416$		0			0
$417$	−43.1846			−2.11476
$418$		0			0
$419$	9.36751	+	16.2250i	0.457633	+	0.792643i	0.998835	−	0.0482492i	$-0.0153642\pi$
$419$	9.36751	+	16.2250i	0.457633	+	0.792643i	−0.541203	+	0.840892i	$0.682031\pi$
$420$		0			0
$421$			7.50063i			0.365558i	0.983154	+	0.182779i	$0.0585093\pi$
$421$			7.50063i			0.365558i	−0.983154	+	0.182779i	$0.941491\pi$
$422$		0			0
$423$	5.04792	+	2.91442i	0.245438	+	0.141704i
$424$		0			0
$425$	−10.3918	+	17.9992i	−0.504077	+	0.873088i
$426$		0			0
$427$	17.3712	−	10.0293i	0.840651	−	0.485350i
$428$		0			0
$429$	21.2969	+	2.41746i	1.02822	+	0.116716i
$430$		0			0
$431$	−9.41341	+	5.43483i	−0.453428	+	0.261787i	−0.709277	−	0.704930i	$-0.750978\pi$
$431$	−9.41341	+	5.43483i	−0.453428	+	0.261787i	0.255849	+	0.966717i	$0.417645\pi$
$432$		0			0
$433$	0.0780169	−	0.135129i	0.00374925	−	0.00649389i	−0.864145	−	0.503243i	$-0.832140\pi$
$433$	0.0780169	−	0.135129i	0.00374925	−	0.00649389i	0.867894	+	0.496750i	$0.165473\pi$
$434$		0			0
$435$	17.2547	+	9.96200i	0.827299	+	0.477641i
$436$		0			0
$437$			18.0933i			0.865520i
$438$		0			0
$439$	3.85435	+	6.67593i	0.183958	+	0.318625i	0.943225	−	0.332155i	$-0.107776\pi$
$439$	3.85435	+	6.67593i	0.183958	+	0.318625i	−0.759267	+	0.650779i	$0.774442\pi$
$440$		0			0
$441$	0.408196			0.0194379
$442$		0			0
$443$	−5.59697			−0.265920			−0.132960	−	0.991121i	$-0.542448\pi$
$443$	−5.59697			−0.265920			−0.132960	+	0.991121i	$0.542448\pi$
$444$		0			0
$445$	−6.47377	−	11.2129i	−0.306886	−	0.531543i
$446$		0			0
$447$		−	3.34659i		−	0.158288i
$448$		0			0
$449$	16.3728	+	9.45283i	0.772679	+	0.446107i	0.833830	−	0.552022i	$-0.186144\pi$
$449$	16.3728	+	9.45283i	0.772679	+	0.446107i	−0.0611504	+	0.998129i	$0.519477\pi$
$450$		0			0
$451$	7.48100	−	12.9575i	0.352266	−	0.610143i
$452$		0			0
$453$	11.0327	−	6.36976i	0.518363	−	0.299277i
$454$		0			0
$455$	1.19079	−	10.4904i	0.0558252	−	0.491798i
$456$		0			0
$457$	−9.11698	+	5.26369i	−0.426474	+	0.246225i	−0.697844	−	0.716250i	$-0.745857\pi$
$457$	−9.11698	+	5.26369i	−0.426474	+	0.246225i	0.271369	+	0.962475i	$0.412524\pi$
$458$		0			0
$459$	5.14460	−	8.91071i	0.240129	−	0.415916i
$460$		0			0
$461$	−1.45515	−	0.840131i	−0.0677731	−	0.0391288i	0.465731	−	0.884927i	$-0.345792\pi$
$461$	−1.45515	−	0.840131i	−0.0677731	−	0.0391288i	−0.533504	+	0.845798i	$0.679125\pi$
$462$		0			0
$463$		−	18.7795i		−	0.872759i	−0.899763	−	0.436379i	$-0.856261\pi$
$463$		−	18.7795i		−	0.872759i	0.899763	−	0.436379i	$-0.143739\pi$
$464$		0			0
$465$	−10.5549	−	18.2815i	−0.489470	−	0.847786i
$466$		0			0
$467$	−16.6604			−0.770949			−0.385475	−	0.922718i	$-0.625962\pi$
$467$	−16.6604			−0.770949			−0.385475	+	0.922718i	$0.625962\pi$
$468$		0			0
$469$	−4.60214			−0.212507
$470$		0			0
$471$	0.489996	+	0.848698i	0.0225778	+	0.0391059i
$472$		0			0
$473$		−	10.5292i		−	0.484131i
$474$		0			0
$475$	25.7426	+	14.8625i	1.18115	+	0.681939i
$476$		0			0
$477$	−10.4305	+	18.0661i	−0.477578	+	0.827189i
$478$		0			0
$479$	−10.6704	+	6.16056i	−0.487543	+	0.281483i	−0.723555	−	0.690267i	$-0.757493\pi$
$479$	−10.6704	+	6.16056i	−0.487543	+	0.281483i	0.236011	+	0.971750i	$0.424160\pi$
$480$		0			0
$481$	7.72143	−	10.4440i	0.352067	−	0.476207i
$482$		0			0
$483$	11.7246	−	6.76922i	0.533489	−	0.308010i
$484$		0			0
$485$	−8.77953	+	15.2066i	−0.398658	+	0.690496i
$486$		0			0
$487$	−32.2215	−	18.6031i	−1.46009	−	0.842986i	−0.461079	−	0.887359i	$-0.652538\pi$
$487$	−32.2215	−	18.6031i	−1.46009	−	0.842986i	−0.999015	+	0.0443730i	$0.985871\pi$
$488$		0			0
$489$			8.38556i			0.379208i
$490$		0			0
$491$	−7.36708	−	12.7602i	−0.332472	−	0.575858i	0.650524	−	0.759486i	$-0.274549\pi$
$491$	−7.36708	−	12.7602i	−0.332472	−	0.575858i	−0.982996	+	0.183628i	$0.941216\pi$
$492$		0			0
$493$	−43.3195			−1.95101
$494$		0			0
$495$	−6.40303			−0.287795
$496$		0			0
$497$	−1.32654	−	2.29764i	−0.0595036	−	0.103063i
$498$		0			0
$499$		−	19.2287i		−	0.860795i	−0.902639	−	0.430397i	$-0.858373\pi$
$499$		−	19.2287i		−	0.860795i	0.902639	−	0.430397i	$-0.141627\pi$
$500$		0			0
$501$	32.4773	+	18.7508i	1.45098	+	0.837723i
$502$		0			0
$503$	17.4040	−	30.1447i	0.776007	−	1.34408i	−0.158219	−	0.987404i	$-0.550575\pi$
$503$	17.4040	−	30.1447i	0.776007	−	1.34408i	0.934226	−	0.356680i	$-0.116091\pi$
$504$		0			0
$505$	15.8876	−	9.17272i	0.706990	−	0.408181i
$506$		0			0
$507$	−28.8533	−	6.63591i	−1.28142	−	0.294711i
$508$		0			0
$509$	−4.52370	+	2.61176i	−0.200510	+	0.115764i	−0.596893	−	0.802321i	$-0.703598\pi$
$509$	−4.52370	+	2.61176i	−0.200510	+	0.115764i	0.396384	+	0.918085i	$0.370265\pi$
$510$		0			0
$511$	−0.421983	+	0.730896i	−0.0186674	+	0.0323329i
$512$		0			0
$513$	−12.7442	−	7.35787i	−0.562670	−	0.324858i
$514$		0			0
$515$		−	2.51694i		−	0.110910i
$516$		0			0
$517$	−3.47894	−	6.02570i	−0.153004	−	0.265010i
$518$		0			0
$519$	54.1559			2.37718
$520$		0			0
$521$	−7.92917			−0.347383			−0.173692	−	0.984800i	$-0.555570\pi$
$521$	−7.92917			−0.347383			−0.173692	+	0.984800i	$0.555570\pi$
$522$		0			0
$523$	−15.9683	−	27.6578i	−0.698243	−	1.20939i	−0.969075	−	0.246766i	$-0.920632\pi$
$523$	−15.9683	−	27.6578i	−0.698243	−	1.20939i	0.270832	−	0.962627i	$-0.412701\pi$
$524$		0			0
$525$		−	22.2420i		−	0.970719i
$526$		0			0
$527$	39.7484	+	22.9487i	1.73147	+	0.999663i
$528$		0			0
$529$	8.90666	−	15.4268i	0.387246	−	0.670730i
$530$		0			0
$531$	−7.25426	+	4.18825i	−0.314808	+	0.181755i
$532$		0			0
$533$	−12.2864	+	16.6186i	−0.532182	+	0.719832i
$534$		0			0
$535$	−10.5238	+	6.07591i	−0.454983	+	0.262685i
$536$		0			0
$537$	5.78001	−	10.0113i	0.249426	−	0.432018i
$538$		0			0
$539$	−0.421983	−	0.243632i	−0.0181761	−	0.0104940i
$540$		0			0
$541$		−	17.1534i		−	0.737483i	−0.929532	−	0.368742i	$-0.879789\pi$
$541$		−	17.1534i		−	0.737483i	0.929532	−	0.368742i	$-0.120211\pi$
$542$		0			0
$543$	−10.4382	−	18.0795i	−0.447946	−	0.775866i
$544$		0			0
$545$	−3.28491			−0.140710
$546$		0			0
$547$	15.4885			0.662241			0.331121	−	0.943588i	$-0.392573\pi$
$547$	15.4885			0.662241			0.331121	+	0.943588i	$0.392573\pi$
$548$		0			0
$549$	8.40183	+	14.5524i	0.358581	+	0.621081i
$550$		0			0
$551$			61.9560i			2.63941i
$552$		0			0
$553$	6.03283	+	3.48306i	0.256542	+	0.148115i
$554$		0			0
$555$	−4.60172	+	7.97041i	−0.195332	+	0.338325i
$556$		0			0
$557$	27.4972	−	15.8755i	1.16509	−	0.672667i	0.212574	−	0.977145i	$-0.431815\pi$
$557$	27.4972	−	15.8755i	1.16509	−	0.672667i	0.952519	+	0.304478i	$0.0984821\pi$
$558$		0			0
$559$	−1.64039	+	14.4513i	−0.0693813	+	0.611223i
$560$		0			0
$561$	28.5975	−	16.5107i	1.20739	−	0.697084i
$562$		0			0
$563$	−17.0739	+	29.5728i	−0.719577	+	1.24634i	0.241590	+	0.970378i	$0.422331\pi$
$563$	−17.0739	+	29.5728i	−0.719577	+	1.24634i	−0.961167	+	0.275966i	$0.911002\pi$
$564$		0			0
$565$	−9.75613	−	5.63270i	−0.410444	−	0.236970i
$566$		0			0
$567$			28.1344i			1.18153i
$568$		0			0
$569$	1.13987	+	1.97431i	0.0477858	+	0.0827674i	0.888929	−	0.458045i	$-0.151450\pi$
$569$	1.13987	+	1.97431i	0.0477858	+	0.0827674i	−0.841143	+	0.540812i	$0.818117\pi$
$570$		0			0
$571$	24.5631			1.02793			0.513967	−	0.857810i	$-0.328176\pi$
$571$	24.5631			1.02793			0.513967	+	0.857810i	$0.328176\pi$
$572$		0			0
$573$	38.6801			1.61588
$574$		0			0
$575$	4.26053	+	7.37945i	0.177676	+	0.307744i
$576$		0			0
$577$			10.6670i			0.444073i	0.975038	+	0.222037i	$0.0712704\pi$
$577$			10.6670i			0.444073i	−0.975038	+	0.222037i	$0.928730\pi$
$578$		0			0
$579$	40.4074	+	23.3292i	1.67928	+	0.969530i
$580$		0			0
$581$	3.62761	−	6.28321i	0.150499	−	0.260672i
$582$		0			0
$583$	21.5655	−	12.4508i	0.893151	−	0.515661i
$584$		0			0
$585$	8.78815	+	0.997563i	0.363345	+	0.0412441i
$586$		0			0
$587$	−1.74262	+	1.00610i	−0.0719258	+	0.0415264i	−0.535532	−	0.844515i	$-0.679889\pi$
$587$	−1.74262	+	1.00610i	−0.0719258	+	0.0415264i	0.463606	+	0.886042i	$0.346555\pi$
$588$		0			0
$589$	32.8216	−	56.8486i	1.35239	−	2.34241i
$590$		0			0
$591$	−30.6528	−	17.6974i	−1.26089	−	0.727975i
$592$		0			0
$593$			38.9058i			1.59767i	0.601552	+	0.798834i	$0.294549\pi$
$593$			38.9058i			1.59767i	−0.601552	+	0.798834i	$0.705451\pi$
$594$		0			0
$595$	−8.13287	−	14.0865i	−0.333415	−	0.577492i
$596$		0			0
$597$	−44.0852			−1.80429
$598$		0			0
$599$	−14.2815			−0.583528			−0.291764	−	0.956490i	$-0.594242\pi$
$599$	−14.2815			−0.583528			−0.291764	+	0.956490i	$0.594242\pi$
$600$		0			0
$601$	−17.0590	−	29.5470i	−0.695850	−	1.20525i	−0.969893	−	0.243530i	$-0.921695\pi$
$601$	−17.0590	−	29.5470i	−0.695850	−	1.20525i	0.274043	−	0.961717i	$-0.411639\pi$
$602$		0			0
$603$		−	3.85536i		−	0.157002i
$604$		0			0
$605$	−4.06744	−	2.34834i	−0.165365	−	0.0954736i
$606$		0			0
$607$	3.28327	−	5.68679i	0.133264	−	0.230820i	−0.791669	−	0.610950i	$-0.790788\pi$
$607$	3.28327	−	5.68679i	0.133264	−	0.230820i	0.924933	+	0.380130i	$0.124121\pi$
$608$		0			0
$609$	40.1481	−	23.1795i	1.62688	−	0.939281i
$610$		0			0
$611$	3.83607	+	8.81227i	0.155191	+	0.356506i
$612$		0			0
$613$	40.0955	−	23.1491i	1.61944	−	0.934985i	0.632378	−	0.774660i	$-0.282079\pi$
$613$	40.0955	−	23.1491i	1.61944	−	0.934985i	0.987064	−	0.160325i	$-0.0512542\pi$
$614$		0			0
$615$	7.32228	−	12.6826i	0.295263	−	0.511410i
$616$		0			0
$617$	17.1021	+	9.87393i	0.688506	+	0.397509i	0.803052	−	0.595909i	$-0.203208\pi$
$617$	17.1021	+	9.87393i	0.688506	+	0.397509i	−0.114546	+	0.993418i	$0.536541\pi$
$618$		0			0
$619$			6.07074i			0.244004i	0.992530	+	0.122002i	$0.0389314\pi$
$619$			6.07074i			0.244004i	−0.992530	+	0.122002i	$0.961069\pi$
$620$		0			0
$621$	−2.10923	−	3.65329i	−0.0846404	−	0.146601i
$622$		0			0
$623$	−30.1263			−1.20698
$624$		0			0
$625$	7.70668			0.308267
$626$		0			0
$627$	−23.6139	−	40.9004i	−0.943047	−	1.63341i
$628$		0			0
$629$		−	20.0104i		−	0.797869i
$630$		0			0
$631$	20.9641	+	12.1036i	0.834566	+	0.481837i	0.855413	−	0.517946i	$-0.173303\pi$
$631$	20.9641	+	12.1036i	0.834566	+	0.481837i	−0.0208475	+	0.999783i	$0.506636\pi$
$632$		0			0
$633$	−22.6312	+	39.1985i	−0.899511	+	1.55800i
$634$		0			0
$635$	0.380197	−	0.219507i	0.0150877	−	0.00871087i
$636$		0			0
$637$	0.541215	+	0.400128i	0.0214437	+	0.0158536i
$638$		0			0
$639$	1.92480	−	1.11129i	0.0761440	−	0.0439618i
$640$		0			0
$641$	16.8871	−	29.2494i	0.667002	−	1.15528i	−0.311737	−	0.950169i	$-0.600911\pi$
$641$	16.8871	−	29.2494i	0.667002	−	1.15528i	0.978738	−	0.205112i	$-0.0657560\pi$
$642$		0			0
$643$	28.4102	+	16.4026i	1.12039	+	0.646856i	0.941500	−	0.337013i	$-0.109417\pi$
$643$	28.4102	+	16.4026i	1.12039	+	0.646856i	0.178888	+	0.983869i	$0.442750\pi$
$644$		0			0
$645$		−	10.3058i		−	0.405789i
$646$		0			0
$647$	−19.0100	−	32.9262i	−0.747359	−	1.29446i	−0.949085	−	0.315021i	$-0.897988\pi$
$647$	−19.0100	−	32.9262i	−0.747359	−	1.29446i	0.201726	−	0.979442i	$-0.435345\pi$
$648$		0			0
$649$	9.99904			0.392497
$650$		0			0
$651$	−49.1179			−1.92508
$652$		0			0
$653$	−10.0005	−	17.3213i	−0.391349	−	0.677836i	0.601279	−	0.799039i	$-0.294658\pi$
$653$	−10.0005	−	17.3213i	−0.391349	−	0.677836i	−0.992628	+	0.121203i	$0.961325\pi$
$654$		0			0
$655$		−	21.7109i		−	0.848315i
$656$		0			0
$657$	−0.612294	−	0.353508i	−0.0238879	−	0.0137917i
$658$		0			0
$659$	−5.59588	+	9.69234i	−0.217984	+	0.377560i	−0.954192	−	0.299196i	$-0.903282\pi$
$659$	−5.59588	+	9.69234i	−0.217984	+	0.377560i	0.736207	+	0.676756i	$0.236615\pi$
$660$		0			0
$661$	−22.5870	+	13.0406i	−0.878531	+	0.507220i	−0.870174	−	0.492745i	$-0.835994\pi$
$661$	−22.5870	+	13.0406i	−0.878531	+	0.507220i	−0.00835740	+	0.999965i	$0.502660\pi$
$662$		0			0
$663$	−41.8223	+	18.2056i	−1.62424	+	0.707048i
$664$		0			0
$665$	−20.1467	+	11.6317i	−0.781257	+	0.451059i
$666$		0			0
$667$	−8.88024	+	15.3810i	−0.343844	+	0.595556i
$668$		0			0
$669$	−34.0733	−	19.6722i	−1.31735	−	0.760573i
$670$		0			0
$671$		−	20.0585i		−	0.774351i
$672$		0			0
$673$	−22.6667	−	39.2598i	−0.873736	−	1.51335i	−0.858103	−	0.513477i	$-0.828357\pi$
$673$	−22.6667	−	39.2598i	−0.873736	−	1.51335i	−0.0156324	−	0.999878i	$-0.504976\pi$
$674$		0			0
$675$	−6.93040			−0.266751
$676$		0			0
$677$	−23.6942			−0.910644			−0.455322	−	0.890327i	$-0.650476\pi$
$677$	−23.6942			−0.910644			−0.455322	+	0.890327i	$0.650476\pi$
$678$		0			0
$679$	20.4282	+	35.3826i	0.783961	+	1.35786i
$680$		0			0
$681$			18.3455i			0.703003i
$682$		0			0
$683$	−37.1501	−	21.4486i	−1.42151	−	0.820709i	−0.425081	−	0.905155i	$-0.639754\pi$
$683$	−37.1501	−	21.4486i	−1.42151	−	0.820709i	−0.996428	+	0.0844466i	$0.973088\pi$
$684$		0			0
$685$	−2.22999	+	3.86246i	−0.0852036	+	0.147577i
$686$		0			0
$687$	−21.5538	+	12.4441i	−0.822329	+	0.474772i
$688$		0			0
$689$	−31.5384	+	13.7290i	−1.20152	+	0.523032i
$690$		0			0
$691$	−41.6801	+	24.0640i	−1.58559	+	0.915439i	−0.591564	+	0.806258i	$0.701489\pi$
$691$	−41.6801	+	24.0640i	−1.58559	+	0.915439i	−0.994022	+	0.109181i	$0.965177\pi$
$692$		0			0
$693$	−7.44926	+	12.9025i	−0.282974	+	0.490125i
$694$		0			0
$695$	18.4220	+	10.6359i	0.698786	+	0.403444i
$696$		0			0
$697$			31.8407i			1.20605i
$698$		0			0
$699$	−5.31639	−	9.20826i	−0.201084	−	0.348288i
$700$		0			0
$701$	21.6433			0.817456			0.408728	−	0.912656i	$-0.365972\pi$
$701$	21.6433			0.817456			0.408728	+	0.912656i	$0.365972\pi$
$702$		0			0
$703$	−28.6192			−1.07939
$704$		0			0
$705$	−3.40513	−	5.89786i	−0.128245	−	0.222126i
$706$		0			0
$707$		−	42.6861i		−	1.60537i
$708$		0			0
$709$	10.5449	+	6.08807i	0.396020	+	0.228642i	0.684765	−	0.728764i	$-0.259905\pi$
$709$	10.5449	+	6.08807i	0.396020	+	0.228642i	−0.288745	+	0.957406i	$0.593238\pi$
$710$		0			0
$711$	−2.91787	+	5.05389i	−0.109428	+	0.189536i
$712$		0			0
$713$	16.2964	−	9.40872i	0.610304	−	0.352359i
$714$		0			0
$715$	−8.48957	−	6.27646i	−0.317492	−	0.234726i
$716$		0			0
$717$	−34.4882	+	19.9118i	−1.28799	+	0.743619i
$718$		0			0
$719$	8.66767	−	15.0129i	0.323250	−	0.559885i	−0.657907	−	0.753099i	$-0.728558\pi$
$719$	8.66767	−	15.0129i	0.323250	−	0.559885i	0.981157	+	0.193214i	$0.0618913\pi$
$720$		0			0
$721$	−5.07180	−	2.92820i	−0.188884	−	0.109052i
$722$		0			0
$723$			32.1312i			1.19497i
$724$		0			0
$725$	14.5891	+	25.2691i	0.541827	+	0.938471i
$726$		0			0
$727$	21.9600			0.814451			0.407225	−	0.913328i	$-0.366496\pi$
$727$	21.9600			0.814451			0.407225	+	0.913328i	$0.366496\pi$
$728$		0			0
$729$	−10.9137			−0.404210
$730$		0			0
$731$	11.2036	+	19.4052i	0.414379	+	0.717726i
$732$		0			0
$733$		−	4.24733i		−	0.156879i	−0.996919	−	0.0784393i	$-0.975006\pi$
$733$		−	4.24733i		−	0.156879i	0.996919	−	0.0784393i	$-0.0249937\pi$
$734$		0			0
$735$	−0.413030	−	0.238463i	−0.0152348	−	0.00879584i
$736$		0			0
$737$	−2.30107	+	3.98557i	−0.0847610	+	0.146810i
$738$		0			0
$739$	12.1138	−	6.99390i	0.445613	−	0.257275i	−0.260363	−	0.965511i	$-0.583842\pi$
$739$	12.1138	−	6.99390i	0.445613	−	0.257275i	0.705976	+	0.708236i	$0.250509\pi$
$740$		0			0
$741$	26.0379	+	59.8147i	0.956527	+	2.19735i
$742$		0			0
$743$	−41.8143	+	24.1415i	−1.53402	+	0.885666i	−0.534848	+	0.844948i	$0.679631\pi$
$743$	−41.8143	+	24.1415i	−1.53402	+	0.885666i	−0.999171	+	0.0407183i	$0.987035\pi$
$744$		0			0
$745$	−0.824233	+	1.42761i	−0.0301976	+	0.0523037i
$746$		0			0
$747$	5.26364	+	3.03896i	0.192587	+	0.111190i
$748$		0			0
$749$			28.2748i			1.03314i
$750$		0			0
$751$	7.90298	+	13.6884i	0.288384	+	0.499496i	0.973424	−	0.229010i	$-0.0735487\pi$
$751$	7.90298	+	13.6884i	0.288384	+	0.499496i	−0.685040	+	0.728505i	$0.740215\pi$
$752$		0			0
$753$	42.2983			1.54144
$754$		0			0
$755$	−6.27524			−0.228379
$756$		0			0
$757$	5.30107	+	9.18172i	0.192671	+	0.333715i	0.946134	−	0.323774i	$-0.104952\pi$
$757$	5.30107	+	9.18172i	0.192671	+	0.333715i	−0.753464	+	0.657489i	$0.771618\pi$
$758$		0			0
$759$		−	13.5384i		−	0.491414i
$760$		0			0
$761$	−30.8970	−	17.8384i	−1.12002	−	0.646641i	−0.178610	−	0.983920i	$-0.557160\pi$
$761$	−30.8970	−	17.8384i	−1.12002	−	0.646641i	−0.941405	+	0.337279i	$0.890493\pi$
$762$		0			0
$763$	−3.82165	+	6.61929i	−0.138353	+	0.239634i
$764$		0			0
$765$	11.8007	−	6.81316i	0.426656	−	0.246330i
$766$		0			0
$767$	−13.7237	−	1.55780i	−0.495533	−	0.0562491i
$768$		0			0
$769$	2.96572	−	1.71226i	0.106947	−	0.0617457i	−0.445573	−	0.895246i	$-0.647000\pi$
$769$	2.96572	−	1.71226i	0.106947	−	0.0617457i	0.552519	+	0.833500i	$0.313667\pi$
$770$		0			0
$771$	−4.93203	+	8.54253i	−0.177623	+	0.307652i
$772$		0			0
$773$	−25.8369	−	14.9169i	−0.929288	−	0.536525i	−0.0427017	−	0.999088i	$-0.513596\pi$
$773$	−25.8369	−	14.9169i	−0.929288	−	0.536525i	−0.886586	+	0.462563i	$0.846930\pi$
$774$		0			0
$775$		−	30.9147i		−	1.11049i
$776$		0			0
$777$	10.7073	+	18.5455i	0.384121	+	0.665316i
$778$		0			0
$779$	45.5390			1.63160
$780$		0			0
$781$	−2.65309			−0.0949349
$782$		0			0
$783$	−7.22253	−	12.5098i	−0.258112	−	0.447063i
$784$		0			0
$785$		−	0.482725i		−	0.0172292i
$786$		0			0
$787$	−25.0330	−	14.4528i	−0.892331	−	0.515188i	−0.0176269	−	0.999845i	$-0.505611\pi$
$787$	−25.0330	−	14.4528i	−0.892331	−	0.515188i	−0.874704	+	0.484657i	$0.838944\pi$
$788$		0			0
$789$	−4.81179	+	8.33427i	−0.171304	+	0.296708i
$790$		0			0
$791$	−22.7005	+	13.1061i	−0.807137	+	0.466001i
$792$		0			0
$793$	−3.12503	+	27.5303i	−0.110973	+	0.977630i
$794$		0			0
$795$	21.1079	−	12.1867i	0.748621	−	0.432217i
$796$		0			0
$797$	−0.225157	+	0.389984i	−0.00797548	+	0.0138139i	−0.869986	−	0.493077i	$-0.835872\pi$
$797$	−0.225157	+	0.389984i	−0.00797548	+	0.0138139i	0.862010	+	0.506891i	$0.169205\pi$
$798$		0			0
$799$	12.8233	+	7.40355i	0.453657	+	0.261919i
$800$		0			0
$801$		−	25.2377i		−	0.891730i
$802$		0			0
$803$	0.421983	+	0.730896i	0.0148915	+	0.0257928i
$804$		0			0
$805$	−6.66877			−0.235043
$806$		0			0
$807$	18.7405			0.659696
$808$		0			0
$809$	−16.2605	−	28.1640i	−0.571688	−	0.990193i	−0.996393	−	0.0848610i	$-0.972955\pi$
$809$	−16.2605	−	28.1640i	−0.571688	−	0.990193i	0.424705	−	0.905332i	$-0.360378\pi$
$810$		0			0
$811$		−	0.00315434i		−	0.000110764i	−1.00000		5.53819e-5i	$-0.999982\pi$
$811$		−	0.00315434i		−	0.000110764i	1.00000		5.53819e-5i	$-1.76286e-5\pi$
$812$		0			0
$813$	15.2261	+	8.79080i	0.534003	+	0.308307i
$814$		0			0
$815$	2.06528	−	3.57717i	0.0723436	−	0.125303i
$816$		0			0
$817$	27.7535	−	16.0235i	0.970972	−	0.560591i
$818$		0			0
$819$	12.2343	−	16.5481i	0.427500	−	0.578238i
$820$		0			0
$821$	37.4594	−	21.6272i	1.30734	−	0.754795i	0.325691	−	0.945476i	$-0.394403\pi$
$821$	37.4594	−	21.6272i	1.30734	−	0.754795i	0.981652	+	0.190682i	$0.0610699\pi$
$822$		0			0
$823$	−20.3934	+	35.3224i	−0.710869	+	1.23126i	0.253662	+	0.967293i	$0.418365\pi$
$823$	−20.3934	+	35.3224i	−0.710869	+	1.23126i	−0.964531	+	0.263969i	$0.914968\pi$
$824$		0			0
$825$	−19.2621	−	11.1210i	−0.670620	−	0.387183i
$826$		0			0
$827$			15.0453i			0.523175i	0.965180	+	0.261588i	$0.0842461\pi$
$827$			15.0453i			0.523175i	−0.965180	+	0.261588i	$0.915754\pi$
$828$		0			0
$829$	17.0196	+	29.4788i	0.591115	+	1.02384i	0.994083	+	0.108626i	$0.0346452\pi$
$829$	17.0196	+	29.4788i	0.591115	+	1.02384i	−0.402968	+	0.915214i	$0.632021\pi$
$830$		0			0
$831$	−21.6425			−0.750771
$832$		0			0
$833$	1.03695			0.0359282
$834$		0			0
$835$	−9.23627	−	15.9977i	−0.319634	−	0.553623i
$836$		0			0
$837$			15.3047i			0.529008i
$838$		0			0
$839$	−38.2873	−	22.1052i	−1.32182	−	0.763156i	−0.337805	−	0.941216i	$-0.609684\pi$
$839$	−38.2873	−	22.1052i	−1.32182	−	0.763156i	−0.984020	+	0.178061i	$0.943018\pi$
$840$		0			0
$841$	−15.9082	+	27.5538i	−0.548558	+	0.950131i
$842$		0			0
$843$	−45.4223	+	26.2246i	−1.56443	+	0.903223i
$844$		0			0
$845$	10.6741	+	9.93708i	0.367200	+	0.341846i
$846$		0			0
$847$	−9.46410	+	5.46410i	−0.325190	+	0.187749i
$848$		0			0
$849$	−15.2261	+	26.3724i	−0.522559	+	0.905099i
$850$		0			0
$851$	−7.10492	−	4.10203i	−0.243553	−	0.140616i
$852$		0			0
$853$			47.0540i			1.61110i	0.592528	+	0.805550i	$0.298130\pi$
$853$			47.0540i			1.61110i	−0.592528	+	0.805550i	$0.701870\pi$
$854$		0			0
$855$	−9.74426	−	16.8776i	−0.333247	−	0.577200i
$856$		0			0
$857$	−7.26478			−0.248160			−0.124080	−	0.992272i	$-0.539598\pi$
$857$	−7.26478			−0.248160			−0.124080	+	0.992272i	$0.539598\pi$
$858$		0			0
$859$	−18.3788			−0.627077			−0.313538	−	0.949575i	$-0.601514\pi$
$859$	−18.3788			−0.627077			−0.313538	+	0.949575i	$0.601514\pi$
$860$		0			0
$861$	−17.0374	−	29.5097i	−0.580634	−	1.00569i
$862$		0			0
$863$		−	15.0390i		−	0.511932i	−0.966686	−	0.255966i	$-0.917606\pi$
$863$		−	15.0390i		−	0.511932i	0.966686	−	0.255966i	$-0.0823936\pi$
$864$		0			0
$865$	−23.1022	−	13.3381i	−0.785499	−	0.453508i
$866$		0			0
$867$	−15.7785	+	27.3291i	−0.535865	+	0.928146i
$868$		0			0
$869$	6.03283	−	3.48306i	0.204650	−	0.118155i
$870$		0			0
$871$	3.77915	−	5.11170i	0.128052	−	0.173203i
$872$		0			0
$873$	−29.6411	+	17.1133i	−1.00320	+	0.579197i
$874$		0			0
$875$	−12.7985	+	22.1676i	−0.432668	+	0.749403i
$876$		0			0
$877$	−22.7305	−	13.1234i	−0.767554	−	0.443147i	0.0644477	−	0.997921i	$-0.479471\pi$
$877$	−22.7305	−	13.1234i	−0.767554	−	0.443147i	−0.832001	+	0.554774i	$0.812805\pi$
$878$		0			0
$879$			39.6195i			1.33633i
$880$		0			0
$881$	7.20353	+	12.4769i	0.242693	+	0.420357i	0.961480	−	0.274873i	$-0.0886359\pi$
$881$	7.20353	+	12.4769i	0.242693	+	0.420357i	−0.718787	+	0.695230i	$0.755303\pi$
$882$		0			0
$883$	−36.9503			−1.24348			−0.621739	−	0.783225i	$-0.713573\pi$
$883$	−36.9503			−1.24348			−0.621739	+	0.783225i	$0.713573\pi$
$884$		0			0
$885$	9.78689			0.328983
$886$		0			0
$887$	−23.9103	−	41.4138i	−0.802828	−	1.39054i	−0.917748	−	0.397164i	$-0.869995\pi$
$887$	−23.9103	−	41.4138i	−0.802828	−	1.39054i	0.114920	−	0.993375i	$-0.463339\pi$
$888$		0			0
$889$		−	1.02150i		−	0.0342599i
$890$		0			0
$891$	24.3651	+	14.0672i	0.816261	+	0.471268i
$892$		0			0
$893$	10.5886	−	18.3401i	0.354336	−	0.613727i
$894$		0			0
$895$	−4.93136	+	2.84712i	−0.164837	+	0.0951687i
$896$		0			0
$897$	−2.10923	+	18.5815i	−0.0704251	+	0.620418i
$898$		0			0
$899$	55.8029	−	32.2178i	1.86113	−	1.07453i
$900$		0			0
$901$	−26.4967	+	45.8936i	−0.882733	+	1.52894i
$902$		0			0
$903$	−20.7667	−	11.9897i	−0.691074	−	0.398992i
$904$		0			0
$905$			10.2833i			0.341829i
$906$		0			0
$907$	10.7353	+	18.5940i	0.356459	+	0.617404i	0.987366	−	0.158453i	$-0.0506508\pi$
$907$	10.7353	+	18.5940i	0.356459	+	0.617404i	−0.630908	+	0.775858i	$0.717317\pi$
$908$		0			0
$909$	35.7594			1.18607
$910$		0			0
$911$	28.2594			0.936277			0.468138	−	0.883655i	$-0.344925\pi$
$911$	28.2594			0.936277			0.468138	+	0.883655i	$0.344925\pi$
$912$		0			0
$913$	−3.62761	−	6.28321i	−0.120056	−	0.207944i
$914$		0			0
$915$		−	19.6330i		−	0.649046i
$916$		0			0
$917$	−43.7488	−	25.2584i	−1.44471	−	0.834105i
$918$		0			0
$919$	22.7232	−	39.3577i	0.749568	−	1.29829i	−0.198462	−	0.980109i	$-0.563595\pi$
$919$	22.7232	−	39.3577i	0.749568	−	1.29829i	0.948030	−	0.318181i	$-0.103072\pi$
$920$		0			0
$921$	−7.89546	+	4.55845i	−0.260164	+	0.150206i
$922$		0			0
$923$	3.64136	+	0.413339i	0.119857	+	0.0136052i
$924$		0			0
$925$	−11.6725	+	6.73912i	−0.383789	+	0.221581i
$926$		0			0
$927$	2.45305	−	4.24880i	0.0805686	−	0.139549i
$928$		0			0
$929$	15.1077	+	8.72243i	0.495667	+	0.286174i	0.726923	−	0.686719i	$-0.240950\pi$
$929$	15.1077	+	8.72243i	0.495667	+	0.286174i	−0.231255	+	0.972893i	$0.574283\pi$
$930$		0			0
$931$		−	1.48306i		−	0.0486052i
$932$		0			0
$933$	−32.4113	−	56.1380i	−1.06110	−	1.83787i
$934$		0			0
$935$	−16.2657			−0.531947
$936$		0			0
$937$	44.7794			1.46288			0.731440	−	0.681906i	$-0.238848\pi$
$937$	44.7794			1.46288			0.731440	+	0.681906i	$0.238848\pi$
$938$		0			0
$939$	4.05275	+	7.01957i	0.132257	+	0.229075i
$940$		0			0
$941$		−	0.525176i		−	0.0171202i	−0.999963	−	0.00856012i	$-0.997275\pi$
$941$		−	0.525176i		−	0.0171202i	0.999963	−	0.00856012i	$-0.00272481\pi$
$942$		0			0
$943$	11.3054	+	6.52716i	0.368154	+	0.212554i
$944$		0			0
$945$	2.71194	−	4.69722i	0.0882194	−	0.152801i
$946$		0			0
$947$	−21.0744	+	12.1673i	−0.684826	+	0.395384i	−0.801671	−	0.597766i	$-0.796055\pi$
$947$	−21.0744	+	12.1673i	−0.684826	+	0.395384i	0.116845	+	0.993150i	$0.462722\pi$
$948$		0			0
$949$	−0.465301	−	1.06890i	−0.0151043	−	0.0346979i
$950$		0			0
$951$	−2.72425	+	1.57285i	−0.0883399	+	0.0510031i
$952$		0			0
$953$	26.5257	−	45.9438i	0.859250	−	1.48827i	−0.0133948	−	0.999910i	$-0.504264\pi$
$953$	26.5257	−	45.9438i	0.859250	−	1.48827i	0.872645	−	0.488355i	$-0.162403\pi$
$954$		0			0
$955$	−16.5004	−	9.52652i	−0.533941	−	0.308271i
$956$		0			0
$957$		−	46.3590i		−	1.49857i
$958$		0			0
$959$	5.18873	+	8.98715i	0.167553	+	0.290210i
$960$		0			0
$961$	−37.2704			−1.20227
$962$		0			0
$963$	−23.6867			−0.763292
$964$		0			0
$965$	−11.4915	−	19.9039i	−0.369925	−	0.640730i
$966$		0			0
$967$			26.5793i			0.854732i	0.904079	+	0.427366i	$0.140558\pi$
$967$			26.5793i			0.854732i	−0.904079	+	0.427366i	$0.859442\pi$
$968$		0			0
$969$	87.0404	+	50.2528i	2.79614	+	1.61435i
$970$		0			0
$971$	27.5500	−	47.7180i	0.884121	−	1.53134i	0.0374027	−	0.999300i	$-0.488092\pi$
$971$	27.5500	−	47.7180i	0.884121	−	1.53134i	0.846718	−	0.532042i	$-0.178575\pi$
$972$		0			0
$973$	42.8642	−	24.7476i	1.37416	−	0.793373i
$974$		0			0
$975$	24.7046	+	18.2645i	0.791181	+	0.584932i
$976$		0			0
$977$	29.5834	−	17.0800i	0.946457	−	0.546437i	0.0544782	−	0.998515i	$-0.482650\pi$
$977$	29.5834	−	17.0800i	0.946457	−	0.546437i	0.891978	+	0.452078i	$0.149317\pi$
$978$		0			0
$979$	−15.0631	+	26.0901i	−0.481420	+	0.833844i
$980$		0			0
$981$	−5.54518	−	3.20151i	−0.177044	−	0.102216i
$982$		0			0
$983$		−	13.8912i		−	0.443059i	−0.975154	−	0.221530i	$-0.928895\pi$
$983$		−	13.8912i		−	0.443059i	0.975154	−	0.221530i	$-0.0711050\pi$
$984$		0			0
$985$	8.71740	+	15.0990i	0.277760	+	0.481094i
$986$		0			0
$987$	−15.8461			−0.504386
$988$		0			0
$989$	9.18667			0.292119
$990$		0			0
$991$	−8.62081	−	14.9317i	−0.273849	−	0.474320i	0.695995	−	0.718047i	$-0.254964\pi$
$991$	−8.62081	−	14.9317i	−0.273849	−	0.474320i	−0.969844	+	0.243726i	$0.921630\pi$
$992$		0			0
$993$		−	21.4708i		−	0.681357i
$994$		0			0
$995$	18.8062	+	10.8578i	0.596196	+	0.344214i
$996$		0			0
$997$	−0.728370	+	1.26157i	−0.0230677	+	0.0399545i	−0.877329	−	0.479890i	$-0.840677\pi$
$997$	−0.728370	+	1.26157i	−0.0230677	+	0.0399545i	0.854261	+	0.519844i	$0.174010\pi$
$998$		0			0
$999$	5.77861	−	3.33628i	0.182827	−	0.105555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.w.i.257.1		8
4.3	odd	2		832.2.w.g.257.4		8
8.3	odd	2		104.2.o.a.49.1	yes	8
8.5	even	2		208.2.w.c.49.4		8
13.4	even	6	inner	832.2.w.i.641.1		8
24.5	odd	2		1872.2.by.n.1297.2		8
24.11	even	2		936.2.bi.b.361.2		8
52.43	odd	6		832.2.w.g.641.4		8
104.3	odd	6		1352.2.f.f.337.7		8
104.11	even	12		1352.2.a.l.1.4		4
104.19	even	12		1352.2.i.k.529.1		8
104.29	even	6		2704.2.f.q.337.1		8
104.35	odd	6		1352.2.o.f.1161.1		8
104.37	odd	12		2704.2.a.be.1.1		4
104.43	odd	6		104.2.o.a.17.1	✓	8
104.51	odd	2		1352.2.o.f.361.1		8
104.59	even	12		1352.2.i.l.529.1		8
104.67	even	12		1352.2.a.k.1.4		4
104.69	even	6		208.2.w.c.17.4		8
104.75	odd	6		1352.2.f.f.337.8		8
104.83	even	4		1352.2.i.k.1329.1		8
104.93	odd	12		2704.2.a.bd.1.1		4
104.99	even	4		1352.2.i.l.1329.1		8
104.101	even	6		2704.2.f.q.337.2		8
312.173	odd	6		1872.2.by.n.433.3		8
312.251	even	6		936.2.bi.b.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.1	✓	8	104.43	odd	6
104.2.o.a.49.1	yes	8	8.3	odd	2
208.2.w.c.17.4		8	104.69	even	6
208.2.w.c.49.4		8	8.5	even	2
832.2.w.g.257.4		8	4.3	odd	2
832.2.w.g.641.4		8	52.43	odd	6
832.2.w.i.257.1		8	1.1	even	1	trivial
832.2.w.i.641.1		8	13.4	even	6	inner
936.2.bi.b.361.2		8	24.11	even	2
936.2.bi.b.433.3		8	312.251	even	6
1352.2.a.k.1.4		4	104.67	even	12
1352.2.a.l.1.4		4	104.11	even	12
1352.2.f.f.337.7		8	104.3	odd	6
1352.2.f.f.337.8		8	104.75	odd	6
1352.2.i.k.529.1		8	104.19	even	12
1352.2.i.k.1329.1		8	104.83	even	4
1352.2.i.l.529.1		8	104.59	even	12
1352.2.i.l.1329.1		8	104.99	even	4
1352.2.o.f.361.1		8	104.51	odd	2
1352.2.o.f.1161.1		8	104.35	odd	6
1872.2.by.n.433.3		8	312.173	odd	6
1872.2.by.n.1297.2		8	24.5	odd	2
2704.2.a.bd.1.1		4	104.93	odd	12
2704.2.a.be.1.1		4	104.37	odd	12
2704.2.f.q.337.1		8	104.29	even	6
2704.2.f.q.337.2		8	104.101	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13871 - 1.97231i) q^{3} +1.12182i q^{5} +(2.26053 + 1.30512i) q^{7} +(-1.09334 + 1.89372i) q^{9} +(2.26053 - 1.30512i) q^{11} +(-3.30591 + 1.43909i) q^{13} +(2.21257 - 1.27743i) q^{15} +(-2.77743 + 4.81064i) q^{17} +(6.88024 + 3.97231i) q^{19} -5.94462i q^{21} +(1.13871 + 1.97231i) q^{23} +3.74153 q^{25} -1.85229 q^{27} +(3.89924 + 6.75369i) q^{29} -8.26259i q^{31} +(-5.14819 - 2.97231i) q^{33} +(-1.46410 + 2.53590i) q^{35} +(-3.11971 + 1.80117i) q^{37} +(6.60282 + 4.88156i) q^{39} +(4.96410 - 2.86603i) q^{41} +(2.01690 - 3.49337i) q^{43} +(-2.12440 - 1.22652i) q^{45} -2.66562i q^{47} +(-0.0933372 - 0.161665i) q^{49} +12.6508 q^{51} +9.54002 q^{53} +(1.46410 + 2.53590i) q^{55} -18.0933i q^{57} +(3.31749 + 1.91535i) q^{59} +(3.84229 - 6.65503i) q^{61} +(-4.94304 + 2.85387i) q^{63} +(-1.61440 - 3.70862i) q^{65} +(-1.52690 + 0.881557i) q^{67} +(2.59334 - 4.49179i) q^{69} +(-0.880242 - 0.508208i) q^{71} +0.323330i q^{73} +(-4.26053 - 7.37945i) q^{75} +6.81333 q^{77} +2.66877 q^{79} +(5.38924 + 9.33444i) q^{81} -2.77953i q^{83} +(-5.39666 - 3.11576i) q^{85} +(8.88024 - 15.3810i) q^{87} +(-9.99531 + 5.77080i) q^{89} +(-9.35128 - 1.06149i) q^{91} +(-16.2964 + 9.40872i) q^{93} +(-4.45620 + 7.71837i) q^{95} +(13.5553 + 7.82618i) q^{97} +5.70773i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{19} - 2 q^{23} - 20 q^{25} - 28 q^{27} + 8 q^{29} + 6 q^{33} + 16 q^{35} + 24 q^{37} + 14 q^{39} + 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49}+ \cdots + 30 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^19 - 2 * q^23 - 20 * q^25 - 28 * q^27 + 8 * q^29 + 6 * q^33 + 16 * q^35 + 24 * q^37 + 14 * q^39 + 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 - 20 * q^53 - 16 * q^55 + 18 * q^59 + 4 * q^61 - 36 * q^63 + 14 * q^65 - 42 * q^67 + 18 * q^69 + 54 * q^71 - 22 * q^75 + 60 * q^77 - 16 * q^79 - 20 * q^81 - 6 * q^85 + 10 * q^87 - 18 * q^89 - 46 * q^91 - 36 * q^93 - 16 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

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