LMFDB - Embedded newform 1232.2.be.b.1167.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1232.815");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1167.2
Character	$\chi$	$=$	1232.1167
Dual form			1232.2.be.b.815.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51694 - 2.62742i) q^{3} +(-0.766106 - 0.442311i) q^{5} +(0.296809 - 2.62905i) q^{7} +(-3.10224 + 5.37323i) q^{9} +O(q^{10})$	\(q+(-1.51694 - 2.62742i) q^{3} +(-0.766106 - 0.442311i) q^{5} +(0.296809 - 2.62905i) q^{7} +(-3.10224 + 5.37323i) q^{9} +(0.866025 - 0.500000i) q^{11} +5.80526i q^{13} +2.68385i q^{15} +(-0.576630 + 0.332917i) q^{17} +(-3.71630 + 6.43682i) q^{19} +(-7.35787 + 3.20828i) q^{21} +(-2.96659 - 1.71276i) q^{23} +(-2.10872 - 3.65241i) q^{25} +9.72202 q^{27} -1.57738 q^{29} +(2.72783 + 4.72475i) q^{31} +(-2.62742 - 1.51694i) q^{33} +(-1.39025 + 1.88285i) q^{35} +(-0.867604 + 1.50273i) q^{37} +(15.2529 - 8.80625i) q^{39} +2.51870i q^{41} +4.40277i q^{43} +(4.75329 - 2.74431i) q^{45} +(2.68759 - 4.65504i) q^{47} +(-6.82381 - 1.56065i) q^{49} +(1.74943 + 1.01003i) q^{51} +(5.74837 + 9.95647i) q^{53} -0.884623 q^{55} +22.5497 q^{57} +(1.50282 + 2.60295i) q^{59} +(-2.33095 - 1.34578i) q^{61} +(13.2057 + 9.75077i) q^{63} +(2.56773 - 4.44744i) q^{65} +(7.18079 - 4.14583i) q^{67} +10.3927i q^{69} -11.9263i q^{71} +(-2.43070 + 1.40336i) q^{73} +(-6.39762 + 11.0810i) q^{75} +(-1.05748 - 2.42523i) q^{77} +(-10.4260 - 6.01945i) q^{79} +(-5.44105 - 9.42418i) q^{81} -12.1174 q^{83} +0.589012 q^{85} +(2.39279 + 4.14444i) q^{87} +(11.6907 + 6.74965i) q^{89} +(15.2623 + 1.72305i) q^{91} +(8.27594 - 14.3344i) q^{93} +(5.69416 - 3.28752i) q^{95} +0.764589i q^{97} +6.20448i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9	$ 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9} + 18 q^{17} - 14 q^{19} - 2 q^{21} + 12 q^{23} + 14 q^{25} + 16 q^{27} + 16 q^{29} - 10 q^{31} - 6 q^{35} - 4 q^{37} - 42 q^{39} - 42 q^{45} - 6 q^{47} - 4 q^{49} + 24 q^{51} - 2 q^{53} - 48 q^{57} + 12 q^{59} - 12 q^{61} + 26 q^{63} + 6 q^{65} + 48 q^{67} + 6 q^{73} + 14 q^{75} + 2 q^{77} - 48 q^{79} - 22 q^{81} + 84 q^{83} + 16 q^{85} - 18 q^{87} + 6 q^{89} + 18 q^{91} + 28 q^{93} + 36 q^{95}+O(q^{100}) $ 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9 + 18 * q^17 - 14 * q^19 - 2 * q^21 + 12 * q^23 + 14 * q^25 + 16 * q^27 + 16 * q^29 - 10 * q^31 - 6 * q^35 - 4 * q^37 - 42 * q^39 - 42 * q^45 - 6 * q^47 - 4 * q^49 + 24 * q^51 - 2 * q^53 - 48 * q^57 + 12 * q^59 - 12 * q^61 + 26 * q^63 + 6 * q^65 + 48 * q^67 + 6 * q^73 + 14 * q^75 + 2 * q^77 - 48 * q^79 - 22 * q^81 + 84 * q^83 + 16 * q^85 - 18 * q^87 + 6 * q^89 + 18 * q^91 + 28 * q^93 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.51694	−	2.62742i	−0.875808	−	1.51694i	−0.855899	−	0.517142i	$-0.826996\pi$
$3$	−1.51694	−	2.62742i	−0.875808	−	1.51694i	−0.0199086	−	0.999802i	$-0.506338\pi$
$4$		0			0
$5$	−0.766106	−	0.442311i	−0.342613	−	0.197808i	0.318814	−	0.947817i	$-0.396715\pi$
$5$	−0.766106	−	0.442311i	−0.342613	−	0.197808i	−0.661427	+	0.750010i	$0.730049\pi$
$6$		0			0
$7$	0.296809	−	2.62905i	0.112183	−	0.993688i
$7$	0.296809	−	2.62905i	0.112183	−	0.993688i
$8$		0			0
$9$	−3.10224	+	5.37323i	−1.03408	+	1.79108i
$10$		0			0
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$		0			0
$13$			5.80526i			1.61009i	0.593215	+	0.805044i	$0.297858\pi$
$13$			5.80526i			1.61009i	−0.593215	+	0.805044i	$0.702142\pi$
$14$		0			0
$15$			2.68385i			0.692966i
$16$		0			0
$17$	−0.576630	+	0.332917i	−0.139853	+	0.0807443i	−0.568294	−	0.822826i	$-0.692396\pi$
$17$	−0.576630	+	0.332917i	−0.139853	+	0.0807443i	0.428441	+	0.903570i	$0.359063\pi$
$18$		0			0
$19$	−3.71630	+	6.43682i	−0.852577	+	1.47671i	0.0262969	+	0.999654i	$0.491628\pi$
$19$	−3.71630	+	6.43682i	−0.852577	+	1.47671i	−0.878874	+	0.477053i	$0.841705\pi$
$20$		0			0
$21$	−7.35787	+	3.20828i	−1.60562	+	0.700104i
$22$		0			0
$23$	−2.96659	−	1.71276i	−0.618577	−	0.357135i	0.157738	−	0.987481i	$-0.449580\pi$
$23$	−2.96659	−	1.71276i	−0.618577	−	0.357135i	−0.776315	+	0.630346i	$0.782913\pi$
$24$		0			0
$25$	−2.10872	−	3.65241i	−0.421744	−	0.730483i
$26$		0			0
$27$	9.72202			1.87100
$28$		0			0
$29$	−1.57738			−0.292912			−0.146456	−	0.989217i	$-0.546787\pi$
$29$	−1.57738			−0.292912			−0.146456	+	0.989217i	$0.546787\pi$
$30$		0			0
$31$	2.72783	+	4.72475i	0.489933	+	0.848590i	0.999933	−	0.0115851i	$-0.00368774\pi$
$31$	2.72783	+	4.72475i	0.489933	+	0.848590i	−0.509999	+	0.860175i	$0.670354\pi$
$32$		0			0
$33$	−2.62742	−	1.51694i	−0.457376	−	0.264066i
$34$		0			0
$35$	−1.39025	+	1.88285i	−0.234994	+	0.318259i
$36$		0			0
$37$	−0.867604	+	1.50273i	−0.142633	+	0.247048i	−0.928487	−	0.371364i	$-0.878890\pi$
$37$	−0.867604	+	1.50273i	−0.142633	+	0.247048i	0.785854	+	0.618412i	$0.212224\pi$
$38$		0			0
$39$	15.2529	−	8.80625i	2.44241	−	1.41013i
$40$		0			0
$41$			2.51870i			0.393355i	0.980468	+	0.196678i	$0.0630152\pi$
$41$			2.51870i			0.393355i	−0.980468	+	0.196678i	$0.936985\pi$
$42$		0			0
$43$			4.40277i			0.671416i	0.941966	+	0.335708i	$0.108976\pi$
$43$			4.40277i			0.671416i	−0.941966	+	0.335708i	$0.891024\pi$
$44$		0			0
$45$	4.75329	−	2.74431i	0.708578	−	0.409098i
$46$		0			0
$47$	2.68759	−	4.65504i	0.392025	−	0.679008i	−0.600691	−	0.799481i	$-0.705108\pi$
$47$	2.68759	−	4.65504i	0.392025	−	0.679008i	0.992717	+	0.120473i	$0.0384412\pi$
$48$		0			0
$49$	−6.82381	−	1.56065i	−0.974830	−	0.222950i
$50$		0			0
$51$	1.74943	+	1.01003i	0.244969	+	0.141433i
$52$		0			0
$53$	5.74837	+	9.95647i	0.789600	+	1.36763i	0.926212	+	0.377002i	$0.123045\pi$
$53$	5.74837	+	9.95647i	0.789600	+	1.36763i	−0.136613	+	0.990625i	$0.543622\pi$
$54$		0			0
$55$	−0.884623			−0.119282
$56$		0			0
$57$	22.5497			2.98678
$58$		0			0
$59$	1.50282	+	2.60295i	0.195650	+	0.338876i	0.947113	−	0.320899i	$-0.103985\pi$
$59$	1.50282	+	2.60295i	0.195650	+	0.338876i	−0.751463	+	0.659775i	$0.770652\pi$
$60$		0			0
$61$	−2.33095	−	1.34578i	−0.298448	−	0.172309i	0.343298	−	0.939227i	$-0.388456\pi$
$61$	−2.33095	−	1.34578i	−0.298448	−	0.172309i	−0.641745	+	0.766918i	$0.721789\pi$
$62$		0			0
$63$	13.2057	+	9.75077i	1.66377	+	1.22848i
$64$		0			0
$65$	2.56773	−	4.44744i	0.318488	−	0.551637i
$66$		0			0
$67$	7.18079	−	4.14583i	0.877273	−	0.506494i	0.00751450	−	0.999972i	$-0.497608\pi$
$67$	7.18079	−	4.14583i	0.877273	−	0.506494i	0.869758	+	0.493478i	$0.164275\pi$
$68$		0			0
$69$			10.3927i			1.25113i
$70$		0			0
$71$		−	11.9263i		−	1.41539i	−0.706517	−	0.707696i	$-0.749735\pi$
$71$		−	11.9263i		−	1.41539i	0.706517	−	0.707696i	$-0.250265\pi$
$72$		0			0
$73$	−2.43070	+	1.40336i	−0.284492	+	0.164251i	−0.635455	−	0.772138i	$-0.719188\pi$
$73$	−2.43070	+	1.40336i	−0.284492	+	0.164251i	0.350963	+	0.936389i	$0.385854\pi$
$74$		0			0
$75$	−6.39762	+	11.0810i	−0.738734	+	1.27952i
$76$		0			0
$77$	−1.05748	−	2.42523i	−0.120511	−	0.276380i
$78$		0			0
$79$	−10.4260	−	6.01945i	−1.17302	−	0.677241i	−0.218628	−	0.975808i	$-0.570158\pi$
$79$	−10.4260	−	6.01945i	−1.17302	−	0.677241i	−0.954389	+	0.298567i	$0.903491\pi$
$80$		0			0
$81$	−5.44105	−	9.42418i	−0.604561	−	1.04713i
$82$		0			0
$83$	−12.1174			−1.33006			−0.665030	−	0.746816i	$-0.731581\pi$
$83$	−12.1174			−1.33006			−0.665030	+	0.746816i	$0.731581\pi$
$84$		0			0
$85$	0.589012			0.0638874
$86$		0			0
$87$	2.39279	+	4.14444i	0.256534	+	0.444331i
$88$		0			0
$89$	11.6907	+	6.74965i	1.23922	+	0.715462i	0.968934	−	0.247319i	$-0.0795497\pi$
$89$	11.6907	+	6.74965i	1.23922	+	0.715462i	0.270282	+	0.962781i	$0.412883\pi$
$90$		0			0
$91$	15.2623	+	1.72305i	1.59992	+	0.180625i
$92$		0			0
$93$	8.27594	−	14.3344i	0.858175	−	1.48640i
$94$		0			0
$95$	5.69416	−	3.28752i	0.584208	−	0.337293i
$96$		0			0
$97$			0.764589i			0.0776322i	0.999246	+	0.0388161i	$0.0123587\pi$
$97$			0.764589i			0.0776322i	−0.999246	+	0.0388161i	$0.987641\pi$
$98$		0			0
$99$			6.20448i			0.623573i
$100$		0			0
$101$	−13.5487	+	7.82233i	−1.34814	+	0.778351i	−0.987987	−	0.154540i	$-0.950610\pi$
$101$	−13.5487	+	7.82233i	−1.34814	+	0.778351i	−0.360158	+	0.932891i	$0.617277\pi$
$102$		0			0
$103$	−4.31722	+	7.47765i	−0.425389	+	0.736795i	−0.996457	−	0.0841079i	$-0.973196\pi$
$103$	−4.31722	+	7.47765i	−0.425389	+	0.736795i	0.571068	+	0.820903i	$0.306529\pi$
$104$		0			0
$105$	7.05597	+	0.796590i	0.688592	+	0.0777392i
$106$		0			0
$107$	10.9765	+	6.33727i	1.06113	+	0.612647i	0.925746	−	0.378146i	$-0.123438\pi$
$107$	10.9765	+	6.33727i	1.06113	+	0.612647i	0.135389	+	0.990793i	$0.456772\pi$
$108$		0			0
$109$	−7.08695	−	12.2750i	−0.678806	−	1.17573i	−0.975341	−	0.220705i	$-0.929164\pi$
$109$	−7.08695	−	12.2750i	−0.678806	−	1.17573i	0.296534	−	0.955022i	$-0.404169\pi$
$110$		0			0
$111$	5.26442			0.499677
$112$		0			0
$113$	17.3199			1.62932			0.814660	−	0.579938i	$-0.196923\pi$
$113$	17.3199			1.62932			0.814660	+	0.579938i	$0.196923\pi$
$114$		0			0
$115$	1.51515	+	2.62431i	0.141288	+	0.244718i
$116$		0			0
$117$	−31.1930	−	18.0093i	−2.88379	−	1.66496i
$118$		0			0
$119$	0.704107	+	1.61480i	0.0645454	+	0.148029i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	6.61770	−	3.82073i	0.596698	−	0.344504i
$124$		0			0
$125$			8.15396i			0.729312i
$126$		0			0
$127$		−	2.06788i		−	0.183495i	−0.995782	−	0.0917475i	$-0.970755\pi$
$127$		−	2.06788i		−	0.183495i	0.995782	−	0.0917475i	$-0.0292453\pi$
$128$		0			0
$129$	11.5679	−	6.67876i	1.01850	−	0.588032i
$130$		0			0
$131$	−9.82744	+	17.0216i	−0.858627	+	1.48719i	0.0146114	+	0.999893i	$0.495349\pi$
$131$	−9.82744	+	17.0216i	−0.858627	+	1.48719i	−0.873239	+	0.487293i	$0.837984\pi$
$132$		0			0
$133$	15.8197	+	11.6808i	1.37174	+	1.01286i
$134$		0			0
$135$	−7.44810	−	4.30016i	−0.641030	−	0.370099i
$136$		0			0
$137$	9.58725	+	16.6056i	0.819094	+	1.41871i	0.906350	+	0.422527i	$0.138857\pi$
$137$	9.58725	+	16.6056i	0.819094	+	1.41871i	−0.0872558	+	0.996186i	$0.527810\pi$
$138$		0			0
$139$	−1.06327			−0.0901857			−0.0450928	−	0.998983i	$-0.514358\pi$
$139$	−1.06327			−0.0901857			−0.0450928	+	0.998983i	$0.514358\pi$
$140$		0			0
$141$	−16.3077			−1.37336
$142$		0			0
$143$	2.90263	+	5.02750i	0.242730	+	0.420421i
$144$		0			0
$145$	1.20844	+	0.697692i	0.100355	+	0.0579402i
$146$		0			0
$147$	6.25084	+	20.2965i	0.515561	+	1.67402i
$148$		0			0
$149$	2.96461	−	5.13486i	0.242871	−	0.420664i	−0.718660	−	0.695362i	$-0.755244\pi$
$149$	2.96461	−	5.13486i	0.242871	−	0.420664i	0.961531	+	0.274697i	$0.0885776\pi$
$150$		0			0
$151$	−17.7645	+	10.2563i	−1.44565	+	0.834648i	−0.998218	−	0.0596695i	$-0.980995\pi$
$151$	−17.7645	+	10.2563i	−1.44565	+	0.834648i	−0.447434	+	0.894317i	$0.647662\pi$
$152$		0			0
$153$		−	4.13116i		−	0.333984i
$154$		0			0
$155$		−	4.82621i		−	0.387650i
$156$		0			0
$157$	−0.431120	+	0.248907i	−0.0344071	+	0.0198650i	−0.517105	−	0.855922i	$-0.672990\pi$
$157$	−0.431120	+	0.248907i	−0.0344071	+	0.0198650i	0.482698	+	0.875787i	$0.339657\pi$
$158$		0			0
$159$	17.4399	−	30.2068i	1.38308	−	2.39556i
$160$		0			0
$161$	−5.38345	+	7.29095i	−0.424275	+	0.574607i
$162$		0			0
$163$	−19.6100	−	11.3218i	−1.53597	−	0.886795i	−0.999068	−	0.0431533i	$-0.986260\pi$
$163$	−19.6100	−	11.3218i	−1.53597	−	0.886795i	−0.536906	−	0.843642i	$-0.680407\pi$
$164$		0			0
$165$	1.34192	+	2.32428i	0.104469	+	0.180945i
$166$		0			0
$167$	14.3679			1.11182			0.555910	−	0.831242i	$-0.312370\pi$
$167$	14.3679			1.11182			0.555910	+	0.831242i	$0.312370\pi$
$168$		0			0
$169$	−20.7010			−1.59238
$170$		0			0
$171$	−23.0577	−	39.9371i	−1.76327	−	3.05407i
$172$		0			0
$173$	−9.00943	−	5.20160i	−0.684974	−	0.395470i	0.116752	−	0.993161i	$-0.462752\pi$
$173$	−9.00943	−	5.20160i	−0.684974	−	0.395470i	−0.801727	+	0.597691i	$0.796085\pi$
$174$		0			0
$175$	−10.2283	+	4.45986i	−0.773184	+	0.337134i
$176$		0			0
$177$	4.55938	−	7.89707i	0.342704	−	0.593580i
$178$		0			0
$179$	5.25927	−	3.03644i	0.393096	−	0.226954i	−0.290404	−	0.956904i	$-0.593790\pi$
$179$	5.25927	−	3.03644i	0.393096	−	0.226954i	0.683501	+	0.729950i	$0.260457\pi$
$180$		0			0
$181$			5.68994i			0.422930i	0.977386	+	0.211465i	$0.0678234\pi$
$181$			5.68994i			0.422930i	−0.977386	+	0.211465i	$0.932177\pi$
$182$		0			0
$183$			8.16586i			0.603638i
$184$		0			0
$185$	1.32935	−	0.767502i	0.0977359	−	0.0564279i
$186$		0			0
$187$	−0.332917	+	0.576630i	−0.0243453	+	0.0421673i
$188$		0			0
$189$	2.88559	−	25.5597i	0.209895	−	1.85919i
$190$		0			0
$191$	−20.2687	−	11.7021i	−1.46659	−	0.846737i	−0.467290	−	0.884104i	$-0.654770\pi$
$191$	−20.2687	−	11.7021i	−1.46659	−	0.846737i	−0.999302	+	0.0373671i	$0.988103\pi$
$192$		0			0
$193$	3.38111	+	5.85625i	0.243377	+	0.421542i	0.961674	−	0.274195i	$-0.0884113\pi$
$193$	3.38111	+	5.85625i	0.243377	+	0.421542i	−0.718297	+	0.695737i	$0.755078\pi$
$194$		0			0
$195$	−15.5804			−1.11574
$196$		0			0
$197$	15.5300			1.10647			0.553235	−	0.833025i	$-0.313393\pi$
$197$	15.5300			1.10647			0.553235	+	0.833025i	$0.313393\pi$
$198$		0			0
$199$	−5.68811	−	9.85209i	−0.403219	−	0.698396i	0.590893	−	0.806750i	$-0.298775\pi$
$199$	−5.68811	−	9.85209i	−0.403219	−	0.698396i	−0.994112	+	0.108354i	$0.965442\pi$
$200$		0			0
$201$	−21.7857	−	12.5780i	−1.53665	−	0.887182i
$202$		0			0
$203$	−0.468180	+	4.14700i	−0.0328598	+	0.291063i
$204$		0			0
$205$	1.11405	−	1.92959i	0.0778086	−	0.134769i
$206$		0			0
$207$	18.4061	−	10.6268i	1.27932	−	0.738613i
$208$		0			0
$209$			7.43260i			0.514124i
$210$		0			0
$211$			17.9893i			1.23843i	0.785221	+	0.619216i	$0.212550\pi$
$211$			17.9893i			1.23843i	−0.785221	+	0.619216i	$0.787450\pi$
$212$		0			0
$213$	−31.3355	+	18.0915i	−2.14707	+	1.23961i
$214$		0			0
$215$	1.94740	−	3.37299i	0.132811	−	0.230036i
$216$		0			0
$217$	13.2312	−	5.76926i	0.898195	−	0.391643i
$218$		0			0
$219$	7.37447	+	4.25765i	0.498320	+	0.287705i
$220$		0			0
$221$	−1.93267	−	3.34748i	−0.130005	−	0.225176i
$222$		0			0
$223$	−18.8373			−1.26144			−0.630719	−	0.776011i	$-0.717240\pi$
$223$	−18.8373			−1.26144			−0.630719	+	0.776011i	$0.717240\pi$
$224$		0			0
$225$	26.1670			1.74447
$226$		0			0
$227$	−11.2362	−	19.4618i	−0.745776	−	1.29172i	−0.949831	−	0.312763i	$-0.898746\pi$
$227$	−11.2362	−	19.4618i	−0.745776	−	1.29172i	0.204055	−	0.978959i	$-0.434588\pi$
$228$		0			0
$229$	−2.92762	−	1.69026i	−0.193463	−	0.111696i	0.400140	−	0.916454i	$-0.368962\pi$
$229$	−2.92762	−	1.69026i	−0.193463	−	0.111696i	−0.593603	+	0.804758i	$0.702295\pi$
$230$		0			0
$231$	−4.76797	+	6.45739i	−0.313709	+	0.424865i
$232$		0			0
$233$	−1.64816	+	2.85470i	−0.107975	+	0.187018i	−0.914950	−	0.403568i	$-0.867770\pi$
$233$	−1.64816	+	2.85470i	−0.107975	+	0.187018i	0.806975	+	0.590586i	$0.201103\pi$
$234$		0			0
$235$	−4.11796	+	2.37750i	−0.268626	+	0.155091i
$236$		0			0
$237$			36.5247i			2.37253i
$238$		0			0
$239$		−	0.172767i		−	0.0111754i	−0.999984	−	0.00558768i	$-0.998221\pi$
$239$		−	0.172767i		−	0.0111754i	0.999984	−	0.00558768i	$-0.00177862\pi$
$240$		0			0
$241$	−18.0433	+	10.4173i	−1.16227	+	0.671039i	−0.951848	−	0.306571i	$-0.900818\pi$
$241$	−18.0433	+	10.4173i	−1.16227	+	0.671039i	−0.210425	+	0.977610i	$0.567485\pi$
$242$		0			0
$243$	−1.92451	+	3.33334i	−0.123457	+	0.213834i
$244$		0			0
$245$	4.53746	+	4.21387i	0.289888	+	0.269214i
$246$		0			0
$247$	−37.3674	−	21.5741i	−2.37763	−	1.37273i
$248$		0			0
$249$	18.3815	+	31.8376i	1.16488	+	2.01763i
$250$		0			0
$251$	20.8033			1.31309			0.656547	−	0.754285i	$-0.272016\pi$
$251$	20.8033			1.31309			0.656547	+	0.754285i	$0.272016\pi$
$252$		0			0
$253$	−3.42552			−0.215361
$254$		0			0
$255$	−0.893499	−	1.54759i	−0.0559531	−	0.0969136i
$256$		0			0
$257$	−17.3974	−	10.0444i	−1.08522	−	0.626554i	−0.152922	−	0.988238i	$-0.548868\pi$
$257$	−17.3974	−	10.0444i	−1.08522	−	0.626554i	−0.932301	+	0.361685i	$0.882202\pi$
$258$		0			0
$259$	3.69325	+	2.72700i	0.229487	+	0.169447i
$260$		0			0
$261$	4.89340	−	8.47562i	0.302894	−	0.524628i
$262$		0			0
$263$	−22.2700	+	12.8576i	−1.37323	+	0.792833i	−0.991333	−	0.131374i	$-0.958061\pi$
$263$	−22.2700	+	12.8576i	−1.37323	+	0.792833i	−0.381893	+	0.924206i	$0.624728\pi$
$264$		0			0
$265$		−	10.1703i		−	0.624755i
$266$		0			0
$267$		−	40.9554i		−	2.50643i
$268$		0			0
$269$	−2.98673	+	1.72439i	−0.182104	+	0.105138i	−0.588281	−	0.808657i	$-0.700195\pi$
$269$	−2.98673	+	1.72439i	−0.182104	+	0.105138i	0.406177	+	0.913794i	$0.366862\pi$
$270$		0			0
$271$	−7.47499	+	12.9471i	−0.454073	+	0.786478i	−0.998634	−	0.0522430i	$-0.983363\pi$
$271$	−7.47499	+	12.9471i	−0.454073	+	0.786478i	0.544561	+	0.838721i	$0.316696\pi$
$272$		0			0
$273$	−18.6249	−	42.7143i	−1.12723	−	2.58519i
$274$		0			0
$275$	−3.65241	−	2.10872i	−0.220249	−	0.127161i
$276$		0			0
$277$	−0.0238068	−	0.0412346i	−0.00143041	−	0.00247755i	0.865309	−	0.501238i	$-0.167122\pi$
$277$	−0.0238068	−	0.0412346i	−0.00143041	−	0.00247755i	−0.866740	+	0.498761i	$0.833789\pi$
$278$		0			0
$279$	−33.8496			−2.02652
$280$		0			0
$281$	−4.28214			−0.255451			−0.127725	−	0.991810i	$-0.540768\pi$
$281$	−4.28214			−0.255451			−0.127725	+	0.991810i	$0.540768\pi$
$282$		0			0
$283$	7.18207	+	12.4397i	0.426930	+	0.739464i	0.996598	−	0.0824104i	$-0.0262618\pi$
$283$	7.18207	+	12.4397i	0.426930	+	0.739464i	−0.569669	+	0.821874i	$0.692928\pi$
$284$		0			0
$285$	−17.2754	−	9.97398i	−1.02331	−	0.590807i
$286$		0			0
$287$	6.62179	+	0.747573i	0.390872	+	0.0441279i
$288$		0			0
$289$	−8.27833	+	14.3385i	−0.486961	+	0.843441i
$290$		0			0
$291$	2.00890	−	1.15984i	0.117764	−	0.0679909i
$292$		0			0
$293$		−	3.11780i		−	0.182144i	−0.995844	−	0.0910718i	$-0.970971\pi$
$293$		−	3.11780i		−	0.182144i	0.995844	−	0.0910718i	$-0.0290293\pi$
$294$		0			0
$295$		−	2.65885i		−	0.154804i
$296$		0			0
$297$	8.41952	−	4.86101i	0.488550	−	0.282065i
$298$		0			0
$299$	9.94302	−	17.2218i	0.575020	−	0.995963i
$300$		0			0
$301$	11.5751	+	1.30678i	0.667178	+	0.0753217i
$302$		0			0
$303$	41.1052	+	23.7321i	2.36143	+	1.36337i
$304$		0			0
$305$	1.19050	+	2.06201i	0.0681680	+	0.118070i
$306$		0			0
$307$	−0.167901			−0.00958260			−0.00479130	−	0.999989i	$-0.501525\pi$
$307$	−0.167901			−0.00958260			−0.00479130	+	0.999989i	$0.501525\pi$
$308$		0			0
$309$	26.1959			1.49024
$310$		0			0
$311$	5.91505	+	10.2452i	0.335412	+	0.580950i	0.983564	−	0.180561i	$-0.0577913\pi$
$311$	5.91505	+	10.2452i	0.335412	+	0.580950i	−0.648152	+	0.761511i	$0.724458\pi$
$312$		0			0
$313$	24.0325	+	13.8751i	1.35839	+	0.784270i	0.989407	−	0.145165i	$-0.0463713\pi$
$313$	24.0325	+	13.8751i	1.35839	+	0.784270i	0.368987	+	0.929434i	$0.379705\pi$
$314$		0			0
$315$	−5.80411	−	13.3112i	−0.327025	−	0.749999i
$316$		0			0
$317$	−15.6861	+	27.1692i	−0.881021	+	1.52597i	−0.0308132	+	0.999525i	$0.509810\pi$
$317$	−15.6861	+	27.1692i	−0.881021	+	1.52597i	−0.850208	+	0.526448i	$0.823524\pi$
$318$		0			0
$319$	−1.36605	+	0.788689i	−0.0764841	+	0.0441581i
$320$		0			0
$321$		−	38.4531i		−	2.14624i
$322$		0			0
$323$		−	4.94888i		−	0.275363i
$324$		0			0
$325$	21.2032	−	12.2417i	1.17614	−	0.679046i
$326$		0			0
$327$	−21.5010	+	37.2408i	−1.18901	+	2.05942i
$328$		0			0
$329$	−11.4406	−	8.44747i	−0.630743	−	0.465724i
$330$		0			0
$331$	1.16861	+	0.674694i	0.0642323	+	0.0370846i	0.531772	−	0.846887i	$-0.321526\pi$
$331$	1.16861	+	0.674694i	0.0642323	+	0.0370846i	−0.467540	+	0.883972i	$0.654860\pi$
$332$		0			0
$333$	−5.38303	−	9.32368i	−0.294988	−	0.510934i
$334$		0			0
$335$	−7.33499			−0.400753
$336$		0			0
$337$	28.3720			1.54552			0.772759	−	0.634699i	$-0.218876\pi$
$337$	28.3720			1.54552			0.772759	+	0.634699i	$0.218876\pi$
$338$		0			0
$339$	−26.2733	−	45.5068i	−1.42697	−	2.47159i
$340$		0			0
$341$	4.72475	+	2.72783i	0.255859	+	0.147720i
$342$		0			0
$343$	−6.12840	+	17.4769i	−0.330903	+	0.943665i
$344$		0			0
$345$	4.59679	−	7.96187i	0.247483	−	0.428653i
$346$		0			0
$347$	−12.5343	+	7.23669i	−0.672878	+	0.388486i	−0.797166	−	0.603760i	$-0.793669\pi$
$347$	−12.5343	+	7.23669i	−0.672878	+	0.388486i	0.124288	+	0.992246i	$0.460335\pi$
$348$		0			0
$349$		−	5.72848i		−	0.306639i	−0.988177	−	0.153319i	$-0.951004\pi$
$349$		−	5.72848i		−	0.306639i	0.988177	−	0.153319i	$-0.0489963\pi$
$350$		0			0
$351$			56.4388i			3.01248i
$352$		0			0
$353$	12.7869	−	7.38254i	0.680580	−	0.392933i	−0.119494	−	0.992835i	$-0.538127\pi$
$353$	12.7869	−	7.38254i	0.680580	−	0.392933i	0.800073	+	0.599902i	$0.204794\pi$
$354$		0			0
$355$	−5.27514	+	9.13681i	−0.279975	+	0.484931i
$356$		0			0
$357$	3.17468	−	4.29955i	0.168022	−	0.227556i
$358$		0			0
$359$	11.5098	+	6.64517i	0.607462	+	0.350719i	0.771972	−	0.635657i	$-0.219271\pi$
$359$	11.5098	+	6.64517i	0.607462	+	0.350719i	−0.164509	+	0.986376i	$0.552604\pi$
$360$		0			0
$361$	−18.1218	−	31.3878i	−0.953777	−	1.65199i
$362$		0			0
$363$	−3.03389			−0.159238
$364$		0			0
$365$	2.48290			0.129961
$366$		0			0
$367$	17.6619	+	30.5914i	0.921945	+	1.59686i	0.796402	+	0.604768i	$0.206734\pi$
$367$	17.6619	+	30.5914i	0.921945	+	1.59686i	0.125544	+	0.992088i	$0.459932\pi$
$368$		0			0
$369$	−13.5336	−	7.81361i	−0.704530	−	0.406760i
$370$		0			0
$371$	27.8822	−	12.1576i	1.44757	−	0.631190i
$372$		0			0
$373$	−4.10727	+	7.11401i	−0.212667	+	0.368349i	−0.952548	−	0.304388i	$-0.901548\pi$
$373$	−4.10727	+	7.11401i	−0.212667	+	0.368349i	0.739882	+	0.672737i	$0.234881\pi$
$374$		0			0
$375$	21.4239	−	12.3691i	1.10633	−	0.638738i
$376$		0			0
$377$		−	9.15708i		−	0.471614i
$378$		0			0
$379$			14.9059i			0.765665i	0.923818	+	0.382832i	$0.125051\pi$
$379$			14.9059i			0.765665i	−0.923818	+	0.382832i	$0.874949\pi$
$380$		0			0
$381$	−5.43321	+	3.13686i	−0.278352	+	0.160706i
$382$		0			0
$383$	8.12686	−	14.0761i	0.415263	−	0.719257i	−0.580193	−	0.814479i	$-0.697023\pi$
$383$	8.12686	−	14.0761i	0.415263	−	0.719257i	0.995456	+	0.0952221i	$0.0303561\pi$
$384$		0			0
$385$	−0.262564	+	2.32572i	−0.0133815	+	0.118530i
$386$		0			0
$387$	−23.6571	−	13.6584i	−1.20256	−	0.694298i
$388$		0			0
$389$	−14.2874	−	24.7465i	−0.724399	−	1.25470i	−0.959221	−	0.282657i	$-0.908784\pi$
$389$	−14.2874	−	24.7465i	−0.724399	−	1.25470i	0.234822	−	0.972038i	$-0.424549\pi$
$390$		0			0
$391$	2.28083			0.115347
$392$		0			0
$393$	59.6307			3.00797
$394$		0			0
$395$	5.32495	+	9.22308i	0.267927	+	0.464063i
$396$		0			0
$397$	−16.7044	−	9.64428i	−0.838369	−	0.484033i	0.0183405	−	0.999832i	$-0.494162\pi$
$397$	−16.7044	−	9.64428i	−0.838369	−	0.484033i	−0.856709	+	0.515799i	$0.827495\pi$
$398$		0			0
$399$	6.69295	−	59.2842i	0.335066	−	2.96792i
$400$		0			0
$401$	11.9815	−	20.7526i	0.598327	−	1.03633i	−0.394741	−	0.918792i	$-0.629166\pi$
$401$	11.9815	−	20.7526i	0.598327	−	1.03633i	0.993068	−	0.117541i	$-0.0375010\pi$
$402$		0			0
$403$	−27.4284	+	15.8358i	−1.36630	+	0.788836i
$404$		0			0
$405$			9.62656i			0.478347i
$406$		0			0
$407$			1.73521i			0.0860110i
$408$		0			0
$409$	1.33938	−	0.773291i	0.0662280	−	0.0382368i	−0.466520	−	0.884510i	$-0.654493\pi$
$409$	1.33938	−	0.773291i	0.0662280	−	0.0382368i	0.532748	+	0.846274i	$0.321159\pi$
$410$		0			0
$411$	29.0867	−	50.3796i	1.43474	−	2.48504i
$412$		0			0
$413$	7.28935	−	3.17840i	0.358685	−	0.156399i
$414$		0			0
$415$	9.28323	+	5.35968i	0.455696	+	0.263096i
$416$		0			0
$417$	1.61293	+	2.79367i	0.0789854	+	0.136807i
$418$		0			0
$419$	−34.6341			−1.69199			−0.845993	−	0.533194i	$-0.820992\pi$
$419$	−34.6341			−1.69199			−0.845993	+	0.533194i	$0.820992\pi$
$420$		0			0
$421$	−7.57711			−0.369286			−0.184643	−	0.982806i	$-0.559113\pi$
$421$	−7.57711			−0.369286			−0.184643	+	0.982806i	$0.559113\pi$
$422$		0			0
$423$	16.6751	+	28.8821i	0.810771	+	1.40430i
$424$		0			0
$425$	2.43190	+	1.40406i	0.117965	+	0.0681069i
$426$		0			0
$427$	−4.22996	+	5.72875i	−0.204702	+	0.277234i
$428$		0			0
$429$	8.80625	−	15.2529i	0.425170	−	0.736415i
$430$		0			0
$431$	−1.19894	+	0.692206i	−0.0577507	+	0.0333424i	−0.528597	−	0.848873i	$-0.677282\pi$
$431$	−1.19894	+	0.692206i	−0.0577507	+	0.0333424i	0.470847	+	0.882215i	$0.343949\pi$
$432$		0			0
$433$			15.4764i			0.743747i	0.928284	+	0.371873i	$0.121284\pi$
$433$			15.4764i			0.743747i	−0.928284	+	0.371873i	$0.878716\pi$
$434$		0			0
$435$		−	4.23344i		−	0.202978i
$436$		0			0
$437$	22.0495	−	12.7303i	1.05477	−	0.608971i
$438$		0			0
$439$	7.92086	−	13.7193i	0.378042	−	0.654788i	−0.612735	−	0.790288i	$-0.709931\pi$
$439$	7.92086	−	13.7193i	0.378042	−	0.654788i	0.990777	+	0.135500i	$0.0432641\pi$
$440$		0			0
$441$	29.5548	−	31.8244i	1.40737	−	1.51545i
$442$		0			0
$443$	8.66477	+	5.00260i	0.411675	+	0.237681i	0.691509	−	0.722368i	$-0.256946\pi$
$443$	8.66477	+	5.00260i	0.411675	+	0.237681i	−0.279834	+	0.960048i	$0.590279\pi$
$444$		0			0
$445$	−5.97090	−	10.3419i	−0.283048	−	0.490253i
$446$		0			0
$447$	−17.9886			−0.850832
$448$		0			0
$449$	29.3617			1.38567			0.692833	−	0.721098i	$-0.256362\pi$
$449$	29.3617			1.38567			0.692833	+	0.721098i	$0.256362\pi$
$450$		0			0
$451$	1.25935	+	2.18126i	0.0593005	+	0.102711i
$452$		0			0
$453$	53.8954	+	31.1165i	2.53223	+	1.46198i
$454$		0			0
$455$	−10.9304	−	8.07073i	−0.512426	−	0.378362i
$456$		0			0
$457$	−4.91450	+	8.51217i	−0.229891	+	0.398182i	−0.957776	−	0.287517i	$-0.907170\pi$
$457$	−4.91450	+	8.51217i	−0.229891	+	0.398182i	0.727885	+	0.685699i	$0.240504\pi$
$458$		0			0
$459$	−5.60601	+	3.23663i	−0.261666	+	0.151073i
$460$		0			0
$461$			28.8901i			1.34554i	0.739850	+	0.672772i	$0.234897\pi$
$461$			28.8901i			1.34554i	−0.739850	+	0.672772i	$0.765103\pi$
$462$		0			0
$463$			16.9310i			0.786849i	0.919357	+	0.393425i	$0.128710\pi$
$463$			16.9310i			0.786849i	−0.919357	+	0.393425i	$0.871290\pi$
$464$		0			0
$465$	−12.6805	+	7.32109i	−0.588044	+	0.339507i
$466$		0			0
$467$	20.8677	−	36.1439i	0.965641	−	1.67254i	0.257757	−	0.966210i	$-0.417016\pi$
$467$	20.8677	−	36.1439i	0.965641	−	1.67254i	0.707883	−	0.706329i	$-0.249650\pi$
$468$		0			0
$469$	−8.76827	−	20.1092i	−0.404881	−	0.928555i
$470$		0			0
$471$	1.30797	+	0.755157i	0.0602681	+	0.0347958i
$472$		0			0
$473$	2.20138	+	3.81291i	0.101220	+	0.175318i
$474$		0			0
$475$	31.3466			1.43828
$476$		0			0
$477$	−71.3313			−3.26604
$478$		0			0
$479$	−8.64784	−	14.9785i	−0.395130	−	0.684385i	0.597988	−	0.801505i	$-0.295967\pi$
$479$	−8.64784	−	14.9785i	−0.395130	−	0.684385i	−0.993118	+	0.117120i	$0.962634\pi$
$480$		0			0
$481$	−8.72375	−	5.03666i	−0.397769	−	0.229652i
$482$		0			0
$483$	27.3228	+	3.08463i	1.24323	+	0.140356i
$484$		0			0
$485$	0.338186	−	0.585756i	0.0153562	−	0.0265978i
$486$		0			0
$487$	−7.53520	+	4.35045i	−0.341452	+	0.197138i	−0.660914	−	0.750462i	$-0.729831\pi$
$487$	−7.53520	+	4.35045i	−0.341452	+	0.197138i	0.319462	+	0.947599i	$0.396498\pi$
$488$		0			0
$489$			68.6984i			3.10665i
$490$		0			0
$491$			5.84010i			0.263560i	0.991279	+	0.131780i	$0.0420692\pi$
$491$			5.84010i			0.263560i	−0.991279	+	0.131780i	$0.957931\pi$
$492$		0			0
$493$	0.909563	−	0.525136i	0.0409647	−	0.0236510i
$494$		0			0
$495$	2.74431	−	4.75329i	0.123348	−	0.213644i
$496$		0			0
$497$	−31.3548	−	3.53984i	−1.40646	−	0.158783i
$498$		0			0
$499$	15.6340	+	9.02630i	0.699875	+	0.404073i	0.807301	−	0.590140i	$-0.200928\pi$
$499$	15.6340	+	9.02630i	0.699875	+	0.404073i	−0.107426	+	0.994213i	$0.534261\pi$
$500$		0			0
$501$	−21.7953	−	37.7505i	−0.973742	−	1.68657i
$502$		0			0
$503$	13.4279			0.598721			0.299360	−	0.954140i	$-0.403227\pi$
$503$	13.4279			0.598721			0.299360	+	0.954140i	$0.403227\pi$
$504$		0			0
$505$	13.8396			0.615855
$506$		0			0
$507$	31.4023	+	54.3903i	1.39462	+	2.41556i
$508$		0			0
$509$	19.2618	+	11.1208i	0.853766	+	0.492922i	0.861920	−	0.507045i	$-0.169262\pi$
$509$	19.2618	+	11.1208i	0.853766	+	0.492922i	−0.00815390	+	0.999967i	$0.502595\pi$
$510$		0			0
$511$	2.96806	+	6.80696i	0.131299	+	0.301122i
$512$		0			0
$513$	−36.1300	+	62.5789i	−1.59518	+	2.76293i
$514$		0			0
$515$	6.61490	−	3.81911i	0.291487	−	0.168290i
$516$		0			0
$517$		−	5.37518i		−	0.236400i
$518$		0			0
$519$			31.5621i			1.38542i
$520$		0			0
$521$	−18.0494	+	10.4208i	−0.790757	+	0.456544i	−0.840229	−	0.542232i	$-0.817579\pi$
$521$	−18.0494	+	10.4208i	−0.790757	+	0.456544i	0.0494720	+	0.998776i	$0.484246\pi$
$522$		0			0
$523$	−4.45030	+	7.70815i	−0.194598	+	0.337054i	−0.946769	−	0.321915i	$-0.895674\pi$
$523$	−4.45030	+	7.70815i	−0.194598	+	0.337054i	0.752171	+	0.658968i	$0.229007\pi$
$524$		0			0
$525$	27.2337	+	20.1086i	1.18857	+	0.877612i
$526$		0			0
$527$	−3.14590	−	1.81629i	−0.137038	−	0.0791187i
$528$		0			0
$529$	−5.63289	−	9.75646i	−0.244908	−	0.424194i
$530$		0			0
$531$	−18.6484			−0.809271
$532$		0			0
$533$	−14.6217			−0.633336
$534$		0			0
$535$	−5.60609	−	9.71003i	−0.242372	−	0.419801i
$536$		0			0
$537$	−15.9560	−	9.21223i	−0.688554	−	0.397537i
$538$		0			0
$539$	−6.68992	+	2.06034i	−0.288155	+	0.0887451i
$540$		0			0
$541$	−11.1631	+	19.3351i	−0.479941	+	0.831282i	−0.999735	−	0.0230096i	$-0.992675\pi$
$541$	−11.1631	+	19.3351i	−0.479941	+	0.831282i	0.519794	+	0.854291i	$0.326009\pi$
$542$		0			0
$543$	14.9499	−	8.63132i	0.641561	−	0.370405i
$544$		0			0
$545$			12.5385i			0.537092i
$546$		0			0
$547$		−	7.46203i		−	0.319053i	−0.987194	−	0.159527i	$-0.949003\pi$
$547$		−	7.46203i		−	0.319053i	0.987194	−	0.159527i	$-0.0509968\pi$
$548$		0			0
$549$	14.4623	−	8.34983i	0.617237	−	0.356362i
$550$		0			0
$551$	5.86201	−	10.1533i	0.249730	−	0.432545i
$552$		0			0
$553$	−18.9200	+	25.6238i	−0.804559	+	1.08964i
$554$		0			0
$555$	−4.03311	−	2.32851i	−0.171196	−	0.0988399i
$556$		0			0
$557$	−14.6505	−	25.3754i	−0.620760	−	1.07519i	−0.989344	−	0.145594i	$-0.953491\pi$
$557$	−14.6505	−	25.3754i	−0.620760	−	1.07519i	0.368584	−	0.929594i	$-0.379843\pi$
$558$		0			0
$559$	−25.5592			−1.08104
$560$		0			0
$561$	2.02007			0.0852873
$562$		0			0
$563$	21.6343	+	37.4717i	0.911777	+	1.57924i	0.811552	+	0.584280i	$0.198623\pi$
$563$	21.6343	+	37.4717i	0.911777	+	1.57924i	0.100225	+	0.994965i	$0.468044\pi$
$564$		0			0
$565$	−13.2689	−	7.66080i	−0.558226	−	0.322292i
$566$		0			0
$567$	−26.3916	+	11.5076i	−1.10834	+	0.483274i
$568$		0			0
$569$	−5.33795	+	9.24560i	−0.223778	+	0.387596i	−0.955952	−	0.293522i	$-0.905173\pi$
$569$	−5.33795	+	9.24560i	−0.223778	+	0.387596i	0.732174	+	0.681118i	$0.238506\pi$
$570$		0			0
$571$	−9.01939	+	5.20735i	−0.377450	+	0.217921i	−0.676708	−	0.736251i	$-0.736594\pi$
$571$	−9.01939	+	5.20735i	−0.377450	+	0.217921i	0.299258	+	0.954172i	$0.403261\pi$
$572$		0			0
$573$			71.0060i			2.96632i
$574$		0			0
$575$			14.4469i			0.602479i
$576$		0			0
$577$	−26.9407	+	15.5542i	−1.12155	+	0.647530i	−0.941797	−	0.336181i	$-0.890864\pi$
$577$	−26.9407	+	15.5542i	−1.12155	+	0.647530i	−0.179757	+	0.983711i	$0.557531\pi$
$578$		0			0
$579$	10.2579	−	17.7672i	0.426304	−	0.738380i
$580$		0			0
$581$	−3.59656	+	31.8573i	−0.149211	+	1.32166i
$582$		0			0
$583$	9.95647	+	5.74837i	0.412355	+	0.238073i
$584$		0			0
$585$	15.9314	+	27.5940i	0.658683	+	1.14087i
$586$		0			0
$587$	3.80480			0.157041			0.0785205	−	0.996913i	$-0.474980\pi$
$587$	3.80480			0.157041			0.0785205	+	0.996913i	$0.474980\pi$
$588$		0			0
$589$	−40.5498			−1.67082
$590$		0			0
$591$	−23.5582	−	40.8040i	−0.969055	−	1.67845i
$592$		0			0
$593$	33.8184	+	19.5250i	1.38875	+	0.801797i	0.993175	−	0.116635i	$-0.0372108\pi$
$593$	33.8184	+	19.5250i	1.38875	+	0.801797i	0.395579	+	0.918432i	$0.370544\pi$
$594$		0			0
$595$	0.174824	−	1.54854i	0.00716710	−	0.0634841i
$596$		0			0
$597$	−17.2571	+	29.8901i	−0.706285	+	1.22332i
$598$		0			0
$599$	−5.54063	+	3.19888i	−0.226384	+	0.130703i	−0.608903	−	0.793245i	$-0.708390\pi$
$599$	−5.54063	+	3.19888i	−0.226384	+	0.130703i	0.382519	+	0.923948i	$0.375057\pi$
$600$		0			0
$601$		−	15.4619i		−	0.630703i	−0.948975	−	0.315352i	$-0.897878\pi$
$601$		−	15.4619i		−	0.630703i	0.948975	−	0.315352i	$-0.102122\pi$
$602$		0			0
$603$			51.4454i			2.09502i
$604$		0			0
$605$	−0.766106	+	0.442311i	−0.0311466	+	0.0179825i
$606$		0			0
$607$	11.8652	−	20.5512i	0.481595	−	0.834146i	−0.518182	−	0.855270i	$-0.673391\pi$
$607$	11.8652	−	20.5512i	0.481595	−	0.834146i	0.999777	+	0.0211239i	$0.00672446\pi$
$608$		0			0
$609$	11.6061	−	5.06067i	0.470305	−	0.205069i
$610$		0			0
$611$	27.0237	+	15.6021i	1.09326	+	0.631195i
$612$		0			0
$613$	−7.97371	−	13.8109i	−0.322055	−	0.557816i	0.658857	−	0.752268i	$-0.271040\pi$
$613$	−7.97371	−	13.8109i	−0.322055	−	0.557816i	−0.980912	+	0.194452i	$0.937707\pi$
$614$		0			0
$615$	−6.75981			−0.272582
$616$		0			0
$617$	−2.58440			−0.104044			−0.0520220	−	0.998646i	$-0.516567\pi$
$617$	−2.58440			−0.104044			−0.0520220	+	0.998646i	$0.516567\pi$
$618$		0			0
$619$	−4.96976	−	8.60788i	−0.199751	−	0.345980i	0.748696	−	0.662913i	$-0.230680\pi$
$619$	−4.96976	−	8.60788i	−0.199751	−	0.345980i	−0.948448	+	0.316933i	$0.897347\pi$
$620$		0			0
$621$	−28.8413	−	16.6515i	−1.15736	−	0.668202i
$622$		0			0
$623$	21.2151	−	28.7322i	0.849965	−	1.15113i
$624$		0			0
$625$	−6.93702	+	12.0153i	−0.277481	+	0.480611i
$626$		0			0
$627$	19.5286	−	11.2748i	0.779897	−	0.450274i
$628$		0			0
$629$		−	1.15536i		−	0.0460673i
$630$		0			0
$631$		−	47.4180i		−	1.88768i	−0.330400	−	0.943841i	$-0.607184\pi$
$631$		−	47.4180i		−	1.88768i	0.330400	−	0.943841i	$-0.392816\pi$
$632$		0			0
$633$	47.2654	−	27.2887i	1.87863	−	1.08463i
$634$		0			0
$635$	−0.914649	+	1.58422i	−0.0362967	+	0.0628678i
$636$		0			0
$637$	9.05998	−	39.6140i	0.358970	−	1.56956i
$638$		0			0
$639$	64.0828	+	36.9982i	2.53508	+	1.46363i
$640$		0			0
$641$	−5.22066	−	9.04245i	−0.206204	−	0.357155i	0.744312	−	0.667832i	$-0.232778\pi$
$641$	−5.22066	−	9.04245i	−0.206204	−	0.357155i	−0.950516	+	0.310677i	$0.899444\pi$
$642$		0			0
$643$	−9.45741			−0.372964			−0.186482	−	0.982458i	$-0.559709\pi$
$643$	−9.45741			−0.372964			−0.186482	+	0.982458i	$0.559709\pi$
$644$		0			0
$645$	−11.8164			−0.465269
$646$		0			0
$647$	−1.92768	−	3.33884i	−0.0757848	−	0.131263i	0.825642	−	0.564194i	$-0.190813\pi$
$647$	−1.92768	−	3.33884i	−0.0757848	−	0.131263i	−0.901427	+	0.432931i	$0.857480\pi$
$648$		0			0
$649$	2.60295	+	1.50282i	0.102175	+	0.0589907i
$650$		0			0
$651$	−35.2294	−	26.0124i	−1.38075	−	1.01951i
$652$		0			0
$653$	17.9036	−	31.0100i	0.700624	−	1.21352i	−0.267624	−	0.963523i	$-0.586239\pi$
$653$	17.9036	−	31.0100i	0.700624	−	1.21352i	0.968248	−	0.249992i	$-0.0804281\pi$
$654$		0			0
$655$	15.0577	−	8.69357i	0.588354	−	0.339686i
$656$		0			0
$657$		−	17.4143i		−	0.679396i
$658$		0			0
$659$		−	33.1431i		−	1.29107i	−0.763730	−	0.645536i	$-0.776634\pi$
$659$		−	33.1431i		−	1.29107i	0.763730	−	0.645536i	$-0.223366\pi$
$660$		0			0
$661$	8.97837	−	5.18366i	0.349218	−	0.201621i	−0.315123	−	0.949051i	$-0.602046\pi$
$661$	8.97837	−	5.18366i	0.349218	−	0.201621i	0.664341	+	0.747430i	$0.268712\pi$
$662$		0			0
$663$	−5.86351	+	10.1559i	−0.227720	+	0.394422i
$664$		0			0
$665$	−6.95298	−	15.9460i	−0.269625	−	0.618359i
$666$		0			0
$667$	4.67943	+	2.70167i	0.181188	+	0.104609i
$668$		0			0
$669$	28.5751	+	49.4936i	1.10478	+	1.91353i
$670$		0			0
$671$	−2.69155			−0.103906
$672$		0			0
$673$	8.15602			0.314392			0.157196	−	0.987567i	$-0.449755\pi$
$673$	8.15602			0.314392			0.157196	+	0.987567i	$0.449755\pi$
$674$		0			0
$675$	−20.5010	−	35.5088i	−0.789085	−	1.36674i
$676$		0			0
$677$	−15.0530	−	8.69088i	−0.578536	−	0.334018i	0.182016	−	0.983296i	$-0.441738\pi$
$677$	−15.0530	−	8.69088i	−0.578536	−	0.334018i	−0.760551	+	0.649278i	$0.775071\pi$
$678$		0			0
$679$	2.01014	+	0.226937i	0.0771422	+	0.00870904i
$680$		0			0
$681$	−34.0895	+	59.0448i	−1.30631	+	2.26260i
$682$		0			0
$683$	−20.2478	+	11.6901i	−0.774760	+	0.447308i	−0.834570	−	0.550902i	$-0.814284\pi$
$683$	−20.2478	+	11.6901i	−0.774760	+	0.447308i	0.0598101	+	0.998210i	$0.480950\pi$
$684$		0			0
$685$		−	16.9622i		−	0.648093i
$686$		0			0
$687$			10.2561i			0.391296i
$688$		0			0
$689$	−57.7999	+	33.3708i	−2.20200	+	1.27133i
$690$		0			0
$691$	4.64879	−	8.05194i	0.176848	−	0.306310i	−0.763951	−	0.645274i	$-0.776743\pi$
$691$	4.64879	−	8.05194i	0.176848	−	0.306310i	0.940799	+	0.338964i	$0.110076\pi$
$692$		0			0
$693$	16.3119	+	1.84155i	0.619637	+	0.0699545i
$694$		0			0
$695$	0.814580	+	0.470298i	0.0308988	+	0.0178394i
$696$		0			0
$697$	−0.838519	−	1.45236i	−0.0317612	−	0.0550120i
$698$		0			0
$699$	10.0007			0.378260
$700$		0			0
$701$	17.6125			0.665216			0.332608	−	0.943065i	$-0.392071\pi$
$701$	17.6125			0.665216			0.332608	+	0.943065i	$0.392071\pi$
$702$		0			0
$703$	−6.44855	−	11.1692i	−0.243212	−	0.421255i
$704$		0			0
$705$	12.4934	+	7.21308i	0.470529	+	0.271660i
$706$		0			0
$707$	16.5439	+	37.9419i	0.622199	+	1.42695i
$708$		0			0
$709$	17.3032	−	29.9701i	0.649837	−	1.12555i	−0.333325	−	0.942812i	$-0.608171\pi$
$709$	17.3032	−	29.9701i	0.649837	−	1.12555i	0.983162	−	0.182738i	$-0.0584962\pi$
$710$		0			0
$711$	64.6879	−	37.3476i	2.42598	−	1.40064i
$712$		0			0
$713$		−	18.6885i		−	0.699890i
$714$		0			0
$715$		−	5.13546i		−	0.192055i
$716$		0			0
$717$	−0.453932	+	0.262078i	−0.0169524	+	0.00978747i
$718$		0			0
$719$	0.622685	−	1.07852i	0.0232222	−	0.0402221i	−0.854181	−	0.519976i	$-0.825941\pi$
$719$	0.622685	−	1.07852i	0.0232222	−	0.0402221i	0.877403	+	0.479754i	$0.159274\pi$
$720$		0			0
$721$	18.3777	+	13.5696i	0.684422	+	0.505360i
$722$		0			0
$723$	54.7414	+	31.6050i	2.03586	+	1.17540i
$724$		0			0
$725$	3.32625	+	5.76123i	0.123534	+	0.213967i
$726$		0			0
$727$	−43.8198			−1.62519			−0.812594	−	0.582830i	$-0.801945\pi$
$727$	−43.8198			−1.62519			−0.812594	+	0.582830i	$0.801945\pi$
$728$		0			0
$729$	−20.9688			−0.776624
$730$		0			0
$731$	−1.46576	−	2.53877i	−0.0542130	−	0.0938997i
$732$		0			0
$733$	−25.5120	−	14.7293i	−0.942307	−	0.544041i	−0.0516240	−	0.998667i	$-0.516440\pi$
$733$	−25.5120	−	14.7293i	−0.942307	−	0.544041i	−0.890683	+	0.454626i	$0.849773\pi$
$734$		0			0
$735$	4.18855	−	18.3141i	0.154497	−	0.675524i
$736$		0			0
$737$	4.14583	−	7.18079i	0.152714	−	0.264508i
$738$		0			0
$739$	−34.8977	+	20.1482i	−1.28373	+	0.741164i	−0.977529	−	0.210801i	$-0.932393\pi$
$739$	−34.8977	+	20.1482i	−1.28373	+	0.741164i	−0.306205	+	0.951966i	$0.599059\pi$
$740$		0			0
$741$			130.907i			4.80897i
$742$		0			0
$743$		−	16.0426i		−	0.588546i	−0.955721	−	0.294273i	$-0.904923\pi$
$743$		−	16.0426i		−	0.588546i	0.955721	−	0.294273i	$-0.0950775\pi$
$744$		0			0
$745$	−4.54242	+	2.62257i	−0.166421	+	0.0960834i
$746$		0			0
$747$	37.5912	−	65.1098i	1.37539	−	2.38224i
$748$		0			0
$749$	19.9189	−	26.9767i	0.727821	−	0.985708i
$750$		0			0
$751$	22.7121	+	13.1128i	0.828776	+	0.478494i	0.853434	−	0.521202i	$-0.174516\pi$
$751$	22.7121	+	13.1128i	0.828776	+	0.478494i	−0.0246571	+	0.999696i	$0.507849\pi$
$752$		0			0
$753$	−31.5575	−	54.6591i	−1.15002	−	1.99189i
$754$		0			0
$755$	18.1459			0.660399
$756$		0			0
$757$	38.0555			1.38315			0.691576	−	0.722303i	$-0.256917\pi$
$757$	38.0555			1.38315			0.691576	+	0.722303i	$0.256917\pi$
$758$		0			0
$759$	5.19633	+	9.00030i	0.188615	+	0.326690i
$760$		0			0
$761$	4.47387	+	2.58299i	0.162178	+	0.0936332i	0.578892	−	0.815404i	$-0.303485\pi$
$761$	4.47387	+	2.58299i	0.162178	+	0.0936332i	−0.416715	+	0.909037i	$0.636819\pi$
$762$		0			0
$763$	−34.3749	+	14.9886i	−1.24446	+	0.542624i
$764$		0			0
$765$	−1.82726	+	3.16490i	−0.0660646	+	0.114427i
$766$		0			0
$767$	−15.1108	+	8.72423i	−0.545620	+	0.315014i
$768$		0			0
$769$		−	53.5221i		−	1.93006i	−0.262143	−	0.965029i	$-0.584429\pi$
$769$		−	53.5221i		−	1.93006i	0.262143	−	0.965029i	$-0.415571\pi$
$770$		0			0
$771$			60.9473i			2.19496i
$772$		0			0
$773$	−33.9926	+	19.6256i	−1.22263	+	0.705885i	−0.965478	−	0.260486i	$-0.916117\pi$
$773$	−33.9926	+	19.6256i	−1.22263	+	0.705885i	−0.257152	+	0.966371i	$0.582784\pi$
$774$		0			0
$775$	11.5045	−	19.9263i	0.413253	−	0.715776i
$776$		0			0
$777$	1.56253	−	13.8404i	0.0560554	−	0.496523i
$778$		0			0
$779$	−16.2124	−	9.36025i	−0.580870	−	0.335366i
$780$		0			0
$781$	−5.96315	−	10.3285i	−0.213378	−	0.369582i
$782$		0			0
$783$	−15.3353			−0.548039
$784$		0			0
$785$	0.440378			0.0157178
$786$		0			0
$787$	19.1109	+	33.1010i	0.681229	+	1.17992i	0.974606	+	0.223927i	$0.0718877\pi$
$787$	19.1109	+	33.1010i	0.681229	+	1.17992i	−0.293377	+	0.955997i	$0.594779\pi$
$788$		0			0
$789$	67.5646	+	39.0085i	2.40537	+	1.38874i
$790$		0			0
$791$	5.14071	−	45.5349i	0.182783	−	1.61904i
$792$		0			0
$793$	7.81257	−	13.5318i	0.277432	−	0.480527i
$794$		0			0
$795$	−26.7216	+	15.4277i	−0.947719	+	0.547166i
$796$		0			0
$797$		−	43.7129i		−	1.54839i	−0.632946	−	0.774196i	$-0.718155\pi$
$797$		−	43.7129i		−	1.54839i	0.632946	−	0.774196i	$-0.281845\pi$
$798$		0			0
$799$			3.57898i			0.126615i
$800$		0			0
$801$	−72.5349	+	41.8781i	−2.56290	+	1.47969i
$802$		0			0
$803$	−1.40336	+	2.43070i	−0.0495237	+	0.0857775i
$804$		0			0
$805$	7.34916	−	3.20448i	0.259024	−	0.112943i
$806$		0			0
$807$	9.06140	+	5.23160i	0.318976	+	0.184161i
$808$		0			0
$809$	3.24769	+	5.62516i	0.114183	+	0.197770i	0.917453	−	0.397845i	$-0.130242\pi$
$809$	3.24769	+	5.62516i	0.114183	+	0.197770i	−0.803270	+	0.595615i	$0.796908\pi$
$810$		0			0
$811$	−0.692067			−0.0243018			−0.0121509	−	0.999926i	$-0.503868\pi$
$811$	−0.692067			−0.0243018			−0.0121509	+	0.999926i	$0.503868\pi$
$812$		0			0
$813$	45.3566			1.59072
$814$		0			0
$815$	10.0156	+	17.3475i	0.350830	+	0.607655i
$816$		0			0
$817$	−28.3398	−	16.3620i	−0.991485	−	0.572434i
$818$		0			0
$819$	−56.6057	+	76.6626i	−1.97796	+	2.67881i
$820$		0			0
$821$	2.09226	−	3.62391i	0.0730205	−	0.126475i	−0.827203	−	0.561903i	$-0.810069\pi$
$821$	2.09226	−	3.62391i	0.0730205	−	0.126475i	0.900224	+	0.435428i	$0.143403\pi$
$822$		0			0
$823$	−0.168118	+	0.0970628i	−0.00586022	+	0.00338340i	−0.502927	−	0.864329i	$-0.667744\pi$
$823$	−0.168118	+	0.0970628i	−0.00586022	+	0.00338340i	0.497067	+	0.867712i	$0.334410\pi$
$824$		0			0
$825$			12.7952i			0.445473i
$826$		0			0
$827$			35.3697i			1.22992i	0.788557	+	0.614962i	$0.210829\pi$
$827$			35.3697i			1.22992i	−0.788557	+	0.614962i	$0.789171\pi$
$828$		0			0
$829$	20.3542	−	11.7515i	0.706930	−	0.408146i	−0.102993	−	0.994682i	$-0.532842\pi$
$829$	20.3542	−	11.7515i	0.706930	−	0.408146i	0.809923	+	0.586536i	$0.199509\pi$
$830$		0			0
$831$	−0.0722272	+	0.125101i	−0.00250553	+	0.00433971i
$832$		0			0
$833$	4.45438	−	1.37185i	0.154335	−	0.0475316i
$834$		0			0
$835$	−11.0073	−	6.35508i	−0.380924	−	0.219927i
$836$		0			0
$837$	26.5201	+	45.9341i	0.916668	+	1.58771i
$838$		0			0
$839$	18.7473			0.647228			0.323614	−	0.946189i	$-0.395102\pi$
$839$	18.7473			0.647228			0.323614	+	0.946189i	$0.395102\pi$
$840$		0			0
$841$	−26.5119			−0.914203
$842$		0			0
$843$	6.49576	+	11.2510i	0.223726	+	0.387505i
$844$		0			0
$845$	15.8592	+	9.15629i	0.545571	+	0.314986i
$846$		0			0
$847$	−2.12842	−	1.57157i	−0.0731334	−	0.0539998i
$848$		0			0
$849$	21.7896	−	37.7407i	0.747817	−	1.29526i
$850$		0			0
$851$	5.14765	−	2.97200i	0.176459	−	0.101879i
$852$		0			0
$853$			16.3087i			0.558400i	0.960233	+	0.279200i	$0.0900693\pi$
$853$			16.3087i			0.558400i	−0.960233	+	0.279200i	$0.909931\pi$
$854$		0			0
$855$			40.7947i			1.39515i
$856$		0			0
$857$	38.2423	−	22.0792i	1.30633	−	0.754212i	0.324851	−	0.945765i	$-0.394686\pi$
$857$	38.2423	−	22.0792i	1.30633	−	0.754212i	0.981482	+	0.191554i	$0.0613526\pi$
$858$		0			0
$859$	−13.3337	+	23.0946i	−0.454939	+	0.787978i	−0.998685	−	0.0512722i	$-0.983672\pi$
$859$	−13.3337	+	23.0946i	−0.454939	+	0.787978i	0.543745	+	0.839250i	$0.317006\pi$
$860$		0			0
$861$	−8.08069	−	18.5323i	−0.275389	−	0.631578i
$862$		0			0
$863$	10.1977	+	5.88767i	0.347135	+	0.200418i	0.663423	−	0.748245i	$-0.269103\pi$
$863$	10.1977	+	5.88767i	0.347135	+	0.200418i	−0.316288	+	0.948663i	$0.602436\pi$
$864$		0			0
$865$	4.60145	+	7.96995i	0.156454	+	0.270986i
$866$		0			0
$867$	50.2311			1.70594
$868$		0			0
$869$	−12.0389			−0.408392
$870$		0			0
$871$	24.0676	+	41.6863i	0.815499	+	1.41249i
$872$		0			0
$873$	−4.10831	−	2.37194i	−0.139045	−	0.0802779i
$874$		0			0
$875$	21.4372	+	2.42017i	0.724709	+	0.0818167i
$876$		0			0
$877$	4.95390	−	8.58041i	0.167281	−	0.289740i	−0.770182	−	0.637825i	$-0.779834\pi$
$877$	4.95390	−	8.58041i	0.167281	−	0.289740i	0.937463	+	0.348085i	$0.113168\pi$
$878$		0			0
$879$	−8.19178	+	4.72952i	−0.276302	+	0.159523i
$880$		0			0
$881$		−	48.3702i		−	1.62963i	−0.579718	−	0.814817i	$-0.696837\pi$
$881$		−	48.3702i		−	1.62963i	0.579718	−	0.814817i	$-0.303163\pi$
$882$		0			0
$883$			17.3911i			0.585256i	0.956226	+	0.292628i	$0.0945297\pi$
$883$			17.3911i			0.585256i	−0.956226	+	0.292628i	$0.905470\pi$
$884$		0			0
$885$	−6.98593	+	4.03333i	−0.234829	+	0.135579i
$886$		0			0
$887$	−17.4880	+	30.2900i	−0.587189	+	1.01704i	0.407410	+	0.913245i	$0.366432\pi$
$887$	−17.4880	+	30.2900i	−0.587189	+	1.01704i	−0.994599	+	0.103795i	$0.966901\pi$
$888$		0			0
$889$	−5.43657	−	0.613767i	−0.182337	−	0.0205851i
$890$		0			0
$891$	−9.42418	−	5.44105i	−0.315722	−	0.182282i
$892$		0			0
$893$	19.9758	+	34.5991i	0.668464	+	1.15781i
$894$		0			0
$895$	−5.37221			−0.179573
$896$		0			0
$897$	−60.3320			−2.01443
$898$		0			0
$899$	−4.30282	−	7.45271i	−0.143507	−	0.248562i
$900$		0			0
$901$	−6.62937	−	3.82747i	−0.220856	−	0.127511i
$902$		0			0
$903$	−14.1253	−	32.3950i	−0.470061	−	1.07804i
$904$		0			0
$905$	2.51672	−	4.35910i	0.0836588	−	0.144901i
$906$		0			0
$907$	−28.9486	+	16.7135i	−0.961222	+	0.554962i	−0.896549	−	0.442945i	$-0.853934\pi$
$907$	−28.9486	+	16.7135i	−0.961222	+	0.554962i	−0.0646732	+	0.997906i	$0.520601\pi$
$908$		0			0
$909$		−	97.0670i		−	3.21951i
$910$		0			0
$911$			15.5057i			0.513727i	0.966448	+	0.256864i	$0.0826891\pi$
$911$			15.5057i			0.513727i	−0.966448	+	0.256864i	$0.917311\pi$
$912$		0			0
$913$	−10.4940	+	6.05872i	−0.347301	+	0.200514i
$914$		0			0
$915$	3.61185	−	6.25591i	0.119404	−	0.206814i
$916$		0			0
$917$	41.8338	+	30.8890i	1.38147	+	1.02004i
$918$		0			0
$919$	7.20611	+	4.16045i	0.237708	+	0.137241i	0.614123	−	0.789211i	$-0.289510\pi$
$919$	7.20611	+	4.16045i	0.237708	+	0.137241i	−0.376415	+	0.926451i	$0.622843\pi$
$920$		0			0
$921$	0.254696	+	0.441146i	0.00839252	+	0.0145363i
$922$		0			0
$923$	69.2352			2.27891
$924$		0			0
$925$	7.31814			0.240619
$926$		0			0
$927$	−26.7861	−	46.3949i	−0.879771	−	1.52381i
$928$		0			0
$929$	20.9341	+	12.0863i	0.686826	+	0.396539i	0.802422	−	0.596757i	$-0.203544\pi$
$929$	20.9341	+	12.0863i	0.686826	+	0.396539i	−0.115596	+	0.993296i	$0.536878\pi$
$930$		0			0
$931$	35.4049	−	38.1238i	1.16035	−	1.24946i
$932$		0			0
$933$	17.9456	−	31.0827i	0.587512	−	1.01760i
$934$		0			0
$935$	0.510100	−	0.294506i	0.0166820	−	0.00963138i
$936$		0			0
$937$		−	39.4466i		−	1.28866i	−0.764746	−	0.644332i	$-0.777135\pi$
$937$		−	39.4466i		−	1.28866i	0.764746	−	0.644332i	$-0.222865\pi$
$938$		0			0
$939$		−	84.1913i		−	2.74748i
$940$		0			0
$941$	−27.7952	+	16.0476i	−0.906099	+	0.523136i	−0.879174	−	0.476501i	$-0.841905\pi$
$941$	−27.7952	+	16.0476i	−0.906099	+	0.523136i	−0.0269249	+	0.999637i	$0.508571\pi$
$942$		0			0
$943$	4.31393	−	7.47195i	0.140481	−	0.243320i
$944$		0			0
$945$	−13.5160	+	18.3051i	−0.439676	+	0.595465i
$946$		0			0
$947$	−28.1997	−	16.2811i	−0.916368	−	0.529065i	−0.0338936	−	0.999425i	$-0.510791\pi$
$947$	−28.1997	−	16.2811i	−0.916368	−	0.529065i	−0.882475	+	0.470360i	$0.844124\pi$
$948$		0			0
$949$	−8.14689	−	14.1108i	−0.264459	−	0.458057i
$950$		0			0
$951$	95.1799			3.08642
$952$		0			0
$953$	3.32173			0.107601			0.0538006	−	0.998552i	$-0.482866\pi$
$953$	3.32173			0.107601			0.0538006	+	0.998552i	$0.482866\pi$
$954$		0			0
$955$	10.3520	+	17.9302i	0.334982	+	0.580206i
$956$		0			0
$957$	4.14444	+	2.39279i	0.133971	+	0.0773480i
$958$		0			0
$959$	46.5026	−	20.2767i	1.50165	−	0.654768i
$960$		0			0
$961$	0.617844	−	1.07014i	0.0199305	−	0.0345206i
$962$		0			0
$963$	−68.1032	+	39.3194i	−2.19460	+	1.26705i
$964$		0			0
$965$		−	5.98201i		−	0.192568i
$966$		0			0
$967$		−	51.0144i		−	1.64051i	−0.571997	−	0.820256i	$-0.693831\pi$
$967$		−	51.0144i		−	1.64051i	0.571997	−	0.820256i	$-0.306169\pi$
$968$		0			0
$969$	−13.0028	+	7.50718i	−0.417710	+	0.241165i
$970$		0			0
$971$	−3.58697	+	6.21281i	−0.115111	+	0.199379i	−0.917824	−	0.396987i	$-0.870056\pi$
$971$	−3.58697	+	6.21281i	−0.115111	+	0.199379i	0.802713	+	0.596366i	$0.203389\pi$
$972$		0			0
$973$	−0.315589	+	2.79540i	−0.0101173	+	0.0896164i
$974$		0			0
$975$	−64.3281	−	37.1398i	−2.06015	−	1.18943i
$976$		0			0
$977$	−9.72080	−	16.8369i	−0.310996	−	0.538661i	0.667582	−	0.744536i	$-0.267329\pi$
$977$	−9.72080	−	16.8369i	−0.310996	−	0.538661i	−0.978578	+	0.205875i	$0.933996\pi$
$978$		0			0
$979$	13.4993			0.431440
$980$		0			0
$981$	87.9416			2.80776
$982$		0			0
$983$	−4.06343	−	7.03806i	−0.129603	−	0.224479i	0.793920	−	0.608023i	$-0.208037\pi$
$983$	−4.06343	−	7.03806i	−0.129603	−	0.224479i	−0.923523	+	0.383543i	$0.874704\pi$
$984$		0			0
$985$	−11.8977	−	6.86911i	−0.379091	−	0.218868i
$986$		0			0
$987$	−4.84027	+	42.8737i	−0.154068	+	1.36469i
$988$		0			0
$989$	7.54090	−	13.0612i	0.239787	−	0.415322i
$990$		0			0
$991$	−8.27614	+	4.77823i	−0.262900	+	0.151785i	−0.625657	−	0.780098i	$-0.715169\pi$
$991$	−8.27614	+	4.77823i	−0.262900	+	0.151785i	0.362757	+	0.931884i	$0.381836\pi$
$992$		0			0
$993$		−	4.09389i		−	0.129916i
$994$		0			0
$995$			10.0637i			0.319039i
$996$		0			0
$997$	10.9012	−	6.29382i	0.345245	−	0.199327i	−0.317344	−	0.948310i	$-0.602791\pi$
$997$	10.9012	−	6.29382i	0.345245	−	0.199327i	0.662589	+	0.748983i	$0.269458\pi$
$998$		0			0
$999$	−8.43486	+	14.6096i	−0.266867	+	0.462228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.be.b.1167.2	yes	28
4.3	odd	2		1232.2.be.c.1167.13	yes	28
7.3	odd	6		1232.2.be.c.815.13	yes	28
28.3	even	6	inner	1232.2.be.b.815.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.be.b.815.2	✓	28	28.3	even	6	inner
1232.2.be.b.1167.2	yes	28	1.1	even	1	trivial
1232.2.be.c.815.13	yes	28	7.3	odd	6
1232.2.be.c.1167.13	yes	28	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.51694 - 2.62742i) q^{3} +(-0.766106 - 0.442311i) q^{5} +(0.296809 - 2.62905i) q^{7} +(-3.10224 + 5.37323i) q^{9} +O(q^{10})\)	\(q+(-1.51694 - 2.62742i) q^{3} +(-0.766106 - 0.442311i) q^{5} +(0.296809 - 2.62905i) q^{7} +(-3.10224 + 5.37323i) q^{9} +(0.866025 - 0.500000i) q^{11} +5.80526i q^{13} +2.68385i q^{15} +(-0.576630 + 0.332917i) q^{17} +(-3.71630 + 6.43682i) q^{19} +(-7.35787 + 3.20828i) q^{21} +(-2.96659 - 1.71276i) q^{23} +(-2.10872 - 3.65241i) q^{25} +9.72202 q^{27} -1.57738 q^{29} +(2.72783 + 4.72475i) q^{31} +(-2.62742 - 1.51694i) q^{33} +(-1.39025 + 1.88285i) q^{35} +(-0.867604 + 1.50273i) q^{37} +(15.2529 - 8.80625i) q^{39} +2.51870i q^{41} +4.40277i q^{43} +(4.75329 - 2.74431i) q^{45} +(2.68759 - 4.65504i) q^{47} +(-6.82381 - 1.56065i) q^{49} +(1.74943 + 1.01003i) q^{51} +(5.74837 + 9.95647i) q^{53} -0.884623 q^{55} +22.5497 q^{57} +(1.50282 + 2.60295i) q^{59} +(-2.33095 - 1.34578i) q^{61} +(13.2057 + 9.75077i) q^{63} +(2.56773 - 4.44744i) q^{65} +(7.18079 - 4.14583i) q^{67} +10.3927i q^{69} -11.9263i q^{71} +(-2.43070 + 1.40336i) q^{73} +(-6.39762 + 11.0810i) q^{75} +(-1.05748 - 2.42523i) q^{77} +(-10.4260 - 6.01945i) q^{79} +(-5.44105 - 9.42418i) q^{81} -12.1174 q^{83} +0.589012 q^{85} +(2.39279 + 4.14444i) q^{87} +(11.6907 + 6.74965i) q^{89} +(15.2623 + 1.72305i) q^{91} +(8.27594 - 14.3344i) q^{93} +(5.69416 - 3.28752i) q^{95} +0.764589i q^{97} +6.20448i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9	\( 28 q - 2 q^{3} + 2 q^{7} - 16 q^{9} + 18 q^{17} - 14 q^{19} - 2 q^{21} + 12 q^{23} + 14 q^{25} + 16 q^{27} + 16 q^{29} - 10 q^{31} - 6 q^{35} - 4 q^{37} - 42 q^{39} - 42 q^{45} - 6 q^{47} - 4 q^{49} + 24 q^{51} - 2 q^{53} - 48 q^{57} + 12 q^{59} - 12 q^{61} + 26 q^{63} + 6 q^{65} + 48 q^{67} + 6 q^{73} + 14 q^{75} + 2 q^{77} - 48 q^{79} - 22 q^{81} + 84 q^{83} + 16 q^{85} - 18 q^{87} + 6 q^{89} + 18 q^{91} + 28 q^{93} + 36 q^{95}+O(q^{100}) \) 28 * q - 2 * q^3 + 2 * q^7 - 16 * q^9 + 18 * q^17 - 14 * q^19 - 2 * q^21 + 12 * q^23 + 14 * q^25 + 16 * q^27 + 16 * q^29 - 10 * q^31 - 6 * q^35 - 4 * q^37 - 42 * q^39 - 42 * q^45 - 6 * q^47 - 4 * q^49 + 24 * q^51 - 2 * q^53 - 48 * q^57 + 12 * q^59 - 12 * q^61 + 26 * q^63 + 6 * q^65 + 48 * q^67 + 6 * q^73 + 14 * q^75 + 2 * q^77 - 48 * q^79 - 22 * q^81 + 84 * q^83 + 16 * q^85 - 18 * q^87 + 6 * q^89 + 18 * q^91 + 28 * q^93 + 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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