LMFDB - Embedded newform 720.2.br.c.239.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(239,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5, 3]))

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

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

chi := DirichletCharacter("720.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.br (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.11
Character	$\chi$	$=$	720.239
Dual form			720.2.br.c.479.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56217 - 0.748070i) q^{3} +(1.74305 - 1.40063i) q^{5} +(-2.45766 - 4.25679i) q^{7} +(1.88078 - 2.33723i) q^{9} +O(q^{10})$	\(q+(1.56217 - 0.748070i) q^{3} +(1.74305 - 1.40063i) q^{5} +(-2.45766 - 4.25679i) q^{7} +(1.88078 - 2.33723i) q^{9} +(1.62292 + 2.81098i) q^{11} +(3.94659 + 2.27856i) q^{13} +(1.67518 - 3.49196i) q^{15} -4.68147 q^{17} +2.29982i q^{19} +(-7.02367 - 4.81135i) q^{21} +(-2.41968 - 1.39700i) q^{23} +(1.07645 - 4.88275i) q^{25} +(1.18969 - 5.05812i) q^{27} +(0.841610 - 0.485904i) q^{29} +(-8.33350 - 4.81135i) q^{31} +(4.63809 + 3.17718i) q^{33} +(-10.2460 - 3.97752i) q^{35} +2.32167i q^{37} +(7.86979 + 0.607189i) q^{39} +(8.23509 + 4.75453i) q^{41} +(0.256227 + 0.443798i) q^{43} +(0.00468816 - 6.70820i) q^{45} +(7.37017 - 4.25517i) q^{47} +(-8.58018 + 14.8613i) q^{49} +(-7.31328 + 3.50207i) q^{51} +9.90660 q^{53} +(6.76598 + 2.62656i) q^{55} +(1.72043 + 3.59272i) q^{57} +(-1.48077 + 2.56476i) q^{59} +(1.67840 + 2.90707i) q^{61} +(-14.5714 - 2.26197i) q^{63} +(10.0705 - 1.55607i) q^{65} +(-4.05210 + 7.01844i) q^{67} +(-4.82501 - 0.372271i) q^{69} +8.66662 q^{71} +3.66953i q^{73} +(-1.97104 - 8.43297i) q^{75} +(7.97717 - 13.8169i) q^{77} +(0.00584899 - 0.00337691i) q^{79} +(-1.92532 - 8.79165i) q^{81} +(2.41968 - 1.39700i) q^{83} +(-8.16004 + 6.55703i) q^{85} +(0.951252 - 1.38865i) q^{87} -0.952424i q^{89} -22.3997i q^{91} +(-16.6176 - 1.28212i) q^{93} +(3.22120 + 4.00870i) q^{95} +(-3.07057 + 1.77279i) q^{97} +(9.62227 + 1.49369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 2 q^{9}+O(q^{10}) $ 24 * q + 3 * q^5 + 2 * q^9	$ 24 q + 3 q^{5} + 2 q^{9} - 6 q^{11} + 9 q^{15} - 18 q^{21} + 3 q^{25} + 12 q^{29} - 18 q^{31} - 30 q^{35} + 6 q^{39} - 12 q^{41} + q^{45} - 12 q^{49} - 36 q^{51} + 6 q^{59} + 3 q^{65} - 12 q^{69} + 96 q^{71} + 9 q^{75} - 18 q^{79} - 14 q^{81} + 24 q^{95} - 18 q^{99}+O(q^{100}) $ 24 * q + 3 * q^5 + 2 * q^9 - 6 * q^11 + 9 * q^15 - 18 * q^21 + 3 * q^25 + 12 * q^29 - 18 * q^31 - 30 * q^35 + 6 * q^39 - 12 * q^41 + q^45 - 12 * q^49 - 36 * q^51 + 6 * q^59 + 3 * q^65 - 12 * q^69 + 96 * q^71 + 9 * q^75 - 18 * q^79 - 14 * q^81 + 24 * q^95 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.56217	−	0.748070i	0.901922	−	0.431899i
$3$	1.56217	−	0.748070i	0.901922	−	0.431899i
$4$		0			0
$5$	1.74305	−	1.40063i	0.779516	−	0.626382i
$5$	1.74305	−	1.40063i	0.779516	−	0.626382i
$6$		0			0
$7$	−2.45766	−	4.25679i	−0.928908	−	1.60892i	−0.785152	−	0.619302i	$-0.787415\pi$
$7$	−2.45766	−	4.25679i	−0.928908	−	1.60892i	−0.143755	−	0.989613i	$-0.545918\pi$
$8$		0			0
$9$	1.88078	−	2.33723i	0.626927	−	0.779078i
$10$		0			0
$11$	1.62292	+	2.81098i	0.489329	+	0.847542i	0.999925	−	0.0122787i	$-0.00390852\pi$
$11$	1.62292	+	2.81098i	0.489329	+	0.847542i	−0.510596	+	0.859821i	$0.670575\pi$
$12$		0			0
$13$	3.94659	+	2.27856i	1.09459	+	0.631960i	0.934794	−	0.355191i	$-0.115584\pi$
$13$	3.94659	+	2.27856i	1.09459	+	0.631960i	0.159793	+	0.987151i	$0.448917\pi$
$14$		0			0
$15$	1.67518	−	3.49196i	0.432529	−	0.901620i
$16$		0			0
$17$	−4.68147			−1.13542			−0.567712	−	0.823227i	$-0.692171\pi$
$17$	−4.68147			−1.13542			−0.567712	+	0.823227i	$0.692171\pi$
$18$		0			0
$19$			2.29982i			0.527615i	0.964575	+	0.263807i	$0.0849783\pi$
$19$			2.29982i			0.527615i	−0.964575	+	0.263807i	$0.915022\pi$
$20$		0			0
$21$	−7.02367	−	4.81135i	−1.53269	−	1.04992i
$22$		0			0
$23$	−2.41968	−	1.39700i	−0.504538	−	0.291295i	0.226048	−	0.974116i	$-0.427419\pi$
$23$	−2.41968	−	1.39700i	−0.504538	−	0.291295i	−0.730585	+	0.682821i	$0.760753\pi$
$24$		0			0
$25$	1.07645	−	4.88275i	0.215290	−	0.976550i
$26$		0			0
$27$	1.18969	−	5.05812i	0.228957	−	0.973437i
$28$		0			0
$29$	0.841610	−	0.485904i	0.156283	−	0.0902301i	−0.419819	−	0.907608i	$-0.637906\pi$
$29$	0.841610	−	0.485904i	0.156283	−	0.0902301i	0.576102	+	0.817378i	$0.304573\pi$
$30$		0			0
$31$	−8.33350	−	4.81135i	−1.49674	−	0.864144i	−0.496748	−	0.867895i	$-0.665473\pi$
$31$	−8.33350	−	4.81135i	−1.49674	−	0.864144i	−0.999993	+	0.00375071i	$0.998806\pi$
$32$		0			0
$33$	4.63809	+	3.17718i	0.807389	+	0.553077i
$34$		0			0
$35$	−10.2460	−	3.97752i	−1.73190	−	0.672324i
$36$		0			0
$37$			2.32167i			0.381679i	0.981621	+	0.190840i	$0.0611211\pi$
$37$			2.32167i			0.381679i	−0.981621	+	0.190840i	$0.938879\pi$
$38$		0			0
$39$	7.86979	+	0.607189i	1.26017	+	0.0972281i
$40$		0			0
$41$	8.23509	+	4.75453i	1.28611	+	0.742533i	0.977957	−	0.208805i	$-0.0669574\pi$
$41$	8.23509	+	4.75453i	1.28611	+	0.742533i	0.308148	+	0.951338i	$0.400291\pi$
$42$		0			0
$43$	0.256227	+	0.443798i	0.0390743	+	0.0676786i	0.884901	−	0.465779i	$-0.154226\pi$
$43$	0.256227	+	0.443798i	0.0390743	+	0.0676786i	−0.845827	+	0.533457i	$0.820892\pi$
$44$		0			0
$45$	0.00468816	−	6.70820i	0.000698869	−	1.00000i
$46$		0			0
$47$	7.37017	−	4.25517i	1.07505	−	0.620680i	0.145493	−	0.989359i	$-0.453523\pi$
$47$	7.37017	−	4.25517i	1.07505	−	0.620680i	0.929557	+	0.368679i	$0.120190\pi$
$48$		0			0
$49$	−8.58018	+	14.8613i	−1.22574	+	2.12304i
$50$		0			0
$51$	−7.31328	+	3.50207i	−1.02406	+	0.490388i
$52$		0			0
$53$	9.90660			1.36078			0.680388	−	0.732852i	$-0.261811\pi$
$53$	9.90660			1.36078			0.680388	+	0.732852i	$0.261811\pi$
$54$		0			0
$55$	6.76598	+	2.62656i	0.912325	+	0.354166i
$56$		0			0
$57$	1.72043	+	3.59272i	0.227876	+	0.475867i
$58$		0			0
$59$	−1.48077	+	2.56476i	−0.192779	+	0.333904i	−0.946170	−	0.323669i	$-0.895083\pi$
$59$	−1.48077	+	2.56476i	−0.192779	+	0.333904i	0.753391	+	0.657573i	$0.228417\pi$
$60$		0			0
$61$	1.67840	+	2.90707i	0.214897	+	0.372212i	0.953241	−	0.302212i	$-0.0977252\pi$
$61$	1.67840	+	2.90707i	0.214897	+	0.372212i	−0.738344	+	0.674424i	$0.764392\pi$
$62$		0			0
$63$	−14.5714	−	2.26197i	−1.83583	−	0.284981i
$64$		0			0
$65$	10.0705	−	1.55607i	1.24910	−	0.193007i
$66$		0			0
$67$	−4.05210	+	7.01844i	−0.495042	+	0.857439i	−0.999984	−	0.00571511i	$-0.998181\pi$
$67$	−4.05210	+	7.01844i	−0.495042	+	0.857439i	0.504941	+	0.863154i	$0.331514\pi$
$68$		0			0
$69$	−4.82501	−	0.372271i	−0.580863	−	0.0448162i
$70$		0			0
$71$	8.66662			1.02854			0.514270	−	0.857629i	$-0.328063\pi$
$71$	8.66662			1.02854			0.514270	+	0.857629i	$0.328063\pi$
$72$		0			0
$73$			3.66953i			0.429486i	0.976671	+	0.214743i	$0.0688914\pi$
$73$			3.66953i			0.429486i	−0.976671	+	0.214743i	$0.931109\pi$
$74$		0			0
$75$	−1.97104	−	8.43297i	−0.227596	−	0.973756i
$76$		0			0
$77$	7.97717	−	13.8169i	0.909083	−	1.57458i
$78$		0			0
$79$	0.00584899	−	0.00337691i	0.000658062	−	0.000379932i	−0.499671	−	0.866215i	$-0.666546\pi$
$79$	0.00584899	−	0.00337691i	0.000658062	−	0.000379932i	0.500329	+	0.865835i	$0.333212\pi$
$80$		0			0
$81$	−1.92532	−	8.79165i	−0.213925	−	0.976850i
$82$		0			0
$83$	2.41968	−	1.39700i	0.265594	−	0.153341i	−0.361290	−	0.932454i	$-0.617663\pi$
$83$	2.41968	−	1.39700i	0.265594	−	0.153341i	0.626884	+	0.779113i	$0.284330\pi$
$84$		0			0
$85$	−8.16004	+	6.55703i	−0.885081	+	0.711210i
$86$		0			0
$87$	0.951252	−	1.38865i	0.101985	−	0.148879i
$88$		0			0
$89$		−	0.952424i		−	0.100957i	−0.998725	−	0.0504784i	$-0.983925\pi$
$89$		−	0.952424i		−	0.100957i	0.998725	−	0.0504784i	$-0.0160746\pi$
$90$		0			0
$91$		−	22.3997i		−	2.34813i
$92$		0			0
$93$	−16.6176	−	1.28212i	−1.72317	−	0.132950i
$94$		0			0
$95$	3.22120	+	4.00870i	0.330489	+	0.411284i
$96$		0			0
$97$	−3.07057	+	1.77279i	−0.311769	+	0.180000i	−0.647718	−	0.761880i	$-0.724276\pi$
$97$	−3.07057	+	1.77279i	−0.311769	+	0.180000i	0.335949	+	0.941880i	$0.390943\pi$
$98$		0			0
$99$	9.62227	+	1.49369i	0.967075	+	0.150122i
$100$		0			0
$101$	5.59275	−	3.22898i	0.556499	−	0.321295i	−0.195240	−	0.980756i	$-0.562549\pi$
$101$	5.59275	−	3.22898i	0.556499	−	0.321295i	0.751739	+	0.659460i	$0.229215\pi$
$102$		0			0
$103$	−3.43413	+	5.94809i	−0.338375	+	0.586083i	−0.984127	−	0.177464i	$-0.943211\pi$
$103$	−3.43413	+	5.94809i	−0.338375	+	0.586083i	0.645752	+	0.763547i	$0.276544\pi$
$104$		0			0
$105$	−18.9816	+	1.45117i	−1.85241	+	0.141620i
$106$		0			0
$107$			8.35683i			0.807886i	0.914784	+	0.403943i	$0.132361\pi$
$107$			8.35683i			0.807886i	−0.914784	+	0.403943i	$0.867639\pi$
$108$		0			0
$109$	−8.40624			−0.805172			−0.402586	−	0.915382i	$-0.631889\pi$
$109$	−8.40624			−0.805172			−0.402586	+	0.915382i	$0.631889\pi$
$110$		0			0
$111$	1.73677	+	3.62685i	0.164847	+	0.344245i
$112$		0			0
$113$	−7.70815	+	13.3509i	−0.725121	+	1.25595i	0.233803	+	0.972284i	$0.424883\pi$
$113$	−7.70815	+	13.3509i	−0.725121	+	1.25595i	−0.958924	+	0.283663i	$0.908450\pi$
$114$		0			0
$115$	−6.17431	+	0.954038i	−0.575757	+	0.0889645i
$116$		0			0
$117$	12.7482	−	4.93862i	1.17857	−	0.456575i
$118$		0			0
$119$	11.5055	+	19.9281i	1.05470	+	1.82680i
$120$		0			0
$121$	0.232264	−	0.402293i	0.0211149	−	0.0365721i
$122$		0			0
$123$	16.4214	+	1.26698i	1.48067	+	0.114240i
$124$		0			0
$125$	−4.96264	−	10.0186i	−0.443872	−	0.896090i
$126$		0			0
$127$	3.57050			0.316830			0.158415	−	0.987373i	$-0.449362\pi$
$127$	3.57050			0.316830			0.158415	+	0.987373i	$0.449362\pi$
$128$		0			0
$129$	0.732264	+	0.501615i	0.0644722	+	0.0441647i
$130$		0			0
$131$	−2.63122	+	4.55740i	−0.229891	+	0.398182i	−0.957775	−	0.287517i	$-0.907170\pi$
$131$	−2.63122	+	4.55740i	−0.229891	+	0.398182i	0.727885	+	0.685699i	$0.240503\pi$
$132$		0			0
$133$	9.78985	−	5.65217i	0.848888	−	0.490105i
$134$		0			0
$135$	−5.01088	−	10.4829i	−0.431268	−	0.902224i
$136$		0			0
$137$	−6.02560	−	10.4366i	−0.514802	−	0.891663i	−0.999852	−	0.0171767i	$-0.994532\pi$
$137$	−6.02560	−	10.4366i	−0.514802	−	0.891663i	0.485051	−	0.874486i	$-0.338801\pi$
$138$		0			0
$139$	15.8635	+	9.15882i	1.34553	+	0.776841i	0.987612	−	0.156913i	$-0.0501542\pi$
$139$	15.8635	+	9.15882i	1.34553	+	0.776841i	0.357916	+	0.933754i	$0.383487\pi$
$140$		0			0
$141$	8.33033	−	12.1607i	0.701540	−	1.02412i
$142$		0			0
$143$			14.7917i			1.23694i
$144$		0			0
$145$	0.786396	−	2.02574i	0.0653066	−	0.168229i
$146$		0			0
$147$	−2.28644	+	29.6345i	−0.188582	+	2.44422i
$148$		0			0
$149$	20.2462	+	11.6891i	1.65863	+	0.957612i	0.973347	+	0.229338i	$0.0736563\pi$
$149$	20.2462	+	11.6891i	1.65863	+	0.957612i	0.685286	+	0.728274i	$0.259677\pi$
$150$		0			0
$151$	−15.4153	+	8.90005i	−1.25448	+	0.724276i	−0.971996	−	0.234996i	$-0.924492\pi$
$151$	−15.4153	+	8.90005i	−1.25448	+	0.724276i	−0.282486	+	0.959272i	$0.591159\pi$
$152$		0			0
$153$	−8.80483	+	10.9417i	−0.711828	+	0.884584i
$154$		0			0
$155$	−21.2647	+	3.28576i	−1.70802	+	0.263919i
$156$		0			0
$157$	−2.22723	−	1.28589i	−0.177753	−	0.102626i	0.408484	−	0.912766i	$-0.366058\pi$
$157$	−2.22723	−	1.28589i	−0.177753	−	0.102626i	−0.586236	+	0.810140i	$0.699391\pi$
$158$		0			0
$159$	15.4758	−	7.41084i	1.22731	−	0.587718i
$160$		0			0
$161$			13.7334i			1.08234i
$162$		0			0
$163$	4.61388			0.361387			0.180694	−	0.983539i	$-0.442166\pi$
$163$	4.61388			0.361387			0.180694	+	0.983539i	$0.442166\pi$
$164$		0			0
$165$	12.5345	−	0.958281i	0.975810	−	0.0746021i
$166$		0			0
$167$	4.72157	+	2.72600i	0.365366	+	0.210944i	0.671432	−	0.741066i	$-0.265680\pi$
$167$	4.72157	+	2.72600i	0.365366	+	0.210944i	−0.306066	+	0.952010i	$0.599013\pi$
$168$		0			0
$169$	3.88370	+	6.72677i	0.298746	+	0.517444i
$170$		0			0
$171$	5.37521	+	4.32546i	0.411053	+	0.330776i
$172$		0			0
$173$	−11.0583	−	19.1535i	−0.840746	−	1.45621i	−0.889265	−	0.457393i	$-0.848783\pi$
$173$	−11.0583	−	19.1535i	−0.840746	−	1.45621i	0.0485189	−	0.998822i	$-0.484550\pi$
$174$		0			0
$175$	−23.4304	+	7.41792i	−1.77117	+	0.560742i
$176$		0			0
$177$	−0.394593	+	5.11432i	−0.0296594	+	0.384416i
$178$		0			0
$179$	9.02225			0.674355			0.337177	−	0.941441i	$-0.390528\pi$
$179$	9.02225			0.674355			0.337177	+	0.941441i	$0.390528\pi$
$180$		0			0
$181$	−13.6415			−1.01396			−0.506982	−	0.861957i	$-0.669239\pi$
$181$	−13.6415			−1.01396			−0.506982	+	0.861957i	$0.669239\pi$
$182$		0			0
$183$	4.79664	+	3.28579i	0.354578	+	0.242893i
$184$		0			0
$185$	3.25180	+	4.04678i	0.239077	+	0.297525i
$186$		0			0
$187$	−7.59766	−	13.1595i	−0.555596	−	0.962320i
$188$		0			0
$189$	−24.4552	+	7.36687i	−1.77886	+	0.535861i
$190$		0			0
$191$	−5.28131	−	9.14750i	−0.382142	−	0.661890i	0.609226	−	0.792997i	$-0.291480\pi$
$191$	−5.28131	−	9.14750i	−0.382142	−	0.661890i	−0.991368	+	0.131107i	$0.958147\pi$
$192$		0			0
$193$	−13.6860	−	7.90162i	−0.985140	−	0.568771i	−0.0813222	−	0.996688i	$-0.525914\pi$
$193$	−13.6860	−	7.90162i	−0.985140	−	0.568771i	−0.903818	+	0.427917i	$0.859248\pi$
$194$		0			0
$195$	14.5679	−	9.96433i	1.04323	−	0.713560i
$196$		0			0
$197$	−19.0230			−1.35533			−0.677666	−	0.735370i	$-0.737008\pi$
$197$	−19.0230			−1.35533			−0.677666	+	0.735370i	$0.737008\pi$
$198$		0			0
$199$			1.43855i			0.101976i	0.998699	+	0.0509881i	$0.0162371\pi$
$199$			1.43855i			0.101976i	−0.998699	+	0.0509881i	$0.983763\pi$
$200$		0			0
$201$	−1.07980	+	13.9953i	−0.0761631	+	0.987151i
$202$		0			0
$203$	−4.13678	−	2.38837i	−0.290345	−	0.167631i
$204$		0			0
$205$	21.0135	−	3.24696i	1.46765	−	0.226777i
$206$		0			0
$207$	−7.81600	+	3.02790i	−0.543250	+	0.210453i
$208$		0			0
$209$	−6.46474	+	3.73242i	−0.447176	+	0.258177i
$210$		0			0
$211$	15.4153	+	8.90005i	1.06124	+	0.612704i	0.925774	−	0.378078i	$-0.123415\pi$
$211$	15.4153	+	8.90005i	1.06124	+	0.612704i	0.135462	+	0.990783i	$0.456748\pi$
$212$		0			0
$213$	13.5388	−	6.48325i	0.927662	−	0.444225i
$214$		0			0
$215$	1.06822	+	0.414683i	0.0728517	+	0.0282811i
$216$		0			0
$217$			47.2986i			3.21084i
$218$		0			0
$219$	2.74507	+	5.73245i	0.185494	+	0.387363i
$220$		0			0
$221$	−18.4758	−	10.6670i	−1.24282	−	0.717542i
$222$		0			0
$223$	−0.772004	−	1.33715i	−0.0516972	−	0.0895422i	0.839019	−	0.544102i	$-0.183130\pi$
$223$	−0.772004	−	1.33715i	−0.0516972	−	0.0895422i	−0.890716	+	0.454560i	$0.849796\pi$
$224$		0			0
$225$	−9.38756	−	11.6993i	−0.625838	−	0.779953i
$226$		0			0
$227$	7.32514	−	4.22917i	0.486187	−	0.280700i	−0.236804	−	0.971557i	$-0.576100\pi$
$227$	7.32514	−	4.22917i	0.486187	−	0.280700i	0.722991	+	0.690857i	$0.242767\pi$
$228$		0			0
$229$	4.13038	−	7.15403i	0.272943	−	0.472752i	−0.696671	−	0.717391i	$-0.745336\pi$
$229$	4.13038	−	7.15403i	0.272943	−	0.472752i	0.969614	+	0.244639i	$0.0786696\pi$
$230$		0			0
$231$	2.12575	−	27.5518i	0.139864	−	1.81278i
$232$		0			0
$233$	14.6573			0.960229			0.480115	−	0.877206i	$-0.340595\pi$
$233$	14.6573			0.960229			0.480115	+	0.877206i	$0.340595\pi$
$234$		0			0
$235$	6.88665	−	17.7399i	0.449235	−	1.15722i
$236$		0			0
$237$	0.00661097	−	0.00965078i	0.000429429	−	0.000626886i
$238$		0			0
$239$	−0.171965	+	0.297852i	−0.0111235	+	0.0192664i	−0.871534	−	0.490336i	$-0.836874\pi$
$239$	−0.171965	+	0.297852i	−0.0111235	+	0.0192664i	0.860410	+	0.509602i	$0.170207\pi$
$240$		0			0
$241$	4.93539	+	8.54834i	0.317916	+	0.550647i	0.980053	−	0.198736i	$-0.0636836\pi$
$241$	4.93539	+	8.54834i	0.317916	+	0.550647i	−0.662137	+	0.749383i	$0.730350\pi$
$242$		0			0
$243$	−9.58447	−	12.2938i	−0.614844	−	0.788649i
$244$		0			0
$245$	5.85956	+	37.9217i	0.374354	+	2.42273i
$246$		0			0
$247$	−5.24028	+	9.07644i	−0.333431	+	0.577520i
$248$		0			0
$249$	2.73490	−	3.99245i	0.173317	−	0.253011i
$250$		0			0
$251$	−16.5795			−1.04649			−0.523243	−	0.852183i	$-0.675278\pi$
$251$	−16.5795			−1.04649			−0.523243	+	0.852183i	$0.675278\pi$
$252$		0			0
$253$		−	9.06888i		−	0.570156i
$254$		0			0
$255$	−7.84230	+	16.3475i	−0.491104	+	1.02372i
$256$		0			0
$257$	7.09105	−	12.2821i	0.442327	−	0.766133i	−0.555534	−	0.831494i	$-0.687486\pi$
$257$	7.09105	−	12.2821i	0.442327	−	0.766133i	0.997862	+	0.0653601i	$0.0208196\pi$
$258$		0			0
$259$	9.88284	−	5.70586i	0.614090	−	0.354545i
$260$		0			0
$261$	0.447214	−	2.88092i	0.0276818	−	0.178324i
$262$		0			0
$263$	4.76712	−	2.75230i	0.293953	−	0.169714i	−0.345770	−	0.938319i	$-0.612382\pi$
$263$	4.76712	−	2.75230i	0.293953	−	0.169714i	0.639723	+	0.768605i	$0.279049\pi$
$264$		0			0
$265$	17.2677	−	13.8755i	1.06075	−	0.852367i
$266$		0			0
$267$	−0.712480	−	1.48785i	−0.0436031	−	0.0910552i
$268$		0			0
$269$			23.3589i			1.42422i	0.702069	+	0.712109i	$0.252260\pi$
$269$			23.3589i			1.42422i	−0.702069	+	0.712109i	$0.747740\pi$
$270$		0			0
$271$			19.4755i			1.18305i	0.806287	+	0.591525i	$0.201474\pi$
$271$			19.4755i			1.18305i	−0.806287	+	0.591525i	$0.798526\pi$
$272$		0			0
$273$	−16.7566	−	34.9923i	−1.01415	−	2.11783i
$274$		0			0
$275$	15.4723	−	4.89843i	0.933015	−	0.295387i
$276$		0			0
$277$	−21.4830	+	12.4032i	−1.29079	+	0.745236i	−0.978794	−	0.204848i	$-0.934330\pi$
$277$	−21.4830	+	12.4032i	−1.29079	+	0.745236i	−0.311994	+	0.950084i	$0.600997\pi$
$278$		0			0
$279$	−26.9187	+	10.4282i	−1.61158	+	0.624323i
$280$		0			0
$281$	22.2519	−	12.8471i	1.32743	−	0.766395i	0.342532	−	0.939506i	$-0.388715\pi$
$281$	22.2519	−	12.8471i	1.32743	−	0.766395i	0.984902	+	0.173112i	$0.0553821\pi$
$282$		0			0
$283$	−7.17373	+	12.4253i	−0.426434	+	0.738605i	−0.996553	−	0.0829568i	$-0.973564\pi$
$283$	−7.17373	+	12.4253i	−0.426434	+	0.738605i	0.570119	+	0.821562i	$0.306897\pi$
$284$		0			0
$285$	8.03088	+	3.85260i	0.475708	+	0.228209i
$286$		0			0
$287$		−	46.7401i		−	2.75898i
$288$		0			0
$289$	4.91619			0.289188
$290$		0			0
$291$	−3.47059	+	5.06642i	−0.203450	+	0.296999i
$292$		0			0
$293$	−8.76145	+	15.1753i	−0.511849	+	0.886549i	0.488056	+	0.872812i	$0.337706\pi$
$293$	−8.76145	+	15.1753i	−0.511849	+	0.886549i	−0.999906	+	0.0137369i	$0.995627\pi$
$294$		0			0
$295$	1.01124	+	6.54452i	0.0588768	+	0.381037i
$296$		0			0
$297$	16.1491	−	4.86473i	0.937064	−	0.282280i
$298$		0			0
$299$	−6.36631	−	11.0268i	−0.368173	−	0.637695i
$300$		0			0
$301$	1.25944	−	2.18141i	0.0725928	−	0.125734i
$302$		0			0
$303$	6.32135	−	9.22800i	0.363152	−	0.530135i
$304$		0			0
$305$	6.99727	+	2.71635i	0.400663	+	0.155538i
$306$		0			0
$307$	−0.415391			−0.0237076			−0.0118538	−	0.999930i	$-0.503773\pi$
$307$	−0.415391			−0.0237076			−0.0118538	+	0.999930i	$0.503773\pi$
$308$		0			0
$309$	−0.915124	+	11.8609i	−0.0520596	+	0.674745i
$310$		0			0
$311$	−10.8799	+	18.8446i	−0.616943	+	1.06858i	0.373097	+	0.927792i	$0.378296\pi$
$311$	−10.8799	+	18.8446i	−0.616943	+	1.06858i	−0.990040	+	0.140784i	$0.955038\pi$
$312$		0			0
$313$	17.8846	−	10.3257i	1.01090	−	0.583641i	0.0994419	−	0.995043i	$-0.468294\pi$
$313$	17.8846	−	10.3257i	1.01090	−	0.583641i	0.911454	+	0.411403i	$0.134961\pi$
$314$		0			0
$315$	−28.5669	+	16.4665i	−1.60956	+	0.927783i
$316$		0			0
$317$	−5.28802	−	9.15912i	−0.297005	−	0.514428i	0.678444	−	0.734652i	$-0.262654\pi$
$317$	−5.28802	−	9.15912i	−0.297005	−	0.514428i	−0.975449	+	0.220224i	$0.929321\pi$
$318$		0			0
$319$	2.73173	+	1.57717i	0.152948	+	0.0883044i
$320$		0			0
$321$	6.25150	+	13.0548i	0.348925	+	0.728650i
$322$		0			0
$323$		−	10.7665i		−	0.599066i
$324$		0			0
$325$	15.3740	−	16.8174i	0.852794	−	0.932864i
$326$		0			0
$327$	−13.1320	+	6.28846i	−0.726203	+	0.347753i
$328$		0			0
$329$	−36.2267	−	20.9155i	−1.99725	−	1.15311i
$330$		0			0
$331$	2.59592	−	1.49876i	0.142685	−	0.0823791i	−0.426958	−	0.904271i	$-0.640415\pi$
$331$	2.59592	−	1.49876i	0.142685	−	0.0823791i	0.569643	+	0.821892i	$0.307082\pi$
$332$		0			0
$333$	5.42627	+	4.36654i	0.297358	+	0.239285i
$334$		0			0
$335$	2.76725	+	17.9090i	0.151191	+	0.978473i
$336$		0			0
$337$	−24.9848	−	14.4250i	−1.36101	−	0.785780i	−0.371252	−	0.928532i	$-0.621072\pi$
$337$	−24.9848	−	14.4250i	−1.36101	−	0.785780i	−0.989758	+	0.142752i	$0.954405\pi$
$338$		0			0
$339$	−2.05406	+	26.6227i	−0.111561	+	1.44595i
$340$		0			0
$341$		−	31.2337i		−	1.69140i
$342$		0			0
$343$	49.9414			2.69658
$344$		0			0
$345$	−8.93166	+	6.10919i	−0.480864	+	0.328908i
$346$		0			0
$347$	7.84132	+	4.52719i	0.420944	+	0.243032i	0.695481	−	0.718544i	$-0.255191\pi$
$347$	7.84132	+	4.52719i	0.420944	+	0.243032i	−0.274537	+	0.961577i	$0.588525\pi$
$348$		0			0
$349$	−7.32154	−	12.6813i	−0.391913	−	0.678813i	0.600789	−	0.799408i	$-0.294853\pi$
$349$	−7.32154	−	12.6813i	−0.391913	−	0.678813i	−0.992702	+	0.120595i	$0.961520\pi$
$350$		0			0
$351$	16.2205	−	17.2515i	0.865786	−	0.920819i
$352$		0			0
$353$	5.20672	+	9.01831i	0.277126	+	0.479996i	0.970669	−	0.240419i	$-0.0772848\pi$
$353$	5.20672	+	9.01831i	0.277126	+	0.479996i	−0.693543	+	0.720415i	$0.743951\pi$
$354$		0			0
$355$	15.1064	−	12.1388i	0.801763	−	0.644259i
$356$		0			0
$357$	32.8811	+	22.5242i	1.74025	+	1.19211i
$358$		0			0
$359$	22.0275			1.16257			0.581283	−	0.813701i	$-0.302551\pi$
$359$	22.0275			1.16257			0.581283	+	0.813701i	$0.302551\pi$
$360$		0			0
$361$	13.7108			0.721623
$362$		0			0
$363$	0.0618935	−	0.802202i	0.00324856	−	0.0421047i
$364$		0			0
$365$	5.13967	+	6.39618i	0.269023	+	0.334791i
$366$		0			0
$367$	−17.7698	−	30.7782i	−0.927577	−	1.60661i	−0.787363	−	0.616490i	$-0.788554\pi$
$367$	−17.7698	−	30.7782i	−0.927577	−	1.60661i	−0.140214	−	0.990121i	$-0.544779\pi$
$368$		0			0
$369$	26.6009	−	10.3051i	1.38479	−	0.536462i
$370$		0			0
$371$	−24.3471	−	42.1703i	−1.26404	−	2.18937i
$372$		0			0
$373$	−5.66594	−	3.27123i	−0.293371	−	0.169378i	0.346090	−	0.938201i	$-0.387509\pi$
$373$	−5.66594	−	3.27123i	−0.293371	−	0.169378i	−0.639461	+	0.768823i	$0.720843\pi$
$374$		0			0
$375$	−15.2471	−	11.9384i	−0.787358	−	0.616496i
$376$		0			0
$377$	4.42865			0.228087
$378$		0			0
$379$		−	14.2443i		−	0.731682i	−0.930677	−	0.365841i	$-0.880781\pi$
$379$		−	14.2443i		−	0.731682i	0.930677	−	0.365841i	$-0.119219\pi$
$380$		0			0
$381$	5.57774	−	2.67098i	0.285756	−	0.136839i
$382$		0			0
$383$	−8.10979	−	4.68219i	−0.414391	−	0.239249i	0.278284	−	0.960499i	$-0.410234\pi$
$383$	−8.10979	−	4.68219i	−0.414391	−	0.239249i	−0.692675	+	0.721250i	$0.743568\pi$
$384$		0			0
$385$	−5.44775	−	35.2566i	−0.277643	−	1.79684i
$386$		0			0
$387$	1.51917	+	0.235825i	0.0772236	+	0.0119877i
$388$		0			0
$389$	−7.64156	+	4.41186i	−0.387442	+	0.223690i	−0.681051	−	0.732236i	$-0.738477\pi$
$389$	−7.64156	+	4.41186i	−0.387442	+	0.223690i	0.293609	+	0.955926i	$0.405144\pi$
$390$		0			0
$391$	11.3277	+	6.54002i	0.572864	+	0.330743i
$392$		0			0
$393$	−0.701164	+	9.08780i	−0.0353691	+	0.458419i
$394$		0			0
$395$	0.00546526	−	0.0140784i	0.000274987	−	0.000708362i
$396$		0			0
$397$			1.68445i			0.0845401i	0.999106	+	0.0422700i	$0.0134590\pi$
$397$			1.68445i			0.0845401i	−0.999106	+	0.0422700i	$0.986541\pi$
$398$		0			0
$399$	11.0652	−	16.1532i	0.553955	−	0.808670i
$400$		0			0
$401$	−13.7375	−	7.93137i	−0.686020	−	0.396074i	0.116099	−	0.993238i	$-0.462961\pi$
$401$	−13.7375	−	7.93137i	−0.686020	−	0.396074i	−0.802119	+	0.597164i	$0.796294\pi$
$402$		0			0
$403$	−21.9259	−	37.9768i	−1.09221	−	1.89176i
$404$		0			0
$405$	−15.6698	−	12.6276i	−0.778640	−	0.627471i
$406$		0			0
$407$	−6.52615	+	3.76788i	−0.323489	+	0.186767i
$408$		0			0
$409$	−0.0555181	+	0.0961601i	−0.00274519	+	0.00475481i	−0.867395	−	0.497621i	$-0.834207\pi$
$409$	−0.0555181	+	0.0961601i	−0.00274519	+	0.00475481i	0.864650	+	0.502376i	$0.167540\pi$
$410$		0			0
$411$	−17.2204	−	11.7963i	−0.849419	−	0.581868i
$412$		0			0
$413$	14.5569			0.716297
$414$		0			0
$415$	2.26093	−	5.82412i	0.110985	−	0.285895i
$416$		0			0
$417$	31.6331	+	2.44063i	1.54908	+	0.119518i
$418$		0			0
$419$	9.66122	−	16.7337i	0.471981	−	0.817496i	−0.527505	−	0.849552i	$-0.676872\pi$
$419$	9.66122	−	16.7337i	0.471981	−	0.817496i	0.999486	+	0.0320563i	$0.0102056\pi$
$420$		0			0
$421$	−18.4323	−	31.9258i	−0.898337	−	1.55597i	−0.829619	−	0.558330i	$-0.811442\pi$
$421$	−18.4323	−	31.9258i	−0.898337	−	1.55597i	−0.0687183	−	0.997636i	$-0.521891\pi$
$422$		0			0
$423$	3.91635	−	25.2289i	0.190420	−	1.22667i
$424$		0			0
$425$	−5.03937	+	22.8585i	−0.244445	+	1.10880i
$426$		0			0
$427$	8.24986	−	14.2892i	0.399239	−	0.691502i
$428$		0			0
$429$	11.0652	+	23.1072i	0.534235	+	1.11563i
$430$		0			0
$431$	15.5407			0.748571			0.374286	−	0.927313i	$-0.377888\pi$
$431$	15.5407			0.748571			0.374286	+	0.927313i	$0.377888\pi$
$432$		0			0
$433$		−	8.23429i		−	0.395715i	−0.980231	−	0.197857i	$-0.936602\pi$
$433$		−	8.23429i		−	0.395715i	0.980231	−	0.197857i	$-0.0633983\pi$
$434$		0			0
$435$	−0.286911	−	3.75284i	−0.0137563	−	0.179935i
$436$		0			0
$437$	3.21285	−	5.56482i	0.153691	−	0.266201i
$438$		0			0
$439$	−28.8199	+	16.6392i	−1.37550	+	0.794145i	−0.991614	−	0.129235i	$-0.958748\pi$
$439$	−28.8199	+	16.6392i	−1.37550	+	0.794145i	−0.383886	+	0.923381i	$0.625414\pi$
$440$		0			0
$441$	18.5969	+	48.0048i	0.885567	+	2.28594i
$442$		0			0
$443$	−11.6345	+	6.71718i	−0.552772	+	0.319143i	−0.750239	−	0.661167i	$-0.770062\pi$
$443$	−11.6345	+	6.71718i	−0.552772	+	0.319143i	0.197467	+	0.980309i	$0.436728\pi$
$444$		0			0
$445$	−1.33400	−	1.66012i	−0.0632376	−	0.0786974i
$446$		0			0
$447$	40.3724	+	3.11491i	1.90955	+	0.147330i
$448$		0			0
$449$		−	30.4331i		−	1.43622i	−0.695927	−	0.718112i	$-0.745006\pi$
$449$		−	30.4331i		−	1.43622i	0.695927	−	0.718112i	$-0.254994\pi$
$450$		0			0
$451$			30.8649i			1.45337i
$452$		0			0
$453$	−17.4236	+	25.4352i	−0.818631	+	1.19505i
$454$		0			0
$455$	−31.3738	−	39.0439i	−1.47083	−	1.83040i
$456$		0			0
$457$	6.90969	−	3.98931i	0.323222	−	0.186612i	−0.329606	−	0.944119i	$-0.606916\pi$
$457$	6.90969	−	3.98931i	0.323222	−	0.186612i	0.652828	+	0.757507i	$0.273583\pi$
$458$		0			0
$459$	−5.56952	+	23.6795i	−0.259963	+	1.10526i
$460$		0			0
$461$	−22.8613	+	13.1990i	−1.06476	+	0.614738i	−0.926745	−	0.375692i	$-0.877405\pi$
$461$	−22.8613	+	13.1990i	−1.06476	+	0.614738i	−0.138014	+	0.990430i	$0.544072\pi$
$462$		0			0
$463$	0.473161	−	0.819539i	0.0219896	−	0.0380872i	−0.854821	−	0.518923i	$-0.826333\pi$
$463$	0.473161	−	0.819539i	0.0219896	−	0.0380872i	0.876811	+	0.480836i	$0.159667\pi$
$464$		0			0
$465$	−30.7611	+	21.0404i	−1.42651	+	0.975725i
$466$		0			0
$467$			34.4606i			1.59464i	0.603554	+	0.797322i	$0.293751\pi$
$467$			34.4606i			1.59464i	−0.603554	+	0.797322i	$0.706249\pi$
$468$		0			0
$469$	39.8347			1.83940
$470$		0			0
$471$	−4.44127	−	0.342664i	−0.204643	−	0.0157891i
$472$		0			0
$473$	−0.831672	+	1.44050i	−0.0382403	+	0.0662342i
$474$		0			0
$475$	11.2294	+	2.47564i	0.515242	+	0.113590i
$476$		0			0
$477$	18.6322	−	23.1540i	0.853108	−	1.06015i
$478$		0			0
$479$	3.07387	+	5.32411i	0.140449	+	0.243265i	0.927666	−	0.373412i	$-0.121812\pi$
$479$	3.07387	+	5.32411i	0.140449	+	0.243265i	−0.787217	+	0.616676i	$0.788479\pi$
$480$		0			0
$481$	−5.29006	+	9.16265i	−0.241206	+	0.417781i
$482$		0			0
$483$	10.2736	+	21.4540i	0.467463	+	0.976190i
$484$		0			0
$485$	−2.86912	+	7.39081i	−0.130280	+	0.335600i
$486$		0			0
$487$	−19.7766			−0.896164			−0.448082	−	0.893992i	$-0.647893\pi$
$487$	−19.7766			−0.896164			−0.448082	+	0.893992i	$0.647893\pi$
$488$		0			0
$489$	7.20769	−	3.45151i	0.325943	−	0.156083i
$490$		0			0
$491$	−3.30861	+	5.73068i	−0.149316	+	0.258622i	−0.930975	−	0.365084i	$-0.881040\pi$
$491$	−3.30861	+	5.73068i	−0.149316	+	0.258622i	0.781659	+	0.623706i	$0.214374\pi$
$492$		0			0
$493$	−3.93998	+	2.27475i	−0.177448	+	0.102449i
$494$		0			0
$495$	18.8642	−	10.8737i	0.847884	−	0.488736i
$496$		0			0
$497$	−21.2996	−	36.8920i	−0.955418	−	1.65483i
$498$		0			0
$499$	−14.7185	−	8.49775i	−0.658892	−	0.380412i	0.132963	−	0.991121i	$-0.457551\pi$
$499$	−14.7185	−	8.49775i	−0.658892	−	0.380412i	−0.791855	+	0.610710i	$0.790884\pi$
$500$		0			0
$501$	9.41515	+	0.726421i	0.420638	+	0.0324541i
$502$		0			0
$503$			15.4892i			0.690631i	0.938487	+	0.345316i	$0.112228\pi$
$503$			15.4892i			0.690631i	−0.938487	+	0.345316i	$0.887772\pi$
$504$		0			0
$505$	5.22583	−	13.4617i	0.232547	−	0.599036i
$506$		0			0
$507$	11.0991	+	7.60311i	0.492929	+	0.337666i
$508$		0			0
$509$	−7.57111	−	4.37118i	−0.335584	−	0.193749i	0.322734	−	0.946490i	$-0.395398\pi$
$509$	−7.57111	−	4.37118i	−0.335584	−	0.193749i	−0.658317	+	0.752741i	$0.728731\pi$
$510$		0			0
$511$	15.6204	−	9.01846i	0.691007	−	0.398953i
$512$		0			0
$513$	11.6328	+	2.73608i	0.513599	+	0.120801i
$514$		0			0
$515$	2.34523	+	15.1778i	0.103343	+	0.668813i
$516$		0			0
$517$	23.9224	+	13.8116i	1.05211	+	0.607433i
$518$		0			0
$519$	−31.6032	−	21.6488i	−1.38722	−	0.950275i
$520$		0			0
$521$			34.5835i			1.51513i	0.652758	+	0.757566i	$0.273612\pi$
$521$			34.5835i			1.51513i	−0.652758	+	0.757566i	$0.726388\pi$
$522$		0			0
$523$	−10.1425			−0.443501			−0.221751	−	0.975103i	$-0.571177\pi$
$523$	−10.1425			−0.443501			−0.221751	+	0.975103i	$0.571177\pi$
$524$		0			0
$525$	−31.0533	+	29.1157i	−1.35528	+	1.27071i
$526$		0			0
$527$	39.0131	+	22.5242i	1.69944	+	0.981170i
$528$		0			0
$529$	−7.59678	−	13.1580i	−0.330295	−	0.572087i
$530$		0			0
$531$	3.20945	+	8.28465i	0.139278	+	0.359523i
$532$		0			0
$533$	21.6670	+	37.5284i	0.938503	+	1.62553i
$534$		0			0
$535$	11.7049	+	14.5664i	0.506045	+	0.629760i
$536$		0			0
$537$	14.0943	−	6.74928i	0.608216	−	0.291253i
$538$		0			0
$539$	−55.6998			−2.39916
$540$		0			0
$541$	21.9906			0.945450			0.472725	−	0.881210i	$-0.343270\pi$
$541$	21.9906			0.945450			0.472725	+	0.881210i	$0.343270\pi$
$542$		0			0
$543$	−21.3104	+	10.2048i	−0.914516	+	0.437929i
$544$		0			0
$545$	−14.6525	+	11.7741i	−0.627645	+	0.504346i
$546$		0			0
$547$	−6.66047	−	11.5363i	−0.284781	−	0.493256i	0.687775	−	0.725924i	$-0.258588\pi$
$547$	−6.66047	−	11.5363i	−0.284781	−	0.493256i	−0.972556	+	0.232668i	$0.925254\pi$
$548$		0			0
$549$	9.95120	+	1.54476i	0.424707	+	0.0659285i
$550$		0			0
$551$	1.11749	+	1.93555i	0.0476067	+	0.0824573i
$552$		0			0
$553$	−0.0287496	−	0.0165986i	−0.00122256	−	0.000705845i
$554$		0			0
$555$	8.10716	+	3.88920i	0.344130	+	0.165087i
$556$		0			0
$557$	−11.2286			−0.475771			−0.237885	−	0.971293i	$-0.576454\pi$
$557$	−11.2286			−0.475771			−0.237885	+	0.971293i	$0.576454\pi$
$558$		0			0
$559$			2.33532i			0.0987735i
$560$		0			0
$561$	−21.7131	−	14.8739i	−0.916729	−	0.627977i
$562$		0			0
$563$	−26.3748	−	15.2275i	−1.11157	−	0.641764i	−0.172332	−	0.985039i	$-0.555130\pi$
$563$	−26.3748	−	15.2275i	−1.11157	−	0.641764i	−0.939235	+	0.343275i	$0.888464\pi$
$564$		0			0
$565$	5.26403	+	34.0676i	0.221460	+	1.43323i
$566$		0			0
$567$	−32.6924	+	29.8026i	−1.37295	+	1.25159i
$568$		0			0
$569$	−21.2927	+	12.2934i	−0.892638	+	0.515365i	−0.874804	−	0.484476i	$-0.839010\pi$
$569$	−21.2927	+	12.2934i	−0.892638	+	0.515365i	−0.0178334	+	0.999841i	$0.505677\pi$
$570$		0			0
$571$	9.86354	+	5.69472i	0.412776	+	0.238317i	0.691982	−	0.721915i	$-0.256738\pi$
$571$	9.86354	+	5.69472i	0.412776	+	0.238317i	−0.279206	+	0.960231i	$0.590071\pi$
$572$		0			0
$573$	−15.0933	−	10.3392i	−0.630532	−	0.431926i
$574$		0			0
$575$	−9.42587	+	10.3109i	−0.393086	+	0.429993i
$576$		0			0
$577$		−	3.96503i		−	0.165066i	−0.996588	−	0.0825331i	$-0.973699\pi$
$577$		−	3.96503i		−	0.165066i	0.996588	−	0.0825331i	$-0.0263010\pi$
$578$		0			0
$579$	−27.2909	−	2.10562i	−1.13417	−	0.0875064i
$580$		0			0
$581$	−11.8935	−	6.86671i	−0.493425	−	0.284879i
$582$		0			0
$583$	16.0776	+	27.8473i	0.665867	+	1.15332i
$584$		0			0
$585$	15.3036	−	26.4638i	0.632725	−	1.09414i
$586$		0			0
$587$	28.6601	−	16.5469i	1.18293	−	0.682965i	0.226240	−	0.974072i	$-0.427357\pi$
$587$	28.6601	−	16.5469i	1.18293	−	0.682965i	0.956691	+	0.291106i	$0.0940233\pi$
$588$		0			0
$589$	11.0652	−	19.1655i	0.455935	−	0.789703i
$590$		0			0
$591$	−29.7172	+	14.2305i	−1.22240	+	0.585366i
$592$		0			0
$593$	−20.4391			−0.839334			−0.419667	−	0.907678i	$-0.637853\pi$
$593$	−20.4391			−0.839334			−0.419667	+	0.907678i	$0.637853\pi$
$594$		0			0
$595$	47.9665	+	18.6207i	1.96644	+	0.763373i
$596$		0			0
$597$	1.07614	+	2.24727i	0.0440434	+	0.0919746i
$598$		0			0
$599$	21.8710	−	37.8817i	0.893625	−	1.54780i	0.0581288	−	0.998309i	$-0.481487\pi$
$599$	21.8710	−	37.8817i	0.893625	−	1.54780i	0.835497	−	0.549496i	$-0.185180\pi$
$600$		0			0
$601$	−11.1919	−	19.3850i	−0.456529	−	0.790732i	0.542246	−	0.840220i	$-0.317574\pi$
$601$	−11.1919	−	19.3850i	−0.456529	−	0.790732i	−0.998775	+	0.0494884i	$0.984241\pi$
$602$		0			0
$603$	8.78262	+	22.6708i	0.357656	+	0.923228i
$604$		0			0
$605$	−0.158617	−	1.02653i	−0.00644871	−	0.0417345i
$606$		0			0
$607$	−12.1622	+	21.0656i	−0.493649	+	0.855025i	−0.999973	−	0.00731837i	$-0.997670\pi$
$607$	−12.1622	+	21.0656i	−0.493649	+	0.855025i	0.506325	+	0.862343i	$0.331004\pi$
$608$		0			0
$609$	−8.24905	−	0.636451i	−0.334268	−	0.0257903i
$610$		0			0
$611$	38.7827			1.56898
$612$		0			0
$613$			15.7753i			0.637157i	0.947896	+	0.318579i	$0.103205\pi$
$613$			15.7753i			0.637157i	−0.947896	+	0.318579i	$0.896795\pi$
$614$		0			0
$615$	30.3979	−	20.7919i	1.22576	−	0.838411i
$616$		0			0
$617$	−3.17947	+	5.50700i	−0.128001	+	0.221703i	−0.922902	−	0.385035i	$-0.874189\pi$
$617$	−3.17947	+	5.50700i	−0.128001	+	0.221703i	0.794901	+	0.606739i	$0.207523\pi$
$618$		0			0
$619$	27.7015	−	15.9935i	1.11342	−	0.642832i	0.173705	−	0.984798i	$-0.444426\pi$
$619$	27.7015	−	15.9935i	1.11342	−	0.642832i	0.939712	+	0.341966i	$0.111093\pi$
$620$		0			0
$621$	−9.94488	+	10.5770i	−0.399074	+	0.424441i
$622$		0			0
$623$	−4.05427	+	2.34073i	−0.162431	+	0.0937795i
$624$		0			0
$625$	−22.6825	−	10.5121i	−0.907300	−	0.420483i
$626$		0			0
$627$	−7.30695	+	10.6668i	−0.291811	+	0.425990i
$628$		0			0
$629$		−	10.8688i		−	0.433368i
$630$		0			0
$631$		−	20.8543i		−	0.830196i	−0.909777	−	0.415098i	$-0.863747\pi$
$631$		−	20.8543i		−	0.830196i	0.909777	−	0.415098i	$-0.136253\pi$
$632$		0			0
$633$	30.7393	+	2.37168i	1.22178	+	0.0942656i
$634$		0			0
$635$	6.22356	−	5.00096i	0.246974	−	0.198457i
$636$		0			0
$637$	−67.7249	+	39.1010i	−2.68336	+	1.54924i
$638$		0			0
$639$	16.3000	−	20.2559i	0.644819	−	0.801312i
$640$		0			0
$641$	−26.5324	+	15.3185i	−1.04797	+	0.605043i	−0.922079	−	0.387002i	$-0.873511\pi$
$641$	−26.5324	+	15.3185i	−1.04797	+	0.605043i	−0.125886	+	0.992045i	$0.540177\pi$
$642$		0			0
$643$	−19.0142	+	32.9335i	−0.749846	+	1.29877i	0.198050	+	0.980192i	$0.436539\pi$
$643$	−19.0142	+	32.9335i	−0.749846	+	1.29877i	−0.947896	+	0.318580i	$0.896794\pi$
$644$		0			0
$645$	1.97895	−	0.151294i	0.0779211	−	0.00595719i
$646$		0			0
$647$		−	28.3431i		−	1.11428i	−0.830417	−	0.557142i	$-0.811898\pi$
$647$		−	28.3431i		−	1.11428i	0.830417	−	0.557142i	$-0.188102\pi$
$648$		0			0
$649$	−9.61266			−0.377330
$650$		0			0
$651$	35.3827	+	73.8887i	1.38676	+	2.89593i
$652$		0			0
$653$	−11.2134	+	19.4221i	−0.438813	+	0.760046i	−0.997598	−	0.0692663i	$-0.977934\pi$
$653$	−11.2134	+	19.4221i	−0.438813	+	0.760046i	0.558785	+	0.829312i	$0.311268\pi$
$654$		0			0
$655$	1.79691	+	11.6292i	0.0702110	+	0.454389i
$656$		0			0
$657$	8.57655	+	6.90158i	0.334603	+	0.269256i
$658$		0			0
$659$	−4.01881	−	6.96078i	−0.156551	−	0.271154i	0.777072	−	0.629412i	$-0.216704\pi$
$659$	−4.01881	−	6.96078i	−0.156551	−	0.271154i	−0.933623	+	0.358258i	$0.883371\pi$
$660$		0			0
$661$	10.1926	−	17.6542i	0.396448	−	0.686668i	−0.596837	−	0.802362i	$-0.703576\pi$
$661$	10.1926	−	17.6542i	0.396448	−	0.686668i	0.993285	+	0.115695i	$0.0369095\pi$
$662$		0			0
$663$	−36.8422	−	2.84254i	−1.43083	−	0.110395i
$664$		0			0
$665$	9.14758	−	23.5640i	0.354728	−	0.913773i
$666$		0			0
$667$	−2.71523			−0.105134
$668$		0			0
$669$	−2.20629	−	1.51135i	−0.0853000	−	0.0584321i
$670$		0			0
$671$	−5.44781	+	9.43588i	−0.210310	+	0.364268i
$672$		0			0
$673$	23.6402	−	13.6487i	0.911264	−	0.526119i	0.0304264	−	0.999537i	$-0.490313\pi$
$673$	23.6402	−	13.6487i	0.911264	−	0.526119i	0.880838	+	0.473418i	$0.156980\pi$
$674$		0			0
$675$	−23.4169	−	11.2538i	−0.901318	−	0.433159i
$676$		0			0
$677$	−18.7854	−	32.5373i	−0.721981	−	1.25051i	−0.960205	−	0.279298i	$-0.909898\pi$
$677$	−18.7854	−	32.5373i	−0.721981	−	1.25051i	0.238223	−	0.971210i	$-0.423435\pi$
$678$		0			0
$679$	15.0928	+	8.71385i	0.579210	+	0.334407i
$680$		0			0
$681$	8.27943	−	12.0864i	0.317269	−	0.463153i
$682$		0			0
$683$			0.779851i			0.0298402i	0.999889	+	0.0149201i	$0.00474938\pi$
$683$			0.779851i			0.0298402i	−0.999889	+	0.0149201i	$0.995251\pi$
$684$		0			0
$685$	−25.1208	−	9.75194i	−0.959818	−	0.372602i
$686$		0			0
$687$	1.10066	−	14.2657i	0.0419928	−	0.544269i
$688$		0			0
$689$	39.0973	+	22.5728i	1.48949	+	0.859956i
$690$		0			0
$691$	22.5980	−	13.0469i	0.859668	−	0.496329i	−0.00423336	−	0.999991i	$-0.501348\pi$
$691$	22.5980	−	13.0469i	0.859668	−	0.496329i	0.863901	+	0.503662i	$0.168014\pi$
$692$		0			0
$693$	−17.2899	−	44.6310i	−0.656790	−	1.69539i
$694$		0			0
$695$	40.4791	−	6.25473i	1.53546	−	0.237255i
$696$		0			0
$697$	−38.5524	−	22.2582i	−1.46028	−	0.843090i
$698$		0			0
$699$	22.8972	−	10.9647i	0.866052	−	0.414722i
$700$		0			0
$701$			16.3745i			0.618458i	0.950988	+	0.309229i	$0.100071\pi$
$701$			16.3745i			0.618458i	−0.950988	+	0.309229i	$0.899929\pi$
$702$		0			0
$703$	−5.33941			−0.201380
$704$		0			0
$705$	−2.51254	−	32.8645i	−0.0946278	−	1.23775i
$706$		0			0
$707$	−27.4901	−	15.8714i	−1.03387	−	0.596907i
$708$		0			0
$709$	9.64926	+	16.7130i	0.362385	+	0.627670i	0.988353	−	0.152179i	$-0.0486291\pi$
$709$	9.64926	+	16.7130i	0.362385	+	0.627670i	−0.625968	+	0.779849i	$0.715296\pi$
$710$		0			0
$711$	0.00310803	−	0.0200217i	0.000116560	−	0.000750872i
$712$		0			0
$713$	13.4429	+	23.2838i	0.503441	+	0.871986i
$714$		0			0
$715$	20.7178	+	25.7827i	0.774800	+	0.964218i
$716$		0			0
$717$	−0.0458250	+	0.593938i	−0.00171137	+	0.0221810i
$718$		0			0
$719$	−46.2738			−1.72572			−0.862860	−	0.505442i	$-0.831329\pi$
$719$	−46.2738			−1.72572			−0.862860	+	0.505442i	$0.831329\pi$
$720$		0			0
$721$	33.7597			1.25728
$722$		0			0
$723$	14.1047	+	9.66199i	0.524559	+	0.359333i
$724$		0			0
$725$	−1.46660	−	4.63243i	−0.0544680	−	0.172044i
$726$		0			0
$727$	9.16075	+	15.8669i	0.339753	+	0.588470i	0.984386	−	0.176022i	$-0.0563231\pi$
$727$	9.16075	+	15.8669i	0.339753	+	0.588470i	−0.644633	+	0.764492i	$0.722990\pi$
$728$		0			0
$729$	−24.1693	−	12.0352i	−0.895158	−	0.445750i
$730$		0			0
$731$	−1.19952	−	2.07763i	−0.0443659	−	0.0768439i
$732$		0			0
$733$	4.01463	+	2.31785i	0.148284	+	0.0856117i	0.572306	−	0.820040i	$-0.306049\pi$
$733$	4.01463	+	2.31785i	0.148284	+	0.0856117i	−0.424022	+	0.905652i	$0.639382\pi$
$734$		0			0
$735$	37.5218	+	54.8570i	1.38401	+	2.02343i
$736$		0			0
$737$	−26.3049			−0.968954
$738$		0			0
$739$			11.4405i			0.420844i	0.977611	+	0.210422i	$0.0674839\pi$
$739$			11.4405i			0.420844i	−0.977611	+	0.210422i	$0.932516\pi$
$740$		0			0
$741$	−1.39643	+	18.0991i	−0.0512990	+	0.664887i
$742$		0			0
$743$	23.6156	+	13.6345i	0.866373	+	0.500201i	0.866141	−	0.499799i	$-0.166593\pi$
$743$	23.6156	+	13.6345i	0.866373	+	0.500201i	0.000231838		1.00000i	$0.499926\pi$
$744$		0			0
$745$	51.6624	−	7.98273i	1.89276	−	0.292465i
$746$		0			0
$747$	1.28576	−	8.28280i	0.0470437	−	0.303052i
$748$		0			0
$749$	35.5733	−	20.5383i	1.29982	−	0.750451i
$750$		0			0
$751$	−24.9256	−	14.3908i	−0.909549	−	0.525128i	−0.0292631	−	0.999572i	$-0.509316\pi$
$751$	−24.9256	−	14.3908i	−0.909549	−	0.525128i	−0.880286	+	0.474443i	$0.842649\pi$
$752$		0			0
$753$	−25.9000	+	12.4026i	−0.943850	+	0.451976i
$754$		0			0
$755$	−14.4040	+	37.1045i	−0.524215	+	1.35037i
$756$		0			0
$757$			38.6191i			1.40363i	0.712357	+	0.701817i	$0.247628\pi$
$757$			38.6191i			1.40363i	−0.712357	+	0.701817i	$0.752372\pi$
$758$		0			0
$759$	−6.78416	−	14.1672i	−0.246249	−	0.514236i
$760$		0			0
$761$	10.7901	+	6.22969i	0.391142	+	0.225826i	0.682655	−	0.730741i	$-0.260825\pi$
$761$	10.7901	+	6.22969i	0.391142	+	0.225826i	−0.291513	+	0.956567i	$0.594159\pi$
$762$		0			0
$763$	20.6597	+	35.7836i	0.747931	+	1.29545i
$764$		0			0
$765$	−0.0219475	+	31.4043i	−0.000793513	+	1.13542i
$766$		0			0
$767$	−11.6879	+	6.74804i	−0.422027	+	0.243658i
$768$		0			0
$769$	20.7262	−	35.8988i	0.747405	−	1.29454i	−0.201657	−	0.979456i	$-0.564633\pi$
$769$	20.7262	−	35.8988i	0.747405	−	1.29454i	0.949062	−	0.315088i	$-0.102034\pi$
$770$		0			0
$771$	1.88961	−	24.4913i	0.0680528	−	0.882033i
$772$		0			0
$773$	−12.8158			−0.460954			−0.230477	−	0.973078i	$-0.574029\pi$
$773$	−12.8158			−0.460954			−0.230477	+	0.973078i	$0.574029\pi$
$774$		0			0
$775$	−32.4632	+	35.5112i	−1.16611	+	1.27560i
$776$		0			0
$777$	11.1703	−	16.3066i	0.400734	−	0.584997i
$778$		0			0
$779$	−10.9346	+	18.9392i	−0.391772	+	0.678568i
$780$		0			0
$781$	14.0652	+	24.3617i	0.503294	+	0.871730i
$782$		0			0
$783$	−1.45650	−	4.83505i	−0.0520512	−	0.172791i
$784$		0			0
$785$	−5.68325	+	0.878161i	−0.202844	+	0.0313429i
$786$		0			0
$787$	1.29742	−	2.24720i	0.0462481	−	0.0801041i	−0.841975	−	0.539517i	$-0.818607\pi$
$787$	1.29742	−	2.24720i	0.0462481	−	0.0801041i	0.888223	+	0.459413i	$0.151940\pi$
$788$		0			0
$789$	5.38817	−	7.86572i	0.191824	−	0.280027i
$790$		0			0
$791$	75.7760			2.69428
$792$		0			0
$793$			15.2973i			0.543225i
$794$		0			0
$795$	16.5953	−	34.5935i	0.588575	−	1.22690i
$796$		0			0
$797$	−1.96403	+	3.40180i	−0.0695695	+	0.120498i	−0.898712	−	0.438540i	$-0.855496\pi$
$797$	−1.96403	+	3.40180i	−0.0695695	+	0.120498i	0.829142	+	0.559038i	$0.188829\pi$
$798$		0			0
$799$	−34.5033	+	19.9205i	−1.22064	+	0.704736i
$800$		0			0
$801$	−2.22604	−	1.79130i	−0.0786532	−	0.0632925i
$802$		0			0
$803$	−10.3150	+	5.95535i	−0.364008	+	0.210160i
$804$		0			0
$805$	19.2355	+	23.9380i	0.677962	+	0.843705i
$806$		0			0
$807$	17.4741	+	36.4907i	0.615118	+	1.28453i
$808$		0			0
$809$		−	23.6490i		−	0.831454i	−0.909489	−	0.415727i	$-0.863527\pi$
$809$		−	23.6490i		−	0.831454i	0.909489	−	0.415727i	$-0.136473\pi$
$810$		0			0
$811$		−	30.1396i		−	1.05834i	−0.848515	−	0.529172i	$-0.822503\pi$
$811$		−	30.1396i		−	1.05834i	0.848515	−	0.529172i	$-0.177497\pi$
$812$		0			0
$813$	14.5690	+	30.4241i	0.510958	+	1.06702i
$814$		0			0
$815$	8.04223	−	6.46236i	0.281707	−	0.226367i
$816$		0			0
$817$	−1.02066	+	0.589276i	−0.0357082	+	0.0206162i
$818$		0			0
$819$	−52.3534	−	42.1290i	−1.82938	−	1.47211i
$820$		0			0
$821$	28.5981	−	16.5111i	0.998081	−	0.576242i	0.0904010	−	0.995905i	$-0.471185\pi$
$821$	28.5981	−	16.5111i	0.998081	−	0.576242i	0.907680	+	0.419663i	$0.137852\pi$
$822$		0			0
$823$	27.3286	−	47.3345i	0.952615	−	1.64998i	0.212881	−	0.977078i	$-0.431715\pi$
$823$	27.3286	−	47.3345i	0.952615	−	1.64998i	0.739734	−	0.672900i	$-0.234951\pi$
$824$		0			0
$825$	20.5061	−	19.2266i	0.713930	−	0.669384i
$826$		0			0
$827$		−	7.83653i		−	0.272503i	−0.990674	−	0.136251i	$-0.956494\pi$
$827$		−	7.83653i		−	0.272503i	0.990674	−	0.136251i	$-0.0435055\pi$
$828$		0			0
$829$	−45.3314			−1.57442			−0.787211	−	0.616683i	$-0.788476\pi$
$829$	−45.3314			−1.57442			−0.787211	+	0.616683i	$0.788476\pi$
$830$		0			0
$831$	−24.2817	+	35.4468i	−0.842323	+	1.22963i
$832$		0			0
$833$	40.1679	−	69.5728i	1.39173	−	2.41056i
$834$		0			0
$835$	12.0481	−	1.86163i	0.416940	−	0.0644245i
$836$		0			0
$837$	−34.2507	+	36.4279i	−1.18388	+	1.25913i
$838$		0			0
$839$	−12.1201	−	20.9926i	−0.418432	−	0.724745i	0.577350	−	0.816497i	$-0.304087\pi$
$839$	−12.1201	−	20.9926i	−0.418432	−	0.724745i	−0.995782	+	0.0917514i	$0.970753\pi$
$840$		0			0
$841$	−14.0278	+	24.2969i	−0.483717	+	0.837823i
$842$		0			0
$843$	25.1507	−	36.7154i	0.866238	−	1.26455i
$844$		0			0
$845$	16.1912	+	6.28546i	0.556995	+	0.216226i
$846$		0			0
$847$	−2.28330			−0.0784552
$848$		0			0
$849$	−1.91165	+	24.7769i	−0.0656076	+	0.850341i
$850$		0			0
$851$	3.24337	−	5.61768i	0.111181	−	0.192572i
$852$		0			0
$853$	−13.9184	+	8.03581i	−0.476558	+	0.275141i	−0.718981	−	0.695030i	$-0.755391\pi$
$853$	−13.9184	+	8.03581i	−0.476558	+	0.275141i	0.242423	+	0.970171i	$0.422058\pi$
$854$		0			0
$855$	15.4277	+	0.0107819i	0.527615	+	0.000368734i
$856$		0			0
$857$	1.14515	+	1.98346i	0.0391177	+	0.0677538i	0.884921	−	0.465740i	$-0.154212\pi$
$857$	1.14515	+	1.98346i	0.0391177	+	0.0677538i	−0.845804	+	0.533494i	$0.820879\pi$
$858$		0			0
$859$	−25.7347	−	14.8579i	−0.878056	−	0.506946i	−0.00803922	−	0.999968i	$-0.502559\pi$
$859$	−25.7347	−	14.8579i	−0.878056	−	0.506946i	−0.870017	+	0.493022i	$0.835892\pi$
$860$		0			0
$861$	−34.9649	−	73.0162i	−1.19160	−	2.48839i
$862$		0			0
$863$			34.7002i			1.18121i	0.806961	+	0.590605i	$0.201111\pi$
$863$			34.7002i			1.18121i	−0.806961	+	0.590605i	$0.798889\pi$
$864$		0			0
$865$	−46.1022	−	17.8969i	−1.56752	−	0.608514i
$866$		0			0
$867$	7.67996	−	3.67766i	0.260825	−	0.124900i
$868$		0			0
$869$	0.0189849	+	0.0109609i	0.000644018	+	0.000371824i
$870$		0			0
$871$	−31.9839	+	18.4659i	−1.08373	+	0.625694i
$872$		0			0
$873$	−1.63164	+	10.5109i	−0.0552225	+	0.355739i
$874$		0			0
$875$	−30.4506	+	45.7472i	−1.02942	+	1.54654i
$876$		0			0
$877$	4.08267	+	2.35713i	0.137862	+	0.0795947i	0.567345	−	0.823480i	$-0.307971\pi$
$877$	4.08267	+	2.35713i	0.137862	+	0.0795947i	−0.429483	+	0.903075i	$0.641304\pi$
$878$		0			0
$879$	−2.33474	+	30.2606i	−0.0787489	+	1.02067i
$880$		0			0
$881$			41.1882i			1.38766i	0.720136	+	0.693832i	$0.244079\pi$
$881$			41.1882i			1.38766i	−0.720136	+	0.693832i	$0.755921\pi$
$882$		0			0
$883$	−26.9479			−0.906870			−0.453435	−	0.891289i	$-0.649802\pi$
$883$	−26.9479			−0.906870			−0.453435	+	0.891289i	$0.649802\pi$
$884$		0			0
$885$	6.47550	+	9.46721i	0.217672	+	0.318237i
$886$		0			0
$887$	−0.0614320	−	0.0354678i	−0.00206269	−	0.00119089i	0.498968	−	0.866620i	$-0.333712\pi$
$887$	−0.0614320	−	0.0354678i	−0.00206269	−	0.00119089i	−0.501031	+	0.865429i	$0.667046\pi$
$888$		0			0
$889$	−8.77507	−	15.1989i	−0.294306	−	0.509753i
$890$		0			0
$891$	21.5885	−	19.6802i	0.723242	−	0.659311i
$892$		0			0
$893$	9.78612	+	16.9501i	0.327480	+	0.567212i
$894$		0			0
$895$	15.7262	−	12.6369i	0.525670	−	0.422404i
$896$		0			0
$897$	−18.1941	−	12.4633i	−0.607483	−	0.416138i
$898$		0			0
$899$	−9.35142			−0.311887
$900$		0			0
$901$	−46.3775			−1.54506
$902$		0			0
$903$	0.335614	−	4.34989i	0.0111685	−	0.144755i
$904$		0			0
$905$	−23.7778	+	19.1067i	−0.790401	+	0.635129i
$906$		0			0
$907$	−18.5017	−	32.0459i	−0.614340	−	1.06407i	−0.990500	−	0.137513i	$-0.956089\pi$
$907$	−18.5017	−	32.0459i	−0.614340	−	1.06407i	0.376160	−	0.926555i	$-0.377244\pi$
$908$		0			0
$909$	2.97187	−	19.1446i	0.0985706	−	0.634985i
$910$		0			0
$911$	16.7405	+	28.9954i	0.554637	+	0.960660i	0.997932	+	0.0642840i	$0.0204763\pi$
$911$	16.7405	+	28.9954i	0.554637	+	0.960660i	−0.443294	+	0.896376i	$0.646190\pi$
$912$		0			0
$913$	7.85388	+	4.53444i	0.259926	+	0.150068i
$914$		0			0
$915$	12.9630	−	0.991039i	0.428543	−	0.0327628i
$916$		0			0
$917$	25.8665			0.854189
$918$		0			0
$919$		−	37.0547i		−	1.22232i	−0.791506	−	0.611161i	$-0.790703\pi$
$919$		−	37.0547i		−	1.22232i	0.791506	−	0.611161i	$-0.209297\pi$
$920$		0			0
$921$	−0.648913	+	0.310742i	−0.0213824	+	0.0102393i
$922$		0			0
$923$	34.2036	+	19.7475i	1.12583	+	0.649995i
$924$		0			0
$925$	11.3361	+	2.49916i	0.372729	+	0.0821718i
$926$		0			0
$927$	7.44323	+	19.2134i	0.244468	+	0.631052i
$928$		0			0
$929$	3.32859	−	1.92176i	0.109208	−	0.0630510i	−0.444401	−	0.895828i	$-0.646584\pi$
$929$	3.32859	−	1.92176i	0.109208	−	0.0630510i	0.553609	+	0.832777i	$0.313250\pi$
$930$		0			0
$931$	−34.1783	−	19.7329i	−1.12015	−	0.646718i
$932$		0			0
$933$	−2.89927	+	37.5774i	−0.0949177	+	1.23023i
$934$		0			0
$935$	−31.6748	−	12.2962i	−1.03588	−	0.402128i
$936$		0			0
$937$			20.6287i			0.673912i	0.941520	+	0.336956i	$0.109397\pi$
$937$			20.6287i			0.673912i	−0.941520	+	0.336956i	$0.890603\pi$
$938$		0			0
$939$	20.2145	−	29.5094i	0.659675	−	0.963003i
$940$		0			0
$941$	−21.3168	−	12.3072i	−0.694907	−	0.401205i	0.110541	−	0.993872i	$-0.464742\pi$
$941$	−21.3168	−	12.3072i	−0.694907	−	0.401205i	−0.805448	+	0.592667i	$0.798075\pi$
$942$		0			0
$943$	−13.2842	−	23.0089i	−0.432592	−	0.749272i
$944$		0			0
$945$	−32.3084	+	47.0937i	−1.05099	+	1.53196i
$946$		0			0
$947$	22.4985	−	12.9895i	0.731104	−	0.422103i	−0.0877216	−	0.996145i	$-0.527959\pi$
$947$	22.4985	−	12.9895i	0.731104	−	0.422103i	0.818826	+	0.574042i	$0.194625\pi$
$948$		0			0
$949$	−8.36126	+	14.4821i	−0.271418	+	0.470110i
$950$		0			0
$951$	−15.1125	−	10.3523i	−0.490056	−	0.335698i
$952$		0			0
$953$	−38.7615			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$953$	−38.7615			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$954$		0			0
$955$	−22.0179	−	8.54737i	−0.712482	−	0.276586i
$956$		0			0
$957$	5.44727	+	0.420282i	0.176085	+	0.0135858i
$958$		0			0
$959$	−29.6177	+	51.2994i	−0.956407	+	1.65655i
$960$		0			0
$961$	30.7982	+	53.3440i	0.993490	+	1.72077i
$962$		0			0
$963$	19.5319	+	15.7174i	0.629406	+	0.506485i
$964$		0			0
$965$	−34.9227	+	5.39616i	−1.12420	+	0.173709i
$966$		0			0
$967$	19.5551	−	33.8704i	0.628849	−	1.08920i	−0.358934	−	0.933363i	$-0.616860\pi$
$967$	19.5551	−	33.8704i	0.628849	−	1.08920i	0.987783	−	0.155835i	$-0.0498068\pi$
$968$		0			0
$969$	−8.05413	−	16.8192i	−0.258736	−	0.540311i
$970$		0			0
$971$	23.5132			0.754574			0.377287	−	0.926096i	$-0.376857\pi$
$971$	23.5132			0.754574			0.377287	+	0.926096i	$0.376857\pi$
$972$		0			0
$973$		−	90.0371i		−	2.88646i
$974$		0			0
$975$	11.4362	−	37.7726i	0.366251	−	1.20969i
$976$		0			0
$977$	19.9499	−	34.5542i	0.638253	−	1.10549i	−0.347563	−	0.937657i	$-0.612991\pi$
$977$	19.9499	−	34.5542i	0.638253	−	1.10549i	0.985816	−	0.167830i	$-0.0536760\pi$
$978$		0			0
$979$	2.67724	−	1.54571i	0.0855651	−	0.0494010i
$980$		0			0
$981$	−15.8103	+	19.6474i	−0.504784	+	0.627292i
$982$		0			0
$983$	−43.2536	+	24.9725i	−1.37958	+	0.796499i	−0.992108	−	0.125384i	$-0.959984\pi$
$983$	−43.2536	+	24.9725i	−1.37958	+	0.796499i	−0.387469	+	0.921883i	$0.626650\pi$
$984$		0			0
$985$	−33.1580	+	26.6442i	−1.05650	+	0.848956i
$986$		0			0
$987$	−72.2388	−	5.57355i	−2.29939	−	0.177408i
$988$		0			0
$989$		−	1.43180i		−	0.0455285i
$990$		0			0
$991$		−	37.3553i		−	1.18663i	−0.804971	−	0.593315i	$-0.797819\pi$
$991$		−	37.3553i		−	1.18663i	0.804971	−	0.593315i	$-0.202181\pi$
$992$		0			0
$993$	2.93411	−	4.28325i	0.0931111	−	0.135925i
$994$		0			0
$995$	2.01488	+	2.50747i	0.0638761	+	0.0794921i
$996$		0			0
$997$	44.6518	−	25.7797i	1.41414	−	0.816452i	0.418361	−	0.908281i	$-0.362605\pi$
$997$	44.6518	−	25.7797i	1.41414	−	0.816452i	0.995775	+	0.0918294i	$0.0292714\pi$
$998$		0			0
$999$	11.7433	+	2.76207i	0.371541	+	0.0873881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.br.c.239.11	yes	24
3.2	odd	2		2160.2.br.d.719.3		24
4.3	odd	2		720.2.br.d.239.2	yes	24
5.4	even	2	inner	720.2.br.c.239.2	✓	24
9.2	odd	6		720.2.br.d.479.11	yes	24
9.7	even	3		2160.2.br.c.1439.7		24
12.11	even	2		2160.2.br.c.719.3		24
15.14	odd	2		2160.2.br.d.719.7		24
20.19	odd	2		720.2.br.d.239.11	yes	24
36.7	odd	6		2160.2.br.d.1439.7		24
36.11	even	6	inner	720.2.br.c.479.2	yes	24
45.29	odd	6		720.2.br.d.479.2	yes	24
45.34	even	6		2160.2.br.c.1439.3		24
60.59	even	2		2160.2.br.c.719.7		24
180.79	odd	6		2160.2.br.d.1439.3		24
180.119	even	6	inner	720.2.br.c.479.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.br.c.239.2	✓	24	5.4	even	2	inner
720.2.br.c.239.11	yes	24	1.1	even	1	trivial
720.2.br.c.479.2	yes	24	36.11	even	6	inner
720.2.br.c.479.11	yes	24	180.119	even	6	inner
720.2.br.d.239.2	yes	24	4.3	odd	2
720.2.br.d.239.11	yes	24	20.19	odd	2
720.2.br.d.479.2	yes	24	45.29	odd	6
720.2.br.d.479.11	yes	24	9.2	odd	6
2160.2.br.c.719.3		24	12.11	even	2
2160.2.br.c.719.7		24	60.59	even	2
2160.2.br.c.1439.3		24	45.34	even	6
2160.2.br.c.1439.7		24	9.7	even	3
2160.2.br.d.719.3		24	3.2	odd	2
2160.2.br.d.719.7		24	15.14	odd	2
2160.2.br.d.1439.3		24	180.79	odd	6
2160.2.br.d.1439.7		24	36.7	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56217 - 0.748070i) q^{3} +(1.74305 - 1.40063i) q^{5} +(-2.45766 - 4.25679i) q^{7} +(1.88078 - 2.33723i) q^{9} +O(q^{10})\)	\(q+(1.56217 - 0.748070i) q^{3} +(1.74305 - 1.40063i) q^{5} +(-2.45766 - 4.25679i) q^{7} +(1.88078 - 2.33723i) q^{9} +(1.62292 + 2.81098i) q^{11} +(3.94659 + 2.27856i) q^{13} +(1.67518 - 3.49196i) q^{15} -4.68147 q^{17} +2.29982i q^{19} +(-7.02367 - 4.81135i) q^{21} +(-2.41968 - 1.39700i) q^{23} +(1.07645 - 4.88275i) q^{25} +(1.18969 - 5.05812i) q^{27} +(0.841610 - 0.485904i) q^{29} +(-8.33350 - 4.81135i) q^{31} +(4.63809 + 3.17718i) q^{33} +(-10.2460 - 3.97752i) q^{35} +2.32167i q^{37} +(7.86979 + 0.607189i) q^{39} +(8.23509 + 4.75453i) q^{41} +(0.256227 + 0.443798i) q^{43} +(0.00468816 - 6.70820i) q^{45} +(7.37017 - 4.25517i) q^{47} +(-8.58018 + 14.8613i) q^{49} +(-7.31328 + 3.50207i) q^{51} +9.90660 q^{53} +(6.76598 + 2.62656i) q^{55} +(1.72043 + 3.59272i) q^{57} +(-1.48077 + 2.56476i) q^{59} +(1.67840 + 2.90707i) q^{61} +(-14.5714 - 2.26197i) q^{63} +(10.0705 - 1.55607i) q^{65} +(-4.05210 + 7.01844i) q^{67} +(-4.82501 - 0.372271i) q^{69} +8.66662 q^{71} +3.66953i q^{73} +(-1.97104 - 8.43297i) q^{75} +(7.97717 - 13.8169i) q^{77} +(0.00584899 - 0.00337691i) q^{79} +(-1.92532 - 8.79165i) q^{81} +(2.41968 - 1.39700i) q^{83} +(-8.16004 + 6.55703i) q^{85} +(0.951252 - 1.38865i) q^{87} -0.952424i q^{89} -22.3997i q^{91} +(-16.6176 - 1.28212i) q^{93} +(3.22120 + 4.00870i) q^{95} +(-3.07057 + 1.77279i) q^{97} +(9.62227 + 1.49369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 2 q^{9}+O(q^{10}) \) 24 * q + 3 * q^5 + 2 * q^9	\( 24 q + 3 q^{5} + 2 q^{9} - 6 q^{11} + 9 q^{15} - 18 q^{21} + 3 q^{25} + 12 q^{29} - 18 q^{31} - 30 q^{35} + 6 q^{39} - 12 q^{41} + q^{45} - 12 q^{49} - 36 q^{51} + 6 q^{59} + 3 q^{65} - 12 q^{69} + 96 q^{71} + 9 q^{75} - 18 q^{79} - 14 q^{81} + 24 q^{95} - 18 q^{99}+O(q^{100}) \) 24 * q + 3 * q^5 + 2 * q^9 - 6 * q^11 + 9 * q^15 - 18 * q^21 + 3 * q^25 + 12 * q^29 - 18 * q^31 - 30 * q^35 + 6 * q^39 - 12 * q^41 + q^45 - 12 * q^49 - 36 * q^51 + 6 * q^59 + 3 * q^65 - 12 * q^69 + 96 * q^71 + 9 * q^75 - 18 * q^79 - 14 * q^81 + 24 * q^95 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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