LMFDB - Embedded newform 720.2.br.c.479.2

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			479.2
Character	$\chi$	$=$	720.479
Dual form			720.2.br.c.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56217 - 0.748070i) q^{3} +(-0.341459 - 2.20984i) q^{5} +(2.45766 - 4.25679i) q^{7} +(1.88078 + 2.33723i) q^{9} +O(q^{10})$	\(q+(-1.56217 - 0.748070i) q^{3} +(-0.341459 - 2.20984i) q^{5} +(2.45766 - 4.25679i) q^{7} +(1.88078 + 2.33723i) q^{9} +(1.62292 - 2.81098i) q^{11} +(-3.94659 + 2.27856i) q^{13} +(-1.11970 + 3.70760i) q^{15} +4.68147 q^{17} -2.29982i q^{19} +(-7.02367 + 4.81135i) q^{21} +(2.41968 - 1.39700i) q^{23} +(-4.76681 + 1.50914i) q^{25} +(-1.18969 - 5.05812i) q^{27} +(0.841610 + 0.485904i) q^{29} +(-8.33350 + 4.81135i) q^{31} +(-4.63809 + 3.17718i) q^{33} +(-10.2460 - 3.97752i) q^{35} +2.32167i q^{37} +(7.86979 - 0.607189i) q^{39} +(8.23509 - 4.75453i) q^{41} +(-0.256227 + 0.443798i) q^{43} +(4.52271 - 4.95430i) q^{45} +(-7.37017 - 4.25517i) q^{47} +(-8.58018 - 14.8613i) q^{49} +(-7.31328 - 3.50207i) q^{51} -9.90660 q^{53} +(-6.76598 - 2.62656i) q^{55} +(-1.72043 + 3.59272i) q^{57} +(-1.48077 - 2.56476i) q^{59} +(1.67840 - 2.90707i) q^{61} +(14.5714 - 2.26197i) q^{63} +(6.38287 + 7.94330i) q^{65} +(4.05210 + 7.01844i) q^{67} +(-4.82501 + 0.372271i) q^{69} +8.66662 q^{71} +3.66953i q^{73} +(8.57554 + 1.20837i) q^{75} +(-7.97717 - 13.8169i) q^{77} +(0.00584899 + 0.00337691i) q^{79} +(-1.92532 + 8.79165i) q^{81} +(-2.41968 - 1.39700i) q^{83} +(-1.59853 - 10.3453i) q^{85} +(-0.951252 - 1.38865i) q^{87} +0.952424i q^{89} +22.3997i q^{91} +(16.6176 - 1.28212i) q^{93} +(-5.08224 + 0.785294i) q^{95} +(3.07057 + 1.77279i) q^{97} +(9.62227 - 1.49369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

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
$5$	−0.341459	−	2.20984i	−0.152705	−	0.988272i
$5$	−0.341459	−	2.20984i	−0.152705	−	0.988272i
$6$		0			0
$7$	2.45766	−	4.25679i	0.928908	−	1.60892i	0.143755	−	0.989613i	$-0.454082\pi$
$7$	2.45766	−	4.25679i	0.928908	−	1.60892i	0.785152	−	0.619302i	$-0.212585\pi$
$8$		0			0
$9$	1.88078	+	2.33723i	0.626927	+	0.779078i
$10$		0			0
$11$	1.62292	−	2.81098i	0.489329	−	0.847542i	−0.510596	−	0.859821i	$-0.670575\pi$
$11$	1.62292	−	2.81098i	0.489329	−	0.847542i	0.999925	+	0.0122787i	$0.00390852\pi$
$12$		0			0
$13$	−3.94659	+	2.27856i	−1.09459	+	0.631960i	−0.934794	−	0.355191i	$-0.884416\pi$
$13$	−3.94659	+	2.27856i	−1.09459	+	0.631960i	−0.159793	+	0.987151i	$0.551083\pi$
$14$		0			0
$15$	−1.11970	+	3.70760i	−0.289105	+	0.957297i
$16$		0			0
$17$	4.68147			1.13542			0.567712	−	0.823227i	$-0.307829\pi$
$17$	4.68147			1.13542			0.567712	+	0.823227i	$0.307829\pi$
$18$		0			0
$19$		−	2.29982i		−	0.527615i	−0.964575	−	0.263807i	$-0.915022\pi$
$19$		−	2.29982i		−	0.527615i	0.964575	−	0.263807i	$-0.0849783\pi$
$20$		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	$-0.572581\pi$
$23$	2.41968	−	1.39700i	0.504538	−	0.291295i	0.730585	+	0.682821i	$0.239247\pi$
$24$		0			0
$25$	−4.76681	+	1.50914i	−0.953362	+	0.301828i
$26$		0			0
$27$	−1.18969	−	5.05812i	−0.228957	−	0.973437i
$28$		0			0
$29$	0.841610	+	0.485904i	0.156283	+	0.0902301i	0.576102	−	0.817378i	$-0.304573\pi$
$29$	0.841610	+	0.485904i	0.156283	+	0.0902301i	−0.419819	+	0.907608i	$0.637906\pi$
$30$		0			0
$31$	−8.33350	+	4.81135i	−1.49674	+	0.864144i	−0.999993	−	0.00375071i	$-0.998806\pi$
$31$	−8.33350	+	4.81135i	−1.49674	+	0.864144i	−0.496748	+	0.867895i	$0.665473\pi$
$32$		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	0.308148	−	0.951338i	$-0.400291\pi$
$41$	8.23509	−	4.75453i	1.28611	−	0.742533i	0.977957	+	0.208805i	$0.0669574\pi$
$42$		0			0
$43$	−0.256227	+	0.443798i	−0.0390743	+	0.0676786i	−0.884901	−	0.465779i	$-0.845774\pi$
$43$	−0.256227	+	0.443798i	−0.0390743	+	0.0676786i	0.845827	+	0.533457i	$0.179108\pi$
$44$		0			0
$45$	4.52271	−	4.95430i	0.674206	−	0.738544i
$46$		0			0
$47$	−7.37017	−	4.25517i	−1.07505	−	0.620680i	−0.145493	−	0.989359i	$-0.546477\pi$
$47$	−7.37017	−	4.25517i	−1.07505	−	0.620680i	−0.929557	+	0.368679i	$0.879810\pi$
$48$		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	$-0.738189\pi$
$53$	−9.90660			−1.36078			−0.680388	+	0.732852i	$0.738189\pi$
$54$		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	0.753391	−	0.657573i	$-0.228417\pi$
$59$	−1.48077	−	2.56476i	−0.192779	−	0.333904i	−0.946170	+	0.323669i	$0.895083\pi$
$60$		0			0
$61$	1.67840	−	2.90707i	0.214897	−	0.372212i	−0.738344	−	0.674424i	$-0.764392\pi$
$61$	1.67840	−	2.90707i	0.214897	−	0.372212i	0.953241	+	0.302212i	$0.0977252\pi$
$62$		0			0
$63$	14.5714	−	2.26197i	1.83583	−	0.284981i
$64$		0			0
$65$	6.38287	+	7.94330i	0.791697	+	0.985245i
$66$		0			0
$67$	4.05210	+	7.01844i	0.495042	+	0.857439i	0.999984	−	0.00571511i	$-0.00181918\pi$
$67$	4.05210	+	7.01844i	0.495042	+	0.857439i	−0.504941	+	0.863154i	$0.668486\pi$
$68$		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
$75$	8.57554	+	1.20837i	0.990218	+	0.139530i
$76$		0			0
$77$	−7.97717	−	13.8169i	−0.909083	−	1.57458i
$78$		0			0
$79$	0.00584899	+	0.00337691i	0.000658062	+	0.000379932i	0.500329	−	0.865835i	$-0.333212\pi$
$79$	0.00584899	+	0.00337691i	0.000658062	+	0.000379932i	−0.499671	+	0.866215i	$0.666546\pi$
$80$		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	$-0.382337\pi$
$83$	−2.41968	−	1.39700i	−0.265594	−	0.153341i	−0.626884	+	0.779113i	$0.715670\pi$
$84$		0			0
$85$	−1.59853	−	10.3453i	−0.173385	−	1.12211i
$86$		0			0
$87$	−0.951252	−	1.38865i	−0.101985	−	0.148879i
$88$		0			0
$89$			0.952424i			0.100957i	0.998725	+	0.0504784i	$0.0160746\pi$
$89$			0.952424i			0.100957i	−0.998725	+	0.0504784i	$0.983925\pi$
$90$		0			0
$91$			22.3997i			2.34813i
$92$		0			0
$93$	16.6176	−	1.28212i	1.72317	−	0.132950i
$94$		0			0
$95$	−5.08224	+	0.785294i	−0.521427	+	0.0805695i
$96$		0			0
$97$	3.07057	+	1.77279i	0.311769	+	0.180000i	0.647718	−	0.761880i	$-0.275724\pi$
$97$	3.07057	+	1.77279i	0.311769	+	0.180000i	−0.335949	+	0.941880i	$0.609057\pi$
$98$		0			0
$99$	9.62227	−	1.49369i	0.967075	−	0.150122i
$100$		0			0
$101$	5.59275	+	3.22898i	0.556499	+	0.321295i	0.751739	−	0.659460i	$-0.229215\pi$
$101$	5.59275	+	3.22898i	0.556499	+	0.321295i	−0.195240	+	0.980756i	$0.562549\pi$
$102$		0			0
$103$	3.43413	+	5.94809i	0.338375	+	0.586083i	0.984127	−	0.177464i	$-0.0567894\pi$
$103$	3.43413	+	5.94809i	0.338375	+	0.586083i	−0.645752	+	0.763547i	$0.723456\pi$
$104$		0			0
$105$	13.0306	+	13.8783i	1.27166	+	1.35439i
$106$		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	0.958924	+	0.283663i	$0.0915497\pi$
$113$	7.70815	+	13.3509i	0.725121	+	1.25595i	−0.233803	+	0.972284i	$0.575117\pi$
$114$		0			0
$115$	−3.91337	−	4.87009i	−0.364924	−	0.454138i
$116$		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	$-0.550638\pi$
$127$	−3.57050			−0.316830			−0.158415	+	0.987373i	$0.550638\pi$
$128$		0			0
$129$	0.732264	−	0.501615i	0.0644722	−	0.0441647i
$130$		0			0
$131$	−2.63122	−	4.55740i	−0.229891	−	0.398182i	0.727885	−	0.685699i	$-0.240503\pi$
$131$	−2.63122	−	4.55740i	−0.229891	−	0.398182i	−0.957775	+	0.287517i	$0.907170\pi$
$132$		0			0
$133$	−9.78985	−	5.65217i	−0.848888	−	0.490105i
$134$		0			0
$135$	−10.7714	+	4.35618i	−0.927057	+	0.374920i
$136$		0			0
$137$	6.02560	−	10.4366i	0.514802	−	0.891663i	−0.485051	−	0.874486i	$-0.661199\pi$
$137$	6.02560	−	10.4366i	0.514802	−	0.891663i	0.999852	−	0.0171767i	$-0.00546779\pi$
$138$		0			0
$139$	15.8635	−	9.15882i	1.34553	−	0.776841i	0.357916	−	0.933754i	$-0.383487\pi$
$139$	15.8635	−	9.15882i	1.34553	−	0.776841i	0.987612	+	0.156913i	$0.0501542\pi$
$140$		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	0.685286	−	0.728274i	$-0.259677\pi$
$149$	20.2462	−	11.6891i	1.65863	−	0.957612i	0.973347	−	0.229338i	$-0.0736563\pi$
$150$		0			0
$151$	−15.4153	−	8.90005i	−1.25448	−	0.724276i	−0.282486	−	0.959272i	$-0.591159\pi$
$151$	−15.4153	−	8.90005i	−1.25448	−	0.724276i	−0.971996	+	0.234996i	$0.924492\pi$
$152$		0			0
$153$	8.80483	+	10.9417i	0.711828	+	0.884584i
$154$		0			0
$155$	13.4779	+	16.7729i	1.08257	+	1.34723i
$156$		0			0
$157$	2.22723	−	1.28589i	0.177753	−	0.102626i	−0.408484	−	0.912766i	$-0.633942\pi$
$157$	2.22723	−	1.28589i	0.177753	−	0.102626i	0.586236	+	0.810140i	$0.300609\pi$
$158$		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	$-0.557834\pi$
$163$	−4.61388			−0.361387			−0.180694	+	0.983539i	$0.557834\pi$
$164$		0			0
$165$	8.60480	+	9.16458i	0.669882	+	0.713462i
$166$		0			0
$167$	−4.72157	+	2.72600i	−0.365366	+	0.210944i	−0.671432	−	0.741066i	$-0.734320\pi$
$167$	−4.72157	+	2.72600i	−0.365366	+	0.210944i	0.306066	+	0.952010i	$0.400987\pi$
$168$		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	−0.0485189	−	0.998822i	$-0.515450\pi$
$173$	11.0583	−	19.1535i	0.840746	−	1.45621i	0.889265	−	0.457393i	$-0.151217\pi$
$174$		0			0
$175$	−5.29110	+	24.0003i	−0.399969	+	1.81425i
$176$		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
$185$	5.13051	−	0.792754i	0.377203	−	0.0582844i
$186$		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	−0.991368	−	0.131107i	$-0.958147\pi$
$191$	−5.28131	+	9.14750i	−0.382142	+	0.661890i	0.609226	+	0.792997i	$0.291480\pi$
$192$		0			0
$193$	13.6860	−	7.90162i	0.985140	−	0.568771i	0.0813222	−	0.996688i	$-0.474086\pi$
$193$	13.6860	−	7.90162i	0.985140	−	0.568771i	0.903818	+	0.427917i	$0.140752\pi$
$194$		0			0
$195$	−4.02900	−	17.1837i	−0.288523	−	1.23055i
$196$		0			0
$197$	19.0230			1.35533			0.677666	−	0.735370i	$-0.262992\pi$
$197$	19.0230			1.35533			0.677666	+	0.735370i	$0.262992\pi$
$198$		0			0
$199$		−	1.43855i		−	0.101976i	−0.998699	−	0.0509881i	$-0.983763\pi$
$199$		−	1.43855i		−	0.101976i	0.998699	−	0.0509881i	$-0.0162371\pi$
$200$		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
$205$	−13.3187	−	16.5748i	−0.930220	−	1.15763i
$206$		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	0.135462	−	0.990783i	$-0.456748\pi$
$211$	15.4153	−	8.90005i	1.06124	−	0.612704i	0.925774	+	0.378078i	$0.123415\pi$
$212$		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	$-0.816870\pi$
$223$	0.772004	−	1.33715i	0.0516972	−	0.0895422i	0.890716	+	0.454560i	$0.150204\pi$
$224$		0			0
$225$	−12.4925	−	8.30279i	−0.832837	−	0.553519i
$226$		0			0
$227$	−7.32514	−	4.22917i	−0.486187	−	0.280700i	0.236804	−	0.971557i	$-0.423900\pi$
$227$	−7.32514	−	4.22917i	−0.486187	−	0.280700i	−0.722991	+	0.690857i	$0.757233\pi$
$228$		0			0
$229$	4.13038	+	7.15403i	0.272943	+	0.472752i	0.969614	−	0.244639i	$-0.0786696\pi$
$229$	4.13038	+	7.15403i	0.272943	+	0.472752i	−0.696671	+	0.717391i	$0.745336\pi$
$230$		0			0
$231$	2.12575	+	27.5518i	0.139864	+	1.81278i
$232$		0			0
$233$	−14.6573			−0.960229			−0.480115	−	0.877206i	$-0.659405\pi$
$233$	−14.6573			−0.960229			−0.480115	+	0.877206i	$0.659405\pi$
$234$		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	0.860410	−	0.509602i	$-0.170207\pi$
$239$	−0.171965	−	0.297852i	−0.0111235	−	0.0192664i	−0.871534	+	0.490336i	$0.836874\pi$
$240$		0			0
$241$	4.93539	−	8.54834i	0.317916	−	0.550647i	−0.662137	−	0.749383i	$-0.730350\pi$
$241$	4.93539	−	8.54834i	0.317916	−	0.550647i	0.980053	+	0.198736i	$0.0636836\pi$
$242$		0			0
$243$	9.58447	−	12.2938i	0.614844	−	0.788649i
$244$		0			0
$245$	−29.9114	+	24.0354i	−1.91097	+	1.53556i
$246$		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
$255$	−5.24184	+	17.3570i	−0.328257	+	1.08694i
$256$		0			0
$257$	−7.09105	−	12.2821i	−0.442327	−	0.766133i	0.555534	−	0.831494i	$-0.312514\pi$
$257$	−7.09105	−	12.2821i	−0.442327	−	0.766133i	−0.997862	+	0.0653601i	$0.979180\pi$
$258$		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	$-0.387618\pi$
$263$	−4.76712	−	2.75230i	−0.293953	−	0.169714i	−0.639723	+	0.768605i	$0.720951\pi$
$264$		0			0
$265$	3.38270	+	21.8920i	0.207798	+	1.34482i
$266$		0			0
$267$	0.712480	−	1.48785i	0.0436031	−	0.0910552i
$268$		0			0
$269$		−	23.3589i		−	1.42422i	−0.702069	−	0.712109i	$-0.747740\pi$
$269$		−	23.3589i		−	1.42422i	0.702069	−	0.712109i	$-0.252260\pi$
$270$		0			0
$271$		−	19.4755i		−	1.18305i	−0.806287	−	0.591525i	$-0.798526\pi$
$271$		−	19.4755i		−	1.18305i	0.806287	−	0.591525i	$-0.201474\pi$
$272$		0			0
$273$	16.7566	−	34.9923i	1.01415	−	2.11783i
$274$		0			0
$275$	−3.49398	+	15.8486i	−0.210695	+	0.955708i
$276$		0			0
$277$	21.4830	+	12.4032i	1.29079	+	0.745236i	0.978794	−	0.204848i	$-0.0656699\pi$
$277$	21.4830	+	12.4032i	1.29079	+	0.745236i	0.311994	+	0.950084i	$0.399003\pi$
$278$		0			0
$279$	−26.9187	−	10.4282i	−1.61158	−	0.624323i
$280$		0			0
$281$	22.2519	+	12.8471i	1.32743	+	0.766395i	0.984902	−	0.173112i	$-0.0553821\pi$
$281$	22.2519	+	12.8471i	1.32743	+	0.766395i	0.342532	+	0.939506i	$0.388715\pi$
$282$		0			0
$283$	7.17373	+	12.4253i	0.426434	+	0.738605i	0.996553	−	0.0829568i	$-0.0264363\pi$
$283$	7.17373	+	12.4253i	0.426434	+	0.738605i	−0.570119	+	0.821562i	$0.693103\pi$
$284$		0			0
$285$	8.52680	+	2.57511i	0.505084	+	0.152536i
$286$		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	0.999906	+	0.0137369i	$0.00437272\pi$
$293$	8.76145	+	15.1753i	0.511849	+	0.886549i	−0.488056	+	0.872812i	$0.662294\pi$
$294$		0			0
$295$	−5.16210	+	4.14802i	−0.300549	+	0.241507i
$296$		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	$-0.496227\pi$
$307$	0.415391			0.0237076			0.0118538	+	0.999930i	$0.496227\pi$
$308$		0			0
$309$	−0.915124	−	11.8609i	−0.0520596	−	0.674745i
$310$		0			0
$311$	−10.8799	−	18.8446i	−0.616943	−	1.06858i	−0.990040	−	0.140784i	$-0.955038\pi$
$311$	−10.8799	−	18.8446i	−0.616943	−	1.06858i	0.373097	−	0.927792i	$-0.378296\pi$
$312$		0			0
$313$	−17.8846	−	10.3257i	−1.01090	−	0.583641i	−0.0994419	−	0.995043i	$-0.531706\pi$
$313$	−17.8846	−	10.3257i	−1.01090	−	0.583641i	−0.911454	+	0.411403i	$0.865039\pi$
$314$		0			0
$315$	−9.97414	−	31.4282i	−0.561979	−	1.77078i
$316$		0			0
$317$	5.28802	−	9.15912i	0.297005	−	0.514428i	−0.678444	−	0.734652i	$-0.737346\pi$
$317$	5.28802	−	9.15912i	0.297005	−	0.514428i	0.975449	+	0.220224i	$0.0706789\pi$
$318$		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	0.569643	−	0.821892i	$-0.307082\pi$
$331$	2.59592	+	1.49876i	0.142685	+	0.0823791i	−0.426958	+	0.904271i	$0.640415\pi$
$332$		0			0
$333$	−5.42627	+	4.36654i	−0.297358	+	0.239285i
$334$		0			0
$335$	14.1260	−	11.3510i	0.771787	−	0.620172i
$336$		0			0
$337$	24.9848	−	14.4250i	1.36101	−	0.785780i	0.371252	−	0.928532i	$-0.378928\pi$
$337$	24.9848	−	14.4250i	1.36101	−	0.785780i	0.989758	+	0.142752i	$0.0455951\pi$
$338$		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
$345$	2.47021	+	10.5354i	0.132991	+	0.567207i
$346$		0			0
$347$	−7.84132	+	4.52719i	−0.420944	+	0.243032i	−0.695481	−	0.718544i	$-0.744809\pi$
$347$	−7.84132	+	4.52719i	−0.420944	+	0.243032i	0.274537	+	0.961577i	$0.411475\pi$
$348$		0			0
$349$	−7.32154	+	12.6813i	−0.391913	+	0.678813i	−0.992702	−	0.120595i	$-0.961520\pi$
$349$	−7.32154	+	12.6813i	−0.391913	+	0.678813i	0.600789	+	0.799408i	$0.294853\pi$
$350$		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	$-0.922715\pi$
$353$	−5.20672	+	9.01831i	−0.277126	+	0.479996i	0.693543	+	0.720415i	$0.256049\pi$
$354$		0			0
$355$	−2.95930	−	19.1519i	−0.157063	−	1.01648i
$356$		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
$365$	8.10909	−	1.25299i	0.424449	−	0.0655847i
$366$		0			0
$367$	17.7698	−	30.7782i	0.927577	−	1.60661i	0.140214	−	0.990121i	$-0.455221\pi$
$367$	17.7698	−	30.7782i	0.927577	−	1.60661i	0.787363	−	0.616490i	$-0.211446\pi$
$368$		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	$-0.612491\pi$
$373$	5.66594	−	3.27123i	0.293371	−	0.169378i	0.639461	+	0.768823i	$0.279157\pi$
$374$		0			0
$375$	−0.257897	−	19.3632i	−0.0133177	−	0.999911i
$376$		0			0
$377$	−4.42865			−0.228087
$378$		0			0
$379$			14.2443i			0.731682i	0.930677	+	0.365841i	$0.119219\pi$
$379$			14.2443i			0.731682i	−0.930677	+	0.365841i	$0.880781\pi$
$380$		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	$-0.589766\pi$
$383$	8.10979	−	4.68219i	0.414391	−	0.239249i	0.692675	+	0.721250i	$0.256432\pi$
$384$		0			0
$385$	−27.8092	+	22.3462i	−1.41729	+	1.13887i
$386$		0			0
$387$	−1.51917	+	0.235825i	−0.0772236	+	0.0119877i
$388$		0			0
$389$	−7.64156	−	4.41186i	−0.387442	−	0.223690i	0.293609	−	0.955926i	$-0.405144\pi$
$389$	−7.64156	−	4.41186i	−0.387442	−	0.223690i	−0.681051	+	0.732236i	$0.738477\pi$
$390$		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	−0.802119	−	0.597164i	$-0.796294\pi$
$401$	−13.7375	+	7.93137i	−0.686020	+	0.396074i	0.116099	+	0.993238i	$0.462961\pi$
$402$		0			0
$403$	21.9259	−	37.9768i	1.09221	−	1.89176i
$404$		0			0
$405$	20.0856	+	1.25267i	0.998061	+	0.0622458i
$406$		0			0
$407$	6.52615	+	3.76788i	0.323489	+	0.186767i
$408$		0			0
$409$	−0.0555181	−	0.0961601i	−0.00274519	−	0.00475481i	0.864650	−	0.502376i	$-0.167540\pi$
$409$	−0.0555181	−	0.0961601i	−0.00274519	−	0.00475481i	−0.867395	+	0.497621i	$0.834207\pi$
$410$		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	0.999486	−	0.0320563i	$-0.0102056\pi$
$419$	9.66122	+	16.7337i	0.471981	+	0.817496i	−0.527505	+	0.849552i	$0.676872\pi$
$420$		0			0
$421$	−18.4323	+	31.9258i	−0.898337	+	1.55597i	−0.0687183	+	0.997636i	$0.521891\pi$
$421$	−18.4323	+	31.9258i	−0.898337	+	1.55597i	−0.829619	+	0.558330i	$0.811442\pi$
$422$		0			0
$423$	−3.91635	−	25.2289i	−0.190420	−	1.22667i
$424$		0			0
$425$	−22.3157	+	7.06501i	−1.08247	+	0.342703i
$426$		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
$435$	−2.74389	+	2.57629i	−0.131559	+	0.123523i
$436$		0			0
$437$	−3.21285	−	5.56482i	−0.153691	−	0.266201i
$438$		0			0
$439$	−28.8199	−	16.6392i	−1.37550	−	0.794145i	−0.383886	−	0.923381i	$-0.625414\pi$
$439$	−28.8199	−	16.6392i	−1.37550	−	0.794145i	−0.991614	+	0.129235i	$0.958748\pi$
$440$		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	$-0.229938\pi$
$443$	11.6345	+	6.71718i	0.552772	+	0.319143i	−0.197467	+	0.980309i	$0.563272\pi$
$444$		0			0
$445$	2.10471	−	0.325214i	0.0997727	−	0.0154166i
$446$		0			0
$447$	−40.3724	+	3.11491i	−1.90955	+	0.147330i
$448$		0			0
$449$			30.4331i			1.43622i	0.695927	+	0.718112i	$0.254994\pi$
$449$			30.4331i			1.43622i	−0.695927	+	0.718112i	$0.745006\pi$
$450$		0			0
$451$		−	30.8649i		−	1.45337i
$452$		0			0
$453$	17.4236	+	25.4352i	0.818631	+	1.19505i
$454$		0			0
$455$	49.4999	−	7.64859i	2.32059	−	0.358572i
$456$		0			0
$457$	−6.90969	−	3.98931i	−0.323222	−	0.186612i	0.329606	−	0.944119i	$-0.393084\pi$
$457$	−6.90969	−	3.98931i	−0.323222	−	0.186612i	−0.652828	+	0.757507i	$0.726417\pi$
$458$		0			0
$459$	−5.56952	−	23.6795i	−0.259963	−	1.10526i
$460$		0			0
$461$	−22.8613	−	13.1990i	−1.06476	−	0.614738i	−0.138014	−	0.990430i	$-0.544072\pi$
$461$	−22.8613	−	13.1990i	−1.06476	−	0.614738i	−0.926745	+	0.375692i	$0.877405\pi$
$462$		0			0
$463$	−0.473161	−	0.819539i	−0.0219896	−	0.0380872i	0.854821	−	0.518923i	$-0.173667\pi$
$463$	−0.473161	−	0.819539i	−0.0219896	−	0.0380872i	−0.876811	+	0.480836i	$0.840333\pi$
$464$		0			0
$465$	−8.50753	−	36.2845i	−0.394527	−	1.68265i
$466$		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
$475$	3.47075	+	10.9628i	0.159249	+	0.503008i
$476$		0			0
$477$	−18.6322	−	23.1540i	−0.853108	−	1.06015i
$478$		0			0
$479$	3.07387	−	5.32411i	0.140449	−	0.243265i	−0.787217	−	0.616676i	$-0.788479\pi$
$479$	3.07387	−	5.32411i	0.140449	−	0.243265i	0.927666	+	0.373412i	$0.121812\pi$
$480$		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	$-0.352107\pi$
$487$	19.7766			0.896164			0.448082	+	0.893992i	$0.352107\pi$
$488$		0			0
$489$	7.20769	+	3.45151i	0.325943	+	0.156083i
$490$		0			0
$491$	−3.30861	−	5.73068i	−0.149316	−	0.258622i	0.781659	−	0.623706i	$-0.214374\pi$
$491$	−3.30861	−	5.73068i	−0.149316	−	0.258622i	−0.930975	+	0.365084i	$0.881040\pi$
$492$		0			0
$493$	3.93998	+	2.27475i	0.177448	+	0.102449i
$494$		0			0
$495$	−6.58644	−	20.7537i	−0.296039	−	0.932808i
$496$		0			0
$497$	21.2996	−	36.8920i	0.955418	−	1.65483i
$498$		0			0
$499$	−14.7185	+	8.49775i	−0.658892	+	0.380412i	−0.791855	−	0.610710i	$-0.790884\pi$
$499$	−14.7185	+	8.49775i	−0.658892	+	0.380412i	0.132963	+	0.991121i	$0.457551\pi$
$500$		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	−0.658317	−	0.752741i	$-0.728731\pi$
$509$	−7.57111	+	4.37118i	−0.335584	+	0.193749i	0.322734	+	0.946490i	$0.395398\pi$
$510$		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
$515$	11.9717	−	9.61993i	0.527538	−	0.423905i
$516$		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	$-0.726388\pi$
$521$		−	34.5835i		−	1.51513i	0.652758	−	0.757566i	$-0.273612\pi$
$522$		0			0
$523$	10.1425			0.443501			0.221751	−	0.975103i	$-0.428823\pi$
$523$	10.1425			0.443501			0.221751	+	0.975103i	$0.428823\pi$
$524$		0			0
$525$	26.2195	−	33.5345i	1.14431	−	1.46357i
$526$		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
$535$	18.4673	−	2.85352i	0.798411	−	0.123368i
$536$		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
$545$	2.87039	+	18.5765i	0.122954	+	0.795729i
$546$		0			0
$547$	6.66047	−	11.5363i	0.284781	−	0.493256i	−0.687775	−	0.725924i	$-0.741412\pi$
$547$	6.66047	−	11.5363i	0.284781	−	0.493256i	0.972556	+	0.232668i	$0.0747457\pi$
$548$		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
$555$	−8.60780	−	2.59957i	−0.365381	−	0.110345i
$556$		0			0
$557$	11.2286			0.475771			0.237885	−	0.971293i	$-0.423546\pi$
$557$	11.2286			0.475771			0.237885	+	0.971293i	$0.423546\pi$
$558$		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	$-0.444870\pi$
$563$	26.3748	−	15.2275i	1.11157	−	0.641764i	0.939235	+	0.343275i	$0.111536\pi$
$564$		0			0
$565$	26.8714	−	21.5926i	1.13049	−	0.908407i
$566$		0			0
$567$	32.6924	+	29.8026i	1.37295	+	1.25159i
$568$		0			0
$569$	−21.2927	−	12.2934i	−0.892638	−	0.515365i	−0.0178334	−	0.999841i	$-0.505677\pi$
$569$	−21.2927	−	12.2934i	−0.892638	−	0.515365i	−0.874804	+	0.484476i	$0.839010\pi$
$570$		0			0
$571$	9.86354	−	5.69472i	0.412776	−	0.238317i	−0.279206	−	0.960231i	$-0.590071\pi$
$571$	9.86354	−	5.69472i	0.412776	−	0.238317i	0.691982	+	0.721915i	$0.256738\pi$
$572$		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
$585$	−6.56058	+	29.8579i	−0.271247	+	1.23447i
$586$		0			0
$587$	−28.6601	−	16.5469i	−1.18293	−	0.682965i	−0.226240	−	0.974072i	$-0.572643\pi$
$587$	−28.6601	−	16.5469i	−1.18293	−	0.682965i	−0.956691	+	0.291106i	$0.905977\pi$
$588$		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	$-0.362147\pi$
$593$	20.4391			0.839334			0.419667	+	0.907678i	$0.362147\pi$
$594$		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	0.835497	+	0.549496i	$0.185180\pi$
$599$	21.8710	+	37.8817i	0.893625	+	1.54780i	0.0581288	+	0.998309i	$0.481487\pi$
$600$		0			0
$601$	−11.1919	+	19.3850i	−0.456529	+	0.790732i	−0.998775	−	0.0494884i	$-0.984241\pi$
$601$	−11.1919	+	19.3850i	−0.456529	+	0.790732i	0.542246	+	0.840220i	$0.317574\pi$
$602$		0			0
$603$	−8.78262	+	22.6708i	−0.357656	+	0.923228i
$604$		0			0
$605$	0.809696	−	0.650633i	0.0329188	−	0.0264520i
$606$		0			0
$607$	12.1622	+	21.0656i	0.493649	+	0.855025i	0.999973	−	0.00731837i	$-0.00232953\pi$
$607$	12.1622	+	21.0656i	0.493649	+	0.855025i	−0.506325	+	0.862343i	$0.668996\pi$
$608$		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
$615$	8.40707	+	35.8561i	0.339006	+	1.44586i
$616$		0			0
$617$	3.17947	+	5.50700i	0.128001	+	0.221703i	0.922902	−	0.385035i	$-0.125811\pi$
$617$	3.17947	+	5.50700i	0.128001	+	0.221703i	−0.794901	+	0.606739i	$0.792477\pi$
$618$		0			0
$619$	27.7015	+	15.9935i	1.11342	+	0.642832i	0.939712	−	0.341966i	$-0.111093\pi$
$619$	27.7015	+	15.9935i	1.11342	+	0.642832i	0.173705	+	0.984798i	$0.444426\pi$
$620$		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
$625$	20.4450	−	14.3876i	0.817799	−	0.575504i
$626$		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	$0.136253\pi$
$631$			20.8543i			0.830196i	−0.909777	+	0.415098i	$0.863747\pi$
$632$		0			0
$633$	−30.7393	+	2.37168i	−1.22178	+	0.0942656i
$634$		0			0
$635$	1.21918	+	7.89024i	0.0483816	+	0.313115i
$636$		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	−0.125886	−	0.992045i	$-0.540177\pi$
$641$	−26.5324	−	15.3185i	−1.04797	−	0.605043i	−0.922079	+	0.387002i	$0.873511\pi$
$642$		0			0
$643$	19.0142	+	32.9335i	0.749846	+	1.29877i	0.947896	+	0.318580i	$0.103206\pi$
$643$	19.0142	+	32.9335i	0.749846	+	1.29877i	−0.198050	+	0.980192i	$0.563461\pi$
$644$		0			0
$645$	−1.35853	−	1.44691i	−0.0534920	−	0.0569719i
$646$		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	$-0.0220658\pi$
$653$	11.2134	+	19.4221i	0.438813	+	0.760046i	−0.558785	+	0.829312i	$0.688732\pi$
$654$		0			0
$655$	−9.17269	+	7.37075i	−0.358407	+	0.287999i
$656$		0			0
$657$	−8.57655	+	6.90158i	−0.334603	+	0.269256i
$658$		0			0
$659$	−4.01881	+	6.96078i	−0.156551	+	0.271154i	−0.933623	−	0.358258i	$-0.883371\pi$
$659$	−4.01881	+	6.96078i	−0.156551	+	0.271154i	0.777072	+	0.629412i	$0.216704\pi$
$660$		0			0
$661$	10.1926	+	17.6542i	0.396448	+	0.686668i	0.993285	−	0.115695i	$-0.0369095\pi$
$661$	10.1926	+	17.6542i	0.396448	+	0.686668i	−0.596837	+	0.802362i	$0.703576\pi$
$662$		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	$-0.509687\pi$
$673$	−23.6402	−	13.6487i	−0.911264	−	0.526119i	−0.880838	+	0.473418i	$0.843020\pi$
$674$		0			0
$675$	13.3045	+	22.3157i	0.512090	+	0.858932i
$676$		0			0
$677$	18.7854	−	32.5373i	0.721981	−	1.25051i	−0.238223	−	0.971210i	$-0.576565\pi$
$677$	18.7854	−	32.5373i	0.721981	−	1.25051i	0.960205	−	0.279298i	$-0.0901017\pi$
$678$		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	0.863901	−	0.503662i	$-0.168014\pi$
$691$	22.5980	+	13.0469i	0.859668	+	0.496329i	−0.00423336	+	0.999991i	$0.501348\pi$
$692$		0			0
$693$	17.2899	−	44.6310i	0.656790	−	1.69539i
$694$		0			0
$695$	−25.6563	−	31.9286i	−0.973199	−	1.21112i
$696$		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	$-0.899929\pi$
$701$		−	16.3745i		−	0.618458i	0.950988	−	0.309229i	$-0.100071\pi$
$702$		0			0
$703$	5.33941			0.201380
$704$		0			0
$705$	24.0288	−	22.5611i	0.904978	−	0.849701i
$706$		0			0
$707$	27.4901	−	15.8714i	1.03387	−	0.596907i
$708$		0			0
$709$	9.64926	−	16.7130i	0.362385	−	0.627670i	−0.625968	−	0.779849i	$-0.715296\pi$
$709$	9.64926	−	16.7130i	0.362385	−	0.627670i	0.988353	+	0.152179i	$0.0486291\pi$
$710$		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
$715$	32.6873	−	5.05076i	1.22244	−	0.188888i
$716$		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
$725$	−4.74510	−	1.04610i	−0.176228	−	0.0388513i
$726$		0			0
$727$	−9.16075	+	15.8669i	−0.339753	+	0.588470i	−0.984386	−	0.176022i	$-0.943677\pi$
$727$	−9.16075	+	15.8669i	−0.339753	+	0.588470i	0.644633	+	0.764492i	$0.277010\pi$
$728$		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	$-0.693951\pi$
$733$	−4.01463	+	2.31785i	−0.148284	+	0.0856117i	0.424022	+	0.905652i	$0.360618\pi$
$734$		0			0
$735$	64.7070	−	15.1717i	2.38675	−	0.559615i
$736$		0			0
$737$	26.3049			0.968954
$738$		0			0
$739$		−	11.4405i		−	0.420844i	−0.977611	−	0.210422i	$-0.932516\pi$
$739$		−	11.4405i		−	0.420844i	0.977611	−	0.210422i	$-0.0674839\pi$
$740$		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	$-0.833407\pi$
$743$	−23.6156	+	13.6345i	−0.866373	+	0.500201i	−0.000231838		1.00000i	$0.500074\pi$
$744$		0			0
$745$	−32.7444	−	40.7495i	−1.19966	−	1.49295i
$746$		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	−0.880286	−	0.474443i	$-0.842649\pi$
$751$	−24.9256	+	14.3908i	−0.909549	+	0.525128i	−0.0292631	+	0.999572i	$0.509316\pi$
$752$		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	−0.291513	−	0.956567i	$-0.594159\pi$
$761$	10.7901	−	6.22969i	0.391142	−	0.225826i	0.682655	+	0.730741i	$0.260825\pi$
$762$		0			0
$763$	−20.6597	+	35.7836i	−0.747931	+	1.29545i
$764$		0			0
$765$	21.1729	−	23.1934i	0.765509	−	0.838560i
$766$		0			0
$767$	11.6879	+	6.74804i	0.422027	+	0.243658i
$768$		0			0
$769$	20.7262	+	35.8988i	0.747405	+	1.29454i	0.949062	+	0.315088i	$0.102034\pi$
$769$	20.7262	+	35.8988i	0.747405	+	1.29454i	−0.201657	+	0.979456i	$0.564633\pi$
$770$		0			0
$771$	1.88961	+	24.4913i	0.0680528	+	0.882033i
$772$		0			0
$773$	12.8158			0.460954			0.230477	−	0.973078i	$-0.425971\pi$
$773$	12.8158			0.460954			0.230477	+	0.973078i	$0.425971\pi$
$774$		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
$785$	−3.60214	−	4.48276i	−0.128566	−	0.159997i
$786$		0			0
$787$	−1.29742	−	2.24720i	−0.0462481	−	0.0801041i	0.841975	−	0.539517i	$-0.181393\pi$
$787$	−1.29742	−	2.24720i	−0.0462481	−	0.0801041i	−0.888223	+	0.459413i	$0.848060\pi$
$788$		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
$795$	11.0924	−	36.7297i	0.393407	−	1.30267i
$796$		0			0
$797$	1.96403	+	3.40180i	0.0695695	+	0.120498i	0.898712	−	0.438540i	$-0.144504\pi$
$797$	1.96403	+	3.40180i	0.0695695	+	0.120498i	−0.829142	+	0.559038i	$0.811171\pi$
$798$		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
$805$	−30.3487	+	4.68940i	−1.06965	+	0.165280i
$806$		0			0
$807$	−17.4741	+	36.4907i	−0.615118	+	1.28453i
$808$		0			0
$809$			23.6490i			0.831454i	0.909489	+	0.415727i	$0.136473\pi$
$809$			23.6490i			0.831454i	−0.909489	+	0.415727i	$0.863527\pi$
$810$		0			0
$811$			30.1396i			1.05834i	0.848515	+	0.529172i	$0.177497\pi$
$811$			30.1396i			1.05834i	−0.848515	+	0.529172i	$0.822503\pi$
$812$		0			0
$813$	−14.5690	+	30.4241i	−0.510958	+	1.06702i
$814$		0			0
$815$	1.57545	+	10.1960i	0.0551857	+	0.357149i
$816$		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	0.907680	−	0.419663i	$-0.137852\pi$
$821$	28.5981	+	16.5111i	0.998081	+	0.576242i	0.0904010	+	0.995905i	$0.471185\pi$
$822$		0			0
$823$	−27.3286	−	47.3345i	−0.952615	−	1.64998i	−0.739734	−	0.672900i	$-0.765049\pi$
$823$	−27.3286	−	47.3345i	−0.952615	−	1.64998i	−0.212881	−	0.977078i	$-0.568285\pi$
$824$		0			0
$825$	17.3141	−	22.1446i	0.602800	−	0.770975i
$826$		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
$835$	7.63625	+	9.50310i	0.264263	+	0.328868i
$836$		0			0
$837$	34.2507	+	36.4279i	1.18388	+	1.25913i
$838$		0			0
$839$	−12.1201	+	20.9926i	−0.418432	+	0.724745i	−0.995782	−	0.0917514i	$-0.970753\pi$
$839$	−12.1201	+	20.9926i	−0.418432	+	0.724745i	0.577350	+	0.816497i	$0.304087\pi$
$840$		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	$-0.244609\pi$
$853$	13.9184	+	8.03581i	0.476558	+	0.275141i	−0.242423	+	0.970171i	$0.577942\pi$
$854$		0			0
$855$	−11.3940	−	10.4014i	−0.389666	−	0.355721i
$856$		0			0
$857$	−1.14515	+	1.98346i	−0.0391177	+	0.0677538i	−0.884921	−	0.465740i	$-0.845788\pi$
$857$	−1.14515	+	1.98346i	−0.0391177	+	0.0677538i	0.845804	+	0.533494i	$0.179121\pi$
$858$		0			0
$859$	−25.7347	+	14.8579i	−0.878056	+	0.506946i	−0.870017	−	0.493022i	$-0.835892\pi$
$859$	−25.7347	+	14.8579i	−0.878056	+	0.506946i	−0.00803922	+	0.999968i	$0.502559\pi$
$860$		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
$875$	54.8435	+	3.49737i	1.85405	+	0.118233i
$876$		0			0
$877$	−4.08267	+	2.35713i	−0.137862	+	0.0795947i	−0.567345	−	0.823480i	$-0.692029\pi$
$877$	−4.08267	+	2.35713i	−0.137862	+	0.0795947i	0.429483	+	0.903075i	$0.358696\pi$
$878$		0			0
$879$	−2.33474	−	30.2606i	−0.0787489	−	1.02067i
$880$		0			0
$881$		−	41.1882i		−	1.38766i	−0.720136	−	0.693832i	$-0.755921\pi$
$881$		−	41.1882i		−	1.38766i	0.720136	−	0.693832i	$-0.244079\pi$
$882$		0			0
$883$	26.9479			0.906870			0.453435	−	0.891289i	$-0.350198\pi$
$883$	26.9479			0.906870			0.453435	+	0.891289i	$0.350198\pi$
$884$		0			0
$885$	11.1671	−	2.61832i	0.375379	−	0.0880139i
$886$		0			0
$887$	0.0614320	−	0.0354678i	0.00206269	−	0.00119089i	−0.498968	−	0.866620i	$-0.666288\pi$
$887$	0.0614320	−	0.0354678i	0.00206269	−	0.00119089i	0.501031	+	0.865429i	$0.332954\pi$
$888$		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
$895$	−3.08073	−	19.9378i	−0.102977	−	0.666446i
$896$		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
$905$	4.65801	+	30.1455i	0.154837	+	1.00207i
$906$		0			0
$907$	18.5017	−	32.0459i	0.614340	−	1.06407i	−0.376160	−	0.926555i	$-0.622756\pi$
$907$	18.5017	−	32.0459i	0.614340	−	1.06407i	0.990500	−	0.137513i	$-0.0439110\pi$
$908$		0			0
$909$	2.97187	+	19.1446i	0.0985706	+	0.634985i
$910$		0			0
$911$	16.7405	−	28.9954i	0.554637	−	0.960660i	−0.443294	−	0.896376i	$-0.646190\pi$
$911$	16.7405	−	28.9954i	0.554637	−	0.960660i	0.997932	−	0.0642840i	$-0.0204763\pi$
$912$		0			0
$913$	−7.85388	+	4.53444i	−0.259926	+	0.150068i
$914$		0			0
$915$	8.89894	+	9.47787i	0.294190	+	0.313329i
$916$		0			0
$917$	−25.8665			−0.854189
$918$		0			0
$919$			37.0547i			1.22232i	0.791506	+	0.611161i	$0.209297\pi$
$919$			37.0547i			1.22232i	−0.791506	+	0.611161i	$0.790703\pi$
$920$		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
$925$	−3.50372	−	11.0669i	−0.115202	−	0.363879i
$926$		0			0
$927$	−7.44323	+	19.2134i	−0.244468	+	0.631052i
$928$		0			0
$929$	3.32859	+	1.92176i	0.109208	+	0.0630510i	0.553609	−	0.832777i	$-0.313250\pi$
$929$	3.32859	+	1.92176i	0.109208	+	0.0630510i	−0.444401	+	0.895828i	$0.646584\pi$
$930$		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	−0.805448	−	0.592667i	$-0.798075\pi$
$941$	−21.3168	+	12.3072i	−0.694907	+	0.401205i	0.110541	+	0.993872i	$0.464742\pi$
$942$		0			0
$943$	13.2842	−	23.0089i	0.432592	−	0.749272i
$944$		0			0
$945$	−7.92916	+	56.5577i	−0.257936	+	1.83982i
$946$		0			0
$947$	−22.4985	−	12.9895i	−0.731104	−	0.422103i	0.0877216	−	0.996145i	$-0.472041\pi$
$947$	−22.4985	−	12.9895i	−0.731104	−	0.422103i	−0.818826	+	0.574042i	$0.805375\pi$
$948$		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	$-0.283954\pi$
$953$	38.7615			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$954$		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
$965$	−22.1346	−	27.5458i	−0.712536	−	0.886732i
$966$		0			0
$967$	−19.5551	−	33.8704i	−0.628849	−	1.08920i	−0.987783	−	0.155835i	$-0.950193\pi$
$967$	−19.5551	−	33.8704i	−0.628849	−	1.08920i	0.358934	−	0.933363i	$-0.383140\pi$
$968$		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
$975$	−36.5975	+	14.7710i	−1.17206	+	0.473050i
$976$		0			0
$977$	−19.9499	−	34.5542i	−0.638253	−	1.10549i	−0.985816	−	0.167830i	$-0.946324\pi$
$977$	−19.9499	−	34.5542i	−0.638253	−	1.10549i	0.347563	−	0.937657i	$-0.387009\pi$
$978$		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	$-0.0400162\pi$
$983$	43.2536	+	24.9725i	1.37958	+	0.796499i	0.387469	+	0.921883i	$0.373350\pi$
$984$		0			0
$985$	−6.49557	−	42.0378i	−0.206966	−	1.33944i
$986$		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	$0.202181\pi$
$991$			37.3553i			1.18663i	−0.804971	+	0.593315i	$0.797819\pi$
$992$		0			0
$993$	−2.93411	−	4.28325i	−0.0931111	−	0.135925i
$994$		0			0
$995$	−3.17897	+	0.491207i	−0.100780	+	0.0155723i
$996$		0			0
$997$	−44.6518	−	25.7797i	−1.41414	−	0.816452i	−0.418361	−	0.908281i	$-0.637395\pi$
$997$	−44.6518	−	25.7797i	−1.41414	−	0.816452i	−0.995775	+	0.0918294i	$0.970729\pi$
$998$		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.479.2	yes	24
3.2	odd	2		2160.2.br.d.1439.7		24
4.3	odd	2		720.2.br.d.479.11	yes	24
5.4	even	2	inner	720.2.br.c.479.11	yes	24
9.4	even	3		2160.2.br.c.719.3		24
9.5	odd	6		720.2.br.d.239.2	yes	24
12.11	even	2		2160.2.br.c.1439.7		24
15.14	odd	2		2160.2.br.d.1439.3		24
20.19	odd	2		720.2.br.d.479.2	yes	24
36.23	even	6	inner	720.2.br.c.239.11	yes	24
36.31	odd	6		2160.2.br.d.719.3		24
45.4	even	6		2160.2.br.c.719.7		24
45.14	odd	6		720.2.br.d.239.11	yes	24
60.59	even	2		2160.2.br.c.1439.3		24
180.59	even	6	inner	720.2.br.c.239.2	✓	24
180.139	odd	6		2160.2.br.d.719.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.br.c.239.2	✓	24	180.59	even	6	inner
720.2.br.c.239.11	yes	24	36.23	even	6	inner
720.2.br.c.479.2	yes	24	1.1	even	1	trivial
720.2.br.c.479.11	yes	24	5.4	even	2	inner
720.2.br.d.239.2	yes	24	9.5	odd	6
720.2.br.d.239.11	yes	24	45.14	odd	6
720.2.br.d.479.2	yes	24	20.19	odd	2
720.2.br.d.479.11	yes	24	4.3	odd	2
2160.2.br.c.719.3		24	9.4	even	3
2160.2.br.c.719.7		24	45.4	even	6
2160.2.br.c.1439.3		24	60.59	even	2
2160.2.br.c.1439.7		24	12.11	even	2
2160.2.br.d.719.3		24	36.31	odd	6
2160.2.br.d.719.7		24	180.139	odd	6
2160.2.br.d.1439.3		24	15.14	odd	2
2160.2.br.d.1439.7		24	3.2	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56217 - 0.748070i) q^{3} +(-0.341459 - 2.20984i) q^{5} +(2.45766 - 4.25679i) q^{7} +(1.88078 + 2.33723i) q^{9} +O(q^{10})\)	\(q+(-1.56217 - 0.748070i) q^{3} +(-0.341459 - 2.20984i) q^{5} +(2.45766 - 4.25679i) q^{7} +(1.88078 + 2.33723i) q^{9} +(1.62292 - 2.81098i) q^{11} +(-3.94659 + 2.27856i) q^{13} +(-1.11970 + 3.70760i) q^{15} +4.68147 q^{17} -2.29982i q^{19} +(-7.02367 + 4.81135i) q^{21} +(2.41968 - 1.39700i) q^{23} +(-4.76681 + 1.50914i) q^{25} +(-1.18969 - 5.05812i) q^{27} +(0.841610 + 0.485904i) q^{29} +(-8.33350 + 4.81135i) q^{31} +(-4.63809 + 3.17718i) q^{33} +(-10.2460 - 3.97752i) q^{35} +2.32167i q^{37} +(7.86979 - 0.607189i) q^{39} +(8.23509 - 4.75453i) q^{41} +(-0.256227 + 0.443798i) q^{43} +(4.52271 - 4.95430i) q^{45} +(-7.37017 - 4.25517i) q^{47} +(-8.58018 - 14.8613i) q^{49} +(-7.31328 - 3.50207i) q^{51} -9.90660 q^{53} +(-6.76598 - 2.62656i) q^{55} +(-1.72043 + 3.59272i) q^{57} +(-1.48077 - 2.56476i) q^{59} +(1.67840 - 2.90707i) q^{61} +(14.5714 - 2.26197i) q^{63} +(6.38287 + 7.94330i) q^{65} +(4.05210 + 7.01844i) q^{67} +(-4.82501 + 0.372271i) q^{69} +8.66662 q^{71} +3.66953i q^{73} +(8.57554 + 1.20837i) q^{75} +(-7.97717 - 13.8169i) q^{77} +(0.00584899 + 0.00337691i) q^{79} +(-1.92532 + 8.79165i) q^{81} +(-2.41968 - 1.39700i) q^{83} +(-1.59853 - 10.3453i) q^{85} +(-0.951252 - 1.38865i) q^{87} +0.952424i q^{89} +22.3997i q^{91} +(16.6176 - 1.28212i) q^{93} +(-5.08224 + 0.785294i) q^{95} +(3.07057 + 1.77279i) q^{97} +(9.62227 - 1.49369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 2 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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