LMFDB - Embedded newform 720.2.bl.b.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(251,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("720.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bl (of order $4$, 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 $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.7
Character	$\chi$	$=$	720.251
Dual form			720.2.bl.b.611.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.219596 - 1.39706i) q^{2} +(-1.90356 - 0.613577i) q^{4} +(-0.707107 + 0.707107i) q^{5} -0.750417 q^{7} +(-1.27522 + 2.52464i) q^{8} +O(q^{10})$	\(q+(0.219596 - 1.39706i) q^{2} +(-1.90356 - 0.613577i) q^{4} +(-0.707107 + 0.707107i) q^{5} -0.750417 q^{7} +(-1.27522 + 2.52464i) q^{8} +(0.832593 + 1.14315i) q^{10} +(2.08285 + 2.08285i) q^{11} +(-1.66519 + 1.66519i) q^{13} +(-0.164788 + 1.04838i) q^{14} +(3.24705 + 2.33596i) q^{16} +1.81077i q^{17} +(-1.22715 - 1.22715i) q^{19} +(1.77988 - 0.912152i) q^{20} +(3.36725 - 2.45248i) q^{22} +9.36690i q^{23} -1.00000i q^{25} +(1.96070 + 2.69203i) q^{26} +(1.42846 + 0.460439i) q^{28} +(4.84824 + 4.84824i) q^{29} -4.95295i q^{31} +(3.97651 - 4.02335i) q^{32} +(2.52975 + 0.397637i) q^{34} +(0.530625 - 0.530625i) q^{35} +(5.94167 + 5.94167i) q^{37} +(-1.98389 + 1.44493i) q^{38} +(-0.883477 - 2.68691i) q^{40} -2.47546 q^{41} +(5.20107 - 5.20107i) q^{43} +(-2.68683 - 5.24281i) q^{44} +(13.0861 + 2.05693i) q^{46} +4.43781 q^{47} -6.43687 q^{49} +(-1.39706 - 0.219596i) q^{50} +(4.19149 - 2.14805i) q^{52} +(-7.54780 + 7.54780i) q^{53} -2.94559 q^{55} +(0.956944 - 1.89453i) q^{56} +(7.83793 - 5.70863i) q^{58} +(0.472792 + 0.472792i) q^{59} +(-4.99164 + 4.99164i) q^{61} +(-6.91958 - 1.08765i) q^{62} +(-4.74764 - 6.43894i) q^{64} -2.35493i q^{65} +(1.95148 + 1.95148i) q^{67} +(1.11105 - 3.44690i) q^{68} +(-0.624792 - 0.857838i) q^{70} +0.418759i q^{71} +3.49594i q^{73} +(9.60564 - 6.99611i) q^{74} +(1.58300 + 3.08891i) q^{76} +(-1.56300 - 1.56300i) q^{77} -3.40726i q^{79} +(-3.94778 + 0.644237i) q^{80} +(-0.543601 + 3.45837i) q^{82} +(-0.548807 + 0.548807i) q^{83} +(-1.28041 - 1.28041i) q^{85} +(-6.12407 - 8.40834i) q^{86} +(-7.91453 + 2.60236i) q^{88} -12.2354 q^{89} +(1.24958 - 1.24958i) q^{91} +(5.74732 - 17.8304i) q^{92} +(0.974525 - 6.19989i) q^{94} +1.73546 q^{95} +6.64896 q^{97} +(-1.41351 + 8.99270i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4} - 8 q^{7}+O(q^{10}) $ 24 * q - 8 * q^4 - 8 * q^7	$ 24 q - 8 q^{4} - 8 q^{7} - 4 q^{16} - 24 q^{19} + 12 q^{22} - 20 q^{28} - 12 q^{34} + 8 q^{37} - 20 q^{40} + 48 q^{43} + 12 q^{46} + 24 q^{49} + 4 q^{52} + 24 q^{55} + 48 q^{58} + 40 q^{61} + 16 q^{64} - 40 q^{67} - 20 q^{70} - 84 q^{76} - 12 q^{82} + 24 q^{85} - 132 q^{88} + 40 q^{91} + 60 q^{94} - 16 q^{97}+O(q^{100}) $ 24 * q - 8 * q^4 - 8 * q^7 - 4 * q^16 - 24 * q^19 + 12 * q^22 - 20 * q^28 - 12 * q^34 + 8 * q^37 - 20 * q^40 + 48 * q^43 + 12 * q^46 + 24 * q^49 + 4 * q^52 + 24 * q^55 + 48 * q^58 + 40 * q^61 + 16 * q^64 - 40 * q^67 - 20 * q^70 - 84 * q^76 - 12 * q^82 + 24 * q^85 - 132 * q^88 + 40 * q^91 + 60 * q^94 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.219596	−	1.39706i	0.155278	−	0.987871i
$2$	0.219596	−	1.39706i	0.155278	−	0.987871i
$3$		0			0
$3$		0			0
$4$	−1.90356	−	0.613577i	−0.951778	−	0.306789i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	−0.750417			−0.283631			−0.141815	−	0.989893i	$-0.545294\pi$
$7$	−0.750417			−0.283631			−0.141815	+	0.989893i	$0.545294\pi$
$8$	−1.27522	+	2.52464i	−0.450857	+	0.892596i
$9$		0			0
$10$	0.832593	+	1.14315i	0.263289	+	0.361495i
$11$	2.08285	+	2.08285i	0.628002	+	0.628002i	0.947565	−	0.319563i	$-0.103536\pi$
$11$	2.08285	+	2.08285i	0.628002	+	0.628002i	−0.319563	+	0.947565i	$0.603536\pi$
$12$		0			0
$13$	−1.66519	+	1.66519i	−0.461840	+	0.461840i	−0.899258	−	0.437418i	$-0.855893\pi$
$13$	−1.66519	+	1.66519i	−0.461840	+	0.461840i	0.437418	+	0.899258i	$0.355893\pi$
$14$	−0.164788	+	1.04838i	−0.0440415	+	0.280191i
$15$		0			0
$16$	3.24705	+	2.33596i	0.811761	+	0.583989i
$17$			1.81077i			0.439176i	0.975593	+	0.219588i	$0.0704712\pi$
$17$			1.81077i			0.439176i	−0.975593	+	0.219588i	$0.929529\pi$
$18$		0			0
$19$	−1.22715	−	1.22715i	−0.281529	−	0.281529i	0.552190	−	0.833718i	$-0.313792\pi$
$19$	−1.22715	−	1.22715i	−0.281529	−	0.281529i	−0.833718	+	0.552190i	$0.813792\pi$
$20$	1.77988	−	0.912152i	0.397994	−	0.203963i
$21$		0			0
$22$	3.36725	−	2.45248i	0.717900	−	0.522870i
$23$			9.36690i			1.95313i	0.215215	+	0.976567i	$0.430955\pi$
$23$			9.36690i			1.95313i	−0.215215	+	0.976567i	$0.569045\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	1.96070	+	2.69203i	0.384524	+	0.527951i
$27$		0			0
$28$	1.42846	+	0.460439i	0.269953	+	0.0870147i
$29$	4.84824	+	4.84824i	0.900295	+	0.900295i	0.995461	−	0.0951663i	$-0.0303383\pi$
$29$	4.84824	+	4.84824i	0.900295	+	0.900295i	−0.0951663	+	0.995461i	$0.530338\pi$
$30$		0			0
$31$		−	4.95295i		−	0.889577i	−0.895636	−	0.444788i	$-0.853279\pi$
$31$		−	4.95295i		−	0.889577i	0.895636	−	0.444788i	$-0.146721\pi$
$32$	3.97651	−	4.02335i	0.702954	−	0.711235i
$33$		0			0
$34$	2.52975	+	0.397637i	0.433849	+	0.0681942i
$35$	0.530625	−	0.530625i	0.0896919	−	0.0896919i
$36$		0			0
$37$	5.94167	+	5.94167i	0.976805	+	0.976805i	0.999737	−	0.0229319i	$-0.00730010\pi$
$37$	5.94167	+	5.94167i	0.976805	+	0.976805i	−0.0229319	+	0.999737i	$0.507300\pi$
$38$	−1.98389	+	1.44493i	−0.321829	+	0.234399i
$39$		0			0
$40$	−0.883477	−	2.68691i	−0.139690	−	0.424837i
$41$	−2.47546			−0.386602			−0.193301	−	0.981139i	$-0.561919\pi$
$41$	−2.47546			−0.386602			−0.193301	+	0.981139i	$0.561919\pi$
$42$		0			0
$43$	5.20107	−	5.20107i	0.793155	−	0.793155i	−0.188851	−	0.982006i	$-0.560476\pi$
$43$	5.20107	−	5.20107i	0.793155	−	0.793155i	0.982006	+	0.188851i	$0.0604762\pi$
$44$	−2.68683	−	5.24281i	−0.405055	−	0.790383i
$45$		0			0
$46$	13.0861	+	2.05693i	1.92944	+	0.303278i
$47$	4.43781			0.647321			0.323661	−	0.946173i	$-0.395086\pi$
$47$	4.43781			0.647321			0.323661	+	0.946173i	$0.395086\pi$
$48$		0			0
$49$	−6.43687			−0.919554
$50$	−1.39706	−	0.219596i	−0.197574	−	0.0310555i
$51$		0			0
$52$	4.19149	−	2.14805i	0.581256	−	0.297881i
$53$	−7.54780	+	7.54780i	−1.03677	+	1.03677i	−0.0374723	+	0.999298i	$0.511931\pi$
$53$	−7.54780	+	7.54780i	−1.03677	+	1.03677i	−0.999298	+	0.0374723i	$0.988069\pi$
$54$		0			0
$55$	−2.94559			−0.397184
$56$	0.956944	−	1.89453i	0.127877	−	0.253168i
$57$		0			0
$58$	7.83793	−	5.70863i	1.02917	−	0.749580i
$59$	0.472792	+	0.472792i	0.0615523	+	0.0615523i	0.737213	−	0.675661i	$-0.236141\pi$
$59$	0.472792	+	0.472792i	0.0615523	+	0.0615523i	−0.675661	+	0.737213i	$0.736141\pi$
$60$		0			0
$61$	−4.99164	+	4.99164i	−0.639114	+	0.639114i	−0.950337	−	0.311223i	$-0.899261\pi$
$61$	−4.99164	+	4.99164i	−0.639114	+	0.639114i	0.311223	+	0.950337i	$0.399261\pi$
$62$	−6.91958	−	1.08765i	−0.878787	−	0.138131i
$63$		0			0
$64$	−4.74764	−	6.43894i	−0.593455	−	0.804867i
$65$		−	2.35493i		−	0.292093i
$66$		0			0
$67$	1.95148	+	1.95148i	0.238412	+	0.238412i	0.816192	−	0.577781i	$-0.196081\pi$
$67$	1.95148	+	1.95148i	0.238412	+	0.238412i	−0.577781	+	0.816192i	$0.696081\pi$
$68$	1.11105	−	3.44690i	0.134734	−	0.417998i
$69$		0			0
$70$	−0.624792	−	0.857838i	−0.0746769	−	0.102531i
$71$			0.418759i			0.0496975i	0.999691	+	0.0248488i	$0.00791042\pi$
$71$			0.418759i			0.0496975i	−0.999691	+	0.0248488i	$0.992090\pi$
$72$		0			0
$73$			3.49594i			0.409168i	0.978849	+	0.204584i	$0.0655842\pi$
$73$			3.49594i			0.409168i	−0.978849	+	0.204584i	$0.934416\pi$
$74$	9.60564	−	6.99611i	1.11663	−	0.813281i
$75$		0			0
$76$	1.58300	+	3.08891i	0.181583	+	0.354322i
$77$	−1.56300	−	1.56300i	−0.178121	−	0.178121i
$78$		0			0
$79$		−	3.40726i		−	0.383347i	−0.981459	−	0.191674i	$-0.938609\pi$
$79$		−	3.40726i		−	0.383347i	0.981459	−	0.191674i	$-0.0613915\pi$
$80$	−3.94778	+	0.644237i	−0.441375	+	0.0720279i
$81$		0			0
$82$	−0.543601	+	3.45837i	−0.0600307	+	0.381913i
$83$	−0.548807	+	0.548807i	−0.0602394	+	0.0602394i	−0.736585	−	0.676345i	$-0.763563\pi$
$83$	−0.548807	+	0.548807i	−0.0602394	+	0.0602394i	0.676345	+	0.736585i	$0.263563\pi$
$84$		0			0
$85$	−1.28041	−	1.28041i	−0.138880	−	0.138880i
$86$	−6.12407	−	8.40834i	−0.660376	−	0.906694i
$87$		0			0
$88$	−7.91453	+	2.60236i	−0.843692	+	0.277413i
$89$	−12.2354			−1.29695			−0.648474	−	0.761237i	$-0.724592\pi$
$89$	−12.2354			−1.29695			−0.648474	+	0.761237i	$0.724592\pi$
$90$		0			0
$91$	1.24958	−	1.24958i	0.130992	−	0.130992i
$92$	5.74732	−	17.8304i	0.599199	−	1.85895i
$93$		0			0
$94$	0.974525	−	6.19989i	0.100515	−	0.639470i
$95$	1.73546			0.178054
$96$		0			0
$97$	6.64896			0.675100			0.337550	−	0.941308i	$-0.390402\pi$
$97$	6.64896			0.675100			0.337550	+	0.941308i	$0.390402\pi$
$98$	−1.41351	+	8.99270i	−0.142786	+	0.908400i
$99$		0			0
$100$	−0.613577	+	1.90356i	−0.0613577	+	0.190356i
$101$	8.50982	−	8.50982i	0.846759	−	0.846759i	−0.142968	−	0.989727i	$-0.545665\pi$
$101$	8.50982	−	8.50982i	0.846759	−	0.846759i	0.989727	+	0.142968i	$0.0456647\pi$
$102$		0			0
$103$	−13.3482			−1.31524			−0.657621	−	0.753349i	$-0.728437\pi$
$103$	−13.3482			−1.31524			−0.657621	+	0.753349i	$0.728437\pi$
$104$	−2.08053	−	6.32747i	−0.204012	−	0.620460i
$105$		0			0
$106$	8.88727	+	12.2022i	0.863208	+	1.18518i
$107$	1.67726	+	1.67726i	0.162147	+	0.162147i	0.783517	−	0.621370i	$-0.213424\pi$
$107$	1.67726	+	1.67726i	0.162147	+	0.162147i	−0.621370	+	0.783517i	$0.713424\pi$
$108$		0			0
$109$	−10.8094	+	10.8094i	−1.03535	+	1.03535i	−0.0360007	+	0.999352i	$0.511462\pi$
$109$	−10.8094	+	10.8094i	−1.03535	+	1.03535i	−0.999352	+	0.0360007i	$0.988538\pi$
$110$	−0.646840	+	4.11517i	−0.0616738	+	0.392366i
$111$		0			0
$112$	−2.43664	−	1.75294i	−0.230241	−	0.165637i
$113$			9.62581i			0.905520i	0.891632	+	0.452760i	$0.149561\pi$
$113$			9.62581i			0.905520i	−0.891632	+	0.452760i	$0.850439\pi$
$114$		0			0
$115$	−6.62340	−	6.62340i	−0.617635	−	0.617635i
$116$	−6.25412	−	12.2037i	−0.580680	−	1.13308i
$117$		0			0
$118$	0.764342	−	0.556696i	0.0703634	−	0.0512480i
$119$		−	1.35883i		−	0.124564i
$120$		0			0
$121$		−	2.32349i		−	0.211226i
$122$	5.87748	+	8.06977i	0.532122	+	0.730602i
$123$		0			0
$124$	−3.03902	+	9.42822i	−0.272912	+	0.846679i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$		−	1.98607i		−	0.176235i	−0.996110	−	0.0881176i	$-0.971915\pi$
$127$		−	1.98607i		−	0.176235i	0.996110	−	0.0881176i	$-0.0280851\pi$
$128$	−10.0381	+	5.21878i	−0.887255	+	0.461279i
$129$		0			0
$130$	−3.28998	−	0.517133i	−0.288550	−	0.0453555i
$131$	14.6078	−	14.6078i	1.27629	−	1.27629i	0.333554	−	0.942731i	$-0.391752\pi$
$131$	14.6078	−	14.6078i	1.27629	−	1.27629i	0.942731	−	0.333554i	$-0.108248\pi$
$132$		0			0
$133$	0.920877	+	0.920877i	0.0798502	+	0.0798502i
$134$	3.15488	−	2.29780i	0.272540	−	0.198500i
$135$		0			0
$136$	−4.57154	−	2.30912i	−0.392006	−	0.198006i
$137$	−17.5298			−1.49767			−0.748837	−	0.662754i	$-0.769387\pi$
$137$	−17.5298			−1.49767			−0.748837	+	0.662754i	$0.769387\pi$
$138$		0			0
$139$	9.60358	−	9.60358i	0.814565	−	0.814565i	−0.170750	−	0.985314i	$-0.554619\pi$
$139$	9.60358	−	9.60358i	0.814565	−	0.814565i	0.985314	+	0.170750i	$0.0546190\pi$
$140$	−1.33565	+	0.684494i	−0.112883	+	0.0578503i
$141$		0			0
$142$	0.585031	+	0.0919577i	0.0490947	+	0.00771692i
$143$	−6.93666			−0.580073
$144$		0			0
$145$	−6.85644			−0.569397
$146$	4.88403	+	0.767693i	0.404206	+	0.0635347i
$147$		0			0
$148$	−7.66463	−	14.9560i	−0.630029	−	1.22937i
$149$	3.85352	−	3.85352i	0.315693	−	0.315693i	−0.531417	−	0.847110i	$-0.678340\pi$
$149$	3.85352	−	3.85352i	0.315693	−	0.315693i	0.847110	+	0.531417i	$0.178340\pi$
$150$		0			0
$151$	−12.1519			−0.988912			−0.494456	−	0.869203i	$-0.664633\pi$
$151$	−12.1519			−0.988912			−0.494456	+	0.869203i	$0.664633\pi$
$152$	4.66302	−	1.53324i	0.378221	−	0.124362i
$153$		0			0
$154$	−2.52684	+	1.84038i	−0.203619	+	0.148302i
$155$	3.50227	+	3.50227i	0.281309	+	0.281309i
$156$		0			0
$157$	−3.49520	+	3.49520i	−0.278947	+	0.278947i	−0.832689	−	0.553741i	$-0.813200\pi$
$157$	−3.49520	+	3.49520i	−0.278947	+	0.278947i	0.553741	+	0.832689i	$0.313200\pi$
$158$	−4.76015	−	0.748221i	−0.378697	−	0.0595253i
$159$		0			0
$160$	0.0331222	+	5.65676i	0.00261854	+	0.447206i
$161$		−	7.02908i		−	0.553969i
$162$		0			0
$163$	6.19907	+	6.19907i	0.485549	+	0.485549i	0.906898	−	0.421349i	$-0.138443\pi$
$163$	6.19907	+	6.19907i	0.485549	+	0.485549i	−0.421349	+	0.906898i	$0.638443\pi$
$164$	4.71218	+	1.51889i	0.367959	+	0.118605i
$165$		0			0
$166$	0.646200	+	0.887232i	0.0501549	+	0.0688625i
$167$			23.9728i			1.85507i	0.373739	+	0.927534i	$0.378076\pi$
$167$			23.9728i			1.85507i	−0.373739	+	0.927534i	$0.621924\pi$
$168$		0			0
$169$			7.45431i			0.573408i
$170$	−2.06998	+	1.50763i	−0.158760	+	0.115630i
$171$		0			0
$172$	−13.0918	+	6.70926i	−0.998239	+	0.511576i
$173$	4.70153	+	4.70153i	0.357450	+	0.357450i	0.862872	−	0.505422i	$-0.168663\pi$
$173$	4.70153	+	4.70153i	0.357450	+	0.357450i	−0.505422	+	0.862872i	$0.668663\pi$
$174$		0			0
$175$			0.750417i			0.0567262i
$176$	1.89766	+	11.6285i	0.143041	+	0.876535i
$177$		0			0
$178$	−2.68684	+	17.0936i	−0.201387	+	1.28122i
$179$	10.9751	−	10.9751i	0.820315	−	0.820315i	−0.165838	−	0.986153i	$-0.553033\pi$
$179$	10.9751	−	10.9751i	0.820315	−	0.820315i	0.986153	+	0.165838i	$0.0530329\pi$
$180$		0			0
$181$	−0.999478	−	0.999478i	−0.0742906	−	0.0742906i	0.668985	−	0.743276i	$-0.266729\pi$
$181$	−0.999478	−	0.999478i	−0.0742906	−	0.0742906i	−0.743276	+	0.668985i	$0.766729\pi$
$182$	−1.47134	−	2.02015i	−0.109063	−	0.149743i
$183$		0			0
$184$	−23.6481	−	11.9448i	−1.74336	−	0.880585i
$185$	−8.40280			−0.617786
$186$		0			0
$187$	−3.77155	+	3.77155i	−0.275803	+	0.275803i
$188$	−8.44762	−	2.72294i	−0.616106	−	0.198591i
$189$		0			0
$190$	0.381100	−	2.42454i	0.0276479	−	0.175895i
$191$	20.6166			1.49177			0.745884	−	0.666076i	$-0.232027\pi$
$191$	20.6166			1.49177			0.745884	+	0.666076i	$0.232027\pi$
$192$		0			0
$193$	−4.05831			−0.292124			−0.146062	−	0.989275i	$-0.546660\pi$
$193$	−4.05831			−0.292124			−0.146062	+	0.989275i	$0.546660\pi$
$194$	1.46008	−	9.28900i	0.104828	−	0.666911i
$195$		0			0
$196$	12.2529	+	3.94952i	0.875211	+	0.282109i
$197$	−4.20746	+	4.20746i	−0.299769	+	0.299769i	−0.840923	−	0.541154i	$-0.817987\pi$
$197$	−4.20746	+	4.20746i	−0.299769	+	0.299769i	0.541154	+	0.840923i	$0.317987\pi$
$198$		0			0
$199$	8.21153			0.582100			0.291050	−	0.956708i	$-0.405995\pi$
$199$	8.21153			0.582100			0.291050	+	0.956708i	$0.405995\pi$
$200$	2.52464	+	1.27522i	0.178519	+	0.0901715i
$201$		0			0
$202$	−10.0200	−	13.7575i	−0.705006	−	0.967971i
$203$	−3.63820	−	3.63820i	−0.255351	−	0.255351i
$204$		0			0
$205$	1.75042	−	1.75042i	0.122254	−	0.122254i
$206$	−2.93122	+	18.6483i	−0.204228	+	1.29929i
$207$		0			0
$208$	−9.29674	+	1.51713i	−0.644613	+	0.105194i
$209$		−	5.11195i		−	0.353601i
$210$		0			0
$211$	2.03421	+	2.03421i	0.140041	+	0.140041i	0.773652	−	0.633611i	$-0.218428\pi$
$211$	2.03421	+	2.03421i	0.140041	+	0.140041i	−0.633611	+	0.773652i	$0.718428\pi$
$212$	18.9988	−	9.73649i	1.30484	−	0.668705i
$213$		0			0
$214$	2.71155	−	1.97491i	0.185358	−	0.135002i
$215$			7.35542i			0.501635i
$216$		0			0
$217$			3.71678i			0.252311i
$218$	12.7277	+	17.4751i	0.862027	+	1.18356i
$219$		0			0
$220$	5.60710	+	1.80735i	0.378030	+	0.121851i
$221$	−3.01526	−	3.01526i	−0.202829	−	0.202829i
$222$		0			0
$223$		−	28.2722i		−	1.89325i	−0.322344	−	0.946623i	$-0.604471\pi$
$223$		−	28.2722i		−	1.89325i	0.322344	−	0.946623i	$-0.395529\pi$
$224$	−2.98404	+	3.01919i	−0.199380	+	0.201728i
$225$		0			0
$226$	13.4478	+	2.11379i	0.894537	+	0.140607i
$227$	7.39231	−	7.39231i	0.490645	−	0.490645i	−0.417864	−	0.908509i	$-0.637221\pi$
$227$	7.39231	−	7.39231i	0.490645	−	0.490645i	0.908509	+	0.417864i	$0.137221\pi$
$228$		0			0
$229$	14.8710	+	14.8710i	0.982706	+	0.982706i	0.999853	−	0.0171469i	$-0.00545829\pi$
$229$	14.8710	+	14.8710i	0.982706	+	0.982706i	−0.0171469	+	0.999853i	$0.505458\pi$
$230$	−10.7078	+	7.79881i	−0.706049	+	0.514239i
$231$		0			0
$232$	−18.4226	+	6.05751i	−1.20950	+	0.397695i
$233$	−19.2128			−1.25867			−0.629336	−	0.777133i	$-0.716673\pi$
$233$	−19.2128			−1.25867			−0.629336	+	0.777133i	$0.716673\pi$
$234$		0			0
$235$	−3.13801	+	3.13801i	−0.204701	+	0.204701i
$236$	−0.609891	−	1.19008i	−0.0397006	−	0.0774677i
$237$		0			0
$238$	−1.89837	−	0.298393i	−0.123053	−	0.0193420i
$239$	−20.9731			−1.35664			−0.678318	−	0.734769i	$-0.737291\pi$
$239$	−20.9731			−1.35664			−0.678318	+	0.734769i	$0.737291\pi$
$240$		0			0
$241$	0.400502			0.0257986			0.0128993	−	0.999917i	$-0.495894\pi$
$241$	0.400502			0.0257986			0.0128993	+	0.999917i	$0.495894\pi$
$242$	−3.24605	−	0.510228i	−0.208664	−	0.0327987i
$243$		0			0
$244$	12.5646	−	6.43911i	0.804367	−	0.412222i
$245$	4.55156	−	4.55156i	0.290788	−	0.290788i
$246$		0			0
$247$	4.08688			0.260042
$248$	12.5044	+	6.31609i	0.794033	+	0.401072i
$249$		0			0
$250$	1.14315	−	0.832593i	0.0722991	−	0.0526578i
$251$	−21.3187	−	21.3187i	−1.34562	−	1.34562i	−0.890354	−	0.455269i	$-0.849543\pi$
$251$	−21.3187	−	21.3187i	−1.34562	−	1.34562i	−0.455269	−	0.890354i	$-0.650457\pi$
$252$		0			0
$253$	−19.5098	+	19.5098i	−1.22657	+	1.22657i
$254$	−2.77466	−	0.436133i	−0.174098	−	0.0273654i
$255$		0			0
$256$	5.08661	+	15.1699i	0.317913	+	0.948120i
$257$		−	23.7762i		−	1.48312i	−0.670887	−	0.741560i	$-0.734086\pi$
$257$		−	23.7762i		−	1.48312i	0.670887	−	0.741560i	$-0.265914\pi$
$258$		0			0
$259$	−4.45873	−	4.45873i	−0.277052	−	0.277052i
$260$	−1.44493	+	4.48274i	−0.0896108	+	0.278008i
$261$		0			0
$262$	−17.2001	−	23.6157i	−1.06263	−	1.45898i
$263$		−	4.83991i		−	0.298441i	−0.988804	−	0.149221i	$-0.952324\pi$
$263$		−	4.83991i		−	0.298441i	0.988804	−	0.149221i	$-0.0476765\pi$
$264$		0			0
$265$		−	10.6742i		−	0.655711i
$266$	1.48874	−	1.08430i	0.0912806	−	0.0664827i
$267$		0			0
$268$	−2.51737	−	4.91214i	−0.153773	−	0.300057i
$269$	20.9861	+	20.9861i	1.27954	+	1.27954i	0.940924	+	0.338619i	$0.109960\pi$
$269$	20.9861	+	20.9861i	1.27954	+	1.27954i	0.338619	+	0.940924i	$0.390040\pi$
$270$		0			0
$271$		−	19.2132i		−	1.16712i	−0.812071	−	0.583559i	$-0.801660\pi$
$271$		−	19.2132i		−	1.16712i	0.812071	−	0.583559i	$-0.198340\pi$
$272$	−4.22987	+	5.87964i	−0.256474	+	0.356506i
$273$		0			0
$274$	−3.84948	+	24.4902i	−0.232555	+	1.47951i
$275$	2.08285	−	2.08285i	0.125600	−	0.125600i
$276$		0			0
$277$	9.81607	+	9.81607i	0.589790	+	0.589790i	0.937575	−	0.347784i	$-0.113066\pi$
$277$	9.81607	+	9.81607i	0.589790	+	0.589790i	−0.347784	+	0.937575i	$0.613066\pi$
$278$	−11.3079	−	15.5257i	−0.678201	−	0.931168i
$279$		0			0
$280$	0.662976	+	2.01630i	0.0396204	+	0.120497i
$281$	8.55344			0.510256			0.255128	−	0.966907i	$-0.417882\pi$
$281$	8.55344			0.510256			0.255128	+	0.966907i	$0.417882\pi$
$282$		0			0
$283$	0.613273	−	0.613273i	0.0364553	−	0.0364553i	−0.688644	−	0.725099i	$-0.741794\pi$
$283$	0.613273	−	0.613273i	0.0364553	−	0.0364553i	0.725099	+	0.688644i	$0.241794\pi$
$284$	0.256941	−	0.797131i	0.0152466	−	0.0473010i
$285$		0			0
$286$	−1.52326	+	9.69093i	−0.0900724	+	0.573037i
$287$	1.85763			0.109652
$288$		0			0
$289$	13.7211			0.807125
$290$	−1.50565	+	9.57886i	−0.0884146	+	0.562490i
$291$		0			0
$292$	2.14503	−	6.65471i	0.125528	−	0.389437i
$293$	15.9327	−	15.9327i	0.930801	−	0.930801i	−0.0669549	−	0.997756i	$-0.521328\pi$
$293$	15.9327	−	15.9327i	0.930801	−	0.930801i	0.997756	+	0.0669549i	$0.0213284\pi$
$294$		0			0
$295$	−0.668629			−0.0389291
$296$	−22.5775	+	7.42368i	−1.31229	+	0.431492i
$297$		0			0
$298$	−4.53738	−	6.22982i	−0.262844	−	0.360884i
$299$	−15.5976	−	15.5976i	−0.902034	−	0.902034i
$300$		0			0
$301$	−3.90297	+	3.90297i	−0.224963	+	0.224963i
$302$	−2.66852	+	16.9770i	−0.153556	+	0.976917i
$303$		0			0
$304$	−1.11805	−	6.85121i	−0.0641244	−	0.392944i
$305$		−	7.05925i		−	0.404211i
$306$		0			0
$307$	24.3353	+	24.3353i	1.38889	+	1.38889i	0.827657	+	0.561235i	$0.189673\pi$
$307$	24.3353	+	24.3353i	1.38889	+	1.38889i	0.561235	+	0.827657i	$0.310327\pi$
$308$	2.01624	+	3.93429i	0.114886	+	0.224177i
$309$		0			0
$310$	5.66196	−	4.12380i	0.321578	−	0.234216i
$311$		−	7.54616i		−	0.427904i	−0.976844	−	0.213952i	$-0.931366\pi$
$311$		−	7.54616i		−	0.427904i	0.976844	−	0.213952i	$-0.0686336\pi$
$312$		0			0
$313$		−	24.9197i		−	1.40855i	−0.709929	−	0.704273i	$-0.751273\pi$
$313$		−	24.9197i		−	1.40855i	0.709929	−	0.704273i	$-0.248727\pi$
$314$	4.11548	+	5.65054i	0.232250	+	0.318878i
$315$		0			0
$316$	−2.09062	+	6.48591i	−0.117607	+	0.364861i
$317$	−12.1374	−	12.1374i	−0.681706	−	0.681706i	0.278679	−	0.960384i	$-0.410104\pi$
$317$	−12.1374	−	12.1374i	−0.681706	−	0.681706i	−0.960384	+	0.278679i	$0.910104\pi$
$318$		0			0
$319$			20.1963i			1.13077i
$320$	7.91010	+	1.19593i	0.442188	+	0.0668543i
$321$		0			0
$322$	−9.82004	−	1.54356i	−0.547250	−	0.0860190i
$323$	2.22209	−	2.22209i	0.123640	−	0.123640i
$324$		0			0
$325$	1.66519	+	1.66519i	0.0923679	+	0.0923679i
$326$	10.0218	−	7.29919i	0.555055	−	0.404265i
$327$		0			0
$328$	3.15675	−	6.24966i	0.174303	−	0.345080i
$329$	−3.33021			−0.183600
$330$		0			0
$331$	14.1985	−	14.1985i	0.780418	−	0.780418i	−0.199483	−	0.979901i	$-0.563926\pi$
$331$	14.1985	−	14.1985i	0.780418	−	0.780418i	0.979901	+	0.199483i	$0.0639264\pi$
$332$	1.38142	−	0.707949i	0.0758152	−	0.0388537i
$333$		0			0
$334$	33.4914	+	5.26432i	1.83257	+	0.288051i
$335$	−2.75981			−0.150785
$336$		0			0
$337$	32.2946			1.75920			0.879600	−	0.475714i	$-0.157810\pi$
$337$	32.2946			1.75920			0.879600	+	0.475714i	$0.157810\pi$
$338$	10.4141	+	1.63694i	0.566453	+	0.0890376i
$339$		0			0
$340$	1.65170	+	3.22295i	0.0895758	+	0.174789i
$341$	10.3163	−	10.3163i	0.558656	−	0.558656i
$342$		0			0
$343$	10.0833			0.544445
$344$	6.49834	+	19.7633i	0.350367	+	1.06557i
$345$		0			0
$346$	7.60075	−	5.53588i	0.408619	−	0.297611i
$347$	11.0493	+	11.0493i	0.593159	+	0.593159i	0.938483	−	0.345324i	$-0.112231\pi$
$347$	11.0493	+	11.0493i	0.593159	+	0.593159i	−0.345324	+	0.938483i	$0.612231\pi$
$348$		0			0
$349$	25.6937	−	25.6937i	1.37535	−	1.37535i	0.523045	−	0.852305i	$-0.324796\pi$
$349$	25.6937	−	25.6937i	1.37535	−	1.37535i	0.852305	−	0.523045i	$-0.175204\pi$
$350$	1.04838	+	0.164788i	0.0560381	+	0.00880831i
$351$		0			0
$352$	16.6625	−	0.0975646i	0.888114	−	0.00520021i
$353$			14.7815i			0.786740i	0.919380	+	0.393370i	$0.128691\pi$
$353$			14.7815i			0.786740i	−0.919380	+	0.393370i	$0.871309\pi$
$354$		0			0
$355$	−0.296107	−	0.296107i	−0.0157157	−	0.0157157i
$356$	23.2907	+	7.50735i	1.23441	+	0.397889i
$357$		0			0
$358$	−12.9228	−	17.7429i	−0.682989	−	0.937742i
$359$			10.4972i			0.554023i	0.960867	+	0.277012i	$0.0893441\pi$
$359$			10.4972i			0.554023i	−0.960867	+	0.277012i	$0.910656\pi$
$360$		0			0
$361$		−	15.9882i		−	0.841483i
$362$	−1.61581	+	1.17685i	−0.0849252	+	0.0618538i
$363$		0			0
$364$	−3.14537	+	1.61194i	−0.164862	+	0.0844884i
$365$	−2.47200	−	2.47200i	−0.129390	−	0.129390i
$366$		0			0
$367$			25.0959i			1.31000i	0.755631	+	0.654998i	$0.227331\pi$
$367$			25.0959i			1.31000i	−0.755631	+	0.654998i	$0.772669\pi$
$368$	−21.8807	+	30.4147i	−1.14061	+	1.58548i
$369$		0			0
$370$	−1.84522	+	11.7392i	−0.0959284	+	0.610293i
$371$	5.66399	−	5.66399i	0.294060	−	0.294060i
$372$		0			0
$373$	0.459192	+	0.459192i	0.0237761	+	0.0237761i	0.718895	−	0.695119i	$-0.244648\pi$
$373$	0.459192	+	0.459192i	0.0237761	+	0.0237761i	−0.695119	+	0.718895i	$0.744648\pi$
$374$	4.44087	+	6.09731i	0.229632	+	0.315284i
$375$		0			0
$376$	−5.65917	+	11.2039i	−0.291850	+	0.577796i
$377$	−16.1464			−0.831584
$378$		0			0
$379$	11.1426	−	11.1426i	0.572356	−	0.572356i	−0.360430	−	0.932786i	$-0.617370\pi$
$379$	11.1426	−	11.1426i	0.572356	−	0.572356i	0.932786	+	0.360430i	$0.117370\pi$
$380$	−3.30354	−	1.06484i	−0.169468	−	0.0546250i
$381$		0			0
$382$	4.52733	−	28.8027i	0.231638	−	1.47367i
$383$	9.51038			0.485957			0.242979	−	0.970032i	$-0.421875\pi$
$383$	9.51038			0.485957			0.242979	+	0.970032i	$0.421875\pi$
$384$		0			0
$385$	2.21042			0.112653
$386$	−0.891189	+	5.66971i	−0.0453603	+	0.288580i
$387$		0			0
$388$	−12.6567	−	4.07965i	−0.642545	−	0.207113i
$389$	−9.53161	+	9.53161i	−0.483272	+	0.483272i	−0.906175	−	0.422903i	$-0.861011\pi$
$389$	−9.53161	+	9.53161i	−0.483272	+	0.483272i	0.422903	+	0.906175i	$0.361011\pi$
$390$		0			0
$391$	−16.9613			−0.857768
$392$	8.20842	−	16.2508i	0.414588	−	0.820790i
$393$		0			0
$394$	4.95413	+	6.80201i	0.249586	+	0.342681i
$395$	2.40930	+	2.40930i	0.121225	+	0.121225i
$396$		0			0
$397$	12.3827	−	12.3827i	0.621469	−	0.621469i	−0.324438	−	0.945907i	$-0.605175\pi$
$397$	12.3827	−	12.3827i	0.621469	−	0.621469i	0.945907	+	0.324438i	$0.105175\pi$
$398$	1.80322	−	11.4720i	0.0903872	−	0.575040i
$399$		0			0
$400$	2.33596	−	3.24705i	0.116798	−	0.162352i
$401$		−	20.2893i		−	1.01320i	−0.862182	−	0.506599i	$-0.830902\pi$
$401$		−	20.2893i		−	1.01320i	0.862182	−	0.506599i	$-0.169098\pi$
$402$		0			0
$403$	8.24759	+	8.24759i	0.410842	+	0.410842i
$404$	−21.4204	+	10.9775i	−1.06570	+	0.546150i
$405$		0			0
$406$	−5.88172	+	4.28385i	−0.291905	+	0.212604i
$407$			24.7512i			1.22687i
$408$		0			0
$409$			26.4946i			1.31008i	0.755596	+	0.655038i	$0.227347\pi$
$409$			26.4946i			1.31008i	−0.755596	+	0.655038i	$0.772653\pi$
$410$	−2.06105	−	2.82982i	−0.101788	−	0.139755i
$411$		0			0
$412$	25.4091	+	8.19018i	1.25182	+	0.403501i
$413$	−0.354791	−	0.354791i	−0.0174581	−	0.0174581i
$414$		0			0
$415$		−	0.776130i		−	0.0380987i
$416$	0.0780005	+	13.3213i	0.00382429	+	0.653129i
$417$		0			0
$418$	−7.14171	−	1.12256i	−0.349312	−	0.0549064i
$419$	5.89550	−	5.89550i	0.288014	−	0.288014i	−0.548280	−	0.836295i	$-0.684717\pi$
$419$	5.89550	−	5.89550i	0.288014	−	0.288014i	0.836295	+	0.548280i	$0.184717\pi$
$420$		0			0
$421$	−17.4387	−	17.4387i	−0.849912	−	0.849912i	0.140210	−	0.990122i	$-0.455222\pi$
$421$	−17.4387	−	17.4387i	−0.849912	−	0.849912i	−0.990122	+	0.140210i	$0.955222\pi$
$422$	3.28862	−	2.39521i	0.160088	−	0.116597i
$423$		0			0
$424$	−9.43041	−	28.6806i	−0.457981	−	1.39285i
$425$	1.81077			0.0878351
$426$		0			0
$427$	3.74581	−	3.74581i	0.181272	−	0.181272i
$428$	−2.16362	−	4.22188i	−0.104583	−	0.204072i
$429$		0			0
$430$	10.2760	+	1.61522i	0.495551	+	0.0778928i
$431$	−14.3547			−0.691442			−0.345721	−	0.938337i	$-0.612366\pi$
$431$	−14.3547			−0.691442			−0.345721	+	0.938337i	$0.612366\pi$
$432$		0			0
$433$	29.6967			1.42713			0.713566	−	0.700588i	$-0.247079\pi$
$433$	29.6967			1.42713			0.713566	+	0.700588i	$0.247079\pi$
$434$	5.19256	+	0.816189i	0.249251	+	0.0391783i
$435$		0			0
$436$	27.2087	−	13.9439i	1.30306	−	0.667791i
$437$	11.4946	−	11.4946i	0.549863	−	0.549863i
$438$		0			0
$439$	27.7682			1.32530			0.662651	−	0.748928i	$-0.269431\pi$
$439$	27.7682			1.32530			0.662651	+	0.748928i	$0.269431\pi$
$440$	3.75627	−	7.43657i	0.179073	−	0.354524i
$441$		0			0
$442$	−4.87465	+	3.55037i	−0.231863	+	0.168874i
$443$	−15.9336	−	15.9336i	−0.757030	−	0.757030i	0.218750	−	0.975781i	$-0.429802\pi$
$443$	−15.9336	−	15.9336i	−0.757030	−	0.757030i	−0.975781	+	0.218750i	$0.929802\pi$
$444$		0			0
$445$	8.65172	−	8.65172i	0.410131	−	0.410131i
$446$	−39.4979	−	6.20845i	−1.87028	−	0.293979i
$447$		0			0
$448$	3.56271	+	4.83188i	0.168322	+	0.228285i
$449$			26.5910i			1.25491i	0.778653	+	0.627455i	$0.215903\pi$
$449$			26.5910i			1.25491i	−0.778653	+	0.627455i	$0.784097\pi$
$450$		0			0
$451$	−5.15601	−	5.15601i	−0.242787	−	0.242787i
$452$	5.90618	−	18.3233i	0.277803	−	0.861854i
$453$		0			0
$454$	−8.70419	−	11.9508i	−0.408508	−	0.560880i
$455$			1.76718i			0.0828466i
$456$		0			0
$457$		−	37.4320i		−	1.75100i	−0.483221	−	0.875499i	$-0.660533\pi$
$457$		−	37.4320i		−	1.75100i	0.483221	−	0.875499i	$-0.339467\pi$
$458$	24.0414	−	17.5101i	1.12338	−	0.818194i
$459$		0			0
$460$	8.54404	+	16.6720i	0.398368	+	0.777335i
$461$	15.6767	+	15.6767i	0.730135	+	0.730135i	0.970646	−	0.240512i	$-0.0773152\pi$
$461$	15.6767	+	15.6767i	0.730135	+	0.730135i	−0.240512	+	0.970646i	$0.577315\pi$
$462$		0			0
$463$			8.33480i			0.387351i	0.981066	+	0.193675i	$0.0620409\pi$
$463$			8.33480i			0.387351i	−0.981066	+	0.193675i	$0.937959\pi$
$464$	4.41718	+	27.0677i	0.205062	+	1.25659i
$465$		0			0
$466$	−4.21905	+	26.8415i	−0.195444	+	1.24341i
$467$	−14.2346	+	14.2346i	−0.658696	+	0.658696i	−0.955072	−	0.296375i	$-0.904222\pi$
$467$	−14.2346	+	14.2346i	−0.658696	+	0.658696i	0.296375	+	0.955072i	$0.404222\pi$
$468$		0			0
$469$	−1.46443	−	1.46443i	−0.0676209	−	0.0676209i
$470$	3.69489	+	5.07308i	0.170433	+	0.234004i
$471$		0			0
$472$	−1.79654	+	0.590718i	−0.0826926	+	0.0271900i
$473$	21.6661			0.996207
$474$		0			0
$475$	−1.22715	+	1.22715i	−0.0563057	+	0.0563057i
$476$	−0.833747	+	2.58661i	−0.0382147	+	0.118557i
$477$		0			0
$478$	−4.60560	+	29.3007i	−0.210655	+	1.34018i
$479$	−25.4854			−1.16446			−0.582228	−	0.813025i	$-0.697819\pi$
$479$	−25.4854			−1.16446			−0.582228	+	0.813025i	$0.697819\pi$
$480$		0			0
$481$	−19.7880			−0.902254
$482$	0.0879486	−	0.559525i	0.00400595	−	0.0254857i
$483$		0			0
$484$	−1.42564	+	4.42289i	−0.0648018	+	0.201040i
$485$	−4.70153	+	4.70153i	−0.213485	+	0.213485i
$486$		0			0
$487$	−27.9781			−1.26781			−0.633905	−	0.773411i	$-0.718549\pi$
$487$	−27.9781			−1.26781			−0.633905	+	0.773411i	$0.718549\pi$
$488$	−6.23668	−	18.9675i	−0.282321	−	0.858620i
$489$		0			0
$490$	−5.35930	−	7.35830i	−0.242108	−	0.332414i
$491$	14.3468	+	14.3468i	0.647461	+	0.647461i	0.952379	−	0.304917i	$-0.0986289\pi$
$491$	14.3468	+	14.3468i	0.647461	+	0.647461i	−0.304917	+	0.952379i	$0.598629\pi$
$492$		0			0
$493$	−8.77903	+	8.77903i	−0.395388	+	0.395388i
$494$	0.897462	−	5.70962i	0.0403787	−	0.256888i
$495$		0			0
$496$	11.5699	−	16.0825i	0.519503	−	0.722124i
$497$		−	0.314244i		−	0.0140958i
$498$		0			0
$499$	13.7825	+	13.7825i	0.616992	+	0.616992i	0.944759	−	0.327767i	$-0.106296\pi$
$499$	13.7825	+	13.7825i	0.616992	+	0.616992i	−0.327767	+	0.944759i	$0.606296\pi$
$500$	−0.912152	−	1.77988i	−0.0407927	−	0.0795987i
$501$		0			0
$502$	−34.4650	+	25.1020i	−1.53825	+	1.12036i
$503$		−	23.6008i		−	1.05231i	−0.850390	−	0.526153i	$-0.823634\pi$
$503$		−	23.6008i		−	1.05231i	0.850390	−	0.526153i	$-0.176366\pi$
$504$		0			0
$505$			12.0347i			0.535537i
$506$	22.9721	+	31.5407i	1.02124	+	1.40215i
$507$		0			0
$508$	−1.21861	+	3.78059i	−0.0540669	+	0.167737i
$509$	25.8588	+	25.8588i	1.14617	+	1.14617i	0.987299	+	0.158874i	$0.0507863\pi$
$509$	25.8588	+	25.8588i	1.14617	+	1.14617i	0.158874	+	0.987299i	$0.449214\pi$
$510$		0			0
$511$		−	2.62341i		−	0.116053i
$512$	22.3103	−	3.77505i	0.985985	−	0.166835i
$513$		0			0
$514$	−33.2168	−	5.22116i	−1.46513	−	0.230295i
$515$	9.43864	−	9.43864i	0.415916	−	0.415916i
$516$		0			0
$517$	9.24328	+	9.24328i	0.406519	+	0.406519i
$518$	−7.20823	+	5.25000i	−0.316712	+	0.230672i
$519$		0			0
$520$	5.94535	+	3.00305i	0.260721	+	0.131692i
$521$	1.61959			0.0709555			0.0354778	−	0.999370i	$-0.488705\pi$
$521$	1.61959			0.0709555			0.0354778	+	0.999370i	$0.488705\pi$
$522$		0			0
$523$	−12.2302	+	12.2302i	−0.534787	+	0.534787i	−0.921993	−	0.387206i	$-0.873440\pi$
$523$	−12.2302	+	12.2302i	−0.534787	+	0.534787i	0.387206	+	0.921993i	$0.373440\pi$
$524$	−36.7696	+	18.8437i	−1.60629	+	0.823190i
$525$		0			0
$526$	−6.76164	−	1.06282i	−0.294822	−	0.0463413i
$527$	8.96865			0.390680
$528$		0			0
$529$	−64.7388			−2.81473
$530$	−14.9125	−	2.34401i	−0.647758	−	0.101817i
$531$		0			0
$532$	−1.18791	−	2.31797i	−0.0515025	−	0.100497i
$533$	4.12211	−	4.12211i	0.178548	−	0.178548i
$534$		0			0
$535$	−2.37200			−0.102550
$536$	−7.41536	+	2.43823i	−0.320295	+	0.105316i
$537$		0			0
$538$	33.9272	−	24.7103i	1.46271	−	1.06534i
$539$	−13.4070	−	13.4070i	−0.577482	−	0.577482i
$540$		0			0
$541$	−14.5843	+	14.5843i	−0.627026	+	0.627026i	−0.947319	−	0.320293i	$-0.896219\pi$
$541$	−14.5843	+	14.5843i	−0.627026	+	0.627026i	0.320293	+	0.947319i	$0.396219\pi$
$542$	−26.8420	−	4.21914i	−1.15296	−	0.181228i
$543$		0			0
$544$	7.28536	+	7.20054i	0.312357	+	0.308720i
$545$		−	15.2868i		−	0.654814i
$546$		0			0
$547$	−5.88016	−	5.88016i	−0.251418	−	0.251418i	0.570134	−	0.821552i	$-0.306891\pi$
$547$	−5.88016	−	5.88016i	−0.251418	−	0.251418i	−0.821552	+	0.570134i	$0.806891\pi$
$548$	33.3690	+	10.7559i	1.42545	+	0.459470i
$549$		0			0
$550$	−2.45248	−	3.36725i	−0.104574	−	0.143580i
$551$		−	11.8991i		−	0.506918i
$552$		0			0
$553$			2.55687i			0.108729i
$554$	15.8692	−	11.5581i	0.674218	−	0.491056i
$555$		0			0
$556$	−24.1735	+	12.3884i	−1.02518	+	0.525385i
$557$	−4.61435	−	4.61435i	−0.195516	−	0.195516i	0.602559	−	0.798075i	$-0.294148\pi$
$557$	−4.61435	−	4.61435i	−0.195516	−	0.195516i	−0.798075	+	0.602559i	$0.794148\pi$
$558$		0			0
$559$			17.3215i			0.732621i
$560$	2.96248	−	0.483446i	0.125188	−	0.0204293i
$561$		0			0
$562$	1.87830	−	11.9497i	0.0792313	−	0.504067i
$563$	−21.9201	+	21.9201i	−0.923821	+	0.923821i	−0.997297	−	0.0734759i	$-0.976591\pi$
$563$	−21.9201	+	21.9201i	−0.923821	+	0.923821i	0.0734759	+	0.997297i	$0.476591\pi$
$564$		0			0
$565$	−6.80648	−	6.80648i	−0.286351	−	0.286351i
$566$	−0.722108	−	0.991452i	−0.0303524	−	0.0416738i
$567$		0			0
$568$	−1.05722	−	0.534009i	−0.0443598	−	0.0224065i
$569$	10.4987			0.440128			0.220064	−	0.975485i	$-0.429373\pi$
$569$	10.4987			0.440128			0.220064	+	0.975485i	$0.429373\pi$
$570$		0			0
$571$	−27.2368	+	27.2368i	−1.13983	+	1.13983i	−0.151344	+	0.988481i	$0.548360\pi$
$571$	−27.2368	+	27.2368i	−1.13983	+	1.13983i	−0.988481	+	0.151344i	$0.951640\pi$
$572$	13.2043	+	4.25618i	0.552100	+	0.177960i
$573$		0			0
$574$	0.407928	−	2.59522i	0.0170266	−	0.108322i
$575$	9.36690			0.390627
$576$		0			0
$577$	5.71248			0.237814			0.118907	−	0.992905i	$-0.462061\pi$
$577$	5.71248			0.237814			0.118907	+	0.992905i	$0.462061\pi$
$578$	3.01310	−	19.1692i	0.125328	−	0.797335i
$579$		0			0
$580$	13.0516	+	4.20696i	0.541939	+	0.174684i
$581$	0.411834	−	0.411834i	0.0170857	−	0.0170857i
$582$		0			0
$583$	−31.4418			−1.30219
$584$	−8.82599	−	4.45808i	−0.365222	−	0.184477i
$585$		0			0
$586$	−18.7602	−	25.7578i	−0.774979	−	1.06404i
$587$	7.81040	+	7.81040i	0.322370	+	0.322370i	0.849676	−	0.527306i	$-0.176798\pi$
$587$	7.81040	+	7.81040i	0.322370	+	0.322370i	−0.527306	+	0.849676i	$0.676798\pi$
$588$		0			0
$589$	−6.07804	+	6.07804i	−0.250441	+	0.250441i
$590$	−0.146828	+	0.934115i	−0.00604482	+	0.0384569i
$591$		0			0
$592$	5.41339	+	33.1724i	0.222489	+	1.36338i
$593$			5.56434i			0.228500i	0.993452	+	0.114250i	$0.0364465\pi$
$593$			5.56434i			0.228500i	−0.993452	+	0.114250i	$0.963554\pi$
$594$		0			0
$595$	0.960838	+	0.960838i	0.0393905	+	0.0393905i
$596$	−9.69982	+	4.97096i	−0.397320	+	0.203618i
$597$		0			0
$598$	−25.2160	+	18.3657i	−1.03116	+	0.751028i
$599$			20.8570i			0.852195i	0.904677	+	0.426098i	$0.140112\pi$
$599$			20.8570i			0.852195i	−0.904677	+	0.426098i	$0.859888\pi$
$600$		0			0
$601$		−	45.8151i		−	1.86884i	−0.356178	−	0.934418i	$-0.615920\pi$
$601$		−	45.8151i		−	1.86884i	0.356178	−	0.934418i	$-0.384080\pi$
$602$	4.59560	+	6.30976i	0.187303	+	0.257166i
$603$		0			0
$604$	23.1319	+	7.45616i	0.941224	+	0.303387i
$605$	1.64295	+	1.64295i	0.0667956	+	0.0667956i
$606$		0			0
$607$			17.6991i			0.718383i	0.933264	+	0.359191i	$0.116947\pi$
$607$			17.6991i			0.718383i	−0.933264	+	0.359191i	$0.883053\pi$
$608$	−9.81707	+	0.0574823i	−0.398135	+	0.00233121i
$609$		0			0
$610$	−9.86219	−	1.55018i	−0.399308	−	0.0627650i
$611$	−7.38978	+	7.38978i	−0.298959	+	0.298959i
$612$		0			0
$613$	−22.8661	−	22.8661i	−0.923552	−	0.923552i	0.0737263	−	0.997279i	$-0.476511\pi$
$613$	−22.8661	−	22.8661i	−0.923552	−	0.923552i	−0.997279	+	0.0737263i	$0.976511\pi$
$614$	39.3419	−	28.6540i	1.58771	−	1.15638i
$615$		0			0
$616$	5.93920	−	1.95286i	0.239297	−	0.0786828i
$617$	−17.0873			−0.687907			−0.343954	−	0.938987i	$-0.611766\pi$
$617$	−17.0873			−0.687907			−0.343954	+	0.938987i	$0.611766\pi$
$618$		0			0
$619$	19.5907	−	19.5907i	0.787419	−	0.787419i	−0.193652	−	0.981070i	$-0.562033\pi$
$619$	19.5907	−	19.5907i	0.787419	−	0.787419i	0.981070	+	0.193652i	$0.0620332\pi$
$620$	−4.51785	−	8.81567i	−0.181441	−	0.354046i
$621$		0			0
$622$	−10.5424	−	1.65711i	−0.422714	−	0.0664439i
$623$	9.18163			0.367854
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−34.8144	−	5.47227i	−1.39146	−	0.218716i
$627$		0			0
$628$	8.79789	−	4.50873i	0.351074	−	0.179918i
$629$	−10.7590	+	10.7590i	−0.428989	+	0.428989i
$630$		0			0
$631$	−3.65602			−0.145544			−0.0727719	−	0.997349i	$-0.523185\pi$
$631$	−3.65602			−0.145544			−0.0727719	+	0.997349i	$0.523185\pi$
$632$	8.60212	+	4.34500i	0.342174	+	0.172835i
$633$		0			0
$634$	−19.6221	+	14.2914i	−0.779291	+	0.567584i
$635$	1.40436	+	1.40436i	0.0557304	+	0.0557304i
$636$		0			0
$637$	10.7186	−	10.7186i	0.424686	−	0.424686i
$638$	28.2154	+	4.43502i	1.11706	+	0.175584i
$639$		0			0
$640$	3.40781	−	10.7883i	0.134705	−	0.426444i
$641$			35.6775i			1.40918i	0.709617	+	0.704588i	$0.248868\pi$
$641$			35.6775i			1.40918i	−0.709617	+	0.704588i	$0.751132\pi$
$642$		0			0
$643$	29.2912	+	29.2912i	1.15513	+	1.15513i	0.985509	+	0.169625i	$0.0542557\pi$
$643$	29.2912	+	29.2912i	1.15513	+	1.15513i	0.169625	+	0.985509i	$0.445744\pi$
$644$	−4.31288	+	13.3802i	−0.169951	+	0.527255i
$645$		0			0
$646$	−2.61643	−	3.59236i	−0.102942	−	0.141339i
$647$		−	11.4778i		−	0.451237i	−0.974216	−	0.225619i	$-0.927560\pi$
$647$		−	11.4778i		−	0.451237i	0.974216	−	0.225619i	$-0.0724403\pi$
$648$		0			0
$649$			1.96951i			0.0773100i
$650$	2.69203	−	1.96070i	0.105590	−	0.0769049i
$651$		0			0
$652$	−7.99667	−	15.6039i	−0.313174	−	0.611096i
$653$	−1.49816	−	1.49816i	−0.0586275	−	0.0586275i	0.677185	−	0.735813i	$-0.263200\pi$
$653$	−1.49816	−	1.49816i	−0.0586275	−	0.0586275i	−0.735813	+	0.677185i	$0.763200\pi$
$654$		0			0
$655$			20.6585i			0.807194i
$656$	−8.03794	−	5.78257i	−0.313829	−	0.225772i
$657$		0			0
$658$	−0.731300	+	4.65250i	−0.0285090	+	0.181373i
$659$	8.88429	−	8.88429i	0.346083	−	0.346083i	−0.512565	−	0.858648i	$-0.671305\pi$
$659$	8.88429	−	8.88429i	0.346083	−	0.346083i	0.858648	+	0.512565i	$0.171305\pi$
$660$		0			0
$661$	3.63603	+	3.63603i	0.141425	+	0.141425i	0.774275	−	0.632850i	$-0.218115\pi$
$661$	3.63603	+	3.63603i	0.141425	+	0.141425i	−0.632850	+	0.774275i	$0.718115\pi$
$662$	−16.7182	−	22.9540i	−0.649771	−	0.892134i
$663$		0			0
$664$	−0.685693	−	2.08539i	−0.0266100	−	0.0809288i
$665$	−1.30232			−0.0505017
$666$		0			0
$667$	−45.4129	+	45.4129i	−1.75840	+	1.75840i
$668$	14.7091	−	45.6335i	0.569114	−	1.76561i
$669$		0			0
$670$	−0.606044	+	3.85563i	−0.0234135	+	0.148956i
$671$	−20.7937			−0.802730
$672$		0			0
$673$	21.2098			0.817577			0.408788	−	0.912629i	$-0.365951\pi$
$673$	21.2098			0.817577			0.408788	+	0.912629i	$0.365951\pi$
$674$	7.09177	−	45.1175i	0.273165	−	1.73786i
$675$		0			0
$676$	4.57380	−	14.1897i	0.175915	−	0.545757i
$677$	−11.3920	+	11.3920i	−0.437831	+	0.437831i	−0.891282	−	0.453450i	$-0.850193\pi$
$677$	−11.3920	+	11.3920i	−0.437831	+	0.437831i	0.453450	+	0.891282i	$0.350193\pi$
$678$		0			0
$679$	−4.98949			−0.191479
$680$	4.86536	−	1.59977i	0.186578	−	0.0613484i
$681$		0			0
$682$	−12.1470	−	16.6778i	−0.465133	−	0.638627i
$683$	−13.9917	−	13.9917i	−0.535379	−	0.535379i	0.386789	−	0.922168i	$-0.373584\pi$
$683$	−13.9917	−	13.9917i	−0.535379	−	0.535379i	−0.922168	+	0.386789i	$0.873584\pi$
$684$		0			0
$685$	12.3955	−	12.3955i	0.473606	−	0.473606i
$686$	2.21424	−	14.0869i	0.0845401	−	0.537841i
$687$		0			0
$688$	29.0376	−	4.73863i	1.10705	−	0.180659i
$689$		−	25.1370i		−	0.957643i
$690$		0			0
$691$	−2.03799	−	2.03799i	−0.0775288	−	0.0775288i	0.667279	−	0.744808i	$-0.267459\pi$
$691$	−2.03799	−	2.03799i	−0.0775288	−	0.0775288i	−0.744808	+	0.667279i	$0.767459\pi$
$692$	−6.06487	−	11.8344i	−0.230552	−	0.449875i
$693$		0			0
$694$	17.8630	−	13.0102i	0.678069	−	0.493860i
$695$			13.5815i			0.515176i
$696$		0			0
$697$		−	4.48249i		−	0.169786i
$698$	−30.2534	−	41.5378i	−1.14511	−	1.57223i
$699$		0			0
$700$	0.460439	−	1.42846i	0.0174029	−	0.0539907i
$701$	3.05142	+	3.05142i	0.115251	+	0.115251i	0.762380	−	0.647130i	$-0.224031\pi$
$701$	3.05142	+	3.05142i	0.115251	+	0.115251i	−0.647130	+	0.762380i	$0.724031\pi$
$702$		0			0
$703$		−	14.5827i		−	0.549997i
$704$	3.52271	−	23.2999i	0.132767	−	0.878150i
$705$		0			0
$706$	20.6507	+	3.24596i	0.777197	+	0.122163i
$707$	−6.38591	+	6.38591i	−0.240167	+	0.240167i
$708$		0			0
$709$	−5.26339	−	5.26339i	−0.197671	−	0.197671i	0.601330	−	0.799001i	$-0.294638\pi$
$709$	−5.26339	−	5.26339i	−0.197671	−	0.197671i	−0.799001	+	0.601330i	$0.794638\pi$
$710$	−0.478704	+	0.348656i	−0.0179654	+	0.0130848i
$711$		0			0
$712$	15.6028	−	30.8900i	0.584738	−	1.15765i
$713$	46.3938			1.73746
$714$		0			0
$715$	4.90496	−	4.90496i	0.183435	−	0.183435i
$716$	−27.6257	+	14.1576i	−1.03242	+	0.529094i
$717$		0			0
$718$	14.6653	+	2.30515i	0.547304	+	0.0860275i
$719$	−47.8137			−1.78315			−0.891575	−	0.452873i	$-0.850399\pi$
$719$	−47.8137			−1.78315			−0.891575	+	0.452873i	$0.850399\pi$
$720$		0			0
$721$	10.0167			0.373043
$722$	−22.3365	−	3.51094i	−0.831277	−	0.130664i
$723$		0			0
$724$	1.28930	+	2.51582i	0.0479166	+	0.0934996i
$725$	4.84824	−	4.84824i	0.180059	−	0.180059i
$726$		0			0
$727$	−9.20719			−0.341476			−0.170738	−	0.985316i	$-0.554615\pi$
$727$	−9.20719			−0.341476			−0.170738	+	0.985316i	$0.554615\pi$
$728$	1.56126	+	4.74824i	0.0578642	+	0.175982i
$729$		0			0
$730$	−3.99637	+	2.91069i	−0.147912	+	0.107730i
$731$	9.41792	+	9.41792i	0.348334	+	0.348334i
$732$		0			0
$733$	−20.8850	+	20.8850i	−0.771405	+	0.771405i	−0.978352	−	0.206947i	$-0.933647\pi$
$733$	−20.8850	+	20.8850i	−0.771405	+	0.771405i	0.206947	+	0.978352i	$0.433647\pi$
$734$	35.0605	+	5.51096i	1.29411	+	0.203413i
$735$		0			0
$736$	37.6863	+	37.2476i	1.38914	+	1.37296i
$737$			8.12929i			0.299446i
$738$		0			0
$739$	−37.2338	−	37.2338i	−1.36967	−	1.36967i	−0.860910	−	0.508757i	$-0.830105\pi$
$739$	−37.2338	−	37.2338i	−1.36967	−	1.36967i	−0.508757	−	0.860910i	$-0.669895\pi$
$740$	15.9952	+	5.15576i	0.587995	+	0.189530i
$741$		0			0
$742$	−6.66915	−	9.15673i	−0.244832	−	0.336154i
$743$		−	4.21038i		−	0.154464i	−0.997013	−	0.0772320i	$-0.975392\pi$
$743$		−	4.21038i		−	0.154464i	0.997013	−	0.0772320i	$-0.0246082\pi$
$744$		0			0
$745$			5.44970i			0.199662i
$746$	0.742355	−	0.540682i	0.0271796	−	0.0197958i
$747$		0			0
$748$	9.49350	−	4.86522i	0.347117	−	0.177890i
$749$	−1.25864	−	1.25864i	−0.0459898	−	0.0459898i
$750$		0			0
$751$			10.9180i			0.398403i	0.979959	+	0.199202i	$0.0638349\pi$
$751$			10.9180i			0.398403i	−0.979959	+	0.199202i	$0.936165\pi$
$752$	14.4098	+	10.3665i	0.525470	+	0.378029i
$753$		0			0
$754$	−3.54569	+	22.5575i	−0.129126	+	0.821497i
$755$	8.59273	−	8.59273i	0.312721	−	0.312721i
$756$		0			0
$757$	−21.3455	−	21.3455i	−0.775814	−	0.775814i	0.203302	−	0.979116i	$-0.434833\pi$
$757$	−21.3455	−	21.3455i	−0.775814	−	0.775814i	−0.979116	+	0.203302i	$0.934833\pi$
$758$	−13.1200	−	18.0137i	−0.476539	−	0.654288i
$759$		0			0
$760$	−2.21309	+	4.38141i	−0.0802771	+	0.158931i
$761$	7.21797			0.261651			0.130826	−	0.991405i	$-0.458237\pi$
$761$	7.21797			0.261651			0.130826	+	0.991405i	$0.458237\pi$
$762$		0			0
$763$	8.11155	−	8.11155i	0.293658	−	0.293658i
$764$	−39.2449	−	12.6499i	−1.41983	−	0.457657i
$765$		0			0
$766$	2.08844	−	13.2866i	0.0754584	−	0.480063i
$767$	−1.57457			−0.0568546
$768$		0			0
$769$	−38.8357			−1.40045			−0.700226	−	0.713921i	$-0.746918\pi$
$769$	−38.8357			−1.40045			−0.700226	+	0.713921i	$0.746918\pi$
$770$	0.485399	−	3.08809i	0.0174926	−	0.111287i
$771$		0			0
$772$	7.72522	+	2.49009i	0.278037	+	0.0896202i
$773$	4.91339	−	4.91339i	0.176722	−	0.176722i	−0.613203	−	0.789925i	$-0.710119\pi$
$773$	4.91339	−	4.91339i	0.176722	−	0.176722i	0.789925	+	0.613203i	$0.210119\pi$
$774$		0			0
$775$	−4.95295			−0.177915
$776$	−8.47887	+	16.7863i	−0.304374	+	0.602591i
$777$		0			0
$778$	11.2231	+	15.4093i	0.402369	+	0.552452i
$779$	3.03778	+	3.03778i	0.108840	+	0.108840i
$780$		0			0
$781$	−0.872211	+	0.872211i	−0.0312102	+	0.0312102i
$782$	−3.72463	+	23.6959i	−0.133192	+	0.847364i
$783$		0			0
$784$	−20.9008	−	15.0363i	−0.746458	−	0.537009i
$785$		−	4.94296i		−	0.176422i
$786$		0			0
$787$	−17.6563	−	17.6563i	−0.629379	−	0.629379i	0.318533	−	0.947912i	$-0.396810\pi$
$787$	−17.6563	−	17.6563i	−0.629379	−	0.629379i	−0.947912	+	0.318533i	$0.896810\pi$
$788$	10.5907	−	5.42753i	0.377279	−	0.193348i
$789$		0			0
$790$	3.89501	−	2.83686i	0.138578	−	0.100931i
$791$		−	7.22337i		−	0.256833i
$792$		0			0
$793$		−	16.6240i		−	0.590336i
$794$	−14.5802	−	20.0185i	−0.517431	−	0.710431i
$795$		0			0
$796$	−15.6311	−	5.03841i	−0.554030	−	0.178582i
$797$	−14.3307	−	14.3307i	−0.507618	−	0.507618i	0.406177	−	0.913795i	$-0.366862\pi$
$797$	−14.3307	−	14.3307i	−0.507618	−	0.507618i	−0.913795	+	0.406177i	$0.866862\pi$
$798$		0			0
$799$			8.03584i			0.284288i
$800$	−4.02335	−	3.97651i	−0.142247	−	0.140591i
$801$		0			0
$802$	−28.3453	−	4.45544i	−1.00091	−	0.157327i
$803$	−7.28150	+	7.28150i	−0.256959	+	0.256959i
$804$		0			0
$805$	4.97031	+	4.97031i	0.175180	+	0.175180i
$806$	13.3335	−	9.71125i	0.469653	−	0.342064i
$807$		0			0
$808$	10.6324	+	32.3361i	0.374046	+	1.13758i
$809$	39.4238			1.38607			0.693034	−	0.720905i	$-0.256274\pi$
$809$	39.4238			1.38607			0.693034	+	0.720905i	$0.256274\pi$
$810$		0			0
$811$	−7.90652	+	7.90652i	−0.277636	+	0.277636i	−0.832164	−	0.554529i	$-0.812898\pi$
$811$	−7.90652	+	7.90652i	−0.277636	+	0.277636i	0.554529	+	0.832164i	$0.312898\pi$
$812$	4.69319	+	9.15783i	0.164699	+	0.321377i
$813$		0			0
$814$	34.5789	+	5.43526i	1.21199	+	0.190506i
$815$	−8.76681			−0.307088
$816$		0			0
$817$	−12.7650			−0.446592
$818$	37.0146	+	5.81811i	1.29419	+	0.203426i
$819$		0			0
$820$	−4.40603	+	2.25800i	−0.153865	+	0.0788527i
$821$	−4.52928	+	4.52928i	−0.158073	+	0.158073i	−0.781712	−	0.623639i	$-0.785653\pi$
$821$	−4.52928	+	4.52928i	−0.158073	+	0.158073i	0.623639	+	0.781712i	$0.285653\pi$
$822$		0			0
$823$	34.2257			1.19303			0.596516	−	0.802601i	$-0.296551\pi$
$823$	34.2257			1.19303			0.596516	+	0.802601i	$0.296551\pi$
$824$	17.0219	−	33.6996i	0.592987	−	1.17398i
$825$		0			0
$826$	−0.573575	+	0.417754i	−0.0199572	+	0.0145355i
$827$	30.4656	+	30.4656i	1.05939	+	1.05939i	0.998121	+	0.0612712i	$0.0195155\pi$
$827$	30.4656	+	30.4656i	1.05939	+	1.05939i	0.0612712	+	0.998121i	$0.480485\pi$
$828$		0			0
$829$	16.5777	−	16.5777i	0.575767	−	0.575767i	−0.357967	−	0.933734i	$-0.616530\pi$
$829$	16.5777	−	16.5777i	0.575767	−	0.575767i	0.933734	+	0.357967i	$0.116530\pi$
$830$	−1.08430	−	0.170435i	−0.0376366	−	0.00591588i
$831$		0			0
$832$	18.6277	+	2.81632i	0.645801	+	0.0976384i
$833$		−	11.6557i		−	0.403845i
$834$		0			0
$835$	−16.9513	−	16.9513i	−0.586624	−	0.586624i
$836$	−3.13658	+	9.73089i	−0.108481	+	0.336550i
$837$		0			0
$838$	−6.94175	−	9.53100i	−0.239799	−	0.329243i
$839$		−	35.8895i		−	1.23904i	−0.784979	−	0.619522i	$-0.787327\pi$
$839$		−	35.8895i		−	1.23904i	0.784979	−	0.619522i	$-0.212673\pi$
$840$		0			0
$841$			18.0108i			0.621062i
$842$	−28.1924	+	20.5335i	−0.971576	+	0.707631i
$843$		0			0
$844$	−2.62409	−	5.12038i	−0.0903248	−	0.176251i
$845$	−5.27099	−	5.27099i	−0.181328	−	0.181328i
$846$		0			0
$847$			1.74358i			0.0599102i
$848$	−42.1394	+	6.87672i	−1.44707	+	0.236147i
$849$		0			0
$850$	0.397637	−	2.52975i	0.0136388	−	0.0867698i
$851$	−55.6550	+	55.6550i	−1.90783	+	1.90783i
$852$		0			0
$853$	24.1542	+	24.1542i	0.827024	+	0.827024i	0.987104	−	0.160080i	$-0.0511752\pi$
$853$	24.1542	+	24.1542i	0.827024	+	0.827024i	−0.160080	+	0.987104i	$0.551175\pi$
$854$	−4.41056	−	6.05569i	−0.150926	−	0.207221i
$855$		0			0
$856$	−6.37334	+	2.09561i	−0.217836	+	0.0716264i
$857$	−5.33820			−0.182349			−0.0911747	−	0.995835i	$-0.529062\pi$
$857$	−5.33820			−0.182349			−0.0911747	+	0.995835i	$0.529062\pi$
$858$		0			0
$859$	−22.3520	+	22.3520i	−0.762641	+	0.762641i	−0.976799	−	0.214158i	$-0.931299\pi$
$859$	−22.3520	+	22.3520i	−0.762641	+	0.762641i	0.214158	+	0.976799i	$0.431299\pi$
$860$	4.51312	−	14.0014i	0.153896	−	0.477445i
$861$		0			0
$862$	−3.15224	+	20.0544i	−0.107366	+	0.683056i
$863$	22.5742			0.768435			0.384217	−	0.923243i	$-0.374471\pi$
$863$	22.5742			0.768435			0.384217	+	0.923243i	$0.374471\pi$
$864$		0			0
$865$	−6.64896			−0.226072
$866$	6.52127	−	41.4881i	0.221602	−	1.40982i
$867$		0			0
$868$	2.28053	−	7.07509i	0.0774063	−	0.240144i
$869$	7.09681	−	7.09681i	0.240743	−	0.240743i
$870$		0			0
$871$	−6.49917			−0.220216
$872$	−13.5055	−	41.0742i	−0.457355	−	1.39095i
$873$		0			0
$874$	−13.5345	−	18.5829i	−0.457812	−	0.628575i
$875$	−0.530625	−	0.530625i	−0.0179384	−	0.0179384i
$876$		0			0
$877$	26.5772	−	26.5772i	0.897447	−	0.897447i	−0.0977631	−	0.995210i	$-0.531169\pi$
$877$	26.5772	−	26.5772i	0.897447	−	0.897447i	0.995210	+	0.0977631i	$0.0311687\pi$
$878$	6.09777	−	38.7938i	0.205790	−	1.30923i
$879$		0			0
$880$	−9.56447	−	6.88078i	−0.322418	−	0.231951i
$881$			49.9704i			1.68355i	0.539831	+	0.841773i	$0.318488\pi$
$881$			49.9704i			1.68355i	−0.539831	+	0.841773i	$0.681512\pi$
$882$		0			0
$883$	33.9156	+	33.9156i	1.14135	+	1.14135i	0.988203	+	0.153147i	$0.0489408\pi$
$883$	33.9156	+	33.9156i	1.14135	+	1.14135i	0.153147	+	0.988203i	$0.451059\pi$
$884$	3.88963	+	7.58982i	0.130822	+	0.255273i
$885$		0			0
$886$	−25.7592	+	18.7613i	−0.865398	+	0.630298i
$887$			44.9975i			1.51087i	0.655226	+	0.755433i	$0.272574\pi$
$887$			44.9975i			1.51087i	−0.655226	+	0.755433i	$0.727426\pi$
$888$		0			0
$889$			1.49038i			0.0499857i
$890$	−10.1871	−	13.9869i	−0.341472	−	0.468840i
$891$		0			0
$892$	−17.3472	+	53.8177i	−0.580826	+	1.80195i
$893$	−5.44588	−	5.44588i	−0.182239	−	0.182239i
$894$		0			0
$895$			15.5211i			0.518813i
$896$	7.53279	−	3.91626i	0.251653	−	0.130833i
$897$		0			0
$898$	37.1493	+	5.83928i	1.23969	+	0.194859i
$899$	24.0131	−	24.0131i	0.800882	−	0.800882i
$900$		0			0
$901$	−13.6673	−	13.6673i	−0.455324	−	0.455324i
$902$	−8.33550	+	6.07102i	−0.277542	+	0.202143i
$903$		0			0
$904$	−24.3017	−	12.2750i	−0.808264	−	0.408261i
$905$	1.41347			0.0469855
$906$		0			0
$907$	−5.29252	+	5.29252i	−0.175735	+	0.175735i	−0.789494	−	0.613759i	$-0.789657\pi$
$907$	−5.29252	+	5.29252i	−0.175735	+	0.175735i	0.613759	+	0.789494i	$0.289657\pi$
$908$	−18.6074	+	9.53592i	−0.617509	+	0.316461i
$909$		0			0
$910$	2.46885	+	0.388065i	0.0818417	+	0.0128642i
$911$	26.4816			0.877373			0.438687	−	0.898640i	$-0.355444\pi$
$911$	26.4816			0.877373			0.438687	+	0.898640i	$0.355444\pi$
$912$		0			0
$913$	−2.28616			−0.0756609
$914$	−52.2948	−	8.21992i	−1.72976	−	0.271891i
$915$		0			0
$916$	−19.1833	−	37.4324i	−0.633835	−	1.23680i
$917$	−10.9619	+	10.9619i	−0.361994	+	0.361994i
$918$		0			0
$919$	46.9764			1.54961			0.774805	−	0.632200i	$-0.217848\pi$
$919$	46.9764			1.54961			0.774805	+	0.632200i	$0.217848\pi$
$920$	25.1680	−	8.27544i	0.829764	−	0.272833i
$921$		0			0
$922$	25.3438	−	18.4587i	0.834652	−	0.607905i
$923$	−0.697311	−	0.697311i	−0.0229523	−	0.0229523i
$924$		0			0
$925$	5.94167	−	5.94167i	0.195361	−	0.195361i
$926$	11.6442	+	1.83029i	0.382653	+	0.0601470i
$927$		0			0
$928$	38.7852	−	0.227101i	1.27319	−	0.00745494i
$929$		−	5.52346i		−	0.181219i	−0.995887	−	0.0906095i	$-0.971118\pi$
$929$		−	5.52346i		−	0.181219i	0.995887	−	0.0906095i	$-0.0288815\pi$
$930$		0			0
$931$	7.89904	+	7.89904i	0.258881	+	0.258881i
$932$	36.5726	+	11.7885i	1.19798	+	0.386147i
$933$		0			0
$934$	16.7607	+	23.0124i	0.548426	+	0.752988i
$935$		−	5.33378i		−	0.174433i
$936$		0			0
$937$			19.8409i			0.648174i	0.946027	+	0.324087i	$0.105057\pi$
$937$			19.8409i			0.648174i	−0.946027	+	0.324087i	$0.894943\pi$
$938$	−2.36747	+	1.72431i	−0.0773007	+	0.0563007i
$939$		0			0
$940$	7.89878	−	4.04796i	0.257630	−	0.132030i
$941$	−32.5548	−	32.5548i	−1.06125	−	1.06125i	−0.997997	−	0.0632574i	$-0.979851\pi$
$941$	−32.5548	−	32.5548i	−1.06125	−	1.06125i	−0.0632574	−	0.997997i	$-0.520149\pi$
$942$		0			0
$943$		−	23.1874i		−	0.755086i
$944$	0.430756	+	2.63960i	0.0140199	+	0.0859117i
$945$		0			0
$946$	4.75778	−	30.2688i	0.154689	−	0.984124i
$947$	−33.4414	+	33.4414i	−1.08670	+	1.08670i	−0.0908334	+	0.995866i	$0.528953\pi$
$947$	−33.4414	+	33.4414i	−1.08670	+	1.08670i	−0.995866	+	0.0908334i	$0.971047\pi$
$948$		0			0
$949$	−5.82139	−	5.82139i	−0.188970	−	0.188970i
$950$	1.44493	+	1.98389i	0.0468798	+	0.0643658i
$951$		0			0
$952$	3.43056	+	1.73280i	0.111185	+	0.0561605i
$953$	7.81474			0.253144			0.126572	−	0.991957i	$-0.459602\pi$
$953$	7.81474			0.253144			0.126572	+	0.991957i	$0.459602\pi$
$954$		0			0
$955$	−14.5782	+	14.5782i	−0.471738	+	0.471738i
$956$	39.9234	+	12.8686i	1.29122	+	0.416200i
$957$		0			0
$958$	−5.59648	+	35.6046i	−0.180814	+	1.15033i
$959$	13.1547			0.424787
$960$		0			0
$961$	6.46825			0.208653
$962$	−4.34536	+	27.6450i	−0.140100	+	0.891311i
$963$		0			0
$964$	−0.762378	−	0.245739i	−0.0245545	−	0.00791472i
$965$	2.86966	−	2.86966i	0.0923776	−	0.0923776i
$966$		0			0
$967$	−6.45064			−0.207439			−0.103719	−	0.994607i	$-0.533074\pi$
$967$	−6.45064			−0.207439			−0.103719	+	0.994607i	$0.533074\pi$
$968$	5.86597	+	2.96295i	0.188540	+	0.0952329i
$969$		0			0
$970$	5.53588	+	7.60075i	0.177746	+	0.244045i
$971$	−16.4783	−	16.4783i	−0.528813	−	0.528813i	0.391405	−	0.920218i	$-0.371989\pi$
$971$	−16.4783	−	16.4783i	−0.528813	−	0.528813i	−0.920218	+	0.391405i	$0.871989\pi$
$972$		0			0
$973$	−7.20668	+	7.20668i	−0.231036	+	0.231036i
$974$	−6.14388	+	39.0871i	−0.196863	+	1.25243i
$975$		0			0
$976$	−27.8683	+	4.54783i	−0.892044	+	0.145572i
$977$			6.49980i			0.207947i	0.994580	+	0.103974i	$0.0331557\pi$
$977$			6.49980i			0.207947i	−0.994580	+	0.103974i	$0.966844\pi$
$978$		0			0
$979$	−25.4844	−	25.4844i	−0.814486	−	0.814486i
$980$	−11.4569	+	5.87141i	−0.365976	+	0.187555i
$981$		0			0
$982$	23.1938	−	16.8928i	0.740145	−	0.539072i
$983$		−	39.3984i		−	1.25661i	−0.777966	−	0.628306i	$-0.783749\pi$
$983$		−	39.3984i		−	1.25661i	0.777966	−	0.628306i	$-0.216251\pi$
$984$		0			0
$985$		−	5.95025i		−	0.189591i
$986$	10.3370	+	14.1927i	0.329197	+	0.451987i
$987$		0			0
$988$	−7.77961	−	2.50762i	−0.247502	−	0.0797780i
$989$	48.7179	+	48.7179i	1.54914	+	1.54914i
$990$		0			0
$991$		−	40.0421i		−	1.27198i	−0.771698	−	0.635989i	$-0.780592\pi$
$991$		−	40.0421i		−	1.27198i	0.771698	−	0.635989i	$-0.219408\pi$
$992$	−19.9275	−	19.6955i	−0.632698	−	0.625332i
$993$		0			0
$994$	−0.439017	−	0.0690066i	−0.0139248	−	0.00218876i
$995$	−5.80643	+	5.80643i	−0.184076	+	0.184076i
$996$		0			0
$997$	−11.8009	−	11.8009i	−0.373737	−	0.373737i	0.495099	−	0.868836i	$-0.335132\pi$
$997$	−11.8009	−	11.8009i	−0.373737	−	0.373737i	−0.868836	+	0.495099i	$0.835132\pi$
$998$	22.2816	−	16.2285i	0.705313	−	0.513703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bl.b.251.7	yes	24
3.2	odd	2	inner	720.2.bl.b.251.6	✓	24
4.3	odd	2		2880.2.bl.b.1871.2		24
12.11	even	2		2880.2.bl.b.1871.11		24
16.3	odd	4	inner	720.2.bl.b.611.6	yes	24
16.13	even	4		2880.2.bl.b.431.11		24
48.29	odd	4		2880.2.bl.b.431.2		24
48.35	even	4	inner	720.2.bl.b.611.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bl.b.251.6	✓	24	3.2	odd	2	inner
720.2.bl.b.251.7	yes	24	1.1	even	1	trivial
720.2.bl.b.611.6	yes	24	16.3	odd	4	inner
720.2.bl.b.611.7	yes	24	48.35	even	4	inner
2880.2.bl.b.431.2		24	48.29	odd	4
2880.2.bl.b.431.11		24	16.13	even	4
2880.2.bl.b.1871.2		24	4.3	odd	2
2880.2.bl.b.1871.11		24	12.11	even	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.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.219596 - 1.39706i) q^{2} +(-1.90356 - 0.613577i) q^{4} +(-0.707107 + 0.707107i) q^{5} -0.750417 q^{7} +(-1.27522 + 2.52464i) q^{8} +O(q^{10})\)	\(q+(0.219596 - 1.39706i) q^{2} +(-1.90356 - 0.613577i) q^{4} +(-0.707107 + 0.707107i) q^{5} -0.750417 q^{7} +(-1.27522 + 2.52464i) q^{8} +(0.832593 + 1.14315i) q^{10} +(2.08285 + 2.08285i) q^{11} +(-1.66519 + 1.66519i) q^{13} +(-0.164788 + 1.04838i) q^{14} +(3.24705 + 2.33596i) q^{16} +1.81077i q^{17} +(-1.22715 - 1.22715i) q^{19} +(1.77988 - 0.912152i) q^{20} +(3.36725 - 2.45248i) q^{22} +9.36690i q^{23} -1.00000i q^{25} +(1.96070 + 2.69203i) q^{26} +(1.42846 + 0.460439i) q^{28} +(4.84824 + 4.84824i) q^{29} -4.95295i q^{31} +(3.97651 - 4.02335i) q^{32} +(2.52975 + 0.397637i) q^{34} +(0.530625 - 0.530625i) q^{35} +(5.94167 + 5.94167i) q^{37} +(-1.98389 + 1.44493i) q^{38} +(-0.883477 - 2.68691i) q^{40} -2.47546 q^{41} +(5.20107 - 5.20107i) q^{43} +(-2.68683 - 5.24281i) q^{44} +(13.0861 + 2.05693i) q^{46} +4.43781 q^{47} -6.43687 q^{49} +(-1.39706 - 0.219596i) q^{50} +(4.19149 - 2.14805i) q^{52} +(-7.54780 + 7.54780i) q^{53} -2.94559 q^{55} +(0.956944 - 1.89453i) q^{56} +(7.83793 - 5.70863i) q^{58} +(0.472792 + 0.472792i) q^{59} +(-4.99164 + 4.99164i) q^{61} +(-6.91958 - 1.08765i) q^{62} +(-4.74764 - 6.43894i) q^{64} -2.35493i q^{65} +(1.95148 + 1.95148i) q^{67} +(1.11105 - 3.44690i) q^{68} +(-0.624792 - 0.857838i) q^{70} +0.418759i q^{71} +3.49594i q^{73} +(9.60564 - 6.99611i) q^{74} +(1.58300 + 3.08891i) q^{76} +(-1.56300 - 1.56300i) q^{77} -3.40726i q^{79} +(-3.94778 + 0.644237i) q^{80} +(-0.543601 + 3.45837i) q^{82} +(-0.548807 + 0.548807i) q^{83} +(-1.28041 - 1.28041i) q^{85} +(-6.12407 - 8.40834i) q^{86} +(-7.91453 + 2.60236i) q^{88} -12.2354 q^{89} +(1.24958 - 1.24958i) q^{91} +(5.74732 - 17.8304i) q^{92} +(0.974525 - 6.19989i) q^{94} +1.73546 q^{95} +6.64896 q^{97} +(-1.41351 + 8.99270i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4} - 8 q^{7}+O(q^{10}) \) 24 * q - 8 * q^4 - 8 * q^7	\( 24 q - 8 q^{4} - 8 q^{7} - 4 q^{16} - 24 q^{19} + 12 q^{22} - 20 q^{28} - 12 q^{34} + 8 q^{37} - 20 q^{40} + 48 q^{43} + 12 q^{46} + 24 q^{49} + 4 q^{52} + 24 q^{55} + 48 q^{58} + 40 q^{61} + 16 q^{64} - 40 q^{67} - 20 q^{70} - 84 q^{76} - 12 q^{82} + 24 q^{85} - 132 q^{88} + 40 q^{91} + 60 q^{94} - 16 q^{97}+O(q^{100}) \) 24 * q - 8 * q^4 - 8 * q^7 - 4 * q^16 - 24 * q^19 + 12 * q^22 - 20 * q^28 - 12 * q^34 + 8 * q^37 - 20 * q^40 + 48 * q^43 + 12 * q^46 + 24 * q^49 + 4 * q^52 + 24 * q^55 + 48 * q^58 + 40 * q^61 + 16 * q^64 - 40 * q^67 - 20 * q^70 - 84 * q^76 - 12 * q^82 + 24 * q^85 - 132 * q^88 + 40 * q^91 + 60 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more