LMFDB - Embedded newform 360.2.bs.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(113,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("360.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bs (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71407 + 0.248907i) q^{3} +(0.528278 - 2.17277i) q^{5} +(-0.980572 - 0.262743i) q^{7} +(2.87609 - 0.853289i) q^{9} +O(q^{10})$	\(q+(-1.71407 + 0.248907i) q^{3} +(0.528278 - 2.17277i) q^{5} +(-0.980572 - 0.262743i) q^{7} +(2.87609 - 0.853289i) q^{9} +(-3.66231 + 2.11444i) q^{11} +(-3.89065 + 1.04250i) q^{13} +(-0.364690 + 3.85578i) q^{15} +(-2.61068 - 2.61068i) q^{17} -0.281469i q^{19} +(1.74617 + 0.206290i) q^{21} +(-2.36908 - 8.84152i) q^{23} +(-4.44185 - 2.29565i) q^{25} +(-4.71744 + 2.17848i) q^{27} +(-2.93812 - 5.08896i) q^{29} +(-0.835561 + 1.44723i) q^{31} +(5.75117 - 4.53587i) q^{33} +(-1.08889 + 1.99175i) q^{35} +(-3.09788 + 3.09788i) q^{37} +(6.40937 - 2.75532i) q^{39} +(10.9685 + 6.33265i) q^{41} +(-2.26685 + 8.45998i) q^{43} +(-0.334624 - 6.69985i) q^{45} +(0.481889 - 1.79843i) q^{47} +(-5.16969 - 2.98472i) q^{49} +(5.12470 + 3.82507i) q^{51} +(1.91696 - 1.91696i) q^{53} +(2.65946 + 9.07436i) q^{55} +(0.0700596 + 0.482459i) q^{57} +(4.31085 - 7.46661i) q^{59} +(2.82244 + 4.88861i) q^{61} +(-3.04441 + 0.0810368i) q^{63} +(0.209760 + 9.00420i) q^{65} +(-1.50752 - 5.62615i) q^{67} +(6.26149 + 14.5653i) q^{69} -1.92890i q^{71} +(4.05914 + 4.05914i) q^{73} +(8.18505 + 2.82931i) q^{75} +(4.14671 - 1.11111i) q^{77} +(3.19722 - 1.84591i) q^{79} +(7.54380 - 4.90827i) q^{81} +(-0.950284 - 0.254628i) q^{83} +(-7.05156 + 4.29323i) q^{85} +(6.30282 + 7.99154i) q^{87} -6.94741 q^{89} +4.08897 q^{91} +(1.07199 - 2.68864i) q^{93} +(-0.611567 - 0.148694i) q^{95} +(3.20533 + 0.858865i) q^{97} +(-8.72891 + 9.20632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.71407	+	0.248907i	−0.989620	+	0.143706i
$3$	−1.71407	+	0.248907i	−0.989620	+	0.143706i
$4$		0			0
$5$	0.528278	−	2.17277i	0.236253	−	0.971692i
$5$	0.528278	−	2.17277i	0.236253	−	0.971692i
$6$		0			0
$7$	−0.980572	−	0.262743i	−0.370621	−	0.0993077i	0.0687007	−	0.997637i	$-0.478115\pi$
$7$	−0.980572	−	0.262743i	−0.370621	−	0.0993077i	−0.439322	+	0.898330i	$0.644781\pi$
$8$		0			0
$9$	2.87609	−	0.853289i	0.958697	−	0.284430i
$10$		0			0
$11$	−3.66231	+	2.11444i	−1.10423	+	0.637526i	−0.937328	−	0.348448i	$-0.886709\pi$
$11$	−3.66231	+	2.11444i	−1.10423	+	0.637526i	−0.166900	+	0.985974i	$0.553376\pi$
$12$		0			0
$13$	−3.89065	+	1.04250i	−1.07907	+	0.289136i	−0.754215	−	0.656627i	$-0.771982\pi$
$13$	−3.89065	+	1.04250i	−1.07907	+	0.289136i	−0.324856	+	0.945764i	$0.605316\pi$
$14$		0			0
$15$	−0.364690	+	3.85578i	−0.0941624	+	0.995557i
$16$		0			0
$17$	−2.61068	−	2.61068i	−0.633182	−	0.633182i	0.315683	−	0.948865i	$-0.397766\pi$
$17$	−2.61068	−	2.61068i	−0.633182	−	0.633182i	−0.948865	+	0.315683i	$0.897766\pi$
$18$		0			0
$19$		−	0.281469i		−	0.0645734i	−0.999479	−	0.0322867i	$-0.989721\pi$
$19$		−	0.281469i		−	0.0645734i	0.999479	−	0.0322867i	$-0.0102790\pi$
$20$		0			0
$21$	1.74617	+	0.206290i	0.381046	+	0.0450163i
$22$		0			0
$23$	−2.36908	−	8.84152i	−0.493987	−	1.84358i	−0.535631	−	0.844452i	$-0.679926\pi$
$23$	−2.36908	−	8.84152i	−0.493987	−	1.84358i	0.0416437	−	0.999133i	$-0.486741\pi$
$24$		0			0
$25$	−4.44185	−	2.29565i	−0.888369	−	0.459130i
$26$		0			0
$27$	−4.71744	+	2.17848i	−0.907872	+	0.419248i
$28$		0			0
$29$	−2.93812	−	5.08896i	−0.545594	−	0.944997i	−0.998569	−	0.0534738i	$-0.982971\pi$
$29$	−2.93812	−	5.08896i	−0.545594	−	0.944997i	0.452975	−	0.891523i	$-0.350363\pi$
$30$		0			0
$31$	−0.835561	+	1.44723i	−0.150071	+	0.259931i	−0.931253	−	0.364372i	$-0.881284\pi$
$31$	−0.835561	+	1.44723i	−0.150071	+	0.259931i	0.781182	+	0.624303i	$0.214617\pi$
$32$		0			0
$33$	5.75117	−	4.53587i	1.00115	−	0.789594i
$34$		0			0
$35$	−1.08889	+	1.99175i	−0.184057	+	0.336668i
$36$		0			0
$37$	−3.09788	+	3.09788i	−0.509289	+	0.509289i	−0.914308	−	0.405019i	$-0.867265\pi$
$37$	−3.09788	+	3.09788i	−0.509289	+	0.509289i	0.405019	+	0.914308i	$0.367265\pi$
$38$		0			0
$39$	6.40937	−	2.75532i	1.02632	−	0.441204i
$40$		0			0
$41$	10.9685	+	6.33265i	1.71299	+	0.988993i	0.930473	+	0.366360i	$0.119396\pi$
$41$	10.9685	+	6.33265i	1.71299	+	0.988993i	0.782514	+	0.622633i	$0.213937\pi$
$42$		0			0
$43$	−2.26685	+	8.45998i	−0.345691	+	1.29014i	0.546113	+	0.837712i	$0.316107\pi$
$43$	−2.26685	+	8.45998i	−0.345691	+	1.29014i	−0.891803	+	0.452423i	$0.850560\pi$
$44$		0			0
$45$	−0.334624	−	6.69985i	−0.0498828	−	0.998755i
$46$		0			0
$47$	0.481889	−	1.79843i	0.0702907	−	0.262329i	−0.921834	−	0.387586i	$-0.873309\pi$
$47$	0.481889	−	1.79843i	0.0702907	−	0.262329i	0.992124	+	0.125257i	$0.0399757\pi$
$48$		0			0
$49$	−5.16969	−	2.98472i	−0.738527	−	0.426389i
$50$		0			0
$51$	5.12470	+	3.82507i	0.717602	+	0.535618i
$52$		0			0
$53$	1.91696	−	1.91696i	0.263315	−	0.263315i	−0.563084	−	0.826399i	$-0.690385\pi$
$53$	1.91696	−	1.91696i	0.263315	−	0.263315i	0.826399	+	0.563084i	$0.190385\pi$
$54$		0			0
$55$	2.65946	+	9.07436i	0.358602	+	1.22359i
$56$		0			0
$57$	0.0700596	+	0.482459i	0.00927962	+	0.0639032i
$58$		0			0
$59$	4.31085	−	7.46661i	0.561225	−	0.972070i	−0.436165	−	0.899867i	$-0.643664\pi$
$59$	4.31085	−	7.46661i	0.561225	−	0.972070i	0.997390	−	0.0722032i	$-0.0230030\pi$
$60$		0			0
$61$	2.82244	+	4.88861i	0.361377	+	0.625923i	0.988188	−	0.153249i	$-0.0489735\pi$
$61$	2.82244	+	4.88861i	0.361377	+	0.625923i	−0.626811	+	0.779171i	$0.715640\pi$
$62$		0			0
$63$	−3.04441	+	0.0810368i	−0.383560	+	0.0102097i
$64$		0			0
$65$	0.209760	+	9.00420i	0.0260175	+	1.11683i
$66$		0			0
$67$	−1.50752	−	5.62615i	−0.184173	−	0.687344i	−0.994806	−	0.101789i	$-0.967543\pi$
$67$	−1.50752	−	5.62615i	−0.184173	−	0.687344i	0.810633	−	0.585555i	$-0.199123\pi$
$68$		0			0
$69$	6.26149	+	14.5653i	0.753795	+	1.75346i
$70$		0			0
$71$		−	1.92890i		−	0.228919i	−0.993428	−	0.114459i	$-0.963486\pi$
$71$		−	1.92890i		−	0.228919i	0.993428	−	0.114459i	$-0.0365136\pi$
$72$		0			0
$73$	4.05914	+	4.05914i	0.475087	+	0.475087i	0.903556	−	0.428470i	$-0.140947\pi$
$73$	4.05914	+	4.05914i	0.475087	+	0.475087i	−0.428470	+	0.903556i	$0.640947\pi$
$74$		0			0
$75$	8.18505	+	2.82931i	0.945128	+	0.326700i
$76$		0			0
$77$	4.14671	−	1.11111i	0.472562	−	0.126623i
$78$		0			0
$79$	3.19722	−	1.84591i	0.359715	−	0.207682i	−0.309241	−	0.950984i	$-0.600075\pi$
$79$	3.19722	−	1.84591i	0.359715	−	0.207682i	0.668956	+	0.743302i	$0.266742\pi$
$80$		0			0
$81$	7.54380	−	4.90827i	0.838200	−	0.545363i
$82$		0			0
$83$	−0.950284	−	0.254628i	−0.104307	−	0.0279490i	0.206288	−	0.978491i	$-0.433862\pi$
$83$	−0.950284	−	0.254628i	−0.104307	−	0.0279490i	−0.310595	+	0.950542i	$0.600528\pi$
$84$		0			0
$85$	−7.05156	+	4.29323i	−0.764849	+	0.465667i
$86$		0			0
$87$	6.30282	+	7.99154i	0.675733	+	0.856783i
$88$		0			0
$89$	−6.94741			−0.736423			−0.368212	−	0.929742i	$-0.620030\pi$
$89$	−6.94741			−0.736423			−0.368212	+	0.929742i	$0.620030\pi$
$90$		0			0
$91$	4.08897			0.428640
$92$		0			0
$93$	1.07199	−	2.68864i	0.111160	−	0.278799i
$94$		0			0
$95$	−0.611567	−	0.148694i	−0.0627455	−	0.0152557i
$96$		0			0
$97$	3.20533	+	0.858865i	0.325452	+	0.0872045i	0.417846	−	0.908518i	$-0.362785\pi$
$97$	3.20533	+	0.858865i	0.325452	+	0.0872045i	−0.0923940	+	0.995723i	$0.529452\pi$
$98$		0			0
$99$	−8.72891	+	9.20632i	−0.877289	+	0.925270i
$100$		0			0
$101$	5.37496	−	3.10323i	0.534828	−	0.308783i	−0.208152	−	0.978096i	$-0.566745\pi$
$101$	5.37496	−	3.10323i	0.534828	−	0.308783i	0.742980	+	0.669313i	$0.233412\pi$
$102$		0			0
$103$	15.5754	−	4.17342i	1.53469	−	0.411219i	0.610146	−	0.792289i	$-0.291111\pi$
$103$	15.5754	−	4.17342i	1.53469	−	0.411219i	0.924546	+	0.381070i	$0.124444\pi$
$104$		0			0
$105$	1.37068	−	3.68505i	0.133765	−	0.359624i
$106$		0			0
$107$	−9.51835	−	9.51835i	−0.920173	−	0.920173i	0.0768681	−	0.997041i	$-0.475508\pi$
$107$	−9.51835	−	9.51835i	−0.920173	−	0.920173i	−0.997041	+	0.0768681i	$0.975508\pi$
$108$		0			0
$109$		−	11.0583i		−	1.05919i	−0.848249	−	0.529597i	$-0.822343\pi$
$109$		−	11.0583i		−	1.05919i	0.848249	−	0.529597i	$-0.177657\pi$
$110$		0			0
$111$	4.53891	−	6.08108i	0.430814	−	0.577191i
$112$		0			0
$113$	−1.42849	−	5.33120i	−0.134381	−	0.501517i	−1.00000		0.000812894i	$-0.999741\pi$
$113$	−1.42849	−	5.33120i	−0.134381	−	0.501517i	0.865619	−	0.500704i	$-0.166925\pi$
$114$		0			0
$115$	−20.4621	+	0.476681i	−1.90810	+	0.0444507i
$116$		0			0
$117$	−10.3003	+	6.31815i	−0.952263	+	0.584114i
$118$		0			0
$119$	1.87402	+	3.24589i	0.171791	+	0.297551i
$120$		0			0
$121$	3.44167	−	5.96116i	0.312880	−	0.541923i
$122$		0			0
$123$	−20.3770	−	8.12449i	−1.83733	−	0.732561i
$124$		0			0
$125$	−7.33444	+	8.43836i	−0.656013	+	0.754750i
$126$		0			0
$127$	7.93844	−	7.93844i	0.704422	−	0.704422i	−0.260934	−	0.965357i	$-0.584031\pi$
$127$	7.93844	−	7.93844i	0.704422	−	0.704422i	0.965357	+	0.260934i	$0.0840306\pi$
$128$		0			0
$129$	1.77979	−	15.0653i	0.156702	−	1.32642i
$130$		0			0
$131$	−5.94678	−	3.43338i	−0.519573	−	0.299975i	0.217187	−	0.976130i	$-0.430312\pi$
$131$	−5.94678	−	3.43338i	−0.519573	−	0.299975i	−0.736760	+	0.676155i	$0.763645\pi$
$132$		0			0
$133$	−0.0739542	+	0.276001i	−0.00641264	+	0.0239323i
$134$		0			0
$135$	2.24121	+	11.4007i	0.192893	+	0.981220i
$136$		0			0
$137$	−5.49250	+	20.4983i	−0.469256	+	1.75129i	0.173125	+	0.984900i	$0.444614\pi$
$137$	−5.49250	+	20.4983i	−0.469256	+	1.75129i	−0.642381	+	0.766386i	$0.722053\pi$
$138$		0			0
$139$	11.7241	+	6.76891i	0.994425	+	0.574132i	0.906594	−	0.422004i	$-0.138673\pi$
$139$	11.7241	+	6.76891i	0.994425	+	0.574132i	0.0878311	+	0.996135i	$0.472006\pi$
$140$		0			0
$141$	−0.378350	+	3.20259i	−0.0318628	+	0.269707i
$142$		0			0
$143$	12.0445	−	12.0445i	1.00721	−	1.00721i
$144$		0			0
$145$	−12.6093	+	3.69546i	−1.04714	+	0.306891i
$146$		0			0
$147$	9.60414	+	3.82926i	0.792136	+	0.315832i
$148$		0			0
$149$	1.79849	−	3.11508i	0.147338	−	0.255198i	−0.782905	−	0.622142i	$-0.786263\pi$
$149$	1.79849	−	3.11508i	0.147338	−	0.255198i	0.930243	+	0.366944i	$0.119596\pi$
$150$		0			0
$151$	2.41050	+	4.17511i	0.196164	+	0.339766i	0.947281	−	0.320403i	$-0.103818\pi$
$151$	2.41050	+	4.17511i	0.196164	+	0.339766i	−0.751117	+	0.660169i	$0.770485\pi$
$152$		0			0
$153$	−9.73620	−	5.28088i	−0.787125	−	0.426934i
$154$		0			0
$155$	2.70310	+	2.58002i	0.217118	+	0.207232i
$156$		0			0
$157$	2.13261	+	7.95901i	0.170201	+	0.635198i	0.997319	+	0.0731706i	$0.0233118\pi$
$157$	2.13261	+	7.95901i	0.170201	+	0.635198i	−0.827119	+	0.562027i	$0.810022\pi$
$158$		0			0
$159$	−2.80867	+	3.76296i	−0.222742	+	0.298422i
$160$		0			0
$161$			9.29221i			0.732329i
$162$		0			0
$163$	−4.95634	−	4.95634i	−0.388210	−	0.388210i	0.485838	−	0.874049i	$-0.338514\pi$
$163$	−4.95634	−	4.95634i	−0.388210	−	0.388210i	−0.874049	+	0.485838i	$0.838514\pi$
$164$		0			0
$165$	−6.81718	−	14.8922i	−0.530717	−	1.15935i
$166$		0			0
$167$	13.8848	−	3.72041i	1.07443	−	0.287894i	0.322121	−	0.946699i	$-0.395604\pi$
$167$	13.8848	−	3.72041i	1.07443	−	0.287894i	0.752314	+	0.658805i	$0.228938\pi$
$168$		0			0
$169$	2.79200	−	1.61196i	0.214769	−	0.123997i
$170$		0			0
$171$	−0.240174	−	0.809531i	−0.0183666	−	0.0619064i
$172$		0			0
$173$	14.0437	+	3.76299i	1.06772	+	0.286095i	0.749556	−	0.661941i	$-0.230267\pi$
$173$	14.0437	+	3.76299i	1.06772	+	0.286095i	0.318164	+	0.948036i	$0.396934\pi$
$174$		0			0
$175$	3.75238	+	3.41812i	0.283653	+	0.258385i
$176$		0			0
$177$	−5.53062	+	13.8713i	−0.415707	+	1.04263i
$178$		0			0
$179$	−21.8707			−1.63469			−0.817347	−	0.576146i	$-0.804556\pi$
$179$	−21.8707			−1.63469			−0.817347	+	0.576146i	$0.804556\pi$
$180$		0			0
$181$	−23.8617			−1.77363			−0.886814	−	0.462127i	$-0.847086\pi$
$181$	−23.8617			−1.77363			−0.886814	+	0.462127i	$0.847086\pi$
$182$		0			0
$183$	−6.05468	−	7.67691i	−0.447575	−	0.567494i
$184$		0			0
$185$	5.09444	+	8.36752i	0.374551	+	0.615193i
$186$		0			0
$187$	15.0812	+	4.04100i	1.10285	+	0.295507i
$188$		0			0
$189$	5.19817	−	0.896677i	0.378111	−	0.0652237i
$190$		0			0
$191$	−14.5962	+	8.42713i	−1.05615	+	0.609766i	−0.924363	−	0.381513i	$-0.875403\pi$
$191$	−14.5962	+	8.42713i	−1.05615	+	0.609766i	−0.131782	+	0.991279i	$0.542070\pi$
$192$		0			0
$193$	−23.6162	+	6.32793i	−1.69993	+	0.455494i	−0.972921	−	0.231136i	$-0.925756\pi$
$193$	−23.6162	+	6.32793i	−1.69993	+	0.455494i	−0.727007	+	0.686631i	$0.759089\pi$
$194$		0			0
$195$	−2.60075	−	15.3816i	−0.186244	−	1.10150i
$196$		0			0
$197$	−13.2754	−	13.2754i	−0.945832	−	0.945832i	0.0527741	−	0.998606i	$-0.483194\pi$
$197$	−13.2754	−	13.2754i	−0.945832	−	0.945832i	−0.998606	+	0.0527741i	$0.983194\pi$
$198$		0			0
$199$		−	25.3515i		−	1.79712i	−0.438852	−	0.898559i	$-0.644615\pi$
$199$		−	25.3515i		−	1.79712i	0.438852	−	0.898559i	$-0.355385\pi$
$200$		0			0
$201$	3.98439	+	9.26840i	0.281037	+	0.653743i
$202$		0			0
$203$	1.54394	+	5.76207i	0.108363	+	0.404418i
$204$		0			0
$205$	19.5538	−	20.4865i	1.36569	−	1.43084i
$206$		0			0
$207$	−14.3581	−	23.4075i	−0.997954	−	1.62693i
$208$		0			0
$209$	0.595148	+	1.03083i	0.0411673	+	0.0713038i
$210$		0			0
$211$	6.35077	−	10.9999i	0.437205	−	0.757261i	−0.560268	−	0.828312i	$-0.689302\pi$
$211$	6.35077	−	10.9999i	0.437205	−	0.757261i	0.997473	+	0.0710502i	$0.0226350\pi$
$212$		0			0
$213$	0.480117	+	3.30628i	0.0328971	+	0.226543i
$214$		0			0
$215$	17.1841	+	9.39455i	1.17194	+	0.640703i
$216$		0			0
$217$	1.19958	−	1.19958i	0.0814327	−	0.0814327i
$218$		0			0
$219$	−7.96801	−	5.94732i	−0.538428	−	0.401882i
$220$		0			0
$221$	12.8788	+	7.43560i	0.866324	+	0.500172i
$222$		0			0
$223$	1.71629	−	6.40529i	0.114931	−	0.428930i	−0.884350	−	0.466824i	$-0.845398\pi$
$223$	1.71629	−	6.40529i	0.114931	−	0.428930i	0.999282	+	0.0378938i	$0.0120648\pi$
$224$		0			0
$225$	−14.7340	−	2.81232i	−0.982267	−	0.187488i
$226$		0			0
$227$	−0.0441550	+	0.164789i	−0.00293067	+	0.0109374i	−0.967376	−	0.253346i	$-0.918469\pi$
$227$	−0.0441550	+	0.164789i	−0.00293067	+	0.0109374i	0.964445	+	0.264284i	$0.0851355\pi$
$228$		0			0
$229$	11.7967	+	6.81084i	0.779550	+	0.450073i	0.836271	−	0.548317i	$-0.184731\pi$
$229$	11.7967	+	6.81084i	0.779550	+	0.450073i	−0.0567210	+	0.998390i	$0.518065\pi$
$230$		0			0
$231$	−6.83120	+	2.93667i	−0.449460	+	0.193218i
$232$		0			0
$233$	5.81013	−	5.81013i	0.380634	−	0.380634i	−0.490697	−	0.871331i	$-0.663258\pi$
$233$	5.81013	−	5.81013i	0.380634	−	0.380634i	0.871331	+	0.490697i	$0.163258\pi$
$234$		0			0
$235$	−3.65301	−	1.99711i	−0.238296	−	0.130277i
$236$		0			0
$237$	−5.02080	+	3.95984i	−0.326136	+	0.257219i
$238$		0			0
$239$	−10.5650	+	18.2991i	−0.683394	+	1.18367i	0.290544	+	0.956861i	$0.406164\pi$
$239$	−10.5650	+	18.2991i	−0.683394	+	1.18367i	−0.973939	+	0.226812i	$0.927170\pi$
$240$		0			0
$241$	−14.2304	−	24.6478i	−0.916662	−	1.58771i	−0.804450	−	0.594021i	$-0.797540\pi$
$241$	−14.2304	−	24.6478i	−0.916662	−	1.58771i	−0.112212	−	0.993684i	$-0.535794\pi$
$242$		0			0
$243$	−11.7089	+	10.2908i	−0.751127	+	0.660157i
$244$		0			0
$245$	−9.21614	+	9.65578i	−0.588798	+	0.616885i
$246$		0			0
$247$	0.293430	+	1.09510i	0.0186705	+	0.0696793i
$248$		0			0
$249$	1.69224	+	0.199919i	0.107241	+	0.0126693i
$250$		0			0
$251$			3.25994i			0.205766i	0.994693	+	0.102883i	$0.0328067\pi$
$251$			3.25994i			0.205766i	−0.994693	+	0.102883i	$0.967193\pi$
$252$		0			0
$253$	27.3711	+	27.3711i	1.72081	+	1.72081i
$254$		0			0
$255$	11.0183	−	9.11409i	0.689991	−	0.570747i
$256$		0			0
$257$	−27.9940	+	7.50097i	−1.74622	+	0.467898i	−0.983812	−	0.179203i	$-0.942648\pi$
$257$	−27.9940	+	7.50097i	−1.74622	+	0.467898i	−0.762405	+	0.647100i	$0.775982\pi$
$258$		0			0
$259$	3.85165	−	2.22375i	0.239330	−	0.138177i
$260$		0			0
$261$	−12.7926	−	12.1293i	−0.791845	−	0.750783i
$262$		0			0
$263$	18.4961	+	4.95600i	1.14052	+	0.305600i	0.779158	−	0.626827i	$-0.215647\pi$
$263$	18.4961	+	4.95600i	1.14052	+	0.305600i	0.361357	+	0.932427i	$0.382314\pi$
$264$		0			0
$265$	−3.15243	−	5.17780i	−0.193652	−	0.318070i
$266$		0			0
$267$	11.9084	−	1.72926i	0.728780	−	0.105829i
$268$		0			0
$269$	−4.67111			−0.284803			−0.142401	−	0.989809i	$-0.545482\pi$
$269$	−4.67111			−0.284803			−0.142401	+	0.989809i	$0.545482\pi$
$270$		0			0
$271$	−13.0525			−0.792886			−0.396443	−	0.918059i	$-0.629756\pi$
$271$	−13.0525			−0.792886			−0.396443	+	0.918059i	$0.629756\pi$
$272$		0			0
$273$	−7.00879	+	1.01777i	−0.424191	+	0.0615983i
$274$		0			0
$275$	21.1214	−	0.984614i	1.27367	−	0.0593745i
$276$		0			0
$277$	24.5784	+	6.58576i	1.47677	+	0.395700i	0.905248	−	0.424885i	$-0.139685\pi$
$277$	24.5784	+	6.58576i	1.47677	+	0.395700i	0.571525	+	0.820585i	$0.306352\pi$
$278$		0			0
$279$	−1.16824	+	4.87535i	−0.0699408	+	0.291880i
$280$		0			0
$281$	2.62412	−	1.51504i	0.156542	−	0.0903796i	−0.419683	−	0.907671i	$-0.637859\pi$
$281$	2.62412	−	1.51504i	0.156542	−	0.0903796i	0.576225	+	0.817291i	$0.304525\pi$
$282$		0			0
$283$	−7.77609	+	2.08360i	−0.462241	+	0.123857i	−0.482421	−	0.875939i	$-0.660243\pi$
$283$	−7.77609	+	2.08360i	−0.462241	+	0.123857i	0.0201806	+	0.999796i	$0.493576\pi$
$284$		0			0
$285$	1.08528	+	0.102649i	0.0642865	+	0.00608039i
$286$		0			0
$287$	−9.09151	−	9.09151i	−0.536655	−	0.536655i
$288$		0			0
$289$		−	3.36874i		−	0.198161i
$290$		0			0
$291$	−5.70794	−	0.674329i	−0.334605	−	0.0395299i
$292$		0			0
$293$	−2.13277	−	7.95962i	−0.124598	−	0.465006i	0.875227	−	0.483712i	$-0.160712\pi$
$293$	−2.13277	−	7.95962i	−0.124598	−	0.465006i	−0.999825	+	0.0187062i	$0.994045\pi$
$294$		0			0
$295$	−13.9459	−	13.3109i	−0.811961	−	0.774992i
$296$		0			0
$297$	12.6705	−	17.9530i	0.735216	−	1.04174i
$298$		0			0
$299$	18.4345	+	31.9295i	1.06609	+	1.84653i
$300$		0			0
$301$	4.44561	−	7.70002i	0.256241	−	0.443822i
$302$		0			0
$303$	−8.44065	+	6.65703i	−0.484903	+	0.382436i
$304$		0			0
$305$	12.1129	−	3.54997i	0.693580	−	0.203271i
$306$		0			0
$307$	−1.15439	+	1.15439i	−0.0658844	+	0.0658844i	−0.739281	−	0.673397i	$-0.764835\pi$
$307$	−1.15439	+	1.15439i	−0.0658844	+	0.0658844i	0.673397	+	0.739281i	$0.264835\pi$
$308$		0			0
$309$	−25.6586	+	11.0304i	−1.45967	+	0.627496i
$310$		0			0
$311$	−4.86996	−	2.81167i	−0.276150	−	0.159435i	0.355529	−	0.934665i	$-0.384301\pi$
$311$	−4.86996	−	2.81167i	−0.276150	−	0.159435i	−0.631679	+	0.775230i	$0.717634\pi$
$312$		0			0
$313$	−3.94609	+	14.7270i	−0.223046	+	0.832420i	0.760131	+	0.649769i	$0.225134\pi$
$313$	−3.94609	+	14.7270i	−0.223046	+	0.832420i	−0.983178	+	0.182651i	$0.941532\pi$
$314$		0			0
$315$	−1.43222	+	6.65761i	−0.0806964	+	0.375114i
$316$		0			0
$317$	7.13440	−	26.6259i	0.400708	−	1.49546i	−0.411129	−	0.911577i	$-0.634865\pi$
$317$	7.13440	−	26.6259i	0.400708	−	1.49546i	0.811837	−	0.583884i	$-0.198468\pi$
$318$		0			0
$319$	21.5206	+	12.4249i	1.20492	+	0.695661i
$320$		0			0
$321$	18.6843	+	13.9460i	1.04286	+	0.778387i
$322$		0			0
$323$	−0.734825	+	0.734825i	−0.0408867	+	0.0408867i
$324$		0			0
$325$	19.6749	+	4.30096i	1.09136	+	0.238574i
$326$		0			0
$327$	2.75249	+	18.9548i	0.152213	+	1.04820i
$328$		0			0
$329$	−0.945053	+	1.63688i	−0.0521025	+	0.0902441i
$330$		0			0
$331$	12.9037	+	22.3499i	0.709253	+	1.22846i	0.965135	+	0.261754i	$0.0843010\pi$
$331$	12.9037	+	22.3499i	0.709253	+	1.22846i	−0.255881	+	0.966708i	$0.582366\pi$
$332$		0			0
$333$	−6.26640	+	11.5532i	−0.343397	+	0.633110i
$334$		0			0
$335$	−13.0207	+	0.303328i	−0.711398	+	0.0165726i
$336$		0			0
$337$	−6.30633	−	23.5355i	−0.343528	−	1.28206i	−0.894323	−	0.447422i	$-0.852342\pi$
$337$	−6.30633	−	23.5355i	−0.343528	−	1.28206i	0.550795	−	0.834640i	$-0.314324\pi$
$338$		0			0
$339$	3.77551	+	8.78250i	0.205057	+	0.477000i
$340$		0			0
$341$		−	7.06696i		−	0.382697i
$342$		0			0
$343$	9.30984	+	9.30984i	0.502684	+	0.502684i
$344$		0			0
$345$	34.9549	−	5.91022i	1.88191	−	0.318196i
$346$		0			0
$347$	1.43538	−	0.384609i	0.0770552	−	0.0206469i	−0.220085	−	0.975481i	$-0.570634\pi$
$347$	1.43538	−	0.384609i	0.0770552	−	0.0206469i	0.297141	+	0.954834i	$0.403967\pi$
$348$		0			0
$349$	11.0207	−	6.36282i	0.589926	−	0.340594i	−0.175142	−	0.984543i	$-0.556039\pi$
$349$	11.0207	−	6.36282i	0.589926	−	0.340594i	0.765068	+	0.643949i	$0.222705\pi$
$350$		0			0
$351$	16.0828	−	13.3936i	0.858438	−	0.714897i
$352$		0			0
$353$	13.6377	+	3.65422i	0.725862	+	0.194494i	0.602786	−	0.797903i	$-0.294057\pi$
$353$	13.6377	+	3.65422i	0.725862	+	0.194494i	0.123077	+	0.992397i	$0.460724\pi$
$354$		0			0
$355$	−4.19106	−	1.01900i	−0.222438	−	0.0540827i
$356$		0			0
$357$	−4.02013	−	5.09724i	−0.212768	−	0.269775i
$358$		0			0
$359$	−23.2014			−1.22452			−0.612262	−	0.790655i	$-0.709740\pi$
$359$	−23.2014			−1.22452			−0.612262	+	0.790655i	$0.709740\pi$
$360$		0			0
$361$	18.9208			0.995830
$362$		0			0
$363$	−4.41551	+	11.0745i	−0.231754	+	0.581261i
$364$		0			0
$365$	10.9639	−	6.67522i	0.573878	−	0.349397i
$366$		0			0
$367$	−10.2481	−	2.74598i	−0.534948	−	0.143339i	−0.0187758	−	0.999824i	$-0.505977\pi$
$367$	−10.2481	−	2.74598i	−0.534948	−	0.143339i	−0.516172	+	0.856485i	$0.672644\pi$
$368$		0			0
$369$	36.9499	+	8.85400i	1.92353	+	0.460921i
$370$		0			0
$371$	−2.38339	+	1.37605i	−0.123739	+	0.0714409i
$372$		0			0
$373$	19.0303	−	5.09915i	0.985351	−	0.264024i	0.270054	−	0.962845i	$-0.412958\pi$
$373$	19.0303	−	5.09915i	0.985351	−	0.264024i	0.715296	+	0.698821i	$0.246292\pi$
$374$		0			0
$375$	10.4714	−	16.2896i	0.540741	−	0.841189i
$376$		0			0
$377$	16.7364	+	16.7364i	0.861968	+	0.861968i
$378$		0			0
$379$		−	10.5293i		−	0.540852i	−0.962741	−	0.270426i	$-0.912835\pi$
$379$		−	10.5293i		−	0.540852i	0.962741	−	0.270426i	$-0.0871646\pi$
$380$		0			0
$381$	−11.6311	+	15.5830i	−0.595881	+	0.798341i
$382$		0			0
$383$	7.55008	+	28.1773i	0.385791	+	1.43979i	0.836916	+	0.547331i	$0.184356\pi$
$383$	7.55008	+	28.1773i	0.385791	+	1.43979i	−0.451125	+	0.892461i	$0.648977\pi$
$384$		0			0
$385$	−0.223565	−	9.59682i	−0.0113940	−	0.489099i
$386$		0			0
$387$	0.699153	+	26.2659i	0.0355399	+	1.33517i
$388$		0			0
$389$	−9.74483	−	16.8785i	−0.494082	−	0.855776i	0.505894	−	0.862595i	$-0.331163\pi$
$389$	−9.74483	−	16.8785i	−0.494082	−	0.855776i	−0.999977	+	0.00681963i	$0.997829\pi$
$390$		0			0
$391$	−16.8975	+	29.2673i	−0.854541	+	1.48011i
$392$		0			0
$393$	11.0478	+	4.40486i	0.557288	+	0.222196i
$394$		0			0
$395$	−2.32173	−	7.92197i	−0.116819	−	0.398597i
$396$		0			0
$397$	0.214255	−	0.214255i	0.0107532	−	0.0107532i	−0.701710	−	0.712463i	$-0.747580\pi$
$397$	0.214255	−	0.214255i	0.0107532	−	0.0107532i	0.712463	+	0.701710i	$0.247580\pi$
$398$		0			0
$399$	0.0580644	−	0.491493i	0.00290686	−	0.0246054i
$400$		0			0
$401$	−10.5015	−	6.06307i	−0.524422	−	0.302775i	0.214320	−	0.976764i	$-0.431247\pi$
$401$	−10.5015	−	6.06307i	−0.524422	−	0.302775i	−0.738742	+	0.673988i	$0.764580\pi$
$402$		0			0
$403$	1.74214	−	6.50174i	0.0867820	−	0.323875i
$404$		0			0
$405$	−6.67932	−	18.9839i	−0.331898	−	0.943315i
$406$		0			0
$407$	4.79513	−	17.8957i	0.237686	−	0.887056i
$408$		0			0
$409$	−16.8210	−	9.71162i	−0.831745	−	0.480208i	0.0227044	−	0.999742i	$-0.492772\pi$
$409$	−16.8210	−	9.71162i	−0.831745	−	0.480208i	−0.854450	+	0.519534i	$0.826106\pi$
$410$		0			0
$411$	4.31238	−	36.5027i	0.212714	−	1.80054i
$412$		0			0
$413$	−6.18890	+	6.18890i	−0.304536	+	0.304536i
$414$		0			0
$415$	−1.05526	+	1.93023i	−0.0518008	+	0.0947514i
$416$		0			0
$417$	−21.7808	−	8.68420i	−1.06661	−	0.425267i
$418$		0			0
$419$	−0.242058	+	0.419257i	−0.0118253	+	0.0204820i	−0.871878	−	0.489724i	$-0.837098\pi$
$419$	−0.242058	+	0.419257i	−0.0118253	+	0.0204820i	0.860052	+	0.510206i	$0.170431\pi$
$420$		0			0
$421$	−8.06103	−	13.9621i	−0.392871	−	0.680472i	0.599956	−	0.800033i	$-0.295185\pi$
$421$	−8.06103	−	13.9621i	−0.392871	−	0.680472i	−0.992827	+	0.119561i	$0.961851\pi$
$422$		0			0
$423$	−0.148627	−	5.58365i	−0.00722648	−	0.271486i
$424$		0			0
$425$	5.60302	+	17.5894i	0.271786	+	0.853212i
$426$		0			0
$427$	−1.48316	−	5.53521i	−0.0717750	−	0.267868i
$428$		0			0
$429$	−17.6471	+	23.6430i	−0.852012	+	1.14150i
$430$		0			0
$431$			20.5311i			0.988949i	0.869192	+	0.494474i	$0.164639\pi$
$431$			20.5311i			0.988949i	−0.869192	+	0.494474i	$0.835361\pi$
$432$		0			0
$433$	18.0908	+	18.0908i	0.869389	+	0.869389i	0.992405	−	0.123016i	$-0.0392566\pi$
$433$	18.0908	+	18.0908i	0.869389	+	0.869389i	−0.123016	+	0.992405i	$0.539257\pi$
$434$		0			0
$435$	20.6934	−	9.47282i	0.992173	−	0.454187i
$436$		0			0
$437$	−2.48862	+	0.666822i	−0.119047	+	0.0318984i
$438$		0			0
$439$	−31.7433	+	18.3270i	−1.51502	+	0.874699i	−0.515179	+	0.857083i	$0.672274\pi$
$439$	−31.7433	+	18.3270i	−1.51502	+	0.874699i	−0.999845	+	0.0176165i	$0.994392\pi$
$440$		0			0
$441$	−17.4153	−	4.17309i	−0.829301	−	0.198719i
$442$		0			0
$443$	−9.05102	−	2.42521i	−0.430027	−	0.115225i	0.0373118	−	0.999304i	$-0.488121\pi$
$443$	−9.05102	−	2.42521i	−0.430027	−	0.115225i	−0.467339	+	0.884078i	$0.654787\pi$
$444$		0			0
$445$	−3.67016	+	15.0951i	−0.173982	+	0.715577i
$446$		0			0
$447$	−2.30738	+	5.78714i	−0.109136	+	0.273722i
$448$		0			0
$449$	6.35277			0.299806			0.149903	−	0.988701i	$-0.452104\pi$
$449$	6.35277			0.299806			0.149903	+	0.988701i	$0.452104\pi$
$450$		0			0
$451$	−53.5599			−2.52204
$452$		0			0
$453$	−5.17099	−	6.55646i	−0.242954	−	0.308049i
$454$		0			0
$455$	2.16011	−	8.88438i	0.101268	−	0.416506i
$456$		0			0
$457$	14.9472	+	4.00508i	0.699199	+	0.187350i	0.590872	−	0.806766i	$-0.298784\pi$
$457$	14.9472	+	4.00508i	0.699199	+	0.187350i	0.108327	+	0.994115i	$0.465451\pi$
$458$		0			0
$459$	18.0030	+	6.62841i	0.840308	+	0.309388i
$460$		0			0
$461$	5.28581	−	3.05176i	0.246185	−	0.142135i	−0.371831	−	0.928300i	$-0.621270\pi$
$461$	5.28581	−	3.05176i	0.246185	−	0.142135i	0.618016	+	0.786166i	$0.287937\pi$
$462$		0			0
$463$	−24.8625	+	6.66190i	−1.15546	+	0.309605i	−0.785151	−	0.619304i	$-0.787415\pi$
$463$	−24.8625	+	6.66190i	−1.15546	+	0.309605i	−0.370309	+	0.928909i	$0.620748\pi$
$464$		0			0
$465$	−5.27549	−	3.74953i	−0.244645	−	0.173880i
$466$		0			0
$467$	24.0615	+	24.0615i	1.11343	+	1.11343i	0.992683	+	0.120749i	$0.0385296\pi$
$467$	24.0615	+	24.0615i	1.11343	+	1.11343i	0.120749	+	0.992683i	$0.461470\pi$
$468$		0			0
$469$			5.91294i			0.273034i
$470$		0			0
$471$	−5.63650	−	13.1115i	−0.259716	−	0.604146i
$472$		0			0
$473$	−9.58620	−	35.7762i	−0.440774	−	1.64499i
$474$		0			0
$475$	−0.646155	+	1.25024i	−0.0296476	+	0.0573651i
$476$		0			0
$477$	3.87763	−	7.14908i	0.177545	−	0.327334i
$478$		0			0
$479$	−15.9283	−	27.5886i	−0.727781	−	1.26055i	−0.957819	−	0.287373i	$-0.907218\pi$
$479$	−15.9283	−	27.5886i	−0.727781	−	1.26055i	0.230037	−	0.973182i	$-0.426115\pi$
$480$		0			0
$481$	8.82324	−	15.2823i	0.402305	−	0.696813i
$482$		0			0
$483$	−2.31289	−	15.9275i	−0.105240	−	0.724727i
$484$		0			0
$485$	3.55942	−	6.51072i	0.161625	−	0.295636i
$486$		0			0
$487$	−0.615541	+	0.615541i	−0.0278928	+	0.0278928i	−0.720916	−	0.693023i	$-0.756278\pi$
$487$	−0.615541	+	0.615541i	−0.0278928	+	0.0278928i	0.693023	+	0.720916i	$0.256278\pi$
$488$		0			0
$489$	9.72919	+	7.26186i	0.439969	+	0.328393i
$490$		0			0
$491$	−21.5023	−	12.4143i	−0.970384	−	0.560252i	−0.0710310	−	0.997474i	$-0.522629\pi$
$491$	−21.5023	−	12.4143i	−0.970384	−	0.560252i	−0.899353	+	0.437222i	$0.855962\pi$
$492$		0			0
$493$	−5.61517	+	20.9561i	−0.252895	+	0.943816i
$494$		0			0
$495$	15.3919	+	23.8294i	0.691815	+	1.07105i
$496$		0			0
$497$	−0.506806	+	1.89143i	−0.0227334	+	0.0848421i
$498$		0			0
$499$	7.45894	+	4.30642i	0.333908	+	0.192782i	0.657575	−	0.753389i	$-0.271582\pi$
$499$	7.45894	+	4.30642i	0.333908	+	0.192782i	−0.323667	+	0.946171i	$0.604916\pi$
$500$		0			0
$501$	−22.8734	+	9.83306i	−1.02191	+	0.439309i
$502$		0			0
$503$	17.0273	−	17.0273i	0.759208	−	0.759208i	−0.216970	−	0.976178i	$-0.569617\pi$
$503$	17.0273	−	17.0273i	0.759208	−	0.759208i	0.976178	+	0.216970i	$0.0696173\pi$
$504$		0			0
$505$	−3.90314	−	13.3179i	−0.173687	−	0.592639i
$506$		0			0
$507$	−4.38446	+	3.45796i	−0.194721	+	0.153574i
$508$		0			0
$509$	2.76039	−	4.78114i	0.122352	−	0.211920i	−0.798343	−	0.602204i	$-0.794290\pi$
$509$	2.76039	−	4.78114i	0.122352	−	0.211920i	0.920695	+	0.390283i	$0.127623\pi$
$510$		0			0
$511$	−2.91377	−	5.04679i	−0.128897	−	0.223257i
$512$		0			0
$513$	0.613174	+	1.32781i	0.0270723	+	0.0586244i
$514$		0			0
$515$	−0.839732	−	36.0465i	−0.0370030	−	1.58840i
$516$		0			0
$517$	2.03785	+	7.60534i	0.0896244	+	0.334483i
$518$		0			0
$519$	−25.0085	−	2.95447i	−1.09775	−	0.129687i
$520$		0			0
$521$		−	20.1806i		−	0.884126i	−0.896984	−	0.442063i	$-0.854247\pi$
$521$		−	20.1806i		−	0.884126i	0.896984	−	0.442063i	$-0.145753\pi$
$522$		0			0
$523$	0.0855088	+	0.0855088i	0.00373904	+	0.00373904i	0.708974	−	0.705235i	$-0.249158\pi$
$523$	0.0855088	+	0.0855088i	0.00373904	+	0.00373904i	−0.705235	+	0.708974i	$0.749158\pi$
$524$		0			0
$525$	−7.28265	−	4.92491i	−0.317841	−	0.214941i
$526$		0			0
$527$	5.95964	−	1.59688i	0.259606	−	0.0695612i
$528$		0			0
$529$	−52.6414	+	30.3925i	−2.28876	+	1.32141i
$530$		0			0
$531$	6.02722	−	25.1530i	0.261559	−	1.09155i
$532$		0			0
$533$	−49.2762	−	13.2035i	−2.13439	−	0.571908i
$534$		0			0
$535$	−25.7095	+	15.6528i	−1.11152	+	0.676731i
$536$		0			0
$537$	37.4880	−	5.44377i	1.61773	−	0.234916i
$538$		0			0
$539$	25.2440			1.08734
$540$		0			0
$541$	−16.7856			−0.721671			−0.360835	−	0.932630i	$-0.617508\pi$
$541$	−16.7856			−0.721671			−0.360835	+	0.932630i	$0.617508\pi$
$542$		0			0
$543$	40.9007	−	5.93934i	1.75522	−	0.254882i
$544$		0			0
$545$	−24.0272	−	5.84186i	−1.02921	−	0.250238i
$546$		0			0
$547$	8.58350	+	2.29994i	0.367004	+	0.0983384i	0.437608	−	0.899166i	$-0.355826\pi$
$547$	8.58350	+	2.29994i	0.367004	+	0.0983384i	−0.0706037	+	0.997504i	$0.522493\pi$
$548$		0			0
$549$	12.2890	+	11.6517i	0.524482	+	0.497284i
$550$		0			0
$551$	−1.43239	+	0.826989i	−0.0610217	+	0.0352309i
$552$		0			0
$553$	−3.62010	+	0.970004i	−0.153942	+	0.0412488i
$554$		0			0
$555$	−10.8150	−	13.0745i	−0.459070	−	0.554982i
$556$		0			0
$557$	0.716676	+	0.716676i	0.0303665	+	0.0303665i	0.722127	−	0.691760i	$-0.243165\pi$
$557$	0.716676	+	0.716676i	0.0303665	+	0.0303665i	−0.691760	+	0.722127i	$0.743165\pi$
$558$		0			0
$559$		−	35.2780i		−	1.49210i
$560$		0			0
$561$	−26.8561	−	3.17275i	−1.13387	−	0.133954i
$562$		0			0
$563$	7.55543	+	28.1972i	0.318423	+	1.18837i	0.920760	+	0.390130i	$0.127570\pi$
$563$	7.55543	+	28.1972i	0.318423	+	1.18837i	−0.602337	+	0.798242i	$0.705764\pi$
$564$		0			0
$565$	−12.3381	+	0.287426i	−0.519067	+	0.0120921i
$566$		0			0
$567$	−8.68685	+	2.83083i	−0.364814	+	0.118884i
$568$		0			0
$569$	−15.1381	−	26.2200i	−0.634623	−	1.09920i	−0.986595	−	0.163189i	$-0.947822\pi$
$569$	−15.1381	−	26.2200i	−0.634623	−	1.09920i	0.351971	−	0.936011i	$-0.385511\pi$
$570$		0			0
$571$	15.2794	−	26.4647i	0.639423	−	1.10751i	−0.346136	−	0.938184i	$-0.612506\pi$
$571$	15.2794	−	26.4647i	0.639423	−	1.10751i	0.985560	−	0.169329i	$-0.0541602\pi$
$572$		0			0
$573$	22.9214	−	18.0778i	0.957555	−	0.755211i
$574$		0			0
$575$	−9.77396	+	44.7113i	−0.407602	+	1.86459i
$576$		0			0
$577$	−7.11358	+	7.11358i	−0.296142	+	0.296142i	−0.839501	−	0.543359i	$-0.817152\pi$
$577$	−7.11358	+	7.11358i	−0.296142	+	0.296142i	0.543359	+	0.839501i	$0.317152\pi$
$578$		0			0
$579$	38.9047	−	16.7248i	1.61683	−	0.695057i
$580$		0			0
$581$	0.864920	+	0.499362i	0.0358829	+	0.0207170i
$582$		0			0
$583$	−2.96722	+	11.0738i	−0.122890	+	0.458630i
$584$		0			0
$585$	8.28647	+	25.7179i	0.342603	+	1.06330i
$586$		0			0
$587$	2.48476	−	9.27324i	0.102557	−	0.382748i	−0.895500	−	0.445062i	$-0.853182\pi$
$587$	2.48476	−	9.27324i	0.102557	−	0.382748i	0.998057	+	0.0623146i	$0.0198482\pi$
$588$		0			0
$589$	0.407352	+	0.235185i	0.0167846	+	0.00969061i
$590$		0			0
$591$	26.0593	+	19.4507i	1.07194	+	0.800093i
$592$		0			0
$593$	−0.723344	+	0.723344i	−0.0297042	+	0.0297042i	−0.721803	−	0.692099i	$-0.756686\pi$
$593$	−0.723344	+	0.723344i	−0.0297042	+	0.0297042i	0.692099	+	0.721803i	$0.256686\pi$
$594$		0			0
$595$	8.04258	−	2.35707i	0.329714	−	0.0966306i
$596$		0			0
$597$	6.31015	+	43.4543i	0.258257	+	1.77847i
$598$		0			0
$599$	−3.49913	+	6.06066i	−0.142970	+	0.247632i	−0.928614	−	0.371047i	$-0.878999\pi$
$599$	−3.49913	+	6.06066i	−0.142970	+	0.247632i	0.785643	+	0.618680i	$0.212332\pi$
$600$		0			0
$601$	4.49249	+	7.78122i	0.183252	+	0.317402i	0.942986	−	0.332832i	$-0.108004\pi$
$601$	4.49249	+	7.78122i	0.183252	+	0.317402i	−0.759734	+	0.650234i	$0.774671\pi$
$602$		0			0
$603$	−9.13651	−	14.8950i	−0.372067	−	0.606570i
$604$		0			0
$605$	−11.1341	−	10.6271i	−0.452664	−	0.432053i
$606$		0			0
$607$	−5.12710	−	19.1346i	−0.208103	−	0.776649i	−0.988481	−	0.151342i	$-0.951640\pi$
$607$	−5.12710	−	19.1346i	−0.208103	−	0.776649i	0.780379	−	0.625307i	$-0.215026\pi$
$608$		0			0
$609$	−4.08064	−	9.49230i	−0.165356	−	0.384648i
$610$		0			0
$611$			7.49944i			0.303395i
$612$		0			0
$613$	−16.6163	−	16.6163i	−0.671124	−	0.671124i	0.286851	−	0.957975i	$-0.407392\pi$
$613$	−16.6163	−	16.6163i	−0.671124	−	0.671124i	−0.957975	+	0.286851i	$0.907392\pi$
$614$		0			0
$615$	−28.4174	+	39.9825i	−1.14590	+	1.61225i
$616$		0			0
$617$	11.3965	−	3.05370i	0.458808	−	0.122937i	−0.0220100	−	0.999758i	$-0.507007\pi$
$617$	11.3965	−	3.05370i	0.458808	−	0.122937i	0.480818	+	0.876821i	$0.340340\pi$
$618$		0			0
$619$	5.05521	−	2.91863i	0.203186	−	0.117309i	−0.394955	−	0.918701i	$-0.629240\pi$
$619$	5.05521	−	2.91863i	0.203186	−	0.117309i	0.598141	+	0.801391i	$0.295906\pi$
$620$		0			0
$621$	30.4370	+	36.5484i	1.22140	+	1.46664i
$622$		0			0
$623$	6.81243	+	1.82539i	0.272934	+	0.0731325i
$624$		0			0
$625$	14.4600	+	20.3938i	0.578399	+	0.815754i
$626$		0			0
$627$	−1.27671	−	1.61878i	−0.0509868	−	0.0646477i
$628$		0			0
$629$	16.1751			0.644945
$630$		0			0
$631$	46.1124			1.83571			0.917853	−	0.396920i	$-0.129921\pi$
$631$	46.1124			1.83571			0.917853	+	0.396920i	$0.129921\pi$
$632$		0			0
$633$	−8.14774	+	20.4353i	−0.323844	+	0.812231i
$634$		0			0
$635$	−13.0547	−	21.4421i	−0.518059	−	0.850903i
$636$		0			0
$637$	23.2250	+	6.22312i	0.920208	+	0.246569i
$638$		0			0
$639$	−1.64591	−	5.54770i	−0.0651112	−	0.219464i
$640$		0			0
$641$	−33.2725	+	19.2099i	−1.31418	+	0.758744i	−0.982786	−	0.184747i	$-0.940854\pi$
$641$	−33.2725	+	19.2099i	−1.31418	+	0.758744i	−0.331398	+	0.943491i	$0.607520\pi$
$642$		0			0
$643$	16.9724	−	4.54774i	0.669326	−	0.179345i	0.0918748	−	0.995771i	$-0.470714\pi$
$643$	16.9724	−	4.54774i	0.669326	−	0.179345i	0.577451	+	0.816425i	$0.304047\pi$
$644$		0			0
$645$	−31.7931	−	11.8257i	−1.25185	−	0.465637i
$646$		0			0
$647$	−22.1467	−	22.1467i	−0.870677	−	0.870677i	0.121870	−	0.992546i	$-0.461111\pi$
$647$	−22.1467	−	22.1467i	−0.870677	−	0.870677i	−0.992546	+	0.121870i	$0.961111\pi$
$648$		0			0
$649$			36.4601i			1.43118i
$650$		0			0
$651$	−1.75758	+	2.35475i	−0.0688851	+	0.0922899i
$652$		0			0
$653$	−8.56014	−	31.9469i	−0.334984	−	1.25018i	−0.903886	−	0.427773i	$-0.859298\pi$
$653$	−8.56014	−	31.9469i	−0.334984	−	1.25018i	0.568902	−	0.822405i	$-0.307368\pi$
$654$		0			0
$655$	−10.6015	+	11.1072i	−0.414234	+	0.433994i
$656$		0			0
$657$	15.1381	+	8.21084i	0.590593	+	0.320335i
$658$		0			0
$659$	−0.0315958	−	0.0547256i	−0.00123080	−	0.00213181i	0.865409	−	0.501066i	$-0.167058\pi$
$659$	−0.0315958	−	0.0547256i	−0.00123080	−	0.00213181i	−0.866640	+	0.498934i	$0.833725\pi$
$660$		0			0
$661$	−0.681072	+	1.17965i	−0.0264906	+	0.0458832i	−0.878967	−	0.476883i	$-0.841767\pi$
$661$	−0.681072	+	1.17965i	−0.0264906	+	0.0458832i	0.852476	+	0.522766i	$0.175100\pi$
$662$		0			0
$663$	−23.9260	−	9.53953i	−0.929210	−	0.370485i
$664$		0			0
$665$	0.560617	+	0.306490i	0.0217398	+	0.0118852i
$666$		0			0
$667$	−38.0336	+	38.0336i	−1.47267	+	1.47267i
$668$		0			0
$669$	−1.34753	+	11.4063i	−0.0520985	+	0.440994i
$670$		0			0
$671$	−20.6733	−	11.9357i	−0.798084	−	0.460774i
$672$		0			0
$673$	6.37147	−	23.7787i	0.245602	−	0.916600i	−0.727478	−	0.686131i	$-0.759307\pi$
$673$	6.37147	−	23.7787i	0.245602	−	0.916600i	0.973080	−	0.230469i	$-0.0740259\pi$
$674$		0			0
$675$	25.9552	+	1.15313i	0.999015	+	0.0443841i
$676$		0			0
$677$	4.45281	−	16.6181i	0.171135	−	0.638686i	−0.826042	−	0.563608i	$-0.809413\pi$
$677$	4.45281	−	16.6181i	0.171135	−	0.638686i	0.997178	−	0.0750779i	$-0.0239205\pi$
$678$		0			0
$679$	−2.91739	−	1.68436i	−0.111959	−	0.0646397i
$680$		0			0
$681$	0.0346678	−	0.293450i	0.00132847	−	0.0112450i
$682$		0			0
$683$	7.80388	−	7.80388i	0.298607	−	0.298607i	−0.541861	−	0.840468i	$-0.682280\pi$
$683$	7.80388	−	7.80388i	0.298607	−	0.298607i	0.840468	+	0.541861i	$0.182280\pi$
$684$		0			0
$685$	41.6364	+	22.7627i	1.59085	+	0.869718i
$686$		0			0
$687$	−21.9157	−	8.73800i	−0.836137	−	0.333375i
$688$		0			0
$689$	−5.45979	+	9.45664i	−0.208002	+	0.360269i
$690$		0			0
$691$	15.3258	+	26.5451i	0.583023	+	1.00982i	0.995119	+	0.0986844i	$0.0314634\pi$
$691$	15.3258	+	26.5451i	0.583023	+	1.00982i	−0.412096	+	0.911140i	$0.635203\pi$
$692$		0			0
$693$	10.9782	−	6.73399i	0.417028	−	0.255803i
$694$		0			0
$695$	20.9009	−	21.8979i	0.792815	−	0.830634i
$696$		0			0
$697$	−12.1026	−	45.1676i	−0.458420	−	1.71085i
$698$		0			0
$699$	−8.51280	+	11.4052i	−0.321984	+	0.431383i
$700$		0			0
$701$		−	9.37006i		−	0.353902i	−0.984220	−	0.176951i	$-0.943377\pi$
$701$		−	9.37006i		−	0.353902i	0.984220	−	0.176951i	$-0.0566234\pi$
$702$		0			0
$703$	0.871958	+	0.871958i	0.0328865	+	0.0328865i
$704$		0			0
$705$	6.75862	+	2.51393i	0.254544	+	0.0946799i
$706$		0			0
$707$	−6.08589	+	1.63071i	−0.228883	+	0.0613291i
$708$		0			0
$709$	1.62031	−	0.935488i	0.0608522	−	0.0351330i	−0.469265	−	0.883057i	$-0.655481\pi$
$709$	1.62031	−	0.935488i	0.0608522	−	0.0351330i	0.530117	+	0.847924i	$0.322148\pi$
$710$		0			0
$711$	7.62039	−	8.03716i	0.285787	−	0.301417i
$712$		0			0
$713$	14.7753	+	3.95902i	0.553338	+	0.148266i
$714$		0			0
$715$	−19.8070	−	32.5326i	−0.740740	−	1.21665i
$716$		0			0
$717$	13.5544	−	33.9958i	0.506199	−	1.26960i
$718$		0			0
$719$	21.7584			0.811452			0.405726	−	0.913995i	$-0.367019\pi$
$719$	21.7584			0.811452			0.405726	+	0.913995i	$0.367019\pi$
$720$		0			0
$721$	−16.3694			−0.609627
$722$		0			0
$723$	30.5270	+	38.7061i	1.13531	+	1.43950i
$724$		0			0
$725$	1.36817	+	29.3493i	0.0508126	+	1.09000i
$726$		0			0
$727$	−15.6944	−	4.20530i	−0.582073	−	0.155966i	−0.0442451	−	0.999021i	$-0.514088\pi$
$727$	−15.6944	−	4.20530i	−0.582073	−	0.155966i	−0.537828	+	0.843055i	$0.680755\pi$
$728$		0			0
$729$	17.5085	−	20.5537i	0.648462	−	0.761247i
$730$		0			0
$731$	28.0043	−	16.1683i	1.03578	−	0.598005i
$732$		0			0
$733$	−43.2446	+	11.5873i	−1.59727	+	0.427988i	−0.944218	−	0.329321i	$-0.893180\pi$
$733$	−43.2446	+	11.5873i	−1.59727	+	0.427988i	−0.653057	+	0.757309i	$0.726514\pi$
$734$		0			0
$735$	13.3937	−	18.8447i	0.494036	−	0.695096i
$736$		0			0
$737$	17.4172	+	17.4172i	0.641569	+	0.641569i
$738$		0			0
$739$		−	15.2703i		−	0.561726i	−0.959748	−	0.280863i	$-0.909379\pi$
$739$		−	15.2703i		−	0.561726i	0.959748	−	0.280863i	$-0.0906206\pi$
$740$		0			0
$741$	−0.775538	−	1.80404i	−0.0284901	−	0.0662730i
$742$		0			0
$743$	3.17205	+	11.8382i	0.116371	+	0.434303i	0.999386	−	0.0350425i	$-0.0111567\pi$
$743$	3.17205	+	11.8382i	0.116371	+	0.434303i	−0.883015	+	0.469345i	$0.844490\pi$
$744$		0			0
$745$	−5.81825	−	5.55334i	−0.213164	−	0.203459i
$746$		0			0
$747$	−2.95038	+	0.0785337i	−0.107949	+	0.00287340i
$748$		0			0
$749$	6.83254	+	11.8343i	0.249656	+	0.432416i
$750$		0			0
$751$	1.95028	−	3.37798i	0.0711667	−	0.123264i	−0.828246	−	0.560364i	$-0.810661\pi$
$751$	1.95028	−	3.37798i	0.0711667	−	0.123264i	0.899413	+	0.437100i	$0.143994\pi$
$752$		0			0
$753$	−0.811421	−	5.58777i	−0.0295698	−	0.203630i
$754$		0			0
$755$	10.3450	−	3.03185i	0.376492	−	0.110340i
$756$		0			0
$757$	−8.02600	+	8.02600i	−0.291710	+	0.291710i	−0.837756	−	0.546045i	$-0.816133\pi$
$757$	−8.02600	+	8.02600i	−0.291710	+	0.291710i	0.546045	+	0.837756i	$0.316133\pi$
$758$		0			0
$759$	−53.7290	−	40.1032i	−1.95024	−	1.45566i
$760$		0			0
$761$	23.0744	+	13.3220i	0.836447	+	0.482923i	0.856055	−	0.516885i	$-0.172908\pi$
$761$	23.0744	+	13.3220i	0.836447	+	0.482923i	−0.0196080	+	0.999808i	$0.506242\pi$
$762$		0			0
$763$	−2.90550	+	10.8435i	−0.105186	+	0.392560i
$764$		0			0
$765$	−16.6176	+	18.3647i	−0.600809	+	0.663979i
$766$		0			0
$767$	−8.98808	+	33.5440i	−0.324541	+	1.21120i
$768$		0			0
$769$	37.3021	+	21.5364i	1.34515	+	0.776621i	0.987558	−	0.157258i	$-0.0502653\pi$
$769$	37.3021	+	21.5364i	1.34515	+	0.776621i	0.357590	+	0.933879i	$0.383599\pi$
$770$		0			0
$771$	46.1167	−	19.8251i	1.66085	−	0.713983i
$772$		0			0
$773$	−1.43913	+	1.43913i	−0.0517620	+	0.0517620i	−0.732514	−	0.680752i	$-0.761653\pi$
$773$	−1.43913	+	1.43913i	−0.0517620	+	0.0517620i	0.680752	+	0.732514i	$0.261653\pi$
$774$		0			0
$775$	7.03378	−	4.51023i	0.252661	−	0.162012i
$776$		0			0
$777$	−6.04849	+	4.77037i	−0.216989	+	0.171136i
$778$		0			0
$779$	1.78244	−	3.08729i	0.0638627	−	0.110613i
$780$		0			0
$781$	4.07854	+	7.06424i	0.145942	+	0.252778i
$782$		0			0
$783$	24.9466	+	17.6063i	0.891518	+	0.629197i
$784$		0			0
$785$	18.4197	−	0.429101i	0.657427	−	0.0153153i
$786$		0			0
$787$	4.88152	+	18.2181i	0.174007	+	0.649405i	0.996719	+	0.0809450i	$0.0257938\pi$
$787$	4.88152	+	18.2181i	0.174007	+	0.649405i	−0.822711	+	0.568460i	$0.807540\pi$
$788$		0			0
$789$	−32.9372	−	3.89116i	−1.17259	−	0.138529i
$790$		0			0
$791$			5.60295i			0.199218i
$792$		0			0
$793$	−16.0775	−	16.0775i	−0.570928	−	0.570928i
$794$		0			0
$795$	6.69228	+	8.09047i	0.237351	+	0.286939i
$796$		0			0
$797$	−22.8838	+	6.13169i	−0.810585	+	0.217196i	−0.640226	−	0.768186i	$-0.721159\pi$
$797$	−22.8838	+	6.13169i	−0.810585	+	0.217196i	−0.170359	+	0.985382i	$0.554493\pi$
$798$		0			0
$799$	−5.95318	+	3.43707i	−0.210609	+	0.121595i
$800$		0			0
$801$	−19.9814	+	5.92814i	−0.706007	+	0.209461i
$802$		0			0
$803$	−23.4486	−	6.28304i	−0.827484	−	0.221724i
$804$		0			0
$805$	20.1898	+	4.90887i	0.711598	+	0.173015i
$806$		0			0
$807$	8.00662	−	1.16267i	0.281846	−	0.0409280i
$808$		0			0
$809$	4.46997			0.157156			0.0785778	−	0.996908i	$-0.474962\pi$
$809$	4.46997			0.157156			0.0785778	+	0.996908i	$0.474962\pi$
$810$		0			0
$811$	43.2622			1.51914			0.759571	−	0.650424i	$-0.225409\pi$
$811$	43.2622			1.51914			0.759571	+	0.650424i	$0.225409\pi$
$812$		0			0
$813$	22.3730	−	3.24887i	0.784656	−	0.113943i
$814$		0			0
$815$	−13.3873	+	8.15065i	−0.468937	+	0.285505i
$816$		0			0
$817$	2.38122	+	0.638047i	0.0833085	+	0.0223224i
$818$		0			0
$819$	11.7602	−	3.48907i	0.410936	−	0.121918i
$820$		0			0
$821$	40.3735	−	23.3097i	1.40905	−	0.813513i	0.413750	−	0.910391i	$-0.364219\pi$
$821$	40.3735	−	23.3097i	1.40905	−	0.813513i	0.995296	+	0.0968772i	$0.0308854\pi$
$822$		0			0
$823$	31.4955	−	8.43920i	1.09787	−	0.294172i	0.335970	−	0.941873i	$-0.390936\pi$
$823$	31.4955	−	8.43920i	1.09787	−	0.294172i	0.761895	+	0.647700i	$0.224269\pi$
$824$		0			0
$825$	−35.9586	+	6.94496i	−1.25192	+	0.241793i
$826$		0			0
$827$	6.08734	+	6.08734i	0.211678	+	0.211678i	0.804980	−	0.593302i	$-0.202176\pi$
$827$	6.08734	+	6.08734i	0.211678	+	0.211678i	−0.593302	+	0.804980i	$0.702176\pi$
$828$		0			0
$829$		−	25.7231i		−	0.893400i	−0.894684	−	0.446700i	$-0.852599\pi$
$829$		−	25.7231i		−	0.893400i	0.894684	−	0.446700i	$-0.147401\pi$
$830$		0			0
$831$	−43.7684	−	5.17075i	−1.51831	−	0.179371i
$832$		0			0
$833$	5.70425	+	21.2885i	0.197640	+	0.737604i
$834$		0			0
$835$	−0.748581	−	32.1338i	−0.0259057	−	1.11203i
$836$		0			0
$837$	0.788942	−	8.64749i	0.0272698	−	0.298901i
$838$		0			0
$839$	−0.00802753	−	0.0139041i	−0.000277141	−	0.000480022i	0.865887	−	0.500240i	$-0.166755\pi$
$839$	−0.00802753	−	0.0139041i	−0.000277141	−	0.000480022i	−0.866164	+	0.499760i	$0.833422\pi$
$840$		0			0
$841$	−2.76504	+	4.78919i	−0.0953462	+	0.165145i
$842$		0			0
$843$	−4.12084	+	3.25005i	−0.141929	+	0.111938i
$844$		0			0
$845$	−2.02747	−	6.91792i	−0.0697469	−	0.237984i
$846$		0			0
$847$	−4.94106	+	4.94106i	−0.169777	+	0.169777i
$848$		0			0
$849$	12.8102	−	5.50696i	0.439644	−	0.188998i
$850$		0			0
$851$	34.7291	+	20.0509i	1.19050	+	0.687335i
$852$		0			0
$853$	2.68364	−	10.0155i	0.0918859	−	0.342923i	−0.904643	−	0.426170i	$-0.859862\pi$
$853$	2.68364	−	10.0155i	0.0918859	−	0.342923i	0.996529	+	0.0832473i	$0.0265291\pi$
$854$		0			0
$855$	−1.88580	+	0.0941863i	−0.0644931	+	0.00322110i
$856$		0			0
$857$	1.23292	−	4.60132i	0.0421157	−	0.157178i	−0.941666	−	0.336550i	$-0.890740\pi$
$857$	1.23292	−	4.60132i	0.0421157	−	0.157178i	0.983781	+	0.179372i	$0.0574066\pi$
$858$		0			0
$859$	31.0689	+	17.9377i	1.06006	+	0.612025i	0.925448	−	0.378874i	$-0.123688\pi$
$859$	31.0689	+	17.9377i	1.06006	+	0.612025i	0.134610	+	0.990899i	$0.457022\pi$
$860$		0			0
$861$	17.8464	+	13.3206i	0.608205	+	0.453964i
$862$		0			0
$863$	−35.1155	+	35.1155i	−1.19535	+	1.19535i	−0.219803	+	0.975544i	$0.570541\pi$
$863$	−35.1155	+	35.1155i	−1.19535	+	1.19535i	−0.975544	+	0.219803i	$0.929459\pi$
$864$		0			0
$865$	15.5950	−	28.5257i	0.530248	−	0.969903i
$866$		0			0
$867$	0.838501	+	5.77426i	0.0284770	+	0.196104i
$868$		0			0
$869$	−7.80613	+	13.5206i	−0.264805	+	0.458656i
$870$		0			0
$871$	11.7305	+	20.3178i	0.397472	+	0.688442i
$872$		0			0
$873$	9.95167	−	0.264896i	0.336813	−	0.00896536i
$874$		0			0
$875$	9.40907	−	6.34734i	0.318085	−	0.214579i
$876$		0			0
$877$	5.52326	+	20.6131i	0.186507	+	0.696055i	0.994303	+	0.106592i	$0.0339939\pi$
$877$	5.52326	+	20.6131i	0.186507	+	0.696055i	−0.807795	+	0.589463i	$0.799339\pi$
$878$		0			0
$879$	5.63694	+	13.1125i	0.190129	+	0.442274i
$880$		0			0
$881$			46.9670i			1.58236i	0.611584	+	0.791180i	$0.290533\pi$
$881$			46.9670i			1.58236i	−0.611584	+	0.791180i	$0.709467\pi$
$882$		0			0
$883$	−19.3061	−	19.3061i	−0.649703	−	0.649703i	0.303218	−	0.952921i	$-0.401939\pi$
$883$	−19.3061	−	19.3061i	−0.649703	−	0.649703i	−0.952921	+	0.303218i	$0.901939\pi$
$884$		0			0
$885$	27.2174	+	19.3447i	0.914904	+	0.650264i
$886$		0			0
$887$	−11.6307	+	3.11644i	−0.390522	+	0.104640i	−0.448736	−	0.893664i	$-0.648126\pi$
$887$	−11.6307	+	3.11644i	−0.390522	+	0.104640i	0.0582149	+	0.998304i	$0.481459\pi$
$888$		0			0
$889$	−9.86998	+	5.69844i	−0.331029	+	0.191119i
$890$		0			0
$891$	−17.2495	+	33.9265i	−0.577880	+	1.13658i
$892$		0			0
$893$	−0.506204	−	0.135637i	−0.0169395	−	0.00453891i
$894$		0			0
$895$	−11.5538	+	47.5200i	−0.386201	+	1.58842i
$896$		0			0
$897$	−39.5455	−	50.1410i	−1.32039	−	1.67416i
$898$		0			0
$899$	9.81990			0.327512
$900$		0			0
$901$	−10.0091			−0.333453
$902$		0			0
$903$	−5.70351	+	14.3049i	−0.189801	+	0.476039i
$904$		0			0
$905$	−12.6056	+	51.8460i	−0.419025	+	1.72342i
$906$		0			0
$907$	−4.14289	−	1.11008i	−0.137562	−	0.0368598i	0.189381	−	0.981904i	$-0.439352\pi$
$907$	−4.14289	−	1.11008i	−0.137562	−	0.0368598i	−0.326943	+	0.945044i	$0.606019\pi$
$908$		0			0
$909$	12.8109	−	13.5116i	0.424911	−	0.448151i
$910$		0			0
$911$	31.7547	−	18.3336i	1.05208	−	0.607419i	0.128849	−	0.991664i	$-0.458872\pi$
$911$	31.7547	−	18.3336i	1.05208	−	0.607419i	0.923231	+	0.384245i	$0.125538\pi$
$912$		0			0
$913$	4.01863	−	1.07679i	0.132997	−	0.0356365i
$914$		0			0
$915$	−19.8787	+	9.09987i	−0.657170	+	0.300833i
$916$		0			0
$917$	4.92915	+	4.92915i	0.162775	+	0.162775i
$918$		0			0
$919$			21.3075i			0.702870i	0.936212	+	0.351435i	$0.114306\pi$
$919$			21.3075i			0.702870i	−0.936212	+	0.351435i	$0.885694\pi$
$920$		0			0
$921$	1.69137	−	2.26604i	0.0557325	−	0.0746685i
$922$		0			0
$923$	2.01087	+	7.50468i	0.0661886	+	0.247019i
$924$		0			0
$925$	20.8720	−	6.64866i	0.686266	−	0.218607i
$926$		0			0
$927$	41.2352	−	25.2935i	1.35434	−	0.830747i
$928$		0			0
$929$	−14.5804	−	25.2540i	−0.478367	−	0.828556i	0.521326	−	0.853358i	$-0.325438\pi$
$929$	−14.5804	−	25.2540i	−0.478367	−	0.828556i	−0.999692	+	0.0248023i	$0.992104\pi$
$930$		0			0
$931$	−0.840107	+	1.45511i	−0.0275334	+	0.0476892i
$932$		0			0
$933$	9.04731	+	3.60724i	0.296196	+	0.118096i
$934$		0			0
$935$	16.7472	−	30.6332i	0.547693	−	1.00181i
$936$		0			0
$937$	13.6450	−	13.6450i	0.445761	−	0.445761i	−0.448181	−	0.893943i	$-0.647928\pi$
$937$	13.6450	−	13.6450i	0.445761	−	0.445761i	0.893943	+	0.448181i	$0.147928\pi$
$938$		0			0
$939$	3.09824	−	26.2254i	0.101107	−	0.855833i
$940$		0			0
$941$	19.1984	+	11.0842i	0.625849	+	0.361334i	0.779143	−	0.626847i	$-0.215655\pi$
$941$	19.1984	+	11.0842i	0.625849	+	0.361334i	−0.153294	+	0.988181i	$0.548988\pi$
$942$		0			0
$943$	30.0051	−	111.980i	0.977100	−	3.64659i
$944$		0			0
$945$	0.797805	−	11.7681i	0.0259526	−	0.382817i
$946$		0			0
$947$	−5.22747	+	19.5092i	−0.169870	+	0.633964i	0.827499	+	0.561468i	$0.189763\pi$
$947$	−5.22747	+	19.5092i	−0.169870	+	0.633964i	−0.997369	+	0.0724959i	$0.976904\pi$
$948$		0			0
$949$	−20.0243	−	11.5610i	−0.650017	−	0.375287i
$950$		0			0
$951$	−5.60150	+	47.4146i	−0.181641	+	1.53752i
$952$		0			0
$953$	−20.3870	+	20.3870i	−0.660399	+	0.660399i	−0.955474	−	0.295075i	$-0.904655\pi$
$953$	−20.3870	+	20.3870i	−0.660399	+	0.660399i	0.295075	+	0.955474i	$0.404655\pi$
$954$		0			0
$955$	10.5993	+	36.1661i	0.342987	+	1.17031i
$956$		0			0
$957$	−39.9805	−	15.9406i	−1.29239	−	0.515286i
$958$		0			0
$959$	10.7716	−	18.6569i	0.347832	−	0.602463i
$960$		0			0
$961$	14.1037	+	24.4283i	0.454957	+	0.788009i
$962$		0			0
$963$	−35.4975	−	19.2537i	−1.14389	−	0.620443i
$964$		0			0
$965$	1.27324	+	54.6553i	0.0409870	+	1.75942i
$966$		0			0
$967$	−6.12383	−	22.8544i	−0.196929	−	0.734949i	−0.991759	−	0.128117i	$-0.959107\pi$
$967$	−6.12383	−	22.8544i	−0.196929	−	0.734949i	0.794830	−	0.606832i	$-0.207560\pi$
$968$		0			0
$969$	1.07664	−	1.44245i	0.0345867	−	0.0463380i
$970$		0			0
$971$		−	32.0761i		−	1.02937i	−0.857379	−	0.514686i	$-0.827908\pi$
$971$		−	32.0761i		−	1.02937i	0.857379	−	0.514686i	$-0.172092\pi$
$972$		0			0
$973$	−9.71784	−	9.71784i	−0.311540	−	0.311540i
$974$		0			0
$975$	−34.7947	−	2.47495i	−1.11432	−	0.0792619i
$976$		0			0
$977$	−23.3058	+	6.24476i	−0.745618	+	0.199788i	−0.611573	−	0.791188i	$-0.709463\pi$
$977$	−23.3058	+	6.24476i	−0.745618	+	0.199788i	−0.134044	+	0.990975i	$0.542796\pi$
$978$		0			0
$979$	25.4435	−	14.6898i	0.813179	−	0.469489i
$980$		0			0
$981$	−9.43594	−	31.8047i	−0.301266	−	1.01545i
$982$		0			0
$983$	−5.39530	−	1.44566i	−0.172083	−	0.0461096i	0.171749	−	0.985141i	$-0.445058\pi$
$983$	−5.39530	−	1.44566i	−0.172083	−	0.0461096i	−0.343832	+	0.939031i	$0.611725\pi$
$984$		0			0
$985$	−35.8574	+	21.8313i	−1.14251	+	0.695602i
$986$		0			0
$987$	1.21246	−	3.04096i	0.0385930	−	0.0967949i
$988$		0			0
$989$	80.1694			2.54924
$990$		0			0
$991$	12.1955			0.387401			0.193701	−	0.981061i	$-0.437951\pi$
$991$	12.1955			0.387401			0.193701	+	0.981061i	$0.437951\pi$
$992$		0			0
$993$	−27.6810	−	35.0976i	−0.878429	−	1.11379i
$994$		0			0
$995$	−55.0829	−	13.3926i	−1.74625	−	0.424575i
$996$		0			0
$997$	−50.3044	−	13.4790i	−1.59316	−	0.426885i	−0.650191	−	0.759771i	$-0.725311\pi$
$997$	−50.3044	−	13.4790i	−1.59316	−	0.426885i	−0.942967	+	0.332886i	$0.891978\pi$
$998$		0			0
$999$	7.86541	−	21.3627i	0.248851	−	0.675887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.2	✓	72
3.2	odd	2		1080.2.bt.a.233.8		72
4.3	odd	2		720.2.cu.e.113.17		72
5.2	odd	4	inner	360.2.bs.a.257.11	yes	72
9.2	odd	6	inner	360.2.bs.a.353.11	yes	72
9.7	even	3		1080.2.bt.a.953.15		72
15.2	even	4		1080.2.bt.a.17.15		72
20.7	even	4		720.2.cu.e.257.8		72
36.11	even	6		720.2.cu.e.353.8		72
45.2	even	12	inner	360.2.bs.a.137.2	yes	72
45.7	odd	12		1080.2.bt.a.737.8		72
180.47	odd	12		720.2.cu.e.497.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.2	✓	72	1.1	even	1	trivial
360.2.bs.a.137.2	yes	72	45.2	even	12	inner
360.2.bs.a.257.11	yes	72	5.2	odd	4	inner
360.2.bs.a.353.11	yes	72	9.2	odd	6	inner
720.2.cu.e.113.17		72	4.3	odd	2
720.2.cu.e.257.8		72	20.7	even	4
720.2.cu.e.353.8		72	36.11	even	6
720.2.cu.e.497.17		72	180.47	odd	12
1080.2.bt.a.17.15		72	15.2	even	4
1080.2.bt.a.233.8		72	3.2	odd	2
1080.2.bt.a.737.8		72	45.7	odd	12
1080.2.bt.a.953.15		72	9.7	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71407 + 0.248907i) q^{3} +(0.528278 - 2.17277i) q^{5} +(-0.980572 - 0.262743i) q^{7} +(2.87609 - 0.853289i) q^{9} +O(q^{10})\)	\(q+(-1.71407 + 0.248907i) q^{3} +(0.528278 - 2.17277i) q^{5} +(-0.980572 - 0.262743i) q^{7} +(2.87609 - 0.853289i) q^{9} +(-3.66231 + 2.11444i) q^{11} +(-3.89065 + 1.04250i) q^{13} +(-0.364690 + 3.85578i) q^{15} +(-2.61068 - 2.61068i) q^{17} -0.281469i q^{19} +(1.74617 + 0.206290i) q^{21} +(-2.36908 - 8.84152i) q^{23} +(-4.44185 - 2.29565i) q^{25} +(-4.71744 + 2.17848i) q^{27} +(-2.93812 - 5.08896i) q^{29} +(-0.835561 + 1.44723i) q^{31} +(5.75117 - 4.53587i) q^{33} +(-1.08889 + 1.99175i) q^{35} +(-3.09788 + 3.09788i) q^{37} +(6.40937 - 2.75532i) q^{39} +(10.9685 + 6.33265i) q^{41} +(-2.26685 + 8.45998i) q^{43} +(-0.334624 - 6.69985i) q^{45} +(0.481889 - 1.79843i) q^{47} +(-5.16969 - 2.98472i) q^{49} +(5.12470 + 3.82507i) q^{51} +(1.91696 - 1.91696i) q^{53} +(2.65946 + 9.07436i) q^{55} +(0.0700596 + 0.482459i) q^{57} +(4.31085 - 7.46661i) q^{59} +(2.82244 + 4.88861i) q^{61} +(-3.04441 + 0.0810368i) q^{63} +(0.209760 + 9.00420i) q^{65} +(-1.50752 - 5.62615i) q^{67} +(6.26149 + 14.5653i) q^{69} -1.92890i q^{71} +(4.05914 + 4.05914i) q^{73} +(8.18505 + 2.82931i) q^{75} +(4.14671 - 1.11111i) q^{77} +(3.19722 - 1.84591i) q^{79} +(7.54380 - 4.90827i) q^{81} +(-0.950284 - 0.254628i) q^{83} +(-7.05156 + 4.29323i) q^{85} +(6.30282 + 7.99154i) q^{87} -6.94741 q^{89} +4.08897 q^{91} +(1.07199 - 2.68864i) q^{93} +(-0.611567 - 0.148694i) q^{95} +(3.20533 + 0.858865i) q^{97} +(-8.72891 + 9.20632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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