LMFDB - Embedded newform 360.2.bs.a.113.3

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			113.3
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66953 - 0.461153i) q^{3} +(-2.18181 - 0.489584i) q^{5} +(1.65362 + 0.443086i) q^{7} +(2.57468 + 1.53982i) q^{9} +O(q^{10})$	\(q+(-1.66953 - 0.461153i) q^{3} +(-2.18181 - 0.489584i) q^{5} +(1.65362 + 0.443086i) q^{7} +(2.57468 + 1.53982i) q^{9} +(-4.34262 + 2.50721i) q^{11} +(2.12477 - 0.569329i) q^{13} +(3.41683 + 1.82352i) q^{15} +(4.30508 + 4.30508i) q^{17} +4.07361i q^{19} +(-2.55644 - 1.50232i) q^{21} +(0.256369 + 0.956784i) q^{23} +(4.52062 + 2.13636i) q^{25} +(-3.58842 - 3.75809i) q^{27} +(4.46015 + 7.72522i) q^{29} +(-4.14951 + 7.18717i) q^{31} +(8.40634 - 2.18326i) q^{33} +(-3.39096 - 1.77631i) q^{35} +(3.83952 - 3.83952i) q^{37} +(-3.80991 - 0.0293274i) q^{39} +(-8.75041 - 5.05205i) q^{41} +(-0.269180 + 1.00459i) q^{43} +(-4.86359 - 4.62011i) q^{45} +(1.71292 - 6.39270i) q^{47} +(-3.52405 - 2.03461i) q^{49} +(-5.20217 - 9.17277i) q^{51} +(-5.41021 + 5.41021i) q^{53} +(10.7023 - 3.34419i) q^{55} +(1.87856 - 6.80103i) q^{57} +(3.43467 - 5.94903i) q^{59} +(1.88941 + 3.27256i) q^{61} +(3.57526 + 3.68707i) q^{63} +(-4.91457 + 0.201919i) q^{65} +(0.874529 + 3.26379i) q^{67} +(0.0132062 - 1.71561i) q^{69} +9.54059i q^{71} +(-1.99102 - 1.99102i) q^{73} +(-6.56213 - 5.65142i) q^{75} +(-8.29194 + 2.22182i) q^{77} +(3.11765 - 1.79998i) q^{79} +(4.25792 + 7.92907i) q^{81} +(1.58191 + 0.423871i) q^{83} +(-7.28519 - 11.5006i) q^{85} +(-3.88387 - 14.9543i) q^{87} -5.37389 q^{89} +3.76581 q^{91} +(10.2421 - 10.0857i) q^{93} +(1.99438 - 8.88787i) q^{95} +(-3.60332 - 0.965508i) q^{97} +(-15.0415 - 0.231582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.66953	−	0.461153i	−0.963905	−	0.266247i
$3$	−1.66953	−	0.461153i	−0.963905	−	0.266247i
$4$		0			0
$5$	−2.18181	−	0.489584i	−0.975736	−	0.218948i
$5$	−2.18181	−	0.489584i	−0.975736	−	0.218948i
$6$		0			0
$7$	1.65362	+	0.443086i	0.625009	+	0.167471i	0.557404	−	0.830242i	$-0.311798\pi$
$7$	1.65362	+	0.443086i	0.625009	+	0.167471i	0.0676051	+	0.997712i	$0.478464\pi$
$8$		0			0
$9$	2.57468	+	1.53982i	0.858226	+	0.513273i
$10$		0			0
$11$	−4.34262	+	2.50721i	−1.30935	+	0.755952i	−0.981987	−	0.188947i	$-0.939493\pi$
$11$	−4.34262	+	2.50721i	−1.30935	+	0.755952i	−0.327361	+	0.944899i	$0.606159\pi$
$12$		0			0
$13$	2.12477	−	0.569329i	0.589304	−	0.157903i	0.0481688	−	0.998839i	$-0.484661\pi$
$13$	2.12477	−	0.569329i	0.589304	−	0.157903i	0.541135	+	0.840936i	$0.317995\pi$
$14$		0			0
$15$	3.41683	+	1.82352i	0.882223	+	0.470832i
$16$		0			0
$17$	4.30508	+	4.30508i	1.04414	+	1.04414i	0.998980	+	0.0451557i	$0.0143784\pi$
$17$	4.30508	+	4.30508i	1.04414	+	1.04414i	0.0451557	+	0.998980i	$0.485622\pi$
$18$		0			0
$19$			4.07361i			0.934551i	0.884112	+	0.467276i	$0.154764\pi$
$19$			4.07361i			0.934551i	−0.884112	+	0.467276i	$0.845236\pi$
$20$		0			0
$21$	−2.55644	−	1.50232i	−0.557861	−	0.327832i
$22$		0			0
$23$	0.256369	+	0.956784i	0.0534567	+	0.199503i	0.987490	−	0.157684i	$-0.0504026\pi$
$23$	0.256369	+	0.956784i	0.0534567	+	0.199503i	−0.934033	+	0.357187i	$0.883736\pi$
$24$		0			0
$25$	4.52062	+	2.13636i	0.904123	+	0.427272i
$26$		0			0
$27$	−3.58842	−	3.75809i	−0.690591	−	0.723246i
$28$		0			0
$29$	4.46015	+	7.72522i	0.828230	+	1.43454i	0.899426	+	0.437074i	$0.143985\pi$
$29$	4.46015	+	7.72522i	0.828230	+	1.43454i	−0.0711955	+	0.997462i	$0.522681\pi$
$30$		0			0
$31$	−4.14951	+	7.18717i	−0.745275	+	1.29085i	0.204792	+	0.978806i	$0.434348\pi$
$31$	−4.14951	+	7.18717i	−0.745275	+	1.29085i	−0.950066	+	0.312048i	$0.898985\pi$
$32$		0			0
$33$	8.40634	−	2.18326i	1.46336	−	0.380057i
$34$		0			0
$35$	−3.39096	−	1.77631i	−0.573176	−	0.300252i
$36$		0			0
$37$	3.83952	−	3.83952i	0.631213	−	0.631213i	−0.317159	−	0.948372i	$-0.602729\pi$
$37$	3.83952	−	3.83952i	0.631213	−	0.631213i	0.948372	+	0.317159i	$0.102729\pi$
$38$		0			0
$39$	−3.80991	−	0.0293274i	−0.610074	−	0.00469614i
$40$		0			0
$41$	−8.75041	−	5.05205i	−1.36659	−	0.788998i	−0.376095	−	0.926581i	$-0.622733\pi$
$41$	−8.75041	−	5.05205i	−1.36659	−	0.788998i	−0.990490	+	0.137583i	$0.956067\pi$
$42$		0			0
$43$	−0.269180	+	1.00459i	−0.0410495	+	0.153199i	−0.983409	−	0.181404i	$-0.941936\pi$
$43$	−0.269180	+	1.00459i	−0.0410495	+	0.153199i	0.942359	+	0.334603i	$0.108602\pi$
$44$		0			0
$45$	−4.86359	−	4.62011i	−0.725022	−	0.688726i
$46$		0			0
$47$	1.71292	−	6.39270i	0.249855	−	0.932471i	−0.721026	−	0.692908i	$-0.756329\pi$
$47$	1.71292	−	6.39270i	0.249855	−	0.932471i	0.970881	−	0.239563i	$-0.0770041\pi$
$48$		0			0
$49$	−3.52405	−	2.03461i	−0.503436	−	0.290659i
$50$		0			0
$51$	−5.20217	−	9.17277i	−0.728450	−	1.28445i
$52$		0			0
$53$	−5.41021	+	5.41021i	−0.743150	+	0.743150i	−0.973183	−	0.230033i	$-0.926117\pi$
$53$	−5.41021	+	5.41021i	−0.743150	+	0.743150i	0.230033	+	0.973183i	$0.426117\pi$
$54$		0			0
$55$	10.7023	−	3.34419i	1.44309	−	0.450930i
$56$		0			0
$57$	1.87856	−	6.80103i	0.248821	−	0.900819i
$58$		0			0
$59$	3.43467	−	5.94903i	0.447156	−	0.774498i	−0.551043	−	0.834477i	$-0.685770\pi$
$59$	3.43467	−	5.94903i	0.447156	−	0.774498i	0.998200	+	0.0599791i	$0.0191034\pi$
$60$		0			0
$61$	1.88941	+	3.27256i	0.241914	+	0.419008i	0.961260	−	0.275645i	$-0.0888914\pi$
$61$	1.88941	+	3.27256i	0.241914	+	0.419008i	−0.719345	+	0.694653i	$0.755558\pi$
$62$		0			0
$63$	3.57526	+	3.68707i	0.450441	+	0.464528i
$64$		0			0
$65$	−4.91457	+	0.201919i	−0.609578	+	0.0250450i
$66$		0			0
$67$	0.874529	+	3.26379i	0.106841	+	0.398735i	0.998547	−	0.0538786i	$-0.0171584\pi$
$67$	0.874529	+	3.26379i	0.106841	+	0.398735i	−0.891707	+	0.452614i	$0.850492\pi$
$68$		0			0
$69$	0.0132062	−	1.71561i	0.00158983	−	0.206535i
$70$		0			0
$71$			9.54059i			1.13226i	0.824316	+	0.566130i	$0.191560\pi$
$71$			9.54059i			1.13226i	−0.824316	+	0.566130i	$0.808440\pi$
$72$		0			0
$73$	−1.99102	−	1.99102i	−0.233032	−	0.233032i	0.580925	−	0.813957i	$-0.302691\pi$
$73$	−1.99102	−	1.99102i	−0.233032	−	0.233032i	−0.813957	+	0.580925i	$0.802691\pi$
$74$		0			0
$75$	−6.56213	−	5.65142i	−0.757729	−	0.652569i
$76$		0			0
$77$	−8.29194	+	2.22182i	−0.944954	+	0.253200i
$78$		0			0
$79$	3.11765	−	1.79998i	0.350763	−	0.202513i	−0.314258	−	0.949338i	$-0.601756\pi$
$79$	3.11765	−	1.79998i	0.350763	−	0.202513i	0.665021	+	0.746824i	$0.268422\pi$
$80$		0			0
$81$	4.25792	+	7.92907i	0.473102	+	0.881008i
$82$		0			0
$83$	1.58191	+	0.423871i	0.173637	+	0.0465259i	0.344590	−	0.938753i	$-0.388018\pi$
$83$	1.58191	+	0.423871i	0.173637	+	0.0465259i	−0.170953	+	0.985279i	$0.554685\pi$
$84$		0			0
$85$	−7.28519	−	11.5006i	−0.790189	−	1.24741i
$86$		0			0
$87$	−3.88387	−	14.9543i	−0.416395	−	1.60327i
$88$		0			0
$89$	−5.37389			−0.569631			−0.284816	−	0.958582i	$-0.591932\pi$
$89$	−5.37389			−0.569631			−0.284816	+	0.958582i	$0.591932\pi$
$90$		0			0
$91$	3.76581			0.394764
$92$		0			0
$93$	10.2421	−	10.0857i	1.06206	−	1.04583i
$94$		0			0
$95$	1.99438	−	8.88787i	0.204619	−	0.911876i
$96$		0			0
$97$	−3.60332	−	0.965508i	−0.365862	−	0.0980325i	0.0712041	−	0.997462i	$-0.477316\pi$
$97$	−3.60332	−	0.965508i	−0.365862	−	0.0980325i	−0.437066	+	0.899429i	$0.643982\pi$
$98$		0			0
$99$	−15.0415	−	0.231582i	−1.51173	−	0.0232749i
$100$		0			0
$101$	8.08725	−	4.66918i	0.804711	−	0.464600i	−0.0404046	−	0.999183i	$-0.512865\pi$
$101$	8.08725	−	4.66918i	0.804711	−	0.464600i	0.845116	+	0.534583i	$0.179531\pi$
$102$		0			0
$103$	1.72941	−	0.463394i	0.170404	−	0.0456595i	−0.172608	−	0.984991i	$-0.555219\pi$
$103$	1.72941	−	0.463394i	0.170404	−	0.0456595i	0.343012	+	0.939331i	$0.388553\pi$
$104$		0			0
$105$	4.84216	+	4.52936i	0.472547	+	0.442021i
$106$		0			0
$107$	1.96744	+	1.96744i	0.190200	+	0.190200i	0.795782	−	0.605583i	$-0.207060\pi$
$107$	1.96744	+	1.96744i	0.190200	+	0.190200i	−0.605583	+	0.795782i	$0.707060\pi$
$108$		0			0
$109$			11.0642i			1.05975i	0.848074	+	0.529877i	$0.177762\pi$
$109$			11.0642i			1.05975i	−0.848074	+	0.529877i	$0.822238\pi$
$110$		0			0
$111$	−8.18081	+	4.63960i	−0.776488	+	0.440371i
$112$		0			0
$113$	0.275679	+	1.02885i	0.0259337	+	0.0967858i	0.977680	−	0.210101i	$-0.0673793\pi$
$113$	0.275679	+	1.02885i	0.0259337	+	0.0967858i	−0.951746	+	0.306887i	$0.900713\pi$
$114$		0			0
$115$	−0.0909244	−	2.21304i	−0.00847875	−	0.206367i
$116$		0			0
$117$	6.34725	+	1.80591i	0.586803	+	0.166957i
$118$		0			0
$119$	5.21144	+	9.02648i	0.477732	+	0.827456i
$120$		0			0
$121$	7.07221	−	12.2494i	0.642928	−	1.11358i
$122$		0			0
$123$	12.2793	+	12.4698i	1.10719	+	1.12437i
$124$		0			0
$125$	−8.81721	−	6.87436i	−0.788635	−	0.614861i
$126$		0			0
$127$	−3.85333	+	3.85333i	−0.341928	+	0.341928i	−0.857092	−	0.515164i	$-0.827731\pi$
$127$	−3.85333	+	3.85333i	−0.341928	+	0.341928i	0.515164	+	0.857092i	$0.327731\pi$
$128$		0			0
$129$	0.912674	−	1.55307i	0.0803565	−	0.136740i
$130$		0			0
$131$	−15.6520	−	9.03669i	−1.36752	−	0.789539i	−0.376911	−	0.926249i	$-0.623014\pi$
$131$	−15.6520	−	9.03669i	−1.36752	−	0.789539i	−0.990611	+	0.136710i	$0.956347\pi$
$132$		0			0
$133$	−1.80496	+	6.73620i	−0.156510	+	0.584103i
$134$		0			0
$135$	5.98935	+	9.95629i	0.515481	+	0.856901i
$136$		0			0
$137$	−3.18980	+	11.9045i	−0.272523	+	1.01707i	0.684961	+	0.728580i	$0.259819\pi$
$137$	−3.18980	+	11.9045i	−0.272523	+	1.01707i	−0.957483	+	0.288489i	$0.906847\pi$
$138$		0			0
$139$	15.9769	+	9.22428i	1.35514	+	0.782393i	0.988965	−	0.148151i	$-0.0473322\pi$
$139$	15.9769	+	9.22428i	1.35514	+	0.782393i	0.366180	+	0.930544i	$0.380666\pi$
$140$		0			0
$141$	−5.80778	+	9.88290i	−0.489103	+	0.832290i
$142$		0			0
$143$	−7.79961	+	7.79961i	−0.652236	+	0.652236i
$144$		0			0
$145$	−5.94908	−	19.0386i	−0.494045	−	1.58107i
$146$		0			0
$147$	4.94525	+	5.02197i	0.407877	+	0.414205i
$148$		0			0
$149$	5.28774	−	9.15863i	0.433188	−	0.750304i	−0.563957	−	0.825804i	$-0.690722\pi$
$149$	5.28774	−	9.15863i	0.433188	−	0.750304i	0.997146	+	0.0754995i	$0.0240551\pi$
$150$		0			0
$151$	4.11092	+	7.12031i	0.334542	+	0.579443i	0.983397	−	0.181469i	$-0.0580852\pi$
$151$	4.11092	+	7.12031i	0.334542	+	0.579443i	−0.648855	+	0.760912i	$0.724752\pi$
$152$		0			0
$153$	4.45515	+	17.7132i	0.360178	+	1.43203i
$154$		0			0
$155$	12.5722	−	13.6495i	1.00982	−	1.09636i
$156$		0			0
$157$	1.89012	+	7.05403i	0.150848	+	0.562973i	0.999425	+	0.0339011i	$0.0107931\pi$
$157$	1.89012	+	7.05403i	0.150848	+	0.562973i	−0.848577	+	0.529072i	$0.822540\pi$
$158$		0			0
$159$	11.5275	−	6.53759i	0.914187	−	0.518465i
$160$		0			0
$161$			1.69575i			0.133644i
$162$		0			0
$163$	−17.6585	−	17.6585i	−1.38312	−	1.38312i	−0.839015	−	0.544109i	$-0.816868\pi$
$163$	−17.6585	−	17.6585i	−1.38312	−	1.38312i	−0.544109	−	0.839015i	$-0.683132\pi$
$164$		0			0
$165$	−19.4100	+	0.647858i	−1.51106	+	0.0504356i
$166$		0			0
$167$	20.5930	−	5.51787i	1.59353	−	0.426986i	0.650451	−	0.759548i	$-0.274580\pi$
$167$	20.5930	−	5.51787i	1.59353	−	0.426986i	0.943081	+	0.332563i	$0.107913\pi$
$168$		0			0
$169$	−7.06784	+	4.08062i	−0.543680	+	0.313894i
$170$		0			0
$171$	−6.27263	+	10.4882i	−0.479680	+	0.802056i
$172$		0			0
$173$	19.4315	+	5.20665i	1.47735	+	0.395854i	0.905444	−	0.424466i	$-0.139538\pi$
$173$	19.4315	+	5.20665i	1.47735	+	0.395854i	0.571905	+	0.820320i	$0.306205\pi$
$174$		0			0
$175$	6.52878	+	5.53574i	0.493529	+	0.418463i
$176$		0			0
$177$	−8.47771	+	8.34819i	−0.637224	+	0.627488i
$178$		0			0
$179$	15.1885			1.13524			0.567620	−	0.823291i	$-0.307864\pi$
$179$	15.1885			1.13524			0.567620	+	0.823291i	$0.307864\pi$
$180$		0			0
$181$	−12.5127			−0.930059			−0.465029	−	0.885295i	$-0.653956\pi$
$181$	−12.5127			−0.930059			−0.465029	+	0.885295i	$0.653956\pi$
$182$		0			0
$183$	−1.64529	−	6.33494i	−0.121623	−	0.468293i
$184$		0			0
$185$	−10.2569	+	6.49735i	−0.754101	+	0.477694i
$186$		0			0
$187$	−29.4891	−	7.90157i	−2.15645	−	0.577820i
$188$		0			0
$189$	−4.26871	−	7.80443i	−0.310503	−	0.567689i
$190$		0			0
$191$	7.98022	−	4.60738i	0.577428	−	0.333378i	−0.182682	−	0.983172i	$-0.558478\pi$
$191$	7.98022	−	4.60738i	0.577428	−	0.333378i	0.760111	+	0.649794i	$0.225145\pi$
$192$		0			0
$193$	0.348966	−	0.0935051i	0.0251191	−	0.00673065i	−0.246238	−	0.969209i	$-0.579194\pi$
$193$	0.348966	−	0.0935051i	0.0251191	−	0.00673065i	0.271357	+	0.962479i	$0.412528\pi$
$194$		0			0
$195$	8.29816	+	1.92926i	0.594243	+	0.138157i
$196$		0			0
$197$	6.41263	+	6.41263i	0.456881	+	0.456881i	0.897630	−	0.440749i	$-0.145287\pi$
$197$	6.41263	+	6.41263i	0.456881	+	0.456881i	−0.440749	+	0.897630i	$0.645287\pi$
$198$		0			0
$199$			20.2580i			1.43605i	0.696017	+	0.718025i	$0.254954\pi$
$199$			20.2580i			1.43605i	−0.696017	+	0.718025i	$0.745046\pi$
$200$		0			0
$201$	0.0450489	−	5.85229i	0.00317751	−	0.412789i
$202$		0			0
$203$	3.95246	+	14.7508i	0.277408	+	1.03530i
$204$		0			0
$205$	16.6184	+	15.3067i	1.16068	+	1.06907i
$206$		0			0
$207$	−0.813205	+	2.85817i	−0.0565216	+	0.198657i
$208$		0			0
$209$	−10.2134	−	17.6901i	−0.706476	−	1.22365i
$210$		0			0
$211$	−4.12445	+	7.14375i	−0.283939	+	0.491796i	−0.972351	−	0.233523i	$-0.924975\pi$
$211$	−4.12445	+	7.14375i	−0.283939	+	0.491796i	0.688413	+	0.725319i	$0.258308\pi$
$212$		0			0
$213$	4.39967	−	15.9283i	0.301460	−	1.09139i
$214$		0			0
$215$	1.07913	−	2.06005i	0.0735962	−	0.140494i
$216$		0			0
$217$	−10.0462	+	10.0462i	−0.681983	+	0.681983i
$218$		0			0
$219$	2.40591	+	4.24224i	0.162577	+	0.286664i
$220$		0			0
$221$	11.5983	+	6.69628i	0.780186	+	0.450441i
$222$		0			0
$223$	7.05515	−	26.3302i	0.472448	−	1.76320i	−0.158484	−	0.987361i	$-0.550661\pi$
$223$	7.05515	−	26.3302i	0.472448	−	1.76320i	0.630932	−	0.775838i	$-0.282673\pi$
$224$		0			0
$225$	8.34952	+	12.4614i	0.556635	+	0.830757i
$226$		0			0
$227$	2.76643	−	10.3245i	0.183615	−	0.685259i	−0.811308	−	0.584619i	$-0.801244\pi$
$227$	2.76643	−	10.3245i	0.183615	−	0.685259i	0.994923	−	0.100641i	$-0.0320892\pi$
$228$		0			0
$229$	−16.2371	−	9.37450i	−1.07298	−	0.619485i	−0.143985	−	0.989580i	$-0.545992\pi$
$229$	−16.2371	−	9.37450i	−1.07298	−	0.619485i	−0.928994	+	0.370095i	$0.879325\pi$
$230$		0			0
$231$	14.8683	+	0.114451i	0.978259	+	0.00753031i
$232$		0			0
$233$	−17.7670	+	17.7670i	−1.16396	+	1.16396i	−0.180354	+	0.983602i	$0.557724\pi$
$233$	−17.7670	+	17.7670i	−1.16396	+	1.16396i	−0.983602	+	0.180354i	$0.942276\pi$
$234$		0			0
$235$	−6.86703	+	13.1091i	−0.447955	+	0.855140i
$236$		0			0
$237$	−6.03509	+	1.56741i	−0.392021	+	0.101814i
$238$		0			0
$239$	1.34253	−	2.32533i	0.0868411	−	0.150413i	−0.819333	−	0.573318i	$-0.805656\pi$
$239$	1.34253	−	2.32533i	0.0868411	−	0.150413i	0.906174	+	0.422904i	$0.138989\pi$
$240$		0			0
$241$	−13.6856	−	23.7042i	−0.881568	−	1.52692i	−0.849597	−	0.527433i	$-0.823155\pi$
$241$	−13.6856	−	23.7042i	−0.881568	−	1.52692i	−0.0319716	−	0.999489i	$-0.510179\pi$
$242$		0			0
$243$	−3.45223	−	15.2014i	−0.221460	−	0.975169i
$244$		0			0
$245$	6.69271	+	6.16446i	0.427581	+	0.393833i
$246$		0			0
$247$	2.31923	+	8.65547i	0.147569	+	0.550735i
$248$		0			0
$249$	−2.44558	−	1.43717i	−0.154982	−	0.0910768i
$250$		0			0
$251$		−	7.19708i		−	0.454276i	−0.973863	−	0.227138i	$-0.927063\pi$
$251$		−	7.19708i		−	0.454276i	0.973863	−	0.227138i	$-0.0729368\pi$
$252$		0			0
$253$	−3.51217	−	3.51217i	−0.220808	−	0.220808i
$254$		0			0
$255$	6.85933	+	22.5602i	0.429548	+	1.41277i
$256$		0			0
$257$	9.07746	−	2.43230i	0.566237	−	0.151723i	0.0356666	−	0.999364i	$-0.488645\pi$
$257$	9.07746	−	2.43230i	0.566237	−	0.151723i	0.530570	+	0.847641i	$0.321978\pi$
$258$		0			0
$259$	8.05033	−	4.64786i	0.500223	−	0.288804i
$260$		0			0
$261$	−0.411969	+	26.7578i	−0.0255002	+	1.65626i
$262$		0			0
$263$	10.0192	+	2.68464i	0.617811	+	0.165542i	0.554132	−	0.832428i	$-0.313050\pi$
$263$	10.0192	+	2.68464i	0.617811	+	0.165542i	0.0636786	+	0.997970i	$0.479717\pi$
$264$		0			0
$265$	14.4528	−	9.15532i	0.887830	−	0.562407i
$266$		0			0
$267$	8.97189	+	2.47818i	0.549071	+	0.151662i
$268$		0			0
$269$	20.8507			1.27129			0.635646	−	0.771981i	$-0.280734\pi$
$269$	20.8507			1.27129			0.635646	+	0.771981i	$0.280734\pi$
$270$		0			0
$271$	27.7079			1.68314			0.841568	−	0.540152i	$-0.181633\pi$
$271$	27.7079			1.68314			0.841568	+	0.540152i	$0.181633\pi$
$272$		0			0
$273$	−6.28714	−	1.73661i	−0.380515	−	0.105105i
$274$		0			0
$275$	−24.9876	+	2.05674i	−1.50681	+	0.124026i
$276$		0			0
$277$	−1.62763	−	0.436123i	−0.0977950	−	0.0262041i	0.209590	−	0.977789i	$-0.432787\pi$
$277$	−1.62763	−	0.436123i	−0.0977950	−	0.0262041i	−0.307385	+	0.951585i	$0.599454\pi$
$278$		0			0
$279$	−21.7506	+	12.1151i	−1.30217	+	0.725315i
$280$		0			0
$281$	15.9538	−	9.21095i	0.951726	−	0.549479i	0.0581096	−	0.998310i	$-0.481493\pi$
$281$	15.9538	−	9.21095i	0.951726	−	0.549479i	0.893617	+	0.448831i	$0.148159\pi$
$282$		0			0
$283$	−11.8943	+	3.18706i	−0.707042	+	0.189451i	−0.594383	−	0.804182i	$-0.702604\pi$
$283$	−11.8943	+	3.18706i	−0.707042	+	0.189451i	−0.112659	+	0.993634i	$0.535937\pi$
$284$		0			0
$285$	−7.42834	+	13.9189i	−0.440017	+	0.824483i
$286$		0			0
$287$	−12.2314	−	12.2314i	−0.721994	−	0.721994i
$288$		0			0
$289$			20.0675i			1.18044i
$290$		0			0
$291$	5.57062	+	3.27363i	0.326556	+	0.191904i
$292$		0			0
$293$	−2.95178	−	11.0162i	−0.172445	−	0.643572i	−0.996973	−	0.0777513i	$-0.975226\pi$
$293$	−2.95178	−	11.0162i	−0.172445	−	0.643572i	0.824528	−	0.565821i	$-0.191441\pi$
$294$		0			0
$295$	−10.4064	+	11.2981i	−0.605882	+	0.657801i
$296$		0			0
$297$	25.0054	+	7.32305i	1.45096	+	0.424926i
$298$		0			0
$299$	1.08945	+	1.88698i	0.0630045	+	0.109127i
$300$		0			0
$301$	−0.890241	+	1.54194i	−0.0513126	+	0.0888761i
$302$		0			0
$303$	−15.6551	+	4.06588i	−0.899363	+	0.233579i
$304$		0			0
$305$	−2.52015	−	8.06513i	−0.144303	−	0.461808i
$306$		0			0
$307$	15.1593	−	15.1593i	0.865185	−	0.865185i	−0.126749	−	0.991935i	$-0.540454\pi$
$307$	15.1593	−	15.1593i	0.865185	−	0.865185i	0.991935	+	0.126749i	$0.0404544\pi$
$308$		0			0
$309$	−3.10100	−	0.0238704i	−0.176410	−	0.00135794i
$310$		0			0
$311$	−4.37900	−	2.52822i	−0.248310	−	0.143362i	0.370680	−	0.928761i	$-0.379125\pi$
$311$	−4.37900	−	2.52822i	−0.248310	−	0.143362i	−0.618990	+	0.785399i	$0.712458\pi$
$312$		0			0
$313$	6.73477	−	25.1345i	0.380672	−	1.42069i	−0.464207	−	0.885727i	$-0.653660\pi$
$313$	6.73477	−	25.1345i	0.380672	−	1.42069i	0.844878	−	0.534959i	$-0.179673\pi$
$314$		0			0
$315$	−5.99542	−	9.79489i	−0.337804	−	0.551880i
$316$		0			0
$317$	3.87765	−	14.4716i	0.217790	−	0.812805i	−0.767375	−	0.641198i	$-0.778438\pi$
$317$	3.87765	−	14.4716i	0.217790	−	0.812805i	0.985166	−	0.171607i	$-0.0548958\pi$
$318$		0			0
$319$	−38.7375	−	22.3651i	−2.16888	−	1.25220i
$320$		0			0
$321$	−2.37742	−	4.19200i	−0.132695	−	0.233975i
$322$		0			0
$323$	−17.5372	+	17.5372i	−0.975798	+	0.975798i
$324$		0			0
$325$	10.8215	+	1.96555i	0.600271	+	0.109029i
$326$		0			0
$327$	5.10226	−	18.4720i	0.282156	−	1.02150i
$328$		0			0
$329$	5.66502	−	9.81211i	0.312323	−	0.540959i
$330$		0			0
$331$	−6.49152	−	11.2436i	−0.356806	−	0.618006i	0.630619	−	0.776092i	$-0.282801\pi$
$331$	−6.49152	−	11.2436i	−0.356806	−	0.618006i	−0.987425	+	0.158086i	$0.949468\pi$
$332$		0			0
$333$	15.7977	−	3.97336i	0.865708	−	0.217739i
$334$		0			0
$335$	−0.310162	−	7.54913i	−0.0169460	−	0.412453i
$336$		0			0
$337$	0.542954	+	2.02633i	0.0295766	+	0.110381i	0.979136	−	0.203206i	$-0.0651360\pi$
$337$	0.542954	+	2.02633i	0.0295766	+	0.110381i	−0.949560	+	0.313587i	$0.898469\pi$
$338$		0			0
$339$	0.0142008	−	1.84482i	0.000771283	−	0.100197i
$340$		0			0
$341$		−	41.6148i		−	2.25357i
$342$		0			0
$343$	−13.3997	−	13.3997i	−0.723513	−	0.723513i
$344$		0			0
$345$	−0.868747	+	3.73667i	−0.0467717	+	0.201175i
$346$		0			0
$347$	15.6073	−	4.18197i	0.837845	−	0.224500i	0.185711	−	0.982604i	$-0.440541\pi$
$347$	15.6073	−	4.18197i	0.837845	−	0.224500i	0.652133	+	0.758105i	$0.273874\pi$
$348$		0			0
$349$	−4.51722	+	2.60802i	−0.241801	+	0.139604i	−0.616004	−	0.787743i	$-0.711250\pi$
$349$	−4.51722	+	2.60802i	−0.241801	+	0.139604i	0.374203	+	0.927347i	$0.377916\pi$
$350$		0			0
$351$	−9.76413	−	5.94208i	−0.521171	−	0.317165i
$352$		0			0
$353$	−30.2795	−	8.11338i	−1.61162	−	0.431831i	−0.663093	−	0.748537i	$-0.730757\pi$
$353$	−30.2795	−	8.11338i	−1.61162	−	0.431831i	−0.948524	+	0.316705i	$0.897423\pi$
$354$		0			0
$355$	4.67092	−	20.8158i	0.247907	−	1.10479i
$356$		0			0
$357$	−4.53809	−	17.4733i	−0.240181	−	0.924784i
$358$		0			0
$359$	−7.29879			−0.385215			−0.192608	−	0.981276i	$-0.561694\pi$
$359$	−7.29879			−0.385215			−0.192608	+	0.981276i	$0.561694\pi$
$360$		0			0
$361$	2.40566			0.126614
$362$		0			0
$363$	−17.4561	+	17.1894i	−0.916209	+	0.902211i
$364$		0			0
$365$	3.36927	+	5.31881i	0.176356	+	0.278399i
$366$		0			0
$367$	−23.7706	−	6.36932i	−1.24082	−	0.332476i	−0.422034	−	0.906580i	$-0.638684\pi$
$367$	−23.7706	−	6.36932i	−1.24082	−	0.332476i	−0.818782	+	0.574104i	$0.805351\pi$
$368$		0			0
$369$	−14.7502	−	26.4815i	−0.767867	−	1.37857i
$370$		0			0
$371$	−11.3436	+	6.54924i	−0.588931	+	0.340020i
$372$		0			0
$373$	−5.20646	+	1.39507i	−0.269580	+	0.0722339i	−0.391077	−	0.920358i	$-0.627897\pi$
$373$	−5.20646	+	1.39507i	−0.269580	+	0.0722339i	0.121496	+	0.992592i	$0.461231\pi$
$374$		0			0
$375$	11.5505	+	15.5430i	0.596465	+	0.802639i
$376$		0			0
$377$	13.8750	+	13.8750i	0.714597	+	0.714597i
$378$		0			0
$379$		−	16.8559i		−	0.865829i	−0.901435	−	0.432914i	$-0.857485\pi$
$379$		−	16.8559i		−	0.865829i	0.901435	−	0.432914i	$-0.142515\pi$
$380$		0			0
$381$	8.21024	−	4.65629i	0.420623	−	0.238549i
$382$		0			0
$383$	−0.241371	−	0.900808i	−0.0123335	−	0.0460292i	0.959485	−	0.281760i	$-0.0909182\pi$
$383$	−0.241371	−	0.900808i	−0.0123335	−	0.0460292i	−0.971818	+	0.235731i	$0.924252\pi$
$384$		0			0
$385$	19.1792	−	0.787994i	0.977464	−	0.0401599i
$386$		0			0
$387$	−2.23994	+	2.17201i	−0.113863	+	0.110410i
$388$		0			0
$389$	−5.95421	−	10.3130i	−0.301890	−	0.522890i	0.674674	−	0.738116i	$-0.264284\pi$
$389$	−5.95421	−	10.3130i	−0.301890	−	0.522890i	−0.976564	+	0.215227i	$0.930951\pi$
$390$		0			0
$391$	−3.01534	+	5.22272i	−0.152492	+	0.264125i
$392$		0			0
$393$	21.9642	+	22.3050i	1.10795	+	1.12514i
$394$		0			0
$395$	−7.68338	+	2.40086i	−0.386593	+	0.120801i
$396$		0			0
$397$	−19.5784	+	19.5784i	−0.982609	+	0.982609i	−0.999851	−	0.0172420i	$-0.994511\pi$
$397$	−19.5784	+	19.5784i	−0.982609	+	0.982609i	0.0172420	+	0.999851i	$0.494511\pi$
$398$		0			0
$399$	6.11986	−	10.4139i	0.306376	−	0.521349i
$400$		0			0
$401$	20.1888	+	11.6560i	1.00818	+	0.582072i	0.910658	−	0.413162i	$-0.135576\pi$
$401$	20.1888	+	11.6560i	1.00818	+	0.582072i	0.0975204	+	0.995234i	$0.468909\pi$
$402$		0			0
$403$	−4.72488	+	17.6335i	−0.235363	+	0.878387i
$404$		0			0
$405$	−5.40804	−	19.3844i	−0.268728	−	0.963216i
$406$		0			0
$407$	−7.04707	+	26.3000i	−0.349310	+	1.30364i
$408$		0			0
$409$	27.9647	+	16.1454i	1.38276	+	0.798339i	0.992486	−	0.122358i	$-0.0390457\pi$
$409$	27.9647	+	16.1454i	1.38276	+	0.798339i	0.390278	+	0.920697i	$0.372379\pi$
$410$		0			0
$411$	10.8153	−	18.4039i	0.533477	−	0.907799i
$412$		0			0
$413$	8.31557	−	8.31557i	0.409182	−	0.409182i
$414$		0			0
$415$	−3.24391	−	1.69928i	−0.159237	−	0.0834146i
$416$		0			0
$417$	−22.4202	−	22.7680i	−1.09792	−	1.11495i
$418$		0			0
$419$	−8.97586	+	15.5467i	−0.438500	+	0.759504i	−0.997574	−	0.0696139i	$-0.977823\pi$
$419$	−8.97586	+	15.5467i	−0.438500	+	0.759504i	0.559074	+	0.829118i	$0.311157\pi$
$420$		0			0
$421$	15.2854	+	26.4750i	0.744964	+	1.29031i	0.950212	+	0.311605i	$0.100867\pi$
$421$	15.2854	+	26.4750i	0.744964	+	1.29031i	−0.205248	+	0.978710i	$0.565800\pi$
$422$		0			0
$423$	14.2538	−	13.8215i	0.693044	−	0.672027i
$424$		0			0
$425$	10.2644	+	28.6588i	0.497897	+	1.39016i
$426$		0			0
$427$	1.67434	+	6.24873i	0.0810271	+	0.302397i
$428$		0			0
$429$	16.6185	−	9.42489i	0.802349	−	0.455038i
$430$		0			0
$431$			7.93690i			0.382307i	0.981560	+	0.191154i	$0.0612229\pi$
$431$			7.93690i			0.382307i	−0.981560	+	0.191154i	$0.938777\pi$
$432$		0			0
$433$	−16.1988	−	16.1988i	−0.778463	−	0.778463i	0.201106	−	0.979569i	$-0.435546\pi$
$433$	−16.1988	−	16.1988i	−0.778463	−	0.778463i	−0.979569	+	0.201106i	$0.935546\pi$
$434$		0			0
$435$	1.15249	+	34.5290i	0.0552579	+	1.65554i
$436$		0			0
$437$	−3.89757	+	1.04435i	−0.186446	+	0.0499581i
$438$		0			0
$439$	11.8492	−	6.84114i	0.565532	−	0.326510i	−0.189831	−	0.981817i	$-0.560794\pi$
$439$	11.8492	−	6.84114i	0.565532	−	0.326510i	0.755363	+	0.655307i	$0.227461\pi$
$440$		0			0
$441$	−5.94036	−	10.6649i	−0.282874	−	0.507851i
$442$		0			0
$443$	−15.0479	−	4.03207i	−0.714947	−	0.191569i	−0.117031	−	0.993128i	$-0.537338\pi$
$443$	−15.0479	−	4.03207i	−0.714947	−	0.191569i	−0.597916	+	0.801559i	$0.704004\pi$
$444$		0			0
$445$	11.7248	+	2.63097i	0.555810	+	0.124720i
$446$		0			0
$447$	−13.0516	+	12.8522i	−0.617318	+	0.607887i
$448$		0			0
$449$	−20.0247			−0.945026			−0.472513	−	0.881324i	$-0.656653\pi$
$449$	−20.0247			−0.945026			−0.472513	+	0.881324i	$0.656653\pi$
$450$		0			0
$451$	50.6662			2.38578
$452$		0			0
$453$	−3.57976	−	13.7834i	−0.168192	−	0.647598i
$454$		0			0
$455$	−8.21630	−	1.84368i	−0.385186	−	0.0864331i
$456$		0			0
$457$	28.5585	+	7.65222i	1.33591	+	0.357956i	0.854915	−	0.518768i	$-0.173609\pi$
$457$	28.5585	+	7.65222i	1.33591	+	0.357956i	0.480994	+	0.876724i	$0.340276\pi$
$458$		0			0
$459$	0.730485	−	31.6273i	0.0340961	−	1.47624i
$460$		0			0
$461$	13.0917	−	7.55849i	0.609741	−	0.352034i	−0.163123	−	0.986606i	$-0.552157\pi$
$461$	13.0917	−	7.55849i	0.609741	−	0.352034i	0.772864	+	0.634572i	$0.218824\pi$
$462$		0			0
$463$	−4.72723	+	1.26666i	−0.219693	+	0.0588665i	−0.366986	−	0.930226i	$-0.619610\pi$
$463$	−4.72723	+	1.26666i	−0.219693	+	0.0588665i	0.147294	+	0.989093i	$0.452944\pi$
$464$		0			0
$465$	−27.2842	+	16.9906i	−1.26527	+	0.787922i
$466$		0			0
$467$	11.2304	+	11.2304i	0.519679	+	0.519679i	0.917474	−	0.397795i	$-0.130225\pi$
$467$	11.2304	+	11.2304i	0.519679	+	0.519679i	−0.397795	+	0.917474i	$0.630225\pi$
$468$		0			0
$469$			5.78455i			0.267106i
$470$		0			0
$471$	0.0973643	−	12.6486i	0.00448631	−	0.582815i
$472$		0			0
$473$	−1.34978	−	5.03745i	−0.0620630	−	0.231622i
$474$		0			0
$475$	−8.70271	+	18.4152i	−0.399308	+	0.844949i
$476$		0			0
$477$	−22.2603	+	5.59881i	−1.01923	+	0.256352i
$478$		0			0
$479$	9.01976	+	15.6227i	0.412123	+	0.713818i	0.995122	−	0.0986549i	$-0.0314540\pi$
$479$	9.01976	+	15.6227i	0.412123	+	0.713818i	−0.582999	+	0.812473i	$0.698121\pi$
$480$		0			0
$481$	5.97213	−	10.3440i	0.272306	−	0.471647i
$482$		0			0
$483$	0.781999	−	2.83111i	0.0355822	−	0.128820i
$484$		0			0
$485$	7.38908	+	3.87069i	0.335521	+	0.175759i
$486$		0			0
$487$	−1.26685	+	1.26685i	−0.0574065	+	0.0574065i	−0.735227	−	0.677821i	$-0.762925\pi$
$487$	−1.26685	+	1.26685i	−0.0574065	+	0.0574065i	0.677821	+	0.735227i	$0.262925\pi$
$488$		0			0
$489$	21.3382	+	37.6248i	0.964948	+	1.70145i
$490$		0			0
$491$	5.66640	+	3.27150i	0.255721	+	0.147641i	0.622381	−	0.782714i	$-0.286165\pi$
$491$	5.66640	+	3.27150i	0.255721	+	0.147641i	−0.366660	+	0.930355i	$0.619499\pi$
$492$		0			0
$493$	−14.0564	+	52.4590i	−0.633066	+	2.36264i
$494$		0			0
$495$	32.7043	+	7.86933i	1.46995	+	0.353700i
$496$		0			0
$497$	−4.22730	+	15.7765i	−0.189620	+	0.707672i
$498$		0			0
$499$	5.07659	+	2.93097i	0.227259	+	0.131208i	0.609307	−	0.792934i	$-0.291448\pi$
$499$	5.07659	+	2.93097i	0.227259	+	0.131208i	−0.382048	+	0.924143i	$0.624781\pi$
$500$		0			0
$501$	−36.9252	−	0.284238i	−1.64970	−	0.0126988i
$502$		0			0
$503$	25.3023	−	25.3023i	1.12817	−	1.12817i	0.137700	−	0.990474i	$-0.456029\pi$
$503$	25.3023	−	25.3023i	1.12817	−	1.12817i	0.990474	−	0.137700i	$-0.0439709\pi$
$504$		0			0
$505$	−19.9308	+	6.22788i	−0.886910	+	0.277137i
$506$		0			0
$507$	13.6818	−	3.55337i	0.607629	−	0.157811i
$508$		0			0
$509$	0.901059	−	1.56068i	0.0399387	−	0.0691759i	−0.845365	−	0.534189i	$-0.820617\pi$
$509$	0.901059	−	1.56068i	0.0399387	−	0.0691759i	0.885304	+	0.465013i	$0.153950\pi$
$510$		0			0
$511$	−2.41020	−	4.17459i	−0.106621	−	0.184673i
$512$		0			0
$513$	15.3090	−	14.6178i	0.675910	−	0.645393i
$514$		0			0
$515$	−4.00012	+	0.164348i	−0.176266	+	0.00724204i
$516$		0			0
$517$	8.58929	+	32.0557i	0.377757	+	1.40981i
$518$		0			0
$519$	−30.0404	−	17.6536i	−1.31863	−	0.774905i
$520$		0			0
$521$			26.5523i			1.16328i	0.813447	+	0.581639i	$0.197588\pi$
$521$			26.5523i			1.16328i	−0.813447	+	0.581639i	$0.802412\pi$
$522$		0			0
$523$	9.25440	+	9.25440i	0.404667	+	0.404667i	0.879874	−	0.475207i	$-0.157627\pi$
$523$	9.25440	+	9.25440i	0.404667	+	0.404667i	−0.475207	+	0.879874i	$0.657627\pi$
$524$		0			0
$525$	−8.34719	−	12.2529i	−0.364301	−	0.534759i
$526$		0			0
$527$	−48.8053	+	13.0774i	−2.12599	+	0.569658i
$528$		0			0
$529$	19.0689	−	11.0094i	0.829081	−	0.478670i
$530$		0			0
$531$	18.0036	−	10.0281i	0.781289	−	0.435180i
$532$		0			0
$533$	−21.4689	−	5.75256i	−0.929920	−	0.249171i
$534$		0			0
$535$	−3.32936	−	5.25582i	−0.143941	−	0.227229i
$536$		0			0
$537$	−25.3576	−	7.00420i	−1.09426	−	0.302253i
$538$		0			0
$539$	20.4048			0.878897
$540$		0			0
$541$	8.33300			0.358264			0.179132	−	0.983825i	$-0.442671\pi$
$541$	8.33300			0.358264			0.179132	+	0.983825i	$0.442671\pi$
$542$		0			0
$543$	20.8903	+	5.77024i	0.896488	+	0.247625i
$544$		0			0
$545$	5.41683	−	24.1399i	0.232032	−	1.03404i
$546$		0			0
$547$	24.7083	+	6.62057i	1.05645	+	0.283075i	0.744915	−	0.667159i	$-0.232490\pi$
$547$	24.7083	+	6.62057i	1.05645	+	0.283075i	0.311536	+	0.950234i	$0.399157\pi$
$548$		0			0
$549$	−0.174518	+	11.3351i	−0.00744825	+	0.483771i
$550$		0			0
$551$	−31.4695	+	18.1690i	−1.34065	+	0.774023i
$552$		0			0
$553$	5.95295	−	1.59509i	0.253145	−	0.0678301i
$554$		0			0
$555$	20.1205	−	6.11755i	0.854066	−	0.259675i
$556$		0			0
$557$	−0.642929	−	0.642929i	−0.0272418	−	0.0272418i	0.693355	−	0.720596i	$-0.256132\pi$
$557$	−0.642929	−	0.642929i	−0.0272418	−	0.0272418i	−0.720596	+	0.693355i	$0.756132\pi$
$558$		0			0
$559$			2.28777i			0.0967626i
$560$		0			0
$561$	45.5891	+	26.7909i	1.92477	+	1.13111i
$562$		0			0
$563$	8.66875	+	32.3522i	0.365344	+	1.36348i	0.866954	+	0.498389i	$0.166075\pi$
$563$	8.66875	+	32.3522i	0.365344	+	1.36348i	−0.501609	+	0.865094i	$0.667258\pi$
$564$		0			0
$565$	−0.0977727	−	2.37972i	−0.00411333	−	0.100116i
$566$		0			0
$567$	3.52772	+	14.9983i	0.148150	+	0.629868i
$568$		0			0
$569$	−12.0301	−	20.8368i	−0.504329	−	0.873524i	−0.999987	−	0.00500614i	$-0.998406\pi$
$569$	−12.0301	−	20.8368i	−0.504329	−	0.873524i	0.495658	−	0.868518i	$-0.334927\pi$
$570$		0			0
$571$	−10.6199	+	18.3943i	−0.444430	+	0.769776i	−0.998012	−	0.0630190i	$-0.979927\pi$
$571$	−10.6199	+	18.3943i	−0.444430	+	0.769776i	0.553582	+	0.832795i	$0.313260\pi$
$572$		0			0
$573$	−15.4479	+	4.01208i	−0.645347	+	0.167607i
$574$		0			0
$575$	−0.885087	+	4.87295i	−0.0369107	+	0.203216i
$576$		0			0
$577$	21.2799	−	21.2799i	0.885895	−	0.885895i	−0.108231	−	0.994126i	$-0.534519\pi$
$577$	21.2799	−	21.2799i	0.885895	−	0.885895i	0.994126	+	0.108231i	$0.0345185\pi$
$578$		0			0
$579$	−0.625730	−	0.00481666i	−0.0260044	−	0.000200173i
$580$		0			0
$581$	2.42806	+	1.40184i	0.100733	+	0.0581582i
$582$		0			0
$583$	9.92993	−	37.0590i	0.411256	−	1.53483i
$584$		0			0
$585$	−12.9644	−	7.04767i	−0.536010	−	0.291385i
$586$		0			0
$587$	−7.21191	+	26.9152i	−0.297667	+	1.11091i	0.641409	+	0.767199i	$0.278350\pi$
$587$	−7.21191	+	26.9152i	−0.297667	+	1.11091i	−0.939076	+	0.343710i	$0.888316\pi$
$588$		0			0
$589$	−29.2778	−	16.9035i	−1.20637	−	0.696497i
$590$		0			0
$591$	−7.74889	−	13.6633i	−0.318747	−	0.562033i
$592$		0			0
$593$	−4.16977	+	4.16977i	−0.171232	+	0.171232i	−0.787520	−	0.616289i	$-0.788636\pi$
$593$	−4.16977	+	4.16977i	−0.171232	+	0.171232i	0.616289	+	0.787520i	$0.288636\pi$
$594$		0			0
$595$	−6.95117	−	22.2455i	−0.284970	−	0.911978i
$596$		0			0
$597$	9.34202	−	33.8214i	0.382344	−	1.38422i
$598$		0			0
$599$	−1.63839	+	2.83778i	−0.0669429	+	0.115949i	−0.897554	−	0.440904i	$-0.854658\pi$
$599$	−1.63839	+	2.83778i	−0.0669429	+	0.115949i	0.830611	+	0.556853i	$0.187991\pi$
$600$		0			0
$601$	−8.17825	−	14.1651i	−0.333598	−	0.577808i	0.649617	−	0.760262i	$-0.274929\pi$
$601$	−8.17825	−	14.1651i	−0.333598	−	0.577808i	−0.983214	+	0.182454i	$0.941596\pi$
$602$		0			0
$603$	−2.77401	+	9.74981i	−0.112966	+	0.397043i
$604$		0			0
$605$	−21.4273	+	23.2635i	−0.871146	+	0.945796i
$606$		0			0
$607$	0.992416	+	3.70375i	0.0402809	+	0.150330i	0.983137	−	0.182869i	$-0.0585384\pi$
$607$	0.992416	+	3.70375i	0.0402809	+	0.150330i	−0.942856	+	0.333199i	$0.891872\pi$
$608$		0			0
$609$	0.203600	−	26.4496i	0.00825029	−	1.07179i
$610$		0			0
$611$		−	14.5582i		−	0.588962i
$612$		0			0
$613$	2.05933	+	2.05933i	0.0831755	+	0.0831755i	0.747470	−	0.664295i	$-0.231268\pi$
$613$	2.05933	+	2.05933i	0.0831755	+	0.0831755i	−0.664295	+	0.747470i	$0.731268\pi$
$614$		0			0
$615$	−20.6862	−	33.2186i	−0.834147	−	1.33950i
$616$		0			0
$617$	−5.13662	+	1.37635i	−0.206792	+	0.0554099i	−0.360728	−	0.932671i	$-0.617472\pi$
$617$	−5.13662	+	1.37635i	−0.206792	+	0.0554099i	0.153936	+	0.988081i	$0.450805\pi$
$618$		0			0
$619$	−9.07976	+	5.24220i	−0.364946	+	0.210702i	−0.671248	−	0.741233i	$-0.734242\pi$
$619$	−9.07976	+	5.24220i	−0.364946	+	0.210702i	0.306302	+	0.951934i	$0.400908\pi$
$620$		0			0
$621$	2.67572	−	4.39680i	0.107373	−	0.176437i
$622$		0			0
$623$	−8.88637	−	2.38109i	−0.356025	−	0.0953965i
$624$		0			0
$625$	15.8719	+	19.3153i	0.634877	+	0.772613i
$626$		0			0
$627$	8.89376	+	34.2442i	0.355183	+	1.36758i
$628$		0			0
$629$	33.0589			1.31814
$630$		0			0
$631$	7.92408			0.315453			0.157726	−	0.987483i	$-0.449584\pi$
$631$	7.92408			0.315453			0.157726	+	0.987483i	$0.449584\pi$
$632$		0			0
$633$	10.1803	−	10.0247i	0.404629	−	0.398447i
$634$		0			0
$635$	10.2938	−	6.52072i	0.408496	−	0.258767i
$636$		0			0
$637$	−8.64614	−	2.31673i	−0.342573	−	0.0917921i
$638$		0			0
$639$	−14.6908	+	24.5639i	−0.581158	+	0.971734i
$640$		0			0
$641$	−33.6813	+	19.4459i	−1.33033	+	0.768068i	−0.985351	−	0.170541i	$-0.945449\pi$
$641$	−33.6813	+	19.4459i	−1.33033	+	0.768068i	−0.344983	+	0.938609i	$0.612115\pi$
$642$		0			0
$643$	22.0078	−	5.89698i	0.867903	−	0.232554i	0.202723	−	0.979236i	$-0.435021\pi$
$643$	22.0078	−	5.89698i	0.867903	−	0.232554i	0.665181	+	0.746682i	$0.268354\pi$
$644$		0			0
$645$	−2.75164	+	2.94167i	−0.108346	+	0.115828i
$646$		0			0
$647$	−8.55724	−	8.55724i	−0.336420	−	0.336420i	0.518598	−	0.855018i	$-0.326454\pi$
$647$	−8.55724	−	8.55724i	−0.336420	−	0.336420i	−0.855018	+	0.518598i	$0.826454\pi$
$648$		0			0
$649$			34.4458i			1.35212i
$650$		0			0
$651$	21.4054	−	12.1397i	0.838943	−	0.475791i
$652$		0			0
$653$	2.83332	+	10.5741i	0.110876	+	0.413796i	0.998945	−	0.0459140i	$-0.0146200\pi$
$653$	2.83332	+	10.5741i	0.110876	+	0.413796i	−0.888069	+	0.459710i	$0.847953\pi$
$654$		0			0
$655$	29.7255	+	27.3793i	1.16147	+	1.06980i
$656$		0			0
$657$	−2.06043	−	8.19206i	−0.0803850	−	0.319603i
$658$		0			0
$659$	5.60975	+	9.71638i	0.218525	+	0.378496i	0.954357	−	0.298667i	$-0.0965421\pi$
$659$	5.60975	+	9.71638i	0.218525	+	0.378496i	−0.735832	+	0.677164i	$0.763209\pi$
$660$		0			0
$661$	−14.1181	+	24.4532i	−0.549130	+	0.951121i	0.449205	+	0.893429i	$0.351707\pi$
$661$	−14.1181	+	24.4532i	−0.549130	+	0.951121i	−0.998334	+	0.0576919i	$0.981626\pi$
$662$		0			0
$663$	−16.2757	−	16.5282i	−0.632097	−	0.641904i
$664$		0			0
$665$	7.23602	−	13.8135i	0.280601	−	0.535663i
$666$		0			0
$667$	−6.24791	+	6.24791i	−0.241920	+	0.241920i
$668$		0			0
$669$	−23.9210	+	40.7056i	−0.924841	+	1.57377i
$670$		0			0
$671$	−16.4100	−	9.47430i	−0.633500	−	0.365751i
$672$		0			0
$673$	−8.64541	+	32.2651i	−0.333256	+	1.24373i	0.572492	+	0.819911i	$0.305977\pi$
$673$	−8.64541	+	32.2651i	−0.333256	+	1.24373i	−0.905748	+	0.423818i	$0.860690\pi$
$674$		0			0
$675$	−8.19320	−	24.6550i	−0.315356	−	0.948973i
$676$		0			0
$677$	5.52060	−	20.6032i	0.212174	−	0.791844i	−0.774969	−	0.632000i	$-0.782234\pi$
$677$	5.52060	−	20.6032i	0.212174	−	0.791844i	0.987142	−	0.159844i	$-0.0510990\pi$
$678$		0			0
$679$	−5.53072	−	3.19316i	−0.212250	−	0.122542i
$680$		0			0
$681$	−9.37981	+	15.9613i	−0.359435	+	0.611638i
$682$		0			0
$683$	30.8694	−	30.8694i	1.18118	−	1.18118i	0.201746	−	0.979438i	$-0.435338\pi$
$683$	30.8694	−	30.8694i	1.18118	−	1.18118i	0.979438	−	0.201746i	$-0.0646617\pi$
$684$		0			0
$685$	12.7878	−	24.4117i	0.488596	−	0.932723i
$686$		0			0
$687$	22.7853	+	23.1388i	0.869314	+	0.882801i
$688$		0			0
$689$	−8.41524	+	14.5756i	−0.320595	+	0.555287i
$690$		0			0
$691$	11.0204	+	19.0879i	0.419237	+	0.726140i	0.995863	−	0.0908685i	$-0.0289643\pi$
$691$	11.0204	+	19.0879i	0.419237	+	0.726140i	−0.576626	+	0.817008i	$0.695631\pi$
$692$		0			0
$693$	−24.7702	−	7.04761i	−0.940944	−	0.267717i
$694$		0			0
$695$	−30.3426	−	27.9477i	−1.15096	−	1.06012i
$696$		0			0
$697$	−15.9217	−	59.4208i	−0.603079	−	2.25072i
$698$		0			0
$699$	37.8559	−	21.4693i	1.43184	−	0.812044i
$700$		0			0
$701$		−	20.0002i		−	0.755399i	−0.925928	−	0.377699i	$-0.876715\pi$
$701$		−	20.0002i		−	0.755399i	0.925928	−	0.377699i	$-0.123285\pi$
$702$		0			0
$703$	15.6407	+	15.6407i	0.589901	+	0.589901i
$704$		0			0
$705$	17.5100	−	18.7192i	0.659465	−	0.705007i
$706$		0			0
$707$	15.4421	−	4.13769i	0.580759	−	0.155614i
$708$		0			0
$709$	21.6603	−	12.5056i	0.813469	−	0.469657i	−0.0346900	−	0.999398i	$-0.511044\pi$
$709$	21.6603	−	12.5056i	0.813469	−	0.469657i	0.848159	+	0.529741i	$0.177711\pi$
$710$		0			0
$711$	10.7986	+	0.166258i	0.404979	+	0.00623515i
$712$		0			0
$713$	−7.94038	−	2.12762i	−0.297369	−	0.0796799i
$714$		0			0
$715$	20.8359	−	13.1987i	0.779217	−	0.493604i
$716$		0			0
$717$	−3.31373	+	3.26311i	−0.123754	+	0.121863i
$718$		0			0
$719$	−24.5853			−0.916877			−0.458439	−	0.888726i	$-0.651591\pi$
$719$	−24.5853			−0.916877			−0.458439	+	0.888726i	$0.651591\pi$
$720$		0			0
$721$	3.06511			0.114150
$722$		0			0
$723$	11.9173	+	45.8861i	0.443211	+	1.70652i
$724$		0			0
$725$	3.65881	+	44.4512i	0.135885	+	1.65088i
$726$		0			0
$727$	−38.5509	−	10.3297i	−1.42977	−	0.383107i	−0.540834	−	0.841129i	$-0.681891\pi$
$727$	−38.5509	−	10.3297i	−1.42977	−	0.383107i	−0.888941	+	0.458022i	$0.848558\pi$
$728$		0			0
$729$	−1.24655	+	26.9712i	−0.0461686	+	0.998934i
$730$		0			0
$731$	−5.48369	+	3.16601i	−0.202822	+	0.117099i
$732$		0			0
$733$	28.6966	−	7.68923i	1.05993	−	0.284008i	0.313582	−	0.949561i	$-0.398471\pi$
$733$	28.6966	−	7.68923i	1.05993	−	0.284008i	0.746351	+	0.665553i	$0.231804\pi$
$734$		0			0
$735$	−8.33093	−	13.3781i	−0.307291	−	0.493459i
$736$		0			0
$737$	−11.9807	−	11.9807i	−0.441316	−	0.441316i
$738$		0			0
$739$		−	35.4557i		−	1.30426i	−0.758108	−	0.652130i	$-0.773876\pi$
$739$		−	35.4557i		−	1.30426i	0.758108	−	0.652130i	$-0.226124\pi$
$740$		0			0
$741$	0.119469	−	15.5201i	0.00438879	−	0.570146i
$742$		0			0
$743$	5.77763	+	21.5624i	0.211961	+	0.791047i	0.987214	+	0.159398i	$0.0509552\pi$
$743$	5.77763	+	21.5624i	0.211961	+	0.791047i	−0.775254	+	0.631650i	$0.782378\pi$
$744$		0			0
$745$	−16.0208	+	17.3936i	−0.586956	+	0.637253i
$746$		0			0
$747$	3.42022	+	3.52718i	0.125139	+	0.129053i
$748$		0			0
$749$	2.38165	+	4.12514i	0.0870237	+	0.150729i
$750$		0			0
$751$	11.9176	−	20.6418i	0.434878	−	0.753230i	−0.562408	−	0.826860i	$-0.690125\pi$
$751$	11.9176	−	20.6418i	0.434878	−	0.753230i	0.997286	+	0.0736296i	$0.0234583\pi$
$752$		0			0
$753$	−3.31895	+	12.0158i	−0.120949	+	0.437879i
$754$		0			0
$755$	−5.48326	−	17.5478i	−0.199556	−	0.638631i
$756$		0			0
$757$	36.9273	−	36.9273i	1.34215	−	1.34215i	0.448228	−	0.893919i	$-0.352055\pi$
$757$	36.9273	−	36.9273i	1.34215	−	1.34215i	0.893919	−	0.448228i	$-0.147945\pi$
$758$		0			0
$759$	4.24404	+	7.48333i	0.154049	+	0.271628i
$760$		0			0
$761$	−2.90682	−	1.67825i	−0.105372	−	0.0608367i	0.446388	−	0.894840i	$-0.352710\pi$
$761$	−2.90682	−	1.67825i	−0.105372	−	0.0608367i	−0.551760	+	0.834003i	$0.686044\pi$
$762$		0			0
$763$	−4.90237	+	18.2959i	−0.177478	+	0.662356i
$764$		0			0
$765$	−1.04819	−	40.8281i	−0.0378976	−	1.47614i
$766$		0			0
$767$	3.91092	−	14.5957i	0.141215	−	0.527022i
$768$		0			0
$769$	−22.5987	−	13.0474i	−0.814930	−	0.470500i	0.0337352	−	0.999431i	$-0.489260\pi$
$769$	−22.5987	−	13.0474i	−0.814930	−	0.470500i	−0.848665	+	0.528931i	$0.822593\pi$
$770$		0			0
$771$	−16.2768	−	0.125293i	−0.586194	−	0.00451232i
$772$		0			0
$773$	−29.7518	+	29.7518i	−1.07010	+	1.07010i	−0.0727487	+	0.997350i	$0.523177\pi$
$773$	−29.7518	+	29.7518i	−1.07010	+	1.07010i	−0.997350	+	0.0727487i	$0.976823\pi$
$774$		0			0
$775$	−34.1127	+	23.6256i	−1.22537	+	0.848656i
$776$		0			0
$777$	−15.5837	+	4.04733i	−0.559061	+	0.145197i
$778$		0			0
$779$	20.5801	−	35.6458i	0.737359	−	1.27714i
$780$		0			0
$781$	−23.9203	−	41.4311i	−0.855934	−	1.48252i
$782$		0			0
$783$	13.0272	−	44.4830i	0.465554	−	1.58969i
$784$		0			0
$785$	−0.670354	−	16.3159i	−0.0239260	−	0.582341i
$786$		0			0
$787$	9.19127	+	34.3023i	0.327633	+	1.22274i	0.911638	+	0.410994i	$0.134818\pi$
$787$	9.19127	+	34.3023i	0.327633	+	1.22274i	−0.584005	+	0.811750i	$0.698515\pi$
$788$		0			0
$789$	−15.4894	−	9.10248i	−0.551436	−	0.324057i
$790$		0			0
$791$			1.82347i			0.0648351i
$792$		0			0
$793$	5.87772	+	5.87772i	0.208724	+	0.208724i
$794$		0			0
$795$	−28.3515	+	8.62015i	−1.00552	+	0.305725i
$796$		0			0
$797$	−0.991094	+	0.265563i	−0.0351063	+	0.00940672i	−0.276329	−	0.961063i	$-0.589118\pi$
$797$	−0.991094	+	0.265563i	−0.0351063	+	0.00940672i	0.241223	+	0.970470i	$0.422451\pi$
$798$		0			0
$799$	34.8953	−	20.1468i	1.23451	−	0.712744i
$800$		0			0
$801$	−13.8360	−	8.27482i	−0.488872	−	0.292376i
$802$		0			0
$803$	13.6382	+	3.65434i	0.481280	+	0.128959i
$804$		0			0
$805$	0.830211	−	3.69981i	0.0292611	−	0.130401i
$806$		0			0
$807$	−34.8110	−	9.61537i	−1.22540	−	0.338477i
$808$		0			0
$809$	2.22409			0.0781948			0.0390974	−	0.999235i	$-0.487552\pi$
$809$	2.22409			0.0781948			0.0390974	+	0.999235i	$0.487552\pi$
$810$		0			0
$811$	−32.1204			−1.12790			−0.563949	−	0.825809i	$-0.690719\pi$
$811$	−32.1204			−1.12790			−0.563949	+	0.825809i	$0.690719\pi$
$812$		0			0
$813$	−46.2592	−	12.7776i	−1.62238	−	0.448129i
$814$		0			0
$815$	29.8823	+	47.1730i	1.04673	+	1.65240i
$816$		0			0
$817$	−4.09232	−	1.09653i	−0.143172	−	0.0383629i
$818$		0			0
$819$	9.69575	+	5.79867i	0.338797	+	0.202622i
$820$		0			0
$821$	17.2136	−	9.93829i	0.600760	−	0.346849i	−0.168581	−	0.985688i	$-0.553918\pi$
$821$	17.2136	−	9.93829i	0.600760	−	0.346849i	0.769340	+	0.638839i	$0.220585\pi$
$822$		0			0
$823$	−3.80617	+	1.01986i	−0.132675	+	0.0355501i	−0.324545	−	0.945870i	$-0.605211\pi$
$823$	−3.80617	+	1.01986i	−0.132675	+	0.0355501i	0.191871	+	0.981420i	$0.438545\pi$
$824$		0			0
$825$	42.6661	+	8.08929i	1.48544	+	0.281633i
$826$		0			0
$827$	9.86529	+	9.86529i	0.343050	+	0.343050i	0.857513	−	0.514463i	$-0.172009\pi$
$827$	9.86529	+	9.86529i	0.343050	+	0.343050i	−0.514463	+	0.857513i	$0.672009\pi$
$828$		0			0
$829$			24.5699i			0.853349i	0.904405	+	0.426675i	$0.140315\pi$
$829$			24.5699i			0.853349i	−0.904405	+	0.426675i	$0.859685\pi$
$830$		0			0
$831$	2.51627	+	1.47871i	0.0872884	+	0.0512958i
$832$		0			0
$833$	−6.41216	−	23.9305i	−0.222168	−	0.829142i
$834$		0			0
$835$	−47.6315	+	1.95698i	−1.64836	+	0.0677240i
$836$		0			0
$837$	41.9002	−	10.1963i	1.44828	−	0.352435i
$838$		0			0
$839$	−5.38475	−	9.32666i	−0.185902	−	0.321992i	0.757978	−	0.652280i	$-0.226187\pi$
$839$	−5.38475	−	9.32666i	−0.185902	−	0.321992i	−0.943880	+	0.330288i	$0.892854\pi$
$840$		0			0
$841$	−25.2860	+	43.7966i	−0.871930	+	1.51023i
$842$		0			0
$843$	−30.8831	+	8.02083i	−1.06367	+	0.276252i
$844$		0			0
$845$	17.4185	−	5.44285i	0.599215	−	0.187240i
$846$		0			0
$847$	17.1223	−	17.1223i	0.588328	−	0.588328i
$848$		0			0
$849$	21.3276	+	0.164173i	0.731962	+	0.00563439i
$850$		0			0
$851$	4.65793	+	2.68925i	0.159672	+	0.0921865i
$852$		0			0
$853$	0.779078	−	2.90756i	0.0266751	−	0.0995529i	−0.951305	−	0.308252i	$-0.900256\pi$
$853$	0.779078	−	2.90756i	0.0266751	−	0.0995529i	0.977980	+	0.208699i	$0.0669228\pi$
$854$		0			0
$855$	18.8206	−	19.8124i	0.643650	−	0.677570i
$856$		0			0
$857$	8.23450	−	30.7316i	0.281285	−	1.04977i	−0.670226	−	0.742157i	$-0.733803\pi$
$857$	8.23450	−	30.7316i	0.281285	−	1.04977i	0.951511	−	0.307614i	$-0.0995305\pi$
$858$		0			0
$859$	−10.4539	−	6.03558i	−0.356683	−	0.205931i	0.310942	−	0.950429i	$-0.399356\pi$
$859$	−10.4539	−	6.03558i	−0.356683	−	0.205931i	−0.667625	+	0.744498i	$0.732689\pi$
$860$		0			0
$861$	14.7801	+	26.0612i	0.503705	+	0.888162i
$862$		0			0
$863$	39.2965	−	39.2965i	1.33767	−	1.33767i	0.439355	−	0.898313i	$-0.355207\pi$
$863$	39.2965	−	39.2965i	1.33767	−	1.33767i	0.898313	−	0.439355i	$-0.144793\pi$
$864$		0			0
$865$	−39.8468	−	20.8733i	−1.35483	−	0.709713i
$866$		0			0
$867$	9.25416	−	33.5033i	0.314288	−	1.13783i
$868$		0			0
$869$	−9.02585	+	15.6332i	−0.306181	+	0.530321i
$870$		0			0
$871$	3.71634	+	6.43689i	0.125923	+	0.218106i
$872$		0			0
$873$	−7.79069	−	8.03434i	−0.263675	−	0.271921i
$874$		0			0
$875$	−11.5344	−	15.2743i	−0.389933	−	0.516367i
$876$		0			0
$877$	3.33188	+	12.4348i	0.112510	+	0.419892i	0.999089	−	0.0426856i	$-0.0135914\pi$
$877$	3.33188	+	12.4348i	0.112510	+	0.419892i	−0.886579	+	0.462577i	$0.846925\pi$
$878$		0			0
$879$	−0.152053	+	19.7531i	−0.00512861	+	0.666255i
$880$		0			0
$881$			12.8747i			0.433761i	0.976198	+	0.216881i	$0.0695882\pi$
$881$			12.8747i			0.433761i	−0.976198	+	0.216881i	$0.930412\pi$
$882$		0			0
$883$	−12.4323	−	12.4323i	−0.418380	−	0.418380i	0.466265	−	0.884645i	$-0.345599\pi$
$883$	−12.4323	−	12.4323i	−0.418380	−	0.418380i	−0.884645	+	0.466265i	$0.845599\pi$
$884$		0			0
$885$	22.5839	−	14.0636i	0.759150	−	0.472744i
$886$		0			0
$887$	41.3915	−	11.0908i	1.38979	−	0.372393i	0.515123	−	0.857116i	$-0.327746\pi$
$887$	41.3915	−	11.0908i	1.38979	−	0.372393i	0.874668	+	0.484723i	$0.161080\pi$
$888$		0			0
$889$	−8.07929	+	4.66458i	−0.270971	+	0.156445i
$890$		0			0
$891$	−38.3704	−	23.7574i	−1.28546	−	0.795902i
$892$		0			0
$893$	26.0414	+	6.97777i	0.871442	+	0.233502i
$894$		0			0
$895$	−33.1384	−	7.43602i	−1.10769	−	0.248559i
$896$		0			0
$897$	−0.948685	−	3.65278i	−0.0316757	−	0.121963i
$898$		0			0
$899$	−74.0299			−2.46904
$900$		0			0
$901$	−46.5828			−1.55190
$902$		0			0
$903$	2.19736	−	2.16379i	0.0731234	−	0.0720063i
$904$		0			0
$905$	27.3003	+	6.12599i	0.907492	+	0.203635i
$906$		0			0
$907$	13.4889	+	3.61433i	0.447891	+	0.120012i	0.475712	−	0.879601i	$-0.342190\pi$
$907$	13.4889	+	3.61433i	0.447891	+	0.120012i	−0.0278216	+	0.999613i	$0.508857\pi$
$908$		0			0
$909$	28.0117	+	0.431275i	0.929091	+	0.0143045i
$910$		0			0
$911$	2.63737	−	1.52269i	0.0873800	−	0.0504489i	−0.455673	−	0.890147i	$-0.650601\pi$
$911$	2.63737	−	1.52269i	0.0873800	−	0.0504489i	0.543053	+	0.839698i	$0.317268\pi$
$912$		0			0
$913$	−7.93236	+	2.12547i	−0.262523	+	0.0703427i
$914$		0			0
$915$	0.488220	+	14.6272i	0.0161400	+	0.483559i
$916$		0			0
$917$	−21.8784	−	21.8784i	−0.722489	−	0.722489i
$918$		0			0
$919$			56.8751i			1.87614i	0.346451	+	0.938068i	$0.387387\pi$
$919$			56.8751i			1.87614i	−0.346451	+	0.938068i	$0.612613\pi$
$920$		0			0
$921$	−32.2996	+	18.3182i	−1.06431	+	0.603604i
$922$		0			0
$923$	5.43174	+	20.2715i	0.178788	+	0.667245i
$924$		0			0
$925$	25.5596	−	9.15440i	0.840394	−	0.300995i
$926$		0			0
$927$	5.16621	+	1.46989i	0.169681	+	0.0482774i
$928$		0			0
$929$	−2.52331	−	4.37050i	−0.0827872	−	0.143392i	0.821659	−	0.569979i	$-0.193049\pi$
$929$	−2.52331	−	4.37050i	−0.0827872	−	0.143392i	−0.904446	+	0.426588i	$0.859715\pi$
$930$		0			0
$931$	8.28822	−	14.3556i	0.271636	−	0.470486i
$932$		0			0
$933$	6.14499	+	6.24033i	0.201178	+	0.204299i
$934$		0			0
$935$	60.4711	+	31.6771i	1.97762	+	1.03595i
$936$		0			0
$937$	10.1617	−	10.1617i	0.331970	−	0.331970i	−0.521364	−	0.853334i	$-0.674577\pi$
$937$	10.1617	−	10.1617i	0.331970	−	0.331970i	0.853334	+	0.521364i	$0.174577\pi$
$938$		0			0
$939$	−22.8347	+	38.8571i	−0.745184	+	1.26805i
$940$		0			0
$941$	21.5910	+	12.4656i	0.703846	+	0.406365i	0.808778	−	0.588114i	$-0.200129\pi$
$941$	21.5910	+	12.4656i	0.703846	+	0.406365i	−0.104932	+	0.994479i	$0.533463\pi$
$942$		0			0
$943$	2.59038	−	9.66745i	0.0843545	−	0.314815i
$944$		0			0
$945$	5.49261	+	19.1177i	0.178675	+	0.621899i
$946$		0			0
$947$	7.38190	−	27.5496i	0.239879	−	0.895242i	−0.736009	−	0.676972i	$-0.763292\pi$
$947$	7.38190	−	27.5496i	0.239879	−	0.895242i	0.975888	−	0.218270i	$-0.0700414\pi$
$948$		0			0
$949$	−5.36401	−	3.09691i	−0.174123	−	0.100530i
$950$		0			0
$951$	−13.1475	+	22.3726i	−0.426336	+	0.725481i
$952$		0			0
$953$	37.8124	−	37.8124i	1.22486	−	1.22486i	0.258982	−	0.965882i	$-0.416613\pi$
$953$	37.8124	−	37.8124i	1.22486	−	1.22486i	0.965882	−	0.258982i	$-0.0833871\pi$
$954$		0			0
$955$	−19.6670	+	6.14546i	−0.636411	+	0.198862i
$956$		0			0
$957$	54.3598	+	55.2031i	1.75720	+	1.78446i
$958$		0			0
$959$	−10.5494	+	18.2721i	−0.340658	+	0.590037i
$960$		0			0
$961$	−18.9369	−	32.7997i	−0.610869	−	1.05806i
$962$		0			0
$963$	2.03603	+	8.09503i	0.0656100	+	0.260859i
$964$		0			0
$965$	−0.807157	+	0.0331627i	−0.0259833	+	0.00106754i
$966$		0			0
$967$	−6.99300	−	26.0982i	−0.224880	−	0.839262i	−0.982453	−	0.186512i	$-0.940282\pi$
$967$	−6.99300	−	26.0982i	−0.224880	−	0.839262i	0.757573	−	0.652750i	$-0.226385\pi$
$968$		0			0
$969$	37.3663	−	21.1917i	1.20038	−	0.680774i
$970$		0			0
$971$			22.1746i			0.711616i	0.934559	+	0.355808i	$0.115794\pi$
$971$			22.1746i			0.711616i	−0.934559	+	0.355808i	$0.884206\pi$
$972$		0			0
$973$	22.3326	+	22.3326i	0.715949	+	0.715949i
$974$		0			0
$975$	−17.1605	−	8.27192i	−0.549576	−	0.264914i
$976$		0			0
$977$	−30.8299	+	8.26085i	−0.986336	+	0.264288i	−0.715711	−	0.698397i	$-0.753897\pi$
$977$	−30.8299	+	8.26085i	−0.986336	+	0.264288i	−0.270625	+	0.962685i	$0.587230\pi$
$978$		0			0
$979$	23.3367	−	13.4735i	0.745846	−	0.430614i
$980$		0			0
$981$	−17.0368	+	28.4866i	−0.543943	+	0.909508i
$982$		0			0
$983$	−2.38481	−	0.639007i	−0.0760635	−	0.0203811i	0.220587	−	0.975367i	$-0.429203\pi$
$983$	−2.38481	−	0.639007i	−0.0760635	−	0.0203811i	−0.296650	+	0.954986i	$0.595870\pi$
$984$		0			0
$985$	−10.8516	−	17.1307i	−0.345762	−	0.545829i
$986$		0			0
$987$	−13.9828	+	13.7692i	−0.445078	+	0.438278i
$988$		0			0
$989$	−1.03019			−0.0327580
$990$		0			0
$991$	−23.5584			−0.748358			−0.374179	−	0.927357i	$-0.622075\pi$
$991$	−23.5584			−0.748358			−0.374179	+	0.927357i	$0.622075\pi$
$992$		0			0
$993$	5.65277	+	21.7652i	0.179385	+	0.690698i
$994$		0			0
$995$	9.91798	−	44.1991i	0.314421	−	1.40121i
$996$		0			0
$997$	−41.3167	−	11.0708i	−1.30851	−	0.350615i	−0.463850	−	0.885914i	$-0.653532\pi$
$997$	−41.3167	−	11.0708i	−1.30851	−	0.350615i	−0.844663	+	0.535299i	$0.820199\pi$
$998$		0			0
$999$	−28.2071	−	0.651488i	−0.892432	−	0.0206122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.3	✓	72
3.2	odd	2		1080.2.bt.a.233.16		72
4.3	odd	2		720.2.cu.e.113.16		72
5.2	odd	4	inner	360.2.bs.a.257.8	yes	72
9.2	odd	6	inner	360.2.bs.a.353.8	yes	72
9.7	even	3		1080.2.bt.a.953.14		72
15.2	even	4		1080.2.bt.a.17.14		72
20.7	even	4		720.2.cu.e.257.11		72
36.11	even	6		720.2.cu.e.353.11		72
45.2	even	12	inner	360.2.bs.a.137.3	yes	72
45.7	odd	12		1080.2.bt.a.737.16		72
180.47	odd	12		720.2.cu.e.497.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.3	✓	72	1.1	even	1	trivial
360.2.bs.a.137.3	yes	72	45.2	even	12	inner
360.2.bs.a.257.8	yes	72	5.2	odd	4	inner
360.2.bs.a.353.8	yes	72	9.2	odd	6	inner
720.2.cu.e.113.16		72	4.3	odd	2
720.2.cu.e.257.11		72	20.7	even	4
720.2.cu.e.353.11		72	36.11	even	6
720.2.cu.e.497.16		72	180.47	odd	12
1080.2.bt.a.17.14		72	15.2	even	4
1080.2.bt.a.233.16		72	3.2	odd	2
1080.2.bt.a.737.16		72	45.7	odd	12
1080.2.bt.a.953.14		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)

\(f(q)\)	\(=\)	\(q+(-1.66953 - 0.461153i) q^{3} +(-2.18181 - 0.489584i) q^{5} +(1.65362 + 0.443086i) q^{7} +(2.57468 + 1.53982i) q^{9} +O(q^{10})\)	\(q+(-1.66953 - 0.461153i) q^{3} +(-2.18181 - 0.489584i) q^{5} +(1.65362 + 0.443086i) q^{7} +(2.57468 + 1.53982i) q^{9} +(-4.34262 + 2.50721i) q^{11} +(2.12477 - 0.569329i) q^{13} +(3.41683 + 1.82352i) q^{15} +(4.30508 + 4.30508i) q^{17} +4.07361i q^{19} +(-2.55644 - 1.50232i) q^{21} +(0.256369 + 0.956784i) q^{23} +(4.52062 + 2.13636i) q^{25} +(-3.58842 - 3.75809i) q^{27} +(4.46015 + 7.72522i) q^{29} +(-4.14951 + 7.18717i) q^{31} +(8.40634 - 2.18326i) q^{33} +(-3.39096 - 1.77631i) q^{35} +(3.83952 - 3.83952i) q^{37} +(-3.80991 - 0.0293274i) q^{39} +(-8.75041 - 5.05205i) q^{41} +(-0.269180 + 1.00459i) q^{43} +(-4.86359 - 4.62011i) q^{45} +(1.71292 - 6.39270i) q^{47} +(-3.52405 - 2.03461i) q^{49} +(-5.20217 - 9.17277i) q^{51} +(-5.41021 + 5.41021i) q^{53} +(10.7023 - 3.34419i) q^{55} +(1.87856 - 6.80103i) q^{57} +(3.43467 - 5.94903i) q^{59} +(1.88941 + 3.27256i) q^{61} +(3.57526 + 3.68707i) q^{63} +(-4.91457 + 0.201919i) q^{65} +(0.874529 + 3.26379i) q^{67} +(0.0132062 - 1.71561i) q^{69} +9.54059i q^{71} +(-1.99102 - 1.99102i) q^{73} +(-6.56213 - 5.65142i) q^{75} +(-8.29194 + 2.22182i) q^{77} +(3.11765 - 1.79998i) q^{79} +(4.25792 + 7.92907i) q^{81} +(1.58191 + 0.423871i) q^{83} +(-7.28519 - 11.5006i) q^{85} +(-3.88387 - 14.9543i) q^{87} -5.37389 q^{89} +3.76581 q^{91} +(10.2421 - 10.0857i) q^{93} +(1.99438 - 8.88787i) q^{95} +(-3.60332 - 0.965508i) q^{97} +(-15.0415 - 0.231582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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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