LMFDB - Embedded newform 504.2.bs.a.353.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(257,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.5
Character	$\chi$	$=$	504.353
Dual form			504.2.bs.a.257.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41991 + 0.991901i) q^{3} +(-1.11047 + 1.92339i) q^{5} +(0.362456 + 2.62081i) q^{7} +(1.03226 - 2.81681i) q^{9} +(-1.01582 + 0.586482i) q^{11} +(-3.12404 + 1.80366i) q^{13} +(-0.331050 - 3.83251i) q^{15} +(3.71178 - 6.42899i) q^{17} +(-3.05231 + 1.76225i) q^{19} +(-3.11423 - 3.36178i) q^{21} +(-5.03374 - 2.90623i) q^{23} +(0.0337168 + 0.0583992i) q^{25} +(1.32828 + 5.02351i) q^{27} +(-6.04430 - 3.48968i) q^{29} +7.95031i q^{31} +(0.860632 - 1.84034i) q^{33} +(-5.44333 - 2.21318i) q^{35} +(-5.54350 - 9.60163i) q^{37} +(2.64678 - 5.65977i) q^{39} +(0.809022 + 1.40127i) q^{41} +(0.904302 - 1.56630i) q^{43} +(4.27153 + 5.11343i) q^{45} -8.52953 q^{47} +(-6.73725 + 1.89985i) q^{49} +(1.10654 + 12.8103i) q^{51} +(9.62611 + 5.55764i) q^{53} -2.60508i q^{55} +(2.58602 - 5.52983i) q^{57} -4.00276 q^{59} +8.18688i q^{61} +(7.75647 + 1.68440i) q^{63} -8.01166i q^{65} +9.92669 q^{67} +(10.0301 - 0.866397i) q^{69} +3.67194i q^{71} +(6.92803 + 3.99990i) q^{73} +(-0.105801 - 0.0494776i) q^{75} +(-1.90525 - 2.44969i) q^{77} -4.51987 q^{79} +(-6.86886 - 5.81539i) q^{81} +(0.390969 - 0.677179i) q^{83} +(8.24363 + 14.2784i) q^{85} +(12.0438 - 1.04033i) q^{87} +(-1.75440 - 3.03870i) q^{89} +(-5.85938 - 7.53375i) q^{91} +(-7.88592 - 11.2887i) q^{93} -7.82772i q^{95} +(3.49226 + 2.01626i) q^{97} +(0.603418 + 3.46677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.41991	+	0.991901i	−0.819783	+	0.572674i
$3$	−1.41991	+	0.991901i	−0.819783	+	0.572674i
$4$		0			0
$5$	−1.11047	+	1.92339i	−0.496617	+	0.860166i	−0.999992	−	0.00390210i	$-0.998758\pi$
$5$	−1.11047	+	1.92339i	−0.496617	+	0.860166i	0.503376	+	0.864068i	$0.332091\pi$
$6$		0			0
$7$	0.362456	+	2.62081i	0.136995	+	0.990572i
$7$	0.362456	+	2.62081i	0.136995	+	0.990572i
$8$		0			0
$9$	1.03226	−	2.81681i	0.344088	−	0.938937i
$10$		0			0
$11$	−1.01582	+	0.586482i	−0.306280	+	0.176831i	−0.645261	−	0.763962i	$-0.723251\pi$
$11$	−1.01582	+	0.586482i	−0.306280	+	0.176831i	0.338980	+	0.940793i	$0.389918\pi$
$12$		0			0
$13$	−3.12404	+	1.80366i	−0.866453	+	0.500247i	−0.866168	−	0.499753i	$-0.833424\pi$
$13$	−3.12404	+	1.80366i	−0.866453	+	0.500247i	−0.000284763		1.00000i	$0.500091\pi$
$14$		0			0
$15$	−0.331050	−	3.83251i	−0.0854767	−	0.989549i
$16$		0			0
$17$	3.71178	−	6.42899i	0.900238	−	1.55926i	0.0730533	−	0.997328i	$-0.476726\pi$
$17$	3.71178	−	6.42899i	0.900238	−	1.55926i	0.827185	−	0.561930i	$-0.189941\pi$
$18$		0			0
$19$	−3.05231	+	1.76225i	−0.700249	+	0.404289i	−0.807440	−	0.589950i	$-0.799148\pi$
$19$	−3.05231	+	1.76225i	−0.700249	+	0.404289i	0.107191	+	0.994238i	$0.465814\pi$
$20$		0			0
$21$	−3.11423	−	3.36178i	−0.679581	−	0.733600i
$22$		0			0
$23$	−5.03374	−	2.90623i	−1.04961	−	0.605991i	−0.127068	−	0.991894i	$-0.540557\pi$
$23$	−5.03374	−	2.90623i	−1.04961	−	0.605991i	−0.922539	+	0.385903i	$0.873890\pi$
$24$		0			0
$25$	0.0337168	+	0.0583992i	0.00674336	+	0.0116798i
$26$		0			0
$27$	1.32828	+	5.02351i	0.255628	+	0.966775i
$28$		0			0
$29$	−6.04430	−	3.48968i	−1.12240	−	0.648017i	−0.180387	−	0.983596i	$-0.557735\pi$
$29$	−6.04430	−	3.48968i	−1.12240	−	0.648017i	−0.942012	+	0.335579i	$0.891068\pi$
$30$		0			0
$31$			7.95031i			1.42792i	0.700187	+	0.713959i	$0.253100\pi$
$31$			7.95031i			1.42792i	−0.700187	+	0.713959i	$0.746900\pi$
$32$		0			0
$33$	0.860632	−	1.84034i	0.149817	−	0.320362i
$34$		0			0
$35$	−5.44333	−	2.21318i	−0.920090	−	0.374096i
$36$		0			0
$37$	−5.54350	−	9.60163i	−0.911346	−	1.57850i	−0.812164	−	0.583429i	$-0.801711\pi$
$37$	−5.54350	−	9.60163i	−0.911346	−	1.57850i	−0.0991818	−	0.995069i	$-0.531623\pi$
$38$		0			0
$39$	2.64678	−	5.65977i	0.423825	−	0.906289i
$40$		0			0
$41$	0.809022	+	1.40127i	0.126348	+	0.218841i	0.922259	−	0.386572i	$-0.126341\pi$
$41$	0.809022	+	1.40127i	0.126348	+	0.218841i	−0.795911	+	0.605414i	$0.793008\pi$
$42$		0			0
$43$	0.904302	−	1.56630i	0.137905	−	0.238858i	−0.788799	−	0.614652i	$-0.789297\pi$
$43$	0.904302	−	1.56630i	0.137905	−	0.238858i	0.926703	+	0.375794i	$0.122630\pi$
$44$		0			0
$45$	4.27153	+	5.11343i	0.636762	+	0.762265i
$46$		0			0
$47$	−8.52953			−1.24416			−0.622080	−	0.782954i	$-0.713712\pi$
$47$	−8.52953			−1.24416			−0.622080	+	0.782954i	$0.713712\pi$
$48$		0			0
$49$	−6.73725	+	1.89985i	−0.962465	+	0.271407i
$50$		0			0
$51$	1.10654	+	12.8103i	0.154947	+	1.79380i
$52$		0			0
$53$	9.62611	+	5.55764i	1.32225	+	0.763400i	0.984087	−	0.177688i	$-0.0568617\pi$
$53$	9.62611	+	5.55764i	1.32225	+	0.763400i	0.338161	+	0.941088i	$0.390195\pi$
$54$		0			0
$55$		−	2.60508i		−	0.351269i
$56$		0			0
$57$	2.58602	−	5.52983i	0.342526	−	0.732444i
$58$		0			0
$59$	−4.00276			−0.521115			−0.260557	−	0.965458i	$-0.583906\pi$
$59$	−4.00276			−0.521115			−0.260557	+	0.965458i	$0.583906\pi$
$60$		0			0
$61$			8.18688i			1.04822i	0.851650	+	0.524111i	$0.175602\pi$
$61$			8.18688i			1.04822i	−0.851650	+	0.524111i	$0.824398\pi$
$62$		0			0
$63$	7.75647	+	1.68440i	0.977223	+	0.212214i
$64$		0			0
$65$		−	8.01166i		−	0.993724i
$66$		0			0
$67$	9.92669			1.21274			0.606369	−	0.795183i	$-0.292625\pi$
$67$	9.92669			1.21274			0.606369	+	0.795183i	$0.292625\pi$
$68$		0			0
$69$	10.0301	−	0.866397i	1.20749	−	0.104302i
$70$		0			0
$71$			3.67194i			0.435779i	0.975973	+	0.217890i	$0.0699172\pi$
$71$			3.67194i			0.435779i	−0.975973	+	0.217890i	$0.930083\pi$
$72$		0			0
$73$	6.92803	+	3.99990i	0.810865	+	0.468153i	0.847256	−	0.531185i	$-0.178253\pi$
$73$	6.92803	+	3.99990i	0.810865	+	0.468153i	−0.0363913	+	0.999338i	$0.511586\pi$
$74$		0			0
$75$	−0.105801	−	0.0494776i	−0.0122168	−	0.00571318i
$76$		0			0
$77$	−1.90525	−	2.44969i	−0.217123	−	0.279168i
$78$		0			0
$79$	−4.51987			−0.508525			−0.254262	−	0.967135i	$-0.581833\pi$
$79$	−4.51987			−0.508525			−0.254262	+	0.967135i	$0.581833\pi$
$80$		0			0
$81$	−6.86886	−	5.81539i	−0.763207	−	0.646155i
$82$		0			0
$83$	0.390969	−	0.677179i	0.0429145	−	0.0743300i	−0.843770	−	0.536704i	$-0.819669\pi$
$83$	0.390969	−	0.677179i	0.0429145	−	0.0743300i	0.886685	+	0.462374i	$0.153002\pi$
$84$		0			0
$85$	8.24363	+	14.2784i	0.894147	+	1.54871i
$86$		0			0
$87$	12.0438	−	1.04033i	1.29123	−	0.111535i
$88$		0			0
$89$	−1.75440	−	3.03870i	−0.185966	−	0.322102i	0.757936	−	0.652329i	$-0.226208\pi$
$89$	−1.75440	−	3.03870i	−0.185966	−	0.322102i	−0.943901	+	0.330227i	$0.892875\pi$
$90$		0			0
$91$	−5.85938	−	7.53375i	−0.614230	−	0.789752i
$92$		0			0
$93$	−7.88592	−	11.2887i	−0.817732	−	1.17058i
$94$		0			0
$95$		−	7.82772i		−	0.803107i
$96$		0			0
$97$	3.49226	+	2.01626i	0.354585	+	0.204720i	0.666703	−	0.745324i	$-0.267705\pi$
$97$	3.49226	+	2.01626i	0.354585	+	0.204720i	−0.312118	+	0.950043i	$0.601038\pi$
$98$		0			0
$99$	0.603418	+	3.46677i	0.0606458	+	0.348424i
$100$		0			0
$101$	1.13904	+	1.97288i	0.113339	+	0.196309i	0.917115	−	0.398624i	$-0.130512\pi$
$101$	1.13904	+	1.97288i	0.113339	+	0.196309i	−0.803775	+	0.594933i	$0.797179\pi$
$102$		0			0
$103$	7.68427	+	4.43651i	0.757153	+	0.437143i	0.828273	−	0.560325i	$-0.189324\pi$
$103$	7.68427	+	4.43651i	0.757153	+	0.437143i	−0.0711195	+	0.997468i	$0.522657\pi$
$104$		0			0
$105$	9.92427	−	2.25673i	0.968509	−	0.220234i
$106$		0			0
$107$	0.574764	−	0.331840i	0.0555646	−	0.0320802i	−0.471960	−	0.881620i	$-0.656453\pi$
$107$	0.574764	−	0.331840i	0.0555646	−	0.0320802i	0.527525	+	0.849540i	$0.323120\pi$
$108$		0			0
$109$	−8.03435	+	13.9159i	−0.769551	+	1.33290i	0.168256	+	0.985743i	$0.446187\pi$
$109$	−8.03435	+	13.9159i	−0.769551	+	1.33290i	−0.937807	+	0.347158i	$0.887147\pi$
$110$		0			0
$111$	17.3951	+	8.13480i	1.65107	+	0.772121i
$112$		0			0
$113$	−4.86666	+	2.80977i	−0.457817	+	0.264321i	−0.711126	−	0.703065i	$-0.751814\pi$
$113$	−4.86666	+	2.80977i	−0.457817	+	0.264321i	0.253309	+	0.967385i	$0.418481\pi$
$114$		0			0
$115$	11.1796	−	6.45456i	1.04250	−	0.601891i
$116$		0			0
$117$	1.85575	+	10.6617i	0.171564	+	0.985674i
$118$		0			0
$119$	18.1945	+	7.39763i	1.66789	+	0.678139i
$120$		0			0
$121$	−4.81208	+	8.33476i	−0.437462	+	0.757706i
$122$		0			0
$123$	−2.53865	−	1.18720i	−0.228903	−	0.107046i
$124$		0			0
$125$	−11.2545			−1.00663
$126$		0			0
$127$	7.74425			0.687191			0.343595	−	0.939118i	$-0.388355\pi$
$127$	7.74425			0.687191			0.343595	+	0.939118i	$0.388355\pi$
$128$		0			0
$129$	0.269588	+	3.12097i	0.0237359	+	0.274786i
$130$		0			0
$131$	−7.81293	+	13.5324i	−0.682619	+	1.18233i	0.291559	+	0.956553i	$0.405826\pi$
$131$	−7.81293	+	13.5324i	−0.682619	+	1.18233i	−0.974179	+	0.225778i	$0.927507\pi$
$132$		0			0
$133$	−5.72486	−	7.36078i	−0.496408	−	0.638261i
$134$		0			0
$135$	−11.1372	−	3.02366i	−0.958536	−	0.260235i
$136$		0			0
$137$	0.931541	−	0.537826i	0.0795870	−	0.0459496i	−0.459678	−	0.888085i	$-0.652035\pi$
$137$	0.931541	−	0.537826i	0.0795870	−	0.0459496i	0.539265	+	0.842136i	$0.318702\pi$
$138$		0			0
$139$	−5.81776	+	3.35889i	−0.493456	+	0.284897i	−0.726007	−	0.687687i	$-0.758626\pi$
$139$	−5.81776	+	3.35889i	−0.493456	+	0.284897i	0.232551	+	0.972584i	$0.425293\pi$
$140$		0			0
$141$	12.1111	−	8.46045i	1.01994	−	0.712498i
$142$		0			0
$143$	2.11563	−	3.66439i	0.176918	−	0.306431i
$144$		0			0
$145$	13.4240	−	7.75036i	1.11480	−	0.643633i
$146$		0			0
$147$	7.68180	−	9.38030i	0.633584	−	0.773674i
$148$		0			0
$149$	15.2105	+	8.78176i	1.24609	+	0.719430i	0.970327	−	0.241796i	$-0.0777365\pi$
$149$	15.2105	+	8.78176i	1.24609	+	0.719430i	0.275762	+	0.961226i	$0.411070\pi$
$150$		0			0
$151$	−0.848028	−	1.46883i	−0.0690115	−	0.119531i	0.829455	−	0.558574i	$-0.188651\pi$
$151$	−0.848028	−	1.46883i	−0.0690115	−	0.119531i	−0.898466	+	0.439042i	$0.855318\pi$
$152$		0			0
$153$	−14.2777	−	17.0918i	−1.15428	−	1.38179i
$154$		0			0
$155$	−15.2915	−	8.82858i	−1.22825	−	0.709128i
$156$		0			0
$157$			7.88233i			0.629078i	0.949244	+	0.314539i	$0.101850\pi$
$157$			7.88233i			0.629078i	−0.949244	+	0.314539i	$0.898150\pi$
$158$		0			0
$159$	−19.1808	+	1.65683i	−1.52114	+	0.131395i
$160$		0			0
$161$	5.79216	−	14.2458i	0.456486	−	1.12273i
$162$		0			0
$163$	−5.69385	−	9.86204i	−0.445977	−	0.772455i	0.552143	−	0.833750i	$-0.313810\pi$
$163$	−5.69385	−	9.86204i	−0.445977	−	0.772455i	−0.998120	+	0.0612949i	$0.980477\pi$
$164$		0			0
$165$	2.58398	+	3.69897i	0.201163	+	0.287964i
$166$		0			0
$167$	−8.05638	−	13.9541i	−0.623422	−	1.07980i	−0.988844	−	0.148956i	$-0.952409\pi$
$167$	−8.05638	−	13.9541i	−0.623422	−	1.07980i	0.365422	−	0.930842i	$-0.380925\pi$
$168$		0			0
$169$	0.00641296	−	0.0111076i	0.000493305	−	0.000854429i
$170$		0			0
$171$	1.81314	+	10.4169i	0.138654	+	0.796601i
$172$		0			0
$173$	6.90364			0.524874			0.262437	−	0.964949i	$-0.415474\pi$
$173$	6.90364			0.524874			0.262437	+	0.964949i	$0.415474\pi$
$174$		0			0
$175$	−0.140832	+	0.109532i	−0.0106459	+	0.00827986i
$176$		0			0
$177$	5.68354	−	3.97034i	0.427201	−	0.298429i
$178$		0			0
$179$	5.28759	+	3.05279i	0.395213	+	0.228176i	0.684416	−	0.729091i	$-0.260057\pi$
$179$	5.28759	+	3.05279i	0.395213	+	0.228176i	−0.289203	+	0.957268i	$0.593390\pi$
$180$		0			0
$181$			5.46329i			0.406083i	0.979170	+	0.203041i	$0.0650826\pi$
$181$			5.46329i			0.406083i	−0.979170	+	0.203041i	$0.934917\pi$
$182$		0			0
$183$	−8.12057	−	11.6246i	−0.600290	−	0.859315i
$184$		0			0
$185$	24.6236			1.81036
$186$		0			0
$187$			8.70756i			0.636760i
$188$		0			0
$189$	−12.6842	+	5.30196i	−0.922640	+	0.385661i
$190$		0			0
$191$			6.01636i			0.435328i	0.976024	+	0.217664i	$0.0698438\pi$
$191$			6.01636i			0.435328i	−0.976024	+	0.217664i	$0.930156\pi$
$192$		0			0
$193$	−5.78034			−0.416078			−0.208039	−	0.978121i	$-0.566708\pi$
$193$	−5.78034			−0.416078			−0.208039	+	0.978121i	$0.566708\pi$
$194$		0			0
$195$	7.94677	+	11.3758i	0.569080	+	0.814638i
$196$		0			0
$197$			7.95354i			0.566666i	0.959022	+	0.283333i	$0.0914402\pi$
$197$			7.95354i			0.566666i	−0.959022	+	0.283333i	$0.908560\pi$
$198$		0			0
$199$	−15.5229	−	8.96214i	−1.10039	−	0.635309i	−0.164065	−	0.986450i	$-0.552461\pi$
$199$	−15.5229	−	8.96214i	−1.10039	−	0.635309i	−0.936323	+	0.351141i	$0.885794\pi$
$200$		0			0
$201$	−14.0950	+	9.84629i	−0.994182	+	0.694504i
$202$		0			0
$203$	6.95498	−	17.1058i	0.488144	−	1.20059i
$204$		0			0
$205$	−3.59358			−0.250986
$206$		0			0
$207$	−13.3825	+	11.1791i	−0.930145	+	0.777001i
$208$		0			0
$209$	2.06706	−	3.58026i	0.142982	−	0.247651i
$210$		0			0
$211$	−4.00200	−	6.93166i	−0.275509	−	0.477195i	0.694755	−	0.719247i	$-0.255513\pi$
$211$	−4.00200	−	6.93166i	−0.275509	−	0.477195i	−0.970263	+	0.242052i	$0.922180\pi$
$212$		0			0
$213$	−3.64220	−	5.21381i	−0.249559	−	0.357244i
$214$		0			0
$215$	2.00840	+	3.47865i	0.136972	+	0.237242i
$216$		0			0
$217$	−20.8362	+	2.88164i	−1.41446	+	0.195618i
$218$		0			0
$219$	−13.8047	+	1.19244i	−0.932832	+	0.0805776i
$220$		0			0
$221$			26.7792i			1.80136i
$222$		0			0
$223$	14.2405	+	8.22177i	0.953616	+	0.550570i	0.894202	−	0.447663i	$-0.147744\pi$
$223$	14.2405	+	8.22177i	0.953616	+	0.550570i	0.0594134	+	0.998233i	$0.481077\pi$
$224$		0			0
$225$	0.199304	−	0.0346904i	0.0132869	−	0.00231269i
$226$		0			0
$227$	−7.99649	−	13.8503i	−0.530746	−	0.919279i	−0.999356	−	0.0358740i	$-0.988578\pi$
$227$	−7.99649	−	13.8503i	−0.530746	−	0.919279i	0.468610	−	0.883405i	$-0.344755\pi$
$228$		0			0
$229$	−13.3898	−	7.73058i	−0.884820	−	0.510851i	−0.0125754	−	0.999921i	$-0.504003\pi$
$229$	−13.3898	−	7.73058i	−0.884820	−	0.510851i	−0.872245	+	0.489070i	$0.837336\pi$
$230$		0			0
$231$	5.13511	+	1.58851i	0.337866	+	0.104516i
$232$		0			0
$233$	−16.5268	+	9.54175i	−1.08271	+	0.625101i	−0.931625	−	0.363421i	$-0.881609\pi$
$233$	−16.5268	+	9.54175i	−1.08271	+	0.625101i	−0.151081	+	0.988521i	$0.548275\pi$
$234$		0			0
$235$	9.47178	−	16.4056i	0.617871	−	1.07018i
$236$		0			0
$237$	6.41778	−	4.48326i	0.416880	−	0.291219i
$238$		0			0
$239$	7.37626	−	4.25868i	0.477130	−	0.275471i	−0.242089	−	0.970254i	$-0.577833\pi$
$239$	7.37626	−	4.25868i	0.477130	−	0.275471i	0.719220	+	0.694783i	$0.244499\pi$
$240$		0			0
$241$	19.6047	−	11.3188i	1.26285	−	0.729107i	0.289225	−	0.957261i	$-0.406602\pi$
$241$	19.6047	−	11.3188i	1.26285	−	0.729107i	0.973625	+	0.228154i	$0.0732690\pi$
$242$		0			0
$243$	15.5214	+	1.44408i	0.995700	+	0.0926377i
$244$		0			0
$245$	3.82736	−	15.0681i	0.244521	−	0.962664i
$246$		0			0
$247$	6.35703	−	11.0107i	0.404488	−	0.700594i
$248$		0			0
$249$	0.116555	+	1.34933i	0.00738635	+	0.0855105i
$250$		0			0
$251$	−7.74235			−0.488693			−0.244346	−	0.969688i	$-0.578573\pi$
$251$	−7.74235			−0.488693			−0.244346	+	0.969688i	$0.578573\pi$
$252$		0			0
$253$	6.81781			0.428632
$254$		0			0
$255$	−25.8679	−	12.0971i	−1.61991	−	0.757549i
$256$		0			0
$257$	−11.8945	+	20.6019i	−0.741958	+	1.28511i	0.209645	+	0.977778i	$0.432769\pi$
$257$	−11.8945	+	20.6019i	−0.741958	+	1.28511i	−0.951603	+	0.307331i	$0.900564\pi$
$258$		0			0
$259$	23.1547	−	18.0086i	1.43877	−	1.11900i
$260$		0			0
$261$	−16.0691	+	13.4234i	−0.994652	+	0.830887i
$262$		0			0
$263$	−17.7831	+	10.2671i	−1.09655	+	0.633094i	−0.935313	−	0.353822i	$-0.884882\pi$
$263$	−17.7831	+	10.2671i	−1.09655	+	0.633094i	−0.161238	+	0.986916i	$0.551549\pi$
$264$		0			0
$265$	−21.3790	+	12.3432i	−1.31330	+	0.758235i
$266$		0			0
$267$	5.50517	+	2.57448i	0.336911	+	0.157556i
$268$		0			0
$269$	−6.17188	+	10.6900i	−0.376306	+	0.651782i	−0.990522	−	0.137357i	$-0.956139\pi$
$269$	−6.17188	+	10.6900i	−0.376306	+	0.651782i	0.614215	+	0.789138i	$0.289473\pi$
$270$		0			0
$271$	−25.3900	+	14.6589i	−1.54233	+	0.890467i	−0.543643	+	0.839317i	$0.682955\pi$
$271$	−25.3900	+	14.6589i	−1.54233	+	0.890467i	−0.998691	+	0.0511505i	$0.983711\pi$
$272$		0			0
$273$	15.7925	+	4.88529i	0.955806	+	0.295671i
$274$		0			0
$275$	−0.0685002	−	0.0395486i	−0.00413072	−	0.00238487i
$276$		0			0
$277$	1.24115	+	2.14974i	0.0745735	+	0.129165i	0.900901	−	0.434025i	$-0.142907\pi$
$277$	1.24115	+	2.14974i	0.0745735	+	0.129165i	−0.826327	+	0.563190i	$0.809574\pi$
$278$		0			0
$279$	22.3945	+	8.20683i	1.34073	+	0.491330i
$280$		0			0
$281$	20.0970	+	11.6030i	1.19889	+	0.692178i	0.960307	−	0.278944i	$-0.0899845\pi$
$281$	20.0970	+	11.6030i	1.19889	+	0.692178i	0.238581	+	0.971123i	$0.423318\pi$
$282$		0			0
$283$		−	27.3000i		−	1.62282i	−0.584480	−	0.811408i	$-0.698702\pi$
$283$		−	27.3000i		−	1.62282i	0.584480	−	0.811408i	$-0.301298\pi$
$284$		0			0
$285$	7.76432	+	11.1146i	0.459919	+	0.658373i
$286$		0			0
$287$	−3.37922	+	2.62819i	−0.199469	+	0.155137i
$288$		0			0
$289$	−19.0546	−	33.0035i	−1.12086	−	1.94138i
$290$		0			0
$291$	−6.95861	+	0.601081i	−0.407921	+	0.0352360i
$292$		0			0
$293$	−4.15628	−	7.19888i	−0.242812	−	0.420563i	0.718702	−	0.695318i	$-0.244737\pi$
$293$	−4.15628	−	7.19888i	−0.242812	−	0.420563i	−0.961514	+	0.274755i	$0.911403\pi$
$294$		0			0
$295$	4.44494	−	7.69886i	0.258794	−	0.448245i
$296$		0			0
$297$	−4.29549	−	4.32396i	−0.249250	−	0.250901i
$298$		0			0
$299$	20.9675			1.21258
$300$		0			0
$301$	4.43273	+	1.80229i	0.255498	+	0.103882i
$302$		0			0
$303$	−3.57424	−	1.67149i	−0.205335	−	0.0960245i
$304$		0			0
$305$	−15.7465	−	9.09127i	−0.901645	−	0.520565i
$306$		0			0
$307$			22.4908i			1.28362i	0.766864	+	0.641810i	$0.221816\pi$
$307$			22.4908i			1.28362i	−0.766864	+	0.641810i	$0.778184\pi$
$308$		0			0
$309$	−15.3115	+	1.32260i	−0.871042	+	0.0752401i
$310$		0			0
$311$	9.67799			0.548789			0.274394	−	0.961617i	$-0.411523\pi$
$311$	9.67799			0.548789			0.274394	+	0.961617i	$0.411523\pi$
$312$		0			0
$313$		−	24.4969i		−	1.38465i	−0.721587	−	0.692324i	$-0.756587\pi$
$313$		−	24.4969i		−	1.38465i	0.721587	−	0.692324i	$-0.243413\pi$
$314$		0			0
$315$	−11.8531	+	13.0482i	−0.667845	+	0.735185i
$316$		0			0
$317$			9.18619i			0.515948i	0.966152	+	0.257974i	$0.0830549\pi$
$317$			9.18619i			0.515948i	−0.966152	+	0.257974i	$0.916945\pi$
$318$		0			0
$319$	8.18654			0.458358
$320$		0			0
$321$	−0.486958	+	1.04129i	−0.0271794	+	0.0581192i
$322$		0			0
$323$			26.1644i			1.45582i
$324$		0			0
$325$	−0.210665	−	0.121628i	−0.0116856	−	0.00674668i
$326$		0			0
$327$	−2.39518	−	27.7285i	−0.132454	−	1.53339i
$328$		0			0
$329$	−3.09157	−	22.3542i	−0.170444	−	1.23243i
$330$		0			0
$331$	25.7197			1.41368			0.706842	−	0.707372i	$-0.250119\pi$
$331$	25.7197			1.41368			0.706842	+	0.707372i	$0.250119\pi$
$332$		0			0
$333$	−32.7683	+	5.70358i	−1.79569	+	0.312554i
$334$		0			0
$335$	−11.0233	+	19.0929i	−0.602266	+	1.04316i
$336$		0			0
$337$	8.80657	+	15.2534i	0.479724	+	0.830907i	0.999730	−	0.0232560i	$-0.00740329\pi$
$337$	8.80657	+	15.2534i	0.479724	+	0.830907i	−0.520005	+	0.854163i	$0.674070\pi$
$338$		0			0
$339$	4.12319	−	8.81685i	0.223941	−	0.478865i
$340$		0			0
$341$	−4.66272	−	8.07606i	−0.252500	−	0.437343i
$342$		0			0
$343$	−7.42110	−	16.9684i	−0.400702	−	0.916209i
$344$		0			0
$345$	−9.47173	+	20.2539i	−0.509941	+	1.09044i
$346$		0			0
$347$		−	8.35297i		−	0.448411i	−0.974542	−	0.224206i	$-0.928021\pi$
$347$		−	8.35297i		−	0.448411i	0.974542	−	0.224206i	$-0.0719787\pi$
$348$		0			0
$349$	16.4062	+	9.47211i	0.878203	+	0.507031i	0.870065	−	0.492936i	$-0.164076\pi$
$349$	16.4062	+	9.47211i	0.878203	+	0.507031i	0.00813729	+	0.999967i	$0.497410\pi$
$350$		0			0
$351$	−13.2103	−	13.2979i	−0.705115	−	0.709788i
$352$		0			0
$353$	12.7486	+	22.0811i	0.678537	+	1.17526i	0.975421	+	0.220347i	$0.0707191\pi$
$353$	12.7486	+	22.0811i	0.678537	+	1.17526i	−0.296884	+	0.954913i	$0.595948\pi$
$354$		0			0
$355$	−7.06257	−	4.07758i	−0.374842	−	0.216415i
$356$		0			0
$357$	−33.1722	+	7.54319i	−1.75566	+	0.399228i
$358$		0			0
$359$	17.4128	−	10.0533i	0.919013	−	0.530592i	0.0356928	−	0.999363i	$-0.488636\pi$
$359$	17.4128	−	10.0533i	0.919013	−	0.530592i	0.883320	+	0.468771i	$0.155303\pi$
$360$		0			0
$361$	−3.28892	+	5.69658i	−0.173101	+	0.299820i
$362$		0			0
$363$	−1.43456	−	16.6077i	−0.0752950	−	0.871677i
$364$		0			0
$365$	−15.3867	+	8.88353i	−0.805378	+	0.464985i
$366$		0			0
$367$	−20.1654	+	11.6425i	−1.05263	+	0.607735i	−0.923384	−	0.383878i	$-0.874588\pi$
$367$	−20.1654	+	11.6425i	−1.05263	+	0.607735i	−0.129244	+	0.991613i	$0.541255\pi$
$368$		0			0
$369$	4.78223	−	0.832384i	0.248953	−	0.0433322i
$370$		0			0
$371$	−11.0765	+	27.2426i	−0.575061	+	1.41436i
$372$		0			0
$373$	12.5625	−	21.7588i	0.650460	−	1.12663i	−0.332551	−	0.943085i	$-0.607909\pi$
$373$	12.5625	−	21.7588i	0.650460	−	1.12663i	0.983011	−	0.183545i	$-0.0587573\pi$
$374$		0			0
$375$	15.9803	−	11.1633i	0.825217	−	0.576471i
$376$		0			0
$377$	25.1768			1.29667
$378$		0			0
$379$	32.3000			1.65914			0.829569	−	0.558404i	$-0.188586\pi$
$379$	32.3000			1.65914			0.829569	+	0.558404i	$0.188586\pi$
$380$		0			0
$381$	−10.9961	+	7.68153i	−0.563347	+	0.393536i
$382$		0			0
$383$	4.77182	−	8.26503i	0.243828	−	0.422323i	−0.717973	−	0.696071i	$-0.754930\pi$
$383$	4.77182	−	8.26503i	0.243828	−	0.422323i	0.961802	+	0.273748i	$0.0882633\pi$
$384$		0			0
$385$	6.82741	−	0.944226i	0.347957	−	0.0481222i
$386$		0			0
$387$	−3.47849	−	4.16408i	−0.176821	−	0.211672i
$388$		0			0
$389$	11.7953	−	6.81005i	0.598048	−	0.345283i	−0.170225	−	0.985405i	$-0.554450\pi$
$389$	11.7953	−	6.81005i	0.598048	−	0.345283i	0.768273	+	0.640122i	$0.221116\pi$
$390$		0			0
$391$	−37.3682	+	21.5746i	−1.88979	+	1.09107i
$392$		0			0
$393$	−2.32917	−	26.9644i	−0.117491	−	1.36017i
$394$		0			0
$395$	5.01917	−	8.69346i	0.252542	−	0.437415i
$396$		0			0
$397$	2.59589	−	1.49874i	0.130284	−	0.0752196i	−0.433441	−	0.901182i	$-0.642701\pi$
$397$	2.59589	−	1.49874i	0.130284	−	0.0752196i	0.563726	+	0.825962i	$0.309368\pi$
$398$		0			0
$399$	15.4299	+	4.77313i	0.772462	+	0.238955i
$400$		0			0
$401$	11.2875	+	6.51682i	0.563669	+	0.325434i	0.754617	−	0.656166i	$-0.227823\pi$
$401$	11.2875	+	6.51682i	0.563669	+	0.325434i	−0.190948	+	0.981600i	$0.561156\pi$
$402$		0			0
$403$	−14.3397	−	24.8371i	−0.714311	−	1.23722i
$404$		0			0
$405$	18.8129	−	6.75367i	0.934821	−	0.335593i
$406$		0			0
$407$	11.2624	+	6.50233i	0.558255	+	0.322309i
$408$		0			0
$409$		−	32.8723i		−	1.62543i	−0.582662	−	0.812714i	$-0.697989\pi$
$409$		−	32.8723i		−	1.62543i	0.582662	−	0.812714i	$-0.302011\pi$
$410$		0			0
$411$	−0.789231	+	1.68766i	−0.0389299	+	0.0832461i
$412$		0			0
$413$	−1.45082	−	10.4905i	−0.0713903	−	0.516201i
$414$		0			0
$415$	0.868319	+	1.50397i	0.0426241	+	0.0738271i
$416$		0			0
$417$	4.92899	−	10.5399i	0.241374	−	0.516144i
$418$		0			0
$419$	−11.0687	−	19.1716i	−0.540742	−	0.936593i	−0.998862	−	0.0477024i	$-0.984810\pi$
$419$	−11.0687	−	19.1716i	−0.540742	−	0.936593i	0.458119	−	0.888891i	$-0.348523\pi$
$420$		0			0
$421$	12.1963	−	21.1245i	0.594409	−	1.02955i	−0.399221	−	0.916855i	$-0.630719\pi$
$421$	12.1963	−	21.1245i	0.594409	−	1.02955i	0.993630	−	0.112692i	$-0.0359472\pi$
$422$		0			0
$423$	−8.80473	+	24.0261i	−0.428101	+	1.16819i
$424$		0			0
$425$	0.500597			0.0242825
$426$		0			0
$427$	−21.4562	+	2.96738i	−1.03834	+	0.143602i
$428$		0			0
$429$	0.630707	+	7.30158i	0.0304508	+	0.352524i
$430$		0			0
$431$	12.2611	+	7.07897i	0.590598	+	0.340982i	0.765334	−	0.643634i	$-0.222574\pi$
$431$	12.2611	+	7.07897i	0.590598	+	0.340982i	−0.174736	+	0.984615i	$0.555907\pi$
$432$		0			0
$433$		−	8.90220i		−	0.427813i	−0.976854	−	0.213906i	$-0.931381\pi$
$433$		−	8.90220i		−	0.427813i	0.976854	−	0.213906i	$-0.0686187\pi$
$434$		0			0
$435$	−11.3733	+	24.3201i	−0.545306	+	1.16606i
$436$		0			0
$437$	20.4861			0.979981
$438$		0			0
$439$			16.1624i			0.771389i	0.922626	+	0.385695i	$0.126038\pi$
$439$			16.1624i			0.771389i	−0.922626	+	0.385695i	$0.873962\pi$
$440$		0			0
$441$	−1.60310	+	20.9387i	−0.0763382	+	0.997082i
$442$		0			0
$443$		−	17.4477i		−	0.828963i	−0.910058	−	0.414482i	$-0.863963\pi$
$443$		−	17.4477i		−	0.828963i	0.910058	−	0.414482i	$-0.136037\pi$
$444$		0			0
$445$	7.79281			0.369415
$446$		0			0
$447$	−30.3080	+	2.61799i	−1.43352	+	0.123827i
$448$		0			0
$449$		−	9.14988i		−	0.431809i	−0.976414	−	0.215905i	$-0.930730\pi$
$449$		−	9.14988i		−	0.431809i	0.976414	−	0.215905i	$-0.0692700\pi$
$450$		0			0
$451$	−1.64364	−	0.948954i	−0.0773958	−	0.0446845i
$452$		0			0
$453$	2.66105	+	1.24444i	0.125027	+	0.0584687i
$454$		0			0
$455$	20.9970	−	2.90387i	0.984354	−	0.136135i
$456$		0			0
$457$	14.1151			0.660279			0.330139	−	0.943932i	$-0.392904\pi$
$457$	14.1151			0.660279			0.330139	+	0.943932i	$0.392904\pi$
$458$		0			0
$459$	37.2264	+	10.1067i	1.73758	+	0.471739i
$460$		0			0
$461$	17.5323	−	30.3668i	0.816561	−	1.41432i	−0.0916412	−	0.995792i	$-0.529211\pi$
$461$	17.5323	−	30.3668i	0.816561	−	1.41432i	0.908202	−	0.418532i	$-0.137455\pi$
$462$		0			0
$463$	15.9985	+	27.7103i	0.743515	+	1.28781i	0.950885	+	0.309543i	$0.100176\pi$
$463$	15.9985	+	27.7103i	0.743515	+	1.28781i	−0.207370	+	0.978263i	$0.566490\pi$
$464$		0			0
$465$	30.4696	−	2.63195i	1.41300	−	0.122054i
$466$		0			0
$467$	8.02671	+	13.9027i	0.371432	+	0.643339i	0.989786	−	0.142561i	$-0.0455337\pi$
$467$	8.02671	+	13.9027i	0.371432	+	0.643339i	−0.618354	+	0.785899i	$0.712200\pi$
$468$		0			0
$469$	3.59798	+	26.0159i	0.166139	+	1.20130i
$470$		0			0
$471$	−7.81849	−	11.1922i	−0.360257	−	0.515708i
$472$		0			0
$473$			2.12143i			0.0975434i
$474$		0			0
$475$	−0.205828	−	0.118835i	−0.00944406	−	0.00545253i
$476$		0			0
$477$	25.5915	−	21.3780i	1.17176	−	0.978831i
$478$		0			0
$479$	15.7481	+	27.2764i	0.719547	+	1.24629i	0.961179	+	0.275925i	$0.0889840\pi$
$479$	15.7481	+	27.2764i	0.719547	+	1.24629i	−0.241632	+	0.970368i	$0.577683\pi$
$480$		0			0
$481$	34.6362	+	19.9972i	1.57928	+	0.911796i
$482$		0			0
$483$	5.90613	+	25.9730i	0.268738	+	1.18181i
$484$		0			0
$485$	−7.75609	+	4.47798i	−0.352186	+	0.203335i
$486$		0			0
$487$	10.7924	−	18.6930i	0.489052	−	0.847062i	−0.510869	−	0.859659i	$-0.670676\pi$
$487$	10.7924	−	18.6930i	0.489052	−	0.847062i	0.999921	+	0.0125963i	$0.00400964\pi$
$488$		0			0
$489$	17.8669	+	8.35543i	0.807969	+	0.377846i
$490$		0			0
$491$	−28.9290	+	16.7022i	−1.30555	+	0.753758i	−0.981349	−	0.192232i	$-0.938427\pi$
$491$	−28.9290	+	16.7022i	−1.30555	+	0.753758i	−0.324197	+	0.945990i	$0.605094\pi$
$492$		0			0
$493$	−44.8702	+	25.9058i	−2.02085	+	1.16674i
$494$		0			0
$495$	−7.33803	−	2.68913i	−0.329820	−	0.120868i
$496$		0			0
$497$	−9.62344	+	1.33091i	−0.431670	+	0.0596997i
$498$		0			0
$499$	−16.0722	+	27.8378i	−0.719489	+	1.24619i	0.241713	+	0.970348i	$0.422291\pi$
$499$	−16.0722	+	27.8378i	−0.719489	+	1.24619i	−0.961202	+	0.275844i	$0.911043\pi$
$500$		0			0
$501$	25.2804	+	11.8223i	1.12944	+	0.528183i
$502$		0			0
$503$	21.7295			0.968872			0.484436	−	0.874827i	$-0.339025\pi$
$503$	21.7295			0.968872			0.484436	+	0.874827i	$0.339025\pi$
$504$		0			0
$505$	−5.05949			−0.225145
$506$		0			0
$507$	0.00191182	+	0.0221327i	8.49067e−5	+	0.000982950i
$508$		0			0
$509$	11.9432	−	20.6862i	0.529373	−	0.916901i	−0.470040	−	0.882645i	$-0.655761\pi$
$509$	11.9432	−	20.6862i	0.529373	−	0.916901i	0.999413	−	0.0342559i	$-0.0109061\pi$
$510$		0			0
$511$	−7.97186	+	19.6068i	−0.352654	+	0.867354i
$512$		0			0
$513$	−12.9070	−	12.9926i	−0.569859	−	0.573636i
$514$		0			0
$515$	−17.0663	+	9.85322i	−0.752030	+	0.434185i
$516$		0			0
$517$	8.66444	−	5.00242i	0.381062	−	0.220006i
$518$		0			0
$519$	−9.80251	+	6.84772i	−0.430283	+	0.300582i
$520$		0			0
$521$	−13.5098	+	23.3996i	−0.591874	+	1.02516i	0.402106	+	0.915593i	$0.368278\pi$
$521$	−13.5098	+	23.3996i	−0.591874	+	1.02516i	−0.993980	+	0.109562i	$0.965055\pi$
$522$		0			0
$523$	27.2136	−	15.7118i	1.18997	−	0.687028i	0.231669	−	0.972795i	$-0.425582\pi$
$523$	27.2136	−	15.7118i	1.18997	−	0.687028i	0.958299	+	0.285766i	$0.0922482\pi$
$524$		0			0
$525$	0.0913232	−	0.295217i	0.00398567	−	0.0128843i
$526$		0			0
$527$	51.1125	+	29.5098i	2.22649	+	1.28547i
$528$		0			0
$529$	5.39234	+	9.33981i	0.234450	+	0.406079i
$530$		0			0
$531$	−4.13190	+	11.2750i	−0.179309	+	0.489294i
$532$		0			0
$533$	−5.05483	−	2.91841i	−0.218949	−	0.126410i
$534$		0			0
$535$			1.47399i			0.0637263i
$536$		0			0
$537$	−10.5359	+	0.910090i	−0.454660	+	0.0392733i
$538$		0			0
$539$	5.72959	−	5.88118i	0.246791	−	0.253320i
$540$		0			0
$541$	−0.0969057	−	0.167846i	−0.00416630	−	0.00721624i	0.863935	−	0.503604i	$-0.167993\pi$
$541$	−0.0969057	−	0.167846i	−0.00416630	−	0.00721624i	−0.868101	+	0.496388i	$0.834660\pi$
$542$		0			0
$543$	−5.41904	−	7.75735i	−0.232553	−	0.332900i
$544$		0			0
$545$	−17.8438	−	30.9064i	−0.764344	−	1.32388i
$546$		0			0
$547$	0.987053	−	1.70963i	0.0422033	−	0.0730983i	−0.844152	−	0.536104i	$-0.819896\pi$
$547$	0.987053	−	1.70963i	0.0422033	−	0.0730983i	0.886355	+	0.463005i	$0.153229\pi$
$548$		0			0
$549$	23.0609	+	8.45102i	0.984215	+	0.360681i
$550$		0			0
$551$	24.5988			1.04794
$552$		0			0
$553$	−1.63825	−	11.8457i	−0.0696655	−	0.503730i
$554$		0			0
$555$	−34.9631	+	24.4241i	−1.48410	+	1.03675i
$556$		0			0
$557$	18.3383	+	10.5876i	0.777018	+	0.448612i	0.835373	−	0.549684i	$-0.185252\pi$
$557$	18.3383	+	10.5876i	0.777018	+	0.448612i	−0.0583543	+	0.998296i	$0.518585\pi$
$558$		0			0
$559$			6.52423i			0.275946i
$560$		0			0
$561$	−8.63704	−	12.3639i	−0.364656	−	0.522005i
$562$		0			0
$563$	−34.1289			−1.43836			−0.719182	−	0.694822i	$-0.755483\pi$
$563$	−34.1289			−1.43836			−0.719182	+	0.694822i	$0.755483\pi$
$564$		0			0
$565$		−	12.4806i		−	0.525064i
$566$		0			0
$567$	12.7514	−	20.1098i	0.535507	−	0.844531i
$568$		0			0
$569$			11.0389i			0.462773i	0.972862	+	0.231387i	$0.0743262\pi$
$569$			11.0389i			0.462773i	−0.972862	+	0.231387i	$0.925674\pi$
$570$		0			0
$571$	41.3233			1.72933			0.864663	−	0.502353i	$-0.167532\pi$
$571$	41.3233			1.72933			0.864663	+	0.502353i	$0.167532\pi$
$572$		0			0
$573$	−5.96763	−	8.54266i	−0.249301	−	0.356875i
$574$		0			0
$575$		−	0.391955i		−	0.0163456i
$576$		0			0
$577$	12.5253	+	7.23151i	0.521437	+	0.301052i	0.737522	−	0.675323i	$-0.235996\pi$
$577$	12.5253	+	7.23151i	0.521437	+	0.301052i	−0.216085	+	0.976374i	$0.569329\pi$
$578$		0			0
$579$	8.20754	−	5.73352i	0.341094	−	0.238277i
$580$		0			0
$581$	1.91646	+	0.779208i	0.0795083	+	0.0323270i
$582$		0			0
$583$	−13.0378			−0.539972
$584$		0			0
$585$	−22.5673	−	8.27015i	−0.933044	−	0.341929i
$586$		0			0
$587$	0.248251	−	0.429983i	0.0102464	−	0.0177473i	−0.860857	−	0.508847i	$-0.830072\pi$
$587$	0.248251	−	0.429983i	0.0102464	−	0.0177473i	0.871103	+	0.491100i	$0.163405\pi$
$588$		0			0
$589$	−14.0105	−	24.2669i	−0.577292	−	0.999898i
$590$		0			0
$591$	−7.88912	−	11.2933i	−0.324515	−	0.464543i
$592$		0			0
$593$	−12.2302	−	21.1834i	−0.502236	−	0.869898i	−0.999997	−	0.00258345i	$-0.999178\pi$
$593$	−12.2302	−	21.1834i	−0.502236	−	0.869898i	0.497761	−	0.867314i	$-0.334156\pi$
$594$		0			0
$595$	−34.4329	+	26.7802i	−1.41161	+	1.09788i
$596$		0			0
$597$	30.9306	−	2.67177i	1.26590	−	0.109348i
$598$		0			0
$599$		−	18.8348i		−	0.769570i	−0.923006	−	0.384785i	$-0.874276\pi$
$599$		−	18.8348i		−	0.769570i	0.923006	−	0.384785i	$-0.125724\pi$
$600$		0			0
$601$	6.37572	+	3.68102i	0.260071	+	0.150152i	0.624367	−	0.781131i	$-0.285357\pi$
$601$	6.37572	+	3.68102i	0.260071	+	0.150152i	−0.364296	+	0.931283i	$0.618690\pi$
$602$		0			0
$603$	10.2470	−	27.9616i	0.417289	−	1.13868i
$604$		0			0
$605$	−10.6873	−	18.5110i	−0.434502	−	0.752579i
$606$		0			0
$607$	−25.1081	−	14.4961i	−1.01910	−	0.588380i	−0.105260	−	0.994445i	$-0.533568\pi$
$607$	−25.1081	−	14.4961i	−1.01910	−	0.588380i	−0.913845	+	0.406064i	$0.866901\pi$
$608$		0			0
$609$	7.09184	+	31.1873i	0.287376	+	1.26377i
$610$		0			0
$611$	26.6466	−	15.3844i	1.07801	−	0.622387i
$612$		0			0
$613$	12.4334	−	21.5352i	0.502179	−	0.869799i	−0.497818	−	0.867282i	$-0.665865\pi$
$613$	12.4334	−	21.5352i	0.502179	−	0.869799i	0.999997	−	0.00251771i	$-0.000801413\pi$
$614$		0			0
$615$	5.10254	−	3.56447i	0.205754	−	0.143733i
$616$		0			0
$617$	−37.4629	+	21.6292i	−1.50820	+	0.870759i	−0.508245	+	0.861213i	$0.669706\pi$
$617$	−37.4629	+	21.6292i	−1.50820	+	0.870759i	−0.999954	+	0.00954684i	$0.996961\pi$
$618$		0			0
$619$	−6.45380	+	3.72610i	−0.259400	+	0.149765i	−0.624061	−	0.781376i	$-0.714518\pi$
$619$	−6.45380	+	3.72610i	−0.259400	+	0.149765i	0.364661	+	0.931140i	$0.381185\pi$
$620$		0			0
$621$	7.91327	−	29.1473i	0.317548	−	1.16964i
$622$		0			0
$623$	7.32796	−	5.69933i	0.293588	−	0.228339i
$624$		0			0
$625$	12.3291	−	21.3547i	0.493166	−	0.854188i
$626$		0			0
$627$	0.616227	+	7.13395i	0.0246097	+	0.284902i
$628$		0			0
$629$	−82.3050			−3.28171
$630$		0			0
$631$	−9.67068			−0.384984			−0.192492	−	0.981299i	$-0.561657\pi$
$631$	−9.67068			−0.384984			−0.192492	+	0.981299i	$0.561657\pi$
$632$		0			0
$633$	12.5580	+	5.87272i	0.499135	+	0.233420i
$634$		0			0
$635$	−8.59975	+	14.8952i	−0.341271	+	0.591098i
$636$		0			0
$637$	17.6207	−	18.0870i	0.698159	−	0.716631i
$638$		0			0
$639$	10.3432	+	3.79041i	0.409169	+	0.149946i
$640$		0			0
$641$	−26.8113	+	15.4795i	−1.05898	+	0.611404i	−0.925151	−	0.379600i	$-0.876062\pi$
$641$	−26.8113	+	15.4795i	−1.05898	+	0.611404i	−0.133832	+	0.991004i	$0.542728\pi$
$642$		0			0
$643$	−6.99262	+	4.03719i	−0.275762	+	0.159211i	−0.631503	−	0.775373i	$-0.717562\pi$
$643$	−6.99262	+	4.03719i	−0.275762	+	0.159211i	0.355741	+	0.934585i	$0.384228\pi$
$644$		0			0
$645$	−6.30221	−	2.94722i	−0.248149	−	0.116047i
$646$		0			0
$647$	−4.54355	+	7.86966i	−0.178625	+	0.309388i	−0.941410	−	0.337265i	$-0.890498\pi$
$647$	−4.54355	+	7.86966i	−0.178625	+	0.309388i	0.762785	+	0.646653i	$0.223832\pi$
$648$		0			0
$649$	4.06607	−	2.34755i	0.159607	−	0.0921492i
$650$		0			0
$651$	26.7272	−	24.7591i	1.04752	−	0.970387i
$652$		0			0
$653$	17.8326	+	10.2957i	0.697844	+	0.402900i	0.806544	−	0.591174i	$-0.201335\pi$
$653$	17.8326	+	10.2957i	0.697844	+	0.402900i	−0.108700	+	0.994075i	$0.534669\pi$
$654$		0			0
$655$	−17.3520	−	30.0546i	−0.678000	−	1.17433i
$656$		0			0
$657$	18.4185	−	15.3860i	0.718575	−	0.600265i
$658$		0			0
$659$	−41.7687	−	24.1152i	−1.62708	−	0.939395i	−0.984959	−	0.172791i	$-0.944722\pi$
$659$	−41.7687	−	24.1152i	−1.62708	−	0.939395i	−0.642121	−	0.766604i	$-0.721945\pi$
$660$		0			0
$661$		−	27.5213i		−	1.07046i	−0.844708	−	0.535228i	$-0.820226\pi$
$661$		−	27.5213i		−	1.07046i	0.844708	−	0.535228i	$-0.179774\pi$
$662$		0			0
$663$	−26.5623	−	38.0239i	−1.03159	−	1.47673i
$664$		0			0
$665$	20.5149	−	2.83720i	0.795535	−	0.110022i
$666$		0			0
$667$	20.2836	+	35.1323i	0.785385	+	1.36033i
$668$		0			0
$669$	−28.3754	+	2.45105i	−1.09706	+	0.0947631i
$670$		0			0
$671$	−4.80146	−	8.31637i	−0.185358	−	0.321050i
$672$		0			0
$673$	−17.5734	+	30.4380i	−0.677404	+	1.17330i	0.298355	+	0.954455i	$0.403562\pi$
$673$	−17.5734	+	30.4380i	−0.677404	+	1.17330i	−0.975760	+	0.218844i	$0.929771\pi$
$674$		0			0
$675$	−0.248584	+	0.246947i	−0.00956799	+	0.00950500i
$676$		0			0
$677$	−43.8855			−1.68666			−0.843329	−	0.537397i	$-0.819408\pi$
$677$	−43.8855			−1.68666			−0.843329	+	0.537397i	$0.819408\pi$
$678$		0			0
$679$	−4.01843	+	9.88334i	−0.154213	+	0.379288i
$680$		0			0
$681$	25.0924	+	11.7344i	0.961544	+	0.449665i
$682$		0			0
$683$	−17.9331	−	10.3537i	−0.686190	−	0.396172i	0.115993	−	0.993250i	$-0.462995\pi$
$683$	−17.9331	−	10.3537i	−0.686190	−	0.396172i	−0.802183	+	0.597078i	$0.796328\pi$
$684$		0			0
$685$			2.38896i			0.0912773i
$686$		0			0
$687$	26.6802	−	2.30462i	1.01791	−	0.0879267i
$688$		0			0
$689$	−40.0965			−1.52755
$690$		0			0
$691$			18.3226i			0.697023i	0.937304	+	0.348512i	$0.113313\pi$
$691$			18.3226i			0.697023i	−0.937304	+	0.348512i	$0.886687\pi$
$692$		0			0
$693$	−8.86702	+	2.83799i	−0.336830	+	0.107806i
$694$		0			0
$695$		−	14.9198i		−	0.565939i
$696$		0			0
$697$	12.0116			0.454973
$698$		0			0
$699$	14.0020	−	29.9413i	0.529605	−	1.13248i
$700$		0			0
$701$			2.62840i			0.0992734i	0.998767	+	0.0496367i	$0.0158064\pi$
$701$			2.62840i			0.0992734i	−0.998767	+	0.0496367i	$0.984194\pi$
$702$		0			0
$703$	33.8410	+	19.5381i	1.27634	+	0.736894i
$704$		0			0
$705$	2.82370	+	32.6895i	0.106347	+	1.23116i
$706$		0			0
$707$	−4.75769	+	3.70030i	−0.178931	+	0.139164i
$708$		0			0
$709$	−16.3327			−0.613387			−0.306693	−	0.951808i	$-0.599223\pi$
$709$	−16.3327			−0.613387			−0.306693	+	0.951808i	$0.599223\pi$
$710$		0			0
$711$	−4.66570	+	12.7316i	−0.174977	+	0.477473i
$712$		0			0
$713$	23.1054	−	40.0198i	0.865305	−	1.49875i
$714$		0			0
$715$	4.69869	+	8.13838i	0.175721	+	0.304358i
$716$		0			0
$717$	−6.24940	+	13.3634i	−0.233388	+	0.499067i
$718$		0			0
$719$	−3.15485	−	5.46436i	−0.117656	−	0.203786i	0.801182	−	0.598420i	$-0.204205\pi$
$719$	−3.15485	−	5.46436i	−0.117656	−	0.203786i	−0.918838	+	0.394634i	$0.870871\pi$
$720$		0			0
$721$	−8.84204	+	21.7470i	−0.329295	+	0.809901i
$722$		0			0
$723$	−16.6097	+	35.5175i	−0.617722	+	1.32091i
$724$		0			0
$725$		−	0.470643i		−	0.0174792i
$726$		0			0
$727$	−14.3318	−	8.27447i	−0.531537	−	0.306883i	0.210105	−	0.977679i	$-0.432619\pi$
$727$	−14.3318	−	8.27447i	−0.531537	−	0.306883i	−0.741642	+	0.670796i	$0.765953\pi$
$728$		0			0
$729$	−23.4713	+	13.3453i	−0.869309	+	0.494269i
$730$		0			0
$731$	−6.71314	−	11.6275i	−0.248294	−	0.430058i
$732$		0			0
$733$	17.2433	+	9.95544i	0.636897	+	0.367713i	0.783418	−	0.621495i	$-0.213474\pi$
$733$	17.2433	+	9.95544i	0.636897	+	0.367713i	−0.146521	+	0.989208i	$0.546808\pi$
$734$		0			0
$735$	9.51156	+	25.1916i	0.350839	+	0.929207i
$736$		0			0
$737$	−10.0837	+	5.82183i	−0.371438	+	0.214450i
$738$		0			0
$739$	−24.1545	+	41.8368i	−0.888536	+	1.53899i	−0.0469307	+	0.998898i	$0.514944\pi$
$739$	−24.1545	+	41.8368i	−0.888536	+	1.53899i	−0.841606	+	0.540092i	$0.818389\pi$
$740$		0			0
$741$	1.89514	+	21.9397i	0.0696197	+	0.805975i
$742$		0			0
$743$	−7.17819	+	4.14433i	−0.263342	+	0.152041i	−0.625858	−	0.779937i	$-0.715251\pi$
$743$	−7.17819	+	4.14433i	−0.263342	+	0.152041i	0.362516	+	0.931978i	$0.381918\pi$
$744$		0			0
$745$	−33.7815	+	19.5037i	−1.23766	+	0.714562i
$746$		0			0
$747$	−1.50390	−	1.80031i	−0.0550249	−	0.0658701i
$748$		0			0
$749$	1.07802	+	1.38607i	0.0393898	+	0.0506458i
$750$		0			0
$751$	12.5114	−	21.6705i	0.456549	−	0.790767i	−0.542227	−	0.840232i	$-0.682419\pi$
$751$	12.5114	−	21.6705i	0.456549	−	0.790767i	0.998776	+	0.0494658i	$0.0157519\pi$
$752$		0			0
$753$	10.9934	−	7.67964i	0.400622	−	0.279862i
$754$		0			0
$755$	3.76683			0.137089
$756$		0			0
$757$	−18.7744			−0.682368			−0.341184	−	0.939997i	$-0.610828\pi$
$757$	−18.7744			−0.682368			−0.341184	+	0.939997i	$0.610828\pi$
$758$		0			0
$759$	−9.68065	+	6.76259i	−0.351385	+	0.245467i
$760$		0			0
$761$	11.5963	−	20.0854i	0.420367	−	0.728097i	−0.575609	−	0.817725i	$-0.695235\pi$
$761$	11.5963	−	20.0854i	0.420367	−	0.728097i	0.995975	+	0.0896289i	$0.0285681\pi$
$762$		0			0
$763$	−39.3830	−	16.0126i	−1.42576	−	0.579694i
$764$		0			0
$765$	48.7291	−	8.48168i	1.76180	−	0.306656i
$766$		0			0
$767$	12.5048	−	7.21963i	0.451521	−	0.260686i
$768$		0			0
$769$	−27.8202	+	16.0620i	−1.00322	+	0.579210i	−0.909200	−	0.416360i	$-0.863305\pi$
$769$	−27.8202	+	16.0620i	−1.00322	+	0.579210i	−0.0940211	+	0.995570i	$0.529972\pi$
$770$		0			0
$771$	−3.54595	−	41.0509i	−0.127704	−	1.47841i
$772$		0			0
$773$	8.14023	−	14.0993i	0.292784	−	0.507116i	−0.681683	−	0.731647i	$-0.738752\pi$
$773$	8.14023	−	14.0993i	0.292784	−	0.507116i	0.974467	+	0.224531i	$0.0720851\pi$
$774$		0			0
$775$	−0.464292	+	0.268059i	−0.0166779	+	0.00962896i
$776$		0			0
$777$	−15.0148	+	48.5377i	−0.538652	+	1.74128i
$778$		0			0
$779$	−4.93878	−	2.85141i	−0.176950	−	0.102162i
$780$		0			0
$781$	−2.15353	−	3.73002i	−0.0770593	−	0.133471i
$782$		0			0
$783$	9.50192	−	34.9989i	0.339571	−	1.25076i
$784$		0			0
$785$	−15.1608	−	8.75308i	−0.541112	−	0.312411i
$786$		0			0
$787$		−	0.922766i		−	0.0328931i	−0.999865	−	0.0164465i	$-0.994765\pi$
$787$		−	0.922766i		−	0.0328931i	0.999865	−	0.0164465i	$-0.00523533\pi$
$788$		0			0
$789$	15.0664	−	32.2173i	0.536377	−	1.14697i
$790$		0			0
$791$	−9.12780	−	11.7362i	−0.324547	−	0.417290i
$792$		0			0
$793$	−14.7664	−	25.5761i	−0.524369	−	0.908235i
$794$		0			0
$795$	18.1130	−	38.7320i	0.642401	−	1.37368i
$796$		0			0
$797$	2.98084	+	5.16296i	0.105587	+	0.182881i	0.913978	−	0.405764i	$-0.132995\pi$
$797$	2.98084	+	5.16296i	0.105587	+	0.182881i	−0.808391	+	0.588646i	$0.799661\pi$
$798$		0			0
$799$	−31.6597	+	54.8362i	−1.12004	+	1.93997i
$800$		0			0
$801$	−10.3705	+	1.80506i	−0.366422	+	0.0637786i
$802$		0			0
$803$	−9.38348			−0.331136
$804$		0			0
$805$	20.9683	+	26.9601i	0.739034	+	0.950220i
$806$		0			0
$807$	−1.83994	−	21.3007i	−0.0647691	−	0.749820i
$808$		0			0
$809$	18.0267	+	10.4077i	0.633784	+	0.365916i	0.782216	−	0.623007i	$-0.214089\pi$
$809$	18.0267	+	10.4077i	0.633784	+	0.365916i	−0.148432	+	0.988923i	$0.547423\pi$
$810$		0			0
$811$		−	11.7101i		−	0.411198i	−0.978636	−	0.205599i	$-0.934086\pi$
$811$		−	11.7101i		−	0.411198i	0.978636	−	0.205599i	$-0.0659142\pi$
$812$		0			0
$813$	21.5112	−	45.9987i	0.754432	−	1.61324i
$814$		0			0
$815$	25.2914			0.885919
$816$		0			0
$817$			6.37444i			0.223013i
$818$		0			0
$819$	−27.2696	+	8.72795i	−0.952877	+	0.304979i
$820$		0			0
$821$			0.558286i			0.0194843i	0.999953	+	0.00974215i	$0.00310107\pi$
$821$			0.558286i			0.0194843i	−0.999953	+	0.00974215i	$0.996899\pi$
$822$		0			0
$823$	41.4087			1.44341			0.721707	−	0.692198i	$-0.243358\pi$
$823$	41.4087			1.44341			0.721707	+	0.692198i	$0.243358\pi$
$824$		0			0
$825$	0.136492	−	0.0117901i	0.00475204	−	0.000410479i
$826$		0			0
$827$		−	8.83309i		−	0.307157i	−0.988136	−	0.153578i	$-0.950920\pi$
$827$		−	8.83309i		−	0.307157i	0.988136	−	0.153578i	$-0.0490797\pi$
$828$		0			0
$829$	−7.60753	−	4.39221i	−0.264220	−	0.152548i	0.362038	−	0.932163i	$-0.382081\pi$
$829$	−7.60753	−	4.39221i	−0.264220	−	0.152548i	−0.626258	+	0.779616i	$0.715414\pi$
$830$		0			0
$831$	−3.89464	−	1.82132i	−0.135104	−	0.0631810i
$832$		0			0
$833$	−12.7931	+	50.3655i	−0.443253	+	1.74506i
$834$		0			0
$835$	35.7855			1.23841
$836$		0			0
$837$	−39.9385	+	10.5602i	−1.38048	+	0.365015i
$838$		0			0
$839$	−11.6778	+	20.2265i	−0.403161	+	0.698295i	−0.994106	−	0.108417i	$-0.965422\pi$
$839$	−11.6778	+	20.2265i	−0.403161	+	0.698295i	0.590944	+	0.806712i	$0.298755\pi$
$840$		0			0
$841$	9.85573	+	17.0706i	0.339853	+	0.588642i
$842$		0			0
$843$	−40.0449	+	3.45906i	−1.37922	+	0.119136i
$844$		0			0
$845$	0.0142428	+	0.0246693i	0.000489967	+	0.000848648i
$846$		0			0
$847$	−23.5880	−	9.59054i	−0.810492	−	0.329535i
$848$		0			0
$849$	27.0789	+	38.7634i	0.929345	+	1.33036i
$850$		0			0
$851$			64.4428i			2.20907i
$852$		0			0
$853$	13.8754	+	8.01099i	0.475086	+	0.274291i	0.718366	−	0.695665i	$-0.244890\pi$
$853$	13.8754	+	8.01099i	0.475086	+	0.274291i	−0.243280	+	0.969956i	$0.578223\pi$
$854$		0			0
$855$	−22.0492	−	8.08027i	−0.754067	−	0.276340i
$856$		0			0
$857$	−8.41205	−	14.5701i	−0.287350	−	0.497705i	0.685826	−	0.727765i	$-0.259441\pi$
$857$	−8.41205	−	14.5701i	−0.287350	−	0.497705i	−0.973176	+	0.230060i	$0.926108\pi$
$858$		0			0
$859$	−41.2188	−	23.7977i	−1.40637	−	0.811966i	−0.411331	−	0.911486i	$-0.634936\pi$
$859$	−41.2188	−	23.7977i	−1.40637	−	0.811966i	−0.995036	+	0.0995201i	$0.968269\pi$
$860$		0			0
$861$	2.19127	−	7.08363i	0.0746782	−	0.241409i
$862$		0			0
$863$	44.7300	−	25.8249i	1.52263	−	0.879089i	0.522985	−	0.852342i	$-0.324818\pi$
$863$	44.7300	−	25.8249i	1.52263	−	0.879089i	0.999642	−	0.0267477i	$-0.00851508\pi$
$864$		0			0
$865$	−7.66628	+	13.2784i	−0.260661	+	0.451478i
$866$		0			0
$867$	59.7919	+	27.9616i	2.03064	+	0.949625i
$868$		0			0
$869$	4.59136	−	2.65082i	0.155751	−	0.0899230i
$870$		0			0
$871$	−31.0114	+	17.9044i	−1.05078	+	0.606668i
$872$		0			0
$873$	9.28435	−	7.75573i	0.314228	−	0.262492i
$874$		0			0
$875$	−4.07924	−	29.4958i	−0.137904	−	0.997138i
$876$		0			0
$877$	−7.15280	+	12.3890i	−0.241533	+	0.418347i	−0.961151	−	0.276023i	$-0.910983\pi$
$877$	−7.15280	+	12.3890i	−0.241533	+	0.418347i	0.719618	+	0.694370i	$0.244317\pi$
$878$		0			0
$879$	13.0421	+	6.09912i	0.439899	+	0.205718i
$880$		0			0
$881$	10.4054			0.350566			0.175283	−	0.984518i	$-0.443916\pi$
$881$	10.4054			0.350566			0.175283	+	0.984518i	$0.443916\pi$
$882$		0			0
$883$	44.9042			1.51115			0.755574	−	0.655064i	$-0.227358\pi$
$883$	44.9042			1.51115			0.755574	+	0.655064i	$0.227358\pi$
$884$		0			0
$885$	1.32511	+	15.3406i	0.0445432	+	0.515668i
$886$		0			0
$887$	0.474260	−	0.821442i	0.0159241	−	0.0275813i	−0.857954	−	0.513727i	$-0.828264\pi$
$887$	0.474260	−	0.821442i	0.0159241	−	0.0275813i	0.873878	+	0.486146i	$0.161598\pi$
$888$		0			0
$889$	2.80695	+	20.2962i	0.0941419	+	0.680712i
$890$		0			0
$891$	10.3881	+	1.87891i	0.348015	+	0.0629458i
$892$		0			0
$893$	26.0348	−	15.0312i	0.871221	−	0.503000i
$894$		0			0
$895$	−11.7434	+	6.78006i	−0.392539	+	0.226632i
$896$		0			0
$897$	−29.7718	+	20.7976i	−0.994052	+	0.694413i
$898$		0			0
$899$	27.7440	−	48.0541i	0.925316	−	1.60269i
$900$		0			0
$901$	71.4600	−	41.2574i	2.38068	−	1.37448i
$902$		0			0
$903$	−8.08175	+	1.83775i	−0.268944	+	0.0611566i
$904$		0			0
$905$	−10.5080	−	6.06681i	−0.349299	−	0.201668i
$906$		0			0
$907$	−17.5275	−	30.3585i	−0.581990	−	1.00804i	−0.995243	−	0.0974205i	$-0.968941\pi$
$907$	−17.5275	−	30.3585i	−0.581990	−	1.00804i	0.413253	−	0.910616i	$-0.364393\pi$
$908$		0			0
$909$	6.73303	−	1.17194i	0.223321	−	0.0388707i
$910$		0			0
$911$	−42.8316	−	24.7288i	−1.41907	−	0.819303i	−0.422857	−	0.906196i	$-0.638973\pi$
$911$	−42.8316	−	24.7288i	−1.41907	−	0.819303i	−0.996218	+	0.0868934i	$0.972306\pi$
$912$		0			0
$913$			0.917186i			0.0303544i
$914$		0			0
$915$	31.3763	−	2.71026i	1.03727	−	0.0895986i
$916$		0			0
$917$	−38.2976	−	15.5713i	−1.26470	−	0.514209i
$918$		0			0
$919$	8.34526	+	14.4544i	0.275285	+	0.476807i	0.970207	−	0.242278i	$-0.0778945\pi$
$919$	8.34526	+	14.4544i	0.275285	+	0.476807i	−0.694922	+	0.719085i	$0.744561\pi$
$920$		0			0
$921$	−22.3087	−	31.9349i	−0.735096	−	1.05229i
$922$		0			0
$923$	−6.62295	−	11.4713i	−0.217997	−	0.377582i
$924$		0			0
$925$	0.373818	−	0.647472i	0.0122911	−	0.0212888i
$926$		0			0
$927$	20.4290	−	17.0655i	0.670977	−	0.560504i
$928$		0			0
$929$	−10.6372			−0.348995			−0.174498	−	0.984658i	$-0.555830\pi$
$929$	−10.6372			−0.348995			−0.174498	+	0.984658i	$0.555830\pi$
$930$		0			0
$931$	17.2162	−	17.6717i	0.564238	−	0.579166i
$932$		0			0
$933$	−13.7418	+	9.59961i	−0.449888	+	0.314277i
$934$		0			0
$935$	−16.7480	−	9.66948i	−0.547719	−	0.316226i
$936$		0			0
$937$			26.7085i			0.872528i	0.899819	+	0.436264i	$0.143699\pi$
$937$			26.7085i			0.872528i	−0.899819	+	0.436264i	$0.856301\pi$
$938$		0			0
$939$	24.2985	+	34.7833i	0.792952	+	1.13511i
$940$		0			0
$941$	6.59067			0.214850			0.107425	−	0.994213i	$-0.465739\pi$
$941$	6.59067			0.214850			0.107425	+	0.994213i	$0.465739\pi$
$942$		0			0
$943$		−	9.40482i		−	0.306263i
$944$		0			0
$945$	3.88768	−	30.2843i	0.126466	−	0.985150i
$946$		0			0
$947$			28.7413i			0.933965i	0.884267	+	0.466983i	$0.154659\pi$
$947$			28.7413i			0.933965i	−0.884267	+	0.466983i	$0.845341\pi$
$948$		0			0
$949$	−28.8579			−0.936768
$950$		0			0
$951$	−9.11179	−	13.0435i	−0.295470	−	0.422965i
$952$		0			0
$953$			18.2616i			0.591550i	0.955258	+	0.295775i	$0.0955778\pi$
$953$			18.2616i			0.591550i	−0.955258	+	0.295775i	$0.904422\pi$
$954$		0			0
$955$	−11.5718	−	6.68098i	−0.374455	−	0.216191i
$956$		0			0
$957$	−11.6241	+	8.12024i	−0.375754	+	0.262490i
$958$		0			0
$959$	1.74718	+	2.24645i	0.0564194	+	0.0725417i
$960$		0			0
$961$	−32.2075			−1.03895
$962$		0			0
$963$	−0.341423	−	1.96155i	−0.0110022	−	0.0632101i
$964$		0			0
$965$	6.41889	−	11.1178i	0.206631	−	0.357896i
$966$		0			0
$967$	12.5899	+	21.8064i	0.404865	+	0.701247i	0.994306	−	0.106565i	$-0.0339851\pi$
$967$	12.5899	+	21.8064i	0.404865	+	0.701247i	−0.589441	+	0.807812i	$0.700652\pi$
$968$		0			0
$969$	−25.9525	−	37.1509i	−0.833714	−	1.19346i
$970$		0			0
$971$	23.7214	+	41.0866i	0.761255	+	1.31853i	0.942204	+	0.335040i	$0.108750\pi$
$971$	23.7214	+	41.0866i	0.761255	+	1.31853i	−0.180949	+	0.983492i	$0.557917\pi$
$972$		0			0
$973$	−10.9117	−	14.0298i	−0.349812	−	0.449774i
$974$		0			0
$975$	0.419767	−	0.0362593i	0.0134433	−	0.00116123i
$976$		0			0
$977$		−	55.3422i		−	1.77055i	−0.465064	−	0.885277i	$-0.653969\pi$
$977$		−	55.3422i		−	1.77055i	0.465064	−	0.885277i	$-0.346031\pi$
$978$		0			0
$979$	3.56429	+	2.05784i	0.113915	+	0.0657690i
$980$		0			0
$981$	30.9049	+	36.9961i	0.986717	+	1.18120i
$982$		0			0
$983$	−12.6750	−	21.9537i	−0.404268	−	0.700213i	0.589968	−	0.807427i	$-0.299140\pi$
$983$	−12.6750	−	21.9537i	−0.404268	−	0.700213i	−0.994236	+	0.107214i	$0.965807\pi$
$984$		0			0
$985$	−15.2977	−	8.83216i	−0.487427	−	0.281416i
$986$		0			0
$987$	26.5629	+	28.6744i	0.845508	+	0.912716i
$988$		0			0
$989$	−9.10404	+	5.25622i	−0.289492	+	0.167138i
$990$		0			0
$991$	−12.9683	+	22.4618i	−0.411953	+	0.713523i	−0.995103	−	0.0988413i	$-0.968486\pi$
$991$	−12.9683	+	22.4618i	−0.411953	+	0.713523i	0.583151	+	0.812364i	$0.301820\pi$
$992$		0			0
$993$	−36.5196	+	25.5114i	−1.15891	+	0.809580i
$994$		0			0
$995$	34.4753	−	19.9043i	1.09294	−	0.631010i
$996$		0			0
$997$	−13.7943	+	7.96414i	−0.436869	+	0.252227i	−0.702269	−	0.711912i	$-0.747830\pi$
$997$	−13.7943	+	7.96414i	−0.436869	+	0.252227i	0.265399	+	0.964139i	$0.414496\pi$
$998$		0			0
$999$	40.8706	−	40.6015i	1.29309	−	1.28457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.353.5	yes	48
3.2	odd	2		1512.2.bs.a.521.20		48
4.3	odd	2		1008.2.ca.e.353.20		48
7.5	odd	6		504.2.cx.a.425.13	yes	48
9.4	even	3		1512.2.cx.a.17.20		48
9.5	odd	6		504.2.cx.a.185.13	yes	48
12.11	even	2		3024.2.ca.e.2033.20		48
21.5	even	6		1512.2.cx.a.89.20		48
28.19	even	6		1008.2.df.e.929.12		48
36.23	even	6		1008.2.df.e.689.12		48
36.31	odd	6		3024.2.df.e.17.20		48
63.5	even	6	inner	504.2.bs.a.257.5	✓	48
63.40	odd	6		1512.2.bs.a.1097.20		48
84.47	odd	6		3024.2.df.e.1601.20		48
252.103	even	6		3024.2.ca.e.2609.20		48
252.131	odd	6		1008.2.ca.e.257.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.5	✓	48	63.5	even	6	inner
504.2.bs.a.353.5	yes	48	1.1	even	1	trivial
504.2.cx.a.185.13	yes	48	9.5	odd	6
504.2.cx.a.425.13	yes	48	7.5	odd	6
1008.2.ca.e.257.20		48	252.131	odd	6
1008.2.ca.e.353.20		48	4.3	odd	2
1008.2.df.e.689.12		48	36.23	even	6
1008.2.df.e.929.12		48	28.19	even	6
1512.2.bs.a.521.20		48	3.2	odd	2
1512.2.bs.a.1097.20		48	63.40	odd	6
1512.2.cx.a.17.20		48	9.4	even	3
1512.2.cx.a.89.20		48	21.5	even	6
3024.2.ca.e.2033.20		48	12.11	even	2
3024.2.ca.e.2609.20		48	252.103	even	6
3024.2.df.e.17.20		48	36.31	odd	6
3024.2.df.e.1601.20		48	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41991 + 0.991901i) q^{3} +(-1.11047 + 1.92339i) q^{5} +(0.362456 + 2.62081i) q^{7} +(1.03226 - 2.81681i) q^{9} +(-1.01582 + 0.586482i) q^{11} +(-3.12404 + 1.80366i) q^{13} +(-0.331050 - 3.83251i) q^{15} +(3.71178 - 6.42899i) q^{17} +(-3.05231 + 1.76225i) q^{19} +(-3.11423 - 3.36178i) q^{21} +(-5.03374 - 2.90623i) q^{23} +(0.0337168 + 0.0583992i) q^{25} +(1.32828 + 5.02351i) q^{27} +(-6.04430 - 3.48968i) q^{29} +7.95031i q^{31} +(0.860632 - 1.84034i) q^{33} +(-5.44333 - 2.21318i) q^{35} +(-5.54350 - 9.60163i) q^{37} +(2.64678 - 5.65977i) q^{39} +(0.809022 + 1.40127i) q^{41} +(0.904302 - 1.56630i) q^{43} +(4.27153 + 5.11343i) q^{45} -8.52953 q^{47} +(-6.73725 + 1.89985i) q^{49} +(1.10654 + 12.8103i) q^{51} +(9.62611 + 5.55764i) q^{53} -2.60508i q^{55} +(2.58602 - 5.52983i) q^{57} -4.00276 q^{59} +8.18688i q^{61} +(7.75647 + 1.68440i) q^{63} -8.01166i q^{65} +9.92669 q^{67} +(10.0301 - 0.866397i) q^{69} +3.67194i q^{71} +(6.92803 + 3.99990i) q^{73} +(-0.105801 - 0.0494776i) q^{75} +(-1.90525 - 2.44969i) q^{77} -4.51987 q^{79} +(-6.86886 - 5.81539i) q^{81} +(0.390969 - 0.677179i) q^{83} +(8.24363 + 14.2784i) q^{85} +(12.0438 - 1.04033i) q^{87} +(-1.75440 - 3.03870i) q^{89} +(-5.85938 - 7.53375i) q^{91} +(-7.88592 - 11.2887i) q^{93} -7.82772i q^{95} +(3.49226 + 2.01626i) q^{97} +(0.603418 + 3.46677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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