LMFDB - Embedded newform 1008.2.ca.e.257.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, 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("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.20
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.e.353.20

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.41991	+	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	0.503376	−	0.864068i	$-0.332091\pi$
$5$	−1.11047	−	1.92339i	−0.496617	−	0.860166i	−0.999992	+	0.00390210i	$0.998758\pi$
$6$		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	$-0.276749\pi$
$11$	1.01582	+	0.586482i	0.306280	+	0.176831i	−0.338980	+	0.940793i	$0.610082\pi$
$12$		0			0
$13$	−3.12404	−	1.80366i	−0.866453	−	0.500247i	−0.000284763	−	1.00000i	$-0.500091\pi$
$13$	−3.12404	−	1.80366i	−0.866453	−	0.500247i	−0.866168	+	0.499753i	$0.833424\pi$
$14$		0			0
$15$	0.331050	−	3.83251i	0.0854767	−	0.989549i
$16$		0			0
$17$	3.71178	+	6.42899i	0.900238	+	1.55926i	0.827185	+	0.561930i	$0.189941\pi$
$17$	3.71178	+	6.42899i	0.900238	+	1.55926i	0.0730533	+	0.997328i	$0.476726\pi$
$18$		0			0
$19$	3.05231	+	1.76225i	0.700249	+	0.404289i	0.807440	−	0.589950i	$-0.200852\pi$
$19$	3.05231	+	1.76225i	0.700249	+	0.404289i	−0.107191	+	0.994238i	$0.534186\pi$
$20$		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	$-0.459443\pi$
$23$	5.03374	−	2.90623i	1.04961	−	0.605991i	0.922539	+	0.385903i	$0.126110\pi$
$24$		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	−0.942012	−	0.335579i	$-0.891068\pi$
$29$	−6.04430	+	3.48968i	−1.12240	+	0.648017i	−0.180387	+	0.983596i	$0.557735\pi$
$30$		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	−0.0991818	+	0.995069i	$0.531623\pi$
$37$	−5.54350	+	9.60163i	−0.911346	+	1.57850i	−0.812164	+	0.583429i	$0.801711\pi$
$38$		0			0
$39$	−2.64678	−	5.65977i	−0.423825	−	0.906289i
$40$		0			0
$41$	0.809022	−	1.40127i	0.126348	−	0.218841i	−0.795911	−	0.605414i	$-0.793008\pi$
$41$	0.809022	−	1.40127i	0.126348	−	0.218841i	0.922259	+	0.386572i	$0.126341\pi$
$42$		0			0
$43$	−0.904302	−	1.56630i	−0.137905	−	0.238858i	0.788799	−	0.614652i	$-0.210703\pi$
$43$	−0.904302	−	1.56630i	−0.137905	−	0.238858i	−0.926703	+	0.375794i	$0.877370\pi$
$44$		0			0
$45$	4.27153	−	5.11343i	0.636762	−	0.762265i
$46$		0			0
$47$	8.52953			1.24416			0.622080	−	0.782954i	$-0.286288\pi$
$47$	8.52953			1.24416			0.622080	+	0.782954i	$0.286288\pi$
$48$		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	0.338161	−	0.941088i	$-0.390195\pi$
$53$	9.62611	−	5.55764i	1.32225	−	0.763400i	0.984087	+	0.177688i	$0.0568617\pi$
$54$		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	$-0.416094\pi$
$59$	4.00276			0.521115			0.260557	+	0.965458i	$0.416094\pi$
$60$		0			0
$61$		−	8.18688i		−	1.04822i	−0.851650	−	0.524111i	$-0.824398\pi$
$61$		−	8.18688i		−	1.04822i	0.851650	−	0.524111i	$-0.175602\pi$
$62$		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	$-0.707375\pi$
$67$	−9.92669			−1.21274			−0.606369	+	0.795183i	$0.707375\pi$
$68$		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	−0.0363913	−	0.999338i	$-0.511586\pi$
$73$	6.92803	−	3.99990i	0.810865	−	0.468153i	0.847256	+	0.531185i	$0.178253\pi$
$74$		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	$-0.418167\pi$
$79$	4.51987			0.508525			0.254262	+	0.967135i	$0.418167\pi$
$80$		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	$-0.180331\pi$
$83$	−0.390969	−	0.677179i	−0.0429145	−	0.0743300i	−0.886685	+	0.462374i	$0.846998\pi$
$84$		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	−0.943901	−	0.330227i	$-0.892875\pi$
$89$	−1.75440	+	3.03870i	−0.185966	+	0.322102i	0.757936	+	0.652329i	$0.226208\pi$
$90$		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	−0.312118	−	0.950043i	$-0.601038\pi$
$97$	3.49226	−	2.01626i	0.354585	−	0.204720i	0.666703	+	0.745324i	$0.267705\pi$
$98$		0			0
$99$	−0.603418	+	3.46677i	−0.0606458	+	0.348424i
$100$		0			0
$101$	1.13904	−	1.97288i	0.113339	−	0.196309i	−0.803775	−	0.594933i	$-0.797179\pi$
$101$	1.13904	−	1.97288i	0.113339	−	0.196309i	0.917115	+	0.398624i	$0.130512\pi$
$102$		0			0
$103$	−7.68427	+	4.43651i	−0.757153	+	0.437143i	−0.828273	−	0.560325i	$-0.810676\pi$
$103$	−7.68427	+	4.43651i	−0.757153	+	0.437143i	0.0711195	+	0.997468i	$0.477343\pi$
$104$		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	$-0.343547\pi$
$107$	−0.574764	−	0.331840i	−0.0555646	−	0.0320802i	−0.527525	+	0.849540i	$0.676880\pi$
$108$		0			0
$109$	−8.03435	−	13.9159i	−0.769551	−	1.33290i	−0.937807	−	0.347158i	$-0.887147\pi$
$109$	−8.03435	−	13.9159i	−0.769551	−	1.33290i	0.168256	−	0.985743i	$-0.446187\pi$
$110$		0			0
$111$	−17.3951	+	8.13480i	−1.65107	+	0.772121i
$112$		0			0
$113$	−4.86666	−	2.80977i	−0.457817	−	0.264321i	0.253309	−	0.967385i	$-0.418481\pi$
$113$	−4.86666	−	2.80977i	−0.457817	−	0.264321i	−0.711126	+	0.703065i	$0.751814\pi$
$114$		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	$-0.611645\pi$
$127$	−7.74425			−0.687191			−0.343595	+	0.939118i	$0.611645\pi$
$128$		0			0
$129$	0.269588	−	3.12097i	0.0237359	−	0.274786i
$130$		0			0
$131$	7.81293	+	13.5324i	0.682619	+	1.18233i	0.974179	+	0.225778i	$0.0724926\pi$
$131$	7.81293	+	13.5324i	0.682619	+	1.18233i	−0.291559	+	0.956553i	$0.594174\pi$
$132$		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	0.539265	−	0.842136i	$-0.318702\pi$
$137$	0.931541	+	0.537826i	0.0795870	+	0.0459496i	−0.459678	+	0.888085i	$0.652035\pi$
$138$		0			0
$139$	5.81776	+	3.35889i	0.493456	+	0.284897i	0.726007	−	0.687687i	$-0.241374\pi$
$139$	5.81776	+	3.35889i	0.493456	+	0.284897i	−0.232551	+	0.972584i	$0.574707\pi$
$140$		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	0.275762	−	0.961226i	$-0.411070\pi$
$149$	15.2105	−	8.78176i	1.24609	−	0.719430i	0.970327	+	0.241796i	$0.0777365\pi$
$150$		0			0
$151$	0.848028	−	1.46883i	0.0690115	−	0.119531i	−0.829455	−	0.558574i	$-0.811349\pi$
$151$	0.848028	−	1.46883i	0.0690115	−	0.119531i	0.898466	+	0.439042i	$0.144682\pi$
$152$		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	$-0.898150\pi$
$157$		−	7.88233i		−	0.629078i	0.949244	−	0.314539i	$-0.101850\pi$
$158$		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	$-0.686190\pi$
$163$	5.69385	−	9.86204i	0.445977	−	0.772455i	0.998120	+	0.0612949i	$0.0195230\pi$
$164$		0			0
$165$	2.58398	−	3.69897i	0.201163	−	0.287964i
$166$		0			0
$167$	8.05638	−	13.9541i	0.623422	−	1.07980i	−0.365422	−	0.930842i	$-0.619075\pi$
$167$	8.05638	−	13.9541i	0.623422	−	1.07980i	0.988844	−	0.148956i	$-0.0475913\pi$
$168$		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	$-0.739943\pi$
$179$	−5.28759	+	3.05279i	−0.395213	+	0.228176i	0.289203	+	0.957268i	$0.406610\pi$
$180$		0			0
$181$		−	5.46329i		−	0.406083i	−0.979170	−	0.203041i	$-0.934917\pi$
$181$		−	5.46329i		−	0.406083i	0.979170	−	0.203041i	$-0.0650826\pi$
$182$		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	$-0.908560\pi$
$197$		−	7.95354i		−	0.566666i	0.959022	−	0.283333i	$-0.0914402\pi$
$198$		0			0
$199$	15.5229	−	8.96214i	1.10039	−	0.635309i	0.164065	−	0.986450i	$-0.447539\pi$
$199$	15.5229	−	8.96214i	1.10039	−	0.635309i	0.936323	+	0.351141i	$0.114206\pi$
$200$		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	$-0.744487\pi$
$211$	4.00200	−	6.93166i	0.275509	−	0.477195i	0.970263	+	0.242052i	$0.0778203\pi$
$212$		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	$-0.852256\pi$
$223$	−14.2405	+	8.22177i	−0.953616	+	0.550570i	−0.0594134	+	0.998233i	$0.518923\pi$
$224$		0			0
$225$	0.199304	+	0.0346904i	0.0132869	+	0.00231269i
$226$		0			0
$227$	7.99649	−	13.8503i	0.530746	−	0.919279i	−0.468610	−	0.883405i	$-0.655245\pi$
$227$	7.99649	−	13.8503i	0.530746	−	0.919279i	0.999356	−	0.0358740i	$-0.0114215\pi$
$228$		0			0
$229$	−13.3898	+	7.73058i	−0.884820	+	0.510851i	−0.872245	−	0.489070i	$-0.837336\pi$
$229$	−13.3898	+	7.73058i	−0.884820	+	0.510851i	−0.0125754	+	0.999921i	$0.504003\pi$
$230$		0			0
$231$	−5.13511	+	1.58851i	−0.337866	+	0.104516i
$232$		0			0
$233$	−16.5268	−	9.54175i	−1.08271	−	0.625101i	−0.151081	−	0.988521i	$-0.548275\pi$
$233$	−16.5268	−	9.54175i	−1.08271	−	0.625101i	−0.931625	+	0.363421i	$0.881609\pi$
$234$		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	$-0.422167\pi$
$239$	−7.37626	−	4.25868i	−0.477130	−	0.275471i	−0.719220	+	0.694783i	$0.755501\pi$
$240$		0			0
$241$	19.6047	+	11.3188i	1.26285	+	0.729107i	0.973625	−	0.228154i	$-0.0732690\pi$
$241$	19.6047	+	11.3188i	1.26285	+	0.729107i	0.289225	+	0.957261i	$0.406602\pi$
$242$		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	$-0.421427\pi$
$251$	7.74235			0.488693			0.244346	+	0.969688i	$0.421427\pi$
$252$		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	−0.951603	−	0.307331i	$-0.900564\pi$
$257$	−11.8945	−	20.6019i	−0.741958	−	1.28511i	0.209645	−	0.977778i	$-0.432769\pi$
$258$		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	$-0.115118\pi$
$263$	17.7831	+	10.2671i	1.09655	+	0.633094i	0.161238	+	0.986916i	$0.448451\pi$
$264$		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	0.614215	−	0.789138i	$-0.289473\pi$
$269$	−6.17188	−	10.6900i	−0.376306	−	0.651782i	−0.990522	+	0.137357i	$0.956139\pi$
$270$		0			0
$271$	25.3900	+	14.6589i	1.54233	+	0.890467i	0.998691	+	0.0511505i	$0.0162888\pi$
$271$	25.3900	+	14.6589i	1.54233	+	0.890467i	0.543643	+	0.839317i	$0.317045\pi$
$272$		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	−0.826327	−	0.563190i	$-0.809574\pi$
$277$	1.24115	−	2.14974i	0.0745735	−	0.129165i	0.900901	+	0.434025i	$0.142907\pi$
$278$		0			0
$279$	−22.3945	+	8.20683i	−1.34073	+	0.491330i
$280$		0			0
$281$	20.0970	−	11.6030i	1.19889	−	0.692178i	0.238581	−	0.971123i	$-0.423318\pi$
$281$	20.0970	−	11.6030i	1.19889	−	0.692178i	0.960307	+	0.278944i	$0.0899845\pi$
$282$		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	−0.961514	−	0.274755i	$-0.911403\pi$
$293$	−4.15628	+	7.19888i	−0.242812	+	0.420563i	0.718702	+	0.695318i	$0.244737\pi$
$294$		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	$-0.588477\pi$
$311$	−9.67799			−0.548789			−0.274394	+	0.961617i	$0.588477\pi$
$312$		0			0
$313$			24.4969i			1.38465i	0.721587	+	0.692324i	$0.243413\pi$
$313$			24.4969i			1.38465i	−0.721587	+	0.692324i	$0.756587\pi$
$314$		0			0
$315$	11.8531	+	13.0482i	0.667845	+	0.735185i
$316$		0			0
$317$		−	9.18619i		−	0.515948i	−0.966152	−	0.257974i	$-0.916945\pi$
$317$		−	9.18619i		−	0.515948i	0.966152	−	0.257974i	$-0.0830549\pi$
$318$		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	$-0.749881\pi$
$331$	−25.7197			−1.41368			−0.706842	+	0.707372i	$0.749881\pi$
$332$		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	−0.520005	−	0.854163i	$-0.674070\pi$
$337$	8.80657	−	15.2534i	0.479724	−	0.830907i	0.999730	+	0.0232560i	$0.00740329\pi$
$338$		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	0.00813729	−	0.999967i	$-0.497410\pi$
$349$	16.4062	−	9.47211i	0.878203	−	0.507031i	0.870065	+	0.492936i	$0.164076\pi$
$350$		0			0
$351$	13.2103	−	13.2979i	0.705115	−	0.709788i
$352$		0			0
$353$	12.7486	−	22.0811i	0.678537	−	1.17526i	−0.296884	−	0.954913i	$-0.595948\pi$
$353$	12.7486	−	22.0811i	0.678537	−	1.17526i	0.975421	−	0.220347i	$-0.0707191\pi$
$354$		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	$-0.511364\pi$
$359$	−17.4128	−	10.0533i	−0.919013	−	0.530592i	−0.883320	+	0.468771i	$0.844697\pi$
$360$		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	$-0.125412\pi$
$367$	20.1654	+	11.6425i	1.05263	+	0.607735i	0.129244	+	0.991613i	$0.458745\pi$
$368$		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	0.983011	+	0.183545i	$0.0587573\pi$
$373$	12.5625	+	21.7588i	0.650460	+	1.12663i	−0.332551	+	0.943085i	$0.607909\pi$
$374$		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	$-0.811414\pi$
$379$	−32.3000			−1.65914			−0.829569	+	0.558404i	$0.811414\pi$
$380$		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	$-0.245070\pi$
$383$	−4.77182	−	8.26503i	−0.243828	−	0.422323i	−0.961802	+	0.273748i	$0.911737\pi$
$384$		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	0.768273	−	0.640122i	$-0.221116\pi$
$389$	11.7953	+	6.81005i	0.598048	+	0.345283i	−0.170225	+	0.985405i	$0.554450\pi$
$390$		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	0.563726	−	0.825962i	$-0.309368\pi$
$397$	2.59589	+	1.49874i	0.130284	+	0.0752196i	−0.433441	+	0.901182i	$0.642701\pi$
$398$		0			0
$399$	−15.4299	+	4.77313i	−0.772462	+	0.238955i
$400$		0			0
$401$	11.2875	−	6.51682i	0.563669	−	0.325434i	−0.190948	−	0.981600i	$-0.561156\pi$
$401$	11.2875	−	6.51682i	0.563669	−	0.325434i	0.754617	+	0.656166i	$0.227823\pi$
$402$		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	$0.302011\pi$
$409$			32.8723i			1.62543i	−0.582662	+	0.812714i	$0.697989\pi$
$410$		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	−0.458119	−	0.888891i	$-0.651477\pi$
$419$	11.0687	−	19.1716i	0.540742	−	0.936593i	0.998862	−	0.0477024i	$-0.0151899\pi$
$420$		0			0
$421$	12.1963	+	21.1245i	0.594409	+	1.02955i	0.993630	+	0.112692i	$0.0359472\pi$
$421$	12.1963	+	21.1245i	0.594409	+	1.02955i	−0.399221	+	0.916855i	$0.630719\pi$
$422$		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	$-0.777426\pi$
$431$	−12.2611	+	7.07897i	−0.590598	+	0.340982i	0.174736	+	0.984615i	$0.444093\pi$
$432$		0			0
$433$			8.90220i			0.427813i	0.976854	+	0.213906i	$0.0686187\pi$
$433$			8.90220i			0.427813i	−0.976854	+	0.213906i	$0.931381\pi$
$434$		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	$0.0692700\pi$
$449$			9.14988i			0.431809i	−0.976414	+	0.215905i	$0.930730\pi$
$450$		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	0.908202	+	0.418532i	$0.137455\pi$
$461$	17.5323	+	30.3668i	0.816561	+	1.41432i	−0.0916412	+	0.995792i	$0.529211\pi$
$462$		0			0
$463$	−15.9985	+	27.7103i	−0.743515	+	1.28781i	0.207370	+	0.978263i	$0.433510\pi$
$463$	−15.9985	+	27.7103i	−0.743515	+	1.28781i	−0.950885	+	0.309543i	$0.899824\pi$
$464$		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	$-0.954466\pi$
$467$	−8.02671	+	13.9027i	−0.371432	+	0.643339i	0.618354	+	0.785899i	$0.287800\pi$
$468$		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	0.241632	+	0.970368i	$0.422317\pi$
$479$	−15.7481	+	27.2764i	−0.719547	+	1.24629i	−0.961179	+	0.275925i	$0.911016\pi$
$480$		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	$-0.329324\pi$
$487$	−10.7924	−	18.6930i	−0.489052	−	0.847062i	−0.999921	+	0.0125963i	$0.995990\pi$
$488$		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	$-0.0615726\pi$
$491$	28.9290	+	16.7022i	1.30555	+	0.753758i	0.324197	+	0.945990i	$0.394906\pi$
$492$		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	0.961202	+	0.275844i	$0.0889574\pi$
$499$	16.0722	+	27.8378i	0.719489	+	1.24619i	−0.241713	+	0.970348i	$0.577709\pi$
$500$		0			0
$501$	25.2804	−	11.8223i	1.12944	−	0.528183i
$502$		0			0
$503$	−21.7295			−0.968872			−0.484436	−	0.874827i	$-0.660975\pi$
$503$	−21.7295			−0.968872			−0.484436	+	0.874827i	$0.660975\pi$
$504$		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	0.999413	+	0.0342559i	$0.0109061\pi$
$509$	11.9432	+	20.6862i	0.529373	+	0.916901i	−0.470040	+	0.882645i	$0.655761\pi$
$510$		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	−0.993980	−	0.109562i	$-0.965055\pi$
$521$	−13.5098	−	23.3996i	−0.591874	−	1.02516i	0.402106	−	0.915593i	$-0.368278\pi$
$522$		0			0
$523$	−27.2136	−	15.7118i	−1.18997	−	0.687028i	−0.231669	−	0.972795i	$-0.574418\pi$
$523$	−27.2136	−	15.7118i	−1.18997	−	0.687028i	−0.958299	+	0.285766i	$0.907752\pi$
$524$		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	−0.868101	−	0.496388i	$-0.834660\pi$
$541$	−0.0969057	+	0.167846i	−0.00416630	+	0.00721624i	0.863935	+	0.503604i	$0.167993\pi$
$542$		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	$-0.180104\pi$
$547$	−0.987053	−	1.70963i	−0.0422033	−	0.0730983i	−0.886355	+	0.463005i	$0.846771\pi$
$548$		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	−0.0583543	−	0.998296i	$-0.518585\pi$
$557$	18.3383	−	10.5876i	0.777018	−	0.448612i	0.835373	+	0.549684i	$0.185252\pi$
$558$		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	$-0.244517\pi$
$563$	34.1289			1.43836			0.719182	+	0.694822i	$0.244517\pi$
$564$		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	$-0.925674\pi$
$569$		−	11.0389i		−	0.462773i	0.972862	−	0.231387i	$-0.0743262\pi$
$570$		0			0
$571$	−41.3233			−1.72933			−0.864663	−	0.502353i	$-0.832468\pi$
$571$	−41.3233			−1.72933			−0.864663	+	0.502353i	$0.832468\pi$
$572$		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	−0.216085	−	0.976374i	$-0.569329\pi$
$577$	12.5253	−	7.23151i	0.521437	−	0.301052i	0.737522	+	0.675323i	$0.235996\pi$
$578$		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	$-0.169928\pi$
$587$	−0.248251	−	0.429983i	−0.0102464	−	0.0177473i	−0.871103	+	0.491100i	$0.836595\pi$
$588$		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	0.497761	+	0.867314i	$0.334156\pi$
$593$	−12.2302	+	21.1834i	−0.502236	+	0.869898i	−0.999997	+	0.00258345i	$0.999178\pi$
$594$		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	−0.364296	−	0.931283i	$-0.618690\pi$
$601$	6.37572	−	3.68102i	0.260071	−	0.150152i	0.624367	+	0.781131i	$0.285357\pi$
$602$		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	$-0.466432\pi$
$607$	25.1081	−	14.4961i	1.01910	−	0.588380i	0.913845	+	0.406064i	$0.133099\pi$
$608$		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	0.999997	+	0.00251771i	$0.000801413\pi$
$613$	12.4334	+	21.5352i	0.502179	+	0.869799i	−0.497818	+	0.867282i	$0.665865\pi$
$614$		0			0
$615$	−5.10254	−	3.56447i	−0.205754	−	0.143733i
$616$		0			0
$617$	−37.4629	−	21.6292i	−1.50820	−	0.870759i	−0.999954	−	0.00954684i	$-0.996961\pi$
$617$	−37.4629	−	21.6292i	−1.50820	−	0.870759i	−0.508245	−	0.861213i	$-0.669706\pi$
$618$		0			0
$619$	6.45380	+	3.72610i	0.259400	+	0.149765i	0.624061	−	0.781376i	$-0.285482\pi$
$619$	6.45380	+	3.72610i	0.259400	+	0.149765i	−0.364661	+	0.931140i	$0.618815\pi$
$620$		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	$-0.438343\pi$
$631$	9.67068			0.384984			0.192492	+	0.981299i	$0.438343\pi$
$632$		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	−0.133832	−	0.991004i	$-0.542728\pi$
$641$	−26.8113	−	15.4795i	−1.05898	−	0.611404i	−0.925151	+	0.379600i	$0.876062\pi$
$642$		0			0
$643$	6.99262	+	4.03719i	0.275762	+	0.159211i	0.631503	−	0.775373i	$-0.282438\pi$
$643$	6.99262	+	4.03719i	0.275762	+	0.159211i	−0.355741	+	0.934585i	$0.615772\pi$
$644$		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	$-0.109502\pi$
$647$	4.54355	+	7.86966i	0.178625	+	0.309388i	−0.762785	+	0.646653i	$0.776168\pi$
$648$		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	−0.108700	−	0.994075i	$-0.534669\pi$
$653$	17.8326	−	10.2957i	0.697844	−	0.402900i	0.806544	+	0.591174i	$0.201335\pi$
$654$		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	0.642121	−	0.766604i	$-0.278055\pi$
$659$	41.7687	−	24.1152i	1.62708	−	0.939395i	0.984959	−	0.172791i	$-0.0552785\pi$
$660$		0			0
$661$			27.5213i			1.07046i	0.844708	+	0.535228i	$0.179774\pi$
$661$			27.5213i			1.07046i	−0.844708	+	0.535228i	$0.820226\pi$
$662$		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	−0.975760	−	0.218844i	$-0.929771\pi$
$673$	−17.5734	−	30.4380i	−0.677404	−	1.17330i	0.298355	−	0.954455i	$-0.403562\pi$
$674$		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	$-0.537005\pi$
$683$	17.9331	−	10.3537i	0.686190	−	0.396172i	0.802183	+	0.597078i	$0.203672\pi$
$684$		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	$-0.984194\pi$
$701$		−	2.62840i		−	0.0992734i	0.998767	−	0.0496367i	$-0.0158064\pi$
$702$		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	$-0.795795\pi$
$719$	3.15485	−	5.46436i	0.117656	−	0.203786i	0.918838	+	0.394634i	$0.129129\pi$
$720$		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	$-0.567381\pi$
$727$	14.3318	−	8.27447i	0.531537	−	0.306883i	0.741642	+	0.670796i	$0.234047\pi$
$728$		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	−0.146521	−	0.989208i	$-0.546808\pi$
$733$	17.2433	−	9.95544i	0.636897	−	0.367713i	0.783418	+	0.621495i	$0.213474\pi$
$734$		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	0.841606	+	0.540092i	$0.181611\pi$
$739$	24.1545	+	41.8368i	0.888536	+	1.53899i	0.0469307	+	0.998898i	$0.485056\pi$
$740$		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	$-0.284749\pi$
$743$	7.17819	+	4.14433i	0.263342	+	0.152041i	−0.362516	+	0.931978i	$0.618082\pi$
$744$		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	$-0.317581\pi$
$751$	−12.5114	−	21.6705i	−0.456549	−	0.790767i	−0.998776	+	0.0494658i	$0.984248\pi$
$752$		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	0.995975	−	0.0896289i	$-0.0285681\pi$
$761$	11.5963	+	20.0854i	0.420367	+	0.728097i	−0.575609	+	0.817725i	$0.695235\pi$
$762$		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	−0.0940211	−	0.995570i	$-0.529972\pi$
$769$	−27.8202	−	16.0620i	−1.00322	−	0.579210i	−0.909200	+	0.416360i	$0.863305\pi$
$770$		0			0
$771$	3.54595	−	41.0509i	0.127704	−	1.47841i
$772$		0			0
$773$	8.14023	+	14.0993i	0.292784	+	0.507116i	0.974467	−	0.224531i	$-0.0720851\pi$
$773$	8.14023	+	14.0993i	0.292784	+	0.507116i	−0.681683	+	0.731647i	$0.738752\pi$
$774$		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	−0.808391	−	0.588646i	$-0.799661\pi$
$797$	2.98084	−	5.16296i	0.105587	−	0.182881i	0.913978	+	0.405764i	$0.132995\pi$
$798$		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	−0.148432	−	0.988923i	$-0.547423\pi$
$809$	18.0267	−	10.4077i	0.633784	−	0.365916i	0.782216	+	0.623007i	$0.214089\pi$
$810$		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	$-0.996899\pi$
$821$		−	0.558286i		−	0.0194843i	0.999953	−	0.00974215i	$-0.00310107\pi$
$822$		0			0
$823$	−41.4087			−1.44341			−0.721707	−	0.692198i	$-0.756642\pi$
$823$	−41.4087			−1.44341			−0.721707	+	0.692198i	$0.756642\pi$
$824$		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	−0.626258	−	0.779616i	$-0.715414\pi$
$829$	−7.60753	+	4.39221i	−0.264220	+	0.152548i	0.362038	+	0.932163i	$0.382081\pi$
$830$		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	$-0.0345781\pi$
$839$	11.6778	+	20.2265i	0.403161	+	0.698295i	−0.590944	+	0.806712i	$0.701245\pi$
$840$		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	−0.243280	−	0.969956i	$-0.578223\pi$
$853$	13.8754	−	8.01099i	0.475086	−	0.274291i	0.718366	+	0.695665i	$0.244890\pi$
$854$		0			0
$855$	22.0492	−	8.08027i	0.754067	−	0.276340i
$856$		0			0
$857$	−8.41205	+	14.5701i	−0.287350	+	0.497705i	−0.973176	−	0.230060i	$-0.926108\pi$
$857$	−8.41205	+	14.5701i	−0.287350	+	0.497705i	0.685826	+	0.727765i	$0.259441\pi$
$858$		0			0
$859$	41.2188	−	23.7977i	1.40637	−	0.811966i	0.411331	−	0.911486i	$-0.365064\pi$
$859$	41.2188	−	23.7977i	1.40637	−	0.811966i	0.995036	+	0.0995201i	$0.0317307\pi$
$860$		0			0
$861$	2.19127	+	7.08363i	0.0746782	+	0.241409i
$862$		0			0
$863$	−44.7300	−	25.8249i	−1.52263	−	0.879089i	−0.999642	−	0.0267477i	$-0.991485\pi$
$863$	−44.7300	−	25.8249i	−1.52263	−	0.879089i	−0.522985	−	0.852342i	$-0.675182\pi$
$864$		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	0.719618	−	0.694370i	$-0.244317\pi$
$877$	−7.15280	−	12.3890i	−0.241533	−	0.418347i	−0.961151	+	0.276023i	$0.910983\pi$
$878$		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	$-0.772642\pi$
$883$	−44.9042			−1.51115			−0.755574	+	0.655064i	$0.772642\pi$
$884$		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	$-0.171736\pi$
$887$	−0.474260	−	0.821442i	−0.0159241	−	0.0275813i	−0.873878	+	0.486146i	$0.838402\pi$
$888$		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	−0.413253	−	0.910616i	$-0.635607\pi$
$907$	17.5275	−	30.3585i	0.581990	−	1.00804i	0.995243	−	0.0974205i	$-0.0310592\pi$
$908$		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	$-0.361027\pi$
$911$	42.8316	−	24.7288i	1.41907	−	0.819303i	0.996218	+	0.0868934i	$0.0276940\pi$
$912$		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	$-0.922105\pi$
$919$	−8.34526	+	14.4544i	−0.275285	+	0.476807i	0.694922	+	0.719085i	$0.255439\pi$
$920$		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	$-0.856301\pi$
$937$		−	26.7085i		−	0.872528i	0.899819	−	0.436264i	$-0.143699\pi$
$938$		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	$-0.904422\pi$
$953$		−	18.2616i		−	0.591550i	0.955258	−	0.295775i	$-0.0955778\pi$
$954$		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	$-0.966015\pi$
$967$	−12.5899	+	21.8064i	−0.404865	+	0.701247i	0.589441	+	0.807812i	$0.299348\pi$
$968$		0			0
$969$	−25.9525	+	37.1509i	−0.833714	+	1.19346i
$970$		0			0
$971$	−23.7214	+	41.0866i	−0.761255	+	1.31853i	0.180949	+	0.983492i	$0.442083\pi$
$971$	−23.7214	+	41.0866i	−0.761255	+	1.31853i	−0.942204	+	0.335040i	$0.891250\pi$
$972$		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	$0.346031\pi$
$977$			55.3422i			1.77055i	−0.465064	+	0.885277i	$0.653969\pi$
$978$		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	$-0.700860\pi$
$983$	12.6750	−	21.9537i	0.404268	−	0.700213i	0.994236	+	0.107214i	$0.0341929\pi$
$984$		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	$-0.0315136\pi$
$991$	12.9683	+	22.4618i	0.411953	+	0.713523i	−0.583151	+	0.812364i	$0.698180\pi$
$992$		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	0.265399	−	0.964139i	$-0.414496\pi$
$997$	−13.7943	−	7.96414i	−0.436869	−	0.252227i	−0.702269	+	0.711912i	$0.747830\pi$
$998$		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	1008.2.ca.e.257.20		48
3.2	odd	2		3024.2.ca.e.2609.20		48
4.3	odd	2		504.2.bs.a.257.5	✓	48
7.3	odd	6		1008.2.df.e.689.12		48
9.2	odd	6		1008.2.df.e.929.12		48
9.7	even	3		3024.2.df.e.1601.20		48
12.11	even	2		1512.2.bs.a.1097.20		48
21.17	even	6		3024.2.df.e.17.20		48
28.3	even	6		504.2.cx.a.185.13	yes	48
36.7	odd	6		1512.2.cx.a.89.20		48
36.11	even	6		504.2.cx.a.425.13	yes	48
63.38	even	6	inner	1008.2.ca.e.353.20		48
63.52	odd	6		3024.2.ca.e.2033.20		48
84.59	odd	6		1512.2.cx.a.17.20		48
252.115	even	6		1512.2.bs.a.521.20		48
252.227	odd	6		504.2.bs.a.353.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.5	✓	48	4.3	odd	2
504.2.bs.a.353.5	yes	48	252.227	odd	6
504.2.cx.a.185.13	yes	48	28.3	even	6
504.2.cx.a.425.13	yes	48	36.11	even	6
1008.2.ca.e.257.20		48	1.1	even	1	trivial
1008.2.ca.e.353.20		48	63.38	even	6	inner
1008.2.df.e.689.12		48	7.3	odd	6
1008.2.df.e.929.12		48	9.2	odd	6
1512.2.bs.a.521.20		48	252.115	even	6
1512.2.bs.a.1097.20		48	12.11	even	2
1512.2.cx.a.17.20		48	84.59	odd	6
1512.2.cx.a.89.20		48	36.7	odd	6
3024.2.ca.e.2033.20		48	63.52	odd	6
3024.2.ca.e.2609.20		48	3.2	odd	2
3024.2.df.e.17.20		48	21.17	even	6
3024.2.df.e.1601.20		48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not 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

Fields

Representations

Groups

Database

Properties

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