LMFDB - Embedded newform 1008.2.cz.i.607.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.14
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.i.367.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60273 + 0.656694i) q^{3} +(2.94743 - 1.70170i) q^{5} +(1.13535 - 2.38977i) q^{7} +(2.13751 + 2.10501i) q^{9} +O(q^{10})$	\(q+(1.60273 + 0.656694i) q^{3} +(2.94743 - 1.70170i) q^{5} +(1.13535 - 2.38977i) q^{7} +(2.13751 + 2.10501i) q^{9} +(4.77030 + 2.75413i) q^{11} +(-1.96711 - 1.13571i) q^{13} +(5.84145 - 0.791810i) q^{15} +(-6.64938 + 3.83902i) q^{17} +(-0.850777 + 1.47359i) q^{19} +(3.38901 - 3.08458i) q^{21} +(1.09863 - 0.634293i) q^{23} +(3.29157 - 5.70117i) q^{25} +(2.04350 + 4.77746i) q^{27} +(-3.04081 - 5.26683i) q^{29} -7.32136 q^{31} +(5.83689 + 7.54677i) q^{33} +(-0.720307 - 8.97570i) q^{35} +(-0.928112 + 1.60754i) q^{37} +(-2.40693 - 3.11203i) q^{39} +(-4.99026 - 2.88113i) q^{41} +(6.68015 - 3.85679i) q^{43} +(9.88225 + 2.56698i) q^{45} +1.64594 q^{47} +(-4.42197 - 5.42643i) q^{49} +(-13.1782 + 1.78632i) q^{51} +(-2.90265 - 5.02754i) q^{53} +18.7469 q^{55} +(-2.33127 + 1.80307i) q^{57} +6.97610 q^{59} +11.1375i q^{61} +(7.45730 - 2.71822i) q^{63} -7.73055 q^{65} +8.24153i q^{67} +(2.17734 - 0.295140i) q^{69} +5.47245i q^{71} +(-12.5641 + 7.25388i) q^{73} +(9.01944 - 6.97590i) q^{75} +(11.9977 - 8.27301i) q^{77} -3.42392i q^{79} +(0.137857 + 8.99894i) q^{81} +(-5.67528 - 9.82987i) q^{83} +(-13.0657 + 22.6305i) q^{85} +(-1.41490 - 10.4382i) q^{87} +(4.67278 + 2.69783i) q^{89} +(-4.94743 + 3.41150i) q^{91} +(-11.7342 - 4.80790i) q^{93} +5.79107i q^{95} +(0.903873 - 0.521851i) q^{97} +(4.39906 + 15.9285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9}+O(q^{10}) $ 32 * q - 4 * q^9	$ 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.60273	+	0.656694i	0.925338	+	0.379143i
$3$	1.60273	+	0.656694i	0.925338	+	0.379143i
$4$		0			0
$5$	2.94743	−	1.70170i	1.31813	−	0.761024i	0.334704	−	0.942323i	$-0.391364\pi$
$5$	2.94743	−	1.70170i	1.31813	−	0.761024i	0.983428	+	0.181299i	$0.0580303\pi$
$6$		0			0
$7$	1.13535	−	2.38977i	0.429121	−	0.903247i
$7$	1.13535	−	2.38977i	0.429121	−	0.903247i
$8$		0			0
$9$	2.13751	+	2.10501i	0.712502	+	0.701670i
$10$		0			0
$11$	4.77030	+	2.75413i	1.43830	+	0.830403i	0.997732	−	0.0673165i	$-0.0214437\pi$
$11$	4.77030	+	2.75413i	1.43830	+	0.830403i	0.440568	+	0.897719i	$0.354777\pi$
$12$		0			0
$13$	−1.96711	−	1.13571i	−0.545577	−	0.314989i	0.201759	−	0.979435i	$-0.435334\pi$
$13$	−1.96711	−	1.13571i	−0.545577	−	0.314989i	−0.747336	+	0.664446i	$0.768668\pi$
$14$		0			0
$15$	5.84145	−	0.791810i	1.50825	−	0.204444i
$16$		0			0
$17$	−6.64938	+	3.83902i	−1.61271	+	0.931099i	−0.623972	+	0.781447i	$0.714482\pi$
$17$	−6.64938	+	3.83902i	−1.61271	+	0.931099i	−0.988739	+	0.149652i	$0.952185\pi$
$18$		0			0
$19$	−0.850777	+	1.47359i	−0.195182	+	0.338064i	−0.946960	−	0.321351i	$-0.895863\pi$
$19$	−0.850777	+	1.47359i	−0.195182	+	0.338064i	0.751778	+	0.659416i	$0.229196\pi$
$20$		0			0
$21$	3.38901	−	3.08458i	0.739542	−	0.673111i
$22$		0			0
$23$	1.09863	−	0.634293i	0.229080	−	0.132259i	−0.381068	−	0.924547i	$-0.624444\pi$
$23$	1.09863	−	0.634293i	0.229080	−	0.132259i	0.610148	+	0.792288i	$0.291110\pi$
$24$		0			0
$25$	3.29157	−	5.70117i	0.658315	−	1.14023i
$26$		0			0
$27$	2.04350	+	4.77746i	0.393272	+	0.919422i
$28$		0			0
$29$	−3.04081	−	5.26683i	−0.564664	−	0.978026i	−0.997081	−	0.0763526i	$-0.975673\pi$
$29$	−3.04081	−	5.26683i	−0.564664	−	0.978026i	0.432417	−	0.901674i	$-0.357661\pi$
$30$		0			0
$31$	−7.32136			−1.31496			−0.657478	−	0.753474i	$-0.728377\pi$
$31$	−7.32136			−1.31496			−0.657478	+	0.753474i	$0.728377\pi$
$32$		0			0
$33$	5.83689	+	7.54677i	1.01607	+	1.31372i
$34$		0			0
$35$	−0.720307	−	8.97570i	−0.121754	−	1.51717i
$36$		0			0
$37$	−0.928112	+	1.60754i	−0.152581	+	0.264278i	−0.932175	−	0.362007i	$-0.882092\pi$
$37$	−0.928112	+	1.60754i	−0.152581	+	0.264278i	0.779595	+	0.626284i	$0.215425\pi$
$38$		0			0
$39$	−2.40693	−	3.11203i	−0.385418	−	0.498323i
$40$		0			0
$41$	−4.99026	−	2.88113i	−0.779347	−	0.449956i	0.0568517	−	0.998383i	$-0.481894\pi$
$41$	−4.99026	−	2.88113i	−0.779347	−	0.449956i	−0.836199	+	0.548426i	$0.815227\pi$
$42$		0			0
$43$	6.68015	−	3.85679i	1.01871	−	0.588155i	0.104983	−	0.994474i	$-0.466521\pi$
$43$	6.68015	−	3.85679i	1.01871	−	0.588155i	0.913731	+	0.406319i	$0.133188\pi$
$44$		0			0
$45$	9.88225	+	2.56698i	1.47316	+	0.382663i
$46$		0			0
$47$	1.64594			0.240085			0.120042	−	0.992769i	$-0.461697\pi$
$47$	1.64594			0.240085			0.120042	+	0.992769i	$0.461697\pi$
$48$		0			0
$49$	−4.42197	−	5.42643i	−0.631710	−	0.775205i
$50$		0			0
$51$	−13.1782	+	1.78632i	−1.84532	+	0.250134i
$52$		0			0
$53$	−2.90265	−	5.02754i	−0.398710	−	0.690585i	0.594857	−	0.803831i	$-0.297209\pi$
$53$	−2.90265	−	5.02754i	−0.398710	−	0.690585i	−0.993567	+	0.113246i	$0.963875\pi$
$54$		0			0
$55$	18.7469			2.52783
$56$		0			0
$57$	−2.33127	+	1.80307i	−0.308784	+	0.238822i
$58$		0			0
$59$	6.97610			0.908211			0.454105	−	0.890948i	$-0.349959\pi$
$59$	6.97610			0.908211			0.454105	+	0.890948i	$0.349959\pi$
$60$		0			0
$61$			11.1375i			1.42602i	0.701155	+	0.713009i	$0.252668\pi$
$61$			11.1375i			1.42602i	−0.701155	+	0.713009i	$0.747332\pi$
$62$		0			0
$63$	7.45730	−	2.71822i	0.939531	−	0.342463i
$64$		0			0
$65$	−7.73055			−0.958857
$66$		0			0
$67$			8.24153i			1.00686i	0.864035	+	0.503431i	$0.167929\pi$
$67$			8.24153i			1.00686i	−0.864035	+	0.503431i	$0.832071\pi$
$68$		0			0
$69$	2.17734	−	0.295140i	0.262121	−	0.0355307i
$70$		0			0
$71$			5.47245i			0.649460i	0.945807	+	0.324730i	$0.105273\pi$
$71$			5.47245i			0.649460i	−0.945807	+	0.324730i	$0.894727\pi$
$72$		0			0
$73$	−12.5641	+	7.25388i	−1.47052	+	0.849002i	−0.999452	−	0.0330971i	$-0.989463\pi$
$73$	−12.5641	+	7.25388i	−1.47052	+	0.849002i	−0.471063	+	0.882099i	$0.656130\pi$
$74$		0			0
$75$	9.01944	−	6.97590i	1.04148	−	0.805508i
$76$		0			0
$77$	11.9977	−	8.27301i	1.36726	−	0.942796i
$78$		0			0
$79$		−	3.42392i		−	0.385221i	−0.981275	−	0.192610i	$-0.938305\pi$
$79$		−	3.42392i		−	0.385221i	0.981275	−	0.192610i	$-0.0616954\pi$
$80$		0			0
$81$	0.137857	+	8.99894i	0.0153175	+	0.999883i
$82$		0			0
$83$	−5.67528	−	9.82987i	−0.622942	−	1.07897i	−0.988935	−	0.148350i	$-0.952604\pi$
$83$	−5.67528	−	9.82987i	−0.622942	−	1.07897i	0.365992	−	0.930618i	$-0.380730\pi$
$84$		0			0
$85$	−13.0657	+	22.6305i	−1.41718	+	2.45462i
$86$		0			0
$87$	−1.41490	−	10.4382i	−0.151694	−	1.11909i
$88$		0			0
$89$	4.67278	+	2.69783i	0.495314	+	0.285970i	0.726776	−	0.686874i	$-0.241018\pi$
$89$	4.67278	+	2.69783i	0.495314	+	0.285970i	−0.231462	+	0.972844i	$0.574351\pi$
$90$		0			0
$91$	−4.94743	+	3.41150i	−0.518632	+	0.357622i
$92$		0			0
$93$	−11.7342	−	4.80790i	−1.21678	−	0.498556i
$94$		0			0
$95$			5.79107i			0.594152i
$96$		0			0
$97$	0.903873	−	0.521851i	0.0917744	−	0.0529860i	−0.453410	−	0.891302i	$-0.649793\pi$
$97$	0.903873	−	0.521851i	0.0917744	−	0.0529860i	0.545185	+	0.838316i	$0.316459\pi$
$98$		0			0
$99$	4.39906	+	15.9285i	0.442122	+	1.60088i
$100$		0			0
$101$	3.00424	+	1.73450i	0.298933	+	0.172589i	0.641964	−	0.766735i	$-0.278120\pi$
$101$	3.00424	+	1.73450i	0.298933	+	0.172589i	−0.343030	+	0.939324i	$0.611453\pi$
$102$		0			0
$103$	6.03820	+	10.4585i	0.594961	+	1.03050i	0.993552	+	0.113374i	$0.0361660\pi$
$103$	6.03820	+	10.4585i	0.594961	+	1.03050i	−0.398591	+	0.917129i	$0.630501\pi$
$104$		0			0
$105$	4.73983	−	14.8587i	0.462560	−	1.45006i
$106$		0			0
$107$	−1.36559	−	0.788422i	−0.132016	−	0.0762196i	0.432537	−	0.901616i	$-0.357618\pi$
$107$	−1.36559	−	0.788422i	−0.132016	−	0.0762196i	−0.564554	+	0.825396i	$0.690952\pi$
$108$		0			0
$109$	−2.76649	−	4.79171i	−0.264982	−	0.458962i	0.702577	−	0.711608i	$-0.252033\pi$
$109$	−2.76649	−	4.79171i	−0.264982	−	0.458962i	−0.967559	+	0.252645i	$0.918699\pi$
$110$		0			0
$111$	−2.54318	+	1.96697i	−0.241388	+	0.186696i
$112$		0			0
$113$	5.31271	−	9.20188i	0.499778	−	0.865640i	−0.500222	−	0.865897i	$-0.666748\pi$
$113$	5.31271	−	9.20188i	0.499778	−	0.865640i	1.00000		0.000256749i	$8.17257e-5\pi$
$114$		0			0
$115$	2.15876	−	3.73907i	0.201305	−	0.348671i
$116$		0			0
$117$	−1.81402	−	6.56836i	−0.167706	−	0.607246i
$118$		0			0
$119$	1.62501	+	20.2491i	0.148964	+	1.85623i
$120$		0			0
$121$	9.67051	+	16.7498i	0.879137	+	1.52271i
$122$		0			0
$123$	−6.10603	−	7.89475i	−0.550562	−	0.711846i
$124$		0			0
$125$		−	5.38810i		−	0.481926i
$126$		0			0
$127$		−	7.63759i		−	0.677726i	−0.940836	−	0.338863i	$-0.889958\pi$
$127$		−	7.63759i		−	0.677726i	0.940836	−	0.338863i	$-0.110042\pi$
$128$		0			0
$129$	13.2392	−	1.79458i	1.16565	−	0.158004i
$130$		0			0
$131$	5.16583	+	8.94749i	0.451341	+	0.781746i	0.998470	−	0.0553030i	$-0.0176125\pi$
$131$	5.16583	+	8.94749i	0.451341	+	0.781746i	−0.547129	+	0.837049i	$0.684279\pi$
$132$		0			0
$133$	2.55561	+	3.70619i	0.221599	+	0.321368i
$134$		0			0
$135$	14.1529	+	10.6038i	1.21809	+	0.912631i
$136$		0			0
$137$	6.58763	−	11.4101i	0.562819	−	0.974831i	−0.434430	−	0.900706i	$-0.643050\pi$
$137$	6.58763	−	11.4101i	0.562819	−	0.974831i	0.997249	−	0.0741257i	$-0.0236166\pi$
$138$		0			0
$139$	0.992238	−	1.71861i	0.0841605	−	0.145770i	−0.820873	−	0.571111i	$-0.806512\pi$
$139$	0.992238	−	1.71861i	0.0841605	−	0.145770i	0.905033	+	0.425341i	$0.139846\pi$
$140$		0			0
$141$	2.63800	+	1.08088i	0.222160	+	0.0910263i
$142$		0			0
$143$	−6.25579	−	10.8353i	−0.523136	−	0.906097i
$144$		0			0
$145$	−17.9252	−	10.3491i	−1.48860	−	0.859445i
$146$		0			0
$147$	−3.52373	−	11.6010i	−0.290632	−	0.956835i
$148$		0			0
$149$	−5.70660	−	9.88411i	−0.467503	−	0.809738i	0.531808	−	0.846865i	$-0.321513\pi$
$149$	−5.70660	−	9.88411i	−0.467503	−	0.809738i	−0.999311	+	0.0371268i	$0.988179\pi$
$150$		0			0
$151$	−1.63122	−	0.941783i	−0.132746	−	0.0766412i	0.432156	−	0.901799i	$-0.357753\pi$
$151$	−1.63122	−	0.941783i	−0.132746	−	0.0766412i	−0.564903	+	0.825158i	$0.691086\pi$
$152$		0			0
$153$	−22.2943	−	5.79109i	−1.80238	−	0.468182i
$154$		0			0
$155$	−21.5792	+	12.4588i	−1.73328	+	1.00071i
$156$		0			0
$157$			11.4704i			0.915438i	0.889097	+	0.457719i	$0.151333\pi$
$157$			11.4704i			0.915438i	−0.889097	+	0.457719i	$0.848667\pi$
$158$		0			0
$159$	−1.35062	−	9.96395i	−0.107111	−	0.790193i
$160$		0			0
$161$	−0.268488	−	3.34561i	−0.0211598	−	0.263671i
$162$		0			0
$163$	−16.5492	−	9.55468i	−1.29623	−	0.748380i	−0.316481	−	0.948599i	$-0.602501\pi$
$163$	−16.5492	−	9.55468i	−1.29623	−	0.748380i	−0.979751	+	0.200219i	$0.935835\pi$
$164$		0			0
$165$	30.0462	+	12.3110i	2.33909	+	0.958406i
$166$		0			0
$167$	12.4065	−	21.4886i	0.960041	−	1.66284i	0.237654	−	0.971350i	$-0.423622\pi$
$167$	12.4065	−	21.4886i	0.960041	−	1.66284i	0.722387	−	0.691489i	$-0.243045\pi$
$168$		0			0
$169$	−3.92033	−	6.79021i	−0.301564	−	0.522324i
$170$		0			0
$171$	−4.92046	+	1.35891i	−0.376277	+	0.103918i
$172$		0			0
$173$		−	16.4190i		−	1.24831i	−0.781301	−	0.624155i	$-0.785443\pi$
$173$		−	16.4190i		−	1.24831i	0.781301	−	0.624155i	$-0.214557\pi$
$174$		0			0
$175$	−9.88740	−	14.3389i	−0.747417	−	1.08392i
$176$		0			0
$177$	11.1808	+	4.58116i	0.840402	+	0.344341i
$178$		0			0
$179$	−9.16446	+	5.29111i	−0.684984	+	0.395476i	−0.801730	−	0.597686i	$-0.796087\pi$
$179$	−9.16446	+	5.29111i	−0.684984	+	0.395476i	0.116746	+	0.993162i	$0.462754\pi$
$180$		0			0
$181$		−	3.03044i		−	0.225251i	−0.993638	−	0.112625i	$-0.964074\pi$
$181$		−	3.03044i		−	0.225251i	0.993638	−	0.112625i	$-0.0359260\pi$
$182$		0			0
$183$	−7.31397	+	17.8505i	−0.540664	+	1.31955i
$184$		0			0
$185$			6.31748i			0.464470i
$186$		0			0
$187$	−42.2927			−3.09275
$188$		0			0
$189$	13.7371	+	0.540585i	0.999227	+	0.0393218i
$190$		0			0
$191$		−	1.47781i		−	0.106931i	−0.998570	−	0.0534653i	$-0.982973\pi$
$191$		−	1.47781i		−	0.106931i	0.998570	−	0.0534653i	$-0.0170266\pi$
$192$		0			0
$193$	21.2569			1.53011			0.765053	−	0.643967i	$-0.222713\pi$
$193$	21.2569			1.53011			0.765053	+	0.643967i	$0.222713\pi$
$194$		0			0
$195$	−12.3900	−	5.07661i	−0.887267	−	0.363544i
$196$		0			0
$197$	5.96607			0.425065			0.212533	−	0.977154i	$-0.431829\pi$
$197$	5.96607			0.425065			0.212533	+	0.977154i	$0.431829\pi$
$198$		0			0
$199$	12.2688	+	21.2502i	0.869712	+	1.50638i	0.862292	+	0.506412i	$0.169029\pi$
$199$	12.2688	+	21.2502i	0.869712	+	1.50638i	0.00741998	+	0.999972i	$0.497638\pi$
$200$		0			0
$201$	−5.41216	+	13.2090i	−0.381745	+	0.931689i
$202$		0			0
$203$	−16.0389	+	1.28713i	−1.12571	+	0.0903390i
$204$		0			0
$205$	−19.6113			−1.36971
$206$		0			0
$207$	3.68352	+	0.956819i	0.256022	+	0.0665035i
$208$		0			0
$209$	−8.11692	+	4.68631i	−0.561459	+	0.324159i
$210$		0			0
$211$	−9.75069	−	5.62956i	−0.671265	−	0.387555i	0.125291	−	0.992120i	$-0.460014\pi$
$211$	−9.75069	−	5.62956i	−0.671265	−	0.387555i	−0.796556	+	0.604565i	$0.793347\pi$
$212$		0			0
$213$	−3.59373	+	8.77087i	−0.246238	+	0.600970i
$214$		0			0
$215$	13.1262	−	22.7353i	0.895200	−	1.55053i
$216$		0			0
$217$	−8.31229	+	17.4963i	−0.564275	+	1.18773i
$218$		0			0
$219$	−24.9005	+	3.37527i	−1.68262	+	0.228079i
$220$		0			0
$221$	17.4400			1.17314
$222$		0			0
$223$	6.53871	+	11.3254i	0.437864	+	0.758403i	0.997525	−	0.0703189i	$-0.0224017\pi$
$223$	6.53871	+	11.3254i	0.437864	+	0.758403i	−0.559660	+	0.828722i	$0.689068\pi$
$224$		0			0
$225$	19.0368	−	5.25749i	1.26912	−	0.350499i
$226$		0			0
$227$	−3.86182	+	6.68888i	−0.256318	+	0.443956i	−0.965253	−	0.261318i	$-0.915843\pi$
$227$	−3.86182	+	6.68888i	−0.256318	+	0.443956i	0.708934	+	0.705274i	$0.249176\pi$
$228$		0			0
$229$	−14.0608	+	8.11803i	−0.929167	+	0.536455i	−0.886548	−	0.462637i	$-0.846903\pi$
$229$	−14.0608	+	8.11803i	−0.929167	+	0.536455i	−0.0426190	+	0.999091i	$0.513570\pi$
$230$		0			0
$231$	24.6619	−	5.38060i	1.62264	−	0.354018i
$232$		0			0
$233$	0.449450	−	0.778470i	0.0294444	−	0.0509993i	−0.850928	−	0.525283i	$-0.823960\pi$
$233$	0.449450	−	0.778470i	0.0294444	−	0.0509993i	0.880372	+	0.474284i	$0.157293\pi$
$234$		0			0
$235$	4.85129	−	2.80089i	0.316463	−	0.182710i
$236$		0			0
$237$	2.24847	−	5.48763i	0.146054	−	0.356460i
$238$		0			0
$239$	5.32245	+	3.07292i	0.344280	+	0.198770i	0.662163	−	0.749360i	$-0.269639\pi$
$239$	5.32245	+	3.07292i	0.344280	+	0.198770i	−0.317883	+	0.948130i	$0.602972\pi$
$240$		0			0
$241$	23.2138	+	13.4025i	1.49533	+	0.863330i	0.999986	−	0.00536600i	$-0.00170806\pi$
$241$	23.2138	+	13.4025i	1.49533	+	0.863330i	0.495346	+	0.868696i	$0.335041\pi$
$242$		0			0
$243$	−5.68861	+	14.5134i	−0.364924	+	0.931037i
$244$		0			0
$245$	−22.2676	−	8.46918i	−1.42263	−	0.541076i
$246$		0			0
$247$	3.34714	−	1.93247i	0.212973	−	0.122960i
$248$		0			0
$249$	−2.64073	−	19.4816i	−0.167350	−	1.23459i
$250$		0			0
$251$	−16.8838			−1.06570			−0.532849	−	0.846210i	$-0.678879\pi$
$251$	−16.8838			−1.06570			−0.532849	+	0.846210i	$0.678879\pi$
$252$		0			0
$253$	6.98772			0.439314
$254$		0			0
$255$	−35.8022	+	27.6905i	−2.24202	+	1.73404i
$256$		0			0
$257$	−11.8562	+	6.84519i	−0.739571	+	0.426991i	−0.821913	−	0.569613i	$-0.807093\pi$
$257$	−11.8562	+	6.84519i	−0.739571	+	0.426991i	0.0823425	+	0.996604i	$0.473760\pi$
$258$		0			0
$259$	2.78791	+	4.04309i	0.173232	+	0.251225i
$260$		0			0
$261$	4.58700	−	17.6588i	0.283928	−	1.09305i
$262$		0			0
$263$	−11.6356	−	6.71780i	−0.717480	−	0.414237i	0.0963442	−	0.995348i	$-0.469285\pi$
$263$	−11.6356	−	6.71780i	−0.717480	−	0.414237i	−0.813825	+	0.581111i	$0.802618\pi$
$264$		0			0
$265$	−17.1107	−	9.87889i	−1.05110	−	0.606855i
$266$		0			0
$267$	5.71757	+	7.39249i	0.349910	+	0.452413i
$268$		0			0
$269$	−7.38133	+	4.26161i	−0.450047	+	0.259835i	−0.707850	−	0.706363i	$-0.750335\pi$
$269$	−7.38133	+	4.26161i	−0.450047	+	0.259835i	0.257803	+	0.966198i	$0.417002\pi$
$270$		0			0
$271$	−14.9978	+	25.9769i	−0.911049	+	1.57798i	−0.0984646	+	0.995141i	$0.531393\pi$
$271$	−14.9978	+	25.9769i	−0.911049	+	1.57798i	−0.812585	+	0.582843i	$0.801940\pi$
$272$		0			0
$273$	−10.1697	+	2.21877i	−0.615500	+	0.134286i
$274$		0			0
$275$	31.4036	−	18.1309i	1.89371	−	1.09333i
$276$		0			0
$277$	−5.51925	+	9.55962i	−0.331619	+	0.574382i	−0.982830	−	0.184516i	$-0.940928\pi$
$277$	−5.51925	+	9.55962i	−0.331619	+	0.574382i	0.651210	+	0.758897i	$0.274262\pi$
$278$		0			0
$279$	−15.6494	−	15.4115i	−0.936908	−	0.922665i
$280$		0			0
$281$	−8.73153	−	15.1235i	−0.520880	−	0.902190i	−0.999705	−	0.0242800i	$-0.992271\pi$
$281$	−8.73153	−	15.1235i	−0.520880	−	0.902190i	0.478826	−	0.877910i	$-0.341063\pi$
$282$		0			0
$283$	7.38373			0.438917			0.219459	−	0.975622i	$-0.429571\pi$
$283$	7.38373			0.438917			0.219459	+	0.975622i	$0.429571\pi$
$284$		0			0
$285$	−3.80296	+	9.28154i	−0.225268	+	0.549791i
$286$		0			0
$287$	−12.5509	+	8.65447i	−0.740856	+	0.510857i
$288$		0			0
$289$	20.9761	−	36.3317i	1.23389	−	2.13716i
$290$		0			0
$291$	1.79136	−	0.242820i	0.105012	−	0.0142344i
$292$		0			0
$293$	−10.2448	−	5.91482i	−0.598506	−	0.345547i	0.169948	−	0.985453i	$-0.445640\pi$
$293$	−10.2448	−	5.91482i	−0.598506	−	0.345547i	−0.768454	+	0.639906i	$0.778973\pi$
$294$		0			0
$295$	20.5616	−	11.8712i	1.19714	−	0.691170i
$296$		0			0
$297$	−3.40965	+	28.4180i	−0.197848	+	1.64898i
$298$		0			0
$299$	−2.88149			−0.166641
$300$		0			0
$301$	−1.63253	−	20.3428i	−0.0940973	−	1.17254i
$302$		0			0
$303$	3.67596	+	4.75281i	0.211179	+	0.273042i
$304$		0			0
$305$	18.9528	+	32.8272i	1.08523	+	1.87968i
$306$		0			0
$307$	8.04614			0.459217			0.229609	−	0.973283i	$-0.426255\pi$
$307$	8.04614			0.459217			0.229609	+	0.973283i	$0.426255\pi$
$308$		0			0
$309$	2.80960	+	20.7274i	0.159833	+	1.17914i
$310$		0			0
$311$	22.1900			1.25828			0.629140	−	0.777292i	$-0.283407\pi$
$311$	22.1900			1.25828			0.629140	+	0.777292i	$0.283407\pi$
$312$		0			0
$313$		−	4.22000i		−	0.238529i	−0.992863	−	0.119264i	$-0.961946\pi$
$313$		−	4.22000i		−	0.238529i	0.992863	−	0.119264i	$-0.0380536\pi$
$314$		0			0
$315$	17.3543	−	20.7019i	0.977803	−	1.16642i
$316$		0			0
$317$	6.83165			0.383704			0.191852	−	0.981424i	$-0.438551\pi$
$317$	6.83165			0.383704			0.191852	+	0.981424i	$0.438551\pi$
$318$		0			0
$319$		−	33.4992i		−	1.87559i
$320$		0			0
$321$	−1.67092	−	2.16040i	−0.0932616	−	0.120582i
$322$		0			0
$323$		−	13.0646i		−	0.726934i
$324$		0			0
$325$	−12.9498	+	7.47654i	−0.718323	+	0.414724i
$326$		0			0
$327$	−1.28726	−	9.49657i	−0.0711858	−	0.525162i
$328$		0			0
$329$	1.86871	−	3.93341i	0.103025	−	0.216856i
$330$		0			0
$331$			22.0862i			1.21397i	0.794714	+	0.606984i	$0.207621\pi$
$331$			22.0862i			1.21397i	−0.794714	+	0.606984i	$0.792379\pi$
$332$		0			0
$333$	−5.36773	+	1.48243i	−0.294150	+	0.0812369i
$334$		0			0
$335$	14.0246	+	24.2914i	0.766247	+	1.32718i
$336$		0			0
$337$	5.15154	−	8.92273i	0.280622	−	0.486052i	−0.690916	−	0.722935i	$-0.742792\pi$
$337$	5.15154	−	8.92273i	0.280622	−	0.486052i	0.971538	+	0.236883i	$0.0761258\pi$
$338$		0			0
$339$	14.5577	−	11.2593i	0.790664	−	0.611523i
$340$		0			0
$341$	−34.9251	−	20.1640i	−1.89130	−	1.09194i
$342$		0			0
$343$	−17.9884	+	4.40659i	−0.971281	+	0.237933i
$344$		0			0
$345$	5.91534	−	4.57510i	0.318471	−	0.246315i
$346$		0			0
$347$			32.6663i			1.75362i	0.480837	+	0.876810i	$0.340333\pi$
$347$			32.6663i			1.75362i	−0.480837	+	0.876810i	$0.659667\pi$
$348$		0			0
$349$	−15.7425	+	9.08892i	−0.842675	+	0.486519i	−0.858173	−	0.513361i	$-0.828400\pi$
$349$	−15.7425	+	9.08892i	−0.842675	+	0.486519i	0.0154978	+	0.999880i	$0.495067\pi$
$350$		0			0
$351$	1.40602	−	11.7186i	0.0750478	−	0.625492i
$352$		0			0
$353$	−2.54798	−	1.47108i	−0.135615	−	0.0782976i	0.430657	−	0.902516i	$-0.358282\pi$
$353$	−2.54798	−	1.47108i	−0.135615	−	0.0782976i	−0.566273	+	0.824218i	$0.691615\pi$
$354$		0			0
$355$	9.31247	+	16.1297i	0.494255	+	0.856074i
$356$		0			0
$357$	−10.6930	+	33.5210i	−0.565934	+	1.77412i
$358$		0			0
$359$	4.61275	+	2.66317i	0.243452	+	0.140557i	0.616762	−	0.787150i	$-0.288444\pi$
$359$	4.61275	+	2.66317i	0.243452	+	0.140557i	−0.373310	+	0.927706i	$0.621777\pi$
$360$		0			0
$361$	8.05236	+	13.9471i	0.423808	+	0.734057i
$362$		0			0
$363$	4.49974	+	33.1961i	0.236175	+	1.74234i
$364$		0			0
$365$	−24.6879	+	42.7607i	−1.29222	+	2.23819i
$366$		0			0
$367$	2.22470	−	3.85329i	0.116128	−	0.201140i	−0.802102	−	0.597187i	$-0.796285\pi$
$367$	2.22470	−	3.85329i	0.116128	−	0.201140i	0.918230	+	0.396047i	$0.129618\pi$
$368$		0			0
$369$	−4.60190	−	16.6630i	−0.239565	−	0.867439i
$370$		0			0
$371$	−15.3102	+	1.22865i	−0.794864	+	0.0637885i
$372$		0			0
$373$	−12.6261	−	21.8690i	−0.653753	−	1.13233i	−0.982205	−	0.187812i	$-0.939860\pi$
$373$	−12.6261	−	21.8690i	−0.653753	−	1.13233i	0.328452	−	0.944521i	$-0.393473\pi$
$374$		0			0
$375$	3.53833	−	8.63568i	0.182719	−	0.445945i
$376$		0			0
$377$			13.8139i			0.711452i
$378$		0			0
$379$		−	28.8437i		−	1.48160i	−0.671725	−	0.740801i	$-0.734446\pi$
$379$		−	28.8437i		−	1.48160i	0.671725	−	0.740801i	$-0.265554\pi$
$380$		0			0
$381$	5.01556	−	12.2410i	0.256955	−	0.627126i
$382$		0			0
$383$	−16.8717	−	29.2226i	−0.862101	−	1.49320i	−0.869897	−	0.493234i	$-0.835815\pi$
$383$	−16.8717	−	29.2226i	−0.862101	−	1.49320i	0.00779544	−	0.999970i	$-0.497519\pi$
$384$		0			0
$385$	21.2842	−	44.8006i	1.08474	−	2.28325i
$386$		0			0
$387$	22.3974	+	5.81789i	1.13853	+	0.295740i
$388$		0			0
$389$	2.18919	−	3.79179i	0.110996	−	0.192251i	−0.805176	−	0.593036i	$-0.797929\pi$
$389$	2.18919	−	3.79179i	0.110996	−	0.192251i	0.916172	+	0.400785i	$0.131262\pi$
$390$		0			0
$391$	−4.87013	+	8.43531i	−0.246293	+	0.426592i
$392$		0			0
$393$	2.40369	+	17.7328i	0.121250	+	0.894502i
$394$		0			0
$395$	−5.82649	−	10.0918i	−0.293162	−	0.507772i
$396$		0			0
$397$	15.1468	+	8.74501i	0.760196	+	0.438900i	0.829366	−	0.558705i	$-0.188702\pi$
$397$	15.1468	+	8.74501i	0.760196	+	0.438900i	−0.0691699	+	0.997605i	$0.522035\pi$
$398$		0			0
$399$	1.66212	+	7.61829i	0.0832099	+	0.381392i
$400$		0			0
$401$	−2.42582	−	4.20164i	−0.121140	−	0.209820i	0.799078	−	0.601228i	$-0.205322\pi$
$401$	−2.42582	−	4.20164i	−0.121140	−	0.209820i	−0.920217	+	0.391408i	$0.871988\pi$
$402$		0			0
$403$	14.4019	+	8.31494i	0.717409	+	0.414197i
$404$		0			0
$405$	15.7198	+	26.2892i	0.781125	+	1.30632i
$406$		0			0
$407$	−8.85475	+	5.11229i	−0.438914	+	0.253407i
$408$		0			0
$409$			2.08009i			0.102854i	0.998677	+	0.0514268i	$0.0163769\pi$
$409$			2.08009i			0.102854i	−0.998677	+	0.0514268i	$0.983623\pi$
$410$		0			0
$411$	18.0512	−	13.9613i	0.890398	−	0.688660i
$412$		0			0
$413$	7.92030	−	16.6712i	0.389732	−	0.820339i
$414$		0			0
$415$	−33.4550	−	19.3152i	−1.64224	−	0.948148i
$416$		0			0
$417$	2.71889	−	2.10287i	0.133145	−	0.102978i
$418$		0			0
$419$	−6.04498	+	10.4702i	−0.295317	+	0.511504i	−0.975059	−	0.221948i	$-0.928759\pi$
$419$	−6.04498	+	10.4702i	−0.295317	+	0.511504i	0.679742	+	0.733452i	$0.262092\pi$
$420$		0			0
$421$	−7.48772	−	12.9691i	−0.364929	−	0.632076i	0.623836	−	0.781555i	$-0.285573\pi$
$421$	−7.48772	−	12.9691i	−0.364929	−	0.632076i	−0.988765	+	0.149480i	$0.952240\pi$
$422$		0			0
$423$	3.51820	+	3.46472i	0.171061	+	0.168460i
$424$		0			0
$425$			50.5457i			2.45183i
$426$		0			0
$427$	26.6161	+	12.6450i	1.28805	+	0.611934i
$428$		0			0
$429$	−2.91085	−	21.4743i	−0.140537	−	1.03679i
$430$		0			0
$431$	−11.8113	+	6.81925i	−0.568929	+	0.328472i	−0.756722	−	0.653737i	$-0.773200\pi$
$431$	−11.8113	+	6.81925i	−0.568929	+	0.328472i	0.187792	+	0.982209i	$0.439867\pi$
$432$		0			0
$433$		−	0.892648i		−	0.0428979i	−0.999770	−	0.0214490i	$-0.993172\pi$
$433$		−	0.892648i		−	0.0428979i	0.999770	−	0.0214490i	$-0.00682794\pi$
$434$		0			0
$435$	−21.9330	−	28.3582i	−1.05161	−	1.35967i
$436$		0			0
$437$			2.15857i			0.103258i
$438$		0			0
$439$	−4.66182			−0.222497			−0.111248	−	0.993793i	$-0.535485\pi$
$439$	−4.66182			−0.222497			−0.111248	+	0.993793i	$0.535485\pi$
$440$		0			0
$441$	1.97072	−	20.9073i	0.0938436	−	0.995587i
$442$		0			0
$443$			25.3912i			1.20637i	0.797600	+	0.603187i	$0.206103\pi$
$443$			25.3912i			1.20637i	−0.797600	+	0.603187i	$0.793897\pi$
$444$		0			0
$445$	18.3636			0.870519
$446$		0			0
$447$	−2.65531	−	19.5891i	−0.125592	−	0.926532i
$448$		0			0
$449$	15.1155			0.713347			0.356673	−	0.934229i	$-0.383911\pi$
$449$	15.1155			0.713347			0.356673	+	0.934229i	$0.383911\pi$
$450$		0			0
$451$	−15.8700	−	27.4877i	−0.747290	−	1.29434i
$452$		0			0
$453$	−1.99594	−	2.58064i	−0.0937774	−	0.121249i
$454$		0			0
$455$	−8.77687	+	18.4742i	−0.411466	+	0.866085i
$456$		0			0
$457$	−3.72227			−0.174121			−0.0870603	−	0.996203i	$-0.527747\pi$
$457$	−3.72227			−0.174121			−0.0870603	+	0.996203i	$0.527747\pi$
$458$		0			0
$459$	−31.9288	−	23.9221i	−1.49031	−	1.11659i
$460$		0			0
$461$	11.5574	−	6.67267i	0.538282	−	0.310777i	−0.206101	−	0.978531i	$-0.566077\pi$
$461$	11.5574	−	6.67267i	0.538282	−	0.310777i	0.744382	+	0.667754i	$0.232744\pi$
$462$		0			0
$463$	11.0980	+	6.40741i	0.515766	+	0.297777i	0.735200	−	0.677850i	$-0.237088\pi$
$463$	11.0980	+	6.40741i	0.515766	+	0.297777i	−0.219435	+	0.975627i	$0.570421\pi$
$464$		0			0
$465$	−42.7673	+	5.79713i	−1.98329	+	0.268835i
$466$		0			0
$467$	12.0842	−	20.9304i	0.559189	−	0.968544i	−0.438375	−	0.898792i	$-0.644446\pi$
$467$	12.0842	−	20.9304i	0.559189	−	0.968544i	0.997564	−	0.0697517i	$-0.0222207\pi$
$468$		0			0
$469$	19.6953	+	9.35700i	0.909446	+	0.432066i
$470$		0			0
$471$	−7.53255	+	18.3840i	−0.347082	+	0.847090i
$472$		0			0
$473$	42.4885			1.95362
$474$		0			0
$475$	5.60079	+	9.70086i	0.256982	+	0.445106i
$476$		0			0
$477$	4.37859	−	16.8565i	0.200482	−	0.771806i
$478$		0			0
$479$	−1.75951	+	3.04757i	−0.0803942	+	0.139247i	−0.903419	−	0.428758i	$-0.858951\pi$
$479$	−1.75951	+	3.04757i	−0.0803942	+	0.139247i	0.823025	+	0.568005i	$0.192285\pi$
$480$		0			0
$481$	3.65139	−	2.10813i	0.166489	−	0.0961225i
$482$		0			0
$483$	1.76673	−	5.53843i	0.0803889	−	0.252007i
$484$		0			0
$485$	1.77607	−	3.07624i	0.0806472	−	0.139685i
$486$		0			0
$487$	32.8616	−	18.9726i	1.48910	−	0.859732i	0.489177	−	0.872185i	$-0.337297\pi$
$487$	32.8616	−	18.9726i	1.48910	−	0.859732i	0.999922	+	0.0124530i	$0.00396402\pi$
$488$		0			0
$489$	−20.2494	−	26.1814i	−0.915711	−	1.18396i
$490$		0			0
$491$	17.2645	+	9.96766i	0.779136	+	0.449834i	0.836124	−	0.548540i	$-0.184816\pi$
$491$	17.2645	+	9.96766i	0.779136	+	0.449834i	−0.0569880	+	0.998375i	$0.518150\pi$
$492$		0			0
$493$	40.4389	+	23.3474i	1.82128	+	1.05152i
$494$		0			0
$495$	40.0715	+	39.4623i	1.80108	+	1.77370i
$496$		0			0
$497$	13.0779	+	6.21313i	0.586623	+	0.278697i
$498$		0			0
$499$	30.4839	−	17.5999i	1.36464	−	0.787878i	0.374407	−	0.927265i	$-0.377846\pi$
$499$	30.4839	−	17.5999i	1.36464	−	0.787878i	0.990238	+	0.139387i	$0.0445131\pi$
$500$		0			0
$501$	33.9957	−	26.2933i	1.51882	−	1.17470i
$502$		0			0
$503$	−17.8170			−0.794419			−0.397209	−	0.917728i	$-0.630021\pi$
$503$	−17.8170			−0.794419			−0.397209	+	0.917728i	$0.630021\pi$
$504$		0			0
$505$	11.8064			0.525378
$506$		0			0
$507$	−1.82415	−	13.4573i	−0.0810133	−	0.597662i
$508$		0			0
$509$	13.5600	−	7.82889i	0.601038	−	0.347009i	−0.168412	−	0.985717i	$-0.553864\pi$
$509$	13.5600	−	7.82889i	0.601038	−	0.347009i	0.769450	+	0.638707i	$0.220531\pi$
$510$		0			0
$511$	3.07047	+	38.2609i	0.135830	+	1.69256i
$512$		0			0
$513$	−8.77857	−	1.05327i	−0.387583	−	0.0465030i
$514$		0			0
$515$	35.5944	+	20.5504i	1.56848	+	0.905560i
$516$		0			0
$517$	7.85162	+	4.53313i	0.345314	+	0.199367i
$518$		0			0
$519$	10.7822	−	26.3152i	0.473288	−	1.15511i
$520$		0			0
$521$	18.6160	−	10.7480i	0.815582	−	0.470877i	−0.0333084	−	0.999445i	$-0.510604\pi$
$521$	18.6160	−	10.7480i	0.815582	−	0.470877i	0.848891	+	0.528568i	$0.177271\pi$
$522$		0			0
$523$	6.97015	−	12.0727i	0.304783	−	0.527901i	−0.672430	−	0.740161i	$-0.734749\pi$
$523$	6.97015	−	12.0727i	0.304783	−	0.527901i	0.977213	+	0.212261i	$0.0680826\pi$
$524$		0			0
$525$	−6.43057	−	29.4744i	−0.280653	−	1.28637i
$526$		0			0
$527$	48.6825	−	28.1068i	2.12064	−	1.22435i
$528$		0			0
$529$	−10.6953	+	18.5249i	−0.465015	+	0.805430i
$530$		0			0
$531$	14.9114	+	14.6848i	0.647102	+	0.637265i
$532$		0			0
$533$	6.54424	+	11.3350i	0.283463	+	0.490972i
$534$		0			0
$535$	−5.36664			−0.232020
$536$		0			0
$537$	−18.1628	+	2.46198i	−0.783784	+	0.106242i
$538$		0			0
$539$	−6.14900	−	38.0644i	−0.264856	−	1.63955i
$540$		0			0
$541$	−20.9294	+	36.2508i	−0.899826	+	1.55854i	−0.0721102	+	0.997397i	$0.522973\pi$
$541$	−20.9294	+	36.2508i	−0.899826	+	1.55854i	−0.827716	+	0.561148i	$0.810360\pi$
$542$		0			0
$543$	1.99007	−	4.85698i	0.0854021	−	0.208433i
$544$		0			0
$545$	−16.3081	−	9.41549i	−0.698563	−	0.403315i
$546$		0			0
$547$	−9.08166	+	5.24330i	−0.388304	+	0.224187i	−0.681425	−	0.731888i	$-0.738639\pi$
$547$	−9.08166	+	5.24330i	−0.388304	+	0.224187i	0.293121	+	0.956075i	$0.405306\pi$
$548$		0			0
$549$	−23.4447	+	23.8066i	−1.00059	+	1.01604i
$550$		0			0
$551$	10.3482			0.440848
$552$		0			0
$553$	−8.18236	−	3.88734i	−0.347950	−	0.165306i
$554$		0			0
$555$	−4.14865	+	10.1252i	−0.176100	+	0.429792i
$556$		0			0
$557$	−10.8727	−	18.8321i	−0.460691	−	0.797941i	0.538304	−	0.842751i	$-0.319065\pi$
$557$	−10.8727	−	18.8321i	−0.460691	−	0.797941i	−0.998996	+	0.0448097i	$0.985732\pi$
$558$		0			0
$559$	−17.5208			−0.741049
$560$		0			0
$561$	−67.7839	−	27.7734i	−2.86184	−	1.17259i
$562$		0			0
$563$	42.2497			1.78061			0.890307	−	0.455361i	$-0.150490\pi$
$563$	42.2497			1.78061			0.890307	+	0.455361i	$0.150490\pi$
$564$		0			0
$565$		−	36.1626i		−	1.52137i
$566$		0			0
$567$	21.6619	+	9.88748i	0.909714	+	0.415235i
$568$		0			0
$569$	27.6412			1.15878			0.579390	−	0.815050i	$-0.303291\pi$
$569$	27.6412			1.15878			0.579390	+	0.815050i	$0.303291\pi$
$570$		0			0
$571$			36.1380i			1.51233i	0.654383	+	0.756164i	$0.272929\pi$
$571$			36.1380i			1.51233i	−0.654383	+	0.756164i	$0.727071\pi$
$572$		0			0
$573$	0.970469	−	2.36853i	0.0405419	−	0.0989469i
$574$		0			0
$575$		−	8.35130i		−	0.348273i
$576$		0			0
$577$	−9.81027	+	5.66396i	−0.408407	+	0.235794i	−0.690105	−	0.723709i	$-0.742436\pi$
$577$	−9.81027	+	5.66396i	−0.408407	+	0.235794i	0.281698	+	0.959503i	$0.409102\pi$
$578$		0			0
$579$	34.0692	+	13.9593i	1.41587	+	0.580129i
$580$		0			0
$581$	−29.9345	+	2.40227i	−1.24189	+	0.0996629i
$582$		0			0
$583$		−	31.9771i		−	1.32436i
$584$		0			0
$585$	−16.5241	−	16.2729i	−0.683187	−	0.672801i
$586$		0			0
$587$	−14.1099	−	24.4391i	−0.582378	−	1.00871i	−0.995197	−	0.0978955i	$-0.968789\pi$
$587$	−14.1099	−	24.4391i	−0.582378	−	1.00871i	0.412818	−	0.910813i	$-0.364544\pi$
$588$		0			0
$589$	6.22884	−	10.7887i	0.256655	−	0.444540i
$590$		0			0
$591$	9.56202	+	3.91789i	0.393329	+	0.161160i
$592$		0			0
$593$	22.0384	+	12.7239i	0.905010	+	0.522508i	0.878822	−	0.477149i	$-0.158330\pi$
$593$	22.0384	+	12.7239i	0.905010	+	0.522508i	0.0261879	+	0.999657i	$0.491663\pi$
$594$		0			0
$595$	39.2475	+	56.9175i	1.60899	+	2.33339i
$596$		0			0
$597$	5.70873	+	42.1152i	0.233643	+	1.72366i
$598$		0			0
$599$		−	5.56315i		−	0.227304i	−0.993521	−	0.113652i	$-0.963745\pi$
$599$		−	5.56315i		−	0.227304i	0.993521	−	0.113652i	$-0.0362549\pi$
$600$		0			0
$601$	−9.11396	+	5.26195i	−0.371766	+	0.214639i	−0.674230	−	0.738522i	$-0.735524\pi$
$601$	−9.11396	+	5.26195i	−0.371766	+	0.214639i	0.302464	+	0.953161i	$0.402191\pi$
$602$		0			0
$603$	−17.3485	+	17.6163i	−0.706486	+	0.717391i
$604$		0			0
$605$	57.0064	+	32.9126i	2.31764	+	1.33809i
$606$		0			0
$607$	−8.07902	−	13.9933i	−0.327917	−	0.567969i	0.654181	−	0.756338i	$-0.273013\pi$
$607$	−8.07902	−	13.9933i	−0.327917	−	0.567969i	−0.982098	+	0.188368i	$0.939680\pi$
$608$		0			0
$609$	−26.5513	−	8.46971i	−1.07591	−	0.343210i
$610$		0			0
$611$	−3.23773	−	1.86931i	−0.130985	−	0.0756241i
$612$		0			0
$613$	−18.1089	−	31.3656i	−0.731413	−	1.26684i	−0.956279	−	0.292455i	$-0.905528\pi$
$613$	−18.1089	−	31.3656i	−0.731413	−	1.26684i	0.224866	−	0.974390i	$-0.427806\pi$
$614$		0			0
$615$	−31.4316	−	12.8786i	−1.26745	−	0.519316i
$616$		0			0
$617$	−10.3991	+	18.0117i	−0.418651	+	0.725125i	−0.995804	−	0.0915111i	$-0.970830\pi$
$617$	−10.3991	+	18.0117i	−0.418651	+	0.725125i	0.577153	+	0.816636i	$0.304164\pi$
$618$		0			0
$619$	4.34530	−	7.52628i	0.174652	−	0.302507i	−0.765389	−	0.643568i	$-0.777453\pi$
$619$	4.34530	−	7.52628i	0.174652	−	0.302507i	0.940041	+	0.341062i	$0.110787\pi$
$620$		0			0
$621$	5.27536	+	3.95247i	0.211693	+	0.158607i
$622$		0			0
$623$	11.7524	−	8.10388i	0.470851	−	0.324675i
$624$		0			0
$625$	7.28894	+	12.6248i	0.291558	+	0.504993i
$626$		0			0
$627$	−16.0867	+	2.18056i	−0.642442	+	0.0870833i
$628$		0			0
$629$		−	14.2522i		−	0.568271i
$630$		0			0
$631$		−	2.24983i		−	0.0895641i	−0.998997	−	0.0447821i	$-0.985741\pi$
$631$		−	2.24983i		−	0.0895641i	0.998997	−	0.0447821i	$-0.0142593\pi$
$632$		0			0
$633$	−11.9309	−	15.4259i	−0.474209	−	0.613125i
$634$		0			0
$635$	−12.9969	−	22.5113i	−0.515766	−	0.893333i
$636$		0			0
$637$	2.53564	+	15.6964i	0.100466	+	0.621916i
$638$		0			0
$639$	−11.5196	+	11.6974i	−0.455707	+	0.462742i
$640$		0			0
$641$	−12.5139	+	21.6746i	−0.494268	+	0.856096i	−0.999978	−	0.00660668i	$-0.997897\pi$
$641$	−12.5139	+	21.6746i	−0.494268	+	0.856096i	0.505711	+	0.862703i	$0.331230\pi$
$642$		0			0
$643$	10.4909	−	18.1708i	0.413721	−	0.716586i	−0.581572	−	0.813495i	$-0.697562\pi$
$643$	10.4909	−	18.1708i	0.413721	−	0.716586i	0.995293	+	0.0969090i	$0.0308956\pi$
$644$		0			0
$645$	35.9679	−	27.8186i	1.41624	−	1.09536i
$646$		0			0
$647$	3.41215	+	5.91002i	0.134146	+	0.232347i	0.925271	−	0.379307i	$-0.123838\pi$
$647$	3.41215	+	5.91002i	0.134146	+	0.232347i	−0.791125	+	0.611654i	$0.790504\pi$
$648$		0			0
$649$	33.2781	+	19.2131i	1.30628	+	0.754181i
$650$		0			0
$651$	−24.8121	+	22.5833i	−0.972464	+	0.885111i
$652$		0			0
$653$	8.17719	+	14.1633i	0.319998	+	0.554253i	0.980487	−	0.196583i	$-0.0629844\pi$
$653$	8.17719	+	14.1633i	0.319998	+	0.554253i	−0.660489	+	0.750836i	$0.729651\pi$
$654$		0			0
$655$	30.4519	+	17.5814i	1.18985	+	0.686963i
$656$		0			0
$657$	−42.1253	−	10.9423i	−1.64346	−	0.426901i
$658$		0			0
$659$	25.5483	−	14.7503i	0.995221	−	0.574591i	0.0883901	−	0.996086i	$-0.471828\pi$
$659$	25.5483	−	14.7503i	0.995221	−	0.574591i	0.906831	+	0.421495i	$0.138494\pi$
$660$		0			0
$661$		−	43.0374i		−	1.67396i	−0.547234	−	0.836980i	$-0.684319\pi$
$661$		−	43.0374i		−	1.67396i	0.547234	−	0.836980i	$-0.315681\pi$
$662$		0			0
$663$	27.9517	+	11.4528i	1.08556	+	0.444789i
$664$		0			0
$665$	13.8393	+	6.57488i	0.536666	+	0.254963i
$666$		0			0
$667$	−6.68143	−	3.85753i	−0.258706	−	0.149364i
$668$		0			0
$669$	3.04249	+	22.4455i	0.117630	+	0.867793i
$670$		0			0
$671$	−30.6743	+	53.1295i	−1.18417	+	2.05104i
$672$		0			0
$673$	−7.69617	−	13.3302i	−0.296665	−	0.513840i	0.678705	−	0.734411i	$-0.262541\pi$
$673$	−7.69617	−	13.3302i	−0.296665	−	0.513840i	−0.975371	+	0.220571i	$0.929208\pi$
$674$		0			0
$675$	33.9635	+	4.07500i	1.30725	+	0.156847i
$676$		0			0
$677$			23.6623i			0.909415i	0.890641	+	0.454707i	$0.150256\pi$
$677$			23.6623i			0.909415i	−0.890641	+	0.454707i	$0.849744\pi$
$678$		0			0
$679$	−0.220893	−	2.75253i	−0.00847708	−	0.105632i
$680$		0			0
$681$	−10.5820	+	8.18444i	−0.405504	+	0.313629i
$682$		0			0
$683$	34.0953	−	19.6850i	1.30462	−	0.753224i	0.323429	−	0.946253i	$-0.395164\pi$
$683$	34.0953	−	19.6850i	1.30462	−	0.753224i	0.981193	+	0.193029i	$0.0618311\pi$
$684$		0			0
$685$		−	44.8407i		−	1.71328i
$686$		0			0
$687$	−27.8669	+	3.77736i	−1.06319	+	0.144115i
$688$		0			0
$689$			13.1863i			0.502357i
$690$		0			0
$691$	−1.26070			−0.0479594			−0.0239797	−	0.999712i	$-0.507634\pi$
$691$	−1.26070			−0.0479594			−0.0239797	+	0.999712i	$0.507634\pi$
$692$		0			0
$693$	43.0599	+	7.57168i	1.63571	+	0.287624i
$694$		0			0
$695$		−	6.75397i		−	0.256193i
$696$		0			0
$697$	44.2428			1.67582
$698$		0			0
$699$	1.23156	−	0.952528i	0.0465820	−	0.0360279i
$700$		0			0
$701$	−2.53754			−0.0958416			−0.0479208	−	0.998851i	$-0.515260\pi$
$701$	−2.53754			−0.0958416			−0.0479208	+	0.998851i	$0.515260\pi$
$702$		0			0
$703$	−1.57923	−	2.73531i	−0.0595619	−	0.103164i
$704$		0			0
$705$	9.61466	−	1.30327i	0.362109	−	0.0490840i
$706$		0			0
$707$	7.55592	−	5.21018i	0.284169	−	0.195949i
$708$		0			0
$709$	−2.21390			−0.0831446			−0.0415723	−	0.999135i	$-0.513237\pi$
$709$	−2.21390			−0.0831446			−0.0415723	+	0.999135i	$0.513237\pi$
$710$		0			0
$711$	7.20738	−	7.31864i	0.270298	−	0.274471i
$712$		0			0
$713$	−8.04346	+	4.64389i	−0.301230	+	0.173915i
$714$		0			0
$715$	−36.8771	−	21.2910i	−1.37912	−	0.796237i
$716$		0			0
$717$	6.51249	+	8.42028i	0.243213	+	0.314461i
$718$		0			0
$719$	−1.90077	+	3.29222i	−0.0708866	+	0.122779i	−0.899290	−	0.437353i	$-0.855916\pi$
$719$	−1.90077	+	3.29222i	−0.0708866	+	0.122779i	0.828404	+	0.560132i	$0.189250\pi$
$720$		0			0
$721$	31.8487	−	2.55589i	1.18611	−	0.0951863i
$722$		0			0
$723$	28.4042	+	36.7250i	1.05636	+	1.36582i
$724$		0			0
$725$	−40.0362			−1.48691
$726$		0			0
$727$	−19.8952	−	34.4595i	−0.737873	−	1.27803i	−0.953451	−	0.301547i	$-0.902497\pi$
$727$	−19.8952	−	34.4595i	−0.737873	−	1.27803i	0.215578	−	0.976487i	$-0.430836\pi$
$728$		0			0
$729$	−18.6482	+	19.5255i	−0.690674	+	0.723166i
$730$		0			0
$731$	−29.6126	+	51.2905i	−1.09526	+	1.89705i
$732$		0			0
$733$	−6.06358	+	3.50081i	−0.223963	+	0.129305i	−0.607784	−	0.794102i	$-0.707941\pi$
$733$	−6.06358	+	3.50081i	−0.223963	+	0.129305i	0.383821	+	0.923408i	$0.374608\pi$
$734$		0			0
$735$	−30.1274	−	28.1969i	−1.11127	−	1.04006i
$736$		0			0
$737$	−22.6983	+	39.3146i	−0.836102	+	1.44817i
$738$		0			0
$739$	13.1489	−	7.59152i	0.483690	−	0.279259i	−0.238263	−	0.971201i	$-0.576578\pi$
$739$	13.1489	−	7.59152i	0.483690	−	0.279259i	0.721953	+	0.691942i	$0.243245\pi$
$740$		0			0
$741$	6.63361	−	0.899188i	0.243692	−	0.0330325i
$742$		0			0
$743$	25.6717	+	14.8216i	0.941803	+	0.543750i	0.890525	−	0.454934i	$-0.150337\pi$
$743$	25.6717	+	14.8216i	0.941803	+	0.543750i	0.0512779	+	0.998684i	$0.483671\pi$
$744$		0			0
$745$	−33.6396	−	19.4218i	−1.23246	−	0.711561i
$746$		0			0
$747$	8.56104	−	32.9579i	0.313232	−	1.20587i
$748$		0			0
$749$	−3.43456	+	2.36830i	−0.125496	+	0.0865358i
$750$		0			0
$751$	−37.0782	+	21.4071i	−1.35300	+	0.781157i	−0.988669	−	0.150112i	$-0.952037\pi$
$751$	−37.0782	+	21.4071i	−1.35300	+	0.781157i	−0.364334	+	0.931268i	$0.618703\pi$
$752$		0			0
$753$	−27.0603	−	11.0875i	−0.986131	−	0.404051i
$754$		0			0
$755$	−6.41053			−0.233303
$756$		0			0
$757$	33.5040			1.21773			0.608863	−	0.793276i	$-0.291626\pi$
$757$	33.5040			1.21773			0.608863	+	0.793276i	$0.291626\pi$
$758$		0			0
$759$	11.1994	+	4.58879i	0.406514	+	0.166563i
$760$		0			0
$761$	1.92673	−	1.11240i	0.0698440	−	0.0403245i	−0.464671	−	0.885483i	$-0.653828\pi$
$761$	1.92673	−	1.11240i	0.0698440	−	0.0403245i	0.534515	+	0.845159i	$0.320494\pi$
$762$		0			0
$763$	−14.5920	+	1.17102i	−0.528266	+	0.0423938i
$764$		0			0
$765$	−75.5655	+	20.8693i	−2.73208	+	0.754532i
$766$		0			0
$767$	−13.7227	−	7.92282i	−0.495499	−	0.286076i
$768$		0			0
$769$	24.7865	+	14.3105i	0.893823	+	0.516049i	0.875191	−	0.483778i	$-0.160736\pi$
$769$	24.7865	+	14.3105i	0.893823	+	0.516049i	0.0186318	+	0.999826i	$0.494069\pi$
$770$		0			0
$771$	−23.4976	+	3.18510i	−0.846244	+	0.114709i
$772$		0			0
$773$	−19.0712	+	11.0108i	−0.685943	+	0.396030i	−0.802091	−	0.597202i	$-0.796279\pi$
$773$	−19.0712	+	11.0108i	−0.685943	+	0.396030i	0.116147	+	0.993232i	$0.462946\pi$
$774$		0			0
$775$	−24.0988	+	41.7404i	−0.865655	+	1.49936i
$776$		0			0
$777$	1.81320	+	8.31079i	0.0650483	+	0.298148i
$778$		0			0
$779$	8.49119	−	4.90239i	0.304228	−	0.175646i
$780$		0			0
$781$	−15.0719	+	26.1052i	−0.539314	+	0.934118i
$782$		0			0
$783$	18.9482	−	25.2901i	0.677153	−	0.903795i
$784$		0			0
$785$	19.5192	+	33.8083i	0.696670	+	1.20667i
$786$		0			0
$787$	−32.2826			−1.15075			−0.575374	−	0.817890i	$-0.695144\pi$
$787$	−32.2826			−1.15075			−0.575374	+	0.817890i	$0.695144\pi$
$788$		0			0
$789$	−14.2372	−	18.4079i	−0.506857	−	0.655337i
$790$		0			0
$791$	−15.9586	−	23.1435i	−0.567422	−	0.822887i
$792$		0			0
$793$	12.6490	−	21.9087i	0.449180	−	0.778002i
$794$		0			0
$795$	−20.9365	−	27.0697i	−0.742542	−	0.960065i
$796$		0			0
$797$	−7.78425	−	4.49424i	−0.275732	−	0.159194i	0.355758	−	0.934578i	$-0.384223\pi$
$797$	−7.78425	−	4.49424i	−0.275732	−	0.159194i	−0.631490	+	0.775384i	$0.717556\pi$
$798$		0			0
$799$	−10.9445	+	6.31879i	−0.387187	+	0.223543i
$800$		0			0
$801$	4.30913	+	15.6029i	0.152256	+	0.551301i
$802$		0			0
$803$	−79.9126			−2.82006
$804$		0			0
$805$	−6.48458	−	9.40407i	−0.228551	−	0.331450i
$806$		0			0
$807$	−14.6289	+	1.98295i	−0.514961	+	0.0698031i
$808$		0			0
$809$	−22.7656	−	39.4312i	−0.800396	−	1.38633i	−0.919356	−	0.393427i	$-0.871289\pi$
$809$	−22.7656	−	39.4312i	−0.800396	−	1.38633i	0.118960	−	0.992899i	$-0.462044\pi$
$810$		0			0
$811$	−11.9150			−0.418394			−0.209197	−	0.977874i	$-0.567085\pi$
$811$	−11.9150			−0.418394			−0.209197	+	0.977874i	$0.567085\pi$
$812$		0			0
$813$	−41.0963	+	31.7851i	−1.44131	+	1.11475i
$814$		0			0
$815$	−65.0368			−2.27814
$816$		0			0
$817$			13.1251i			0.459188i
$818$		0			0
$819$	−17.7564	−	3.12230i	−0.620459	−	0.109102i
$820$		0			0
$821$	−15.9351			−0.556139			−0.278070	−	0.960561i	$-0.589695\pi$
$821$	−15.9351			−0.556139			−0.278070	+	0.960561i	$0.589695\pi$
$822$		0			0
$823$		−	0.879238i		−	0.0306483i	−0.999883	−	0.0153242i	$-0.995122\pi$
$823$		−	0.879238i		−	0.0306483i	0.999883	−	0.0153242i	$-0.00487802\pi$
$824$		0			0
$825$	62.2380	−	8.43639i	2.16685	−	0.293717i
$826$		0			0
$827$		−	6.14006i		−	0.213511i	−0.994285	−	0.106755i	$-0.965954\pi$
$827$		−	6.14006i		−	0.213511i	0.994285	−	0.106755i	$-0.0340462\pi$
$828$		0			0
$829$	1.71187	−	0.988351i	0.0594558	−	0.0343268i	−0.469977	−	0.882678i	$-0.655738\pi$
$829$	1.71187	−	0.988351i	0.0594558	−	0.0343268i	0.529433	+	0.848352i	$0.322405\pi$
$830$		0			0
$831$	−15.1236	+	11.6971i	−0.524633	+	0.405766i
$832$		0			0
$833$	50.2355	+	19.1064i	1.74056	+	0.661996i
$834$		0			0
$835$		−	84.4484i		−	2.92246i
$836$		0			0
$837$	−14.9612	−	34.9775i	−0.517135	−	1.20900i
$838$		0			0
$839$	24.4737	+	42.3897i	0.844926	+	1.46345i	0.885685	+	0.464286i	$0.153689\pi$
$839$	24.4737	+	42.3897i	0.844926	+	1.46345i	−0.0407595	+	0.999169i	$0.512978\pi$
$840$		0			0
$841$	−3.99302	+	6.91611i	−0.137690	+	0.238487i
$842$		0			0
$843$	−4.06283	−	29.9728i	−0.139931	−	1.03232i
$844$		0			0
$845$	−23.1098	−	13.3425i	−0.795002	−	0.458995i
$846$		0			0
$847$	51.0076	−	4.09340i	1.75264	−	0.140651i
$848$		0			0
$849$	11.8342	+	4.84886i	0.406147	+	0.166412i
$850$		0			0
$851$			2.35478i			0.0807209i
$852$		0			0
$853$	−16.2267	+	9.36851i	−0.555593	+	0.320772i	−0.751375	−	0.659876i	$-0.770609\pi$
$853$	−16.2267	+	9.36851i	−0.555593	+	0.320772i	0.195782	+	0.980647i	$0.437276\pi$
$854$		0			0
$855$	−12.1903	+	12.3784i	−0.416898	+	0.423334i
$856$		0			0
$857$	−30.6545	−	17.6984i	−1.04714	−	0.604565i	−0.125290	−	0.992120i	$-0.539986\pi$
$857$	−30.6545	−	17.6984i	−1.04714	−	0.604565i	−0.921846	+	0.387556i	$0.873320\pi$
$858$		0			0
$859$	−6.22098	−	10.7750i	−0.212257	−	0.367640i	0.740164	−	0.672427i	$-0.234748\pi$
$859$	−6.22098	−	10.7750i	−0.212257	−	0.367640i	−0.952421	+	0.304787i	$0.901415\pi$
$860$		0			0
$861$	−25.7991	+	5.62870i	−0.879230	+	0.191826i
$862$		0			0
$863$	40.9185	+	23.6243i	1.39288	+	0.804180i	0.993633	−	0.112662i	$-0.0359379\pi$
$863$	40.9185	+	23.6243i	1.39288	+	0.804180i	0.399248	+	0.916843i	$0.369271\pi$
$864$		0			0
$865$	−27.9402	−	48.3938i	−0.949994	−	1.64544i
$866$		0			0
$867$	57.4780	−	44.4552i	1.95206	−	1.50978i
$868$		0			0
$869$	9.42993	−	16.3331i	0.319888	−	0.554063i
$870$		0			0
$871$	9.35998	−	16.2120i	0.317151	−	0.549321i
$872$		0			0
$873$	3.03053	+	0.787202i	0.102568	+	0.0266428i
$874$		0			0
$875$	−12.8763	−	6.11736i	−0.435298	−	0.206805i
$876$		0			0
$877$	−21.6295	−	37.4635i	−0.730378	−	1.26505i	−0.956722	−	0.291004i	$-0.906011\pi$
$877$	−21.6295	−	37.4635i	−0.730378	−	1.26505i	0.226344	−	0.974047i	$-0.427323\pi$
$878$		0			0
$879$	−12.5354	−	16.2076i	−0.422808	−	0.546667i
$880$		0			0
$881$			33.4300i			1.12629i	0.826359	+	0.563143i	$0.190408\pi$
$881$			33.4300i			1.12629i	−0.826359	+	0.563143i	$0.809592\pi$
$882$		0			0
$883$			41.0826i			1.38254i	0.722597	+	0.691270i	$0.242948\pi$
$883$			41.0826i			1.38254i	−0.722597	+	0.691270i	$0.757052\pi$
$884$		0			0
$885$	40.7505	−	5.52375i	1.36981	−	0.185679i
$886$		0			0
$887$	−17.1994	−	29.7902i	−0.577498	−	1.00026i	−0.995765	−	0.0919318i	$-0.970696\pi$
$887$	−17.1994	−	29.7902i	−0.577498	−	1.00026i	0.418267	−	0.908324i	$-0.362638\pi$
$888$		0			0
$889$	−18.2521	−	8.67132i	−0.612154	−	0.290827i
$890$		0			0
$891$	−24.1267	+	43.3073i	−0.808274	+	1.45085i
$892$		0			0
$893$	−1.40033	+	2.42544i	−0.0468601	+	0.0811641i
$894$		0			0
$895$	−18.0078	+	31.1904i	−0.601933	+	1.04258i
$896$		0			0
$897$	−4.61826	−	1.89226i	−0.154199	−	0.0631807i
$898$		0			0
$899$	22.2628	+	38.5604i	0.742508	+	1.28606i
$900$		0			0
$901$	38.6016	+	22.2867i	1.28601	+	0.742476i
$902$		0			0
$903$	10.7425	−	33.6762i	0.357488	−	1.12067i
$904$		0			0
$905$	−5.15690	−	8.93201i	−0.171421	−	0.296910i
$906$		0			0
$907$	4.26984	+	2.46520i	0.141778	+	0.0818555i	0.569211	−	0.822191i	$-0.307249\pi$
$907$	4.26984	+	2.46520i	0.141778	+	0.0818555i	−0.427433	+	0.904047i	$0.640582\pi$
$908$		0			0
$909$	2.77044	+	10.0315i	0.0918898	+	0.332723i
$910$		0			0
$911$	11.5141	−	6.64764i	0.381478	−	0.220246i	−0.296983	−	0.954883i	$-0.595981\pi$
$911$	11.5141	−	6.64764i	0.381478	−	0.220246i	0.678461	+	0.734636i	$0.262647\pi$
$912$		0			0
$913$		−	62.5219i		−	2.06917i
$914$		0			0
$915$	8.81882	+	65.0594i	0.291541	+	2.15080i
$916$		0			0
$917$	27.2474	−	2.18663i	0.899789	−	0.0722088i
$918$		0			0
$919$	−6.70092	−	3.86878i	−0.221043	−	0.127619i	0.385390	−	0.922754i	$-0.374067\pi$
$919$	−6.70092	−	3.86878i	−0.221043	−	0.127619i	−0.606433	+	0.795135i	$0.707400\pi$
$920$		0			0
$921$	12.8958	+	5.28385i	0.424931	+	0.174109i
$922$		0			0
$923$	6.21511	−	10.7649i	0.204573	−	0.354331i
$924$		0			0
$925$	6.10990	+	10.5827i	0.200892	+	0.347956i
$926$		0			0
$927$	−9.10851	+	35.0655i	−0.299163	+	1.15170i
$928$		0			0
$929$			16.7712i			0.550247i	0.961409	+	0.275123i	$0.0887187\pi$
$929$			16.7712i			0.550247i	−0.961409	+	0.275123i	$0.911281\pi$
$930$		0			0
$931$	11.7584	−	1.89948i	0.385367	−	0.0622530i
$932$		0			0
$933$	35.5647	+	14.5721i	1.16434	+	0.477068i
$934$		0			0
$935$	−124.655	+	71.9695i	−4.07665	+	2.35366i
$936$		0			0
$937$			17.0639i			0.557452i	0.960371	+	0.278726i	$0.0899121\pi$
$937$			17.0639i			0.557452i	−0.960371	+	0.278726i	$0.910088\pi$
$938$		0			0
$939$	2.77125	−	6.76354i	0.0904364	−	0.220720i
$940$		0			0
$941$			23.1103i			0.753374i	0.926341	+	0.376687i	$0.122937\pi$
$941$			23.1103i			0.753374i	−0.926341	+	0.376687i	$0.877063\pi$
$942$		0			0
$943$	−7.30992			−0.238044
$944$		0			0
$945$	41.4091	−	21.7831i	1.34704	−	0.708604i
$946$		0			0
$947$			2.50258i			0.0813229i	0.999173	+	0.0406614i	$0.0129465\pi$
$947$			2.50258i			0.0813229i	−0.999173	+	0.0406614i	$0.987053\pi$
$948$		0			0
$949$	32.9532			1.06971
$950$		0			0
$951$	10.9493	+	4.48631i	0.355056	+	0.145478i
$952$		0			0
$953$	10.5408			0.341450			0.170725	−	0.985319i	$-0.445389\pi$
$953$	10.5408			0.341450			0.170725	+	0.985319i	$0.445389\pi$
$954$		0			0
$955$	−2.51479	−	4.35574i	−0.0813767	−	0.140949i
$956$		0			0
$957$	21.9987	−	53.6902i	0.711117	−	1.73556i
$958$		0			0
$959$	−19.7882	−	28.6973i	−0.638996	−	0.926685i
$960$		0			0
$961$	22.6023			0.729107
$962$		0			0
$963$	−1.25931	−	4.55983i	−0.0405808	−	0.146939i
$964$		0			0
$965$	62.6533	−	36.1729i	2.01688	−	1.16445i
$966$		0			0
$967$	40.2896	+	23.2612i	1.29563	+	0.748031i	0.979646	−	0.200734i	$-0.0643328\pi$
$967$	40.2896	+	23.2612i	1.29563	+	0.748031i	0.315982	+	0.948765i	$0.397666\pi$
$968$		0			0
$969$	8.57945	−	20.9391i	0.275612	−	0.672659i
$970$		0			0
$971$	15.9949	−	27.7040i	0.513301	−	0.889063i	−0.486580	−	0.873636i	$-0.661756\pi$
$971$	15.9949	−	27.7040i	0.513301	−	0.889063i	0.999881	−	0.0154270i	$-0.00491075\pi$
$972$		0			0
$973$	−2.98053	−	4.32243i	−0.0955515	−	0.138571i
$974$		0			0
$975$	−25.6648	+	3.47887i	−0.821931	+	0.111413i
$976$		0			0
$977$	−36.7497			−1.17573			−0.587864	−	0.808960i	$-0.700031\pi$
$977$	−36.7497			−1.17573			−0.587864	+	0.808960i	$0.700031\pi$
$978$		0			0
$979$	14.8604	+	25.7389i	0.474940	+	0.822620i
$980$		0			0
$981$	4.17320	−	16.0658i	0.133240	−	0.512942i
$982$		0			0
$983$	30.0864	−	52.1111i	0.959606	−	1.66209i	0.236149	−	0.971717i	$-0.424115\pi$
$983$	30.0864	−	52.1111i	0.959606	−	1.66209i	0.723457	−	0.690369i	$-0.242552\pi$
$984$		0			0
$985$	17.5846	−	10.1525i	0.560292	−	0.323485i
$986$		0			0
$987$	5.57809	−	5.07703i	0.177553	−	0.161604i
$988$		0			0
$989$	4.89267	−	8.47435i	0.155578	−	0.269469i
$990$		0			0
$991$	14.8725	−	8.58665i	0.472441	−	0.272764i	−0.244820	−	0.969569i	$-0.578729\pi$
$991$	14.8725	−	8.58665i	0.472441	−	0.272764i	0.717261	+	0.696805i	$0.245396\pi$
$992$		0			0
$993$	−14.5039	+	35.3983i	−0.460267	+	1.12333i
$994$		0			0
$995$	72.3229	+	41.7556i	2.29279	+	1.32374i
$996$		0			0
$997$	13.3621	+	7.71463i	0.423183	+	0.244325i	0.696438	−	0.717617i	$-0.254767\pi$
$997$	13.3621	+	7.71463i	0.423183	+	0.244325i	−0.273255	+	0.961942i	$0.588100\pi$
$998$		0			0
$999$	−9.57654	−	1.14901i	−0.302988	−	0.0363531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.i.607.14	yes	32
3.2	odd	2		3024.2.cz.i.1279.2		32
4.3	odd	2	inner	1008.2.cz.i.607.3	yes	32
7.3	odd	6		1008.2.bf.i.31.9	yes	32
9.2	odd	6		3024.2.bf.i.2287.1		32
9.7	even	3		1008.2.bf.i.943.8	yes	32
12.11	even	2		3024.2.cz.i.1279.1		32
21.17	even	6		3024.2.bf.i.1711.15		32
28.3	even	6		1008.2.bf.i.31.8	✓	32
36.7	odd	6		1008.2.bf.i.943.9	yes	32
36.11	even	6		3024.2.bf.i.2287.2		32
63.38	even	6		3024.2.cz.i.2719.1		32
63.52	odd	6	inner	1008.2.cz.i.367.3	yes	32
84.59	odd	6		3024.2.bf.i.1711.16		32
252.115	even	6	inner	1008.2.cz.i.367.14	yes	32
252.227	odd	6		3024.2.cz.i.2719.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.8	✓	32	28.3	even	6
1008.2.bf.i.31.9	yes	32	7.3	odd	6
1008.2.bf.i.943.8	yes	32	9.7	even	3
1008.2.bf.i.943.9	yes	32	36.7	odd	6
1008.2.cz.i.367.3	yes	32	63.52	odd	6	inner
1008.2.cz.i.367.14	yes	32	252.115	even	6	inner
1008.2.cz.i.607.3	yes	32	4.3	odd	2	inner
1008.2.cz.i.607.14	yes	32	1.1	even	1	trivial
3024.2.bf.i.1711.15		32	21.17	even	6
3024.2.bf.i.1711.16		32	84.59	odd	6
3024.2.bf.i.2287.1		32	9.2	odd	6
3024.2.bf.i.2287.2		32	36.11	even	6
3024.2.cz.i.1279.1		32	12.11	even	2
3024.2.cz.i.1279.2		32	3.2	odd	2
3024.2.cz.i.2719.1		32	63.38	even	6
3024.2.cz.i.2719.2		32	252.227	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60273 + 0.656694i) q^{3} +(2.94743 - 1.70170i) q^{5} +(1.13535 - 2.38977i) q^{7} +(2.13751 + 2.10501i) q^{9} +O(q^{10})\)	\(q+(1.60273 + 0.656694i) q^{3} +(2.94743 - 1.70170i) q^{5} +(1.13535 - 2.38977i) q^{7} +(2.13751 + 2.10501i) q^{9} +(4.77030 + 2.75413i) q^{11} +(-1.96711 - 1.13571i) q^{13} +(5.84145 - 0.791810i) q^{15} +(-6.64938 + 3.83902i) q^{17} +(-0.850777 + 1.47359i) q^{19} +(3.38901 - 3.08458i) q^{21} +(1.09863 - 0.634293i) q^{23} +(3.29157 - 5.70117i) q^{25} +(2.04350 + 4.77746i) q^{27} +(-3.04081 - 5.26683i) q^{29} -7.32136 q^{31} +(5.83689 + 7.54677i) q^{33} +(-0.720307 - 8.97570i) q^{35} +(-0.928112 + 1.60754i) q^{37} +(-2.40693 - 3.11203i) q^{39} +(-4.99026 - 2.88113i) q^{41} +(6.68015 - 3.85679i) q^{43} +(9.88225 + 2.56698i) q^{45} +1.64594 q^{47} +(-4.42197 - 5.42643i) q^{49} +(-13.1782 + 1.78632i) q^{51} +(-2.90265 - 5.02754i) q^{53} +18.7469 q^{55} +(-2.33127 + 1.80307i) q^{57} +6.97610 q^{59} +11.1375i q^{61} +(7.45730 - 2.71822i) q^{63} -7.73055 q^{65} +8.24153i q^{67} +(2.17734 - 0.295140i) q^{69} +5.47245i q^{71} +(-12.5641 + 7.25388i) q^{73} +(9.01944 - 6.97590i) q^{75} +(11.9977 - 8.27301i) q^{77} -3.42392i q^{79} +(0.137857 + 8.99894i) q^{81} +(-5.67528 - 9.82987i) q^{83} +(-13.0657 + 22.6305i) q^{85} +(-1.41490 - 10.4382i) q^{87} +(4.67278 + 2.69783i) q^{89} +(-4.94743 + 3.41150i) q^{91} +(-11.7342 - 4.80790i) q^{93} +5.79107i q^{95} +(0.903873 - 0.521851i) q^{97} +(4.39906 + 15.9285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9}+O(q^{10}) \) 32 * q - 4 * q^9	\( 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Introduction

L-functions

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