LMFDB - Embedded newform 756.2.bp.a.193.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.15
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557871 - 1.63975i) q^{3} +(2.46711 - 0.897956i) q^{5} +(1.73437 + 1.99799i) q^{7} +(-2.37756 - 1.82954i) q^{9} +O(q^{10})$	\(q+(0.557871 - 1.63975i) q^{3} +(2.46711 - 0.897956i) q^{5} +(1.73437 + 1.99799i) q^{7} +(-2.37756 - 1.82954i) q^{9} +(3.00283 + 1.09294i) q^{11} +(0.390189 - 0.142017i) q^{13} +(-0.0960930 - 4.54639i) q^{15} +(2.86379 + 4.96022i) q^{17} +(1.85458 - 3.21223i) q^{19} +(4.24376 - 1.72932i) q^{21} +(-0.155436 + 0.881523i) q^{23} +(1.45011 - 1.21678i) q^{25} +(-4.32635 + 2.87796i) q^{27} +(-4.60734 - 1.67693i) q^{29} +(-0.238899 + 0.0869523i) q^{31} +(3.46734 - 4.31417i) q^{33} +(6.07300 + 3.37187i) q^{35} -1.34314 q^{37} +(-0.0151977 - 0.719039i) q^{39} +(-5.30846 + 1.93212i) q^{41} +(-1.43117 - 8.11658i) q^{43} +(-7.50856 - 2.37873i) q^{45} +(-7.90833 - 2.87840i) q^{47} +(-0.983909 + 6.93051i) q^{49} +(9.73115 - 1.92873i) q^{51} +(-0.258931 + 0.448481i) q^{53} +8.38974 q^{55} +(-4.23264 - 4.83307i) q^{57} +(-6.95855 - 5.83892i) q^{59} +(13.2831 + 4.83465i) q^{61} +(-0.468182 - 7.92343i) q^{63} +(0.835115 - 0.700744i) q^{65} +(2.75811 - 15.6420i) q^{67} +(1.35876 + 0.746652i) q^{69} +(0.980331 - 1.69798i) q^{71} -9.60609 q^{73} +(-1.18625 - 3.05662i) q^{75} +(3.02434 + 7.89519i) q^{77} +(0.965357 + 5.47481i) q^{79} +(2.30559 + 8.69967i) q^{81} +(-11.4405 - 4.16401i) q^{83} +(11.5194 + 9.66588i) q^{85} +(-5.32005 + 6.61937i) q^{87} +(3.64522 - 6.31370i) q^{89} +(0.960480 + 0.533281i) q^{91} +(0.00930503 + 0.440243i) q^{93} +(1.69103 - 9.59028i) q^{95} +(1.87320 + 10.6234i) q^{97} +(-5.13984 - 8.09232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.557871	−	1.63975i	0.322087	−	0.946710i
$3$	0.557871	−	1.63975i	0.322087	−	0.946710i
$4$		0			0
$5$	2.46711	−	0.897956i	1.10333	−	0.401578i	0.274785	−	0.961506i	$-0.411393\pi$
$5$	2.46711	−	0.897956i	1.10333	−	0.401578i	0.828542	+	0.559927i	$0.189171\pi$
$6$		0			0
$7$	1.73437	+	1.99799i	0.655531	+	0.755168i
$7$	1.73437	+	1.99799i	0.655531	+	0.755168i
$8$		0			0
$9$	−2.37756	−	1.82954i	−0.792520	−	0.609846i
$10$		0			0
$11$	3.00283	+	1.09294i	0.905388	+	0.329534i	0.752410	−	0.658695i	$-0.228891\pi$
$11$	3.00283	+	1.09294i	0.905388	+	0.329534i	0.152978	+	0.988230i	$0.451114\pi$
$12$		0			0
$13$	0.390189	−	0.142017i	0.108219	−	0.0393884i	−0.287343	−	0.957828i	$-0.592772\pi$
$13$	0.390189	−	0.142017i	0.108219	−	0.0393884i	0.395562	+	0.918439i	$0.370550\pi$
$14$		0			0
$15$	−0.0960930	−	4.54639i	−0.0248111	−	1.17387i
$16$		0			0
$17$	2.86379	+	4.96022i	0.694570	+	1.20303i	0.970325	+	0.241803i	$0.0777388\pi$
$17$	2.86379	+	4.96022i	0.694570	+	1.20303i	−0.275755	+	0.961228i	$0.588928\pi$
$18$		0			0
$19$	1.85458	−	3.21223i	0.425471	−	0.736937i	−0.570994	−	0.820955i	$-0.693442\pi$
$19$	1.85458	−	3.21223i	0.425471	−	0.736937i	0.996464	+	0.0840176i	$0.0267752\pi$
$20$		0			0
$21$	4.24376	−	1.72932i	0.926063	−	0.377368i
$22$		0			0
$23$	−0.155436	+	0.881523i	−0.0324107	+	0.183810i	−0.996715	−	0.0809852i	$-0.974193\pi$
$23$	−0.155436	+	0.881523i	−0.0324107	+	0.183810i	0.964305	+	0.264795i	$0.0853044\pi$
$24$		0			0
$25$	1.45011	−	1.21678i	0.290021	−	0.243357i
$26$		0			0
$27$	−4.32635	+	2.87796i	−0.832607	+	0.553864i
$28$		0			0
$29$	−4.60734	−	1.67693i	−0.855561	−	0.311399i	−0.123255	−	0.992375i	$-0.539333\pi$
$29$	−4.60734	−	1.67693i	−0.855561	−	0.311399i	−0.732305	+	0.680976i	$0.761556\pi$
$30$		0			0
$31$	−0.238899	+	0.0869523i	−0.0429076	+	0.0156171i	−0.363385	−	0.931639i	$-0.618379\pi$
$31$	−0.238899	+	0.0869523i	−0.0429076	+	0.0156171i	0.320477	+	0.947256i	$0.396157\pi$
$32$		0			0
$33$	3.46734	−	4.31417i	0.603587	−	0.751001i
$34$		0			0
$35$	6.07300	+	3.37187i	1.02652	+	0.569951i
$36$		0			0
$37$	−1.34314			−0.220811			−0.110405	−	0.993887i	$-0.535215\pi$
$37$	−1.34314			−0.220811			−0.110405	+	0.993887i	$0.535215\pi$
$38$		0			0
$39$	−0.0151977	−	0.719039i	−0.00243358	−	0.115138i
$40$		0			0
$41$	−5.30846	+	1.93212i	−0.829042	+	0.301747i	−0.721466	−	0.692450i	$-0.756531\pi$
$41$	−5.30846	+	1.93212i	−0.829042	+	0.301747i	−0.107576	+	0.994197i	$0.534309\pi$
$42$		0			0
$43$	−1.43117	−	8.11658i	−0.218252	−	1.23777i	−0.875174	−	0.483809i	$-0.839253\pi$
$43$	−1.43117	−	8.11658i	−0.218252	−	1.23777i	0.656922	−	0.753959i	$-0.271858\pi$
$44$		0			0
$45$	−7.50856	−	2.37873i	−1.11931	−	0.354600i
$46$		0			0
$47$	−7.90833	−	2.87840i	−1.15355	−	0.419857i	−0.306760	−	0.951787i	$-0.599245\pi$
$47$	−7.90833	−	2.87840i	−1.15355	−	0.419857i	−0.846788	+	0.531930i	$0.821467\pi$
$48$		0			0
$49$	−0.983909	+	6.93051i	−0.140558	+	0.990072i
$50$		0			0
$51$	9.73115	−	1.92873i	1.36263	−	0.270076i
$52$		0			0
$53$	−0.258931	+	0.448481i	−0.0355669	+	0.0616036i	−0.883261	−	0.468882i	$-0.844657\pi$
$53$	−0.258931	+	0.448481i	−0.0355669	+	0.0616036i	0.847694	+	0.530485i	$0.177990\pi$
$54$		0			0
$55$	8.38974			1.13127
$56$		0			0
$57$	−4.23264	−	4.83307i	−0.560627	−	0.640155i
$58$		0			0
$59$	−6.95855	−	5.83892i	−0.905926	−	0.760162i	0.0654133	−	0.997858i	$-0.479163\pi$
$59$	−6.95855	−	5.83892i	−0.905926	−	0.760162i	−0.971340	+	0.237696i	$0.923608\pi$
$60$		0			0
$61$	13.2831	+	4.83465i	1.70073	+	0.619013i	0.995908	−	0.0903755i	$-0.0288067\pi$
$61$	13.2831	+	4.83465i	1.70073	+	0.619013i	0.704817	+	0.709389i	$0.251029\pi$
$62$		0			0
$63$	−0.468182	−	7.92343i	−0.0589854	−	0.998259i
$64$		0			0
$65$	0.835115	−	0.700744i	0.103583	−	0.0869166i
$66$		0			0
$67$	2.75811	−	15.6420i	0.336956	−	1.91097i	−0.0700388	−	0.997544i	$-0.522312\pi$
$67$	2.75811	−	15.6420i	0.336956	−	1.91097i	0.406995	−	0.913430i	$-0.366577\pi$
$68$		0			0
$69$	1.35876	+	0.746652i	0.163576	+	0.0898864i
$70$		0			0
$71$	0.980331	−	1.69798i	0.116344	−	0.201514i	−0.801972	−	0.597361i	$-0.796216\pi$
$71$	0.980331	−	1.69798i	0.116344	−	0.201514i	0.918316	+	0.395848i	$0.129549\pi$
$72$		0			0
$73$	−9.60609			−1.12431			−0.562154	−	0.827033i	$-0.690027\pi$
$73$	−9.60609			−1.12431			−0.562154	+	0.827033i	$0.690027\pi$
$74$		0			0
$75$	−1.18625	−	3.05662i	−0.136976	−	0.352948i
$76$		0			0
$77$	3.02434	+	7.89519i	0.344656	+	0.899740i
$78$		0			0
$79$	0.965357	+	5.47481i	0.108611	+	0.615965i	0.989716	+	0.143044i	$0.0456891\pi$
$79$	0.965357	+	5.47481i	0.108611	+	0.615965i	−0.881105	+	0.472920i	$0.843200\pi$
$80$		0			0
$81$	2.30559	+	8.69967i	0.256177	+	0.966630i
$82$		0			0
$83$	−11.4405	−	4.16401i	−1.25576	−	0.457059i	−0.373416	−	0.927664i	$-0.621814\pi$
$83$	−11.4405	−	4.16401i	−1.25576	−	0.457059i	−0.882344	+	0.470604i	$0.844036\pi$
$84$		0			0
$85$	11.5194	+	9.66588i	1.24945	+	1.04841i
$86$		0			0
$87$	−5.32005	+	6.61937i	−0.570369	+	0.709671i
$88$		0			0
$89$	3.64522	−	6.31370i	0.386392	−	0.669251i	−0.605569	−	0.795793i	$-0.707054\pi$
$89$	3.64522	−	6.31370i	0.386392	−	0.669251i	0.991961	+	0.126542i	$0.0403878\pi$
$90$		0			0
$91$	0.960480	+	0.533281i	0.100686	+	0.0559031i
$92$		0			0
$93$	0.00930503	+	0.440243i	0.000964887	+	0.0456511i
$94$		0			0
$95$	1.69103	−	9.59028i	0.173496	−	0.983942i
$96$		0			0
$97$	1.87320	+	10.6234i	0.190195	+	1.07865i	0.919098	+	0.394030i	$0.128919\pi$
$97$	1.87320	+	10.6234i	0.190195	+	1.07865i	−0.728903	+	0.684617i	$0.759969\pi$
$98$		0			0
$99$	−5.13984	−	8.09232i	−0.516573	−	0.813309i
$100$		0			0
$101$	1.66307	+	9.43175i	0.165482	+	0.938495i	0.948566	+	0.316579i	$0.102534\pi$
$101$	1.66307	+	9.43175i	0.165482	+	0.938495i	−0.783084	+	0.621916i	$0.786355\pi$
$102$		0			0
$103$	1.34689	−	0.490227i	0.132713	−	0.0483035i	−0.274810	−	0.961499i	$-0.588615\pi$
$103$	1.34689	−	0.490227i	0.132713	−	0.0483035i	0.407523	+	0.913195i	$0.366393\pi$
$104$		0			0
$105$	8.91698	−	8.07713i	0.870208	−	0.788247i
$106$		0			0
$107$	0.592492	+	1.02623i	0.0572784	+	0.0992091i	0.893243	−	0.449575i	$-0.148424\pi$
$107$	0.592492	+	1.02623i	0.0572784	+	0.0992091i	−0.835964	+	0.548784i	$0.815091\pi$
$108$		0			0
$109$	8.61322	−	14.9185i	0.824997	−	1.42894i	−0.0769242	−	0.997037i	$-0.524510\pi$
$109$	8.61322	−	14.9185i	0.824997	−	1.42894i	0.901921	−	0.431900i	$-0.142157\pi$
$110$		0			0
$111$	−0.749298	+	2.20241i	−0.0711202	+	0.209044i
$112$		0			0
$113$	−3.18869	+	18.0839i	−0.299966	+	1.70119i	0.346334	+	0.938111i	$0.387426\pi$
$113$	−3.18869	+	18.0839i	−0.299966	+	1.70119i	−0.646301	+	0.763083i	$0.723685\pi$
$114$		0			0
$115$	0.408090	+	2.31439i	0.0380546	+	0.215818i
$116$		0			0
$117$	−1.18752	−	0.376210i	−0.109786	−	0.0347806i
$118$		0			0
$119$	−4.94359	+	14.3247i	−0.453179	+	1.31314i
$120$		0			0
$121$	−0.604015	−	0.506829i	−0.0549105	−	0.0460754i
$122$		0			0
$123$	0.206762	+	9.78242i	0.0186431	+	0.882051i
$124$		0			0
$125$	−4.07866	+	7.06445i	−0.364807	+	0.631864i
$126$		0			0
$127$	0.455860	+	0.789573i	0.0404511	+	0.0700633i	0.885542	−	0.464559i	$-0.153787\pi$
$127$	0.455860	+	0.789573i	0.0404511	+	0.0700633i	−0.845091	+	0.534622i	$0.820454\pi$
$128$		0			0
$129$	−14.1076	−	2.18124i	−1.24210	−	0.192047i
$130$		0			0
$131$	−1.49350	+	8.47006i	−0.130488	+	0.740033i	0.847408	+	0.530941i	$0.178162\pi$
$131$	−1.49350	+	8.47006i	−0.130488	+	0.740033i	−0.977896	+	0.209091i	$0.932950\pi$
$132$		0			0
$133$	9.63454	−	1.86577i	0.835421	−	0.161783i
$134$		0			0
$135$	−8.08933	+	10.9851i	−0.696219	+	0.945450i
$136$		0			0
$137$	−12.8333	+	10.7684i	−1.09642	+	0.920006i	−0.997179	−	0.0750579i	$-0.976086\pi$
$137$	−12.8333	+	10.7684i	−1.09642	+	0.920006i	−0.0992408	+	0.995063i	$0.531641\pi$
$138$		0			0
$139$	−5.02132	−	4.21339i	−0.425903	−	0.357375i	0.404501	−	0.914538i	$-0.367445\pi$
$139$	−5.02132	−	4.21339i	−0.425903	−	0.357375i	−0.830403	+	0.557163i	$0.811890\pi$
$140$		0			0
$141$	−9.13167	+	11.3619i	−0.769026	+	0.956845i
$142$		0			0
$143$	1.32689			0.110960
$144$		0			0
$145$	−12.8726			−1.06901
$146$		0			0
$147$	10.8154	+	5.47969i	0.892040	+	0.451957i
$148$		0			0
$149$	−8.63225	−	7.24332i	−0.707182	−	0.593396i	0.216625	−	0.976255i	$-0.430495\pi$
$149$	−8.63225	−	7.24332i	−0.707182	−	0.593396i	−0.923807	+	0.382859i	$0.874940\pi$
$150$		0			0
$151$	5.17057	+	1.88193i	0.420775	+	0.153150i	0.543725	−	0.839263i	$-0.317013\pi$
$151$	5.17057	+	1.88193i	0.420775	+	0.153150i	−0.122950	+	0.992413i	$0.539236\pi$
$152$		0			0
$153$	2.26609	−	17.0326i	0.183202	−	1.37701i
$154$		0			0
$155$	−0.511313	+	0.429042i	−0.0410696	+	0.0344615i
$156$		0			0
$157$	6.02757	+	5.05773i	0.481052	+	0.403651i	0.850807	−	0.525479i	$-0.176114\pi$
$157$	6.02757	+	5.05773i	0.481052	+	0.403651i	−0.369754	+	0.929130i	$0.620558\pi$
$158$		0			0
$159$	0.590947	+	0.674776i	0.0468652	+	0.0535132i
$160$		0			0
$161$	−2.03086	+	1.21833i	−0.160054	+	0.0960178i
$162$		0			0
$163$	8.00021	+	13.8568i	0.626625	+	1.08535i	0.988224	+	0.153012i	$0.0488974\pi$
$163$	8.00021	+	13.8568i	0.626625	+	1.08535i	−0.361600	+	0.932333i	$0.617769\pi$
$164$		0			0
$165$	4.68039	−	13.7571i	0.364368	−	1.07099i
$166$		0			0
$167$	2.93501	−	16.6453i	0.227118	−	1.28805i	−0.631476	−	0.775395i	$-0.717551\pi$
$167$	2.93501	−	16.6453i	0.227118	−	1.28805i	0.858594	−	0.512656i	$-0.171338\pi$
$168$		0			0
$169$	−9.82650	+	8.24541i	−0.755885	+	0.634262i
$170$		0			0
$171$	−10.2863	+	4.24425i	−0.786612	+	0.324566i
$172$		0			0
$173$	−6.48292	+	5.43982i	−0.492887	+	0.413582i	−0.855060	−	0.518529i	$-0.826480\pi$
$173$	−6.48292	+	5.43982i	−0.492887	+	0.413582i	0.362172	+	0.932111i	$0.382035\pi$
$174$		0			0
$175$	4.94614	+	0.786939i	0.373893	+	0.0594870i
$176$		0			0
$177$	−13.4563	+	8.15293i	−1.01144	+	0.612811i
$178$		0			0
$179$	9.65383	+	16.7209i	0.721561	+	1.24978i	0.960374	+	0.278715i	$0.0899086\pi$
$179$	9.65383	+	16.7209i	0.721561	+	1.24978i	−0.238812	+	0.971066i	$0.576758\pi$
$180$		0			0
$181$	−9.35641	−	16.2058i	−0.695457	−	1.20457i	−0.970026	−	0.242999i	$-0.921869\pi$
$181$	−9.35641	−	16.2058i	−0.695457	−	1.20457i	0.274570	−	0.961567i	$-0.411465\pi$
$182$		0			0
$183$	15.3379	−	19.0838i	1.13381	−	1.41072i
$184$		0			0
$185$	−3.31368	+	1.20608i	−0.243626	+	0.0886727i
$186$		0			0
$187$	3.17823	+	18.0247i	0.232416	+	1.31809i
$188$		0			0
$189$	−13.2536	−	3.65255i	−0.964060	−	0.265684i
$190$		0			0
$191$	2.43903	+	13.8325i	0.176482	+	1.00088i	0.936419	+	0.350884i	$0.114119\pi$
$191$	2.43903	+	13.8325i	0.176482	+	1.00088i	−0.759937	+	0.649997i	$0.774770\pi$
$192$		0			0
$193$	23.7802	−	8.65528i	1.71174	−	0.623021i	0.714662	−	0.699470i	$-0.246581\pi$
$193$	23.7802	−	8.65528i	1.71174	−	0.623021i	0.997073	+	0.0764495i	$0.0243584\pi$
$194$		0			0
$195$	−0.683160	−	1.76030i	−0.0489221	−	0.126058i
$196$		0			0
$197$	7.17369	+	12.4252i	0.511104	+	0.885259i	0.999917	+	0.0128700i	$0.00409675\pi$
$197$	7.17369	+	12.4252i	0.511104	+	0.885259i	−0.488813	+	0.872389i	$0.662570\pi$
$198$		0			0
$199$	−8.89708	−	15.4102i	−0.630697	−	1.09240i	−0.987409	−	0.158185i	$-0.949436\pi$
$199$	−8.89708	−	15.4102i	−0.630697	−	1.09240i	0.356713	−	0.934214i	$-0.383898\pi$
$200$		0			0
$201$	−24.1103	−	13.2488i	−1.70061	−	0.934500i
$202$		0			0
$203$	−4.64034	−	12.1138i	−0.325688	−	0.850224i
$204$		0			0
$205$	−11.3616	+	9.53353i	−0.793530	+	0.665851i
$206$		0			0
$207$	1.98234	−	1.81150i	0.137782	−	0.125908i
$208$		0			0
$209$	9.07978	−	7.61884i	0.628062	−	0.527006i
$210$		0			0
$211$	2.60301	−	14.7624i	0.179199	−	1.01629i	−0.753987	−	0.656890i	$-0.771872\pi$
$211$	2.60301	−	14.7624i	0.179199	−	1.01629i	0.933185	−	0.359396i	$-0.117017\pi$
$212$		0			0
$213$	−2.23737	−	2.55475i	−0.153302	−	0.175049i
$214$		0			0
$215$	−10.8192	−	18.7394i	−0.737863	−	1.27802i
$216$		0			0
$217$	−0.588070	−	0.326510i	−0.0399208	−	0.0221650i
$218$		0			0
$219$	−5.35895	+	15.7516i	−0.362125	+	1.06439i
$220$		0			0
$221$	1.82185	+	1.52872i	0.122551	+	0.102833i
$222$		0			0
$223$	−10.8131	+	9.07328i	−0.724099	+	0.607592i	−0.928516	−	0.371292i	$-0.878915\pi$
$223$	−10.8131	+	9.07328i	−0.724099	+	0.607592i	0.204417	+	0.978884i	$0.434470\pi$
$224$		0			0
$225$	−5.67386	+	0.239954i	−0.378258	+	0.0159969i
$226$		0			0
$227$	12.5573	+	4.57049i	0.833458	+	0.303354i	0.723277	−	0.690558i	$-0.242635\pi$
$227$	12.5573	+	4.57049i	0.833458	+	0.303354i	0.110181	+	0.993912i	$0.464857\pi$
$228$		0			0
$229$	7.89603	+	6.62556i	0.521784	+	0.437829i	0.865253	−	0.501335i	$-0.167158\pi$
$229$	7.89603	+	6.62556i	0.521784	+	0.437829i	−0.343469	+	0.939164i	$0.611602\pi$
$230$		0			0
$231$	14.6333	−	0.554674i	0.962802	−	0.0364949i
$232$		0			0
$233$	0.103979			0.00681186			0.00340593	−	0.999994i	$-0.498916\pi$
$233$	0.103979			0.00681186			0.00340593	+	0.999994i	$0.498916\pi$
$234$		0			0
$235$	−22.0954			−1.44135
$236$		0			0
$237$	9.51587	+	1.47129i	0.618122	+	0.0955707i
$238$		0			0
$239$	3.02560	+	2.53878i	0.195710	+	0.164220i	0.735376	−	0.677659i	$-0.237005\pi$
$239$	3.02560	+	2.53878i	0.195710	+	0.164220i	−0.539667	+	0.841879i	$0.681450\pi$
$240$		0			0
$241$	−8.30250	+	6.96662i	−0.534811	+	0.448760i	−0.869759	−	0.493477i	$-0.835726\pi$
$241$	−8.30250	+	6.96662i	−0.534811	+	0.448760i	0.334948	+	0.942237i	$0.391281\pi$
$242$		0			0
$243$	15.5515	+	1.07270i	0.997630	+	0.0688137i
$244$		0			0
$245$	3.79588	+	17.9819i	0.242510	+	1.14882i
$246$		0			0
$247$	0.267446	−	1.51676i	0.0170172	−	0.0965091i
$248$		0			0
$249$	−13.2103	+	16.4366i	−0.837167	+	1.04163i
$250$		0			0
$251$	−4.22540	−	7.31861i	−0.266705	−	0.461947i	0.701304	−	0.712862i	$-0.252602\pi$
$251$	−4.22540	−	7.31861i	−0.266705	−	0.461947i	−0.968009	+	0.250916i	$0.919268\pi$
$252$		0			0
$253$	−1.43020	+	2.47718i	−0.0899160	+	0.155739i
$254$		0			0
$255$	22.2759	−	13.4965i	1.39497	−	0.845186i
$256$		0			0
$257$	−7.52905	−	6.31762i	−0.469649	−	0.394082i	0.377018	−	0.926206i	$-0.376950\pi$
$257$	−7.52905	−	6.31762i	−0.469649	−	0.394082i	−0.846667	+	0.532124i	$0.821394\pi$
$258$		0			0
$259$	−2.32950	−	2.68357i	−0.144748	−	0.166749i
$260$		0			0
$261$	7.88621	+	12.4163i	0.488144	+	0.768550i
$262$		0			0
$263$	2.09442	+	11.8781i	0.129148	+	0.732433i	0.978757	+	0.205021i	$0.0657264\pi$
$263$	2.09442	+	11.8781i	0.129148	+	0.732433i	−0.849610	+	0.527412i	$0.823162\pi$
$264$		0			0
$265$	−0.236095	+	1.33896i	−0.0145032	+	0.0822518i
$266$		0			0
$267$	−8.31933	−	9.49947i	−0.509135	−	0.581358i
$268$		0			0
$269$	−3.70714	+	6.42095i	−0.226028	+	0.391492i	−0.956627	−	0.291314i	$-0.905907\pi$
$269$	−3.70714	+	6.42095i	−0.226028	+	0.391492i	0.730599	+	0.682806i	$0.239241\pi$
$270$		0			0
$271$	3.38967	+	5.87109i	0.205908	+	0.356643i	0.950422	−	0.310964i	$-0.100652\pi$
$271$	3.38967	+	5.87109i	0.205908	+	0.356643i	−0.744514	+	0.667607i	$0.767319\pi$
$272$		0			0
$273$	1.41027	−	1.27745i	0.0853535	−	0.0773145i
$274$		0			0
$275$	5.68429	−	2.06891i	0.342776	−	0.124760i
$276$		0			0
$277$	−0.369187	−	2.09376i	−0.0221823	−	0.125802i	0.971706	−	0.236195i	$-0.0759003\pi$
$277$	−0.369187	−	2.09376i	−0.0221823	−	0.125802i	−0.993888	+	0.110393i	$0.964789\pi$
$278$		0			0
$279$	0.727080	+	0.230341i	0.0435292	+	0.0137902i
$280$		0			0
$281$	−0.325917	−	1.84837i	−0.0194426	−	0.110264i	0.973542	−	0.228508i	$-0.0733847\pi$
$281$	−0.325917	−	1.84837i	−0.0194426	−	0.110264i	−0.992985	+	0.118244i	$0.962274\pi$
$282$		0			0
$283$	−1.40831	+	7.98694i	−0.0837155	+	0.474774i	0.913911	+	0.405915i	$0.133047\pi$
$283$	−1.40831	+	7.98694i	−0.0837155	+	0.474774i	−0.997626	+	0.0688594i	$0.978064\pi$
$284$		0			0
$285$	−14.7823	−	8.12300i	−0.875628	−	0.481165i
$286$		0			0
$287$	−13.0672	−	7.25522i	−0.771332	−	0.428262i
$288$		0			0
$289$	−7.90254	+	13.6876i	−0.464856	+	0.805153i
$290$		0			0
$291$	18.4648	+	2.85493i	1.08243	+	0.167359i
$292$		0			0
$293$	−13.1522	−	11.0360i	−0.768361	−	0.644731i	0.171928	−	0.985110i	$-0.445000\pi$
$293$	−13.1522	−	11.0360i	−0.768361	−	0.644731i	−0.940289	+	0.340378i	$0.889445\pi$
$294$		0			0
$295$	−22.4106	−	8.15680i	−1.30480	−	0.474908i
$296$		0			0
$297$	−16.1368	+	3.91358i	−0.936349	+	0.227089i
$298$		0			0
$299$	0.0645418	+	0.366035i	0.00373255	+	0.0211683i
$300$		0			0
$301$	13.7346	−	16.9366i	0.791652	−	0.976212i
$302$		0			0
$303$	16.3935	+	2.53468i	0.941782	+	0.145613i
$304$		0			0
$305$	37.1122			2.12504
$306$		0			0
$307$	−8.82039	+	15.2774i	−0.503406	+	0.871925i	0.496586	+	0.867988i	$0.334587\pi$
$307$	−8.82039	+	15.2774i	−0.503406	+	0.871925i	−0.999992	+	0.00393774i	$0.998747\pi$
$308$		0			0
$309$	−0.0524607	−	2.48204i	−0.00298439	−	0.141199i
$310$		0			0
$311$	5.94061	−	33.6909i	0.336861	−	1.91043i	−0.0711660	−	0.997464i	$-0.522672\pi$
$311$	5.94061	−	33.6909i	0.336861	−	1.91043i	0.408027	−	0.912970i	$-0.366217\pi$
$312$		0			0
$313$	8.35516	−	7.01081i	0.472262	−	0.396275i	−0.375357	−	0.926880i	$-0.622480\pi$
$313$	8.35516	−	7.01081i	0.472262	−	0.396275i	0.847619	+	0.530606i	$0.178035\pi$
$314$		0			0
$315$	−8.26996	−	19.1276i	−0.465959	−	1.07772i
$316$		0			0
$317$	20.6558	+	7.51811i	1.16015	+	0.422259i	0.849150	−	0.528152i	$-0.177115\pi$
$317$	20.6558	+	7.51811i	1.16015	+	0.422259i	0.310997	+	0.950411i	$0.399337\pi$
$318$		0			0
$319$	−12.0023	−	10.0711i	−0.671998	−	0.563873i
$320$		0			0
$321$	2.01329	−	0.399038i	0.112371	−	0.0222721i
$322$		0			0
$323$	21.2445			1.18208
$324$		0			0
$325$	0.393011	−	0.680714i	0.0218003	−	0.0377592i
$326$		0			0
$327$	−19.6576	−	22.4462i	−1.08707	−	1.24127i
$328$		0			0
$329$	−7.96498	−	20.7929i	−0.439124	−	1.14635i
$330$		0			0
$331$	−0.777831	−	0.283107i	−0.0427535	−	0.0155610i	0.320555	−	0.947230i	$-0.396131\pi$
$331$	−0.777831	−	0.283107i	−0.0427535	−	0.0155610i	−0.363308	+	0.931669i	$0.618353\pi$
$332$		0			0
$333$	3.19339	+	2.45732i	0.174997	+	0.134660i
$334$		0			0
$335$	−7.24127	−	41.0673i	−0.395633	−	2.24374i
$336$		0			0
$337$	3.49602	−	1.27245i	0.190440	−	0.0693146i	−0.245039	−	0.969513i	$-0.578801\pi$
$337$	3.49602	−	1.27245i	0.190440	−	0.0693146i	0.435480	+	0.900198i	$0.356579\pi$
$338$		0			0
$339$	27.8743	+	15.3171i	1.51392	+	0.831913i
$340$		0			0
$341$	−0.812408			−0.0439944
$342$		0			0
$343$	−15.5535	+	10.0542i	−0.839812	+	0.542878i
$344$		0			0
$345$	4.02269	+	0.621966i	0.216574	+	0.0334855i
$346$		0			0
$347$	13.3651	−	4.86451i	0.717477	−	0.261140i	0.0426227	−	0.999091i	$-0.486429\pi$
$347$	13.3651	−	4.86451i	0.717477	−	0.261140i	0.674854	+	0.737951i	$0.264206\pi$
$348$		0			0
$349$	−30.7387	−	11.1880i	−1.64540	−	0.598878i	−0.657432	−	0.753514i	$-0.728357\pi$
$349$	−30.7387	−	11.1880i	−1.64540	−	0.598878i	−0.987971	+	0.154636i	$0.950579\pi$
$350$		0			0
$351$	−1.27937	+	1.73736i	−0.0682880	+	0.0927336i
$352$		0			0
$353$	−10.1343	+	8.50366i	−0.539393	+	0.452604i	−0.871330	−	0.490697i	$-0.836742\pi$
$353$	−10.1343	+	8.50366i	−0.539393	+	0.452604i	0.331938	+	0.943301i	$0.392298\pi$
$354$		0			0
$355$	0.893875	−	5.06942i	0.0474419	−	0.269057i
$356$		0			0
$357$	20.7310	+	16.0976i	1.09720	+	0.851974i
$358$		0			0
$359$	0.764398	−	1.32398i	0.0403434	−	0.0698768i	−0.845149	−	0.534531i	$-0.820488\pi$
$359$	0.764398	−	1.32398i	0.0403434	−	0.0698768i	0.885492	+	0.464655i	$0.153821\pi$
$360$		0			0
$361$	2.62104	+	4.53977i	0.137949	+	0.238935i
$362$		0			0
$363$	−1.16804	+	0.707689i	−0.0613060	+	0.0371440i
$364$		0			0
$365$	−23.6993	+	8.62585i	−1.24048	+	0.451497i
$366$		0			0
$367$	25.6333	+	9.32977i	1.33805	+	0.487010i	0.909198	−	0.416365i	$-0.136696\pi$
$367$	25.6333	+	9.32977i	1.33805	+	0.487010i	0.428852	+	0.903375i	$0.358918\pi$
$368$		0			0
$369$	16.1561	+	5.11829i	0.841052	+	0.266447i
$370$		0			0
$371$	−1.34514	+	0.260493i	−0.0698363	+	0.0135241i
$372$		0			0
$373$	22.7640	−	8.28544i	1.17868	−	0.429004i	0.322943	−	0.946418i	$-0.395328\pi$
$373$	22.7640	−	8.28544i	1.17868	−	0.429004i	0.855735	+	0.517415i	$0.173106\pi$
$374$		0			0
$375$	9.30857	+	10.6290i	0.480692	+	0.548881i
$376$		0			0
$377$	−2.03588			−0.104853
$378$		0			0
$379$	12.8522			0.660174			0.330087	−	0.943951i	$-0.392922\pi$
$379$	12.8522			0.660174			0.330087	+	0.943951i	$0.392922\pi$
$380$		0			0
$381$	1.54901	−	0.307017i	0.0793584	−	0.0157290i
$382$		0			0
$383$	32.0235	−	11.6556i	1.63632	−	0.595573i	0.649934	−	0.759991i	$-0.274797\pi$
$383$	32.0235	−	11.6556i	1.63632	−	0.595573i	0.986391	+	0.164418i	$0.0525745\pi$
$384$		0			0
$385$	14.5509	+	16.7626i	0.741584	+	0.854301i
$386$		0			0
$387$	−11.4469	+	21.9161i	−0.581878	+	1.11406i
$388$		0			0
$389$	−17.7196	−	6.44941i	−0.898419	−	0.326998i	−0.148800	−	0.988867i	$-0.547541\pi$
$389$	−17.7196	−	6.44941i	−0.898419	−	0.326998i	−0.749619	+	0.661869i	$0.769763\pi$
$390$		0			0
$391$	−4.81769	+	1.75349i	−0.243641	+	0.0886780i
$392$		0			0
$393$	13.0556	+	7.17416i	0.658568	+	0.361889i
$394$		0			0
$395$	7.29779	+	12.6401i	0.367192	+	0.635995i
$396$		0			0
$397$	19.5129	−	33.7973i	0.979324	−	1.69624i	0.314467	−	0.949268i	$-0.398174\pi$
$397$	19.5129	−	33.7973i	0.979324	−	1.69624i	0.664857	−	0.746971i	$-0.268493\pi$
$398$		0			0
$399$	2.31543	−	16.8391i	0.115916	−	0.843009i
$400$		0			0
$401$	−3.45766	+	19.6093i	−0.172667	+	0.979244i	0.768135	+	0.640288i	$0.221185\pi$
$401$	−3.45766	+	19.6093i	−0.172667	+	0.979244i	−0.940802	+	0.338956i	$0.889926\pi$
$402$		0			0
$403$	−0.0808671	+	0.0678556i	−0.00402828	+	0.00338013i
$404$		0			0
$405$	13.5001	+	19.3928i	0.670824	+	0.963634i
$406$		0			0
$407$	−4.03322	−	1.46797i	−0.199919	−	0.0727646i
$408$		0			0
$409$	30.5507	−	11.1196i	1.51064	−	0.549826i	0.551847	−	0.833946i	$-0.313923\pi$
$409$	30.5507	−	11.1196i	1.51064	−	0.549826i	0.958789	+	0.284119i	$0.0917011\pi$
$410$		0			0
$411$	10.4982	+	27.0507i	0.517836	+	1.33431i
$412$		0			0
$413$	−0.402630	−	24.0300i	−0.0198121	−	1.18244i
$414$		0			0
$415$	−31.9642			−1.56906
$416$		0			0
$417$	−9.71015	+	5.88318i	−0.475508	+	0.288101i
$418$		0			0
$419$	13.3228	−	4.84909i	0.650860	−	0.236894i	0.00457461	−	0.999990i	$-0.498544\pi$
$419$	13.3228	−	4.84909i	0.650860	−	0.236894i	0.646285	+	0.763096i	$0.276322\pi$
$420$		0			0
$421$	−2.90098	−	16.4522i	−0.141385	−	0.801833i	−0.970199	−	0.242309i	$-0.922095\pi$
$421$	−2.90098	−	16.4522i	−0.141385	−	0.801833i	0.828814	−	0.559524i	$-0.189016\pi$
$422$		0			0
$423$	13.5364	+	21.3121i	0.658162	+	1.03623i
$424$		0			0
$425$	10.1883	+	3.70824i	0.494205	+	0.179876i
$426$		0			0
$427$	13.3782	+	34.9245i	0.647419	+	1.69012i
$428$		0			0
$429$	0.740231	−	2.17576i	0.0357387	−	0.105047i
$430$		0			0
$431$	16.2908	−	28.2165i	0.784700	−	1.35914i	−0.144477	−	0.989508i	$-0.546150\pi$
$431$	16.2908	−	28.2165i	0.784700	−	1.35914i	0.929178	−	0.369633i	$-0.120517\pi$
$432$		0			0
$433$	−29.9161			−1.43768			−0.718838	−	0.695177i	$-0.755326\pi$
$433$	−29.9161			−1.43768			−0.718838	+	0.695177i	$0.755326\pi$
$434$		0			0
$435$	−7.18127	+	21.1079i	−0.344315	+	1.01205i
$436$		0			0
$437$	2.54339	+	2.13416i	0.121667	+	0.102091i
$438$		0			0
$439$	9.44991	+	3.43949i	0.451020	+	0.164158i	0.557535	−	0.830153i	$-0.311747\pi$
$439$	9.44991	+	3.43949i	0.451020	+	0.164158i	−0.106516	+	0.994311i	$0.533969\pi$
$440$		0			0
$441$	15.0189	−	14.6776i	0.715187	−	0.698933i
$442$		0			0
$443$	−4.43538	+	3.72173i	−0.210731	+	0.176825i	−0.742044	−	0.670351i	$-0.766143\pi$
$443$	−4.43538	+	3.72173i	−0.210731	+	0.176825i	0.531313	+	0.847176i	$0.321699\pi$
$444$		0			0
$445$	3.32374	−	18.8499i	0.157560	−	0.893569i
$446$		0			0
$447$	−16.6929	+	10.1139i	−0.789548	+	0.478371i
$448$		0			0
$449$	5.79529	−	10.0377i	0.273496	−	0.473710i	−0.696258	−	0.717791i	$-0.745153\pi$
$449$	5.79529	−	10.0377i	0.273496	−	0.473710i	0.969755	+	0.244082i	$0.0784865\pi$
$450$		0			0
$451$	−18.0521			−0.850040
$452$		0			0
$453$	5.97041	−	7.42856i	0.280514	−	0.349024i
$454$		0			0
$455$	2.84848	+	0.453197i	0.133539	+	0.0212462i
$456$		0			0
$457$	−1.67961	−	9.52554i	−0.0785688	−	0.445586i	−0.998560	−	0.0536469i	$-0.982915\pi$
$457$	−1.67961	−	9.52554i	−0.0785688	−	0.445586i	0.919991	−	0.391939i	$-0.128196\pi$
$458$		0			0
$459$	−26.6651	−	13.2178i	−1.24462	−	0.616955i
$460$		0			0
$461$	−9.54990	−	3.47588i	−0.444783	−	0.161888i	0.109912	−	0.993941i	$-0.464943\pi$
$461$	−9.54990	−	3.47588i	−0.444783	−	0.161888i	−0.554695	+	0.832053i	$0.687165\pi$
$462$		0			0
$463$	−5.50110	−	4.61597i	−0.255658	−	0.214522i	0.505946	−	0.862565i	$-0.331143\pi$
$463$	−5.50110	−	4.61597i	−0.255658	−	0.214522i	−0.761604	+	0.648043i	$0.775588\pi$
$464$		0			0
$465$	0.418276	+	1.07778i	0.0193971	+	0.0499806i
$466$		0			0
$467$	−15.5922	+	27.0065i	−0.721520	+	1.24971i	0.238870	+	0.971052i	$0.423223\pi$
$467$	−15.5922	+	27.0065i	−0.721520	+	1.24971i	−0.960390	+	0.278658i	$0.910110\pi$
$468$		0			0
$469$	36.0361	−	21.6184i	1.66399	−	0.998244i
$470$		0			0
$471$	11.6560	−	7.06215i	0.537081	−	0.325407i
$472$		0			0
$473$	4.57338	−	25.9369i	0.210284	−	1.19258i
$474$		0			0
$475$	−1.21925	−	6.91470i	−0.0559430	−	0.317268i
$476$		0			0
$477$	1.43614	−	0.592568i	0.0657562	−	0.0271318i
$478$		0			0
$479$	−2.08210	−	11.8082i	−0.0951335	−	0.539529i	−0.994706	−	0.102758i	$-0.967233\pi$
$479$	−2.08210	−	11.8082i	−0.0951335	−	0.539529i	0.899573	−	0.436771i	$-0.143878\pi$
$480$		0			0
$481$	−0.524077	+	0.190749i	−0.0238959	+	0.00869738i
$482$		0			0
$483$	0.864800	+	4.00977i	0.0393497	+	0.182451i
$484$		0			0
$485$	14.1608	+	24.5272i	0.643008	+	1.11372i
$486$		0			0
$487$	1.62021	−	2.80628i	0.0734187	−	0.127165i	−0.826979	−	0.562233i	$-0.809942\pi$
$487$	1.62021	−	2.80628i	0.0734187	−	0.127165i	0.900398	+	0.435068i	$0.143276\pi$
$488$		0			0
$489$	27.1847	−	5.38806i	1.22934	−	0.243656i
$490$		0			0
$491$	6.76320	−	38.3560i	0.305219	−	1.73098i	−0.317254	−	0.948341i	$-0.602761\pi$
$491$	6.76320	−	38.3560i	0.305219	−	1.73098i	0.622473	−	0.782642i	$-0.286128\pi$
$492$		0			0
$493$	−4.87646	−	27.6558i	−0.219625	−	1.24555i
$494$		0			0
$495$	−19.9471	−	15.3493i	−0.896556	−	0.689902i
$496$		0			0
$497$	5.09281	−	0.986245i	0.228444	−	0.0442392i
$498$		0			0
$499$	−32.1539	−	26.9803i	−1.43941	−	1.20780i	−0.939880	−	0.341505i	$-0.889063\pi$
$499$	−32.1539	−	26.9803i	−1.43941	−	1.20780i	−0.499526	−	0.866299i	$-0.666492\pi$
$500$		0			0
$501$	−25.6568	−	14.0986i	−1.14626	−	0.629879i
$502$		0			0
$503$	13.6439	−	23.6319i	0.608352	−	1.05370i	−0.383161	−	0.923682i	$-0.625164\pi$
$503$	13.6439	−	23.6319i	0.608352	−	1.05370i	0.991512	−	0.130014i	$-0.0415023\pi$
$504$		0			0
$505$	12.5723	+	21.7758i	0.559460	+	0.969013i
$506$		0			0
$507$	8.03850	+	20.7129i	0.357002	+	0.919891i
$508$		0			0
$509$	−6.32944	+	35.8960i	−0.280548	+	1.59106i	0.440222	+	0.897889i	$0.354900\pi$
$509$	−6.32944	+	35.8960i	−0.280548	+	1.59106i	−0.720769	+	0.693175i	$0.756211\pi$
$510$		0			0
$511$	−16.6605	−	19.1928i	−0.737018	−	0.849041i
$512$		0			0
$513$	1.22109	+	19.2347i	0.0539126	+	0.849232i
$514$		0			0
$515$	2.88272	−	2.41889i	0.127028	−	0.106589i
$516$		0			0
$517$	−20.6015	−	17.2867i	−0.906051	−	0.760267i
$518$		0			0
$519$	5.30331	+	13.6651i	0.232789	+	0.599831i
$520$		0			0
$521$	−2.90849			−0.127423			−0.0637115	−	0.997968i	$-0.520294\pi$
$521$	−2.90849			−0.127423			−0.0637115	+	0.997968i	$0.520294\pi$
$522$		0			0
$523$	10.6606			0.466154			0.233077	−	0.972458i	$-0.425121\pi$
$523$	10.6606			0.466154			0.233077	+	0.972458i	$0.425121\pi$
$524$		0			0
$525$	4.04969	−	7.67142i	0.176743	−	0.334808i
$526$		0			0
$527$	−1.11546	−	0.935982i	−0.0485902	−	0.0407720i
$528$		0			0
$529$	20.8600	+	7.59242i	0.906957	+	0.330105i
$530$		0			0
$531$	5.86186	+	26.6133i	0.254383	+	1.15492i
$532$		0			0
$533$	−1.79691	+	1.50778i	−0.0778326	+	0.0653093i
$534$		0			0
$535$	2.38325	+	1.99979i	0.103037	+	0.0864583i
$536$		0			0
$537$	32.8037	−	6.50176i	1.41559	−	0.280572i
$538$		0			0
$539$	−10.5291	+	19.7358i	−0.453522	+	0.850080i
$540$		0			0
$541$	−13.9070	−	24.0877i	−0.597909	−	1.03561i	−0.993129	−	0.117023i	$-0.962665\pi$
$541$	−13.9070	−	24.0877i	−0.597909	−	1.03561i	0.395220	−	0.918587i	$-0.370668\pi$
$542$		0			0
$543$	−31.7931	+	6.30145i	−1.36437	+	0.270421i
$544$		0			0
$545$	7.85361	−	44.5400i	0.336412	−	1.90789i
$546$		0			0
$547$	−18.4284	+	15.4633i	−0.787943	+	0.661163i	−0.945236	−	0.326389i	$-0.894168\pi$
$547$	−18.4284	+	15.4633i	−0.787943	+	0.661163i	0.157292	+	0.987552i	$0.449724\pi$
$548$		0			0
$549$	−22.7362	−	35.7966i	−0.970356	−	1.52776i
$550$		0			0
$551$	−13.9314	+	11.6898i	−0.593497	+	0.498003i
$552$		0			0
$553$	−9.26432	+	11.4241i	−0.393959	+	0.485804i
$554$		0			0
$555$	0.129066	+	6.10644i	0.00547856	+	0.259204i
$556$		0			0
$557$	14.4761	+	25.0734i	0.613374	+	1.06240i	0.990667	+	0.136301i	$0.0435215\pi$
$557$	14.4761	+	25.0734i	0.613374	+	1.06240i	−0.377293	+	0.926094i	$0.623145\pi$
$558$		0			0
$559$	−1.71112	−	2.96375i	−0.0723727	−	0.125353i
$560$		0			0
$561$	31.3290	+	4.84392i	1.32271	+	0.204510i
$562$		0			0
$563$	−25.2541	+	9.19175i	−1.06433	+	0.387386i	−0.814055	−	0.580788i	$-0.802745\pi$
$563$	−25.2541	+	9.19175i	−1.06433	+	0.387386i	−0.250279	+	0.968174i	$0.580522\pi$
$564$		0			0
$565$	8.37173	+	47.4784i	0.352201	+	1.99743i
$566$		0			0
$567$	−13.3831	+	19.6950i	−0.562037	+	0.827112i
$568$		0			0
$569$	−4.19761	−	23.8058i	−0.175973	−	0.997992i	−0.937015	−	0.349289i	$-0.886423\pi$
$569$	−4.19761	−	23.8058i	−0.175973	−	0.997992i	0.761042	−	0.648702i	$-0.224688\pi$
$570$		0			0
$571$	−42.3904	+	15.4289i	−1.77398	+	0.645678i	−0.774064	+	0.633107i	$0.781779\pi$
$571$	−42.3904	+	15.4289i	−1.77398	+	0.645678i	−0.999921	+	0.0125703i	$0.995999\pi$
$572$		0			0
$573$	24.0424	+	3.71731i	1.00439	+	0.155293i
$574$		0			0
$575$	0.847223	+	1.46743i	0.0353316	+	0.0611962i
$576$		0			0
$577$	−15.7885	−	27.3465i	−0.657283	−	1.13845i	−0.981316	−	0.192402i	$-0.938372\pi$
$577$	−15.7885	−	27.3465i	−0.657283	−	1.13845i	0.324033	−	0.946046i	$-0.394961\pi$
$578$		0			0
$579$	−0.926228	−	43.8221i	−0.0384927	−	1.82118i
$580$		0			0
$581$	−11.5225	−	30.0800i	−0.478033	−	1.24793i
$582$		0			0
$583$	−1.26769	+	1.06372i	−0.0525023	+	0.0440547i
$584$		0			0
$585$	−3.26757	+	0.138189i	−0.135098	+	0.00571342i
$586$		0			0
$587$	−29.5451	+	24.7913i	−1.21946	+	1.02325i	−0.220606	+	0.975363i	$0.570803\pi$
$587$	−29.5451	+	24.7913i	−1.21946	+	1.02325i	−0.998853	+	0.0478842i	$0.984752\pi$
$588$		0			0
$589$	−0.163748	+	0.928661i	−0.00674712	+	0.0382648i
$590$		0			0
$591$	24.3762	−	4.83141i	1.00270	−	0.198738i
$592$		0			0
$593$	−9.22056	−	15.9705i	−0.378643	−	0.655829i	0.612222	−	0.790686i	$-0.290276\pi$
$593$	−9.22056	−	15.9705i	−0.378643	−	0.655829i	−0.990865	+	0.134857i	$0.956943\pi$
$594$		0			0
$595$	0.666524	+	39.7798i	0.0273248	+	1.63081i
$596$		0			0
$597$	−30.2323	+	5.99209i	−1.23732	+	0.245240i
$598$		0			0
$599$	9.43063	+	7.91324i	0.385325	+	0.323326i	0.814789	−	0.579758i	$-0.196853\pi$
$599$	9.43063	+	7.91324i	0.385325	+	0.323326i	−0.429464	+	0.903084i	$0.641297\pi$
$600$		0			0
$601$	−19.6100	+	16.4548i	−0.799910	+	0.671204i	−0.948177	−	0.317743i	$-0.897075\pi$
$601$	−19.6100	+	16.4548i	−0.799910	+	0.671204i	0.148267	+	0.988947i	$0.452630\pi$
$602$		0			0
$603$	−35.1752	+	32.1437i	−1.43244	+	1.30899i
$604$		0			0
$605$	−1.94529	−	0.708026i	−0.0790871	−	0.0287853i
$606$		0			0
$607$	−18.3970	−	15.4369i	−0.746712	−	0.626566i	0.187919	−	0.982184i	$-0.439826\pi$
$607$	−18.3970	−	15.4369i	−0.746712	−	0.626566i	−0.934631	+	0.355619i	$0.884270\pi$
$608$		0			0
$609$	−22.4524	+	0.851054i	−0.909816	+	0.0344864i
$610$		0			0
$611$	−3.49452			−0.141373
$612$		0			0
$613$	−13.6138			−0.549857			−0.274928	−	0.961465i	$-0.588654\pi$
$613$	−13.6138			−0.549857			−0.274928	+	0.961465i	$0.588654\pi$
$614$		0			0
$615$	9.29429	+	23.9487i	0.374782	+	0.965704i
$616$		0			0
$617$	22.9958	+	19.2957i	0.925774	+	0.776817i	0.975054	−	0.221968i	$-0.0712481\pi$
$617$	22.9958	+	19.2957i	0.925774	+	0.776817i	−0.0492797	+	0.998785i	$0.515693\pi$
$618$		0			0
$619$	−26.7327	+	22.4314i	−1.07448	+	0.901593i	−0.995451	−	0.0952791i	$-0.969626\pi$
$619$	−26.7327	+	22.4314i	−1.07448	+	0.901593i	−0.0790266	+	0.996873i	$0.525181\pi$
$620$		0			0
$621$	−1.86452	−	4.26112i	−0.0748204	−	0.170993i
$622$		0			0
$623$	18.9369	−	3.66721i	0.758689	−	0.146924i
$624$		0			0
$625$	−5.36252	+	30.4124i	−0.214501	+	1.21649i
$626$		0			0
$627$	−7.42765	−	19.1389i	−0.296632	−	0.764334i
$628$		0			0
$629$	−3.84646	−	6.66227i	−0.153368	−	0.265642i
$630$		0			0
$631$	21.3274	−	36.9402i	0.849032	−	1.47057i	−0.0330420	−	0.999454i	$-0.510520\pi$
$631$	21.3274	−	36.9402i	0.849032	−	1.47057i	0.882074	−	0.471112i	$-0.156147\pi$
$632$		0			0
$633$	−22.7545	−	12.5038i	−0.904410	−	0.496981i
$634$		0			0
$635$	1.83366	+	1.53862i	0.0727666	+	0.0610585i
$636$		0			0
$637$	0.600340	+	2.84394i	0.0237863	+	0.112681i
$638$		0			0
$639$	−5.43732	+	2.24351i	−0.215097	+	0.0887518i
$640$		0			0
$641$	1.81413	+	10.2885i	0.0716539	+	0.406369i	0.999446	+	0.0332726i	$0.0105929\pi$
$641$	1.81413	+	10.2885i	0.0716539	+	0.406369i	−0.927792	+	0.373097i	$0.878296\pi$
$642$		0			0
$643$	−6.88702	+	39.0582i	−0.271598	+	1.54031i	0.477968	+	0.878377i	$0.341373\pi$
$643$	−6.88702	+	39.0582i	−0.271598	+	1.54031i	−0.749566	+	0.661930i	$0.769738\pi$
$644$		0			0
$645$	−36.7637	+	7.28662i	−1.44757	+	0.286910i
$646$		0			0
$647$	−2.42155	+	4.19426i	−0.0952011	+	0.164893i	−0.909693	−	0.415282i	$-0.863683\pi$
$647$	−2.42155	+	4.19426i	−0.0952011	+	0.164893i	0.814491	+	0.580176i	$0.197016\pi$
$648$		0			0
$649$	−14.5138	−	25.1386i	−0.569715	−	0.986775i
$650$		0			0
$651$	−0.863463	+	0.782137i	−0.0338418	+	0.0306544i
$652$		0			0
$653$	27.3286	−	9.94681i	1.06945	−	0.389249i	0.253480	−	0.967341i	$-0.418425\pi$
$653$	27.3286	−	9.94681i	1.06945	−	0.389249i	0.815972	+	0.578092i	$0.196203\pi$
$654$		0			0
$655$	3.92111	+	22.2377i	0.153210	+	0.868899i
$656$		0			0
$657$	22.8391	+	17.5747i	0.891036	+	0.685654i
$658$		0			0
$659$	−5.05141	−	28.6480i	−0.196775	−	1.11597i	−0.909868	−	0.414898i	$-0.863817\pi$
$659$	−5.05141	−	28.6480i	−0.196775	−	1.11597i	0.713093	−	0.701070i	$-0.247294\pi$
$660$		0			0
$661$	−4.37430	+	24.8079i	−0.170141	+	0.964915i	0.773464	+	0.633840i	$0.218522\pi$
$661$	−4.37430	+	24.8079i	−0.170141	+	0.964915i	−0.943604	+	0.331075i	$0.892589\pi$
$662$		0			0
$663$	3.52307	−	2.13456i	0.136825	−	0.0828993i
$664$		0			0
$665$	22.0941	−	13.2545i	0.856774	−	0.513986i
$666$		0			0
$667$	2.19440	−	3.80082i	0.0849676	−	0.147168i
$668$		0			0
$669$	8.84559	+	22.7925i	0.341990	+	0.881209i
$670$		0			0
$671$	34.6029	+	29.0353i	1.33583	+	1.12089i
$672$		0			0
$673$	38.6067	+	14.0517i	1.48818	+	0.541652i	0.952969	−	0.303067i	$-0.0980108\pi$
$673$	38.6067	+	14.0517i	1.48818	+	0.541652i	0.535209	+	0.844720i	$0.320233\pi$
$674$		0			0
$675$	−2.77182	+	9.43758i	−0.106687	+	0.363253i
$676$		0			0
$677$	4.86999	+	27.6191i	0.187169	+	1.06149i	0.923137	+	0.384471i	$0.125616\pi$
$677$	4.86999	+	27.6191i	0.187169	+	1.06149i	−0.735968	+	0.677016i	$0.763273\pi$
$678$		0			0
$679$	−17.9767	+	22.1676i	−0.689882	+	0.850715i
$680$		0			0
$681$	14.4998	−	18.0411i	0.555634	−	0.691337i
$682$		0			0
$683$	36.2993			1.38896			0.694478	−	0.719514i	$-0.255636\pi$
$683$	36.2993			1.38896			0.694478	+	0.719514i	$0.255636\pi$
$684$		0			0
$685$	−21.9916	+	38.0906i	−0.840256	+	1.45537i
$686$		0			0
$687$	15.2692	−	9.25131i	0.582557	−	0.352960i
$688$		0			0
$689$	−0.0373398	+	0.211765i	−0.00142253	+	0.00806759i
$690$		0			0
$691$	−12.7131	+	10.6676i	−0.483629	+	0.405813i	−0.851737	−	0.523970i	$-0.824450\pi$
$691$	−12.7131	+	10.6676i	−0.483629	+	0.405813i	0.368107	+	0.929783i	$0.380006\pi$
$692$		0			0
$693$	7.25397	−	24.3044i	0.275556	−	0.923249i
$694$		0			0
$695$	−16.1716	−	5.88598i	−0.613424	−	0.223268i
$696$		0			0
$697$	−24.7860	−	20.7980i	−0.938839	−	0.787779i
$698$		0			0
$699$	0.0580066	−	0.170499i	0.00219401	−	0.00644886i
$700$		0			0
$701$	4.04117			0.152633			0.0763164	−	0.997084i	$-0.475684\pi$
$701$	4.04117			0.152633			0.0763164	+	0.997084i	$0.475684\pi$
$702$		0			0
$703$	−2.49096	+	4.31447i	−0.0939485	+	0.162724i
$704$		0			0
$705$	−12.3264	+	36.2310i	−0.464239	+	1.36454i
$706$		0			0
$707$	−15.9601	+	19.6810i	−0.600243	+	0.740179i
$708$		0			0
$709$	19.2649	+	7.01186i	0.723509	+	0.263336i	0.677415	−	0.735601i	$-0.263100\pi$
$709$	19.2649	+	7.01186i	0.723509	+	0.263336i	0.0460946	+	0.998937i	$0.485322\pi$
$710$		0			0
$711$	7.72118	−	14.7829i	0.289567	−	0.554400i
$712$		0			0
$713$	−0.0395168	−	0.224111i	−0.00147992	−	0.00839302i
$714$		0			0
$715$	3.27358	−	1.19149i	0.122425	−	0.0445590i
$716$		0			0
$717$	5.85085	−	3.54491i	0.218504	−	0.132387i
$718$		0			0
$719$	−9.77344			−0.364488			−0.182244	−	0.983253i	$-0.558336\pi$
$719$	−9.77344			−0.364488			−0.182244	+	0.983253i	$0.558336\pi$
$720$		0			0
$721$	3.31547	+	1.84083i	0.123475	+	0.0685561i
$722$		0			0
$723$	6.79180	+	17.5005i	0.252590	+	0.650851i
$724$		0			0
$725$	−8.72159	+	3.17440i	−0.323912	+	0.117894i
$726$		0			0
$727$	12.6552	+	4.60612i	0.469356	+	0.170831i	0.565860	−	0.824501i	$-0.308544\pi$
$727$	12.6552	+	4.60612i	0.469356	+	0.170831i	−0.0965048	+	0.995333i	$0.530766\pi$
$728$		0			0
$729$	10.4347	−	24.9022i	0.386470	−	0.922302i
$730$		0			0
$731$	36.1615	−	30.3431i	1.33748	−	1.12228i
$732$		0			0
$733$	1.75797	−	9.96996i	0.0649322	−	0.368249i	−0.934976	−	0.354711i	$-0.884579\pi$
$733$	1.75797	−	9.96996i	0.0649322	−	0.368249i	0.999908	−	0.0135383i	$-0.00430952\pi$
$734$		0			0
$735$	31.6034	+	3.80726i	1.16571	+	0.140433i
$736$		0			0
$737$	25.3779	−	43.9558i	0.934807	−	1.61913i
$738$		0			0
$739$	−0.529716	−	0.917494i	−0.0194859	−	0.0337506i	0.856118	−	0.516780i	$-0.172870\pi$
$739$	−0.529716	−	0.917494i	−0.0194859	−	0.0337506i	−0.875604	+	0.483030i	$0.839536\pi$
$740$		0			0
$741$	−2.33791	−	1.28470i	−0.0858851	−	0.0471946i
$742$		0			0
$743$	−44.2613	+	16.1098i	−1.62379	+	0.591011i	−0.984099	−	0.177622i	$-0.943159\pi$
$743$	−44.2613	+	16.1098i	−1.62379	+	0.591011i	−0.639690	+	0.768633i	$0.720937\pi$
$744$		0			0
$745$	−27.8009	−	10.1187i	−1.01855	−	0.370721i
$746$		0			0
$747$	19.5823	+	30.8310i	0.716480	+	1.12805i
$748$		0			0
$749$	−1.02279	+	2.96365i	−0.0373718	+	0.108289i
$750$		0			0
$751$	−13.6532	+	4.96935i	−0.498212	+	0.181334i	−0.578890	−	0.815406i	$-0.696514\pi$
$751$	−13.6532	+	4.96935i	−0.498212	+	0.181334i	0.0806777	+	0.996740i	$0.474292\pi$
$752$		0			0
$753$	−14.3579	+	2.84577i	−0.523232	+	0.103705i
$754$		0			0
$755$	14.4463			0.525754
$756$		0			0
$757$	6.18709			0.224874			0.112437	−	0.993659i	$-0.464134\pi$
$757$	6.18709			0.224874			0.112437	+	0.993659i	$0.464134\pi$
$758$		0			0
$759$	3.26409	+	3.72712i	0.118479	+	0.135286i
$760$		0			0
$761$	−26.2780	+	9.56442i	−0.952578	+	0.346710i	−0.771121	−	0.636689i	$-0.780304\pi$
$761$	−26.2780	+	9.56442i	−0.952578	+	0.346710i	−0.181457	+	0.983399i	$0.558081\pi$
$762$		0			0
$763$	44.7456	−	8.66518i	1.61990	−	0.313701i
$764$		0			0
$765$	−9.70387	−	44.0563i	−0.350844	−	1.59286i
$766$		0			0
$767$	−3.54437	−	1.29005i	−0.127980	−	0.0465809i
$768$		0			0
$769$	5.14416	−	1.87232i	0.185503	−	0.0675176i	−0.247598	−	0.968863i	$-0.579641\pi$
$769$	5.14416	−	1.87232i	0.185503	−	0.0675176i	0.433102	+	0.901345i	$0.357419\pi$
$770$		0			0
$771$	−14.5596	+	8.82134i	−0.524349	+	0.317693i
$772$		0			0
$773$	−13.9664	−	24.1905i	−0.502336	−	0.870072i	−0.999996	−	0.00269986i	$-0.999141\pi$
$773$	−13.9664	−	24.1905i	−0.502336	−	0.870072i	0.497660	−	0.867372i	$-0.334193\pi$
$774$		0			0
$775$	−0.240627	+	0.416779i	−0.00864359	+	0.0149711i
$776$		0			0
$777$	−5.69995	+	2.32271i	−0.204485	+	0.0833269i
$778$		0			0
$779$	−3.63856	+	20.6353i	−0.130365	+	0.739336i
$780$		0			0
$781$	4.79957	−	4.02731i	0.171742	−	0.144109i
$782$		0			0
$783$	24.7591	−	6.00472i	0.884819	−	0.214591i
$784$		0			0
$785$	19.4123	+	7.06551i	0.692856	+	0.252179i
$786$		0			0
$787$	18.8883	−	6.87476i	0.673294	−	0.245059i	0.0173283	−	0.999850i	$-0.494484\pi$
$787$	18.8883	−	6.87476i	0.673294	−	0.245059i	0.655965	+	0.754791i	$0.272262\pi$
$788$		0			0
$789$	20.6455	+	3.19210i	0.734999	+	0.113642i
$790$		0			0
$791$	−41.6619	+	24.9933i	−1.48133	+	0.888660i
$792$		0			0
$793$	5.86951			0.208432
$794$		0			0
$795$	2.06385	+	1.13411i	0.0731973	+	0.0402226i
$796$		0			0
$797$	4.76658	−	1.73489i	0.168841	−	0.0614530i	−0.256217	−	0.966619i	$-0.582476\pi$
$797$	4.76658	−	1.73489i	0.168841	−	0.0614530i	0.425058	+	0.905166i	$0.360254\pi$
$798$		0			0
$799$	−8.37027	−	47.4702i	−0.296119	−	1.67937i
$800$		0			0
$801$	−20.2179	+	8.34215i	−0.714363	+	0.294755i
$802$		0			0
$803$	−28.8455	−	10.4989i	−1.01793	−	0.370498i
$804$		0			0
$805$	−3.91635	+	4.82938i	−0.138033	+	0.170213i
$806$		0			0
$807$	8.46065	+	9.66084i	0.297829	+	0.340078i
$808$		0			0
$809$	3.03665	−	5.25964i	0.106763	−	0.184919i	−0.807694	−	0.589602i	$-0.799285\pi$
$809$	3.03665	−	5.25964i	0.106763	−	0.184919i	0.914457	+	0.404683i	$0.132618\pi$
$810$		0			0
$811$	−50.6545			−1.77872			−0.889360	−	0.457208i	$-0.848849\pi$
$811$	−50.6545			−1.77872			−0.889360	+	0.457208i	$0.848849\pi$
$812$		0			0
$813$	11.5181	−	2.28291i	0.403958	−	0.0800652i
$814$		0			0
$815$	32.1802	+	27.0024i	1.12722	+	0.945852i
$816$		0			0
$817$	−28.7266	−	10.4556i	−1.00502	−	0.365796i
$818$		0			0
$819$	−1.30794	−	3.02514i	−0.0457032	−	0.105707i
$820$		0			0
$821$	23.9994	−	20.1379i	0.837585	−	0.702817i	−0.119434	−	0.992842i	$-0.538108\pi$
$821$	23.9994	−	20.1379i	0.837585	−	0.702817i	0.957019	+	0.290025i	$0.0936636\pi$
$822$		0			0
$823$	7.92695	−	44.9560i	0.276316	−	1.56707i	−0.458434	−	0.888728i	$-0.651590\pi$
$823$	7.92695	−	44.9560i	0.276316	−	1.56707i	0.734750	−	0.678338i	$-0.237299\pi$
$824$		0			0
$825$	−0.221401	−	10.4750i	−0.00770819	−	0.364693i
$826$		0			0
$827$	−6.21353	+	10.7622i	−0.216066	+	0.374237i	−0.953602	−	0.301071i	$-0.902656\pi$
$827$	−6.21353	+	10.7622i	−0.216066	+	0.374237i	0.737536	+	0.675308i	$0.235989\pi$
$828$		0			0
$829$	34.9368			1.21341			0.606703	−	0.794928i	$-0.292492\pi$
$829$	34.9368			1.21341			0.606703	+	0.794928i	$0.292492\pi$
$830$		0			0
$831$	−3.63921	−	0.562675i	−0.126243	−	0.0195190i
$832$		0			0
$833$	−37.1946	+	14.9671i	−1.28872	+	0.518579i
$834$		0			0
$835$	−7.70573	−	43.7013i	−0.266668	−	1.51235i
$836$		0			0
$837$	0.783318	−	1.06373i	0.0270754	−	0.0367679i
$838$		0			0
$839$	0.266824	+	0.0971159i	0.00921178	+	0.00335281i	0.346622	−	0.938005i	$-0.387329\pi$
$839$	0.266824	+	0.0971159i	0.00921178	+	0.00335281i	−0.337410	+	0.941358i	$0.609551\pi$
$840$		0			0
$841$	−3.79984	−	3.18845i	−0.131029	−	0.109946i
$842$		0			0
$843$	−3.21268	−	0.496727i	−0.110651	−	0.0171082i
$844$		0			0
$845$	−16.8391	+	29.1661i	−0.579282	+	1.00335i
$846$		0			0
$847$	−0.0349491	−	2.08585i	−0.00120086	−	0.0716705i
$848$		0			0
$849$	12.3109	+	6.76496i	0.422510	+	0.232173i
$850$		0			0
$851$	0.208772	−	1.18401i	0.00715663	−	0.0405872i
$852$		0			0
$853$	6.54395	+	37.1126i	0.224061	+	1.27071i	0.864473	+	0.502679i	$0.167652\pi$
$853$	6.54395	+	37.1126i	0.224061	+	1.27071i	−0.640412	+	0.768031i	$0.721237\pi$
$854$		0			0
$855$	−21.5663	+	19.7077i	−0.737552	+	0.673989i
$856$		0			0
$857$	5.42748	+	30.7807i	0.185399	+	1.05145i	0.925442	+	0.378890i	$0.123694\pi$
$857$	5.42748	+	30.7807i	0.185399	+	1.05145i	−0.740043	+	0.672560i	$0.765195\pi$
$858$		0			0
$859$	29.6462	−	10.7903i	1.01152	−	0.368162i	0.217501	−	0.976060i	$-0.430209\pi$
$859$	29.6462	−	10.7903i	1.01152	−	0.368162i	0.794015	+	0.607898i	$0.207987\pi$
$860$		0			0
$861$	−19.1866	+	17.3795i	−0.653876	+	0.592291i
$862$		0			0
$863$	−1.88049	−	3.25711i	−0.0640127	−	0.110873i	0.832243	−	0.554411i	$-0.187056\pi$
$863$	−1.88049	−	3.25711i	−0.0640127	−	0.110873i	−0.896256	+	0.443538i	$0.853723\pi$
$864$		0			0
$865$	−11.1094	+	19.2420i	−0.377731	+	0.654249i
$866$		0			0
$867$	18.0357	+	20.5941i	0.612523	+	0.699413i
$868$		0			0
$869$	−3.08484	+	17.4950i	−0.104646	+	0.593478i
$870$		0			0
$871$	−1.14525	−	6.49503i	−0.0388053	−	0.220076i
$872$		0			0
$873$	14.9823	−	28.6850i	0.507075	−	0.970839i
$874$		0			0
$875$	−21.1886	+	4.10327i	−0.716305	+	0.138716i
$876$		0			0
$877$	34.0752	+	28.5925i	1.15064	+	0.965501i	0.999734	−	0.0230478i	$-0.00733698\pi$
$877$	34.0752	+	28.5925i	1.15064	+	0.965501i	0.150904	+	0.988548i	$0.451781\pi$
$878$		0			0
$879$	−25.4335	+	15.4097i	−0.857852	+	0.519755i
$880$		0			0
$881$	−0.846357	+	1.46593i	−0.0285145	+	0.0493886i	−0.879931	−	0.475102i	$-0.842411\pi$
$881$	−0.846357	+	1.46593i	−0.0285145	+	0.0493886i	0.851416	+	0.524491i	$0.175744\pi$
$882$		0			0
$883$	12.6797	+	21.9618i	0.426705	+	0.739075i	0.996578	−	0.0826579i	$-0.0263409\pi$
$883$	12.6797	+	21.9618i	0.426705	+	0.739075i	−0.569873	+	0.821733i	$0.693008\pi$
$884$		0			0
$885$	−25.8774	+	32.1974i	−0.869858	+	1.08230i
$886$		0			0
$887$	−7.69115	+	43.6187i	−0.258243	+	1.46457i	0.529364	+	0.848395i	$0.322430\pi$
$887$	−7.69115	+	43.6187i	−0.258243	+	1.46457i	−0.787608	+	0.616177i	$0.788681\pi$
$888$		0			0
$889$	−0.786926	+	2.28022i	−0.0263927	+	0.0764760i
$890$		0			0
$891$	−2.58493	+	28.6435i	−0.0865984	+	0.959594i
$892$		0			0
$893$	−23.9127	+	20.0652i	−0.800209	+	0.671455i
$894$		0			0
$895$	38.8318	+	32.5837i	1.29800	+	1.08915i
$896$		0			0
$897$	0.636211	+	0.0983676i	0.0212425	+	0.00328440i
$898$		0			0
$899$	1.24650			0.0415732
$900$		0			0
$901$	−2.96609			−0.0988147
$902$		0			0
$903$	−20.1097	−	31.9698i	−0.669209	−	1.06389i
$904$		0			0
$905$	−37.6354	−	31.5799i	−1.25104	−	1.04975i
$906$		0			0
$907$	19.7905	+	7.20316i	0.657133	+	0.239177i	0.648998	−	0.760790i	$-0.275188\pi$
$907$	19.7905	+	7.20316i	0.657133	+	0.239177i	0.00813501	+	0.999967i	$0.497411\pi$
$908$		0			0
$909$	13.3017	−	25.4672i	0.441189	−	0.844694i
$910$		0			0
$911$	14.2445	−	11.9526i	0.471941	−	0.396006i	−0.375561	−	0.926798i	$-0.622550\pi$
$911$	14.2445	−	11.9526i	0.471941	−	0.396006i	0.847502	+	0.530792i	$0.178105\pi$
$912$		0			0
$913$	−29.8029	−	25.0076i	−0.986333	−	0.827632i
$914$		0			0
$915$	20.7038	−	60.8547i	0.684447	−	2.01180i
$916$		0			0
$917$	−19.5134	+	11.7062i	−0.644388	+	0.386574i
$918$		0			0
$919$	−17.8536	−	30.9233i	−0.588934	−	1.02006i	−0.994372	−	0.105942i	$-0.966214\pi$
$919$	−17.8536	−	30.9233i	−0.588934	−	1.02006i	0.405438	−	0.914123i	$-0.367119\pi$
$920$		0			0
$921$	20.1304	+	22.9860i	0.663320	+	0.757415i
$922$		0			0
$923$	0.141371	−	0.801758i	0.00465330	−	0.0263902i
$924$		0			0
$925$	−1.94769	+	1.63431i	−0.0640397	+	0.0537357i
$926$		0			0
$927$	−4.09920	−	1.29864i	−0.134635	−	0.0426528i
$928$		0			0
$929$	−3.34897	+	2.81012i	−0.109876	+	0.0921971i	−0.696071	−	0.717973i	$-0.745070\pi$
$929$	−3.34897	+	2.81012i	−0.109876	+	0.0921971i	0.586194	+	0.810170i	$0.300625\pi$
$930$		0			0
$931$	20.4377	+	16.0138i	0.669817	+	0.524830i
$932$		0			0
$933$	−51.9305	−	28.5363i	−1.70013	−	0.934235i
$934$		0			0
$935$	24.0264	+	41.6150i	0.785748	+	1.36096i
$936$		0			0
$937$	20.4060	+	35.3442i	0.666635	+	1.15465i	0.978839	+	0.204630i	$0.0655992\pi$
$937$	20.4060	+	35.3442i	0.666635	+	1.15465i	−0.312205	+	0.950015i	$0.601067\pi$
$938$		0			0
$939$	−6.83488	−	17.6115i	−0.223048	−	0.574730i
$940$		0			0
$941$	4.94368	−	1.79935i	0.161159	−	0.0586572i	−0.260181	−	0.965560i	$-0.583782\pi$
$941$	4.94368	−	1.79935i	0.161159	−	0.0586572i	0.421340	+	0.906903i	$0.361560\pi$
$942$		0			0
$943$	−0.878082	−	4.97985i	−0.0285943	−	0.162166i
$944$		0			0
$945$	−35.9781	+	2.88993i	−1.17037	+	0.0940094i
$946$		0			0
$947$	−5.91581	−	33.5502i	−0.192238	−	1.09024i	−0.916297	−	0.400499i	$-0.868837\pi$
$947$	−5.91581	−	33.5502i	−0.192238	−	1.09024i	0.724059	−	0.689738i	$-0.242274\pi$
$948$		0			0
$949$	−3.74818	+	1.36423i	−0.121671	+	0.0442847i
$950$		0			0
$951$	23.8511	−	29.6763i	0.773425	−	0.962319i
$952$		0			0
$953$	−23.3597	−	40.4601i	−0.756694	−	1.31063i	−0.944528	−	0.328432i	$-0.893480\pi$
$953$	−23.3597	−	40.4601i	−0.756694	−	1.31063i	0.187834	−	0.982201i	$-0.439853\pi$
$954$		0			0
$955$	18.4383	+	31.9361i	0.596650	+	1.03343i
$956$		0			0
$957$	−23.2098	+	14.0623i	−0.750266	+	0.454571i
$958$		0			0
$959$	−43.7728	−	6.96432i	−1.41350	−	0.224889i
$960$		0			0
$961$	−23.6979	+	19.8849i	−0.764447	+	0.641447i
$962$		0			0
$963$	0.468833	−	3.52390i	0.0151079	−	0.113556i
$964$		0			0
$965$	50.8964	−	42.7071i	1.63841	−	1.37479i
$966$		0			0
$967$	−3.44027	+	19.5107i	−0.110632	+	0.627423i	0.878189	+	0.478314i	$0.158752\pi$
$967$	−3.44027	+	19.5107i	−0.110632	+	0.627423i	−0.988821	+	0.149110i	$0.952359\pi$
$968$		0			0
$969$	11.8517	−	34.8357i	0.380731	−	1.11908i
$970$		0			0
$971$	−4.92490	−	8.53018i	−0.158048	−	0.273746i	0.776117	−	0.630589i	$-0.217187\pi$
$971$	−4.92490	−	8.53018i	−0.158048	−	0.273746i	−0.934165	+	0.356843i	$0.883853\pi$
$972$		0			0
$973$	−0.290540	−	17.3401i	−0.00931427	−	0.555898i
$974$		0			0
$975$	−0.896952	−	1.02419i	−0.0287255	−	0.0328003i
$976$		0			0
$977$	18.6614	+	15.6588i	0.597031	+	0.500968i	0.890490	−	0.455003i	$-0.150362\pi$
$977$	18.6614	+	15.6588i	0.597031	+	0.500968i	−0.293459	+	0.955972i	$0.594806\pi$
$978$		0			0
$979$	17.8465	−	14.9750i	0.570376	−	0.478602i
$980$		0			0
$981$	−47.7725	+	19.7115i	−1.52526	+	0.629341i
$982$		0			0
$983$	−15.2541	−	5.55202i	−0.486529	−	0.177082i	0.0870964	−	0.996200i	$-0.472241\pi$
$983$	−15.2541	−	5.55202i	−0.486529	−	0.177082i	−0.573625	+	0.819118i	$0.694463\pi$
$984$		0			0
$985$	28.8556	+	24.2127i	0.919416	+	0.771481i
$986$		0			0
$987$	−38.5387	+	1.46080i	−1.22670	+	0.0464979i
$988$		0			0
$989$	7.37741			0.234588
$990$		0			0
$991$	35.9204			1.14105			0.570524	−	0.821281i	$-0.306740\pi$
$991$	35.9204			1.14105			0.570524	+	0.821281i	$0.306740\pi$
$992$		0			0
$993$	−0.898155	+	1.11751i	−0.0285021	+	0.0354632i
$994$		0			0
$995$	−35.7878	−	30.0295i	−1.13455	−	0.951999i
$996$		0			0
$997$	29.1303	−	24.4432i	0.922566	−	0.774125i	−0.0519015	−	0.998652i	$-0.516528\pi$
$997$	29.1303	−	24.4432i	0.922566	−	0.774125i	0.974468	+	0.224527i	$0.0720837\pi$
$998$		0			0
$999$	5.81089	−	3.86550i	0.183849	−	0.122299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.15	✓	144
7.2	even	3		756.2.bq.a.625.18	yes	144
27.7	even	9		756.2.bq.a.277.18	yes	144
189.142	even	9	inner	756.2.bp.a.709.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.15	✓	144	1.1	even	1	trivial
756.2.bp.a.709.15	yes	144	189.142	even	9	inner
756.2.bq.a.277.18	yes	144	27.7	even	9
756.2.bq.a.625.18	yes	144	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.557871 - 1.63975i) q^{3} +(2.46711 - 0.897956i) q^{5} +(1.73437 + 1.99799i) q^{7} +(-2.37756 - 1.82954i) q^{9} +O(q^{10})\)	\(q+(0.557871 - 1.63975i) q^{3} +(2.46711 - 0.897956i) q^{5} +(1.73437 + 1.99799i) q^{7} +(-2.37756 - 1.82954i) q^{9} +(3.00283 + 1.09294i) q^{11} +(0.390189 - 0.142017i) q^{13} +(-0.0960930 - 4.54639i) q^{15} +(2.86379 + 4.96022i) q^{17} +(1.85458 - 3.21223i) q^{19} +(4.24376 - 1.72932i) q^{21} +(-0.155436 + 0.881523i) q^{23} +(1.45011 - 1.21678i) q^{25} +(-4.32635 + 2.87796i) q^{27} +(-4.60734 - 1.67693i) q^{29} +(-0.238899 + 0.0869523i) q^{31} +(3.46734 - 4.31417i) q^{33} +(6.07300 + 3.37187i) q^{35} -1.34314 q^{37} +(-0.0151977 - 0.719039i) q^{39} +(-5.30846 + 1.93212i) q^{41} +(-1.43117 - 8.11658i) q^{43} +(-7.50856 - 2.37873i) q^{45} +(-7.90833 - 2.87840i) q^{47} +(-0.983909 + 6.93051i) q^{49} +(9.73115 - 1.92873i) q^{51} +(-0.258931 + 0.448481i) q^{53} +8.38974 q^{55} +(-4.23264 - 4.83307i) q^{57} +(-6.95855 - 5.83892i) q^{59} +(13.2831 + 4.83465i) q^{61} +(-0.468182 - 7.92343i) q^{63} +(0.835115 - 0.700744i) q^{65} +(2.75811 - 15.6420i) q^{67} +(1.35876 + 0.746652i) q^{69} +(0.980331 - 1.69798i) q^{71} -9.60609 q^{73} +(-1.18625 - 3.05662i) q^{75} +(3.02434 + 7.89519i) q^{77} +(0.965357 + 5.47481i) q^{79} +(2.30559 + 8.69967i) q^{81} +(-11.4405 - 4.16401i) q^{83} +(11.5194 + 9.66588i) q^{85} +(-5.32005 + 6.61937i) q^{87} +(3.64522 - 6.31370i) q^{89} +(0.960480 + 0.533281i) q^{91} +(0.00930503 + 0.440243i) q^{93} +(1.69103 - 9.59028i) q^{95} +(1.87320 + 10.6234i) q^{97} +(-5.13984 - 8.09232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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