LMFDB - Embedded newform 804.2.s.b.161.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	804.161
Dual form			804.2.s.b.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17979 + 1.26810i) q^{3} +(2.83063 + 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-0.216176 - 2.99220i) q^{9} +O(q^{10})$	\(q+(-1.17979 + 1.26810i) q^{3} +(2.83063 + 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-0.216176 - 2.99220i) q^{9} +(-3.88931 - 1.14200i) q^{11} +(-0.777890 + 1.21042i) q^{13} +(-4.39353 + 2.60895i) q^{15} +(-5.27916 + 0.759028i) q^{17} +(-0.130434 + 0.150529i) q^{19} +(0.231790 - 6.55625i) q^{21} +(0.694228 + 0.317043i) q^{23} +(3.11537 + 2.00213i) q^{25} +(4.04946 + 3.25605i) q^{27} -8.71464i q^{29} +(3.86518 + 6.01434i) q^{31} +(6.03676 - 3.58472i) q^{33} +(-10.1642 + 4.64183i) q^{35} -2.50144 q^{37} +(-0.617189 - 2.41449i) q^{39} +(-0.0416445 - 0.289644i) q^{41} +(-6.85998 + 0.986316i) q^{43} +(1.87505 - 8.64948i) q^{45} +(-6.89272 - 3.14780i) q^{47} +(1.04545 - 7.27129i) q^{49} +(5.26579 - 7.59001i) q^{51} +(-0.173569 + 1.20720i) q^{53} +(-10.0600 - 6.46518i) q^{55} +(-0.0370010 - 0.342996i) q^{57} +(0.206913 + 0.321963i) q^{59} +(3.48314 + 11.8625i) q^{61} +(8.04055 + 8.02896i) q^{63} +(-3.20795 + 2.77971i) q^{65} +(-8.15987 - 0.645356i) q^{67} +(-1.22109 + 0.506307i) q^{69} +(-0.756392 - 0.108753i) q^{71} +(-11.2432 + 3.30131i) q^{73} +(-6.21440 + 1.58852i) q^{75} +(13.9657 - 6.37792i) q^{77} +(8.00157 - 12.4507i) q^{79} +(-8.90654 + 1.29368i) q^{81} +(-3.51473 + 11.9701i) q^{83} +(-15.5742 - 2.23923i) q^{85} +(11.0511 + 10.2815i) q^{87} +(-0.0142974 + 0.00652940i) q^{89} +(-0.775578 - 5.39427i) q^{91} +(-12.1869 - 2.19423i) q^{93} +(-0.494321 + 0.317681i) q^{95} +15.9958i q^{97} +(-2.57633 + 11.8845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

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
$3$	−1.17979	+	1.26810i	−0.681154	+	0.732140i
$3$	−1.17979	+	1.26810i	−0.681154	+	0.732140i
$4$		0			0
$5$	2.83063	+	0.831147i	1.26589	+	0.371700i	0.844685	−	0.535263i	$-0.179788\pi$
$5$	2.83063	+	0.831147i	1.26589	+	0.371700i	0.421209	+	0.906964i	$0.361606\pi$
$6$		0			0
$7$	−2.86249	+	2.48036i	−1.08192	+	0.937489i	−0.998258	−	0.0590050i	$-0.981207\pi$
$7$	−2.86249	+	2.48036i	−1.08192	+	0.937489i	−0.0836625	+	0.996494i	$0.526662\pi$
$8$		0			0
$9$	−0.216176	−	2.99220i	−0.0720585	−	0.997400i
$10$		0			0
$11$	−3.88931	−	1.14200i	−1.17267	−	0.344327i	−0.363327	−	0.931662i	$-0.618359\pi$
$11$	−3.88931	−	1.14200i	−1.17267	−	0.344327i	−0.809344	+	0.587334i	$0.800177\pi$
$12$		0			0
$13$	−0.777890	+	1.21042i	−0.215748	+	0.335710i	−0.932211	−	0.361914i	$-0.882123\pi$
$13$	−0.777890	+	1.21042i	−0.215748	+	0.335710i	0.716464	+	0.697625i	$0.245760\pi$
$14$		0			0
$15$	−4.39353	+	2.60895i	−1.13441	+	0.673627i
$16$		0			0
$17$	−5.27916	+	0.759028i	−1.28038	+	0.184091i	−0.748732	−	0.662872i	$-0.769337\pi$
$17$	−5.27916	+	0.759028i	−1.28038	+	0.184091i	−0.531651	+	0.846964i	$0.678428\pi$
$18$		0			0
$19$	−0.130434	+	0.150529i	−0.0299236	+	0.0345336i	−0.770514	−	0.637423i	$-0.780000\pi$
$19$	−0.130434	+	0.150529i	−0.0299236	+	0.0345336i	0.740591	+	0.671957i	$0.234546\pi$
$20$		0			0
$21$	0.231790	−	6.55625i	0.0505807	−	1.43069i
$22$		0			0
$23$	0.694228	+	0.317043i	0.144756	+	0.0661081i	0.486476	−	0.873694i	$-0.338282\pi$
$23$	0.694228	+	0.317043i	0.144756	+	0.0661081i	−0.341720	+	0.939802i	$0.611009\pi$
$24$		0			0
$25$	3.11537	+	2.00213i	0.623074	+	0.400425i
$26$		0			0
$27$	4.04946	+	3.25605i	0.779320	+	0.626626i
$28$		0			0
$29$		−	8.71464i		−	1.61827i	−0.587624	−	0.809134i	$-0.699937\pi$
$29$		−	8.71464i		−	1.61827i	0.587624	−	0.809134i	$-0.300063\pi$
$30$		0			0
$31$	3.86518	+	6.01434i	0.694207	+	1.08021i	0.992081	+	0.125602i	$0.0400864\pi$
$31$	3.86518	+	6.01434i	0.694207	+	1.08021i	−0.297873	+	0.954605i	$0.596277\pi$
$32$		0			0
$33$	6.03676	−	3.58472i	1.05087	−	0.624020i
$34$		0			0
$35$	−10.1642	+	4.64183i	−1.71806	+	0.784612i
$36$		0			0
$37$	−2.50144			−0.411234			−0.205617	−	0.978633i	$-0.565920\pi$
$37$	−2.50144			−0.411234			−0.205617	+	0.978633i	$0.565920\pi$
$38$		0			0
$39$	−0.617189	−	2.41449i	−0.0988294	−	0.386628i
$40$		0			0
$41$	−0.0416445	−	0.289644i	−0.00650378	−	0.0452348i	0.986311	−	0.164895i	$-0.0527286\pi$
$41$	−0.0416445	−	0.289644i	−0.00650378	−	0.0452348i	−0.992815	+	0.119660i	$0.961819\pi$
$42$		0			0
$43$	−6.85998	+	0.986316i	−1.04614	+	0.150412i	−0.643889	−	0.765119i	$-0.722680\pi$
$43$	−6.85998	+	0.986316i	−1.04614	+	0.150412i	−0.402248	+	0.915531i	$0.631771\pi$
$44$		0			0
$45$	1.87505	−	8.64948i	0.279515	−	1.28939i
$46$		0			0
$47$	−6.89272	−	3.14780i	−1.00541	−	0.459154i	−0.156489	−	0.987680i	$-0.550018\pi$
$47$	−6.89272	−	3.14780i	−1.00541	−	0.459154i	−0.848917	+	0.528526i	$0.822745\pi$
$48$		0			0
$49$	1.04545	−	7.27129i	0.149351	−	1.03876i
$50$		0			0
$51$	5.26579	−	7.59001i	0.737357	−	1.06281i
$52$		0			0
$53$	−0.173569	+	1.20720i	−0.0238415	+	0.165821i	−0.998264	−	0.0589041i	$-0.981239\pi$
$53$	−0.173569	+	1.20720i	−0.0238415	+	0.165821i	0.974422	+	0.224725i	$0.0721485\pi$
$54$		0			0
$55$	−10.0600	−	6.46518i	−1.35649	−	0.871764i
$56$		0			0
$57$	−0.0370010	−	0.342996i	−0.00490091	−	0.0454310i
$58$		0			0
$59$	0.206913	+	0.321963i	0.0269378	+	0.0419160i	0.854461	−	0.519515i	$-0.173887\pi$
$59$	0.206913	+	0.321963i	0.0269378	+	0.0419160i	−0.827524	+	0.561431i	$0.810251\pi$
$60$		0			0
$61$	3.48314	+	11.8625i	0.445970	+	1.51883i	0.809425	+	0.587223i	$0.199779\pi$
$61$	3.48314	+	11.8625i	0.445970	+	1.51883i	−0.363456	+	0.931612i	$0.618403\pi$
$62$		0			0
$63$	8.04055	+	8.02896i	1.01301	+	1.01155i
$64$		0			0
$65$	−3.20795	+	2.77971i	−0.397897	+	0.344780i
$66$		0			0
$67$	−8.15987	−	0.645356i	−0.996887	−	0.0788428i
$67$	−8.15987	−	0.645356i	−0.996887	−	0.0788428i
$68$		0			0
$69$	−1.22109	+	0.506307i	−0.147002	+	0.0609523i
$70$		0			0
$71$	−0.756392	−	0.108753i	−0.0897672	−	0.0129066i	0.0972849	−	0.995257i	$-0.468984\pi$
$71$	−0.756392	−	0.108753i	−0.0897672	−	0.0129066i	−0.187052	+	0.982350i	$0.559893\pi$
$72$		0			0
$73$	−11.2432	+	3.30131i	−1.31592	+	0.386390i	−0.863020	−	0.505170i	$-0.831430\pi$
$73$	−11.2432	+	3.30131i	−1.31592	+	0.386390i	−0.452903	+	0.891560i	$0.649612\pi$
$74$		0			0
$75$	−6.21440	+	1.58852i	−0.717577	+	0.183426i
$76$		0			0
$77$	13.9657	−	6.37792i	1.59154	−	0.726832i
$78$		0			0
$79$	8.00157	−	12.4507i	0.900247	−	1.40081i	−0.0158579	−	0.999874i	$-0.505048\pi$
$79$	8.00157	−	12.4507i	0.900247	−	1.40081i	0.916105	−	0.400938i	$-0.131316\pi$
$80$		0			0
$81$	−8.90654	+	1.29368i	−0.989615	+	0.143742i
$82$		0			0
$83$	−3.51473	+	11.9701i	−0.385792	+	1.31389i	0.506428	+	0.862282i	$0.330966\pi$
$83$	−3.51473	+	11.9701i	−0.385792	+	1.31389i	−0.892219	+	0.451603i	$0.850852\pi$
$84$		0			0
$85$	−15.5742	−	2.23923i	−1.68926	−	0.242878i
$86$		0			0
$87$	11.0511	+	10.2815i	1.18480	+	1.10229i
$88$		0			0
$89$	−0.0142974	+	0.00652940i	−0.00151552	+	0.000692115i	−0.416173	−	0.909286i	$-0.636629\pi$
$89$	−0.0142974	+	0.00652940i	−0.00151552	+	0.000692115i	0.414657	+	0.909978i	$0.363902\pi$
$90$		0			0
$91$	−0.775578	−	5.39427i	−0.0813027	−	0.565473i
$92$		0			0
$93$	−12.1869	−	2.19423i	−1.26373	−	0.227531i
$94$		0			0
$95$	−0.494321	+	0.317681i	−0.0507162	+	0.0325933i
$96$		0			0
$97$			15.9958i			1.62413i	0.583566	+	0.812066i	$0.301657\pi$
$97$			15.9958i			1.62413i	−0.583566	+	0.812066i	$0.698343\pi$
$98$		0			0
$99$	−2.57633	+	11.8845i	−0.258931	+	1.19443i
$100$		0			0
$101$	9.07482	−	10.4729i	0.902979	−	1.04209i	−0.0959301	−	0.995388i	$-0.530583\pi$
$101$	9.07482	−	10.4729i	0.902979	−	1.04209i	0.998909	−	0.0467048i	$-0.0148720\pi$
$102$		0			0
$103$	0.156435	−	0.100534i	0.0154140	−	0.00990596i	−0.532911	−	0.846171i	$-0.678902\pi$
$103$	0.156435	−	0.100534i	0.0154140	−	0.00990596i	0.548325	+	0.836265i	$0.315266\pi$
$104$		0			0
$105$	6.10532	−	18.3656i	0.595818	−	1.79230i
$106$		0			0
$107$	−3.20448	−	10.9135i	−0.309789	−	1.05504i	−0.956360	−	0.292191i	$-0.905616\pi$
$107$	−3.20448	−	10.9135i	−0.309789	−	1.05504i	0.646571	−	0.762854i	$-0.276202\pi$
$108$		0			0
$109$	−7.91640	+	12.3182i	−0.758254	+	1.17987i	0.220612	+	0.975362i	$0.429195\pi$
$109$	−7.91640	+	12.3182i	−0.758254	+	1.17987i	−0.978866	+	0.204504i	$0.934442\pi$
$110$		0			0
$111$	2.95118	−	3.17209i	0.280114	−	0.301081i
$112$		0			0
$113$	13.2015	−	3.87631i	1.24189	−	0.364653i	0.406166	−	0.913799i	$-0.366865\pi$
$113$	13.2015	−	3.87631i	1.24189	−	0.364653i	0.835726	+	0.549147i	$0.185047\pi$
$114$		0			0
$115$	1.70159	+	1.47444i	0.158674	+	0.137492i
$116$		0			0
$117$	3.78998	+	2.06594i	0.350384	+	0.190996i
$118$		0			0
$119$	13.2289	−	15.2669i	1.21269	−	1.39952i
$120$		0			0
$121$	4.56877	+	2.93617i	0.415343	+	0.266925i
$122$		0			0
$123$	0.416431	+	0.288911i	0.0375483	+	0.0260502i
$124$		0			0
$125$	−2.50523	−	2.89118i	−0.224074	−	0.258595i
$126$		0			0
$127$	2.59056	+	2.98967i	0.229875	+	0.265290i	0.858956	−	0.512050i	$-0.171114\pi$
$127$	2.59056	+	2.98967i	0.229875	+	0.265290i	−0.629080	+	0.777340i	$0.716568\pi$
$128$		0			0
$129$	6.84261	−	9.86282i	0.602458	−	0.868372i
$130$		0			0
$131$	3.04712	+	1.39157i	0.266228	+	0.121582i	0.544057	−	0.839048i	$-0.316888\pi$
$131$	3.04712	+	1.39157i	0.266228	+	0.121582i	−0.277829	+	0.960631i	$0.589615\pi$
$132$		0			0
$133$		−	0.754410i		−	0.0654157i
$134$		0			0
$135$	8.75627	+	12.5823i	0.753620	+	1.08292i
$136$		0			0
$137$	−6.27585	+	13.7422i	−0.536182	+	1.17407i	0.426760	+	0.904365i	$0.359655\pi$
$137$	−6.27585	+	13.7422i	−0.536182	+	1.17407i	−0.962942	+	0.269710i	$0.913072\pi$
$138$		0			0
$139$	−4.37634	+	14.9044i	−0.371196	+	1.26418i	0.536268	+	0.844048i	$0.319834\pi$
$139$	−4.37634	+	14.9044i	−0.371196	+	1.26418i	−0.907464	+	0.420130i	$0.861985\pi$
$140$		0			0
$141$	12.1237	−	5.02693i	1.02100	−	0.423344i
$142$		0			0
$143$	4.40776	−	3.81935i	0.368595	−	0.319390i
$144$		0			0
$145$	7.24315	−	24.6679i	0.601510	−	2.04856i
$146$		0			0
$147$	7.98733	+	9.90436i	0.658784	+	0.816898i
$148$		0			0
$149$	13.7776	+	11.9383i	1.12870	+	0.978026i	0.999907	−	0.0136454i	$-0.00434360\pi$
$149$	13.7776	+	11.9383i	1.12870	+	0.978026i	0.128795	+	0.991671i	$0.458889\pi$
$150$		0			0
$151$	−0.470875	−	3.27501i	−0.0383192	−	0.266516i	0.961651	−	0.274277i	$-0.0884386\pi$
$151$	−0.470875	−	3.27501i	−0.0383192	−	0.266516i	−0.999970	+	0.00776115i	$0.997530\pi$
$152$		0			0
$153$	3.41239	+	15.6322i	0.275875	+	1.26379i
$154$		0			0
$155$	5.94209	+	20.2369i	0.477280	+	1.62547i
$156$		0			0
$157$	−4.94188	+	10.8212i	−0.394405	+	0.863626i	0.603402	+	0.797437i	$0.293811\pi$
$157$	−4.94188	+	10.8212i	−0.394405	+	0.863626i	−0.997807	+	0.0661893i	$0.978916\pi$
$158$		0			0
$159$	−1.32607	−	1.64434i	−0.105165	−	0.130405i
$160$		0			0
$161$	−2.77360	+	0.814403i	−0.218591	+	0.0641840i
$162$		0			0
$163$	17.8684			1.39956			0.699781	−	0.714357i	$-0.253281\pi$
$163$	17.8684			1.39956			0.699781	+	0.714357i	$0.253281\pi$
$164$		0			0
$165$	20.0672	−	5.12957i	1.56223	−	0.399336i
$166$		0			0
$167$	0.518218	+	0.449039i	0.0401009	+	0.0347477i	0.674681	−	0.738110i	$-0.264281\pi$
$167$	0.518218	+	0.449039i	0.0401009	+	0.0347477i	−0.634580	+	0.772857i	$0.718827\pi$
$168$		0			0
$169$	4.54039	+	9.94207i	0.349261	+	0.764775i
$170$		0			0
$171$	0.478609	+	0.357744i	0.0366001	+	0.0273573i
$172$		0			0
$173$	11.6014	+	18.0521i	0.882037	+	1.37248i	0.927624	+	0.373516i	$0.121848\pi$
$173$	11.6014	+	18.0521i	0.882037	+	1.37248i	−0.0455864	+	0.998960i	$0.514516\pi$
$174$		0			0
$175$	−13.8837	+	1.99618i	−1.04951	+	0.150897i
$176$		0			0
$177$	−0.652398	−	0.117463i	−0.0490372	−	0.00882903i
$178$		0			0
$179$	−1.38815	−	3.03963i	−0.103755	−	0.227192i	0.850633	−	0.525759i	$-0.176219\pi$
$179$	−1.38815	−	3.03963i	−0.103755	−	0.227192i	−0.954389	+	0.298567i	$0.903491\pi$
$180$		0			0
$181$	−1.03125	+	2.25813i	−0.0766526	+	0.167846i	−0.944079	−	0.329720i	$-0.893046\pi$
$181$	−1.03125	+	2.25813i	−0.0766526	+	0.167846i	0.867426	+	0.497566i	$0.165773\pi$
$182$		0			0
$183$	−19.1522	−	9.57829i	−1.41577	−	0.708047i
$184$		0			0
$185$	−7.08064	−	2.07906i	−0.520579	−	0.152856i
$186$		0			0
$187$	21.3991	+	3.07672i	1.56486	+	0.224992i
$188$		0			0
$189$	−19.6677	+	0.723740i	−1.43062	+	0.0526443i
$190$		0			0
$191$	2.31794	+	5.07558i	0.167720	+	0.367256i	0.974765	−	0.223235i	$-0.0716616\pi$
$191$	2.31794	+	5.07558i	0.167720	+	0.367256i	−0.807045	+	0.590491i	$0.798934\pi$
$192$		0			0
$193$	17.2923	−	11.1131i	1.24473	−	0.799938i	0.258609	−	0.965982i	$-0.416736\pi$
$193$	17.2923	−	11.1131i	1.24473	−	0.799938i	0.986118	+	0.166044i	$0.0530994\pi$
$194$		0			0
$195$	0.259763	−	7.34749i	0.0186020	−	0.526165i
$196$		0			0
$197$	−0.352396	+	2.45097i	−0.0251072	+	0.174624i	−0.998517	−	0.0544480i	$-0.982660\pi$
$197$	−0.352396	+	2.45097i	−0.0251072	+	0.174624i	0.973409	+	0.229072i	$0.0735692\pi$
$198$		0			0
$199$	−3.29690	−	3.80483i	−0.233711	−	0.269717i	0.626764	−	0.779209i	$-0.284379\pi$
$199$	−3.29690	−	3.80483i	−0.233711	−	0.269717i	−0.860476	+	0.509492i	$0.829833\pi$
$200$		0			0
$201$	10.4453	−	9.58618i	0.736758	−	0.676157i
$202$		0			0
$203$	21.6155	+	24.9456i	1.51711	+	1.75084i
$204$		0			0
$205$	0.122857	−	0.854487i	0.00858068	−	0.0596800i
$206$		0			0
$207$	0.798582	−	2.14581i	0.0555053	−	0.149144i
$208$		0			0
$209$	0.679202	−	0.436497i	0.0469814	−	0.0301931i
$210$		0			0
$211$	−9.04523	−	19.8063i	−0.622699	−	1.36352i	−0.913540	−	0.406750i	$-0.866662\pi$
$211$	−9.04523	−	19.8063i	−0.622699	−	1.36352i	0.290840	−	0.956772i	$-0.406065\pi$
$212$		0			0
$213$	1.03030	−	0.830878i	0.0705947	−	0.0569308i
$214$		0			0
$215$	−20.2378	−	2.90976i	−1.38021	−	0.198444i
$216$		0			0
$217$	−25.9818	−	7.62895i	−1.76376	−	0.517887i
$218$		0			0
$219$	9.07830	−	18.1525i	0.613454	−	1.22663i
$220$		0			0
$221$	3.18786	−	6.98043i	0.214439	−	0.469555i
$222$		0			0
$223$	9.31921	+	20.4062i	0.624060	+	1.36650i	0.912529	+	0.409012i	$0.134127\pi$
$223$	9.31921	+	20.4062i	0.624060	+	1.36650i	−0.288469	+	0.957489i	$0.593146\pi$
$224$		0			0
$225$	5.31730	−	9.75462i	0.354487	−	0.650308i
$226$		0			0
$227$	−4.40653	+	0.633564i	−0.292472	+	0.0420511i	−0.286989	−	0.957934i	$-0.592654\pi$
$227$	−4.40653	+	0.633564i	−0.292472	+	0.0420511i	−0.00548275	+	0.999985i	$0.501745\pi$
$228$		0			0
$229$	8.29963	+	12.9145i	0.548455	+	0.853413i	0.999230	−	0.0392245i	$-0.0124888\pi$
$229$	8.29963	+	12.9145i	0.548455	+	0.853413i	−0.450775	+	0.892638i	$0.648852\pi$
$230$		0			0
$231$	−8.38877	+	25.2346i	−0.551941	+	1.66031i
$232$		0			0
$233$	−5.70613	−	12.4947i	−0.373821	−	0.818553i	−0.999267	−	0.0382859i	$-0.987810\pi$
$233$	−5.70613	−	12.4947i	−0.373821	−	0.818553i	0.625446	−	0.780267i	$-0.284917\pi$
$234$		0			0
$235$	−16.8944	−	14.6391i	−1.10207	−	0.954950i
$236$		0			0
$237$	6.34857	+	24.8361i	0.412384	+	1.61328i
$238$		0			0
$239$	−23.3595			−1.51100			−0.755500	−	0.655148i	$-0.772606\pi$
$239$	−23.3595			−1.51100			−0.755500	+	0.655148i	$0.772606\pi$
$240$		0			0
$241$	2.15759	−	0.633526i	0.138983	−	0.0408090i	−0.211501	−	0.977378i	$-0.567835\pi$
$241$	2.15759	−	0.633526i	0.138983	−	0.0408090i	0.350484	+	0.936569i	$0.386017\pi$
$242$		0			0
$243$	8.86735	−	12.8207i	0.568841	−	0.822448i
$244$		0			0
$245$	9.00280	−	19.7134i	0.575168	−	1.25944i
$246$		0			0
$247$	−0.0807398	−	0.274974i	−0.00513735	−	0.0174962i
$248$		0			0
$249$	−11.0326	−	18.5792i	−0.699165	−	1.17741i
$250$		0			0
$251$	2.12352	+	14.7694i	0.134035	+	0.932237i	0.940219	+	0.340571i	$0.110620\pi$
$251$	2.12352	+	14.7694i	0.134035	+	0.932237i	−0.806183	+	0.591666i	$0.798470\pi$
$252$		0			0
$253$	−2.33800	−	2.02589i	−0.146989	−	0.127367i
$254$		0			0
$255$	21.2139	−	17.1078i	1.32846	−	1.07134i
$256$		0			0
$257$	3.22142	−	10.9711i	0.200947	−	0.684361i	−0.795930	−	0.605389i	$-0.793018\pi$
$257$	3.22142	−	10.9711i	0.200947	−	0.684361i	0.996877	−	0.0789730i	$-0.0251641\pi$
$258$		0			0
$259$	7.16035	−	6.20448i	0.444923	−	0.385528i
$260$		0			0
$261$	−26.0760	+	1.88389i	−1.61406	+	0.116610i
$262$		0			0
$263$	−4.21240	+	14.3461i	−0.259747	+	0.884619i	0.721589	+	0.692321i	$0.243412\pi$
$263$	−4.21240	+	14.3461i	−0.259747	+	0.884619i	−0.981337	+	0.192297i	$0.938406\pi$
$264$		0			0
$265$	−1.49466	+	3.27286i	−0.0918165	+	0.201050i
$266$		0			0
$267$	0.00858801	−	0.0258339i	0.000525578	−	0.00158101i
$268$		0			0
$269$			20.8104i			1.26884i	0.772990	+	0.634418i	$0.218760\pi$
$269$			20.8104i			1.26884i	−0.772990	+	0.634418i	$0.781240\pi$
$270$		0			0
$271$	−26.4716	−	12.0892i	−1.60804	−	0.734366i	−0.609734	−	0.792606i	$-0.708724\pi$
$271$	−26.4716	−	12.0892i	−1.60804	−	0.734366i	−0.998303	+	0.0582400i	$0.981451\pi$
$272$		0			0
$273$	7.75551	+	5.38060i	0.469385	+	0.325649i
$274$		0			0
$275$	−9.83020	−	11.3447i	−0.592784	−	0.684109i
$276$		0			0
$277$	−16.1014	−	18.5820i	−0.967440	−	1.11648i	−0.993154	−	0.116815i	$-0.962731\pi$
$277$	−16.1014	−	18.5820i	−0.967440	−	1.11648i	0.0257141	−	0.999669i	$-0.491814\pi$
$278$		0			0
$279$	17.1606	−	12.8656i	1.02738	−	0.770241i
$280$		0			0
$281$	−27.7394	−	17.8271i	−1.65480	−	1.06347i	−0.925116	−	0.379685i	$-0.876032\pi$
$281$	−27.7394	−	17.8271i	−1.65480	−	1.06347i	−0.729681	−	0.683788i	$-0.760331\pi$
$282$		0			0
$283$	3.38795	−	3.90990i	0.201393	−	0.232420i	−0.646065	−	0.763282i	$-0.723587\pi$
$283$	3.38795	−	3.90990i	0.201393	−	0.232420i	0.847458	+	0.530863i	$0.178132\pi$
$284$		0			0
$285$	0.180344	−	1.00165i	0.0106827	−	0.0593325i
$286$		0			0
$287$	0.837630	+	0.725810i	0.0494437	+	0.0428432i
$288$		0			0
$289$	10.9820	−	3.22460i	0.645999	−	0.189682i
$290$		0			0
$291$	−20.2844	−	18.8718i	−1.18909	−	1.10628i
$292$		0			0
$293$	−1.03101	+	1.60428i	−0.0602322	+	0.0937231i	−0.870063	−	0.492940i	$-0.835922\pi$
$293$	−1.03101	+	1.60428i	−0.0602322	+	0.0937231i	0.809831	+	0.586663i	$0.199559\pi$
$294$		0			0
$295$	0.318095	+	1.08333i	0.0185202	+	0.0630741i
$296$		0			0
$297$	−12.0312	−	17.2883i	−0.698121	−	1.00317i
$298$		0			0
$299$	−0.923788	+	0.593682i	−0.0534240	+	0.0343335i
$300$		0			0
$301$	17.1902	−	19.8386i	0.990827	−	1.14348i
$302$		0			0
$303$	2.57432	+	23.8637i	0.147891	+	1.37093i
$304$		0			0
$305$			36.4732i			2.08845i
$306$		0			0
$307$	2.28977	−	1.47155i	0.130684	−	0.0839857i	−0.473665	−	0.880705i	$-0.657069\pi$
$307$	2.28977	−	1.47155i	0.130684	−	0.0839857i	0.604350	+	0.796719i	$0.293433\pi$
$308$		0			0
$309$	−0.0570724	+	0.316985i	−0.00324674	+	0.0180327i
$310$		0			0
$311$	−0.224559	−	1.56184i	−0.0127336	−	0.0885639i	0.982464	−	0.186454i	$-0.0596996\pi$
$311$	−0.224559	−	1.56184i	−0.0127336	−	0.0885639i	−0.995197	+	0.0978904i	$0.968791\pi$
$312$		0			0
$313$	2.15289	−	0.983191i	0.121688	−	0.0555732i	−0.353640	−	0.935381i	$-0.615056\pi$
$313$	2.15289	−	0.983191i	0.121688	−	0.0555732i	0.475329	+	0.879808i	$0.342329\pi$
$314$		0			0
$315$	16.0865	+	29.4098i	0.906374	+	1.65706i
$316$		0			0
$317$	1.60985	+	0.231462i	0.0904183	+	0.0130002i	0.187375	−	0.982288i	$-0.440002\pi$
$317$	1.60985	+	0.231462i	0.0904183	+	0.0130002i	−0.0969572	+	0.995289i	$0.530911\pi$
$318$		0			0
$319$	−9.95216	+	33.8939i	−0.557214	+	1.89770i
$320$		0			0
$321$	17.6200	+	8.81201i	0.983454	+	0.491839i
$322$		0			0
$323$	0.574325	−	0.893667i	0.0319563	−	0.0497250i
$324$		0			0
$325$	−4.84683	+	2.21347i	−0.268854	+	0.122781i
$326$		0			0
$327$	−6.28099	−	24.5717i	−0.347340	−	1.35882i
$328$		0			0
$329$	27.5380	−	8.08590i	1.51822	−	0.445790i
$330$		0			0
$331$	28.3260	+	4.07266i	1.55694	+	0.223853i	0.866365	−	0.499412i	$-0.166450\pi$
$331$	28.3260	+	4.07266i	1.55694	+	0.223853i	0.690570	+	0.723265i	$0.257360\pi$
$332$		0			0
$333$	0.540750	+	7.48481i	0.0296329	+	0.410165i
$334$		0			0
$335$	−22.5612	−	8.60881i	−1.23265	−	0.470350i
$336$		0			0
$337$	−15.2316	+	13.1983i	−0.829719	+	0.718956i	−0.962234	−	0.272225i	$-0.912240\pi$
$337$	−15.2316	+	13.1983i	−0.829719	+	0.718956i	0.132514	+	0.991181i	$0.457695\pi$
$338$		0			0
$339$	−10.6595	+	21.3141i	−0.578943	+	1.15762i
$340$		0			0
$341$	−8.16449	−	27.8057i	−0.442132	−	1.50576i
$342$		0			0
$343$	0.708644	+	1.10267i	0.0382632	+	0.0595387i
$344$		0			0
$345$	−3.87726	+	0.418263i	−0.208745	+	0.0225185i
$346$		0			0
$347$	24.7044	+	15.8765i	1.32620	+	0.852297i	0.995801	−	0.0915445i	$-0.0291804\pi$
$347$	24.7044	+	15.8765i	1.32620	+	0.852297i	0.330399	+	0.943841i	$0.392817\pi$
$348$		0			0
$349$	−2.66838	+	18.5590i	−0.142835	+	0.993439i	0.784746	+	0.619817i	$0.212793\pi$
$349$	−2.66838	+	18.5590i	−0.142835	+	0.993439i	−0.927581	+	0.373622i	$0.878116\pi$
$350$		0			0
$351$	−7.09122	+	2.36871i	−0.378501	+	0.126432i
$352$		0			0
$353$	1.25495	−	8.72836i	0.0667942	−	0.464564i	−0.928784	−	0.370623i	$-0.879144\pi$
$353$	1.25495	−	8.72836i	0.0667942	−	0.464564i	0.995578	−	0.0939411i	$-0.0299465\pi$
$354$		0			0
$355$	−2.05067	−	0.936511i	−0.108838	−	0.0497048i
$356$		0			0
$357$	3.75272	+	34.7874i	0.198615	+	1.84115i
$358$		0			0
$359$	4.63866	−	0.666939i	0.244819	−	0.0351997i	−0.0188128	−	0.999823i	$-0.505989\pi$
$359$	4.63866	−	0.666939i	0.244819	−	0.0351997i	0.263632	+	0.964623i	$0.415080\pi$
$360$		0			0
$361$	2.69834	+	18.7673i	0.142018	+	0.987755i
$362$		0			0
$363$	−9.11358	+	2.32960i	−0.478339	+	0.122272i
$364$		0			0
$365$	−34.5693			−1.80944
$366$		0			0
$367$	10.3001	−	4.70390i	0.537661	−	0.245541i	−0.128029	−	0.991770i	$-0.540865\pi$
$367$	10.3001	−	4.70390i	0.537661	−	0.245541i	0.665689	+	0.746229i	$0.268138\pi$
$368$		0			0
$369$	−0.857671	+	0.187223i	−0.0446486	+	0.00974643i
$370$		0			0
$371$	−2.49745	−	3.88610i	−0.129661	−	0.201756i
$372$		0			0
$373$		−	27.8273i		−	1.44084i	−0.693538	−	0.720420i	$-0.743949\pi$
$373$		−	27.8273i		−	1.44084i	0.693538	−	0.720420i	$-0.256051\pi$
$374$		0			0
$375$	6.62197	+	0.234113i	0.341957	+	0.0120896i
$376$		0			0
$377$	10.5484	+	6.77903i	0.543269	+	0.349138i
$378$		0			0
$379$	33.4407	+	15.2718i	1.71773	+	0.784461i	0.995704	+	0.0925970i	$0.0295168\pi$
$379$	33.4407	+	15.2718i	1.71773	+	0.784461i	0.722027	+	0.691865i	$0.243210\pi$
$380$		0			0
$381$	−6.84754	−	0.242088i	−0.350810	−	0.0124025i
$382$		0			0
$383$	12.5766	−	14.5142i	0.642634	−	0.741639i	−0.337205	−	0.941431i	$-0.609481\pi$
$383$	12.5766	−	14.5142i	0.642634	−	0.741639i	0.979838	+	0.199793i	$0.0640269\pi$
$384$		0			0
$385$	44.8327	−	6.44597i	2.28488	−	0.328517i
$386$		0			0
$387$	4.43422	+	20.3132i	0.225404	+	1.03258i
$388$		0			0
$389$	10.8893	−	16.9441i	0.552109	−	0.859098i	−0.447268	−	0.894400i	$-0.647603\pi$
$389$	10.8893	−	16.9441i	0.552109	−	0.859098i	0.999377	+	0.0353022i	$0.0112394\pi$
$390$		0			0
$391$	−3.90558	−	1.14678i	−0.197514	−	0.0579952i
$392$		0			0
$393$	−5.35963	+	2.22230i	−0.270357	+	0.112100i
$394$		0			0
$395$	32.9978	−	28.5928i	1.66030	−	1.43866i
$396$		0			0
$397$	−12.5930	−	3.69765i	−0.632026	−	0.185580i	−0.0499993	−	0.998749i	$-0.515922\pi$
$397$	−12.5930	−	3.69765i	−0.632026	−	0.185580i	−0.582027	+	0.813170i	$0.697740\pi$
$398$		0			0
$399$	0.956671	+	0.890048i	0.0478934	+	0.0445581i
$400$		0			0
$401$	−30.6091			−1.52854			−0.764272	−	0.644894i	$-0.776901\pi$
$401$	−30.6091			−1.52854			−0.764272	+	0.644894i	$0.776901\pi$
$402$		0			0
$403$	−10.2866			−0.512410
$404$		0			0
$405$	−26.2863	−	3.74071i	−1.30618	−	0.185877i
$406$		0			0
$407$	9.72888	+	2.85666i	0.482243	+	0.141599i
$408$		0			0
$409$	6.14065	−	5.32091i	0.303636	−	0.263102i	−0.489694	−	0.871895i	$-0.662891\pi$
$409$	6.14065	−	5.32091i	0.303636	−	0.263102i	0.793329	+	0.608793i	$0.208346\pi$
$410$		0			0
$411$	−10.0223	−	24.1714i	−0.494365	−	1.19229i
$412$		0			0
$413$	−1.39087	−	0.408397i	−0.0684404	−	0.0200959i
$414$		0			0
$415$	−19.8978	+	30.9615i	−0.976743	+	1.51984i
$416$		0			0
$417$	−13.7372	−	23.1338i	−0.672713	−	1.13287i
$418$		0			0
$419$	−19.7307	+	2.83685i	−0.963908	+	0.138589i	−0.606259	−	0.795267i	$-0.707331\pi$
$419$	−19.7307	+	2.83685i	−0.963908	+	0.138589i	−0.357649	+	0.933856i	$0.616421\pi$
$420$		0			0
$421$	−4.74306	+	5.47379i	−0.231163	+	0.266776i	−0.859467	−	0.511192i	$-0.829204\pi$
$421$	−4.74306	+	5.47379i	−0.231163	+	0.266776i	0.628304	+	0.777968i	$0.283750\pi$
$422$		0			0
$423$	−7.92881	+	21.3049i	−0.385512	+	1.03588i
$424$		0			0
$425$	−17.9662	−	8.20488i	−0.871488	−	0.397995i
$426$		0			0
$427$	−39.3937	−	25.3168i	−1.90639	−	1.22517i
$428$		0			0
$429$	−0.356918	+	10.0955i	−0.0172322	+	0.487417i
$430$		0			0
$431$		−	10.6012i		−	0.510640i	−0.966857	−	0.255320i	$-0.917819\pi$
$431$		−	10.6012i		−	0.510640i	0.966857	−	0.255320i	$-0.0821809\pi$
$432$		0			0
$433$	12.1735	+	18.9423i	0.585021	+	0.910310i	1.00000		0.000479079i	$0.000152496\pi$
$433$	12.1735	+	18.9423i	0.585021	+	0.910310i	−0.414979	+	0.909831i	$0.636211\pi$
$434$		0			0
$435$	22.7360	+	38.2881i	1.09011	+	1.83577i
$436$		0			0
$437$	−0.138275	+	0.0631480i	−0.00661458	+	0.00302078i
$438$		0			0
$439$	−13.7539			−0.656438			−0.328219	−	0.944602i	$-0.606448\pi$
$439$	−13.7539			−0.656438			−0.328219	+	0.944602i	$0.606448\pi$
$440$		0			0
$441$	−21.9832	−	1.55633i	−1.04682	−	0.0741110i
$442$		0			0
$443$	2.76881	+	19.2575i	0.131550	+	0.914950i	0.943535	+	0.331272i	$0.107478\pi$
$443$	2.76881	+	19.2575i	0.131550	+	0.914950i	−0.811985	+	0.583678i	$0.801613\pi$
$444$		0			0
$445$	−0.0458975	+	0.00659906i	−0.00217575	+	0.000312825i
$446$		0			0
$447$	−31.3937	+	3.38663i	−1.48487	+	0.160182i
$448$		0			0
$449$	−38.1025	−	17.4008i	−1.79817	−	0.821196i	−0.962163	−	0.272473i	$-0.912158\pi$
$449$	−38.1025	−	17.4008i	−1.79817	−	0.821196i	−0.836005	−	0.548722i	$-0.815114\pi$
$450$		0			0
$451$	−0.168806	+	1.17407i	−0.00794878	+	0.0552850i
$452$		0			0
$453$	4.70858	+	3.26671i	0.221228	+	0.153483i
$454$		0			0
$455$	2.28805	−	15.9138i	0.107266	−	0.746049i
$456$		0			0
$457$	−11.0054	−	7.07271i	−0.514809	−	0.330848i	0.257307	−	0.966330i	$-0.417165\pi$
$457$	−11.0054	−	7.07271i	−0.514809	−	0.330848i	−0.772115	+	0.635482i	$0.780801\pi$
$458$		0			0
$459$	−23.8492	−	14.1155i	−1.11318	−	0.658856i
$460$		0			0
$461$	−11.9303	−	18.5639i	−0.555649	−	0.864607i	0.443855	−	0.896099i	$-0.353611\pi$
$461$	−11.9303	−	18.5639i	−0.555649	−	0.864607i	−0.999504	+	0.0314915i	$0.989974\pi$
$462$		0			0
$463$	−11.2952	−	38.4680i	−0.524934	−	1.78776i	−0.611185	−	0.791488i	$-0.709307\pi$
$463$	−11.2952	−	38.4680i	−0.524934	−	1.78776i	0.0862514	−	0.996273i	$-0.472511\pi$
$464$		0			0
$465$	−32.6729	−	16.3402i	−1.51517	−	0.757757i
$466$		0			0
$467$	17.4693	−	15.1372i	0.808382	−	0.700467i	−0.149144	−	0.988816i	$-0.547652\pi$
$467$	17.4693	−	15.1372i	0.808382	−	0.700467i	0.957525	+	0.288349i	$0.0931062\pi$
$468$		0			0
$469$	24.9583	−	18.3921i	1.15247	−	0.849269i
$470$		0			0
$471$	−7.89202	−	19.0336i	−0.363645	−	0.877022i
$472$		0			0
$473$	27.8070	+	3.99804i	1.27857	+	0.183830i
$474$		0			0
$475$	−0.707727	+	0.207807i	−0.0324727	+	0.00953486i
$476$		0			0
$477$	3.64969	+	0.258386i	0.167108	+	0.0118307i
$478$		0			0
$479$	−23.8724	+	10.9021i	−1.09076	+	0.498132i	−0.877848	−	0.478940i	$-0.841021\pi$
$479$	−23.8724	+	10.9021i	−1.09076	+	0.498132i	−0.212909	+	0.977072i	$0.568294\pi$
$480$		0			0
$481$	1.94584	−	3.02779i	0.0887229	−	0.138055i
$482$		0			0
$483$	2.23953	−	4.47804i	0.101902	−	0.203758i
$484$		0			0
$485$	−13.2949	+	45.2782i	−0.603690	+	2.05598i
$486$		0			0
$487$	−1.33732	−	0.192278i	−0.0605997	−	0.00871293i	0.111948	−	0.993714i	$-0.464291\pi$
$487$	−1.33732	−	0.192278i	−0.0605997	−	0.00871293i	−0.172548	+	0.985001i	$0.555200\pi$
$488$		0			0
$489$	−21.0810	+	22.6590i	−0.953318	+	1.02468i
$490$		0			0
$491$	29.2186	−	13.3437i	1.31862	−	0.602193i	0.373109	−	0.927788i	$-0.378292\pi$
$491$	29.2186	−	13.3437i	1.31862	−	0.602193i	0.945509	+	0.325595i	$0.105565\pi$
$492$		0			0
$493$	6.61466	+	46.0059i	0.297909	+	2.07200i
$494$		0			0
$495$	−17.1704	+	31.4992i	−0.771751	+	1.41578i
$496$		0			0
$497$	2.43491	−	1.56482i	0.109221	−	0.0701919i
$498$		0			0
$499$			12.9260i			0.578646i	0.957231	+	0.289323i	$0.0934302\pi$
$499$			12.9260i			0.578646i	−0.957231	+	0.289323i	$0.906570\pi$
$500$		0			0
$501$	−1.18082	+	0.127382i	−0.0527551	+	0.00569100i
$502$		0			0
$503$	12.5972	−	14.5380i	0.561682	−	0.648215i	−0.401883	−	0.915691i	$-0.631644\pi$
$503$	12.5972	−	14.5380i	0.561682	−	0.648215i	0.963565	+	0.267476i	$0.0861895\pi$
$504$		0			0
$505$	34.3919	−	22.1024i	1.53042	−	0.983542i
$506$		0			0
$507$	−17.9643	−	5.97190i	−0.797823	−	0.265221i
$508$		0			0
$509$	5.63479	+	19.1903i	0.249758	+	0.850597i	0.984965	+	0.172754i	$0.0552666\pi$
$509$	5.63479	+	19.1903i	0.249758	+	0.850597i	−0.735207	+	0.677842i	$0.762915\pi$
$510$		0			0
$511$	23.9952	−	37.3373i	1.06149	−	1.65171i
$512$		0			0
$513$	−1.01832	+	0.184862i	−0.0449597	+	0.00816186i
$514$		0			0
$515$	0.526367	−	0.154555i	0.0231945	−	0.00681052i
$516$		0			0
$517$	23.2131	+	20.1143i	1.02091	+	0.884625i
$518$		0			0
$519$	−36.5792	−	6.58599i	−1.60565	−	0.289093i
$520$		0			0
$521$	14.3488	−	16.5594i	0.628632	−	0.725480i	−0.348690	−	0.937238i	$-0.613373\pi$
$521$	14.3488	−	16.5594i	0.628632	−	0.725480i	0.977322	+	0.211758i	$0.0679189\pi$
$522$		0			0
$523$	−1.74778	−	1.12323i	−0.0764251	−	0.0491154i	0.501870	−	0.864943i	$-0.332645\pi$
$523$	−1.74778	−	1.12323i	−0.0764251	−	0.0491154i	−0.578295	+	0.815828i	$0.696282\pi$
$524$		0			0
$525$	13.8486	−	19.9611i	0.604401	−	0.871173i
$526$		0			0
$527$	−24.9700	−	28.8169i	−1.08771	−	1.25528i
$528$		0			0
$529$	−14.6804	−	16.9420i	−0.638277	−	0.736610i
$530$		0			0
$531$	0.918649	−	0.688727i	0.0398660	−	0.0298882i
$532$		0			0
$533$	0.382986	+	0.174904i	0.0165890	+	0.00757592i
$534$		0			0
$535$		−	33.5553i		−	1.45072i
$536$		0			0
$537$	5.49229	+	1.82581i	0.237010	+	0.0787895i
$538$		0			0
$539$	−12.3699	+	27.0864i	−0.532811	+	1.16669i
$540$		0			0
$541$	−10.1591	+	34.5988i	−0.436775	+	1.48752i	0.387788	+	0.921748i	$0.373239\pi$
$541$	−10.1591	+	34.5988i	−0.436775	+	1.48752i	−0.824563	+	0.565770i	$0.808579\pi$
$542$		0			0
$543$	−1.64688	−	3.97187i	−0.0706744	−	0.170449i
$544$		0			0
$545$	−32.6466	+	28.2884i	−1.39843	+	1.21174i
$546$		0			0
$547$	7.92881	−	27.0031i	0.339012	−	1.15457i	−0.596895	−	0.802319i	$-0.703599\pi$
$547$	7.92881	−	27.0031i	0.339012	−	1.15457i	0.935907	−	0.352248i	$-0.114583\pi$
$548$		0			0
$549$	34.7419	−	12.9866i	1.48275	−	0.554256i
$550$		0			0
$551$	1.31180	+	1.13668i	0.0558847	+	0.0484244i
$552$		0			0
$553$	7.97780	+	55.4868i	0.339251	+	2.35954i
$554$		0			0
$555$	10.9902	−	6.52612i	0.466506	−	0.277019i
$556$		0			0
$557$	6.49987	+	22.1365i	0.275409	+	0.937955i	0.974775	+	0.223192i	$0.0716476\pi$
$557$	6.49987	+	22.1365i	0.275409	+	0.937955i	−0.699366	+	0.714764i	$0.746534\pi$
$558$		0			0
$559$	4.14245	−	9.07070i	0.175207	−	0.383650i
$560$		0			0
$561$	−29.1481	+	23.5064i	−1.23063	+	0.992440i
$562$		0			0
$563$	−23.5092	+	6.90294i	−0.990797	+	0.290924i	−0.736674	−	0.676248i	$-0.763605\pi$
$563$	−23.5092	+	6.90294i	−0.990797	+	0.290924i	−0.254123	+	0.967172i	$0.581787\pi$
$564$		0			0
$565$	40.5903			1.70765
$566$		0			0
$567$	22.2861	−	25.7946i	0.935928	−	1.08327i
$568$		0			0
$569$	4.98397	+	4.31864i	0.208939	+	0.181047i	0.753043	−	0.657971i	$-0.228585\pi$
$569$	4.98397	+	4.31864i	0.208939	+	0.181047i	−0.544104	+	0.839018i	$0.683130\pi$
$570$		0			0
$571$	8.65212	+	18.9455i	0.362080	+	0.792844i	0.999746	+	0.0225316i	$0.00717263\pi$
$571$	8.65212	+	18.9455i	0.362080	+	0.792844i	−0.637666	+	0.770313i	$0.720100\pi$
$572$		0			0
$573$	−9.17105	−	3.04875i	−0.383126	−	0.127363i
$574$		0			0
$575$	1.52802	+	2.37764i	0.0637226	+	0.0991544i
$576$		0			0
$577$	20.2236	−	2.90771i	0.841918	−	0.121049i	0.292156	−	0.956371i	$-0.405627\pi$
$577$	20.2236	−	2.90771i	0.841918	−	0.121049i	0.549762	+	0.835321i	$0.314718\pi$
$578$		0			0
$579$	−6.30879	+	35.0396i	−0.262185	+	1.45620i
$580$		0			0
$581$	−19.6292	−	42.9820i	−0.814358	−	1.78319i
$582$		0			0
$583$	2.05369	−	4.49694i	0.0850550	−	0.186244i
$584$		0			0
$585$	9.01092	+	8.99793i	0.372556	+	0.372019i
$586$		0			0
$587$	−13.5582	−	3.98104i	−0.559606	−	0.164315i	−0.0103159	−	0.999947i	$-0.503284\pi$
$587$	−13.5582	−	3.98104i	−0.559606	−	0.164315i	−0.549290	+	0.835632i	$0.685102\pi$
$588$		0			0
$589$	−1.40948	−	0.202653i	−0.0580767	−	0.00835017i
$590$		0			0
$591$	−2.69233	−	3.33851i	−0.110748	−	0.137328i
$592$		0			0
$593$	8.23739	+	18.0374i	0.338269	+	0.740706i	0.999959	−	0.00907163i	$-0.00288763\pi$
$593$	8.23739	+	18.0374i	0.338269	+	0.740706i	−0.661690	+	0.749778i	$0.730160\pi$
$594$		0			0
$595$	50.1351	−	32.2198i	2.05534	−	1.32088i
$596$		0			0
$597$	8.71458	+	0.308095i	0.356664	+	0.0126095i
$598$		0			0
$599$	−3.41470	+	23.7497i	−0.139521	+	0.970388i	0.792987	+	0.609239i	$0.208525\pi$
$599$	−3.41470	+	23.7497i	−0.139521	+	0.970388i	−0.932508	+	0.361150i	$0.882384\pi$
$600$		0			0
$601$	−13.9003	−	16.0418i	−0.567004	−	0.654358i	0.397755	−	0.917492i	$-0.369789\pi$
$601$	−13.9003	−	16.0418i	−0.567004	−	0.654358i	−0.964759	+	0.263134i	$0.915244\pi$
$602$		0			0
$603$	−0.167069	+	24.5555i	−0.00680358	+	0.999977i
$604$		0			0
$605$	10.4921	+	12.1085i	0.426564	+	0.492281i
$606$		0			0
$607$	2.80749	−	19.5266i	0.113953	−	0.792558i	−0.850057	−	0.526691i	$-0.823433\pi$
$607$	2.80749	−	19.5266i	0.113953	−	0.792558i	0.964010	−	0.265867i	$-0.0856583\pi$
$608$		0			0
$609$	−57.1354	−	2.01997i	−2.31524	−	0.0818532i
$610$		0			0
$611$	9.17194	−	5.89445i	0.371057	−	0.238464i
$612$		0			0
$613$	−3.16626	−	6.93315i	−0.127884	−	0.280027i	0.834850	−	0.550478i	$-0.185555\pi$
$613$	−3.16626	−	6.93315i	−0.127884	−	0.280027i	−0.962734	+	0.270451i	$0.912827\pi$
$614$		0			0
$615$	0.938633	+	1.16391i	0.0378493	+	0.0469335i
$616$		0			0
$617$	3.30061	+	0.474556i	0.132877	+	0.0191049i	0.208433	−	0.978037i	$-0.433164\pi$
$617$	3.30061	+	0.474556i	0.132877	+	0.0191049i	−0.0755552	+	0.997142i	$0.524073\pi$
$618$		0			0
$619$	45.2582	+	13.2890i	1.81908	+	0.534130i	0.999259	−	0.0384883i	$-0.0122542\pi$
$619$	45.2582	+	13.2890i	1.81908	+	0.534130i	0.819822	+	0.572619i	$0.194072\pi$
$620$		0			0
$621$	1.77894	+	3.54429i	0.0713865	+	0.142228i
$622$		0			0
$623$	0.0247309	−	0.0541531i	0.000990822	−	0.00216960i
$624$		0			0
$625$	−12.3803	−	27.1090i	−0.495211	−	1.08436i
$626$		0			0
$627$	−0.247795	+	1.37627i	−0.00989597	+	0.0549631i
$628$		0			0
$629$	13.2055	−	1.89866i	0.526537	−	0.0757046i
$630$		0			0
$631$	−19.5180	−	30.3706i	−0.776999	−	1.20903i	−0.973535	−	0.228537i	$-0.926606\pi$
$631$	−19.5180	−	30.3706i	−0.776999	−	1.20903i	0.196537	−	0.980496i	$-0.437031\pi$
$632$		0			0
$633$	35.7879	+	11.8970i	1.42244	+	0.472865i
$634$		0			0
$635$	4.84806	+	10.6158i	0.192389	+	0.421274i
$636$		0			0
$637$	7.98807	+	6.92170i	0.316499	+	0.274248i
$638$		0			0
$639$	−0.161897	+	2.28679i	−0.00640453	+	0.0904638i
$640$		0			0
$641$	19.0369			0.751914			0.375957	−	0.926637i	$-0.377314\pi$
$641$	19.0369			0.751914			0.375957	+	0.926637i	$0.377314\pi$
$642$		0			0
$643$	−26.1566	+	7.68027i	−1.03152	+	0.302880i	−0.753327	−	0.657646i	$-0.771552\pi$
$643$	−26.1566	+	7.68027i	−1.03152	+	0.302880i	−0.278189	+	0.960526i	$0.589734\pi$
$644$		0			0
$645$	27.5663	−	22.2307i	1.08542	−	0.875334i
$646$		0			0
$647$	19.9666	−	43.7207i	0.784968	−	1.71884i	0.0944441	−	0.995530i	$-0.469893\pi$
$647$	19.9666	−	43.7207i	0.784968	−	1.71884i	0.690524	−	0.723310i	$-0.257380\pi$
$648$		0			0
$649$	−0.437066	−	1.48851i	−0.0171564	−	0.0584292i
$650$		0			0
$651$	40.3275	−	23.9471i	1.58056	−	0.938559i
$652$		0			0
$653$	1.49965	+	10.4303i	0.0586860	+	0.408170i	0.997896	+	0.0648281i	$0.0206499\pi$
$653$	1.49965	+	10.4303i	0.0586860	+	0.408170i	−0.939210	+	0.343342i	$0.888441\pi$
$654$		0			0
$655$	7.46865	+	6.47162i	0.291824	+	0.252867i
$656$		0			0
$657$	12.3087	+	32.9284i	0.480209	+	1.28466i
$658$		0			0
$659$	3.84876	−	13.1077i	0.149926	−	0.510602i	−0.849941	−	0.526878i	$-0.823363\pi$
$659$	3.84876	−	13.1077i	0.149926	−	0.510602i	0.999868	+	0.0162753i	$0.00518083\pi$
$660$		0			0
$661$	−6.20052	+	5.37278i	−0.241172	+	0.208977i	−0.767057	−	0.641579i	$-0.778280\pi$
$661$	−6.20052	+	5.37278i	−0.241172	+	0.208977i	0.525885	+	0.850556i	$0.323734\pi$
$662$		0			0
$663$	5.09090	+	12.2780i	0.197714	+	0.476838i
$664$		0			0
$665$	0.627026	−	2.13545i	0.0243150	−	0.0828093i
$666$		0			0
$667$	2.76292	−	6.04994i	0.106981	−	0.234255i
$668$		0			0
$669$	−36.8719	−	12.2574i	−1.42555	−	0.473898i
$670$		0			0
$671$		−	50.1146i		−	1.93465i
$672$		0			0
$673$	12.7092	+	5.80409i	0.489903	+	0.223731i	0.645021	−	0.764165i	$-0.276849\pi$
$673$	12.7092	+	5.80409i	0.489903	+	0.223731i	−0.155118	+	0.987896i	$0.549576\pi$
$674$		0			0
$675$	6.09657	+	18.2513i	0.234657	+	0.702494i
$676$		0			0
$677$	1.10341	+	1.27340i	0.0424073	+	0.0489407i	0.776557	−	0.630047i	$-0.216964\pi$
$677$	1.10341	+	1.27340i	0.0424073	+	0.0489407i	−0.734150	+	0.678988i	$0.762419\pi$
$678$		0			0
$679$	−39.6755	−	45.7880i	−1.52261	−	1.75718i
$680$		0			0
$681$	4.39537	−	6.33541i	0.168431	−	0.242774i
$682$		0			0
$683$	12.0221	+	7.72614i	0.460013	+	0.295633i	0.750048	−	0.661384i	$-0.230030\pi$
$683$	12.0221	+	7.72614i	0.460013	+	0.295633i	−0.290035	+	0.957016i	$0.593667\pi$
$684$		0			0
$685$	−29.1864	+	33.6828i	−1.11515	+	1.28696i
$686$		0			0
$687$	−26.1688	−	4.71162i	−0.998400	−	0.179760i
$688$		0			0
$689$	−1.32620	−	1.14916i	−0.0505241	−	0.0437794i
$690$		0			0
$691$	−16.0896	+	4.72433i	−0.612077	+	0.179722i	−0.573056	−	0.819516i	$-0.694242\pi$
$691$	−16.0896	+	4.72433i	−0.612077	+	0.179722i	−0.0390213	+	0.999238i	$0.512424\pi$
$692$		0			0
$693$	−22.1031	−	40.4094i	−0.839626	−	1.53503i
$694$		0			0
$695$	−24.7755	+	38.5515i	−0.939790	+	1.46234i
$696$		0			0
$697$	0.439696	+	1.49747i	0.0166547	+	0.0567206i
$698$		0			0
$699$	22.5766	+	7.50517i	0.853925	+	0.283872i
$700$		0			0
$701$	14.5696	−	9.36331i	0.550286	−	0.353647i	−0.235764	−	0.971810i	$-0.575759\pi$
$701$	14.5696	−	9.36331i	0.550286	−	0.353647i	0.786050	+	0.618163i	$0.212123\pi$
$702$		0			0
$703$	0.326272	−	0.376538i	0.0123056	−	0.0142014i
$704$		0			0
$705$	38.4958	−	4.15277i	1.44984	−	0.156403i
$706$		0			0
$707$			52.4875i			1.97399i
$708$		0			0
$709$	20.9318	−	13.4520i	0.786110	−	0.505202i	−0.0849464	−	0.996386i	$-0.527072\pi$
$709$	20.9318	−	13.4520i	0.786110	−	0.505202i	0.871056	+	0.491183i	$0.163436\pi$
$710$		0			0
$711$	−38.9847	−	21.2508i	−1.46204	−	0.796967i
$712$		0			0
$713$	0.776511	+	5.40075i	0.0290806	+	0.202260i
$714$		0			0
$715$	15.6512	−	7.14764i	0.585320	−	0.267307i
$716$		0			0
$717$	27.5594	−	29.6223i	1.02922	−	1.10626i
$718$		0			0
$719$	−6.05908	−	0.871164i	−0.225966	−	0.0324889i	0.0284019	−	0.999597i	$-0.490958\pi$
$719$	−6.05908	−	0.871164i	−0.225966	−	0.0324889i	−0.254367	+	0.967108i	$0.581867\pi$
$720$		0			0
$721$	−0.198431	+	0.675794i	−0.00738996	+	0.0251679i
$722$		0			0
$723$	−1.74214	+	3.48348i	−0.0647907	+	0.129552i
$724$		0			0
$725$	17.4478	−	27.1493i	0.647996	−	1.00830i
$726$		0			0
$727$	−14.1305	+	6.45316i	−0.524070	+	0.239335i	−0.659840	−	0.751406i	$-0.729376\pi$
$727$	−14.1305	+	6.45316i	−0.524070	+	0.239335i	0.135771	+	0.990740i	$0.456649\pi$
$728$		0			0
$729$	5.79633	+	26.3705i	0.214679	+	0.976685i
$730$		0			0
$731$	35.4663	−	10.4138i	1.31177	−	0.385169i
$732$		0			0
$733$	−25.2314	−	3.62773i	−0.931944	−	0.133993i	−0.340414	−	0.940276i	$-0.610567\pi$
$733$	−25.2314	−	3.62773i	−0.931944	−	0.133993i	−0.591531	+	0.806282i	$0.701476\pi$
$734$		0			0
$735$	14.3772	+	34.6742i	0.530310	+	1.27898i
$736$		0			0
$737$	30.9993	+	11.8286i	1.14187	+	0.435712i
$738$		0			0
$739$	−14.2599	+	12.3563i	−0.524558	+	0.454532i	−0.876439	−	0.481512i	$-0.840088\pi$
$739$	−14.2599	+	12.3563i	−0.524558	+	0.454532i	0.351881	+	0.936045i	$0.385542\pi$
$740$		0			0
$741$	0.443952	+	0.222027i	0.0163090	+	0.00815635i
$742$		0			0
$743$	11.9043	+	40.5424i	0.436728	+	1.48736i	0.824638	+	0.565661i	$0.191379\pi$
$743$	11.9043	+	40.5424i	0.436728	+	1.48736i	−0.387910	+	0.921697i	$0.626803\pi$
$744$		0			0
$745$	29.0766	+	45.2441i	1.06529	+	1.65762i
$746$		0			0
$747$	36.5766	+	7.92914i	1.33827	+	0.290112i
$748$		0			0
$749$	36.2422	+	23.2914i	1.32426	+	0.851050i
$750$		0			0
$751$	0.861200	−	5.98978i	0.0314256	−	0.218570i	−0.968057	−	0.250730i	$-0.919329\pi$
$751$	0.861200	−	5.98978i	0.0314256	−	0.218570i	0.999483	+	0.0321598i	$0.0102385\pi$
$752$		0			0
$753$	−21.2345	−	14.7320i	−0.773827	−	0.536864i
$754$		0			0
$755$	1.38914	−	9.66168i	0.0505560	−	0.351625i
$756$		0			0
$757$	0.504090	+	0.230210i	0.0183215	+	0.00836714i	0.424555	−	0.905402i	$-0.360431\pi$
$757$	0.504090	+	0.230210i	0.0183215	+	0.00836714i	−0.406233	+	0.913769i	$0.633158\pi$
$758$		0			0
$759$	5.32740	−	0.574698i	0.193372	−	0.0208602i
$760$		0			0
$761$	1.51723	−	0.218144i	0.0549995	−	0.00790773i	−0.114760	−	0.993393i	$-0.536610\pi$
$761$	1.51723	−	0.218144i	0.0549995	−	0.00790773i	0.169760	+	0.985485i	$0.445701\pi$
$762$		0			0
$763$	−7.89288	−	54.8962i	−0.285741	−	1.98738i
$764$		0			0
$765$	−3.33347	+	47.0851i	−0.120522	+	1.70237i
$766$		0			0
$767$	−0.550666			−0.0198834
$768$		0			0
$769$	5.52872	−	2.52488i	0.199371	−	0.0910496i	−0.313228	−	0.949678i	$-0.601410\pi$
$769$	5.52872	−	2.52488i	0.199371	−	0.0910496i	0.512598	+	0.858629i	$0.328683\pi$
$770$		0			0
$771$	10.1119	+	17.0288i	0.364173	+	0.613277i
$772$		0			0
$773$	−16.8998	−	26.2967i	−0.607845	−	0.945825i	−0.999668	−	0.0257841i	$-0.991792\pi$
$773$	−16.8998	−	26.2967i	−0.607845	−	0.945825i	0.391823	−	0.920041i	$-0.371845\pi$
$774$		0			0
$775$			26.4755i			0.951028i
$776$		0			0
$777$	−0.579809	+	16.4001i	−0.0208005	+	0.588349i
$778$		0			0
$779$	0.0490316	+	0.0315107i	0.00175674	+	0.00112899i
$780$		0			0
$781$	2.81765	+	1.28678i	0.100823	+	0.0460445i
$782$		0			0
$783$	28.3753	−	35.2896i	1.01405	−	1.26115i
$784$		0			0
$785$	−22.9826	+	26.5234i	−0.820285	+	0.946659i
$786$		0			0
$787$	−24.4189	+	3.51090i	−0.870438	+	0.125150i	−0.563039	−	0.826430i	$-0.690368\pi$
$787$	−24.4189	+	3.51090i	−0.870438	+	0.125150i	−0.307399	+	0.951581i	$0.599459\pi$
$788$		0			0
$789$	−13.2226	−	22.2672i	−0.470737	−	0.792733i
$790$		0			0
$791$	−28.1745	+	43.8404i	−1.00177	+	1.55879i
$792$		0			0
$793$	−17.0681	−	5.01164i	−0.606105	−	0.177968i
$794$		0			0
$795$	−2.38693	−	5.75669i	−0.0846557	−	0.204169i
$796$		0			0
$797$	−37.9773	+	32.9075i	−1.34522	+	1.16564i	−0.374013	+	0.927423i	$0.622019\pi$
$797$	−37.9773	+	32.9075i	−1.34522	+	1.16564i	−0.971211	+	0.238220i	$0.923436\pi$
$798$		0			0
$799$	38.7770	+	11.3860i	1.37183	+	0.402806i
$800$		0			0
$801$	0.0226280	+	0.0413692i	0.000799522	+	0.00146171i
$802$		0			0
$803$	47.4986			1.67619
$804$		0			0
$805$	−8.52792			−0.300570
$806$		0			0
$807$	−26.3898	−	24.5520i	−0.928965	−	0.864272i
$808$		0			0
$809$	15.9590	+	4.68600i	0.561090	+	0.164751i	0.549966	−	0.835187i	$-0.314641\pi$
$809$	15.9590	+	4.68600i	0.561090	+	0.164751i	0.0111243	+	0.999938i	$0.496459\pi$
$810$		0			0
$811$	−31.8586	+	27.6056i	−1.11871	+	0.969365i	−0.999723	−	0.0235312i	$-0.992509\pi$
$811$	−31.8586	+	27.6056i	−1.11871	+	0.969365i	−0.118984	+	0.992896i	$0.537964\pi$
$812$		0			0
$813$	46.5614	−	19.3060i	1.63298	−	0.677092i
$814$		0			0
$815$	50.5788	+	14.8513i	1.77170	+	0.520218i
$816$		0			0
$817$	0.746304	−	1.16127i	0.0261099	−	0.0406278i
$818$		0			0
$819$	−15.9731	+	3.48680i	−0.558144	+	0.121838i
$820$		0			0
$821$	−33.2770	+	4.78451i	−1.16137	+	0.166980i	−0.695939	−	0.718101i	$-0.745011\pi$
$821$	−33.2770	+	4.78451i	−1.16137	+	0.166980i	−0.465436	+	0.885082i	$0.654102\pi$
$822$		0			0
$823$	5.30667	−	6.12422i	0.184979	−	0.213477i	−0.655685	−	0.755035i	$-0.727620\pi$
$823$	5.30667	−	6.12422i	0.184979	−	0.213477i	0.840663	+	0.541558i	$0.182165\pi$
$824$		0			0
$825$	25.9838	+	0.918632i	0.904640	+	0.0319827i
$826$		0			0
$827$	−24.7893	−	11.3209i	−0.862008	−	0.393666i	−0.0651809	−	0.997873i	$-0.520762\pi$
$827$	−24.7893	−	11.3209i	−0.862008	−	0.393666i	−0.796827	+	0.604208i	$0.793490\pi$
$828$		0			0
$829$	−2.65572	−	1.70673i	−0.0922369	−	0.0592771i	0.493709	−	0.869627i	$-0.335641\pi$
$829$	−2.65572	−	1.70673i	−0.0922369	−	0.0592771i	−0.585946	+	0.810350i	$0.699277\pi$
$830$		0			0
$831$	42.5602	+	1.50468i	1.47640	+	0.0521966i
$832$		0			0
$833$			39.1798i			1.35750i
$834$		0			0
$835$	1.09367	+	1.70178i	0.0378478	+	0.0588924i
$836$		0			0
$837$	−3.93105	+	36.9401i	−0.135877	+	1.27684i
$838$		0			0
$839$	−21.6673	+	9.89514i	−0.748040	+	0.341618i	−0.752694	−	0.658371i	$-0.771246\pi$
$839$	−21.6673	+	9.89514i	−0.748040	+	0.341618i	0.00465394	+	0.999989i	$0.498519\pi$
$840$		0			0
$841$	−46.9450			−1.61879
$842$		0			0
$843$	55.3334	−	14.1443i	1.90578	−	0.487154i
$844$		0			0
$845$	4.58883	+	31.9160i	0.157861	+	1.09794i
$846$		0			0
$847$	−20.3608	+	2.92745i	−0.699607	+	0.100588i
$848$		0			0
$849$	0.961083	+	8.90915i	0.0329843	+	0.305761i
$850$		0			0
$851$	−1.73657	−	0.793064i	−0.0595288	−	0.0271859i
$852$		0			0
$853$	5.84235	−	40.6345i	0.200038	−	1.39130i	−0.604125	−	0.796889i	$-0.706477\pi$
$853$	5.84235	−	40.6345i	0.200038	−	1.39130i	0.804164	−	0.594408i	$-0.202614\pi$
$854$		0			0
$855$	1.05742	+	1.41043i	0.0361632	+	0.0482358i
$856$		0			0
$857$	6.06500	−	42.1830i	0.207177	−	1.44094i	−0.575136	−	0.818058i	$-0.695051\pi$
$857$	6.06500	−	42.1830i	0.207177	−	1.44094i	0.782312	−	0.622886i	$-0.214040\pi$
$858$		0			0
$859$	15.5190	+	9.97347i	0.529502	+	0.340290i	0.777921	−	0.628362i	$-0.216275\pi$
$859$	15.5190	+	9.97347i	0.529502	+	0.340290i	−0.248419	+	0.968653i	$0.579911\pi$
$860$		0			0
$861$	−1.90863	+	0.205896i	−0.0650460	+	0.00701690i
$862$		0			0
$863$	−7.30510	−	11.3670i	−0.248668	−	0.386936i	0.694371	−	0.719618i	$-0.255683\pi$
$863$	−7.30510	−	11.3670i	−0.248668	−	0.386936i	−0.943039	+	0.332682i	$0.892046\pi$
$864$		0			0
$865$	17.8352	+	60.7412i	0.606416	+	2.06526i
$866$		0			0
$867$	−8.86734	+	17.7307i	−0.301151	+	0.602164i
$868$		0			0
$869$	−45.3393	+	39.2868i	−1.53803	+	1.33271i
$870$		0			0
$871$	7.12863	−	9.37486i	0.241544	−	0.317655i
$872$		0			0
$873$	47.8628	−	3.45791i	1.61991	−	0.117033i
$874$		0			0
$875$	14.3424	+	2.06212i	0.484861	+	0.0697124i
$876$		0			0
$877$	−15.3290	+	4.50101i	−0.517624	+	0.151988i	−0.530102	−	0.847934i	$-0.677846\pi$
$877$	−15.3290	+	4.50101i	−0.517624	+	0.151988i	0.0124776	+	0.999922i	$0.496028\pi$
$878$		0			0
$879$	−0.818018	−	3.20015i	−0.0275911	−	0.107938i
$880$		0			0
$881$	−15.1214	+	6.90569i	−0.509452	+	0.232659i	−0.653520	−	0.756909i	$-0.726709\pi$
$881$	−15.1214	+	6.90569i	−0.509452	+	0.232659i	0.144069	+	0.989568i	$0.453981\pi$
$882$		0			0
$883$	−13.6674	+	21.2668i	−0.459943	+	0.715686i	−0.991323	−	0.131448i	$-0.958037\pi$
$883$	−13.6674	+	21.2668i	−0.459943	+	0.715686i	0.531380	+	0.847134i	$0.321674\pi$
$884$		0			0
$885$	−1.74907	−	0.874731i	−0.0587942	−	0.0294038i
$886$		0			0
$887$	14.8180	−	50.4653i	0.497538	−	1.69446i	−0.201595	−	0.979469i	$-0.564613\pi$
$887$	14.8180	−	50.4653i	0.497538	−	1.69446i	0.699134	−	0.714991i	$-0.253569\pi$
$888$		0			0
$889$	−14.8309	−	2.13237i	−0.497413	−	0.0715172i
$890$		0			0
$891$	36.1177	+	5.13977i	1.20999	+	0.172189i
$892$		0			0
$893$	1.37288	−	0.626972i	0.0459416	−	0.0209808i
$894$		0			0
$895$	−1.40296	−	9.75780i	−0.0468958	−	0.326167i
$896$		0			0
$897$	0.337028	−	1.87188i	0.0112530	−	0.0625003i
$898$		0			0
$899$	52.4128	−	33.6837i	1.74807	−	1.12341i
$900$		0			0
$901$		−	6.50472i		−	0.216704i
$902$		0			0
$903$	4.87646	+	45.2044i	0.162279	+	1.50431i
$904$		0			0
$905$	−4.79594	+	5.53481i	−0.159422	+	0.183983i
$906$		0			0
$907$	41.5788	−	26.7211i	1.38060	−	0.887259i	0.381294	−	0.924454i	$-0.375478\pi$
$907$	41.5788	−	26.7211i	1.38060	−	0.887259i	0.999308	+	0.0371944i	$0.0118421\pi$
$908$		0			0
$909$	−33.2988	−	24.8897i	−1.10445	−	0.825540i
$910$		0			0
$911$	8.68233	+	29.5693i	0.287659	+	0.979675i	0.968866	+	0.247585i	$0.0796369\pi$
$911$	8.68233	+	29.5693i	0.287659	+	0.979675i	−0.681208	+	0.732090i	$0.738545\pi$
$912$		0			0
$913$	27.3397	−	42.5415i	0.904813	−	1.40792i
$914$		0			0
$915$	−46.2518	−	43.0309i	−1.52904	−	1.42256i
$916$		0			0
$917$	−12.1740	+	3.57460i	−0.402019	+	0.118044i
$918$		0			0
$919$	35.9822	+	31.1787i	1.18694	+	1.02849i	0.998926	+	0.0463247i	$0.0147509\pi$
$919$	35.9822	+	31.1787i	1.18694	+	1.02849i	0.188015	+	0.982166i	$0.439795\pi$
$920$		0			0
$921$	−0.835383	+	4.63979i	−0.0275268	+	0.152886i
$922$		0			0
$923$	0.720026	−	0.830954i	0.0236999	−	0.0273512i
$924$		0			0
$925$	−7.79291	−	5.00820i	−0.256229	−	0.164669i
$926$		0			0
$927$	−0.334637	−	0.446351i	−0.0109909	−	0.0146601i
$928$		0			0
$929$	−34.8473	−	40.2159i	−1.14330	−	1.31944i	−0.940332	−	0.340258i	$-0.889486\pi$
$929$	−34.8473	−	40.2159i	−1.14330	−	1.31944i	−0.202971	−	0.979185i	$-0.565060\pi$
$930$		0			0
$931$	0.958175	+	1.10579i	0.0314029	+	0.0362409i
$932$		0			0
$933$	2.24551	+	1.55789i	0.0735147	+	0.0510029i
$934$		0			0
$935$	58.0156	+	26.4948i	1.89731	+	0.866474i
$936$		0			0
$937$		−	23.3787i		−	0.763748i	−0.924214	−	0.381874i	$-0.875279\pi$
$937$		−	23.3787i		−	0.763748i	0.924214	−	0.381874i	$-0.124721\pi$
$938$		0			0
$939$	−1.29317	+	3.89005i	−0.0422012	+	0.126947i
$940$		0			0
$941$	−6.54190	+	14.3248i	−0.213260	+	0.466974i	−0.985785	−	0.168010i	$-0.946266\pi$
$941$	−6.54190	+	14.3248i	−0.213260	+	0.466974i	0.772526	+	0.634984i	$0.218993\pi$
$942$		0			0
$943$	0.0629189	−	0.214282i	0.00204892	−	0.00697798i
$944$		0			0
$945$	−56.2735	−	14.2981i	−1.83058	−	0.465118i
$946$		0			0
$947$	−1.36387	+	1.18180i	−0.0443198	+	0.0384034i	−0.676739	−	0.736223i	$-0.736607\pi$
$947$	−1.36387	+	1.18180i	−0.0443198	+	0.0384034i	0.632419	+	0.774626i	$0.282062\pi$
$948$		0			0
$949$	4.75003	−	16.1771i	0.154192	−	0.525131i
$950$		0			0
$951$	−2.19281	+	1.76838i	−0.0711067	+	0.0573437i
$952$		0			0
$953$	26.8276	+	23.2462i	0.869031	+	0.753020i	0.970317	−	0.241838i	$-0.0777502\pi$
$953$	26.8276	+	23.2462i	0.869031	+	0.753020i	−0.101286	+	0.994857i	$0.532296\pi$
$954$		0			0
$955$	2.34267	+	16.2936i	0.0758069	+	0.527249i
$956$		0			0
$957$	−31.2396	−	52.6082i	−1.00983	−	1.70058i
$958$		0			0
$959$	−16.1211	−	54.9033i	−0.520576	−	1.77292i
$960$		0			0
$961$	−8.35481	+	18.2945i	−0.269510	+	0.590145i
$962$		0			0
$963$	−31.9625	+	11.9477i	−1.02998	+	0.385009i
$964$		0			0
$965$	58.1847	−	17.0846i	1.87303	−	0.549972i
$966$		0			0
$967$	−21.1933			−0.681530			−0.340765	−	0.940149i	$-0.610686\pi$
$967$	−21.1933			−0.681530			−0.340765	+	0.940149i	$0.610686\pi$
$968$		0			0
$969$	0.455678	+	1.78265i	0.0146385	+	0.0572668i
$970$		0			0
$971$	−13.2617	−	11.4913i	−0.425587	−	0.368774i	0.415573	−	0.909560i	$-0.363581\pi$
$971$	−13.2617	−	11.4913i	−0.425587	−	0.368774i	−0.841160	+	0.540787i	$0.818127\pi$
$972$		0			0
$973$	−24.4412	−	53.5187i	−0.783548	−	1.71573i
$974$		0			0
$975$	2.91134	−	8.75772i	0.0932376	−	0.280472i
$976$		0			0
$977$	7.36138	+	11.4545i	0.235511	+	0.366463i	0.938812	−	0.344429i	$-0.111928\pi$
$977$	7.36138	+	11.4545i	0.235511	+	0.366463i	−0.703301	+	0.710892i	$0.748291\pi$
$978$		0			0
$979$	0.0630636	−	0.00906718i	0.00201552	−	0.000289788i
$980$		0			0
$981$	38.5697	+	21.0246i	1.23144	+	0.671263i
$982$		0			0
$983$	−19.7227	−	43.1868i	−0.629058	−	1.37744i	−0.908744	−	0.417353i	$-0.862958\pi$
$983$	−19.7227	−	43.1868i	−0.629058	−	1.37744i	0.279686	−	0.960091i	$-0.409770\pi$
$984$		0			0
$985$	−3.03462	+	6.64488i	−0.0966909	+	0.211723i
$986$		0			0
$987$	−22.2354	+	44.4608i	−0.707762	+	1.41520i
$988$		0			0
$989$	−5.07509	−	1.49018i	−0.161379	−	0.0473850i
$990$		0			0
$991$	13.7419	+	1.97579i	0.436527	+	0.0627631i	0.357075	−	0.934076i	$-0.383774\pi$
$991$	13.7419	+	1.97579i	0.436527	+	0.0627631i	0.0794517	+	0.996839i	$0.474683\pi$
$992$		0			0
$993$	−38.5833	+	31.1154i	−1.22440	+	0.987416i
$994$		0			0
$995$	−6.16993	−	13.5103i	−0.195600	−	0.428304i
$996$		0			0
$997$	2.72231	−	1.74952i	0.0862165	−	0.0554080i	−0.496822	−	0.867852i	$-0.665500\pi$
$997$	2.72231	−	1.74952i	0.0862165	−	0.0554080i	0.583039	+	0.812444i	$0.301864\pi$
$998$		0			0
$999$	−10.1295	−	8.14480i	−0.320483	−	0.257690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.161.6	yes	200
3.2	odd	2	inner	804.2.s.b.161.12	yes	200
67.5	odd	22	inner	804.2.s.b.5.12	yes	200
201.5	even	22	inner	804.2.s.b.5.6	✓	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.6	✓	200	201.5	even	22	inner
804.2.s.b.5.12	yes	200	67.5	odd	22	inner
804.2.s.b.161.6	yes	200	1.1	even	1	trivial
804.2.s.b.161.12	yes	200	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17979 + 1.26810i) q^{3} +(2.83063 + 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-0.216176 - 2.99220i) q^{9} +O(q^{10})\)	\(q+(-1.17979 + 1.26810i) q^{3} +(2.83063 + 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-0.216176 - 2.99220i) q^{9} +(-3.88931 - 1.14200i) q^{11} +(-0.777890 + 1.21042i) q^{13} +(-4.39353 + 2.60895i) q^{15} +(-5.27916 + 0.759028i) q^{17} +(-0.130434 + 0.150529i) q^{19} +(0.231790 - 6.55625i) q^{21} +(0.694228 + 0.317043i) q^{23} +(3.11537 + 2.00213i) q^{25} +(4.04946 + 3.25605i) q^{27} -8.71464i q^{29} +(3.86518 + 6.01434i) q^{31} +(6.03676 - 3.58472i) q^{33} +(-10.1642 + 4.64183i) q^{35} -2.50144 q^{37} +(-0.617189 - 2.41449i) q^{39} +(-0.0416445 - 0.289644i) q^{41} +(-6.85998 + 0.986316i) q^{43} +(1.87505 - 8.64948i) q^{45} +(-6.89272 - 3.14780i) q^{47} +(1.04545 - 7.27129i) q^{49} +(5.26579 - 7.59001i) q^{51} +(-0.173569 + 1.20720i) q^{53} +(-10.0600 - 6.46518i) q^{55} +(-0.0370010 - 0.342996i) q^{57} +(0.206913 + 0.321963i) q^{59} +(3.48314 + 11.8625i) q^{61} +(8.04055 + 8.02896i) q^{63} +(-3.20795 + 2.77971i) q^{65} +(-8.15987 - 0.645356i) q^{67} +(-1.22109 + 0.506307i) q^{69} +(-0.756392 - 0.108753i) q^{71} +(-11.2432 + 3.30131i) q^{73} +(-6.21440 + 1.58852i) q^{75} +(13.9657 - 6.37792i) q^{77} +(8.00157 - 12.4507i) q^{79} +(-8.90654 + 1.29368i) q^{81} +(-3.51473 + 11.9701i) q^{83} +(-15.5742 - 2.23923i) q^{85} +(11.0511 + 10.2815i) q^{87} +(-0.0142974 + 0.00652940i) q^{89} +(-0.775578 - 5.39427i) q^{91} +(-12.1869 - 2.19423i) q^{93} +(-0.494321 + 0.317681i) q^{95} +15.9958i q^{97} +(-2.57633 + 11.8845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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