LMFDB - Embedded newform 810.2.s.a.773.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			773.13
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.529859 - 2.17238i) q^{5} +(1.88653 + 1.32096i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.529859 - 2.17238i) q^{5} +(1.88653 + 1.32096i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.338507 - 2.21030i) q^{10} +(0.0819834 - 0.225247i) q^{11} +(0.178036 + 2.03496i) q^{13} +(1.76422 + 1.48036i) q^{14} +(0.939693 + 0.342020i) q^{16} +(6.39398 - 1.71326i) q^{17} +(1.24940 - 0.721342i) q^{19} +(-0.144579 - 2.23139i) q^{20} +(0.101303 - 0.217245i) q^{22} +(-2.29713 - 3.28065i) q^{23} +(-4.43850 + 2.30211i) q^{25} +2.04273i q^{26} +(1.62849 + 1.62849i) q^{28} +(6.94075 - 5.82398i) q^{29} +(0.853954 - 4.84302i) q^{31} +(0.906308 + 0.422618i) q^{32} +(6.51897 - 1.14947i) q^{34} +(1.87004 - 4.79819i) q^{35} +(0.998014 + 3.72464i) q^{37} +(1.30752 - 0.609704i) q^{38} +(0.0504497 - 2.23550i) q^{40} +(-5.73269 + 6.83195i) q^{41} +(-0.464803 - 0.996773i) q^{43} +(0.119852 - 0.207589i) q^{44} +(-2.00247 - 3.46837i) q^{46} +(1.98990 - 2.84187i) q^{47} +(-0.580090 - 1.59378i) q^{49} +(-4.62225 + 1.90651i) q^{50} +(-0.178036 + 2.03496i) q^{52} +(-4.45596 + 4.45596i) q^{53} +(-0.532763 - 0.0587499i) q^{55} +(1.48036 + 1.76422i) q^{56} +(7.42193 - 5.19689i) q^{58} +(-7.55529 + 2.74990i) q^{59} +(1.84255 + 10.4496i) q^{61} +(1.27280 - 4.75016i) q^{62} +(0.866025 + 0.500000i) q^{64} +(4.32637 - 1.46500i) q^{65} +(8.05202 - 0.704460i) q^{67} +(6.59434 - 0.576930i) q^{68} +(2.28111 - 4.61694i) q^{70} +(-6.87978 - 3.97204i) q^{71} +(1.37861 - 5.14504i) q^{73} +(0.669592 + 3.79745i) q^{74} +(1.35568 - 0.493427i) q^{76} +(0.452207 - 0.316639i) q^{77} +(5.84837 + 6.96981i) q^{79} +(0.245094 - 2.22260i) q^{80} +(-6.30632 + 6.30632i) q^{82} +(-1.26085 + 14.4115i) q^{83} +(-7.10977 - 12.9824i) q^{85} +(-0.376160 - 1.03349i) q^{86} +(0.137488 - 0.196353i) q^{88} +(1.89691 + 3.28554i) q^{89} +(-2.35223 + 4.07418i) q^{91} +(-1.69256 - 3.62970i) q^{92} +(2.23001 - 2.65763i) q^{94} +(-2.22904 - 2.33197i) q^{95} +(-8.93186 + 4.16500i) q^{97} +(-0.438975 - 1.63828i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−0.529859	−	2.17238i	−0.236960	−	0.971519i
$5$	−0.529859	−	2.17238i	−0.236960	−	0.971519i
$6$		0			0
$7$	1.88653	+	1.32096i	0.713041	+	0.499277i	0.872922	−	0.487860i	$-0.162222\pi$
$7$	1.88653	+	1.32096i	0.713041	+	0.499277i	−0.159881	+	0.987136i	$0.551111\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	−0.338507	−	2.21030i	−0.107045	−	0.698957i
$11$	0.0819834	−	0.225247i	0.0247189	−	0.0679147i	−0.926719	−	0.375754i	$-0.877384\pi$
$11$	0.0819834	−	0.225247i	0.0247189	−	0.0679147i	0.951438	+	0.307839i	$0.0996060\pi$
$12$		0			0
$13$	0.178036	+	2.03496i	0.0493782	+	0.564396i	0.980078	+	0.198612i	$0.0636434\pi$
$13$	0.178036	+	2.03496i	0.0493782	+	0.564396i	−0.930700	+	0.365784i	$0.880801\pi$
$14$	1.76422	+	1.48036i	0.471508	+	0.395642i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	6.39398	−	1.71326i	1.55077	−	0.415527i	0.621041	−	0.783778i	$-0.286710\pi$
$17$	6.39398	−	1.71326i	1.55077	−	0.415527i	0.929726	+	0.368251i	$0.120043\pi$
$18$		0			0
$19$	1.24940	−	0.721342i	0.286632	−	0.165487i	−0.349790	−	0.936828i	$-0.613747\pi$
$19$	1.24940	−	0.721342i	0.286632	−	0.165487i	0.636422	+	0.771341i	$0.280414\pi$
$20$	−0.144579	−	2.23139i	−0.0323288	−	0.498954i
$21$		0			0
$22$	0.101303	−	0.217245i	0.0215979	−	0.0463168i
$23$	−2.29713	−	3.28065i	−0.478986	−	0.684063i	0.504835	−	0.863216i	$-0.331553\pi$
$23$	−2.29713	−	3.28065i	−0.478986	−	0.684063i	−0.983821	+	0.179153i	$0.942664\pi$
$24$		0			0
$25$	−4.43850	+	2.30211i	−0.887700	+	0.460423i
$26$			2.04273i			0.400613i
$27$		0			0
$28$	1.62849	+	1.62849i	0.307755	+	0.307755i
$29$	6.94075	−	5.82398i	1.28887	−	1.08149i	0.296909	−	0.954906i	$-0.404044\pi$
$29$	6.94075	−	5.82398i	1.28887	−	1.08149i	0.991956	−	0.126581i	$-0.0404003\pi$
$30$		0			0
$31$	0.853954	−	4.84302i	0.153375	−	0.869831i	−0.806882	−	0.590713i	$-0.798847\pi$
$31$	0.853954	−	4.84302i	0.153375	−	0.869831i	0.960257	−	0.279119i	$-0.0900423\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	6.51897	−	1.14947i	1.11799	−	0.197132i
$35$	1.87004	−	4.79819i	0.316095	−	0.811042i
$36$		0			0
$37$	0.998014	+	3.72464i	0.164072	+	0.612327i	0.998157	+	0.0606896i	$0.0193300\pi$
$37$	0.998014	+	3.72464i	0.164072	+	0.612327i	−0.834084	+	0.551637i	$0.814003\pi$
$38$	1.30752	−	0.609704i	0.212107	−	0.0989071i
$39$		0			0
$40$	0.0504497	−	2.23550i	0.00797680	−	0.353463i
$41$	−5.73269	+	6.83195i	−0.895296	+	1.06697i	0.102095	+	0.994775i	$0.467445\pi$
$41$	−5.73269	+	6.83195i	−0.895296	+	1.06697i	−0.997390	+	0.0721970i	$0.976999\pi$
$42$		0			0
$43$	−0.464803	−	0.996773i	−0.0708818	−	0.152006i	0.867674	−	0.497133i	$-0.165614\pi$
$43$	−0.464803	−	0.996773i	−0.0708818	−	0.152006i	−0.938556	+	0.345126i	$0.887836\pi$
$44$	0.119852	−	0.207589i	0.0180683	−	0.0312952i
$45$		0			0
$46$	−2.00247	−	3.46837i	−0.295248	−	0.511384i
$47$	1.98990	−	2.84187i	0.290257	−	0.414530i	−0.647369	−	0.762177i	$-0.724131\pi$
$47$	1.98990	−	2.84187i	0.290257	−	0.414530i	0.937625	+	0.347648i	$0.113019\pi$
$48$		0			0
$49$	−0.580090	−	1.59378i	−0.0828700	−	0.227683i
$50$	−4.62225	+	1.90651i	−0.653685	+	0.269622i
$51$		0			0
$52$	−0.178036	+	2.03496i	−0.0246891	+	0.282198i
$53$	−4.45596	+	4.45596i	−0.612073	+	0.612073i	−0.943486	−	0.331413i	$-0.892475\pi$
$53$	−4.45596	+	4.45596i	−0.612073	+	0.612073i	0.331413	+	0.943486i	$0.392475\pi$
$54$		0			0
$55$	−0.532763	−	0.0587499i	−0.0718378	−	0.00792184i
$56$	1.48036	+	1.76422i	0.197821	+	0.235754i
$57$		0			0
$58$	7.42193	−	5.19689i	0.974548	−	0.682386i
$59$	−7.55529	+	2.74990i	−0.983616	+	0.358007i	−0.783245	−	0.621713i	$-0.786437\pi$
$59$	−7.55529	+	2.74990i	−0.983616	+	0.358007i	−0.200371	+	0.979720i	$0.564215\pi$
$60$		0			0
$61$	1.84255	+	10.4496i	0.235914	+	1.33793i	0.840680	+	0.541532i	$0.182155\pi$
$61$	1.84255	+	10.4496i	0.235914	+	1.33793i	−0.604766	+	0.796403i	$0.706734\pi$
$62$	1.27280	−	4.75016i	0.161646	−	0.603271i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	4.32637	−	1.46500i	0.536621	−	0.181711i
$66$		0			0
$67$	8.05202	−	0.704460i	0.983711	−	0.0860635i	0.416064	−	0.909335i	$-0.363409\pi$
$67$	8.05202	−	0.704460i	0.983711	−	0.0860635i	0.567647	+	0.823272i	$0.307854\pi$
$68$	6.59434	−	0.576930i	0.799681	−	0.0699631i
$69$		0			0
$70$	2.28111	−	4.61694i	0.272645	−	0.551830i
$71$	−6.87978	−	3.97204i	−0.816480	−	0.471395i	0.0327212	−	0.999465i	$-0.489583\pi$
$71$	−6.87978	−	3.97204i	−0.816480	−	0.471395i	−0.849201	+	0.528070i	$0.822916\pi$
$72$		0			0
$73$	1.37861	−	5.14504i	0.161354	−	0.602181i	−0.837123	−	0.547014i	$-0.815764\pi$
$73$	1.37861	−	5.14504i	0.161354	−	0.602181i	0.998477	−	0.0551667i	$-0.0175690\pi$
$74$	0.669592	+	3.79745i	0.0778385	+	0.441444i
$75$		0			0
$76$	1.35568	−	0.493427i	0.155507	−	0.0565999i
$77$	0.452207	−	0.316639i	0.0515338	−	0.0360843i
$78$		0			0
$79$	5.84837	+	6.96981i	0.657993	+	0.784165i	0.987096	−	0.160129i	$-0.0511910\pi$
$79$	5.84837	+	6.96981i	0.657993	+	0.784165i	−0.329104	+	0.944294i	$0.606747\pi$
$80$	0.245094	−	2.22260i	0.0274024	−	0.248494i
$81$		0			0
$82$	−6.30632	+	6.30632i	−0.696416	+	0.696416i
$83$	−1.26085	+	14.4115i	−0.138396	+	1.58187i	0.536463	+	0.843924i	$0.319760\pi$
$83$	−1.26085	+	14.4115i	−0.138396	+	1.58187i	−0.674859	+	0.737947i	$0.735795\pi$
$84$		0			0
$85$	−7.10977	−	12.9824i	−0.771162	−	1.40814i
$86$	−0.376160	−	1.03349i	−0.0405623	−	0.111444i
$87$		0			0
$88$	0.137488	−	0.196353i	0.0146563	−	0.0209313i
$89$	1.89691	+	3.28554i	0.201072	+	0.348267i	0.948874	−	0.315655i	$-0.102224\pi$
$89$	1.89691	+	3.28554i	0.201072	+	0.348267i	−0.747802	+	0.663922i	$0.768891\pi$
$90$		0			0
$91$	−2.35223	+	4.07418i	−0.246581	+	0.427091i
$92$	−1.69256	−	3.62970i	−0.176461	−	0.378423i
$93$		0			0
$94$	2.23001	−	2.65763i	0.230008	−	0.274113i
$95$	−2.22904	−	2.33197i	−0.228694	−	0.239255i
$96$		0			0
$97$	−8.93186	+	4.16500i	−0.906893	+	0.422891i	−0.819366	−	0.573271i	$-0.805674\pi$
$97$	−8.93186	+	4.16500i	−0.906893	+	0.422891i	−0.0875273	+	0.996162i	$0.527897\pi$
$98$	−0.438975	−	1.63828i	−0.0443432	−	0.165491i
$99$		0			0
$100$	−4.77083	+	1.49640i	−0.477083	+	0.149640i
$101$	−16.0221	+	2.82513i	−1.59426	+	0.281111i	−0.899100	−	0.437743i	$-0.855778\pi$
$101$	−16.0221	+	2.82513i	−1.59426	+	0.281111i	−0.695161	+	0.718855i	$0.744667\pi$
$102$		0			0
$103$	−3.34004	−	1.55749i	−0.329104	−	0.153464i	0.251042	−	0.967976i	$-0.419227\pi$
$103$	−3.34004	−	1.55749i	−0.329104	−	0.153464i	−0.580146	+	0.814512i	$0.697005\pi$
$104$	−0.354717	+	2.01170i	−0.0347828	+	0.197263i
$105$		0			0
$106$	−4.82737	+	4.05064i	−0.468875	+	0.393433i
$107$	−13.4628	−	13.4628i	−1.30149	−	1.30149i	−0.927384	−	0.374111i	$-0.877948\pi$
$107$	−13.4628	−	13.4628i	−1.30149	−	1.30149i	−0.374111	−	0.927384i	$-0.622052\pi$
$108$		0			0
$109$			18.9996i			1.81984i	0.414788	+	0.909918i	$0.363856\pi$
$109$			18.9996i			1.81984i	−0.414788	+	0.909918i	$0.636144\pi$
$110$	−0.525616	−	0.104960i	−0.0501155	−	0.0100075i
$111$		0			0
$112$	1.32096	+	1.88653i	0.124819	+	0.178260i
$113$	0.618148	−	1.32562i	0.0581505	−	0.124704i	−0.875085	−	0.483969i	$-0.839195\pi$
$113$	0.618148	−	1.32562i	0.0581505	−	0.124704i	0.933236	+	0.359265i	$0.116973\pi$
$114$		0			0
$115$	−5.90967	+	6.72854i	−0.551079	+	0.627439i
$116$	7.84663	−	4.53025i	0.728541	−	0.420624i
$117$		0			0
$118$	−7.76621	+	2.08095i	−0.714938	+	0.191567i
$119$	14.3256	+	5.21408i	1.31322	+	0.477974i
$120$		0			0
$121$	8.38247	+	7.03373i	0.762043	+	0.639430i
$122$	0.924793	+	10.5704i	0.0837268	+	0.957001i
$123$		0			0
$124$	1.68196	−	4.62115i	0.151045	−	0.414992i
$125$	7.35285	+	8.42233i	0.657659	+	0.753316i
$126$		0			0
$127$	−3.92295	−	1.05115i	−0.348106	−	0.0932747i	0.0805296	−	0.996752i	$-0.474339\pi$
$127$	−3.92295	−	1.05115i	−0.348106	−	0.0932747i	−0.428635	+	0.903478i	$0.641006\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	4.43759	−	1.08236i	0.389203	−	0.0949292i
$131$	−18.9884	−	3.34816i	−1.65902	−	0.292530i	−0.735916	−	0.677073i	$-0.763248\pi$
$131$	−18.9884	−	3.34816i	−1.65902	−	0.292530i	−0.923107	+	0.384543i	$0.874359\pi$
$132$		0			0
$133$	3.30989	+	0.289578i	0.287004	+	0.0251096i
$134$	8.08278			0.698246
$135$		0			0
$136$	6.61953			0.567620
$137$	19.2804	+	1.68681i	1.64723	+	0.144114i	0.872646	−	0.488353i	$-0.162402\pi$
$137$	19.2804	+	1.68681i	1.64723	+	0.144114i	0.774587	+	0.632467i	$0.217958\pi$
$138$		0			0
$139$	−16.3123	−	2.87629i	−1.38359	−	0.243964i	−0.568206	−	0.822887i	$-0.692362\pi$
$139$	−16.3123	−	2.87629i	−1.38359	−	0.243964i	−0.815382	+	0.578923i	$0.803473\pi$
$140$	2.67483	−	4.40056i	0.226064	−	0.371915i
$141$		0			0
$142$	−6.50742	−	4.55654i	−0.546090	−	0.382376i
$143$	0.472965	+	0.126731i	0.0395513	+	0.0105977i
$144$		0			0
$145$	−16.3295	−	11.9921i	−1.35609	−	0.995889i
$146$	1.82178	−	5.00530i	0.150772	−	0.414242i
$147$		0			0
$148$	0.336075	+	3.84135i	0.0276252	+	0.315757i
$149$	−8.16866	−	6.85432i	−0.669203	−	0.561528i	0.243626	−	0.969869i	$-0.421663\pi$
$149$	−8.16866	−	6.85432i	−0.669203	−	0.561528i	−0.912829	+	0.408341i	$0.866107\pi$
$150$		0			0
$151$	−0.337006	−	0.122660i	−0.0274251	−	0.00998193i	0.328271	−	0.944584i	$-0.393534\pi$
$151$	−0.337006	−	0.122660i	−0.0274251	−	0.00998193i	−0.355696	+	0.934602i	$0.615756\pi$
$152$	1.39353	−	0.373394i	0.113030	−	0.0302862i
$153$		0			0
$154$	0.478083	−	0.276022i	0.0385250	−	0.0222424i
$155$	−10.9734	+	0.710999i	−0.881402	+	0.0571088i
$156$		0			0
$157$	10.1799	−	21.8309i	0.812444	−	1.74229i	0.156226	−	0.987721i	$-0.450067\pi$
$157$	10.1799	−	21.8309i	0.812444	−	1.74229i	0.656218	−	0.754571i	$-0.272155\pi$
$158$	5.21865	+	7.45301i	0.415174	+	0.592929i
$159$		0			0
$160$	0.437874	−	2.19278i	0.0346169	−	0.173354i
$161$		−	9.22346i		−	0.726911i
$162$		0			0
$163$	−4.31127	−	4.31127i	−0.337685	−	0.337685i	0.517810	−	0.855495i	$-0.326747\pi$
$163$	−4.31127	−	4.31127i	−0.337685	−	0.337685i	−0.855495	+	0.517810i	$0.826747\pi$
$164$	−6.83195	+	5.73269i	−0.533486	+	0.447648i
$165$		0			0
$166$	−2.51210	+	14.2468i	−0.194976	+	1.10577i
$167$	−10.9075	−	5.08624i	−0.844046	−	0.393585i	−0.0480189	−	0.998846i	$-0.515291\pi$
$167$	−10.9075	−	5.08624i	−0.844046	−	0.393585i	−0.796027	+	0.605262i	$0.793069\pi$
$168$		0			0
$169$	8.69314	−	1.53284i	0.668703	−	0.117910i
$170$	−5.95122	−	13.5526i	−0.456438	−	1.03944i
$171$		0			0
$172$	−0.284654	−	1.06234i	−0.0217046	−	0.0810028i
$173$	1.06790	−	0.497970i	0.0811910	−	0.0378600i	−0.381599	−	0.924328i	$-0.624626\pi$
$173$	1.06790	−	0.497970i	0.0811910	−	0.0378600i	0.462790	+	0.886468i	$0.346849\pi$
$174$		0			0
$175$	−11.4144	−	1.52008i	−0.862844	−	0.114907i
$176$	0.154078	−	0.183623i	0.0116141	−	0.0138411i
$177$		0			0
$178$	1.60334	+	3.43837i	0.120175	+	0.257717i
$179$	−5.27250	+	9.13224i	−0.394085	+	0.682576i	−0.992984	−	0.118249i	$-0.962272\pi$
$179$	−5.27250	+	9.13224i	−0.394085	+	0.682576i	0.598899	+	0.800825i	$0.295605\pi$
$180$		0			0
$181$	−4.64926	−	8.05275i	−0.345577	−	0.598556i	0.639882	−	0.768473i	$-0.278983\pi$
$181$	−4.64926	−	8.05275i	−0.345577	−	0.598556i	−0.985458	+	0.169917i	$0.945650\pi$
$182$	−2.69837	+	3.85367i	−0.200016	+	0.285653i
$183$		0			0
$184$	−1.36977	−	3.76341i	−0.100981	−	0.277442i
$185$	7.56253	−	4.14160i	0.556009	−	0.304497i
$186$		0			0
$187$	0.138292	−	1.58069i	0.0101129	−	0.115591i
$188$	2.45315	−	2.45315i	0.178915	−	0.178915i
$189$		0			0
$190$	−2.01731	−	2.51737i	−0.146351	−	0.182629i
$191$	14.4035	+	17.1654i	1.04220	+	1.24205i	0.969602	+	0.244687i	$0.0786852\pi$
$191$	14.4035	+	17.1654i	1.04220	+	1.24205i	0.0726001	+	0.997361i	$0.476870\pi$
$192$		0			0
$193$	−3.28128	+	2.29758i	−0.236192	+	0.165383i	−0.685680	−	0.727903i	$-0.740495\pi$
$193$	−3.28128	+	2.29758i	−0.236192	+	0.165383i	0.449488	+	0.893286i	$0.351606\pi$
$194$	−9.26088	+	3.37068i	−0.664892	+	0.242001i
$195$		0			0
$196$	−0.294519	−	1.67030i	−0.0210371	−	0.119307i
$197$	−1.51589	+	5.65739i	−0.108003	+	0.403073i	−0.998669	−	0.0515865i	$-0.983572\pi$
$197$	−1.51589	+	5.65739i	−0.108003	+	0.403073i	0.890666	+	0.454659i	$0.150239\pi$
$198$		0			0
$199$	4.01337	+	2.31712i	0.284500	+	0.164256i	0.635459	−	0.772135i	$-0.280811\pi$
$199$	4.01337	+	2.31712i	0.284500	+	0.164256i	−0.350959	+	0.936391i	$0.614144\pi$
$200$	−4.88309	+	1.07490i	−0.345287	+	0.0760071i
$201$		0			0
$202$	−16.2074	+	1.41796i	−1.14035	+	0.0997674i
$203$	20.7872	−	1.81864i	1.45897	−	0.127644i
$204$		0			0
$205$	17.8791	+	8.83363i	1.24873	+	0.616967i
$206$	−3.19159	−	1.84266i	−0.222369	−	0.128385i
$207$		0			0
$208$	−0.528698	+	1.97313i	−0.0366586	+	0.136812i
$209$	−0.0600503	−	0.340562i	−0.00415377	−	0.0235572i
$210$		0			0
$211$	−24.0313	+	8.74669i	−1.65438	+	0.602147i	−0.989466	−	0.144769i	$-0.953756\pi$
$211$	−24.0313	+	8.74669i	−1.65438	+	0.602147i	−0.664919	+	0.746915i	$0.731534\pi$
$212$	−5.16203	+	3.61450i	−0.354530	+	0.248245i
$213$		0			0
$214$	−12.2382	−	14.5849i	−0.836585	−	0.997003i
$215$	−1.91909	+	1.53788i	−0.130881	+	0.104882i
$216$		0			0
$217$	8.00845	−	8.00845i	0.543649	−	0.543649i
$218$	−1.65593	+	18.9273i	−0.112154	+	1.28192i
$219$		0			0
$220$	−0.514468	−	0.150371i	−0.0346854	−	0.0101380i
$221$	4.62477	+	12.7065i	0.311096	+	0.854728i
$222$		0			0
$223$	9.63356	−	13.7581i	0.645111	−	0.921314i	−0.354796	−	0.934944i	$-0.615450\pi$
$223$	9.63356	−	13.7581i	0.645111	−	0.921314i	0.999907	+	0.0136298i	$0.00433864\pi$
$224$	1.15151	+	1.99448i	0.0769387	+	0.133262i
$225$		0			0
$226$	0.731331	−	1.26670i	0.0486474	−	0.0842598i
$227$	−1.20184	−	2.57735i	−0.0797688	−	0.171065i	0.862378	−	0.506264i	$-0.168974\pi$
$227$	−1.20184	−	2.57735i	−0.0797688	−	0.171065i	−0.942147	+	0.335200i	$0.891196\pi$
$228$		0			0
$229$	10.0216	−	11.9433i	0.662246	−	0.789234i	−0.325460	−	0.945556i	$-0.605519\pi$
$229$	10.0216	−	11.9433i	0.662246	−	0.789234i	0.987706	+	0.156322i	$0.0499637\pi$
$230$	−6.47361	+	6.18787i	−0.426857	+	0.408016i
$231$		0			0
$232$	8.21161	−	3.82914i	0.539119	−	0.251395i
$233$	2.06299	+	7.69919i	0.135151	+	0.504391i	0.999997	+	0.00235377i	$0.000749228\pi$
$233$	2.06299	+	7.69919i	0.135151	+	0.504391i	−0.864846	+	0.502037i	$0.832584\pi$
$234$		0			0
$235$	−7.22800	−	2.81703i	−0.471503	−	0.183763i
$236$	−7.91803	+	1.39616i	−0.515420	+	0.0908824i
$237$		0			0
$238$	13.8166	+	6.44280i	0.895599	+	0.417624i
$239$	−2.84653	+	16.1435i	−0.184127	+	1.04424i	0.742945	+	0.669352i	$0.233428\pi$
$239$	−2.84653	+	16.1435i	−0.184127	+	1.04424i	−0.927072	+	0.374883i	$0.877683\pi$
$240$		0			0
$241$	−2.40426	+	2.01741i	−0.154872	+	0.129953i	−0.716931	−	0.697144i	$-0.754454\pi$
$241$	−2.40426	+	2.01741i	−0.154872	+	0.129953i	0.562059	+	0.827097i	$0.310009\pi$
$242$	7.73755	+	7.73755i	0.497388	+	0.497388i
$243$		0			0
$244$			10.6108i			0.679287i
$245$	−3.15494	+	2.10466i	−0.201562	+	0.134462i
$246$		0			0
$247$	1.69034	+	2.41405i	0.107554	+	0.153602i
$248$	2.07832	−	4.45698i	0.131974	−	0.283018i
$249$		0			0
$250$	6.59082	+	9.03112i	0.416840	+	0.571178i
$251$	−14.7673	+	8.52590i	−0.932103	+	0.538150i	−0.887476	−	0.460854i	$-0.847543\pi$
$251$	−14.7673	+	8.52590i	−0.932103	+	0.538150i	−0.0446271	+	0.999004i	$0.514210\pi$
$252$		0			0
$253$	−0.927285	+	0.248465i	−0.0582979	+	0.0156209i
$254$	−3.81641	−	1.38906i	−0.239463	−	0.0871574i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.116062	−	1.32659i	−0.00723974	−	0.0827507i	0.991715	−	0.128456i	$-0.0410021\pi$
$257$	−0.116062	−	1.32659i	−0.00723974	−	0.0827507i	−0.998955	+	0.0457052i	$0.985447\pi$
$258$		0			0
$259$	−3.03732	+	8.34497i	−0.188730	+	0.518531i
$260$	4.51504	−	0.691479i	0.280011	−	0.0428837i
$261$		0			0
$262$	−18.6243	−	4.99037i	−1.15061	−	0.308306i
$263$	−2.58514	−	1.81013i	−0.159406	−	0.111617i	0.491152	−	0.871074i	$-0.336576\pi$
$263$	−2.58514	−	1.81013i	−0.159406	−	0.111617i	−0.650558	+	0.759457i	$0.725465\pi$
$264$		0			0
$265$	12.0411	+	7.31902i	0.739678	+	0.449604i
$266$	3.27206	+	0.576953i	0.200623	+	0.0353752i
$267$		0			0
$268$	8.05202	+	0.704460i	0.491855	+	0.0430318i
$269$	3.59173			0.218992			0.109496	−	0.993987i	$-0.465076\pi$
$269$	3.59173			0.218992			0.109496	+	0.993987i	$0.465076\pi$
$270$		0			0
$271$	−0.268997			−0.0163404			−0.00817022	−	0.999967i	$-0.502601\pi$
$271$	−0.268997			−0.0163404			−0.00817022	+	0.999967i	$0.502601\pi$
$272$	6.59434	+	0.576930i	0.399841	+	0.0349815i
$273$		0			0
$274$	19.0600	+	3.36079i	1.15146	+	0.203033i
$275$	0.154662	+	1.18850i	0.00932648	+	0.0716690i
$276$		0			0
$277$	−17.3332	−	12.1368i	−1.04145	−	0.729233i	−0.0779565	−	0.996957i	$-0.524840\pi$
$277$	−17.3332	−	12.1368i	−1.04145	−	0.729233i	−0.963496	+	0.267724i	$0.913728\pi$
$278$	−15.9995	−	4.28705i	−0.959587	−	0.257120i
$279$		0			0
$280$	3.04818	−	4.15069i	0.182164	−	0.248051i
$281$	8.10418	−	22.2660i	0.483455	−	1.32828i	−0.423058	−	0.906103i	$-0.639043\pi$
$281$	8.10418	−	22.2660i	0.483455	−	1.32828i	0.906513	−	0.422178i	$-0.138734\pi$
$282$		0			0
$283$	1.11397	+	12.7328i	0.0662189	+	0.756886i	0.954622	+	0.297821i	$0.0962598\pi$
$283$	1.11397	+	12.7328i	0.0662189	+	0.756886i	−0.888403	+	0.459065i	$0.848185\pi$
$284$	−6.08552	−	5.10636i	−0.361109	−	0.303007i
$285$		0			0
$286$	0.460120	+	0.167470i	0.0272075	+	0.00990271i
$287$	−19.8396	+	5.31601i	−1.17110	+	0.313794i
$288$		0			0
$289$	23.2252	−	13.4091i	1.36619	−	0.788771i
$290$	−15.2222	−	13.3697i	−0.893880	−	0.785094i
$291$		0			0
$292$	2.25109	−	4.82748i	0.131735	−	0.282507i
$293$	7.84514	+	11.2040i	0.458318	+	0.654546i	0.980093	−	0.198537i	$-0.0636191\pi$
$293$	7.84514	+	11.2040i	0.458318	+	0.654546i	−0.521776	+	0.853083i	$0.674730\pi$
$294$		0			0
$295$	9.97708	+	14.9559i	0.580888	+	0.870768i
$296$			3.85603i			0.224127i
$297$		0			0
$298$	−7.54019	−	7.54019i	−0.436791	−	0.436791i
$299$	6.26701	−	5.25865i	0.362431	−	0.304115i
$300$		0			0
$301$	0.439835	−	2.49443i	0.0253517	−	0.143776i
$302$	−0.325033	−	0.151565i	−0.0187035	−	0.00872160i
$303$		0			0
$304$	1.42077	−	0.250519i	0.0814865	−	0.0143683i
$305$	21.7243	−	9.53953i	1.24393	−	0.546232i
$306$		0			0
$307$	0.879501	+	3.28234i	0.0501958	+	0.187333i	0.986472	−	0.163933i	$-0.0524180\pi$
$307$	0.879501	+	3.28234i	0.0501958	+	0.187333i	−0.936276	+	0.351266i	$0.885751\pi$
$308$	0.500321	−	0.233303i	0.0285084	−	0.0132937i
$309$		0			0
$310$	−10.9936	−	0.248098i	−0.624393	−	0.0140910i
$311$	4.72942	−	5.63630i	0.268181	−	0.319605i	−0.615101	−	0.788449i	$-0.710885\pi$
$311$	4.72942	−	5.63630i	0.268181	−	0.319605i	0.883281	+	0.468843i	$0.155329\pi$
$312$		0			0
$313$	−2.54862	−	5.46554i	−0.144057	−	0.308931i	0.821019	−	0.570900i	$-0.193406\pi$
$313$	−2.54862	−	5.46554i	−0.144057	−	0.308931i	−0.965076	+	0.261970i	$0.915628\pi$
$314$	12.0438	−	20.8606i	0.679674	−	1.17723i
$315$		0			0
$316$	4.54922	+	7.87948i	0.255914	+	0.443256i
$317$	1.97295	−	2.81766i	0.110812	−	0.158255i	−0.759916	−	0.650022i	$-0.774760\pi$
$317$	1.97295	−	2.81766i	0.110812	−	0.158255i	0.870727	+	0.491766i	$0.163649\pi$
$318$		0			0
$319$	−0.742811	−	2.04086i	−0.0415894	−	0.114266i
$320$	0.627320	−	2.14627i	0.0350683	−	0.119980i
$321$		0			0
$322$	0.803878	−	9.18837i	0.0447984	−	0.512048i
$323$	6.75279	−	6.75279i	0.375735	−	0.375735i
$324$		0			0
$325$	−5.47492	−	8.62230i	−0.303694	−	0.478279i
$326$	−3.91911	−	4.67062i	−0.217060	−	0.258682i
$327$		0			0
$328$	−7.30559	+	5.11543i	−0.403384	+	0.282452i
$329$	7.50801	−	2.73269i	0.413930	−	0.150658i
$330$		0			0
$331$	2.45650	+	13.9315i	0.135021	+	0.765744i	0.974845	+	0.222885i	$0.0715473\pi$
$331$	2.45650	+	13.9315i	0.135021	+	0.765744i	−0.839823	+	0.542860i	$0.817342\pi$
$332$	−3.74423	+	13.9736i	−0.205491	+	0.766903i
$333$		0			0
$334$	−10.4227	−	6.01753i	−0.570303	−	0.329265i
$335$	−5.79679	−	17.1188i	−0.316713	−	0.935301i
$336$		0			0
$337$	14.3020	−	1.25126i	0.779077	−	0.0681604i	0.309322	−	0.950957i	$-0.399898\pi$
$337$	14.3020	−	1.25126i	0.779077	−	0.0681604i	0.469755	+	0.882797i	$0.344342\pi$
$338$	8.79366	−	0.769346i	0.478312	−	0.0418469i
$339$		0			0
$340$	−4.74739	−	14.0197i	−0.257463	−	0.760328i
$341$	−1.02087	−	0.589398i	−0.0552830	−	0.0319177i
$342$		0			0
$343$	5.18344	−	19.3449i	0.279880	−	1.04452i
$344$	−0.190981	−	1.08311i	−0.0102970	−	0.0583973i
$345$		0			0
$346$	1.10724	−	0.403002i	0.0595255	−	0.0216655i
$347$	29.7351	−	20.8207i	1.59626	−	1.11772i	0.669027	−	0.743238i	$-0.266711\pi$
$347$	29.7351	−	20.8207i	1.59626	−	1.11772i	0.927236	−	0.374477i	$-0.122178\pi$
$348$		0			0
$349$	−4.12275	−	4.91331i	−0.220686	−	0.263003i	0.644330	−	0.764747i	$-0.277136\pi$
$349$	−4.12275	−	4.91331i	−0.220686	−	0.263003i	−0.865016	+	0.501744i	$0.832692\pi$
$350$	−11.2384	−	2.50913i	−0.600720	−	0.134118i
$351$		0			0
$352$	0.169496	−	0.169496i	0.00903416	−	0.00903416i
$353$	0.0622490	−	0.711510i	0.00331318	−	0.0378698i	−0.994358	−	0.106075i	$-0.966172\pi$
$353$	0.0622490	−	0.711510i	0.00331318	−	0.0378698i	0.997671	+	0.0682051i	$0.0217272\pi$
$354$		0			0
$355$	−4.98349	+	17.0501i	−0.264496	+	0.904928i
$356$	1.29756	+	3.56502i	0.0687707	+	0.188946i
$357$		0			0
$358$	−6.04836	+	8.63796i	−0.319666	+	0.456530i
$359$	4.37105	+	7.57089i	0.230695	+	0.399576i	0.958013	−	0.286725i	$-0.0925666\pi$
$359$	4.37105	+	7.57089i	0.230695	+	0.399576i	−0.727318	+	0.686301i	$0.759233\pi$
$360$		0			0
$361$	−8.45933	+	14.6520i	−0.445228	+	0.771158i
$362$	−3.92972	−	8.42732i	−0.206542	−	0.442930i
$363$		0			0
$364$	−3.02397	+	3.60383i	−0.158499	+	0.188892i
$365$	−11.9075	−	0.268722i	−0.623265	−	0.0140655i
$366$		0			0
$367$	−2.42271	+	1.12973i	−0.126464	+	0.0589714i	−0.484821	−	0.874614i	$-0.661115\pi$
$367$	−2.42271	+	1.12973i	−0.126464	+	0.0589714i	0.358356	+	0.933585i	$0.383337\pi$
$368$	−1.03655	−	3.86847i	−0.0540340	−	0.201658i
$369$		0			0
$370$	7.89472	−	3.46672i	0.410427	−	0.180226i
$371$	−14.2925	+	2.52014i	−0.742027	+	0.130839i
$372$		0			0
$373$	17.3611	+	8.09560i	0.898922	+	0.419174i	0.816448	−	0.577419i	$-0.195940\pi$
$373$	17.3611	+	8.09560i	0.898922	+	0.419174i	0.0824740	+	0.996593i	$0.473718\pi$
$374$	0.275532	−	1.56262i	0.0142474	−	0.0808010i
$375$		0			0
$376$	2.65763	−	2.23001i	0.137057	−	0.115004i
$377$	13.0873	+	13.0873i	0.674028	+	0.674028i
$378$		0			0
$379$			30.8761i			1.58600i	0.609222	+	0.793000i	$0.291482\pi$
$379$			30.8761i			1.58600i	−0.609222	+	0.793000i	$0.708518\pi$
$380$	−1.79023	−	2.68361i	−0.0918369	−	0.137666i
$381$		0			0
$382$	12.8526	+	18.3555i	0.657598	+	0.939148i
$383$	12.7958	−	27.4407i	0.653836	−	1.40216i	−0.247436	−	0.968904i	$-0.579588\pi$
$383$	12.7958	−	27.4407i	0.653836	−	1.40216i	0.901273	−	0.433252i	$-0.142634\pi$
$384$		0			0
$385$	−0.927467	−	0.814593i	−0.0472681	−	0.0415155i
$386$	−3.46904	+	2.00285i	−0.176570	+	0.101943i
$387$		0			0
$388$	−9.51941	+	2.55072i	−0.483275	+	0.129493i
$389$	23.3694	+	8.50576i	1.18487	+	0.431259i	0.857921	−	0.513781i	$-0.171756\pi$
$389$	23.3694	+	8.50576i	1.18487	+	0.431259i	0.326953	+	0.945040i	$0.393978\pi$
$390$		0			0
$391$	−20.3084	−	17.0408i	−1.02704	−	0.861790i
$392$	−0.147822	−	1.68962i	−0.00746615	−	0.0853385i
$393$		0			0
$394$	−2.00320	+	5.50375i	−0.100920	+	0.277275i
$395$	12.0423	−	16.3979i	0.605914	−	0.825068i
$396$		0			0
$397$	30.2800	+	8.11350i	1.51971	+	0.407205i	0.919646	−	0.392747i	$-0.128475\pi$
$397$	30.2800	+	8.11350i	1.51971	+	0.407205i	0.600064	+	0.799952i	$0.295142\pi$
$398$	3.79615	+	2.65809i	0.190284	+	0.133238i
$399$		0			0
$400$	−4.95819	+	0.645223i	−0.247910	+	0.0322612i
$401$	1.41560	+	0.249609i	0.0706919	+	0.0124649i	0.208882	−	0.977941i	$-0.433017\pi$
$401$	1.41560	+	0.249609i	0.0706919	+	0.0124649i	−0.138190	+	0.990406i	$0.544129\pi$
$402$		0			0
$403$	10.0074	+	0.875531i	0.498503	+	0.0436133i
$404$	−16.2693			−0.809427
$405$		0			0
$406$	20.8666			1.03559
$407$	0.920786	+	0.0805583i	0.0456416	+	0.00399313i
$408$		0			0
$409$	−3.51476	−	0.619747i	−0.173794	−	0.0306445i	0.0860740	−	0.996289i	$-0.472568\pi$
$409$	−3.51476	−	0.619747i	−0.173794	−	0.0306445i	−0.259868	+	0.965644i	$0.583679\pi$
$410$	17.0412	+	10.3583i	0.841605	+	0.511559i
$411$		0			0
$412$	−3.01885	−	2.11382i	−0.148728	−	0.104140i
$413$	−17.8858	−	4.79248i	−0.880102	−	0.235823i
$414$		0			0
$415$	31.9754	−	4.89704i	1.56961	−	0.240386i
$416$	−0.698655	+	1.91954i	−0.0342544	+	0.0941132i
$417$		0			0
$418$	−0.0301398	−	0.344500i	−0.00147419	−	0.0168500i
$419$	−10.8184	−	9.07767i	−0.528511	−	0.443473i	0.339076	−	0.940759i	$-0.389886\pi$
$419$	−10.8184	−	9.07767i	−0.528511	−	0.443473i	−0.867587	+	0.497286i	$0.834330\pi$
$420$		0			0
$421$	−15.9110	−	5.79114i	−0.775456	−	0.282243i	−0.0761796	−	0.997094i	$-0.524272\pi$
$421$	−15.9110	−	5.79114i	−0.775456	−	0.282243i	−0.699277	+	0.714851i	$0.746494\pi$
$422$	−24.7022	+	6.61893i	−1.20248	+	0.322205i
$423$		0			0
$424$	−5.45741	+	3.15084i	−0.265035	+	0.153018i
$425$	−24.4355	+	22.3240i	−1.18530	+	1.08287i
$426$		0			0
$427$	−10.3275	+	22.1474i	−0.499783	+	1.07179i
$428$	−10.9205	−	15.5960i	−0.527860	−	0.753862i
$429$		0			0
$430$	−2.04583	+	1.36477i	−0.0986584	+	0.0658149i
$431$		−	1.97868i		−	0.0953096i	−0.998864	−	0.0476548i	$-0.984825\pi$
$431$		−	1.97868i		−	0.0953096i	0.998864	−	0.0476548i	$-0.0151747\pi$
$432$		0			0
$433$	−19.7905	−	19.7905i	−0.951069	−	0.951069i	0.0477880	−	0.998857i	$-0.484783\pi$
$433$	−19.7905	−	19.7905i	−0.951069	−	0.951069i	−0.998857	+	0.0477880i	$0.984783\pi$
$434$	8.67596	−	7.27999i	0.416459	−	0.349451i
$435$		0			0
$436$	−3.29925	+	18.7110i	−0.158006	+	0.896094i
$437$	−5.23651	−	2.44182i	−0.250496	−	0.116808i
$438$		0			0
$439$	−26.0950	+	4.60125i	−1.24545	+	0.219606i	−0.757248	−	0.653127i	$-0.773457\pi$
$439$	−26.0950	+	4.60125i	−1.24545	+	0.219606i	−0.488198	+	0.872733i	$0.662345\pi$
$440$	−0.499404	−	0.194637i	−0.0238082	−	0.00927897i
$441$		0			0
$442$	3.49973	+	13.0612i	0.166465	+	0.621257i
$443$	8.94617	−	4.17167i	0.425045	−	0.198202i	−0.198312	−	0.980139i	$-0.563546\pi$
$443$	8.94617	−	4.17167i	0.425045	−	0.198202i	0.623357	+	0.781937i	$0.285768\pi$
$444$		0			0
$445$	6.13237	−	5.86169i	0.290702	−	0.277871i
$446$	10.7960	−	12.8662i	0.511206	−	0.609231i
$447$		0			0
$448$	0.973301	+	2.08725i	0.0459841	+	0.0986133i
$449$	−5.81494	+	10.0718i	−0.274424	+	0.475316i	−0.969990	−	0.243146i	$-0.921820\pi$
$449$	−5.81494	+	10.0718i	−0.274424	+	0.475316i	0.695566	+	0.718462i	$0.255154\pi$
$450$		0			0
$451$	1.06889	+	1.85138i	0.0503323	+	0.0871781i
$452$	0.838949	−	1.19814i	0.0394608	−	0.0563559i
$453$		0			0
$454$	−0.972634	−	2.67229i	−0.0456480	−	0.125417i
$455$	10.0970	+	2.95121i	0.473357	+	0.138355i
$456$		0			0
$457$	1.04510	−	11.9456i	0.0488879	−	0.558791i	−0.931768	−	0.363053i	$-0.881734\pi$
$457$	1.04510	−	11.9456i	0.0488879	−	0.558791i	0.980656	−	0.195738i	$-0.0627101\pi$
$458$	11.0244	−	11.0244i	0.515136	−	0.515136i
$459$		0			0
$460$	−6.98829	+	5.60011i	−0.325831	+	0.261107i
$461$	−1.18520	−	1.41247i	−0.0552004	−	0.0657853i	0.737738	−	0.675087i	$-0.235894\pi$
$461$	−1.18520	−	1.41247i	−0.0552004	−	0.0657853i	−0.792938	+	0.609302i	$0.791450\pi$
$462$		0			0
$463$	16.4460	−	11.5156i	0.764312	−	0.535177i	−0.125176	−	0.992135i	$-0.539950\pi$
$463$	16.4460	−	11.5156i	0.764312	−	0.535177i	0.889489	+	0.456957i	$0.151061\pi$
$464$	8.51409	−	3.09888i	0.395257	−	0.143862i
$465$		0			0
$466$	1.38411	+	7.84970i	0.0641178	+	0.363630i
$467$	−4.95699	+	18.4997i	−0.229382	+	0.856066i	0.751219	+	0.660053i	$0.229466\pi$
$467$	−4.95699	+	18.4997i	−0.229382	+	0.856066i	−0.980601	+	0.196013i	$0.937201\pi$
$468$		0			0
$469$	16.1209	+	9.30742i	0.744395	+	0.429777i
$470$	−6.95498	−	3.43628i	−0.320809	−	0.158504i
$471$		0			0
$472$	−8.00958	+	0.700748i	−0.368671	+	0.0322545i
$473$	−0.262627	+	0.0229769i	−0.0120756	+	0.00105648i
$474$		0			0
$475$	−3.88485	+	6.07794i	−0.178249	+	0.278875i
$476$	13.2025	+	7.62248i	0.605136	+	0.349376i
$477$		0			0
$478$	−4.24270	+	15.8340i	−0.194057	+	0.724229i
$479$	0.621407	+	3.52418i	0.0283928	+	0.161024i	0.995708	−	0.0925551i	$-0.0295034\pi$
$479$	0.621407	+	3.52418i	0.0283928	+	0.161024i	−0.967315	+	0.253579i	$0.918392\pi$
$480$		0			0
$481$	−7.40180	+	2.69403i	−0.337493	+	0.122837i
$482$	−2.57094	+	1.80019i	−0.117103	+	0.0819964i
$483$		0			0
$484$	7.03373	+	8.38247i	0.319715	+	0.381022i
$485$	13.7806	+	17.1966i	0.625745	+	0.780856i
$486$		0			0
$487$	23.7449	−	23.7449i	1.07598	−	1.07598i	0.0791168	−	0.996865i	$-0.474790\pi$
$487$	23.7449	−	23.7449i	1.07598	−	1.07598i	0.996865	−	0.0791168i	$-0.0252100\pi$
$488$	−0.924793	+	10.5704i	−0.0418634	+	0.478501i
$489$		0			0
$490$	−3.32637	+	1.82168i	−0.150270	+	0.0822951i
$491$	12.3418	+	33.9088i	0.556977	+	1.53028i	0.823998	+	0.566592i	$0.191739\pi$
$491$	12.3418	+	33.9088i	0.556977	+	1.53028i	−0.267021	+	0.963691i	$0.586039\pi$
$492$		0			0
$493$	34.4010	−	49.1297i	1.54934	−	2.21269i
$494$	1.47351	+	2.55219i	0.0662962	+	0.114828i
$495$		0			0
$496$	2.45886	−	4.25888i	0.110406	−	0.191229i
$497$	−7.73199	−	16.5813i	−0.346827	−	0.743773i
$498$		0			0
$499$	11.0072	−	13.1178i	0.492748	−	0.587234i	−0.461166	−	0.887314i	$-0.652569\pi$
$499$	11.0072	−	13.1178i	0.492748	−	0.587234i	0.953914	+	0.300079i	$0.0970132\pi$
$500$	5.77862	+	9.57118i	0.258428	+	0.428036i
$501$		0			0
$502$	−15.4542	+	7.20640i	−0.689754	+	0.321637i
$503$	−6.30725	−	23.5390i	−0.281227	−	1.04955i	−0.951553	−	0.307485i	$-0.900513\pi$
$503$	−6.30725	−	23.5390i	−0.281227	−	1.04955i	0.670326	−	0.742066i	$-0.266154\pi$
$504$		0			0
$505$	14.6267	+	33.3093i	0.650881	+	1.48224i
$506$	−0.945411	+	0.166701i	−0.0420286	+	0.00741078i
$507$		0			0
$508$	−3.68082	−	1.71640i	−0.163310	−	0.0761528i
$509$	1.96537	−	11.1461i	0.0871133	−	0.494044i	−0.909767	−	0.415119i	$-0.863740\pi$
$509$	1.96537	−	11.1461i	0.0871133	−	0.494044i	0.996881	−	0.0789253i	$-0.0251489\pi$
$510$		0			0
$511$	9.39718	−	7.88517i	0.415707	−	0.348819i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	1.33166i		−	0.0587371i
$515$	−1.61371	+	8.08110i	−0.0711085	+	0.356096i
$516$		0			0
$517$	−0.476986	−	0.681206i	−0.0209778	−	0.0299594i
$518$	−3.75308	+	8.04850i	−0.164901	+	0.353631i
$519$		0			0
$520$	4.55813	−	0.295336i	0.199887	−	0.0129513i
$521$	14.8677	−	8.58387i	0.651366	−	0.376066i	−0.137614	−	0.990486i	$-0.543943\pi$
$521$	14.8677	−	8.58387i	0.651366	−	0.376066i	0.788979	+	0.614420i	$0.210610\pi$
$522$		0			0
$523$	−1.61457	+	0.432622i	−0.0706000	+	0.0189172i	−0.293946	−	0.955822i	$-0.594969\pi$
$523$	−1.61457	+	0.432622i	−0.0706000	+	0.0189172i	0.223346	+	0.974739i	$0.428302\pi$
$524$	−18.1185	−	6.59460i	−0.791510	−	0.288086i
$525$		0			0
$526$	−2.41753	−	2.02855i	−0.105410	−	0.0884491i
$527$	−2.83719	−	32.4292i	−0.123590	−	1.41264i
$528$		0			0
$529$	2.38064	−	6.54075i	0.103506	−	0.284380i
$530$	11.3574	+	8.34062i	0.493333	+	0.362293i
$531$		0			0
$532$	3.20932	+	0.859936i	0.139142	+	0.0372830i
$533$	−14.9234	−	10.4494i	−0.646402	−	0.452616i
$534$		0			0
$535$	−22.1129	+	36.3797i	−0.956025	+	1.57283i
$536$	7.95998	+	1.40356i	0.343819	+	0.0606245i
$537$		0			0
$538$	3.57806	+	0.313040i	0.154261	+	0.0134961i
$539$	−0.406554			−0.0175115
$540$		0			0
$541$	36.5213			1.57017			0.785086	−	0.619387i	$-0.212619\pi$
$541$	36.5213			1.57017			0.785086	+	0.619387i	$0.212619\pi$
$542$	−0.267974	−	0.0234447i	−0.0115105	−	0.00100703i
$543$		0			0
$544$	6.51897	+	1.14947i	0.279498	+	0.0492831i
$545$	41.2745	−	10.0671i	1.76801	−	0.431229i
$546$		0			0
$547$	−18.0827	−	12.6616i	−0.773158	−	0.541371i	0.119108	−	0.992881i	$-0.461997\pi$
$547$	−18.0827	−	12.6616i	−0.773158	−	0.541371i	−0.892266	+	0.451510i	$0.850886\pi$
$548$	18.6945	+	5.00919i	0.798592	+	0.213982i
$549$		0			0
$550$	0.0504894	+	1.19745i	0.00215288	+	0.0510596i
$551$	4.47070	−	12.2831i	0.190458	−	0.523279i
$552$		0			0
$553$	1.82626	+	20.8742i	0.0776604	+	0.887662i
$554$	−16.2095	−	13.6014i	−0.688674	−	0.577866i
$555$		0			0
$556$	−15.5650	−	5.66519i	−0.660102	−	0.240258i
$557$	4.98077	−	1.33459i	0.211042	−	0.0565485i	−0.151749	−	0.988419i	$-0.548491\pi$
$557$	4.98077	−	1.33459i	0.211042	−	0.0565485i	0.362791	+	0.931871i	$0.381824\pi$
$558$		0			0
$559$	1.94564	−	1.12332i	0.0822918	−	0.0475112i
$560$	3.39834	−	3.86923i	0.143606	−	0.163505i
$561$		0			0
$562$	10.0140	−	21.4750i	0.422413	−	0.905868i
$563$	−16.7912	−	23.9803i	−0.707665	−	1.01065i	−0.998547	−	0.0538917i	$-0.982837\pi$
$563$	−16.7912	−	23.9803i	−0.707665	−	1.01065i	0.290881	−	0.956759i	$-0.406051\pi$
$564$		0			0
$565$	−3.20729	−	0.640461i	−0.134932	−	0.0269444i
$566$			12.7814i			0.537243i
$567$		0			0
$568$	−5.61732	−	5.61732i	−0.235697	−	0.235697i
$569$	−28.4203	+	23.8475i	−1.19144	+	0.999737i	−0.191608	+	0.981472i	$0.561370\pi$
$569$	−28.4203	+	23.8475i	−1.19144	+	0.999737i	−0.999833	+	0.0182658i	$0.994185\pi$
$570$		0			0
$571$	3.91898	−	22.2257i	0.164004	−	0.930115i	−0.786081	−	0.618124i	$-0.787893\pi$
$571$	3.91898	−	22.2257i	0.164004	−	0.930115i	0.950085	−	0.311991i	$-0.100996\pi$
$572$	0.443773	+	0.206935i	0.0185551	+	0.00865238i
$573$		0			0
$574$	−20.2275	+	3.56665i	−0.844278	+	0.148869i
$575$	17.7483	+	9.27289i	0.740153	+	0.386706i
$576$		0			0
$577$	4.15516	+	15.5073i	0.172982	+	0.645577i	0.996887	+	0.0788485i	$0.0251243\pi$
$577$	4.15516	+	15.5073i	0.172982	+	0.645577i	−0.823905	+	0.566728i	$0.808209\pi$
$578$	24.3055	−	11.3339i	1.01098	−	0.471426i
$579$		0			0
$580$	−13.9991	−	14.6455i	−0.581279	−	0.608121i
$581$	−21.4157	+	25.5222i	−0.888473	+	1.05884i
$582$		0			0
$583$	0.638379	+	1.36901i	0.0264390	+	0.0566985i
$584$	2.66327	−	4.61291i	0.110207	−	0.190884i
$585$		0			0
$586$	6.83879	+	11.8451i	0.282508	+	0.489318i
$587$	6.53473	−	9.33256i	0.269717	−	0.385196i	−0.661330	−	0.750095i	$-0.730008\pi$
$587$	6.53473	−	9.33256i	0.269717	−	0.385196i	0.931047	+	0.364899i	$0.118897\pi$
$588$		0			0
$589$	−2.42654	−	6.66686i	−0.0999838	−	0.274703i
$590$	8.63562	+	15.7686i	0.355523	+	0.649182i
$591$		0			0
$592$	−0.336075	+	3.84135i	−0.0138126	+	0.157879i
$593$	−29.6232	+	29.6232i	−1.21648	+	1.21648i	−0.247623	+	0.968856i	$0.579649\pi$
$593$	−29.6232	+	29.6232i	−1.21648	+	1.21648i	−0.968856	+	0.247623i	$0.920351\pi$
$594$		0			0
$595$	3.73645	−	33.8834i	0.153180	−	1.38908i
$596$	−6.85432	−	8.16866i	−0.280764	−	0.334602i
$597$		0			0
$598$	6.70148	−	4.69243i	0.274044	−	0.191888i
$599$	−18.7566	+	6.82683i	−0.766372	+	0.278937i	−0.695478	−	0.718547i	$-0.744807\pi$
$599$	−18.7566	+	6.82683i	−0.766372	+	0.278937i	−0.0708939	+	0.997484i	$0.522585\pi$
$600$		0			0
$601$	−3.32165	−	18.8380i	−0.135493	−	0.768419i	−0.974515	−	0.224322i	$-0.927983\pi$
$601$	−3.32165	−	18.8380i	−0.135493	−	0.768419i	0.839022	−	0.544097i	$-0.183128\pi$
$602$	0.655565	−	2.44660i	0.0267188	−	0.0997160i
$603$		0			0
$604$	−0.310586	−	0.179317i	−0.0126376	−	0.00729631i
$605$	10.8384	−	21.9368i	0.440645	−	0.891859i
$606$		0			0
$607$	15.5809	−	1.36315i	0.632410	−	0.0553287i	0.233556	−	0.972343i	$-0.424964\pi$
$607$	15.5809	−	1.36315i	0.632410	−	0.0553287i	0.398853	+	0.917015i	$0.369408\pi$
$608$	1.43719	−	0.125738i	0.0582859	−	0.00509935i
$609$		0			0
$610$	22.4730	−	7.60984i	0.909906	−	0.308113i
$611$	6.13736	+	3.54341i	0.248291	+	0.143351i
$612$		0			0
$613$	−11.2842	+	42.1132i	−0.455765	+	1.70094i	0.230065	+	0.973175i	$0.426106\pi$
$613$	−11.2842	+	42.1132i	−0.455765	+	1.70094i	−0.685830	+	0.727762i	$0.740561\pi$
$614$	0.590079	+	3.34651i	0.0238137	+	0.135054i
$615$		0			0
$616$	0.518751	−	0.188810i	0.0209011	−	0.00760737i
$617$	6.45432	−	4.51936i	0.259841	−	0.181943i	−0.436396	−	0.899755i	$-0.643745\pi$
$617$	6.45432	−	4.51936i	0.259841	−	0.181943i	0.696237	+	0.717812i	$0.254856\pi$
$618$		0			0
$619$	−27.7023	−	33.0143i	−1.11345	−	1.32696i	−0.939634	−	0.342181i	$-0.888835\pi$
$619$	−27.7023	−	33.0143i	−1.11345	−	1.32696i	−0.173816	−	0.984778i	$-0.555610\pi$
$620$	−10.9301	−	1.20531i	−0.438964	−	0.0484063i
$621$		0			0
$622$	5.20266	−	5.20266i	0.208608	−	0.208608i
$623$	−0.761503	+	8.70402i	−0.0305090	+	0.348719i
$624$		0			0
$625$	14.4005	−	20.4359i	0.576022	−	0.817434i
$626$	−2.06257	−	5.66687i	−0.0824370	−	0.226494i
$627$		0			0
$628$	13.8161	−	19.7315i	0.551324	−	0.787372i
$629$	12.7626	+	22.1054i	0.508876	+	0.881399i
$630$		0			0
$631$	11.2152	−	19.4253i	0.446469	−	0.773308i	−0.551684	−	0.834053i	$-0.686015\pi$
$631$	11.2152	−	19.4253i	0.446469	−	0.773308i	0.998153	+	0.0607456i	$0.0193478\pi$
$632$	3.84517	+	8.24599i	0.152953	+	0.328008i
$633$		0			0
$634$	2.21101	−	2.63498i	0.0878105	−	0.104649i
$635$	−0.204893	+	9.07912i	−0.00813094	+	0.360294i
$636$		0			0
$637$	3.14001	−	1.46421i	0.124412	−	0.0580141i
$638$	−0.562112	−	2.09783i	−0.0222542	−	0.0830539i
$639$		0			0
$640$	0.811993	−	2.08343i	0.0320968	−	0.0823547i
$641$	24.7409	−	4.36249i	0.977207	−	0.172308i	0.337835	−	0.941205i	$-0.390305\pi$
$641$	24.7409	−	4.36249i	0.977207	−	0.172308i	0.639372	+	0.768897i	$0.279194\pi$
$642$		0			0
$643$	−10.0482	−	4.68557i	−0.396264	−	0.184781i	0.214264	−	0.976776i	$-0.431265\pi$
$643$	−10.0482	−	4.68557i	−0.396264	−	0.184781i	−0.610528	+	0.791995i	$0.709043\pi$
$644$	1.60164	−	9.08334i	0.0631134	−	0.357934i
$645$		0			0
$646$	7.31564	−	6.13855i	0.287830	−	0.241518i
$647$	28.0668	+	28.0668i	1.10342	+	1.10342i	0.993995	+	0.109423i	$0.0349004\pi$
$647$	28.0668	+	28.0668i	1.10342	+	1.10342i	0.109423	+	0.993995i	$0.465100\pi$
$648$		0			0
$649$			1.92726i			0.0756515i
$650$	−4.70260	−	9.06666i	−0.184451	−	0.355624i
$651$		0			0
$652$	−3.49713	−	4.99442i	−0.136958	−	0.195597i
$653$	−9.09985	+	19.5147i	−0.356105	+	0.763669i	−0.999999	−	0.00144573i	$-0.999540\pi$
$653$	−9.09985	+	19.5147i	−0.356105	+	0.763669i	0.643894	+	0.765114i	$0.277318\pi$
$654$		0			0
$655$	2.78767	+	43.0241i	0.108923	+	1.68109i
$656$	−7.72363	+	4.45924i	−0.301557	+	0.174104i
$657$		0			0
$658$	7.71761	−	2.06793i	0.300864	−	0.0806162i
$659$	−22.2802	−	8.10932i	−0.867912	−	0.315894i	−0.130591	−	0.991436i	$-0.541687\pi$
$659$	−22.2802	−	8.10932i	−0.867912	−	0.315894i	−0.737321	+	0.675542i	$0.763910\pi$
$660$		0			0
$661$	1.87402	+	1.57249i	0.0728908	+	0.0611626i	0.678505	−	0.734596i	$-0.262628\pi$
$661$	1.87402	+	1.57249i	0.0728908	+	0.0611626i	−0.605614	+	0.795758i	$0.707073\pi$
$662$	1.23294	+	14.0926i	0.0479196	+	0.547724i
$663$		0			0
$664$	−4.94786	+	13.5941i	−0.192014	+	0.527555i
$665$	−1.12470	−	7.34380i	−0.0436141	−	0.284780i
$666$		0			0
$667$	−35.0503	−	9.39170i	−1.35715	−	0.363648i
$668$	−9.85855	−	6.90303i	−0.381439	−	0.267086i
$669$		0			0
$670$	−4.28273	−	17.5589i	−0.165456	−	0.678359i
$671$	2.50480	+	0.441665i	0.0966969	+	0.0170503i
$672$		0			0
$673$	−27.9591	−	2.44610i	−1.07774	−	0.0942902i	−0.465567	−	0.885012i	$-0.654150\pi$
$673$	−27.9591	−	2.44610i	−1.07774	−	0.0942902i	−0.612175	+	0.790722i	$0.709705\pi$
$674$	14.3566			0.552995
$675$		0			0
$676$	8.82725			0.339510
$677$	12.8045	+	1.12025i	0.492116	+	0.0430546i	0.330513	−	0.943801i	$-0.392778\pi$
$677$	12.8045	+	1.12025i	0.492116	+	0.0430546i	0.161603	+	0.986856i	$0.448334\pi$
$678$		0			0
$679$	−22.3520	−	3.94126i	−0.857792	−	0.151252i
$680$	−3.50742	−	14.3802i	−0.134503	−	0.551454i
$681$		0			0
$682$	−0.965613	−	0.676129i	−0.0369752	−	0.0258903i
$683$	−36.5389	−	9.79056i	−1.39812	−	0.374625i	−0.520451	−	0.853891i	$-0.674236\pi$
$683$	−36.5389	−	9.79056i	−1.39812	−	0.374625i	−0.877670	+	0.479266i	$0.840903\pi$
$684$		0			0
$685$	−6.55147	−	42.7781i	−0.250319	−	1.63447i
$686$	6.84973	−	18.8195i	0.261524	−	0.718531i
$687$		0			0
$688$	−0.0958554	−	1.09563i	−0.00365445	−	0.0417706i
$689$	−9.86101	−	8.27437i	−0.375675	−	0.315228i
$690$		0			0
$691$	19.4452	+	7.07747i	0.739730	+	0.269240i	0.684278	−	0.729222i	$-0.260118\pi$
$691$	19.4452	+	7.07747i	0.739730	+	0.269240i	0.0554523	+	0.998461i	$0.482340\pi$
$692$	1.13815	−	0.304966i	0.0432659	−	0.0115931i
$693$		0			0
$694$	31.4366	−	18.1499i	1.19332	−	0.688961i
$695$	2.39479	+	36.9605i	0.0908396	+	1.40199i
$696$		0			0
$697$	−24.9498	+	53.5049i	−0.945040	+	2.02664i
$698$	−3.67884	−	5.25393i	−0.139246	−	0.198864i
$699$		0			0
$700$	−10.9770	−	3.47907i	−0.414891	−	0.131497i
$701$		−	12.9458i		−	0.488956i	−0.969655	−	0.244478i	$-0.921383\pi$
$701$		−	12.9458i		−	0.488956i	0.969655	−	0.244478i	$-0.0786166\pi$
$702$		0			0
$703$	3.93365	+	3.93365i	0.148361	+	0.148361i
$704$	0.183623	−	0.154078i	0.00692057	−	0.00580705i
$705$		0			0
$706$	0.124024	−	0.703377i	0.00466772	−	0.0264719i
$707$	−33.9581	−	15.8349i	−1.27713	−	0.595533i
$708$		0			0
$709$	−2.18879	+	0.385942i	−0.0822016	+	0.0144944i	−0.214598	−	0.976703i	$-0.568844\pi$
$709$	−2.18879	+	0.385942i	−0.0822016	+	0.0144944i	0.132396	+	0.991197i	$0.457733\pi$
$710$	−6.45054	+	16.5509i	−0.242085	+	0.621145i
$711$		0			0
$712$	0.981913	+	3.66455i	0.0367987	+	0.137335i
$713$	−17.8499	+	8.32354i	−0.668483	+	0.311719i
$714$		0			0
$715$	0.0247027	−	1.09461i	0.000923827	−	0.0409361i
$716$	−6.77820	+	8.07794i	−0.253313	+	0.301887i
$717$		0			0
$718$	3.69457	+	7.92304i	0.137880	+	0.295685i
$719$	−11.3478	+	19.6551i	−0.423203	+	0.733010i	−0.996251	−	0.0865125i	$-0.972428\pi$
$719$	−11.3478	+	19.6551i	−0.423203	+	0.733010i	0.573047	+	0.819522i	$0.305761\pi$
$720$		0			0
$721$	−4.24371	−	7.35031i	−0.158044	−	0.273740i
$722$	−9.70415	+	13.8590i	−0.361151	+	0.515777i
$723$		0			0
$724$	−3.18028	−	8.73775i	−0.118194	−	0.324736i
$725$	−17.3991	+	41.8281i	−0.646185	+	1.55346i
$726$		0			0
$727$	−0.915329	+	10.4623i	−0.0339477	+	0.388024i	0.960146	+	0.279499i	$0.0901683\pi$
$727$	−0.915329	+	10.4623i	−0.0339477	+	0.388024i	−0.994094	+	0.108525i	$0.965387\pi$
$728$	−3.32656	+	3.32656i	−0.123290	+	0.123290i
$729$		0			0
$730$	−11.8387	−	1.30550i	−0.438171	−	0.0483188i
$731$	−4.67967	−	5.57701i	−0.173084	−	0.206273i
$732$		0			0
$733$	−22.0817	+	15.4618i	−0.815606	+	0.571094i	−0.905250	−	0.424880i	$-0.860316\pi$
$733$	−22.0817	+	15.4618i	−0.815606	+	0.571094i	0.0896432	+	0.995974i	$0.471427\pi$
$734$	−2.51195	+	0.914277i	−0.0927179	+	0.0337466i
$735$		0			0
$736$	−0.695449	−	3.94409i	−0.0256346	−	0.145381i
$737$	0.501454	−	1.87145i	0.0184713	−	0.0689358i
$738$		0			0
$739$	−22.3950	−	12.9298i	−0.823814	−	0.475629i	0.0279158	−	0.999610i	$-0.491113\pi$
$739$	−22.3950	−	12.9298i	−0.823814	−	0.475629i	−0.851730	+	0.523981i	$0.824446\pi$
$740$	8.16682	−	2.76546i	0.300218	−	0.101660i
$741$		0			0
$742$	−14.4577	+	1.26489i	−0.530759	+	0.0464354i
$743$	48.9387	−	4.28158i	1.79539	−	0.157076i	0.859906	−	0.510452i	$-0.170522\pi$
$743$	48.9387	−	4.28158i	1.79539	−	0.157076i	0.935481	+	0.353376i	$0.114966\pi$
$744$		0			0
$745$	−10.5620	+	21.3773i	−0.386961	+	0.783203i
$746$	16.5894	+	9.57791i	0.607382	+	0.350672i
$747$		0			0
$748$	0.410674	−	1.53266i	0.0150157	−	0.0560395i
$749$	−7.61410	−	43.1817i	−0.278213	−	1.57782i
$750$		0			0
$751$	−1.34694	+	0.490245i	−0.0491505	+	0.0178893i	−0.366478	−	0.930427i	$-0.619437\pi$
$751$	−1.34694	+	0.490245i	−0.0491505	+	0.0178893i	0.317328	+	0.948316i	$0.397214\pi$
$752$	2.84187	−	1.98990i	0.103632	−	0.0725642i
$753$		0			0
$754$	11.8968	+	14.1781i	0.433257	+	0.516336i
$755$	−0.0878991	+	0.797098i	−0.00319898	+	0.0290094i
$756$		0			0
$757$	−15.6406	+	15.6406i	−0.568469	+	0.568469i	−0.931699	−	0.363231i	$-0.881674\pi$
$757$	−15.6406	+	15.6406i	−0.568469	+	0.568469i	0.363231	+	0.931699i	$0.381674\pi$
$758$	−2.69103	+	30.7586i	−0.0977427	+	1.11720i
$759$		0			0
$760$	−1.54953	−	2.82942i	−0.0562072	−	0.102634i
$761$	−0.420811	−	1.15617i	−0.0152544	−	0.0419111i	0.931832	−	0.362891i	$-0.118210\pi$
$761$	−0.420811	−	1.15617i	−0.0152544	−	0.0419111i	−0.947086	+	0.320980i	$0.895988\pi$
$762$		0			0
$763$	−25.0978	+	35.8434i	−0.908602	+	1.29762i
$764$	11.2040	+	19.4058i	0.405345	+	0.702078i
$765$		0			0
$766$	15.1388	−	26.2211i	0.546986	−	0.947407i
$767$	−6.94105	−	14.8851i	−0.250627	−	0.537471i
$768$		0			0
$769$	−27.2951	+	32.5290i	−0.984286	+	1.17303i	0.000630919		1.00000i	$0.499799\pi$
$769$	−27.2951	+	32.5290i	−0.984286	+	1.17303i	−0.984917	+	0.173027i	$0.944645\pi$
$770$	−0.852941	−	0.892328i	−0.0307379	−	0.0321573i
$771$		0			0
$772$	−3.63040	+	1.69288i	−0.130661	+	0.0609282i
$773$	0.801998	+	2.99310i	0.0288458	+	0.107654i	0.978848	−	0.204590i	$-0.0655860\pi$
$773$	0.801998	+	2.99310i	0.0288458	+	0.107654i	−0.950002	+	0.312244i	$0.898919\pi$
$774$		0			0
$775$	7.35890	+	23.4616i	0.264339	+	0.842766i
$776$	−9.70550	+	1.71134i	−0.348407	+	0.0614336i
$777$		0			0
$778$	22.5391	+	10.5102i	0.808067	+	0.376808i
$779$	−2.23425	+	12.6711i	−0.0800504	+	0.453988i
$780$		0			0
$781$	−1.45872	+	1.22401i	−0.0521971	+	0.0437986i
$782$	−18.7459	−	18.7459i	−0.670354	−	0.670354i
$783$		0			0
$784$		−	1.69607i		−	0.0605739i
$785$	−52.8189	−	10.5474i	−1.88519	−	0.376452i
$786$		0			0
$787$	−0.876396	−	1.25162i	−0.0312401	−	0.0446155i	0.803228	−	0.595671i	$-0.203114\pi$
$787$	−0.876396	−	1.25162i	−0.0312401	−	0.0446155i	−0.834468	+	0.551056i	$0.814225\pi$
$788$	−2.47526	+	5.30821i	−0.0881775	+	0.189097i
$789$		0			0
$790$	13.4256	−	15.2860i	0.477663	−	0.543850i
$791$	2.91725	−	1.68428i	0.103725	−	0.0598859i
$792$		0			0
$793$	−20.9365	+	5.60991i	−0.743476	+	0.199214i
$794$	29.4576	+	10.7217i	1.04541	+	0.380499i
$795$		0			0
$796$	3.55004	+	2.97883i	0.125828	+	0.105582i
$797$	2.55604	+	29.2157i	0.0905397	+	1.03487i	0.896541	+	0.442960i	$0.146072\pi$
$797$	2.55604	+	29.2157i	0.0905397	+	1.03487i	−0.806002	+	0.591913i	$0.798373\pi$
$798$		0			0
$799$	7.85451	−	21.5801i	0.277872	−	0.763448i
$800$	−4.99556	+	0.210633i	−0.176620	+	0.00744700i
$801$		0			0
$802$	1.38846	+	0.372037i	0.0490283	+	0.0131371i
$803$	−1.04588	−	0.732335i	−0.0369084	−	0.0258436i
$804$		0			0
$805$	−20.0369	+	4.88714i	−0.706208	+	0.172249i
$806$	9.89298	+	1.74440i	0.348465	+	0.0614438i
$807$		0			0
$808$	−16.2074	−	1.41796i	−0.570174	−	0.0498837i
$809$	36.0963			1.26908			0.634538	−	0.772891i	$-0.281190\pi$
$809$	36.0963			1.26908			0.634538	+	0.772891i	$0.281190\pi$
$810$		0			0
$811$	−24.7458			−0.868943			−0.434471	−	0.900686i	$-0.643065\pi$
$811$	−24.7458			−0.868943			−0.434471	+	0.900686i	$0.643065\pi$
$812$	20.7872	+	1.81864i	0.729487	+	0.0638219i
$813$		0			0
$814$	0.910261	+	0.160503i	0.0319046	+	0.00562564i
$815$	−7.08137	+	11.6501i	−0.248050	+	0.408085i
$816$		0			0
$817$	−1.29974	−	0.910087i	−0.0454721	−	0.0318399i
$818$	−3.44737	−	0.923721i	−0.120535	−	0.0322971i
$819$		0			0
$820$	16.0736	+	11.8041i	0.561313	+	0.412217i
$821$	8.51495	−	23.3946i	0.297174	−	0.816478i	−0.697796	−	0.716297i	$-0.745836\pi$
$821$	8.51495	−	23.3946i	0.297174	−	0.816478i	0.994969	−	0.100181i	$-0.0319422\pi$
$822$		0			0
$823$	2.28161	+	26.0789i	0.0795318	+	0.909052i	0.926225	+	0.376971i	$0.123034\pi$
$823$	2.28161	+	26.0789i	0.0795318	+	0.909052i	−0.846693	+	0.532081i	$0.821410\pi$
$824$	−2.82313	−	2.36888i	−0.0983483	−	0.0825240i
$825$		0			0
$826$	−17.4000	−	6.33310i	−0.605425	−	0.220357i
$827$	−19.2351	+	5.15404i	−0.668872	+	0.179224i	−0.577246	−	0.816570i	$-0.695873\pi$
$827$	−19.2351	+	5.15404i	−0.668872	+	0.179224i	−0.0916251	+	0.995794i	$0.529206\pi$
$828$		0			0
$829$	−23.0699	+	13.3194i	−0.801251	+	0.462603i	−0.843908	−	0.536487i	$-0.819751\pi$
$829$	−23.0699	+	13.3194i	−0.801251	+	0.462603i	0.0426573	+	0.999090i	$0.486418\pi$
$830$	32.2806	−	2.09156i	1.12047	−	0.0725992i
$831$		0			0
$832$	−0.863295	+	1.85134i	−0.0299294	+	0.0641838i
$833$	−6.43965	−	9.19677i	−0.223121	−	0.318649i
$834$		0			0
$835$	−5.26984	+	26.3902i	−0.182370	+	0.913271i
$836$		−	0.345816i		−	0.0119603i
$837$		0			0
$838$	−9.98601	−	9.98601i	−0.344961	−	0.344961i
$839$	22.5062	−	18.8849i	0.777000	−	0.651980i	−0.165491	−	0.986211i	$-0.552921\pi$
$839$	22.5062	−	18.8849i	0.777000	−	0.651980i	0.942491	+	0.334231i	$0.108477\pi$
$840$		0			0
$841$	9.21947	−	52.2862i	0.317913	−	1.80297i
$842$	−15.3458	−	7.15584i	−0.528850	−	0.246607i
$843$		0			0
$844$	−25.1851	+	4.44081i	−0.866906	+	0.152859i
$845$	−7.93605	−	18.0727i	−0.273008	−	0.621718i
$846$		0			0
$847$	6.52249	+	24.3423i	0.224115	+	0.836410i
$848$	−5.71126	+	2.66321i	−0.196126	+	0.0914548i
$849$		0			0
$850$	−26.2882	+	20.1093i	−0.901678	+	0.689744i
$851$	9.92665	−	11.8301i	0.340281	−	0.405531i
$852$		0			0
$853$	−9.08625	−	19.4855i	−0.311107	−	0.667172i	0.687129	−	0.726535i	$-0.258871\pi$
$853$	−9.08625	−	19.4855i	−0.311107	−	0.667172i	−0.998236	+	0.0593635i	$0.981093\pi$
$854$	−12.2185	+	21.1630i	−0.418108	+	0.724184i
$855$		0			0
$856$	−9.51961	−	16.4885i	−0.325374	−	0.563564i
$857$	−7.33298	+	10.4726i	−0.250490	+	0.357736i	−0.924630	−	0.380867i	$-0.875626\pi$
$857$	−7.33298	+	10.4726i	−0.250490	+	0.357736i	0.674140	+	0.738604i	$0.264514\pi$
$858$		0			0
$859$	−5.55404	−	15.2596i	−0.189501	−	0.520651i	0.808163	−	0.588959i	$-0.200462\pi$
$859$	−5.55404	−	15.2596i	−0.189501	−	0.520651i	−0.997664	+	0.0683083i	$0.978240\pi$
$860$	−2.15699	+	1.18127i	−0.0735527	+	0.0402809i
$861$		0			0
$862$	0.172453	−	1.97115i	0.00587378	−	0.0671376i
$863$	−15.0219	+	15.0219i	−0.511352	+	0.511352i	−0.914940	−	0.403589i	$-0.867763\pi$
$863$	−15.0219	+	15.0219i	−0.511352	+	0.511352i	0.403589	+	0.914940i	$0.367763\pi$
$864$		0			0
$865$	−1.64762	−	2.05604i	−0.0560208	−	0.0699073i
$866$	−17.9903	−	21.4400i	−0.611336	−	0.728561i
$867$		0			0
$868$	9.27743	−	6.49613i	0.314897	−	0.220493i
$869$	2.04940	−	0.745921i	0.0695212	−	0.0253036i
$870$		0			0
$871$	2.86709	+	16.2601i	0.0971478	+	0.550953i
$872$	−4.91747	+	18.3523i	−0.166527	+	0.621486i
$873$		0			0
$874$	−5.00376	−	2.88892i	−0.169255	−	0.0977193i
$875$	2.74580	+	25.6018i	0.0928249	+	0.865499i
$876$		0			0
$877$	48.7345	−	4.26371i	1.64565	−	0.143975i	0.773692	−	0.633562i	$-0.218408\pi$
$877$	48.7345	−	4.26371i	1.64565	−	0.143975i	0.871955	+	0.489587i	$0.162852\pi$
$878$	−26.3967	+	2.30941i	−0.890846	+	0.0779389i
$879$		0			0
$880$	−0.480540	−	0.237423i	−0.0161990	−	0.00800352i
$881$	13.5253	+	7.80885i	0.455680	+	0.263087i	0.710226	−	0.703974i	$-0.248593\pi$
$881$	13.5253	+	7.80885i	0.455680	+	0.263087i	−0.254546	+	0.967061i	$0.581926\pi$
$882$		0			0
$883$	−12.8472	+	47.9463i	−0.432342	+	1.61352i	0.315007	+	0.949090i	$0.397993\pi$
$883$	−12.8472	+	47.9463i	−0.432342	+	1.61352i	−0.747348	+	0.664432i	$0.768673\pi$
$884$	2.34806	+	13.3165i	0.0789737	+	0.447882i
$885$		0			0
$886$	9.27571	−	3.37608i	0.311624	−	0.113422i
$887$	12.4855	−	8.74243i	0.419222	−	0.293542i	−0.344869	−	0.938651i	$-0.612077\pi$
$887$	12.4855	−	8.74243i	0.419222	−	0.293542i	0.764091	+	0.645109i	$0.223188\pi$
$888$		0			0
$889$	−6.01223	−	7.16510i	−0.201644	−	0.240310i
$890$	6.61991	−	5.30491i	0.221900	−	0.177821i
$891$		0			0
$892$	11.8763	−	11.8763i	0.397647	−	0.397647i
$893$	0.436221	−	4.98603i	0.0145976	−	0.166851i
$894$		0			0
$895$	22.6324	+	6.61509i	0.756518	+	0.221118i
$896$	0.787681	+	2.16414i	0.0263146	+	0.0722987i
$897$		0			0
$898$	−6.67062	+	9.52664i	−0.222602	+	0.317908i
$899$	−22.2786	−	38.5876i	−0.743032	−	1.28697i
$900$		0			0
$901$	−20.8571	+	36.1255i	−0.694850	+	1.20352i
$902$	0.903469	+	1.93750i	0.0300822	+	0.0645115i
$903$		0			0
$904$	0.940181	−	1.12046i	0.0312700	−	0.0372661i
$905$	−15.0302	+	14.3668i	−0.499621	+	0.477568i
$906$		0			0
$907$	20.1927	−	9.41600i	0.670487	−	0.312653i	−0.0573992	−	0.998351i	$-0.518281\pi$
$907$	20.1927	−	9.41600i	0.670487	−	0.312653i	0.727886	+	0.685698i	$0.240503\pi$
$908$	−0.736027	−	2.74689i	−0.0244259	−	0.0911588i
$909$		0			0
$910$	9.80141	+	3.81999i	0.324913	+	0.126631i
$911$	−5.70901	+	1.00665i	−0.189148	+	0.0333519i	−0.267420	−	0.963580i	$-0.586171\pi$
$911$	−5.70901	+	1.00665i	−0.189148	+	0.0333519i	0.0782716	+	0.996932i	$0.475060\pi$
$912$		0			0
$913$	3.14279	+	1.46551i	0.104011	+	0.0485012i
$914$	2.08225	−	11.8090i	0.0688748	−	0.390608i
$915$		0			0
$916$	11.9433	−	10.0216i	0.394617	−	0.331123i
$917$	−31.3993	−	31.3993i	−1.03690	−	1.03690i
$918$		0			0
$919$			9.30883i			0.307070i	0.988143	+	0.153535i	$0.0490658\pi$
$919$			9.30883i			0.307070i	−0.988143	+	0.153535i	$0.950934\pi$
$920$	−7.44978	+	4.96973i	−0.245612	+	0.163847i
$921$		0			0
$922$	−1.05759	−	1.51039i	−0.0348298	−	0.0497422i
$923$	6.85810	−	14.7072i	0.225737	−	0.484094i
$924$		0			0
$925$	−13.0042	−	14.2343i	−0.427576	−	0.468020i
$926$	17.3871	−	10.0385i	0.571376	−	0.329884i
$927$		0			0
$928$	8.75178	−	2.34503i	0.287291	−	0.0769795i
$929$	−16.1059	−	5.86206i	−0.528417	−	0.192328i	0.0640144	−	0.997949i	$-0.479610\pi$
$929$	−16.1059	−	5.86206i	−0.528417	−	0.192328i	−0.592431	+	0.805621i	$0.701832\pi$
$930$		0			0
$931$	−1.87443	−	1.57283i	−0.0614319	−	0.0515475i
$932$	0.694700	+	7.94046i	0.0227557	+	0.260098i
$933$		0			0
$934$	−6.55049	+	17.9973i	−0.214338	+	0.588890i
$935$	−3.50713	+	0.537117i	−0.114695	+	0.0175656i
$936$		0			0
$937$	−22.0789	−	5.91602i	−0.721286	−	0.193268i	−0.120541	−	0.992708i	$-0.538463\pi$
$937$	−22.0789	−	5.91602i	−0.721286	−	0.193268i	−0.600745	+	0.799440i	$0.705129\pi$
$938$	15.2484	+	10.6770i	0.497878	+	0.348618i
$939$		0			0
$940$	−6.62902	−	4.02937i	−0.216215	−	0.131423i
$941$	−30.0461	−	5.29794i	−0.979475	−	0.172708i	−0.339083	−	0.940756i	$-0.610117\pi$
$941$	−30.0461	−	5.29794i	−0.979475	−	0.172708i	−0.640392	+	0.768049i	$0.721228\pi$
$942$		0			0
$943$	35.5820	+	3.11302i	1.15871	+	0.101374i
$944$	−8.04018			−0.261685
$945$		0			0
$946$	−0.263630			−0.00857135
$947$	−34.5912	−	3.02634i	−1.12406	−	0.0983428i	−0.490071	−	0.871682i	$-0.663029\pi$
$947$	−34.5912	−	3.02634i	−1.12406	−	0.0983428i	−0.633992	+	0.773339i	$0.718585\pi$
$948$		0			0
$949$	10.7154	+	1.88941i	0.347836	+	0.0613328i
$950$	−4.39980	+	5.71622i	−0.142748	+	0.185459i
$951$		0			0
$952$	12.4879	+	8.74415i	0.404736	+	0.283399i
$953$	−16.6356	−	4.45750i	−0.538880	−	0.144393i	−0.0208944	−	0.999782i	$-0.506651\pi$
$953$	−16.6356	−	4.45750i	−0.538880	−	0.144393i	−0.517986	+	0.855389i	$0.673318\pi$
$954$		0			0
$955$	29.6581	−	40.3852i	0.959714	−	1.30684i
$956$	−5.60658	+	15.4039i	−0.181330	+	0.498199i
$957$		0			0
$958$	0.311890	+	3.56492i	0.0100767	+	0.115177i
$959$	34.1448	+	28.6509i	1.10259	+	0.925184i
$960$		0			0
$961$	6.40490	+	2.33119i	0.206610	+	0.0751998i
$962$	−7.60843	+	2.03867i	−0.245306	+	0.0657295i
$963$		0			0
$964$	−2.71805	+	1.56927i	−0.0875425	+	0.0505427i
$965$	6.72984	+	5.91081i	0.216641	+	0.190276i
$966$		0			0
$967$	7.03618	−	15.0891i	0.226268	−	0.485234i	−0.760096	−	0.649811i	$-0.774848\pi$
$967$	7.03618	−	15.0891i	0.226268	−	0.485234i	0.986364	+	0.164577i	$0.0526259\pi$
$968$	6.27638	+	8.96361i	0.201731	+	0.288101i
$969$		0			0
$970$	12.2294	+	18.3322i	0.392662	+	0.588611i
$971$		−	10.6683i		−	0.342361i	−0.985240	−	0.171180i	$-0.945242\pi$
$971$		−	10.6683i		−	0.342361i	0.985240	−	0.171180i	$-0.0547581\pi$
$972$		0			0
$973$	−26.9741	−	26.9741i	−0.864749	−	0.864749i
$974$	25.7240	−	21.5850i	0.824250	−	0.691628i
$975$		0			0
$976$	−1.84255	+	10.4496i	−0.0589785	+	0.334484i
$977$	−3.13210	−	1.46052i	−0.100205	−	0.0467263i	0.371870	−	0.928285i	$-0.378717\pi$
$977$	−3.13210	−	1.46052i	−0.100205	−	0.0467263i	−0.472074	+	0.881559i	$0.656495\pi$
$978$		0			0
$979$	0.895575	−	0.157914i	0.0286227	−	0.00504696i
$980$	−3.47248	+	1.52483i	−0.110924	+	0.0487090i
$981$		0			0
$982$	9.33948	+	34.8554i	0.298035	+	1.11228i
$983$	−48.8746	+	22.7906i	−1.55886	+	0.726908i	−0.995085	−	0.0990223i	$-0.968428\pi$
$983$	−48.8746	+	22.7906i	−1.55886	+	0.726908i	−0.563773	+	0.825930i	$0.690651\pi$
$984$		0			0
$985$	13.0932	+	0.295482i	0.417185	+	0.00941484i
$986$	38.5520	−	45.9445i	1.22775	−	1.46317i
$987$		0			0
$988$	1.24546	+	2.67090i	0.0396234	+	0.0849727i
$989$	−2.20235	+	3.81458i	−0.0700306	+	0.121296i
$990$		0			0
$991$	−24.7704	−	42.9037i	−0.786859	−	1.36288i	−0.927882	−	0.372873i	$-0.878373\pi$
$991$	−24.7704	−	42.9037i	−0.786859	−	1.36288i	0.141023	−	0.990006i	$-0.454961\pi$
$992$	2.82069	−	4.02837i	0.0895571	−	0.127901i
$993$		0			0
$994$	−6.25741	−	17.1921i	−0.198473	−	0.545300i
$995$	2.90715	−	9.94633i	0.0921630	−	0.315320i
$996$		0			0
$997$	−0.536622	+	6.13362i	−0.0169950	+	0.194254i	0.982951	+	0.183867i	$0.0588617\pi$
$997$	−0.536622	+	6.13362i	−0.0169950	+	0.194254i	−0.999946	+	0.0103863i	$0.996694\pi$
$998$	12.1086	−	12.1086i	0.383290	−	0.383290i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.13		216
3.2	odd	2		270.2.r.a.113.3	✓	216
5.2	odd	4	inner	810.2.s.a.287.4		216
15.2	even	4		270.2.r.a.167.16	yes	216
27.11	odd	18	inner	810.2.s.a.683.4		216
27.16	even	9		270.2.r.a.173.16	yes	216
135.92	even	36	inner	810.2.s.a.197.13		216
135.97	odd	36		270.2.r.a.227.3	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.3	✓	216	3.2	odd	2
270.2.r.a.167.16	yes	216	15.2	even	4
270.2.r.a.173.16	yes	216	27.16	even	9
270.2.r.a.227.3	yes	216	135.97	odd	36
810.2.s.a.197.13		216	135.92	even	36	inner
810.2.s.a.287.4		216	5.2	odd	4	inner
810.2.s.a.683.4		216	27.11	odd	18	inner
810.2.s.a.773.13		216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.529859 - 2.17238i) q^{5} +(1.88653 + 1.32096i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.529859 - 2.17238i) q^{5} +(1.88653 + 1.32096i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.338507 - 2.21030i) q^{10} +(0.0819834 - 0.225247i) q^{11} +(0.178036 + 2.03496i) q^{13} +(1.76422 + 1.48036i) q^{14} +(0.939693 + 0.342020i) q^{16} +(6.39398 - 1.71326i) q^{17} +(1.24940 - 0.721342i) q^{19} +(-0.144579 - 2.23139i) q^{20} +(0.101303 - 0.217245i) q^{22} +(-2.29713 - 3.28065i) q^{23} +(-4.43850 + 2.30211i) q^{25} +2.04273i q^{26} +(1.62849 + 1.62849i) q^{28} +(6.94075 - 5.82398i) q^{29} +(0.853954 - 4.84302i) q^{31} +(0.906308 + 0.422618i) q^{32} +(6.51897 - 1.14947i) q^{34} +(1.87004 - 4.79819i) q^{35} +(0.998014 + 3.72464i) q^{37} +(1.30752 - 0.609704i) q^{38} +(0.0504497 - 2.23550i) q^{40} +(-5.73269 + 6.83195i) q^{41} +(-0.464803 - 0.996773i) q^{43} +(0.119852 - 0.207589i) q^{44} +(-2.00247 - 3.46837i) q^{46} +(1.98990 - 2.84187i) q^{47} +(-0.580090 - 1.59378i) q^{49} +(-4.62225 + 1.90651i) q^{50} +(-0.178036 + 2.03496i) q^{52} +(-4.45596 + 4.45596i) q^{53} +(-0.532763 - 0.0587499i) q^{55} +(1.48036 + 1.76422i) q^{56} +(7.42193 - 5.19689i) q^{58} +(-7.55529 + 2.74990i) q^{59} +(1.84255 + 10.4496i) q^{61} +(1.27280 - 4.75016i) q^{62} +(0.866025 + 0.500000i) q^{64} +(4.32637 - 1.46500i) q^{65} +(8.05202 - 0.704460i) q^{67} +(6.59434 - 0.576930i) q^{68} +(2.28111 - 4.61694i) q^{70} +(-6.87978 - 3.97204i) q^{71} +(1.37861 - 5.14504i) q^{73} +(0.669592 + 3.79745i) q^{74} +(1.35568 - 0.493427i) q^{76} +(0.452207 - 0.316639i) q^{77} +(5.84837 + 6.96981i) q^{79} +(0.245094 - 2.22260i) q^{80} +(-6.30632 + 6.30632i) q^{82} +(-1.26085 + 14.4115i) q^{83} +(-7.10977 - 12.9824i) q^{85} +(-0.376160 - 1.03349i) q^{86} +(0.137488 - 0.196353i) q^{88} +(1.89691 + 3.28554i) q^{89} +(-2.35223 + 4.07418i) q^{91} +(-1.69256 - 3.62970i) q^{92} +(2.23001 - 2.65763i) q^{94} +(-2.22904 - 2.33197i) q^{95} +(-8.93186 + 4.16500i) q^{97} +(-0.438975 - 1.63828i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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