LMFDB - Embedded newform 405.2.p.a.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(19,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16, 9]))

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

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

chi := DirichletCharacter("405.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.p (of order $18$, degree $6$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	405.289
Dual form			405.2.p.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06000 + 1.26326i) q^{2} +(-0.124928 - 0.708504i) q^{4} +(0.908813 + 2.04305i) q^{5} +(-1.22191 - 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +O(q^{10})$	\(q+(-1.06000 + 1.26326i) q^{2} +(-0.124928 - 0.708504i) q^{4} +(0.908813 + 2.04305i) q^{5} +(-1.22191 - 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +(-3.54425 - 1.01757i) q^{10} +(-3.30366 + 1.20243i) q^{11} +(0.380059 + 0.452936i) q^{13} +(1.56741 - 1.31521i) q^{14} +(4.62449 - 1.68318i) q^{16} +(-4.46967 + 2.58056i) q^{17} +(-1.41748 + 2.45515i) q^{19} +(1.33397 - 0.899132i) q^{20} +(1.98290 - 5.44797i) q^{22} +(6.59324 - 1.16257i) q^{23} +(-3.34812 + 3.71350i) q^{25} -0.975040 q^{26} +0.892646i q^{28} +(-7.21421 - 6.05345i) q^{29} +(0.196771 + 1.11595i) q^{31} +(-1.33116 + 3.65733i) q^{32} +(1.47793 - 8.38176i) q^{34} +(-0.670302 - 2.69224i) q^{35} +(-4.06570 + 2.34734i) q^{37} +(-1.59896 - 4.39311i) q^{38} +(0.495142 - 4.69597i) q^{40} +(-4.43129 + 3.71830i) q^{41} +(-0.739520 - 2.03181i) q^{43} +(1.26465 + 2.19044i) q^{44} +(-5.52022 + 9.56131i) q^{46} +(6.14268 + 1.08312i) q^{47} +(-5.13120 - 1.86760i) q^{49} +(-1.14211 - 8.16587i) q^{50} +(0.273427 - 0.325858i) q^{52} -8.21098i q^{53} +(-5.45905 - 5.65676i) q^{55} +(2.00717 + 1.68421i) q^{56} +(15.2942 - 2.69677i) q^{58} +(12.6981 + 4.62173i) q^{59} +(-1.38440 + 7.85133i) q^{61} +(-1.61831 - 0.934331i) q^{62} +(1.71215 + 2.96553i) q^{64} +(-0.579970 + 1.18811i) q^{65} +(2.83000 + 3.37266i) q^{67} +(2.38673 + 2.84439i) q^{68} +(4.11152 + 2.00701i) q^{70} +(3.43788 + 5.95458i) q^{71} +(1.23957 + 0.715668i) q^{73} +(1.34436 - 7.62423i) q^{74} +(1.91656 + 0.697573i) q^{76} +(4.29586 - 0.757476i) q^{77} +(-0.970806 - 0.814603i) q^{79} +(7.64162 + 7.91838i) q^{80} -9.53928i q^{82} +(0.982501 - 1.17090i) q^{83} +(-9.33432 - 6.78651i) q^{85} +(3.35061 + 1.21952i) q^{86} +(7.31144 + 1.28920i) q^{88} +(-6.52774 + 11.3064i) q^{89} +(-0.366811 - 0.635335i) q^{91} +(-1.64736 - 4.52610i) q^{92} +(-7.87952 + 6.61170i) q^{94} +(-6.30422 - 0.664715i) q^{95} +(4.74011 + 13.0234i) q^{97} +(7.79835 - 4.50238i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} + 9 q^{5}+O(q^{10}) $ 96 * q - 12 * q^4 + 9 * q^5	$ 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46} - 30 q^{49} - 84 q^{50} - 12 q^{55} + 96 q^{56} - 66 q^{59} + 6 q^{61} - 45 q^{65} - 33 q^{70} + 90 q^{71} - 66 q^{74} + 12 q^{76} + 24 q^{79} - 30 q^{80} - 21 q^{85} - 18 q^{86} - 96 q^{89} - 6 q^{91} + 24 q^{94} - 87 q^{95}+O(q^{100}) $ 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.06000	+	1.26326i	−0.749535	+	0.893261i	−0.997138	−	0.0756008i	$-0.975913\pi$
$2$	−1.06000	+	1.26326i	−0.749535	+	0.893261i	0.247604	+	0.968861i	$0.420357\pi$
$3$		0			0
$3$		0			0
$4$	−0.124928	−	0.708504i	−0.0624641	−	0.354252i
$5$	0.908813	+	2.04305i	0.406434	+	0.913680i
$5$	0.908813	+	2.04305i	0.406434	+	0.913680i
$6$		0			0
$7$	−1.22191	−	0.215456i	−0.461840	−	0.0814348i	−0.0621128	−	0.998069i	$-0.519784\pi$
$7$	−1.22191	−	0.215456i	−0.461840	−	0.0814348i	−0.399727	+	0.916634i	$0.630895\pi$
$8$	−1.82882	−	1.05587i	−0.646587	−	0.373307i
$9$		0			0
$10$	−3.54425	−	1.01757i	−1.12079	−	0.321784i
$11$	−3.30366	+	1.20243i	−0.996092	+	0.362548i	−0.788076	−	0.615578i	$-0.788923\pi$
$11$	−3.30366	+	1.20243i	−0.996092	+	0.362548i	−0.208016	+	0.978125i	$0.566701\pi$
$12$		0			0
$13$	0.380059	+	0.452936i	0.105409	+	0.125622i	0.816170	−	0.577812i	$-0.196093\pi$
$13$	0.380059	+	0.452936i	0.105409	+	0.125622i	−0.710760	+	0.703434i	$0.751649\pi$
$14$	1.56741	−	1.31521i	0.418907	−	0.351505i
$15$		0			0
$16$	4.62449	−	1.68318i	1.15612	−	0.420794i
$17$	−4.46967	+	2.58056i	−1.08405	+	0.625879i	−0.931987	−	0.362491i	$-0.881926\pi$
$17$	−4.46967	+	2.58056i	−1.08405	+	0.625879i	−0.152067	+	0.988370i	$0.548593\pi$
$18$		0			0
$19$	−1.41748	+	2.45515i	−0.325192	+	0.563250i	−0.981551	−	0.191199i	$-0.938762\pi$
$19$	−1.41748	+	2.45515i	−0.325192	+	0.563250i	0.656359	+	0.754449i	$0.272096\pi$
$20$	1.33397	−	0.899132i	0.298285	−	0.201052i
$21$		0			0
$22$	1.98290	−	5.44797i	0.422756	−	1.16151i
$23$	6.59324	−	1.16257i	1.37479	−	0.242412i	0.563043	−	0.826427i	$-0.309630\pi$
$23$	6.59324	−	1.16257i	1.37479	−	0.242412i	0.811742	+	0.584016i	$0.198519\pi$
$24$		0			0
$25$	−3.34812	+	3.71350i	−0.669624	+	0.742701i
$26$	−0.975040			−0.191221
$27$		0			0
$28$			0.892646i			0.168694i
$29$	−7.21421	−	6.05345i	−1.33965	−	1.12410i	−0.981717	−	0.190348i	$-0.939038\pi$
$29$	−7.21421	−	6.05345i	−1.33965	−	1.12410i	−0.357929	−	0.933749i	$-0.616517\pi$
$30$		0			0
$31$	0.196771	+	1.11595i	0.0353412	+	0.200430i	0.997366	−	0.0725319i	$-0.0231079\pi$
$31$	0.196771	+	1.11595i	0.0353412	+	0.200430i	−0.962025	+	0.272962i	$0.911997\pi$
$32$	−1.33116	+	3.65733i	−0.235318	+	0.646531i
$33$		0			0
$34$	1.47793	−	8.38176i	0.253463	−	1.43746i
$35$	−0.670302	−	2.69224i	−0.113302	−	0.455072i
$36$		0			0
$37$	−4.06570	+	2.34734i	−0.668398	+	0.385900i	−0.795469	−	0.605994i	$-0.792776\pi$
$37$	−4.06570	+	2.34734i	−0.668398	+	0.385900i	0.127072	+	0.991894i	$0.459442\pi$
$38$	−1.59896	−	4.39311i	−0.259386	−	0.712657i
$39$		0			0
$40$	0.495142	−	4.69597i	0.0782888	−	0.742498i
$41$	−4.43129	+	3.71830i	−0.692052	+	0.580700i	−0.919500	−	0.393090i	$-0.871406\pi$
$41$	−4.43129	+	3.71830i	−0.692052	+	0.580700i	0.227448	+	0.973790i	$0.426962\pi$
$42$		0			0
$43$	−0.739520	−	2.03181i	−0.112776	−	0.309849i	0.870446	−	0.492264i	$-0.163831\pi$
$43$	−0.739520	−	2.03181i	−0.112776	−	0.309849i	−0.983222	+	0.182415i	$0.941608\pi$
$44$	1.26465	+	2.19044i	0.190653	+	0.330221i
$45$		0			0
$46$	−5.52022	+	9.56131i	−0.813913	+	1.40974i
$47$	6.14268	+	1.08312i	0.896002	+	0.157989i	0.602641	−	0.798012i	$-0.294115\pi$
$47$	6.14268	+	1.08312i	0.896002	+	0.157989i	0.293361	+	0.956002i	$0.405226\pi$
$48$		0			0
$49$	−5.13120	−	1.86760i	−0.733029	−	0.266801i
$50$	−1.14211	−	8.16587i	−0.161519	−	1.15483i
$51$		0			0
$52$	0.273427	−	0.325858i	0.0379175	−	0.0451883i
$53$		−	8.21098i		−	1.12787i	−0.825821	−	0.563933i	$-0.809288\pi$
$53$		−	8.21098i		−	1.12787i	0.825821	−	0.563933i	$-0.190712\pi$
$54$		0			0
$55$	−5.45905	−	5.65676i	−0.736098	−	0.762758i
$56$	2.00717	+	1.68421i	0.268219	+	0.225063i
$57$		0			0
$58$	15.2942	−	2.69677i	2.00822	−	0.354104i
$59$	12.6981	+	4.62173i	1.65315	+	0.601698i	0.989265	−	0.146136i	$-0.0466836\pi$
$59$	12.6981	+	4.62173i	1.65315	+	0.601698i	0.663886	+	0.747833i	$0.268906\pi$
$60$		0			0
$61$	−1.38440	+	7.85133i	−0.177254	+	1.00526i	0.758255	+	0.651958i	$0.226052\pi$
$61$	−1.38440	+	7.85133i	−0.177254	+	1.00526i	−0.935509	+	0.353302i	$0.885059\pi$
$62$	−1.61831	−	0.934331i	−0.205525	−	0.118660i
$63$		0			0
$64$	1.71215	+	2.96553i	0.214019	+	0.370691i
$65$	−0.579970	+	1.18811i	−0.0719364	+	0.147367i
$66$		0			0
$67$	2.83000	+	3.37266i	0.345739	+	0.412036i	0.910691	−	0.413088i	$-0.135550\pi$
$67$	2.83000	+	3.37266i	0.345739	+	0.412036i	−0.564952	+	0.825124i	$0.691105\pi$
$68$	2.38673	+	2.84439i	0.289433	+	0.344933i
$69$		0			0
$70$	4.11152	+	2.00701i	0.491421	+	0.239884i
$71$	3.43788	+	5.95458i	0.408001	+	0.706679i	0.994666	−	0.103151i	$-0.0328925\pi$
$71$	3.43788	+	5.95458i	0.408001	+	0.706679i	−0.586664	+	0.809830i	$0.699559\pi$
$72$		0			0
$73$	1.23957	+	0.715668i	0.145081	+	0.0837626i	0.570783	−	0.821101i	$-0.306640\pi$
$73$	1.23957	+	0.715668i	0.145081	+	0.0837626i	−0.425702	+	0.904863i	$0.639973\pi$
$74$	1.34436	−	7.62423i	0.156278	−	0.886298i
$75$		0			0
$76$	1.91656	+	0.697573i	0.219845	+	0.0800171i
$77$	4.29586	−	0.757476i	0.489559	−	0.0863224i
$78$		0			0
$79$	−0.970806	−	0.814603i	−0.109224	−	0.0916500i	0.586540	−	0.809920i	$-0.300490\pi$
$79$	−0.970806	−	0.814603i	−0.109224	−	0.0916500i	−0.695764	+	0.718270i	$0.744934\pi$
$80$	7.64162	+	7.91838i	0.854359	+	0.885302i
$81$		0			0
$82$		−	9.53928i		−	1.05344i
$83$	0.982501	−	1.17090i	0.107844	−	0.128523i	−0.709423	−	0.704783i	$-0.751044\pi$
$83$	0.982501	−	1.17090i	0.107844	−	0.128523i	0.817266	+	0.576260i	$0.195489\pi$
$84$		0			0
$85$	−9.33432	−	6.78651i	−1.01245	−	0.736101i
$86$	3.35061	+	1.21952i	0.361305	+	0.131504i
$87$		0			0
$88$	7.31144	+	1.28920i	0.779402	+	0.137430i
$89$	−6.52774	+	11.3064i	−0.691939	+	1.19847i	0.279262	+	0.960215i	$0.409910\pi$
$89$	−6.52774	+	11.3064i	−0.691939	+	1.19847i	−0.971202	+	0.238259i	$0.923423\pi$
$90$		0			0
$91$	−0.366811	−	0.635335i	−0.0384522	−	0.0666012i
$92$	−1.64736	−	4.52610i	−0.171750	−	0.471878i
$93$		0			0
$94$	−7.87952	+	6.61170i	−0.812711	+	0.681945i
$95$	−6.30422	−	0.664715i	−0.646799	−	0.0681983i
$96$		0			0
$97$	4.74011	+	13.0234i	0.481286	+	1.32232i	0.908392	+	0.418120i	$0.137311\pi$
$97$	4.74011	+	13.0234i	0.481286	+	1.32232i	−0.427106	+	0.904202i	$0.640467\pi$
$98$	7.79835	−	4.50238i	0.787753	−	0.454809i
$99$		0			0
$100$	3.04930	+	1.90823i	0.304930	+	0.190823i
$101$	−2.04974	+	11.6247i	−0.203957	+	1.15670i	0.695115	+	0.718898i	$0.255353\pi$
$101$	−2.04974	+	11.6247i	−0.203957	+	1.15670i	−0.899072	+	0.437800i	$0.855758\pi$
$102$		0			0
$103$	−0.837596	+	2.30128i	−0.0825308	+	0.226751i	−0.974093	−	0.226146i	$-0.927387\pi$
$103$	−0.837596	+	2.30128i	−0.0825308	+	0.226751i	0.891563	+	0.452897i	$0.149610\pi$
$104$	−0.216818	−	1.22963i	−0.0212607	−	0.120576i
$105$		0			0
$106$	10.3726	+	8.70366i	1.00748	+	0.845374i
$107$			6.83945i			0.661195i	0.943772	+	0.330597i	$0.107250\pi$
$107$			6.83945i			0.661195i	−0.943772	+	0.330597i	$0.892750\pi$
$108$		0			0
$109$	18.7944			1.80018			0.900088	−	0.435708i	$-0.143502\pi$
$109$	18.7944			1.80018			0.900088	+	0.435708i	$0.143502\pi$
$110$	12.9326	−	0.900022i	1.23307	−	0.0858137i
$111$		0			0
$112$	−6.01338	+	1.06032i	−0.568211	+	0.100191i
$113$	−4.71959	+	12.9670i	−0.443982	+	1.21983i	0.492870	+	0.870103i	$0.335948\pi$
$113$	−4.71959	+	12.9670i	−0.443982	+	1.21983i	−0.936852	+	0.349727i	$0.886274\pi$
$114$		0			0
$115$	8.36720	+	12.4138i	0.780246	+	1.15759i
$116$	−3.38763	+	5.86754i	−0.314533	+	0.544788i
$117$		0			0
$118$	−19.2985	+	11.1420i	−1.77657	+	1.02570i
$119$	6.01754	−	2.19021i	0.551627	−	0.200776i
$120$		0			0
$121$	1.04185	−	0.874216i	0.0947136	−	0.0794742i
$122$	−8.45081	−	10.0713i	−0.765101	−	0.911811i
$123$		0			0
$124$	0.766069	−	0.278826i	0.0687950	−	0.0250393i
$125$	−10.6297	−	3.46550i	−0.950748	−	0.309964i
$126$		0			0
$127$	7.40277	+	4.27399i	0.656890	+	0.379255i	0.791091	−	0.611699i	$-0.209514\pi$
$127$	7.40277	+	4.27399i	0.656890	+	0.379255i	−0.134201	+	0.990954i	$0.542847\pi$
$128$	−13.2270	−	2.33227i	−1.16911	−	0.206146i
$129$		0			0
$130$	−0.886129	−	1.99206i	−0.0777187	−	0.174715i
$131$	−1.68189	−	9.53845i	−0.146947	−	0.833379i	−0.965783	−	0.259351i	$-0.916491\pi$
$131$	−1.68189	−	9.53845i	−0.146947	−	0.833379i	0.818836	−	0.574028i	$-0.194620\pi$
$132$		0			0
$133$	2.26101	−	2.69457i	0.196055	−	0.233649i
$134$	−7.26035			−0.627198
$135$		0			0
$136$	10.8990			0.934580
$137$	9.51323	−	11.3374i	0.812770	−	0.968622i	−0.187136	−	0.982334i	$-0.559920\pi$
$137$	9.51323	−	11.3374i	0.812770	−	0.968622i	0.999906	+	0.0137123i	$0.00436489\pi$
$138$		0			0
$139$	−0.474713	−	2.69223i	−0.0402646	−	0.228352i	0.958034	−	0.286653i	$-0.0925428\pi$
$139$	−0.474713	−	2.69223i	−0.0402646	−	0.228352i	−0.998299	+	0.0583011i	$0.981432\pi$
$140$	−1.82372	+	0.811248i	−0.154133	+	0.0685630i
$141$		0			0
$142$	−11.1664	−	1.96893i	−0.937060	−	0.165229i
$143$	−1.80021	−	1.03935i	−0.150541	−	0.0869151i
$144$		0			0
$145$	5.81113	−	20.2405i	0.482588	−	1.68088i
$146$	−2.21803	+	0.807296i	−0.183565	+	0.0668123i
$147$		0			0
$148$	2.17102	+	2.58732i	0.178456	+	0.212676i
$149$	14.9253	−	12.5238i	1.22273	−	1.02599i	0.224054	−	0.974577i	$-0.428071\pi$
$149$	14.9253	−	12.5238i	1.22273	−	1.02599i	0.998677	−	0.0514162i	$-0.0163735\pi$
$150$		0			0
$151$	−12.9070	+	4.69775i	−1.05035	+	0.382297i	−0.808796	−	0.588089i	$-0.799880\pi$
$151$	−12.9070	+	4.69775i	−1.05035	+	0.382297i	−0.241557	+	0.970387i	$0.577658\pi$
$152$	5.18465	−	2.99336i	0.420530	−	0.242793i
$153$		0			0
$154$	−3.59673	+	6.22972i	−0.289833	+	0.502005i
$155$	−2.10110	+	1.41620i	−0.168765	+	0.113752i
$156$		0			0
$157$	−4.04287	+	11.1077i	−0.322656	+	0.886491i	0.667258	+	0.744826i	$0.267468\pi$
$157$	−4.04287	+	11.1077i	−0.322656	+	0.886491i	−0.989915	+	0.141665i	$0.954755\pi$
$158$	2.05811	−	0.362901i	0.163735	−	0.0288708i
$159$		0			0
$160$	−8.68189	+	0.604203i	−0.686364	+	0.0477664i
$161$	−8.30684			−0.654671
$162$		0			0
$163$		−	13.4522i		−	1.05366i	−0.849972	−	0.526828i	$-0.823381\pi$
$163$		−	13.4522i		−	1.05366i	0.849972	−	0.526828i	$-0.176619\pi$
$164$	3.18802	+	2.67507i	0.248943	+	0.208888i
$165$		0			0
$166$	0.437699	+	2.48231i	0.0339720	+	0.192665i
$167$	0.885201	−	2.43207i	0.0684989	−	0.188199i	−0.900720	−	0.434401i	$-0.856960\pi$
$167$	0.885201	−	2.43207i	0.0684989	−	0.188199i	0.969219	+	0.246201i	$0.0791824\pi$
$168$		0			0
$169$	2.19672	−	12.4582i	0.168978	−	0.958324i
$170$	18.4675	−	4.59797i	1.41640	−	0.352648i
$171$		0			0
$172$	−1.34716	+	0.777784i	−0.102720	+	0.0593055i
$173$	5.65820	+	15.5458i	0.430185	+	1.18192i	0.945699	+	0.325042i	$0.105379\pi$
$173$	5.65820	+	15.5458i	0.430185	+	1.18192i	−0.515515	+	0.856881i	$0.672399\pi$
$174$		0			0
$175$	4.89120	−	3.81620i	0.369740	−	0.288478i
$176$	−13.2539	+	11.1213i	−0.999047	+	0.838300i
$177$		0			0
$178$	−7.36349	−	20.2310i	−0.551917	−	1.51638i
$179$	0.606831	+	1.05106i	0.0453567	+	0.0785601i	0.887812	−	0.460205i	$-0.152224\pi$
$179$	0.606831	+	1.05106i	0.0453567	+	0.0785601i	−0.842456	+	0.538765i	$0.818891\pi$
$180$		0			0
$181$	1.84215	−	3.19070i	0.136926	−	0.237163i	−0.789405	−	0.613872i	$-0.789611\pi$
$181$	1.84215	−	3.19070i	0.136926	−	0.237163i	0.926332	+	0.376709i	$0.122944\pi$
$182$	1.19141	+	0.210078i	0.0883135	+	0.0155720i
$183$		0			0
$184$	−13.2854	−	4.83549i	−0.979413	−	0.356477i
$185$	−8.49069	−	6.17315i	−0.624248	−	0.453859i
$186$		0			0
$187$	11.6633	−	13.8998i	0.852906	−	1.01645i
$188$		−	4.48743i		−	0.327279i
$189$		0			0
$190$	7.52219	−	7.25928i	0.545717	−	0.526643i
$191$	−2.91058	−	2.44226i	−0.210602	−	0.176716i	0.531385	−	0.847131i	$-0.321672\pi$
$191$	−2.91058	−	2.44226i	−0.210602	−	0.176716i	−0.741987	+	0.670415i	$0.766116\pi$
$192$		0			0
$193$	−8.95492	+	1.57899i	−0.644589	+	0.113658i	−0.486380	−	0.873747i	$-0.661683\pi$
$193$	−8.95492	+	1.57899i	−0.644589	+	0.113658i	−0.158209	+	0.987406i	$0.550572\pi$
$194$	−21.4764	−	7.81678i	−1.54192	−	0.561212i
$195$		0			0
$196$	−0.682172	+	3.86879i	−0.0487266	+	0.276342i
$197$	5.83859	+	3.37091i	0.415982	+	0.240167i	0.693357	−	0.720594i	$-0.256131\pi$
$197$	5.83859	+	3.37091i	0.415982	+	0.240167i	−0.277375	+	0.960762i	$0.589464\pi$
$198$		0			0
$199$	−5.30284	−	9.18479i	−0.375909	−	0.651093i	0.614554	−	0.788875i	$-0.289336\pi$
$199$	−5.30284	−	9.18479i	−0.375909	−	0.651093i	−0.990463	+	0.137782i	$0.956003\pi$
$200$	10.0441	−	3.25616i	0.710225	−	0.230245i
$201$		0			0
$202$	−12.5123	−	14.9115i	−0.880360	−	1.04917i
$203$	7.51089	+	8.95113i	0.527161	+	0.628246i
$204$		0			0
$205$	−11.6239	−	5.67412i	−0.811847	−	0.396298i
$206$	−2.01926	−	3.49746i	−0.140688	−	0.243680i
$207$		0			0
$208$	2.51995	+	1.45489i	0.174727	+	0.100879i
$209$	1.73072	−	9.81541i	0.119717	−	0.678946i
$210$		0			0
$211$	16.7832	+	6.10860i	1.15541	+	0.420534i	0.847454	−	0.530868i	$-0.178134\pi$
$211$	16.7832	+	6.10860i	1.15541	+	0.420534i	0.307952	+	0.951402i	$0.400356\pi$
$212$	−5.81751	+	1.02578i	−0.399548	+	0.0704511i
$213$		0			0
$214$	−8.64002	−	7.24983i	−0.590619	−	0.495588i
$215$	3.47902	−	3.35742i	0.237267	−	0.228974i
$216$		0			0
$217$		−	1.40598i		−	0.0954443i
$218$	−19.9221	+	23.7422i	−1.34929	+	1.60803i
$219$		0			0
$220$	−3.32585	+	4.57445i	−0.224229	+	0.308409i
$221$	−2.86757	−	1.04371i	−0.192894	−	0.0702075i
$222$		0			0
$223$	−19.2137	−	3.38789i	−1.28664	−	0.226870i	−0.511844	−	0.859078i	$-0.671037\pi$
$223$	−19.2137	−	3.38789i	−1.28664	−	0.226870i	−0.774798	+	0.632209i	$0.782149\pi$
$224$	2.41456	−	4.18213i	0.161329	−	0.279431i
$225$		0			0
$226$	−11.3779	−	19.7071i	−0.756846	−	1.31090i
$227$	1.25836	+	3.45732i	0.0835203	+	0.229470i	0.974422	−	0.224726i	$-0.0721487\pi$
$227$	1.25836	+	3.45732i	0.0835203	+	0.229470i	−0.890902	+	0.454196i	$0.849927\pi$
$228$		0			0
$229$	−3.32291	+	2.78825i	−0.219584	+	0.184253i	−0.745943	−	0.666009i	$-0.768001\pi$
$229$	−3.32291	+	2.78825i	−0.219584	+	0.184253i	0.526360	+	0.850262i	$0.323557\pi$
$230$	−24.5511	−	2.58866i	−1.61885	−	0.170691i
$231$		0			0
$232$	6.80187	+	18.6880i	0.446564	+	1.22693i
$233$	−6.83118	+	3.94398i	−0.447525	+	0.258379i	−0.706784	−	0.707429i	$-0.749855\pi$
$233$	−6.83118	+	3.94398i	−0.447525	+	0.258379i	0.259259	+	0.965808i	$0.416522\pi$
$234$		0			0
$235$	3.36968	+	13.5342i	0.219814	+	0.882872i
$236$	1.68816	−	9.57403i	0.109890	−	0.623216i
$237$		0			0
$238$	−3.61180	+	9.92335i	−0.234119	+	0.643235i
$239$	4.95815	+	28.1191i	0.320716	+	1.81887i	0.538210	+	0.842811i	$0.319101\pi$
$239$	4.95815	+	28.1191i	0.320716	+	1.81887i	−0.217493	+	0.976062i	$0.569788\pi$
$240$		0			0
$241$	−10.0815	−	8.45937i	−0.649405	−	0.544916i	0.257485	−	0.966282i	$-0.417106\pi$
$241$	−10.0815	−	8.45937i	−0.649405	−	0.544916i	−0.906890	+	0.421367i	$0.861551\pi$
$242$			2.24280i			0.144173i
$243$		0			0
$244$	5.73565			0.367187
$245$	−0.847690	−	12.1806i	−0.0541569	−	0.778190i
$246$		0			0
$247$	−1.65075	+	0.291072i	−0.105035	+	0.0185205i
$248$	0.818435	−	2.24863i	0.0519707	−	0.142788i
$249$		0			0
$250$	15.6453	−	9.75464i	0.989497	−	0.616938i
$251$	13.5512	−	23.4713i	0.855341	−	1.48149i	−0.0209869	−	0.999780i	$-0.506681\pi$
$251$	13.5512	−	23.4713i	0.855341	−	1.48149i	0.876328	−	0.481715i	$-0.159986\pi$
$252$		0			0
$253$	−20.3839	+	11.7687i	−1.28153	+	0.739890i
$254$	−13.2461	+	4.82119i	−0.831135	+	0.302509i
$255$		0			0
$256$	11.7205	−	9.83471i	0.732534	−	0.614669i
$257$	1.21645	+	1.44970i	0.0758798	+	0.0904300i	0.802649	−	0.596452i	$-0.203423\pi$
$257$	1.21645	+	1.44970i	0.0758798	+	0.0904300i	−0.726769	+	0.686882i	$0.758979\pi$
$258$		0			0
$259$	5.47368	−	1.99226i	0.340118	−	0.123793i
$260$	0.914238	+	0.262482i	0.0566986	+	0.0162784i
$261$		0			0
$262$	13.8324	+	7.98612i	0.854566	+	0.493384i
$263$	−20.7228	−	3.65398i	−1.27782	−	0.225314i	−0.506766	−	0.862084i	$-0.669159\pi$
$263$	−20.7228	−	3.65398i	−1.27782	−	0.225314i	−0.771054	+	0.636770i	$0.780270\pi$
$264$		0			0
$265$	16.7755	−	7.46225i	1.03051	−	0.458402i
$266$	1.00727	+	5.71250i	0.0617596	+	0.350256i
$267$		0			0
$268$	2.03599	−	2.42640i	0.124368	−	0.148216i
$269$	−1.06528			−0.0649512			−0.0324756	−	0.999473i	$-0.510339\pi$
$269$	−1.06528			−0.0649512			−0.0324756	+	0.999473i	$0.510339\pi$
$270$		0			0
$271$	−5.32687			−0.323585			−0.161792	−	0.986825i	$-0.551727\pi$
$271$	−5.32687			−0.323585			−0.161792	+	0.986825i	$0.551727\pi$
$272$	−16.3264	+	19.4571i	−0.989934	+	1.17976i
$273$		0			0
$274$	4.23809	+	24.0354i	0.256032	+	1.45203i
$275$	6.59581	−	16.2941i	0.397742	−	0.982569i
$276$		0			0
$277$	−16.9171	−	2.98294i	−1.01645	−	0.179228i	−0.359487	−	0.933150i	$-0.617048\pi$
$277$	−16.9171	−	2.98294i	−1.01645	−	0.179228i	−0.656963	+	0.753923i	$0.728159\pi$
$278$	3.90419	+	2.25408i	0.234158	+	0.135191i
$279$		0			0
$280$	−1.61680	+	5.63139i	−0.0966221	+	0.336540i
$281$	11.6900	−	4.25480i	0.697365	−	0.253820i	0.0310798	−	0.999517i	$-0.490105\pi$
$281$	11.6900	−	4.25480i	0.697365	−	0.253820i	0.666286	+	0.745697i	$0.267883\pi$
$282$		0			0
$283$	13.3156	+	15.8689i	0.791528	+	0.943306i	0.999393	−	0.0348514i	$-0.0110958\pi$
$283$	13.3156	+	15.8689i	0.791528	+	0.943306i	−0.207865	+	0.978158i	$0.566651\pi$
$284$	3.78936	−	3.17965i	0.224857	−	0.188677i
$285$		0			0
$286$	3.22120	−	1.17242i	0.190474	−	0.0693268i
$287$	6.21578	−	3.58868i	0.366906	−	0.211833i
$288$		0			0
$289$	4.81863	−	8.34611i	0.283449	−	0.490948i
$290$	19.4092	+	28.7959i	1.13975	+	1.69095i
$291$		0			0
$292$	0.352196	−	0.967650i	0.0206107	−	0.0566274i
$293$	6.16081	−	1.08632i	0.359919	−	0.0634634i	0.00923499	−	0.999957i	$-0.497060\pi$
$293$	6.16081	−	1.08632i	0.359919	−	0.0634634i	0.350684	+	0.936494i	$0.385949\pi$
$294$		0			0
$295$	2.09776	+	30.1431i	0.122137	+	1.75500i
$296$	9.91394			0.576236
$297$		0			0
$298$			32.1299i			1.86123i
$299$	3.03239	+	2.54448i	0.175367	+	0.147151i
$300$		0			0
$301$	0.465862	+	2.64203i	0.0268518	+	0.152284i
$302$	7.74692	−	21.2845i	0.445785	−	1.22478i
$303$		0			0
$304$	−2.42268	+	13.7397i	−0.138950	+	0.788025i
$305$	−17.2988	+	4.30699i	−0.990528	+	0.246617i
$306$		0			0
$307$	15.8040	−	9.12444i	0.901981	−	0.520759i	0.0241389	−	0.999709i	$-0.492316\pi$
$307$	15.8040	−	9.12444i	0.901981	−	0.520759i	0.877843	+	0.478949i	$0.158982\pi$
$308$	−1.07335	−	2.94900i	−0.0611597	−	0.168035i
$309$		0			0
$310$	0.438146	−	4.15542i	0.0248850	−	0.236012i
$311$	3.62362	−	3.04058i	0.205477	−	0.172416i	−0.534242	−	0.845332i	$-0.679403\pi$
$311$	3.62362	−	3.04058i	0.205477	−	0.172416i	0.739719	+	0.672916i	$0.234958\pi$
$312$		0			0
$313$	−11.8489	−	32.5545i	−0.669737	−	1.84009i	−0.526026	−	0.850469i	$-0.676319\pi$
$313$	−11.8489	−	32.5545i	−0.669737	−	1.84009i	−0.143711	−	0.989620i	$-0.545904\pi$
$314$	−9.74647	−	16.8814i	−0.550025	−	0.952672i
$315$		0			0
$316$	−0.455868	+	0.789587i	−0.0256446	+	0.0444177i
$317$	−1.01556	−	0.179070i	−0.0570395	−	0.0100576i	0.145056	−	0.989424i	$-0.453664\pi$
$317$	−1.01556	−	0.179070i	−0.0570395	−	0.0100576i	−0.202095	+	0.979366i	$0.564775\pi$
$318$		0			0
$319$	31.1122	+	11.3239i	1.74195	+	0.634018i
$320$	−4.50270	+	6.19312i	−0.251709	+	0.346206i
$321$		0			0
$322$	8.80527	−	10.4937i	0.490699	−	0.584792i
$323$		−	14.6316i		−	0.814124i
$324$		0			0
$325$	−2.95446	−	0.105135i	−0.163884	−	0.00583185i
$326$	16.9936	+	14.2593i	0.941189	+	0.789752i
$327$		0			0
$328$	12.0301	−	2.12123i	0.664251	−	0.117125i
$329$	−7.27246	−	2.64696i	−0.400943	−	0.145931i
$330$		0			0
$331$	2.20443	−	12.5020i	0.121167	−	0.687170i	−0.862344	−	0.506322i	$-0.831005\pi$
$331$	2.20443	−	12.5020i	0.121167	−	0.687170i	0.983511	−	0.180848i	$-0.0578842\pi$
$332$	−0.952329	−	0.549827i	−0.0522658	−	0.0301757i
$333$		0			0
$334$	2.13403	+	3.69624i	0.116769	+	0.202249i
$335$	−4.31857	+	8.84694i	−0.235949	+	0.483360i
$336$		0			0
$337$	5.97195	+	7.11709i	0.325313	+	0.387693i	0.903769	−	0.428021i	$-0.140789\pi$
$337$	5.97195	+	7.11709i	0.325313	+	0.387693i	−0.578456	+	0.815714i	$0.696345\pi$
$338$	13.4095	+	15.9808i	0.729378	+	0.869239i
$339$		0			0
$340$	−3.64215	+	7.46123i	−0.197523	+	0.404642i
$341$	−1.99192	−	3.45010i	−0.107868	−	0.186833i
$342$		0			0
$343$	13.3892	+	7.73027i	0.722950	+	0.417395i
$344$	−0.792885	+	4.49667i	−0.0427495	+	0.242444i
$345$		0			0
$346$	−25.6361	−	9.33077i	−1.37820	−	0.501625i
$347$	−24.7495	+	4.36400i	−1.32862	+	0.234272i	−0.792502	−	0.609870i	$-0.791222\pi$
$347$	−24.7495	+	4.36400i	−1.32862	+	0.234272i	−0.536120	+	0.844142i	$0.680111\pi$
$348$		0			0
$349$	−1.83471	−	1.53950i	−0.0982096	−	0.0824076i	0.592361	−	0.805673i	$-0.298196\pi$
$349$	−1.83471	−	1.53950i	−0.0982096	−	0.0824076i	−0.690570	+	0.723265i	$0.742640\pi$
$350$	−0.363825	+	10.2241i	−0.0194473	+	0.546499i
$351$		0			0
$352$		−	13.6832i		−	0.729319i
$353$	−8.23024	+	9.80842i	−0.438051	+	0.522049i	−0.939227	−	0.343296i	$-0.888457\pi$
$353$	−8.23024	+	9.80842i	−0.438051	+	0.522049i	0.501176	+	0.865346i	$0.332901\pi$
$354$		0			0
$355$	−9.04113	+	12.4354i	−0.479853	+	0.660001i
$356$	8.82611	+	3.21244i	0.467783	+	0.170259i
$357$		0			0
$358$	−1.97101	−	0.347542i	−0.104171	−	0.0183682i
$359$	−0.774475	+	1.34143i	−0.0408753	+	0.0707980i	−0.885739	−	0.464183i	$-0.846348\pi$
$359$	−0.774475	+	1.34143i	−0.0408753	+	0.0707980i	0.844864	+	0.534981i	$0.179681\pi$
$360$		0			0
$361$	5.48150	+	9.49423i	0.288500	+	0.499696i
$362$	2.07800	+	5.70927i	0.109218	+	0.300073i
$363$		0			0
$364$	−0.404312	+	0.339258i	−0.0211917	+	0.0177819i
$365$	−0.335606	+	3.18292i	−0.0175664	+	0.166602i
$366$		0			0
$367$	1.69337	+	4.65249i	0.0883931	+	0.242858i	0.976011	−	0.217723i	$-0.0698631\pi$
$367$	1.69337	+	4.65249i	0.0883931	+	0.242858i	−0.887617	+	0.460582i	$0.847641\pi$
$368$	28.5336	−	16.4739i	1.48742	−	0.858760i
$369$		0			0
$370$	16.7985	−	4.18241i	0.873310	−	0.217433i
$371$	−1.76911	+	10.0331i	−0.0918474	+	0.520893i
$372$		0			0
$373$	5.91918	−	16.2628i	0.306484	−	0.842057i	−0.686852	−	0.726798i	$-0.741008\pi$
$373$	5.91918	−	16.2628i	0.306484	−	0.842057i	0.993335	−	0.115260i	$-0.0367700\pi$
$374$	5.19594	+	29.4676i	0.268676	+	1.52374i
$375$		0			0
$376$	−10.0903	−	8.46673i	−0.520365	−	0.436638i
$377$		−	5.56825i		−	0.286779i
$378$		0			0
$379$	−8.91774			−0.458073			−0.229037	−	0.973418i	$-0.573558\pi$
$379$	−8.91774			−0.458073			−0.229037	+	0.973418i	$0.573558\pi$
$380$	0.316622	+	4.54960i	0.0162424	+	0.233390i
$381$		0			0
$382$	6.17043	−	1.08801i	0.315707	−	0.0556676i
$383$	8.44098	−	23.1914i	0.431314	−	1.18502i	−0.513693	−	0.857974i	$-0.671723\pi$
$383$	8.44098	−	23.1914i	0.431314	−	1.18502i	0.945007	−	0.327051i	$-0.106055\pi$
$384$		0			0
$385$	5.45169	+	8.08826i	0.277844	+	0.412216i
$386$	7.49755	−	12.9861i	0.381615	−	0.660977i
$387$		0			0
$388$	8.63492	−	4.98537i	0.438372	−	0.253094i
$389$	6.71441	−	2.44385i	0.340434	−	0.123908i	−0.166145	−	0.986101i	$-0.553132\pi$
$389$	6.71441	−	2.44385i	0.340434	−	0.123908i	0.506579	+	0.862193i	$0.330910\pi$
$390$		0			0
$391$	−26.4695	+	22.2106i	−1.33862	+	1.12324i
$392$	7.41211	+	8.83341i	0.374368	+	0.446155i
$393$		0			0
$394$	−10.4473	+	3.80249i	−0.526325	+	0.191567i
$395$	0.781995	−	2.72373i	0.0393464	−	0.137046i
$396$		0			0
$397$	−3.87921	−	2.23966i	−0.194692	−	0.112405i	0.399485	−	0.916740i	$-0.369189\pi$
$397$	−3.87921	−	2.23966i	−0.194692	−	0.112405i	−0.594177	+	0.804334i	$0.702522\pi$
$398$	17.2238	+	3.03702i	0.863352	+	0.152232i
$399$		0			0
$400$	−9.23286	+	22.8085i	−0.461643	+	1.14043i
$401$	−0.799427	−	4.53377i	−0.0399215	−	0.226406i	0.958319	−	0.285700i	$-0.0922261\pi$
$401$	−0.799427	−	4.53377i	−0.0399215	−	0.226406i	−0.998241	+	0.0592942i	$0.981115\pi$
$402$		0			0
$403$	−0.430668	+	0.513250i	−0.0214531	+	0.0255668i
$404$	8.49220			0.422503
$405$		0			0
$406$	−19.2692			−0.956313
$407$	10.6092	−	12.6435i	0.525878	−	0.626717i
$408$		0			0
$409$	−2.13917	−	12.1318i	−0.105775	−	0.599880i	−0.990908	−	0.134542i	$-0.957044\pi$
$409$	−2.13917	−	12.1318i	−0.105775	−	0.599880i	0.885133	−	0.465339i	$-0.154067\pi$
$410$	19.4892	−	8.66942i	0.962505	−	0.428152i
$411$		0			0
$412$	1.73510	+	0.305945i	0.0854823	+	0.0150728i
$413$	−14.5202	−	8.38323i	−0.714491	−	0.412512i
$414$		0			0
$415$	3.28512	+	0.943172i	0.161260	+	0.0462985i
$416$	−2.16246	+	0.787071i	−0.106023	+	0.0385893i
$417$		0			0
$418$	10.5649	+	12.5907i	0.516744	+	0.615832i
$419$	12.8029	−	10.7429i	0.625462	−	0.524825i	−0.274053	−	0.961715i	$-0.588364\pi$
$419$	12.8029	−	10.7429i	0.625462	−	0.524825i	0.899515	+	0.436890i	$0.143920\pi$
$420$		0			0
$421$	7.93497	−	2.88809i	0.386727	−	0.140757i	−0.141338	−	0.989961i	$-0.545140\pi$
$421$	7.93497	−	2.88809i	0.386727	−	0.140757i	0.528064	+	0.849205i	$0.322918\pi$
$422$	−25.5070	+	14.7265i	−1.24166	+	0.716875i
$423$		0			0
$424$	−8.66975	+	15.0164i	−0.421040	+	0.729263i
$425$	5.38204	−	25.2382i	0.261068	−	1.22423i
$426$		0			0
$427$	3.38323	−	9.29536i	0.163726	−	0.449834i
$428$	4.84578	−	0.854441i	0.234229	−	0.0413010i
$429$		0			0
$430$	0.553530	+	7.95378i	0.0266936	+	0.383565i
$431$	11.6530			0.561306			0.280653	−	0.959809i	$-0.409449\pi$
$431$	11.6530			0.561306			0.280653	+	0.959809i	$0.409449\pi$
$432$		0			0
$433$			10.8242i			0.520178i	0.965585	+	0.260089i	$0.0837519\pi$
$433$			10.8242i			0.520178i	−0.965585	+	0.260089i	$0.916248\pi$
$434$	1.77612	+	1.49034i	0.0852567	+	0.0715388i
$435$		0			0
$436$	−2.34795	−	13.3159i	−0.112446	−	0.637716i
$437$	−6.49152	+	17.8353i	−0.310531	+	0.853178i
$438$		0			0
$439$	−4.86673	+	27.6006i	−0.232276	+	1.31731i	0.615998	+	0.787748i	$0.288753\pi$
$439$	−4.86673	+	27.6006i	−0.232276	+	1.31731i	−0.848274	+	0.529557i	$0.822358\pi$
$440$	4.01082	+	16.1093i	0.191208	+	0.767980i
$441$		0			0
$442$	4.35811	−	2.51615i	0.207294	−	0.119681i
$443$	−9.57265	−	26.3006i	−0.454810	−	1.24958i	−0.929302	−	0.369321i	$-0.879590\pi$
$443$	−9.57265	−	26.3006i	−0.454810	−	1.24958i	0.474491	−	0.880260i	$-0.342632\pi$
$444$		0			0
$445$	−29.0320	−	3.06113i	−1.37625	−	0.145111i
$446$	24.6463	−	20.6807i	1.16704	−	0.979260i
$447$		0			0
$448$	−1.45315	−	3.99251i	−0.0686551	−	0.188628i
$449$	12.5470	+	21.7321i	0.592130	+	1.02560i	0.993945	+	0.109878i	$0.0350461\pi$
$449$	12.5470	+	21.7321i	0.592130	+	1.02560i	−0.401815	+	0.915721i	$0.631621\pi$
$450$		0			0
$451$	10.1685	−	17.6123i	0.478815	−	0.829333i
$452$	9.77675	+	1.72391i	0.459860	+	0.0810857i
$453$		0			0
$454$	−5.70136	−	2.07512i	−0.267578	−	0.0973904i
$455$	0.964659	−	1.32681i	0.0452239	−	0.0622020i
$456$		0			0
$457$	10.7750	−	12.8412i	0.504036	−	0.600686i	−0.452694	−	0.891666i	$-0.649537\pi$
$457$	10.7750	−	12.8412i	0.504036	−	0.600686i	0.956729	+	0.290980i	$0.0939813\pi$
$458$		−	7.15325i		−	0.334249i
$459$		0			0
$460$	7.74990	−	7.47903i	0.361341	−	0.348711i
$461$	−19.8382	−	16.6462i	−0.923956	−	0.775291i	0.0507663	−	0.998711i	$-0.483834\pi$
$461$	−19.8382	−	16.6462i	−0.923956	−	0.775291i	−0.974722	+	0.223419i	$0.928278\pi$
$462$		0			0
$463$	17.0551	−	3.00727i	0.792616	−	0.139760i	0.237341	−	0.971426i	$-0.423724\pi$
$463$	17.0551	−	3.00727i	0.792616	−	0.139760i	0.555275	+	0.831667i	$0.312613\pi$
$464$	−43.5511	−	15.8513i	−2.02181	−	0.735878i
$465$		0			0
$466$	2.25878	−	12.8102i	0.104636	−	0.593420i
$467$	10.7327	+	6.19652i	0.496649	+	0.286741i	0.727329	−	0.686289i	$-0.240762\pi$
$467$	10.7327	+	6.19652i	0.496649	+	0.286741i	−0.230679	+	0.973030i	$0.574095\pi$
$468$		0			0
$469$	−2.73135	−	4.73083i	−0.126122	−	0.218449i
$470$	−20.6691	−	10.0895i	−0.953393	−	0.465392i
$471$		0			0
$472$	−18.3426	−	21.8599i	−0.844288	−	1.00618i
$473$	4.88625	+	5.82321i	0.224670	+	0.267751i
$474$		0			0
$475$	−4.37131	−	13.4839i	−0.200569	−	0.618686i
$476$	−2.30353	−	3.98983i	−0.105582	−	0.182874i
$477$		0			0
$478$	−40.7774	−	23.5429i	−1.86512	−	1.07682i
$479$	−3.96462	+	22.4845i	−0.181148	+	1.02734i	0.749657	+	0.661826i	$0.230218\pi$
$479$	−3.96462	+	22.4845i	−0.181148	+	1.02734i	−0.930805	+	0.365515i	$0.880893\pi$
$480$		0			0
$481$	−2.60840	−	0.949380i	−0.118933	−	0.0432880i
$482$	21.3728	−	3.76860i	0.973503	−	0.171655i
$483$		0			0
$484$	−0.749542	−	0.628940i	−0.0340701	−	0.0285882i
$485$	−22.2995	+	21.5201i	−1.01257	+	0.977177i
$486$		0			0
$487$			3.22215i			0.146009i	0.997332	+	0.0730047i	$0.0232588\pi$
$487$			3.22215i			0.146009i	−0.997332	+	0.0730047i	$0.976741\pi$
$488$	10.8218	−	12.8970i	0.489881	−	0.583818i
$489$		0			0
$490$	16.2858	+	11.8406i	0.735719	+	0.534904i
$491$	−24.5814	−	8.94691i	−1.10934	−	0.403768i	−0.278591	−	0.960410i	$-0.589868\pi$
$491$	−24.5814	−	8.94691i	−1.10934	−	0.403768i	−0.830753	+	0.556641i	$0.812090\pi$
$492$		0			0
$493$	47.8665	+	8.44015i	2.15580	+	0.380125i
$494$	1.38210	−	2.39387i	0.0621836	−	0.107705i
$495$		0			0
$496$	2.78830	+	4.82948i	0.125198	+	0.216850i
$497$	−2.91784	−	8.01669i	−0.130883	−	0.359598i
$498$		0			0
$499$	26.2418	−	22.0195i	1.17474	−	0.985727i	0.174745	−	0.984614i	$-0.444090\pi$
$499$	26.2418	−	22.0195i	1.17474	−	0.985727i	0.999999	−	0.00111367i	$-0.000354492\pi$
$500$	−1.12737	+	7.96411i	−0.0504174	+	0.356166i
$501$		0			0
$502$	15.2861	+	41.9983i	0.682253	+	1.87447i
$503$	13.7378	−	7.93150i	0.612537	−	0.353648i	−0.161421	−	0.986886i	$-0.551608\pi$
$503$	13.7378	−	7.93150i	0.612537	−	0.353648i	0.773958	+	0.633237i	$0.218274\pi$
$504$		0			0
$505$	−25.6126	+	6.37692i	−1.13975	+	0.283769i
$506$	6.74011	−	38.2250i	0.299634	−	1.69931i
$507$		0			0
$508$	2.10332	−	5.77883i	0.0933198	−	0.256394i
$509$	2.38054	+	13.5007i	0.105516	+	0.598410i	0.991013	+	0.133765i	$0.0427068\pi$
$509$	2.38054	+	13.5007i	0.105516	+	0.598410i	−0.885497	+	0.464645i	$0.846182\pi$
$510$		0			0
$511$	−1.36046	−	1.14156i	−0.0601830	−	0.0504995i
$512$		−	1.63110i		−	0.0720849i
$513$		0			0
$514$	−3.12079			−0.137652
$515$	−5.46284	+	0.380178i	−0.240722	+	0.0167526i
$516$		0			0
$517$	−21.5957	+	3.80791i	−0.949779	+	0.167472i
$518$	−3.28537	+	9.02649i	−0.144351	+	0.396601i
$519$		0			0
$520$	2.31516	−	1.56048i	0.101526	−	0.0684315i
$521$	−13.9166	+	24.1042i	−0.609697	+	1.05603i	0.381593	+	0.924330i	$0.375375\pi$
$521$	−13.9166	+	24.1042i	−0.609697	+	1.05603i	−0.991290	+	0.131696i	$0.957958\pi$
$522$		0			0
$523$	7.94269	−	4.58572i	0.347310	−	0.200519i	−0.316190	−	0.948696i	$-0.602404\pi$
$523$	7.94269	−	4.58572i	0.347310	−	0.200519i	0.663500	+	0.748177i	$0.269070\pi$
$524$	−6.54791	+	2.38325i	−0.286047	+	0.104113i
$525$		0			0
$526$	26.5821	−	22.3050i	1.15903	−	0.972545i
$527$	−3.75927	−	4.48012i	−0.163756	−	0.195157i
$528$		0			0
$529$	20.5063	−	7.46369i	0.891579	−	0.324508i
$530$	−8.35525	+	29.1018i	−0.362929	+	1.26410i
$531$		0			0
$532$	−2.19158	−	1.26531i	−0.0950170	−	0.0548581i
$533$	−3.36830	−	0.593923i	−0.145897	−	0.0257257i
$534$		0			0
$535$	−13.9734	+	6.21578i	−0.604121	+	0.268732i
$536$	−1.61447	−	9.15611i	−0.0697345	−	0.395484i
$537$		0			0
$538$	1.12920	−	1.34572i	0.0486832	−	0.0580183i
$539$	19.1974			0.826892
$540$		0			0
$541$	25.6800			1.10407			0.552035	−	0.833821i	$-0.313852\pi$
$541$	25.6800			1.10407			0.552035	+	0.833821i	$0.313852\pi$
$542$	5.64650	−	6.72923i	0.242538	−	0.289045i
$543$		0			0
$544$	−3.48814	−	19.7822i	−0.149553	−	0.848155i
$545$	17.0806	+	38.3979i	0.731652	+	1.64479i
$546$		0			0
$547$	−38.7852	−	6.83888i	−1.65834	−	0.292409i	−0.735477	−	0.677549i	$-0.763042\pi$
$547$	−38.7852	−	6.83888i	−1.65834	−	0.292409i	−0.922858	+	0.385140i	$0.874153\pi$
$548$	−9.22108	−	5.32379i	−0.393905	−	0.227421i
$549$		0			0
$550$	13.5921	+	25.6040i	0.579568	+	1.09176i
$551$	25.0881	−	9.13133i	1.06879	−	0.389008i
$552$		0			0
$553$	1.01073	+	1.20454i	0.0429806	+	0.0512222i
$554$	21.7004	−	18.2088i	0.921962	−	0.773618i
$555$		0			0
$556$	−1.84815	+	0.672672i	−0.0783790	+	0.0285276i
$557$	3.57754	−	2.06550i	0.151585	−	0.0875178i	−0.422289	−	0.906461i	$-0.638773\pi$
$557$	3.57754	−	2.06550i	0.151585	−	0.0875178i	0.573874	+	0.818944i	$0.305440\pi$
$558$		0			0
$559$	0.639222	−	1.10716i	0.0270362	−	0.0468281i
$560$	−7.63132	−	11.3220i	−0.322482	−	0.478442i
$561$		0			0
$562$	−7.01647	+	19.2776i	−0.295972	+	0.813176i
$563$	−17.1381	+	3.02191i	−0.722286	+	0.127358i	−0.522694	−	0.852521i	$-0.675073\pi$
$563$	−17.1381	+	3.02191i	−0.722286	+	0.127358i	−0.199592	+	0.979879i	$0.563962\pi$
$564$		0			0
$565$	−30.7814	+	2.14218i	−1.29498	+	0.0901223i
$566$	−34.1610			−1.43590
$567$		0			0
$568$		−	14.5199i		−	0.609239i
$569$	3.52883	+	2.96104i	0.147936	+	0.124133i	0.713752	−	0.700398i	$-0.246994\pi$
$569$	3.52883	+	2.96104i	0.147936	+	0.124133i	−0.565816	+	0.824532i	$0.691439\pi$
$570$		0			0
$571$	−2.79686	−	15.8618i	−0.117045	−	0.663794i	−0.985717	−	0.168407i	$-0.946138\pi$
$571$	−2.79686	−	15.8618i	−0.117045	−	0.663794i	0.868673	−	0.495386i	$-0.164974\pi$
$572$	−0.511488	+	1.40530i	−0.0213864	+	0.0587586i
$573$		0			0
$574$	−2.05530	+	11.6562i	−0.0857864	+	0.486519i
$575$	−17.7578	+	28.3764i	−0.740549	+	1.18338i
$576$		0			0
$577$	−23.9756	+	13.8423i	−0.998116	+	0.576262i	−0.907690	−	0.419641i	$-0.862156\pi$
$577$	−23.9756	+	13.8423i	−0.998116	+	0.576262i	−0.0904254	+	0.995903i	$0.528823\pi$
$578$	5.43556	+	14.9341i	0.226089	+	0.621176i
$579$		0			0
$580$	−15.0664	−	1.58860i	−0.625599	−	0.0659629i
$581$	−1.45281	+	1.21905i	−0.0602726	+	0.0505748i
$582$		0			0
$583$	9.87317	+	27.1263i	0.408905	+	1.12346i
$584$	−1.51131	−	2.61766i	−0.0625384	−	0.108320i
$585$		0			0
$586$	−5.15817	+	8.93422i	−0.213082	+	0.369069i
$587$	−16.8114	−	2.96430i	−0.693880	−	0.122350i	−0.184424	−	0.982847i	$-0.559042\pi$
$587$	−16.8114	−	2.96430i	−0.693880	−	0.122350i	−0.509455	+	0.860497i	$0.670153\pi$
$588$		0			0
$589$	−3.01873	−	1.09873i	−0.124385	−	0.0452723i
$590$	−40.3023	−	29.3018i	−1.65922	−	1.20633i
$591$		0			0
$592$	−14.8508	+	17.6985i	−0.610366	+	0.727405i
$593$		−	7.85373i		−	0.322514i	−0.986912	−	0.161257i	$-0.948445\pi$
$593$		−	7.85373i		−	0.322514i	0.986912	−	0.161257i	$-0.0515548\pi$
$594$		0			0
$595$	9.94353	+	10.3037i	0.407645	+	0.422409i
$596$	−10.7378	−	9.01007i	−0.439837	−	0.369067i
$597$		0			0
$598$	−6.42867	+	1.13355i	−0.262888	+	0.0463543i
$599$	−45.0491	−	16.3965i	−1.84066	−	0.669944i	−0.989404	−	0.145188i	$-0.953621\pi$
$599$	−45.0491	−	16.3965i	−1.84066	−	0.669944i	−0.851253	−	0.524756i	$-0.824157\pi$
$600$		0			0
$601$	4.31451	−	24.4688i	0.175993	−	0.998104i	−0.760999	−	0.648753i	$-0.775291\pi$
$601$	4.31451	−	24.4688i	0.175993	−	0.998104i	0.936992	−	0.349351i	$-0.113598\pi$
$602$	−3.83139	−	2.21206i	−0.156156	−	0.0901567i
$603$		0			0
$604$	4.94082	+	8.55775i	0.201039	+	0.348210i
$605$	2.73291	+	1.33405i	0.111109	+	0.0542370i
$606$		0			0
$607$	28.6468	+	34.1399i	1.16274	+	1.38570i	0.908148	+	0.418648i	$0.137496\pi$
$607$	28.6468	+	34.1399i	1.16274	+	1.38570i	0.254590	+	0.967049i	$0.418060\pi$
$608$	−7.09240	−	8.45239i	−0.287635	−	0.342790i
$609$		0			0
$610$	12.8959	−	26.4184i	0.522142	−	1.06965i
$611$	1.84400	+	3.19389i	0.0746001	+	0.129211i
$612$		0			0
$613$	5.10015	+	2.94457i	0.205993	+	0.118930i	0.599448	−	0.800414i	$-0.295387\pi$
$613$	5.10015	+	2.94457i	0.205993	+	0.118930i	−0.393455	+	0.919344i	$0.628720\pi$
$614$	−5.22571	+	29.6365i	−0.210893	+	1.19603i
$615$		0			0
$616$	−8.65617	−	3.15059i	−0.348767	−	0.126941i
$617$	−30.2359	+	5.33141i	−1.21725	+	0.214635i	−0.745143	−	0.666905i	$-0.767619\pi$
$617$	−30.2359	+	5.33141i	−1.21725	+	0.214635i	−0.472110	+	0.881539i	$0.656508\pi$
$618$		0			0
$619$	34.9350	+	29.3139i	1.40416	+	1.17823i	0.959219	+	0.282666i	$0.0912187\pi$
$619$	34.9350	+	29.3139i	1.40416	+	1.17823i	0.444938	+	0.895561i	$0.353226\pi$
$620$	1.26587	+	1.31172i	0.0508385	+	0.0526798i
$621$		0			0
$622$			7.80060i			0.312776i
$623$	10.4124	−	12.4090i	0.417162	−	0.497155i
$624$		0			0
$625$	−2.58021	−	24.8665i	−0.103208	−	0.994660i
$626$	53.6846	+	19.5396i	2.14567	+	0.780960i
$627$		0			0
$628$	8.37491	+	1.47672i	0.334195	+	0.0589277i
$629$	12.1149	−	20.9836i	0.483053	−	0.836672i
$630$		0			0
$631$	−6.80759	−	11.7911i	−0.271006	−	0.469396i	0.698114	−	0.715987i	$-0.254023\pi$
$631$	−6.80759	−	11.7911i	−0.271006	−	0.469396i	−0.969120	+	0.246591i	$0.920690\pi$
$632$	0.915317	+	2.51481i	0.0364094	+	0.100034i
$633$		0			0
$634$	1.30271	−	1.09310i	0.0517371	−	0.0434126i
$635$	−2.00425	+	19.0085i	−0.0795362	+	0.754329i
$636$		0			0
$637$	−1.10425	−	3.03391i	−0.0437520	−	0.120208i
$638$	−47.2841	+	27.2995i	−1.87199	+	1.08080i
$639$		0			0
$640$	−7.25589	−	29.1430i	−0.286814	−	1.15198i
$641$	−1.38566	+	7.85848i	−0.0547304	+	0.310391i	−0.999867	−	0.0162827i	$-0.994817\pi$
$641$	−1.38566	+	7.85848i	−0.0547304	+	0.310391i	0.945137	+	0.326674i	$0.105928\pi$
$642$		0			0
$643$	5.16505	−	14.1909i	0.203690	−	0.559633i	−0.795220	−	0.606321i	$-0.792645\pi$
$643$	5.16505	−	14.1909i	0.203690	−	0.559633i	0.998909	+	0.0466885i	$0.0148668\pi$
$644$	1.03776	+	5.88543i	0.0408935	+	0.231918i
$645$		0			0
$646$	18.4835	+	15.5095i	0.727225	+	0.610214i
$647$			44.8366i			1.76271i	0.472455	+	0.881355i	$0.343368\pi$
$647$			44.8366i			1.76271i	−0.472455	+	0.881355i	$0.656632\pi$
$648$		0			0
$649$	−47.5075			−1.86483
$650$	3.26455	−	3.62081i	0.128046	−	0.142020i
$651$		0			0
$652$	−9.53092	+	1.68056i	−0.373260	+	0.0658157i
$653$	−6.37556	+	17.5167i	−0.249495	+	0.685482i	0.750210	+	0.661199i	$0.229952\pi$
$653$	−6.37556	+	17.5167i	−0.249495	+	0.685482i	−0.999705	+	0.0242823i	$0.992270\pi$
$654$		0			0
$655$	17.9590	−	12.1049i	0.701717	−	0.472976i
$656$	−14.2339	+	24.6539i	−0.555742	+	0.962573i
$657$		0			0
$658$	11.0526	−	6.38123i	0.430876	−	0.248766i
$659$	8.86949	−	3.22823i	0.345506	−	0.125754i	−0.163438	−	0.986554i	$-0.552258\pi$
$659$	8.86949	−	3.22823i	0.345506	−	0.125754i	0.508944	+	0.860800i	$0.330036\pi$
$660$		0			0
$661$	−21.0425	+	17.6567i	−0.818457	+	0.686767i	−0.952610	−	0.304194i	$-0.901613\pi$
$661$	−21.0425	+	17.6567i	−0.818457	+	0.686767i	0.134153	+	0.990961i	$0.457169\pi$
$662$	13.4565	+	16.0369i	0.523003	+	0.623291i
$663$		0			0
$664$	−3.03314	+	1.10397i	−0.117709	+	0.0428425i
$665$	7.55999	+	2.17051i	0.293164	+	0.0841686i
$666$		0			0
$667$	−54.6026	−	31.5248i	−2.11422	−	1.22065i
$668$	−1.83372	−	0.323334i	−0.0709486	−	0.0125102i
$669$		0			0
$670$	−6.59830	−	14.8333i	−0.254914	−	0.573059i
$671$	−4.86712	−	27.6028i	−0.187893	−	1.06559i
$672$		0			0
$673$	−17.1645	+	20.4558i	−0.661642	+	0.788514i	−0.987620	−	0.156863i	$-0.949862\pi$
$673$	−17.1645	+	20.4558i	−0.661642	+	0.788514i	0.325979	+	0.945377i	$0.394306\pi$
$674$	−15.3210			−0.590144
$675$		0			0
$676$	−9.10112			−0.350043
$677$	21.7428	−	25.9121i	0.835645	−	0.995883i	−0.164310	−	0.986409i	$-0.552540\pi$
$677$	21.7428	−	25.9121i	0.835645	−	0.995883i	0.999955	−	0.00947415i	$-0.00301576\pi$
$678$		0			0
$679$	−2.98604	−	16.9347i	−0.114594	−	0.649894i
$680$	9.90514	+	22.2672i	0.379845	+	0.853908i
$681$		0			0
$682$	6.46982	+	1.14080i	0.247742	+	0.0436836i
$683$	15.0388	+	8.68268i	0.575445	+	0.332233i	0.759321	−	0.650716i	$-0.225531\pi$
$683$	15.0388	+	8.68268i	0.575445	+	0.332233i	−0.183876	+	0.982949i	$0.558864\pi$
$684$		0			0
$685$	31.8087	+	9.13242i	1.21535	+	0.348932i
$686$	−23.9579	+	8.71998i	−0.914718	+	0.332930i
$687$		0			0
$688$	−6.83981	−	8.15137i	−0.260765	−	0.310768i
$689$	3.71905	−	3.12066i	0.141685	−	0.118888i
$690$		0			0
$691$	−13.7800	+	5.01549i	−0.524214	+	0.190798i	−0.590553	−	0.806999i	$-0.701090\pi$
$691$	−13.7800	+	5.01549i	−0.524214	+	0.190798i	0.0663389	+	0.997797i	$0.478868\pi$
$692$	10.3074	−	5.95096i	0.391827	−	0.226222i
$693$		0			0
$694$	20.7216	−	35.8909i	0.786582	−	1.36240i
$695$	5.06894	−	3.41660i	0.192276	−	0.129599i
$696$		0			0
$697$	10.2111	−	28.0548i	0.386773	−	1.06265i
$698$	3.88958	−	0.685839i	0.147223	−	0.0259594i
$699$		0			0
$700$	−3.31484	−	2.98868i	−0.125289	−	0.112962i
$701$	28.8893			1.09113			0.545567	−	0.838067i	$-0.316314\pi$
$701$	28.8893			1.09113			0.545567	+	0.838067i	$0.316314\pi$
$702$		0			0
$703$		−	13.3092i		−	0.501966i
$704$	−9.22221	−	7.73836i	−0.347575	−	0.291650i
$705$		0			0
$706$	−3.66652	−	20.7939i	−0.137991	−	0.782588i
$707$	5.00922	−	13.7627i	0.188391	−	0.517600i
$708$		0			0
$709$	−0.360524	+	2.04463i	−0.0135398	+	0.0767878i	−0.990829	−	0.135122i	$-0.956857\pi$
$709$	−0.360524	+	2.04463i	−0.0135398	+	0.0767878i	0.977289	+	0.211910i	$0.0679684\pi$
$710$	−6.12550	−	24.6028i	−0.229886	−	0.923328i
$711$		0			0
$712$	23.8762	−	13.7849i	0.894798	−	0.516612i
$713$	2.59472	+	7.12893i	0.0971730	+	0.266981i
$714$		0			0
$715$	0.487396	−	4.62251i	0.0182276	−	0.172872i
$716$	0.668871	−	0.561249i	0.0249969	−	0.0209749i
$717$		0			0
$718$	−0.873632	−	2.40028i	−0.0326037	−	0.0895778i
$719$	−9.24248	−	16.0084i	−0.344686	−	0.597014i	0.640610	−	0.767866i	$-0.278681\pi$
$719$	−9.24248	−	16.0084i	−0.344686	−	0.597014i	−0.985297	+	0.170852i	$0.945348\pi$
$720$		0			0
$721$	1.51929	−	2.63149i	0.0565814	−	0.0980019i
$722$	−17.8041	−	3.13934i	−0.662600	−	0.116834i
$723$		0			0
$724$	−2.49076	−	0.906563i	−0.0925684	−	0.0336921i
$725$	46.6335	−	6.52236i	1.73193	−	0.242234i
$726$		0			0
$727$	26.3979	−	31.4598i	0.979045	−	1.16678i	−0.00694522	−	0.999976i	$-0.502211\pi$
$727$	26.3979	−	31.4598i	0.979045	−	1.16678i	0.985990	−	0.166804i	$-0.0533448\pi$
$728$			1.54922i			0.0574179i
$729$		0			0
$730$	−3.66512	−	3.79786i	−0.135652	−	0.140565i
$731$	8.54864	+	7.17316i	0.316183	+	0.265309i
$732$		0			0
$733$	−3.29255	+	0.580566i	−0.121613	+	0.0214437i	−0.234123	−	0.972207i	$-0.575222\pi$
$733$	−3.29255	+	0.580566i	−0.121613	+	0.0214437i	0.112510	+	0.993651i	$0.464111\pi$
$734$	−7.67229	−	2.79248i	−0.283189	−	0.103072i
$735$		0			0
$736$	−4.52477	+	25.6612i	−0.166785	+	0.945886i
$737$	−13.4048	−	7.73924i	−0.493770	−	0.285078i
$738$		0			0
$739$	9.86291	+	17.0831i	0.362813	+	0.628411i	0.988423	−	0.151726i	$-0.0484830\pi$
$739$	9.86291	+	17.0831i	0.362813	+	0.628411i	−0.625610	+	0.780136i	$0.715150\pi$
$740$	−3.31297	+	6.78689i	−0.121787	+	0.249491i
$741$		0			0
$742$	−10.7992	−	12.8700i	−0.396450	−	0.472471i
$743$	14.4345	+	17.2023i	0.529549	+	0.631092i	0.962811	−	0.270176i	$-0.0870820\pi$
$743$	14.4345	+	17.2023i	0.529549	+	0.631092i	−0.433262	+	0.901268i	$0.642638\pi$
$744$		0			0
$745$	39.1512	+	19.1114i	1.43439	+	0.700187i
$746$	14.2698	+	24.7161i	0.522456	+	0.904921i
$747$		0			0
$748$	−11.3051	−	6.52702i	−0.413357	−	0.238652i
$749$	1.47360	−	8.35721i	0.0538442	−	0.305366i
$750$		0			0
$751$	−23.9497	−	8.71699i	−0.873938	−	0.318088i	−0.134177	−	0.990957i	$-0.542839\pi$
$751$	−23.9497	−	8.71699i	−0.873938	−	0.318088i	−0.739761	+	0.672870i	$0.765061\pi$
$752$	30.2299	−	5.33034i	1.10237	−	0.194378i
$753$		0			0
$754$	7.03415	+	5.90235i	0.256169	+	0.214951i
$755$	−21.3278	−	22.1002i	−0.776197	−	0.804309i
$756$		0			0
$757$			43.0981i			1.56643i	0.621753	+	0.783214i	$0.286421\pi$
$757$			43.0981i			1.56643i	−0.621753	+	0.783214i	$0.713579\pi$
$758$	9.45282	−	11.2654i	0.343342	−	0.409179i
$759$		0			0
$760$	10.8275	+	7.87210i	0.392753	+	0.285551i
$761$	26.5013	+	9.64570i	0.960673	+	0.349656i	0.774297	−	0.632822i	$-0.218104\pi$
$761$	26.5013	+	9.64570i	0.960673	+	0.349656i	0.186376	+	0.982479i	$0.440326\pi$
$762$		0			0
$763$	−22.9651	−	4.04937i	−0.831393	−	0.146597i
$764$	−1.36674	+	2.36726i	−0.0494469	+	0.0856445i
$765$		0			0
$766$	20.3493	+	35.2461i	0.735251	+	1.27349i
$767$	2.73267	+	7.50796i	0.0986711	+	0.271097i
$768$		0			0
$769$	0.986304	−	0.827608i	0.0355670	−	0.0298443i	−0.624831	−	0.780760i	$-0.714832\pi$
$769$	0.986304	−	0.827608i	0.0355670	−	0.0298443i	0.660398	+	0.750916i	$0.270388\pi$
$770$	−15.9964	−	1.68665i	−0.576470	−	0.0607828i
$771$		0			0
$772$	2.23745	+	6.14733i	0.0805274	+	0.221247i
$773$	4.24332	−	2.44988i	0.152622	−	0.0881162i	−0.421744	−	0.906715i	$-0.638582\pi$
$773$	4.24332	−	2.44988i	0.152622	−	0.0881162i	0.574366	+	0.818599i	$0.305249\pi$
$774$		0			0
$775$	−4.80288	−	3.00561i	−0.172524	−	0.107965i
$776$	5.08217	−	28.8224i	0.182439	−	1.03466i
$777$		0			0
$778$	−4.03007	+	11.0725i	−0.144485	+	0.396970i
$779$	−2.84770	−	16.1501i	−0.102029	−	0.578637i
$780$		0			0
$781$	−18.5176	−	15.5381i	−0.662612	−	0.555997i
$782$		−	56.9812i		−	2.03764i
$783$		0			0
$784$	−26.8727			−0.959739
$785$	−26.3678	+	1.83503i	−0.941108	+	0.0654949i
$786$		0			0
$787$	31.1341	−	5.48979i	1.10981	−	0.195690i	0.411448	−	0.911433i	$-0.365023\pi$
$787$	31.1341	−	5.48979i	1.10981	−	0.195690i	0.698363	+	0.715743i	$0.253912\pi$
$788$	1.65890	−	4.55778i	0.0590958	−	0.162364i
$789$		0			0
$790$	2.61186	+	3.87502i	0.0929260	+	0.137867i
$791$	8.56074	−	14.8276i	0.304385	−	0.527210i
$792$		0			0
$793$	−4.08231	+	2.35692i	−0.144967	+	0.0836967i
$794$	6.94125	−	2.52641i	0.246336	−	0.0896589i
$795$		0			0
$796$	−5.84498	+	4.90452i	−0.207170	+	0.173836i
$797$	−16.6580	−	19.8522i	−0.590057	−	0.703202i	0.385560	−	0.922683i	$-0.374008\pi$
$797$	−16.6580	−	19.8522i	−0.590057	−	0.703202i	−0.975617	+	0.219480i	$0.929564\pi$
$798$		0			0
$799$	−30.2508	+	11.0104i	−1.07020	+	0.389520i
$800$	−9.12464	−	17.1884i	−0.322605	−	0.607703i
$801$		0			0
$802$	6.57473	+	3.79592i	0.232162	+	0.134039i
$803$	−4.95568	−	0.873820i	−0.174882	−	0.0308364i
$804$		0			0
$805$	−7.54937	−	16.9713i	−0.266080	−	0.598160i
$806$	−0.191860	−	1.08809i	−0.00675797	−	0.0383264i
$807$		0			0
$808$	16.0228	−	19.0952i	0.563680	−	0.671768i
$809$	−16.8506			−0.592435			−0.296217	−	0.955121i	$-0.595725\pi$
$809$	−16.8506			−0.592435			−0.296217	+	0.955121i	$0.595725\pi$
$810$		0			0
$811$	−26.5505			−0.932313			−0.466156	−	0.884702i	$-0.654362\pi$
$811$	−26.5505			−0.932313			−0.466156	+	0.884702i	$0.654362\pi$
$812$	5.40358	−	6.43974i	0.189629	−	0.225991i
$813$		0			0
$814$	4.72633	+	26.8044i	0.165658	+	0.939493i
$815$	27.4835	−	12.2255i	0.962705	−	0.428241i
$816$		0			0
$817$	6.03666	+	1.06443i	0.211196	+	0.0372396i
$818$	17.5932	+	10.1574i	0.615132	+	0.355146i
$819$		0			0
$820$	−2.56798	+	8.94442i	−0.0896779	+	0.312353i
$821$	−43.6959	+	15.9040i	−1.52500	+	0.555054i	−0.962390	−	0.271670i	$-0.912424\pi$
$821$	−43.6959	+	15.9040i	−1.52500	+	0.555054i	−0.562608	+	0.826724i	$0.690202\pi$
$822$		0			0
$823$	−0.257495	−	0.306870i	−0.00897570	−	0.0106968i	0.761538	−	0.648120i	$-0.224445\pi$
$823$	−0.257495	−	0.306870i	−0.00897570	−	0.0106968i	−0.770514	+	0.637424i	$0.780000\pi$
$824$	3.96167	−	3.32424i	0.138011	−	0.115805i
$825$		0			0
$826$	25.9816	−	9.45654i	0.904017	−	0.329035i
$827$	−0.954191	+	0.550903i	−0.0331805	+	0.0191568i	−0.516498	−	0.856288i	$-0.672765\pi$
$827$	−0.954191	+	0.550903i	−0.0331805	+	0.0191568i	0.483318	+	0.875445i	$0.339431\pi$
$828$		0			0
$829$	−2.63061	+	4.55635i	−0.0913648	+	0.158249i	−0.908086	−	0.418784i	$-0.862456\pi$
$829$	−2.63061	+	4.55635i	−0.0913648	+	0.158249i	0.816721	+	0.577033i	$0.195790\pi$
$830$	−4.67371	+	3.15020i	−0.162227	+	0.109345i
$831$		0			0
$832$	−0.692479	+	1.90257i	−0.0240074	+	0.0659597i
$833$	27.7542	−	4.89382i	0.961627	−	0.169561i
$834$		0			0
$835$	5.77333	−	0.401785i	0.199794	−	0.0139044i
$836$	−7.17047			−0.247996
$837$		0			0
$838$			27.5609i			0.952075i
$839$	27.5648	+	23.1296i	0.951642	+	0.798523i	0.979573	−	0.201087i	$-0.0644474\pi$
$839$	27.5648	+	23.1296i	0.951642	+	0.798523i	−0.0279310	+	0.999610i	$0.508892\pi$
$840$		0			0
$841$	10.3649	+	58.7823i	0.357410	+	2.02698i
$842$	−4.76267	+	13.0853i	−0.164132	+	0.450950i
$843$		0			0
$844$	2.23126	−	12.6541i	0.0768033	−	0.435573i
$845$	27.4492	−	6.83418i	0.944281	−	0.235103i
$846$		0			0
$847$	−1.46140	+	0.843742i	−0.0502145	+	0.0289913i
$848$	−13.8205	−	37.9716i	−0.474599	−	1.30395i
$849$		0			0
$850$	26.1774	+	33.5514i	0.897878	+	1.15080i
$851$	−24.0772	+	20.2032i	−0.825357	+	0.692557i
$852$		0			0
$853$	−0.137118	−	0.376728i	−0.00469483	−	0.0128989i	0.937323	−	0.348462i	$-0.113296\pi$
$853$	−0.137118	−	0.376728i	−0.00469483	−	0.0128989i	−0.942018	+	0.335563i	$0.891074\pi$
$854$	8.15623	+	14.1270i	0.279101	+	0.483416i
$855$		0			0
$856$	7.22159	−	12.5082i	0.246829	−	0.427520i
$857$	38.0088	+	6.70198i	1.29836	+	0.228935i	0.779757	−	0.626083i	$-0.215343\pi$
$857$	38.0088	+	6.70198i	1.29836	+	0.228935i	0.518599	+	0.855018i	$0.326454\pi$
$858$		0			0
$859$	16.0641	+	5.84684i	0.548099	+	0.199492i	0.601202	−	0.799097i	$-0.294689\pi$
$859$	16.0641	+	5.84684i	0.548099	+	0.199492i	−0.0531029	+	0.998589i	$0.516911\pi$
$860$	−2.81337	−	2.04546i	−0.0959351	−	0.0697496i
$861$		0			0
$862$	−12.3522	+	14.7208i	−0.420719	+	0.501393i
$863$			23.2510i			0.791472i	0.918364	+	0.395736i	$0.129511\pi$
$863$			23.2510i			0.791472i	−0.918364	+	0.395736i	$0.870489\pi$
$864$		0			0
$865$	−26.6186	+	25.6882i	−0.905058	+	0.873425i
$866$	−13.6738	−	11.4737i	−0.464654	−	0.389891i
$867$		0			0
$868$	−0.996144	+	0.175647i	−0.0338113	+	0.00596185i
$869$	4.18672	+	1.52384i	0.142025	+	0.0516928i
$870$		0			0
$871$	−0.452035	+	2.56362i	−0.0153166	+	0.0868648i
$872$	−34.3716	−	19.8445i	−1.16397	−	0.672019i
$873$		0			0
$874$	−15.6496	−	27.1059i	−0.529356	−	0.916872i
$875$	12.2419	+	6.52477i	0.413851	+	0.220577i
$876$		0			0
$877$	−0.503887	−	0.600510i	−0.0170151	−	0.0202778i	0.757470	−	0.652870i	$-0.226435\pi$
$877$	−0.503887	−	0.600510i	−0.0170151	−	0.0202778i	−0.774485	+	0.632592i	$0.781991\pi$
$878$	−29.7080	−	35.4047i	−1.00260	−	1.19485i
$879$		0			0
$880$	−34.7667	−	16.9711i	−1.17198	−	0.572096i
$881$	−4.60962	−	7.98410i	−0.155302	−	0.268991i	0.777867	−	0.628429i	$-0.216302\pi$
$881$	−4.60962	−	7.98410i	−0.155302	−	0.268991i	−0.933169	+	0.359438i	$0.882968\pi$
$882$		0			0
$883$	31.4539	+	18.1599i	1.05851	+	0.611129i	0.925019	−	0.379921i	$-0.124049\pi$
$883$	31.4539	+	18.1599i	1.05851	+	0.611129i	0.133488	+	0.991050i	$0.457382\pi$
$884$	−0.381232	+	2.16207i	−0.0128222	+	0.0727183i
$885$		0			0
$886$	43.3716	+	15.7860i	1.45710	+	0.530340i
$887$	33.0505	−	5.82770i	1.10973	−	0.195675i	0.411401	−	0.911454i	$-0.365040\pi$
$887$	33.0505	−	5.82770i	1.10973	−	0.195675i	0.698326	+	0.715779i	$0.253928\pi$
$888$		0			0
$889$	−8.12468	−	6.81741i	−0.272493	−	0.228649i
$890$	34.6410	−	33.4302i	1.16117	−	1.12058i
$891$		0			0
$892$			14.0362i			0.469967i
$893$	−11.3664	+	13.5459i	−0.380361	+	0.453296i
$894$		0			0
$895$	−1.59588	+	2.19501i	−0.0533443	+	0.0733709i
$896$	15.6597	+	5.69966i	0.523154	+	0.190412i
$897$		0			0
$898$	−40.7531	−	7.18587i	−1.35995	−	0.239796i
$899$	5.33576	−	9.24181i	0.177958	−	0.308232i
$900$		0			0
$901$	21.1890	+	36.7004i	0.705907	+	1.22267i
$902$	11.4704	+	31.5146i	0.381921	+	1.04932i
$903$		0			0
$904$	22.3228	−	18.7310i	0.742444	−	0.622985i
$905$	8.19294	+	0.863861i	0.272343	+	0.0287157i
$906$		0			0
$907$	−3.34276	−	9.18415i	−0.110994	−	0.304955i	0.871742	−	0.489965i	$-0.162990\pi$
$907$	−3.34276	−	9.18415i	−0.110994	−	0.304955i	−0.982737	+	0.185010i	$0.940768\pi$
$908$	2.29232	−	1.32347i	0.0760732	−	0.0439209i
$909$		0			0
$910$	0.653571	+	2.62504i	0.0216657	+	0.0870193i
$911$	−6.63575	+	37.6332i	−0.219852	+	1.24684i	0.652433	+	0.757847i	$0.273748\pi$
$911$	−6.63575	+	37.6332i	−0.219852	+	1.24684i	−0.872285	+	0.488998i	$0.837363\pi$
$912$		0			0
$913$	−1.83792	+	5.04965i	−0.0608264	+	0.167119i
$914$	4.80022	+	27.2234i	0.158777	+	0.900470i
$915$		0			0
$916$	2.39061	+	2.00596i	0.0789880	+	0.0662788i
$917$			12.0175i			0.396854i
$918$		0			0
$919$	−15.3144			−0.505176			−0.252588	−	0.967574i	$-0.581282\pi$
$919$	−15.3144			−0.505176			−0.252588	+	0.967574i	$0.581282\pi$
$920$	−2.19479	−	31.5373i	−0.0723600	−	1.03975i
$921$		0			0
$922$	42.0570	−	7.41579i	1.38507	−	0.244226i
$923$	−1.39045	+	3.82023i	−0.0457673	+	0.125745i
$924$		0			0
$925$	4.89562	−	22.9572i	0.160967	−	0.754827i
$926$	−14.2794	+	24.7327i	−0.469252	+	0.812768i
$927$		0			0
$928$	31.7427	−	18.3267i	1.04201	−	0.601603i
$929$	−0.281736	+	0.102544i	−0.00924347	+	0.00336435i	−0.346638	−	0.937999i	$-0.612677\pi$
$929$	−0.281736	+	0.102544i	−0.00924347	+	0.00336435i	0.337394	+	0.941363i	$0.390454\pi$
$930$		0			0
$931$	11.8586	−	9.95056i	0.388651	−	0.326117i
$932$	3.64773	+	4.34720i	0.119485	+	0.142397i
$933$		0			0
$934$	−19.2045	+	6.98986i	−0.628390	+	0.228715i
$935$	38.9978	+	11.1964i	1.27536	+	0.366163i
$936$		0			0
$937$	13.1951	+	7.61820i	0.431065	+	0.248876i	0.699800	−	0.714338i	$-0.253272\pi$
$937$	13.1951	+	7.61820i	0.431065	+	0.248876i	−0.268735	+	0.963214i	$0.586606\pi$
$938$	8.87151	+	1.56429i	0.289665	+	0.0510758i
$939$		0			0
$940$	9.16804	−	4.07823i	0.299029	−	0.133017i
$941$	1.63828	+	9.29115i	0.0534064	+	0.302883i	0.999797	−	0.0201414i	$-0.00641163\pi$
$941$	1.63828	+	9.29115i	0.0534064	+	0.302883i	−0.946391	+	0.323024i	$0.895301\pi$
$942$		0			0
$943$	−24.8938	+	29.6673i	−0.810654	+	0.966100i
$944$	66.5014			2.16444
$945$		0			0
$946$	−12.5357			−0.407570
$947$	−36.2626	+	43.2160i	−1.17837	+	1.40433i	−0.282941	+	0.959137i	$0.591310\pi$
$947$	−36.2626	+	43.2160i	−1.17837	+	1.40433i	−0.895433	+	0.445195i	$0.853134\pi$
$948$		0			0
$949$	0.146959	+	0.833444i	0.00477048	+	0.0270547i
$950$	21.6673	+	8.77090i	0.702981	+	0.284566i
$951$		0			0
$952$	−13.3176	−	2.34825i	−0.431626	−	0.0761073i
$953$	−13.0557	−	7.53769i	−0.422915	−	0.244170i	0.273409	−	0.961898i	$-0.411849\pi$
$953$	−13.0557	−	7.53769i	−0.422915	−	0.244170i	−0.696324	+	0.717728i	$0.745182\pi$
$954$		0			0
$955$	2.34450	−	8.16602i	0.0758663	−	0.264246i
$956$	19.3031	−	7.02574i	0.624306	−	0.227229i
$957$		0			0
$958$	−24.2012	−	28.8419i	−0.781907	−	0.931840i
$959$	−14.0671	+	11.8037i	−0.454249	+	0.381160i
$960$		0			0
$961$	27.9239	−	10.1635i	0.900770	−	0.327853i
$962$	3.96422	−	2.28875i	0.127812	−	0.0737921i
$963$		0			0
$964$	−4.73403	+	8.19958i	−0.152473	+	0.264091i
$965$	−11.3643	−	16.8603i	−0.365830	−	0.542754i
$966$		0			0
$967$	3.00739	−	8.26273i	0.0967110	−	0.265711i	−0.881898	−	0.471440i	$-0.843734\pi$
$967$	3.00739	−	8.26273i	0.0967110	−	0.265711i	0.978609	+	0.205729i	$0.0659565\pi$
$968$	−2.82842	+	0.498727i	−0.0909089	+	0.0160297i
$969$		0			0
$970$	−3.54797	−	50.9815i	−0.113919	−	1.63692i
$971$	1.79910			0.0577358			0.0288679	−	0.999583i	$-0.490810\pi$
$971$	1.79910			0.0577358			0.0288679	+	0.999583i	$0.490810\pi$
$972$		0			0
$973$			3.39195i			0.108741i
$974$	−4.07041	−	3.41548i	−0.130424	−	0.109439i
$975$		0			0
$976$	6.81303	+	38.6386i	0.218080	+	1.23679i
$977$	−4.35167	+	11.9561i	−0.139222	+	0.382510i	−0.989635	−	0.143606i	$-0.954130\pi$
$977$	−4.35167	+	11.9561i	−0.139222	+	0.382510i	0.850413	+	0.526116i	$0.176352\pi$
$978$		0			0
$979$	7.97027	−	45.2017i	0.254731	−	1.44465i
$980$	−8.52410	+	2.12229i	−0.272292	+	0.0677942i
$981$		0			0
$982$	37.3586	−	21.5690i	1.19216	−	0.688295i
$983$	17.9343	+	49.2740i	0.572015	+	1.57160i	0.801315	+	0.598242i	$0.204134\pi$
$983$	17.9343	+	49.2740i	0.572015	+	1.57160i	−0.229301	+	0.973356i	$0.573644\pi$
$984$		0			0
$985$	−1.58076	+	14.9921i	−0.0503672	+	0.477687i
$986$	−61.4007	+	51.5213i	−1.95540	+	1.64077i
$987$		0			0
$988$	0.412451	+	1.13320i	0.0131218	+	0.0360519i
$989$	−7.23795	−	12.5365i	−0.230154	−	0.398638i
$990$		0			0
$991$	−7.43264	+	12.8737i	−0.236106	+	0.408947i	−0.959593	−	0.281390i	$-0.909204\pi$
$991$	−7.43264	+	12.8737i	−0.236106	+	0.408947i	0.723488	+	0.690337i	$0.242538\pi$
$992$	−4.34332	−	0.765844i	−0.137900	−	0.0243156i
$993$		0			0
$994$	13.2201	+	4.81172i	0.419316	+	0.152618i
$995$	13.9457	−	19.1812i	0.442109	−	0.608086i
$996$		0			0
$997$	14.5685	−	17.3621i	0.461390	−	0.549864i	−0.484313	−	0.874895i	$-0.660930\pi$
$997$	14.5685	−	17.3621i	0.461390	−	0.549864i	0.945703	+	0.325031i	$0.105375\pi$
$998$			56.4909i			1.78819i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.p.a.289.4		96
3.2	odd	2		135.2.p.a.124.13	yes	96
5.4	even	2	inner	405.2.p.a.289.13		96
15.2	even	4		675.2.l.h.151.13		96
15.8	even	4		675.2.l.h.151.4		96
15.14	odd	2		135.2.p.a.124.4	yes	96
27.5	odd	18		135.2.p.a.49.4	✓	96
27.22	even	9	inner	405.2.p.a.199.13		96
135.32	even	36		675.2.l.h.76.13		96
135.49	even	18	inner	405.2.p.a.199.4		96
135.59	odd	18		135.2.p.a.49.13	yes	96
135.113	even	36		675.2.l.h.76.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.4	✓	96	27.5	odd	18
135.2.p.a.49.13	yes	96	135.59	odd	18
135.2.p.a.124.4	yes	96	15.14	odd	2
135.2.p.a.124.13	yes	96	3.2	odd	2
405.2.p.a.199.4		96	135.49	even	18	inner
405.2.p.a.199.13		96	27.22	even	9	inner
405.2.p.a.289.4		96	1.1	even	1	trivial
405.2.p.a.289.13		96	5.4	even	2	inner
675.2.l.h.76.4		96	135.113	even	36
675.2.l.h.76.13		96	135.32	even	36
675.2.l.h.151.4		96	15.8	even	4
675.2.l.h.151.13		96	15.2	even	4

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.p (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06000 + 1.26326i) q^{2} +(-0.124928 - 0.708504i) q^{4} +(0.908813 + 2.04305i) q^{5} +(-1.22191 - 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +O(q^{10})\)	\(q+(-1.06000 + 1.26326i) q^{2} +(-0.124928 - 0.708504i) q^{4} +(0.908813 + 2.04305i) q^{5} +(-1.22191 - 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +(-3.54425 - 1.01757i) q^{10} +(-3.30366 + 1.20243i) q^{11} +(0.380059 + 0.452936i) q^{13} +(1.56741 - 1.31521i) q^{14} +(4.62449 - 1.68318i) q^{16} +(-4.46967 + 2.58056i) q^{17} +(-1.41748 + 2.45515i) q^{19} +(1.33397 - 0.899132i) q^{20} +(1.98290 - 5.44797i) q^{22} +(6.59324 - 1.16257i) q^{23} +(-3.34812 + 3.71350i) q^{25} -0.975040 q^{26} +0.892646i q^{28} +(-7.21421 - 6.05345i) q^{29} +(0.196771 + 1.11595i) q^{31} +(-1.33116 + 3.65733i) q^{32} +(1.47793 - 8.38176i) q^{34} +(-0.670302 - 2.69224i) q^{35} +(-4.06570 + 2.34734i) q^{37} +(-1.59896 - 4.39311i) q^{38} +(0.495142 - 4.69597i) q^{40} +(-4.43129 + 3.71830i) q^{41} +(-0.739520 - 2.03181i) q^{43} +(1.26465 + 2.19044i) q^{44} +(-5.52022 + 9.56131i) q^{46} +(6.14268 + 1.08312i) q^{47} +(-5.13120 - 1.86760i) q^{49} +(-1.14211 - 8.16587i) q^{50} +(0.273427 - 0.325858i) q^{52} -8.21098i q^{53} +(-5.45905 - 5.65676i) q^{55} +(2.00717 + 1.68421i) q^{56} +(15.2942 - 2.69677i) q^{58} +(12.6981 + 4.62173i) q^{59} +(-1.38440 + 7.85133i) q^{61} +(-1.61831 - 0.934331i) q^{62} +(1.71215 + 2.96553i) q^{64} +(-0.579970 + 1.18811i) q^{65} +(2.83000 + 3.37266i) q^{67} +(2.38673 + 2.84439i) q^{68} +(4.11152 + 2.00701i) q^{70} +(3.43788 + 5.95458i) q^{71} +(1.23957 + 0.715668i) q^{73} +(1.34436 - 7.62423i) q^{74} +(1.91656 + 0.697573i) q^{76} +(4.29586 - 0.757476i) q^{77} +(-0.970806 - 0.814603i) q^{79} +(7.64162 + 7.91838i) q^{80} -9.53928i q^{82} +(0.982501 - 1.17090i) q^{83} +(-9.33432 - 6.78651i) q^{85} +(3.35061 + 1.21952i) q^{86} +(7.31144 + 1.28920i) q^{88} +(-6.52774 + 11.3064i) q^{89} +(-0.366811 - 0.635335i) q^{91} +(-1.64736 - 4.52610i) q^{92} +(-7.87952 + 6.61170i) q^{94} +(-6.30422 - 0.664715i) q^{95} +(4.74011 + 13.0234i) q^{97} +(7.79835 - 4.50238i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} + 9 q^{5}+O(q^{10}) \) 96 * q - 12 * q^4 + 9 * q^5	\( 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46} - 30 q^{49} - 84 q^{50} - 12 q^{55} + 96 q^{56} - 66 q^{59} + 6 q^{61} - 45 q^{65} - 33 q^{70} + 90 q^{71} - 66 q^{74} + 12 q^{76} + 24 q^{79} - 30 q^{80} - 21 q^{85} - 18 q^{86} - 96 q^{89} - 6 q^{91} + 24 q^{94} - 87 q^{95}+O(q^{100}) \) 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Introduction

L-functions

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