LMFDB - Embedded newform 432.2.v.a.395.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(35,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("432.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			395.3
Character	$\chi$	$=$	432.395
Dual form			432.2.v.a.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20346 - 0.742754i) q^{2} +(0.896632 + 1.78775i) q^{4} +(0.206232 + 0.769670i) q^{5} +(-2.17574 - 3.76849i) q^{7} +(0.248799 - 2.81746i) q^{8} +O(q^{10})$	\(q+(-1.20346 - 0.742754i) q^{2} +(0.896632 + 1.78775i) q^{4} +(0.206232 + 0.769670i) q^{5} +(-2.17574 - 3.76849i) q^{7} +(0.248799 - 2.81746i) q^{8} +(0.323483 - 1.07945i) q^{10} +(-1.05570 + 3.93991i) q^{11} +(-0.454903 - 1.69772i) q^{13} +(-0.180648 + 6.15127i) q^{14} +(-2.39210 + 3.20591i) q^{16} -6.68683i q^{17} +(-0.708282 - 0.708282i) q^{19} +(-1.19106 + 1.05880i) q^{20} +(4.19687 - 3.95740i) q^{22} +(-3.88191 - 2.24122i) q^{23} +(3.78027 - 2.18254i) q^{25} +(-0.713532 + 2.38102i) q^{26} +(4.78628 - 7.26863i) q^{28} +(1.06907 - 3.98981i) q^{29} +(-4.94177 - 2.85313i) q^{31} +(5.26000 - 2.08144i) q^{32} +(-4.96668 + 8.04734i) q^{34} +(2.45179 - 2.45179i) q^{35} +(-1.51665 - 1.51665i) q^{37} +(0.326309 + 1.37847i) q^{38} +(2.21983 - 0.389559i) q^{40} +(-1.36389 + 2.36233i) q^{41} +(-8.60436 - 2.30553i) q^{43} +(-7.99014 + 1.64533i) q^{44} +(3.00704 + 5.58052i) q^{46} +(-1.23164 - 2.13327i) q^{47} +(-5.96768 + 10.3363i) q^{49} +(-6.17049 - 0.181213i) q^{50} +(2.62722 - 2.33548i) q^{52} +(-1.68291 + 1.68291i) q^{53} -3.25015 q^{55} +(-11.1589 + 5.19247i) q^{56} +(-4.25002 + 4.00752i) q^{58} +(1.00516 - 0.269331i) q^{59} +(1.97401 + 0.528935i) q^{61} +(3.82804 + 7.10415i) q^{62} +(-7.87620 - 1.40197i) q^{64} +(1.21287 - 0.700250i) q^{65} +(8.01120 - 2.14659i) q^{67} +(11.9544 - 5.99563i) q^{68} +(-4.77170 + 1.12955i) q^{70} -8.05218i q^{71} +9.73126i q^{73} +(0.698727 + 2.95172i) q^{74} +(0.631163 - 1.90130i) q^{76} +(17.1444 - 4.59383i) q^{77} +(11.9835 - 6.91865i) q^{79} +(-2.96082 - 1.17997i) q^{80} +(3.39603 - 1.82994i) q^{82} +(-3.05012 - 0.817277i) q^{83} +(5.14666 - 1.37904i) q^{85} +(8.64256 + 9.16554i) q^{86} +(10.8379 + 3.95463i) q^{88} -1.71120 q^{89} +(-5.40809 + 5.40809i) q^{91} +(0.526101 - 8.94943i) q^{92} +(-0.102261 + 3.48211i) q^{94} +(0.399073 - 0.691214i) q^{95} +(3.66561 + 6.34903i) q^{97} +(14.8592 - 8.00683i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.20346	−	0.742754i	−0.850975	−	0.525207i
$2$	−1.20346	−	0.742754i	−0.850975	−	0.525207i
$3$		0			0
$3$		0			0
$4$	0.896632	+	1.78775i	0.448316	+	0.893875i
$5$	0.206232	+	0.769670i	0.0922300	+	0.344207i	0.996585	−	0.0825742i	$-0.0263142\pi$
$5$	0.206232	+	0.769670i	0.0922300	+	0.344207i	−0.904355	+	0.426781i	$0.859647\pi$
$6$		0			0
$7$	−2.17574	−	3.76849i	−0.822352	−	1.42436i	−0.903926	−	0.427688i	$-0.859328\pi$
$7$	−2.17574	−	3.76849i	−0.822352	−	1.42436i	0.0815745	−	0.996667i	$-0.474005\pi$
$8$	0.248799	−	2.81746i	0.0879638	−	0.996124i
$9$		0			0
$10$	0.323483	−	1.07945i	0.102294	−	0.341351i
$11$	−1.05570	+	3.93991i	−0.318304	+	1.18793i	0.602570	+	0.798066i	$0.294144\pi$
$11$	−1.05570	+	3.93991i	−0.318304	+	1.18793i	−0.920874	+	0.389861i	$0.872523\pi$
$12$		0			0
$13$	−0.454903	−	1.69772i	−0.126167	−	0.470863i	0.873711	−	0.486445i	$-0.161707\pi$
$13$	−0.454903	−	1.69772i	−0.126167	−	0.470863i	−0.999879	+	0.0155820i	$0.995040\pi$
$14$	−0.180648	+	6.15127i	−0.0482803	+	1.64400i
$15$		0			0
$16$	−2.39210	+	3.20591i	−0.598026	+	0.801477i
$17$		−	6.68683i		−	1.62180i	−0.585188	−	0.810898i	$-0.698979\pi$
$17$		−	6.68683i		−	1.62180i	0.585188	−	0.810898i	$-0.301021\pi$
$18$		0			0
$19$	−0.708282	−	0.708282i	−0.162491	−	0.162491i	0.621178	−	0.783669i	$-0.286654\pi$
$19$	−0.708282	−	0.708282i	−0.162491	−	0.162491i	−0.783669	+	0.621178i	$0.786654\pi$
$20$	−1.19106	+	1.05880i	−0.266330	+	0.236755i
$21$		0			0
$22$	4.19687	−	3.95740i	0.894776	−	0.843720i
$23$	−3.88191	−	2.24122i	−0.809433	−	0.467327i	0.0373258	−	0.999303i	$-0.488116\pi$
$23$	−3.88191	−	2.24122i	−0.809433	−	0.467327i	−0.846759	+	0.531977i	$0.821449\pi$
$24$		0			0
$25$	3.78027	−	2.18254i	0.756053	−	0.436508i
$26$	−0.713532	+	2.38102i	−0.139935	+	0.466956i
$27$		0			0
$28$	4.78628	−	7.26863i	0.904523	−	1.37364i
$29$	1.06907	−	3.98981i	0.198520	−	0.740888i	−0.792807	−	0.609473i	$-0.791381\pi$
$29$	1.06907	−	3.98981i	0.198520	−	0.740888i	0.991327	−	0.131415i	$-0.0419522\pi$
$30$		0			0
$31$	−4.94177	−	2.85313i	−0.887568	−	0.512437i	−0.0144215	−	0.999896i	$-0.504591\pi$
$31$	−4.94177	−	2.85313i	−0.887568	−	0.512437i	−0.873146	+	0.487459i	$0.837924\pi$
$32$	5.26000	−	2.08144i	0.929846	−	0.367949i
$33$		0			0
$34$	−4.96668	+	8.04734i	−0.851778	+	1.38011i
$35$	2.45179	−	2.45179i	0.414427	−	0.414427i
$36$		0			0
$37$	−1.51665	−	1.51665i	−0.249335	−	0.249335i	0.571363	−	0.820698i	$-0.306415\pi$
$37$	−1.51665	−	1.51665i	−0.249335	−	0.249335i	−0.820698	+	0.571363i	$0.806415\pi$
$38$	0.326309	+	1.37847i	0.0529344	+	0.223617i
$39$		0			0
$40$	2.21983	−	0.389559i	0.350986	−	0.0615947i
$41$	−1.36389	+	2.36233i	−0.213005	+	0.368935i	−0.952653	−	0.304058i	$-0.901658\pi$
$41$	−1.36389	+	2.36233i	−0.213005	+	0.368935i	0.739649	+	0.672993i	$0.234992\pi$
$42$		0			0
$43$	−8.60436	−	2.30553i	−1.31215	−	0.351590i	−0.466120	−	0.884722i	$-0.654348\pi$
$43$	−8.60436	−	2.30553i	−1.31215	−	0.351590i	−0.846033	+	0.533131i	$0.821015\pi$
$44$	−7.99014	+	1.64533i	−1.20456	+	0.248042i
$45$		0			0
$46$	3.00704	+	5.58052i	0.443364	+	0.822803i
$47$	−1.23164	−	2.13327i	−0.179654	−	0.311169i	0.762108	−	0.647449i	$-0.224164\pi$
$47$	−1.23164	−	2.13327i	−0.179654	−	0.311169i	−0.941762	+	0.336280i	$0.890831\pi$
$48$		0			0
$49$	−5.96768	+	10.3363i	−0.852525	+	1.47662i
$50$	−6.17049	−	0.181213i	−0.872639	−	0.0256274i
$51$		0			0
$52$	2.62722	−	2.33548i	0.364330	−	0.323873i
$53$	−1.68291	+	1.68291i	−0.231165	+	0.231165i	−0.813179	−	0.582014i	$-0.802265\pi$
$53$	−1.68291	+	1.68291i	−0.231165	+	0.231165i	0.582014	+	0.813179i	$0.302265\pi$
$54$		0			0
$55$	−3.25015			−0.438250
$56$	−11.1589	+	5.19247i	−1.49117	+	0.693872i
$57$		0			0
$58$	−4.25002	+	4.00752i	−0.558055	+	0.526213i
$59$	1.00516	−	0.269331i	0.130860	−	0.0350640i	−0.192794	−	0.981239i	$-0.561755\pi$
$59$	1.00516	−	0.269331i	0.130860	−	0.0350640i	0.323655	+	0.946175i	$0.395088\pi$
$60$		0			0
$61$	1.97401	+	0.528935i	0.252747	+	0.0677232i	0.382968	−	0.923762i	$-0.374902\pi$
$61$	1.97401	+	0.528935i	0.252747	+	0.0677232i	−0.130221	+	0.991485i	$0.541569\pi$
$62$	3.82804	+	7.10415i	0.486162	+	0.902228i
$63$		0			0
$64$	−7.87620	−	1.40197i	−0.984525	−	0.175246i
$65$	1.21287	−	0.700250i	0.150438	−	0.0868553i
$66$		0			0
$67$	8.01120	−	2.14659i	0.978723	−	0.262248i	0.266217	−	0.963913i	$-0.414226\pi$
$67$	8.01120	−	2.14659i	0.978723	−	0.262248i	0.712507	+	0.701665i	$0.247560\pi$
$68$	11.9544	−	5.99563i	1.44968	−	0.727077i
$69$		0			0
$70$	−4.77170	+	1.12955i	−0.570327	+	0.135007i
$71$		−	8.05218i		−	0.955618i	−0.878464	−	0.477809i	$-0.841431\pi$
$71$		−	8.05218i		−	0.955618i	0.878464	−	0.477809i	$-0.158569\pi$
$72$		0			0
$73$			9.73126i			1.13896i	0.822006	+	0.569479i	$0.192855\pi$
$73$			9.73126i			1.13896i	−0.822006	+	0.569479i	$0.807145\pi$
$74$	0.698727	+	2.95172i	0.0812254	+	0.343130i
$75$		0			0
$76$	0.631163	−	1.90130i	0.0723994	−	0.218094i
$77$	17.1444	−	4.59383i	1.95379	−	0.523516i
$78$		0			0
$79$	11.9835	−	6.91865i	1.34824	−	0.778409i	0.360243	−	0.932858i	$-0.382694\pi$
$79$	11.9835	−	6.91865i	1.34824	−	0.778409i	0.988001	+	0.154449i	$0.0493604\pi$
$80$	−2.96082	−	1.17997i	−0.331030	−	0.131924i
$81$		0			0
$82$	3.39603	−	1.82994i	0.375028	−	0.202083i
$83$	−3.05012	−	0.817277i	−0.334794	−	0.0897078i	0.0875058	−	0.996164i	$-0.472110\pi$
$83$	−3.05012	−	0.817277i	−0.334794	−	0.0897078i	−0.422300	+	0.906456i	$0.638777\pi$
$84$		0			0
$85$	5.14666	−	1.37904i	0.558233	−	0.149578i
$86$	8.64256	+	9.16554i	0.931951	+	0.988346i
$87$		0			0
$88$	10.8379	+	3.95463i	1.15532	+	0.421565i
$89$	−1.71120			−0.181386			−0.0906932	−	0.995879i	$-0.528908\pi$
$89$	−1.71120			−0.181386			−0.0906932	+	0.995879i	$0.528908\pi$
$90$		0			0
$91$	−5.40809	+	5.40809i	−0.566922	+	0.566922i
$92$	0.526101	−	8.94943i	0.0548498	−	0.933042i
$93$		0			0
$94$	−0.102261	+	3.48211i	−0.0105475	+	0.359152i
$95$	0.399073	−	0.691214i	0.0409440	−	0.0709171i
$96$		0			0
$97$	3.66561	+	6.34903i	0.372187	+	0.644646i	0.989902	−	0.141756i	$-0.0452748\pi$
$97$	3.66561	+	6.34903i	0.372187	+	0.644646i	−0.617715	+	0.786402i	$0.711941\pi$
$98$	14.8592	−	8.00683i	1.50101	−	0.808812i
$99$		0			0
$100$	7.29134	+	4.80124i	0.729134	+	0.480124i
$101$	14.0255	+	3.75813i	1.39559	+	0.373948i	0.876760	−	0.480928i	$-0.159700\pi$
$101$	14.0255	+	3.75813i	1.39559	+	0.373948i	0.518833	+	0.854876i	$0.326367\pi$
$102$		0			0
$103$	−7.43866	+	12.8841i	−0.732953	+	1.26951i	0.222663	+	0.974895i	$0.428525\pi$
$103$	−7.43866	+	12.8841i	−0.732953	+	1.26951i	−0.955616	+	0.294616i	$0.904808\pi$
$104$	−4.89644	+	0.859280i	−0.480136	+	0.0842594i
$105$		0			0
$106$	3.27530	−	0.775325i	0.318125	−	0.0753062i
$107$	0.0974799	+	0.0974799i	0.00942374	+	0.00942374i	0.711803	−	0.702379i	$-0.247879\pi$
$107$	0.0974799	+	0.0974799i	0.00942374	+	0.00942374i	−0.702379	+	0.711803i	$0.747879\pi$
$108$		0			0
$109$	8.80665	−	8.80665i	0.843524	−	0.843524i	−0.145791	−	0.989315i	$-0.546573\pi$
$109$	8.80665	−	8.80665i	0.843524	−	0.843524i	0.989315	+	0.145791i	$0.0465728\pi$
$110$	3.91142	+	2.41406i	0.372939	+	0.230172i
$111$		0			0
$112$	17.2860	+	2.03940i	1.63338	+	0.192705i
$113$	−7.22037	−	4.16868i	−0.679235	−	0.392157i	0.120331	−	0.992734i	$-0.461604\pi$
$113$	−7.22037	−	4.16868i	−0.679235	−	0.392157i	−0.799567	+	0.600577i	$0.794938\pi$
$114$		0			0
$115$	0.924424	−	3.45000i	0.0862030	−	0.321714i
$116$	8.09133	−	1.66616i	0.751262	−	0.154699i
$117$		0			0
$118$	−1.40971	−	0.422456i	−0.129775	−	0.0388903i
$119$	−25.1993	+	14.5488i	−2.31001	+	1.33369i
$120$		0			0
$121$	−4.88210	−	2.81868i	−0.443827	−	0.256244i
$122$	−1.98278	−	2.10276i	−0.179512	−	0.190375i
$123$		0			0
$124$	0.669740	−	11.3929i	0.0601445	−	1.02311i
$125$	5.27664	+	5.27664i	0.471957	+	0.471957i
$126$		0			0
$127$			4.84829i			0.430216i	0.976590	+	0.215108i	$0.0690103\pi$
$127$			4.84829i			0.430216i	−0.976590	+	0.215108i	$0.930990\pi$
$128$	8.43737	+	7.53729i	0.745765	+	0.666209i
$129$		0			0
$130$	−1.97975	−	0.0581407i	−0.173636	−	0.00509928i
$131$	5.49193	+	20.4961i	0.479832	+	1.79076i	0.602284	+	0.798282i	$0.294258\pi$
$131$	5.49193	+	20.4961i	0.479832	+	1.79076i	−0.122452	+	0.992474i	$0.539076\pi$
$132$		0			0
$133$	−1.12812	+	4.21019i	−0.0978201	+	0.365070i
$134$	−11.2355	−	3.36701i	−0.970603	−	0.290866i
$135$		0			0
$136$	−18.8399	−	1.66368i	−1.61551	−	0.142659i
$137$	2.93860	+	5.08981i	0.251062	+	0.434852i	0.963818	−	0.266560i	$-0.0858869\pi$
$137$	2.93860	+	5.08981i	0.251062	+	0.434852i	−0.712757	+	0.701411i	$0.752554\pi$
$138$		0			0
$139$	−1.86863	−	6.97384i	−0.158496	−	0.591513i	−0.998781	−	0.0493686i	$-0.984279\pi$
$139$	−1.86863	−	6.97384i	−0.158496	−	0.591513i	0.840285	−	0.542145i	$-0.182388\pi$
$140$	6.58153	+	2.18483i	0.556241	+	0.184652i
$141$		0			0
$142$	−5.98079	+	9.69047i	−0.501897	+	0.813206i
$143$	7.16910			0.599510
$144$		0			0
$145$	3.29131			0.273328
$146$	7.22794	−	11.7112i	0.598188	−	0.969224i
$147$		0			0
$148$	1.35151	−	4.07126i	0.111094	−	0.334655i
$149$	−1.16425	−	4.34504i	−0.0953792	−	0.355960i	0.901698	−	0.432367i	$-0.142322\pi$
$149$	−1.16425	−	4.34504i	−0.0953792	−	0.355960i	−0.997077	+	0.0764076i	$0.975655\pi$
$150$		0			0
$151$	−4.23499	−	7.33521i	−0.344638	−	0.596931i	0.640650	−	0.767833i	$-0.278665\pi$
$151$	−4.23499	−	7.33521i	−0.344638	−	0.596931i	−0.985288	+	0.170902i	$0.945332\pi$
$152$	−2.17178	+	1.81934i	−0.176154	+	0.147568i
$153$		0			0
$154$	−24.0447	−	7.20560i	−1.93758	−	0.580644i
$155$	1.17682	−	4.39194i	0.0945241	−	0.352769i
$156$		0			0
$157$	−4.38117	−	16.3507i	−0.349655	−	1.30493i	−0.887079	−	0.461618i	$-0.847269\pi$
$157$	−4.38117	−	16.3507i	−0.349655	−	1.30493i	0.537423	−	0.843313i	$-0.319398\pi$
$158$	−19.5605	−	0.574445i	−1.55615	−	0.0457004i
$159$		0			0
$160$	2.68680	+	3.61921i	0.212410	+	0.286123i
$161$			19.5052i			1.53723i
$162$		0			0
$163$	13.6982	+	13.6982i	1.07293	+	1.07293i	0.997123	+	0.0758059i	$0.0241529\pi$
$163$	13.6982	+	13.6982i	1.07293	+	1.07293i	0.0758059	+	0.997123i	$0.475847\pi$
$164$	−5.44618	−	0.320159i	−0.425275	−	0.0250002i
$165$		0			0
$166$	3.06366	+	3.24905i	0.237786	+	0.252175i
$167$	7.11859	+	4.10992i	0.550853	+	0.318035i	0.749466	−	0.662043i	$-0.230310\pi$
$167$	7.11859	+	4.10992i	0.550853	+	0.318035i	−0.198613	+	0.980078i	$0.563644\pi$
$168$		0			0
$169$	8.58301	−	4.95540i	0.660232	−	0.381185i
$170$	−7.21808	−	2.16308i	−0.553602	−	0.165901i
$171$		0			0
$172$	−3.59323	−	17.4497i	−0.273981	−	1.33052i
$173$	2.52258	−	9.41440i	0.191788	−	0.715764i	−0.801287	−	0.598281i	$-0.795851\pi$
$173$	2.52258	−	9.41440i	0.191788	−	0.715764i	0.993075	−	0.117483i	$-0.0374826\pi$
$174$		0			0
$175$	−16.4497	−	9.49727i	−1.24348	−	0.717926i
$176$	−10.1056	−	12.8091i	−0.761742	−	0.965524i
$177$		0			0
$178$	2.05936	+	1.27100i	0.154355	+	0.0952654i
$179$	−2.59887	+	2.59887i	−0.194248	+	0.194248i	−0.797529	−	0.603281i	$-0.793860\pi$
$179$	−2.59887	+	2.59887i	−0.194248	+	0.194248i	0.603281	+	0.797529i	$0.293860\pi$
$180$		0			0
$181$	6.92926	+	6.92926i	0.515048	+	0.515048i	0.916069	−	0.401021i	$-0.131345\pi$
$181$	6.92926	+	6.92926i	0.515048	+	0.515048i	−0.401021	+	0.916069i	$0.631345\pi$
$182$	10.5253	−	2.49154i	0.780188	−	0.184685i
$183$		0			0
$184$	−7.28037	+	10.3795i	−0.536716	+	0.765188i
$185$	0.854536	−	1.48010i	0.0628267	−	0.108819i
$186$		0			0
$187$	26.3455	+	7.05926i	1.92657	+	0.516224i
$188$	2.70942	−	4.11462i	0.197605	−	0.300090i
$189$		0			0
$190$	−0.993670	+	0.535435i	−0.0720884	+	0.0388446i
$191$	−6.96728	−	12.0677i	−0.504135	−	0.873187i	−0.999989	−	0.00478132i	$-0.998478\pi$
$191$	−6.96728	−	12.0677i	−0.504135	−	0.873187i	0.495854	−	0.868406i	$-0.334855\pi$
$192$		0			0
$193$	−1.34094	+	2.32257i	−0.0965226	+	0.167182i	−0.910243	−	0.414074i	$-0.864105\pi$
$193$	−1.34094	+	2.32257i	−0.0965226	+	0.167182i	0.813720	+	0.581256i	$0.197439\pi$
$194$	0.304350	−	10.3635i	0.0218511	−	0.744053i
$195$		0			0
$196$	−23.8296	−	1.40085i	−1.70211	−	0.100060i
$197$	−14.2363	+	14.2363i	−1.01430	+	1.01430i	−0.0144009	+	0.999896i	$0.504584\pi$
$197$	−14.2363	+	14.2363i	−1.01430	+	1.01430i	−0.999896	+	0.0144009i	$0.995416\pi$
$198$		0			0
$199$	7.90078			0.560072			0.280036	−	0.959990i	$-0.409654\pi$
$199$	7.90078			0.560072			0.280036	+	0.959990i	$0.409654\pi$
$200$	−5.20869	−	11.1938i	−0.368310	−	0.791520i
$201$		0			0
$202$	−14.0878	−	14.9403i	−0.991214	−	1.05119i
$203$	−17.3615	+	4.65201i	−1.21854	+	0.326507i
$204$		0			0
$205$	−2.09950	−	0.562559i	−0.146635	−	0.0392908i
$206$	18.5219	−	9.98044i	1.29048	−	0.695370i
$207$		0			0
$208$	6.53091	+	2.60275i	0.452837	+	0.180468i
$209$	3.53830	−	2.04284i	0.244749	−	0.141306i
$210$		0			0
$211$	13.2108	−	3.53982i	0.909469	−	0.243691i	0.226391	−	0.974037i	$-0.427307\pi$
$211$	13.2108	−	3.53982i	0.909469	−	0.243691i	0.683078	+	0.730345i	$0.260641\pi$
$212$	−4.51757	−	1.49967i	−0.310268	−	0.102998i
$213$		0			0
$214$	−0.0449095	−	0.189717i	−0.00306995	−	0.0129688i
$215$		−	7.09799i		−	0.484079i
$216$		0			0
$217$			24.8307i			1.68562i
$218$	−17.1396	+	4.05727i	−1.16084	+	0.274793i
$219$		0			0
$220$	−2.91418	−	5.81045i	−0.196474	−	0.391741i
$221$	−11.3524	+	3.04186i	−0.763643	+	0.204618i
$222$		0			0
$223$	−24.3372	+	14.0511i	−1.62974	+	0.940931i	−0.645570	+	0.763701i	$0.723380\pi$
$223$	−24.3372	+	14.0511i	−1.62974	+	0.940931i	−0.984169	+	0.177230i	$0.943286\pi$
$224$	−19.2883	−	15.2936i	−1.28875	−	1.02185i
$225$		0			0
$226$	5.59312	+	10.3798i	0.372049	+	0.690454i
$227$	−0.489998	−	0.131295i	−0.0325223	−	0.00871433i	0.242521	−	0.970146i	$-0.422026\pi$
$227$	−0.489998	−	0.131295i	−0.0325223	−	0.00871433i	−0.275044	+	0.961432i	$0.588692\pi$
$228$		0			0
$229$	−14.6181	+	3.91690i	−0.965988	+	0.258836i	−0.707133	−	0.707080i	$-0.750012\pi$
$229$	−14.6181	+	3.91690i	−0.965988	+	0.258836i	−0.258855	+	0.965916i	$0.583345\pi$
$230$	−3.67501	+	3.46531i	−0.242323	+	0.228496i
$231$		0			0
$232$	−10.9751	−	4.00471i	−0.720554	−	0.262922i
$233$	−15.4968			−1.01523			−0.507614	−	0.861584i	$-0.669473\pi$
$233$	−15.4968			−1.01523			−0.507614	+	0.861584i	$0.669473\pi$
$234$		0			0
$235$	1.38791	−	1.38791i	0.0905371	−	0.0905371i
$236$	1.38275	+	1.55548i	0.0900096	+	0.101253i
$237$		0			0
$238$	41.1325	+	1.20797i	2.66622	+	0.0783007i
$239$	7.61709	−	13.1932i	0.492709	−	0.853397i	−0.507256	−	0.861796i	$-0.669340\pi$
$239$	7.61709	−	13.1932i	0.492709	−	0.853397i	0.999965	+	0.00839869i	$0.00267342\pi$
$240$		0			0
$241$	−9.10697	−	15.7737i	−0.586632	−	1.01608i	−0.994670	−	0.103111i	$-0.967120\pi$
$241$	−9.10697	−	15.7737i	−0.586632	−	1.01608i	0.408038	−	0.912965i	$-0.366213\pi$
$242$	3.78182	+	7.01837i	0.243105	+	0.451158i
$243$		0			0
$244$	0.824359	+	4.00330i	0.0527742	+	0.256285i
$245$	−9.18628	−	2.46146i	−0.586890	−	0.157257i
$246$		0			0
$247$	−0.880265	+	1.52466i	−0.0560099	+	0.0970121i
$248$	−9.26810	+	13.2134i	−0.588525	+	0.839051i
$249$		0			0
$250$	−2.43097	−	10.2695i	−0.153748	−	0.649498i
$251$	−2.18418	−	2.18418i	−0.137864	−	0.137864i	0.634807	−	0.772671i	$-0.281080\pi$
$251$	−2.18418	−	2.18418i	−0.137864	−	0.137864i	−0.772671	+	0.634807i	$0.781080\pi$
$252$		0			0
$253$	12.9283	−	12.9283i	0.812796	−	0.812796i
$254$	3.60109	−	5.83472i	0.225952	−	0.366103i
$255$		0			0
$256$	−4.55568	−	15.3377i	−0.284730	−	0.958608i
$257$	−16.6777	−	9.62887i	−1.04033	−	0.600633i	−0.120400	−	0.992725i	$-0.538418\pi$
$257$	−16.6777	−	9.62887i	−1.04033	−	0.600633i	−0.919926	+	0.392093i	$0.871751\pi$
$258$		0			0
$259$	−2.41564	+	9.01529i	−0.150101	+	0.560183i
$260$	2.33937	+	1.54044i	0.145081	+	0.0955340i
$261$		0			0
$262$	8.61429	−	28.7454i	0.532193	−	1.77590i
$263$	22.8254	−	13.1782i	1.40747	−	0.812605i	0.412329	−	0.911035i	$-0.364715\pi$
$263$	22.8254	−	13.1782i	1.40747	−	0.812605i	0.995144	+	0.0984300i	$0.0313821\pi$
$264$		0			0
$265$	−1.64235	−	0.948214i	−0.100889	−	0.0582483i
$266$	4.48478	−	4.22888i	0.274980	−	0.259289i
$267$		0			0
$268$	11.0207	+	12.3973i	0.673194	+	0.757287i
$269$	0.605506	+	0.605506i	0.0369184	+	0.0369184i	0.725325	−	0.688407i	$-0.241690\pi$
$269$	0.605506	+	0.605506i	0.0369184	+	0.0369184i	−0.688407	+	0.725325i	$0.741690\pi$
$270$		0			0
$271$		−	19.1084i		−	1.16075i	−0.814349	−	0.580376i	$-0.802906\pi$
$271$		−	19.1084i		−	1.16075i	0.814349	−	0.580376i	$-0.197094\pi$
$272$	21.4374	+	15.9956i	1.29983	+	0.969876i
$273$		0			0
$274$	0.243988	−	8.30804i	0.0147398	−	0.501907i
$275$	4.60819	+	17.1980i	0.277884	+	1.03708i
$276$		0			0
$277$	−1.82792	+	6.82191i	−0.109829	+	0.409889i	−0.998848	−	0.0479819i	$-0.984721\pi$
$277$	−1.82792	+	6.82191i	−0.109829	+	0.409889i	0.889019	+	0.457871i	$0.151388\pi$
$278$	−2.93102	+	9.78067i	−0.175791	+	0.586606i
$279$		0			0
$280$	−6.29781	−	7.51782i	−0.376366	−	0.449276i
$281$	11.8490	+	20.5230i	0.706849	+	1.22430i	0.966020	+	0.258467i	$0.0832174\pi$
$281$	11.8490	+	20.5230i	0.706849	+	1.22430i	−0.259171	+	0.965831i	$0.583449\pi$
$282$		0			0
$283$	−0.194826	−	0.727099i	−0.0115812	−	0.0432215i	0.959893	−	0.280365i	$-0.0904555\pi$
$283$	−0.194826	−	0.727099i	−0.0115812	−	0.0432215i	−0.971475	+	0.237143i	$0.923789\pi$
$284$	14.3953	−	7.21984i	0.854203	−	0.428419i
$285$		0			0
$286$	−8.62772	−	5.32488i	−0.510168	−	0.314867i
$287$	11.8699			0.700659
$288$		0			0
$289$	−27.7137			−1.63022
$290$	−3.96096	−	2.44463i	−0.232596	−	0.143554i
$291$		0			0
$292$	−17.3971	+	8.72536i	−1.01809	+	0.510613i
$293$	−5.31070	−	19.8198i	−0.310255	−	1.15789i	−0.928327	−	0.371765i	$-0.878753\pi$
$293$	−5.31070	−	19.8198i	−0.310255	−	1.15789i	0.618072	−	0.786121i	$-0.287914\pi$
$294$		0			0
$295$	0.414592	+	0.718095i	0.0241385	+	0.0418091i
$296$	−4.65044	+	3.89576i	−0.270301	+	0.226436i
$297$		0			0
$298$	−1.82617	+	6.09384i	−0.105787	+	0.353007i
$299$	−2.03907	+	7.60993i	−0.117923	+	0.440093i
$300$		0			0
$301$	10.0325	+	37.4417i	0.578262	+	2.15810i
$302$	−0.351624	+	11.9732i	−0.0202337	+	0.688979i
$303$		0			0
$304$	3.96497	−	0.576403i	0.227407	−	0.0330590i
$305$			1.62842i			0.0932432i
$306$		0			0
$307$	−15.3450	−	15.3450i	−0.875783	−	0.875783i	0.117312	−	0.993095i	$-0.462572\pi$
$307$	−15.3450	−	15.3450i	−0.875783	−	0.875783i	−0.993095	+	0.117312i	$0.962572\pi$
$308$	23.5849	+	26.5310i	1.34387	+	1.51174i
$309$		0			0
$310$	−4.67838	+	4.41144i	−0.265714	+	0.250553i
$311$	−0.576605	−	0.332903i	−0.0326963	−	0.0188772i	0.483563	−	0.875310i	$-0.339342\pi$
$311$	−0.576605	−	0.332903i	−0.0326963	−	0.0188772i	−0.516259	+	0.856432i	$0.672676\pi$
$312$		0			0
$313$	14.3283	−	8.27244i	0.809882	−	0.467586i	−0.0370327	−	0.999314i	$-0.511791\pi$
$313$	14.3283	−	8.27244i	0.809882	−	0.467586i	0.846915	+	0.531728i	$0.178457\pi$
$314$	−6.87202	+	22.9316i	−0.387811	+	1.29410i
$315$		0			0
$316$	23.1136	+	15.2199i	1.30024	+	0.856189i
$317$	1.75927	−	6.56570i	0.0988107	−	0.368767i	−0.898759	−	0.438443i	$-0.855530\pi$
$317$	1.75927	−	6.56570i	0.0988107	−	0.368767i	0.997570	+	0.0696766i	$0.0221967\pi$
$318$		0			0
$319$	14.5909	+	8.42404i	0.816931	+	0.471656i
$320$	−0.545277	−	6.35120i	−0.0304819	−	0.355043i
$321$		0			0
$322$	14.4876	−	23.4738i	0.807362	−	1.30814i
$323$	−4.73616	+	4.73616i	−0.263527	+	0.263527i
$324$		0			0
$325$	−5.42499	−	5.42499i	−0.300924	−	0.300924i
$326$	−6.31085	−	26.6597i	−0.349526	−	1.47654i
$327$		0			0
$328$	6.31645	+	4.43047i	0.348768	+	0.244632i
$329$	−5.35946	+	9.28286i	−0.295477	+	0.511781i
$330$		0			0
$331$	9.39568	+	2.51757i	0.516434	+	0.138378i	0.507616	−	0.861583i	$-0.330527\pi$
$331$	9.39568	+	2.51757i	0.516434	+	0.138378i	0.00881711	+	0.999961i	$0.497193\pi$
$332$	−1.27375	−	6.18565i	−0.0699059	−	0.339481i
$333$		0			0
$334$	−5.51427	−	10.2335i	−0.301728	−	0.559951i
$335$	3.30434	+	5.72328i	0.180535	+	0.312696i
$336$		0			0
$337$	13.5580	−	23.4832i	0.738553	−	1.27921i	−0.214593	−	0.976704i	$-0.568843\pi$
$337$	13.5580	−	23.4832i	0.738553	−	1.27921i	0.953147	−	0.302509i	$-0.0978241\pi$
$338$	−14.0100	−	0.411440i	−0.762041	−	0.0223794i
$339$		0			0
$340$	7.08004	+	7.96444i	0.383969	+	0.431933i
$341$	16.4581	−	16.4581i	0.891254	−	0.891254i
$342$		0			0
$343$	21.4761			1.15960
$344$	−8.63651	+	23.6689i	−0.465649	+	1.27614i
$345$		0			0
$346$	−10.0284	+	9.45620i	−0.539131	+	0.508368i
$347$	30.1679	−	8.08347i	1.61950	−	0.433944i	0.668645	−	0.743582i	$-0.266875\pi$
$347$	30.1679	−	8.08347i	1.61950	−	0.433944i	0.950854	+	0.309638i	$0.100208\pi$
$348$		0			0
$349$	−31.6714	−	8.48634i	−1.69533	−	0.454263i	−0.723576	−	0.690245i	$-0.757503\pi$
$349$	−31.6714	−	8.48634i	−1.69533	−	0.454263i	−0.971757	+	0.235982i	$0.924169\pi$
$350$	12.7425	+	23.6477i	0.681114	+	1.26402i
$351$		0			0
$352$	2.64771	+	22.9213i	0.141123	+	1.22171i
$353$	3.48989	−	2.01489i	0.185748	−	0.107242i	−0.404243	−	0.914652i	$-0.632465\pi$
$353$	3.48989	−	2.01489i	0.185748	−	0.107242i	0.589990	+	0.807410i	$0.299131\pi$
$354$		0			0
$355$	6.19752	−	1.66062i	0.328930	−	0.0881366i
$356$	−1.53431	−	3.05919i	−0.0813184	−	0.162137i
$357$		0			0
$358$	5.05795	−	1.19731i	0.267321	−	0.0632799i
$359$			14.8043i			0.781342i	0.920530	+	0.390671i	$0.127757\pi$
$359$			14.8043i			0.781342i	−0.920530	+	0.390671i	$0.872243\pi$
$360$		0			0
$361$		−	17.9967i		−	0.947193i
$362$	−3.19235	−	13.4858i	−0.167786	−	0.708800i
$363$		0			0
$364$	−14.5174	−	4.81925i	−0.760918	−	0.252597i
$365$	−7.48986	+	2.00690i	−0.392037	+	0.105046i
$366$		0			0
$367$	−2.66934	+	1.54114i	−0.139338	+	0.0804470i	−0.568049	−	0.822995i	$-0.692301\pi$
$367$	−2.66934	+	1.54114i	−0.139338	+	0.0804470i	0.428710	+	0.903442i	$0.358968\pi$
$368$	16.4711	−	7.08380i	0.858613	−	0.369269i
$369$		0			0
$370$	−2.12775	+	1.14653i	−0.110616	+	0.0596052i
$371$	10.0036	+	2.68045i	0.519361	+	0.139162i
$372$		0			0
$373$	28.2816	−	7.57804i	1.46437	−	0.392376i	0.563372	−	0.826204i	$-0.309504\pi$
$373$	28.2816	−	7.57804i	1.46437	−	0.392376i	0.900996	+	0.433828i	$0.142837\pi$
$374$	−26.4625	−	28.0638i	−1.36834	−	1.45114i
$375$		0			0
$376$	−6.31683	+	2.93935i	−0.325766	+	0.151585i
$377$	−7.25990			−0.373904
$378$		0			0
$379$	−13.0654	+	13.0654i	−0.671124	+	0.671124i	−0.957975	−	0.286851i	$-0.907392\pi$
$379$	−13.0654	+	13.0654i	−0.671124	+	0.671124i	0.286851	+	0.957975i	$0.407392\pi$
$380$	1.59354	+	0.0936778i	0.0817468	+	0.00480557i
$381$		0			0
$382$	−0.578483	+	19.6980i	−0.0295978	+	1.00784i
$383$	−1.66394	+	2.88203i	−0.0850235	+	0.147265i	−0.905401	−	0.424557i	$-0.860430\pi$
$383$	−1.66394	+	2.88203i	−0.0850235	+	0.147265i	0.820378	+	0.571822i	$0.193763\pi$
$384$		0			0
$385$	7.07147	+	12.2481i	0.360396	+	0.624223i
$386$	3.33886	−	1.79913i	0.169943	−	0.0915734i
$387$		0			0
$388$	−8.06378	+	12.2459i	−0.409376	+	0.621694i
$389$	6.62255	+	1.77451i	0.335777	+	0.0899711i	0.422768	−	0.906238i	$-0.361059\pi$
$389$	6.62255	+	1.77451i	0.335777	+	0.0899711i	−0.0869912	+	0.996209i	$0.527725\pi$
$390$		0			0
$391$	−14.9867	+	25.9577i	−0.757908	+	1.31274i
$392$	27.6374	+	19.3854i	1.39590	+	0.979110i
$393$		0			0
$394$	27.7070	−	6.55876i	1.39586	−	0.330426i
$395$	7.79645	+	7.79645i	0.392282	+	0.392282i
$396$		0			0
$397$	2.33820	−	2.33820i	0.117351	−	0.117351i	−0.645993	−	0.763344i	$-0.723556\pi$
$397$	2.33820	−	2.33820i	0.117351	−	0.117351i	0.763344	+	0.645993i	$0.223556\pi$
$398$	−9.50828	−	5.86834i	−0.476607	−	0.294153i
$399$		0			0
$400$	−2.04577	+	17.3400i	−0.102289	+	0.867002i
$401$	−3.32787	−	1.92135i	−0.166186	−	0.0959474i	0.414600	−	0.910004i	$-0.363921\pi$
$401$	−3.32787	−	1.92135i	−0.166186	−	0.0959474i	−0.580786	+	0.814056i	$0.697255\pi$
$402$		0			0
$403$	−2.59579	+	9.68764i	−0.129306	+	0.482575i
$404$	5.85714	+	28.4438i	0.291404	+	1.41513i
$405$		0			0
$406$	24.3492	+	7.29686i	1.20843	+	0.362137i
$407$	7.57656	−	4.37433i	0.375556	−	0.216828i
$408$		0			0
$409$	4.36888	+	2.52237i	0.216027	+	0.124723i	0.604109	−	0.796901i	$-0.293529\pi$
$409$	4.36888	+	2.52237i	0.216027	+	0.124723i	−0.388082	+	0.921625i	$0.626862\pi$
$410$	2.10882	+	2.23643i	0.104147	+	0.110449i
$411$		0			0
$412$	−29.7034	−	1.74614i	−1.46338	−	0.0860262i
$413$	−3.20193	−	3.20193i	−0.157557	−	0.157557i
$414$		0			0
$415$		−	2.51613i		−	0.123512i
$416$	−5.92649	−	7.98316i	−0.290570	−	0.391407i
$417$		0			0
$418$	−5.77552	−	0.169614i	−0.282490	−	0.00829607i
$419$	−5.72083	−	21.3504i	−0.279481	−	1.04304i	−0.952779	−	0.303665i	$-0.901790\pi$
$419$	−5.72083	−	21.3504i	−0.279481	−	1.04304i	0.673298	−	0.739371i	$-0.264877\pi$
$420$		0			0
$421$	2.13099	−	7.95298i	0.103858	−	0.387604i	−0.894355	−	0.447358i	$-0.852365\pi$
$421$	2.13099	−	7.95298i	0.103858	−	0.387604i	0.998213	+	0.0597538i	$0.0190316\pi$
$422$	−18.5279	−	5.55234i	−0.901923	−	0.270284i
$423$		0			0
$424$	4.32283	+	5.16024i	0.209935	+	0.250603i
$425$	−14.5943	−	25.2780i	−0.707926	−	1.22616i
$426$		0			0
$427$	−2.30165	−	8.58988i	−0.111385	−	0.415693i
$428$	−0.0868662	+	0.261673i	−0.00419884	+	0.0126485i
$429$		0			0
$430$	−5.27207	+	8.54215i	−0.254242	+	0.411939i
$431$	1.08094			0.0520671			0.0260336	−	0.999661i	$-0.491712\pi$
$431$	1.08094			0.0520671			0.0260336	+	0.999661i	$0.491712\pi$
$432$		0			0
$433$	−15.5307			−0.746359			−0.373179	−	0.927759i	$-0.621732\pi$
$433$	−15.5307			−0.746359			−0.373179	+	0.927759i	$0.621732\pi$
$434$	18.4431	−	29.8827i	0.885297	−	1.43442i
$435$		0			0
$436$	23.6404	+	7.84777i	1.13217	+	0.375840i
$437$	1.16207	+	4.33690i	0.0555893	+	0.207462i
$438$		0			0
$439$	−2.26321	−	3.91999i	−0.108017	−	0.187091i	0.806950	−	0.590620i	$-0.201117\pi$
$439$	−2.26321	−	3.91999i	−0.108017	−	0.187091i	−0.914967	+	0.403529i	$0.867783\pi$
$440$	−0.808634	+	9.15717i	−0.0385501	+	0.436551i
$441$		0			0
$442$	15.9215	+	4.77127i	0.757308	+	0.226946i
$443$	6.82958	−	25.4883i	0.324483	−	1.21099i	−0.590347	−	0.807149i	$-0.701009\pi$
$443$	6.82958	−	25.4883i	0.324483	−	1.21099i	0.914830	−	0.403838i	$-0.132324\pi$
$444$		0			0
$445$	−0.352904	−	1.31706i	−0.0167293	−	0.0624345i
$446$	39.7254	+	1.16664i	1.88105	+	0.0552420i
$447$		0			0
$448$	11.8533	+	32.7317i	0.560014	+	1.54643i
$449$			5.94688i			0.280650i	0.990105	+	0.140325i	$0.0448148\pi$
$449$			5.94688i			0.280650i	−0.990105	+	0.140325i	$0.955185\pi$
$450$		0			0
$451$	−7.86752	−	7.86752i	−0.370467	−	0.370467i
$452$	0.978552	−	16.6460i	0.0460272	−	0.782962i
$453$		0			0
$454$	0.492173	+	0.521956i	0.0230988	+	0.0244966i
$455$	−5.27777	−	3.04712i	−0.247426	−	0.142851i
$456$		0			0
$457$	−18.2318	+	10.5261i	−0.852846	+	0.492391i	−0.861610	−	0.507571i	$-0.830544\pi$
$457$	−18.2318	+	10.5261i	−0.852846	+	0.492391i	0.00876413	+	0.999962i	$0.497210\pi$
$458$	20.5015	+	6.14380i	0.957974	+	0.287081i
$459$		0			0
$460$	6.99660	−	1.44074i	0.326218	−	0.0671747i
$461$	−10.2518	+	38.2603i	−0.477475	+	1.78196i	0.134314	+	0.990939i	$0.457117\pi$
$461$	−10.2518	+	38.2603i	−0.477475	+	1.78196i	−0.611788	+	0.791021i	$0.709550\pi$
$462$		0			0
$463$	9.98020	+	5.76207i	0.463819	+	0.267786i	0.713649	−	0.700504i	$-0.247041\pi$
$463$	9.98020	+	5.76207i	0.463819	+	0.267786i	−0.249829	+	0.968290i	$0.580375\pi$
$464$	10.2336	+	12.9714i	0.475085	+	0.602180i
$465$		0			0
$466$	18.6498	+	11.5103i	0.863934	+	0.533205i
$467$	25.1476	−	25.1476i	1.16369	−	1.16369i	0.180032	−	0.983661i	$-0.442380\pi$
$467$	25.1476	−	25.1476i	1.16369	−	1.16369i	0.983661	−	0.180032i	$-0.0576202\pi$
$468$		0			0
$469$	−25.5197	−	25.5197i	−1.17839	−	1.17839i
$470$	−2.70116	+	0.639416i	−0.124595	+	0.0294941i
$471$		0			0
$472$	−0.508748	−	2.89901i	−0.0234170	−	0.133438i
$473$	18.1672	−	31.4664i	0.835327	−	1.44683i
$474$		0			0
$475$	−4.22335	−	1.13164i	−0.193780	−	0.0519233i
$476$	−48.6041	−	32.0051i	−2.22776	−	1.46695i
$477$		0			0
$478$	−18.9662	+	10.2199i	−0.867493	+	0.467445i
$479$	−2.64784	−	4.58619i	−0.120983	−	0.209548i	0.799173	−	0.601101i	$-0.205271\pi$
$479$	−2.64784	−	4.58619i	−0.120983	−	0.209548i	−0.920155	+	0.391553i	$0.871938\pi$
$480$		0			0
$481$	−1.88491	+	3.26477i	−0.0859447	+	0.148861i
$482$	−0.756138	+	25.7473i	−0.0344412	+	1.17276i
$483$		0			0
$484$	0.661654	−	11.2553i	0.0300752	−	0.511604i
$485$	−4.13069	+	4.13069i	−0.187565	+	0.187565i
$486$		0			0
$487$	1.85543			0.0840775			0.0420387	−	0.999116i	$-0.486615\pi$
$487$	1.85543			0.0840775			0.0420387	+	0.999116i	$0.486615\pi$
$488$	1.98139	−	5.43011i	0.0896933	−	0.245810i
$489$		0			0
$490$	9.22707	+	9.78542i	0.416836	+	0.442060i
$491$	3.49505	−	0.936497i	0.157730	−	0.0422635i	−0.179090	−	0.983833i	$-0.557315\pi$
$491$	3.49505	−	0.936497i	0.157730	−	0.0422635i	0.336820	+	0.941569i	$0.390649\pi$
$492$		0			0
$493$	−26.6792	−	7.14866i	−1.20157	−	0.321960i
$494$	2.19182	−	1.18105i	0.0986144	−	0.0531380i
$495$		0			0
$496$	20.9681	−	9.01786i	0.941495	−	0.404914i
$497$	−30.3446	+	17.5194i	−1.36114	+	0.785854i
$498$		0			0
$499$	−12.0253	+	3.22216i	−0.538325	+	0.144244i	−0.517730	−	0.855544i	$-0.673223\pi$
$499$	−12.0253	+	3.22216i	−0.538325	+	0.144244i	−0.0205953	+	0.999788i	$0.506556\pi$
$500$	−4.70211	+	14.1645i	−0.210285	+	0.633456i
$501$		0			0
$502$	1.00626	+	4.25088i	0.0449118	+	0.189726i
$503$		−	16.6233i		−	0.741198i	−0.928793	−	0.370599i	$-0.879152\pi$
$503$		−	16.6233i		−	0.741198i	0.928793	−	0.370599i	$-0.120848\pi$
$504$		0			0
$505$			11.5701i			0.514862i
$506$	−25.1613	+	5.95614i	−1.11855	+	0.264783i
$507$		0			0
$508$	−8.66753	+	4.34713i	−0.384559	+	0.192873i
$509$	−15.1091	+	4.04848i	−0.669700	+	0.179446i	−0.577620	−	0.816306i	$-0.696018\pi$
$509$	−15.1091	+	4.04848i	−0.669700	+	0.179446i	−0.0920802	+	0.995752i	$0.529352\pi$
$510$		0			0
$511$	36.6722	−	21.1727i	1.62228	−	0.936624i
$512$	−5.90958	+	21.8421i	−0.261169	+	0.965293i
$513$		0			0
$514$	12.9191	+	23.9754i	0.569835	+	1.05751i
$515$	−11.4506	−	3.06819i	−0.504575	−	0.135200i
$516$		0			0
$517$	9.70511	−	2.60048i	0.426830	−	0.114369i
$518$	9.60328	−	9.05532i	0.421944	−	0.397868i
$519$		0			0
$520$	−1.67117	−	3.59143i	−0.0732856	−	0.157495i
$521$	40.4461			1.77198			0.885988	−	0.463709i	$-0.153482\pi$
$521$	40.4461			1.77198			0.885988	+	0.463709i	$0.153482\pi$
$522$		0			0
$523$	7.69126	−	7.69126i	0.336315	−	0.336315i	−0.518663	−	0.854979i	$-0.673570\pi$
$523$	7.69126	−	7.69126i	0.336315	−	0.336315i	0.854979	+	0.518663i	$0.173570\pi$
$524$	−31.7178	+	28.1957i	−1.38560	+	1.23173i
$525$		0			0
$526$	−37.2576	−	1.09417i	−1.62451	−	0.0477080i
$527$	−19.0784	+	33.0448i	−0.831069	+	1.43945i
$528$		0			0
$529$	−1.45387	−	2.51818i	−0.0632119	−	0.109486i
$530$	1.27222	+	2.36100i	0.0552616	+	0.102555i
$531$		0			0
$532$	−8.53827	+	1.75820i	−0.370181	+	0.0762275i
$533$	4.63102	+	1.24088i	0.200592	+	0.0537484i
$534$		0			0
$535$	−0.0549239	+	0.0951309i	−0.00237457	+	0.00411287i
$536$	−4.05477	−	23.1053i	−0.175139	−	0.997998i
$537$		0			0
$538$	−0.278960	−	1.17844i	−0.0120268	−	0.0508063i
$539$	−34.4241	−	34.4241i	−1.48275	−	1.48275i
$540$		0			0
$541$	−17.0176	+	17.0176i	−0.731643	+	0.731643i	−0.970945	−	0.239302i	$-0.923081\pi$
$541$	−17.0176	+	17.0176i	−0.731643	+	0.731643i	0.239302	+	0.970945i	$0.423081\pi$
$542$	−14.1928	+	22.9962i	−0.609635	+	0.987771i
$543$		0			0
$544$	−13.9182	−	35.1728i	−0.596739	−	1.50802i
$545$	8.59443	+	4.96200i	0.368145	+	0.212549i
$546$		0			0
$547$	−5.77510	+	21.5530i	−0.246926	+	0.921539i	0.725480	+	0.688243i	$0.241618\pi$
$547$	−5.77510	+	21.5530i	−0.246926	+	0.921539i	−0.972406	+	0.233296i	$0.925049\pi$
$548$	−6.46447	+	9.81718i	−0.276148	+	0.419369i
$549$		0			0
$550$	7.22812	−	24.1199i	0.308208	−	1.02847i
$551$	−3.58311	+	2.06871i	−0.152645	+	0.0881299i
$552$		0			0
$553$	−52.1457	−	30.1064i	−2.21746	−	1.28025i
$554$	7.26683	−	6.85219i	0.308738	−	0.291122i
$555$		0			0
$556$	10.7920	−	9.59362i	0.457683	−	0.406860i
$557$	11.6516	+	11.6516i	0.493695	+	0.493695i	0.909468	−	0.415773i	$-0.136489\pi$
$557$	11.6516	+	11.6516i	0.493695	+	0.493695i	−0.415773	+	0.909468i	$0.636489\pi$
$558$		0			0
$559$			15.6566i			0.662203i
$560$	1.99527	+	13.7251i	0.0843157	+	0.579992i
$561$		0			0
$562$	0.983800	−	33.4994i	0.0414991	−	1.41309i
$563$	1.30826	+	4.88249i	0.0551365	+	0.205772i	0.987999	−	0.154460i	$-0.0493639\pi$
$563$	1.30826	+	4.88249i	0.0551365	+	0.205772i	−0.932862	+	0.360233i	$0.882697\pi$
$564$		0			0
$565$	1.71944	−	6.41702i	0.0723372	−	0.269966i
$566$	−0.305591	+	1.01974i	−0.0128450	+	0.0428629i
$567$		0			0
$568$	−22.6867	−	2.00338i	−0.951913	−	0.0840598i
$569$	−2.79764	−	4.84565i	−0.117283	−	0.203140i	0.801407	−	0.598119i	$-0.204085\pi$
$569$	−2.79764	−	4.84565i	−0.117283	−	0.203140i	−0.918690	+	0.394979i	$0.870752\pi$
$570$		0			0
$571$	−2.31993	−	8.65808i	−0.0970859	−	0.362329i	0.900242	−	0.435391i	$-0.143390\pi$
$571$	−2.31993	−	8.65808i	−0.0970859	−	0.362329i	−0.997327	+	0.0730613i	$0.976723\pi$
$572$	6.42804	+	12.8166i	0.268770	+	0.535887i
$573$		0			0
$574$	−14.2850	−	8.81643i	−0.596243	−	0.367991i
$575$	−19.5662			−0.815966
$576$		0			0
$577$	16.6893			0.694785			0.347393	−	0.937720i	$-0.387067\pi$
$577$	16.6893			0.694785			0.347393	+	0.937720i	$0.387067\pi$
$578$	33.3524	+	20.5845i	1.38728	+	0.856203i
$579$		0			0
$580$	2.95109	+	5.88404i	0.122537	+	0.244321i
$581$	3.55636	+	13.2725i	0.147543	+	0.550637i
$582$		0			0
$583$	−4.85387	−	8.40714i	−0.201027	−	0.348188i
$584$	27.4175	+	2.42113i	1.13454	+	0.100187i
$585$		0			0
$586$	−8.33004	+	27.7969i	−0.344111	+	1.14828i
$587$	−1.34545	+	5.02128i	−0.0555325	+	0.207250i	−0.988118	−	0.153700i	$-0.950881\pi$
$587$	−1.34545	+	5.02128i	−0.0555325	+	0.207250i	0.932585	+	0.360950i	$0.117548\pi$
$588$		0			0
$589$	1.47934	+	5.52099i	0.0609553	+	0.227488i
$590$	0.0344230	−	1.17214i	0.00141717	−	0.0482562i
$591$		0			0
$592$	8.49020	−	1.23425i	0.348945	−	0.0507275i
$593$		−	44.7927i		−	1.83942i	−0.392602	−	0.919708i	$-0.628425\pi$
$593$		−	44.7927i		−	1.83942i	0.392602	−	0.919708i	$-0.371575\pi$
$594$		0			0
$595$	−16.3947	−	16.3947i	−0.672116	−	0.672116i
$596$	6.72395	−	5.97729i	0.275424	−	0.244840i
$597$		0			0
$598$	8.10625	−	7.64371i	0.331489	−	0.312575i
$599$	27.1165	+	15.6557i	1.10795	+	0.639674i	0.938297	−	0.345830i	$-0.112403\pi$
$599$	27.1165	+	15.6557i	1.10795	+	0.639674i	0.169651	+	0.985504i	$0.445736\pi$
$600$		0			0
$601$	15.4248	−	8.90549i	0.629189	−	0.363262i	−0.151249	−	0.988496i	$-0.548330\pi$
$601$	15.4248	−	8.90549i	0.629189	−	0.363262i	0.780438	+	0.625233i	$0.214996\pi$
$602$	15.7363	−	52.5112i	0.641364	−	2.14020i
$603$		0			0
$604$	9.31630	−	14.1481i	0.379075	−	0.575677i
$605$	1.16261	−	4.33891i	0.0472667	−	0.176402i
$606$		0			0
$607$	29.3159	+	16.9255i	1.18989	+	0.686986i	0.958283	−	0.285823i	$-0.0922668\pi$
$607$	29.3159	+	16.9255i	1.18989	+	0.686986i	0.231612	+	0.972808i	$0.425600\pi$
$608$	−5.19981	−	2.25132i	−0.210880	−	0.0913031i
$609$		0			0
$610$	1.20952	−	1.95974i	0.0489720	−	0.0793476i
$611$	−3.06141	+	3.06141i	−0.123852	+	0.123852i
$612$		0			0
$613$	−11.3734	−	11.3734i	−0.459367	−	0.459367i	0.439081	−	0.898448i	$-0.355304\pi$
$613$	−11.3734	−	11.3734i	−0.459367	−	0.459367i	−0.898448	+	0.439081i	$0.855304\pi$
$614$	7.06951	+	29.8646i	0.285302	+	1.20524i
$615$		0			0
$616$	−8.67744	−	49.4467i	−0.349624	−	1.99226i
$617$	−18.0269	+	31.2236i	−0.725738	+	1.25701i	0.232932	+	0.972493i	$0.425168\pi$
$617$	−18.0269	+	31.2236i	−0.725738	+	1.25701i	−0.958670	+	0.284521i	$0.908165\pi$
$618$		0			0
$619$	16.0209	+	4.29280i	0.643936	+	0.172542i	0.565986	−	0.824415i	$-0.308496\pi$
$619$	16.0209	+	4.29280i	0.643936	+	0.172542i	0.0779503	+	0.996957i	$0.475162\pi$
$620$	8.90686	−	1.83410i	0.357708	−	0.0736591i
$621$		0			0
$622$	0.446656	+	0.828912i	0.0179093	+	0.0332363i
$623$	3.72312	+	6.44863i	0.149163	+	0.258359i
$624$		0			0
$625$	7.93964	−	13.7519i	0.317585	−	0.550074i
$626$	−23.3879	−	0.686848i	−0.934769	−	0.0274520i
$627$		0			0
$628$	25.3027	−	22.4930i	1.00969	−	0.897569i
$629$	−10.1416	+	10.1416i	−0.404371	+	0.404371i
$630$		0			0
$631$	24.4330			0.972664			0.486332	−	0.873774i	$-0.338335\pi$
$631$	24.4330			0.972664			0.486332	+	0.873774i	$0.338335\pi$
$632$	−16.5116	−	35.4843i	−0.656795	−	1.41149i
$633$		0			0
$634$	−6.99392	+	6.59485i	−0.277764	+	0.261915i
$635$	−3.73158	+	0.999874i	−0.148083	+	0.0396788i
$636$		0			0
$637$	20.2629	+	5.42943i	0.802845	+	0.215122i
$638$	−11.3025	−	20.9754i	−0.447471	−	0.830425i
$639$		0			0
$640$	−4.06117	+	8.04843i	−0.160532	+	0.318142i
$641$	40.0952	−	23.1490i	1.58366	−	0.914329i	0.589346	−	0.807881i	$-0.299385\pi$
$641$	40.0952	−	23.1490i	1.58366	−	0.914329i	0.994318	−	0.106448i	$-0.0339479\pi$
$642$		0			0
$643$	10.5870	−	2.83678i	0.417511	−	0.111872i	−0.0439466	−	0.999034i	$-0.513993\pi$
$643$	10.5870	−	2.83678i	0.417511	−	0.111872i	0.461458	+	0.887162i	$0.347326\pi$
$644$	−34.8705	+	17.4890i	−1.37409	+	0.689163i
$645$		0			0
$646$	9.21759	−	2.18198i	0.362661	−	0.0858487i
$647$		−	10.0479i		−	0.395025i	−0.980300	−	0.197512i	$-0.936714\pi$
$647$		−	10.0479i		−	0.395025i	0.980300	−	0.197512i	$-0.0632863\pi$
$648$		0			0
$649$			4.24456i			0.166614i
$650$	2.49932	+	10.5582i	0.0980316	+	0.414127i
$651$		0			0
$652$	−12.2068	+	36.7713i	−0.478053	+	1.44008i
$653$	25.5935	−	6.85777i	1.00155	−	0.268365i	0.279457	−	0.960158i	$-0.409846\pi$
$653$	25.5935	−	6.85777i	1.00155	−	0.268365i	0.722096	+	0.691793i	$0.243179\pi$
$654$		0			0
$655$	−14.6427	+	8.45394i	−0.572136	+	0.330323i
$656$	−4.31085	−	10.0235i	−0.168310	−	0.391351i
$657$		0			0
$658$	13.3448	−	7.19079i	0.520234	−	0.280326i
$659$	−6.76233	−	1.81196i	−0.263423	−	0.0705840i	0.124690	−	0.992196i	$-0.460206\pi$
$659$	−6.76233	−	1.81196i	−0.263423	−	0.0705840i	−0.388113	+	0.921612i	$0.626873\pi$
$660$		0			0
$661$	20.1902	−	5.40993i	0.785306	−	0.210422i	0.156183	−	0.987728i	$-0.450081\pi$
$661$	20.1902	−	5.40993i	0.785306	−	0.210422i	0.629123	+	0.777306i	$0.283414\pi$
$662$	−9.43740	−	10.0085i	−0.366795	−	0.388990i
$663$		0			0
$664$	−3.06151	+	8.39026i	−0.118810	+	0.325605i
$665$	−3.47311			−0.134681
$666$		0			0
$667$	−13.0920	+	13.0920i	−0.506926	+	0.506926i
$668$	−0.964757	+	16.4113i	−0.0373276	+	0.634974i
$669$		0			0
$670$	0.274354	−	9.34205i	0.0105992	−	0.360915i
$671$	−4.16791	+	7.21904i	−0.160901	+	0.278688i
$672$		0			0
$673$	3.86200	+	6.68918i	0.148869	+	0.257849i	0.930810	−	0.365504i	$-0.119103\pi$
$673$	3.86200	+	6.68918i	0.148869	+	0.257849i	−0.781941	+	0.623353i	$0.785770\pi$
$674$	−33.7588	+	18.1908i	−1.30034	+	0.700684i
$675$		0			0
$676$	16.5548	+	10.9011i	0.636724	+	0.419274i
$677$	−7.62160	−	2.04220i	−0.292922	−	0.0784882i	0.109366	−	0.994002i	$-0.465118\pi$
$677$	−7.62160	−	2.04220i	−0.292922	−	0.0784882i	−0.402287	+	0.915513i	$0.631785\pi$
$678$		0			0
$679$	15.9508	−	27.6277i	0.612137	−	1.06025i
$680$	−2.60492	−	14.8436i	−0.0998940	−	0.569227i
$681$		0			0
$682$	−32.0309	+	7.58232i	−1.22653	+	0.290342i
$683$	23.0318	+	23.0318i	0.881288	+	0.881288i	0.993666	−	0.112378i	$-0.0358467\pi$
$683$	23.0318	+	23.0318i	0.881288	+	0.881288i	−0.112378	+	0.993666i	$0.535847\pi$
$684$		0			0
$685$	−3.31144	+	3.31144i	−0.126524	+	0.126524i
$686$	−25.8456	−	15.9515i	−0.986790	−	0.609029i
$687$		0			0
$688$	27.9738	−	22.0697i	1.06649	−	0.841400i
$689$	3.62267	+	2.09155i	0.138013	+	0.0796816i
$690$		0			0
$691$	−6.66520	+	24.8749i	−0.253556	+	0.946285i	0.715332	+	0.698785i	$0.246276\pi$
$691$	−6.66520	+	24.8749i	−0.253556	+	0.946285i	−0.968888	+	0.247500i	$0.920391\pi$
$692$	19.0924	−	3.93151i	0.725785	−	0.149453i
$693$		0			0
$694$	−42.3099	−	12.6792i	−1.60606	−	0.481297i
$695$	4.98218	−	2.87646i	0.188985	−	0.109111i
$696$		0			0
$697$	15.7965	+	9.12014i	0.598337	+	0.345450i
$698$	31.8120	+	33.7371i	1.20410	+	1.27697i
$699$		0			0
$700$	2.22938	−	37.9236i	0.0842625	−	1.43338i
$701$	−35.0396	−	35.0396i	−1.32343	−	1.32343i	−0.910983	−	0.412443i	$-0.864675\pi$
$701$	−35.0396	−	35.0396i	−1.32343	−	1.32343i	−0.412443	−	0.910983i	$-0.635325\pi$
$702$		0			0
$703$			2.14843i			0.0810295i
$704$	13.8385	−	29.5514i	0.521557	−	1.11376i
$705$		0			0
$706$	−5.69650	−	0.167293i	−0.214391	−	0.00629616i
$707$	−16.3534	−	61.0318i	−0.615034	−	2.29534i
$708$		0			0
$709$	−12.2110	+	45.5722i	−0.458595	+	1.71150i	0.218702	+	0.975792i	$0.429818\pi$
$709$	−12.2110	+	45.5722i	−0.458595	+	1.71150i	−0.677297	+	0.735710i	$0.736849\pi$
$710$	−8.69190	−	2.60474i	−0.326201	−	0.0977543i
$711$		0			0
$712$	−0.425744	+	4.82123i	−0.0159554	+	0.180683i
$713$	12.7890	+	22.1512i	0.478951	+	0.829568i
$714$		0			0
$715$	1.47850	+	5.51784i	0.0552928	+	0.206356i
$716$	−6.97635	−	2.31590i	−0.260719	−	0.0865492i
$717$		0			0
$718$	10.9960	−	17.8164i	0.410366	−	0.664902i
$719$	−26.0582			−0.971806			−0.485903	−	0.874013i	$-0.661509\pi$
$719$	−26.0582			−0.971806			−0.485903	+	0.874013i	$0.661509\pi$
$720$		0			0
$721$	64.7383			2.41098
$722$	−13.3671	+	21.6583i	−0.497472	+	0.806038i
$723$		0			0
$724$	−6.17480	+	18.6008i	−0.229484	+	0.691293i
$725$	−4.66655	−	17.4158i	−0.173311	−	0.646807i
$726$		0			0
$727$	−4.96698	−	8.60307i	−0.184215	−	0.319070i	0.759097	−	0.650978i	$-0.225641\pi$
$727$	−4.96698	−	8.60307i	−0.184215	−	0.319070i	−0.943312	+	0.331908i	$0.892308\pi$
$728$	13.8916	+	16.5826i	0.514856	+	0.614593i
$729$		0			0
$730$	10.5044	+	3.14790i	0.388785	+	0.116509i
$731$	−15.4167	+	57.5359i	−0.570207	+	2.12804i
$732$		0			0
$733$	3.40512	+	12.7081i	0.125771	+	0.469384i	0.999866	−	0.0163712i	$-0.00521135\pi$
$733$	3.40512	+	12.7081i	0.125771	+	0.469384i	−0.874095	+	0.485755i	$0.838545\pi$
$734$	4.35713	+	0.127959i	0.160825	+	0.00472305i
$735$		0			0
$736$	−25.0838	−	3.70888i	−0.924601	−	0.136711i
$737$			33.8295i			1.24613i
$738$		0			0
$739$	−32.6637	−	32.6637i	−1.20155	−	1.20155i	−0.973694	−	0.227861i	$-0.926827\pi$
$739$	−32.6637	−	32.6637i	−1.20155	−	1.20155i	−0.227861	−	0.973694i	$-0.573173\pi$
$740$	3.41225	+	0.200593i	0.125437	+	0.00737393i
$741$		0			0
$742$	−10.0480	−	10.6560i	−0.368874	−	0.391195i
$743$	8.76936	+	5.06299i	0.321717	+	0.185743i	0.652157	−	0.758084i	$-0.273864\pi$
$743$	8.76936	+	5.06299i	0.321717	+	0.185743i	−0.330441	+	0.943827i	$0.607197\pi$
$744$		0			0
$745$	3.10414	−	1.79218i	0.113727	−	0.0656603i
$746$	−39.6644	−	11.8864i	−1.45222	−	0.435193i
$747$		0			0
$748$	11.0020	+	53.4287i	0.402274	+	1.95355i
$749$	0.155261	−	0.579443i	0.00567312	−	0.0211724i
$750$		0			0
$751$	−22.6187	−	13.0589i	−0.825368	−	0.476526i	0.0268964	−	0.999638i	$-0.491438\pi$
$751$	−22.6187	−	13.0589i	−0.825368	−	0.476526i	−0.852264	+	0.523112i	$0.824771\pi$
$752$	9.78527	+	1.15446i	0.356832	+	0.0420990i
$753$		0			0
$754$	8.73699	+	5.39232i	0.318183	+	0.196377i
$755$	4.77230	−	4.77230i	0.173682	−	0.173682i
$756$		0			0
$757$	2.39808	+	2.39808i	0.0871596	+	0.0871596i	0.749342	−	0.662183i	$-0.230370\pi$
$757$	2.39808	+	2.39808i	0.0871596	+	0.0871596i	−0.662183	+	0.749342i	$0.730370\pi$
$758$	25.4281	−	6.01930i	0.923589	−	0.218631i
$759$		0			0
$760$	−1.84818	−	1.29635i	−0.0670406	−	0.0470234i
$761$	23.1857	−	40.1589i	0.840482	−	1.45576i	−0.0490055	−	0.998799i	$-0.515605\pi$
$761$	23.1857	−	40.1589i	0.840482	−	1.45576i	0.889488	−	0.456959i	$-0.151061\pi$
$762$		0			0
$763$	−52.3487	−	14.0268i	−1.89515	−	0.507804i
$764$	15.3269	−	23.2760i	0.554509	−	0.842098i
$765$		0			0
$766$	4.14313	−	2.23251i	0.149697	−	0.0806639i
$767$	−0.914499	−	1.58396i	−0.0330206	−	0.0571934i
$768$		0			0
$769$	−7.38255	+	12.7870i	−0.266222	+	0.461109i	−0.967883	−	0.251401i	$-0.919109\pi$
$769$	−7.38255	+	12.7870i	−0.266222	+	0.461109i	0.701661	+	0.712511i	$0.252442\pi$
$770$	0.587134	−	19.9925i	0.0211588	−	0.720480i
$771$		0			0
$772$	−5.35450	−	0.314770i	−0.192713	−	0.0113288i
$773$	−22.1409	+	22.1409i	−0.796353	+	0.796353i	−0.982518	−	0.186165i	$-0.940394\pi$
$773$	−22.1409	+	22.1409i	−0.796353	+	0.796353i	0.186165	+	0.982518i	$0.440394\pi$
$774$		0			0
$775$	−24.9083			−0.894731
$776$	18.8002	−	8.74810i	0.674887	−	0.314038i
$777$		0			0
$778$	−6.65195	−	7.05448i	−0.238484	−	0.252915i
$779$	2.63922	−	0.707177i	0.0945599	−	0.0253372i
$780$		0			0
$781$	31.7248	+	8.50064i	1.13520	+	0.304177i
$782$	37.3160	−	20.1076i	1.33442	−	0.719046i
$783$		0			0
$784$	−18.8620	−	43.8574i	−0.673642	−	1.56633i
$785$	11.6811	−	6.74410i	0.416917	−	0.240707i
$786$		0			0
$787$	−4.18136	+	1.12039i	−0.149050	+	0.0399377i	−0.332572	−	0.943078i	$-0.607917\pi$
$787$	−4.18136	+	1.12039i	−0.149050	+	0.0399377i	0.183523	+	0.983015i	$0.441250\pi$
$788$	−38.2158	−	12.6863i	−1.36138	−	0.451930i
$789$		0			0
$790$	−3.59187	−	15.1736i	−0.127793	−	0.539851i
$791$			36.2799i			1.28996i
$792$		0			0
$793$		−	3.59194i		−	0.127553i
$794$	−4.55064	+	1.07722i	−0.161496	+	0.0382292i
$795$		0			0
$796$	7.08409	+	14.1246i	0.251089	+	0.500634i
$797$	−51.5141	+	13.8032i	−1.82472	+	0.488933i	−0.997352	−	0.0727237i	$-0.976831\pi$
$797$	−51.5141	+	13.8032i	−1.82472	+	0.488933i	−0.827370	+	0.561657i	$0.810164\pi$
$798$		0			0
$799$	−14.2648	+	8.23579i	−0.504652	+	0.291361i
$800$	15.3414	−	19.3485i	0.542400	−	0.684074i
$801$		0			0
$802$	2.57787	+	4.78405i	0.0910277	+	0.168931i
$803$	−38.3403	−	10.2732i	−1.35300	−	0.362535i
$804$		0			0
$805$	−15.0126	+	4.02261i	−0.529124	+	0.141778i
$806$	10.3195	−	9.73064i	0.363488	−	0.342747i
$807$		0			0
$808$	14.0779	−	38.5814i	0.495260	−	1.35729i
$809$	−30.1140			−1.05875			−0.529375	−	0.848388i	$-0.677574\pi$
$809$	−30.1140			−1.05875			−0.529375	+	0.848388i	$0.677574\pi$
$810$		0			0
$811$	20.5672	−	20.5672i	0.722214	−	0.722214i	−0.246842	−	0.969056i	$-0.579393\pi$
$811$	20.5672	−	20.5672i	0.722214	−	0.722214i	0.969056	+	0.246842i	$0.0793929\pi$
$812$	−23.8836	−	26.8670i	−0.838148	−	0.942846i
$813$		0			0
$814$	−12.3671	−	0.363194i	−0.433468	−	0.0127299i
$815$	−7.71810	+	13.3681i	−0.270353	+	0.468265i
$816$		0			0
$817$	4.46135	+	7.72728i	0.156083	+	0.270343i
$818$	−3.38426	−	6.28057i	−0.118328	−	0.219595i
$819$		0			0
$820$	−0.876761	−	4.25779i	−0.0306178	−	0.148688i
$821$	−31.8546	−	8.53541i	−1.11173	−	0.297888i	−0.344199	−	0.938897i	$-0.611849\pi$
$821$	−31.8546	−	8.53541i	−1.11173	−	0.297888i	−0.767533	+	0.641009i	$0.778516\pi$
$822$		0			0
$823$	4.71220	−	8.16178i	0.164257	−	0.284502i	−0.772134	−	0.635460i	$-0.780811\pi$
$823$	4.71220	−	8.16178i	0.164257	−	0.284502i	0.936391	+	0.350958i	$0.114144\pi$
$824$	34.4498	+	24.1637i	1.20012	+	0.841783i
$825$		0			0
$826$	1.47515	+	6.23165i	0.0513270	+	0.216827i
$827$	38.7468	+	38.7468i	1.34736	+	1.34736i	0.888518	+	0.458841i	$0.151735\pi$
$827$	38.7468	+	38.7468i	1.34736	+	1.34736i	0.458841	+	0.888518i	$0.348265\pi$
$828$		0			0
$829$	11.0569	−	11.0569i	0.384021	−	0.384021i	−0.488528	−	0.872548i	$-0.662466\pi$
$829$	11.0569	−	11.0569i	0.384021	−	0.384021i	0.872548	+	0.488528i	$0.162466\pi$
$830$	−1.86887	+	3.02807i	−0.0648694	+	0.105106i
$831$		0			0
$832$	1.20276	+	14.0093i	0.0416982	+	0.485686i
$833$	69.1173	+	39.9049i	2.39477	+	1.38262i
$834$		0			0
$835$	−1.69520	+	6.32656i	−0.0586647	+	0.218940i
$836$	6.82463	+	4.49392i	0.236035	+	0.155425i
$837$		0			0
$838$	−8.97333	+	29.9435i	−0.309978	+	1.03438i
$839$	−25.3695	+	14.6471i	−0.875853	+	0.505674i	−0.869289	−	0.494305i	$-0.835423\pi$
$839$	−25.3695	+	14.6471i	−0.875853	+	0.505674i	−0.00656388	+	0.999978i	$0.502089\pi$
$840$		0			0
$841$	10.3391	+	5.96927i	0.356520	+	0.205837i
$842$	−8.47167	+	7.98828i	−0.291953	+	0.275294i
$843$		0			0
$844$	18.1735	+	20.4437i	0.625559	+	0.703701i
$845$	5.58412	+	5.58412i	0.192100	+	0.192100i
$846$		0			0
$847$			24.5309i			0.842891i
$848$	−1.36956	−	9.42094i	−0.0470308	−	0.323516i
$849$		0			0
$850$	−1.21174	+	41.2610i	−0.0415623	+	1.41524i
$851$	2.48834	+	9.28662i	0.0852992	+	0.318341i
$852$		0			0
$853$	−10.9035	+	40.6922i	−0.373327	+	1.39328i	0.482447	+	0.875925i	$0.339748\pi$
$853$	−10.9035	+	40.6922i	−0.373327	+	1.39328i	−0.855774	+	0.517350i	$0.826918\pi$
$854$	−3.61022	+	12.0471i	−0.123539	+	0.412244i
$855$		0			0
$856$	0.298899	−	0.250393i	0.0102162	−	0.00855826i
$857$	−14.2207	−	24.6310i	−0.485769	−	0.841377i	0.514097	−	0.857732i	$-0.328127\pi$
$857$	−14.2207	−	24.6310i	−0.485769	−	0.841377i	−0.999866	+	0.0163548i	$0.994794\pi$
$858$		0			0
$859$	−0.896437	−	3.34555i	−0.0305860	−	0.114149i	0.948945	−	0.315441i	$-0.102152\pi$
$859$	−0.896437	−	3.34555i	−0.0305860	−	0.114149i	−0.979531	+	0.201293i	$0.935486\pi$
$860$	12.6894	−	6.36428i	0.432706	−	0.217020i
$861$		0			0
$862$	−1.30087	−	0.802875i	−0.0443078	−	0.0273460i
$863$	11.1356			0.379062			0.189531	−	0.981875i	$-0.439303\pi$
$863$	11.1356			0.379062			0.189531	+	0.981875i	$0.439303\pi$
$864$		0			0
$865$	7.76622			0.264059
$866$	18.6906	+	11.5355i	0.635133	+	0.391993i
$867$		0			0
$868$	−44.3910	+	22.2640i	−1.50673	+	0.755688i
$869$	14.6080	+	54.5177i	0.495541	+	1.84939i
$870$		0			0
$871$	−7.28863	−	12.6243i	−0.246966	−	0.427757i
$872$	−22.6213	−	27.0035i	−0.766055	−	0.914454i
$873$		0			0
$874$	1.82275	−	6.08242i	0.0616554	−	0.205741i
$875$	8.40437	−	31.3655i	0.284119	−	1.06035i
$876$		0			0
$877$	7.32539	+	27.3387i	0.247361	+	0.923163i	0.972182	+	0.234226i	$0.0752557\pi$
$877$	7.32539	+	27.3387i	0.247361	+	0.923163i	−0.724821	+	0.688937i	$0.758078\pi$
$878$	−0.187911	+	6.39856i	−0.00634168	+	0.215941i
$879$		0			0
$880$	7.77469	−	10.4197i	0.262085	−	0.351247i
$881$			4.86363i			0.163860i	0.996638	+	0.0819299i	$0.0261084\pi$
$881$			4.86363i			0.163860i	−0.996638	+	0.0819299i	$0.973892\pi$
$882$		0			0
$883$	8.56478	+	8.56478i	0.288228	+	0.288228i	0.836379	−	0.548151i	$-0.184668\pi$
$883$	8.56478	+	8.56478i	0.288228	+	0.288228i	−0.548151	+	0.836379i	$0.684668\pi$
$884$	−15.6170	−	17.5678i	−0.525256	−	0.590869i
$885$		0			0
$886$	−27.1507	+	25.6015i	−0.912146	+	0.860099i
$887$	−3.99885	−	2.30874i	−0.134268	−	0.0775199i	0.431361	−	0.902179i	$-0.358033\pi$
$887$	−3.99885	−	2.30874i	−0.134268	−	0.0775199i	−0.565630	+	0.824659i	$0.691367\pi$
$888$		0			0
$889$	18.2707	−	10.5486i	0.612780	−	0.353789i
$890$	−0.553543	+	1.84715i	−0.0185548	+	0.0619165i
$891$		0			0
$892$	−46.9414	−	30.9102i	−1.57171	−	1.03495i
$893$	−0.638605	+	2.38330i	−0.0213701	+	0.0797543i
$894$		0			0
$895$	−2.53624	−	1.46430i	−0.0847772	−	0.0489461i
$896$	10.0467	−	48.1953i	0.335636	−	1.61009i
$897$		0			0
$898$	4.41707	−	7.15683i	0.147399	−	0.238826i
$899$	−16.6665	+	16.6665i	−0.555859	+	0.555859i
$900$		0			0
$901$	11.2533	+	11.2533i	0.374903	+	0.374903i
$902$	3.62461	+	15.3119i	0.120686	+	0.509830i
$903$		0			0
$904$	−13.5415	+	19.3060i	−0.450385	+	0.642107i
$905$	−3.90421	+	6.76228i	−0.129780	+	0.224786i
$906$		0			0
$907$	8.35931	+	2.23987i	0.277566	+	0.0743737i	0.394917	−	0.918717i	$-0.370773\pi$
$907$	8.35931	+	2.23987i	0.277566	+	0.0743737i	−0.117350	+	0.993091i	$0.537440\pi$
$908$	−0.204626	−	0.993717i	−0.00679075	−	0.0329777i
$909$		0			0
$910$	4.08832	+	7.58718i	0.135527	+	0.251512i
$911$	23.9969	+	41.5638i	0.795052	+	1.37707i	0.922806	+	0.385264i	$0.125890\pi$
$911$	23.9969	+	41.5638i	0.795052	+	1.37707i	−0.127755	+	0.991806i	$0.540777\pi$
$912$		0			0
$913$	6.43999	−	11.1544i	0.213133	−	0.369156i
$914$	29.7595	+	0.873967i	0.984357	+	0.0289083i
$915$		0			0
$916$	−20.1094	−	22.6214i	−0.664435	−	0.747433i
$917$	65.2905	−	65.2905i	2.15608	−	2.15608i
$918$		0			0
$919$	51.8939			1.71182			0.855910	−	0.517124i	$-0.172997\pi$
$919$	51.8939			1.71182			0.855910	+	0.517124i	$0.172997\pi$
$920$	−9.49025	−	3.46289i	−0.312884	−	0.114168i
$921$		0			0
$922$	40.7557	−	38.4302i	1.34222	−	1.26563i
$923$	−13.6703	+	3.66296i	−0.449965	+	0.120568i
$924$		0			0
$925$	−9.04347	−	2.42319i	−0.297347	−	0.0796740i
$926$	−7.73097	−	14.3473i	−0.254055	−	0.471480i
$927$		0			0
$928$	−2.68124	−	23.2116i	−0.0880160	−	0.761957i
$929$	−8.80130	+	5.08143i	−0.288761	+	0.166716i	−0.637383	−	0.770547i	$-0.719983\pi$
$929$	−8.80130	+	5.08143i	−0.288761	+	0.166716i	0.348622	+	0.937263i	$0.386650\pi$
$930$		0			0
$931$	11.5478	−	3.09423i	0.378465	−	0.101409i
$932$	−13.8949	−	27.7044i	−0.455143	−	0.907488i
$933$		0			0
$934$	−48.9427	+	11.5856i	−1.60145	+	0.379094i
$935$			21.7332i			0.710751i
$936$		0			0
$937$		−	37.8157i		−	1.23539i	−0.786420	−	0.617693i	$-0.788068\pi$
$937$		−	37.8157i		−	1.23539i	0.786420	−	0.617693i	$-0.211932\pi$
$938$	11.7571	+	49.6668i	0.383882	+	1.62168i
$939$		0			0
$940$	3.72567	+	1.23679i	0.121518	+	0.0403396i
$941$	34.3731	−	9.21025i	1.12053	−	0.300246i	0.349433	−	0.936961i	$-0.386374\pi$
$941$	34.3731	−	9.21025i	1.12053	−	0.300246i	0.771099	+	0.636716i	$0.219707\pi$
$942$		0			0
$943$	10.5890	−	6.11357i	0.344826	−	0.199085i
$944$	−1.54099	+	3.86671i	−0.0501550	+	0.125851i
$945$		0			0
$946$	−45.2353	+	24.3749i	−1.47073	+	0.792495i
$947$	10.0399	+	2.69018i	0.326253	+	0.0874191i	0.418228	−	0.908342i	$-0.362651\pi$
$947$	10.0399	+	2.69018i	0.326253	+	0.0874191i	−0.0919752	+	0.995761i	$0.529318\pi$
$948$		0			0
$949$	16.5210	−	4.42678i	0.536293	−	0.143699i
$950$	4.24210	+	4.49880i	0.137632	+	0.145960i
$951$		0			0
$952$	34.7212	+	74.6177i	1.12532	+	2.41837i
$953$	24.6743			0.799280			0.399640	−	0.916672i	$-0.369135\pi$
$953$	24.6743			0.799280			0.399640	+	0.916672i	$0.369135\pi$
$954$		0			0
$955$	7.85126	−	7.85126i	0.254061	−	0.254061i
$956$	30.4159	+	1.78803i	0.983719	+	0.0578289i
$957$		0			0
$958$	−0.219846	+	7.48599i	−0.00710290	+	0.241861i
$959$	12.7873	−	22.1482i	0.412922	−	0.715203i
$960$		0			0
$961$	0.780708	+	1.35223i	0.0251841	+	0.0436202i
$962$	4.69334	−	2.52899i	0.151319	−	0.0815379i
$963$		0			0
$964$	20.0339	−	30.4242i	0.645249	−	0.979898i
$965$	−2.06416	−	0.553089i	−0.0664475	−	0.0178046i
$966$		0			0
$967$	12.5371	−	21.7150i	0.403167	−	0.698306i	−0.590939	−	0.806716i	$-0.701243\pi$
$967$	12.5371	−	21.7150i	0.403167	−	0.698306i	0.994106	+	0.108410i	$0.0345759\pi$
$968$	−9.15620	+	13.0539i	−0.294291	+	0.419567i
$969$		0			0
$970$	8.03921	−	1.90303i	0.258123	−	0.0611027i
$971$	−18.9203	−	18.9203i	−0.607180	−	0.607180i	0.335028	−	0.942208i	$-0.391254\pi$
$971$	−18.9203	−	18.9203i	−0.607180	−	0.607180i	−0.942208	+	0.335028i	$0.891254\pi$
$972$		0			0
$973$	−22.2152	+	22.2152i	−0.712186	+	0.712186i
$974$	−2.23293	−	1.37813i	−0.0715478	−	0.0441581i
$975$		0			0
$976$	−6.41776	+	5.06324i	−0.205428	+	0.162070i
$977$	12.1897	+	7.03771i	0.389982	+	0.225156i	0.682152	−	0.731210i	$-0.261044\pi$
$977$	12.1897	+	7.03771i	0.389982	+	0.225156i	−0.292170	+	0.956366i	$0.594377\pi$
$978$		0			0
$979$	1.80650	−	6.74196i	0.0577360	−	0.215474i
$980$	−3.83624	−	18.6298i	−0.122544	−	0.595107i
$981$		0			0
$982$	−4.90175	−	1.46893i	−0.156421	−	0.0468755i
$983$	0.562149	−	0.324557i	0.0179298	−	0.0103518i	−0.491008	−	0.871155i	$-0.663372\pi$
$983$	0.562149	−	0.324557i	0.0179298	−	0.0103518i	0.508938	+	0.860803i	$0.330038\pi$
$984$		0			0
$985$	−13.8933	−	8.02129i	−0.442677	−	0.255579i
$986$	26.7976	+	28.4192i	0.853410	+	0.905052i
$987$		0			0
$988$	−3.51499	−	0.206632i	−0.111827	−	0.00657385i
$989$	28.2341	+	28.2341i	0.897792	+	0.897792i
$990$		0			0
$991$			36.5529i			1.16114i	0.814210	+	0.580571i	$0.197171\pi$
$991$			36.5529i			1.16114i	−0.814210	+	0.580571i	$0.802829\pi$
$992$	−31.9323	−	4.72150i	−1.01385	−	0.149908i
$993$		0			0
$994$	49.5311	+	1.45461i	1.57103	+	0.0461375i
$995$	1.62940	+	6.08100i	0.0516554	+	0.192781i
$996$		0			0
$997$	−2.07498	+	7.74395i	−0.0657154	+	0.245253i	−0.990968	−	0.134098i	$-0.957186\pi$
$997$	−2.07498	+	7.74395i	−0.0657154	+	0.245253i	0.925253	+	0.379352i	$0.123853\pi$
$998$	16.8652	+	5.05408i	0.533859	+	0.159984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.395.3		88
3.2	odd	2		144.2.u.a.59.20	yes	88
4.3	odd	2		1728.2.z.a.719.13		88
9.2	odd	6	inner	432.2.v.a.251.11		88
9.7	even	3		144.2.u.a.11.12	✓	88
12.11	even	2		576.2.y.a.527.8		88
16.3	odd	4	inner	432.2.v.a.179.11		88
16.13	even	4		1728.2.z.a.1583.13		88
36.7	odd	6		576.2.y.a.335.4		88
36.11	even	6		1728.2.z.a.143.13		88
48.29	odd	4		576.2.y.a.239.4		88
48.35	even	4		144.2.u.a.131.12	yes	88
144.29	odd	12		1728.2.z.a.1007.13		88
144.61	even	12		576.2.y.a.47.8		88
144.83	even	12	inner	432.2.v.a.35.3		88
144.115	odd	12		144.2.u.a.83.20	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.12	✓	88	9.7	even	3
144.2.u.a.59.20	yes	88	3.2	odd	2
144.2.u.a.83.20	yes	88	144.115	odd	12
144.2.u.a.131.12	yes	88	48.35	even	4
432.2.v.a.35.3		88	144.83	even	12	inner
432.2.v.a.179.11		88	16.3	odd	4	inner
432.2.v.a.251.11		88	9.2	odd	6	inner
432.2.v.a.395.3		88	1.1	even	1	trivial
576.2.y.a.47.8		88	144.61	even	12
576.2.y.a.239.4		88	48.29	odd	4
576.2.y.a.335.4		88	36.7	odd	6
576.2.y.a.527.8		88	12.11	even	2
1728.2.z.a.143.13		88	36.11	even	6
1728.2.z.a.719.13		88	4.3	odd	2
1728.2.z.a.1007.13		88	144.29	odd	12
1728.2.z.a.1583.13		88	16.13	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20346 - 0.742754i) q^{2} +(0.896632 + 1.78775i) q^{4} +(0.206232 + 0.769670i) q^{5} +(-2.17574 - 3.76849i) q^{7} +(0.248799 - 2.81746i) q^{8} +O(q^{10})\)	\(q+(-1.20346 - 0.742754i) q^{2} +(0.896632 + 1.78775i) q^{4} +(0.206232 + 0.769670i) q^{5} +(-2.17574 - 3.76849i) q^{7} +(0.248799 - 2.81746i) q^{8} +(0.323483 - 1.07945i) q^{10} +(-1.05570 + 3.93991i) q^{11} +(-0.454903 - 1.69772i) q^{13} +(-0.180648 + 6.15127i) q^{14} +(-2.39210 + 3.20591i) q^{16} -6.68683i q^{17} +(-0.708282 - 0.708282i) q^{19} +(-1.19106 + 1.05880i) q^{20} +(4.19687 - 3.95740i) q^{22} +(-3.88191 - 2.24122i) q^{23} +(3.78027 - 2.18254i) q^{25} +(-0.713532 + 2.38102i) q^{26} +(4.78628 - 7.26863i) q^{28} +(1.06907 - 3.98981i) q^{29} +(-4.94177 - 2.85313i) q^{31} +(5.26000 - 2.08144i) q^{32} +(-4.96668 + 8.04734i) q^{34} +(2.45179 - 2.45179i) q^{35} +(-1.51665 - 1.51665i) q^{37} +(0.326309 + 1.37847i) q^{38} +(2.21983 - 0.389559i) q^{40} +(-1.36389 + 2.36233i) q^{41} +(-8.60436 - 2.30553i) q^{43} +(-7.99014 + 1.64533i) q^{44} +(3.00704 + 5.58052i) q^{46} +(-1.23164 - 2.13327i) q^{47} +(-5.96768 + 10.3363i) q^{49} +(-6.17049 - 0.181213i) q^{50} +(2.62722 - 2.33548i) q^{52} +(-1.68291 + 1.68291i) q^{53} -3.25015 q^{55} +(-11.1589 + 5.19247i) q^{56} +(-4.25002 + 4.00752i) q^{58} +(1.00516 - 0.269331i) q^{59} +(1.97401 + 0.528935i) q^{61} +(3.82804 + 7.10415i) q^{62} +(-7.87620 - 1.40197i) q^{64} +(1.21287 - 0.700250i) q^{65} +(8.01120 - 2.14659i) q^{67} +(11.9544 - 5.99563i) q^{68} +(-4.77170 + 1.12955i) q^{70} -8.05218i q^{71} +9.73126i q^{73} +(0.698727 + 2.95172i) q^{74} +(0.631163 - 1.90130i) q^{76} +(17.1444 - 4.59383i) q^{77} +(11.9835 - 6.91865i) q^{79} +(-2.96082 - 1.17997i) q^{80} +(3.39603 - 1.82994i) q^{82} +(-3.05012 - 0.817277i) q^{83} +(5.14666 - 1.37904i) q^{85} +(8.64256 + 9.16554i) q^{86} +(10.8379 + 3.95463i) q^{88} -1.71120 q^{89} +(-5.40809 + 5.40809i) q^{91} +(0.526101 - 8.94943i) q^{92} +(-0.102261 + 3.48211i) q^{94} +(0.399073 - 0.691214i) q^{95} +(3.66561 + 6.34903i) q^{97} +(14.8592 - 8.00683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

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