LMFDB - Embedded newform 432.2.v.a.179.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			179.11
Character	$\chi$	$=$	432.179
Dual form			432.2.v.a.251.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0415142 + 1.41360i) q^{2} +(-1.99655 + 0.117369i) q^{4} +(0.769670 - 0.206232i) q^{5} +(-2.17574 - 3.76849i) q^{7} +(-0.248799 - 2.81746i) q^{8} +(0.323483 + 1.07945i) q^{10} +(-3.93991 - 1.05570i) q^{11} +(1.69772 - 0.454903i) q^{13} +(5.23683 - 3.23208i) q^{14} +(3.97245 - 0.468669i) q^{16} -6.68683i q^{17} +(-0.708282 + 0.708282i) q^{19} +(-1.51248 + 0.502090i) q^{20} +(1.32877 - 5.61330i) q^{22} +(-3.88191 - 2.24122i) q^{23} +(-3.78027 + 2.18254i) q^{25} +(0.713532 + 2.38102i) q^{26} +(4.78628 + 7.26863i) q^{28} +(3.98981 + 1.06907i) q^{29} +(4.94177 + 2.85313i) q^{31} +(0.827425 + 5.59601i) q^{32} +(9.45254 - 0.277599i) q^{34} +(-2.45179 - 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(-1.03063 - 0.971827i) q^{38} +(-0.772546 - 2.11721i) q^{40} +(1.36389 - 2.36233i) q^{41} +(2.30553 - 8.60436i) q^{43} +(7.99014 + 1.64533i) q^{44} +(3.00704 - 5.58052i) q^{46} +(1.23164 + 2.13327i) q^{47} +(-5.96768 + 10.3363i) q^{49} +(-3.24218 - 5.25319i) q^{50} +(-3.33620 + 1.10750i) q^{52} +(1.68291 + 1.68291i) q^{53} -3.25015 q^{55} +(-10.0763 + 7.06766i) q^{56} +(-1.34560 + 5.68439i) q^{58} +(0.269331 + 1.00516i) q^{59} +(-0.528935 + 1.97401i) q^{61} +(-3.82804 + 7.10415i) q^{62} +(-7.87620 + 1.40197i) q^{64} +(1.21287 - 0.700250i) q^{65} +(-2.14659 - 8.01120i) q^{67} +(0.784830 + 13.3506i) q^{68} +(3.36407 - 3.56764i) q^{70} -8.05218i q^{71} -9.73126i q^{73} +(-2.20690 - 2.08098i) q^{74} +(1.33099 - 1.49725i) q^{76} +(4.59383 + 17.1444i) q^{77} +(-11.9835 + 6.91865i) q^{79} +(2.96082 - 1.17997i) q^{80} +(3.39603 + 1.82994i) q^{82} +(-0.817277 + 3.05012i) q^{83} +(-1.37904 - 5.14666i) q^{85} +(12.2589 + 2.90190i) q^{86} +(-1.99414 + 11.3632i) q^{88} +1.71120 q^{89} +(-5.40809 - 5.40809i) q^{91} +(8.01348 + 4.01910i) q^{92} +(-2.96446 + 1.82962i) q^{94} +(-0.399073 + 0.691214i) q^{95} +(3.66561 + 6.34903i) q^{97} +(-14.8592 - 8.00683i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 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}+ \cdots - 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

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.0415142	+	1.41360i	0.0293550	+	0.999569i
$2$	0.0415142	+	1.41360i	0.0293550	+	0.999569i
$3$		0			0
$3$		0			0
$4$	−1.99655	+	0.117369i	−0.998277	+	0.0586847i
$5$	0.769670	−	0.206232i	0.344207	−	0.0922300i	−0.0825742	−	0.996585i	$-0.526314\pi$
$5$	0.769670	−	0.206232i	0.344207	−	0.0922300i	0.426781	+	0.904355i	$0.359647\pi$
$6$		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
$11$	−3.93991	−	1.05570i	−1.18793	−	0.318304i	−0.389861	−	0.920874i	$-0.627477\pi$
$11$	−3.93991	−	1.05570i	−1.18793	−	0.318304i	−0.798066	+	0.602570i	$0.794144\pi$
$12$		0			0
$13$	1.69772	−	0.454903i	0.470863	−	0.126167i	−0.0155820	−	0.999879i	$-0.504960\pi$
$13$	1.69772	−	0.454903i	0.470863	−	0.126167i	0.486445	+	0.873711i	$0.338293\pi$
$14$	5.23683	−	3.23208i	1.39960	−	0.863809i
$15$		0			0
$16$	3.97245	−	0.468669i	0.993112	−	0.117167i
$17$		−	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	−0.783669	−	0.621178i	$-0.786654\pi$
$19$	−0.708282	+	0.708282i	−0.162491	+	0.162491i	0.621178	+	0.783669i	$0.286654\pi$
$20$	−1.51248	+	0.502090i	−0.338201	+	0.112271i
$21$		0			0
$22$	1.32877	−	5.61330i	0.283295	−	1.19676i
$23$	−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
$29$	3.98981	+	1.06907i	0.740888	+	0.198520i	0.609473	−	0.792807i	$-0.291381\pi$
$29$	3.98981	+	1.06907i	0.740888	+	0.198520i	0.131415	+	0.991327i	$0.458048\pi$
$30$		0			0
$31$	4.94177	+	2.85313i	0.887568	+	0.512437i	0.873146	−	0.487459i	$-0.162076\pi$
$31$	4.94177	+	2.85313i	0.887568	+	0.512437i	0.0144215	+	0.999896i	$0.495409\pi$
$32$	0.827425	+	5.59601i	0.146269	+	0.989245i
$33$		0			0
$34$	9.45254	−	0.277599i	1.62110	−	0.0476078i
$35$	−2.45179	−	2.45179i	−0.414427	−	0.414427i
$36$		0			0
$37$	−1.51665	+	1.51665i	−0.249335	+	0.249335i	−0.820698	−	0.571363i	$-0.806415\pi$
$37$	−1.51665	+	1.51665i	−0.249335	+	0.249335i	0.571363	+	0.820698i	$0.306415\pi$
$38$	−1.03063	−	0.971827i	−0.167191	−	0.157651i
$39$		0			0
$40$	−0.772546	−	2.11721i	−0.122150	−	0.334760i
$41$	1.36389	−	2.36233i	0.213005	−	0.368935i	−0.739649	−	0.672993i	$-0.765008\pi$
$41$	1.36389	−	2.36233i	0.213005	−	0.368935i	0.952653	+	0.304058i	$0.0983418\pi$
$42$		0			0
$43$	2.30553	−	8.60436i	0.351590	−	1.31215i	−0.533131	−	0.846033i	$-0.678985\pi$
$43$	2.30553	−	8.60436i	0.351590	−	1.31215i	0.884722	−	0.466120i	$-0.154348\pi$
$44$	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	0.941762	−	0.336280i	$-0.109169\pi$
$47$	1.23164	+	2.13327i	0.179654	+	0.311169i	−0.762108	+	0.647449i	$0.775836\pi$
$48$		0			0
$49$	−5.96768	+	10.3363i	−0.852525	+	1.47662i
$50$	−3.24218	−	5.25319i	−0.458513	−	0.742914i
$51$		0			0
$52$	−3.33620	+	1.10750i	−0.462647	+	0.153582i
$53$	1.68291	+	1.68291i	0.231165	+	0.231165i	0.813179	−	0.582014i	$-0.197735\pi$
$53$	1.68291	+	1.68291i	0.231165	+	0.231165i	−0.582014	+	0.813179i	$0.697735\pi$
$54$		0			0
$55$	−3.25015			−0.438250
$56$	−10.0763	+	7.06766i	−1.34650	+	0.944456i
$57$		0			0
$58$	−1.34560	+	5.68439i	−0.176686	+	0.746397i
$59$	0.269331	+	1.00516i	0.0350640	+	0.130860i	0.981239	−	0.192794i	$-0.0617550\pi$
$59$	0.269331	+	1.00516i	0.0350640	+	0.130860i	−0.946175	+	0.323655i	$0.895088\pi$
$60$		0			0
$61$	−0.528935	+	1.97401i	−0.0677232	+	0.252747i	−0.991485	−	0.130221i	$-0.958431\pi$
$61$	−0.528935	+	1.97401i	−0.0677232	+	0.252747i	0.923762	+	0.382968i	$0.125098\pi$
$62$	−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
$67$	−2.14659	−	8.01120i	−0.262248	−	0.978723i	−0.963913	−	0.266217i	$-0.914226\pi$
$67$	−2.14659	−	8.01120i	−0.262248	−	0.978723i	0.701665	−	0.712507i	$-0.252440\pi$
$68$	0.784830	+	13.3506i	0.0951746	+	1.61900i
$69$		0			0
$70$	3.36407	−	3.56764i	0.402083	−	0.426414i
$71$		−	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	$-0.807145\pi$
$73$		−	9.73126i		−	1.13896i	0.822006	−	0.569479i	$-0.192855\pi$
$74$	−2.20690	−	2.08098i	−0.256547	−	0.241908i
$75$		0			0
$76$	1.33099	−	1.49725i	0.152675	−	0.171747i
$77$	4.59383	+	17.1444i	0.523516	+	1.95379i
$78$		0			0
$79$	−11.9835	+	6.91865i	−1.34824	+	0.778409i	−0.988001	−	0.154449i	$-0.950640\pi$
$79$	−11.9835	+	6.91865i	−1.34824	+	0.778409i	−0.360243	+	0.932858i	$0.617306\pi$
$80$	2.96082	−	1.17997i	0.331030	−	0.131924i
$81$		0			0
$82$	3.39603	+	1.82994i	0.375028	+	0.202083i
$83$	−0.817277	+	3.05012i	−0.0897078	+	0.334794i	−0.996164	−	0.0875058i	$-0.972110\pi$
$83$	−0.817277	+	3.05012i	−0.0897078	+	0.334794i	0.906456	+	0.422300i	$0.138777\pi$
$84$		0			0
$85$	−1.37904	−	5.14666i	−0.149578	−	0.558233i
$86$	12.2589	+	2.90190i	1.32191	+	0.312920i
$87$		0			0
$88$	−1.99414	+	11.3632i	−0.212576	+	1.21132i
$89$	1.71120			0.181386			0.0906932	−	0.995879i	$-0.471092\pi$
$89$	1.71120			0.181386			0.0906932	+	0.995879i	$0.471092\pi$
$90$		0			0
$91$	−5.40809	−	5.40809i	−0.566922	−	0.566922i
$92$	8.01348	+	4.01910i	0.835463	+	0.419020i
$93$		0			0
$94$	−2.96446	+	1.82962i	−0.305761	+	0.188710i
$95$	−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
$101$	3.75813	−	14.0255i	0.373948	−	1.39559i	−0.480928	−	0.876760i	$-0.659700\pi$
$101$	3.75813	−	14.0255i	0.373948	−	1.39559i	0.854876	−	0.518833i	$-0.173633\pi$
$102$		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	$0.904808\pi$
$104$	−1.70406	−	4.67009i	−0.167097	−	0.457940i
$105$		0			0
$106$	−2.30910	+	2.44883i	−0.224280	+	0.237851i
$107$	−0.0974799	+	0.0974799i	−0.00942374	+	0.00942374i	−0.711803	−	0.702379i	$-0.752121\pi$
$107$	−0.0974799	+	0.0974799i	−0.00942374	+	0.00942374i	0.702379	+	0.711803i	$0.252121\pi$
$108$		0			0
$109$	8.80665	+	8.80665i	0.843524	+	0.843524i	0.989315	−	0.145791i	$-0.0465728\pi$
$109$	8.80665	+	8.80665i	0.843524	+	0.843524i	−0.145791	+	0.989315i	$0.546573\pi$
$110$	−0.134927	−	4.59442i	−0.0128648	−	0.438061i
$111$		0			0
$112$	−10.4092	−	13.9504i	−0.983575	−	1.31819i
$113$	−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
$115$	−3.45000	−	0.924424i	−0.321714	−	0.0862030i
$116$	−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
$122$	−2.81243	−	0.665756i	−0.254626	−	0.0602747i
$123$		0			0
$124$	−10.2014	−	5.11641i	−0.916110	−	0.459468i
$125$	−5.27664	+	5.27664i	−0.471957	+	0.471957i
$126$		0			0
$127$		−	4.84829i		−	0.430216i	−0.976590	−	0.215108i	$-0.930990\pi$
$127$		−	4.84829i		−	0.430216i	0.976590	−	0.215108i	$-0.0690103\pi$
$128$	−2.30880	−	11.0756i	−0.204071	−	0.978956i
$129$		0			0
$130$	1.04023	+	1.68545i	0.0912340	+	0.147823i
$131$	20.4961	−	5.49193i	1.79076	−	0.479832i	0.798282	−	0.602284i	$-0.205742\pi$
$131$	20.4961	−	5.49193i	1.79076	−	0.479832i	0.992474	+	0.122452i	$0.0390758\pi$
$132$		0			0
$133$	4.21019	+	1.12812i	0.365070	+	0.0978201i
$134$	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	0.712757	−	0.701411i	$-0.247446\pi$
$137$	−2.93860	−	5.08981i	−0.251062	−	0.434852i	−0.963818	+	0.266560i	$0.914113\pi$
$138$		0			0
$139$	6.97384	−	1.86863i	0.591513	−	0.158496i	0.0493686	−	0.998781i	$-0.484279\pi$
$139$	6.97384	−	1.86863i	0.591513	−	0.158496i	0.542145	+	0.840285i	$0.317612\pi$
$140$	5.18288	+	4.60736i	0.438034	+	0.389393i
$141$		0			0
$142$	11.3826	−	0.334280i	0.955206	−	0.0280522i
$143$	−7.16910			−0.599510
$144$		0			0
$145$	3.29131			0.273328
$146$	13.7562	−	0.403986i	1.13847	−	0.0334341i
$147$		0			0
$148$	2.85006	−	3.20607i	0.234273	−	0.263538i
$149$	−4.34504	+	1.16425i	−0.355960	+	0.0953792i	−0.432367	−	0.901698i	$-0.642322\pi$
$149$	−4.34504	+	1.16425i	−0.355960	+	0.0953792i	0.0764076	+	0.997077i	$0.475655\pi$
$150$		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
$155$	4.39194	+	1.17682i	0.352769	+	0.0945241i
$156$		0			0
$157$	16.3507	−	4.38117i	1.30493	−	0.349655i	0.461618	−	0.887079i	$-0.347269\pi$
$157$	16.3507	−	4.38117i	1.30493	−	0.349655i	0.843313	+	0.537423i	$0.180602\pi$
$158$	−10.2777	−	16.6526i	−0.817651	−	1.32481i
$159$		0			0
$160$	1.79092	+	4.13644i	0.141585	+	0.327014i
$161$			19.5052i			1.53723i
$162$		0			0
$163$	13.6982	−	13.6982i	1.07293	−	1.07293i	0.0758059	−	0.997123i	$-0.475847\pi$
$163$	13.6982	−	13.6982i	1.07293	−	1.07293i	0.997123	−	0.0758059i	$-0.0241529\pi$
$164$	−2.44582	+	4.87661i	−0.190987	+	0.380799i
$165$		0			0
$166$	−4.34559	−	1.02868i	−0.337283	−	0.0798412i
$167$	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
$173$	9.41440	+	2.52258i	0.715764	+	0.191788i	0.598281	−	0.801287i	$-0.295851\pi$
$173$	9.41440	+	2.52258i	0.715764	+	0.191788i	0.117483	+	0.993075i	$0.462517\pi$
$174$		0			0
$175$	16.4497	+	9.49727i	1.24348	+	0.717926i
$176$	−16.1459	−	2.34718i	−1.21704	−	0.176926i
$177$		0			0
$178$	0.0710390	+	2.41895i	0.00532460	+	0.181308i
$179$	2.59887	+	2.59887i	0.194248	+	0.194248i	0.797529	−	0.603281i	$-0.206140\pi$
$179$	2.59887	+	2.59887i	0.194248	+	0.194248i	−0.603281	+	0.797529i	$0.706140\pi$
$180$		0			0
$181$	6.92926	−	6.92926i	0.515048	−	0.515048i	−0.401021	−	0.916069i	$-0.631345\pi$
$181$	6.92926	−	6.92926i	0.515048	−	0.515048i	0.916069	+	0.401021i	$0.131345\pi$
$182$	7.42039	−	7.86941i	0.550036	−	0.583320i
$183$		0			0
$184$	−5.34874	+	11.4947i	−0.394314	+	0.847403i
$185$	−0.854536	+	1.48010i	−0.0628267	+	0.108819i
$186$		0			0
$187$	−7.05926	+	26.3455i	−0.516224	+	1.92657i
$188$	−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	$0.00152195\pi$
$191$	6.96728	+	12.0677i	0.504135	+	0.873187i	−0.495854	+	0.868406i	$0.665145\pi$
$192$		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	$0.197439\pi$
$194$	−8.82284	+	5.44530i	−0.633443	+	0.390950i
$195$		0			0
$196$	10.7016	−	21.3374i	0.764401	−	1.52410i
$197$	14.2363	+	14.2363i	1.01430	+	1.01430i	0.999896	+	0.0144009i	$0.00458410\pi$
$197$	14.2363	+	14.2363i	1.01430	+	1.01430i	0.0144009	+	0.999896i	$0.495416\pi$
$198$		0			0
$199$	7.90078			0.560072			0.280036	−	0.959990i	$-0.409654\pi$
$199$	7.90078			0.560072			0.280036	+	0.959990i	$0.409654\pi$
$200$	7.08975	+	10.1077i	0.501321	+	0.714726i
$201$		0			0
$202$	19.9826	+	4.73025i	1.40597	+	0.332819i
$203$	−4.65201	−	17.3615i	−0.326507	−	1.21854i
$204$		0			0
$205$	0.562559	−	2.09950i	0.0392908	−	0.146635i
$206$	−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
$211$	−3.53982	−	13.2108i	−0.243691	−	0.909469i	−0.974037	−	0.226391i	$-0.927307\pi$
$211$	−3.53982	−	13.2108i	−0.243691	−	0.909469i	0.730345	−	0.683078i	$-0.239359\pi$
$212$	−3.55754	−	3.16249i	−0.244333	−	0.217201i
$213$		0			0
$214$	−0.141845	−	0.133751i	−0.00969631	−	0.00914305i
$215$		−	7.09799i		−	0.484079i
$216$		0			0
$217$		−	24.8307i		−	1.68562i
$218$	−12.0835	+	12.8147i	−0.818399	+	0.867922i
$219$		0			0
$220$	6.48909	−	0.381468i	0.437494	−	0.0257186i
$221$	−3.04186	−	11.3524i	−0.204618	−	0.763643i
$222$		0			0
$223$	24.3372	−	14.0511i	1.62974	−	0.940931i	0.645570	−	0.763701i	$-0.276620\pi$
$223$	24.3372	−	14.0511i	1.62974	−	0.940931i	0.984169	−	0.177230i	$-0.0567136\pi$
$224$	19.2883	−	15.2936i	1.28875	−	1.02185i
$225$		0			0
$226$	5.59312	−	10.3798i	0.372049	−	0.690454i
$227$	−0.131295	+	0.489998i	−0.00871433	+	0.0325223i	−0.970146	−	0.242521i	$-0.922026\pi$
$227$	−0.131295	+	0.489998i	−0.00871433	+	0.0325223i	0.961432	+	0.275044i	$0.0886923\pi$
$228$		0			0
$229$	3.91690	+	14.6181i	0.258836	+	0.965988i	0.965916	+	0.258855i	$0.0833452\pi$
$229$	3.91690	+	14.6181i	0.258836	+	0.965988i	−0.707080	+	0.707133i	$0.749988\pi$
$230$	1.16355	−	4.91531i	0.0767219	−	0.324106i
$231$		0			0
$232$	2.01939	−	11.5071i	0.132580	−	0.755479i
$233$	15.4968			1.01523			0.507614	−	0.861584i	$-0.330527\pi$
$233$	15.4968			1.01523			0.507614	+	0.861584i	$0.330527\pi$
$234$		0			0
$235$	1.38791	+	1.38791i	0.0905371	+	0.0905371i
$236$	−0.655709	−	1.97524i	−0.0426830	−	0.128577i
$237$		0			0
$238$	−21.6124	−	35.0178i	−1.40092	−	2.26987i
$239$	−7.61709	+	13.1932i	−0.492709	+	0.853397i	−0.999965	−	0.00839869i	$-0.997327\pi$
$239$	−7.61709	+	13.1932i	−0.492709	+	0.853397i	0.507256	+	0.861796i	$0.330660\pi$
$240$		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
$245$	−2.46146	+	9.18628i	−0.157257	+	0.586890i
$246$		0			0
$247$	−0.880265	+	1.52466i	−0.0560099	+	0.0970121i
$248$	6.80908	−	14.6331i	0.432377	−	0.929203i
$249$		0			0
$250$	−7.67813	−	7.24002i	−0.485608	−	0.457899i
$251$	2.18418	−	2.18418i	0.137864	−	0.137864i	−0.634807	−	0.772671i	$-0.718920\pi$
$251$	2.18418	−	2.18418i	0.137864	−	0.137864i	0.772671	+	0.634807i	$0.218920\pi$
$252$		0			0
$253$	12.9283	+	12.9283i	0.812796	+	0.812796i
$254$	6.85356	−	0.201273i	0.430030	−	0.0126290i
$255$		0			0
$256$	15.5607	−	3.72352i	0.972544	−	0.232720i
$257$	−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
$259$	9.01529	+	2.41564i	0.560183	+	0.150101i
$260$	−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
$266$	−1.41993	+	5.99837i	−0.0870614	+	0.367784i
$267$		0			0
$268$	5.22606	+	15.7428i	0.319232	+	0.961647i
$269$	−0.605506	+	0.605506i	−0.0369184	+	0.0369184i	−0.725325	−	0.688407i	$-0.758310\pi$
$269$	−0.605506	+	0.605506i	−0.0369184	+	0.0369184i	0.688407	+	0.725325i	$0.258310\pi$
$270$		0			0
$271$			19.1084i			1.16075i	0.814349	+	0.580376i	$0.197094\pi$
$271$			19.1084i			1.16075i	−0.814349	+	0.580376i	$0.802906\pi$
$272$	−3.13391	−	26.5631i	−0.190021	−	1.61062i
$273$		0			0
$274$	7.07298	−	4.36532i	0.427295	−	0.263719i
$275$	17.1980	−	4.60819i	1.03708	−	0.277884i
$276$		0			0
$277$	6.82191	+	1.82792i	0.409889	+	0.109829i	0.457871	−	0.889019i	$-0.348612\pi$
$277$	6.82191	+	1.82792i	0.409889	+	0.109829i	−0.0479819	+	0.998848i	$0.515279\pi$
$278$	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	$-0.916783\pi$
$281$	−11.8490	−	20.5230i	−0.706849	−	1.22430i	0.259171	−	0.965831i	$-0.416551\pi$
$282$		0			0
$283$	0.727099	−	0.194826i	0.0432215	−	0.0115812i	−0.237143	−	0.971475i	$-0.576211\pi$
$283$	0.727099	−	0.194826i	0.0432215	−	0.0115812i	0.280365	+	0.959893i	$0.409544\pi$
$284$	0.945079	+	16.0766i	0.0560801	+	0.953971i
$285$		0			0
$286$	−0.297620	−	10.1343i	−0.0175986	−	0.599252i
$287$	−11.8699			−0.700659
$288$		0			0
$289$	−27.7137			−1.63022
$290$	0.136636	+	4.65261i	0.00802356	+	0.273211i
$291$		0			0
$292$	1.14215	+	19.4290i	0.0668394	+	1.13699i
$293$	−19.8198	+	5.31070i	−1.15789	+	0.310255i	−0.786121	−	0.618072i	$-0.787914\pi$
$293$	−19.8198	+	5.31070i	−1.15789	+	0.310255i	−0.371765	+	0.928327i	$0.621247\pi$
$294$		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
$299$	−7.60993	−	2.03907i	−0.440093	−	0.117923i
$300$		0			0
$301$	−37.4417	+	10.0325i	−2.15810	+	0.578262i
$302$	10.1933	−	6.29111i	0.586557	−	0.362013i
$303$		0			0
$304$	−2.48166	+	3.14556i	−0.142333	+	0.180410i
$305$			1.62842i			0.0932432i
$306$		0			0
$307$	−15.3450	+	15.3450i	−0.875783	+	0.875783i	−0.993095	−	0.117312i	$-0.962572\pi$
$307$	−15.3450	+	15.3450i	−0.875783	+	0.875783i	0.117312	+	0.993095i	$0.462572\pi$
$308$	−11.1841	−	33.6906i	−0.637271	−	1.91970i
$309$		0			0
$310$	−1.48122	+	6.25732i	−0.0841279	+	0.355392i
$311$	−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	−0.846915	−	0.531728i	$-0.821543\pi$
$313$	−14.3283	+	8.27244i	−0.809882	+	0.467586i	0.0370327	+	0.999314i	$0.488209\pi$
$314$	6.87202	+	22.9316i	0.387811	+	1.29410i
$315$		0			0
$316$	23.1136	−	15.2199i	1.30024	−	0.856189i
$317$	6.56570	+	1.75927i	0.368767	+	0.0988107i	0.438443	−	0.898759i	$-0.355530\pi$
$317$	6.56570	+	1.75927i	0.368767	+	0.0988107i	−0.0696766	+	0.997570i	$0.522197\pi$
$318$		0			0
$319$	−14.5909	−	8.42404i	−0.816931	−	0.471656i
$320$	−5.77294	+	2.70338i	−0.322717	+	0.151123i
$321$		0			0
$322$	−27.5727	+	0.809745i	−1.53656	+	0.0451253i
$323$	4.73616	+	4.73616i	0.263527	+	0.263527i
$324$		0			0
$325$	−5.42499	+	5.42499i	−0.300924	+	0.300924i
$326$	19.9326	+	18.7952i	1.10396	+	1.04097i
$327$		0			0
$328$	−6.99513	−	3.25498i	−0.386241	−	0.179726i
$329$	5.35946	−	9.28286i	0.295477	−	0.511781i
$330$		0			0
$331$	−2.51757	+	9.39568i	−0.138378	+	0.516434i	0.861583	+	0.507616i	$0.169473\pi$
$331$	−2.51757	+	9.39568i	−0.138378	+	0.516434i	−0.999961	+	0.00881711i	$0.997193\pi$
$332$	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	$-0.0978241\pi$
$338$	−7.36130	−	11.9273i	−0.400402	−	0.648758i
$339$		0			0
$340$	3.35739	+	10.1137i	0.182080	+	0.548493i
$341$	−16.4581	−	16.4581i	−0.891254	−	0.891254i
$342$		0			0
$343$	21.4761			1.15960
$344$	−24.8161	−	4.35499i	−1.33799	−	0.234805i
$345$		0			0
$346$	−3.17510	+	13.4130i	−0.170694	+	0.721085i
$347$	8.08347	+	30.1679i	0.433944	+	1.61950i	0.743582	+	0.668645i	$0.233125\pi$
$347$	8.08347	+	30.1679i	0.433944	+	1.61950i	−0.309638	+	0.950854i	$0.600208\pi$
$348$		0			0
$349$	8.48634	−	31.6714i	0.454263	−	1.69533i	−0.235982	−	0.971757i	$-0.575831\pi$
$349$	8.48634	−	31.6714i	0.454263	−	1.69533i	0.690245	−	0.723576i	$-0.257503\pi$
$350$	−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
$355$	−1.66062	−	6.19752i	−0.0881366	−	0.328930i
$356$	−3.41649	+	0.200842i	−0.181074	+	0.0106446i
$357$		0			0
$358$	−3.56588	+	3.78166i	−0.188463	+	0.199867i
$359$			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
$362$	10.0829	+	9.50757i	0.529945	+	0.499707i
$363$		0			0
$364$	11.4323	+	10.1628i	0.599215	+	0.532675i
$365$	−2.00690	−	7.48986i	−0.105046	−	0.392037i
$366$		0			0
$367$	2.66934	−	1.54114i	0.139338	−	0.0804470i	−0.428710	−	0.903442i	$-0.641032\pi$
$367$	2.66934	−	1.54114i	0.139338	−	0.0804470i	0.568049	+	0.822995i	$0.307699\pi$
$368$	−16.4711	−	7.08380i	−0.858613	−	0.369269i
$369$		0			0
$370$	−2.12775	−	1.14653i	−0.110616	−	0.0596052i
$371$	2.68045	−	10.0036i	0.139162	−	0.519361i
$372$		0			0
$373$	−7.57804	−	28.2816i	−0.392376	−	1.46437i	−0.826204	−	0.563372i	$-0.809504\pi$
$373$	−7.57804	−	28.2816i	−0.392376	−	1.46437i	0.433828	−	0.900996i	$-0.357163\pi$
$374$	−37.5352	−	8.88528i	−1.94090	−	0.459447i
$375$		0			0
$376$	5.70397	−	4.00086i	0.294160	−	0.206329i
$377$	7.25990			0.373904
$378$		0			0
$379$	−13.0654	−	13.0654i	−0.671124	−	0.671124i	0.286851	−	0.957975i	$-0.407392\pi$
$379$	−13.0654	−	13.0654i	−0.671124	−	0.671124i	−0.957975	+	0.286851i	$0.907392\pi$
$380$	0.715642	−	1.42688i	0.0367117	−	0.0731976i
$381$		0			0
$382$	−16.7697	+	10.3500i	−0.858012	+	0.529550i
$383$	1.66394	−	2.88203i	0.0850235	−	0.147265i	−0.820378	−	0.571822i	$-0.806237\pi$
$383$	1.66394	−	2.88203i	0.0850235	−	0.147265i	0.905401	+	0.424557i	$0.139570\pi$
$384$		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
$389$	1.77451	−	6.62255i	0.0899711	−	0.335777i	−0.906238	−	0.422768i	$-0.861059\pi$
$389$	1.77451	−	6.62255i	0.0899711	−	0.335777i	0.996209	+	0.0869912i	$0.0277252\pi$
$390$		0			0
$391$	−14.9867	+	25.9577i	−0.757908	+	1.31274i
$392$	30.6070	+	14.2420i	1.54588	+	0.719332i
$393$		0			0
$394$	−19.5335	+	20.7156i	−0.984085	+	1.04363i
$395$	−7.79645	+	7.79645i	−0.392282	+	0.392282i
$396$		0			0
$397$	2.33820	+	2.33820i	0.117351	+	0.117351i	0.763344	−	0.645993i	$-0.223556\pi$
$397$	2.33820	+	2.33820i	0.117351	+	0.117351i	−0.645993	+	0.763344i	$0.723556\pi$
$398$	0.327995	+	11.1686i	0.0164409	+	0.559830i
$399$		0			0
$400$	−13.9940	+	10.4417i	−0.699702	+	0.522086i
$401$	−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
$403$	9.68764	+	2.59579i	0.482575	+	0.129306i
$404$	−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	0.388082	−	0.921625i	$-0.373138\pi$
$409$	−4.36888	−	2.52237i	−0.216027	−	0.124723i	−0.604109	+	0.796901i	$0.706471\pi$
$410$	2.99121	+	0.708076i	0.147725	+	0.0349694i
$411$		0			0
$412$	13.3395	−	26.5969i	0.657189	−	1.31034i
$413$	3.20193	−	3.20193i	0.157557	−	0.157557i
$414$		0			0
$415$			2.51613i			0.123512i
$416$	3.95038	+	9.12407i	0.193683	+	0.447344i
$417$		0			0
$418$	3.03465	+	4.91694i	0.148430	+	0.240495i
$419$	−21.3504	+	5.72083i	−1.04304	+	0.279481i	−0.739371	−	0.673298i	$-0.764877\pi$
$419$	−21.3504	+	5.72083i	−1.04304	+	0.279481i	−0.303665	+	0.952779i	$0.598210\pi$
$420$		0			0
$421$	−7.95298	−	2.13099i	−0.387604	−	0.103858i	0.0597538	−	0.998213i	$-0.480968\pi$
$421$	−7.95298	−	2.13099i	−0.387604	−	0.103858i	−0.447358	+	0.894355i	$0.647635\pi$
$422$	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
$427$	8.58988	−	2.30165i	0.415693	−	0.111385i
$428$	0.183183	−	0.206065i	0.00885447	−	0.00996053i
$429$		0			0
$430$	10.0338	−	0.294668i	0.483870	−	0.0142101i
$431$	−1.08094			−0.0520671			−0.0260336	−	0.999661i	$-0.508288\pi$
$431$	−1.08094			−0.0520671			−0.0260336	+	0.999661i	$0.508288\pi$
$432$		0			0
$433$	−15.5307			−0.746359			−0.373179	−	0.927759i	$-0.621732\pi$
$433$	−15.5307			−0.746359			−0.373179	+	0.927759i	$0.621732\pi$
$434$	35.1007	−	1.03083i	1.68489	−	0.0494812i
$435$		0			0
$436$	−18.6166	−	16.5493i	−0.891572	−	0.792568i
$437$	4.33690	−	1.16207i	0.207462	−	0.0555893i
$438$		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
$443$	25.4883	+	6.82958i	1.21099	+	0.324483i	0.807149	−	0.590347i	$-0.201009\pi$
$443$	25.4883	+	6.82958i	1.21099	+	0.324483i	0.403838	+	0.914830i	$0.367676\pi$
$444$		0			0
$445$	1.31706	−	0.352904i	0.0624345	−	0.0167293i
$446$	20.8730	+	33.8199i	0.988366	+	1.60142i
$447$		0			0
$448$	22.4198	+	26.6311i	1.05924	+	1.25820i
$449$			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
$452$	14.9051	+	7.47555i	0.701078	+	0.351620i
$453$		0			0
$454$	−0.698114	−	0.165257i	−0.0327641	−	0.00775588i
$455$	−5.27777	−	3.04712i	−0.247426	−	0.142851i
$456$		0			0
$457$	18.2318	−	10.5261i	0.852846	−	0.492391i	−0.00876413	−	0.999962i	$-0.502790\pi$
$457$	18.2318	−	10.5261i	0.852846	−	0.492391i	0.861610	+	0.507571i	$0.169456\pi$
$458$	−20.5015	+	6.14380i	−0.957974	+	0.287081i
$459$		0			0
$460$	6.99660	+	1.44074i	0.326218	+	0.0671747i
$461$	−38.2603	−	10.2518i	−1.78196	−	0.477475i	−0.791021	−	0.611788i	$-0.790450\pi$
$461$	−38.2603	−	10.2518i	−1.78196	−	0.477475i	−0.990939	+	0.134314i	$0.957117\pi$
$462$		0			0
$463$	−9.98020	−	5.76207i	−0.463819	−	0.267786i	0.249829	−	0.968290i	$-0.419625\pi$
$463$	−9.98020	−	5.76207i	−0.463819	−	0.267786i	−0.713649	+	0.700504i	$0.752959\pi$
$464$	16.3503	+	2.37691i	0.759045	+	0.110345i
$465$		0			0
$466$	0.643338	+	21.9063i	0.0298020	+	1.01479i
$467$	−25.1476	−	25.1476i	−1.16369	−	1.16369i	−0.983661	−	0.180032i	$-0.942380\pi$
$467$	−25.1476	−	25.1476i	−1.16369	−	1.16369i	−0.180032	−	0.983661i	$-0.557620\pi$
$468$		0			0
$469$	−25.5197	+	25.5197i	−1.17839	+	1.17839i
$470$	−1.90433	+	2.01957i	−0.0878403	+	0.0931558i
$471$		0			0
$472$	2.76499	−	1.00891i	0.127269	−	0.0464390i
$473$	−18.1672	+	31.4664i	−0.835327	+	1.44683i
$474$		0			0
$475$	1.13164	−	4.22335i	0.0519233	−	0.193780i
$476$	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	0.920155	−	0.391553i	$-0.128062\pi$
$479$	2.64784	+	4.58619i	0.120983	+	0.209548i	−0.799173	+	0.601101i	$0.794729\pi$
$480$		0			0
$481$	−1.88491	+	3.26477i	−0.0859447	+	0.148861i
$482$	21.9198	−	13.5285i	0.998417	−	0.616206i
$483$		0			0
$484$	−10.0782	−	5.05464i	−0.458100	−	0.229756i
$485$	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	$0.486615\pi$
$488$	5.69331	+	0.999123i	0.257724	+	0.0452282i
$489$		0			0
$490$	−13.0880	−	3.09816i	−0.591253	−	0.139961i
$491$	0.936497	+	3.49505i	0.0422635	+	0.157730i	0.983833	−	0.179090i	$-0.0573154\pi$
$491$	0.936497	+	3.49505i	0.0422635	+	0.157730i	−0.941569	+	0.336820i	$0.890649\pi$
$492$		0			0
$493$	7.14866	−	26.6792i	0.321960	−	1.20157i
$494$	−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
$499$	3.22216	+	12.0253i	0.144244	+	0.538325i	0.999788	+	0.0205953i	$0.00655616\pi$
$499$	3.22216	+	12.0253i	0.144244	+	0.538325i	−0.855544	+	0.517730i	$0.826777\pi$
$500$	9.91577	−	11.1544i	0.443447	−	0.498840i
$501$		0			0
$502$	3.17824	+	2.99689i	0.141852	+	0.133758i
$503$		−	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
$506$	−17.7388	+	18.8122i	−0.788586	+	0.836305i
$507$		0			0
$508$	0.569041	+	9.67986i	0.0252471	+	0.429474i
$509$	−4.04848	−	15.1091i	−0.179446	−	0.669700i	−0.995752	−	0.0920802i	$-0.970648\pi$
$509$	−4.04848	−	15.1091i	−0.179446	−	0.669700i	0.816306	−	0.577620i	$-0.196018\pi$
$510$		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
$515$	−3.06819	+	11.4506i	−0.135200	+	0.504575i
$516$		0			0
$517$	−2.60048	−	9.70511i	−0.114369	−	0.426830i
$518$	−3.04050	+	12.8443i	−0.133592	+	0.564348i
$519$		0			0
$520$	−2.27469	−	3.24299i	−0.0997517	−	0.142215i
$521$	−40.4461			−1.77198			−0.885988	−	0.463709i	$-0.846518\pi$
$521$	−40.4461			−1.77198			−0.885988	+	0.463709i	$0.846518\pi$
$522$		0			0
$523$	7.69126	+	7.69126i	0.336315	+	0.336315i	0.854979	−	0.518663i	$-0.173570\pi$
$523$	7.69126	+	7.69126i	0.336315	+	0.336315i	−0.518663	+	0.854979i	$0.673570\pi$
$524$	−40.2771	+	13.3705i	−1.75951	+	0.584095i
$525$		0			0
$526$	19.5764	+	31.7190i	0.853571	+	1.38301i
$527$	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
$533$	1.24088	−	4.63102i	0.0537484	−	0.200592i
$534$		0			0
$535$	−0.0549239	+	0.0951309i	−0.00237457	+	0.00411287i
$536$	−22.0372	+	8.04113i	−0.951861	+	0.347324i
$537$		0			0
$538$	−0.881083	−	0.830809i	−0.0379862	−	0.0358187i
$539$	34.4241	−	34.4241i	1.48275	−	1.48275i
$540$		0			0
$541$	−17.0176	−	17.0176i	−0.731643	−	0.731643i	0.239302	−	0.970945i	$-0.423081\pi$
$541$	−17.0176	−	17.0176i	−0.731643	−	0.731643i	−0.970945	+	0.239302i	$0.923081\pi$
$542$	−27.0117	+	0.793270i	−1.16025	+	0.0340739i
$543$		0			0
$544$	37.4196	−	5.53285i	1.60435	−	0.237219i
$545$	8.59443	+	4.96200i	0.368145	+	0.212549i
$546$		0			0
$547$	21.5530	+	5.77510i	0.921539	+	0.246926i	0.688243	−	0.725480i	$-0.258382\pi$
$547$	21.5530	+	5.77510i	0.921539	+	0.246926i	0.233296	+	0.972406i	$0.425049\pi$
$548$	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
$554$	−2.30075	+	9.71936i	−0.0977497	+	0.412936i
$555$		0			0
$556$	−13.7043	+	4.54934i	−0.581193	+	0.192935i
$557$	−11.6516	+	11.6516i	−0.493695	+	0.493695i	−0.909468	−	0.415773i	$-0.863511\pi$
$557$	−11.6516	+	11.6516i	−0.493695	+	0.493695i	0.415773	+	0.909468i	$0.363511\pi$
$558$		0			0
$559$		−	15.6566i		−	0.662203i
$560$	−10.8887	−	8.59052i	−0.460130	−	0.363016i
$561$		0			0
$562$	28.5195	−	17.6017i	1.20302	−	0.742484i
$563$	4.88249	−	1.30826i	0.205772	−	0.0551365i	−0.154460	−	0.987999i	$-0.549364\pi$
$563$	4.88249	−	1.30826i	0.205772	−	0.0551365i	0.360233	+	0.932862i	$0.382697\pi$
$564$		0			0
$565$	−6.41702	−	1.71944i	−0.269966	−	0.0723372i
$566$	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	0.918690	−	0.394979i	$-0.129248\pi$
$569$	2.79764	+	4.84565i	0.117283	+	0.203140i	−0.801407	+	0.598119i	$0.795915\pi$
$570$		0			0
$571$	8.65808	−	2.31993i	0.362329	−	0.0970859i	−0.0730613	−	0.997327i	$-0.523277\pi$
$571$	8.65808	−	2.31993i	0.362329	−	0.0970859i	0.435391	+	0.900242i	$0.356610\pi$
$572$	14.3135	−	0.841433i	0.598477	−	0.0351821i
$573$		0			0
$574$	−0.492770	−	16.7794i	−0.0205678	−	0.700357i
$575$	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	$0.387067\pi$
$578$	−1.15052	−	39.1763i	−0.0478551	−	1.62952i
$579$		0			0
$580$	−6.57127	+	0.386299i	−0.272857	+	0.0160402i
$581$	13.2725	−	3.55636i	0.550637	−	0.147543i
$582$		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
$587$	−5.02128	−	1.34545i	−0.207250	−	0.0555325i	0.153700	−	0.988118i	$-0.450881\pi$
$587$	−5.02128	−	1.34545i	−0.207250	−	0.0555325i	−0.360950	+	0.932585i	$0.617548\pi$
$588$		0			0
$589$	−5.52099	+	1.47934i	−0.227488	+	0.0609553i
$590$	−0.997891	+	0.615881i	−0.0410825	+	0.0253554i
$591$		0			0
$592$	−5.31400	+	6.73561i	−0.218404	+	0.276832i
$593$		−	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
$596$	8.53846	−	2.83446i	0.349749	−	0.116104i
$597$		0			0
$598$	2.56652	−	10.8421i	0.104953	−	0.443365i
$599$	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	−0.780438	−	0.625233i	$-0.785004\pi$
$601$	−15.4248	+	8.90549i	−0.629189	+	0.363262i	0.151249	+	0.988496i	$0.451670\pi$
$602$	−15.7363	−	52.5112i	−0.641364	−	2.14020i
$603$		0			0
$604$	9.31630	+	14.1481i	0.379075	+	0.575677i
$605$	4.33891	+	1.16261i	0.176402	+	0.0472667i
$606$		0			0
$607$	−29.3159	−	16.9255i	−1.18989	−	0.686986i	−0.231612	−	0.972808i	$-0.574400\pi$
$607$	−29.3159	−	16.9255i	−1.18989	−	0.686986i	−0.958283	+	0.285823i	$0.907733\pi$
$608$	−4.54961	−	3.37751i	−0.184511	−	0.136976i
$609$		0			0
$610$	−2.30195	+	0.0676027i	−0.0932030	+	0.00273715i
$611$	3.06141	+	3.06141i	0.123852	+	0.123852i
$612$		0			0
$613$	−11.3734	+	11.3734i	−0.459367	+	0.459367i	−0.898448	−	0.439081i	$-0.855304\pi$
$613$	−11.3734	+	11.3734i	−0.459367	+	0.459367i	0.439081	+	0.898448i	$0.355304\pi$
$614$	−22.3287	−	21.0547i	−0.901115	−	0.849697i
$615$		0			0
$616$	47.1608	−	17.2085i	1.90016	−	0.693349i
$617$	18.0269	−	31.2236i	0.725738	−	1.25701i	−0.232932	−	0.972493i	$-0.574832\pi$
$617$	18.0269	−	31.2236i	0.725738	−	1.25701i	0.958670	−	0.284521i	$-0.0918346\pi$
$618$		0			0
$619$	−4.29280	+	16.0209i	−0.172542	+	0.643936i	0.824415	+	0.565986i	$0.191504\pi$
$619$	−4.29280	+	16.0209i	−0.172542	+	0.643936i	−0.996957	+	0.0779503i	$0.975162\pi$
$620$	−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
$626$	−12.2888	−	19.9111i	−0.491158	−	0.795807i
$627$		0			0
$628$	−32.1309	+	10.6663i	−1.28216	+	0.425632i
$629$	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	$0.338335\pi$
$632$	22.4745	+	32.0416i	0.893988	+	1.27455i
$633$		0			0
$634$	−2.21435	+	9.35434i	−0.0879430	+	0.371508i
$635$	−0.999874	−	3.73158i	−0.0396788	−	0.148083i
$636$		0			0
$637$	−5.42943	+	20.2629i	−0.215122	+	0.802845i
$638$	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
$643$	−2.83678	−	10.5870i	−0.111872	−	0.417511i	0.887162	−	0.461458i	$-0.152674\pi$
$643$	−2.83678	−	10.5870i	−0.111872	−	0.417511i	−0.999034	+	0.0439466i	$0.986007\pi$
$644$	−2.28932	−	38.9432i	−0.0902117	−	1.53458i
$645$		0			0
$646$	−6.49844	+	6.89168i	−0.255678	+	0.271149i
$647$		−	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
$650$	−7.89401	−	7.44358i	−0.309628	−	0.291961i
$651$		0			0
$652$	−25.7415	+	28.9570i	−1.00811	+	1.13404i
$653$	6.85777	+	25.5935i	0.268365	+	1.00155i	0.960158	+	0.279457i	$0.0901544\pi$
$653$	6.85777	+	25.5935i	0.268365	+	1.00155i	−0.691793	+	0.722096i	$0.743179\pi$
$654$		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
$659$	−1.81196	+	6.76233i	−0.0705840	+	0.263423i	−0.992196	−	0.124690i	$-0.960206\pi$
$659$	−1.81196	+	6.76233i	−0.0705840	+	0.263423i	0.921612	+	0.388113i	$0.126873\pi$
$660$		0			0
$661$	−5.40993	−	20.1902i	−0.210422	−	0.785306i	−0.987728	−	0.156183i	$-0.950081\pi$
$661$	−5.40993	−	20.1902i	−0.210422	−	0.785306i	0.777306	−	0.629123i	$-0.216586\pi$
$662$	−13.3863	−	3.16879i	−0.520273	−	0.123158i
$663$		0			0
$664$	8.79693	+	1.54378i	0.341387	+	0.0599103i
$665$	3.47311			0.134681
$666$		0			0
$667$	−13.0920	−	13.0920i	−0.506926	−	0.506926i
$668$	−14.6950	−	7.37017i	−0.568567	−	0.285160i
$669$		0			0
$670$	7.95328	−	4.90862i	0.307262	−	0.189637i
$671$	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
$677$	−2.04220	+	7.62160i	−0.0784882	+	0.292922i	−0.994002	−	0.109366i	$-0.965118\pi$
$677$	−2.04220	+	7.62160i	−0.0784882	+	0.292922i	0.915513	+	0.402287i	$0.131785\pi$
$678$		0			0
$679$	15.9508	−	27.6277i	0.612137	−	1.06025i
$680$	−14.1574	+	5.16588i	−0.542912	+	0.198103i
$681$		0			0
$682$	22.5820	−	23.9484i	0.864708	−	0.917033i
$683$	−23.0318	+	23.0318i	−0.881288	+	0.881288i	−0.993666	−	0.112378i	$-0.964153\pi$
$683$	−23.0318	+	23.0318i	−0.881288	+	0.881288i	0.112378	+	0.993666i	$0.464153\pi$
$684$		0			0
$685$	−3.31144	−	3.31144i	−0.126524	−	0.126524i
$686$	0.891563	+	30.3587i	0.0340400	+	1.15910i
$687$		0			0
$688$	5.12601	−	35.2609i	0.195427	−	1.34431i
$689$	3.62267	+	2.09155i	0.138013	+	0.0796816i
$690$		0			0
$691$	24.8749	+	6.66520i	0.946285	+	0.253556i	0.698785	−	0.715332i	$-0.253724\pi$
$691$	24.8749	+	6.66520i	0.946285	+	0.253556i	0.247500	+	0.968888i	$0.420391\pi$
$692$	−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
$698$	45.1232	+	10.6815i	1.70794	+	0.404301i
$699$		0			0
$700$	−33.9575	−	17.0311i	−1.28347	−	0.643715i
$701$	35.0396	−	35.0396i	1.32343	−	1.32343i	0.412443	−	0.910983i	$-0.364675\pi$
$701$	35.0396	−	35.0396i	1.32343	−	1.32343i	0.910983	−	0.412443i	$-0.135325\pi$
$702$		0			0
$703$		−	2.14843i		−	0.0810295i
$704$	32.5115	+	2.79125i	1.22532	+	0.105199i
$705$		0			0
$706$	2.99313	+	4.84967i	0.112648	+	0.182520i
$707$	−61.0318	+	16.3534i	−2.29534	+	0.615034i
$708$		0			0
$709$	45.5722	+	12.2110i	1.71150	+	0.458595i	0.975792	−	0.218702i	$-0.0701821\pi$
$709$	45.5722	+	12.2110i	1.71150	+	0.458595i	0.735710	+	0.677297i	$0.236849\pi$
$710$	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
$715$	−5.51784	+	1.47850i	−0.206356	+	0.0552928i
$716$	−5.49380	−	4.88375i	−0.205313	−	0.182514i
$717$		0			0
$718$	−20.9274	+	0.614590i	−0.781005	+	0.0229363i
$719$	26.0582			0.971806			0.485903	−	0.874013i	$-0.338491\pi$
$719$	26.0582			0.971806			0.485903	+	0.874013i	$0.338491\pi$
$720$		0			0
$721$	64.7383			2.41098
$722$	−25.4402	+	0.747118i	−0.946785	+	0.0278049i
$723$		0			0
$724$	−13.0214	+	14.6479i	−0.483935	+	0.544386i
$725$	−17.4158	+	4.66655i	−0.646807	+	0.173311i
$726$		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
$731$	−57.5359	−	15.4167i	−2.12804	−	0.570207i
$732$		0			0
$733$	−12.7081	+	3.40512i	−0.469384	+	0.125771i	−0.485755	−	0.874095i	$-0.661455\pi$
$733$	−12.7081	+	3.40512i	−0.469384	+	0.125771i	0.0163712	+	0.999866i	$0.494789\pi$
$734$	2.28938	+	3.70941i	0.0845026	+	0.136917i
$735$		0			0
$736$	9.32991	−	23.5776i	0.343905	−	0.869083i
$737$			33.8295i			1.24613i
$738$		0			0
$739$	−32.6637	+	32.6637i	−1.20155	+	1.20155i	−0.227861	+	0.973694i	$0.573173\pi$
$739$	−32.6637	+	32.6637i	−1.20155	+	1.20155i	−0.973694	+	0.227861i	$0.926827\pi$
$740$	1.53241	−	3.05539i	0.0563324	−	0.112318i
$741$		0			0
$742$	14.2524	+	3.37381i	0.523222	+	0.123856i
$743$	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
$749$	0.579443	+	0.155261i	0.0211724	+	0.00567312i
$750$		0			0
$751$	22.6187	+	13.0589i	0.825368	+	0.476526i	0.852264	−	0.523112i	$-0.175229\pi$
$751$	22.6187	+	13.0589i	0.825368	+	0.476526i	−0.0268964	+	0.999638i	$0.508562\pi$
$752$	5.89243	+	7.89706i	0.214875	+	0.287976i
$753$		0			0
$754$	0.301389	+	10.2626i	0.0109759	+	0.373742i
$755$	−4.77230	−	4.77230i	−0.173682	−	0.173682i
$756$		0			0
$757$	2.39808	−	2.39808i	0.0871596	−	0.0871596i	−0.662183	−	0.749342i	$-0.730370\pi$
$757$	2.39808	−	2.39808i	0.0871596	−	0.0871596i	0.749342	+	0.662183i	$0.230370\pi$
$758$	17.9269	−	19.0117i	0.651134	−	0.690536i
$759$		0			0
$760$	2.04676	+	0.952399i	0.0742438	+	0.0345471i
$761$	−23.1857	+	40.1589i	−0.840482	+	1.45576i	0.0490055	+	0.998799i	$0.484395\pi$
$761$	−23.1857	+	40.1589i	−0.840482	+	1.45576i	−0.889488	+	0.456959i	$0.848939\pi$
$762$		0			0
$763$	14.0268	−	52.3487i	0.507804	−	1.89515i
$764$	−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	$0.252442\pi$
$770$	−17.0205	+	10.5047i	−0.613375	+	0.378564i
$771$		0			0
$772$	2.40465	−	4.79452i	0.0865453	−	0.172558i
$773$	22.1409	+	22.1409i	0.796353	+	0.796353i	0.982518	−	0.186165i	$-0.0596060\pi$
$773$	22.1409	+	22.1409i	0.796353	+	0.796353i	−0.186165	+	0.982518i	$0.559606\pi$
$774$		0			0
$775$	−24.9083			−0.894731
$776$	16.9762	−	11.9074i	0.609409	−	0.427450i
$777$		0			0
$778$	9.43533	+	2.23352i	0.338273	+	0.0800756i
$779$	0.707177	+	2.63922i	0.0253372	+	0.0945599i
$780$		0			0
$781$	−8.50064	+	31.7248i	−0.304177	+	1.13520i
$782$	−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
$787$	1.12039	+	4.18136i	0.0399377	+	0.149050i	0.983015	−	0.183523i	$-0.0587501\pi$
$787$	1.12039	+	4.18136i	0.0399377	+	0.149050i	−0.943078	+	0.332572i	$0.892083\pi$
$788$	−30.0945	−	26.7527i	−1.07207	−	0.953025i
$789$		0			0
$790$	−11.3448	−	10.6974i	−0.403629	−	0.380598i
$791$			36.2799i			1.28996i
$792$		0			0
$793$			3.59194i			0.127553i
$794$	−3.20822	+	3.40236i	−0.113856	+	0.120745i
$795$		0			0
$796$	−15.7743	+	0.927310i	−0.559106	+	0.0328676i
$797$	−13.8032	−	51.5141i	−0.488933	−	1.82472i	−0.561657	−	0.827370i	$-0.689836\pi$
$797$	−13.8032	−	51.5141i	−0.488933	−	1.82472i	0.0727237	−	0.997352i	$-0.476831\pi$
$798$		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
$803$	−10.2732	+	38.3403i	−0.362535	+	1.35300i
$804$		0			0
$805$	4.02261	+	15.0126i	0.141778	+	0.529124i
$806$	−3.26725	+	13.8022i	−0.115084	+	0.486163i
$807$		0			0
$808$	−40.4514	−	7.09885i	−1.42308	−	0.249737i
$809$	30.1140			1.05875			0.529375	−	0.848388i	$-0.322426\pi$
$809$	30.1140			1.05875			0.529375	+	0.848388i	$0.322426\pi$
$810$		0			0
$811$	20.5672	+	20.5672i	0.722214	+	0.722214i	0.969056	−	0.246842i	$-0.0793929\pi$
$811$	20.5672	+	20.5672i	0.722214	+	0.722214i	−0.246842	+	0.969056i	$0.579393\pi$
$812$	11.3257	+	34.1173i	0.397454	+	1.19728i
$813$		0			0
$814$	6.49811	+	10.5287i	0.227759	+	0.369030i
$815$	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
$821$	−8.53541	+	31.8546i	−0.297888	+	1.11173i	0.641009	+	0.767533i	$0.278516\pi$
$821$	−8.53541	+	31.8546i	−0.297888	+	1.11173i	−0.938897	+	0.344199i	$0.888151\pi$
$822$		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	$0.114144\pi$
$824$	38.1513	+	17.7526i	1.32906	+	0.618440i
$825$		0			0
$826$	4.65919	+	4.39334i	0.162114	+	0.152864i
$827$	−38.7468	+	38.7468i	−1.34736	+	1.34736i	−0.458841	+	0.888518i	$0.651735\pi$
$827$	−38.7468	+	38.7468i	−1.34736	+	1.34736i	−0.888518	+	0.458841i	$0.848265\pi$
$828$		0			0
$829$	11.0569	+	11.0569i	0.384021	+	0.384021i	0.872548	−	0.488528i	$-0.162466\pi$
$829$	11.0569	+	11.0569i	0.384021	+	0.384021i	−0.488528	+	0.872548i	$0.662466\pi$
$830$	−3.55682	+	0.104455i	−0.123459	+	0.00362570i
$831$		0			0
$832$	−12.7338	+	5.96305i	−0.441466	+	0.206732i
$833$	69.1173	+	39.9049i	2.39477	+	1.38262i
$834$		0			0
$835$	6.32656	+	1.69520i	0.218940	+	0.0586647i
$836$	−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
$842$	2.68222	−	11.3308i	0.0924354	−	0.390486i
$843$		0			0
$844$	8.61799	+	25.9606i	0.296643	+	0.893601i
$845$	−5.58412	+	5.58412i	−0.192100	+	0.192100i
$846$		0			0
$847$		−	24.5309i		−	0.842891i
$848$	7.47399	+	5.89654i	0.256658	+	0.202488i
$849$		0			0
$850$	−35.1272	+	21.6799i	−1.20485	+	0.743615i
$851$	9.28662	−	2.48834i	0.318341	−	0.0852992i
$852$		0			0
$853$	40.6922	+	10.9035i	1.39328	+	0.373327i	0.875925	−	0.482447i	$-0.160252\pi$
$853$	40.6922	+	10.9035i	1.39328	+	0.373327i	0.517350	+	0.855774i	$0.326918\pi$
$854$	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	0.999866	−	0.0163548i	$-0.00520611\pi$
$857$	14.2207	+	24.6310i	0.485769	+	0.841377i	−0.514097	+	0.857732i	$0.671873\pi$
$858$		0			0
$859$	3.34555	−	0.896437i	0.114149	−	0.0305860i	−0.201293	−	0.979531i	$-0.564514\pi$
$859$	3.34555	−	0.896437i	0.114149	−	0.0305860i	0.315441	+	0.948945i	$0.397848\pi$
$860$	0.833087	+	14.1715i	0.0284080	+	0.483245i
$861$		0			0
$862$	−0.0448745	−	1.52802i	−0.00152843	−	0.0520447i
$863$	−11.1356			−0.379062			−0.189531	−	0.981875i	$-0.560697\pi$
$863$	−11.1356			−0.379062			−0.189531	+	0.981875i	$0.560697\pi$
$864$		0			0
$865$	7.76622			0.264059
$866$	−0.644746	−	21.9543i	−0.0219094	−	0.746037i
$867$		0			0
$868$	2.91436	+	49.5757i	0.0989198	+	1.68271i
$869$	54.5177	−	14.6080i	1.84939	−	0.495541i
$870$		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
$875$	31.3655	+	8.40437i	1.06035	+	0.284119i
$876$		0			0
$877$	−27.3387	+	7.32539i	−0.923163	+	0.247361i	−0.688937	−	0.724821i	$-0.741922\pi$
$877$	−27.3387	+	7.32539i	−0.923163	+	0.247361i	−0.234226	+	0.972182i	$0.575256\pi$
$878$	5.44736	−	3.36202i	0.183839	−	0.113463i
$879$		0			0
$880$	−12.9110	+	1.52324i	−0.435231	+	0.0513485i
$881$			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	−0.548151	−	0.836379i	$-0.684668\pi$
$883$	8.56478	−	8.56478i	0.288228	−	0.288228i	0.836379	+	0.548151i	$0.184668\pi$
$884$	7.40566	+	22.3086i	0.249079	+	0.750319i
$885$		0			0
$886$	−8.59619	+	36.3139i	−0.288795	+	1.21999i
$887$	−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
$893$	−2.38330	−	0.638605i	−0.0797543	−	0.0213701i
$894$		0			0
$895$	2.53624	+	1.46430i	0.0847772	+	0.0489461i
$896$	−36.7150	+	32.7983i	−1.22656	+	1.09572i
$897$		0			0
$898$	−8.40653	+	0.246880i	−0.280529	+	0.00823849i
$899$	16.6665	+	16.6665i	0.555859	+	0.555859i
$900$		0			0
$901$	11.2533	−	11.2533i	0.374903	−	0.374903i
$902$	−11.4482	−	10.7949i	−0.381183	−	0.359433i
$903$		0			0
$904$	−9.94869	+	21.3803i	−0.330888	+	0.711098i
$905$	3.90421	−	6.76228i	0.129780	−	0.224786i
$906$		0			0
$907$	−2.23987	+	8.35931i	−0.0743737	+	0.277566i	−0.993091	−	0.117350i	$-0.962560\pi$
$907$	−2.23987	+	8.35931i	−0.0743737	+	0.277566i	0.918717	+	0.394917i	$0.129227\pi$
$908$	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	$-0.874110\pi$
$911$	−23.9969	−	41.5638i	−0.795052	−	1.37707i	0.127755	−	0.991806i	$-0.459223\pi$
$912$		0			0
$913$	6.43999	−	11.1544i	0.213133	−	0.369156i
$914$	15.6366	+	25.3355i	0.517214	+	0.838024i
$915$		0			0
$916$	−9.53600	−	28.7260i	−0.315078	−	0.949134i
$917$	−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	$0.172997\pi$
$920$	−1.74617	+	9.95024i	−0.0575697	+	0.328050i
$921$		0			0
$922$	12.9037	−	54.5105i	0.424960	−	1.79521i
$923$	−3.66296	−	13.6703i	−0.120568	−	0.449965i
$924$		0			0
$925$	2.42319	−	9.04347i	0.0796740	−	0.297347i
$926$	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
$931$	−3.09423	−	11.5478i	−0.101409	−	0.378465i
$932$	−30.9402	+	1.81885i	−1.01348	+	0.0595784i
$933$		0			0
$934$	34.5048	−	36.5928i	1.12903	−	1.19735i
$935$			21.7332i			0.710751i
$936$		0			0
$937$			37.8157i			1.23539i	0.786420	+	0.617693i	$0.211932\pi$
$937$			37.8157i			1.23539i	−0.786420	+	0.617693i	$0.788068\pi$
$938$	−37.1342	−	35.0153i	−1.21247	−	1.14329i
$939$		0			0
$940$	−2.93393	−	2.60813i	−0.0956942	−	0.0850679i
$941$	9.21025	+	34.3731i	0.300246	+	1.12053i	0.936961	+	0.349433i	$0.113626\pi$
$941$	9.21025	+	34.3731i	0.300246	+	1.12053i	−0.636716	+	0.771099i	$0.719707\pi$
$942$		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
$947$	2.69018	−	10.0399i	0.0874191	−	0.326253i	−0.908342	−	0.418228i	$-0.862651\pi$
$947$	2.69018	−	10.0399i	0.0874191	−	0.326253i	0.995761	+	0.0919752i	$0.0293181\pi$
$948$		0			0
$949$	−4.42678	−	16.5210i	−0.143699	−	0.536293i
$950$	6.01712	+	1.42437i	0.195221	+	0.0462125i
$951$		0			0
$952$	47.2603	+	67.3783i	1.53171	+	2.18374i
$953$	−24.6743			−0.799280			−0.399640	−	0.916672i	$-0.630865\pi$
$953$	−24.6743			−0.799280			−0.399640	+	0.916672i	$0.630865\pi$
$954$		0			0
$955$	7.85126	+	7.85126i	0.254061	+	0.254061i
$956$	13.6595	−	27.2349i	0.441778	−	0.880841i
$957$		0			0
$958$	−6.37313	+	3.93339i	−0.205907	+	0.127082i
$959$	−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
$965$	−0.553089	+	2.06416i	−0.0178046	+	0.0664475i
$966$		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	$0.0345759\pi$
$968$	6.72687	−	14.4564i	0.216210	−	0.464647i
$969$		0			0
$970$	−5.66768	+	6.01064i	−0.181978	+	0.192990i
$971$	18.9203	−	18.9203i	0.607180	−	0.607180i	−0.335028	−	0.942208i	$-0.608746\pi$
$971$	18.9203	−	18.9203i	0.607180	−	0.607180i	0.942208	+	0.335028i	$0.108746\pi$
$972$		0			0
$973$	−22.2152	−	22.2152i	−0.712186	−	0.712186i
$974$	0.0770267	+	2.62284i	0.00246809	+	0.0840412i
$975$		0			0
$976$	−1.17601	+	8.08956i	−0.0376432	+	0.258941i
$977$	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
$979$	−6.74196	−	1.80650i	−0.215474	−	0.0577360i
$980$	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
$986$	38.0106	+	8.99781i	1.21050	+	0.286549i
$987$		0			0
$988$	1.57855	−	3.14739i	0.0502203	−	0.100132i
$989$	−28.2341	+	28.2341i	−0.897792	+	0.897792i
$990$		0			0
$991$		−	36.5529i		−	1.16114i	−0.814210	−	0.580571i	$-0.802829\pi$
$991$		−	36.5529i		−	1.16114i	0.814210	−	0.580571i	$-0.197171\pi$
$992$	−11.8772	+	30.0149i	−0.377102	+	0.952976i
$993$		0			0
$994$	−26.0253	−	42.1679i	−0.825472	−	1.33748i
$995$	6.08100	−	1.62940i	0.192781	−	0.0516554i
$996$		0			0
$997$	7.74395	+	2.07498i	0.245253	+	0.0657154i	0.379352	−	0.925253i	$-0.376147\pi$
$997$	7.74395	+	2.07498i	0.245253	+	0.0657154i	−0.134098	+	0.990968i	$0.542814\pi$
$998$	−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.179.11		88
3.2	odd	2		144.2.u.a.131.12	yes	88
4.3	odd	2		1728.2.z.a.1583.13		88
9.2	odd	6	inner	432.2.v.a.35.3		88
9.7	even	3		144.2.u.a.83.20	yes	88
12.11	even	2		576.2.y.a.239.4		88
16.5	even	4		1728.2.z.a.719.13		88
16.11	odd	4	inner	432.2.v.a.395.3		88
36.7	odd	6		576.2.y.a.47.8		88
36.11	even	6		1728.2.z.a.1007.13		88
48.5	odd	4		576.2.y.a.527.8		88
48.11	even	4		144.2.u.a.59.20	yes	88
144.11	even	12	inner	432.2.v.a.251.11		88
144.43	odd	12		144.2.u.a.11.12	✓	88
144.101	odd	12		1728.2.z.a.143.13		88
144.133	even	12		576.2.y.a.335.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.12	✓	88	144.43	odd	12
144.2.u.a.59.20	yes	88	48.11	even	4
144.2.u.a.83.20	yes	88	9.7	even	3
144.2.u.a.131.12	yes	88	3.2	odd	2
432.2.v.a.35.3		88	9.2	odd	6	inner
432.2.v.a.179.11		88	1.1	even	1	trivial
432.2.v.a.251.11		88	144.11	even	12	inner
432.2.v.a.395.3		88	16.11	odd	4	inner
576.2.y.a.47.8		88	36.7	odd	6
576.2.y.a.239.4		88	12.11	even	2
576.2.y.a.335.4		88	144.133	even	12
576.2.y.a.527.8		88	48.5	odd	4
1728.2.z.a.143.13		88	144.101	odd	12
1728.2.z.a.719.13		88	16.5	even	4
1728.2.z.a.1007.13		88	36.11	even	6
1728.2.z.a.1583.13		88	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0415142 + 1.41360i) q^{2} +(-1.99655 + 0.117369i) q^{4} +(0.769670 - 0.206232i) q^{5} +(-2.17574 - 3.76849i) q^{7} +(-0.248799 - 2.81746i) q^{8} +(0.323483 + 1.07945i) q^{10} +(-3.93991 - 1.05570i) q^{11} +(1.69772 - 0.454903i) q^{13} +(5.23683 - 3.23208i) q^{14} +(3.97245 - 0.468669i) q^{16} -6.68683i q^{17} +(-0.708282 + 0.708282i) q^{19} +(-1.51248 + 0.502090i) q^{20} +(1.32877 - 5.61330i) q^{22} +(-3.88191 - 2.24122i) q^{23} +(-3.78027 + 2.18254i) q^{25} +(0.713532 + 2.38102i) q^{26} +(4.78628 + 7.26863i) q^{28} +(3.98981 + 1.06907i) q^{29} +(4.94177 + 2.85313i) q^{31} +(0.827425 + 5.59601i) q^{32} +(9.45254 - 0.277599i) q^{34} +(-2.45179 - 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(-1.03063 - 0.971827i) q^{38} +(-0.772546 - 2.11721i) q^{40} +(1.36389 - 2.36233i) q^{41} +(2.30553 - 8.60436i) q^{43} +(7.99014 + 1.64533i) q^{44} +(3.00704 - 5.58052i) q^{46} +(1.23164 + 2.13327i) q^{47} +(-5.96768 + 10.3363i) q^{49} +(-3.24218 - 5.25319i) q^{50} +(-3.33620 + 1.10750i) q^{52} +(1.68291 + 1.68291i) q^{53} -3.25015 q^{55} +(-10.0763 + 7.06766i) q^{56} +(-1.34560 + 5.68439i) q^{58} +(0.269331 + 1.00516i) q^{59} +(-0.528935 + 1.97401i) q^{61} +(-3.82804 + 7.10415i) q^{62} +(-7.87620 + 1.40197i) q^{64} +(1.21287 - 0.700250i) q^{65} +(-2.14659 - 8.01120i) q^{67} +(0.784830 + 13.3506i) q^{68} +(3.36407 - 3.56764i) q^{70} -8.05218i q^{71} -9.73126i q^{73} +(-2.20690 - 2.08098i) q^{74} +(1.33099 - 1.49725i) q^{76} +(4.59383 + 17.1444i) q^{77} +(-11.9835 + 6.91865i) q^{79} +(2.96082 - 1.17997i) q^{80} +(3.39603 + 1.82994i) q^{82} +(-0.817277 + 3.05012i) q^{83} +(-1.37904 - 5.14666i) q^{85} +(12.2589 + 2.90190i) q^{86} +(-1.99414 + 11.3632i) q^{88} +1.71120 q^{89} +(-5.40809 - 5.40809i) q^{91} +(8.01348 + 4.01910i) q^{92} +(-2.96446 + 1.82962i) q^{94} +(-0.399073 + 0.691214i) q^{95} +(3.66561 + 6.34903i) q^{97} +(-14.8592 - 8.00683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 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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