LMFDB - Embedded newform 432.2.v.a.35.20

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			35.20
Character	$\chi$	$=$	432.35
Dual form			432.2.v.a.395.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35029 - 0.420387i) q^{2} +(1.64655 - 1.13529i) q^{4} +(-0.619079 + 2.31044i) q^{5} +(2.51270 - 4.35213i) q^{7} +(1.74605 - 2.22515i) q^{8} +O(q^{10})$	\(q+(1.35029 - 0.420387i) q^{2} +(1.64655 - 1.13529i) q^{4} +(-0.619079 + 2.31044i) q^{5} +(2.51270 - 4.35213i) q^{7} +(1.74605 - 2.22515i) q^{8} +(0.135344 + 3.38000i) q^{10} +(0.276313 + 1.03121i) q^{11} +(-1.07325 + 4.00543i) q^{13} +(1.56329 - 6.93293i) q^{14} +(1.42225 - 3.73861i) q^{16} -2.22468i q^{17} +(-0.697254 + 0.697254i) q^{19} +(1.60366 + 4.50708i) q^{20} +(0.806611 + 1.27628i) q^{22} +(2.20833 - 1.27498i) q^{23} +(-0.624725 - 0.360685i) q^{25} +(0.234635 + 5.85966i) q^{26} +(-0.803629 - 10.0186i) q^{28} +(-0.157969 - 0.589549i) q^{29} +(-0.190501 + 0.109986i) q^{31} +(0.348774 - 5.64609i) q^{32} +(-0.935228 - 3.00396i) q^{34} +(8.49974 + 8.49974i) q^{35} +(-5.16341 + 5.16341i) q^{37} +(-0.648376 + 1.23461i) q^{38} +(4.06012 + 5.41169i) q^{40} +(0.828296 + 1.43465i) q^{41} +(-4.98067 + 1.33457i) q^{43} +(1.62569 + 1.38425i) q^{44} +(2.44589 - 2.64994i) q^{46} +(-5.76715 + 9.98900i) q^{47} +(-9.12734 - 15.8090i) q^{49} +(-0.995185 - 0.224402i) q^{50} +(2.78015 + 7.81358i) q^{52} +(-7.80379 - 7.80379i) q^{53} -2.55361 q^{55} +(-5.29683 - 13.1902i) q^{56} +(-0.461143 - 0.729652i) q^{58} +(-5.09824 - 1.36607i) q^{59} +(-6.48859 + 1.73861i) q^{61} +(-0.210995 + 0.228597i) q^{62} +(-1.90260 - 7.77046i) q^{64} +(-8.58985 - 4.95935i) q^{65} +(8.22431 + 2.20370i) q^{67} +(-2.52565 - 3.66304i) q^{68} +(15.0503 + 7.90391i) q^{70} +12.0321i q^{71} +10.3710i q^{73} +(-4.80145 + 9.14272i) q^{74} +(-0.356479 + 1.93965i) q^{76} +(5.18226 + 1.38858i) q^{77} +(-7.74084 - 4.46918i) q^{79} +(7.75734 + 5.60050i) q^{80} +(1.72155 + 1.58899i) q^{82} +(5.55149 - 1.48752i) q^{83} +(5.13998 + 1.37725i) q^{85} +(-6.16430 + 3.89586i) q^{86} +(2.77706 + 1.18571i) q^{88} +6.56588 q^{89} +(14.7354 + 14.7354i) q^{91} +(2.18866 - 4.60641i) q^{92} +(-3.58806 + 15.9125i) q^{94} +(-1.17930 - 2.04262i) q^{95} +(-1.51787 + 2.62902i) q^{97} +(-18.9704 - 17.5097i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.35029	−	0.420387i	0.954797	−	0.297259i
$2$	1.35029	−	0.420387i	0.954797	−	0.297259i
$3$		0			0
$3$		0			0
$4$	1.64655	−	1.13529i	0.823274	−	0.567644i
$5$	−0.619079	+	2.31044i	−0.276861	+	1.03326i	0.677724	+	0.735317i	$0.262967\pi$
$5$	−0.619079	+	2.31044i	−0.276861	+	1.03326i	−0.954584	+	0.297941i	$0.903700\pi$
$6$		0			0
$7$	2.51270	−	4.35213i	0.949712	−	1.64495i	0.203681	−	0.979037i	$-0.434709\pi$
$7$	2.51270	−	4.35213i	0.949712	−	1.64495i	0.746030	−	0.665912i	$-0.231957\pi$
$8$	1.74605	−	2.22515i	0.617323	−	0.786710i
$9$		0			0
$10$	0.135344	+	3.38000i	0.0427994	+	1.06885i
$11$	0.276313	+	1.03121i	0.0833114	+	0.310922i	0.994989	−	0.0999837i	$-0.0318791\pi$
$11$	0.276313	+	1.03121i	0.0833114	+	0.310922i	−0.911678	+	0.410906i	$0.865212\pi$
$12$		0			0
$13$	−1.07325	+	4.00543i	−0.297666	+	1.11091i	0.641411	+	0.767198i	$0.278350\pi$
$13$	−1.07325	+	4.00543i	−0.297666	+	1.11091i	−0.939077	+	0.343708i	$0.888317\pi$
$14$	1.56329	−	6.93293i	0.417806	−	1.85290i
$15$		0			0
$16$	1.42225	−	3.73861i	0.355561	−	0.934653i
$17$		−	2.22468i		−	0.539564i	−0.962921	−	0.269782i	$-0.913048\pi$
$17$		−	2.22468i		−	0.539564i	0.962921	−	0.269782i	$-0.0869517\pi$
$18$		0			0
$19$	−0.697254	+	0.697254i	−0.159961	+	0.159961i	−0.782549	−	0.622588i	$-0.786081\pi$
$19$	−0.697254	+	0.697254i	−0.159961	+	0.159961i	0.622588	+	0.782549i	$0.286081\pi$
$20$	1.60366	+	4.50708i	0.358590	+	1.00781i
$21$		0			0
$22$	0.806611	+	1.27628i	0.171970	+	0.272103i
$23$	2.20833	−	1.27498i	0.460469	−	0.265852i	−0.251773	−	0.967786i	$-0.581013\pi$
$23$	2.20833	−	1.27498i	0.460469	−	0.265852i	0.712241	+	0.701935i	$0.247680\pi$
$24$		0			0
$25$	−0.624725	−	0.360685i	−0.124945	−	0.0721370i
$26$	0.234635	+	5.85966i	0.0460157	+	1.14917i
$27$		0			0
$28$	−0.803629	−	10.0186i	−0.151872	−	1.89334i
$29$	−0.157969	−	0.589549i	−0.0293342	−	0.109477i	0.949707	−	0.313141i	$-0.101381\pi$
$29$	−0.157969	−	0.589549i	−0.0293342	−	0.109477i	−0.979041	+	0.203665i	$0.934715\pi$
$30$		0			0
$31$	−0.190501	+	0.109986i	−0.0342150	+	0.0197541i	−0.517010	−	0.855979i	$-0.672955\pi$
$31$	−0.190501	+	0.109986i	−0.0342150	+	0.0197541i	0.482795	+	0.875733i	$0.339622\pi$
$32$	0.348774	−	5.64609i	0.0616551	−	0.998098i
$33$		0			0
$34$	−0.935228	−	3.00396i	−0.160390	−	0.515174i
$35$	8.49974	+	8.49974i	1.43672	+	1.43672i
$36$		0			0
$37$	−5.16341	+	5.16341i	−0.848859	+	0.848859i	−0.989991	−	0.141132i	$-0.954926\pi$
$37$	−5.16341	+	5.16341i	−0.848859	+	0.848859i	0.141132	+	0.989991i	$0.454926\pi$
$38$	−0.648376	+	1.23461i	−0.105180	+	0.200280i
$39$		0			0
$40$	4.06012	+	5.41169i	0.641962	+	0.855663i
$41$	0.828296	+	1.43465i	0.129358	+	0.224055i	0.923428	−	0.383772i	$-0.125375\pi$
$41$	0.828296	+	1.43465i	0.129358	+	0.224055i	−0.794070	+	0.607826i	$0.792042\pi$
$42$		0			0
$43$	−4.98067	+	1.33457i	−0.759545	+	0.203519i	−0.617748	−	0.786376i	$-0.711955\pi$
$43$	−4.98067	+	1.33457i	−0.759545	+	0.203519i	−0.141797	+	0.989896i	$0.545288\pi$
$44$	1.62569	+	1.38425i	0.245081	+	0.208683i
$45$		0			0
$46$	2.44589	−	2.64994i	0.360627	−	0.390713i
$47$	−5.76715	+	9.98900i	−0.841226	+	1.45705i	0.0476333	+	0.998865i	$0.484832\pi$
$47$	−5.76715	+	9.98900i	−0.841226	+	1.45705i	−0.888859	+	0.458181i	$0.848501\pi$
$48$		0			0
$49$	−9.12734	−	15.8090i	−1.30391	−	2.25843i
$50$	−0.995185	−	0.224402i	−0.140740	−	0.0317352i
$51$		0			0
$52$	2.78015	+	7.81358i	0.385537	+	1.08355i
$53$	−7.80379	−	7.80379i	−1.07193	−	1.07193i	−0.997204	−	0.0747298i	$-0.976191\pi$
$53$	−7.80379	−	7.80379i	−1.07193	−	1.07193i	−0.0747298	−	0.997204i	$-0.523809\pi$
$54$		0			0
$55$	−2.55361			−0.344329
$56$	−5.29683	−	13.1902i	−0.707819	−	1.76261i
$57$		0			0
$58$	−0.461143	−	0.729652i	−0.0605510	−	0.0958080i
$59$	−5.09824	−	1.36607i	−0.663735	−	0.177847i	−0.0888039	−	0.996049i	$-0.528304\pi$
$59$	−5.09824	−	1.36607i	−0.663735	−	0.177847i	−0.574931	+	0.818202i	$0.694971\pi$
$60$		0			0
$61$	−6.48859	+	1.73861i	−0.830779	+	0.222606i	−0.649053	−	0.760743i	$-0.724835\pi$
$61$	−6.48859	+	1.73861i	−0.830779	+	0.222606i	−0.181725	+	0.983349i	$0.558168\pi$
$62$	−0.210995	+	0.228597i	−0.0267963	+	0.0290318i
$63$		0			0
$64$	−1.90260	−	7.77046i	−0.237825	−	0.971308i
$65$	−8.58985	−	4.95935i	−1.06544	−	0.615132i
$66$		0			0
$67$	8.22431	+	2.20370i	1.00476	+	0.269224i	0.723438	−	0.690389i	$-0.242561\pi$
$67$	8.22431	+	2.20370i	1.00476	+	0.269224i	0.281321	+	0.959614i	$0.409227\pi$
$68$	−2.52565	−	3.66304i	−0.306280	−	0.444209i
$69$		0			0
$70$	15.0503	+	7.90391i	1.79885	+	0.944698i
$71$			12.0321i			1.42795i	0.700171	+	0.713975i	$0.253107\pi$
$71$			12.0321i			1.42795i	−0.700171	+	0.713975i	$0.746893\pi$
$72$		0			0
$73$			10.3710i			1.21383i	0.794766	+	0.606917i	$0.207594\pi$
$73$			10.3710i			1.21383i	−0.794766	+	0.606917i	$0.792406\pi$
$74$	−4.80145	+	9.14272i	−0.558157	+	1.06282i
$75$		0			0
$76$	−0.356479	+	1.93965i	−0.0408910	+	0.222493i
$77$	5.18226	+	1.38858i	0.590574	+	0.158244i
$78$		0			0
$79$	−7.74084	−	4.46918i	−0.870913	−	0.502822i	−0.00326134	−	0.999995i	$-0.501038\pi$
$79$	−7.74084	−	4.46918i	−0.870913	−	0.502822i	−0.867651	+	0.497173i	$0.834371\pi$
$80$	7.75734	+	5.60050i	0.867297	+	0.626155i
$81$		0			0
$82$	1.72155	+	1.58899i	0.190113	+	0.175474i
$83$	5.55149	−	1.48752i	0.609355	−	0.163276i	0.0590710	−	0.998254i	$-0.481186\pi$
$83$	5.55149	−	1.48752i	0.609355	−	0.163276i	0.550284	+	0.834978i	$0.314520\pi$
$84$		0			0
$85$	5.13998	+	1.37725i	0.557509	+	0.149384i
$86$	−6.16430	+	3.89586i	−0.664713	+	0.420101i
$87$		0			0
$88$	2.77706	+	1.18571i	0.296036	+	0.126398i
$89$	6.56588			0.695982			0.347991	−	0.937498i	$-0.386864\pi$
$89$	6.56588			0.695982			0.347991	+	0.937498i	$0.386864\pi$
$90$		0			0
$91$	14.7354	+	14.7354i	1.54469	+	1.54469i
$92$	2.18866	−	4.60641i	0.228183	−	0.480251i
$93$		0			0
$94$	−3.58806	+	15.9125i	−0.370080	+	1.64124i
$95$	−1.17930	−	2.04262i	−0.120994	−	0.209568i
$96$		0			0
$97$	−1.51787	+	2.62902i	−0.154116	+	0.266936i	−0.932737	−	0.360558i	$-0.882586\pi$
$97$	−1.51787	+	2.62902i	−0.154116	+	0.266936i	0.778621	+	0.627495i	$0.215920\pi$
$98$	−18.9704	−	17.5097i	−1.91630	−	1.76874i
$99$		0			0
$100$	−1.43812	+	0.115357i	−0.143812	+	0.0115357i
$101$	0.413922	−	0.110910i	0.0411868	−	0.0110360i	−0.238167	−	0.971224i	$-0.576547\pi$
$101$	0.413922	−	0.110910i	0.0411868	−	0.0110360i	0.279354	+	0.960188i	$0.409880\pi$
$102$		0			0
$103$	4.07491	+	7.05795i	0.401513	+	0.695440i	0.993909	−	0.110207i	$-0.0351513\pi$
$103$	4.07491	+	7.05795i	0.401513	+	0.695440i	−0.592396	+	0.805647i	$0.701818\pi$
$104$	7.03873	+	9.38183i	0.690204	+	0.919964i
$105$		0			0
$106$	−13.8180	−	7.25674i	−1.34212	−	0.704837i
$107$	10.5385	−	10.5385i	1.01879	−	1.01879i	0.0189732	−	0.999820i	$-0.493960\pi$
$107$	10.5385	−	10.5385i	1.01879	−	1.01879i	0.999820	−	0.0189732i	$-0.00603973\pi$
$108$		0			0
$109$	−7.21559	−	7.21559i	−0.691128	−	0.691128i	0.271352	−	0.962480i	$-0.412529\pi$
$109$	−7.21559	−	7.21559i	−0.691128	−	0.691128i	−0.962480	+	0.271352i	$0.912529\pi$
$110$	−3.44811	+	1.07351i	−0.328764	+	0.102355i
$111$		0			0
$112$	−12.6972	−	15.5838i	−1.19978	−	1.47253i
$113$	−2.83876	+	1.63896i	−0.267048	+	0.154180i	−0.627545	−	0.778580i	$-0.715940\pi$
$113$	−2.83876	+	1.63896i	−0.267048	+	0.154180i	0.360497	+	0.932760i	$0.382607\pi$
$114$		0			0
$115$	1.57863	+	5.89152i	0.147208	+	0.549387i
$116$	−0.929412	−	0.791381i	−0.0862937	−	0.0734779i
$117$		0			0
$118$	−7.45837	+	0.298651i	−0.686599	+	0.0274931i
$119$	−9.68209	−	5.58996i	−0.887555	−	0.512430i
$120$		0			0
$121$	8.53923	−	4.93013i	0.776293	−	0.448193i
$122$	−8.03056	+	5.07535i	−0.727053	+	0.459500i
$123$		0			0
$124$	−0.188804	+	0.397371i	−0.0169551	+	0.0356850i
$125$	−7.23669	+	7.23669i	−0.647269	+	0.647269i
$126$		0			0
$127$		−	6.21746i		−	0.551710i	−0.961199	−	0.275855i	$-0.911039\pi$
$127$		−	6.21746i		−	0.551710i	0.961199	−	0.275855i	$-0.0889610\pi$
$128$	−5.83566	−	9.69252i	−0.515805	−	0.856706i
$129$		0			0
$130$	−13.6836	−	3.08548i	−1.20013	−	0.270615i
$131$	3.25160	−	12.1351i	0.284093	−	1.06025i	−0.665406	−	0.746482i	$-0.731742\pi$
$131$	3.25160	−	12.1351i	0.284093	−	1.06025i	0.949499	−	0.313769i	$-0.101592\pi$
$132$		0			0
$133$	1.28255	+	4.78653i	0.111211	+	0.415045i
$134$	12.0316	−	0.481774i	1.03937	−	0.0416189i
$135$		0			0
$136$	−4.95025	−	3.88441i	−0.424480	−	0.333085i
$137$	1.22043	−	2.11385i	0.104269	−	0.180598i	−0.809171	−	0.587574i	$-0.800083\pi$
$137$	1.22043	−	2.11385i	0.104269	−	0.180598i	0.913439	+	0.406975i	$0.133417\pi$
$138$		0			0
$139$	3.77577	−	14.0914i	0.320257	−	1.19521i	−0.598738	−	0.800945i	$-0.704331\pi$
$139$	3.77577	−	14.0914i	0.320257	−	1.19521i	0.918995	−	0.394270i	$-0.129002\pi$
$140$	23.6449	+	4.34559i	1.99836	+	0.367270i
$141$		0			0
$142$	5.05815	+	16.2468i	0.424471	+	1.36340i
$143$	−4.42700			−0.370204
$144$		0			0
$145$	1.45991			0.121239
$146$	4.35984	+	14.0038i	0.360823	+	1.15896i
$147$		0			0
$148$	−2.63985	+	14.3638i	−0.216994	+	1.18069i
$149$	0.0621341	−	0.231888i	0.00509023	−	0.0189970i	−0.963334	−	0.268305i	$-0.913536\pi$
$149$	0.0621341	−	0.231888i	0.00509023	−	0.0189970i	0.968424	+	0.249308i	$0.0802032\pi$
$150$		0			0
$151$	1.91034	−	3.30881i	0.155462	−	0.269267i	−0.777765	−	0.628555i	$-0.783647\pi$
$151$	1.91034	−	3.30881i	0.155462	−	0.269267i	0.933227	+	0.359287i	$0.116980\pi$
$152$	0.334054	+	2.76894i	0.0270954	+	0.224591i
$153$		0			0
$154$	7.58128	−	0.303573i	0.610917	−	0.0244626i
$155$	−0.136180	−	0.508231i	−0.0109382	−	0.0408221i
$156$		0			0
$157$	0.0542841	−	0.202591i	0.00433234	−	0.0161685i	−0.963726	−	0.266894i	$-0.914003\pi$
$157$	0.0542841	−	0.202591i	0.00433234	−	0.0161685i	0.968058	+	0.250726i	$0.0806692\pi$
$158$	−12.3311	−	2.78052i	−0.981013	−	0.221206i
$159$		0			0
$160$	12.8290	+	4.30120i	1.01422	+	0.340040i
$161$		−	12.8146i		−	1.00993i
$162$		0			0
$163$	7.63956	−	7.63956i	0.598377	−	0.598377i	−0.341504	−	0.939880i	$-0.610936\pi$
$163$	7.63956	−	7.63956i	0.598377	−	0.598377i	0.939880	+	0.341504i	$0.110936\pi$
$164$	2.99257	+	1.42187i	0.233681	+	0.111029i
$165$		0			0
$166$	6.87077	−	4.34235i	0.533275	−	0.337032i
$167$	−3.93638	+	2.27267i	−0.304607	+	0.175865i	−0.644510	−	0.764595i	$-0.722939\pi$
$167$	−3.93638	+	2.27267i	−0.304607	+	0.175865i	0.339904	+	0.940460i	$0.389605\pi$
$168$		0			0
$169$	−3.63324	−	2.09765i	−0.279480	−	0.161358i
$170$	7.51943	−	0.301096i	0.576714	−	0.0230930i
$171$		0			0
$172$	−6.68580	+	7.85192i	−0.509787	+	0.598703i
$173$	4.50521	+	16.8137i	0.342525	+	1.27832i	0.895478	+	0.445107i	$0.146834\pi$
$173$	4.50521	+	16.8137i	0.342525	+	1.27832i	−0.552953	+	0.833212i	$0.686499\pi$
$174$		0			0
$175$	−3.13949	+	1.81259i	−0.237323	+	0.137019i
$176$	4.24829	+	0.433612i	0.320227	+	0.0326848i
$177$		0			0
$178$	8.86582	−	2.76021i	0.664521	−	0.206887i
$179$	0.113028	+	0.113028i	0.00844808	+	0.00844808i	0.711318	−	0.702870i	$-0.248099\pi$
$179$	0.113028	+	0.113028i	0.00844808	+	0.00844808i	−0.702870	+	0.711318i	$0.748099\pi$
$180$		0			0
$181$	6.17637	−	6.17637i	0.459086	−	0.459086i	−0.439270	−	0.898355i	$-0.644763\pi$
$181$	6.17637	−	6.17637i	0.459086	−	0.459086i	0.898355	+	0.439270i	$0.144763\pi$
$182$	26.0915	+	13.7024i	1.93403	+	1.01569i
$183$		0			0
$184$	1.01884	−	7.14006i	0.0751096	−	0.526372i
$185$	−8.73316	−	15.1263i	−0.642075	−	1.11211i
$186$		0			0
$187$	2.29412	−	0.614707i	0.167763	−	0.0449519i
$188$	1.84449	+	22.9948i	0.134523	+	1.67706i
$189$		0			0
$190$	−2.45109	−	2.26235i	−0.177821	−	0.164128i
$191$	1.91222	−	3.31206i	0.138363	−	0.239653i	−0.788514	−	0.615017i	$-0.789149\pi$
$191$	1.91222	−	3.31206i	0.138363	−	0.239653i	0.926877	+	0.375364i	$0.122482\pi$
$192$		0			0
$193$	4.69587	+	8.13348i	0.338016	+	0.585461i	0.984059	−	0.177840i	$-0.0569109\pi$
$193$	4.69587	+	8.13348i	0.338016	+	0.585461i	−0.646044	+	0.763300i	$0.723578\pi$
$194$	−0.944346	+	4.18802i	−0.0678001	+	0.300682i
$195$		0			0
$196$	−32.9764	−	15.6682i	−2.35545	−	1.11915i
$197$	6.00916	+	6.00916i	0.428135	+	0.428135i	0.887993	−	0.459858i	$-0.152100\pi$
$197$	6.00916	+	6.00916i	0.428135	+	0.428135i	−0.459858	+	0.887993i	$0.652100\pi$
$198$		0			0
$199$	17.0487			1.20855			0.604274	−	0.796776i	$-0.293463\pi$
$199$	17.0487			1.20855			0.604274	+	0.796776i	$0.293463\pi$
$200$	−1.89338	+	0.760333i	−0.133882	+	0.0537636i
$201$		0			0
$202$	0.512288	−	0.323768i	0.0360445	−	0.0227802i
$203$	−2.96272	−	0.793859i	−0.207942	−	0.0557180i
$204$		0			0
$205$	−3.82745	+	1.02556i	−0.267321	+	0.0716284i
$206$	8.46937	+	7.81721i	0.590089	+	0.544651i
$207$		0			0
$208$	13.4483	+	9.70917i	0.932472	+	0.673210i
$209$	−0.911678	−	0.526357i	−0.0630621	−	0.0364089i
$210$		0			0
$211$	−0.646700	−	0.173283i	−0.0445207	−	0.0119293i	0.236490	−	0.971634i	$-0.424003\pi$
$211$	−0.646700	−	0.173283i	−0.0445207	−	0.0119293i	−0.281011	+	0.959705i	$0.590670\pi$
$212$	−21.7089	−	3.98978i	−1.49097	−	0.274019i
$213$		0			0
$214$	9.79972	−	18.6602i	0.669895	−	1.27559i
$215$		−	12.3337i		−	0.841152i
$216$		0			0
$217$			1.10545i			0.0750426i
$218$	−12.7765	−	6.70977i	−0.865331	−	0.454443i
$219$		0			0
$220$	−4.20464	+	2.89908i	−0.283477	+	0.195456i
$221$	8.91079	+	2.38764i	0.599405	+	0.160610i
$222$		0			0
$223$	−10.6472	−	6.14716i	−0.712989	−	0.411644i	0.0991778	−	0.995070i	$-0.468379\pi$
$223$	−10.6472	−	6.14716i	−0.712989	−	0.411644i	−0.812167	+	0.583425i	$0.801712\pi$
$224$	−23.6961	−	15.7049i	−1.58327	−	1.04932i
$225$		0			0
$226$	−3.14414	+	3.40645i	−0.209145	+	0.226593i
$227$	18.2009	−	4.87693i	1.20804	−	0.323693i	0.402047	−	0.915619i	$-0.368299\pi$
$227$	18.2009	−	4.87693i	1.20804	−	0.323693i	0.805992	+	0.591926i	$0.201632\pi$
$228$		0			0
$229$	−6.76830	−	1.81356i	−0.447262	−	0.119843i	0.0281561	−	0.999604i	$-0.491036\pi$
$229$	−6.76830	−	1.81356i	−0.447262	−	0.119843i	−0.475418	+	0.879760i	$0.657703\pi$
$230$	4.60832	+	7.29161i	0.303864	+	0.480794i
$231$		0			0
$232$	−1.58766	−	0.677878i	−0.104235	−	0.0445049i
$233$	−24.5688			−1.60956			−0.804779	−	0.593575i	$-0.797716\pi$
$233$	−24.5688			−1.60956			−0.804779	+	0.593575i	$0.797716\pi$
$234$		0			0
$235$	−19.5086	−	19.5086i	−1.27260	−	1.27260i
$236$	−9.94539	+	3.53867i	−0.647390	+	0.230348i
$237$		0			0
$238$	−15.4235	−	3.47782i	−0.999760	−	0.225433i
$239$	1.70661	+	2.95593i	0.110391	+	0.191203i	0.915928	−	0.401343i	$-0.131456\pi$
$239$	1.70661	+	2.95593i	0.110391	+	0.191203i	−0.805537	+	0.592546i	$0.798123\pi$
$240$		0			0
$241$	12.9443	−	22.4201i	0.833813	−	1.44421i	−0.0611802	−	0.998127i	$-0.519486\pi$
$241$	12.9443	−	22.4201i	0.833813	−	1.44421i	0.894993	−	0.446080i	$-0.147180\pi$
$242$	9.45784	−	10.2469i	0.607973	−	0.658694i
$243$		0			0
$244$	−8.70995	+	10.2291i	−0.557598	+	0.654852i
$245$	42.1762	−	11.3011i	2.69454	−	0.722000i
$246$		0			0
$247$	−2.04447	−	3.54113i	−0.130087	−	0.225317i
$248$	−0.0878897	+	0.615935i	−0.00558100	+	0.0391119i
$249$		0			0
$250$	−6.72939	+	12.8138i	−0.425604	+	0.810417i
$251$	−19.0153	+	19.0153i	−1.20024	+	1.20024i	−0.226140	+	0.974095i	$0.572611\pi$
$251$	−19.0153	+	19.0153i	−1.20024	+	1.20024i	−0.974095	+	0.226140i	$0.927389\pi$
$252$		0			0
$253$	1.92497	+	1.92497i	0.121022	+	0.121022i
$254$	−2.61374	−	8.39535i	−0.164001	−	0.526771i
$255$		0			0
$256$	−11.9544	−	10.6344i	−0.747152	−	0.664653i
$257$	1.47472	−	0.851429i	0.0919904	−	0.0531107i	−0.453299	−	0.891358i	$-0.649753\pi$
$257$	1.47472	−	0.851429i	0.0919904	−	0.0531107i	0.545290	+	0.838248i	$0.316420\pi$
$258$		0			0
$259$	9.49770	+	35.4459i	0.590159	+	2.20250i
$260$	−19.7739	+	1.58613i	−1.22633	+	0.0983678i
$261$		0			0
$262$	−0.710866	−	17.7528i	−0.0439174	−	1.09677i
$263$	1.41474	+	0.816800i	0.0872366	+	0.0503661i	0.542984	−	0.839743i	$-0.317295\pi$
$263$	1.41474	+	0.816800i	0.0872366	+	0.0503661i	−0.455747	+	0.890109i	$0.650628\pi$
$264$		0			0
$265$	22.8613	−	13.1990i	1.40436	−	0.810808i
$266$	3.74400	+	5.92402i	0.229560	+	0.363225i
$267$		0			0
$268$	16.0436	−	5.70846i	0.980016	−	0.348700i
$269$	−1.20285	+	1.20285i	−0.0733392	+	0.0733392i	−0.742825	−	0.669486i	$-0.766515\pi$
$269$	−1.20285	+	1.20285i	−0.0733392	+	0.0733392i	0.669486	+	0.742825i	$0.266515\pi$
$270$		0			0
$271$			22.9432i			1.39370i	0.717218	+	0.696849i	$0.245415\pi$
$271$			22.9432i			1.39370i	−0.717218	+	0.696849i	$0.754585\pi$
$272$	−8.31721	−	3.16404i	−0.504305	−	0.191848i
$273$		0			0
$274$	0.759297	−	3.36736i	0.0458708	−	0.203429i
$275$	0.199324	−	0.743886i	0.0120197	−	0.0448580i
$276$		0			0
$277$	1.03947	+	3.87936i	0.0624558	+	0.233088i	0.990097	−	0.140384i	$-0.0448338\pi$
$277$	1.03947	+	3.87936i	0.0624558	+	0.233088i	−0.927641	+	0.373472i	$0.878167\pi$
$278$	−0.825462	−	20.6147i	−0.0495079	−	1.23639i
$279$		0			0
$280$	33.7542	−	4.07222i	2.01720	−	0.243362i
$281$	15.2214	−	26.3642i	0.908031	−	1.57276i	0.0912360	−	0.995829i	$-0.470918\pi$
$281$	15.2214	−	26.3642i	0.908031	−	1.57276i	0.816795	−	0.576927i	$-0.195748\pi$
$282$		0			0
$283$	3.10051	−	11.5713i	0.184306	−	0.687841i	−0.810472	−	0.585778i	$-0.800789\pi$
$283$	3.10051	−	11.5713i	0.184306	−	0.687841i	0.994778	−	0.102063i	$-0.0325442\pi$
$284$	13.6599	+	19.8115i	0.810567	+	1.17559i
$285$		0			0
$286$	−5.97772	+	1.86106i	−0.353470	+	0.110047i
$287$	8.32505			0.491412
$288$		0			0
$289$	12.0508			0.708871
$290$	1.97130	−	0.613728i	0.115759	−	0.0360394i
$291$		0			0
$292$	11.7741	+	17.0763i	0.689025	+	0.999318i
$293$	−5.00638	+	18.6841i	−0.292476	+	1.09153i	0.650726	+	0.759313i	$0.274465\pi$
$293$	−5.00638	+	18.6841i	−0.292476	+	1.09153i	−0.943201	+	0.332222i	$0.892202\pi$
$294$		0			0
$295$	6.31244	−	10.9335i	0.367524	−	0.636571i
$296$	2.47379	+	20.5050i	0.143786	+	1.19183i
$297$		0			0
$298$	−0.0135838	−	0.339235i	−0.000786889	−	0.0196514i
$299$	2.73675	+	10.2137i	0.158270	+	0.590672i
$300$		0			0
$301$	−6.70673	+	25.0299i	−0.386570	+	1.44270i
$302$	1.18853	−	5.27093i	0.0683922	−	0.303308i
$303$		0			0
$304$	1.61510	+	3.59843i	0.0926321	+	0.206384i
$305$		−	16.0678i		−	0.920040i
$306$		0			0
$307$	2.25289	−	2.25289i	0.128579	−	0.128579i	−0.639889	−	0.768468i	$-0.721020\pi$
$307$	2.25289	−	2.25289i	0.128579	−	0.128579i	0.768468	+	0.639889i	$0.221020\pi$
$308$	10.1093	−	3.59699i	0.576030	−	0.204957i
$309$		0			0
$310$	−0.397536	−	0.629009i	−0.0225785	−	0.0357253i
$311$	24.7389	−	14.2830i	1.40281	−	0.809914i	0.408132	−	0.912923i	$-0.366180\pi$
$311$	24.7389	−	14.2830i	1.40281	−	0.809914i	0.994680	+	0.103009i	$0.0328469\pi$
$312$		0			0
$313$	−18.1750	−	10.4933i	−1.02731	−	0.593119i	−0.111099	−	0.993809i	$-0.535437\pi$
$313$	−18.1750	−	10.4933i	−1.02731	−	0.593119i	−0.916214	+	0.400690i	$0.868770\pi$
$314$	−0.0118676	−	0.296376i	−0.000669729	−	0.0167255i
$315$		0			0
$316$	−17.8195	+	1.42936i	−1.00242	+	0.0804079i
$317$	−3.07456	−	11.4744i	−0.172684	−	0.644466i	−0.996934	−	0.0782407i	$-0.975070\pi$
$317$	−3.07456	−	11.4744i	−0.172684	−	0.644466i	0.824250	−	0.566226i	$-0.191597\pi$
$318$		0			0
$319$	0.564302	−	0.325800i	0.0315949	−	0.0182413i
$320$	19.1310	+	0.414694i	1.06946	+	0.0231821i
$321$		0			0
$322$	−5.38709	−	17.3034i	−0.300211	−	0.964279i
$323$	1.55117	+	1.55117i	0.0863093	+	0.0863093i
$324$		0			0
$325$	2.11518	−	2.11518i	0.117329	−	0.117329i
$326$	7.10402	−	13.5272i	0.393456	−	0.749201i
$327$		0			0
$328$	4.63857	+	0.661891i	0.256122	+	0.0365468i
$329$	28.9823	+	50.1988i	1.59784	+	2.76755i
$330$		0			0
$331$	6.38080	−	1.70973i	0.350720	−	0.0939753i	−0.0791579	−	0.996862i	$-0.525223\pi$
$331$	6.38080	−	1.70973i	0.350720	−	0.0939753i	0.429878	+	0.902887i	$0.358556\pi$
$332$	7.45203	−	8.75180i	0.408984	−	0.480317i
$333$		0			0
$334$	−4.35984	+	4.72357i	−0.238560	+	0.258462i
$335$	−10.1830	+	17.6375i	−0.556357	+	0.963638i
$336$		0			0
$337$	13.3790	+	23.1731i	0.728801	+	1.26232i	0.957390	+	0.288798i	$0.0932555\pi$
$337$	13.3790	+	23.1731i	0.728801	+	1.26232i	−0.228589	+	0.973523i	$0.573411\pi$
$338$	−5.78775	−	1.30506i	−0.314812	−	0.0709861i
$339$		0			0
$340$	10.0268	−	3.56764i	0.543780	−	0.193482i
$341$	−0.166057	−	0.166057i	−0.00899248	−	0.00899248i
$342$		0			0
$343$	−56.5593			−3.05391
$344$	−5.72690	+	13.4130i	−0.308774	+	0.723179i
$345$		0			0
$346$	13.1516	+	20.8093i	0.707033	+	1.11872i
$347$	2.96361	+	0.794096i	0.159095	+	0.0426293i	0.337487	−	0.941330i	$-0.390423\pi$
$347$	2.96361	+	0.794096i	0.159095	+	0.0426293i	−0.178393	+	0.983959i	$0.557090\pi$
$348$		0			0
$349$	22.6749	−	6.07573i	1.21376	−	0.325226i	0.405524	−	0.914084i	$-0.367089\pi$
$349$	22.6749	−	6.07573i	1.21376	−	0.325226i	0.808236	+	0.588858i	$0.200422\pi$
$350$	−3.47723	+	3.76732i	−0.185866	+	0.201372i
$351$		0			0
$352$	5.91870	−	1.20043i	0.315468	−	0.0639830i
$353$	−2.70837	−	1.56368i	−0.144152	−	0.0832262i	0.426189	−	0.904634i	$-0.359856\pi$
$353$	−2.70837	−	1.56368i	−0.144152	−	0.0832262i	−0.570341	+	0.821408i	$0.693189\pi$
$354$		0			0
$355$	−27.7994	−	7.44884i	−1.47544	−	0.395343i
$356$	10.8110	−	7.45416i	0.572984	−	0.395070i
$357$		0			0
$358$	0.200135	+	0.105104i	0.0105775	+	0.00555494i
$359$		−	25.4807i		−	1.34482i	−0.740180	−	0.672409i	$-0.765260\pi$
$359$		−	25.4807i		−	1.34482i	0.740180	−	0.672409i	$-0.234740\pi$
$360$		0			0
$361$			18.0277i			0.948825i
$362$	5.74340	−	10.9363i	0.301866	−	0.574801i
$363$		0			0
$364$	40.9914	+	7.53362i	2.14853	+	0.394869i
$365$	−23.9615	−	6.42047i	−1.25420	−	0.336063i
$366$		0			0
$367$	−27.1264	−	15.6614i	−1.41599	−	0.817520i	−0.420043	−	0.907504i	$-0.637985\pi$
$367$	−27.1264	−	15.6614i	−1.41599	−	0.817520i	−0.995943	+	0.0899840i	$0.971318\pi$
$368$	−1.62587	−	10.0694i	−0.0847542	−	0.524905i
$369$		0			0
$370$	−18.1512	−	16.7535i	−0.943635	−	0.870973i
$371$	−53.5717	+	14.3545i	−2.78130	+	0.745248i
$372$		0			0
$373$	−11.5188	−	3.08646i	−0.596423	−	0.159811i	−0.0520359	−	0.998645i	$-0.516571\pi$
$373$	−11.5188	−	3.08646i	−0.596423	−	0.159811i	−0.544387	+	0.838834i	$0.683238\pi$
$374$	2.83930	−	1.79445i	0.146817	−	0.0927888i
$375$		0			0
$376$	12.1573	+	30.2741i	0.626965	+	1.56127i
$377$	2.53094			0.130350
$378$		0			0
$379$	3.76992	+	3.76992i	0.193648	+	0.193648i	0.797270	−	0.603623i	$-0.206277\pi$
$379$	3.76992	+	3.76992i	0.193648	+	0.193648i	−0.603623	+	0.797270i	$0.706277\pi$
$380$	−4.26074	−	2.02442i	−0.218571	−	0.103850i
$381$		0			0
$382$	1.18970	−	5.27611i	0.0608702	−	0.269949i
$383$	−9.14036	−	15.8316i	−0.467051	−	0.808956i	0.532241	−	0.846593i	$-0.321350\pi$
$383$	−9.14036	−	15.8316i	−0.467051	−	0.808956i	−0.999291	+	0.0376375i	$0.988017\pi$
$384$		0			0
$385$	−6.41646	+	11.1136i	−0.327013	+	0.566403i
$386$	9.75998	+	9.00844i	0.496770	+	0.458518i
$387$		0			0
$388$	0.485454	+	6.05202i	0.0246452	+	0.307245i
$389$	−24.6006	+	6.59172i	−1.24730	+	0.334214i	−0.821294	−	0.570506i	$-0.806747\pi$
$389$	−24.6006	+	6.59172i	−1.24730	+	0.334214i	−0.426008	+	0.904719i	$0.640081\pi$
$390$		0			0
$391$	−2.83642	−	4.91283i	−0.143444	−	0.248452i
$392$	−51.1143	−	7.29365i	−2.58166	−	0.368385i
$393$		0			0
$394$	10.6403	+	5.58791i	0.536049	+	0.281515i
$395$	15.1179	−	15.1179i	0.760666	−	0.760666i
$396$		0			0
$397$	−4.35736	−	4.35736i	−0.218689	−	0.218689i	0.589257	−	0.807946i	$-0.299421\pi$
$397$	−4.35736	−	4.35736i	−0.218689	−	0.218689i	−0.807946	+	0.589257i	$0.799421\pi$
$398$	23.0206	−	7.16705i	1.15392	−	0.359252i
$399$		0			0
$400$	−2.23697	+	1.82262i	−0.111849	+	0.0911310i
$401$	−31.6292	+	18.2611i	−1.57948	+	0.911916i	−0.584553	+	0.811355i	$0.698730\pi$
$401$	−31.6292	+	18.2611i	−1.57948	+	0.911916i	−0.994931	+	0.100561i	$0.967936\pi$
$402$		0			0
$403$	−0.236085	−	0.881081i	−0.0117602	−	0.0438898i
$404$	0.555628	−	0.652539i	0.0276435	−	0.0324650i
$405$		0			0
$406$	−4.33425	+	0.173554i	−0.215105	+	0.00861334i
$407$	−6.75129	−	3.89786i	−0.334649	−	0.193210i
$408$		0			0
$409$	6.64716	−	3.83774i	0.328681	−	0.189764i	−0.326574	−	0.945172i	$-0.605894\pi$
$409$	6.64716	−	3.83774i	0.328681	−	0.189764i	0.655255	+	0.755407i	$0.272561\pi$
$410$	−4.73702	+	2.99382i	−0.233945	+	0.147854i
$411$		0			0
$412$	14.7223	+	6.99506i	0.725317	+	0.344622i
$413$	−18.7557	+	18.7557i	−0.922907	+	0.922907i
$414$		0			0
$415$			13.7472i			0.674826i
$416$	22.2407	+	7.45666i	1.09044	+	0.365593i
$417$		0			0
$418$	−1.45230	−	0.327476i	−0.0710343	−	0.0160174i
$419$	1.66712	−	6.22178i	0.0814442	−	0.303954i	−0.913173	−	0.407572i	$-0.866375\pi$
$419$	1.66712	−	6.22178i	0.0814442	−	0.303954i	0.994617	+	0.103618i	$0.0330421\pi$
$420$		0			0
$421$	2.94683	+	10.9977i	0.143620	+	0.535996i	0.999813	+	0.0193401i	$0.00615652\pi$
$421$	2.94683	+	10.9977i	0.143620	+	0.535996i	−0.856193	+	0.516655i	$0.827177\pi$
$422$	−0.946077	+	0.0378832i	−0.0460543	+	0.00184413i
$423$		0			0
$424$	−30.9905	+	3.73879i	−1.50503	+	0.181572i
$425$	−0.802409	+	1.38981i	−0.0389225	+	0.0674158i
$426$		0			0
$427$	−8.73722	+	32.6078i	−0.422824	+	1.57800i
$428$	5.38792	−	29.3163i	0.260435	−	1.41706i
$429$		0			0
$430$	−5.18494	−	16.6541i	−0.250040	−	0.803130i
$431$	8.35135			0.402270			0.201135	−	0.979564i	$-0.435537\pi$
$431$	8.35135			0.402270			0.201135	+	0.979564i	$0.435537\pi$
$432$		0			0
$433$	−1.97345			−0.0948380			−0.0474190	−	0.998875i	$-0.515100\pi$
$433$	−1.97345			−0.0948380			−0.0474190	+	0.998875i	$0.515100\pi$
$434$	0.464716	+	1.49267i	0.0223071	+	0.0716505i
$435$		0			0
$436$	−20.0726	−	3.68905i	−0.961303	−	0.176674i
$437$	−0.650783	+	2.42875i	−0.0311312	+	0.116183i
$438$		0			0
$439$	0.292649	−	0.506883i	0.0139674	−	0.0241922i	−0.858957	−	0.512047i	$-0.828887\pi$
$439$	0.292649	−	0.506883i	0.0139674	−	0.0241922i	0.872925	+	0.487855i	$0.162221\pi$
$440$	−4.45874	+	5.68217i	−0.212562	+	0.270887i
$441$		0			0
$442$	13.0359	−	0.521987i	0.620052	−	0.0248284i
$443$	−7.27885	−	27.1650i	−0.345829	−	1.29065i	−0.891641	−	0.452743i	$-0.850446\pi$
$443$	−7.27885	−	27.1650i	−0.345829	−	1.29065i	0.545812	−	0.837907i	$-0.316221\pi$
$444$		0			0
$445$	−4.06480	+	15.1700i	−0.192690	+	0.719129i
$446$	−16.9610	−	3.82448i	−0.803125	−	0.181095i
$447$		0			0
$448$	−38.5987	−	11.2445i	−1.82362	−	0.531252i
$449$			31.8656i			1.50383i	0.659258	+	0.751916i	$0.270870\pi$
$449$			31.8656i			1.50383i	−0.659258	+	0.751916i	$0.729130\pi$
$450$		0			0
$451$	−1.25056	+	1.25056i	−0.0588867	+	0.0588867i
$452$	−2.81347	+	5.92144i	−0.132334	+	0.278521i
$453$		0			0
$454$	22.5263	−	14.2367i	1.05721	−	0.668162i
$455$	−43.1675	+	24.9227i	−2.02372	+	1.16840i
$456$		0			0
$457$	12.6310	+	7.29251i	0.590854	+	0.341129i	0.765435	−	0.643513i	$-0.222524\pi$
$457$	12.6310	+	7.29251i	0.590854	+	0.341129i	−0.174581	+	0.984643i	$0.555857\pi$
$458$	−9.90154	+	0.396482i	−0.462669	+	0.0185264i
$459$		0			0
$460$	9.28786	+	7.90848i	0.433049	+	0.368735i
$461$	−0.978401	−	3.65144i	−0.0455687	−	0.170065i	0.939391	−	0.342847i	$-0.111391\pi$
$461$	−0.978401	−	3.65144i	−0.0455687	−	0.170065i	−0.984960	+	0.172782i	$0.944724\pi$
$462$		0			0
$463$	15.8368	−	9.14339i	0.735999	−	0.424929i	−0.0846136	−	0.996414i	$-0.526966\pi$
$463$	15.8368	−	9.14339i	0.735999	−	0.424929i	0.820613	+	0.571484i	$0.193632\pi$
$464$	−2.42877	−	0.247898i	−0.112753	−	0.0115084i
$465$		0			0
$466$	−33.1750	+	10.3284i	−1.53680	+	0.478455i
$467$	10.9698	+	10.9698i	0.507621	+	0.507621i	0.913795	−	0.406175i	$-0.133138\pi$
$467$	10.9698	+	10.9698i	0.507621	+	0.507621i	−0.406175	+	0.913795i	$0.633138\pi$
$468$		0			0
$469$	30.2560	−	30.2560i	1.39709	−	1.39709i
$470$	−34.5434	−	18.1410i	−1.59337	−	0.836784i
$471$		0			0
$472$	−11.9415	+	8.95914i	−0.549653	+	0.412378i
$473$	−2.75244	−	4.76737i	−0.126558	−	0.219204i
$474$		0			0
$475$	0.687081	−	0.184103i	0.0315254	−	0.00844722i
$476$	−22.2882	+	1.78782i	−1.02158	+	0.0819444i
$477$		0			0
$478$	3.54704	+	3.27392i	0.162238	+	0.149745i
$479$	−6.26251	+	10.8470i	−0.286142	+	0.495612i	−0.972885	−	0.231288i	$-0.925706\pi$
$479$	−6.26251	+	10.8470i	−0.286142	+	0.495612i	0.686744	+	0.726900i	$0.259039\pi$
$480$		0			0
$481$	−15.1400	−	26.2233i	−0.690326	−	1.19568i
$482$	8.05333	−	35.7152i	0.366819	−	1.62678i
$483$		0			0
$484$	8.46315	−	17.8122i	0.384688	−	0.809644i
$485$	−5.13450	−	5.13450i	−0.233146	−	0.233146i
$486$		0			0
$487$	−12.7213			−0.576459			−0.288230	−	0.957561i	$-0.593067\pi$
$487$	−12.7213			−0.576459			−0.288230	+	0.957561i	$0.593067\pi$
$488$	−7.46074	+	17.4738i	−0.337732	+	0.791002i
$489$		0			0
$490$	52.1992	−	32.9901i	2.35812	−	1.49034i
$491$	10.5795	+	2.83477i	0.477446	+	0.127931i	0.489513	−	0.871996i	$-0.337175\pi$
$491$	10.5795	+	2.83477i	0.477446	+	0.127931i	−0.0120673	+	0.999927i	$0.503841\pi$
$492$		0			0
$493$	−1.31156	+	0.351431i	−0.0590696	+	0.0158277i
$494$	−4.24927	−	3.92207i	−0.191184	−	0.176462i
$495$		0			0
$496$	0.140255	+	0.868637i	0.00629764	+	0.0390030i
$497$	52.3653	+	30.2331i	2.34891	+	1.35614i
$498$		0			0
$499$	−23.1524	−	6.20368i	−1.03645	−	0.277715i	−0.299806	−	0.954000i	$-0.596922\pi$
$499$	−23.1524	−	6.20368i	−1.03645	−	0.277715i	−0.736639	+	0.676286i	$0.763589\pi$
$500$	−3.69984	+	20.1313i	−0.165462	+	0.900298i
$501$		0			0
$502$	−17.6823	+	33.6699i	−0.789200	+	1.50276i
$503$			27.6712i			1.23380i	0.787042	+	0.616899i	$0.211611\pi$
$503$			27.6712i			1.23380i	−0.787042	+	0.616899i	$0.788389\pi$
$504$		0			0
$505$			1.02500i			0.0456120i
$506$	3.40849	+	1.79003i	0.151526	+	0.0795763i
$507$		0			0
$508$	−7.05860	−	10.2373i	−0.313175	−	0.454209i
$509$	27.5074	+	7.37058i	1.21924	+	0.326695i	0.810383	−	0.585901i	$-0.199259\pi$
$509$	27.5074	+	7.37058i	1.21924	+	0.326695i	0.408861	+	0.912597i	$0.365926\pi$
$510$		0			0
$511$	45.1359	+	26.0592i	1.99669	+	1.15279i
$512$	−20.6125	−	9.33406i	−0.910953	−	0.412511i
$513$		0			0
$514$	1.63336	−	1.76963i	0.0720446	−	0.0780549i
$515$	−18.8296	+	5.04538i	−0.829732	+	0.222326i
$516$		0			0
$517$	−11.8943	−	3.18708i	−0.523112	−	0.140167i
$518$	27.7256	+	43.8694i	1.21819	+	1.92751i
$519$		0			0
$520$	−26.0336	+	10.4544i	−1.14165	+	0.458457i
$521$	13.7107			0.600678			0.300339	−	0.953832i	$-0.402900\pi$
$521$	13.7107			0.600678			0.300339	+	0.953832i	$0.402900\pi$
$522$		0			0
$523$	4.42816	+	4.42816i	0.193630	+	0.193630i	0.797262	−	0.603633i	$-0.206281\pi$
$523$	4.42816	+	4.42816i	0.193630	+	0.193630i	−0.603633	+	0.797262i	$0.706281\pi$
$524$	−8.42294	−	23.6726i	−0.367958	−	1.03414i
$525$		0			0
$526$	2.25368	+	0.508176i	0.0982650	+	0.0221575i
$527$	0.244683	+	0.423804i	0.0106586	+	0.0184612i
$528$		0			0
$529$	−8.24885	+	14.2874i	−0.358646	+	0.621192i
$530$	25.3207	−	27.4330i	1.09986	−	1.19162i
$531$		0			0
$532$	7.54586	+	6.42519i	0.327155	+	0.278568i
$533$	−6.63536	+	1.77794i	−0.287409	+	0.0770111i
$534$		0			0
$535$	17.8243	+	30.8726i	0.770613	+	1.33474i
$536$	19.2636	−	14.4526i	0.832062	−	0.624256i
$537$		0			0
$538$	−1.11853	+	2.12986i	−0.0482233	+	0.0918248i
$539$	13.7805	−	13.7805i	0.593566	−	0.593566i
$540$		0			0
$541$	−23.9889	−	23.9889i	−1.03136	−	1.03136i	−0.999492	−	0.0318715i	$-0.989853\pi$
$541$	−23.9889	−	23.9889i	−1.03136	−	1.03136i	−0.0318715	−	0.999492i	$-0.510147\pi$
$542$	9.64502	+	30.9799i	0.414289	+	1.33070i
$543$		0			0
$544$	−12.5607	−	0.775910i	−0.538538	−	0.0332669i
$545$	21.1382	−	12.2041i	0.905460	−	0.522768i
$546$		0			0
$547$	−0.642523	−	2.39793i	−0.0274723	−	0.102528i	0.950828	−	0.309718i	$-0.100235\pi$
$547$	−0.642523	−	2.39793i	−0.0274723	−	0.102528i	−0.978301	+	0.207190i	$0.933568\pi$
$548$	−0.390326	−	4.86610i	−0.0166739	−	0.207869i
$549$		0			0
$550$	−0.0435763	−	1.08825i	−0.00185810	−	0.0464033i
$551$	0.521210	+	0.300921i	0.0222043	+	0.0128197i
$552$		0			0
$553$	−38.9008	+	22.4594i	−1.65423	+	0.955071i
$554$	3.03442	+	4.80127i	0.128920	+	0.203986i
$555$		0			0
$556$	−9.78076	−	27.4887i	−0.414797	−	1.16578i
$557$	32.9289	−	32.9289i	1.39524	−	1.39524i	0.582186	−	0.813056i	$-0.302198\pi$
$557$	32.9289	−	32.9289i	1.39524	−	1.39524i	0.813056	−	0.582186i	$-0.197802\pi$
$558$		0			0
$559$		−	21.3820i		−	0.904363i
$560$	43.8660	−	19.6885i	1.85368	−	0.831992i
$561$		0			0
$562$	9.47005	−	41.9981i	0.399470	−	1.77158i
$563$	−1.92423	+	7.18131i	−0.0810964	+	0.302656i	−0.994546	−	0.104295i	$-0.966741\pi$
$563$	−1.92423	+	7.18131i	−0.0810964	+	0.302656i	0.913450	+	0.406951i	$0.133408\pi$
$564$		0			0
$565$	−2.02929	−	7.57342i	−0.0853730	−	0.318616i
$566$	−0.677836	−	16.9279i	−0.0284916	−	0.711535i
$567$		0			0
$568$	26.7733	+	21.0087i	1.12338	+	0.881506i
$569$	−13.9011	+	24.0775i	−0.582766	+	1.00938i	0.412383	+	0.911010i	$0.364696\pi$
$569$	−13.9011	+	24.0775i	−0.582766	+	1.00938i	−0.995150	+	0.0983706i	$0.968637\pi$
$570$		0			0
$571$	−1.02058	+	3.80886i	−0.0427100	+	0.159396i	−0.983987	−	0.178239i	$-0.942960\pi$
$571$	−1.02058	+	3.80886i	−0.0427100	+	0.159396i	0.941277	+	0.337635i	$0.109627\pi$
$572$	−7.28927	+	5.02592i	−0.304780	+	0.210144i
$573$		0			0
$574$	11.2412	−	3.49974i	0.469199	−	0.146077i
$575$	−1.83947			−0.0767110
$576$		0			0
$577$	−10.6180			−0.442032			−0.221016	−	0.975270i	$-0.570937\pi$
$577$	−10.6180			−0.442032			−0.221016	+	0.975270i	$0.570937\pi$
$578$	16.2720	−	5.06601i	0.676827	−	0.210718i
$579$		0			0
$580$	2.40381	−	1.65742i	0.0998130	−	0.0688206i
$581$	7.47537	−	27.8985i	0.310131	−	1.15742i
$582$		0			0
$583$	5.89109	−	10.2037i	0.243984	−	0.422593i
$584$	23.0770	+	18.1083i	0.954935	+	0.749327i
$585$		0			0
$586$	1.09450	+	27.3335i	0.0452133	+	1.12913i
$587$	−0.889198	−	3.31853i	−0.0367011	−	0.136970i	0.945144	−	0.326653i	$-0.105921\pi$
$587$	−0.889198	−	3.31853i	−0.0367011	−	0.136970i	−0.981845	+	0.189682i	$0.939254\pi$
$588$		0			0
$589$	0.0561396	−	0.209516i	0.00231319	−	0.00863295i
$590$	3.92731	−	17.4170i	0.161685	−	0.717045i
$591$		0			0
$592$	11.9603	+	26.6476i	0.491567	+	1.09521i
$593$			27.5541i			1.13151i	0.824573	+	0.565755i	$0.191415\pi$
$593$			27.5541i			1.13151i	−0.824573	+	0.565755i	$0.808585\pi$
$594$		0			0
$595$	18.9092	−	18.9092i	0.775202	−	0.775202i
$596$	−0.160952	−	0.452355i	−0.00659286	−	0.0185292i
$597$		0			0
$598$	7.98910	+	12.6409i	0.326699	+	0.516925i
$599$	14.5840	−	8.42008i	0.595886	−	0.344035i	−0.171535	−	0.985178i	$-0.554873\pi$
$599$	14.5840	−	8.42008i	0.595886	−	0.344035i	0.767422	+	0.641143i	$0.221539\pi$
$600$		0			0
$601$	−22.6011	−	13.0487i	−0.921916	−	0.532269i	−0.0376703	−	0.999290i	$-0.511994\pi$
$601$	−22.6011	−	13.0487i	−0.921916	−	0.532269i	−0.884246	+	0.467022i	$0.845327\pi$
$602$	1.46623	+	36.6169i	0.0597591	+	1.49239i
$603$		0			0
$604$	−0.610979	−	7.61691i	−0.0248604	−	0.309928i
$605$	6.10428	+	22.7815i	0.248174	+	0.926198i
$606$		0			0
$607$	−14.0103	+	8.08887i	−0.568662	+	0.328317i	−0.756615	−	0.653861i	$-0.773148\pi$
$607$	−14.0103	+	8.08887i	−0.568662	+	0.328317i	0.187953	+	0.982178i	$0.439815\pi$
$608$	3.69358	+	4.17995i	0.149794	+	0.169519i
$609$		0			0
$610$	−6.75470	−	21.6961i	−0.273490	−	0.878451i
$611$	−33.8206	−	33.8206i	−1.36824	−	1.36824i
$612$		0			0
$613$	−0.969385	+	0.969385i	−0.0391531	+	0.0391531i	−0.726412	−	0.687259i	$-0.758814\pi$
$613$	−0.969385	+	0.969385i	−0.0391531	+	0.0391531i	0.687259	+	0.726412i	$0.258814\pi$
$614$	2.09496	−	3.98913i	0.0845456	−	0.160988i
$615$		0			0
$616$	12.1383	−	9.10678i	0.489066	−	0.366923i
$617$	−12.4805	−	21.6168i	−0.502445	−	0.870260i	−0.999996	−	0.00282568i	$-0.999101\pi$
$617$	−12.4805	−	21.6168i	−0.502445	−	0.870260i	0.497551	−	0.867435i	$-0.334233\pi$
$618$		0			0
$619$	−9.79499	+	2.62456i	−0.393694	+	0.105490i	−0.450235	−	0.892910i	$-0.648660\pi$
$619$	−9.79499	+	2.62456i	−0.393694	+	0.105490i	0.0565406	+	0.998400i	$0.481993\pi$
$620$	−0.801215	−	0.682223i	−0.0321776	−	0.0273987i
$621$		0			0
$622$	27.4002	−	29.6860i	1.09865	−	1.19030i
$623$	16.4981	−	28.5755i	0.660982	−	1.14485i
$624$		0			0
$625$	−14.0432	−	24.3236i	−0.561730	−	0.972944i
$626$	−28.9527	−	6.52848i	−1.15718	−	0.260931i
$627$		0			0
$628$	−0.140618	−	0.395204i	−0.00561125	−	0.0157704i
$629$	11.4869	+	11.4869i	0.458014	+	0.458014i
$630$		0			0
$631$	14.5051			0.577440			0.288720	−	0.957414i	$-0.406770\pi$
$631$	14.5051			0.577440			0.288720	+	0.957414i	$0.406770\pi$
$632$	−23.4605	+	9.42113i	−0.933209	+	0.374753i
$633$		0			0
$634$	−8.97523	−	14.2012i	−0.356452	−	0.564003i
$635$	14.3650	+	3.84910i	0.570059	+	0.152747i
$636$		0			0
$637$	73.1177	−	19.5918i	2.89703	−	0.776257i
$638$	0.625007	−	0.677149i	0.0247443	−	0.0268086i
$639$		0			0
$640$	26.0067	−	7.48248i	1.02800	−	0.295771i
$641$	−16.9507	−	9.78651i	−0.669514	−	0.386544i	0.126379	−	0.991982i	$-0.459665\pi$
$641$	−16.9507	−	9.78651i	−0.669514	−	0.386544i	−0.795892	+	0.605438i	$0.792998\pi$
$642$		0			0
$643$	−37.6479	−	10.0877i	−1.48469	−	0.397821i	−0.576748	−	0.816922i	$-0.695679\pi$
$643$	−37.6479	−	10.0877i	−1.48469	−	0.397821i	−0.907940	+	0.419101i	$0.862345\pi$
$644$	−14.5482	−	21.0998i	−0.573281	−	0.831450i
$645$		0			0
$646$	2.74661	+	1.44243i	0.108064	+	0.0567516i
$647$		−	3.37402i		−	0.132647i	−0.997798	−	0.0663233i	$-0.978873\pi$
$647$		−	3.37402i		−	0.132647i	0.997798	−	0.0663233i	$-0.0211269\pi$
$648$		0			0
$649$		−	5.63484i		−	0.221187i
$650$	1.96691	−	3.74530i	0.0771485	−	0.146903i
$651$		0			0
$652$	3.90581	−	21.2520i	0.152963	−	0.832293i
$653$	−26.5132	−	7.10419i	−1.03754	−	0.278008i	−0.300447	−	0.953798i	$-0.597136\pi$
$653$	−26.5132	−	7.10419i	−1.03754	−	0.278008i	−0.737094	+	0.675790i	$0.763803\pi$
$654$		0			0
$655$	26.0244	+	15.0252i	1.01686	+	0.587083i
$656$	6.54165	−	1.05625i	0.255408	−	0.0412397i
$657$		0			0
$658$	60.2373	+	55.5989i	2.34829	+	2.16747i
$659$	48.7287	−	13.0568i	1.89820	−	0.508621i	0.901003	−	0.433813i	$-0.142832\pi$
$659$	48.7287	−	13.0568i	1.89820	−	0.508621i	0.997198	−	0.0748080i	$-0.0238344\pi$
$660$		0			0
$661$	4.89081	+	1.31049i	0.190230	+	0.0509721i	0.352676	−	0.935745i	$-0.385272\pi$
$661$	4.89081	+	1.31049i	0.190230	+	0.0509721i	−0.162446	+	0.986717i	$0.551938\pi$
$662$	7.89716	−	4.99103i	0.306932	−	0.193982i
$663$		0			0
$664$	6.38324	−	14.9502i	0.247718	−	0.580180i
$665$	−11.8530			−0.459638
$666$		0			0
$667$	−1.10051	−	1.10051i	−0.0426120	−	0.0426120i
$668$	−3.90131	+	8.21099i	−0.150946	+	0.317693i
$669$		0			0
$670$	−6.33540	+	28.0965i	−0.244758	+	1.08546i
$671$	−3.58576	−	6.21072i	−0.138427	−	0.239762i
$672$		0			0
$673$	−17.6472	+	30.5658i	−0.680249	+	1.17823i	0.294656	+	0.955603i	$0.404795\pi$
$673$	−17.6472	+	30.5658i	−0.680249	+	1.17823i	−0.974905	+	0.222622i	$0.928538\pi$
$674$	27.8072	+	25.6660i	1.07109	+	0.988617i
$675$		0			0
$676$	−8.36375	+	0.670885i	−0.321683	+	0.0258033i
$677$	−44.1766	+	11.8371i	−1.69785	+	0.454936i	−0.972396	−	0.233338i	$-0.925035\pi$
$677$	−44.1766	+	11.8371i	−1.69785	+	0.454936i	−0.725450	+	0.688275i	$0.758368\pi$
$678$		0			0
$679$	7.62788	+	13.2119i	0.292731	+	0.507025i
$680$	12.0393	−	9.03248i	0.461685	−	0.346380i
$681$		0			0
$682$	−0.294033	−	0.154416i	−0.0112591	−	0.00591290i
$683$	−29.7527	+	29.7527i	−1.13845	+	1.13845i	−0.149727	+	0.988727i	$0.547839\pi$
$683$	−29.7527	+	29.7527i	−1.13845	+	1.13845i	−0.988727	+	0.149727i	$0.952161\pi$
$684$		0			0
$685$	4.12837	+	4.12837i	0.157737	+	0.157737i
$686$	−76.3712	+	23.7768i	−2.91587	+	0.907802i
$687$		0			0
$688$	−2.09431	+	20.5189i	−0.0798448	+	0.782274i
$689$	39.6330	−	22.8821i	1.50990	−	0.871738i
$690$		0			0
$691$	−9.78609	−	36.5222i	−0.372280	−	1.38937i	−0.857278	−	0.514854i	$-0.827846\pi$
$691$	−9.78609	−	36.5222i	−0.372280	−	1.38937i	0.484997	−	0.874516i	$-0.338821\pi$
$692$	26.5064	+	22.5698i	1.00762	+	0.857975i
$693$		0			0
$694$	4.33555	−	0.173606i	0.164575	−	0.00658999i
$695$	30.2197	+	17.4474i	1.14630	+	0.661816i
$696$		0			0
$697$	3.19164	−	1.84269i	0.120892	−	0.0697970i
$698$	28.0635	−	17.7362i	1.06222	−	0.671326i
$699$		0			0
$700$	−3.11152	+	6.54874i	−0.117604	+	0.247519i
$701$	19.2180	−	19.2180i	0.725854	−	0.725854i	−0.243937	−	0.969791i	$-0.578439\pi$
$701$	19.2180	−	19.2180i	0.725854	−	0.725854i	0.969791	+	0.243937i	$0.0784390\pi$
$702$		0			0
$703$		−	7.20042i		−	0.271569i
$704$	7.48729	−	4.10907i	0.282188	−	0.154866i
$705$		0			0
$706$	−4.31443	−	0.972849i	−0.162376	−	0.0366137i
$707$	0.557368	−	2.08013i	0.0209620	−	0.0782312i
$708$		0			0
$709$	8.13238	+	30.3504i	0.305418	+	1.13983i	0.932585	+	0.360950i	$0.117548\pi$
$709$	8.13238	+	30.3504i	0.305418	+	1.13983i	−0.627167	+	0.778885i	$0.715786\pi$
$710$	−40.6686	+	1.62847i	−1.52627	+	0.0611154i
$711$		0			0
$712$	11.4644	−	14.6101i	0.429645	−	0.547536i
$713$	−0.280460	+	0.485771i	−0.0105033	+	0.0181923i
$714$		0			0
$715$	2.74066	−	10.2283i	0.102495	−	0.382517i
$716$	0.314424	+	0.0577867i	0.0117506	+	0.00215959i
$717$		0			0
$718$	−10.7118	−	34.4062i	−0.399759	−	1.28403i
$719$	19.9203			0.742903			0.371452	−	0.928452i	$-0.378860\pi$
$719$	19.9203			0.742903			0.371452	+	0.928452i	$0.378860\pi$
$720$		0			0
$721$	40.9561			1.52528
$722$	7.57861	+	24.3425i	0.282047	+	0.905935i
$723$		0			0
$724$	3.15774	−	17.1816i	0.117356	−	0.638551i
$725$	−0.113954	+	0.425283i	−0.00423216	+	0.0157946i
$726$		0			0
$727$	11.2366	−	19.4624i	0.416743	−	0.721819i	−0.578867	−	0.815422i	$-0.696505\pi$
$727$	11.2366	−	19.4624i	0.416743	−	0.721819i	0.995610	+	0.0936026i	$0.0298383\pi$
$728$	58.5171	−	7.05970i	2.16879	−	0.261650i
$729$		0			0
$730$	−35.0540	+	1.40365i	−1.29741	+	0.0519513i
$731$	2.96898	+	11.0804i	0.109812	+	0.409823i
$732$		0			0
$733$	10.8684	−	40.5613i	0.401432	−	1.49817i	−0.409109	−	0.912485i	$-0.634161\pi$
$733$	10.8684	−	40.5613i	0.401432	−	1.49817i	0.810542	−	0.585681i	$-0.199173\pi$
$734$	−43.2123	−	9.74383i	−1.59499	−	0.359651i
$735$		0			0
$736$	−6.42845	−	12.9131i	−0.236956	−	0.475984i
$737$			9.08993i			0.334832i
$738$		0			0
$739$	−4.75917	+	4.75917i	−0.175069	+	0.175069i	−0.789202	−	0.614133i	$-0.789506\pi$
$739$	−4.75917	+	4.75917i	−0.175069	+	0.175069i	0.614133	+	0.789202i	$0.289506\pi$
$740$	−31.5523	−	14.9915i	−1.15988	−	0.551099i
$741$		0			0
$742$	−66.3027	+	41.9036i	−2.43405	+	1.53833i
$743$	26.1387	−	15.0912i	0.958936	−	0.553642i	0.0630904	−	0.998008i	$-0.479904\pi$
$743$	26.1387	−	15.0912i	0.958936	−	0.553642i	0.895845	+	0.444366i	$0.146571\pi$
$744$		0			0
$745$	0.497296	+	0.287114i	0.0182195	+	0.0105190i
$746$	−16.8512	+	0.674765i	−0.616968	+	0.0247049i
$747$		0			0
$748$	3.07951	−	3.61663i	0.112598	−	0.132237i
$749$	−19.3847	−	72.3448i	−0.708303	−	2.64342i
$750$		0			0
$751$	30.3572	−	17.5267i	1.10775	−	0.639559i	0.169503	−	0.985530i	$-0.445784\pi$
$751$	30.3572	−	17.5267i	1.10775	−	0.639559i	0.938245	+	0.345971i	$0.112450\pi$
$752$	29.1427	+	35.7680i	1.06272	+	1.30432i
$753$		0			0
$754$	3.41749	−	1.06397i	0.124458	−	0.0387477i
$755$	6.46214	+	6.46214i	0.235182	+	0.235182i
$756$		0			0
$757$	−24.7520	+	24.7520i	−0.899626	+	0.899626i	−0.995403	−	0.0957772i	$-0.969466\pi$
$757$	−24.7520	+	24.7520i	−0.899626	+	0.899626i	0.0957772	+	0.995403i	$0.469466\pi$
$758$	6.67530	+	3.50564i	0.242458	+	0.127331i
$759$		0			0
$760$	−6.60426	−	0.942382i	−0.239562	−	0.0341838i
$761$	−24.7912	−	42.9396i	−0.898681	−	1.55656i	−0.829182	−	0.558978i	$-0.811193\pi$
$761$	−24.7912	−	42.9396i	−0.898681	−	1.55656i	−0.0694983	−	0.997582i	$-0.522140\pi$
$762$		0			0
$763$	−49.5338	+	13.2725i	−1.79324	+	0.480498i
$764$	−0.611579	−	7.62440i	−0.0221262	−	0.275841i
$765$		0			0
$766$	−18.9975	−	17.5347i	−0.686408	−	0.633553i
$767$	10.9434	−	18.9545i	0.395143	−	0.684408i
$768$		0			0
$769$	23.4383	+	40.5964i	0.845208	+	1.46394i	0.885440	+	0.464754i	$0.153857\pi$
$769$	23.4383	+	40.5964i	0.845208	+	1.46394i	−0.0402316	+	0.999190i	$0.512810\pi$
$770$	−3.99203	+	17.7040i	−0.143863	+	0.638008i
$771$		0			0
$772$	16.9658	+	8.06101i	0.610613	+	0.290122i
$773$	12.8895	+	12.8895i	0.463605	+	0.463605i	0.899835	−	0.436230i	$-0.143687\pi$
$773$	12.8895	+	12.8895i	0.463605	+	0.463605i	−0.436230	+	0.899835i	$0.643687\pi$
$774$		0			0
$775$	0.158681			0.00569999
$776$	3.19970	+	7.96789i	0.114862	+	0.286030i
$777$		0			0
$778$	−30.4468	+	19.2425i	−1.09157	+	0.689878i
$779$	−1.57785	−	0.422784i	−0.0565323	−	0.0151478i
$780$		0			0
$781$	−12.4077	+	3.32463i	−0.443982	+	0.118965i
$782$	−5.89528	−	5.44133i	−0.210815	−	0.194582i
$783$		0			0
$784$	−72.0851	+	11.6393i	−2.57447	+	0.415688i
$785$	0.434467	+	0.250840i	0.0155068	+	0.00895285i
$786$		0			0
$787$	34.1116	+	9.14019i	1.21595	+	0.325812i	0.809093	−	0.587680i	$-0.199959\pi$
$787$	34.1116	+	9.14019i	1.21595	+	0.325812i	0.406855	+	0.913493i	$0.366625\pi$
$788$	16.7165	+	3.07225i	0.595501	+	0.109444i
$789$		0			0
$790$	14.0582	−	26.7689i	0.500167	−	0.952396i
$791$			16.4729i			0.585708i
$792$		0			0
$793$		−	27.8555i		−	0.989179i
$794$	−7.71546	−	4.05190i	−0.273811	−	0.143797i
$795$		0			0
$796$	28.0715	−	19.3552i	0.994967	−	0.686025i
$797$	7.89416	+	2.11523i	0.279625	+	0.0749254i	0.395906	−	0.918291i	$-0.370431\pi$
$797$	7.89416	+	2.11523i	0.279625	+	0.0749254i	−0.116281	+	0.993216i	$0.537097\pi$
$798$		0			0
$799$	22.2223	+	12.8301i	0.786170	+	0.453895i
$800$	−2.25435	+	3.40146i	−0.0797033	+	0.120260i
$801$		0			0
$802$	−35.0317	+	37.9542i	−1.23701	+	1.34021i
$803$	−10.6947	+	2.86564i	−0.377408	+	0.101126i
$804$		0			0
$805$	29.6073	+	7.93324i	1.04352	+	0.279610i
$806$	−0.689178	−	1.09047i	−0.0242753	−	0.0384100i
$807$		0			0
$808$	0.475938	−	1.11469i	0.0167434	−	0.0392148i
$809$	−17.8123			−0.626248			−0.313124	−	0.949712i	$-0.601375\pi$
$809$	−17.8123			−0.626248			−0.313124	+	0.949712i	$0.601375\pi$
$810$		0			0
$811$	15.4533	+	15.4533i	0.542639	+	0.542639i	0.924302	−	0.381663i	$-0.124648\pi$
$811$	15.4533	+	15.4533i	0.542639	+	0.542639i	−0.381663	+	0.924302i	$0.624648\pi$
$812$	−5.77953	+	2.05641i	−0.202822	+	0.0721660i
$813$		0			0
$814$	−10.7548	−	2.42507i	−0.376955	−	0.0849987i
$815$	12.9212	+	22.3802i	0.452611	+	0.783945i
$816$		0			0
$817$	2.54226	−	4.40332i	0.0889424	−	0.154053i
$818$	7.36224	−	7.97644i	0.257415	−	0.278890i
$819$		0			0
$820$	−5.13778	+	6.03389i	−0.179419	+	0.210713i
$821$	6.17527	−	1.65466i	0.215518	−	0.0577480i	−0.149444	−	0.988770i	$-0.547748\pi$
$821$	6.17527	−	1.65466i	0.215518	−	0.0577480i	0.364963	+	0.931022i	$0.381082\pi$
$822$		0			0
$823$	16.7762	+	29.0572i	0.584782	+	1.01287i	0.994903	+	0.100840i	$0.0321532\pi$
$823$	16.7762	+	29.0572i	0.584782	+	1.01287i	−0.410121	+	0.912031i	$0.634514\pi$
$824$	22.8200	+	3.25626i	0.794973	+	0.113437i
$825$		0			0
$826$	−17.4409	+	33.2102i	−0.606846	+	1.15553i
$827$	−14.6929	+	14.6929i	−0.510921	+	0.510921i	−0.914809	−	0.403888i	$-0.867659\pi$
$827$	−14.6929	+	14.6929i	−0.510921	+	0.510921i	0.403888	+	0.914809i	$0.367659\pi$
$828$		0			0
$829$	18.8540	+	18.8540i	0.654827	+	0.654827i	0.954151	−	0.299324i	$-0.0967612\pi$
$829$	18.8540	+	18.8540i	0.654827	+	0.654827i	−0.299324	+	0.954151i	$0.596761\pi$
$830$	5.77917	+	18.5627i	0.200598	+	0.644321i
$831$		0			0
$832$	33.1660	+	0.718924i	1.14982	+	0.0249242i
$833$	−35.1700	+	20.3054i	−1.21857	+	0.703540i
$834$		0			0
$835$	−2.81393	−	10.5017i	−0.0973800	−	0.363427i
$836$	−2.09869	+	0.168343i	−0.0725847	+	0.00582227i
$837$		0			0
$838$	−0.364467	−	9.10203i	−0.0125903	−	0.314424i
$839$	22.2713	+	12.8583i	0.768891	+	0.443919i	0.832479	−	0.554057i	$-0.186921\pi$
$839$	22.2713	+	12.8583i	0.768891	+	0.443919i	−0.0635881	+	0.997976i	$0.520254\pi$
$840$		0			0
$841$	24.7921	−	14.3137i	0.854901	−	0.493577i
$842$	8.60236	+	13.6113i	0.296457	+	0.469075i
$843$		0			0
$844$	−1.26155	+	0.448872i	−0.0434243	+	0.0154508i
$845$	7.09576	−	7.09576i	0.244101	−	0.244101i
$846$		0			0
$847$		−	49.5517i		−	1.70262i
$848$	−40.2743	+	18.0764i	−1.38302	+	0.620748i
$849$		0			0
$850$	−0.499222	+	2.21397i	−0.0171232	+	0.0759385i
$851$	−4.81927	+	17.9858i	−0.165202	+	0.616544i
$852$		0			0
$853$	−11.6194	−	43.3641i	−0.397840	−	1.48476i	−0.816889	−	0.576795i	$-0.804303\pi$
$853$	−11.6194	−	43.3641i	−0.397840	−	1.48476i	0.419049	−	0.907963i	$-0.362363\pi$
$854$	1.91014	+	47.7029i	0.0653636	+	1.63236i
$855$		0			0
$856$	−5.04898	−	41.8505i	−0.172571	−	1.43042i
$857$	−13.0424	+	22.5901i	−0.445520	+	0.771663i	−0.998088	−	0.0618046i	$-0.980314\pi$
$857$	−13.0424	+	22.5901i	−0.445520	+	0.771663i	0.552569	+	0.833467i	$0.313648\pi$
$858$		0			0
$859$	8.14400	−	30.3938i	0.277870	−	1.03702i	−0.676024	−	0.736879i	$-0.736299\pi$
$859$	8.14400	−	30.3938i	0.277870	−	1.03702i	0.953894	−	0.300144i	$-0.0970347\pi$
$860$	−14.0023	−	20.3081i	−0.477475	−	0.692499i
$861$		0			0
$862$	11.2767	−	3.51080i	0.384086	−	0.119578i
$863$	−30.7225			−1.04581			−0.522903	−	0.852392i	$-0.675151\pi$
$863$	−30.7225			−1.04581			−0.522903	+	0.852392i	$0.675151\pi$
$864$		0			0
$865$	−41.6360			−1.41566
$866$	−2.66472	+	0.829614i	−0.0905510	+	0.0281914i
$867$		0			0
$868$	1.25500	+	1.82017i	0.0425975	+	0.0617807i
$869$	2.46978	−	9.21735i	0.0837816	−	0.312677i
$870$		0			0
$871$	−17.6535	+	30.5767i	−0.598166	+	1.03605i
$872$	−28.6546	+	3.45699i	−0.970367	+	0.117068i
$873$		0			0
$874$	0.142274	+	3.55309i	0.00481251	+	0.120185i
$875$	13.3113	+	49.6786i	0.450005	+	1.67944i
$876$		0			0
$877$	−5.32228	+	19.8630i	−0.179720	+	0.670726i	0.815979	+	0.578082i	$0.196199\pi$
$877$	−5.32228	+	19.8630i	−0.179720	+	0.670726i	−0.995699	+	0.0926441i	$0.970468\pi$
$878$	0.182073	−	0.807463i	0.00614466	−	0.0272505i
$879$		0			0
$880$	−3.63186	+	9.54696i	−0.122430	+	0.321828i
$881$		−	42.7006i		−	1.43862i	−0.694689	−	0.719310i	$-0.744458\pi$
$881$		−	42.7006i		−	1.43862i	0.694689	−	0.719310i	$-0.255542\pi$
$882$		0			0
$883$	20.6871	−	20.6871i	0.696177	−	0.696177i	−0.267407	−	0.963584i	$-0.586167\pi$
$883$	20.6871	−	20.6871i	0.696177	−	0.696177i	0.963584	+	0.267407i	$0.0861667\pi$
$884$	17.3827	−	6.18494i	0.584644	−	0.208022i
$885$		0			0
$886$	−21.2484	−	33.6207i	−0.713853	−	1.12951i
$887$	−34.2924	+	19.7987i	−1.15143	+	0.664777i	−0.949235	−	0.314569i	$-0.898140\pi$
$887$	−34.2924	+	19.7987i	−1.15143	+	0.664777i	−0.202192	+	0.979346i	$0.564807\pi$
$888$		0			0
$889$	−27.0592	−	15.6226i	−0.907535	−	0.523966i
$890$	0.888649	+	22.1927i	0.0297876	+	0.743901i
$891$		0			0
$892$	−24.5099	+	1.96603i	−0.820653	+	0.0658274i
$893$	−2.94370	−	10.9860i	−0.0985072	−	0.367634i
$894$		0			0
$895$	−0.331116	+	0.191170i	−0.0110680	+	0.00639011i
$896$	−56.8464	+	1.04313i	−1.89910	+	0.0348484i
$897$		0			0
$898$	13.3959	+	43.0278i	0.447028	+	1.43586i
$899$	0.0949355	+	0.0949355i	0.00316628	+	0.00316628i
$900$		0			0
$901$	−17.3609	+	17.3609i	−0.578377	+	0.578377i
$902$	−1.16290	+	2.21434i	−0.0387202	+	0.0737294i
$903$		0			0
$904$	−1.30969	+	9.17839i	−0.0435597	+	0.305269i
$905$	10.4464	+	18.0938i	0.347251	+	0.601457i
$906$		0			0
$907$	−0.845385	+	0.226520i	−0.0280705	+	0.00752148i	−0.272827	−	0.962063i	$-0.587959\pi$
$907$	−0.845385	+	0.226520i	−0.0280705	+	0.00752148i	0.244756	+	0.969585i	$0.421292\pi$
$908$	24.4320	−	28.6934i	0.810805	−	0.952224i
$909$		0			0
$910$	−47.8112	+	51.7999i	−1.58493	+	1.71715i
$911$	26.3505	−	45.6405i	0.873032	−	1.51214i	0.0141881	−	0.999899i	$-0.495484\pi$
$911$	26.3505	−	45.6405i	0.873032	−	1.51214i	0.858844	−	0.512237i	$-0.171183\pi$
$912$		0			0
$913$	3.06789	+	5.31375i	0.101532	+	0.175859i
$914$	20.1212	+	4.53707i	0.665549	+	0.150073i
$915$		0			0
$916$	−13.2032	+	4.69785i	−0.436248	+	0.155221i
$917$	−44.6433	−	44.6433i	−1.47425	−	1.47425i
$918$		0			0
$919$	17.0903			0.563758			0.281879	−	0.959450i	$-0.409042\pi$
$919$	17.0903			0.563758			0.281879	+	0.959450i	$0.409042\pi$
$920$	15.8659	+	6.77422i	0.523083	+	0.223339i
$921$		0			0
$922$	−2.85614	−	4.51919i	−0.0940620	−	0.148831i
$923$	−48.1938	−	12.9135i	−1.58632	−	0.425053i
$924$		0			0
$925$	5.08807	−	1.36335i	0.167295	−	0.0448265i
$926$	17.5405	−	19.0038i	0.576416	−	0.624504i
$927$		0			0
$928$	−3.38375	+	0.686290i	−0.111077	+	0.0225286i
$929$	−23.0709	−	13.3200i	−0.756933	−	0.437015i	0.0712608	−	0.997458i	$-0.477298\pi$
$929$	−23.0709	−	13.3200i	−0.756933	−	0.437015i	−0.828193	+	0.560442i	$0.810631\pi$
$930$		0			0
$931$	17.3870	+	4.65882i	0.569835	+	0.152687i
$932$	−40.4538	+	27.8927i	−1.32511	+	0.913655i
$933$		0			0
$934$	19.4239	+	10.2008i	0.635570	+	0.333780i
$935$			5.68097i			0.185787i
$936$		0			0
$937$			26.2397i			0.857214i	0.903491	+	0.428607i	$0.140995\pi$
$937$			26.2397i			0.857214i	−0.903491	+	0.428607i	$0.859005\pi$
$938$	28.1350	−	53.5735i	0.918641	−	1.74924i
$939$		0			0
$940$	−54.2698	−	9.97400i	−1.77008	−	0.325316i
$941$	−25.4022	−	6.80651i	−0.828089	−	0.221886i	−0.180209	−	0.983628i	$-0.557678\pi$
$941$	−25.4022	−	6.80651i	−0.828089	−	0.221886i	−0.647880	+	0.761742i	$0.724344\pi$
$942$		0			0
$943$	3.65831	+	2.11212i	0.119131	+	0.0687802i
$944$	−12.3582	+	17.1175i	−0.402224	+	0.557126i
$945$		0			0
$946$	−5.72073	−	5.28023i	−0.185997	−	0.171675i
$947$	−16.5153	+	4.42526i	−0.536675	+	0.143802i	−0.516969	−	0.856004i	$-0.672940\pi$
$947$	−16.5153	+	4.42526i	−0.536675	+	0.143802i	−0.0197060	+	0.999806i	$0.506273\pi$
$948$		0			0
$949$	−41.5403	−	11.1307i	−1.34845	−	0.361317i
$950$	0.850362	−	0.537432i	0.0275894	−	0.0174366i
$951$		0			0
$952$	−29.3439	+	11.7838i	−0.951042	+	0.381914i
$953$	47.3557			1.53400			0.767001	−	0.641646i	$-0.221748\pi$
$953$	47.3557			1.53400			0.767001	+	0.641646i	$0.221748\pi$
$954$		0			0
$955$	6.46849	+	6.46849i	0.209316	+	0.209316i
$956$	6.16584	+	2.92959i	0.199417	+	0.0947498i
$957$		0			0
$958$	−3.89625	+	17.2792i	−0.125882	+	0.558267i
$959$	−6.13316	−	10.6229i	−0.198050	−	0.343033i
$960$		0			0
$961$	−15.4758	+	26.8049i	−0.499220	+	0.864674i
$962$	−31.4673	−	29.0443i	−1.01455	−	0.936425i
$963$		0			0
$964$	−4.13992	−	51.6113i	−0.133338	−	1.66229i
$965$	−21.6990	+	5.81423i	−0.698515	+	0.187167i
$966$		0			0
$967$	−5.54783	−	9.60912i	−0.178406	−	0.309009i	0.762929	−	0.646483i	$-0.223761\pi$
$967$	−5.54783	−	9.60912i	−0.178406	−	0.309009i	−0.941335	+	0.337474i	$0.890427\pi$
$968$	3.93966	−	27.6093i	0.126626	−	0.887398i
$969$		0			0
$970$	−9.09153	−	4.77457i	−0.291911	−	0.153302i
$971$	11.1100	−	11.1100i	0.356538	−	0.356538i	−0.505997	−	0.862535i	$-0.668875\pi$
$971$	11.1100	−	11.1100i	0.356538	−	0.356538i	0.862535	+	0.505997i	$0.168875\pi$
$972$		0			0
$973$	−51.8401	−	51.8401i	−1.66192	−	1.66192i
$974$	−17.1775	+	5.34789i	−0.550401	+	0.171358i
$975$		0			0
$976$	−2.72837	+	26.7310i	−0.0873330	+	0.855640i
$977$	37.8418	−	21.8480i	1.21067	−	0.698979i	0.247762	−	0.968821i	$-0.420305\pi$
$977$	37.8418	−	21.8480i	1.21067	−	0.698979i	0.962905	+	0.269842i	$0.0869715\pi$
$978$		0			0
$979$	1.81424	+	6.77082i	0.0579832	+	0.216396i
$980$	56.6152	−	66.4899i	1.80851	−	2.12394i
$981$		0			0
$982$	15.4770	−	0.619738i	0.493892	−	0.0197766i
$983$	4.32758	+	2.49853i	0.138028	+	0.0796907i	0.567424	−	0.823426i	$-0.307940\pi$
$983$	4.32758	+	2.49853i	0.138028	+	0.0796907i	−0.429396	+	0.903116i	$0.641273\pi$
$984$		0			0
$985$	−17.6039	+	10.1636i	−0.560908	+	0.323840i
$986$	−1.62324	+	1.02590i	−0.0516946	+	0.0326712i
$987$		0			0
$988$	−7.38652	−	3.50958i	−0.234997	−	0.111655i
$989$	−9.29742	+	9.29742i	−0.295641	+	0.295641i
$990$		0			0
$991$			36.5019i			1.15952i	0.814787	+	0.579760i	$0.196854\pi$
$991$			36.5019i			1.15952i	−0.814787	+	0.579760i	$0.803146\pi$
$992$	0.554549	+	1.11395i	0.0176069	+	0.0353679i
$993$		0			0
$994$	83.4178	+	18.8097i	2.64585	+	0.596607i
$995$	−10.5545	+	39.3899i	−0.334600	+	1.24874i
$996$		0			0
$997$	1.74992	+	6.53078i	0.0554204	+	0.206832i	0.988084	−	0.153915i	$-0.0491884\pi$
$997$	1.74992	+	6.53078i	0.0554204	+	0.206832i	−0.932664	+	0.360747i	$0.882522\pi$
$998$	−33.8704	+	1.35625i	−1.07215	+	0.0429314i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.35.20		88
3.2	odd	2		144.2.u.a.83.3	yes	88
4.3	odd	2		1728.2.z.a.1007.4		88
9.4	even	3		144.2.u.a.131.11	yes	88
9.5	odd	6	inner	432.2.v.a.179.12		88
12.11	even	2		576.2.y.a.47.6		88
16.5	even	4		1728.2.z.a.143.4		88
16.11	odd	4	inner	432.2.v.a.251.12		88
36.23	even	6		1728.2.z.a.1583.4		88
36.31	odd	6		576.2.y.a.239.17		88
48.5	odd	4		576.2.y.a.335.17		88
48.11	even	4		144.2.u.a.11.11	✓	88
144.5	odd	12		1728.2.z.a.719.4		88
144.59	even	12	inner	432.2.v.a.395.20		88
144.85	even	12		576.2.y.a.527.6		88
144.139	odd	12		144.2.u.a.59.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.11	✓	88	48.11	even	4
144.2.u.a.59.3	yes	88	144.139	odd	12
144.2.u.a.83.3	yes	88	3.2	odd	2
144.2.u.a.131.11	yes	88	9.4	even	3
432.2.v.a.35.20		88	1.1	even	1	trivial
432.2.v.a.179.12		88	9.5	odd	6	inner
432.2.v.a.251.12		88	16.11	odd	4	inner
432.2.v.a.395.20		88	144.59	even	12	inner
576.2.y.a.47.6		88	12.11	even	2
576.2.y.a.239.17		88	36.31	odd	6
576.2.y.a.335.17		88	48.5	odd	4
576.2.y.a.527.6		88	144.85	even	12
1728.2.z.a.143.4		88	16.5	even	4
1728.2.z.a.719.4		88	144.5	odd	12
1728.2.z.a.1007.4		88	4.3	odd	2
1728.2.z.a.1583.4		88	36.23	even	6

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)

\(f(q)\)	\(=\)	\(q+(1.35029 - 0.420387i) q^{2} +(1.64655 - 1.13529i) q^{4} +(-0.619079 + 2.31044i) q^{5} +(2.51270 - 4.35213i) q^{7} +(1.74605 - 2.22515i) q^{8} +O(q^{10})\)	\(q+(1.35029 - 0.420387i) q^{2} +(1.64655 - 1.13529i) q^{4} +(-0.619079 + 2.31044i) q^{5} +(2.51270 - 4.35213i) q^{7} +(1.74605 - 2.22515i) q^{8} +(0.135344 + 3.38000i) q^{10} +(0.276313 + 1.03121i) q^{11} +(-1.07325 + 4.00543i) q^{13} +(1.56329 - 6.93293i) q^{14} +(1.42225 - 3.73861i) q^{16} -2.22468i q^{17} +(-0.697254 + 0.697254i) q^{19} +(1.60366 + 4.50708i) q^{20} +(0.806611 + 1.27628i) q^{22} +(2.20833 - 1.27498i) q^{23} +(-0.624725 - 0.360685i) q^{25} +(0.234635 + 5.85966i) q^{26} +(-0.803629 - 10.0186i) q^{28} +(-0.157969 - 0.589549i) q^{29} +(-0.190501 + 0.109986i) q^{31} +(0.348774 - 5.64609i) q^{32} +(-0.935228 - 3.00396i) q^{34} +(8.49974 + 8.49974i) q^{35} +(-5.16341 + 5.16341i) q^{37} +(-0.648376 + 1.23461i) q^{38} +(4.06012 + 5.41169i) q^{40} +(0.828296 + 1.43465i) q^{41} +(-4.98067 + 1.33457i) q^{43} +(1.62569 + 1.38425i) q^{44} +(2.44589 - 2.64994i) q^{46} +(-5.76715 + 9.98900i) q^{47} +(-9.12734 - 15.8090i) q^{49} +(-0.995185 - 0.224402i) q^{50} +(2.78015 + 7.81358i) q^{52} +(-7.80379 - 7.80379i) q^{53} -2.55361 q^{55} +(-5.29683 - 13.1902i) q^{56} +(-0.461143 - 0.729652i) q^{58} +(-5.09824 - 1.36607i) q^{59} +(-6.48859 + 1.73861i) q^{61} +(-0.210995 + 0.228597i) q^{62} +(-1.90260 - 7.77046i) q^{64} +(-8.58985 - 4.95935i) q^{65} +(8.22431 + 2.20370i) q^{67} +(-2.52565 - 3.66304i) q^{68} +(15.0503 + 7.90391i) q^{70} +12.0321i q^{71} +10.3710i q^{73} +(-4.80145 + 9.14272i) q^{74} +(-0.356479 + 1.93965i) q^{76} +(5.18226 + 1.38858i) q^{77} +(-7.74084 - 4.46918i) q^{79} +(7.75734 + 5.60050i) q^{80} +(1.72155 + 1.58899i) q^{82} +(5.55149 - 1.48752i) q^{83} +(5.13998 + 1.37725i) q^{85} +(-6.16430 + 3.89586i) q^{86} +(2.77706 + 1.18571i) q^{88} +6.56588 q^{89} +(14.7354 + 14.7354i) q^{91} +(2.18866 - 4.60641i) q^{92} +(-3.58806 + 15.9125i) q^{94} +(-1.17930 - 2.04262i) q^{95} +(-1.51787 + 2.62902i) q^{97} +(-18.9704 - 17.5097i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 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

Introduction

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