LMFDB - Embedded newform 972.2.l.a.107.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(107,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("972.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			107.13
Character	$\chi$	$=$	972.107
Dual form			972.2.l.a.863.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14898 - 0.824528i) q^{2} +(0.640306 - 1.89473i) q^{4} +(-0.840877 + 2.31029i) q^{5} +(-3.82489 - 0.674430i) q^{7} +(-0.826562 - 2.70496i) q^{8} +O(q^{10})$	\(q+(1.14898 - 0.824528i) q^{2} +(0.640306 - 1.89473i) q^{4} +(-0.840877 + 2.31029i) q^{5} +(-3.82489 - 0.674430i) q^{7} +(-0.826562 - 2.70496i) q^{8} +(0.938750 + 3.34780i) q^{10} +(0.0547511 - 0.0199278i) q^{11} +(-3.53434 + 2.96567i) q^{13} +(-4.95080 + 2.37882i) q^{14} +(-3.18002 - 2.42642i) q^{16} +(-1.79249 + 1.03489i) q^{17} +(-2.46167 - 1.42125i) q^{19} +(3.83896 + 3.07253i) q^{20} +(0.0464768 - 0.0680404i) q^{22} +(-0.991876 - 5.62521i) q^{23} +(-0.800144 - 0.671401i) q^{25} +(-1.61561 + 6.32166i) q^{26} +(-3.72696 + 6.81529i) q^{28} +(-2.57867 + 3.07314i) q^{29} +(-7.51076 + 1.32435i) q^{31} +(-5.65442 - 0.165888i) q^{32} +(-1.20623 + 2.66703i) q^{34} +(4.77439 - 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(-4.00027 + 0.396735i) q^{38} +(6.94427 + 0.364939i) q^{40} +(0.705325 + 0.840573i) q^{41} +(3.29941 + 9.06505i) q^{43} +(-0.00270032 - 0.116498i) q^{44} +(-5.77779 - 5.64542i) q^{46} +(0.948548 - 5.37948i) q^{47} +(7.59704 + 2.76510i) q^{49} +(-1.47294 - 0.111684i) q^{50} +(3.35608 + 8.59557i) q^{52} -10.5337i q^{53} +0.143248i q^{55} +(1.33720 + 10.9036i) q^{56} +(-0.428948 + 5.65716i) q^{58} +(-1.50332 - 0.547162i) q^{59} +(-0.366631 + 2.07927i) q^{61} +(-7.53775 + 7.71449i) q^{62} +(-6.63359 + 4.47163i) q^{64} +(-3.87960 - 10.6591i) q^{65} +(-4.85766 - 5.78913i) q^{67} +(0.813104 + 4.05893i) q^{68} +(-1.33275 - 13.4381i) q^{70} +(-4.08357 - 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(6.21214 + 2.80960i) q^{74} +(-4.26910 + 3.75417i) q^{76} +(-0.222856 + 0.0392956i) q^{77} +(-4.45402 + 5.30809i) q^{79} +(8.27973 - 5.30644i) q^{80} +(1.50348 + 0.384241i) q^{82} +(8.72941 + 7.32485i) q^{83} +(-0.883642 - 5.01138i) q^{85} +(11.2653 + 7.69510i) q^{86} +(-0.0991589 - 0.131628i) q^{88} +(1.85844 + 1.07297i) q^{89} +(15.5186 - 8.95967i) q^{91} +(-11.2934 - 1.72252i) q^{92} +(-3.34567 - 6.96302i) q^{94} +(5.35345 - 4.49208i) q^{95} +(4.84352 - 1.76290i) q^{97} +(11.0087 - 3.08694i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} - 33 q^{14} + 3 q^{16} + 18 q^{17} + 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 30 q^{29} - 33 q^{32} + 15 q^{34} - 6 q^{37} + 63 q^{38} + 33 q^{40} + 24 q^{41} - 63 q^{44} - 3 q^{46} + 6 q^{49} + 21 q^{50} + 57 q^{52} + 18 q^{56} + 57 q^{58} + 6 q^{61} - 90 q^{62} - 3 q^{64} - 30 q^{65} + 102 q^{68} + 51 q^{70} - 6 q^{73} - 75 q^{74} + 27 q^{76} + 42 q^{77} - 12 q^{82} - 24 q^{85} + 111 q^{86} + 27 q^{88} - 147 q^{92} + 30 q^{94} - 12 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 - 33 * q^14 + 3 * q^16 + 18 * q^17 + 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 30 * q^29 - 33 * q^32 + 15 * q^34 - 6 * q^37 + 63 * q^38 + 33 * q^40 + 24 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 21 * q^50 + 57 * q^52 + 18 * q^56 + 57 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 - 30 * q^65 + 102 * q^68 + 51 * q^70 - 6 * q^73 - 75 * q^74 + 27 * q^76 + 42 * q^77 - 12 * q^82 - 24 * q^85 + 111 * q^86 + 27 * q^88 - 147 * q^92 + 30 * q^94 - 12 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	1.14898	−	0.824528i	0.812451	−	0.583030i
$2$	1.14898	−	0.824528i	0.812451	−	0.583030i
$3$		0			0
$3$		0			0
$4$	0.640306	−	1.89473i	0.320153	−	0.947366i
$5$	−0.840877	+	2.31029i	−0.376052	+	1.03319i	0.596927	+	0.802296i	$0.296388\pi$
$5$	−0.840877	+	2.31029i	−0.376052	+	1.03319i	−0.972978	+	0.230897i	$0.925834\pi$
$6$		0			0
$7$	−3.82489	−	0.674430i	−1.44567	−	0.254911i	−0.604900	−	0.796302i	$-0.706787\pi$
$7$	−3.82489	−	0.674430i	−1.44567	−	0.254911i	−0.840771	+	0.541391i	$0.817898\pi$
$8$	−0.826562	−	2.70496i	−0.292234	−	0.956347i
$9$		0			0
$10$	0.938750	+	3.34780i	0.296859	+	1.05867i
$11$	0.0547511	−	0.0199278i	0.0165081	−	0.00600845i	−0.333753	−	0.942661i	$-0.608315\pi$
$11$	0.0547511	−	0.0199278i	0.0165081	−	0.00600845i	0.350261	+	0.936652i	$0.386093\pi$
$12$		0			0
$13$	−3.53434	+	2.96567i	−0.980251	+	0.822528i	−0.984127	−	0.177465i	$-0.943210\pi$
$13$	−3.53434	+	2.96567i	−0.980251	+	0.822528i	0.00387662	+	0.999992i	$0.498766\pi$
$14$	−4.95080	+	2.37882i	−1.32316	+	0.635766i
$15$		0			0
$16$	−3.18002	−	2.42642i	−0.795004	−	0.606604i
$17$	−1.79249	+	1.03489i	−0.434742	+	0.250998i	−0.701365	−	0.712803i	$-0.747426\pi$
$17$	−1.79249	+	1.03489i	−0.434742	+	0.250998i	0.266623	+	0.963801i	$0.414092\pi$
$18$		0			0
$19$	−2.46167	−	1.42125i	−0.564746	−	0.326056i	0.190302	−	0.981726i	$-0.439053\pi$
$19$	−2.46167	−	1.42125i	−0.564746	−	0.326056i	−0.755048	+	0.655669i	$0.772387\pi$
$20$	3.83896	+	3.07253i	0.858418	+	0.687038i
$21$		0			0
$22$	0.0464768	−	0.0680404i	0.00990889	−	0.0145063i
$23$	−0.991876	−	5.62521i	−0.206820	−	1.17294i	−0.894549	−	0.446969i	$-0.852503\pi$
$23$	−0.991876	−	5.62521i	−0.206820	−	1.17294i	0.687729	−	0.725968i	$-0.258608\pi$
$24$		0			0
$25$	−0.800144	−	0.671401i	−0.160029	−	0.134280i
$26$	−1.61561	+	6.32166i	−0.316847	+	1.23978i
$27$		0			0
$28$	−3.72696	+	6.81529i	−0.704330	+	1.28797i
$29$	−2.57867	+	3.07314i	−0.478847	+	0.570668i	−0.950345	−	0.311200i	$-0.899269\pi$
$29$	−2.57867	+	3.07314i	−0.478847	+	0.570668i	0.471497	+	0.881867i	$0.343714\pi$
$30$		0			0
$31$	−7.51076	+	1.32435i	−1.34897	+	0.237860i	−0.801014	−	0.598645i	$-0.795706\pi$
$31$	−7.51076	+	1.32435i	−1.34897	+	0.237860i	−0.547958	+	0.836506i	$0.684595\pi$
$32$	−5.65442	−	0.165888i	−0.999570	−	0.0293251i
$33$		0			0
$34$	−1.20623	+	2.66703i	−0.206867	+	0.457391i
$35$	4.77439	−	8.26948i	0.807019	−	1.39780i
$36$		0			0
$37$	2.41051	+	4.17513i	0.396286	+	0.686387i	0.993264	−	0.115870i	$-0.0369656\pi$
$37$	2.41051	+	4.17513i	0.396286	+	0.686387i	−0.596979	+	0.802257i	$0.703632\pi$
$38$	−4.00027	+	0.396735i	−0.648929	+	0.0643589i
$39$		0			0
$40$	6.94427	+	0.364939i	1.09799	+	0.0577019i
$41$	0.705325	+	0.840573i	0.110153	+	0.131275i	0.818304	−	0.574786i	$-0.194915\pi$
$41$	0.705325	+	0.840573i	0.110153	+	0.131275i	−0.708151	+	0.706061i	$0.750470\pi$
$42$		0			0
$43$	3.29941	+	9.06505i	0.503155	+	1.38241i	0.888178	+	0.459500i	$0.151972\pi$
$43$	3.29941	+	9.06505i	0.503155	+	1.38241i	−0.385022	+	0.922907i	$0.625806\pi$
$44$	−0.00270032	−	0.116498i	−0.000407088	−	0.0175628i
$45$		0			0
$46$	−5.77779	−	5.64542i	−0.851888	−	0.832371i
$47$	0.948548	−	5.37948i	0.138360	−	0.784678i	−0.834101	−	0.551612i	$-0.814013\pi$
$47$	0.948548	−	5.37948i	0.138360	−	0.784678i	0.972461	−	0.233066i	$-0.0748759\pi$
$48$		0			0
$49$	7.59704	+	2.76510i	1.08529	+	0.395014i
$50$	−1.47294	−	0.111684i	−0.208305	−	0.0157945i
$51$		0			0
$52$	3.35608	+	8.59557i	0.465405	+	1.19199i
$53$		−	10.5337i		−	1.44692i	−0.690367	−	0.723459i	$-0.742551\pi$
$53$		−	10.5337i		−	1.44692i	0.690367	−	0.723459i	$-0.257449\pi$
$54$		0			0
$55$			0.143248i			0.0193155i
$56$	1.33720	+	10.9036i	0.178691	+	1.45706i
$57$		0			0
$58$	−0.428948	+	5.65716i	−0.0563236	+	0.742821i
$59$	−1.50332	−	0.547162i	−0.195715	−	0.0712344i	0.242303	−	0.970201i	$-0.422097\pi$
$59$	−1.50332	−	0.547162i	−0.195715	−	0.0712344i	−0.438018	+	0.898966i	$0.644319\pi$
$60$		0			0
$61$	−0.366631	+	2.07927i	−0.0469423	+	0.266223i	−0.999241	−	0.0389431i	$-0.987601\pi$
$61$	−0.366631	+	2.07927i	−0.0469423	+	0.266223i	0.952299	+	0.305166i	$0.0987120\pi$
$62$	−7.53775	+	7.71449i	−0.957295	+	0.979741i
$63$		0			0
$64$	−6.63359	+	4.47163i	−0.829199	+	0.558954i
$65$	−3.87960	−	10.6591i	−0.481205	−	1.32210i
$66$		0			0
$67$	−4.85766	−	5.78913i	−0.593457	−	0.707255i	0.382809	−	0.923827i	$-0.374957\pi$
$67$	−4.85766	−	5.78913i	−0.593457	−	0.707255i	−0.976266	+	0.216573i	$0.930512\pi$
$68$	0.813104	+	4.05893i	0.0986034	+	0.492218i
$69$		0			0
$70$	−1.33275	−	13.4381i	−0.159294	−	1.60616i
$71$	−4.08357	−	7.07295i	−0.484630	−	0.839404i	0.515214	−	0.857062i	$-0.327712\pi$
$71$	−4.08357	−	7.07295i	−0.484630	−	0.839404i	−0.999844	+	0.0176575i	$0.994379\pi$
$72$		0			0
$73$	3.26625	−	5.65731i	0.382286	−	0.662138i	−0.609103	−	0.793091i	$-0.708470\pi$
$73$	3.26625	−	5.65731i	0.382286	−	0.662138i	0.991389	+	0.130953i	$0.0418037\pi$
$74$	6.21214	+	2.80960i	0.722147	+	0.326610i
$75$		0			0
$76$	−4.26910	+	3.75417i	−0.489700	+	0.430633i
$77$	−0.222856	+	0.0392956i	−0.0253968	+	0.00447815i
$78$		0			0
$79$	−4.45402	+	5.30809i	−0.501116	+	0.597207i	−0.956008	−	0.293340i	$-0.905233\pi$
$79$	−4.45402	+	5.30809i	−0.501116	+	0.597207i	0.454892	+	0.890546i	$0.349678\pi$
$80$	8.27973	−	5.30644i	0.925702	−	0.593278i
$81$		0			0
$82$	1.50348	+	0.384241i	0.166032	+	0.0424323i
$83$	8.72941	+	7.32485i	0.958178	+	0.804006i	0.980656	−	0.195741i	$-0.0627111\pi$
$83$	8.72941	+	7.32485i	0.958178	+	0.804006i	−0.0224781	+	0.999747i	$0.507156\pi$
$84$		0			0
$85$	−0.883642	−	5.01138i	−0.0958444	−	0.543561i
$86$	11.2653	+	7.69510i	1.21477	+	0.829784i
$87$		0			0
$88$	−0.0991589	−	0.131628i	−0.0105704	−	0.0140316i
$89$	1.85844	+	1.07297i	0.196995	+	0.113735i	0.595253	−	0.803538i	$-0.297052\pi$
$89$	1.85844	+	1.07297i	0.196995	+	0.113735i	−0.398258	+	0.917273i	$0.630385\pi$
$90$		0			0
$91$	15.5186	−	8.95967i	1.62679	−	0.939228i
$92$	−11.2934	−	1.72252i	−1.17741	−	0.179585i
$93$		0			0
$94$	−3.34567	−	6.96302i	−0.345080	−	0.718180i
$95$	5.35345	−	4.49208i	0.549253	−	0.460878i
$96$		0			0
$97$	4.84352	−	1.76290i	0.491785	−	0.178995i	−0.0842102	−	0.996448i	$-0.526837\pi$
$97$	4.84352	−	1.76290i	0.491785	−	0.178995i	0.575996	+	0.817453i	$0.304615\pi$
$98$	11.0087	−	3.08694i	1.11205	−	0.311828i
$99$		0			0
$100$	−1.78446	+	1.08616i	−0.178446	+	0.108616i
$101$	13.0167	+	2.29520i	1.29521	+	0.228381i	0.778427	−	0.627735i	$-0.216018\pi$
$101$	13.0167	+	2.29520i	1.29521	+	0.228381i	0.516784	+	0.856116i	$0.327129\pi$
$102$		0			0
$103$	−0.356687	+	0.979989i	−0.0351454	+	0.0965612i	−0.956024	−	0.293288i	$-0.905251\pi$
$103$	−0.356687	+	0.979989i	−0.0351454	+	0.0965612i	0.920879	+	0.389849i	$0.127473\pi$
$104$	10.9434	+	7.10894i	1.07308	+	0.697089i
$105$		0			0
$106$	−8.68535	−	12.1030i	−0.843596	−	1.17555i
$107$	12.4850			1.20697			0.603485	−	0.797375i	$-0.293778\pi$
$107$	12.4850			1.20697			0.603485	+	0.797375i	$0.293778\pi$
$108$		0			0
$109$	−19.2545			−1.84425			−0.922123	−	0.386896i	$-0.873547\pi$
$109$	−19.2545			−1.84425			−0.922123	+	0.386896i	$0.873547\pi$
$110$	0.118112	+	0.164589i	0.0112615	+	0.0156929i
$111$		0			0
$112$	10.5267	+	11.4255i	0.994684	+	1.07960i
$113$	1.78289	−	4.89846i	0.167721	−	0.460809i	−0.827148	−	0.561984i	$-0.810038\pi$
$113$	1.78289	−	4.89846i	0.167721	−	0.460809i	0.994869	+	0.101176i	$0.0322604\pi$
$114$		0			0
$115$	13.8299	+	2.43859i	1.28965	+	0.227399i
$116$	4.17164	+	6.85364i	0.387327	+	0.636344i
$117$		0			0
$118$	−2.17843	+	0.610848i	−0.200541	+	0.0562331i
$119$	7.55402	−	2.74944i	0.692476	−	0.252041i
$120$		0			0
$121$	−8.42389	+	7.06848i	−0.765808	+	0.642589i
$122$	1.29316	+	2.69133i	0.117078	+	0.243662i
$123$		0			0
$124$	−2.29990	+	15.0789i	−0.206537	+	1.35412i
$125$	−8.42192	+	4.86240i	−0.753279	+	0.434906i
$126$		0			0
$127$	1.67801	+	0.968801i	0.148900	+	0.0859672i	0.572599	−	0.819836i	$-0.305935\pi$
$127$	1.67801	+	0.968801i	0.148900	+	0.0859672i	−0.423699	+	0.905803i	$0.639269\pi$
$128$	−3.93487	+	10.6074i	−0.347797	+	0.937570i
$129$		0			0
$130$	−13.2463	−	9.04826i	−1.16178	−	0.793585i
$131$	0.0812185	+	0.460613i	0.00709609	+	0.0402440i	0.988150	−	0.153490i	$-0.0490513\pi$
$131$	0.0812185	+	0.460613i	0.00709609	+	0.0402440i	−0.981054	+	0.193734i	$0.937940\pi$
$132$		0			0
$133$	8.45707	+	7.09633i	0.733321	+	0.615330i
$134$	−10.3546	−	2.64631i	−0.894505	−	0.228607i
$135$		0			0
$136$	4.28094	+	3.99320i	0.367088	+	0.342414i
$137$	−2.82207	+	3.36321i	−0.241105	+	0.287338i	−0.873004	−	0.487713i	$-0.837831\pi$
$137$	−2.82207	+	3.36321i	−0.241105	+	0.287338i	0.631899	+	0.775051i	$0.282276\pi$
$138$		0			0
$139$	−8.31937	+	1.46693i	−0.705639	+	0.124423i	−0.514941	−	0.857225i	$-0.672186\pi$
$139$	−8.31937	+	1.46693i	−0.705639	+	0.124423i	−0.190698	+	0.981649i	$0.561075\pi$
$140$	−12.6114	−	14.3412i	−1.06586	−	1.21205i
$141$		0			0
$142$	−10.5238	−	4.75965i	−0.883136	−	0.399421i
$143$	−0.134410	+	0.232805i	−0.0112399	+	0.0194681i
$144$		0			0
$145$	−4.93150	−	8.54161i	−0.409539	−	0.709342i
$146$	−0.911761	−	9.19325i	−0.0754578	−	0.760839i
$147$		0			0
$148$	9.45422	−	1.89391i	0.777132	−	0.155679i
$149$	−6.53498	−	7.78809i	−0.535367	−	0.638025i	0.428776	−	0.903411i	$-0.358945\pi$
$149$	−6.53498	−	7.78809i	−0.535367	−	0.638025i	−0.964142	+	0.265386i	$0.914501\pi$
$150$		0			0
$151$	−0.816192	−	2.24247i	−0.0664208	−	0.182490i	0.902042	−	0.431649i	$-0.142068\pi$
$151$	−0.816192	−	2.24247i	−0.0664208	−	0.182490i	−0.968463	+	0.249159i	$0.919846\pi$
$152$	−1.80969	+	7.83346i	−0.146785	+	0.635378i
$153$		0			0
$154$	−0.223657	+	0.228901i	−0.0180228	+	0.0184454i
$155$	3.25599	−	18.4657i	0.261528	−	1.48320i
$156$		0			0
$157$	5.11743	+	1.86259i	0.408416	+	0.148651i	0.538054	−	0.842910i	$-0.319160\pi$
$157$	5.11743	+	1.86259i	0.408416	+	0.148651i	−0.129639	+	0.991561i	$0.541382\pi$
$158$	−0.740901	+	9.77135i	−0.0589429	+	0.777367i
$159$		0			0
$160$	5.13792	−	12.9239i	0.406188	−	1.02172i
$161$			22.1847i			1.74840i
$162$		0			0
$163$		−	9.76328i		−	0.764719i	−0.924014	−	0.382360i	$-0.875112\pi$
$163$		−	9.76328i		−	0.764719i	0.924014	−	0.382360i	$-0.124888\pi$
$164$	2.04428	−	0.798177i	0.159632	−	0.0623271i
$165$		0			0
$166$	16.0695	+	1.21845i	1.24723	+	0.0945699i
$167$	4.36568	+	1.58898i	0.337826	+	0.122959i	0.505362	−	0.862907i	$-0.331359\pi$
$167$	4.36568	+	1.58898i	0.337826	+	0.122959i	−0.167536	+	0.985866i	$0.553581\pi$
$168$		0			0
$169$	1.43898	−	8.16087i	0.110691	−	0.627759i
$170$	−5.14731	−	5.02939i	−0.394781	−	0.385736i
$171$		0			0
$172$	19.2885	−	0.447088i	1.47073	−	0.0340901i
$173$	0.301382	+	0.828041i	0.0229137	+	0.0629548i	0.950622	−	0.310351i	$-0.100447\pi$
$173$	0.301382	+	0.828041i	0.0229137	+	0.0629548i	−0.927708	+	0.373306i	$0.878224\pi$
$174$		0			0
$175$	2.60765	+	3.10767i	0.197120	+	0.234918i
$176$	−0.222462	−	0.0694783i	−0.0167687	−	0.00523712i
$177$		0			0
$178$	3.02001	−	0.299516i	0.226359	−	0.0224497i
$179$	6.34874	+	10.9963i	0.474527	+	0.821905i	0.999575	−	0.0291678i	$-0.00928571\pi$
$179$	6.34874	+	10.9963i	0.474527	+	0.821905i	−0.525047	+	0.851073i	$0.675952\pi$
$180$		0			0
$181$	−3.30529	+	5.72493i	−0.245680	+	0.425530i	−0.962323	−	0.271910i	$-0.912345\pi$
$181$	−3.30529	+	5.72493i	−0.245680	+	0.425530i	0.716643	+	0.697441i	$0.245678\pi$
$182$	10.4430	−	23.0900i	0.774090	−	1.71154i
$183$		0			0
$184$	−14.3961	+	7.33256i	−1.06129	+	0.540564i
$185$	−11.6727	+	2.05821i	−0.858194	+	0.151323i
$186$		0			0
$187$	−0.0775175	+	0.0923817i	−0.00566864	+	0.00675562i
$188$	−9.58531	−	5.24176i	−0.699081	−	0.382294i
$189$		0			0
$190$	2.44716	−	9.57538i	0.177535	−	0.694671i
$191$	−19.5133	−	16.3736i	−1.41193	−	1.18475i	−0.955500	−	0.294990i	$-0.904684\pi$
$191$	−19.5133	−	16.3736i	−1.41193	−	1.18475i	−0.456429	−	0.889760i	$-0.650872\pi$
$192$		0			0
$193$	−3.57625	−	20.2819i	−0.257424	−	1.45993i	−0.789772	−	0.613400i	$-0.789801\pi$
$193$	−3.57625	−	20.2819i	−0.257424	−	1.45993i	0.532348	−	0.846526i	$-0.321310\pi$
$194$	4.11155	−	6.01916i	0.295192	−	0.432150i
$195$		0			0
$196$	10.1036	−	12.6239i	0.721682	−	0.901704i
$197$	−6.00833	−	3.46891i	−0.428076	−	0.247150i	0.270451	−	0.962734i	$-0.412827\pi$
$197$	−6.00833	−	3.46891i	−0.428076	−	0.247150i	−0.698526	+	0.715584i	$0.746161\pi$
$198$		0			0
$199$	−10.0244	+	5.78756i	−0.710608	+	0.410270i	−0.811286	−	0.584650i	$-0.801232\pi$
$199$	−10.0244	+	5.78756i	−0.710608	+	0.410270i	0.100678	+	0.994919i	$0.467899\pi$
$200$	−1.15474	+	2.71931i	−0.0816526	+	0.192284i
$201$		0			0
$202$	16.8484	−	8.09551i	1.18545	−	0.569598i
$203$	11.9357	−	10.0153i	0.837725	−	0.702934i
$204$		0			0
$205$	−2.53506	+	0.922686i	−0.177056	+	0.0644432i
$206$	0.398203	+	1.42009i	0.0277441	+	0.0989421i
$207$		0			0
$208$	18.4352	−	0.855080i	1.27825	−	0.0592891i
$209$	−0.163101	−	0.0287592i	−0.0112820	−	0.00198931i
$210$		0			0
$211$	5.16932	−	14.2026i	0.355871	−	0.977747i	−0.624576	−	0.780964i	$-0.714728\pi$
$211$	5.16932	−	14.2026i	0.355871	−	0.977747i	0.980447	−	0.196783i	$-0.0630494\pi$
$212$	−19.9586	−	6.74481i	−1.37076	−	0.463235i
$213$		0			0
$214$	14.3450	−	10.2942i	0.980603	−	0.703699i
$215$	−23.7173			−1.61751
$216$		0			0
$217$	29.6210			2.01080
$218$	−22.1230	+	15.8759i	−1.49836	+	1.07525i
$219$		0			0
$220$	0.271416	+	0.0917223i	0.0182989	+	0.00618392i
$221$	3.26612	−	8.97359i	0.219703	−	0.603629i
$222$		0			0
$223$	1.61660	+	0.285051i	0.108256	+	0.0190884i	0.227514	−	0.973775i	$-0.426940\pi$
$223$	1.61660	+	0.285051i	0.108256	+	0.0190884i	−0.119258	+	0.992863i	$0.538051\pi$
$224$	21.5156	+	4.44802i	1.43757	+	0.297196i
$225$		0			0
$226$	−1.99041	−	7.09828i	−0.132400	−	0.472170i
$227$	−25.6644	+	9.34108i	−1.70341	+	0.619989i	−0.996206	−	0.0870239i	$-0.972264\pi$
$227$	−25.6644	+	9.34108i	−1.70341	+	0.619989i	−0.707200	+	0.707013i	$0.750042\pi$
$228$		0			0
$229$	−4.83939	+	4.06073i	−0.319796	+	0.268340i	−0.788527	−	0.615000i	$-0.789156\pi$
$229$	−4.83939	+	4.06073i	−0.319796	+	0.268340i	0.468731	+	0.883341i	$0.344711\pi$
$230$	17.9010	−	8.60127i	1.18035	−	0.567151i
$231$		0			0
$232$	10.4441	+	4.43505i	0.685692	+	0.291176i
$233$	25.6785	−	14.8255i	1.68226	−	0.971251i	0.722099	−	0.691790i	$-0.243178\pi$
$233$	25.6785	−	14.8255i	1.68226	−	0.971251i	0.960157	−	0.279461i	$-0.0901558\pi$
$234$		0			0
$235$	11.6306	+	6.71490i	0.758693	+	0.438032i
$236$	−1.99931	+	2.49803i	−0.130144	+	0.162608i
$237$		0			0
$238$	6.41242	−	9.38755i	0.415656	−	0.608505i
$239$	1.61593	+	9.16442i	0.104526	+	0.592797i	0.991409	+	0.130802i	$0.0417552\pi$
$239$	1.61593	+	9.16442i	0.104526	+	0.592797i	−0.886882	+	0.461995i	$0.847134\pi$
$240$		0			0
$241$	−10.7714	−	9.03831i	−0.693849	−	0.582209i	0.226167	−	0.974089i	$-0.427380\pi$
$241$	−10.7714	−	9.03831i	−0.693849	−	0.582209i	−0.920016	+	0.391880i	$0.871825\pi$
$242$	−3.85071	+	15.0673i	−0.247533	+	0.968561i
$243$		0			0
$244$	3.70490	+	2.02604i	0.237182	+	0.129704i
$245$	−12.7764	+	15.2263i	−0.816251	+	0.972771i
$246$		0			0
$247$	12.9153	−	2.27732i	0.821783	−	0.144902i
$248$	9.79042	+	19.2216i	0.621692	+	1.22058i
$249$		0			0
$250$	−5.66743	+	12.5309i	−0.358439	+	0.792524i
$251$	−7.60386	+	13.1703i	−0.479951	+	0.831300i	−0.999736	−	0.0229974i	$-0.992679\pi$
$251$	−7.60386	+	13.1703i	−0.479951	+	0.831300i	0.519784	+	0.854298i	$0.326012\pi$
$252$		0			0
$253$	−0.166404	−	0.288220i	−0.0104617	−	0.0181203i
$254$	2.72680	−	0.270437i	0.171095	−	0.0169687i
$255$		0			0
$256$	4.22501	+	15.4321i	0.264063	+	0.964505i
$257$	4.55275	+	5.42575i	0.283992	+	0.338449i	0.889115	−	0.457683i	$-0.151321\pi$
$257$	4.55275	+	5.42575i	0.283992	+	0.338449i	−0.605123	+	0.796132i	$0.706876\pi$
$258$		0			0
$259$	−6.40410	−	17.5951i	−0.397931	−	1.09331i
$260$	−22.6803	+	0.525707i	−1.40657	+	0.0326030i
$261$		0			0
$262$	0.473107	+	0.462268i	0.0292286	+	0.0285590i
$263$	−0.345233	+	1.95791i	−0.0212880	+	0.120730i	−0.993600	−	0.112957i	$-0.963968\pi$
$263$	−0.345233	+	1.95791i	−0.0212880	+	0.120730i	0.972312	+	0.233687i	$0.0750790\pi$
$264$		0			0
$265$	24.3360	+	8.85756i	1.49495	+	0.544116i
$266$	15.5681	+	1.18044i	0.954543	+	0.0723771i
$267$		0			0
$268$	−14.0792	+	5.49714i	−0.860026	+	0.335791i
$269$			1.18433i			0.0722097i	0.999348	+	0.0361048i	$0.0114950\pi$
$269$			1.18433i			0.0722097i	−0.999348	+	0.0361048i	$0.988505\pi$
$270$		0			0
$271$			10.9019i			0.662245i	0.943588	+	0.331122i	$0.107427\pi$
$271$			10.9019i			0.662245i	−0.943588	+	0.331122i	$0.892573\pi$
$272$	8.21122	+	1.05834i	0.497878	+	0.0641715i
$273$		0			0
$274$	−0.469435	+	6.19113i	−0.0283596	+	0.374020i
$275$	−0.0571883	−	0.0208148i	−0.00344858	−	0.00125518i
$276$		0			0
$277$	−0.982411	+	5.57153i	−0.0590274	+	0.334761i	−0.999993	−	0.00374124i	$-0.998809\pi$
$277$	−0.982411	+	5.57153i	−0.0590274	+	0.334761i	0.940966	+	0.338502i	$0.109920\pi$
$278$	−8.34925	+	8.54502i	−0.500755	+	0.512496i
$279$		0			0
$280$	−26.3149	−	6.07928i	−1.57262	−	0.363306i
$281$	−4.23708	−	11.6413i	−0.252763	−	0.694460i	−0.999567	−	0.0294162i	$-0.990635\pi$
$281$	−4.23708	−	11.6413i	−0.252763	−	0.694460i	0.746805	−	0.665044i	$-0.231587\pi$
$282$		0			0
$283$	14.4882	+	17.2663i	0.861233	+	1.02638i	0.999353	+	0.0359618i	$0.0114495\pi$
$283$	14.4882	+	17.2663i	0.861233	+	1.02638i	−0.138120	+	0.990415i	$0.544106\pi$
$284$	−16.0161	+	3.20841i	−0.950379	+	0.190384i
$285$		0			0
$286$	0.0375200	+	0.378313i	0.00221860	+	0.0223701i
$287$	−2.13088	−	3.69079i	−0.125782	−	0.217860i
$288$		0			0
$289$	−6.35799	+	11.0124i	−0.374000	+	0.647786i
$290$	−12.7090	−	5.74797i	−0.746298	−	0.337532i
$291$		0			0
$292$	−8.62769	−	9.81108i	−0.504897	−	0.574150i
$293$	24.7027	−	4.35575i	1.44315	−	0.254466i	0.603398	−	0.797440i	$-0.293813\pi$
$293$	24.7027	−	4.35575i	1.44315	−	0.254466i	0.839749	+	0.542975i	$0.182702\pi$
$294$		0			0
$295$	2.52821	−	3.01300i	0.147198	−	0.175424i
$296$	9.30111	−	9.97134i	0.540616	−	0.579572i
$297$		0			0
$298$	−13.9301	−	3.56007i	−0.806946	−	0.206229i
$299$	20.1881	+	16.9398i	1.16751	+	0.979657i
$300$		0			0
$301$	−6.50611	−	36.8980i	−0.375006	−	2.12677i
$302$	−2.78677	−	1.90358i	−0.160360	−	0.109539i
$303$		0			0
$304$	4.37962	+	10.4926i	0.251188	+	0.601793i
$305$	−4.49542	−	2.59543i	−0.257407	−	0.148614i
$306$		0			0
$307$	−7.99858	+	4.61798i	−0.456503	+	0.263562i	−0.710573	−	0.703624i	$-0.751564\pi$
$307$	−7.99858	+	4.61798i	−0.456503	+	0.263562i	0.254070	+	0.967186i	$0.418231\pi$
$308$	−0.0682417	+	0.447414i	−0.00388843	+	0.0254938i
$309$		0			0
$310$	−11.4844	−	23.9013i	−0.652269	−	1.35750i
$311$	−19.9420	+	16.7333i	−1.13080	+	0.948858i	−0.999099	−	0.0424309i	$-0.986490\pi$
$311$	−19.9420	+	16.7333i	−1.13080	+	0.948858i	−0.131706	+	0.991289i	$0.542045\pi$
$312$		0			0
$313$	−21.0105	+	7.64718i	−1.18758	+	0.432244i	−0.858874	−	0.512187i	$-0.828835\pi$
$313$	−21.0105	+	7.64718i	−1.18758	+	0.432244i	−0.328708	+	0.944432i	$0.606613\pi$
$314$	7.41558	−	2.07939i	0.418486	−	0.117347i
$315$		0			0
$316$	7.20547	+	11.8380i	0.405340	+	0.665938i
$317$	−11.4763	−	2.02358i	−0.644574	−	0.113656i	−0.158201	−	0.987407i	$-0.550569\pi$
$317$	−11.4763	−	2.02358i	−0.644574	−	0.113656i	−0.486373	+	0.873751i	$0.661680\pi$
$318$		0			0
$319$	−0.0799442	+	0.219645i	−0.00447601	+	0.0122977i
$320$	−4.75273	−	19.0856i	−0.265686	−	1.06692i
$321$		0			0
$322$	18.2919	+	25.4898i	1.01937	+	1.42049i
$323$	5.88335			0.327358
$324$		0			0
$325$	4.81914			0.267318
$326$	−8.05010	−	11.2178i	−0.445854	−	0.621297i
$327$		0			0
$328$	1.69072	−	2.60266i	0.0933544	−	0.143708i
$329$	−7.25617	+	19.9362i	−0.400046	+	1.09912i
$330$		0			0
$331$	−4.32184	−	0.762057i	−0.237550	−	0.0418864i	0.0536058	−	0.998562i	$-0.482929\pi$
$331$	−4.32184	−	0.762057i	−0.237550	−	0.0418864i	−0.291155	+	0.956676i	$0.594040\pi$
$332$	19.4681	−	11.8498i	1.06845	−	0.650340i
$333$		0			0
$334$	6.32623	−	1.77392i	0.346156	−	0.0970648i
$335$	17.4593	−	6.35465i	0.953901	−	0.347192i
$336$		0			0
$337$	−25.7716	+	21.6249i	−1.40387	+	1.17799i	−0.444517	+	0.895771i	$0.646625\pi$
$337$	−25.7716	+	21.6249i	−1.40387	+	1.17799i	−0.959351	+	0.282214i	$0.908931\pi$
$338$	−5.07551	−	10.5631i	−0.276071	−	0.574560i
$339$		0			0
$340$	−10.0610	−	1.53455i	−0.545636	−	0.0832229i
$341$	−0.384831	+	0.222182i	−0.0208398	+	0.0120318i
$342$		0			0
$343$	−3.64812	−	2.10624i	−0.196980	−	0.113726i
$344$	21.7934	−	16.4176i	1.17502	−	0.885177i
$345$		0			0
$346$	1.02903	+	0.702903i	0.0553207	+	0.0377883i
$347$	−2.59951	−	14.7425i	−0.139549	−	0.791421i	−0.971583	−	0.236697i	$-0.923935\pi$
$347$	−2.59951	−	14.7425i	−0.139549	−	0.791421i	0.832035	−	0.554724i	$-0.187176\pi$
$348$		0			0
$349$	−8.14865	−	6.83753i	−0.436187	−	0.366005i	0.398093	−	0.917345i	$-0.369672\pi$
$349$	−8.14865	−	6.83753i	−0.436187	−	0.366005i	−0.834280	+	0.551340i	$0.814117\pi$
$350$	5.55850	+	1.42057i	0.297114	+	0.0759328i
$351$		0			0
$352$	−0.312891	+	0.103597i	−0.0166772	+	0.00552176i
$353$	7.07097	−	8.42685i	0.376350	−	0.448516i	−0.544309	−	0.838885i	$-0.683208\pi$
$353$	7.07097	−	8.42685i	0.376350	−	0.448516i	0.920659	+	0.390369i	$0.127652\pi$
$354$		0			0
$355$	19.7743	−	3.48675i	1.04951	−	0.185057i
$356$	3.22297	−	2.83422i	0.170817	−	0.150213i
$357$		0			0
$358$	16.3614	+	7.39985i	0.864725	+	0.391094i
$359$	−8.75833	+	15.1699i	−0.462247	+	0.800636i	−0.999073	−	0.0430578i	$-0.986290\pi$
$359$	−8.75833	+	15.1699i	−0.462247	+	0.800636i	0.536825	+	0.843693i	$0.319623\pi$
$360$		0			0
$361$	−5.46012	−	9.45721i	−0.287375	−	0.497748i
$362$	0.922657	+	9.30312i	0.0484938	+	0.488961i
$363$		0			0
$364$	−7.03951	−	35.1405i	−0.368971	−	1.84186i
$365$	10.3235	+	12.3031i	0.540358	+	0.643973i
$366$		0			0
$367$	1.77877	+	4.88714i	0.0928511	+	0.255106i	0.977421	−	0.211301i	$-0.0677702\pi$
$367$	1.77877	+	4.88714i	0.0928511	+	0.255106i	−0.884570	+	0.466408i	$0.845548\pi$
$368$	−10.4949	+	20.2950i	−0.547085	+	1.05795i
$369$		0			0
$370$	−11.7146	+	11.9893i	−0.609015	+	0.623295i
$371$	−7.10426	+	40.2903i	−0.368835	+	2.09177i
$372$		0			0
$373$	14.9141	+	5.42829i	0.772223	+	0.281066i	0.697926	−	0.716170i	$-0.254107\pi$
$373$	14.9141	+	5.42829i	0.772223	+	0.281066i	0.0742970	+	0.997236i	$0.476329\pi$
$374$	−0.0128946	+	0.170060i	−0.000666764	+	0.00879360i
$375$		0			0
$376$	−15.3353	+	1.88069i	−0.790858	+	0.0969893i
$377$		−	18.5090i		−	0.953262i
$378$		0			0
$379$		−	13.3564i		−	0.686073i	−0.939322	−	0.343037i	$-0.888544\pi$
$379$		−	13.3564i		−	0.686073i	0.939322	−	0.343037i	$-0.111456\pi$
$380$	−5.08344	−	13.0197i	−0.260775	−	0.667894i
$381$		0			0
$382$	−35.9208	−	2.72365i	−1.83787	−	0.139354i
$383$	7.59874	+	2.76571i	0.388277	+	0.141321i	0.528780	−	0.848759i	$-0.322650\pi$
$383$	7.59874	+	2.76571i	0.388277	+	0.141321i	−0.140503	+	0.990080i	$0.544872\pi$
$384$		0			0
$385$	0.0966106	−	0.547906i	0.00492373	−	0.0279239i
$386$	−20.8321	−	20.3548i	−1.06032	−	1.03603i
$387$		0			0
$388$	−0.238882	−	10.3060i	−0.0121274	−	0.523207i
$389$	6.72162	+	18.4675i	0.340799	+	0.936339i	0.985163	+	0.171620i	$0.0549000\pi$
$389$	6.72162	+	18.4675i	0.340799	+	0.936339i	−0.644364	+	0.764719i	$0.722878\pi$
$390$		0			0
$391$	7.59941	+	9.05663i	0.384319	+	0.458013i
$392$	1.20005	−	22.8352i	0.0606115	−	1.15335i
$393$		0			0
$394$	−9.76366	+	0.968332i	−0.491886	+	0.0487839i
$395$	−8.51795	−	14.7535i	−0.428585	−	0.742330i
$396$		0			0
$397$	12.3726	−	21.4299i	0.620961	−	1.07554i	−0.368346	−	0.929689i	$-0.620076\pi$
$397$	12.3726	−	21.4299i	0.620961	−	1.07554i	0.989307	−	0.145848i	$-0.0465910\pi$
$398$	−6.74576	+	14.9152i	−0.338135	+	0.747629i
$399$		0			0
$400$	0.915374	+	4.07655i	0.0457687	+	0.203827i
$401$	−11.9917	+	2.11446i	−0.598836	+	0.105591i	−0.464846	−	0.885392i	$-0.653890\pi$
$401$	−11.9917	+	2.11446i	−0.598836	+	0.105591i	−0.133990	+	0.990983i	$0.542779\pi$
$402$		0			0
$403$	22.6180	−	26.9551i	1.12668	−	1.34273i
$404$	12.6835	−	23.1935i	0.631026	−	1.15392i
$405$		0			0
$406$	5.45604	−	21.3487i	0.270779	−	1.05952i
$407$	0.215179	+	0.180557i	0.0106660	+	0.00894986i
$408$		0			0
$409$	5.39760	+	30.6113i	0.266894	+	1.51363i	0.763586	+	0.645706i	$0.223437\pi$
$409$	5.39760	+	30.6113i	0.266894	+	1.51363i	−0.496692	+	0.867927i	$0.665452\pi$
$410$	−2.15195	+	3.15037i	−0.106277	+	0.155586i
$411$		0			0
$412$	1.62843	+	1.30332i	0.0802269	+	0.0642099i
$413$	5.38099	+	3.10671i	0.264781	+	0.152871i
$414$		0			0
$415$	−24.2629	+	14.0082i	−1.19102	+	0.687635i
$416$	20.4766	−	16.1828i	1.00395	−	0.793428i
$417$		0			0
$418$	−0.211113	+	0.101438i	−0.0103259	+	0.00496149i
$419$	−28.2403	+	23.6964i	−1.37963	+	1.15765i	−0.410281	+	0.911959i	$0.634569\pi$
$419$	−28.2403	+	23.6964i	−1.37963	+	1.15765i	−0.969349	+	0.245688i	$0.920986\pi$
$420$		0			0
$421$	34.6191	−	12.6003i	1.68723	−	0.614102i	0.692960	−	0.720976i	$-0.256306\pi$
$421$	34.6191	−	12.6003i	1.68723	−	0.614102i	0.994273	+	0.106874i	$0.0340842\pi$
$422$	−5.77100	−	20.5807i	−0.280928	−	1.00185i
$423$		0			0
$424$	−28.4933	+	8.70677i	−1.38376	+	0.422838i
$425$	2.12908	+	0.375414i	0.103275	+	0.0182102i
$426$		0			0
$427$	2.80464	−	7.70569i	0.135726	−	0.372905i
$428$	7.99421	−	23.6557i	0.386415	−	1.14344i
$429$		0			0
$430$	−27.2507	+	19.5556i	−1.31414	+	0.943054i
$431$	11.3781			0.548063			0.274032	−	0.961721i	$-0.411643\pi$
$431$	11.3781			0.548063			0.274032	+	0.961721i	$0.411643\pi$
$432$		0			0
$433$	−7.27646			−0.349684			−0.174842	−	0.984596i	$-0.555941\pi$
$433$	−7.27646			−0.349684			−0.174842	+	0.984596i	$0.555941\pi$
$434$	34.0339	−	24.4233i	1.63368	−	1.17236i
$435$		0			0
$436$	−12.3288	+	36.4821i	−0.590441	+	1.74718i
$437$	−5.55313	+	15.2571i	−0.265642	+	0.729846i
$438$		0			0
$439$	−29.3104	−	5.16822i	−1.39891	−	0.246665i	−0.577214	−	0.816593i	$-0.695860\pi$
$439$	−29.3104	−	5.16822i	−1.39891	−	0.246665i	−0.821695	+	0.569927i	$0.806971\pi$
$440$	0.387479	−	0.118403i	0.0184723	−	0.00564464i
$441$		0			0
$442$	−3.64627	−	13.0035i	−0.173436	−	0.618512i
$443$	−16.1633	+	5.88296i	−0.767941	+	0.279508i	−0.696135	−	0.717911i	$-0.745099\pi$
$443$	−16.1633	+	5.88296i	−0.767941	+	0.279508i	−0.0718063	+	0.997419i	$0.522876\pi$
$444$		0			0
$445$	−4.04160	+	3.39131i	−0.191590	+	0.160763i
$446$	2.09248	−	1.00542i	0.0990817	−	0.0476080i
$447$		0			0
$448$	28.3885	−	12.6296i	1.34123	−	0.596691i
$449$	−18.8763	+	10.8982i	−0.890826	+	0.514319i	−0.874213	−	0.485543i	$-0.838622\pi$
$449$	−18.8763	+	10.8982i	−0.890826	+	0.514319i	−0.0166137	+	0.999862i	$0.505289\pi$
$450$		0			0
$451$	0.0553680	+	0.0319667i	0.00260718	+	0.00150525i
$452$	−8.13967	−	6.51462i	−0.382858	−	0.306422i
$453$		0			0
$454$	−21.7859	+	31.8937i	−1.02246	+	1.49685i
$455$	7.65020	+	43.3864i	0.358647	+	2.03399i
$456$		0			0
$457$	7.39792	+	6.20759i	0.346060	+	0.290379i	0.799206	−	0.601058i	$-0.205254\pi$
$457$	7.39792	+	6.20759i	0.346060	+	0.290379i	−0.453146	+	0.891436i	$0.649698\pi$
$458$	−2.21217	+	8.65590i	−0.103368	+	0.404464i
$459$		0			0
$460$	13.4758	−	24.6425i	0.628314	−	1.14896i
$461$	21.0745	−	25.1156i	0.981536	−	1.16975i	−0.00395005	−	0.999992i	$-0.501257\pi$
$461$	21.0745	−	25.1156i	0.981536	−	1.16975i	0.985486	−	0.169757i	$-0.0542982\pi$
$462$		0			0
$463$	−37.7572	+	6.65762i	−1.75473	+	0.309406i	−0.956235	−	0.292599i	$-0.905480\pi$
$463$	−37.7572	+	6.65762i	−1.75473	+	0.309406i	−0.798493	+	0.602005i	$0.794369\pi$
$464$	15.6569	−	3.51571i	0.726855	−	0.163213i
$465$		0			0
$466$	17.2800	−	38.2069i	0.800482	−	1.76990i
$467$	5.79199	−	10.0320i	0.268021	−	0.464227i	−0.700329	−	0.713820i	$-0.746964\pi$
$467$	5.79199	−	10.0320i	0.268021	−	0.464227i	0.968351	+	0.249593i	$0.0802969\pi$
$468$		0			0
$469$	14.6756	+	25.4189i	0.677657	+	1.17374i
$470$	18.8999	−	1.87444i	0.871787	−	0.0864613i
$471$		0			0
$472$	−0.237467	+	4.51867i	−0.0109303	+	0.207989i
$473$	0.361292	+	0.430571i	0.0166122	+	0.0197977i
$474$		0			0
$475$	1.01547	+	2.78997i	0.0465928	+	0.128013i
$476$	−0.372564	−	16.0733i	−0.0170764	−	0.736720i
$477$		0			0
$478$	9.41300	+	9.19735i	0.430541	+	0.420677i
$479$	−3.11270	+	17.6530i	−0.142223	+	0.806585i	0.827332	+	0.561713i	$0.189857\pi$
$479$	−3.11270	+	17.6530i	−0.142223	+	0.806585i	−0.969555	+	0.244873i	$0.921254\pi$
$480$		0			0
$481$	−20.9016	−	7.60757i	−0.953032	−	0.346875i
$482$	−19.8285	−	1.50347i	−0.903163	−	0.0684813i
$483$		0			0
$484$	7.99901	+	20.4870i	0.363591	+	0.931227i
$485$			12.6723i			0.575421i
$486$		0			0
$487$			22.6464i			1.02621i	0.858327	+	0.513104i	$0.171504\pi$
$487$			22.6464i			1.02621i	−0.858327	+	0.513104i	$0.828496\pi$
$488$	5.92737	−	0.726922i	0.268320	−	0.0329062i
$489$		0			0
$490$	−2.12528	+	28.0291i	−0.0960102	+	1.26623i
$491$	−24.1565	−	8.79224i	−1.09017	−	0.396788i	−0.266484	−	0.963839i	$-0.585862\pi$
$491$	−24.1565	−	8.79224i	−1.09017	−	0.396788i	−0.823683	+	0.567051i	$0.808084\pi$
$492$		0			0
$493$	1.44186	−	8.17721i	0.0649382	−	0.368283i
$494$	12.9617	−	13.2656i	0.583176	−	0.596850i
$495$		0			0
$496$	27.0978	+	14.0128i	1.21673	+	0.629192i
$497$	10.8490	+	29.8073i	0.486643	+	1.33704i
$498$		0			0
$499$	4.64688	+	5.53794i	0.208023	+	0.247912i	0.859961	−	0.510360i	$-0.170488\pi$
$499$	4.64688	+	5.53794i	0.208023	+	0.247912i	−0.651938	+	0.758273i	$0.726044\pi$
$500$	3.82033	+	19.0707i	0.170851	+	0.852868i
$501$		0			0
$502$	2.12259	+	21.4020i	0.0947357	+	0.955217i
$503$	19.3621	+	33.5362i	0.863314	+	1.49530i	0.868712	+	0.495318i	$0.164949\pi$
$503$	19.3621	+	33.5362i	0.863314	+	1.49530i	−0.00539768	+	0.999985i	$0.501718\pi$
$504$		0			0
$505$	−16.2480	+	28.1424i	−0.723027	+	1.25232i
$506$	−0.428841	−	0.193954i	−0.0190643	−	0.00862232i
$507$		0			0
$508$	2.91006	−	2.55905i	0.129113	−	0.113540i
$509$	18.8059	−	3.31600i	0.833559	−	0.146979i	0.259449	−	0.965757i	$-0.416459\pi$
$509$	18.8059	−	3.31600i	0.833559	−	0.146979i	0.574110	+	0.818778i	$0.305348\pi$
$510$		0			0
$511$	−16.3085	+	19.4357i	−0.721446	+	0.859785i
$512$	17.5786	+	14.2475i	0.776873	+	0.629657i
$513$		0			0
$514$	9.70469	+	2.48021i	0.428056	+	0.109397i
$515$	−1.96413	−	1.64810i	−0.0865499	−	0.0726240i
$516$		0			0
$517$	−0.0552670	−	0.313435i	−0.00243064	−	0.0137848i
$518$	−21.8658	−	14.9361i	−0.960730	−	0.656253i
$519$		0			0
$520$	−25.6257	+	19.3046i	−1.12376	+	0.846562i
$521$	19.0779	+	11.0146i	0.835817	+	0.482559i	0.855840	−	0.517240i	$-0.173041\pi$
$521$	19.0779	+	11.0146i	0.835817	+	0.482559i	−0.0200233	+	0.999800i	$0.506374\pi$
$522$		0			0
$523$	−3.75661	+	2.16888i	−0.164265	+	0.0948384i	−0.579879	−	0.814703i	$-0.696900\pi$
$523$	−3.75661	+	2.16888i	−0.164265	+	0.0948384i	0.415614	+	0.909541i	$0.363567\pi$
$524$	0.924743	+	0.141046i	0.0403976	+	0.00616162i
$525$		0			0
$526$	1.21769	+	2.53425i	0.0530938	+	0.110499i
$527$	12.0924	−	10.1467i	0.526752	−	0.441998i
$528$		0			0
$529$	−9.04622	+	3.29256i	−0.393314	+	0.143155i
$530$	35.2648	−	9.88853i	1.53181	−	0.429530i
$531$		0			0
$532$	18.8608	−	11.4801i	0.817717	−	0.497724i
$533$	−4.98572	−	0.879117i	−0.215955	−	0.0380788i
$534$		0			0
$535$	−10.4983	+	28.8439i	−0.453883	+	1.24703i
$536$	−11.6442	+	17.9248i	−0.502953	+	0.774234i
$537$		0			0
$538$	0.976511	+	1.36077i	0.0421004	+	0.0586668i
$539$	0.471048			0.0202895
$540$		0			0
$541$	−2.88802			−0.124166			−0.0620829	−	0.998071i	$-0.519774\pi$
$541$	−2.88802			−0.124166			−0.0620829	+	0.998071i	$0.519774\pi$
$542$	8.98895	+	12.5261i	0.386108	+	0.538042i
$543$		0			0
$544$	10.3072	−	5.55437i	0.441916	−	0.238142i
$545$	16.1907	−	44.4835i	0.693532	−	1.90546i
$546$		0			0
$547$	−22.9975	−	4.05508i	−0.983303	−	0.173383i	−0.341191	−	0.939994i	$-0.610830\pi$
$547$	−22.9975	−	4.05508i	−0.983303	−	0.173383i	−0.642112	+	0.766611i	$0.721941\pi$
$548$	4.56539	+	7.50054i	0.195024	+	0.320407i
$549$		0			0
$550$	−0.0828705	+	0.0232375i	−0.00353361	+	0.000990852i
$551$	10.7155	−	3.90013i	0.456497	−	0.166151i
$552$		0			0
$553$	20.6160	−	17.2989i	0.876683	−	0.735625i
$554$	3.46512	+	7.21160i	0.147219	+	0.306391i
$555$		0			0
$556$	−2.54750	+	16.7022i	−0.108038	+	0.708333i
$557$	7.72227	−	4.45845i	0.327203	−	0.188911i	−0.327396	−	0.944887i	$-0.606171\pi$
$557$	7.72227	−	4.45845i	0.327203	−	0.188911i	0.654599	+	0.755977i	$0.272838\pi$
$558$		0			0
$559$	−38.5452	−	22.2541i	−1.63029	−	0.941247i
$560$	−35.2478	+	14.7124i	−1.48949	+	0.621714i
$561$		0			0
$562$	−14.4669	−	9.88199i	−0.610248	−	0.416846i
$563$	−3.80400	−	21.5736i	−0.160320	−	0.909218i	−0.953760	−	0.300570i	$-0.902823\pi$
$563$	−3.80400	−	21.5736i	−0.160320	−	0.909218i	0.793440	−	0.608648i	$-0.208288\pi$
$564$		0			0
$565$	9.81767	+	8.23801i	0.413033	+	0.346576i
$566$	30.8832	+	7.89275i	1.29812	+	0.331757i
$567$		0			0
$568$	−15.7567	+	16.8921i	−0.661136	+	0.708777i
$569$	12.7365	−	15.1788i	0.533943	−	0.636329i	−0.429875	−	0.902888i	$-0.641442\pi$
$569$	12.7365	−	15.1788i	0.533943	−	0.636329i	0.963818	+	0.266560i	$0.0858869\pi$
$570$		0			0
$571$	27.0599	−	4.77140i	1.13242	−	0.199677i	0.424134	−	0.905599i	$-0.360579\pi$
$571$	27.0599	−	4.77140i	1.13242	−	0.199677i	0.708289	+	0.705923i	$0.249467\pi$
$572$	0.355039	+	0.403737i	0.0148449	+	0.0168811i
$573$		0			0
$574$	−5.49149	−	2.48367i	−0.229210	−	0.103666i
$575$	−2.98313	+	5.16693i	−0.124405	+	0.215476i
$576$		0			0
$577$	1.20328	+	2.08414i	0.0500931	+	0.0867638i	0.889985	−	0.455990i	$-0.150715\pi$
$577$	1.20328	+	2.08414i	0.0500931	+	0.0867638i	−0.839892	+	0.542754i	$0.817382\pi$
$578$	1.77481	+	17.8953i	0.0738223	+	0.744347i
$579$		0			0
$580$	−19.3417	+	3.87463i	−0.803121	+	0.160885i
$581$	−28.4489	−	33.9041i	−1.18026	−	1.40658i
$582$		0			0
$583$	−0.209913	−	0.576733i	−0.00869373	−	0.0238858i
$584$	−18.0025	−	4.15895i	−0.744951	−	0.172099i
$585$		0			0
$586$	24.7914	−	25.3727i	1.02412	−	1.04814i
$587$	−2.24123	+	12.7106i	−0.0925054	+	0.524624i	0.902978	+	0.429687i	$0.141376\pi$
$587$	−2.24123	+	12.7106i	−0.0925054	+	0.524624i	−0.995483	+	0.0949372i	$0.969735\pi$
$588$		0			0
$589$	20.3712	+	7.41453i	0.839383	+	0.305510i
$590$	0.420553	−	5.54645i	0.0173139	−	0.228344i
$591$		0			0
$592$	2.46513	−	19.1259i	0.101316	−	0.786069i
$593$		−	27.2738i		−	1.12000i	−0.828493	−	0.560000i	$-0.810801\pi$
$593$		−	27.2738i		−	1.12000i	0.828493	−	0.560000i	$-0.189199\pi$
$594$		0			0
$595$			19.7639i			0.810242i
$596$	−18.9407	+	7.39528i	−0.775842	+	0.302922i
$597$		0			0
$598$	37.1631	+	2.81785i	1.51971	+	0.115230i
$599$	19.1994	+	6.98801i	0.784466	+	0.285522i	0.703034	−	0.711157i	$-0.251828\pi$
$599$	19.1994	+	6.98801i	0.784466	+	0.285522i	0.0814322	+	0.996679i	$0.474051\pi$
$600$		0			0
$601$	−7.63059	+	43.2752i	−0.311258	+	1.76523i	0.281216	+	0.959645i	$0.409262\pi$
$601$	−7.63059	+	43.2752i	−0.311258	+	1.76523i	−0.592474	+	0.805589i	$0.701849\pi$
$602$	−37.8988	−	37.0306i	−1.54464	−	1.50925i
$603$		0			0
$604$	−4.77149	+	0.110598i	−0.194149	+	0.00450019i
$605$	−9.24679	−	25.4053i	−0.375935	−	1.03287i
$606$		0			0
$607$	−24.2266	−	28.8721i	−0.983326	−	1.17188i	−0.985117	−	0.171884i	$-0.945015\pi$
$607$	−24.2266	−	28.8721i	−0.983326	−	1.17188i	0.00179117	−	0.999998i	$-0.499430\pi$
$608$	13.6836	+	8.44468i	0.554941	+	0.342477i
$609$		0			0
$610$	−7.30515	+	0.724504i	−0.295777	+	0.0293343i
$611$	12.6013	+	21.8260i	0.509792	+	0.882986i
$612$		0			0
$613$	1.70832	−	2.95890i	0.0689984	−	0.119509i	−0.829462	−	0.558563i	$-0.811353\pi$
$613$	1.70832	−	2.95890i	0.0689984	−	0.119509i	0.898461	+	0.439054i	$0.144686\pi$
$614$	−5.38255	+	11.9010i	−0.217222	+	0.480286i
$615$		0			0
$616$	0.290498	+	0.570337i	0.0117045	+	0.0229795i
$617$	−28.4409	+	5.01489i	−1.14499	+	0.201892i	−0.713786	−	0.700364i	$-0.753021\pi$
$617$	−28.4409	+	5.01489i	−1.14499	+	0.201892i	−0.431200	+	0.902256i	$0.641910\pi$
$618$		0			0
$619$	11.5574	−	13.7736i	0.464533	−	0.553609i	−0.482019	−	0.876161i	$-0.660096\pi$
$619$	11.5574	−	13.7736i	0.464533	−	0.553609i	0.946552	+	0.322552i	$0.104541\pi$
$620$	−32.9026	−	17.9929i	−1.32140	−	0.722612i
$621$		0			0
$622$	−9.11582	+	35.6689i	−0.365511	+	1.43019i
$623$	−6.38469	−	5.35739i	−0.255797	−	0.214639i
$624$		0			0
$625$	−5.05864	−	28.6890i	−0.202346	−	1.14756i
$626$	−17.8353	+	26.1102i	−0.712840	+	1.04357i
$627$		0			0
$628$	6.80584	−	8.50353i	0.271582	−	0.339328i
$629$	−8.64162	−	4.98924i	−0.344564	−	0.198934i
$630$		0			0
$631$	−10.4847	+	6.05333i	−0.417388	+	0.240979i	−0.693959	−	0.720014i	$-0.744135\pi$
$631$	−10.4847	+	6.05333i	−0.417388	+	0.240979i	0.276571	+	0.960994i	$0.410802\pi$
$632$	18.0397	+	7.66046i	0.717580	+	0.304717i
$633$		0			0
$634$	−14.8545	+	7.13749i	−0.589949	+	0.283466i
$635$	−3.64921	+	3.06205i	−0.144815	+	0.121514i
$636$		0			0
$637$	−35.0509	+	12.7575i	−1.38877	+	0.505470i
$638$	0.0892492	+	0.318284i	0.00353341	+	0.0126010i
$639$		0			0
$640$	−21.1974	−	18.0102i	−0.837901	−	0.711916i
$641$	18.9399	+	3.33962i	0.748081	+	0.131907i	0.534676	−	0.845057i	$-0.320434\pi$
$641$	18.9399	+	3.33962i	0.748081	+	0.131907i	0.213405	+	0.976964i	$0.431545\pi$
$642$		0			0
$643$	0.978566	−	2.68859i	0.0385909	−	0.106028i	−0.918901	−	0.394489i	$-0.870922\pi$
$643$	0.978566	−	2.68859i	0.0385909	−	0.106028i	0.957491	+	0.288462i	$0.0931438\pi$
$644$	42.0341	+	14.2050i	1.65638	+	0.559756i
$645$		0			0
$646$	6.75984	−	4.85099i	0.265963	−	0.190860i
$647$	−36.4238			−1.43197			−0.715984	−	0.698117i	$-0.754022\pi$
$647$	−36.4238			−1.43197			−0.715984	+	0.698117i	$0.754022\pi$
$648$		0			0
$649$	−0.0932118			−0.00365888
$650$	5.53709	−	3.97351i	0.217182	−	0.155854i
$651$		0			0
$652$	−18.4988	−	6.25149i	−0.724469	−	0.244827i
$653$	−7.46684	+	20.5150i	−0.292200	+	0.802813i	0.703544	+	0.710652i	$0.251600\pi$
$653$	−7.46684	+	20.5150i	−0.292200	+	0.802813i	−0.995744	+	0.0921615i	$0.970622\pi$
$654$		0			0
$655$	−1.13244	−	0.199681i	−0.0442483	−	0.00780216i
$656$	−0.203364	−	4.38445i	−0.00794001	−	0.171184i
$657$		0			0
$658$	8.10075	+	28.8892i	0.315800	+	1.12622i
$659$	−0.310964	+	0.113182i	−0.0121134	+	0.00440894i	−0.348070	−	0.937469i	$-0.613163\pi$
$659$	−0.310964	+	0.113182i	−0.0121134	+	0.00440894i	0.335956	+	0.941878i	$0.390941\pi$
$660$		0			0
$661$	18.1399	−	15.2212i	0.705561	−	0.592036i	−0.217789	−	0.975996i	$-0.569884\pi$
$661$	18.1399	−	15.2212i	0.705561	−	0.592036i	0.923350	+	0.383960i	$0.125440\pi$
$662$	−5.59404	+	2.68789i	−0.217418	+	0.104468i
$663$		0			0
$664$	12.5980	−	29.6671i	0.488897	−	1.15131i
$665$	−23.5059	+	13.5712i	−0.911521	+	0.526267i
$666$		0			0
$667$	19.8448	+	11.4574i	0.768393	+	0.443632i
$668$	5.80606	−	7.25436i	0.224643	−	0.280680i
$669$		0			0
$670$	14.8207	−	21.6970i	0.572575	−	0.838229i
$671$	0.0213617	+	0.121148i	0.000824660	+	0.00467688i
$672$		0			0
$673$	2.82408	+	2.36968i	0.108860	+	0.0913446i	0.695593	−	0.718436i	$-0.255142\pi$
$673$	2.82408	+	2.36968i	0.108860	+	0.0913446i	−0.586733	+	0.809781i	$0.699586\pi$
$674$	−11.7806	+	46.0960i	−0.453774	+	1.77555i
$675$		0			0
$676$	−14.5413	−	7.95194i	−0.559280	−	0.305844i
$677$	6.13883	−	7.31597i	0.235934	−	0.281176i	−0.635066	−	0.772458i	$-0.719027\pi$
$677$	6.13883	−	7.31597i	0.235934	−	0.281176i	0.871001	+	0.491282i	$0.163472\pi$
$678$		0			0
$679$	−19.7149	+	3.47627i	−0.756588	+	0.133407i
$680$	−12.8252	+	6.53243i	−0.491824	+	0.250507i
$681$		0			0
$682$	−0.258967	+	0.572587i	−0.00991636	+	0.0219255i
$683$	14.0206	−	24.2843i	0.536482	−	0.929214i	−0.462608	−	0.886563i	$-0.653086\pi$
$683$	14.0206	−	24.2843i	0.536482	−	0.929214i	0.999090	−	0.0426510i	$-0.0135804\pi$
$684$		0			0
$685$	−5.39697	−	9.34783i	−0.206208	−	0.357162i
$686$	−5.92827	+	0.587949i	−0.226342	+	0.0224480i
$687$		0			0
$688$	11.5034	−	36.8328i	0.438564	−	1.40424i
$689$	31.2395	+	37.2298i	1.19013	+	1.41834i
$690$		0			0
$691$	−13.8412	−	38.0284i	−0.526545	−	1.44667i	−0.863113	−	0.505011i	$-0.831488\pi$
$691$	−13.8412	−	38.0284i	−0.526545	−	1.44667i	0.336568	−	0.941659i	$-0.390734\pi$
$692$	1.76189	−	0.0408389i	0.0669771	−	0.00155246i
$693$		0			0
$694$	−15.1424	−	14.7955i	−0.574798	−	0.561630i
$695$	3.60653	−	20.4537i	0.136804	−	0.775851i
$696$		0			0
$697$	−2.13419	−	0.776781i	−0.0808381	−	0.0294227i
$698$	−15.0004	−	1.13739i	−0.567772	−	0.0430507i
$699$		0			0
$700$	7.55790	−	2.95093i	0.285662	−	0.111535i
$701$			13.2691i			0.501165i	0.968095	+	0.250583i	$0.0806222\pi$
$701$			13.2691i			0.501165i	−0.968095	+	0.250583i	$0.919378\pi$
$702$		0			0
$703$		−	13.7037i		−	0.516846i
$704$	−0.274087	+	0.377019i	−0.0103300	+	0.0142094i
$705$		0			0
$706$	1.17622	−	15.5125i	0.0442675	−	0.583820i
$707$	−48.2395	−	17.5577i	−1.81423	−	0.660326i
$708$		0			0
$709$	2.29730	−	13.0286i	0.0862768	−	0.489300i	−0.910797	−	0.412855i	$-0.864532\pi$
$709$	2.29730	−	13.0286i	0.0862768	−	0.489300i	0.997074	−	0.0764456i	$-0.0243571\pi$
$710$	19.8454	−	20.3107i	0.744784	−	0.762247i
$711$		0			0
$712$	1.36623	−	5.91389i	0.0512016	−	0.221632i
$713$	14.8995	+	40.9360i	0.557990	+	1.53307i
$714$		0			0
$715$	−0.424825	−	0.506286i	−0.0158875	−	0.0189340i
$716$	24.9003	−	4.98814i	0.930566	−	0.186415i
$717$		0			0
$718$	2.44485	+	24.6514i	0.0912411	+	0.919981i
$719$	−20.7715	−	35.9773i	−0.774647	−	1.34173i	−0.934992	−	0.354668i	$-0.884594\pi$
$719$	−20.7715	−	35.9773i	−0.774647	−	1.34173i	0.160345	−	0.987061i	$-0.448739\pi$
$720$		0			0
$721$	2.02522	−	3.50779i	0.0754232	−	0.130637i
$722$	−14.0713	−	6.36411i	−0.523679	−	0.236848i
$723$		0			0
$724$	8.73080	+	9.92834i	0.324478	+	0.368984i
$725$	4.12662	−	0.727634i	0.153259	−	0.0270236i
$726$		0			0
$727$	−22.0411	+	26.2675i	−0.817458	+	0.974208i	−0.999960	−	0.00899729i	$-0.997136\pi$
$727$	−22.0411	+	26.2675i	−0.817458	+	0.974208i	0.182502	+	0.983206i	$0.441580\pi$
$728$	−37.0626	−	34.5714i	−1.37363	−	1.28130i
$729$		0			0
$730$	22.0058	+	5.62396i	0.814470	+	0.208152i
$731$	−15.2955	−	12.8345i	−0.565725	−	0.474699i
$732$		0			0
$733$	3.79927	+	21.5467i	0.140329	+	0.795846i	0.970999	+	0.239082i	$0.0768464\pi$
$733$	3.79927	+	21.5467i	0.140329	+	0.795846i	−0.830670	+	0.556765i	$0.812043\pi$
$734$	6.07335	+	4.14857i	0.224172	+	0.153126i
$735$		0			0
$736$	4.67533	+	31.9718i	0.172335	+	1.17850i
$737$	−0.381326	−	0.220159i	−0.0140463	−	0.00810965i
$738$		0			0
$739$	23.8855	−	13.7903i	0.878644	−	0.507285i	0.00843293	−	0.999964i	$-0.497316\pi$
$739$	23.8855	−	13.7903i	0.878644	−	0.507285i	0.870211	+	0.492679i	$0.163982\pi$
$740$	−3.57434	+	23.4345i	−0.131395	+	0.861470i
$741$		0			0
$742$	25.0578	+	52.1504i	0.919902	+	1.91450i
$743$	16.1814	−	13.5778i	0.593637	−	0.498121i	−0.295756	−	0.955263i	$-0.595572\pi$
$743$	16.1814	−	13.5778i	0.593637	−	0.498121i	0.889393	+	0.457143i	$0.151127\pi$
$744$		0			0
$745$	23.4879	−	8.54888i	0.860528	−	0.313207i
$746$	21.6118	−	6.06011i	0.791263	−	0.221876i
$747$		0			0
$748$	0.125404	+	0.206027i	0.00458521	+	0.00753311i
$749$	−47.7537	−	8.42026i	−1.74488	−	0.307670i
$750$		0			0
$751$	5.22592	−	14.3581i	0.190696	−	0.523934i	−0.807090	−	0.590428i	$-0.798959\pi$
$751$	5.22592	−	14.3581i	0.190696	−	0.523934i	0.997787	+	0.0664938i	$0.0211813\pi$
$752$	−16.0693	+	14.8053i	−0.585986	+	0.539893i
$753$		0			0
$754$	−15.2612	−	21.2665i	−0.555780	−	0.774479i
$755$	5.86707			0.213525
$756$		0			0
$757$	−29.8309			−1.08422			−0.542112	−	0.840306i	$-0.682375\pi$
$757$	−29.8309			−1.08422			−0.542112	+	0.840306i	$0.682375\pi$
$758$	−11.0127	−	15.3463i	−0.400001	−	0.557401i
$759$		0			0
$760$	−16.5758	−	10.7679i	−0.601269	−	0.390592i
$761$	−3.25292	+	8.93733i	−0.117918	+	0.323978i	−0.984584	−	0.174911i	$-0.944036\pi$
$761$	−3.25292	+	8.93733i	−0.117918	+	0.323978i	0.866666	+	0.498889i	$0.166258\pi$
$762$		0			0
$763$	73.6463	+	12.9858i	2.66617	+	0.470118i
$764$	−43.5180	+	26.4883i	−1.57442	+	0.958313i
$765$		0			0
$766$	11.0112	−	3.08763i	0.397851	−	0.111560i
$767$	6.93593	−	2.52447i	0.250442	−	0.0911534i
$768$		0			0
$769$	4.27261	−	3.58514i	0.154074	−	0.129284i	−0.562492	−	0.826803i	$-0.690157\pi$
$769$	4.27261	−	3.58514i	0.154074	−	0.129284i	0.716566	+	0.697519i	$0.245713\pi$
$770$	−0.340760	−	0.709190i	−0.0122802	−	0.0255575i
$771$		0			0
$772$	−40.7187	−	6.21061i	−1.46550	−	0.223525i
$773$	−15.2614	+	8.81115i	−0.548913	+	0.316915i	−0.748683	−	0.662928i	$-0.769314\pi$
$773$	−15.2614	+	8.81115i	−0.548913	+	0.316915i	0.199770	+	0.979843i	$0.435980\pi$
$774$		0			0
$775$	6.89886	+	3.98306i	0.247815	+	0.143076i
$776$	−8.77204	−	11.6444i	−0.314898	−	0.418009i
$777$		0			0
$778$	22.9500	+	15.6766i	0.822796	+	0.562033i
$779$	−0.541615	−	3.07165i	−0.0194054	−	0.110053i
$780$		0			0
$781$	−0.364528	−	0.305875i	−0.0130438	−	0.0109451i
$782$	16.1990	+	4.13994i	0.579275	+	0.148044i
$783$		0			0
$784$	−17.4494	−	27.2266i	−0.623194	−	0.972380i
$785$	−8.60626	+	10.2565i	−0.307171	+	0.366072i
$786$		0			0
$787$	38.0897	−	6.71624i	1.35775	−	0.239408i	0.553080	−	0.833128i	$-0.313453\pi$
$787$	38.0897	−	6.71624i	1.35775	−	0.239408i	0.804672	+	0.593720i	$0.202341\pi$
$788$	−10.4198	+	9.16301i	−0.371191	+	0.326419i
$789$		0			0
$790$	−21.9516	−	9.92820i	−0.781004	−	0.353229i
$791$	−10.1230	+	17.5336i	−0.359934	+	0.623424i
$792$		0			0
$793$	−4.87062	−	8.43615i	−0.172961	−	0.299577i
$794$	−3.45375	−	34.8241i	−0.122569	−	1.23586i
$795$		0			0
$796$	4.54723	+	22.6993i	0.161172	+	0.804554i
$797$	2.14341	+	2.55442i	0.0759236	+	0.0904822i	0.802669	−	0.596425i	$-0.203413\pi$
$797$	2.14341	+	2.55442i	0.0759236	+	0.0904822i	−0.726746	+	0.686907i	$0.758968\pi$
$798$		0			0
$799$	3.86693	+	10.6243i	0.136802	+	0.375861i
$800$	4.41298	+	3.92912i	0.156022	+	0.138915i
$801$		0			0
$802$	−12.0348	+	12.3170i	−0.424962	+	0.434927i
$803$	0.0660932	−	0.374833i	0.00233238	−	0.0132276i
$804$		0			0
$805$	−51.2532	−	18.6546i	−1.80644	−	0.657489i
$806$	3.76239	−	49.6201i	0.132524	−	1.74779i
$807$		0			0
$808$	−4.55070	−	37.1068i	−0.160093	−	1.30541i
$809$			5.26208i			0.185005i	0.995712	+	0.0925025i	$0.0294866\pi$
$809$			5.26208i			0.185005i	−0.995712	+	0.0925025i	$0.970513\pi$
$810$		0			0
$811$			3.33372i			0.117063i	0.998286	+	0.0585314i	$0.0186418\pi$
$811$			3.33372i			0.117063i	−0.998286	+	0.0585314i	$0.981358\pi$
$812$	−11.3337	−	29.0279i	−0.397736	−	1.01868i
$813$		0			0
$814$	0.396110	+	0.0300346i	0.0138837	+	0.00105271i
$815$	22.5560	+	8.20972i	0.790103	+	0.287574i
$816$		0			0
$817$	4.76161	−	27.0044i	0.166588	−	0.944766i
$818$	31.4416	+	30.7213i	1.09933	+	1.07415i
$819$		0			0
$820$	0.125029	+	5.39406i	0.00436620	+	0.188369i
$821$	8.98195	+	24.6777i	0.313472	+	0.861258i	0.991949	+	0.126636i	$0.0404182\pi$
$821$	8.98195	+	24.6777i	0.313472	+	0.861258i	−0.678477	+	0.734622i	$0.737360\pi$
$822$		0			0
$823$	24.7575	+	29.5048i	0.862991	+	1.02847i	0.999285	+	0.0378043i	$0.0120364\pi$
$823$	24.7575	+	29.5048i	0.862991	+	1.02847i	−0.136294	+	0.990668i	$0.543519\pi$
$824$	2.94565	+	0.154801i	0.102617	+	0.00539276i
$825$		0			0
$826$	8.74421	−	0.867226i	0.304250	−	0.0301747i
$827$	−16.3619	−	28.3397i	−0.568960	−	0.985467i	−0.996669	−	0.0815507i	$-0.974013\pi$
$827$	−16.3619	−	28.3397i	−0.568960	−	0.985467i	0.427710	−	0.903916i	$-0.359321\pi$
$828$		0			0
$829$	13.4083	−	23.2238i	0.465688	−	0.806595i	−0.533544	−	0.845772i	$-0.679140\pi$
$829$	13.4083	−	23.2238i	0.465688	−	0.806595i	0.999232	+	0.0391769i	$0.0124736\pi$
$830$	−16.3274	+	36.1005i	−0.566732	+	1.25307i
$831$		0			0
$832$	10.1840	−	35.4773i	0.353068	−	1.22995i
$833$	−16.4792	+	2.90572i	−0.570970	+	0.100677i
$834$		0			0
$835$	−7.34200	+	8.74985i	−0.254080	+	0.302801i
$836$	−0.158926	+	0.290619i	−0.00549656	+	0.0100513i
$837$		0			0
$838$	−12.9091	+	50.5117i	−0.445939	+	1.74490i
$839$	−4.82314	−	4.04709i	−0.166513	−	0.139721i	0.555723	−	0.831367i	$-0.312441\pi$
$839$	−4.82314	−	4.04709i	−0.166513	−	0.139721i	−0.722237	+	0.691646i	$0.756886\pi$
$840$		0			0
$841$	2.24115	+	12.7102i	0.0772811	+	0.438283i
$842$	29.3873	−	43.0219i	1.01275	−	1.48263i
$843$		0			0
$844$	−23.6001	−	18.8885i	−0.812351	−	0.650168i
$845$	17.6440	+	10.1867i	0.606971	+	0.350435i
$846$		0			0
$847$	36.9876	−	21.3548i	1.27091	−	0.733760i
$848$	−25.5592	+	33.4974i	−0.877706	+	1.15031i
$849$		0			0
$850$	2.75580	−	1.32414i	0.0945233	−	0.0454177i
$851$	21.0950	−	17.7008i	0.723129	−	0.606777i
$852$		0			0
$853$	−0.675411	+	0.245829i	−0.0231256	+	0.00841704i	−0.353557	−	0.935413i	$-0.615028\pi$
$853$	−0.675411	+	0.245829i	−0.0231256	+	0.00841704i	0.330431	+	0.943830i	$0.392806\pi$
$854$	−3.13109	−	11.1662i	−0.107144	−	0.382099i
$855$		0			0
$856$	−10.3196	−	33.7714i	−0.352717	−	1.15428i
$857$	−53.7149	−	9.47138i	−1.83486	−	0.323536i	−0.854307	−	0.519768i	$-0.826018\pi$
$857$	−53.7149	−	9.47138i	−1.83486	−	0.323536i	−0.980557	+	0.196232i	$0.937129\pi$
$858$		0			0
$859$	10.4149	−	28.6147i	0.355352	−	0.976322i	−0.625269	−	0.780409i	$-0.715011\pi$
$859$	10.4149	−	28.6147i	0.355352	−	0.976322i	0.980621	−	0.195913i	$-0.0627670\pi$
$860$	−15.1863	+	44.9379i	−0.517850	+	1.53237i
$861$		0			0
$862$	13.0732	−	9.38156i	0.445275	−	0.319537i
$863$	30.5772			1.04086			0.520430	−	0.853904i	$-0.325772\pi$
$863$	30.5772			1.04086			0.520430	+	0.853904i	$0.325772\pi$
$864$		0			0
$865$	−2.16644			−0.0736612
$866$	−8.36050	+	5.99964i	−0.284101	+	0.203876i
$867$		0			0
$868$	18.9665	−	56.1238i	0.643765	−	1.90497i
$869$	−0.138084	+	0.379382i	−0.00468417	+	0.0128697i
$870$		0			0
$871$	34.3372	+	6.05458i	1.16347	+	0.205152i
$872$	15.9150	+	52.0826i	0.538951	+	1.76374i
$873$		0			0
$874$	6.19948	+	22.1088i	0.209701	+	0.747842i
$875$	35.4922	−	12.9181i	1.19986	−	0.436712i
$876$		0			0
$877$	−25.9234	+	21.7523i	−0.875372	+	0.734524i	−0.965222	−	0.261431i	$-0.915806\pi$
$877$	−25.9234	+	21.7523i	−0.875372	+	0.734524i	0.0898503	+	0.995955i	$0.471361\pi$
$878$	−37.9384	+	18.2291i	−1.28036	+	0.615202i
$879$		0			0
$880$	0.347578	−	0.455530i	0.0117169	−	0.0153559i
$881$	10.3117	−	5.95348i	0.347411	−	0.200578i	−0.316133	−	0.948715i	$-0.602385\pi$
$881$	10.3117	−	5.95348i	0.347411	−	0.200578i	0.663544	+	0.748137i	$0.269051\pi$
$882$		0			0
$883$	−10.5936	−	6.11620i	−0.356502	−	0.205827i	0.311043	−	0.950396i	$-0.399322\pi$
$883$	−10.5936	−	6.11620i	−0.356502	−	0.205827i	−0.667545	+	0.744569i	$0.732655\pi$
$884$	−14.9112	−	11.9343i	−0.501519	−	0.401393i
$885$		0			0
$886$	−13.7206	+	20.0865i	−0.460953	+	0.674819i
$887$	2.31672	+	13.1388i	0.0777879	+	0.441157i	0.998681	+	0.0513422i	$0.0163499\pi$
$887$	2.31672	+	13.1388i	0.0777879	+	0.441157i	−0.920893	+	0.389815i	$0.872539\pi$
$888$		0			0
$889$	−5.76482	−	4.83725i	−0.193346	−	0.162236i
$890$	−1.84749	+	7.22896i	−0.0619279	+	0.242315i
$891$		0			0
$892$	1.57522	−	2.88051i	0.0527422	−	0.0964467i
$893$	−9.98058	+	11.8944i	−0.333987	+	0.398031i
$894$		0			0
$895$	−30.7433	+	5.42086i	−1.02763	+	0.181200i
$896$	22.2044	−	37.9183i	0.741796	−	1.26676i
$897$		0			0
$898$	−12.7026	+	28.0859i	−0.423890	+	0.937237i
$899$	15.2979	−	26.4967i	0.510212	−	0.883714i
$900$		0			0
$901$	10.9013	+	18.8816i	0.363174	+	0.629036i
$902$	0.0899742	−	0.00892338i	0.00299581	−	0.000297116i
$903$		0			0
$904$	−14.7238	−	0.773772i	−0.489706	−	0.0257353i
$905$	−10.4469	−	12.4501i	−0.347267	−	0.413856i
$906$		0			0
$907$	6.89696	+	18.9492i	0.229010	+	0.629199i	0.999970	−	0.00768346i	$-0.00244575\pi$
$907$	6.89696	+	18.9492i	0.229010	+	0.629199i	−0.770961	+	0.636883i	$0.780224\pi$
$908$	1.26577	+	54.6083i	0.0420060	+	1.81224i
$909$		0			0
$910$	44.5633	+	43.5423i	1.47726	+	1.44341i
$911$	5.48881	−	31.1286i	0.181852	−	1.03134i	−0.748081	−	0.663607i	$-0.769025\pi$
$911$	5.48881	−	31.1286i	0.181852	−	1.03134i	0.929933	−	0.367728i	$-0.119864\pi$
$912$		0			0
$913$	0.623912	+	0.227086i	0.0206485	+	0.00751544i
$914$	13.6184	+	1.03260i	0.450456	+	0.0341553i
$915$		0			0
$916$	4.59530	+	11.7695i	0.151833	+	0.388874i
$917$		−	1.81657i		−	0.0599884i
$918$		0			0
$919$			3.86720i			0.127567i	0.997964	+	0.0637835i	$0.0203167\pi$
$919$			3.86720i			0.127567i	−0.997964	+	0.0637835i	$0.979683\pi$
$920$	−4.83500	−	39.4250i	−0.159405	−	1.29980i
$921$		0			0
$922$	3.50562	−	46.2338i	0.115452	−	1.52263i
$923$	35.4087	+	12.8877i	1.16549	+	0.424205i
$924$		0			0
$925$	0.874428	−	4.95913i	0.0287510	−	0.163055i
$926$	−37.8929	+	38.7814i	−1.24524	+	1.27444i
$927$		0			0
$928$	15.0907	−	16.9491i	0.495376	−	0.556380i
$929$	−17.2575	−	47.4145i	−0.566200	−	1.55562i	−0.810388	−	0.585893i	$-0.800744\pi$
$929$	−17.2575	−	47.4145i	−0.566200	−	1.55562i	0.244189	−	0.969728i	$-0.421478\pi$
$930$		0			0
$931$	−14.7715	−	17.6040i	−0.484117	−	0.576949i
$932$	−11.6482	−	58.1468i	−0.381551	−	1.90466i
$933$		0			0
$934$	−1.61681	−	16.3022i	−0.0529037	−	0.533426i
$935$	−0.148246	−	0.256770i	−0.00484816	−	0.00839726i
$936$		0			0
$937$	24.0457	−	41.6483i	0.785538	−	1.36059i	−0.143139	−	0.989703i	$-0.545720\pi$
$937$	24.0457	−	41.6483i	0.785538	−	1.36059i	0.928677	−	0.370890i	$-0.120947\pi$
$938$	37.8206	+	17.1053i	1.23489	+	0.558509i
$939$		0			0
$940$	20.1700	−	17.7372i	0.657874	−	0.578523i
$941$	7.23098	−	1.27502i	0.235723	−	0.0415644i	−0.0545385	−	0.998512i	$-0.517369\pi$
$941$	7.23098	−	1.27502i	0.235723	−	0.0415644i	0.290262	+	0.956947i	$0.406258\pi$
$942$		0			0
$943$	4.02880	−	4.80134i	0.131196	−	0.156353i
$944$	3.45292	+	5.38765i	0.112383	+	0.175353i
$945$		0			0
$946$	0.770136	+	0.196822i	0.0250393	+	0.00639923i
$947$	−24.3956	−	20.4704i	−0.792752	−	0.665198i	0.153673	−	0.988122i	$-0.450890\pi$
$947$	−24.3956	−	20.4704i	−0.792752	−	0.665198i	−0.946425	+	0.322924i	$0.895334\pi$
$948$		0			0
$949$	5.23365	+	29.6815i	0.169891	+	0.963502i
$950$	3.46716	+	2.36834i	0.112489	+	0.0768390i
$951$		0			0
$952$	−13.6810	−	18.1607i	−0.443403	−	0.588592i
$953$	−13.1967	−	7.61912i	−0.427483	−	0.246807i	0.270791	−	0.962638i	$-0.412715\pi$
$953$	−13.1967	−	7.61912i	−0.427483	−	0.246807i	−0.698274	+	0.715831i	$0.746048\pi$
$954$		0			0
$955$	54.2359	−	31.3131i	1.75503	−	1.01327i
$956$	18.3988	+	2.80627i	0.595060	+	0.0907613i
$957$		0			0
$958$	10.9790	+	22.8494i	0.354714	+	0.738231i
$959$	13.0623	−	10.9606i	0.421804	−	0.353936i
$960$		0			0
$961$	25.5272	−	9.29113i	0.823457	−	0.299714i
$962$	−30.2882	+	8.49304i	−0.976530	+	0.273827i
$963$		0			0
$964$	−24.0222	+	14.6217i	−0.773703	+	0.470933i
$965$	49.8644	+	8.79243i	1.60519	+	0.283038i
$966$		0			0
$967$	−14.7610	+	40.5556i	−0.474683	+	1.30418i	0.439268	+	0.898356i	$0.355238\pi$
$967$	−14.7610	+	40.5556i	−0.474683	+	1.30418i	−0.913951	+	0.405825i	$0.866984\pi$
$968$	26.0828	+	16.9437i	0.838333	+	0.544592i
$969$		0			0
$970$	10.4487	+	14.5602i	0.335487	+	0.467501i
$971$	32.9105			1.05615			0.528074	−	0.849198i	$-0.322914\pi$
$971$	32.9105			1.05615			0.528074	+	0.849198i	$0.322914\pi$
$972$		0			0
$973$	32.8100			1.05184
$974$	18.6726	+	26.0203i	0.598309	+	0.833743i
$975$		0			0
$976$	6.21106	−	5.72251i	0.198811	−	0.183173i
$977$	19.4179	−	53.3502i	0.621234	−	1.70683i	−0.0827138	−	0.996573i	$-0.526359\pi$
$977$	19.4179	−	53.3502i	0.621234	−	1.70683i	0.703947	−	0.710252i	$-0.251419\pi$
$978$		0			0
$979$	0.123134	+	0.0217118i	0.00393537	+	0.000693912i
$980$	20.6689	+	33.9572i	0.660244	+	1.08472i
$981$		0			0
$982$	−35.0048	+	9.81561i	−1.11705	+	0.313229i
$983$	30.4707	−	11.0904i	0.971864	−	0.353730i	0.193192	−	0.981161i	$-0.438116\pi$
$983$	30.4707	−	11.0904i	0.971864	−	0.353730i	0.778672	+	0.627431i	$0.215894\pi$
$984$		0			0
$985$	13.0665	−	10.9641i	0.416332	−	0.349344i
$986$	−5.08567	−	10.5843i	−0.161961	−	0.337073i
$987$		0			0
$988$	3.95485	−	25.9293i	0.125821	−	0.824920i
$989$	47.7202	−	27.5513i	1.51741	−	0.876080i
$990$		0			0
$991$	36.6324	+	21.1497i	1.16367	+	0.671843i	0.952180	−	0.305539i	$-0.0988365\pi$
$991$	36.6324	+	21.1497i	1.16367	+	0.671843i	0.211486	+	0.977381i	$0.432170\pi$
$992$	42.6887	−	6.24249i	1.35537	−	0.198199i
$993$		0			0
$994$	37.0422	+	25.3027i	1.17491	+	0.802552i
$995$	−4.94170	−	28.0258i	−0.156663	−	0.888477i
$996$		0			0
$997$	−25.8985	−	21.7314i	−0.820213	−	0.688241i	0.132809	−	0.991142i	$-0.457600\pi$
$997$	−25.8985	−	21.7314i	−0.820213	−	0.688241i	−0.953022	+	0.302901i	$0.902045\pi$
$998$	9.90536	+	2.53149i	0.313549	+	0.0801329i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.a.107.13		96
3.2	odd	2		972.2.l.d.107.4		96
4.3	odd	2	inner	972.2.l.a.107.11		96
9.2	odd	6		972.2.l.c.755.15		96
9.4	even	3		324.2.l.a.143.10		96
9.5	odd	6		108.2.l.a.47.7	yes	96
9.7	even	3		972.2.l.b.755.2		96
12.11	even	2		972.2.l.d.107.6		96
27.4	even	9		972.2.l.c.215.16		96
27.5	odd	18	inner	972.2.l.a.863.11		96
27.13	even	9		108.2.l.a.23.6	✓	96
27.14	odd	18		324.2.l.a.179.11		96
27.22	even	9		972.2.l.d.863.6		96
27.23	odd	18		972.2.l.b.215.1		96
36.7	odd	6		972.2.l.b.755.1		96
36.11	even	6		972.2.l.c.755.16		96
36.23	even	6		108.2.l.a.47.6	yes	96
36.31	odd	6		324.2.l.a.143.11		96
108.23	even	18		972.2.l.b.215.2		96
108.31	odd	18		972.2.l.c.215.15		96
108.59	even	18	inner	972.2.l.a.863.13		96
108.67	odd	18		108.2.l.a.23.7	yes	96
108.95	even	18		324.2.l.a.179.10		96
108.103	odd	18		972.2.l.d.863.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.6	✓	96	27.13	even	9
108.2.l.a.23.7	yes	96	108.67	odd	18
108.2.l.a.47.6	yes	96	36.23	even	6
108.2.l.a.47.7	yes	96	9.5	odd	6
324.2.l.a.143.10		96	9.4	even	3
324.2.l.a.143.11		96	36.31	odd	6
324.2.l.a.179.10		96	108.95	even	18
324.2.l.a.179.11		96	27.14	odd	18
972.2.l.a.107.11		96	4.3	odd	2	inner
972.2.l.a.107.13		96	1.1	even	1	trivial
972.2.l.a.863.11		96	27.5	odd	18	inner
972.2.l.a.863.13		96	108.59	even	18	inner
972.2.l.b.215.1		96	27.23	odd	18
972.2.l.b.215.2		96	108.23	even	18
972.2.l.b.755.1		96	36.7	odd	6
972.2.l.b.755.2		96	9.7	even	3
972.2.l.c.215.15		96	108.31	odd	18
972.2.l.c.215.16		96	27.4	even	9
972.2.l.c.755.15		96	9.2	odd	6
972.2.l.c.755.16		96	36.11	even	6
972.2.l.d.107.4		96	3.2	odd	2
972.2.l.d.107.6		96	12.11	even	2
972.2.l.d.863.4		96	108.103	odd	18
972.2.l.d.863.6		96	27.22	even	9

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14898 - 0.824528i) q^{2} +(0.640306 - 1.89473i) q^{4} +(-0.840877 + 2.31029i) q^{5} +(-3.82489 - 0.674430i) q^{7} +(-0.826562 - 2.70496i) q^{8} +O(q^{10})\)	\(q+(1.14898 - 0.824528i) q^{2} +(0.640306 - 1.89473i) q^{4} +(-0.840877 + 2.31029i) q^{5} +(-3.82489 - 0.674430i) q^{7} +(-0.826562 - 2.70496i) q^{8} +(0.938750 + 3.34780i) q^{10} +(0.0547511 - 0.0199278i) q^{11} +(-3.53434 + 2.96567i) q^{13} +(-4.95080 + 2.37882i) q^{14} +(-3.18002 - 2.42642i) q^{16} +(-1.79249 + 1.03489i) q^{17} +(-2.46167 - 1.42125i) q^{19} +(3.83896 + 3.07253i) q^{20} +(0.0464768 - 0.0680404i) q^{22} +(-0.991876 - 5.62521i) q^{23} +(-0.800144 - 0.671401i) q^{25} +(-1.61561 + 6.32166i) q^{26} +(-3.72696 + 6.81529i) q^{28} +(-2.57867 + 3.07314i) q^{29} +(-7.51076 + 1.32435i) q^{31} +(-5.65442 - 0.165888i) q^{32} +(-1.20623 + 2.66703i) q^{34} +(4.77439 - 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(-4.00027 + 0.396735i) q^{38} +(6.94427 + 0.364939i) q^{40} +(0.705325 + 0.840573i) q^{41} +(3.29941 + 9.06505i) q^{43} +(-0.00270032 - 0.116498i) q^{44} +(-5.77779 - 5.64542i) q^{46} +(0.948548 - 5.37948i) q^{47} +(7.59704 + 2.76510i) q^{49} +(-1.47294 - 0.111684i) q^{50} +(3.35608 + 8.59557i) q^{52} -10.5337i q^{53} +0.143248i q^{55} +(1.33720 + 10.9036i) q^{56} +(-0.428948 + 5.65716i) q^{58} +(-1.50332 - 0.547162i) q^{59} +(-0.366631 + 2.07927i) q^{61} +(-7.53775 + 7.71449i) q^{62} +(-6.63359 + 4.47163i) q^{64} +(-3.87960 - 10.6591i) q^{65} +(-4.85766 - 5.78913i) q^{67} +(0.813104 + 4.05893i) q^{68} +(-1.33275 - 13.4381i) q^{70} +(-4.08357 - 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(6.21214 + 2.80960i) q^{74} +(-4.26910 + 3.75417i) q^{76} +(-0.222856 + 0.0392956i) q^{77} +(-4.45402 + 5.30809i) q^{79} +(8.27973 - 5.30644i) q^{80} +(1.50348 + 0.384241i) q^{82} +(8.72941 + 7.32485i) q^{83} +(-0.883642 - 5.01138i) q^{85} +(11.2653 + 7.69510i) q^{86} +(-0.0991589 - 0.131628i) q^{88} +(1.85844 + 1.07297i) q^{89} +(15.5186 - 8.95967i) q^{91} +(-11.2934 - 1.72252i) q^{92} +(-3.34567 - 6.96302i) q^{94} +(5.35345 - 4.49208i) q^{95} +(4.84352 - 1.76290i) q^{97} +(11.0087 - 3.08694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} - 33 q^{14} + 3 q^{16} + 18 q^{17} + 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 30 q^{29} - 33 q^{32} + 15 q^{34} - 6 q^{37} + 63 q^{38} + 33 q^{40} + 24 q^{41} - 63 q^{44} - 3 q^{46} + 6 q^{49} + 21 q^{50} + 57 q^{52} + 18 q^{56} + 57 q^{58} + 6 q^{61} - 90 q^{62} - 3 q^{64} - 30 q^{65} + 102 q^{68} + 51 q^{70} - 6 q^{73} - 75 q^{74} + 27 q^{76} + 42 q^{77} - 12 q^{82} - 24 q^{85} + 111 q^{86} + 27 q^{88} - 147 q^{92} + 30 q^{94} - 12 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 - 33 * q^14 + 3 * q^16 + 18 * q^17 + 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 30 * q^29 - 33 * q^32 + 15 * q^34 - 6 * q^37 + 63 * q^38 + 33 * q^40 + 24 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 21 * q^50 + 57 * q^52 + 18 * q^56 + 57 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 - 30 * q^65 + 102 * q^68 + 51 * q^70 - 6 * q^73 - 75 * q^74 + 27 * q^76 + 42 * q^77 - 12 * q^82 - 24 * q^85 + 111 * q^86 + 27 * q^88 - 147 * q^92 + 30 * q^94 - 12 * q^97 + 180 * q^98

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