LMFDB - Embedded newform 945.2.ce.a.748.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(118,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("945.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.ce (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			748.14
Character	$\chi$	$=$	945.748
Dual form			945.2.ce.a.307.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388459 - 1.44975i) q^{2} +(-0.218820 + 0.126336i) q^{4} +(1.66955 - 1.48748i) q^{5} +(2.18265 - 1.49535i) q^{7} +(-1.85442 - 1.85442i) q^{8} +O(q^{10})$	\(q+(-0.388459 - 1.44975i) q^{2} +(-0.218820 + 0.126336i) q^{4} +(1.66955 - 1.48748i) q^{5} +(2.18265 - 1.49535i) q^{7} +(-1.85442 - 1.85442i) q^{8} +(-2.80503 - 1.84260i) q^{10} +(-1.50520 + 2.60709i) q^{11} +(-5.41932 - 1.45210i) q^{13} +(-3.01574 - 2.58341i) q^{14} +(-2.22075 + 3.84645i) q^{16} +(-1.04847 - 1.04847i) q^{17} -7.21291 q^{19} +(-0.177409 + 0.536415i) q^{20} +(4.36433 + 1.16942i) q^{22} +(1.46083 - 5.45189i) q^{23} +(0.574793 - 4.96685i) q^{25} +8.42074i q^{26} +(-0.288691 + 0.602958i) q^{28} +(4.88990 + 2.82318i) q^{29} +(4.98189 - 2.87630i) q^{31} +(1.37268 + 0.367810i) q^{32} +(-1.11273 + 1.92730i) q^{34} +(1.41973 - 5.74320i) q^{35} +(2.33216 - 2.33216i) q^{37} +(2.80192 + 10.4569i) q^{38} +(-5.85447 - 0.337630i) q^{40} +(3.05504 - 1.76383i) q^{41} +(2.96236 - 0.793762i) q^{43} -0.760643i q^{44} -8.47134 q^{46} +(-5.88834 + 1.57778i) q^{47} +(2.52788 - 6.52762i) q^{49} +(-7.42397 + 1.09611i) q^{50} +(1.36931 - 0.366905i) q^{52} +(6.84756 + 6.84756i) q^{53} +(1.36499 + 6.59162i) q^{55} +(-6.82055 - 1.27454i) q^{56} +(2.19338 - 8.18581i) q^{58} +(-2.39004 - 4.13968i) q^{59} +(-5.10293 - 2.94618i) q^{61} +(-6.10517 - 6.10517i) q^{62} +6.75007i q^{64} +(-11.2078 + 5.63679i) q^{65} +(3.23103 + 0.865752i) q^{67} +(0.361884 + 0.0969666i) q^{68} +(-8.87771 + 0.172741i) q^{70} +7.34107 q^{71} +(3.61212 - 3.61212i) q^{73} +(-4.28699 - 2.47509i) q^{74} +(1.57833 - 0.911248i) q^{76} +(0.613175 + 7.94114i) q^{77} +(-8.69380 - 5.01937i) q^{79} +(2.01388 + 9.72517i) q^{80} +(-3.74386 - 3.74386i) q^{82} +(0.149805 + 0.559080i) q^{83} +(-3.31004 - 0.190892i) q^{85} +(-2.30151 - 3.98633i) q^{86} +(7.62592 - 2.04336i) q^{88} -0.259914 q^{89} +(-13.9999 + 4.93434i) q^{91} +(0.369110 + 1.37754i) q^{92} +(4.57476 + 7.92371i) q^{94} +(-12.0423 + 10.7291i) q^{95} +(12.3966 - 3.32166i) q^{97} +(-10.4454 - 1.12908i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8}+O(q^{10}) $ 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8	$ 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8} + 12 q^{11} + 56 q^{16} + 12 q^{22} + 12 q^{23} - 4 q^{25} - 32 q^{28} - 48 q^{32} + 8 q^{35} - 16 q^{37} - 4 q^{43} - 80 q^{46} + 76 q^{50} - 64 q^{53} + 52 q^{56} - 44 q^{58} - 20 q^{65} - 4 q^{67} + 18 q^{70} + 64 q^{71} - 26 q^{77} - 4 q^{85} - 80 q^{86} - 60 q^{88} - 16 q^{91} + 68 q^{92} - 40 q^{95} + 120 q^{98}+O(q^{100}) $ 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8 + 12 * q^11 + 56 * q^16 + 12 * q^22 + 12 * q^23 - 4 * q^25 - 32 * q^28 - 48 * q^32 + 8 * q^35 - 16 * q^37 - 4 * q^43 - 80 * q^46 + 76 * q^50 - 64 * q^53 + 52 * q^56 - 44 * q^58 - 20 * q^65 - 4 * q^67 + 18 * q^70 + 64 * q^71 - 26 * q^77 - 4 * q^85 - 80 * q^86 - 60 * q^88 - 16 * q^91 + 68 * q^92 - 40 * q^95 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.388459	−	1.44975i	−0.274682	−	1.02513i	−0.956054	−	0.293190i	$-0.905283\pi$
$2$	−0.388459	−	1.44975i	−0.274682	−	1.02513i	0.681372	−	0.731937i	$-0.261384\pi$
$3$		0			0
$3$		0			0
$4$	−0.218820	+	0.126336i	−0.109410	+	0.0631679i
$5$	1.66955	−	1.48748i	0.746645	−	0.665222i
$5$	1.66955	−	1.48748i	0.746645	−	0.665222i
$6$		0			0
$7$	2.18265	−	1.49535i	0.824962	−	0.565188i
$7$	2.18265	−	1.49535i	0.824962	−	0.565188i
$8$	−1.85442	−	1.85442i	−0.655637	−	0.655637i
$9$		0			0
$10$	−2.80503	−	1.84260i	−0.887027	−	0.582682i
$11$	−1.50520	+	2.60709i	−0.453836	+	0.786066i	−0.998620	−	0.0525096i	$-0.983278\pi$
$11$	−1.50520	+	2.60709i	−0.453836	+	0.786066i	0.544785	+	0.838576i	$0.316611\pi$
$12$		0			0
$13$	−5.41932	−	1.45210i	−1.50305	−	0.402741i	−0.588930	−	0.808184i	$-0.700451\pi$
$13$	−5.41932	−	1.45210i	−1.50305	−	0.402741i	−0.914120	+	0.405443i	$0.867117\pi$
$14$	−3.01574	−	2.58341i	−0.805992	−	0.690444i
$15$		0			0
$16$	−2.22075	+	3.84645i	−0.555188	+	0.961613i
$17$	−1.04847	−	1.04847i	−0.254291	−	0.254291i	0.568437	−	0.822727i	$-0.307548\pi$
$17$	−1.04847	−	1.04847i	−0.254291	−	0.254291i	−0.822727	+	0.568437i	$0.807548\pi$
$18$		0			0
$19$	−7.21291			−1.65475			−0.827377	−	0.561646i	$-0.810168\pi$
$19$	−7.21291			−1.65475			−0.827377	+	0.561646i	$0.810168\pi$
$20$	−0.177409	+	0.536415i	−0.0396698	+	0.119946i
$21$		0			0
$22$	4.36433	+	1.16942i	0.930478	+	0.249321i
$23$	1.46083	−	5.45189i	0.304604	−	1.13680i	−0.628682	−	0.777663i	$-0.716405\pi$
$23$	1.46083	−	5.45189i	0.304604	−	1.13680i	0.933286	−	0.359134i	$-0.116928\pi$
$24$		0			0
$25$	0.574793	−	4.96685i	0.114959	−	0.993370i
$26$			8.42074i			1.65144i
$27$		0			0
$28$	−0.288691	+	0.602958i	−0.0545574	+	0.113948i
$29$	4.88990	+	2.82318i	0.908031	+	0.524252i	0.879797	−	0.475349i	$-0.157678\pi$
$29$	4.88990	+	2.82318i	0.908031	+	0.524252i	0.0282341	+	0.999601i	$0.491012\pi$
$30$		0			0
$31$	4.98189	−	2.87630i	0.894775	−	0.516598i	0.0192734	−	0.999814i	$-0.493865\pi$
$31$	4.98189	−	2.87630i	0.894775	−	0.516598i	0.875501	+	0.483216i	$0.160531\pi$
$32$	1.37268	+	0.367810i	0.242659	+	0.0650202i
$33$		0			0
$34$	−1.11273	+	1.92730i	−0.190831	+	0.330529i
$35$	1.41973	−	5.74320i	0.239979	−	0.970778i
$36$		0			0
$37$	2.33216	−	2.33216i	0.383404	−	0.383404i	−0.488923	−	0.872327i	$-0.662610\pi$
$37$	2.33216	−	2.33216i	0.383404	−	0.383404i	0.872327	+	0.488923i	$0.162610\pi$
$38$	2.80192	+	10.4569i	0.454531	+	1.69633i
$39$		0			0
$40$	−5.85447	−	0.337630i	−0.925673	−	0.0533840i
$41$	3.05504	−	1.76383i	0.477117	−	0.275464i	−0.242097	−	0.970252i	$-0.577835\pi$
$41$	3.05504	−	1.76383i	0.477117	−	0.275464i	0.719214	+	0.694788i	$0.244502\pi$
$42$		0			0
$43$	2.96236	−	0.793762i	0.451755	−	0.121048i	−0.0257652	−	0.999668i	$-0.508202\pi$
$43$	2.96236	−	0.793762i	0.451755	−	0.121048i	0.477521	+	0.878621i	$0.341536\pi$
$44$		−	0.760643i		−	0.114671i
$45$		0			0
$46$	−8.47134			−1.24903
$47$	−5.88834	+	1.57778i	−0.858903	+	0.230142i	−0.661283	−	0.750137i	$-0.729988\pi$
$47$	−5.88834	+	1.57778i	−0.858903	+	0.230142i	−0.197620	+	0.980279i	$0.563321\pi$
$48$		0			0
$49$	2.52788	−	6.52762i	0.361126	−	0.932517i
$50$	−7.42397	+	1.09611i	−1.04991	+	0.155014i
$51$		0			0
$52$	1.36931	−	0.366905i	0.189889	−	0.0508806i
$53$	6.84756	+	6.84756i	0.940585	+	0.940585i	0.998331	−	0.0577465i	$-0.0183915\pi$
$53$	6.84756	+	6.84756i	0.940585	+	0.940585i	−0.0577465	+	0.998331i	$0.518392\pi$
$54$		0			0
$55$	1.36499	+	6.59162i	0.184055	+	0.888814i
$56$	−6.82055	−	1.27454i	−0.911434	−	0.170318i
$57$		0			0
$58$	2.19338	−	8.18581i	0.288005	−	1.07485i
$59$	−2.39004	−	4.13968i	−0.311157	−	0.538940i	0.667456	−	0.744649i	$-0.267383\pi$
$59$	−2.39004	−	4.13968i	−0.311157	−	0.538940i	−0.978613	+	0.205709i	$0.934050\pi$
$60$		0			0
$61$	−5.10293	−	2.94618i	−0.653364	−	0.377220i	0.136380	−	0.990657i	$-0.456453\pi$
$61$	−5.10293	−	2.94618i	−0.653364	−	0.377220i	−0.789744	+	0.613437i	$0.789786\pi$
$62$	−6.10517	−	6.10517i	−0.775358	−	0.775358i
$63$		0			0
$64$			6.75007i			0.843759i
$65$	−11.2078	+	5.63679i	−1.39016	+	0.699158i
$66$		0			0
$67$	3.23103	+	0.865752i	0.394733	+	0.105768i	0.450725	−	0.892663i	$-0.351165\pi$
$67$	3.23103	+	0.865752i	0.394733	+	0.105768i	−0.0559921	+	0.998431i	$0.517832\pi$
$68$	0.361884	+	0.0969666i	0.0438849	+	0.0117589i
$69$		0			0
$70$	−8.87771	+	0.172741i	−1.06109	+	0.0206464i
$71$	7.34107			0.871225			0.435613	−	0.900134i	$-0.356532\pi$
$71$	7.34107			0.871225			0.435613	+	0.900134i	$0.356532\pi$
$72$		0			0
$73$	3.61212	−	3.61212i	0.422767	−	0.422767i	−0.463389	−	0.886155i	$-0.653367\pi$
$73$	3.61212	−	3.61212i	0.422767	−	0.422767i	0.886155	+	0.463389i	$0.153367\pi$
$74$	−4.28699	−	2.47509i	−0.498352	−	0.287724i
$75$		0			0
$76$	1.57833	−	0.911248i	0.181047	−	0.104527i
$77$	0.613175	+	7.94114i	0.0698778	+	0.904977i
$78$		0			0
$79$	−8.69380	−	5.01937i	−0.978128	−	0.564723i	−0.0764239	−	0.997075i	$-0.524350\pi$
$79$	−8.69380	−	5.01937i	−0.978128	−	0.564723i	−0.901705	+	0.432353i	$0.857684\pi$
$80$	2.01388	+	9.72517i	0.225158	+	1.08731i
$81$		0			0
$82$	−3.74386	−	3.74386i	−0.413441	−	0.413441i
$83$	0.149805	+	0.559080i	0.0164432	+	0.0613670i	0.973660	−	0.228005i	$-0.0732202\pi$
$83$	0.149805	+	0.559080i	0.0164432	+	0.0613670i	−0.957217	+	0.289372i	$0.906554\pi$
$84$		0			0
$85$	−3.31004	−	0.190892i	−0.359025	−	0.0207051i
$86$	−2.30151	−	3.98633i	−0.248178	−	0.429857i
$87$		0			0
$88$	7.62592	−	2.04336i	0.812926	−	0.217823i
$89$	−0.259914			−0.0275508			−0.0137754	−	0.999905i	$-0.504385\pi$
$89$	−0.259914			−0.0275508			−0.0137754	+	0.999905i	$0.504385\pi$
$90$		0			0
$91$	−13.9999	+	4.93434i	−1.46758	+	0.517259i
$92$	0.369110	+	1.37754i	0.0384824	+	0.143618i
$93$		0			0
$94$	4.57476	+	7.92371i	0.471850	+	0.817268i
$95$	−12.0423	+	10.7291i	−1.23552	+	1.10078i
$96$		0			0
$97$	12.3966	−	3.32166i	1.25868	−	0.337263i	0.432999	−	0.901395i	$-0.357456\pi$
$97$	12.3966	−	3.32166i	1.25868	−	0.337263i	0.825685	+	0.564131i	$0.190789\pi$
$98$	−10.4454	−	1.12908i	−1.05514	−	0.114054i
$99$		0			0
$100$	0.501715	+	1.15946i	0.0501715	+	0.115946i
$101$	−2.10970	−	1.21804i	−0.209923	−	0.121199i	0.391352	−	0.920241i	$-0.372007\pi$
$101$	−2.10970	−	1.21804i	−0.209923	−	0.121199i	−0.601276	+	0.799042i	$0.705341\pi$
$102$		0			0
$103$	4.80703	+	1.28804i	0.473651	+	0.126914i	0.487745	−	0.872986i	$-0.337820\pi$
$103$	4.80703	+	1.28804i	0.473651	+	0.126914i	−0.0140938	+	0.999901i	$0.504486\pi$
$104$	7.35690	+	12.7425i	0.721403	+	1.24951i
$105$		0			0
$106$	7.26725	−	12.5872i	0.705857	−	1.22258i
$107$	2.36251	−	2.36251i	0.228392	−	0.228392i	−0.583628	−	0.812021i	$-0.698368\pi$
$107$	2.36251	−	2.36251i	0.228392	−	0.228392i	0.812021	+	0.583628i	$0.198368\pi$
$108$		0			0
$109$			19.8506i			1.90134i	0.310197	+	0.950672i	$0.399605\pi$
$109$			19.8506i			1.90134i	−0.310197	+	0.950672i	$0.600395\pi$
$110$	9.02596	−	4.53946i	0.860591	−	0.432821i
$111$		0			0
$112$	0.904668	+	11.7162i	0.0854831	+	1.10708i
$113$	3.60530	−	13.4552i	0.339159	−	1.26576i	−0.560131	−	0.828404i	$-0.689249\pi$
$113$	3.60530	−	13.4552i	0.339159	−	1.26576i	0.899290	−	0.437353i	$-0.144084\pi$
$114$		0			0
$115$	−5.67066	−	11.2752i	−0.528792	−	1.05141i
$116$	−1.42668			−0.132464
$117$		0			0
$118$	−5.07306	+	5.07306i	−0.467013	+	0.467013i
$119$	−3.85625	−	0.720610i	−0.353502	−	0.0660582i
$120$		0			0
$121$	0.968732	+	1.67789i	0.0880665	+	0.152536i
$122$	−2.28894	+	8.54244i	−0.207231	+	0.773396i
$123$		0			0
$124$	−0.726759	+	1.25878i	−0.0652648	+	0.113042i
$125$	−6.42846	−	9.14740i	−0.574979	−	0.818168i
$126$		0			0
$127$	3.90612	−	3.90612i	0.346612	−	0.346612i	−0.512234	−	0.858846i	$-0.671182\pi$
$127$	3.90612	−	3.90612i	0.346612	−	0.346612i	0.858846	+	0.512234i	$0.171182\pi$
$128$	12.5313	−	3.35775i	1.10762	−	0.296786i
$129$		0			0
$130$	12.5257	+	14.0588i	1.09858	+	1.23304i
$131$	−0.235360	+	0.135885i	−0.0205635	+	0.0118724i	−0.510247	−	0.860028i	$-0.670446\pi$
$131$	−0.235360	+	0.135885i	−0.0205635	+	0.0118724i	0.489683	+	0.871901i	$0.337113\pi$
$132$		0			0
$133$	−15.7432	+	10.7858i	−1.36511	+	0.935247i
$134$		−	5.02049i		−	0.433704i
$135$		0			0
$136$			3.88860i			0.333445i
$137$	1.36633	+	5.09921i	0.116733	+	0.435655i	0.999411	−	0.0343246i	$-0.0109280\pi$
$137$	1.36633	+	5.09921i	0.116733	+	0.435655i	−0.882677	+	0.469979i	$0.844261\pi$
$138$		0			0
$139$	6.88691	+	11.9285i	0.584140	+	1.01176i	0.994982	+	0.100053i	$0.0319014\pi$
$139$	6.88691	+	11.9285i	0.584140	+	1.01176i	−0.410842	+	0.911706i	$0.634765\pi$
$140$	0.414905	+	1.43609i	0.0350659	+	0.121372i
$141$		0			0
$142$	−2.85171	−	10.6427i	−0.239310	−	0.893116i
$143$	11.9429	−	11.9429i	0.998719	−	0.998719i
$144$		0			0
$145$	12.3634	−	2.56019i	1.02672	−	0.212612i
$146$	−6.63983	−	3.83351i	−0.549516	−	0.317263i
$147$		0			0
$148$	−0.215688	+	0.804957i	−0.0177294	+	0.0661670i
$149$	16.0919	−	9.29066i	1.31830	−	0.761120i	0.334844	−	0.942274i	$-0.391316\pi$
$149$	16.0919	−	9.29066i	1.31830	−	0.761120i	0.983455	+	0.181153i	$0.0579830\pi$
$150$		0			0
$151$	−7.74118	+	13.4081i	−0.629969	+	1.09114i	0.357589	+	0.933879i	$0.383599\pi$
$151$	−7.74118	+	13.4081i	−0.629969	+	1.09114i	−0.987557	+	0.157258i	$0.949734\pi$
$152$	13.3758	+	13.3758i	1.08492	+	1.08492i
$153$		0			0
$154$	11.2745	−	3.97376i	0.908523	−	0.320215i
$155$	4.03908	−	12.2126i	0.324427	−	0.980940i
$156$		0			0
$157$	−2.15749	+	8.05187i	−0.172187	+	0.642609i	0.824827	+	0.565385i	$0.191272\pi$
$157$	−2.15749	+	8.05187i	−0.172187	+	0.642609i	−0.997014	+	0.0772243i	$0.975394\pi$
$158$	−3.89964	+	14.5536i	−0.310238	+	1.15783i
$159$		0			0
$160$	2.83888	−	1.42777i	0.224433	−	0.112875i
$161$	−4.96399	−	14.0840i	−0.391217	−	1.10997i
$162$		0			0
$163$	5.84122	+	5.84122i	0.457520	+	0.457520i	0.897841	−	0.440321i	$-0.145135\pi$
$163$	5.84122	+	5.84122i	0.457520	+	0.457520i	−0.440321	+	0.897841i	$0.645135\pi$
$164$	−0.445669	+	0.771921i	−0.0348009	+	0.0602769i
$165$		0			0
$166$	0.752332	−	0.434359i	0.0583923	−	0.0337128i
$167$	1.52522	−	5.69220i	0.118025	−	0.440475i	−0.881470	−	0.472239i	$-0.843446\pi$
$167$	1.52522	−	5.69220i	0.118025	−	0.440475i	0.999495	+	0.0317639i	$0.0101125\pi$
$168$		0			0
$169$	16.0021	+	9.23884i	1.23093	+	0.710680i
$170$	1.00907	+	4.87288i	0.0773922	+	0.373733i
$171$		0			0
$172$	−0.547943	+	0.547943i	−0.0417802	+	0.0417802i
$173$	−0.346725	−	1.29400i	−0.0263610	−	0.0983808i	0.951492	−	0.307674i	$-0.0995505\pi$
$173$	−0.346725	−	1.29400i	−0.0263610	−	0.0983808i	−0.977853	+	0.209293i	$0.932884\pi$
$174$		0			0
$175$	−6.17259	−	11.7004i	−0.466604	−	0.884466i
$176$	−6.68536	−	11.5794i	−0.503928	−	0.872828i
$177$		0			0
$178$	0.100966	+	0.376810i	0.00756772	+	0.0282431i
$179$			15.1327i			1.13107i	0.824724	+	0.565535i	$0.191330\pi$
$179$			15.1327i			1.13107i	−0.824724	+	0.565535i	$0.808670\pi$
$180$		0			0
$181$		−	17.1083i		−	1.27165i	−0.771834	−	0.635825i	$-0.780660\pi$
$181$		−	17.1083i		−	1.27165i	0.771834	−	0.635825i	$-0.219340\pi$
$182$	12.5919	+	18.3795i	0.933375	+	1.36238i
$183$		0			0
$184$	−12.8191	+	7.40110i	−0.945036	+	0.545617i
$185$	0.424610	−	7.36269i	0.0312180	−	0.541316i
$186$		0			0
$187$	4.31160	−	1.15529i	0.315295	−	0.0844831i
$188$	1.08916	−	1.08916i	0.0794349	−	0.0794349i
$189$		0			0
$190$	20.2324	+	13.2905i	1.46781	+	0.964196i
$191$	5.33828	−	9.24617i	0.386264	−	0.669029i	−0.605679	−	0.795709i	$-0.707099\pi$
$191$	5.33828	−	9.24617i	0.386264	−	0.669029i	0.991944	+	0.126679i	$0.0404319\pi$
$192$		0			0
$193$	5.08177	−	18.9654i	0.365793	−	1.36516i	−0.500548	−	0.865709i	$-0.666868\pi$
$193$	5.08177	−	18.9654i	0.365793	−	1.36516i	0.866342	−	0.499451i	$-0.166465\pi$
$194$	−9.63114	−	16.6816i	−0.691475	−	1.19767i
$195$		0			0
$196$	0.271521	+	1.74773i	0.0193944	+	0.124838i
$197$	−6.33933	+	6.33933i	−0.451659	+	0.451659i	−0.895905	−	0.444246i	$-0.853472\pi$
$197$	−6.33933	+	6.33933i	−0.451659	+	0.451659i	0.444246	+	0.895905i	$0.353472\pi$
$198$		0			0
$199$	−20.6723			−1.46542			−0.732710	−	0.680541i	$-0.761745\pi$
$199$	−20.6723			−1.46542			−0.732710	+	0.680541i	$0.761745\pi$
$200$	−10.2765	+	8.14473i	−0.726662	+	0.575919i
$201$		0			0
$202$	−0.946315	+	3.53170i	−0.0665825	+	0.248489i
$203$	14.8945	−	1.15008i	1.04539	−	0.0807199i
$204$		0			0
$205$	2.47688	−	7.48911i	0.172993	−	0.523062i
$206$		−	7.46934i		−	0.520413i
$207$		0			0
$208$	17.6204	−	17.6204i	1.22176	−	1.22176i
$209$	10.8569	−	18.8047i	0.750987	−	1.30075i
$210$		0			0
$211$	−4.00114	−	6.93018i	−0.275450	−	0.477094i	0.694798	−	0.719204i	$-0.255494\pi$
$211$	−4.00114	−	6.93018i	−0.275450	−	0.477094i	−0.970249	+	0.242111i	$0.922160\pi$
$212$	−2.36347	−	0.633291i	−0.162324	−	0.0434946i
$213$		0			0
$214$	−4.34278	−	2.50731i	−0.296866	−	0.171396i
$215$	3.76510	−	5.73168i	0.256778	−	0.390897i
$216$		0			0
$217$	6.57265	−	13.7276i	0.446180	−	0.931890i
$218$	28.7784	−	7.71115i	1.94912	−	0.522265i
$219$		0			0
$220$	−1.13144	−	1.26993i	−0.0762819	−	0.0856188i
$221$	4.15950	+	7.20446i	0.279798	+	0.484625i
$222$		0			0
$223$	1.92131	+	7.17043i	0.128661	+	0.480168i	0.999944	−	0.0106130i	$-0.00337830\pi$
$223$	1.92131	+	7.17043i	0.128661	+	0.480168i	−0.871283	+	0.490781i	$0.836712\pi$
$224$	3.54609	−	1.24984i	0.236933	−	0.0835085i
$225$		0			0
$226$	−20.9071			−1.39072
$227$	9.12876	−	2.44604i	0.605897	−	0.162350i	0.0571887	−	0.998363i	$-0.481786\pi$
$227$	9.12876	−	2.44604i	0.605897	−	0.162350i	0.548709	+	0.836014i	$0.315120\pi$
$228$		0			0
$229$	−2.96181	−	5.13000i	−0.195722	−	0.339000i	0.751415	−	0.659830i	$-0.229372\pi$
$229$	−2.96181	−	5.13000i	−0.195722	−	0.339000i	−0.947137	+	0.320830i	$0.896038\pi$
$230$	−14.1433	+	12.6010i	−0.932583	+	0.830883i
$231$		0			0
$232$	−3.83256	−	14.3033i	−0.251620	−	0.939058i
$233$	−6.93556	−	6.93556i	−0.454364	−	0.454364i	0.442436	−	0.896800i	$-0.354114\pi$
$233$	−6.93556	−	6.93556i	−0.454364	−	0.454364i	−0.896800	+	0.442436i	$0.854114\pi$
$234$		0			0
$235$	−7.48396	+	11.3930i	−0.488200	+	0.743196i
$236$	1.04598	+	0.603896i	0.0680874	+	0.0393103i
$237$		0			0
$238$	0.453292	+	5.87052i	0.0293826	+	0.380529i
$239$	−12.0682	+	6.96756i	−0.780625	+	0.450694i	−0.836652	−	0.547735i	$-0.815490\pi$
$239$	−12.0682	+	6.96756i	−0.780625	+	0.450694i	0.0560266	+	0.998429i	$0.482157\pi$
$240$		0			0
$241$	11.0801	+	6.39710i	0.713732	+	0.412073i	0.812441	−	0.583043i	$-0.198138\pi$
$241$	11.0801	+	6.39710i	0.713732	+	0.412073i	−0.0987094	+	0.995116i	$0.531471\pi$
$242$	2.05621	−	2.05621i	0.132178	−	0.132178i
$243$		0			0
$244$	1.48883			0.0953127
$245$	−5.48930	−	14.6584i	−0.350698	−	0.936488i
$246$		0			0
$247$	39.0891	+	10.4739i	2.48718	+	0.666438i
$248$	−14.5724	−	3.90466i	−0.925349	−	0.247946i
$249$		0			0
$250$	−10.7642	+	12.8730i	−0.680790	+	0.814162i
$251$			27.3432i			1.72589i	0.505298	+	0.862945i	$0.331383\pi$
$251$			27.3432i			1.72589i	−0.505298	+	0.862945i	$0.668617\pi$
$252$		0			0
$253$	12.0147	+	12.0147i	0.755358	+	0.755358i
$254$	−7.18026	−	4.14553i	−0.450530	−	0.260113i
$255$		0			0
$256$	−2.98570	−	5.17139i	−0.186606	−	0.323212i
$257$	3.08480	−	11.5126i	0.192425	−	0.718138i	−0.800494	−	0.599341i	$-0.795429\pi$
$257$	3.08480	−	11.5126i	0.192425	−	0.718138i	0.992919	−	0.118797i	$-0.0379039\pi$
$258$		0			0
$259$	1.60289	−	8.57765i	0.0995986	−	0.532989i
$260$	1.74036	−	2.64939i	0.107933	−	0.164308i
$261$		0			0
$262$	0.288427	+	0.288427i	0.0178191	+	0.0178191i
$263$	−15.7989	+	4.23331i	−0.974205	+	0.261037i	−0.710602	−	0.703594i	$-0.751577\pi$
$263$	−15.7989	+	4.23331i	−0.974205	+	0.261037i	−0.263602	+	0.964631i	$0.584911\pi$
$264$		0			0
$265$	21.6180	+	1.24672i	1.32798	+	0.0765853i
$266$	21.7523	+	18.6339i	1.33372	+	1.14252i
$267$		0			0
$268$	−0.816389	+	0.218751i	−0.0498689	+	0.0133623i
$269$	4.70963			0.287151			0.143576	−	0.989639i	$-0.454140\pi$
$269$	4.70963			0.287151			0.143576	+	0.989639i	$0.454140\pi$
$270$		0			0
$271$			0.261497i			0.0158848i	0.999968	+	0.00794242i	$0.00252818\pi$
$271$			0.261497i			0.0158848i	−0.999968	+	0.00794242i	$0.997472\pi$
$272$	6.36126	−	1.70449i	0.385708	−	0.103350i
$273$		0			0
$274$	6.86181	−	3.96167i	0.414537	−	0.239333i
$275$	12.0838	+	8.97465i	0.728683	+	0.541192i
$276$		0			0
$277$	2.68878	+	10.0347i	0.161553	+	0.602924i	0.998455	+	0.0555711i	$0.0176979\pi$
$277$	2.68878	+	10.0347i	0.161553	+	0.602924i	−0.836902	+	0.547353i	$0.815635\pi$
$278$	14.6180	−	14.6180i	0.876730	−	0.876730i
$279$		0			0
$280$	−13.2831	+	8.01753i	−0.793817	+	0.479139i
$281$	9.18006	−	15.9003i	0.547636	−	0.948534i	−0.450800	−	0.892625i	$-0.648861\pi$
$281$	9.18006	−	15.9003i	0.547636	−	0.948534i	0.998436	−	0.0559087i	$-0.0178056\pi$
$282$		0			0
$283$	4.41271	+	1.18238i	0.262308	+	0.0702853i	0.387576	−	0.921838i	$-0.373312\pi$
$283$	4.41271	+	1.18238i	0.262308	+	0.0702853i	−0.125268	+	0.992123i	$0.539979\pi$
$284$	−1.60637	+	0.927440i	−0.0953207	+	0.0550334i
$285$		0			0
$286$	−21.9536	−	12.6749i	−1.29814	−	0.749484i
$287$	4.03053	−	8.41815i	0.237915	−	0.496908i
$288$		0			0
$289$		−	14.8014i		−	0.870673i
$290$	−8.51429	−	16.9292i	−0.499976	−	0.994119i
$291$		0			0
$292$	−0.334064	+	1.24674i	−0.0195496	+	0.0729602i
$293$	−23.4140	−	6.27377i	−1.36786	−	0.366518i	−0.501165	−	0.865352i	$-0.667095\pi$
$293$	−23.4140	−	6.27377i	−1.36786	−	0.366518i	−0.866697	+	0.498834i	$0.833762\pi$
$294$		0			0
$295$	−10.1480	−	3.35625i	−0.590839	−	0.195409i
$296$	−8.64960			−0.502748
$297$		0			0
$298$	−19.7202	−	19.7202i	−1.14236	−	1.14236i
$299$	−15.8334	+	27.4243i	−0.915670	+	1.58599i
$300$		0			0
$301$	5.27883	−	6.16225i	0.304267	−	0.355186i
$302$	22.4455	+	6.01426i	1.29160	+	0.346082i
$303$		0			0
$304$	16.0181	−	27.7441i	0.918699	−	1.59123i
$305$	−12.9020	+	2.67173i	−0.738766	+	0.152983i
$306$		0			0
$307$	−0.347114	−	0.347114i	−0.0198109	−	0.0198109i	0.697132	−	0.716943i	$-0.254459\pi$
$307$	−0.347114	−	0.347114i	−0.0198109	−	0.0198109i	−0.716943	+	0.697132i	$0.754459\pi$
$308$	−1.13743	−	1.66021i	−0.0648108	−	0.0945995i
$309$		0			0
$310$	−19.2742	−	1.11155i	−1.09470	−	0.0631320i
$311$	21.7696	−	12.5687i	1.23444	−	0.712706i	0.266490	−	0.963838i	$-0.414136\pi$
$311$	21.7696	−	12.5687i	1.23444	−	0.712706i	0.967953	+	0.251131i	$0.0808026\pi$
$312$		0			0
$313$	3.05557	+	11.4035i	0.172711	+	0.644566i	0.996930	+	0.0782951i	$0.0249476\pi$
$313$	3.05557	+	11.4035i	0.172711	+	0.644566i	−0.824219	+	0.566271i	$0.808386\pi$
$314$	12.5113			0.706053
$315$		0			0
$316$	2.53650			0.142689
$317$	−1.42134	−	5.30450i	−0.0798303	−	0.297931i	0.914455	−	0.404688i	$-0.132620\pi$
$317$	−1.42134	−	5.30450i	−0.0798303	−	0.297931i	−0.994285	+	0.106757i	$0.965953\pi$
$318$		0			0
$319$	−14.7206	+	8.49893i	−0.824194	+	0.475849i
$320$	10.0406	+	11.2696i	0.561287	+	0.629989i
$321$		0			0
$322$	−18.4899	+	12.6676i	−1.03040	+	0.705937i
$323$	7.56250	+	7.56250i	0.420789	+	0.420789i
$324$		0			0
$325$	−10.3274	+	26.0823i	−0.572860	+	1.44679i
$326$	6.19923	−	10.7374i	0.343343	−	0.594688i
$327$		0			0
$328$	−8.93621	−	2.39445i	−0.493420	−	0.132211i
$329$	−10.4928	+	12.2488i	−0.578489	+	0.675300i
$330$		0			0
$331$	5.21617	−	9.03467i	0.286706	−	0.496590i	−0.686315	−	0.727304i	$-0.740773\pi$
$331$	5.21617	−	9.03467i	0.286706	−	0.496590i	0.973022	+	0.230714i	$0.0741062\pi$
$332$	−0.103412	−	0.103412i	−0.00567548	−	0.00567548i
$333$		0			0
$334$	−8.84474			−0.483963
$335$	6.68215	−	3.36068i	0.365085	−	0.183614i
$336$		0			0
$337$	−7.40667	−	1.98461i	−0.403467	−	0.108109i	0.0513780	−	0.998679i	$-0.483639\pi$
$337$	−7.40667	−	1.98461i	−0.403467	−	0.108109i	−0.454845	+	0.890571i	$0.650305\pi$
$338$	7.17782	−	26.7880i	0.390422	−	1.45707i
$339$		0			0
$340$	0.748420	−	0.376406i	0.0405888	−	0.0204135i
$341$			17.3176i			0.937803i
$342$		0			0
$343$	−4.24359	−	18.0275i	−0.229132	−	0.973395i
$344$	−6.96543	−	4.02149i	−0.375551	−	0.216824i
$345$		0			0
$346$	−1.74128	+	1.00533i	−0.0936119	+	0.0540468i
$347$	31.4710	+	8.43262i	1.68945	+	0.452687i	0.970248	−	0.242115i	$-0.0778410\pi$
$347$	31.4710	+	8.43262i	1.68945	+	0.452687i	0.719202	+	0.694801i	$0.244508\pi$
$348$		0			0
$349$	11.1908	−	19.3830i	0.599028	−	1.03755i	−0.393937	−	0.919137i	$-0.628887\pi$
$349$	11.1908	−	19.3830i	0.599028	−	1.03755i	0.992965	−	0.118409i	$-0.0377795\pi$
$350$	−14.5648	+	13.4938i	−0.778523	+	0.721275i
$351$		0			0
$352$	−3.02508	+	3.02508i	−0.161237	+	0.161237i
$353$	−2.57319	−	9.60326i	−0.136957	−	0.511130i	−0.999982	−	0.00596923i	$-0.998100\pi$
$353$	−2.57319	−	9.60326i	−0.136957	−	0.511130i	0.863025	−	0.505161i	$-0.168567\pi$
$354$		0			0
$355$	12.2563	−	10.9197i	0.650496	−	0.579558i
$356$	0.0568744	−	0.0328364i	0.00301434	−	0.00174033i
$357$		0			0
$358$	21.9386	−	5.87843i	1.15949	−	0.310685i
$359$			21.1671i			1.11716i	0.829452	+	0.558578i	$0.188653\pi$
$359$			21.1671i			1.11716i	−0.829452	+	0.558578i	$0.811347\pi$
$360$		0			0
$361$	33.0261			1.73821
$362$	−24.8027	+	6.64587i	−1.30360	+	0.349299i
$363$		0			0
$364$	2.44006	−	2.84841i	0.127894	−	0.149297i
$365$	0.657650	−	11.4036i	0.0344230	−	0.596891i
$366$		0			0
$367$	−16.0941	+	4.31241i	−0.840107	+	0.225106i	−0.653118	−	0.757256i	$-0.726539\pi$
$367$	−16.0941	+	4.31241i	−0.840107	+	0.225106i	−0.186989	+	0.982362i	$0.559873\pi$
$368$	17.7263	+	17.7263i	0.924046	+	0.924046i
$369$		0			0
$370$	−10.8390	+	2.24453i	−0.563493	+	0.116687i
$371$	25.1853	+	4.70632i	1.30755	+	0.244340i
$372$		0			0
$373$	−0.366437	+	1.36756i	−0.0189734	+	0.0708096i	−0.974763	−	0.223240i	$-0.928337\pi$
$373$	−0.366437	+	1.36756i	−0.0189734	+	0.0708096i	0.955790	+	0.294050i	$0.0950032\pi$
$374$	−3.34976	−	5.80195i	−0.173212	−	0.300012i
$375$		0			0
$376$	13.8453	+	7.99360i	0.714018	+	0.412239i
$377$	−22.4004	−	22.4004i	−1.15368	−	1.15368i
$378$		0			0
$379$			12.7908i			0.657019i	0.944501	+	0.328510i	$0.106546\pi$
$379$			12.7908i			0.657019i	−0.944501	+	0.328510i	$0.893454\pi$
$380$	1.27963	−	3.86911i	0.0656437	−	0.198481i
$381$		0			0
$382$	−15.4783	−	4.14741i	−0.791940	−	0.212200i
$383$	2.97391	+	0.796856i	0.151960	+	0.0407174i	0.333997	−	0.942574i	$-0.391603\pi$
$383$	2.97391	+	0.796856i	0.151960	+	0.0407174i	−0.182037	+	0.983292i	$0.558269\pi$
$384$		0			0
$385$	12.8360	+	12.3460i	0.654185	+	0.629213i
$386$	−29.4691			−1.49994
$387$		0			0
$388$	−2.29298	+	2.29298i	−0.116408	+	0.116408i
$389$	2.13469	+	1.23247i	0.108233	+	0.0624885i	0.553139	−	0.833089i	$-0.313430\pi$
$389$	2.13469	+	1.23247i	0.108233	+	0.0624885i	−0.444906	+	0.895577i	$0.646763\pi$
$390$		0			0
$391$	−7.24775	+	4.18449i	−0.366535	+	0.211619i
$392$	−16.7927	+	7.41721i	−0.848160	+	0.374625i
$393$		0			0
$394$	11.6530	+	6.72787i	0.587070	+	0.338945i
$395$	−21.9809	+	4.55179i	−1.10598	+	0.229025i
$396$		0			0
$397$	21.2368	+	21.2368i	1.06585	+	1.06585i	0.997674	+	0.0681729i	$0.0217170\pi$
$397$	21.2368	+	21.2368i	1.06585	+	1.06585i	0.0681729	+	0.997674i	$0.478283\pi$
$398$	8.03034	+	29.9696i	0.402524	+	1.50224i
$399$		0			0
$400$	17.8283	+	13.2411i	0.891414	+	0.662053i
$401$	−0.663976	−	1.15004i	−0.0331574	−	0.0574302i	0.848971	−	0.528440i	$-0.177223\pi$
$401$	−0.663976	−	1.15004i	−0.0331574	−	0.0574302i	−0.882128	+	0.471010i	$0.843890\pi$
$402$		0			0
$403$	−31.1752	+	8.35337i	−1.55295	+	0.416111i
$404$	0.615527			0.0306236
$405$		0			0
$406$	−7.45325	−	21.1466i	−0.369899	−	1.04949i
$407$	2.56977	+	9.59050i	0.127379	+	0.475383i
$408$		0			0
$409$	2.10020	+	3.63765i	0.103848	+	0.179870i	0.913267	−	0.407361i	$-0.133551\pi$
$409$	2.10020	+	3.63765i	0.103848	+	0.179870i	−0.809419	+	0.587232i	$0.800218\pi$
$410$	−11.8195	−	0.681636i	−0.583723	−	0.0336636i
$411$		0			0
$412$	−1.21460	+	0.325451i	−0.0598390	+	0.0160338i
$413$	−11.4069	−	5.46151i	−0.561296	−	0.268743i
$414$		0			0
$415$	1.08173	+	0.710580i	0.0531000	+	0.0348810i
$416$	−6.90492	−	3.98656i	−0.338542	−	0.195457i
$417$		0			0
$418$	−31.4795	−	8.43491i	−1.53971	−	0.412565i
$419$	9.60886	+	16.6430i	0.469424	+	0.813065i	0.999389	−	0.0349539i	$-0.0111284\pi$
$419$	9.60886	+	16.6430i	0.469424	+	0.813065i	−0.529965	+	0.848019i	$0.677795\pi$
$420$		0			0
$421$	7.94820	−	13.7667i	0.387371	−	0.670947i	−0.604724	−	0.796435i	$-0.706716\pi$
$421$	7.94820	−	13.7667i	0.387371	−	0.670947i	0.992095	+	0.125488i	$0.0400498\pi$
$422$	−8.49275	+	8.49275i	−0.413420	+	0.413420i
$423$		0			0
$424$		−	25.3965i		−	1.23336i
$425$	−5.81023	+	4.60493i	−0.281838	+	0.223372i
$426$		0			0
$427$	−15.5434	+	1.20019i	−0.752200	+	0.0580811i
$428$	−0.218495	+	0.815433i	−0.0105613	+	0.0394155i
$429$		0			0
$430$	−9.77208	−	3.23192i	−0.471252	−	0.155857i
$431$	−13.1962			−0.635638			−0.317819	−	0.948151i	$-0.602950\pi$
$431$	−13.1962			−0.635638			−0.317819	+	0.948151i	$0.602950\pi$
$432$		0			0
$433$	9.58308	−	9.58308i	0.460533	−	0.460533i	−0.438297	−	0.898830i	$-0.644418\pi$
$433$	9.58308	−	9.58308i	0.460533	−	0.460533i	0.898830	+	0.438297i	$0.144418\pi$
$434$	−22.4548	−	4.19608i	−1.07786	−	0.201418i
$435$		0			0
$436$	−2.50784	−	4.34371i	−0.120104	−	0.208026i
$437$	−10.5368	+	39.3240i	−0.504045	+	1.88112i
$438$		0			0
$439$	−15.0035	+	25.9868i	−0.716079	+	1.24028i	0.246464	+	0.969152i	$0.420731\pi$
$439$	−15.0035	+	25.9868i	−0.716079	+	1.24028i	−0.962542	+	0.271132i	$0.912602\pi$
$440$	9.69239	−	14.7549i	0.462067	−	0.703413i
$441$		0			0
$442$	8.82887	−	8.82887i	0.419946	−	0.419946i
$443$	−32.7879	+	8.78548i	−1.55780	+	0.417411i	−0.931966	−	0.362547i	$-0.881907\pi$
$443$	−32.7879	+	8.78548i	−1.55780	+	0.417411i	−0.625833	+	0.779957i	$0.715241\pi$
$444$		0			0
$445$	−0.433940	+	0.386618i	−0.0205707	+	0.0183274i
$446$	9.64897	−	5.57084i	0.456892	−	0.263787i
$447$		0			0
$448$	10.0937	+	14.7330i	0.476882	+	0.696070i
$449$		−	6.04212i		−	0.285145i	−0.989784	−	0.142573i	$-0.954463\pi$
$449$		−	6.04212i		−	0.285145i	0.989784	−	0.142573i	$-0.0455375\pi$
$450$		0			0
$451$			10.6197i			0.500061i
$452$	0.910958	+	3.39974i	0.0428478	+	0.159910i
$453$		0			0
$454$	−7.09230	−	12.2842i	−0.332858	−	0.576527i
$455$	−16.0337	+	29.0627i	−0.751672	+	1.36248i
$456$		0			0
$457$	5.71993	+	21.3471i	0.267567	+	0.998573i	0.960660	+	0.277726i	$0.0895806\pi$
$457$	5.71993	+	21.3471i	0.267567	+	0.998573i	−0.693094	+	0.720848i	$0.743753\pi$
$458$	−6.28667	+	6.28667i	−0.293757	+	0.293757i
$459$		0			0
$460$	2.66531	+	1.75082i	0.124271	+	0.0816325i
$461$	6.38312	+	3.68530i	0.297291	+	0.171641i	0.641225	−	0.767353i	$-0.278426\pi$
$461$	6.38312	+	3.68530i	0.297291	+	0.171641i	−0.343934	+	0.938994i	$0.611760\pi$
$462$		0			0
$463$	4.25388	−	15.8757i	0.197695	−	0.737807i	−0.793858	−	0.608103i	$-0.791931\pi$
$463$	4.25388	−	15.8757i	0.197695	−	0.737807i	0.991553	−	0.129704i	$-0.0414026\pi$
$464$	−21.7185	+	12.5392i	−1.00826	+	0.582116i
$465$		0			0
$466$	−7.36064	+	12.7490i	−0.340975	+	0.590586i
$467$	−5.96079	−	5.96079i	−0.275832	−	0.275832i	0.555610	−	0.831443i	$-0.312485\pi$
$467$	−5.96079	−	5.96079i	−0.275832	−	0.275832i	−0.831443	+	0.555610i	$0.812485\pi$
$468$		0			0
$469$	8.34679	−	2.94188i	0.385419	−	0.135843i
$470$	19.4242	+	6.42416i	0.895970	+	0.296324i
$471$		0			0
$472$	−3.24456	+	12.1089i	−0.149343	+	0.557356i
$473$	−2.38954	+	8.91790i	−0.109871	+	0.410045i
$474$		0			0
$475$	−4.14593	+	35.8255i	−0.190228	+	1.64378i
$476$	0.934864	−	0.329499i	0.0428494	−	0.0151025i
$477$		0			0
$478$	14.7892	+	14.7892i	0.676442	+	0.676442i
$479$	−19.1885	+	33.2355i	−0.876747	+	1.51857i	−0.0218561	+	0.999761i	$0.506958\pi$
$479$	−19.1885	+	33.2355i	−0.876747	+	1.51857i	−0.854891	+	0.518808i	$0.826376\pi$
$480$		0			0
$481$	−16.0252	+	9.25218i	−0.730688	+	0.421863i
$482$	4.97002	−	18.5484i	0.226378	−	0.844855i
$483$		0			0
$484$	−0.423956	−	0.244771i	−0.0192707	−	0.0111259i
$485$	15.7558	−	23.9854i	0.715435	−	1.08912i
$486$		0			0
$487$	−6.98374	+	6.98374i	−0.316463	+	0.316463i	−0.847407	−	0.530944i	$-0.821838\pi$
$487$	−6.98374	+	6.98374i	−0.316463	+	0.316463i	0.530944	+	0.847407i	$0.321838\pi$
$488$	3.99953	+	14.9264i	0.181050	+	0.675689i
$489$		0			0
$490$	−19.1186	+	13.6523i	−0.863689	+	0.616747i
$491$	−18.6711	−	32.3394i	−0.842617	−	1.45945i	−0.887675	−	0.460471i	$-0.847681\pi$
$491$	−18.6711	−	32.3394i	−0.842617	−	1.45945i	0.0450583	−	0.998984i	$-0.485653\pi$
$492$		0			0
$493$	−2.16688	−	8.08691i	−0.0975914	−	0.364216i
$494$		−	60.7380i		−	2.73273i
$495$		0			0
$496$			25.5502i			1.14724i
$497$	16.0230	−	10.9774i	0.718728	−	0.492406i
$498$		0			0
$499$	12.8750	−	7.43339i	0.576365	−	0.332764i	−0.183323	−	0.983053i	$-0.558685\pi$
$499$	12.8750	−	7.43339i	0.576365	−	0.332764i	0.759687	+	0.650288i	$0.225352\pi$
$500$	2.56232	+	1.18949i	0.114590	+	0.0531956i
$501$		0			0
$502$	39.6408	−	10.6217i	1.76926	−	0.474071i
$503$	−17.1033	+	17.1033i	−0.762598	+	0.762598i	−0.976791	−	0.214193i	$-0.931288\pi$
$503$	−17.1033	+	17.1033i	−0.762598	+	0.762598i	0.214193	+	0.976791i	$0.431288\pi$
$504$		0			0
$505$	−5.33406	+	1.10457i	−0.237363	+	0.0491528i
$506$	12.7511	−	22.0855i	0.566855	−	0.981821i
$507$		0			0
$508$	−0.361254	+	1.34822i	−0.0160281	+	0.0598176i
$509$	−20.1407	−	34.8848i	−0.892722	−	1.54624i	−0.836598	−	0.547817i	$-0.815459\pi$
$509$	−20.1407	−	34.8848i	−0.892722	−	1.54624i	−0.0561241	−	0.998424i	$-0.517874\pi$
$510$		0			0
$511$	2.48261	−	13.2853i	0.109824	−	0.587709i
$512$	12.0097	−	12.0097i	0.530758	−	0.530758i
$513$		0			0
$514$	−17.8887			−0.789038
$515$	9.94152	−	4.99993i	0.438076	−	0.220323i
$516$		0			0
$517$	4.74974	−	17.7263i	0.208893	−	0.779601i
$518$	−13.0581	+	1.00828i	−0.573740	+	0.0443013i
$519$		0			0
$520$	31.2370	+	10.3310i	1.36983	+	0.453045i
$521$			28.7800i			1.26088i	0.776240	+	0.630438i	$0.217125\pi$
$521$			28.7800i			1.26088i	−0.776240	+	0.630438i	$0.782875\pi$
$522$		0			0
$523$	−1.01735	+	1.01735i	−0.0444858	+	0.0444858i	−0.729000	−	0.684514i	$-0.760014\pi$
$523$	−1.01735	+	1.01735i	−0.0444858	+	0.0444858i	0.684514	+	0.729000i	$0.260014\pi$
$524$	0.0343343	−	0.0594688i	0.00149990	−	0.00259791i
$525$		0			0
$526$	12.2745	+	21.2600i	0.535193	+	0.926981i
$527$	−8.23905	−	2.20765i	−0.358899	−	0.0961667i
$528$		0			0
$529$	−7.67047	−	4.42855i	−0.333499	−	0.192545i
$530$	−6.59026	−	31.8249i	−0.286263	−	1.38239i
$531$		0			0
$532$	2.08230	−	4.34908i	0.0902791	−	0.188556i
$533$	−19.1175	+	5.12252i	−0.828071	+	0.221881i
$534$		0			0
$535$	0.430136	−	7.45852i	0.0185964	−	0.322460i
$536$	−4.38622	−	7.59716i	−0.189456	−	0.328147i
$537$		0			0
$538$	−1.82950	−	6.82778i	−0.0788753	−	0.294366i
$539$	13.2131	+	16.4158i	0.569129	+	0.707078i
$540$		0			0
$541$	27.2918			1.17337			0.586683	−	0.809817i	$-0.300433\pi$
$541$	27.2918			1.17337			0.586683	+	0.809817i	$0.300433\pi$
$542$	0.379105	−	0.101581i	0.0162840	−	0.00436328i
$543$		0			0
$544$	−1.05358	−	1.82485i	−0.0451718	−	0.0782398i
$545$	29.5274	+	33.1416i	1.26482	+	1.41963i
$546$		0			0
$547$	−0.324482	−	1.21098i	−0.0138738	−	0.0517779i	0.958642	−	0.284615i	$-0.0918658\pi$
$547$	−0.324482	−	1.21098i	−0.0138738	−	0.0517779i	−0.972516	+	0.232837i	$0.925199\pi$
$548$	−0.943192	−	0.943192i	−0.0402912	−	0.0402912i
$549$		0			0
$550$	8.31692	−	21.0048i	0.354635	−	0.895648i
$551$	−35.2704	−	20.3634i	−1.50257	−	0.867509i
$552$		0			0
$553$	−26.4812	+	2.04474i	−1.12609	+	0.0869512i
$554$	13.5033	−	7.79611i	0.573698	−	0.331225i
$555$		0			0
$556$	−3.01399	−	1.74013i	−0.127821	−	0.0737977i
$557$	1.67807	−	1.67807i	0.0711020	−	0.0711020i	−0.670662	−	0.741764i	$-0.733990\pi$
$557$	1.67807	−	1.67807i	0.0711020	−	0.0711020i	0.741764	+	0.670662i	$0.233990\pi$
$558$		0			0
$559$	−17.2066			−0.727762
$560$	18.9381	+	18.2152i	0.800280	+	0.769731i
$561$		0			0
$562$	−26.6175	−	7.13215i	−1.12279	−	0.300852i
$563$	24.2179	+	6.48916i	1.02066	+	0.273485i	0.730078	−	0.683364i	$-0.239484\pi$
$563$	24.2179	+	6.48916i	1.02066	+	0.273485i	0.290584	+	0.956850i	$0.406150\pi$
$564$		0			0
$565$	−13.9951	−	27.8269i	−0.588779	−	1.17069i
$566$		−	6.85662i		−	0.288205i
$567$		0			0
$568$	−13.6134	−	13.6134i	−0.571207	−	0.571207i
$569$	22.1958	+	12.8148i	0.930498	+	0.537223i	0.886969	−	0.461829i	$-0.152807\pi$
$569$	22.1958	+	12.8148i	0.930498	+	0.537223i	0.0435292	+	0.999052i	$0.486140\pi$
$570$		0			0
$571$	−14.0363	−	24.3116i	−0.587400	−	1.01741i	−0.994572	−	0.104055i	$-0.966818\pi$
$571$	−14.0363	−	24.3116i	−0.587400	−	1.01741i	0.407171	−	0.913352i	$-0.366515\pi$
$572$	−1.10453	+	4.12217i	−0.0461828	+	0.172357i
$573$		0			0
$574$	−13.7699	−	2.57315i	−0.574744	−	0.107401i
$575$	−26.2390	−	10.3894i	−1.09424	−	0.433269i
$576$		0			0
$577$	−10.6783	−	10.6783i	−0.444542	−	0.444542i	0.448993	−	0.893535i	$-0.351783\pi$
$577$	−10.6783	−	10.6783i	−0.444542	−	0.444542i	−0.893535	+	0.448993i	$0.851783\pi$
$578$	−21.4584	+	5.74975i	−0.892550	+	0.239158i
$579$		0			0
$580$	−2.38191	+	2.12216i	−0.0989033	+	0.0881177i
$581$	1.16299	+	0.996263i	0.0482489	+	0.0413320i
$582$		0			0
$583$	−28.1592	+	7.54522i	−1.16623	+	0.312491i
$584$	−13.3968			−0.554363
$585$		0			0
$586$			36.3816i			1.50291i
$587$	−3.33709	+	0.894170i	−0.137736	+	0.0369064i	−0.327029	−	0.945014i	$-0.606047\pi$
$587$	−3.33709	+	0.894170i	−0.137736	+	0.0369064i	0.189292	+	0.981921i	$0.439381\pi$
$588$		0			0
$589$	−35.9340	+	20.7465i	−1.48063	+	0.854844i
$590$	−0.923640	+	16.0158i	−0.0380257	+	0.659361i
$591$		0			0
$592$	3.79139	+	14.1497i	0.155825	+	0.581547i
$593$	5.25283	−	5.25283i	0.215708	−	0.215708i	−0.590979	−	0.806687i	$-0.701258\pi$
$593$	5.25283	−	5.25283i	0.215708	−	0.215708i	0.806687	+	0.590979i	$0.201258\pi$
$594$		0			0
$595$	−7.51010	+	4.53301i	−0.307884	+	0.185835i
$596$	−2.34748	+	4.06596i	−0.0961567	+	0.166548i
$597$		0			0
$598$	45.9089	+	12.3013i	1.87736	+	0.503036i
$599$	17.9987	−	10.3916i	0.735408	−	0.424588i	−0.0849891	−	0.996382i	$-0.527086\pi$
$599$	17.9987	−	10.3916i	0.735408	−	0.424588i	0.820397	+	0.571794i	$0.193752\pi$
$600$		0			0
$601$	−22.0101	−	12.7076i	−0.897812	−	0.518352i	−0.0213224	−	0.999773i	$-0.506788\pi$
$601$	−22.0101	−	12.7076i	−0.897812	−	0.518352i	−0.876490	+	0.481421i	$0.840121\pi$
$602$	−10.9843	−	5.25919i	−0.447688	−	0.214349i
$603$		0			0
$604$		−	3.91195i		−	0.159175i
$605$	4.11318	+	1.36035i	0.167225	+	0.0553063i
$606$		0			0
$607$	3.41228	−	12.7348i	0.138500	−	0.516889i	−0.861459	−	0.507827i	$-0.830449\pi$
$607$	3.41228	−	12.7348i	0.138500	−	0.516889i	0.999959	−	0.00906195i	$-0.00288455\pi$
$608$	−9.90105	−	2.65298i	−0.401541	−	0.107592i
$609$		0			0
$610$	8.88523	+	17.6668i	0.359752	+	0.715307i
$611$	34.2019			1.38366
$612$		0			0
$613$	−33.5992	−	33.5992i	−1.35706	−	1.35706i	−0.877523	−	0.479535i	$-0.840805\pi$
$613$	−33.5992	−	33.5992i	−1.35706	−	1.35706i	−0.479535	−	0.877523i	$-0.659195\pi$
$614$	−0.368389	+	0.638068i	−0.0148670	+	0.0257503i
$615$		0			0
$616$	13.5891	−	15.8633i	0.547522	−	0.639151i
$617$	−20.6724	−	5.53916i	−0.832240	−	0.222998i	−0.182550	−	0.983197i	$-0.558435\pi$
$617$	−20.6724	−	5.53916i	−0.832240	−	0.222998i	−0.649691	+	0.760199i	$0.725102\pi$
$618$		0			0
$619$	5.07651	−	8.79277i	0.204042	−	0.353411i	−0.745785	−	0.666187i	$-0.767925\pi$
$619$	5.07651	−	8.79277i	0.204042	−	0.353411i	0.949827	+	0.312776i	$0.101259\pi$
$620$	0.659057	+	3.18264i	0.0264684	+	0.127818i
$621$		0			0
$622$	−26.6781	−	26.6781i	−1.06969	−	1.06969i
$623$	−0.567300	+	0.388662i	−0.0227284	+	0.0155714i
$624$		0			0
$625$	−24.3392	−	5.70983i	−0.973569	−	0.228393i
$626$	15.3453	−	8.85961i	0.613321	−	0.354101i
$627$		0			0
$628$	−0.545137	−	2.03448i	−0.0217533	−	0.0811845i
$629$	−4.89038			−0.194992
$630$		0			0
$631$	9.71655			0.386810			0.193405	−	0.981119i	$-0.438047\pi$
$631$	9.71655			0.386810			0.193405	+	0.981119i	$0.438047\pi$
$632$	6.81394	+	25.4300i	0.271044	+	1.01155i
$633$		0			0
$634$	−7.13807	+	4.12116i	−0.283489	+	0.163672i
$635$	0.711178	−	12.3317i	0.0282222	−	0.489370i
$636$		0			0
$637$	−23.1782	+	31.7045i	−0.918353	+	1.25618i
$638$	18.0396	+	18.0396i	0.714196	+	0.714196i
$639$		0			0
$640$	15.9270	−	24.2460i	0.629570	−	0.958406i
$641$	−6.43683	+	11.1489i	−0.254239	+	0.440356i	−0.964689	−	0.263393i	$-0.915158\pi$
$641$	−6.43683	+	11.1489i	−0.254239	+	0.440356i	0.710449	+	0.703748i	$0.248492\pi$
$642$		0			0
$643$	−24.8205	−	6.65065i	−0.978827	−	0.262276i	−0.266276	−	0.963897i	$-0.585793\pi$
$643$	−24.8205	−	6.65065i	−0.978827	−	0.262276i	−0.712550	+	0.701621i	$0.752460\pi$
$644$	2.86553	+	2.45473i	0.112918	+	0.0967298i
$645$		0			0
$646$	8.02600	−	13.9014i	0.315779	−	0.546945i
$647$	18.7373	+	18.7373i	0.736638	+	0.736638i	0.971926	−	0.235288i	$-0.0756032\pi$
$647$	18.7373	+	18.7373i	0.736638	+	0.736638i	−0.235288	+	0.971926i	$0.575603\pi$
$648$		0			0
$649$	14.3900			0.564857
$650$	41.8246	+	4.84019i	1.64049	+	0.189848i
$651$		0			0
$652$	−2.01613	−	0.540220i	−0.0789578	−	0.0211567i
$653$	−9.49156	+	35.4230i	−0.371433	+	1.38621i	0.487053	+	0.873372i	$0.338072\pi$
$653$	−9.49156	+	35.4230i	−0.371433	+	1.38621i	−0.858487	+	0.512836i	$0.828595\pi$
$654$		0			0
$655$	−0.190819	+	0.576962i	−0.00745590	+	0.0225438i
$656$			15.6681i			0.611736i
$657$		0			0
$658$	21.8338	+	10.4538i	0.851169	+	0.407532i
$659$	1.28824	+	0.743765i	0.0501826	+	0.0289730i	0.524881	−	0.851175i	$-0.324110\pi$
$659$	1.28824	+	0.743765i	0.0501826	+	0.0289730i	−0.474699	+	0.880148i	$0.657443\pi$
$660$		0			0
$661$	38.9886	−	22.5101i	1.51648	−	0.875541i	0.516670	−	0.856185i	$-0.327172\pi$
$661$	38.9886	−	22.5101i	1.51648	−	0.875541i	0.999813	−	0.0193567i	$-0.00616180\pi$
$662$	−15.1243	−	4.05253i	−0.587821	−	0.157506i
$663$		0			0
$664$	0.758968	−	1.31457i	0.0294537	−	0.0510153i
$665$	−10.2404	+	41.4252i	−0.397106	+	1.60640i
$666$		0			0
$667$	22.5350	−	22.5350i	0.872558	−	0.872558i
$668$	0.385380	+	1.43826i	0.0149108	+	0.0556478i
$669$		0			0
$670$	−7.46789	−	8.38196i	−0.288510	−	0.323823i
$671$	15.3619	−	8.86919i	0.593039	−	0.342391i
$672$		0			0
$673$	−17.1957	+	4.60757i	−0.662845	+	0.177609i	−0.574529	−	0.818484i	$-0.694815\pi$
$673$	−17.1957	+	4.60757i	−0.662845	+	0.177609i	−0.0883151	+	0.996093i	$0.528148\pi$
$674$			11.5087i			0.443300i
$675$		0			0
$676$	−4.66878			−0.179569
$677$	22.3425	−	5.98665i	0.858691	−	0.230085i	0.197500	−	0.980303i	$-0.436718\pi$
$677$	22.3425	−	5.98665i	0.858691	−	0.230085i	0.661191	+	0.750218i	$0.270051\pi$
$678$		0			0
$679$	22.0903	−	25.7872i	0.847749	−	0.989622i
$680$	5.78422	+	6.49221i	0.221815	+	0.248965i
$681$		0			0
$682$	25.1062	−	6.72719i	0.961367	−	0.257598i
$683$	−22.8715	−	22.8715i	−0.875154	−	0.875154i	0.117875	−	0.993028i	$-0.462392\pi$
$683$	−22.8715	−	22.8715i	−0.875154	−	0.875154i	−0.993028	+	0.117875i	$0.962392\pi$
$684$		0			0
$685$	9.86614	+	6.48099i	0.376966	+	0.247626i
$686$	−24.4869	+	13.1551i	−0.934915	+	0.502264i
$687$		0			0
$688$	−3.52549	+	13.1573i	−0.134408	+	0.501618i
$689$	−27.1658	−	47.0525i	−1.03493	−	1.79256i
$690$		0			0
$691$	21.8834	+	12.6344i	0.832485	+	0.480636i	0.854703	−	0.519118i	$-0.173739\pi$
$691$	21.8834	+	12.6344i	0.832485	+	0.480636i	−0.0222176	+	0.999753i	$0.507073\pi$
$692$	0.239348	+	0.239348i	0.00909866	+	0.00909866i
$693$		0			0
$694$		−	48.9007i		−	1.85625i
$695$	29.2414	+	9.67103i	1.10919	+	0.366843i
$696$		0			0
$697$	−5.05242	−	1.35379i	−0.191374	−	0.0512785i
$698$	−32.4476	−	8.69431i	−1.22816	−	0.329084i
$699$		0			0
$700$	2.82886	+	1.78046i	0.106921	+	0.0672950i
$701$	47.6479			1.79964			0.899818	−	0.436266i	$-0.143699\pi$
$701$	47.6479			1.79964			0.899818	+	0.436266i	$0.143699\pi$
$702$		0			0
$703$	−16.8216	+	16.8216i	−0.634440	+	0.634440i
$704$	−17.5980	−	10.1602i	−0.663251	−	0.382928i
$705$		0			0
$706$	−12.9227	+	7.46094i	−0.486353	+	0.280796i
$707$	−6.42612	+	0.496193i	−0.241679	+	0.0186612i
$708$		0			0
$709$	26.7407	+	15.4388i	1.00427	+	0.579815i	0.909509	−	0.415685i	$-0.136458\pi$
$709$	26.7407	+	15.4388i	1.00427	+	0.579815i	0.0947608	+	0.995500i	$0.469791\pi$
$710$	−20.5919	−	13.5267i	−0.772800	−	0.507647i
$711$		0			0
$712$	0.481990	+	0.481990i	0.0180634	+	0.0180634i
$713$	−8.40356	−	31.3625i	−0.314716	−	1.17454i
$714$		0			0
$715$	2.17442	−	37.7042i	0.0813188	−	1.41006i
$716$	−1.91180	−	3.31134i	−0.0714473	−	0.123750i
$717$		0			0
$718$	30.6870	−	8.22255i	1.14523	−	0.306863i
$719$	17.2432			0.643061			0.321531	−	0.946899i	$-0.395803\pi$
$719$	17.2432			0.643061			0.321531	+	0.946899i	$0.395803\pi$
$720$		0			0
$721$	12.4181	−	4.37684i	0.462475	−	0.163002i
$722$	−12.8293	−	47.8795i	−0.477456	−	1.78189i
$723$		0			0
$724$	2.16139	+	3.74363i	0.0803274	+	0.139131i
$725$	16.8330	−	22.6646i	0.625163	−	0.841744i
$726$		0			0
$727$	−2.52439	+	0.676408i	−0.0936244	+	0.0250866i	−0.305327	−	0.952248i	$-0.598766\pi$
$727$	−2.52439	+	0.676408i	−0.0936244	+	0.0250866i	0.211703	+	0.977334i	$0.432099\pi$
$728$	35.1120	+	16.8113i	1.30134	+	0.623068i
$729$		0			0
$730$	−16.7878	+	3.47640i	−0.621344	+	0.128667i
$731$	−3.93817	−	2.27370i	−0.145658	−	0.0840959i
$732$		0			0
$733$	−16.1897	−	4.33803i	−0.597982	−	0.160229i	−0.0528833	−	0.998601i	$-0.516841\pi$
$733$	−16.1897	−	4.33803i	−0.597982	−	0.160229i	−0.545099	+	0.838372i	$0.683508\pi$
$734$	12.5038	+	21.6572i	0.461524	+	0.799384i
$735$		0			0
$736$	4.01051	−	6.94641i	0.147829	−	0.256048i
$737$	−7.12044	+	7.12044i	−0.262285	+	0.262285i
$738$		0			0
$739$		−	19.4170i		−	0.714265i	−0.934054	−	0.357132i	$-0.883754\pi$
$739$		−	19.4170i		−	0.714265i	0.934054	−	0.357132i	$-0.116246\pi$
$740$	0.837258	+	1.66475i	0.0307782	+	0.0611973i
$741$		0			0
$742$	−2.96046	−	38.3405i	−0.108682	−	1.40752i
$743$	8.47189	−	31.6175i	0.310804	−	1.15993i	−0.617030	−	0.786940i	$-0.711664\pi$
$743$	8.47189	−	31.6175i	0.310804	−	1.15993i	0.927833	−	0.372995i	$-0.121669\pi$
$744$		0			0
$745$	13.0465	−	39.4476i	0.477988	−	1.44525i
$746$	2.12497			0.0778005
$747$		0			0
$748$	−0.797509	+	0.797509i	−0.0291598	+	0.0291598i
$749$	1.62375	−	8.68929i	0.0593305	−	0.317500i
$750$		0			0
$751$	−1.68889	−	2.92525i	−0.0616286	−	0.106744i	0.833565	−	0.552422i	$-0.186296\pi$
$751$	−1.68889	−	2.92525i	−0.0616286	−	0.106744i	−0.895194	+	0.445678i	$0.852963\pi$
$752$	7.00769	−	26.1531i	0.255544	−	0.953704i
$753$		0			0
$754$	−23.7733	+	41.1766i	−0.865772	+	1.49956i
$755$	7.02005	+	33.9004i	0.255486	+	1.23376i
$756$		0			0
$757$	−17.8925	+	17.8925i	−0.650313	+	0.650313i	−0.953068	−	0.302755i	$-0.902093\pi$
$757$	−17.8925	+	17.8925i	−0.650313	+	0.650313i	0.302755	+	0.953068i	$0.402093\pi$
$758$	18.5434	−	4.96870i	0.673528	−	0.180471i
$759$		0			0
$760$	42.2278	+	2.43530i	1.53176	+	0.0883375i
$761$	−9.86040	+	5.69290i	−0.357439	+	0.206368i	−0.667957	−	0.744200i	$-0.732831\pi$
$761$	−9.86040	+	5.69290i	−0.357439	+	0.206368i	0.310518	+	0.950568i	$0.399498\pi$
$762$		0			0
$763$	29.6835	+	43.3269i	1.07462	+	1.56854i
$764$			2.69766i			0.0975980i
$765$		0			0
$766$		−	4.62096i		−	0.166962i
$767$	6.94118	+	25.9049i	0.250632	+	0.935370i
$768$		0			0
$769$	24.3209	+	42.1251i	0.877035	+	1.51907i	0.854579	+	0.519322i	$0.173815\pi$
$769$	24.3209	+	42.1251i	0.877035	+	1.51907i	0.0224562	+	0.999748i	$0.492851\pi$
$770$	12.9124	−	23.4050i	0.465330	−	0.843456i
$771$		0			0
$772$	1.28402	+	4.79202i	0.0462128	+	0.172468i
$773$	30.6490	−	30.6490i	1.10237	−	1.10237i	0.108245	−	0.994124i	$-0.465477\pi$
$773$	30.6490	−	30.6490i	1.10237	−	1.10237i	0.994124	−	0.108245i	$-0.0345230\pi$
$774$		0			0
$775$	−11.4226	−	26.3976i	−0.410311	−	0.948230i
$776$	−29.1483	−	16.8288i	−1.04636	−	0.604117i
$777$		0			0
$778$	0.957525	−	3.57353i	0.0343289	−	0.128117i
$779$	−22.0357	+	12.7223i	−0.789511	+	0.455825i
$780$		0			0
$781$	−11.0498	+	19.1388i	−0.395393	+	0.684841i
$782$	8.88192	+	8.88192i	0.317617	+	0.317617i
$783$		0			0
$784$	19.4944	+	24.2196i	0.696228	+	0.864985i
$785$	8.37498	+	16.6522i	0.298916	+	0.594344i
$786$		0			0
$787$	−11.8340	+	44.1650i	−0.421835	+	1.57431i	0.348903	+	0.937159i	$0.386554\pi$
$787$	−11.8340	+	44.1650i	−0.421835	+	1.57431i	−0.770738	+	0.637152i	$0.780112\pi$
$788$	0.586288	−	2.18806i	0.0208856	−	0.0779463i
$789$		0			0
$790$	15.1376	+	30.0987i	0.538573	+	1.07086i
$791$	−12.2511	−	34.7591i	−0.435597	−	1.23589i
$792$		0			0
$793$	23.3763	+	23.3763i	0.830116	+	0.830116i
$794$	22.5384	−	39.0377i	0.799859	−	1.38540i
$795$		0			0
$796$	4.52351	−	2.61165i	0.160332	−	0.0925675i
$797$	3.10125	−	11.5740i	0.109852	−	0.409972i	−0.888999	−	0.457910i	$-0.848598\pi$
$797$	3.10125	−	11.5740i	0.109852	−	0.409972i	0.998850	+	0.0479376i	$0.0152649\pi$
$798$		0			0
$799$	7.82797	+	4.51948i	0.276934	+	0.159888i
$800$	2.61587	−	6.60651i	0.0924848	−	0.233575i
$801$		0			0
$802$	−1.40934	+	1.40934i	−0.0497656	+	0.0497656i
$803$	3.98014	+	14.8541i	0.140456	+	0.524189i
$804$		0			0
$805$	−29.2373	−	16.1301i	−1.03048	−	0.568510i
$806$	24.2206	+	41.9512i	0.853133	+	1.47767i
$807$		0			0
$808$	1.65352	+	6.17103i	0.0581708	+	0.217096i
$809$			37.0882i			1.30395i	0.758240	+	0.651976i	$0.226060\pi$
$809$			37.0882i			1.30395i	−0.758240	+	0.651976i	$0.773940\pi$
$810$		0			0
$811$			7.45819i			0.261892i	0.991389	+	0.130946i	$0.0418015\pi$
$811$			7.45819i			0.261892i	−0.991389	+	0.130946i	$0.958198\pi$
$812$	−3.11393	+	2.13337i	−0.109277	+	0.0748668i
$813$		0			0
$814$	12.9056	−	7.45103i	0.452340	−	0.261159i
$815$	18.4409	+	1.06350i	0.645957	+	0.0372527i
$816$		0			0
$817$	−21.3672	+	5.72533i	−0.747545	+	0.200304i
$818$	4.45784	−	4.45784i	0.155865	−	0.155865i
$819$		0			0
$820$	0.404153	+	1.95169i	0.0141136	+	0.0681558i
$821$	−16.8906	+	29.2554i	−0.589486	+	1.02102i	0.404814	+	0.914399i	$0.367336\pi$
$821$	−16.8906	+	29.2554i	−0.589486	+	1.02102i	−0.994300	+	0.106621i	$0.965997\pi$
$822$		0			0
$823$	−12.1231	+	45.2440i	−0.422585	+	1.57711i	0.346556	+	0.938029i	$0.387351\pi$
$823$	−12.1231	+	45.2440i	−0.422585	+	1.57711i	−0.769141	+	0.639079i	$0.779316\pi$
$824$	−6.52569	−	11.3028i	−0.227333	−	0.393753i
$825$		0			0
$826$	−3.48671	+	18.6587i	−0.121318	+	0.649218i
$827$	−5.53246	+	5.53246i	−0.192383	+	0.192383i	−0.796725	−	0.604342i	$-0.793436\pi$
$827$	−5.53246	+	5.53246i	−0.192383	+	0.192383i	0.604342	+	0.796725i	$0.293436\pi$
$828$		0			0
$829$	11.3905			0.395609			0.197805	−	0.980241i	$-0.436619\pi$
$829$	11.3905			0.395609			0.197805	+	0.980241i	$0.436619\pi$
$830$	0.609955	−	1.84427i	0.0211718	−	0.0640154i
$831$		0			0
$832$	9.80181	−	36.5808i	0.339816	−	1.26821i
$833$	−9.49439	+	4.19360i	−0.328961	+	0.145299i
$834$		0			0
$835$	−5.92061	−	11.7721i	−0.204891	−	0.407392i
$836$			5.48645i			0.189753i
$837$		0			0
$838$	20.3956	−	20.3956i	0.704553	−	0.704553i
$839$	−5.35271	+	9.27116i	−0.184796	+	0.320076i	−0.943508	−	0.331351i	$-0.892496\pi$
$839$	−5.35271	+	9.27116i	−0.184796	+	0.320076i	0.758712	+	0.651426i	$0.225829\pi$
$840$		0			0
$841$	1.44074	+	2.49543i	0.0496805	+	0.0860492i
$842$	−23.0458	−	6.17510i	−0.794210	−	0.212808i
$843$		0			0
$844$	1.75106	+	1.01098i	0.0602740	+	0.0347992i
$845$	40.4590	−	8.37819i	1.39183	−	0.288219i
$846$		0			0
$847$	4.62343	+	2.21365i	0.158863	+	0.0760621i
$848$	−41.5455	+	11.1321i	−1.42668	+	0.382278i
$849$		0			0
$850$	8.93302	+	6.63455i	0.306400	+	0.227563i
$851$	−9.30777	−	16.1215i	−0.319066	−	0.552639i
$852$		0			0
$853$	−14.1658	−	52.8674i	−0.485027	−	1.81015i	−0.579940	−	0.814660i	$-0.696924\pi$
$853$	−14.1658	−	52.8674i	−0.485027	−	1.81015i	0.0949126	−	0.995486i	$-0.469743\pi$
$854$	7.77796	+	22.0679i	0.266156	+	0.755147i
$855$		0			0
$856$	−8.76218			−0.299485
$857$	−11.1987	+	3.00069i	−0.382542	+	0.102502i	−0.444965	−	0.895548i	$-0.646784\pi$
$857$	−11.1987	+	3.00069i	−0.382542	+	0.102502i	0.0624231	+	0.998050i	$0.480117\pi$
$858$		0			0
$859$	−1.72732	−	2.99181i	−0.0589355	−	0.102079i	0.835052	−	0.550171i	$-0.185437\pi$
$859$	−1.72732	−	2.99181i	−0.0589355	−	0.102079i	−0.893988	+	0.448091i	$0.852104\pi$
$860$	−0.0997626	+	1.72987i	−0.00340188	+	0.0589882i
$861$		0			0
$862$	5.12618	+	19.1312i	0.174598	+	0.651610i
$863$	−13.6278	−	13.6278i	−0.463897	−	0.463897i	0.436034	−	0.899930i	$-0.356383\pi$
$863$	−13.6278	−	13.6278i	−0.463897	−	0.463897i	−0.899930	+	0.436034i	$0.856383\pi$
$864$		0			0
$865$	−2.50367	−	1.64464i	−0.0851274	−	0.0559196i
$866$	−17.6157	−	10.1704i	−0.598605	−	0.345605i
$867$		0			0
$868$	0.296060	+	3.83423i	0.0100489	+	0.130142i
$869$	26.1718	−	15.1103i	0.887819	−	0.512583i
$870$		0			0
$871$	−16.2528	−	9.38358i	−0.550706	−	0.317950i
$872$	36.8114	−	36.8114i	1.24659	−	1.24659i
$873$		0			0
$874$	61.1030			2.06684
$875$	−27.7096	−	10.3528i	−0.936754	−	0.349987i
$876$		0			0
$877$	−9.57755	−	2.56630i	−0.323411	−	0.0866577i	0.0934610	−	0.995623i	$-0.470207\pi$
$877$	−9.57755	−	2.56630i	−0.323411	−	0.0866577i	−0.416872	+	0.908965i	$0.636874\pi$
$878$	43.5026	+	11.6565i	1.46814	+	0.393388i
$879$		0			0
$880$	−28.3857	−	9.38800i	−0.956880	−	0.316469i
$881$			6.90193i			0.232532i	0.993218	+	0.116266i	$0.0370925\pi$
$881$			6.90193i			0.232532i	−0.993218	+	0.116266i	$0.962907\pi$
$882$		0			0
$883$	9.91036	+	9.91036i	0.333510	+	0.333510i	0.853918	−	0.520408i	$-0.174220\pi$
$883$	9.91036	+	9.91036i	0.333510	+	0.333510i	−0.520408	+	0.853918i	$0.674220\pi$
$884$	−1.82036	−	1.05099i	−0.0612254	−	0.0353485i
$885$		0			0
$886$	25.4735	+	44.1214i	0.855798	+	1.48229i
$887$	−7.28938	+	27.2043i	−0.244753	+	0.913432i	0.728754	+	0.684776i	$0.240100\pi$
$887$	−7.28938	+	27.2043i	−0.244753	+	0.913432i	−0.973507	+	0.228656i	$0.926567\pi$
$888$		0			0
$889$	2.68467	−	14.3667i	0.0900410	−	0.481843i
$890$	0.729066	+	0.478918i	0.0244384	+	0.0160534i
$891$		0			0
$892$	−1.32630	−	1.32630i	−0.0444079	−	0.0444079i
$893$	42.4721	−	11.3804i	1.42127	−	0.380829i
$894$		0			0
$895$	22.5096	+	25.2648i	0.752414	+	0.844509i
$896$	22.3303	−	26.0674i	0.746004	−	0.870850i
$897$		0			0
$898$	−8.75956	+	2.34712i	−0.292310	+	0.0783243i
$899$	32.4813			1.08331
$900$		0			0
$901$		−	14.3589i		−	0.478364i
$902$	15.3958	−	4.12531i	0.512626	−	0.137358i
$903$		0			0
$904$	−31.6373	+	18.2658i	−1.05224	+	0.607512i
$905$	−25.4483	−	28.5631i	−0.845929	−	0.949471i
$906$		0			0
$907$	−14.5908	−	54.4535i	−0.484479	−	1.80810i	−0.582396	−	0.812905i	$-0.697885\pi$
$907$	−14.5908	−	54.4535i	−0.484479	−	1.80810i	0.0979168	−	0.995195i	$-0.468782\pi$
$908$	−1.68853	+	1.68853i	−0.0560359	+	0.0560359i
$909$		0			0
$910$	48.3620	+	11.9552i	1.60318	+	0.396311i
$911$	−3.23617	+	5.60520i	−0.107219	+	0.185709i	−0.914643	−	0.404263i	$-0.867528\pi$
$911$	−3.23617	+	5.60520i	−0.107219	+	0.185709i	0.807424	+	0.589972i	$0.200861\pi$
$912$		0			0
$913$	−1.68306	−	0.450974i	−0.0557011	−	0.0149251i
$914$	28.7259	−	16.5849i	0.950169	−	0.548580i
$915$		0			0
$916$	1.29621	+	0.748364i	0.0428278	+	0.0247267i
$917$	−0.310512	+	0.648535i	−0.0102540	+	0.0214165i
$918$		0			0
$919$			21.4278i			0.706839i	0.935465	+	0.353420i	$0.114981\pi$
$919$			21.4278i			0.706839i	−0.935465	+	0.353420i	$0.885019\pi$
$920$	−10.3931	+	31.4247i	−0.342650	+	1.03604i
$921$		0			0
$922$	2.86317	−	10.6855i	0.0942935	−	0.351908i
$923$	−39.7836	−	10.6600i	−1.30949	−	0.350878i
$924$		0			0
$925$	−10.2430	−	12.9240i	−0.336787	−	0.424938i
$926$	−24.6683			−0.810649
$927$		0			0
$928$	5.67389	+	5.67389i	0.186255	+	0.186255i
$929$	8.45190	−	14.6391i	0.277298	−	0.480294i	−0.693415	−	0.720539i	$-0.743894\pi$
$929$	8.45190	−	14.6391i	0.277298	−	0.480294i	0.970712	+	0.240245i	$0.0772278\pi$
$930$		0			0
$931$	−18.2334	+	47.0831i	−0.597574	+	1.54309i
$932$	2.39385	+	0.641430i	0.0784132	+	0.0210107i
$933$		0			0
$934$	−6.32612	+	10.9572i	−0.206997	+	0.358530i
$935$	5.47996	−	8.34224i	0.179214	−	0.272820i
$936$		0			0
$937$	−7.14404	−	7.14404i	−0.233386	−	0.233386i	0.580719	−	0.814104i	$-0.302772\pi$
$937$	−7.14404	−	7.14404i	−0.233386	−	0.233386i	−0.814104	+	0.580719i	$0.802772\pi$
$938$	−7.50737	−	10.9579i	−0.245124	−	0.357790i
$939$		0			0
$940$	0.198300	−	3.43850i	0.00646784	−	0.112152i
$941$	−40.8266	+	23.5713i	−1.33091	+	0.768401i	−0.985439	−	0.170028i	$-0.945614\pi$
$941$	−40.8266	+	23.5713i	−1.33091	+	0.768401i	−0.345471	+	0.938430i	$0.612281\pi$
$942$		0			0
$943$	−5.15330	−	19.2324i	−0.167815	−	0.626292i
$944$	21.2308			0.691003
$945$		0			0
$946$	13.8570			0.450528
$947$	−7.77368	−	29.0118i	−0.252611	−	0.942755i	−0.969404	−	0.245470i	$-0.921058\pi$
$947$	−7.77368	−	29.0118i	−0.252611	−	0.942755i	0.716794	−	0.697285i	$-0.245609\pi$
$948$		0			0
$949$	−24.8204	+	14.3301i	−0.805705	+	0.465174i
$950$	53.5484	−	7.90616i	1.73734	−	0.256510i
$951$		0			0
$952$	5.81480	+	8.48743i	0.188459	+	0.275079i
$953$	0.938800	+	0.938800i	0.0304107	+	0.0304107i	0.722149	−	0.691738i	$-0.243155\pi$
$953$	0.938800	+	0.938800i	0.0304107	+	0.0304107i	−0.691738	+	0.722149i	$0.743155\pi$
$954$		0			0
$955$	−4.84099	−	23.3775i	−0.156651	−	0.756479i
$956$	1.76050	−	3.04928i	0.0569388	−	0.0986209i
$957$		0			0
$958$	55.6371	+	14.9079i	1.79755	+	0.481653i
$959$	10.6073	+	9.08663i	0.342527	+	0.293423i
$960$		0			0
$961$	1.04618	−	1.81204i	0.0337478	−	0.0584530i
$962$	19.6385	+	19.6385i	0.633170	+	0.633170i
$963$		0			0
$964$	−3.23273			−0.104119
$965$	−19.7264	−	39.2227i	−0.635017	−	1.26262i
$966$		0			0
$967$	−15.7040	−	4.20788i	−0.505007	−	0.135316i	−0.00268441	−	0.999996i	$-0.500854\pi$
$967$	−15.7040	−	4.20788i	−0.505007	−	0.135316i	−0.502323	+	0.864680i	$0.667521\pi$
$968$	1.31508	−	4.90796i	0.0422684	−	0.157748i
$969$		0			0
$970$	−40.8933	−	13.5246i	−1.31300	−	0.434250i
$971$			37.3169i			1.19755i	0.800915	+	0.598777i	$0.204347\pi$
$971$			37.3169i			1.19755i	−0.800915	+	0.598777i	$0.795653\pi$
$972$		0			0
$973$	32.8689	+	15.7373i	1.05373	+	0.504515i
$974$	12.8376	+	7.41177i	0.411342	+	0.237488i
$975$		0			0
$976$	22.6647	−	13.0855i	0.725479	−	0.418855i
$977$	−43.8114	−	11.7392i	−1.40165	−	0.375572i	−0.522714	−	0.852508i	$-0.675081\pi$
$977$	−43.8114	−	11.7392i	−1.40165	−	0.375572i	−0.878938	+	0.476936i	$0.841747\pi$
$978$		0			0
$979$	0.391223	−	0.677619i	0.0125036	−	0.0216568i
$980$	3.05304	+	2.51405i	0.0975259	+	0.0803083i
$981$		0			0
$982$	−39.6310	+	39.6310i	−1.26468	+	1.26468i
$983$	4.82947	+	18.0238i	0.154036	+	0.574871i	0.999186	+	0.0403415i	$0.0128446\pi$
$983$	4.82947	+	18.0238i	0.154036	+	0.574871i	−0.845150	+	0.534530i	$0.820489\pi$
$984$		0			0
$985$	−1.15419	+	20.0135i	−0.0367755	+	0.637682i
$986$	−10.8822	+	6.28287i	−0.346561	+	0.200087i
$987$		0			0
$988$	−9.87670	+	2.64645i	−0.314220	+	0.0841949i
$989$		−	17.3100i		−	0.550426i
$990$		0			0
$991$	11.6129			0.368897			0.184449	−	0.982842i	$-0.440950\pi$
$991$	11.6129			0.368897			0.184449	+	0.982842i	$0.440950\pi$
$992$	7.89650	−	2.11586i	0.250714	−	0.0671786i
$993$		0			0
$994$	−22.1388	−	18.9650i	−0.702200	−	0.601532i
$995$	−34.5134	+	30.7497i	−1.09415	+	0.974830i
$996$		0			0
$997$	5.48047	−	1.46849i	0.173568	−	0.0465074i	−0.170988	−	0.985273i	$-0.554696\pi$
$997$	5.48047	−	1.46849i	0.173568	−	0.0465074i	0.344556	+	0.938766i	$0.388029\pi$
$998$	−15.7780	−	15.7780i	−0.499443	−	0.499443i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.ce.a.748.14		176
3.2	odd	2		315.2.cb.a.223.32	yes	176
5.2	odd	4	inner	945.2.ce.a.937.32		176
7.6	odd	2	inner	945.2.ce.a.748.13		176
9.4	even	3	inner	945.2.ce.a.118.31		176
9.5	odd	6		315.2.cb.a.13.13	✓	176
15.2	even	4		315.2.cb.a.97.14	yes	176
21.20	even	2		315.2.cb.a.223.31	yes	176
35.27	even	4	inner	945.2.ce.a.937.31		176
45.22	odd	12	inner	945.2.ce.a.307.13		176
45.32	even	12		315.2.cb.a.202.31	yes	176
63.13	odd	6	inner	945.2.ce.a.118.32		176
63.41	even	6		315.2.cb.a.13.14	yes	176
105.62	odd	4		315.2.cb.a.97.13	yes	176
315.167	odd	12		315.2.cb.a.202.32	yes	176
315.202	even	12	inner	945.2.ce.a.307.14		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cb.a.13.13	✓	176	9.5	odd	6
315.2.cb.a.13.14	yes	176	63.41	even	6
315.2.cb.a.97.13	yes	176	105.62	odd	4
315.2.cb.a.97.14	yes	176	15.2	even	4
315.2.cb.a.202.31	yes	176	45.32	even	12
315.2.cb.a.202.32	yes	176	315.167	odd	12
315.2.cb.a.223.31	yes	176	21.20	even	2
315.2.cb.a.223.32	yes	176	3.2	odd	2
945.2.ce.a.118.31		176	9.4	even	3	inner
945.2.ce.a.118.32		176	63.13	odd	6	inner
945.2.ce.a.307.13		176	45.22	odd	12	inner
945.2.ce.a.307.14		176	315.202	even	12	inner
945.2.ce.a.748.13		176	7.6	odd	2	inner
945.2.ce.a.748.14		176	1.1	even	1	trivial
945.2.ce.a.937.31		176	35.27	even	4	inner
945.2.ce.a.937.32		176	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.ce (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.388459 - 1.44975i) q^{2} +(-0.218820 + 0.126336i) q^{4} +(1.66955 - 1.48748i) q^{5} +(2.18265 - 1.49535i) q^{7} +(-1.85442 - 1.85442i) q^{8} +O(q^{10})\)	\(q+(-0.388459 - 1.44975i) q^{2} +(-0.218820 + 0.126336i) q^{4} +(1.66955 - 1.48748i) q^{5} +(2.18265 - 1.49535i) q^{7} +(-1.85442 - 1.85442i) q^{8} +(-2.80503 - 1.84260i) q^{10} +(-1.50520 + 2.60709i) q^{11} +(-5.41932 - 1.45210i) q^{13} +(-3.01574 - 2.58341i) q^{14} +(-2.22075 + 3.84645i) q^{16} +(-1.04847 - 1.04847i) q^{17} -7.21291 q^{19} +(-0.177409 + 0.536415i) q^{20} +(4.36433 + 1.16942i) q^{22} +(1.46083 - 5.45189i) q^{23} +(0.574793 - 4.96685i) q^{25} +8.42074i q^{26} +(-0.288691 + 0.602958i) q^{28} +(4.88990 + 2.82318i) q^{29} +(4.98189 - 2.87630i) q^{31} +(1.37268 + 0.367810i) q^{32} +(-1.11273 + 1.92730i) q^{34} +(1.41973 - 5.74320i) q^{35} +(2.33216 - 2.33216i) q^{37} +(2.80192 + 10.4569i) q^{38} +(-5.85447 - 0.337630i) q^{40} +(3.05504 - 1.76383i) q^{41} +(2.96236 - 0.793762i) q^{43} -0.760643i q^{44} -8.47134 q^{46} +(-5.88834 + 1.57778i) q^{47} +(2.52788 - 6.52762i) q^{49} +(-7.42397 + 1.09611i) q^{50} +(1.36931 - 0.366905i) q^{52} +(6.84756 + 6.84756i) q^{53} +(1.36499 + 6.59162i) q^{55} +(-6.82055 - 1.27454i) q^{56} +(2.19338 - 8.18581i) q^{58} +(-2.39004 - 4.13968i) q^{59} +(-5.10293 - 2.94618i) q^{61} +(-6.10517 - 6.10517i) q^{62} +6.75007i q^{64} +(-11.2078 + 5.63679i) q^{65} +(3.23103 + 0.865752i) q^{67} +(0.361884 + 0.0969666i) q^{68} +(-8.87771 + 0.172741i) q^{70} +7.34107 q^{71} +(3.61212 - 3.61212i) q^{73} +(-4.28699 - 2.47509i) q^{74} +(1.57833 - 0.911248i) q^{76} +(0.613175 + 7.94114i) q^{77} +(-8.69380 - 5.01937i) q^{79} +(2.01388 + 9.72517i) q^{80} +(-3.74386 - 3.74386i) q^{82} +(0.149805 + 0.559080i) q^{83} +(-3.31004 - 0.190892i) q^{85} +(-2.30151 - 3.98633i) q^{86} +(7.62592 - 2.04336i) q^{88} -0.259914 q^{89} +(-13.9999 + 4.93434i) q^{91} +(0.369110 + 1.37754i) q^{92} +(4.57476 + 7.92371i) q^{94} +(-12.0423 + 10.7291i) q^{95} +(12.3966 - 3.32166i) q^{97} +(-10.4454 - 1.12908i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8}+O(q^{10}) \) 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8	\( 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8} + 12 q^{11} + 56 q^{16} + 12 q^{22} + 12 q^{23} - 4 q^{25} - 32 q^{28} - 48 q^{32} + 8 q^{35} - 16 q^{37} - 4 q^{43} - 80 q^{46} + 76 q^{50} - 64 q^{53} + 52 q^{56} - 44 q^{58} - 20 q^{65} - 4 q^{67} + 18 q^{70} + 64 q^{71} - 26 q^{77} - 4 q^{85} - 80 q^{86} - 60 q^{88} - 16 q^{91} + 68 q^{92} - 40 q^{95} + 120 q^{98}+O(q^{100}) \) 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8 + 12 * q^11 + 56 * q^16 + 12 * q^22 + 12 * q^23 - 4 * q^25 - 32 * q^28 - 48 * q^32 + 8 * q^35 - 16 * q^37 - 4 * q^43 - 80 * q^46 + 76 * q^50 - 64 * q^53 + 52 * q^56 - 44 * q^58 - 20 * q^65 - 4 * q^67 + 18 * q^70 + 64 * q^71 - 26 * q^77 - 4 * q^85 - 80 * q^86 - 60 * q^88 - 16 * q^91 + 68 * q^92 - 40 * q^95 + 120 * q^98

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