LMFDB - Embedded newform 630.2.bv.b.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(73,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("630.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.1
Root			$-1.09227 - 0.838128i$ of defining polynomial
Character	$\chi$	$=$	630.577
Dual form			630.2.bv.b.523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-2.14315 - 0.637899i) q^{5} +(0.153213 - 2.64131i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-2.14315 - 0.637899i) q^{5} +(0.153213 - 2.64131i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.17085 - 1.90502i) q^{10} +(-2.27722 + 3.94427i) q^{11} +(1.77772 + 1.77772i) q^{13} +(2.51166 + 0.831614i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.06747 + 3.98386i) q^{17} +(1.88956 + 3.27281i) q^{19} +(1.53707 + 1.62401i) q^{20} +(-3.22048 - 3.22048i) q^{22} +(7.77857 + 2.08426i) q^{23} +(4.18617 + 2.73423i) q^{25} +(-2.17725 + 1.25704i) q^{26} +(-1.45334 + 2.21084i) q^{28} -1.55563i q^{29} +(3.37208 + 1.94687i) q^{31} +(-0.965926 + 0.258819i) q^{32} -4.12440 q^{34} +(-2.01325 + 5.56299i) q^{35} +(-2.95980 + 11.0461i) q^{37} +(-3.65035 + 0.978107i) q^{38} +(-1.96650 + 1.06437i) q^{40} -11.3796i q^{41} +(0.367260 - 0.367260i) q^{43} +(3.94427 - 2.27722i) q^{44} +(-4.02648 + 6.97408i) q^{46} +(-4.87829 - 1.30713i) q^{47} +(-6.95305 - 0.809365i) q^{49} +(-3.72452 + 3.33586i) q^{50} +(-0.650691 - 2.42841i) q^{52} +(2.18307 + 8.14732i) q^{53} +(7.39647 - 7.00051i) q^{55} +(-1.75935 - 1.97603i) q^{56} +(1.50262 + 0.402626i) q^{58} +(0.221511 - 0.383668i) q^{59} +(7.09442 - 4.09597i) q^{61} +(-2.75329 + 2.75329i) q^{62} -1.00000i q^{64} +(-2.67591 - 4.94392i) q^{65} +(-8.99808 + 2.41103i) q^{67} +(1.06747 - 3.98386i) q^{68} +(-4.85237 - 3.38446i) q^{70} +6.68403 q^{71} +(-4.20080 + 1.12560i) q^{73} +(-9.90370 - 5.71790i) q^{74} -3.77912i q^{76} +(10.0691 + 6.61917i) q^{77} +(-4.08283 + 2.35722i) q^{79} +(-0.519137 - 2.17497i) q^{80} +(10.9919 + 2.94527i) q^{82} +(3.21718 + 3.21718i) q^{83} +(0.253550 - 9.21894i) q^{85} +(0.259692 + 0.449799i) q^{86} +(1.17878 + 4.39926i) q^{88} +(-3.02425 - 5.23816i) q^{89} +(4.96788 - 4.42314i) q^{91} +(-5.69431 - 5.69431i) q^{92} +(2.52519 - 4.37376i) q^{94} +(-1.96188 - 8.21947i) q^{95} +(0.462652 - 0.462652i) q^{97} +(2.58137 - 6.50665i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 4 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 4 * q^7	$ 16 q - 12 q^{5} - 4 q^{7} + 4 q^{10} - 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} - 8 q^{20} + 4 q^{22} + 40 q^{23} + 16 q^{25} + 12 q^{26} - 4 q^{28} - 24 q^{31} - 16 q^{34} + 44 q^{35} - 8 q^{37} + 20 q^{38} - 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{52} + 28 q^{53} + 56 q^{55} - 8 q^{56} - 12 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} - 16 q^{65} - 84 q^{67} - 12 q^{68} + 4 q^{70} + 32 q^{71} + 16 q^{73} - 24 q^{74} - 44 q^{77} - 12 q^{79} - 12 q^{80} + 36 q^{82} - 16 q^{83} + 8 q^{85} + 8 q^{86} - 4 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 8 q^{94} - 72 q^{95} - 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q - 12 * q^5 - 4 * q^7 + 4 * q^10 - 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 - 8 * q^20 + 4 * q^22 + 40 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^31 - 16 * q^34 + 44 * q^35 - 8 * q^37 + 20 * q^38 - 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^52 + 28 * q^53 + 56 * q^55 - 8 * q^56 - 12 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 - 16 * q^65 - 84 * q^67 - 12 * q^68 + 4 * q^70 + 32 * q^71 + 16 * q^73 - 24 * q^74 - 44 * q^77 - 12 * q^79 - 12 * q^80 + 36 * q^82 - 16 * q^83 + 8 * q^85 + 8 * q^86 - 4 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 8 * q^94 - 72 * q^95 - 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.14315	−	0.637899i	−0.958445	−	0.285277i
$5$	−2.14315	−	0.637899i	−0.958445	−	0.285277i
$6$		0			0
$7$	0.153213	−	2.64131i	0.0579090	−	0.998322i
$7$	0.153213	−	2.64131i	0.0579090	−	0.998322i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	1.17085	−	1.90502i	0.370256	−	0.602421i
$11$	−2.27722	+	3.94427i	−0.686609	+	1.18924i	0.286319	+	0.958134i	$0.407568\pi$
$11$	−2.27722	+	3.94427i	−0.686609	+	1.18924i	−0.972928	+	0.231107i	$0.925765\pi$
$12$		0			0
$13$	1.77772	+	1.77772i	0.493051	+	0.493051i	0.909266	−	0.416215i	$-0.136644\pi$
$13$	1.77772	+	1.77772i	0.493051	+	0.493051i	−0.416215	+	0.909266i	$0.636644\pi$
$14$	2.51166	+	0.831614i	0.671268	+	0.222258i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.06747	+	3.98386i	0.258900	+	0.966228i	0.965879	+	0.258993i	$0.0833908\pi$
$17$	1.06747	+	3.98386i	0.258900	+	0.966228i	−0.706979	+	0.707234i	$0.749943\pi$
$18$		0			0
$19$	1.88956	+	3.27281i	0.433494	+	0.750834i	0.997171	−	0.0751610i	$-0.0239471\pi$
$19$	1.88956	+	3.27281i	0.433494	+	0.750834i	−0.563677	+	0.825995i	$0.690614\pi$
$20$	1.53707	+	1.62401i	0.343700	+	0.363140i
$21$		0			0
$22$	−3.22048	−	3.22048i	−0.686609	−	0.686609i
$23$	7.77857	+	2.08426i	1.62194	+	0.434599i	0.951572	−	0.307426i	$-0.0994677\pi$
$23$	7.77857	+	2.08426i	1.62194	+	0.434599i	0.670372	+	0.742025i	$0.266134\pi$
$24$		0			0
$25$	4.18617	+	2.73423i	0.837234	+	0.546845i
$26$	−2.17725	+	1.25704i	−0.426995	+	0.246525i
$27$		0			0
$28$	−1.45334	+	2.21084i	−0.274656	+	0.417809i
$29$		−	1.55563i		−	0.288873i	−0.989514	−	0.144436i	$-0.953863\pi$
$29$		−	1.55563i		−	0.288873i	0.989514	−	0.144436i	$-0.0461369\pi$
$30$		0			0
$31$	3.37208	+	1.94687i	0.605643	+	0.349668i	0.771258	−	0.636522i	$-0.219628\pi$
$31$	3.37208	+	1.94687i	0.605643	+	0.349668i	−0.165615	+	0.986190i	$0.552961\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−4.12440			−0.707328
$35$	−2.01325	+	5.56299i	−0.340301	+	0.940317i
$36$		0			0
$37$	−2.95980	+	11.0461i	−0.486589	+	1.81597i	0.0862078	+	0.996277i	$0.472525\pi$
$37$	−2.95980	+	11.0461i	−0.486589	+	1.81597i	−0.572797	+	0.819697i	$0.694142\pi$
$38$	−3.65035	+	0.978107i	−0.592164	+	0.158670i
$39$		0			0
$40$	−1.96650	+	1.06437i	−0.310931	+	0.168292i
$41$		−	11.3796i		−	1.77720i	−0.458682	−	0.888600i	$-0.651678\pi$
$41$		−	11.3796i		−	1.77720i	0.458682	−	0.888600i	$-0.348322\pi$
$42$		0			0
$43$	0.367260	−	0.367260i	0.0560066	−	0.0560066i	−0.678549	−	0.734555i	$-0.737391\pi$
$43$	0.367260	−	0.367260i	0.0560066	−	0.0560066i	0.734555	+	0.678549i	$0.237391\pi$
$44$	3.94427	−	2.27722i	0.594621	−	0.343304i
$45$		0			0
$46$	−4.02648	+	6.97408i	−0.593673	+	1.02827i
$47$	−4.87829	−	1.30713i	−0.711572	−	0.190665i	−0.115164	−	0.993347i	$-0.536739\pi$
$47$	−4.87829	−	1.30713i	−0.711572	−	0.190665i	−0.596408	+	0.802681i	$0.703406\pi$
$48$		0			0
$49$	−6.95305	−	0.809365i	−0.993293	−	0.115624i
$50$	−3.72452	+	3.33586i	−0.526727	+	0.471762i
$51$		0			0
$52$	−0.650691	−	2.42841i	−0.0902346	−	0.336760i
$53$	2.18307	+	8.14732i	0.299868	+	1.11912i	0.937274	+	0.348593i	$0.113341\pi$
$53$	2.18307	+	8.14732i	0.299868	+	1.11912i	−0.637407	+	0.770528i	$0.719993\pi$
$54$		0			0
$55$	7.39647	−	7.00051i	0.997340	−	0.943949i
$56$	−1.75935	−	1.97603i	−0.235103	−	0.264058i
$57$		0			0
$58$	1.50262	+	0.402626i	0.197304	+	0.0528674i
$59$	0.221511	−	0.383668i	0.0288383	−	0.0499493i	−0.851246	−	0.524767i	$-0.824153\pi$
$59$	0.221511	−	0.383668i	0.0288383	−	0.0499493i	0.880084	+	0.474817i	$0.157486\pi$
$60$		0			0
$61$	7.09442	−	4.09597i	0.908348	−	0.524435i	0.0284488	−	0.999595i	$-0.490943\pi$
$61$	7.09442	−	4.09597i	0.908348	−	0.524435i	0.879899	+	0.475160i	$0.157610\pi$
$62$	−2.75329	+	2.75329i	−0.349668	+	0.349668i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.67591	−	4.94392i	−0.331906	−	0.613218i
$66$		0			0
$67$	−8.99808	+	2.41103i	−1.09929	+	0.294554i	−0.762476	−	0.647017i	$-0.776016\pi$
$67$	−8.99808	+	2.41103i	−1.09929	+	0.294554i	−0.336815	+	0.941571i	$0.609350\pi$
$68$	1.06747	−	3.98386i	0.129450	−	0.483114i
$69$		0			0
$70$	−4.85237	−	3.38446i	−0.579969	−	0.404520i
$71$	6.68403			0.793248			0.396624	−	0.917981i	$-0.370182\pi$
$71$	6.68403			0.793248			0.396624	+	0.917981i	$0.370182\pi$
$72$		0			0
$73$	−4.20080	+	1.12560i	−0.491666	+	0.131742i	−0.496130	−	0.868249i	$-0.665246\pi$
$73$	−4.20080	+	1.12560i	−0.491666	+	0.131742i	0.00446349	+	0.999990i	$0.498579\pi$
$74$	−9.90370	−	5.71790i	−1.15128	−	0.664693i
$75$		0			0
$76$		−	3.77912i		−	0.433494i
$77$	10.0691	+	6.61917i	1.14748	+	0.754324i
$78$		0			0
$79$	−4.08283	+	2.35722i	−0.459354	+	0.265208i	−0.711773	−	0.702410i	$-0.752107\pi$
$79$	−4.08283	+	2.35722i	−0.459354	+	0.265208i	0.252418	+	0.967618i	$0.418774\pi$
$80$	−0.519137	−	2.17497i	−0.0580413	−	0.243169i
$81$		0			0
$82$	10.9919	+	2.94527i	1.21385	+	0.325250i
$83$	3.21718	+	3.21718i	0.353131	+	0.353131i	0.861273	−	0.508142i	$-0.169668\pi$
$83$	3.21718	+	3.21718i	0.353131	+	0.353131i	−0.508142	+	0.861273i	$0.669668\pi$
$84$		0			0
$85$	0.253550	−	9.21894i	0.0275014	−	0.999935i
$86$	0.259692	+	0.449799i	0.0280033	+	0.0485031i
$87$		0			0
$88$	1.17878	+	4.39926i	0.125658	+	0.468963i
$89$	−3.02425	−	5.23816i	−0.320570	−	0.555244i	0.660035	−	0.751234i	$-0.270541\pi$
$89$	−3.02425	−	5.23816i	−0.320570	−	0.555244i	−0.980606	+	0.195990i	$0.937208\pi$
$90$		0			0
$91$	4.96788	−	4.42314i	0.520775	−	0.463671i
$92$	−5.69431	−	5.69431i	−0.593673	−	0.593673i
$93$		0			0
$94$	2.52519	−	4.37376i	0.260453	−	0.451118i
$95$	−1.96188	−	8.21947i	−0.201285	−	0.843299i
$96$		0			0
$97$	0.462652	−	0.462652i	0.0469752	−	0.0469752i	−0.683229	−	0.730204i	$-0.739425\pi$
$97$	0.462652	−	0.462652i	0.0469752	−	0.0469752i	0.730204	+	0.683229i	$0.239425\pi$
$98$	2.58137	−	6.50665i	0.260758	−	0.657271i
$99$		0			0
$100$	−2.25822	−	4.46099i	−0.225822	−	0.446099i
$101$	4.85151	+	2.80102i	0.482743	+	0.278712i	0.721559	−	0.692353i	$-0.243426\pi$
$101$	4.85151	+	2.80102i	0.482743	+	0.278712i	−0.238816	+	0.971065i	$0.576759\pi$
$102$		0			0
$103$	−1.43852	+	5.36863i	−0.141742	+	0.528987i	0.858137	+	0.513420i	$0.171622\pi$
$103$	−1.43852	+	5.36863i	−0.141742	+	0.528987i	−0.999879	+	0.0155666i	$0.995045\pi$
$104$	2.51408			0.246525
$105$		0			0
$106$	−8.43473			−0.819253
$107$	−1.93865	+	7.23514i	−0.187416	+	0.699447i	0.806684	+	0.590983i	$0.201260\pi$
$107$	−1.93865	+	7.23514i	−0.187416	+	0.699447i	−0.994100	+	0.108464i	$0.965407\pi$
$108$		0			0
$109$	1.27034	+	0.733433i	0.121677	+	0.0702501i	0.559603	−	0.828761i	$-0.310954\pi$
$109$	1.27034	+	0.733433i	0.121677	+	0.0702501i	−0.437926	+	0.899011i	$0.644287\pi$
$110$	4.84763	+	8.95631i	0.462203	+	0.853951i
$111$		0			0
$112$	2.36405	−	1.18797i	0.223382	−	0.112253i
$113$	−7.08834	+	7.08834i	−0.666815	+	0.666815i	−0.956977	−	0.290163i	$-0.906291\pi$
$113$	−7.08834	+	7.08834i	−0.666815	+	0.666815i	0.290163	+	0.956977i	$0.406291\pi$
$114$		0			0
$115$	−15.3411	−	9.42883i	−1.43056	−	0.879243i
$116$	−0.777814	+	1.34721i	−0.0722182	+	0.125086i
$117$		0			0
$118$	0.313264	+	0.313264i	0.0288383	+	0.0288383i
$119$	10.6862	−	2.20915i	0.979599	−	0.202512i
$120$		0			0
$121$	−4.87150	−	8.43768i	−0.442863	−	0.767062i
$122$	2.12023	+	7.91280i	0.191957	+	0.716391i
$123$		0			0
$124$	−1.94687	−	3.37208i	−0.174834	−	0.302821i
$125$	−7.22742	−	8.53020i	−0.646440	−	0.762965i
$126$		0			0
$127$	12.9176	+	12.9176i	1.14625	+	1.14625i	0.987283	+	0.158971i	$0.0508176\pi$
$127$	12.9176	+	12.9176i	1.14625	+	1.14625i	0.158971	+	0.987283i	$0.449182\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	5.46804	−	1.30515i	0.479579	−	0.114469i
$131$	−0.323655	+	0.186862i	−0.0282779	+	0.0163262i	−0.514072	−	0.857747i	$-0.671864\pi$
$131$	−0.323655	+	0.186862i	−0.0282779	+	0.0163262i	0.485794	+	0.874073i	$0.338530\pi$
$132$		0			0
$133$	8.93402	−	4.48947i	0.774677	−	0.389287i
$134$		−	9.31550i		−	0.804737i
$135$		0			0
$136$	3.57183	+	2.06220i	0.306282	+	0.176832i
$137$	−2.56800	+	0.688094i	−0.219399	+	0.0587878i	−0.366844	−	0.930282i	$-0.619562\pi$
$137$	−2.56800	+	0.688094i	−0.219399	+	0.0587878i	0.147445	+	0.989070i	$0.452895\pi$
$138$		0			0
$139$	4.58070			0.388530			0.194265	−	0.980949i	$-0.437768\pi$
$139$	4.58070			0.388530			0.194265	+	0.980949i	$0.437768\pi$
$140$	4.52502	−	3.81106i	0.382434	−	0.322094i
$141$		0			0
$142$	−1.72995	+	6.45627i	−0.145174	+	0.541798i
$143$	−11.0601	+	2.96354i	−0.924889	+	0.247823i
$144$		0			0
$145$	−0.992333	+	3.33394i	−0.0824088	+	0.276869i
$146$		−	4.34898i		−	0.359925i
$147$		0			0
$148$	8.08634	−	8.08634i	0.664693	−	0.664693i
$149$	−14.9338	+	8.62203i	−1.22342	+	0.706344i	−0.965646	−	0.259860i	$-0.916324\pi$
$149$	−14.9338	+	8.62203i	−1.22342	+	0.706344i	−0.257778	+	0.966204i	$0.582990\pi$
$150$		0			0
$151$	2.78385	−	4.82177i	0.226546	−	0.392390i	−0.730236	−	0.683195i	$-0.760590\pi$
$151$	2.78385	−	4.82177i	0.226546	−	0.392390i	0.956782	+	0.290805i	$0.0939231\pi$
$152$	3.65035	+	0.978107i	0.296082	+	0.0793350i
$153$		0			0
$154$	−8.99971	+	8.01287i	−0.725217	+	0.645696i
$155$	−5.98495	−	6.32347i	−0.480723	−	0.507914i
$156$		0			0
$157$	−1.06916	−	3.99014i	−0.0853279	−	0.318448i	0.910048	−	0.414503i	$-0.136044\pi$
$157$	−1.06916	−	3.99014i	−0.0853279	−	0.318448i	−0.995376	+	0.0960544i	$0.969378\pi$
$158$	−1.22019	−	4.55381i	−0.0970730	−	0.362281i
$159$		0			0
$160$	2.23522	+	0.0614757i	0.176710	+	0.00486008i
$161$	6.69696	−	20.2263i	0.527795	−	1.59406i
$162$		0			0
$163$	20.9982	+	5.62644i	1.64470	+	0.440697i	0.958123	−	0.286357i	$-0.0924445\pi$
$163$	20.9982	+	5.62644i	1.64470	+	0.440697i	0.686580	+	0.727054i	$0.259111\pi$
$164$	−5.68982	+	9.85506i	−0.444300	+	0.769551i
$165$		0			0
$166$	−3.94022	+	2.27489i	−0.305821	+	0.176566i
$167$	17.4949	−	17.4949i	1.35380	−	1.35380i	0.472425	−	0.881371i	$-0.343379\pi$
$167$	17.4949	−	17.4949i	1.35380	−	1.35380i	0.881371	−	0.472425i	$-0.156621\pi$
$168$		0			0
$169$		−	6.67942i		−	0.513802i
$170$	8.83919	+	2.63095i	0.677935	+	0.201785i
$171$		0			0
$172$	−0.501686	+	0.134426i	−0.0382532	+	0.0102499i
$173$	4.28763	−	16.0017i	0.325982	−	1.21658i	−0.587338	−	0.809342i	$-0.699824\pi$
$173$	4.28763	−	16.0017i	0.325982	−	1.21658i	0.913321	−	0.407241i	$-0.133509\pi$
$174$		0			0
$175$	7.86331	−	10.6381i	0.594411	−	0.804162i
$176$	−4.55445			−0.343304
$177$		0			0
$178$	5.84241	−	1.56547i	0.437907	−	0.117337i
$179$	11.0222	+	6.36367i	0.823837	+	0.475643i	0.851738	−	0.523968i	$-0.175549\pi$
$179$	11.0222	+	6.36367i	0.823837	+	0.475643i	−0.0279007	+	0.999611i	$0.508882\pi$
$180$		0			0
$181$		−	9.09951i		−	0.676361i	−0.941081	−	0.338180i	$-0.890189\pi$
$181$		−	9.09951i		−	0.676361i	0.941081	−	0.338180i	$-0.109811\pi$
$182$	2.98665	+	5.94340i	0.221385	+	0.440554i
$183$		0			0
$184$	6.97408	−	4.02648i	0.514136	−	0.296836i
$185$	13.3896	−	21.7855i	0.984425	−	1.60170i
$186$		0			0
$187$	−18.1443	−	4.86175i	−1.32684	−	0.355526i
$188$	3.57116	+	3.57116i	0.260453	+	0.260453i
$189$		0			0
$190$	8.44717	+	0.232324i	0.612822	+	0.0168545i
$191$	9.10308	+	15.7670i	0.658676	+	1.14086i	0.980959	+	0.194216i	$0.0622164\pi$
$191$	9.10308	+	15.7670i	0.658676	+	1.14086i	−0.322283	+	0.946643i	$0.604450\pi$
$192$		0			0
$193$	−2.60664	−	9.72810i	−0.187630	−	0.700244i	−0.994052	−	0.108904i	$-0.965266\pi$
$193$	−2.60664	−	9.72810i	−0.187630	−	0.700244i	0.806422	−	0.591340i	$-0.201401\pi$
$194$	0.327144	+	0.566631i	0.0234876	+	0.0406817i
$195$		0			0
$196$	5.61684	+	4.17746i	0.401203	+	0.298390i
$197$	−16.2439	−	16.2439i	−1.15733	−	1.15733i	−0.985048	−	0.172283i	$-0.944886\pi$
$197$	−16.2439	−	16.2439i	−1.15733	−	1.15733i	−0.172283	−	0.985048i	$-0.555114\pi$
$198$		0			0
$199$	−12.6984	+	21.9943i	−0.900168	+	1.55914i	−0.0728933	+	0.997340i	$0.523223\pi$
$199$	−12.6984	+	21.9943i	−0.900168	+	1.55914i	−0.827275	+	0.561797i	$0.810110\pi$
$200$	4.89346	−	1.02668i	0.346020	−	0.0725972i
$201$		0			0
$202$	−3.96124	+	3.96124i	−0.278712	+	0.278712i
$203$	−4.10890	−	0.238342i	−0.288388	−	0.0167283i
$204$		0			0
$205$	−7.25906	+	24.3883i	−0.506995	+	1.70335i
$206$	−4.81338	−	2.77901i	−0.335364	−	0.193623i
$207$		0			0
$208$	−0.650691	+	2.42841i	−0.0451173	+	0.168380i
$209$	−17.2118			−1.19056
$210$		0			0
$211$	−13.6182			−0.937517			−0.468759	−	0.883326i	$-0.655299\pi$
$211$	−13.6182			−0.937517			−0.468759	+	0.883326i	$0.655299\pi$
$212$	2.18307	−	8.14732i	0.149934	−	0.559560i
$213$		0			0
$214$	−6.48684	−	3.74518i	−0.443432	−	0.256015i
$215$	−1.02137	+	0.552817i	−0.0696566	+	0.0377018i
$216$		0			0
$217$	5.65893	−	8.60842i	0.384153	−	0.584378i
$218$	−1.03723	+	1.03723i	−0.0702501	+	0.0702501i
$219$		0			0
$220$	−9.90579	+	2.36438i	−0.667848	+	0.159407i
$221$	−5.18452	+	8.97985i	−0.348749	+	0.604050i
$222$		0			0
$223$	15.8412	+	15.8412i	1.06081	+	1.06081i	0.998027	+	0.0627803i	$0.0199968\pi$
$223$	15.8412	+	15.8412i	1.06081	+	1.06081i	0.0627803	+	0.998027i	$0.480003\pi$
$224$	0.535629	+	2.59097i	0.0357883	+	0.173116i
$225$		0			0
$226$	−5.01221	−	8.68141i	−0.333407	−	0.577479i
$227$	2.83476	+	10.5795i	0.188150	+	0.702184i	0.993934	+	0.109976i	$0.0350772\pi$
$227$	2.83476	+	10.5795i	0.188150	+	0.702184i	−0.805785	+	0.592209i	$0.798256\pi$
$228$		0			0
$229$	−14.4722	−	25.0665i	−0.956347	−	1.65644i	−0.731255	−	0.682104i	$-0.761065\pi$
$229$	−14.4722	−	25.0665i	−0.956347	−	1.65644i	−0.225092	−	0.974338i	$-0.572268\pi$
$230$	13.0781	−	12.3780i	0.862345	−	0.816180i
$231$		0			0
$232$	−1.09999	−	1.09999i	−0.0722182	−	0.0722182i
$233$	1.36397	+	0.365476i	0.0893569	+	0.0239431i	0.303220	−	0.952920i	$-0.401938\pi$
$233$	1.36397	+	0.365476i	0.0893569	+	0.0239431i	−0.213864	+	0.976864i	$0.568605\pi$
$234$		0			0
$235$	9.62108	+	5.91324i	0.627610	+	0.385737i
$236$	−0.383668	+	0.221511i	−0.0249747	+	0.0144191i
$237$		0			0
$238$	−0.631910	+	10.8938i	−0.0409606	+	0.706141i
$239$		−	4.36430i		−	0.282303i	−0.989988	−	0.141152i	$-0.954920\pi$
$239$		−	4.36430i		−	0.282303i	0.989988	−	0.141152i	$-0.0450805\pi$
$240$		0			0
$241$	−2.65862	−	1.53496i	−0.171257	−	0.0988752i	0.411922	−	0.911219i	$-0.364858\pi$
$241$	−2.65862	−	1.53496i	−0.171257	−	0.0988752i	−0.583178	+	0.812344i	$0.698191\pi$
$242$	9.41101	−	2.52167i	0.604963	−	0.162099i
$243$		0			0
$244$	−8.19194			−0.524435
$245$	14.3851	+	6.16994i	0.919032	+	0.394183i
$246$		0			0
$247$	−2.45904	+	9.17725i	−0.156465	+	0.583934i
$248$	3.76106	−	1.00777i	0.238828	−	0.0639937i
$249$		0			0
$250$	10.1101	−	4.77337i	0.639421	−	0.301895i
$251$		−	1.25355i		−	0.0791234i	−0.999217	−	0.0395617i	$-0.987404\pi$
$251$		−	1.25355i		−	0.0791234i	0.999217	−	0.0395617i	$-0.0125962\pi$
$252$		0			0
$253$	−25.9344	+	25.9344i	−1.63048	+	1.63048i
$254$	−15.8208	+	9.13414i	−0.992685	+	0.573127i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.81783	−	1.82683i	−0.425285	−	0.113955i	0.0398273	−	0.999207i	$-0.487319\pi$
$257$	−6.81783	−	1.82683i	−0.425285	−	0.113955i	−0.465112	+	0.885252i	$0.653986\pi$
$258$		0			0
$259$	28.7228	+	9.51018i	1.78475	+	0.590934i
$260$	−0.154555	+	5.61952i	−0.00958507	+	0.348508i
$261$		0			0
$262$	−0.0967271	−	0.360990i	−0.00597582	−	0.0223021i
$263$	1.47214	+	5.49409i	0.0907758	+	0.338780i	0.996345	−	0.0854182i	$-0.0272226\pi$
$263$	1.47214	+	5.49409i	0.0907758	+	0.338780i	−0.905569	+	0.424198i	$0.860556\pi$
$264$		0			0
$265$	0.518531	−	18.8535i	0.0318531	−	1.15816i
$266$	2.02421	+	9.79156i	0.124112	+	0.600359i
$267$		0			0
$268$	8.99808	+	2.41103i	0.549645	+	0.147277i
$269$	−3.85391	+	6.67517i	−0.234977	+	0.406992i	−0.959266	−	0.282504i	$-0.908835\pi$
$269$	−3.85391	+	6.67517i	−0.234977	+	0.406992i	0.724289	+	0.689496i	$0.242168\pi$
$270$		0			0
$271$	−15.4900	+	8.94316i	−0.940951	+	0.543258i	−0.890258	−	0.455456i	$-0.849476\pi$
$271$	−15.4900	+	8.94316i	−0.940951	+	0.543258i	−0.0506925	+	0.998714i	$0.516143\pi$
$272$	−2.91639	+	2.91639i	−0.176832	+	0.176832i
$273$		0			0
$274$		−	2.65859i		−	0.160611i
$275$	−20.3174	+	10.2849i	−1.22518	+	0.620205i
$276$		0			0
$277$	−14.2439	+	3.81664i	−0.855832	+	0.229319i	−0.659951	−	0.751308i	$-0.729423\pi$
$277$	−14.2439	+	3.81664i	−0.855832	+	0.229319i	−0.195881	+	0.980628i	$0.562756\pi$
$278$	−1.18557	+	4.42461i	−0.0711059	+	0.265371i
$279$		0			0
$280$	2.51004	+	5.35721i	0.150004	+	0.320154i
$281$	−0.587402			−0.0350415			−0.0175207	−	0.999847i	$-0.505577\pi$
$281$	−0.587402			−0.0350415			−0.0175207	+	0.999847i	$0.505577\pi$
$282$		0			0
$283$	17.9809	−	4.81795i	1.06885	−	0.286398i	0.318830	−	0.947812i	$-0.396710\pi$
$283$	17.9809	−	4.81795i	1.06885	−	0.286398i	0.750021	+	0.661414i	$0.230043\pi$
$284$	−5.78854	−	3.34201i	−0.343486	−	0.198312i
$285$		0			0
$286$		−	11.4502i		−	0.677066i
$287$	−30.0572	−	1.74351i	−1.77422	−	0.102916i
$288$		0			0
$289$	−0.00921092	+	0.00531793i	−0.000541819	+	0.000312819i
$290$	−2.96350	−	1.82141i	−0.174023	−	0.106957i
$291$		0			0
$292$	4.20080	+	1.12560i	0.245833	+	0.0658708i
$293$	20.6736	+	20.6736i	1.20777	+	1.20777i	0.971749	+	0.236018i	$0.0758423\pi$
$293$	20.6736	+	20.6736i	1.20777	+	1.20777i	0.236018	+	0.971749i	$0.424158\pi$
$294$		0			0
$295$	−0.719472	+	0.680956i	−0.0418893	+	0.0396468i
$296$	5.71790	+	9.90370i	0.332346	+	0.575641i
$297$		0			0
$298$	−4.46309	−	16.6565i	−0.258540	−	0.964884i
$299$	10.1229	+	17.5334i	0.585422	+	1.01398i
$300$		0			0
$301$	−0.913778	−	1.02632i	−0.0526693	−	0.0591559i
$302$	3.93696	+	3.93696i	0.226546	+	0.226546i
$303$		0			0
$304$	−1.88956	+	3.27281i	−0.108374	+	0.187709i
$305$	−17.8172	+	4.25274i	−1.02021	+	0.243511i
$306$		0			0
$307$	−1.63464	+	1.63464i	−0.0932937	+	0.0932937i	−0.752213	−	0.658920i	$-0.771014\pi$
$307$	−1.63464	+	1.63464i	−0.0932937	+	0.0932937i	0.658920	+	0.752213i	$0.271014\pi$
$308$	−5.41055	−	10.7669i	−0.308294	−	0.613503i
$309$		0			0
$310$	7.65703	−	4.14439i	0.434890	−	0.235385i
$311$	−12.0239	−	6.94197i	−0.681810	−	0.393643i	0.118727	−	0.992927i	$-0.462119\pi$
$311$	−12.0239	−	6.94197i	−0.681810	−	0.393643i	−0.800537	+	0.599284i	$0.795452\pi$
$312$		0			0
$313$	3.49157	−	13.0307i	0.197355	−	0.736540i	−0.794289	−	0.607540i	$-0.792157\pi$
$313$	3.49157	−	13.0307i	0.197355	−	0.736540i	0.991645	−	0.129000i	$-0.0411768\pi$
$314$	4.13090			0.233120
$315$		0			0
$316$	4.71445			0.265208
$317$	−3.55024	+	13.2497i	−0.199401	+	0.744175i	0.791682	+	0.610933i	$0.209206\pi$
$317$	−3.55024	+	13.2497i	−0.199401	+	0.744175i	−0.991083	+	0.133242i	$0.957461\pi$
$318$		0			0
$319$	6.13581	+	3.54251i	0.343539	+	0.198343i
$320$	−0.637899	+	2.14315i	−0.0356596	+	0.119806i
$321$		0			0
$322$	17.8038	+	11.7037i	0.992167	+	0.652223i
$323$	−11.0214	+	11.0214i	−0.613245	+	0.613245i
$324$		0			0
$325$	2.58115	+	12.3025i	0.143176	+	0.682421i
$326$	−10.8694	+	18.8264i	−0.602003	+	1.04270i
$327$		0			0
$328$	−8.04662	−	8.04662i	−0.444300	−	0.444300i
$329$	−4.19996	+	12.6848i	−0.231552	+	0.699336i
$330$		0			0
$331$	−16.6194	−	28.7856i	−0.913483	−	1.58220i	−0.809108	−	0.587660i	$-0.800049\pi$
$331$	−16.6194	−	28.7856i	−0.913483	−	1.58220i	−0.104375	−	0.994538i	$-0.533284\pi$
$332$	−1.17757	−	4.39475i	−0.0646275	−	0.241193i
$333$		0			0
$334$	12.3708	+	21.4268i	0.676898	+	1.17242i
$335$	20.8222	+	0.572677i	1.13764	+	0.0312887i
$336$		0			0
$337$	−17.0329	−	17.0329i	−0.927842	−	0.927842i	0.0697246	−	0.997566i	$-0.477788\pi$
$337$	−17.0329	−	17.0329i	−0.927842	−	0.927842i	−0.997566	+	0.0697246i	$0.977788\pi$
$338$	6.45183	+	1.72876i	0.350933	+	0.0940323i
$339$		0			0
$340$	−4.82905	+	7.85706i	−0.261892	+	0.426109i
$341$	−15.3579	+	8.86691i	−0.831679	+	0.480170i
$342$		0			0
$343$	−3.20308	+	18.2412i	−0.172950	+	0.984931i
$344$		−	0.519384i		−	0.0280033i
$345$		0			0
$346$	14.3467	+	8.28306i	0.771283	+	0.445300i
$347$	1.98700	−	0.532414i	0.106668	−	0.0285815i	−0.205090	−	0.978743i	$-0.565749\pi$
$347$	1.98700	−	0.532414i	0.106668	−	0.0285815i	0.311758	+	0.950162i	$0.399082\pi$
$348$		0			0
$349$	−11.7250			−0.627627			−0.313814	−	0.949485i	$-0.601607\pi$
$349$	−11.7250			−0.627627			−0.313814	+	0.949485i	$0.601607\pi$
$350$	8.24040	+	10.3487i	0.440468	+	0.553162i
$351$		0			0
$352$	1.17878	−	4.39926i	0.0628291	−	0.234481i
$353$	11.0334	−	2.95640i	0.587250	−	0.157353i	0.0470542	−	0.998892i	$-0.485017\pi$
$353$	11.0334	−	2.95640i	0.587250	−	0.157353i	0.540196	+	0.841539i	$0.318350\pi$
$354$		0			0
$355$	−14.3249	−	4.26373i	−0.760285	−	0.226296i
$356$			6.04851i			0.320570i
$357$		0			0
$358$	−8.99958	+	8.99958i	−0.475643	+	0.475643i
$359$	−2.08846	+	1.20577i	−0.110225	+	0.0636383i	−0.554099	−	0.832451i	$-0.686937\pi$
$359$	−2.08846	+	1.20577i	−0.110225	+	0.0636383i	0.443874	+	0.896089i	$0.353604\pi$
$360$		0			0
$361$	2.35914	−	4.08615i	0.124165	−	0.215061i
$362$	8.78945	+	2.35513i	0.461963	+	0.123783i
$363$		0			0
$364$	−6.51388	+	1.34661i	−0.341420	+	0.0705817i
$365$	9.72095	+	0.267357i	0.508818	+	0.0139941i
$366$		0			0
$367$	1.34815	+	5.03135i	0.0703727	+	0.262635i	0.992144	−	0.125099i	$-0.0399248\pi$
$367$	1.34815	+	5.03135i	0.0703727	+	0.262635i	−0.921772	+	0.387733i	$0.873258\pi$
$368$	2.08426	+	7.77857i	0.108650	+	0.405486i
$369$		0			0
$370$	17.5777	+	18.5719i	0.913819	+	0.965506i
$371$	21.8541	−	4.51789i	1.13461	−	0.234557i
$372$		0			0
$373$	0.141659	+	0.0379573i	0.00733480	+	0.00196535i	0.262485	−	0.964936i	$-0.415458\pi$
$373$	0.141659	+	0.0379573i	0.00733480	+	0.00196535i	−0.255150	+	0.966902i	$0.582125\pi$
$374$	9.39217	−	16.2677i	0.485658	−	0.841184i
$375$		0			0
$376$	−4.37376	+	2.52519i	−0.225559	+	0.130227i
$377$	2.76547	−	2.76547i	0.142429	−	0.142429i
$378$		0			0
$379$		−	18.5438i		−	0.952530i	−0.879302	−	0.476265i	$-0.841990\pi$
$379$		−	18.5438i		−	0.952530i	0.879302	−	0.476265i	$-0.158010\pi$
$380$	−2.41069	+	8.09921i	−0.123666	+	0.415481i
$381$		0			0
$382$	−17.5858	+	4.71210i	−0.899768	+	0.241092i
$383$	0.996351	−	3.71843i	0.0509112	−	0.190003i	−0.935787	−	0.352566i	$-0.885309\pi$
$383$	0.996351	−	3.71843i	0.0509112	−	0.190003i	0.986698	+	0.162563i	$0.0519760\pi$
$384$		0			0
$385$	−17.3573	−	20.6090i	−0.884610	−	1.05033i
$386$	10.0713			0.512614
$387$		0			0
$388$	−0.631994	+	0.169342i	−0.0320847	+	0.00859706i
$389$	15.4340	+	8.91085i	0.782537	+	0.451798i	0.837329	−	0.546700i	$-0.184116\pi$
$389$	15.4340	+	8.91085i	0.782537	+	0.451798i	−0.0547917	+	0.998498i	$0.517449\pi$
$390$		0			0
$391$			33.2136i			1.67969i
$392$	−5.48886	+	4.34424i	−0.277229	+	0.219417i
$393$		0			0
$394$	19.8946	−	11.4862i	1.00228	−	0.578665i
$395$	10.2538	−	2.44745i	0.515924	−	0.123144i
$396$		0			0
$397$	24.7725	+	6.63778i	1.24330	+	0.333141i	0.819744	−	0.572730i	$-0.194116\pi$
$397$	24.7725	+	6.63778i	1.24330	+	0.333141i	0.423554	+	0.905871i	$0.360782\pi$
$398$	−17.9583	−	17.9583i	−0.900168	−	0.900168i
$399$		0			0
$400$	−0.274824	+	4.99244i	−0.0137412	+	0.249622i
$401$	−2.63060	−	4.55632i	−0.131366	−	0.227532i	0.792838	−	0.609433i	$-0.208603\pi$
$401$	−2.63060	−	4.55632i	−0.131366	−	0.227532i	−0.924203	+	0.381901i	$0.875270\pi$
$402$		0			0
$403$	2.53362	+	9.45560i	0.126209	+	0.471017i
$404$	−2.80102	−	4.85151i	−0.139356	−	0.241371i
$405$		0			0
$406$	1.29368	−	3.90720i	0.0642043	−	0.193911i
$407$	−36.8288	−	36.8288i	−1.82554	−	1.82554i
$408$		0			0
$409$	−4.18773	+	7.25336i	−0.207070	+	0.358655i	−0.950790	−	0.309835i	$-0.899726\pi$
$409$	−4.18773	+	7.25336i	−0.207070	+	0.358655i	0.743720	+	0.668491i	$0.233059\pi$
$410$	−21.6785	−	13.3239i	−1.07062	−	0.658018i
$411$		0			0
$412$	3.93011	−	3.93011i	0.193623	−	0.193623i
$413$	−0.979449	−	0.643862i	−0.0481955	−	0.0316824i
$414$		0			0
$415$	−4.84265	−	8.94712i	−0.237717	−	0.439197i
$416$	−2.17725	−	1.25704i	−0.106749	−	0.0616313i
$417$		0			0
$418$	4.45474	−	16.6253i	0.217888	−	0.813170i
$419$	9.53078			0.465609			0.232805	−	0.972524i	$-0.425210\pi$
$419$	9.53078			0.465609			0.232805	+	0.972524i	$0.425210\pi$
$420$		0			0
$421$	16.8461			0.821027			0.410514	−	0.911854i	$-0.365349\pi$
$421$	16.8461			0.821027			0.410514	+	0.911854i	$0.365349\pi$
$422$	3.52466	−	13.1542i	0.171578	−	0.640336i
$423$		0			0
$424$	7.30469	+	4.21737i	0.354747	+	0.204813i
$425$	−6.42415	+	19.5958i	−0.311617	+	0.950537i
$426$		0			0
$427$	−9.73177	−	19.3661i	−0.470953	−	0.937193i
$428$	5.29649	−	5.29649i	0.256015	−	0.256015i
$429$		0			0
$430$	−0.269631	−	1.12964i	−0.0130028	−	0.0544763i
$431$	10.7791	−	18.6699i	0.519209	−	0.899297i	−0.480541	−	0.876972i	$-0.659560\pi$
$431$	10.7791	−	18.6699i	0.519209	−	0.899297i	0.999751	−	0.0223251i	$-0.00710689\pi$
$432$		0			0
$433$	−25.8823	−	25.8823i	−1.24382	−	1.24382i	−0.958402	−	0.285422i	$-0.907866\pi$
$433$	−25.8823	−	25.8823i	−1.24382	−	1.24382i	−0.285422	−	0.958402i	$-0.592134\pi$
$434$	6.85045	+	7.69413i	0.328832	+	0.369330i
$435$		0			0
$436$	−0.733433	−	1.27034i	−0.0351251	−	0.0608384i
$437$	7.87667	+	29.3961i	0.376792	+	1.40621i
$438$		0			0
$439$	−10.5899	−	18.3422i	−0.505426	−	0.875424i	−0.999980	−	0.00627716i	$-0.998002\pi$
$439$	−10.5899	−	18.3422i	−0.505426	−	0.875424i	0.494554	−	0.869147i	$-0.335331\pi$
$440$	0.279988	−	10.1802i	0.0133479	−	0.485322i
$441$		0			0
$442$	−7.33202	−	7.33202i	−0.348749	−	0.348749i
$443$	−4.00895	−	1.07420i	−0.190471	−	0.0510366i	0.162322	−	0.986738i	$-0.448102\pi$
$443$	−4.00895	−	1.07420i	−0.190471	−	0.0510366i	−0.352794	+	0.935701i	$0.614768\pi$
$444$		0			0
$445$	3.14001	+	13.1553i	0.148851	+	0.623622i
$446$	−19.4015	+	11.2014i	−0.918686	+	0.530404i
$447$		0			0
$448$	−2.64131	−	0.153213i	−0.124790	−	0.00723862i
$449$			29.3795i			1.38651i	0.720694	+	0.693253i	$0.243823\pi$
$449$			29.3795i			1.38651i	−0.720694	+	0.693253i	$0.756177\pi$
$450$		0			0
$451$	44.8843	+	25.9140i	2.11352	+	1.22024i
$452$	9.68285	−	2.59451i	0.455443	−	0.122036i
$453$		0			0
$454$	−10.9527			−0.514035
$455$	−13.4684	+	6.31044i	−0.631410	+	0.295838i
$456$		0			0
$457$	−0.121995	+	0.455291i	−0.00570668	+	0.0212976i	−0.968720	−	0.248155i	$-0.920176\pi$
$457$	−0.121995	+	0.455291i	−0.00570668	+	0.0212976i	0.963014	+	0.269452i	$0.0868426\pi$
$458$	27.9581	−	7.49134i	1.30639	−	0.350047i
$459$		0			0
$460$	8.57135	+	15.8361i	0.399641	+	0.738364i
$461$		−	26.3199i		−	1.22584i	−0.790145	−	0.612920i	$-0.789995\pi$
$461$		−	26.3199i		−	1.22584i	0.790145	−	0.612920i	$-0.210005\pi$
$462$		0			0
$463$	−1.02619	+	1.02619i	−0.0476909	+	0.0476909i	−0.730550	−	0.682859i	$-0.760736\pi$
$463$	−1.02619	+	1.02619i	−0.0476909	+	0.0476909i	0.682859	+	0.730550i	$0.260736\pi$
$464$	1.34721	−	0.777814i	0.0625428	−	0.0361091i
$465$		0			0
$466$	−0.706045	+	1.22291i	−0.0327069	+	0.0566500i
$467$	29.9569	+	8.02693i	1.38624	+	0.371442i	0.873384	−	0.487033i	$-0.161921\pi$
$467$	29.9569	+	8.02693i	1.38624	+	0.371442i	0.512856	+	0.858475i	$0.328587\pi$
$468$		0			0
$469$	4.98966	+	24.1361i	0.230401	+	1.11450i
$470$	−8.20187	+	7.76279i	−0.378324	+	0.358071i
$471$		0			0
$472$	−0.114663	−	0.427926i	−0.00527777	−	0.0196969i
$473$	0.612238	+	2.28490i	0.0281507	+	0.105060i
$474$		0			0
$475$	−1.03859	+	18.8670i	−0.0476538	+	0.865678i
$476$	−10.3591	−	3.42990i	−0.474807	−	0.157209i
$477$		0			0
$478$	4.21559	+	1.12956i	0.192817	+	0.0516650i
$479$	16.6760	−	28.8837i	0.761945	−	1.31973i	−0.179901	−	0.983685i	$-0.557578\pi$
$479$	16.6760	−	28.8837i	0.761945	−	1.31973i	0.941847	−	0.336043i	$-0.109089\pi$
$480$		0			0
$481$	−24.8987	+	14.3752i	−1.13528	+	0.655455i
$482$	2.17075	−	2.17075i	0.0988752	−	0.0988752i
$483$		0			0
$484$			9.74299i			0.442863i
$485$	−1.28666	+	0.696407i	−0.0584241	+	0.0316222i
$486$		0			0
$487$	3.19111	−	0.855056i	0.144603	−	0.0387463i	−0.185791	−	0.982589i	$-0.559485\pi$
$487$	3.19111	−	0.855056i	0.144603	−	0.0387463i	0.330395	+	0.943843i	$0.392818\pi$
$488$	2.12023	−	7.91280i	0.0959783	−	0.358196i
$489$		0			0
$490$	−9.68285	+	12.2981i	−0.437426	+	0.555570i
$491$	−3.61649			−0.163210			−0.0816051	−	0.996665i	$-0.526005\pi$
$491$	−3.61649			−0.163210			−0.0816051	+	0.996665i	$0.526005\pi$
$492$		0			0
$493$	6.19740	−	1.66059i	0.279117	−	0.0747891i
$494$	−8.22809	−	4.75049i	−0.370199	−	0.213735i
$495$		0			0
$496$			3.89374i			0.174834i
$497$	1.02408	−	17.6546i	0.0459362	−	0.791917i
$498$		0			0
$499$	0.561004	−	0.323896i	0.0251140	−	0.0144996i	−0.487390	−	0.873184i	$-0.662051\pi$
$499$	0.561004	−	0.323896i	0.0251140	−	0.0144996i	0.512504	+	0.858685i	$0.328718\pi$
$500$	1.99403	+	11.0011i	0.0891757	+	0.491983i
$501$		0			0
$502$	1.21084	+	0.324443i	0.0540423	+	0.0144806i
$503$	−12.9189	−	12.9189i	−0.576027	−	0.576027i	0.357779	−	0.933806i	$-0.383534\pi$
$503$	−12.9189	−	12.9189i	−0.576027	−	0.576027i	−0.933806	+	0.357779i	$0.883534\pi$
$504$		0			0
$505$	−8.61073	−	9.09777i	−0.383172	−	0.404845i
$506$	−18.3384	−	31.7631i	−0.815242	−	1.41204i
$507$		0			0
$508$	−4.72818	−	17.6458i	−0.209779	−	0.782906i
$509$	−10.1554	−	17.5896i	−0.450128	−	0.779645i	0.548265	−	0.836304i	$-0.315288\pi$
$509$	−10.1554	−	17.5896i	−0.450128	−	0.779645i	−0.998394	+	0.0566595i	$0.981955\pi$
$510$		0			0
$511$	2.32944	+	11.2681i	0.103049	+	0.498470i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	3.52917	−	6.11270i	0.155665	−	0.269620i
$515$	6.50761	−	10.5881i	0.286760	−	0.466569i
$516$		0			0
$517$	16.2646	−	16.2646i	0.715318	−	0.715318i
$518$	−16.6201	+	25.2827i	−0.730247	+	1.11086i
$519$		0			0
$520$	−5.38804	−	1.60373i	−0.236281	−	0.0703281i
$521$	−1.07875	−	0.622814i	−0.0472607	−	0.0272860i	0.476183	−	0.879346i	$-0.342020\pi$
$521$	−1.07875	−	0.622814i	−0.0472607	−	0.0272860i	−0.523444	+	0.852060i	$0.675353\pi$
$522$		0			0
$523$	5.25224	−	19.6016i	0.229664	−	0.857119i	−0.750818	−	0.660509i	$-0.770340\pi$
$523$	5.25224	−	19.6016i	0.229664	−	0.857119i	0.980482	−	0.196609i	$-0.0629930\pi$
$524$	0.373725			0.0163262
$525$		0			0
$526$	−5.68790			−0.248004
$527$	−4.15646	+	15.5121i	−0.181058	+	0.675718i
$528$		0			0
$529$	36.2434	+	20.9252i	1.57580	+	0.909790i
$530$	18.0769	+	5.38051i	0.785209	+	0.233714i
$531$		0			0
$532$	−9.98182	−	0.579009i	−0.432767	−	0.0251032i
$533$	20.2298	−	20.2298i	0.876250	−	0.876250i
$534$		0			0
$535$	8.77010	−	14.2693i	0.379164	−	0.616916i
$536$	−4.65775	+	8.06746i	−0.201184	+	0.348461i
$537$		0			0
$538$	−5.45025	−	5.45025i	−0.234977	−	0.234977i
$539$	19.0260	−	25.5816i	0.819508	−	1.10188i
$540$		0			0
$541$	17.0068	+	29.4566i	0.731178	+	1.26644i	0.956380	+	0.292126i	$0.0943625\pi$
$541$	17.0068	+	29.4566i	0.731178	+	1.26644i	−0.225202	+	0.974312i	$0.572304\pi$
$542$	−4.62932	−	17.2769i	−0.198846	−	0.742104i
$543$		0			0
$544$	−2.06220	−	3.57183i	−0.0884160	−	0.153141i
$545$	−2.25468	−	2.38221i	−0.0965798	−	0.102043i
$546$		0			0
$547$	27.8171	+	27.8171i	1.18937	+	1.18937i	0.977241	+	0.212132i	$0.0680407\pi$
$547$	27.8171	+	27.8171i	1.18937	+	1.18937i	0.212132	+	0.977241i	$0.431959\pi$
$548$	2.56800	+	0.688094i	0.109700	+	0.0293939i
$549$		0			0
$550$	−4.67596	−	22.2870i	−0.199384	−	0.950321i
$551$	5.09127	−	2.93945i	0.216896	−	0.125225i
$552$		0			0
$553$	5.60062	+	11.1452i	0.238163	+	0.473941i
$554$		−	14.7464i		−	0.626512i
$555$		0			0
$556$	−3.96700	−	2.29035i	−0.168238	−	0.0971324i
$557$	1.36512	−	0.365782i	0.0578419	−	0.0154987i	−0.229782	−	0.973242i	$-0.573801\pi$
$557$	1.36512	−	0.365782i	0.0578419	−	0.0154987i	0.287624	+	0.957743i	$0.407135\pi$
$558$		0			0
$559$	1.30577			0.0552282
$560$	−5.82431	+	1.03797i	−0.246122	+	0.0438622i
$561$		0			0
$562$	0.152031	−	0.567387i	0.00641303	−	0.0239338i
$563$	−36.9530	+	9.90152i	−1.55738	+	0.417299i	−0.931834	−	0.362886i	$-0.881791\pi$
$563$	−36.9530	+	9.90152i	−1.55738	+	0.417299i	−0.625548	+	0.780185i	$0.715125\pi$
$564$		0			0
$565$	19.7130	−	10.6697i	0.829332	−	0.448878i
$566$			18.6151i			0.782453i
$567$		0			0
$568$	4.72632	−	4.72632i	0.198312	−	0.198312i
$569$	31.1820	−	18.0029i	1.30722	−	0.754723i	0.325587	−	0.945512i	$-0.394438\pi$
$569$	31.1820	−	18.0029i	1.30722	−	0.754723i	0.981631	+	0.190789i	$0.0611047\pi$
$570$		0			0
$571$	17.1990	−	29.7895i	0.719756	−	1.24665i	−0.241341	−	0.970440i	$-0.577587\pi$
$571$	17.1990	−	29.7895i	0.719756	−	1.24665i	0.961096	−	0.276213i	$-0.0890795\pi$
$572$	11.0601	+	2.96354i	0.462445	+	0.123912i
$573$		0			0
$574$	9.46346	−	28.5817i	0.394997	−	1.19298i
$575$	26.8636	+	29.9934i	1.12029	+	1.25081i
$576$		0			0
$577$	−11.5727	−	43.1900i	−0.481779	−	1.79802i	−0.594148	−	0.804355i	$-0.702511\pi$
$577$	−11.5727	−	43.1900i	−0.481779	−	1.79802i	0.112370	−	0.993666i	$-0.464156\pi$
$578$	−0.00275276	−	0.0102734i	−0.000114500	−	0.000427319i
$579$		0			0
$580$	2.52636	−	2.39111i	0.104901	−	0.0992854i
$581$	8.99048	−	8.00466i	0.372988	−	0.332089i
$582$		0			0
$583$	−37.1066	−	9.94267i	−1.53680	−	0.411783i
$584$	−2.17449	+	3.76633i	−0.0899811	+	0.155852i
$585$		0			0
$586$	−25.3199	+	14.6185i	−1.04596	+	0.603883i
$587$	−19.7182	+	19.7182i	−0.813859	+	0.813859i	−0.985210	−	0.171351i	$-0.945187\pi$
$587$	−19.7182	+	19.7182i	−0.813859	+	0.813859i	0.171351	+	0.985210i	$0.445187\pi$
$588$		0			0
$589$			14.7149i			0.606316i
$590$	−0.471540	−	0.871201i	−0.0194130	−	0.0358668i
$591$		0			0
$592$	−11.0461	+	2.95980i	−0.453994	+	0.121647i
$593$	2.57961	−	9.62724i	0.105932	−	0.395343i	−0.892517	−	0.451013i	$-0.851063\pi$
$593$	2.57961	−	9.62724i	0.105932	−	0.395343i	0.998449	+	0.0556699i	$0.0177294\pi$
$594$		0			0
$595$	−24.3112	−	2.08216i	−0.996664	−	0.0853604i
$596$	17.2441			0.706344
$597$		0			0
$598$	−19.5559	+	5.23999i	−0.799701	+	0.214279i
$599$	−14.2556	−	8.23048i	−0.582469	−	0.336288i	0.179645	−	0.983731i	$-0.442505\pi$
$599$	−14.2556	−	8.23048i	−0.582469	−	0.336288i	−0.762114	+	0.647443i	$0.775838\pi$
$600$		0			0
$601$		−	34.0216i		−	1.38777i	−0.720086	−	0.693885i	$-0.755898\pi$
$601$		−	34.0216i		−	1.38777i	0.720086	−	0.693885i	$-0.244102\pi$
$602$	1.22785	−	0.617012i	0.0500434	−	0.0251475i
$603$		0			0
$604$	−4.82177	+	2.78385i	−0.196195	+	0.113273i
$605$	5.05795	+	21.1907i	0.205635	+	0.861525i
$606$		0			0
$607$	34.7707	+	9.31678i	1.41130	+	0.378156i	0.882389	−	0.470521i	$-0.155934\pi$
$607$	34.7707	+	9.31678i	1.41130	+	0.378156i	0.528910	+	0.848678i	$0.322601\pi$
$608$	−2.67224	−	2.67224i	−0.108374	−	0.108374i
$609$		0			0
$610$	0.503605	−	18.3108i	0.0203904	−	0.741383i
$611$	−6.34852	−	10.9960i	−0.256833	−	0.444849i
$612$		0			0
$613$	−8.52125	−	31.8017i	−0.344170	−	1.28446i	−0.893579	−	0.448906i	$-0.851814\pi$
$613$	−8.52125	−	31.8017i	−0.344170	−	1.28446i	0.549409	−	0.835554i	$-0.314853\pi$
$614$	−1.15586	−	2.00201i	−0.0466469	−	0.0807947i
$615$		0			0
$616$	11.8004	−	2.43950i	0.475452	−	0.0982901i
$617$	10.3705	+	10.3705i	0.417499	+	0.417499i	0.884341	−	0.466842i	$-0.154608\pi$
$617$	10.3705	+	10.3705i	0.417499	+	0.417499i	−0.466842	+	0.884341i	$0.654608\pi$
$618$		0			0
$619$	−2.58828	+	4.48304i	−0.104032	+	0.180188i	−0.913342	−	0.407193i	$-0.866508\pi$
$619$	−2.58828	+	4.48304i	−0.104032	+	0.180188i	0.809310	+	0.587381i	$0.199841\pi$
$620$	2.02138	+	8.46877i	0.0811808	+	0.340114i
$621$		0			0
$622$	9.81743	−	9.81743i	0.393643	−	0.393643i
$623$	−14.2990	+	7.18544i	−0.572876	+	0.287879i
$624$		0			0
$625$	10.0480	+	22.8919i	0.401921	+	0.915674i
$626$	11.6830	+	6.74520i	0.466948	+	0.269592i
$627$		0			0
$628$	−1.06916	+	3.99014i	−0.0426640	+	0.159224i
$629$	−47.1658			−1.88062
$630$		0			0
$631$	14.5385			0.578769			0.289384	−	0.957213i	$-0.406549\pi$
$631$	14.5385			0.578769			0.289384	+	0.957213i	$0.406549\pi$
$632$	−1.22019	+	4.55381i	−0.0485365	+	0.181141i
$633$		0			0
$634$	−11.8793	−	6.85853i	−0.471788	−	0.272387i
$635$	−19.4442	−	35.9245i	−0.771621	−	1.42562i
$636$		0			0
$637$	−10.9218	−	13.7994i	−0.432736	−	0.546752i
$638$	−5.00987	+	5.00987i	−0.198343	+	0.198343i
$639$		0			0
$640$	−1.90502	−	1.17085i	−0.0753026	−	0.0462819i
$641$	20.8743	−	36.1553i	0.824484	−	1.42805i	−0.0778281	−	0.996967i	$-0.524799\pi$
$641$	20.8743	−	36.1553i	0.824484	−	1.42805i	0.902313	−	0.431082i	$-0.141868\pi$
$642$		0			0
$643$	−15.5128	−	15.5128i	−0.611766	−	0.611766i	0.331640	−	0.943406i	$-0.392398\pi$
$643$	−15.5128	−	15.5128i	−0.611766	−	0.611766i	−0.943406	+	0.331640i	$0.892398\pi$
$644$	−15.9129	+	14.1680i	−0.627056	+	0.558298i
$645$		0			0
$646$	−7.79328	−	13.4984i	−0.306623	−	0.531086i
$647$	3.70148	+	13.8141i	0.145520	+	0.543089i	0.999732	+	0.0231633i	$0.00737377\pi$
$647$	3.70148	+	13.8141i	0.145520	+	0.543089i	−0.854211	+	0.519926i	$0.825960\pi$
$648$		0			0
$649$	1.00886	+	1.74740i	0.0396012	+	0.0685913i
$650$	−12.5514	−	0.690928i	−0.492305	−	0.0271004i
$651$		0			0
$652$	−15.3717	−	15.3717i	−0.602003	−	0.602003i
$653$	14.7451	+	3.95094i	0.577021	+	0.154612i	0.535515	−	0.844526i	$-0.320118\pi$
$653$	14.7451	+	3.95094i	0.577021	+	0.154612i	0.0415062	+	0.999138i	$0.486784\pi$
$654$		0			0
$655$	0.812840	−	0.194014i	0.0317603	−	0.00758077i
$656$	9.85506	−	5.68982i	0.384775	−	0.222150i
$657$		0			0
$658$	−11.1656	−	7.33993i	−0.435279	−	0.286140i
$659$			18.9116i			0.736690i	0.929689	+	0.368345i	$0.120076\pi$
$659$			18.9116i			0.736690i	−0.929689	+	0.368345i	$0.879924\pi$
$660$		0			0
$661$	19.5815	+	11.3054i	0.761632	+	0.439728i	0.829881	−	0.557940i	$-0.188408\pi$
$661$	19.5815	+	11.3054i	0.761632	+	0.439728i	−0.0682495	+	0.997668i	$0.521741\pi$
$662$	32.1061	−	8.60281i	1.24784	−	0.334358i
$663$		0			0
$664$	4.54978			0.176566
$665$	−22.0108	+	3.92261i	−0.853540	+	0.152112i
$666$		0			0
$667$	3.24233	−	12.1006i	0.125544	−	0.468535i
$668$	−23.8985	+	6.40358i	−0.924660	+	0.247762i
$669$		0			0
$670$	−5.94235	+	19.9645i	−0.229573	+	0.771296i
$671$			37.3097i			1.44033i
$672$		0			0
$673$	−24.2623	+	24.2623i	−0.935243	+	0.935243i	−0.998027	−	0.0627838i	$-0.980002\pi$
$673$	−24.2623	+	24.2623i	−0.935243	+	0.935243i	0.0627838	+	0.998027i	$0.480002\pi$
$674$	20.8610	−	12.0441i	0.803534	−	0.463921i
$675$		0			0
$676$	−3.33971	+	5.78455i	−0.128450	+	0.222483i
$677$	−8.59870	−	2.30402i	−0.330475	−	0.0885505i	0.0897664	−	0.995963i	$-0.471388\pi$
$677$	−8.59870	−	2.30402i	−0.330475	−	0.0885505i	−0.420241	+	0.907412i	$0.638055\pi$
$678$		0			0
$679$	−1.15112	−	1.29289i	−0.0441761	−	0.0496166i
$680$	−6.33949	−	6.69806i	−0.243108	−	0.256859i
$681$		0			0
$682$	−4.58985	−	17.1296i	−0.175755	−	0.655925i
$683$	−12.3979	−	46.2697i	−0.474394	−	1.77046i	−0.623693	−	0.781669i	$-0.714368\pi$
$683$	−12.3979	−	46.2697i	−0.474394	−	1.77046i	0.149299	−	0.988792i	$-0.452298\pi$
$684$		0			0
$685$	5.94254	+	0.163439i	0.227053	+	0.00624467i
$686$	−16.7906	−	7.81510i	−0.641068	−	0.298382i
$687$		0			0
$688$	0.501686	+	0.134426i	0.0191266	+	0.00512496i
$689$	−10.6028	+	18.3645i	−0.403934	+	0.699633i
$690$		0			0
$691$	−22.3848	+	12.9239i	−0.851559	+	0.491648i	−0.861177	−	0.508306i	$-0.830272\pi$
$691$	−22.3848	+	12.9239i	−0.851559	+	0.491648i	0.00961738	+	0.999954i	$0.496939\pi$
$692$	−11.7140	+	11.7140i	−0.445300	+	0.445300i
$693$		0			0
$694$			2.05709i			0.0780861i
$695$	−9.81711	−	2.92202i	−0.372384	−	0.110839i
$696$		0			0
$697$	45.3349	−	12.1474i	1.71718	−	0.460117i
$698$	3.03467	−	11.3255i	0.114864	−	0.428677i
$699$		0			0
$700$	−12.1289	+	5.28117i	−0.458428	+	0.199610i
$701$	−3.95788			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$701$	−3.95788			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$702$		0			0
$703$	−41.7447	+	11.1854i	−1.57443	+	0.421867i
$704$	3.94427	+	2.27722i	0.148655	+	0.0858261i
$705$		0			0
$706$			11.4227i			0.429897i
$707$	8.14167	−	12.3852i	0.306199	−	0.465793i
$708$		0			0
$709$	−25.1665	+	14.5299i	−0.945148	+	0.545682i	−0.891570	−	0.452882i	$-0.850396\pi$
$709$	−25.1665	+	14.5299i	−0.945148	+	0.545682i	−0.0535778	+	0.998564i	$0.517063\pi$
$710$	7.82600	−	12.7332i	0.293704	−	0.477869i
$711$		0			0
$712$	−5.84241	−	1.56547i	−0.218954	−	0.0586684i
$713$	22.1722	+	22.1722i	0.830354	+	0.830354i
$714$		0			0
$715$	25.5938	+	0.703911i	0.957154	+	0.0263248i
$716$	−6.36367	−	11.0222i	−0.237821	−	0.411919i
$717$		0			0
$718$	−0.624155	−	2.32938i	−0.0232932	−	0.0869316i
$719$	10.1319	+	17.5490i	0.377857	+	0.654467i	0.990750	−	0.135699i	$-0.0433279\pi$
$719$	10.1319	+	17.5490i	0.377857	+	0.654467i	−0.612893	+	0.790166i	$0.709995\pi$
$720$		0			0
$721$	13.9598	+	4.62212i	0.519891	+	0.172137i
$722$	3.33633	+	3.33633i	0.124165	+	0.124165i
$723$		0			0
$724$	−4.54975	+	7.88040i	−0.169090	+	0.292873i
$725$	4.25343	−	6.51212i	0.157969	−	0.241854i
$726$		0			0
$727$	−2.80940	+	2.80940i	−0.104195	+	0.104195i	−0.757282	−	0.653088i	$-0.773473\pi$
$727$	−2.80940	+	2.80940i	−0.104195	+	0.104195i	0.653088	+	0.757282i	$0.273473\pi$
$728$	0.385189	−	6.64046i	0.0142760	−	0.246112i
$729$		0			0
$730$	−2.77421	+	9.32052i	−0.102678	+	0.344968i
$731$	1.85515	+	1.07107i	0.0686152	+	0.0396150i
$732$		0			0
$733$	−0.451275	+	1.68418i	−0.0166682	+	0.0622066i	−0.973759	−	0.227582i	$-0.926918\pi$
$733$	−0.451275	+	1.68418i	−0.0166682	+	0.0622066i	0.957091	+	0.289788i	$0.0935848\pi$
$734$	−5.20884			−0.192262
$735$		0			0
$736$	−8.05297			−0.296836
$737$	10.9809	−	40.9813i	0.404487	−	1.50957i
$738$		0			0
$739$	−20.2692	−	11.7024i	−0.745615	−	0.430481i	0.0784926	−	0.996915i	$-0.474989\pi$
$739$	−20.2692	−	11.7024i	−0.745615	−	0.430481i	−0.824107	+	0.566434i	$0.808323\pi$
$740$	−22.4885	+	12.1720i	−0.826693	+	0.447450i
$741$		0			0
$742$	−1.29231	+	22.2787i	−0.0474421	+	0.817879i
$743$	−1.84057	+	1.84057i	−0.0675240	+	0.0675240i	−0.740062	−	0.672538i	$-0.765204\pi$
$743$	−1.84057	+	1.84057i	−0.0675240	+	0.0675240i	0.672538	+	0.740062i	$0.265204\pi$
$744$		0			0
$745$	37.5053	−	8.95203i	1.37409	−	0.327977i
$746$	−0.0733279	+	0.127008i	−0.00268472	+	0.00465008i
$747$		0			0
$748$	13.2825	+	13.2825i	0.485658	+	0.485658i
$749$	18.8132	+	6.22909i	0.687420	+	0.227606i
$750$		0			0
$751$	−21.1862	−	36.6956i	−0.773096	−	1.33904i	−0.935858	−	0.352376i	$-0.885374\pi$
$751$	−21.1862	−	36.6956i	−0.773096	−	1.33904i	0.162762	−	0.986665i	$-0.447960\pi$
$752$	−1.30713	−	4.87829i	−0.0476663	−	0.177893i
$753$		0			0
$754$	1.95548	+	3.38699i	0.0712145	+	0.123347i
$755$	−9.04201	+	8.55795i	−0.329072	+	0.311456i
$756$		0			0
$757$	10.2470	+	10.2470i	0.372434	+	0.372434i	0.868363	−	0.495929i	$-0.165172\pi$
$757$	10.2470	+	10.2470i	0.372434	+	0.372434i	−0.495929	+	0.868363i	$0.665172\pi$
$758$	17.9119	+	4.79948i	0.650590	+	0.174325i
$759$		0			0
$760$	−7.19930	−	4.42478i	−0.261146	−	0.160504i
$761$	−13.4082	+	7.74124i	−0.486048	+	0.280620i	−0.722933	−	0.690918i	$-0.757207\pi$
$761$	−13.4082	+	7.74124i	−0.486048	+	0.280620i	0.236886	+	0.971538i	$0.423873\pi$
$762$		0			0
$763$	2.13186	−	3.24300i	0.0771784	−	0.117404i
$764$		−	18.2062i		−	0.658676i
$765$		0			0
$766$	3.33386	+	1.92480i	0.120457	+	0.0695460i
$767$	1.07584	−	0.288270i	0.0388463	−	0.0104088i
$768$		0			0
$769$	15.9644			0.575691			0.287846	−	0.957677i	$-0.407061\pi$
$769$	15.9644			0.575691			0.287846	+	0.957677i	$0.407061\pi$
$770$	24.3991	−	11.4319i	0.879283	−	0.411976i
$771$		0			0
$772$	−2.60664	+	9.72810i	−0.0938149	+	0.350122i
$773$	−22.3797	+	5.99662i	−0.804941	+	0.215683i	−0.637752	−	0.770241i	$-0.720136\pi$
$773$	−22.3797	+	5.99662i	−0.804941	+	0.215683i	−0.167189	+	0.985925i	$0.553469\pi$
$774$		0			0
$775$	8.79290	+	17.3699i	0.315850	+	0.623947i
$776$		−	0.654289i		−	0.0234876i
$777$		0			0
$778$	−12.6018	+	12.6018i	−0.451798	+	0.451798i
$779$	37.2434	−	21.5025i	1.33438	−	0.770406i
$780$		0			0
$781$	−15.2210	+	26.3636i	−0.544651	+	0.943363i
$782$	−32.0819	−	8.59632i	−1.14725	−	0.307404i
$783$		0			0
$784$	−2.77559	−	6.42620i	−0.0991284	−	0.229507i
$785$	−0.253950	+	9.23348i	−0.00906386	+	0.329557i
$786$		0			0
$787$	−0.544910	−	2.03363i	−0.0194239	−	0.0724912i	0.955534	−	0.294882i	$-0.0952805\pi$
$787$	−0.544910	−	2.03363i	−0.0194239	−	0.0724912i	−0.974958	+	0.222391i	$0.928614\pi$
$788$	5.94568	+	22.1896i	0.211806	+	0.790471i
$789$		0			0
$790$	−0.289824	+	10.5378i	−0.0103115	+	0.374920i
$791$	17.6365	+	19.8085i	0.627081	+	0.704310i
$792$		0			0
$793$	19.8934	+	5.33042i	0.706435	+	0.189289i
$794$	−12.8232	+	22.2105i	−0.455079	+	0.788219i
$795$		0			0
$796$	21.9943	−	12.6984i	0.779569	−	0.450084i
$797$	23.6759	−	23.6759i	0.838642	−	0.838642i	−0.150038	−	0.988680i	$-0.547940\pi$
$797$	23.6759	−	23.6759i	0.838642	−	0.838642i	0.988680	+	0.150038i	$0.0479397\pi$
$798$		0			0
$799$		−	20.8298i		−	0.736904i
$800$	−4.75120	−	1.55760i	−0.167980	−	0.0550694i
$801$		0			0
$802$	5.08192	−	1.36170i	0.179449	−	0.0480832i
$803$	5.12649	−	19.1323i	0.180910	−	0.675164i
$804$		0			0
$805$	−27.2549	+	39.0760i	−0.960610	+	1.37725i
$806$	−9.78915			−0.344808
$807$		0			0
$808$	5.41115	−	1.44991i	0.190364	−	0.0510078i
$809$	−1.15441	−	0.666500i	−0.0405869	−	0.0234329i	0.479569	−	0.877504i	$-0.340793\pi$
$809$	−1.15441	−	0.666500i	−0.0405869	−	0.0234329i	−0.520156	+	0.854071i	$0.674126\pi$
$810$		0			0
$811$			41.6705i			1.46325i	0.681708	+	0.731624i	$0.261237\pi$
$811$			41.6705i			1.46325i	−0.681708	+	0.731624i	$0.738763\pi$
$812$	3.43924	+	2.26086i	0.120694	+	0.0793406i
$813$		0			0
$814$	45.1059	−	26.0419i	1.58096	−	0.912768i
$815$	−41.4131	−	25.4530i	−1.45064	−	0.891580i
$816$		0			0
$817$	1.89593	+	0.508013i	0.0663302	+	0.0177731i
$818$	−5.92234	−	5.92234i	−0.207070	−	0.207070i
$819$		0			0
$820$	18.4807	−	17.4913i	0.645373	−	0.610823i
$821$	−16.0833	−	27.8571i	−0.561312	−	0.972221i	−0.997382	−	0.0723083i	$-0.976963\pi$
$821$	−16.0833	−	27.8571i	−0.561312	−	0.972221i	0.436070	−	0.899913i	$-0.356370\pi$
$822$		0			0
$823$	3.82988	+	14.2933i	0.133501	+	0.498233i	1.00000		0.000946758i	$-0.000301363\pi$
$823$	3.82988	+	14.2933i	0.133501	+	0.498233i	−0.866498	+	0.499180i	$0.833635\pi$
$824$	2.77901	+	4.81338i	0.0968113	+	0.167682i
$825$		0			0
$826$	0.875423	−	0.779431i	0.0304599	−	0.0271199i
$827$	34.2632	+	34.2632i	1.19145	+	1.19145i	0.976661	+	0.214788i	$0.0689062\pi$
$827$	34.2632	+	34.2632i	1.19145	+	1.19145i	0.214788	+	0.976661i	$0.431094\pi$
$828$		0			0
$829$	25.2456	−	43.7267i	0.876817	−	1.51869i	0.0220025	−	0.999758i	$-0.492996\pi$
$829$	25.2456	−	43.7267i	0.876817	−	1.51869i	0.854814	−	0.518934i	$-0.173671\pi$
$830$	9.89563	−	2.36196i	0.343482	−	0.0819848i
$831$		0			0
$832$	1.77772	−	1.77772i	0.0616313	−	0.0616313i
$833$	−4.19779	−	28.5640i	−0.145445	−	0.989682i
$834$		0			0
$835$	−48.6541	+	26.3342i	−1.68375	+	0.911332i
$836$	14.9058	+	8.60589i	0.515529	+	0.297641i
$837$		0			0
$838$	−2.46675	+	9.20603i	−0.0852124	+	0.318017i
$839$	22.4313			0.774414			0.387207	−	0.921993i	$-0.373440\pi$
$839$	22.4313			0.774414			0.387207	+	0.921993i	$0.373440\pi$
$840$		0			0
$841$	26.5800			0.916553
$842$	−4.36008	+	16.2721i	−0.150258	+	0.560772i
$843$		0			0
$844$	11.7937	+	6.80911i	0.405957	+	0.234379i
$845$	−4.26080	+	14.3150i	−0.146576	+	0.492451i
$846$		0			0
$847$	−23.0329	+	11.5744i	−0.791420	+	0.397700i
$848$	−5.96425	+	5.96425i	−0.204813	+	0.204813i
$849$		0			0
$850$	−17.2654	−	11.2770i	−0.592199	−	0.386799i
$851$	−46.0461	+	79.7542i	−1.57844	+	2.73394i
$852$		0			0
$853$	24.4497	+	24.4497i	0.837140	+	0.837140i	0.988482	−	0.151341i	$-0.0483592\pi$
$853$	24.4497	+	24.4497i	0.837140	+	0.837140i	−0.151341	+	0.988482i	$0.548359\pi$
$854$	21.2250	−	4.38784i	0.726305	−	0.150149i
$855$		0			0
$856$	3.74518	+	6.48684i	0.128008	+	0.221716i
$857$	−3.75655	−	14.0196i	−0.128321	−	0.478901i	0.871615	−	0.490191i	$-0.163073\pi$
$857$	−3.75655	−	14.0196i	−0.128321	−	0.478901i	−0.999936	+	0.0112896i	$0.996406\pi$
$858$		0			0
$859$	8.65502	+	14.9909i	0.295306	+	0.511484i	0.975056	−	0.221959i	$-0.0712452\pi$
$859$	8.65502	+	14.9909i	0.295306	+	0.511484i	−0.679750	+	0.733444i	$0.737912\pi$
$860$	1.16094	+	0.0319295i	0.0395877	+	0.00108879i
$861$		0			0
$862$	15.2439	+	15.2439i	0.519209	+	0.519209i
$863$	−9.04469	−	2.42352i	−0.307885	−	0.0824975i	0.101568	−	0.994829i	$-0.467614\pi$
$863$	−9.04469	−	2.42352i	−0.307885	−	0.0824975i	−0.409453	+	0.912331i	$0.634281\pi$
$864$		0			0
$865$	−19.3965	+	31.5588i	−0.659500	+	1.07303i
$866$	31.6992	−	18.3016i	1.07718	−	0.621912i
$867$		0			0
$868$	−9.20499	+	4.62564i	−0.312438	+	0.157005i
$869$		−	21.4717i		−	0.728378i
$870$		0			0
$871$	−20.2822	−	11.7099i	−0.687236	−	0.396776i
$872$	1.41688	−	0.379653i	0.0479817	−	0.0128567i
$873$		0			0
$874$	−30.4331			−1.02942
$875$	−23.6383	+	17.7829i	−0.799119	+	0.601173i
$876$		0			0
$877$	−9.68626	+	36.1496i	−0.327082	+	1.22069i	0.585120	+	0.810946i	$0.301047\pi$
$877$	−9.68626	+	36.1496i	−0.327082	+	1.22069i	−0.912202	+	0.409740i	$0.865619\pi$
$878$	20.4580	−	5.48171i	0.690425	−	0.184999i
$879$		0			0
$880$	9.76086	+	2.90528i	0.329038	+	0.0979369i
$881$			49.1425i			1.65565i	0.560984	+	0.827827i	$0.310423\pi$
$881$			49.1425i			1.65565i	−0.560984	+	0.827827i	$0.689577\pi$
$882$		0			0
$883$	22.9167	−	22.9167i	0.771207	−	0.771207i	−0.207110	−	0.978318i	$-0.566406\pi$
$883$	22.9167	−	22.9167i	0.771207	−	0.771207i	0.978318	+	0.207110i	$0.0664060\pi$
$884$	8.97985	−	5.18452i	0.302025	−	0.174374i
$885$		0			0
$886$	2.07519	−	3.59433i	0.0697173	−	0.120754i
$887$	25.3392	+	6.78961i	0.850806	+	0.227973i	0.657770	−	0.753219i	$-0.271500\pi$
$887$	25.3392	+	6.78961i	0.850806	+	0.227973i	0.193036	+	0.981192i	$0.438167\pi$
$888$		0			0
$889$	36.0986	−	32.1403i	1.21071	−	1.07795i
$890$	−13.5198	−	0.371836i	−0.453184	−	0.0124640i
$891$		0			0
$892$	−5.79830	−	21.6395i	−0.194141	−	0.724545i
$893$	−4.93981	−	18.4356i	−0.165304	−	0.616925i
$894$		0			0
$895$	−19.5628	−	20.6693i	−0.653913	−	0.690899i
$896$	0.831614	−	2.51166i	0.0277823	−	0.0839086i
$897$		0			0
$898$	−28.3785	−	7.60399i	−0.947002	−	0.253748i
$899$	3.02860	−	5.24569i	0.101010	−	0.174954i
$900$		0			0
$901$	−30.1274	+	17.3941i	−1.00369	+	0.579481i
$902$	−36.6479	+	36.6479i	−1.22024	+	1.22024i
$903$		0			0
$904$			10.0244i			0.333407i
$905$	−5.80457	+	19.5016i	−0.192950	+	0.648255i
$906$		0			0
$907$	−1.22193	+	0.327416i	−0.0405736	+	0.0108717i	−0.279049	−	0.960277i	$-0.590019\pi$
$907$	−1.22193	+	0.327416i	−0.0405736	+	0.0108717i	0.238475	+	0.971149i	$0.423352\pi$
$908$	2.83476	−	10.5795i	0.0940749	−	0.351092i
$909$		0			0
$910$	−2.60953	−	14.6428i	−0.0865052	−	0.485403i
$911$	49.7996			1.64993			0.824967	−	0.565182i	$-0.191194\pi$
$911$	49.7996			1.64993			0.824967	+	0.565182i	$0.191194\pi$
$912$		0			0
$913$	−20.0156	+	5.36318i	−0.662421	+	0.177495i
$914$	−0.408203	−	0.235676i	−0.0135021	−	0.00779547i
$915$		0			0
$916$			28.9443i			0.956347i
$917$	0.443974	+	0.883504i	0.0146613	+	0.0291759i
$918$		0			0
$919$	43.6221	−	25.1852i	1.43896	−	0.830784i	0.441182	−	0.897418i	$-0.354559\pi$
$919$	43.6221	−	25.1852i	1.43896	−	0.830784i	0.997777	+	0.0666338i	$0.0212259\pi$
$920$	−17.5150	+	4.18060i	−0.577452	+	0.137830i
$921$		0			0
$922$	25.4231	+	6.81209i	0.837264	+	0.224344i
$923$	11.8823	+	11.8823i	0.391112	+	0.391112i
$924$		0			0
$925$	−42.5929	+	38.1482i	−1.40045	+	1.25431i
$926$	−0.725623	−	1.25682i	−0.0238455	−	0.0413015i
$927$		0			0
$928$	0.402626	+	1.50262i	0.0132168	+	0.0493259i
$929$	−11.4115	−	19.7652i	−0.374398	−	0.648476i	0.615839	−	0.787872i	$-0.288817\pi$
$929$	−11.4115	−	19.7652i	−0.374398	−	0.648476i	−0.990237	+	0.139396i	$0.955484\pi$
$930$		0			0
$931$	−10.4893	−	24.2854i	−0.343773	−	0.795921i
$932$	−0.998499	−	0.998499i	−0.0327069	−	0.0327069i
$933$		0			0
$934$	−15.5068	+	26.8586i	−0.507399	+	0.878841i
$935$	35.7846	+	21.9937i	1.17028	+	0.719270i
$936$		0			0
$937$	−24.9461	+	24.9461i	−0.814954	+	0.814954i	−0.985372	−	0.170418i	$-0.945488\pi$
$937$	−24.9461	+	24.9461i	−0.814954	+	0.814954i	0.170418	+	0.985372i	$0.445488\pi$
$938$	−24.6051	−	1.42725i	−0.803386	−	0.0466015i
$939$		0			0
$940$	−5.37548	−	9.93156i	−0.175329	−	0.323932i
$941$	16.1409	+	9.31896i	0.526179	+	0.303789i	0.739459	−	0.673202i	$-0.235081\pi$
$941$	16.1409	+	9.31896i	0.526179	+	0.303789i	−0.213280	+	0.976991i	$0.568415\pi$
$942$		0			0
$943$	23.7181	−	88.5173i	0.772369	−	2.88252i
$944$	0.443022			0.0144191
$945$		0			0
$946$	−2.36551			−0.0769092
$947$	−0.657006	+	2.45198i	−0.0213498	+	0.0796786i	−0.975779	−	0.218760i	$-0.929799\pi$
$947$	−0.657006	+	2.45198i	−0.0213498	+	0.0796786i	0.954429	+	0.298438i	$0.0964656\pi$
$948$		0			0
$949$	−9.46884	−	5.46684i	−0.307372	−	0.177461i
$950$	−17.9553	−	5.88634i	−0.582548	−	0.190978i
$951$		0			0
$952$	5.99416	−	9.11836i	0.194272	−	0.295528i
$953$	−31.1031	+	31.1031i	−1.00753	+	1.00753i	−0.00755624	+	0.999971i	$0.502405\pi$
$953$	−31.1031	+	31.1031i	−1.00753	+	1.00753i	−0.999971	+	0.00755624i	$0.997595\pi$
$954$		0			0
$955$	−9.45149	−	39.5979i	−0.305843	−	1.28136i
$956$	−2.18215	+	3.77959i	−0.0705758	+	0.122241i
$957$		0			0
$958$	23.5834	+	23.5834i	0.761945	+	0.761945i
$959$	1.42402	+	6.88831i	0.0459840	+	0.222435i
$960$		0			0
$961$	−7.91940	−	13.7168i	−0.255465	−	0.442477i
$962$	−7.44117	−	27.7708i	−0.239913	−	0.895368i
$963$		0			0
$964$	1.53496	+	2.65862i	0.0494376	+	0.0856284i
$965$	−0.619139	+	22.5115i	−0.0199308	+	0.724672i
$966$		0			0
$967$	−14.7707	−	14.7707i	−0.474993	−	0.474993i	0.428533	−	0.903526i	$-0.359031\pi$
$967$	−14.7707	−	14.7707i	−0.474993	−	0.474993i	−0.903526	+	0.428533i	$0.859031\pi$
$968$	−9.41101	−	2.52167i	−0.302481	−	0.0810496i
$969$		0			0
$970$	−0.339666	−	1.42306i	−0.0109060	−	0.0456917i
$971$	−9.39194	+	5.42244i	−0.301402	+	0.174014i	−0.643072	−	0.765805i	$-0.722341\pi$
$971$	−9.39194	+	5.42244i	−0.301402	+	0.174014i	0.341671	+	0.939820i	$0.389007\pi$
$972$		0			0
$973$	0.701821	−	12.0990i	0.0224994	−	0.387878i
$974$			3.30368i			0.105857i
$975$		0			0
$976$	7.09442	+	4.09597i	0.227087	+	0.131109i
$977$	16.5560	−	4.43616i	0.529673	−	0.141925i	0.0159356	−	0.999873i	$-0.494927\pi$
$977$	16.5560	−	4.43616i	0.529673	−	0.141925i	0.513737	+	0.857948i	$0.328261\pi$
$978$		0			0
$979$	27.5476			0.880426
$980$	−9.37292	−	12.5359i	−0.299407	−	0.400444i
$981$		0			0
$982$	0.936018	−	3.49327i	0.0298695	−	0.111475i
$983$	1.62331	−	0.434966i	0.0517757	−	0.0138732i	−0.232838	−	0.972515i	$-0.574801\pi$
$983$	1.62331	−	0.434966i	0.0517757	−	0.0138732i	0.284614	+	0.958642i	$0.408135\pi$
$984$		0			0
$985$	24.4511	+	45.1751i	0.779077	+	1.43940i
$986$			6.41602i			0.204328i
$987$		0			0
$988$	6.71821	−	6.71821i	0.213735	−	0.213735i
$989$	3.62222	−	2.09129i	0.115180	−	0.0664992i
$990$		0			0
$991$	8.40392	−	14.5560i	0.266959	−	0.462387i	−0.701116	−	0.713047i	$-0.747314\pi$
$991$	8.40392	−	14.5560i	0.266959	−	0.462387i	0.968075	+	0.250660i	$0.0806478\pi$
$992$	−3.76106	−	1.00777i	−0.119414	−	0.0319968i
$993$		0			0
$994$	16.7880	+	5.55853i	0.532482	+	0.176306i
$995$	41.2448	−	39.0368i	1.30755	−	1.23755i
$996$		0			0
$997$	4.51978	+	16.8680i	0.143143	+	0.534216i	0.999831	+	0.0183818i	$0.00585143\pi$
$997$	4.51978	+	16.8680i	0.143143	+	0.534216i	−0.856688	+	0.515835i	$0.827482\pi$
$998$	0.167661	+	0.625718i	0.00530721	+	0.0198068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.b.577.1		16
3.2	odd	2		210.2.u.b.157.4	yes	16
5.3	odd	4		630.2.bv.a.73.3		16
7.5	odd	6		630.2.bv.a.397.3		16
15.2	even	4		1050.2.bc.h.493.4		16
15.8	even	4		210.2.u.a.73.2	✓	16
15.14	odd	2		1050.2.bc.g.157.1		16
21.5	even	6		210.2.u.a.187.2	yes	16
21.11	odd	6		1470.2.m.e.97.5		16
21.17	even	6		1470.2.m.d.97.8		16
35.33	even	12	inner	630.2.bv.b.523.1		16
105.38	odd	12		1470.2.m.e.1273.5		16
105.47	odd	12		1050.2.bc.g.943.1		16
105.53	even	12		1470.2.m.d.1273.8		16
105.68	odd	12		210.2.u.b.103.4	yes	16
105.89	even	6		1050.2.bc.h.607.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.2	✓	16	15.8	even	4
210.2.u.a.187.2	yes	16	21.5	even	6
210.2.u.b.103.4	yes	16	105.68	odd	12
210.2.u.b.157.4	yes	16	3.2	odd	2
630.2.bv.a.73.3		16	5.3	odd	4
630.2.bv.a.397.3		16	7.5	odd	6
630.2.bv.b.523.1		16	35.33	even	12	inner
630.2.bv.b.577.1		16	1.1	even	1	trivial
1050.2.bc.g.157.1		16	15.14	odd	2
1050.2.bc.g.943.1		16	105.47	odd	12
1050.2.bc.h.493.4		16	15.2	even	4
1050.2.bc.h.607.4		16	105.89	even	6
1470.2.m.d.97.8		16	21.17	even	6
1470.2.m.d.1273.8		16	105.53	even	12
1470.2.m.e.97.5		16	21.11	odd	6
1470.2.m.e.1273.5		16	105.38	odd	12

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-2.14315 - 0.637899i) q^{5} +(0.153213 - 2.64131i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-2.14315 - 0.637899i) q^{5} +(0.153213 - 2.64131i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.17085 - 1.90502i) q^{10} +(-2.27722 + 3.94427i) q^{11} +(1.77772 + 1.77772i) q^{13} +(2.51166 + 0.831614i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.06747 + 3.98386i) q^{17} +(1.88956 + 3.27281i) q^{19} +(1.53707 + 1.62401i) q^{20} +(-3.22048 - 3.22048i) q^{22} +(7.77857 + 2.08426i) q^{23} +(4.18617 + 2.73423i) q^{25} +(-2.17725 + 1.25704i) q^{26} +(-1.45334 + 2.21084i) q^{28} -1.55563i q^{29} +(3.37208 + 1.94687i) q^{31} +(-0.965926 + 0.258819i) q^{32} -4.12440 q^{34} +(-2.01325 + 5.56299i) q^{35} +(-2.95980 + 11.0461i) q^{37} +(-3.65035 + 0.978107i) q^{38} +(-1.96650 + 1.06437i) q^{40} -11.3796i q^{41} +(0.367260 - 0.367260i) q^{43} +(3.94427 - 2.27722i) q^{44} +(-4.02648 + 6.97408i) q^{46} +(-4.87829 - 1.30713i) q^{47} +(-6.95305 - 0.809365i) q^{49} +(-3.72452 + 3.33586i) q^{50} +(-0.650691 - 2.42841i) q^{52} +(2.18307 + 8.14732i) q^{53} +(7.39647 - 7.00051i) q^{55} +(-1.75935 - 1.97603i) q^{56} +(1.50262 + 0.402626i) q^{58} +(0.221511 - 0.383668i) q^{59} +(7.09442 - 4.09597i) q^{61} +(-2.75329 + 2.75329i) q^{62} -1.00000i q^{64} +(-2.67591 - 4.94392i) q^{65} +(-8.99808 + 2.41103i) q^{67} +(1.06747 - 3.98386i) q^{68} +(-4.85237 - 3.38446i) q^{70} +6.68403 q^{71} +(-4.20080 + 1.12560i) q^{73} +(-9.90370 - 5.71790i) q^{74} -3.77912i q^{76} +(10.0691 + 6.61917i) q^{77} +(-4.08283 + 2.35722i) q^{79} +(-0.519137 - 2.17497i) q^{80} +(10.9919 + 2.94527i) q^{82} +(3.21718 + 3.21718i) q^{83} +(0.253550 - 9.21894i) q^{85} +(0.259692 + 0.449799i) q^{86} +(1.17878 + 4.39926i) q^{88} +(-3.02425 - 5.23816i) q^{89} +(4.96788 - 4.42314i) q^{91} +(-5.69431 - 5.69431i) q^{92} +(2.52519 - 4.37376i) q^{94} +(-1.96188 - 8.21947i) q^{95} +(0.462652 - 0.462652i) q^{97} +(2.58137 - 6.50665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 4 * q^7	\( 16 q - 12 q^{5} - 4 q^{7} + 4 q^{10} - 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} - 8 q^{20} + 4 q^{22} + 40 q^{23} + 16 q^{25} + 12 q^{26} - 4 q^{28} - 24 q^{31} - 16 q^{34} + 44 q^{35} - 8 q^{37} + 20 q^{38} - 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{52} + 28 q^{53} + 56 q^{55} - 8 q^{56} - 12 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} - 16 q^{65} - 84 q^{67} - 12 q^{68} + 4 q^{70} + 32 q^{71} + 16 q^{73} - 24 q^{74} - 44 q^{77} - 12 q^{79} - 12 q^{80} + 36 q^{82} - 16 q^{83} + 8 q^{85} + 8 q^{86} - 4 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 8 q^{94} - 72 q^{95} - 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 12 * q^5 - 4 * q^7 + 4 * q^10 - 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 - 8 * q^20 + 4 * q^22 + 40 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^31 - 16 * q^34 + 44 * q^35 - 8 * q^37 + 20 * q^38 - 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^52 + 28 * q^53 + 56 * q^55 - 8 * q^56 - 12 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 - 16 * q^65 - 84 * q^67 - 12 * q^68 + 4 * q^70 + 32 * q^71 + 16 * q^73 - 24 * q^74 - 44 * q^77 - 12 * q^79 - 12 * q^80 + 36 * q^82 - 16 * q^83 + 8 * q^85 + 8 * q^86 - 4 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 8 * q^94 - 72 * q^95 - 44 * q^97 - 24 * q^98

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