LMFDB - Embedded newform 450.2.h.d.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1064390625.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 $ x^8 - 2x^7 - 3x^6 - 5x^5 + 36x^4 - 35x^3 + 23x^2 - 171*x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.2
Root			$1.31557 - 1.28500i$ of defining polynomial
Character	$\chi$	$=$	450.181
Dual form			450.2.h.d.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.12459 + 0.697217i) q^{5} -4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.12459 + 0.697217i) q^{5} -4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.00655751 + 2.23606i) q^{10} +(1.51061 + 4.64918i) q^{11} +(-1.43361 + 4.41219i) q^{13} +(-1.31557 - 4.04892i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.815575 - 0.592550i) q^{17} +(1.00000 + 0.726543i) q^{19} +(-2.12864 + 0.684743i) q^{20} +(-3.95483 + 2.87335i) q^{22} +(1.38197 + 4.25325i) q^{23} +(4.02778 + 2.96260i) q^{25} -4.63925 q^{26} +(3.44422 - 2.50237i) q^{28} +(3.42049 - 2.48513i) q^{29} +(-0.826185 - 0.600258i) q^{31} +1.00000 q^{32} +(0.311522 - 0.958765i) q^{34} +(-9.04500 - 2.96825i) q^{35} +(3.31152 - 10.1918i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(-1.30902 - 1.81286i) q^{40} +(-1.42049 + 4.37183i) q^{41} -10.4984 q^{43} +(-3.95483 - 2.87335i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-1.63925 + 1.19099i) q^{47} +11.1245 q^{49} +(-1.57295 + 4.74614i) q^{50} +(-1.43361 - 4.41219i) q^{52} +(8.94413 - 6.49829i) q^{53} +(-0.0320560 + 10.9308i) q^{55} +(3.44422 + 2.50237i) q^{56} +(3.42049 + 2.48513i) q^{58} +(0.656508 - 2.02052i) q^{59} +(1.19754 + 3.68565i) q^{61} +(0.315575 - 0.971238i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-6.12209 + 8.37457i) q^{65} +(-3.03434 - 2.20457i) q^{67} +1.00811 q^{68} +(0.0279172 - 9.51955i) q^{70} +(10.1457 - 7.37130i) q^{71} +(1.05975 + 3.26157i) q^{73} +10.7163 q^{74} -1.23607 q^{76} +(-6.43110 - 19.7929i) q^{77} +(-5.16968 + 3.75599i) q^{79} +(1.31963 - 1.80515i) q^{80} -4.59681 q^{82} +(5.70151 + 4.14239i) q^{83} +(-1.31963 - 1.82756i) q^{85} +(-3.24417 - 9.98454i) q^{86} +(1.51061 - 4.64918i) q^{88} +(-0.693488 - 2.13434i) q^{89} +(6.10328 - 18.7840i) q^{91} +(-3.61803 - 2.62866i) q^{92} +(-1.63925 - 1.19099i) q^{94} +(1.61803 + 2.24082i) q^{95} +(6.49586 - 4.71952i) q^{97} +(3.43766 + 10.5800i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8 + 4 * q^10 + 5 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^19 - q^20 + 20 * q^23 + 14 * q^25 - 14 * q^26 + 3 * q^28 + 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 + 4 * q^35 + 21 * q^37 - 12 * q^38 - 6 * q^40 - 2 * q^41 - 32 * q^43 - 20 * q^46 + 10 * q^47 + 22 * q^49 - 26 * q^50 + 6 * q^52 - 7 * q^53 - 40 * q^55 + 3 * q^56 + 18 * q^58 + 25 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^64 - 37 * q^65 - 2 * q^67 + 2 * q^68 - 11 * q^70 - 24 * q^73 + 26 * q^74 + 8 * q^76 - 35 * q^77 - 6 * q^79 - q^80 - 42 * q^82 - 11 * q^83 + q^85 - 2 * q^86 + 5 * q^88 - 9 * q^89 - 4 * q^91 - 20 * q^92 + 10 * q^94 + 4 * q^95 + q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.12459	+	0.697217i	0.950146	+	0.311805i
$5$	2.12459	+	0.697217i	0.950146	+	0.311805i
$6$		0			0
$7$	−4.25729			−1.60910			−0.804552	−	0.593882i	$-0.797594\pi$
$7$	−4.25729			−1.60910			−0.804552	+	0.593882i	$0.797594\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$	−0.00655751	+	2.23606i	−0.00207367	+	0.707104i
$11$	1.51061	+	4.64918i	0.455466	+	1.40178i	0.870587	+	0.492014i	$0.163739\pi$
$11$	1.51061	+	4.64918i	0.455466	+	1.40178i	−0.415121	+	0.909766i	$0.636261\pi$
$12$		0			0
$13$	−1.43361	+	4.41219i	−0.397611	+	1.22372i	0.529298	+	0.848436i	$0.322456\pi$
$13$	−1.43361	+	4.41219i	−0.397611	+	1.22372i	−0.926909	+	0.375286i	$0.877544\pi$
$14$	−1.31557	−	4.04892i	−0.351602	−	1.08212i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.815575	−	0.592550i	−0.197806	−	0.143714i	0.484473	−	0.874806i	$-0.339011\pi$
$17$	−0.815575	−	0.592550i	−0.197806	−	0.143714i	−0.682279	+	0.731092i	$0.739011\pi$
$18$		0			0
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	0.696555	−	0.717504i	$-0.254715\pi$
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	−0.467139	+	0.884184i	$0.654715\pi$
$20$	−2.12864	+	0.684743i	−0.475979	+	0.153113i
$21$		0			0
$22$	−3.95483	+	2.87335i	−0.843172	+	0.612601i
$23$	1.38197	+	4.25325i	0.288160	+	0.886865i	0.985434	+	0.170060i	$0.0543961\pi$
$23$	1.38197	+	4.25325i	0.288160	+	0.886865i	−0.697274	+	0.716805i	$0.745604\pi$
$24$		0			0
$25$	4.02778	+	2.96260i	0.805556	+	0.592520i
$26$	−4.63925			−0.909833
$27$		0			0
$28$	3.44422	−	2.50237i	0.650896	−	0.472904i
$29$	3.42049	−	2.48513i	0.635170	−	0.461478i	−0.223018	−	0.974814i	$-0.571591\pi$
$29$	3.42049	−	2.48513i	0.635170	−	0.461478i	0.858187	+	0.513337i	$0.171591\pi$
$30$		0			0
$31$	−0.826185	−	0.600258i	−0.148387	−	0.107810i	0.511115	−	0.859513i	$-0.329233\pi$
$31$	−0.826185	−	0.600258i	−0.148387	−	0.107810i	−0.659502	+	0.751703i	$0.729233\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.311522	−	0.958765i	0.0534255	−	0.164427i
$35$	−9.04500	−	2.96825i	−1.52888	−	0.501726i
$36$		0			0
$37$	3.31152	−	10.1918i	0.544411	−	1.67552i	−0.177976	−	0.984035i	$-0.556955\pi$
$37$	3.31152	−	10.1918i	0.544411	−	1.67552i	0.722387	−	0.691489i	$-0.243045\pi$
$38$	−0.381966	+	1.17557i	−0.0619631	+	0.190703i
$39$		0			0
$40$	−1.30902	−	1.81286i	−0.206974	−	0.286639i
$41$	−1.42049	+	4.37183i	−0.221844	+	0.682765i	0.776753	+	0.629806i	$0.216865\pi$
$41$	−1.42049	+	4.37183i	−0.221844	+	0.682765i	−0.998597	+	0.0529595i	$0.983135\pi$
$42$		0			0
$43$	−10.4984			−1.60099			−0.800493	−	0.599342i	$-0.795429\pi$
$43$	−10.4984			−1.60099			−0.800493	+	0.599342i	$0.795429\pi$
$44$	−3.95483	−	2.87335i	−0.596213	−	0.433174i
$45$		0			0
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	−1.63925	+	1.19099i	−0.239110	+	0.173723i	−0.700887	−	0.713273i	$-0.747212\pi$
$47$	−1.63925	+	1.19099i	−0.239110	+	0.173723i	0.461777	+	0.886996i	$0.347212\pi$
$48$		0			0
$49$	11.1245			1.58922
$50$	−1.57295	+	4.74614i	−0.222449	+	0.671205i
$51$		0			0
$52$	−1.43361	−	4.41219i	−0.198806	−	0.611861i
$53$	8.94413	−	6.49829i	1.22857	−	0.892609i	0.231789	−	0.972766i	$-0.425542\pi$
$53$	8.94413	−	6.49829i	1.22857	−	0.892609i	0.996782	+	0.0801570i	$0.0255422\pi$
$54$		0			0
$55$	−0.0320560	+	10.9308i	−0.00432242	+	1.47391i
$56$	3.44422	+	2.50237i	0.460253	+	0.334393i
$57$		0			0
$58$	3.42049	+	2.48513i	0.449133	+	0.326314i
$59$	0.656508	−	2.02052i	0.0854701	−	0.263050i	−0.899183	−	0.437573i	$-0.855838\pi$
$59$	0.656508	−	2.02052i	0.0854701	−	0.263050i	0.984653	+	0.174523i	$0.0558383\pi$
$60$		0			0
$61$	1.19754	+	3.68565i	0.153329	+	0.471899i	0.997988	−	0.0634064i	$-0.0201964\pi$
$61$	1.19754	+	3.68565i	0.153329	+	0.471899i	−0.844658	+	0.535306i	$0.820196\pi$
$62$	0.315575	−	0.971238i	0.0400780	−	0.123347i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−6.12209	+	8.37457i	−0.759351	+	1.03874i
$66$		0			0
$67$	−3.03434	−	2.20457i	−0.370703	−	0.269332i	0.386799	−	0.922164i	$-0.373581\pi$
$67$	−3.03434	−	2.20457i	−0.370703	−	0.269332i	−0.757502	+	0.652832i	$0.773581\pi$
$68$	1.00811			0.122251
$69$		0			0
$70$	0.0279172	−	9.51955i	0.00333674	−	1.13780i
$71$	10.1457	−	7.37130i	1.20408	−	0.874813i	0.209397	−	0.977831i	$-0.432850\pi$
$71$	10.1457	−	7.37130i	1.20408	−	0.874813i	0.994679	+	0.103018i	$0.0328500\pi$
$72$		0			0
$73$	1.05975	+	3.26157i	0.124034	+	0.381738i	0.993724	−	0.111861i	$-0.0356811\pi$
$73$	1.05975	+	3.26157i	0.124034	+	0.381738i	−0.869690	+	0.493599i	$0.835681\pi$
$74$	10.7163			1.24575
$75$		0			0
$76$	−1.23607			−0.141787
$77$	−6.43110	−	19.7929i	−0.732892	−	2.25561i
$78$		0			0
$79$	−5.16968	+	3.75599i	−0.581634	+	0.422582i	−0.839313	−	0.543649i	$-0.817042\pi$
$79$	−5.16968	+	3.75599i	−0.581634	+	0.422582i	0.257679	+	0.966231i	$0.417042\pi$
$80$	1.31963	−	1.80515i	0.147539	−	0.201822i
$81$		0			0
$82$	−4.59681			−0.507633
$83$	5.70151	+	4.14239i	0.625822	+	0.454686i	0.854950	−	0.518710i	$-0.173588\pi$
$83$	5.70151	+	4.14239i	0.625822	+	0.454686i	−0.229128	+	0.973396i	$0.573588\pi$
$84$		0			0
$85$	−1.31963	−	1.82756i	−0.143134	−	0.198226i
$86$	−3.24417	−	9.98454i	−0.349828	−	1.07666i
$87$		0			0
$88$	1.51061	−	4.64918i	0.161032	−	0.495604i
$89$	−0.693488	−	2.13434i	−0.0735096	−	0.226239i	0.907551	−	0.419943i	$-0.137950\pi$
$89$	−0.693488	−	2.13434i	−0.0735096	−	0.226239i	−0.981060	+	0.193704i	$0.937950\pi$
$90$		0			0
$91$	6.10328	−	18.7840i	0.639798	−	1.96910i
$92$	−3.61803	−	2.62866i	−0.377206	−	0.274056i
$93$		0			0
$94$	−1.63925	−	1.19099i	−0.169076	−	0.122841i
$95$	1.61803	+	2.24082i	0.166007	+	0.229904i
$96$		0			0
$97$	6.49586	−	4.71952i	0.659555	−	0.479195i	−0.206958	−	0.978350i	$-0.566356\pi$
$97$	6.49586	−	4.71952i	0.659555	−	0.479195i	0.866513	+	0.499155i	$0.166356\pi$
$98$	3.43766	+	10.5800i	0.347256	+	1.06874i
$99$		0			0
$100$	−4.99991	−	0.0293259i	−0.499991	−	0.00293259i
$101$	17.6310			1.75435			0.877174	−	0.480173i	$-0.159426\pi$
$101$	17.6310			1.75435			0.877174	+	0.480173i	$0.159426\pi$
$102$		0			0
$103$	15.9376	−	11.5793i	1.57038	−	1.14094i	0.643580	−	0.765378i	$-0.277448\pi$
$103$	15.9376	−	11.5793i	1.57038	−	1.14094i	0.926795	−	0.375566i	$-0.122552\pi$
$104$	3.75324	−	2.72689i	0.368035	−	0.267393i
$105$		0			0
$106$	8.94413	+	6.49829i	0.868731	+	0.631170i
$107$	−6.16695			−0.596181			−0.298091	−	0.954538i	$-0.596350\pi$
$107$	−6.16695			−0.596181			−0.298091	+	0.954538i	$0.596350\pi$
$108$		0			0
$109$	2.44982	−	7.53977i	0.234650	−	0.722179i	−0.762517	−	0.646968i	$-0.776037\pi$
$109$	2.44982	−	7.53977i	0.234650	−	0.722179i	0.997168	−	0.0752113i	$-0.0239631\pi$
$110$	−10.4057	+	3.34733i	−0.992149	+	0.319155i
$111$		0			0
$112$	−1.31557	+	4.04892i	−0.124310	+	0.382587i
$113$	−2.08857	+	6.42795i	−0.196476	+	0.604691i	0.803480	+	0.595332i	$0.202979\pi$
$113$	−2.08857	+	6.42795i	−0.196476	+	0.604691i	−0.999956	+	0.00935951i	$0.997021\pi$
$114$		0			0
$115$	−0.0293261	+	9.99996i	−0.00273467	+	0.932501i
$116$	−1.30651	+	4.02103i	−0.121307	+	0.373343i
$117$		0			0
$118$	2.12451			0.195577
$119$	3.47214	+	2.52265i	0.318290	+	0.231251i
$120$		0			0
$121$	−10.4337	+	7.58056i	−0.948523	+	0.689142i
$122$	−3.13520	+	2.27786i	−0.283848	+	0.206228i
$123$		0			0
$124$	1.02122			0.0917083
$125$	6.49181	+	9.10255i	0.580645	+	0.814157i
$126$		0			0
$127$	3.12054	+	9.60403i	0.276903	+	0.852220i	0.988710	+	0.149844i	$0.0478773\pi$
$127$	3.12054	+	9.60403i	0.276903	+	0.852220i	−0.711807	+	0.702376i	$0.752123\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	−9.85652	−	3.23457i	−0.864474	−	0.283690i
$131$	5.43780	+	3.95079i	0.475103	+	0.345182i	0.799427	−	0.600764i	$-0.205137\pi$
$131$	5.43780	+	3.95079i	0.475103	+	0.345182i	−0.324324	+	0.945946i	$0.605137\pi$
$132$		0			0
$133$	−4.25729	−	3.09310i	−0.369154	−	0.268206i
$134$	1.15901	−	3.56708i	0.100123	−	0.308148i
$135$		0			0
$136$	0.311522	+	0.958765i	0.0267128	+	0.0822134i
$137$	−5.44672	+	16.7633i	−0.465345	+	1.43218i	0.393203	+	0.919452i	$0.371367\pi$
$137$	−5.44672	+	16.7633i	−0.465345	+	1.43218i	−0.858548	+	0.512733i	$0.828633\pi$
$138$		0			0
$139$	−2.51976	−	7.75502i	−0.213723	−	0.657772i	−0.999242	−	0.0389342i	$-0.987604\pi$
$139$	−2.51976	−	7.75502i	−0.213723	−	0.657772i	0.785519	−	0.618838i	$-0.212396\pi$
$140$	9.06225	−	2.91515i	0.765900	−	0.246375i
$141$		0			0
$142$	10.1457	+	7.37130i	0.851410	+	0.618586i
$143$	−22.6787			−1.89649
$144$		0			0
$145$	8.99983	−	2.89507i	0.747395	−	0.240422i
$146$	−2.77446	+	2.01576i	−0.229616	+	0.166826i
$147$		0			0
$148$	3.31152	+	10.1918i	0.272205	+	0.837762i
$149$	−10.2230			−0.837497			−0.418748	−	0.908102i	$-0.637531\pi$
$149$	−10.2230			−0.837497			−0.418748	+	0.908102i	$0.637531\pi$
$150$		0			0
$151$	17.2016			1.39984			0.699922	−	0.714220i	$-0.253218\pi$
$151$	17.2016			1.39984			0.699922	+	0.714220i	$0.253218\pi$
$152$	−0.381966	−	1.17557i	−0.0309815	−	0.0953514i
$153$		0			0
$154$	16.8368	−	12.2327i	1.35675	−	0.985738i
$155$	−1.33680	−	1.85133i	−0.107374	−	0.148703i
$156$		0			0
$157$	−18.7425			−1.49582			−0.747909	−	0.663802i	$-0.768942\pi$
$157$	−18.7425			−1.49582			−0.747909	+	0.663802i	$0.768942\pi$
$158$	−5.16968	−	3.75599i	−0.411277	−	0.298811i
$159$		0			0
$160$	2.12459	+	0.697217i	0.167964	+	0.0551198i
$161$	−5.88343	−	18.1073i	−0.463679	−	1.42706i
$162$		0			0
$163$	−4.32624	+	13.3148i	−0.338857	+	1.04289i	0.625934	+	0.779876i	$0.284718\pi$
$163$	−4.32624	+	13.3148i	−0.338857	+	1.04289i	−0.964791	+	0.263019i	$0.915282\pi$
$164$	−1.42049	−	4.37183i	−0.110922	−	0.341383i
$165$		0			0
$166$	−2.17778	+	6.70252i	−0.169029	+	0.520217i
$167$	−10.9309	−	7.94175i	−0.845857	−	0.614551i	0.0781438	−	0.996942i	$-0.475101\pi$
$167$	−10.9309	−	7.94175i	−0.845857	−	0.614551i	−0.924001	+	0.382391i	$0.875101\pi$
$168$		0			0
$169$	−6.89500	−	5.00951i	−0.530384	−	0.385347i
$170$	1.33032	−	1.81979i	0.102031	−	0.139571i
$171$		0			0
$172$	8.49336	−	6.17078i	0.647612	−	0.470518i
$173$	2.77609	+	8.54393i	0.211062	+	0.649583i	0.999410	+	0.0343526i	$0.0109369\pi$
$173$	2.77609	+	8.54393i	0.211062	+	0.649583i	−0.788348	+	0.615230i	$0.789063\pi$
$174$		0			0
$175$	−17.1474	−	12.6126i	−1.29622	−	0.953426i
$176$	4.88844			0.368480
$177$		0			0
$178$	1.81557	−	1.31909i	0.136083	−	0.0988701i
$179$	5.68029	−	4.12697i	0.424565	−	0.308464i	−0.354907	−	0.934902i	$-0.615488\pi$
$179$	5.68029	−	4.12697i	0.424565	−	0.308464i	0.779472	+	0.626437i	$0.215488\pi$
$180$		0			0
$181$	9.66968	+	7.02543i	0.718741	+	0.522196i	0.885982	−	0.463720i	$-0.153486\pi$
$181$	9.66968	+	7.02543i	0.718741	+	0.522196i	−0.167240	+	0.985916i	$0.553486\pi$
$182$	19.7506			1.46402
$183$		0			0
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$	14.1415	−	19.3446i	1.03971	−	1.42224i
$186$		0			0
$187$	1.52285	−	4.68686i	0.111362	−	0.342737i
$188$	0.626140	−	1.92706i	0.0456659	−	0.140545i
$189$		0			0
$190$	−1.63115	+	2.23129i	−0.118336	+	0.161875i
$191$	−1.00000	+	3.07768i	−0.0723575	+	0.222693i	−0.980695	−	0.195545i	$-0.937352\pi$
$191$	−1.00000	+	3.07768i	−0.0723575	+	0.222693i	0.908337	+	0.418239i	$0.137352\pi$
$192$		0			0
$193$	−7.60802			−0.547637			−0.273818	−	0.961781i	$-0.588287\pi$
$193$	−7.60802			−0.547637			−0.273818	+	0.961781i	$0.588287\pi$
$194$	6.49586	+	4.71952i	0.466376	+	0.338842i
$195$		0			0
$196$	−8.99991	+	6.53882i	−0.642851	+	0.467059i
$197$	3.81549	−	2.77211i	0.271842	−	0.197505i	−0.443509	−	0.896270i	$-0.646267\pi$
$197$	3.81549	−	2.77211i	0.271842	−	0.197505i	0.715351	+	0.698765i	$0.246267\pi$
$198$		0			0
$199$	−15.9276			−1.12908			−0.564539	−	0.825406i	$-0.690946\pi$
$199$	−15.9276			−1.12908			−0.564539	+	0.825406i	$0.690946\pi$
$200$	−1.51717	−	4.76426i	−0.107280	−	0.336884i
$201$		0			0
$202$	5.44827	+	16.7681i	0.383339	+	1.17980i
$203$	−14.5620	+	10.5799i	−1.02205	+	0.742566i
$204$		0			0
$205$	−6.06608	+	8.29796i	−0.423673	+	0.579555i
$206$	15.9376	+	11.5793i	1.11042	+	0.806770i
$207$		0			0
$208$	3.75324	+	2.72689i	0.260240	+	0.189075i
$209$	−1.86722	+	5.74670i	−0.129158	+	0.397508i
$210$		0			0
$211$	−3.73443	−	11.4934i	−0.257089	−	0.791239i	−0.993411	−	0.114607i	$-0.963439\pi$
$211$	−3.73443	−	11.4934i	−0.257089	−	0.791239i	0.736322	−	0.676631i	$-0.236561\pi$
$212$	−3.41635	+	10.5145i	−0.234636	+	0.722136i
$213$		0			0
$214$	−1.90569	−	5.86511i	−0.130270	−	0.400931i
$215$	−22.3047	−	7.31963i	−1.52117	−	0.499195i
$216$		0			0
$217$	3.51731	+	2.55547i	0.238770	+	0.173477i
$218$	7.92778			0.536937
$219$		0			0
$220$	−6.39905	−	8.86207i	−0.431424	−	0.597481i
$221$	3.78366	−	2.74899i	0.254516	−	0.184917i
$222$		0			0
$223$	−2.89258	−	8.90243i	−0.193701	−	0.596151i	−0.999989	−	0.00462801i	$-0.998527\pi$
$223$	−2.89258	−	8.90243i	−0.193701	−	0.596151i	0.806288	−	0.591523i	$-0.201473\pi$
$224$	−4.25729			−0.284452
$225$		0			0
$226$	−6.75875			−0.449585
$227$	−3.12864	−	9.62898i	−0.207655	−	0.639098i	−0.999594	−	0.0284967i	$-0.990928\pi$
$227$	−3.12864	−	9.62898i	−0.207655	−	0.639098i	0.791938	−	0.610601i	$-0.209072\pi$
$228$		0			0
$229$	−5.99741	+	4.35737i	−0.396320	+	0.287943i	−0.768040	−	0.640401i	$-0.778768\pi$
$229$	−5.99741	+	4.35737i	−0.396320	+	0.287943i	0.371720	+	0.928345i	$0.378768\pi$
$230$	−9.51959	+	3.06227i	−0.627703	+	0.201920i
$231$		0			0
$232$	−4.22796			−0.277579
$233$	−4.79568	−	3.48426i	−0.314175	−	0.228262i	0.419511	−	0.907750i	$-0.362202\pi$
$233$	−4.79568	−	3.48426i	−0.314175	−	0.228262i	−0.733686	+	0.679489i	$0.762202\pi$
$234$		0			0
$235$	−4.31312	+	1.38745i	−0.281357	+	0.0905071i
$236$	0.656508	+	2.02052i	0.0427351	+	0.131525i
$237$		0			0
$238$	−1.32624	+	4.08174i	−0.0859672	+	0.264580i
$239$	5.10328	+	15.7063i	0.330104	+	1.01596i	0.969084	+	0.246732i	$0.0793568\pi$
$239$	5.10328	+	15.7063i	0.330104	+	1.01596i	−0.638980	+	0.769224i	$0.720643\pi$
$240$		0			0
$241$	−2.48120	+	7.63634i	−0.159828	+	0.491900i	−0.998618	−	0.0525550i	$-0.983264\pi$
$241$	−2.48120	+	7.63634i	−0.159828	+	0.491900i	0.838790	+	0.544455i	$0.183264\pi$
$242$	−10.4337	−	7.58056i	−0.670707	−	0.487297i
$243$		0			0
$244$	−3.13520	−	2.27786i	−0.200711	−	0.145825i
$245$	23.6350	+	7.75619i	1.50999	+	0.495525i
$246$		0			0
$247$	−4.63925	+	3.37062i	−0.295189	+	0.214467i
$248$	0.315575	+	0.971238i	0.0200390	+	0.0616737i
$249$		0			0
$250$	−6.65096	+	8.98692i	−0.420644	+	0.568383i
$251$	−14.4639			−0.912951			−0.456475	−	0.889736i	$-0.650888\pi$
$251$	−14.4639			−0.912951			−0.456475	+	0.889736i	$0.650888\pi$
$252$		0			0
$253$	−17.6865	+	12.8500i	−1.11194	+	0.807874i
$254$	−8.16968	+	5.93562i	−0.512611	+	0.372434i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	1.36075			0.0848810			0.0424405	−	0.999099i	$-0.486487\pi$
$257$	1.36075			0.0848810			0.0424405	+	0.999099i	$0.486487\pi$
$258$		0			0
$259$	−14.0981	+	43.3895i	−0.876014	+	2.69609i
$260$	0.0304219	−	10.3736i	0.00188669	−	0.643346i
$261$		0			0
$262$	−2.07705	+	6.39252i	−0.128321	+	0.394931i
$263$	2.09518	−	6.44830i	0.129194	−	0.397619i	−0.865448	−	0.500999i	$-0.832966\pi$
$263$	2.09518	−	6.44830i	0.129194	−	0.397619i	0.994642	+	0.103380i	$0.0329659\pi$
$264$		0			0
$265$	23.5333	−	7.57022i	1.44564	−	0.465035i
$266$	1.62614	−	5.00474i	0.0997050	−	0.306860i
$267$		0			0
$268$	3.75065			0.229107
$269$	−3.19745	−	2.32309i	−0.194952	−	0.141641i	0.486027	−	0.873944i	$-0.338446\pi$
$269$	−3.19745	−	2.32309i	−0.194952	−	0.141641i	−0.680979	+	0.732303i	$0.738446\pi$
$270$		0			0
$271$	−8.28521	+	6.01955i	−0.503290	+	0.365662i	−0.810272	−	0.586053i	$-0.800681\pi$
$271$	−8.28521	+	6.01955i	−0.503290	+	0.365662i	0.306982	+	0.951715i	$0.400681\pi$
$272$	−0.815575	+	0.592550i	−0.0494515	+	0.0359286i
$273$		0			0
$274$	−17.6260			−1.06482
$275$	−7.68926	+	23.2012i	−0.463680	+	1.39909i
$276$		0			0
$277$	−3.18684	−	9.80810i	−0.191479	−	0.589311i	−1.00000		0.000843804i	$-0.999731\pi$
$277$	−3.18684	−	9.80810i	−0.191479	−	0.589311i	0.808521	−	0.588468i	$-0.200269\pi$
$278$	6.59681	−	4.79287i	0.395651	−	0.287457i
$279$		0			0
$280$	5.57286	+	7.71788i	0.333042	+	0.461232i
$281$	−2.88602	−	2.09682i	−0.172165	−	0.125086i	0.498366	−	0.866967i	$-0.333934\pi$
$281$	−2.88602	−	2.09682i	−0.172165	−	0.125086i	−0.670531	+	0.741881i	$0.733934\pi$
$282$		0			0
$283$	23.2571	+	16.8973i	1.38249	+	1.00444i	0.996642	+	0.0818776i	$0.0260917\pi$
$283$	23.2571	+	16.8973i	1.38249	+	1.00444i	0.385850	+	0.922562i	$0.373908\pi$
$284$	−3.87532	+	11.9270i	−0.229958	+	0.707738i
$285$		0			0
$286$	−7.00811	−	21.5687i	−0.414398	−	1.27539i
$287$	6.04745	−	18.6121i	0.356970	−	1.09864i
$288$		0			0
$289$	−4.93924	−	15.2014i	−0.290544	−	0.894201i
$290$	5.53447	+	7.66472i	0.324996	+	0.450088i
$291$		0			0
$292$	−2.77446	−	2.01576i	−0.162363	−	0.117963i
$293$	−1.78543			−0.104306			−0.0521530	−	0.998639i	$-0.516608\pi$
$293$	−1.78543			−0.104306			−0.0521530	+	0.998639i	$0.516608\pi$
$294$		0			0
$295$	2.80356	−	3.83506i	0.163229	−	0.223286i
$296$	−8.66968	+	6.29889i	−0.503915	+	0.366115i
$297$		0			0
$298$	−3.15907	−	9.72261i	−0.183000	−	0.563215i
$299$	−20.7474			−1.19985
$300$		0			0
$301$	44.6946			2.57615
$302$	5.31557	+	16.3597i	0.305877	+	0.941392i
$303$		0			0
$304$	1.00000	−	0.726543i	0.0573539	−	0.0416701i
$305$	−0.0254125	+	8.66545i	−0.00145511	+	0.496182i
$306$		0			0
$307$	16.2752			0.928877			0.464439	−	0.885605i	$-0.346256\pi$
$307$	16.2752			0.928877			0.464439	+	0.885605i	$0.346256\pi$
$308$	16.8368	+	12.2327i	0.959368	+	0.697022i
$309$		0			0
$310$	1.34763	−	1.84346i	0.0765403	−	0.104702i
$311$	−4.00501	−	12.3262i	−0.227103	−	0.698952i	−0.998071	−	0.0620781i	$-0.980227\pi$
$311$	−4.00501	−	12.3262i	−0.227103	−	0.698952i	0.770968	−	0.636874i	$-0.219773\pi$
$312$		0			0
$313$	−1.29075	+	3.97253i	−0.0729577	+	0.224541i	−0.980885	−	0.194586i	$-0.937664\pi$
$313$	−1.29075	+	3.97253i	−0.0729577	+	0.224541i	0.907928	+	0.419127i	$0.137664\pi$
$314$	−5.79176	−	17.8252i	−0.326848	−	1.00594i
$315$		0			0
$316$	1.97464	−	6.07732i	0.111082	−	0.341876i
$317$	24.4480	+	17.7625i	1.37314	+	0.997643i	0.997485	+	0.0708820i	$0.0225814\pi$
$317$	24.4480	+	17.7625i	1.37314	+	0.997643i	0.375653	+	0.926761i	$0.377419\pi$
$318$		0			0
$319$	16.7209	+	12.1484i	0.936189	+	0.680181i
$320$	−0.00655751	+	2.23606i	−0.000366576	+	0.124999i
$321$		0			0
$322$	15.4030	−	11.1909i	0.858376	−	0.623647i
$323$	−0.385062	−	1.18510i	−0.0214254	−	0.0659407i
$324$		0			0
$325$	−18.8458	+	13.5241i	−1.04538	+	0.750183i
$326$	−14.0000			−0.775388
$327$		0			0
$328$	3.71890	−	2.70194i	0.205342	−	0.149190i
$329$	6.97878	−	5.07038i	0.384753	−	0.279539i
$330$		0			0
$331$	−11.3949	−	8.27889i	−0.626321	−	0.455049i	0.228803	−	0.973473i	$-0.426519\pi$
$331$	−11.3949	−	8.27889i	−0.626321	−	0.455049i	−0.855124	+	0.518424i	$0.826519\pi$
$332$	−7.04745			−0.386779
$333$		0			0
$334$	4.17522	−	12.8500i	0.228458	−	0.703122i
$335$	−4.90966	−	6.79941i	−0.268243	−	0.371491i
$336$		0			0
$337$	4.15155	−	12.7772i	0.226149	−	0.696016i	−0.772023	−	0.635594i	$-0.780755\pi$
$337$	4.15155	−	12.7772i	0.226149	−	0.696016i	0.998173	−	0.0604224i	$-0.0192448\pi$
$338$	2.63365	−	8.10555i	0.143252	−	0.440884i
$339$		0			0
$340$	2.14181	+	0.702868i	0.116156	+	0.0381184i
$341$	1.54267	−	4.74784i	0.0835401	−	0.257110i
$342$		0			0
$343$	−17.5592			−0.948108
$344$	8.49336	+	6.17078i	0.457931	+	0.332706i
$345$		0			0
$346$	−7.26790	+	5.28044i	−0.390725	+	0.283878i
$347$	4.55975	−	3.31285i	0.244780	−	0.177843i	−0.458630	−	0.888627i	$-0.651660\pi$
$347$	4.55975	−	3.31285i	0.244780	−	0.177843i	0.703410	+	0.710784i	$0.251660\pi$
$348$		0			0
$349$	24.1159			1.29090			0.645449	−	0.763804i	$-0.276670\pi$
$349$	24.1159			1.29090			0.645449	+	0.763804i	$0.276670\pi$
$350$	6.69650	−	20.2057i	0.357943	−	1.08004i
$351$		0			0
$352$	1.51061	+	4.64918i	0.0805158	+	0.247802i
$353$	19.1672	−	13.9258i	1.02017	−	0.741196i	0.0538510	−	0.998549i	$-0.482850\pi$
$353$	19.1672	−	13.9258i	1.02017	−	0.741196i	0.966317	+	0.257353i	$0.0828504\pi$
$354$		0			0
$355$	26.6949	−	8.58724i	1.41682	−	0.455763i
$356$	1.81557	+	1.31909i	0.0962253	+	0.0699117i
$357$		0			0
$358$	5.68029	+	4.12697i	0.300212	+	0.218117i
$359$	0.849092	−	2.61324i	0.0448134	−	0.137921i	−0.926146	−	0.377164i	$-0.876899\pi$
$359$	0.849092	−	2.61324i	0.0448134	−	0.137921i	0.970960	+	0.239243i	$0.0768992\pi$
$360$		0			0
$361$	−5.39919	−	16.6170i	−0.284168	−	0.874578i
$362$	−3.69349	+	11.3674i	−0.194125	+	0.597457i
$363$		0			0
$364$	6.10328	+	18.7840i	0.319899	+	0.984548i
$365$	−0.0224884	+	7.66838i	−0.00117710	+	0.401381i
$366$		0			0
$367$	4.33266	+	3.14786i	0.226163	+	0.164317i	0.695096	−	0.718917i	$-0.255362\pi$
$367$	4.33266	+	3.14786i	0.226163	+	0.164317i	−0.468934	+	0.883233i	$0.655362\pi$
$368$	4.47214			0.233126
$369$		0			0
$370$	22.7678	+	7.47159i	1.18364	+	0.388429i
$371$	−38.0778	+	27.6651i	−1.97690	+	1.43630i
$372$		0			0
$373$	−8.66048	−	26.6542i	−0.448422	−	1.38010i	−0.878687	−	0.477399i	$-0.841580\pi$
$373$	−8.66048	−	26.6542i	−0.448422	−	1.38010i	0.430264	−	0.902703i	$-0.358420\pi$
$374$	4.92806			0.254824
$375$		0			0
$376$	2.02623			0.104495
$377$	6.06124	+	18.6546i	0.312170	+	0.960760i
$378$		0			0
$379$	2.20145	−	1.59945i	0.113081	−	0.0821582i	−0.529807	−	0.848118i	$-0.677736\pi$
$379$	2.20145	−	1.59945i	0.113081	−	0.0821582i	0.642889	+	0.765960i	$0.277736\pi$
$380$	−2.62614	−	0.861807i	−0.134718	−	0.0442098i
$381$		0			0
$382$	−3.23607			−0.165572
$383$	13.6522	+	9.91890i	0.697595	+	0.506832i	0.879148	−	0.476549i	$-0.158112\pi$
$383$	13.6522	+	9.91890i	0.697595	+	0.506832i	−0.181553	+	0.983381i	$0.558112\pi$
$384$		0			0
$385$	0.136471	−	46.5357i	0.00695523	−	2.37168i
$386$	−2.35101	−	7.23565i	−0.119663	−	0.368285i
$387$		0			0
$388$	−2.48120	+	7.63634i	−0.125964	+	0.387677i
$389$	−11.9654	−	36.8258i	−0.606672	−	1.86714i	−0.484862	−	0.874590i	$-0.661130\pi$
$389$	−11.9654	−	36.8258i	−0.606672	−	1.86714i	−0.121810	−	0.992553i	$-0.538870\pi$
$390$		0			0
$391$	1.39317	−	4.28773i	0.0704555	−	0.216840i
$392$	−8.99991	−	6.53882i	−0.454564	−	0.330260i
$393$		0			0
$394$	3.81549	+	2.77211i	0.192222	+	0.139657i
$395$	−13.6022	+	4.37556i	−0.684400	+	0.220158i
$396$		0			0
$397$	−20.0261	+	14.5498i	−1.00508	+	0.730233i	−0.963171	−	0.268889i	$-0.913344\pi$
$397$	−20.0261	+	14.5498i	−1.00508	+	0.730233i	−0.0419078	+	0.999121i	$0.513344\pi$
$398$	−4.92190	−	15.1481i	−0.246713	−	0.759304i
$399$		0			0
$400$	4.06225	−	2.91515i	0.203113	−	0.145758i
$401$	3.31830			0.165708			0.0828541	−	0.996562i	$-0.473596\pi$
$401$	3.31830			0.165708			0.0828541	+	0.996562i	$0.473596\pi$
$402$		0			0
$403$	3.83288	−	2.78475i	0.190929	−	0.138718i
$404$	−14.2638	+	10.3632i	−0.709649	+	0.515590i
$405$		0			0
$406$	−14.5620	−	10.5799i	−0.722701	−	0.525073i
$407$	52.3860			2.59668
$408$		0			0
$409$	−8.76950	+	26.9897i	−0.433624	+	1.33456i	0.460866	+	0.887470i	$0.347539\pi$
$409$	−8.76950	+	26.9897i	−0.433624	+	1.33456i	−0.894490	+	0.447087i	$0.852461\pi$
$410$	−9.76635	−	3.20497i	−0.482326	−	0.158282i
$411$		0			0
$412$	−6.08761	+	18.7357i	−0.299915	+	0.923044i
$413$	−2.79495	+	8.60196i	−0.137530	+	0.423275i
$414$		0			0
$415$	9.22523	+	12.7761i	0.452849	+	0.627152i
$416$	−1.43361	+	4.41219i	−0.0702884	+	0.216326i
$417$		0			0
$418$	−6.04244			−0.295545
$419$	11.9931	+	8.71352i	0.585903	+	0.425683i	0.840847	−	0.541272i	$-0.182057\pi$
$419$	11.9931	+	8.71352i	0.585903	+	0.425683i	−0.254945	+	0.966956i	$0.582057\pi$
$420$		0			0
$421$	−14.7255	+	10.6987i	−0.717677	+	0.521423i	−0.885641	−	0.464370i	$-0.846281\pi$
$421$	−14.7255	+	10.6987i	−0.717677	+	0.521423i	0.167964	+	0.985793i	$0.446281\pi$
$422$	9.77688	−	7.10332i	0.475931	−	0.345784i
$423$		0			0
$424$	−11.0556			−0.536905
$425$	−1.52947	−	4.80288i	−0.0741900	−	0.232974i
$426$		0			0
$427$	−5.09828	−	15.6909i	−0.246723	−	0.759335i
$428$	4.98916	−	3.62484i	0.241160	−	0.175213i
$429$		0			0
$430$	0.0688431	−	23.4750i	0.00331991	−	1.13206i
$431$	14.3606	+	10.4336i	0.691724	+	0.502567i	0.877227	−	0.480077i	$-0.159391\pi$
$431$	14.3606	+	10.4336i	0.691724	+	0.502567i	−0.185502	+	0.982644i	$0.559391\pi$
$432$		0			0
$433$	−17.5703	−	12.7656i	−0.844373	−	0.613473i	0.0792155	−	0.996858i	$-0.474758\pi$
$433$	−17.5703	−	12.7656i	−0.844373	−	0.613473i	−0.923589	+	0.383384i	$0.874758\pi$
$434$	−1.34349	+	4.13484i	−0.0644897	+	0.198479i
$435$		0			0
$436$	2.44982	+	7.53977i	0.117325	+	0.361089i
$437$	−1.70820	+	5.25731i	−0.0817145	+	0.251491i
$438$		0			0
$439$	3.31399	+	10.1994i	0.158168	+	0.486792i	0.998468	−	0.0553300i	$-0.0176211\pi$
$439$	3.31399	+	10.1994i	0.158168	+	0.486792i	−0.840300	+	0.542122i	$0.817621\pi$
$440$	6.45092	−	8.82439i	0.307535	−	0.420686i
$441$		0			0
$442$	3.78366	+	2.74899i	0.179970	+	0.130756i
$443$	−25.5092			−1.21198			−0.605990	−	0.795472i	$-0.707223\pi$
$443$	−25.5092			−1.21198			−0.605990	+	0.795472i	$0.707223\pi$
$444$		0			0
$445$	0.0147162	−	5.01810i	0.000697614	−	0.237881i
$446$	7.57286	−	5.50201i	0.358585	−	0.260528i
$447$		0			0
$448$	−1.31557	−	4.04892i	−0.0621551	−	0.191294i
$449$	12.5619			0.592831			0.296415	−	0.955059i	$-0.404209\pi$
$449$	12.5619			0.592831			0.296415	+	0.955059i	$0.404209\pi$
$450$		0			0
$451$	−22.4712			−1.05813
$452$	−2.08857	−	6.42795i	−0.0982380	−	0.302346i
$453$		0			0
$454$	8.19090	−	5.95104i	0.384418	−	0.279296i
$455$	26.0635	−	35.6530i	1.22188	−	1.67144i
$456$		0			0
$457$	3.04289			0.142340			0.0711702	−	0.997464i	$-0.477327\pi$
$457$	3.04289			0.142340			0.0711702	+	0.997464i	$0.477327\pi$
$458$	−5.99741	−	4.35737i	−0.280241	−	0.203607i
$459$		0			0
$460$	−5.85410	−	8.10737i	−0.272949	−	0.378008i
$461$	8.52674	+	26.2426i	0.397130	+	1.22224i	0.927291	+	0.374342i	$0.122132\pi$
$461$	8.52674	+	26.2426i	0.397130	+	1.22224i	−0.530161	+	0.847897i	$0.677868\pi$
$462$		0			0
$463$	9.33417	−	28.7276i	0.433796	−	1.33509i	−0.460520	−	0.887649i	$-0.652337\pi$
$463$	9.33417	−	28.7276i	0.433796	−	1.33509i	0.894316	−	0.447437i	$-0.147663\pi$
$464$	−1.30651	−	4.02103i	−0.0606533	−	0.186672i
$465$		0			0
$466$	1.83179	−	5.63766i	0.0848558	−	0.261159i
$467$	24.1271	+	17.5293i	1.11647	+	0.811161i	0.983670	−	0.179982i	$-0.0576040\pi$
$467$	24.1271	+	17.5293i	1.11647	+	0.811161i	0.132797	+	0.991143i	$0.457604\pi$
$468$		0			0
$469$	12.9180	+	9.38551i	0.596500	+	0.433382i
$470$	−2.65237	−	3.67328i	−0.122345	−	0.169436i
$471$		0			0
$472$	−1.71876	+	1.24875i	−0.0791124	+	0.0574785i
$473$	−15.8589	−	48.8088i	−0.729195	−	2.24423i
$474$		0			0
$475$	1.87532	+	5.88895i	0.0860457	+	0.270204i
$476$	−4.29180			−0.196714
$477$		0			0
$478$	−13.3606	+	9.70702i	−0.611098	+	0.443989i
$479$	5.27040	−	3.82917i	0.240811	−	0.174959i	−0.460834	−	0.887487i	$-0.652450\pi$
$479$	5.27040	−	3.82917i	0.240811	−	0.174959i	0.701644	+	0.712527i	$0.252450\pi$
$480$		0			0
$481$	40.2208	+	29.2221i	1.83391	+	1.33242i
$482$	−8.02933			−0.365726
$483$		0			0
$484$	3.98534	−	12.2656i	0.181152	−	0.557528i
$485$	17.0916	−	5.49803i	0.776089	−	0.249653i
$486$		0			0
$487$	12.4222	−	38.2315i	0.562903	−	1.73244i	−0.111199	−	0.993798i	$-0.535469\pi$
$487$	12.4222	−	38.2315i	0.562903	−	1.73244i	0.674102	−	0.738638i	$-0.264531\pi$
$488$	1.19754	−	3.68565i	0.0542101	−	0.166842i
$489$		0			0
$490$	−0.0729490	+	24.8750i	−0.00329550	+	1.12374i
$491$	11.3187	−	34.8353i	0.510804	−	1.57209i	−0.279984	−	0.960005i	$-0.590329\pi$
$491$	11.3187	−	34.8353i	0.510804	−	1.57209i	0.790788	−	0.612090i	$-0.209671\pi$
$492$		0			0
$493$	−4.26223			−0.191961
$494$	−4.63925	−	3.37062i	−0.208730	−	0.151651i
$495$		0			0
$496$	−0.826185	+	0.600258i	−0.0370968	+	0.0269524i
$497$	−43.1933	+	31.3818i	−1.93748	+	1.40766i
$498$		0			0
$499$	−24.9343			−1.11621			−0.558105	−	0.829770i	$-0.688471\pi$
$499$	−24.9343			−1.11621			−0.558105	+	0.829770i	$0.688471\pi$
$500$	−10.6023	−	3.54833i	−0.474151	−	0.158686i
$501$		0			0
$502$	−4.46958	−	13.7559i	−0.199487	−	0.613958i
$503$	34.9784	−	25.4133i	1.55961	−	1.13312i	0.623284	−	0.781996i	$-0.285798\pi$
$503$	34.9784	−	25.4133i	1.55961	−	1.13312i	0.936327	−	0.351128i	$-0.114202\pi$
$504$		0			0
$505$	37.4586	+	12.2926i	1.66689	+	0.547014i
$506$	−17.6865	−	12.8500i	−0.786262	−	0.571253i
$507$		0			0
$508$	−8.16968	−	5.93562i	−0.362471	−	0.263350i
$509$	−9.55465	+	29.4062i	−0.423503	+	1.30341i	0.480918	+	0.876765i	$0.340303\pi$
$509$	−9.55465	+	29.4062i	−0.423503	+	1.30341i	−0.904421	+	0.426641i	$0.859697\pi$
$510$		0			0
$511$	−4.51165	−	13.8854i	−0.199584	−	0.614256i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	0.420493	+	1.29415i	0.0185472	+	0.0570823i
$515$	41.9341	−	13.4894i	1.84784	−	0.594414i
$516$		0			0
$517$	−8.01339	−	5.82207i	−0.352429	−	0.256054i
$518$	−45.6224			−2.00453
$519$		0			0
$520$	9.87532	−	3.17670i	0.433062	−	0.139307i
$521$	−23.9548	+	17.4042i	−1.04948	+	0.762491i	−0.972113	−	0.234512i	$-0.924651\pi$
$521$	−23.9548	+	17.4042i	−1.04948	+	0.762491i	−0.0773654	+	0.997003i	$0.524651\pi$
$522$		0			0
$523$	3.64736	+	11.2254i	0.159488	+	0.490853i	0.998588	−	0.0531238i	$-0.0169178\pi$
$523$	3.64736	+	11.2254i	0.159488	+	0.490853i	−0.839100	+	0.543977i	$0.816918\pi$
$524$	−6.72149			−0.293630
$525$		0			0
$526$	6.78014			0.295628
$527$	0.318132	+	0.979111i	0.0138581	+	0.0426507i
$528$		0			0
$529$	2.42705	−	1.76336i	0.105524	−	0.0766676i
$530$	14.4719	+	20.0422i	0.628620	+	0.870578i
$531$		0			0
$532$	5.26230			0.228150
$533$	−17.2529	−	12.5350i	−0.747307	−	0.542950i
$534$		0			0
$535$	−13.1022	−	4.29970i	−0.566459	−	0.185892i
$536$	1.15901	+	3.56708i	0.0500617	+	0.154074i
$537$		0			0
$538$	1.22132	−	3.75883i	0.0526548	−	0.162055i
$539$	16.8048	+	51.7198i	0.723834	+	2.22773i
$540$		0			0
$541$	4.69039	−	14.4355i	0.201656	−	0.620632i	−0.798178	−	0.602421i	$-0.794203\pi$
$541$	4.69039	−	14.4355i	0.201656	−	0.620632i	0.999834	−	0.0182113i	$-0.00579717\pi$
$542$	−8.28521	−	6.01955i	−0.355880	−	0.258562i
$543$		0			0
$544$	−0.815575	−	0.592550i	−0.0349675	−	0.0254054i
$545$	10.4617	−	14.3109i	0.448131	−	0.613011i
$546$		0			0
$547$	−28.2147	+	20.4992i	−1.20637	+	0.876481i	−0.994896	−	0.100902i	$-0.967827\pi$
$547$	−28.2147	+	20.4992i	−1.20637	+	0.876481i	−0.211476	+	0.977383i	$0.567827\pi$
$548$	−5.44672	−	16.7633i	−0.232672	−	0.716092i
$549$		0			0
$550$	−24.4418	−	0.143358i	−1.04220	−	0.00611281i
$551$	5.22605			0.222637
$552$		0			0
$553$	22.0088	−	15.9903i	0.935910	−	0.679978i
$554$	8.34327	−	6.06174i	0.354471	−	0.257539i
$555$		0			0
$556$	6.59681	+	4.79287i	0.279767	+	0.203263i
$557$	−31.4820			−1.33393			−0.666967	−	0.745087i	$-0.732408\pi$
$557$	−31.4820			−1.33393			−0.666967	+	0.745087i	$0.732408\pi$
$558$		0			0
$559$	15.0505	−	46.3208i	0.636570	−	1.95916i
$560$	−5.61803	+	7.68506i	−0.237405	+	0.324753i
$561$		0			0
$562$	1.10236	−	3.39272i	0.0465003	−	0.143113i
$563$	−0.272961	+	0.840089i	−0.0115040	+	0.0354055i	−0.956644	−	0.291261i	$-0.905925\pi$
$563$	−0.272961	+	0.840089i	−0.0115040	+	0.0354055i	0.945140	+	0.326666i	$0.105925\pi$
$564$		0			0
$565$	−8.91903	+	12.2006i	−0.375226	+	0.513283i
$566$	−8.88343	+	27.3404i	−0.373398	+	1.14920i
$567$		0			0
$568$	−12.5408			−0.526201
$569$	−4.94008	−	3.58918i	−0.207099	−	0.150466i	0.479401	−	0.877596i	$-0.340854\pi$
$569$	−4.94008	−	3.58918i	−0.207099	−	0.150466i	−0.686500	+	0.727130i	$0.740854\pi$
$570$		0			0
$571$	0.0293261	−	0.0213066i	0.00122726	−	0.000891655i	−0.587171	−	0.809463i	$-0.699759\pi$
$571$	0.0293261	−	0.0213066i	0.00122726	−	0.000891655i	0.588399	+	0.808571i	$0.299759\pi$
$572$	18.3475	−	13.3302i	0.767146	−	0.557364i
$573$		0			0
$574$	19.5700			0.816834
$575$	−7.03444	+	21.2254i	−0.293357	+	0.885159i
$576$		0			0
$577$	12.3368	+	37.9688i	0.513587	+	1.58066i	0.785837	+	0.618433i	$0.212232\pi$
$577$	12.3368	+	37.9688i	0.513587	+	1.58066i	−0.272250	+	0.962227i	$0.587768\pi$
$578$	12.9311	−	9.39500i	0.537863	−	0.390780i
$579$		0			0
$580$	−5.57933	+	7.63213i	−0.231669	+	0.316907i
$581$	−24.2730	−	17.6353i	−1.00701	−	0.731637i
$582$		0			0
$583$	43.7228	+	31.7665i	1.81081	+	1.31563i
$584$	1.05975	−	3.26157i	0.0438527	−	0.134965i
$585$		0			0
$586$	−0.551728	−	1.69805i	−0.0227917	−	0.0701456i
$587$	5.39111	−	16.5921i	0.222515	−	0.684831i	−0.776019	−	0.630709i	$-0.782764\pi$
$587$	5.39111	−	16.5921i	0.222515	−	0.684831i	0.998534	−	0.0541218i	$-0.0172359\pi$
$588$		0			0
$589$	−0.390072	−	1.20052i	−0.0160726	−	0.0494664i
$590$	4.51371	+	1.48124i	0.185826	+	0.0609817i
$591$		0			0
$592$	−8.66968	−	6.29889i	−0.356322	−	0.258883i
$593$	5.43780			0.223304			0.111652	−	0.993747i	$-0.464386\pi$
$593$	5.43780			0.223304			0.111652	+	0.993747i	$0.464386\pi$
$594$		0			0
$595$	5.61803	+	7.78044i	0.230317	+	0.318967i
$596$	8.27054	−	6.00890i	0.338775	−	0.246134i
$597$		0			0
$598$	−6.41129	−	19.7319i	−0.262177	−	0.806899i
$599$	−28.7804			−1.17593			−0.587967	−	0.808885i	$-0.700071\pi$
$599$	−28.7804			−1.17593			−0.587967	+	0.808885i	$0.700071\pi$
$600$		0			0
$601$	−41.4162			−1.68940			−0.844702	−	0.535237i	$-0.820222\pi$
$601$	−41.4162			−1.68940			−0.844702	+	0.535237i	$0.820222\pi$
$602$	13.8114	+	42.5071i	0.562910	+	1.73246i
$603$		0			0
$604$	−13.9164	+	10.1108i	−0.566248	+	0.411404i
$605$	−27.4527	+	8.83101i	−1.11611	+	0.359032i
$606$		0			0
$607$	23.9868			0.973595			0.486797	−	0.873515i	$-0.338165\pi$
$607$	23.9868			0.973595			0.486797	+	0.873515i	$0.338165\pi$
$608$	1.00000	+	0.726543i	0.0405554	+	0.0294652i
$609$		0			0
$610$	−8.24918	+	2.65360i	−0.334000	+	0.107441i
$611$	−2.90482	−	8.94012i	−0.117516	−	0.361678i
$612$		0			0
$613$	0.131288	−	0.404063i	0.00530268	−	0.0163200i	−0.948370	−	0.317166i	$-0.897269\pi$
$613$	0.131288	−	0.404063i	0.00530268	−	0.0163200i	0.953673	+	0.300846i	$0.0972689\pi$
$614$	5.02933	+	15.4787i	0.202967	+	0.624668i
$615$		0			0
$616$	−6.43110	+	19.7929i	−0.259117	+	0.797479i
$617$	26.5991	+	19.3253i	1.07084	+	0.778009i	0.976063	−	0.217489i	$-0.0697868\pi$
$617$	26.5991	+	19.3253i	1.07084	+	0.778009i	0.0947752	+	0.995499i	$0.469787\pi$
$618$		0			0
$619$	−9.53580	−	6.92816i	−0.383276	−	0.278466i	0.379419	−	0.925225i	$-0.376124\pi$
$619$	−9.53580	−	6.92816i	−0.383276	−	0.278466i	−0.762695	+	0.646759i	$0.776124\pi$
$620$	2.16968	+	0.712012i	0.0871363	+	0.0285951i
$621$		0			0
$622$	10.4853	−	7.61798i	0.420420	−	0.305453i
$623$	2.95238	+	9.08648i	0.118285	+	0.364042i
$624$		0			0
$625$	7.44599	+	23.8654i	0.297840	+	0.954616i
$626$	−4.17697			−0.166945
$627$		0			0
$628$	15.1630	−	11.0166i	0.605071	−	0.439610i
$629$	−8.73995	+	6.34994i	−0.348485	+	0.253189i
$630$		0			0
$631$	−27.0900	−	19.6820i	−1.07844	−	0.783529i	−0.101026	−	0.994884i	$-0.532213\pi$
$631$	−27.0900	−	19.6820i	−1.07844	−	0.783529i	−0.977410	+	0.211354i	$0.932213\pi$
$632$	6.39007			0.254183
$633$		0			0
$634$	−9.33831	+	28.7404i	−0.370872	+	1.14143i
$635$	−0.0662195	+	22.5803i	−0.00262784	+	0.896073i
$636$		0			0
$637$	−15.9482	+	49.0835i	−0.631890	+	1.94476i
$638$	−6.38680	+	19.6566i	−0.252856	+	0.778211i
$639$		0			0
$640$	−2.12864	+	0.684743i	−0.0841421	+	0.0270669i
$641$	5.17714	−	15.9336i	0.204485	−	0.629339i	−0.795250	−	0.606282i	$-0.792660\pi$
$641$	5.17714	−	15.9336i	0.204485	−	0.629339i	0.999734	−	0.0230567i	$-0.00733983\pi$
$642$		0			0
$643$	14.5246			0.572794			0.286397	−	0.958111i	$-0.407542\pi$
$643$	14.5246			0.572794			0.286397	+	0.958111i	$0.407542\pi$
$644$	15.4030	+	11.1909i	0.606964	+	0.440985i
$645$		0			0
$646$	1.00811	−	0.732432i	0.0396634	−	0.0288171i
$647$	12.8965	−	9.36989i	0.507015	−	0.368368i	−0.304675	−	0.952456i	$-0.598548\pi$
$647$	12.8965	−	9.36989i	0.507015	−	0.368368i	0.811690	+	0.584088i	$0.198548\pi$
$648$		0			0
$649$	10.3855			0.407667
$650$	−18.6859	−	13.7443i	−0.732921	−	0.539094i
$651$		0			0
$652$	−4.32624	−	13.3148i	−0.169429	−	0.521447i
$653$	−20.3233	+	14.7657i	−0.795312	+	0.577828i	−0.909535	−	0.415627i	$-0.863562\pi$
$653$	−20.3233	+	14.7657i	−0.795312	+	0.577828i	0.114223	+	0.993455i	$0.463562\pi$
$654$		0			0
$655$	8.79855	+	12.1851i	0.343788	+	0.476113i
$656$	3.71890	+	2.70194i	0.145199	+	0.105493i
$657$		0			0
$658$	6.97878	+	5.07038i	0.272061	+	0.197664i
$659$	3.40766	−	10.4877i	0.132744	−	0.408543i	−0.862489	−	0.506076i	$-0.831095\pi$
$659$	3.40766	−	10.4877i	0.132744	−	0.408543i	0.995232	+	0.0975338i	$0.0310954\pi$
$660$		0			0
$661$	−4.20173	−	12.9316i	−0.163428	−	0.502981i	0.835489	−	0.549508i	$-0.185185\pi$
$661$	−4.20173	−	12.9316i	−0.163428	−	0.502981i	−0.998917	+	0.0465267i	$0.985185\pi$
$662$	4.35247	−	13.3955i	0.169163	−	0.520632i
$663$		0			0
$664$	−2.17778	−	6.70252i	−0.0845143	−	0.260108i
$665$	−6.88844	−	9.53983i	−0.267122	−	0.369939i
$666$		0			0
$667$	15.2969	+	11.1139i	0.592299	+	0.430330i
$668$	13.5113			0.522768
$669$		0			0
$670$	4.94945	−	6.77049i	0.191214	−	0.261567i
$671$	−15.3262	+	11.1352i	−0.591663	+	0.429868i
$672$		0			0
$673$	−6.81053	−	20.9607i	−0.262527	−	0.807974i	−0.992253	−	0.124235i	$-0.960352\pi$
$673$	−6.81053	−	20.9607i	−0.262527	−	0.807974i	0.729726	−	0.683740i	$-0.239648\pi$
$674$	13.4347			0.517485
$675$		0			0
$676$	8.52268			0.327795
$677$	−10.3185	−	31.7571i	−0.396572	−	1.22052i	−0.927730	−	0.373251i	$-0.878243\pi$
$677$	−10.3185	−	31.7571i	−0.396572	−	1.22052i	0.531158	−	0.847273i	$-0.321757\pi$
$678$		0			0
$679$	−27.6548	+	20.0924i	−1.06129	+	0.771074i
$680$	−0.00661066	+	2.25418i	−0.000253507	+	0.0864440i
$681$		0			0
$682$	4.99217			0.191160
$683$	2.88616	+	2.09692i	0.110436	+	0.0802363i	0.641632	−	0.767012i	$-0.278257\pi$
$683$	2.88616	+	2.09692i	0.110436	+	0.0802363i	−0.531197	+	0.847249i	$0.678257\pi$
$684$		0			0
$685$	−23.2597	+	31.8176i	−0.888708	+	1.21569i
$686$	−5.42609	−	16.6998i	−0.207169	−	0.637601i
$687$		0			0
$688$	−3.24417	+	9.98454i	−0.123683	+	0.380657i
$689$	15.8493	+	48.7792i	0.603812	+	1.85834i
$690$		0			0
$691$	−11.6129	+	35.7407i	−0.441774	+	1.35964i	0.444210	+	0.895923i	$0.353485\pi$
$691$	−11.6129	+	35.7407i	−0.441774	+	1.35964i	−0.885983	+	0.463717i	$0.846515\pi$
$692$	−7.26790	−	5.28044i	−0.276284	−	0.200732i
$693$		0			0
$694$	4.55975	+	3.31285i	0.173086	+	0.125754i
$695$	0.0534706	−	18.2331i	0.00202826	−	0.691620i
$696$		0			0
$697$	3.74904	−	2.72384i	0.142005	−	0.103173i
$698$	7.45224	+	22.9356i	0.282071	+	0.868126i
$699$		0			0
$700$	21.2861	+	0.124849i	0.804538	+	0.00471885i
$701$	−26.4948			−1.00070			−0.500348	−	0.865825i	$-0.666795\pi$
$701$	−26.4948			−1.00070			−0.500348	+	0.865825i	$0.666795\pi$
$702$		0			0
$703$	10.7163	−	7.78585i	0.404173	−	0.293649i
$704$	−3.95483	+	2.87335i	−0.149053	+	0.108294i
$705$		0			0
$706$	19.1672	+	13.9258i	0.721368	+	0.524105i
$707$	−75.0602			−2.82293
$708$		0			0
$709$	11.5055	−	35.4104i	0.432100	−	1.32987i	−0.463930	−	0.885872i	$-0.653561\pi$
$709$	11.5055	−	35.4104i	0.432100	−	1.32987i	0.896029	−	0.443995i	$-0.146439\pi$
$710$	16.4161	+	22.7348i	0.616086	+	0.853221i
$711$		0			0
$712$	−0.693488	+	2.13434i	−0.0259896	+	0.0799876i
$713$	1.41129	−	4.34351i	0.0528533	−	0.162666i
$714$		0			0
$715$	−48.1830	−	15.8120i	−1.80194	−	0.591334i
$716$	−2.16968	+	6.67758i	−0.0810846	+	0.249553i
$717$		0			0
$718$	2.74772			0.102544
$719$	−0.501912	−	0.364661i	−0.0187182	−	0.0135995i	0.578387	−	0.815763i	$-0.303682\pi$
$719$	−0.501912	−	0.364661i	−0.0187182	−	0.0135995i	−0.597105	+	0.802163i	$0.703682\pi$
$720$		0			0
$721$	−67.8509	+	49.2965i	−2.52690	+	1.83590i
$722$	14.1353	−	10.2699i	0.526060	−	0.382205i
$723$		0			0
$724$	−11.9524			−0.444207
$725$	21.1394	+	0.123989i	0.785099	+	0.00460483i
$726$		0			0
$727$	−0.0770549	−	0.237151i	−0.00285781	−	0.00879543i	0.949617	−	0.313411i	$-0.101472\pi$
$727$	−0.0770549	−	0.237151i	−0.00285781	−	0.00879543i	−0.952475	+	0.304616i	$0.901472\pi$
$728$	−15.9786	+	11.6091i	−0.592207	+	0.430263i
$729$		0			0
$730$	−7.30001	+	2.34827i	−0.270185	+	0.0869134i
$731$	8.56220	+	6.22080i	0.316684	+	0.230085i
$732$		0			0
$733$	−34.4927	−	25.0604i	−1.27402	−	0.925628i	−0.274663	−	0.961540i	$-0.588566\pi$
$733$	−34.4927	−	25.0604i	−1.27402	−	0.925628i	−0.999355	+	0.0359121i	$0.988566\pi$
$734$	−1.65493	+	5.09334i	−0.0610845	+	0.187999i
$735$		0			0
$736$	1.38197	+	4.25325i	0.0509399	+	0.156777i
$737$	5.66576	−	17.4374i	0.208701	−	0.642316i
$738$		0			0
$739$	4.86029	+	14.9584i	0.178789	+	0.550255i	0.999786	−	0.0206765i	$-0.00658202\pi$
$739$	4.86029	+	14.9584i	0.178789	+	0.550255i	−0.820997	+	0.570932i	$0.806582\pi$
$740$	−0.0702723	+	23.9623i	−0.00258326	+	0.880871i
$741$		0			0
$742$	−38.0778	−	27.6651i	−1.39788	−	1.01562i
$743$	45.9731			1.68659			0.843294	−	0.537452i	$-0.180613\pi$
$743$	45.9731			1.68659			0.843294	+	0.537452i	$0.180613\pi$
$744$		0			0
$745$	−21.7196	−	7.12761i	−0.795745	−	0.261136i
$746$	22.6734	−	16.4732i	0.830133	−	0.603127i
$747$		0			0
$748$	1.52285	+	4.68686i	0.0556811	+	0.171369i
$749$	26.2545			0.959317
$750$		0			0
$751$	7.09608			0.258940			0.129470	−	0.991583i	$-0.458672\pi$
$751$	7.09608			0.258940			0.129470	+	0.991583i	$0.458672\pi$
$752$	0.626140	+	1.92706i	0.0228330	+	0.0702726i
$753$		0			0
$754$	−15.8685	+	11.5292i	−0.577898	+	0.419868i
$755$	36.5463	+	11.9932i	1.33006	+	0.436478i
$756$		0			0
$757$	23.7795			0.864281			0.432141	−	0.901806i	$-0.357758\pi$
$757$	23.7795			0.864281			0.432141	+	0.901806i	$0.357758\pi$
$758$	2.20145	+	1.59945i	0.0799604	+	0.0580946i
$759$		0			0
$760$	0.00810552	−	2.76392i	0.000294018	−	0.100258i
$761$	−1.62195	−	4.99184i	−0.0587956	−	0.180954i	0.917345	−	0.398093i	$-0.130328\pi$
$761$	−1.62195	−	4.99184i	−0.0587956	−	0.180954i	−0.976141	+	0.217138i	$0.930328\pi$
$762$		0			0
$763$	−10.4296	+	32.0990i	−0.377576	+	1.16206i
$764$	−1.00000	−	3.07768i	−0.0361787	−	0.111347i
$765$		0			0
$766$	−5.21468	+	16.0491i	−0.188414	+	0.579878i
$767$	7.97377	+	5.79328i	0.287916	+	0.209183i
$768$		0			0
$769$	4.43639	+	3.22323i	0.159980	+	0.116233i	0.664895	−	0.746937i	$-0.268476\pi$
$769$	4.43639	+	3.22323i	0.159980	+	0.116233i	−0.504915	+	0.863169i	$0.668476\pi$
$770$	44.3003	−	14.2505i	1.59647	−	0.513553i
$771$		0			0
$772$	6.15501	−	4.47188i	0.221524	−	0.160946i
$773$	3.60661	+	11.1000i	0.129721	+	0.399239i	0.994732	−	0.102514i	$-0.0326886\pi$
$773$	3.60661	+	11.1000i	0.129721	+	0.399239i	−0.865011	+	0.501753i	$0.832689\pi$
$774$		0			0
$775$	−1.54936	−	4.86536i	−0.0556548	−	0.174769i
$776$	−8.02933			−0.288236
$777$		0			0
$778$	31.3259	−	22.7596i	1.12309	−	0.815972i
$779$	−4.59681	+	3.33978i	−0.164698	+	0.119660i
$780$		0			0
$781$	49.5967	+	36.0341i	1.77471	+	1.28940i
$782$	4.50838			0.161220
$783$		0			0
$784$	3.43766	−	10.5800i	0.122774	−	0.377858i
$785$	−39.8202	−	13.0676i	−1.42125	−	0.466403i
$786$		0			0
$787$	−7.63108	+	23.4861i	−0.272019	+	0.837188i	0.717974	+	0.696070i	$0.245070\pi$
$787$	−7.63108	+	23.4861i	−0.272019	+	0.837188i	−0.989993	+	0.141118i	$0.954930\pi$
$788$	−1.45739	+	4.48538i	−0.0519173	+	0.159785i
$789$		0			0
$790$	−8.36471	−	11.5843i	−0.297603	−	0.412152i
$791$	8.89164	−	27.3657i	0.316150	−	0.973011i
$792$		0			0
$793$	−17.9786			−0.638439
$794$	−20.0261	−	14.5498i	−0.710698	−	0.516352i
$795$		0			0
$796$	12.8857	−	9.36201i	0.456722	−	0.331828i
$797$	16.7427	−	12.1643i	0.593056	−	0.430880i	−0.250351	−	0.968155i	$-0.580546\pi$
$797$	16.7427	−	12.1643i	0.593056	−	0.430880i	0.843407	+	0.537275i	$0.180546\pi$
$798$		0			0
$799$	2.04265			0.0722639
$800$	4.02778	+	2.96260i	0.142403	+	0.104744i
$801$		0			0
$802$	1.02541	+	3.15590i	0.0362086	+	0.111439i
$803$	−13.5628	+	9.85392i	−0.478619	+	0.347737i
$804$		0			0
$805$	0.124850	−	42.5727i	0.00440037	−	1.50049i
$806$	3.83288	+	2.78475i	0.135007	+	0.0980887i
$807$		0			0
$808$	−14.2638	−	10.3632i	−0.501797	−	0.364577i
$809$	0.948863	−	2.92030i	0.0333602	−	0.102672i	−0.932990	−	0.359903i	$-0.882810\pi$
$809$	0.948863	−	2.92030i	0.0333602	−	0.102672i	0.966350	+	0.257230i	$0.0828099\pi$
$810$		0			0
$811$	−14.3668	−	44.2164i	−0.504485	−	1.55265i	−0.801634	−	0.597815i	$-0.796036\pi$
$811$	−14.3668	−	44.2164i	−0.504485	−	1.55265i	0.297149	−	0.954831i	$-0.403964\pi$
$812$	5.56220	−	17.1187i	0.195195	−	0.600748i
$813$		0			0
$814$	16.1882	+	49.8221i	0.567395	+	1.74626i
$815$	−18.4748	+	25.2722i	−0.647143	+	0.885245i
$816$		0			0
$817$	−10.4984	−	7.62751i	−0.367291	−	0.266853i
$818$	−28.3787			−0.992238
$819$		0			0
$820$	0.0301436	−	10.2787i	0.00105266	−	0.358949i
$821$	−14.3885	+	10.4539i	−0.502162	+	0.364842i	−0.809842	−	0.586648i	$-0.800447\pi$
$821$	−14.3885	+	10.4539i	−0.502162	+	0.364842i	0.307680	+	0.951490i	$0.400447\pi$
$822$		0			0
$823$	1.89759	+	5.84017i	0.0661457	+	0.203575i	0.978667	−	0.205454i	$-0.0658672\pi$
$823$	1.89759	+	5.84017i	0.0661457	+	0.203575i	−0.912521	+	0.409030i	$0.865867\pi$
$824$	−19.6999			−0.686279
$825$		0			0
$826$	−9.04463			−0.314703
$827$	9.06121	+	27.8875i	0.315089	+	0.969745i	0.975718	+	0.219032i	$0.0702898\pi$
$827$	9.06121	+	27.8875i	0.315089	+	0.969745i	−0.660629	+	0.750713i	$0.729710\pi$
$828$		0			0
$829$	40.1826	−	29.1944i	1.39560	−	1.01396i	0.400374	−	0.916352i	$-0.368880\pi$
$829$	40.1826	−	29.1944i	1.39560	−	1.01396i	0.995225	−	0.0976102i	$-0.0311199\pi$
$830$	−9.30001	+	12.7217i	−0.322808	+	0.441578i
$831$		0			0
$832$	−4.63925			−0.160837
$833$	−9.07286	−	6.59182i	−0.314356	−	0.228393i
$834$		0			0
$835$	−17.6865	−	24.4942i	−0.612068	−	0.847655i
$836$	−1.86722	−	5.74670i	−0.0645790	−	0.198754i
$837$		0			0
$838$	−4.58097	+	14.0988i	−0.158247	+	0.487034i
$839$	−8.60481	−	26.4829i	−0.297071	−	0.914291i	−0.982518	−	0.186168i	$-0.940393\pi$
$839$	−8.60481	−	26.4829i	−0.297071	−	0.914291i	0.685447	−	0.728123i	$-0.259607\pi$
$840$		0			0
$841$	−3.43761	+	10.5799i	−0.118538	+	0.364823i
$842$	−14.7255	−	10.6987i	−0.507475	−	0.368702i
$843$		0			0
$844$	9.77688	+	7.10332i	0.336534	+	0.244506i
$845$	−11.1563	−	15.4505i	−0.383790	−	0.531512i
$846$		0			0
$847$	44.4195	−	32.2726i	1.52627	−	1.10890i
$848$	−3.41635	−	10.5145i	−0.117318	−	0.361068i
$849$		0			0
$850$	4.09518	−	2.93878i	0.140463	−	0.100799i
$851$	47.9248			1.64284
$852$		0			0
$853$	25.8857	−	18.8070i	0.886309	−	0.643941i	−0.0486043	−	0.998818i	$-0.515477\pi$
$853$	25.8857	−	18.8070i	0.886309	−	0.643941i	0.934913	+	0.354877i	$0.115477\pi$
$854$	13.3475	−	9.69750i	0.456741	−	0.331841i
$855$		0			0
$856$	4.98916	+	3.62484i	0.170526	+	0.123894i
$857$	−31.7769			−1.08548			−0.542739	−	0.839902i	$-0.682613\pi$
$857$	−31.7769			−1.08548			−0.542739	+	0.839902i	$0.682613\pi$
$858$		0			0
$859$	2.55910	−	7.87611i	0.0873155	−	0.268729i	−0.897859	−	0.440282i	$-0.854878\pi$
$859$	2.55910	−	7.87611i	0.0873155	−	0.268729i	0.985175	+	0.171553i	$0.0548784\pi$
$860$	22.3473	−	7.18869i	0.762036	−	0.245132i
$861$		0			0
$862$	−5.48525	+	16.8819i	−0.186828	+	0.574999i
$863$	5.98671	−	18.4252i	0.203790	−	0.627201i	−0.795971	−	0.605335i	$-0.793039\pi$
$863$	5.98671	−	18.4252i	0.203790	−	0.627201i	0.999761	−	0.0218664i	$-0.00696084\pi$
$864$		0			0
$865$	−0.0589101	+	20.0879i	−0.00200300	+	0.683009i
$866$	6.71125	−	20.6551i	0.228057	−	0.701889i
$867$		0			0
$868$	−4.34763			−0.147568
$869$	−25.2716	−	18.3609i	−0.857282	−	0.622852i
$870$		0			0
$871$	14.0771	−	10.2276i	0.476983	−	0.346548i
$872$	−6.41371	+	4.65983i	−0.217196	+	0.157802i
$873$		0			0
$874$	−5.52786			−0.186983
$875$	−27.6375	−	38.7522i	−0.934318	−	1.31006i
$876$		0			0
$877$	−9.18634	−	28.2726i	−0.310201	−	0.954699i	−0.977685	−	0.210076i	$-0.932629\pi$
$877$	−9.18634	−	28.2726i	−0.310201	−	0.954699i	0.667485	−	0.744624i	$-0.267371\pi$
$878$	−8.67615	+	6.30359i	−0.292806	+	0.212736i
$879$		0			0
$880$	10.3859	+	3.40830i	0.350110	+	0.114894i
$881$	13.8537	+	10.0653i	0.466741	+	0.339107i	0.796170	−	0.605073i	$-0.206856\pi$
$881$	13.8537	+	10.0653i	0.466741	+	0.339107i	−0.329429	+	0.944180i	$0.606856\pi$
$882$		0			0
$883$	2.34718	+	1.70533i	0.0789889	+	0.0573888i	0.626579	−	0.779358i	$-0.284455\pi$
$883$	2.34718	+	1.70533i	0.0789889	+	0.0573888i	−0.547590	+	0.836747i	$0.684455\pi$
$884$	−1.44523	+	4.44796i	−0.0486083	+	0.149601i
$885$		0			0
$886$	−7.88278	−	24.2607i	−0.264827	−	0.815055i
$887$	8.80338	−	27.0940i	0.295589	−	0.909728i	−0.687434	−	0.726246i	$-0.741263\pi$
$887$	8.80338	−	27.0940i	0.295589	−	0.909728i	0.983023	−	0.183482i	$-0.0587369\pi$
$888$		0			0
$889$	−13.2850	−	40.8871i	−0.445566	−	1.37131i
$890$	4.77705	−	1.53668i	0.160127	−	0.0515097i
$891$		0			0
$892$	7.57286	+	5.50201i	0.253558	+	0.184221i
$893$	−2.50456			−0.0838118
$894$		0			0
$895$	14.9457	−	4.80773i	0.499579	−	0.160705i
$896$	3.44422	−	2.50237i	0.115063	−	0.0835984i
$897$		0			0
$898$	3.88183	+	11.9470i	0.129538	+	0.398678i
$899$	−4.31768			−0.144003
$900$		0			0
$901$	−11.1452			−0.371299
$902$	−6.94399	−	21.3714i	−0.231210	−	0.711590i
$903$		0			0
$904$	5.46794	−	3.97269i	0.181861	−	0.132130i
$905$	15.6459	+	21.6680i	0.520086	+	0.720270i
$906$		0			0
$907$	55.7343			1.85063			0.925314	−	0.379203i	$-0.123802\pi$
$907$	55.7343			1.85063			0.925314	+	0.379203i	$0.123802\pi$
$908$	8.19090	+	5.95104i	0.271824	+	0.197492i
$909$		0			0
$910$	41.9621	+	13.7705i	1.39103	+	0.456487i
$911$	−0.506472	−	1.55876i	−0.0167801	−	0.0516440i	0.942316	−	0.334725i	$-0.108643\pi$
$911$	−0.506472	−	1.55876i	−0.0167801	−	0.0516440i	−0.959096	+	0.283081i	$0.908643\pi$
$912$		0			0
$913$	−10.6460	+	32.7649i	−0.352330	+	1.08436i
$914$	0.940305	+	2.89396i	0.0311025	+	0.0957237i
$915$		0			0
$916$	2.29081	−	7.05038i	0.0756904	−	0.232951i
$917$	−23.1503	−	16.8197i	−0.764490	−	0.555434i
$918$		0			0
$919$	−28.5965	−	20.7766i	−0.943310	−	0.685355i	0.00590477	−	0.999983i	$-0.498120\pi$
$919$	−28.5965	−	20.7766i	−0.943310	−	0.685355i	−0.949215	+	0.314627i	$0.898120\pi$
$920$	5.90155	−	8.07290i	0.194568	−	0.266156i
$921$		0			0
$922$	−22.3233	+	16.2188i	−0.735178	+	0.534138i
$923$	17.9786	+	55.3325i	0.591773	+	1.82129i
$924$		0			0
$925$	43.5324	−	31.2397i	1.43134	−	1.02715i
$926$	30.2060			0.992631
$927$		0			0
$928$	3.42049	−	2.48513i	0.112283	−	0.0815785i
$929$	−7.50256	+	5.45093i	−0.246151	+	0.178839i	−0.704019	−	0.710181i	$-0.748613\pi$
$929$	−7.50256	+	5.45093i	−0.246151	+	0.178839i	0.457868	+	0.889020i	$0.348613\pi$
$930$		0			0
$931$	11.1245	+	8.08243i	0.364591	+	0.264891i
$932$	5.92778			0.194171
$933$		0			0
$934$	−9.21572	+	28.3631i	−0.301548	+	0.928068i
$935$	6.50320	−	8.89591i	0.212677	−	0.290927i
$936$		0			0
$937$	−3.03856	+	9.35173i	−0.0992654	+	0.305508i	−0.988342	−	0.152251i	$-0.951348\pi$
$937$	−3.03856	+	9.35173i	−0.0992654	+	0.305508i	0.889076	+	0.457759i	$0.151348\pi$
$938$	−4.93425	+	15.1861i	−0.161109	+	0.495843i
$939$		0			0
$940$	2.67387	−	3.65766i	0.0872120	−	0.119300i
$941$	−18.0203	+	55.4607i	−0.587444	+	1.80797i	0.00178292	+	0.999998i	$0.499432\pi$
$941$	−18.0203	+	55.4607i	−0.587444	+	1.80797i	−0.589227	+	0.807968i	$0.700568\pi$
$942$		0			0
$943$	−20.5576			−0.669447
$944$	−1.71876	−	1.24875i	−0.0559409	−	0.0406434i
$945$		0			0
$946$	41.5192	−	30.1655i	1.34991	−	0.980765i
$947$	−35.0917	+	25.4956i	−1.14033	+	0.828496i	−0.987165	−	0.159705i	$-0.948946\pi$
$947$	−35.0917	+	25.4956i	−1.14033	+	0.828496i	−0.153162	+	0.988201i	$0.548946\pi$
$948$		0			0
$949$	−15.9099			−0.516458
$950$	−5.02122	+	3.60332i	−0.162910	+	0.116907i
$951$		0			0
$952$	−1.32624	−	4.08174i	−0.0429836	−	0.132290i
$953$	−8.14992	+	5.92126i	−0.264002	+	0.191808i	−0.711909	−	0.702271i	$-0.752169\pi$
$953$	−8.14992	+	5.92126i	−0.264002	+	0.191808i	0.447908	+	0.894080i	$0.352169\pi$
$954$		0			0
$955$	−4.27040	+	5.84160i	−0.138187	+	0.189030i
$956$	−13.3606	−	9.70702i	−0.432112	−	0.313948i
$957$		0			0
$958$	5.27040	+	3.82917i	0.170279	+	0.123715i
$959$	23.1883	−	71.3662i	0.748788	−	2.30453i
$960$		0			0
$961$	−9.25726	−	28.4909i	−0.298621	−	0.919061i
$962$	−15.3630	+	47.2824i	−0.495323	+	1.52445i
$963$		0			0
$964$	−2.48120	−	7.63634i	−0.0799140	−	0.245950i
$965$	−16.1639	−	5.30443i	−0.520335	−	0.170756i
$966$		0			0
$967$	11.3754	+	8.26469i	0.365807	+	0.265775i	0.755470	−	0.655183i	$-0.227408\pi$
$967$	11.3754	+	8.26469i	0.365807	+	0.265775i	−0.389663	+	0.920958i	$0.627408\pi$
$968$	12.8968			0.414520
$969$		0			0
$970$	10.5105	+	14.5561i	0.337473	+	0.467367i
$971$	−24.3406	+	17.6845i	−0.781127	+	0.567522i	−0.905317	−	0.424737i	$-0.860367\pi$
$971$	−24.3406	+	17.6845i	−0.781127	+	0.567522i	0.124190	+	0.992258i	$0.460367\pi$
$972$		0			0
$973$	10.7273	+	33.0154i	0.343903	+	1.05842i
$974$	40.1990			1.28806
$975$		0			0
$976$	3.87532			0.124046
$977$	3.66766	+	11.2879i	0.117339	+	0.361131i	0.992428	−	0.122831i	$-0.0391972\pi$
$977$	3.66766	+	11.2879i	0.117339	+	0.361131i	−0.875089	+	0.483962i	$0.839197\pi$
$978$		0			0
$979$	8.87532	−	6.44830i	0.283657	−	0.206089i
$980$	−23.6801	+	7.61743i	−0.756434	+	0.243330i
$981$		0			0
$982$	36.6280			1.16885
$983$	−27.7898	−	20.1905i	−0.886358	−	0.643976i	0.0485682	−	0.998820i	$-0.484534\pi$
$983$	−27.7898	−	20.1905i	−0.886358	−	0.643976i	−0.934926	+	0.354843i	$0.884534\pi$
$984$		0			0
$985$	10.0391	−	3.22939i	0.319873	−	0.102897i
$986$	−1.31710	−	4.05362i	−0.0419451	−	0.129094i
$987$		0			0
$988$	1.77204	−	5.45377i	0.0563760	−	0.173508i
$989$	−14.5084	−	44.6522i	−0.461340	−	1.41986i
$990$		0			0
$991$	8.76632	−	26.9800i	0.278471	−	0.857046i	−0.709809	−	0.704394i	$-0.751219\pi$
$991$	8.76632	−	26.9800i	0.278471	−	0.857046i	0.988280	−	0.152652i	$-0.0487814\pi$
$992$	−0.826185	−	0.600258i	−0.0262314	−	0.0190582i
$993$		0			0
$994$	−43.1933	−	31.3818i	−1.37001	−	0.995369i
$995$	−33.8397	−	11.1050i	−1.07279	−	0.352052i
$996$		0			0
$997$	−37.0128	+	26.8914i	−1.17221	+	0.851658i	−0.991271	−	0.131837i	$-0.957912\pi$
$997$	−37.0128	+	26.8914i	−1.17221	+	0.851658i	−0.180935	+	0.983495i	$0.557912\pi$
$998$	−7.70511	−	23.7139i	−0.243901	−	0.750650i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.d.181.2		8
3.2	odd	2		150.2.g.c.31.1	✓	8
15.2	even	4		750.2.h.e.349.3		16
15.8	even	4		750.2.h.e.349.2		16
15.14	odd	2		750.2.g.d.151.2		8
25.21	even	5	inner	450.2.h.d.271.2		8
75.2	even	20		3750.2.c.h.1249.1		8
75.11	odd	10		3750.2.a.l.1.1		4
75.14	odd	10		3750.2.a.q.1.4		4
75.23	even	20		3750.2.c.h.1249.8		8
75.29	odd	10		750.2.g.d.601.2		8
75.47	even	20		750.2.h.e.649.1		16
75.53	even	20		750.2.h.e.649.4		16
75.71	odd	10		150.2.g.c.121.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.31.1	✓	8	3.2	odd	2
150.2.g.c.121.1	yes	8	75.71	odd	10
450.2.h.d.181.2		8	1.1	even	1	trivial
450.2.h.d.271.2		8	25.21	even	5	inner
750.2.g.d.151.2		8	15.14	odd	2
750.2.g.d.601.2		8	75.29	odd	10
750.2.h.e.349.2		16	15.8	even	4
750.2.h.e.349.3		16	15.2	even	4
750.2.h.e.649.1		16	75.47	even	20
750.2.h.e.649.4		16	75.53	even	20
3750.2.a.l.1.1		4	75.11	odd	10
3750.2.a.q.1.4		4	75.14	odd	10
3750.2.c.h.1249.1		8	75.2	even	20
3750.2.c.h.1249.8		8	75.23	even	20

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.12459 + 0.697217i) q^{5} -4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.12459 + 0.697217i) q^{5} -4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.00655751 + 2.23606i) q^{10} +(1.51061 + 4.64918i) q^{11} +(-1.43361 + 4.41219i) q^{13} +(-1.31557 - 4.04892i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.815575 - 0.592550i) q^{17} +(1.00000 + 0.726543i) q^{19} +(-2.12864 + 0.684743i) q^{20} +(-3.95483 + 2.87335i) q^{22} +(1.38197 + 4.25325i) q^{23} +(4.02778 + 2.96260i) q^{25} -4.63925 q^{26} +(3.44422 - 2.50237i) q^{28} +(3.42049 - 2.48513i) q^{29} +(-0.826185 - 0.600258i) q^{31} +1.00000 q^{32} +(0.311522 - 0.958765i) q^{34} +(-9.04500 - 2.96825i) q^{35} +(3.31152 - 10.1918i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(-1.30902 - 1.81286i) q^{40} +(-1.42049 + 4.37183i) q^{41} -10.4984 q^{43} +(-3.95483 - 2.87335i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-1.63925 + 1.19099i) q^{47} +11.1245 q^{49} +(-1.57295 + 4.74614i) q^{50} +(-1.43361 - 4.41219i) q^{52} +(8.94413 - 6.49829i) q^{53} +(-0.0320560 + 10.9308i) q^{55} +(3.44422 + 2.50237i) q^{56} +(3.42049 + 2.48513i) q^{58} +(0.656508 - 2.02052i) q^{59} +(1.19754 + 3.68565i) q^{61} +(0.315575 - 0.971238i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-6.12209 + 8.37457i) q^{65} +(-3.03434 - 2.20457i) q^{67} +1.00811 q^{68} +(0.0279172 - 9.51955i) q^{70} +(10.1457 - 7.37130i) q^{71} +(1.05975 + 3.26157i) q^{73} +10.7163 q^{74} -1.23607 q^{76} +(-6.43110 - 19.7929i) q^{77} +(-5.16968 + 3.75599i) q^{79} +(1.31963 - 1.80515i) q^{80} -4.59681 q^{82} +(5.70151 + 4.14239i) q^{83} +(-1.31963 - 1.82756i) q^{85} +(-3.24417 - 9.98454i) q^{86} +(1.51061 - 4.64918i) q^{88} +(-0.693488 - 2.13434i) q^{89} +(6.10328 - 18.7840i) q^{91} +(-3.61803 - 2.62866i) q^{92} +(-1.63925 - 1.19099i) q^{94} +(1.61803 + 2.24082i) q^{95} +(6.49586 - 4.71952i) q^{97} +(3.43766 + 10.5800i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8 + 4 * q^10 + 5 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^19 - q^20 + 20 * q^23 + 14 * q^25 - 14 * q^26 + 3 * q^28 + 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 + 4 * q^35 + 21 * q^37 - 12 * q^38 - 6 * q^40 - 2 * q^41 - 32 * q^43 - 20 * q^46 + 10 * q^47 + 22 * q^49 - 26 * q^50 + 6 * q^52 - 7 * q^53 - 40 * q^55 + 3 * q^56 + 18 * q^58 + 25 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^64 - 37 * q^65 - 2 * q^67 + 2 * q^68 - 11 * q^70 - 24 * q^73 + 26 * q^74 + 8 * q^76 - 35 * q^77 - 6 * q^79 - q^80 - 42 * q^82 - 11 * q^83 + q^85 - 2 * q^86 + 5 * q^88 - 9 * q^89 - 4 * q^91 - 20 * q^92 + 10 * q^94 + 4 * q^95 + q^97 + 7 * q^98

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