LMFDB - Embedded newform 990.2.ba.b.829.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(289,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			829.1
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	990.829
Dual form			990.2.ba.b.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-1.03025 + 1.98459i) q^{5} +(0.587785 - 0.190983i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.00000 - 2.00000i) q^{10} +(-1.69098 - 2.85317i) q^{11} +(1.40008 - 1.92705i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.80423 - 5.23607i) q^{17} +(-1.11803 + 3.44095i) q^{19} +(2.20582 + 0.366554i) q^{20} +(3.30220 + 0.309017i) q^{22} -4.61803i q^{23} +(-2.87718 - 4.08924i) q^{25} +(0.736068 + 2.26538i) q^{26} +(-0.363271 - 0.500000i) q^{28} +(1.38197 + 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} -1.00000i q^{32} +6.47214 q^{34} +(-0.226543 + 1.36327i) q^{35} +(5.34307 - 1.73607i) q^{37} +(-2.12663 - 2.92705i) q^{38} +(-1.59310 + 1.56909i) q^{40} +(-0.190983 + 0.587785i) q^{41} -8.47214i q^{43} +(-2.19098 + 2.48990i) q^{44} +(3.73607 + 2.71441i) q^{46} +(9.59632 + 3.11803i) q^{47} +(-5.35410 + 3.88998i) q^{49} +(4.99942 + 0.0759100i) q^{50} +(-2.26538 - 0.736068i) q^{52} +(4.16750 - 5.73607i) q^{53} +(7.40450 - 0.416429i) q^{55} +0.618034 q^{56} +(-4.25325 - 1.38197i) q^{58} +(-3.35410 - 10.3229i) q^{59} +(5.61803 - 4.08174i) q^{61} +(1.90211 - 0.618034i) q^{62} +(0.809017 + 0.587785i) q^{64} +(2.38197 + 4.76393i) q^{65} -9.23607i q^{67} +(-3.80423 + 5.23607i) q^{68} +(-0.969751 - 0.984587i) q^{70} +(1.61803 - 1.17557i) q^{71} +(-1.45309 + 0.472136i) q^{73} +(-1.73607 + 5.34307i) q^{74} +3.61803 q^{76} +(-1.53884 - 1.35410i) q^{77} +(-5.00000 - 3.63271i) q^{79} +(-0.333023 - 2.21113i) q^{80} +(-0.363271 - 0.500000i) q^{82} +(-5.98385 - 8.23607i) q^{83} +(14.3107 - 2.15537i) q^{85} +(6.85410 + 4.97980i) q^{86} +(-0.726543 - 3.23607i) q^{88} +11.3820 q^{89} +(0.454915 - 1.40008i) q^{91} +(-4.39201 + 1.42705i) q^{92} +(-8.16312 + 5.93085i) q^{94} +(-5.67702 - 5.76388i) q^{95} +(-5.42882 + 7.47214i) q^{97} -6.61803i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 4 q^{5} - 8 q^{10} - 18 q^{11} - 6 q^{14} - 2 q^{16} + 4 q^{20} - 6 q^{25} - 12 q^{26} + 20 q^{29} - 4 q^{31} + 16 q^{34} + 4 q^{35} - 2 q^{40} - 6 q^{41} - 22 q^{44} + 12 q^{46} - 16 q^{49}+ \cdots - 34 q^{94}+O(q^{100}) $ 8 * q + 2 * q^4 - 4 * q^5 - 8 * q^10 - 18 * q^11 - 6 * q^14 - 2 * q^16 + 4 * q^20 - 6 * q^25 - 12 * q^26 + 20 * q^29 - 4 * q^31 + 16 * q^34 + 4 * q^35 - 2 * q^40 - 6 * q^41 - 22 * q^44 + 12 * q^46 - 16 * q^49 + 8 * q^50 + 4 * q^55 - 4 * q^56 + 36 * q^61 + 2 * q^64 + 28 * q^65 - 12 * q^70 + 4 * q^71 + 4 * q^74 + 20 * q^76 - 40 * q^79 - 4 * q^80 + 16 * q^85 + 28 * q^86 + 100 * q^89 + 26 * q^91 - 34 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.03025	+	1.98459i	−0.460741	+	0.887535i
$5$	−1.03025	+	1.98459i	−0.460741	+	0.887535i
$6$		0			0
$7$	0.587785	−	0.190983i	0.222162	−	0.0721848i	−0.195821	−	0.980640i	$-0.562737\pi$
$7$	0.587785	−	0.190983i	0.222162	−	0.0721848i	0.417983	+	0.908455i	$0.362737\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		0			0
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$12$		0			0
$13$	1.40008	−	1.92705i	0.388314	−	0.534468i	−0.569449	−	0.822026i	$-0.692844\pi$
$13$	1.40008	−	1.92705i	0.388314	−	0.534468i	0.957763	+	0.287559i	$0.0928436\pi$
$14$	−0.190983	+	0.587785i	−0.0510424	+	0.157092i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.80423	−	5.23607i	−0.922660	−	1.26993i	−0.962654	−	0.270733i	$-0.912734\pi$
$17$	−3.80423	−	5.23607i	−0.922660	−	1.26993i	0.0399941	−	0.999200i	$-0.487266\pi$
$18$		0			0
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	0.737037	+	0.675852i	$0.236224\pi$
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	−0.993532	+	0.113557i	$0.963776\pi$
$20$	2.20582	+	0.366554i	0.493236	+	0.0819639i
$21$		0			0
$22$	3.30220	+	0.309017i	0.704031	+	0.0658826i
$23$		−	4.61803i		−	0.962927i	−0.876466	−	0.481463i	$-0.840105\pi$
$23$		−	4.61803i		−	0.962927i	0.876466	−	0.481463i	$-0.159895\pi$
$24$		0			0
$25$	−2.87718	−	4.08924i	−0.575435	−	0.817848i
$26$	0.736068	+	2.26538i	0.144355	+	0.444278i
$27$		0			0
$28$	−0.363271	−	0.500000i	−0.0686518	−	0.0944911i
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	0.993505	+	0.113787i	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$		0			0
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	6.47214			1.10996
$35$	−0.226543	+	1.36327i	−0.0382927	+	0.230435i
$36$		0			0
$37$	5.34307	−	1.73607i	0.878395	−	0.285408i	0.165104	−	0.986276i	$-0.447204\pi$
$37$	5.34307	−	1.73607i	0.878395	−	0.285408i	0.713291	+	0.700868i	$0.247204\pi$
$38$	−2.12663	−	2.92705i	−0.344984	−	0.474830i
$39$		0			0
$40$	−1.59310	+	1.56909i	−0.251891	+	0.248095i
$41$	−0.190983	+	0.587785i	−0.0298265	+	0.0917966i	−0.964862	−	0.262759i	$-0.915368\pi$
$41$	−0.190983	+	0.587785i	−0.0298265	+	0.0917966i	0.935035	+	0.354555i	$0.115368\pi$
$42$		0			0
$43$		−	8.47214i		−	1.29199i	−0.763342	−	0.645994i	$-0.776443\pi$
$43$		−	8.47214i		−	1.29199i	0.763342	−	0.645994i	$-0.223557\pi$
$44$	−2.19098	+	2.48990i	−0.330303	+	0.375366i
$45$		0			0
$46$	3.73607	+	2.71441i	0.550853	+	0.400218i
$47$	9.59632	+	3.11803i	1.39977	+	0.454812i	0.909116	−	0.416544i	$-0.136759\pi$
$47$	9.59632	+	3.11803i	1.39977	+	0.454812i	0.490652	+	0.871356i	$0.336759\pi$
$48$		0			0
$49$	−5.35410	+	3.88998i	−0.764872	+	0.555712i
$50$	4.99942	+	0.0759100i	0.707025	+	0.0107353i
$51$		0			0
$52$	−2.26538	−	0.736068i	−0.314152	−	0.102074i
$53$	4.16750	−	5.73607i	0.572450	−	0.787910i	−0.420393	−	0.907342i	$-0.638108\pi$
$53$	4.16750	−	5.73607i	0.572450	−	0.787910i	0.992842	+	0.119433i	$0.0381076\pi$
$54$		0			0
$55$	7.40450	−	0.416429i	0.998422	−	0.0561513i
$56$	0.618034			0.0825883
$57$		0			0
$58$	−4.25325	−	1.38197i	−0.558480	−	0.181461i
$59$	−3.35410	−	10.3229i	−0.436667	−	1.34392i	−0.891369	−	0.453279i	$-0.850254\pi$
$59$	−3.35410	−	10.3229i	−0.436667	−	1.34392i	0.454702	−	0.890644i	$-0.349746\pi$
$60$		0			0
$61$	5.61803	−	4.08174i	0.719316	−	0.522613i	−0.166850	−	0.985982i	$-0.553360\pi$
$61$	5.61803	−	4.08174i	0.719316	−	0.522613i	0.886165	+	0.463369i	$0.153360\pi$
$62$	1.90211	−	0.618034i	0.241569	−	0.0784904i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	2.38197	+	4.76393i	0.295447	+	0.590893i
$66$		0			0
$67$		−	9.23607i		−	1.12837i	−0.825650	−	0.564183i	$-0.809191\pi$
$67$		−	9.23607i		−	1.12837i	0.825650	−	0.564183i	$-0.190809\pi$
$68$	−3.80423	+	5.23607i	−0.461330	+	0.634967i
$69$		0			0
$70$	−0.969751	−	0.984587i	−0.115907	−	0.117681i
$71$	1.61803	−	1.17557i	0.192025	−	0.139515i	−0.487619	−	0.873057i	$-0.662134\pi$
$71$	1.61803	−	1.17557i	0.192025	−	0.139515i	0.679644	+	0.733542i	$0.262134\pi$
$72$		0			0
$73$	−1.45309	+	0.472136i	−0.170071	+	0.0552593i	−0.392815	−	0.919618i	$-0.628499\pi$
$73$	−1.45309	+	0.472136i	−0.170071	+	0.0552593i	0.222744	+	0.974877i	$0.428499\pi$
$74$	−1.73607	+	5.34307i	−0.201814	+	0.621119i
$75$		0			0
$76$	3.61803			0.415017
$77$	−1.53884	−	1.35410i	−0.175367	−	0.154314i
$78$		0			0
$79$	−5.00000	−	3.63271i	−0.562544	−	0.408712i	0.269845	−	0.962904i	$-0.413027\pi$
$79$	−5.00000	−	3.63271i	−0.562544	−	0.408712i	−0.832389	+	0.554192i	$0.813027\pi$
$80$	−0.333023	−	2.21113i	−0.0372331	−	0.247212i
$81$		0			0
$82$	−0.363271	−	0.500000i	−0.0401166	−	0.0552158i
$83$	−5.98385	−	8.23607i	−0.656813	−	0.904026i	0.342557	−	0.939497i	$-0.388707\pi$
$83$	−5.98385	−	8.23607i	−0.656813	−	0.904026i	−0.999371	+	0.0354710i	$0.988707\pi$
$84$		0			0
$85$	14.3107	−	2.15537i	1.55222	−	0.233782i
$86$	6.85410	+	4.97980i	0.739097	+	0.536985i
$87$		0			0
$88$	−0.726543	−	3.23607i	−0.0774497	−	0.344966i
$89$	11.3820			1.20649			0.603243	−	0.797557i	$-0.293875\pi$
$89$	11.3820			1.20649			0.603243	+	0.797557i	$0.293875\pi$
$90$		0			0
$91$	0.454915	−	1.40008i	0.0476881	−	0.146769i
$92$	−4.39201	+	1.42705i	−0.457899	+	0.148780i
$93$		0			0
$94$	−8.16312	+	5.93085i	−0.841961	+	0.611721i
$95$	−5.67702	−	5.76388i	−0.582450	−	0.591361i
$96$		0			0
$97$	−5.42882	+	7.47214i	−0.551214	+	0.758680i	−0.990176	−	0.139825i	$-0.955346\pi$
$97$	−5.42882	+	7.47214i	−0.551214	+	0.758680i	0.438963	+	0.898505i	$0.355346\pi$
$98$		−	6.61803i		−	0.668522i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−15.9443	−	11.5842i	−1.58651	−	1.15267i	−0.908710	−	0.417428i	$-0.862932\pi$
$101$	−15.9443	−	11.5842i	−1.58651	−	1.15267i	−0.677804	−	0.735242i	$-0.737068\pi$
$102$		0			0
$103$	−6.51864	+	2.11803i	−0.642301	+	0.208696i	−0.612016	−	0.790845i	$-0.709641\pi$
$103$	−6.51864	+	2.11803i	−0.642301	+	0.208696i	−0.0302843	+	0.999541i	$0.509641\pi$
$104$	1.92705	−	1.40008i	0.188963	−	0.137290i
$105$		0			0
$106$	2.19098	+	6.74315i	0.212807	+	0.654953i
$107$	14.6619	+	4.76393i	1.41742	+	0.460547i	0.914781	−	0.403951i	$-0.132363\pi$
$107$	14.6619	+	4.76393i	1.41742	+	0.460547i	0.502636	+	0.864498i	$0.332363\pi$
$108$		0			0
$109$	5.52786			0.529473			0.264737	−	0.964321i	$-0.414715\pi$
$109$	5.52786			0.529473			0.264737	+	0.964321i	$0.414715\pi$
$110$	−4.01536	+	6.23514i	−0.382849	+	0.594497i
$111$		0			0
$112$	−0.363271	+	0.500000i	−0.0343259	+	0.0472456i
$113$	−8.95554	−	2.90983i	−0.842466	−	0.273734i	−0.144179	−	0.989552i	$-0.546054\pi$
$113$	−8.95554	−	2.90983i	−0.842466	−	0.273734i	−0.698287	+	0.715818i	$0.746054\pi$
$114$		0			0
$115$	9.16489	+	4.75772i	0.854631	+	0.443660i
$116$	3.61803	−	2.62866i	0.335926	−	0.244065i
$117$		0			0
$118$	10.3229	+	3.35410i	0.950297	+	0.308770i
$119$	−3.23607	−	2.35114i	−0.296650	−	0.215529i
$120$		0			0
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$			6.94427i			0.628705i
$123$		0			0
$124$	−0.618034	+	1.90211i	−0.0555011	+	0.170815i
$125$	11.0797	−	1.49707i	0.990995	−	0.133902i
$126$		0			0
$127$	1.67760	+	2.30902i	0.148863	+	0.204892i	0.876936	−	0.480608i	$-0.159584\pi$
$127$	1.67760	+	2.30902i	0.148863	+	0.204892i	−0.728073	+	0.685500i	$0.759584\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	−5.25419	−	0.873118i	−0.460823	−	0.0765775i
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$			2.23607i			0.193892i
$134$	7.47214	+	5.42882i	0.645494	+	0.468979i
$135$		0			0
$136$	−2.00000	−	6.15537i	−0.171499	−	0.527818i
$137$	12.5882	+	17.3262i	1.07549	+	1.48028i	0.864394	+	0.502814i	$0.167702\pi$
$137$	12.5882	+	17.3262i	1.07549	+	1.48028i	0.211092	+	0.977466i	$0.432298\pi$
$138$		0			0
$139$	−0.100813	−	0.310271i	−0.00855085	−	0.0263168i	0.946690	−	0.322146i	$-0.104404\pi$
$139$	−0.100813	−	0.310271i	−0.00855085	−	0.0263168i	−0.955241	+	0.295829i	$0.904404\pi$
$140$	1.36655	−	0.205819i	0.115495	−	0.0173949i
$141$		0			0
$142$			2.00000i			0.167836i
$143$	−7.86572	−	0.736068i	−0.657765	−	0.0615531i
$144$		0			0
$145$	−9.86472	−	1.63928i	−0.819221	−	0.136135i
$146$	0.472136	−	1.45309i	0.0390742	−	0.120258i
$147$		0			0
$148$	−3.30220	−	4.54508i	−0.271439	−	0.373604i
$149$	−17.5623	+	12.7598i	−1.43876	+	1.04532i	−0.450460	+	0.892796i	$0.648740\pi$
$149$	−17.5623	+	12.7598i	−1.43876	+	1.04532i	−0.988300	+	0.152524i	$0.951260\pi$
$150$		0			0
$151$	4.23607	−	13.0373i	0.344726	−	1.06096i	−0.617004	−	0.786960i	$-0.711654\pi$
$151$	4.23607	−	13.0373i	0.344726	−	1.06096i	0.961730	−	0.273998i	$-0.0883463\pi$
$152$	−2.12663	+	2.92705i	−0.172492	+	0.237415i
$153$		0			0
$154$	2.00000	−	0.449028i	0.161165	−	0.0361837i
$155$	4.00000	−	2.00000i	0.321288	−	0.160644i
$156$		0			0
$157$	−5.84510	−	1.89919i	−0.466489	−	0.151572i	0.0663350	−	0.997797i	$-0.478869\pi$
$157$	−5.84510	−	1.89919i	−0.466489	−	0.151572i	−0.532824	+	0.846226i	$0.678869\pi$
$158$	5.87785	−	1.90983i	0.467617	−	0.151938i
$159$		0			0
$160$	1.98459	+	1.03025i	0.156895	+	0.0814483i
$161$	−0.881966	−	2.71441i	−0.0695087	−	0.213926i
$162$		0			0
$163$	5.53483	−	7.61803i	0.433521	−	0.596690i	−0.535236	−	0.844703i	$-0.679777\pi$
$163$	5.53483	−	7.61803i	0.433521	−	0.596690i	0.968757	+	0.248012i	$0.0797773\pi$
$164$	0.618034			0.0482603
$165$		0			0
$166$	10.1803			0.790148
$167$	−7.83297	+	10.7812i	−0.606133	+	0.834271i	−0.996252	−	0.0864937i	$-0.972434\pi$
$167$	−7.83297	+	10.7812i	−0.606133	+	0.834271i	0.390119	+	0.920764i	$0.372434\pi$
$168$		0			0
$169$	2.26393	+	6.96767i	0.174149	+	0.535974i
$170$	−6.66791	+	12.8445i	−0.511405	+	0.985130i
$171$		0			0
$172$	−8.05748	+	2.61803i	−0.614377	+	0.199623i
$173$	−1.76336	−	0.572949i	−0.134065	−	0.0435605i	0.241216	−	0.970472i	$-0.422454\pi$
$173$	−1.76336	−	0.572949i	−0.134065	−	0.0435605i	−0.375281	+	0.926911i	$0.622454\pi$
$174$		0			0
$175$	−2.47214	−	1.85410i	−0.186876	−	0.140157i
$176$	3.04508	+	1.31433i	0.229532	+	0.0990712i
$177$		0			0
$178$	−6.69015	+	9.20820i	−0.501448	+	0.690184i
$179$	−2.86475	+	8.81678i	−0.214121	+	0.658997i	0.785094	+	0.619377i	$0.212615\pi$
$179$	−2.86475	+	8.81678i	−0.214121	+	0.658997i	−0.999215	+	0.0396200i	$0.987385\pi$
$180$		0			0
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.993883	−	0.110442i	$-0.964773\pi$
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.202090	+	0.979367i	$0.564773\pi$
$182$	0.865300	+	1.19098i	0.0641403	+	0.0882815i
$183$		0			0
$184$	1.42705	−	4.39201i	0.105204	−	0.323783i
$185$	−2.05931	+	12.3924i	−0.151403	+	0.911105i
$186$		0			0
$187$	−8.50651	+	19.7082i	−0.622057	+	1.44121i
$188$		−	10.0902i		−	0.735901i
$189$		0			0
$190$	7.99994	−	1.20489i	0.580377	−	0.0874117i
$191$	2.79837	+	8.61251i	0.202483	+	0.623179i	0.999807	+	0.0196279i	$0.00624817\pi$
$191$	2.79837	+	8.61251i	0.202483	+	0.623179i	−0.797324	+	0.603551i	$0.793752\pi$
$192$		0			0
$193$	−7.77997	−	10.7082i	−0.560014	−	0.770793i	0.431314	−	0.902202i	$-0.358050\pi$
$193$	−7.77997	−	10.7082i	−0.560014	−	0.770793i	−0.991328	+	0.131408i	$0.958050\pi$
$194$	−2.85410	−	8.78402i	−0.204913	−	0.630656i
$195$		0			0
$196$	5.35410	+	3.88998i	0.382436	+	0.277856i
$197$		−	26.2148i		−	1.86773i	−0.357631	−	0.933863i	$-0.616415\pi$
$197$		−	26.2148i		−	1.86773i	0.357631	−	0.933863i	$-0.383585\pi$
$198$		0			0
$199$	5.52786			0.391860			0.195930	−	0.980618i	$-0.437227\pi$
$199$	5.52786			0.391860			0.195930	+	0.980618i	$0.437227\pi$
$200$	−1.47271	−	4.77819i	−0.104136	−	0.337869i
$201$		0			0
$202$	18.7436	−	6.09017i	1.31880	−	0.428503i
$203$	1.62460	+	2.23607i	0.114024	+	0.156941i
$204$		0			0
$205$	−0.969751	−	0.984587i	−0.0677304	−	0.0687666i
$206$	2.11803	−	6.51864i	0.147570	−	0.454175i
$207$		0			0
$208$			2.38197i			0.165160i
$209$	11.7082	−	2.62866i	0.809873	−	0.181828i
$210$		0			0
$211$	−21.4164	−	15.5599i	−1.47437	−	1.07119i	−0.979319	−	0.202324i	$-0.935151\pi$
$211$	−21.4164	−	15.5599i	−1.47437	−	1.07119i	−0.495048	−	0.868866i	$-0.664849\pi$
$212$	−6.74315	−	2.19098i	−0.463122	−	0.150477i
$213$		0			0
$214$	−12.4721	+	9.06154i	−0.852578	+	0.619434i
$215$	16.8137	+	8.72841i	1.14668	+	0.595272i
$216$		0			0
$217$	−1.17557	−	0.381966i	−0.0798029	−	0.0259295i
$218$	−3.24920	+	4.47214i	−0.220063	+	0.302891i
$219$		0			0
$220$	−2.68416	−	6.91341i	−0.180966	−	0.466102i
$221$	−15.4164			−1.03702
$222$		0			0
$223$	18.1558	+	5.89919i	1.21580	+	0.395039i	0.845552	−	0.533893i	$-0.179271\pi$
$223$	18.1558	+	5.89919i	1.21580	+	0.395039i	0.370252	+	0.928931i	$0.379271\pi$
$224$	−0.190983	−	0.587785i	−0.0127606	−	0.0392731i
$225$		0			0
$226$	7.61803	−	5.53483i	0.506744	−	0.368171i
$227$	−11.4127	+	3.70820i	−0.757486	+	0.246122i	−0.662199	−	0.749328i	$-0.730377\pi$
$227$	−11.4127	+	3.70820i	−0.757486	+	0.246122i	−0.0952867	+	0.995450i	$0.530377\pi$
$228$		0			0
$229$	−5.85410	−	4.25325i	−0.386850	−	0.281063i	0.377314	−	0.926086i	$-0.376848\pi$
$229$	−5.85410	−	4.25325i	−0.386850	−	0.281063i	−0.764163	+	0.645023i	$0.776848\pi$
$230$	−9.23607	+	4.61803i	−0.609008	+	0.304504i
$231$		0			0
$232$			4.47214i			0.293610i
$233$	11.2412	−	15.4721i	0.736433	−	1.01361i	−0.262383	−	0.964964i	$-0.584508\pi$
$233$	11.2412	−	15.4721i	0.736433	−	1.01361i	0.998816	−	0.0486494i	$-0.0154917\pi$
$234$		0			0
$235$	−16.0746	+	15.8324i	−1.04859	+	1.03279i
$236$	−8.78115	+	6.37988i	−0.571604	+	0.415295i
$237$		0			0
$238$	3.80423	−	1.23607i	0.246591	−	0.0801224i
$239$	2.23607	−	6.88191i	0.144639	−	0.445154i	−0.852325	−	0.523012i	$-0.824808\pi$
$239$	2.23607	−	6.88191i	0.144639	−	0.445154i	0.996964	+	0.0778584i	$0.0248082\pi$
$240$		0			0
$241$	−4.90983			−0.316270			−0.158135	−	0.987418i	$-0.550548\pi$
$241$	−4.90983			−0.316270			−0.158135	+	0.987418i	$0.550548\pi$
$242$	−4.70228	−	9.94427i	−0.302274	−	0.639242i
$243$		0			0
$244$	−5.61803	−	4.08174i	−0.359658	−	0.261307i
$245$	−2.20395	−	14.6333i	−0.140805	−	0.934889i
$246$		0			0
$247$	5.06555	+	6.97214i	0.322313	+	0.443626i
$248$	−1.17557	−	1.61803i	−0.0746488	−	0.102745i
$249$		0			0
$250$	−5.30130	+	9.84359i	−0.335284	+	0.622563i
$251$	5.50000	+	3.99598i	0.347157	+	0.252224i	0.747675	−	0.664064i	$-0.231170\pi$
$251$	5.50000	+	3.99598i	0.347157	+	0.252224i	−0.400518	+	0.916289i	$0.631170\pi$
$252$		0			0
$253$	−13.1760	+	7.80902i	−0.828370	+	0.490949i
$254$	−2.85410			−0.179082
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−19.9192	+	6.47214i	−1.24252	+	0.403721i	−0.855236	−	0.518238i	$-0.826588\pi$
$257$	−19.9192	+	6.47214i	−1.24252	+	0.403721i	−0.387288	+	0.921959i	$0.626588\pi$
$258$		0			0
$259$	2.80902	−	2.04087i	0.174544	−	0.126814i
$260$	3.79470	−	3.73752i	0.235337	−	0.231791i
$261$		0			0
$262$	−4.70228	+	6.47214i	−0.290508	+	0.399850i
$263$		−	5.14590i		−	0.317310i	−0.987334	−	0.158655i	$-0.949284\pi$
$263$		−	5.14590i		−	0.317310i	0.987334	−	0.158655i	$-0.0507157\pi$
$264$		0			0
$265$	7.09017	+	14.1803i	0.435546	+	0.871091i
$266$	−1.80902	−	1.31433i	−0.110918	−	0.0805866i
$267$		0			0
$268$	−8.78402	+	2.85410i	−0.536570	+	0.174342i
$269$	−18.0902	+	13.1433i	−1.10298	+	0.801360i	−0.981543	−	0.191240i	$-0.938749\pi$
$269$	−18.0902	+	13.1433i	−1.10298	+	0.801360i	−0.121434	+	0.992600i	$0.538749\pi$
$270$		0			0
$271$	−0.437694	−	1.34708i	−0.0265880	−	0.0818295i	0.936882	−	0.349646i	$-0.113698\pi$
$271$	−0.437694	−	1.34708i	−0.0265880	−	0.0818295i	−0.963470	+	0.267816i	$0.913698\pi$
$272$	6.15537	+	2.00000i	0.373224	+	0.121268i
$273$		0			0
$274$	−21.4164			−1.29381
$275$	−6.80203	+	15.1239i	−0.410178	+	0.912005i
$276$		0			0
$277$	0.0202444	−	0.0278640i	0.00121637	−	0.00167419i	−0.808408	−	0.588622i	$-0.799671\pi$
$277$	0.0202444	−	0.0278640i	0.00121637	−	0.00167419i	0.809625	+	0.586948i	$0.199671\pi$
$278$	0.310271	+	0.100813i	0.0186088	+	0.00604637i
$279$		0			0
$280$	−0.636729	+	1.22654i	−0.0380518	+	0.0732999i
$281$	−7.32624	+	5.32282i	−0.437047	+	0.317533i	−0.784460	−	0.620179i	$-0.787060\pi$
$281$	−7.32624	+	5.32282i	−0.437047	+	0.317533i	0.347414	+	0.937712i	$0.387060\pi$
$282$		0			0
$283$	−0.171513	−	0.0557281i	−0.0101954	−	0.00331269i	0.303915	−	0.952699i	$-0.401706\pi$
$283$	−0.171513	−	0.0557281i	−0.0101954	−	0.00331269i	−0.314110	+	0.949387i	$0.601706\pi$
$284$	−1.61803	−	1.17557i	−0.0960127	−	0.0697573i
$285$		0			0
$286$	5.21885	−	5.93085i	0.308597	−	0.350699i
$287$			0.381966i			0.0225467i
$288$		0			0
$289$	−7.69098	+	23.6704i	−0.452411	+	1.39238i
$290$	7.12454	−	7.01719i	0.418368	−	0.412063i
$291$		0			0
$292$	0.898056	+	1.23607i	0.0525547	+	0.0723354i
$293$	−28.3929	+	9.22542i	−1.65873	+	0.538955i	−0.980606	−	0.195990i	$-0.937208\pi$
$293$	−28.3929	+	9.22542i	−1.65873	+	0.538955i	−0.678127	+	0.734945i	$0.737208\pi$
$294$		0			0
$295$	23.9422	+	3.97861i	1.39397	+	0.231644i
$296$	5.61803			0.326542
$297$		0			0
$298$		−	21.7082i		−	1.25752i
$299$	−8.89919	−	6.46564i	−0.514653	−	0.373917i
$300$		0			0
$301$	−1.61803	−	4.97980i	−0.0932619	−	0.287031i
$302$	8.05748	+	11.0902i	0.463656	+	0.638168i
$303$		0			0
$304$	−1.11803	−	3.44095i	−0.0641236	−	0.197352i
$305$	2.31260	+	15.3547i	0.132419	+	0.879207i
$306$		0			0
$307$			15.2361i			0.869568i	0.900535	+	0.434784i	$0.143175\pi$
$307$			15.2361i			0.869568i	−0.900535	+	0.434784i	$0.856825\pi$
$308$	−0.812299	+	1.88197i	−0.0462850	+	0.107235i
$309$		0			0
$310$	−0.733107	+	4.41164i	−0.0416377	+	0.250564i
$311$	1.29180	−	3.97574i	0.0732510	−	0.225444i	−0.907727	−	0.419561i	$-0.862184\pi$
$311$	1.29180	−	3.97574i	0.0732510	−	0.225444i	0.980978	+	0.194117i	$0.0621842\pi$
$312$		0			0
$313$	−6.77591	−	9.32624i	−0.382997	−	0.527150i	0.573378	−	0.819291i	$-0.305632\pi$
$313$	−6.77591	−	9.32624i	−0.382997	−	0.527150i	−0.956375	+	0.292141i	$0.905632\pi$
$314$	4.97214	−	3.61247i	0.280594	−	0.203863i
$315$		0			0
$316$	−1.90983	+	5.87785i	−0.107436	+	0.330655i
$317$	−8.45351	+	11.6353i	−0.474796	+	0.653501i	−0.977494	−	0.210961i	$-0.932341\pi$
$317$	−8.45351	+	11.6353i	−0.474796	+	0.653501i	0.502698	+	0.864462i	$0.332341\pi$
$318$		0			0
$319$	9.79837	−	11.1352i	0.548604	−	0.623449i
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$		0			0
$322$	2.71441	+	0.881966i	0.151268	+	0.0491500i
$323$	22.2703	−	7.23607i	1.23915	−	0.402626i
$324$		0			0
$325$	−11.9085	−	0.180815i	−0.660562	−	0.0100298i
$326$	2.90983	+	8.95554i	0.161161	+	0.496001i
$327$		0			0
$328$	−0.363271	+	0.500000i	−0.0200583	+	0.0276079i
$329$	6.23607			0.343806
$330$		0			0
$331$	−6.09017			−0.334746			−0.167373	−	0.985894i	$-0.553528\pi$
$331$	−6.09017			−0.334746			−0.167373	+	0.985894i	$0.553528\pi$
$332$	−5.98385	+	8.23607i	−0.328407	+	0.452013i
$333$		0			0
$334$	−4.11803	−	12.6740i	−0.225329	−	0.693491i
$335$	18.3298	+	9.51545i	1.00146	+	0.519884i
$336$		0			0
$337$	−1.73060	+	0.562306i	−0.0942718	+	0.0306308i	−0.355773	−	0.934572i	$-0.615782\pi$
$337$	−1.73060	+	0.562306i	−0.0942718	+	0.0306308i	0.261501	+	0.965203i	$0.415782\pi$
$338$	−6.96767	−	2.26393i	−0.378991	−	0.123142i
$339$		0			0
$340$	−6.47214	−	12.9443i	−0.351001	−	0.702002i
$341$	−0.618034	+	6.60440i	−0.0334684	+	0.357648i
$342$		0			0
$343$	−4.94704	+	6.80902i	−0.267115	+	0.367652i
$344$	2.61803	−	8.05748i	0.141155	−	0.434430i
$345$		0			0
$346$	1.50000	−	1.08981i	0.0806405	−	0.0585888i
$347$	−1.55909	−	2.14590i	−0.0836961	−	0.115198i	0.765116	−	0.643893i	$-0.222682\pi$
$347$	−1.55909	−	2.14590i	−0.0836961	−	0.115198i	−0.848812	+	0.528695i	$0.822682\pi$
$348$		0			0
$349$	2.23607	−	6.88191i	0.119694	−	0.368380i	−0.873203	−	0.487356i	$-0.837961\pi$
$349$	2.23607	−	6.88191i	0.119694	−	0.368380i	0.992897	+	0.118976i	$0.0379612\pi$
$350$	2.95309	−	0.910186i	0.157849	−	0.0486515i
$351$		0			0
$352$	−2.85317	+	1.69098i	−0.152074	+	0.0901297i
$353$		−	16.0000i		−	0.851594i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$		−	16.0000i		−	0.851594i	0.904819	−	0.425797i	$-0.140006\pi$
$354$		0			0
$355$	0.666045	+	4.42226i	0.0353500	+	0.234709i
$356$	−3.51722	−	10.8249i	−0.186412	−	0.573718i
$357$		0			0
$358$	−5.44907	−	7.50000i	−0.287992	−	0.396387i
$359$	−10.0000	−	30.7768i	−0.527780	−	1.62434i	−0.758753	−	0.651379i	$-0.774191\pi$
$359$	−10.0000	−	30.7768i	−0.527780	−	1.62434i	0.230973	−	0.972960i	$-0.425809\pi$
$360$		0			0
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$		−	19.8885i		−	1.04532i
$363$		0			0
$364$	−1.47214			−0.0771609
$365$	0.560044	−	3.37019i	0.0293140	−	0.176404i
$366$		0			0
$367$	28.4257	−	9.23607i	1.48381	−	0.482119i	0.548561	−	0.836111i	$-0.315176\pi$
$367$	28.4257	−	9.23607i	1.48381	−	0.482119i	0.935248	+	0.353992i	$0.115176\pi$
$368$	2.71441	+	3.73607i	0.141499	+	0.194756i
$369$		0			0
$370$	−8.81520	−	8.95007i	−0.458281	−	0.465292i
$371$	1.35410	−	4.16750i	0.0703015	−	0.216366i
$372$		0			0
$373$		−	6.56231i		−	0.339783i	−0.985463	−	0.169892i	$-0.945658\pi$
$373$		−	6.56231i		−	0.339783i	0.985463	−	0.169892i	$-0.0543418\pi$
$374$	−10.9443	−	18.4661i	−0.565915	−	0.954859i
$375$		0			0
$376$	8.16312	+	5.93085i	0.420981	+	0.305860i
$377$	10.1311	+	3.29180i	0.521779	+	0.169536i
$378$		0			0
$379$	25.9164	−	18.8294i	1.33124	−	0.967200i	0.331519	−	0.943449i	$-0.392439\pi$
$379$	25.9164	−	18.8294i	1.33124	−	0.967200i	0.999718	−	0.0237512i	$-0.00756095\pi$
$380$	−3.72747	+	7.18031i	−0.191215	+	0.368342i
$381$		0			0
$382$	−8.61251	−	2.79837i	−0.440654	−	0.143177i
$383$	13.0575	−	17.9721i	0.667208	−	0.918333i	−0.332485	−	0.943109i	$-0.607887\pi$
$383$	13.0575	−	17.9721i	0.667208	−	0.918333i	0.999693	+	0.0247753i	$0.00788704\pi$
$384$		0			0
$385$	4.27272	−	1.65890i	0.217758	−	0.0845456i
$386$	13.2361			0.673698
$387$		0			0
$388$	8.78402	+	2.85410i	0.445941	+	0.144895i
$389$	7.76393	+	23.8949i	0.393647	+	1.21152i	0.930010	+	0.367534i	$0.119798\pi$
$389$	7.76393	+	23.8949i	0.393647	+	1.21152i	−0.536363	+	0.843987i	$0.680202\pi$
$390$		0			0
$391$	−24.1803	+	17.5680i	−1.22285	+	0.888454i
$392$	−6.29412	+	2.04508i	−0.317901	+	0.103292i
$393$		0			0
$394$	21.2082	+	15.4087i	1.06845	+	0.776277i
$395$	12.3607	−	6.18034i	0.621933	−	0.310967i
$396$		0			0
$397$		−	12.3262i		−	0.618636i	−0.950959	−	0.309318i	$-0.899899\pi$
$397$		−	12.3262i		−	0.618636i	0.950959	−	0.309318i	$-0.100101\pi$
$398$	−3.24920	+	4.47214i	−0.162868	+	0.224168i
$399$		0			0
$400$	4.73128	+	1.61710i	0.236564	+	0.0808551i
$401$	0.0729490	−	0.0530006i	0.00364290	−	0.00264672i	−0.585962	−	0.810338i	$-0.699283\pi$
$401$	0.0729490	−	0.0530006i	0.00364290	−	0.00264672i	0.589605	+	0.807692i	$0.299283\pi$
$402$		0			0
$403$	−4.53077	+	1.47214i	−0.225694	+	0.0733323i
$404$	−6.09017	+	18.7436i	−0.302997	+	0.932530i
$405$		0			0
$406$	−2.76393			−0.137172
$407$	−13.9883	−	12.3090i	−0.693376	−	0.610135i
$408$		0			0
$409$	21.0172	+	15.2699i	1.03923	+	0.755048i	0.970136	−	0.242562i	$-0.0779877\pi$
$409$	21.0172	+	15.2699i	1.03923	+	0.755048i	0.0690987	+	0.997610i	$0.477988\pi$
$410$	1.36655	−	0.205819i	0.0674893	−	0.0101647i
$411$		0			0
$412$	4.02874	+	5.54508i	0.198482	+	0.273187i
$413$	−3.94298	−	5.42705i	−0.194022	−	0.267048i
$414$		0			0
$415$	22.5101	−	3.39028i	1.10498	−	0.166422i
$416$	−1.92705	−	1.40008i	−0.0944814	−	0.0686448i
$417$		0			0
$418$	−4.75528	+	11.0172i	−0.232588	+	0.538870i
$419$	35.9787			1.75768			0.878838	−	0.477121i	$-0.158320\pi$
$419$	35.9787			1.75768			0.878838	+	0.477121i	$0.158320\pi$
$420$		0			0
$421$	0.618034	−	1.90211i	0.0301211	−	0.0927033i	−0.934866	−	0.355001i	$-0.884480\pi$
$421$	0.618034	−	1.90211i	0.0301211	−	0.0927033i	0.964987	+	0.262298i	$0.0844804\pi$
$422$	25.1765	−	8.18034i	1.22557	−	0.398213i
$423$		0			0
$424$	5.73607	−	4.16750i	0.278568	−	0.202392i
$425$	−10.4661	+	30.6215i	−0.507680	+	1.48536i
$426$		0			0
$427$	2.52265	−	3.47214i	0.122080	−	0.168028i
$428$		−	15.4164i		−	0.745180i
$429$		0			0
$430$	−16.9443	+	8.47214i	−0.817125	+	0.408563i
$431$	22.7984	+	16.5640i	1.09816	+	0.797859i	0.980758	−	0.195225i	$-0.0625438\pi$
$431$	22.7984	+	16.5640i	1.09816	+	0.797859i	0.117401	+	0.993085i	$0.462544\pi$
$432$		0			0
$433$	7.05342	−	2.29180i	0.338966	−	0.110137i	−0.134588	−	0.990902i	$-0.542971\pi$
$433$	7.05342	−	2.29180i	0.338966	−	0.110137i	0.473554	+	0.880765i	$0.342971\pi$
$434$	1.00000	−	0.726543i	0.0480015	−	0.0348752i
$435$		0			0
$436$	−1.70820	−	5.25731i	−0.0818081	−	0.251780i
$437$	15.8904	+	5.16312i	0.760143	+	0.246985i
$438$		0			0
$439$	6.18034			0.294972			0.147486	−	0.989064i	$-0.452882\pi$
$439$	6.18034			0.294972			0.147486	+	0.989064i	$0.452882\pi$
$440$	7.17078	+	1.89207i	0.341854	+	0.0902008i
$441$		0			0
$442$	9.06154	−	12.4721i	0.431013	−	0.593239i
$443$	0.171513	+	0.0557281i	0.00814885	+	0.00264772i	0.313089	−	0.949724i	$-0.398636\pi$
$443$	0.171513	+	0.0557281i	0.00814885	+	0.00264772i	−0.304940	+	0.952372i	$0.598636\pi$
$444$		0			0
$445$	−11.7263	+	22.5885i	−0.555878	+	1.07080i
$446$	−15.4443	+	11.2209i	−0.731307	+	0.531326i
$447$		0			0
$448$	0.587785	+	0.190983i	0.0277702	+	0.00902310i
$449$	16.8713	+	12.2577i	0.796207	+	0.578478i	0.909799	−	0.415049i	$-0.136236\pi$
$449$	16.8713	+	12.2577i	0.796207	+	0.578478i	−0.113592	+	0.993527i	$0.536236\pi$
$450$		0			0
$451$	2.00000	−	0.449028i	0.0941763	−	0.0211439i
$452$			9.41641i			0.442911i
$453$		0			0
$454$	3.70820	−	11.4127i	0.174035	−	0.535624i
$455$	2.30991	+	2.34525i	0.108290	+	0.109947i
$456$		0			0
$457$	4.80828	+	6.61803i	0.224922	+	0.309579i	0.906532	−	0.422137i	$-0.138720\pi$
$457$	4.80828	+	6.61803i	0.224922	+	0.309579i	−0.681610	+	0.731716i	$0.738720\pi$
$458$	6.88191	−	2.23607i	0.321571	−	0.104485i
$459$		0			0
$460$	1.69276	−	10.1865i	0.0789252	−	0.474950i
$461$	9.70820			0.452156			0.226078	−	0.974109i	$-0.427410\pi$
$461$	9.70820			0.452156			0.226078	+	0.974109i	$0.427410\pi$
$462$		0			0
$463$			1.32624i			0.0616355i	0.999525	+	0.0308178i	$0.00981115\pi$
$463$			1.32624i			0.0616355i	−0.999525	+	0.0308178i	$0.990189\pi$
$464$	−3.61803	−	2.62866i	−0.167963	−	0.122032i
$465$		0			0
$466$	5.90983	+	18.1886i	0.273768	+	0.842570i
$467$	10.9637	+	15.0902i	0.507337	+	0.698290i	0.983467	−	0.181085i	$-0.0579609\pi$
$467$	10.9637	+	15.0902i	0.507337	+	0.698290i	−0.476130	+	0.879375i	$0.657961\pi$
$468$		0			0
$469$	−1.76393	−	5.42882i	−0.0814508	−	0.250680i
$470$	−3.36025	−	22.3107i	−0.154997	−	1.02911i
$471$		0			0
$472$		−	10.8541i		−	0.499601i
$473$	−24.1724	+	14.3262i	−1.11145	+	0.658721i
$474$		0			0
$475$	17.2877	−	5.32832i	0.793212	−	0.244480i
$476$	−1.23607	+	3.80423i	−0.0566551	+	0.174366i
$477$		0			0
$478$	4.25325	+	5.85410i	0.194539	+	0.267760i
$479$	22.0344	−	16.0090i	1.00678	−	0.731468i	0.0432482	−	0.999064i	$-0.486229\pi$
$479$	22.0344	−	16.0090i	1.00678	−	0.731468i	0.963531	+	0.267596i	$0.0862294\pi$
$480$		0			0
$481$	4.13525	−	12.7270i	0.188551	−	0.580302i
$482$	2.88593	−	3.97214i	0.131450	−	0.180926i
$483$		0			0
$484$	10.8090	+	2.04087i	0.491319	+	0.0927668i
$485$	−9.23607	−	18.4721i	−0.419388	−	0.838776i
$486$		0			0
$487$	−38.9403	−	12.6525i	−1.76455	−	0.573338i	−0.766898	−	0.641769i	$-0.778201\pi$
$487$	−38.9403	−	12.6525i	−1.76455	−	0.573338i	−0.997656	+	0.0684303i	$0.978201\pi$
$488$	6.60440	−	2.14590i	0.298967	−	0.0971402i
$489$		0			0
$490$	13.1341	+	6.81822i	0.593337	+	0.308016i
$491$	−8.11803	−	24.9847i	−0.366362	−	1.12755i	−0.949124	−	0.314903i	$-0.898028\pi$
$491$	−8.11803	−	24.9847i	−0.366362	−	1.12755i	0.582762	−	0.812643i	$-0.301972\pi$
$492$		0			0
$493$	17.0130	−	23.4164i	0.766228	−	1.05462i
$494$	−8.61803			−0.387744
$495$		0			0
$496$	2.00000			0.0898027
$497$	0.726543	−	1.00000i	0.0325899	−	0.0448561i
$498$		0			0
$499$	0.100813	+	0.310271i	0.00451301	+	0.0138896i	0.953288	−	0.302064i	$-0.0976756\pi$
$499$	0.100813	+	0.310271i	0.00451301	+	0.0138896i	−0.948775	+	0.315954i	$0.897676\pi$
$500$	−4.84760	−	10.0748i	−0.216791	−	0.450557i
$501$		0			0
$502$	−6.46564	+	2.10081i	−0.288576	+	0.0937639i
$503$	−11.7759	−	3.82624i	−0.525064	−	0.170604i	0.0344785	−	0.999405i	$-0.489023\pi$
$503$	−11.7759	−	3.82624i	−0.525064	−	0.170604i	−0.559542	+	0.828802i	$0.689023\pi$
$504$		0			0
$505$	39.4164	−	19.7082i	1.75401	−	0.877004i
$506$	1.42705	−	15.2497i	0.0634402	−	0.677930i
$507$		0			0
$508$	1.67760	−	2.30902i	0.0744314	−	0.102446i
$509$	−3.61803	+	11.1352i	−0.160367	+	0.493557i	−0.998665	−	0.0516541i	$-0.983551\pi$
$509$	−3.61803	+	11.1352i	−0.160367	+	0.493557i	0.838298	+	0.545212i	$0.183551\pi$
$510$		0			0
$511$	−0.763932	+	0.555029i	−0.0337944	+	0.0245530i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$		0			0
$514$	6.47214	−	19.9192i	0.285474	−	0.878598i
$515$	2.51240	−	15.1189i	0.110709	−	0.666219i
$516$		0			0
$517$	−7.33094	−	32.6525i	−0.322414	−	1.43605i
$518$			3.47214i			0.152557i
$519$		0			0
$520$	0.793248	+	5.26684i	0.0347862	+	0.230966i
$521$	9.60739	+	29.5685i	0.420907	+	1.29542i	0.906859	+	0.421434i	$0.138473\pi$
$521$	9.60739	+	29.5685i	0.420907	+	1.29542i	−0.485952	+	0.873986i	$0.661527\pi$
$522$		0			0
$523$	−0.661030	−	0.909830i	−0.0289048	−	0.0397841i	0.794320	−	0.607500i	$-0.207827\pi$
$523$	−0.661030	−	0.909830i	−0.0289048	−	0.0397841i	−0.823225	+	0.567716i	$0.807827\pi$
$524$	−2.47214	−	7.60845i	−0.107996	−	0.332377i
$525$		0			0
$526$	4.16312	+	3.02468i	0.181521	+	0.131882i
$527$			12.9443i			0.563861i
$528$		0			0
$529$	1.67376			0.0727723
$530$	−15.6396	−	2.59893i	−0.679342	−	0.112890i
$531$		0			0
$532$	2.12663	−	0.690983i	0.0922010	−	0.0299579i
$533$	0.865300	+	1.19098i	0.0374803	+	0.0515872i
$534$		0			0
$535$	−24.5598	+	24.1897i	−1.06181	+	1.04581i
$536$	2.85410	−	8.78402i	0.123278	−	0.379412i
$537$		0			0
$538$		−	22.3607i		−	0.964037i
$539$	20.1525	+	8.69827i	0.868029	+	0.374661i
$540$		0			0
$541$	−12.7984	−	9.29856i	−0.550245	−	0.399776i	0.277631	−	0.960688i	$-0.410451\pi$
$541$	−12.7984	−	9.29856i	−0.550245	−	0.399776i	−0.827876	+	0.560911i	$0.810451\pi$
$542$	1.34708	+	0.437694i	0.0578622	+	0.0188006i
$543$		0			0
$544$	−5.23607	+	3.80423i	−0.224495	+	0.163105i
$545$	−5.69507	+	10.9705i	−0.243950	+	0.469926i
$546$		0			0
$547$	−18.9151	−	6.14590i	−0.808753	−	0.262780i	−0.124683	−	0.992197i	$-0.539791\pi$
$547$	−18.9151	−	6.14590i	−0.808753	−	0.262780i	−0.684069	+	0.729417i	$0.739791\pi$
$548$	12.5882	−	17.3262i	0.537743	−	0.740140i
$549$		0			0
$550$	−8.23736	−	14.3926i	−0.351242	−	0.613701i
$551$	−16.1803			−0.689306
$552$		0			0
$553$	−3.63271	−	1.18034i	−0.154479	−	0.0501932i
$554$	0.0106431	+	0.0327561i	0.000452183	+	0.00139168i
$555$		0			0
$556$	−0.263932	+	0.191758i	−0.0111932	+	0.00813234i
$557$	10.0453	−	3.26393i	0.425635	−	0.138297i	−0.0883634	−	0.996088i	$-0.528164\pi$
$557$	10.0453	−	3.26393i	0.425635	−	0.138297i	0.513999	+	0.857791i	$0.328164\pi$
$558$		0			0
$559$	−16.3262	−	11.8617i	−0.690526	−	0.501697i
$560$	−0.618034	−	1.23607i	−0.0261167	−	0.0522334i
$561$		0			0
$562$		−	9.05573i		−	0.381993i
$563$	−26.8011	+	36.8885i	−1.12953	+	1.55467i	−0.340575	+	0.940217i	$0.610622\pi$
$563$	−26.8011	+	36.8885i	−1.12953	+	1.55467i	−0.788956	+	0.614450i	$0.789378\pi$
$564$		0			0
$565$	15.0012	−	14.7752i	0.631107	−	0.621597i
$566$	0.145898	−	0.106001i	0.00613255	−	0.00445556i
$567$		0			0
$568$	1.90211	−	0.618034i	0.0798109	−	0.0259321i
$569$	1.80902	−	5.56758i	0.0758379	−	0.233405i	−0.905950	−	0.423384i	$-0.860842\pi$
$569$	1.80902	−	5.56758i	0.0758379	−	0.233405i	0.981788	+	0.189979i	$0.0608420\pi$
$570$		0			0
$571$	44.6869			1.87009			0.935045	−	0.354530i	$-0.115359\pi$
$571$	44.6869			1.87009			0.935045	+	0.354530i	$0.115359\pi$
$572$	1.73060	+	7.70820i	0.0723600	+	0.322296i
$573$		0			0
$574$	−0.309017	−	0.224514i	−0.0128981	−	0.00937103i
$575$	−18.8842	+	13.2869i	−0.787527	+	0.554102i
$576$		0			0
$577$	10.3026	+	14.1803i	0.428904	+	0.590335i	0.967701	−	0.252100i	$-0.0811212\pi$
$577$	10.3026	+	14.1803i	0.428904	+	0.590335i	−0.538797	+	0.842435i	$0.681121\pi$
$578$	−14.6291	−	20.1353i	−0.608491	−	0.837516i
$579$		0			0
$580$	1.48932	+	9.88847i	0.0618407	+	0.410597i
$581$	−5.09017	−	3.69822i	−0.211176	−	0.153428i
$582$		0			0
$583$	−23.4131	−	2.19098i	−0.969673	−	0.0907412i
$584$	−1.52786			−0.0632235
$585$		0			0
$586$	9.22542	−	28.3929i	0.381099	−	1.17290i
$587$	22.9969	−	7.47214i	0.949182	−	0.308408i	0.206799	−	0.978383i	$-0.433695\pi$
$587$	22.9969	−	7.47214i	0.949182	−	0.308408i	0.742383	+	0.669975i	$0.233695\pi$
$588$		0			0
$589$	5.85410	−	4.25325i	0.241214	−	0.175252i
$590$	−17.2916	+	17.0311i	−0.711885	+	0.701158i
$591$		0			0
$592$	−3.30220	+	4.54508i	−0.135719	+	0.186802i
$593$			6.11146i			0.250967i	0.992096	+	0.125484i	$0.0400483\pi$
$593$			6.11146i			0.250967i	−0.992096	+	0.125484i	$0.959952\pi$
$594$		0			0
$595$	8.00000	−	4.00000i	0.327968	−	0.163984i
$596$	17.5623	+	12.7598i	0.719380	+	0.522660i
$597$		0			0
$598$	10.4616	−	3.39919i	0.427808	−	0.139003i
$599$	5.00000	−	3.63271i	0.204294	−	0.148429i	−0.480934	−	0.876757i	$-0.659702\pi$
$599$	5.00000	−	3.63271i	0.204294	−	0.148429i	0.685228	+	0.728328i	$0.259702\pi$
$600$		0			0
$601$	0.0278640	+	0.0857567i	0.00113660	+	0.00349809i	0.951623	−	0.307267i	$-0.0994146\pi$
$601$	0.0278640	+	0.0857567i	0.00113660	+	0.00349809i	−0.950487	+	0.310766i	$0.899415\pi$
$602$	4.97980	+	1.61803i	0.202961	+	0.0659461i
$603$		0			0
$604$	−13.7082			−0.557779
$605$	−13.7090	−	20.4221i	−0.557351	−	0.830277i
$606$		0			0
$607$	19.7072	−	27.1246i	0.799890	−	1.10095i	−0.192916	−	0.981215i	$-0.561794\pi$
$607$	19.7072	−	27.1246i	0.799890	−	1.10095i	0.992805	−	0.119739i	$-0.0382057\pi$
$608$	3.44095	+	1.11803i	0.139549	+	0.0453423i
$609$		0			0
$610$	−13.7815	−	7.15433i	−0.557997	−	0.289670i
$611$	19.4443	−	14.1271i	0.786631	−	0.571521i
$612$		0			0
$613$	5.70634	+	1.85410i	0.230477	+	0.0748865i	0.421979	−	0.906606i	$-0.361336\pi$
$613$	5.70634	+	1.85410i	0.230477	+	0.0748865i	−0.191502	+	0.981492i	$0.561336\pi$
$614$	−12.3262	−	8.95554i	−0.497446	−	0.361416i
$615$		0			0
$616$	−1.04508	−	1.76336i	−0.0421077	−	0.0710476i
$617$		−	9.05573i		−	0.364570i	−0.983246	−	0.182285i	$-0.941651\pi$
$617$		−	9.05573i		−	0.364570i	0.983246	−	0.182285i	$-0.0583493\pi$
$618$		0			0
$619$	2.29837	−	7.07367i	0.0923794	−	0.284315i	−0.894182	−	0.447703i	$-0.852242\pi$
$619$	2.29837	−	7.07367i	0.0923794	−	0.284315i	0.986562	+	0.163388i	$0.0522423\pi$
$620$	−3.13818	−	3.18619i	−0.126032	−	0.127961i
$621$		0			0
$622$	2.45714	+	3.38197i	0.0985224	+	0.135604i
$623$	6.69015	−	2.17376i	0.268035	−	0.0870899i
$624$		0			0
$625$	−8.44373	+	23.5309i	−0.337749	+	0.941236i
$626$	11.5279			0.460746
$627$		0			0
$628$			6.14590i			0.245248i
$629$	−29.4164	−	21.3723i	−1.17291	−	0.852168i
$630$		0			0
$631$	8.38197	+	25.7970i	0.333681	+	1.02696i	0.967368	+	0.253375i	$0.0815406\pi$
$631$	8.38197	+	25.7970i	0.333681	+	1.02696i	−0.633687	+	0.773589i	$0.718459\pi$
$632$	−3.63271	−	5.00000i	−0.144502	−	0.198889i
$633$		0			0
$634$	−4.44427	−	13.6781i	−0.176505	−	0.543225i
$635$	−6.31079	+	0.950480i	−0.250436	+	0.0377187i
$636$		0			0
$637$			15.7639i			0.624590i
$638$	3.24920	+	14.4721i	0.128637	+	0.572957i
$639$		0			0
$640$	0.366554	−	2.20582i	0.0144893	−	0.0871927i
$641$	−9.50000	+	29.2380i	−0.375227	+	1.15483i	0.568098	+	0.822961i	$0.307680\pi$
$641$	−9.50000	+	29.2380i	−0.375227	+	1.15483i	−0.943325	+	0.331870i	$0.892320\pi$
$642$		0			0
$643$	12.2452	+	16.8541i	0.482904	+	0.664661i	0.979060	−	0.203573i	$-0.0652554\pi$
$643$	12.2452	+	16.8541i	0.482904	+	0.664661i	−0.496155	+	0.868234i	$0.665255\pi$
$644$	−2.30902	+	1.67760i	−0.0909880	+	0.0661067i
$645$		0			0
$646$	−7.23607	+	22.2703i	−0.284699	+	0.876214i
$647$	16.3270	−	22.4721i	0.641879	−	0.883471i	−0.356835	−	0.934167i	$-0.616144\pi$
$647$	16.3270	−	22.4721i	0.641879	−	0.883471i	0.998714	+	0.0506966i	$0.0161442\pi$
$648$		0			0
$649$	−23.7812	+	27.0256i	−0.933492	+	1.06085i
$650$	7.14590	−	9.52786i	0.280285	−	0.373714i
$651$		0			0
$652$	−8.95554	−	2.90983i	−0.350726	−	0.113958i
$653$	27.7849	−	9.02786i	1.08731	−	0.353288i	0.290102	−	0.956996i	$-0.406311\pi$
$653$	27.7849	−	9.02786i	1.08731	−	0.353288i	0.797205	+	0.603708i	$0.206311\pi$
$654$		0			0
$655$	−8.24199	+	15.8767i	−0.322041	+	0.620354i
$656$	−0.190983	−	0.587785i	−0.00745663	−	0.0229492i
$657$		0			0
$658$	−3.66547	+	5.04508i	−0.142895	+	0.196678i
$659$	−11.3820			−0.443378			−0.221689	−	0.975117i	$-0.571157\pi$
$659$	−11.3820			−0.443378			−0.221689	+	0.975117i	$0.571157\pi$
$660$		0			0
$661$	−5.88854			−0.229038			−0.114519	−	0.993421i	$-0.536533\pi$
$661$	−5.88854			−0.229038			−0.114519	+	0.993421i	$0.536533\pi$
$662$	3.57971	−	4.92705i	0.139129	−	0.191495i
$663$		0			0
$664$	−3.14590	−	9.68208i	−0.122085	−	0.375738i
$665$	−4.43767	−	2.30371i	−0.172086	−	0.0893339i
$666$		0			0
$667$	19.6417	−	6.38197i	0.760529	−	0.247111i
$668$	12.6740	+	4.11803i	0.490372	+	0.159332i
$669$		0			0
$670$	−18.4721	+	9.23607i	−0.713641	+	0.356820i
$671$	−21.1459	−	9.12705i	−0.816328	−	0.352346i
$672$		0			0
$673$	1.28157	−	1.76393i	0.0494010	−	0.0679946i	−0.783602	−	0.621263i	$-0.786620\pi$
$673$	1.28157	−	1.76393i	0.0494010	−	0.0679946i	0.833003	+	0.553269i	$0.186620\pi$
$674$	0.562306	−	1.73060i	0.0216592	−	0.0666602i
$675$		0			0
$676$	5.92705	−	4.30625i	0.227963	−	0.165625i
$677$	−9.68208	−	13.3262i	−0.372113	−	0.512169i	0.581361	−	0.813646i	$-0.302520\pi$
$677$	−9.68208	−	13.3262i	−0.372113	−	0.512169i	−0.953474	+	0.301477i	$0.902520\pi$
$678$		0			0
$679$	−1.76393	+	5.42882i	−0.0676935	+	0.208339i
$680$	14.2764	+	2.37238i	0.547473	+	0.0909768i
$681$		0			0
$682$	−4.97980	−	4.38197i	−0.190686	−	0.167794i
$683$		−	15.5967i		−	0.596793i	−0.954442	−	0.298396i	$-0.903548\pi$
$683$		−	15.5967i		−	0.596793i	0.954442	−	0.298396i	$-0.0964518\pi$
$684$		0			0
$685$	−47.3545	+	7.13215i	−1.80932	+	0.272505i
$686$	−2.60081	−	8.00448i	−0.0992995	−	0.305612i
$687$		0			0
$688$	4.97980	+	6.85410i	0.189853	+	0.261310i
$689$	−5.21885	−	16.0620i	−0.198822	−	0.611912i
$690$		0			0
$691$	−31.6803	−	23.0171i	−1.20518	−	0.875612i	−0.210393	−	0.977617i	$-0.567474\pi$
$691$	−31.6803	−	23.0171i	−1.20518	−	0.875612i	−0.994784	+	0.102005i	$0.967474\pi$
$692$			1.85410i			0.0704824i
$693$		0			0
$694$	2.65248			0.100687
$695$	0.719622	+	0.119584i	0.0272968	+	0.00453607i
$696$		0			0
$697$	3.80423	−	1.23607i	0.144095	−	0.0468194i
$698$	4.25325	+	5.85410i	0.160988	+	0.221581i
$699$		0			0
$700$	−0.999424	+	2.92409i	−0.0377747	+	0.110520i
$701$	8.20163	−	25.2420i	0.309771	−	0.953378i	−0.668082	−	0.744087i	$-0.732885\pi$
$701$	8.20163	−	25.2420i	0.309771	−	0.953378i	0.977854	−	0.209290i	$-0.0671154\pi$
$702$		0			0
$703$			20.3262i			0.766619i
$704$	0.309017	−	3.30220i	0.0116465	−	0.124456i
$705$		0			0
$706$	12.9443	+	9.40456i	0.487164	+	0.353945i
$707$	−11.5842	−	3.76393i	−0.435668	−	0.141557i
$708$		0			0
$709$	−3.61803	+	2.62866i	−0.135878	+	0.0987212i	−0.653648	−	0.756799i	$-0.726762\pi$
$709$	−3.61803	+	2.62866i	−0.135878	+	0.0987212i	0.517770	+	0.855520i	$0.326762\pi$
$710$	−3.96917	−	2.06050i	−0.148960	−	0.0773291i
$711$		0			0
$712$	10.8249	+	3.51722i	0.405680	+	0.131813i
$713$	−5.42882	+	7.47214i	−0.203311	+	0.279834i
$714$		0			0
$715$	9.56444	−	14.8519i	0.357690	−	0.555429i
$716$	9.27051			0.346455
$717$		0			0
$718$	30.7768	+	10.0000i	1.14858	+	0.373197i
$719$	6.05573	+	18.6376i	0.225841	+	0.695066i	0.998205	+	0.0598864i	$0.0190738\pi$
$719$	6.05573	+	18.6376i	0.225841	+	0.695066i	−0.772365	+	0.635179i	$0.780926\pi$
$720$		0			0
$721$	−3.42705	+	2.48990i	−0.127630	+	0.0927287i
$722$	−5.62058	+	1.82624i	−0.209176	+	0.0679655i
$723$		0			0
$724$	16.0902	+	11.6902i	0.597986	+	0.434463i
$725$	13.4164	−	17.8885i	0.498273	−	0.664364i
$726$		0			0
$727$			31.7426i			1.17727i	0.808399	+	0.588635i	$0.200334\pi$
$727$			31.7426i			1.17727i	−0.808399	+	0.588635i	$0.799666\pi$
$728$	0.865300	−	1.19098i	0.0320701	−	0.0441408i
$729$		0			0
$730$	2.39736	+	2.43403i	0.0887302	+	0.0900876i
$731$	−44.3607	+	32.2299i	−1.64074	+	1.19207i
$732$		0			0
$733$	−8.95554	+	2.90983i	−0.330780	+	0.107477i	−0.469699	−	0.882827i	$-0.655637\pi$
$733$	−8.95554	+	2.90983i	−0.330780	+	0.107477i	0.138918	+	0.990304i	$0.455637\pi$
$734$	−9.23607	+	28.4257i	−0.340909	+	1.04921i
$735$		0			0
$736$	−4.61803			−0.170223
$737$	−26.3521	+	15.6180i	−0.970691	+	0.575298i
$738$		0			0
$739$	6.97214	+	5.06555i	0.256474	+	0.186339i	0.708591	−	0.705619i	$-0.249331\pi$
$739$	6.97214	+	5.06555i	0.256474	+	0.186339i	−0.452117	+	0.891959i	$0.649331\pi$
$740$	12.4222	−	1.87093i	0.456649	−	0.0687768i
$741$		0			0
$742$	2.57565	+	3.54508i	0.0945553	+	0.130144i
$743$	9.21281	+	12.6803i	0.337985	+	0.465197i	0.943852	−	0.330370i	$-0.107173\pi$
$743$	9.21281	+	12.6803i	0.337985	+	0.465197i	−0.605867	+	0.795566i	$0.707173\pi$
$744$		0			0
$745$	−7.22932	−	47.9997i	−0.264862	−	1.75857i
$746$	5.30902	+	3.85723i	0.194377	+	0.141223i
$747$		0			0
$748$	21.3723	+	2.00000i	0.781448	+	0.0731272i
$749$	9.52786			0.348141
$750$		0			0
$751$	−7.14590	+	21.9928i	−0.260758	+	0.802529i	0.731883	+	0.681430i	$0.238642\pi$
$751$	−7.14590	+	21.9928i	−0.260758	+	0.802529i	−0.992640	+	0.121099i	$0.961358\pi$
$752$	−9.59632	+	3.11803i	−0.349942	+	0.113703i
$753$		0			0
$754$	−8.61803	+	6.26137i	−0.313850	+	0.228026i
$755$	21.5094	+	21.8385i	0.782808	+	0.794784i
$756$		0			0
$757$	−4.54328	+	6.25329i	−0.165128	+	0.227280i	−0.883560	−	0.468318i	$-0.844860\pi$
$757$	−4.54328	+	6.25329i	−0.165128	+	0.227280i	0.718432	+	0.695597i	$0.244860\pi$
$758$			32.0344i			1.16354i
$759$		0			0
$760$	−3.61803	−	7.23607i	−0.131240	−	0.262480i
$761$	−8.38197	−	6.08985i	−0.303846	−	0.220757i	0.425405	−	0.905003i	$-0.360132\pi$
$761$	−8.38197	−	6.08985i	−0.303846	−	0.220757i	−0.729251	+	0.684246i	$0.760132\pi$
$762$		0			0
$763$	3.24920	−	1.05573i	0.117629	−	0.0382199i
$764$	7.32624	−	5.32282i	0.265054	−	0.192573i
$765$		0			0
$766$	6.86475	+	21.1275i	0.248033	+	0.763368i
$767$	−24.5887	−	7.98936i	−0.887847	−	0.288479i
$768$		0			0
$769$	37.0344			1.33550			0.667748	−	0.744387i	$-0.267258\pi$
$769$	37.0344			1.33550			0.667748	+	0.744387i	$0.267258\pi$
$770$	−1.16936	+	4.43179i	−0.0421409	+	0.159710i
$771$		0			0
$772$	−7.77997	+	10.7082i	−0.280007	+	0.385397i
$773$	37.5200	+	12.1910i	1.34950	+	0.438479i	0.892524	−	0.451000i	$-0.148932\pi$
$773$	37.5200	+	12.1910i	1.34950	+	0.438479i	0.456976	+	0.889479i	$0.348932\pi$
$774$		0			0
$775$	−0.151820	+	9.99885i	−0.00545353	+	0.359169i
$776$	−7.47214	+	5.42882i	−0.268234	+	0.194883i
$777$		0			0
$778$	−23.8949	−	7.76393i	−0.856675	−	0.278350i
$779$	−1.80902	−	1.31433i	−0.0648148	−	0.0470907i
$780$		0			0
$781$	−6.09017	−	2.62866i	−0.217923	−	0.0940607i
$782$		−	29.8885i		−	1.06881i
$783$		0			0
$784$	2.04508	−	6.29412i	0.0730387	−	0.224790i
$785$	9.79101	−	9.64347i	0.349456	−	0.344190i
$786$		0			0
$787$	−10.9637	−	15.0902i	−0.390812	−	0.537906i	0.567596	−	0.823307i	$-0.307873\pi$
$787$	−10.9637	−	15.0902i	−0.390812	−	0.537906i	−0.958408	+	0.285400i	$0.907873\pi$
$788$	−24.9317	+	8.10081i	−0.888156	+	0.288580i
$789$		0			0
$790$	−2.26543	+	13.6327i	−0.0806002	+	0.485030i
$791$	−5.81966			−0.206923
$792$		0			0
$793$		−	16.5410i		−	0.587389i
$794$	9.97214	+	7.24518i	0.353898	+	0.257122i
$795$		0			0
$796$	−1.70820	−	5.25731i	−0.0605457	−	0.186340i
$797$	−3.30220	−	4.54508i	−0.116970	−	0.160995i	0.746517	−	0.665366i	$-0.231724\pi$
$797$	−3.30220	−	4.54508i	−0.116970	−	0.160995i	−0.863487	+	0.504371i	$0.831724\pi$
$798$		0			0
$799$	−20.1803	−	62.1087i	−0.713929	−	2.19725i
$800$	−4.08924	+	2.87718i	−0.144576	+	0.101724i
$801$		0			0
$802$			0.0901699i			0.00318401i
$803$	3.80423	+	3.34752i	0.134248	+	0.118132i
$804$		0			0
$805$	6.29563	+	1.04618i	0.221892	+	0.0368730i
$806$	1.47214	−	4.53077i	0.0518538	−	0.159590i
$807$		0			0
$808$	−11.5842	−	15.9443i	−0.407530	−	0.560918i
$809$	2.07295	−	1.50609i	0.0728810	−	0.0529512i	−0.550748	−	0.834671i	$-0.685658\pi$
$809$	2.07295	−	1.50609i	0.0728810	−	0.0529512i	0.623629	+	0.781720i	$0.285658\pi$
$810$		0			0
$811$	−13.0238	+	40.0831i	−0.457327	+	1.40751i	0.411053	+	0.911611i	$0.365161\pi$
$811$	−13.0238	+	40.0831i	−0.457327	+	1.40751i	−0.868381	+	0.495898i	$0.834839\pi$
$812$	1.62460	−	2.23607i	0.0570122	−	0.0784706i
$813$		0			0
$814$	18.1803	−	4.08174i	0.637221	−	0.143065i
$815$	9.41641	+	18.8328i	0.329842	+	0.659685i
$816$		0			0
$817$	29.1522	+	9.47214i	1.01991	+	0.331388i
$818$	−24.7072	+	8.02786i	−0.863868	+	0.280688i
$819$		0			0
$820$	−0.636729	+	1.22654i	−0.0222355	+	0.0428327i
$821$	−0.819660	−	2.52265i	−0.0286063	−	0.0880412i	0.935734	−	0.352706i	$-0.114739\pi$
$821$	−0.819660	−	2.52265i	−0.0286063	−	0.0880412i	−0.964340	+	0.264665i	$0.914739\pi$
$822$		0			0
$823$	3.79171	−	5.21885i	0.132171	−	0.181918i	−0.737802	−	0.675017i	$-0.764136\pi$
$823$	3.79171	−	5.21885i	0.132171	−	0.181918i	0.869973	+	0.493100i	$0.164136\pi$
$824$	−6.85410			−0.238774
$825$		0			0
$826$	6.70820			0.233408
$827$	5.19180	−	7.14590i	0.180537	−	0.248487i	−0.709152	−	0.705056i	$-0.750922\pi$
$827$	5.19180	−	7.14590i	0.180537	−	0.248487i	0.889688	+	0.456569i	$0.150922\pi$
$828$		0			0
$829$	7.88854	+	24.2784i	0.273980	+	0.843225i	0.989487	+	0.144619i	$0.0461958\pi$
$829$	7.88854	+	24.2784i	0.273980	+	0.843225i	−0.715507	+	0.698606i	$0.753804\pi$
$830$	−10.4883	+	20.2038i	−0.364054	+	0.701283i
$831$		0			0
$832$	2.26538	−	0.736068i	0.0785381	−	0.0255186i
$833$	40.7364	+	13.2361i	1.41143	+	0.458603i
$834$		0			0
$835$	−13.3262	−	26.6525i	−0.461173	−	0.922347i
$836$	−6.11803	−	10.3229i	−0.211597	−	0.357024i
$837$		0			0
$838$	−21.1478	+	29.1074i	−0.730537	+	1.00550i
$839$	−2.23607	+	6.88191i	−0.0771976	+	0.237590i	−0.982207	−	0.187802i	$-0.939864\pi$
$839$	−2.23607	+	6.88191i	−0.0771976	+	0.237590i	0.905009	+	0.425392i	$0.139864\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	1.17557	+	1.61803i	0.0405128	+	0.0557611i
$843$		0			0
$844$	−8.18034	+	25.1765i	−0.281579	+	0.866611i
$845$	−16.1604	−	2.68546i	−0.555933	−	0.0923826i
$846$		0			0
$847$	−1.26133	+	6.68034i	−0.0433397	+	0.229539i
$848$			7.09017i			0.243477i
$849$		0			0
$850$	−18.6215	−	26.4661i	−0.638711	−	0.907780i
$851$	−8.01722	−	24.6745i	−0.274827	−	0.845830i
$852$		0			0
$853$	−3.09793	−	4.26393i	−0.106071	−	0.145994i	0.752682	−	0.658385i	$-0.228760\pi$
$853$	−3.09793	−	4.26393i	−0.106071	−	0.145994i	−0.858753	+	0.512391i	$0.828760\pi$
$854$	1.32624	+	4.08174i	0.0453829	+	0.139674i
$855$		0			0
$856$	12.4721	+	9.06154i	0.426289	+	0.309717i
$857$			8.18034i			0.279435i	0.990191	+	0.139718i	$0.0446195\pi$
$857$			8.18034i			0.279435i	−0.990191	+	0.139718i	$0.955381\pi$
$858$		0			0
$859$	−8.61803			−0.294044			−0.147022	−	0.989133i	$-0.546969\pi$
$859$	−8.61803			−0.294044			−0.147022	+	0.989133i	$0.546969\pi$
$860$	3.10549	−	18.6880i	0.105896	−	0.637256i
$861$		0			0
$862$	−26.8011	+	8.70820i	−0.912849	+	0.296603i
$863$	13.5393	+	18.6353i	0.460883	+	0.634351i	0.974692	−	0.223554i	$-0.0717658\pi$
$863$	13.5393	+	18.6353i	0.460883	+	0.634351i	−0.513808	+	0.857905i	$0.671766\pi$
$864$		0			0
$865$	2.95376	−	2.90925i	0.100431	−	0.0989176i
$866$	−2.29180	+	7.05342i	−0.0778784	+	0.239685i
$867$		0			0
$868$			1.23607i			0.0419549i
$869$	−1.90983	+	20.4087i	−0.0647865	+	0.692318i
$870$		0			0
$871$	−17.7984	−	12.9313i	−0.603075	−	0.438160i
$872$	5.25731	+	1.70820i	0.178035	+	0.0578471i
$873$		0			0
$874$	−13.5172	+	9.82084i	−0.457227	+	0.332195i
$875$	6.22654	−	2.99598i	0.210496	−	0.101283i
$876$		0			0
$877$	49.3287	+	16.0279i	1.66571	+	0.541223i	0.982057	−	0.188583i	$-0.0603896\pi$
$877$	49.3287	+	16.0279i	1.66571	+	0.541223i	0.683654	+	0.729806i	$0.260390\pi$
$878$	−3.63271	+	5.00000i	−0.122598	+	0.168742i
$879$		0			0
$880$	−5.74559	+	4.68915i	−0.193684	+	0.158071i
$881$	−6.79837			−0.229043			−0.114522	−	0.993421i	$-0.536533\pi$
$881$	−6.79837			−0.229043			−0.114522	+	0.993421i	$0.536533\pi$
$882$		0			0
$883$	13.5923	+	4.41641i	0.457418	+	0.148624i	0.528657	−	0.848835i	$-0.322696\pi$
$883$	13.5923	+	4.41641i	0.457418	+	0.148624i	−0.0712400	+	0.997459i	$0.522696\pi$
$884$	4.76393	+	14.6619i	0.160228	+	0.493132i
$885$		0			0
$886$	−0.145898	+	0.106001i	−0.00490154	+	0.00356118i
$887$	−37.2425	+	12.1008i	−1.25048	+	0.406306i	−0.858093	−	0.513495i	$-0.828351\pi$
$887$	−37.2425	+	12.1008i	−1.25048	+	0.406306i	−0.392387	+	0.919800i	$0.628351\pi$
$888$		0			0
$889$	1.42705	+	1.03681i	0.0478618	+	0.0347736i
$890$	−11.3820	−	22.7639i	−0.381524	−	0.763049i
$891$		0			0
$892$		−	19.0902i		−	0.639186i
$893$	−21.4580	+	29.5344i	−0.718066	+	0.988332i
$894$		0			0
$895$	−14.5463	−	14.7688i	−0.486228	−	0.493667i
$896$	−0.500000	+	0.363271i	−0.0167038	+	0.0121360i
$897$		0			0
$898$	−19.8334	+	6.44427i	−0.661850	+	0.215048i
$899$	2.76393	−	8.50651i	0.0921823	−	0.283708i
$900$		0			0
$901$	−45.8885			−1.52877
$902$	−0.812299	+	1.88197i	−0.0270466	+	0.0626626i
$903$		0			0
$904$	−7.61803	−	5.53483i	−0.253372	−	0.184086i
$905$	−6.62333	−	43.9762i	−0.220167	−	1.46182i
$906$		0			0
$907$	17.3310	+	23.8541i	0.575467	+	0.792062i	0.993189	−	0.116512i	$-0.0371715\pi$
$907$	17.3310	+	23.8541i	0.575467	+	0.792062i	−0.417722	+	0.908575i	$0.637171\pi$
$908$	7.05342	+	9.70820i	0.234076	+	0.322178i
$909$		0			0
$910$	−3.25508	+	0.490254i	−0.107905	+	0.0162518i
$911$	−19.5623	−	14.2128i	−0.648128	−	0.470893i	0.214505	−	0.976723i	$-0.431186\pi$
$911$	−19.5623	−	14.2128i	−0.648128	−	0.470893i	−0.862633	+	0.505830i	$0.831186\pi$
$912$		0			0
$913$	−13.3803	+	31.0000i	−0.442823	+	1.02595i
$914$	−8.18034			−0.270582
$915$		0			0
$916$	−2.23607	+	6.88191i	−0.0738818	+	0.227385i
$917$	4.70228	−	1.52786i	0.155283	−	0.0504545i
$918$		0			0
$919$	8.09017	−	5.87785i	0.266870	−	0.193892i	−0.446300	−	0.894883i	$-0.647259\pi$
$919$	8.09017	−	5.87785i	0.266870	−	0.193892i	0.713170	+	0.700991i	$0.247259\pi$
$920$	7.24611	+	7.35697i	0.238897	+	0.242552i
$921$		0			0
$922$	−5.70634	+	7.85410i	−0.187928	+	0.258661i
$923$		−	4.76393i		−	0.156807i
$924$		0			0
$925$	−22.4721	−	16.8541i	−0.738879	−	0.554159i
$926$	−1.07295	−	0.779543i	−0.0352593	−	0.0256174i
$927$		0			0
$928$	4.25325	−	1.38197i	0.139620	−	0.0453653i
$929$	5.26393	−	3.82447i	0.172704	−	0.125477i	−0.498075	−	0.867134i	$-0.665960\pi$
$929$	5.26393	−	3.82447i	0.172704	−	0.125477i	0.670779	+	0.741657i	$0.265960\pi$
$930$		0			0
$931$	−7.39919	−	22.7724i	−0.242499	−	0.746334i
$932$	−18.1886	−	5.90983i	−0.595787	−	0.193583i
$933$		0			0
$934$	−18.6525			−0.610328
$935$	−30.3488	−	37.1863i	−0.992513	−	1.21612i
$936$		0			0
$937$	−31.3319	+	43.1246i	−1.02357	+	1.40882i	−0.113895	+	0.993493i	$0.536333\pi$
$937$	−31.3319	+	43.1246i	−1.02357	+	1.40882i	−0.909672	+	0.415327i	$0.863667\pi$
$938$	5.42882	+	1.76393i	0.177257	+	0.0575944i
$939$		0			0
$940$	20.0248	+	10.3954i	0.653138	+	0.339060i
$941$	16.0902	−	11.6902i	0.524525	−	0.381089i	−0.293781	−	0.955873i	$-0.594914\pi$
$941$	16.0902	−	11.6902i	0.524525	−	0.381089i	0.818306	+	0.574783i	$0.194914\pi$
$942$		0			0
$943$	2.71441	+	0.881966i	0.0883934	+	0.0287208i
$944$	8.78115	+	6.37988i	0.285802	+	0.207647i
$945$		0			0
$946$	2.61803	−	27.9767i	0.0851196	−	0.909600i
$947$		−	28.0000i		−	0.909878i	−0.890523	−	0.454939i	$-0.849661\pi$
$947$		−	28.0000i		−	0.909878i	0.890523	−	0.454939i	$-0.150339\pi$
$948$		0			0
$949$	−1.12461	+	3.46120i	−0.0365064	+	0.112355i
$950$	−5.85073	+	17.1179i	−0.189823	+	0.555379i
$951$		0			0
$952$	−2.35114	−	3.23607i	−0.0762009	−	0.104882i
$953$	−6.43288	+	2.09017i	−0.208381	+	0.0677072i	−0.411348	−	0.911478i	$-0.634942\pi$
$953$	−6.43288	+	2.09017i	−0.208381	+	0.0677072i	0.202966	+	0.979186i	$0.434942\pi$
$954$		0			0
$955$	−19.9753	−	3.31941i	−0.646386	−	0.107414i
$956$	−7.23607			−0.234031
$957$		0			0
$958$			27.2361i			0.879957i
$959$	10.7082	+	7.77997i	0.345786	+	0.251228i
$960$		0			0
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	7.86572	+	10.8262i	0.253601	+	0.349052i
$963$		0			0
$964$	1.51722	+	4.66953i	0.0488664	+	0.150395i
$965$	29.2667	−	4.40791i	0.942127	−	0.141896i
$966$		0			0
$967$		−	44.5623i		−	1.43303i	−0.697573	−	0.716514i	$-0.745737\pi$
$967$		−	44.5623i		−	1.43303i	0.697573	−	0.716514i	$-0.254263\pi$
$968$	−8.00448	+	7.54508i	−0.257274	+	0.242508i
$969$		0			0
$970$	20.3731	+	3.38551i	0.654141	+	0.108702i
$971$	10.8647	−	33.4382i	0.348666	−	1.07308i	−0.610925	−	0.791688i	$-0.709202\pi$
$971$	10.8647	−	33.4382i	0.348666	−	1.07308i	0.959592	−	0.281396i	$-0.0907975\pi$
$972$		0			0
$973$	−0.118513	−	0.163119i	−0.00379935	−	0.00522935i
$974$	33.1246	−	24.0664i	1.06138	−	0.771138i
$975$		0			0
$976$	−2.14590	+	6.60440i	−0.0686885	+	0.211402i
$977$	5.19180	−	7.14590i	0.166100	−	0.228618i	−0.717851	−	0.696197i	$-0.754874\pi$
$977$	5.19180	−	7.14590i	0.166100	−	0.228618i	0.883951	+	0.467580i	$0.154874\pi$
$978$		0			0
$979$	−19.2467	−	32.4747i	−0.615128	−	1.03790i
$980$	−13.2361	+	6.61803i	−0.422811	+	0.211405i
$981$		0			0
$982$	24.9847	+	8.11803i	0.797295	+	0.259057i
$983$	−21.1275	+	6.86475i	−0.673863	+	0.218951i	−0.625907	−	0.779898i	$-0.715271\pi$
$983$	−21.1275	+	6.86475i	−0.673863	+	0.218951i	−0.0479565	+	0.998849i	$0.515271\pi$
$984$		0			0
$985$	52.0255	+	27.0077i	1.65767	+	0.860538i
$986$	8.94427	+	27.5276i	0.284844	+	0.876659i
$987$		0			0
$988$	5.06555	−	6.97214i	0.161157	−	0.221813i
$989$	−39.1246			−1.24409
$990$		0			0
$991$	35.8197			1.13785			0.568925	−	0.822390i	$-0.307360\pi$
$991$	35.8197			1.13785			0.568925	+	0.822390i	$0.307360\pi$
$992$	−1.17557	+	1.61803i	−0.0373244	+	0.0513726i
$993$		0			0
$994$	0.381966	+	1.17557i	0.0121152	+	0.0372868i
$995$	−5.69507	+	10.9705i	−0.180546	+	0.347789i
$996$		0			0
$997$	−25.6255	+	8.32624i	−0.811569	+	0.263695i	−0.685262	−	0.728297i	$-0.740312\pi$
$997$	−25.6255	+	8.32624i	−0.811569	+	0.263695i	−0.126307	+	0.991991i	$0.540312\pi$
$998$	−0.310271	−	0.100813i	−0.00982145	−	0.00319118i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.ba.b.829.1		8
3.2	odd	2		110.2.j.a.59.2	yes	8
5.4	even	2	inner	990.2.ba.b.829.2		8
11.3	even	5	inner	990.2.ba.b.289.2		8
12.11	even	2		880.2.cd.a.609.2		8
15.2	even	4		550.2.h.e.301.1		4
15.8	even	4		550.2.h.d.301.1		4
15.14	odd	2		110.2.j.a.59.1	✓	8
33.5	odd	10		1210.2.b.f.969.3		4
33.14	odd	10		110.2.j.a.69.1	yes	8
33.17	even	10		1210.2.b.g.969.1		4
55.14	even	10	inner	990.2.ba.b.289.1		8
60.59	even	2		880.2.cd.a.609.1		8
132.47	even	10		880.2.cd.a.289.1		8
165.14	odd	10		110.2.j.a.69.2	yes	8
165.17	odd	20		6050.2.a.ct.1.1		2
165.38	even	20		6050.2.a.cl.1.2		2
165.47	even	20		550.2.h.e.201.1		4
165.83	odd	20		6050.2.a.bv.1.2		2
165.104	odd	10		1210.2.b.f.969.2		4
165.113	even	20		550.2.h.d.201.1		4
165.137	even	20		6050.2.a.ce.1.1		2
165.149	even	10		1210.2.b.g.969.4		4
660.179	even	10		880.2.cd.a.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.a.59.1	✓	8	15.14	odd	2
110.2.j.a.59.2	yes	8	3.2	odd	2
110.2.j.a.69.1	yes	8	33.14	odd	10
110.2.j.a.69.2	yes	8	165.14	odd	10
550.2.h.d.201.1		4	165.113	even	20
550.2.h.d.301.1		4	15.8	even	4
550.2.h.e.201.1		4	165.47	even	20
550.2.h.e.301.1		4	15.2	even	4
880.2.cd.a.289.1		8	132.47	even	10
880.2.cd.a.289.2		8	660.179	even	10
880.2.cd.a.609.1		8	60.59	even	2
880.2.cd.a.609.2		8	12.11	even	2
990.2.ba.b.289.1		8	55.14	even	10	inner
990.2.ba.b.289.2		8	11.3	even	5	inner
990.2.ba.b.829.1		8	1.1	even	1	trivial
990.2.ba.b.829.2		8	5.4	even	2	inner
1210.2.b.f.969.2		4	165.104	odd	10
1210.2.b.f.969.3		4	33.5	odd	10
1210.2.b.g.969.1		4	33.17	even	10
1210.2.b.g.969.4		4	165.149	even	10
6050.2.a.bv.1.2		2	165.83	odd	20
6050.2.a.ce.1.1		2	165.137	even	20
6050.2.a.cl.1.2		2	165.38	even	20
6050.2.a.ct.1.1		2	165.17	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-1.03025 + 1.98459i) q^{5} +(0.587785 - 0.190983i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.00000 - 2.00000i) q^{10} +(-1.69098 - 2.85317i) q^{11} +(1.40008 - 1.92705i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.80423 - 5.23607i) q^{17} +(-1.11803 + 3.44095i) q^{19} +(2.20582 + 0.366554i) q^{20} +(3.30220 + 0.309017i) q^{22} -4.61803i q^{23} +(-2.87718 - 4.08924i) q^{25} +(0.736068 + 2.26538i) q^{26} +(-0.363271 - 0.500000i) q^{28} +(1.38197 + 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} -1.00000i q^{32} +6.47214 q^{34} +(-0.226543 + 1.36327i) q^{35} +(5.34307 - 1.73607i) q^{37} +(-2.12663 - 2.92705i) q^{38} +(-1.59310 + 1.56909i) q^{40} +(-0.190983 + 0.587785i) q^{41} -8.47214i q^{43} +(-2.19098 + 2.48990i) q^{44} +(3.73607 + 2.71441i) q^{46} +(9.59632 + 3.11803i) q^{47} +(-5.35410 + 3.88998i) q^{49} +(4.99942 + 0.0759100i) q^{50} +(-2.26538 - 0.736068i) q^{52} +(4.16750 - 5.73607i) q^{53} +(7.40450 - 0.416429i) q^{55} +0.618034 q^{56} +(-4.25325 - 1.38197i) q^{58} +(-3.35410 - 10.3229i) q^{59} +(5.61803 - 4.08174i) q^{61} +(1.90211 - 0.618034i) q^{62} +(0.809017 + 0.587785i) q^{64} +(2.38197 + 4.76393i) q^{65} -9.23607i q^{67} +(-3.80423 + 5.23607i) q^{68} +(-0.969751 - 0.984587i) q^{70} +(1.61803 - 1.17557i) q^{71} +(-1.45309 + 0.472136i) q^{73} +(-1.73607 + 5.34307i) q^{74} +3.61803 q^{76} +(-1.53884 - 1.35410i) q^{77} +(-5.00000 - 3.63271i) q^{79} +(-0.333023 - 2.21113i) q^{80} +(-0.363271 - 0.500000i) q^{82} +(-5.98385 - 8.23607i) q^{83} +(14.3107 - 2.15537i) q^{85} +(6.85410 + 4.97980i) q^{86} +(-0.726543 - 3.23607i) q^{88} +11.3820 q^{89} +(0.454915 - 1.40008i) q^{91} +(-4.39201 + 1.42705i) q^{92} +(-8.16312 + 5.93085i) q^{94} +(-5.67702 - 5.76388i) q^{95} +(-5.42882 + 7.47214i) q^{97} -6.61803i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 4 q^{5} - 8 q^{10} - 18 q^{11} - 6 q^{14} - 2 q^{16} + 4 q^{20} - 6 q^{25} - 12 q^{26} + 20 q^{29} - 4 q^{31} + 16 q^{34} + 4 q^{35} - 2 q^{40} - 6 q^{41} - 22 q^{44} + 12 q^{46} - 16 q^{49}+ \cdots - 34 q^{94}+O(q^{100}) \) 8 * q + 2 * q^4 - 4 * q^5 - 8 * q^10 - 18 * q^11 - 6 * q^14 - 2 * q^16 + 4 * q^20 - 6 * q^25 - 12 * q^26 + 20 * q^29 - 4 * q^31 + 16 * q^34 + 4 * q^35 - 2 * q^40 - 6 * q^41 - 22 * q^44 + 12 * q^46 - 16 * q^49 + 8 * q^50 + 4 * q^55 - 4 * q^56 + 36 * q^61 + 2 * q^64 + 28 * q^65 - 12 * q^70 + 4 * q^71 + 4 * q^74 + 20 * q^76 - 40 * q^79 - 4 * q^80 + 16 * q^85 + 28 * q^86 + 100 * q^89 + 26 * q^91 - 34 * q^94

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