LMFDB - Embedded newform 990.2.ba.h.289.1

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 = [16,0,0,4,6,0,0] 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.1
Root			$1.89162 - 1.19237i$ of defining polynomial
Character	$\chi$	$=$	990.289
Dual form			990.2.ba.h.829.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-1.71856 + 1.43058i) q^{5} +(-4.76878 - 1.54947i) q^{7} +(0.951057 - 0.309017i) q^{8} +(2.16751 + 0.549472i) q^{10} +(0.969425 - 3.17178i) q^{11} +(1.37249 + 1.88906i) q^{13} +(1.54947 + 4.76878i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.0359433 + 0.0494717i) q^{17} +(0.636930 + 1.96027i) q^{19} +(-0.829496 - 2.07652i) q^{20} +(-3.13584 + 1.08005i) q^{22} +3.91525i q^{23} +(0.906896 - 4.91707i) q^{25} +(0.721558 - 2.22073i) q^{26} +(2.94727 - 4.05657i) q^{28} +(-1.27844 + 3.93464i) q^{29} +(7.18170 - 5.21781i) q^{31} +1.00000i q^{32} +0.0611504 q^{34} +(10.4121 - 4.15925i) q^{35} +(4.33385 + 1.40815i) q^{37} +(1.21151 - 1.66751i) q^{38} +(-1.19237 + 1.89162i) q^{40} +(1.41525 + 4.35570i) q^{41} -3.61803i q^{43} +(2.71698 + 1.90211i) q^{44} +(3.16751 - 2.30133i) q^{46} +(8.44260 - 2.74317i) q^{47} +(14.6773 + 10.6637i) q^{49} +(-4.51105 + 2.15649i) q^{50} +(-2.22073 + 0.721558i) q^{52} +(-1.30598 - 1.79753i) q^{53} +(2.87147 + 6.83774i) q^{55} -5.01420 q^{56} +(3.93464 - 1.27844i) q^{58} +(0.599137 - 1.84396i) q^{59} +(7.84211 + 5.69763i) q^{61} +(-8.44260 - 2.74317i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-5.06115 - 1.28302i) q^{65} +2.49573i q^{67} +(-0.0359433 - 0.0494717i) q^{68} +(-9.48497 - 5.97880i) q^{70} +(7.13254 + 5.18210i) q^{71} +(-5.13205 - 1.66751i) q^{73} +(-1.40815 - 4.33385i) q^{74} -2.06115 q^{76} +(-9.53757 + 13.6235i) q^{77} +(-5.38417 + 3.91183i) q^{79} +(2.23122 - 0.147217i) q^{80} +(2.69197 - 3.70518i) q^{82} +(6.49620 - 8.94125i) q^{83} +(-0.00900240 - 0.136440i) q^{85} +(-2.92705 + 2.12663i) q^{86} +(-0.0581575 - 3.31611i) q^{88} +6.09017 q^{89} +(-3.61803 - 11.1352i) q^{91} +(-3.72363 - 1.20988i) q^{92} +(-7.18170 - 5.21781i) q^{94} +(-3.89892 - 2.45766i) q^{95} +(4.29216 + 5.90765i) q^{97} -18.1422i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 6 q^{5} + 4 q^{10} + 20 q^{11} + 12 q^{14} - 4 q^{16} - 16 q^{19} - 6 q^{20} + 16 q^{26} - 16 q^{29} - 4 q^{31} - 8 q^{34} + 48 q^{35} - 4 q^{40} - 40 q^{41} + 20 q^{46} + 84 q^{49} - 4 q^{50}+ \cdots + 50 q^{95}+O(q^{100}) $ 16 * q + 4 * q^4 + 6 * q^5 + 4 * q^10 + 20 * q^11 + 12 * q^14 - 4 * q^16 - 16 * q^19 - 6 * q^20 + 16 * q^26 - 16 * q^29 - 4 * q^31 - 8 * q^34 + 48 * q^35 - 4 * q^40 - 40 * q^41 + 20 * q^46 + 84 * q^49 - 4 * q^50 + 32 * q^55 + 8 * q^56 + 20 * q^61 + 4 * q^64 - 72 * q^65 + 36 * q^70 + 56 * q^71 - 4 * q^74 - 24 * q^76 + 36 * q^79 - 4 * q^80 - 54 * q^85 - 20 * q^86 + 8 * q^89 - 40 * q^91 + 4 * q^94 + 50 * q^95

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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
$5$	−1.71856	+	1.43058i	−0.768563	+	0.639774i
$5$	−1.71856	+	1.43058i	−0.768563	+	0.639774i
$6$		0			0
$7$	−4.76878	−	1.54947i	−1.80243	−	0.585645i	−0.802491	−	0.596664i	$-0.796493\pi$
$7$	−4.76878	−	1.54947i	−1.80243	−	0.585645i	−0.999939	+	0.0110184i	$0.996493\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$		0			0
$10$	2.16751	+	0.549472i	0.685425	+	0.173758i
$11$	0.969425	−	3.17178i	0.292293	−	0.956329i
$11$	0.969425	−	3.17178i	0.292293	−	0.956329i
$12$		0			0
$13$	1.37249	+	1.88906i	0.380659	+	0.523932i	0.955759	−	0.294151i	$-0.0950369\pi$
$13$	1.37249	+	1.88906i	0.380659	+	0.523932i	−0.575100	+	0.818083i	$0.695037\pi$
$14$	1.54947	+	4.76878i	0.414114	+	1.27451i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.0359433	+	0.0494717i	−0.00871753	+	0.0119986i	−0.813354	−	0.581770i	$-0.802360\pi$
$17$	−0.0359433	+	0.0494717i	−0.00871753	+	0.0119986i	0.804636	+	0.593768i	$0.202360\pi$
$18$		0			0
$19$	0.636930	+	1.96027i	0.146122	+	0.449717i	0.997154	−	0.0753974i	$-0.0240226\pi$
$19$	0.636930	+	1.96027i	0.146122	+	0.449717i	−0.851032	+	0.525114i	$0.824023\pi$
$20$	−0.829496	−	2.07652i	−0.185481	−	0.464324i
$21$		0			0
$22$	−3.13584	+	1.08005i	−0.668564	+	0.230267i
$23$			3.91525i			0.816387i	0.912896	+	0.408193i	$0.133841\pi$
$23$			3.91525i			0.816387i	−0.912896	+	0.408193i	$0.866159\pi$
$24$		0			0
$25$	0.906896	−	4.91707i	0.181379	−	0.983413i
$26$	0.721558	−	2.22073i	0.141509	−	0.435521i
$27$		0			0
$28$	2.94727	−	4.05657i	0.556982	−	0.766620i
$29$	−1.27844	+	3.93464i	−0.237401	+	0.730644i	0.759393	+	0.650632i	$0.225496\pi$
$29$	−1.27844	+	3.93464i	−0.237401	+	0.730644i	−0.996794	+	0.0800122i	$0.974504\pi$
$30$		0			0
$31$	7.18170	−	5.21781i	1.28987	−	0.937147i	0.290069	−	0.957006i	$-0.406322\pi$
$31$	7.18170	−	5.21781i	1.28987	−	0.937147i	0.999803	+	0.0198592i	$0.00632179\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.0611504			0.0104872
$35$	10.4121	−	4.15925i	1.75996	−	0.703042i
$36$		0			0
$37$	4.33385	+	1.40815i	0.712481	+	0.231499i	0.642760	−	0.766067i	$-0.277789\pi$
$37$	4.33385	+	1.40815i	0.712481	+	0.231499i	0.0697209	+	0.997567i	$0.477789\pi$
$38$	1.21151	−	1.66751i	0.196533	−	0.270505i
$39$		0			0
$40$	−1.19237	+	1.89162i	−0.188531	+	0.299092i
$41$	1.41525	+	4.35570i	0.221025	+	0.680246i	0.998671	+	0.0515429i	$0.0164139\pi$
$41$	1.41525	+	4.35570i	0.221025	+	0.680246i	−0.777646	+	0.628703i	$0.783586\pi$
$42$		0			0
$43$		−	3.61803i		−	0.551745i	−0.961194	−	0.275873i	$-0.911033\pi$
$43$		−	3.61803i		−	0.551745i	0.961194	−	0.275873i	$-0.0889668\pi$
$44$	2.71698	+	1.90211i	0.409600	+	0.286754i
$45$		0			0
$46$	3.16751	−	2.30133i	0.467023	−	0.339312i
$47$	8.44260	−	2.74317i	1.23148	−	0.400132i	0.380229	−	0.924892i	$-0.375845\pi$
$47$	8.44260	−	2.74317i	1.23148	−	0.400132i	0.851250	+	0.524760i	$0.175845\pi$
$48$		0			0
$49$	14.6773	+	10.6637i	2.09676	+	1.52338i
$50$	−4.51105	+	2.15649i	−0.637959	+	0.304973i
$51$		0			0
$52$	−2.22073	+	0.721558i	−0.307960	+	0.100062i
$53$	−1.30598	−	1.79753i	−0.179391	−	0.246910i	0.709847	−	0.704356i	$-0.248764\pi$
$53$	−1.30598	−	1.79753i	−0.179391	−	0.246910i	−0.889237	+	0.457446i	$0.848764\pi$
$54$		0			0
$55$	2.87147	+	6.83774i	0.387189	+	0.922000i
$56$	−5.01420			−0.670050
$57$		0			0
$58$	3.93464	−	1.27844i	0.516643	−	0.167868i
$59$	0.599137	−	1.84396i	0.0780011	−	0.240063i	−0.904451	−	0.426577i	$-0.859719\pi$
$59$	0.599137	−	1.84396i	0.0780011	−	0.240063i	0.982452	+	0.186515i	$0.0597192\pi$
$60$		0			0
$61$	7.84211	+	5.69763i	1.00408	+	0.729506i	0.962959	−	0.269648i	$-0.0869073\pi$
$61$	7.84211	+	5.69763i	1.00408	+	0.729506i	0.0411202	+	0.999154i	$0.486907\pi$
$62$	−8.44260	−	2.74317i	−1.07221	−	0.348382i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−5.06115	−	1.28302i	−0.627758	−	0.159139i
$66$		0			0
$67$			2.49573i			0.304902i	0.988311	+	0.152451i	$0.0487167\pi$
$67$			2.49573i			0.304902i	−0.988311	+	0.152451i	$0.951283\pi$
$68$	−0.0359433	−	0.0494717i	−0.00435876	−	0.00599932i
$69$		0			0
$70$	−9.48497	−	5.97880i	−1.13367	−	0.714603i
$71$	7.13254	+	5.18210i	0.846477	+	0.615002i	0.924172	−	0.381975i	$-0.124756\pi$
$71$	7.13254	+	5.18210i	0.846477	+	0.615002i	−0.0776953	+	0.996977i	$0.524756\pi$
$72$		0			0
$73$	−5.13205	−	1.66751i	−0.600662	−	0.195167i	−0.00712611	−	0.999975i	$-0.502268\pi$
$73$	−5.13205	−	1.66751i	−0.600662	−	0.195167i	−0.593535	+	0.804808i	$0.702268\pi$
$74$	−1.40815	−	4.33385i	−0.163695	−	0.503800i
$75$		0			0
$76$	−2.06115			−0.236430
$77$	−9.53757	+	13.6235i	−1.08691	+	1.55254i
$78$		0			0
$79$	−5.38417	+	3.91183i	−0.605766	+	0.440115i	−0.847921	−	0.530123i	$-0.822146\pi$
$79$	−5.38417	+	3.91183i	−0.605766	+	0.440115i	0.242155	+	0.970238i	$0.422146\pi$
$80$	2.23122	−	0.147217i	0.249458	−	0.0164594i
$81$		0			0
$82$	2.69197	−	3.70518i	0.297278	−	0.409169i
$83$	6.49620	−	8.94125i	0.713050	−	0.981429i	−0.286676	−	0.958028i	$-0.592550\pi$
$83$	6.49620	−	8.94125i	0.713050	−	0.981429i	0.999726	−	0.0234017i	$-0.00744968\pi$
$84$		0			0
$85$	−0.00900240	−	0.136440i	−0.000976448	−	0.0147990i
$86$	−2.92705	+	2.12663i	−0.315632	+	0.229320i
$87$		0			0
$88$	−0.0581575	−	3.31611i	−0.00619961	−	0.353499i
$89$	6.09017			0.645557			0.322778	−	0.946475i	$-0.395383\pi$
$89$	6.09017			0.645557			0.322778	+	0.946475i	$0.395383\pi$
$90$		0			0
$91$	−3.61803	−	11.1352i	−0.379273	−	1.16728i
$92$	−3.72363	−	1.20988i	−0.388215	−	0.126139i
$93$		0			0
$94$	−7.18170	−	5.21781i	−0.740736	−	0.538176i
$95$	−3.89892	−	2.45766i	−0.400021	−	0.252151i
$96$		0			0
$97$	4.29216	+	5.90765i	0.435802	+	0.599831i	0.969273	−	0.245988i	$-0.0791124\pi$
$97$	4.29216	+	5.90765i	0.435802	+	0.599831i	−0.533470	+	0.845819i	$0.679112\pi$
$98$		−	18.1422i		−	1.83263i
$99$		0			0
$100$	4.39616	+	2.38197i	0.439616	+	0.238197i
$101$	−0.179498	+	0.130413i	−0.0178608	+	0.0129766i	−0.596680	−	0.802479i	$-0.703514\pi$
$101$	−0.179498	+	0.130413i	−0.0178608	+	0.0129766i	0.578819	+	0.815456i	$0.303514\pi$
$102$		0			0
$103$	−0.538341	−	0.174918i	−0.0530443	−	0.0172351i	0.282375	−	0.959304i	$-0.408878\pi$
$103$	−0.538341	−	0.174918i	−0.0530443	−	0.0172351i	−0.335419	+	0.942069i	$0.608878\pi$
$104$	1.88906	+	1.37249i	0.185238	+	0.134583i
$105$		0			0
$106$	−0.686596	+	2.11313i	−0.0666881	+	0.205245i
$107$	−2.12087	+	0.689113i	−0.205033	+	0.0666191i	−0.409733	−	0.912206i	$-0.634378\pi$
$107$	−2.12087	+	0.689113i	−0.205033	+	0.0666191i	0.204700	+	0.978825i	$0.434378\pi$
$108$		0			0
$109$	−7.86288			−0.753127			−0.376563	−	0.926391i	$-0.622894\pi$
$109$	−7.86288			−0.753127			−0.376563	+	0.926391i	$0.622894\pi$
$110$	3.84404	−	6.34219i	0.366515	−	0.604704i
$111$		0			0
$112$	2.94727	+	4.05657i	0.278491	+	0.383310i
$113$	11.9469	−	3.88177i	1.12387	−	0.365166i	0.312624	−	0.949877i	$-0.398792\pi$
$113$	11.9469	−	3.88177i	1.12387	−	0.365166i	0.811242	+	0.584710i	$0.198792\pi$
$114$		0			0
$115$	−5.60107	−	6.72860i	−0.522303	−	0.627445i
$116$	−3.34700	−	2.43174i	−0.310762	−	0.225781i
$117$		0			0
$118$	−1.84396	+	0.599137i	−0.169750	+	0.0551551i
$119$	0.248061	−	0.180227i	0.0227397	−	0.0165214i
$120$		0			0
$121$	−9.12043	−	6.14961i	−0.829130	−	0.559056i
$122$		−	9.69338i		−	0.877597i
$123$		0			0
$124$	2.74317	+	8.44260i	0.246344	+	0.758168i
$125$	5.47569	+	9.74766i	0.489761	+	0.871857i
$126$		0			0
$127$	8.50112	−	11.7008i	0.754353	−	1.03828i	−0.243310	−	0.969949i	$-0.578233\pi$
$127$	8.50112	−	11.7008i	0.754353	−	1.03828i	0.997663	−	0.0683289i	$-0.0217667\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$		0			0
$130$	1.93688	+	4.84870i	0.169876	+	0.425259i
$131$	−15.3256			−1.33900			−0.669502	−	0.742810i	$-0.733493\pi$
$131$	−15.3256			−1.33900			−0.669502	+	0.742810i	$0.733493\pi$
$132$		0			0
$133$		−	10.3350i		−	0.896159i
$134$	2.01909	−	1.46696i	0.174423	−	0.126726i
$135$		0			0
$136$	−0.0188965	+	0.0581575i	−0.00162036	+	0.00498696i
$137$	0.649130	−	0.893451i	0.0554589	−	0.0763326i	−0.780387	−	0.625297i	$-0.784978\pi$
$137$	0.649130	−	0.893451i	0.0554589	−	0.0763326i	0.835846	+	0.548964i	$0.184978\pi$
$138$		0			0
$139$	3.06115	−	9.42125i	0.259643	−	0.799100i	−0.733236	−	0.679974i	$-0.761991\pi$
$139$	3.06115	−	9.42125i	0.259643	−	0.799100i	0.992879	−	0.119126i	$-0.0380092\pi$
$140$	0.738177	+	11.1878i	0.0623874	+	0.945538i
$141$		0			0
$142$		−	8.81631i		−	0.739848i
$143$	7.32222	−	2.52192i	0.612315	−	0.210894i
$144$		0			0
$145$	−3.43173	−	8.59082i	−0.284990	−	0.713429i
$146$	1.66751	+	5.13205i	0.138004	+	0.424732i
$147$		0			0
$148$	−2.67847	+	3.68660i	−0.220169	+	0.303036i
$149$	−7.11314	−	5.16800i	−0.582731	−	0.423379i	0.256977	−	0.966418i	$-0.417274\pi$
$149$	−7.11314	−	5.16800i	−0.582731	−	0.423379i	−0.839708	+	0.543039i	$0.817274\pi$
$150$		0			0
$151$	6.67177	+	20.5336i	0.542941	+	1.67100i	0.725835	+	0.687868i	$0.241453\pi$
$151$	6.67177	+	20.5336i	0.542941	+	1.67100i	−0.182894	+	0.983133i	$0.558547\pi$
$152$	1.21151	+	1.66751i	0.0982667	+	0.135253i
$153$		0			0
$154$	16.6276	−	0.291613i	1.33989	−	0.0234988i
$155$	−4.87770	+	19.2411i	−0.391786	+	1.54548i
$156$		0			0
$157$	−3.24760	+	1.05521i	−0.259186	+	0.0842148i	−0.435728	−	0.900078i	$-0.643509\pi$
$157$	−3.24760	+	1.05521i	−0.259186	+	0.0842148i	0.176542	+	0.984293i	$0.443509\pi$
$158$	6.32947	+	2.05657i	0.503546	+	0.163612i
$159$		0			0
$160$	−1.43058	−	1.71856i	−0.113097	−	0.135864i
$161$	6.06657	−	18.6710i	0.478113	−	1.47148i
$162$		0			0
$163$	10.2336	+	14.0853i	0.801554	+	1.10324i	0.992572	+	0.121657i	$0.0388209\pi$
$163$	10.2336	+	14.0853i	0.801554	+	1.10324i	−0.191019	+	0.981586i	$0.561179\pi$
$164$	−4.57985			−0.357626
$165$		0			0
$166$	−11.0520			−0.857801
$167$	1.94321	+	2.67460i	0.150370	+	0.206967i	0.877556	−	0.479473i	$-0.159172\pi$
$167$	1.94321	+	2.67460i	0.150370	+	0.206967i	−0.727186	+	0.686440i	$0.759172\pi$
$168$		0			0
$169$	2.33237	−	7.17831i	0.179413	−	0.552178i
$170$	−0.105091	+	0.0874803i	−0.00806008	+	0.00670944i
$171$		0			0
$172$	3.44095	+	1.11803i	0.262370	+	0.0852493i
$173$	−4.87758	+	1.58482i	−0.370836	+	0.120492i	−0.488505	−	0.872561i	$-0.662458\pi$
$173$	−4.87758	+	1.58482i	−0.370836	+	0.120492i	0.117670	+	0.993053i	$0.462458\pi$
$174$		0			0
$175$	−11.9436	+	22.0432i	−0.902855	+	1.66631i
$176$	−2.64861	+	1.99621i	−0.199646	+	0.150470i
$177$		0			0
$178$	−3.57971	−	4.92705i	−0.268311	−	0.369298i
$179$	−4.46201	−	13.7327i	−0.333507	−	1.02643i	−0.967453	−	0.253051i	$-0.918566\pi$
$179$	−4.46201	−	13.7327i	−0.333507	−	1.02643i	0.633947	−	0.773377i	$-0.281434\pi$
$180$		0			0
$181$	−9.63223	−	6.99822i	−0.715958	−	0.520174i	0.169132	−	0.985593i	$-0.445903\pi$
$181$	−9.63223	−	6.99822i	−0.715958	−	0.520174i	−0.885090	+	0.465419i	$0.845903\pi$
$182$	−6.88191	+	9.47214i	−0.510121	+	0.702121i
$183$		0			0
$184$	1.20988	+	3.72363i	0.0891935	+	0.274509i
$185$	−9.46246	+	3.77992i	−0.695694	+	0.277905i
$186$		0			0
$187$	0.122069	+	0.161963i	0.00892658	+	0.0118439i
$188$			8.87707i			0.647427i
$189$		0			0
$190$	0.303437	+	4.59887i	0.0220137	+	0.333637i
$191$	−3.25026	+	10.0033i	−0.235181	+	0.723812i	0.761917	+	0.647675i	$0.224259\pi$
$191$	−3.25026	+	10.0033i	−0.235181	+	0.723812i	−0.997097	+	0.0761369i	$0.975741\pi$
$192$		0			0
$193$	−2.86174	+	3.93885i	−0.205993	+	0.283525i	−0.899496	−	0.436929i	$-0.856066\pi$
$193$	−2.86174	+	3.93885i	−0.205993	+	0.283525i	0.693503	+	0.720453i	$0.256066\pi$
$194$	2.25652	−	6.94485i	0.162009	−	0.498612i
$195$		0			0
$196$	−14.6773	+	10.6637i	−1.04838	+	0.761692i
$197$			15.9760i			1.13824i	0.822253	+	0.569122i	$0.192717\pi$
$197$			15.9760i			1.13824i	−0.822253	+	0.569122i	$0.807283\pi$
$198$		0			0
$199$	−16.7076			−1.18437			−0.592184	−	0.805803i	$-0.701734\pi$
$199$	−16.7076			−1.18437			−0.592184	+	0.805803i	$0.701734\pi$
$200$	−0.656948	−	4.95665i	−0.0464532	−	0.350488i
$201$		0			0
$202$	0.211013	+	0.0685623i	0.0148468	+	0.00482403i
$203$	12.1932	−	16.7825i	0.855797	−	1.17790i
$204$		0			0
$205$	−8.66336	−	5.46090i	−0.605075	−	0.381406i
$206$	0.174918	+	0.538341i	0.0121871	+	0.0375080i
$207$		0			0
$208$		−	2.33501i		−	0.161904i
$209$	6.83501	−	0.119871i	0.472788	−	0.00829167i
$210$		0			0
$211$	12.7388	−	9.25526i	0.876974	−	0.637159i	−0.0554754	−	0.998460i	$-0.517667\pi$
$211$	12.7388	−	9.25526i	0.876974	−	0.637159i	0.932449	+	0.361301i	$0.117667\pi$
$212$	2.11313	−	0.686596i	0.145130	−	0.0471556i
$213$		0			0
$214$	1.80412	+	1.31077i	0.123327	+	0.0896025i
$215$	5.17588	+	6.21781i	0.352992	+	0.424051i
$216$		0			0
$217$	−42.3328	+	13.7548i	−2.87374	+	0.933735i
$218$	4.62168	+	6.36120i	0.313020	+	0.430835i
$219$		0			0
$220$	−7.39041	+	0.617952i	−0.498261	+	0.0416623i
$221$	−0.142787			−0.00960488
$222$		0			0
$223$	13.8432	−	4.49794i	0.927011	−	0.301204i	0.193671	−	0.981067i	$-0.437961\pi$
$223$	13.8432	−	4.49794i	0.927011	−	0.301204i	0.733340	+	0.679862i	$0.237961\pi$
$224$	1.54947	−	4.76878i	0.103528	−	0.318628i
$225$		0			0
$226$	−10.1626	−	7.38357i	−0.676007	−	0.491148i
$227$	9.35512	+	3.03966i	0.620921	+	0.201749i	0.602549	−	0.798082i	$-0.294152\pi$
$227$	9.35512	+	3.03966i	0.620921	+	0.201749i	0.0183719	+	0.999831i	$0.494152\pi$
$228$		0			0
$229$	−12.5785	+	9.13881i	−0.831210	+	0.603909i	−0.919901	−	0.392150i	$-0.871732\pi$
$229$	−12.5785	+	9.13881i	−0.831210	+	0.603909i	0.0886913	+	0.996059i	$0.471732\pi$
$230$	−2.15132	+	8.48633i	−0.141854	+	0.559572i
$231$		0			0
$232$			4.13712i			0.271616i
$233$	−15.2217	−	20.9509i	−0.997206	−	1.37254i	−0.927024	−	0.375002i	$-0.877642\pi$
$233$	−15.2217	−	20.9509i	−0.997206	−	1.37254i	−0.0701824	−	0.997534i	$-0.522358\pi$
$234$		0			0
$235$	−10.5848	+	16.7921i	−0.690476	+	1.09539i
$236$	1.56856	+	1.13963i	0.102105	+	0.0741834i
$237$		0			0
$238$	−0.291613	−	0.0947508i	−0.0189025	−	0.00614178i
$239$	6.17911	+	19.0173i	0.399693	+	1.23013i	0.925246	+	0.379369i	$0.123859\pi$
$239$	6.17911	+	19.0173i	0.399693	+	1.23013i	−0.525552	+	0.850761i	$0.676141\pi$
$240$		0			0
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$	0.385714	+	10.9932i	0.0247946	+	0.706672i
$243$		0			0
$244$	−7.84211	+	5.69763i	−0.502040	+	0.364753i
$245$	−40.4791	+	2.67084i	−2.58611	+	0.170634i
$246$		0			0
$247$	−2.82890	+	3.89364i	−0.179998	+	0.247747i
$248$	5.21781	−	7.18170i	0.331331	−	0.456038i
$249$		0			0
$250$	4.66749	−	10.1595i	0.295198	−	0.642540i
$251$	1.06115	−	0.770971i	0.0669792	−	0.0486632i	−0.553792	−	0.832655i	$-0.686820\pi$
$251$	1.06115	−	0.770971i	0.0669792	−	0.0486632i	0.620771	+	0.783992i	$0.286820\pi$
$252$		0			0
$253$	12.4183	+	3.79554i	0.780734	+	0.238624i
$254$	−14.4630			−0.907488
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.24551	−	1.37945i	−0.264827	−	0.0860477i	0.173594	−	0.984817i	$-0.444462\pi$
$257$	−4.24551	−	1.37945i	−0.264827	−	0.0860477i	−0.438421	+	0.898770i	$0.644462\pi$
$258$		0			0
$259$	−18.4853	−	13.4304i	−1.14862	−	0.834522i
$260$	2.78421	−	4.41696i	0.172669	−	0.273928i
$261$		0			0
$262$	9.00817	+	12.3987i	0.556526	+	0.765993i
$263$			14.1791i			0.874320i	0.899384	+	0.437160i	$0.144016\pi$
$263$			14.1791i			0.874320i	−0.899384	+	0.437160i	$0.855984\pi$
$264$		0			0
$265$	4.81592	+	1.22086i	0.295840	+	0.0749966i
$266$	−8.36120	+	6.07477i	−0.512658	+	0.372468i
$267$		0			0
$268$	−2.37358	−	0.771224i	−0.144990	−	0.0471100i
$269$	25.8847	+	18.8063i	1.57822	+	1.14664i	0.918702	+	0.394952i	$0.129239\pi$
$269$	25.8847	+	18.8063i	1.57822	+	1.14664i	0.659516	+	0.751691i	$0.270761\pi$
$270$		0			0
$271$	0.327988	−	1.00944i	0.0199238	−	0.0613192i	−0.940600	−	0.339516i	$-0.889737\pi$
$271$	0.327988	−	1.00944i	0.0199238	−	0.0613192i	0.960524	+	0.278197i	$0.0897367\pi$
$272$	0.0581575	−	0.0188965i	0.00352631	−	0.00114577i
$273$		0			0
$274$	−1.10437			−0.0667172
$275$	−14.7167	−	7.64320i	−0.887451	−	0.460902i
$276$		0			0
$277$	3.89892	+	5.36641i	0.234264	+	0.322436i	0.909923	−	0.414778i	$-0.136141\pi$
$277$	3.89892	+	5.36641i	0.234264	+	0.322436i	−0.675659	+	0.737214i	$0.736141\pi$
$278$	−9.42125	+	3.06115i	−0.565049	+	0.183596i
$279$		0			0
$280$	8.61720	−	7.17320i	0.514976	−	0.428680i
$281$	12.6582	+	9.19674i	0.755126	+	0.548631i	0.897412	−	0.441194i	$-0.145445\pi$
$281$	12.6582	+	9.19674i	0.755126	+	0.548631i	−0.142285	+	0.989826i	$0.545445\pi$
$282$		0			0
$283$	21.3993	−	6.95305i	1.27205	−	0.413316i	0.406280	−	0.913749i	$-0.366826\pi$
$283$	21.3993	−	6.95305i	1.27205	−	0.413316i	0.865775	+	0.500433i	$0.166826\pi$
$284$	−7.13254	+	5.18210i	−0.423239	+	0.307501i
$285$		0			0
$286$	−6.34417	−	4.44146i	−0.375139	−	0.262629i
$287$		−	22.9643i		−	1.35554i
$288$		0			0
$289$	5.25213	+	16.1644i	0.308949	+	0.950847i
$290$	−4.93300	+	7.82589i	−0.289676	+	0.459552i
$291$		0			0
$292$	3.17178	−	4.36559i	0.185615	−	0.255477i
$293$	17.2985	+	5.62063i	1.01059	+	0.328360i	0.767089	−	0.641540i	$-0.221704\pi$
$293$	17.2985	+	5.62063i	1.01059	+	0.328360i	0.243500	+	0.969901i	$0.421704\pi$
$294$		0			0
$295$	1.60827	+	4.02606i	0.0936370	+	0.234406i
$296$	4.55688			0.264863
$297$		0			0
$298$			8.79232i			0.509326i
$299$	−7.39616	+	5.37363i	−0.427731	+	0.310765i
$300$		0			0
$301$	−5.60604	+	17.2536i	−0.323127	+	0.994482i
$302$	12.6905	−	17.4669i	0.730254	−	1.00511i
$303$		0			0
$304$	0.636930	−	1.96027i	0.0365305	−	0.112429i
$305$	−21.6280	+	1.42703i	−1.23842	+	0.0817118i
$306$		0			0
$307$		−	12.3820i		−	0.706676i	−0.935496	−	0.353338i	$-0.885047\pi$
$307$		−	12.3820i		−	0.706676i	0.935496	−	0.353338i	$-0.114953\pi$
$308$	−10.0094	−	13.2806i	−0.570339	−	0.756735i
$309$		0			0
$310$	18.4334	−	7.36349i	1.04695	−	0.418218i
$311$	−2.90784	−	8.94941i	−0.164889	−	0.507475i	0.834140	−	0.551553i	$-0.185965\pi$
$311$	−2.90784	−	8.94941i	−0.164889	−	0.507475i	−0.999028	+	0.0440788i	$0.985965\pi$
$312$		0			0
$313$	8.95297	−	12.3227i	0.506052	−	0.696520i	−0.477196	−	0.878797i	$-0.658347\pi$
$313$	8.95297	−	12.3227i	0.506052	−	0.696520i	0.983247	+	0.182277i	$0.0583467\pi$
$314$	2.76257	+	2.00712i	0.155901	+	0.113269i
$315$		0			0
$316$	−2.05657	−	6.32947i	−0.115691	−	0.356061i
$317$	7.90964	+	10.8867i	0.444250	+	0.611457i	0.971150	−	0.238470i	$-0.0766459\pi$
$317$	7.90964	+	10.8867i	0.444250	+	0.611457i	−0.526900	+	0.849927i	$0.676646\pi$
$318$		0			0
$319$	11.2405	+	7.86928i	0.629346	+	0.440595i
$320$	−0.549472	+	2.16751i	−0.0307164	+	0.121167i
$321$		0			0
$322$	−18.6710	+	6.06657i	−1.04049	+	0.338077i
$323$	−0.119871	−	0.0389485i	−0.00666982	−	0.00216715i
$324$		0			0
$325$	10.5334	−	5.03542i	0.584285	−	0.279315i
$326$	5.38010	−	16.5582i	0.297976	−	0.917076i
$327$		0			0
$328$	2.69197	+	3.70518i	0.148639	+	0.204584i
$329$	−44.5114			−2.45399
$330$		0			0
$331$	−3.82236			−0.210096			−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236			−0.210096			−0.105048	+	0.994467i	$0.533500\pi$
$332$	6.49620	+	8.94125i	0.356525	+	0.490715i
$333$		0			0
$334$	1.02161	−	3.14419i	0.0558999	−	0.172042i
$335$	−3.57034	−	4.28907i	−0.195069	−	0.234337i
$336$		0			0
$337$	9.00338	+	2.92538i	0.490445	+	0.159355i	0.543791	−	0.839221i	$-0.316988\pi$
$337$	9.00338	+	2.92538i	0.490445	+	0.159355i	−0.0533455	+	0.998576i	$0.516988\pi$
$338$	−7.17831	+	2.33237i	−0.390449	+	0.126864i
$339$		0			0
$340$	0.132544	+	0.0336004i	0.00718820	+	0.00182224i
$341$	−9.58765	−	27.8371i	−0.519201	−	1.50746i
$342$		0			0
$343$	−32.8390	−	45.1989i	−1.77314	−	2.44051i
$344$	−1.11803	−	3.44095i	−0.0602804	−	0.185524i
$345$		0			0
$346$	4.14912	+	3.01451i	0.223058	+	0.162061i
$347$	−9.72341	+	13.3831i	−0.521980	+	0.718444i	−0.985882	−	0.167443i	$-0.946449\pi$
$347$	−9.72341	+	13.3831i	−0.521980	+	0.718444i	0.463902	+	0.885887i	$0.346449\pi$
$348$		0			0
$349$	−9.03161	−	27.7964i	−0.483451	−	1.48791i	−0.834212	−	0.551444i	$-0.814077\pi$
$349$	−9.03161	−	27.7964i	−0.483451	−	1.48791i	0.350761	−	0.936465i	$-0.385923\pi$
$350$	24.8536	−	3.29407i	1.32848	−	0.176075i
$351$		0			0
$352$	3.17178	+	0.969425i	0.169057	+	0.0516705i
$353$		−	27.9200i		−	1.48603i	−0.669272	−	0.743017i	$-0.733394\pi$
$353$		−	27.9200i		−	1.48603i	0.669272	−	0.743017i	$-0.266606\pi$
$354$		0			0
$355$	−19.6711	+	1.29791i	−1.04403	+	0.0688862i
$356$	−1.88197	+	5.79210i	−0.0997440	+	0.306980i
$357$		0			0
$358$	−8.48725	+	11.6817i	−0.448565	+	0.617397i
$359$	5.25768	−	16.1815i	0.277490	−	0.854025i	−0.711060	−	0.703131i	$-0.751785\pi$
$359$	5.25768	−	16.1815i	0.277490	−	0.854025i	0.988550	−	0.150894i	$-0.0482152\pi$
$360$		0			0
$361$	11.9343	−	8.67081i	0.628123	−	0.456358i
$362$			11.9061i			0.625770i
$363$		0			0
$364$	11.7082			0.613677
$365$	11.2052	−	4.47609i	0.586509	−	0.234289i
$366$		0			0
$367$	27.9983	+	9.09719i	1.46150	+	0.474870i	0.928527	−	0.371264i	$-0.121075\pi$
$367$	27.9983	+	9.09719i	1.46150	+	0.474870i	0.532971	+	0.846133i	$0.321075\pi$
$368$	2.30133	−	3.16751i	0.119965	−	0.165118i
$369$		0			0
$370$	8.61991	+	5.43351i	0.448128	+	0.282475i
$371$	3.44273	+	10.5956i	0.178738	+	0.550098i
$372$		0			0
$373$			16.0743i			0.832297i	0.909297	+	0.416149i	$0.136620\pi$
$373$			16.0743i			0.832297i	−0.909297	+	0.416149i	$0.863380\pi$
$374$	0.0592807	−	0.193956i	0.00306533	−	0.0100292i
$375$		0			0
$376$	7.18170	−	5.21781i	0.370368	−	0.269088i
$377$	−9.18743	+	2.98518i	−0.473177	+	0.153744i
$378$		0			0
$379$	14.6618	+	10.6524i	0.753125	+	0.547178i	0.896794	−	0.442448i	$-0.145890\pi$
$379$	14.6618	+	10.6524i	0.753125	+	0.547178i	−0.143669	+	0.989626i	$0.545890\pi$
$380$	3.54221	−	2.94864i	0.181712	−	0.151262i
$381$		0			0
$382$	10.0033	−	3.25026i	0.511812	−	0.166298i
$383$	−7.76587	−	10.6888i	−0.396817	−	0.546172i	0.563124	−	0.826372i	$-0.309599\pi$
$383$	−7.76587	−	10.6888i	−0.396817	−	0.546172i	−0.959942	+	0.280200i	$0.909599\pi$
$384$		0			0
$385$	−3.09853	−	37.0570i	−0.157916	−	1.88860i
$386$	4.86869			0.247810
$387$		0			0
$388$	−6.94485	+	2.25652i	−0.352572	+	0.114557i
$389$	−8.19653	+	25.2263i	−0.415580	+	1.27902i	0.496150	+	0.868237i	$0.334746\pi$
$389$	−8.19653	+	25.2263i	−0.415580	+	1.27902i	−0.911731	+	0.410788i	$0.865254\pi$
$390$		0			0
$391$	−0.193694	−	0.140727i	−0.00979553	−	0.00711687i
$392$	17.2542	+	5.60624i	0.871470	+	0.283158i
$393$		0			0
$394$	12.9249	−	9.39047i	0.651145	−	0.473085i
$395$	3.65684	−	14.4252i	0.183996	−	0.725810i
$396$		0			0
$397$			30.3246i			1.52195i	0.648783	+	0.760974i	$0.275278\pi$
$397$			30.3246i			1.52195i	−0.648783	+	0.760974i	$0.724722\pi$
$398$	9.82047	+	13.5167i	0.492256	+	0.677532i
$399$		0			0
$400$	−3.62387	+	3.44493i	−0.181194	+	0.172247i
$401$	15.7565	+	11.4478i	0.786844	+	0.571676i	0.907025	−	0.421076i	$-0.138348\pi$
$401$	15.7565	+	11.4478i	0.786844	+	0.571676i	−0.120181	+	0.992752i	$0.538348\pi$
$402$		0			0
$403$	19.7136	+	6.40532i	0.982002	+	0.319072i
$404$	−0.0685623	−	0.211013i	−0.00341110	−	0.0104983i
$405$		0			0
$406$	−20.7444			−1.02952
$407$	8.66771	−	12.3809i	0.429642	−	0.613701i
$408$		0			0
$409$	−22.9197	+	16.6521i	−1.13330	+	0.823394i	−0.986172	−	0.165723i	$-0.947004\pi$
$409$	−22.9197	+	16.6521i	−1.13330	+	0.823394i	−0.147132	+	0.989117i	$0.547004\pi$
$410$	0.674234	+	10.2186i	0.0332981	+	0.504663i
$411$		0			0
$412$	0.332713	−	0.457940i	0.0163916	−	0.0225611i
$413$	−5.71431	+	7.86508i	−0.281183	+	0.387015i
$414$		0			0
$415$	1.62705	+	24.6594i	0.0798685	+	1.21048i
$416$	−1.88906	+	1.37249i	−0.0926190	+	0.0672916i
$417$		0			0
$418$	−4.11450	−	5.45918i	−0.201247	−	0.267017i
$419$	−15.4826			−0.756374			−0.378187	−	0.925729i	$-0.623452\pi$
$419$	−15.4826			−0.756374			−0.378187	+	0.925729i	$0.623452\pi$
$420$		0			0
$421$	6.63964	+	20.4347i	0.323596	+	0.995927i	0.972070	+	0.234690i	$0.0754076\pi$
$421$	6.63964	+	20.4347i	0.323596	+	0.995927i	−0.648474	+	0.761237i	$0.724592\pi$
$422$	−14.9753	−	4.86578i	−0.728988	−	0.236862i
$423$		0			0
$424$	−1.79753	−	1.30598i	−0.0872959	−	0.0634242i
$425$	0.210659	+	0.221601i	0.0102185	+	0.0107492i
$426$		0			0
$427$	−28.5690	−	39.3219i	−1.38255	−	1.90292i
$428$		−	2.23002i		−	0.107792i
$429$		0			0
$430$	1.98801	−	7.84211i	0.0958702	−	0.378180i
$431$	21.3896	−	15.5404i	1.03030	−	0.748557i	0.0619316	−	0.998080i	$-0.480274\pi$
$431$	21.3896	−	15.5404i	1.03030	−	0.748557i	0.968369	+	0.249523i	$0.0802739\pi$
$432$		0			0
$433$	−31.2725	−	10.1611i	−1.50286	−	0.488309i	−0.562010	−	0.827130i	$-0.689972\pi$
$433$	−31.2725	−	10.1611i	−1.50286	−	0.488309i	−0.940851	+	0.338821i	$0.889972\pi$
$434$	36.0105	+	26.1631i	1.72856	+	1.25587i
$435$		0			0
$436$	2.42976	−	7.47804i	0.116365	−	0.358133i
$437$	−7.67495	+	2.49374i	−0.367143	+	0.119292i
$438$		0			0
$439$	12.1796			0.581299			0.290649	−	0.956830i	$-0.406129\pi$
$439$	12.1796			0.581299			0.290649	+	0.956830i	$0.406129\pi$
$440$	4.84391	+	5.61574i	0.230924	+	0.267720i
$441$		0			0
$442$	0.0839280	+	0.115517i	0.00399205	+	0.00549458i
$443$	15.7961	−	5.13247i	0.750496	−	0.243851i	0.0913015	−	0.995823i	$-0.470897\pi$
$443$	15.7961	−	5.13247i	0.750496	−	0.243851i	0.659195	+	0.751972i	$0.270897\pi$
$444$		0			0
$445$	−10.4663	+	8.71246i	−0.496151	+	0.413010i
$446$	−11.7757	−	8.55558i	−0.557598	−	0.405119i
$447$		0			0
$448$	−4.76878	+	1.54947i	−0.225304	+	0.0732057i
$449$	4.33928	−	3.15267i	0.204783	−	0.148784i	−0.480667	−	0.876903i	$-0.659605\pi$
$449$	4.33928	−	3.15267i	0.204783	−	0.148784i	0.685450	+	0.728119i	$0.259605\pi$
$450$		0			0
$451$	15.1873	−	0.266353i	0.715143	−	0.0125421i
$452$			12.5617i			0.590852i
$453$		0			0
$454$	−3.03966	−	9.35512i	−0.142658	−	0.439058i
$455$	22.1475	+	13.9606i	1.03829	+	0.654481i
$456$		0			0
$457$	−2.12330	+	2.92247i	−0.0993237	+	0.136707i	−0.855786	−	0.517330i	$-0.826926\pi$
$457$	−2.12330	+	2.92247i	−0.0993237	+	0.136707i	0.756462	+	0.654037i	$0.226926\pi$
$458$	14.7869	+	4.80456i	0.690947	+	0.224502i
$459$		0			0
$460$	8.13010	−	3.24769i	0.379068	−	0.151424i
$461$	40.6625			1.89384			0.946922	−	0.321464i	$-0.104175\pi$
$461$	40.6625			1.89384			0.946922	+	0.321464i	$0.104175\pi$
$462$		0			0
$463$			2.11880i			0.0984690i	0.998787	+	0.0492345i	$0.0156782\pi$
$463$			2.11880i			0.0984690i	−0.998787	+	0.0492345i	$0.984322\pi$
$464$	3.34700	−	2.43174i	0.155381	−	0.112891i
$465$		0			0
$466$	−8.00252	+	24.6292i	−0.370709	+	1.14093i
$467$	8.08494	−	11.1280i	0.374126	−	0.514941i	−0.579890	−	0.814695i	$-0.696905\pi$
$467$	8.08494	−	11.1280i	0.374126	−	0.514941i	0.954017	+	0.299754i	$0.0969046\pi$
$468$		0			0
$469$	3.86707	−	11.9016i	0.178565	−	0.549565i
$470$	19.8067	−	1.30686i	0.913613	−	0.0602810i
$471$		0			0
$472$		−	1.93885i		−	0.0892428i
$473$	−11.4756	−	3.50741i	−0.527650	−	0.161271i
$474$		0			0
$475$	10.2164	−	1.35407i	0.468761	−	0.0621289i
$476$	0.0947508	+	0.291613i	0.00434289	+	0.0133661i
$477$		0			0
$478$	11.7534	−	16.1771i	0.537586	−	0.739924i
$479$	−25.4118	−	18.4628i	−1.16110	−	0.843586i	−0.171180	−	0.985240i	$-0.554758\pi$
$479$	−25.4118	−	18.4628i	−1.16110	−	0.843586i	−0.989916	+	0.141654i	$0.954758\pi$
$480$		0			0
$481$	3.28806	+	10.1196i	0.149922	+	0.461414i
$482$	−5.29818	−	7.29232i	−0.241326	−	0.332156i
$483$		0			0
$484$	8.66700	−	6.77371i	0.393954	−	0.307896i
$485$	−15.8277	−	4.01238i	−0.718698	−	0.182193i
$486$		0			0
$487$	7.14274	−	2.32082i	0.323668	−	0.105166i	−0.142676	−	0.989769i	$-0.545571\pi$
$487$	7.14274	−	2.32082i	0.323668	−	0.105166i	0.466344	+	0.884603i	$0.345571\pi$
$488$	9.21895	+	2.99542i	0.417322	+	0.135596i
$489$		0			0
$490$	25.9538	+	31.1784i	1.17247	+	1.40850i
$491$	−3.48008	+	10.7106i	−0.157054	+	0.483361i	−0.998363	−	0.0571923i	$-0.981785\pi$
$491$	−3.48008	+	10.7106i	−0.157054	+	0.483361i	0.841310	+	0.540554i	$0.181785\pi$
$492$		0			0
$493$	−0.148702	−	0.204671i	−0.00669719	−	0.00921790i
$494$	4.81281			0.216539
$495$		0			0
$496$	−8.87707			−0.398592
$497$	−25.9840	−	35.7640i	−1.16554	−	1.60423i
$498$		0			0
$499$	8.33753	−	25.6603i	0.373239	−	1.14871i	−0.571420	−	0.820658i	$-0.693607\pi$
$499$	8.33753	−	25.6603i	0.373239	−	1.14871i	0.944659	−	0.328054i	$-0.106393\pi$
$500$	−10.9627	+	2.19550i	−0.490265	+	0.0981857i
$501$		0			0
$502$	−1.24746	−	0.405323i	−0.0556767	−	0.0180905i
$503$	30.5818	−	9.93662i	1.36357	−	0.443052i	0.466339	−	0.884606i	$-0.345573\pi$
$503$	30.5818	−	9.93662i	1.36357	−	0.443052i	0.897235	+	0.441554i	$0.145573\pi$
$504$		0			0
$505$	0.121913	−	0.480909i	0.00542504	−	0.0214002i
$506$	−4.22866	−	12.2776i	−0.187987	−	0.545806i
$507$		0			0
$508$	8.50112	+	11.7008i	0.377176	+	0.519139i
$509$	3.64048	+	11.2043i	0.161362	+	0.496620i	0.998750	−	0.0499888i	$-0.0159186\pi$
$509$	3.64048	+	11.2043i	0.161362	+	0.496620i	−0.837388	+	0.546609i	$0.815919\pi$
$510$		0			0
$511$	21.8899	+	15.9039i	0.968352	+	0.703549i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$		0			0
$514$	1.37945	+	4.24551i	0.0608449	+	0.187261i
$515$	1.17540	−	0.469532i	0.0517945	−	0.0206901i
$516$		0			0
$517$	−0.516268	−	29.4374i	−0.0227054	−	1.29465i
$518$			22.8491i			1.00393i
$519$		0			0
$520$	−5.20992	+	0.343754i	−0.228470	+	0.0150746i
$521$	−0.718847	+	2.21238i	−0.0314933	+	0.0969263i	−0.965568	−	0.260152i	$-0.916227\pi$
$521$	−0.718847	+	2.21238i	−0.0314933	+	0.0969263i	0.934074	+	0.357079i	$0.116227\pi$
$522$		0			0
$523$	−0.901612	+	1.24096i	−0.0394248	+	0.0542635i	−0.828274	−	0.560323i	$-0.810677\pi$
$523$	−0.901612	+	1.24096i	−0.0394248	+	0.0542635i	0.788850	+	0.614586i	$0.210677\pi$
$524$	4.73587	−	14.5755i	0.206888	−	0.636735i
$525$		0			0
$526$	11.4711	−	8.33426i	0.500165	−	0.363391i
$527$			0.542836i			0.0236463i
$528$		0			0
$529$	7.67080			0.333513
$530$	−1.84303	−	4.61376i	−0.0800563	−	0.200409i
$531$		0			0
$532$	9.82918	+	3.19369i	0.426149	+	0.138464i
$533$	−6.28578	+	8.65163i	−0.272267	+	0.374744i
$534$		0			0
$535$	2.65902	−	4.21836i	0.114959	−	0.182375i
$536$	0.771224	+	2.37358i	0.0333118	+	0.102523i
$537$		0			0
$538$		−	31.9952i		−	1.37941i
$539$	48.0515	−	36.2156i	2.06972	−	1.55992i
$540$		0			0
$541$	12.4927	−	9.07650i	0.537104	−	0.390229i	−0.285904	−	0.958258i	$-0.592294\pi$
$541$	12.4927	−	9.07650i	0.537104	−	0.390229i	0.823008	+	0.568029i	$0.192294\pi$
$542$	−1.00944	+	0.327988i	−0.0433593	+	0.0140883i
$543$		0			0
$544$	−0.0494717	−	0.0359433i	−0.00212108	−	0.00154106i
$545$	13.5128	−	11.2485i	0.578826	−	0.481831i
$546$		0			0
$547$	10.1261	−	3.29017i	0.432960	−	0.140677i	−0.0844251	−	0.996430i	$-0.526905\pi$
$547$	10.1261	−	3.29017i	0.432960	−	0.140677i	0.517385	+	0.855752i	$0.326905\pi$
$548$	0.649130	+	0.893451i	0.0277295	+	0.0381663i
$549$		0			0
$550$	2.46678	+	16.3986i	0.105184	+	0.699240i
$551$	−8.52724			−0.363272
$552$		0			0
$553$	31.7372	−	10.3120i	1.34960	−	0.438513i
$554$	2.04979	−	6.30859i	0.0870871	−	0.268026i
$555$		0			0
$556$	8.01420	+	5.82265i	0.339878	+	0.246936i
$557$	−32.2595	−	10.4818i	−1.36688	−	0.444126i	−0.468545	−	0.883439i	$-0.655222\pi$
$557$	−32.2595	−	10.4818i	−1.36688	−	0.444126i	−0.898334	+	0.439313i	$0.855222\pi$
$558$		0			0
$559$	6.83470	−	4.96570i	0.289077	−	0.210027i
$560$	−10.8683	−	2.75516i	−0.459269	−	0.116427i
$561$		0			0
$562$		−	15.6464i		−	0.660005i
$563$	−0.789857	−	1.08714i	−0.0332885	−	0.0458177i	0.792048	−	0.610458i	$-0.209015\pi$
$563$	−0.789857	−	1.08714i	−0.0332885	−	0.0458177i	−0.825337	+	0.564641i	$0.809015\pi$
$564$		0			0
$565$	−14.9782	+	23.7620i	−0.630139	+	0.999674i
$566$	−18.2033	−	13.2255i	−0.765142	−	0.555908i
$567$		0			0
$568$	8.38481	+	2.72439i	0.351819	+	0.114313i
$569$	−9.70595	−	29.8718i	−0.406894	−	1.25229i	−0.919303	−	0.393550i	$-0.871247\pi$
$569$	−9.70595	−	29.8718i	−0.406894	−	1.25229i	0.512409	−	0.858742i	$-0.328753\pi$
$570$		0			0
$571$	9.25361			0.387252			0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361			0.387252			0.193626	+	0.981075i	$0.437975\pi$
$572$	0.135798	+	7.74317i	0.00567801	+	0.323758i
$573$		0			0
$574$	−18.5785	+	13.4981i	−0.775451	+	0.563398i
$575$	19.2516	+	3.55073i	0.802845	+	0.148075i
$576$		0			0
$577$	25.4998	−	35.0975i	1.06157	−	1.46113i	0.183244	−	0.983068i	$-0.441340\pi$
$577$	25.4998	−	35.0975i	1.06157	−	1.46113i	0.878327	−	0.478060i	$-0.158660\pi$
$578$	9.99015	−	13.7503i	0.415536	−	0.571936i
$579$		0			0
$580$	9.23082	−	0.609057i	0.383289	−	0.0252897i
$581$	−44.8332	+	32.5732i	−1.85999	+	1.35136i
$582$		0			0
$583$	−6.96744	+	2.39973i	−0.288562	+	0.0993865i
$584$	−5.39616			−0.223295
$585$		0			0
$586$	−5.62063	−	17.2985i	−0.232186	−	0.714595i
$587$	3.05524	+	0.992708i	0.126103	+	0.0409734i	0.371389	−	0.928477i	$-0.378882\pi$
$587$	3.05524	+	0.992708i	0.126103	+	0.0409734i	−0.245285	+	0.969451i	$0.578882\pi$
$588$		0			0
$589$	14.8026	+	10.7547i	0.609929	+	0.443139i
$590$	2.31184	−	3.66758i	0.0951768	−	0.150992i
$591$		0			0
$592$	−2.67847	−	3.68660i	−0.110084	−	0.151518i
$593$			0.0315027i			0.00129366i	1.00000		0.000646829i	$0.000205892\pi$
$593$			0.0315027i			0.00129366i	−1.00000		0.000646829i	$0.999794\pi$
$594$		0			0
$595$	−0.168479	+	0.664600i	−0.00690696	+	0.0272460i
$596$	7.11314	−	5.16800i	0.291366	−	0.211689i
$597$		0			0
$598$	8.69471	+	2.82508i	0.355553	+	0.115526i
$599$	8.50993	+	6.18283i	0.347706	+	0.252623i	0.747906	−	0.663804i	$-0.231059\pi$
$599$	8.50993	+	6.18283i	0.347706	+	0.252623i	−0.400200	+	0.916428i	$0.631059\pi$
$600$		0			0
$601$	7.45305	−	22.9381i	0.304016	−	0.935665i	−0.676026	−	0.736877i	$-0.736300\pi$
$601$	7.45305	−	22.9381i	0.304016	−	0.935665i	0.980043	−	0.198788i	$-0.0637005\pi$
$602$	17.2536	−	5.60604i	0.703205	−	0.228485i
$603$		0			0
$604$	−21.5903			−0.878497
$605$	24.4715	−	2.47901i	0.994908	−	0.100786i
$606$		0			0
$607$	−1.46340	−	2.01420i	−0.0593975	−	0.0817537i	0.778285	−	0.627911i	$-0.216090\pi$
$607$	−1.46340	−	2.01420i	−0.0593975	−	0.0817537i	−0.837682	+	0.546158i	$0.816090\pi$
$608$	−1.96027	+	0.636930i	−0.0794995	+	0.0258309i
$609$		0			0
$610$	13.8671	+	16.6587i	0.561464	+	0.674489i
$611$	16.7694	+	12.1836i	0.678415	+	0.492898i
$612$		0			0
$613$	−35.7338	+	11.6106i	−1.44328	+	0.468949i	−0.922917	−	0.384999i	$-0.874202\pi$
$613$	−35.7338	+	11.6106i	−1.44328	+	0.468949i	−0.520359	+	0.853948i	$0.674202\pi$
$614$	−10.0172	+	7.27794i	−0.404262	+	0.293714i
$615$		0			0
$616$	−4.86089	+	15.9039i	−0.195851	+	0.640788i
$617$			45.5803i			1.83499i	0.397744	+	0.917496i	$0.369793\pi$
$617$			45.5803i			1.83499i	−0.397744	+	0.917496i	$0.630207\pi$
$618$		0			0
$619$	−1.77382	−	5.45924i	−0.0712957	−	0.219425i	0.909059	−	0.416667i	$-0.136802\pi$
$619$	−1.77382	−	5.45924i	−0.0712957	−	0.219425i	−0.980355	+	0.197241i	$0.936802\pi$
$620$	−16.7921	−	10.5848i	−0.674386	−	0.425096i
$621$		0			0
$622$	−5.53104	+	7.61283i	−0.221775	+	0.305246i
$623$	−29.0427	−	9.43655i	−1.16357	−	0.378067i
$624$		0			0
$625$	−23.3551	−	8.91853i	−0.934203	−	0.356741i
$626$	−15.2317			−0.608781
$627$		0			0
$628$		−	3.41472i		−	0.136262i
$629$	−0.225437	+	0.163789i	−0.00898875	+	0.00653071i
$630$		0			0
$631$	3.70103	−	11.3906i	0.147336	−	0.453453i	−0.849968	−	0.526834i	$-0.823379\pi$
$631$	3.70103	−	11.3906i	0.147336	−	0.453453i	0.997304	+	0.0733811i	$0.0233790\pi$
$632$	−3.91183	+	5.38417i	−0.155604	+	0.214171i
$633$		0			0
$634$	4.15834	−	12.7981i	0.165149	−	0.508276i
$635$	2.12920	+	32.2700i	0.0844948	+	1.28060i
$636$		0			0
$637$			42.3621i			1.67845i
$638$	−0.240605	−	13.7192i	−0.00952563	−	0.543148i
$639$		0			0
$640$	2.07652	−	0.829496i	0.0820817	−	0.0327887i
$641$	10.8526	+	33.4007i	0.428650	+	1.31925i	0.899455	+	0.437013i	$0.143964\pi$
$641$	10.8526	+	33.4007i	0.428650	+	1.31925i	−0.470805	+	0.882237i	$0.656036\pi$
$642$		0			0
$643$	−20.9529	+	28.8392i	−0.826302	+	1.13731i	0.162298	+	0.986742i	$0.448109\pi$
$643$	−20.9529	+	28.8392i	−0.826302	+	1.13731i	−0.988600	+	0.150565i	$0.951891\pi$
$644$	15.8825	+	11.5393i	0.625858	+	0.454712i
$645$		0			0
$646$	0.0389485	+	0.119871i	0.00153241	+	0.00471627i
$647$	−11.8476	−	16.3068i	−0.465778	−	0.641088i	0.509917	−	0.860224i	$-0.329676\pi$
$647$	−11.8476	−	16.3068i	−0.465778	−	0.641088i	−0.975694	+	0.219136i	$0.929676\pi$
$648$		0			0
$649$	−5.26781	−	3.68791i	−0.206780	−	0.144763i
$650$	−10.2651	−	5.56192i	−0.402630	−	0.218156i
$651$		0			0
$652$	−16.5582	+	5.38010i	−0.648470	+	0.210701i
$653$	−23.1905	−	7.53504i	−0.907513	−	0.294869i	−0.182178	−	0.983266i	$-0.558315\pi$
$653$	−23.1905	−	7.53504i	−0.907513	−	0.294869i	−0.725334	+	0.688397i	$0.758315\pi$
$654$		0			0
$655$	26.3380	−	21.9245i	1.02911	−	0.856660i
$656$	1.41525	−	4.35570i	0.0552563	−	0.170061i
$657$		0			0
$658$	26.1631	+	36.0105i	1.01994	+	1.40383i
$659$	−6.98788			−0.272209			−0.136104	−	0.990694i	$-0.543458\pi$
$659$	−6.98788			−0.272209			−0.136104	+	0.990694i	$0.543458\pi$
$660$		0			0
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$	2.24673	+	3.09235i	0.0873215	+	0.120188i
$663$		0			0
$664$	3.41525	−	10.5111i	0.132537	−	0.407908i
$665$	14.7850	+	17.7613i	0.573339	+	0.688755i
$666$		0			0
$667$	−15.4051	−	5.00542i	−0.596488	−	0.193811i
$668$	−3.14419	+	1.02161i	−0.121652	+	0.0395272i
$669$		0			0
$670$	−1.37133	+	5.40952i	−0.0529793	+	0.208988i
$671$	25.6740	−	19.3501i	0.991133	−	0.747001i
$672$		0			0
$673$	−4.68377	−	6.44665i	−0.180546	−	0.248500i	0.709146	−	0.705062i	$-0.249081\pi$
$673$	−4.68377	−	6.44665i	−0.180546	−	0.248500i	−0.889692	+	0.456562i	$0.849081\pi$
$674$	−2.92538	−	9.00338i	−0.112681	−	0.346797i
$675$		0			0
$676$	6.10624	+	4.43644i	0.234855	+	0.170632i
$677$	8.48443	−	11.6778i	0.326083	−	0.448815i	−0.614229	−	0.789128i	$-0.710533\pi$
$677$	8.48443	−	11.6778i	0.326083	−	0.448815i	0.940312	+	0.340313i	$0.110533\pi$
$678$		0			0
$679$	−11.3146	−	34.8229i	−0.434216	−	1.33638i
$680$	−0.0507240	−	0.126980i	−0.00194518	−	0.00486946i
$681$		0			0
$682$	−16.8852	+	24.1188i	−0.646567	+	0.923557i
$683$			29.6723i			1.13538i	0.823242	+	0.567690i	$0.192163\pi$
$683$			29.6723i			1.13538i	−0.823242	+	0.567690i	$0.807837\pi$
$684$		0			0
$685$	0.162582	+	2.46408i	0.00621194	+	0.0941476i
$686$	−17.2645	+	53.1345i	−0.659160	+	2.02869i
$687$		0			0
$688$	−2.12663	+	2.92705i	−0.0810769	+	0.111593i
$689$	1.60321	−	4.93417i	0.0610774	−	0.187977i
$690$		0			0
$691$	−26.1812	+	19.0218i	−0.995980	+	0.723622i	−0.961223	−	0.275774i	$-0.911066\pi$
$691$	−26.1812	+	19.0218i	−0.995980	+	0.723622i	−0.0347577	+	0.999396i	$0.511066\pi$
$692$		−	5.12859i		−	0.194960i
$693$		0			0
$694$	16.5424			0.627943
$695$	8.21706	+	20.5702i	0.311691	+	0.780272i
$696$		0			0
$697$	−0.266353	−	0.0865432i	−0.0100888	−	0.00327806i
$698$	−17.1791	+	23.6451i	−0.650240	+	0.894979i
$699$		0			0
$700$	−17.2736	−	18.1708i	−0.652879	−	0.686792i
$701$	−5.86089	−	18.0380i	−0.221363	−	0.681284i	−0.998640	−	0.0521266i	$-0.983400\pi$
$701$	−5.86089	−	18.0380i	−0.221363	−	0.681284i	0.777278	−	0.629157i	$-0.216600\pi$
$702$		0			0
$703$			9.39242i			0.354242i
$704$	−1.08005	−	3.13584i	−0.0407058	−	0.118186i
$705$		0			0
$706$	−22.5878	+	16.4110i	−0.850103	+	0.617636i
$707$	1.05806	−	0.343785i	0.0397925	−	0.0129294i
$708$		0			0
$709$	6.78617	+	4.93044i	0.254860	+	0.185167i	0.707878	−	0.706335i	$-0.249653\pi$
$709$	6.78617	+	4.93044i	0.254860	+	0.185167i	−0.453018	+	0.891501i	$0.649653\pi$
$710$	12.6124	+	15.1514i	0.473335	+	0.568620i
$711$		0			0
$712$	5.79210	−	1.88197i	0.217068	−	0.0705297i
$713$	20.4290	+	28.1182i	0.765074	+	1.05303i
$714$		0			0
$715$	−8.97588	+	14.8091i	−0.335679	+	0.553828i
$716$	14.4394			0.539625
$717$		0			0
$718$	−16.1815	+	5.25768i	−0.603887	+	0.196215i
$719$	2.33218	−	7.17771i	0.0869756	−	0.267684i	−0.898104	−	0.439783i	$-0.855055\pi$
$719$	2.33218	−	7.17771i	0.0869756	−	0.267684i	0.985079	+	0.172100i	$0.0550552\pi$
$720$		0			0
$721$	2.29620	+	1.66829i	0.0855150	+	0.0621303i
$722$	−14.0297	−	4.55851i	−0.522130	−	0.169650i
$723$		0			0
$724$	9.63223	−	6.99822i	0.357979	−	0.260087i
$725$	18.1875	+	9.85449i	0.675466	+	0.365987i
$726$		0			0
$727$			24.2826i			0.900593i	0.892879	+	0.450297i	$0.148682\pi$
$727$			24.2826i			0.900593i	−0.892879	+	0.450297i	$0.851318\pi$
$728$	−6.88191	−	9.47214i	−0.255061	−	0.351061i
$729$		0			0
$730$	−10.2075	−	6.43425i	−0.377797	−	0.238142i
$731$	0.178990	+	0.130044i	0.00662019	+	0.00480985i
$732$		0			0
$733$	−20.3541	−	6.61345i	−0.751796	−	0.244273i	−0.0920424	−	0.995755i	$-0.529340\pi$
$733$	−20.3541	−	6.61345i	−0.751796	−	0.244273i	−0.659754	+	0.751482i	$0.729340\pi$
$734$	−9.09719	−	27.9983i	−0.335784	−	1.03344i
$735$		0			0
$736$	−3.91525			−0.144318
$737$	7.91593	+	2.41943i	0.291587	+	0.0891207i
$738$		0			0
$739$	28.4419	−	20.6642i	1.04625	−	0.760147i	0.0747558	−	0.997202i	$-0.476182\pi$
$739$	28.4419	−	20.6642i	1.04625	−	0.760147i	0.971496	+	0.237055i	$0.0761823\pi$
$740$	−0.670853	−	10.1674i	−0.0246610	−	0.373761i
$741$		0			0
$742$	6.54846	−	9.01318i	0.240401	−	0.330884i
$743$	−20.0435	+	27.5875i	−0.735324	+	1.01209i	0.263550	+	0.964646i	$0.415107\pi$
$743$	−20.0435	+	27.5875i	−0.735324	+	1.01209i	−0.998874	+	0.0474407i	$0.984893\pi$
$744$		0			0
$745$	19.6176	−	1.29438i	0.718732	−	0.0474225i
$746$	13.0044	−	9.44825i	0.476125	−	0.345925i
$747$		0			0
$748$	−0.191758	+	0.0660453i	−0.00701136	+	0.00241485i
$749$	11.1817			0.408572
$750$		0			0
$751$	−11.0690	−	34.0669i	−0.403914	−	1.24312i	−0.921799	−	0.387669i	$-0.873280\pi$
$751$	−11.0690	−	34.0669i	−0.403914	−	1.24312i	0.517884	−	0.855451i	$-0.326720\pi$
$752$	−8.44260	−	2.74317i	−0.307870	−	0.100033i
$753$		0			0
$754$	7.81529	+	5.67814i	0.284616	+	0.206786i
$755$	−40.8408	−	25.7437i	−1.48635	−	0.936911i
$756$		0			0
$757$	−14.2408	−	19.6008i	−0.517592	−	0.712404i	0.467584	−	0.883948i	$-0.345124\pi$
$757$	−14.2408	−	19.6008i	−0.517592	−	0.712404i	−0.985176	+	0.171544i	$0.945124\pi$
$758$		−	18.1230i		−	0.658256i
$759$		0			0
$760$	−4.46756	−	1.13254i	−0.162055	−	0.0410817i
$761$	8.62191	−	6.26419i	0.312544	−	0.227077i	−0.420443	−	0.907319i	$-0.638125\pi$
$761$	8.62191	−	6.26419i	0.312544	−	0.227077i	0.732987	+	0.680242i	$0.238125\pi$
$762$		0			0
$763$	37.4964	+	12.1833i	1.35746	+	0.441065i
$764$	−8.50930	−	6.18237i	−0.307856	−	0.223670i
$765$		0			0
$766$	−4.08276	+	12.5654i	−0.147516	+	0.454008i
$767$	4.30566	−	1.39899i	0.155468	−	0.0505147i
$768$		0			0
$769$	−25.8297			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$769$	−25.8297			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$770$	−28.1584	+	24.2883i	−1.01476	+	0.875289i
$771$		0			0
$772$	−2.86174	−	3.93885i	−0.102996	−	0.141762i
$773$	11.4679	−	3.72614i	0.412471	−	0.134020i	−0.0954286	−	0.995436i	$-0.530422\pi$
$773$	11.4679	−	3.72614i	0.412471	−	0.134020i	0.507899	+	0.861416i	$0.330422\pi$
$774$		0			0
$775$	−19.1433	−	40.0449i	−0.687647	−	1.43846i
$776$	5.90765	+	4.29216i	0.212072	+	0.154079i
$777$		0			0
$778$	25.2263	−	8.19653i	0.904407	−	0.293860i
$779$	−7.63693	+	5.54855i	−0.273621	+	0.198798i
$780$		0			0
$781$	23.3510	−	17.5992i	0.835563	−	0.629750i
$782$			0.239419i			0.00856161i
$783$		0			0
$784$	−5.60624	−	17.2542i	−0.200223	−	0.616222i
$785$	4.07163	−	6.45938i	0.145323	−	0.230545i
$786$		0			0
$787$	−10.6725	+	14.6895i	−0.380435	+	0.523624i	−0.955700	−	0.294343i	$-0.904899\pi$
$787$	−10.6725	+	14.6895i	−0.380435	+	0.523624i	0.575265	+	0.817967i	$0.304899\pi$
$788$	−15.1941	−	4.93686i	−0.541267	−	0.175868i
$789$		0			0
$790$	−13.8197	+	5.52046i	−0.491681	+	0.196409i
$791$	−62.9867			−2.23955
$792$		0			0
$793$			22.6342i			0.803762i
$794$	24.5331	−	17.8243i	0.870648	−	0.632562i
$795$		0			0
$796$	5.16292	−	15.8898i	0.182995	−	0.563201i
$797$	−0.946725	+	1.30306i	−0.0335347	+	0.0461566i	−0.825455	−	0.564468i	$-0.809081\pi$
$797$	−0.946725	+	1.30306i	−0.0335347	+	0.0461566i	0.791920	+	0.610624i	$0.209081\pi$
$798$		0			0
$799$	−0.167746	+	0.516268i	−0.00593441	+	0.0182642i
$800$	4.91707	+	0.906896i	0.173845	+	0.0320636i
$801$		0			0
$802$		−	19.4762i		−	0.687727i
$803$	−10.2641	+	14.6612i	−0.362213	+	0.517384i
$804$		0			0
$805$	16.2845	+	40.7659i	0.573954	+	1.43681i
$806$	−6.40532	−	19.7136i	−0.225618	−	0.694380i
$807$		0			0
$808$	−0.130413	+	0.179498i	−0.00458792	+	0.00631473i
$809$	−20.7273	−	15.0593i	−0.728733	−	0.529455i	0.160429	−	0.987047i	$-0.448712\pi$
$809$	−20.7273	−	15.0593i	−0.728733	−	0.529455i	−0.889162	+	0.457592i	$0.848712\pi$
$810$		0			0
$811$	13.5506	+	41.7045i	0.475827	+	1.46444i	0.844839	+	0.535020i	$0.179696\pi$
$811$	13.5506	+	41.7045i	0.475827	+	1.46444i	−0.369012	+	0.929424i	$0.620304\pi$
$812$	12.1932	+	16.7825i	0.427898	+	0.588951i
$813$		0			0
$814$	−15.1111	+	0.265017i	−0.529646	+	0.00928883i
$815$	−37.7370	−	9.56650i	−1.32187	−	0.335100i
$816$		0			0
$817$	7.09233	−	2.30444i	0.248129	−	0.0806220i
$818$	26.9437	+	8.75453i	0.942063	+	0.306095i
$819$		0			0
$820$	7.87075	−	6.55183i	0.274859	−	0.228800i
$821$	5.43938	−	16.7407i	0.189836	−	0.584254i	−0.810163	−	0.586205i	$-0.800621\pi$
$821$	5.43938	−	16.7407i	0.189836	−	0.584254i	0.999998	+	0.00195152i	$0.000621189\pi$
$822$		0			0
$823$	−7.43854	−	10.2383i	−0.259291	−	0.356884i	0.659447	−	0.751751i	$-0.270791\pi$
$823$	−7.43854	−	10.2383i	−0.259291	−	0.356884i	−0.918738	+	0.394867i	$0.870791\pi$
$824$	−0.566045			−0.0197191
$825$		0			0
$826$	9.72177			0.338264
$827$	5.19856	+	7.15520i	0.180772	+	0.248811i	0.889780	−	0.456389i	$-0.150857\pi$
$827$	5.19856	+	7.15520i	0.180772	+	0.248811i	−0.709009	+	0.705200i	$0.750857\pi$
$828$		0			0
$829$	−11.6571	+	35.8767i	−0.404866	+	1.24605i	0.516141	+	0.856504i	$0.327368\pi$
$829$	−11.6571	+	35.8767i	−0.404866	+	1.24605i	−0.921007	+	0.389546i	$0.872632\pi$
$830$	18.9935	−	15.8107i	0.659274	−	0.548798i
$831$		0			0
$832$	2.22073	+	0.721558i	0.0769899	+	0.0250155i
$833$	−1.05510	+	0.342823i	−0.0365571	+	0.0118781i
$834$		0			0
$835$	−7.16576	−	1.81655i	−0.247981	−	0.0628643i
$836$	−1.99813	+	6.53752i	−0.0691068	+	0.226105i
$837$		0			0
$838$	9.10044	+	12.5257i	0.314369	+	0.432692i
$839$	−11.8934	−	36.6041i	−0.410606	−	1.26372i	−0.916123	−	0.400898i	$-0.868698\pi$
$839$	−11.8934	−	36.6041i	−0.410606	−	1.26372i	0.505517	−	0.862817i	$-0.331302\pi$
$840$		0			0
$841$	9.61452	+	6.98536i	0.331535	+	0.240874i
$842$	12.6293	−	17.3828i	0.435236	−	0.599051i
$843$		0			0
$844$	4.86578	+	14.9753i	0.167487	+	0.515472i
$845$	6.26080	+	15.6730i	0.215378	+	0.539168i
$846$		0			0
$847$	33.9647	+	43.4580i	1.16704	+	1.49324i
$848$			2.22187i			0.0762994i
$849$		0			0
$850$	0.0554570	−	0.300680i	0.00190216	−	0.0103133i
$851$	−5.51328	+	16.9681i	−0.188993	+	0.581660i
$852$		0			0
$853$	−29.9122	+	41.1706i	−1.02417	+	1.40965i	−0.114936	+	0.993373i	$0.536666\pi$
$853$	−29.9122	+	41.1706i	−1.02417	+	1.40965i	−0.909237	+	0.416280i	$0.863334\pi$
$854$	−15.0196	+	46.2256i	−0.513961	+	1.58181i
$855$		0			0
$856$	−1.80412	+	1.31077i	−0.0616636	+	0.0448012i
$857$		−	11.5197i		−	0.393506i	−0.980453	−	0.196753i	$-0.936960\pi$
$857$		−	11.5197i		−	0.393506i	0.980453	−	0.196753i	$-0.0630397\pi$
$858$		0			0
$859$	−23.9497			−0.817153			−0.408577	−	0.912724i	$-0.633975\pi$
$859$	−23.9497			−0.817153			−0.408577	+	0.912724i	$0.633975\pi$
$860$	−7.51292	+	3.00114i	−0.256188	+	0.102338i
$861$		0			0
$862$	−25.1450	−	8.17010i	−0.856441	−	0.278275i
$863$	−23.5170	+	32.3684i	−0.800530	+	1.10183i	0.192187	+	0.981358i	$0.438442\pi$
$863$	−23.5170	+	32.3684i	−0.800530	+	1.10183i	−0.992716	+	0.120476i	$0.961558\pi$
$864$		0			0
$865$	6.11520	−	9.70137i	0.207923	−	0.329856i
$866$	10.1611	+	31.2725i	0.345287	+	1.06268i
$867$		0			0
$868$		−	44.5114i		−	1.51081i
$869$	7.18793	+	20.8696i	0.243834	+	0.707954i
$870$		0			0
$871$	−4.71460	+	3.42536i	−0.159748	+	0.116064i
$872$	−7.47804	+	2.42976i	−0.253238	+	0.0822821i
$873$		0			0
$874$	6.52871	+	4.74338i	0.220837	+	0.160447i
$875$	−11.0087	−	54.9689i	−0.372161	−	1.85829i
$876$		0			0
$877$	24.7104	−	8.02891i	0.834413	−	0.271117i	0.139510	−	0.990221i	$-0.455447\pi$
$877$	24.7104	−	8.02891i	0.834413	−	0.271117i	0.694903	+	0.719104i	$0.255447\pi$
$878$	−7.15897	−	9.85347i	−0.241603	−	0.332539i
$879$		0			0
$880$	1.69605	−	7.21965i	0.0571740	−	0.243374i
$881$	−25.1372			−0.846893			−0.423446	−	0.905921i	$-0.639180\pi$
$881$	−25.1372			−0.846893			−0.423446	+	0.905921i	$0.639180\pi$
$882$		0			0
$883$	41.3431	−	13.4332i	1.39131	−	0.452063i	0.484937	−	0.874549i	$-0.338843\pi$
$883$	41.3431	−	13.4332i	1.39131	−	0.452063i	0.906369	+	0.422486i	$0.138843\pi$
$884$	0.0441236	−	0.135798i	0.00148404	−	0.00456739i
$885$		0			0
$886$	−13.4370	−	9.76254i	−0.451424	−	0.327979i
$887$	27.2078	+	8.84036i	0.913549	+	0.296830i	0.727818	−	0.685770i	$-0.240535\pi$
$887$	27.2078	+	8.84036i	0.913549	+	0.296830i	0.185731	+	0.982601i	$0.440535\pi$
$888$		0			0
$889$	−58.6701	+	42.6263i	−1.96773	+	1.42964i
$890$	13.2005	+	3.34638i	0.442481	+	0.112171i
$891$		0			0
$892$			14.5556i			0.487358i
$893$	10.7547	+	14.8026i	0.359892	+	0.495349i
$894$		0			0
$895$	27.3139	+	17.2171i	0.913002	+	0.575506i
$896$	4.05657	+	2.94727i	0.135520	+	0.0984614i
$897$		0			0
$898$	−5.10113	−	1.65746i	−0.170227	−	0.0553100i
$899$	11.3488	+	34.9281i	0.378504	+	1.16492i
$900$		0			0
$901$	0.135868			0.00452643
$902$	−9.14237	−	12.1302i	−0.304407	−	0.403893i
$903$		0			0
$904$	10.1626	−	7.38357i	0.338003	−	0.245574i
$905$	26.5651	−	1.75278i	0.883053	−	0.0582645i
$906$		0			0
$907$	−28.0438	+	38.5990i	−0.931179	+	1.28166i	0.0282187	+	0.999602i	$0.491017\pi$
$907$	−28.0438	+	38.5990i	−0.931179	+	1.28166i	−0.959398	+	0.282056i	$0.908983\pi$
$908$	−5.78178	+	7.95794i	−0.191875	+	0.264094i
$909$		0			0
$910$	−1.72365	−	26.1235i	−0.0571385	−	0.865987i
$911$	40.3003	−	29.2799i	1.33521	−	0.970085i	0.335602	−	0.942004i	$-0.391060\pi$
$911$	40.3003	−	29.2799i	1.33521	−	0.970085i	0.999606	−	0.0280809i	$-0.00893959\pi$
$912$		0			0
$913$	−22.0621	−	29.2724i	−0.730150	−	0.968775i
$914$	3.61237			0.119487
$915$		0			0
$916$	−4.80456	−	14.7869i	−0.158747	−	0.488573i
$917$	73.0845	+	23.7466i	2.41346	+	0.784182i
$918$		0			0
$919$	−34.7058	−	25.2153i	−1.14484	−	0.831775i	−0.157053	−	0.987590i	$-0.550199\pi$
$919$	−34.7058	−	25.2153i	−1.14484	−	0.831775i	−0.987786	+	0.155815i	$0.950199\pi$
$920$	−7.40619	−	4.66845i	−0.244175	−	0.153914i
$921$		0			0
$922$	−23.9008	−	32.8967i	−0.787132	−	1.08339i
$923$			20.5862i			0.677602i
$924$		0			0
$925$	10.8543	−	20.0328i	0.356889	−	0.658674i
$926$	1.71415	−	1.24540i	0.0563303	−	0.0409264i
$927$		0			0
$928$	−3.93464	−	1.27844i	−0.129161	−	0.0419669i
$929$	3.20719	+	2.33016i	0.105224	+	0.0764500i	0.639153	−	0.769079i	$-0.279285\pi$
$929$	3.20719	+	2.33016i	0.105224	+	0.0764500i	−0.533929	+	0.845529i	$0.679285\pi$
$930$		0			0
$931$	−11.5553	+	35.5635i	−0.378709	+	1.16555i
$932$	24.6292	−	8.00252i	0.806757	−	0.262131i
$933$		0			0
$934$	−13.7549			−0.450075
$935$	−0.441484	−	0.103714i	−0.0144381	−	0.00339182i
$936$		0			0
$937$	−1.24563	−	1.71446i	−0.0406929	−	0.0560090i	0.788186	−	0.615437i	$-0.211021\pi$
$937$	−1.24563	−	1.71446i	−0.0406929	−	0.0560090i	−0.828879	+	0.559429i	$0.811021\pi$
$938$	−11.9016	+	3.86707i	−0.388601	+	0.126264i
$939$		0			0
$940$	−12.6993	−	15.2558i	−0.414207	−	0.497589i
$941$	4.08118	+	2.96515i	0.133043	+	0.0966612i	0.652316	−	0.757947i	$-0.273797\pi$
$941$	4.08118	+	2.96515i	0.133043	+	0.0966612i	−0.519274	+	0.854608i	$0.673797\pi$
$942$		0			0
$943$	−17.0537	+	5.54107i	−0.555344	+	0.180442i
$944$	−1.56856	+	1.13963i	−0.0510524	+	0.0370917i
$945$		0			0
$946$	3.90765	+	11.3456i	0.127049	+	0.368877i
$947$		−	0.986192i		−	0.0320470i	−0.999872	−	0.0160235i	$-0.994899\pi$
$947$		−	0.986192i		−	0.0320470i	0.999872	−	0.0160235i	$-0.00510065\pi$
$948$		0			0
$949$	−3.89364	−	11.9834i	−0.126393	−	0.388998i
$950$	−7.10052	−	7.46935i	−0.230371	−	0.242338i
$951$		0			0
$952$	0.180227	−	0.248061i	0.00584118	−	0.00803969i
$953$	−21.8386	−	7.09580i	−0.707422	−	0.229855i	−0.0668608	−	0.997762i	$-0.521298\pi$
$953$	−21.8386	−	7.09580i	−0.707422	−	0.229855i	−0.640562	+	0.767907i	$0.721298\pi$
$954$		0			0
$955$	−8.72470	−	21.8410i	−0.282325	−	0.706758i
$956$	−19.9960			−0.646718
$957$		0			0
$958$			31.4107i			1.01484i
$959$	−4.47994	+	3.25486i	−0.144665	+	0.105105i
$960$		0			0
$961$	14.7718	−	45.4628i	0.476508	−	1.46654i
$962$	6.25426	−	8.60824i	0.201645	−	0.277541i
$963$		0			0
$964$	−2.78542	+	8.57264i	−0.0897123	+	0.276106i
$965$	−0.716756	−	10.8631i	−0.0230732	−	0.349695i
$966$		0			0
$967$		−	20.1267i		−	0.647231i	−0.946189	−	0.323616i	$-0.895102\pi$
$967$		−	20.1267i		−	0.647231i	0.946189	−	0.323616i	$-0.104898\pi$
$968$	−10.5744	−	3.03026i	−0.339873	−	0.0973963i
$969$		0			0
$970$	6.05719	+	15.1633i	0.194485	+	0.486863i
$971$	6.77852	+	20.8621i	0.217533	+	0.669498i	0.998964	+	0.0455060i	$0.0144900\pi$
$971$	6.77852	+	20.8621i	0.217533	+	0.669498i	−0.781431	+	0.623991i	$0.785510\pi$
$972$		0			0
$973$	−29.1959	+	40.1847i	−0.935978	+	1.28826i
$974$	−6.07597	−	4.41445i	−0.194687	−	0.141448i
$975$		0			0
$976$	−2.99542	−	9.21895i	−0.0958810	−	0.295091i
$977$	−34.7133	−	47.7788i	−1.11058	−	1.52858i	−0.820562	−	0.571557i	$-0.806340\pi$
$977$	−34.7133	−	47.7788i	−1.11058	−	1.52858i	−0.290015	−	0.957022i	$-0.593660\pi$
$978$		0			0
$979$	5.90396	−	19.3167i	0.188691	−	0.617365i
$980$	9.96860	−	39.3232i	0.318435	−	1.25613i
$981$		0			0
$982$	10.7106	−	3.48008i	0.341788	−	0.111054i
$983$	−45.9751	−	14.9382i	−1.46638	−	0.476455i	−0.536367	−	0.843985i	$-0.680204\pi$
$983$	−45.9751	−	14.9382i	−1.46638	−	0.476455i	−0.930012	+	0.367530i	$0.880204\pi$
$984$		0			0
$985$	−22.8549	−	27.4557i	−0.728219	−	0.874813i
$986$	−0.0781772	+	0.240605i	−0.00248967	+	0.00766241i
$987$		0			0
$988$	−2.82890	−	3.89364i	−0.0899992	−	0.123873i
$989$	14.1655			0.450437
$990$		0			0
$991$	−55.0154			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$992$	5.21781	+	7.18170i	0.165666	+	0.228019i
$993$		0			0
$994$	−13.6606	+	42.0431i	−0.433289	+	1.33353i
$995$	28.7130	−	23.9015i	0.910262	−	0.757728i
$996$		0			0
$997$	21.8457	+	7.09810i	0.691861	+	0.224799i	0.633781	−	0.773513i	$-0.281502\pi$
$997$	21.8457	+	7.09810i	0.691861	+	0.224799i	0.0580799	+	0.998312i	$0.481502\pi$
$998$	−25.6603	+	8.33753i	−0.812262	+	0.263920i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.ba.h.289.1		16
3.2	odd	2		110.2.j.b.69.4	yes	16
5.4	even	2	inner	990.2.ba.h.289.3		16
11.4	even	5	inner	990.2.ba.h.829.3		16
12.11	even	2		880.2.cd.b.289.2		16
15.2	even	4		550.2.h.j.201.2		8
15.8	even	4		550.2.h.n.201.1		8
15.14	odd	2		110.2.j.b.69.2	yes	16
33.2	even	10		1210.2.b.l.969.5		8
33.20	odd	10		1210.2.b.k.969.1		8
33.26	odd	10		110.2.j.b.59.2	✓	16
55.4	even	10	inner	990.2.ba.h.829.1		16
60.59	even	2		880.2.cd.b.289.4		16
132.59	even	10		880.2.cd.b.609.4		16
165.2	odd	20		6050.2.a.da.1.1		4
165.53	even	20		6050.2.a.dd.1.3		4
165.59	odd	10		110.2.j.b.59.4	yes	16
165.68	odd	20		6050.2.a.dl.1.4		4
165.92	even	20		550.2.h.j.301.2		8
165.119	odd	10		1210.2.b.k.969.7		8
165.134	even	10		1210.2.b.l.969.3		8
165.152	even	20		6050.2.a.di.1.2		4
165.158	even	20		550.2.h.n.301.1		8
660.59	even	10		880.2.cd.b.609.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	33.26	odd	10
110.2.j.b.59.4	yes	16	165.59	odd	10
110.2.j.b.69.2	yes	16	15.14	odd	2
110.2.j.b.69.4	yes	16	3.2	odd	2
550.2.h.j.201.2		8	15.2	even	4
550.2.h.j.301.2		8	165.92	even	20
550.2.h.n.201.1		8	15.8	even	4
550.2.h.n.301.1		8	165.158	even	20
880.2.cd.b.289.2		16	12.11	even	2
880.2.cd.b.289.4		16	60.59	even	2
880.2.cd.b.609.2		16	660.59	even	10
880.2.cd.b.609.4		16	132.59	even	10
990.2.ba.h.289.1		16	1.1	even	1	trivial
990.2.ba.h.289.3		16	5.4	even	2	inner
990.2.ba.h.829.1		16	55.4	even	10	inner
990.2.ba.h.829.3		16	11.4	even	5	inner
1210.2.b.k.969.1		8	33.20	odd	10
1210.2.b.k.969.7		8	165.119	odd	10
1210.2.b.l.969.3		8	165.134	even	10
1210.2.b.l.969.5		8	33.2	even	10
6050.2.a.da.1.1		4	165.2	odd	20
6050.2.a.dd.1.3		4	165.53	even	20
6050.2.a.di.1.2		4	165.152	even	20
6050.2.a.dl.1.4		4	165.68	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)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-1.71856 + 1.43058i) q^{5} +(-4.76878 - 1.54947i) q^{7} +(0.951057 - 0.309017i) q^{8} +(2.16751 + 0.549472i) q^{10} +(0.969425 - 3.17178i) q^{11} +(1.37249 + 1.88906i) q^{13} +(1.54947 + 4.76878i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.0359433 + 0.0494717i) q^{17} +(0.636930 + 1.96027i) q^{19} +(-0.829496 - 2.07652i) q^{20} +(-3.13584 + 1.08005i) q^{22} +3.91525i q^{23} +(0.906896 - 4.91707i) q^{25} +(0.721558 - 2.22073i) q^{26} +(2.94727 - 4.05657i) q^{28} +(-1.27844 + 3.93464i) q^{29} +(7.18170 - 5.21781i) q^{31} +1.00000i q^{32} +0.0611504 q^{34} +(10.4121 - 4.15925i) q^{35} +(4.33385 + 1.40815i) q^{37} +(1.21151 - 1.66751i) q^{38} +(-1.19237 + 1.89162i) q^{40} +(1.41525 + 4.35570i) q^{41} -3.61803i q^{43} +(2.71698 + 1.90211i) q^{44} +(3.16751 - 2.30133i) q^{46} +(8.44260 - 2.74317i) q^{47} +(14.6773 + 10.6637i) q^{49} +(-4.51105 + 2.15649i) q^{50} +(-2.22073 + 0.721558i) q^{52} +(-1.30598 - 1.79753i) q^{53} +(2.87147 + 6.83774i) q^{55} -5.01420 q^{56} +(3.93464 - 1.27844i) q^{58} +(0.599137 - 1.84396i) q^{59} +(7.84211 + 5.69763i) q^{61} +(-8.44260 - 2.74317i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-5.06115 - 1.28302i) q^{65} +2.49573i q^{67} +(-0.0359433 - 0.0494717i) q^{68} +(-9.48497 - 5.97880i) q^{70} +(7.13254 + 5.18210i) q^{71} +(-5.13205 - 1.66751i) q^{73} +(-1.40815 - 4.33385i) q^{74} -2.06115 q^{76} +(-9.53757 + 13.6235i) q^{77} +(-5.38417 + 3.91183i) q^{79} +(2.23122 - 0.147217i) q^{80} +(2.69197 - 3.70518i) q^{82} +(6.49620 - 8.94125i) q^{83} +(-0.00900240 - 0.136440i) q^{85} +(-2.92705 + 2.12663i) q^{86} +(-0.0581575 - 3.31611i) q^{88} +6.09017 q^{89} +(-3.61803 - 11.1352i) q^{91} +(-3.72363 - 1.20988i) q^{92} +(-7.18170 - 5.21781i) q^{94} +(-3.89892 - 2.45766i) q^{95} +(4.29216 + 5.90765i) q^{97} -18.1422i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 6 q^{5} + 4 q^{10} + 20 q^{11} + 12 q^{14} - 4 q^{16} - 16 q^{19} - 6 q^{20} + 16 q^{26} - 16 q^{29} - 4 q^{31} - 8 q^{34} + 48 q^{35} - 4 q^{40} - 40 q^{41} + 20 q^{46} + 84 q^{49} - 4 q^{50}+ \cdots + 50 q^{95}+O(q^{100}) \) 16 * q + 4 * q^4 + 6 * q^5 + 4 * q^10 + 20 * q^11 + 12 * q^14 - 4 * q^16 - 16 * q^19 - 6 * q^20 + 16 * q^26 - 16 * q^29 - 4 * q^31 - 8 * q^34 + 48 * q^35 - 4 * q^40 - 40 * q^41 + 20 * q^46 + 84 * q^49 - 4 * q^50 + 32 * q^55 + 8 * q^56 + 20 * q^61 + 4 * q^64 - 72 * q^65 + 36 * q^70 + 56 * q^71 - 4 * q^74 - 24 * q^76 + 36 * q^79 - 4 * q^80 - 54 * q^85 - 20 * q^86 + 8 * q^89 - 40 * q^91 + 4 * q^94 + 50 * q^95

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