LMFDB - Embedded newform 567.2.v.b.442.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(64,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("567.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.v (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			442.4
Character	$\chi$	$=$	567.442
Dual form			567.2.v.b.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.786541 + 0.659987i) q^{2} +(-0.164231 + 0.931402i) q^{4} +(-3.56827 + 1.29874i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.51229 - 2.61937i) q^{8} +O(q^{10})$	\(q+(-0.786541 + 0.659987i) q^{2} +(-0.164231 + 0.931402i) q^{4} +(-3.56827 + 1.29874i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.51229 - 2.61937i) q^{8} +(1.94944 - 3.37653i) q^{10} +(1.53871 + 0.560043i) q^{11} +(-4.81098 - 4.03689i) q^{13} +(-0.786541 - 0.659987i) q^{14} +(1.14077 + 0.415205i) q^{16} +(-0.424366 + 0.735023i) q^{17} +(2.19397 + 3.80006i) q^{19} +(-0.623631 - 3.53679i) q^{20} +(-1.57988 + 0.575028i) q^{22} +(0.517102 - 2.93263i) q^{23} +(7.21559 - 6.05460i) q^{25} +6.44833 q^{26} -0.945770 q^{28} +(5.54559 - 4.65331i) q^{29} +(-0.831089 + 4.71334i) q^{31} +(4.51308 - 1.64263i) q^{32} +(-0.151324 - 0.858202i) q^{34} +(-1.89864 - 3.28853i) q^{35} +(4.25038 - 7.36187i) q^{37} +(-4.23363 - 1.54092i) q^{38} +(8.79817 + 7.38254i) q^{40} +(-3.46354 - 2.90626i) q^{41} +(-7.40891 - 2.69662i) q^{43} +(-0.774329 + 1.34118i) q^{44} +(1.52878 + 2.64792i) q^{46} +(-0.0270638 - 0.153487i) q^{47} +(-0.939693 + 0.342020i) q^{49} +(-1.67941 + 9.52438i) q^{50} +(4.55008 - 3.81797i) q^{52} -12.6703 q^{53} -6.21787 q^{55} +(2.31697 - 1.94417i) q^{56} +(-1.29072 + 7.32003i) q^{58} +(-3.14407 + 1.14435i) q^{59} +(-1.76396 - 10.0039i) q^{61} +(-2.45705 - 4.25574i) q^{62} +(-3.67959 + 6.37324i) q^{64} +(22.4098 + 8.15649i) q^{65} +(-3.56045 - 2.98758i) q^{67} +(-0.614908 - 0.515969i) q^{68} +(3.66374 + 1.33349i) q^{70} +(2.71831 - 4.70826i) q^{71} +(0.756070 + 1.30955i) q^{73} +(1.51564 + 8.59561i) q^{74} +(-3.89970 + 1.41938i) q^{76} +(-0.284341 + 1.61258i) q^{77} +(-4.73453 + 3.97274i) q^{79} -4.60980 q^{80} +4.64231 q^{82} +(-1.62520 + 1.36370i) q^{83} +(0.559645 - 3.17390i) q^{85} +(7.60715 - 2.76878i) q^{86} +(-0.860016 - 4.87739i) q^{88} +(0.415312 + 0.719341i) q^{89} +(3.14014 - 5.43889i) q^{91} +(2.64654 + 0.963260i) q^{92} +(0.122586 + 0.102862i) q^{94} +(-12.7640 - 10.7102i) q^{95} +(-8.94079 - 3.25418i) q^{97} +(0.513378 - 0.889197i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) $ 54 * q + 3 * q^5 + 27 * q^8	$ 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) $ 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−0.786541	+	0.659987i	−0.556169	+	0.466681i	−0.877024	−	0.480447i	$-0.840474\pi$
$2$	−0.786541	+	0.659987i	−0.556169	+	0.466681i	0.320855	+	0.947128i	$0.396030\pi$
$3$		0			0
$3$		0			0
$4$	−0.164231	+	0.931402i	−0.0821157	+	0.465701i
$5$	−3.56827	+	1.29874i	−1.59578	+	0.580816i	−0.978557	−	0.205974i	$-0.933964\pi$
$5$	−3.56827	+	1.29874i	−1.59578	+	0.580816i	−0.617221	+	0.786790i	$0.711742\pi$
$6$		0			0
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$8$	−1.51229	−	2.61937i	−0.534677	−	0.926088i
$9$		0			0
$10$	1.94944	−	3.37653i	0.616466	−	1.06775i
$11$	1.53871	+	0.560043i	0.463937	+	0.168859i	0.563404	−	0.826182i	$-0.309491\pi$
$11$	1.53871	+	0.560043i	0.463937	+	0.168859i	−0.0994668	+	0.995041i	$0.531714\pi$
$12$		0			0
$13$	−4.81098	−	4.03689i	−1.33433	−	1.11963i	−0.983045	−	0.183362i	$-0.941302\pi$
$13$	−4.81098	−	4.03689i	−1.33433	−	1.11963i	−0.351281	−	0.936270i	$-0.614254\pi$
$14$	−0.786541	−	0.659987i	−0.210212	−	0.176389i
$15$		0			0
$16$	1.14077	+	0.415205i	0.285191	+	0.103801i
$17$	−0.424366	+	0.735023i	−0.102924	+	0.178269i	−0.912888	−	0.408210i	$-0.866153\pi$
$17$	−0.424366	+	0.735023i	−0.102924	+	0.178269i	0.809964	+	0.586479i	$0.199486\pi$
$18$		0			0
$19$	2.19397	+	3.80006i	0.503330	+	0.871794i	0.999993	+	0.00384981i	$0.00122544\pi$
$19$	2.19397	+	3.80006i	0.503330	+	0.871794i	−0.496662	+	0.867944i	$0.665441\pi$
$20$	−0.623631	−	3.53679i	−0.139448	−	0.790850i
$21$		0			0
$22$	−1.57988	+	0.575028i	−0.336831	+	0.122596i
$23$	0.517102	−	2.93263i	0.107823	−	0.611496i	−0.882232	−	0.470815i	$-0.843960\pi$
$23$	0.517102	−	2.93263i	0.107823	−	0.611496i	0.990055	−	0.140681i	$-0.0449291\pi$
$24$		0			0
$25$	7.21559	−	6.05460i	1.44312	−	1.21092i
$26$	6.44833			1.26462
$27$		0			0
$28$	−0.945770			−0.178734
$29$	5.54559	−	4.65331i	1.02979	−	0.864097i	0.0389647	−	0.999241i	$-0.487594\pi$
$29$	5.54559	−	4.65331i	1.02979	−	0.864097i	0.990826	+	0.135144i	$0.0431496\pi$
$30$		0			0
$31$	−0.831089	+	4.71334i	−0.149268	+	0.846541i	0.814573	+	0.580062i	$0.196971\pi$
$31$	−0.831089	+	4.71334i	−0.149268	+	0.846541i	−0.963841	+	0.266479i	$0.914140\pi$
$32$	4.51308	−	1.64263i	0.797807	−	0.290378i
$33$		0			0
$34$	−0.151324	−	0.858202i	−0.0259519	−	0.147180i
$35$	−1.89864	−	3.28853i	−0.320928	−	0.555864i
$36$		0			0
$37$	4.25038	−	7.36187i	0.698758	−	1.21028i	−0.270140	−	0.962821i	$-0.587070\pi$
$37$	4.25038	−	7.36187i	0.698758	−	1.21028i	0.968897	−	0.247463i	$-0.0795967\pi$
$38$	−4.23363	−	1.54092i	−0.686786	−	0.249970i
$39$		0			0
$40$	8.79817	+	7.38254i	1.39111	+	1.16728i
$41$	−3.46354	−	2.90626i	−0.540915	−	0.453881i	0.330936	−	0.943653i	$-0.392636\pi$
$41$	−3.46354	−	2.90626i	−0.540915	−	0.453881i	−0.871851	+	0.489772i	$0.837080\pi$
$42$		0			0
$43$	−7.40891	−	2.69662i	−1.12985	−	0.411231i	−0.291611	−	0.956537i	$-0.594191\pi$
$43$	−7.40891	−	2.69662i	−1.12985	−	0.411231i	−0.838237	+	0.545306i	$0.816414\pi$
$44$	−0.774329	+	1.34118i	−0.116734	+	0.202190i
$45$		0			0
$46$	1.52878	+	2.64792i	0.225406	+	0.390414i
$47$	−0.0270638	−	0.153487i	−0.00394767	−	0.0223883i	0.982770	−	0.184831i	$-0.0591738\pi$
$47$	−0.0270638	−	0.153487i	−0.00394767	−	0.0223883i	−0.986718	+	0.162443i	$0.948063\pi$
$48$		0			0
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	−1.67941	+	9.52438i	−0.237504	+	1.34695i
$51$		0			0
$52$	4.55008	−	3.81797i	0.630983	−	0.529458i
$53$	−12.6703			−1.74040			−0.870200	−	0.492699i	$-0.836010\pi$
$53$	−12.6703			−1.74040			−0.870200	+	0.492699i	$0.836010\pi$
$54$		0			0
$55$	−6.21787			−0.838417
$56$	2.31697	−	1.94417i	0.309618	−	0.259800i
$57$		0			0
$58$	−1.29072	+	7.32003i	−0.169480	+	0.961168i
$59$	−3.14407	+	1.14435i	−0.409323	+	0.148981i	−0.538471	−	0.842644i	$-0.680998\pi$
$59$	−3.14407	+	1.14435i	−0.409323	+	0.148981i	0.129148	+	0.991625i	$0.458776\pi$
$60$		0			0
$61$	−1.76396	−	10.0039i	−0.225852	−	1.28087i	−0.861050	−	0.508521i	$-0.830192\pi$
$61$	−1.76396	−	10.0039i	−0.225852	−	1.28087i	0.635197	−	0.772350i	$-0.280919\pi$
$62$	−2.45705	−	4.25574i	−0.312046	−	0.540480i
$63$		0			0
$64$	−3.67959	+	6.37324i	−0.459949	+	0.796655i
$65$	22.4098	+	8.15649i	2.77959	+	1.01169i
$66$		0			0
$67$	−3.56045	−	2.98758i	−0.434979	−	0.364990i	0.398848	−	0.917017i	$-0.369410\pi$
$67$	−3.56045	−	2.98758i	−0.434979	−	0.364990i	−0.833826	+	0.552027i	$0.813855\pi$
$68$	−0.614908	−	0.515969i	−0.0745686	−	0.0625704i
$69$		0			0
$70$	3.66374	+	1.33349i	0.437901	+	0.159383i
$71$	2.71831	−	4.70826i	0.322604	−	0.558767i	−0.658420	−	0.752651i	$-0.728775\pi$
$71$	2.71831	−	4.70826i	0.322604	−	0.558767i	0.981025	+	0.193883i	$0.0621083\pi$
$72$		0			0
$73$	0.756070	+	1.30955i	0.0884913	+	0.153271i	0.906874	−	0.421403i	$-0.138462\pi$
$73$	0.756070	+	1.30955i	0.0884913	+	0.153271i	−0.818382	+	0.574674i	$0.805129\pi$
$74$	1.51564	+	8.59561i	0.176189	+	0.999219i
$75$		0			0
$76$	−3.89970	+	1.41938i	−0.447327	+	0.162814i
$77$	−0.284341	+	1.61258i	−0.0324037	+	0.183770i
$78$		0			0
$79$	−4.73453	+	3.97274i	−0.532677	+	0.446969i	−0.869024	−	0.494769i	$-0.835253\pi$
$79$	−4.73453	+	3.97274i	−0.532677	+	0.446969i	0.336348	+	0.941738i	$0.390808\pi$
$80$	−4.60980			−0.515392
$81$		0			0
$82$	4.64231			0.512658
$83$	−1.62520	+	1.36370i	−0.178389	+	0.149686i	−0.727610	−	0.685991i	$-0.759369\pi$
$83$	−1.62520	+	1.36370i	−0.178389	+	0.149686i	0.549221	+	0.835677i	$0.314924\pi$
$84$		0			0
$85$	0.559645	−	3.17390i	0.0607020	−	0.344258i
$86$	7.60715	−	2.76878i	0.820300	−	0.298565i
$87$		0			0
$88$	−0.860016	−	4.87739i	−0.0916780	−	0.519932i
$89$	0.415312	+	0.719341i	0.0440229	+	0.0762500i	0.887197	−	0.461390i	$-0.152649\pi$
$89$	0.415312	+	0.719341i	0.0440229	+	0.0762500i	−0.843174	+	0.537640i	$0.819316\pi$
$90$		0			0
$91$	3.14014	−	5.43889i	0.329177	−	0.570151i
$92$	2.64654	+	0.963260i	0.275920	+	0.100427i
$93$		0			0
$94$	0.122586	+	0.102862i	0.0126438	+	0.0106094i
$95$	−12.7640	−	10.7102i	−1.30956	−	1.09885i
$96$		0			0
$97$	−8.94079	−	3.25418i	−0.907800	−	0.330412i	−0.154426	−	0.988004i	$-0.549353\pi$
$97$	−8.94079	−	3.25418i	−0.907800	−	0.330412i	−0.753374	+	0.657592i	$0.771575\pi$
$98$	0.513378	−	0.889197i	0.0518591	−	0.0898225i
$99$		0			0
$100$	4.45424	+	7.71497i	0.445424	+	0.771497i
$101$	1.09098	+	6.18723i	0.108556	+	0.615652i	0.989740	+	0.142879i	$0.0456360\pi$
$101$	1.09098	+	6.18723i	0.108556	+	0.615652i	−0.881184	+	0.472773i	$0.843253\pi$
$102$		0			0
$103$	5.73622	−	2.08781i	0.565207	−	0.205718i	−0.0435833	−	0.999050i	$-0.513877\pi$
$103$	5.73622	−	2.08781i	0.565207	−	0.205718i	0.608790	+	0.793331i	$0.291655\pi$
$104$	−3.29850	+	18.7067i	−0.323444	+	1.83434i
$105$		0			0
$106$	9.96571	−	8.36223i	0.967956	−	0.812211i
$107$	−2.17406			−0.210175			−0.105087	−	0.994463i	$-0.533512\pi$
$107$	−2.17406			−0.210175			−0.105087	+	0.994463i	$0.533512\pi$
$108$		0			0
$109$	−3.76714			−0.360827			−0.180413	−	0.983591i	$-0.557744\pi$
$109$	−3.76714			−0.360827			−0.180413	+	0.983591i	$0.557744\pi$
$110$	4.89061	−	4.10371i	0.466301	−	0.391273i
$111$		0			0
$112$	−0.210805	+	1.19553i	−0.0199192	+	0.112967i
$113$	5.26699	−	1.91703i	0.495477	−	0.180339i	−0.0821816	−	0.996617i	$-0.526189\pi$
$113$	5.26699	−	1.91703i	0.495477	−	0.180339i	0.577659	+	0.816279i	$0.303967\pi$
$114$		0			0
$115$	1.96358	+	11.1360i	0.183105	+	1.03844i
$116$	3.42334	+	5.92940i	0.317849	+	0.550531i
$117$		0			0
$118$	1.71769	−	2.97512i	0.158126	−	0.273882i
$119$	−0.797547	−	0.290283i	−0.0731110	−	0.0266102i
$120$		0			0
$121$	−6.37252	−	5.34718i	−0.579320	−	0.486107i
$122$	7.98988	+	6.70431i	0.723370	+	0.606979i
$123$		0			0
$124$	−4.25352	−	1.54816i	−0.381978	−	0.139029i
$125$	−8.39061	+	14.5330i	−0.750479	+	1.29987i
$126$		0			0
$127$	2.50078	+	4.33148i	0.221908	+	0.384356i	0.955387	−	0.295356i	$-0.0954381\pi$
$127$	2.50078	+	4.33148i	0.221908	+	0.384356i	−0.733479	+	0.679712i	$0.762105\pi$
$128$	0.355866	+	2.01822i	0.0314544	+	0.178387i
$129$		0			0
$130$	−23.0094	+	8.37473i	−2.01806	+	0.734512i
$131$	−3.26034	+	18.4903i	−0.284858	+	1.61551i	0.420936	+	0.907090i	$0.361702\pi$
$131$	−3.26034	+	18.4903i	−0.284858	+	1.61551i	−0.705794	+	0.708417i	$0.749409\pi$
$132$		0			0
$133$	−3.36135	+	2.82051i	−0.291466	+	0.244569i
$134$	4.77220			0.412256
$135$		0			0
$136$	2.56707			0.220124
$137$	−6.28285	+	5.27194i	−0.536780	+	0.450412i	−0.870435	−	0.492283i	$-0.836162\pi$
$137$	−6.28285	+	5.27194i	−0.536780	+	0.450412i	0.333655	+	0.942695i	$0.391718\pi$
$138$		0			0
$139$	1.63090	−	9.24931i	0.138331	−	0.784516i	−0.834150	−	0.551537i	$-0.814041\pi$
$139$	1.63090	−	9.24931i	0.138331	−	0.784516i	0.972482	−	0.232979i	$-0.0748474\pi$
$140$	3.37476	−	1.22831i	0.285220	−	0.103811i
$141$		0			0
$142$	0.969320	+	5.49729i	0.0813436	+	0.461322i
$143$	−5.14185	−	8.90594i	−0.429983	−	0.744753i
$144$		0			0
$145$	−13.7447	+	23.8066i	−1.14144	+	1.97703i
$146$	−1.45897	−	0.531020i	−0.120745	−	0.0439475i
$147$		0			0
$148$	6.15881	+	5.16786i	0.506251	+	0.424795i
$149$	−5.91863	−	4.96632i	−0.484873	−	0.406857i	0.367312	−	0.930098i	$-0.380278\pi$
$149$	−5.91863	−	4.96632i	−0.484873	−	0.406857i	−0.852185	+	0.523241i	$0.824723\pi$
$150$		0			0
$151$	−13.0432	−	4.74735i	−1.06144	−	0.386334i	−0.248473	−	0.968639i	$-0.579929\pi$
$151$	−13.0432	−	4.74735i	−1.06144	−	0.386334i	−0.812970	+	0.582305i	$0.802151\pi$
$152$	6.63585	−	11.4936i	0.538238	−	0.932256i
$153$		0			0
$154$	−0.840635	−	1.45602i	−0.0677403	−	0.117330i
$155$	−3.15587	−	17.8978i	−0.253486	−	1.43759i
$156$		0			0
$157$	2.15757	−	0.785291i	0.172193	−	0.0626731i	−0.254485	−	0.967077i	$-0.581906\pi$
$157$	2.15757	−	0.785291i	0.172193	−	0.0626731i	0.426678	+	0.904404i	$0.359684\pi$
$158$	1.10195	−	6.24946i	0.0876662	−	0.497180i
$159$		0			0
$160$	−13.9705	+	11.7227i	−1.10447	+	0.926759i
$161$	2.97787			0.234689
$162$		0			0
$163$	15.3511			1.20239			0.601196	−	0.799102i	$-0.294691\pi$
$163$	15.3511			1.20239			0.601196	+	0.799102i	$0.294691\pi$
$164$	3.27572	−	2.74865i	0.255791	−	0.214634i
$165$		0			0
$166$	0.378260	−	2.14522i	0.0293587	−	0.166501i
$167$	−7.28311	+	2.65084i	−0.563584	+	0.205128i	−0.608072	−	0.793882i	$-0.708057\pi$
$167$	−7.28311	+	2.65084i	−0.563584	+	0.205128i	0.0444876	+	0.999010i	$0.485834\pi$
$168$		0			0
$169$	4.59161	+	26.0403i	0.353201	+	2.00310i
$170$	1.65455	+	2.86576i	0.126898	+	0.219794i
$171$		0			0
$172$	3.72842	−	6.45780i	0.284289	−	0.492403i
$173$	−23.1418	−	8.42291i	−1.75944	−	0.640382i	−0.759487	−	0.650522i	$-0.774550\pi$
$173$	−23.1418	−	8.42291i	−1.75944	−	0.640382i	−0.999949	+	0.0101400i	$0.996772\pi$
$174$		0			0
$175$	7.21559	+	6.05460i	0.545447	+	0.457685i
$176$	1.52277	+	1.27776i	0.114783	+	0.0963144i
$177$		0			0
$178$	−0.801415	−	0.291691i	−0.0600686	−	0.0218632i
$179$	9.86874	−	17.0932i	0.737624	−	1.27760i	−0.215938	−	0.976407i	$-0.569281\pi$
$179$	9.86874	−	17.0932i	0.737624	−	1.27760i	0.953562	−	0.301196i	$-0.0973858\pi$
$180$		0			0
$181$	−9.02723	−	15.6356i	−0.670989	−	1.16219i	−0.977624	−	0.210359i	$-0.932537\pi$
$181$	−9.02723	−	15.6356i	−0.670989	−	1.16219i	0.306635	−	0.951827i	$-0.400797\pi$
$182$	1.11974	+	6.35037i	0.0830007	+	0.470720i
$183$		0			0
$184$	−8.46366	+	3.08052i	−0.623950	+	0.227099i
$185$	−5.60531	+	31.7893i	−0.412110	+	2.33719i
$186$		0			0
$187$	−1.06462	+	0.893321i	−0.0778526	+	0.0653261i
$188$	0.147402			0.0107504
$189$		0			0
$190$	17.1080			1.24114
$191$	−8.15072	+	6.83926i	−0.589765	+	0.494872i	−0.888138	−	0.459578i	$-0.848001\pi$
$191$	−8.15072	+	6.83926i	−0.589765	+	0.494872i	0.298372	+	0.954450i	$0.403556\pi$
$192$		0			0
$193$	−2.99805	+	17.0028i	−0.215805	+	1.22389i	0.663700	+	0.747999i	$0.268985\pi$
$193$	−2.99805	+	17.0028i	−0.215805	+	1.22389i	−0.879505	+	0.475890i	$0.842126\pi$
$194$	9.18002	−	3.34125i	0.659087	−	0.239888i
$195$		0			0
$196$	−0.164231	−	0.931402i	−0.0117308	−	0.0665287i
$197$	0.358511	+	0.620959i	0.0255428	+	0.0442415i	0.878514	−	0.477716i	$-0.158535\pi$
$197$	0.358511	+	0.620959i	0.0255428	+	0.0442415i	−0.852971	+	0.521958i	$0.825202\pi$
$198$		0			0
$199$	−2.58197	+	4.47210i	−0.183031	+	0.317018i	−0.942911	−	0.333044i	$-0.891924\pi$
$199$	−2.58197	+	4.47210i	−0.183031	+	0.317018i	0.759880	+	0.650063i	$0.225257\pi$
$200$	−26.7713	−	9.74397i	−1.89302	−	0.689003i
$201$		0			0
$202$	−4.94159	−	4.14648i	−0.347689	−	0.291745i
$203$	5.54559	+	4.65331i	0.389224	+	0.326598i
$204$		0			0
$205$	16.1333	+	5.87206i	1.12680	+	0.410122i
$206$	−3.13385	+	5.42798i	−0.218345	+	0.378185i
$207$		0			0
$208$	−3.81206	−	6.60269i	−0.264319	−	0.457814i
$209$	1.24767	+	7.07589i	0.0863032	+	0.489450i
$210$		0			0
$211$	2.23549	−	0.813652i	0.153897	−	0.0560141i	−0.263923	−	0.964544i	$-0.585016\pi$
$211$	2.23549	−	0.813652i	0.153897	−	0.0560141i	0.417820	+	0.908530i	$0.362794\pi$
$212$	2.08086	−	11.8011i	0.142914	−	0.810506i
$213$		0			0
$214$	1.70999	−	1.43485i	0.116893	−	0.0980845i
$215$	29.9392			2.04184
$216$		0			0
$217$	−4.78605			−0.324898
$218$	2.96301	−	2.48626i	0.200681	−	0.168391i
$219$		0			0
$220$	1.02117	−	5.79134i	0.0688472	−	0.390452i
$221$	5.00883	−	1.82306i	0.336930	−	0.122633i
$222$		0			0
$223$	−1.63131	−	9.25162i	−0.109241	−	0.619535i	−0.989441	−	0.144933i	$-0.953703\pi$
$223$	−1.63131	−	9.25162i	−0.109241	−	0.619535i	0.880201	−	0.474601i	$-0.157408\pi$
$224$	2.40136	+	4.15928i	0.160448	+	0.277903i
$225$		0			0
$226$	−2.87749	+	4.98397i	−0.191408	+	0.331528i
$227$	19.8649	+	7.23025i	1.31848	+	0.479888i	0.902972	−	0.429700i	$-0.141381\pi$
$227$	19.8649	+	7.23025i	1.31848	+	0.479888i	0.415511	+	0.909588i	$0.363603\pi$
$228$		0			0
$229$	−6.21523	−	5.21520i	−0.410714	−	0.344630i	0.413903	−	0.910321i	$-0.364165\pi$
$229$	−6.21523	−	5.21520i	−0.410714	−	0.344630i	−0.824617	+	0.565691i	$0.808610\pi$
$230$	−8.89405	−	7.46299i	−0.586456	−	0.492095i
$231$		0			0
$232$	−20.5753	−	7.48880i	−1.35084	−	0.491664i
$233$	4.51226	−	7.81546i	0.295608	−	0.512008i	−0.679518	−	0.733659i	$-0.737811\pi$
$233$	4.51226	−	7.81546i	0.295608	−	0.512008i	0.975126	+	0.221651i	$0.0711445\pi$
$234$		0			0
$235$	0.295911	+	0.512533i	0.0193031	+	0.0334339i
$236$	−0.549493	−	3.11633i	−0.0357690	−	0.202856i
$237$		0			0
$238$	0.818887	−	0.298050i	0.0530806	−	0.0193197i
$239$	1.06860	−	6.06031i	0.0691217	−	0.392009i	−0.930545	−	0.366179i	$-0.880666\pi$
$239$	1.06860	−	6.06031i	0.0691217	−	0.392009i	0.999666	−	0.0258303i	$-0.00822295\pi$
$240$		0			0
$241$	13.7022	−	11.4975i	0.882639	−	0.740622i	−0.0840812	−	0.996459i	$-0.526796\pi$
$241$	13.7022	−	11.4975i	0.882639	−	0.740622i	0.966720	+	0.255837i	$0.0823511\pi$
$242$	8.54132			0.549057
$243$		0			0
$244$	9.60737			0.615049
$245$	2.90888	−	2.44084i	0.185842	−	0.155940i
$246$		0			0
$247$	4.78531	−	27.1388i	0.304482	−	1.72680i
$248$	13.6028	−	4.95103i	0.863781	−	0.314391i
$249$		0			0
$250$	−2.99200	−	16.9685i	−0.189231	−	1.07318i
$251$	−13.4328	−	23.2663i	−0.847870	−	1.46855i	−0.883106	−	0.469174i	$-0.844552\pi$
$251$	−13.4328	−	23.2663i	−0.847870	−	1.46855i	0.0352362	−	0.999379i	$-0.488782\pi$
$252$		0			0
$253$	2.43807	−	4.22286i	0.153280	−	0.265489i
$254$	−4.82568	−	1.75640i	−0.302790	−	0.110207i
$255$		0			0
$256$	−12.8868	−	10.8133i	−0.805426	−	0.675833i
$257$	−10.8465	−	9.10130i	−0.676587	−	0.567724i	0.238420	−	0.971162i	$-0.423370\pi$
$257$	−10.8465	−	9.10130i	−0.676587	−	0.567724i	−0.915007	+	0.403438i	$0.867815\pi$
$258$		0			0
$259$	7.98809	+	2.90743i	0.496356	+	0.180659i
$260$	−11.2774	+	19.5330i	−0.699392	+	1.21138i
$261$		0			0
$262$	−9.63897	−	16.6952i	−0.595498	−	1.03143i
$263$	1.35568	+	7.68844i	0.0835947	+	0.474089i	0.997651	+	0.0685019i	$0.0218219\pi$
$263$	1.35568	+	7.68844i	0.0835947	+	0.474089i	−0.914056	+	0.405587i	$0.867067\pi$
$264$		0			0
$265$	45.2110	−	16.4555i	2.77729	−	1.01085i
$266$	0.782344	−	4.43689i	0.0479686	−	0.272043i
$267$		0			0
$268$	3.36737	−	2.82556i	0.205695	−	0.172599i
$269$	−6.34578			−0.386909			−0.193455	−	0.981109i	$-0.561969\pi$
$269$	−6.34578			−0.386909			−0.193455	+	0.981109i	$0.561969\pi$
$270$		0			0
$271$	17.3780			1.05564			0.527818	−	0.849357i	$-0.323010\pi$
$271$	17.3780			1.05564			0.527818	+	0.849357i	$0.323010\pi$
$272$	−0.789287	+	0.662291i	−0.0478576	+	0.0401573i
$273$		0			0
$274$	1.46231	−	8.29319i	0.0883416	−	0.501010i
$275$	14.4935	−	5.27520i	0.873991	−	0.318107i
$276$		0			0
$277$	−2.28304	−	12.9478i	−0.137174	−	0.777955i	−0.973321	−	0.229449i	$-0.926308\pi$
$277$	−2.28304	−	12.9478i	−0.137174	−	0.777955i	0.836146	−	0.548506i	$-0.184803\pi$
$278$	4.82165	+	8.35134i	0.289183	+	0.500880i
$279$		0			0
$280$	−5.74260	+	9.94647i	−0.343186	+	0.594415i
$281$	3.20684	+	1.16719i	0.191304	+	0.0696290i	0.435896	−	0.899997i	$-0.356432\pi$
$281$	3.20684	+	1.16719i	0.191304	+	0.0696290i	−0.244592	+	0.969626i	$0.578654\pi$
$282$		0			0
$283$	−1.24498	−	1.04466i	−0.0740063	−	0.0620987i	0.605034	−	0.796200i	$-0.293159\pi$
$283$	−1.24498	−	1.04466i	−0.0740063	−	0.0620987i	−0.679040	+	0.734101i	$0.737604\pi$
$284$	3.93885	+	3.30509i	0.233728	+	0.196121i
$285$		0			0
$286$	9.92208	+	3.61134i	0.586705	+	0.213543i
$287$	2.26067	−	3.91559i	0.133443	−	0.231130i
$288$		0			0
$289$	8.13983	+	14.0986i	0.478813	+	0.829329i
$290$	−4.90121	−	27.7962i	−0.287809	−	1.63225i
$291$		0			0
$292$	−1.34389	+	0.489136i	−0.0786451	+	0.0286245i
$293$	1.96516	−	11.1450i	0.114806	−	0.651096i	−0.872041	−	0.489434i	$-0.837204\pi$
$293$	1.96516	−	11.1450i	0.114806	−	0.651096i	0.986846	−	0.161662i	$-0.0516854\pi$
$294$		0			0
$295$	9.73268	−	8.16669i	0.566658	−	0.475483i
$296$	−25.7113			−1.49444
$297$		0			0
$298$	7.93295			0.459544
$299$	−14.3265	+	12.0214i	−0.828522	+	0.695213i
$300$		0			0
$301$	1.36911	−	7.76462i	0.0789143	−	0.447545i
$302$	13.3922	−	4.87437i	0.770636	−	0.280489i
$303$		0			0
$304$	0.924998	+	5.24592i	0.0530523	+	0.300874i
$305$	19.2868	+	33.4058i	1.10436	+	1.91281i
$306$		0			0
$307$	−0.844810	+	1.46325i	−0.0482158	+	0.0835123i	−0.889126	−	0.457662i	$-0.848687\pi$
$307$	−0.844810	+	1.46325i	−0.0482158	+	0.0835123i	0.840910	+	0.541175i	$0.182020\pi$
$308$	−1.45526	−	0.529672i	−0.0829213	−	0.0301809i
$309$		0			0
$310$	14.2946	+	11.9946i	0.811876	+	0.681245i
$311$	−12.9294	−	10.8491i	−0.733159	−	0.615194i	0.197832	−	0.980236i	$-0.436610\pi$
$311$	−12.9294	−	10.8491i	−0.733159	−	0.615194i	−0.930991	+	0.365042i	$0.881055\pi$
$312$		0			0
$313$	28.6924	+	10.4432i	1.62179	+	0.590284i	0.983723	−	0.179694i	$-0.0575106\pi$
$313$	28.6924	+	10.4432i	1.62179	+	0.590284i	0.638070	+	0.769978i	$0.279733\pi$
$314$	−1.17874	+	2.04163i	−0.0665199	+	0.115216i
$315$		0			0
$316$	−2.92266	−	5.06220i	−0.164413	−	0.284771i
$317$	−1.65848	−	9.40570i	−0.0931494	−	0.528276i	−0.995299	−	0.0968526i	$-0.969122\pi$
$317$	−1.65848	−	9.40570i	−0.0931494	−	0.528276i	0.902149	−	0.431424i	$-0.141989\pi$
$318$		0			0
$319$	11.1391	−	4.05430i	0.623669	−	0.226997i
$320$	4.85257	−	27.5203i	0.271267	−	1.53843i
$321$		0			0
$322$	−2.34222	+	1.96536i	−0.130527	+	0.109525i
$323$	−3.72418			−0.207219
$324$		0			0
$325$	−59.1558			−3.28137
$326$	−12.0743	+	10.1315i	−0.668732	+	0.561133i
$327$		0			0
$328$	−2.37467	+	13.4674i	−0.131119	+	0.743614i
$329$	0.146455	−	0.0533053i	0.00807434	−	0.00293882i
$330$		0			0
$331$	3.29017	+	18.6595i	0.180844	+	1.02562i	0.931180	+	0.364560i	$0.118781\pi$
$331$	3.29017	+	18.6595i	0.180844	+	1.02562i	−0.750336	+	0.661057i	$0.770108\pi$
$332$	−1.00325	−	1.73768i	−0.0550604	−	0.0953674i
$333$		0			0
$334$	3.97895	−	6.89175i	0.217719	−	0.377100i
$335$	16.5848	+	6.03636i	0.906122	+	0.329801i
$336$		0			0
$337$	8.81703	+	7.39837i	0.480294	+	0.403015i	0.850533	−	0.525922i	$-0.176280\pi$
$337$	8.81703	+	7.39837i	0.480294	+	0.403015i	−0.370238	+	0.928937i	$0.620724\pi$
$338$	−20.7978	−	17.4514i	−1.13125	−	0.949231i
$339$		0			0
$340$	2.86427	+	1.04251i	0.155337	+	0.0565380i
$341$	−3.91847	+	6.78700i	−0.212197	+	0.367536i
$342$		0			0
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	4.14100	+	23.4848i	0.223268	+	1.26621i
$345$		0			0
$346$	23.7610	−	8.64828i	1.27740	−	0.464935i
$347$	0.113298	−	0.642546i	0.00608217	−	0.0344937i	−0.981616	−	0.190868i	$-0.938870\pi$
$347$	0.113298	−	0.642546i	0.00608217	−	0.0344937i	0.987698	+	0.156375i	$0.0499807\pi$
$348$		0			0
$349$	−27.8354	+	23.3566i	−1.48999	+	1.25025i	−0.595353	+	0.803464i	$0.702988\pi$
$349$	−27.8354	+	23.3566i	−1.48999	+	1.25025i	−0.894640	+	0.446788i	$0.852568\pi$
$350$	−9.67131			−0.516953
$351$		0			0
$352$	7.86424			0.419166
$353$	−1.15497	+	0.969131i	−0.0614726	+	0.0515817i	−0.673006	−	0.739637i	$-0.734997\pi$
$353$	−1.15497	+	0.969131i	−0.0614726	+	0.0515817i	0.611534	+	0.791218i	$0.290553\pi$
$354$		0			0
$355$	−3.58485	+	20.3307i	−0.190264	+	1.07904i
$356$	−0.738202	+	0.268684i	−0.0391247	+	0.0142402i
$357$		0			0
$358$	3.51908	+	19.9577i	0.185989	+	1.05480i
$359$	18.6210	+	32.2526i	0.982781	+	1.70223i	0.651409	+	0.758727i	$0.274178\pi$
$359$	18.6210	+	32.2526i	0.982781	+	1.70223i	0.331372	+	0.943500i	$0.392489\pi$
$360$		0			0
$361$	−0.126974	+	0.219925i	−0.00668284	+	0.0115750i
$362$	17.4196	+	6.34021i	0.915553	+	0.333234i
$363$		0			0
$364$	4.55008	+	3.81797i	0.238489	+	0.200116i
$365$	−4.39863	−	3.69089i	−0.230235	−	0.193190i
$366$		0			0
$367$	−31.7489	−	11.5556i	−1.65728	−	0.603200i	−0.667346	−	0.744748i	$-0.732570\pi$
$367$	−31.7489	−	11.5556i	−1.65728	−	0.603200i	−0.989931	+	0.141549i	$0.954792\pi$
$368$	1.80754	−	3.13074i	0.0942243	−	0.163201i
$369$		0			0
$370$	−16.5717	−	28.7030i	−0.861521	−	1.49220i
$371$	−2.20017	−	12.4778i	−0.114227	−	0.647816i
$372$		0			0
$373$	−4.52370	+	1.64649i	−0.234228	+	0.0852522i	−0.456468	−	0.889740i	$-0.650886\pi$
$373$	−4.52370	+	1.64649i	−0.234228	+	0.0852522i	0.222239	+	0.974992i	$0.428663\pi$
$374$	0.247787	−	1.40527i	0.0128127	−	0.0726647i
$375$		0			0
$376$	−0.361110	+	0.303007i	−0.0186228	+	0.0156264i
$377$	−45.4646			−2.34155
$378$		0			0
$379$	−25.8902			−1.32989			−0.664946	−	0.746892i	$-0.731545\pi$
$379$	−25.8902			−1.32989			−0.664946	+	0.746892i	$0.731545\pi$
$380$	12.0718	−	10.1294i	0.619269	−	0.519629i
$381$		0			0
$382$	1.89705	−	10.7587i	0.0970617	−	0.550464i
$383$	19.1495	−	6.96983i	0.978491	−	0.356142i	0.197238	−	0.980356i	$-0.436803\pi$
$383$	19.1495	−	6.96983i	0.978491	−	0.356142i	0.781253	+	0.624214i	$0.214581\pi$
$384$		0			0
$385$	−1.07972	−	6.12340i	−0.0550277	−	0.312078i
$386$	−8.86353	−	15.3521i	−0.451142	−	0.781400i
$387$		0			0
$388$	4.49931	−	7.79303i	0.228418	−	0.395631i
$389$	−5.24106	−	1.90759i	−0.265732	−	0.0967186i	0.205718	−	0.978611i	$-0.434047\pi$
$389$	−5.24106	−	1.90759i	−0.265732	−	0.0967186i	−0.471450	+	0.881893i	$0.656269\pi$
$390$		0			0
$391$	1.93611	+	1.62459i	0.0979134	+	0.0821591i
$392$	2.31697	+	1.94417i	0.117025	+	0.0981954i
$393$		0			0
$394$	−0.691808	−	0.251798i	−0.0348528	−	0.0126854i
$395$	11.7345	−	20.3248i	0.590427	−	1.02265i
$396$		0			0
$397$	−6.96118	−	12.0571i	−0.349371	−	0.605129i	0.636766	−	0.771057i	$-0.280272\pi$
$397$	−6.96118	−	12.0571i	−0.349371	−	0.605129i	−0.986138	+	0.165928i	$0.946938\pi$
$398$	−0.920700	−	5.22155i	−0.0461505	−	0.261733i
$399$		0			0
$400$	10.7452	−	3.91093i	0.537260	−	0.195547i
$401$	−0.134854	+	0.764794i	−0.00673428	+	0.0381920i	−0.987990	−	0.154520i	$-0.950617\pi$
$401$	−0.134854	+	0.764794i	−0.00673428	+	0.0381920i	0.981255	+	0.192712i	$0.0617282\pi$
$402$		0			0
$403$	23.0256	−	19.3208i	1.14699	−	0.962436i
$404$	−5.94197			−0.295624
$405$		0			0
$406$	−7.43296			−0.368891
$407$	10.6630	−	8.94735i	0.528547	−	0.443504i
$408$		0			0
$409$	−2.69427	+	15.2800i	−0.133223	+	0.755546i	0.842857	+	0.538137i	$0.180872\pi$
$409$	−2.69427	+	15.2800i	−0.133223	+	0.755546i	−0.976081	+	0.217409i	$0.930239\pi$
$410$	−16.5650	+	6.02917i	−0.818088	+	0.297760i
$411$		0			0
$412$	1.00253	+	5.68561i	0.0493910	+	0.280110i
$413$	−1.67293	−	2.89759i	−0.0823193	−	0.142581i
$414$		0			0
$415$	4.02805	−	6.97678i	0.197729	−	0.342477i
$416$	−28.3435	−	10.3162i	−1.38965	−	0.505792i
$417$		0			0
$418$	−5.65134	−	4.74203i	−0.276416	−	0.231940i
$419$	8.84945	+	7.42557i	0.432324	+	0.362763i	0.832828	−	0.553532i	$-0.186720\pi$
$419$	8.84945	+	7.42557i	0.432324	+	0.362763i	−0.400504	+	0.916295i	$0.631165\pi$
$420$		0			0
$421$	25.5735	+	9.30801i	1.24638	+	0.453645i	0.879176	−	0.476497i	$-0.158094\pi$
$421$	25.5735	+	9.30801i	1.24638	+	0.453645i	0.367202	+	0.930141i	$0.380316\pi$
$422$	−1.22131	+	2.11536i	−0.0594522	+	0.102974i
$423$		0			0
$424$	19.1612	+	33.1882i	0.930552	+	1.61176i
$425$	1.38822	+	7.87299i	0.0673386	+	0.381896i
$426$		0			0
$427$	9.54563	−	3.47433i	0.461945	−	0.168134i
$428$	0.357049	−	2.02493i	0.0172586	−	0.0978786i
$429$		0			0
$430$	−23.5484	+	19.7595i	−1.13561	+	0.952887i
$431$	37.5351			1.80800			0.904001	−	0.427531i	$-0.140617\pi$
$431$	37.5351			1.80800			0.904001	+	0.427531i	$0.140617\pi$
$432$		0			0
$433$	−32.9932			−1.58555			−0.792777	−	0.609512i	$-0.791366\pi$
$433$	−32.9932			−1.58555			−0.792777	+	0.609512i	$0.791366\pi$
$434$	3.76443	−	3.15873i	0.180698	−	0.151624i
$435$		0			0
$436$	0.618683	−	3.50872i	0.0296295	−	0.168037i
$437$	12.2787	−	4.46908i	0.587369	−	0.213785i
$438$		0			0
$439$	−0.424336	−	2.40653i	−0.0202525	−	0.114857i	0.973006	−	0.230781i	$-0.0741282\pi$
$439$	−0.424336	−	2.40653i	−0.0202525	−	0.114857i	−0.993258	+	0.115924i	$0.963017\pi$
$440$	9.40325	+	16.2869i	0.448282	+	0.776448i
$441$		0			0
$442$	−2.73645	+	4.73967i	−0.130160	+	0.225443i
$443$	−26.2421	−	9.55136i	−1.24680	−	0.453799i	−0.367482	−	0.930031i	$-0.619780\pi$
$443$	−26.2421	−	9.55136i	−1.24680	−	0.453799i	−0.879320	+	0.476232i	$0.842002\pi$
$444$		0			0
$445$	−2.41618	−	2.02742i	−0.114538	−	0.0961088i
$446$	7.38904	+	6.20014i	0.349881	+	0.293585i
$447$		0			0
$448$	−6.91537	−	2.51699i	−0.326720	−	0.118917i
$449$	−7.90135	+	13.6855i	−0.372888	+	0.645861i	−0.990008	−	0.141008i	$-0.954966\pi$
$449$	−7.90135	+	13.6855i	−0.372888	+	0.645861i	0.617121	+	0.786869i	$0.288299\pi$
$450$		0			0
$451$	−3.70174	−	6.41161i	−0.174308	−	0.301911i
$452$	0.920519	+	5.22052i	0.0432976	+	0.245553i
$453$		0			0
$454$	−20.3965	+	7.42371i	−0.957254	+	0.348412i
$455$	−4.14116	+	23.4857i	−0.194140	+	1.10103i
$456$		0			0
$457$	−29.9480	+	25.1293i	−1.40091	+	1.17550i	−0.440212	+	0.897894i	$0.645097\pi$
$457$	−29.9480	+	25.1293i	−1.40091	+	1.17550i	−0.960695	+	0.277606i	$0.910459\pi$
$458$	8.33050			0.389259
$459$		0			0
$460$	−10.6946			−0.498637
$461$	15.2551	−	12.8006i	0.710503	−	0.596183i	−0.214237	−	0.976782i	$-0.568727\pi$
$461$	15.2551	−	12.8006i	0.710503	−	0.596183i	0.924740	+	0.380599i	$0.124282\pi$
$462$		0			0
$463$	2.87004	−	16.2768i	0.133382	−	0.756447i	−0.842591	−	0.538554i	$-0.818971\pi$
$463$	2.87004	−	16.2768i	0.133382	−	0.756447i	0.975973	−	0.217893i	$-0.0699183\pi$
$464$	8.25830	−	3.00577i	0.383382	−	0.139540i
$465$		0			0
$466$	1.60902	+	9.12521i	0.0745365	+	0.422717i
$467$	−15.1595	−	26.2570i	−0.701497	−	1.21503i	−0.967941	−	0.251178i	$-0.919182\pi$
$467$	−15.1595	−	26.2570i	−0.701497	−	1.21503i	0.266444	−	0.963850i	$-0.414151\pi$
$468$		0			0
$469$	2.32392	−	4.02515i	0.107309	−	0.185864i
$470$	−0.571011	−	0.207831i	−0.0263388	−	0.00958653i
$471$		0			0
$472$	7.75224	+	6.50490i	0.356826	+	0.299412i
$473$	−9.88991	−	8.29862i	−0.454738	−	0.381571i
$474$		0			0
$475$	38.8386	+	14.1361i	1.78204	+	0.648608i
$476$	0.401353	−	0.695163i	0.0183960	−	0.0318628i
$477$		0			0
$478$	3.15923	+	5.47194i	0.144500	+	0.250281i
$479$	−2.92440	−	16.5851i	−0.133619	−	0.757792i	−0.975811	−	0.218614i	$-0.929846\pi$
$479$	−2.92440	−	16.5851i	−0.133619	−	0.757792i	0.842192	−	0.539177i	$-0.181265\pi$
$480$		0			0
$481$	−50.1676	+	18.2595i	−2.28744	+	0.832561i
$482$	−3.18915	+	18.0866i	−0.145262	+	0.823821i
$483$		0			0
$484$	6.02694	−	5.05721i	0.273952	−	0.229873i
$485$	36.1295			1.64056
$486$		0			0
$487$	16.6758			0.755654			0.377827	−	0.925876i	$-0.376671\pi$
$487$	16.6758			0.755654			0.377827	+	0.925876i	$0.376671\pi$
$488$	−23.5364	+	19.7493i	−1.06544	+	0.894011i
$489$		0			0
$490$	−0.677033	+	3.83964i	−0.0305852	+	0.173457i
$491$	−8.19449	+	2.98255i	−0.369812	+	0.134601i	−0.520240	−	0.854020i	$-0.674157\pi$
$491$	−8.19449	+	2.98255i	−0.369812	+	0.134601i	0.150427	+	0.988621i	$0.451935\pi$
$492$		0			0
$493$	1.06693	+	6.05084i	0.0480520	+	0.272516i
$494$	14.1474	+	24.5040i	0.636522	+	1.10249i
$495$		0			0
$496$	−2.90508	+	5.03174i	−0.130442	+	0.225932i
$497$	5.10876	+	1.85944i	0.229159	+	0.0834071i
$498$		0			0
$499$	−0.910677	−	0.764149i	−0.0407675	−	0.0342080i	0.622176	−	0.782877i	$-0.286249\pi$
$499$	−0.910677	−	0.764149i	−0.0407675	−	0.0342080i	−0.662944	+	0.748669i	$0.730693\pi$
$500$	−12.1580	−	10.2018i	−0.543724	−	0.456238i
$501$		0			0
$502$	25.9209	+	9.43442i	1.15690	+	0.421079i
$503$	−9.32422	+	16.1500i	−0.415747	+	0.720094i	−0.995507	−	0.0946931i	$-0.969813\pi$
$503$	−9.32422	+	16.1500i	−0.415747	+	0.720094i	0.579760	+	0.814787i	$0.303146\pi$
$504$		0			0
$505$	−11.9285	−	20.6608i	−0.530812	−	0.919394i
$506$	0.869388	+	4.93054i	0.0386490	+	0.219189i
$507$		0			0
$508$	−4.44505	+	1.61787i	−0.197217	+	0.0717812i
$509$	−0.201799	+	1.14446i	−0.00894457	+	0.0507272i	−0.988953	−	0.148227i	$-0.952643\pi$
$509$	−0.201799	+	1.14446i	−0.00894457	+	0.0507272i	0.980009	+	0.198954i	$0.0637545\pi$
$510$		0			0
$511$	−1.15837	+	0.971984i	−0.0512431	+	0.0429981i
$512$	13.1740			0.582212
$513$		0			0
$514$	14.5380			0.641242
$515$	−17.7569	+	14.8998i	−0.782460	+	0.656562i
$516$		0			0
$517$	0.0443158	−	0.251328i	0.00194901	−	0.0110534i
$518$	−8.20183	+	2.98522i	−0.360368	+	0.131163i
$519$		0			0
$520$	−12.5253	−	71.0345i	−0.549271	−	3.11507i
$521$	9.77759	+	16.9353i	0.428364	+	0.741949i	0.996728	−	0.0808288i	$-0.0257567\pi$
$521$	9.77759	+	16.9353i	0.428364	+	0.741949i	−0.568364	+	0.822777i	$0.692423\pi$
$522$		0			0
$523$	16.4835	−	28.5503i	0.720775	−	1.24842i	−0.239914	−	0.970794i	$-0.577119\pi$
$523$	16.4835	−	28.5503i	0.720775	−	1.24842i	0.960689	−	0.277625i	$-0.0895473\pi$
$524$	−16.6865	−	6.07338i	−0.728952	−	0.265317i
$525$		0			0
$526$	−6.14056	−	5.15254i	−0.267741	−	0.224662i
$527$	−3.11173	−	2.61105i	−0.135549	−	0.113739i
$528$		0			0
$529$	13.2800	+	4.83352i	0.577391	+	0.210153i
$530$	−24.7000	+	42.7816i	−1.07290	+	1.85831i
$531$		0			0
$532$	−2.07499	−	3.59399i	−0.0899621	−	0.155819i
$533$	4.93079	+	27.9639i	0.213576	+	1.21125i
$534$		0			0
$535$	7.75765	−	2.82355i	0.335392	−	0.122073i
$536$	−2.44111	+	13.8442i	−0.105440	+	0.597980i
$537$		0			0
$538$	4.99122	−	4.18813i	0.215187	−	0.180563i
$539$	−1.63746			−0.0705302
$540$		0			0
$541$	−22.5335			−0.968792			−0.484396	−	0.874849i	$-0.660961\pi$
$541$	−22.5335			−0.968792			−0.484396	+	0.874849i	$0.660961\pi$
$542$	−13.6685	+	11.4692i	−0.587112	+	0.492646i
$543$		0			0
$544$	−0.707828	+	4.01429i	−0.0303479	+	0.172111i
$545$	13.4422	−	4.89255i	0.575800	−	0.209574i
$546$		0			0
$547$	7.32502	+	41.5423i	0.313195	+	1.77622i	0.582165	+	0.813070i	$0.302206\pi$
$547$	7.32502	+	41.5423i	0.313195	+	1.77622i	−0.268970	+	0.963149i	$0.586683\pi$
$548$	−3.87845	−	6.71768i	−0.165679	−	0.286965i
$549$		0			0
$550$	−7.91817	+	13.7147i	−0.337632	+	0.584796i
$551$	29.8497	+	10.8644i	1.27164	+	0.462839i
$552$		0			0
$553$	−4.73453	−	3.97274i	−0.201333	−	0.168938i
$554$	10.3410	+	8.67717i	0.439349	+	0.368657i
$555$		0			0
$556$	8.34698	+	3.03805i	0.353991	+	0.128842i
$557$	5.00101	−	8.66200i	0.211900	−	0.367021i	−0.740409	−	0.672156i	$-0.765368\pi$
$557$	5.00101	−	8.66200i	0.211900	−	0.367021i	0.952309	+	0.305135i	$0.0987017\pi$
$558$		0			0
$559$	24.7582	+	42.8824i	1.04716	+	1.81373i
$560$	−0.800484	−	4.53977i	−0.0338266	−	0.191840i
$561$		0			0
$562$	−3.29265	+	1.19843i	−0.138892	+	0.0505525i
$563$	1.92456	−	10.9147i	0.0811104	−	0.460000i	−0.917018	−	0.398846i	$-0.869411\pi$
$563$	1.92456	−	10.9147i	0.0811104	−	0.460000i	0.998128	−	0.0611539i	$-0.0194780\pi$
$564$		0			0
$565$	−16.3043	+	13.6809i	−0.685928	+	0.575562i
$566$	1.66869			0.0701402
$567$		0			0
$568$	−16.4436			−0.689957
$569$	−4.51145	+	3.78556i	−0.189130	+	0.158699i	−0.732436	−	0.680836i	$-0.761617\pi$
$569$	−4.51145	+	3.78556i	−0.189130	+	0.158699i	0.543306	+	0.839535i	$0.317172\pi$
$570$		0			0
$571$	−3.77217	+	21.3930i	−0.157860	+	0.895270i	0.798264	+	0.602308i	$0.205752\pi$
$571$	−3.77217	+	21.3930i	−0.157860	+	0.895270i	−0.956124	+	0.292962i	$0.905359\pi$
$572$	9.13947	−	3.32649i	0.382140	−	0.139088i
$573$		0			0
$574$	0.806129	+	4.57178i	0.0336472	+	0.190823i
$575$	−14.0247	−	24.2915i	−0.584871	−	1.01303i
$576$		0			0
$577$	−4.78131	+	8.28148i	−0.199049	+	0.344762i	−0.948220	−	0.317614i	$-0.897119\pi$
$577$	−4.78131	+	8.28148i	−0.199049	+	0.344762i	0.749172	+	0.662376i	$0.230452\pi$
$578$	−15.7072	−	5.71695i	−0.653333	−	0.237794i
$579$		0			0
$580$	−19.9162	−	16.7116i	−0.826973	−	0.693913i
$581$	−1.62520	−	1.36370i	−0.0674246	−	0.0565760i
$582$		0			0
$583$	−19.4959	−	7.09591i	−0.807436	−	0.293883i
$584$	2.28680	−	3.96085i	0.0946285	−	0.163901i
$585$		0			0
$586$	5.80985	+	10.0629i	0.240003	+	0.415697i
$587$	0.579987	+	3.28927i	0.0239386	+	0.135763i	0.994435	−	0.105354i	$-0.0335975\pi$
$587$	0.579987	+	3.28927i	0.0239386	+	0.135763i	−0.970496	+	0.241117i	$0.922486\pi$
$588$		0			0
$589$	−19.7344	+	7.18272i	−0.813140	+	0.295959i
$590$	−2.26525	+	12.8469i	−0.0932589	+	0.528897i
$591$		0			0
$592$	7.90537	−	6.63339i	0.324909	−	0.272631i
$593$	24.3048			0.998080			0.499040	−	0.866579i	$-0.333686\pi$
$593$	24.3048			0.998080			0.499040	+	0.866579i	$0.333686\pi$
$594$		0			0
$595$	3.22287			0.132125
$596$	5.59767	−	4.69700i	0.229289	−	0.192397i
$597$		0			0
$598$	3.33445	−	18.9106i	0.136356	−	0.773311i
$599$	22.8148	−	8.30390i	0.932187	−	0.339288i	0.169111	−	0.985597i	$-0.445910\pi$
$599$	22.8148	−	8.30390i	0.932187	−	0.339288i	0.763076	+	0.646309i	$0.223688\pi$
$600$		0			0
$601$	2.79563	+	15.8548i	0.114036	+	0.646730i	0.987223	+	0.159345i	$0.0509382\pi$
$601$	2.79563	+	15.8548i	0.114036	+	0.646730i	−0.873187	+	0.487385i	$0.837951\pi$
$602$	4.04768	+	7.01079i	0.164971	+	0.285738i
$603$		0			0
$604$	6.56380	−	11.3688i	0.267077	−	0.462591i
$605$	29.6835	+	10.8039i	1.20681	+	0.439241i
$606$		0			0
$607$	7.84648	+	6.58398i	0.318479	+	0.267236i	0.787986	−	0.615693i	$-0.211124\pi$
$607$	7.84648	+	6.58398i	0.318479	+	0.267236i	−0.469507	+	0.882929i	$0.655568\pi$
$608$	16.1436	+	13.5461i	0.654711	+	0.549367i
$609$		0			0
$610$	−37.2172	−	13.5460i	−1.50688	−	0.548460i
$611$	−0.489405	+	0.847675i	−0.0197992	+	0.0342933i
$612$		0			0
$613$	15.3227	+	26.5396i	0.618876	+	1.07192i	0.989691	+	0.143218i	$0.0457450\pi$
$613$	15.3227	+	26.5396i	0.618876	+	1.07192i	−0.370815	+	0.928707i	$0.620922\pi$
$614$	−0.301250	−	1.70847i	−0.0121575	−	0.0689483i
$615$		0			0
$616$	4.65395	−	1.69390i	0.187513	−	0.0682492i
$617$	−2.48396	+	14.0872i	−0.100000	+	0.567131i	0.893099	+	0.449859i	$0.148526\pi$
$617$	−2.48396	+	14.0872i	−0.100000	+	0.567131i	−0.993100	+	0.117271i	$0.962585\pi$
$618$		0			0
$619$	−7.70903	+	6.46864i	−0.309852	+	0.259997i	−0.784431	−	0.620216i	$-0.787045\pi$
$619$	−7.70903	+	6.46864i	−0.309852	+	0.259997i	0.474579	+	0.880213i	$0.342600\pi$
$620$	17.1884			0.690302
$621$		0			0
$622$	17.3297			0.694860
$623$	−0.636294	+	0.533914i	−0.0254926	+	0.0213908i
$624$		0			0
$625$	2.88715	−	16.3739i	0.115486	−	0.654955i
$626$	−29.4602	+	10.7226i	−1.17747	+	0.428562i
$627$		0			0
$628$	0.377081	+	2.13853i	0.0150472	+	0.0853368i
$629$	3.60743	+	6.24825i	0.143838	+	0.249134i
$630$		0			0
$631$	20.1736	−	34.9417i	0.803099	−	1.39101i	−0.114468	−	0.993427i	$-0.536516\pi$
$631$	20.1736	−	34.9417i	0.803099	−	1.39101i	0.917567	−	0.397581i	$-0.130150\pi$
$632$	17.5661	+	6.39354i	0.698742	+	0.254321i
$633$		0			0
$634$	7.51209	+	6.30340i	0.298343	+	0.250340i
$635$	−14.5489	−	12.2080i	−0.577357	−	0.484460i
$636$		0			0
$637$	5.90154	+	2.14799i	0.233828	+	0.0851063i
$638$	−6.08557	+	10.5405i	−0.240930	+	0.417303i
$639$		0			0
$640$	−3.89097	−	6.73936i	−0.153804	−	0.266397i
$641$	−3.74680	−	21.2491i	−0.147990	−	0.839291i	−0.964918	−	0.262552i	$-0.915436\pi$
$641$	−3.74680	−	21.2491i	−0.147990	−	0.839291i	0.816928	−	0.576739i	$-0.195675\pi$
$642$		0			0
$643$	26.3560	−	9.59278i	1.03938	−	0.378302i	0.234733	−	0.972060i	$-0.424578\pi$
$643$	26.3560	−	9.59278i	1.03938	−	0.378302i	0.804644	+	0.593757i	$0.202356\pi$
$644$	−0.489060	+	2.77360i	−0.0192717	+	0.109295i
$645$		0			0
$646$	2.92922	−	2.45791i	0.115249	−	0.0967051i
$647$	−34.8829			−1.37139			−0.685695	−	0.727889i	$-0.740501\pi$
$647$	−34.8829			−1.37139			−0.685695	+	0.727889i	$0.740501\pi$
$648$		0			0
$649$	−5.47868			−0.215057
$650$	46.5285	−	39.0420i	1.82500	−	1.53136i
$651$		0			0
$652$	−2.52113	+	14.2980i	−0.0987351	+	0.559955i
$653$	−40.3590	+	14.6895i	−1.57937	+	0.574844i	−0.975067	−	0.221910i	$-0.928771\pi$
$653$	−40.3590	+	14.6895i	−1.57937	+	0.574844i	−0.604304	+	0.796754i	$0.706549\pi$
$654$		0			0
$655$	−12.3804	−	70.2128i	−0.483743	−	2.74344i
$656$	−2.74440	−	4.75344i	−0.107151	−	0.185591i
$657$		0			0
$658$	−0.0800123	+	0.138585i	−0.00311920	+	0.00540262i
$659$	2.84942	+	1.03711i	0.110998	+	0.0403999i	0.396922	−	0.917852i	$-0.370078\pi$
$659$	2.84942	+	1.03711i	0.110998	+	0.0403999i	−0.285924	+	0.958252i	$0.592301\pi$
$660$		0			0
$661$	17.7441	+	14.8890i	0.690164	+	0.579116i	0.918956	−	0.394359i	$-0.129033\pi$
$661$	17.7441	+	14.8890i	0.690164	+	0.579116i	−0.228793	+	0.973475i	$0.573478\pi$
$662$	−14.9029	−	12.5050i	−0.579216	−	0.486020i
$663$		0			0
$664$	6.02983	+	2.19468i	0.234003	+	0.0851701i
$665$	8.33109	−	14.4299i	0.323066	−	0.559566i
$666$		0			0
$667$	−10.7788	−	18.6694i	−0.417357	−	0.722883i
$668$	−1.27288	−	7.21886i	−0.0492492	−	0.279306i
$669$		0			0
$670$	−17.0285	+	6.19787i	−0.657869	+	0.239445i
$671$	2.88841	−	16.3810i	0.111506	−	0.632381i
$672$		0			0
$673$	−18.0612	+	15.1551i	−0.696208	+	0.584188i	−0.920692	−	0.390290i	$-0.872375\pi$
$673$	−18.0612	+	15.1551i	−0.696208	+	0.584188i	0.224484	+	0.974478i	$0.427930\pi$
$674$	−11.8178			−0.455204
$675$		0			0
$676$	−25.0081			−0.961850
$677$	−9.98972	+	8.38237i	−0.383936	+	0.322161i	−0.814245	−	0.580521i	$-0.802849\pi$
$677$	−9.98972	+	8.38237i	−0.383936	+	0.322161i	0.430309	+	0.902682i	$0.358405\pi$
$678$		0			0
$679$	1.65219	−	9.37004i	0.0634053	−	0.359589i
$680$	−9.15998	+	3.33396i	−0.351269	+	0.127852i
$681$		0			0
$682$	−1.39728	−	7.92439i	−0.0535048	−	0.303441i
$683$	−11.2143	−	19.4238i	−0.429104	−	0.743230i	0.567690	−	0.823242i	$-0.307837\pi$
$683$	−11.2143	−	19.4238i	−0.429104	−	0.743230i	−0.996794	+	0.0800127i	$0.974504\pi$
$684$		0			0
$685$	15.5720	−	26.9715i	0.594976	−	1.03053i
$686$	0.964836	+	0.351172i	0.0368376	+	0.0134078i
$687$		0			0
$688$	−7.33218	−	6.15243i	−0.279537	−	0.234559i
$689$	60.9566	+	51.1486i	2.32226	+	1.94861i
$690$		0			0
$691$	−15.4584	−	5.62641i	−0.588067	−	0.214039i	0.0308123	−	0.999525i	$-0.490191\pi$
$691$	−15.4584	−	5.62641i	−0.588067	−	0.214039i	−0.618879	+	0.785486i	$0.712413\pi$
$692$	11.6457	−	20.1710i	0.442704	−	0.766786i
$693$		0			0
$694$	0.334958	+	0.580164i	0.0127148	+	0.0220227i
$695$	6.19298	+	35.1222i	0.234913	+	1.33226i
$696$		0			0
$697$	3.60598	−	1.31247i	0.136586	−	0.0497133i
$698$	6.47859	−	36.7419i	0.245218	−	1.39070i
$699$		0			0
$700$	−6.82429	+	5.72626i	−0.257934	+	0.216432i
$701$	−22.8729			−0.863899			−0.431949	−	0.901898i	$-0.642174\pi$
$701$	−22.8729			−0.863899			−0.431949	+	0.901898i	$0.642174\pi$
$702$		0			0
$703$	37.3007			1.40682
$704$	−9.23109	+	7.74581i	−0.347910	+	0.291931i
$705$		0			0
$706$	0.268815	−	1.52452i	0.0101170	−	0.0573762i
$707$	−5.90378	+	2.14880i	−0.222035	+	0.0808140i
$708$		0			0
$709$	1.16037	+	6.58080i	0.0435787	+	0.247147i	0.998813	−	0.0487022i	$-0.0155085\pi$
$709$	1.16037	+	6.58080i	0.0435787	+	0.247147i	−0.955235	+	0.295849i	$0.904397\pi$
$710$	−10.5984	−	18.3569i	−0.397750	−	0.688923i
$711$		0			0
$712$	1.25615	−	2.17571i	0.0470761	−	0.0815382i
$713$	13.3927	+	4.87456i	0.501562	+	0.182554i
$714$		0			0
$715$	29.9140	+	25.1009i	1.11872	+	0.938719i
$716$	14.2999	+	11.9990i	0.534411	+	0.448424i
$717$		0			0
$718$	−35.9325	−	13.0784i	−1.34099	−	0.488080i
$719$	−16.4784	+	28.5413i	−0.614539	+	1.06441i	0.375926	+	0.926650i	$0.377325\pi$
$719$	−16.4784	+	28.5413i	−0.614539	+	1.06441i	−0.990465	+	0.137763i	$0.956009\pi$
$720$		0			0
$721$	3.05218	+	5.28653i	0.113669	+	0.196881i
$722$	−0.0452775	−	0.256782i	−0.00168505	−	0.00955642i
$723$		0			0
$724$	16.0456	−	5.84012i	0.596330	−	0.217046i
$725$	11.8408	−	67.1527i	0.439757	−	2.49399i
$726$		0			0
$727$	12.4578	−	10.4534i	0.462035	−	0.387694i	−0.381844	−	0.924227i	$-0.624711\pi$
$727$	12.4578	−	10.4534i	0.462035	−	0.387694i	0.843879	+	0.536533i	$0.180266\pi$
$728$	−18.9953			−0.704013
$729$		0			0
$730$	5.89564			0.218208
$731$	5.12617	−	4.30137i	0.189598	−	0.159092i
$732$		0			0
$733$	7.99914	−	45.3654i	0.295455	−	1.67561i	−0.369892	−	0.929075i	$-0.620605\pi$
$733$	7.99914	−	45.3654i	0.295455	−	1.67561i	0.665347	−	0.746534i	$-0.268284\pi$
$734$	32.5984	−	11.8648i	1.20323	−	0.437939i
$735$		0			0
$736$	−2.48350	−	14.0846i	−0.0915429	−	0.519166i
$737$	−3.80532	−	6.59101i	−0.140171	−	0.242783i
$738$		0			0
$739$	−23.3972	+	40.5251i	−0.860679	+	1.49074i	0.0105964	+	0.999944i	$0.496627\pi$
$739$	−23.3972	+	40.5251i	−0.860679	+	1.49074i	−0.871275	+	0.490795i	$0.836706\pi$
$740$	−28.6880	−	10.4416i	−1.05459	−	0.383840i
$741$		0			0
$742$	9.96571	+	8.36223i	0.365853	+	0.306987i
$743$	−12.6273	−	10.5955i	−0.463249	−	0.388712i	0.381076	−	0.924544i	$-0.375554\pi$
$743$	−12.6273	−	10.5955i	−0.463249	−	0.388712i	−0.844325	+	0.535832i	$0.819998\pi$
$744$		0			0
$745$	27.5692	+	10.0344i	1.01006	+	0.367631i
$746$	2.47142	−	4.28062i	0.0904849	−	0.156725i
$747$		0			0
$748$	−0.657198	−	1.13830i	−0.0240295	−	0.0416204i
$749$	−0.377522	−	2.14103i	−0.0137944	−	0.0782317i
$750$		0			0
$751$	−40.0385	+	14.5728i	−1.46102	+	0.531769i	−0.945647	−	0.325194i	$-0.894570\pi$
$751$	−40.0385	+	14.5728i	−1.46102	+	0.531769i	−0.515377	+	0.856963i	$0.672348\pi$
$752$	0.0328549	−	0.186329i	0.00119809	−	0.00679473i
$753$		0			0
$754$	35.7598	−	30.0060i	1.30230	−	1.09276i
$755$	52.7074			1.91822
$756$		0			0
$757$	24.6290			0.895155			0.447578	−	0.894245i	$-0.352287\pi$
$757$	24.6290			0.895155			0.447578	+	0.894245i	$0.352287\pi$
$758$	20.3637	−	17.0872i	0.739644	−	0.620635i
$759$		0			0
$760$	−8.75122	+	49.6306i	−0.317440	+	1.80029i
$761$	−24.8848	+	9.05734i	−0.902074	+	0.328328i	−0.751084	−	0.660207i	$-0.770469\pi$
$761$	−24.8848	+	9.05734i	−0.902074	+	0.328328i	−0.150991	+	0.988535i	$0.548246\pi$
$762$		0			0
$763$	−0.654157	−	3.70991i	−0.0236821	−	0.134308i
$764$	−5.03150	−	8.71482i	−0.182033	−	0.315291i
$765$		0			0
$766$	−10.4618	+	18.1204i	−0.378002	+	0.654718i
$767$	19.7457	+	7.18684i	0.712975	+	0.259502i
$768$		0			0
$769$	−9.23195	−	7.74652i	−0.332913	−	0.279347i	0.460973	−	0.887414i	$-0.347501\pi$
$769$	−9.23195	−	7.74652i	−0.332913	−	0.279347i	−0.793885	+	0.608067i	$0.791945\pi$
$770$	4.89061	+	4.10371i	0.176245	+	0.147887i
$771$		0			0
$772$	−15.3441	−	5.58479i	−0.552245	−	0.201001i
$773$	6.38630	−	11.0614i	0.229699	−	0.397851i	−0.728020	−	0.685556i	$-0.759559\pi$
$773$	6.38630	−	11.0614i	0.229699	−	0.397851i	0.957719	+	0.287705i	$0.0928924\pi$
$774$		0			0
$775$	22.5406	+	39.0414i	0.809681	+	1.40241i
$776$	4.99720	+	28.3405i	0.179389	+	1.01737i
$777$		0			0
$778$	5.38129	−	1.95863i	0.192929	−	0.0702203i
$779$	3.44506	−	19.5379i	0.123432	−	0.700018i
$780$		0			0
$781$	6.81951	−	5.72225i	0.244021	−	0.204758i
$782$	−2.59504			−0.0927985
$783$		0			0
$784$	−1.21398			−0.0433563
$785$	−6.67890	+	5.60426i	−0.238380	+	0.200025i
$786$		0			0
$787$	1.73622	−	9.84659i	0.0618895	−	0.350993i	−0.938100	−	0.346365i	$-0.887416\pi$
$787$	1.73622	−	9.84659i	0.0618895	−	0.350993i	0.999989	−	0.00462780i	$-0.00147308\pi$
$788$	−0.637241	+	0.231937i	−0.0227008	+	0.00826241i
$789$		0			0
$790$	4.18440	+	23.7309i	0.148874	+	0.844307i
$791$	2.80251	+	4.85409i	0.0996457	+	0.172591i
$792$		0			0
$793$	−31.8984	+	55.2496i	−1.13274	+	1.96197i
$794$	13.4328	+	4.88913i	0.476712	+	0.173509i
$795$		0			0
$796$	−3.74128	−	3.13931i	−0.132606	−	0.111270i
$797$	33.1759	+	27.8379i	1.17515	+	0.986069i	0.999999	+	0.00152789i	$0.000486342\pi$
$797$	33.1759	+	27.8379i	1.17515	+	0.986069i	0.175153	+	0.984541i	$0.443958\pi$
$798$		0			0
$799$	0.124301	+	0.0452419i	0.00439746	+	0.00160054i
$800$	22.6191	−	39.1774i	0.799706	−	1.38513i
$801$		0			0
$802$	−0.398686	−	0.690544i	−0.0140781	−	0.0243840i
$803$	0.429964	+	2.43844i	0.0151731	+	0.0860508i
$804$		0			0
$805$	−10.6259	+	3.86749i	−0.374512	+	0.136311i
$806$	−5.35914	+	30.3932i	−0.188768	+	1.07055i
$807$		0			0
$808$	14.5568	−	12.2146i	0.512106	−	0.429708i
$809$	−19.6620			−0.691278			−0.345639	−	0.938367i	$-0.612338\pi$
$809$	−19.6620			−0.691278			−0.345639	+	0.938367i	$0.612338\pi$
$810$		0			0
$811$	−6.55208			−0.230075			−0.115037	−	0.993361i	$-0.536699\pi$
$811$	−6.55208			−0.230075			−0.115037	+	0.993361i	$0.536699\pi$
$812$	−5.24486	+	4.40096i	−0.184058	+	0.154443i
$813$		0			0
$814$	−2.48179	+	14.0749i	−0.0869867	+	0.493326i
$815$	−54.7769	+	19.9371i	−1.91875	+	0.698368i
$816$		0			0
$817$	−6.00757	−	34.0706i	−0.210178	−	1.19198i
$818$	−7.96542	−	13.7965i	−0.278504	−	0.482384i
$819$		0			0
$820$	−8.11885	+	14.0623i	−0.283522	+	0.491075i
$821$	−45.5151	−	16.5662i	−1.58849	−	0.578163i	−0.611461	−	0.791274i	$-0.709418\pi$
$821$	−45.5151	−	16.5662i	−1.58849	−	0.578163i	−0.977028	+	0.213111i	$0.931640\pi$
$822$		0			0
$823$	−34.8141	−	29.2125i	−1.21354	−	1.01828i	−0.999137	−	0.0415387i	$-0.986774\pi$
$823$	−34.8141	−	29.2125i	−1.21354	−	1.01828i	−0.214406	−	0.976745i	$-0.568782\pi$
$824$	−14.1436	−	11.8679i	−0.492716	−	0.413438i
$825$		0			0
$826$	3.22820	+	1.17497i	0.112323	+	0.0408823i
$827$	18.7421	−	32.4622i	0.651725	−	1.12882i	−0.330979	−	0.943638i	$-0.607379\pi$
$827$	18.7421	−	32.4622i	0.651725	−	1.12882i	0.982704	−	0.185183i	$-0.0592879\pi$
$828$		0			0
$829$	6.33851	+	10.9786i	0.220146	+	0.381303i	0.954852	−	0.297082i	$-0.0960134\pi$
$829$	6.33851	+	10.9786i	0.220146	+	0.381303i	−0.734706	+	0.678385i	$0.762680\pi$
$830$	1.43636	+	8.14599i	0.0498567	+	0.282751i
$831$		0			0
$832$	43.4305	−	15.8074i	1.50568	−	0.548023i
$833$	0.147381	−	0.835838i	0.00510644	−	0.0289601i
$834$		0			0
$835$	22.5454	−	18.9178i	0.780214	−	0.654677i
$836$	−6.79540			−0.235024
$837$		0			0
$838$	−11.8612			−0.409740
$839$	−7.69628	+	6.45794i	−0.265705	+	0.222953i	−0.765900	−	0.642960i	$-0.777706\pi$
$839$	−7.69628	+	6.45794i	−0.265705	+	0.222953i	0.500195	+	0.865913i	$0.333262\pi$
$840$		0			0
$841$	4.06456	−	23.0512i	0.140157	−	0.794871i
$842$	−26.2578	+	9.55706i	−0.904904	+	0.329358i
$843$		0			0
$844$	0.390699	+	2.21577i	0.0134484	+	0.0762698i
$845$	−50.2038	−	86.9556i	−1.72706	−	2.99136i
$846$		0			0
$847$	4.15937	−	7.20424i	0.142918	−	0.247541i
$848$	−14.4538	−	5.26077i	−0.496347	−	0.180656i
$849$		0			0
$850$	−6.28796	−	5.27623i	−0.215675	−	0.180973i
$851$	−19.3918	−	16.2716i	−0.664741	−	0.557784i
$852$		0			0
$853$	−7.77992	−	2.83166i	−0.266379	−	0.0969542i	0.205377	−	0.978683i	$-0.434158\pi$
$853$	−7.77992	−	2.83166i	−0.266379	−	0.0969542i	−0.471757	+	0.881729i	$0.656380\pi$
$854$	−5.21503	+	9.03269i	−0.178454	+	0.309092i
$855$		0			0
$856$	3.28783	+	5.69468i	0.112376	+	0.194640i
$857$	−5.61976	−	31.8712i	−0.191967	−	1.08870i	−0.916672	−	0.399641i	$-0.869135\pi$
$857$	−5.61976	−	31.8712i	−0.191967	−	1.08870i	0.724704	−	0.689060i	$-0.241976\pi$
$858$		0			0
$859$	−26.9649	+	9.81442i	−0.920031	+	0.334864i	−0.758251	−	0.651963i	$-0.773946\pi$
$859$	−26.9649	+	9.81442i	−0.920031	+	0.334864i	−0.161780	+	0.986827i	$0.551723\pi$
$860$	−4.91696	+	27.8854i	−0.167667	+	0.950886i
$861$		0			0
$862$	−29.5229	+	24.7727i	−1.00555	+	0.843760i
$863$	−42.3613			−1.44200			−0.720998	−	0.692937i	$-0.756316\pi$
$863$	−42.3613			−1.44200			−0.720998	+	0.692937i	$0.756316\pi$
$864$		0			0
$865$	93.5153			3.17961
$866$	25.9506	−	21.7751i	0.881836	−	0.739948i
$867$		0			0
$868$	0.786019	−	4.45774i	0.0266792	−	0.151305i
$869$	−9.50996	+	3.46134i	−0.322603	+	0.117418i
$870$		0			0
$871$	5.06876	+	28.7463i	0.171748	+	0.974033i
$872$	5.69703	+	9.86754i	0.192926	+	0.334157i
$873$		0			0
$874$	−6.70816	+	11.6189i	−0.226907	+	0.393014i
$875$	−15.7692	−	5.73952i	−0.533096	−	0.194031i
$876$		0			0
$877$	3.60840	+	3.02781i	0.121847	+	0.102242i	0.701675	−	0.712497i	$-0.252436\pi$
$877$	3.60840	+	3.02781i	0.121847	+	0.102242i	−0.579828	+	0.814739i	$0.696880\pi$
$878$	1.92203	+	1.61278i	0.0648655	+	0.0544286i
$879$		0			0
$880$	−7.09313	−	2.58169i	−0.239109	−	0.0870287i
$881$	13.0334	−	22.5746i	0.439107	−	0.760556i	−0.558513	−	0.829495i	$-0.688628\pi$
$881$	13.0334	−	22.5746i	0.439107	−	0.760556i	0.997621	+	0.0689391i	$0.0219614\pi$
$882$		0			0
$883$	−15.8514	−	27.4555i	−0.533443	−	0.923951i	−0.999237	−	0.0390577i	$-0.987564\pi$
$883$	−15.8514	−	27.4555i	−0.533443	−	0.923951i	0.465794	−	0.884893i	$-0.345769\pi$
$884$	0.875399	+	4.96464i	0.0294429	+	0.166979i
$885$		0			0
$886$	26.9443	−	9.80692i	0.905211	−	0.329470i
$887$	−3.07385	+	17.4327i	−0.103210	+	0.585332i	0.888710	+	0.458469i	$0.151602\pi$
$887$	−3.07385	+	17.4327i	−0.103210	+	0.585332i	−0.991920	+	0.126863i	$0.959509\pi$
$888$		0			0
$889$	−3.83142	+	3.21494i	−0.128502	+	0.107826i
$890$	3.23850			0.108555
$891$		0			0
$892$	8.88489			0.297488
$893$	0.523881	−	0.439589i	0.0175310	−	0.0147103i
$894$		0			0
$895$	−13.0147	+	73.8100i	−0.435033	+	2.46720i
$896$	−1.92576	+	0.700920i	−0.0643351	+	0.0234161i
$897$		0			0
$898$	−2.81753	−	15.9790i	−0.0940223	−	0.533227i
$899$	17.3237	+	30.0056i	0.577779	+	1.00074i
$900$		0			0
$901$	5.37684	−	9.31297i	0.179129	−	0.310260i
$902$	7.14315	+	2.59989i	0.237841	+	0.0865670i
$903$		0			0
$904$	−12.9867	−	10.8971i	−0.431930	−	0.362432i
$905$	52.5182	+	44.0680i	1.74577	+	1.46487i
$906$		0			0
$907$	−0.423479	−	0.154134i	−0.0140614	−	0.00511792i	0.334980	−	0.942225i	$-0.391270\pi$
$907$	−0.423479	−	0.154134i	−0.0140614	−	0.00511792i	−0.349041	+	0.937107i	$0.613493\pi$
$908$	−9.99671	+	17.3148i	−0.331753	+	0.574612i
$909$		0			0
$910$	−12.2430	−	21.2056i	−0.405853	−	0.702957i
$911$	−6.95902	−	39.4665i	−0.230563	−	1.30759i	−0.851760	−	0.523931i	$-0.824465\pi$
$911$	−6.95902	−	39.4665i	−0.230563	−	1.30759i	0.621198	−	0.783654i	$-0.286646\pi$
$912$		0			0
$913$	−3.26444	+	1.18816i	−0.108037	+	0.0393223i
$914$	6.97029	−	39.5305i	0.230557	−	1.30755i
$915$		0			0
$916$	5.87818	−	4.93238i	0.194221	−	0.162970i
$917$	−18.7756			−0.620024
$918$		0			0
$919$	7.56702			0.249613			0.124807	−	0.992181i	$-0.460169\pi$
$919$	7.56702			0.249613			0.124807	+	0.992181i	$0.460169\pi$
$920$	26.1998	−	21.9843i	0.863783	−	0.724800i
$921$		0			0
$922$	−3.55059	+	20.1364i	−0.116932	+	0.663156i
$923$	−32.0845	+	11.6778i	−1.05607	+	0.384379i
$924$		0			0
$925$	−13.9042	−	78.8545i	−0.457167	−	2.59272i
$926$	8.48507	+	14.6966i	0.278837	+	0.482959i
$927$		0			0
$928$	17.3841	−	30.1101i	0.570660	−	0.988412i
$929$	12.2038	+	4.44181i	0.400393	+	0.145731i	0.534365	−	0.845254i	$-0.320551\pi$
$929$	12.2038	+	4.44181i	0.400393	+	0.145731i	−0.133972	+	0.990985i	$0.542773\pi$
$930$		0			0
$931$	−3.36135	−	2.82051i	−0.110164	−	0.0924384i
$932$	6.53828	+	5.48627i	0.214169	+	0.179709i
$933$		0			0
$934$	29.2528	+	10.6472i	0.957181	+	0.348386i
$935$	2.63865	−	4.57028i	0.0862931	−	0.149464i
$936$		0			0
$937$	−3.38631	−	5.86525i	−0.110626	−	0.191609i	0.805397	−	0.592736i	$-0.201952\pi$
$937$	−3.38631	−	5.86525i	−0.110626	−	0.191609i	−0.916023	+	0.401126i	$0.868619\pi$
$938$	0.828685	+	4.69970i	0.0270575	+	0.153451i
$939$		0			0
$940$	−0.525972	+	0.191438i	−0.0171553	+	0.00624402i
$941$	−6.31504	+	35.8144i	−0.205864	+	1.16751i	0.690209	+	0.723610i	$0.257518\pi$
$941$	−6.31504	+	35.8144i	−0.205864	+	1.16751i	−0.896074	+	0.443905i	$0.853593\pi$
$942$		0			0
$943$	−10.3140	+	8.65447i	−0.335870	+	0.281828i
$944$	−4.06179			−0.132200
$945$		0			0
$946$	13.2558			0.430983
$947$	−28.0374	+	23.5262i	−0.911093	+	0.764498i	−0.972327	−	0.233626i	$-0.924941\pi$
$947$	−28.0374	+	23.5262i	−0.911093	+	0.764498i	0.0612337	+	0.998123i	$0.480496\pi$
$948$		0			0
$949$	1.64908	−	9.35240i	0.0535314	−	0.303592i
$950$	−39.8778	+	14.5143i	−1.29381	+	0.470907i
$951$		0			0
$952$	0.445766	+	2.52807i	0.0144474	+	0.0819351i
$953$	20.0649	+	34.7534i	0.649965	+	1.12577i	0.983131	+	0.182904i	$0.0585499\pi$
$953$	20.0649	+	34.7534i	0.649965	+	1.12577i	−0.333165	+	0.942868i	$0.608117\pi$
$954$		0			0
$955$	20.2015	−	34.9900i	0.653705	−	1.13225i
$956$	5.46909	+	1.99059i	0.176883	+	0.0643801i
$957$		0			0
$958$	13.2461	+	11.1148i	0.427962	+	0.359102i
$959$	−6.28285	−	5.27194i	−0.202884	−	0.170240i
$960$		0			0
$961$	7.60561	+	2.76822i	0.245342	+	0.0892973i
$962$	27.4078	−	47.4718i	0.883664	−	1.53055i
$963$		0			0
$964$	8.45850	+	14.6505i	0.272430	+	0.471862i
$965$	−11.3844	−	64.5643i	−0.366478	−	2.07840i
$966$		0			0
$967$	−7.62789	+	2.77632i	−0.245296	+	0.0892806i	−0.461743	−	0.887014i	$-0.652776\pi$
$967$	−7.62789	+	2.77632i	−0.245296	+	0.0892806i	0.216446	+	0.976295i	$0.430553\pi$
$968$	−4.36912	+	24.7785i	−0.140429	+	0.796412i
$969$		0			0
$970$	−28.4174	+	23.8450i	−0.912426	+	0.765616i
$971$	43.0646			1.38201			0.691004	−	0.722851i	$-0.257169\pi$
$971$	43.0646			1.38201			0.691004	+	0.722851i	$0.257169\pi$
$972$		0			0
$973$	9.39200			0.301094
$974$	−13.1162	+	11.0058i	−0.420271	+	0.352649i
$975$		0			0
$976$	2.14141	−	12.1445i	0.0685448	−	0.388737i
$977$	−3.42289	+	1.24583i	−0.109508	+	0.0398576i	−0.396193	−	0.918167i	$-0.629669\pi$
$977$	−3.42289	+	1.24583i	−0.109508	+	0.0398576i	0.286685	+	0.958025i	$0.407447\pi$
$978$		0			0
$979$	0.236180	+	1.33945i	0.00754836	+	0.0428089i
$980$	1.79567	+	3.11020i	0.0573607	+	0.0993517i
$981$		0			0
$982$	4.47686	−	7.75416i	0.142862	−	0.247445i
$983$	45.1557	+	16.4353i	1.44024	+	0.524205i	0.939848	−	0.341593i	$-0.110966\pi$
$983$	45.1557	+	16.4353i	1.44024	+	0.524205i	0.500394	+	0.865798i	$0.333188\pi$
$984$		0			0
$985$	−2.08573	−	1.75014i	−0.0664569	−	0.0557640i
$986$	−4.83266	−	4.05508i	−0.153903	−	0.129140i
$987$		0			0
$988$	24.4913	+	8.91409i	0.779171	+	0.283595i
$989$	−11.7394	+	20.3332i	−0.373290	+	0.646557i
$990$		0			0
$991$	−20.1097	−	34.8310i	−0.638806	−	1.10644i	−0.985695	−	0.168538i	$-0.946095\pi$
$991$	−20.1097	−	34.8310i	−0.638806	−	1.10644i	0.346889	−	0.937906i	$-0.387238\pi$
$992$	3.99149	+	22.6369i	0.126730	+	0.718721i
$993$		0			0
$994$	−5.24545	+	1.90919i	−0.166376	+	0.0605558i
$995$	3.40504	−	19.3110i	0.107947	−	0.612198i
$996$		0			0
$997$	−4.96978	+	4.17014i	−0.157394	+	0.132070i	−0.718084	−	0.695957i	$-0.754981\pi$
$997$	−4.96978	+	4.17014i	−0.157394	+	0.132070i	0.560689	+	0.828026i	$0.310536\pi$
$998$	1.22061			0.0386378
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.v.b.442.4		54
3.2	odd	2		189.2.v.a.22.6	✓	54
27.4	even	9		5103.2.a.f.1.12		27
27.11	odd	18		189.2.v.a.43.6	yes	54
27.16	even	9	inner	567.2.v.b.127.4		54
27.23	odd	18		5103.2.a.i.1.16		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.6	✓	54	3.2	odd	2
189.2.v.a.43.6	yes	54	27.11	odd	18
567.2.v.b.127.4		54	27.16	even	9	inner
567.2.v.b.442.4		54	1.1	even	1	trivial
5103.2.a.f.1.12		27	27.4	even	9
5103.2.a.i.1.16		27	27.23	odd	18

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.786541 + 0.659987i) q^{2} +(-0.164231 + 0.931402i) q^{4} +(-3.56827 + 1.29874i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.51229 - 2.61937i) q^{8} +O(q^{10})\)	\(q+(-0.786541 + 0.659987i) q^{2} +(-0.164231 + 0.931402i) q^{4} +(-3.56827 + 1.29874i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.51229 - 2.61937i) q^{8} +(1.94944 - 3.37653i) q^{10} +(1.53871 + 0.560043i) q^{11} +(-4.81098 - 4.03689i) q^{13} +(-0.786541 - 0.659987i) q^{14} +(1.14077 + 0.415205i) q^{16} +(-0.424366 + 0.735023i) q^{17} +(2.19397 + 3.80006i) q^{19} +(-0.623631 - 3.53679i) q^{20} +(-1.57988 + 0.575028i) q^{22} +(0.517102 - 2.93263i) q^{23} +(7.21559 - 6.05460i) q^{25} +6.44833 q^{26} -0.945770 q^{28} +(5.54559 - 4.65331i) q^{29} +(-0.831089 + 4.71334i) q^{31} +(4.51308 - 1.64263i) q^{32} +(-0.151324 - 0.858202i) q^{34} +(-1.89864 - 3.28853i) q^{35} +(4.25038 - 7.36187i) q^{37} +(-4.23363 - 1.54092i) q^{38} +(8.79817 + 7.38254i) q^{40} +(-3.46354 - 2.90626i) q^{41} +(-7.40891 - 2.69662i) q^{43} +(-0.774329 + 1.34118i) q^{44} +(1.52878 + 2.64792i) q^{46} +(-0.0270638 - 0.153487i) q^{47} +(-0.939693 + 0.342020i) q^{49} +(-1.67941 + 9.52438i) q^{50} +(4.55008 - 3.81797i) q^{52} -12.6703 q^{53} -6.21787 q^{55} +(2.31697 - 1.94417i) q^{56} +(-1.29072 + 7.32003i) q^{58} +(-3.14407 + 1.14435i) q^{59} +(-1.76396 - 10.0039i) q^{61} +(-2.45705 - 4.25574i) q^{62} +(-3.67959 + 6.37324i) q^{64} +(22.4098 + 8.15649i) q^{65} +(-3.56045 - 2.98758i) q^{67} +(-0.614908 - 0.515969i) q^{68} +(3.66374 + 1.33349i) q^{70} +(2.71831 - 4.70826i) q^{71} +(0.756070 + 1.30955i) q^{73} +(1.51564 + 8.59561i) q^{74} +(-3.89970 + 1.41938i) q^{76} +(-0.284341 + 1.61258i) q^{77} +(-4.73453 + 3.97274i) q^{79} -4.60980 q^{80} +4.64231 q^{82} +(-1.62520 + 1.36370i) q^{83} +(0.559645 - 3.17390i) q^{85} +(7.60715 - 2.76878i) q^{86} +(-0.860016 - 4.87739i) q^{88} +(0.415312 + 0.719341i) q^{89} +(3.14014 - 5.43889i) q^{91} +(2.64654 + 0.963260i) q^{92} +(0.122586 + 0.102862i) q^{94} +(-12.7640 - 10.7102i) q^{95} +(-8.94079 - 3.25418i) q^{97} +(0.513378 - 0.889197i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) \) 54 * q + 3 * q^5 + 27 * q^8	\( 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) \) 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

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