LMFDB - Embedded newform 567.2.bd.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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([11, 3]))

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, 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:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0159182 + 0.00280680i) q^{2} +(-1.87914 + 0.683951i) q^{4} +(-3.75147 + 1.36542i) q^{5} +(0.157938 + 2.64103i) q^{7} +(0.0559891 - 0.0323253i) q^{8} +O(q^{10})$	\(q+(-0.0159182 + 0.00280680i) q^{2} +(-1.87914 + 0.683951i) q^{4} +(-3.75147 + 1.36542i) q^{5} +(0.157938 + 2.64103i) q^{7} +(0.0559891 - 0.0323253i) q^{8} +(0.0558840 - 0.0322646i) q^{10} +(1.76436 - 4.84753i) q^{11} +(-0.220791 - 0.606618i) q^{13} +(-0.00992693 - 0.0415971i) q^{14} +(3.06298 - 2.57014i) q^{16} +(-1.69383 - 2.93380i) q^{17} +(0.328436 + 0.189623i) q^{19} +(6.11565 - 5.13164i) q^{20} +(-0.0144792 + 0.0821158i) q^{22} +(0.993035 + 0.175099i) q^{23} +(8.37891 - 7.03074i) q^{25} +(0.00521724 + 0.00903653i) q^{26} +(-2.10312 - 4.85485i) q^{28} +(-1.97120 + 5.41582i) q^{29} +(-2.20741 - 6.06480i) q^{31} +(-0.124656 + 0.148560i) q^{32} +(0.0351973 + 0.0419465i) q^{34} +(-4.19863 - 9.69210i) q^{35} +6.16814 q^{37} +(-0.00576033 - 0.00209659i) q^{38} +(-0.165904 + 0.197716i) q^{40} +(-0.266252 + 0.0969077i) q^{41} +(-1.45052 - 8.22633i) q^{43} +10.3159i q^{44} -0.0162988 q^{46} +(-6.91258 - 2.51597i) q^{47} +(-6.95011 + 0.834239i) q^{49} +(-0.113643 + 0.135434i) q^{50} +(0.829794 + 0.988910i) q^{52} +(-1.71989 - 0.992981i) q^{53} +20.5944i q^{55} +(0.0942150 + 0.142764i) q^{56} +(0.0161767 - 0.0917427i) q^{58} +(2.62371 + 2.20155i) q^{59} +(-2.75545 + 7.57053i) q^{61} +(0.0521605 + 0.0903447i) q^{62} +(-3.99687 + 6.92277i) q^{64} +(1.65658 + 1.97424i) q^{65} +(1.63911 - 9.29584i) q^{67} +(5.18952 + 4.35453i) q^{68} +(0.0940381 + 0.142496i) q^{70} +(-8.57363 - 4.94999i) q^{71} -7.08887i q^{73} +(-0.0981854 + 0.0173127i) q^{74} +(-0.746871 - 0.131693i) q^{76} +(13.0811 + 3.89411i) q^{77} +(-0.222353 - 1.26102i) q^{79} +(-7.98133 + 13.8241i) q^{80} +(0.00396624 - 0.00228991i) q^{82} +(8.07527 + 2.93916i) q^{83} +(10.3602 + 8.69327i) q^{85} +(0.0461793 + 0.126877i) q^{86} +(-0.0579132 - 0.328442i) q^{88} +(2.67849 - 4.63928i) q^{89} +(1.56723 - 0.678924i) q^{91} +(-1.98581 + 0.350152i) q^{92} +(0.117097 + 0.0206474i) q^{94} +(-1.49103 - 0.262910i) q^{95} +(-7.39427 + 1.30381i) q^{97} +(0.108291 - 0.0327871i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.0159182	+	0.00280680i	−0.0112558	+	0.00198471i	−0.179273	−	0.983799i	$-0.557375\pi$
$2$	−0.0159182	+	0.00280680i	−0.0112558	+	0.00198471i	0.168017	+	0.985784i	$0.446264\pi$
$3$		0			0
$3$		0			0
$4$	−1.87914	+	0.683951i	−0.939570	+	0.341975i
$5$	−3.75147	+	1.36542i	−1.67771	+	0.610636i	−0.992993	−	0.118175i	$-0.962296\pi$
$5$	−3.75147	+	1.36542i	−1.67771	+	0.610636i	−0.684715	+	0.728811i	$0.740073\pi$
$6$		0			0
$7$	0.157938	+	2.64103i	0.0596949	+	0.998217i
$7$	0.157938	+	2.64103i	0.0596949	+	0.998217i
$8$	0.0559891	−	0.0323253i	0.0197951	−	0.0114287i
$9$		0			0
$10$	0.0558840	−	0.0322646i	0.0176721	−	0.0102030i
$11$	1.76436	−	4.84753i	0.531973	−	1.46158i	−0.324746	−	0.945801i	$-0.605279\pi$
$11$	1.76436	−	4.84753i	0.531973	−	1.46158i	0.856719	−	0.515783i	$-0.172499\pi$
$12$		0			0
$13$	−0.220791	−	0.606618i	−0.0612364	−	0.168246i	0.905301	−	0.424770i	$-0.139645\pi$
$13$	−0.220791	−	0.606618i	−0.0612364	−	0.168246i	−0.966538	+	0.256524i	$0.917423\pi$
$14$	−0.00992693	−	0.0415971i	−0.00265308	−	0.0111173i
$15$		0			0
$16$	3.06298	−	2.57014i	0.765744	−	0.642536i
$17$	−1.69383	−	2.93380i	−0.410815	−	0.711552i	0.584165	−	0.811635i	$-0.301422\pi$
$17$	−1.69383	−	2.93380i	−0.410815	−	0.711552i	−0.994979	+	0.100084i	$0.968089\pi$
$18$		0			0
$19$	0.328436	+	0.189623i	0.0753485	+	0.0435025i	0.537201	−	0.843454i	$-0.319482\pi$
$19$	0.328436	+	0.189623i	0.0753485	+	0.0435025i	−0.461852	+	0.886957i	$0.652815\pi$
$20$	6.11565	−	5.13164i	1.36750	−	1.14747i
$21$		0			0
$22$	−0.0144792	+	0.0821158i	−0.00308698	+	0.0175072i
$23$	0.993035	+	0.175099i	0.207062	+	0.0365106i	0.276217	−	0.961095i	$-0.410919\pi$
$23$	0.993035	+	0.175099i	0.207062	+	0.0365106i	−0.0691549	+	0.997606i	$0.522030\pi$
$24$		0			0
$25$	8.37891	−	7.03074i	1.67578	−	1.40615i
$26$	0.00521724	+	0.00903653i	0.00102318	+	0.00177221i
$27$		0			0
$28$	−2.10312	−	4.85485i	−0.397453	−	0.917480i
$29$	−1.97120	+	5.41582i	−0.366042	+	1.00569i	0.610810	+	0.791777i	$0.290844\pi$
$29$	−1.97120	+	5.41582i	−0.366042	+	1.00569i	−0.976852	+	0.213916i	$0.931378\pi$
$30$		0			0
$31$	−2.20741	−	6.06480i	−0.396462	−	1.08927i	−0.963995	−	0.265920i	$-0.914324\pi$
$31$	−2.20741	−	6.06480i	−0.396462	−	1.08927i	0.567533	−	0.823351i	$-0.307898\pi$
$32$	−0.124656	+	0.148560i	−0.0220363	+	0.0262619i
$33$		0			0
$34$	0.0351973	+	0.0419465i	0.00603628	+	0.00719376i
$35$	−4.19863	−	9.69210i	−0.709697	−	1.63826i
$36$		0			0
$37$	6.16814			1.01404			0.507018	−	0.861936i	$-0.330748\pi$
$37$	6.16814			1.01404			0.507018	+	0.861936i	$0.330748\pi$
$38$	−0.00576033	−	0.00209659i	−0.000934449	−	0.000340112i
$39$		0			0
$40$	−0.165904	+	0.197716i	−0.0262317	+	0.0312617i
$41$	−0.266252	+	0.0969077i	−0.0415816	+	0.0151344i	−0.362727	−	0.931895i	$-0.618154\pi$
$41$	−0.266252	+	0.0969077i	−0.0415816	+	0.0151344i	0.321146	+	0.947030i	$0.395932\pi$
$42$		0			0
$43$	−1.45052	−	8.22633i	−0.221203	−	1.25450i	−0.869812	−	0.493383i	$-0.835760\pi$
$43$	−1.45052	−	8.22633i	−0.221203	−	1.25450i	0.648610	−	0.761121i	$-0.275351\pi$
$44$			10.3159i			1.55518i
$45$		0			0
$46$	−0.0162988			−0.00240312
$47$	−6.91258	−	2.51597i	−1.00830	−	0.366992i	−0.215522	−	0.976499i	$-0.569145\pi$
$47$	−6.91258	−	2.51597i	−1.00830	−	0.366992i	−0.792781	+	0.609507i	$0.791368\pi$
$48$		0			0
$49$	−6.95011	+	0.834239i	−0.992873	+	0.119177i
$50$	−0.113643	+	0.135434i	−0.0160715	+	0.0191533i
$51$		0			0
$52$	0.829794	+	0.988910i	0.115072	+	0.137137i
$53$	−1.71989	−	0.992981i	−0.236246	−	0.136396i	0.377204	−	0.926130i	$-0.376885\pi$
$53$	−1.71989	−	0.992981i	−0.236246	−	0.136396i	−0.613450	+	0.789734i	$0.710219\pi$
$54$		0			0
$55$			20.5944i			2.77695i
$56$	0.0942150	+	0.142764i	0.0125900	+	0.0190776i
$57$		0			0
$58$	0.0161767	−	0.0917427i	0.00212411	−	0.0120464i
$59$	2.62371	+	2.20155i	0.341578	+	0.286618i	0.797398	−	0.603454i	$-0.206209\pi$
$59$	2.62371	+	2.20155i	0.341578	+	0.286618i	−0.455820	+	0.890072i	$0.650654\pi$
$60$		0			0
$61$	−2.75545	+	7.57053i	−0.352799	+	0.969307i	0.628668	+	0.777674i	$0.283601\pi$
$61$	−2.75545	+	7.57053i	−0.352799	+	0.969307i	−0.981467	+	0.191633i	$0.938622\pi$
$62$	0.0521605	+	0.0903447i	0.00662439	+	0.0114738i
$63$		0			0
$64$	−3.99687	+	6.92277i	−0.499608	+	0.865347i
$65$	1.65658	+	1.97424i	0.205474	+	0.244874i
$66$		0			0
$67$	1.63911	−	9.29584i	0.200249	−	1.13567i	−0.704494	−	0.709710i	$-0.748826\pi$
$67$	1.63911	−	9.29584i	0.200249	−	1.13567i	0.904743	−	0.425958i	$-0.140063\pi$
$68$	5.18952	+	4.35453i	0.629322	+	0.528064i
$69$		0			0
$70$	0.0940381	+	0.142496i	0.0112397	+	0.0170315i
$71$	−8.57363	−	4.94999i	−1.01750	−	0.587456i	−0.104123	−	0.994564i	$-0.533204\pi$
$71$	−8.57363	−	4.94999i	−1.01750	−	0.587456i	−0.913380	+	0.407109i	$0.866537\pi$
$72$		0			0
$73$		−	7.08887i		−	0.829690i	−0.909892	−	0.414845i	$-0.863836\pi$
$73$		−	7.08887i		−	0.829690i	0.909892	−	0.414845i	$-0.136164\pi$
$74$	−0.0981854	+	0.0173127i	−0.0114138	+	0.00201256i
$75$		0			0
$76$	−0.746871	−	0.131693i	−0.0856719	−	0.0151063i
$77$	13.0811	+	3.89411i	1.49073	+	0.443775i
$78$		0			0
$79$	−0.222353	−	1.26102i	−0.0250166	−	0.141876i	0.969741	−	0.244135i	$-0.0785041\pi$
$79$	−0.222353	−	1.26102i	−0.0250166	−	0.141876i	−0.994758	+	0.102259i	$0.967393\pi$
$80$	−7.98133	+	13.8241i	−0.892340	+	1.54558i
$81$		0			0
$82$	0.00396624	−	0.00228991i	0.000437998	−	0.000252878i
$83$	8.07527	+	2.93916i	0.886376	+	0.322614i	0.744780	−	0.667310i	$-0.232554\pi$
$83$	8.07527	+	2.93916i	0.886376	+	0.322614i	0.141596	+	0.989925i	$0.454777\pi$
$84$		0			0
$85$	10.3602	+	8.69327i	1.12373	+	0.942918i
$86$	0.0461793	+	0.126877i	0.00497964	+	0.0136815i
$87$		0			0
$88$	−0.0579132	−	0.328442i	−0.00617356	−	0.0350120i
$89$	2.67849	−	4.63928i	0.283920	−	0.491763i	−0.688427	−	0.725306i	$-0.741698\pi$
$89$	2.67849	−	4.63928i	0.283920	−	0.491763i	0.972347	+	0.233543i	$0.0750318\pi$
$90$		0			0
$91$	1.56723	−	0.678924i	0.164290	−	0.0711706i
$92$	−1.98581	+	0.350152i	−0.207035	+	0.0365059i
$93$		0			0
$94$	0.117097	+	0.0206474i	0.0120777	+	0.00212962i
$95$	−1.49103	−	0.262910i	−0.152977	−	0.0269739i
$96$		0			0
$97$	−7.39427	+	1.30381i	−0.750774	+	0.132382i	−0.535925	−	0.844265i	$-0.680037\pi$
$97$	−7.39427	+	1.30381i	−0.750774	+	0.132382i	−0.214849	+	0.976647i	$0.568926\pi$
$98$	0.108291	−	0.0327871i	0.0109391	−	0.00331200i
$99$		0			0
$100$	−10.9365	+	18.9425i	−1.09365	+	1.89425i
$101$	−1.98008	−	11.2296i	−0.197025	−	1.11738i	−0.909505	−	0.415693i	$-0.863539\pi$
$101$	−1.98008	−	11.2296i	−0.197025	−	1.11738i	0.712480	−	0.701692i	$-0.247572\pi$
$102$		0			0
$103$	−3.27445	−	8.99648i	−0.322641	−	0.886449i	−0.989918	−	0.141640i	$-0.954763\pi$
$103$	−3.27445	−	8.99648i	−0.322641	−	0.886449i	0.667277	−	0.744810i	$-0.267460\pi$
$104$	−0.0319710	−	0.0268269i	−0.00313502	−	0.00263059i
$105$		0			0
$106$	0.0301646	+	0.0109790i	0.00292985	+	0.00106638i
$107$	12.0916	−	6.98107i	1.16894	−	0.674885i	0.215507	−	0.976502i	$-0.430860\pi$
$107$	12.0916	−	6.98107i	1.16894	−	0.674885i	0.953429	+	0.301617i	$0.0975264\pi$
$108$		0			0
$109$	0.912496	−	1.58049i	0.0874012	−	0.151383i	−0.819011	−	0.573778i	$-0.805477\pi$
$109$	0.912496	−	1.58049i	0.0874012	−	0.151383i	0.906412	+	0.422395i	$0.138810\pi$
$110$	−0.0578044	−	0.327825i	−0.00551144	−	0.0312569i
$111$		0			0
$112$	7.27159	+	7.68350i	0.687101	+	0.726023i
$113$	−4.07591	−	0.718692i	−0.383429	−	0.0676089i	−0.0213886	−	0.999771i	$-0.506809\pi$
$113$	−4.07591	−	0.718692i	−0.383429	−	0.0676089i	−0.362041	+	0.932162i	$0.617920\pi$
$114$		0			0
$115$	−3.96442	+	0.699035i	−0.369684	+	0.0651853i
$116$		−	11.5253i		−	1.07010i
$117$		0			0
$118$	−0.0479439	−	0.0276804i	−0.00441360	−	0.00254819i
$119$	7.48075	−	4.93682i	0.685759	−	0.452558i
$120$		0			0
$121$	−11.9591	−	10.0349i	−1.08719	−	0.912259i
$122$	0.0226127	−	0.128243i	0.00204726	−	0.0116106i
$123$		0			0
$124$	8.29605	+	9.88685i	0.745008	+	0.887866i
$125$	−11.8527	+	20.5295i	−1.06014	+	1.83622i
$126$		0			0
$127$	−3.16383	−	5.47991i	−0.280744	−	0.486263i	0.690824	−	0.723023i	$-0.257248\pi$
$127$	−3.16383	−	5.47991i	−0.280744	−	0.486263i	−0.971568	+	0.236760i	$0.923915\pi$
$128$	0.176848	−	0.485887i	0.0156313	−	0.0429467i
$129$		0			0
$130$	−0.0319110	−	0.0267765i	−0.00279878	−	0.00234845i
$131$	−0.681494	+	3.86494i	−0.0595424	+	0.337682i	−0.999997	−	0.00223629i	$-0.999288\pi$
$131$	−0.681494	+	3.86494i	−0.0595424	+	0.337682i	0.940455	+	0.339918i	$0.110399\pi$
$132$		0			0
$133$	−0.448928	+	0.897360i	−0.0389270	+	0.0778110i
$134$			0.152573i			0.0131803i
$135$		0			0
$136$	−0.189672	−	0.109507i	−0.0162643	−	0.00939017i
$137$	−4.16810	−	4.96735i	−0.356105	−	0.424389i	0.558017	−	0.829830i	$-0.311563\pi$
$137$	−4.16810	−	4.96735i	−0.356105	−	0.424389i	−0.914121	+	0.405441i	$0.867118\pi$
$138$		0			0
$139$	−3.60990	+	4.30212i	−0.306188	+	0.364901i	−0.897094	−	0.441840i	$-0.854326\pi$
$139$	−3.60990	+	4.30212i	−0.306188	+	0.364901i	0.590906	+	0.806740i	$0.298770\pi$
$140$	14.5187	+	15.3412i	1.22706	+	1.29656i
$141$		0			0
$142$	0.150370	+	0.0547302i	0.0126188	+	0.00459286i
$143$	−3.33015			−0.278481
$144$		0			0
$145$		−	23.0088i		−	1.91078i
$146$	0.0198970	+	0.112842i	0.00164669	+	0.00933885i
$147$		0			0
$148$	−11.5908	+	4.21870i	−0.952757	+	0.346775i
$149$	−2.28030	+	2.71756i	−0.186810	+	0.222631i	−0.851318	−	0.524649i	$-0.824196\pi$
$149$	−2.28030	+	2.71756i	−0.186810	+	0.222631i	0.664509	+	0.747280i	$0.268641\pi$
$150$		0			0
$151$	15.0731	+	5.48616i	1.22663	+	0.446457i	0.872442	−	0.488717i	$-0.162535\pi$
$151$	15.0731	+	5.48616i	1.22663	+	0.446457i	0.354188	+	0.935174i	$0.384757\pi$
$152$	0.0245185			0.00198871
$153$		0			0
$154$	−0.219157	−	0.0252709i	−0.0176602	−	0.00203639i
$155$	16.5620	+	19.7379i	1.33030	+	1.58538i
$156$		0			0
$157$	−3.94390	+	4.70015i	−0.314757	+	0.375113i	−0.900108	−	0.435667i	$-0.856512\pi$
$157$	−3.94390	+	4.70015i	−0.314757	+	0.375113i	0.585351	+	0.810780i	$0.300957\pi$
$158$	0.00707889	+	0.0194491i	0.000563166	+	0.00154729i
$159$		0			0
$160$	0.264798	−	0.727525i	0.0209341	−	0.0575159i
$161$	−0.305604	+	2.65029i	−0.0240850	+	0.208872i
$162$		0			0
$163$	−1.58197	−	2.74005i	−0.123910	−	0.214618i	0.797397	−	0.603456i	$-0.206210\pi$
$163$	−1.58197	−	2.74005i	−0.123910	−	0.214618i	−0.921306	+	0.388838i	$0.872877\pi$
$164$	0.434044	−	0.364206i	0.0338932	−	0.0284397i
$165$		0			0
$166$	−0.136793	−	0.0241203i	−0.0106172	−	0.00187210i
$167$	−1.33048	+	7.54555i	−0.102956	+	0.583892i	0.889061	+	0.457788i	$0.151358\pi$
$167$	−1.33048	+	7.54555i	−0.102956	+	0.583892i	−0.992017	+	0.126104i	$0.959753\pi$
$168$		0			0
$169$	9.63934	−	8.08837i	0.741488	−	0.622182i
$170$	−0.189316	−	0.109302i	−0.0145199	−	0.00838306i
$171$		0			0
$172$	8.35214	+	14.4663i	0.636845	+	1.10305i
$173$	−1.21193	+	1.01693i	−0.0921413	+	0.0773157i	−0.687695	−	0.726000i	$-0.741377\pi$
$173$	−1.21193	+	1.01693i	−0.0921413	+	0.0773157i	0.595553	+	0.803316i	$0.296933\pi$
$174$		0			0
$175$	19.8918	+	21.0186i	1.50368	+	1.58885i
$176$	−7.05465	−	19.3825i	−0.531765	−	1.46101i
$177$		0			0
$178$	−0.0296151	+	0.0813668i	−0.00221975	+	0.00609870i
$179$	−7.54113	+	4.35388i	−0.563651	+	0.325424i	−0.754610	−	0.656174i	$-0.772174\pi$
$179$	−7.54113	+	4.35388i	−0.563651	+	0.325424i	0.190959	+	0.981598i	$0.438840\pi$
$180$		0			0
$181$	1.08680	−	0.627465i	0.0807813	−	0.0466391i	−0.459065	−	0.888403i	$-0.651816\pi$
$181$	1.08680	−	0.627465i	0.0807813	−	0.0466391i	0.539847	+	0.841763i	$0.318482\pi$
$182$	−0.0230418	+	0.0152061i	−0.00170797	+	0.00112715i
$183$		0			0
$184$	0.0612593	−	0.0222965i	0.00451609	−	0.00164372i
$185$	−23.1396	+	8.42212i	−1.70126	+	0.619206i
$186$		0			0
$187$	−17.2102	+	3.03462i	−1.25853	+	0.221914i
$188$	14.7105			1.07287
$189$		0			0
$190$	0.0244724			0.00177542
$191$	−8.73361	+	1.53997i	−0.631942	+	0.111428i	−0.480439	−	0.877028i	$-0.659523\pi$
$191$	−8.73361	+	1.53997i	−0.631942	+	0.111428i	−0.151503	+	0.988457i	$0.548411\pi$
$192$		0			0
$193$	−23.6910	+	8.62281i	−1.70531	+	0.620684i	−0.996413	−	0.0846240i	$-0.973031\pi$
$193$	−23.6910	+	8.62281i	−1.70531	+	0.620684i	−0.708901	+	0.705308i	$0.750809\pi$
$194$	0.114044	−	0.0415085i	0.00818785	−	0.00298013i
$195$		0			0
$196$	12.4897	−	6.32119i	0.892118	−	0.451513i
$197$	11.0546	−	6.38238i	0.787608	−	0.454726i	−0.0515117	−	0.998672i	$-0.516404\pi$
$197$	11.0546	−	6.38238i	0.787608	−	0.454726i	0.839120	+	0.543947i	$0.183071\pi$
$198$		0			0
$199$	−17.6420	+	10.1856i	−1.25061	+	0.722038i	−0.971230	−	0.238144i	$-0.923461\pi$
$199$	−17.6420	+	10.1856i	−1.25061	+	0.722038i	−0.279377	+	0.960182i	$0.590128\pi$
$200$	0.241857	−	0.664496i	0.0171019	−	0.0469870i
$201$		0			0
$202$	0.0630384	+	0.173196i	0.00443536	+	0.0121861i
$203$	−14.6147	−	4.35064i	−1.02575	−	0.305355i
$204$		0			0
$205$	0.866515	−	0.727093i	0.0605201	−	0.0507824i
$206$	0.0773745	+	0.134017i	0.00539094	+	0.00933738i
$207$		0			0
$208$	−2.23537	−	1.29059i	−0.154995	−	0.0894866i
$209$	1.49868	−	1.25754i	0.103666	−	0.0869860i
$210$		0			0
$211$	−0.149574	+	0.848277i	−0.0102971	+	0.0583978i	−0.989523	−	0.144373i	$-0.953884\pi$
$211$	−0.149574	+	0.848277i	−0.0102971	+	0.0583978i	0.979226	+	0.202771i	$0.0649946\pi$
$212$	3.91107	+	0.689627i	0.268613	+	0.0473638i
$213$		0			0
$214$	−0.172881	+	0.145064i	−0.0118179	+	0.00991639i
$215$	16.6740	+	28.8802i	1.13716	+	1.96962i
$216$		0			0
$217$	15.6687	−	6.78770i	1.06366	−	0.460779i
$218$	−0.0100891	+	0.0277197i	−0.000683322	+	0.00187741i
$219$		0			0
$220$	−14.0856	−	38.6998i	−0.949650	−	2.60914i
$221$	−1.40572	+	1.67527i	−0.0945586	+	0.112691i
$222$		0			0
$223$	−10.1302	−	12.0727i	−0.678367	−	0.808446i	0.311530	−	0.950236i	$-0.399159\pi$
$223$	−10.1302	−	12.0727i	−0.678367	−	0.808446i	−0.989897	+	0.141790i	$0.954714\pi$
$224$	−0.412039	−	0.305758i	−0.0275305	−	0.0204293i
$225$		0			0
$226$	0.0668981			0.00445000
$227$	−8.89407	−	3.23718i	−0.590320	−	0.214859i	0.0295500	−	0.999563i	$-0.490593\pi$
$227$	−8.89407	−	3.23718i	−0.590320	−	0.214859i	−0.619870	+	0.784704i	$0.712815\pi$
$228$		0			0
$229$	−1.18329	+	1.41019i	−0.0781938	+	0.0931878i	−0.803723	−	0.595004i	$-0.797151\pi$
$229$	−1.18329	+	1.41019i	−0.0781938	+	0.0931878i	0.725529	+	0.688191i	$0.241595\pi$
$230$	0.0611442	−	0.0222547i	0.00403173	−	0.00146743i
$231$		0			0
$232$	0.0647026	+	0.366947i	0.00424793	+	0.0240912i
$233$		−	10.5523i		−	0.691304i	−0.938363	−	0.345652i	$-0.887658\pi$
$233$		−	10.5523i		−	0.691304i	0.938363	−	0.345652i	$-0.112342\pi$
$234$		0			0
$235$	29.3677			1.91574
$236$	−6.43607	−	2.34254i	−0.418953	−	0.152486i
$237$		0			0
$238$	−0.105223	+	0.0995821i	−0.00682059	+	0.00645495i
$239$	3.07353	−	3.66289i	0.198810	−	0.236933i	−0.657424	−	0.753521i	$-0.728354\pi$
$239$	3.07353	−	3.66289i	0.198810	−	0.236933i	0.856234	+	0.516588i	$0.172798\pi$
$240$		0			0
$241$	−5.60988	−	6.68559i	−0.361364	−	0.430657i	0.554476	−	0.832199i	$-0.312919\pi$
$241$	−5.60988	−	6.68559i	−0.361364	−	0.430657i	−0.915840	+	0.401543i	$0.868474\pi$
$242$	0.218532	+	0.126170i	0.0140478	+	0.00811049i
$243$		0			0
$244$		−	16.1107i		−	1.03138i
$245$	24.9340	−	12.6195i	1.59298	−	0.806228i
$246$		0			0
$247$	0.0425129	−	0.241103i	0.00270503	−	0.0153410i
$248$	−0.319637	−	0.268208i	−0.0202970	−	0.0170312i
$249$		0			0
$250$	0.131051	−	0.360060i	0.00828840	−	0.0227722i
$251$	−5.48464	−	9.49967i	−0.346187	−	0.599614i	0.639382	−	0.768890i	$-0.279190\pi$
$251$	−5.48464	−	9.49967i	−0.346187	−	0.599614i	−0.985569	+	0.169276i	$0.945857\pi$
$252$		0			0
$253$	2.60086	−	4.50483i	0.163515	−	0.283216i
$254$	0.0657433	+	0.0783498i	0.00412510	+	0.00491610i
$255$		0			0
$256$	2.77474	−	15.7363i	0.173421	−	0.983522i
$257$	9.83062	+	8.24887i	0.613217	+	0.514550i	0.895663	−	0.444733i	$-0.146701\pi$
$257$	9.83062	+	8.24887i	0.613217	+	0.514550i	−0.282446	+	0.959283i	$0.591146\pi$
$258$		0			0
$259$	0.974183	+	16.2903i	0.0605328	+	1.01223i
$260$	−4.46323	−	2.57685i	−0.276798	−	0.159809i
$261$		0			0
$262$		−	0.0634356i		−	0.00391906i
$263$	2.43598	−	0.429529i	0.150209	−	0.0264859i	−0.0980380	−	0.995183i	$-0.531257\pi$
$263$	2.43598	−	0.429529i	0.150209	−	0.0264859i	0.248247	+	0.968697i	$0.420146\pi$
$264$		0			0
$265$	7.80796	+	1.37675i	0.479639	+	0.0845734i
$266$	0.00462739	−	0.0155444i	0.000283723	−	0.000953086i
$267$		0			0
$268$	3.27779	+	18.5893i	0.200223	+	1.13552i
$269$	13.2754	−	22.9936i	0.809413	−	1.40195i	−0.103858	−	0.994592i	$-0.533119\pi$
$269$	13.2754	−	22.9936i	0.809413	−	1.40195i	0.913271	−	0.407353i	$-0.133548\pi$
$270$		0			0
$271$	−17.4414	+	10.0698i	−1.05949	+	0.611698i	−0.925292	−	0.379257i	$-0.876180\pi$
$271$	−17.4414	+	10.0698i	−1.05949	+	0.611698i	−0.134200	+	0.990954i	$0.542846\pi$
$272$	−12.7285	−	4.63278i	−0.771776	−	0.280904i
$273$		0			0
$274$	0.0802908	+	0.0673720i	0.00485054	+	0.00407009i
$275$	−19.2983	−	53.0217i	−1.16373	−	3.19733i
$276$		0			0
$277$	−4.06457	−	23.0513i	−0.244216	−	1.38502i	−0.822306	−	0.569046i	$-0.807313\pi$
$277$	−4.06457	−	23.0513i	−0.244216	−	1.38502i	0.578090	−	0.815973i	$-0.303798\pi$
$278$	0.0453878	−	0.0786140i	0.00272218	−	0.00471496i
$279$		0			0
$280$	−0.548377	−	0.406930i	−0.0327718	−	0.0243187i
$281$	−8.66178	+	1.52731i	−0.516719	+	0.0911114i	−0.425925	−	0.904758i	$-0.640051\pi$
$281$	−8.66178	+	1.52731i	−0.516719	+	0.0911114i	−0.0907933	+	0.995870i	$0.528940\pi$
$282$		0			0
$283$	29.3925	+	5.18270i	1.74721	+	0.308079i	0.953762	−	0.300564i	$-0.0971748\pi$
$283$	29.3925	+	5.18270i	1.74721	+	0.308079i	0.793444	+	0.608643i	$0.208286\pi$
$284$	19.4966	+	3.43778i	1.15691	+	0.203995i
$285$		0			0
$286$	0.0530099	−	0.00934707i	0.00313454	−	0.000552704i
$287$	−0.297988	−	0.687874i	−0.0175897	−	0.0406039i
$288$		0			0
$289$	2.76187	−	4.78370i	0.162463	−	0.281394i
$290$	0.0645811	+	0.366258i	0.00379233	+	0.0215074i
$291$		0			0
$292$	4.84844	+	13.3210i	0.283734	+	0.779552i
$293$	−1.70777	−	1.43299i	−0.0997691	−	0.0837162i	0.591539	−	0.806277i	$-0.298521\pi$
$293$	−1.70777	−	1.43299i	−0.0997691	−	0.0837162i	−0.691308	+	0.722560i	$0.742965\pi$
$294$		0			0
$295$	−12.8488	−	4.67659i	−0.748087	−	0.272281i
$296$	0.345348	−	0.199387i	0.0200730	−	0.0115891i
$297$		0			0
$298$	0.0286706	−	0.0496589i	0.00166084	−	0.00287666i
$299$	−0.113035	−	0.641054i	−0.00653698	−	0.0370731i
$300$		0			0
$301$	21.4969	−	5.13013i	1.23906	−	0.295696i
$302$	−0.255334	−	0.0450223i	−0.0146928	−	0.00259074i
$303$		0			0
$304$	1.49335	−	0.263318i	0.0856495	−	0.0151023i
$305$		−	32.1630i		−	1.84165i
$306$		0			0
$307$	12.9614	+	7.48325i	0.739744	+	0.427091i	0.821976	−	0.569522i	$-0.192872\pi$
$307$	12.9614	+	7.48325i	0.739744	+	0.427091i	−0.0822321	+	0.996613i	$0.526205\pi$
$308$	−27.2447	+	1.62927i	−1.55241	+	0.0928365i
$309$		0			0
$310$	−0.319037	−	0.267704i	−0.0181201	−	0.0152046i
$311$	−0.786394	+	4.45986i	−0.0445923	+	0.252896i	−0.998952	−	0.0457630i	$-0.985428\pi$
$311$	−0.786394	+	4.45986i	−0.0445923	+	0.252896i	0.954360	+	0.298659i	$0.0965392\pi$
$312$		0			0
$313$	−7.81741	−	9.31643i	−0.441866	−	0.526596i	0.498440	−	0.866924i	$-0.333906\pi$
$313$	−7.81741	−	9.31643i	−0.441866	−	0.526596i	−0.940307	+	0.340328i	$0.889462\pi$
$314$	0.0495872	−	0.0858875i	0.00279836	−	0.00484691i
$315$		0			0
$316$	1.28031	+	2.21756i	0.0720231	+	0.124748i
$317$	−11.6274	+	31.9461i	−0.653061	+	1.79427i	−0.0469397	+	0.998898i	$0.514947\pi$
$317$	−11.6274	+	31.9461i	−0.653061	+	1.79427i	−0.606121	+	0.795372i	$0.707275\pi$
$318$		0			0
$319$	22.7755	+	19.1109i	1.27518	+	1.07000i
$320$	5.54160	−	31.4280i	0.309785	−	1.75688i
$321$		0			0
$322$	−0.00257419	−	0.0430455i	−0.000143454	−	0.00239883i
$323$		−	1.28476i		−	0.0714858i
$324$		0			0
$325$	−6.11497	−	3.53048i	−0.339197	−	0.195836i
$326$	0.0328728	+	0.0391763i	0.00182066	+	0.00216978i
$327$		0			0
$328$	−0.0117746	+	0.0140325i	−0.000650145	+	0.000774813i
$329$	5.55301	−	18.6537i	0.306147	−	1.02841i
$330$		0			0
$331$	31.2817	+	11.3856i	1.71940	+	0.625810i	0.997787	−	0.0664891i	$-0.0211798\pi$
$331$	31.2817	+	11.3856i	1.71940	+	0.625810i	0.721611	+	0.692299i	$0.243402\pi$
$332$	−17.1848			−0.943138
$333$		0			0
$334$		−	0.123846i		−	0.00677653i
$335$	6.54370	+	37.1111i	0.357520	+	2.02760i
$336$		0			0
$337$	−26.0769	+	9.49121i	−1.42050	+	0.517019i	−0.934192	−	0.356770i	$-0.883878\pi$
$337$	−26.0769	+	9.49121i	−1.42050	+	0.517019i	−0.486306	+	0.873789i	$0.661656\pi$
$338$	−0.130738	+	0.155808i	−0.00711121	+	0.00847481i
$339$		0			0
$340$	−25.4141	−	9.24998i	−1.37827	−	0.501650i
$341$	−33.2939			−1.80297
$342$		0			0
$343$	−3.30094	−	18.2237i	−0.178234	−	0.983988i
$344$	−0.347132	−	0.413696i	−0.0187161	−	0.0223050i
$345$		0			0
$346$	0.0164374	−	0.0195893i	0.000883678	−	0.00105313i
$347$	−4.17679	−	11.4756i	−0.224222	−	0.616044i	0.775664	−	0.631146i	$-0.217415\pi$
$347$	−4.17679	−	11.4756i	−0.224222	−	0.616044i	−0.999886	+	0.0151019i	$0.995193\pi$
$348$		0			0
$349$	−3.80673	+	10.4589i	−0.203770	+	0.559853i	−0.998915	−	0.0465660i	$-0.985172\pi$
$349$	−3.80673	+	10.4589i	−0.203770	+	0.559853i	0.795145	+	0.606419i	$0.207394\pi$
$350$	−0.375635	−	0.278744i	−0.0200785	−	0.0148995i
$351$		0			0
$352$	0.500209	+	0.866387i	0.0266612	+	0.0461786i
$353$	−15.0431	+	12.6227i	−0.800664	+	0.671837i	−0.948360	−	0.317196i	$-0.897259\pi$
$353$	−15.0431	+	12.6227i	−0.800664	+	0.671837i	0.147696	+	0.989033i	$0.452814\pi$
$354$		0			0
$355$	38.9225	+	6.86309i	2.06579	+	0.364255i
$356$	−1.86022	+	10.5498i	−0.0985913	+	0.559139i
$357$		0			0
$358$	0.107820	−	0.0904721i	0.00569849	−	0.00478160i
$359$	25.9840	+	15.0019i	1.37138	+	0.791768i	0.991102	−	0.133103i	$-0.0424940\pi$
$359$	25.9840	+	15.0019i	1.37138	+	0.791768i	0.380281	+	0.924871i	$0.375827\pi$
$360$		0			0
$361$	−9.42809	−	16.3299i	−0.496215	−	0.859470i
$362$	−0.0155387	+	0.0130385i	−0.000816695	+	0.000685289i
$363$		0			0
$364$	−2.48069	+	2.34770i	−0.130023	+	0.123053i
$365$	9.67931	+	26.5937i	0.506638	+	1.39198i
$366$		0			0
$367$	−0.00927887	+	0.0254935i	−0.000484353	+	0.00133075i	−0.939935	−	0.341355i	$-0.889114\pi$
$367$	−0.00927887	+	0.0254935i	−0.000484353	+	0.00133075i	0.939450	+	0.342685i	$0.111336\pi$
$368$	3.49167	−	2.01592i	0.182016	−	0.105087i
$369$		0			0
$370$	0.344700	−	0.199013i	0.0179201	−	0.0103462i
$371$	2.35086	−	4.69912i	0.122051	−	0.243966i
$372$		0			0
$373$	26.4258	−	9.61822i	1.36828	−	0.498012i	0.449674	−	0.893193i	$-0.351540\pi$
$373$	26.4258	−	9.61822i	1.36828	−	0.498012i	0.918604	+	0.395180i	$0.129318\pi$
$374$	0.265437	−	0.0966112i	0.0137254	−	0.00499565i
$375$		0			0
$376$	−0.468359	+	0.0825843i	−0.0241538	+	0.00425896i
$377$	3.72056			0.191619
$378$		0			0
$379$	0.592745			0.0304473			0.0152236	−	0.999884i	$-0.495154\pi$
$379$	0.592745			0.0304473			0.0152236	+	0.999884i	$0.495154\pi$
$380$	2.98168	−	0.525750i	0.152957	−	0.0269704i
$381$		0			0
$382$	0.134701	−	0.0490270i	0.00689188	−	0.00250844i
$383$	11.0275	−	4.01368i	0.563478	−	0.205089i	−0.0445466	−	0.999007i	$-0.514184\pi$
$383$	11.0275	−	4.01368i	0.563478	−	0.205089i	0.608025	+	0.793918i	$0.291962\pi$
$384$		0			0
$385$	−54.3906	+	3.25264i	−2.77200	+	0.165770i
$386$	0.352914	−	0.203755i	0.0179629	−	0.0103709i
$387$		0			0
$388$	13.0031	−	7.50736i	0.660134	−	0.381128i
$389$	5.24004	−	14.3969i	0.265680	−	0.729951i	−0.733078	−	0.680144i	$-0.761917\pi$
$389$	5.24004	−	14.3969i	0.265680	−	0.729951i	0.998759	−	0.0498070i	$-0.0158606\pi$
$390$		0			0
$391$	−1.16833	−	3.20996i	−0.0590849	−	0.162335i
$392$	−0.362163	+	0.271373i	−0.0182920	+	0.0137064i
$393$		0			0
$394$	−0.158055	+	0.132624i	−0.00796269	+	0.00668149i
$395$	2.55598	+	4.42709i	0.128605	+	0.222751i
$396$		0			0
$397$	−19.7438	−	11.3991i	−0.990914	−	0.572104i	−0.0853663	−	0.996350i	$-0.527206\pi$
$397$	−19.7438	−	11.3991i	−0.990914	−	0.572104i	−0.905547	+	0.424245i	$0.860539\pi$
$398$	0.252239	−	0.211653i	0.0126436	−	0.0106092i
$399$		0			0
$400$	7.59440	−	43.0700i	0.379720	−	2.15350i
$401$	−2.88795	−	0.509224i	−0.144218	−	0.0254294i	0.101073	−	0.994879i	$-0.467772\pi$
$401$	−2.88795	−	0.509224i	−0.144218	−	0.0254294i	−0.245291	+	0.969450i	$0.578883\pi$
$402$		0			0
$403$	−3.19164	+	2.67811i	−0.158987	+	0.133406i
$404$	11.4013	+	19.7477i	0.567237	+	0.982483i
$405$		0			0
$406$	0.244850	+	0.0282336i	0.0121517	+	0.00140121i
$407$	10.8828	−	29.9002i	0.539440	−	1.48210i
$408$		0			0
$409$	6.88596	+	18.9190i	0.340489	+	0.935485i	0.985253	+	0.171103i	$0.0547332\pi$
$409$	6.88596	+	18.9190i	0.340489	+	0.935485i	−0.644764	+	0.764381i	$0.723045\pi$
$410$	−0.0117525	+	0.0140061i	−0.000580416	+	0.000691712i
$411$		0			0
$412$	12.3063	+	14.6661i	0.606288	+	0.722546i
$413$	−5.39999	+	7.27701i	−0.265716	+	0.358078i
$414$		0			0
$415$	−34.3073			−1.68408
$416$	0.117642	+	0.0428182i	0.00576787	+	0.00209933i
$417$		0			0
$418$	−0.0203265	+	0.0242242i	−0.000994204	+	0.00118485i
$419$	13.5738	−	4.94048i	0.663126	−	0.241358i	0.0115404	−	0.999933i	$-0.496326\pi$
$419$	13.5738	−	4.94048i	0.663126	−	0.241358i	0.651585	+	0.758575i	$0.274104\pi$
$420$		0			0
$421$	1.54410	+	8.75701i	0.0752547	+	0.426791i	0.999037	+	0.0438728i	$0.0139696\pi$
$421$	1.54410	+	8.75701i	0.0752547	+	0.426791i	−0.923782	+	0.382918i	$0.874919\pi$
$422$		−	0.0139228i		−	0.000677753i
$423$		0			0
$424$	−0.128394			−0.00623535
$425$	−34.8193	−	12.6732i	−1.68898	−	0.614740i
$426$		0			0
$427$	−20.4292	−	6.08155i	−0.988639	−	0.294307i
$428$	−17.9470	+	21.3884i	−0.867503	+	1.03385i
$429$		0			0
$430$	−0.346481	−	0.412919i	−0.0167088	−	0.0199127i
$431$	27.2881	+	15.7548i	1.31442	+	0.758881i	0.982825	−	0.184541i	$-0.0590798\pi$
$431$	27.2881	+	15.7548i	1.31442	+	0.758881i	0.331595	+	0.943422i	$0.392413\pi$
$432$		0			0
$433$		−	35.8271i		−	1.72174i	−0.508824	−	0.860870i	$-0.669920\pi$
$433$		−	35.8271i		−	1.72174i	0.508824	−	0.860870i	$-0.330080\pi$
$434$	−0.230365	+	0.152027i	−0.0110579	+	0.00729751i
$435$		0			0
$436$	−0.633730	+	3.59406i	−0.0303502	+	0.172124i
$437$	0.292946	+	0.245811i	0.0140135	+	0.0117587i
$438$		0			0
$439$	−12.3813	+	34.0174i	−0.590928	+	1.62356i	0.177858	+	0.984056i	$0.443083\pi$
$439$	−12.3813	+	34.0174i	−0.590928	+	1.62356i	−0.768786	+	0.639506i	$0.779139\pi$
$440$	0.665722	+	1.15306i	0.0317370	+	0.0549701i
$441$		0			0
$442$	0.0176743	−	0.0306127i	0.000840678	−	0.00145610i
$443$	15.4246	+	18.3824i	0.732847	+	0.873373i	0.995811	−	0.0914326i	$-0.0291446\pi$
$443$	15.4246	+	18.3824i	0.732847	+	0.873373i	−0.262964	+	0.964806i	$0.584700\pi$
$444$		0			0
$445$	−3.71369	+	21.0614i	−0.176046	+	0.998406i
$446$	0.195139	+	0.163741i	0.00924011	+	0.00775338i
$447$		0			0
$448$	−18.9145	−	9.46248i	−0.893628	−	0.447060i
$449$	27.8837	+	16.0987i	1.31591	+	0.759743i	0.983069	−	0.183238i	$-0.0586580\pi$
$449$	27.8837	+	16.0987i	1.31591	+	0.759743i	0.332845	+	0.942981i	$0.391991\pi$
$450$		0			0
$451$			1.46164i			0.0688261i
$452$	8.15075	−	1.43720i	0.383379	−	0.0676001i
$453$		0			0
$454$	0.150663	+	0.0265660i	0.00707098	+	0.00124680i
$455$	−4.95239	+	4.68689i	−0.232171	+	0.219725i
$456$		0			0
$457$	0.192143	+	1.08970i	0.00898809	+	0.0509740i	0.988972	−	0.148103i	$-0.0473167\pi$
$457$	0.192143	+	1.08970i	0.00898809	+	0.0509740i	−0.979984	+	0.199077i	$0.936206\pi$
$458$	0.0148776	−	0.0257688i	0.000695186	−	0.00120410i
$459$		0			0
$460$	6.97160	−	4.02506i	0.325053	−	0.187669i
$461$	−19.7443	−	7.18634i	−0.919584	−	0.334701i	−0.161511	−	0.986871i	$-0.551637\pi$
$461$	−19.7443	−	7.18634i	−0.919584	−	0.334701i	−0.758073	+	0.652170i	$0.773859\pi$
$462$		0			0
$463$	−17.5556	−	14.7309i	−0.815876	−	0.684601i	0.136126	−	0.990691i	$-0.456535\pi$
$463$	−17.5556	−	14.7309i	−0.815876	−	0.684601i	−0.952003	+	0.306090i	$0.900979\pi$
$464$	7.88170	+	21.6548i	0.365899	+	1.00530i
$465$		0			0
$466$	0.0296182	+	0.167973i	0.00137203	+	0.00778120i
$467$	−17.0089	+	29.4602i	−0.787076	+	1.36326i	0.140674	+	0.990056i	$0.455073\pi$
$467$	−17.0089	+	29.4602i	−0.787076	+	1.36326i	−0.927751	+	0.373200i	$0.878260\pi$
$468$		0			0
$469$	24.8095	+	2.86077i	1.14560	+	0.132098i
$470$	−0.467479	+	0.0824292i	−0.0215632	+	0.00380218i
$471$		0			0
$472$	0.218065	+	0.0384507i	0.0100373	+	0.00176984i
$473$	−42.4366	−	7.48272i	−1.95124	−	0.344056i
$474$		0			0
$475$	4.08513	−	0.720319i	0.187439	−	0.0330505i
$476$	−10.6808	+	14.3934i	−0.489555	+	0.659723i
$477$		0			0
$478$	−0.0386439	+	0.0669333i	−0.00176753	+	0.00306146i
$479$	6.61372	+	37.5083i	0.302189	+	1.71380i	0.636451	+	0.771317i	$0.280402\pi$
$479$	6.61372	+	37.5083i	0.302189	+	1.71380i	−0.334263	+	0.942480i	$0.608487\pi$
$480$		0			0
$481$	−1.36187	−	3.74171i	−0.0620959	−	0.170607i
$482$	0.108064	+	0.0906764i	0.00492218	+	0.00413020i
$483$		0			0
$484$	29.3361	+	10.6775i	1.33346	+	0.485340i
$485$	25.9591	−	14.9875i	1.17874	−	0.680548i
$486$		0			0
$487$	10.4173	−	18.0433i	0.472053	−	0.817619i	−0.527436	−	0.849595i	$-0.676847\pi$
$487$	10.4173	−	18.0433i	0.472053	−	0.817619i	0.999489	+	0.0319755i	$0.0101799\pi$
$488$	0.0904448	+	0.512938i	0.00409424	+	0.0232196i
$489$		0			0
$490$	−0.361483	+	0.270863i	−0.0163302	+	0.0122364i
$491$	−2.73237	−	0.481790i	−0.123310	−	0.0217429i	0.111653	−	0.993747i	$-0.464386\pi$
$491$	−2.73237	−	0.481790i	−0.123310	−	0.0217429i	−0.234962	+	0.972004i	$0.575497\pi$
$492$		0			0
$493$	19.2278	−	3.39039i	0.865978	−	0.152695i
$494$			0.00395723i			0.000178044i
$495$		0			0
$496$	−22.3486	−	12.9030i	−1.00348	−	0.579362i
$497$	11.7190	−	23.4250i	0.525668	−	1.05076i
$498$		0			0
$499$	−3.11754	−	2.61593i	−0.139560	−	0.117105i	0.570335	−	0.821412i	$-0.306813\pi$
$499$	−3.11754	−	2.61593i	−0.139560	−	0.117105i	−0.709895	+	0.704307i	$0.751258\pi$
$500$	8.23174	−	46.6845i	0.368134	−	2.08779i
$501$		0			0
$502$	0.113969	+	0.135823i	0.00508668	+	0.00606207i
$503$	20.5736	−	35.6344i	0.917329	−	1.58886i	0.113875	−	0.993495i	$-0.463674\pi$
$503$	20.5736	−	35.6344i	0.917329	−	1.58886i	0.803455	−	0.595366i	$-0.202993\pi$
$504$		0			0
$505$	22.7613	+	39.4238i	1.01287	+	1.75433i
$506$	−0.0287568	+	0.0790086i	−0.00127840	+	0.00351236i
$507$		0			0
$508$	9.69326	+	8.13361i	0.430069	+	0.360871i
$509$	6.67420	−	37.8513i	0.295829	−	1.67773i	−0.367986	−	0.929831i	$-0.619952\pi$
$509$	6.67420	−	37.8513i	0.295829	−	1.67773i	0.663814	−	0.747897i	$-0.268936\pi$
$510$		0			0
$511$	18.7219	−	1.11960i	0.828210	−	0.0495283i
$512$			1.29242i			0.0571175i
$513$		0			0
$514$	−0.179638	−	0.103714i	−0.00792350	−	0.00457463i
$515$	24.5680	+	29.2790i	1.08260	+	1.29019i
$516$		0			0
$517$	−24.3925	+	29.0698i	−1.07278	+	1.27849i
$518$	−0.0612307	−	0.256576i	−0.00269032	−	0.0112733i
$519$		0			0
$520$	0.156568	+	0.0569862i	0.00686597	+	0.00249901i
$521$	27.2574			1.19417			0.597084	−	0.802178i	$-0.296326\pi$
$521$	27.2574			1.19417			0.597084	+	0.802178i	$0.296326\pi$
$522$		0			0
$523$			14.0528i			0.614487i	0.951631	+	0.307244i	$0.0994067\pi$
$523$			14.0528i			0.614487i	−0.951631	+	0.307244i	$0.900593\pi$
$524$	−1.36281	−	7.72887i	−0.0595346	−	0.337637i
$525$		0			0
$526$	−0.0375707	+	0.0136746i	−0.00163816	+	0.000596241i
$527$	−14.0540	+	16.7489i	−0.612200	+	0.729591i
$528$		0			0
$529$	−20.6575	−	7.51870i	−0.898151	−	0.326900i
$530$	−0.128153			−0.00556659
$531$		0			0
$532$	0.229847	−	1.99331i	0.00996515	−	0.0864209i
$533$	0.117572	+	0.140117i	0.00509261	+	0.00606914i
$534$		0			0
$535$	−35.8290	+	42.6994i	−1.54902	+	1.84605i
$536$	−0.208719	−	0.573451i	−0.00901528	−	0.0247693i
$537$		0			0
$538$	−0.146781	+	0.403277i	−0.00632817	+	0.0173865i
$539$	−8.21847	+	35.1627i	−0.353995	+	1.51457i
$540$		0			0
$541$	10.7693	+	18.6530i	0.463010	+	0.801957i	0.999109	−	0.0421981i	$-0.0134361\pi$
$541$	10.7693	+	18.6530i	0.463010	+	0.801957i	−0.536099	+	0.844155i	$0.680103\pi$
$542$	0.249371	−	0.209247i	0.0107114	−	0.00898795i
$543$		0			0
$544$	0.646991	+	0.114082i	0.0277395	+	0.00489123i
$545$	−1.26516	+	7.17510i	−0.0541936	+	0.307347i
$546$		0			0
$547$	−20.2027	+	16.9521i	−0.863805	+	0.724819i	−0.962784	−	0.270271i	$-0.912887\pi$
$547$	−20.2027	+	16.9521i	−0.863805	+	0.724819i	0.0989790	+	0.995090i	$0.468442\pi$
$548$	11.2299	+	6.48357i	0.479716	+	0.276964i
$549$		0			0
$550$	0.456015	+	0.789841i	0.0194445	+	0.0336789i
$551$	−1.67438	+	1.40497i	−0.0713309	+	0.0598537i
$552$		0			0
$553$	3.29529	−	0.786404i	0.140130	−	0.0334413i
$554$	0.129401	+	0.355526i	0.00549771	+	0.0151048i
$555$		0			0
$556$	3.84108	−	10.5533i	0.162898	−	0.447559i
$557$	−26.6538	+	15.3886i	−1.12936	+	0.652036i	−0.943774	−	0.330592i	$-0.892752\pi$
$557$	−26.6538	+	15.3886i	−1.12936	+	0.652036i	−0.185586	+	0.982628i	$0.559418\pi$
$558$		0			0
$559$	−4.66998	+	2.69621i	−0.197519	+	0.114038i
$560$	−37.7704	−	18.8956i	−1.59609	−	0.798485i
$561$		0			0
$562$	0.133593	−	0.0486238i	0.00563527	−	0.00205107i
$563$	18.2008	−	6.62454i	0.767071	−	0.279191i	0.0713000	−	0.997455i	$-0.477285\pi$
$563$	18.2008	−	6.62454i	0.767071	−	0.279191i	0.695771	+	0.718264i	$0.255063\pi$
$564$		0			0
$565$	16.2720	−	2.86919i	0.684566	−	0.120708i
$566$	−0.482422			−0.0202777
$567$		0			0
$568$	−0.640040			−0.0268555
$569$	−41.8969	+	7.38755i	−1.75641	+	0.309702i	−0.956784	−	0.290799i	$-0.906079\pi$
$569$	−41.8969	+	7.38755i	−1.75641	+	0.309702i	−0.799624	+	0.600501i	$0.794968\pi$
$570$		0			0
$571$	−28.7214	+	10.4537i	−1.20195	+	0.437476i	−0.863906	−	0.503653i	$-0.831989\pi$
$571$	−28.7214	+	10.4537i	−1.20195	+	0.437476i	−0.338048	+	0.941129i	$0.609767\pi$
$572$	6.25782	−	2.27766i	0.261653	−	0.0952338i
$573$		0			0
$574$	0.00667414	+	0.0101133i	0.000278573	+	0.000422121i
$575$	9.55163	−	5.51464i	0.398331	−	0.229976i
$576$		0			0
$577$	6.22559	−	3.59435i	0.259175	−	0.149635i	−0.364783	−	0.931092i	$-0.618857\pi$
$577$	6.22559	−	3.59435i	0.259175	−	0.149635i	0.623958	+	0.781458i	$0.285524\pi$
$578$	−0.0305370	+	0.0838996i	−0.00127017	+	0.00348976i
$579$		0			0
$580$	15.7369	+	43.2368i	0.653439	+	1.79531i
$581$	−6.48702	+	21.7913i	−0.269127	+	0.904054i
$582$		0			0
$583$	−7.84800	+	6.58526i	−0.325031	+	0.272733i
$584$	−0.229150	−	0.396900i	−0.00948230	−	0.0164238i
$585$		0			0
$586$	0.0312067	+	0.0180172i	0.00128914	+	0.000744283i
$587$	17.1076	−	14.3550i	0.706107	−	0.592495i	−0.217396	−	0.976083i	$-0.569756\pi$
$587$	17.1076	−	14.3550i	0.706107	−	0.592495i	0.923504	+	0.383589i	$0.125312\pi$
$588$		0			0
$589$	0.425032	−	2.41048i	0.0175131	−	0.0993220i
$590$	0.217656	+	0.0383786i	0.00896074	+	0.00158002i
$591$		0			0
$592$	18.8929	−	15.8530i	0.776492	−	0.651554i
$593$	−17.8613	−	30.9367i	−0.733476	−	1.27042i	−0.955389	−	0.295351i	$-0.904564\pi$
$593$	−17.8613	−	30.9367i	−0.733476	−	1.27042i	0.221913	−	0.975066i	$-0.428770\pi$
$594$		0			0
$595$	−21.3229	+	28.7347i	−0.874155	+	1.17801i
$596$	2.42633	−	6.66629i	0.0993863	−	0.273062i
$597$		0			0
$598$	0.00359862	+	0.00988712i	0.000147158	+	0.000404314i
$599$	−23.8068	+	28.3718i	−0.972718	+	1.15924i	0.0145052	+	0.999895i	$0.495383\pi$
$599$	−23.8068	+	28.3718i	−0.972718	+	1.15924i	−0.987223	+	0.159345i	$0.949062\pi$
$600$		0			0
$601$	1.43732	+	1.71293i	0.0586295	+	0.0698719i	0.794562	−	0.607183i	$-0.207700\pi$
$601$	1.43732	+	1.71293i	0.0586295	+	0.0698719i	−0.735933	+	0.677055i	$0.763256\pi$
$602$	−0.327792	+	0.142000i	−0.0133598	+	0.00578748i
$603$		0			0
$604$	−32.0767			−1.30518
$605$	58.5659	+	21.3162i	2.38104	+	0.866628i
$606$		0			0
$607$	20.5333	−	24.4707i	0.833422	−	0.993233i	−0.166552	−	0.986033i	$-0.553263\pi$
$607$	20.5333	−	24.4707i	0.833422	−	0.993233i	0.999974	−	0.00720065i	$-0.00229206\pi$
$608$	−0.0691120	+	0.0251547i	−0.00280286	+	0.00102016i
$609$		0			0
$610$	0.0902750	+	0.511975i	0.00365513	+	0.0207293i
$611$			4.74880i			0.192116i
$612$		0			0
$613$	−10.0436			−0.405657			−0.202828	−	0.979214i	$-0.565013\pi$
$613$	−10.0436			−0.405657			−0.202828	+	0.979214i	$0.565013\pi$
$614$	−0.227325	−	0.0827395i	−0.00917409	−	0.00333909i
$615$		0			0
$616$	0.858279	−	0.204824i	0.0345811	−	0.00825260i
$617$	−20.1274	+	23.9869i	−0.810298	+	0.965675i	−0.999869	−	0.0161920i	$-0.994846\pi$
$617$	−20.1274	+	23.9869i	−0.810298	+	0.965675i	0.189571	+	0.981867i	$0.439290\pi$
$618$		0			0
$619$	18.5528	+	22.1104i	0.745701	+	0.888691i	0.996854	−	0.0792558i	$-0.0252544\pi$
$619$	18.5528	+	22.1104i	0.745701	+	0.888691i	−0.251154	+	0.967947i	$0.580810\pi$
$620$	−44.6221	−	25.7626i	−1.79207	−	1.03465i
$621$		0			0
$622$		−	0.0732000i		−	0.00293505i
$623$	12.6755	+	6.34127i	0.507835	+	0.254057i
$624$		0			0
$625$	6.93691	−	39.3412i	0.277476	−	1.57365i
$626$	0.150588	+	0.126358i	0.00601871	+	0.00505030i
$627$		0			0
$628$	4.19646	−	11.5297i	0.167457	−	0.460084i
$629$	−10.4478	−	18.0961i	−0.416581	−	0.721539i
$630$		0			0
$631$	4.47416	−	7.74947i	0.178113	−	0.308501i	−0.763121	−	0.646256i	$-0.776334\pi$
$631$	4.47416	−	7.74947i	0.178113	−	0.308501i	0.941234	+	0.337754i	$0.109667\pi$
$632$	−0.0532123	−	0.0634160i	−0.00211667	−	0.00252255i
$633$		0			0
$634$	0.0954208	−	0.541158i	0.00378964	−	0.0214921i
$635$	19.3514	+	16.2377i	0.767937	+	0.644375i
$636$		0			0
$637$	2.04059	+	4.03187i	0.0808510	+	0.159749i
$638$	−0.416183	−	0.240284i	−0.0164769	−	0.00951292i
$639$		0			0
$640$			2.06426i			0.0815971i
$641$	28.5119	−	5.02742i	1.12615	−	0.198571i	0.420613	−	0.907240i	$-0.361815\pi$
$641$	28.5119	−	5.02742i	1.12615	−	0.198571i	0.705541	+	0.708669i	$0.250704\pi$
$642$		0			0
$643$	−12.3352	−	2.17502i	−0.486451	−	0.0857744i	−0.0749567	−	0.997187i	$-0.523882\pi$
$643$	−12.3352	−	2.17502i	−0.486451	−	0.0857744i	−0.411494	+	0.911412i	$0.634993\pi$
$644$	−1.23840	−	5.18929i	−0.0487997	−	0.204487i
$645$		0			0
$646$	0.00360605	+	0.0204509i	0.000141878	+	0.000804632i
$647$	4.53468	−	7.85429i	0.178277	−	0.308784i	−0.763014	−	0.646382i	$-0.776281\pi$
$647$	4.53468	−	7.85429i	0.178277	−	0.308784i	0.941290	+	0.337598i	$0.109615\pi$
$648$		0			0
$649$	15.3012	−	8.83418i	0.600626	−	0.346772i
$650$	0.107248	+	0.0390352i	0.00420662	+	0.00153109i
$651$		0			0
$652$	4.84681	+	4.06695i	0.189816	+	0.159274i
$653$	−8.08778	−	22.2210i	−0.316499	−	0.869575i	−0.991306	−	0.131580i	$-0.957995\pi$
$653$	−8.08778	−	22.2210i	−0.316499	−	0.869575i	0.674806	−	0.737995i	$-0.264227\pi$
$654$		0			0
$655$	−2.72068	−	15.4297i	−0.106306	−	0.602890i
$656$	−0.566457	+	0.981131i	−0.0221164	+	0.0383067i
$657$		0			0
$658$	−0.0360364	+	0.312519i	−0.00140484	+	0.0121833i
$659$	−42.5738	+	7.50690i	−1.65844	+	0.292427i	−0.922895	−	0.385051i	$-0.874184\pi$
$659$	−42.5738	+	7.50690i	−1.65844	+	0.292427i	−0.735543	+	0.677478i	$0.763073\pi$
$660$		0			0
$661$	−15.4143	−	2.71796i	−0.599548	−	0.105717i	−0.134367	−	0.990932i	$-0.542900\pi$
$661$	−15.4143	−	2.71796i	−0.599548	−	0.105717i	−0.465182	+	0.885215i	$0.654011\pi$
$662$	−0.529904	−	0.0934364i	−0.0205953	−	0.00363151i
$663$		0			0
$664$	0.547136	−	0.0964749i	0.0212330	−	0.00374395i
$665$	0.458862	−	3.97939i	0.0177939	−	0.154314i
$666$		0			0
$667$	−2.90577	+	5.03295i	−0.112512	+	0.194877i
$668$	−2.66062	−	15.0891i	−0.102942	−	0.583816i
$669$		0			0
$670$	−0.208327	−	0.572374i	−0.00804838	−	0.0221127i
$671$	31.8368	+	26.7142i	1.22904	+	1.03129i
$672$		0			0
$673$	0.784137	+	0.285403i	0.0302263	+	0.0110015i	0.357089	−	0.934070i	$-0.383769\pi$
$673$	0.784137	+	0.285403i	0.0302263	+	0.0110015i	−0.326863	+	0.945072i	$0.605991\pi$
$674$	0.388456	−	0.224275i	0.0149628	−	0.00863875i
$675$		0			0
$676$	−12.5816	+	21.7920i	−0.483909	+	0.838154i
$677$	3.61744	+	20.5155i	0.139029	+	0.788475i	0.971969	+	0.235111i	$0.0755452\pi$
$677$	3.61744	+	20.5155i	0.139029	+	0.788475i	−0.832939	+	0.553364i	$0.813344\pi$
$678$		0			0
$679$	−4.61124	−	19.3226i	−0.176963	−	0.741533i
$680$	0.861073	+	0.151830i	0.0330206	+	0.00582243i
$681$		0			0
$682$	0.529978	−	0.0934494i	0.0202939	−	0.00357836i
$683$			17.5517i			0.671596i	0.941934	+	0.335798i	$0.109006\pi$
$683$			17.5517i			0.671596i	−0.941934	+	0.335798i	$0.890994\pi$
$684$		0			0
$685$	22.4190	+	12.9436i	0.856587	+	0.494551i
$686$	0.103695	+	0.280823i	0.00395910	+	0.0107219i
$687$		0			0
$688$	−25.5858	−	21.4690i	−0.975448	−	0.818498i
$689$	−0.222623	+	1.26256i	−0.00848128	+	0.0480997i
$690$		0			0
$691$	−16.8826	−	20.1199i	−0.642245	−	0.765398i	0.342478	−	0.939526i	$-0.388734\pi$
$691$	−16.8826	−	20.1199i	−0.642245	−	0.765398i	−0.984723	+	0.174128i	$0.944289\pi$
$692$	1.58186	−	2.73985i	0.0601331	−	0.104154i
$693$		0			0
$694$	0.0986965	+	0.170947i	0.00374647	+	0.00648907i
$695$	7.66823	−	21.0683i	0.290873	−	0.799166i
$696$		0			0
$697$	0.735294	+	0.616985i	0.0278512	+	0.0233700i
$698$	0.0312401	−	0.177171i	0.00118245	−	0.00670603i
$699$		0			0
$700$	−51.7551	−	25.8918i	−1.95616	−	0.978619i
$701$		−	8.38616i		−	0.316741i	−0.987380	−	0.158370i	$-0.949376\pi$
$701$		−	8.38616i		−	0.316741i	0.987380	−	0.158370i	$-0.0506240\pi$
$702$		0			0
$703$	2.02584	+	1.16962i	0.0764060	+	0.0441130i
$704$	26.5064	+	31.5891i	0.998999	+	1.19056i
$705$		0			0
$706$	0.204029	−	0.243152i	0.00767874	−	0.00915116i
$707$	29.3450	−	7.00303i	1.10363	−	0.263376i
$708$		0			0
$709$	7.49554	+	2.72815i	0.281501	+	0.102458i	0.478912	−	0.877863i	$-0.341031\pi$
$709$	7.49554	+	2.72815i	0.281501	+	0.102458i	−0.197411	+	0.980321i	$0.563253\pi$
$710$	−0.638838			−0.0239752
$711$		0			0
$712$		−	0.346332i		−	0.0129794i
$713$	−1.13009	−	6.40908i	−0.0423223	−	0.240022i
$714$		0			0
$715$	12.4930	−	4.54706i	0.467210	−	0.170051i
$716$	11.1930	−	13.3393i	0.418302	−	0.498513i
$717$		0			0
$718$	−0.455725	−	0.165870i	−0.0170075	−	0.00619022i
$719$	49.6729			1.85249			0.926243	−	0.376926i	$-0.123019\pi$
$719$	49.6729			1.85249			0.926243	+	0.376926i	$0.123019\pi$
$720$		0			0
$721$	23.2428	−	10.0688i	0.865608	−	0.374982i
$722$	0.195913	+	0.233479i	0.00729111	+	0.00868921i
$723$		0			0
$724$	−1.61310	+	1.92241i	−0.0599502	+	0.0714459i
$725$	21.5608	+	59.2377i	0.800747	+	2.20003i
$726$		0			0
$727$	10.9113	−	29.9786i	0.404678	−	1.11184i	−0.555271	−	0.831669i	$-0.687386\pi$
$727$	10.9113	−	29.9786i	0.404678	−	1.11184i	0.959949	−	0.280174i	$-0.0903923\pi$
$728$	0.0658012	−	0.0886735i	0.00243875	−	0.00328646i
$729$		0			0
$730$	−0.228720	−	0.396154i	−0.00846530	−	0.0146623i
$731$	−21.6775	+	18.1896i	−0.801771	+	0.672766i
$732$		0			0
$733$	36.7025	+	6.47164i	1.35564	+	0.239035i	0.803792	−	0.594911i	$-0.202813\pi$
$733$	36.7025	+	6.47164i	1.35564	+	0.239035i	0.551845	+	0.833946i	$0.313924\pi$
$734$	7.61473e−5	0	0.000431853i	2.81065e−6	0	1.59400e-5i
$735$		0			0
$736$	−0.149801	+	0.125698i	−0.00552173	+	0.00463328i
$737$	−42.1699	−	24.3468i	−1.55335	−	0.896826i
$738$		0			0
$739$	24.4802	+	42.4009i	0.900518	+	1.55974i	0.826823	+	0.562462i	$0.190146\pi$
$739$	24.4802	+	42.4009i	0.900518	+	1.55974i	0.0736953	+	0.997281i	$0.476521\pi$
$740$	37.7222	−	31.6527i	1.38670	−	1.16358i
$741$		0			0
$742$	−0.0242318	+	0.0813998i	−0.000889578	+	0.00298828i
$743$	−13.1684	−	36.1798i	−0.483100	−	1.32731i	−0.906821	−	0.421515i	$-0.861499\pi$
$743$	−13.1684	−	36.1798i	−0.483100	−	1.32731i	0.423721	−	0.905793i	$-0.360724\pi$
$744$		0			0
$745$	4.84387	−	13.3084i	0.177465	−	0.487582i
$746$	−0.393654	+	0.227276i	−0.0144127	+	0.00832117i
$747$		0			0
$748$	30.2648	−	17.4734i	1.10659	−	0.638891i
$749$	20.3470	+	30.8317i	0.743461	+	1.12656i
$750$		0			0
$751$	4.12197	−	1.50028i	0.150413	−	0.0547458i	−0.265717	−	0.964051i	$-0.585609\pi$
$751$	4.12197	−	1.50028i	0.150413	−	0.0547458i	0.416129	+	0.909305i	$0.363386\pi$
$752$	−27.6395	+	10.0599i	−1.00791	+	0.366849i
$753$		0			0
$754$	−0.0592244	+	0.0104429i	−0.00215683	+	0.000380307i
$755$	−64.0371			−2.33055
$756$		0			0
$757$	2.14305			0.0778906			0.0389453	−	0.999241i	$-0.487600\pi$
$757$	2.14305			0.0778906			0.0389453	+	0.999241i	$0.487600\pi$
$758$	−0.00943540	+	0.00166372i	−0.000342709	+	6.04289e-5i
$759$		0			0
$760$	−0.0919803	+	0.0334781i	−0.00333648	+	0.00121438i
$761$	22.3023	−	8.11738i	0.808459	−	0.294255i	0.0954716	−	0.995432i	$-0.469564\pi$
$761$	22.3023	−	8.11738i	0.808459	−	0.294255i	0.712987	+	0.701177i	$0.247342\pi$
$762$		0			0
$763$	4.31824	+	2.16031i	0.156331	+	0.0782085i
$764$	15.3584	−	8.86719i	0.555648	−	0.320804i
$765$		0			0
$766$	−0.164272	+	0.0948423i	−0.00593537	+	0.00342679i
$767$	0.756211	−	2.07767i	0.0273052	−	0.0750204i
$768$		0			0
$769$	−15.4284	−	42.3891i	−0.556362	−	1.52859i	−0.824875	−	0.565315i	$-0.808755\pi$
$769$	−15.4284	−	42.3891i	−0.556362	−	1.52859i	0.268513	−	0.963276i	$-0.413468\pi$
$770$	0.856668	−	0.204439i	0.0308722	−	0.00736749i
$771$		0			0
$772$	38.6211	−	32.4069i	1.39000	−	1.16635i
$773$	−3.09960	−	5.36866i	−0.111485	−	0.193097i	0.804884	−	0.593432i	$-0.202227\pi$
$773$	−3.09960	−	5.36866i	−0.111485	−	0.193097i	−0.916369	+	0.400334i	$0.868894\pi$
$774$		0			0
$775$	−61.1357	−	35.2967i	−2.19606	−	1.26790i
$776$	−0.371852	+	0.312021i	−0.0133487	+	0.0112009i
$777$		0			0
$778$	−0.0430025	+	0.243880i	−0.00154172	+	0.00874351i
$779$	−0.105823	−	0.0186594i	−0.00379149	−	0.000668542i
$780$		0			0
$781$	−39.1221	+	32.8274i	−1.39990	+	1.17466i
$782$	0.0276073	+	0.0478173i	0.000987236	+	0.00170994i
$783$		0			0
$784$	−19.1439	+	20.4180i	−0.683711	+	0.729215i
$785$	8.37771	−	23.0176i	0.299013	−	0.821532i
$786$		0			0
$787$	−0.817076	−	2.24490i	−0.0291256	−	0.0800219i	0.924278	−	0.381721i	$-0.124668\pi$
$787$	−0.817076	−	2.24490i	−0.0291256	−	0.0800219i	−0.953403	+	0.301699i	$0.902446\pi$
$788$	−16.4079	+	19.5542i	−0.584508	+	0.696589i
$789$		0			0
$790$	−0.0531124	−	0.0632969i	−0.00188966	−	0.00225200i
$791$	1.25435	−	10.8781i	0.0445996	−	0.386781i
$792$		0			0
$793$	5.20080			0.184686
$794$	0.346280	+	0.126036i	0.0122890	+	0.00447284i
$795$		0			0
$796$	26.1853	−	31.2064i	0.928113	−	1.10608i
$797$	3.93456	−	1.43206i	0.139369	−	0.0507263i	−0.271394	−	0.962468i	$-0.587485\pi$
$797$	3.93456	−	1.43206i	0.139369	−	0.0507263i	0.410763	+	0.911742i	$0.365262\pi$
$798$		0			0
$799$	4.32738	+	24.5418i	0.153092	+	0.868226i
$800$			2.12119i			0.0749956i
$801$		0			0
$802$	0.0474002			0.00167376
$803$	−34.3635	−	12.5073i	−1.21266	−	0.441373i
$804$		0			0
$805$	−2.47231	−	10.3598i	−0.0871374	−	0.365134i
$806$	0.0432882	−	0.0515888i	0.00152476	−	0.00181714i
$807$		0			0
$808$	−0.473862	−	0.564727i	−0.0166704	−	0.0198670i
$809$	−30.6187	−	17.6777i	−1.07650	−	0.621516i	−0.146547	−	0.989204i	$-0.546816\pi$
$809$	−30.6187	−	17.6777i	−1.07650	−	0.621516i	−0.929949	+	0.367688i	$0.880149\pi$
$810$		0			0
$811$			30.5126i			1.07144i	0.844395	+	0.535722i	$0.179960\pi$
$811$			30.5126i			1.07144i	−0.844395	+	0.535722i	$0.820040\pi$
$812$	30.4387	−	1.82028i	1.06819	−	0.0638794i
$813$		0			0
$814$	−0.0893100	+	0.506502i	−0.00313031	+	0.0177529i
$815$	9.67605	+	8.11917i	0.338937	+	0.284402i
$816$		0			0
$817$	1.08350	−	2.97688i	0.0379067	−	0.104148i
$818$	−0.162714	−	0.281828i	−0.00568915	−	0.00985389i
$819$		0			0
$820$	−1.13101	+	1.95896i	−0.0394965	+	0.0684099i
$821$	−5.20426	−	6.20219i	−0.181630	−	0.216458i	0.667546	−	0.744569i	$-0.267345\pi$
$821$	−5.20426	−	6.20219i	−0.181630	−	0.216458i	−0.849175	+	0.528111i	$0.822900\pi$
$822$		0			0
$823$	−2.63420	+	14.9393i	−0.0918225	+	0.520751i	0.903852	+	0.427845i	$0.140727\pi$
$823$	−2.63420	+	14.9393i	−0.0918225	+	0.520751i	−0.995675	+	0.0929068i	$0.970384\pi$
$824$	−0.474147	−	0.397857i	−0.0165177	−	0.0138600i
$825$		0			0
$826$	0.0655328	−	0.130993i	0.00228018	−	0.00455784i
$827$	−28.1258	−	16.2385i	−0.978031	−	0.564667i	−0.0763561	−	0.997081i	$-0.524329\pi$
$827$	−28.1258	−	16.2385i	−0.978031	−	0.564667i	−0.901675	+	0.432414i	$0.857662\pi$
$828$		0			0
$829$			53.6133i			1.86207i	0.364936	+	0.931033i	$0.381091\pi$
$829$			53.6133i			1.86207i	−0.364936	+	0.931033i	$0.618909\pi$
$830$	0.546109	−	0.0962937i	0.0189557	−	0.00334240i
$831$		0			0
$832$	5.08195	+	0.896085i	0.176185	+	0.0310662i
$833$	14.2198	+	18.9772i	0.492687	+	0.657521i
$834$		0			0
$835$	−5.31160	−	30.1236i	−0.183815	−	1.04247i
$836$	−1.95613	+	3.38812i	−0.0676542	+	0.117181i
$837$		0			0
$838$	−0.202204	+	0.116742i	−0.00698501	+	0.00403280i
$839$	−45.4329	−	16.5362i	−1.56852	−	0.570893i	−0.595849	−	0.803096i	$-0.703184\pi$
$839$	−45.4329	−	16.5362i	−1.56852	−	0.570893i	−0.972667	+	0.232203i	$0.925407\pi$
$840$		0			0
$841$	−3.23023	−	2.71049i	−0.111387	−	0.0934651i
$842$	−0.0491583	−	0.135061i	−0.00169411	−	0.00465452i
$843$		0			0
$844$	−0.299109	−	1.69633i	−0.0102958	−	0.0583902i
$845$	−25.1176	+	43.5050i	−0.864073	+	1.49662i
$846$		0			0
$847$	24.6136	−	33.1692i	0.845733	−	1.13971i
$848$	−7.82010	+	1.37889i	−0.268543	+	0.0473514i
$849$		0			0
$850$	0.589830	+	0.104003i	0.0202310	+	0.00356727i
$851$	6.12518	+	1.08003i	0.209968	+	0.0370231i
$852$		0			0
$853$	23.9167	−	4.21716i	0.818892	−	0.144393i	0.251518	−	0.967853i	$-0.419070\pi$
$853$	23.9167	−	4.21716i	0.818892	−	0.144393i	0.567374	+	0.823460i	$0.307959\pi$
$854$	0.342265	+	0.0394664i	0.0117121	+	0.00135051i
$855$		0			0
$856$	0.451331	−	0.781727i	0.0154262	−	0.0267189i
$857$	−6.93629	−	39.3377i	−0.236939	−	1.34375i	−0.838491	−	0.544915i	$-0.816562\pi$
$857$	−6.93629	−	39.3377i	−0.236939	−	1.34375i	0.601552	−	0.798834i	$-0.294549\pi$
$858$		0			0
$859$	−1.98439	−	5.45208i	−0.0677066	−	0.186022i	0.901225	−	0.433352i	$-0.142669\pi$
$859$	−1.98439	−	5.45208i	−0.0677066	−	0.186022i	−0.968931	+	0.247329i	$0.920447\pi$
$860$	−51.0855	−	42.8658i	−1.74200	−	1.46171i
$861$		0			0
$862$	−0.478596	−	0.174195i	−0.0163011	−	0.00593310i
$863$	−18.5008	+	10.6815i	−0.629776	+	0.363601i	−0.780665	−	0.624949i	$-0.785120\pi$
$863$	−18.5008	+	10.6815i	−0.629776	+	0.363601i	0.150889	+	0.988551i	$0.451786\pi$
$864$		0			0
$865$	3.15798	−	5.46978i	0.107374	−	0.185978i
$866$	0.100559	+	0.570301i	0.00341715	+	0.0193796i
$867$		0			0
$868$	−24.8012	+	23.4717i	−0.841809	+	0.796680i
$869$	−6.50516	−	1.14703i	−0.220672	−	0.0389105i
$870$		0			0
$871$	−6.00093	+	1.05813i	−0.203334	+	0.0358532i
$872$		−	0.117987i		−	0.00399554i
$873$		0			0
$874$	−0.00535310	−	0.00309062i	−0.000181071	−	0.000104542i
$875$	−56.0911	−	28.0610i	−1.89623	−	0.948636i
$876$		0			0
$877$	−7.58986	−	6.36865i	−0.256291	−	0.215054i	0.505584	−	0.862777i	$-0.331277\pi$
$877$	−7.58986	−	6.36865i	−0.256291	−	0.215054i	−0.761876	+	0.647723i	$0.775721\pi$
$878$	0.101608	−	0.576246i	0.00342909	−	0.0194474i
$879$		0			0
$880$	52.9306	+	63.0803i	1.78429	+	2.12644i
$881$	4.16378	−	7.21189i	0.140281	−	0.242975i	−0.787321	−	0.616543i	$-0.788533\pi$
$881$	4.16378	−	7.21189i	0.140281	−	0.242975i	0.927603	+	0.373569i	$0.121866\pi$
$882$		0			0
$883$	−8.57726	−	14.8562i	−0.288648	−	0.499953i	0.684839	−	0.728694i	$-0.259872\pi$
$883$	−8.57726	−	14.8562i	−0.288648	−	0.499953i	−0.973487	+	0.228741i	$0.926539\pi$
$884$	1.49574	−	4.10950i	0.0503070	−	0.138217i
$885$		0			0
$886$	−0.297127	−	0.249320i	−0.00998219	−	0.00837605i
$887$	2.61306	−	14.8194i	0.0877378	−	0.497586i	−0.908994	−	0.416809i	$-0.863149\pi$
$887$	2.61306	−	14.8194i	0.0877378	−	0.497586i	0.996732	−	0.0807775i	$-0.0257403\pi$
$888$		0			0
$889$	13.9729	−	9.22126i	0.468637	−	0.309271i
$890$		−	0.345682i		−	0.0115873i
$891$		0			0
$892$	27.2931	+	15.7577i	0.913842	+	0.527607i
$893$	−1.79326	−	2.13712i	−0.0600090	−	0.0715160i
$894$		0			0
$895$	22.3454	−	26.6303i	0.746926	−	0.890152i
$896$	1.31117	+	0.390322i	0.0438033	+	0.0130398i
$897$		0			0
$898$	−0.489043	−	0.177997i	−0.0163196	−	0.00593984i
$899$	37.1971			1.24059
$900$		0			0
$901$			6.72777i			0.224135i
$902$	−0.00410254	−	0.0232666i	−0.000136600	−	0.000774694i
$903$		0			0
$904$	−0.251438	+	0.0915161i	−0.00836271	+	0.00304378i
$905$	−3.22034	+	3.83786i	−0.107048	+	0.127575i
$906$		0			0
$907$	25.0503	+	9.11758i	0.831783	+	0.302744i	0.722591	−	0.691276i	$-0.242951\pi$
$907$	25.0503	+	9.11758i	0.831783	+	0.302744i	0.109193	+	0.994021i	$0.465173\pi$
$908$	18.9273			0.628124
$909$		0			0
$910$	0.0656777	−	0.0885070i	0.00217719	−	0.00293398i
$911$	0.769727	+	0.917325i	0.0255022	+	0.0303923i	0.778645	−	0.627465i	$-0.215907\pi$
$911$	0.769727	+	0.917325i	0.0255022	+	0.0303923i	−0.753143	+	0.657857i	$0.771463\pi$
$912$		0			0
$913$	28.4953	−	33.9594i	0.943056	−	1.12389i
$914$	−0.00611714	−	0.0168067i	−0.000202337	−	0.000555916i
$915$		0			0
$916$	1.25906	−	3.45925i	0.0416006	−	0.114297i
$917$	−10.3151	−	1.18943i	−0.340634	−	0.0392783i
$918$		0			0
$919$	−19.4234	−	33.6423i	−0.640718	−	1.10976i	−0.985273	−	0.170990i	$-0.945303\pi$
$919$	−19.4234	−	33.6423i	−0.640718	−	1.10976i	0.344555	−	0.938766i	$-0.388030\pi$
$920$	−0.199368	+	0.167290i	−0.00657297	+	0.00551537i
$921$		0			0
$922$	0.334464	+	0.0589750i	0.0110150	+	0.00194224i
$923$	−1.10977	+	6.29384i	−0.0365286	+	0.207164i
$924$		0			0
$925$	51.6823	−	43.3666i	1.69930	−	1.42589i
$926$	0.320799	+	0.185213i	0.0105421	+	0.00608648i
$927$		0			0
$928$	−0.558850	−	0.967957i	−0.0183452	−	0.0317747i
$929$	14.8623	−	12.4709i	0.487616	−	0.409158i	−0.365555	−	0.930790i	$-0.619121\pi$
$929$	14.8623	−	12.4709i	0.487616	−	0.409158i	0.853171	+	0.521631i	$0.174676\pi$
$930$		0			0
$931$	−2.44086	−	1.04391i	−0.0799960	−	0.0342126i
$932$	7.21725	+	19.8292i	0.236409	+	0.649528i
$933$		0			0
$934$	0.188061	−	0.516693i	0.00615354	−	0.0169067i
$935$	60.4200	−	34.8835i	1.97594	−	1.14081i
$936$		0			0
$937$	−6.25895	+	3.61361i	−0.204471	+	0.118051i	−0.598739	−	0.800944i	$-0.704331\pi$
$937$	−6.25895	+	3.61361i	−0.204471	+	0.118051i	0.394268	+	0.918995i	$0.370998\pi$
$938$	−0.402951	+	0.0240971i	−0.0131568	+	0.000786799i
$939$		0			0
$940$	−55.1860	+	20.0861i	−1.79997	+	0.655135i
$941$	34.1651	−	12.4351i	1.11375	−	0.405373i	0.281384	−	0.959595i	$-0.409207\pi$
$941$	34.1651	−	12.4351i	1.11375	−	0.405373i	0.832368	+	0.554223i	$0.186984\pi$
$942$		0			0
$943$	−0.281366	+	0.0496124i	−0.00916253	+	0.00161560i
$944$	13.6947			0.445723
$945$		0			0
$946$	0.696515			0.0226456
$947$	42.9579	−	7.57464i	1.39594	−	0.246143i	0.575469	−	0.817824i	$-0.304820\pi$
$947$	42.9579	−	7.57464i	1.39594	−	0.246143i	0.820476	+	0.571681i	$0.193709\pi$
$948$		0			0
$949$	−4.30024	+	1.56516i	−0.139592	+	0.0508072i
$950$	−0.0630059	+	0.0229323i	−0.00204418	+	0.000744021i
$951$		0			0
$952$	0.259256	−	0.518226i	0.00840253	−	0.0167958i
$953$	−43.3242	+	25.0133i	−1.40341	+	0.810259i	−0.994741	−	0.102424i	$-0.967340\pi$
$953$	−43.3242	+	25.0133i	−1.40341	+	0.810259i	−0.408669	+	0.912683i	$0.634007\pi$
$954$		0			0
$955$	30.6612	−	17.7022i	0.992172	−	0.572831i
$956$	−3.27036	+	8.98523i	−0.105771	+	0.290603i
$957$		0			0
$958$	−0.210556	−	0.578499i	−0.00680277	−	0.0186905i
$959$	12.4606	−	11.7926i	0.402375	−	0.380804i
$960$		0			0
$961$	−8.16180	+	6.84857i	−0.263284	+	0.220922i
$962$	0.0321807	+	0.0557385i	0.00103755	+	0.00179708i
$963$		0			0
$964$	15.1144	+	8.72628i	0.486801	+	0.281054i
$965$	77.1022	−	64.6964i	2.48201	−	2.08265i
$966$		0			0
$967$	−3.26924	+	18.5408i	−0.105132	+	0.596231i	0.886036	+	0.463616i	$0.153448\pi$
$967$	−3.26924	+	18.5408i	−0.105132	+	0.596231i	−0.991168	+	0.132615i	$0.957663\pi$
$968$	−0.993957	−	0.175261i	−0.0319470	−	0.00563312i
$969$		0			0
$970$	−0.371154	+	0.311435i	−0.0119170	+	0.00999959i
$971$	−2.80491	−	4.85825i	−0.0900140	−	0.155909i	0.817503	−	0.575925i	$-0.195358\pi$
$971$	−2.80491	−	4.85825i	−0.0900140	−	0.155909i	−0.907517	+	0.420016i	$0.862025\pi$
$972$		0			0
$973$	−11.9322	−	8.85441i	−0.382528	−	0.283859i
$974$	−0.115180	+	0.316455i	−0.00369061	+	0.0101399i
$975$		0			0
$976$	11.0175	+	30.2703i	0.352661	+	0.968927i
$977$	−17.7765	+	21.1852i	−0.568720	+	0.677774i	−0.971368	−	0.237581i	$-0.923646\pi$
$977$	−17.7765	+	21.1852i	−0.568720	+	0.677774i	0.402648	+	0.915355i	$0.368090\pi$
$978$		0			0
$979$	−17.7632	−	21.1694i	−0.567715	−	0.676577i
$980$	−38.2234	+	40.7674i	−1.22100	+	1.30227i
$981$		0			0
$982$	0.0448465			0.00143111
$983$	−31.8837	−	11.6047i	−1.01693	−	0.370132i	−0.220840	−	0.975310i	$-0.570880\pi$
$983$	−31.8837	−	11.6047i	−1.01693	−	0.370132i	−0.796091	+	0.605178i	$0.793102\pi$
$984$		0			0
$985$	−32.7564	+	39.0375i	−1.04370	+	1.24384i
$986$	−0.296555	+	0.107937i	−0.00944425	+	0.00343743i
$987$		0			0
$988$	0.0850146	+	0.482142i	0.00270468	+	0.0153390i
$989$		−	8.42302i		−	0.267837i
$990$		0			0
$991$	−24.8565			−0.789593			−0.394796	−	0.918769i	$-0.629185\pi$
$991$	−24.8565			−0.789593			−0.394796	+	0.918769i	$0.629185\pi$
$992$	1.17615	+	0.428084i	0.0373429	+	0.0135917i
$993$		0			0
$994$	−0.120795	+	0.405776i	−0.00383139	+	0.0128704i
$995$	52.2757	−	62.2997i	1.65725	−	1.97503i
$996$		0			0
$997$	−37.3905	−	44.5602i	−1.18417	−	1.41124i	−0.890291	−	0.455393i	$-0.849499\pi$
$997$	−37.3905	−	44.5602i	−1.18417	−	1.41124i	−0.293877	−	0.955843i	$-0.594946\pi$
$998$	0.0569679	+	0.0328904i	0.00180329	+	0.00104113i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.11		132
3.2	odd	2		189.2.bd.a.185.12	yes	132
7.5	odd	6		567.2.ba.a.341.12		132
21.5	even	6		189.2.ba.a.131.11	yes	132
27.7	even	9		189.2.ba.a.101.11	✓	132
27.20	odd	18		567.2.ba.a.143.12		132
189.47	even	18	inner	567.2.bd.a.467.11		132
189.61	odd	18		189.2.bd.a.47.12	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.11	✓	132	27.7	even	9
189.2.ba.a.131.11	yes	132	21.5	even	6
189.2.bd.a.47.12	yes	132	189.61	odd	18
189.2.bd.a.185.12	yes	132	3.2	odd	2
567.2.ba.a.143.12		132	27.20	odd	18
567.2.ba.a.341.12		132	7.5	odd	6
567.2.bd.a.17.11		132	1.1	even	1	trivial
567.2.bd.a.467.11		132	189.47	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0159182 + 0.00280680i) q^{2} +(-1.87914 + 0.683951i) q^{4} +(-3.75147 + 1.36542i) q^{5} +(0.157938 + 2.64103i) q^{7} +(0.0559891 - 0.0323253i) q^{8} +O(q^{10})\)	\(q+(-0.0159182 + 0.00280680i) q^{2} +(-1.87914 + 0.683951i) q^{4} +(-3.75147 + 1.36542i) q^{5} +(0.157938 + 2.64103i) q^{7} +(0.0559891 - 0.0323253i) q^{8} +(0.0558840 - 0.0322646i) q^{10} +(1.76436 - 4.84753i) q^{11} +(-0.220791 - 0.606618i) q^{13} +(-0.00992693 - 0.0415971i) q^{14} +(3.06298 - 2.57014i) q^{16} +(-1.69383 - 2.93380i) q^{17} +(0.328436 + 0.189623i) q^{19} +(6.11565 - 5.13164i) q^{20} +(-0.0144792 + 0.0821158i) q^{22} +(0.993035 + 0.175099i) q^{23} +(8.37891 - 7.03074i) q^{25} +(0.00521724 + 0.00903653i) q^{26} +(-2.10312 - 4.85485i) q^{28} +(-1.97120 + 5.41582i) q^{29} +(-2.20741 - 6.06480i) q^{31} +(-0.124656 + 0.148560i) q^{32} +(0.0351973 + 0.0419465i) q^{34} +(-4.19863 - 9.69210i) q^{35} +6.16814 q^{37} +(-0.00576033 - 0.00209659i) q^{38} +(-0.165904 + 0.197716i) q^{40} +(-0.266252 + 0.0969077i) q^{41} +(-1.45052 - 8.22633i) q^{43} +10.3159i q^{44} -0.0162988 q^{46} +(-6.91258 - 2.51597i) q^{47} +(-6.95011 + 0.834239i) q^{49} +(-0.113643 + 0.135434i) q^{50} +(0.829794 + 0.988910i) q^{52} +(-1.71989 - 0.992981i) q^{53} +20.5944i q^{55} +(0.0942150 + 0.142764i) q^{56} +(0.0161767 - 0.0917427i) q^{58} +(2.62371 + 2.20155i) q^{59} +(-2.75545 + 7.57053i) q^{61} +(0.0521605 + 0.0903447i) q^{62} +(-3.99687 + 6.92277i) q^{64} +(1.65658 + 1.97424i) q^{65} +(1.63911 - 9.29584i) q^{67} +(5.18952 + 4.35453i) q^{68} +(0.0940381 + 0.142496i) q^{70} +(-8.57363 - 4.94999i) q^{71} -7.08887i q^{73} +(-0.0981854 + 0.0173127i) q^{74} +(-0.746871 - 0.131693i) q^{76} +(13.0811 + 3.89411i) q^{77} +(-0.222353 - 1.26102i) q^{79} +(-7.98133 + 13.8241i) q^{80} +(0.00396624 - 0.00228991i) q^{82} +(8.07527 + 2.93916i) q^{83} +(10.3602 + 8.69327i) q^{85} +(0.0461793 + 0.126877i) q^{86} +(-0.0579132 - 0.328442i) q^{88} +(2.67849 - 4.63928i) q^{89} +(1.56723 - 0.678924i) q^{91} +(-1.98581 + 0.350152i) q^{92} +(0.117097 + 0.0206474i) q^{94} +(-1.49103 - 0.262910i) q^{95} +(-7.39427 + 1.30381i) q^{97} +(0.108291 - 0.0327871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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