LMFDB - Embedded newform 567.2.bd.a.17.15

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			17.15
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.910598 - 0.160563i) q^{2} +(-1.07598 + 0.391623i) q^{4} +(0.473927 - 0.172495i) q^{5} +(-2.46079 - 0.971863i) q^{7} +(-2.51844 + 1.45402i) q^{8} +O(q^{10})$	\(q+(0.910598 - 0.160563i) q^{2} +(-1.07598 + 0.391623i) q^{4} +(0.473927 - 0.172495i) q^{5} +(-2.46079 - 0.971863i) q^{7} +(-2.51844 + 1.45402i) q^{8} +(0.403861 - 0.233169i) q^{10} +(-1.66156 + 4.56510i) q^{11} +(1.60911 + 4.42100i) q^{13} +(-2.39684 - 0.489865i) q^{14} +(-0.305533 + 0.256373i) q^{16} +(2.38696 + 4.13434i) q^{17} +(-5.51758 - 3.18557i) q^{19} +(-0.442381 + 0.371202i) q^{20} +(-0.780028 + 4.42376i) q^{22} +(3.53298 + 0.622960i) q^{23} +(-3.63537 + 3.05044i) q^{25} +(2.17510 + 3.76739i) q^{26} +(3.02836 + 0.0819996i) q^{28} +(-0.997075 + 2.73944i) q^{29} +(-0.268468 - 0.737610i) q^{31} +(3.50145 - 4.17286i) q^{32} +(2.83739 + 3.38147i) q^{34} +(-1.33388 - 0.0361178i) q^{35} -5.47451 q^{37} +(-5.53578 - 2.01486i) q^{38} +(-0.942744 + 1.12352i) q^{40} +(5.44849 - 1.98309i) q^{41} +(-1.36729 - 7.75429i) q^{43} -5.56264i q^{44} +3.31715 q^{46} +(-7.22256 - 2.62880i) q^{47} +(5.11096 + 4.78310i) q^{49} +(-2.82057 + 3.36143i) q^{50} +(-3.46273 - 4.12672i) q^{52} +(-4.26125 - 2.46023i) q^{53} +2.45014i q^{55} +(7.61045 - 1.13046i) q^{56} +(-0.468082 + 2.65462i) q^{58} +(4.08557 + 3.42820i) q^{59} +(-2.45624 + 6.74846i) q^{61} +(-0.362900 - 0.628561i) q^{62} +(2.91725 - 5.05283i) q^{64} +(1.52520 + 1.81767i) q^{65} +(1.51964 - 8.61830i) q^{67} +(-4.18742 - 3.51366i) q^{68} +(-1.22043 + 0.181283i) q^{70} +(11.3110 + 6.53043i) q^{71} +9.73306i q^{73} +(-4.98508 + 0.879004i) q^{74} +(7.18433 + 1.26679i) q^{76} +(8.52540 - 9.61893i) q^{77} +(-0.825069 - 4.67920i) q^{79} +(-0.100577 + 0.174205i) q^{80} +(4.64298 - 2.68063i) q^{82} +(2.75845 + 1.00400i) q^{83} +(1.84440 + 1.54764i) q^{85} +(-2.49011 - 6.84151i) q^{86} +(-2.45321 - 13.9128i) q^{88} +(-5.60470 + 9.70762i) q^{89} +(0.336922 - 12.4430i) q^{91} +(-4.04537 + 0.713308i) q^{92} +(-6.99893 - 1.23410i) q^{94} +(-3.16443 - 0.557974i) q^{95} +(2.41733 - 0.426241i) q^{97} +(5.42202 + 3.53485i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.910598	−	0.160563i	0.643890	−	0.113535i	0.157838	−	0.987465i	$-0.449548\pi$
$2$	0.910598	−	0.160563i	0.643890	−	0.113535i	0.486052	+	0.873930i	$0.338436\pi$
$3$		0			0
$3$		0			0
$4$	−1.07598	+	0.391623i	−0.537988	+	0.195812i
$5$	0.473927	−	0.172495i	0.211947	−	0.0771423i	−0.233865	−	0.972269i	$-0.575137\pi$
$5$	0.473927	−	0.172495i	0.211947	−	0.0771423i	0.445812	+	0.895127i	$0.352915\pi$
$6$		0			0
$7$	−2.46079	−	0.971863i	−0.930091	−	0.367330i
$7$	−2.46079	−	0.971863i	−0.930091	−	0.367330i
$8$	−2.51844	+	1.45402i	−0.890401	+	0.514073i
$9$		0			0
$10$	0.403861	−	0.233169i	0.127712	−	0.0737346i
$11$	−1.66156	+	4.56510i	−0.500979	+	1.37643i	0.389341	+	0.921094i	$0.372703\pi$
$11$	−1.66156	+	4.56510i	−0.500979	+	1.37643i	−0.890320	+	0.455335i	$0.849519\pi$
$12$		0			0
$13$	1.60911	+	4.42100i	0.446287	+	1.22616i	0.935290	+	0.353882i	$0.115138\pi$
$13$	1.60911	+	4.42100i	0.446287	+	1.22616i	−0.489003	+	0.872282i	$0.662639\pi$
$14$	−2.39684	−	0.489865i	−0.640581	−	0.130922i
$15$		0			0
$16$	−0.305533	+	0.256373i	−0.0763833	+	0.0640932i
$17$	2.38696	+	4.13434i	0.578923	+	1.00272i	0.995603	+	0.0936714i	$0.0298603\pi$
$17$	2.38696	+	4.13434i	0.578923	+	1.00272i	−0.416680	+	0.909053i	$0.636806\pi$
$18$		0			0
$19$	−5.51758	−	3.18557i	−1.26582	−	0.730821i	−0.291625	−	0.956533i	$-0.594196\pi$
$19$	−5.51758	−	3.18557i	−1.26582	−	0.730821i	−0.974194	+	0.225712i	$0.927529\pi$
$20$	−0.442381	+	0.371202i	−0.0989195	+	0.0830033i
$21$		0			0
$22$	−0.780028	+	4.42376i	−0.166302	+	0.943148i
$23$	3.53298	+	0.622960i	0.736677	+	0.129896i	0.529383	−	0.848383i	$-0.322423\pi$
$23$	3.53298	+	0.622960i	0.736677	+	0.129896i	0.207294	+	0.978279i	$0.433534\pi$
$24$		0			0
$25$	−3.63537	+	3.05044i	−0.727074	+	0.610087i
$26$	2.17510	+	3.76739i	0.426573	+	0.738846i
$27$		0			0
$28$	3.02836	+	0.0819996i	0.572305	+	0.0154965i
$29$	−0.997075	+	2.73944i	−0.185152	+	0.508701i	−0.997191	−	0.0749022i	$-0.976136\pi$
$29$	−0.997075	+	2.73944i	−0.185152	+	0.508701i	0.812039	+	0.583604i	$0.198358\pi$
$30$		0			0
$31$	−0.268468	−	0.737610i	−0.0482183	−	0.132479i	0.913246	−	0.407409i	$-0.133568\pi$
$31$	−0.268468	−	0.737610i	−0.0482183	−	0.132479i	−0.961464	+	0.274930i	$0.911345\pi$
$32$	3.50145	−	4.17286i	0.618975	−	0.737665i
$33$		0			0
$34$	2.83739	+	3.38147i	0.486608	+	0.579916i
$35$	−1.33388	−	0.0361178i	−0.225466	−	0.00610501i
$36$		0			0
$37$	−5.47451			−0.900004			−0.450002	−	0.893028i	$-0.648577\pi$
$37$	−5.47451			−0.900004			−0.450002	+	0.893028i	$0.648577\pi$
$38$	−5.53578	−	2.01486i	−0.898022	−	0.326853i
$39$		0			0
$40$	−0.942744	+	1.12352i	−0.149061	+	0.177644i
$41$	5.44849	−	1.98309i	0.850912	−	0.309707i	0.120500	−	0.992713i	$-0.461550\pi$
$41$	5.44849	−	1.98309i	0.850912	−	0.309707i	0.730412	+	0.683007i	$0.239328\pi$
$42$		0			0
$43$	−1.36729	−	7.75429i	−0.208510	−	1.18252i	−0.891820	−	0.452390i	$-0.850571\pi$
$43$	−1.36729	−	7.75429i	−0.208510	−	1.18252i	0.683310	−	0.730128i	$-0.260540\pi$
$44$		−	5.56264i		−	0.838600i
$45$		0			0
$46$	3.31715			0.489087
$47$	−7.22256	−	2.62880i	−1.05352	−	0.383449i	−0.243529	−	0.969894i	$-0.578305\pi$
$47$	−7.22256	−	2.62880i	−1.05352	−	0.383449i	−0.809989	+	0.586445i	$0.800527\pi$
$48$		0			0
$49$	5.11096	+	4.78310i	0.730138	+	0.683300i
$50$	−2.82057	+	3.36143i	−0.398889	+	0.475378i
$51$		0			0
$52$	−3.46273	−	4.12672i	−0.480194	−	0.572273i
$53$	−4.26125	−	2.46023i	−0.585328	−	0.337939i	0.177920	−	0.984045i	$-0.443063\pi$
$53$	−4.26125	−	2.46023i	−0.585328	−	0.337939i	−0.763248	+	0.646106i	$0.776396\pi$
$54$		0			0
$55$			2.45014i			0.330376i
$56$	7.61045	−	1.13046i	1.01699	−	0.151064i
$57$		0			0
$58$	−0.468082	+	2.65462i	−0.0614621	+	0.348569i
$59$	4.08557	+	3.42820i	0.531896	+	0.446313i	0.868755	−	0.495241i	$-0.164920\pi$
$59$	4.08557	+	3.42820i	0.531896	+	0.446313i	−0.336860	+	0.941555i	$0.609365\pi$
$60$		0			0
$61$	−2.45624	+	6.74846i	−0.314489	+	0.864052i	0.677247	+	0.735756i	$0.263173\pi$
$61$	−2.45624	+	6.74846i	−0.314489	+	0.864052i	−0.991736	+	0.128296i	$0.959049\pi$
$62$	−0.362900	−	0.628561i	−0.0460883	−	0.0798273i
$63$		0			0
$64$	2.91725	−	5.05283i	0.364656	−	0.631603i
$65$	1.52520	+	1.81767i	0.189178	+	0.225454i
$66$		0			0
$67$	1.51964	−	8.61830i	0.185653	−	1.05289i	−0.739460	−	0.673201i	$-0.764919\pi$
$67$	1.51964	−	8.61830i	0.185653	−	1.05289i	0.925113	−	0.379692i	$-0.123970\pi$
$68$	−4.18742	−	3.51366i	−0.507799	−	0.426094i
$69$		0			0
$70$	−1.22043	+	0.181283i	−0.145869	+	0.0216674i
$71$	11.3110	+	6.53043i	1.34237	+	0.775019i	0.987155	−	0.159764i	$-0.0510735\pi$
$71$	11.3110	+	6.53043i	1.34237	+	0.775019i	0.355217	+	0.934784i	$0.384407\pi$
$72$		0			0
$73$			9.73306i			1.13917i	0.821933	+	0.569584i	$0.192896\pi$
$73$			9.73306i			1.13917i	−0.821933	+	0.569584i	$0.807104\pi$
$74$	−4.98508	+	0.879004i	−0.579504	+	0.102182i
$75$		0			0
$76$	7.18433	+	1.26679i	0.824099	+	0.145311i
$77$	8.52540	−	9.61893i	0.971560	−	1.09618i
$78$		0			0
$79$	−0.825069	−	4.67920i	−0.0928275	−	0.526451i	−0.995391	−	0.0958952i	$-0.969429\pi$
$79$	−0.825069	−	4.67920i	−0.0928275	−	0.526451i	0.902564	−	0.430556i	$-0.141682\pi$
$80$	−0.100577	+	0.174205i	−0.0112449	+	0.0194767i
$81$		0			0
$82$	4.64298	−	2.68063i	0.512731	−	0.296026i
$83$	2.75845	+	1.00400i	0.302780	+	0.110203i	0.488942	−	0.872316i	$-0.337383\pi$
$83$	2.75845	+	1.00400i	0.302780	+	0.110203i	−0.186163	+	0.982519i	$0.559605\pi$
$84$		0			0
$85$	1.84440	+	1.54764i	0.200053	+	0.167865i
$86$	−2.49011	−	6.84151i	−0.268515	−	0.737739i
$87$		0			0
$88$	−2.45321	−	13.9128i	−0.261513	−	1.48311i
$89$	−5.60470	+	9.70762i	−0.594097	+	1.02901i	0.399577	+	0.916700i	$0.369157\pi$
$89$	−5.60470	+	9.70762i	−0.594097	+	1.02901i	−0.993674	+	0.112306i	$0.964176\pi$
$90$		0			0
$91$	0.336922	−	12.4430i	0.0353190	−	1.30438i
$92$	−4.04537	+	0.713308i	−0.421759	+	0.0743675i
$93$		0			0
$94$	−6.99893	−	1.23410i	−0.721885	−	0.127288i
$95$	−3.16443	−	0.557974i	−0.324663	−	0.0572469i
$96$		0			0
$97$	2.41733	−	0.426241i	0.245443	−	0.0432783i	−0.0495730	−	0.998771i	$-0.515786\pi$
$97$	2.41733	−	0.426241i	0.245443	−	0.0432783i	0.295016	+	0.955492i	$0.404675\pi$
$98$	5.42202	+	3.53485i	0.547707	+	0.357074i
$99$		0			0
$100$	2.71695	−	4.70589i	0.271695	−	0.470589i
$101$	1.05002	+	5.95496i	0.104481	+	0.592540i	0.991426	+	0.130666i	$0.0417116\pi$
$101$	1.05002	+	5.95496i	0.104481	+	0.592540i	−0.886946	+	0.461874i	$0.847177\pi$
$102$		0			0
$103$	3.34509	+	9.19055i	0.329601	+	0.905572i	0.988212	+	0.153089i	$0.0489220\pi$
$103$	3.34509	+	9.19055i	0.329601	+	0.905572i	−0.658611	+	0.752483i	$0.728856\pi$
$104$	−10.4807	−	8.79431i	−1.02771	−	0.862354i
$105$		0			0
$106$	−4.27531	−	1.55609i	−0.415255	−	0.151140i
$107$	13.9175	−	8.03528i	1.34546	−	0.776800i	0.357855	−	0.933777i	$-0.383508\pi$
$107$	13.9175	−	8.03528i	1.34546	−	0.776800i	0.987602	+	0.156977i	$0.0501749\pi$
$108$		0			0
$109$	7.22285	−	12.5103i	0.691823	−	1.19827i	−0.279417	−	0.960170i	$-0.590141\pi$
$109$	7.22285	−	12.5103i	0.691823	−	1.19827i	0.971240	−	0.238103i	$-0.0765256\pi$
$110$	0.393401	+	2.23109i	0.0375093	+	0.212726i
$111$		0			0
$112$	1.00101	−	0.333943i	0.0945867	−	0.0315546i
$113$	1.50934	+	0.266138i	0.141987	+	0.0250361i	0.244190	−	0.969727i	$-0.421478\pi$
$113$	1.50934	+	0.266138i	0.141987	+	0.0250361i	−0.102203	+	0.994764i	$0.532589\pi$
$114$		0			0
$115$	1.78183	−	0.314185i	0.166157	−	0.0292979i
$116$		−	3.33805i		−	0.309930i
$117$		0			0
$118$	4.27075	+	2.46572i	0.393155	+	0.226988i
$119$	−1.85580	−	12.4935i	−0.170121	−	1.14528i
$120$		0			0
$121$	−9.65286	−	8.09971i	−0.877532	−	0.736337i
$122$	−1.15309	+	6.53952i	−0.104396	+	0.592060i
$123$		0			0
$124$	0.577731	+	0.688513i	0.0518818	+	0.0618303i
$125$	−2.45757	+	4.25664i	−0.219812	+	0.380725i
$126$		0			0
$127$	5.33708	+	9.24410i	0.473590	+	0.820281i	0.999543	−	0.0302322i	$-0.00962466\pi$
$127$	5.33708	+	9.24410i	0.473590	+	0.820281i	−0.525953	+	0.850513i	$0.676291\pi$
$128$	−1.88102	+	5.16805i	−0.166260	+	0.456796i
$129$		0			0
$130$	1.68070	+	1.41027i	0.147407	+	0.123689i
$131$	1.59928	−	9.06999i	0.139730	−	0.792449i	−0.831718	−	0.555198i	$-0.812643\pi$
$131$	1.59928	−	9.06999i	0.139730	−	0.792449i	0.971448	−	0.237251i	$-0.0762463\pi$
$132$		0			0
$133$	10.4816	+	13.2014i	0.908874	+	1.14470i
$134$		−	8.09180i		−	0.699025i
$135$		0			0
$136$	−12.0228	−	6.94138i	−1.03095	−	0.595218i
$137$	−9.57049	−	11.4057i	−0.817663	−	0.974452i	0.182299	−	0.983243i	$-0.441646\pi$
$137$	−9.57049	−	11.4057i	−0.817663	−	0.974452i	−0.999961	+	0.00879090i	$0.997202\pi$
$138$		0			0
$139$	−6.89067	+	8.21198i	−0.584459	+	0.696531i	−0.974531	−	0.224254i	$-0.928006\pi$
$139$	−6.89067	+	8.21198i	−0.584459	+	0.696531i	0.390072	+	0.920784i	$0.372450\pi$
$140$	1.44936	−	0.483516i	0.122494	−	0.0408645i
$141$		0			0
$142$	11.3484	+	4.13046i	0.952333	+	0.346621i
$143$	−22.8559			−1.91131
$144$		0			0
$145$			1.47029i			0.122101i
$146$	1.56277	+	8.86290i	0.129336	+	0.733499i
$147$		0			0
$148$	5.89045	−	2.14395i	0.484192	−	0.176231i
$149$	−1.37019	+	1.63293i	−0.112250	+	0.133775i	−0.819244	−	0.573445i	$-0.805606\pi$
$149$	−1.37019	+	1.63293i	−0.112250	+	0.133775i	0.706994	+	0.707220i	$0.250051\pi$
$150$		0			0
$151$	−6.24885	−	2.27439i	−0.508524	−	0.185088i	0.0750000	−	0.997184i	$-0.476104\pi$
$151$	−6.24885	−	2.27439i	−0.508524	−	0.185088i	−0.583524	+	0.812096i	$0.698327\pi$
$152$	18.5276			1.50278
$153$		0			0
$154$	6.21877	−	10.1278i	0.501123	−	0.816125i
$155$	−0.254469	−	0.303264i	−0.0204394	−	0.0243588i
$156$		0			0
$157$	−0.380802	+	0.453822i	−0.0303913	+	0.0362189i	−0.781026	−	0.624499i	$-0.785303\pi$
$157$	−0.380802	+	0.453822i	−0.0303913	+	0.0362189i	0.750635	+	0.660717i	$0.229748\pi$
$158$	−1.50261	−	4.12840i	−0.119541	−	0.328438i
$159$		0			0
$160$	0.939632	−	2.58162i	0.0742844	−	0.204095i
$161$	−8.08848	−	4.96655i	−0.637462	−	0.391419i
$162$		0			0
$163$	9.38783	+	16.2602i	0.735311	+	1.27360i	0.954587	+	0.297934i	$0.0962975\pi$
$163$	9.38783	+	16.2602i	0.735311	+	1.27360i	−0.219275	+	0.975663i	$0.570369\pi$
$164$	−5.08583	+	4.26752i	−0.397136	+	0.333237i
$165$		0			0
$166$	2.67305	+	0.471331i	0.207469	+	0.0365823i
$167$	−2.39928	+	13.6070i	−0.185662	+	1.05294i	0.739441	+	0.673221i	$0.235090\pi$
$167$	−2.39928	+	13.6070i	−0.185662	+	1.05294i	−0.925102	+	0.379718i	$0.876021\pi$
$168$		0			0
$169$	−6.99739	+	5.87151i	−0.538261	+	0.451654i
$170$	1.92800	+	1.11313i	0.147871	+	0.0853734i
$171$		0			0
$172$	4.50794	+	7.80797i	0.343727	+	0.595352i
$173$	−3.37313	+	2.83039i	−0.256454	+	0.215191i	−0.761946	−	0.647641i	$-0.775756\pi$
$173$	−3.37313	+	2.83039i	−0.256454	+	0.215191i	0.505491	+	0.862832i	$0.331311\pi$
$174$		0			0
$175$	11.9105	−	3.97340i	0.900348	−	0.300361i
$176$	−0.662705	−	1.82077i	−0.0499533	−	0.137246i
$177$		0			0
$178$	−3.54494	+	9.73965i	−0.265705	+	0.730017i
$179$	2.60964	−	1.50667i	0.195053	−	0.112614i	−0.399293	−	0.916823i	$-0.630744\pi$
$179$	2.60964	−	1.50667i	0.195053	−	0.112614i	0.594346	+	0.804209i	$0.297411\pi$
$180$		0			0
$181$	−1.98157	+	1.14406i	−0.147289	+	0.0850373i	−0.571833	−	0.820370i	$-0.693768\pi$
$181$	−1.98157	+	1.14406i	−0.147289	+	0.0850373i	0.424544	+	0.905407i	$0.360434\pi$
$182$	−1.69108	−	11.3846i	−0.125351	−	0.843886i
$183$		0			0
$184$	−9.80338	+	3.56814i	−0.722715	+	0.263047i
$185$	−2.59452	+	0.944328i	−0.190753	+	0.0694284i
$186$		0			0
$187$	−22.8398	+	4.02726i	−1.67021	+	0.294503i
$188$	8.80080			0.641864
$189$		0			0
$190$	−2.97111			−0.215547
$191$	−12.9505	+	2.28352i	−0.937063	+	0.165229i	−0.621268	−	0.783598i	$-0.713382\pi$
$191$	−12.9505	+	2.28352i	−0.937063	+	0.165229i	−0.315795	+	0.948828i	$0.602271\pi$
$192$		0			0
$193$	0.0352236	−	0.0128203i	0.00253545	−	0.000922827i	−0.340752	−	0.940153i	$-0.610682\pi$
$193$	0.0352236	−	0.0128203i	0.00253545	−	0.000922827i	0.343288	+	0.939230i	$0.388459\pi$
$194$	2.13278	−	0.776269i	0.153125	−	0.0557329i
$195$		0			0
$196$	−7.37245	−	3.14493i	−0.526604	−	0.224638i
$197$	4.43094	−	2.55821i	0.315692	−	0.182265i	−0.333779	−	0.942651i	$-0.608324\pi$
$197$	4.43094	−	2.55821i	0.315692	−	0.182265i	0.649471	+	0.760387i	$0.274991\pi$
$198$		0			0
$199$	5.34761	−	3.08744i	0.379082	−	0.218863i	−0.298337	−	0.954461i	$-0.596432\pi$
$199$	5.34761	−	3.08744i	0.379082	−	0.218863i	0.677419	+	0.735598i	$0.263099\pi$
$200$	4.72005	−	12.9682i	0.333758	−	0.916992i
$201$		0			0
$202$	1.91229	+	5.25398i	0.134548	+	0.369669i
$203$	5.11595	−	5.77216i	0.359069	−	0.405126i
$204$		0			0
$205$	2.24012	−	1.87968i	0.156457	−	0.131283i
$206$	4.52169	+	7.83180i	0.315041	+	0.545668i
$207$		0			0
$208$	−1.62506	−	0.938229i	−0.112678	−	0.0650545i
$209$	23.7103	−	19.8953i	1.64007	−	1.37618i
$210$		0			0
$211$	0.583521	−	3.30931i	0.0401712	−	0.227822i	−0.958112	−	0.286394i	$-0.907543\pi$
$211$	0.583521	−	3.30931i	0.0401712	−	0.227822i	0.998283	+	0.0585715i	$0.0186546\pi$
$212$	5.54849	+	0.978349i	0.381072	+	0.0671933i
$213$		0			0
$214$	11.3831	−	9.55155i	0.778133	−	0.652931i
$215$	−1.98558	−	3.43912i	−0.135415	−	0.234546i
$216$		0			0
$217$	−0.0562129	+	2.07602i	−0.00381598	+	0.140929i
$218$	4.56841	−	12.5516i	0.309412	−	0.850103i
$219$		0			0
$220$	−0.959531	−	2.63629i	−0.0646915	−	0.177739i
$221$	−14.4370	+	17.2054i	−0.971139	+	1.15736i
$222$		0			0
$223$	4.25268	+	5.06814i	0.284780	+	0.339388i	0.889403	−	0.457124i	$-0.151120\pi$
$223$	4.25268	+	5.06814i	0.284780	+	0.339388i	−0.604623	+	0.796512i	$0.706676\pi$
$224$	−12.6718	+	6.86561i	−0.846669	+	0.458728i
$225$		0			0
$226$	1.41714			0.0942665
$227$	9.85012	+	3.58515i	0.653775	+	0.237955i	0.647547	−	0.762026i	$-0.275795\pi$
$227$	9.85012	+	3.58515i	0.653775	+	0.237955i	0.00622869	+	0.999981i	$0.498017\pi$
$228$		0			0
$229$	11.2293	−	13.3825i	0.742052	−	0.884343i	−0.254521	−	0.967067i	$-0.581918\pi$
$229$	11.2293	−	13.3825i	0.742052	−	0.884343i	0.996572	+	0.0827244i	$0.0263621\pi$
$230$	1.57209	−	0.572193i	0.103660	−	0.0377293i
$231$		0			0
$232$	−1.47213	−	8.34887i	−0.0966501	−	0.548130i
$233$			10.2714i			0.672900i	0.941701	+	0.336450i	$0.109226\pi$
$233$			10.2714i			0.672900i	−0.941701	+	0.336450i	$0.890774\pi$
$234$		0			0
$235$	−3.87642			−0.252870
$236$	−5.73854	−	2.08866i	−0.373547	−	0.135960i
$237$		0			0
$238$	−3.69589	−	11.0786i	−0.239569	−	0.718120i
$239$	−14.4600	+	17.2328i	−0.935342	+	1.11470i	0.0578640	+	0.998324i	$0.481571\pi$
$239$	−14.4600	+	17.2328i	−0.935342	+	1.11470i	−0.993206	+	0.116372i	$0.962873\pi$
$240$		0			0
$241$	5.50391	+	6.55931i	0.354538	+	0.422522i	0.913606	−	0.406600i	$-0.133286\pi$
$241$	5.50391	+	6.55931i	0.354538	+	0.422522i	−0.559068	+	0.829121i	$0.688841\pi$
$242$	−10.0904	−	5.82569i	−0.648635	−	0.374489i
$243$		0			0
$244$		−	8.22310i		−	0.526430i
$245$	3.24729	+	1.38522i	0.207462	+	0.0884987i
$246$		0			0
$247$	5.20502	−	29.5191i	0.331187	−	1.87826i
$248$	1.74862	+	1.46727i	0.111037	+	0.0931715i
$249$		0			0
$250$	−1.55440	+	4.27068i	−0.0983090	+	0.270102i
$251$	8.90861	+	15.4302i	0.562307	+	0.973943i	0.997295	+	0.0735073i	$0.0234192\pi$
$251$	8.90861	+	15.4302i	0.562307	+	0.973943i	−0.434988	+	0.900436i	$0.643247\pi$
$252$		0			0
$253$	−8.71413	+	15.0933i	−0.547853	+	0.948909i
$254$	6.34420	+	7.56072i	0.398071	+	0.474402i
$255$		0			0
$256$	−2.90935	+	16.4998i	−0.181835	+	1.03124i
$257$	18.3114	+	15.3650i	1.14223	+	0.958445i	0.999509	−	0.0313176i	$-0.00997034\pi$
$257$	18.3114	+	15.3650i	1.14223	+	0.958445i	0.142721	+	0.989763i	$0.454415\pi$
$258$		0			0
$259$	13.4716	+	5.32048i	0.837086	+	0.330598i
$260$	−2.35292	−	1.35846i	−0.145922	−	0.0842482i
$261$		0			0
$262$		−	8.51590i		−	0.526114i
$263$	8.75677	−	1.54405i	0.539965	−	0.0952104i	0.102987	−	0.994683i	$-0.467160\pi$
$263$	8.75677	−	1.54405i	0.539965	−	0.0952104i	0.436978	+	0.899472i	$0.356049\pi$
$264$		0			0
$265$	−2.44390	−	0.430926i	−0.150128	−	0.0264716i
$266$	11.6642	+	10.3382i	0.715179	+	0.633874i
$267$		0			0
$268$	1.74003	+	9.86821i	0.106289	+	0.602797i
$269$	0.579284	−	1.00335i	0.0353195	−	0.0611752i	−0.847825	−	0.530276i	$-0.822088\pi$
$269$	0.579284	−	1.00335i	0.0353195	−	0.0611752i	0.883145	+	0.469100i	$0.155422\pi$
$270$		0			0
$271$	−22.8894	+	13.2152i	−1.39043	+	0.802766i	−0.993363	−	0.115023i	$-0.963306\pi$
$271$	−22.8894	+	13.2152i	−1.39043	+	0.802766i	−0.397069	+	0.917789i	$0.629973\pi$
$272$	−1.78923	−	0.651226i	−0.108488	−	0.0394864i
$273$		0			0
$274$	−10.5462	−	8.84932i	−0.637120	−	0.534607i
$275$	−7.88516	−	21.6643i	−0.475493	−	1.30641i
$276$		0			0
$277$	−1.90615	−	10.8103i	−0.114529	−	0.649529i	−0.986982	−	0.160830i	$-0.948583\pi$
$277$	−1.90615	−	10.8103i	−0.114529	−	0.649529i	0.872453	−	0.488699i	$-0.162528\pi$
$278$	−4.95609	+	8.58420i	−0.297246	+	0.514846i
$279$		0			0
$280$	3.41180	−	1.84852i	0.203894	−	0.110470i
$281$	−0.726106	+	0.128032i	−0.0433159	+	0.00763776i	−0.195264	−	0.980751i	$-0.562556\pi$
$281$	−0.726106	+	0.128032i	−0.0433159	+	0.00763776i	0.151948	+	0.988388i	$0.451445\pi$
$282$		0			0
$283$	−9.06936	−	1.59917i	−0.539117	−	0.0950609i	−0.102542	−	0.994729i	$-0.532698\pi$
$283$	−9.06936	−	1.59917i	−0.539117	−	0.0950609i	−0.436575	+	0.899668i	$0.643809\pi$
$284$	−14.7279	−	2.59692i	−0.873939	−	0.154099i
$285$		0			0
$286$	−20.8126	+	3.66982i	−1.23067	+	0.217001i
$287$	−15.3349	−	0.415227i	−0.905190	−	0.0245101i
$288$		0			0
$289$	−2.89518	+	5.01460i	−0.170305	+	0.294976i
$290$	0.236074	+	1.33884i	0.0138627	+	0.0786194i
$291$		0			0
$292$	−3.81169	−	10.4725i	−0.223062	−	0.612859i
$293$	17.3436	+	14.5530i	1.01322	+	0.850196i	0.988761	−	0.149505i	$-0.0477679\pi$
$293$	17.3436	+	14.5530i	1.01322	+	0.850196i	0.0244632	+	0.999701i	$0.492212\pi$
$294$		0			0
$295$	2.52761	+	0.919975i	0.147163	+	0.0535630i
$296$	13.7872	−	7.96005i	0.801365	−	0.462668i
$297$		0			0
$298$	−0.985503	+	1.70694i	−0.0570887	+	0.0988805i
$299$	2.93085	+	16.6217i	0.169496	+	0.961258i
$300$		0			0
$301$	−4.17150	+	20.4105i	−0.240441	+	1.17644i
$302$	−6.05537	−	1.06773i	−0.348448	−	0.0614407i
$303$		0			0
$304$	2.50250	−	0.441258i	0.143528	−	0.0253079i
$305$			3.62197i			0.207393i
$306$		0			0
$307$	−18.3264	−	10.5807i	−1.04594	−	0.603875i	−0.124432	−	0.992228i	$-0.539711\pi$
$307$	−18.3264	−	10.5807i	−1.04594	−	0.603875i	−0.921511	+	0.388353i	$0.873044\pi$
$308$	−5.40613	+	13.6885i	−0.308043	+	0.779974i
$309$		0			0
$310$	−0.280412	−	0.235293i	−0.0159263	−	0.0133638i
$311$	1.43987	−	8.16591i	0.0816476	−	0.463046i	−0.916382	−	0.400304i	$-0.868904\pi$
$311$	1.43987	−	8.16591i	0.0816476	−	0.463046i	0.998030	−	0.0627420i	$-0.0199845\pi$
$312$		0			0
$313$	18.3841	+	21.9093i	1.03913	+	1.23839i	0.970589	+	0.240741i	$0.0773904\pi$
$313$	18.3841	+	21.9093i	1.03913	+	1.23839i	0.0685426	+	0.997648i	$0.478165\pi$
$314$	−0.273890	+	0.474392i	−0.0154565	+	0.0267715i
$315$		0			0
$316$	2.72024	+	4.71159i	0.153025	+	0.265048i
$317$	−6.91030	+	18.9859i	−0.388121	+	1.06635i	0.579725	+	0.814812i	$0.303160\pi$
$317$	−6.91030	+	18.9859i	−0.388121	+	1.06635i	−0.967846	+	0.251542i	$0.919062\pi$
$318$		0			0
$319$	−10.8491	−	9.10349i	−0.607434	−	0.509698i
$320$	0.510975	−	2.89788i	0.0285644	−	0.161997i
$321$		0			0
$322$	−8.16280	−	3.22382i	−0.454895	−	0.179656i
$323$		−	30.4154i		−	1.69236i
$324$		0			0
$325$	−19.3357	−	11.1635i	−1.07255	−	0.619238i
$326$	11.1593	+	13.2992i	0.618058	+	0.736573i
$327$		0			0
$328$	−10.8382	+	12.9165i	−0.598441	+	0.713194i
$329$	15.2184	+	13.4882i	0.839015	+	0.743631i
$330$		0			0
$331$	14.0414	+	5.11066i	0.771786	+	0.280907i	0.697743	−	0.716348i	$-0.254188\pi$
$331$	14.0414	+	5.11066i	0.771786	+	0.280907i	0.0740427	+	0.997255i	$0.476410\pi$
$332$	−3.36122			−0.184471
$333$		0			0
$334$			12.7757i			0.699056i
$335$	−0.766419	−	4.34658i	−0.0418739	−	0.237479i
$336$		0			0
$337$	−10.4942	+	3.81956i	−0.571653	+	0.208065i	−0.611641	−	0.791136i	$-0.709490\pi$
$337$	−10.4942	+	3.81956i	−0.571653	+	0.208065i	0.0399880	+	0.999200i	$0.487268\pi$
$338$	−5.42906	+	6.47011i	−0.295302	+	0.351927i
$339$		0			0
$340$	−2.59062	−	0.942910i	−0.140496	−	0.0511365i
$341$	3.81334			0.206504
$342$		0			0
$343$	−7.92848	−	16.7374i	−0.428098	−	0.903732i
$344$	14.7183	+	17.5406i	0.793559	+	0.945727i
$345$		0			0
$346$	−2.61711	+	3.11895i	−0.140697	+	0.167676i
$347$	6.22372	+	17.0995i	0.334107	+	0.917950i	0.987031	+	0.160528i	$0.0513196\pi$
$347$	6.22372	+	17.0995i	0.334107	+	0.917950i	−0.652925	+	0.757423i	$0.726458\pi$
$348$		0			0
$349$	8.74024	−	24.0136i	0.467854	−	1.28542i	−0.451599	−	0.892221i	$-0.649146\pi$
$349$	8.74024	−	24.0136i	0.467854	−	1.28542i	0.919454	−	0.393198i	$-0.128631\pi$
$350$	10.2077	−	5.53055i	0.545624	−	0.295621i
$351$		0			0
$352$	13.2317	+	22.9179i	0.705250	+	1.22153i
$353$	−9.82463	+	8.24385i	−0.522913	+	0.438776i	−0.865646	−	0.500657i	$-0.833092\pi$
$353$	−9.82463	+	8.24385i	−0.522913	+	0.438776i	0.342733	+	0.939433i	$0.388647\pi$
$354$		0			0
$355$	6.48708	+	1.14385i	0.344298	+	0.0607091i
$356$	2.22879	−	12.6401i	0.118126	−	0.669924i
$357$		0			0
$358$	2.13441	−	1.79099i	0.112807	−	0.0946565i
$359$	−18.5666	−	10.7194i	−0.979908	−	0.565750i	−0.0776659	−	0.996979i	$-0.524747\pi$
$359$	−18.5666	−	10.7194i	−0.979908	−	0.565750i	−0.902242	+	0.431229i	$0.858080\pi$
$360$		0			0
$361$	10.7958	+	18.6988i	0.568199	+	0.984149i
$362$	−1.62072	+	1.35995i	−0.0851831	+	0.0714771i
$363$		0			0
$364$	4.51044	+	13.5203i	0.236411	+	0.708656i
$365$	1.67891	+	4.61276i	0.0878780	+	0.241443i
$366$		0			0
$367$	2.38366	−	6.54905i	0.124426	−	0.341858i	−0.861803	−	0.507243i	$-0.830665\pi$
$367$	2.38366	−	6.54905i	0.124426	−	0.341858i	0.986229	+	0.165385i	$0.0528868\pi$
$368$	−1.23915	+	0.715425i	−0.0645953	+	0.0372941i
$369$		0			0
$370$	−2.21094	+	1.27649i	−0.114941	+	0.0663614i
$371$	8.09503	+	10.1955i	0.420273	+	0.529322i
$372$		0			0
$373$	10.8547	−	3.95079i	0.562035	−	0.204564i	−0.0453508	−	0.998971i	$-0.514441\pi$
$373$	10.8547	−	3.95079i	0.562035	−	0.204564i	0.607386	+	0.794407i	$0.292218\pi$
$374$	−20.1512	+	7.33444i	−1.04199	+	0.379255i
$375$		0			0
$376$	22.0119	−	3.88128i	1.13518	−	0.200162i
$377$	−13.7155			−0.706382
$378$		0			0
$379$	6.46443			0.332055			0.166028	−	0.986121i	$-0.446906\pi$
$379$	6.46443			0.332055			0.166028	+	0.986121i	$0.446906\pi$
$380$	3.62337	−	0.638897i	0.185875	−	0.0327747i
$381$		0			0
$382$	−11.4260	+	4.15873i	−0.584606	+	0.212779i
$383$	2.18674	−	0.795907i	0.111737	−	0.0406690i	−0.285547	−	0.958365i	$-0.592175\pi$
$383$	2.18674	−	0.795907i	0.111737	−	0.0406690i	0.397284	+	0.917696i	$0.369953\pi$
$384$		0			0
$385$	2.38120	−	6.02927i	0.121357	−	0.307280i
$386$	0.0300160	−	0.0173298i	0.00152778	−	0.000882062i
$387$		0			0
$388$	−2.43407	+	1.40531i	−0.123571	+	0.0713438i
$389$	11.2737	−	30.9741i	0.571597	−	1.57045i	−0.230383	−	0.973100i	$-0.573998\pi$
$389$	11.2737	−	30.9741i	0.571597	−	1.57045i	0.801980	−	0.597351i	$-0.203780\pi$
$390$		0			0
$391$	5.85756	+	16.0935i	0.296230	+	0.813884i
$392$	−19.8264	−	4.61449i	−1.00138	−	0.233067i
$393$		0			0
$394$	3.62406	−	3.04094i	0.182577	−	0.153201i
$395$	−1.19816	−	2.07528i	−0.0602861	−	0.104419i
$396$		0			0
$397$	−21.9971	−	12.7000i	−1.10400	−	0.637397i	−0.166734	−	0.986002i	$-0.553322\pi$
$397$	−21.9971	−	12.7000i	−1.10400	−	0.637397i	−0.937270	+	0.348605i	$0.886656\pi$
$398$	4.37379	−	3.67005i	0.219238	−	0.183963i
$399$		0			0
$400$	0.328677	−	1.86402i	0.0164339	−	0.0932010i
$401$	−19.2008	−	3.38563i	−0.958844	−	0.169070i	−0.327740	−	0.944768i	$-0.606287\pi$
$401$	−19.2008	−	3.38563i	−0.958844	−	0.169070i	−0.631104	+	0.775698i	$0.717398\pi$
$402$		0			0
$403$	2.82898	−	2.37379i	0.140921	−	0.118247i
$404$	−3.46190	−	5.99618i	−0.172236	−	0.298321i
$405$		0			0
$406$	3.73178	−	6.07756i	0.185205	−	0.301624i
$407$	9.09623	−	24.9917i	0.450883	−	1.23879i
$408$		0			0
$409$	−5.92119	−	16.2683i	−0.292784	−	0.804417i	−0.995657	−	0.0931015i	$-0.970322\pi$
$409$	−5.92119	−	16.2683i	−0.292784	−	0.804417i	0.702873	−	0.711316i	$-0.251900\pi$
$410$	1.73804	−	2.07131i	0.0858356	−	0.102295i
$411$		0			0
$412$	−7.19847	−	8.57880i	−0.354643	−	0.422647i
$413$	−6.72198	−	12.4067i	−0.330767	−	0.610493i
$414$		0			0
$415$	1.48049			0.0726745
$416$	24.0824	+	8.76529i	1.18074	+	0.429754i
$417$		0			0
$418$	18.3961	−	21.9236i	0.899781	−	1.07232i
$419$	3.08710	−	1.12361i	0.150815	−	0.0548920i	−0.265510	−	0.964108i	$-0.585540\pi$
$419$	3.08710	−	1.12361i	0.150815	−	0.0548920i	0.416324	+	0.909216i	$0.363318\pi$
$420$		0			0
$421$	−0.564741	−	3.20281i	−0.0275238	−	0.156095i	0.967948	−	0.251150i	$-0.0808086\pi$
$421$	−0.564741	−	3.20281i	−0.0275238	−	0.156095i	−0.995472	+	0.0950543i	$0.969698\pi$
$422$		−	3.10714i		−	0.151253i
$423$		0			0
$424$	14.3089			0.694902
$425$	−21.2890	−	7.74858i	−1.03267	−	0.375861i
$426$		0			0
$427$	12.6029	−	14.2194i	0.609895	−	0.688125i
$428$	−11.8281	+	14.0962i	−0.571734	+	0.681366i
$429$		0			0
$430$	−2.36026	−	2.81285i	−0.113822	−	0.135648i
$431$	−29.6610	−	17.1248i	−1.42872	−	0.824872i	−0.431700	−	0.902017i	$-0.642086\pi$
$431$	−29.6610	−	17.1248i	−1.42872	−	0.824872i	−0.997020	+	0.0771457i	$0.975419\pi$
$432$		0			0
$433$			27.4243i			1.31793i	0.752174	+	0.658965i	$0.229005\pi$
$433$			27.4243i			1.31793i	−0.752174	+	0.658965i	$0.770995\pi$
$434$	0.282144	+	1.89944i	0.0135434	+	0.0911762i
$435$		0			0
$436$	−2.87227	+	16.2895i	−0.137557	+	0.780124i
$437$	−17.5090	−	14.6918i	−0.837569	−	0.702804i
$438$		0			0
$439$	1.29268	−	3.55162i	0.0616964	−	0.169510i	−0.905014	−	0.425381i	$-0.860140\pi$
$439$	1.29268	−	3.55162i	0.0616964	−	0.169510i	0.966711	+	0.255871i	$0.0823624\pi$
$440$	−3.56255	−	6.17051i	−0.169838	−	0.294168i
$441$		0			0
$442$	−10.3838	+	17.9852i	−0.493906	+	0.855470i
$443$	13.8797	+	16.5412i	0.659444	+	0.785894i	0.987306	−	0.158831i	$-0.0507726\pi$
$443$	13.8797	+	16.5412i	0.659444	+	0.785894i	−0.327862	+	0.944726i	$0.606328\pi$
$444$		0			0
$445$	−0.981699	+	5.56749i	−0.0465370	+	0.263924i
$446$	4.68624	+	3.93222i	0.221900	+	0.186196i
$447$		0			0
$448$	−12.0894	+	9.59877i	−0.571170	+	0.453499i
$449$	15.0109	+	8.66655i	0.708408	+	0.409000i	0.810471	−	0.585778i	$-0.199211\pi$
$449$	15.0109	+	8.66655i	0.708408	+	0.409000i	−0.102063	+	0.994778i	$0.532544\pi$
$450$		0			0
$451$			28.1679i			1.32638i
$452$	−1.72824	+	0.304736i	−0.0812897	+	0.0143336i
$453$		0			0
$454$	9.54514	+	1.68307i	0.447976	+	0.0789902i
$455$	−1.98668	−	5.95518i	−0.0931370	−	0.279183i
$456$		0			0
$457$	5.69846	+	32.3176i	0.266563	+	1.51175i	0.764548	+	0.644567i	$0.222962\pi$
$457$	5.69846	+	32.3176i	0.266563	+	1.51175i	−0.497985	+	0.867186i	$0.665927\pi$
$458$	8.07662	−	13.9891i	0.377396	−	0.653669i
$459$		0			0
$460$	−1.79417	+	1.03586i	−0.0836535	+	0.0482974i
$461$	−0.748682	−	0.272498i	−0.0348696	−	0.0126915i	0.324526	−	0.945877i	$-0.394795\pi$
$461$	−0.748682	−	0.272498i	−0.0348696	−	0.0126915i	−0.359396	+	0.933185i	$0.617017\pi$
$462$		0			0
$463$	8.79280	+	7.37804i	0.408636	+	0.342887i	0.823820	−	0.566851i	$-0.191838\pi$
$463$	8.79280	+	7.37804i	0.408636	+	0.342887i	−0.415184	+	0.909737i	$0.636283\pi$
$464$	−0.397679	−	1.09261i	−0.0184618	−	0.0507233i
$465$		0			0
$466$	1.64920	+	9.35309i	0.0763978	+	0.433273i
$467$	−2.59486	+	4.49443i	−0.120076	+	0.207977i	−0.919797	−	0.392394i	$-0.871647\pi$
$467$	−2.59486	+	4.49443i	−0.120076	+	0.207977i	0.799722	+	0.600371i	$0.204980\pi$
$468$		0			0
$469$	−12.1153	+	19.7309i	−0.559433	+	0.911090i
$470$	−3.52986	+	0.622410i	−0.162820	+	0.0287096i
$471$		0			0
$472$	−15.2739	−	2.69320i	−0.703039	−	0.123965i
$473$	37.6710	+	6.64241i	1.73211	+	0.305418i
$474$		0			0
$475$	29.7758	−	5.25028i	1.36621	−	0.240899i
$476$	6.88956	+	12.7160i	0.315782	+	0.582836i
$477$		0			0
$478$	−10.4003	+	18.0139i	−0.475700	+	0.823937i
$479$	−3.21688	−	18.2438i	−0.146983	−	0.833582i	−0.965754	−	0.259461i	$-0.916455\pi$
$479$	−3.21688	−	18.2438i	−0.146983	−	0.833582i	0.818771	−	0.574121i	$-0.194656\pi$
$480$		0			0
$481$	−8.80910	−	24.2028i	−0.401660	−	1.10355i
$482$	6.06503	+	5.08917i	0.276255	+	0.231805i
$483$		0			0
$484$	13.5583	+	4.93481i	0.616285	+	0.224310i
$485$	1.07212	−	0.618987i	0.0486823	−	0.0281067i
$486$		0			0
$487$	12.9714	−	22.4672i	0.587792	−	1.01809i	−0.406729	−	0.913549i	$-0.633331\pi$
$487$	12.9714	−	22.4672i	0.587792	−	1.01809i	0.994521	−	0.104537i	$-0.0333360\pi$
$488$	−3.62651	−	20.5670i	−0.164165	−	0.931023i
$489$		0			0
$490$	3.17939	+	0.739988i	0.143630	+	0.0334293i
$491$	−17.9073	−	3.15754i	−0.808146	−	0.142498i	−0.245715	−	0.969342i	$-0.579023\pi$
$491$	−17.9073	−	3.15754i	−0.808146	−	0.142498i	−0.562431	+	0.826844i	$0.690134\pi$
$492$		0			0
$493$	−13.7058	+	2.41669i	−0.617276	+	0.108842i
$494$		−	27.7158i		−	1.24699i
$495$		0			0
$496$	0.271129	+	0.156536i	0.0121741	+	0.00702870i
$497$	−21.4874	−	27.0628i	−0.963841	−	1.21393i
$498$		0			0
$499$	−18.7234	−	15.7108i	−0.838173	−	0.703311i	0.118979	−	0.992897i	$-0.462038\pi$
$499$	−18.7234	−	15.7108i	−0.838173	−	0.703311i	−0.957152	+	0.289586i	$0.906482\pi$
$500$	0.977290	−	5.54249i	0.0437057	−	0.247868i
$501$		0			0
$502$	10.5897	+	12.6203i	0.472641	+	0.563271i
$503$	−7.81528	+	13.5365i	−0.348466	+	0.603561i	−0.985977	−	0.166880i	$-0.946631\pi$
$503$	−7.81528	+	13.5365i	−0.348466	+	0.603561i	0.637511	+	0.770441i	$0.279964\pi$
$504$		0			0
$505$	1.52484	+	2.64109i	0.0678543	+	0.117527i
$506$	−5.51164	+	15.1431i	−0.245022	+	0.673194i
$507$		0			0
$508$	−9.36278	−	7.85631i	−0.415406	−	0.348567i
$509$	4.24348	−	24.0660i	0.188089	−	1.06671i	−0.733833	−	0.679330i	$-0.762271\pi$
$509$	4.24348	−	24.0660i	0.188089	−	1.06671i	0.921922	−	0.387375i	$-0.126618\pi$
$510$		0			0
$511$	9.45920	−	23.9510i	0.418450	−	1.05953i
$512$			4.49234i			0.198535i
$513$		0			0
$514$	19.1413	+	11.0513i	0.844288	+	0.487450i
$515$	3.17066	+	3.77864i	0.139716	+	0.166507i
$516$		0			0
$517$	24.0014	−	28.6038i	1.05558	−	1.25799i
$518$	13.1215	+	2.68177i	0.576526	+	0.117830i
$519$		0			0
$520$	−6.48405	−	2.36000i	−0.284344	−	0.103493i
$521$	33.1998			1.45451			0.727255	−	0.686367i	$-0.240796\pi$
$521$	33.1998			1.45451			0.727255	+	0.686367i	$0.240796\pi$
$522$		0			0
$523$		−	39.1939i		−	1.71383i	−0.515458	−	0.856915i	$-0.672378\pi$
$523$		−	39.1939i		−	1.71383i	0.515458	−	0.856915i	$-0.327622\pi$
$524$	1.83123	+	10.3854i	0.0799976	+	0.453689i
$525$		0			0
$526$	7.72598	−	2.81203i	0.336869	−	0.122610i
$527$	2.40871	−	2.87059i	0.104925	−	0.125045i
$528$		0			0
$529$	−9.51906	−	3.46466i	−0.413872	−	0.150637i
$530$	−2.29460			−0.0996712
$531$		0			0
$532$	−16.4480	−	10.0995i	−0.713110	−	0.437869i
$533$	17.5345	+	20.8968i	0.759502	+	0.905139i
$534$		0			0
$535$	5.20984	−	6.20885i	0.225241	−	0.268432i
$536$	8.70406	+	23.9142i	0.375958	+	1.03294i
$537$		0			0
$538$	0.366394	−	1.00666i	0.0157964	−	0.0434002i
$539$	−30.3275	+	15.3846i	−1.30630	+	0.662663i
$540$		0			0
$541$	−22.2029	−	38.4566i	−0.954578	−	1.65338i	−0.735330	−	0.677709i	$-0.762973\pi$
$541$	−22.2029	−	38.4566i	−0.954578	−	1.65338i	−0.219248	−	0.975669i	$-0.570360\pi$
$542$	−18.7212	+	15.7089i	−0.804143	+	0.674756i
$543$		0			0
$544$	25.6099	+	4.51571i	1.09801	+	0.193609i
$545$	1.26513	−	7.17490i	0.0541921	−	0.307339i
$546$		0			0
$547$	10.6883	−	8.96856i	0.456999	−	0.383468i	−0.385026	−	0.922906i	$-0.625808\pi$
$547$	10.6883	−	8.96856i	0.456999	−	0.383468i	0.842025	+	0.539438i	$0.181363\pi$
$548$	14.7644	+	8.52420i	0.630702	+	0.364136i
$549$		0			0
$550$	−10.6587	−	18.4614i	−0.454489	−	0.787197i
$551$	14.2281	−	11.9388i	0.606139	−	0.508611i
$552$		0			0
$553$	−2.51722	+	12.3164i	−0.107043	+	0.523746i
$554$	−3.47147	−	9.53780i	−0.147489	−	0.405222i
$555$		0			0
$556$	4.19819	−	11.5344i	0.178043	−	0.489169i
$557$	−10.3785	+	5.99202i	−0.439750	+	0.253890i	−0.703492	−	0.710704i	$-0.748377\pi$
$557$	−10.3785	+	5.99202i	−0.439750	+	0.253890i	0.263741	+	0.964593i	$0.415043\pi$
$558$		0			0
$559$	32.0816	−	18.5223i	1.35691	−	0.783410i
$560$	0.416803	−	0.330935i	0.0176132	−	0.0139845i
$561$		0			0
$562$	−0.640634	+	0.233172i	−0.0270235	+	0.00983576i
$563$	0.925935	−	0.337013i	0.0390235	−	0.0142034i	−0.322435	−	0.946592i	$-0.604501\pi$
$563$	0.925935	−	0.337013i	0.0390235	−	0.0142034i	0.361458	+	0.932388i	$0.382279\pi$
$564$		0			0
$565$	0.761226	−	0.134225i	0.0320250	−	0.00564688i
$566$	−8.51531			−0.357925
$567$		0			0
$568$	−37.9815			−1.59367
$569$	−5.45358	+	0.961613i	−0.228626	+	0.0403129i	−0.286787	−	0.957994i	$-0.592587\pi$
$569$	−5.45358	+	0.961613i	−0.228626	+	0.0403129i	0.0581614	+	0.998307i	$0.481476\pi$
$570$		0			0
$571$	12.4065	−	4.51560i	0.519196	−	0.188972i	−0.0691118	−	0.997609i	$-0.522017\pi$
$571$	12.4065	−	4.51560i	0.519196	−	0.188972i	0.588308	+	0.808637i	$0.299794\pi$
$572$	24.5924	−	8.95091i	1.02826	−	0.374256i
$573$		0			0
$574$	−14.0306	+	2.08411i	−0.585626	+	0.0869891i
$575$	−14.7440	+	8.51244i	−0.614867	+	0.354993i
$576$		0			0
$577$	16.5747	−	9.56942i	0.690015	−	0.398380i	−0.113603	−	0.993526i	$-0.536239\pi$
$577$	16.5747	−	9.56942i	0.690015	−	0.398380i	0.803617	+	0.595146i	$0.202906\pi$
$578$	−1.83119	+	5.03114i	−0.0761673	+	0.209268i
$579$		0			0
$580$	−0.575799	−	1.58199i	−0.0239087	−	0.0656887i
$581$	−5.81223	−	5.15146i	−0.241132	−	0.213719i
$582$		0			0
$583$	18.3115	−	15.3652i	0.758386	−	0.636362i
$584$	−14.1521	−	24.5121i	−0.585616	−	1.01432i
$585$		0			0
$586$	18.1297	+	10.4672i	0.748932	+	0.432396i
$587$	20.7501	−	17.4114i	0.856450	−	0.718647i	−0.104750	−	0.994499i	$-0.533404\pi$
$587$	20.7501	−	17.4114i	0.856450	−	0.718647i	0.961200	+	0.275852i	$0.0889598\pi$
$588$		0			0
$589$	−0.868419	+	4.92505i	−0.0357826	+	0.202933i
$590$	2.44935	+	0.431887i	0.100838	+	0.0177805i
$591$		0			0
$592$	1.67265	−	1.40352i	0.0687453	−	0.0576841i
$593$	21.3668	+	37.0083i	0.877428	+	1.51975i	0.854154	+	0.520020i	$0.174076\pi$
$593$	21.3668	+	37.0083i	0.877428	+	1.51975i	0.0232738	+	0.999729i	$0.492591\pi$
$594$		0			0
$595$	−3.03459	−	5.60091i	−0.124406	−	0.229615i
$596$	0.834798	−	2.29359i	0.0341946	−	0.0939490i
$597$		0			0
$598$	5.33766	+	14.6651i	0.218273	+	0.599701i
$599$	−20.1380	+	23.9996i	−0.822817	+	0.980595i	−0.999994	−	0.00358376i	$-0.998859\pi$
$599$	−20.1380	+	23.9996i	−0.822817	+	0.980595i	0.177176	+	0.984179i	$0.443304\pi$
$600$		0			0
$601$	−3.68912	−	4.39652i	−0.150482	−	0.179338i	0.685537	−	0.728038i	$-0.259567\pi$
$601$	−3.68912	−	4.39652i	−0.150482	−	0.179338i	−0.836019	+	0.548700i	$0.815123\pi$
$602$	−0.521388	+	19.2556i	−0.0212502	+	0.784798i
$603$		0			0
$604$	7.61432			0.309822
$605$	−5.97191	−	2.17360i	−0.242793	−	0.0883694i
$606$		0			0
$607$	−8.69875	+	10.3668i	−0.353071	+	0.420774i	−0.913123	−	0.407683i	$-0.866337\pi$
$607$	−8.69875	+	10.3668i	−0.353071	+	0.420774i	0.560052	+	0.828457i	$0.310781\pi$
$608$	−32.6125	+	11.8700i	−1.32261	+	0.481391i
$609$		0			0
$610$	0.581554	+	3.29816i	0.0235464	+	0.133539i
$611$		−	36.1609i		−	1.46291i
$612$		0			0
$613$	1.85353			0.0748633			0.0374316	−	0.999299i	$-0.488082\pi$
$613$	1.85353			0.0748633			0.0374316	+	0.999299i	$0.488082\pi$
$614$	−18.3869	−	6.69227i	−0.742033	−	0.270078i
$615$		0			0
$616$	−7.48455	+	36.6208i	−0.301561	+	1.47549i
$617$	30.5178	−	36.3698i	1.22860	−	1.46419i	0.388779	−	0.921331i	$-0.372897\pi$
$617$	30.5178	−	36.3698i	1.22860	−	1.46419i	0.839823	−	0.542860i	$-0.182659\pi$
$618$		0			0
$619$	−1.98050	−	2.36027i	−0.0796031	−	0.0948672i	0.724773	−	0.688988i	$-0.241945\pi$
$619$	−1.98050	−	2.36027i	−0.0796031	−	0.0948672i	−0.804376	+	0.594121i	$0.797500\pi$
$620$	0.392568	+	0.226649i	0.0157659	+	0.00910245i
$621$		0			0
$622$		−	7.66706i		−	0.307421i
$623$	23.2264	−	18.4414i	0.930548	−	0.738839i
$624$		0			0
$625$	3.68990	−	20.9264i	0.147596	−	0.837058i
$626$	20.2584	+	16.9988i	0.809688	+	0.679409i
$627$		0			0
$628$	0.232006	−	0.637432i	0.00925806	−	0.0254363i
$629$	−13.0675	−	22.6335i	−0.521033	−	0.902456i
$630$		0			0
$631$	12.7919	−	22.1562i	0.509238	−	0.882026i	−0.490705	−	0.871326i	$-0.663261\pi$
$631$	12.7919	−	22.1562i	0.509238	−	0.882026i	0.999943	−	0.0106999i	$-0.00340596\pi$
$632$	8.88153	+	10.5846i	0.353288	+	0.421033i
$633$		0			0
$634$	−3.24407	+	18.3981i	−0.128839	+	0.730680i
$635$	4.12395	+	3.46041i	0.163654	+	0.137322i
$636$		0			0
$637$	−12.9220	+	30.2921i	−0.511987	+	1.20022i
$638$	−11.3409	−	6.54765i	−0.448989	−	0.259224i
$639$		0			0
$640$			2.77375i			0.109642i
$641$	12.9851	−	2.28962i	0.512879	−	0.0904345i	0.0887820	−	0.996051i	$-0.471703\pi$
$641$	12.9851	−	2.28962i	0.512879	−	0.0904345i	0.424097	+	0.905617i	$0.360591\pi$
$642$		0			0
$643$	−39.9985	−	7.05281i	−1.57739	−	0.278136i	−0.684703	−	0.728822i	$-0.740068\pi$
$643$	−39.9985	−	7.05281i	−1.57739	−	0.278136i	−0.892682	+	0.450686i	$0.851179\pi$
$644$	10.6480	+	2.17625i	0.419591	+	0.0857561i
$645$		0			0
$646$	−4.88359	−	27.6962i	−0.192142	−	1.08969i
$647$	20.0184	−	34.6729i	0.787006	−	1.36313i	−0.140788	−	0.990040i	$-0.544964\pi$
$647$	20.0184	−	34.6729i	0.787006	−	1.36313i	0.927794	−	0.373094i	$-0.121703\pi$
$648$		0			0
$649$	−22.4385	+	12.9549i	−0.880787	+	0.508523i
$650$	−19.3995	−	7.06083i	−0.760910	−	0.276949i
$651$		0			0
$652$	−16.4690	−	13.8191i	−0.644974	−	0.541198i
$653$	4.72454	+	12.9806i	0.184885	+	0.507968i	0.997160	−	0.0753061i	$-0.0239934\pi$
$653$	4.72454	+	12.9806i	0.184885	+	0.507968i	−0.812275	+	0.583275i	$0.801771\pi$
$654$		0			0
$655$	−0.806587	−	4.57438i	−0.0315160	−	0.178736i
$656$	−1.15629	+	2.00275i	−0.0451454	+	0.0781941i
$657$		0			0
$658$	16.0235	+	9.83887i	0.624662	+	0.383559i
$659$	−36.6031	+	6.45411i	−1.42585	+	0.251417i	−0.832723	−	0.553690i	$-0.813219\pi$
$659$	−36.6031	+	6.45411i	−1.42585	+	0.251417i	−0.593131	+	0.805106i	$0.702108\pi$
$660$		0			0
$661$	44.4693	+	7.84114i	1.72966	+	0.304985i	0.947893	−	0.318589i	$-0.103209\pi$
$661$	44.4693	+	7.84114i	1.72966	+	0.304985i	0.781764	+	0.623575i	$0.214320\pi$
$662$	13.6067	+	2.39922i	0.528838	+	0.0932484i
$663$		0			0
$664$	−8.40682	+	1.48235i	−0.326248	+	0.0575263i
$665$	7.24471	+	4.44845i	0.280938	+	0.172503i
$666$		0			0
$667$	−5.22921	+	9.05725i	−0.202476	+	0.350698i
$668$	−2.74724	−	15.5804i	−0.106294	−	0.602823i
$669$		0			0
$670$	−1.39580	−	3.83493i	−0.0539244	−	0.148156i
$671$	−26.7262	−	22.4259i	−1.03175	−	0.865744i
$672$		0			0
$673$	4.43681	+	1.61487i	0.171026	+	0.0622485i	0.426114	−	0.904669i	$-0.359882\pi$
$673$	4.43681	+	1.61487i	0.171026	+	0.0622485i	−0.255088	+	0.966918i	$0.582104\pi$
$674$	−8.94268	+	5.16306i	−0.344459	+	0.198874i
$675$		0			0
$676$	5.22961	−	9.05794i	0.201139	−	0.348382i
$677$	1.83606	+	10.4128i	0.0705656	+	0.400197i	0.999548	+	0.0300728i	$0.00957391\pi$
$677$	1.83606	+	10.4128i	0.0705656	+	0.400197i	−0.928982	+	0.370125i	$0.879315\pi$
$678$		0			0
$679$	−6.36280	−	1.30043i	−0.244182	−	0.0499059i
$680$	−6.89530	−	1.21583i	−0.264423	−	0.0466248i
$681$		0			0
$682$	3.47242	−	0.612281i	0.132966	−	0.0234455i
$683$		−	9.29154i		−	0.355531i	−0.984073	−	0.177765i	$-0.943113\pi$
$683$		−	9.29154i		−	0.355531i	0.984073	−	0.177765i	$-0.0568868\pi$
$684$		0			0
$685$	−6.50314	−	3.75459i	−0.248472	−	0.143456i
$686$	−9.90706	−	13.9680i	−0.378253	−	0.533300i
$687$		0			0
$688$	2.40574	+	2.01866i	0.0917181	+	0.0769606i
$689$	4.01986	−	22.7978i	0.153144	−	0.868526i
$690$		0			0
$691$	−6.66743	−	7.94594i	−0.253641	−	0.302278i	0.624166	−	0.781292i	$-0.285439\pi$
$691$	−6.66743	−	7.94594i	−0.253641	−	0.302278i	−0.877807	+	0.479014i	$0.840994\pi$
$692$	2.52096	−	4.36643i	0.0958325	−	0.165987i
$693$		0			0
$694$	8.41286	+	14.5715i	0.319348	+	0.553126i
$695$	−1.84915	+	5.08049i	−0.0701421	+	0.192714i
$696$		0			0
$697$	21.2041	+	17.7924i	0.803163	+	0.673934i
$698$	4.10315	−	23.2701i	0.155306	−	0.880787i
$699$		0			0
$700$	−11.2593	+	8.93971i	−0.425563	+	0.337889i
$701$			32.6042i			1.23144i	0.787964	+	0.615721i	$0.211135\pi$
$701$			32.6042i			1.23144i	−0.787964	+	0.615721i	$0.788865\pi$
$702$		0			0
$703$	30.2060	+	17.4395i	1.13924	+	0.657742i
$704$	18.2195	+	21.7131i	0.686672	+	0.818344i
$705$		0			0
$706$	−7.62264	+	9.08431i	−0.286882	+	0.341892i
$707$	3.20353	−	15.6744i	0.120481	−	0.589495i
$708$		0			0
$709$	11.3943	+	4.14720i	0.427923	+	0.155751i	0.546998	−	0.837134i	$-0.315771\pi$
$709$	11.3943	+	4.14720i	0.427923	+	0.155751i	−0.119075	+	0.992885i	$0.537993\pi$
$710$	6.09078			0.228583
$711$		0			0
$712$		−	32.5973i		−	1.22164i
$713$	−0.488991	−	2.77321i	−0.0183129	−	0.103857i
$714$		0			0
$715$	−10.8320	+	3.94254i	−0.405095	+	0.147443i
$716$	−2.21786	+	2.64314i	−0.0828852	+	0.0987788i
$717$		0			0
$718$	−18.6279	−	6.77999i	−0.695186	−	0.253027i
$719$	10.2736			0.383139			0.191570	−	0.981479i	$-0.438642\pi$
$719$	10.2736			0.383139			0.191570	+	0.981479i	$0.438642\pi$
$720$		0			0
$721$	0.700407	−	25.8670i	0.0260845	−	0.963337i
$722$	12.8330	+	15.2937i	0.477593	+	0.569173i
$723$		0			0
$724$	1.68408	−	2.00701i	0.0625884	−	0.0745899i
$725$	−4.73176	−	13.0004i	−0.175733	−	0.482822i
$726$		0			0
$727$	−12.1820	+	33.4698i	−0.451806	+	1.24133i	0.479646	+	0.877462i	$0.340765\pi$
$727$	−12.1820	+	33.4698i	−0.451806	+	1.24133i	−0.931452	+	0.363865i	$0.881457\pi$
$728$	17.2438	+	31.8267i	0.639098	+	1.17958i
$729$		0			0
$730$	2.26945	+	3.93080i	0.0839961	+	0.145485i
$731$	28.7952	−	24.1621i	1.06503	−	0.893666i
$732$		0			0
$733$	9.19455	+	1.62125i	0.339608	+	0.0598821i	0.340852	−	0.940117i	$-0.389285\pi$
$733$	9.19455	+	1.62125i	0.339608	+	0.0598821i	−0.00124322	+	0.999999i	$0.500396\pi$
$734$	1.11902	−	6.34628i	0.0413038	−	0.234246i
$735$		0			0
$736$	14.9701	−	12.5614i	0.551804	−	0.463019i
$737$	36.8184	+	21.2571i	1.35622	+	0.783016i
$738$		0			0
$739$	24.9361	+	43.1905i	0.917288	+	1.58879i	0.803517	+	0.595282i	$0.202959\pi$
$739$	24.9361	+	43.1905i	0.917288	+	1.58879i	0.113770	+	0.993507i	$0.463707\pi$
$740$	2.42182	−	2.03215i	0.0890279	−	0.0747033i
$741$		0			0
$742$	9.00833	+	7.98422i	0.330706	+	0.293110i
$743$	13.7749	+	37.8461i	0.505350	+	1.38844i	0.885985	+	0.463713i	$0.153483\pi$
$743$	13.7749	+	37.8461i	0.505350	+	1.38844i	−0.380635	+	0.924725i	$0.624295\pi$
$744$		0			0
$745$	−0.367697	+	1.01024i	−0.0134714	+	0.0370123i
$746$	9.24992	−	5.34044i	0.338664	−	0.195527i
$747$		0			0
$748$	22.9979	−	13.2778i	0.840885	−	0.485485i
$749$	−42.0573	+	6.24721i	−1.53674	+	0.228268i
$750$		0			0
$751$	−38.2116	+	13.9079i	−1.39436	+	0.507506i	−0.926500	−	0.376295i	$-0.877198\pi$
$751$	−38.2116	+	13.9079i	−1.39436	+	0.507506i	−0.467862	+	0.883801i	$0.654976\pi$
$752$	2.88068	−	1.04848i	0.105048	−	0.0382342i
$753$		0			0
$754$	−12.4893	+	2.20220i	−0.454833	+	0.0801992i
$755$	−3.35382			−0.122058
$756$		0			0
$757$	38.9341			1.41508			0.707542	−	0.706671i	$-0.249804\pi$
$757$	38.9341			1.41508			0.707542	+	0.706671i	$0.249804\pi$
$758$	5.88650	−	1.03795i	0.213807	−	0.0377000i
$759$		0			0
$760$	8.78071	−	3.19592i	0.318510	−	0.115928i
$761$	−35.9569	+	13.0872i	−1.30344	+	0.474412i	−0.898115	−	0.439761i	$-0.855063\pi$
$761$	−35.9569	+	13.0872i	−1.30344	+	0.474412i	−0.405322	+	0.914174i	$0.632841\pi$
$762$		0			0
$763$	−29.9322	+	23.7657i	−1.08362	+	0.860375i
$764$	13.0401	−	7.52871i	0.471775	−	0.272379i
$765$		0			0
$766$	1.86345	−	1.07586i	0.0673291	−	0.0388724i
$767$	−8.58192	+	23.5786i	−0.309875	+	0.851375i
$768$		0			0
$769$	−2.38576	−	6.55481i	−0.0860326	−	0.236373i	0.889214	−	0.457491i	$-0.151252\pi$
$769$	−2.38576	−	6.55481i	−0.0860326	−	0.236373i	−0.975247	+	0.221118i	$0.929029\pi$
$770$	1.20024	−	5.87257i	0.0432535	−	0.211633i
$771$		0			0
$772$	−0.0328790	+	0.0275887i	−0.00118334	+	0.000992940i
$773$	13.0179	+	22.5477i	0.468222	+	0.810985i	0.999340	−	0.0363129i	$-0.0115613\pi$
$773$	13.0179	+	22.5477i	0.468222	+	0.810985i	−0.531118	+	0.847298i	$0.678228\pi$
$774$		0			0
$775$	3.22601	+	1.86254i	0.115882	+	0.0669044i
$776$	−5.46814	+	4.58831i	−0.196295	+	0.164711i
$777$		0			0
$778$	5.29248	−	30.0151i	0.189744	−	1.07609i
$779$	−36.3798	−	6.41474i	−1.30344	−	0.229832i
$780$		0			0
$781$	−48.6060	+	40.7853i	−1.73926	+	1.45941i
$782$	7.91791	+	13.7142i	0.283144	+	0.490420i
$783$		0			0
$784$	−2.78783	−	0.151084i	−0.0995652	−	0.00539587i
$785$	−0.102190	+	0.280765i	−0.00364732	+	0.0100209i
$786$		0			0
$787$	9.54357	+	26.2208i	0.340192	+	0.934669i	0.985339	+	0.170610i	$0.0545739\pi$
$787$	9.54357	+	26.2208i	0.340192	+	0.934669i	−0.645147	+	0.764059i	$0.723204\pi$
$788$	−3.76574	+	4.48783i	−0.134149	+	0.159872i
$789$		0			0
$790$	−1.42426	−	1.69737i	−0.0506729	−	0.0603896i
$791$	−3.45552	−	2.12178i	−0.122864	−	0.0754420i
$792$		0			0
$793$	−33.7873			−1.19982
$794$	−22.0697	−	8.03272i	−0.783225	−	0.285070i
$795$		0			0
$796$	−4.54478	+	5.41626i	−0.161086	+	0.191974i
$797$	10.0467	−	3.65670i	0.355873	−	0.129527i	−0.157896	−	0.987456i	$-0.550471\pi$
$797$	10.0467	−	3.65670i	0.355873	−	0.129527i	0.513769	+	0.857929i	$0.328249\pi$
$798$		0			0
$799$	−6.37163	−	36.1353i	−0.225412	−	1.27838i
$800$			25.8509i			0.913966i
$801$		0			0
$802$	−18.0279			−0.636586
$803$	−44.4324	−	16.1721i	−1.56798	−	0.570699i
$804$		0			0
$805$	−4.69006	−	0.958555i	−0.165303	−	0.0337846i
$806$	2.19492	−	2.61580i	0.0773127	−	0.0921377i
$807$		0			0
$808$	−11.3030	−	13.4704i	−0.397639	−	0.473888i
$809$	43.9114	+	25.3522i	1.54384	+	0.891338i	0.998591	+	0.0530646i	$0.0168989\pi$
$809$	43.9114	+	25.3522i	1.54384	+	0.891338i	0.545251	+	0.838273i	$0.316434\pi$
$810$		0			0
$811$			4.10320i			0.144083i	0.997402	+	0.0720414i	$0.0229514\pi$
$811$			4.10320i			0.144083i	−0.997402	+	0.0720414i	$0.977049\pi$
$812$	−3.24413	+	8.21424i	−0.113847	+	0.288263i
$813$		0			0
$814$	4.27027	−	24.2179i	0.149673	−	0.848837i
$815$	7.25396	+	6.08679i	0.254095	+	0.213211i
$816$		0			0
$817$	−17.1577	+	47.1405i	−0.600274	+	1.64924i
$818$	−8.00392	−	13.8632i	−0.279850	−	0.484715i
$819$		0			0
$820$	−1.67419	+	2.89977i	−0.0584651	+	0.101265i
$821$	−22.3237	−	26.6043i	−0.779102	−	0.928498i	0.219790	−	0.975547i	$-0.429463\pi$
$821$	−22.3237	−	26.6043i	−0.779102	−	0.928498i	−0.998893	+	0.0470490i	$0.985018\pi$
$822$		0			0
$823$	−6.70773	+	38.0415i	−0.233817	+	1.32604i	0.611274	+	0.791419i	$0.290657\pi$
$823$	−6.70773	+	38.0415i	−0.233817	+	1.32604i	−0.845091	+	0.534623i	$0.820454\pi$
$824$	−21.7876	−	18.2820i	−0.759008	−	0.636883i
$825$		0			0
$826$	−8.11308	−	10.2182i	−0.282290	−	0.355537i
$827$	−28.4168	−	16.4064i	−0.988148	−	0.570508i	−0.0834279	−	0.996514i	$-0.526587\pi$
$827$	−28.4168	−	16.4064i	−0.988148	−	0.570508i	−0.904720	+	0.426006i	$0.859920\pi$
$828$		0			0
$829$		−	10.5842i		−	0.367605i	−0.982963	−	0.183803i	$-0.941159\pi$
$829$		−	10.5842i		−	0.367605i	0.982963	−	0.183803i	$-0.0588407\pi$
$830$	1.34813	−	0.237712i	0.0467944	−	0.00825111i
$831$		0			0
$832$	27.0327	+	4.76660i	0.937190	+	0.165252i
$833$	−7.57529	+	32.5475i	−0.262468	+	1.12771i
$834$		0			0
$835$	1.21006	+	6.86258i	0.0418758	+	0.237489i
$836$	−17.7202	+	30.6923i	−0.612867	+	1.06152i
$837$		0			0
$838$	2.63070	−	1.51883i	0.0908759	−	0.0524672i
$839$	−40.4225	−	14.7126i	−1.39554	−	0.507934i	−0.468687	−	0.883364i	$-0.655273\pi$
$839$	−40.4225	−	14.7126i	−1.39554	−	0.507934i	−0.926851	+	0.375430i	$0.877495\pi$
$840$		0			0
$841$	15.7049	+	13.1780i	0.541549	+	0.454413i
$842$	−1.02851	−	2.82579i	−0.0354446	−	0.0973833i
$843$		0			0
$844$	0.668149	+	3.78926i	0.0229986	+	0.130432i
$845$	−2.30345	+	3.98968i	−0.0792409	+	0.137249i
$846$		0			0
$847$	15.8818	+	29.3129i	0.545706	+	1.00720i
$848$	1.93269	−	0.340786i	0.0663689	−	0.0117026i
$849$		0			0
$850$	−20.6299	−	3.63761i	−0.707600	−	0.124769i
$851$	−19.3413	−	3.41040i	−0.663012	−	0.116907i
$852$		0			0
$853$	−35.0998	+	6.18904i	−1.20179	+	0.211909i	−0.738473	−	0.674283i	$-0.764453\pi$
$853$	−35.0998	+	6.18904i	−1.20179	+	0.211909i	−0.463320	+	0.886191i	$0.653342\pi$
$854$	9.19303	−	14.9717i	0.314579	−	0.512322i
$855$		0			0
$856$	−23.3669	+	40.4727i	−0.798665	+	1.38333i
$857$	6.80319	+	38.5828i	0.232393	+	1.31796i	0.848036	+	0.529939i	$0.177785\pi$
$857$	6.80319	+	38.5828i	0.232393	+	1.31796i	−0.615643	+	0.788025i	$0.711104\pi$
$858$		0			0
$859$	5.56866	+	15.2998i	0.190000	+	0.522021i	0.997716	−	0.0675511i	$-0.0215186\pi$
$859$	5.56866	+	15.2998i	0.190000	+	0.522021i	−0.807716	+	0.589572i	$0.799296\pi$
$860$	3.48327	+	2.92281i	0.118779	+	0.0996671i
$861$		0			0
$862$	−29.7589	−	10.8313i	−1.01359	−	0.368917i
$863$	30.6409	−	17.6905i	1.04303	−	0.602193i	0.122339	−	0.992488i	$-0.460960\pi$
$863$	30.6409	−	17.6905i	1.04303	−	0.602193i	0.920690	+	0.390295i	$0.127627\pi$
$864$		0			0
$865$	−1.11039	+	1.92325i	−0.0377543	+	0.0653924i
$866$	4.40333	+	24.9726i	0.149631	+	0.848602i
$867$		0			0
$868$	−0.752533	−	2.25576i	−0.0255426	−	0.0765655i
$869$	22.7319	+	4.00825i	0.771127	+	0.135971i
$870$		0			0
$871$	40.5467	−	7.14948i	1.37387	−	0.242251i
$872$			42.0086i			1.42259i
$873$		0			0
$874$	−18.3026	−	10.5670i	−0.619096	−	0.357435i
$875$	10.1844	−	8.08627i	0.344297	−	0.273366i
$876$		0			0
$877$	−20.4975	−	17.1995i	−0.692153	−	0.580785i	0.227376	−	0.973807i	$-0.426985\pi$
$877$	−20.4975	−	17.1995i	−0.692153	−	0.580785i	−0.919529	+	0.393022i	$0.871430\pi$
$878$	0.606857	−	3.44166i	0.0204804	−	0.116150i
$879$		0			0
$880$	−0.628148	−	0.748598i	−0.0211749	−	0.0252352i
$881$	−0.302257	+	0.523525i	−0.0101833	+	0.0176380i	−0.871072	−	0.491155i	$-0.836575\pi$
$881$	−0.302257	+	0.523525i	−0.0101833	+	0.0176380i	0.860889	+	0.508793i	$0.169908\pi$
$882$		0			0
$883$	−10.2674	−	17.7836i	−0.345525	−	0.598466i	0.639924	−	0.768438i	$-0.278966\pi$
$883$	−10.2674	−	17.7836i	−0.345525	−	0.598466i	−0.985449	+	0.169972i	$0.945632\pi$
$884$	8.79586	−	24.1664i	0.295837	−	0.812805i
$885$		0			0
$886$	15.2947	+	12.8338i	0.513836	+	0.431160i
$887$	2.47534	−	14.0384i	0.0831139	−	0.471362i	−0.914634	−	0.404283i	$-0.867521\pi$
$887$	2.47534	−	14.0384i	0.0831139	−	0.471362i	0.997748	−	0.0670790i	$-0.0213680\pi$
$888$		0			0
$889$	−4.14943	−	27.9347i	−0.139168	−	0.936900i
$890$			5.22737i			0.175222i
$891$		0			0
$892$	−6.56058	−	3.78775i	−0.219665	−	0.126823i
$893$	31.4768	+	37.5126i	1.05333	+	1.25531i
$894$		0			0
$895$	0.976883	−	1.16420i	0.0326536	−	0.0389150i
$896$	9.65143	−	10.8894i	0.322432	−	0.363789i
$897$		0			0
$898$	15.0604	+	5.48155i	0.502573	+	0.182922i
$899$	2.28832			0.0763198
$900$		0			0
$901$		−	23.4899i		−	0.782564i
$902$	4.52273	+	25.6497i	0.150590	+	0.854041i
$903$		0			0
$904$	−4.18815	+	1.52436i	−0.139296	+	0.0506995i
$905$	−0.741774	+	0.884012i	−0.0246574	+	0.0293856i
$906$		0			0
$907$	−26.5353	−	9.65807i	−0.881091	−	0.320691i	−0.138441	−	0.990371i	$-0.544209\pi$
$907$	−26.5353	−	9.65807i	−0.881091	−	0.320691i	−0.742650	+	0.669680i	$0.766431\pi$
$908$	−12.0025			−0.398318
$909$		0			0
$910$	−2.76525	−	5.10379i	−0.0916671	−	0.169189i
$911$	−20.6579	−	24.6191i	−0.684426	−	0.815667i	0.306244	−	0.951953i	$-0.400928\pi$
$911$	−20.6579	−	24.6191i	−0.684426	−	0.815667i	−0.990670	+	0.136286i	$0.956483\pi$
$912$		0			0
$913$	−9.16667	+	10.9244i	−0.303373	+	0.361545i
$914$	10.3780	+	28.5134i	0.343274	+	0.943139i
$915$		0			0
$916$	−6.84153	+	18.7969i	−0.226050	+	0.621068i
$917$	−12.7503	+	20.7650i	−0.421052	+	0.685722i
$918$		0			0
$919$	7.94398	+	13.7594i	0.262048	+	0.453880i	0.966786	−	0.255587i	$-0.0822688\pi$
$919$	7.94398	+	13.7594i	0.262048	+	0.453880i	−0.704738	+	0.709468i	$0.748936\pi$
$920$	−4.03060	+	3.38208i	−0.132885	+	0.111504i
$921$		0			0
$922$	−0.725501	−	0.127925i	−0.0238931	−	0.00421300i
$923$	−10.6703	+	60.5142i	−0.351217	+	1.99185i
$924$		0			0
$925$	19.9019	−	16.6997i	0.654370	−	0.549081i
$926$	9.19135	+	5.30663i	0.302047	+	0.174387i
$927$		0			0
$928$	7.94011	+	13.7527i	0.260647	+	0.451453i
$929$	−25.0074	+	20.9837i	−0.820466	+	0.688452i	−0.953081	−	0.302715i	$-0.902107\pi$
$929$	−25.0074	+	20.9837i	−0.820466	+	0.688452i	0.132615	+	0.991168i	$0.457662\pi$
$930$		0			0
$931$	−12.9632	−	42.6725i	−0.424852	−	1.39853i
$932$	−4.02251	−	11.0517i	−0.131762	−	0.362012i
$933$		0			0
$934$	−1.64123	+	4.50926i	−0.0537028	+	0.147547i
$935$	−10.1297	+	5.84838i	−0.331276	+	0.191263i
$936$		0			0
$937$	−3.11413	+	1.79794i	−0.101734	+	0.0587362i	−0.550004	−	0.835162i	$-0.685374\pi$
$937$	−3.11413	+	1.79794i	−0.101734	+	0.0587362i	0.448270	+	0.893898i	$0.352040\pi$
$938$	−7.86413	+	19.9122i	−0.256773	+	0.650157i
$939$		0			0
$940$	4.17094	−	1.51810i	0.136041	−	0.0495149i
$941$	18.8278	−	6.85277i	0.613770	−	0.223394i	−0.0163822	−	0.999866i	$-0.505215\pi$
$941$	18.8278	−	6.85277i	0.613770	−	0.223394i	0.630152	+	0.776472i	$0.282993\pi$
$942$		0			0
$943$	20.4848	−	3.61202i	0.667077	−	0.117624i
$944$	−2.12717			−0.0692336
$945$		0			0
$946$	35.3696			1.14997
$947$	−48.3743	+	8.52970i	−1.57195	+	0.277178i	−0.890604	−	0.454779i	$-0.849718\pi$
$947$	−48.3743	+	8.52970i	−1.57195	+	0.277178i	−0.681350	+	0.731957i	$0.738607\pi$
$948$		0			0
$949$	−43.0298	+	15.6616i	−1.39681	+	0.508396i
$950$	26.2708	−	9.56180i	0.852338	−	0.310226i
$951$		0			0
$952$	22.8396	+	28.7658i	0.740234	+	0.932305i
$953$	27.6214	−	15.9472i	0.894744	−	0.516581i	0.0192530	−	0.999815i	$-0.493871\pi$
$953$	27.6214	−	15.9472i	0.894744	−	0.516581i	0.875491	+	0.483234i	$0.160538\pi$
$954$		0			0
$955$	−5.74368	+	3.31612i	−0.185861	+	0.107307i
$956$	8.80989	−	24.2050i	0.284932	−	0.782845i
$957$		0			0
$958$	−5.85857	−	16.0963i	−0.189282	−	0.520048i
$959$	12.4662	+	37.3682i	0.402555	+	1.20668i
$960$		0			0
$961$	23.2754	−	19.5304i	0.750819	−	0.630012i
$962$	−11.9076	−	20.6246i	−0.383917	−	0.664964i
$963$		0			0
$964$	−8.49086	−	4.90220i	−0.273472	−	0.157889i
$965$	0.0144820	−	0.0121518i	0.000466191	−	0.000391180i
$966$		0			0
$967$	−7.25864	+	41.1658i	−0.233422	+	1.32380i	0.612489	+	0.790479i	$0.290168\pi$
$967$	−7.25864	+	41.1658i	−0.233422	+	1.32380i	−0.845911	+	0.533323i	$0.820943\pi$
$968$	36.0872	+	6.36315i	1.15989	+	0.204519i
$969$		0			0
$970$	0.876881	−	0.735790i	0.0281549	−	0.0236248i
$971$	23.9484	+	41.4799i	0.768542	+	1.33115i	0.938353	+	0.345677i	$0.112351\pi$
$971$	23.9484	+	41.4799i	0.768542	+	1.33115i	−0.169811	+	0.985477i	$0.554316\pi$
$972$		0			0
$973$	24.9374	−	13.5112i	0.799456	−	0.433148i
$974$	8.20437	−	22.5413i	0.262885	−	0.722270i
$975$		0			0
$976$	−0.979659	−	2.69159i	−0.0313581	−	0.0861557i
$977$	15.1762	−	18.0863i	0.485529	−	0.578631i	−0.466546	−	0.884497i	$-0.654502\pi$
$977$	15.1762	−	18.0863i	0.485529	−	0.578631i	0.952074	+	0.305866i	$0.0989461\pi$
$978$		0			0
$979$	−35.0037	−	41.7158i	−1.11872	−	1.33324i
$980$	−4.03649	−	0.218755i	−0.128941	−	0.00698787i
$981$		0			0
$982$	−16.8134			−0.536536
$983$	57.8632	+	21.0605i	1.84555	+	0.671725i	0.987382	+	0.158356i	$0.0506193\pi$
$983$	57.8632	+	21.0605i	1.84555	+	0.671725i	0.858168	+	0.513369i	$0.171603\pi$
$984$		0			0
$985$	1.65867	−	1.97672i	0.0528495	−	0.0629836i
$986$	−12.0924	+	4.40128i	−0.385101	+	0.140165i
$987$		0			0
$988$	5.95990	+	33.8003i	0.189610	+	1.07533i
$989$		−	28.2475i		−	0.898219i
$990$		0			0
$991$	−6.39641			−0.203189			−0.101594	−	0.994826i	$-0.532394\pi$
$991$	−6.39641			−0.203189			−0.101594	+	0.994826i	$0.532394\pi$
$992$	−4.01797	−	1.46242i	−0.127571	−	0.0464320i
$993$		0			0
$994$	−23.9117	−	21.1932i	−0.758432	−	0.672209i
$995$	2.00181	−	2.38566i	0.0634615	−	0.0756305i
$996$		0			0
$997$	23.1587	+	27.5994i	0.733442	+	0.874082i	0.995863	−	0.0908715i	$-0.0289653\pi$
$997$	23.1587	+	27.5994i	0.733442	+	0.874082i	−0.262421	+	0.964954i	$0.584521\pi$
$998$	−19.5720	−	11.2999i	−0.619542	−	0.357693i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.15		132
3.2	odd	2		189.2.bd.a.185.8	yes	132
7.5	odd	6		567.2.ba.a.341.8		132
21.5	even	6		189.2.ba.a.131.15	yes	132
27.7	even	9		189.2.ba.a.101.15	✓	132
27.20	odd	18		567.2.ba.a.143.8		132
189.47	even	18	inner	567.2.bd.a.467.15		132
189.61	odd	18		189.2.bd.a.47.8	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.15	✓	132	27.7	even	9
189.2.ba.a.131.15	yes	132	21.5	even	6
189.2.bd.a.47.8	yes	132	189.61	odd	18
189.2.bd.a.185.8	yes	132	3.2	odd	2
567.2.ba.a.143.8		132	27.20	odd	18
567.2.ba.a.341.8		132	7.5	odd	6
567.2.bd.a.17.15		132	1.1	even	1	trivial
567.2.bd.a.467.15		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)

\(f(q)\)	\(=\)	\(q+(0.910598 - 0.160563i) q^{2} +(-1.07598 + 0.391623i) q^{4} +(0.473927 - 0.172495i) q^{5} +(-2.46079 - 0.971863i) q^{7} +(-2.51844 + 1.45402i) q^{8} +O(q^{10})\)	\(q+(0.910598 - 0.160563i) q^{2} +(-1.07598 + 0.391623i) q^{4} +(0.473927 - 0.172495i) q^{5} +(-2.46079 - 0.971863i) q^{7} +(-2.51844 + 1.45402i) q^{8} +(0.403861 - 0.233169i) q^{10} +(-1.66156 + 4.56510i) q^{11} +(1.60911 + 4.42100i) q^{13} +(-2.39684 - 0.489865i) q^{14} +(-0.305533 + 0.256373i) q^{16} +(2.38696 + 4.13434i) q^{17} +(-5.51758 - 3.18557i) q^{19} +(-0.442381 + 0.371202i) q^{20} +(-0.780028 + 4.42376i) q^{22} +(3.53298 + 0.622960i) q^{23} +(-3.63537 + 3.05044i) q^{25} +(2.17510 + 3.76739i) q^{26} +(3.02836 + 0.0819996i) q^{28} +(-0.997075 + 2.73944i) q^{29} +(-0.268468 - 0.737610i) q^{31} +(3.50145 - 4.17286i) q^{32} +(2.83739 + 3.38147i) q^{34} +(-1.33388 - 0.0361178i) q^{35} -5.47451 q^{37} +(-5.53578 - 2.01486i) q^{38} +(-0.942744 + 1.12352i) q^{40} +(5.44849 - 1.98309i) q^{41} +(-1.36729 - 7.75429i) q^{43} -5.56264i q^{44} +3.31715 q^{46} +(-7.22256 - 2.62880i) q^{47} +(5.11096 + 4.78310i) q^{49} +(-2.82057 + 3.36143i) q^{50} +(-3.46273 - 4.12672i) q^{52} +(-4.26125 - 2.46023i) q^{53} +2.45014i q^{55} +(7.61045 - 1.13046i) q^{56} +(-0.468082 + 2.65462i) q^{58} +(4.08557 + 3.42820i) q^{59} +(-2.45624 + 6.74846i) q^{61} +(-0.362900 - 0.628561i) q^{62} +(2.91725 - 5.05283i) q^{64} +(1.52520 + 1.81767i) q^{65} +(1.51964 - 8.61830i) q^{67} +(-4.18742 - 3.51366i) q^{68} +(-1.22043 + 0.181283i) q^{70} +(11.3110 + 6.53043i) q^{71} +9.73306i q^{73} +(-4.98508 + 0.879004i) q^{74} +(7.18433 + 1.26679i) q^{76} +(8.52540 - 9.61893i) q^{77} +(-0.825069 - 4.67920i) q^{79} +(-0.100577 + 0.174205i) q^{80} +(4.64298 - 2.68063i) q^{82} +(2.75845 + 1.00400i) q^{83} +(1.84440 + 1.54764i) q^{85} +(-2.49011 - 6.84151i) q^{86} +(-2.45321 - 13.9128i) q^{88} +(-5.60470 + 9.70762i) q^{89} +(0.336922 - 12.4430i) q^{91} +(-4.04537 + 0.713308i) q^{92} +(-6.99893 - 1.23410i) q^{94} +(-3.16443 - 0.557974i) q^{95} +(2.41733 - 0.426241i) q^{97} +(5.42202 + 3.53485i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 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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