LMFDB - Embedded newform 216.2.n.b.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(37,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("216.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.n (of order $6$, degree $2$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.1
Root			$-0.722180 - 1.21592i$ of defining polynomial
Character	$\chi$	$=$	216.181
Dual form			216.2.n.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41411 - 0.0174668i) q^{2} +(1.99939 + 0.0493999i) q^{4} +(3.17262 - 1.83171i) q^{5} +(-0.191926 + 0.332426i) q^{7} +(-2.82649 - 0.104780i) q^{8} +O(q^{10})$	\(q+(-1.41411 - 0.0174668i) q^{2} +(1.99939 + 0.0493999i) q^{4} +(3.17262 - 1.83171i) q^{5} +(-0.191926 + 0.332426i) q^{7} +(-2.82649 - 0.104780i) q^{8} +(-4.51841 + 2.53482i) q^{10} +(-1.73849 - 1.00372i) q^{11} +(0.397799 - 0.229669i) q^{13} +(0.277210 - 0.466733i) q^{14} +(3.99512 + 0.197539i) q^{16} +4.08495 q^{17} -4.72398i q^{19} +(6.43379 - 3.50558i) q^{20} +(2.44087 + 1.44973i) q^{22} +(2.97594 + 5.15447i) q^{23} +(4.21034 - 7.29252i) q^{25} +(-0.566541 + 0.317828i) q^{26} +(-0.400157 + 0.655168i) q^{28} +(-2.03783 - 1.17654i) q^{29} +(0.592083 + 1.02552i) q^{31} +(-5.64607 - 0.349123i) q^{32} +(-5.77656 - 0.0713512i) q^{34} +1.40621i q^{35} +5.74432i q^{37} +(-0.0825129 + 6.68021i) q^{38} +(-9.15929 + 4.84488i) q^{40} +(-4.75281 - 8.23212i) q^{41} +(-1.03633 - 0.598327i) q^{43} +(-3.42633 - 2.09270i) q^{44} +(-4.11825 - 7.34095i) q^{46} +(-3.27688 + 5.67572i) q^{47} +(3.42633 + 5.93458i) q^{49} +(-6.08124 + 10.2389i) q^{50} +(0.806700 - 0.439547i) q^{52} +7.63807i q^{53} -7.35407 q^{55} +(0.577308 - 0.919487i) q^{56} +(2.86116 + 1.69935i) q^{58} +(0.603703 - 0.348548i) q^{59} +(-4.23774 - 2.44666i) q^{61} +(-0.819356 - 1.46053i) q^{62} +(7.97804 + 0.592316i) q^{64} +(0.841376 - 1.45731i) q^{65} +(-8.87932 + 5.12648i) q^{67} +(8.16741 + 0.201796i) q^{68} +(0.0245621 - 1.98853i) q^{70} +3.73792 q^{71} -2.68275 q^{73} +(0.100335 - 8.12307i) q^{74} +(0.233364 - 9.44508i) q^{76} +(0.667322 - 0.385279i) q^{77} +(-5.35979 + 9.28342i) q^{79} +(13.0368 - 6.69119i) q^{80} +(6.57719 + 11.7241i) q^{82} +(-5.49039 - 3.16988i) q^{83} +(12.9600 - 7.48246i) q^{85} +(1.45503 + 0.864199i) q^{86} +(4.80864 + 3.01915i) q^{88} -7.56802 q^{89} +0.176318i q^{91} +(5.69542 + 10.4528i) q^{92} +(4.73299 - 7.96883i) q^{94} +(-8.65297 - 14.9874i) q^{95} +(-2.98511 + 5.17036i) q^{97} +(-4.74153 - 8.45196i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41411	−	0.0174668i	−0.999924	−	0.0123509i
$2$	−1.41411	−	0.0174668i	−0.999924	−	0.0123509i
$3$		0			0
$3$		0			0
$4$	1.99939	+	0.0493999i	0.999695	+	0.0246999i
$5$	3.17262	−	1.83171i	1.41884	−	0.819167i	0.422641	−	0.906297i	$-0.361103\pi$
$5$	3.17262	−	1.83171i	1.41884	−	0.819167i	0.996197	+	0.0871306i	$0.0277697\pi$
$6$		0			0
$7$	−0.191926	+	0.332426i	−0.0725413	+	0.125645i	−0.900014	−	0.435860i	$-0.856444\pi$
$7$	−0.191926	+	0.332426i	−0.0725413	+	0.125645i	0.827473	+	0.561505i	$0.189778\pi$
$8$	−2.82649	−	0.104780i	−0.999314	−	0.0370452i
$9$		0			0
$10$	−4.51841	+	2.53482i	−1.42885	+	0.801580i
$11$	−1.73849	−	1.00372i	−0.524173	−	0.302632i	0.214467	−	0.976731i	$-0.431199\pi$
$11$	−1.73849	−	1.00372i	−0.524173	−	0.302632i	−0.738640	+	0.674100i	$0.764532\pi$
$12$		0			0
$13$	0.397799	−	0.229669i	0.110330	−	0.0636988i	−0.443820	−	0.896116i	$-0.646377\pi$
$13$	0.397799	−	0.229669i	0.110330	−	0.0636988i	0.554149	+	0.832417i	$0.313044\pi$
$14$	0.277210	−	0.466733i	0.0740876	−	0.124740i
$15$		0			0
$16$	3.99512	+	0.197539i	0.998780	+	0.0493848i
$17$	4.08495			0.990747			0.495373	−	0.868680i	$-0.335031\pi$
$17$	4.08495			0.990747			0.495373	+	0.868680i	$0.335031\pi$
$18$		0			0
$19$		−	4.72398i		−	1.08376i	−0.840457	−	0.541878i	$-0.817714\pi$
$19$		−	4.72398i		−	1.08376i	0.840457	−	0.541878i	$-0.182286\pi$
$20$	6.43379	−	3.50558i	1.43864	−	0.783871i
$21$		0			0
$22$	2.44087	+	1.44973i	0.520396	+	0.309083i
$23$	2.97594	+	5.15447i	0.620525	+	1.07478i	0.989388	+	0.145298i	$0.0464140\pi$
$23$	2.97594	+	5.15447i	0.620525	+	1.07478i	−0.368863	+	0.929484i	$0.620253\pi$
$24$		0			0
$25$	4.21034	−	7.29252i	0.842068	−	1.45850i
$26$	−0.566541	+	0.317828i	−0.111108	+	0.0623313i
$27$		0			0
$28$	−0.400157	+	0.655168i	−0.0756226	+	0.123815i
$29$	−2.03783	−	1.17654i	−0.378416	−	0.218479i	0.298713	−	0.954343i	$-0.403443\pi$
$29$	−2.03783	−	1.17654i	−0.378416	−	0.218479i	−0.677129	+	0.735864i	$0.736776\pi$
$30$		0			0
$31$	0.592083	+	1.02552i	0.106341	+	0.184188i	0.914285	−	0.405071i	$-0.132753\pi$
$31$	0.592083	+	1.02552i	0.106341	+	0.184188i	−0.807944	+	0.589259i	$0.799420\pi$
$32$	−5.64607	−	0.349123i	−0.998094	−	0.0617169i
$33$		0			0
$34$	−5.77656	−	0.0713512i	−0.990671	−	0.0122366i
$35$			1.40621i			0.237693i
$36$		0			0
$37$			5.74432i			0.944360i	0.881502	+	0.472180i	$0.156533\pi$
$37$			5.74432i			0.944360i	−0.881502	+	0.472180i	$0.843467\pi$
$38$	−0.0825129	+	6.68021i	−0.0133854	+	1.08367i
$39$		0			0
$40$	−9.15929	+	4.84488i	−1.44821	+	0.766043i
$41$	−4.75281	−	8.23212i	−0.742265	−	1.28564i	−0.951462	−	0.307767i	$-0.900418\pi$
$41$	−4.75281	−	8.23212i	−0.742265	−	1.28564i	0.209197	−	0.977874i	$-0.432915\pi$
$42$		0			0
$43$	−1.03633	−	0.598327i	−0.158039	−	0.0912440i	0.418895	−	0.908035i	$-0.362418\pi$
$43$	−1.03633	−	0.598327i	−0.158039	−	0.0912440i	−0.576934	+	0.816791i	$0.695751\pi$
$44$	−3.42633	−	2.09270i	−0.516538	−	0.315486i
$45$		0			0
$46$	−4.11825	−	7.34095i	−0.607204	−	1.08236i
$47$	−3.27688	+	5.67572i	−0.477982	+	0.827889i	−0.999681	−	0.0252403i	$-0.991965\pi$
$47$	−3.27688	+	5.67572i	−0.477982	+	0.827889i	0.521699	+	0.853129i	$0.325298\pi$
$48$		0			0
$49$	3.42633	+	5.93458i	0.489476	+	0.847796i
$50$	−6.08124	+	10.2389i	−0.860017	+	1.44799i
$51$		0			0
$52$	0.806700	−	0.439547i	0.111869	−	0.0609542i
$53$			7.63807i			1.04917i	0.851358	+	0.524585i	$0.175779\pi$
$53$			7.63807i			1.04917i	−0.851358	+	0.524585i	$0.824221\pi$
$54$		0			0
$55$	−7.35407			−0.991623
$56$	0.577308	−	0.919487i	0.0771460	−	0.122872i
$57$		0			0
$58$	2.86116	+	1.69935i	0.375689	+	0.223136i
$59$	0.603703	−	0.348548i	0.0785954	−	0.0453771i	−0.460187	−	0.887822i	$-0.652218\pi$
$59$	0.603703	−	0.348548i	0.0785954	−	0.0453771i	0.538783	+	0.842445i	$0.318884\pi$
$60$		0			0
$61$	−4.23774	−	2.44666i	−0.542587	−	0.313263i	0.203540	−	0.979067i	$-0.434755\pi$
$61$	−4.23774	−	2.44666i	−0.542587	−	0.313263i	−0.746127	+	0.665804i	$0.768089\pi$
$62$	−0.819356	−	1.46053i	−0.104058	−	0.185488i
$63$		0			0
$64$	7.97804	+	0.592316i	0.997255	+	0.0740395i
$65$	0.841376	−	1.45731i	0.104360	−	0.180757i
$66$		0			0
$67$	−8.87932	+	5.12648i	−1.08478	+	0.626299i	−0.932182	−	0.361989i	$-0.882098\pi$
$67$	−8.87932	+	5.12648i	−1.08478	+	0.626299i	−0.152599	+	0.988288i	$0.548764\pi$
$68$	8.16741	+	0.201796i	0.990444	+	0.0244714i
$69$		0			0
$70$	0.0245621	−	1.98853i	0.00293573	−	0.237675i
$71$	3.73792			0.443610			0.221805	−	0.975091i	$-0.428805\pi$
$71$	3.73792			0.443610			0.221805	+	0.975091i	$0.428805\pi$
$72$		0			0
$73$	−2.68275			−0.313992			−0.156996	−	0.987599i	$-0.550181\pi$
$73$	−2.68275			−0.313992			−0.156996	+	0.987599i	$0.550181\pi$
$74$	0.100335	−	8.12307i	0.0116637	−	0.944288i
$75$		0			0
$76$	0.233364	−	9.44508i	0.0267687	−	1.08342i
$77$	0.667322	−	0.385279i	0.0760484	−	0.0439066i
$78$		0			0
$79$	−5.35979	+	9.28342i	−0.603023	+	1.04447i	0.389337	+	0.921095i	$0.372704\pi$
$79$	−5.35979	+	9.28342i	−0.603023	+	1.04447i	−0.992361	+	0.123372i	$0.960629\pi$
$80$	13.0368	−	6.69119i	1.45756	−	0.748098i
$81$		0			0
$82$	6.57719	+	11.7241i	0.726329	+	1.29471i
$83$	−5.49039	−	3.16988i	−0.602648	−	0.347939i	0.167434	−	0.985883i	$-0.446452\pi$
$83$	−5.49039	−	3.16988i	−0.602648	−	0.347939i	−0.770083	+	0.637944i	$0.779785\pi$
$84$		0			0
$85$	12.9600	−	7.48246i	1.40571	−	0.811586i
$86$	1.45503	+	0.864199i	0.156900	+	0.0931890i
$87$		0			0
$88$	4.80864	+	3.01915i	0.512603	+	0.321842i
$89$	−7.56802			−0.802208			−0.401104	−	0.916032i	$-0.631373\pi$
$89$	−7.56802			−0.802208			−0.401104	+	0.916032i	$0.631373\pi$
$90$		0			0
$91$			0.176318i			0.0184832i
$92$	5.69542	+	10.4528i	0.593789	+	1.08978i
$93$		0			0
$94$	4.73299	−	7.96883i	0.488171	−	0.821922i
$95$	−8.65297	−	14.9874i	−0.887776	−	1.53767i
$96$		0			0
$97$	−2.98511	+	5.17036i	−0.303092	+	0.524971i	−0.976835	−	0.213995i	$-0.931352\pi$
$97$	−2.98511	+	5.17036i	−0.303092	+	0.524971i	0.673743	+	0.738966i	$0.264686\pi$
$98$	−4.74153	−	8.45196i	−0.478967	−	0.853777i
$99$		0			0
$100$	8.77836	−	14.3726i	0.877836	−	1.43726i
$101$	4.81265	+	2.77859i	0.478877	+	0.276480i	0.719948	−	0.694028i	$-0.244165\pi$
$101$	4.81265	+	2.77859i	0.478877	+	0.276480i	−0.241071	+	0.970507i	$0.577499\pi$
$102$		0			0
$103$	−6.14380	−	10.6414i	−0.605366	−	1.04853i	−0.991993	−	0.126289i	$-0.959693\pi$
$103$	−6.14380	−	10.6414i	−0.605366	−	1.04853i	0.386627	−	0.922236i	$-0.373640\pi$
$104$	−1.14844	+	0.607476i	−0.112614	+	0.0595679i
$105$		0			0
$106$	0.133413	−	10.8010i	0.0129582	−	1.04909i
$107$			6.61773i			0.639760i	0.947458	+	0.319880i	$0.103643\pi$
$107$			6.61773i			0.639760i	−0.947458	+	0.319880i	$0.896357\pi$
$108$		0			0
$109$			7.01563i			0.671975i	0.941866	+	0.335988i	$0.109070\pi$
$109$			7.01563i			0.671975i	−0.941866	+	0.335988i	$0.890930\pi$
$110$	10.3994	+	0.128452i	0.991547	+	0.0122474i
$111$		0			0
$112$	−0.832435	+	1.29017i	−0.0786577	+	0.121909i
$113$	4.09419	+	7.09135i	0.385149	+	0.667098i	0.991790	−	0.127878i	$-0.0408167\pi$
$113$	4.09419	+	7.09135i	0.385149	+	0.667098i	−0.606641	+	0.794976i	$0.707483\pi$
$114$		0			0
$115$	18.8830	+	10.9021i	1.76085	+	1.01663i
$116$	−4.01630	−	2.45304i	−0.372905	−	0.227759i
$117$		0			0
$118$	−0.859788	+	0.482339i	−0.0791499	+	0.0444029i
$119$	−0.784009	+	1.35794i	−0.0718700	+	0.124483i
$120$		0			0
$121$	−3.48511	−	6.03639i	−0.316828	−	0.548762i
$122$	5.94988	+	3.53386i	0.538676	+	0.319940i
$123$		0			0
$124$	1.13314	+	2.07966i	0.101759	+	0.186759i
$125$		−	12.5314i		−	1.12084i
$126$		0			0
$127$	21.0113			1.86445			0.932224	−	0.361882i	$-0.117866\pi$
$127$	21.0113			1.86445			0.932224	+	0.361882i	$0.117866\pi$
$128$	−11.2714	−	0.976949i	−0.996265	−	0.0863509i
$129$		0			0
$130$	−1.21525	+	2.04609i	−0.106584	+	0.179454i
$131$	5.49039	−	3.16988i	0.479697	−	0.276953i	−0.240593	−	0.970626i	$-0.577342\pi$
$131$	5.49039	−	3.16988i	0.479697	−	0.276953i	0.720290	+	0.693673i	$0.244009\pi$
$132$		0			0
$133$	1.57037	+	0.906655i	0.136169	+	0.0786170i
$134$	12.6458	−	7.09429i	1.09243	−	0.612853i
$135$		0			0
$136$	−11.5461	−	0.428020i	−0.990067	−	0.0367024i
$137$	−0.483695	+	0.837785i	−0.0413249	+	0.0715768i	−0.885948	−	0.463784i	$-0.846491\pi$
$137$	−0.483695	+	0.837785i	−0.0413249	+	0.0715768i	0.844623	+	0.535361i	$0.179825\pi$
$138$		0			0
$139$	5.18167	−	2.99164i	0.439503	−	0.253747i	−0.263884	−	0.964554i	$-0.585004\pi$
$139$	5.18167	−	2.99164i	0.439503	−	0.253747i	0.703387	+	0.710807i	$0.251670\pi$
$140$	−0.0694668	+	2.81157i	−0.00587101	+	0.237621i
$141$		0			0
$142$	−5.28582	−	0.0652897i	−0.443576	−	0.00547899i
$143$	−0.922090			−0.0771091
$144$		0			0
$145$	−8.62036			−0.715882
$146$	3.79369	+	0.0468592i	0.313968	+	0.00387809i
$147$		0			0
$148$	−0.283769	+	11.4851i	−0.0233256	+	0.944072i
$149$	−6.43764	+	3.71678i	−0.527392	+	0.304490i	−0.739954	−	0.672658i	$-0.765153\pi$
$149$	−6.43764	+	3.71678i	−0.527392	+	0.304490i	0.212562	+	0.977148i	$0.431819\pi$
$150$		0			0
$151$	−0.492870	+	0.853676i	−0.0401092	+	0.0694711i	−0.885383	−	0.464862i	$-0.846104\pi$
$151$	−0.492870	+	0.853676i	−0.0401092	+	0.0694711i	0.845274	+	0.534333i	$0.179437\pi$
$152$	−0.494977	+	13.3523i	−0.0401479	+	1.08301i
$153$		0			0
$154$	−0.950393	+	0.533169i	−0.0765849	+	0.0429639i
$155$	3.75691	+	2.16905i	0.301762	+	0.174222i
$156$		0			0
$157$	−15.2336	+	8.79510i	−1.21577	+	0.701925i	−0.964010	−	0.265864i	$-0.914343\pi$
$157$	−15.2336	+	8.79510i	−1.21577	+	0.701925i	−0.251760	+	0.967790i	$0.581009\pi$
$158$	7.74146	−	13.0341i	0.615877	−	1.03694i
$159$		0			0
$160$	−18.5523	+	9.23434i	−1.46669	+	0.730039i
$161$	−2.28464			−0.180055
$162$		0			0
$163$		−	17.8852i		−	1.40088i	−0.713711	−	0.700440i	$-0.752987\pi$
$163$		−	17.8852i		−	1.40088i	0.713711	−	0.700440i	$-0.247013\pi$
$164$	−9.09606	−	16.6940i	−0.710283	−	1.30358i
$165$		0			0
$166$	7.70862	+	4.57844i	0.598305	+	0.355356i
$167$	1.04037	+	1.80197i	0.0805062	+	0.139441i	0.903467	−	0.428657i	$-0.141013\pi$
$167$	1.04037	+	1.80197i	0.0805062	+	0.139441i	−0.822961	+	0.568097i	$0.807680\pi$
$168$		0			0
$169$	−6.39450	+	11.0756i	−0.491885	+	0.851970i
$170$	−18.4575	+	10.3546i	−1.41563	+	0.794163i
$171$		0			0
$172$	−2.04248	−	1.24748i	−0.155737	−	0.0951198i
$173$	−16.4718	−	9.51000i	−1.25233	−	0.723032i	−0.280757	−	0.959779i	$-0.590585\pi$
$173$	−16.4718	−	9.51000i	−1.25233	−	0.723032i	−0.971571	+	0.236747i	$0.923919\pi$
$174$		0			0
$175$	1.61615	+	2.79925i	0.122169	+	0.211603i
$176$	−6.74719	−	4.35338i	−0.508588	−	0.328149i
$177$		0			0
$178$	10.7020	+	0.132189i	0.802147	+	0.00990800i
$179$			2.12111i			0.158539i	0.996853	+	0.0792697i	$0.0252588\pi$
$179$			2.12111i			0.158539i	−0.996853	+	0.0792697i	$0.974741\pi$
$180$		0			0
$181$		−	1.66297i		−	0.123608i	−0.998088	−	0.0618039i	$-0.980315\pi$
$181$		−	1.66297i		−	0.123608i	0.998088	−	0.0618039i	$-0.0196853\pi$
$182$	0.00307972	−	0.249332i	0.000228284	−	0.0184818i
$183$		0			0
$184$	−7.87135	−	14.8809i	−0.580284	−	1.09703i
$185$	10.5219	+	18.2245i	0.773588	+	1.33989i
$186$		0			0
$187$	−7.10164	−	4.10013i	−0.519323	−	0.299831i
$188$	−6.83214	+	11.1861i	−0.498285	+	0.815830i
$189$		0			0
$190$	11.9744	+	21.3449i	0.868717	+	1.54852i
$191$	8.69755	−	15.0646i	0.629333	−	1.09004i	−0.358353	−	0.933586i	$-0.616662\pi$
$191$	8.69755	−	15.0646i	0.629333	−	1.09004i	0.987686	−	0.156450i	$-0.0500052\pi$
$192$		0			0
$193$	−1.41709	−	2.45447i	−0.102004	−	0.176677i	0.810506	−	0.585730i	$-0.199192\pi$
$193$	−1.41709	−	2.45447i	−0.102004	−	0.176677i	−0.912510	+	0.409054i	$0.865859\pi$
$194$	4.31157	−	7.25930i	0.309553	−	0.521187i
$195$		0			0
$196$	6.55740	+	12.0348i	0.468386	+	0.859628i
$197$			12.5991i			0.897646i	0.893621	+	0.448823i	$0.148157\pi$
$197$			12.5991i			0.897646i	−0.893621	+	0.448823i	$0.851843\pi$
$198$		0			0
$199$	17.2733			1.22447			0.612237	−	0.790674i	$-0.290270\pi$
$199$	17.2733			1.22447			0.612237	+	0.790674i	$0.290270\pi$
$200$	−12.6646	+	20.1710i	−0.895520	+	1.42631i
$201$		0			0
$202$	−6.75707	−	4.01328i	−0.475426	−	0.282373i
$203$	0.782227	−	0.451619i	0.0549016	−	0.0316975i
$204$		0			0
$205$	−30.1577	−	17.4116i	−2.10631	−	1.21608i
$206$	8.50211	+	15.1553i	0.592370	+	1.05592i
$207$		0			0
$208$	1.63462	−	0.838975i	0.113341	−	0.0581725i
$209$	−4.74153	+	8.21258i	−0.327979	+	0.568076i
$210$		0			0
$211$	−15.2192	+	8.78678i	−1.04773	+	0.604907i	−0.922013	−	0.387159i	$-0.873456\pi$
$211$	−15.2192	+	8.78678i	−1.04773	+	0.604907i	−0.125717	+	0.992066i	$0.540123\pi$
$212$	−0.377320	+	15.2715i	−0.0259144	+	1.04885i
$213$		0			0
$214$	0.115591	−	9.35817i	0.00790162	−	0.639711i
$215$	−4.38385			−0.298976
$216$		0			0
$217$	−0.454545			−0.0308565
$218$	0.122541	−	9.92084i	0.00829951	−	0.671924i
$219$		0			0
$220$	−14.7037	−	0.363290i	−0.991320	−	0.0244930i
$221$	1.62499	−	0.938188i	0.109309	−	0.0631094i
$222$		0			0
$223$	12.3137	−	21.3280i	0.824587	−	1.42823i	−0.0776484	−	0.996981i	$-0.524741\pi$
$223$	12.3137	−	21.3280i	0.824587	−	1.42823i	0.902235	−	0.431245i	$-0.141926\pi$
$224$	1.19969	−	1.80989i	0.0801574	−	0.120929i
$225$		0			0
$226$	−5.66575	−	10.0994i	−0.376880	−	0.671804i
$227$	16.9918	+	9.81024i	1.12779	+	0.651128i	0.943378	−	0.331721i	$-0.107629\pi$
$227$	16.9918	+	9.81024i	1.12779	+	0.651128i	0.184410	+	0.982849i	$0.440963\pi$
$228$		0			0
$229$	21.3431	−	12.3224i	1.41039	−	0.814289i	0.414965	−	0.909837i	$-0.363794\pi$
$229$	21.3431	−	12.3224i	1.41039	−	0.814289i	0.995425	+	0.0955486i	$0.0304605\pi$
$230$	−26.5122	−	15.7466i	−1.74816	−	1.03830i
$231$		0			0
$232$	5.63663	+	3.53901i	0.370063	+	0.232347i
$233$	20.9222			1.37066			0.685330	−	0.728233i	$-0.259658\pi$
$233$	20.9222			1.37066			0.685330	+	0.728233i	$0.259658\pi$
$234$		0			0
$235$			24.0092i			1.56619i
$236$	1.22426	−	0.667060i	0.0796922	−	0.0434219i
$237$		0			0
$238$	1.13239	−	1.90658i	0.0734020	−	0.123585i
$239$	5.14584	+	8.91286i	0.332857	+	0.576525i	0.983071	−	0.183226i	$-0.0586541\pi$
$239$	5.14584	+	8.91286i	0.332857	+	0.576525i	−0.650214	+	0.759751i	$0.725321\pi$
$240$		0			0
$241$	10.2379	−	17.7326i	0.659483	−	1.14226i	−0.321267	−	0.946989i	$-0.604109\pi$
$241$	10.2379	−	17.7326i	0.659483	−	1.14226i	0.980750	−	0.195269i	$-0.0625579\pi$
$242$	4.82288	+	8.59696i	0.310026	+	0.552634i
$243$		0			0
$244$	−8.35203	−	5.10117i	−0.534684	−	0.326569i
$245$	21.7409	+	12.5521i	1.38897	+	0.801924i
$246$		0			0
$247$	−1.08495	−	1.87919i	−0.0690339	−	0.119570i
$248$	−1.56606	−	2.96065i	−0.0994450	−	0.188001i
$249$		0			0
$250$	−0.218884	+	17.7207i	−0.0138434	+	1.12076i
$251$		−	28.0987i		−	1.77358i	−0.462177	−	0.886788i	$-0.652932\pi$
$251$		−	28.0987i		−	1.77358i	0.462177	−	0.886788i	$-0.347068\pi$
$252$		0			0
$253$		−	11.9480i		−	0.751163i
$254$	−29.7121	−	0.367000i	−1.86431	−	0.0230276i
$255$		0			0
$256$	15.9220	+	1.57839i	0.995122	+	0.0986491i
$257$	−5.53682	−	9.59006i	−0.345378	−	0.598211i	0.640045	−	0.768338i	$-0.278916\pi$
$257$	−5.53682	−	9.59006i	−0.345378	−	0.598211i	−0.985422	+	0.170126i	$0.945582\pi$
$258$		0			0
$259$	−1.90956	−	1.10248i	−0.118654	−	0.0685050i
$260$	1.75423	−	2.87216i	0.108793	−	0.178124i
$261$		0			0
$262$	−7.81936	+	4.38664i	−0.483081	+	0.271008i
$263$	12.7620	−	22.1044i	0.786938	−	1.36302i	−0.140897	−	0.990024i	$-0.544998\pi$
$263$	12.7620	−	22.1044i	0.786938	−	1.36302i	0.927834	−	0.372992i	$-0.121668\pi$
$264$		0			0
$265$	13.9907	+	24.2327i	0.859444	+	1.48860i
$266$	−2.20484	−	1.30954i	−0.135187	−	0.0802928i
$267$		0			0
$268$	−18.0065	+	9.81119i	−1.09992	+	0.599314i
$269$		−	18.3998i		−	1.12185i	−0.827865	−	0.560927i	$-0.810445\pi$
$269$		−	18.3998i		−	1.12185i	0.827865	−	0.560927i	$-0.189555\pi$
$270$		0			0
$271$	−22.4135			−1.36152			−0.680760	−	0.732506i	$-0.738350\pi$
$271$	−22.4135			−1.36152			−0.680760	+	0.732506i	$0.738350\pi$
$272$	16.3199	+	0.806938i	0.989538	+	0.0489278i
$273$		0			0
$274$	0.698630	−	1.17627i	0.0422058	−	0.0710609i
$275$	−14.6392	+	8.45196i	−0.882779	+	0.509673i
$276$		0			0
$277$	20.2421	+	11.6868i	1.21623	+	0.702190i	0.964109	−	0.265506i	$-0.0855391\pi$
$277$	20.2421	+	11.6868i	1.21623	+	0.702190i	0.252119	+	0.967696i	$0.418872\pi$
$278$	−7.37968	+	4.13998i	−0.442604	+	0.248300i
$279$		0			0
$280$	0.147343	−	3.97464i	0.00880540	−	0.237530i
$281$	−5.29466	+	9.17062i	−0.315853	+	0.547073i	−0.979618	−	0.200867i	$-0.935624\pi$
$281$	−5.29466	+	9.17062i	−0.315853	+	0.547073i	0.663765	+	0.747941i	$0.268957\pi$
$282$		0			0
$283$	7.69029	−	4.43999i	0.457140	−	0.263930i	−0.253701	−	0.967283i	$-0.581648\pi$
$283$	7.69029	−	4.43999i	0.457140	−	0.263930i	0.710841	+	0.703353i	$0.248314\pi$
$284$	7.47357	+	0.184653i	0.443475	+	0.0109571i
$285$		0			0
$286$	1.30393	+	0.0161060i	0.0771032	+	0.000952367i
$287$	3.64876			0.215379
$288$		0			0
$289$	−0.313160			−0.0184212
$290$	12.1901	+	0.150570i	0.715827	+	0.00884180i
$291$		0			0
$292$	−5.36387	−	0.132528i	−0.313897	−	0.00775559i
$293$	−9.82117	+	5.67026i	−0.573759	+	0.331260i	−0.758649	−	0.651499i	$-0.774140\pi$
$293$	−9.82117	+	5.67026i	−0.573759	+	0.331260i	0.184890	+	0.982759i	$0.440807\pi$
$294$		0			0
$295$	1.27688	−	2.21162i	0.0743428	−	0.128765i
$296$	0.601887	−	16.2362i	0.0349840	−	0.943712i
$297$		0			0
$298$	9.16843	−	5.14347i	0.531113	−	0.297953i
$299$	2.36765	+	1.36696i	0.136925	+	0.0790534i
$300$		0			0
$301$	0.397799	−	0.229669i	0.0229287	−	0.0132379i
$302$	0.711881	−	1.19858i	0.0409642	−	0.0689705i
$303$		0			0
$304$	0.933171	−	18.8729i	0.0535210	−	1.08243i
$305$	−17.9263			−1.02646
$306$		0			0
$307$			0.628678i			0.0358805i	0.999839	+	0.0179403i	$0.00571087\pi$
$307$			0.628678i			0.0358805i	−0.999839	+	0.0179403i	$0.994289\pi$
$308$	1.35327	−	0.737356i	0.0771097	−	0.0420148i
$309$		0			0
$310$	−5.27478	−	3.13289i	−0.299587	−	0.177936i
$311$	9.64443	+	16.7046i	0.546885	+	0.947233i	0.998486	+	0.0550127i	$0.0175199\pi$
$311$	9.64443	+	16.7046i	0.546885	+	0.947233i	−0.451600	+	0.892220i	$0.649147\pi$
$312$		0			0
$313$	−2.86959	+	4.97028i	−0.162199	+	0.280937i	−0.935657	−	0.352911i	$-0.885192\pi$
$313$	−2.86959	+	4.97028i	−0.162199	+	0.280937i	0.773458	+	0.633847i	$0.218525\pi$
$314$	21.6955	−	12.1711i	1.22435	−	0.686856i
$315$		0			0
$316$	−11.1749	+	18.2964i	−0.628638	+	1.02925i
$317$	−10.8187	−	6.24618i	−0.607639	−	0.350821i	0.164402	−	0.986393i	$-0.447431\pi$
$317$	−10.8187	−	6.24618i	−0.607639	−	0.350821i	−0.772041	+	0.635573i	$0.780764\pi$
$318$		0			0
$319$	2.36183	+	4.09081i	0.132237	+	0.229042i
$320$	26.3962	−	12.7343i	1.47559	−	0.711868i
$321$		0			0
$322$	3.23072	+	0.0399054i	0.180041	+	0.00222384i
$323$		−	19.2972i		−	1.07373i
$324$		0			0
$325$		−	3.86794i		−	0.214555i
$326$	−0.312398	+	25.2916i	−0.0173021	+	1.40077i
$327$		0			0
$328$	12.5712	+	23.7660i	0.694129	+	1.31226i
$329$	−1.25784	−	2.17864i	−0.0693468	−	0.120112i
$330$		0			0
$331$	3.00014	+	1.73213i	0.164902	+	0.0952065i	0.580180	−	0.814488i	$-0.302982\pi$
$331$	3.00014	+	1.73213i	0.164902	+	0.0952065i	−0.415278	+	0.909695i	$0.636316\pi$
$332$	−10.8208	−	6.60904i	−0.593870	−	0.362718i
$333$		0			0
$334$	−1.43972	−	2.56635i	−0.0787778	−	0.140425i
$335$	−18.7805	+	32.5287i	−1.02609	+	1.77723i
$336$		0			0
$337$	−9.30453	−	16.1159i	−0.506850	−	0.877890i	−0.999969	−	0.00792778i	$-0.997476\pi$
$337$	−9.30453	−	16.1159i	−0.506850	−	0.877890i	0.493119	−	0.869962i	$-0.335857\pi$
$338$	9.23596	−	15.5504i	0.502370	−	0.845829i
$339$		0			0
$340$	26.2817	−	14.3201i	1.42533	−	0.776618i
$341$		−	2.37713i		−	0.128729i
$342$		0			0
$343$	−5.31737			−0.287111
$344$	2.86649	+	1.79975i	0.154551	+	0.0970360i
$345$		0			0
$346$	23.1268	+	13.7359i	1.24330	+	0.738444i
$347$	−0.0408752	+	0.0235993i	−0.00219430	+	0.00126688i	−0.501097	−	0.865391i	$-0.667070\pi$
$347$	−0.0408752	+	0.0235993i	−0.00219430	+	0.00126688i	0.498902	+	0.866658i	$0.333737\pi$
$348$		0			0
$349$	12.8884	+	7.44113i	0.689901	+	0.398314i	0.803575	−	0.595204i	$-0.202929\pi$
$349$	12.8884	+	7.44113i	0.689901	+	0.398314i	−0.113674	+	0.993518i	$0.536262\pi$
$350$	−2.23651	−	3.98666i	−0.119546	−	0.213096i
$351$		0			0
$352$	9.46520	+	6.27400i	0.504497	+	0.334405i
$353$	9.25423	−	16.0288i	0.492553	−	0.853127i	−0.507410	−	0.861705i	$-0.669397\pi$
$353$	9.25423	−	16.0288i	0.492553	−	0.853127i	0.999963	+	0.00857792i	$0.00273047\pi$
$354$		0			0
$355$	11.8590	−	6.84680i	0.629411	−	0.363390i
$356$	−15.1314	−	0.373859i	−0.801964	−	0.0198145i
$357$		0			0
$358$	0.0370491	−	2.99948i	0.00195811	−	0.158527i
$359$	−31.3426			−1.65420			−0.827101	−	0.562054i	$-0.810011\pi$
$359$	−31.3426			−1.65420			−0.827101	+	0.562054i	$0.810011\pi$
$360$		0			0
$361$	−3.31599			−0.174526
$362$	−0.0290468	+	2.35162i	−0.00152667	+	0.123598i
$363$		0			0
$364$	−0.00871009	+	0.352529i	−0.000456533	+	0.0184775i
$365$	−8.51135	+	4.91403i	−0.445504	+	0.257212i
$366$		0			0
$367$	−10.2308	+	17.7203i	−0.534043	+	0.924990i	0.465166	+	0.885224i	$0.345995\pi$
$367$	−10.2308	+	17.7203i	−0.534043	+	0.924990i	−0.999209	+	0.0397663i	$0.987339\pi$
$368$	10.8710	+	21.1806i	0.566690	+	1.10411i
$369$		0			0
$370$	−14.5608	−	25.9552i	−0.756980	−	1.34935i
$371$	−2.53909	−	1.46594i	−0.131823	−	0.0761081i
$372$		0			0
$373$	−20.6021	+	11.8946i	−1.06674	+	0.615880i	−0.927288	−	0.374349i	$-0.877866\pi$
$373$	−20.6021	+	11.8946i	−1.06674	+	0.615880i	−0.139448	+	0.990229i	$0.544533\pi$
$374$	9.97085	+	5.92206i	0.515580	+	0.306223i
$375$		0			0
$376$	9.85675	−	15.6990i	0.508323	−	0.809614i
$377$	−1.08086			−0.0556673
$378$		0			0
$379$		−	24.0988i		−	1.23787i	−0.785441	−	0.618937i	$-0.787564\pi$
$379$		−	24.0988i		−	1.23787i	0.785441	−	0.618937i	$-0.212436\pi$
$380$	−16.5603	−	30.3931i	−0.849525	−	1.55913i
$381$		0			0
$382$	−12.5624	+	21.1510i	−0.642748	+	1.08218i
$383$	−9.39161	−	16.2667i	−0.479889	−	0.831192i	0.519845	−	0.854261i	$-0.325990\pi$
$383$	−9.39161	−	16.2667i	−0.479889	−	0.831192i	−0.999734	+	0.0230686i	$0.992656\pi$
$384$		0			0
$385$	1.41144	−	2.44468i	0.0719336	−	0.124593i
$386$	1.96105	+	3.49564i	0.0998146	+	0.177923i
$387$		0			0
$388$	−6.22381	+	10.1901i	−0.315966	+	0.517324i
$389$	15.0467	+	8.68720i	0.762897	+	0.440459i	0.830335	−	0.557265i	$-0.188149\pi$
$389$	15.0467	+	8.68720i	0.762897	+	0.440459i	−0.0674382	+	0.997723i	$0.521483\pi$
$390$		0			0
$391$	12.1566	+	21.0558i	0.614783	+	1.06484i
$392$	−9.06265	−	17.1330i	−0.457733	−	0.865347i
$393$		0			0
$394$	0.220066	−	17.8164i	0.0110867	−	0.897578i
$395$			39.2703i			1.97591i
$396$		0			0
$397$			26.2401i			1.31696i	0.752600	+	0.658478i	$0.228799\pi$
$397$			26.2401i			1.31696i	−0.752600	+	0.658478i	$0.771201\pi$
$398$	−24.4263	−	0.301710i	−1.22438	−	0.0151234i
$399$		0			0
$400$	18.2614	−	28.3028i	0.913068	−	1.41514i
$401$	−10.8194	−	18.7398i	−0.540296	−	0.935820i	−0.998887	−	0.0471725i	$-0.984979\pi$
$401$	−10.8194	−	18.7398i	−0.540296	−	0.935820i	0.458591	−	0.888648i	$-0.348354\pi$
$402$		0			0
$403$	0.471060	+	0.271967i	0.0234652	+	0.0135476i
$404$	9.48511	+	5.79322i	0.471902	+	0.288224i
$405$		0			0
$406$	−1.11404	+	0.624974i	−0.0552889	+	0.0310170i
$407$	5.76566	−	9.98642i	0.285793	−	0.495008i
$408$		0			0
$409$	−6.00563	−	10.4021i	−0.296959	−	0.514348i	0.678480	−	0.734619i	$-0.262639\pi$
$409$	−6.00563	−	10.4021i	−0.296959	−	0.514348i	−0.975439	+	0.220271i	$0.929306\pi$
$410$	42.3421	+	25.1486i	2.09113	+	1.24200i
$411$		0			0
$412$	−11.7582	−	21.5797i	−0.579283	−	1.06316i
$413$			0.267582i			0.0131668i
$414$		0			0
$415$	−23.2252			−1.14008
$416$	−2.32618	+	1.15785i	−0.114051	+	0.0567682i
$417$		0			0
$418$	6.84848	−	11.5306i	0.334970	−	0.563982i
$419$	−1.38092	+	0.797277i	−0.0674625	+	0.0389495i	−0.533352	−	0.845893i	$-0.679068\pi$
$419$	−1.38092	+	0.797277i	−0.0674625	+	0.0389495i	0.465889	+	0.884843i	$0.345734\pi$
$420$		0			0
$421$	15.6612	+	9.04197i	0.763278	+	0.440679i	0.830471	−	0.557061i	$-0.188071\pi$
$421$	15.6612	+	9.04197i	0.763278	+	0.440679i	−0.0671934	+	0.997740i	$0.521404\pi$
$422$	21.6750	−	12.1596i	1.05512	−	0.591920i
$423$		0			0
$424$	0.800314	−	21.5889i	0.0388667	−	1.04845i
$425$	17.1990	−	29.7896i	0.834276	−	1.44501i
$426$		0			0
$427$	1.62667	−	0.939156i	0.0787199	−	0.0454489i
$428$	−0.326915	+	13.2314i	−0.0158020	+	0.639565i
$429$		0			0
$430$	6.19923	+	0.0765720i	0.298953	+	0.00369263i
$431$	34.7451			1.67361			0.836806	−	0.547499i	$-0.184420\pi$
$431$	34.7451			1.67361			0.836806	+	0.547499i	$0.184420\pi$
$432$		0			0
$433$	12.7197			0.611270			0.305635	−	0.952149i	$-0.401131\pi$
$433$	12.7197			0.611270			0.305635	+	0.952149i	$0.401131\pi$
$434$	0.642774	+	0.00793946i	0.0308542	+	0.000381106i
$435$		0			0
$436$	−0.346571	+	14.0270i	−0.0165978	+	0.671770i
$437$	24.3496	−	14.0583i	1.16480	−	0.672498i
$438$		0			0
$439$	−7.45900	+	12.9194i	−0.355999	+	0.616608i	−0.987288	−	0.158939i	$-0.949193\pi$
$439$	−7.45900	+	12.9194i	−0.355999	+	0.616608i	0.631290	+	0.775547i	$0.282526\pi$
$440$	20.7862	+	0.770557i	0.990942	+	0.0367349i
$441$		0			0
$442$	−2.31429	+	1.29831i	−0.110080	+	0.0617545i
$443$	−3.48405	−	2.01152i	−0.165532	−	0.0955702i	0.414945	−	0.909846i	$-0.363801\pi$
$443$	−3.48405	−	2.01152i	−0.165532	−	0.0955702i	−0.580478	+	0.814276i	$0.697134\pi$
$444$		0			0
$445$	−24.0104	+	13.8624i	−1.13820	+	0.657142i
$446$	−17.7854	+	29.9449i	−0.842164	+	1.41793i
$447$		0			0
$448$	−1.72810	+	2.53843i	−0.0816449	+	0.119929i
$449$	−10.9179			−0.515246			−0.257623	−	0.966245i	$-0.582939\pi$
$449$	−10.9179			−0.515246			−0.257623	+	0.966245i	$0.582939\pi$
$450$		0			0
$451$			19.0819i			0.898531i
$452$	7.83557	+	14.3806i	0.368554	+	0.676407i
$453$		0			0
$454$	−23.8569	−	14.1695i	−1.11966	−	0.665008i
$455$	0.322964	+	0.559390i	0.0151408	+	0.0262246i
$456$		0			0
$457$	−0.815204	+	1.41197i	−0.0381336	+	0.0660494i	−0.884462	−	0.466612i	$-0.845475\pi$
$457$	−0.815204	+	1.41197i	−0.0381336	+	0.0660494i	0.846329	+	0.532661i	$0.178808\pi$
$458$	−30.3966	+	17.0524i	−1.42034	+	0.796807i
$459$		0			0
$460$	37.2159	+	22.7304i	1.73520	+	1.05981i
$461$	10.1812	+	5.87811i	0.474185	+	0.273771i	0.717990	−	0.696054i	$-0.245062\pi$
$461$	10.1812	+	5.87811i	0.474185	+	0.273771i	−0.243805	+	0.969824i	$0.578396\pi$
$462$		0			0
$463$	−10.6473	−	18.4416i	−0.494820	−	0.857053i	0.505162	−	0.863024i	$-0.331433\pi$
$463$	−10.6473	−	18.4416i	−0.494820	−	0.857053i	−0.999982	+	0.00597113i	$0.998099\pi$
$464$	−7.90898	−	5.10299i	−0.367165	−	0.236900i
$465$		0			0
$466$	−29.5862	−	0.365445i	−1.37056	−	0.0169289i
$467$			18.9230i			0.875650i	0.899060	+	0.437825i	$0.144251\pi$
$467$			18.9230i			0.875650i	−0.899060	+	0.437825i	$0.855749\pi$
$468$		0			0
$469$		−	3.93562i		−	0.181730i
$470$	0.419364	−	33.9515i	0.0193438	−	1.56607i
$471$		0			0
$472$	−1.74288	+	0.921910i	−0.0802225	+	0.0424344i
$473$	1.20110	+	2.08037i	0.0552267	+	0.0956554i
$474$		0			0
$475$	−34.4497	−	19.8896i	−1.58066	−	0.912595i
$476$	−1.63462	+	2.67633i	−0.0749228	+	0.122669i
$477$		0			0
$478$	−7.12108	−	12.6936i	−0.325711	−	0.580592i
$479$	−14.9759	+	25.9391i	−0.684268	+	1.18519i	0.289398	+	0.957209i	$0.406545\pi$
$479$	−14.9759	+	25.9391i	−0.684268	+	1.18519i	−0.973666	+	0.227978i	$0.926789\pi$
$480$		0			0
$481$	1.31929	+	2.28508i	0.0601546	+	0.104191i
$482$	−14.7872	+	24.8970i	−0.673540	+	1.13403i
$483$		0			0
$484$	−6.66990	−	12.2413i	−0.303177	−	0.556421i
$485$			21.8714i			0.993131i
$486$		0			0
$487$	−17.3370			−0.785614			−0.392807	−	0.919621i	$-0.628496\pi$
$487$	−17.3370			−0.785614			−0.392807	+	0.919621i	$0.628496\pi$
$488$	11.7215	+	7.35948i	0.530610	+	0.333148i
$489$		0			0
$490$	−30.5246	−	18.1297i	−1.37896	−	0.819018i
$491$	−31.1204	+	17.9674i	−1.40444	+	0.810856i	−0.994845	−	0.101409i	$-0.967665\pi$
$491$	−31.1204	+	17.9674i	−1.40444	+	0.810856i	−0.409599	+	0.912265i	$0.634332\pi$
$492$		0			0
$493$	−8.32446	−	4.80613i	−0.374915	−	0.216457i
$494$	1.50141	+	2.67633i	0.0675518	+	0.120414i
$495$		0			0
$496$	2.16286	+	4.21403i	0.0971154	+	0.189215i
$497$	−0.717405	+	1.24258i	−0.0321800	+	0.0557374i
$498$		0			0
$499$	10.4956	−	6.05962i	0.469846	−	0.271266i	−0.246329	−	0.969186i	$-0.579224\pi$
$499$	10.4956	−	6.05962i	0.469846	−	0.271266i	0.716175	+	0.697920i	$0.245891\pi$
$500$	0.619049	−	25.0551i	0.0276847	−	1.12050i
$501$		0			0
$502$	−0.490795	+	39.7346i	−0.0219053	+	1.77344i
$503$	−32.3442			−1.44215			−0.721077	−	0.692855i	$-0.756353\pi$
$503$	−32.3442			−1.44215			−0.721077	+	0.692855i	$0.756353\pi$
$504$		0			0
$505$	20.3583			0.905932
$506$	−0.208693	+	16.8957i	−0.00927754	+	0.751105i
$507$		0			0
$508$	42.0097	+	1.03795i	1.86388	+	0.0460517i
$509$	−2.90310	+	1.67610i	−0.128677	+	0.0742919i	−0.562957	−	0.826486i	$-0.690336\pi$
$509$	−2.90310	+	1.67610i	−0.128677	+	0.0742919i	0.434280	+	0.900778i	$0.357003\pi$
$510$		0			0
$511$	0.514890	−	0.891816i	0.0227774	−	0.0394516i
$512$	−22.4878	−	2.51011i	−0.993828	−	0.110932i
$513$		0			0
$514$	7.66215	+	13.6581i	0.337963	+	0.602432i
$515$	−38.9838	−	22.5073i	−1.71783	−	0.991792i
$516$		0			0
$517$	11.3936	−	6.57811i	0.501091	−	0.289305i
$518$	2.68106	+	1.59238i	0.117799	+	0.0699653i
$519$		0			0
$520$	−2.53083	+	4.03089i	−0.110984	+	0.176766i
$521$	−21.5651			−0.944786			−0.472393	−	0.881388i	$-0.656610\pi$
$521$	−21.5651			−0.944786			−0.472393	+	0.881388i	$0.656610\pi$
$522$		0			0
$523$			24.9549i			1.09120i	0.838046	+	0.545600i	$0.183698\pi$
$523$			24.9549i			1.09120i	−0.838046	+	0.545600i	$0.816302\pi$
$524$	11.1340	−	6.06659i	0.486392	−	0.265020i
$525$		0			0
$526$	−18.4329	+	31.0351i	−0.803712	+	1.35319i
$527$	2.41863	+	4.18919i	0.105357	+	0.182484i
$528$		0			0
$529$	−6.21238	+	10.7602i	−0.270104	+	0.467833i
$530$	−19.3611	−	34.5119i	−0.840993	−	1.49910i
$531$		0			0
$532$	3.09500	+	1.89033i	0.134185	+	0.0819564i
$533$	−3.78133	−	2.18315i	−0.163787	−	0.0945627i
$534$		0			0
$535$	12.1218	+	20.9955i	0.524070	+	0.907716i
$536$	25.6344	−	13.5595i	1.10724	−	0.585683i
$537$		0			0
$538$	−0.321386	+	26.0192i	−0.0138559	+	1.12177i
$539$		−	13.7562i		−	0.592523i
$540$		0			0
$541$		−	41.9065i		−	1.80170i	−0.434131	−	0.900850i	$-0.642945\pi$
$541$		−	41.9065i		−	1.80170i	0.434131	−	0.900850i	$-0.357055\pi$
$542$	31.6950	+	0.391492i	1.36142	+	0.0168160i
$543$		0			0
$544$	−23.0639	−	1.42615i	−0.988858	−	0.0611458i
$545$	12.8506	+	22.2579i	0.550460	+	0.953424i
$546$		0			0
$547$	−25.7251	−	14.8524i	−1.09993	−	0.635043i	−0.163726	−	0.986506i	$-0.552351\pi$
$547$	−25.7251	−	14.8524i	−1.09993	−	0.635043i	−0.936202	+	0.351462i	$0.885684\pi$
$548$	−1.00848	+	1.65116i	−0.0430802	+	0.0705342i
$549$		0			0
$550$	20.8490	−	11.6963i	0.889006	−	0.498731i
$551$	−5.55797	+	9.62669i	−0.236778	+	0.410111i
$552$		0			0
$553$	−2.05737	−	3.56346i	−0.0874881	−	0.151534i
$554$	−28.4203	−	16.8799i	−1.20746	−	0.717158i
$555$		0			0
$556$	10.5080	−	5.72547i	0.445637	−	0.242814i
$557$		−	21.9632i		−	0.930609i	−0.885151	−	0.465305i	$-0.845945\pi$
$557$		−	21.9632i		−	0.930609i	0.885151	−	0.465305i	$-0.154055\pi$
$558$		0			0
$559$	−0.549669			−0.0232485
$560$	−0.277782	+	5.61799i	−0.0117384	+	0.237403i
$561$		0			0
$562$	7.64739	−	12.8757i	0.322586	−	0.543131i
$563$	23.8394	−	13.7637i	1.00471	−	0.580069i	0.0950710	−	0.995470i	$-0.469692\pi$
$563$	23.8394	−	13.7637i	1.00471	−	0.580069i	0.909638	+	0.415401i	$0.136359\pi$
$564$		0			0
$565$	25.9786	+	14.9988i	1.09293	+	0.631002i
$566$	−10.9524	+	6.14429i	−0.460365	+	0.258264i
$567$		0			0
$568$	−10.5652	−	0.391658i	−0.443305	−	0.0164336i
$569$	−8.83572	+	15.3039i	−0.370413	+	0.641574i	−0.989629	−	0.143647i	$-0.954117\pi$
$569$	−8.83572	+	15.3039i	−0.370413	+	0.641574i	0.619216	+	0.785221i	$0.287450\pi$
$570$		0			0
$571$	3.92630	−	2.26685i	0.164311	−	0.0948648i	−0.415590	−	0.909552i	$-0.636425\pi$
$571$	3.92630	−	2.26685i	0.164311	−	0.0948648i	0.579900	+	0.814687i	$0.303091\pi$
$572$	−1.84362	−	0.0455512i	−0.0770855	−	0.00190459i
$573$		0			0
$574$	−5.15973	−	0.0637322i	−0.215363	−	0.00266013i
$575$	50.1188			2.09010
$576$		0			0
$577$	23.3909			0.973776			0.486888	−	0.873464i	$-0.338132\pi$
$577$	23.3909			0.973776			0.486888	+	0.873464i	$0.338132\pi$
$578$	0.442841	+	0.00546991i	0.0184198	+	0.000227518i
$579$		0			0
$580$	−17.2355	−	0.425845i	−0.715664	−	0.0176822i
$581$	2.10750	−	1.21676i	0.0874337	−	0.0504799i
$582$		0			0
$583$	7.66645	−	13.2787i	0.317512	−	0.549947i
$584$	7.58276	+	0.281098i	0.313777	+	0.0116319i
$585$		0			0
$586$	13.9872	−	7.84680i	0.577807	−	0.324148i
$587$	−7.18259	−	4.14687i	−0.296457	−	0.171160i	0.344393	−	0.938826i	$-0.388085\pi$
$587$	−7.18259	−	4.14687i	−0.296457	−	0.171160i	−0.640850	+	0.767666i	$0.721418\pi$
$588$		0			0
$589$	4.84453	−	2.79699i	0.199615	−	0.115248i
$590$	−1.84427	+	3.10516i	−0.0759275	+	0.127837i
$591$		0			0
$592$	−1.13473	+	22.9492i	−0.0466370	+	0.943208i
$593$	43.5169			1.78702			0.893512	−	0.449039i	$-0.148234\pi$
$593$	43.5169			1.78702			0.893512	+	0.449039i	$0.148234\pi$
$594$		0			0
$595$			5.74432i			0.235494i
$596$	−13.0550	+	7.11326i	−0.534752	+	0.291371i
$597$		0			0
$598$	−3.32423	−	1.97438i	−0.135938	−	0.0807385i
$599$	−0.527649	−	0.913915i	−0.0215592	−	0.0373416i	0.855045	−	0.518555i	$-0.173530\pi$
$599$	−0.527649	−	0.913915i	−0.0215592	−	0.0373416i	−0.876604	+	0.481213i	$0.840196\pi$
$600$		0			0
$601$	17.9922	−	31.1633i	0.733915	−	1.27118i	−0.221282	−	0.975210i	$-0.571024\pi$
$601$	17.9922	−	31.1633i	0.733915	−	1.27118i	0.955198	−	0.295969i	$-0.0956424\pi$
$602$	−0.566541	+	0.317828i	−0.0230905	+	0.0129537i
$603$		0			0
$604$	−1.02761	+	1.68248i	−0.0418129	+	0.0684592i
$605$	−22.1138	−	12.7674i	−0.899056	−	0.519070i
$606$		0			0
$607$	−9.81512	−	17.0003i	−0.398383	−	0.690020i	0.595143	−	0.803620i	$-0.297095\pi$
$607$	−9.81512	−	17.0003i	−0.398383	−	0.690020i	−0.993527	+	0.113599i	$0.963762\pi$
$608$	−1.64925	+	26.6719i	−0.0668860	+	1.08169i
$609$		0			0
$610$	25.3497	+	0.313116i	1.02638	+	0.0126777i
$611$			3.01039i			0.121787i
$612$		0			0
$613$		−	0.0630655i		−	0.00254719i	−0.999999	−	0.00127360i	$-0.999595\pi$
$613$		−	0.0630655i		−	0.00254719i	0.999999	−	0.00127360i	$-0.000405399\pi$
$614$	0.0109810	−	0.889017i	0.000443157	−	0.0358778i
$615$		0			0
$616$	−1.92655	+	1.01906i	−0.0776227	+	0.0410592i
$617$	−15.0926	−	26.1412i	−0.607606	−	1.05240i	−0.991634	−	0.129083i	$-0.958797\pi$
$617$	−15.0926	−	26.1412i	−0.607606	−	1.05240i	0.384028	−	0.923322i	$-0.374537\pi$
$618$		0			0
$619$	38.2663	+	22.0930i	1.53805	+	0.887994i	0.998953	+	0.0457517i	$0.0145683\pi$
$619$	38.2663	+	22.0930i	1.53805	+	0.887994i	0.539099	+	0.842243i	$0.318765\pi$
$620$	7.40437	+	4.52237i	0.297367	+	0.181623i
$621$		0			0
$622$	−13.3465	−	23.7906i	−0.535144	−	0.953915i
$623$	1.45250	−	2.51580i	0.0581932	−	0.100794i
$624$		0			0
$625$	−1.90220	−	3.29471i	−0.0760881	−	0.131788i
$626$	4.14472	−	6.97838i	0.165656	−	0.278912i
$627$		0			0
$628$	−30.8923	+	16.8323i	−1.23274	+	0.671682i
$629$			23.4653i			0.935621i
$630$		0			0
$631$	19.6743			0.783221			0.391610	−	0.920131i	$-0.371918\pi$
$631$	19.6743			0.783221			0.391610	+	0.920131i	$0.371918\pi$
$632$	16.1221	−	25.6779i	0.641302	−	1.02141i
$633$		0			0
$634$	15.1897	+	9.02173i	0.603260	+	0.358299i
$635$	66.6607	−	38.4866i	2.64535	−	1.52729i
$636$		0			0
$637$	2.72598	+	1.57384i	0.108007	+	0.0623580i
$638$	−3.26843	−	5.82610i	−0.129398	−	0.230657i
$639$		0			0
$640$	−37.5495	+	17.5466i	−1.48427	+	0.693589i
$641$	0.994371	−	1.72230i	0.0392753	−	0.0680268i	−0.845720	−	0.533628i	$-0.820828\pi$
$641$	0.994371	−	1.72230i	0.0392753	−	0.0680268i	0.884995	+	0.465601i	$0.154162\pi$
$642$		0			0
$643$	12.9370	−	7.46917i	0.510185	−	0.294555i	−0.222725	−	0.974881i	$-0.571495\pi$
$643$	12.9370	−	7.46917i	0.510185	−	0.294555i	0.732910	+	0.680326i	$0.238162\pi$
$644$	−4.56788	−	0.112861i	−0.180000	−	0.00444734i
$645$		0			0
$646$	−0.337061	+	27.2883i	−0.0132615	+	1.07365i
$647$	8.81283			0.346468			0.173234	−	0.984881i	$-0.444578\pi$
$647$	8.81283			0.346468			0.173234	+	0.984881i	$0.444578\pi$
$648$		0			0
$649$	−1.39937			−0.0549302
$650$	−0.0675606	+	5.46968i	−0.00264995	+	0.214538i
$651$		0			0
$652$	0.883529	−	35.7596i	0.0346017	−	1.40045i
$653$	18.1802	−	10.4964i	0.711447	−	0.410754i	−0.100150	−	0.994972i	$-0.531932\pi$
$653$	18.1802	−	10.4964i	0.711447	−	0.410754i	0.811597	+	0.584218i	$0.198599\pi$
$654$		0			0
$655$	11.6126	−	20.1136i	0.453742	−	0.785904i
$656$	−17.3619	−	33.8272i	−0.677868	−	1.32073i
$657$		0			0
$658$	1.74066	+	3.10280i	0.0678580	+	0.120960i
$659$	40.6209	+	23.4525i	1.58237	+	0.913580i	0.994513	+	0.104612i	$0.0333601\pi$
$659$	40.6209	+	23.4525i	1.58237	+	0.913580i	0.587853	+	0.808968i	$0.299973\pi$
$660$		0			0
$661$	0.736985	−	0.425498i	0.0286654	−	0.0165500i	−0.485599	−	0.874182i	$-0.661398\pi$
$661$	0.736985	−	0.425498i	0.0286654	−	0.0165500i	0.514264	+	0.857632i	$0.328065\pi$
$662$	−4.21226	−	2.50182i	−0.163714	−	0.0972359i
$663$		0			0
$664$	15.1864	+	9.53489i	0.589345	+	0.370026i
$665$	6.64293			0.257602
$666$		0			0
$667$		−	14.0053i		−	0.542287i
$668$	1.99109	+	3.65424i	0.0770375	+	0.141387i
$669$		0			0
$670$	27.1257	−	45.6710i	1.04796	−	1.76442i
$671$	4.91150	+	8.50697i	0.189606	+	0.328408i
$672$		0			0
$673$	−22.4873	+	38.9491i	−0.866820	+	1.50138i	−0.00159139	+	0.999999i	$0.500507\pi$
$673$	−22.4873	+	38.9491i	−0.866820	+	1.50138i	−0.865229	+	0.501378i	$0.832827\pi$
$674$	12.8761	+	22.9521i	0.495969	+	0.884083i
$675$		0			0
$676$	−13.3322	+	21.8286i	−0.512778	+	0.839560i
$677$	−7.29713	−	4.21300i	−0.280451	−	0.161919i	0.353176	−	0.935557i	$-0.385102\pi$
$677$	−7.29713	−	4.21300i	−0.280451	−	0.161919i	−0.633628	+	0.773638i	$0.718435\pi$
$678$		0			0
$679$	−1.14584	−	1.98466i	−0.0439733	−	0.0761641i
$680$	−37.4153	+	19.7911i	−1.43481	+	0.758955i
$681$		0			0
$682$	−0.0415210	+	3.36152i	−0.00158992	+	0.128719i
$683$		−	23.3602i		−	0.893853i	−0.894571	−	0.446926i	$-0.852519\pi$
$683$		−	23.3602i		−	0.893853i	0.894571	−	0.446926i	$-0.147481\pi$
$684$		0			0
$685$			3.54396i			0.135408i
$686$	7.51933	+	0.0928776i	0.287089	+	0.00354609i
$687$		0			0
$688$	−4.02208	−	2.59510i	−0.153340	−	0.0989374i
$689$	1.75423	+	3.03841i	0.0668308	+	0.115754i
$690$		0			0
$691$	−25.9304	−	14.9709i	−0.986439	−	0.569521i	−0.0822311	−	0.996613i	$-0.526205\pi$
$691$	−25.9304	−	14.9709i	−0.986439	−	0.569521i	−0.904208	+	0.427092i	$0.859538\pi$
$692$	−32.4638	−	19.8279i	−1.23409	−	0.753744i
$693$		0			0
$694$	0.0582141	−	0.0326580i	0.00220978	−	0.00123968i
$695$	10.9596	−	18.9826i	0.415722	−	0.720052i
$696$		0			0
$697$	−19.4150	−	33.6278i	−0.735396	−	1.27374i
$698$	−18.0956	−	10.7477i	−0.684929	−	0.406805i
$699$		0			0
$700$	3.09303	+	5.67663i	0.116905	+	0.214556i
$701$			0.718775i			0.0271478i	0.999908	+	0.0135739i	$0.00432083\pi$
$701$			0.718775i			0.0271478i	−0.999908	+	0.0135739i	$0.995679\pi$
$702$		0			0
$703$	27.1360			1.02346
$704$	−13.2752	−	9.03742i	−0.500328	−	0.340611i
$705$		0			0
$706$	−13.3664	+	22.5048i	−0.503052	+	0.846978i
$707$	−1.84735	+	1.06657i	−0.0694767	+	0.0401124i
$708$		0			0
$709$	−10.9918	−	6.34613i	−0.412807	−	0.238334i	0.279188	−	0.960236i	$-0.409935\pi$
$709$	−10.9918	−	6.34613i	−0.412807	−	0.238334i	−0.691995	+	0.721902i	$0.743268\pi$
$710$	−16.8895	+	9.47496i	−0.633851	+	0.355589i
$711$		0			0
$712$	21.3909	+	0.792974i	0.801658	+	0.0297180i
$713$	−3.52400	+	6.10375i	−0.131975	+	0.228587i
$714$		0			0
$715$	−2.92544	+	1.68900i	−0.109405	+	0.0631652i
$716$	−0.104783	+	4.24093i	−0.00391591	+	0.158491i
$717$		0			0
$718$	44.3218	+	0.547456i	1.65408	+	0.0204309i
$719$	−7.74226			−0.288738			−0.144369	−	0.989524i	$-0.546115\pi$
$719$	−7.74226			−0.288738			−0.144369	+	0.989524i	$0.546115\pi$
$720$		0			0
$721$	4.71662			0.175656
$722$	4.68916	+	0.0579198i	0.174512	+	0.00215555i
$723$		0			0
$724$	0.0821506	−	3.32493i	0.00305310	−	0.123570i
$725$	−17.1599	+	9.90730i	−0.637304	+	0.367948i
$726$		0			0
$727$	9.91355	−	17.1708i	0.367673	−	0.636828i	−0.621528	−	0.783392i	$-0.713488\pi$
$727$	9.91355	−	17.1708i	0.367673	−	0.636828i	0.989201	+	0.146563i	$0.0468212\pi$
$728$	0.0184745	−	0.498361i	0.000684712	−	0.0184705i
$729$		0			0
$730$	12.1218	−	6.80029i	0.448647	−	0.251690i
$731$	−4.23337	−	2.44414i	−0.156577	−	0.0903997i
$732$		0			0
$733$	−32.7535	+	18.9102i	−1.20978	+	0.698466i	−0.962711	−	0.270532i	$-0.912800\pi$
$733$	−32.7535	+	18.9102i	−1.20978	+	0.698466i	−0.247068	+	0.968998i	$0.579467\pi$
$734$	14.7769	−	24.8796i	0.545427	−	0.918323i
$735$		0			0
$736$	−15.0028	−	30.1415i	−0.553010	−	1.11103i
$737$	20.5821			0.758152
$738$		0			0
$739$			6.61431i			0.243311i	0.992572	+	0.121656i	$0.0388204\pi$
$739$			6.61431i			0.243311i	−0.992572	+	0.121656i	$0.961180\pi$
$740$	20.1372	+	36.9577i	0.740257	+	1.35859i
$741$		0			0
$742$	3.56494	+	2.11735i	0.130873	+	0.0777304i
$743$	3.30245	+	5.72000i	0.121155	+	0.209847i	0.920223	−	0.391394i	$-0.128007\pi$
$743$	3.30245	+	5.72000i	0.121155	+	0.209847i	−0.799068	+	0.601240i	$0.794674\pi$
$744$		0			0
$745$	−13.6161	+	23.5838i	−0.498856	+	0.864044i
$746$	29.3413	−	16.4604i	1.07426	−	0.602658i
$747$		0			0
$748$	−13.9964	−	8.54858i	−0.511759	−	0.312567i
$749$	−2.19990	−	1.27012i	−0.0803828	−	0.0464090i
$750$		0			0
$751$	12.8675	+	22.2871i	0.469540	+	0.813268i	0.999394	−	0.0348217i	$-0.0110863\pi$
$751$	12.8675	+	22.2871i	0.469540	+	0.813268i	−0.529853	+	0.848089i	$0.677753\pi$
$752$	−14.2127	+	22.0279i	−0.518284	+	0.803274i
$753$		0			0
$754$	1.52846	+	0.0188793i	0.0556631	+	0.000687542i
$755$			3.61118i			0.131424i
$756$		0			0
$757$		−	48.0424i		−	1.74613i	−0.487602	−	0.873066i	$-0.662128\pi$
$757$		−	48.0424i		−	1.74613i	0.487602	−	0.873066i	$-0.337872\pi$
$758$	−0.420930	+	34.0783i	−0.0152889	+	1.23778i
$759$		0			0
$760$	22.8871	+	43.2683i	0.830203	+	1.56951i
$761$	1.20688	+	2.09038i	0.0437493	+	0.0757761i	0.887071	−	0.461633i	$-0.152736\pi$
$761$	1.20688	+	2.09038i	0.0437493	+	0.0757761i	−0.843322	+	0.537409i	$0.819403\pi$
$762$		0			0
$763$	−2.33218	−	1.34648i	−0.0844305	−	0.0487459i
$764$	18.1340	−	29.6904i	0.656065	−	1.07416i
$765$		0			0
$766$	12.9966	+	23.1669i	0.469586	+	0.837056i
$767$	0.160101	−	0.277304i	0.00578093	−	0.0100129i
$768$		0			0
$769$	16.8464	+	29.1788i	0.607496	+	1.05221i	0.991652	+	0.128945i	$0.0411592\pi$
$769$	16.8464	+	29.1788i	0.607496	+	1.05221i	−0.384156	+	0.923268i	$0.625507\pi$
$770$	−2.03862	+	3.43239i	−0.0734669	+	0.123695i
$771$		0			0
$772$	−2.71207	−	4.97746i	−0.0976094	−	0.179143i
$773$		−	18.8545i		−	0.678149i	−0.940759	−	0.339075i	$-0.889886\pi$
$773$		−	18.8545i		−	0.678149i	0.940759	−	0.339075i	$-0.110114\pi$
$774$		0			0
$775$	9.97148			0.358186
$776$	8.97912	−	14.3012i	0.322332	−	0.513382i
$777$		0			0
$778$	−21.1258	−	12.5474i	−0.757398	−	0.449847i
$779$	−38.8884	+	22.4522i	−1.39332	+	0.804434i
$780$		0			0
$781$	−6.49833	−	3.75181i	−0.232529	−	0.134250i
$782$	−16.8229	−	29.9874i	−0.601585	−	1.07235i
$783$		0			0
$784$	12.5163	+	24.3862i	0.447010	+	0.870935i
$785$	−32.2202	+	55.8070i	−1.14999	+	1.99184i
$786$		0			0
$787$	14.8124	−	8.55193i	0.528004	−	0.304843i	−0.212199	−	0.977226i	$-0.568063\pi$
$787$	14.8124	−	8.55193i	0.528004	−	0.304843i	0.740203	+	0.672383i	$0.234729\pi$
$788$	−0.622392	+	25.1904i	−0.0221718	+	0.897372i
$789$		0			0
$790$	0.685928	−	55.5324i	0.0244042	−	1.97576i
$791$	−3.14313			−0.111757
$792$		0			0
$793$	−2.24769			−0.0798178
$794$	0.458332	−	37.1063i	0.0162656	−	1.31685i
$795$		0			0
$796$	34.5361	+	0.853301i	1.22410	+	0.0302444i
$797$	3.11800	−	1.80018i	0.110445	−	0.0637656i	−0.443760	−	0.896146i	$-0.646356\pi$
$797$	3.11800	−	1.80018i	0.110445	−	0.0637656i	0.554205	+	0.832380i	$0.313022\pi$
$798$		0			0
$799$	−13.3859	+	23.1851i	−0.473559	+	0.820228i
$800$	−26.3179	+	39.7042i	−0.930477	+	1.40375i
$801$		0			0
$802$	14.9725	+	26.6890i	0.528697	+	0.942422i
$803$	4.66393	+	2.69272i	0.164586	+	0.0950240i
$804$		0			0
$805$	−7.24829	+	4.18480i	−0.255469	+	0.147495i
$806$	−0.661378	−	0.392817i	−0.0232960	−	0.0138364i
$807$		0			0
$808$	−13.3118	−	8.35790i	−0.468306	−	0.294030i
$809$	−13.5918			−0.477864			−0.238932	−	0.971036i	$-0.576797\pi$
$809$	−13.5918			−0.477864			−0.238932	+	0.971036i	$0.576797\pi$
$810$		0			0
$811$			10.0627i			0.353349i	0.984269	+	0.176674i	$0.0565339\pi$
$811$			10.0627i			0.353349i	−0.984269	+	0.176674i	$0.943466\pi$
$812$	1.58629	−	0.864321i	0.0556678	−	0.0303317i
$813$		0			0
$814$	−8.32768	+	14.0211i	−0.291885	+	0.491441i
$815$	−32.7606	−	56.7430i	−1.14755	−	1.98762i
$816$		0			0
$817$	−2.82649	+	4.89562i	−0.0988862	+	0.171276i
$818$	8.31090	+	14.8145i	0.290584	+	0.517977i
$819$		0			0
$820$	−59.4369	−	36.3023i	−2.07563	−	1.26773i
$821$	−33.4098	−	19.2891i	−1.16601	−	0.673196i	−0.213273	−	0.976993i	$-0.568412\pi$
$821$	−33.4098	−	19.2891i	−1.16601	−	0.673196i	−0.952737	+	0.303797i	$0.901746\pi$
$822$		0			0
$823$	−16.1120	−	27.9068i	−0.561628	−	0.972768i	−0.997355	−	0.0726892i	$-0.976842\pi$
$823$	−16.1120	−	27.9068i	−0.561628	−	0.972768i	0.435727	−	0.900079i	$-0.356491\pi$
$824$	16.2504	+	30.7214i	0.566108	+	1.07023i
$825$		0			0
$826$	0.00467381	−	0.378389i	0.000162623	−	0.0131658i
$827$			27.7190i			0.963886i	0.876203	+	0.481943i	$0.160069\pi$
$827$			27.7190i			0.963886i	−0.876203	+	0.481943i	$0.839931\pi$
$828$		0			0
$829$			10.3137i			0.358208i	0.983830	+	0.179104i	$0.0573199\pi$
$829$			10.3137i			0.358208i	−0.983830	+	0.179104i	$0.942680\pi$
$830$	32.8429	+	0.405671i	1.13999	+	0.0140810i
$831$		0			0
$832$	3.30969	−	1.59669i	0.114743	−	0.0553552i
$833$	13.9964	+	24.2425i	0.484946	+	0.839951i
$834$		0			0
$835$	6.60139	+	3.81131i	0.228451	+	0.131896i
$836$	−9.88587	+	16.1859i	−0.341910	+	0.559801i
$837$		0			0
$838$	1.96670	−	1.10331i	0.0679385	−	0.0381133i
$839$	19.1961	−	33.2487i	0.662724	−	1.14787i	−0.317173	−	0.948368i	$-0.602733\pi$
$839$	19.1961	−	33.2487i	0.662724	−	1.14787i	0.979897	−	0.199504i	$-0.0639332\pi$
$840$		0			0
$841$	−11.7315	−	20.3195i	−0.404534	−	0.700673i
$842$	−21.9886	−	13.0599i	−0.757777	−	0.450072i
$843$		0			0
$844$	−30.8631	+	16.8164i	−1.06235	+	0.578844i
$845$			46.8516i			1.61174i
$846$		0			0
$847$	2.67553			0.0919325
$848$	−1.50882	+	30.5150i	−0.0518130	+	1.04789i
$849$		0			0
$850$	−24.8416	+	41.8252i	−0.852059	+	1.43459i
$851$	−29.6089	+	17.0947i	−1.01498	+	0.585999i
$852$		0			0
$853$	−24.4212	−	14.0996i	−0.836166	−	0.482761i	0.0197931	−	0.999804i	$-0.493699\pi$
$853$	−24.4212	−	14.0996i	−0.836166	−	0.482761i	−0.855959	+	0.517043i	$0.827033\pi$
$854$	−2.31668	+	1.29965i	−0.0792752	+	0.0444732i
$855$		0			0
$856$	0.693403	−	18.7049i	0.0237000	−	0.639321i
$857$	−15.7011	+	27.1951i	−0.536339	+	0.928966i	0.462759	+	0.886484i	$0.346860\pi$
$857$	−15.7011	+	27.1951i	−0.536339	+	0.928966i	−0.999097	+	0.0424814i	$0.986474\pi$
$858$		0			0
$859$	−41.6368	+	24.0390i	−1.42063	+	0.820201i	−0.996353	−	0.0853309i	$-0.972805\pi$
$859$	−41.6368	+	24.0390i	−1.42063	+	0.820201i	−0.424278	+	0.905532i	$0.639472\pi$
$860$	−8.76503	−	0.216562i	−0.298885	−	0.00738469i
$861$		0			0
$862$	−49.1332	−	0.606887i	−1.67348	−	0.0206706i
$863$	−37.6968			−1.28321			−0.641607	−	0.767034i	$-0.721732\pi$
$863$	−37.6968			−1.28321			−0.641607	+	0.767034i	$0.721732\pi$
$864$		0			0
$865$	−69.6783			−2.36913
$866$	−17.9870	−	0.222173i	−0.611223	−	0.00754974i
$867$		0			0
$868$	−0.908812	−	0.0224545i	−0.0308471	−	0.000762154i
$869$	18.6358	−	10.7594i	0.632177	−	0.364988i
$870$		0			0
$871$	−2.35479	+	4.07861i	−0.0797890	+	0.138199i
$872$	0.735095	−	19.8296i	0.0248935	−	0.671514i
$873$		0			0
$874$	−34.6785	+	19.4546i	−1.17302	+	0.658060i
$875$	4.16576	+	2.40510i	0.140828	+	0.0813072i
$876$		0			0
$877$	21.6823	−	12.5183i	0.732158	−	0.422711i	−0.0870533	−	0.996204i	$-0.527745\pi$
$877$	21.6823	−	12.5183i	0.732158	−	0.422711i	0.819211	+	0.573492i	$0.194412\pi$
$878$	10.7735	−	18.1391i	0.363587	−	0.612164i
$879$		0			0
$880$	−29.3804	−	1.45272i	−0.990413	−	0.0489711i
$881$	21.0382			0.708795			0.354398	−	0.935095i	$-0.384686\pi$
$881$	21.0382			0.708795			0.354398	+	0.935095i	$0.384686\pi$
$882$		0			0
$883$			55.5904i			1.87077i	0.353636	+	0.935383i	$0.384945\pi$
$883$			55.5904i			1.87077i	−0.353636	+	0.935383i	$0.615055\pi$
$884$	3.29533	−	1.79553i	0.110834	−	0.0603902i
$885$		0			0
$886$	4.89169	+	2.90536i	0.164339	+	0.0976074i
$887$	−0.695385	−	1.20444i	−0.0233487	−	0.0404412i	0.854115	−	0.520084i	$-0.174099\pi$
$887$	−0.695385	−	1.20444i	−0.0233487	−	0.0404412i	−0.877464	+	0.479643i	$0.840766\pi$
$888$		0			0
$889$	−4.03261	+	6.98468i	−0.135249	+	0.234259i
$890$	34.1954	−	19.1836i	1.14623	−	0.643034i
$891$		0			0
$892$	25.6735	−	42.0346i	0.859612	−	1.40742i
$893$	26.8120	+	15.4799i	0.897229	+	0.518015i
$894$		0			0
$895$	3.88527	+	6.72948i	0.129870	+	0.224942i
$896$	2.48805	−	3.55942i	0.0831199	−	0.118912i
$897$		0			0
$898$	15.4390	+	0.190701i	0.515207	+	0.00636376i
$899$		−	2.78645i		−	0.0929332i
$900$		0			0
$901$			31.2011i			1.03946i
$902$	0.333300	−	26.9838i	0.0110977	−	0.898463i
$903$		0			0
$904$	−10.8291	−	20.4726i	−0.360172	−	0.680908i
$905$	−3.04608	−	5.27597i	−0.101255	−	0.175379i
$906$		0			0
$907$	37.3197	+	21.5465i	1.23918	+	0.715440i	0.968926	−	0.247349i	$-0.0795595\pi$
$907$	37.3197	+	21.5465i	1.23918	+	0.715440i	0.270252	+	0.962789i	$0.412893\pi$
$908$	33.4887	+	20.4539i	1.11136	+	0.678786i
$909$		0			0
$910$	−0.446934	−	0.796678i	−0.0148157	−	0.0264096i
$911$	3.96463	−	6.86694i	0.131354	−	0.227512i	−0.792845	−	0.609424i	$-0.791401\pi$
$911$	3.96463	−	6.86694i	0.131354	−	0.227512i	0.924199	+	0.381912i	$0.124734\pi$
$912$		0			0
$913$	6.36331	+	11.0216i	0.210595	+	0.364761i
$914$	1.17745	−	1.98244i	0.0389465	−	0.0655734i
$915$		0			0
$916$	43.2818	−	23.5830i	1.43007	−	0.779204i
$917$			2.43353i			0.0803622i
$918$		0			0
$919$	1.66862			0.0550426			0.0275213	−	0.999621i	$-0.491239\pi$
$919$	1.66862			0.0550426			0.0275213	+	0.999621i	$0.491239\pi$
$920$	−52.2302	−	32.7932i	−1.72198	−	1.08116i
$921$		0			0
$922$	−14.2946	−	8.49010i	−0.470767	−	0.279606i
$923$	1.48694	−	0.858486i	0.0489433	−	0.0282574i
$924$		0			0
$925$	41.8905	+	24.1855i	1.37735	+	0.795215i
$926$	14.7342	+	26.2643i	0.484197	+	0.863099i
$927$		0			0
$928$	11.0950	+	7.35431i	0.364211	+	0.241417i
$929$	23.3838	−	40.5020i	0.767199	−	1.32883i	−0.171878	−	0.985118i	$-0.554983\pi$
$929$	23.3838	−	40.5020i	0.767199	−	1.32883i	0.939076	−	0.343709i	$-0.111683\pi$
$930$		0			0
$931$	28.0348	−	16.1859i	0.918804	−	0.530472i
$932$	41.8317	+	1.03355i	1.37024	+	0.0338552i
$933$		0			0
$934$	0.330524	−	26.7591i	0.0108151	−	0.875583i
$935$	−30.0410			−0.982447
$936$		0			0
$937$	−9.30185			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$937$	−9.30185			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$938$	−0.0687428	+	5.56538i	−0.00224453	+	0.181716i
$939$		0			0
$940$	−1.18605	+	48.0037i	−0.0386847	+	1.56571i
$941$	−5.42009	+	3.12929i	−0.176690	+	0.102012i	−0.585736	−	0.810502i	$-0.699195\pi$
$941$	−5.42009	+	3.12929i	−0.176690	+	0.102012i	0.409047	+	0.912513i	$0.365861\pi$
$942$		0			0
$943$	28.2881	−	48.9965i	0.921188	−	1.59555i
$944$	2.48072	−	1.27324i	0.0807404	−	0.0414403i
$945$		0			0
$946$	−1.66215	−	2.96284i	−0.0540410	−	0.0963302i
$947$	−38.4243	−	22.1843i	−1.24862	−	0.720893i	−0.277789	−	0.960642i	$-0.589601\pi$
$947$	−38.4243	−	22.1843i	−1.24862	−	0.720893i	−0.970835	+	0.239749i	$0.922935\pi$
$948$		0			0
$949$	−1.06720	+	0.616146i	−0.0346426	+	0.0200009i
$950$	48.3681	+	28.7277i	1.56927	+	0.932048i
$951$		0			0
$952$	2.35828	−	3.75606i	0.0764322	−	0.121735i
$953$	−6.11599			−0.198116			−0.0990582	−	0.995082i	$-0.531583\pi$
$953$	−6.11599			−0.198116			−0.0990582	+	0.995082i	$0.531583\pi$
$954$		0			0
$955$		−	63.7257i		−	2.06211i
$956$	9.84825	+	18.0745i	0.318515	+	0.584571i
$957$		0			0
$958$	21.6306	−	36.4190i	0.698854	−	1.17665i
$959$	−0.185668	−	0.321586i	−0.00599552	−	0.0103845i
$960$		0			0
$961$	14.7989	−	25.6324i	0.477383	−	0.826852i
$962$	−1.82571	−	3.25439i	−0.0588631	−	0.104926i
$963$		0			0
$964$	21.3456	−	34.9486i	0.687495	−	1.12562i
$965$	−8.99178	−	5.19141i	−0.289456	−	0.167117i
$966$		0			0
$967$	16.9985	+	29.4423i	0.546635	+	0.946799i	0.998502	+	0.0547141i	$0.0174248\pi$
$967$	16.9985	+	29.4423i	0.546635	+	0.946799i	−0.451867	+	0.892085i	$0.649242\pi$
$968$	9.21812	+	17.4269i	0.296282	+	0.560123i
$969$		0			0
$970$	0.382025	−	30.9285i	0.0122661	−	0.993055i
$971$			42.4798i			1.36324i	0.731706	+	0.681621i	$0.238725\pi$
$971$			42.4798i			1.36324i	−0.731706	+	0.681621i	$0.761275\pi$
$972$		0			0
$973$			2.29669i			0.0736286i
$974$	24.5163	+	0.302822i	0.785554	+	0.00970304i
$975$		0			0
$976$	−16.4470	−	10.6118i	−0.526454	−	0.339676i
$977$	−7.66569	−	13.2774i	−0.245247	−	0.424781i	0.716954	−	0.697121i	$-0.245536\pi$
$977$	−7.66569	−	13.2774i	−0.245247	−	0.424781i	−0.962201	+	0.272340i	$0.912202\pi$
$978$		0			0
$979$	13.1569	+	7.59614i	0.420496	+	0.242774i
$980$	42.8484	+	26.1705i	1.36874	+	0.835987i
$981$		0			0
$982$	44.3214	−	24.8642i	1.41435	−	0.793448i
$983$	14.8653	−	25.7474i	0.474129	−	0.821216i	−0.525432	−	0.850836i	$-0.676096\pi$
$983$	14.8653	−	25.7474i	0.474129	−	0.821216i	0.999561	+	0.0296198i	$0.00942964\pi$
$984$		0			0
$985$	23.0779	+	39.9720i	0.735322	+	1.27361i
$986$	11.6877	+	6.94178i	0.372213	+	0.221071i
$987$		0			0
$988$	−2.07641	−	3.81084i	−0.0660595	−	0.121239i
$989$		−	7.12233i		−	0.226477i
$990$		0			0
$991$	−49.5495			−1.57399			−0.786996	−	0.616958i	$-0.788365\pi$
$991$	−49.5495			−1.57399			−0.786996	+	0.616958i	$0.788365\pi$
$992$	−2.98491	−	5.99686i	−0.0947710	−	0.190400i
$993$		0			0
$994$	1.03619	−	1.74461i	0.0328660	−	0.0553357i
$995$	54.8017	−	31.6398i	1.73733	−	1.00305i
$996$		0			0
$997$	−34.4541	−	19.8921i	−1.09117	−	0.629988i	−0.157284	−	0.987553i	$-0.550274\pi$
$997$	−34.4541	−	19.8921i	−1.09117	−	0.629988i	−0.933888	+	0.357565i	$0.883607\pi$
$998$	−14.9477	+	8.38562i	−0.473161	+	0.265442i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.n.b.181.1		16
3.2	odd	2		72.2.n.b.61.8	yes	16
4.3	odd	2		864.2.r.b.721.8		16
8.3	odd	2		864.2.r.b.721.1		16
8.5	even	2	inner	216.2.n.b.181.6		16
9.2	odd	6		648.2.d.j.325.3		8
9.4	even	3	inner	216.2.n.b.37.6		16
9.5	odd	6		72.2.n.b.13.3	✓	16
9.7	even	3		648.2.d.k.325.6		8
12.11	even	2		288.2.r.b.241.5		16
24.5	odd	2		72.2.n.b.61.3	yes	16
24.11	even	2		288.2.r.b.241.4		16
36.7	odd	6		2592.2.d.k.1297.8		8
36.11	even	6		2592.2.d.j.1297.1		8
36.23	even	6		288.2.r.b.49.4		16
36.31	odd	6		864.2.r.b.145.1		16
72.5	odd	6		72.2.n.b.13.8	yes	16
72.11	even	6		2592.2.d.j.1297.8		8
72.13	even	6	inner	216.2.n.b.37.1		16
72.29	odd	6		648.2.d.j.325.4		8
72.43	odd	6		2592.2.d.k.1297.1		8
72.59	even	6		288.2.r.b.49.5		16
72.61	even	6		648.2.d.k.325.5		8
72.67	odd	6		864.2.r.b.145.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.3	✓	16	9.5	odd	6
72.2.n.b.13.8	yes	16	72.5	odd	6
72.2.n.b.61.3	yes	16	24.5	odd	2
72.2.n.b.61.8	yes	16	3.2	odd	2
216.2.n.b.37.1		16	72.13	even	6	inner
216.2.n.b.37.6		16	9.4	even	3	inner
216.2.n.b.181.1		16	1.1	even	1	trivial
216.2.n.b.181.6		16	8.5	even	2	inner
288.2.r.b.49.4		16	36.23	even	6
288.2.r.b.49.5		16	72.59	even	6
288.2.r.b.241.4		16	24.11	even	2
288.2.r.b.241.5		16	12.11	even	2
648.2.d.j.325.3		8	9.2	odd	6
648.2.d.j.325.4		8	72.29	odd	6
648.2.d.k.325.5		8	72.61	even	6
648.2.d.k.325.6		8	9.7	even	3
864.2.r.b.145.1		16	36.31	odd	6
864.2.r.b.145.8		16	72.67	odd	6
864.2.r.b.721.1		16	8.3	odd	2
864.2.r.b.721.8		16	4.3	odd	2
2592.2.d.j.1297.1		8	36.11	even	6
2592.2.d.j.1297.8		8	72.11	even	6
2592.2.d.k.1297.1		8	72.43	odd	6
2592.2.d.k.1297.8		8	36.7	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41411 - 0.0174668i) q^{2} +(1.99939 + 0.0493999i) q^{4} +(3.17262 - 1.83171i) q^{5} +(-0.191926 + 0.332426i) q^{7} +(-2.82649 - 0.104780i) q^{8} +O(q^{10})\)	\(q+(-1.41411 - 0.0174668i) q^{2} +(1.99939 + 0.0493999i) q^{4} +(3.17262 - 1.83171i) q^{5} +(-0.191926 + 0.332426i) q^{7} +(-2.82649 - 0.104780i) q^{8} +(-4.51841 + 2.53482i) q^{10} +(-1.73849 - 1.00372i) q^{11} +(0.397799 - 0.229669i) q^{13} +(0.277210 - 0.466733i) q^{14} +(3.99512 + 0.197539i) q^{16} +4.08495 q^{17} -4.72398i q^{19} +(6.43379 - 3.50558i) q^{20} +(2.44087 + 1.44973i) q^{22} +(2.97594 + 5.15447i) q^{23} +(4.21034 - 7.29252i) q^{25} +(-0.566541 + 0.317828i) q^{26} +(-0.400157 + 0.655168i) q^{28} +(-2.03783 - 1.17654i) q^{29} +(0.592083 + 1.02552i) q^{31} +(-5.64607 - 0.349123i) q^{32} +(-5.77656 - 0.0713512i) q^{34} +1.40621i q^{35} +5.74432i q^{37} +(-0.0825129 + 6.68021i) q^{38} +(-9.15929 + 4.84488i) q^{40} +(-4.75281 - 8.23212i) q^{41} +(-1.03633 - 0.598327i) q^{43} +(-3.42633 - 2.09270i) q^{44} +(-4.11825 - 7.34095i) q^{46} +(-3.27688 + 5.67572i) q^{47} +(3.42633 + 5.93458i) q^{49} +(-6.08124 + 10.2389i) q^{50} +(0.806700 - 0.439547i) q^{52} +7.63807i q^{53} -7.35407 q^{55} +(0.577308 - 0.919487i) q^{56} +(2.86116 + 1.69935i) q^{58} +(0.603703 - 0.348548i) q^{59} +(-4.23774 - 2.44666i) q^{61} +(-0.819356 - 1.46053i) q^{62} +(7.97804 + 0.592316i) q^{64} +(0.841376 - 1.45731i) q^{65} +(-8.87932 + 5.12648i) q^{67} +(8.16741 + 0.201796i) q^{68} +(0.0245621 - 1.98853i) q^{70} +3.73792 q^{71} -2.68275 q^{73} +(0.100335 - 8.12307i) q^{74} +(0.233364 - 9.44508i) q^{76} +(0.667322 - 0.385279i) q^{77} +(-5.35979 + 9.28342i) q^{79} +(13.0368 - 6.69119i) q^{80} +(6.57719 + 11.7241i) q^{82} +(-5.49039 - 3.16988i) q^{83} +(12.9600 - 7.48246i) q^{85} +(1.45503 + 0.864199i) q^{86} +(4.80864 + 3.01915i) q^{88} -7.56802 q^{89} +0.176318i q^{91} +(5.69542 + 10.4528i) q^{92} +(4.73299 - 7.96883i) q^{94} +(-8.65297 - 14.9874i) q^{95} +(-2.98511 + 5.17036i) q^{97} +(-4.74153 - 8.45196i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

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