LMFDB - Embedded newform 441.2.u.d.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	441.64
Dual form			441.2.u.d.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.132418 - 0.580160i) q^{2} +(1.48289 + 0.714121i) q^{4} +(-0.595901 + 0.747236i) q^{5} +(-0.416022 - 2.61284i) q^{7} +(1.35272 - 1.69625i) q^{8} +O(q^{10})$	\(q+(0.132418 - 0.580160i) q^{2} +(1.48289 + 0.714121i) q^{4} +(-0.595901 + 0.747236i) q^{5} +(-0.416022 - 2.61284i) q^{7} +(1.35272 - 1.69625i) q^{8} +(0.354609 + 0.444665i) q^{10} +(0.770373 - 3.37522i) q^{11} +(0.0986100 - 0.432039i) q^{13} +(-1.57095 - 0.104627i) q^{14} +(1.24740 + 1.56420i) q^{16} +(1.92202 - 0.925595i) q^{17} +3.99082 q^{19} +(-1.41727 + 0.682522i) q^{20} +(-1.85616 - 0.893879i) q^{22} +(5.89801 + 2.84033i) q^{23} +(0.909341 + 3.98408i) q^{25} +(-0.237594 - 0.114419i) q^{26} +(1.24897 - 4.17163i) q^{28} +(2.93677 - 1.41427i) q^{29} -8.81506 q^{31} +(4.98213 - 2.39927i) q^{32} +(-0.282484 - 1.23764i) q^{34} +(2.20032 + 1.24613i) q^{35} +(0.164550 - 0.0792429i) q^{37} +(0.528456 - 2.31531i) q^{38} +(0.461417 + 2.02160i) q^{40} +(-6.84489 + 8.58321i) q^{41} +(-5.25323 - 6.58735i) q^{43} +(3.55269 - 4.45494i) q^{44} +(2.42885 - 3.04568i) q^{46} +(-0.430650 + 1.88680i) q^{47} +(-6.65385 + 2.17400i) q^{49} +2.43182 q^{50} +(0.454755 - 0.570245i) q^{52} +(-6.76016 - 3.25552i) q^{53} +(2.06302 + 2.58695i) q^{55} +(-4.99480 - 2.82875i) q^{56} +(-0.431624 - 1.89107i) q^{58} +(-5.19927 - 6.51968i) q^{59} +(1.37935 - 0.664259i) q^{61} +(-1.16727 + 5.11415i) q^{62} +(0.158151 + 0.692903i) q^{64} +(0.264073 + 0.331137i) q^{65} +6.48189 q^{67} +3.51112 q^{68} +(1.01431 - 1.11153i) q^{70} +(-3.77982 - 1.82027i) q^{71} +(2.13993 + 9.37566i) q^{73} +(-0.0241843 - 0.105958i) q^{74} +(5.91794 + 2.84993i) q^{76} +(-9.13941 - 0.608691i) q^{77} -2.59260 q^{79} -1.91215 q^{80} +(4.07325 + 5.10770i) q^{82} +(1.73474 + 7.60038i) q^{83} +(-0.453694 + 1.98776i) q^{85} +(-4.51734 + 2.17543i) q^{86} +(-4.68314 - 5.87247i) q^{88} +(-1.43356 - 6.28082i) q^{89} +(-1.16987 - 0.0779142i) q^{91} +(6.71774 + 8.42377i) q^{92} +(1.03762 + 0.499692i) q^{94} +(-2.37814 + 2.98209i) q^{95} -0.578609 q^{97} +(0.380179 + 4.14817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	0.132418	−	0.580160i	0.0936335	−	0.410235i	−0.906289	−	0.422658i	$-0.861097\pi$
$2$	0.132418	−	0.580160i	0.0936335	−	0.410235i	0.999923	+	0.0124227i	$0.00395438\pi$
$3$		0			0
$3$		0			0
$4$	1.48289	+	0.714121i	0.741443	+	0.357060i
$5$	−0.595901	+	0.747236i	−0.266495	+	0.334174i	−0.897016	−	0.441998i	$-0.854270\pi$
$5$	−0.595901	+	0.747236i	−0.266495	+	0.334174i	0.630521	+	0.776172i	$0.282841\pi$
$6$		0			0
$7$	−0.416022	−	2.61284i	−0.157242	−	0.987560i
$7$	−0.416022	−	2.61284i	−0.157242	−	0.987560i
$8$	1.35272	−	1.69625i	0.478258	−	0.599716i
$9$		0			0
$10$	0.354609	+	0.444665i	0.112137	+	0.140616i
$11$	0.770373	−	3.37522i	0.232276	−	1.01767i	−0.715470	−	0.698643i	$-0.753787\pi$
$11$	0.770373	−	3.37522i	0.232276	−	1.01767i	0.947746	−	0.319025i	$-0.103355\pi$
$12$		0			0
$13$	0.0986100	−	0.432039i	0.0273495	−	0.119826i	−0.959410	−	0.282013i	$-0.908998\pi$
$13$	0.0986100	−	0.432039i	0.0273495	−	0.119826i	0.986760	+	0.162187i	$0.0518549\pi$
$14$	−1.57095	−	0.104627i	−0.419855	−	0.0279626i
$15$		0			0
$16$	1.24740	+	1.56420i	0.311851	+	0.391049i
$17$	1.92202	−	0.925595i	0.466158	−	0.224490i	−0.186035	−	0.982543i	$-0.559564\pi$
$17$	1.92202	−	0.925595i	0.466158	−	0.224490i	0.652192	+	0.758053i	$0.273849\pi$
$18$		0			0
$19$	3.99082			0.915557			0.457779	−	0.889066i	$-0.348645\pi$
$19$	3.99082			0.915557			0.457779	+	0.889066i	$0.348645\pi$
$20$	−1.41727	+	0.682522i	−0.316911	+	0.152616i
$21$		0			0
$22$	−1.85616	−	0.893879i	−0.395734	−	0.190576i
$23$	5.89801	+	2.84033i	1.22982	+	0.592250i	0.932030	−	0.362382i	$-0.118036\pi$
$23$	5.89801	+	2.84033i	1.22982	+	0.592250i	0.297789	+	0.954632i	$0.403751\pi$
$24$		0			0
$25$	0.909341	+	3.98408i	0.181868	+	0.796816i
$26$	−0.237594	−	0.114419i	−0.0465960	−	0.0224394i
$27$		0			0
$28$	1.24897	−	4.17163i	0.236033	−	0.788365i
$29$	2.93677	−	1.41427i	0.545344	−	0.262624i	−0.140864	−	0.990029i	$-0.544988\pi$
$29$	2.93677	−	1.41427i	0.545344	−	0.262624i	0.686208	+	0.727405i	$0.259274\pi$
$30$		0			0
$31$	−8.81506			−1.58323			−0.791616	−	0.611019i	$-0.790760\pi$
$31$	−8.81506			−1.58323			−0.791616	+	0.611019i	$0.790760\pi$
$32$	4.98213	−	2.39927i	0.880724	−	0.424134i
$33$		0			0
$34$	−0.282484	−	1.23764i	−0.0484456	−	0.212254i
$35$	2.20032	+	1.24613i	0.371921	+	0.210634i
$36$		0			0
$37$	0.164550	−	0.0792429i	0.0270518	−	0.0130275i	−0.420309	−	0.907381i	$-0.638078\pi$
$37$	0.164550	−	0.0792429i	0.0270518	−	0.0130275i	0.447361	+	0.894354i	$0.352364\pi$
$38$	0.528456	−	2.31531i	0.0857268	−	0.375594i
$39$		0			0
$40$	0.461417	+	2.02160i	0.0729564	+	0.319643i
$41$	−6.84489	+	8.58321i	−1.06899	+	1.34047i	−0.131949	+	0.991256i	$0.542124\pi$
$41$	−6.84489	+	8.58321i	−1.06899	+	1.34047i	−0.937042	+	0.349216i	$0.886448\pi$
$42$		0			0
$43$	−5.25323	−	6.58735i	−0.801111	−	1.00456i	−0.999700	−	0.0244784i	$-0.992208\pi$
$43$	−5.25323	−	6.58735i	−0.801111	−	1.00456i	0.198590	−	0.980083i	$-0.436364\pi$
$44$	3.55269	−	4.45494i	0.535589	−	0.671607i
$45$		0			0
$46$	2.42885	−	3.04568i	0.358114	−	0.449061i
$47$	−0.430650	+	1.88680i	−0.0628168	+	0.275218i	−0.996576	−	0.0826841i	$-0.973651\pi$
$47$	−0.430650	+	1.88680i	−0.0628168	+	0.275218i	0.933759	+	0.357902i	$0.116508\pi$
$48$		0			0
$49$	−6.65385	+	2.17400i	−0.950550	+	0.310571i
$50$	2.43182			0.343911
$51$		0			0
$52$	0.454755	−	0.570245i	0.0630632	−	0.0790787i
$53$	−6.76016	−	3.25552i	−0.928579	−	0.447180i	−0.0924528	−	0.995717i	$-0.529471\pi$
$53$	−6.76016	−	3.25552i	−0.928579	−	0.447180i	−0.836126	+	0.548537i	$0.815185\pi$
$54$		0			0
$55$	2.06302	+	2.58695i	0.278178	+	0.348824i
$56$	−4.99480	−	2.82875i	−0.667458	−	0.378008i
$57$		0			0
$58$	−0.431624	−	1.89107i	−0.0566751	−	0.248310i
$59$	−5.19927	−	6.51968i	−0.676887	−	0.848790i	0.318176	−	0.948032i	$-0.396930\pi$
$59$	−5.19927	−	6.51968i	−0.676887	−	0.848790i	−0.995063	+	0.0992420i	$0.968358\pi$
$60$		0			0
$61$	1.37935	−	0.664259i	0.176608	−	0.0850497i	−0.343491	−	0.939156i	$-0.611610\pi$
$61$	1.37935	−	0.664259i	0.176608	−	0.0850497i	0.520099	+	0.854106i	$0.325895\pi$
$62$	−1.16727	+	5.11415i	−0.148244	+	0.649497i
$63$		0			0
$64$	0.158151	+	0.692903i	0.0197688	+	0.0866129i
$65$	0.264073	+	0.331137i	0.0327542	+	0.0410725i
$66$		0			0
$67$	6.48189			0.791889			0.395945	−	0.918274i	$-0.370417\pi$
$67$	6.48189			0.791889			0.395945	+	0.918274i	$0.370417\pi$
$68$	3.51112			0.425786
$69$		0			0
$70$	1.01431	−	1.11153i	0.121234	−	0.132853i
$71$	−3.77982	−	1.82027i	−0.448582	−	0.216026i	0.195933	−	0.980617i	$-0.437226\pi$
$71$	−3.77982	−	1.82027i	−0.448582	−	0.216026i	−0.644515	+	0.764592i	$0.722941\pi$
$72$		0			0
$73$	2.13993	+	9.37566i	0.250460	+	1.09734i	0.931113	+	0.364732i	$0.118839\pi$
$73$	2.13993	+	9.37566i	0.250460	+	1.09734i	−0.680652	+	0.732607i	$0.738304\pi$
$74$	−0.0241843	−	0.105958i	−0.00281137	−	0.0123174i
$75$		0			0
$76$	5.91794	+	2.84993i	0.678834	+	0.326909i
$77$	−9.13941	−	0.608691i	−1.04153	−	0.0693668i
$78$		0			0
$79$	−2.59260			−0.291690			−0.145845	−	0.989307i	$-0.546590\pi$
$79$	−2.59260			−0.291690			−0.145845	+	0.989307i	$0.546590\pi$
$80$	−1.91215			−0.213785
$81$		0			0
$82$	4.07325	+	5.10770i	0.449816	+	0.564051i
$83$	1.73474	+	7.60038i	0.190412	+	0.834250i	0.976393	+	0.216000i	$0.0693011\pi$
$83$	1.73474	+	7.60038i	0.190412	+	0.834250i	−0.785981	+	0.618250i	$0.787842\pi$
$84$		0			0
$85$	−0.453694	+	1.98776i	−0.0492101	+	0.215603i
$86$	−4.51734	+	2.17543i	−0.487117	+	0.234583i
$87$		0			0
$88$	−4.68314	−	5.87247i	−0.499224	−	0.626008i
$89$	−1.43356	−	6.28082i	−0.151957	−	0.665766i	−0.992315	−	0.123735i	$-0.960513\pi$
$89$	−1.43356	−	6.28082i	−0.151957	−	0.665766i	0.840359	−	0.542031i	$-0.182344\pi$
$90$		0			0
$91$	−1.16987	−	0.0779142i	−0.122636	−	0.00816763i
$92$	6.71774	+	8.42377i	0.700372	+	0.878239i
$93$		0			0
$94$	1.03762	+	0.499692i	0.107022	+	0.0515393i
$95$	−2.37814	+	2.98209i	−0.243992	+	0.305956i
$96$		0			0
$97$	−0.578609			−0.0587488			−0.0293744	−	0.999568i	$-0.509352\pi$
$97$	−0.578609			−0.0587488			−0.0293744	+	0.999568i	$0.509352\pi$
$98$	0.380179	+	4.14817i	0.0384039	+	0.419029i
$99$		0			0
$100$	−1.49667	+	6.55732i	−0.149667	+	0.655732i
$101$	−12.1427	+	15.2265i	−1.20825	+	1.51510i	−0.410780	+	0.911734i	$0.634744\pi$
$101$	−12.1427	+	15.2265i	−1.20825	+	1.51510i	−0.797468	+	0.603361i	$0.793828\pi$
$102$		0			0
$103$	5.68835	−	7.13297i	0.560490	−	0.702832i	−0.418158	−	0.908374i	$-0.637324\pi$
$103$	5.68835	−	7.13297i	0.560490	−	0.702832i	0.978648	+	0.205542i	$0.0658958\pi$
$104$	−0.599455	−	0.751693i	−0.0587814	−	0.0737096i
$105$		0			0
$106$	−2.78389	+	3.49088i	−0.270395	+	0.339065i
$107$	3.88114	+	17.0044i	0.375204	+	1.64388i	0.711913	+	0.702267i	$0.247829\pi$
$107$	3.88114	+	17.0044i	0.375204	+	1.64388i	−0.336709	+	0.941609i	$0.609314\pi$
$108$		0			0
$109$	−2.70231	+	11.8396i	−0.258834	+	1.13403i	0.663666	+	0.748029i	$0.269000\pi$
$109$	−2.70231	+	11.8396i	−0.258834	+	1.13403i	−0.922500	+	0.385997i	$0.873857\pi$
$110$	1.77403	−	0.854326i	0.169147	−	0.0814568i
$111$		0			0
$112$	3.56804	−	3.91001i	0.337148	−	0.369461i
$113$	−0.532517	−	2.33311i	−0.0500950	−	0.219481i	0.943684	−	0.330847i	$-0.107334\pi$
$113$	−0.532517	−	2.33311i	−0.0500950	−	0.219481i	−0.993779	+	0.111366i	$0.964477\pi$
$114$		0			0
$115$	−5.63703	+	2.71465i	−0.525655	+	0.253142i
$116$	5.36486			0.498114
$117$		0			0
$118$	−4.47093	+	2.15309i	−0.411583	+	0.198208i
$119$	−3.21803	−	4.63685i	−0.294997	−	0.425060i
$120$		0			0
$121$	−0.888008	−	0.427642i	−0.0807280	−	0.0388766i
$122$	−0.202726	−	0.888203i	−0.0183540	−	0.0804141i
$123$		0			0
$124$	−13.0717	−	6.29502i	−1.17388	−	0.565309i
$125$	−7.82444	−	3.76805i	−0.699839	−	0.337025i
$126$		0			0
$127$	10.7608	−	5.18214i	0.954869	−	0.459841i	0.109478	−	0.993989i	$-0.465082\pi$
$127$	10.7608	−	5.18214i	0.954869	−	0.459841i	0.845391	+	0.534148i	$0.179368\pi$
$128$	11.4824			1.01491
$129$		0			0
$130$	0.227080	−	0.109356i	0.0199163	−	0.00959117i
$131$	9.12744	+	11.4454i	0.797468	+	0.999993i	0.999786	+	0.0206731i	$0.00658093\pi$
$131$	9.12744	+	11.4454i	0.797468	+	0.999993i	−0.202319	+	0.979320i	$0.564848\pi$
$132$		0			0
$133$	−1.66027	−	10.4274i	−0.143964	−	0.904168i
$134$	0.858317	−	3.76053i	0.0741473	−	0.324861i
$135$		0			0
$136$	1.02990	−	4.51230i	0.0883134	−	0.386926i
$137$	−14.0090	−	17.5668i	−1.19687	−	1.50083i	−0.817841	−	0.575444i	$-0.804829\pi$
$137$	−14.0090	−	17.5668i	−1.19687	−	1.50083i	−0.379030	−	0.925384i	$-0.623742\pi$
$138$		0			0
$139$	−10.1071	+	12.6739i	−0.857272	+	1.07498i	0.139134	+	0.990274i	$0.455568\pi$
$139$	−10.1071	+	12.6739i	−0.857272	+	1.07498i	−0.996406	+	0.0847113i	$0.973003\pi$
$140$	2.37294	+	3.41916i	0.200550	+	0.288971i
$141$		0			0
$142$	−1.55656	+	1.95186i	−0.130624	+	0.163797i
$143$	−1.38226	−	0.665662i	−0.115590	−	0.0556654i
$144$		0			0
$145$	−0.693227	+	3.03723i	−0.0575694	+	0.252228i
$146$	5.72275			0.473618
$147$		0			0
$148$	0.300598			0.0247090
$149$	0.228166	−	0.999659i	0.0186921	−	0.0818953i	−0.964722	−	0.263272i	$-0.915198\pi$
$149$	0.228166	−	0.999659i	0.0186921	−	0.0818953i	0.983414	+	0.181377i	$0.0580554\pi$
$150$		0			0
$151$	−15.9654	−	7.68853i	−1.29925	−	0.625684i	−0.348982	−	0.937130i	$-0.613472\pi$
$151$	−15.9654	−	7.68853i	−1.29925	−	0.625684i	−0.950264	+	0.311446i	$0.899187\pi$
$152$	5.39845	−	6.76945i	0.437872	−	0.549075i
$153$		0			0
$154$	−1.56336	+	5.22172i	−0.125979	+	0.420778i
$155$	5.25291	−	6.58694i	0.421924	−	0.529075i
$156$		0			0
$157$	−3.62182	−	4.54161i	−0.289052	−	0.362460i	0.616011	−	0.787738i	$-0.288748\pi$
$157$	−3.62182	−	4.54161i	−0.289052	−	0.362460i	−0.905063	+	0.425278i	$0.860176\pi$
$158$	−0.343306	+	1.50412i	−0.0273120	+	0.119662i
$159$		0			0
$160$	−1.17604	+	5.15255i	−0.0929738	+	0.407345i
$161$	4.96762	−	16.5922i	0.391503	−	1.30765i
$162$		0			0
$163$	12.6619	+	15.8775i	0.991757	+	1.24362i	0.969809	+	0.243865i	$0.0784153\pi$
$163$	12.6619	+	15.8775i	0.991757	+	1.24362i	0.0219477	+	0.999759i	$0.493013\pi$
$164$	−16.2796	+	7.83986i	−1.27123	+	0.612190i
$165$		0			0
$166$	4.63915			0.360068
$167$	7.19043	−	3.46273i	0.556412	−	0.267954i	−0.134475	−	0.990917i	$-0.542935\pi$
$167$	7.19043	−	3.46273i	0.556412	−	0.267954i	0.690887	+	0.722963i	$0.257220\pi$
$168$		0			0
$169$	11.5357	+	5.55528i	0.887359	+	0.427329i
$170$	1.09314	+	0.526430i	0.0838403	+	0.0403754i
$171$		0			0
$172$	−3.08579	−	13.5197i	−0.235289	−	1.03087i
$173$	11.4096	+	5.49455i	0.867452	+	0.417743i	0.814026	−	0.580829i	$-0.197271\pi$
$173$	11.4096	+	5.49455i	0.867452	+	0.417743i	0.0534264	+	0.998572i	$0.482986\pi$
$174$		0			0
$175$	10.0315	−	4.03343i	0.758307	−	0.304898i
$176$	6.24048	−	3.00526i	0.470394	−	0.226530i
$177$		0			0
$178$	−3.83371			−0.287349
$179$	9.62990	−	4.63751i	0.719772	−	0.346624i	−0.0378802	−	0.999282i	$-0.512061\pi$
$179$	9.62990	−	4.63751i	0.719772	−	0.346624i	0.757652	+	0.652658i	$0.226346\pi$
$180$		0			0
$181$	−1.67289	−	7.32939i	−0.124345	−	0.544789i	−0.998274	−	0.0587357i	$-0.981293\pi$
$181$	−1.67289	−	7.32939i	−0.124345	−	0.544789i	0.873929	−	0.486054i	$-0.161564\pi$
$182$	−0.200114	+	0.668395i	−0.0148335	+	0.0495447i
$183$		0			0
$184$	12.7963	−	6.16235i	0.943352	−	0.454294i
$185$	−0.0388421	+	0.170178i	−0.00285573	+	0.0125118i
$186$		0			0
$187$	−1.64342	−	7.20029i	−0.120179	−	0.526538i
$188$	−1.98601	+	2.49038i	−0.144845	+	0.181629i
$189$		0			0
$190$	1.41518	+	1.77458i	0.102668	+	0.128742i
$191$	−15.1326	+	18.9756i	−1.09495	+	1.37303i	−0.173367	+	0.984857i	$0.555465\pi$
$191$	−15.1326	+	18.9756i	−1.09495	+	1.37303i	−0.921587	+	0.388172i	$0.873107\pi$
$192$		0			0
$193$	9.40791	−	11.7972i	0.677197	−	0.849178i	−0.317896	−	0.948126i	$-0.602976\pi$
$193$	9.40791	−	11.7972i	0.677197	−	0.849178i	0.995093	+	0.0989480i	$0.0315477\pi$
$194$	−0.0766181	+	0.335686i	−0.00550086	+	0.0241008i
$195$		0			0
$196$	−11.4194	−	1.52786i	−0.815672	−	0.109133i
$197$	−0.799611			−0.0569699			−0.0284850	−	0.999594i	$-0.509068\pi$
$197$	−0.799611			−0.0569699			−0.0284850	+	0.999594i	$0.509068\pi$
$198$		0			0
$199$	6.89002	−	8.63981i	0.488421	−	0.612460i	−0.475153	−	0.879903i	$-0.657607\pi$
$199$	6.89002	−	8.63981i	0.488421	−	0.612460i	0.963574	+	0.267443i	$0.0861787\pi$
$200$	7.98809	+	3.84686i	0.564843	+	0.272014i
$201$		0			0
$202$	7.22590	+	9.06100i	0.508413	+	0.637529i
$203$	−4.91703	−	7.08493i	−0.345108	−	0.497265i
$204$		0			0
$205$	−2.33482	−	10.2295i	−0.163071	−	0.714459i
$206$	−3.38502	−	4.24468i	−0.235846	−	0.295741i
$207$		0			0
$208$	0.798799	−	0.384681i	0.0553868	−	0.0266729i
$209$	3.07442	−	13.4699i	0.212662	−	0.931734i
$210$		0			0
$211$	3.25650	+	14.2676i	0.224186	+	0.982225i	0.954289	+	0.298887i	$0.0966153\pi$
$211$	3.25650	+	14.2676i	0.224186	+	0.982225i	−0.730102	+	0.683338i	$0.760528\pi$
$212$	−7.69971	−	9.65514i	−0.528819	−	0.663117i
$213$		0			0
$214$	10.3792			0.709507
$215$	8.05271			0.549191
$216$		0			0
$217$	3.66726	+	23.0323i	0.248950	+	1.56354i
$218$	6.51102	+	3.13554i	0.440982	+	0.212366i
$219$		0			0
$220$	1.21184	+	5.30940i	0.0817020	+	0.357960i
$221$	−0.210363	−	0.921659i	−0.0141505	−	0.0619975i
$222$		0			0
$223$	−17.3626	−	8.36139i	−1.16269	−	0.559920i	−0.249865	−	0.968281i	$-0.580386\pi$
$223$	−17.3626	−	8.36139i	−1.16269	−	0.559920i	−0.912821	+	0.408360i	$0.866101\pi$
$224$	−8.34157	−	12.0193i	−0.557345	−	0.803076i
$225$		0			0
$226$	−1.42409			−0.0947292
$227$	14.5925			0.968537			0.484269	−	0.874919i	$-0.339086\pi$
$227$	14.5925			0.968537			0.484269	+	0.874919i	$0.339086\pi$
$228$		0			0
$229$	−0.0729523	−	0.0914793i	−0.00482082	−	0.00604512i	0.779415	−	0.626508i	$-0.215516\pi$
$229$	−0.0729523	−	0.0914793i	−0.00482082	−	0.00604512i	−0.784236	+	0.620463i	$0.786945\pi$
$230$	0.828488	+	3.62984i	0.0546289	+	0.239345i
$231$		0			0
$232$	1.57365	−	6.89461i	0.103315	−	0.452654i
$233$	−21.1971	+	10.2080i	−1.38867	+	0.668746i	−0.970828	−	0.239776i	$-0.922926\pi$
$233$	−21.1971	+	10.2080i	−1.38867	+	0.668746i	−0.417837	+	0.908522i	$0.637212\pi$
$234$		0			0
$235$	−1.15326	−	1.44614i	−0.0752305	−	0.0943360i
$236$	−3.05409	−	13.3808i	−0.198804	−	0.871019i
$237$		0			0
$238$	−3.11624	+	1.25297i	−0.201996	+	0.0812181i
$239$	−8.79462	−	11.0281i	−0.568877	−	0.713349i	0.411294	−	0.911503i	$-0.365077\pi$
$239$	−8.79462	−	11.0281i	−0.568877	−	0.713349i	−0.980171	+	0.198154i	$0.936506\pi$
$240$		0			0
$241$	−17.5184	−	8.43642i	−1.12846	−	0.543438i	−0.225964	−	0.974136i	$-0.572553\pi$
$241$	−17.5184	−	8.43642i	−1.12846	−	0.543438i	−0.902496	+	0.430698i	$0.858268\pi$
$242$	−0.365689	+	0.458559i	−0.0235074	+	0.0294773i
$243$		0			0
$244$	2.51978			0.161312
$245$	2.34055	−	6.26749i	0.149532	−	0.400415i
$246$		0			0
$247$	0.393535	−	1.72419i	0.0250400	−	0.109707i
$248$	−11.9243	+	14.9526i	−0.757193	+	0.949490i
$249$		0			0
$250$	−3.22217	+	4.04047i	−0.203788	+	0.255542i
$251$	7.93579	+	9.95117i	0.500903	+	0.628112i	0.966433	−	0.256920i	$-0.0827077\pi$
$251$	7.93579	+	9.95117i	0.500903	+	0.628112i	−0.465530	+	0.885032i	$0.654136\pi$
$252$		0			0
$253$	14.1304	−	17.7190i	0.888372	−	1.11398i
$254$	−1.58155	−	6.92921i	−0.0992351	−	0.434777i
$255$		0			0
$256$	1.20418	−	5.27584i	0.0752609	−	0.329740i
$257$	10.8075	−	5.20462i	0.674153	−	0.324655i	−0.0652973	−	0.997866i	$-0.520800\pi$
$257$	10.8075	−	5.20462i	0.674153	−	0.324655i	0.739451	+	0.673211i	$0.235085\pi$
$258$		0			0
$259$	−0.275505	−	0.396975i	−0.0171191	−	0.0246668i
$260$	0.155119	+	0.679619i	0.00962005	+	0.0421482i
$261$		0			0
$262$	7.84882	−	3.77979i	0.484902	−	0.233516i
$263$	−4.94044			−0.304641			−0.152320	−	0.988331i	$-0.548675\pi$
$263$	−4.94044			−0.304641			−0.152320	+	0.988331i	$0.548675\pi$
$264$		0			0
$265$	6.46103	−	3.11147i	0.396898	−	0.191136i
$266$	−6.26939	−	0.417546i	−0.384401	−	0.0256014i
$267$		0			0
$268$	9.61191	+	4.62885i	0.587141	+	0.282752i
$269$	−0.525741	−	2.30342i	−0.0320550	−	0.140442i	0.956368	−	0.292164i	$-0.0943753\pi$
$269$	−0.525741	−	2.30342i	−0.0320550	−	0.140442i	−0.988423	+	0.151722i	$0.951518\pi$
$270$		0			0
$271$	19.6067	+	9.44207i	1.19102	+	0.573565i	0.921103	−	0.389319i	$-0.127289\pi$
$271$	19.6067	+	9.44207i	1.19102	+	0.573565i	0.269917	+	0.962884i	$0.413004\pi$
$272$	3.84534	+	1.85182i	0.233158	+	0.112283i
$273$		0			0
$274$	−12.0466	+	5.80132i	−0.727760	+	0.350471i
$275$	14.1477			0.853138
$276$		0			0
$277$	−11.5461	+	5.56032i	−0.693740	+	0.334087i	−0.747309	−	0.664477i	$-0.768655\pi$
$277$	−11.5461	+	5.56032i	−0.693740	+	0.334087i	0.0535692	+	0.998564i	$0.482940\pi$
$278$	6.01452	+	7.54197i	0.360727	+	0.452337i
$279$		0			0
$280$	5.09015	−	2.04664i	0.304195	−	0.122310i
$281$	4.25239	−	18.6309i	0.253676	−	1.11143i	−0.674203	−	0.738546i	$-0.735513\pi$
$281$	4.25239	−	18.6309i	0.253676	−	1.11143i	0.927879	−	0.372882i	$-0.121630\pi$
$282$		0			0
$283$	3.46097	−	15.1635i	0.205733	−	0.901376i	−0.761636	−	0.648005i	$-0.775603\pi$
$283$	3.46097	−	15.1635i	0.205733	−	0.901376i	0.967369	−	0.253371i	$-0.0815394\pi$
$284$	−4.30516	−	5.39849i	−0.255464	−	0.320342i
$285$		0			0
$286$	−0.569226	+	0.713787i	−0.0336590	+	0.0422071i
$287$	25.2742	+	14.3138i	1.49189	+	0.844915i
$288$		0			0
$289$	−7.76190	+	9.73312i	−0.456582	+	0.572536i
$290$	1.67028	+	0.804365i	0.0980823	+	0.0472340i
$291$		0			0
$292$	−3.52208	+	15.4312i	−0.206114	+	0.903044i
$293$	0.246213			0.0143839			0.00719197	−	0.999974i	$-0.497711\pi$
$293$	0.246213			0.0143839			0.00719197	+	0.999974i	$0.497711\pi$
$294$		0			0
$295$	7.96999			0.464031
$296$	0.0881730	−	0.386311i	0.00512495	−	0.0224539i
$297$		0			0
$298$	−0.549749	−	0.264745i	−0.0318461	−	0.0153363i
$299$	1.80873	−	2.26808i	0.104602	−	0.131166i
$300$		0			0
$301$	−15.0262	+	16.4663i	−0.866097	+	0.949104i
$302$	−6.57468	+	8.24439i	−0.378330	+	0.474411i
$303$		0			0
$304$	4.97817	+	6.24242i	0.285518	+	0.358028i
$305$	−0.325597	+	1.42653i	−0.0186436	+	0.0816830i
$306$		0			0
$307$	3.07070	−	13.4536i	0.175254	−	0.767840i	−0.808526	−	0.588461i	$-0.799734\pi$
$307$	3.07070	−	13.4536i	0.175254	−	0.767840i	0.983780	−	0.179379i	$-0.0574088\pi$
$308$	−13.1180	−	7.42926i	−0.747469	−	0.423321i
$309$		0			0
$310$	−3.12590	−	3.91975i	−0.177539	−	0.222627i
$311$	19.8399	−	9.55437i	1.12502	−	0.541779i	0.223577	−	0.974686i	$-0.428227\pi$
$311$	19.8399	−	9.55437i	1.12502	−	0.541779i	0.901438	+	0.432907i	$0.142512\pi$
$312$		0			0
$313$	−18.6212			−1.05253			−0.526266	−	0.850320i	$-0.676408\pi$
$313$	−18.6212			−1.05253			−0.526266	+	0.850320i	$0.676408\pi$
$314$	−3.11445	+	1.49984i	−0.175759	+	0.0846410i
$315$		0			0
$316$	−3.84453	−	1.85143i	−0.216272	−	0.104151i
$317$	22.8434	+	11.0008i	1.28301	+	0.617866i	0.946162	−	0.323693i	$-0.104925\pi$
$317$	22.8434	+	11.0008i	1.28301	+	0.617866i	0.336849	+	0.941559i	$0.390639\pi$
$318$		0			0
$319$	−2.51108	−	11.0018i	−0.140594	−	0.615981i
$320$	−0.612005	−	0.294726i	−0.0342121	−	0.0164757i
$321$		0			0
$322$	−8.96832	−	5.07911i	−0.499785	−	0.283048i
$323$	7.67043	−	3.69388i	0.426794	−	0.205533i
$324$		0			0
$325$	1.81095			0.100453
$326$	10.8882	−	5.24346i	0.603040	−	0.290409i
$327$		0			0
$328$	5.30011	+	23.2213i	0.292650	+	1.28218i
$329$	5.10907	+	0.340267i	0.281672	+	0.0187596i
$330$		0			0
$331$	6.21838	−	2.99461i	0.341793	−	0.164599i	−0.255110	−	0.966912i	$-0.582112\pi$
$331$	6.21838	−	2.99461i	0.341793	−	0.164599i	0.596904	+	0.802313i	$0.296398\pi$
$332$	−2.85517	+	12.5093i	−0.156698	+	0.686538i
$333$		0			0
$334$	−1.05680	−	4.63012i	−0.0578253	−	0.253349i
$335$	−3.86257	+	4.84351i	−0.211035	+	0.264629i
$336$		0			0
$337$	−3.57699	−	4.48540i	−0.194851	−	0.244336i	0.674802	−	0.737999i	$-0.264229\pi$
$337$	−3.57699	−	4.48540i	−0.194851	−	0.244336i	−0.869653	+	0.493663i	$0.835658\pi$
$338$	4.75048	−	5.95691i	0.258392	−	0.324013i
$339$		0			0
$340$	−2.09228	+	2.62364i	−0.113470	+	0.142287i
$341$	−6.79089	+	29.7528i	−0.367747	+	1.61121i
$342$		0			0
$343$	8.44846	+	16.4810i	0.456174	+	0.889891i
$344$	−18.2800			−0.985589
$345$		0			0
$346$	4.69854	−	5.89179i	0.252595	−	0.316745i
$347$	18.5608	+	8.93840i	0.996394	+	0.479838i	0.859713	−	0.510777i	$-0.170642\pi$
$347$	18.5608	+	8.93840i	0.996394	+	0.479838i	0.136681	+	0.990615i	$0.456356\pi$
$348$		0			0
$349$	−19.3857	−	24.3089i	−1.03769	−	1.30123i	−0.952394	−	0.304871i	$-0.901387\pi$
$349$	−19.3857	−	24.3089i	−1.03769	−	1.30123i	−0.0852995	−	0.996355i	$-0.527185\pi$
$350$	−1.01169	−	6.35395i	−0.0540771	−	0.339633i
$351$		0			0
$352$	−4.25997	−	18.6641i	−0.227057	−	0.994801i
$353$	−6.39535	−	8.01952i	−0.340390	−	0.426836i	0.581944	−	0.813229i	$-0.302292\pi$
$353$	−6.39535	−	8.01952i	−0.340390	−	0.426836i	−0.922334	+	0.386393i	$0.873721\pi$
$354$		0			0
$355$	3.61257	−	1.73972i	0.191735	−	0.0923348i
$356$	2.35946	−	10.3375i	0.125051	−	0.547886i
$357$		0			0
$358$	−1.41533	−	6.20097i	−0.0748025	−	0.327731i
$359$	−13.4761	−	16.8985i	−0.711243	−	0.891871i	0.286564	−	0.958061i	$-0.407487\pi$
$359$	−13.4761	−	16.8985i	−0.711243	−	0.891871i	−0.997807	+	0.0661904i	$0.978916\pi$
$360$		0			0
$361$	−3.07334			−0.161755
$362$	−4.47374			−0.235135
$363$		0			0
$364$	−1.67915	−	0.950967i	−0.0880111	−	0.0498442i
$365$	−8.28103	−	3.98793i	−0.433449	−	0.208738i
$366$		0			0
$367$	7.67976	+	33.6472i	0.400880	+	1.75637i	0.623848	+	0.781546i	$0.285568\pi$
$367$	7.67976	+	33.6472i	0.400880	+	1.75637i	−0.222968	+	0.974826i	$0.571574\pi$
$368$	2.91437	+	12.7687i	0.151922	+	0.665613i
$369$		0			0
$370$	0.0935873	+	0.0450693i	0.00486537	+	0.00234304i
$371$	−5.69377	+	19.0176i	−0.295606	+	0.987343i
$372$		0			0
$373$	−9.33686			−0.483444			−0.241722	−	0.970345i	$-0.577712\pi$
$373$	−9.33686			−0.483444			−0.241722	+	0.970345i	$0.577712\pi$
$374$	−4.39494			−0.227257
$375$		0			0
$376$	2.61795	+	3.28280i	0.135010	+	0.169297i
$377$	−0.321426	−	1.40826i	−0.0165543	−	0.0725290i
$378$		0			0
$379$	−3.56800	+	15.6324i	−0.183276	+	0.802984i	0.796781	+	0.604268i	$0.206534\pi$
$379$	−3.56800	+	15.6324i	−0.183276	+	0.802984i	−0.980057	+	0.198716i	$0.936323\pi$
$380$	−5.65607	+	2.72382i	−0.290151	+	0.139729i
$381$		0			0
$382$	9.00509	+	11.2920i	0.460740	+	0.577750i
$383$	−3.16291	−	13.8576i	−0.161617	−	0.708090i	−0.989179	−	0.146716i	$-0.953130\pi$
$383$	−3.16291	−	13.8576i	−0.161617	−	0.708090i	0.827562	−	0.561375i	$-0.189727\pi$
$384$		0			0
$385$	5.90102	−	6.46658i	0.300744	−	0.329567i
$386$	−5.59846	−	7.02025i	−0.284954	−	0.357321i
$387$		0			0
$388$	−0.858012	−	0.413197i	−0.0435589	−	0.0209769i
$389$	−12.1289	+	15.2091i	−0.614959	+	0.771134i	−0.987625	−	0.156831i	$-0.949872\pi$
$389$	−12.1289	+	15.2091i	−0.614959	+	0.771134i	0.372666	+	0.927965i	$0.378444\pi$
$390$		0			0
$391$	13.9651			0.706244
$392$	−5.31312	+	14.2274i	−0.268353	+	0.718593i
$393$		0			0
$394$	−0.105883	+	0.463902i	−0.00533429	+	0.0233711i
$395$	1.54493	−	1.93728i	0.0777340	−	0.0974754i
$396$		0			0
$397$	1.70744	−	2.14106i	0.0856937	−	0.107457i	−0.737136	−	0.675744i	$-0.763822\pi$
$397$	1.70744	−	2.14106i	0.0856937	−	0.107457i	0.822830	+	0.568288i	$0.192394\pi$
$398$	−4.10011	−	5.14138i	−0.205520	−	0.257714i
$399$		0			0
$400$	−5.09757	+	6.39215i	−0.254878	+	0.319607i
$401$	−1.72806	−	7.57112i	−0.0862951	−	0.378083i	0.913277	−	0.407339i	$-0.133543\pi$
$401$	−1.72806	−	7.57112i	−0.0862951	−	0.378083i	−0.999572	+	0.0292559i	$0.990686\pi$
$402$		0			0
$403$	−0.869253	+	3.80845i	−0.0433006	+	0.189712i
$404$	−28.8799	+	13.9078i	−1.43683	+	0.691940i
$405$		0			0
$406$	−4.76149	+	1.91449i	−0.236309	+	0.0950147i
$407$	−0.140698	−	0.616439i	−0.00697415	−	0.0305557i
$408$		0			0
$409$	8.53001	−	4.10784i	0.421782	−	0.203119i	−0.210939	−	0.977499i	$-0.567652\pi$
$409$	8.53001	−	4.10784i	0.421782	−	0.203119i	0.632721	+	0.774380i	$0.281938\pi$
$410$	−6.24391			−0.308365
$411$		0			0
$412$	13.5290	−	6.51521i	0.666525	−	0.320981i
$413$	−14.8719	+	16.2972i	−0.731796	+	0.801932i
$414$		0			0
$415$	−6.71301	−	3.23282i	−0.329529	−	0.158693i
$416$	−0.545288	−	2.38906i	−0.0267349	−	0.117133i
$417$		0			0
$418$	−7.40760	−	3.56731i	−0.362318	−	0.174483i
$419$	−11.9283	−	5.74439i	−0.582738	−	0.280632i	0.119200	−	0.992870i	$-0.461967\pi$
$419$	−11.9283	−	5.74439i	−0.582738	−	0.280632i	−0.701937	+	0.712239i	$0.747681\pi$
$420$		0			0
$421$	20.3959	−	9.82217i	0.994037	−	0.478703i	0.135126	−	0.990828i	$-0.456856\pi$
$421$	20.3959	−	9.82217i	0.994037	−	0.478703i	0.858911	+	0.512125i	$0.171142\pi$
$422$	8.70873			0.423934
$423$		0			0
$424$	−14.6668	+	7.06314i	−0.712281	+	0.343017i
$425$	5.43541	+	6.81579i	0.263656	+	0.330615i
$426$		0			0
$427$	−2.30944	−	3.32767i	−0.111762	−	0.161037i
$428$	−6.38789	+	27.9872i	−0.308770	+	1.35281i
$429$		0			0
$430$	1.06632	−	4.67186i	0.0514226	−	0.225297i
$431$	−5.83813	−	7.32079i	−0.281213	−	0.352630i	0.621085	−	0.783743i	$-0.286692\pi$
$431$	−5.83813	−	7.32079i	−0.281213	−	0.352630i	−0.902298	+	0.431114i	$0.858121\pi$
$432$		0			0
$433$	−4.32216	+	5.41982i	−0.207710	+	0.260460i	−0.874764	−	0.484550i	$-0.838984\pi$
$433$	−4.32216	+	5.41982i	−0.207710	+	0.260460i	0.667054	+	0.745009i	$0.267555\pi$
$434$	13.8480	+	0.922290i	0.664728	+	0.0442713i
$435$		0			0
$436$	−12.4621	+	15.6270i	−0.596827	+	0.748397i
$437$	23.5379	+	11.3353i	1.12597	+	0.542239i
$438$		0			0
$439$	−0.575253	+	2.52035i	−0.0274553	+	0.120290i	−0.986799	−	0.161952i	$-0.948221\pi$
$439$	−0.575253	+	2.52035i	−0.0274553	+	0.120290i	0.959343	+	0.282242i	$0.0910781\pi$
$440$	7.17881			0.342236
$441$		0			0
$442$	−0.562565			−0.0267585
$443$	1.93981	−	8.49888i	0.0921633	−	0.403794i	−0.907712	−	0.419594i	$-0.862172\pi$
$443$	1.93981	−	8.49888i	0.0921633	−	0.403794i	0.999875	+	0.0158003i	$0.00502959\pi$
$444$		0			0
$445$	5.54752	+	2.67154i	0.262978	+	0.126643i
$446$	−7.15006	+	8.96589i	−0.338565	+	0.424547i
$447$		0			0
$448$	1.74465	−	0.701486i	0.0824270	−	0.0331421i
$449$	−8.93164	+	11.1999i	−0.421510	+	0.528557i	−0.946566	−	0.322511i	$-0.895473\pi$
$449$	−8.93164	+	11.1999i	−0.421510	+	0.528557i	0.525056	+	0.851068i	$0.324045\pi$
$450$		0			0
$451$	23.6972	+	29.7153i	1.11586	+	1.39924i
$452$	0.876460	−	3.84002i	0.0412252	−	0.180619i
$453$		0			0
$454$	1.93230	−	8.46598i	0.0906875	−	0.397328i
$455$	0.755348	−	0.827741i	0.0354112	−	0.0388051i
$456$		0			0
$457$	14.9254	+	18.7158i	0.698179	+	0.875489i	0.996886	−	0.0788559i	$-0.0251267\pi$
$457$	14.9254	+	18.7158i	0.698179	+	0.875489i	−0.298707	+	0.954345i	$0.596555\pi$
$458$	−0.0627328	+	0.0302105i	−0.00293131	+	0.00141165i
$459$		0			0
$460$	−10.2977			−0.480131
$461$	−35.7884	+	17.2348i	−1.66683	+	0.802704i	−0.668577	+	0.743643i	$0.733096\pi$
$461$	−35.7884	+	17.2348i	−1.66683	+	0.802704i	−0.998254	+	0.0590612i	$0.981189\pi$
$462$		0			0
$463$	−33.6609	−	16.2102i	−1.56435	−	0.753353i	−0.566841	−	0.823827i	$-0.691835\pi$
$463$	−33.6609	−	16.2102i	−1.56435	−	0.753353i	−0.997514	+	0.0704739i	$0.977549\pi$
$464$	5.87554	+	2.82951i	0.272765	+	0.131357i
$465$		0			0
$466$	3.11539	+	13.6494i	0.144317	+	0.632296i
$467$	−29.4227	−	14.1692i	−1.36152	−	0.655675i	−0.396547	−	0.918015i	$-0.629792\pi$
$467$	−29.4227	−	14.1692i	−1.36152	−	0.655675i	−0.964975	+	0.262340i	$0.915506\pi$
$468$		0			0
$469$	−2.69661	−	16.9361i	−0.124518	−	0.782038i
$470$	−0.991707	+	0.477581i	−0.0457440	+	0.0220292i
$471$		0			0
$472$	−18.0922			−0.832759
$473$	−26.2807	+	12.6561i	−1.20839	+	0.581930i
$474$		0			0
$475$	3.62902	+	15.8998i	0.166511	+	0.729531i
$476$	−1.46070	−	9.17399i	−0.0669513	−	0.420489i
$477$		0			0
$478$	−7.56263	+	3.64197i	−0.345907	+	0.166580i
$479$	4.50467	−	19.7362i	0.205824	−	0.901772i	−0.761488	−	0.648179i	$-0.775531\pi$
$479$	4.50467	−	19.7362i	0.205824	−	0.901772i	0.967311	−	0.253592i	$-0.0816122\pi$
$480$		0			0
$481$	−0.0180098	−	0.0789059i	−0.000821175	−	0.00359780i
$482$	−7.21422	+	9.04635i	−0.328599	+	0.412050i
$483$		0			0
$484$	−1.01143	−	1.26829i	−0.0459740	−	0.0576495i
$485$	0.344794	−	0.432358i	0.0156563	−	0.0196324i
$486$		0			0
$487$	−17.2359	+	21.6131i	−0.781031	+	0.979382i	0.218962	+	0.975733i	$0.429733\pi$
$487$	−17.2359	+	21.6131i	−0.781031	+	0.979382i	−0.999993	+	0.00364875i	$0.998839\pi$
$488$	0.739116	−	3.23828i	0.0334582	−	0.146590i
$489$		0			0
$490$	−3.32622	−	2.18782i	−0.150263	−	0.0988355i
$491$	32.0427			1.44607			0.723033	−	0.690814i	$-0.242748\pi$
$491$	32.0427			1.44607			0.723033	+	0.690814i	$0.242748\pi$
$492$		0			0
$493$	4.33548	−	5.43651i	0.195260	−	0.244848i
$494$	−0.948194	−	0.456626i	−0.0426613	−	0.0205446i
$495$		0			0
$496$	−10.9959	−	13.7885i	−0.493733	−	0.619121i
$497$	−3.18357	+	10.6333i	−0.142803	+	0.476970i
$498$		0			0
$499$	−7.96912	−	34.9150i	−0.356747	−	1.56301i	−0.761241	−	0.648470i	$-0.775409\pi$
$499$	−7.96912	−	34.9150i	−0.356747	−	1.56301i	0.404494	−	0.914541i	$-0.367448\pi$
$500$	−8.91191	−	11.1752i	−0.398553	−	0.499769i
$501$		0			0
$502$	6.82411	−	3.28632i	0.304575	−	0.146676i
$503$	9.53631	−	41.7813i	0.425203	−	1.86294i	−0.0752370	−	0.997166i	$-0.523971\pi$
$503$	9.53631	−	41.7813i	0.425203	−	1.86294i	0.500440	−	0.865771i	$-0.333172\pi$
$504$		0			0
$505$	−4.14193	−	18.1470i	−0.184314	−	0.807531i
$506$	−8.40872	−	10.5442i	−0.373813	−	0.468747i
$507$		0			0
$508$	19.6578			0.872172
$509$	−7.97767			−0.353604			−0.176802	−	0.984246i	$-0.556575\pi$
$509$	−7.97767			−0.353604			−0.176802	+	0.984246i	$0.556575\pi$
$510$		0			0
$511$	23.6068	−	9.49179i	1.04431	−	0.419892i
$512$	17.7892	+	8.56685i	0.786181	+	0.378605i
$513$		0			0
$514$	−1.58841	−	6.95926i	−0.0700616	−	0.306960i
$515$	1.94032	+	8.50108i	0.0855006	+	0.374603i
$516$		0			0
$517$	6.03662	+	2.90708i	0.265490	+	0.127853i
$518$	−0.266791	+	0.107271i	−0.0117221	+	0.00471320i
$519$		0			0
$520$	0.918909			0.0402968
$521$	39.4222			1.72712			0.863559	−	0.504247i	$-0.168230\pi$
$521$	39.4222			1.72712			0.863559	+	0.504247i	$0.168230\pi$
$522$		0			0
$523$	7.92023	+	9.93165i	0.346327	+	0.434281i	0.924237	−	0.381820i	$-0.124703\pi$
$523$	7.92023	+	9.93165i	0.346327	+	0.434281i	−0.577909	+	0.816101i	$0.696131\pi$
$524$	5.36153	+	23.4904i	0.234219	+	1.02618i
$525$		0			0
$526$	−0.654202	+	2.86625i	−0.0285246	+	0.124974i
$527$	−16.9427	+	8.15918i	−0.738036	+	0.355419i
$528$		0			0
$529$	12.3787	+	15.5224i	0.538206	+	0.674889i
$530$	−0.949594	−	4.16044i	−0.0412477	−	0.180718i
$531$		0			0
$532$	4.98441	−	16.6482i	0.216101	−	0.721793i
$533$	3.03331	+	3.80364i	0.131387	+	0.164754i
$534$		0			0
$535$	−15.0191	−	7.23280i	−0.649331	−	0.312701i
$536$	8.76817	−	10.9949i	0.378727	−	0.474909i
$537$		0			0
$538$	−1.40597			−0.0606157
$539$	2.21179	+	24.1330i	0.0952684	+	1.03948i
$540$		0			0
$541$	−2.13876	+	9.37054i	−0.0919527	+	0.402871i	−0.999867	−	0.0162840i	$-0.994816\pi$
$541$	−2.13876	+	9.37054i	−0.0919527	+	0.402871i	0.907915	+	0.419155i	$0.137674\pi$
$542$	8.07418	−	10.1247i	0.346816	−	0.434893i
$543$		0			0
$544$	7.35499	−	9.22286i	0.315343	−	0.395427i
$545$	−7.23666	−	9.07448i	−0.309984	−	0.388708i
$546$		0			0
$547$	−6.86316	+	8.60613i	−0.293448	+	0.367972i	−0.906599	−	0.421994i	$-0.861330\pi$
$547$	−6.86316	+	8.60613i	−0.293448	+	0.367972i	0.613151	+	0.789966i	$0.289902\pi$
$548$	−8.22900	−	36.0536i	−0.351526	−	1.54013i
$549$		0			0
$550$	1.87341	−	8.20793i	0.0798823	−	0.349987i
$551$	11.7201	−	5.64411i	0.499294	−	0.240447i
$552$		0			0
$553$	1.07858	+	6.77404i	0.0458659	+	0.288062i
$554$	1.69696	+	7.43489i	0.0720971	+	0.315878i
$555$		0			0
$556$	−24.0383	+	11.5763i	−1.01945	+	0.490943i
$557$	−2.12989			−0.0902463			−0.0451231	−	0.998981i	$-0.514368\pi$
$557$	−2.12989			−0.0902463			−0.0451231	+	0.998981i	$0.514368\pi$
$558$		0			0
$559$	−3.36401	+	1.62002i	−0.142282	+	0.0685196i
$560$	0.795499	+	4.99615i	0.0336160	+	0.211126i
$561$		0			0
$562$	−10.2458	−	4.93413i	−0.432194	−	0.208134i
$563$	−7.53910	−	33.0309i	−0.317735	−	1.39209i	−0.841514	−	0.540235i	$-0.818336\pi$
$563$	−7.53910	−	33.0309i	−0.317735	−	1.39209i	0.523779	−	0.851854i	$-0.324522\pi$
$564$		0			0
$565$	2.06071	+	0.992387i	0.0866949	+	0.0417501i
$566$	−8.33896	−	4.01583i	−0.350513	−	0.168798i
$567$		0			0
$568$	−8.20066	+	3.94923i	−0.344092	+	0.165706i
$569$	31.4390			1.31799			0.658996	−	0.752147i	$-0.270981\pi$
$569$	31.4390			1.31799			0.658996	+	0.752147i	$0.270981\pi$
$570$		0			0
$571$	23.1342	−	11.1408i	0.968135	−	0.466229i	0.118127	−	0.992999i	$-0.462311\pi$
$571$	23.1342	−	11.1408i	0.968135	−	0.466229i	0.850008	+	0.526769i	$0.176597\pi$
$572$	−1.57437	−	1.97420i	−0.0658278	−	0.0825455i
$573$		0			0
$574$	11.6510	−	12.7677i	0.486304	−	0.532912i
$575$	−5.95281	+	26.0810i	−0.248249	+	1.08765i
$576$		0			0
$577$	0.368597	−	1.61493i	0.0153449	−	0.0672304i	−0.966676	−	0.256004i	$-0.917594\pi$
$577$	0.368597	−	1.61493i	0.0153449	−	0.0672304i	0.982021	+	0.188773i	$0.0604512\pi$
$578$	4.61895	+	5.79198i	0.192123	+	0.240915i
$579$		0			0
$580$	−3.19692	+	4.00882i	−0.132745	+	0.166457i
$581$	19.1369	−	7.69452i	0.793931	−	0.319222i
$582$		0			0
$583$	−16.1960	+	20.3091i	−0.670768	+	0.841116i
$584$	18.7982	+	9.05275i	0.777876	+	0.374605i
$585$		0			0
$586$	0.0326030	−	0.142843i	0.00134682	−	0.00590080i
$587$	44.4284			1.83376			0.916878	−	0.399167i	$-0.130701\pi$
$587$	44.4284			1.83376			0.916878	+	0.399167i	$0.130701\pi$
$588$		0			0
$589$	−35.1793			−1.44954
$590$	1.05537	−	4.62387i	0.0434488	−	0.190362i
$591$		0			0
$592$	0.329211	+	0.158540i	0.0135305	+	0.00651595i
$593$	16.9542	−	21.2599i	0.696226	−	0.873040i	−0.300509	−	0.953779i	$-0.597157\pi$
$593$	16.9542	−	21.2599i	0.696226	−	0.873040i	0.996735	+	0.0807391i	$0.0257280\pi$
$594$		0			0
$595$	5.38245	+	0.358475i	0.220659	+	0.0146961i
$596$	1.05222	−	1.31944i	0.0431007	−	0.0540465i
$597$		0			0
$598$	−1.07634	−	1.34969i	−0.0440149	−	0.0551929i
$599$	0.580045	−	2.54134i	0.0237000	−	0.103837i	−0.961695	−	0.274123i	$-0.911612\pi$
$599$	0.580045	−	2.54134i	0.0237000	−	0.103837i	0.985395	+	0.170287i	$0.0544695\pi$
$600$		0			0
$601$	8.51766	−	37.3183i	0.347443	−	1.52225i	−0.435521	−	0.900179i	$-0.643436\pi$
$601$	8.51766	−	37.3183i	0.347443	−	1.52225i	0.782964	−	0.622067i	$-0.213707\pi$
$602$	7.56337	+	10.8980i	0.308260	+	0.444171i
$603$		0			0
$604$	−18.1843	−	22.8024i	−0.739910	−	0.927818i
$605$	0.848715	−	0.408720i	0.0345052	−	0.0166168i
$606$		0			0
$607$	35.0635			1.42318			0.711592	−	0.702593i	$-0.247975\pi$
$607$	35.0635			1.42318			0.711592	+	0.702593i	$0.247975\pi$
$608$	19.8828	−	9.57504i	0.806353	−	0.388319i
$609$		0			0
$610$	0.784502	+	0.377796i	0.0317636	+	0.0152965i
$611$	0.772704	+	0.372115i	0.0312603	+	0.0150542i
$612$		0			0
$613$	−2.58896	−	11.3430i	−0.104567	−	0.458138i	−0.999918	−	0.0127776i	$-0.995933\pi$
$613$	−2.58896	−	11.3430i	−0.104567	−	0.458138i	0.895351	−	0.445361i	$-0.146924\pi$
$614$	−7.39864	−	3.56300i	−0.298585	−	0.143791i
$615$		0			0
$616$	−13.3955	+	14.6794i	−0.539721	+	0.591449i
$617$	0.340484	−	0.163969i	0.0137074	−	0.00660112i	−0.427017	−	0.904243i	$-0.640436\pi$
$617$	0.340484	−	0.163969i	0.0137074	−	0.00660112i	0.440725	+	0.897642i	$0.354721\pi$
$618$		0			0
$619$	34.0256			1.36761			0.683803	−	0.729667i	$-0.260325\pi$
$619$	34.0256			1.36761			0.683803	+	0.729667i	$0.260325\pi$
$620$	12.4933	−	6.01647i	0.501744	−	0.241627i
$621$		0			0
$622$	−2.91592	−	12.7755i	−0.116918	−	0.512249i
$623$	−15.8144	+	6.35862i	−0.633590	+	0.254753i
$624$		0			0
$625$	−10.9310	+	5.26410i	−0.437240	+	0.210564i
$626$	−2.46578	+	10.8033i	−0.0985522	+	0.431786i
$627$		0			0
$628$	−2.12748	−	9.32111i	−0.0848958	−	0.371953i
$629$	0.242921	−	0.304613i	0.00968587	−	0.0121457i
$630$		0			0
$631$	8.66470	+	10.8652i	0.344936	+	0.432536i	0.923793	−	0.382893i	$-0.125072\pi$
$631$	8.66470	+	10.8652i	0.344936	+	0.432536i	−0.578856	+	0.815429i	$0.696501\pi$
$632$	−3.50705	+	4.39771i	−0.139503	+	0.174931i
$633$		0			0
$634$	9.40708	−	11.7961i	0.373603	−	0.468483i
$635$	−2.54010	+	11.1289i	−0.100801	+	0.441638i
$636$		0			0
$637$	0.283115	+	3.08910i	0.0112174	+	0.122395i
$638$	−6.71530			−0.265861
$639$		0			0
$640$	−6.84239	+	8.58009i	−0.270469	+	0.339158i
$641$	−9.67487	−	4.65917i	−0.382134	−	0.184026i	0.232948	−	0.972489i	$-0.425163\pi$
$641$	−9.67487	−	4.65917i	−0.382134	−	0.184026i	−0.615082	+	0.788463i	$0.710877\pi$
$642$		0			0
$643$	13.1151	+	16.4458i	0.517210	+	0.648560i	0.970014	−	0.243050i	$-0.0781478\pi$
$643$	13.1151	+	16.4458i	0.517210	+	0.648560i	−0.452804	+	0.891610i	$0.649576\pi$
$644$	19.2152	−	21.0568i	0.757186	−	0.829756i
$645$		0			0
$646$	−1.12734	−	4.93921i	−0.0443547	−	0.194331i
$647$	1.85517	+	2.32631i	0.0729344	+	0.0914568i	0.816960	−	0.576694i	$-0.195658\pi$
$647$	1.85517	+	2.32631i	0.0729344	+	0.0914568i	−0.744026	+	0.668151i	$0.767086\pi$
$648$		0			0
$649$	−26.0107	+	12.5261i	−1.02101	+	0.491693i
$650$	0.239801	−	1.05064i	0.00940579	−	0.0412094i
$651$		0			0
$652$	7.43770	+	32.5867i	0.291283	+	1.27619i
$653$	−12.3990	−	15.5478i	−0.485209	−	0.608432i	0.477613	−	0.878570i	$-0.341502\pi$
$653$	−12.3990	−	15.5478i	−0.485209	−	0.608432i	−0.962822	+	0.270138i	$0.912931\pi$
$654$		0			0
$655$	−13.9915			−0.546693
$656$	−21.9642			−0.857556
$657$		0			0
$658$	0.873940	−	2.91902i	0.0340697	−	0.113795i
$659$	−33.8467	−	16.2997i	−1.31848	−	0.634946i	−0.363493	−	0.931597i	$-0.618416\pi$
$659$	−33.8467	−	16.2997i	−1.31848	−	0.634946i	−0.954986	+	0.296651i	$0.904130\pi$
$660$		0			0
$661$	−5.58185	−	24.4557i	−0.217109	−	0.951215i	−0.959602	−	0.281361i	$-0.909214\pi$
$661$	−5.58185	−	24.4557i	−0.217109	−	0.951215i	0.742493	−	0.669854i	$-0.233643\pi$
$662$	−0.913932	−	4.00420i	−0.0355210	−	0.155627i
$663$		0			0
$664$	15.2388	+	7.33861i	0.591379	+	0.284793i
$665$	8.78107	+	4.97307i	0.340515	+	0.192847i
$666$		0			0
$667$	21.3381			0.826214
$668$	13.1354			0.508224
$669$		0			0
$670$	2.29854	+	2.88227i	0.0888002	+	0.111352i
$671$	−1.17941	−	5.16734i	−0.0455307	−	0.199483i
$672$		0			0
$673$	−2.40040	+	10.5169i	−0.0925288	+	0.405395i	−0.999888	−	0.0149609i	$-0.995238\pi$
$673$	−2.40040	+	10.5169i	−0.0925288	+	0.405395i	0.907359	+	0.420356i	$0.138095\pi$
$674$	−3.07591	+	1.48128i	−0.118480	+	0.0570567i
$675$		0			0
$676$	13.1389	+	16.4757i	0.505344	+	0.633681i
$677$	−0.549180	−	2.40611i	−0.0211067	−	0.0924744i	0.963278	−	0.268508i	$-0.0865305\pi$
$677$	−0.549180	−	2.40611i	−0.0211067	−	0.0924744i	−0.984384	+	0.176033i	$0.943673\pi$
$678$		0			0
$679$	0.240714	+	1.51181i	0.00923777	+	0.0580180i
$680$	2.75803	+	3.45846i	0.105766	+	0.132626i
$681$		0			0
$682$	16.3622	+	7.87960i	0.626539	+	0.301725i
$683$	−8.73617	+	10.9548i	−0.334280	+	0.419174i	−0.920356	−	0.391082i	$-0.872101\pi$
$683$	−8.73617	+	10.9548i	−0.334280	+	0.419174i	0.586076	+	0.810256i	$0.300672\pi$
$684$		0			0
$685$	21.4745			0.820499
$686$	10.6803	−	2.71908i	0.407777	−	0.103815i
$687$		0			0
$688$	3.75099	−	16.4342i	0.143005	−	0.626547i
$689$	−2.07313	+	2.59962i	−0.0789799	+	0.0990377i
$690$		0			0
$691$	−9.33256	+	11.7027i	−0.355027	+	0.445190i	−0.926988	−	0.375091i	$-0.877612\pi$
$691$	−9.33256	+	11.7027i	−0.355027	+	0.445190i	0.571961	+	0.820281i	$0.306183\pi$
$692$	12.9953	+	16.2956i	0.494007	+	0.619465i
$693$		0			0
$694$	7.64347	−	9.58461i	0.290142	−	0.363827i
$695$	−3.44756	−	15.1048i	−0.130774	−	0.572956i
$696$		0			0
$697$	−5.21141	+	22.8327i	−0.197396	+	0.864849i
$698$	−16.6701	+	8.02788i	−0.630971	+	0.303860i
$699$		0			0
$700$	17.7559	+	1.18255i	0.671109	+	0.0446963i
$701$	5.90449	+	25.8692i	0.223009	+	0.977068i	0.955198	+	0.295966i	$0.0956416\pi$
$701$	5.90449	+	25.8692i	0.223009	+	0.977068i	−0.732189	+	0.681102i	$0.761501\pi$
$702$		0			0
$703$	0.656688	−	0.316244i	0.0247675	−	0.0119274i
$704$	2.46054			0.0927351
$705$		0			0
$706$	−5.49946	+	2.64840i	−0.206975	+	0.0996739i
$707$	44.8361	+	25.3925i	1.68623	+	0.954982i
$708$		0			0
$709$	33.4392	+	16.1035i	1.25584	+	0.604779i	0.939070	−	0.343725i	$-0.111689\pi$
$709$	33.4392	+	16.1035i	1.25584	+	0.604779i	0.316766	+	0.948504i	$0.397403\pi$
$710$	−0.530948	−	2.32624i	−0.0199261	−	0.0873021i
$711$		0			0
$712$	−12.5931	−	6.06450i	−0.471945	−	0.227277i
$713$	−51.9913	−	25.0377i	−1.94709	−	0.937669i
$714$		0			0
$715$	1.32110	−	0.636207i	0.0494062	−	0.0237928i
$716$	17.5918			0.657436
$717$		0			0
$718$	−11.5883	+	5.58065i	−0.432473	+	0.208268i
$719$	−18.3949	−	23.0665i	−0.686015	−	0.860235i	0.309878	−	0.950776i	$-0.399712\pi$
$719$	−18.3949	−	23.0665i	−0.686015	−	0.860235i	−0.995893	+	0.0905410i	$0.971140\pi$
$720$		0			0
$721$	−21.0038	−	11.8953i	−0.782221	−	0.443003i
$722$	−0.406965	+	1.78303i	−0.0151457	+	0.0663575i
$723$		0			0
$724$	2.75337	−	12.0633i	0.102328	−	0.448329i
$725$	8.30510	+	10.4143i	0.308444	+	0.386776i
$726$		0			0
$727$	6.52257	−	8.17905i	0.241909	−	0.303344i	−0.646024	−	0.763317i	$-0.723569\pi$
$727$	6.52257	−	8.17905i	0.241909	−	0.303344i	0.887933	+	0.459973i	$0.152141\pi$
$728$	−1.71467	+	1.87900i	−0.0635498	+	0.0696404i
$729$		0			0
$730$	−3.41019	+	4.27625i	−0.126217	+	0.158271i
$731$	−16.1940	−	7.79863i	−0.598958	−	0.288443i
$732$		0			0
$733$	3.68137	−	16.1291i	0.135975	−	0.595743i	−0.860321	−	0.509752i	$-0.829737\pi$
$733$	3.68137	−	16.1291i	0.135975	−	0.595743i	0.996296	−	0.0859913i	$-0.0274057\pi$
$734$	20.5377			0.758061
$735$		0			0
$736$	36.1993			1.33432
$737$	4.99347	−	21.8778i	0.183937	−	0.805881i
$738$		0			0
$739$	−0.255374	−	0.122982i	−0.00939409	−	0.00452396i	0.429181	−	0.903219i	$-0.358802\pi$
$739$	−0.255374	−	0.122982i	−0.00939409	−	0.00452396i	−0.438575	+	0.898695i	$0.644517\pi$
$740$	−0.179126	+	0.224617i	−0.00658482	+	0.00825710i
$741$		0			0
$742$	10.2793	+	5.82156i	0.377364	+	0.213716i
$743$	4.73333	−	5.93541i	0.173649	−	0.217749i	−0.687389	−	0.726289i	$-0.741243\pi$
$743$	4.73333	−	5.93541i	0.173649	−	0.217749i	0.861038	+	0.508540i	$0.169815\pi$
$744$		0			0
$745$	0.611018	+	0.766192i	0.0223859	+	0.0280711i
$746$	−1.23637	+	5.41687i	−0.0452666	+	0.198326i
$747$		0			0
$748$	2.70487	−	11.8508i	0.0988999	−	0.433309i
$749$	42.8151	−	17.2150i	1.56443	−	0.629022i
$750$		0			0
$751$	−32.4467	−	40.6869i	−1.18400	−	1.48469i	−0.837330	−	0.546697i	$-0.815885\pi$
$751$	−32.4467	−	40.6869i	−1.18400	−	1.48469i	−0.346667	−	0.937988i	$-0.612687\pi$
$752$	−3.48852	+	1.67998i	−0.127213	+	0.0612627i
$753$		0			0
$754$	−0.859577			−0.0313040
$755$	15.2589	−	7.34832i	0.555330	−	0.267433i
$756$		0			0
$757$	−3.61912	−	1.74288i	−0.131539	−	0.0633460i	0.366957	−	0.930238i	$-0.380400\pi$
$757$	−3.61912	−	1.74288i	−0.131539	−	0.0633460i	−0.498496	+	0.866892i	$0.666114\pi$
$758$	8.59684	+	4.14002i	0.312251	+	0.150372i
$759$		0			0
$760$	1.84143	+	8.06784i	0.0667958	+	0.292651i
$761$	−42.0151	−	20.2334i	−1.52305	−	0.733461i	−0.529653	−	0.848214i	$-0.677678\pi$
$761$	−42.0151	−	20.2334i	−1.52305	−	0.733461i	−0.993394	+	0.114754i	$0.963392\pi$
$762$		0			0
$763$	32.0591	+	2.13516i	1.16062	+	0.0772980i
$764$	−35.9908	+	17.3322i	−1.30210	+	0.627059i
$765$		0			0
$766$	−8.45845			−0.305616
$767$	−3.32945	+	1.60338i	−0.120220	+	0.0578947i
$768$		0			0
$769$	4.17506	+	18.2921i	0.150556	+	0.659631i	0.992724	+	0.120414i	$0.0384223\pi$
$769$	4.17506	+	18.2921i	0.150556	+	0.659631i	−0.842167	+	0.539216i	$0.818721\pi$
$770$	−2.97025	−	4.27983i	−0.107040	−	0.154234i
$771$		0			0
$772$	22.3755	−	10.7755i	0.805310	−	0.387817i
$773$	3.49156	−	15.2975i	0.125583	−	0.550213i	−0.872517	−	0.488585i	$-0.837513\pi$
$773$	3.49156	−	15.2975i	0.125583	−	0.550213i	0.998099	−	0.0616288i	$-0.0196295\pi$
$774$		0			0
$775$	−8.01589	−	35.1199i	−0.287939	−	1.26155i
$776$	−0.782694	+	0.981468i	−0.0280971	+	0.0352326i
$777$		0			0
$778$	7.21766	+	9.05066i	0.258766	+	0.324482i
$779$	−27.3167	+	34.2541i	−0.978723	+	1.22728i
$780$		0			0
$781$	−9.05568	+	11.3555i	−0.324038	+	0.406330i
$782$	1.84922	−	8.10197i	0.0661280	−	0.289726i
$783$		0			0
$784$	−11.7006	−	7.69607i	−0.417879	−	0.274860i
$785$	5.55190			0.198156
$786$		0			0
$787$	9.60435	−	12.0435i	0.342358	−	0.429303i	−0.580609	−	0.814183i	$-0.697185\pi$
$787$	9.60435	−	12.0435i	0.342358	−	0.429303i	0.922967	+	0.384879i	$0.125757\pi$
$788$	−1.18573	−	0.571019i	−0.0422400	−	0.0203417i
$789$		0			0
$790$	−0.919359	−	1.15284i	−0.0327093	−	0.0410162i
$791$	−5.87450	+	2.36201i	−0.208873	+	0.0839834i
$792$		0			0
$793$	−0.150968	−	0.661434i	−0.00536103	−	0.0234882i
$794$	−1.01606	−	1.27410i	−0.0360586	−	0.0452161i
$795$		0			0
$796$	16.3870	−	7.89156i	0.580821	−	0.279709i
$797$	8.44242	−	36.9887i	0.299046	−	1.31021i	−0.572505	−	0.819901i	$-0.694028\pi$
$797$	8.44242	−	36.9887i	0.299046	−	1.31021i	0.871551	−	0.490305i	$-0.163115\pi$
$798$		0			0
$799$	0.918696	+	4.02507i	0.0325011	+	0.142397i
$800$	14.0893	+	17.6675i	0.498133	+	0.624639i
$801$		0			0
$802$	−4.62128			−0.163183
$803$	33.2935			1.17490
$804$		0			0
$805$	9.43807	+	13.5993i	0.332648	+	0.479312i
$806$	2.09440	+	1.00861i	0.0737722	+	0.0355268i
$807$		0			0
$808$	9.40234	+	41.1943i	0.330773	+	1.44921i
$809$	7.29576	+	31.9648i	0.256505	+	1.12382i	0.924958	+	0.380069i	$0.124100\pi$
$809$	7.29576	+	31.9648i	0.256505	+	1.12382i	−0.668453	+	0.743754i	$0.733043\pi$
$810$		0			0
$811$	−33.3557	−	16.0632i	−1.17128	−	0.564057i	−0.255918	−	0.966698i	$-0.582378\pi$
$811$	−33.3557	−	16.0632i	−1.17128	−	0.564057i	−0.915358	+	0.402642i	$0.868092\pi$
$812$	−2.23190	−	14.0175i	−0.0783243	−	0.491918i
$813$		0			0
$814$	−0.376264			−0.0131880
$815$	−19.4095			−0.679885
$816$		0			0
$817$	−20.9647	−	26.2889i	−0.733463	−	0.919733i
$818$	−1.25368	−	5.49272i	−0.0438338	−	0.192049i
$819$		0			0
$820$	3.84283	−	16.8365i	0.134197	−	0.587957i
$821$	−23.3386	+	11.2393i	−0.814522	+	0.392253i	−0.794287	−	0.607542i	$-0.792156\pi$
$821$	−23.3386	+	11.2393i	−0.814522	+	0.392253i	−0.0202343	+	0.999795i	$0.506441\pi$
$822$		0			0
$823$	−23.5378	−	29.5155i	−0.820476	−	1.02884i	−0.998991	−	0.0449076i	$-0.985701\pi$
$823$	−23.5378	−	29.5155i	−0.820476	−	1.02884i	0.178515	−	0.983937i	$-0.442871\pi$
$824$	−4.40459	−	19.2978i	−0.153441	−	0.672270i
$825$		0			0
$826$	7.48567	+	10.7861i	0.260460	+	0.375296i
$827$	−12.3433	−	15.4780i	−0.429219	−	0.538223i	0.519448	−	0.854502i	$-0.326138\pi$
$827$	−12.3433	−	15.4780i	−0.429219	−	0.538223i	−0.948666	+	0.316279i	$0.897566\pi$
$828$		0			0
$829$	−20.8686	−	10.0498i	−0.724796	−	0.349043i	0.0348393	−	0.999393i	$-0.488908\pi$
$829$	−20.8686	−	10.0498i	−0.724796	−	0.349043i	−0.759635	+	0.650350i	$0.774622\pi$
$830$	−2.76447	+	3.46654i	−0.0959562	+	0.120325i
$831$		0			0
$832$	0.314956			0.0109191
$833$	−10.7766	+	10.3372i	−0.373386	+	0.358164i
$834$		0			0
$835$	−1.69731	+	7.43639i	−0.0587378	+	0.257347i
$836$	14.1782	−	17.7789i	0.490362	−	0.614895i
$837$		0			0
$838$	−4.91219	+	6.15969i	−0.169689	+	0.212783i
$839$	7.72639	+	9.68859i	0.266745	+	0.334487i	0.897107	−	0.441814i	$-0.145665\pi$
$839$	7.72639	+	9.68859i	0.266745	+	0.334487i	−0.630362	+	0.776301i	$0.717093\pi$
$840$		0			0
$841$	−11.4568	+	14.3663i	−0.395061	+	0.495391i
$842$	−2.99764	−	13.1335i	−0.103306	−	0.452612i
$843$		0			0
$844$	−5.35980	+	23.4828i	−0.184492	+	0.808312i
$845$	−11.0252	+	5.30947i	−0.379279	+	0.182651i
$846$		0			0
$847$	−0.747929	+	2.49813i	−0.0256991	+	0.0858368i
$848$	−3.34038	−	14.6352i	−0.114709	−	0.502573i
$849$		0			0
$850$	4.67400	−	2.25088i	0.160317	−	0.0772045i
$851$	1.19559			0.0409843
$852$		0			0
$853$	−10.0439	+	4.83688i	−0.343896	+	0.165612i	−0.597857	−	0.801603i	$-0.703981\pi$
$853$	−10.0439	+	4.83688i	−0.343896	+	0.165612i	0.253961	+	0.967215i	$0.418267\pi$
$854$	−2.23639	+	0.899204i	−0.0765277	+	0.0307701i
$855$		0			0
$856$	34.0938	+	16.4187i	1.16530	+	0.561180i
$857$	11.1773	+	48.9709i	0.381809	+	1.67282i	0.691810	+	0.722079i	$0.256813\pi$
$857$	11.1773	+	48.9709i	0.381809	+	1.67282i	−0.310001	+	0.950736i	$0.600329\pi$
$858$		0			0
$859$	−4.66353	−	2.24584i	−0.159118	−	0.0766271i	0.352630	−	0.935763i	$-0.385287\pi$
$859$	−4.66353	−	2.24584i	−0.159118	−	0.0766271i	−0.511748	+	0.859136i	$0.671002\pi$
$860$	11.9413	+	5.75061i	0.407194	+	0.196094i
$861$		0			0
$862$	−5.02030	+	2.41765i	−0.170992	+	0.0823454i
$863$	−10.6674			−0.363122			−0.181561	−	0.983380i	$-0.558115\pi$
$863$	−10.6674			−0.363122			−0.181561	+	0.983380i	$0.558115\pi$
$864$		0			0
$865$	−10.9047	+	5.25142i	−0.370771	+	0.178554i
$866$	2.57203	+	3.22522i	0.0874011	+	0.109598i
$867$		0			0
$868$	−11.0097	+	36.7732i	−0.373695	+	1.24816i
$869$	−1.99727	+	8.75061i	−0.0677527	+	0.296844i
$870$		0			0
$871$	0.639179	−	2.80043i	0.0216578	−	0.0948888i
$872$	16.4275	+	20.5994i	0.556304	+	0.697584i
$873$		0			0
$874$	9.69309	−	12.1548i	0.327874	−	0.411141i
$875$	−6.59017	+	22.0116i	−0.222788	+	0.744127i
$876$		0			0
$877$	−0.317596	+	0.398253i	−0.0107244	+	0.0134480i	−0.787165	−	0.616743i	$-0.788452\pi$
$877$	−0.317596	+	0.398253i	−0.0107244	+	0.0134480i	0.776440	+	0.630191i	$0.217023\pi$
$878$	1.38603	+	0.667478i	0.0467763	+	0.0225263i
$879$		0			0
$880$	−1.47307	+	6.45395i	−0.0496572	+	0.217562i
$881$	5.66988			0.191023			0.0955116	−	0.995428i	$-0.469551\pi$
$881$	5.66988			0.191023			0.0955116	+	0.995428i	$0.469551\pi$
$882$		0			0
$883$	−48.0572			−1.61725			−0.808627	−	0.588322i	$-0.799789\pi$
$883$	−48.0572			−1.61725			−0.808627	+	0.588322i	$0.799789\pi$
$884$	0.346231	−	1.51694i	0.0116450	−	0.0510202i
$885$		0			0
$886$	−4.67384	−	2.25080i	−0.157021	−	0.0756172i
$887$	11.8040	−	14.8018i	0.396341	−	0.496996i	−0.543118	−	0.839656i	$-0.682756\pi$
$887$	11.8040	−	14.8018i	0.396341	−	0.496996i	0.939459	+	0.342660i	$0.111328\pi$
$888$		0			0
$889$	−18.0168	−	25.9604i	−0.604266	−	0.870685i
$890$	2.28451	−	2.86469i	0.0765770	−	0.0960246i
$891$		0			0
$892$	−19.7757	−	24.7980i	−0.662141	−	0.830298i
$893$	−1.71865	+	7.52989i	−0.0575123	+	0.251978i
$894$		0			0
$895$	−2.27315	+	9.95931i	−0.0759829	+	0.332903i
$896$	−4.77695	−	30.0017i	−0.159587	−	1.00229i
$897$		0			0
$898$	5.31504	+	6.66485i	0.177365	+	0.222409i
$899$	−25.8878	+	12.4669i	−0.863406	+	0.415795i
$900$		0			0
$901$	−16.0064			−0.533252
$902$	20.3776	−	9.81331i	0.678498	−	0.326748i
$903$		0			0
$904$	−4.67789	−	2.25276i	−0.155584	−	0.0749255i
$905$	6.47366	+	3.11755i	0.215192	+	0.103631i
$906$		0			0
$907$	1.04593	+	4.58254i	0.0347297	+	0.152161i	0.989320	−	0.145762i	$-0.0465634\pi$
$907$	1.04593	+	4.58254i	0.0347297	+	0.152161i	−0.954590	+	0.297923i	$0.903706\pi$
$908$	21.6390	+	10.4208i	0.718116	+	0.345826i
$909$		0			0
$910$	−0.380201	−	0.547830i	−0.0126035	−	0.0181604i
$911$	−21.0104	+	10.1181i	−0.696107	+	0.335227i	−0.748254	−	0.663412i	$-0.769108\pi$
$911$	−21.0104	+	10.1181i	−0.696107	+	0.335227i	0.0521474	+	0.998639i	$0.483393\pi$
$912$		0			0
$913$	26.9894			0.893218
$914$	12.8346	−	6.18079i	0.424529	−	0.204442i
$915$		0			0
$916$	−0.0428528	−	0.187750i	−0.00141589	−	0.00620344i
$917$	26.1079	−	28.6101i	0.862158	−	0.944788i
$918$		0			0
$919$	−11.3190	+	5.45093i	−0.373379	+	0.179810i	−0.611156	−	0.791510i	$-0.709295\pi$
$919$	−11.3190	+	5.45093i	−0.373379	+	0.179810i	0.237778	+	0.971320i	$0.423581\pi$
$920$	−3.02057	+	13.2340i	−0.0995852	+	0.436311i
$921$		0			0
$922$	5.25991	+	23.0452i	0.173226	+	0.758953i
$923$	−1.15915	+	1.45353i	−0.0381540	+	0.0478436i
$924$		0			0
$925$	0.465342	+	0.583520i	0.0153004	+	0.0191860i
$926$	−13.8618	+	17.3822i	−0.455528	+	0.571214i
$927$		0			0
$928$	11.2381	−	14.0922i	0.368910	−	0.462598i
$929$	−2.21011	+	9.68312i	−0.0725113	+	0.317693i	−0.998156	−	0.0607010i	$-0.980666\pi$
$929$	−2.21011	+	9.68312i	−0.0725113	+	0.317693i	0.925645	+	0.378394i	$0.123524\pi$
$930$		0			0
$931$	−26.5543	+	8.67604i	−0.870283	+	0.284346i
$932$	−38.7225			−1.26840
$933$		0			0
$934$	−12.1165	+	15.1936i	−0.396465	+	0.497151i
$935$	6.35964	+	3.06264i	0.207982	+	0.100159i
$936$		0			0
$937$	9.15697	+	11.4825i	0.299145	+	0.375116i	0.908574	−	0.417725i	$-0.137172\pi$
$937$	9.15697	+	11.4825i	0.299145	+	0.375116i	−0.609428	+	0.792841i	$0.708601\pi$
$938$	−10.1827	−	0.678178i	−0.332478	−	0.0221433i
$939$		0			0
$940$	−0.677435	−	2.96804i	−0.0220955	−	0.0968067i
$941$	32.2813	+	40.4794i	1.05234	+	1.31959i	0.945610	+	0.325303i	$0.105466\pi$
$941$	32.2813	+	40.4794i	1.05234	+	1.31959i	0.106729	+	0.994288i	$0.465962\pi$
$942$		0			0
$943$	−64.7503	+	31.1821i	−2.10856	+	1.01543i
$944$	3.71246	−	16.2653i	0.120830	−	0.529392i
$945$		0			0
$946$	3.86255	+	16.9229i	0.125582	+	0.550212i
$947$	−15.8052	−	19.8191i	−0.513601	−	0.644035i	0.455636	−	0.890166i	$-0.349412\pi$
$947$	−15.8052	−	19.8191i	−0.513601	−	0.644035i	−0.969236	+	0.246131i	$0.920841\pi$
$948$		0			0
$949$	4.26167			0.138340
$950$	9.70495			0.314870
$951$		0			0
$952$	−12.2184	−	0.813752i	−0.396000	−	0.0263739i
$953$	−5.98729	−	2.88333i	−0.193948	−	0.0934002i	0.334389	−	0.942435i	$-0.391470\pi$
$953$	−5.98729	−	2.88333i	−0.193948	−	0.0934002i	−0.528337	+	0.849035i	$0.677184\pi$
$954$		0			0
$955$	−5.16177	−	22.6152i	−0.167031	−	0.731811i
$956$	−5.16603	−	22.6339i	−0.167081	−	0.732031i
$957$		0			0
$958$	−10.8537	−	5.22686i	−0.350666	−	0.168872i
$959$	−40.0710	+	43.9115i	−1.29396	+	1.41797i
$960$		0			0
$961$	46.7053			1.50662
$962$	−0.0481629			−0.00155283
$963$		0			0
$964$	−19.9532	−	25.0205i	−0.642649	−	0.805857i
$965$	3.20907	+	14.0599i	0.103304	+	0.452603i
$966$		0			0
$967$	−5.34400	+	23.4136i	−0.171851	+	0.752930i	0.813384	+	0.581727i	$0.197623\pi$
$967$	−5.34400	+	23.4136i	−0.171851	+	0.752930i	−0.985236	+	0.171203i	$0.945234\pi$
$968$	−1.92661	+	0.927808i	−0.0619237	+	0.0298209i
$969$		0			0
$970$	−0.205180	−	0.257287i	−0.00658793	−	0.00826100i
$971$	10.8604	+	47.5825i	0.348526	+	1.52699i	0.780528	+	0.625121i	$0.214950\pi$
$971$	10.8604	+	47.5825i	0.348526	+	1.52699i	−0.432002	+	0.901873i	$0.642193\pi$
$972$		0			0
$973$	37.3196	+	21.1356i	1.19641	+	0.677575i
$974$	10.2567	+	12.8615i	0.328646	+	0.412109i
$975$		0			0
$976$	2.75964	+	1.32897i	0.0883338	+	0.0425393i
$977$	−29.3091	+	36.7524i	−0.937680	+	1.17581i	0.0465497	+	0.998916i	$0.485177\pi$
$977$	−29.3091	+	36.7524i	−0.937680	+	1.17581i	−0.984229	+	0.176897i	$0.943394\pi$
$978$		0			0
$979$	−22.3036			−0.712825
$980$	7.94651	−	7.62254i	0.253842	−	0.243493i
$981$		0			0
$982$	4.24302	−	18.5899i	0.135400	−	0.593227i
$983$	8.95159	−	11.2249i	0.285512	−	0.358020i	−0.618307	−	0.785937i	$-0.712181\pi$
$983$	8.95159	−	11.2249i	0.285512	−	0.358020i	0.903818	+	0.427917i	$0.140752\pi$
$984$		0			0
$985$	0.476489	−	0.597498i	0.0151822	−	0.0190379i
$986$	−2.57995	−	3.23516i	−0.0821625	−	0.103028i
$987$		0			0
$988$	1.81485	−	2.27575i	0.0577379	−	0.0724011i
$989$	−12.2734	−	53.7731i	−0.390270	−	1.70989i
$990$		0			0
$991$	6.56416	−	28.7595i	0.208518	−	0.913575i	−0.757037	−	0.653373i	$-0.773354\pi$
$991$	6.56416	−	28.7595i	0.208518	−	0.913575i	0.965554	−	0.260202i	$-0.0837893\pi$
$992$	−43.9178	+	21.1497i	−1.39439	+	0.671503i
$993$		0			0
$994$	5.74747	+	3.25502i	0.182299	+	0.103243i
$995$	2.35021	+	10.2969i	0.0745067	+	0.326435i
$996$		0			0
$997$	5.41116	−	2.60588i	0.171373	−	0.0825290i	−0.346230	−	0.938150i	$-0.612538\pi$
$997$	5.41116	−	2.60588i	0.171373	−	0.0825290i	0.517604	+	0.855620i	$0.326824\pi$
$998$	−21.3115			−0.674605
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.64.4		36
3.2	odd	2		147.2.i.b.64.3	✓	36
49.36	even	7	inner	441.2.u.d.379.4		36
147.92	odd	14		7203.2.a.h.1.10		18
147.104	even	14		7203.2.a.g.1.10		18
147.134	odd	14		147.2.i.b.85.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.64.3	✓	36	3.2	odd	2
147.2.i.b.85.3	yes	36	147.134	odd	14
441.2.u.d.64.4		36	1.1	even	1	trivial
441.2.u.d.379.4		36	49.36	even	7	inner
7203.2.a.g.1.10		18	147.104	even	14
7203.2.a.h.1.10		18	147.92	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.132418 - 0.580160i) q^{2} +(1.48289 + 0.714121i) q^{4} +(-0.595901 + 0.747236i) q^{5} +(-0.416022 - 2.61284i) q^{7} +(1.35272 - 1.69625i) q^{8} +O(q^{10})\)	\(q+(0.132418 - 0.580160i) q^{2} +(1.48289 + 0.714121i) q^{4} +(-0.595901 + 0.747236i) q^{5} +(-0.416022 - 2.61284i) q^{7} +(1.35272 - 1.69625i) q^{8} +(0.354609 + 0.444665i) q^{10} +(0.770373 - 3.37522i) q^{11} +(0.0986100 - 0.432039i) q^{13} +(-1.57095 - 0.104627i) q^{14} +(1.24740 + 1.56420i) q^{16} +(1.92202 - 0.925595i) q^{17} +3.99082 q^{19} +(-1.41727 + 0.682522i) q^{20} +(-1.85616 - 0.893879i) q^{22} +(5.89801 + 2.84033i) q^{23} +(0.909341 + 3.98408i) q^{25} +(-0.237594 - 0.114419i) q^{26} +(1.24897 - 4.17163i) q^{28} +(2.93677 - 1.41427i) q^{29} -8.81506 q^{31} +(4.98213 - 2.39927i) q^{32} +(-0.282484 - 1.23764i) q^{34} +(2.20032 + 1.24613i) q^{35} +(0.164550 - 0.0792429i) q^{37} +(0.528456 - 2.31531i) q^{38} +(0.461417 + 2.02160i) q^{40} +(-6.84489 + 8.58321i) q^{41} +(-5.25323 - 6.58735i) q^{43} +(3.55269 - 4.45494i) q^{44} +(2.42885 - 3.04568i) q^{46} +(-0.430650 + 1.88680i) q^{47} +(-6.65385 + 2.17400i) q^{49} +2.43182 q^{50} +(0.454755 - 0.570245i) q^{52} +(-6.76016 - 3.25552i) q^{53} +(2.06302 + 2.58695i) q^{55} +(-4.99480 - 2.82875i) q^{56} +(-0.431624 - 1.89107i) q^{58} +(-5.19927 - 6.51968i) q^{59} +(1.37935 - 0.664259i) q^{61} +(-1.16727 + 5.11415i) q^{62} +(0.158151 + 0.692903i) q^{64} +(0.264073 + 0.331137i) q^{65} +6.48189 q^{67} +3.51112 q^{68} +(1.01431 - 1.11153i) q^{70} +(-3.77982 - 1.82027i) q^{71} +(2.13993 + 9.37566i) q^{73} +(-0.0241843 - 0.105958i) q^{74} +(5.91794 + 2.84993i) q^{76} +(-9.13941 - 0.608691i) q^{77} -2.59260 q^{79} -1.91215 q^{80} +(4.07325 + 5.10770i) q^{82} +(1.73474 + 7.60038i) q^{83} +(-0.453694 + 1.98776i) q^{85} +(-4.51734 + 2.17543i) q^{86} +(-4.68314 - 5.87247i) q^{88} +(-1.43356 - 6.28082i) q^{89} +(-1.16987 - 0.0779142i) q^{91} +(6.71774 + 8.42377i) q^{92} +(1.03762 + 0.499692i) q^{94} +(-2.37814 + 2.98209i) q^{95} -0.578609 q^{97} +(0.380179 + 4.14817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

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