LMFDB - Embedded newform 441.2.u.d.190.5

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			190.5
Character	$\chi$	$=$	441.190
Dual form			441.2.u.d.253.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.894323 - 1.12145i) q^{2} +(-0.0127847 - 0.0560133i) q^{4} +(-1.03743 - 0.499602i) q^{5} +(2.02504 + 1.70270i) q^{7} +(2.51042 + 1.20895i) q^{8} +O(q^{10})$	\(q+(0.894323 - 1.12145i) q^{2} +(-0.0127847 - 0.0560133i) q^{4} +(-1.03743 - 0.499602i) q^{5} +(2.02504 + 1.70270i) q^{7} +(2.51042 + 1.20895i) q^{8} +(-1.48808 + 0.716620i) q^{10} +(3.40939 - 4.27524i) q^{11} +(-2.42908 + 3.04598i) q^{13} +(3.72053 - 0.748207i) q^{14} +(3.70443 - 1.78396i) q^{16} +(-0.517762 + 2.26846i) q^{17} +5.93712 q^{19} +(-0.0147211 + 0.0644973i) q^{20} +(-1.74535 - 7.64689i) q^{22} +(-1.30327 - 5.71000i) q^{23} +(-2.29078 - 2.87255i) q^{25} +(1.24351 + 5.44817i) q^{26} +(0.0694846 - 0.135198i) q^{28} +(-1.30216 + 5.70515i) q^{29} +3.41224 q^{31} +(0.0722988 - 0.316762i) q^{32} +(2.08091 + 2.60938i) q^{34} +(-1.25017 - 2.77816i) q^{35} +(1.54018 - 6.74795i) q^{37} +(5.30970 - 6.65815i) q^{38} +(-2.00040 - 2.50842i) q^{40} +(-8.31265 - 4.00316i) q^{41} +(-3.93366 + 1.89435i) q^{43} +(-0.283058 - 0.136314i) q^{44} +(-7.56900 - 3.64504i) q^{46} +(-4.53196 + 5.68289i) q^{47} +(1.20159 + 6.89610i) q^{49} -5.27011 q^{50} +(0.201670 + 0.0971192i) q^{52} +(1.38065 + 6.04902i) q^{53} +(-5.67293 + 2.73194i) q^{55} +(3.02521 + 6.72268i) q^{56} +(5.23346 + 6.56255i) q^{58} +(-3.94095 + 1.89786i) q^{59} +(-0.988544 + 4.33109i) q^{61} +(3.05164 - 3.82664i) q^{62} +(4.83652 + 6.06480i) q^{64} +(4.04179 - 1.94642i) q^{65} -12.5372 q^{67} +0.133683 q^{68} +(-4.23361 - 1.08257i) q^{70} +(-0.126470 - 0.554102i) q^{71} +(-9.13117 - 11.4501i) q^{73} +(-6.19004 - 7.76207i) q^{74} +(-0.0759041 - 0.332557i) q^{76} +(14.1836 - 2.85236i) q^{77} +9.54103 q^{79} -4.73437 q^{80} +(-11.9235 + 5.74206i) q^{82} +(-2.58004 - 3.23527i) q^{83} +(1.67047 - 2.09471i) q^{85} +(-1.39355 + 6.10555i) q^{86} +(13.7276 - 6.61085i) q^{88} +(1.54504 + 1.93742i) q^{89} +(-10.1054 + 2.03222i) q^{91} +(-0.303174 + 0.146001i) q^{92} +(2.32002 + 10.1647i) q^{94} +(-6.15937 - 2.96619i) q^{95} +11.7472 q^{97} +(8.80821 + 4.81982i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.894323	−	1.12145i	0.632382	−	0.792982i	−0.357645	−	0.933857i	$-0.616420\pi$
$2$	0.894323	−	1.12145i	0.632382	−	0.792982i	0.990027	+	0.140876i	$0.0449918\pi$
$3$		0			0
$3$		0			0
$4$	−0.0127847	−	0.0560133i	−0.00639233	−	0.0280066i
$5$	−1.03743	−	0.499602i	−0.463954	−	0.223429i	0.187278	−	0.982307i	$-0.440033\pi$
$5$	−1.03743	−	0.499602i	−0.463954	−	0.223429i	−0.651233	+	0.758878i	$0.725748\pi$
$6$		0			0
$7$	2.02504	+	1.70270i	0.765394	+	0.643562i
$7$	2.02504	+	1.70270i	0.765394	+	0.643562i
$8$	2.51042	+	1.20895i	0.887567	+	0.427430i
$9$		0			0
$10$	−1.48808	+	0.716620i	−0.470571	+	0.226615i
$11$	3.40939	−	4.27524i	1.02797	−	1.28903i	0.0714255	−	0.997446i	$-0.477245\pi$
$11$	3.40939	−	4.27524i	1.02797	−	1.28903i	0.956544	−	0.291587i	$-0.0941834\pi$
$12$		0			0
$13$	−2.42908	+	3.04598i	−0.673707	+	0.844802i	−0.994758	−	0.102260i	$-0.967393\pi$
$13$	−2.42908	+	3.04598i	−0.673707	+	0.844802i	0.321051	+	0.947062i	$0.395964\pi$
$14$	3.72053	−	0.748207i	0.994354	−	0.199967i
$15$		0			0
$16$	3.70443	−	1.78396i	0.926107	−	0.445990i
$17$	−0.517762	+	2.26846i	−0.125576	+	0.550183i	0.872524	+	0.488570i	$0.162481\pi$
$17$	−0.517762	+	2.26846i	−0.125576	+	0.550183i	−0.998100	+	0.0616126i	$0.980376\pi$
$18$		0			0
$19$	5.93712			1.36207			0.681034	−	0.732252i	$-0.261531\pi$
$19$	5.93712			1.36207			0.681034	+	0.732252i	$0.261531\pi$
$20$	−0.0147211	+	0.0644973i	−0.00329174	+	0.0144220i
$21$		0			0
$22$	−1.74535	−	7.64689i	−0.372110	−	1.63032i
$23$	−1.30327	−	5.71000i	−0.271751	−	1.19062i	−0.907945	−	0.419089i	$-0.862349\pi$
$23$	−1.30327	−	5.71000i	−0.271751	−	1.19062i	0.636194	−	0.771529i	$-0.280508\pi$
$24$		0			0
$25$	−2.29078	−	2.87255i	−0.458156	−	0.574510i
$26$	1.24351	+	5.44817i	0.243872	+	1.06847i
$27$		0			0
$28$	0.0694846	−	0.135198i	0.0131313	−	0.0255500i
$29$	−1.30216	+	5.70515i	−0.241806	+	1.05942i	0.697567	+	0.716520i	$0.254266\pi$
$29$	−1.30216	+	5.70515i	−0.241806	+	1.05942i	−0.939372	+	0.342899i	$0.888591\pi$
$30$		0			0
$31$	3.41224			0.612856			0.306428	−	0.951894i	$-0.400866\pi$
$31$	3.41224			0.612856			0.306428	+	0.951894i	$0.400866\pi$
$32$	0.0722988	−	0.316762i	0.0127807	−	0.0559961i
$33$		0			0
$34$	2.08091	+	2.60938i	0.356873	+	0.447505i
$35$	−1.25017	−	2.77816i	−0.211318	−	0.469594i
$36$		0			0
$37$	1.54018	−	6.74795i	0.253203	−	1.10936i	−0.675157	−	0.737674i	$-0.735924\pi$
$37$	1.54018	−	6.74795i	0.253203	−	1.10936i	0.928360	−	0.371682i	$-0.121219\pi$
$38$	5.30970	−	6.65815i	0.861347	−	1.08010i
$39$		0			0
$40$	−2.00040	−	2.50842i	−0.316291	−	0.396616i
$41$	−8.31265	−	4.00316i	−1.29822	−	0.625189i	−0.348210	−	0.937416i	$-0.613211\pi$
$41$	−8.31265	−	4.00316i	−1.29822	−	0.625189i	−0.950007	+	0.312228i	$0.898925\pi$
$42$		0			0
$43$	−3.93366	+	1.89435i	−0.599878	+	0.288886i	−0.709074	−	0.705134i	$-0.750887\pi$
$43$	−3.93366	+	1.89435i	−0.599878	+	0.288886i	0.109196	+	0.994020i	$0.465172\pi$
$44$	−0.283058	−	0.136314i	−0.0426726	−	0.0205500i
$45$		0			0
$46$	−7.56900	−	3.64504i	−1.11599	−	0.537432i
$47$	−4.53196	+	5.68289i	−0.661054	+	0.828935i	−0.993458	−	0.114202i	$-0.963569\pi$
$47$	−4.53196	+	5.68289i	−0.661054	+	0.828935i	0.332404	+	0.943137i	$0.392140\pi$
$48$		0			0
$49$	1.20159	+	6.89610i	0.171656	+	0.985157i
$50$	−5.27011			−0.745306
$51$		0			0
$52$	0.201670	+	0.0971192i	0.0279666	+	0.0134680i
$53$	1.38065	+	6.04902i	0.189647	+	0.830897i	0.976802	+	0.214143i	$0.0686958\pi$
$53$	1.38065	+	6.04902i	0.189647	+	0.830897i	−0.787155	+	0.616755i	$0.788447\pi$
$54$		0			0
$55$	−5.67293	+	2.73194i	−0.764938	+	0.368375i
$56$	3.02521	+	6.72268i	0.404261	+	0.898357i
$57$		0			0
$58$	5.23346	+	6.56255i	0.687187	+	0.861705i
$59$	−3.94095	+	1.89786i	−0.513068	+	0.247080i	−0.672458	−	0.740135i	$-0.734761\pi$
$59$	−3.94095	+	1.89786i	−0.513068	+	0.247080i	0.159390	+	0.987216i	$0.449047\pi$
$60$		0			0
$61$	−0.988544	+	4.33109i	−0.126570	+	0.554540i	0.871384	+	0.490602i	$0.163223\pi$
$61$	−0.988544	+	4.33109i	−0.126570	+	0.554540i	−0.997954	+	0.0639378i	$0.979634\pi$
$62$	3.05164	−	3.82664i	0.387559	−	0.485984i
$63$		0			0
$64$	4.83652	+	6.06480i	0.604565	+	0.758100i
$65$	4.04179	−	1.94642i	0.501322	−	0.241424i
$66$		0			0
$67$	−12.5372			−1.53166			−0.765829	−	0.643044i	$-0.777671\pi$
$67$	−12.5372			−1.53166			−0.765829	+	0.643044i	$0.777671\pi$
$68$	0.133683			0.0162115
$69$		0			0
$70$	−4.23361	−	1.08257i	−0.506013	−	0.129392i
$71$	−0.126470	−	0.554102i	−0.0150092	−	0.0657598i	0.966869	−	0.255274i	$-0.0821658\pi$
$71$	−0.126470	−	0.554102i	−0.0150092	−	0.0657598i	−0.981878	+	0.189514i	$0.939309\pi$
$72$		0			0
$73$	−9.13117	−	11.4501i	−1.06872	−	1.34014i	−0.937188	−	0.348824i	$-0.886581\pi$
$73$	−9.13117	−	11.4501i	−1.06872	−	1.34014i	−0.131534	−	0.991312i	$-0.541990\pi$
$74$	−6.19004	−	7.76207i	−0.719578	−	0.902322i
$75$		0			0
$76$	−0.0759041	−	0.332557i	−0.00870679	−	0.0381470i
$77$	14.1836	−	2.85236i	1.61637	−	0.325056i
$78$		0			0
$79$	9.54103			1.07345			0.536725	−	0.843757i	$-0.319661\pi$
$79$	9.54103			1.07345			0.536725	+	0.843757i	$0.319661\pi$
$80$	−4.73437			−0.529319
$81$		0			0
$82$	−11.9235	+	5.74206i	−1.31673	+	0.634105i
$83$	−2.58004	−	3.23527i	−0.283196	−	0.355117i	0.619804	−	0.784756i	$-0.287212\pi$
$83$	−2.58004	−	3.23527i	−0.283196	−	0.355117i	−0.903000	+	0.429640i	$0.858641\pi$
$84$		0			0
$85$	1.67047	−	2.09471i	0.181188	−	0.227203i
$86$	−1.39355	+	6.10555i	−0.150271	+	0.658379i
$87$		0			0
$88$	13.7276	−	6.61085i	1.46336	−	0.704719i
$89$	1.54504	+	1.93742i	0.163774	+	0.205366i	0.856946	−	0.515406i	$-0.172359\pi$
$89$	1.54504	+	1.93742i	0.163774	+	0.205366i	−0.693172	+	0.720772i	$0.743787\pi$
$90$		0			0
$91$	−10.1054	+	2.03222i	−1.05933	+	0.213034i
$92$	−0.303174	+	0.146001i	−0.0316081	+	0.0152217i
$93$		0			0
$94$	2.32002	+	10.1647i	0.239292	+	1.04841i
$95$	−6.15937	−	2.96619i	−0.631938	−	0.304325i
$96$		0			0
$97$	11.7472			1.19275			0.596374	−	0.802707i	$-0.296608\pi$
$97$	11.7472			1.19275			0.596374	+	0.802707i	$0.296608\pi$
$98$	8.80821	+	4.81982i	0.889764	+	0.486875i
$99$		0			0
$100$	−0.131614	+	0.165039i	−0.0131614	+	0.0165039i
$101$	−7.69817	−	3.70724i	−0.765997	−	0.368885i	0.00973082	−	0.999953i	$-0.496903\pi$
$101$	−7.69817	−	3.70724i	−0.765997	−	0.368885i	−0.775727	+	0.631068i	$0.782617\pi$
$102$		0			0
$103$	−1.17606	−	0.566358i	−0.115880	−	0.0558049i	0.375046	−	0.927006i	$-0.377627\pi$
$103$	−1.17606	−	0.566358i	−0.115880	−	0.0558049i	−0.490926	+	0.871201i	$0.663341\pi$
$104$	−9.78046	+	4.71002i	−0.959053	+	0.461856i
$105$		0			0
$106$	8.01840	+	3.86146i	0.778816	+	0.375058i
$107$	−5.78142	−	7.24967i	−0.558911	−	0.700852i	0.419445	−	0.907781i	$-0.362225\pi$
$107$	−5.78142	−	7.24967i	−0.558911	−	0.700852i	−0.978356	+	0.206929i	$0.933653\pi$
$108$		0			0
$109$	−0.372169	+	0.466685i	−0.0356473	+	0.0447004i	−0.799336	−	0.600885i	$-0.794815\pi$
$109$	−0.372169	+	0.466685i	−0.0356473	+	0.0447004i	0.763688	+	0.645585i	$0.223386\pi$
$110$	−2.00971	+	8.80512i	−0.191619	+	0.839536i
$111$		0			0
$112$	10.5392	+	2.69496i	0.995859	+	0.254649i
$113$	−0.865882	−	1.08578i	−0.0814554	−	0.102142i	0.739434	−	0.673229i	$-0.235093\pi$
$113$	−0.865882	−	1.08578i	−0.0814554	−	0.102142i	−0.820889	+	0.571087i	$0.806522\pi$
$114$		0			0
$115$	−1.50067	+	6.57487i	−0.139938	+	0.613109i
$116$	0.336212			0.0312165
$117$		0			0
$118$	−1.39613	+	6.11686i	−0.128525	+	0.563103i
$119$	−4.91101	+	3.71214i	−0.450192	+	0.340291i
$120$		0			0
$121$	−4.20600	−	18.4277i	−0.382364	−	1.67525i
$122$	3.97301	+	4.98200i	0.359699	+	0.451049i
$123$		0			0
$124$	−0.0436243	−	0.191131i	−0.00391758	−	0.0171640i
$125$	2.22253	+	9.73753i	0.198789	+	0.870951i
$126$		0			0
$127$	−0.625337	+	2.73978i	−0.0554897	+	0.243116i	−0.995065	−	0.0992264i	$-0.968363\pi$
$127$	−0.625337	+	2.73978i	−0.0554897	+	0.243116i	0.939575	+	0.342343i	$0.111220\pi$
$128$	11.7766			1.04091
$129$		0			0
$130$	1.43186	−	6.27338i	0.125582	−	0.550211i
$131$	3.05281	−	1.47015i	0.266725	−	0.128448i	−0.295742	−	0.955268i	$-0.595567\pi$
$131$	3.05281	−	1.47015i	0.266725	−	0.128448i	0.562467	+	0.826820i	$0.309852\pi$
$132$		0			0
$133$	12.0229	+	10.1092i	1.04252	+	0.876575i
$134$	−11.2123	+	14.0597i	−0.968593	+	1.21458i
$135$		0			0
$136$	−4.04227	+	5.06884i	−0.346621	+	0.434650i
$137$	−7.38767	+	3.55771i	−0.631171	+	0.303956i	−0.721982	−	0.691912i	$-0.756769\pi$
$137$	−7.38767	+	3.55771i	−0.631171	+	0.303956i	0.0908104	+	0.995868i	$0.471054\pi$
$138$		0			0
$139$	−5.10671	−	2.45926i	−0.433146	−	0.208592i	0.204589	−	0.978848i	$-0.434414\pi$
$139$	−5.10671	−	2.45926i	−0.433146	−	0.208592i	−0.637735	+	0.770256i	$0.720128\pi$
$140$	−0.139631	+	0.105544i	−0.0118009	+	0.00892011i
$141$		0			0
$142$	−0.734500	−	0.353716i	−0.0616379	−	0.0296832i
$143$	4.74058	+	20.7698i	0.396427	+	1.73686i
$144$		0			0
$145$	4.20121	−	5.26815i	0.348891	−	0.437496i
$146$	−21.0069			−1.73854
$147$		0			0
$148$	−0.397665			−0.0326879
$149$	5.31975	−	6.67076i	0.435811	−	0.546490i	−0.514623	−	0.857417i	$-0.672068\pi$
$149$	5.31975	−	6.67076i	0.435811	−	0.546490i	0.950434	+	0.310927i	$0.100639\pi$
$150$		0			0
$151$	0.0531802	+	0.232998i	0.00432774	+	0.0189611i	0.977046	−	0.213030i	$-0.0683332\pi$
$151$	0.0531802	+	0.232998i	0.00432774	+	0.0189611i	−0.972718	+	0.231991i	$0.925476\pi$
$152$	14.9047	+	7.17770i	1.20893	+	0.582189i
$153$		0			0
$154$	9.48598	−	18.4571i	0.764402	−	1.48732i
$155$	−3.53997	−	1.70476i	−0.284337	−	0.136930i
$156$		0			0
$157$	−4.62961	+	2.22950i	−0.369483	+	0.177934i	−0.609406	−	0.792858i	$-0.708592\pi$
$157$	−4.62961	+	2.22950i	−0.369483	+	0.177934i	0.239923	+	0.970792i	$0.422878\pi$
$158$	8.53276	−	10.6997i	0.678830	−	0.851226i
$159$		0			0
$160$	−0.233260	+	0.292499i	−0.0184408	+	0.0231241i
$161$	7.08327	−	13.7821i	0.558240	−	1.08618i
$162$		0			0
$163$	−16.2425	+	7.82198i	−1.27221	+	0.612665i	−0.943377	−	0.331722i	$-0.892370\pi$
$163$	−16.2425	+	7.82198i	−1.27221	+	0.612665i	−0.328835	+	0.944387i	$0.606656\pi$
$164$	−0.117956	+	0.516798i	−0.00921079	+	0.0403551i
$165$		0			0
$166$	−5.93556			−0.460689
$167$	0.863100	−	3.78149i	0.0667887	−	0.292620i	−0.930492	−	0.366311i	$-0.880621\pi$
$167$	0.863100	−	3.78149i	0.0667887	−	0.292620i	0.997281	+	0.0736907i	$0.0234778\pi$
$168$		0			0
$169$	−0.484743	−	2.12380i	−0.0372879	−	0.163369i
$170$	−0.855157	−	3.74669i	−0.0655875	−	0.287358i
$171$		0			0
$172$	0.156400	+	0.196119i	0.0119254	+	0.0149539i
$173$	−2.88333	−	12.6327i	−0.219216	−	0.960446i	−0.958059	−	0.286569i	$-0.907485\pi$
$173$	−2.88333	−	12.6327i	−0.219216	−	0.960446i	0.738844	−	0.673877i	$-0.235372\pi$
$174$		0			0
$175$	0.252173	−	9.71756i	0.0190625	−	0.734579i
$176$	5.00299	−	21.9195i	0.377115	−	1.65225i
$177$		0			0
$178$	3.55447			0.266419
$179$	1.41639	−	6.20563i	0.105866	−	0.463831i	−0.894009	−	0.448049i	$-0.852119\pi$
$179$	1.41639	−	6.20563i	0.105866	−	0.463831i	0.999875	−	0.0157819i	$-0.00502375\pi$
$180$		0			0
$181$	−15.6172	−	19.5833i	−1.16081	−	1.45561i	−0.865989	−	0.500064i	$-0.833310\pi$
$181$	−15.6172	−	19.5833i	−1.16081	−	1.45561i	−0.294825	−	0.955551i	$-0.595261\pi$
$182$	−6.75847	+	13.1501i	−0.500971	+	0.974751i
$183$		0			0
$184$	3.63138	−	15.9101i	0.267709	−	1.17291i
$185$	−4.96912	+	6.23108i	−0.365337	+	0.458118i
$186$		0			0
$187$	7.93297	+	9.94763i	0.580116	+	0.727443i
$188$	0.376257	+	0.181196i	0.0274414	+	0.0132151i
$189$		0			0
$190$	−8.83489	+	4.25466i	−0.640950	+	0.308665i
$191$	24.3917	+	11.7464i	1.76492	+	0.849940i	0.969955	+	0.243283i	$0.0782244\pi$
$191$	24.3917	+	11.7464i	1.76492	+	0.849940i	0.794964	+	0.606657i	$0.207490\pi$
$192$		0			0
$193$	13.0611	+	6.28991i	0.940161	+	0.452758i	0.840226	−	0.542236i	$-0.182422\pi$
$193$	13.0611	+	6.28991i	0.940161	+	0.452758i	0.0999350	+	0.994994i	$0.468137\pi$
$194$	10.5058	−	13.1738i	0.754272	−	0.945827i
$195$		0			0
$196$	0.370911	−	0.155470i	0.0264936	−	0.0111050i
$197$	−5.61172			−0.399818			−0.199909	−	0.979814i	$-0.564065\pi$
$197$	−5.61172			−0.399818			−0.199909	+	0.979814i	$0.564065\pi$
$198$		0			0
$199$	12.6258	+	6.08025i	0.895017	+	0.431017i	0.824086	−	0.566464i	$-0.191689\pi$
$199$	12.6258	+	6.08025i	0.895017	+	0.431017i	0.0709301	+	0.997481i	$0.477403\pi$
$200$	−2.27804	−	9.98075i	−0.161082	−	0.705746i
$201$		0			0
$202$	−11.0421	+	5.31761i	−0.776921	+	0.374145i
$203$	−12.3511	+	9.33597i	−0.866878	+	0.655256i
$204$		0			0
$205$	6.62384	+	8.30603i	0.462629	+	0.580118i
$206$	−1.68691	+	0.812375i	−0.117533	+	0.0566008i
$207$		0			0
$208$	−3.56448	+	15.6170i	−0.247152	+	1.08284i
$209$	20.2419	−	25.3826i	1.40016	−	1.75575i
$210$		0			0
$211$	4.13552	+	5.18578i	0.284701	+	0.357004i	0.903532	−	0.428520i	$-0.140965\pi$
$211$	4.13552	+	5.18578i	0.284701	+	0.357004i	−0.618831	+	0.785524i	$0.712394\pi$
$212$	0.321174	−	0.154669i	0.0220584	−	0.0106227i
$213$		0			0
$214$	−13.3006			−0.909208
$215$	5.02734			0.342862
$216$		0			0
$217$	6.90993	+	5.81003i	0.469076	+	0.394411i
$218$	0.190523	+	0.834735i	0.0129038	+	0.0565354i
$219$		0			0
$220$	0.225551	+	0.282833i	0.0152067	+	0.0190686i
$221$	−5.65199	−	7.08738i	−0.380194	−	0.476749i
$222$		0			0
$223$	−4.94505	−	21.6657i	−0.331145	−	1.45084i	−0.816916	−	0.576756i	$-0.804318\pi$
$223$	−4.94505	−	21.6657i	−0.331145	−	1.45084i	0.485771	−	0.874086i	$-0.338539\pi$
$224$	0.685760	−	0.518353i	0.0458193	−	0.0346339i
$225$		0			0
$226$	−1.99202			−0.132507
$227$	−10.5400			−0.699567			−0.349784	−	0.936831i	$-0.613745\pi$
$227$	−10.5400			−0.699567			−0.349784	+	0.936831i	$0.613745\pi$
$228$		0			0
$229$	9.49863	−	4.57430i	0.627687	−	0.302278i	−0.0928651	−	0.995679i	$-0.529603\pi$
$229$	9.49863	−	4.57430i	0.627687	−	0.302278i	0.720553	+	0.693400i	$0.243888\pi$
$230$	6.03127	+	7.56297i	0.397690	+	0.498688i
$231$		0			0
$232$	−10.1662	+	12.7481i	−0.667446	+	0.836951i
$233$	3.06082	−	13.4103i	0.200521	−	0.878541i	−0.770099	−	0.637924i	$-0.779793\pi$
$233$	3.06082	−	13.4103i	0.200521	−	0.878541i	0.970620	−	0.240617i	$-0.0773496\pi$
$234$		0			0
$235$	7.54079	−	3.63145i	0.491907	−	0.236890i
$236$	0.156689	+	0.196482i	0.0101996	+	0.0127899i
$237$		0			0
$238$	−0.229070	+	8.82728i	−0.0148484	+	0.572188i
$239$	−6.94644	+	3.34523i	−0.449328	+	0.216385i	−0.644842	−	0.764316i	$-0.723077\pi$
$239$	−6.94644	+	3.34523i	−0.449328	+	0.216385i	0.195514	+	0.980701i	$0.437363\pi$
$240$		0			0
$241$	−6.35492	−	27.8427i	−0.409356	−	1.79351i	−0.587194	−	0.809447i	$-0.699767\pi$
$241$	−6.35492	−	27.8427i	−0.409356	−	1.79351i	0.177837	−	0.984060i	$-0.443090\pi$
$242$	−24.4272	−	11.7635i	−1.57024	−	0.756188i
$243$		0			0
$244$	0.255237			0.0163399
$245$	2.19873	−	7.75456i	0.140472	−	0.495421i
$246$		0			0
$247$	−14.4218	+	18.0843i	−0.917635	+	1.15068i
$248$	8.56615	+	4.12524i	0.543951	+	0.261953i
$249$		0			0
$250$	12.9078	+	6.21606i	0.816359	+	0.393138i
$251$	−2.90959	+	1.40119i	−0.183652	+	0.0884420i	−0.523450	−	0.852056i	$-0.675355\pi$
$251$	−2.90959	+	1.40119i	−0.183652	+	0.0884420i	0.339798	+	0.940498i	$0.389641\pi$
$252$		0			0
$253$	−28.8550	−	13.8958i	−1.81410	−	0.873623i
$254$	2.51326	+	3.15153i	0.157696	+	0.197745i
$255$		0			0
$256$	0.859021	−	1.07718i	0.0536888	−	0.0673237i
$257$	−3.64442	+	15.9672i	−0.227333	+	0.996009i	0.724472	+	0.689304i	$0.242084\pi$
$257$	−3.64442	+	15.9672i	−0.227333	+	0.996009i	−0.951805	+	0.306705i	$0.900774\pi$
$258$		0			0
$259$	14.6087	−	11.0424i	0.907739	−	0.686143i
$260$	−0.160698	−	0.201509i	−0.00996609	−	0.0124971i
$261$		0			0
$262$	1.08150	−	4.73835i	0.0668151	−	0.292736i
$263$	31.4275			1.93790			0.968950	−	0.247257i	$-0.0795293\pi$
$263$	31.4275			1.93790			0.968950	+	0.247257i	$0.0795293\pi$
$264$		0			0
$265$	1.58977	−	6.96524i	0.0976588	−	0.427871i
$266$	22.0892	−	4.44219i	1.35438	−	0.272368i
$267$		0			0
$268$	0.160283	+	0.702247i	0.00979087	+	0.0428966i
$269$	14.0805	+	17.6564i	0.858503	+	1.07653i	0.996289	+	0.0860670i	$0.0274299\pi$
$269$	14.0805	+	17.6564i	0.858503	+	1.07653i	−0.137786	+	0.990462i	$0.543999\pi$
$270$		0			0
$271$	−1.96958	−	8.62928i	−0.119643	−	0.524191i	−0.998859	−	0.0477666i	$-0.984790\pi$
$271$	−1.96958	−	8.62928i	−0.119643	−	0.524191i	0.879215	−	0.476425i	$-0.158068\pi$
$272$	2.12883	+	9.32703i	0.129079	+	0.565534i
$273$		0			0
$274$	−2.61718	+	11.4666i	−0.158110	+	0.692724i
$275$	−20.0910			−1.21153
$276$		0			0
$277$	−4.44792	+	19.4876i	−0.267250	+	1.17090i	0.645949	+	0.763381i	$0.276462\pi$
$277$	−4.44792	+	19.4876i	−0.267250	+	1.17090i	−0.913198	+	0.407516i	$0.866395\pi$
$278$	−7.32498	+	3.52753i	−0.439323	+	0.211567i
$279$		0			0
$280$	0.220207	−	8.48574i	0.0131599	−	0.507120i
$281$	4.54573	−	5.70016i	0.271175	−	0.340043i	−0.627533	−	0.778590i	$-0.715935\pi$
$281$	4.54573	−	5.70016i	0.271175	−	0.340043i	0.898708	+	0.438547i	$0.144507\pi$
$282$		0			0
$283$	−6.94160	+	8.70449i	−0.412635	+	0.517428i	−0.944103	−	0.329650i	$-0.893069\pi$
$283$	−6.94160	+	8.70449i	−0.412635	+	0.517428i	0.531468	+	0.847078i	$0.321641\pi$
$284$	−0.0294202	+	0.0141680i	−0.00174577	+	0.000840717i
$285$		0			0
$286$	27.5318	+	13.2586i	1.62799	+	0.784000i
$287$	−10.0173	−	22.2606i	−0.591301	−	1.31400i
$288$		0			0
$289$	10.4386	+	5.02698i	0.614037	+	0.295705i
$290$	−2.15071	−	9.42285i	−0.126294	−	0.553329i
$291$		0			0
$292$	−0.524620	+	0.657853i	−0.0307011	+	0.0384979i
$293$	5.67555			0.331569			0.165785	−	0.986162i	$-0.446984\pi$
$293$	5.67555			0.331569			0.165785	+	0.986162i	$0.446984\pi$
$294$		0			0
$295$	5.03665			0.293245
$296$	12.0244	−	15.0782i	0.698907	−	0.876401i
$297$		0			0
$298$	−2.72331	−	11.9316i	−0.157757	−	0.691180i
$299$	20.5583	+	9.90035i	1.18892	+	0.572552i
$300$		0			0
$301$	−11.1914	−	2.86172i	−0.645059	−	0.164947i
$302$	0.308854	+	0.148736i	0.0177726	+	0.00855882i
$303$		0			0
$304$	21.9936	−	10.5916i	1.26142	−	0.607469i
$305$	3.18937	−	3.99934i	0.182623	−	0.229002i
$306$		0			0
$307$	6.88047	−	8.62783i	0.392689	−	0.492416i	−0.545708	−	0.837975i	$-0.683739\pi$
$307$	6.88047	−	8.62783i	0.392689	−	0.492416i	0.938397	+	0.345559i	$0.112311\pi$
$308$	−0.341103	−	0.758005i	−0.0194361	−	0.0431914i
$309$		0			0
$310$	−5.07767	+	2.44528i	−0.288392	+	0.138882i
$311$	−2.13106	+	9.33677i	−0.120841	+	0.529439i	0.877880	+	0.478881i	$0.158957\pi$
$311$	−2.13106	+	9.33677i	−0.120841	+	0.529439i	−0.998721	+	0.0505587i	$0.983900\pi$
$312$		0			0
$313$	24.7541			1.39918			0.699592	−	0.714543i	$-0.253365\pi$
$313$	24.7541			1.39918			0.699592	+	0.714543i	$0.253365\pi$
$314$	−1.64010	+	7.18576i	−0.0925563	+	0.405516i
$315$		0			0
$316$	−0.121979	−	0.534424i	−0.00686185	−	0.0300637i
$317$	−0.931316	−	4.08036i	−0.0523079	−	0.229176i	0.942016	−	0.335567i	$-0.108928\pi$
$317$	−0.931316	−	4.08036i	−0.0523079	−	0.229176i	−0.994324	+	0.106391i	$0.966071\pi$
$318$		0			0
$319$	19.9513	+	25.0181i	1.11706	+	1.40075i
$320$	−1.98758	−	8.70816i	−0.111109	−	0.486801i
$321$		0			0
$322$	−9.12113	−	20.2691i	−0.508301	−	1.12955i
$323$	−3.07401	+	13.4681i	−0.171043	+	0.749387i
$324$		0			0
$325$	14.3142			0.794010
$326$	−5.75413	+	25.2105i	−0.318692	+	1.39628i
$327$		0			0
$328$	−16.0286	−	20.0992i	−0.885031	−	1.10979i
$329$	−18.8537	+	3.79152i	−1.03944	+	0.209033i
$330$		0			0
$331$	0.191761	−	0.840158i	0.0105401	−	0.0461793i	−0.969384	−	0.245548i	$-0.921032\pi$
$331$	0.191761	−	0.840158i	0.0105401	−	0.0461793i	0.979925	+	0.199369i	$0.0638892\pi$
$332$	−0.148233	+	0.185878i	−0.00813534	+	0.0102014i
$333$		0			0
$334$	−3.46884	−	4.34979i	−0.189807	−	0.238010i
$335$	13.0065	+	6.26359i	0.710620	+	0.342216i
$336$		0			0
$337$	14.7428	−	7.09974i	0.803090	−	0.386748i	0.0131357	−	0.999914i	$-0.495819\pi$
$337$	14.7428	−	7.09974i	0.803090	−	0.386748i	0.789954	+	0.613166i	$0.210104\pi$
$338$	−2.81524	−	1.35575i	−0.153129	−	0.0737430i
$339$		0			0
$340$	−0.138688	−	0.0667885i	−0.00752140	−	0.00362211i
$341$	11.6336	−	14.5881i	0.629997	−	0.789992i
$342$		0			0
$343$	−9.30874	+	16.0109i	−0.502625	+	0.864505i
$344$	−12.1653			−0.655911
$345$		0			0
$346$	−16.7455	−	8.06421i	−0.900244	−	0.433535i
$347$	7.02581	+	30.7821i	0.377165	+	1.65247i	0.706096	+	0.708116i	$0.250455\pi$
$347$	7.02581	+	30.7821i	0.377165	+	1.65247i	−0.328931	+	0.944354i	$0.606688\pi$
$348$		0			0
$349$	−18.1634	+	8.74701i	−0.972262	+	0.468217i	−0.851437	−	0.524457i	$-0.824268\pi$
$349$	−18.1634	+	8.74701i	−0.972262	+	0.468217i	−0.120825	+	0.992674i	$0.538554\pi$
$350$	−10.6722	−	8.97344i	−0.570453	−	0.479650i
$351$		0			0
$352$	−1.10774	−	1.38906i	−0.0590426	−	0.0740371i
$353$	−21.7920	+	10.4945i	−1.15987	+	0.558565i	−0.911985	−	0.410224i	$-0.865451\pi$
$353$	−21.7920	+	10.4945i	−1.15987	+	0.558565i	−0.247888	+	0.968789i	$0.579736\pi$
$354$		0			0
$355$	−0.145626	+	0.638028i	−0.00772902	+	0.0338630i
$356$	0.0887684	−	0.111312i	0.00470471	−	0.00589952i
$357$		0			0
$358$	−5.69256	−	7.13825i	−0.300861	−	0.377268i
$359$	−23.2745	+	11.2084i	−1.22838	+	0.591557i	−0.931633	−	0.363400i	$-0.881616\pi$
$359$	−23.2745	+	11.2084i	−1.22838	+	0.591557i	−0.296747	+	0.954956i	$0.595902\pi$
$360$		0			0
$361$	16.2494			0.855230
$362$	−35.9284			−1.88835
$363$		0			0
$364$	0.243025	+	0.540055i	0.0127380	+	0.0283066i
$365$	3.75248	+	16.4407i	0.196414	+	0.860545i
$366$		0			0
$367$	20.4280	+	25.6159i	1.06633	+	1.33714i	0.938475	+	0.345347i	$0.112239\pi$
$367$	20.4280	+	25.6159i	1.06633	+	1.33714i	0.127858	+	0.991792i	$0.459190\pi$
$368$	−15.0143	−	18.8273i	−0.782674	−	0.981442i
$369$		0			0
$370$	2.54382	+	11.1452i	0.132247	+	0.579411i
$371$	−7.50383	+	14.6004i	−0.389579	+	0.758013i
$372$		0			0
$373$	−9.40984			−0.487223			−0.243612	−	0.969873i	$-0.578332\pi$
$373$	−9.40984			−0.487223			−0.243612	+	0.969873i	$0.578332\pi$
$374$	18.2504			0.943704
$375$		0			0
$376$	−18.2475	+	8.78751i	−0.941041	+	0.453181i
$377$	−14.2147	−	17.8246i	−0.732093	−	0.918016i
$378$		0			0
$379$	13.0234	−	16.3309i	0.668968	−	0.838859i	−0.325318	−	0.945605i	$-0.605471\pi$
$379$	13.0234	−	16.3309i	0.668968	−	0.838859i	0.994286	+	0.106745i	$0.0340429\pi$
$380$	−0.0874008	+	0.382928i	−0.00448357	+	0.0196438i
$381$		0			0
$382$	34.9870	−	16.8488i	1.79009	−	0.862062i
$383$	12.0836	+	15.1524i	0.617445	+	0.774252i	0.987982	−	0.154566i	$-0.0493979\pi$
$383$	12.0836	+	15.1524i	0.617445	+	0.774252i	−0.370537	+	0.928818i	$0.620826\pi$
$384$		0			0
$385$	−16.1396	−	4.12703i	−0.822551	−	0.210333i
$386$	18.7347	−	9.02214i	0.953569	−	0.459215i
$387$		0			0
$388$	−0.150184	−	0.657999i	−0.00762444	−	0.0334048i
$389$	15.9846	+	7.69776i	0.810449	+	0.390292i	0.792747	−	0.609551i	$-0.208650\pi$
$389$	15.9846	+	7.69776i	0.810449	+	0.390292i	0.0177029	+	0.999843i	$0.494365\pi$
$390$		0			0
$391$	13.6277			0.689183
$392$	−5.32056	+	18.7648i	−0.268729	+	0.947764i
$393$		0			0
$394$	−5.01869	+	6.29324i	−0.252838	+	0.317049i
$395$	−9.89819	−	4.76672i	−0.498032	−	0.239840i
$396$		0			0
$397$	−10.8813	−	5.24014i	−0.546115	−	0.262995i	0.140420	−	0.990092i	$-0.455155\pi$
$397$	−10.8813	−	5.24014i	−0.546115	−	0.262995i	−0.686535	+	0.727097i	$0.740869\pi$
$398$	18.1102	−	8.72140i	0.907781	−	0.437164i
$399$		0			0
$400$	−13.6106	−	6.55450i	−0.680528	−	0.327725i
$401$	5.22308	+	6.54953i	0.260828	+	0.327068i	0.894951	−	0.446164i	$-0.147210\pi$
$401$	5.22308	+	6.54953i	0.260828	+	0.327068i	−0.634123	+	0.773232i	$0.718639\pi$
$402$		0			0
$403$	−8.28861	+	10.3936i	−0.412885	+	0.517742i
$404$	−0.109236	+	0.478596i	−0.00543471	+	0.0238110i
$405$		0			0
$406$	−0.576107	+	22.2005i	−0.0285917	+	1.10179i
$407$	−23.5980	−	29.5910i	−1.16971	−	1.46677i
$408$		0			0
$409$	−6.65813	+	29.1712i	−0.329223	+	1.44242i	0.491391	+	0.870939i	$0.336489\pi$
$409$	−6.65813	+	29.1712i	−0.329223	+	1.44242i	−0.820614	+	0.571483i	$0.806368\pi$
$410$	15.2386			0.752581
$411$		0			0
$412$	−0.0166881	+	0.0731154i	−0.000822164	+	0.00360214i
$413$	−11.2121	−	2.86702i	−0.551711	−	0.141077i
$414$		0			0
$415$	1.06027	+	4.64537i	0.0520468	+	0.228032i
$416$	0.789229	+	0.989662i	0.0386951	+	0.0485221i
$417$		0			0
$418$	−10.3624	−	45.4005i	−0.506840	−	2.22061i
$419$	4.67764	+	20.4941i	0.228517	+	1.00120i	0.950849	+	0.309654i	$0.100213\pi$
$419$	4.67764	+	20.4941i	0.228517	+	1.00120i	−0.722332	+	0.691547i	$0.756930\pi$
$420$		0			0
$421$	−4.26845	+	18.7013i	−0.208032	+	0.911446i	0.757843	+	0.652437i	$0.226253\pi$
$421$	−4.26845	+	18.7013i	−0.208032	+	0.911446i	−0.965875	+	0.259010i	$0.916604\pi$
$422$	9.51405			0.463137
$423$		0			0
$424$	−3.84698	+	16.8547i	−0.186826	+	0.818538i
$425$	7.70235	−	3.70926i	0.373619	−	0.179925i
$426$		0			0
$427$	−9.37642	+	7.08745i	−0.453757	+	0.342986i
$428$	−0.332164	+	0.416521i	−0.0160558	+	0.0201333i
$429$		0			0
$430$	4.49606	−	5.63789i	0.216819	−	0.271883i
$431$	10.6154	−	5.11212i	0.511327	−	0.246242i	−0.160385	−	0.987055i	$-0.551274\pi$
$431$	10.6154	−	5.11212i	0.511327	−	0.246242i	0.671712	+	0.740813i	$0.265559\pi$
$432$		0			0
$433$	24.1782	+	11.6436i	1.16193	+	0.559557i	0.912597	−	0.408860i	$-0.134074\pi$
$433$	24.1782	+	11.6436i	1.16193	+	0.559557i	0.249335	+	0.968417i	$0.419788\pi$
$434$	12.6953	−	2.55306i	0.609396	−	0.122551i
$435$		0			0
$436$	0.0308986	+	0.0148800i	0.00147978	+	0.000712623i
$437$	−7.73767	−	33.9010i	−0.370143	−	1.62170i
$438$		0			0
$439$	4.04339	−	5.07025i	0.192980	−	0.241990i	−0.675922	−	0.736973i	$-0.736254\pi$
$439$	4.04339	−	5.07025i	0.192980	−	0.241990i	0.868902	+	0.494983i	$0.164826\pi$
$440$	−17.5442			−0.836388
$441$		0			0
$442$	−13.0028			−0.618481
$443$	−23.8807	+	29.9455i	−1.13461	+	1.42275i	−0.242951	+	0.970038i	$0.578116\pi$
$443$	−23.8807	+	29.9455i	−1.13461	+	1.42275i	−0.891656	+	0.452714i	$0.850456\pi$
$444$		0			0
$445$	−0.634939	−	2.78185i	−0.0300990	−	0.131872i
$446$	−28.7194	−	13.8305i	−1.35990	−	0.654894i
$447$		0			0
$448$	−0.532411	+	20.5166i	−0.0251541	+	0.969320i
$449$	15.9950	+	7.70278i	0.754850	+	0.363517i	0.771403	−	0.636346i	$-0.219555\pi$
$449$	15.9950	+	7.70278i	0.754850	+	0.363517i	−0.0165534	+	0.999863i	$0.505269\pi$
$450$		0			0
$451$	−45.4555	+	21.8902i	−2.14042	+	1.03077i
$452$	−0.0497482	+	0.0623823i	−0.00233996	+	0.00293422i
$453$		0			0
$454$	−9.42620	+	11.8201i	−0.442394	+	0.554744i
$455$	11.4990	+	2.94038i	0.539080	+	0.137847i
$456$		0			0
$457$	−14.2995	+	6.88629i	−0.668904	+	0.322127i	−0.737334	−	0.675529i	$-0.763915\pi$
$457$	−14.2995	+	6.88629i	−0.668904	+	0.322127i	0.0684297	+	0.997656i	$0.478201\pi$
$458$	3.36502	−	14.7431i	0.157237	−	0.688900i
$459$		0			0
$460$	0.387465			0.0180657
$461$	4.09287	−	17.9321i	0.190624	−	0.835179i	−0.785655	−	0.618665i	$-0.787674\pi$
$461$	4.09287	−	17.9321i	0.190624	−	0.835179i	0.976279	−	0.216514i	$-0.0694689\pi$
$462$		0			0
$463$	0.0239558	+	0.104957i	0.00111332	+	0.00487778i	0.975482	−	0.220081i	$-0.0706323\pi$
$463$	0.0239558	+	0.104957i	0.00111332	+	0.00487778i	−0.974368	+	0.224959i	$0.927775\pi$
$464$	5.35398	+	23.4573i	0.248552	+	1.08898i
$465$		0			0
$466$	−12.3016	−	15.4257i	−0.569861	−	0.714583i
$467$	−7.22263	−	31.6444i	−0.334223	−	1.46433i	−0.810866	−	0.585231i	$-0.801004\pi$
$467$	−7.22263	−	31.6444i	−0.334223	−	1.46433i	0.476643	−	0.879097i	$-0.341853\pi$
$468$		0			0
$469$	−25.3883	−	21.3471i	−1.17232	−	0.985717i
$470$	2.67142	−	11.7043i	0.123224	−	0.539878i
$471$		0			0
$472$	−12.1879			−0.560992
$473$	−5.31258	+	23.2759i	−0.244273	+	1.07023i
$474$		0			0
$475$	−13.6006	−	17.0547i	−0.624040	−	0.782522i
$476$	0.270715	+	0.227623i	0.0124082	+	0.0104331i
$477$		0			0
$478$	−2.46087	+	10.7818i	−0.112558	+	0.493147i
$479$	10.5137	−	13.1838i	0.480384	−	0.602382i	−0.481296	−	0.876558i	$-0.659834\pi$
$479$	10.5137	−	13.1838i	0.480384	−	0.602382i	0.961680	+	0.274176i	$0.0884051\pi$
$480$		0			0
$481$	16.8129	+	21.0827i	0.766601	+	0.961287i
$482$	−36.9074	−	17.7737i	−1.68109	−	0.809569i
$483$		0			0
$484$	−0.978424	+	0.471184i	−0.0444738	+	0.0214175i
$485$	−12.1869	−	5.86892i	−0.553380	−	0.266494i
$486$		0			0
$487$	−31.3586	−	15.1015i	−1.42099	−	0.684314i	−0.443693	−	0.896179i	$-0.646332\pi$
$487$	−31.3586	−	15.1015i	−1.42099	−	0.684314i	−0.977299	+	0.211865i	$0.932046\pi$
$488$	−7.71775	+	9.67776i	−0.349366	+	0.438091i
$489$		0			0
$490$	−6.72995	−	9.40084i	−0.304028	−	0.424687i
$491$	−18.6284			−0.840689			−0.420344	−	0.907365i	$-0.638091\pi$
$491$	−18.6284			−0.840689			−0.420344	+	0.907365i	$0.638091\pi$
$492$		0			0
$493$	−12.2677	−	5.90782i	−0.552510	−	0.266075i
$494$	7.38286	+	32.3464i	0.332171	+	1.45533i
$495$		0			0
$496$	12.6404	−	6.08729i	0.567570	−	0.273328i
$497$	0.687364	−	1.33742i	0.0308325	−	0.0599915i
$498$		0			0
$499$	−13.8001	−	17.3048i	−0.617779	−	0.774670i	0.370251	−	0.928932i	$-0.379272\pi$
$499$	−13.8001	−	17.3048i	−0.617779	−	0.774670i	−0.988030	+	0.154261i	$0.950700\pi$
$500$	0.517017	−	0.248982i	0.0231217	−	0.0111348i
$501$		0			0
$502$	−1.03076	+	4.51606i	−0.0460051	+	0.201562i
$503$	−10.3586	+	12.9892i	−0.461866	+	0.579162i	−0.957158	−	0.289565i	$-0.906490\pi$
$503$	−10.3586	+	12.9892i	−0.461866	+	0.579162i	0.495292	+	0.868726i	$0.335061\pi$
$504$		0			0
$505$	6.13420	+	7.69204i	0.272968	+	0.342291i
$506$	−41.3891	+	19.9319i	−1.83997	+	0.886083i
$507$		0			0
$508$	0.161459			0.00716358
$509$	35.5269			1.57470			0.787352	−	0.616504i	$-0.211452\pi$
$509$	35.5269			1.57470			0.787352	+	0.616504i	$0.211452\pi$
$510$		0			0
$511$	1.00517	−	38.7347i	0.0444662	−	1.71352i
$512$	4.80131	+	21.0359i	0.212190	+	0.929665i
$513$		0			0
$514$	14.6471	+	18.3669i	0.646056	+	0.810129i
$515$	0.937126	+	1.17512i	0.0412947	+	0.0517819i
$516$		0			0
$517$	8.84452	+	38.7504i	0.388982	+	1.70424i
$518$	0.681409	−	26.2583i	0.0299394	−	1.15372i
$519$		0			0
$520$	12.4997			0.548149
$521$	34.4241			1.50815			0.754074	−	0.656790i	$-0.228086\pi$
$521$	34.4241			1.50815			0.754074	+	0.656790i	$0.228086\pi$
$522$		0			0
$523$	29.4420	−	14.1785i	1.28741	−	0.619982i	0.340124	−	0.940381i	$-0.389531\pi$
$523$	29.4420	−	14.1785i	1.28741	−	0.619982i	0.947283	+	0.320398i	$0.103817\pi$
$524$	−0.121377	−	0.152202i	−0.00530239	−	0.00664899i
$525$		0			0
$526$	28.1063	−	35.2442i	1.22549	−	1.53672i
$527$	−1.76673	+	7.74053i	−0.0769598	+	0.337183i
$528$		0			0
$529$	−10.1833	+	4.90404i	−0.442754	+	0.213219i
$530$	−6.38937	−	8.01201i	−0.277536	−	0.348020i
$531$		0			0
$532$	0.412538	−	0.802685i	0.0178858	−	0.0348008i
$533$	32.3857	−	15.5961i	1.40278	−	0.675542i
$534$		0			0
$535$	2.37589	+	10.4095i	0.102719	+	0.450040i
$536$	−31.4735	−	15.1569i	−1.35945	−	0.654676i
$537$		0			0
$538$	32.3932			1.39657
$539$	33.5792	+	18.3744i	1.44636	+	0.791441i
$540$		0			0
$541$	18.2904	−	22.9355i	0.786368	−	0.986074i	−0.213590	−	0.976923i	$-0.568516\pi$
$541$	18.2904	−	22.9355i	0.786368	−	0.986074i	0.999958	−	0.00915067i	$-0.00291279\pi$
$542$	−11.4387	−	5.50859i	−0.491334	−	0.236614i
$543$		0			0
$544$	0.681129	+	0.328014i	0.0292032	+	0.0140635i
$545$	0.619258	−	0.298219i	0.0265261	−	0.0127743i
$546$		0			0
$547$	2.25551	+	1.08620i	0.0964386	+	0.0464424i	0.481481	−	0.876456i	$-0.340099\pi$
$547$	2.25551	+	1.08620i	0.0964386	+	0.0464424i	−0.385043	+	0.922899i	$0.625813\pi$
$548$	0.293728	+	0.368323i	0.0125474	+	0.0157340i
$549$		0			0
$550$	−17.9679	+	22.5310i	−0.766152	+	0.960724i
$551$	−7.73109	+	33.8721i	−0.329356	+	1.44300i
$552$		0			0
$553$	19.3210	+	16.2456i	0.821612	+	0.690831i
$554$	17.8764	+	22.4163i	0.759496	+	0.952378i
$555$		0			0
$556$	−0.0724638	+	0.317485i	−0.00307315	+	0.0134644i
$557$	−16.4674			−0.697745			−0.348872	−	0.937170i	$-0.613435\pi$
$557$	−16.4674			−0.697745			−0.348872	+	0.937170i	$0.613435\pi$
$558$		0			0
$559$	3.78505	−	16.5834i	0.160091	−	0.701403i
$560$	−9.58730	−	8.06123i	−0.405137	−	0.340649i
$561$		0			0
$562$	−2.32707	−	10.1956i	−0.0981616	−	0.430074i
$563$	−1.79330	−	2.24872i	−0.0755784	−	0.0947724i	0.742605	−	0.669730i	$-0.233590\pi$
$563$	−1.79330	−	2.24872i	−0.0755784	−	0.0947724i	−0.818183	+	0.574957i	$0.805019\pi$
$564$		0			0
$565$	0.355837	+	1.55902i	0.0149702	+	0.0655886i
$566$	3.55358	+	15.5692i	0.149368	+	0.654424i
$567$		0			0
$568$	0.352390	−	1.54392i	0.0147860	−	0.0647816i
$569$	−9.02763			−0.378458			−0.189229	−	0.981933i	$-0.560599\pi$
$569$	−9.02763			−0.378458			−0.189229	+	0.981933i	$0.560599\pi$
$570$		0			0
$571$	1.83702	−	8.04851i	0.0768769	−	0.336820i	−0.921834	−	0.387586i	$-0.873309\pi$
$571$	1.83702	−	8.04851i	0.0768769	−	0.336820i	0.998711	+	0.0507661i	$0.0161663\pi$
$572$	1.10278	−	0.531071i	0.0461095	−	0.0222052i
$573$		0			0
$574$	−33.9227	−	8.67431i	−1.41591	−	0.362059i
$575$	−13.4168	+	16.8241i	−0.559518	+	0.701613i
$576$		0			0
$577$	17.2203	−	21.5936i	0.716892	−	0.898954i	−0.281266	−	0.959630i	$-0.590754\pi$
$577$	17.2203	−	21.5936i	0.716892	−	0.898954i	0.998158	+	0.0606760i	$0.0193257\pi$
$578$	14.9730	−	7.21061i	0.622794	−	0.299922i
$579$		0			0
$580$	−0.348797	−	0.167972i	−0.0144830	−	0.00697466i
$581$	0.284015	−	10.9446i	0.0117829	−	0.454058i
$582$		0			0
$583$	30.5682	+	14.7209i	1.26601	+	0.609676i
$584$	−9.08038	−	39.7838i	−0.375749	−	1.64626i
$585$		0			0
$586$	5.07578	−	6.36482i	0.209678	−	0.262928i
$587$	23.2756			0.960686			0.480343	−	0.877081i	$-0.340512\pi$
$587$	23.2756			0.960686			0.480343	+	0.877081i	$0.340512\pi$
$588$		0			0
$589$	20.2589			0.834752
$590$	4.50439	−	5.64833i	0.185443	−	0.232538i
$591$		0			0
$592$	−6.33259	−	27.7449i	−0.260268	−	1.14031i
$593$	−6.06601	−	2.92124i	−0.249101	−	0.119961i	0.305167	−	0.952299i	$-0.401288\pi$
$593$	−6.06601	−	2.92124i	−0.249101	−	0.119961i	−0.554268	+	0.832338i	$0.687002\pi$
$594$		0			0
$595$	6.94944	−	1.39755i	0.284899	−	0.0572939i
$596$	−0.441662	−	0.212693i	−0.0180912	−	0.00871226i
$597$		0			0
$598$	29.4884	−	14.2009i	1.20587	−	0.580717i
$599$	−4.87528	+	6.11341i	−0.199199	+	0.249787i	−0.871391	−	0.490590i	$-0.836781\pi$
$599$	−4.87528	+	6.11341i	−0.199199	+	0.249787i	0.672192	+	0.740377i	$0.265353\pi$
$600$		0			0
$601$	5.09939	−	6.39443i	0.208008	−	0.260834i	−0.666873	−	0.745171i	$-0.732368\pi$
$601$	5.09939	−	6.39443i	0.208008	−	0.260834i	0.874882	+	0.484337i	$0.160939\pi$
$602$	−13.2180	+	9.99120i	−0.538724	+	0.407211i
$603$		0			0
$604$	0.0123711	−	0.00595759i	0.000503372	−	0.000242411i
$605$	−4.84307	+	21.2189i	−0.196899	+	0.862669i
$606$		0			0
$607$	−46.8789			−1.90276			−0.951378	−	0.308025i	$-0.900332\pi$
$607$	−46.8789			−1.90276			−0.951378	+	0.308025i	$0.900332\pi$
$608$	0.429247	−	1.88065i	0.0174082	−	0.0762705i
$609$		0			0
$610$	−1.63272	−	7.15341i	−0.0661069	−	0.289633i
$611$	−6.30145	−	27.6084i	−0.254929	−	1.11692i
$612$		0			0
$613$	6.34629	+	7.95799i	0.256324	+	0.321420i	0.893298	−	0.449465i	$-0.148385\pi$
$613$	6.34629	+	7.95799i	0.256324	+	0.321420i	−0.636974	+	0.770886i	$0.719814\pi$
$614$	−3.52228	−	15.4321i	−0.142148	−	0.622790i
$615$		0			0
$616$	39.0552	+	9.98674i	1.57358	+	0.402377i
$617$	−3.10789	+	13.6166i	−0.125119	+	0.548182i	0.873047	+	0.487637i	$0.162141\pi$
$617$	−3.10789	+	13.6166i	−0.125119	+	0.548182i	−0.998165	+	0.0605449i	$0.980716\pi$
$618$		0			0
$619$	−10.9377			−0.439624			−0.219812	−	0.975542i	$-0.570544\pi$
$619$	−10.9377			−0.439624			−0.219812	+	0.975542i	$0.570544\pi$
$620$	−0.0502318	+	0.220080i	−0.00201736	+	0.00883863i
$621$		0			0
$622$	8.56482	+	10.7399i	0.343418	+	0.430633i
$623$	−0.170080	+	6.55410i	−0.00681412	+	0.262585i
$624$		0			0
$625$	−1.52869	+	6.69763i	−0.0611476	+	0.267905i
$626$	22.1382	−	27.7604i	0.884819	−	1.10953i
$627$		0			0
$628$	0.184070	+	0.230816i	0.00734519	+	0.00921058i
$629$	14.5100	+	6.98766i	0.578553	+	0.278616i
$630$		0			0
$631$	−9.66760	+	4.65567i	−0.384861	+	0.185339i	−0.616302	−	0.787510i	$-0.711370\pi$
$631$	−9.66760	+	4.65567i	−0.384861	+	0.185339i	0.231441	+	0.972849i	$0.425656\pi$
$632$	23.9520	+	11.5347i	0.952759	+	0.458825i
$633$		0			0
$634$	−5.40880	−	2.60474i	−0.214811	−	0.103447i
$635$	2.01754	−	2.52992i	0.0800638	−	0.100397i
$636$		0			0
$637$	−23.9241	−	13.0912i	−0.947908	−	0.518691i
$638$	45.8994			1.81717
$639$		0			0
$640$	−12.2174	−	5.88359i	−0.482935	−	0.232569i
$641$	8.05408	+	35.2872i	0.318117	+	1.39376i	0.840852	+	0.541266i	$0.182055\pi$
$641$	8.05408	+	35.2872i	0.318117	+	1.39376i	−0.522735	+	0.852495i	$0.675088\pi$
$642$		0			0
$643$	−24.0748	+	11.5938i	−0.949416	+	0.457215i	−0.843481	−	0.537158i	$-0.819498\pi$
$643$	−24.0748	+	11.5938i	−0.949416	+	0.457215i	−0.105935	+	0.994373i	$0.533783\pi$
$644$	−0.862537	−	0.220558i	−0.0339887	−	0.00869119i
$645$		0			0
$646$	12.3546	+	15.4922i	0.486086	+	0.609532i
$647$	35.5080	−	17.0998i	1.39596	−	0.672261i	0.423626	−	0.905837i	$-0.360757\pi$
$647$	35.5080	−	17.0998i	1.39596	−	0.672261i	0.972339	+	0.233576i	$0.0750427\pi$
$648$		0			0
$649$	−5.32242	+	23.3191i	−0.208923	+	0.915353i
$650$	12.8015	−	16.0526i	0.502118	−	0.629635i
$651$		0			0
$652$	0.645790	+	0.809795i	0.0252911	+	0.0317140i
$653$	39.6333	−	19.0864i	1.55097	−	0.746908i	0.554607	−	0.832112i	$-0.312868\pi$
$653$	39.6333	−	19.0864i	1.55097	−	0.746908i	0.996364	+	0.0852039i	$0.0271542\pi$
$654$		0			0
$655$	−3.90158			−0.152447
$656$	−37.9351			−1.48112
$657$		0			0
$658$	−12.6093	+	24.5342i	−0.491562	+	0.956444i
$659$	−6.98034	−	30.5829i	−0.271915	−	1.19134i	−0.907749	−	0.419513i	$-0.862201\pi$
$659$	−6.98034	−	30.5829i	−0.271915	−	1.19134i	0.635834	−	0.771826i	$-0.280656\pi$
$660$		0			0
$661$	2.46626	+	3.09259i	0.0959262	+	0.120288i	0.827478	−	0.561498i	$-0.189775\pi$
$661$	2.46626	+	3.09259i	0.0959262	+	0.120288i	−0.731552	+	0.681786i	$0.761203\pi$
$662$	−0.770695	−	0.966421i	−0.0299539	−	0.0375610i
$663$		0			0
$664$	−2.56569	−	11.2410i	−0.0995681	−	0.436236i
$665$	−7.42243	−	16.4943i	−0.287829	−	0.639620i
$666$		0			0
$667$	34.2735			1.32707
$668$	−0.222848			−0.00862225
$669$		0			0
$670$	18.6563	−	8.98438i	0.720754	−	0.347097i
$671$	15.1461	+	18.9927i	0.584710	+	0.733203i
$672$		0			0
$673$	−15.9674	+	20.0225i	−0.615498	+	0.771810i	−0.987703	−	0.156340i	$-0.950030\pi$
$673$	−15.9674	+	20.0225i	−0.615498	+	0.771810i	0.372205	+	0.928151i	$0.378602\pi$
$674$	5.22282	−	22.8827i	0.201176	−	0.881408i
$675$		0			0
$676$	−0.112764	+	0.0543041i	−0.00433706	+	0.00208862i
$677$	−7.94629	−	9.96434i	−0.305401	−	0.382961i	0.605320	−	0.795982i	$-0.293045\pi$
$677$	−7.94629	−	9.96434i	−0.305401	−	0.382961i	−0.910721	+	0.413021i	$0.864474\pi$
$678$		0			0
$679$	23.7886	+	20.0020i	0.912922	+	0.767607i
$680$	6.72599	−	3.23906i	0.257930	−	0.124212i
$681$		0			0
$682$	−5.95556	−	26.0930i	−0.228050	−	0.999153i
$683$	11.9171	+	5.73898i	0.455996	+	0.219596i	0.647759	−	0.761845i	$-0.275706\pi$
$683$	11.9171	+	5.73898i	0.455996	+	0.219596i	−0.191763	+	0.981441i	$0.561421\pi$
$684$		0			0
$685$	9.44166			0.360747
$686$	9.63028	+	24.7581i	0.367686	+	0.945269i
$687$		0			0
$688$	−11.1925	+	14.0350i	−0.426711	+	0.535079i
$689$	−21.7789	−	10.4882i	−0.829710	−	0.399567i
$690$		0			0
$691$	−27.1495	−	13.0745i	−1.03282	−	0.497378i	−0.160867	−	0.986976i	$-0.551429\pi$
$691$	−27.1495	−	13.0745i	−1.03282	−	0.497378i	−0.871948	+	0.489599i	$0.837143\pi$
$692$	−0.670736	+	0.323010i	−0.0254976	+	0.0122790i
$693$		0			0
$694$	40.8038	+	19.6501i	1.54889	+	0.745907i
$695$	4.06923	+	5.10265i	0.154355	+	0.193554i
$696$		0			0
$697$	13.3850	−	16.7843i	0.506993	−	0.635749i
$698$	−6.43461	+	28.1919i	−0.243554	+	1.06708i
$699$		0			0
$700$	−0.547536	+	0.110111i	−0.0206949	+	0.00416179i
$701$	−1.15249	−	1.44517i	−0.0435288	−	0.0545834i	0.759591	−	0.650401i	$-0.225399\pi$
$701$	−1.15249	−	1.44517i	−0.0435288	−	0.0545834i	−0.803119	+	0.595818i	$0.796828\pi$
$702$		0			0
$703$	9.14420	−	40.0634i	0.344880	−	1.51102i
$704$	42.4180			1.59869
$705$		0			0
$706$	−7.72012	+	33.8240i	−0.290550	+	1.27298i
$707$	−9.27678	−	20.6150i	−0.348889	−	0.775308i
$708$		0			0
$709$	−3.92471	−	17.1953i	−0.147395	−	0.645782i	−0.993603	−	0.112928i	$-0.963977\pi$
$709$	−3.92471	−	17.1953i	−0.147395	−	0.645782i	0.846208	−	0.532853i	$-0.178880\pi$
$710$	0.585278	+	0.733915i	0.0219651	+	0.0275433i
$711$		0			0
$712$	1.53645	+	6.73162i	0.0575808	+	0.252278i
$713$	−4.44707	−	19.4839i	−0.166544	−	0.729677i
$714$		0			0
$715$	5.45861	−	23.9157i	0.204140	−	0.894397i
$716$	−0.365706			−0.0136671
$717$		0			0
$718$	−8.24529	+	36.1250i	−0.307712	+	1.34817i
$719$	18.4179	−	8.86960i	0.686872	−	0.330780i	−0.0576888	−	0.998335i	$-0.518373\pi$
$719$	18.4179	−	8.86960i	0.686872	−	0.330780i	0.744561	+	0.667554i	$0.232659\pi$
$720$		0			0
$721$	−1.41722	−	3.14937i	−0.0527801	−	0.117289i
$722$	14.5322	−	18.2228i	0.540832	−	0.678182i
$723$		0			0
$724$	−0.897264	+	1.12513i	−0.0333466	+	0.0418153i
$725$	19.3713	−	9.32872i	0.719432	−	0.346460i
$726$		0			0
$727$	28.1812	+	13.5713i	1.04518	+	0.503333i	0.876030	−	0.482257i	$-0.160183\pi$
$727$	28.1812	+	13.5713i	1.04518	+	0.503333i	0.169152	+	0.985590i	$0.445897\pi$
$728$	−27.8256	−	7.11524i	−1.03129	−	0.263708i
$729$		0			0
$730$	21.7933	+	10.4951i	0.806605	+	0.388440i
$731$	−2.26057	−	9.90420i	−0.0836101	−	0.366320i
$732$		0			0
$733$	30.0096	−	37.6308i	1.10843	−	1.38993i	0.196043	−	0.980595i	$-0.437191\pi$
$733$	30.0096	−	37.6308i	1.10843	−	1.38993i	0.912386	−	0.409330i	$-0.134238\pi$
$734$	46.9961			1.73466
$735$		0			0
$736$	−1.90294			−0.0701431
$737$	−42.7441	+	53.5994i	−1.57450	+	1.97436i
$738$		0			0
$739$	3.14325	+	13.7715i	0.115626	+	0.506593i	0.999262	+	0.0384169i	$0.0122315\pi$
$739$	3.14325	+	13.7715i	0.115626	+	0.506593i	−0.883635	+	0.468176i	$0.844911\pi$
$740$	0.412551	+	0.198674i	0.0151657	+	0.00730341i
$741$		0			0
$742$	9.66268	+	21.4726i	0.354728	+	0.788283i
$743$	16.2701	+	7.83527i	0.596892	+	0.287448i	0.707834	−	0.706379i	$-0.249672\pi$
$743$	16.2701	+	7.83527i	0.596892	+	0.287448i	−0.110942	+	0.993827i	$0.535387\pi$
$744$		0			0
$745$	−8.85161	+	4.26271i	−0.324298	+	0.156174i
$746$	−8.41544	+	10.5526i	−0.308111	+	0.386359i
$747$		0			0
$748$	0.455779	−	0.571529i	0.0166649	−	0.0208972i
$749$	0.636427	−	24.5249i	0.0232545	−	0.896121i
$750$		0			0
$751$	−23.1730	+	11.1595i	−0.845596	+	0.407217i	−0.805941	−	0.591996i	$-0.798340\pi$
$751$	−23.1730	+	11.1595i	−0.845596	+	0.407217i	−0.0396548	+	0.999213i	$0.512626\pi$
$752$	−6.65026	+	29.1367i	−0.242510	+	1.06251i
$753$		0			0
$754$	−32.7019			−1.19093
$755$	0.0612351	−	0.268288i	0.00222857	−	0.00976402i
$756$		0			0
$757$	0.232750	+	1.01975i	0.00845945	+	0.0370633i	0.978981	−	0.203949i	$-0.0653777\pi$
$757$	0.232750	+	1.01975i	0.00845945	+	0.0370633i	−0.970522	+	0.241012i	$0.922521\pi$
$758$	−6.66702	−	29.2101i	−0.242157	−	1.06096i
$759$		0			0
$760$	−11.8766	−	14.8928i	−0.430809	−	0.540218i
$761$	−7.58634	−	33.2379i	−0.275005	−	1.20487i	−0.904023	−	0.427483i	$-0.859400\pi$
$761$	−7.58634	−	33.2379i	−0.275005	−	1.20487i	0.629019	−	0.777390i	$-0.283457\pi$
$762$		0			0
$763$	−1.54829	+	0.311364i	−0.0560517	+	0.0112721i
$764$	0.346115	−	1.51643i	0.0125220	−	0.0548625i
$765$		0			0
$766$	27.7993			1.00443
$767$	3.79206	−	16.6141i	0.136923	−	0.599900i
$768$		0			0
$769$	−14.6710	−	18.3969i	−0.529051	−	0.663409i	0.443452	−	0.896298i	$-0.353754\pi$
$769$	−14.6710	−	18.3969i	−0.529051	−	0.663409i	−0.972503	+	0.232889i	$0.925182\pi$
$770$	−19.0623	+	14.4088i	−0.686957	+	0.519257i
$771$		0			0
$772$	0.185336	−	0.812011i	0.00667040	−	0.0292249i
$773$	−6.37052	+	7.98838i	−0.229132	+	0.287322i	−0.883085	−	0.469213i	$-0.844538\pi$
$773$	−6.37052	+	7.98838i	−0.229132	+	0.287322i	0.653953	+	0.756535i	$0.273109\pi$
$774$		0			0
$775$	−7.81669	−	9.80182i	−0.280784	−	0.352092i
$776$	29.4904	+	14.2018i	1.05864	+	0.509816i
$777$		0			0
$778$	22.9280	−	11.0415i	0.822008	−	0.395858i
$779$	−49.3532	−	23.7672i	−1.76826	−	0.851550i
$780$		0			0
$781$	−2.80010	−	1.34846i	−0.100196	−	0.0482516i
$782$	12.1876	−	15.2827i	0.435827	−	0.546510i
$783$		0			0
$784$	16.7536	+	23.4025i	0.598342	+	0.835804i
$785$	5.91678			0.211179
$786$		0			0
$787$	5.93167	+	2.85654i	0.211441	+	0.101825i	0.536607	−	0.843832i	$-0.319706\pi$
$787$	5.93167	+	2.85654i	0.211441	+	0.101825i	−0.325166	+	0.945657i	$0.605420\pi$
$788$	0.0717439	+	0.314331i	0.00255577	+	0.0111976i
$789$		0			0
$790$	−14.1978	+	6.83730i	−0.505135	+	0.243260i
$791$	0.0953176	−	3.67310i	0.00338910	−	0.130600i
$792$		0			0
$793$	−10.7911	−	13.5317i	−0.383205	−	0.480524i
$794$	−15.6079	+	7.51637i	−0.553904	+	0.266746i
$795$		0			0
$796$	0.179158	−	0.784944i	0.00635010	−	0.0278216i
$797$	3.16816	−	3.97275i	0.112222	−	0.140722i	−0.722548	−	0.691321i	$-0.757029\pi$
$797$	3.16816	−	3.97275i	0.112222	−	0.140722i	0.834770	+	0.550599i	$0.185601\pi$
$798$		0			0
$799$	−10.5450	−	13.2230i	−0.373054	−	0.467795i
$800$	−1.07553	+	0.517950i	−0.0380259	+	0.0183123i
$801$		0			0
$802$	12.0161			0.424302
$803$	−80.0837			−2.82609
$804$		0			0
$805$	−14.2340	+	10.7592i	−0.501682	+	0.379211i
$806$	4.24315	+	18.5905i	0.149459	+	0.654821i
$807$		0			0
$808$	−14.8437	−	18.6135i	−0.522201	−	0.654820i
$809$	−20.8733	−	26.1743i	−0.733868	−	0.920241i	0.265165	−	0.964203i	$-0.414573\pi$
$809$	−20.8733	−	26.1743i	−0.733868	−	0.920241i	−0.999033	+	0.0439618i	$0.986002\pi$
$810$		0			0
$811$	5.07211	+	22.2224i	0.178106	+	0.780333i	0.982504	+	0.186242i	$0.0596309\pi$
$811$	5.07211	+	22.2224i	0.178106	+	0.780333i	−0.804398	+	0.594091i	$0.797512\pi$
$812$	0.680843	+	0.572469i	0.0238929	+	0.0200897i
$813$		0			0
$814$	−54.2890			−1.90283
$815$	20.7584			0.727136
$816$		0			0
$817$	−23.3546	+	11.2470i	−0.817075	+	0.393483i
$818$	26.7594	+	33.5552i	0.935619	+	1.17323i
$819$		0			0
$820$	0.380564	−	0.477213i	0.0132899	−	0.0166650i
$821$	−2.67652	+	11.7266i	−0.0934110	+	0.409261i	−0.999916	−	0.0129339i	$-0.995883\pi$
$821$	−2.67652	+	11.7266i	−0.0934110	+	0.409261i	0.906505	+	0.422194i	$0.138740\pi$
$822$		0			0
$823$	−13.4200	+	6.46274i	−0.467793	+	0.225277i	−0.652904	−	0.757440i	$-0.726450\pi$
$823$	−13.4200	+	6.46274i	−0.467793	+	0.225277i	0.185112	+	0.982717i	$0.440735\pi$
$824$	−2.26769	−	2.84359i	−0.0789987	−	0.0990613i
$825$		0			0
$826$	−13.2424	+	10.0097i	−0.460763	+	0.348282i
$827$	−14.0346	+	6.75869i	−0.488029	+	0.235023i	−0.661682	−	0.749784i	$-0.730157\pi$
$827$	−14.0346	+	6.75869i	−0.488029	+	0.235023i	0.173653	+	0.984807i	$0.444443\pi$
$828$		0			0
$829$	0.849458	+	3.72172i	0.0295029	+	0.129261i	0.987535	−	0.157401i	$-0.0503116\pi$
$829$	0.849458	+	3.72172i	0.0295029	+	0.129261i	−0.958032	+	0.286662i	$0.907454\pi$
$830$	6.15775	+	2.96542i	0.213739	+	0.102931i
$831$		0			0
$832$	−30.2215			−1.04774
$833$	−16.2657	−	0.844764i	−0.563572	−	0.0292694i
$834$		0			0
$835$	−2.78465	+	3.49184i	−0.0963667	+	0.120840i
$836$	−1.68055	−	0.809310i	−0.0581230	−	0.0279906i
$837$		0			0
$838$	27.1663	+	13.0826i	0.938444	+	0.451931i
$839$	−12.6854	+	6.10894i	−0.437947	+	0.210904i	−0.639848	−	0.768502i	$-0.721003\pi$
$839$	−12.6854	+	6.10894i	−0.437947	+	0.210904i	0.201900	+	0.979406i	$0.435288\pi$
$840$		0			0
$841$	−4.72498	−	2.27543i	−0.162930	−	0.0784632i
$842$	17.1551	+	21.5119i	0.591205	+	0.741348i
$843$		0			0
$844$	0.237601	−	0.297942i	0.00817857	−	0.0102556i
$845$	−0.558164	+	2.44548i	−0.0192014	+	0.0841270i
$846$		0			0
$847$	22.8596	−	44.4785i	0.785465	−	1.52830i
$848$	15.9057	+	19.9452i	0.546205	+	0.684920i
$849$		0			0
$850$	2.72866	−	11.9550i	0.0935923	−	0.410055i
$851$	−40.5381			−1.38963
$852$		0			0
$853$	−2.45479	+	10.7551i	−0.0840505	+	0.368249i	−0.999408	−	0.0343918i	$-0.989051\pi$
$853$	−2.45479	+	10.7551i	−0.0840505	+	0.368249i	0.915358	+	0.402641i	$0.131908\pi$
$854$	−0.437355	+	16.8536i	−0.0149660	+	0.576719i
$855$		0			0
$856$	−5.74926	−	25.1892i	−0.196506	−	0.860948i
$857$	−21.4064	−	26.8427i	−0.731228	−	0.916930i	0.267687	−	0.963506i	$-0.413741\pi$
$857$	−21.4064	−	26.8427i	−0.731228	−	0.916930i	−0.998915	+	0.0465754i	$0.985169\pi$
$858$		0			0
$859$	−5.88273	−	25.7739i	−0.200716	−	0.879396i	−0.970502	−	0.241093i	$-0.922494\pi$
$859$	−5.88273	−	25.7739i	−0.200716	−	0.879396i	0.769786	−	0.638302i	$-0.220363\pi$
$860$	−0.0642728	−	0.281598i	−0.00219169	−	0.00960240i
$861$		0			0
$862$	3.76065	−	16.4765i	0.128088	−	0.561192i
$863$	21.7413			0.740084			0.370042	−	0.929015i	$-0.379343\pi$
$863$	21.7413			0.740084			0.370042	+	0.929015i	$0.379343\pi$
$864$		0			0
$865$	−3.32005	+	14.5461i	−0.112885	+	0.494582i
$866$	34.6808	−	16.7014i	1.17850	−	0.567537i
$867$		0			0
$868$	0.237098	−	0.461327i	0.00804763	−	0.0156585i
$869$	32.5291	−	40.7902i	1.10347	−	1.38371i
$870$		0			0
$871$	30.4538	−	38.1879i	1.03189	−	1.29395i
$872$	−1.49850	+	0.721640i	−0.0507457	+	0.0244378i
$873$		0			0
$874$	−44.9381	−	21.6410i	−1.52005	−	0.732019i
$875$	−12.0794	+	23.5032i	−0.408359	+	0.794554i
$876$		0			0
$877$	3.63713	+	1.75155i	0.122817	+	0.0591456i	0.494283	−	0.869301i	$-0.335431\pi$
$877$	3.63713	+	1.75155i	0.122817	+	0.0591456i	−0.371466	+	0.928446i	$0.621145\pi$
$878$	−2.06991	−	9.06888i	−0.0698562	−	0.306060i
$879$		0			0
$880$	−16.1413	+	20.2406i	−0.544123	+	0.682309i
$881$	−41.8324			−1.40937			−0.704685	−	0.709520i	$-0.748912\pi$
$881$	−41.8324			−1.40937			−0.704685	+	0.709520i	$0.748912\pi$
$882$		0			0
$883$	50.0791			1.68530			0.842648	−	0.538465i	$-0.180995\pi$
$883$	50.0791			1.68530			0.842648	+	0.538465i	$0.180995\pi$
$884$	−0.324728	+	0.407196i	−0.0109218	+	0.0136955i
$885$		0			0
$886$	12.2251	+	53.5619i	0.410712	+	1.79945i
$887$	19.6235	+	9.45019i	0.658893	+	0.317306i	0.733284	−	0.679923i	$-0.237987\pi$
$887$	19.6235	+	9.45019i	0.658893	+	0.317306i	−0.0743904	+	0.997229i	$0.523701\pi$
$888$		0			0
$889$	−5.93137	+	4.48341i	−0.198932	+	0.150369i
$890$	−3.68753	−	1.77582i	−0.123606	−	0.0595257i
$891$		0			0
$892$	−1.15035	+	0.553977i	−0.0385164	+	0.0185485i
$893$	−26.9068	+	33.7400i	−0.900400	+	1.12907i
$894$		0			0
$895$	−4.56976	+	5.73030i	−0.152750	+	0.191543i
$896$	23.8481	+	20.0520i	0.796707	+	0.669891i
$897$		0			0
$898$	22.9429	−	11.0487i	0.765615	−	0.368701i
$899$	−4.44329	+	19.4673i	−0.148192	+	0.649271i
$900$		0			0
$901$	−14.4368			−0.480961
$902$	−16.1032	+	70.5528i	−0.536179	+	2.34915i
$903$		0			0
$904$	−0.861067	−	3.77258i	−0.0286387	−	0.125474i
$905$	6.41792	+	28.1187i	0.213339	+	0.934698i
$906$		0			0
$907$	−23.2458	−	29.1493i	−0.771863	−	0.967886i	0.228120	−	0.973633i	$-0.426742\pi$
$907$	−23.2458	−	29.1493i	−0.771863	−	0.967886i	−0.999983	+	0.00574733i	$0.998171\pi$
$908$	0.134751	+	0.590382i	0.00447187	+	0.0195925i
$909$		0			0
$910$	13.5813	−	10.2658i	0.450215	−	0.340309i
$911$	12.2320	−	53.5919i	0.405264	−	1.77558i	−0.200251	−	0.979745i	$-0.564176\pi$
$911$	12.2320	−	53.5919i	0.405264	−	1.77558i	0.605515	−	0.795834i	$-0.292967\pi$
$912$		0			0
$913$	−22.6279			−0.748874
$914$	−5.06580	+	22.1947i	−0.167562	+	0.734136i
$915$		0			0
$916$	−0.377658	−	0.473569i	−0.0124782	−	0.0156472i
$917$	8.68530	+	2.22090i	0.286814	+	0.0733407i
$918$		0			0
$919$	−2.72060	+	11.9197i	−0.0897442	+	0.393195i	−0.999772	−	0.0213522i	$-0.993203\pi$
$919$	−2.72060	+	11.9197i	−0.0897442	+	0.393195i	0.910028	+	0.414547i	$0.136060\pi$
$920$	−11.7160	+	14.6914i	−0.386266	+	0.484362i
$921$		0			0
$922$	−16.4495	−	20.6270i	−0.541734	−	0.679314i
$923$	1.99499	+	0.960735i	0.0656658	+	0.0316230i
$924$		0			0
$925$	−22.9120	+	11.0339i	−0.753343	+	0.362791i
$926$	0.139128	+	0.0670006i	0.00457204	+	0.00220178i
$927$		0			0
$928$	1.71303	+	0.824951i	0.0562329	+	0.0270803i
$929$	16.1324	−	20.2294i	0.529287	−	0.663705i	−0.443265	−	0.896391i	$-0.646180\pi$
$929$	16.1324	−	20.2294i	0.529287	−	0.663705i	0.972552	+	0.232685i	$0.0747513\pi$
$930$		0			0
$931$	7.13401	+	40.9429i	0.233808	+	1.34185i
$932$	−0.790289			−0.0258868
$933$		0			0
$934$	−41.9468	−	20.2005i	−1.37254	−	0.660982i
$935$	−3.26008	−	14.2833i	−0.106616	−	0.467115i
$936$		0			0
$937$	2.64576	−	1.27413i	0.0864331	−	0.0416240i	−0.390168	−	0.920744i	$-0.627583\pi$
$937$	2.64576	−	1.27413i	0.0864331	−	0.0416240i	0.476601	+	0.879120i	$0.341869\pi$
$938$	−46.6449	+	9.38039i	−1.52301	+	0.306281i
$939$		0			0
$940$	−0.299816	−	0.375957i	−0.00977892	−	0.0122624i
$941$	−30.3246	+	14.6036i	−0.988555	+	0.476063i	−0.857039	−	0.515251i	$-0.827699\pi$
$941$	−30.3246	+	14.6036i	−0.988555	+	0.476063i	−0.131515	+	0.991314i	$0.541984\pi$
$942$		0			0
$943$	−12.0244	+	52.6825i	−0.391569	+	1.71558i
$944$	−11.2133	+	14.0610i	−0.364961	+	0.457646i
$945$		0			0
$946$	21.3515	+	26.7740i	0.694199	+	0.870497i
$947$	7.92148	−	3.81478i	0.257413	−	0.123964i	−0.300727	−	0.953710i	$-0.597229\pi$
$947$	7.92148	−	3.81478i	0.257413	−	0.123964i	0.558140	+	0.829746i	$0.311515\pi$
$948$		0			0
$949$	57.0572			1.85215
$950$	−31.2893			−1.01516
$951$		0			0
$952$	−16.8165	+	3.38183i	−0.545026	+	0.109606i
$953$	−6.71498	−	29.4202i	−0.217520	−	0.953015i	−0.959304	−	0.282377i	$-0.908877\pi$
$953$	−6.71498	−	29.4202i	−0.217520	−	0.953015i	0.741784	−	0.670639i	$-0.233980\pi$
$954$		0			0
$955$	−19.4362	−	24.3722i	−0.628941	−	0.788667i
$956$	0.276185	+	0.346325i	0.00893247	+	0.0112010i
$957$		0			0
$958$	−5.38224	−	23.5811i	−0.173892	−	0.761871i
$959$	−21.0181	−	5.37450i	−0.678709	−	0.173552i
$960$		0			0
$961$	−19.3566			−0.624408
$962$	38.6792			1.24707
$963$		0			0
$964$	−1.47832	+	0.711919i	−0.0476133	+	0.0229294i
$965$	−10.4076	−	13.0507i	−0.335033	−	0.420118i
$966$		0			0
$967$	−8.51798	+	10.6812i	−0.273920	+	0.343485i	−0.899695	−	0.436519i	$-0.856211\pi$
$967$	−8.51798	+	10.6812i	−0.273920	+	0.343485i	0.625775	+	0.780003i	$0.284783\pi$
$968$	11.7194	−	51.3461i	0.376676	−	1.65033i
$969$		0			0
$970$	−17.4807	+	8.41828i	−0.561273	+	0.270295i
$971$	15.1546	+	19.0033i	0.486336	+	0.609845i	0.963086	−	0.269193i	$-0.0867570\pi$
$971$	15.1546	+	19.0033i	0.486336	+	0.609845i	−0.476751	+	0.879039i	$0.658186\pi$
$972$		0			0
$973$	−6.15391	−	13.6753i	−0.197285	−	0.438411i
$974$	−44.9802	+	21.6613i	−1.44126	+	0.694073i
$975$		0			0
$976$	4.06450	+	17.8078i	0.130102	+	0.570012i
$977$	−21.6239	−	10.4135i	−0.691810	−	0.333158i	0.0547277	−	0.998501i	$-0.482571\pi$
$977$	−21.6239	−	10.4135i	−0.691810	−	0.333158i	−0.746538	+	0.665343i	$0.768285\pi$
$978$		0			0
$979$	13.5506			0.433078
$980$	−0.462469	−	0.0240185i	−0.0147730	−	0.000767242i
$981$		0			0
$982$	−16.6598	+	20.8908i	−0.531636	+	0.666651i
$983$	−3.05665	−	1.47200i	−0.0974919	−	0.0469496i	0.384502	−	0.923124i	$-0.374373\pi$
$983$	−3.05665	−	1.47200i	−0.0974919	−	0.0469496i	−0.481994	+	0.876174i	$0.660087\pi$
$984$		0			0
$985$	5.82179	+	2.80362i	0.185498	+	0.0893309i
$986$	−17.5966	+	8.47407i	−0.560389	+	0.269869i
$987$		0			0
$988$	1.19734	+	0.576608i	0.0380924	+	0.0183443i
$989$	15.9434	+	19.9924i	0.506970	+	0.635721i
$990$		0			0
$991$	23.2896	−	29.2043i	0.739819	−	0.927704i	−0.259456	−	0.965755i	$-0.583543\pi$
$991$	23.2896	−	29.2043i	0.739819	−	0.927704i	0.999276	+	0.0380506i	$0.0121148\pi$
$992$	0.246701	−	1.08087i	0.00783276	−	0.0343175i
$993$		0			0
$994$	−0.885119	−	1.96693i	−0.0280743	−	0.0623871i
$995$	−10.0607	−	12.6157i	−0.318945	−	0.399945i
$996$		0			0
$997$	5.06234	−	22.1795i	0.160326	−	0.702433i	−0.829305	−	0.558797i	$-0.811263\pi$
$997$	5.06234	−	22.1795i	0.160326	−	0.702433i	0.989631	−	0.143637i	$-0.0458796\pi$
$998$	−31.7482			−1.00497
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.190.5		36
3.2	odd	2		147.2.i.b.43.2	✓	36
49.8	even	7	inner	441.2.u.d.253.5		36
147.8	odd	14		147.2.i.b.106.2	yes	36
147.20	even	14		7203.2.a.g.1.6		18
147.29	odd	14		7203.2.a.h.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.43.2	✓	36	3.2	odd	2
147.2.i.b.106.2	yes	36	147.8	odd	14
441.2.u.d.190.5		36	1.1	even	1	trivial
441.2.u.d.253.5		36	49.8	even	7	inner
7203.2.a.g.1.6		18	147.20	even	14
7203.2.a.h.1.6		18	147.29	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)

\(f(q)\)	\(=\)	\(q+(0.894323 - 1.12145i) q^{2} +(-0.0127847 - 0.0560133i) q^{4} +(-1.03743 - 0.499602i) q^{5} +(2.02504 + 1.70270i) q^{7} +(2.51042 + 1.20895i) q^{8} +O(q^{10})\)	\(q+(0.894323 - 1.12145i) q^{2} +(-0.0127847 - 0.0560133i) q^{4} +(-1.03743 - 0.499602i) q^{5} +(2.02504 + 1.70270i) q^{7} +(2.51042 + 1.20895i) q^{8} +(-1.48808 + 0.716620i) q^{10} +(3.40939 - 4.27524i) q^{11} +(-2.42908 + 3.04598i) q^{13} +(3.72053 - 0.748207i) q^{14} +(3.70443 - 1.78396i) q^{16} +(-0.517762 + 2.26846i) q^{17} +5.93712 q^{19} +(-0.0147211 + 0.0644973i) q^{20} +(-1.74535 - 7.64689i) q^{22} +(-1.30327 - 5.71000i) q^{23} +(-2.29078 - 2.87255i) q^{25} +(1.24351 + 5.44817i) q^{26} +(0.0694846 - 0.135198i) q^{28} +(-1.30216 + 5.70515i) q^{29} +3.41224 q^{31} +(0.0722988 - 0.316762i) q^{32} +(2.08091 + 2.60938i) q^{34} +(-1.25017 - 2.77816i) q^{35} +(1.54018 - 6.74795i) q^{37} +(5.30970 - 6.65815i) q^{38} +(-2.00040 - 2.50842i) q^{40} +(-8.31265 - 4.00316i) q^{41} +(-3.93366 + 1.89435i) q^{43} +(-0.283058 - 0.136314i) q^{44} +(-7.56900 - 3.64504i) q^{46} +(-4.53196 + 5.68289i) q^{47} +(1.20159 + 6.89610i) q^{49} -5.27011 q^{50} +(0.201670 + 0.0971192i) q^{52} +(1.38065 + 6.04902i) q^{53} +(-5.67293 + 2.73194i) q^{55} +(3.02521 + 6.72268i) q^{56} +(5.23346 + 6.56255i) q^{58} +(-3.94095 + 1.89786i) q^{59} +(-0.988544 + 4.33109i) q^{61} +(3.05164 - 3.82664i) q^{62} +(4.83652 + 6.06480i) q^{64} +(4.04179 - 1.94642i) q^{65} -12.5372 q^{67} +0.133683 q^{68} +(-4.23361 - 1.08257i) q^{70} +(-0.126470 - 0.554102i) q^{71} +(-9.13117 - 11.4501i) q^{73} +(-6.19004 - 7.76207i) q^{74} +(-0.0759041 - 0.332557i) q^{76} +(14.1836 - 2.85236i) q^{77} +9.54103 q^{79} -4.73437 q^{80} +(-11.9235 + 5.74206i) q^{82} +(-2.58004 - 3.23527i) q^{83} +(1.67047 - 2.09471i) q^{85} +(-1.39355 + 6.10555i) q^{86} +(13.7276 - 6.61085i) q^{88} +(1.54504 + 1.93742i) q^{89} +(-10.1054 + 2.03222i) q^{91} +(-0.303174 + 0.146001i) q^{92} +(2.32002 + 10.1647i) q^{94} +(-6.15937 - 2.96619i) q^{95} +11.7472 q^{97} +(8.80821 + 4.81982i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 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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