LMFDB - Embedded newform 531.2.i.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	531.19
Dual form			531.2.i.c.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.655840 + 1.23705i) q^{2} +(0.0222185 + 0.0327698i) q^{4} +(-2.32817 + 0.512469i) q^{5} +(-1.36308 + 1.03619i) q^{7} +(-2.83899 + 0.308758i) q^{8} +O(q^{10})$	\(q+(-0.655840 + 1.23705i) q^{2} +(0.0222185 + 0.0327698i) q^{4} +(-2.32817 + 0.512469i) q^{5} +(-1.36308 + 1.03619i) q^{7} +(-2.83899 + 0.308758i) q^{8} +(0.892959 - 3.21615i) q^{10} +(-0.846770 - 2.12523i) q^{11} +(-0.224453 - 4.13980i) q^{13} +(-0.387849 - 2.36577i) q^{14} +(1.45066 - 3.64089i) q^{16} +(2.30690 + 1.75366i) q^{17} +(-1.04728 + 0.352870i) q^{19} +(-0.0685219 - 0.0649074i) q^{20} +(3.18436 + 0.346320i) q^{22} +(4.30312 - 2.58910i) q^{23} +(0.619866 - 0.286781i) q^{25} +(5.26832 + 2.43739i) q^{26} +(-0.0642415 - 0.0216455i) q^{28} +(-2.49387 - 4.70395i) q^{29} +(-2.74214 - 0.923934i) q^{31} +(-0.144971 - 0.170673i) q^{32} +(-3.68231 + 1.70362i) q^{34} +(2.64248 - 3.11096i) q^{35} +(-9.84258 - 1.07044i) q^{37} +(0.250332 - 1.52696i) q^{38} +(6.45141 - 2.17373i) q^{40} +(3.19256 + 1.92090i) q^{41} +(0.835041 - 2.09579i) q^{43} +(0.0508296 - 0.0749680i) q^{44} +(0.380678 + 7.02120i) q^{46} +(-7.54956 - 1.66178i) q^{47} +(-1.08839 + 3.92002i) q^{49} +(-0.0517724 + 0.954885i) q^{50} +(0.130673 - 0.0993354i) q^{52} +(1.24085 + 4.46915i) q^{53} +(3.06054 + 4.51396i) q^{55} +(3.54985 - 3.36259i) q^{56} +7.45458 q^{58} +(-5.56257 - 5.29696i) q^{59} +(5.85104 - 11.0362i) q^{61} +(2.94135 - 2.78620i) q^{62} +(7.96145 - 1.75245i) q^{64} +(2.64408 + 9.52312i) q^{65} +(-8.79018 + 0.955990i) q^{67} +(-0.00621128 + 0.114560i) q^{68} +(2.11536 + 5.30916i) q^{70} +(8.56393 + 1.88506i) q^{71} +(0.561736 + 3.42644i) q^{73} +(7.77934 - 11.4737i) q^{74} +(-0.0348325 - 0.0264790i) q^{76} +(3.35637 + 2.01946i) q^{77} +(-9.43853 - 8.94065i) q^{79} +(-1.51155 + 9.22003i) q^{80} +(-4.47005 + 2.68954i) q^{82} +(-11.2514 + 13.2461i) q^{83} +(-6.26954 - 2.90060i) q^{85} +(2.04494 + 2.40749i) q^{86} +(3.06015 + 5.77206i) q^{88} +(-0.366787 - 0.691834i) q^{89} +(4.59557 + 5.41032i) q^{91} +(0.180453 + 0.0834867i) q^{92} +(7.00700 - 8.24928i) q^{94} +(2.25741 - 1.35824i) q^{95} +(-0.438334 + 2.67372i) q^{97} +(-4.13543 - 3.91729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{19}{29}\right)$

Coefficient data

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

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

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

$2$	−0.655840	+	1.23705i	−0.463749	+	0.874723i	0.535790	+	0.844351i	$0.320014\pi$
$2$	−0.655840	+	1.23705i	−0.463749	+	0.874723i	−0.999539	+	0.0303719i	$0.990331\pi$
$3$		0			0
$3$		0			0
$4$	0.0222185	+	0.0327698i	0.0111092	+	0.0163849i
$5$	−2.32817	+	0.512469i	−1.04119	+	0.229183i	−0.702476	−	0.711707i	$-0.747922\pi$
$5$	−2.32817	+	0.512469i	−1.04119	+	0.229183i	−0.338712	+	0.940890i	$0.609991\pi$
$6$		0			0
$7$	−1.36308	+	1.03619i	−0.515198	+	0.391643i	−0.830215	−	0.557443i	$-0.811783\pi$
$7$	−1.36308	+	1.03619i	−0.515198	+	0.391643i	0.315018	+	0.949086i	$0.397990\pi$
$8$	−2.83899	+	0.308758i	−1.00373	+	0.109163i
$9$		0			0
$10$	0.892959	−	3.21615i	0.282378	−	1.01704i
$11$	−0.846770	−	2.12523i	−0.255311	−	0.640782i	0.744324	−	0.667819i	$-0.232772\pi$
$11$	−0.846770	−	2.12523i	−0.255311	−	0.640782i	−0.999634	+	0.0270373i	$0.991393\pi$
$12$		0			0
$13$	−0.224453	−	4.13980i	−0.0622521	−	1.14817i	−0.848129	−	0.529790i	$-0.822271\pi$
$13$	−0.224453	−	4.13980i	−0.0622521	−	1.14817i	0.785877	−	0.618383i	$-0.212212\pi$
$14$	−0.387849	−	2.36577i	−0.103657	−	0.632280i
$15$		0			0
$16$	1.45066	−	3.64089i	0.362666	−	0.910223i
$17$	2.30690	+	1.75366i	0.559505	+	0.425325i	0.846330	−	0.532658i	$-0.178807\pi$
$17$	2.30690	+	1.75366i	0.559505	+	0.425325i	−0.286825	+	0.957983i	$0.592600\pi$
$18$		0			0
$19$	−1.04728	+	0.352870i	−0.240262	+	0.0809538i	−0.436857	−	0.899531i	$-0.643908\pi$
$19$	−1.04728	+	0.352870i	−0.240262	+	0.0809538i	0.196594	+	0.980485i	$0.437012\pi$
$20$	−0.0685219	−	0.0649074i	−0.0153220	−	0.0145137i
$21$		0			0
$22$	3.18436	+	0.346320i	0.678907	+	0.0738356i
$23$	4.30312	−	2.58910i	0.897264	−	0.539866i	0.00939142	−	0.999956i	$-0.497011\pi$
$23$	4.30312	−	2.58910i	0.897264	−	0.539866i	0.887872	+	0.460090i	$0.152183\pi$
$24$		0			0
$25$	0.619866	−	0.286781i	0.123973	−	0.0573561i
$26$	5.26832	+	2.43739i	1.03320	+	0.478011i
$27$		0			0
$28$	−0.0642415	−	0.0216455i	−0.0121405	−	0.00409061i
$29$	−2.49387	−	4.70395i	−0.463101	−	0.873501i	−0.999563	−	0.0295763i	$-0.990584\pi$
$29$	−2.49387	−	4.70395i	−0.463101	−	0.873501i	0.536462	−	0.843925i	$-0.319761\pi$
$30$		0			0
$31$	−2.74214	−	0.923934i	−0.492502	−	0.165943i	0.0620817	−	0.998071i	$-0.480226\pi$
$31$	−2.74214	−	0.923934i	−0.492502	−	0.165943i	−0.554584	+	0.832128i	$0.687123\pi$
$32$	−0.144971	−	0.170673i	−0.0256275	−	0.0301710i
$33$		0			0
$34$	−3.68231	+	1.70362i	−0.631511	+	0.292168i
$35$	2.64248	−	3.11096i	0.446660	−	0.525849i
$36$		0			0
$37$	−9.84258	−	1.07044i	−1.61811	−	0.175980i	−0.746226	−	0.665693i	$-0.768136\pi$
$37$	−9.84258	−	1.07044i	−1.61811	−	0.175980i	−0.871884	+	0.489713i	$0.837102\pi$
$38$	0.250332	−	1.52696i	0.0406092	−	0.247705i
$39$		0			0
$40$	6.45141	−	2.17373i	1.02006	−	0.343697i
$41$	3.19256	+	1.92090i	0.498594	+	0.299994i	0.742548	−	0.669793i	$-0.233617\pi$
$41$	3.19256	+	1.92090i	0.498594	+	0.299994i	−0.243954	+	0.969787i	$0.578445\pi$
$42$		0			0
$43$	0.835041	−	2.09579i	0.127343	−	0.319606i	−0.851458	−	0.524423i	$-0.824281\pi$
$43$	0.835041	−	2.09579i	0.127343	−	0.319606i	0.978800	+	0.204818i	$0.0656602\pi$
$44$	0.0508296	−	0.0749680i	0.00766285	−	0.0113019i
$45$		0			0
$46$	0.380678	+	7.02120i	0.0561280	+	1.03522i
$47$	−7.54956	−	1.66178i	−1.10122	−	0.242396i	−0.373060	−	0.927807i	$-0.621691\pi$
$47$	−7.54956	−	1.66178i	−1.10122	−	0.242396i	−0.728156	+	0.685411i	$0.759622\pi$
$48$		0			0
$49$	−1.08839	+	3.92002i	−0.155484	+	0.560003i
$50$	−0.0517724	+	0.954885i	−0.00732172	+	0.135041i
$51$		0			0
$52$	0.130673	−	0.0993354i	0.0181211	−	0.0137753i
$53$	1.24085	+	4.46915i	0.170444	+	0.613885i	0.998576	+	0.0533509i	$0.0169902\pi$
$53$	1.24085	+	4.46915i	0.170444	+	0.613885i	−0.828132	+	0.560534i	$0.810596\pi$
$54$		0			0
$55$	3.06054	+	4.51396i	0.412683	+	0.608662i
$56$	3.54985	−	3.36259i	0.474368	−	0.449345i
$57$		0			0
$58$	7.45458			0.978834
$59$	−5.56257	−	5.29696i	−0.724185	−	0.689606i
$59$	−5.56257	−	5.29696i	−0.724185	−	0.689606i
$60$		0			0
$61$	5.85104	−	11.0362i	0.749148	−	1.41304i	−0.155917	−	0.987770i	$-0.549833\pi$
$61$	5.85104	−	11.0362i	0.749148	−	1.41304i	0.905065	−	0.425273i	$-0.139822\pi$
$62$	2.94135	−	2.78620i	0.373552	−	0.353847i
$63$		0			0
$64$	7.96145	−	1.75245i	0.995181	−	0.219056i
$65$	2.64408	+	9.52312i	0.327958	+	1.18120i
$66$		0			0
$67$	−8.79018	+	0.955990i	−1.07389	+	0.116793i	−0.627938	−	0.778263i	$-0.716101\pi$
$67$	−8.79018	+	0.955990i	−1.07389	+	0.116793i	−0.445953	+	0.895056i	$0.647135\pi$
$68$	−0.00621128	+	0.114560i	−0.000753229	+	0.0138925i
$69$		0			0
$70$	2.11536	+	5.30916i	0.252834	+	0.634566i
$71$	8.56393	+	1.88506i	1.01635	+	0.223716i	0.691751	−	0.722136i	$-0.256839\pi$
$71$	8.56393	+	1.88506i	1.01635	+	0.223716i	0.324600	+	0.945852i	$0.394770\pi$
$72$		0			0
$73$	0.561736	+	3.42644i	0.0657463	+	0.401034i	0.999113	+	0.0421103i	$0.0134081\pi$
$73$	0.561736	+	3.42644i	0.0657463	+	0.401034i	−0.933367	+	0.358924i	$0.883144\pi$
$74$	7.77934	−	11.4737i	0.904330	−	1.33379i
$75$		0			0
$76$	−0.0348325	−	0.0264790i	−0.00399556	−	0.00303734i
$77$	3.35637	+	2.01946i	0.382493	+	0.230139i
$78$		0			0
$79$	−9.43853	−	8.94065i	−1.06192	−	1.00590i	−0.999969	−	0.00782238i	$-0.997510\pi$
$79$	−9.43853	−	8.94065i	−1.06192	−	1.00590i	−0.0619482	−	0.998079i	$-0.519731\pi$
$80$	−1.51155	+	9.22003i	−0.168996	+	1.03083i
$81$		0			0
$82$	−4.47005	+	2.68954i	−0.493634	+	0.297010i
$83$	−11.2514	+	13.2461i	−1.23500	+	1.45395i	−0.388598	+	0.921407i	$0.627041\pi$
$83$	−11.2514	+	13.2461i	−1.23500	+	1.45395i	−0.846401	+	0.532546i	$0.821235\pi$
$84$		0			0
$85$	−6.26954	−	2.90060i	−0.680027	−	0.314614i
$86$	2.04494	+	2.40749i	0.220512	+	0.259606i
$87$		0			0
$88$	3.06015	+	5.77206i	0.326213	+	0.615304i
$89$	−0.366787	−	0.691834i	−0.0388793	−	0.0733342i	0.863311	−	0.504672i	$-0.168387\pi$
$89$	−0.366787	−	0.691834i	−0.0388793	−	0.0733342i	−0.902191	+	0.431338i	$0.858042\pi$
$90$		0			0
$91$	4.59557	+	5.41032i	0.481746	+	0.567156i
$92$	0.180453	+	0.0834867i	0.0188136	+	0.00870409i
$93$		0			0
$94$	7.00700	−	8.24928i	0.722717	−	0.850849i
$95$	2.25741	−	1.35824i	0.231605	−	0.139352i
$96$		0			0
$97$	−0.438334	+	2.67372i	−0.0445061	+	0.271475i	−0.999700	−	0.0245068i	$-0.992198\pi$
$97$	−0.438334	+	2.67372i	−0.0445061	+	0.271475i	0.955194	+	0.295982i	$0.0956468\pi$
$98$	−4.13543	−	3.91729i	−0.417742	−	0.395706i
$99$		0			0
$100$	0.0231703	+	0.0139411i	0.00231703	+	0.00139411i
$101$	−12.2591	−	9.31916i	−1.21983	−	0.927291i	−0.220983	−	0.975278i	$-0.570926\pi$
$101$	−12.2591	−	9.31916i	−1.21983	−	0.927291i	−0.998848	+	0.0479867i	$0.984719\pi$
$102$		0			0
$103$	4.09784	−	6.04386i	0.403772	−	0.595519i	−0.570389	−	0.821375i	$-0.693208\pi$
$103$	4.09784	−	6.04386i	0.403772	−	0.595519i	0.974161	+	0.225856i	$0.0725179\pi$
$104$	1.91542	+	11.6835i	0.187822	+	1.14566i
$105$		0			0
$106$	−6.34234	−	1.39605i	−0.616023	−	0.135597i
$107$	−0.117180	−	0.294099i	−0.0113282	−	0.0284316i	0.923204	−	0.384311i	$-0.125561\pi$
$107$	−0.117180	−	0.294099i	−0.0113282	−	0.0284316i	−0.934532	+	0.355879i	$0.884182\pi$
$108$		0			0
$109$	−0.766186	+	14.1315i	−0.0733873	+	1.35355i	0.697503	+	0.716582i	$0.254294\pi$
$109$	−0.766186	+	14.1315i	−0.0733873	+	1.35355i	−0.770890	+	0.636968i	$0.780188\pi$
$110$	−7.59119	+	0.825592i	−0.723792	+	0.0787171i
$111$		0			0
$112$	1.79528	+	6.46601i	0.169638	+	0.610980i
$113$	−18.4186	+	4.05424i	−1.73268	+	0.381391i	−0.965573	−	0.260131i	$-0.916234\pi$
$113$	−18.4186	+	4.05424i	−1.73268	+	0.381391i	−0.767104	+	0.641522i	$0.778303\pi$
$114$		0			0
$115$	−8.69156	+	8.23309i	−0.810492	+	0.767739i
$116$	0.0987374	−	0.186239i	0.00916754	−	0.0172918i
$117$		0			0
$118$	10.2007	−	3.40719i	0.939054	−	0.313658i
$119$	−4.96162			−0.454831
$120$		0			0
$121$	4.18635	−	3.96553i	0.380578	−	0.360502i
$122$	9.81497	+	14.4760i	0.888606	+	1.31060i
$123$		0			0
$124$	−0.0306490	−	0.110388i	−0.00275236	−	0.00991312i
$125$	8.19285	−	6.22805i	0.732791	−	0.557053i
$126$		0			0
$127$	−1.00323	+	18.5035i	−0.0890225	+	1.64192i	0.523899	+	0.851780i	$0.324477\pi$
$127$	−1.00323	+	18.5035i	−0.0890225	+	1.64192i	−0.612922	+	0.790144i	$0.710006\pi$
$128$	−2.93376	+	10.5665i	−0.259310	+	0.933952i
$129$		0			0
$130$	−13.5146	−	2.97479i	−1.18531	−	0.260907i
$131$	−0.619653	−	11.4288i	−0.0541393	−	0.998541i	−0.891823	−	0.452385i	$-0.850573\pi$
$131$	−0.619653	−	11.4288i	−0.0541393	−	0.998541i	0.837684	−	0.546156i	$-0.183909\pi$
$132$		0			0
$133$	1.06189	−	1.56617i	0.0920776	−	0.135804i
$134$	4.58235	−	11.5008i	0.395855	−	0.993520i
$135$		0			0
$136$	−7.09071	−	4.26634i	−0.608023	−	0.365835i
$137$	−8.91212	+	3.00284i	−0.761414	+	0.256550i	−0.673109	−	0.739543i	$-0.735041\pi$
$137$	−8.91212	+	3.00284i	−0.761414	+	0.256550i	−0.0883047	+	0.996094i	$0.528145\pi$
$138$		0			0
$139$	−1.77805	+	10.8457i	−0.150813	+	0.919916i	0.797672	+	0.603092i	$0.206065\pi$
$139$	−1.77805	+	10.8457i	−0.150813	+	0.919916i	−0.948484	+	0.316824i	$0.897383\pi$
$140$	0.160658	+	0.0174726i	0.0135780	+	0.00147670i
$141$		0			0
$142$	−7.94847	+	9.35767i	−0.667021	+	0.785278i
$143$	−8.60797	+	3.98247i	−0.719835	+	0.333031i
$144$		0			0
$145$	8.21679	+	9.67355i	0.682367	+	0.803344i
$146$	−4.60707	−	1.55230i	−0.381284	−	0.128470i
$147$		0			0
$148$	−0.183609	−	0.346323i	−0.0150926	−	0.0284676i
$149$	−10.1911	−	3.43378i	−0.834886	−	0.281306i	−0.130790	−	0.991410i	$-0.541751\pi$
$149$	−10.1911	−	3.43378i	−0.834886	−	0.281306i	−0.704097	+	0.710104i	$0.748648\pi$
$150$		0			0
$151$	11.7806	+	5.45029i	0.958692	+	0.443538i	0.835892	−	0.548894i	$-0.184951\pi$
$151$	11.7806	+	5.45029i	0.958692	+	0.443538i	0.122799	+	0.992432i	$0.460813\pi$
$152$	2.86426	−	1.32515i	0.232322	−	0.107484i
$153$		0			0
$154$	−4.69940	+	2.82754i	−0.378689	+	0.227849i
$155$	6.85764	+	0.745814i	0.550819	+	0.0599052i
$156$		0			0
$157$	−6.64463	−	6.29413i	−0.530299	−	0.502326i	0.375044	−	0.927007i	$-0.377628\pi$
$157$	−6.64463	−	6.29413i	−0.530299	−	0.502326i	−0.905343	+	0.424681i	$0.860386\pi$
$158$	17.2502	−	5.81226i	1.37235	−	0.462398i
$159$		0			0
$160$	0.424982	+	0.323063i	0.0335977	+	0.0255403i
$161$	−3.18272	+	7.98802i	−0.250833	+	0.629545i
$162$		0			0
$163$	−1.41716	−	8.64428i	−0.111000	−	0.677072i	−0.982441	−	0.186572i	$-0.940262\pi$
$163$	−1.41716	−	8.64428i	−0.111000	−	0.677072i	0.871441	−	0.490500i	$-0.163186\pi$
$164$	0.00798633	+	0.147299i	0.000623627	+	0.0115021i
$165$		0			0
$166$	−9.00698	−	22.6058i	−0.699077	−	1.75455i
$167$	−2.79465	+	10.0654i	−0.216257	+	0.778887i	0.773213	+	0.634147i	$0.218648\pi$
$167$	−2.79465	+	10.0654i	−0.216257	+	0.778887i	−0.989470	+	0.144740i	$0.953765\pi$
$168$		0			0
$169$	−4.16375	+	0.452835i	−0.320288	+	0.0348334i
$170$	7.69999	−	5.85338i	0.590562	−	0.448934i
$171$		0			0
$172$	0.0872322	−	0.0192013i	0.00665139	−	0.00146408i
$173$	5.81422	+	8.57533i	0.442047	+	0.651970i	0.981814	−	0.189844i	$-0.0607982\pi$
$173$	5.81422	+	8.57533i	0.442047	+	0.651970i	−0.539768	+	0.841814i	$0.681488\pi$
$174$		0			0
$175$	−0.547771	+	1.03321i	−0.0414076	+	0.0781030i
$176$	−8.96612			−0.675847
$177$		0			0
$178$	1.09638			0.0821774
$179$	2.91165	−	5.49195i	0.217627	−	0.410488i	−0.750529	−	0.660838i	$-0.770201\pi$
$179$	2.91165	−	5.49195i	0.217627	−	0.410488i	0.968155	+	0.250350i	$0.0805458\pi$
$180$		0			0
$181$	9.39115	+	13.8509i	0.698038	+	1.02953i	0.997160	+	0.0753146i	$0.0239961\pi$
$181$	9.39115	+	13.8509i	0.698038	+	1.02953i	−0.299121	+	0.954215i	$0.596694\pi$
$182$	−9.70677	+	2.13662i	−0.719513	+	0.158377i
$183$		0			0
$184$	−11.4171	+	8.67905i	−0.841680	+	0.639828i
$185$	23.4637	−	2.55184i	1.72509	−	0.187615i
$186$		0			0
$187$	1.77352	−	6.38764i	0.129693	−	0.467111i
$188$	−0.113283	−	0.284320i	−0.00826205	−	0.0207362i
$189$		0			0
$190$	0.199703	+	3.68330i	0.0144880	+	0.267215i
$191$	−2.32159	−	14.1611i	−0.167985	−	1.02466i	−0.927405	−	0.374060i	$-0.877965\pi$
$191$	−2.32159	−	14.1611i	−0.167985	−	1.02466i	0.759420	−	0.650601i	$-0.225483\pi$
$192$		0			0
$193$	−3.54190	+	8.88950i	−0.254952	+	0.639881i	−0.999620	−	0.0275539i	$-0.991228\pi$
$193$	−3.54190	+	8.88950i	−0.254952	+	0.639881i	0.744669	+	0.667434i	$0.232608\pi$
$194$	−3.02003	−	2.29577i	−0.216826	−	0.164827i
$195$		0			0
$196$	−0.152641	+	0.0514307i	−0.0109029	+	0.00367362i
$197$	13.5737	+	12.8577i	0.967085	+	0.916072i	0.996508	−	0.0834951i	$-0.0266083\pi$
$197$	13.5737	+	12.8577i	0.967085	+	0.916072i	−0.0294228	+	0.999567i	$0.509367\pi$
$198$		0			0
$199$	−10.8835	−	1.18365i	−0.771511	−	0.0839069i	−0.286108	−	0.958197i	$-0.592362\pi$
$199$	−10.8835	−	1.18365i	−0.771511	−	0.0839069i	−0.485403	+	0.874291i	$0.661327\pi$
$200$	−1.67125	+	1.00556i	−0.118175	+	0.0711035i
$201$		0			0
$202$	19.5683	−	9.05324i	1.37682	−	0.636984i
$203$	8.27355	+	3.82775i	0.580689	+	0.268655i
$204$		0			0
$205$	−8.41721	−	2.83609i	−0.587884	−	0.198081i
$206$	4.78900	+	9.03301i	0.333665	+	0.629360i
$207$		0			0
$208$	−15.3982	−	5.18824i	−1.06767	−	0.359740i
$209$	1.63674	+	1.92691i	0.113215	+	0.133287i
$210$		0			0
$211$	−22.1300	+	10.2384i	−1.52349	+	0.704842i	−0.990014	−	0.140971i	$-0.954977\pi$
$211$	−22.1300	+	10.2384i	−1.52349	+	0.704842i	−0.533478	+	0.845814i	$0.679115\pi$
$212$	−0.118883	+	0.139960i	−0.00816494	+	0.00961251i
$213$		0			0
$214$	0.440665	+	0.0479252i	0.0301233	+	0.00327610i
$215$	−0.870087	+	5.30729i	−0.0593394	+	0.361954i
$216$		0			0
$217$	4.69514	−	1.58198i	0.318727	−	0.107392i
$218$	−16.9788	−	10.2158i	−1.14995	−	0.691901i
$219$		0			0
$220$	−0.0799210	+	0.200587i	−0.00538828	+	0.0135236i
$221$	6.74200	−	9.94371i	0.453516	−	0.668886i
$222$		0			0
$223$	−1.06471	−	19.6374i	−0.0712980	−	1.31501i	−0.787149	−	0.616762i	$-0.788444\pi$
$223$	−1.06471	−	19.6374i	−0.0712980	−	1.31501i	0.715851	−	0.698253i	$-0.246039\pi$
$224$	0.374458	+	0.0824244i	0.0250195	+	0.00550721i
$225$		0			0
$226$	7.06438	−	25.4436i	0.469916	−	1.69248i
$227$	0.676956	−	12.4857i	0.0449311	−	0.828706i	−0.886039	−	0.463611i	$-0.846554\pi$
$227$	0.676956	−	12.4857i	0.0449311	−	0.828706i	0.930970	−	0.365095i	$-0.118964\pi$
$228$		0			0
$229$	22.9269	−	17.4286i	1.51505	−	1.15171i	0.571444	−	0.820641i	$-0.306383\pi$
$229$	22.9269	−	17.4286i	1.51505	−	1.15171i	0.943606	−	0.331070i	$-0.107410\pi$
$230$	−4.48443	−	16.1514i	−0.295694	−	1.06499i
$231$		0			0
$232$	8.53246	+	12.5844i	0.560183	+	0.826209i
$233$	2.81047	−	2.66222i	0.184120	−	0.174408i	−0.590088	−	0.807339i	$-0.700907\pi$
$233$	2.81047	−	2.66222i	0.184120	−	0.174408i	0.774208	+	0.632931i	$0.218148\pi$
$234$		0			0
$235$	18.4283			1.20213
$236$	0.0499886	−	0.299975i	0.00325398	−	0.0195267i
$237$		0			0
$238$	3.25403	−	6.13775i	0.210928	−	0.397852i
$239$	−1.59222	+	1.50823i	−0.102992	+	0.0975592i	−0.737463	−	0.675387i	$-0.763977\pi$
$239$	−1.59222	+	1.50823i	−0.102992	+	0.0975592i	0.634471	+	0.772946i	$0.281218\pi$
$240$		0			0
$241$	25.8579	−	5.69175i	1.66565	−	0.366638i	0.720547	−	0.693406i	$-0.243891\pi$
$241$	25.8579	−	5.69175i	1.66565	−	0.366638i	0.945105	+	0.326768i	$0.105960\pi$
$242$	2.15996	+	7.77946i	0.138847	+	0.500083i
$243$		0			0
$244$	0.491656	−	0.0534709i	0.0314751	−	0.00342312i
$245$	0.525064	−	9.68423i	0.0335451	−	0.618703i
$246$		0			0
$247$	1.69587	+	4.25632i	0.107906	+	0.270823i
$248$	8.07016	+	1.77638i	0.512456	+	0.112800i
$249$		0			0
$250$	2.33117	+	14.2195i	0.147436	+	0.899322i
$251$	3.78710	−	5.58555i	0.239039	−	0.352557i	−0.689180	−	0.724590i	$-0.742029\pi$
$251$	3.78710	−	5.58555i	0.239039	−	0.352557i	0.928219	+	0.372034i	$0.121339\pi$
$252$		0			0
$253$	−9.14621	−	6.95277i	−0.575017	−	0.437117i
$254$	−22.2318	−	13.3764i	−1.39494	−	0.839310i
$255$		0			0
$256$	0.689574	+	0.653199i	0.0430984	+	0.0408250i
$257$	−0.0481822	+	0.293898i	−0.00300552	+	0.0183329i	−0.988287	−	0.152609i	$-0.951233\pi$
$257$	−0.0481822	+	0.293898i	−0.00300552	+	0.0183329i	0.985281	+	0.170941i	$0.0546809\pi$
$258$		0			0
$259$	14.5255	−	8.73967i	0.902568	−	0.543057i
$260$	−0.253324	+	0.298236i	−0.0157105	+	0.0184958i
$261$		0			0
$262$	14.5444	+	6.72894i	0.898554	+	0.415715i
$263$	−4.79419	−	5.64415i	−0.295622	−	0.348033i	0.594219	−	0.804303i	$-0.297461\pi$
$263$	−4.79419	−	5.64415i	−0.295622	−	0.348033i	−0.889842	+	0.456270i	$0.849185\pi$
$264$		0			0
$265$	−5.17921	−	9.76903i	−0.318156	−	0.600107i
$266$	1.24100	+	2.34077i	0.0760903	+	0.143522i
$267$		0			0
$268$	−0.226632	−	0.266812i	−0.0138438	−	0.0162981i
$269$	25.9639	+	12.0122i	1.58305	+	0.732395i	0.996964	−	0.0778578i	$-0.0248080\pi$
$269$	25.9639	+	12.0122i	1.58305	+	0.732395i	0.586081	+	0.810253i	$0.300670\pi$
$270$		0			0
$271$	18.8640	−	22.2084i	1.14590	−	1.34906i	0.218130	−	0.975920i	$-0.430004\pi$
$271$	18.8640	−	22.2084i	1.14590	−	1.34906i	0.927774	−	0.373143i	$-0.121720\pi$
$272$	9.73141	−	5.85520i	0.590054	−	0.355023i
$273$		0			0
$274$	2.13027	−	12.9941i	0.128694	−	0.785001i
$275$	−1.13436	−	1.07452i	−0.0684045	−	0.0647962i
$276$		0			0
$277$	2.76509	+	1.66370i	0.166138	+	0.0999619i	0.596194	−	0.802840i	$-0.296679\pi$
$277$	2.76509	+	1.66370i	0.166138	+	0.0999619i	−0.430056	+	0.902802i	$0.641506\pi$
$278$	−12.2504	−	9.31255i	−0.734733	−	0.558529i
$279$		0			0
$280$	−6.54142	+	9.64787i	−0.390924	+	0.576570i
$281$	2.26039	+	13.7878i	0.134844	+	0.822509i	0.964470	+	0.264191i	$0.0851049\pi$
$281$	2.26039	+	13.7878i	0.134844	+	0.822509i	−0.829627	+	0.558318i	$0.811447\pi$
$282$		0			0
$283$	−10.9289	−	2.40563i	−0.649655	−	0.143000i	−0.122096	−	0.992518i	$-0.538962\pi$
$283$	−10.9289	−	2.40563i	−0.649655	−	0.143000i	−0.527559	+	0.849519i	$0.676893\pi$
$284$	0.128504	+	0.322522i	0.00762533	+	0.0191381i
$285$		0			0
$286$	0.718954	−	13.2603i	0.0425126	−	0.784099i
$287$	−6.34215	+	0.689750i	−0.374365	+	0.0407146i
$288$		0			0
$289$	−2.30152	−	8.28932i	−0.135383	−	0.487607i
$290$	−17.3555	+	3.82024i	−1.01915	+	0.224332i
$291$		0			0
$292$	−0.0998029	+	0.0945384i	−0.00584053	+	0.00553244i
$293$	5.38655	−	10.1601i	0.314685	−	0.593560i	−0.674832	−	0.737971i	$-0.735784\pi$
$293$	5.38655	−	10.1601i	0.314685	−	0.593560i	0.989518	+	0.144412i	$0.0461289\pi$
$294$		0			0
$295$	15.6651	+	9.48158i	0.912059	+	0.552039i
$296$	28.2734			1.64336
$297$		0			0
$298$	10.9315	−	10.3548i	0.633242	−	0.599839i
$299$	−11.6842	−	17.2329i	−0.675716	−	0.996606i
$300$		0			0
$301$	1.03341	+	3.72201i	0.0595648	+	0.214533i
$302$	−14.4684	+	10.9986i	−0.832565	+	0.632900i
$303$		0			0
$304$	−0.234491	+	4.32493i	−0.0134490	+	0.248052i
$305$	−7.96648	+	28.6927i	−0.456159	+	1.64294i
$306$		0			0
$307$	−21.7881	−	4.79592i	−1.24351	−	0.273718i	−0.455979	−	0.889990i	$-0.650711\pi$
$307$	−21.7881	−	4.79592i	−1.24351	−	0.273718i	−0.787533	+	0.616273i	$0.788642\pi$
$308$	0.00839610	+	0.154857i	0.000478412	+	0.00882379i
$309$		0			0
$310$	−5.42012	+	7.99408i	−0.307842	+	0.454034i
$311$	−0.914478	+	2.29517i	−0.0518553	+	0.130147i	−0.952622	−	0.304155i	$-0.901626\pi$
$311$	−0.914478	+	2.29517i	−0.0518553	+	0.130147i	0.900767	+	0.434302i	$0.143005\pi$
$312$		0			0
$313$	9.35011	+	5.62577i	0.528499	+	0.317988i	0.754675	−	0.656099i	$-0.227795\pi$
$313$	9.35011	+	5.62577i	0.528499	+	0.317988i	−0.226175	+	0.974087i	$0.572622\pi$
$314$	12.1439	−	4.09177i	0.685322	−	0.230912i
$315$		0			0
$316$	0.0832737	−	0.507947i	0.00468451	−	0.0285742i
$317$	−1.58790	−	0.172695i	−0.0891854	−	0.00969949i	0.0634175	−	0.997987i	$-0.479800\pi$
$317$	−1.58790	−	0.172695i	−0.0891854	−	0.00969949i	−0.152603	+	0.988288i	$0.548766\pi$
$318$		0			0
$319$	−7.88524	+	9.28323i	−0.441489	+	0.519761i
$320$	−17.6375	+	8.15998i	−0.985967	+	0.456157i
$321$		0			0
$322$	−7.79420	−	9.17604i	−0.434354	−	0.511361i
$323$	−3.03478	−	1.02254i	−0.168860	−	0.0568955i
$324$		0			0
$325$	−1.32634	−	2.50175i	−0.0735724	−	0.138772i
$326$	11.6228	+	3.91618i	0.643727	+	0.216897i
$327$		0			0
$328$	−9.65672	−	4.46767i	−0.533203	−	0.246686i
$329$	12.0126	−	5.55763i	0.662277	−	0.306402i
$330$		0			0
$331$	−10.7754	+	6.48334i	−0.592269	+	0.356357i	−0.779920	−	0.625879i	$-0.784740\pi$
$331$	−10.7754	+	6.48334i	−0.592269	+	0.356357i	0.187651	+	0.982236i	$0.439913\pi$
$332$	−0.684063	−	0.0743963i	−0.0375428	−	0.00408303i
$333$		0			0
$334$	−10.6186	−	10.0584i	−0.581021	−	0.550373i
$335$	19.9751	−	6.73040i	1.09136	−	0.367721i
$336$		0			0
$337$	17.7400	+	13.4856i	0.966358	+	0.734606i	0.964141	−	0.265391i	$-0.0855011\pi$
$337$	17.7400	+	13.4856i	0.966358	+	0.734606i	0.00221723	+	0.999998i	$0.499294\pi$
$338$	2.17057	−	5.44773i	0.118064	−	0.296317i
$339$		0			0
$340$	−0.0442477	−	0.269899i	−0.00239967	−	0.0146373i
$341$	0.358386	+	6.61004i	0.0194077	+	0.357954i
$342$		0			0
$343$	−7.01462	−	17.6054i	−0.378754	−	0.950601i
$344$	−1.72357	+	6.20776i	−0.0929289	+	0.334700i
$345$		0			0
$346$	−14.4213	+	1.56841i	−0.775292	+	0.0843181i
$347$	−18.4226	+	14.0045i	−0.988976	+	0.751800i	−0.968761	−	0.247996i	$-0.920228\pi$
$347$	−18.4226	+	14.0045i	−0.988976	+	0.751800i	−0.0202148	+	0.999796i	$0.506435\pi$
$348$		0			0
$349$	−6.76264	+	1.48857i	−0.361996	+	0.0796813i	−0.392244	−	0.919861i	$-0.628301\pi$
$349$	−6.76264	+	1.48857i	−0.361996	+	0.0796813i	0.0302484	+	0.999542i	$0.490370\pi$
$350$	−0.918872	−	1.35524i	−0.0491158	−	0.0724404i
$351$		0			0
$352$	−0.239963	+	0.452618i	−0.0127901	+	0.0241246i
$353$	16.4594			0.876046			0.438023	−	0.898964i	$-0.355679\pi$
$353$	16.4594			0.876046			0.438023	+	0.898964i	$0.355679\pi$
$354$		0			0
$355$	−20.9043			−1.10948
$356$	0.0145218	−	0.0273911i	0.000769655	−	0.00145172i
$357$		0			0
$358$	4.88422	+	7.20368i	0.258139	+	0.380726i
$359$	6.61869	−	1.45688i	0.349321	−	0.0768914i	−0.0368441	−	0.999321i	$-0.511730\pi$
$359$	6.61869	−	1.45688i	0.349321	−	0.0768914i	0.386165	+	0.922430i	$0.373799\pi$
$360$		0			0
$361$	−14.1535	+	10.7592i	−0.744921	+	0.566274i
$362$	−23.2933	+	2.53330i	−1.22427	+	0.133147i
$363$		0			0
$364$	−0.0751887	+	0.270805i	−0.00394096	+	0.0141940i
$365$	−3.06376	−	7.68946i	−0.160365	−	0.402485i
$366$		0			0
$367$	−1.48058	−	27.3077i	−0.0772857	−	1.42545i	−0.737993	−	0.674808i	$-0.764226\pi$
$367$	−1.48058	−	27.3077i	−0.0772857	−	1.42545i	0.660708	−	0.750643i	$-0.270256\pi$
$368$	−3.18426	−	19.4231i	−0.165991	−	1.01250i
$369$		0			0
$370$	−12.2317	+	30.6993i	−0.635897	+	1.59598i
$371$	−6.32228	−	4.80607i	−0.328236	−	0.249519i
$372$		0			0
$373$	18.0246	−	6.07320i	0.933279	−	0.314458i	0.188732	−	0.982029i	$-0.439562\pi$
$373$	18.0246	−	6.07320i	0.933279	−	0.314458i	0.744547	+	0.667570i	$0.232666\pi$
$374$	6.73866	+	6.38320i	0.348448	+	0.330067i
$375$		0			0
$376$	21.9462	+	2.38679i	1.13179	+	0.123089i
$377$	−18.9136	+	11.3800i	−0.974101	+	0.586097i
$378$		0			0
$379$	−17.5036	+	8.09804i	−0.899101	+	0.415968i	−0.814310	−	0.580431i	$-0.802884\pi$
$379$	−17.5036	+	8.09804i	−0.899101	+	0.415968i	−0.0847908	+	0.996399i	$0.527022\pi$
$380$	0.0946655	+	0.0437969i	0.00485624	+	0.00224673i
$381$		0			0
$382$	19.0405	+	6.41550i	0.974197	+	0.328245i
$383$	2.94442	+	5.55377i	0.150453	+	0.283785i	0.947270	−	0.320436i	$-0.103829\pi$
$383$	2.94442	+	5.55377i	0.150453	+	0.283785i	−0.796817	+	0.604221i	$0.793485\pi$
$384$		0			0
$385$	−8.84909	−	2.98161i	−0.450992	−	0.151957i
$386$	−8.67380	−	10.2116i	−0.441485	−	0.519756i
$387$		0			0
$388$	−0.0973564	+	0.0450419i	−0.00494252	+	0.00228666i
$389$	0.370781	−	0.436517i	0.0187994	−	0.0221323i	−0.752682	−	0.658384i	$-0.771240\pi$
$389$	0.370781	−	0.436517i	0.0187994	−	0.0221323i	0.771481	+	0.636252i	$0.219516\pi$
$390$		0			0
$391$	14.4673	+	1.57341i	0.731642	+	0.0795708i
$392$	1.87958	−	11.4649i	0.0949331	−	0.579066i
$393$		0			0
$394$	−24.8077	+	8.35869i	−1.24979	+	0.421105i
$395$	26.5563	+	15.9784i	1.33619	+	0.803960i
$396$		0			0
$397$	−6.20244	+	15.5670i	−0.311292	+	0.781283i	0.687205	+	0.726464i	$0.258838\pi$
$397$	−6.20244	+	15.5670i	−0.311292	+	0.781283i	−0.998496	+	0.0548192i	$0.982542\pi$
$398$	8.60207	−	12.6871i	0.431183	−	0.635947i
$399$		0			0
$400$	−0.144920	−	2.67289i	−0.00724599	−	0.133644i
$401$	−17.0686	−	3.75709i	−0.852367	−	0.187620i	−0.232762	−	0.972534i	$-0.574776\pi$
$401$	−17.0686	−	3.75709i	−0.852367	−	0.187620i	−0.619605	+	0.784914i	$0.712707\pi$
$402$		0			0
$403$	−3.20942	+	11.5593i	−0.159872	+	0.575808i
$404$	0.0330075	−	0.608788i	0.00164219	−	0.0302883i
$405$		0			0
$406$	−10.1612	+	7.72436i	−0.504293	+	0.383354i
$407$	6.05946	+	21.8242i	0.300356	+	1.08178i
$408$		0			0
$409$	11.9735	+	17.6597i	0.592054	+	0.873214i	0.999194	−	0.0401521i	$-0.0127842\pi$
$409$	11.9735	+	17.6597i	0.592054	+	0.873214i	−0.407140	+	0.913366i	$0.633474\pi$
$410$	9.02872	−	8.55246i	0.445897	−	0.422376i
$411$		0			0
$412$	0.289104			0.0142431
$413$	13.0709	+	1.45633i	0.643178	+	0.0716612i
$414$		0			0
$415$	19.4069	−	36.6052i	0.952646	−	1.79688i
$416$	−0.674013	+	0.638459i	−0.0330462	+	0.0313030i
$417$		0			0
$418$	−3.45712	+	0.760969i	−0.169093	+	0.0372202i
$419$	−1.29001	−	4.64620i	−0.0630212	−	0.226982i	0.925332	−	0.379157i	$-0.123786\pi$
$419$	−1.29001	−	4.64620i	−0.0630212	−	0.226982i	−0.988354	+	0.152175i	$0.951372\pi$
$420$		0			0
$421$	12.6165	−	1.37213i	0.614892	−	0.0668735i	0.204627	−	0.978840i	$-0.434402\pi$
$421$	12.6165	−	1.37213i	0.614892	−	0.0668735i	0.410265	+	0.911966i	$0.365436\pi$
$422$	1.84834	−	34.0906i	0.0899757	−	1.65950i
$423$		0			0
$424$	−4.90265	−	12.3047i	−0.238094	−	0.597570i
$425$	1.93288	+	0.425460i	0.0937587	+	0.0206378i
$426$		0			0
$427$	3.46017	+	21.1061i	0.167449	+	1.02140i
$428$	0.00703402	−	0.0103744i	0.000340002	−	0.000501466i
$429$		0			0
$430$	−5.99473	−	4.55707i	−0.289091	−	0.219762i
$431$	−24.2220	−	14.5739i	−1.16673	−	0.702001i	−0.205751	−	0.978604i	$-0.565964\pi$
$431$	−24.2220	−	14.5739i	−1.16673	−	0.702001i	−0.960984	+	0.276603i	$0.910791\pi$
$432$		0			0
$433$	−12.9823	−	12.2974i	−0.623888	−	0.590978i	0.309037	−	0.951050i	$-0.399993\pi$
$433$	−12.9823	−	12.2974i	−0.623888	−	0.590978i	−0.932924	+	0.360072i	$0.882752\pi$
$434$	−1.12228	+	6.84562i	−0.0538713	+	0.328600i
$435$		0			0
$436$	−0.480110	+	0.288872i	−0.0229931	+	0.0138345i
$437$	−3.59296	+	4.22996i	−0.171875	+	0.202346i
$438$		0			0
$439$	−29.3160	−	13.5630i	−1.39918	−	0.647329i	−0.432104	−	0.901824i	$-0.642229\pi$
$439$	−29.3160	−	13.5630i	−1.39918	−	0.647329i	−0.967074	+	0.254495i	$0.918091\pi$
$440$	−10.0825	−	11.8701i	−0.480667	−	0.565884i
$441$		0			0
$442$	7.87914	+	14.8616i	0.374773	+	0.706896i
$443$	−8.16714	−	15.4049i	−0.388032	−	0.731907i	0.610143	−	0.792291i	$-0.291112\pi$
$443$	−8.16714	−	15.4049i	−0.388032	−	0.731907i	−0.998175	+	0.0603848i	$0.980767\pi$
$444$		0			0
$445$	1.20848	+	1.42274i	0.0572877	+	0.0674443i
$446$	24.9906	+	11.5619i	1.18334	+	0.547471i
$447$		0			0
$448$	−9.03626	+	10.6383i	−0.426923	+	0.502613i
$449$	11.0018	−	6.61954i	0.519205	−	0.312395i	−0.231720	−	0.972782i	$-0.574435\pi$
$449$	11.0018	−	6.61954i	0.519205	−	0.312395i	0.750925	+	0.660387i	$0.229608\pi$
$450$		0			0
$451$	1.37899	−	8.41149i	0.0649343	−	0.396082i
$452$	−0.542091	−	0.513496i	−0.0254978	−	0.0241528i
$453$		0			0
$454$	15.0014	+	9.02605i	0.704051	+	0.423614i
$455$	−13.4719	−	10.2410i	−0.631571	−	0.480108i
$456$		0			0
$457$	−20.8107	+	30.6935i	−0.973483	+	1.43578i	−0.0747918	+	0.997199i	$0.523829\pi$
$457$	−20.8107	+	30.6935i	−0.973483	+	1.43578i	−0.898692	+	0.438581i	$0.855481\pi$
$458$	6.52356	+	39.7919i	0.304826	+	1.85935i
$459$		0			0
$460$	−0.462910	−	0.101894i	−0.0215833	−	0.00475085i
$461$	−8.60746	−	21.6031i	−0.400889	−	1.00616i	−0.981412	−	0.191912i	$-0.938531\pi$
$461$	−8.60746	−	21.6031i	−0.400889	−	1.00616i	0.580523	−	0.814244i	$-0.302848\pi$
$462$		0			0
$463$	−0.318232	+	5.86944i	−0.0147895	+	0.272776i	0.981780	+	0.190020i	$0.0608551\pi$
$463$	−0.318232	+	5.86944i	−0.0147895	+	0.272776i	−0.996570	+	0.0827565i	$0.973628\pi$
$464$	−20.7443	+	2.25608i	−0.963031	+	0.104736i
$465$		0			0
$466$	1.45007	+	5.22267i	0.0671731	+	0.241936i
$467$	16.1589	−	3.55684i	0.747744	−	0.164591i	0.175278	−	0.984519i	$-0.443918\pi$
$467$	16.1589	−	3.55684i	0.747744	−	0.164591i	0.572466	+	0.819928i	$0.305987\pi$
$468$		0			0
$469$	10.9912	−	10.4114i	0.507525	−	0.480753i
$470$	−12.0860	+	22.7966i	−0.557485	+	1.05153i
$471$		0			0
$472$	17.4275	+	13.3205i	0.802168	+	0.613126i
$473$	−5.16114			−0.237309
$474$		0			0
$475$	−0.547977	+	0.519072i	−0.0251429	+	0.0238166i
$476$	−0.110240	−	0.162592i	−0.00505283	−	0.00745237i
$477$		0			0
$478$	−0.821508	−	2.95880i	−0.0375749	−	0.135332i
$479$	−27.7991	+	21.1323i	−1.27017	+	0.965561i	−0.270178	+	0.962810i	$0.587082\pi$
$479$	−27.7991	+	21.1323i	−1.27017	+	0.965561i	−0.999996	+	0.00275063i	$0.999124\pi$
$480$		0			0
$481$	−2.22222	+	40.9865i	−0.101325	+	1.86882i
$482$	−9.91768	+	35.7202i	−0.451738	+	1.62701i
$483$		0			0
$484$	0.222964	+	0.0490781i	0.0101347	+	0.00223082i
$485$	−0.349682	−	6.44950i	−0.0158782	−	0.292857i
$486$		0			0
$487$	16.1872	−	23.8744i	0.733513	−	1.08185i	−0.259717	−	0.965685i	$-0.583629\pi$
$487$	16.1872	−	23.8744i	0.733513	−	1.08185i	0.993230	−	0.116166i	$-0.0370604\pi$
$488$	−13.2035	+	33.1382i	−0.597693	+	1.50010i
$489$		0			0
$490$	11.6355	+	7.00083i	0.525637	+	0.316265i
$491$	17.2765	−	5.82114i	0.779679	−	0.262704i	0.0988067	−	0.995107i	$-0.468497\pi$
$491$	17.2765	−	5.82114i	0.779679	−	0.262704i	0.680872	+	0.732402i	$0.261601\pi$
$492$		0			0
$493$	2.49600	−	15.2249i	0.112414	−	0.685697i
$494$	−6.37749	−	0.693594i	−0.286937	−	0.0312062i
$495$		0			0
$496$	−7.34186	+	8.64351i	−0.329659	+	0.388105i
$497$	−13.6266	+	6.30436i	−0.611238	+	0.282789i
$498$		0			0
$499$	−17.0104	−	20.0262i	−0.761491	−	0.896497i	0.235667	−	0.971834i	$-0.424273\pi$
$499$	−17.0104	−	20.0262i	−0.761491	−	0.896497i	−0.997158	+	0.0753371i	$0.975997\pi$
$500$	0.386125	+	0.130101i	0.0172680	+	0.00581828i
$501$		0			0
$502$	4.42585	+	8.34804i	0.197535	+	0.372591i
$503$	−20.9797	−	7.06888i	−0.935438	−	0.315186i	−0.190018	−	0.981781i	$-0.560855\pi$
$503$	−20.9797	−	7.06888i	−0.935438	−	0.315186i	−0.745420	+	0.666595i	$0.767751\pi$
$504$		0			0
$505$	33.3171	+	15.4141i	1.48259	+	0.685920i
$506$	14.5993	−	6.75437i	0.649020	−	0.300269i
$507$		0			0
$508$	−0.628648	+	0.378245i	−0.0278918	+	0.0167819i
$509$	40.6966	+	4.42602i	1.80385	+	0.196180i	0.947399	−	0.320055i	$-0.103701\pi$
$509$	40.6966	+	4.42602i	1.80385	+	0.196180i	0.856447	+	0.516235i	$0.172667\pi$
$510$		0			0
$511$	−4.31614	−	4.08846i	−0.190935	−	0.180863i
$512$	−22.0445	+	7.42767i	−0.974240	+	0.328260i
$513$		0			0
$514$	−0.331966	−	0.252354i	−0.0146424	−	0.0111308i
$515$	−6.44317	+	16.1711i	−0.283920	+	0.712585i
$516$		0			0
$517$	2.86106	+	17.4517i	0.125829	+	0.767526i
$518$	1.28500	+	23.7005i	0.0564598	+	1.04134i
$519$		0			0
$520$	−10.4468	−	26.2196i	−0.458125	−	1.14981i
$521$	−10.1814	+	36.6701i	−0.446056	+	1.60655i	0.309119	+	0.951023i	$0.399966\pi$
$521$	−10.1814	+	36.6701i	−0.446056	+	1.60655i	−0.755174	+	0.655524i	$0.772448\pi$
$522$		0			0
$523$	1.74038	−	0.189277i	0.0761014	−	0.00827652i	−0.0699891	−	0.997548i	$-0.522296\pi$
$523$	1.74038	−	0.189277i	0.0761014	−	0.00827652i	0.146090	+	0.989271i	$0.453331\pi$
$524$	0.360753	−	0.274237i	0.0157596	−	0.0119801i
$525$		0			0
$526$	10.1263	−	2.22897i	0.441527	−	0.0971875i
$527$	−4.70557	−	6.94020i	−0.204978	−	0.302320i
$528$		0			0
$529$	1.04003	−	1.96170i	0.0452186	−	0.0852913i
$530$	15.4815			0.672472
$531$		0			0
$532$	0.0749168			0.00324806
$533$	7.23555	−	13.6477i	0.313406	−	0.591147i
$534$		0			0
$535$	0.423531	+	0.624661i	0.0183108	+	0.0270065i
$536$	24.6600	−	5.42808i	1.06515	−	0.234457i
$537$		0			0
$538$	−31.8877	+	24.2404i	−1.37478	+	1.04508i
$539$	9.25257	−	1.00628i	0.398536	−	0.0433434i
$540$		0			0
$541$	2.52361	−	9.08920i	0.108498	−	0.390775i	−0.889283	−	0.457358i	$-0.848796\pi$
$541$	2.52361	−	9.08920i	0.108498	−	0.390775i	0.997781	+	0.0665826i	$0.0212096\pi$
$542$	15.1010	+	37.9007i	0.648645	+	1.62798i
$543$		0			0
$544$	−0.0351311	−	0.647955i	−0.00150623	−	0.0277809i
$545$	−5.45813	−	33.2931i	−0.233800	−	1.42612i
$546$		0			0
$547$	−9.08155	+	22.7930i	−0.388299	+	0.974557i	0.596773	+	0.802410i	$0.296449\pi$
$547$	−9.08155	+	22.7930i	−0.388299	+	0.974557i	−0.985071	+	0.172146i	$0.944930\pi$
$548$	−0.296417	−	0.225330i	−0.0126623	−	0.00962562i
$549$		0			0
$550$	2.07319	−	0.698540i	0.0884012	−	0.0297858i
$551$	4.27166	+	4.04634i	0.181979	+	0.172380i
$552$		0			0
$553$	22.1297	+	2.40675i	0.941052	+	0.102346i
$554$	−3.87152	+	2.32942i	−0.164485	+	0.0989675i
$555$		0			0
$556$	−0.394916	+	0.182708i	−0.0167482	+	0.00774853i
$557$	−9.39288	−	4.34561i	−0.397989	−	0.184129i	0.210677	−	0.977556i	$-0.432433\pi$
$557$	−9.39288	−	4.34561i	−0.397989	−	0.184129i	−0.608666	+	0.793426i	$0.708295\pi$
$558$		0			0
$559$	−8.86359	−	2.98649i	−0.374890	−	0.126315i
$560$	−7.49333	−	14.1339i	−0.316651	−	0.597267i
$561$		0			0
$562$	−18.5385	−	6.24636i	−0.782001	−	0.263487i
$563$	14.3134	+	16.8510i	0.603237	+	0.710185i	0.976007	−	0.217738i	$-0.0698679\pi$
$563$	14.3134	+	16.8510i	0.603237	+	0.710185i	−0.372770	+	0.927924i	$0.621592\pi$
$564$		0			0
$565$	40.8040	−	18.8779i	1.71664	−	0.794200i
$566$	10.1435	−	11.9418i	0.426362	−	0.501952i
$567$		0			0
$568$	−24.8949	−	2.70748i	−1.04457	−	0.113603i
$569$	−1.77925	+	10.8530i	−0.0745901	+	0.454980i	0.922952	+	0.384914i	$0.125769\pi$
$569$	−1.77925	+	10.8530i	−0.0745901	+	0.454980i	−0.997542	+	0.0700653i	$0.977679\pi$
$570$		0			0
$571$	4.16619	−	1.40375i	0.174349	−	0.0587452i	−0.230773	−	0.973008i	$-0.574125\pi$
$571$	4.16619	−	1.40375i	0.174349	−	0.0587452i	0.405122	+	0.914262i	$0.367229\pi$
$572$	−0.321761	−	0.193597i	−0.0134535	−	0.00809471i
$573$		0			0
$574$	3.30618	−	8.29789i	0.137997	−	0.346347i
$575$	1.92486	−	2.83895i	0.0802721	−	0.118392i
$576$		0			0
$577$	0.945429	+	17.4374i	0.0393587	+	0.725929i	0.949908	+	0.312529i	$0.101176\pi$
$577$	0.945429	+	17.4374i	0.0393587	+	0.725929i	−0.910550	+	0.413400i	$0.864341\pi$
$578$	11.7637	+	2.58939i	0.489305	+	0.107704i
$579$		0			0
$580$	−0.134436	+	0.484194i	−0.00558215	+	0.0201051i
$581$	1.61106	−	29.7142i	0.0668379	−	1.23275i
$582$		0			0
$583$	8.44726	−	6.42144i	0.349850	−	0.265949i
$584$	−2.65270	−	9.55417i	−0.109770	−	0.395354i
$585$		0			0
$586$	9.03580	+	13.3268i	0.373265	+	0.550525i
$587$	32.7948	−	31.0649i	1.35359	−	1.28219i	0.427935	−	0.903810i	$-0.359241\pi$
$587$	32.7948	−	31.0649i	1.35359	−	1.28219i	0.925652	−	0.378376i	$-0.123517\pi$
$588$		0			0
$589$	3.19781			0.131764
$590$	−22.0030	+	13.1601i	−0.905848	+	0.541792i
$591$		0			0
$592$	−18.1756	+	34.2829i	−0.747014	+	1.40902i
$593$	15.5827	−	14.7607i	0.639903	−	0.606148i	−0.297362	−	0.954765i	$-0.596107\pi$
$593$	15.5827	−	14.7607i	0.639903	−	0.606148i	0.937266	+	0.348616i	$0.113348\pi$
$594$		0			0
$595$	11.5515	−	2.54268i	0.473565	−	0.104240i
$596$	−0.113906	−	0.410254i	−0.00466578	−	0.0168046i
$597$		0			0
$598$	28.9809	−	3.15186i	1.18512	−	0.128889i
$599$	−1.55026	+	28.5928i	−0.0633418	+	1.16827i	0.778177	+	0.628044i	$0.216144\pi$
$599$	−1.55026	+	28.5928i	−0.0633418	+	1.16827i	−0.841519	+	0.540227i	$0.818338\pi$
$600$		0			0
$601$	−5.83171	−	14.6365i	−0.237880	−	0.597035i	0.760767	−	0.649025i	$-0.224823\pi$
$601$	−5.83171	−	14.6365i	−0.237880	−	0.597035i	−0.998648	+	0.0519899i	$0.983444\pi$
$602$	−5.28204	−	1.16267i	−0.215280	−	0.0473867i
$603$		0			0
$604$	0.0831423	+	0.507145i	0.00338301	+	0.0206355i
$605$	−7.71433	+	11.3778i	−0.313632	+	0.462573i
$606$		0			0
$607$	9.70681	+	7.37892i	0.393987	+	0.299501i	0.783347	−	0.621584i	$-0.213511\pi$
$607$	9.70681	+	7.37892i	0.393987	+	0.299501i	−0.389360	+	0.921086i	$0.627304\pi$
$608$	0.212051	+	0.127587i	0.00859979	+	0.00517432i
$609$		0			0
$610$	−30.2694	−	28.6727i	−1.22557	−	1.16092i
$611$	−5.18492	+	31.6266i	−0.209760	+	1.27948i
$612$		0			0
$613$	36.5023	−	21.9627i	1.47431	−	0.887066i	0.474337	−	0.880343i	$-0.342688\pi$
$613$	36.5023	−	21.9627i	1.47431	−	0.887066i	0.999977	−	0.00672228i	$-0.00213978\pi$
$614$	20.2223	−	23.8075i	0.816105	−	0.960793i
$615$		0			0
$616$	−10.1522	−	4.69691i	−0.409044	−	0.189244i
$617$	−16.6373	−	19.5869i	−0.669792	−	0.788540i	0.317364	−	0.948304i	$-0.397202\pi$
$617$	−16.6373	−	19.5869i	−0.669792	−	0.788540i	−0.987155	+	0.159764i	$0.948927\pi$
$618$		0			0
$619$	10.0326	+	18.9235i	0.403245	+	0.760601i	0.999097	−	0.0424935i	$-0.0135302\pi$
$619$	10.0326	+	18.9235i	0.403245	+	0.760601i	−0.595852	+	0.803095i	$0.703185\pi$
$620$	0.127926	+	0.241295i	0.00513765	+	0.00969063i
$621$		0			0
$622$	−2.23948	−	2.63651i	−0.0897948	−	0.105715i
$623$	1.21683	+	0.562967i	0.0487514	+	0.0225548i
$624$		0			0
$625$	−18.0935	+	21.3013i	−0.723739	+	0.852051i
$626$	−13.0915	+	7.87690i	−0.523242	+	0.314824i
$627$		0			0
$628$	0.0586238	−	0.357589i	0.00233935	−	0.0142694i
$629$	−20.8286	−	19.7299i	−0.830492	−	0.786684i
$630$		0			0
$631$	−37.5786	−	22.6103i	−1.49598	−	0.900102i	−0.999486	−	0.0320623i	$-0.989793\pi$
$631$	−37.5786	−	22.6103i	−1.49598	−	0.900102i	−0.496495	−	0.868040i	$-0.665380\pi$
$632$	29.5563	+	22.4682i	1.17569	+	0.893735i
$633$		0			0
$634$	1.25504	−	1.85104i	0.0498440	−	0.0735144i
$635$	−7.14679	−	43.5935i	−0.283612	−	1.72995i
$636$		0			0
$637$	16.4724	+	3.62584i	0.652659	+	0.143661i
$638$	−6.31232	−	15.8427i	−0.249907	−	0.627219i
$639$		0			0
$640$	1.41531	−	26.1039i	0.0559452	−	1.03185i
$641$	44.3028	−	4.81822i	1.74985	−	0.190308i	0.823590	−	0.567185i	$-0.191968\pi$
$641$	44.3028	−	4.81822i	1.74985	−	0.190308i	0.926263	+	0.376877i	$0.123002\pi$
$642$		0			0
$643$	−0.326914	−	1.17744i	−0.0128922	−	0.0464336i	0.956824	−	0.290667i	$-0.0938773\pi$
$643$	−0.326914	−	1.17744i	−0.0128922	−	0.0464336i	−0.969716	+	0.244234i	$0.921464\pi$
$644$	−0.332482	+	0.0731847i	−0.0131016	+	0.00288388i
$645$		0			0
$646$	3.25526	−	3.08354i	0.128076	−	0.121320i
$647$	−6.25160	+	11.7918i	−0.245776	+	0.463582i	−0.975452	−	0.220210i	$-0.929326\pi$
$647$	−6.25160	+	11.7918i	−0.245776	+	0.463582i	0.729677	+	0.683792i	$0.239671\pi$
$648$		0			0
$649$	−6.54706	+	16.3071i	−0.256995	+	0.640108i
$650$	3.96465			0.155506
$651$		0			0
$652$	0.251784	−	0.238503i	0.00986064	−	0.00934050i
$653$	1.61204	+	2.37758i	0.0630840	+	0.0930420i	0.857923	−	0.513779i	$-0.171755\pi$
$653$	1.61204	+	2.37758i	0.0630840	+	0.0930420i	−0.794839	+	0.606821i	$0.792445\pi$
$654$		0			0
$655$	7.29957	+	26.2907i	0.285218	+	1.02726i
$656$	11.6251	−	8.83718i	0.453884	−	0.345034i
$657$		0			0
$658$	−1.00332	+	18.5051i	−0.0391133	+	0.721402i
$659$	2.96750	−	10.6880i	0.115597	−	0.416344i	−0.882995	−	0.469382i	$-0.844477\pi$
$659$	2.96750	−	10.6880i	0.115597	−	0.416344i	0.998593	+	0.0530379i	$0.0168904\pi$
$660$		0			0
$661$	−17.0814	−	3.75991i	−0.664391	−	0.146244i	−0.130043	−	0.991508i	$-0.541512\pi$
$661$	−17.0814	−	3.75991i	−0.664391	−	0.146244i	−0.534348	+	0.845265i	$0.679443\pi$
$662$	−0.953251	−	17.5817i	−0.0370492	−	0.683332i
$663$		0			0
$664$	27.8526	−	41.0796i	1.08089	−	1.59420i
$665$	−1.66965	+	4.19050i	−0.0647461	+	0.162501i
$666$		0			0
$667$	−22.9105	−	13.7848i	−0.887097	−	0.533748i
$668$	−0.391936	+	0.132058i	−0.0151644	+	0.00510950i
$669$		0			0
$670$	−4.77467	+	29.1242i	−0.184461	+	1.12517i
$671$	−28.4090	−	3.08967i	−1.09672	−	0.119275i
$672$		0			0
$673$	−13.0111	+	15.3179i	−0.501542	+	0.590461i	−0.953430	−	0.301614i	$-0.902475\pi$
$673$	−13.0111	+	15.3179i	−0.501542	+	0.590461i	0.451888	+	0.892074i	$0.350751\pi$
$674$	−28.3169	+	13.1008i	−1.09072	+	0.504623i
$675$		0			0
$676$	−0.107352	−	0.126384i	−0.00412890	−	0.00486092i
$677$	−12.4007	−	4.17828i	−0.476597	−	0.160584i	0.0707427	−	0.997495i	$-0.477463\pi$
$677$	−12.4007	−	4.17828i	−0.476597	−	0.160584i	−0.547340	+	0.836910i	$0.684360\pi$
$678$		0			0
$679$	−2.17299	−	4.09870i	−0.0833919	−	0.157294i
$680$	18.6947	+	6.29899i	0.716910	+	0.241555i
$681$		0			0
$682$	−8.41197	−	3.89179i	−0.322111	−	0.149024i
$683$	14.3895	−	6.65729i	0.550599	−	0.254734i	−0.124806	−	0.992181i	$-0.539831\pi$
$683$	14.3895	−	6.65729i	0.550599	−	0.254734i	0.675405	+	0.737447i	$0.263969\pi$
$684$		0			0
$685$	19.2100	−	11.5583i	0.733978	−	0.441620i
$686$	26.3791	+	2.86890i	1.00716	+	0.109535i
$687$		0			0
$688$	−6.41919	−	6.08058i	−0.244729	−	0.231820i
$689$	18.2229	−	6.13999i	0.694235	−	0.233915i
$690$		0			0
$691$	8.63356	+	6.56306i	0.328436	+	0.249671i	0.756377	−	0.654136i	$-0.226968\pi$
$691$	8.63356	+	6.56306i	0.328436	+	0.249671i	−0.427941	+	0.903807i	$0.640761\pi$
$692$	−0.151829	+	0.381062i	−0.00577167	+	0.0144858i
$693$		0			0
$694$	−5.24192	−	31.9743i	−0.198980	−	1.21373i
$695$	−1.41845	−	26.1617i	−0.0538047	−	0.992370i
$696$		0			0
$697$	3.99631	+	10.0300i	0.151371	+	0.379912i
$698$	2.59378	−	9.34196i	0.0981761	−	0.353598i
$699$		0			0
$700$	−0.0460286	+	0.00500592i	−0.00173972	+	0.000189206i
$701$	−21.6219	+	16.4366i	−0.816649	+	0.620800i	−0.927831	−	0.373000i	$-0.878329\pi$
$701$	−21.6219	+	16.4366i	−0.816649	+	0.620800i	0.111183	+	0.993800i	$0.464536\pi$
$702$		0			0
$703$	10.6857	−	2.35209i	0.403017	−	0.0887108i
$704$	−10.4659	−	15.4360i	−0.394447	−	0.581766i
$705$		0			0
$706$	−10.7947	+	20.3610i	−0.406265	+	0.766298i
$707$	26.3667			0.991621
$708$		0			0
$709$	−14.5471			−0.546329			−0.273165	−	0.961967i	$-0.588070\pi$
$709$	−14.5471			−0.546329			−0.273165	+	0.961967i	$0.588070\pi$
$710$	13.7099	−	25.8596i	0.514522	−	0.970492i
$711$		0			0
$712$	1.25491	+	1.85086i	0.0470298	+	0.0693638i
$713$	−14.1919	+	3.12388i	−0.531492	+	0.116990i
$714$		0			0
$715$	17.9999	−	13.6832i	0.673159	−	0.511722i
$716$	0.244663	−	0.0266087i	0.00914347	−	0.000994413i
$717$		0			0
$718$	−2.53857	+	9.14310i	−0.0947386	+	0.341218i
$719$	14.3204	+	35.9414i	0.534059	+	1.34039i	0.910332	+	0.413878i	$0.135826\pi$
$719$	14.3204	+	35.9414i	0.534059	+	1.34039i	−0.376273	+	0.926509i	$0.622795\pi$
$720$		0			0
$721$	0.676886	+	12.4844i	0.0252086	+	0.464944i
$722$	−4.02720	−	24.5648i	−0.149877	−	0.914208i
$723$		0			0
$724$	−0.245235	+	0.615493i	−0.00911408	+	0.0228746i
$725$	−2.89487	−	2.20062i	−0.107513	−	0.0817291i
$726$		0			0
$727$	31.3393	−	10.5594i	1.16231	−	0.391628i	0.328944	−	0.944349i	$-0.393307\pi$
$727$	31.3393	−	10.5594i	1.16231	−	0.391628i	0.833366	+	0.552721i	$0.186411\pi$
$728$	−14.7172	−	13.9409i	−0.545457	−	0.516684i
$729$		0			0
$730$	11.5215	+	1.25304i	0.426432	+	0.0463772i
$731$	5.60166	−	3.37041i	0.207185	−	0.124659i
$732$		0			0
$733$	−38.7096	+	17.9090i	−1.42977	+	0.661483i	−0.973569	−	0.228392i	$-0.926653\pi$
$733$	−38.7096	+	17.9090i	−1.42977	+	0.661483i	−0.456203	+	0.889875i	$0.650791\pi$
$734$	34.7519	+	16.0780i	1.28272	+	0.593448i
$735$		0			0
$736$	−1.06572	−	0.359083i	−0.0392829	−	0.0132360i
$737$	9.47496	+	17.8717i	0.349015	+	0.658312i
$738$		0			0
$739$	−6.50174	−	2.19069i	−0.239170	−	0.0805859i	0.197164	−	0.980371i	$-0.436827\pi$
$739$	−6.50174	−	2.19069i	−0.239170	−	0.0805859i	−0.436334	+	0.899785i	$0.643723\pi$
$740$	0.604952	+	0.712205i	0.0222385	+	0.0261812i
$741$		0			0
$742$	10.0917	−	4.66893i	0.370479	−	0.171402i
$743$	−26.5094	+	31.2093i	−0.972537	+	1.14496i	0.0168794	+	0.999858i	$0.494627\pi$
$743$	−26.5094	+	31.2093i	−0.972537	+	1.14496i	−0.989417	+	0.145102i	$0.953649\pi$
$744$		0			0
$745$	25.4863	+	2.77180i	0.933744	+	0.101551i
$746$	−4.30844	+	26.2803i	−0.157743	+	0.962190i
$747$		0			0
$748$	0.248727	−	0.0838059i	0.00909436	−	0.00306425i
$749$	0.464469	+	0.279462i	0.0169713	+	0.0102113i
$750$		0			0
$751$	7.40022	−	18.5732i	0.270038	−	0.677744i	−0.729946	−	0.683505i	$-0.760455\pi$
$751$	7.40022	−	18.5732i	0.270038	−	0.677744i	0.999983	+	0.00576134i	$0.00183390\pi$
$752$	−17.0022	+	25.0764i	−0.620008	+	0.914443i
$753$		0			0
$754$	−1.67320	−	30.8604i	−0.0609345	−	1.12387i
$755$	−30.2203	−	6.65199i	−1.09983	−	0.242091i
$756$		0			0
$757$	−10.0447	+	36.1777i	−0.365081	+	1.31490i	0.521865	+	0.853028i	$0.325236\pi$
$757$	−10.0447	+	36.1777i	−0.365081	+	1.31490i	−0.886946	+	0.461873i	$0.847177\pi$
$758$	1.46193	−	26.9638i	0.0530998	−	0.979369i
$759$		0			0
$760$	−5.98938	+	4.55301i	−0.217258	+	0.165155i
$761$	−1.18765	−	4.27754i	−0.0430524	−	0.155061i	0.938900	−	0.344191i	$-0.111847\pi$
$761$	−1.18765	−	4.27754i	−0.0430524	−	0.155061i	−0.981952	+	0.189130i	$0.939433\pi$
$762$		0			0
$763$	−13.5985	−	20.0563i	−0.492299	−	0.726087i
$764$	0.412474	−	0.390716i	0.0149228	−	0.0141356i
$765$		0			0
$766$	−8.80134			−0.318005
$767$	−20.6798	+	24.2168i	−0.746705	+	0.874419i
$768$		0			0
$769$	16.2491	−	30.6490i	0.585957	−	1.10523i	−0.396375	−	0.918089i	$-0.629732\pi$
$769$	16.2491	−	30.6490i	0.585957	−	1.10523i	0.982332	−	0.187144i	$-0.0599231\pi$
$770$	9.49197	−	8.99127i	0.342067	−	0.324023i
$771$		0			0
$772$	−0.370003	+	0.0814439i	−0.0133167	+	0.00293123i
$773$	−12.9837	−	46.7632i	−0.466992	−	1.68195i	−0.703800	−	0.710398i	$-0.748515\pi$
$773$	−12.9837	−	46.7632i	−0.466992	−	1.68195i	0.236808	−	0.971556i	$-0.423899\pi$
$774$		0			0
$775$	−1.96472	+	0.213677i	−0.0705750	+	0.00767549i
$776$	0.418891	−	7.72599i	0.0150373	−	0.277347i
$777$		0			0
$778$	0.296819	+	0.744959i	0.0106415	+	0.0267081i
$779$	−4.02133	−	0.885161i	−0.144079	−	0.0317142i
$780$		0			0
$781$	−3.24548	−	19.7966i	−0.116132	−	0.708376i
$782$	−11.4346	+	16.8648i	−0.408901	+	0.603083i
$783$		0			0
$784$	12.6935	+	9.64933i	0.453338	+	0.344619i
$785$	18.6954	+	11.2486i	0.667266	+	0.401481i
$786$		0			0
$787$	−24.2094	−	22.9323i	−0.862971	−	0.817449i	0.121574	−	0.992582i	$-0.461206\pi$
$787$	−24.2094	−	22.9323i	−0.862971	−	0.817449i	−0.984545	+	0.175133i	$0.943964\pi$
$788$	−0.119757	+	0.730486i	−0.00426617	+	0.0260225i
$789$		0			0
$790$	−37.1827	+	22.3721i	−1.32290	+	0.795963i
$791$	20.9052	−	24.6115i	0.743302	−	0.875083i
$792$		0			0
$793$	−47.0010	−	21.7450i	−1.66905	−	0.772187i
$794$	−15.1892	−	17.8821i	−0.539045	−	0.634613i
$795$		0			0
$796$	−0.203027	−	0.382949i	−0.00719610	−	0.0135733i
$797$	7.48275	+	14.1140i	0.265053	+	0.499942i	0.979939	−	0.199299i	$-0.0638664\pi$
$797$	7.48275	+	14.1140i	0.265053	+	0.499942i	−0.714886	+	0.699241i	$0.753522\pi$
$798$		0			0
$799$	−14.5019	−	17.0729i	−0.513039	−	0.603996i
$800$	−0.138808	−	0.0642196i	−0.00490762	−	0.00227051i
$801$		0			0
$802$	15.8420	−	18.6506i	0.559400	−	0.658576i
$803$	6.80632	−	4.09523i	0.240190	−	0.144517i
$804$		0			0
$805$	3.31630	−	20.2285i	0.116884	−	0.712961i
$806$	−12.1945	−	11.5512i	−0.429532	−	0.406875i
$807$		0			0
$808$	37.6809	+	22.6718i	1.32561	+	0.797593i
$809$	−26.8351	−	20.3995i	−0.943471	−	0.717208i	0.0157471	−	0.999876i	$-0.494987\pi$
$809$	−26.8351	−	20.3995i	−0.943471	−	0.717208i	−0.959218	+	0.282668i	$0.908780\pi$
$810$		0			0
$811$	7.76832	−	11.4574i	0.272783	−	0.402324i	−0.666480	−	0.745523i	$-0.732200\pi$
$811$	7.76832	−	11.4574i	0.272783	−	0.402324i	0.939263	+	0.343198i	$0.111510\pi$
$812$	0.0583911	+	0.356170i	0.00204912	+	0.0124991i
$813$		0			0
$814$	−30.9715	−	6.81735i	−1.08555	−	0.238948i
$815$	7.72930	+	19.3991i	0.270746	+	0.679520i
$816$		0			0
$817$	−0.134979	+	2.48954i	−0.00472232	+	0.0870981i
$818$	−29.6985	+	3.22991i	−1.03838	+	0.112931i
$819$		0			0
$820$	−0.0940797	−	0.338844i	−0.00328540	−	0.0118330i
$821$	−35.7770	+	7.87511i	−1.24863	+	0.274843i	−0.789623	−	0.613592i	$-0.789724\pi$
$821$	−35.7770	+	7.87511i	−1.24863	+	0.274843i	−0.459002	+	0.888435i	$0.651793\pi$
$822$		0			0
$823$	−27.8177	+	26.3503i	−0.969665	+	0.918515i	−0.996704	−	0.0811193i	$-0.974151\pi$
$823$	−27.8177	+	26.3503i	−0.969665	+	0.918515i	0.0270398	+	0.999634i	$0.491392\pi$
$824$	−9.76761	+	18.4237i	−0.340271	+	0.641819i
$825$		0			0
$826$	−10.3740	+	15.2142i	−0.360957	+	0.529370i
$827$	32.4735			1.12921			0.564607	−	0.825360i	$-0.309028\pi$
$827$	32.4735			1.12921			0.564607	+	0.825360i	$0.309028\pi$
$828$		0			0
$829$	17.4713	−	16.5497i	0.606804	−	0.574795i	−0.321364	−	0.946956i	$-0.604141\pi$
$829$	17.4713	−	16.5497i	0.606804	−	0.574795i	0.928169	+	0.372160i	$0.121383\pi$
$830$	32.5545	+	48.0144i	1.12998	+	1.66660i
$831$		0			0
$832$	−9.04175	−	32.5654i	−0.313466	−	1.12900i
$833$	−9.38518	+	7.13443i	−0.325177	+	0.247193i
$834$		0			0
$835$	1.34821	−	24.8662i	0.0466566	−	0.860530i
$836$	−0.0267788	+	0.0964487i	−0.000926166	+	0.00333575i
$837$		0			0
$838$	6.59361	+	1.45136i	0.227772	+	0.0501365i
$839$	0.146322	+	2.69876i	0.00505161	+	0.0931715i	0.999972	−	0.00749422i	$-0.00238551\pi$
$839$	0.146322	+	2.69876i	0.00505161	+	0.0931715i	−0.994920	+	0.100666i	$0.967903\pi$
$840$		0			0
$841$	0.366718	−	0.540868i	0.0126454	−	0.0186506i
$842$	−6.57704	+	16.5071i	−0.226660	+	0.568873i
$843$		0			0
$844$	−0.827207	−	0.497714i	−0.0284736	−	0.0171320i
$845$	9.46184	−	3.18806i	0.325497	−	0.109673i
$846$		0			0
$847$	−1.59732	+	9.74321i	−0.0548845	+	0.334781i
$848$	18.0717	+	1.96542i	0.620586	+	0.0674928i
$849$		0			0
$850$	−1.79398	+	2.11203i	−0.0615329	+	0.0724421i
$851$	−45.1253	+	20.8772i	−1.54688	+	0.715661i
$852$		0			0
$853$	22.2779	+	26.2275i	0.762780	+	0.898014i	0.997250	−	0.0741094i	$-0.0236114\pi$
$853$	22.2779	+	26.2275i	0.762780	+	0.898014i	−0.234470	+	0.972123i	$0.575336\pi$
$854$	−28.3785	−	9.56184i	−0.971093	−	0.327199i
$855$		0			0
$856$	0.423477	+	0.798763i	0.0144742	+	0.0273012i
$857$	11.8243	+	3.98406i	0.403909	+	0.136093i	0.513921	−	0.857837i	$-0.328192\pi$
$857$	11.8243	+	3.98406i	0.403909	+	0.136093i	−0.110012	+	0.993930i	$0.535089\pi$
$858$		0			0
$859$	−20.3127	−	9.39768i	−0.693062	−	0.320645i	0.0415458	−	0.999137i	$-0.486772\pi$
$859$	−20.3127	−	9.39768i	−0.693062	−	0.320645i	−0.734608	+	0.678492i	$0.762634\pi$
$860$	−0.193251	+	0.0894075i	−0.00658981	+	0.00304877i
$861$		0			0
$862$	33.9144	−	20.4056i	1.15513	−	0.695018i
$863$	−22.4002	−	2.43617i	−0.762511	−	0.0829281i	−0.281404	−	0.959590i	$-0.590800\pi$
$863$	−22.4002	−	2.43617i	−0.762511	−	0.0829281i	−0.481108	+	0.876661i	$0.659765\pi$
$864$		0			0
$865$	−17.9311	−	16.9852i	−0.609674	−	0.577514i
$866$	23.7268	−	7.99449i	0.806269	−	0.271664i
$867$		0			0
$868$	0.156160	+	0.118710i	0.00530042	+	0.00402927i
$869$	−11.0087	+	27.6298i	−0.373445	+	0.937275i
$870$		0			0
$871$	5.93059	+	36.1750i	0.200950	+	1.22574i
$872$	−2.18802	−	40.3556i	−0.0740956	−	1.36661i
$873$		0			0
$874$	−2.87624	−	7.21883i	−0.0972904	−	0.244181i
$875$	−4.71412	+	16.9787i	−0.159366	+	0.573985i
$876$		0			0
$877$	2.21594	−	0.240998i	0.0748271	−	0.00813793i	−0.0706289	−	0.997503i	$-0.522501\pi$
$877$	2.21594	−	0.240998i	0.0748271	−	0.00813793i	0.145456	+	0.989365i	$0.453535\pi$
$878$	36.0047	−	27.3701i	1.21510	−	0.923696i
$879$		0			0
$880$	20.8746	−	4.59485i	0.703684	−	0.154893i
$881$	−8.07233	−	11.9058i	−0.271964	−	0.401116i	0.667041	−	0.745021i	$-0.267561\pi$
$881$	−8.07233	−	11.9058i	−0.271964	−	0.401116i	−0.939005	+	0.343905i	$0.888250\pi$
$882$		0			0
$883$	10.9804	−	20.7113i	0.369521	−	0.696990i	−0.627117	−	0.778925i	$-0.715765\pi$
$883$	10.9804	−	20.7113i	0.369521	−	0.696990i	0.996638	+	0.0819351i	$0.0261100\pi$
$884$	0.475651			0.0159979
$885$		0			0
$886$	24.4128			0.820165
$887$	4.96111	−	9.35765i	0.166578	−	0.314199i	−0.786144	−	0.618044i	$-0.787925\pi$
$887$	4.96111	−	9.35765i	0.166578	−	0.314199i	0.952722	+	0.303844i	$0.0982703\pi$
$888$		0			0
$889$	−17.8057	−	26.2614i	−0.597184	−	0.880780i
$890$	−2.55256	+	0.561862i	−0.0855622	+	0.0188337i
$891$		0			0
$892$	0.619857	−	0.471203i	0.0207543	−	0.0157770i
$893$	8.49289	−	0.923658i	0.284204	−	0.0309090i
$894$		0			0
$895$	−3.96435	+	14.2783i	−0.132514	+	0.477271i
$896$	−6.94989	−	17.4429i	−0.232180	−	0.582727i
$897$		0			0
$898$	0.973277	+	17.9510i	0.0324787	+	0.599034i
$899$	2.49241	+	15.2030i	0.0831266	+	0.507050i
$900$		0			0
$901$	−4.97484	+	12.4859i	−0.165736	+	0.415966i
$902$	9.50100	+	7.22247i	0.316349	+	0.240482i
$903$		0			0
$904$	51.0384	−	17.1968i	1.69751	−	0.571958i
$905$	−28.9623	−	27.4346i	−0.962740	−	0.911956i
$906$		0			0
$907$	37.8560	+	4.11709i	1.25699	+	0.136706i	0.712265	−	0.701911i	$-0.247669\pi$
$907$	37.8560	+	4.11709i	1.25699	+	0.136706i	0.544723	+	0.838616i	$0.316635\pi$
$908$	0.424196	−	0.255230i	0.0140774	−	0.00847011i
$909$		0			0
$910$	21.5040	−	9.94883i	0.712852	−	0.329800i
$911$	0.630495	+	0.291698i	0.0208892	+	0.00966439i	0.430306	−	0.902683i	$-0.358406\pi$
$911$	0.630495	+	0.291698i	0.0208892	+	0.00966439i	−0.409417	+	0.912348i	$0.634268\pi$
$912$		0			0
$913$	37.6785	+	12.6954i	1.24698	+	0.420155i
$914$	−24.3207	−	45.8738i	−0.804459	−	1.51737i
$915$		0			0
$916$	1.08053	+	0.364073i	0.0357018	+	0.0120293i
$917$	12.6871	+	14.9364i	0.418964	+	0.493243i
$918$		0			0
$919$	30.7289	−	14.2167i	1.01365	−	0.468966i	0.158510	−	0.987357i	$-0.449331\pi$
$919$	30.7289	−	14.2167i	1.01365	−	0.468966i	0.855143	+	0.518392i	$0.173469\pi$
$920$	22.1332	−	26.0572i	0.729710	−	0.859081i
$921$		0			0
$922$	32.3691	+	3.52036i	1.06602	+	0.115937i
$923$	5.88158	−	35.8760i	0.193594	−	1.18087i
$924$		0			0
$925$	−6.40806	+	2.15913i	−0.210696	+	0.0709917i
$926$	−7.05206	−	4.24308i	−0.231745	−	0.139436i
$927$		0			0
$928$	−0.441298	+	1.10757i	−0.0144863	+	0.0363579i
$929$	3.70306	−	5.46161i	0.121494	−	0.179190i	−0.762079	−	0.647484i	$-0.775821\pi$
$929$	3.70306	−	5.46161i	0.121494	−	0.179190i	0.883572	+	0.468295i	$0.155131\pi$
$930$		0			0
$931$	−0.243409	−	4.48942i	−0.00797741	−	0.147135i
$932$	0.149685	+	0.0329481i	0.00490309	+	0.00107925i
$933$		0			0
$934$	−6.19767	+	22.3220i	−0.202794	+	0.730398i
$935$	−0.855587	+	15.7804i	−0.0279807	+	0.516074i
$936$		0			0
$937$	−22.4702	+	17.0814i	−0.734068	+	0.558024i	−0.904052	−	0.427423i	$-0.859422\pi$
$937$	−22.4702	+	17.0814i	−0.734068	+	0.558024i	0.169983	+	0.985447i	$0.445629\pi$
$938$	5.67092	+	20.4248i	0.185162	+	0.666893i
$939$		0			0
$940$	0.409448	+	0.603891i	0.0133547	+	0.0196967i
$941$	−34.7938	+	32.9584i	−1.13425	+	1.07441i	−0.137775	+	0.990464i	$0.543995\pi$
$941$	−34.7938	+	32.9584i	−1.13425	+	1.07441i	−0.996470	+	0.0839506i	$0.973246\pi$
$942$		0			0
$943$	18.7114			0.609327
$944$	−27.3551	+	12.5686i	−0.890332	+	0.409073i
$945$		0			0
$946$	3.38488	−	6.38456i	0.110052	−	0.207580i
$947$	11.5675	−	10.9573i	0.375892	−	0.356064i	−0.476309	−	0.879278i	$-0.658026\pi$
$947$	11.5675	−	10.9573i	0.375892	−	0.356064i	0.852201	+	0.523214i	$0.175267\pi$
$948$		0			0
$949$	14.0587	−	3.09455i	0.456364	−	0.100453i
$950$	−0.282730	−	1.01830i	−0.00917297	−	0.0330380i
$951$		0			0
$952$	14.0860	−	1.53194i	0.456529	−	0.0496505i
$953$	−2.24371	+	41.3827i	−0.0726808	+	1.34052i	0.703809	+	0.710389i	$0.251481\pi$
$953$	−2.24371	+	41.3827i	−0.0726808	+	1.34052i	−0.776490	+	0.630129i	$0.783002\pi$
$954$		0			0
$955$	12.6622	+	31.7797i	0.409738	+	1.02837i
$956$	−0.0848011	−	0.0186661i	−0.00274266	−	0.000603706i
$957$		0			0
$958$	−7.90989	−	48.2482i	−0.255557	−	1.55883i
$959$	9.03646	−	13.3278i	0.291802	−	0.430376i
$960$		0			0
$961$	−18.0132	−	13.6933i	−0.581072	−	0.441719i
$962$	−49.2448	−	29.6296i	−1.58772	−	0.955297i
$963$		0			0
$964$	0.761041	+	0.720896i	0.0245115	+	0.0232185i
$965$	3.69055	−	22.5114i	0.118803	−	0.724667i
$966$		0			0
$967$	−15.1850	+	9.13651i	−0.488317	+	0.293810i	−0.738339	−	0.674430i	$-0.764390\pi$
$967$	−15.1850	+	9.13651i	−0.488317	+	0.293810i	0.250022	+	0.968240i	$0.419562\pi$
$968$	−10.6606	+	12.5506i	−0.342645	+	0.403393i
$969$		0			0
$970$	8.20766	+	3.79727i	0.263532	+	0.121923i
$971$	0.129481	+	0.152436i	0.00415523	+	0.00489192i	0.764236	−	0.644937i	$-0.223116\pi$
$971$	0.129481	+	0.152436i	0.00415523	+	0.00489192i	−0.760081	+	0.649829i	$0.774841\pi$
$972$		0			0
$973$	−8.81452	−	16.6259i	−0.282581	−	0.533003i
$974$	18.9175	+	35.6821i	0.606154	+	1.14333i
$975$		0			0
$976$	−31.6938	−	37.3128i	−1.01449	−	1.19435i
$977$	50.1470	+	23.2005i	1.60434	+	0.742249i	0.998574	−	0.0533906i	$-0.0170029\pi$
$977$	50.1470	+	23.2005i	1.60434	+	0.742249i	0.605771	+	0.795639i	$0.292865\pi$
$978$		0			0
$979$	−1.15972	+	1.36533i	−0.0370649	+	0.0436362i
$980$	0.329017	−	0.197963i	0.0105101	−	0.00632369i
$981$		0			0
$982$	−4.12962	+	25.1896i	−0.131782	+	0.803832i
$983$	19.2584	+	18.2426i	0.614248	+	0.581847i	0.930257	−	0.366909i	$-0.119584\pi$
$983$	19.2584	+	18.2426i	0.614248	+	0.581847i	−0.316008	+	0.948756i	$0.602343\pi$
$984$		0			0
$985$	−38.1910	−	22.9788i	−1.21687	−	0.732164i
$986$	17.1970	+	13.0728i	0.547663	+	0.416322i
$987$		0			0
$988$	−0.101799	+	0.150143i	−0.00323866	+	0.00477667i
$989$	−1.83295	−	11.1805i	−0.0582843	−	0.355518i
$990$		0			0
$991$	29.0332	+	6.39069i	0.922271	+	0.203007i	0.650633	−	0.759392i	$-0.274504\pi$
$991$	29.0332	+	6.39069i	0.922271	+	0.203007i	0.271638	+	0.962400i	$0.412435\pi$
$992$	0.239840	+	0.601953i	0.00761493	+	0.0191120i
$993$		0			0
$994$	1.13812	−	20.9914i	0.0360990	−	0.665808i
$995$	25.9452	−	2.82171i	0.822518	−	0.0894543i
$996$		0			0
$997$	11.0533	+	39.8105i	0.350062	+	1.26081i	0.903741	+	0.428080i	$0.140810\pi$
$997$	11.0533	+	39.8105i	0.350062	+	1.26081i	−0.553678	+	0.832731i	$0.686776\pi$
$998$	35.9295	−	7.90867i	1.13733	−	0.250345i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.19.2		140
3.2	odd	2		177.2.e.a.19.4	✓	140
59.28	even	29	inner	531.2.i.c.28.2		140
177.146	odd	58		177.2.e.a.28.4	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.19.4	✓	140	3.2	odd	2
177.2.e.a.28.4	yes	140	177.146	odd	58
531.2.i.c.19.2		140	1.1	even	1	trivial
531.2.i.c.28.2		140	59.28	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.655840 + 1.23705i) q^{2} +(0.0222185 + 0.0327698i) q^{4} +(-2.32817 + 0.512469i) q^{5} +(-1.36308 + 1.03619i) q^{7} +(-2.83899 + 0.308758i) q^{8} +O(q^{10})\)	\(q+(-0.655840 + 1.23705i) q^{2} +(0.0222185 + 0.0327698i) q^{4} +(-2.32817 + 0.512469i) q^{5} +(-1.36308 + 1.03619i) q^{7} +(-2.83899 + 0.308758i) q^{8} +(0.892959 - 3.21615i) q^{10} +(-0.846770 - 2.12523i) q^{11} +(-0.224453 - 4.13980i) q^{13} +(-0.387849 - 2.36577i) q^{14} +(1.45066 - 3.64089i) q^{16} +(2.30690 + 1.75366i) q^{17} +(-1.04728 + 0.352870i) q^{19} +(-0.0685219 - 0.0649074i) q^{20} +(3.18436 + 0.346320i) q^{22} +(4.30312 - 2.58910i) q^{23} +(0.619866 - 0.286781i) q^{25} +(5.26832 + 2.43739i) q^{26} +(-0.0642415 - 0.0216455i) q^{28} +(-2.49387 - 4.70395i) q^{29} +(-2.74214 - 0.923934i) q^{31} +(-0.144971 - 0.170673i) q^{32} +(-3.68231 + 1.70362i) q^{34} +(2.64248 - 3.11096i) q^{35} +(-9.84258 - 1.07044i) q^{37} +(0.250332 - 1.52696i) q^{38} +(6.45141 - 2.17373i) q^{40} +(3.19256 + 1.92090i) q^{41} +(0.835041 - 2.09579i) q^{43} +(0.0508296 - 0.0749680i) q^{44} +(0.380678 + 7.02120i) q^{46} +(-7.54956 - 1.66178i) q^{47} +(-1.08839 + 3.92002i) q^{49} +(-0.0517724 + 0.954885i) q^{50} +(0.130673 - 0.0993354i) q^{52} +(1.24085 + 4.46915i) q^{53} +(3.06054 + 4.51396i) q^{55} +(3.54985 - 3.36259i) q^{56} +7.45458 q^{58} +(-5.56257 - 5.29696i) q^{59} +(5.85104 - 11.0362i) q^{61} +(2.94135 - 2.78620i) q^{62} +(7.96145 - 1.75245i) q^{64} +(2.64408 + 9.52312i) q^{65} +(-8.79018 + 0.955990i) q^{67} +(-0.00621128 + 0.114560i) q^{68} +(2.11536 + 5.30916i) q^{70} +(8.56393 + 1.88506i) q^{71} +(0.561736 + 3.42644i) q^{73} +(7.77934 - 11.4737i) q^{74} +(-0.0348325 - 0.0264790i) q^{76} +(3.35637 + 2.01946i) q^{77} +(-9.43853 - 8.94065i) q^{79} +(-1.51155 + 9.22003i) q^{80} +(-4.47005 + 2.68954i) q^{82} +(-11.2514 + 13.2461i) q^{83} +(-6.26954 - 2.90060i) q^{85} +(2.04494 + 2.40749i) q^{86} +(3.06015 + 5.77206i) q^{88} +(-0.366787 - 0.691834i) q^{89} +(4.59557 + 5.41032i) q^{91} +(0.180453 + 0.0834867i) q^{92} +(7.00700 - 8.24928i) q^{94} +(2.25741 - 1.35824i) q^{95} +(-0.438334 + 2.67372i) q^{97} +(-4.13543 - 3.91729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

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