LMFDB - Embedded newform 531.2.i.c.28.2

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			28.2
Character	$\chi$	$=$	531.28
Dual form			531.2.i.c.19.2

$q$-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 $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{10}{29}\right)$

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	−0.999539	−	0.0303719i	$-0.990331\pi$
$2$	−0.655840	−	1.23705i	−0.463749	−	0.874723i	0.535790	−	0.844351i	$-0.320014\pi$
$3$		0			0
$3$		0			0
$4$	0.0222185	−	0.0327698i	0.0111092	−	0.0163849i
$5$	−2.32817	−	0.512469i	−1.04119	−	0.229183i	−0.338712	−	0.940890i	$-0.609991\pi$
$5$	−2.32817	−	0.512469i	−1.04119	−	0.229183i	−0.702476	+	0.711707i	$0.747922\pi$
$6$		0			0
$7$	−1.36308	−	1.03619i	−0.515198	−	0.391643i	0.315018	−	0.949086i	$-0.397990\pi$
$7$	−1.36308	−	1.03619i	−0.515198	−	0.391643i	−0.830215	+	0.557443i	$0.811783\pi$
$8$	−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	−0.999634	−	0.0270373i	$-0.991393\pi$
$11$	−0.846770	+	2.12523i	−0.255311	+	0.640782i	0.744324	+	0.667819i	$0.232772\pi$
$12$		0			0
$13$	−0.224453	+	4.13980i	−0.0622521	+	1.14817i	0.785877	+	0.618383i	$0.212212\pi$
$13$	−0.224453	+	4.13980i	−0.0622521	+	1.14817i	−0.848129	+	0.529790i	$0.822271\pi$
$14$	−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	−0.286825	−	0.957983i	$-0.592600\pi$
$17$	2.30690	−	1.75366i	0.559505	−	0.425325i	0.846330	+	0.532658i	$0.178807\pi$
$18$		0			0
$19$	−1.04728	−	0.352870i	−0.240262	−	0.0809538i	0.196594	−	0.980485i	$-0.437012\pi$
$19$	−1.04728	−	0.352870i	−0.240262	−	0.0809538i	−0.436857	+	0.899531i	$0.643908\pi$
$20$	−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	0.887872	−	0.460090i	$-0.152183\pi$
$23$	4.30312	+	2.58910i	0.897264	+	0.539866i	0.00939142	+	0.999956i	$0.497011\pi$
$24$		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	0.536462	+	0.843925i	$0.319761\pi$
$29$	−2.49387	+	4.70395i	−0.463101	+	0.873501i	−0.999563	+	0.0295763i	$0.990584\pi$
$30$		0			0
$31$	−2.74214	+	0.923934i	−0.492502	+	0.165943i	−0.554584	−	0.832128i	$-0.687123\pi$
$31$	−2.74214	+	0.923934i	−0.492502	+	0.165943i	0.0620817	+	0.998071i	$0.480226\pi$
$32$	−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	−0.871884	−	0.489713i	$-0.837102\pi$
$37$	−9.84258	+	1.07044i	−1.61811	+	0.175980i	−0.746226	+	0.665693i	$0.768136\pi$
$38$	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	−0.243954	−	0.969787i	$-0.578445\pi$
$41$	3.19256	−	1.92090i	0.498594	−	0.299994i	0.742548	+	0.669793i	$0.233617\pi$
$42$		0			0
$43$	0.835041	+	2.09579i	0.127343	+	0.319606i	0.978800	−	0.204818i	$-0.0656602\pi$
$43$	0.835041	+	2.09579i	0.127343	+	0.319606i	−0.851458	+	0.524423i	$0.824281\pi$
$44$	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	−0.728156	−	0.685411i	$-0.759622\pi$
$47$	−7.54956	+	1.66178i	−1.10122	+	0.242396i	−0.373060	+	0.927807i	$0.621691\pi$
$48$		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	−0.828132	−	0.560534i	$-0.810596\pi$
$53$	1.24085	−	4.46915i	0.170444	−	0.613885i	0.998576	−	0.0533509i	$-0.0169902\pi$
$54$		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	0.905065	+	0.425273i	$0.139822\pi$
$61$	5.85104	+	11.0362i	0.749148	+	1.41304i	−0.155917	+	0.987770i	$0.549833\pi$
$62$	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	−0.445953	−	0.895056i	$-0.647135\pi$
$67$	−8.79018	−	0.955990i	−1.07389	−	0.116793i	−0.627938	+	0.778263i	$0.716101\pi$
$68$	−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	0.324600	−	0.945852i	$-0.394770\pi$
$71$	8.56393	−	1.88506i	1.01635	−	0.223716i	0.691751	+	0.722136i	$0.256839\pi$
$72$		0			0
$73$	0.561736	−	3.42644i	0.0657463	−	0.401034i	−0.933367	−	0.358924i	$-0.883144\pi$
$73$	0.561736	−	3.42644i	0.0657463	−	0.401034i	0.999113	−	0.0421103i	$-0.0134081\pi$
$74$	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	−0.0619482	+	0.998079i	$0.519731\pi$
$79$	−9.43853	+	8.94065i	−1.06192	+	1.00590i	−0.999969	+	0.00782238i	$0.997510\pi$
$80$	−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	−0.846401	−	0.532546i	$-0.821235\pi$
$83$	−11.2514	−	13.2461i	−1.23500	−	1.45395i	−0.388598	−	0.921407i	$-0.627041\pi$
$84$		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	−0.902191	−	0.431338i	$-0.858042\pi$
$89$	−0.366787	+	0.691834i	−0.0388793	+	0.0733342i	0.863311	+	0.504672i	$0.168387\pi$
$90$		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	0.955194	−	0.295982i	$-0.0956468\pi$
$97$	−0.438334	−	2.67372i	−0.0445061	−	0.271475i	−0.999700	+	0.0245068i	$0.992198\pi$
$98$	−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	−0.998848	−	0.0479867i	$-0.984719\pi$
$101$	−12.2591	+	9.31916i	−1.21983	+	0.927291i	−0.220983	+	0.975278i	$0.570926\pi$
$102$		0			0
$103$	4.09784	+	6.04386i	0.403772	+	0.595519i	0.974161	−	0.225856i	$-0.0725179\pi$
$103$	4.09784	+	6.04386i	0.403772	+	0.595519i	−0.570389	+	0.821375i	$0.693208\pi$
$104$	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	−0.934532	−	0.355879i	$-0.884182\pi$
$107$	−0.117180	+	0.294099i	−0.0113282	+	0.0284316i	0.923204	+	0.384311i	$0.125561\pi$
$108$		0			0
$109$	−0.766186	−	14.1315i	−0.0733873	−	1.35355i	−0.770890	−	0.636968i	$-0.780188\pi$
$109$	−0.766186	−	14.1315i	−0.0733873	−	1.35355i	0.697503	−	0.716582i	$-0.254294\pi$
$110$	−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	−0.767104	−	0.641522i	$-0.778303\pi$
$113$	−18.4186	−	4.05424i	−1.73268	−	0.381391i	−0.965573	+	0.260131i	$0.916234\pi$
$114$		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	−0.612922	−	0.790144i	$-0.710006\pi$
$127$	−1.00323	−	18.5035i	−0.0890225	−	1.64192i	0.523899	−	0.851780i	$-0.324477\pi$
$128$	−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	0.837684	+	0.546156i	$0.183909\pi$
$131$	−0.619653	+	11.4288i	−0.0541393	+	0.998541i	−0.891823	+	0.452385i	$0.850573\pi$
$132$		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	−0.0883047	−	0.996094i	$-0.528145\pi$
$137$	−8.91212	−	3.00284i	−0.761414	−	0.256550i	−0.673109	+	0.739543i	$0.735041\pi$
$138$		0			0
$139$	−1.77805	−	10.8457i	−0.150813	−	0.919916i	−0.948484	−	0.316824i	$-0.897383\pi$
$139$	−1.77805	−	10.8457i	−0.150813	−	0.919916i	0.797672	−	0.603092i	$-0.206065\pi$
$140$	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	−0.704097	−	0.710104i	$-0.748648\pi$
$149$	−10.1911	+	3.43378i	−0.834886	+	0.281306i	−0.130790	+	0.991410i	$0.541751\pi$
$150$		0			0
$151$	11.7806	−	5.45029i	0.958692	−	0.443538i	0.122799	−	0.992432i	$-0.460813\pi$
$151$	11.7806	−	5.45029i	0.958692	−	0.443538i	0.835892	+	0.548894i	$0.184951\pi$
$152$	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	−0.905343	−	0.424681i	$-0.860386\pi$
$157$	−6.64463	+	6.29413i	−0.530299	+	0.502326i	0.375044	+	0.927007i	$0.377628\pi$
$158$	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	0.871441	+	0.490500i	$0.163186\pi$
$163$	−1.41716	+	8.64428i	−0.111000	+	0.677072i	−0.982441	+	0.186572i	$0.940262\pi$
$164$	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	−0.989470	−	0.144740i	$-0.953765\pi$
$167$	−2.79465	−	10.0654i	−0.216257	−	0.778887i	0.773213	−	0.634147i	$-0.218648\pi$
$168$		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	−0.539768	−	0.841814i	$-0.681488\pi$
$173$	5.81422	−	8.57533i	0.442047	−	0.651970i	0.981814	+	0.189844i	$0.0607982\pi$
$174$		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	0.968155	−	0.250350i	$-0.0805458\pi$
$179$	2.91165	+	5.49195i	0.217627	+	0.410488i	−0.750529	+	0.660838i	$0.770201\pi$
$180$		0			0
$181$	9.39115	−	13.8509i	0.698038	−	1.02953i	−0.299121	−	0.954215i	$-0.596694\pi$
$181$	9.39115	−	13.8509i	0.698038	−	1.02953i	0.997160	−	0.0753146i	$-0.0239961\pi$
$182$	−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	0.759420	+	0.650601i	$0.225483\pi$
$191$	−2.32159	+	14.1611i	−0.167985	+	1.02466i	−0.927405	+	0.374060i	$0.877965\pi$
$192$		0			0
$193$	−3.54190	−	8.88950i	−0.254952	−	0.639881i	0.744669	−	0.667434i	$-0.232608\pi$
$193$	−3.54190	−	8.88950i	−0.254952	−	0.639881i	−0.999620	+	0.0275539i	$0.991228\pi$
$194$	−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	−0.0294228	−	0.999567i	$-0.509367\pi$
$197$	13.5737	−	12.8577i	0.967085	−	0.916072i	0.996508	+	0.0834951i	$0.0266083\pi$
$198$		0			0
$199$	−10.8835	+	1.18365i	−0.771511	+	0.0839069i	−0.485403	−	0.874291i	$-0.661327\pi$
$199$	−10.8835	+	1.18365i	−0.771511	+	0.0839069i	−0.286108	+	0.958197i	$0.592362\pi$
$200$	−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	−0.533478	−	0.845814i	$-0.679115\pi$
$211$	−22.1300	−	10.2384i	−1.52349	−	0.704842i	−0.990014	+	0.140971i	$0.954977\pi$
$212$	−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	0.715851	+	0.698253i	$0.246039\pi$
$223$	−1.06471	+	19.6374i	−0.0712980	+	1.31501i	−0.787149	+	0.616762i	$0.788444\pi$
$224$	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	0.930970	+	0.365095i	$0.118964\pi$
$227$	0.676956	+	12.4857i	0.0449311	+	0.828706i	−0.886039	+	0.463611i	$0.846554\pi$
$228$		0			0
$229$	22.9269	+	17.4286i	1.51505	+	1.15171i	0.943606	+	0.331070i	$0.107410\pi$
$229$	22.9269	+	17.4286i	1.51505	+	1.15171i	0.571444	+	0.820641i	$0.306383\pi$
$230$	−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	0.774208	−	0.632931i	$-0.218148\pi$
$233$	2.81047	+	2.66222i	0.184120	+	0.174408i	−0.590088	+	0.807339i	$0.700907\pi$
$234$		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	0.634471	−	0.772946i	$-0.281218\pi$
$239$	−1.59222	−	1.50823i	−0.102992	−	0.0975592i	−0.737463	+	0.675387i	$0.763977\pi$
$240$		0			0
$241$	25.8579	+	5.69175i	1.66565	+	0.366638i	0.945105	−	0.326768i	$-0.105960\pi$
$241$	25.8579	+	5.69175i	1.66565	+	0.366638i	0.720547	+	0.693406i	$0.243891\pi$
$242$	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	0.928219	−	0.372034i	$-0.121339\pi$
$251$	3.78710	+	5.58555i	0.239039	+	0.352557i	−0.689180	+	0.724590i	$0.742029\pi$
$252$		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	0.985281	−	0.170941i	$-0.0546809\pi$
$257$	−0.0481822	−	0.293898i	−0.00300552	−	0.0183329i	−0.988287	+	0.152609i	$0.951233\pi$
$258$		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	−0.889842	−	0.456270i	$-0.849185\pi$
$263$	−4.79419	+	5.64415i	−0.295622	+	0.348033i	0.594219	+	0.804303i	$0.297461\pi$
$264$		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	0.586081	−	0.810253i	$-0.300670\pi$
$269$	25.9639	−	12.0122i	1.58305	−	0.732395i	0.996964	+	0.0778578i	$0.0248080\pi$
$270$		0			0
$271$	18.8640	+	22.2084i	1.14590	+	1.34906i	0.927774	+	0.373143i	$0.121720\pi$
$271$	18.8640	+	22.2084i	1.14590	+	1.34906i	0.218130	+	0.975920i	$0.430004\pi$
$272$	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	−0.430056	−	0.902802i	$-0.641506\pi$
$277$	2.76509	−	1.66370i	0.166138	−	0.0999619i	0.596194	+	0.802840i	$0.296679\pi$
$278$	−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	−0.829627	−	0.558318i	$-0.811447\pi$
$281$	2.26039	−	13.7878i	0.134844	−	0.822509i	0.964470	−	0.264191i	$-0.0851049\pi$
$282$		0			0
$283$	−10.9289	+	2.40563i	−0.649655	+	0.143000i	−0.527559	−	0.849519i	$-0.676893\pi$
$283$	−10.9289	+	2.40563i	−0.649655	+	0.143000i	−0.122096	+	0.992518i	$0.538962\pi$
$284$	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	0.989518	−	0.144412i	$-0.0461289\pi$
$293$	5.38655	+	10.1601i	0.314685	+	0.593560i	−0.674832	+	0.737971i	$0.735784\pi$
$294$		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	−0.787533	−	0.616273i	$-0.788642\pi$
$307$	−21.7881	+	4.79592i	−1.24351	+	0.273718i	−0.455979	+	0.889990i	$0.650711\pi$
$308$	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	0.900767	−	0.434302i	$-0.143005\pi$
$311$	−0.914478	−	2.29517i	−0.0518553	−	0.130147i	−0.952622	+	0.304155i	$0.901626\pi$
$312$		0			0
$313$	9.35011	−	5.62577i	0.528499	−	0.317988i	−0.226175	−	0.974087i	$-0.572622\pi$
$313$	9.35011	−	5.62577i	0.528499	−	0.317988i	0.754675	+	0.656099i	$0.227795\pi$
$314$	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	−0.152603	−	0.988288i	$-0.548766\pi$
$317$	−1.58790	+	0.172695i	−0.0891854	+	0.00969949i	0.0634175	+	0.997987i	$0.479800\pi$
$318$		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	0.187651	−	0.982236i	$-0.439913\pi$
$331$	−10.7754	−	6.48334i	−0.592269	−	0.356357i	−0.779920	+	0.625879i	$0.784740\pi$
$332$	−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	0.00221723	−	0.999998i	$-0.499294\pi$
$337$	17.7400	−	13.4856i	0.966358	−	0.734606i	0.964141	+	0.265391i	$0.0855011\pi$
$338$	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	−0.0202148	−	0.999796i	$-0.506435\pi$
$347$	−18.4226	−	14.0045i	−0.988976	−	0.751800i	−0.968761	+	0.247996i	$0.920228\pi$
$348$		0			0
$349$	−6.76264	−	1.48857i	−0.361996	−	0.0796813i	0.0302484	−	0.999542i	$-0.490370\pi$
$349$	−6.76264	−	1.48857i	−0.361996	−	0.0796813i	−0.392244	+	0.919861i	$0.628301\pi$
$350$	−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	0.386165	−	0.922430i	$-0.373799\pi$
$359$	6.61869	+	1.45688i	0.349321	+	0.0768914i	−0.0368441	+	0.999321i	$0.511730\pi$
$360$		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	0.660708	+	0.750643i	$0.270256\pi$
$367$	−1.48058	+	27.3077i	−0.0772857	+	1.42545i	−0.737993	+	0.674808i	$0.764226\pi$
$368$	−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	0.744547	−	0.667570i	$-0.232666\pi$
$373$	18.0246	+	6.07320i	0.933279	+	0.314458i	0.188732	+	0.982029i	$0.439562\pi$
$374$	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	−0.0847908	−	0.996399i	$-0.527022\pi$
$379$	−17.5036	−	8.09804i	−0.899101	−	0.415968i	−0.814310	+	0.580431i	$0.802884\pi$
$380$	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	−0.796817	−	0.604221i	$-0.793485\pi$
$383$	2.94442	−	5.55377i	0.150453	−	0.283785i	0.947270	+	0.320436i	$0.103829\pi$
$384$		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	0.771481	−	0.636252i	$-0.219516\pi$
$389$	0.370781	+	0.436517i	0.0187994	+	0.0221323i	−0.752682	+	0.658384i	$0.771240\pi$
$390$		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	−0.998496	−	0.0548192i	$-0.982542\pi$
$397$	−6.20244	−	15.5670i	−0.311292	−	0.781283i	0.687205	−	0.726464i	$-0.258838\pi$
$398$	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	−0.619605	−	0.784914i	$-0.712707\pi$
$401$	−17.0686	+	3.75709i	−0.852367	+	0.187620i	−0.232762	+	0.972534i	$0.574776\pi$
$402$		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	−0.407140	−	0.913366i	$-0.633474\pi$
$409$	11.9735	−	17.6597i	0.592054	−	0.873214i	0.999194	+	0.0401521i	$0.0127842\pi$
$410$	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	−0.988354	−	0.152175i	$-0.951372\pi$
$419$	−1.29001	+	4.64620i	−0.0630212	+	0.226982i	0.925332	+	0.379157i	$0.123786\pi$
$420$		0			0
$421$	12.6165	+	1.37213i	0.614892	+	0.0668735i	0.410265	−	0.911966i	$-0.365436\pi$
$421$	12.6165	+	1.37213i	0.614892	+	0.0668735i	0.204627	+	0.978840i	$0.434402\pi$
$422$	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	−0.960984	−	0.276603i	$-0.910791\pi$
$431$	−24.2220	+	14.5739i	−1.16673	+	0.702001i	−0.205751	+	0.978604i	$0.565964\pi$
$432$		0			0
$433$	−12.9823	+	12.2974i	−0.623888	+	0.590978i	−0.932924	−	0.360072i	$-0.882752\pi$
$433$	−12.9823	+	12.2974i	−0.623888	+	0.590978i	0.309037	+	0.951050i	$0.399993\pi$
$434$	−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	−0.967074	−	0.254495i	$-0.918091\pi$
$439$	−29.3160	+	13.5630i	−1.39918	+	0.647329i	−0.432104	+	0.901824i	$0.642229\pi$
$440$	−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	−0.998175	−	0.0603848i	$-0.980767\pi$
$443$	−8.16714	+	15.4049i	−0.388032	+	0.731907i	0.610143	+	0.792291i	$0.291112\pi$
$444$		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	0.750925	−	0.660387i	$-0.229608\pi$
$449$	11.0018	+	6.61954i	0.519205	+	0.312395i	−0.231720	+	0.972782i	$0.574435\pi$
$450$		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	−0.898692	−	0.438581i	$-0.855481\pi$
$457$	−20.8107	−	30.6935i	−0.973483	−	1.43578i	−0.0747918	−	0.997199i	$-0.523829\pi$
$458$	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	0.580523	+	0.814244i	$0.302848\pi$
$461$	−8.60746	+	21.6031i	−0.400889	+	1.00616i	−0.981412	+	0.191912i	$0.938531\pi$
$462$		0			0
$463$	−0.318232	−	5.86944i	−0.0147895	−	0.272776i	−0.996570	−	0.0827565i	$-0.973628\pi$
$463$	−0.318232	−	5.86944i	−0.0147895	−	0.272776i	0.981780	−	0.190020i	$-0.0608551\pi$
$464$	−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	0.572466	−	0.819928i	$-0.305987\pi$
$467$	16.1589	+	3.55684i	0.747744	+	0.164591i	0.175278	+	0.984519i	$0.443918\pi$
$468$		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	−0.999996	−	0.00275063i	$-0.999124\pi$
$479$	−27.7991	−	21.1323i	−1.27017	−	0.965561i	−0.270178	−	0.962810i	$-0.587082\pi$
$480$		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	0.993230	+	0.116166i	$0.0370604\pi$
$487$	16.1872	+	23.8744i	0.733513	+	1.08185i	−0.259717	+	0.965685i	$0.583629\pi$
$488$	−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	0.680872	−	0.732402i	$-0.261601\pi$
$491$	17.2765	+	5.82114i	0.779679	+	0.262704i	0.0988067	+	0.995107i	$0.468497\pi$
$492$		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	−0.997158	−	0.0753371i	$-0.975997\pi$
$499$	−17.0104	+	20.0262i	−0.761491	+	0.896497i	0.235667	+	0.971834i	$0.424273\pi$
$500$	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	−0.745420	−	0.666595i	$-0.767751\pi$
$503$	−20.9797	+	7.06888i	−0.935438	+	0.315186i	−0.190018	+	0.981781i	$0.560855\pi$
$504$		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	0.856447	−	0.516235i	$-0.172667\pi$
$509$	40.6966	−	4.42602i	1.80385	−	0.196180i	0.947399	+	0.320055i	$0.103701\pi$
$510$		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	−0.755174	−	0.655524i	$-0.772448\pi$
$521$	−10.1814	−	36.6701i	−0.446056	−	1.60655i	0.309119	−	0.951023i	$-0.399966\pi$
$522$		0			0
$523$	1.74038	+	0.189277i	0.0761014	+	0.00827652i	0.146090	−	0.989271i	$-0.453331\pi$
$523$	1.74038	+	0.189277i	0.0761014	+	0.00827652i	−0.0699891	+	0.997548i	$0.522296\pi$
$524$	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	0.997781	−	0.0665826i	$-0.0212096\pi$
$541$	2.52361	+	9.08920i	0.108498	+	0.390775i	−0.889283	+	0.457358i	$0.848796\pi$
$542$	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	−0.985071	−	0.172146i	$-0.944930\pi$
$547$	−9.08155	−	22.7930i	−0.388299	−	0.974557i	0.596773	−	0.802410i	$-0.296449\pi$
$548$	−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	−0.608666	−	0.793426i	$-0.708295\pi$
$557$	−9.39288	+	4.34561i	−0.397989	+	0.184129i	0.210677	+	0.977556i	$0.432433\pi$
$558$		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	−0.372770	−	0.927924i	$-0.621592\pi$
$563$	14.3134	−	16.8510i	0.603237	−	0.710185i	0.976007	+	0.217738i	$0.0698679\pi$
$564$		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	−0.997542	−	0.0700653i	$-0.977679\pi$
$569$	−1.77925	−	10.8530i	−0.0745901	−	0.454980i	0.922952	−	0.384914i	$-0.125769\pi$
$570$		0			0
$571$	4.16619	+	1.40375i	0.174349	+	0.0587452i	0.405122	−	0.914262i	$-0.367229\pi$
$571$	4.16619	+	1.40375i	0.174349	+	0.0587452i	−0.230773	+	0.973008i	$0.574125\pi$
$572$	−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	−0.910550	−	0.413400i	$-0.864341\pi$
$577$	0.945429	−	17.4374i	0.0393587	−	0.725929i	0.949908	−	0.312529i	$-0.101176\pi$
$578$	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	0.925652	+	0.378376i	$0.123517\pi$
$587$	32.7948	+	31.0649i	1.35359	+	1.28219i	0.427935	+	0.903810i	$0.359241\pi$
$588$		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	0.937266	−	0.348616i	$-0.113348\pi$
$593$	15.5827	+	14.7607i	0.639903	+	0.606148i	−0.297362	+	0.954765i	$0.596107\pi$
$594$		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	−0.841519	−	0.540227i	$-0.818338\pi$
$599$	−1.55026	−	28.5928i	−0.0633418	−	1.16827i	0.778177	−	0.628044i	$-0.216144\pi$
$600$		0			0
$601$	−5.83171	+	14.6365i	−0.237880	+	0.597035i	−0.998648	−	0.0519899i	$-0.983444\pi$
$601$	−5.83171	+	14.6365i	−0.237880	+	0.597035i	0.760767	+	0.649025i	$0.224823\pi$
$602$	−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	−0.389360	−	0.921086i	$-0.627304\pi$
$607$	9.70681	−	7.37892i	0.393987	−	0.299501i	0.783347	+	0.621584i	$0.213511\pi$
$608$	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	0.999977	+	0.00672228i	$0.00213978\pi$
$613$	36.5023	+	21.9627i	1.47431	+	0.887066i	0.474337	+	0.880343i	$0.342688\pi$
$614$	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	−0.987155	−	0.159764i	$-0.948927\pi$
$617$	−16.6373	+	19.5869i	−0.669792	+	0.788540i	0.317364	+	0.948304i	$0.397202\pi$
$618$		0			0
$619$	10.0326	−	18.9235i	0.403245	−	0.760601i	−0.595852	−	0.803095i	$-0.703185\pi$
$619$	10.0326	−	18.9235i	0.403245	−	0.760601i	0.999097	+	0.0424935i	$0.0135302\pi$
$620$	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	−0.496495	+	0.868040i	$0.665380\pi$
$631$	−37.5786	+	22.6103i	−1.49598	+	0.900102i	−0.999486	+	0.0320623i	$0.989793\pi$
$632$	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	0.926263	−	0.376877i	$-0.123002\pi$
$641$	44.3028	+	4.81822i	1.74985	+	0.190308i	0.823590	+	0.567185i	$0.191968\pi$
$642$		0			0
$643$	−0.326914	+	1.17744i	−0.0128922	+	0.0464336i	−0.969716	−	0.244234i	$-0.921464\pi$
$643$	−0.326914	+	1.17744i	−0.0128922	+	0.0464336i	0.956824	+	0.290667i	$0.0938773\pi$
$644$	−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	0.729677	−	0.683792i	$-0.239671\pi$
$647$	−6.25160	−	11.7918i	−0.245776	−	0.463582i	−0.975452	+	0.220210i	$0.929326\pi$
$648$		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	−0.794839	−	0.606821i	$-0.792445\pi$
$653$	1.61204	−	2.37758i	0.0630840	−	0.0930420i	0.857923	+	0.513779i	$0.171755\pi$
$654$		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	0.998593	−	0.0530379i	$-0.0168904\pi$
$659$	2.96750	+	10.6880i	0.115597	+	0.416344i	−0.882995	+	0.469382i	$0.844477\pi$
$660$		0			0
$661$	−17.0814	+	3.75991i	−0.664391	+	0.146244i	−0.534348	−	0.845265i	$-0.679443\pi$
$661$	−17.0814	+	3.75991i	−0.664391	+	0.146244i	−0.130043	+	0.991508i	$0.541512\pi$
$662$	−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	0.451888	−	0.892074i	$-0.350751\pi$
$673$	−13.0111	−	15.3179i	−0.501542	−	0.590461i	−0.953430	+	0.301614i	$0.902475\pi$
$674$	−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	−0.547340	−	0.836910i	$-0.684360\pi$
$677$	−12.4007	+	4.17828i	−0.476597	+	0.160584i	0.0707427	+	0.997495i	$0.477463\pi$
$678$		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	0.675405	−	0.737447i	$-0.263969\pi$
$683$	14.3895	+	6.65729i	0.550599	+	0.254734i	−0.124806	+	0.992181i	$0.539831\pi$
$684$		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	−0.427941	−	0.903807i	$-0.640761\pi$
$691$	8.63356	−	6.56306i	0.328436	−	0.249671i	0.756377	+	0.654136i	$0.226968\pi$
$692$	−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	0.111183	−	0.993800i	$-0.464536\pi$
$701$	−21.6219	−	16.4366i	−0.816649	−	0.620800i	−0.927831	+	0.373000i	$0.878329\pi$
$702$		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	−0.376273	−	0.926509i	$-0.622795\pi$
$719$	14.3204	−	35.9414i	0.534059	−	1.34039i	0.910332	−	0.413878i	$-0.135826\pi$
$720$		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	0.833366	−	0.552721i	$-0.186411\pi$
$727$	31.3393	+	10.5594i	1.16231	+	0.391628i	0.328944	+	0.944349i	$0.393307\pi$
$728$	−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	−0.456203	−	0.889875i	$-0.650791\pi$
$733$	−38.7096	−	17.9090i	−1.42977	−	0.661483i	−0.973569	+	0.228392i	$0.926653\pi$
$734$	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	−0.436334	−	0.899785i	$-0.643723\pi$
$739$	−6.50174	+	2.19069i	−0.239170	+	0.0805859i	0.197164	+	0.980371i	$0.436827\pi$
$740$	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	−0.989417	−	0.145102i	$-0.953649\pi$
$743$	−26.5094	−	31.2093i	−0.972537	−	1.14496i	0.0168794	−	0.999858i	$-0.494627\pi$
$744$		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	0.999983	−	0.00576134i	$-0.00183390\pi$
$751$	7.40022	+	18.5732i	0.270038	+	0.677744i	−0.729946	+	0.683505i	$0.760455\pi$
$752$	−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	−0.886946	−	0.461873i	$-0.847177\pi$
$757$	−10.0447	−	36.1777i	−0.365081	−	1.31490i	0.521865	−	0.853028i	$-0.325236\pi$
$758$	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	−0.981952	−	0.189130i	$-0.939433\pi$
$761$	−1.18765	+	4.27754i	−0.0430524	+	0.155061i	0.938900	+	0.344191i	$0.111847\pi$
$762$		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	0.982332	+	0.187144i	$0.0599231\pi$
$769$	16.2491	+	30.6490i	0.585957	+	1.10523i	−0.396375	+	0.918089i	$0.629732\pi$
$770$	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	0.236808	+	0.971556i	$0.423899\pi$
$773$	−12.9837	+	46.7632i	−0.466992	+	1.68195i	−0.703800	+	0.710398i	$0.748515\pi$
$774$		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	−0.984545	−	0.175133i	$-0.943964\pi$
$787$	−24.2094	+	22.9323i	−0.862971	+	0.817449i	0.121574	+	0.992582i	$0.461206\pi$
$788$	−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	−0.714886	−	0.699241i	$-0.753522\pi$
$797$	7.48275	−	14.1140i	0.265053	−	0.499942i	0.979939	+	0.199299i	$0.0638664\pi$
$798$		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	−0.959218	−	0.282668i	$-0.908780\pi$
$809$	−26.8351	+	20.3995i	−0.943471	+	0.717208i	0.0157471	+	0.999876i	$0.494987\pi$
$810$		0			0
$811$	7.76832	+	11.4574i	0.272783	+	0.402324i	0.939263	−	0.343198i	$-0.111510\pi$
$811$	7.76832	+	11.4574i	0.272783	+	0.402324i	−0.666480	+	0.745523i	$0.732200\pi$
$812$	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	−0.459002	−	0.888435i	$-0.651793\pi$
$821$	−35.7770	−	7.87511i	−1.24863	−	0.274843i	−0.789623	+	0.613592i	$0.789724\pi$
$822$		0			0
$823$	−27.8177	−	26.3503i	−0.969665	−	0.918515i	0.0270398	−	0.999634i	$-0.491392\pi$
$823$	−27.8177	−	26.3503i	−0.969665	−	0.918515i	−0.996704	+	0.0811193i	$0.974151\pi$
$824$	−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	0.928169	−	0.372160i	$-0.121383\pi$
$829$	17.4713	+	16.5497i	0.606804	+	0.574795i	−0.321364	+	0.946956i	$0.604141\pi$
$830$	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	−0.994920	−	0.100666i	$-0.967903\pi$
$839$	0.146322	−	2.69876i	0.00505161	−	0.0931715i	0.999972	+	0.00749422i	$0.00238551\pi$
$840$		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	−0.234470	−	0.972123i	$-0.575336\pi$
$853$	22.2779	−	26.2275i	0.762780	−	0.898014i	0.997250	+	0.0741094i	$0.0236114\pi$
$854$	−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	−0.110012	−	0.993930i	$-0.535089\pi$
$857$	11.8243	−	3.98406i	0.403909	−	0.136093i	0.513921	+	0.857837i	$0.328192\pi$
$858$		0			0
$859$	−20.3127	+	9.39768i	−0.693062	+	0.320645i	−0.734608	−	0.678492i	$-0.762634\pi$
$859$	−20.3127	+	9.39768i	−0.693062	+	0.320645i	0.0415458	+	0.999137i	$0.486772\pi$
$860$	−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	−0.481108	−	0.876661i	$-0.659765\pi$
$863$	−22.4002	+	2.43617i	−0.762511	+	0.0829281i	−0.281404	+	0.959590i	$0.590800\pi$
$864$		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	0.145456	−	0.989365i	$-0.453535\pi$
$877$	2.21594	+	0.240998i	0.0748271	+	0.00813793i	−0.0706289	+	0.997503i	$0.522501\pi$
$878$	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	−0.939005	−	0.343905i	$-0.888250\pi$
$881$	−8.07233	+	11.9058i	−0.271964	+	0.401116i	0.667041	+	0.745021i	$0.267561\pi$
$882$		0			0
$883$	10.9804	+	20.7113i	0.369521	+	0.696990i	0.996638	−	0.0819351i	$-0.0261100\pi$
$883$	10.9804	+	20.7113i	0.369521	+	0.696990i	−0.627117	+	0.778925i	$0.715765\pi$
$884$	0.475651			0.0159979
$885$		0			0
$886$	24.4128			0.820165
$887$	4.96111	+	9.35765i	0.166578	+	0.314199i	0.952722	−	0.303844i	$-0.0982703\pi$
$887$	4.96111	+	9.35765i	0.166578	+	0.314199i	−0.786144	+	0.618044i	$0.787925\pi$
$888$		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	0.544723	−	0.838616i	$-0.316635\pi$
$907$	37.8560	−	4.11709i	1.25699	−	0.136706i	0.712265	+	0.701911i	$0.247669\pi$
$908$	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	−0.409417	−	0.912348i	$-0.634268\pi$
$911$	0.630495	−	0.291698i	0.0208892	−	0.00966439i	0.430306	+	0.902683i	$0.358406\pi$
$912$		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	0.855143	−	0.518392i	$-0.173469\pi$
$919$	30.7289	+	14.2167i	1.01365	+	0.468966i	0.158510	+	0.987357i	$0.449331\pi$
$920$	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	0.883572	−	0.468295i	$-0.155131\pi$
$929$	3.70306	+	5.46161i	0.121494	+	0.179190i	−0.762079	+	0.647484i	$0.775821\pi$
$930$		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	0.169983	−	0.985447i	$-0.445629\pi$
$937$	−22.4702	−	17.0814i	−0.734068	−	0.558024i	−0.904052	+	0.427423i	$0.859422\pi$
$938$	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	−0.996470	−	0.0839506i	$-0.973246\pi$
$941$	−34.7938	−	32.9584i	−1.13425	−	1.07441i	−0.137775	−	0.990464i	$-0.543995\pi$
$942$		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	0.852201	−	0.523214i	$-0.175267\pi$
$947$	11.5675	+	10.9573i	0.375892	+	0.356064i	−0.476309	+	0.879278i	$0.658026\pi$
$948$		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	−0.776490	−	0.630129i	$-0.783002\pi$
$953$	−2.24371	−	41.3827i	−0.0726808	−	1.34052i	0.703809	−	0.710389i	$-0.251481\pi$
$954$		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	0.250022	−	0.968240i	$-0.419562\pi$
$967$	−15.1850	−	9.13651i	−0.488317	−	0.293810i	−0.738339	+	0.674430i	$0.764390\pi$
$968$	−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	−0.760081	−	0.649829i	$-0.774841\pi$
$971$	0.129481	−	0.152436i	0.00415523	−	0.00489192i	0.764236	+	0.644937i	$0.223116\pi$
$972$		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	0.605771	−	0.795639i	$-0.292865\pi$
$977$	50.1470	−	23.2005i	1.60434	−	0.742249i	0.998574	+	0.0533906i	$0.0170029\pi$
$978$		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	−0.316008	−	0.948756i	$-0.602343\pi$
$983$	19.2584	−	18.2426i	0.614248	−	0.581847i	0.930257	+	0.366909i	$0.119584\pi$
$984$		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	0.271638	−	0.962400i	$-0.412435\pi$
$991$	29.0332	−	6.39069i	0.922271	−	0.203007i	0.650633	+	0.759392i	$0.274504\pi$
$992$	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	−0.553678	−	0.832731i	$-0.686776\pi$
$997$	11.0533	−	39.8105i	0.350062	−	1.26081i	0.903741	−	0.428080i	$-0.140810\pi$
$998$	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.28.2		140
3.2	odd	2		177.2.e.a.28.4	yes	140
59.19	even	29	inner	531.2.i.c.19.2		140
177.137	odd	58		177.2.e.a.19.4	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.19.4	✓	140	177.137	odd	58
177.2.e.a.28.4	yes	140	3.2	odd	2
531.2.i.c.19.2		140	59.19	even	29	inner
531.2.i.c.28.2		140	1.1	even	1	trivial

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

L-functions

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