LMFDB - Embedded newform 531.2.i.a.433.2

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:	$112$
Relative dimension:	$4$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 59)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			433.2
Character	$\chi$	$=$	531.433
Dual form			531.2.i.a.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.554859 + 0.256705i) q^{2} +(-1.05280 - 1.23945i) q^{4} +(2.81882 - 1.69603i) q^{5} +(0.0467597 + 0.862432i) q^{7} +(-0.593097 - 2.13614i) q^{8} +O(q^{10})$	\(q+(0.554859 + 0.256705i) q^{2} +(-1.05280 - 1.23945i) q^{4} +(2.81882 - 1.69603i) q^{5} +(0.0467597 + 0.862432i) q^{7} +(-0.593097 - 2.13614i) q^{8} +(1.99943 - 0.217451i) q^{10} +(-0.631059 - 3.84929i) q^{11} +(-1.31325 - 0.998305i) q^{13} +(-0.195446 + 0.490531i) q^{14} +(-0.306918 + 1.87211i) q^{16} +(-0.182290 + 3.36214i) q^{17} +(-3.16614 - 2.99913i) q^{19} +(-5.06981 - 1.70822i) q^{20} +(0.637984 - 2.29781i) q^{22} +(2.04440 + 0.450007i) q^{23} +(2.72721 - 5.14406i) q^{25} +(-0.472397 - 0.891036i) q^{26} +(1.01972 - 0.965926i) q^{28} +(3.93910 - 1.82242i) q^{29} +(5.88624 - 5.57574i) q^{31} +(-3.13912 + 4.62986i) q^{32} +(-0.964222 + 1.81872i) q^{34} +(1.59452 + 2.35174i) q^{35} +(-0.331878 + 1.19532i) q^{37} +(-0.986869 - 2.47686i) q^{38} +(-5.29479 - 5.01550i) q^{40} +(3.25469 - 0.716412i) q^{41} +(-0.471222 + 2.87433i) q^{43} +(-4.10664 + 4.83471i) q^{44} +(1.01884 + 0.774499i) q^{46} +(-5.86181 - 3.52693i) q^{47} +(6.21736 - 0.676179i) q^{49} +(2.83372 - 2.15414i) q^{50} +(0.145236 + 2.67873i) q^{52} +(-2.19994 - 0.239258i) q^{53} +(-8.30736 - 9.78018i) q^{55} +(1.81454 - 0.611391i) q^{56} +2.65347 q^{58} +(3.82919 + 6.65863i) q^{59} +(10.6495 + 4.92699i) q^{61} +(4.69735 - 1.58272i) q^{62} +(0.320821 - 0.193031i) q^{64} +(-5.39497 - 0.586739i) q^{65} +(1.13948 + 4.10403i) q^{67} +(4.35913 - 3.31372i) q^{68} +(0.281029 + 1.71420i) q^{70} +(9.08556 + 5.46660i) q^{71} +(-4.53863 + 11.3911i) q^{73} +(-0.490989 + 0.578038i) q^{74} +(-0.383962 + 7.08177i) q^{76} +(3.29024 - 0.724237i) q^{77} +(-9.88675 - 3.33123i) q^{79} +(2.31002 + 5.79770i) q^{80} +(1.98980 + 0.437988i) q^{82} +(-3.22744 - 4.76012i) q^{83} +(5.18844 + 9.78644i) q^{85} +(-0.999317 + 1.47388i) q^{86} +(-7.84835 + 3.63103i) q^{88} +(-2.24597 + 1.03910i) q^{89} +(0.799563 - 1.17927i) q^{91} +(-1.59459 - 3.00771i) q^{92} +(-2.34709 - 3.46170i) q^{94} +(-14.0114 - 3.08414i) q^{95} +(3.53517 + 8.87260i) q^{97} +(3.62334 + 1.22084i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 26 q^{2} - 30 q^{4} + 25 q^{5} - 23 q^{7} + 8 q^{8}+O(q^{10}) $ 112 * q + 26 * q^2 - 30 * q^4 + 25 * q^5 - 23 * q^7 + 8 * q^8	$ 112 q + 26 q^{2} - 30 q^{4} + 25 q^{5} - 23 q^{7} + 8 q^{8} - 3 q^{10} + 15 q^{11} - 23 q^{13} - 13 q^{14} - 8 q^{16} + 10 q^{17} - 15 q^{19} - 7 q^{20} - q^{22} - 3 q^{23} - 5 q^{25} - 5 q^{26} + 29 q^{28} + 13 q^{29} + 3 q^{31} - 36 q^{32} + 27 q^{34} - 28 q^{35} - 9 q^{37} - 31 q^{38} + 79 q^{40} - 23 q^{41} + 19 q^{43} - 43 q^{44} - 31 q^{46} - 10 q^{47} - 31 q^{49} + 60 q^{50} - 75 q^{52} + 23 q^{53} - 24 q^{55} + 103 q^{56} + 12 q^{58} + 33 q^{59} - 47 q^{61} + 39 q^{62} - 152 q^{64} + 16 q^{65} - 19 q^{67} + 5 q^{68} + 23 q^{70} + 18 q^{71} + 24 q^{73} - 19 q^{74} + 97 q^{76} - 65 q^{77} + 41 q^{79} - 107 q^{80} + 145 q^{82} - 49 q^{83} + 39 q^{85} - 111 q^{86} + 175 q^{88} - 51 q^{89} + 77 q^{91} - 135 q^{92} + 151 q^{94} - 65 q^{95} + 91 q^{97} - 31 q^{98}+O(q^{100}) $ 112 * q + 26 * q^2 - 30 * q^4 + 25 * q^5 - 23 * q^7 + 8 * q^8 - 3 * q^10 + 15 * q^11 - 23 * q^13 - 13 * q^14 - 8 * q^16 + 10 * q^17 - 15 * q^19 - 7 * q^20 - q^22 - 3 * q^23 - 5 * q^25 - 5 * q^26 + 29 * q^28 + 13 * q^29 + 3 * q^31 - 36 * q^32 + 27 * q^34 - 28 * q^35 - 9 * q^37 - 31 * q^38 + 79 * q^40 - 23 * q^41 + 19 * q^43 - 43 * q^44 - 31 * q^46 - 10 * q^47 - 31 * q^49 + 60 * q^50 - 75 * q^52 + 23 * q^53 - 24 * q^55 + 103 * q^56 + 12 * q^58 + 33 * q^59 - 47 * q^61 + 39 * q^62 - 152 * q^64 + 16 * q^65 - 19 * q^67 + 5 * q^68 + 23 * q^70 + 18 * q^71 + 24 * q^73 - 19 * q^74 + 97 * q^76 - 65 * q^77 + 41 * q^79 - 107 * q^80 + 145 * q^82 - 49 * q^83 + 39 * q^85 - 111 * q^86 + 175 * q^88 - 51 * q^89 + 77 * q^91 - 135 * q^92 + 151 * q^94 - 65 * q^95 + 91 * q^97 - 31 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{4}{29}\right)$

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 $

$2$	0.554859	+	0.256705i	0.392344	+	0.181518i	0.606135	−	0.795362i	$-0.292719\pi$
$2$	0.554859	+	0.256705i	0.392344	+	0.181518i	−0.213791	+	0.976879i	$0.568581\pi$
$3$		0			0
$3$		0			0
$4$	−1.05280	−	1.23945i	−0.526401	−	0.619727i
$5$	2.81882	−	1.69603i	1.26062	−	0.758488i	0.281066	−	0.959688i	$-0.409312\pi$
$5$	2.81882	−	1.69603i	1.26062	−	0.758488i	0.979550	+	0.201201i	$0.0644843\pi$
$6$		0			0
$7$	0.0467597	+	0.862432i	0.0176735	+	0.325969i	0.993979	+	0.109571i	$0.0349478\pi$
$7$	0.0467597	+	0.862432i	0.0176735	+	0.325969i	−0.976305	+	0.216397i	$0.930569\pi$
$8$	−0.593097	−	2.13614i	−0.209691	−	0.755240i
$9$		0			0
$10$	1.99943	−	0.217451i	0.632275	−	0.0687640i
$11$	−0.631059	−	3.84929i	−0.190272	−	1.16061i	−0.893306	−	0.449449i	$-0.851620\pi$
$11$	−0.631059	−	3.84929i	−0.190272	−	1.16061i	0.703034	−	0.711156i	$-0.251828\pi$
$12$		0			0
$13$	−1.31325	−	0.998305i	−0.364230	−	0.276880i	0.407012	−	0.913423i	$-0.366571\pi$
$13$	−1.31325	−	0.998305i	−0.364230	−	0.276880i	−0.771241	+	0.636543i	$0.780364\pi$
$14$	−0.195446	+	0.490531i	−0.0522350	+	0.131100i
$15$		0			0
$16$	−0.306918	+	1.87211i	−0.0767294	+	0.468029i
$17$	−0.182290	+	3.36214i	−0.0442117	+	0.815438i	0.889395	+	0.457139i	$0.151126\pi$
$17$	−0.182290	+	3.36214i	−0.0442117	+	0.815438i	−0.933607	+	0.358299i	$0.883357\pi$
$18$		0			0
$19$	−3.16614	−	2.99913i	−0.726362	−	0.688047i	0.232284	−	0.972648i	$-0.425380\pi$
$19$	−3.16614	−	2.99913i	−0.726362	−	0.688047i	−0.958646	+	0.284601i	$0.908139\pi$
$20$	−5.06981	−	1.70822i	−1.13364	−	0.381969i
$21$		0			0
$22$	0.637984	−	2.29781i	0.136019	−	0.489895i
$23$	2.04440	+	0.450007i	0.426287	+	0.0938330i	0.422932	−	0.906161i	$-0.361001\pi$
$23$	2.04440	+	0.450007i	0.426287	+	0.0938330i	0.00335541	+	0.999994i	$0.498932\pi$
$24$		0			0
$25$	2.72721	−	5.14406i	0.545442	−	1.02881i
$26$	−0.472397	−	0.891036i	−0.0926447	−	0.174747i
$27$		0			0
$28$	1.01972	−	0.965926i	0.192708	−	0.182543i
$29$	3.93910	−	1.82242i	0.731472	−	0.338415i	−0.0185498	−	0.999828i	$-0.505905\pi$
$29$	3.93910	−	1.82242i	0.731472	−	0.338415i	0.750022	+	0.661413i	$0.230043\pi$
$30$		0			0
$31$	5.88624	−	5.57574i	1.05720	−	1.00143i	0.0572045	−	0.998362i	$-0.481781\pi$
$31$	5.88624	−	5.57574i	1.05720	−	1.00143i	0.999995	−	0.00307034i	$-0.000977320\pi$
$32$	−3.13912	+	4.62986i	−0.554924	+	0.818451i
$33$		0			0
$34$	−0.964222	+	1.81872i	−0.165363	+	0.311907i
$35$	1.59452	+	2.35174i	0.269523	+	0.397516i
$36$		0			0
$37$	−0.331878	+	1.19532i	−0.0545604	+	0.196509i	−0.985808	−	0.167879i	$-0.946308\pi$
$37$	−0.331878	+	1.19532i	−0.0545604	+	0.196509i	0.931247	+	0.364388i	$0.118722\pi$
$38$	−0.986869	−	2.47686i	−0.160091	−	0.401799i
$39$		0			0
$40$	−5.29479	−	5.01550i	−0.837180	−	0.793019i
$41$	3.25469	−	0.716412i	0.508297	−	0.111885i	0.0465849	−	0.998914i	$-0.485166\pi$
$41$	3.25469	−	0.716412i	0.508297	−	0.111885i	0.461713	+	0.887030i	$0.347235\pi$
$42$		0			0
$43$	−0.471222	+	2.87433i	−0.0718607	+	0.438331i	0.926251	+	0.376907i	$0.123012\pi$
$43$	−0.471222	+	2.87433i	−0.0718607	+	0.438331i	−0.998112	+	0.0614239i	$0.980436\pi$
$44$	−4.10664	+	4.83471i	−0.619099	+	0.728860i
$45$		0			0
$46$	1.01884	+	0.774499i	0.150219	+	0.114194i
$47$	−5.86181	−	3.52693i	−0.855032	−	0.514456i	0.0192832	−	0.999814i	$-0.493862\pi$
$47$	−5.86181	−	3.52693i	−0.855032	−	0.514456i	−0.874315	+	0.485358i	$0.838689\pi$
$48$		0			0
$49$	6.21736	−	0.676179i	0.888195	−	0.0965970i
$50$	2.83372	−	2.15414i	0.400749	−	0.304641i
$51$		0			0
$52$	0.145236	+	2.67873i	0.0201407	+	0.371473i
$53$	−2.19994	−	0.239258i	−0.302185	−	0.0328645i	−0.0442293	−	0.999021i	$-0.514083\pi$
$53$	−2.19994	−	0.239258i	−0.302185	−	0.0328645i	−0.257955	+	0.966157i	$0.583049\pi$
$54$		0			0
$55$	−8.30736	−	9.78018i	−1.12016	−	1.31876i
$56$	1.81454	−	0.611391i	0.242478	−	0.0817005i
$57$		0			0
$58$	2.65347			0.348417
$59$	3.82919	+	6.65863i	0.498518	+	0.866879i
$59$	3.82919	+	6.65863i	0.498518	+	0.866879i
$60$		0			0
$61$	10.6495	+	4.92699i	1.36353	+	0.630837i	0.958927	−	0.283655i	$-0.0915469\pi$
$61$	10.6495	+	4.92699i	1.36353	+	0.630837i	0.404605	+	0.914491i	$0.367409\pi$
$62$	4.69735	−	1.58272i	0.596564	−	0.201006i
$63$		0			0
$64$	0.320821	−	0.193031i	0.0401026	−	0.0241289i
$65$	−5.39497	−	0.586739i	−0.669164	−	0.0727760i
$66$		0			0
$67$	1.13948	+	4.10403i	0.139209	+	0.501387i	0.999971	−	0.00762130i	$-0.00242596\pi$
$67$	1.13948	+	4.10403i	0.139209	+	0.501387i	−0.860761	+	0.509009i	$0.830012\pi$
$68$	4.35913	−	3.31372i	0.528622	−	0.401848i
$69$		0			0
$70$	0.281029	+	1.71420i	0.0335894	+	0.204886i
$71$	9.08556	+	5.46660i	1.07826	+	0.648766i	0.939842	−	0.341608i	$-0.110972\pi$
$71$	9.08556	+	5.46660i	1.07826	+	0.648766i	0.138415	+	0.990374i	$0.455799\pi$
$72$		0			0
$73$	−4.53863	+	11.3911i	−0.531207	+	1.33323i	0.381408	+	0.924407i	$0.375439\pi$
$73$	−4.53863	+	11.3911i	−0.531207	+	1.33323i	−0.912614	+	0.408822i	$0.865940\pi$
$74$	−0.490989	+	0.578038i	−0.0570764	+	0.0671955i
$75$		0			0
$76$	−0.383962	+	7.08177i	−0.0440435	+	0.812335i
$77$	3.29024	−	0.724237i	0.374958	−	0.0825345i
$78$		0			0
$79$	−9.88675	−	3.33123i	−1.11235	−	0.374793i	−0.297647	−	0.954676i	$-0.596202\pi$
$79$	−9.88675	−	3.33123i	−1.11235	−	0.374793i	−0.814700	+	0.579883i	$0.803098\pi$
$80$	2.31002	+	5.79770i	0.258268	+	0.648203i
$81$		0			0
$82$	1.98980	+	0.437988i	0.219737	+	0.0483677i
$83$	−3.22744	−	4.76012i	−0.354258	−	0.522491i	0.608250	−	0.793746i	$-0.291872\pi$
$83$	−3.22744	−	4.76012i	−0.354258	−	0.522491i	−0.962508	+	0.271254i	$0.912562\pi$
$84$		0			0
$85$	5.18844	+	9.78644i	0.562765	+	1.06149i
$86$	−0.999317	+	1.47388i	−0.107759	+	0.158933i
$87$		0			0
$88$	−7.84835	+	3.63103i	−0.836637	+	0.387069i
$89$	−2.24597	+	1.03910i	−0.238073	+	0.110144i	−0.535298	−	0.844663i	$-0.679801\pi$
$89$	−2.24597	+	1.03910i	−0.238073	+	0.110144i	0.297225	+	0.954807i	$0.403939\pi$
$90$		0			0
$91$	0.799563	−	1.17927i	0.0838170	−	0.123621i
$92$	−1.59459	−	3.00771i	−0.166247	−	0.313576i
$93$		0			0
$94$	−2.34709	−	3.46170i	−0.242084	−	0.357047i
$95$	−14.0114	−	3.08414i	−1.43754	−	0.316426i
$96$		0			0
$97$	3.53517	+	8.87260i	0.358942	+	0.900876i	0.991938	+	0.126721i	$0.0404454\pi$
$97$	3.53517	+	8.87260i	0.358942	+	0.900876i	−0.632997	+	0.774155i	$0.718175\pi$
$98$	3.62334	+	1.22084i	0.366012	+	0.123324i
$99$		0			0
$100$	−9.24704	+	2.03543i	−0.924704	+	0.203543i
$101$	−0.496317	+	9.15403i	−0.0493854	+	0.910860i	0.863931	+	0.503610i	$0.167995\pi$
$101$	−0.496317	+	9.15403i	−0.0493854	+	0.910860i	−0.913317	+	0.407250i	$0.866488\pi$
$102$		0			0
$103$	0.373198	−	0.439363i	0.0367723	−	0.0432917i	−0.743468	−	0.668771i	$-0.766821\pi$
$103$	0.373198	−	0.439363i	0.0367723	−	0.0432917i	0.780241	+	0.625479i	$0.215097\pi$
$104$	−1.35364	+	3.39737i	−0.132735	+	0.333140i
$105$		0			0
$106$	−1.15924	−	0.697489i	−0.112595	−	0.0677461i
$107$	−0.758075	−	4.62405i	−0.0732859	−	0.447024i	−0.997824	−	0.0659343i	$-0.978997\pi$
$107$	−0.758075	−	4.62405i	−0.0732859	−	0.447024i	0.924538	−	0.381090i	$-0.124451\pi$
$108$		0			0
$109$	−3.62962	+	2.75917i	−0.347655	+	0.264280i	−0.764399	−	0.644743i	$-0.776964\pi$
$109$	−3.62962	+	2.75917i	−0.347655	+	0.264280i	0.416744	+	0.909024i	$0.363171\pi$
$110$	−2.09879	−	7.55916i	−0.200112	−	0.720738i
$111$		0			0
$112$	−1.62892	−	0.177156i	−0.153919	−	0.0167397i
$113$	−6.98819	+	4.20465i	−0.657393	+	0.395540i	−0.804809	−	0.593534i	$-0.797732\pi$
$113$	−6.98819	+	4.20465i	−0.657393	+	0.395540i	0.147415	+	0.989075i	$0.452905\pi$
$114$		0			0
$115$	6.52604	−	2.19888i	0.608556	−	0.205046i
$116$	−6.40590	−	2.96368i	−0.594773	−	0.275171i
$117$		0			0
$118$	0.415355	+	4.67757i	0.0382366	+	0.430605i
$119$	−2.90814			−0.266588
$120$		0			0
$121$	−3.99463	+	1.34595i	−0.363148	+	0.122359i
$122$	4.64420	+	5.46757i	0.420466	+	0.495011i
$123$		0			0
$124$	−13.1079	−	1.42557i	−1.17713	−	0.128020i
$125$	−0.146451	−	2.70113i	−0.0130990	−	0.241597i
$126$		0			0
$127$	−6.40397	+	4.86817i	−0.568260	+	0.431980i	−0.849448	−	0.527673i	$-0.823065\pi$
$127$	−6.40397	+	4.86817i	−0.568260	+	0.431980i	0.281188	+	0.959653i	$0.409272\pi$
$128$	11.3494	−	1.23432i	1.00316	−	0.109100i
$129$		0			0
$130$	−2.84283	−	1.71047i	−0.249333	−	0.150018i
$131$	6.48615	+	4.93064i	0.566697	+	0.430792i	0.848893	−	0.528565i	$-0.177270\pi$
$131$	6.48615	+	4.93064i	0.566697	+	0.430792i	−0.282196	+	0.959357i	$0.591063\pi$
$132$		0			0
$133$	2.43849	−	2.87082i	0.211444	−	0.248931i
$134$	−0.421276	+	2.56967i	−0.0363927	+	0.221985i
$135$		0			0
$136$	7.29011	−	1.60467i	0.625122	−	0.137600i
$137$	5.89436	+	5.58343i	0.503589	+	0.477025i	0.896808	−	0.442420i	$-0.145880\pi$
$137$	5.89436	+	5.58343i	0.503589	+	0.477025i	−0.393219	+	0.919445i	$0.628639\pi$
$138$		0			0
$139$	1.57818	+	3.96094i	0.133860	+	0.335963i	0.980593	−	0.196055i	$-0.0628132\pi$
$139$	1.57818	+	3.96094i	0.133860	+	0.335963i	−0.846733	+	0.532018i	$0.821434\pi$
$140$	1.23616	−	4.45224i	0.104475	−	0.376283i
$141$		0			0
$142$	3.63790	+	5.36550i	0.305286	+	0.450263i
$143$	−3.01403	+	5.68507i	−0.252046	+	0.475409i
$144$		0			0
$145$	8.01275	−	11.8179i	0.665422	−	0.981424i
$146$	−5.44246	+	5.15537i	−0.450421	+	0.426661i
$147$		0			0
$148$	1.83094	−	0.847084i	0.150503	−	0.0696299i
$149$	6.70502	−	6.35133i	0.549296	−	0.520321i	−0.361942	−	0.932201i	$-0.617886\pi$
$149$	6.70502	−	6.35133i	0.549296	−	0.520321i	0.911238	+	0.411880i	$0.135128\pi$
$150$		0			0
$151$	−10.4138	−	19.6425i	−0.847464	−	1.59849i	−0.800301	−	0.599599i	$-0.795327\pi$
$151$	−10.4138	−	19.6425i	−0.847464	−	1.59849i	−0.0471626	−	0.998887i	$-0.515018\pi$
$152$	−4.52873	+	8.54209i	−0.367328	+	0.692855i
$153$		0			0
$154$	2.01154	+	0.442773i	0.162094	+	0.0356796i
$155$	7.13565	−	25.7003i	0.573149	−	2.06430i
$156$		0			0
$157$	7.71264	+	2.59869i	0.615536	+	0.207398i	0.609761	−	0.792585i	$-0.291265\pi$
$157$	7.71264	+	2.59869i	0.615536	+	0.207398i	0.00577445	+	0.999983i	$0.498162\pi$
$158$	−4.63061	−	4.38634i	−0.368391	−	0.348959i
$159$		0			0
$160$	−0.996253	+	18.3748i	−0.0787607	+	1.45266i
$161$	−0.292505	+	1.78420i	−0.0230526	+	0.140615i
$162$		0			0
$163$	5.39519	−	13.5409i	0.422584	−	1.06061i	−0.551451	−	0.834207i	$-0.685926\pi$
$163$	5.39519	−	13.5409i	0.422584	−	1.06061i	0.974035	−	0.226398i	$-0.0726950\pi$
$164$	−4.31450	−	3.27980i	−0.336906	−	0.256109i
$165$		0			0
$166$	−0.568828	−	3.46970i	−0.0441496	−	0.269301i
$167$	−16.8909	+	1.83700i	−1.30706	+	0.142151i	−0.735004	−	0.678063i	$-0.762820\pi$
$167$	−16.8909	+	1.83700i	−1.30706	+	0.142151i	−0.572056	+	0.820215i	$0.693854\pi$
$168$		0			0
$169$	−2.74986	−	9.90410i	−0.211528	−	0.761854i
$170$	0.366624	+	6.76199i	0.0281188	+	0.518621i
$171$		0			0
$172$	4.05870	−	2.44204i	0.309473	−	0.186204i
$173$	−12.2858	−	14.4639i	−0.934071	−	1.09967i	−0.994833	−	0.101521i	$-0.967629\pi$
$173$	−12.2858	−	14.4639i	−0.934071	−	1.09967i	0.0607624	−	0.998152i	$-0.480647\pi$
$174$		0			0
$175$	4.56392	+	2.11150i	0.345000	+	0.159614i
$176$	7.40000			0.557796
$177$		0			0
$178$	−1.51294			−0.113400
$179$	16.2981	+	7.54030i	1.21818	+	0.563588i	0.920374	−	0.391039i	$-0.127884\pi$
$179$	16.2981	+	7.54030i	1.21818	+	0.563588i	0.297802	+	0.954628i	$0.403746\pi$
$180$		0			0
$181$	15.3849	+	18.1125i	1.14355	+	1.34629i	0.929220	+	0.369526i	$0.120480\pi$
$181$	15.3849	+	18.1125i	1.14355	+	1.34629i	0.214327	+	0.976762i	$0.431244\pi$
$182$	0.746369	−	0.449075i	0.0553245	−	0.0332877i
$183$		0			0
$184$	−0.251250	−	4.63403i	−0.0185224	−	0.341625i
$185$	1.09179	+	3.93226i	0.0802698	+	0.289106i
$186$		0			0
$187$	13.0569	−	1.42002i	0.954813	−	0.103842i
$188$	1.79985	+	10.9786i	0.131268	+	0.800697i
$189$		0			0
$190$	−6.98263	−	5.30806i	−0.506573	−	0.385087i
$191$	1.82504	−	4.58050i	0.132055	−	0.331433i	−0.848049	−	0.529918i	$-0.822223\pi$
$191$	1.82504	−	4.58050i	0.132055	−	0.331433i	0.980104	+	0.198485i	$0.0636020\pi$
$192$		0			0
$193$	−3.09323	+	18.8679i	−0.222656	+	1.35814i	0.604696	+	0.796456i	$0.293294\pi$
$193$	−3.09323	+	18.8679i	−0.222656	+	1.35814i	−0.827352	+	0.561684i	$0.810154\pi$
$194$	−0.316122	+	5.83053i	−0.0226963	+	0.418608i
$195$		0			0
$196$	−7.38374	−	6.99425i	−0.527410	−	0.499590i
$197$	8.62732	+	2.90688i	0.614671	+	0.207107i	0.609379	−	0.792879i	$-0.291419\pi$
$197$	8.62732	+	2.90688i	0.614671	+	0.207107i	0.00529224	+	0.999986i	$0.498315\pi$
$198$		0			0
$199$	2.53614	−	9.13434i	0.179782	−	0.647517i	−0.817638	−	0.575733i	$-0.804717\pi$
$199$	2.53614	−	9.13434i	0.179782	−	0.647517i	0.997420	−	0.0717840i	$-0.0228692\pi$
$200$	−12.6059	−	2.77478i	−0.891374	−	0.196206i
$201$		0			0
$202$	−2.62527	+	4.95179i	−0.184713	+	0.348407i
$203$	1.75590	+	3.31199i	0.123240	+	0.232456i
$204$		0			0
$205$	7.95935	−	7.53949i	0.555905	−	0.526581i
$206$	0.319859	−	0.147982i	0.0222856	−	0.0103104i
$207$		0			0
$208$	2.27200	−	2.15215i	0.157535	−	0.149225i
$209$	−9.54649	+	14.0800i	−0.660345	+	0.973935i
$210$		0			0
$211$	−13.0562	+	24.6267i	−0.898828	+	1.69537i	−0.200367	+	0.979721i	$0.564213\pi$
$211$	−13.0562	+	24.6267i	−0.898828	+	1.69537i	−0.698461	+	0.715648i	$0.746132\pi$
$212$	2.01955	+	2.97861i	0.138703	+	0.204572i
$213$		0			0
$214$	0.766393	−	2.76030i	0.0523895	−	0.188690i
$215$	3.54666	+	8.90144i	0.241880	+	0.607073i
$216$		0			0
$217$	5.08394	+	4.81576i	0.345120	+	0.326915i
$218$	−2.72222	+	0.599206i	−0.184372	+	0.0405834i
$219$		0			0
$220$	−3.37608	+	20.5932i	−0.227615	+	1.38839i
$221$	3.59583	−	4.23334i	0.241882	−	0.284765i
$222$		0			0
$223$	−2.30497	−	1.75219i	−0.154352	−	0.117336i	0.525148	−	0.851011i	$-0.324010\pi$
$223$	−2.30497	−	1.75219i	−0.154352	−	0.117336i	−0.679500	+	0.733676i	$0.737803\pi$
$224$	−4.13972	−	2.49079i	−0.276597	−	0.166423i
$225$		0			0
$226$	−4.95681	+	0.539086i	−0.329722	+	0.0358595i
$227$	13.3785	−	10.1700i	0.887960	−	0.675010i	−0.0583409	−	0.998297i	$-0.518581\pi$
$227$	13.3785	−	10.1700i	0.887960	−	0.675010i	0.946301	+	0.323287i	$0.104788\pi$
$228$		0			0
$229$	−0.880892	−	16.2471i	−0.0582110	−	1.07364i	−0.871064	−	0.491169i	$-0.836570\pi$
$229$	−0.880892	−	16.2471i	−0.0582110	−	1.07364i	0.812853	−	0.582469i	$-0.197913\pi$
$230$	4.18549	+	0.455200i	0.275983	+	0.0300150i
$231$		0			0
$232$	−6.22921	−	7.33360i	−0.408968	−	0.481474i
$233$	−5.77225	+	1.94490i	−0.378153	+	0.127414i	−0.501958	−	0.864892i	$-0.667387\pi$
$233$	−5.77225	+	1.94490i	−0.378153	+	0.127414i	0.123805	+	0.992307i	$0.460490\pi$
$234$		0			0
$235$	−22.5052			−1.46808
$236$	4.22169	−	11.7563i	0.274808	−	0.765271i
$237$		0			0
$238$	−1.61360	−	0.746533i	−0.104594	−	0.0483905i
$239$	−4.28355	+	1.44330i	−0.277080	+	0.0933592i	−0.454411	−	0.890792i	$-0.650150\pi$
$239$	−4.28355	+	1.44330i	−0.277080	+	0.0933592i	0.177331	+	0.984151i	$0.443254\pi$
$240$		0			0
$241$	24.1172	−	14.5108i	1.55352	−	0.934724i	0.559119	−	0.829087i	$-0.311139\pi$
$241$	24.1172	−	14.5108i	1.55352	−	0.934724i	0.994405	−	0.105637i	$-0.0336881\pi$
$242$	−2.56197	−	0.278631i	−0.164689	−	0.0179111i
$243$		0			0
$244$	−5.10505	−	18.3867i	−0.326818	−	1.17709i
$245$	16.3788	−	12.4509i	1.04641	−	0.795457i
$246$		0			0
$247$	1.16388	+	7.09937i	0.0740561	+	0.451722i
$248$	−15.4017	−	9.26688i	−0.978007	−	0.588448i
$249$		0			0
$250$	0.612134	−	1.53634i	0.0387148	−	0.0971668i
$251$	3.53436	−	4.16097i	0.223087	−	0.262638i	−0.639220	−	0.769024i	$-0.720743\pi$
$251$	3.53436	−	4.16097i	0.223087	−	0.262638i	0.862307	+	0.506385i	$0.169019\pi$
$252$		0			0
$253$	0.442069	−	8.15349i	0.0277926	−	0.512605i
$254$	−4.80298	+	1.05722i	−0.301366	+	0.0663356i
$255$		0			0
$256$	5.90455	+	1.98947i	0.369034	+	0.124342i
$257$	2.21814	+	5.56710i	0.138364	+	0.347266i	0.981788	−	0.189982i	$-0.0608430\pi$
$257$	2.21814	+	5.56710i	0.138364	+	0.347266i	−0.843424	+	0.537249i	$0.819464\pi$
$258$		0			0
$259$	−1.04640	−	0.230330i	−0.0650200	−	0.0143120i
$260$	4.95260	+	7.30454i	0.307147	+	0.453008i
$261$		0			0
$262$	2.33317	+	4.40083i	0.144144	+	0.271884i
$263$	−4.32309	+	6.37609i	−0.266573	+	0.393166i	−0.937292	−	0.348546i	$-0.886676\pi$
$263$	−4.32309	+	6.37609i	−0.266573	+	0.393166i	0.670718	+	0.741712i	$0.265986\pi$
$264$		0			0
$265$	−6.60702	+	3.05673i	−0.405866	+	0.187774i
$266$	2.08997	−	0.966924i	0.128144	−	0.0592859i
$267$		0			0
$268$	3.88711	−	5.73306i	0.237443	−	0.350203i
$269$	2.56485	+	4.83783i	0.156382	+	0.294968i	0.949306	−	0.314352i	$-0.101787\pi$
$269$	2.56485	+	4.83783i	0.156382	+	0.294968i	−0.792924	+	0.609320i	$0.791443\pi$
$270$		0			0
$271$	−5.05394	−	7.45400i	−0.307005	−	0.452798i	0.642621	−	0.766184i	$-0.277847\pi$
$271$	−5.05394	−	7.45400i	−0.307005	−	0.452798i	−0.949626	+	0.313386i	$0.898537\pi$
$272$	−6.23836	−	1.37317i	−0.378256	−	0.0832604i
$273$		0			0
$274$	1.83724	+	4.61113i	0.110992	+	0.278569i
$275$	−21.5220	−	7.25161i	−1.29783	−	0.437289i
$276$		0			0
$277$	9.76763	−	2.15002i	0.586880	−	0.129182i	0.0884027	−	0.996085i	$-0.471824\pi$
$277$	9.76763	−	2.15002i	0.586880	−	0.129182i	0.498477	+	0.866903i	$0.333893\pi$
$278$	−0.141125	+	2.60289i	−0.00846410	+	0.156111i
$279$		0			0
$280$	4.07794	−	4.80092i	0.243703	−	0.286910i
$281$	4.69259	−	11.7775i	0.279937	−	0.702588i	−0.720026	−	0.693947i	$-0.755870\pi$
$281$	4.69259	−	11.7775i	0.279937	−	0.702588i	0.999963	−	0.00864103i	$-0.00275056\pi$
$282$		0			0
$283$	−26.5719	−	15.9878i	−1.57953	−	0.950374i	−0.989750	−	0.142814i	$-0.954385\pi$
$283$	−26.5719	−	15.9878i	−1.57953	−	0.950374i	−0.589785	−	0.807561i	$-0.700787\pi$
$284$	−2.78969	−	17.0164i	−0.165538	−	1.00974i
$285$		0			0
$286$	−3.13175	+	2.38069i	−0.185184	+	0.140773i
$287$	0.770045	+	2.77345i	0.0454543	+	0.163712i
$288$		0			0
$289$	5.62962	+	0.612258i	0.331154	+	0.0360152i
$290$	7.47966	−	4.50036i	0.439221	−	0.264270i
$291$		0			0
$292$	18.8970	−	6.36715i	1.10587	−	0.372609i
$293$	4.59598	+	2.12633i	0.268500	+	0.124221i	0.549520	−	0.835481i	$-0.314811\pi$
$293$	4.59598	+	2.12633i	0.268500	+	0.124221i	−0.281020	+	0.959702i	$0.590673\pi$
$294$		0			0
$295$	22.0870	+	12.2751i	1.28596	+	0.714683i
$296$	2.75020			0.159852
$297$		0			0
$298$	5.35075	−	1.80288i	0.309961	−	0.104438i
$299$	−2.23556	−	2.63191i	−0.129286	−	0.152207i
$300$		0			0
$301$	−2.50095	−	0.271994i	−0.144152	−	0.0156775i
$302$	−0.735858	−	13.5721i	−0.0423439	−	0.780987i
$303$		0			0
$304$	6.58645	−	5.00689i	0.377759	−	0.287165i
$305$	38.3755	−	4.17358i	2.19737	−	0.238979i
$306$		0			0
$307$	−4.14617	−	2.49467i	−0.236635	−	0.142378i	0.392298	−	0.919838i	$-0.371680\pi$
$307$	−4.14617	−	2.49467i	−0.236635	−	0.142378i	−0.628932	+	0.777460i	$0.716508\pi$
$308$	−4.36163	−	3.31563i	−0.248527	−	0.188925i
$309$		0			0
$310$	10.5567	−	12.4283i	0.599578	−	0.705878i
$311$	−3.92141	+	23.9195i	−0.222362	+	1.35635i	0.605690	+	0.795701i	$0.292897\pi$
$311$	−3.92141	+	23.9195i	−0.222362	+	1.35635i	−0.828053	+	0.560650i	$0.810551\pi$
$312$		0			0
$313$	−33.1029	+	7.28650i	−1.87109	+	0.411857i	−0.997233	−	0.0743338i	$-0.976317\pi$
$313$	−33.1029	+	7.28650i	−1.87109	+	0.411857i	−0.873853	+	0.486191i	$0.838386\pi$
$314$	3.61233	+	3.42178i	0.203855	+	0.193102i
$315$		0			0
$316$	6.27988	+	15.7613i	0.353271	+	0.886643i
$317$	5.88706	−	21.2033i	0.330650	−	1.19090i	−0.592217	−	0.805778i	$-0.701747\pi$
$317$	5.88706	−	21.2033i	0.330650	−	1.19090i	0.922868	−	0.385117i	$-0.125839\pi$
$318$		0			0
$319$	−9.50084	−	14.0127i	−0.531945	−	0.784560i
$320$	0.576950	−	1.08824i	0.0322525	−	0.0608346i
$321$		0			0
$322$	−0.620312	+	0.914892i	−0.0345686	+	0.0509849i
$323$	10.6606	−	10.0983i	0.593173	−	0.561883i
$324$		0			0
$325$	−8.71685	+	4.03284i	−0.483524	+	0.223702i
$326$	6.46958	−	6.12832i	0.358317	−	0.339416i
$327$		0			0
$328$	−3.46070	−	6.52758i	−0.191085	−	0.360425i
$329$	2.76764	−	5.22033i	0.152585	−	0.287806i
$330$		0			0
$331$	−1.85821	−	0.409024i	−0.102137	−	0.0224820i	0.163608	−	0.986525i	$-0.447687\pi$
$331$	−1.85821	−	0.409024i	−0.102137	−	0.0224820i	−0.265745	+	0.964043i	$0.585618\pi$
$332$	−2.50209	+	9.01173i	−0.137320	+	0.494583i
$333$		0			0
$334$	−9.84365	−	3.31671i	−0.538620	−	0.181482i
$335$	10.1726	+	9.63595i	0.555786	+	0.526468i
$336$		0			0
$337$	1.17193	−	21.6150i	0.0638392	−	1.17744i	−0.774601	−	0.632450i	$-0.782049\pi$
$337$	1.17193	−	21.6150i	0.0638392	−	1.17744i	0.838440	−	0.544994i	$-0.183468\pi$
$338$	1.01665	−	6.20128i	0.0552984	−	0.337305i
$339$		0			0
$340$	6.66744	−	16.7340i	0.361593	−	0.907529i
$341$	−25.1772	−	19.1392i	−1.36342	−	1.03645i
$342$		0			0
$343$	1.85200	+	11.2967i	0.0999984	+	0.609963i
$344$	6.41945	−	0.698158i	0.346114	−	0.0376421i
$345$		0			0
$346$	−3.10391	−	11.1793i	−0.166867	−	0.601001i
$347$	0.0961070	+	1.77259i	0.00515929	+	0.0951576i	0.999979	−	0.00649863i	$-0.00206859\pi$
$347$	0.0961070	+	1.77259i	0.00515929	+	0.0951576i	−0.994820	+	0.101656i	$0.967586\pi$
$348$		0			0
$349$	−0.965567	+	0.580962i	−0.0516856	+	0.0310982i	−0.541162	−	0.840918i	$-0.682015\pi$
$349$	−0.965567	+	0.580962i	−0.0516856	+	0.0310982i	0.489477	+	0.872016i	$0.337188\pi$
$350$	1.99030	+	2.34316i	0.106386	+	0.125247i
$351$		0			0
$352$	19.8027	+	9.16168i	1.05549	+	0.488319i
$353$	−33.0859			−1.76098			−0.880491	−	0.474062i	$-0.842787\pi$
$353$	−33.0859			−1.76098			−0.880491	+	0.474062i	$0.842787\pi$
$354$		0			0
$355$	34.8821			1.85135
$356$	3.65248	+	1.68982i	0.193581	+	0.0895601i
$357$		0			0
$358$	7.10750	+	8.36760i	0.375643	+	0.442241i
$359$	−9.44626	+	5.68363i	−0.498555	+	0.299970i	−0.742532	−	0.669811i	$-0.766375\pi$
$359$	−9.44626	+	5.68363i	−0.498555	+	0.299970i	0.243977	+	0.969781i	$0.421548\pi$
$360$		0			0
$361$	0.00103907	+	0.0191644i	5.46877e−5	+	0.00100865i
$362$	3.88686	+	13.9992i	0.204289	+	0.735783i
$363$		0			0
$364$	−2.30343	+	0.250513i	−0.120733	+	0.0131305i
$365$	6.52606	+	39.8072i	0.341589	+	2.08360i
$366$		0			0
$367$	−1.82954	−	1.39078i	−0.0955014	−	0.0725983i	0.556334	−	0.830959i	$-0.312208\pi$
$367$	−1.82954	−	1.39078i	−0.0955014	−	0.0725983i	−0.651835	+	0.758361i	$0.726001\pi$
$368$	−1.46993	+	3.68924i	−0.0766253	+	0.192315i
$369$		0			0
$370$	−0.403644	+	2.46212i	−0.0209844	+	0.127999i
$371$	0.103475	−	1.90848i	0.00537215	−	0.0990835i
$372$		0			0
$373$	0.723584	+	0.685415i	0.0374658	+	0.0354895i	0.706203	−	0.708009i	$-0.250406\pi$
$373$	0.723584	+	0.685415i	0.0374658	+	0.0354895i	−0.668738	+	0.743498i	$0.733165\pi$
$374$	7.60925	+	2.56385i	0.393465	+	0.132574i
$375$		0			0
$376$	−4.05740	+	14.6135i	−0.209245	+	0.753631i
$377$	−6.99235	−	1.53913i	−0.360124	−	0.0792693i
$378$		0			0
$379$	−9.54753	+	18.0086i	−0.490424	+	0.925037i	0.507563	+	0.861615i	$0.330546\pi$
$379$	−9.54753	+	18.0086i	−0.490424	+	0.925037i	−0.997987	+	0.0634226i	$0.979798\pi$
$380$	10.9286	+	20.6135i	0.560624	+	1.05745i
$381$		0			0
$382$	2.18847	−	2.07303i	0.111972	−	0.106066i
$383$	23.5937	−	10.9156i	1.20558	−	0.557760i	0.288890	−	0.957362i	$-0.406714\pi$
$383$	23.5937	−	10.9156i	1.20558	−	0.557760i	0.916689	+	0.399602i	$0.130852\pi$
$384$		0			0
$385$	8.04629	−	7.62185i	0.410077	−	0.388445i
$386$	−6.55979	+	9.67496i	−0.333884	+	0.492442i
$387$		0			0
$388$	7.27535	−	13.7228i	0.369350	−	0.696668i
$389$	−13.6598	−	20.1467i	−0.692580	−	1.02148i	−0.997607	−	0.0691350i	$-0.977976\pi$
$389$	−13.6598	−	20.1467i	−0.692580	−	1.02148i	0.305028	−	0.952343i	$-0.401334\pi$
$390$		0			0
$391$	−1.88566	+	6.79153i	−0.0953618	+	0.343462i
$392$	−5.13191	−	12.8801i	−0.259201	−	0.650545i
$393$		0			0
$394$	4.04073	+	3.82759i	0.203569	+	0.192831i
$395$	−33.5189	+	7.37806i	−1.68652	+	0.371231i
$396$		0			0
$397$	−2.12527	+	12.9636i	−0.106664	+	0.650623i	0.878333	+	0.478050i	$0.158656\pi$
$397$	−2.12527	+	12.9636i	−0.106664	+	0.650623i	−0.984997	+	0.172573i	$0.944792\pi$
$398$	3.75203	−	4.41723i	0.188072	−	0.221416i
$399$		0			0
$400$	8.79325	+	6.68445i	0.439662	+	0.334223i
$401$	−17.8154	−	10.7192i	−0.889660	−	0.535291i	−0.00419205	−	0.999991i	$-0.501334\pi$
$401$	−17.8154	−	10.7192i	−0.889660	−	0.535291i	−0.885468	+	0.464701i	$0.846162\pi$
$402$		0			0
$403$	−13.2964	+	1.44607i	−0.662340	+	0.0720338i
$404$	11.8685	−	9.02222i	0.590481	−	0.448872i
$405$		0			0
$406$	0.124075	+	2.28844i	0.00615776	+	0.113573i
$407$	4.81056	+	0.523180i	0.238451	+	0.0259331i
$408$		0			0
$409$	−23.1163	−	27.2147i	−1.14303	−	1.34568i	−0.929535	−	0.368734i	$-0.879791\pi$
$409$	−23.1163	−	27.2147i	−1.14303	−	1.34568i	−0.213495	−	0.976944i	$-0.568485\pi$
$410$	6.35174	−	2.14015i	0.313690	−	0.105694i
$411$		0			0
$412$	−0.937473			−0.0461860
$413$	−5.56356	+	3.61377i	−0.273765	+	0.177822i
$414$		0			0
$415$	−17.1709	−	7.94410i	−0.842886	−	0.389961i
$416$	8.74446	−	2.94635i	0.428733	−	0.144457i
$417$		0			0
$418$	−8.91137	+	5.36179i	−0.435869	+	0.262254i
$419$	−27.2597	−	2.96467i	−1.33172	−	0.144834i	−0.585578	−	0.810616i	$-0.699132\pi$
$419$	−27.2597	−	2.96467i	−1.33172	−	0.144834i	−0.746146	+	0.665782i	$0.768098\pi$
$420$		0			0
$421$	−1.28680	−	4.63464i	−0.0627148	−	0.225878i	0.925551	−	0.378623i	$-0.123602\pi$
$421$	−1.28680	−	4.63464i	−0.0627148	−	0.225878i	−0.988266	+	0.152745i	$0.951189\pi$
$422$	−13.5661	+	10.3127i	−0.660390	+	0.502015i
$423$		0			0
$424$	0.793687	+	4.84128i	0.0385449	+	0.235113i
$425$	16.7979	+	10.1070i	0.814817	+	0.490259i
$426$		0			0
$427$	−3.75123	+	9.41487i	−0.181535	+	0.455618i
$428$	−4.93320	+	5.80781i	−0.238455	+	0.280731i
$429$		0			0
$430$	−0.317150	+	5.84948i	−0.0152943	+	0.282087i
$431$	−1.70525	+	0.375355i	−0.0821392	+	0.0180802i	−0.255850	−	0.966717i	$-0.582355\pi$
$431$	−1.70525	+	0.375355i	−0.0821392	+	0.0180802i	0.173711	+	0.984797i	$0.444424\pi$
$432$		0			0
$433$	21.0612	+	7.09634i	1.01214	+	0.341028i	0.776028	−	0.630699i	$-0.217232\pi$
$433$	21.0612	+	7.09634i	1.01214	+	0.341028i	0.236108	+	0.971727i	$0.424128\pi$
$434$	1.58464	+	3.97714i	0.0760650	+	0.190909i
$435$		0			0
$436$	7.24114	+	1.59389i	0.346788	+	0.0763337i
$437$	−5.12324	−	7.55621i	−0.245078	−	0.361462i
$438$		0			0
$439$	6.10646	+	11.5180i	0.291446	+	0.549725i	0.985392	−	0.170302i	$-0.0544743\pi$
$439$	6.10646	+	11.5180i	0.291446	+	0.549725i	−0.693946	+	0.720027i	$0.744130\pi$
$440$	−15.9648	+	23.5463i	−0.761091	+	1.12253i
$441$		0			0
$442$	3.08190	−	1.42584i	0.146591	−	0.0678202i
$443$	−37.6159	+	17.4030i	−1.78719	+	0.826840i	−0.820171	+	0.572119i	$0.806122\pi$
$443$	−37.6159	+	17.4030i	−1.78719	+	0.826840i	−0.967015	+	0.254721i	$0.918016\pi$
$444$		0			0
$445$	−4.56866	+	6.73827i	−0.216575	+	0.319425i
$446$	−0.829137	−	1.56392i	−0.0392608	−	0.0740537i
$447$		0			0
$448$	0.181478	+	0.267660i	0.00857402	+	0.0126457i
$449$	−6.58499	−	1.44947i	−0.310765	−	0.0684046i	0.0568497	−	0.998383i	$-0.481894\pi$
$449$	−6.58499	−	1.44947i	−0.310765	−	0.0684046i	−0.367615	+	0.929978i	$0.619825\pi$
$450$		0			0
$451$	−4.81158	−	12.0762i	−0.226569	−	0.568644i
$452$	12.5686	+	4.23487i	0.591180	+	0.199192i
$453$		0			0
$454$	10.0339	−	2.20862i	0.470912	−	0.103656i
$455$	0.253755	−	4.68023i	0.0118962	−	0.219413i
$456$		0			0
$457$	−19.9001	+	23.4282i	−0.930889	+	1.09593i	0.0642983	+	0.997931i	$0.479519\pi$
$457$	−19.9001	+	23.4282i	−0.930889	+	1.09593i	−0.995187	+	0.0979960i	$0.968757\pi$
$458$	3.68194	−	9.24097i	0.172046	−	0.431802i
$459$		0			0
$460$	−9.59603	−	5.77374i	−0.447417	−	0.269202i
$461$	5.30727	+	32.3729i	0.247184	+	1.50776i	0.760377	+	0.649482i	$0.225014\pi$
$461$	5.30727	+	32.3729i	0.247184	+	1.50776i	−0.513193	+	0.858273i	$0.671537\pi$
$462$		0			0
$463$	0.0515587	−	0.0391939i	0.00239614	−	0.00182150i	−0.603975	−	0.797003i	$-0.706418\pi$
$463$	0.0515587	−	0.0391939i	0.00239614	−	0.00182150i	0.606372	+	0.795181i	$0.292624\pi$
$464$	2.20280	+	7.93378i	0.102263	+	0.368316i
$465$		0			0
$466$	−3.70205	−	0.402622i	−0.171494	−	0.0186511i
$467$	22.3545	−	13.4503i	1.03444	−	0.622404i	0.106188	−	0.994346i	$-0.466136\pi$
$467$	22.3545	−	13.4503i	1.03444	−	0.622404i	0.928256	+	0.371942i	$0.121308\pi$
$468$		0			0
$469$	−3.48616	+	1.17463i	−0.160976	+	0.0542392i
$470$	−12.4872	−	5.77719i	−0.575991	−	0.266482i
$471$		0			0
$472$	11.9527	−	12.1289i	0.550167	−	0.558278i
$473$	11.3615			0.522403
$474$		0			0
$475$	−24.0624	+	8.10757i	−1.10406	+	0.372001i
$476$	3.06169	+	3.60450i	0.140332	+	0.165212i
$477$		0			0
$478$	−2.74727	−	0.298784i	−0.125657	−	0.0136660i
$479$	0.163608	+	3.01758i	0.00747545	+	0.137877i	0.999889	+	0.0149285i	$0.00475208\pi$
$479$	0.163608	+	3.01758i	0.00747545	+	0.137877i	−0.992413	+	0.122948i	$0.960765\pi$
$480$		0			0
$481$	1.62913	−	1.23843i	0.0742820	−	0.0564677i
$482$	17.1066	−	1.86046i	0.779186	−	0.0847415i
$483$		0			0
$484$	5.87379	+	3.53414i	0.266991	+	0.160643i
$485$	25.0132	+	19.0145i	1.13579	+	0.863406i
$486$		0			0
$487$	−11.2027	+	13.1889i	−0.507645	+	0.597646i	−0.954961	−	0.296730i	$-0.904104\pi$
$487$	−11.2027	+	13.1889i	−0.507645	+	0.597646i	0.447317	+	0.894376i	$0.352380\pi$
$488$	4.20856	−	25.6711i	0.190512	−	1.16207i
$489$		0			0
$490$	12.2841	−	2.70394i	0.554941	−	0.122152i
$491$	11.7240	+	11.1056i	0.529098	+	0.501188i	0.904965	−	0.425485i	$-0.139897\pi$
$491$	11.7240	+	11.1056i	0.529098	+	0.501188i	−0.375867	+	0.926673i	$0.622655\pi$
$492$		0			0
$493$	5.40917	+	13.5760i	0.243617	+	0.611432i
$494$	−1.17665	+	4.23792i	−0.0529401	+	0.190673i
$495$		0			0
$496$	8.63184	+	12.7310i	0.387581	+	0.571639i
$497$	−4.28973	+	8.09129i	−0.192421	+	0.362944i
$498$		0			0
$499$	2.09302	−	3.08697i	0.0936963	−	0.138192i	−0.777952	−	0.628324i	$-0.783741\pi$
$499$	2.09302	−	3.08697i	0.0936963	−	0.138192i	0.871648	+	0.490132i	$0.163052\pi$
$500$	−3.19375	+	3.02528i	−0.142829	+	0.135294i
$501$		0			0
$502$	3.02922	−	1.40146i	0.135200	−	0.0625504i
$503$	12.9800	−	12.2953i	0.578750	−	0.548222i	−0.341334	−	0.939942i	$-0.610879\pi$
$503$	12.9800	−	12.2953i	0.578750	−	0.548222i	0.920084	+	0.391721i	$0.128120\pi$
$504$		0			0
$505$	14.1265	+	26.6454i	0.628620	+	1.18570i
$506$	2.33833	−	4.41055i	0.103951	−	0.196073i
$507$		0			0
$508$	12.7760	+	2.81221i	0.566842	+	0.124771i
$509$	8.85505	−	31.8930i	0.392493	−	1.41363i	−0.458612	−	0.888637i	$-0.651653\pi$
$509$	8.85505	−	31.8930i	0.392493	−	1.41363i	0.851105	−	0.524996i	$-0.175933\pi$
$510$		0			0
$511$	−10.0363	−	3.38162i	−0.443979	−	0.149594i
$512$	−13.8109	−	13.0824i	−0.610363	−	0.578167i
$513$		0			0
$514$	−0.198351	+	3.65836i	−0.00874887	+	0.161363i
$515$	0.306807	−	1.87144i	0.0135195	−	0.0824655i
$516$		0			0
$517$	−9.87704	+	24.7895i	−0.434392	+	1.09024i
$518$	−0.521476	−	0.396416i	−0.0229124	−	0.0174175i
$519$		0			0
$520$	1.94638	+	11.8724i	0.0853546	+	0.520640i
$521$	17.5054	−	1.90383i	0.766926	−	0.0834082i	0.283711	−	0.958910i	$-0.408434\pi$
$521$	17.5054	−	1.90383i	0.766926	−	0.0834082i	0.483215	+	0.875502i	$0.339469\pi$
$522$		0			0
$523$	−2.68104	−	9.65623i	−0.117234	−	0.422237i	0.881520	−	0.472146i	$-0.156521\pi$
$523$	−2.68104	−	9.65623i	−0.117234	−	0.422237i	−0.998754	+	0.0499091i	$0.984107\pi$
$524$	−0.717324	−	13.2303i	−0.0313365	−	0.577967i
$525$		0			0
$526$	−4.03548	+	2.42807i	−0.175955	+	0.105869i
$527$	17.6734	+	20.8067i	0.769865	+	0.906355i
$528$		0			0
$529$	−16.8972	−	7.81746i	−0.734659	−	0.339889i
$530$	−4.45064			−0.193324
$531$		0			0
$532$	−6.12550			−0.265574
$533$	−4.98942	−	2.30835i	−0.216116	−	0.0999857i
$534$		0			0
$535$	−9.97941	−	11.7487i	−0.431448	−	0.507939i
$536$	8.09097	−	4.86817i	0.349477	−	0.210273i
$537$		0			0
$538$	0.181237	+	3.34272i	0.00781369	+	0.144115i
$539$	−6.52634	−	23.5057i	−0.281109	−	1.01246i
$540$		0			0
$541$	−1.04324	+	0.113459i	−0.0448523	+	0.00487799i	−0.130518	−	0.991446i	$-0.541664\pi$
$541$	−1.04324	+	0.113459i	−0.0448523	+	0.00487799i	0.0856653	+	0.996324i	$0.472698\pi$
$542$	−0.890742	−	5.43329i	−0.0382607	−	0.233380i
$543$		0			0
$544$	−14.9940	−	11.3981i	−0.642862	−	0.488691i
$545$	−5.55164	+	13.9336i	−0.237806	+	0.596848i
$546$		0			0
$547$	−5.26270	+	32.1010i	−0.225017	+	1.37254i	0.596618	+	0.802526i	$0.296511\pi$
$547$	−5.26270	+	32.1010i	−0.225017	+	1.37254i	−0.821634	+	0.570015i	$0.806937\pi$
$548$	0.714818	−	13.1840i	0.0305355	−	0.563194i
$549$		0			0
$550$	−10.0802	−	9.54843i	−0.429819	−	0.407147i
$551$	−17.9374	−	6.04382i	−0.764159	−	0.257475i
$552$		0			0
$553$	2.41066	−	8.68242i	0.102512	−	0.369214i
$554$	5.97158	+	1.31444i	0.253708	+	0.0558453i
$555$		0			0
$556$	3.24789	−	6.12617i	0.137741	−	0.259808i
$557$	9.43266	+	17.7919i	0.399675	+	0.753866i	0.998909	−	0.0467076i	$-0.0148729\pi$
$557$	9.43266	+	17.7919i	0.399675	+	0.753866i	−0.599234	+	0.800574i	$0.704528\pi$
$558$		0			0
$559$	3.48829	−	3.30428i	0.147539	−	0.139756i
$560$	−4.89211	+	2.26333i	−0.206729	+	0.0956432i
$561$		0			0
$562$	5.62708	−	5.33025i	0.237364	−	0.224843i
$563$	−12.6330	+	18.6324i	−0.532420	+	0.785260i	−0.994846	−	0.101398i	$-0.967669\pi$
$563$	−12.6330	+	18.6324i	−0.532420	+	0.785260i	0.462426	+	0.886658i	$0.346979\pi$
$564$		0			0
$565$	−12.5673	+	23.7044i	−0.528708	+	0.997250i
$566$	−10.6395	−	15.6921i	−0.447212	−	0.659588i
$567$		0			0
$568$	6.28881	−	22.6502i	0.263873	−	0.950383i
$569$	−9.68713	−	24.3129i	−0.406105	−	1.01925i	−0.979765	−	0.200154i	$-0.935856\pi$
$569$	−9.68713	−	24.3129i	−0.406105	−	1.01925i	0.573659	−	0.819094i	$-0.305523\pi$
$570$		0			0
$571$	2.96218	+	2.80592i	0.123963	+	0.117424i	0.747170	−	0.664633i	$-0.231412\pi$
$571$	2.96218	+	2.80592i	0.123963	+	0.117424i	−0.623207	+	0.782057i	$0.714171\pi$
$572$	10.2196	−	2.24949i	0.427301	−	0.0940561i
$573$		0			0
$574$	−0.284693	+	1.73655i	−0.0118828	+	0.0724821i
$575$	7.89038	−	9.28927i	0.329051	−	0.387389i
$576$		0			0
$577$	29.8122	+	22.6627i	1.24110	+	0.943460i	0.999637	−	0.0269505i	$-0.00857965\pi$
$577$	29.8122	+	22.6627i	1.24110	+	0.943460i	0.241463	+	0.970410i	$0.422373\pi$
$578$	2.96648	+	1.78487i	0.123389	+	0.0742408i
$579$		0			0
$580$	−23.0836	+	2.51049i	−0.958494	+	0.104243i
$581$	3.95436	−	3.00603i	0.164055	−	0.124711i
$582$		0			0
$583$	0.467319	+	8.61919i	0.0193544	+	0.356970i
$584$	27.0249	+	2.93913i	1.11830	+	0.121622i
$585$		0			0
$586$	2.00428	+	2.35962i	0.0827962	+	0.0974752i
$587$	0.957172	−	0.322509i	0.0395067	−	0.0133114i	−0.299479	−	0.954103i	$-0.596813\pi$
$587$	0.957172	−	0.322509i	0.0395067	−	0.0133114i	0.338986	+	0.940792i	$0.389916\pi$
$588$		0			0
$589$	−35.3590			−1.45694
$590$	9.10411	+	12.4808i	0.374810	+	0.513826i
$591$		0			0
$592$	−2.13591	−	0.988178i	−0.0877855	−	0.0406139i
$593$	−0.117791	+	0.0396884i	−0.00483710	+	0.00162981i	−0.321719	−	0.946835i	$-0.604261\pi$
$593$	−0.117791	+	0.0396884i	−0.00483710	+	0.00162981i	0.316882	+	0.948465i	$0.397364\pi$
$594$		0			0
$595$	−8.19752	+	4.93229i	−0.336066	+	0.202204i
$596$	−14.9312	−	1.62387i	−0.611607	−	0.0665163i
$597$		0			0
$598$	−0.564798	−	2.03422i	−0.0230963	−	0.0831854i
$599$	−28.1892	+	21.4289i	−1.15178	+	0.875561i	−0.993723	−	0.111869i	$-0.964316\pi$
$599$	−28.1892	+	21.4289i	−1.15178	+	0.875561i	−0.158057	+	0.987430i	$0.550523\pi$
$600$		0			0
$601$	−1.82016	−	11.1025i	−0.0742460	−	0.452880i	−0.997618	−	0.0689749i	$-0.978027\pi$
$601$	−1.82016	−	11.1025i	−0.0742460	−	0.452880i	0.923372	−	0.383905i	$-0.125421\pi$
$602$	−1.31785	−	0.792924i	−0.0537116	−	0.0323172i
$603$		0			0
$604$	−13.3823	+	33.5871i	−0.544519	+	1.36664i
$605$	−8.97739	+	10.5690i	−0.364983	+	0.429691i
$606$		0			0
$607$	1.95540	−	36.0652i	0.0793672	−	1.46384i	−0.639552	−	0.768748i	$-0.720880\pi$
$607$	1.95540	−	36.0652i	0.0793672	−	1.46384i	0.718919	−	0.695094i	$-0.244637\pi$
$608$	23.8244	−	5.24415i	0.966208	−	0.212679i
$609$		0			0
$610$	22.3643	+	7.53542i	0.905506	+	0.305100i
$611$	4.17705	+	10.4836i	0.168985	+	0.424121i
$612$		0			0
$613$	20.8802	+	4.59608i	0.843343	+	0.185634i	0.615572	−	0.788081i	$-0.288925\pi$
$613$	20.8802	+	4.59608i	0.843343	+	0.185634i	0.227771	+	0.973715i	$0.426856\pi$
$614$	−1.66015	−	2.44853i	−0.0669980	−	0.0988147i
$615$		0			0
$616$	−3.49851	−	6.59888i	−0.140959	−	0.265876i
$617$	−22.4267	+	33.0769i	−0.902863	+	1.33162i	0.0402627	+	0.999189i	$0.487181\pi$
$617$	−22.4267	+	33.0769i	−0.902863	+	1.33162i	−0.943126	+	0.332435i	$0.892130\pi$
$618$		0			0
$619$	5.22870	−	2.41905i	0.210159	−	0.0972300i	−0.311986	−	0.950087i	$-0.600994\pi$
$619$	5.22870	−	2.41905i	0.210159	−	0.0972300i	0.522145	+	0.852857i	$0.325132\pi$
$620$	−39.3667	+	18.2130i	−1.58101	+	0.731451i
$621$		0			0
$622$	−8.31608	+	12.2653i	−0.333445	+	0.491794i
$623$	−1.00117	−	1.88841i	−0.0401111	−	0.0756576i
$624$		0			0
$625$	11.3429	+	16.7296i	0.453718	+	0.669183i
$626$	−20.2379	−	4.45470i	−0.808870	−	0.178046i
$627$		0			0
$628$	−4.89892	−	12.2954i	−0.195488	−	0.490639i
$629$	−3.95832	−	1.33371i	−0.157829	−	0.0531786i
$630$		0			0
$631$	−17.7841	+	3.91458i	−0.707975	+	0.155837i	−0.554340	−	0.832291i	$-0.687029\pi$
$631$	−17.7841	+	3.91458i	−0.707975	+	0.155837i	−0.153635	+	0.988128i	$0.549098\pi$
$632$	−1.25219	+	23.0952i	−0.0498093	+	0.918679i
$633$		0			0
$634$	8.70948	−	10.2536i	0.345898	−	0.407222i
$635$	−9.79510	+	24.5838i	−0.388707	+	0.975580i
$636$		0			0
$637$	−8.83998	−	5.31884i	−0.350253	−	0.210740i
$638$	−1.67450	−	10.2140i	−0.0662939	−	0.404375i
$639$		0			0
$640$	29.8986	−	22.7283i	1.18184	−	0.898415i
$641$	7.33079	+	26.4031i	0.289549	+	1.04286i	0.955045	+	0.296460i	$0.0958061\pi$
$641$	7.33079	+	26.4031i	0.289549	+	1.04286i	−0.665496	+	0.746401i	$0.731780\pi$
$642$		0			0
$643$	32.4751	+	3.53188i	1.28069	+	0.139284i	0.723049	−	0.690797i	$-0.242740\pi$
$643$	32.4751	+	3.53188i	1.28069	+	0.139284i	0.557643	+	0.830081i	$0.311706\pi$
$644$	2.51938	−	1.51586i	0.0992776	−	0.0597334i
$645$		0			0
$646$	8.50742	−	2.86648i	0.334720	−	0.112780i
$647$	−11.9292	−	5.51901i	−0.468983	−	0.216975i	0.171140	−	0.985247i	$-0.445255\pi$
$647$	−11.9292	−	5.51901i	−0.468983	−	0.216975i	−0.640124	+	0.768272i	$0.721117\pi$
$648$		0			0
$649$	23.2146	−	18.9417i	0.911251	−	0.743525i
$650$	−5.87187			−0.230314
$651$		0			0
$652$	−22.4634	+	7.56880i	−0.879734	+	0.296417i
$653$	18.4221	+	21.6882i	0.720912	+	0.848723i	0.993550	−	0.113394i	$-0.0361721\pi$
$653$	18.4221	+	21.6882i	0.720912	+	0.848723i	−0.272638	+	0.962117i	$0.587896\pi$
$654$		0			0
$655$	26.6458	+	2.89791i	1.04114	+	0.113231i
$656$	0.342283	+	6.31304i	0.0133639	+	0.246483i
$657$		0			0
$658$	2.87573	−	2.18608i	0.112108	−	0.0852221i
$659$	2.36068	−	0.256739i	0.0919590	−	0.0100011i	−0.0620238	−	0.998075i	$-0.519755\pi$
$659$	2.36068	−	0.256739i	0.0919590	−	0.0100011i	0.153983	+	0.988074i	$0.450790\pi$
$660$		0			0
$661$	−2.79652	−	1.68261i	−0.108772	−	0.0654461i	0.460128	−	0.887852i	$-0.347803\pi$
$661$	−2.79652	−	1.68261i	−0.108772	−	0.0654461i	−0.568900	+	0.822406i	$0.692631\pi$
$662$	−0.926048	−	0.703963i	−0.0359919	−	0.0273603i
$663$		0			0
$664$	−8.25410	+	9.71748i	−0.320321	+	0.377111i
$665$	2.00469	−	12.2281i	0.0777387	−	0.474185i
$666$		0			0
$667$	8.87321	−	1.95314i	0.343572	−	0.0756259i
$668$	20.0597	+	19.0015i	0.776132	+	0.735192i
$669$		0			0
$670$	3.17073	+	7.95794i	0.122496	+	0.307442i
$671$	12.2450	−	44.1024i	0.472711	−	1.70255i
$672$		0			0
$673$	−1.19515	−	1.76272i	−0.0460698	−	0.0679479i	0.803957	−	0.594688i	$-0.202724\pi$
$673$	−1.19515	−	1.76272i	−0.0460698	−	0.0679479i	−0.850026	+	0.526740i	$0.823414\pi$
$674$	6.19893	−	11.6924i	0.238774	−	0.450376i
$675$		0			0
$676$	−9.38062	+	13.8354i	−0.360793	+	0.532130i
$677$	−22.8644	+	21.6583i	−0.878750	+	0.832396i	−0.986832	−	0.161746i	$-0.948288\pi$
$677$	−22.8644	+	21.6583i	−0.878750	+	0.832396i	0.108082	+	0.994142i	$0.465529\pi$
$678$		0			0
$679$	−7.48671	+	3.46372i	−0.287313	+	0.132925i
$680$	17.8280	−	16.8875i	0.683671	−	0.647608i
$681$		0			0
$682$	−9.05667	−	17.0827i	−0.346798	−	0.654130i
$683$	5.55731	−	10.4822i	0.212644	−	0.401090i	−0.754128	−	0.656727i	$-0.771940\pi$
$683$	5.55731	−	10.4822i	0.212644	−	0.401090i	0.966773	+	0.255637i	$0.0822852\pi$
$684$		0			0
$685$	26.0848	+	5.74171i	0.996650	+	0.219379i
$686$	−1.87232	+	6.74348i	−0.0714854	+	0.257467i
$687$		0			0
$688$	−5.23645	−	1.76437i	−0.199638	−	0.0672658i
$689$	2.65021	+	2.51041i	0.100965	+	0.0956391i
$690$		0			0
$691$	1.54514	−	28.4984i	0.0587799	−	1.08413i	−0.809200	−	0.587533i	$-0.800099\pi$
$691$	1.54514	−	28.4984i	0.0587799	−	1.08413i	0.867980	−	0.496599i	$-0.165418\pi$
$692$	−4.99290	+	30.4553i	−0.189802	+	1.15774i
$693$		0			0
$694$	−0.401707	+	1.00821i	−0.0152486	+	0.0382710i
$695$	11.1665	+	8.48855i	0.423569	+	0.321989i
$696$		0			0
$697$	1.81538	+	11.0733i	0.0687623	+	0.419431i
$698$	−0.684889	+	0.0744862i	−0.0259234	+	0.00281934i
$699$		0			0
$700$	−2.18781	−	7.87976i	−0.0826913	−	0.297827i
$701$	0.137246	+	2.53135i	0.00518371	+	0.0956079i	0.999980	−	0.00627291i	$-0.00199674\pi$
$701$	0.137246	+	2.53135i	0.00518371	+	0.0956079i	−0.994797	+	0.101881i	$0.967514\pi$
$702$		0			0
$703$	4.63568	−	2.78920i	0.174838	−	0.105197i
$704$	−0.945491	−	1.11312i	−0.0356345	−	0.0419522i
$705$		0			0
$706$	−18.3580	−	8.49331i	−0.690912	−	0.319650i
$707$	−7.91794			−0.297785
$708$		0			0
$709$	−8.23468			−0.309260			−0.154630	−	0.987972i	$-0.549419\pi$
$709$	−8.23468			−0.309260			−0.154630	+	0.987972i	$0.549419\pi$
$710$	19.3546	+	8.95441i	0.726367	+	0.336053i
$711$		0			0
$712$	3.55174	+	4.18143i	0.133107	+	0.156706i
$713$	14.5430	−	8.75021i	0.544638	−	0.327698i
$714$		0			0
$715$	1.14602	+	21.1371i	0.0428587	+	0.790482i
$716$	−7.81280	−	28.1392i	−0.291978	−	1.05161i
$717$		0			0
$718$	−6.70036	+	0.728708i	−0.250055	+	0.0271951i
$719$	−1.97588	−	12.0523i	−0.0736878	−	0.449475i	−0.997739	−	0.0672070i	$-0.978591\pi$
$719$	−1.97588	−	12.0523i	−0.0736878	−	0.449475i	0.924051	−	0.382269i	$-0.124857\pi$
$720$		0			0
$721$	0.396371	+	0.301313i	0.0147616	+	0.0112215i
$722$	−0.00434307	+	0.0109003i	−0.000161632	+	0.000405667i
$723$		0			0
$724$	6.25235	−	38.1376i	0.232367	−	1.41737i
$725$	1.36810	−	25.2331i	0.0508099	−	0.937133i
$726$		0			0
$727$	−1.46664	−	1.38927i	−0.0543946	−	0.0515253i	0.660019	−	0.751249i	$-0.270548\pi$
$727$	−1.46664	−	1.38927i	−0.0543946	−	0.0515253i	−0.714414	+	0.699723i	$0.753307\pi$
$728$	−2.99330	−	1.00856i	−0.110939	−	0.0373797i
$729$		0			0
$730$	−6.59766	+	23.7626i	−0.244191	+	0.879495i
$731$	−9.57799	−	2.10827i	−0.354255	−	0.0779773i
$732$		0			0
$733$	21.4119	−	40.3871i	0.790866	−	1.49173i	−0.0781477	−	0.996942i	$-0.524901\pi$
$733$	21.4119	−	40.3871i	0.790866	−	1.49173i	0.869013	−	0.494789i	$-0.164755\pi$
$734$	−0.658117	−	1.24134i	−0.0242916	−	0.0458187i
$735$		0			0
$736$	−8.50110	+	8.05267i	−0.313355	+	0.296825i
$737$	15.0785	−	6.97607i	0.555425	−	0.256967i
$738$		0			0
$739$	15.8300	−	14.9950i	0.582316	−	0.551599i	−0.338814	−	0.940853i	$-0.610026\pi$
$739$	15.8300	−	14.9950i	0.582316	−	0.551599i	0.921130	+	0.389254i	$0.127267\pi$
$740$	3.72443	−	5.49312i	0.136913	−	0.201931i
$741$		0			0
$742$	0.547331	−	1.03238i	0.0200932	−	0.0378997i
$743$	10.2596	+	15.1318i	0.376389	+	0.555132i	0.967955	−	0.251124i	$-0.0808003\pi$
$743$	10.2596	+	15.1318i	0.376389	+	0.555132i	−0.591566	+	0.806257i	$0.701490\pi$
$744$		0			0
$745$	8.12821	−	29.2752i	0.297795	−	1.07256i
$746$	0.225537	+	0.566056i	0.00825751	+	0.0207248i
$747$		0			0
$748$	−15.5064	−	14.6884i	−0.566968	−	0.537061i
$749$	3.95248	−	0.870007i	0.144421	−	0.0317894i
$750$		0			0
$751$	−3.12564	+	19.0655i	−0.114056	+	0.695711i	0.866456	+	0.499253i	$0.166392\pi$
$751$	−3.12564	+	19.0655i	−0.114056	+	0.695711i	−0.980512	+	0.196458i	$0.937056\pi$
$752$	8.40191	−	9.89150i	0.306386	−	0.360706i
$753$		0			0
$754$	−3.48466	−	2.64897i	−0.126904	−	0.0964699i
$755$	−62.6690	−	37.7067i	−2.28076	−	1.37229i
$756$		0			0
$757$	25.2047	−	2.74118i	0.916080	−	0.0996297i	0.362081	−	0.932147i	$-0.382066\pi$
$757$	25.2047	−	2.74118i	0.916080	−	0.0996297i	0.554000	+	0.832517i	$0.313101\pi$
$758$	−9.92042	+	7.54130i	−0.360326	+	0.273912i
$759$		0			0
$760$	1.72195	+	31.7595i	0.0624617	+	1.15204i
$761$	−28.8725	−	3.14007i	−1.04663	−	0.113827i	−0.431386	−	0.902167i	$-0.641975\pi$
$761$	−28.8725	−	3.14007i	−1.04663	−	0.113827i	−0.615240	+	0.788340i	$0.710941\pi$
$762$		0			0
$763$	−2.54931	−	3.00128i	−0.0922914	−	0.108654i
$764$	−7.59872	+	2.56031i	−0.274912	+	0.0926286i
$765$		0			0
$766$	15.8932			0.574246
$767$	1.61867	−	12.5671i	0.0584468	−	0.453773i
$768$		0			0
$769$	−23.7797	−	11.0016i	−0.857517	−	0.396730i	−0.0586798	−	0.998277i	$-0.518689\pi$
$769$	−23.7797	−	11.0016i	−0.857517	−	0.396730i	−0.798837	+	0.601547i	$0.794551\pi$
$770$	6.42112	−	2.16353i	0.231401	−	0.0779681i
$771$		0			0
$772$	26.6424	−	16.0302i	0.958882	−	0.576940i
$773$	11.1976	+	1.21781i	0.402748	+	0.0438015i	0.307252	−	0.951628i	$-0.400591\pi$
$773$	11.1976	+	1.21781i	0.402748	+	0.0438015i	0.0954964	+	0.995430i	$0.469556\pi$
$774$		0			0
$775$	−12.6290	−	45.4854i	−0.453645	−	1.63388i
$776$	16.8564	−	12.8139i	0.605110	−	0.459993i
$777$		0			0
$778$	−2.40750	−	14.6851i	−0.0863132	−	0.526487i
$779$	−12.4534	−	7.49297i	−0.446190	−	0.268464i
$780$		0			0
$781$	15.3090	−	38.4227i	0.547799	−	1.37487i
$782$	−2.78969	+	3.28428i	−0.0997592	+	0.117446i
$783$		0			0
$784$	−0.642334	+	11.8472i	−0.0229405	+	0.423113i
$785$	26.1480	−	5.75562i	0.933263	−	0.205427i
$786$		0			0
$787$	2.53734	+	0.854929i	0.0904463	+	0.0304749i	0.364161	−	0.931336i	$-0.381356\pi$
$787$	2.53734	+	0.854929i	0.0904463	+	0.0304749i	−0.273715	+	0.961811i	$0.588252\pi$
$788$	−5.47991	−	13.7535i	−0.195214	−	0.489949i
$789$		0			0
$790$	−20.4922	−	4.51068i	−0.729081	−	0.160483i
$791$	−3.95299	−	5.83023i	−0.140552	−	0.207299i
$792$		0			0
$793$	−9.06682	−	17.1018i	−0.321972	−	0.607304i
$794$	−4.50704	+	6.64738i	−0.159949	+	0.235907i
$795$		0			0
$796$	−13.9917	+	6.47323i	−0.495921	+	0.229437i
$797$	44.8844	−	20.7658i	1.58989	−	0.735561i	0.592350	−	0.805681i	$-0.298200\pi$
$797$	44.8844	−	20.7658i	1.58989	−	0.735561i	0.997539	+	0.0701197i	$0.0223381\pi$
$798$		0			0
$799$	12.9266	−	19.0653i	0.457309	−	0.674480i
$800$	15.2552	+	28.7744i	0.539354	+	1.01733i
$801$		0			0
$802$	−7.13338	−	10.5209i	−0.251888	−	0.371507i
$803$	46.7119	+	10.2821i	1.64843	+	0.362846i
$804$		0			0
$805$	2.20154	+	5.52544i	0.0775940	+	0.194746i
$806$	−7.74883	−	2.61089i	−0.272941	−	0.0919645i
$807$		0			0
$808$	19.8487	−	4.36902i	0.698274	−	0.153702i
$809$	2.76044	−	50.9133i	0.0970518	−	1.79001i	−0.394228	−	0.919013i	$-0.628988\pi$
$809$	2.76044	−	50.9133i	0.0970518	−	1.79001i	0.491279	−	0.871002i	$-0.336529\pi$
$810$		0			0
$811$	19.6189	−	23.0971i	0.688911	−	0.811049i	−0.300867	−	0.953666i	$-0.597276\pi$
$811$	19.6189	−	23.0971i	0.688911	−	0.811049i	0.989778	+	0.142617i	$0.0455517\pi$
$812$	2.25644	−	5.66323i	0.0791854	−	0.198740i
$813$		0			0
$814$	2.53488	+	1.52519i	0.0888475	+	0.0534577i
$815$	−7.75769	−	47.3198i	−0.271740	−	1.65754i
$816$		0			0
$817$	10.1124	−	7.68727i	0.353789	−	0.268944i
$818$	−5.84016	−	21.0344i	−0.204197	−	0.735450i
$819$		0			0
$820$	−17.7245	−	1.92765i	−0.618965	−	0.0673165i
$821$	−28.1561	+	16.9410i	−0.982656	+	0.591244i	−0.913706	−	0.406376i	$-0.866792\pi$
$821$	−28.1561	+	16.9410i	−0.982656	+	0.591244i	−0.0689495	+	0.997620i	$0.521965\pi$
$822$		0			0
$823$	−0.0856482	+	0.0288582i	−0.00298551	+	0.00100593i	−0.320794	−	0.947149i	$-0.603950\pi$
$823$	−0.0856482	+	0.0288582i	−0.00298551	+	0.00100593i	0.317808	+	0.948155i	$0.397053\pi$
$824$	−1.15988	−	0.536619i	−0.0404064	−	0.0186940i
$825$		0			0
$826$	−4.01466	+	0.576937i	−0.139688	+	0.0200742i
$827$	−22.6616			−0.788021			−0.394011	−	0.919106i	$-0.628913\pi$
$827$	−22.6616			−0.788021			−0.394011	+	0.919106i	$0.628913\pi$
$828$		0			0
$829$	2.20038	−	0.741395i	0.0764225	−	0.0257497i	−0.280831	−	0.959757i	$-0.590610\pi$
$829$	2.20038	−	0.741395i	0.0764225	−	0.0257497i	0.357253	+	0.934008i	$0.383713\pi$
$830$	−7.48813	−	8.81571i	−0.259917	−	0.305998i
$831$		0			0
$832$	−0.614021	−	0.0667788i	−0.0212874	−	0.00231514i
$833$	1.14004	+	21.0269i	0.0395002	+	0.728538i
$834$		0			0
$835$	−44.4970	+	33.8257i	−1.53988	+	1.17059i
$836$	27.5021	−	2.99103i	0.951180	−	0.103447i
$837$		0			0
$838$	−14.3642	−	8.64268i	−0.496205	−	0.298556i
$839$	3.25521	+	2.47454i	0.112382	+	0.0854308i	0.659856	−	0.751392i	$-0.270617\pi$
$839$	3.25521	+	2.47454i	0.112382	+	0.0854308i	−0.547474	+	0.836823i	$0.684410\pi$
$840$		0			0
$841$	−6.57892	+	7.74531i	−0.226859	+	0.267080i
$842$	0.475742	−	2.90190i	0.0163951	−	0.100006i
$843$		0			0
$844$	44.2692	−	9.74439i	1.52381	−	0.335416i
$845$	−24.5490	−	23.2541i	−0.844512	−	0.799965i
$846$		0			0
$847$	−1.34758	−	3.38216i	−0.0463032	−	0.116212i
$848$	1.12312	−	4.04510i	0.0385680	−	0.138909i
$849$		0			0
$850$	6.72595	+	9.92003i	0.230698	+	0.340254i
$851$	−1.21639	+	2.29436i	−0.0416974	+	0.0786497i
$852$		0			0
$853$	−14.4324	+	21.2861i	−0.494155	+	0.728824i	−0.990228	−	0.139457i	$-0.955464\pi$
$853$	−14.4324	+	21.2861i	−0.494155	+	0.728824i	0.496073	+	0.868281i	$0.334775\pi$
$854$	−4.49825	+	4.26097i	−0.153927	+	0.145807i
$855$		0			0
$856$	−9.42801	+	4.36186i	−0.322243	+	0.149085i
$857$	9.45774	−	8.95885i	0.323070	−	0.306028i	−0.508925	−	0.860811i	$-0.669957\pi$
$857$	9.45774	−	8.95885i	0.323070	−	0.306028i	0.831996	+	0.554782i	$0.187198\pi$
$858$		0			0
$859$	15.8610	+	29.9171i	0.541171	+	1.02076i	0.991770	+	0.128031i	$0.0408656\pi$
$859$	15.8610	+	29.9171i	0.541171	+	1.02076i	−0.450599	+	0.892726i	$0.648790\pi$
$860$	7.29900	−	13.7674i	0.248894	−	0.469463i
$861$		0			0
$862$	−1.04253	−	0.229478i	−0.0355087	−	0.00781606i
$863$	9.41164	−	33.8977i	0.320376	−	1.15389i	−0.611540	−	0.791214i	$-0.709449\pi$
$863$	9.41164	−	33.8977i	0.320376	−	1.15389i	0.931915	−	0.362676i	$-0.118137\pi$
$864$		0			0
$865$	−59.1628	−	19.9343i	−2.01159	−	0.677785i
$866$	9.86432	+	9.34398i	0.335203	+	0.317521i
$867$		0			0
$868$	0.616536	−	11.3713i	0.0209266	−	0.385969i
$869$	−6.58377	+	40.1592i	−0.223339	+	1.36231i
$870$		0			0
$871$	2.60066	−	6.52716i	0.0881199	−	0.221164i
$872$	8.04669	+	6.11693i	0.272495	+	0.207146i
$873$		0			0
$874$	−0.902956	−	5.50779i	−0.0305429	−	0.186304i
$875$	2.32269	−	0.252608i	0.0785214	−	0.00853972i
$876$		0			0
$877$	9.63720	+	34.7101i	0.325425	+	1.17208i	0.927558	+	0.373679i	$0.121904\pi$
$877$	9.63720	+	34.7101i	0.325425	+	1.17208i	−0.602133	+	0.798396i	$0.705682\pi$
$878$	0.431493	+	7.95843i	0.0145622	+	0.268584i
$879$		0			0
$880$	20.8593	−	12.5506i	0.703167	−	0.423081i
$881$	13.4962	+	15.8889i	0.454698	+	0.535312i	0.940967	−	0.338497i	$-0.109919\pi$
$881$	13.4962	+	15.8889i	0.454698	+	0.535312i	−0.486270	+	0.873809i	$0.661643\pi$
$882$		0			0
$883$	−1.53759	−	0.711363i	−0.0517439	−	0.0239393i	0.393847	−	0.919176i	$-0.371144\pi$
$883$	−1.53759	−	0.711363i	−0.0517439	−	0.0239393i	−0.445590	+	0.895237i	$0.647006\pi$
$884$	−9.03272			−0.303803
$885$		0			0
$886$	−25.3389			−0.851278
$887$	−33.4483	−	15.4748i	−1.12308	−	0.519594i	−0.231675	−	0.972793i	$-0.574421\pi$
$887$	−33.4483	−	15.4748i	−1.12308	−	0.519594i	−0.891409	+	0.453199i	$0.850283\pi$
$888$		0			0
$889$	−4.49791	−	5.29535i	−0.150855	−	0.177600i
$890$	−4.26471	+	2.56599i	−0.142953	+	0.0860122i
$891$		0			0
$892$	0.254914	+	4.70162i	0.00853516	+	0.157422i
$893$	7.98158	+	28.7470i	0.267093	+	0.961983i
$894$		0			0
$895$	58.7300	−	6.38727i	1.96313	−	0.213503i
$896$	1.59522	+	9.73038i	0.0532924	+	0.325069i
$897$		0			0
$898$	−3.28166	−	2.49465i	−0.109510	−	0.0832475i
$899$	13.0251	−	32.6906i	0.434412	−	1.09029i
$900$		0			0
$901$	1.20544	−	7.35287i	0.0401591	−	0.244960i
$902$	0.430262	−	7.93572i	0.0143262	−	0.264231i
$903$		0			0
$904$	13.1264	+	12.4340i	0.436578	+	0.413548i
$905$	74.0865	+	24.9626i	2.46272	+	0.829786i
$906$		0			0
$907$	3.16656	−	11.4049i	0.105144	−	0.378694i	−0.892191	−	0.451659i	$-0.850832\pi$
$907$	3.16656	−	11.4049i	0.105144	−	0.378694i	0.997334	+	0.0729651i	$0.0232462\pi$
$908$	−26.6902	−	5.87495i	−0.885745	−	0.194967i
$909$		0			0
$910$	1.34224	−	2.53173i	0.0444947	−	0.0839259i
$911$	21.2453	+	40.0729i	0.703888	+	1.32767i	0.934966	+	0.354738i	$0.115430\pi$
$911$	21.2453	+	40.0729i	0.703888	+	1.32767i	−0.231078	+	0.972935i	$0.574225\pi$
$912$		0			0
$913$	−16.2864	+	15.4273i	−0.539001	+	0.510569i
$914$	−17.0559	+	7.89090i	−0.564159	+	0.261008i
$915$		0			0
$916$	−19.2101	+	18.1968i	−0.634720	+	0.601239i
$917$	−3.94905	+	5.82441i	−0.130409	+	0.192339i
$918$		0			0
$919$	−27.1248	+	51.1628i	−0.894764	+	1.68770i	−0.185643	+	0.982617i	$0.559437\pi$
$919$	−27.1248	+	51.1628i	−0.894764	+	1.68770i	−0.709121	+	0.705086i	$0.750908\pi$
$920$	−8.56768	−	12.6364i	−0.282468	−	0.416609i
$921$		0			0
$922$	−5.36550	+	19.3248i	−0.176703	+	0.636428i
$923$	−6.47426	−	16.2492i	−0.213103	−	0.534848i
$924$		0			0
$925$	5.24368	+	4.96708i	0.172411	+	0.163317i
$926$	0.0386691	−	0.00851171i	0.00127075	−	0.000279712i
$927$		0			0
$928$	−3.92776	+	23.9583i	−0.128935	+	0.786469i
$929$	−3.14956	+	3.70795i	−0.103334	+	0.121654i	−0.811398	−	0.584494i	$-0.801293\pi$
$929$	−3.14956	+	3.70795i	−0.103334	+	0.121654i	0.708064	+	0.706148i	$0.249569\pi$
$930$		0			0
$931$	−21.7130	−	16.5058i	−0.711614	−	0.540955i
$932$	8.48764	+	5.10685i	0.278022	+	0.167280i
$933$		0			0
$934$	15.8563	−	1.72448i	0.518836	−	0.0564268i
$935$	34.3966	−	26.1476i	1.12489	−	0.855119i
$936$		0			0
$937$	−1.98456	−	36.6030i	−0.0648326	−	1.19577i	−0.832169	−	0.554522i	$-0.812901\pi$
$937$	−1.98456	−	36.6030i	−0.0648326	−	1.19577i	0.767336	−	0.641245i	$-0.221582\pi$
$938$	−2.23586	−	0.243165i	−0.0730035	−	0.00793961i
$939$		0			0
$940$	23.6935	+	27.8941i	0.772797	+	0.909806i
$941$	−35.8735	+	12.0872i	−1.16944	+	0.394031i	−0.835995	−	0.548737i	$-0.815109\pi$
$941$	−35.8735	+	12.0872i	−1.16944	+	0.394031i	−0.333448	+	0.942769i	$0.608212\pi$
$942$		0			0
$943$	6.97629			0.227179
$944$	−13.6410	+	5.12503i	−0.443975	+	0.166805i
$945$		0			0
$946$	6.30403	+	2.91655i	0.204962	+	0.0948254i
$947$	29.5903	−	9.97014i	0.961556	−	0.323986i	0.205620	−	0.978632i	$-0.434079\pi$
$947$	29.5903	−	9.97014i	0.961556	−	0.323986i	0.755936	+	0.654646i	$0.227182\pi$
$948$		0			0
$949$	17.3322	−	10.4284i	0.562626	−	0.338521i
$950$	−15.4325	−	1.67838i	−0.500696	−	0.0544540i
$951$		0			0
$952$	1.72481	+	6.21219i	0.0559013	+	0.201338i
$953$	−15.7000	+	11.9349i	−0.508574	+	0.386608i	−0.827758	−	0.561085i	$-0.810384\pi$
$953$	−15.7000	+	11.9349i	−0.508574	+	0.386608i	0.319184	+	0.947693i	$0.396591\pi$
$954$		0			0
$955$	−2.62420	−	16.0069i	−0.0849172	−	0.517972i
$956$	6.29864	+	3.78976i	0.203712	+	0.122570i
$957$		0			0
$958$	−0.683847	+	1.71633i	−0.0220941	+	0.0554520i
$959$	−4.53971	+	5.34456i	−0.146595	+	0.172585i
$960$		0			0
$961$	1.88061	−	34.6858i	0.0606648	−	1.11890i
$962$	1.22185	−	0.268949i	0.0393940	−	0.00867127i
$963$		0			0
$964$	−43.3761	−	14.6151i	−1.39705	−	0.470721i
$965$	23.2812	+	58.4314i	0.749449	+	1.88097i
$966$		0			0
$967$	21.6134	+	4.75746i	0.695039	+	0.152990i	0.548420	−	0.836203i	$-0.315230\pi$
$967$	21.6134	+	4.75746i	0.695039	+	0.152990i	0.146620	+	0.989193i	$0.453161\pi$
$968$	5.24434	+	7.73482i	0.168559	+	0.248606i
$969$		0			0
$970$	8.99767	+	16.9714i	0.288898	+	0.544919i
$971$	2.95958	−	4.36506i	0.0949775	−	0.140081i	−0.777231	−	0.629215i	$-0.783377\pi$
$971$	2.95958	−	4.36506i	0.0949775	−	0.140081i	0.872209	+	0.489133i	$0.162687\pi$
$972$		0			0
$973$	−3.34225	+	1.54629i	−0.107148	+	0.0495717i
$974$	−9.60159	+	4.44217i	−0.307655	+	0.142336i
$975$		0			0
$976$	−12.4924	+	18.4250i	−0.399873	+	0.589768i
$977$	−2.72270	−	5.13555i	−0.0871068	−	0.164301i	0.836131	−	0.548530i	$-0.184812\pi$
$977$	−2.72270	−	5.13555i	−0.0871068	−	0.164301i	−0.923238	+	0.384229i	$0.874467\pi$
$978$		0			0
$979$	5.41714	+	7.98968i	0.173132	+	0.255351i
$980$	−32.6759	−	7.19252i	−1.04379	−	0.229757i
$981$		0			0
$982$	3.65432	+	9.17165i	0.116614	+	0.292679i
$983$	−46.3529	−	15.6181i	−1.47843	−	0.498140i	−0.539419	−	0.842037i	$-0.681356\pi$
$983$	−46.3529	−	15.6181i	−1.47843	−	0.498140i	−0.939007	+	0.343898i	$0.888253\pi$
$984$		0			0
$985$	29.2491	−	6.43820i	0.931952	−	0.205138i
$986$	−0.483700	+	8.92132i	−0.0154041	+	0.284113i
$987$		0			0
$988$	7.57401	−	8.91681i	0.240961	−	0.283682i
$989$	−2.25684	+	5.66423i	−0.0717632	+	0.180112i
$990$		0			0
$991$	8.32741	+	5.01044i	0.264529	+	0.159162i	0.641639	−	0.767007i	$-0.278255\pi$
$991$	8.32741	+	5.01044i	0.264529	+	0.159162i	−0.377110	+	0.926168i	$0.623082\pi$
$992$	7.33728	+	44.7554i	0.232959	+	1.42099i
$993$		0			0
$994$	−4.45727	+	3.38833i	−0.141376	+	0.107471i
$995$	−8.34320	−	30.0495i	−0.264497	−	0.952633i
$996$		0			0
$997$	−2.19246	−	0.238444i	−0.0694359	−	0.00755161i	0.0733351	−	0.997307i	$-0.476636\pi$
$997$	−2.19246	−	0.238444i	−0.0694359	−	0.00755161i	−0.142771	+	0.989756i	$0.545601\pi$
$998$	1.95377	−	1.17554i	0.0618455	−	0.0372112i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.a.433.2		112
3.2	odd	2		59.2.c.a.20.3	yes	112
12.11	even	2		944.2.m.c.433.1		112
59.3	even	29	inner	531.2.i.a.298.2		112
177.11	even	58		3481.2.a.q.1.30		56
177.62	odd	58		59.2.c.a.3.3	✓	112
177.107	odd	58		3481.2.a.p.1.27		56
708.239	even	58		944.2.m.c.593.1		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.3.3	✓	112	177.62	odd	58
59.2.c.a.20.3	yes	112	3.2	odd	2
531.2.i.a.298.2		112	59.3	even	29	inner
531.2.i.a.433.2		112	1.1	even	1	trivial
944.2.m.c.433.1		112	12.11	even	2
944.2.m.c.593.1		112	708.239	even	58
3481.2.a.p.1.27		56	177.107	odd	58
3481.2.a.q.1.30		56	177.11	even	58

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)

\(f(q)\)	\(=\)	\(q+(0.554859 + 0.256705i) q^{2} +(-1.05280 - 1.23945i) q^{4} +(2.81882 - 1.69603i) q^{5} +(0.0467597 + 0.862432i) q^{7} +(-0.593097 - 2.13614i) q^{8} +O(q^{10})\)	\(q+(0.554859 + 0.256705i) q^{2} +(-1.05280 - 1.23945i) q^{4} +(2.81882 - 1.69603i) q^{5} +(0.0467597 + 0.862432i) q^{7} +(-0.593097 - 2.13614i) q^{8} +(1.99943 - 0.217451i) q^{10} +(-0.631059 - 3.84929i) q^{11} +(-1.31325 - 0.998305i) q^{13} +(-0.195446 + 0.490531i) q^{14} +(-0.306918 + 1.87211i) q^{16} +(-0.182290 + 3.36214i) q^{17} +(-3.16614 - 2.99913i) q^{19} +(-5.06981 - 1.70822i) q^{20} +(0.637984 - 2.29781i) q^{22} +(2.04440 + 0.450007i) q^{23} +(2.72721 - 5.14406i) q^{25} +(-0.472397 - 0.891036i) q^{26} +(1.01972 - 0.965926i) q^{28} +(3.93910 - 1.82242i) q^{29} +(5.88624 - 5.57574i) q^{31} +(-3.13912 + 4.62986i) q^{32} +(-0.964222 + 1.81872i) q^{34} +(1.59452 + 2.35174i) q^{35} +(-0.331878 + 1.19532i) q^{37} +(-0.986869 - 2.47686i) q^{38} +(-5.29479 - 5.01550i) q^{40} +(3.25469 - 0.716412i) q^{41} +(-0.471222 + 2.87433i) q^{43} +(-4.10664 + 4.83471i) q^{44} +(1.01884 + 0.774499i) q^{46} +(-5.86181 - 3.52693i) q^{47} +(6.21736 - 0.676179i) q^{49} +(2.83372 - 2.15414i) q^{50} +(0.145236 + 2.67873i) q^{52} +(-2.19994 - 0.239258i) q^{53} +(-8.30736 - 9.78018i) q^{55} +(1.81454 - 0.611391i) q^{56} +2.65347 q^{58} +(3.82919 + 6.65863i) q^{59} +(10.6495 + 4.92699i) q^{61} +(4.69735 - 1.58272i) q^{62} +(0.320821 - 0.193031i) q^{64} +(-5.39497 - 0.586739i) q^{65} +(1.13948 + 4.10403i) q^{67} +(4.35913 - 3.31372i) q^{68} +(0.281029 + 1.71420i) q^{70} +(9.08556 + 5.46660i) q^{71} +(-4.53863 + 11.3911i) q^{73} +(-0.490989 + 0.578038i) q^{74} +(-0.383962 + 7.08177i) q^{76} +(3.29024 - 0.724237i) q^{77} +(-9.88675 - 3.33123i) q^{79} +(2.31002 + 5.79770i) q^{80} +(1.98980 + 0.437988i) q^{82} +(-3.22744 - 4.76012i) q^{83} +(5.18844 + 9.78644i) q^{85} +(-0.999317 + 1.47388i) q^{86} +(-7.84835 + 3.63103i) q^{88} +(-2.24597 + 1.03910i) q^{89} +(0.799563 - 1.17927i) q^{91} +(-1.59459 - 3.00771i) q^{92} +(-2.34709 - 3.46170i) q^{94} +(-14.0114 - 3.08414i) q^{95} +(3.53517 + 8.87260i) q^{97} +(3.62334 + 1.22084i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 26 q^{2} - 30 q^{4} + 25 q^{5} - 23 q^{7} + 8 q^{8}+O(q^{10}) \) 112 * q + 26 * q^2 - 30 * q^4 + 25 * q^5 - 23 * q^7 + 8 * q^8	\( 112 q + 26 q^{2} - 30 q^{4} + 25 q^{5} - 23 q^{7} + 8 q^{8} - 3 q^{10} + 15 q^{11} - 23 q^{13} - 13 q^{14} - 8 q^{16} + 10 q^{17} - 15 q^{19} - 7 q^{20} - q^{22} - 3 q^{23} - 5 q^{25} - 5 q^{26} + 29 q^{28} + 13 q^{29} + 3 q^{31} - 36 q^{32} + 27 q^{34} - 28 q^{35} - 9 q^{37} - 31 q^{38} + 79 q^{40} - 23 q^{41} + 19 q^{43} - 43 q^{44} - 31 q^{46} - 10 q^{47} - 31 q^{49} + 60 q^{50} - 75 q^{52} + 23 q^{53} - 24 q^{55} + 103 q^{56} + 12 q^{58} + 33 q^{59} - 47 q^{61} + 39 q^{62} - 152 q^{64} + 16 q^{65} - 19 q^{67} + 5 q^{68} + 23 q^{70} + 18 q^{71} + 24 q^{73} - 19 q^{74} + 97 q^{76} - 65 q^{77} + 41 q^{79} - 107 q^{80} + 145 q^{82} - 49 q^{83} + 39 q^{85} - 111 q^{86} + 175 q^{88} - 51 q^{89} + 77 q^{91} - 135 q^{92} + 151 q^{94} - 65 q^{95} + 91 q^{97} - 31 q^{98}+O(q^{100}) \) 112 * q + 26 * q^2 - 30 * q^4 + 25 * q^5 - 23 * q^7 + 8 * q^8 - 3 * q^10 + 15 * q^11 - 23 * q^13 - 13 * q^14 - 8 * q^16 + 10 * q^17 - 15 * q^19 - 7 * q^20 - q^22 - 3 * q^23 - 5 * q^25 - 5 * q^26 + 29 * q^28 + 13 * q^29 + 3 * q^31 - 36 * q^32 + 27 * q^34 - 28 * q^35 - 9 * q^37 - 31 * q^38 + 79 * q^40 - 23 * q^41 + 19 * q^43 - 43 * q^44 - 31 * q^46 - 10 * q^47 - 31 * q^49 + 60 * q^50 - 75 * q^52 + 23 * q^53 - 24 * q^55 + 103 * q^56 + 12 * q^58 + 33 * q^59 - 47 * q^61 + 39 * q^62 - 152 * q^64 + 16 * q^65 - 19 * q^67 + 5 * q^68 + 23 * q^70 + 18 * q^71 + 24 * q^73 - 19 * q^74 + 97 * q^76 - 65 * q^77 + 41 * q^79 - 107 * q^80 + 145 * q^82 - 49 * q^83 + 39 * q^85 - 111 * q^86 + 175 * q^88 - 51 * q^89 + 77 * q^91 - 135 * q^92 + 151 * q^94 - 65 * q^95 + 91 * q^97 - 31 * q^98

Introduction

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