LMFDB - Embedded newform 531.2.i.c.46.3

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			46.3
Character	$\chi$	$=$	531.46
Dual form			531.2.i.c.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.398193 - 0.468789i) q^{2} +(0.262358 - 1.60032i) q^{4} +(-0.780962 + 1.47305i) q^{5} +(-2.98728 + 0.324887i) q^{7} +(-1.90875 + 1.14846i) q^{8} +O(q^{10})$	\(q+(-0.398193 - 0.468789i) q^{2} +(0.262358 - 1.60032i) q^{4} +(-0.780962 + 1.47305i) q^{5} +(-2.98728 + 0.324887i) q^{7} +(-1.90875 + 1.14846i) q^{8} +(1.00152 - 0.220452i) q^{10} +(1.75843 - 0.592483i) q^{11} +(0.815468 + 2.93705i) q^{13} +(1.34182 + 1.27104i) q^{14} +(-1.77514 - 0.598116i) q^{16} +(-7.12450 - 0.774836i) q^{17} +(0.410857 + 7.57780i) q^{19} +(2.15245 + 1.63625i) q^{20} +(-0.977944 - 0.588409i) q^{22} +(-0.864818 - 0.400107i) q^{23} +(1.24596 + 1.83765i) q^{25} +(1.05214 - 1.55180i) q^{26} +(-0.263818 + 4.86583i) q^{28} +(-1.96982 + 2.31905i) q^{29} +(0.0521205 - 0.961307i) q^{31} +(2.07551 + 5.20914i) q^{32} +(2.47369 + 3.64842i) q^{34} +(1.85438 - 4.65414i) q^{35} +(-5.56000 - 3.34534i) q^{37} +(3.38879 - 3.21003i) q^{38} +(-0.201074 - 3.70858i) q^{40} +(6.70373 - 3.10148i) q^{41} +(-4.42184 - 1.48989i) q^{43} +(-0.486822 - 2.96948i) q^{44} +(0.156798 + 0.564737i) q^{46} +(4.93991 + 9.31766i) q^{47} +(1.98197 - 0.436264i) q^{49} +(0.365339 - 1.31583i) q^{50} +(4.91415 - 0.534447i) q^{52} +(-2.12328 - 0.467370i) q^{53} +(-0.500507 + 3.05296i) q^{55} +(5.32885 - 4.05089i) q^{56} +1.87151 q^{58} +(-6.97832 + 3.20984i) q^{59} +(1.23671 + 1.45597i) q^{61} +(-0.471404 + 0.358352i) q^{62} +(-0.139312 + 0.262771i) q^{64} +(-4.96328 - 1.09250i) q^{65} +(-11.4113 + 6.86593i) q^{67} +(-3.10915 + 11.1982i) q^{68} +(-2.92021 + 0.983934i) q^{70} +(-0.675826 - 1.27474i) q^{71} +(-8.21281 - 7.77959i) q^{73} +(0.645694 + 3.93856i) q^{74} +(12.2347 + 1.33060i) q^{76} +(-5.06043 + 2.34121i) q^{77} +(8.52956 + 6.48400i) q^{79} +(2.26738 - 2.14777i) q^{80} +(-4.12332 - 1.90765i) q^{82} +(3.67816 - 9.23148i) q^{83} +(6.70533 - 9.88963i) q^{85} +(1.06230 + 2.66618i) q^{86} +(-2.67596 + 3.15038i) q^{88} +(3.10924 - 3.66048i) q^{89} +(-3.39024 - 8.50887i) q^{91} +(-0.867190 + 1.27901i) q^{92} +(2.40098 - 6.02600i) q^{94} +(-11.4834 - 5.31277i) q^{95} +(10.4433 - 9.89242i) q^{97} +(-0.993721 - 0.755407i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{8}{29}\right)$

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 $

$2$	−0.398193	−	0.468789i	−0.281565	−	0.331484i	0.603140	−	0.797635i	$-0.293916\pi$
$2$	−0.398193	−	0.468789i	−0.281565	−	0.331484i	−0.884705	+	0.466151i	$0.845640\pi$
$3$		0			0
$3$		0			0
$4$	0.262358	−	1.60032i	0.131179	−	0.800158i
$5$	−0.780962	+	1.47305i	−0.349257	+	0.658768i	−0.994445	−	0.105255i	$-0.966434\pi$
$5$	−0.780962	+	1.47305i	−0.349257	+	0.658768i	0.645188	+	0.764024i	$0.276779\pi$
$6$		0			0
$7$	−2.98728	+	0.324887i	−1.12909	+	0.122796i	−0.653538	−	0.756894i	$-0.726716\pi$
$7$	−2.98728	+	0.324887i	−1.12909	+	0.122796i	−0.475549	+	0.879689i	$0.657751\pi$
$8$	−1.90875	+	1.14846i	−0.674844	+	0.406040i
$9$		0			0
$10$	1.00152	−	0.220452i	0.316710	−	0.0697131i
$11$	1.75843	−	0.592483i	0.530186	−	0.178640i	−0.0414610	−	0.999140i	$-0.513201\pi$
$11$	1.75843	−	0.592483i	0.530186	−	0.178640i	0.571647	+	0.820500i	$0.306305\pi$
$12$		0			0
$13$	0.815468	+	2.93705i	0.226170	+	0.814591i	0.986320	+	0.164843i	$0.0527118\pi$
$13$	0.815468	+	2.93705i	0.226170	+	0.814591i	−0.760150	+	0.649748i	$0.774874\pi$
$14$	1.34182	+	1.27104i	0.358616	+	0.339699i
$15$		0			0
$16$	−1.77514	−	0.598116i	−0.443786	−	0.149529i
$17$	−7.12450	−	0.774836i	−1.72794	−	0.187925i	−0.810486	−	0.585758i	$-0.800797\pi$
$17$	−7.12450	−	0.774836i	−1.72794	−	0.187925i	−0.917458	+	0.397833i	$0.869762\pi$
$18$		0			0
$19$	0.410857	+	7.57780i	0.0942570	+	1.73847i	0.538557	+	0.842589i	$0.318970\pi$
$19$	0.410857	+	7.57780i	0.0942570	+	1.73847i	−0.444300	+	0.895878i	$0.646547\pi$
$20$	2.15245	+	1.63625i	0.481303	+	0.365877i
$21$		0			0
$22$	−0.977944	−	0.588409i	−0.208498	−	0.125449i
$23$	−0.864818	−	0.400107i	−0.180327	−	0.0834281i	0.327648	−	0.944800i	$-0.393744\pi$
$23$	−0.864818	−	0.400107i	−0.180327	−	0.0834281i	−0.507975	+	0.861372i	$0.669606\pi$
$24$		0			0
$25$	1.24596	+	1.83765i	0.249192	+	0.367530i
$26$	1.05214	−	1.55180i	0.206342	−	0.304332i
$27$		0			0
$28$	−0.263818	+	4.86583i	−0.0498569	+	0.919556i
$29$	−1.96982	+	2.31905i	−0.365786	+	0.430637i	−0.914008	−	0.405696i	$-0.867029\pi$
$29$	−1.96982	+	2.31905i	−0.365786	+	0.430637i	0.548222	+	0.836333i	$0.315305\pi$
$30$		0			0
$31$	0.0521205	−	0.961307i	0.00936112	−	0.172656i	−0.990114	−	0.140264i	$-0.955205\pi$
$31$	0.0521205	−	0.961307i	0.00936112	−	0.172656i	0.999475	−	0.0323917i	$-0.0103124\pi$
$32$	2.07551	+	5.20914i	0.366902	+	0.920854i
$33$		0			0
$34$	2.47369	+	3.64842i	0.424234	+	0.625699i
$35$	1.85438	−	4.65414i	0.313447	−	0.786694i
$36$		0			0
$37$	−5.56000	−	3.34534i	−0.914059	−	0.549971i	−0.0209345	−	0.999781i	$-0.506664\pi$
$37$	−5.56000	−	3.34534i	−0.914059	−	0.549971i	−0.893124	+	0.449810i	$0.851492\pi$
$38$	3.38879	−	3.21003i	0.549735	−	0.520736i
$39$		0			0
$40$	−0.201074	−	3.70858i	−0.0317925	−	0.586378i
$41$	6.70373	−	3.10148i	1.04695	−	0.484369i	0.180467	−	0.983581i	$-0.442239\pi$
$41$	6.70373	−	3.10148i	1.04695	−	0.484369i	0.866480	+	0.499212i	$0.166377\pi$
$42$		0			0
$43$	−4.42184	−	1.48989i	−0.674325	−	0.227206i	−0.0387536	−	0.999249i	$-0.512339\pi$
$43$	−4.42184	−	1.48989i	−0.674325	−	0.227206i	−0.635571	+	0.772042i	$0.719235\pi$
$44$	−0.486822	−	2.96948i	−0.0733912	−	0.447666i
$45$		0			0
$46$	0.156798	+	0.564737i	0.0231187	+	0.0832659i
$47$	4.93991	+	9.31766i	0.720560	+	1.35912i	0.924896	+	0.380219i	$0.124151\pi$
$47$	4.93991	+	9.31766i	0.720560	+	1.35912i	−0.204337	+	0.978901i	$0.565504\pi$
$48$		0			0
$49$	1.98197	−	0.436264i	0.283138	−	0.0623234i
$50$	0.365339	−	1.31583i	0.0516667	−	0.186087i
$51$		0			0
$52$	4.91415	−	0.534447i	0.681471	−	0.0741144i
$53$	−2.12328	−	0.467370i	−0.291655	−	0.0641981i	0.0667329	−	0.997771i	$-0.478742\pi$
$53$	−2.12328	−	0.467370i	−0.291655	−	0.0641981i	−0.358388	+	0.933573i	$0.616674\pi$
$54$		0			0
$55$	−0.500507	+	3.05296i	−0.0674884	+	0.411661i
$56$	5.32885	−	4.05089i	0.712098	−	0.541323i
$57$		0			0
$58$	1.87151			0.245742
$59$	−6.97832	+	3.20984i	−0.908500	+	0.417886i
$59$	−6.97832	+	3.20984i	−0.908500	+	0.417886i
$60$		0			0
$61$	1.23671	+	1.45597i	0.158345	+	0.186418i	0.835614	−	0.549318i	$-0.185112\pi$
$61$	1.23671	+	1.45597i	0.158345	+	0.186418i	−0.677269	+	0.735736i	$0.736836\pi$
$62$	−0.471404	+	0.358352i	−0.0598684	+	0.0455108i
$63$		0			0
$64$	−0.139312	+	0.262771i	−0.0174141	+	0.0328464i
$65$	−4.96328	−	1.09250i	−0.615619	−	0.135508i
$66$		0			0
$67$	−11.4113	+	6.86593i	−1.39411	+	0.838807i	−0.996881	−	0.0789134i	$-0.974855\pi$
$67$	−11.4113	+	6.86593i	−1.39411	+	0.838807i	−0.397227	+	0.917720i	$0.630027\pi$
$68$	−3.10915	+	11.1982i	−0.377040	+	1.35798i
$69$		0			0
$70$	−2.92021	+	0.983934i	−0.349032	+	0.117603i
$71$	−0.675826	−	1.27474i	−0.0802058	−	0.151284i	0.840165	−	0.542331i	$-0.182458\pi$
$71$	−0.675826	−	1.27474i	−0.0802058	−	0.151284i	−0.920371	+	0.391046i	$0.872113\pi$
$72$		0			0
$73$	−8.21281	−	7.77959i	−0.961237	−	0.910532i	0.0348072	−	0.999394i	$-0.488918\pi$
$73$	−8.21281	−	7.77959i	−0.961237	−	0.910532i	−0.996044	+	0.0888622i	$0.971677\pi$
$74$	0.645694	+	3.93856i	0.0750604	+	0.457848i
$75$		0			0
$76$	12.2347	+	1.33060i	1.40341	+	0.152630i
$77$	−5.06043	+	2.34121i	−0.576690	+	0.266805i
$78$		0			0
$79$	8.52956	+	6.48400i	0.959650	+	0.729507i	0.962723	−	0.270488i	$-0.0871850\pi$
$79$	8.52956	+	6.48400i	0.959650	+	0.729507i	−0.00307289	+	0.999995i	$0.500978\pi$
$80$	2.26738	−	2.14777i	0.253500	−	0.240128i
$81$		0			0
$82$	−4.12332	−	1.90765i	−0.455344	−	0.210665i
$83$	3.67816	−	9.23148i	0.403730	−	1.01329i	−0.576794	−	0.816890i	$-0.695696\pi$
$83$	3.67816	−	9.23148i	0.403730	−	1.01329i	0.980524	−	0.196397i	$-0.0629242\pi$
$84$		0			0
$85$	6.70533	−	9.88963i	0.727295	−	1.07268i
$86$	1.06230	+	2.66618i	0.114551	+	0.287501i
$87$		0			0
$88$	−2.67596	+	3.15038i	−0.285258	+	0.335831i
$89$	3.10924	−	3.66048i	0.329579	−	0.388010i	−0.572268	−	0.820067i	$-0.693936\pi$
$89$	3.10924	−	3.66048i	0.329579	−	0.388010i	0.901846	+	0.432057i	$0.142212\pi$
$90$		0			0
$91$	−3.39024	−	8.50887i	−0.355394	−	0.891972i
$92$	−0.867190	+	1.27901i	−0.0904108	+	0.133346i
$93$		0			0
$94$	2.40098	−	6.02600i	0.247642	−	0.621535i
$95$	−11.4834	−	5.31277i	−1.17817	−	0.545078i
$96$		0			0
$97$	10.4433	−	9.89242i	1.06036	−	1.00442i	0.0603761	−	0.998176i	$-0.480770\pi$
$97$	10.4433	−	9.89242i	1.06036	−	1.00442i	0.999980	−	0.00624738i	$-0.00198862\pi$
$98$	−0.993721	−	0.755407i	−0.100381	−	0.0763076i
$99$		0			0
$100$	3.26771	−	1.51180i	0.326771	−	0.151180i
$101$	−1.84672	−	0.200843i	−0.183755	−	0.0199846i	0.0157785	−	0.999876i	$-0.494977\pi$
$101$	−1.84672	−	0.200843i	−0.183755	−	0.0199846i	−0.199534	+	0.979891i	$0.563943\pi$
$102$		0			0
$103$	−2.21113	−	13.4873i	−0.217869	−	1.32894i	−0.838526	−	0.544862i	$-0.816582\pi$
$103$	−2.21113	−	13.4873i	−0.217869	−	1.32894i	0.620656	−	0.784083i	$-0.286866\pi$
$104$	−4.92960	−	4.66956i	−0.483387	−	0.457888i
$105$		0			0
$106$	0.626378	+	1.18147i	0.0608392	+	0.114755i
$107$	−13.5018	+	4.54928i	−1.30527	+	0.439796i	−0.884147	−	0.467209i	$-0.845259\pi$
$107$	−13.5018	+	4.54928i	−1.30527	+	0.439796i	−0.421120	+	0.907005i	$0.638363\pi$
$108$		0			0
$109$	2.91116	−	10.4851i	0.278839	−	1.00429i	−0.682943	−	0.730471i	$-0.739300\pi$
$109$	2.91116	−	10.4851i	0.278839	−	1.00429i	0.961782	−	0.273815i	$-0.0882857\pi$
$110$	1.63049	−	0.981035i	0.155461	−	0.0935380i
$111$		0			0
$112$	5.49718	+	1.21002i	0.519435	+	0.114336i
$113$	5.75458	−	10.8543i	0.541345	−	1.02108i	−0.450396	−	0.892829i	$-0.648717\pi$
$113$	5.75458	−	10.8543i	0.541345	−	1.02108i	0.991741	−	0.128256i	$-0.0409379\pi$
$114$		0			0
$115$	1.26477	−	0.961452i	0.117940	−	0.0896558i
$116$	3.19442	+	3.76076i	0.296594	+	0.349177i
$117$		0			0
$118$	4.28346	+	1.99322i	0.394324	+	0.183491i
$119$	21.5346			1.97408
$120$		0			0
$121$	−6.01599	+	4.57324i	−0.546908	+	0.415749i
$122$	0.190093	−	1.15952i	0.0172102	−	0.104978i
$123$		0			0
$124$	−1.52472	−	0.335616i	−0.136924	−	0.0301392i
$125$	−11.9675	+	1.30154i	−1.07040	+	0.116413i
$126$		0			0
$127$	−3.98255	+	14.3439i	−0.353394	+	1.27281i	0.546778	+	0.837278i	$0.315854\pi$
$127$	−3.98255	+	14.3439i	−0.353394	+	1.27281i	−0.900172	+	0.435534i	$0.856560\pi$
$128$	11.1313	−	2.45017i	0.983873	−	0.216567i
$129$		0			0
$130$	1.46419	+	2.76176i	0.128418	+	0.242222i
$131$	1.24265	+	4.47562i	0.108571	+	0.391037i	0.997790	−	0.0664442i	$-0.0211655\pi$
$131$	1.24265	+	4.47562i	0.108571	+	0.391037i	−0.889219	+	0.457481i	$0.848752\pi$
$132$		0			0
$133$	−3.68927	−	22.5036i	−0.319901	−	1.95131i
$134$	7.76256	+	2.61551i	0.670583	+	0.225946i
$135$		0			0
$136$	14.4887	−	6.70320i	1.24240	−	0.574795i
$137$	−0.231122	−	4.26280i	−0.0197461	−	0.364196i	−0.991662	−	0.128867i	$-0.958866\pi$
$137$	−0.231122	−	4.26280i	−0.0197461	−	0.364196i	0.971916	−	0.235329i	$-0.0756167\pi$
$138$		0			0
$139$	−0.680088	+	0.644214i	−0.0576843	+	0.0546415i	−0.715999	−	0.698102i	$-0.754028\pi$
$139$	−0.680088	+	0.644214i	−0.0576843	+	0.0546415i	0.658314	+	0.752743i	$0.271270\pi$
$140$	−6.96159	−	4.18865i	−0.588362	−	0.354005i
$141$		0			0
$142$	−0.328477	+	0.824414i	−0.0275651	+	0.0691833i
$143$	3.17410	+	4.68144i	0.265431	+	0.391482i
$144$		0			0
$145$	−1.87773	−	4.71273i	−0.155937	−	0.391371i
$146$	−0.376702	+	6.94785i	−0.0311761	+	0.575008i
$147$		0			0
$148$	−6.81232	+	8.02008i	−0.559969	+	0.659247i
$149$	0.179588	−	3.31230i	0.0147124	−	0.271354i	−0.981917	−	0.189314i	$-0.939374\pi$
$149$	0.179588	−	3.31230i	0.0147124	−	0.271354i	0.996629	−	0.0820401i	$-0.0261436\pi$
$150$		0			0
$151$	−4.55719	+	6.72135i	−0.370859	+	0.546975i	−0.966629	−	0.256179i	$-0.917536\pi$
$151$	−4.55719	+	6.72135i	−0.370859	+	0.546975i	0.595771	+	0.803155i	$0.296847\pi$
$152$	−9.48699	−	13.9923i	−0.769497	−	1.13492i
$153$		0			0
$154$	3.11256	+	1.44002i	0.250817	+	0.116040i
$155$	1.37535	+	0.827520i	0.110471	+	0.0664680i
$156$		0			0
$157$	7.77973	+	5.91399i	0.620890	+	0.471988i	0.867708	−	0.497074i	$-0.165592\pi$
$157$	7.77973	+	5.91399i	0.620890	+	0.471988i	−0.246819	+	0.969062i	$0.579385\pi$
$158$	−0.356782	−	6.58045i	−0.0283840	−	0.523512i
$159$		0			0
$160$	−9.29422	−	1.01081i	−0.734773	−	0.0799114i
$161$	2.71344	+	0.914266i	0.213849	+	0.0720543i
$162$		0			0
$163$	−10.1922	−	9.65453i	−0.798311	−	0.756201i	0.175275	−	0.984520i	$-0.443919\pi$
$163$	−10.1922	−	9.65453i	−0.798311	−	0.756201i	−0.973586	+	0.228319i	$0.926677\pi$
$164$	−3.20456	−	11.5418i	−0.250234	−	0.901262i
$165$		0			0
$166$	−5.79224	+	1.95163i	−0.449565	+	0.151476i
$167$	19.5257	−	4.29793i	1.51094	−	0.332584i	0.619240	−	0.785202i	$-0.287441\pi$
$167$	19.5257	−	4.29793i	1.51094	−	0.332584i	0.891705	+	0.452618i	$0.149510\pi$
$168$		0			0
$169$	3.17786	−	1.91206i	0.244451	−	0.147081i
$170$	−7.30617	+	0.794593i	−0.560357	+	0.0609425i
$171$		0			0
$172$	−3.54441	+	6.68546i	−0.270258	+	0.509761i
$173$	−2.37020	+	14.4576i	−0.180203	+	1.09919i	0.729516	+	0.683963i	$0.239745\pi$
$173$	−2.37020	+	14.4576i	−0.180203	+	1.09919i	−0.909719	+	0.415224i	$0.863703\pi$
$174$		0			0
$175$	−4.31906	−	5.08479i	−0.326490	−	0.384374i
$176$	−3.47584			−0.262001
$177$		0			0
$178$	−2.95407			−0.221417
$179$	−7.47895	−	8.80490i	−0.559003	−	0.658109i	0.407968	−	0.912996i	$-0.366238\pi$
$179$	−7.47895	−	8.80490i	−0.559003	−	0.658109i	−0.966971	+	0.254887i	$0.917962\pi$
$180$		0			0
$181$	−2.26445	+	13.8125i	−0.168315	+	1.02668i	0.758642	+	0.651508i	$0.225863\pi$
$181$	−2.26445	+	13.8125i	−0.168315	+	1.02668i	−0.926957	+	0.375168i	$0.877585\pi$
$182$	−2.63889	+	4.97748i	−0.195608	+	0.368955i
$183$		0			0
$184$	2.11022	−	0.229501i	0.155568	−	0.0169190i
$185$	9.27001	−	5.57758i	0.681545	−	0.410072i
$186$		0			0
$187$	−12.9870	+	2.85865i	−0.949703	+	0.209045i
$188$	16.2072	−	5.46085i	1.18203	−	0.398273i
$189$		0			0
$190$	2.08203	+	7.49878i	0.151046	+	0.544019i
$191$	11.7148	+	11.0969i	0.847655	+	0.802942i	0.982175	−	0.187969i	$-0.0601906\pi$
$191$	11.7148	+	11.0969i	0.847655	+	0.802942i	−0.134520	+	0.990911i	$0.542949\pi$
$192$		0			0
$193$	11.1458	+	3.75547i	0.802294	+	0.270324i	0.690430	−	0.723399i	$-0.257421\pi$
$193$	11.1458	+	3.75547i	0.802294	+	0.270324i	0.111864	+	0.993724i	$0.464318\pi$
$194$	−8.79591	−	0.956613i	−0.631509	−	0.0686808i
$195$		0			0
$196$	−0.178174	−	3.28623i	−0.0127267	−	0.234731i
$197$	1.78896	+	1.35993i	0.127458	+	0.0968909i	0.666961	−	0.745093i	$-0.267595\pi$
$197$	1.78896	+	1.35993i	0.127458	+	0.0968909i	−0.539503	+	0.841984i	$0.681388\pi$
$198$		0			0
$199$	−1.56897	−	0.944019i	−0.111221	−	0.0669197i	0.458856	−	0.888511i	$-0.348259\pi$
$199$	−1.56897	−	0.944019i	−0.111221	−	0.0669197i	−0.570078	+	0.821591i	$0.693087\pi$
$200$	−4.48868	−	2.07669i	−0.317398	−	0.146844i
$201$		0			0
$202$	0.641198	+	0.945696i	0.0451145	+	0.0665390i
$203$	5.13098	−	7.56763i	0.360124	−	0.531143i
$204$		0			0
$205$	−0.666728	+	12.2971i	−0.0465663	+	0.858865i
$206$	−5.44225	+	6.40711i	−0.379180	+	0.446405i
$207$		0			0
$208$	0.309123	−	5.70144i	0.0214338	−	0.395323i
$209$	5.21219	+	13.0816i	0.360534	+	0.904873i
$210$		0			0
$211$	2.60834	+	3.84701i	0.179565	+	0.264839i	0.906810	−	0.421539i	$-0.138510\pi$
$211$	2.60834	+	3.84701i	0.179565	+	0.264839i	−0.727245	+	0.686378i	$0.759200\pi$
$212$	−1.30500	+	3.27530i	−0.0896278	+	0.224949i
$213$		0			0
$214$	7.50897	+	4.51800i	0.513303	+	0.308844i
$215$	5.64798	−	5.35005i	0.385189	−	0.364870i
$216$		0			0
$217$	0.156617	+	2.88863i	0.0106318	+	0.196093i
$218$	−6.07449	+	2.81036i	−0.411416	+	0.190341i
$219$		0			0
$220$	4.75439	+	1.60194i	0.320541	+	0.108003i
$221$	−3.53407	−	21.5569i	−0.237727	−	1.45007i
$222$		0			0
$223$	−1.97684	−	7.11993i	−0.132379	−	0.476786i	0.867404	−	0.497604i	$-0.165787\pi$
$223$	−1.97684	−	7.11993i	−0.132379	−	0.476786i	−0.999783	+	0.0208180i	$0.993373\pi$
$224$	−7.89252	−	14.8869i	−0.527341	−	0.994671i
$225$		0			0
$226$	−7.37980	+	1.62442i	−0.490897	+	0.108055i
$227$	−5.96609	+	21.4879i	−0.395983	+	1.42620i	0.450017	+	0.893020i	$0.351418\pi$
$227$	−5.96609	+	21.4879i	−0.395983	+	1.42620i	−0.846000	+	0.533183i	$0.820996\pi$
$228$		0			0
$229$	15.2934	−	1.66325i	1.01061	−	0.109911i	0.412196	−	0.911095i	$-0.364762\pi$
$229$	15.2934	−	1.66325i	1.01061	−	0.109911i	0.598417	+	0.801184i	$0.295796\pi$
$230$	−0.954340	−	0.210066i	−0.0629273	−	0.0138513i
$231$		0			0
$232$	1.09656	−	6.68873i	0.0719928	−	0.439137i
$233$	−15.0808	+	11.4641i	−0.987974	+	0.751038i	−0.968562	−	0.248774i	$-0.919972\pi$
$233$	−15.0808	+	11.4641i	−0.987974	+	0.751038i	−0.0194119	+	0.999812i	$0.506179\pi$
$234$		0			0
$235$	−17.5833			−1.14701
$236$	3.30594	+	12.0096i	0.215198	+	0.781761i
$237$		0			0
$238$	−8.57494	−	10.0952i	−0.555831	−	0.654374i
$239$	−18.8184	+	14.3054i	−1.21726	+	0.925337i	−0.998724	−	0.0504920i	$-0.983921\pi$
$239$	−18.8184	+	14.3054i	−1.21726	+	0.925337i	−0.218536	+	0.975829i	$0.570128\pi$
$240$		0			0
$241$	4.70049	−	8.86607i	0.302785	−	0.571114i	−0.684700	−	0.728825i	$-0.740067\pi$
$241$	4.70049	−	8.86607i	0.302785	−	0.571114i	0.987485	+	0.157712i	$0.0504116\pi$
$242$	4.53941	+	0.999200i	0.291804	+	0.0642310i
$243$		0			0
$244$	2.65448	−	1.59715i	0.169936	−	0.102247i
$245$	−0.905201	+	3.26024i	−0.0578312	+	0.208289i
$246$		0			0
$247$	−21.9214	+	7.38617i	−1.39482	+	0.469971i
$248$	1.00453	+	1.89475i	0.0637879	+	0.120317i
$249$		0			0
$250$	5.37551	+	5.09195i	0.339977	+	0.322043i
$251$	−2.39862	−	14.6309i	−0.151400	−	0.923496i	−0.947832	−	0.318769i	$-0.896731\pi$
$251$	−2.39862	−	14.6309i	−0.151400	−	0.923496i	0.796433	−	0.604727i	$-0.206718\pi$
$252$		0			0
$253$	−1.75778	−	0.191170i	−0.110510	−	0.0120187i
$254$	8.31007	−	3.84465i	0.521420	−	0.241235i
$255$		0			0
$256$	−5.10746	−	3.88259i	−0.319216	−	0.242662i
$257$	4.62745	−	4.38336i	0.288653	−	0.273426i	−0.529647	−	0.848218i	$-0.677676\pi$
$257$	4.62745	−	4.38336i	0.288653	−	0.273426i	0.818300	+	0.574792i	$0.194917\pi$
$258$		0			0
$259$	17.6962	+	8.18711i	1.09959	+	0.508723i
$260$	−3.05050	+	7.65618i	−0.189184	+	0.474816i
$261$		0			0
$262$	1.60331	−	2.36470i	0.0990528	−	0.146092i
$263$	5.35881	+	13.4496i	0.330438	+	0.829337i	0.996512	+	0.0834512i	$0.0265943\pi$
$263$	5.35881	+	13.4496i	0.330438	+	0.829337i	−0.666074	+	0.745886i	$0.732026\pi$
$264$		0			0
$265$	2.34666	−	2.76270i	0.144154	−	0.169712i
$266$	−9.08038	+	10.6903i	−0.556754	+	0.655462i
$267$		0			0
$268$	7.99382	+	20.0630i	0.488300	+	1.22554i
$269$	−16.3775	+	24.1550i	−0.998555	+	1.47276i	−0.121369	+	0.992607i	$0.538729\pi$
$269$	−16.3775	+	24.1550i	−0.998555	+	1.47276i	−0.877186	+	0.480151i	$0.840582\pi$
$270$		0			0
$271$	−0.859841	+	2.15804i	−0.0522316	+	0.131092i	−0.952777	−	0.303670i	$-0.901788\pi$
$271$	−0.859841	+	2.15804i	−0.0522316	+	0.131092i	0.900546	+	0.434761i	$0.143167\pi$
$272$	12.1836	+	5.63672i	0.738737	+	0.341776i
$273$		0			0
$274$	−1.90632	+	1.80577i	−0.115165	+	0.109090i
$275$	3.27971	+	2.49317i	0.197774	+	0.150344i
$276$		0			0
$277$	−6.16796	+	2.85360i	−0.370597	+	0.171456i	−0.596343	−	0.802730i	$-0.703380\pi$
$277$	−6.16796	+	2.85360i	−0.370597	+	0.171456i	0.225746	+	0.974186i	$0.427518\pi$
$278$	0.572807	+	0.0622965i	0.0343547	+	0.00373630i
$279$		0			0
$280$	1.80553	+	11.0133i	0.107901	+	0.658168i
$281$	−3.17117	−	3.00389i	−0.189176	−	0.179197i	0.587250	−	0.809406i	$-0.300211\pi$
$281$	−3.17117	−	3.00389i	−0.189176	−	0.179197i	−0.776426	+	0.630209i	$0.782969\pi$
$282$		0			0
$283$	12.8414	+	24.2214i	0.763341	+	1.43981i	0.893850	+	0.448367i	$0.147994\pi$
$283$	12.8414	+	24.2214i	0.763341	+	1.43981i	−0.130509	+	0.991447i	$0.541661\pi$
$284$	−2.21730	+	0.747096i	−0.131573	+	0.0443320i
$285$		0			0
$286$	0.930706	−	3.35210i	0.0550338	−	0.198214i
$287$	−19.0183	+	11.4429i	−1.12262	+	0.675455i
$288$		0			0
$289$	33.5555	+	7.38613i	1.97385	+	0.434478i
$290$	−1.46158	+	2.75684i	−0.0858270	+	0.161887i
$291$		0			0
$292$	−14.6045	+	11.1021i	−0.854664	+	0.649698i
$293$	18.6645	+	21.9736i	1.09039	+	1.28371i	0.956186	+	0.292759i	$0.0945733\pi$
$293$	18.6645	+	21.9736i	1.09039	+	1.28371i	0.134208	+	0.990953i	$0.457151\pi$
$294$		0			0
$295$	0.721545	−	12.7862i	0.0420100	−	0.744440i
$296$	14.4546			0.840158
$297$		0			0
$298$	−1.62428	+	1.23474i	−0.0940920	+	0.0715269i
$299$	0.469904	−	2.86629i	0.0271753	−	0.165762i
$300$		0			0
$301$	13.6933	+	3.01413i	0.789271	+	0.173732i
$302$	4.96553	−	0.540034i	0.285734	−	0.0310755i
$303$		0			0
$304$	3.80308	−	13.6974i	0.218121	−	0.785602i
$305$	−3.11055	+	0.684683i	−0.178109	+	0.0392049i
$306$		0			0
$307$	2.33392	+	4.40224i	0.133204	+	0.251249i	0.941137	−	0.338025i	$-0.109759\pi$
$307$	2.33392	+	4.40224i	0.133204	+	0.251249i	−0.807933	+	0.589274i	$0.799414\pi$
$308$	2.41902	+	8.71253i	0.137837	+	0.496442i
$309$		0			0
$310$	−0.159722	−	0.974262i	−0.00907160	−	0.0553343i
$311$	5.67760	+	1.91301i	0.321947	+	0.108477i	0.475635	−	0.879643i	$-0.342218\pi$
$311$	5.67760	+	1.91301i	0.321947	+	0.108477i	−0.153688	+	0.988119i	$0.549115\pi$
$312$		0			0
$313$	3.41385	−	1.57942i	0.192962	−	0.0892738i	−0.321029	−	0.947069i	$-0.604029\pi$
$313$	3.41385	−	1.57942i	0.192962	−	0.0892738i	0.513991	+	0.857796i	$0.328167\pi$
$314$	−0.325417	−	6.00196i	−0.0183643	−	0.338710i
$315$		0			0
$316$	12.6143	−	11.9489i	0.709607	−	0.672176i
$317$	8.49321	+	5.11020i	0.477026	+	0.287017i	0.733691	−	0.679483i	$-0.237796\pi$
$317$	8.49321	+	5.11020i	0.477026	+	0.287017i	−0.256665	+	0.966501i	$0.582624\pi$
$318$		0			0
$319$	−2.08979	+	5.24497i	−0.117006	+	0.293662i
$320$	−0.278277	−	0.410429i	−0.0155562	−	0.0229437i
$321$		0			0
$322$	−0.651877	−	1.63609i	−0.0363277	−	0.0911756i
$323$	2.94441	−	54.3064i	0.163831	−	3.02169i
$324$		0			0
$325$	−4.38124	+	5.15799i	−0.243027	+	0.286114i
$326$	−0.467490	+	8.62234i	−0.0258919	+	0.477547i
$327$		0			0
$328$	−9.23382	+	13.6189i	−0.509853	+	0.751976i
$329$	−17.7841	−	26.2296i	−0.980469	−	1.44608i
$330$		0			0
$331$	3.76413	+	1.74147i	0.206895	+	0.0957198i	0.520600	−	0.853801i	$-0.325708\pi$
$331$	3.76413	+	1.74147i	0.206895	+	0.0957198i	−0.313705	+	0.949520i	$0.601570\pi$
$332$	−13.8083	−	8.30817i	−0.757829	−	0.455970i
$333$		0			0
$334$	−9.78983	−	7.44203i	−0.535676	−	0.407210i
$335$	−1.20210	−	22.1714i	−0.0656777	−	1.21135i
$336$		0			0
$337$	−23.2182	−	2.52514i	−1.26478	−	0.137553i	−0.548965	−	0.835845i	$-0.684978\pi$
$337$	−23.2182	−	2.52514i	−1.26478	−	0.137553i	−0.715813	+	0.698292i	$0.753944\pi$
$338$	−2.16175	−	0.728380i	−0.117584	−	0.0396186i
$339$		0			0
$340$	−14.0673	−	13.3253i	−0.762908	−	0.722665i
$341$	−0.477908	−	1.72127i	−0.0258802	−	0.0932119i
$342$		0			0
$343$	14.1543	−	4.76912i	0.764258	−	0.257508i
$344$	10.1513	−	2.23446i	0.547319	−	0.120474i
$345$		0			0
$346$	7.72134	−	4.64578i	0.415102	−	0.249759i
$347$	15.7346	−	1.71124i	0.844676	−	0.0918640i	0.324461	−	0.945899i	$-0.394817\pi$
$347$	15.7346	−	1.71124i	0.844676	−	0.0918640i	0.520215	+	0.854035i	$0.325852\pi$
$348$		0			0
$349$	−11.5391	+	21.7650i	−0.617672	+	1.16505i	0.355436	+	0.934701i	$0.384332\pi$
$349$	−11.5391	+	21.7650i	−0.617672	+	1.16505i	−0.973107	+	0.230352i	$0.926012\pi$
$350$	−0.663875	+	4.04946i	−0.0354856	+	0.216453i
$351$		0			0
$352$	6.73596	+	7.93019i	0.359028	+	0.422681i
$353$	24.5491			1.30662			0.653308	−	0.757092i	$-0.273381\pi$
$353$	24.5491			1.30662			0.653308	+	0.757092i	$0.273381\pi$
$354$		0			0
$355$	2.40556			0.127674
$356$	−5.04219	−	5.93612i	−0.267236	−	0.314614i
$357$		0			0
$358$	−1.14958	+	7.01210i	−0.0607570	+	0.370601i
$359$	−13.3179	+	25.1201i	−0.702890	+	1.32579i	0.232647	+	0.972561i	$0.425261\pi$
$359$	−13.3179	+	25.1201i	−0.702890	+	1.32579i	−0.935537	+	0.353229i	$0.885084\pi$
$360$		0			0
$361$	−38.3657	+	4.17252i	−2.01925	+	0.219606i
$362$	7.37684	−	4.43850i	0.387718	−	0.233282i
$363$		0			0
$364$	−14.5063	+	3.19309i	−0.760339	+	0.167363i
$365$	17.8736	−	6.02232i	0.935548	−	0.315223i
$366$		0			0
$367$	2.37199	+	8.54313i	0.123817	+	0.445948i	0.999304	−	0.0372929i	$-0.0118735\pi$
$367$	2.37199	+	8.54313i	0.123817	+	0.445948i	−0.875488	+	0.483241i	$0.839460\pi$
$368$	1.29587	+	1.22751i	0.0675517	+	0.0639884i
$369$		0			0
$370$	−6.30596	−	2.12473i	−0.327831	−	0.110459i
$371$	6.49468	+	0.706340i	0.337187	+	0.0366713i
$372$		0			0
$373$	−0.200379	−	3.69578i	−0.0103753	−	0.191360i	−0.999126	−	0.0417903i	$-0.986694\pi$
$373$	−0.200379	−	3.69578i	−0.0103753	−	0.191360i	0.988751	−	0.149570i	$-0.0477889\pi$
$374$	6.51143	+	4.94986i	0.336698	+	0.255951i
$375$		0			0
$376$	−20.1300	−	12.1118i	−1.03812	−	0.624618i
$377$	−8.41750	−	3.89435i	−0.433523	−	0.200569i
$378$		0			0
$379$	14.0091	+	20.6619i	0.719600	+	1.06133i	0.994988	+	0.0999971i	$0.0318834\pi$
$379$	14.0091	+	20.6619i	0.719600	+	1.06133i	−0.275388	+	0.961333i	$0.588806\pi$
$380$	−11.5149	+	16.9831i	−0.590700	+	0.871217i
$381$		0			0
$382$	0.537331	−	9.91048i	0.0274922	−	0.507064i
$383$	−22.1521	+	26.0794i	−1.13192	+	1.33260i	−0.195908	+	0.980622i	$0.562765\pi$
$383$	−22.1521	+	26.0794i	−1.13192	+	1.33260i	−0.936010	+	0.351974i	$0.885510\pi$
$384$		0			0
$385$	0.503292	−	9.28267i	0.0256501	−	0.473088i
$386$	−2.67767	−	6.72044i	−0.136290	−	0.342062i
$387$		0			0
$388$	−13.0911	−	19.3079i	−0.664600	−	0.980212i
$389$	14.3445	−	36.0020i	0.727296	−	1.82538i	0.190445	−	0.981698i	$-0.439007\pi$
$389$	14.3445	−	36.0020i	0.727296	−	1.82538i	0.536851	−	0.843677i	$-0.319614\pi$
$390$		0			0
$391$	5.85137	+	3.52065i	0.295917	+	0.178047i
$392$	−3.28204	+	3.10892i	−0.165768	+	0.157024i
$393$		0			0
$394$	−0.0748300	−	1.38016i	−0.00376988	−	0.0695313i
$395$	−16.2125	+	7.50071i	−0.815741	+	0.377402i
$396$		0			0
$397$	31.8745	+	10.7398i	1.59973	+	0.539013i	0.971097	−	0.238686i	$-0.0767166\pi$
$397$	31.8745	+	10.7398i	1.59973	+	0.539013i	0.628637	+	0.777699i	$0.283613\pi$
$398$	0.182208	+	1.11142i	0.00913325	+	0.0557104i
$399$		0			0
$400$	−1.11263	−	4.00733i	−0.0556314	−	0.200366i
$401$	−6.87341	−	12.9646i	−0.343242	−	0.647423i	0.650452	−	0.759547i	$-0.274579\pi$
$401$	−6.87341	−	12.9646i	−0.343242	−	0.647423i	−0.993694	+	0.112124i	$0.964235\pi$
$402$		0			0
$403$	2.86591	−	0.630834i	0.142761	−	0.0314241i
$404$	−0.805915	+	2.90264i	−0.0400958	+	0.144412i
$405$		0			0
$406$	−5.59074	+	0.608030i	−0.277464	+	0.0301760i
$407$	−11.7589	−	2.58833i	−0.582868	−	0.128299i
$408$		0			0
$409$	4.89277	−	29.8446i	0.241932	−	1.47572i	−0.534312	−	0.845288i	$-0.679429\pi$
$409$	4.89277	−	29.8446i	0.241932	−	1.47572i	0.776244	−	0.630433i	$-0.217123\pi$
$410$	6.03022	−	4.58405i	0.297811	−	0.226390i
$411$		0			0
$412$	−22.1641			−1.09195
$413$	19.8034	−	11.8559i	0.974461	−	0.583389i
$414$		0			0
$415$	10.7259	+	12.6276i	0.526516	+	0.619862i
$416$	−13.6070	+	10.3438i	−0.667138	+	0.507145i
$417$		0			0
$418$	4.05706	−	7.65242i	0.198437	−	0.374292i
$419$	−0.527064	−	0.116015i	−0.0257487	−	0.00566773i	0.202077	−	0.979370i	$-0.435231\pi$
$419$	−0.527064	−	0.116015i	−0.0257487	−	0.00566773i	−0.227826	+	0.973702i	$0.573162\pi$
$420$		0			0
$421$	−12.7785	+	7.68855i	−0.622784	+	0.374717i	−0.791697	−	0.610914i	$-0.790802\pi$
$421$	−12.7785	+	7.68855i	−0.622784	+	0.374717i	0.168912	+	0.985631i	$0.445974\pi$
$422$	0.764815	−	2.75461i	0.0372306	−	0.134093i
$423$		0			0
$424$	4.58956	−	1.54640i	0.222889	−	0.0751000i
$425$	−7.45295	−	14.0578i	−0.361521	−	0.681901i
$426$		0			0
$427$	−4.16744	−	3.94761i	−0.201677	−	0.191038i
$428$	3.73798	+	22.8007i	0.180682	+	1.10211i
$429$		0			0
$430$	−4.75703	−	0.517358i	−0.229404	−	0.0249492i
$431$	16.6034	−	7.68156i	0.799758	−	0.370008i	0.0229435	−	0.999737i	$-0.492696\pi$
$431$	16.6034	−	7.68156i	0.799758	−	0.370008i	0.776815	+	0.629729i	$0.216834\pi$
$432$		0			0
$433$	−21.5168	−	16.3567i	−1.03403	−	0.786051i	−0.0568344	−	0.998384i	$-0.518101\pi$
$433$	−21.5168	−	16.3567i	−1.03403	−	0.786051i	−0.977197	+	0.212333i	$0.931894\pi$
$434$	1.29179	−	1.22365i	0.0620081	−	0.0587372i
$435$		0			0
$436$	−16.0156	−	7.40962i	−0.767010	−	0.354857i
$437$	2.67662	−	6.71781i	0.128040	−	0.321356i
$438$		0			0
$439$	4.74442	−	6.99750i	0.226439	−	0.333972i	−0.697450	−	0.716634i	$-0.745682\pi$
$439$	4.74442	−	6.99750i	0.226439	−	0.333972i	0.923889	+	0.382661i	$0.124992\pi$
$440$	−2.55085	−	6.40214i	−0.121607	−	0.305210i
$441$		0			0
$442$	−8.69838	+	10.2405i	−0.413740	+	0.487092i
$443$	3.71123	−	4.36920i	0.176326	−	0.207587i	−0.666899	−	0.745149i	$-0.732379\pi$
$443$	3.71123	−	4.36920i	0.176326	−	0.207587i	0.843225	+	0.537562i	$0.180654\pi$
$444$		0			0
$445$	2.96387	+	7.43877i	0.140501	+	0.352631i
$446$	−2.55058	+	3.76183i	−0.120774	+	0.178128i
$447$		0			0
$448$	0.330795	−	0.830233i	0.0156286	−	0.0392248i
$449$	−15.7160	−	7.27098i	−0.741682	−	0.343139i	0.0123962	−	0.999923i	$-0.496054\pi$
$449$	−15.7160	−	7.27098i	−0.741682	−	0.343139i	−0.754078	+	0.656784i	$0.771916\pi$
$450$		0			0
$451$	9.95045	−	9.42557i	0.468549	−	0.443833i
$452$	−15.8605	−	12.0569i	−0.746016	−	0.567107i
$453$		0			0
$454$	12.4490	−	5.75950i	0.584259	−	0.270307i
$455$	15.1816	+	1.65110i	0.711727	+	0.0774049i
$456$		0			0
$457$	−0.265306	−	1.61829i	−0.0124105	−	0.0757005i	0.979895	−	0.199513i	$-0.0639361\pi$
$457$	−0.265306	−	1.61829i	−0.0124105	−	0.0757005i	−0.992306	+	0.123813i	$0.960488\pi$
$458$	−6.86942	−	6.50706i	−0.320987	−	0.304055i
$459$		0			0
$460$	−1.20680	−	2.27627i	−0.0562675	−	0.106132i
$461$	21.2302	−	7.15329i	0.988789	−	0.333162i	0.221990	−	0.975049i	$-0.428745\pi$
$461$	21.2302	−	7.15329i	0.988789	−	0.333162i	0.766799	+	0.641887i	$0.221848\pi$
$462$		0			0
$463$	−6.70775	+	24.1591i	−0.311736	+	1.12277i	0.627251	+	0.778817i	$0.284180\pi$
$463$	−6.70775	+	24.1591i	−0.311736	+	1.12277i	−0.938987	+	0.343953i	$0.888234\pi$
$464$	4.88378	−	2.93847i	0.226724	−	0.136415i
$465$		0			0
$466$	11.3793	+	2.50477i	0.527136	+	0.116031i
$467$	−14.5746	+	27.4906i	−0.674432	+	1.27211i	0.275993	+	0.961160i	$0.410993\pi$
$467$	−14.5746	+	27.4906i	−0.674432	+	1.27211i	−0.950425	+	0.310954i	$0.899351\pi$
$468$		0			0
$469$	31.8580	−	24.2179i	1.47107	−	1.11828i
$470$	7.00153	+	8.24284i	0.322957	+	0.380214i
$471$		0			0
$472$	9.63349	−	14.1411i	0.443417	−	0.650895i
$473$	−8.65823			−0.398106
$474$		0			0
$475$	−13.4135	+	10.1966i	−0.615452	+	0.467854i
$476$	5.64979	−	34.4622i	0.258958	−	1.57957i
$477$		0			0
$478$	14.1995	+	3.12556i	0.649472	+	0.142960i
$479$	−36.2911	+	3.94690i	−1.65818	+	0.180338i	−0.888752	−	0.458389i	$-0.848427\pi$
$479$	−36.2911	+	3.94690i	−1.65818	+	0.180338i	−0.769433	+	0.638728i	$0.779461\pi$
$480$		0			0
$481$	5.29144	−	19.0580i	0.241269	−	0.868971i
$482$	−6.02802	+	1.32687i	−0.274569	+	0.0604371i
$483$		0			0
$484$	5.74028	+	10.8273i	0.260922	+	0.492151i
$485$	6.41621	+	23.1091i	0.291345	+	1.04933i
$486$		0			0
$487$	−5.60906	−	34.2137i	−0.254171	−	1.55037i	−0.737751	−	0.675073i	$-0.764112\pi$
$487$	−5.60906	−	34.2137i	−0.254171	−	1.55037i	0.483580	−	0.875300i	$-0.339336\pi$
$488$	−4.03269	−	1.35877i	−0.182552	−	0.0615088i
$489$		0			0
$490$	1.88881	−	0.873857i	0.0853278	−	0.0394768i
$491$	−1.43036	−	26.3815i	−0.0645514	−	1.19058i	−0.833961	−	0.551824i	$-0.813932\pi$
$491$	−1.43036	−	26.3815i	−0.0645514	−	1.19058i	0.769409	−	0.638756i	$-0.220551\pi$
$492$		0			0
$493$	15.8309	−	14.9958i	0.712986	−	0.675376i
$494$	12.1915	+	7.33538i	0.548521	+	0.330034i
$495$		0			0
$496$	−0.667494	+	1.67528i	−0.0299714	+	0.0752225i
$497$	2.43303	+	3.58845i	0.109136	+	0.160964i
$498$		0			0
$499$	3.93228	+	9.86929i	0.176033	+	0.441810i	0.990346	−	0.138616i	$-0.0442653\pi$
$499$	3.93228	+	9.86929i	0.176033	+	0.441810i	−0.814313	+	0.580426i	$0.802886\pi$
$500$	−1.05689	+	19.4932i	−0.0472656	+	0.871762i
$501$		0			0
$502$	−5.90371	+	6.95038i	−0.263495	+	0.310211i
$503$	−1.93400	+	35.6705i	−0.0862327	+	1.59047i	0.560764	+	0.827975i	$0.310507\pi$
$503$	−1.93400	+	35.6705i	−0.0862327	+	1.59047i	−0.646997	+	0.762492i	$0.723975\pi$
$504$		0			0
$505$	1.73807	−	2.56346i	0.0773431	−	0.114073i
$506$	0.610316	+	0.900149i	0.0271319	+	0.0400165i
$507$		0			0
$508$	21.9099	+	10.1366i	0.972092	+	0.449738i
$509$	6.28832	+	3.78356i	0.278725	+	0.167703i	0.648052	−	0.761596i	$-0.275584\pi$
$509$	6.28832	+	3.78356i	0.278725	+	0.167703i	−0.369327	+	0.929300i	$0.620412\pi$
$510$		0			0
$511$	27.0615	+	20.5716i	1.19713	+	0.910034i
$512$	−1.02048	−	18.8217i	−0.0450993	−	0.831808i
$513$		0			0
$514$	−3.89749	−	0.423877i	−0.171911	−	0.0186964i
$515$	21.5943	+	7.27597i	0.951559	+	0.320618i
$516$		0			0
$517$	14.2070	+	13.4576i	0.624824	+	0.591865i
$518$	−3.20846	−	11.5558i	−0.140972	−	0.507734i
$519$		0			0
$520$	10.7283	−	3.61479i	0.470468	−	0.158519i
$521$	16.4294	−	3.61639i	0.719786	−	0.158437i	0.160051	−	0.987109i	$-0.448834\pi$
$521$	16.4294	−	3.61639i	0.719786	−	0.158437i	0.559735	+	0.828672i	$0.310903\pi$
$522$		0			0
$523$	32.2937	−	19.4304i	1.41210	−	0.849634i	0.413945	−	0.910302i	$-0.364151\pi$
$523$	32.2937	−	19.4304i	1.41210	−	0.849634i	0.998158	+	0.0606677i	$0.0193230\pi$
$524$	7.48843	−	0.814416i	0.327134	−	0.0355779i
$525$		0			0
$526$	4.17118	−	7.86768i	0.181872	−	0.343047i
$527$	−1.11619	+	6.80844i	−0.0486219	+	0.296580i
$528$		0			0
$529$	−14.3021	−	16.8377i	−0.621829	−	0.732073i
$530$	−2.22955			−0.0968454
$531$		0			0
$532$	−36.9807			−1.60332
$533$	14.5759	+	17.1600i	0.631351	+	0.743284i
$534$		0			0
$535$	3.84306	−	23.4416i	0.166150	−	1.01347i
$536$	13.8960	−	26.2107i	0.600217	−	1.13213i
$537$		0			0
$538$	17.8450	−	1.94076i	0.769354	−	0.0836723i
$539$	3.22666	−	1.94142i	0.138982	−	0.0836229i
$540$		0			0
$541$	3.35385	−	0.738239i	0.144193	−	0.0317394i	−0.142287	−	0.989825i	$-0.545446\pi$
$541$	3.35385	−	0.738239i	0.144193	−	0.0317394i	0.286481	+	0.958086i	$0.407515\pi$
$542$	1.35405	−	0.456232i	0.0581613	−	0.0195968i
$543$		0			0
$544$	−10.7507	−	38.7207i	−0.460934	−	1.66014i
$545$	13.1715	+	12.4767i	0.564206	+	0.534444i
$546$		0			0
$547$	−17.4064	−	5.86489i	−0.744243	−	0.250765i	−0.0784675	−	0.996917i	$-0.525003\pi$
$547$	−17.4064	−	5.86489i	−0.744243	−	0.250765i	−0.665776	+	0.746152i	$0.731899\pi$
$548$	−6.88246	−	0.748513i	−0.294004	−	0.0319749i
$549$		0			0
$550$	−0.137186	−	2.53025i	−0.00584965	−	0.107890i
$551$	−18.3826	−	13.9741i	−0.783126	−	0.595317i
$552$		0			0
$553$	−27.5868	−	16.5984i	−1.17311	−	0.705836i
$554$	3.79378	+	1.75519i	0.161182	+	0.0745708i
$555$		0			0
$556$	0.852519	+	1.25737i	0.0361548	+	0.0533244i
$557$	−3.60039	+	5.31018i	−0.152554	+	0.225000i	−0.896285	−	0.443479i	$-0.853744\pi$
$557$	−3.60039	+	5.31018i	−0.152554	+	0.225000i	0.743731	+	0.668479i	$0.233054\pi$
$558$		0			0
$559$	0.770017	−	14.2021i	0.0325683	−	0.600686i
$560$	−6.07551	+	7.15264i	−0.256737	+	0.302254i
$561$		0			0
$562$	−0.145454	+	2.68274i	−0.00613560	+	0.113165i
$563$	−9.17965	−	23.0392i	−0.386876	−	0.970985i	−0.985457	−	0.169923i	$-0.945648\pi$
$563$	−9.17965	−	23.0392i	−0.386876	−	0.970985i	0.598581	−	0.801062i	$-0.295731\pi$
$564$		0			0
$565$	11.4948	+	16.9536i	0.483590	+	0.713242i
$566$	6.24139	−	15.6647i	0.262345	−	0.658436i
$567$		0			0
$568$	2.75397	+	1.65701i	0.115554	+	0.0695265i
$569$	3.15620	−	2.98971i	0.132315	−	0.125335i	−0.618681	−	0.785642i	$-0.712333\pi$
$569$	3.15620	−	2.98971i	0.132315	−	0.125335i	0.750995	+	0.660307i	$0.229574\pi$
$570$		0			0
$571$	1.75233	+	32.3199i	0.0733328	+	1.35254i	0.771326	+	0.636440i	$0.219594\pi$
$571$	1.75233	+	32.3199i	0.0733328	+	1.35254i	−0.697993	+	0.716104i	$0.745923\pi$
$572$	8.32454	−	3.85134i	0.348066	−	0.161033i
$573$		0			0
$574$	12.9373	+	4.35908i	0.539992	+	0.181944i
$575$	−0.342269	−	2.08775i	−0.0142736	−	0.0870652i
$576$		0			0
$577$	−3.57414	−	12.8729i	−0.148793	−	0.535905i	−0.999940	−	0.0109766i	$-0.996506\pi$
$577$	−3.57414	−	12.8729i	−0.148793	−	0.535905i	0.851147	−	0.524928i	$-0.175908\pi$
$578$	−9.89904	−	18.6716i	−0.411746	−	0.776635i
$579$		0			0
$580$	−8.03450	+	1.76853i	−0.333615	+	0.0734341i
$581$	−7.98852	+	28.7720i	−0.331420	+	1.19367i
$582$		0			0
$583$	−4.01055	+	0.436173i	−0.166100	+	0.0180644i
$584$	24.6107	+	5.41722i	1.01840	+	0.224166i
$585$		0			0
$586$	2.86889	−	17.4995i	0.118513	−	0.722897i
$587$	−13.7162	+	10.4268i	−0.566130	+	0.430361i	−0.848691	−	0.528888i	$-0.822609\pi$
$587$	−13.7162	+	10.4268i	−0.566130	+	0.430361i	0.282561	+	0.959249i	$0.408816\pi$
$588$		0			0
$589$	7.30601			0.301039
$590$	−6.28134	+	4.75312i	−0.258599	+	0.195683i
$591$		0			0
$592$	7.86891	+	9.26399i	0.323410	+	0.380748i
$593$	34.7463	−	26.4135i	1.42686	−	1.08467i	0.444901	−	0.895580i	$-0.353239\pi$
$593$	34.7463	−	26.4135i	1.42686	−	1.08467i	0.981959	−	0.189092i	$-0.0605544\pi$
$594$		0			0
$595$	−16.8177	+	31.7216i	−0.689459	+	1.30046i
$596$	−5.25360	−	1.15641i	−0.215196	−	0.0473682i
$597$		0			0
$598$	−1.53080	+	0.921050i	−0.0625990	+	0.0376645i
$599$	−5.63464	+	20.2942i	−0.230225	+	0.829197i	0.754679	+	0.656095i	$0.227793\pi$
$599$	−5.63464	+	20.2942i	−0.230225	+	0.829197i	−0.984904	+	0.173102i	$0.944621\pi$
$600$		0			0
$601$	27.6183	−	9.30567i	1.12657	−	0.379586i	0.306514	−	0.951866i	$-0.400837\pi$
$601$	27.6183	−	9.30567i	1.12657	−	0.379586i	0.820058	+	0.572280i	$0.193941\pi$
$602$	−4.03960	−	7.61950i	−0.164642	−	0.310547i
$603$		0			0
$604$	9.56066	+	9.05634i	0.389018	+	0.368497i
$605$	−2.03835	−	12.4334i	−0.0828707	−	0.505489i
$606$		0			0
$607$	2.11295	+	0.229797i	0.0857618	+	0.00932716i	0.150899	−	0.988549i	$-0.451783\pi$
$607$	2.11295	+	0.229797i	0.0857618	+	0.00932716i	−0.0651375	+	0.997876i	$0.520749\pi$
$608$	−38.6211	+	17.8680i	−1.56629	+	0.724644i
$609$		0			0
$610$	1.55957	+	1.18555i	0.0631452	+	0.0480017i
$611$	−23.3381	+	22.1070i	−0.944158	+	0.894354i
$612$		0			0
$613$	14.0748	+	6.51167i	0.568474	+	0.263004i	0.683003	−	0.730416i	$-0.260674\pi$
$613$	14.0748	+	6.51167i	0.568474	+	0.263004i	−0.114529	+	0.993420i	$0.536536\pi$
$614$	1.13437	−	2.84706i	0.0457796	−	0.114898i
$615$		0			0
$616$	6.97032	−	10.2805i	0.280842	−	0.414211i
$617$	−1.42480	−	3.57598i	−0.0573603	−	0.143963i	0.897504	−	0.441007i	$-0.145379\pi$
$617$	−1.42480	−	3.57598i	−0.0573603	−	0.143963i	−0.954864	+	0.297044i	$0.903999\pi$
$618$		0			0
$619$	6.81756	−	8.02625i	0.274021	−	0.322602i	−0.607888	−	0.794023i	$-0.707983\pi$
$619$	6.81756	−	8.02625i	0.274021	−	0.322602i	0.881908	+	0.471421i	$0.156259\pi$
$620$	1.68513	−	1.98389i	0.0676764	−	0.0796748i
$621$		0			0
$622$	−1.36398	−	3.42334i	−0.0546908	−	0.137264i
$623$	−8.09894	+	11.9450i	−0.324477	+	0.478568i
$624$		0			0
$625$	3.31996	−	8.33248i	0.132799	−	0.333299i
$626$	−2.09978	−	0.971464i	−0.0839243	−	0.0388275i
$627$		0			0
$628$	11.5053	−	10.8984i	0.459113	−	0.434895i
$629$	37.0201	+	28.1420i	1.47609	+	1.12209i
$630$		0			0
$631$	−25.6569	+	11.8701i	−1.02138	+	0.472542i	−0.857798	−	0.513987i	$-0.828168\pi$
$631$	−25.6569	+	11.8701i	−1.02138	+	0.472542i	−0.163586	+	0.986529i	$0.552306\pi$
$632$	−23.7274	−	2.58051i	−0.943824	−	0.102647i
$633$		0			0
$634$	−0.986334	−	6.01637i	−0.0391723	−	0.238941i
$635$	−18.0190	−	17.0685i	−0.715063	−	0.677343i
$636$		0			0
$637$	2.89756	+	5.46538i	0.114805	+	0.216546i
$638$	3.29092	−	1.10884i	0.130289	−	0.0438994i
$639$		0			0
$640$	−5.08386	+	18.3104i	−0.200957	+	0.723782i
$641$	−15.0213	+	9.03802i	−0.593306	+	0.356980i	−0.780323	−	0.625376i	$-0.784945\pi$
$641$	−15.0213	+	9.03802i	−0.593306	+	0.356980i	0.187017	+	0.982357i	$0.440118\pi$
$642$		0			0
$643$	−11.2445	−	2.47510i	−0.443440	−	0.0976086i	−0.0123629	−	0.999924i	$-0.503935\pi$
$643$	−11.2445	−	2.47510i	−0.443440	−	0.0976086i	−0.431077	+	0.902315i	$0.641866\pi$
$644$	2.17501	−	4.10250i	0.0857074	−	0.161661i
$645$		0			0
$646$	−26.6307	+	20.2441i	−1.04777	+	0.796494i
$647$	2.39944	+	2.82484i	0.0943318	+	0.111056i	0.807302	−	0.590138i	$-0.200927\pi$
$647$	2.39944	+	2.82484i	0.0943318	+	0.111056i	−0.712971	+	0.701194i	$0.752651\pi$
$648$		0			0
$649$	−10.3691	+	9.77881i	−0.407023	+	0.383852i
$650$	4.16259			0.163270
$651$		0			0
$652$	−18.1243	+	13.7777i	−0.709802	+	0.539577i
$653$	0.745228	−	4.54569i	0.0291630	−	0.177887i	−0.968229	−	0.250067i	$-0.919547\pi$
$653$	0.745228	−	4.54569i	0.0291630	−	0.177887i	0.997392	+	0.0721803i	$0.0229957\pi$
$654$		0			0
$655$	−7.56328	−	1.66480i	−0.295522	−	0.0650493i
$656$	−13.7551	+	1.49596i	−0.537048	+	0.0584075i
$657$		0			0
$658$	−5.21464	+	18.7814i	−0.203288	+	0.732176i
$659$	−4.59591	+	1.01164i	−0.179031	+	0.0394077i	−0.303581	−	0.952806i	$-0.598182\pi$
$659$	−4.59591	+	1.01164i	−0.179031	+	0.0394077i	0.124550	+	0.992213i	$0.460251\pi$
$660$		0			0
$661$	−22.4727	−	42.3881i	−0.874088	−	1.64870i	−0.754907	−	0.655832i	$-0.772318\pi$
$661$	−22.4727	−	42.3881i	−0.874088	−	1.64870i	−0.119181	−	0.992873i	$-0.538027\pi$
$662$	−0.682467	−	2.45802i	−0.0265248	−	0.0955338i
$663$		0			0
$664$	3.58127	+	21.8448i	0.138980	+	0.847742i
$665$	36.0301	+	12.1399i	1.39719	+	0.470767i
$666$		0			0
$667$	2.63140	−	1.21742i	0.101888	−	0.0471386i
$668$	−1.75532	−	32.3749i	−0.0679152	−	1.25262i
$669$		0			0
$670$	−9.91505	+	9.39203i	−0.383052	+	0.362846i
$671$	3.03731	+	1.82749i	0.117254	+	0.0705495i
$672$		0			0
$673$	−5.08659	+	12.7664i	−0.196074	+	0.492108i	−0.993835	−	0.110865i	$-0.964638\pi$
$673$	−5.08659	+	12.7664i	−0.196074	+	0.492108i	0.797762	+	0.602973i	$0.206017\pi$
$674$	8.06158	+	11.8899i	0.310521	+	0.457984i
$675$		0			0
$676$	−2.22615	−	5.58723i	−0.0856213	−	0.214893i
$677$	1.79708	−	33.1452i	0.0690675	−	1.27388i	−0.734478	−	0.678632i	$-0.762573\pi$
$677$	1.79708	−	33.1452i	0.0690675	−	1.27388i	0.803546	−	0.595243i	$-0.202944\pi$
$678$		0			0
$679$	−27.9832	+	32.9443i	−1.07390	+	1.26429i
$680$	−1.44099	+	26.5776i	−0.0552596	+	1.01920i
$681$		0			0
$682$	−0.616613	+	0.909436i	−0.0236113	+	0.0348241i
$683$	2.96459	+	4.37244i	0.113437	+	0.167307i	0.880169	−	0.474660i	$-0.157429\pi$
$683$	2.96459	+	4.37244i	0.113437	+	0.167307i	−0.766732	+	0.641967i	$0.778119\pi$
$684$		0			0
$685$	6.45982	+	2.98863i	0.246817	+	0.114190i
$686$	−7.87184	−	4.73633i	−0.300548	−	0.180834i
$687$		0			0
$688$	6.95828	+	5.28955i	0.265282	+	0.201662i
$689$	−0.358780	−	6.61731i	−0.0136684	−	0.252099i
$690$		0			0
$691$	−20.6362	−	2.24433i	−0.785040	−	0.0853782i	−0.293185	−	0.956056i	$-0.594715\pi$
$691$	−20.6362	−	2.24433i	−0.785040	−	0.0853782i	−0.491855	+	0.870677i	$0.663681\pi$
$692$	22.5148	+	7.58613i	0.855885	+	0.288381i
$693$		0			0
$694$	−7.06761	−	6.69479i	−0.268283	−	0.254131i
$695$	−0.417836	−	1.50491i	−0.0158494	−	0.0570845i
$696$		0			0
$697$	−50.1638	+	16.9022i	−1.90009	+	0.640215i
$698$	14.7980	−	3.25728i	0.560111	−	0.123290i
$699$		0			0
$700$	−9.27041	+	5.57782i	−0.350389	+	0.210822i
$701$	−14.7831	+	1.60776i	−0.558352	+	0.0607244i	−0.382944	−	0.923771i	$-0.625090\pi$
$701$	−14.7831	+	1.60776i	−0.558352	+	0.0607244i	−0.175408	+	0.984496i	$0.556124\pi$
$702$		0			0
$703$	23.0660	−	43.5071i	0.869950	−	1.64090i
$704$	−0.0892834	+	0.544604i	−0.00336499	+	0.0205256i
$705$		0			0
$706$	−9.77528	−	11.5083i	−0.367897	−	0.433122i
$707$	5.58193			0.209930
$708$		0			0
$709$	−36.5688			−1.37337			−0.686685	−	0.726955i	$-0.740935\pi$
$709$	−36.5688			−1.37337			−0.686685	+	0.726955i	$0.740935\pi$
$710$	−0.957876	−	1.12770i	−0.0359484	−	0.0423218i
$711$		0			0
$712$	−1.73086	+	10.5578i	−0.0648666	+	0.395669i
$713$	−0.429701	+	0.810501i	−0.0160924	+	0.0303535i
$714$		0			0
$715$	−9.37485	+	1.01958i	−0.350600	+	0.0381300i
$716$	−16.0528	+	9.65864i	−0.599921	+	0.360961i
$717$		0			0
$718$	17.0791	−	3.75940i	0.637387	−	0.140300i
$719$	35.2433	−	11.8749i	1.31435	−	0.442857i	0.427127	−	0.904191i	$-0.359526\pi$
$719$	35.2433	−	11.8749i	1.31435	−	0.442857i	0.887226	+	0.461334i	$0.152629\pi$
$720$		0			0
$721$	10.9871	+	39.5721i	0.409182	+	1.47374i
$722$	17.2330	+	16.3240i	0.641345	+	0.607515i
$723$		0			0
$724$	21.5103	+	7.24766i	0.799424	+	0.269357i
$725$	−6.71592	−	0.730400i	−0.249423	−	0.0271264i
$726$		0			0
$727$	0.327349	+	6.03760i	0.0121407	+	0.223922i	0.998307	+	0.0581636i	$0.0185245\pi$
$727$	0.327349	+	6.03760i	0.0121407	+	0.223922i	−0.986166	+	0.165759i	$0.946993\pi$
$728$	16.2432	+	12.3477i	0.602012	+	0.457638i
$729$		0			0
$730$	−9.94035	−	5.98091i	−0.367909	−	0.221363i
$731$	30.3490	+	14.0409i	1.12250	+	0.519323i
$732$		0			0
$733$	15.3441	+	22.6308i	0.566747	+	0.835889i	0.997790	−	0.0664419i	$-0.0211647\pi$
$733$	15.3441	+	22.6308i	0.566747	+	0.835889i	−0.431043	+	0.902331i	$0.641854\pi$
$734$	3.06042	−	4.51378i	0.112962	−	0.166607i
$735$		0			0
$736$	0.289276	−	5.33538i	0.0106629	−	0.196665i
$737$	−15.9979	+	18.8342i	−0.589292	+	0.693768i
$738$		0			0
$739$	1.57736	−	29.0926i	0.0580240	−	1.07019i	−0.814044	−	0.580804i	$-0.802738\pi$
$739$	1.57736	−	29.0926i	0.0580240	−	1.07019i	0.872068	−	0.489385i	$-0.162779\pi$
$740$	−6.49382	−	16.2983i	−0.238718	−	0.599136i
$741$		0			0
$742$	−2.25501	−	3.32590i	−0.0827842	−	0.122098i
$743$	7.41630	−	18.6135i	0.272078	−	0.682863i	−0.727918	−	0.685664i	$-0.759512\pi$
$743$	7.41630	−	18.6135i	0.272078	−	0.682863i	0.999996	+	0.00280029i	$0.000891362\pi$
$744$		0			0
$745$	4.73893	+	2.85132i	0.173621	+	0.104464i
$746$	−1.65275	+	1.56557i	−0.0605116	+	0.0573196i
$747$		0			0
$748$	1.16750	+	21.5333i	0.0426880	+	0.787335i
$749$	38.8557	−	17.9765i	1.41975	−	0.656849i
$750$		0			0
$751$	8.92616	+	3.00757i	0.325720	+	0.109748i	0.477411	−	0.878680i	$-0.341575\pi$
$751$	8.92616	+	3.00757i	0.325720	+	0.109748i	−0.151691	+	0.988428i	$0.548472\pi$
$752$	−3.19601	−	19.4948i	−0.116547	−	0.710903i
$753$		0			0
$754$	1.52616	+	5.49673i	0.0555795	+	0.200179i
$755$	−6.34190	−	11.9621i	−0.230805	−	0.435345i
$756$		0			0
$757$	7.24559	−	1.59488i	0.263346	−	0.0579667i	−0.0813349	−	0.996687i	$-0.525918\pi$
$757$	7.24559	−	1.59488i	0.263346	−	0.0579667i	0.344680	+	0.938720i	$0.387987\pi$
$758$	4.10774	−	14.7947i	0.149200	−	0.537369i
$759$		0			0
$760$	28.0203	−	3.04739i	1.01640	−	0.110541i
$761$	−37.8663	−	8.33501i	−1.37265	−	0.302144i	−0.533390	−	0.845869i	$-0.679082\pi$
$761$	−37.8663	−	8.33501i	−1.37265	−	0.302144i	−0.839263	+	0.543725i	$0.817013\pi$
$762$		0			0
$763$	−5.29001	+	32.2676i	−0.191511	+	1.16817i
$764$	20.8320	−	15.8361i	0.753675	−	0.572929i
$765$		0			0
$766$	21.0465			0.760443
$767$	−15.1181	−	17.8782i	−0.545882	−	0.645543i
$768$		0			0
$769$	31.2907	+	36.8382i	1.12837	+	1.32842i	0.937971	+	0.346714i	$0.112703\pi$
$769$	31.2907	+	36.8382i	1.12837	+	1.32842i	0.190400	+	0.981707i	$0.439022\pi$
$770$	−4.55202	+	3.46036i	−0.164043	+	0.124703i
$771$		0			0
$772$	8.93414	−	16.8516i	0.321547	−	0.606501i
$773$	−48.5796	−	10.6932i	−1.74729	−	0.384607i	−0.777562	−	0.628806i	$-0.783544\pi$
$773$	−48.5796	−	10.6932i	−1.74729	−	0.384607i	−0.969725	+	0.244199i	$0.921475\pi$
$774$		0			0
$775$	1.83149	−	1.10197i	0.0657889	−	0.0395839i
$776$	−8.57262	+	30.8758i	−0.307739	+	1.10838i
$777$		0			0
$778$	−22.5892	+	7.61120i	−0.809864	+	0.272875i
$779$	26.2566	+	49.5253i	0.940742	+	1.77443i
$780$		0			0
$781$	−1.94366	−	1.84113i	−0.0695495	−	0.0658808i
$782$	−0.679532	−	4.14496i	−0.0243000	−	0.148223i
$783$		0			0
$784$	−3.77921	−	0.411014i	−0.134972	−	0.0146791i
$785$	−14.7873	+	6.84133i	−0.527781	+	0.244177i
$786$		0			0
$787$	13.0215	+	9.89870i	0.464167	+	0.352850i	0.810970	−	0.585087i	$-0.198940\pi$
$787$	13.0215	+	9.89870i	0.464167	+	0.352850i	−0.346803	+	0.937938i	$0.612733\pi$
$788$	2.64566	−	2.50611i	0.0942479	−	0.0892763i
$789$		0			0
$790$	9.97197	+	4.61352i	0.354787	+	0.164142i
$791$	−13.6641	+	34.2944i	−0.485841	+	1.21937i
$792$		0			0
$793$	−3.26776	+	4.81959i	−0.116042	+	0.171149i
$794$	−7.65751	−	19.2189i	−0.271755	−	0.682053i
$795$		0			0
$796$	−1.92236	+	2.26318i	−0.0681363	+	0.0802162i
$797$	−19.3161	+	22.7407i	−0.684213	+	0.805518i	−0.989158	−	0.146852i	$-0.953086\pi$
$797$	−19.3161	+	22.7407i	−0.684213	+	0.805518i	0.304946	+	0.952370i	$0.401362\pi$
$798$		0			0
$799$	−27.9747	−	70.2112i	−0.989674	−	2.48389i
$800$	−6.98658	+	10.3044i	−0.247013	+	0.364317i
$801$		0			0
$802$	−3.34073	+	8.38461i	−0.117965	+	0.296071i
$803$	−19.0509	−	8.81389i	−0.672292	−	0.311035i
$804$		0			0
$805$	−3.46586	+	3.28303i	−0.122155	+	0.115712i
$806$	−1.43691	−	1.09231i	−0.0506131	−	0.0384751i
$807$		0			0
$808$	3.75558	−	1.73752i	0.132121	−	0.0611256i
$809$	10.3735	+	1.12818i	0.364711	+	0.0396647i	0.288640	−	0.957438i	$-0.406797\pi$
$809$	10.3735	+	1.12818i	0.364711	+	0.0396647i	0.0760711	+	0.997102i	$0.475762\pi$
$810$		0			0
$811$	5.78301	+	35.2748i	0.203069	+	1.23867i	0.869814	+	0.493380i	$0.164239\pi$
$811$	5.78301	+	35.2748i	0.203069	+	1.23867i	−0.666745	+	0.745286i	$0.732313\pi$
$812$	−10.7644	−	10.1966i	−0.377758	−	0.357831i
$813$		0			0
$814$	3.46894	+	6.54311i	0.121586	+	0.229336i
$815$	22.1813	−	7.47375i	0.776977	−	0.261794i
$816$		0			0
$817$	9.47337	−	34.1200i	0.331431	−	1.19371i
$818$	−15.9391	+	9.59023i	−0.557297	+	0.335315i
$819$		0			0
$820$	19.5043	+	4.29322i	0.681119	+	0.149926i
$821$	21.5525	−	40.6524i	0.752188	−	1.41878i	−0.150557	−	0.988601i	$-0.548107\pi$
$821$	21.5525	−	40.6524i	0.752188	−	1.41878i	0.902745	−	0.430176i	$-0.141548\pi$
$822$		0			0
$823$	23.2145	−	17.6472i	0.809208	−	0.615144i	−0.116582	−	0.993181i	$-0.537194\pi$
$823$	23.2145	−	17.6472i	0.809208	−	0.615144i	0.925791	+	0.378037i	$0.123401\pi$
$824$	19.7101	+	23.2045i	0.686633	+	0.808367i
$825$		0			0
$826$	−13.4435	−	4.56269i	−0.467758	−	0.158756i
$827$	−34.7172			−1.20724			−0.603618	−	0.797274i	$-0.706275\pi$
$827$	−34.7172			−1.20724			−0.603618	+	0.797274i	$0.706275\pi$
$828$		0			0
$829$	−12.4510	+	9.46502i	−0.432442	+	0.328734i	−0.798646	−	0.601801i	$-0.794450\pi$
$829$	−12.4510	+	9.46502i	−0.432442	+	0.328734i	0.366205	+	0.930534i	$0.380657\pi$
$830$	1.64866	−	10.0564i	0.0572260	−	0.349063i
$831$		0			0
$832$	−0.885377	−	0.194886i	−0.0306949	−	0.00675647i
$833$	−14.4585	+	1.57246i	−0.500959	+	0.0544825i
$834$		0			0
$835$	−8.91776	+	32.1189i	−0.308612	+	1.11152i
$836$	22.3022	−	4.90907i	0.771336	−	0.169784i
$837$		0			0
$838$	0.155486	+	0.293278i	0.00537118	+	0.0101311i
$839$	−9.68603	−	34.8859i	−0.334399	−	1.20440i	−0.919387	−	0.393354i	$-0.871315\pi$
$839$	−9.68603	−	34.8859i	−0.334399	−	1.20440i	0.584988	−	0.811042i	$-0.301099\pi$
$840$		0			0
$841$	3.19387	+	19.4817i	0.110133	+	0.671784i
$842$	8.69261	+	2.92888i	0.299567	+	0.100936i
$843$		0			0
$844$	6.84075	−	3.16487i	0.235468	−	0.108939i
$845$	0.334766	+	6.17439i	0.0115163	+	0.212406i
$846$		0			0
$847$	16.4857	−	15.6161i	0.566455	−	0.536575i
$848$	3.48959	+	2.09962i	0.119833	+	0.0721011i
$849$		0			0
$850$	−3.62241	+	9.09156i	−0.124248	+	0.311838i
$851$	3.46989	+	5.11771i	0.118946	+	0.175433i
$852$		0			0
$853$	11.1742	+	28.0451i	0.382597	+	0.960246i	0.986584	+	0.163252i	$0.0521985\pi$
$853$	11.1742	+	28.0451i	0.382597	+	0.960246i	−0.603987	+	0.796994i	$0.706422\pi$
$854$	−0.191150	+	3.52556i	−0.00654103	+	0.120642i
$855$		0			0
$856$	20.5469	−	24.1896i	0.702277	−	0.826785i
$857$	−1.46317	+	26.9866i	−0.0499810	+	0.921846i	0.860797	+	0.508949i	$0.169966\pi$
$857$	−1.46317	+	26.9866i	−0.0499810	+	0.921846i	−0.910778	+	0.412897i	$0.864517\pi$
$858$		0			0
$859$	4.83941	−	7.13759i	0.165119	−	0.243532i	−0.736124	−	0.676847i	$-0.763346\pi$
$859$	4.83941	−	7.13759i	0.165119	−	0.243532i	0.901242	+	0.433315i	$0.142656\pi$
$860$	−7.07997	−	10.4422i	−0.241425	−	0.356075i
$861$		0			0
$862$	−10.2124	−	4.72476i	−0.347836	−	0.160926i
$863$	0.248106	+	0.149280i	0.00844562	+	0.00508156i	0.519770	−	0.854306i	$-0.326017\pi$
$863$	0.248106	+	0.149280i	0.00844562	+	0.00508156i	−0.511325	+	0.859388i	$0.670845\pi$
$864$		0			0
$865$	−19.4457	−	14.7822i	−0.661173	−	0.502611i
$866$	0.900023	+	16.6000i	0.0305840	+	0.564089i
$867$		0			0
$868$	4.66381	+	0.507220i	0.158300	+	0.0172162i
$869$	18.8403	+	6.34803i	0.639113	+	0.215342i
$870$		0			0
$871$	−29.4711	−	27.9165i	−0.998591	−	0.945915i
$872$	6.48495	+	23.3567i	0.219608	+	0.790957i
$873$		0			0
$874$	−4.21505	+	1.42021i	−0.142576	+	0.0480395i
$875$	35.3274	−	7.77614i	1.19428	−	0.262882i
$876$		0			0
$877$	−22.5678	+	13.5786i	−0.762060	+	0.458517i	−0.842805	−	0.538218i	$-0.819098\pi$
$877$	−22.5678	+	13.5786i	−0.762060	+	0.458517i	0.0807451	+	0.996735i	$0.474270\pi$
$878$	−5.16955	+	0.562222i	−0.174464	+	0.0189741i
$879$		0			0
$880$	2.71450	−	5.12009i	0.0915057	−	0.172598i
$881$	−4.64889	+	28.3570i	−0.156625	+	0.955371i	0.785194	+	0.619250i	$0.212563\pi$
$881$	−4.64889	+	28.3570i	−0.156625	+	0.955371i	−0.941819	+	0.336121i	$0.890885\pi$
$882$		0			0
$883$	28.4934	+	33.5450i	0.958879	+	1.12888i	0.991591	+	0.129414i	$0.0413097\pi$
$883$	28.4934	+	33.5450i	0.958879	+	1.12888i	−0.0327120	+	0.999465i	$0.510414\pi$
$884$	−35.4250			−1.19147
$885$		0			0
$886$	−3.52602			−0.118459
$887$	25.2838	+	29.7663i	0.848945	+	0.999456i	0.999940	+	0.0109211i	$0.00347638\pi$
$887$	25.2838	+	29.7663i	0.848945	+	0.999456i	−0.150995	+	0.988535i	$0.548248\pi$
$888$		0			0
$889$	7.23689	−	44.1431i	0.242717	−	1.48051i
$890$	2.30702	−	4.35150i	0.0773314	−	0.145863i
$891$		0			0
$892$	−11.9128	+	1.29559i	−0.398870	+	0.0433797i
$893$	−68.5778	+	41.2619i	−2.29487	+	1.38078i
$894$		0			0
$895$	18.8108	−	4.14058i	0.628777	−	0.138404i
$896$	−32.4562	+	10.9358i	−1.08428	+	0.365338i
$897$		0			0
$898$	2.84943	+	10.2627i	0.0950868	+	0.342472i
$899$	2.12665	+	2.01447i	0.0709278	+	0.0671864i
$900$		0			0
$901$	14.7652	+	4.97497i	0.491899	+	0.165740i
$902$	−8.38081	−	0.911468i	−0.279050	−	0.0303486i
$903$		0			0
$904$	1.48162	+	27.3270i	0.0492781	+	0.908881i
$905$	−18.5781	−	14.1227i	−0.617557	−	0.469454i
$906$		0			0
$907$	8.52840	+	5.13137i	0.283181	+	0.170384i	0.650057	−	0.759886i	$-0.274745\pi$
$907$	8.52840	+	5.13137i	0.283181	+	0.170384i	−0.366876	+	0.930270i	$0.619573\pi$
$908$	32.8222	+	15.1852i	1.08924	+	0.503938i
$909$		0			0
$910$	−5.27121	−	7.77445i	−0.174739	−	0.257720i
$911$	−8.26605	+	12.1915i	−0.273867	+	0.403923i	−0.939604	−	0.342263i	$-0.888807\pi$
$911$	−8.26605	+	12.1915i	−0.273867	+	0.403923i	0.665738	+	0.746186i	$0.268117\pi$
$912$		0			0
$913$	0.998278	−	18.4121i	0.0330382	−	0.609353i
$914$	−0.652995	+	0.768765i	−0.0215992	+	0.0254285i
$915$		0			0
$916$	1.35061	−	24.9106i	0.0446255	−	0.823068i
$917$	−5.16622	−	12.9662i	−0.170604	−	0.428183i
$918$		0			0
$919$	16.6023	+	24.4866i	0.547661	+	0.807739i	0.996297	−	0.0859749i	$-0.0274005\pi$
$919$	16.6023	+	24.4866i	0.547661	+	0.807739i	−0.448636	+	0.893714i	$0.648090\pi$
$920$	−1.30994	+	3.28770i	−0.0431874	+	0.108392i
$921$		0			0
$922$	−11.8071	−	7.10410i	−0.388846	−	0.233961i
$923$	3.19287	−	3.02445i	0.105095	−	0.0995509i
$924$		0			0
$925$	−0.779959	−	14.3855i	−0.0256449	−	0.472993i
$926$	13.9965	−	6.47548i	0.459954	−	0.212798i
$927$		0			0
$928$	−16.1686	−	5.44785i	−0.530762	−	0.178834i
$929$	−4.85859	−	29.6361i	−0.159405	−	0.972328i	−0.938464	−	0.345377i	$-0.887751\pi$
$929$	−4.85859	−	29.6361i	−0.159405	−	0.972328i	0.779059	−	0.626951i	$-0.215697\pi$
$930$		0			0
$931$	4.12022	+	14.8397i	0.135035	+	0.486352i
$932$	14.3896	+	27.1417i	0.471347	+	0.889056i
$933$		0			0
$934$	18.6908	−	4.11416i	0.611582	−	0.134619i
$935$	5.93141	−	21.3630i	0.193978	−	0.698645i
$936$		0			0
$937$	−54.0019	+	5.87306i	−1.76417	+	0.191865i	−0.931950	−	0.362588i	$-0.881893\pi$
$937$	−54.0019	+	5.87306i	−1.76417	+	0.191865i	−0.832216	+	0.554452i	$0.812928\pi$
$938$	−24.0387	−	5.29132i	−0.784892	−	0.172768i
$939$		0			0
$940$	−4.61312	+	28.1388i	−0.150463	+	0.917786i
$941$	42.6201	−	32.3990i	1.38938	−	1.05618i	0.399123	−	0.916897i	$-0.369315\pi$
$941$	42.6201	−	32.3990i	1.38938	−	1.05618i	0.990253	−	0.139279i	$-0.0444784\pi$
$942$		0			0
$943$	−7.03843			−0.229203
$944$	14.3074	−	1.52409i	0.465666	−	0.0496048i
$945$		0			0
$946$	3.44765	+	4.05888i	0.112093	+	0.131966i
$947$	−42.9537	+	32.6525i	−1.39581	+	1.06106i	−0.406749	+	0.913540i	$0.633338\pi$
$947$	−42.9537	+	32.6525i	−1.39581	+	1.06106i	−0.989058	+	0.147525i	$0.952869\pi$
$948$		0			0
$949$	16.1518	−	30.4655i	0.524308	−	0.988950i
$950$	10.1212	+	2.22785i	0.328376	+	0.0722810i
$951$		0			0
$952$	−41.1042	+	24.7316i	−1.33219	+	0.801554i
$953$	2.77857	−	10.0075i	0.0900067	−	0.324175i	−0.904816	−	0.425803i	$-0.859992\pi$
$953$	2.77857	−	10.0075i	0.0900067	−	0.324175i	0.994822	+	0.101629i	$0.0324053\pi$
$954$		0			0
$955$	−25.4951	+	8.59030i	−0.825002	+	0.277975i
$956$	17.9559	+	33.8685i	0.580736	+	1.09539i
$957$		0			0
$958$	16.3011	+	15.4413i	0.526666	+	0.498885i
$959$	2.07535	+	12.6591i	0.0670167	+	0.408784i
$960$		0			0
$961$	29.8969	+	3.25148i	0.964416	+	0.104887i
$962$	−11.0412	+	5.10821i	−0.355983	+	0.164695i
$963$		0			0
$964$	−12.9553	−	9.84836i	−0.417262	−	0.317194i
$965$	−14.2365	+	13.4855i	−0.458288	+	0.434113i
$966$		0			0
$967$	5.89184	+	2.72586i	0.189469	+	0.0876576i	0.512330	−	0.858789i	$-0.328783\pi$
$967$	5.89184	+	2.72586i	0.189469	+	0.0876576i	−0.322861	+	0.946446i	$0.604645\pi$
$968$	6.23085	−	15.6383i	0.200267	−	0.502633i
$969$		0			0
$970$	8.27841	−	12.2097i	0.265804	−	0.392031i
$971$	−4.99583	−	12.5386i	−0.160324	−	0.402383i	0.826767	−	0.562545i	$-0.190178\pi$
$971$	−4.99583	−	12.5386i	−0.160324	−	0.402383i	−0.987091	+	0.160162i	$0.948798\pi$
$972$		0			0
$973$	1.82232	−	2.14540i	0.0584209	−	0.0687784i
$974$	−13.8055	+	16.2531i	−0.442358	+	0.520784i
$975$		0			0
$976$	−1.32451	−	3.32426i	−0.0423964	−	0.106407i
$977$	23.7290	−	34.9977i	0.759159	−	1.11968i	−0.230052	−	0.973178i	$-0.573890\pi$
$977$	23.7290	−	34.9977i	0.759159	−	1.11968i	0.989211	−	0.146497i	$-0.0467999\pi$
$978$		0			0
$979$	3.29860	−	8.27886i	0.105424	−	0.264594i
$980$	4.97993	+	2.30396i	0.159078	+	0.0735973i
$981$		0			0
$982$	−11.7978	+	11.1755i	−0.376483	+	0.356624i
$983$	−6.98326	−	5.30854i	−0.222731	−	0.169316i	0.487858	−	0.872923i	$-0.337778\pi$
$983$	−6.98326	−	5.30854i	−0.222731	−	0.169316i	−0.710589	+	0.703607i	$0.751572\pi$
$984$		0			0
$985$	−3.40035	+	1.57317i	−0.108344	+	0.0501254i
$986$	−13.3336	−	1.45012i	−0.424628	−	0.0461811i
$987$		0			0
$988$	6.06894	+	37.0189i	0.193079	+	1.17773i
$989$	3.22797	+	3.05770i	0.102643	+	0.0972291i
$990$		0			0
$991$	−11.9933	−	22.6218i	−0.380980	−	0.718605i	0.616663	−	0.787228i	$-0.288484\pi$
$991$	−11.9933	−	22.6218i	−0.380980	−	0.718605i	−0.997643	+	0.0686228i	$0.978139\pi$
$992$	5.11576	−	1.72370i	0.162425	−	0.0547275i
$993$		0			0
$994$	0.713411	−	2.56948i	0.0226280	−	0.0814988i
$995$	2.61589	−	1.57393i	0.0829294	−	0.0498970i
$996$		0			0
$997$	−49.9714	−	10.9995i	−1.58261	−	0.348359i	−0.665313	−	0.746564i	$-0.731702\pi$
$997$	−49.9714	−	10.9995i	−1.58261	−	0.348359i	−0.917296	+	0.398205i	$0.869633\pi$
$998$	3.06081	−	5.77330i	0.0968882	−	0.182750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.46.3		140
3.2	odd	2		177.2.e.a.46.3	✓	140
59.9	even	29	inner	531.2.i.c.127.3		140
177.68	odd	58		177.2.e.a.127.3	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.46.3	✓	140	3.2	odd	2
177.2.e.a.127.3	yes	140	177.68	odd	58
531.2.i.c.46.3		140	1.1	even	1	trivial
531.2.i.c.127.3		140	59.9	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.398193 - 0.468789i) q^{2} +(0.262358 - 1.60032i) q^{4} +(-0.780962 + 1.47305i) q^{5} +(-2.98728 + 0.324887i) q^{7} +(-1.90875 + 1.14846i) q^{8} +O(q^{10})\)	\(q+(-0.398193 - 0.468789i) q^{2} +(0.262358 - 1.60032i) q^{4} +(-0.780962 + 1.47305i) q^{5} +(-2.98728 + 0.324887i) q^{7} +(-1.90875 + 1.14846i) q^{8} +(1.00152 - 0.220452i) q^{10} +(1.75843 - 0.592483i) q^{11} +(0.815468 + 2.93705i) q^{13} +(1.34182 + 1.27104i) q^{14} +(-1.77514 - 0.598116i) q^{16} +(-7.12450 - 0.774836i) q^{17} +(0.410857 + 7.57780i) q^{19} +(2.15245 + 1.63625i) q^{20} +(-0.977944 - 0.588409i) q^{22} +(-0.864818 - 0.400107i) q^{23} +(1.24596 + 1.83765i) q^{25} +(1.05214 - 1.55180i) q^{26} +(-0.263818 + 4.86583i) q^{28} +(-1.96982 + 2.31905i) q^{29} +(0.0521205 - 0.961307i) q^{31} +(2.07551 + 5.20914i) q^{32} +(2.47369 + 3.64842i) q^{34} +(1.85438 - 4.65414i) q^{35} +(-5.56000 - 3.34534i) q^{37} +(3.38879 - 3.21003i) q^{38} +(-0.201074 - 3.70858i) q^{40} +(6.70373 - 3.10148i) q^{41} +(-4.42184 - 1.48989i) q^{43} +(-0.486822 - 2.96948i) q^{44} +(0.156798 + 0.564737i) q^{46} +(4.93991 + 9.31766i) q^{47} +(1.98197 - 0.436264i) q^{49} +(0.365339 - 1.31583i) q^{50} +(4.91415 - 0.534447i) q^{52} +(-2.12328 - 0.467370i) q^{53} +(-0.500507 + 3.05296i) q^{55} +(5.32885 - 4.05089i) q^{56} +1.87151 q^{58} +(-6.97832 + 3.20984i) q^{59} +(1.23671 + 1.45597i) q^{61} +(-0.471404 + 0.358352i) q^{62} +(-0.139312 + 0.262771i) q^{64} +(-4.96328 - 1.09250i) q^{65} +(-11.4113 + 6.86593i) q^{67} +(-3.10915 + 11.1982i) q^{68} +(-2.92021 + 0.983934i) q^{70} +(-0.675826 - 1.27474i) q^{71} +(-8.21281 - 7.77959i) q^{73} +(0.645694 + 3.93856i) q^{74} +(12.2347 + 1.33060i) q^{76} +(-5.06043 + 2.34121i) q^{77} +(8.52956 + 6.48400i) q^{79} +(2.26738 - 2.14777i) q^{80} +(-4.12332 - 1.90765i) q^{82} +(3.67816 - 9.23148i) q^{83} +(6.70533 - 9.88963i) q^{85} +(1.06230 + 2.66618i) q^{86} +(-2.67596 + 3.15038i) q^{88} +(3.10924 - 3.66048i) q^{89} +(-3.39024 - 8.50887i) q^{91} +(-0.867190 + 1.27901i) q^{92} +(2.40098 - 6.02600i) q^{94} +(-11.4834 - 5.31277i) q^{95} +(10.4433 - 9.89242i) q^{97} +(-0.993721 - 0.755407i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

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