LMFDB - Embedded newform 414.2.i.g.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$-0.842658 + 0.247427i$ of defining polynomial
Character	$\chi$	$=$	414.127
Dual form			414.2.i.g.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(-3.68019 + 1.08060i) q^{5} +(3.32796 + 3.84067i) q^{7} +(-0.142315 - 0.989821i) q^{8} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(-3.68019 + 1.08060i) q^{5} +(3.32796 + 3.84067i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-2.51176 + 2.89872i) q^{10} +(3.79996 + 2.44208i) q^{11} +(2.18035 - 2.51626i) q^{13} +(4.87608 + 1.43175i) q^{14} +(-0.654861 - 0.755750i) q^{16} +(-0.0640134 - 0.140170i) q^{17} +(-2.18106 + 4.77585i) q^{19} +(-0.545857 + 3.79652i) q^{20} +4.51702 q^{22} +(2.86337 + 3.84723i) q^{23} +(8.16983 - 5.25043i) q^{25} +(0.473835 - 3.29560i) q^{26} +(4.87608 - 1.43175i) q^{28} +(-2.17420 - 4.76083i) q^{29} +(-0.180489 - 1.25533i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-0.129633 - 0.0833101i) q^{34} +(-16.3978 - 10.5382i) q^{35} +(-4.27738 - 1.25595i) q^{37} +(0.747197 + 5.19687i) q^{38} +(1.59335 + 3.48894i) q^{40} +(-2.12194 + 0.623058i) q^{41} +(-0.375521 + 2.61181i) q^{43} +(3.79996 - 2.44208i) q^{44} +(4.48878 + 1.68844i) q^{46} +1.10906 q^{47} +(-2.67923 + 18.6344i) q^{49} +(4.03430 - 8.83388i) q^{50} +(-1.38312 - 3.02861i) q^{52} +(-2.80579 - 3.23806i) q^{53} +(-16.6235 - 4.88109i) q^{55} +(3.32796 - 3.84067i) q^{56} +(-4.40295 - 2.82960i) q^{58} +(-2.11382 + 2.43948i) q^{59} +(-1.87001 - 13.0062i) q^{61} +(-0.830518 - 0.958469i) q^{62} +(-0.959493 + 0.281733i) q^{64} +(-5.30503 + 11.6164i) q^{65} +(8.81965 - 5.66805i) q^{67} -0.154095 q^{68} -19.4920 q^{70} +(11.9951 - 7.70881i) q^{71} +(2.57736 - 5.64363i) q^{73} +(-4.27738 + 1.25595i) q^{74} +(3.43822 + 3.96792i) q^{76} +(3.26686 + 22.7215i) q^{77} +(-1.91015 + 2.20444i) q^{79} +(3.22668 + 2.07366i) q^{80} +(-1.44824 + 1.67136i) q^{82} +(-2.23941 - 0.657551i) q^{83} +(0.387049 + 0.446678i) q^{85} +(1.09614 + 2.40021i) q^{86} +(1.87644 - 4.10882i) q^{88} +(-0.783871 + 5.45194i) q^{89} +16.9202 q^{91} +(4.68904 - 1.00641i) q^{92} +(0.933001 - 0.599603i) q^{94} +(2.86591 - 19.9329i) q^{95} +(-12.6220 + 3.70615i) q^{97} +(7.82063 + 17.1248i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8	$ 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8} - 2 q^{10} + 2 q^{11} + 18 q^{14} - 2 q^{16} - 18 q^{17} + 16 q^{19} - 2 q^{20} + 24 q^{22} + 2 q^{23} + 38 q^{25} + 18 q^{28} + 30 q^{29} + 14 q^{31} - 2 q^{32} + 4 q^{34} - 48 q^{35} - 20 q^{37} + 16 q^{38} - 2 q^{40} + 12 q^{41} - 28 q^{43} + 2 q^{44} + 2 q^{46} - 32 q^{47} + 6 q^{49} - 6 q^{50} + 46 q^{53} - 28 q^{55} - 4 q^{56} - 14 q^{58} - 50 q^{61} - 8 q^{62} - 2 q^{64} - 16 q^{65} - 8 q^{67} + 48 q^{68} - 48 q^{70} - 12 q^{71} - 18 q^{73} - 20 q^{74} - 6 q^{76} + 4 q^{77} - 18 q^{79} - 2 q^{80} - 10 q^{82} + 44 q^{83} + 32 q^{85} - 28 q^{86} + 2 q^{88} + 44 q^{91} + 2 q^{92} + 12 q^{94} - 64 q^{95} + 14 q^{97} + 28 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8 - 2 * q^10 + 2 * q^11 + 18 * q^14 - 2 * q^16 - 18 * q^17 + 16 * q^19 - 2 * q^20 + 24 * q^22 + 2 * q^23 + 38 * q^25 + 18 * q^28 + 30 * q^29 + 14 * q^31 - 2 * q^32 + 4 * q^34 - 48 * q^35 - 20 * q^37 + 16 * q^38 - 2 * q^40 + 12 * q^41 - 28 * q^43 + 2 * q^44 + 2 * q^46 - 32 * q^47 + 6 * q^49 - 6 * q^50 + 46 * q^53 - 28 * q^55 - 4 * q^56 - 14 * q^58 - 50 * q^61 - 8 * q^62 - 2 * q^64 - 16 * q^65 - 8 * q^67 + 48 * q^68 - 48 * q^70 - 12 * q^71 - 18 * q^73 - 20 * q^74 - 6 * q^76 + 4 * q^77 - 18 * q^79 - 2 * q^80 - 10 * q^82 + 44 * q^83 + 32 * q^85 - 28 * q^86 + 2 * q^88 + 44 * q^91 + 2 * q^92 + 12 * q^94 - 64 * q^95 + 14 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$		0			0
$3$		0			0
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−3.68019	+	1.08060i	−1.64583	+	0.483259i	−0.967789	−	0.251764i	$-0.918989\pi$
$5$	−3.68019	+	1.08060i	−1.64583	+	0.483259i	−0.678042	+	0.735023i	$0.737171\pi$
$6$		0			0
$7$	3.32796	+	3.84067i	1.25785	+	1.45164i	0.839508	+	0.543347i	$0.182843\pi$
$7$	3.32796	+	3.84067i	1.25785	+	1.45164i	0.418343	+	0.908289i	$0.362611\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$		0			0
$10$	−2.51176	+	2.89872i	−0.794287	+	0.916656i
$11$	3.79996	+	2.44208i	1.14573	+	0.736316i	0.968784	−	0.247905i	$-0.0797420\pi$
$11$	3.79996	+	2.44208i	1.14573	+	0.736316i	0.176945	+	0.984221i	$0.443378\pi$
$12$		0			0
$13$	2.18035	−	2.51626i	0.604720	−	0.697884i	−0.368011	−	0.929822i	$-0.619961\pi$
$13$	2.18035	−	2.51626i	0.604720	−	0.697884i	0.972731	+	0.231937i	$0.0745064\pi$
$14$	4.87608	+	1.43175i	1.30319	+	0.382650i
$15$		0			0
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.0640134	−	0.140170i	−0.0155255	−	0.0339962i	0.901710	−	0.432341i	$-0.142312\pi$
$17$	−0.0640134	−	0.140170i	−0.0155255	−	0.0339962i	−0.917236	+	0.398344i	$0.869585\pi$
$18$		0			0
$19$	−2.18106	+	4.77585i	−0.500369	+	1.09565i	0.475981	+	0.879456i	$0.342093\pi$
$19$	−2.18106	+	4.77585i	−0.500369	+	1.09565i	−0.976349	+	0.216199i	$0.930634\pi$
$20$	−0.545857	+	3.79652i	−0.122057	+	0.848927i
$21$		0			0
$22$	4.51702			0.963031
$23$	2.86337	+	3.84723i	0.597053	+	0.802202i
$23$	2.86337	+	3.84723i	0.597053	+	0.802202i
$24$		0			0
$25$	8.16983	−	5.25043i	1.63397	−	1.05009i
$26$	0.473835	−	3.29560i	0.0929267	−	0.646320i
$27$		0			0
$28$	4.87608	−	1.43175i	0.921493	−	0.270575i
$29$	−2.17420	−	4.76083i	−0.403738	−	0.884063i	−0.996878	−	0.0789635i	$-0.974839\pi$
$29$	−2.17420	−	4.76083i	−0.403738	−	0.884063i	0.593139	−	0.805100i	$-0.297888\pi$
$30$		0			0
$31$	−0.180489	−	1.25533i	−0.0324168	−	0.225464i	0.967173	−	0.254121i	$-0.0817860\pi$
$31$	−0.180489	−	1.25533i	−0.0324168	−	0.225464i	−0.999589	+	0.0286571i	$0.990877\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$		0			0
$34$	−0.129633	−	0.0833101i	−0.0222319	−	0.0142876i
$35$	−16.3978	−	10.5382i	−2.77173	−	1.78128i
$36$		0			0
$37$	−4.27738	−	1.25595i	−0.703196	−	0.206477i	−0.0894626	−	0.995990i	$-0.528515\pi$
$37$	−4.27738	−	1.25595i	−0.703196	−	0.206477i	−0.613734	+	0.789513i	$0.710333\pi$
$38$	0.747197	+	5.19687i	0.121211	+	0.843043i
$39$		0			0
$40$	1.59335	+	3.48894i	0.251930	+	0.551651i
$41$	−2.12194	+	0.623058i	−0.331392	+	0.0973053i	−0.443196	−	0.896425i	$-0.646155\pi$
$41$	−2.12194	+	0.623058i	−0.331392	+	0.0973053i	0.111804	+	0.993730i	$0.464337\pi$
$42$		0			0
$43$	−0.375521	+	2.61181i	−0.0572665	+	0.398297i	0.940947	+	0.338553i	$0.109937\pi$
$43$	−0.375521	+	2.61181i	−0.0572665	+	0.398297i	−0.998214	+	0.0597439i	$0.980972\pi$
$44$	3.79996	−	2.44208i	0.572865	−	0.368158i
$45$		0			0
$46$	4.48878	+	1.68844i	0.661835	+	0.248947i
$47$	1.10906			0.161773			0.0808865	−	0.996723i	$-0.474225\pi$
$47$	1.10906			0.161773			0.0808865	+	0.996723i	$0.474225\pi$
$48$		0			0
$49$	−2.67923	+	18.6344i	−0.382747	+	2.66206i
$50$	4.03430	−	8.83388i	0.570536	−	1.24930i
$51$		0			0
$52$	−1.38312	−	3.02861i	−0.191804	−	0.419992i
$53$	−2.80579	−	3.23806i	−0.385406	−	0.444782i	0.529585	−	0.848257i	$-0.322348\pi$
$53$	−2.80579	−	3.23806i	−0.385406	−	0.444782i	−0.914991	+	0.403475i	$0.867802\pi$
$54$		0			0
$55$	−16.6235	−	4.88109i	−2.24151	−	0.658166i
$56$	3.32796	−	3.84067i	0.444717	−	0.513231i
$57$		0			0
$58$	−4.40295	−	2.82960i	−0.578135	−	0.371545i
$59$	−2.11382	+	2.43948i	−0.275196	+	0.317594i	−0.876476	−	0.481445i	$-0.840112\pi$
$59$	−2.11382	+	2.43948i	−0.275196	+	0.317594i	0.601280	+	0.799038i	$0.294658\pi$
$60$		0			0
$61$	−1.87001	−	13.0062i	−0.239430	−	1.66527i	−0.654940	−	0.755681i	$-0.727306\pi$
$61$	−1.87001	−	13.0062i	−0.239430	−	1.66527i	0.415510	−	0.909589i	$-0.363603\pi$
$62$	−0.830518	−	0.958469i	−0.105476	−	0.121726i
$63$		0			0
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−5.30503	+	11.6164i	−0.658008	+	1.44084i
$66$		0			0
$67$	8.81965	−	5.66805i	1.07749	−	0.692462i	0.123515	−	0.992343i	$-0.460583\pi$
$67$	8.81965	−	5.66805i	1.07749	−	0.692462i	0.953977	+	0.299880i	$0.0969468\pi$
$68$	−0.154095			−0.0186868
$69$		0			0
$70$	−19.4920			−2.32975
$71$	11.9951	−	7.70881i	1.42356	−	0.914867i	0.423601	−	0.905849i	$-0.360766\pi$
$71$	11.9951	−	7.70881i	1.42356	−	0.914867i	0.999959	−	0.00901832i	$-0.00287066\pi$
$72$		0			0
$73$	2.57736	−	5.64363i	0.301657	−	0.660537i	−0.696729	−	0.717335i	$-0.745362\pi$
$73$	2.57736	−	5.64363i	0.301657	−	0.660537i	0.998386	+	0.0567981i	$0.0180891\pi$
$74$	−4.27738	+	1.25595i	−0.497235	+	0.146001i
$75$		0			0
$76$	3.43822	+	3.96792i	0.394391	+	0.455151i
$77$	3.26686	+	22.7215i	0.372294	+	2.58936i
$78$		0			0
$79$	−1.91015	+	2.20444i	−0.214909	+	0.248018i	−0.852961	−	0.521975i	$-0.825195\pi$
$79$	−1.91015	+	2.20444i	−0.214909	+	0.248018i	0.638051	+	0.769994i	$0.279741\pi$
$80$	3.22668	+	2.07366i	0.360753	+	0.231842i
$81$		0			0
$82$	−1.44824	+	1.67136i	−0.159931	+	0.184571i
$83$	−2.23941	−	0.657551i	−0.245807	−	0.0721756i	0.156508	−	0.987677i	$-0.449976\pi$
$83$	−2.23941	−	0.657551i	−0.245807	−	0.0721756i	−0.402315	+	0.915501i	$0.631794\pi$
$84$		0			0
$85$	0.387049	+	0.446678i	0.0419814	+	0.0484491i
$86$	1.09614	+	2.40021i	0.118200	+	0.258822i
$87$		0			0
$88$	1.87644	−	4.10882i	0.200029	−	0.438002i
$89$	−0.783871	+	5.45194i	−0.0830902	+	0.577905i	0.905161	+	0.425068i	$0.139750\pi$
$89$	−0.783871	+	5.45194i	−0.0830902	+	0.577905i	−0.988251	+	0.152837i	$0.951159\pi$
$90$		0			0
$91$	16.9202			1.77372
$92$	4.68904	−	1.00641i	0.488867	−	0.104926i
$93$		0			0
$94$	0.933001	−	0.599603i	0.0962317	−	0.0618444i
$95$	2.86591	−	19.9329i	0.294037	−	2.04507i
$96$		0			0
$97$	−12.6220	+	3.70615i	−1.28157	+	0.376303i	−0.850481	−	0.526006i	$-0.823689\pi$
$97$	−12.6220	+	3.70615i	−1.28157	+	0.376303i	−0.431089	+	0.902309i	$0.641871\pi$
$98$	7.82063	+	17.1248i	0.790003	+	1.72986i
$99$		0			0
$100$	−1.38209	−	9.61264i	−0.138209	−	0.961264i
$101$	6.25289	+	1.83602i	0.622186	+	0.182690i	0.577606	−	0.816315i	$-0.303987\pi$
$101$	6.25289	+	1.83602i	0.622186	+	0.182690i	0.0445798	+	0.999006i	$0.485805\pi$
$102$		0			0
$103$	−4.74908	−	3.05205i	−0.467941	−	0.300727i	0.285340	−	0.958426i	$-0.407893\pi$
$103$	−4.74908	−	3.05205i	−0.467941	−	0.300727i	−0.753281	+	0.657699i	$0.771530\pi$
$104$	−2.80094	−	1.80006i	−0.274655	−	0.176510i
$105$		0			0
$106$	−4.11101	−	1.20710i	−0.399297	−	0.117244i
$107$	−0.966896	−	6.72491i	−0.0934734	−	0.650122i	−0.981660	−	0.190639i	$-0.938944\pi$
$107$	−0.966896	−	6.72491i	−0.0934734	−	0.650122i	0.888187	−	0.459483i	$-0.151965\pi$
$108$		0			0
$109$	−2.42305	−	5.30574i	−0.232086	−	0.508198i	0.757378	−	0.652977i	$-0.226480\pi$
$109$	−2.42305	−	5.30574i	−0.232086	−	0.508198i	−0.989464	+	0.144779i	$0.953753\pi$
$110$	−16.6235	+	4.88109i	−1.58499	+	0.465394i
$111$		0			0
$112$	0.723235	−	5.03021i	0.0683393	−	0.475310i
$113$	12.3314	−	7.92493i	1.16004	−	0.745515i	0.188430	−	0.982087i	$-0.439660\pi$
$113$	12.3314	−	7.92493i	1.16004	−	0.745515i	0.971614	+	0.236572i	$0.0760239\pi$
$114$		0			0
$115$	−14.6950	−	11.0644i	−1.37032	−	1.03176i
$116$	−5.23379			−0.485946
$117$		0			0
$118$	−0.459378	+	3.19504i	−0.0422891	+	0.294127i
$119$	0.325312	−	0.712334i	0.0298213	−	0.0652995i
$120$		0			0
$121$	3.90633	+	8.55367i	0.355121	+	0.777606i
$122$	−8.60482	−	9.93049i	−0.779044	−	0.899064i
$123$		0			0
$124$	−1.21686	−	0.357304i	−0.109278	−	0.0320868i
$125$	−11.8341	+	13.6573i	−1.05848	+	1.22155i
$126$		0			0
$127$	−9.34570	−	6.00612i	−0.829297	−	0.532957i	0.0557577	−	0.998444i	$-0.482243\pi$
$127$	−9.34570	−	6.00612i	−0.829297	−	0.532957i	−0.885054	+	0.465488i	$0.845879\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$		0			0
$130$	1.81742	+	12.6404i	0.159398	+	1.10864i
$131$	−1.36232	−	1.57220i	−0.119027	−	0.137364i	0.693109	−	0.720833i	$-0.256240\pi$
$131$	−1.36232	−	1.57220i	−0.119027	−	0.137364i	−0.812135	+	0.583469i	$0.801695\pi$
$132$		0			0
$133$	−25.6009	+	7.51711i	−2.21988	+	0.651816i
$134$	4.35519	−	9.53653i	0.376231	−	0.823831i
$135$		0			0
$136$	−0.129633	+	0.0833101i	−0.0111159	+	0.00714378i
$137$	16.5855			1.41699			0.708496	−	0.705714i	$-0.249374\pi$
$137$	16.5855			1.41699			0.708496	+	0.705714i	$0.249374\pi$
$138$		0			0
$139$	4.74700			0.402635			0.201318	−	0.979526i	$-0.435478\pi$
$139$	4.74700			0.402635			0.201318	+	0.979526i	$0.435478\pi$
$140$	−16.3978	+	10.5382i	−1.38586	+	0.890640i
$141$		0			0
$142$	5.92326	−	12.9701i	0.497069	−	1.08843i
$143$	14.4301	−	4.23707i	1.20671	−	0.354322i
$144$		0			0
$145$	13.1460	+	15.1713i	1.09172	+	1.25991i
$146$	−0.882964	−	6.14115i	−0.0730746	−	0.508245i
$147$		0			0
$148$	−2.91934	+	3.36910i	−0.239968	+	0.276938i
$149$	−14.3210	−	9.20353i	−1.17322	−	0.753982i	−0.199092	−	0.979981i	$-0.563799\pi$
$149$	−14.3210	−	9.20353i	−1.17322	−	0.753982i	−0.974128	+	0.225998i	$0.927436\pi$
$150$		0			0
$151$	4.61693	−	5.32822i	0.375720	−	0.433604i	−0.536125	−	0.844139i	$-0.680112\pi$
$151$	4.61693	−	5.32822i	0.375720	−	0.433604i	0.911845	+	0.410534i	$0.134658\pi$
$152$	5.03763	+	1.47918i	0.408606	+	0.119978i
$153$		0			0
$154$	15.0324	+	17.3484i	1.21135	+	1.39797i
$155$	2.02074	+	4.42481i	0.162310	+	0.355409i
$156$		0			0
$157$	2.54014	−	5.56213i	0.202725	−	0.443906i	−0.780775	−	0.624812i	$-0.785176\pi$
$157$	2.54014	−	5.56213i	0.202725	−	0.443906i	0.983500	+	0.180906i	$0.0579029\pi$
$158$	−0.415116	+	2.88720i	−0.0330249	+	0.229693i
$159$		0			0
$160$	3.83556			0.303227
$161$	−5.24676	+	23.8006i	−0.413503	+	1.87575i
$162$		0			0
$163$	−5.04923	+	3.24494i	−0.395486	+	0.254164i	−0.723236	−	0.690601i	$-0.757346\pi$
$163$	−5.04923	+	3.24494i	−0.395486	+	0.254164i	0.327750	+	0.944765i	$0.393710\pi$
$164$	−0.314733	+	2.18901i	−0.0245765	+	0.170933i
$165$		0			0
$166$	−2.23941	+	0.657551i	−0.173812	+	0.0510358i
$167$	−5.18764	−	11.3593i	−0.401431	−	0.879012i	−0.997123	−	0.0757988i	$-0.975849\pi$
$167$	−5.18764	−	11.3593i	−0.401431	−	0.879012i	0.595692	−	0.803213i	$-0.296878\pi$
$168$		0			0
$169$	0.272465	+	1.89504i	0.0209589	+	0.145772i
$170$	0.567099	+	0.166515i	0.0434945	+	0.0127711i
$171$		0			0
$172$	2.21979	+	1.42657i	0.169257	+	0.108775i
$173$	3.18912	+	2.04952i	0.242464	+	0.155822i	0.656230	−	0.754561i	$-0.272150\pi$
$173$	3.18912	+	2.04952i	0.242464	+	0.155822i	−0.413765	+	0.910384i	$0.635787\pi$
$174$		0			0
$175$	47.3540	+	13.9044i	3.57963	+	1.05107i
$176$	−0.642838	−	4.47104i	−0.0484558	−	0.337017i
$177$		0			0
$178$	2.28811	+	5.01026i	0.171501	+	0.375535i
$179$	0.435048	−	0.127742i	0.0325170	−	0.00954785i	−0.265434	−	0.964129i	$-0.585515\pi$
$179$	0.435048	−	0.127742i	0.0325170	−	0.00954785i	0.297951	+	0.954581i	$0.403697\pi$
$180$		0			0
$181$	1.11511	−	7.75578i	0.0828857	−	0.576482i	−0.905480	−	0.424388i	$-0.860489\pi$
$181$	1.11511	−	7.75578i	0.0828857	−	0.576482i	0.988366	−	0.152094i	$-0.0486017\pi$
$182$	14.2342	−	9.14777i	1.05511	−	0.678078i
$183$		0			0
$184$	3.40057	−	3.38174i	0.250693	−	0.249305i
$185$	17.0987			1.25712
$186$		0			0
$187$	0.0990582	−	0.688965i	0.00724385	−	0.0503821i
$188$	0.460720	−	1.00884i	0.0336015	−	0.0735770i
$189$		0			0
$190$	−8.36556	−	18.3180i	−0.606902	−	1.32893i
$191$	10.0626	+	11.6128i	0.728101	+	0.840274i	0.992256	−	0.124207i	$-0.0396386\pi$
$191$	10.0626	+	11.6128i	0.728101	+	0.840274i	−0.264155	+	0.964480i	$0.585093\pi$
$192$		0			0
$193$	−8.42212	−	2.47296i	−0.606237	−	0.178007i	−0.0358144	−	0.999358i	$-0.511403\pi$
$193$	−8.42212	−	2.47296i	−0.606237	−	0.178007i	−0.570423	+	0.821351i	$0.693221\pi$
$194$	−8.61461	+	9.94179i	−0.618493	+	0.713779i
$195$		0			0
$196$	15.8375	+	10.1781i	1.13125	+	0.727010i
$197$	5.25179	−	6.06089i	0.374175	−	0.431821i	−0.537164	−	0.843478i	$-0.680504\pi$
$197$	5.25179	−	6.06089i	0.374175	−	0.431821i	0.911339	+	0.411657i	$0.135050\pi$
$198$		0			0
$199$	−0.882773	−	6.13982i	−0.0625781	−	0.435241i	−0.996891	−	0.0787876i	$-0.974895\pi$
$199$	−0.882773	−	6.13982i	−0.0625781	−	0.435241i	0.934313	−	0.356453i	$-0.116014\pi$
$200$	−6.35967	−	7.33946i	−0.449697	−	0.518978i
$201$		0			0
$202$	6.25289	−	1.83602i	0.439952	−	0.129182i
$203$	11.0491	−	24.1942i	0.775497	−	1.69810i
$204$		0			0
$205$	7.13587	−	4.58594i	0.498391	−	0.320296i
$206$	−5.64524			−0.393322
$207$		0			0
$208$	−3.32949			−0.230858
$209$	−19.9509	+	12.8217i	−1.38003	+	0.886895i
$210$		0			0
$211$	−6.70359	+	14.6788i	−0.461494	+	1.01053i	0.525651	+	0.850701i	$0.323822\pi$
$211$	−6.70359	+	14.6788i	−0.461494	+	1.01053i	−0.987145	+	0.159830i	$0.948905\pi$
$212$	−4.11101	+	1.20710i	−0.282345	+	0.0829041i
$213$		0			0
$214$	−4.44917	−	5.13461i	−0.304139	−	0.350995i
$215$	−1.44033	−	10.0177i	−0.0982299	−	0.683204i
$216$		0			0
$217$	4.22064	−	4.87088i	0.286516	−	0.330657i
$218$	−4.90690	−	3.15347i	−0.332337	−	0.213580i
$219$		0			0
$220$	−11.3456	+	13.0936i	−0.764923	+	0.882768i
$221$	−0.492275	−	0.144545i	−0.0331140	−	0.00972314i
$222$		0			0
$223$	5.99677	+	6.92064i	0.401573	+	0.463440i	0.920136	−	0.391599i	$-0.128078\pi$
$223$	5.99677	+	6.92064i	0.401573	+	0.463440i	−0.518563	+	0.855040i	$0.673533\pi$
$224$	−2.11111	−	4.62269i	−0.141055	−	0.308866i
$225$		0			0
$226$	6.08932	−	13.3338i	0.405056	−	0.886948i
$227$	−1.33838	+	9.30862i	−0.0888313	+	0.617835i	0.895965	+	0.444124i	$0.146485\pi$
$227$	−1.33838	+	9.30862i	−0.0888313	+	0.617835i	−0.984797	+	0.173711i	$0.944424\pi$
$228$		0			0
$229$	3.61058			0.238594			0.119297	−	0.992859i	$-0.461936\pi$
$229$	3.61058			0.238594			0.119297	+	0.992859i	$0.461936\pi$
$230$	−18.3441	−	1.36319i	−1.20957	−	0.0898864i
$231$		0			0
$232$	−4.40295	+	2.82960i	−0.289068	+	0.185773i
$233$	−0.0794969	+	0.552913i	−0.00520802	+	0.0362225i	−0.992260	−	0.124180i	$-0.960370\pi$
$233$	−0.0794969	+	0.552913i	−0.00520802	+	0.0362225i	0.987052	+	0.160402i	$0.0512792\pi$
$234$		0			0
$235$	−4.08155	+	1.19845i	−0.266251	+	0.0781784i
$236$	1.34092	+	2.93620i	0.0872863	+	0.191130i
$237$		0			0
$238$	−0.111447	−	0.775130i	−0.00722403	−	0.0502442i
$239$	18.2994	+	5.37320i	1.18369	+	0.347563i	0.813596	−	0.581430i	$-0.197507\pi$
$239$	18.2994	+	5.37320i	1.18369	+	0.347563i	0.370096	+	0.928994i	$0.379325\pi$
$240$		0			0
$241$	16.5286	+	10.6223i	1.06470	+	0.684240i	0.950974	−	0.309272i	$-0.100085\pi$
$241$	16.5286	+	10.6223i	1.06470	+	0.684240i	0.113725	+	0.993512i	$0.463722\pi$
$242$	7.91067	+	5.08388i	0.508517	+	0.326804i
$243$		0			0
$244$	−12.6077	−	3.70194i	−0.807123	−	0.236993i
$245$	−10.2763	−	71.4734i	−0.656531	−	4.56627i
$246$		0			0
$247$	7.26180	+	15.9011i	0.462057	+	1.01176i
$248$	−1.21686	+	0.357304i	−0.0772709	+	0.0226888i
$249$		0			0
$250$	−2.57180	+	17.8873i	−0.162655	+	1.13129i
$251$	−16.0765	+	10.3317i	−1.01474	+	0.652133i	−0.938615	−	0.344966i	$-0.887891\pi$
$251$	−16.0765	+	10.3317i	−1.01474	+	0.652133i	−0.0761230	+	0.997098i	$0.524254\pi$
$252$		0			0
$253$	1.48542	+	21.6119i	0.0933873	+	1.35873i
$254$	−11.1093			−0.697056
$255$		0			0
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−10.7562	+	23.5529i	−0.670955	+	1.46919i	0.200995	+	0.979592i	$0.435583\pi$
$257$	−10.7562	+	23.5529i	−0.670955	+	1.46919i	−0.871950	+	0.489595i	$0.837145\pi$
$258$		0			0
$259$	−9.41124	−	20.6077i	−0.584786	−	1.28050i
$260$	8.36285	+	9.65125i	0.518642	+	0.598545i
$261$		0			0
$262$	−1.99605	−	0.586094i	−0.123317	−	0.0362090i
$263$	−13.2246	+	15.2620i	−0.815462	+	0.941094i	−0.999122	−	0.0418963i	$-0.986660\pi$
$263$	−13.2246	+	15.2620i	−0.815462	+	0.941094i	0.183660	+	0.982990i	$0.441206\pi$
$264$		0			0
$265$	13.8249	+	8.88473i	0.849257	+	0.545784i
$266$	−17.4728	+	20.1647i	−1.07133	+	1.23638i
$267$		0			0
$268$	−1.49202	−	10.3772i	−0.0911397	−	0.633890i
$269$	−18.1253	−	20.9177i	−1.10512	−	1.27537i	−0.958161	−	0.286230i	$-0.907598\pi$
$269$	−18.1253	−	20.9177i	−1.10512	−	1.27537i	−0.146956	−	0.989143i	$-0.546948\pi$
$270$		0			0
$271$	9.19444	−	2.69973i	0.558522	−	0.163997i	0.00972542	−	0.999953i	$-0.496904\pi$
$271$	9.19444	−	2.69973i	0.558522	−	0.163997i	0.548797	+	0.835956i	$0.315086\pi$
$272$	−0.0640134	+	0.140170i	−0.00388138	+	0.00849904i
$273$		0			0
$274$	13.9526	−	8.96678i	0.842907	−	0.541703i
$275$	43.8670			2.64528
$276$		0			0
$277$	20.7038			1.24397			0.621986	−	0.783028i	$-0.286326\pi$
$277$	20.7038			1.24397			0.621986	+	0.783028i	$0.286326\pi$
$278$	3.99343	−	2.56642i	0.239510	−	0.153924i
$279$		0			0
$280$	−8.09729	+	17.7306i	−0.483906	+	1.05961i
$281$	25.9855	−	7.63002i	1.55016	−	0.455169i	0.609014	−	0.793160i	$-0.291565\pi$
$281$	25.9855	−	7.63002i	1.55016	−	0.455169i	0.941149	+	0.337991i	$0.109747\pi$
$282$		0			0
$283$	−11.8750	−	13.7045i	−0.705898	−	0.814650i	0.283639	−	0.958931i	$-0.408458\pi$
$283$	−11.8750	−	13.7045i	−0.705898	−	0.814650i	−0.989537	+	0.144281i	$0.953913\pi$
$284$	−2.02922	−	14.1135i	−0.120412	−	0.837483i
$285$		0			0
$286$	9.84867	−	11.3660i	0.582364	−	0.672084i
$287$	−9.45470	−	6.07616i	−0.558093	−	0.358665i
$288$		0			0
$289$	11.1171	−	12.8298i	0.653946	−	0.754694i
$290$	19.2614	+	5.65564i	1.13107	+	0.332111i
$291$		0			0
$292$	−4.06295	−	4.68890i	−0.237766	−	0.274397i
$293$	9.24079	+	20.2345i	0.539853	+	1.18211i	0.961362	+	0.275289i	$0.0887735\pi$
$293$	9.24079	+	20.2345i	0.539853	+	1.18211i	−0.421509	+	0.906824i	$0.638499\pi$
$294$		0			0
$295$	5.14316	−	11.2620i	0.299447	−	0.655696i
$296$	−0.634433	+	4.41258i	−0.0368757	+	0.256476i
$297$		0			0
$298$	−17.0234			−0.986137
$299$	15.9237	+	1.18333i	0.920894	+	0.0684338i
$300$		0			0
$301$	−11.2808	+	7.24974i	−0.650215	+	0.417868i
$302$	1.00335	−	6.97848i	0.0577366	−	0.401567i
$303$		0			0
$304$	5.03763	−	1.47918i	0.288928	−	0.0848369i
$305$	20.9365	+	45.8445i	1.19882	+	2.62505i
$306$		0			0
$307$	1.57438	+	10.9500i	0.0898544	+	0.624951i	0.984132	+	0.177438i	$0.0567810\pi$
$307$	1.57438	+	10.9500i	0.0898544	+	0.624951i	−0.894278	+	0.447513i	$0.852310\pi$
$308$	22.0253	+	6.46722i	1.25501	+	0.368504i
$309$		0			0
$310$	4.09219	+	2.62989i	0.232421	+	0.149368i
$311$	−7.83646	−	5.03619i	−0.444365	−	0.285576i	0.299262	−	0.954171i	$-0.403260\pi$
$311$	−7.83646	−	5.03619i	−0.444365	−	0.285576i	−0.743627	+	0.668595i	$0.766896\pi$
$312$		0			0
$313$	−23.9745	−	7.03954i	−1.35512	−	0.397898i	−0.478078	−	0.878317i	$-0.658667\pi$
$313$	−23.9745	−	7.03954i	−1.35512	−	0.397898i	−0.877039	+	0.480419i	$0.840485\pi$
$314$	−0.870213	−	6.05246i	−0.0491090	−	0.341560i
$315$		0			0
$316$	1.21172	+	2.65329i	0.0681645	+	0.149259i
$317$	−17.1568	+	5.03770i	−0.963623	+	0.282945i	−0.725448	−	0.688277i	$-0.758367\pi$
$317$	−17.1568	+	5.03770i	−0.963623	+	0.282945i	−0.238175	+	0.971222i	$0.576549\pi$
$318$		0			0
$319$	3.36448	−	23.4005i	0.188375	−	1.31018i
$320$	3.22668	−	2.07366i	0.180377	−	0.115921i
$321$		0			0
$322$	8.45375	+	22.8590i	0.471109	+	1.27388i
$323$	0.809046			0.0450165
$324$		0			0
$325$	4.60165	−	32.0052i	0.255253	−	1.77533i
$326$	−2.49334	+	5.45964i	−0.138093	+	0.302382i
$327$		0			0
$328$	0.918700	+	2.01167i	0.0507267	+	0.111076i
$329$	3.69091	+	4.25953i	0.203486	+	0.234836i
$330$		0			0
$331$	4.22896	+	1.24173i	0.232444	+	0.0682518i	0.395880	−	0.918302i	$-0.370440\pi$
$331$	4.22896	+	1.24173i	0.232444	+	0.0682518i	−0.163436	+	0.986554i	$0.552258\pi$
$332$	−1.52841	+	1.76388i	−0.0838827	+	0.0968057i
$333$		0			0
$334$	−10.5054	−	6.75144i	−0.574832	−	0.369422i
$335$	−26.3331	+	30.3900i	−1.43873	+	1.66038i
$336$		0			0
$337$	1.92585	+	13.3946i	0.104908	+	0.729650i	0.972589	+	0.232529i	$0.0747002\pi$
$337$	1.92585	+	13.3946i	0.104908	+	0.729650i	−0.867682	+	0.497120i	$0.834391\pi$
$338$	1.25375	+	1.44690i	0.0681949	+	0.0787011i
$339$		0			0
$340$	0.567099	−	0.166515i	0.0307553	−	0.00903056i
$341$	2.37977	−	5.21096i	0.128872	−	0.282189i
$342$		0			0
$343$	−50.5587	+	32.4921i	−2.72991	+	1.75441i
$344$	2.63867			0.142267
$345$		0			0
$346$	3.79092			0.203801
$347$	−15.6449	+	10.0544i	−0.839862	+	0.539746i	−0.888397	−	0.459075i	$-0.848181\pi$
$347$	−15.6449	+	10.0544i	−0.839862	+	0.539746i	0.0485359	+	0.998821i	$0.484544\pi$
$348$		0			0
$349$	0.0738157	−	0.161634i	0.00395126	−	0.00865206i	−0.907646	−	0.419736i	$-0.862123\pi$
$349$	0.0738157	−	0.161634i	0.00395126	−	0.00865206i	0.911597	+	0.411084i	$0.134850\pi$
$350$	47.3540	−	13.9044i	2.53118	−	0.743221i
$351$		0			0
$352$	−2.95802	−	3.41373i	−0.157663	−	0.181953i
$353$	−1.92686	−	13.4016i	−0.102557	−	0.713297i	−0.974614	−	0.223893i	$-0.928123\pi$
$353$	−1.92686	−	13.4016i	−0.102557	−	0.713297i	0.872057	−	0.489404i	$-0.162786\pi$
$354$		0			0
$355$	−35.8142	+	41.3318i	−1.90082	+	2.19367i
$356$	4.63363	+	2.97785i	0.245582	+	0.157826i
$357$		0			0
$358$	0.296923	−	0.342668i	0.0156929	−	0.0181106i
$359$	−16.0185	−	4.70346i	−0.845425	−	0.248239i	−0.169794	−	0.985479i	$-0.554310\pi$
$359$	−16.0185	−	4.70346i	−0.845425	−	0.248239i	−0.675631	+	0.737240i	$0.736129\pi$
$360$		0			0
$361$	−5.60936	−	6.47354i	−0.295229	−	0.340713i
$362$	−3.25500	−	7.12745i	−0.171079	−	0.374610i
$363$		0			0
$364$	7.02892	−	15.3912i	0.368415	−	0.806717i
$365$	−3.38666	+	23.5547i	−0.177266	+	1.23291i
$366$		0			0
$367$	−28.8815			−1.50760			−0.753800	−	0.657104i	$-0.771781\pi$
$367$	−28.8815			−1.50760			−0.753800	+	0.657104i	$0.771781\pi$
$368$	1.03243	−	4.68338i	0.0538193	−	0.244138i
$369$		0			0
$370$	14.3844	−	9.24427i	0.747808	−	0.480587i
$371$	3.09875	−	21.5523i	0.160879	−	1.11894i
$372$		0			0
$373$	−30.3137	+	8.90090i	−1.56958	+	0.460871i	−0.946880	−	0.321587i	$-0.895784\pi$
$373$	−30.3137	+	8.90090i	−1.56958	+	0.460871i	−0.622703	+	0.782458i	$0.713966\pi$
$374$	−0.289150	−	0.633149i	−0.0149516	−	0.0327394i
$375$		0			0
$376$	−0.157836	−	1.09777i	−0.00813976	−	0.0566132i
$377$	−16.7200	−	4.90943i	−0.861122	−	0.252848i
$378$		0			0
$379$	12.3361	+	7.92793i	0.633663	+	0.407230i	0.817664	−	0.575696i	$-0.195269\pi$
$379$	12.3361	+	7.92793i	0.633663	+	0.407230i	−0.184001	+	0.982926i	$0.558905\pi$
$380$	−16.9410	−	10.8873i	−0.869057	−	0.558509i
$381$		0			0
$382$	14.7435	+	4.32909i	0.754344	+	0.221495i
$383$	0.995188	+	6.92168i	0.0508517	+	0.353681i	0.999322	+	0.0368156i	$0.0117214\pi$
$383$	0.995188	+	6.92168i	0.0508517	+	0.353681i	−0.948470	+	0.316866i	$0.897370\pi$
$384$		0			0
$385$	−36.5756	−	80.0894i	−1.86406	−	4.08173i
$386$	−8.42212	+	2.47296i	−0.428675	+	0.125870i
$387$		0			0
$388$	−1.87213	+	13.0210i	−0.0950431	+	0.661040i
$389$	−22.5596	+	14.4982i	−1.14382	+	0.735088i	−0.968399	−	0.249406i	$-0.919765\pi$
$389$	−22.5596	+	14.4982i	−1.14382	+	0.735088i	−0.175420	+	0.984494i	$0.556128\pi$
$390$		0			0
$391$	0.355971	−	0.647631i	0.0180022	−	0.0327521i
$392$	18.8261			0.950860
$393$		0			0
$394$	1.14132	−	7.93808i	0.0574990	−	0.399915i
$395$	4.64762	−	10.1769i	0.233847	−	0.512053i
$396$		0			0
$397$	−3.11296	−	6.81642i	−0.156235	−	0.342106i	0.815287	−	0.579057i	$-0.196579\pi$
$397$	−3.11296	−	6.81642i	−0.156235	−	0.342106i	−0.971522	+	0.236951i	$0.923852\pi$
$398$	−4.06208	−	4.68788i	−0.203613	−	0.234982i
$399$		0			0
$400$	−9.31811	−	2.73604i	−0.465905	−	0.136802i
$401$	21.2579	−	24.5329i	1.06157	−	1.22511i	0.0881412	−	0.996108i	$-0.471907\pi$
$401$	21.2579	−	24.5329i	1.06157	−	1.22511i	0.973425	−	0.229005i	$-0.0735472\pi$
$402$		0			0
$403$	−3.55226	−	2.28290i	−0.176951	−	0.113719i
$404$	4.26764	−	4.92512i	0.212323	−	0.245034i
$405$		0			0
$406$	−3.78526	−	26.3271i	−0.187859	−	1.30659i
$407$	−13.1867	−	15.2183i	−0.653641	−	0.754341i
$408$		0			0
$409$	11.9474	−	3.50809i	0.590763	−	0.173464i	0.0273315	−	0.999626i	$-0.491299\pi$
$409$	11.9474	−	3.50809i	0.590763	−	0.173464i	0.563432	+	0.826163i	$0.309481\pi$
$410$	3.52373	−	7.71588i	0.174024	−	0.381060i
$411$		0			0
$412$	−4.74908	+	3.05205i	−0.233970	+	0.150364i
$413$	−16.4040			−0.807186
$414$		0			0
$415$	8.95201			0.439437
$416$	−2.80094	+	1.80006i	−0.137327	+	0.0882550i
$417$		0			0
$418$	−9.85187	+	21.5726i	−0.481871	+	1.05515i
$419$	36.0999	−	10.5999i	1.76360	−	0.517838i	0.770739	−	0.637151i	$-0.219887\pi$
$419$	36.0999	−	10.5999i	1.76360	−	0.517838i	0.992857	+	0.119312i	$0.0380690\pi$
$420$		0			0
$421$	19.2959	+	22.2687i	0.940426	+	1.08531i	0.996220	+	0.0868670i	$0.0276855\pi$
$421$	19.2959	+	22.2687i	0.940426	+	1.08531i	−0.0557940	+	0.998442i	$0.517769\pi$
$422$	2.29655	+	15.9728i	0.111794	+	0.777545i
$423$		0			0
$424$	−2.80579	+	3.23806i	−0.136261	+	0.157254i
$425$	−1.25893	−	0.809065i	−0.0610671	−	0.0392454i
$426$		0			0
$427$	43.7291	−	50.4661i	2.11620	−	2.44223i
$428$	−6.51886	−	1.91411i	−0.315101	−	0.0925220i
$429$		0			0
$430$	−6.62768	−	7.64875i	−0.319615	−	0.368856i
$431$	−10.9672	−	24.0148i	−0.528272	−	1.15675i	−0.966212	−	0.257750i	$-0.917019\pi$
$431$	−10.9672	−	24.0148i	−0.528272	−	1.15675i	0.437940	−	0.899004i	$-0.355708\pi$
$432$		0			0
$433$	1.94160	−	4.25152i	0.0933075	−	0.204315i	−0.857224	−	0.514944i	$-0.827813\pi$
$433$	1.94160	−	4.25152i	0.0933075	−	0.204315i	0.950531	+	0.310629i	$0.100540\pi$
$434$	0.917233	−	6.37949i	0.0440286	−	0.306226i
$435$		0			0
$436$	−5.83285			−0.279343
$437$	−24.6189	+	5.28398i	−1.17768	+	0.252767i
$438$		0			0
$439$	−15.9800	+	10.2697i	−0.762685	+	0.490148i	−0.863246	−	0.504783i	$-0.831573\pi$
$439$	−15.9800	+	10.2697i	−0.762685	+	0.490148i	0.100561	+	0.994931i	$0.467936\pi$
$440$	−2.46564	+	17.1489i	−0.117545	+	0.817543i
$441$		0			0
$442$	−0.492275	+	0.144545i	−0.0234151	+	0.00687530i
$443$	−2.89004	−	6.32831i	−0.137310	−	0.300667i	0.828468	−	0.560036i	$-0.189213\pi$
$443$	−2.89004	−	6.32831i	−0.137310	−	0.300667i	−0.965778	+	0.259369i	$0.916485\pi$
$444$		0			0
$445$	−3.00658	−	20.9112i	−0.142526	−	0.991287i
$446$	8.78638	+	2.57991i	0.416047	+	0.122162i
$447$		0			0
$448$	−4.27520	−	2.74750i	−0.201984	−	0.129807i
$449$	−16.1820	−	10.3995i	−0.763676	−	0.490785i	0.0999035	−	0.994997i	$-0.468147\pi$
$449$	−16.1820	−	10.3995i	−0.763676	−	0.490785i	−0.863580	+	0.504212i	$0.831783\pi$
$450$		0			0
$451$	−9.58484	−	2.81436i	−0.451333	−	0.132523i
$452$	−2.08611	−	14.5092i	−0.0981223	−	0.682455i
$453$		0			0
$454$	3.90671	+	8.55450i	0.183351	+	0.401482i
$455$	−62.2696	+	18.2840i	−2.91925	+	0.857168i
$456$		0			0
$457$	−2.11293	+	14.6957i	−0.0988386	+	0.687438i	0.878807	+	0.477178i	$0.158340\pi$
$457$	−2.11293	+	14.6957i	−0.0988386	+	0.687438i	−0.977646	+	0.210260i	$0.932569\pi$
$458$	3.03741	−	1.95203i	0.141929	−	0.0912122i
$459$		0			0
$460$	−16.1690	+	8.77078i	−0.753885	+	0.408940i
$461$	5.15752			0.240209			0.120105	−	0.992761i	$-0.461677\pi$
$461$	5.15752			0.240209			0.120105	+	0.992761i	$0.461677\pi$
$462$		0			0
$463$	2.62828	−	18.2801i	0.122147	−	0.849548i	−0.832970	−	0.553318i	$-0.813361\pi$
$463$	2.62828	−	18.2801i	0.122147	−	0.849548i	0.955117	−	0.296230i	$-0.0957294\pi$
$464$	−2.17420	+	4.76083i	−0.100935	+	0.221016i
$465$		0			0
$466$	0.232050	+	0.508119i	0.0107495	+	0.0235382i
$467$	−21.7577	−	25.1097i	−1.00683	−	1.16194i	−0.986768	−	0.162140i	$-0.948160\pi$
$467$	−21.7577	−	25.1097i	−1.00683	−	1.16194i	−0.0200578	−	0.999799i	$-0.506385\pi$
$468$		0			0
$469$	51.1205	+	15.0103i	2.36053	+	0.693113i
$470$	−2.78569	+	3.21486i	−0.128494	+	0.148290i
$471$		0			0
$472$	2.71548	+	1.74513i	0.124990	+	0.0803263i
$473$	−7.80522	+	9.00770i	−0.358884	+	0.414175i
$474$		0			0
$475$	7.25639	+	50.4693i	0.332946	+	2.31569i
$476$	−0.512822	−	0.591828i	−0.0235052	−	0.0271264i
$477$		0			0
$478$	18.2994	−	5.37320i	0.836997	−	0.245764i
$479$	8.38605	−	18.3629i	0.383168	−	0.839022i	−0.615535	−	0.788110i	$-0.711060\pi$
$479$	8.38605	−	18.3629i	0.383168	−	0.839022i	0.998703	−	0.0509120i	$-0.0162128\pi$
$480$		0			0
$481$	−12.4865	+	8.02457i	−0.569334	+	0.365889i
$482$	19.6475			0.894921
$483$		0			0
$484$	9.40343			0.427429
$485$	42.4465	−	27.2787i	1.92740	−	1.23866i
$486$		0			0
$487$	−0.429295	+	0.940024i	−0.0194532	+	0.0425966i	−0.919109	−	0.394003i	$-0.871090\pi$
$487$	−0.429295	+	0.940024i	−0.0194532	+	0.0425966i	0.899656	+	0.436599i	$0.143817\pi$
$488$	−12.6077	+	3.70194i	−0.570722	+	0.167579i
$489$		0			0
$490$	−47.2865	−	54.5715i	−2.13618	−	2.46529i
$491$	1.24891	+	8.68634i	0.0563624	+	0.392009i	0.998402	+	0.0565079i	$0.0179966\pi$
$491$	1.24891	+	8.68634i	0.0563624	+	0.392009i	−0.942040	+	0.335501i	$0.891094\pi$
$492$		0			0
$493$	−0.528146	+	0.609513i	−0.0237865	+	0.0274511i
$494$	14.7058	+	9.45085i	0.661645	+	0.425214i
$495$		0			0
$496$	−0.830518	+	0.958469i	−0.0372914	+	0.0430365i
$497$	69.5263	+	20.4148i	3.11868	+	0.915727i
$498$		0			0
$499$	−21.6009	−	24.9287i	−0.966988	−	1.11596i	−0.993213	−	0.116308i	$-0.962894\pi$
$499$	−21.6009	−	24.9287i	−0.966988	−	1.11596i	0.0262248	−	0.999656i	$-0.491651\pi$
$500$	7.50704	+	16.4381i	0.335725	+	0.735136i
$501$		0			0
$502$	−7.93864	+	17.3832i	−0.354319	+	0.775850i
$503$	−6.15220	+	42.7895i	−0.274313	+	1.90789i	0.126922	+	0.991913i	$0.459490\pi$
$503$	−6.15220	+	42.7895i	−0.274313	+	1.90789i	−0.401235	+	0.915975i	$0.631419\pi$
$504$		0			0
$505$	−24.9958			−1.11230
$506$	12.9339	+	17.3780i	0.574980	+	0.772545i
$507$		0			0
$508$	−9.34570	+	6.00612i	−0.414648	+	0.266478i
$509$	3.28765	−	22.8661i	0.145722	−	1.01352i	−0.777398	−	0.629009i	$-0.783461\pi$
$509$	3.28765	−	22.8661i	0.145722	−	1.01352i	0.923120	−	0.384512i	$-0.125630\pi$
$510$		0			0
$511$	30.2527	−	8.88298i	1.33830	−	0.392960i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$		0			0
$514$	3.68492	+	25.6292i	0.162535	+	1.13046i
$515$	20.7756	+	6.10025i	0.915480	+	0.268809i
$516$		0			0
$517$	4.21438	+	2.70842i	0.185348	+	0.119116i
$518$	−19.0586	−	12.2482i	−0.837388	−	0.538157i
$519$		0			0
$520$	12.2531	+	3.59785i	0.537336	+	0.157776i
$521$	−2.22405	−	15.4686i	−0.0974373	−	0.677691i	−0.978735	−	0.205130i	$-0.934238\pi$
$521$	−2.22405	−	15.4686i	−0.0974373	−	0.677691i	0.881297	−	0.472562i	$-0.156671\pi$
$522$		0			0
$523$	9.07336	+	19.8679i	0.396750	+	0.868762i	0.997589	+	0.0693920i	$0.0221059\pi$
$523$	9.07336	+	19.8679i	0.396750	+	0.868762i	−0.600839	+	0.799370i	$0.705167\pi$
$524$	−1.99605	+	0.586094i	−0.0871980	+	0.0256036i
$525$		0			0
$526$	−2.87397	+	19.9889i	−0.125311	+	0.871559i
$527$	−0.164405	+	0.105657i	−0.00716161	+	0.00460249i
$528$		0			0
$529$	−6.60228	+	22.0320i	−0.287056	+	0.957914i
$530$	16.4337			0.713834
$531$		0			0
$532$	−3.79720	+	26.4101i	−0.164630	+	1.14502i
$533$	−3.05880	+	6.69784i	−0.132491	+	0.290115i
$534$		0			0
$535$	10.8253	+	23.7041i	0.468019	+	1.02482i
$536$	−6.86552	−	7.92324i	−0.296545	−	0.342232i
$537$		0			0
$538$	−26.5569	−	7.79781i	−1.14495	−	0.336187i
$539$	−55.6878	+	64.2671i	−2.39864	+	2.76818i
$540$		0			0
$541$	22.9569	+	14.7535i	0.986993	+	0.634302i	0.931341	−	0.364149i	$-0.118640\pi$
$541$	22.9569	+	14.7535i	0.986993	+	0.634302i	0.0556517	+	0.998450i	$0.482276\pi$
$542$	6.27527	−	7.24204i	0.269546	−	0.311072i
$543$		0			0
$544$	0.0219300	+	0.152527i	0.000940242	+	0.00653952i
$545$	14.6507	+	16.9078i	0.627566	+	0.724250i
$546$		0			0
$547$	4.01024	−	1.17751i	0.171465	−	0.0503468i	−0.194873	−	0.980828i	$-0.562429\pi$
$547$	4.01024	−	1.17751i	0.171465	−	0.0503468i	0.366338	+	0.930482i	$0.380611\pi$
$548$	6.88986	−	15.0867i	0.294320	−	0.644471i
$549$		0			0
$550$	36.9032	−	23.7163i	1.57356	−	1.01127i
$551$	27.4790			1.17065
$552$		0			0
$553$	−14.8234			−0.630356
$554$	17.4172	−	11.1933i	0.739984	−	0.475559i
$555$		0			0
$556$	1.97198	−	4.31802i	0.0836304	−	0.183125i
$557$	−23.6327	+	6.93919i	−1.00135	+	0.294023i	−0.741010	−	0.671494i	$-0.765653\pi$
$557$	−23.6327	+	6.93919i	−1.00135	+	0.294023i	−0.260340	+	0.965517i	$0.583835\pi$
$558$		0			0
$559$	5.75321	+	6.63956i	0.243335	+	0.280824i
$560$	2.77401	+	19.2936i	0.117223	+	0.815305i
$561$		0			0
$562$	17.7353	−	20.4676i	0.748117	−	0.863373i
$563$	6.66415	+	4.28279i	0.280860	+	0.180498i	0.673485	−	0.739201i	$-0.264797\pi$
$563$	6.66415	+	4.28279i	0.280860	+	0.180498i	−0.392625	+	0.919699i	$0.628433\pi$
$564$		0			0
$565$	−36.8183	+	42.4906i	−1.54896	+	1.78759i
$566$	−17.3992	−	5.10885i	−0.731341	−	0.214741i
$567$		0			0
$568$	−9.33743	−	10.7760i	−0.391790	−	0.452149i
$569$	−11.6550	−	25.5210i	−0.488605	−	1.06990i	−0.980007	−	0.198963i	$-0.936243\pi$
$569$	−11.6550	−	25.5210i	−0.488605	−	1.06990i	0.491402	−	0.870933i	$-0.336484\pi$
$570$		0			0
$571$	13.9088	−	30.4560i	0.582064	−	1.27454i	−0.358056	−	0.933700i	$-0.616560\pi$
$571$	13.9088	−	30.4560i	0.582064	−	1.27454i	0.940120	−	0.340843i	$-0.110712\pi$
$572$	2.14032	−	14.8863i	0.0894913	−	0.622426i
$573$		0			0
$574$	−11.2388			−0.469099
$575$	43.5928	+	16.3973i	1.81794	+	0.683813i
$576$		0			0
$577$	22.6292	−	14.5429i	0.942067	−	0.605430i	0.0230868	−	0.999733i	$-0.492651\pi$
$577$	22.6292	−	14.5429i	0.942067	−	0.605430i	0.918980	+	0.394304i	$0.129014\pi$
$578$	2.41597	−	16.8035i	0.100491	−	0.698932i
$579$		0			0
$580$	19.2614	−	5.65564i	0.799784	−	0.234838i
$581$	−4.92724	−	10.7891i	−0.204416	−	0.447609i
$582$		0			0
$583$	−2.75428	−	19.1565i	−0.114071	−	0.793380i
$584$	−5.95298	−	1.74795i	−0.246336	−	0.0723308i
$585$		0			0
$586$	18.7135	+	12.0264i	0.773046	+	0.496806i
$587$	−23.4106	−	15.0451i	−0.966260	−	0.620977i	−0.0405361	−	0.999178i	$-0.512907\pi$
$587$	−23.4106	−	15.0451i	−0.966260	−	0.620977i	−0.925724	+	0.378201i	$0.876543\pi$
$588$		0			0
$589$	6.38891	+	1.87595i	0.263250	+	0.0772973i
$590$	−1.76197	−	12.2548i	−0.0725391	−	0.504521i
$591$		0			0
$592$	1.85190	+	4.05510i	0.0761127	+	0.166664i
$593$	−24.8226	+	7.28856i	−1.01934	+	0.299305i	−0.748370	−	0.663282i	$-0.769163\pi$
$593$	−24.8226	+	7.28856i	−1.01934	+	0.299305i	−0.270971	+	0.962587i	$0.587345\pi$
$594$		0			0
$595$	−0.427461	+	2.97306i	−0.0175242	+	0.121883i
$596$	−14.3210	+	9.20353i	−0.586610	+	0.376991i
$597$		0			0
$598$	14.0357	−	7.61354i	0.573961	−	0.311341i
$599$	−22.3667			−0.913878			−0.456939	−	0.889498i	$-0.651054\pi$
$599$	−22.3667			−0.913878			−0.456939	+	0.889498i	$0.651054\pi$
$600$		0			0
$601$	3.97190	−	27.6252i	0.162017	−	1.12686i	−0.732807	−	0.680437i	$-0.761790\pi$
$601$	3.97190	−	27.6252i	0.162017	−	1.12686i	0.894824	−	0.446419i	$-0.147301\pi$
$602$	−5.57052	+	12.1977i	−0.227037	+	0.497143i
$603$		0			0
$604$	−2.92878	−	6.41313i	−0.119170	−	0.260946i
$605$	−23.6191	−	27.2579i	−0.960254	−	1.10819i
$606$		0			0
$607$	10.6536	+	3.12817i	0.432414	+	0.126968i	0.490694	−	0.871332i	$-0.336743\pi$
$607$	10.6536	+	3.12817i	0.432414	+	0.126968i	−0.0582796	+	0.998300i	$0.518561\pi$
$608$	3.43822	−	3.96792i	0.139438	−	0.160920i
$609$		0			0
$610$	42.3983	+	27.2477i	1.71666	+	1.10323i
$611$	2.41814	−	2.79068i	0.0978274	−	0.112899i
$612$		0			0
$613$	0.353036	+	2.45542i	0.0142590	+	0.0991733i	0.995708	−	0.0925495i	$-0.0295016\pi$
$613$	0.353036	+	2.45542i	0.0142590	+	0.0991733i	−0.981449	+	0.191723i	$0.938593\pi$
$614$	7.24448	+	8.36058i	0.292363	+	0.337405i
$615$		0			0
$616$	22.0253	−	6.46722i	0.887426	−	0.260572i
$617$	−7.59482	+	16.6303i	−0.305756	+	0.669512i	−0.998673	−	0.0515056i	$-0.983598\pi$
$617$	−7.59482	+	16.6303i	−0.305756	+	0.669512i	0.692917	+	0.721017i	$0.256325\pi$
$618$		0			0
$619$	27.4318	−	17.6293i	1.10258	−	0.708583i	0.142913	−	0.989735i	$-0.454353\pi$
$619$	27.4318	−	17.6293i	1.10258	−	0.708583i	0.959663	+	0.281152i	$0.0907166\pi$
$620$	4.86439			0.195359
$621$		0			0
$622$	−9.31522			−0.373506
$623$	−23.5478	+	15.1333i	−0.943423	+	0.606301i
$624$		0			0
$625$	8.62219	−	18.8800i	0.344888	−	0.755199i
$626$	−23.9745	+	7.03954i	−0.958213	+	0.281357i
$627$		0			0
$628$	−4.00428	−	4.62118i	−0.159788	−	0.184405i
$629$	0.0977630	+	0.679957i	0.00389807	+	0.0271116i
$630$		0			0
$631$	7.34061	−	8.47152i	0.292225	−	0.337246i	−0.590585	−	0.806975i	$-0.701103\pi$
$631$	7.34061	−	8.47152i	0.292225	−	0.337246i	0.882810	+	0.469729i	$0.155649\pi$
$632$	2.45384	+	1.57699i	0.0976086	+	0.0627292i
$633$		0			0
$634$	−11.7097	+	13.5137i	−0.465050	+	0.536696i
$635$	40.8842	+	12.0047i	1.62244	+	0.476391i
$636$		0			0
$637$	41.0474	+	47.3712i	1.62636	+	1.87692i
$638$	−9.82088	−	21.5047i	−0.388812	−	0.851380i
$639$		0			0
$640$	1.59335	−	3.48894i	0.0629826	−	0.137913i
$641$	−0.777722	+	5.40918i	−0.0307182	+	0.213650i	−0.999399	−	0.0346588i	$-0.988966\pi$
$641$	−0.777722	+	5.40918i	−0.0307182	+	0.213650i	0.968681	+	0.248308i	$0.0798747\pi$
$642$		0			0
$643$	13.2191			0.521310			0.260655	−	0.965432i	$-0.416061\pi$
$643$	13.2191			0.521310			0.260655	+	0.965432i	$0.416061\pi$
$644$	19.4702	+	14.6598i	0.767235	+	0.577676i
$645$		0			0
$646$	0.680613	−	0.437403i	0.0267784	−	0.0172094i
$647$	−2.65809	+	18.4874i	−0.104500	+	0.726815i	0.868446	+	0.495783i	$0.165119\pi$
$647$	−2.65809	+	18.4874i	−0.104500	+	0.726815i	−0.972946	+	0.231031i	$0.925790\pi$
$648$		0			0
$649$	−13.9899	+	4.10779i	−0.549150	+	0.161245i
$650$	−13.4321	−	29.4123i	−0.526852	−	1.15364i
$651$		0			0
$652$	0.854179	+	5.94094i	0.0334522	+	0.232665i
$653$	7.03544	+	2.06579i	0.275318	+	0.0808407i	0.416477	−	0.909146i	$-0.363265\pi$
$653$	7.03544	+	2.06579i	0.275318	+	0.0808407i	−0.141159	+	0.989987i	$0.545083\pi$
$654$		0			0
$655$	6.71252	+	4.31388i	0.262280	+	0.168557i
$656$	1.86045	+	1.19564i	0.0726385	+	0.0466819i
$657$		0			0
$658$	5.40787	+	1.58789i	0.210821	+	0.0619025i
$659$	6.35871	+	44.2258i	0.247700	+	1.72279i	0.611438	+	0.791292i	$0.290591\pi$
$659$	6.35871	+	44.2258i	0.247700	+	1.72279i	−0.363738	+	0.931501i	$0.618500\pi$
$660$		0			0
$661$	8.72297	+	19.1006i	0.339284	+	0.742929i	0.999970	−	0.00773351i	$-0.00246168\pi$
$661$	8.72297	+	19.1006i	0.339284	+	0.742929i	−0.660686	+	0.750663i	$0.729734\pi$
$662$	4.22896	−	1.24173i	0.164363	−	0.0482613i
$663$		0			0
$664$	−0.332156	+	2.31020i	−0.0128902	+	0.0896530i
$665$	86.0932	−	55.3288i	3.33855	−	2.14556i
$666$		0			0
$667$	12.0905	−	21.9966i	0.468144	−	0.851712i
$668$	−12.4878			−0.483169
$669$		0			0
$670$	−5.72273	+	39.8025i	−0.221088	+	1.53770i
$671$	24.6562	−	53.9896i	0.951843	−	2.08425i
$672$		0			0
$673$	11.6361	+	25.4795i	0.448538	+	0.982161i	0.989952	+	0.141405i	$0.0451620\pi$
$673$	11.6361	+	25.4795i	0.448538	+	0.982161i	−0.541414	+	0.840756i	$0.682111\pi$
$674$	8.86179	+	10.2271i	0.341343	+	0.393931i
$675$		0			0
$676$	1.83697	+	0.539384i	0.0706529	+	0.0207456i
$677$	28.2912	−	32.6498i	1.08732	−	1.25483i	0.122347	−	0.992487i	$-0.460958\pi$
$677$	28.2912	−	32.6498i	1.08732	−	1.25483i	0.964973	−	0.262348i	$-0.0844967\pi$
$678$		0			0
$679$	−56.2396	−	36.1430i	−2.15828	−	1.38704i
$680$	0.387049	−	0.446678i	0.0148427	−	0.0171293i
$681$		0			0
$682$	−0.815271	−	5.67034i	−0.0312183	−	0.217128i
$683$	15.1548	+	17.4896i	0.579884	+	0.669222i	0.967580	−	0.252566i	$-0.0812743\pi$
$683$	15.1548	+	17.4896i	0.579884	+	0.669222i	−0.387696	+	0.921787i	$0.626729\pi$
$684$		0			0
$685$	−61.0377	+	17.9223i	−2.33213	+	0.684775i
$686$	−24.9661	+	54.6682i	−0.953212	+	2.08724i
$687$		0			0
$688$	2.21979	−	1.42657i	0.0846286	−	0.0543875i
$689$	−14.2654			−0.543469
$690$		0			0
$691$	31.0298			1.18043			0.590215	−	0.807246i	$-0.299043\pi$
$691$	31.0298			1.18043			0.590215	+	0.807246i	$0.299043\pi$
$692$	3.18912	−	2.04952i	0.121232	−	0.0779112i
$693$		0			0
$694$	−7.72552	+	16.9165i	−0.293257	+	0.642143i
$695$	−17.4699	+	5.12962i	−0.662670	+	0.194577i
$696$		0			0
$697$	0.223167	+	0.257548i	0.00845304	+	0.00975533i
$698$	−0.0252881	−	0.175883i	−0.000957169	−	0.00665726i
$699$		0			0
$700$	32.3195	−	37.2986i	1.22156	−	1.40976i
$701$	−11.2227	−	7.21241i	−0.423877	−	0.272409i	0.311264	−	0.950323i	$-0.399248\pi$
$701$	−11.2227	−	7.21241i	−0.423877	−	0.272409i	−0.735141	+	0.677915i	$0.762884\pi$
$702$		0			0
$703$	15.3274	−	17.6888i	0.578085	−	0.667146i
$704$	−4.33405	−	1.27259i	−0.163345	−	0.0479626i
$705$		0			0
$706$	−8.86645	−	10.2324i	−0.333693	−	0.385102i
$707$	13.7578	+	30.1255i	0.517417	+	1.13299i
$708$		0			0
$709$	−17.9000	+	39.1955i	−0.672248	+	1.47202i	0.198405	+	0.980120i	$0.436424\pi$
$709$	−17.9000	+	39.1955i	−0.672248	+	1.47202i	−0.870653	+	0.491898i	$0.836303\pi$
$710$	−7.78318	+	54.1332i	−0.292097	+	2.03158i
$711$		0			0
$712$	5.50801			0.206421
$713$	4.31272	−	4.28884i	0.161513	−	0.160618i
$714$		0			0
$715$	−48.5271	+	31.1865i	−1.81481	+	1.16631i
$716$	0.0645276	−	0.448799i	0.00241151	−	0.0167724i
$717$		0			0
$718$	−16.0185	+	4.70346i	−0.597806	+	0.175532i
$719$	8.48367	+	18.5766i	0.316387	+	0.692792i	0.999288	−	0.0377191i	$-0.0120092\pi$
$719$	8.48367	+	18.5766i	0.316387	+	0.692792i	−0.682901	+	0.730511i	$0.739282\pi$
$720$		0			0
$721$	−4.08283	−	28.3967i	−0.152053	−	1.05755i
$722$	−8.21875	−	2.41324i	−0.305870	−	0.0898116i
$723$		0			0
$724$	−6.59167	−	4.23621i	−0.244977	−	0.157437i
$725$	−42.7592	−	27.4797i	−1.58804	−	1.02057i
$726$		0			0
$727$	−14.2668	−	4.18910i	−0.529125	−	0.155365i	0.00624850	−	0.999980i	$-0.498011\pi$
$727$	−14.2668	−	4.18910i	−0.529125	−	0.155365i	−0.535374	+	0.844615i	$0.679829\pi$
$728$	−2.40800	−	16.7480i	−0.0892464	−	0.620722i
$729$		0			0
$730$	9.88560	+	21.6465i	0.365883	+	0.801171i
$731$	0.390135	−	0.114554i	0.0144297	−	0.00423693i
$732$		0			0
$733$	3.75763	−	26.1349i	0.138791	−	0.965314i	−0.794774	−	0.606906i	$-0.792410\pi$
$733$	3.75763	−	26.1349i	0.138791	−	0.965314i	0.933565	−	0.358408i	$-0.116680\pi$
$734$	−24.2966	+	15.6145i	−0.896805	+	0.576341i
$735$		0			0
$736$	−1.66349	−	4.49809i	−0.0613171	−	0.165802i
$737$	47.3561			1.74439
$738$		0			0
$739$	1.27828	−	8.89062i	0.0470222	−	0.327047i	−0.952709	−	0.303883i	$-0.901717\pi$
$739$	1.27828	−	8.89062i	0.0470222	−	0.327047i	0.999732	−	0.0231641i	$-0.00737402\pi$
$740$	7.10307	−	15.5536i	0.261114	−	0.571760i
$741$		0			0
$742$	−9.04520	−	19.8062i	−0.332060	−	0.727109i
$743$	1.57647	+	1.81935i	0.0578353	+	0.0667454i	0.783930	−	0.620849i	$-0.213212\pi$
$743$	1.57647	+	1.81935i	0.0578353	+	0.0667454i	−0.726095	+	0.687595i	$0.758667\pi$
$744$		0			0
$745$	62.6492	+	18.3955i	2.29529	+	0.673958i
$746$	−20.6893	+	23.8767i	−0.757489	+	0.874189i
$747$		0			0
$748$	−0.585554	−	0.376313i	−0.0214100	−	0.0137594i
$749$	22.6104	−	26.0938i	0.826165	−	0.953445i
$750$		0			0
$751$	4.09723	+	28.4968i	0.149510	+	1.03986i	0.917024	+	0.398832i	$0.130584\pi$
$751$	4.09723	+	28.4968i	0.149510	+	1.03986i	−0.767514	+	0.641032i	$0.778506\pi$
$752$	−0.726280	−	0.838172i	−0.0264847	−	0.0305650i
$753$		0			0
$754$	−16.7200	+	4.90943i	−0.608906	+	0.178791i
$755$	−11.2335	+	24.5979i	−0.408829	+	0.895210i
$756$		0			0
$757$	−28.5527	+	18.3497i	−1.03776	+	0.666930i	−0.944433	−	0.328705i	$-0.893388\pi$
$757$	−28.5527	+	18.3497i	−1.03776	+	0.666930i	−0.0933311	+	0.995635i	$0.529751\pi$
$758$	14.6640			0.532619
$759$		0			0
$760$	−20.1378			−0.730476
$761$	−28.4298	+	18.2707i	−1.03058	+	0.662314i	−0.942640	−	0.333812i	$-0.891665\pi$
$761$	−28.4298	+	18.2707i	−1.03058	+	0.662314i	−0.0879404	+	0.996126i	$0.528029\pi$
$762$		0			0
$763$	12.3138	−	26.9634i	0.445789	−	0.976142i
$764$	14.7435	−	4.32909i	0.533402	−	0.156621i
$765$		0			0
$766$	4.57935	+	5.28485i	0.165459	+	0.190949i
$767$	1.52949	+	10.6378i	0.0552267	+	0.384110i
$768$		0			0
$769$	−34.5790	+	39.9063i	−1.24695	+	1.43906i	−0.392313	+	0.919832i	$0.628325\pi$
$769$	−34.5790	+	39.9063i	−1.24695	+	1.43906i	−0.854637	+	0.519225i	$0.826221\pi$
$770$	−74.0689	−	47.6012i	−2.66926	−	1.71543i
$771$		0			0
$772$	−5.74815	+	6.63372i	−0.206881	+	0.238753i
$773$	1.40343	+	0.412085i	0.0504779	+	0.0148217i	0.306874	−	0.951750i	$-0.400717\pi$
$773$	1.40343	+	0.412085i	0.0504779	+	0.0148217i	−0.256396	+	0.966572i	$0.582535\pi$
$774$		0			0
$775$	−8.06557	−	9.30817i	−0.289724	−	0.334359i
$776$	5.46473	+	11.9661i	0.196172	+	0.429558i
$777$		0			0
$778$	−11.1401	+	24.3933i	−0.399390	+	0.874543i
$779$	1.65244	−	11.4930i	0.0592049	−	0.411779i
$780$		0			0
$781$	64.4065			2.30465
$782$	−0.0506740	−	0.737275i	−0.00181210	−	0.0263649i
$783$		0			0
$784$	15.8375	−	10.1781i	0.565625	−	0.363505i
$785$	−3.33775	+	23.2146i	−0.119129	+	0.828563i
$786$		0			0
$787$	16.6618	−	4.89234i	0.593928	−	0.174393i	0.0290648	−	0.999578i	$-0.490747\pi$
$787$	16.6618	−	4.89234i	0.593928	−	0.174393i	0.564863	+	0.825184i	$0.308929\pi$
$788$	−3.33151	−	7.29498i	−0.118680	−	0.259873i
$789$		0			0
$790$	−1.59220	−	11.0740i	−0.0566480	−	0.393996i
$791$	71.4755	+	20.9871i	2.54138	+	0.746216i
$792$		0			0
$793$	−36.8041	−	23.6526i	−1.30695	−	0.839928i
$794$	−6.30402	−	4.05135i	−0.223721	−	0.143777i
$795$		0			0
$796$	−5.95170	−	1.74758i	−0.210952	−	0.0619412i
$797$	−7.47464	−	51.9872i	−0.264765	−	1.84148i	−0.495676	−	0.868507i	$-0.665080\pi$
$797$	−7.47464	−	51.9872i	−0.264765	−	1.84148i	0.230911	−	0.972975i	$-0.425829\pi$
$798$		0			0
$799$	−0.0709947	−	0.155457i	−0.00251161	−	0.00549966i
$800$	−9.31811	+	2.73604i	−0.329445	+	0.0967337i
$801$		0			0
$802$	4.61977	−	32.1312i	0.163130	−	1.13459i
$803$	23.5761	−	15.1514i	0.831981	−	0.534682i
$804$		0			0
$805$	−6.40994	−	93.2605i	−0.225921	−	3.28700i
$806$	−4.22258			−0.148734
$807$		0			0
$808$	0.927448	−	6.45054i	0.0326275	−	0.226929i
$809$	15.2150	−	33.3162i	0.534932	−	1.17134i	−0.428539	−	0.903523i	$-0.640972\pi$
$809$	15.2150	−	33.3162i	0.534932	−	1.17134i	0.963471	−	0.267814i	$-0.0863011\pi$
$810$		0			0
$811$	16.4742	+	36.0734i	0.578486	+	1.26671i	0.942155	+	0.335179i	$0.108797\pi$
$811$	16.4742	+	36.0734i	0.578486	+	1.26671i	−0.363669	+	0.931528i	$0.618476\pi$
$812$	−17.4179	−	20.1013i	−0.611247	−	0.705417i
$813$		0			0
$814$	−19.3210	−	5.67315i	−0.677200	−	0.198844i
$815$	15.0756	−	17.3982i	0.528077	−	0.609433i
$816$		0			0
$817$	−11.6546	−	7.48993i	−0.407742	−	0.262040i
$818$	8.15422	−	9.41047i	0.285105	−	0.329029i
$819$		0			0
$820$	−1.20717	−	8.39608i	−0.0421564	−	0.293204i
$821$	−20.1284	−	23.2294i	−0.702484	−	0.810710i	0.286602	−	0.958050i	$-0.407474\pi$
$821$	−20.1284	−	23.2294i	−0.702484	−	0.810710i	−0.989086	+	0.147340i	$0.952929\pi$
$822$		0			0
$823$	−15.5325	+	4.56075i	−0.541429	+	0.158978i	−0.541001	−	0.841022i	$-0.681954\pi$
$823$	−15.5325	+	4.56075i	−0.541429	+	0.158978i	−0.000428046		1.00000i	$0.500136\pi$
$824$	−2.34512	+	5.13509i	−0.0816960	+	0.178889i
$825$		0			0
$826$	−13.7999	+	8.86865i	−0.480160	+	0.308580i
$827$	−53.7834			−1.87023			−0.935115	−	0.354344i	$-0.884704\pi$
$827$	−53.7834			−1.87023			−0.935115	+	0.354344i	$0.884704\pi$
$828$		0			0
$829$	6.11983			0.212550			0.106275	−	0.994337i	$-0.466108\pi$
$829$	6.11983			0.212550			0.106275	+	0.994337i	$0.466108\pi$
$830$	7.53091	−	4.83982i	0.261402	−	0.167993i
$831$		0			0
$832$	−1.38312	+	3.02861i	−0.0479510	+	0.104998i
$833$	2.78349	−	0.817307i	0.0964423	−	0.0283180i
$834$		0			0
$835$	31.3664	+	36.1987i	1.08548	+	1.25271i
$836$	3.37510	+	23.4743i	0.116730	+	0.811877i
$837$		0			0
$838$	24.6384	−	28.4343i	0.851121	−	0.982246i
$839$	27.0132	+	17.3603i	0.932598	+	0.599344i	0.916287	−	0.400523i	$-0.131172\pi$
$839$	27.0132	+	17.3603i	0.932598	+	0.599344i	0.0163108	+	0.999867i	$0.494808\pi$
$840$		0			0
$841$	1.05262	−	1.21479i	0.0362972	−	0.0418893i
$842$	28.2721	+	8.30145i	0.974322	+	0.286087i
$843$		0			0
$844$	10.5675	+	12.1956i	0.363750	+	0.419790i
$845$	−3.05051	−	6.67968i	−0.104941	−	0.229788i
$846$		0			0
$847$	−19.8517	+	43.4692i	−0.682113	+	1.49362i
$848$	−0.609757	+	4.24096i	−0.0209392	+	0.145635i
$849$		0			0
$850$	−1.49649			−0.0513293
$851$	−7.41576	−	20.0523i	−0.254209	−	0.687383i
$852$		0			0
$853$	20.9941	−	13.4921i	0.718825	−	0.461961i	−0.129403	−	0.991592i	$-0.541306\pi$
$853$	20.9941	−	13.4921i	0.718825	−	0.461961i	0.848228	+	0.529631i	$0.177670\pi$
$854$	9.50325	−	66.0965i	0.325194	−	2.26178i
$855$		0			0
$856$	−6.51886	+	1.91411i	−0.222810	+	0.0654229i
$857$	18.8156	+	41.2005i	0.642730	+	1.40738i	0.897776	+	0.440453i	$0.145182\pi$
$857$	18.8156	+	41.2005i	0.642730	+	1.40738i	−0.255046	+	0.966929i	$0.582091\pi$
$858$		0			0
$859$	8.05041	+	55.9918i	0.274676	+	1.91042i	0.396806	+	0.917903i	$0.370119\pi$
$859$	8.05041	+	55.9918i	0.274676	+	1.91042i	−0.122129	+	0.992514i	$0.538972\pi$
$860$	−9.71079	−	2.85135i	−0.331135	−	0.0972301i
$861$		0			0
$862$	−22.2096	−	14.2732i	−0.756462	−	0.486149i
$863$	−9.35900	−	6.01466i	−0.318584	−	0.204741i	0.371568	−	0.928406i	$-0.378820\pi$
$863$	−9.35900	−	6.01466i	−0.318584	−	0.204741i	−0.690152	+	0.723664i	$0.742456\pi$
$864$		0			0
$865$	−13.9513	−	4.09647i	−0.474358	−	0.139284i
$866$	−0.665164	−	4.62632i	−0.0226032	−	0.157209i
$867$		0			0
$868$	−2.67739	−	5.86267i	−0.0908765	−	0.198992i
$869$	−12.6419	+	3.71200i	−0.428848	+	0.125921i
$870$		0			0
$871$	4.96766	−	34.5508i	0.168323	−	1.17071i
$872$	−4.90690	+	3.15347i	−0.166169	+	0.106790i
$873$		0			0
$874$	−17.8540	+	17.7552i	−0.603921	+	0.600577i
$875$	−91.8366			−3.10464
$876$		0			0
$877$	5.70529	−	39.6811i	0.192654	−	1.33994i	−0.632294	−	0.774728i	$-0.717887\pi$
$877$	5.70529	−	39.6811i	0.192654	−	1.33994i	0.824948	−	0.565208i	$-0.191204\pi$
$878$	−7.89101	+	17.2789i	−0.266309	+	0.583135i
$879$		0			0
$880$	7.19718	+	15.7596i	0.242617	+	0.531257i
$881$	−28.9947	−	33.4617i	−0.976857	−	1.12735i	−0.991843	−	0.127466i	$-0.959316\pi$
$881$	−28.9947	−	33.4617i	−0.976857	−	1.12735i	0.0149857	−	0.999888i	$-0.495230\pi$
$882$		0			0
$883$	−43.8954	−	12.8889i	−1.47720	−	0.433745i	−0.558768	−	0.829324i	$-0.688726\pi$
$883$	−43.8954	−	12.8889i	−1.47720	−	0.433745i	−0.918432	+	0.395579i	$0.870544\pi$
$884$	−0.335981	+	0.387743i	−0.0113003	+	0.0130412i
$885$		0			0
$886$	−5.85261	−	3.76124i	−0.196622	−	0.126361i
$887$	−0.751262	+	0.867002i	−0.0252249	+	0.0291111i	−0.768222	−	0.640184i	$-0.778858\pi$
$887$	−0.751262	+	0.867002i	−0.0252249	+	0.0291111i	0.742997	+	0.669295i	$0.233404\pi$
$888$		0			0
$889$	−8.03460	−	55.8818i	−0.269472	−	1.87422i
$890$	−13.8348	−	15.9662i	−0.463742	−	0.535187i
$891$		0			0
$892$	8.78638	−	2.57991i	0.294190	−	0.0863819i
$893$	−2.41892	+	5.29670i	−0.0809462	+	0.177247i
$894$		0			0
$895$	−1.46302	+	0.940226i	−0.0489034	+	0.0314283i
$896$	−5.08193			−0.169776
$897$		0			0
$898$	−19.2356			−0.641900
$899$	−5.58398	+	3.58861i	−0.186236	+	0.119687i
$900$		0			0
$901$	−0.274270	+	0.600567i	−0.00913725	+	0.0200078i
$902$	−9.58484	+	2.81436i	−0.319140	+	0.0937081i
$903$		0			0
$904$	−9.59921	−	11.0781i	−0.319265	−	0.368451i
$905$	4.27708	+	29.7477i	0.142175	+	0.988848i
$906$		0			0
$907$	0.859844	−	0.992312i	0.0285506	−	0.0329492i	−0.741295	−	0.671180i	$-0.765788\pi$
$907$	0.859844	−	0.992312i	0.0285506	−	0.0329492i	0.769845	+	0.638231i	$0.220333\pi$
$908$	7.91144	+	5.08437i	0.262550	+	0.168731i
$909$		0			0
$910$	−42.4995	+	49.0470i	−1.40884	+	1.62589i
$911$	−29.5463	−	8.67558i	−0.978913	−	0.287435i	−0.247138	−	0.968980i	$-0.579490\pi$
$911$	−29.5463	−	8.67558i	−0.978913	−	0.287435i	−0.731776	+	0.681545i	$0.761308\pi$
$912$		0			0
$913$	−6.90387	−	7.96750i	−0.228485	−	0.263686i
$914$	6.16761	+	13.5052i	0.204006	+	0.446711i
$915$		0			0
$916$	1.49989	−	3.28430i	0.0495577	−	0.108516i
$917$	1.50456	−	10.4644i	0.0496850	−	0.345567i
$918$		0			0
$919$	13.9421			0.459906			0.229953	−	0.973202i	$-0.426143\pi$
$919$	13.9421			0.459906			0.229953	+	0.973202i	$0.426143\pi$
$920$	−8.86042	+	16.1201i	−0.292119	+	0.531464i
$921$		0			0
$922$	4.33878	−	2.78836i	0.142890	−	0.0918299i
$923$	6.75625	−	46.9907i	0.222385	−	1.54672i
$924$		0			0
$925$	−41.5397	+	12.1972i	−1.36582	+	0.401040i
$926$	−7.67191	−	16.7991i	−0.252115	−	0.552054i
$927$		0			0
$928$	0.744847	+	5.18052i	0.0244508	+	0.170059i
$929$	20.3866	+	5.98604i	0.668862	+	0.196396i	0.598496	−	0.801126i	$-0.295765\pi$
$929$	20.3866	+	5.98604i	0.668862	+	0.196396i	0.0703660	+	0.997521i	$0.477583\pi$
$930$		0			0
$931$	−83.1517	−	53.4383i	−2.72519	−	1.75137i
$932$	0.469923	+	0.302001i	0.0153929	+	0.00989238i
$933$		0			0
$934$	−31.8791	−	9.36054i	−1.04311	−	0.306286i
$935$	0.379943	+	2.64256i	0.0124255	+	0.0864211i
$936$		0			0
$937$	−2.43970	−	5.34221i	−0.0797017	−	0.174522i	0.865586	−	0.500760i	$-0.166946\pi$
$937$	−2.43970	−	5.34221i	−0.0797017	−	0.174522i	−0.945288	+	0.326238i	$0.894219\pi$
$938$	51.1205	−	15.0103i	1.66915	−	0.490105i
$939$		0			0
$940$	−0.605388	+	4.21056i	−0.0197456	+	0.137333i
$941$	20.9374	−	13.4557i	0.682540	−	0.438642i	−0.152886	−	0.988244i	$-0.548857\pi$
$941$	20.9374	−	13.4557i	0.682540	−	0.438642i	0.835427	+	0.549602i	$0.185220\pi$
$942$		0			0
$943$	−8.47294	−	6.37954i	−0.275917	−	0.207747i
$944$	3.22790			0.105059
$945$		0			0
$946$	−1.69624	+	11.7976i	−0.0551494	+	0.383572i
$947$	−20.3853	+	44.6375i	−0.662433	+	1.45053i	0.217805	+	0.975992i	$0.430110\pi$
$947$	−20.3853	+	44.6375i	−0.662433	+	1.45053i	−0.880238	+	0.474533i	$0.842617\pi$
$948$		0			0
$949$	−8.58128	−	18.7904i	−0.278560	−	0.609961i
$950$	33.3902	+	38.5344i	1.08332	+	1.25022i
$951$		0			0
$952$	−0.751380	−	0.220625i	−0.0243524	−	0.00715050i
$953$	−18.3971	+	21.2314i	−0.595941	+	0.687753i	−0.970954	−	0.239267i	$-0.923093\pi$
$953$	−18.3971	+	21.2314i	−0.595941	+	0.687753i	0.375013	+	0.927020i	$0.377638\pi$
$954$		0			0
$955$	−49.5809	−	31.8637i	−1.60440	−	1.03109i
$956$	12.4895	−	14.4136i	0.403939	−	0.466171i
$957$		0			0
$958$	−2.87293	−	19.9817i	−0.0928202	−	0.645579i
$959$	55.1958	+	63.6993i	1.78236	+	2.05696i
$960$		0			0
$961$	28.2010	−	8.28056i	0.909710	−	0.267115i
$962$	−6.16588	+	13.5014i	−0.198796	+	0.435302i
$963$		0			0
$964$	16.5286	−	10.6223i	0.532349	−	0.342120i
$965$	33.6673			1.08379
$966$		0			0
$967$	−25.6391			−0.824498			−0.412249	−	0.911071i	$-0.635257\pi$
$967$	−25.6391			−0.824498			−0.412249	+	0.911071i	$0.635257\pi$
$968$	7.91067	−	5.08388i	0.254259	−	0.163402i
$969$		0			0
$970$	20.9603	−	45.8966i	0.672994	−	1.47365i
$971$	8.10494	−	2.37983i	0.260100	−	0.0763722i	−0.149083	−	0.988825i	$-0.547632\pi$
$971$	8.10494	−	2.37983i	0.260100	−	0.0763722i	0.409183	+	0.912452i	$0.365814\pi$
$972$		0			0
$973$	15.7978	+	18.2317i	0.506455	+	0.584480i
$974$	0.147070	+	1.02289i	0.00471242	+	0.0327756i
$975$		0			0
$976$	−8.60482	+	9.93049i	−0.275433	+	0.317867i
$977$	31.8210	+	20.4501i	1.01804	+	0.654257i	0.939463	−	0.342651i	$-0.111325\pi$
$977$	31.8210	+	20.4501i	1.01804	+	0.654257i	0.0785809	+	0.996908i	$0.474961\pi$
$978$		0			0
$979$	−16.2928	+	18.8029i	−0.520719	+	0.600942i
$980$	−69.2835	−	20.3435i	−2.21318	−	0.649848i
$981$		0			0
$982$	5.74684	+	6.63221i	0.183389	+	0.211642i
$983$	0.324247	+	0.710003i	0.0103419	+	0.0226456i	0.914732	−	0.404060i	$-0.132401\pi$
$983$	0.324247	+	0.710003i	0.0103419	+	0.0226456i	−0.904391	+	0.426706i	$0.859674\pi$
$984$		0			0
$985$	−12.7782	+	27.9803i	−0.407147	+	0.891527i
$986$	−0.114777	+	0.798293i	−0.00365525	+	0.0254228i
$987$		0			0
$988$	17.4808			0.556139
$989$	−11.1235	+	6.03384i	−0.353706	+	0.191865i
$990$		0			0
$991$	32.8890	−	21.1365i	1.04475	−	0.671422i	0.0985951	−	0.995128i	$-0.468565\pi$
$991$	32.8890	−	21.1365i	1.04475	−	0.671422i	0.946158	+	0.323706i	$0.104929\pi$
$992$	−0.180489	+	1.25533i	−0.00573053	+	0.0398567i
$993$		0			0
$994$	69.5263	−	20.4148i	2.20524	−	0.647517i
$995$	9.88347	+	21.6418i	0.313327	+	0.686091i
$996$		0			0
$997$	5.82237	+	40.4955i	0.184396	+	1.28250i	0.846216	+	0.532841i	$0.178875\pi$
$997$	5.82237	+	40.4955i	0.184396	+	1.28250i	−0.661819	+	0.749663i	$0.730215\pi$
$998$	−31.6493	−	9.29308i	−1.00184	−	0.294167i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.g.127.1	✓	20
3.2	odd	2		414.2.i.h.127.2	yes	20
23.2	even	11	inner	414.2.i.g.163.1	yes	20
23.5	odd	22		9522.2.a.ci.1.2		10
23.18	even	11		9522.2.a.cj.1.9		10
69.2	odd	22		414.2.i.h.163.2	yes	20
69.5	even	22		9522.2.a.ch.1.9		10
69.41	odd	22		9522.2.a.cg.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.127.1	✓	20	1.1	even	1	trivial
414.2.i.g.163.1	yes	20	23.2	even	11	inner
414.2.i.h.127.2	yes	20	3.2	odd	2
414.2.i.h.163.2	yes	20	69.2	odd	22
9522.2.a.cg.1.2		10	69.41	odd	22
9522.2.a.ch.1.9		10	69.5	even	22
9522.2.a.ci.1.2		10	23.5	odd	22
9522.2.a.cj.1.9		10	23.18	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(-3.68019 + 1.08060i) q^{5} +(3.32796 + 3.84067i) q^{7} +(-0.142315 - 0.989821i) q^{8} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(-3.68019 + 1.08060i) q^{5} +(3.32796 + 3.84067i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-2.51176 + 2.89872i) q^{10} +(3.79996 + 2.44208i) q^{11} +(2.18035 - 2.51626i) q^{13} +(4.87608 + 1.43175i) q^{14} +(-0.654861 - 0.755750i) q^{16} +(-0.0640134 - 0.140170i) q^{17} +(-2.18106 + 4.77585i) q^{19} +(-0.545857 + 3.79652i) q^{20} +4.51702 q^{22} +(2.86337 + 3.84723i) q^{23} +(8.16983 - 5.25043i) q^{25} +(0.473835 - 3.29560i) q^{26} +(4.87608 - 1.43175i) q^{28} +(-2.17420 - 4.76083i) q^{29} +(-0.180489 - 1.25533i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-0.129633 - 0.0833101i) q^{34} +(-16.3978 - 10.5382i) q^{35} +(-4.27738 - 1.25595i) q^{37} +(0.747197 + 5.19687i) q^{38} +(1.59335 + 3.48894i) q^{40} +(-2.12194 + 0.623058i) q^{41} +(-0.375521 + 2.61181i) q^{43} +(3.79996 - 2.44208i) q^{44} +(4.48878 + 1.68844i) q^{46} +1.10906 q^{47} +(-2.67923 + 18.6344i) q^{49} +(4.03430 - 8.83388i) q^{50} +(-1.38312 - 3.02861i) q^{52} +(-2.80579 - 3.23806i) q^{53} +(-16.6235 - 4.88109i) q^{55} +(3.32796 - 3.84067i) q^{56} +(-4.40295 - 2.82960i) q^{58} +(-2.11382 + 2.43948i) q^{59} +(-1.87001 - 13.0062i) q^{61} +(-0.830518 - 0.958469i) q^{62} +(-0.959493 + 0.281733i) q^{64} +(-5.30503 + 11.6164i) q^{65} +(8.81965 - 5.66805i) q^{67} -0.154095 q^{68} -19.4920 q^{70} +(11.9951 - 7.70881i) q^{71} +(2.57736 - 5.64363i) q^{73} +(-4.27738 + 1.25595i) q^{74} +(3.43822 + 3.96792i) q^{76} +(3.26686 + 22.7215i) q^{77} +(-1.91015 + 2.20444i) q^{79} +(3.22668 + 2.07366i) q^{80} +(-1.44824 + 1.67136i) q^{82} +(-2.23941 - 0.657551i) q^{83} +(0.387049 + 0.446678i) q^{85} +(1.09614 + 2.40021i) q^{86} +(1.87644 - 4.10882i) q^{88} +(-0.783871 + 5.45194i) q^{89} +16.9202 q^{91} +(4.68904 - 1.00641i) q^{92} +(0.933001 - 0.599603i) q^{94} +(2.86591 - 19.9329i) q^{95} +(-12.6220 + 3.70615i) q^{97} +(7.82063 + 17.1248i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8	\( 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8} - 2 q^{10} + 2 q^{11} + 18 q^{14} - 2 q^{16} - 18 q^{17} + 16 q^{19} - 2 q^{20} + 24 q^{22} + 2 q^{23} + 38 q^{25} + 18 q^{28} + 30 q^{29} + 14 q^{31} - 2 q^{32} + 4 q^{34} - 48 q^{35} - 20 q^{37} + 16 q^{38} - 2 q^{40} + 12 q^{41} - 28 q^{43} + 2 q^{44} + 2 q^{46} - 32 q^{47} + 6 q^{49} - 6 q^{50} + 46 q^{53} - 28 q^{55} - 4 q^{56} - 14 q^{58} - 50 q^{61} - 8 q^{62} - 2 q^{64} - 16 q^{65} - 8 q^{67} + 48 q^{68} - 48 q^{70} - 12 q^{71} - 18 q^{73} - 20 q^{74} - 6 q^{76} + 4 q^{77} - 18 q^{79} - 2 q^{80} - 10 q^{82} + 44 q^{83} + 32 q^{85} - 28 q^{86} + 2 q^{88} + 44 q^{91} + 2 q^{92} + 12 q^{94} - 64 q^{95} + 14 q^{97} + 28 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8 - 2 * q^10 + 2 * q^11 + 18 * q^14 - 2 * q^16 - 18 * q^17 + 16 * q^19 - 2 * q^20 + 24 * q^22 + 2 * q^23 + 38 * q^25 + 18 * q^28 + 30 * q^29 + 14 * q^31 - 2 * q^32 + 4 * q^34 - 48 * q^35 - 20 * q^37 + 16 * q^38 - 2 * q^40 + 12 * q^41 - 28 * q^43 + 2 * q^44 + 2 * q^46 - 32 * q^47 + 6 * q^49 - 6 * q^50 + 46 * q^53 - 28 * q^55 - 4 * q^56 - 14 * q^58 - 50 * q^61 - 8 * q^62 - 2 * q^64 - 16 * q^65 - 8 * q^67 + 48 * q^68 - 48 * q^70 - 12 * q^71 - 18 * q^73 - 20 * q^74 - 6 * q^76 + 4 * q^77 - 18 * q^79 - 2 * q^80 - 10 * q^82 + 44 * q^83 + 32 * q^85 - 28 * q^86 + 2 * q^88 + 44 * q^91 + 2 * q^92 + 12 * q^94 - 64 * q^95 + 14 * q^97 + 28 * q^98

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