LMFDB - Embedded newform 387.2.y.c.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

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("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	387.109
Dual form			387.2.y.c.316.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72039 + 2.15730i) q^{2} +(-1.24917 + 5.47296i) q^{4} +(-0.0684907 + 0.913945i) q^{5} +(-0.971539 - 1.68276i) q^{7} +(-8.98382 + 4.32638i) q^{8} +O(q^{10})$	\(q+(1.72039 + 2.15730i) q^{2} +(-1.24917 + 5.47296i) q^{4} +(-0.0684907 + 0.913945i) q^{5} +(-0.971539 - 1.68276i) q^{7} +(-8.98382 + 4.32638i) q^{8} +(-2.08949 + 1.42459i) q^{10} +(0.100377 + 0.439781i) q^{11} +(2.90116 + 1.97798i) q^{13} +(1.95879 - 4.99091i) q^{14} +(-14.6735 - 7.06637i) q^{16} +(-0.142476 - 1.90121i) q^{17} +(2.97713 + 2.76237i) q^{19} +(-4.91643 - 1.51652i) q^{20} +(-0.776053 + 0.973140i) q^{22} +(1.77211 + 0.546623i) q^{23} +(4.11355 + 0.620018i) q^{25} +(0.724035 + 9.66157i) q^{26} +(10.4233 - 3.21515i) q^{28} +(1.90792 - 4.86129i) q^{29} +(0.920034 - 0.138673i) q^{31} +(-5.56217 - 24.3695i) q^{32} +(3.85637 - 3.57819i) q^{34} +(1.60449 - 0.772681i) q^{35} +(0.277212 - 0.480145i) q^{37} +(-0.837445 + 11.1749i) q^{38} +(-3.33877 - 8.50704i) q^{40} +(-0.111290 - 0.139553i) q^{41} +(-6.30773 + 1.79236i) q^{43} -2.53229 q^{44} +(1.86949 + 4.76338i) q^{46} +(-1.72810 + 7.57131i) q^{47} +(1.61222 - 2.79245i) q^{49} +(5.73935 + 9.94085i) q^{50} +(-14.4494 + 13.4071i) q^{52} +(8.52328 - 5.81107i) q^{53} +(-0.408811 + 0.0616183i) q^{55} +(16.0084 + 10.9143i) q^{56} +(13.7696 - 4.24737i) q^{58} +(-9.19536 - 4.42825i) q^{59} +(-5.55516 - 0.837306i) q^{61} +(1.88198 + 1.74622i) q^{62} +(22.6945 - 28.4580i) q^{64} +(-2.00646 + 2.51603i) q^{65} +(-0.807046 - 0.748830i) q^{67} +(10.5832 + 1.59516i) q^{68} +(4.42726 + 2.13205i) q^{70} +(5.41606 - 1.67063i) q^{71} +(11.7207 + 7.99101i) q^{73} +(1.51273 - 0.228008i) q^{74} +(-18.8373 + 12.8430i) q^{76} +(0.642524 - 0.596175i) q^{77} +(1.13115 + 1.95921i) q^{79} +(7.46327 - 12.9268i) q^{80} +(0.109596 - 0.480173i) q^{82} +(-5.11608 - 13.0356i) q^{83} +1.74736 q^{85} +(-14.7184 - 10.5241i) q^{86} +(-2.80443 - 3.51664i) q^{88} +(-0.143414 - 0.365414i) q^{89} +(0.509861 - 6.80362i) q^{91} +(-5.20531 + 9.01586i) q^{92} +(-19.3066 + 9.29758i) q^{94} +(-2.72856 + 2.53173i) q^{95} +(-3.76302 - 16.4869i) q^{97} +(8.79782 - 1.32606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{8}{21}\right)$	$1$

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 $

$2$	1.72039	+	2.15730i	1.21650	+	1.52544i	0.780051	+	0.625716i	$0.215193\pi$
$2$	1.72039	+	2.15730i	1.21650	+	1.52544i	0.436450	+	0.899729i	$0.356236\pi$
$3$		0			0
$3$		0			0
$4$	−1.24917	+	5.47296i	−0.624584	+	2.73648i
$5$	−0.0684907	+	0.913945i	−0.0306300	+	0.408729i	0.960723	+	0.277508i	$0.0895086\pi$
$5$	−0.0684907	+	0.913945i	−0.0306300	+	0.408729i	−0.991353	+	0.131220i	$0.958110\pi$
$6$		0			0
$7$	−0.971539	−	1.68276i	−0.367207	−	0.636022i	0.621920	−	0.783080i	$-0.286353\pi$
$7$	−0.971539	−	1.68276i	−0.367207	−	0.636022i	−0.989128	+	0.147059i	$0.953019\pi$
$8$	−8.98382	+	4.32638i	−3.17626	+	1.52961i
$9$		0			0
$10$	−2.08949	+	1.42459i	−0.660754	+	0.450495i
$11$	0.100377	+	0.439781i	0.0302648	+	0.132599i	0.987803	−	0.155706i	$-0.0497653\pi$
$11$	0.100377	+	0.439781i	0.0302648	+	0.132599i	−0.957539	+	0.288305i	$0.906908\pi$
$12$		0			0
$13$	2.90116	+	1.97798i	0.804637	+	0.548592i	0.894346	−	0.447376i	$-0.147641\pi$
$13$	2.90116	+	1.97798i	0.804637	+	0.548592i	−0.0897094	+	0.995968i	$0.528594\pi$
$14$	1.95879	−	4.99091i	0.523508	−	1.33388i
$15$		0			0
$16$	−14.6735	−	7.06637i	−3.66837	−	1.76659i
$17$	−0.142476	−	1.90121i	−0.0345555	−	0.461111i	−0.987463	−	0.157850i	$-0.949544\pi$
$17$	−0.142476	−	1.90121i	−0.0345555	−	0.461111i	0.952908	−	0.303261i	$-0.0980753\pi$
$18$		0			0
$19$	2.97713	+	2.76237i	0.683000	+	0.633731i	0.943356	−	0.331781i	$-0.107650\pi$
$19$	2.97713	+	2.76237i	0.683000	+	0.633731i	−0.260357	+	0.965513i	$0.583840\pi$
$20$	−4.91643	−	1.51652i	−1.09935	−	0.339104i
$21$		0			0
$22$	−0.776053	+	0.973140i	−0.165455	+	0.207474i
$23$	1.77211	+	0.546623i	0.369510	+	0.113979i	0.473949	−	0.880553i	$-0.342828\pi$
$23$	1.77211	+	0.546623i	0.369510	+	0.113979i	−0.104438	+	0.994531i	$0.533304\pi$
$24$		0			0
$25$	4.11355	+	0.620018i	0.822710	+	0.124004i
$26$	0.724035	+	9.66157i	0.141995	+	1.89479i
$27$		0			0
$28$	10.4233	−	3.21515i	1.96981	−	0.607607i
$29$	1.90792	−	4.86129i	0.354291	−	0.902719i	−0.636980	−	0.770880i	$-0.719817\pi$
$29$	1.90792	−	4.86129i	0.354291	−	0.902719i	0.991271	−	0.131839i	$-0.0420880\pi$
$30$		0			0
$31$	0.920034	−	0.138673i	0.165243	−	0.0249064i	−0.0658996	−	0.997826i	$-0.520992\pi$
$31$	0.920034	−	0.138673i	0.165243	−	0.0249064i	0.231143	+	0.972920i	$0.425754\pi$
$32$	−5.56217	−	24.3695i	−0.983262	−	4.30795i
$33$		0			0
$34$	3.85637	−	3.57819i	0.661362	−	0.613654i
$35$	1.60449	−	0.772681i	0.271208	−	0.130607i
$36$		0			0
$37$	0.277212	−	0.480145i	0.0455734	−	0.0789354i	−0.842339	−	0.538948i	$-0.818822\pi$
$37$	0.277212	−	0.480145i	0.0455734	−	0.0789354i	0.887912	+	0.460013i	$0.152155\pi$
$38$	−0.837445	+	11.1749i	−0.135852	+	1.81281i
$39$		0			0
$40$	−3.33877	−	8.50704i	−0.527905	−	1.34508i
$41$	−0.111290	−	0.139553i	−0.0173806	−	0.0217945i	0.773065	−	0.634327i	$-0.218723\pi$
$41$	−0.111290	−	0.139553i	−0.0173806	−	0.0217945i	−0.790446	+	0.612532i	$0.790151\pi$
$42$		0			0
$43$	−6.30773	+	1.79236i	−0.961920	+	0.273333i
$43$	−6.30773	+	1.79236i	−0.961920	+	0.273333i
$44$	−2.53229			−0.381757
$45$		0			0
$46$	1.86949	+	4.76338i	0.275641	+	0.702323i
$47$	−1.72810	+	7.57131i	−0.252069	+	1.10439i	0.677436	+	0.735581i	$0.263091\pi$
$47$	−1.72810	+	7.57131i	−0.252069	+	1.10439i	−0.929506	+	0.368807i	$0.879766\pi$
$48$		0			0
$49$	1.61222	−	2.79245i	0.230317	−	0.398922i
$50$	5.73935	+	9.94085i	0.811667	+	1.40585i
$51$		0			0
$52$	−14.4494	+	13.4071i	−2.00377	+	1.85923i
$53$	8.52328	−	5.81107i	1.17076	−	0.798212i	0.187834	−	0.982201i	$-0.439853\pi$
$53$	8.52328	−	5.81107i	1.17076	−	0.798212i	0.982928	+	0.183989i	$0.0589011\pi$
$54$		0			0
$55$	−0.408811	+	0.0616183i	−0.0551240	+	0.00830861i
$56$	16.0084	+	10.9143i	2.13921	+	1.45849i
$57$		0			0
$58$	13.7696	−	4.24737i	1.80804	−	0.557707i
$59$	−9.19536	−	4.42825i	−1.19713	−	0.576509i	−0.274276	−	0.961651i	$-0.588438\pi$
$59$	−9.19536	−	4.42825i	−1.19713	−	0.576509i	−0.922857	+	0.385142i	$0.874152\pi$
$60$		0			0
$61$	−5.55516	−	0.837306i	−0.711266	−	0.107206i	−0.216563	−	0.976269i	$-0.569485\pi$
$61$	−5.55516	−	0.837306i	−0.711266	−	0.107206i	−0.494702	+	0.869063i	$0.664723\pi$
$62$	1.88198	+	1.74622i	0.239012	+	0.221770i
$63$		0			0
$64$	22.6945	−	28.4580i	2.83681	−	3.55725i
$65$	−2.00646	+	2.51603i	−0.248871	+	0.312075i
$66$		0			0
$67$	−0.807046	−	0.748830i	−0.0985964	−	0.0914841i	0.629335	−	0.777134i	$-0.283327\pi$
$67$	−0.807046	−	0.748830i	−0.0985964	−	0.0914841i	−0.727931	+	0.685650i	$0.759518\pi$
$68$	10.5832	+	1.59516i	1.28340	+	0.193442i
$69$		0			0
$70$	4.42726	+	2.13205i	0.529158	+	0.254829i
$71$	5.41606	−	1.67063i	0.642768	−	0.198268i	0.0437996	−	0.999040i	$-0.486054\pi$
$71$	5.41606	−	1.67063i	0.642768	−	0.198268i	0.598968	+	0.800773i	$0.295578\pi$
$72$		0			0
$73$	11.7207	+	7.99101i	1.37180	+	0.935277i	0.999976	+	0.00697295i	$0.00221958\pi$
$73$	11.7207	+	7.99101i	1.37180	+	0.935277i	0.371823	+	0.928304i	$0.378733\pi$
$74$	1.51273	−	0.228008i	0.175852	−	0.0265054i
$75$		0			0
$76$	−18.8373	+	12.8430i	−2.16078	+	1.47320i
$77$	0.642524	−	0.596175i	0.0732224	−	0.0679404i
$78$		0			0
$79$	1.13115	+	1.95921i	0.127264	+	0.220429i	0.922616	−	0.385720i	$-0.126047\pi$
$79$	1.13115	+	1.95921i	0.127264	+	0.220429i	−0.795351	+	0.606149i	$0.792714\pi$
$80$	7.46327	−	12.9268i	0.834419	−	1.44526i
$81$		0			0
$82$	0.109596	−	0.480173i	0.0121029	−	0.0530262i
$83$	−5.11608	−	13.0356i	−0.561563	−	1.43084i	−0.876349	−	0.481676i	$-0.840028\pi$
$83$	−5.11608	−	13.0356i	−0.561563	−	1.43084i	0.314786	−	0.949163i	$-0.398067\pi$
$84$		0			0
$85$	1.74736			0.189528
$86$	−14.7184	−	10.5241i	−1.58713	−	1.13484i
$87$		0			0
$88$	−2.80443	−	3.51664i	−0.298953	−	0.374876i
$89$	−0.143414	−	0.365414i	−0.0152019	−	0.0387338i	0.923071	−	0.384629i	$-0.125671\pi$
$89$	−0.143414	−	0.365414i	−0.0152019	−	0.0387338i	−0.938273	+	0.345895i	$0.887575\pi$
$90$		0			0
$91$	0.509861	−	6.80362i	0.0534480	−	0.713213i
$92$	−5.20531	+	9.01586i	−0.542691	+	0.939969i
$93$		0			0
$94$	−19.3066	+	9.29758i	−1.99133	+	0.958972i
$95$	−2.72856	+	2.53173i	−0.279944	+	0.259750i
$96$		0			0
$97$	−3.76302	−	16.4869i	−0.382077	−	1.67399i	−0.690963	−	0.722891i	$-0.742813\pi$
$97$	−3.76302	−	16.4869i	−0.382077	−	1.67399i	0.308885	−	0.951099i	$-0.400044\pi$
$98$	8.79782	−	1.32606i	0.888714	−	0.133952i
$99$		0			0
$100$	−8.53185	+	21.7388i	−0.853185	+	2.17388i
$101$	−5.90279	+	1.82077i	−0.587349	+	0.181173i	−0.574165	−	0.818740i	$-0.694673\pi$
$101$	−5.90279	+	1.82077i	−0.587349	+	0.181173i	−0.0131846	+	0.999913i	$0.504197\pi$
$102$		0			0
$103$	0.712752	+	9.51101i	0.0702295	+	0.937148i	0.915373	+	0.402608i	$0.131896\pi$
$103$	0.712752	+	9.51101i	0.0702295	+	0.937148i	−0.845143	+	0.534540i	$0.820485\pi$
$104$	−34.6210	−	5.21827i	−3.39487	−	0.511694i
$105$		0			0
$106$	27.1996	+	8.38997i	2.64186	+	0.814906i
$107$	2.82868	−	3.54705i	0.273459	−	0.342906i	−0.626071	−	0.779766i	$-0.715338\pi$
$107$	2.82868	−	3.54705i	0.273459	−	0.342906i	0.899530	+	0.436860i	$0.143909\pi$
$108$		0			0
$109$	−15.3056	−	4.72117i	−1.46601	−	0.452206i	−0.543909	−	0.839144i	$-0.683056\pi$
$109$	−15.3056	−	4.72117i	−1.46601	−	0.452206i	−0.922106	+	0.386939i	$0.873533\pi$
$110$	−0.836244	−	0.775921i	−0.0797327	−	0.0739812i
$111$		0			0
$112$	2.36488	+	31.5571i	0.223460	+	2.98187i
$113$	11.7135	+	5.64091i	1.10191	+	0.530652i	0.894258	−	0.447551i	$-0.147704\pi$
$113$	11.7135	+	5.64091i	1.10191	+	0.530652i	0.207652	+	0.978203i	$0.433418\pi$
$114$		0			0
$115$	−0.620957	+	1.58217i	−0.0579045	+	0.147538i
$116$	24.2223	+	16.5145i	2.24899	+	1.53333i
$117$		0			0
$118$	−6.26654	−	27.4555i	−0.576882	−	2.52748i
$119$	−3.06085	+	2.08685i	−0.280588	+	0.191301i
$120$		0			0
$121$	9.72733	−	4.68443i	0.884302	−	0.425858i
$122$	−7.75074	−	13.4247i	−0.701719	−	1.21541i
$123$		0			0
$124$	−0.390326	+	5.20854i	−0.0350523	+	0.467741i
$125$	−1.86811	+	8.18474i	−0.167089	+	0.732065i
$126$		0			0
$127$	−8.20396	−	10.2874i	−0.727983	−	0.912862i	0.270777	−	0.962642i	$-0.412719\pi$
$127$	−8.20396	−	10.2874i	−0.727983	−	0.912862i	−0.998760	+	0.0497798i	$0.984148\pi$
$128$	50.4437			4.45864
$129$		0			0
$130$	−8.87974			−0.778805
$131$	−1.89745	−	2.37933i	−0.165781	−	0.207883i	0.692001	−	0.721897i	$-0.256729\pi$
$131$	−1.89745	−	2.37933i	−0.165781	−	0.207883i	−0.857782	+	0.514014i	$0.828158\pi$
$132$		0			0
$133$	1.75600	−	7.69353i	0.152264	−	0.667113i
$134$	0.227017	−	3.02933i	0.0196112	−	0.261694i
$135$		0			0
$136$	9.50533	+	16.4637i	0.815075	+	1.41175i
$137$	−10.9381	+	5.26750i	−0.934503	+	0.450033i	−0.838227	−	0.545322i	$-0.816407\pi$
$137$	−10.9381	+	5.26750i	−0.934503	+	0.450033i	−0.0962759	+	0.995355i	$0.530693\pi$
$138$		0			0
$139$	−3.71295	+	2.53144i	−0.314928	+	0.214714i	−0.710459	−	0.703738i	$-0.751513\pi$
$139$	−3.71295	+	2.53144i	−0.314928	+	0.214714i	0.395531	+	0.918452i	$0.370560\pi$
$140$	2.22458	+	9.74651i	0.188011	+	0.823730i
$141$		0			0
$142$	12.9218	+	8.80994i	1.08437	+	0.739314i
$143$	−0.578666	+	1.47442i	−0.0483905	+	0.123297i
$144$		0			0
$145$	4.31228	+	2.07668i	0.358115	+	0.172459i
$146$	2.92509	+	39.0327i	0.242083	+	3.23037i
$147$		0			0
$148$	2.28153	+	2.11695i	0.187541	+	0.174012i
$149$	8.97878	+	2.76959i	0.735571	+	0.226893i	0.639834	−	0.768513i	$-0.279003\pi$
$149$	8.97878	+	2.76959i	0.735571	+	0.226893i	0.0957367	+	0.995407i	$0.469479\pi$
$150$		0			0
$151$	−5.17636	+	6.49094i	−0.421246	+	0.528226i	−0.946493	−	0.322724i	$-0.895401\pi$
$151$	−5.17636	+	6.49094i	−0.421246	+	0.528226i	0.525247	+	0.850950i	$0.323973\pi$
$152$	−38.6970	−	11.9365i	−3.13874	−	0.968174i
$153$		0			0
$154$	2.39152	+	0.360464i	0.192714	+	0.0290470i
$155$	0.0637256	+	0.850359i	0.00511856	+	0.0683025i
$156$		0			0
$157$	−9.31783	+	2.87417i	−0.743644	+	0.229384i	−0.643348	−	0.765574i	$-0.722455\pi$
$157$	−9.31783	+	2.87417i	−0.743644	+	0.229384i	−0.100296	+	0.994958i	$0.531979\pi$
$158$	−2.28059	+	5.81085i	−0.181434	+	0.462286i
$159$		0			0
$160$	22.6533	−	3.41444i	1.79090	−	0.269935i
$161$	−0.801841	−	3.51309i	−0.0631939	−	0.276871i
$162$		0			0
$163$	−1.63792	+	1.51977i	−0.128292	+	0.119037i	−0.741709	−	0.670721i	$-0.765985\pi$
$163$	−1.63792	+	1.51977i	−0.128292	+	0.119037i	0.613418	+	0.789759i	$0.289794\pi$
$164$	0.902789	−	0.434760i	0.0704960	−	0.0339491i
$165$		0			0
$166$	19.3200	−	33.4632i	1.49952	−	2.59725i
$167$	1.74279	−	23.2559i	0.134861	−	1.79959i	−0.362431	−	0.932011i	$-0.618053\pi$
$167$	1.74279	−	23.2559i	0.134861	−	1.79959i	0.497292	−	0.867583i	$-0.334328\pi$
$168$		0			0
$169$	−0.245104	−	0.624515i	−0.0188542	−	0.0480396i
$170$	3.00614	+	3.76958i	0.230561	+	0.289114i
$171$		0			0
$172$	−1.93013	−	36.7609i	−0.147171	−	2.80299i
$173$	1.53451			0.116666			0.0583332	−	0.998297i	$-0.481421\pi$
$173$	1.53451			0.116666			0.0583332	+	0.998297i	$0.481421\pi$
$174$		0			0
$175$	−2.95314	−	7.52447i	−0.223236	−	0.568797i
$176$	1.63477	−	7.16241i	0.123226	−	0.539887i
$177$		0			0
$178$	0.541580	−	0.938044i	0.0405931	−	0.0703094i
$179$	−3.26451	−	5.65429i	−0.244001	−	0.422621i	0.717850	−	0.696198i	$-0.245127\pi$
$179$	−3.26451	−	5.65429i	−0.244001	−	0.422621i	−0.961850	+	0.273577i	$0.911793\pi$
$180$		0			0
$181$	−13.9680	+	12.9604i	−1.03823	+	0.963336i	−0.999355	−	0.0359077i	$-0.988568\pi$
$181$	−13.9680	+	12.9604i	−1.03823	+	0.963336i	−0.0388746	+	0.999244i	$0.512377\pi$
$182$	15.5546	−	10.6050i	1.15299	−	0.786093i
$183$		0			0
$184$	−18.2852	+	2.75605i	−1.34800	+	0.203179i
$185$	0.419840	+	0.286242i	0.0308672	+	0.0210449i
$186$		0			0
$187$	0.821814	−	0.253496i	0.0600970	−	0.0185375i
$188$	−39.2788	−	18.9157i	−2.86470	−	1.37957i
$189$		0			0
$190$	−10.1559	−	1.53076i	−0.736787	−	0.111053i
$191$	−11.7580	−	10.9099i	−0.850781	−	0.789410i	0.128544	−	0.991704i	$-0.458970\pi$
$191$	−11.7580	−	10.9099i	−0.850781	−	0.789410i	−0.979325	+	0.202294i	$0.935160\pi$
$192$		0			0
$193$	−3.90963	+	4.90253i	−0.281422	+	0.352892i	−0.902372	−	0.430959i	$-0.858176\pi$
$193$	−3.90963	+	4.90253i	−0.281422	+	0.352892i	0.620950	+	0.783850i	$0.286747\pi$
$194$	29.0933	−	36.4819i	2.08878	−	2.61925i
$195$		0			0
$196$	13.2690	+	12.3119i	0.947789	+	0.879419i
$197$	10.7637	+	1.62237i	0.766884	+	0.115589i	0.520822	−	0.853665i	$-0.325625\pi$
$197$	10.7637	+	1.62237i	0.766884	+	0.115589i	0.246062	+	0.969254i	$0.420863\pi$
$198$		0			0
$199$	4.32905	+	2.08476i	0.306878	+	0.147785i	0.580984	−	0.813915i	$-0.302668\pi$
$199$	4.32905	+	2.08476i	0.306878	+	0.147785i	−0.274106	+	0.961699i	$0.588382\pi$
$200$	−39.6378	+	12.2267i	−2.80282	+	0.864555i
$201$		0			0
$202$	−14.0831	−	9.60167i	−0.990881	−	0.675571i
$203$	−10.0340	+	1.51238i	−0.704247	+	0.106148i
$204$		0			0
$205$	0.135166	−	0.0921548i	0.00944042	−	0.00643637i
$206$	−19.2919	+	17.9003i	−1.34413	+	1.24717i
$207$		0			0
$208$	−28.5929	−	49.5244i	−1.98256	−	3.43390i
$209$	−0.916002	+	1.58656i	−0.0633612	+	0.109745i
$210$		0			0
$211$	4.43696	−	19.4396i	0.305453	−	1.33828i	−0.556313	−	0.830973i	$-0.687785\pi$
$211$	4.43696	−	19.4396i	0.305453	−	1.33828i	0.861766	−	0.507305i	$-0.169358\pi$
$212$	21.1568	+	53.9066i	1.45305	+	3.70232i
$213$		0			0
$214$	12.5185			0.855747
$215$	−1.20610	−	5.88768i	−0.0822554	−	0.401536i
$216$		0			0
$217$	−1.12720	−	1.41347i	−0.0765195	−	0.0959524i
$218$	−16.1467	−	41.1412i	−1.09359	−	2.78643i
$219$		0			0
$220$	0.173439	−	2.31438i	0.0116932	−	0.156035i
$221$	3.34720	−	5.79752i	0.225157	−	0.389983i
$222$		0			0
$223$	1.34141	−	0.645989i	0.0898274	−	0.0432586i	−0.388431	−	0.921478i	$-0.626983\pi$
$223$	1.34141	−	0.645989i	0.0898274	−	0.0432586i	0.478258	+	0.878219i	$0.341268\pi$
$224$	−35.6040	+	33.0357i	−2.37889	+	2.20729i
$225$		0			0
$226$	7.98261	+	34.9741i	0.530995	+	2.32644i
$227$	−24.3967	+	3.67721i	−1.61927	+	0.244065i	−0.895200	−	0.445665i	$-0.852967\pi$
$227$	−24.3967	+	3.67721i	−1.61927	+	0.244065i	−0.724067	+	0.689730i	$0.757729\pi$
$228$		0			0
$229$	5.63673	−	14.3622i	0.372486	−	0.949078i	−0.614594	−	0.788844i	$-0.710680\pi$
$229$	5.63673	−	14.3622i	0.372486	−	0.949078i	0.987079	−	0.160234i	$-0.0512248\pi$
$230$	−4.48151	+	1.38236i	−0.295502	+	0.0911504i
$231$		0			0
$232$	3.89142	+	51.9273i	0.255484	+	3.40920i
$233$	20.2723	+	3.05556i	1.32808	+	0.200176i	0.774476	−	0.632603i	$-0.218013\pi$
$233$	20.2723	+	3.05556i	1.32808	+	0.200176i	0.553606	+	0.832779i	$0.313251\pi$
$234$		0			0
$235$	−6.80140	−	2.09795i	−0.443674	−	0.136855i
$236$	35.7222	−	44.7942i	2.32532	−	2.91585i
$237$		0			0
$238$	−9.76783	−	3.01298i	−0.633155	−	0.195302i
$239$	9.45056	+	8.76884i	0.611306	+	0.567209i	0.923879	−	0.382685i	$-0.125000\pi$
$239$	9.45056	+	8.76884i	0.611306	+	0.567209i	−0.312573	+	0.949894i	$0.601191\pi$
$240$		0			0
$241$	−0.568011	−	7.57957i	−0.0365888	−	0.488243i	−0.985155	−	0.171665i	$-0.945085\pi$
$241$	−0.568011	−	7.57957i	−0.0365888	−	0.488243i	0.948567	−	0.316578i	$-0.102534\pi$
$242$	26.8406	+	12.9257i	1.72538	+	0.830898i
$243$		0			0
$244$	11.5219	−	29.3573i	0.737612	−	1.87941i
$245$	2.44172	+	1.66474i	0.155996	+	0.106356i
$246$		0			0
$247$	3.17321	+	13.9028i	0.201907	+	0.884611i
$248$	−7.66547	+	5.22623i	−0.486758	+	0.331866i
$249$		0			0
$250$	−20.8709	+	10.0509i	−1.31999	+	0.635673i
$251$	7.99653	+	13.8504i	0.504736	+	0.874229i	0.999985	+	0.00547772i	$0.00174362\pi$
$251$	7.99653	+	13.8504i	0.504736	+	0.874229i	−0.495249	+	0.868751i	$0.664923\pi$
$252$		0			0
$253$	−0.0625153	+	0.834208i	−0.00393030	+	0.0524462i
$254$	8.07910	−	35.3969i	0.506928	−	2.22100i
$255$		0			0
$256$	41.3940	+	51.9064i	2.58712	+	3.24415i
$257$	2.70015			0.168431			0.0842154	−	0.996448i	$-0.473162\pi$
$257$	2.70015			0.168431			0.0842154	+	0.996448i	$0.473162\pi$
$258$		0			0
$259$	−1.07729			−0.0669395
$260$	−11.2637	−	14.1242i	−0.698545	−	0.875948i
$261$		0			0
$262$	1.86857	−	8.18675i	0.115441	−	0.505779i
$263$	−1.38065	+	18.4235i	−0.0851345	+	1.13604i	0.777048	+	0.629442i	$0.216716\pi$
$263$	−1.38065	+	18.4235i	−0.0851345	+	1.13604i	−0.862182	+	0.506599i	$0.830903\pi$
$264$		0			0
$265$	4.72723	+	8.18781i	0.290392	+	0.502973i
$266$	19.6183	−	9.44767i	1.20287	−	0.579274i
$267$		0			0
$268$	5.10645	−	3.48152i	0.311926	−	0.212668i
$269$	2.87587	+	12.6000i	0.175345	+	0.768236i	0.983740	+	0.179596i	$0.0574792\pi$
$269$	2.87587	+	12.6000i	0.175345	+	0.768236i	−0.808395	+	0.588640i	$0.799664\pi$
$270$		0			0
$271$	−12.7456	−	8.68981i	−0.774240	−	0.527868i	0.110543	−	0.993871i	$-0.464741\pi$
$271$	−12.7456	−	8.68981i	−0.774240	−	0.527868i	−0.884783	+	0.466003i	$0.845694\pi$
$272$	−11.3440	+	28.9041i	−0.687832	+	1.75257i
$273$		0			0
$274$	−30.1814	−	14.5346i	−1.82332	−	0.878066i
$275$	0.140234	+	1.87130i	0.00845645	+	0.112843i
$276$		0			0
$277$	17.5390	+	16.2738i	1.05382	+	0.977798i	0.999785	−	0.0207410i	$-0.00660253\pi$
$277$	17.5390	+	16.2738i	1.05382	+	0.977798i	0.0540310	+	0.998539i	$0.482793\pi$
$278$	−11.8488	−	3.65488i	−0.710645	−	0.219205i
$279$		0			0
$280$	−11.0715	+	13.8833i	−0.661650	+	0.829683i
$281$	−9.50488	−	2.93187i	−0.567013	−	0.174900i	−0.00202302	−	0.999998i	$-0.500644\pi$
$281$	−9.50488	−	2.93187i	−0.567013	−	0.174900i	−0.564990	+	0.825097i	$0.691120\pi$
$282$		0			0
$283$	13.7960	+	2.07941i	0.820084	+	0.123608i	0.545666	−	0.838003i	$-0.316277\pi$
$283$	13.7960	+	2.07941i	0.820084	+	0.123608i	0.274418	+	0.961610i	$0.411515\pi$
$284$	2.37774	+	31.7288i	0.141093	+	1.88276i
$285$		0			0
$286$	−4.17630	+	1.28822i	−0.246950	+	0.0761739i
$287$	−0.126711	+	0.322855i	−0.00747953	+	0.0190575i
$288$		0			0
$289$	13.2158	−	1.99197i	0.777402	−	0.117174i
$290$	2.93877	+	12.8756i	0.172571	+	0.756081i
$291$		0			0
$292$	−58.3755	+	54.1646i	−3.41617	+	3.16974i
$293$	−15.4513	+	7.44096i	−0.902676	+	0.434706i	−0.826855	−	0.562416i	$-0.809872\pi$
$293$	−15.4513	+	7.44096i	−0.902676	+	0.434706i	−0.0758211	+	0.997121i	$0.524158\pi$
$294$		0			0
$295$	4.67697	−	8.10076i	0.272304	−	0.471644i
$296$	−0.413132	+	5.51286i	−0.0240128	+	0.320429i
$297$		0			0
$298$	9.47219	+	24.1347i	0.548709	+	1.39809i
$299$	4.05996	+	5.09103i	0.234794	+	0.294422i
$300$		0			0
$301$	9.14432	+	8.87301i	0.527070	+	0.511432i
$302$	−22.9083			−1.31822
$303$		0			0
$304$	−24.1648	−	61.5710i	−1.38595	−	3.53134i
$305$	1.14573	−	5.01977i	0.0656042	−	0.287431i
$306$		0			0
$307$	−10.5428	+	18.2606i	−0.601707	+	1.04219i	0.390855	+	0.920452i	$0.372179\pi$
$307$	−10.5428	+	18.2606i	−0.601707	+	1.04219i	−0.992563	+	0.121736i	$0.961154\pi$
$308$	2.46022	+	4.26123i	0.140184	+	0.242806i
$309$		0			0
$310$	−1.72485	+	1.60043i	−0.0979648	+	0.0908981i
$311$	−5.32355	+	3.62953i	−0.301871	+	0.205812i	−0.704776	−	0.709430i	$-0.748953\pi$
$311$	−5.32355	+	3.62953i	−0.301871	+	0.205812i	0.402906	+	0.915242i	$0.368000\pi$
$312$		0			0
$313$	−6.81682	+	1.02747i	−0.385310	+	0.0580761i	−0.338841	−	0.940844i	$-0.610035\pi$
$313$	−6.81682	+	1.02747i	−0.385310	+	0.0580761i	−0.0464687	+	0.998920i	$0.514797\pi$
$314$	−22.2308	−	15.1567i	−1.25456	−	0.855341i
$315$		0			0
$316$	−12.1357	+	3.74336i	−0.682686	+	0.210581i
$317$	1.03153	+	0.496760i	0.0579367	+	0.0279008i	0.462628	−	0.886553i	$-0.346907\pi$
$317$	1.03153	+	0.496760i	0.0579367	+	0.0279008i	−0.404691	+	0.914453i	$0.632621\pi$
$318$		0			0
$319$	2.32941	+	0.351103i	0.130422	+	0.0196580i
$320$	24.4547	+	22.6907i	1.36706	+	1.26845i
$321$		0			0
$322$	6.19933	−	7.77371i	0.345475	−	0.433212i
$323$	4.82767	−	6.05371i	0.268619	−	0.336837i
$324$		0			0
$325$	10.7077	+	9.93527i	0.593955	+	0.551110i
$326$	−6.09646	−	0.918893i	−0.337652	−	0.0508928i
$327$		0			0
$328$	1.60357	+	0.772238i	0.0885423	+	0.0426397i
$329$	14.4196	−	4.44785i	0.794977	−	0.245218i
$330$		0			0
$331$	−8.16250	−	5.56510i	−0.448651	−	0.305885i	0.317835	−	0.948146i	$-0.397044\pi$
$331$	−8.16250	−	5.56510i	−0.448651	−	0.305885i	−0.766486	+	0.642261i	$0.777997\pi$
$332$	77.7340	−	11.7165i	4.26621	−	0.643027i
$333$		0			0
$334$	53.1683	−	36.2495i	2.90924	−	1.98349i
$335$	0.739664	−	0.686308i	0.0404122	−	0.0374970i
$336$		0			0
$337$	11.5821	+	20.0608i	0.630919	+	1.09278i	0.987364	+	0.158468i	$0.0506554\pi$
$337$	11.5821	+	20.0608i	0.630919	+	1.09278i	−0.356445	+	0.934316i	$0.616011\pi$
$338$	0.925594	−	1.60318i	0.0503457	−	0.0872012i
$339$		0			0
$340$	−2.18274	+	9.56323i	−0.118376	+	0.518639i
$341$	0.153336	+	0.390694i	0.00830362	+	0.0211573i
$342$		0			0
$343$	−19.8669			−1.07271
$344$	48.9131	−	43.3919i	2.63722	−	2.33954i
$345$		0			0
$346$	2.63996	+	3.31040i	0.141925	+	0.177968i
$347$	6.10329	+	15.5509i	0.327642	+	0.834818i	0.995864	+	0.0908560i	$0.0289603\pi$
$347$	6.10329	+	15.5509i	0.327642	+	0.834818i	−0.668222	+	0.743962i	$0.732944\pi$
$348$		0			0
$349$	−1.53538	+	20.4883i	−0.0821871	+	1.09671i	0.791806	+	0.610773i	$0.209141\pi$
$349$	−1.53538	+	20.4883i	−0.0821871	+	1.09671i	−0.873993	+	0.485938i	$0.838478\pi$
$350$	11.1520	−	19.3159i	0.596100	−	1.03248i
$351$		0			0
$352$	10.1589	−	4.89227i	0.541472	−	0.260759i
$353$	7.38749	−	6.85459i	0.393196	−	0.364833i	−0.458657	−	0.888613i	$-0.651669\pi$
$353$	7.38749	−	6.85459i	0.393196	−	0.364833i	0.851853	+	0.523781i	$0.175479\pi$
$354$		0			0
$355$	1.15592	+	5.06440i	0.0613497	+	0.268791i
$356$	2.17905	−	0.328438i	0.115489	−	0.0174072i
$357$		0			0
$358$	6.58179	−	16.7701i	0.347858	−	0.886329i
$359$	−14.5648	+	4.49265i	−0.768701	+	0.237113i	−0.654211	−	0.756312i	$-0.726999\pi$
$359$	−14.5648	+	4.49265i	−0.768701	+	0.237113i	−0.114489	+	0.993424i	$0.536523\pi$
$360$		0			0
$361$	−0.187276	−	2.49903i	−0.00985663	−	0.131528i
$362$	−51.9898	−	7.83620i	−2.73252	−	0.411862i
$363$		0			0
$364$	36.5991	+	11.2893i	1.91831	+	0.591721i
$365$	−8.10610	+	10.1647i	−0.424292	+	0.532046i
$366$		0			0
$367$	−11.2654	−	3.47491i	−0.588047	−	0.181389i	−0.0135684	−	0.999908i	$-0.504319\pi$
$367$	−11.2654	−	3.47491i	−0.588047	−	0.181389i	−0.574479	+	0.818519i	$0.694795\pi$
$368$	−22.1403	−	20.5432i	−1.15415	−	1.07089i
$369$		0			0
$370$	0.104778	+	1.39817i	0.00544717	+	0.0726874i
$371$	−18.0593	−	8.69691i	−0.937593	−	0.451521i
$372$		0			0
$373$	−4.44434	+	11.3240i	−0.230119	+	0.586335i	−0.998563	−	0.0535823i	$-0.982936\pi$
$373$	−4.44434	+	11.3240i	−0.230119	+	0.586335i	0.768444	+	0.639917i	$0.221031\pi$
$374$	1.96071	+	1.33679i	0.101386	+	0.0691238i
$375$		0			0
$376$	−17.2314	−	75.4957i	−0.888642	−	3.89339i
$377$	15.1507	−	10.3296i	0.780300	−	0.531999i
$378$		0			0
$379$	7.27433	−	3.50313i	0.373657	−	0.179944i	−0.237624	−	0.971357i	$-0.576369\pi$
$379$	7.27433	−	3.50313i	0.373657	−	0.179944i	0.611281	+	0.791413i	$0.290654\pi$
$380$	−10.4477	−	18.0959i	−0.535953	−	0.928298i
$381$		0			0
$382$	3.30745	−	44.1349i	0.169224	−	2.25814i
$383$	−5.78751	+	25.3567i	−0.295728	+	1.29567i	0.580693	+	0.814123i	$0.302782\pi$
$383$	−5.78751	+	25.3567i	−0.295728	+	1.29567i	−0.876421	+	0.481546i	$0.840075\pi$
$384$		0			0
$385$	0.500864	+	0.628064i	0.0255264	+	0.0320091i
$386$	−17.3023			−0.880666
$387$		0			0
$388$	94.9328			4.81948
$389$	2.28337	+	2.86325i	0.115771	+	0.145173i	0.836340	−	0.548211i	$-0.184691\pi$
$389$	2.28337	+	2.86325i	0.115771	+	0.145173i	−0.720569	+	0.693383i	$0.756119\pi$
$390$		0			0
$391$	0.786762	−	3.44703i	0.0397883	−	0.174324i
$392$	−2.40271	+	32.0620i	−0.121355	+	1.61937i
$393$		0			0
$394$	15.0179	+	26.0117i	0.756590	+	1.31045i
$395$	−1.86809	+	0.899623i	−0.0939936	+	0.0452649i
$396$		0			0
$397$	21.5184	−	14.6710i	1.07998	−	0.736315i	0.113620	−	0.993524i	$-0.463755\pi$
$397$	21.5184	−	14.6710i	1.07998	−	0.736315i	0.966356	+	0.257209i	$0.0828028\pi$
$398$	2.95020	+	12.9257i	0.147880	+	0.647905i
$399$		0			0
$400$	−55.9787	−	38.1657i	−2.79894	−	1.90828i
$401$	5.05268	−	12.8740i	0.252319	−	0.642897i	−0.747452	−	0.664316i	$-0.768723\pi$
$401$	5.05268	−	12.8740i	0.252319	−	0.642897i	0.999771	+	0.0214185i	$0.00681823\pi$
$402$		0			0
$403$	2.94346	+	1.41749i	0.146624	+	0.0706104i
$404$	−2.59143	−	34.5802i	−0.128928	−	1.72043i
$405$		0			0
$406$	−20.5250	−	19.0445i	−1.01864	−	0.945160i
$407$	0.238984	+	0.0737170i	0.0118460	+	0.00365401i
$408$		0			0
$409$	4.23419	−	5.30951i	0.209367	−	0.262538i	−0.666049	−	0.745908i	$-0.732016\pi$
$409$	4.23419	−	5.30951i	0.209367	−	0.262538i	0.875416	+	0.483370i	$0.160587\pi$
$410$	0.431345	+	0.133052i	0.0213026	+	0.00657099i
$411$		0			0
$412$	−52.9438	−	7.97999i	−2.60835	−	0.393146i
$413$	1.48199	+	19.7758i	0.0729239	+	0.973101i
$414$		0			0
$415$	12.2642	−	3.78300i	0.602026	−	0.185700i
$416$	32.0655	−	81.7015i	1.57214	−	4.00575i
$417$		0			0
$418$	−4.99858	+	0.753415i	−0.244489	+	0.0368507i
$419$	−2.65456	−	11.6304i	−0.129684	−	0.568181i	−0.997460	−	0.0712267i	$-0.977309\pi$
$419$	−2.65456	−	11.6304i	−0.129684	−	0.568181i	0.867776	−	0.496955i	$-0.165549\pi$
$420$		0			0
$421$	−5.95716	+	5.52743i	−0.290334	+	0.269391i	−0.811869	−	0.583839i	$-0.801550\pi$
$421$	−5.95716	+	5.52743i	−0.290334	+	0.269391i	0.521535	+	0.853230i	$0.325359\pi$
$422$	49.5705	−	23.8719i	2.41305	−	1.16206i
$423$		0			0
$424$	−51.4307	+	89.0806i	−2.49770	+	4.32613i
$425$	0.592702	−	7.90905i	0.0287502	−	0.383645i
$426$		0			0
$427$	3.98808	+	10.1615i	0.192997	+	0.491747i
$428$	15.8794	+	19.9121i	0.767559	+	0.962488i
$429$		0			0
$430$	10.6265	−	12.7310i	0.512457	−	0.613945i
$431$	13.4125			0.646056			0.323028	−	0.946389i	$-0.395299\pi$
$431$	13.4125			0.646056			0.323028	+	0.946389i	$0.395299\pi$
$432$		0			0
$433$	3.83290	+	9.76607i	0.184197	+	0.469327i	0.992909	−	0.118878i	$-0.0379298\pi$
$433$	3.83290	+	9.76607i	0.184197	+	0.469327i	−0.808711	+	0.588206i	$0.799835\pi$
$434$	1.11005	−	4.86344i	0.0532840	−	0.233452i
$435$		0			0
$436$	44.9581	−	77.8697i	2.15310	−	3.72928i
$437$	3.76582	+	6.52259i	0.180143	+	0.312018i
$438$		0			0
$439$	17.6465	−	16.3735i	0.842220	−	0.781466i	−0.135633	−	0.990759i	$-0.543307\pi$
$439$	17.6465	−	16.3735i	0.842220	−	0.781466i	0.977853	+	0.209293i	$0.0671163\pi$
$440$	3.40610	−	2.32224i	0.162379	−	0.110708i
$441$		0			0
$442$	18.2655	−	2.75308i	0.868802	−	0.130951i
$443$	14.5647	+	9.93004i	0.691990	+	0.471791i	0.857544	−	0.514410i	$-0.171989\pi$
$443$	14.5647	+	9.93004i	0.691990	+	0.471791i	−0.165555	+	0.986201i	$0.552941\pi$
$444$		0			0
$445$	0.343791	−	0.106045i	0.0162972	−	0.00502704i
$446$	3.70134	+	1.78247i	0.175264	+	0.0844025i
$447$		0			0
$448$	−69.9365	−	10.5412i	−3.30419	−	0.498027i
$449$	16.9841	+	15.7590i	0.801531	+	0.743712i	0.970290	−	0.241945i	$-0.0777855\pi$
$449$	16.9841	+	15.7590i	0.801531	+	0.743712i	−0.168759	+	0.985657i	$0.553976\pi$
$450$		0			0
$451$	0.0502019	−	0.0629512i	0.00236391	−	0.00296425i
$452$	−45.5046	+	57.0609i	−2.14035	+	2.68392i
$453$		0			0
$454$	−49.9048	−	46.3049i	−2.34215	−	2.17319i
$455$	6.18322	+	0.931970i	0.289874	+	0.0436914i
$456$		0			0
$457$	−20.4097	−	9.82881i	−0.954727	−	0.459772i	−0.109386	−	0.993999i	$-0.534889\pi$
$457$	−20.4097	−	9.82881i	−0.954727	−	0.459772i	−0.845341	+	0.534227i	$0.820603\pi$
$458$	40.6809	−	12.5484i	1.90089	−	0.586348i
$459$		0			0
$460$	−7.88349	−	5.37487i	−0.367570	−	0.250605i
$461$	−27.2692	+	4.11018i	−1.27006	+	0.191430i	−0.749274	−	0.662260i	$-0.769597\pi$
$461$	−27.2692	+	4.11018i	−1.27006	+	0.191430i	−0.520781	+	0.853690i	$0.674359\pi$
$462$		0			0
$463$	8.81026	−	6.00673i	0.409447	−	0.279156i	−0.341030	−	0.940052i	$-0.610776\pi$
$463$	8.81026	−	6.00673i	0.409447	−	0.279156i	0.750478	+	0.660896i	$0.229823\pi$
$464$	−62.3474	+	57.8499i	−2.89440	+	2.68561i
$465$		0			0
$466$	28.2845	+	48.9903i	1.31026	+	2.26943i
$467$	2.52919	−	4.38068i	0.117037	−	0.202714i	−0.801555	−	0.597921i	$-0.795994\pi$
$467$	2.52919	−	4.38068i	0.117037	−	0.202714i	0.918592	+	0.395207i	$0.129327\pi$
$468$		0			0
$469$	−0.476020	+	2.08558i	−0.0219806	+	0.0963031i
$470$	−7.17515	−	18.2820i	−0.330965	−	0.843285i
$471$		0			0
$472$	101.768			4.68424
$473$	−1.42140	−	2.59411i	−0.0653560	−	0.119277i
$474$		0			0
$475$	10.5338	+	13.2090i	0.483326	+	0.606071i
$476$	−7.59774	−	19.3587i	−0.348242	−	0.887306i
$477$		0			0
$478$	−2.65838	+	35.4736i	−0.121591	+	1.62252i
$479$	−17.3338	+	30.0230i	−0.792001	+	1.37179i	0.132726	+	0.991153i	$0.457627\pi$
$479$	−17.3338	+	30.0230i	−0.792001	+	1.37179i	−0.924726	+	0.380633i	$0.875706\pi$
$480$		0			0
$481$	1.75395	−	0.844659i	0.0799733	−	0.0385131i
$482$	15.3742	−	14.2652i	0.700278	−	0.649763i
$483$		0			0
$484$	13.4867	+	59.0889i	0.613030	+	2.68586i
$485$	15.3258	−	2.31000i	0.695911	−	0.104892i
$486$		0			0
$487$	−8.75751	+	22.3138i	−0.396841	+	1.01113i	0.583199	+	0.812330i	$0.301801\pi$
$487$	−8.75751	+	22.3138i	−0.396841	+	1.01113i	−0.980039	+	0.198804i	$0.936294\pi$
$488$	53.5291	−	16.5115i	2.42315	−	0.747442i
$489$		0			0
$490$	0.609375	+	8.13155i	0.0275288	+	0.367346i
$491$	−2.48484	−	0.374530i	−0.112139	−	0.0169023i	0.0927327	−	0.995691i	$-0.470440\pi$
$491$	−2.48484	−	0.374530i	−0.112139	−	0.0169023i	−0.204872	+	0.978789i	$0.565678\pi$
$492$		0			0
$493$	−9.51415	−	2.93473i	−0.428496	−	0.132174i
$494$	−24.5333	+	30.7638i	−1.10381	+	1.38413i
$495$		0			0
$496$	−14.4800	−	4.46649i	−0.650171	−	0.200551i
$497$	−8.07318	−	7.49082i	−0.362132	−	0.336009i
$498$		0			0
$499$	1.13941	+	15.2043i	0.0510068	+	0.680638i	0.962839	+	0.270076i	$0.0870487\pi$
$499$	1.13941	+	15.2043i	0.0510068	+	0.680638i	−0.911832	+	0.410563i	$0.865332\pi$
$500$	−42.4612	−	20.4482i	−1.89892	−	0.914472i
$501$		0			0
$502$	−16.1223	+	41.0790i	−0.719575	+	1.83345i
$503$	−1.84862	−	1.26037i	−0.0824261	−	0.0561971i	0.521406	−	0.853309i	$-0.325408\pi$
$503$	−1.84862	−	1.26037i	−0.0824261	−	0.0561971i	−0.603832	+	0.797112i	$0.706360\pi$
$504$		0			0
$505$	−1.25980	−	5.51953i	−0.0560602	−	0.245616i
$506$	−1.90719	+	1.30030i	−0.0847850	+	0.0578055i
$507$		0			0
$508$	66.5509	−	32.0492i	2.95272	−	1.42195i
$509$	17.6153	+	30.5107i	0.780786	+	1.35236i	0.931484	+	0.363782i	$0.118515\pi$
$509$	17.6153	+	30.5107i	0.780786	+	1.35236i	−0.150698	+	0.988580i	$0.548152\pi$
$510$		0			0
$511$	2.05983	−	27.4866i	0.0911217	−	1.21593i
$512$	−18.3144	+	80.2408i	−0.809391	+	3.54618i
$513$		0			0
$514$	4.64532	+	5.82505i	0.204896	+	0.256932i
$515$	−8.74136			−0.385190
$516$		0			0
$517$	−3.50318			−0.154070
$518$	−1.85336	−	2.32404i	−0.0814320	−	0.102112i
$519$		0			0
$520$	7.14043	−	31.2843i	0.313129	−	1.37191i
$521$	3.20580	−	42.7785i	0.140449	−	1.87416i	−0.270799	−	0.962636i	$-0.587288\pi$
$521$	3.20580	−	42.7785i	0.140449	−	1.87416i	0.411247	−	0.911524i	$-0.365093\pi$
$522$		0			0
$523$	7.69902	+	13.3351i	0.336655	+	0.583103i	0.983801	−	0.179263i	$-0.0573712\pi$
$523$	7.69902	+	13.3351i	0.336655	+	0.583103i	−0.647147	+	0.762366i	$0.724038\pi$
$524$	15.3922	−	7.41250i	0.672412	−	0.323816i
$525$		0			0
$526$	−42.1203	+	28.7171i	−1.83653	+	1.25213i
$527$	−0.394729	−	1.72942i	−0.0171947	−	0.0753347i
$528$		0			0
$529$	−16.1619	−	11.0190i	−0.702692	−	0.479087i
$530$	−9.53090	+	24.2843i	−0.413996	+	1.05484i
$531$		0			0
$532$	39.9129	+	19.2210i	1.73044	+	0.833337i
$533$	−0.0468369	−	0.624995i	−0.00202873	−	0.0270715i
$534$		0			0
$535$	3.04807	+	2.82820i	0.131780	+	0.122274i
$536$	10.4901	+	3.23576i	0.453103	+	0.139764i
$537$		0			0
$538$	−22.2344	+	27.8811i	−0.958594	+	1.20204i
$539$	1.38990	+	0.428726i	0.0598671	+	0.0184666i
$540$		0			0
$541$	32.2484	+	4.86067i	1.38647	+	0.208976i	0.799516	−	0.600645i	$-0.205090\pi$
$541$	32.2484	+	4.86067i	1.38647	+	0.208976i	0.586952	+	0.809622i	$0.300328\pi$
$542$	−3.18089	−	42.4460i	−0.136631	−	1.82321i
$543$		0			0
$544$	−45.5390	+	14.0469i	−1.95247	+	0.602256i
$545$	5.36318	−	13.6652i	0.229733	−	0.585351i
$546$		0			0
$547$	−4.56008	+	0.687322i	−0.194975	+	0.0293878i	−0.245804	−	0.969320i	$-0.579052\pi$
$547$	−4.56008	+	0.687322i	−0.194975	+	0.0293878i	0.0508287	+	0.998707i	$0.483814\pi$
$548$	−15.1653	−	66.4436i	−0.647831	−	2.83833i
$549$		0			0
$550$	−3.79570	+	3.52189i	−0.161849	+	0.150174i
$551$	19.1088	−	9.20230i	0.814061	−	0.392031i
$552$		0			0
$553$	2.19792	−	3.80690i	0.0934649	−	0.161886i
$554$	−4.93360	+	65.8343i	−0.209608	+	2.79703i
$555$		0			0
$556$	−9.21640	−	23.4830i	−0.390863	−	0.995902i
$557$	−2.71786	−	3.40809i	−0.115159	−	0.144405i	0.720911	−	0.693028i	$-0.243724\pi$
$557$	−2.71786	−	3.40809i	−0.115159	−	0.144405i	−0.836070	+	0.548623i	$0.815152\pi$
$558$		0			0
$559$	−21.8450	−	7.27661i	−0.923944	−	0.307768i
$560$	−29.0034			−1.22562
$561$		0			0
$562$	−10.0272	−	25.5489i	−0.422972	−	1.07771i
$563$	6.19136	−	27.1261i	0.260935	−	1.14323i	−0.659306	−	0.751875i	$-0.729150\pi$
$563$	6.19136	−	27.1261i	0.260935	−	1.14323i	0.920240	−	0.391354i	$-0.127993\pi$
$564$		0			0
$565$	−5.95774	+	10.3191i	−0.250644	+	0.434128i
$566$	19.2485	+	33.3395i	0.809077	+	1.40136i
$567$		0			0
$568$	−41.4291	+	38.4406i	−1.73833	+	1.61293i
$569$	−1.04489	+	0.712395i	−0.0438042	+	0.0298652i	−0.585024	−	0.811016i	$-0.698915\pi$
$569$	−1.04489	+	0.712395i	−0.0438042	+	0.0298652i	0.541220	+	0.840881i	$0.317963\pi$
$570$		0			0
$571$	−20.4623	+	3.08420i	−0.856322	+	0.129070i	−0.562507	−	0.826792i	$-0.690163\pi$
$571$	−20.4623	+	3.08420i	−0.856322	+	0.129070i	−0.293815	+	0.955862i	$0.594925\pi$
$572$	−7.34658	−	5.00881i	−0.307176	−	0.209429i
$573$		0			0
$574$	−0.914490	+	0.282083i	−0.0381701	+	0.0117739i
$575$	6.95074	+	3.34730i	0.289866	+	0.139592i
$576$		0			0
$577$	−11.3836	−	1.71580i	−0.473905	−	0.0714297i	−0.0922528	−	0.995736i	$-0.529407\pi$
$577$	−11.3836	−	1.71580i	−0.473905	−	0.0714297i	−0.381653	+	0.924306i	$0.624645\pi$
$578$	27.0337	+	25.0836i	1.12445	+	1.04334i
$579$		0			0
$580$	−16.7524	+	21.0068i	−0.695604	+	0.872260i
$581$	−16.9652	+	21.2737i	−0.703835	+	0.882581i
$582$		0			0
$583$	3.41114	+	3.16508i	0.141275	+	0.131084i
$584$	−139.868	−	21.0818i	−5.78780	−	0.872370i
$585$		0			0
$586$	−42.6348	−	20.5318i	−1.76123	−	0.848161i
$587$	−29.3343	+	9.04842i	−1.21075	+	0.373468i	−0.833437	−	0.552615i	$-0.813630\pi$
$587$	−29.3343	+	9.04842i	−1.21075	+	0.373468i	−0.377318	+	0.926084i	$0.623154\pi$
$588$		0			0
$589$	3.12212	+	2.12863i	0.128645	+	0.0877086i
$590$	25.5220	−	3.84683i	1.05073	−	0.158371i
$591$		0			0
$592$	−7.46054	+	5.08651i	−0.306626	+	0.209054i
$593$	2.70312	−	2.50813i	0.111004	−	0.102997i	−0.622718	−	0.782446i	$-0.713972\pi$
$593$	2.70312	−	2.50813i	0.111004	−	0.102997i	0.733722	+	0.679449i	$0.237781\pi$
$594$		0			0
$595$	−1.69763	−	2.94038i	−0.0695959	−	0.120544i
$596$	−26.3739	+	45.6809i	−1.08032	+	1.87116i
$597$		0			0
$598$	−3.99817	+	17.5171i	−0.163497	+	0.716329i
$599$	−11.9286	−	30.3935i	−0.487388	−	1.24184i	−0.937222	−	0.348732i	$-0.886612\pi$
$599$	−11.9286	−	30.3935i	−0.487388	−	1.24184i	0.449834	−	0.893112i	$-0.351483\pi$
$600$		0			0
$601$	−33.8084			−1.37907			−0.689536	−	0.724251i	$-0.742186\pi$
$601$	−33.8084			−1.37907			−0.689536	+	0.724251i	$0.742186\pi$
$602$	−3.40997	+	34.9921i	−0.138980	+	1.42617i
$603$		0			0
$604$	−29.0586	−	36.4383i	−1.18238	−	1.48265i
$605$	3.61508	+	9.21108i	0.146974	+	0.374484i
$606$		0			0
$607$	−1.39787	+	18.6532i	−0.0567376	+	0.757111i	0.894188	+	0.447691i	$0.147754\pi$
$607$	−1.39787	+	18.6532i	−0.0567376	+	0.757111i	−0.950926	+	0.309419i	$0.899865\pi$
$608$	50.7582	−	87.9157i	2.05852	−	3.56545i
$609$		0			0
$610$	12.8003	−	6.16428i	0.518267	−	0.249584i
$611$	−19.9894	+	18.5474i	−0.808683	+	0.750348i
$612$		0			0
$613$	−4.20791	−	18.4361i	−0.169956	−	0.744626i	−0.986015	−	0.166657i	$-0.946703\pi$
$613$	−4.20791	−	18.4361i	−0.169956	−	0.744626i	0.816059	−	0.577969i	$-0.196154\pi$
$614$	−57.5314	+	8.67146i	−2.32178	+	0.349952i
$615$		0			0
$616$	−3.19304	+	8.13573i	−0.128651	+	0.327798i
$617$	24.4540	−	7.54305i	0.984479	−	0.303672i	0.239601	−	0.970872i	$-0.422983\pi$
$617$	24.4540	−	7.54305i	0.984479	−	0.303672i	0.744879	+	0.667200i	$0.232507\pi$
$618$		0			0
$619$	−3.08108	−	41.1142i	−0.123839	−	1.65252i	−0.620231	−	0.784419i	$-0.712961\pi$
$619$	−3.08108	−	41.1142i	−0.123839	−	1.65252i	0.496392	−	0.868099i	$-0.334658\pi$
$620$	−4.73358	−	0.713473i	−0.190105	−	0.0286538i
$621$		0			0
$622$	−16.9886	−	5.24029i	−0.681181	−	0.210116i
$623$	−0.475570	+	0.596346i	−0.0190533	+	0.0238921i
$624$		0			0
$625$	12.5235	+	3.86300i	0.500941	+	0.154520i
$626$	−13.9442	−	12.9383i	−0.557321	−	0.517119i
$627$		0			0
$628$	−4.09069	−	54.5864i	−0.163236	−	2.17824i
$629$	−0.952352	−	0.458629i	−0.0379728	−	0.0182867i
$630$		0			0
$631$	8.41507	−	21.4412i	0.334998	−	0.853562i	−0.659776	−	0.751463i	$-0.729349\pi$
$631$	8.41507	−	21.4412i	0.334998	−	0.853562i	0.994774	−	0.102100i	$-0.0325560\pi$
$632$	−18.6384	−	12.7074i	−0.741394	−	0.505474i
$633$		0			0
$634$	0.702979	+	3.07995i	0.0279189	+	0.122321i
$635$	9.96405	−	6.79337i	0.395411	−	0.269587i
$636$		0			0
$637$	10.2007	−	4.91240i	0.404167	−	0.194637i
$638$	3.25007	+	5.62929i	0.128672	+	0.222866i
$639$		0			0
$640$	−3.45493	+	46.1028i	−0.136568	+	1.82237i
$641$	7.22296	−	31.6459i	0.285290	−	1.24994i	−0.605619	−	0.795755i	$-0.707074\pi$
$641$	7.22296	−	31.6459i	0.285290	−	1.24994i	0.890909	−	0.454182i	$-0.150068\pi$
$642$		0			0
$643$	25.0195	+	31.3734i	0.986671	+	1.23725i	0.971421	+	0.237362i	$0.0762829\pi$
$643$	25.0195	+	31.3734i	0.986671	+	1.23725i	0.0152498	+	0.999884i	$0.495146\pi$
$644$	20.2287			0.797121
$645$		0			0
$646$	21.3652			0.840602
$647$	−0.798384	−	1.00114i	−0.0313877	−	0.0393590i	0.765890	−	0.642972i	$-0.222299\pi$
$647$	−0.798384	−	1.00114i	−0.0313877	−	0.0393590i	−0.797278	+	0.603613i	$0.793727\pi$
$648$		0			0
$649$	1.02446	−	4.48844i	0.0402134	−	0.176187i
$650$	−3.01200	+	40.1923i	−0.118140	+	1.57647i
$651$		0			0
$652$	−6.27159	−	10.8627i	−0.245614	−	0.425416i
$653$	−15.6506	+	7.53694i	−0.612456	+	0.294943i	−0.714281	−	0.699859i	$-0.753246\pi$
$653$	−15.6506	+	7.53694i	−0.612456	+	0.294943i	0.101825	+	0.994802i	$0.467532\pi$
$654$		0			0
$655$	2.30453	−	1.57120i	0.0900455	−	0.0613920i
$656$	0.646875	+	2.83414i	0.0252562	+	0.110655i
$657$		0			0
$658$	34.4027	+	23.4554i	1.34116	+	0.914385i
$659$	14.1869	−	36.1477i	0.552645	−	1.40812i	−0.332635	−	0.943056i	$-0.607938\pi$
$659$	14.1869	−	36.1477i	0.552645	−	1.40812i	0.885279	−	0.465060i	$-0.153967\pi$
$660$		0			0
$661$	−31.3625	−	15.1034i	−1.21986	−	0.587454i	−0.290587	−	0.956848i	$-0.593851\pi$
$661$	−31.3625	−	15.1034i	−1.21986	−	0.587454i	−0.929273	+	0.369395i	$0.879565\pi$
$662$	−2.03709	−	27.1831i	−0.0791739	−	1.05650i
$663$		0			0
$664$	102.359	+	94.9751i	3.97229	+	3.68575i
$665$	6.91119	+	2.13182i	0.268005	+	0.0826685i
$666$		0			0
$667$	6.03833	−	7.57182i	0.233805	−	0.293182i
$668$	125.102	+	38.5887i	4.84032	+	1.49304i
$669$		0			0
$670$	2.75309	+	0.414961i	0.106361	+	0.0160314i
$671$	−0.189380	−	2.52710i	−0.00731094	−	0.0975577i
$672$		0			0
$673$	20.4975	−	6.32264i	0.790120	−	0.243720i	0.126675	−	0.991944i	$-0.459570\pi$
$673$	20.4975	−	6.32264i	0.790120	−	0.243720i	0.663446	+	0.748225i	$0.269093\pi$
$674$	−23.3515	+	59.4987i	−0.899467	+	2.29181i
$675$		0			0
$676$	3.72412	−	0.561321i	0.143236	−	0.0215893i
$677$	8.90216	+	39.0029i	0.342138	+	1.49900i	0.794552	+	0.607196i	$0.207706\pi$
$677$	8.90216	+	39.0029i	0.342138	+	1.49900i	−0.452414	+	0.891808i	$0.649437\pi$
$678$		0			0
$679$	−24.0875	+	22.3499i	−0.924393	+	0.857711i
$680$	−15.6980	+	7.55974i	−0.601989	+	0.289903i
$681$		0			0
$682$	−0.579047	+	1.00294i	−0.0221729	+	0.0384045i
$683$	−0.0581079	+	0.775395i	−0.00222344	+	0.0296697i	−0.998205	−	0.0598870i	$-0.980926\pi$
$683$	−0.0581079	+	0.775395i	−0.00222344	+	0.0296697i	0.995982	+	0.0895567i	$0.0285450\pi$
$684$		0			0
$685$	−4.06505	−	10.3576i	−0.155317	−	0.395742i
$686$	−34.1789	−	42.8589i	−1.30496	−	1.63636i
$687$		0			0
$688$	105.222	+	18.2725i	4.01154	+	0.696634i
$689$	36.2215			1.37993
$690$		0			0
$691$	−13.6014	−	34.6557i	−0.517420	−	1.31836i	−0.915981	−	0.401223i	$-0.868585\pi$
$691$	−13.6014	−	34.6557i	−0.517420	−	1.31836i	0.398561	−	0.917142i	$-0.369510\pi$
$692$	−1.91686	+	8.39830i	−0.0728680	+	0.319256i
$693$		0			0
$694$	−23.0480	+	39.9204i	−0.874891	+	1.51536i
$695$	−2.05930	−	3.56681i	−0.0781136	−	0.135297i
$696$		0			0
$697$	−0.249464	+	0.231468i	−0.00944911	+	0.00876749i
$698$	−46.8408	+	31.9356i	−1.77295	+	1.20878i
$699$		0			0
$700$	44.8701	−	6.76308i	1.69593	−	0.255620i
$701$	−32.1515	−	21.9205i	−1.21434	−	0.827926i	−0.225119	−	0.974331i	$-0.572277\pi$
$701$	−32.1515	−	21.9205i	−1.21434	−	0.827926i	−0.989225	+	0.146405i	$0.953230\pi$
$702$		0			0
$703$	2.15163	−	0.663691i	0.0811504	−	0.0250316i
$704$	14.7933	+	7.12408i	0.557544	+	0.268499i
$705$		0			0
$706$	27.4968	+	4.14448i	1.03486	+	0.155979i
$707$	8.79870	+	8.16400i	0.330909	+	0.307039i
$708$		0			0
$709$	4.24430	−	5.32218i	0.159398	−	0.199879i	−0.695719	−	0.718314i	$-0.744914\pi$
$709$	4.24430	−	5.32218i	0.159398	−	0.199879i	0.855117	+	0.518436i	$0.173485\pi$
$710$	−8.93682	+	11.2064i	−0.335393	+	0.420570i
$711$		0			0
$712$	2.86933	+	2.66235i	0.107533	+	0.0997758i
$713$	1.70620	+	0.257169i	0.0638978	+	0.00963105i
$714$		0			0
$715$	−1.30790	−	0.629853i	−0.0489128	−	0.0235552i
$716$	35.0236	−	10.8034i	1.30889	−	0.403740i
$717$		0			0
$718$	−34.7492	−	23.6916i	−1.29683	−	0.884162i
$719$	9.10645	−	1.37258i	0.339613	−	0.0511885i	0.0229784	−	0.999736i	$-0.492685\pi$
$719$	9.10645	−	1.37258i	0.339613	−	0.0511885i	0.316635	+	0.948547i	$0.397447\pi$
$720$		0			0
$721$	15.3122	−	10.4397i	0.570258	−	0.388795i
$722$	5.06897	−	4.70332i	0.188647	−	0.175039i
$723$		0			0
$724$	−53.4833	−	92.6357i	−1.98769	−	3.44278i
$725$	10.8624	−	18.8142i	0.403419	−	0.698742i
$726$		0			0
$727$	−4.20129	+	18.4071i	−0.155817	+	0.682680i	0.835312	+	0.549777i	$0.185287\pi$
$727$	−4.20129	+	18.4071i	−0.155817	+	0.682680i	−0.991129	+	0.132904i	$0.957570\pi$
$728$	24.8546	+	63.3284i	0.921171	+	2.34711i
$729$		0			0
$730$	−35.8741			−1.32776
$731$	4.30636	+	11.7369i	0.159276	+	0.434106i
$732$		0			0
$733$	14.2106	+	17.8195i	0.524880	+	0.658178i	0.971637	−	0.236477i	$-0.0759927\pi$
$733$	14.2106	+	17.8195i	0.524880	+	0.658178i	−0.446757	+	0.894655i	$0.647421\pi$
$734$	−11.8844	−	30.2810i	−0.438662	−	1.11769i
$735$		0			0
$736$	3.46414	−	46.2258i	0.127690	−	1.70390i
$737$	0.248312	−	0.430089i	0.00914669	−	0.0158425i
$738$		0			0
$739$	−21.1790	+	10.1993i	−0.779083	+	0.375187i	−0.780775	−	0.624812i	$-0.785176\pi$
$739$	−21.1790	+	10.1993i	−0.779083	+	0.375187i	0.00169199	+	0.999999i	$0.499461\pi$
$740$	−2.09104	+	1.94020i	−0.0768682	+	0.0713233i
$741$		0			0
$742$	−12.3072	−	53.9215i	−0.451813	−	1.97952i
$743$	−27.3290	+	4.11919i	−1.00260	+	0.151118i	−0.629772	−	0.776780i	$-0.716852\pi$
$743$	−27.3290	+	4.11919i	−1.00260	+	0.151118i	−0.372833	+	0.927899i	$0.621613\pi$
$744$		0			0
$745$	−3.14621	+	8.01642i	−0.115268	+	0.293699i
$746$	−32.0753	+	9.89393i	−1.17436	+	0.362242i
$747$		0			0
$748$	0.360791	+	4.81442i	0.0131918	+	0.176032i
$749$	−8.71699	−	1.31388i	−0.318512	−	0.0480079i
$750$		0			0
$751$	−19.8284	−	6.11625i	−0.723549	−	0.223185i	−0.0889600	−	0.996035i	$-0.528354\pi$
$751$	−19.8284	−	6.11625i	−0.723549	−	0.223185i	−0.634589	+	0.772850i	$0.718831\pi$
$752$	78.8589	−	98.8859i	2.87569	−	3.60600i
$753$		0			0
$754$	48.3491	+	14.9137i	1.76077	+	0.543126i
$755$	−5.57783	−	5.17547i	−0.202998	−	0.188355i
$756$		0			0
$757$	−1.60398	−	21.4036i	−0.0582975	−	0.777926i	−0.947366	−	0.320152i	$-0.896266\pi$
$757$	−1.60398	−	21.4036i	−0.0582975	−	0.777926i	0.889069	−	0.457774i	$-0.151353\pi$
$758$	20.0720	+	9.66618i	0.729049	+	0.351091i
$759$		0			0
$760$	13.5597	−	34.5494i	0.491860	−	1.25324i
$761$	−9.83792	−	6.70738i	−0.356624	−	0.243142i	0.371733	−	0.928340i	$-0.378764\pi$
$761$	−9.83792	−	6.70738i	−0.356624	−	0.243142i	−0.728357	+	0.685197i	$0.759716\pi$
$762$		0			0
$763$	6.92547	+	30.3425i	0.250719	+	1.09847i
$764$	74.3970	−	50.7230i	2.69159	−	1.83509i
$765$		0			0
$766$	−64.6590	+	31.1381i	−2.33622	+	1.12507i
$767$	−17.9182	−	31.0353i	−0.646989	−	1.12062i
$768$		0			0
$769$	2.45417	−	32.7486i	0.0884996	−	1.18094i	−0.759341	−	0.650693i	$-0.774478\pi$
$769$	2.45417	−	32.7486i	0.0884996	−	1.18094i	0.847840	−	0.530252i	$-0.177903\pi$
$770$	−0.493242	+	2.16103i	−0.0177752	+	0.0778782i
$771$		0			0
$772$	−21.9476	−	27.5214i	−0.789910	−	0.990515i
$773$	−16.1263			−0.580024			−0.290012	−	0.957023i	$-0.593659\pi$
$773$	−16.1263			−0.580024			−0.290012	+	0.957023i	$0.593659\pi$
$774$		0			0
$775$	3.87059			0.139036
$776$	105.135	+	131.835i	3.77412	+	4.73260i
$777$		0			0
$778$	−2.24862	+	9.85183i	−0.0806168	+	0.353205i
$779$	0.0541732	−	0.722892i	0.00194096	−	0.0259003i
$780$		0			0
$781$	1.27836	+	2.21419i	0.0457434	+	0.0792298i
$782$	8.78983	−	4.23296i	0.314324	−	0.151370i
$783$		0			0
$784$	−43.3894	+	29.5824i	−1.54962	+	1.05651i
$785$	−1.98865	−	8.71284i	−0.0709779	−	0.310975i
$786$		0			0
$787$	5.84489	+	3.98498i	0.208348	+	0.142049i	0.662999	−	0.748621i	$-0.269284\pi$
$787$	5.84489	+	3.98498i	0.208348	+	0.142049i	−0.454651	+	0.890670i	$0.650236\pi$
$788$	−22.3249	+	56.8829i	−0.795291	+	2.02637i
$789$		0			0
$790$	−5.15460	−	2.48232i	−0.183392	−	0.0883171i
$791$	−1.88782	−	25.1913i	−0.0671233	−	0.895698i
$792$		0			0
$793$	−14.4602	−	13.4171i	−0.513498	−	0.476456i
$794$	68.6698	+	21.1818i	2.43700	+	0.751715i
$795$		0			0
$796$	−16.8175	+	21.0885i	−0.596081	+	0.747462i
$797$	−47.8168	−	14.7495i	−1.69376	−	0.522455i	−0.710347	−	0.703852i	$-0.751462\pi$
$797$	−47.8168	−	14.7495i	−1.69376	−	0.522455i	−0.983410	+	0.181397i	$0.941938\pi$
$798$		0			0
$799$	14.6408	+	2.20675i	0.517956	+	0.0780693i
$800$	−7.77076	−	103.694i	−0.274738	−	3.66612i
$801$		0			0
$802$	36.4657	−	11.2482i	1.28765	−	0.397187i
$803$	−2.33781	+	5.95664i	−0.0824994	+	0.210205i
$804$		0			0
$805$	3.26569	−	0.492224i	0.115101	−	0.0173486i
$806$	2.00594	+	8.78858i	0.0706561	+	0.309564i
$807$		0			0
$808$	45.1523	−	41.8952i	1.58845	−	1.47387i
$809$	−22.2720	+	10.7256i	−0.783041	+	0.377093i	−0.782296	−	0.622907i	$-0.785951\pi$
$809$	−22.2720	+	10.7256i	−0.783041	+	0.377093i	−0.000745138		1.00000i	$0.500237\pi$
$810$		0			0
$811$	11.1420	−	19.2986i	0.391249	−	0.677664i	−0.601365	−	0.798974i	$-0.705376\pi$
$811$	11.1420	−	19.2986i	0.391249	−	0.677664i	0.992615	+	0.121310i	$0.0387097\pi$
$812$	4.25693	−	56.8048i	0.149389	−	1.99346i
$813$		0			0
$814$	0.252117	+	0.642384i	0.00883670	+	0.0225156i
$815$	−1.27680	−	1.60106i	−0.0447244	−	0.0560826i
$816$		0			0
$817$	−23.7301	−	12.0882i	−0.830210	−	0.422912i
$818$	18.7387			0.655183
$819$		0			0
$820$	0.335514	+	0.854877i	0.0117167	+	0.0298536i
$821$	11.3396	−	49.6819i	0.395753	−	1.73391i	−0.248077	−	0.968740i	$-0.579798\pi$
$821$	11.3396	−	49.6819i	0.395753	−	1.73391i	0.643830	−	0.765169i	$-0.277344\pi$
$822$		0			0
$823$	7.72992	−	13.3886i	0.269448	−	0.466698i	−0.699271	−	0.714856i	$-0.746492\pi$
$823$	7.72992	−	13.3886i	0.269448	−	0.466698i	0.968719	+	0.248158i	$0.0798254\pi$
$824$	−47.5515	−	82.3616i	−1.65653	−	2.86920i
$825$		0			0
$826$	−40.1127	+	37.2192i	−1.39570	+	1.29502i
$827$	−15.9404	+	10.8680i	−0.554304	+	0.377918i	−0.807834	−	0.589409i	$-0.799360\pi$
$827$	−15.9404	+	10.8680i	−0.554304	+	0.377918i	0.253531	+	0.967327i	$0.418408\pi$
$828$		0			0
$829$	−32.4810	+	4.89573i	−1.12811	+	0.170036i	−0.686472	−	0.727156i	$-0.740841\pi$
$829$	−32.4810	+	4.89573i	−1.12811	+	0.170036i	−0.441641	+	0.897192i	$0.645603\pi$
$830$	29.2603	+	19.9493i	1.01564	+	0.692452i
$831$		0			0
$832$	122.130	−	37.6720i	4.23408	−	1.30604i
$833$	−5.53873	−	2.66731i	−0.191906	−	0.0924169i
$834$		0			0
$835$	21.1352	+	3.18562i	0.731415	+	0.110243i
$836$	−7.53896	−	6.99513i	−0.260740	−	0.241932i
$837$		0			0
$838$	20.5234	−	25.7355i	0.708969	−	0.889019i
$839$	4.90787	−	6.15427i	0.169438	−	0.212469i	−0.689861	−	0.723942i	$-0.742328\pi$
$839$	4.90787	−	6.15427i	0.169438	−	0.212469i	0.859300	+	0.511473i	$0.170900\pi$
$840$		0			0
$841$	1.26652	+	1.17516i	0.0436730	+	0.0405226i
$842$	−22.1730	−	3.34204i	−0.764132	−	0.115174i
$843$		0			0
$844$	100.850	+	48.5667i	3.47139	+	1.67173i
$845$	0.587560	−	0.181238i	0.0202127	−	0.00623479i
$846$		0			0
$847$	−17.3332	−	11.8176i	−0.595577	−	0.406058i
$848$	−166.129	+	25.0399i	−5.70490	+	0.859875i
$849$		0			0
$850$	18.0819	−	12.3280i	0.620204	−	0.422848i
$851$	0.753708	−	0.699339i	0.0258368	−	0.0239730i
$852$		0			0
$853$	0.698964	+	1.21064i	0.0239321	+	0.0414516i	0.877743	−	0.479131i	$-0.159048\pi$
$853$	0.698964	+	1.21064i	0.0239321	+	0.0414516i	−0.853811	+	0.520583i	$0.825715\pi$
$854$	−15.0603	+	26.0852i	−0.515353	+	0.892617i
$855$		0			0
$856$	−10.0665	+	44.1040i	−0.344064	+	1.50744i
$857$	20.5503	+	52.3614i	0.701986	+	1.78863i	0.609307	+	0.792934i	$0.291448\pi$
$857$	20.5503	+	52.3614i	0.701986	+	1.78863i	0.0926784	+	0.995696i	$0.470457\pi$
$858$		0			0
$859$	−13.0903			−0.446635			−0.223317	−	0.974746i	$-0.571689\pi$
$859$	−13.0903			−0.446635			−0.223317	+	0.974746i	$0.571689\pi$
$860$	33.7297	+	0.753753i	1.15017	+	0.0257027i
$861$		0			0
$862$	23.0747	+	28.9348i	0.785927	+	0.985522i
$863$	10.2189	+	26.0374i	0.347856	+	0.886322i	0.992545	+	0.121877i	$0.0388914\pi$
$863$	10.2189	+	26.0374i	0.347856	+	0.886322i	−0.644690	+	0.764445i	$0.723013\pi$
$864$		0			0
$865$	−0.105100	+	1.40246i	−0.00357349	+	0.0476849i
$866$	−14.4743	+	25.0702i	−0.491856	+	0.851920i
$867$		0			0
$868$	9.14392	−	4.40348i	0.310365	−	0.149464i
$869$	−0.748082	+	0.694119i	−0.0253770	+	0.0235464i
$870$		0			0
$871$	−0.860202	−	3.76879i	−0.0291468	−	0.127701i
$872$	157.929	−	23.8039i	5.34814	−	0.806103i
$873$		0			0
$874$	−7.59252	+	19.3454i	−0.256821	+	0.654369i
$875$	15.5879	−	4.80822i	0.526966	−	0.162547i
$876$		0			0
$877$	−2.80162	−	37.3850i	−0.0946039	−	1.26240i	−0.819313	−	0.573347i	$-0.805645\pi$
$877$	−2.80162	−	37.3850i	−0.0946039	−	1.26240i	0.724709	−	0.689055i	$-0.241974\pi$
$878$	65.6815	+	9.89990i	2.21664	+	0.334105i
$879$		0			0
$880$	6.43408	+	1.98465i	0.216893	+	0.0669026i
$881$	−20.0677	+	25.1641i	−0.676098	+	0.847800i	−0.994988	−	0.0999917i	$-0.968118\pi$
$881$	−20.0677	+	25.1641i	−0.676098	+	0.847800i	0.318890	+	0.947792i	$0.396690\pi$
$882$		0			0
$883$	−5.12237	−	1.58004i	−0.172381	−	0.0531726i	0.207363	−	0.978264i	$-0.433512\pi$
$883$	−5.12237	−	1.58004i	−0.172381	−	0.0531726i	−0.379744	+	0.925091i	$0.623988\pi$
$884$	27.5484	+	25.5612i	0.926553	+	0.859715i
$885$		0			0
$886$	3.63488	+	48.5040i	0.122116	+	1.62953i
$887$	−37.9003	−	18.2518i	−1.27257	−	0.612836i	−0.329098	−	0.944296i	$-0.606745\pi$
$887$	−37.9003	−	18.2518i	−1.27257	−	0.612836i	−0.943470	+	0.331459i	$0.892459\pi$
$888$		0			0
$889$	−9.34077	+	23.7999i	−0.313280	+	0.798223i
$890$	0.820227	+	0.559222i	0.0274941	+	0.0187451i
$891$		0			0
$892$	1.85983	+	8.14843i	0.0622716	+	0.272830i
$893$	−26.0595	+	17.7671i	−0.872049	+	0.594553i
$894$		0			0
$895$	5.39130	−	2.59631i	0.180211	−	0.0867852i
$896$	−49.0081	−	84.8845i	−1.63725	−	2.83579i
$897$		0			0
$898$	−4.77752	+	63.7516i	−0.159428	+	2.12742i
$899$	1.08122	−	4.73713i	0.0360607	−	0.157992i
$900$		0			0
$901$	−12.2624	−	15.3766i	−0.408520	−	0.512268i
$902$	0.222172			0.00739751
$903$		0			0
$904$	−129.636			−4.31164
$905$	−10.8884	−	13.6536i	−0.361942	−	0.453861i
$906$		0			0
$907$	11.0757	−	48.5257i	0.367762	−	1.61127i	−0.365151	−	0.930948i	$-0.618983\pi$
$907$	11.0757	−	48.5257i	0.367762	−	1.61127i	0.732913	−	0.680322i	$-0.238160\pi$
$908$	10.3503	−	138.116i	0.343488	−	4.58353i
$909$		0			0
$910$	8.62702	+	14.9424i	0.285983	+	0.495337i
$911$	30.3278	−	14.6051i	1.00481	−	0.483889i	0.142239	−	0.989832i	$-0.454570\pi$
$911$	30.3278	−	14.6051i	1.00481	−	0.483889i	0.862567	+	0.505943i	$0.168856\pi$
$912$		0			0
$913$	5.21926	−	3.55843i	0.172732	−	0.117767i
$914$	−13.9090	−	60.9394i	−0.460070	−	2.01570i
$915$		0			0
$916$	71.5623	+	48.7903i	2.36448	+	1.61208i
$917$	−2.16038	+	5.50456i	−0.0713420	+	0.181776i
$918$		0			0
$919$	−1.21942	−	0.587240i	−0.0402248	−	0.0193712i	0.413663	−	0.910430i	$-0.364249\pi$
$919$	−1.21942	−	0.587240i	−0.0402248	−	0.0193712i	−0.453888	+	0.891059i	$0.649963\pi$
$920$	−1.26651	−	16.9004i	−0.0417557	−	0.557191i
$921$		0			0
$922$	−55.7807	−	51.7569i	−1.83704	−	1.70452i
$923$	19.0173	+	5.86606i	0.625963	+	0.193084i
$924$		0			0
$925$	1.43802	−	1.80322i	0.0472819	−	0.0592897i
$926$	28.1154	+	8.67247i	0.923931	+	0.284995i
$927$		0			0
$928$	−129.079	−	19.4556i	−4.23723	−	0.638660i
$929$	−2.76821	−	36.9392i	−0.0908219	−	1.21193i	−0.837383	−	0.546617i	$-0.815915\pi$
$929$	−2.76821	−	36.9392i	−0.0908219	−	1.21193i	0.746561	−	0.665317i	$-0.231704\pi$
$930$		0			0
$931$	12.5136	−	3.85992i	0.410116	−	0.126504i
$932$	−42.0464	+	107.133i	−1.37728	+	3.50924i
$933$		0			0
$934$	13.8017	−	2.08026i	0.451604	−	0.0680683i
$935$	0.175395	+	0.768455i	0.00573602	+	0.0251312i
$936$		0			0
$937$	−1.98566	+	1.84242i	−0.0648686	+	0.0601893i	−0.711941	−	0.702239i	$-0.752184\pi$
$937$	−1.98566	+	1.84242i	−0.0648686	+	0.0601893i	0.647072	+	0.762429i	$0.275993\pi$
$938$	−5.31817	+	2.56110i	−0.173644	+	0.0836227i
$939$		0			0
$940$	19.9781	−	34.6031i	0.651614	−	1.12863i
$941$	−1.22530	+	16.3505i	−0.0399436	+	0.533011i	0.940960	+	0.338517i	$0.109925\pi$
$941$	−1.22530	+	16.3505i	−0.0399436	+	0.533011i	−0.980904	+	0.194493i	$0.937694\pi$
$942$		0			0
$943$	−0.120935	−	0.308137i	−0.00393818	−	0.0100343i
$944$	103.636	+	129.956i	3.37307	+	4.22969i
$945$		0			0
$946$	3.15091	−	7.52927i	0.102445	−	0.244798i
$947$	−13.5238			−0.439463			−0.219731	−	0.975560i	$-0.570518\pi$
$947$	−13.5238			−0.439463			−0.219731	+	0.975560i	$0.570518\pi$
$948$		0			0
$949$	18.1975	+	46.3663i	0.590714	+	1.50512i
$950$	−10.3735	+	45.4494i	−0.336562	+	1.47457i
$951$		0			0
$952$	18.4696	−	31.9903i	0.598603	−	1.03681i
$953$	−15.5635	−	26.9569i	−0.504153	−	0.873218i	−0.999988	−	0.00480189i	$-0.998472\pi$
$953$	−15.5635	−	26.9569i	−0.504153	−	0.873218i	0.495836	−	0.868416i	$-0.334862\pi$
$954$		0			0
$955$	10.7763	−	9.99897i	0.348714	−	0.323559i
$956$	−59.7969	+	40.7688i	−1.93397	+	1.31856i
$957$		0			0
$958$	−94.5896	+	14.2571i	−3.05605	+	0.460626i
$959$	19.4907	+	13.2885i	0.629387	+	0.429109i
$960$		0			0
$961$	−28.7955	+	8.88224i	−0.928888	+	0.286524i
$962$	4.83967	+	2.33066i	0.156037	+	0.0751436i
$963$		0			0
$964$	42.1923	+	6.35946i	1.35892	+	0.204824i
$965$	−4.21287	−	3.90897i	−0.135617	−	0.125834i
$966$		0			0
$967$	−0.697559	+	0.874712i	−0.0224320	+	0.0281288i	−0.792921	−	0.609324i	$-0.791441\pi$
$967$	−0.697559	+	0.874712i	−0.0224320	+	0.0281288i	0.770489	+	0.637453i	$0.220012\pi$
$968$	−67.1219	+	84.1682i	−2.15738	+	2.70527i
$969$		0			0
$970$	31.3498	+	29.0884i	1.00658	+	0.933972i
$971$	42.2187	+	6.36345i	1.35486	+	0.204213i	0.786004	−	0.618222i	$-0.212147\pi$
$971$	42.2187	+	6.36345i	1.35486	+	0.204213i	0.568860	+	0.822435i	$0.307385\pi$
$972$		0			0
$973$	7.86708	+	3.78858i	0.252207	+	0.121456i
$974$	−63.2039	+	19.4958i	−2.02519	+	0.624687i
$975$		0			0
$976$	75.5968	+	51.5410i	2.41979	+	1.64979i
$977$	−11.1357	+	1.67844i	−0.356264	+	0.0536981i	−0.324736	−	0.945805i	$-0.605275\pi$
$977$	−11.1357	+	1.67844i	−0.356264	+	0.0536981i	−0.0315278	+	0.999503i	$0.510037\pi$
$978$		0			0
$979$	0.146307	−	0.0997501i	0.00467598	−	0.00318803i
$980$	−12.1612	+	11.2839i	−0.388475	+	0.360452i
$981$		0			0
$982$	−3.46693	−	6.00490i	−0.110634	−	0.191624i
$983$	4.19746	−	7.27021i	0.133878	−	0.231884i	−0.791290	−	0.611441i	$-0.790590\pi$
$983$	4.19746	−	7.27021i	0.133878	−	0.231884i	0.925168	+	0.379557i	$0.123924\pi$
$984$		0			0
$985$	−2.21997	+	9.72634i	−0.0707342	+	0.309907i
$986$	−10.0370	−	25.5738i	−0.319643	−	0.814436i
$987$		0			0
$988$	−80.0531			−2.54683
$989$	−12.1577	−	0.271687i	−0.386593	−	0.00863916i
$990$		0			0
$991$	25.7233	+	32.2560i	0.817129	+	1.02465i	0.999145	+	0.0413515i	$0.0131663\pi$
$991$	25.7233	+	32.2560i	0.817129	+	1.02465i	−0.182016	+	0.983296i	$0.558262\pi$
$992$	−8.49677	−	21.6494i	−0.269773	−	0.687370i
$993$		0			0
$994$	2.27093	−	30.3035i	0.0720295	−	0.961167i
$995$	−2.20185	+	3.81372i	−0.0698035	+	0.120903i
$996$		0			0
$997$	−54.1007	+	26.0535i	−1.71339	+	0.825124i	−0.722352	+	0.691526i	$0.756939\pi$
$997$	−54.1007	+	26.0535i	−1.71339	+	0.825124i	−0.991036	+	0.133598i	$0.957347\pi$
$998$	−30.8401	+	28.6154i	−0.976226	+	0.905805i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.109.3		36
3.2	odd	2		43.2.g.a.23.1	yes	36
12.11	even	2		688.2.bg.c.625.2		36
43.15	even	21	inner	387.2.y.c.316.3		36
129.74	odd	42		1849.2.a.n.1.1		18
129.98	even	42		1849.2.a.o.1.18		18
129.101	odd	42		43.2.g.a.15.1	✓	36
516.359	even	42		688.2.bg.c.273.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.15.1	✓	36	129.101	odd	42
43.2.g.a.23.1	yes	36	3.2	odd	2
387.2.y.c.109.3		36	1.1	even	1	trivial
387.2.y.c.316.3		36	43.15	even	21	inner
688.2.bg.c.273.2		36	516.359	even	42
688.2.bg.c.625.2		36	12.11	even	2
1849.2.a.n.1.1		18	129.74	odd	42
1849.2.a.o.1.18		18	129.98	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72039 + 2.15730i) q^{2} +(-1.24917 + 5.47296i) q^{4} +(-0.0684907 + 0.913945i) q^{5} +(-0.971539 - 1.68276i) q^{7} +(-8.98382 + 4.32638i) q^{8} +O(q^{10})\)	\(q+(1.72039 + 2.15730i) q^{2} +(-1.24917 + 5.47296i) q^{4} +(-0.0684907 + 0.913945i) q^{5} +(-0.971539 - 1.68276i) q^{7} +(-8.98382 + 4.32638i) q^{8} +(-2.08949 + 1.42459i) q^{10} +(0.100377 + 0.439781i) q^{11} +(2.90116 + 1.97798i) q^{13} +(1.95879 - 4.99091i) q^{14} +(-14.6735 - 7.06637i) q^{16} +(-0.142476 - 1.90121i) q^{17} +(2.97713 + 2.76237i) q^{19} +(-4.91643 - 1.51652i) q^{20} +(-0.776053 + 0.973140i) q^{22} +(1.77211 + 0.546623i) q^{23} +(4.11355 + 0.620018i) q^{25} +(0.724035 + 9.66157i) q^{26} +(10.4233 - 3.21515i) q^{28} +(1.90792 - 4.86129i) q^{29} +(0.920034 - 0.138673i) q^{31} +(-5.56217 - 24.3695i) q^{32} +(3.85637 - 3.57819i) q^{34} +(1.60449 - 0.772681i) q^{35} +(0.277212 - 0.480145i) q^{37} +(-0.837445 + 11.1749i) q^{38} +(-3.33877 - 8.50704i) q^{40} +(-0.111290 - 0.139553i) q^{41} +(-6.30773 + 1.79236i) q^{43} -2.53229 q^{44} +(1.86949 + 4.76338i) q^{46} +(-1.72810 + 7.57131i) q^{47} +(1.61222 - 2.79245i) q^{49} +(5.73935 + 9.94085i) q^{50} +(-14.4494 + 13.4071i) q^{52} +(8.52328 - 5.81107i) q^{53} +(-0.408811 + 0.0616183i) q^{55} +(16.0084 + 10.9143i) q^{56} +(13.7696 - 4.24737i) q^{58} +(-9.19536 - 4.42825i) q^{59} +(-5.55516 - 0.837306i) q^{61} +(1.88198 + 1.74622i) q^{62} +(22.6945 - 28.4580i) q^{64} +(-2.00646 + 2.51603i) q^{65} +(-0.807046 - 0.748830i) q^{67} +(10.5832 + 1.59516i) q^{68} +(4.42726 + 2.13205i) q^{70} +(5.41606 - 1.67063i) q^{71} +(11.7207 + 7.99101i) q^{73} +(1.51273 - 0.228008i) q^{74} +(-18.8373 + 12.8430i) q^{76} +(0.642524 - 0.596175i) q^{77} +(1.13115 + 1.95921i) q^{79} +(7.46327 - 12.9268i) q^{80} +(0.109596 - 0.480173i) q^{82} +(-5.11608 - 13.0356i) q^{83} +1.74736 q^{85} +(-14.7184 - 10.5241i) q^{86} +(-2.80443 - 3.51664i) q^{88} +(-0.143414 - 0.365414i) q^{89} +(0.509861 - 6.80362i) q^{91} +(-5.20531 + 9.01586i) q^{92} +(-19.3066 + 9.29758i) q^{94} +(-2.72856 + 2.53173i) q^{95} +(-3.76302 - 16.4869i) q^{97} +(8.79782 - 1.32606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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