LMFDB - Embedded newform 81.2.e.a.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			64.2
Root			$0.500000 - 1.27297i$ of defining polynomial
Character	$\chi$	$=$	81.64
Dual form			81.2.e.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57954 + 0.574906i) q^{2} +(0.632343 + 0.530599i) q^{4} +(0.196143 - 1.11238i) q^{5} +(-2.99441 + 2.51261i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})$	\(q+(1.57954 + 0.574906i) q^{2} +(0.632343 + 0.530599i) q^{4} +(0.196143 - 1.11238i) q^{5} +(-2.99441 + 2.51261i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(0.324801 + 1.84204i) q^{11} +(0.688417 - 0.250563i) q^{13} +(-6.17430 + 2.24726i) q^{14} +(-0.862951 - 4.89404i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(0.714260 - 0.599335i) q^{20} +(-0.545962 + 3.09631i) q^{22} +(4.46428 + 3.74597i) q^{23} +(3.49954 + 1.27373i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(-4.99910 - 1.81953i) q^{29} +(1.02696 + 0.861722i) q^{31} +(0.764882 - 4.33786i) q^{32} +(2.43321 - 2.04170i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(-0.800605 - 4.54046i) q^{38} +(-2.09556 + 0.762721i) q^{40} +(1.68800 - 0.614382i) q^{41} +(0.873477 + 4.95373i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(-1.30892 + 1.09832i) q^{47} +(1.43775 - 8.15389i) q^{49} +(4.79539 + 4.02381i) q^{50} +(0.568265 + 0.206831i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(7.25193 + 2.63949i) q^{56} +(-6.85023 - 5.74803i) q^{58} +(1.95529 - 11.0890i) q^{59} +(4.00710 - 3.36235i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(-0.143694 - 0.814930i) q^{65} +(1.77511 - 0.646086i) q^{67} +(1.46577 - 0.533495i) q^{68} +(1.28877 + 7.30898i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(-4.37302 + 3.66940i) q^{74} +(0.393163 - 2.22974i) q^{76} +(-5.60091 - 4.69972i) q^{77} +(-11.6079 - 4.22493i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(-10.9786 - 3.99588i) q^{83} +(-1.63507 - 1.37199i) q^{85} +(-1.46824 + 8.32679i) q^{86} +(2.82886 - 2.37370i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(0.835346 + 4.73748i) q^{92} +(-2.69893 + 0.982329i) q^{94} +(-2.91133 + 1.05964i) q^{95} +(-0.0596270 - 0.338162i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	1.57954	+	0.574906i	1.11690	+	0.406520i	0.833521	−	0.552487i	$-0.186321\pi$
$2$	1.57954	+	0.574906i	1.11690	+	0.406520i	0.283383	+	0.959007i	$0.408543\pi$
$3$		0			0
$3$		0			0
$4$	0.632343	+	0.530599i	0.316172	+	0.265300i
$5$	0.196143	−	1.11238i	0.0877179	−	0.497473i	−0.909019	−	0.416755i	$-0.863167\pi$
$5$	0.196143	−	1.11238i	0.0877179	−	0.497473i	0.996737	−	0.0807185i	$-0.0257215\pi$
$6$		0			0
$7$	−2.99441	+	2.51261i	−1.13178	+	0.949676i	−0.999139	−	0.0414879i	$-0.986790\pi$
$7$	−2.99441	+	2.51261i	−1.13178	+	0.949676i	−0.132641	+	0.991164i	$0.542346\pi$
$8$	−0.987144	−	1.70978i	−0.349008	−	0.604500i
$9$		0			0
$10$	0.949332	−	1.64429i	0.300205	−	0.519971i
$11$	0.324801	+	1.84204i	0.0979313	+	0.555396i	0.993810	+	0.111096i	$0.0354362\pi$
$11$	0.324801	+	1.84204i	0.0979313	+	0.555396i	−0.895878	+	0.444299i	$0.853453\pi$
$12$		0			0
$13$	0.688417	−	0.250563i	0.190932	−	0.0694937i	−0.244784	−	0.969578i	$-0.578717\pi$
$13$	0.688417	−	0.250563i	0.190932	−	0.0694937i	0.435717	+	0.900084i	$0.356495\pi$
$14$	−6.17430	+	2.24726i	−1.65015	+	0.600606i
$15$		0			0
$16$	−0.862951	−	4.89404i	−0.215738	−	1.22351i
$17$	0.944822	−	1.63648i	0.229153	−	0.396905i	−0.728404	−	0.685147i	$-0.759738\pi$
$17$	0.944822	−	1.63648i	0.229153	−	0.396905i	0.957557	+	0.288243i	$0.0930711\pi$
$18$		0			0
$19$	−1.37143	−	2.37538i	−0.314627	−	0.544950i	0.664731	−	0.747083i	$-0.268546\pi$
$19$	−1.37143	−	2.37538i	−0.314627	−	0.544950i	−0.979358	+	0.202133i	$0.935213\pi$
$20$	0.714260	−	0.599335i	0.159713	−	0.134015i
$21$		0			0
$22$	−0.545962	+	3.09631i	−0.116400	+	0.660135i
$23$	4.46428	+	3.74597i	0.930866	+	0.781089i	0.975973	−	0.217893i	$-0.0699183\pi$
$23$	4.46428	+	3.74597i	0.930866	+	0.781089i	−0.0451066	+	0.998982i	$0.514363\pi$
$24$		0			0
$25$	3.49954	+	1.27373i	0.699908	+	0.254746i
$26$	1.23143			0.241504
$27$		0			0
$28$	−3.22668			−0.609786
$29$	−4.99910	−	1.81953i	−0.928310	−	0.337877i	−0.166771	−	0.985996i	$-0.553334\pi$
$29$	−4.99910	−	1.81953i	−0.928310	−	0.337877i	−0.761540	+	0.648118i	$0.775556\pi$
$30$		0			0
$31$	1.02696	+	0.861722i	0.184447	+	0.154770i	0.730336	−	0.683088i	$-0.239363\pi$
$31$	1.02696	+	0.861722i	0.184447	+	0.154770i	−0.545889	+	0.837858i	$0.683808\pi$
$32$	0.764882	−	4.33786i	0.135213	−	0.766833i
$33$		0			0
$34$	2.43321	−	2.04170i	0.417291	−	0.350149i
$35$	2.20765	+	3.82376i	0.373161	+	0.646334i
$36$		0			0
$37$	−1.69806	+	2.94112i	−0.279159	+	0.483517i	−0.971176	−	0.238364i	$-0.923389\pi$
$37$	−1.69806	+	2.94112i	−0.279159	+	0.483517i	0.692017	+	0.721881i	$0.256722\pi$
$38$	−0.800605	−	4.54046i	−0.129875	−	0.736559i
$39$		0			0
$40$	−2.09556	+	0.762721i	−0.331337	+	0.120597i
$41$	1.68800	−	0.614382i	0.263621	−	0.0959503i	−0.206828	−	0.978377i	$-0.566314\pi$
$41$	1.68800	−	0.614382i	0.263621	−	0.0959503i	0.470449	+	0.882427i	$0.344092\pi$
$42$		0			0
$43$	0.873477	+	4.95373i	0.133204	+	0.755437i	0.976094	+	0.217351i	$0.0697415\pi$
$43$	0.873477	+	4.95373i	0.133204	+	0.755437i	−0.842890	+	0.538087i	$0.819147\pi$
$44$	−0.771999	+	1.33714i	−0.116383	+	0.201582i
$45$		0			0
$46$	4.89793	+	8.48346i	0.722160	+	1.25082i
$47$	−1.30892	+	1.09832i	−0.190926	+	0.160206i	−0.733240	−	0.679970i	$-0.761993\pi$
$47$	−1.30892	+	1.09832i	−0.190926	+	0.160206i	0.542314	+	0.840176i	$0.317548\pi$
$48$		0			0
$49$	1.43775	−	8.15389i	0.205393	−	1.16484i
$50$	4.79539	+	4.02381i	0.678170	+	0.569053i
$51$		0			0
$52$	0.568265	+	0.206831i	0.0788041	+	0.0286824i
$53$	−2.84494			−0.390783			−0.195391	−	0.980725i	$-0.562598\pi$
$53$	−2.84494			−0.390783			−0.195391	+	0.980725i	$0.562598\pi$
$54$		0			0
$55$	2.11276			0.284885
$56$	7.25193	+	2.63949i	0.969080	+	0.352716i
$57$		0			0
$58$	−6.85023	−	5.74803i	−0.899480	−	0.754753i
$59$	1.95529	−	11.0890i	0.254557	−	1.44366i	−0.542652	−	0.839958i	$-0.682580\pi$
$59$	1.95529	−	11.0890i	0.254557	−	1.44366i	0.797208	−	0.603704i	$-0.206309\pi$
$60$		0			0
$61$	4.00710	−	3.36235i	0.513056	−	0.430505i	−0.349147	−	0.937068i	$-0.613529\pi$
$61$	4.00710	−	3.36235i	0.513056	−	0.430505i	0.862203	+	0.506563i	$0.169084\pi$
$62$	1.12672	+	1.95153i	0.143093	+	0.247844i
$63$		0			0
$64$	−1.26751	+	2.19540i	−0.158439	+	0.274425i
$65$	−0.143694	−	0.814930i	−0.0178231	−	0.101080i
$66$		0			0
$67$	1.77511	−	0.646086i	0.216864	−	0.0789319i	−0.231304	−	0.972882i	$-0.574299\pi$
$67$	1.77511	−	0.646086i	0.216864	−	0.0789319i	0.448167	+	0.893950i	$0.352077\pi$
$68$	1.46577	−	0.533495i	0.177750	−	0.0646958i
$69$		0			0
$70$	1.28877	+	7.30898i	0.154038	+	0.873590i
$71$	−6.09193	+	10.5515i	−0.722980	+	1.25224i	0.236821	+	0.971553i	$0.423895\pi$
$71$	−6.09193	+	10.5515i	−0.722980	+	1.25224i	−0.959800	+	0.280684i	$0.909439\pi$
$72$		0			0
$73$	−4.94384	−	8.56298i	−0.578633	−	1.00222i	−0.995637	−	0.0933164i	$-0.970253\pi$
$73$	−4.94384	−	8.56298i	−0.578633	−	1.00222i	0.417004	−	0.908905i	$-0.363080\pi$
$74$	−4.37302	+	3.66940i	−0.508353	+	0.426559i
$75$		0			0
$76$	0.393163	−	2.22974i	0.0450989	−	0.255768i
$77$	−5.60091	−	4.69972i	−0.638283	−	0.535583i
$78$		0			0
$79$	−11.6079	−	4.22493i	−1.30599	−	0.475342i	−0.407048	−	0.913407i	$-0.633442\pi$
$79$	−11.6079	−	4.22493i	−1.30599	−	0.475342i	−0.898943	+	0.438065i	$0.855664\pi$
$80$	−5.61331			−0.627587
$81$		0			0
$82$	3.01948			0.333445
$83$	−10.9786	−	3.99588i	−1.20506	−	0.438605i	−0.340070	−	0.940400i	$-0.610451\pi$
$83$	−10.9786	−	3.99588i	−1.20506	−	0.438605i	−0.864986	+	0.501796i	$0.832673\pi$
$84$		0			0
$85$	−1.63507	−	1.37199i	−0.177349	−	0.148813i
$86$	−1.46824	+	8.32679i	−0.158324	+	0.897901i
$87$		0			0
$88$	2.82886	−	2.37370i	0.301558	−	0.253037i
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	0.673331	−	0.739341i	$-0.264863\pi$
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	−0.976954	+	0.213452i	$0.931529\pi$
$90$		0			0
$91$	−1.43183	+	2.48001i	−0.150097	+	0.259976i
$92$	0.835346	+	4.73748i	0.0870908	+	0.493917i
$93$		0			0
$94$	−2.69893	+	0.982329i	−0.278373	+	0.101319i
$95$	−2.91133	+	1.05964i	−0.298697	+	0.108717i
$96$		0			0
$97$	−0.0596270	−	0.338162i	−0.00605421	−	0.0343351i	0.981631	−	0.190789i	$-0.0611047\pi$
$97$	−0.0596270	−	0.338162i	−0.00605421	−	0.0343351i	−0.987685	+	0.156454i	$0.949994\pi$
$98$	6.95870	−	12.0528i	0.702935	−	1.21752i
$99$		0			0
$100$	1.53707	+	2.66228i	0.153707	+	0.266228i
$101$	13.3309	−	11.1860i	1.32647	−	1.11304i	0.341586	−	0.939850i	$-0.389036\pi$
$101$	13.3309	−	11.1860i	1.32647	−	1.11304i	0.984888	−	0.173194i	$-0.0554086\pi$
$102$		0			0
$103$	−2.74590	+	15.5728i	−0.270561	+	1.53443i	0.482155	+	0.876086i	$0.339854\pi$
$103$	−2.74590	+	15.5728i	−0.270561	+	1.53443i	−0.752717	+	0.658345i	$0.771257\pi$
$104$	−1.10798	−	0.929702i	−0.108646	−	0.0911648i
$105$		0			0
$106$	−4.49370	−	1.63557i	−0.436467	−	0.158861i
$107$	16.5298			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$107$	16.5298			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$108$		0			0
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$	3.33719	+	1.21464i	0.318189	+	0.115811i
$111$		0			0
$112$	14.8808	+	12.4865i	1.40611	+	1.17986i
$113$	−3.46338	+	19.6418i	−0.325807	+	1.84775i	0.178132	+	0.984007i	$0.442995\pi$
$113$	−3.46338	+	19.6418i	−0.325807	+	1.84775i	−0.503939	+	0.863739i	$0.668116\pi$
$114$		0			0
$115$	5.04260	−	4.23124i	0.470225	−	0.394565i
$116$	−2.19571	−	3.80308i	−0.203867	−	0.353108i
$117$		0			0
$118$	9.46357	−	16.3914i	0.871193	−	1.50895i
$119$	1.28265	+	7.27425i	0.117580	+	0.666830i
$120$		0			0
$121$	7.04901	−	2.56563i	0.640819	−	0.233239i
$122$	8.26241	−	3.00727i	0.748043	−	0.272266i
$123$		0			0
$124$	0.192163	+	1.08981i	0.0172567	+	0.0978676i
$125$	4.92714	−	8.53407i	0.440697	−	0.763310i
$126$		0			0
$127$	−0.534728	−	0.926176i	−0.0474495	−	0.0821849i	0.841325	−	0.540529i	$-0.181776\pi$
$127$	−0.534728	−	0.926176i	−0.0474495	−	0.0821849i	−0.888775	+	0.458344i	$0.848443\pi$
$128$	−10.0128	+	8.40170i	−0.885011	+	0.742612i
$129$		0			0
$130$	0.241537	−	1.36983i	0.0211842	−	0.120142i
$131$	−5.85281	−	4.91109i	−0.511362	−	0.429084i	0.350246	−	0.936658i	$-0.386098\pi$
$131$	−5.85281	−	4.91109i	−0.511362	−	0.429084i	−0.861608	+	0.507574i	$0.830542\pi$
$132$		0			0
$133$	10.0750	+	3.66701i	0.873615	+	0.317970i
$134$	3.17529			0.274303
$135$		0			0
$136$	−3.73070			−0.319905
$137$	14.7067	+	5.35279i	1.25647	+	0.457319i	0.882585	−	0.470154i	$-0.155801\pi$
$137$	14.7067	+	5.35279i	1.25647	+	0.457319i	0.373890	+	0.927473i	$0.378024\pi$
$138$		0			0
$139$	6.63160	+	5.56457i	0.562485	+	0.471981i	0.879142	−	0.476559i	$-0.158116\pi$
$139$	6.63160	+	5.56457i	0.562485	+	0.471981i	−0.316658	+	0.948540i	$0.602561\pi$
$140$	−0.632892	+	3.58931i	−0.0534891	+	0.303352i
$141$		0			0
$142$	−15.6886	+	13.1643i	−1.31656	+	1.10472i
$143$	0.685146	+	1.18671i	0.0572948	+	0.0992375i
$144$		0			0
$145$	−3.00455	+	5.20403i	−0.249514	+	0.432172i
$146$	−2.88609	−	16.3678i	−0.238854	−	1.35461i
$147$		0			0
$148$	−2.63431	+	0.958811i	−0.216539	+	0.0788137i
$149$	−2.31524	+	0.842677i	−0.189672	+	0.0690348i	−0.435110	−	0.900377i	$-0.643290\pi$
$149$	−2.31524	+	0.842677i	−0.189672	+	0.0690348i	0.245438	+	0.969412i	$0.421068\pi$
$150$		0			0
$151$	−1.82563	−	10.3537i	−0.148568	−	0.842571i	−0.964433	−	0.264328i	$-0.914850\pi$
$151$	−1.82563	−	10.3537i	−0.148568	−	0.842571i	0.815865	−	0.578243i	$-0.196261\pi$
$152$	−2.70760	+	4.68969i	−0.219615	+	0.380384i
$153$		0			0
$154$	−6.14497	−	10.6434i	−0.495176	−	0.857669i
$155$	1.16000	−	0.973353i	0.0931731	−	0.0781816i
$156$		0			0
$157$	0.0625044	−	0.354480i	0.00498840	−	0.0282906i	−0.982212	−	0.187776i	$-0.939872\pi$
$157$	0.0625044	−	0.354480i	0.00498840	−	0.0282906i	0.987200	+	0.159485i	$0.0509833\pi$
$158$	−15.9062	−	13.3469i	−1.26543	−	1.06182i
$159$		0			0
$160$	−4.67534	−	1.70168i	−0.369618	−	0.134530i
$161$	−22.7800			−1.79532
$162$		0			0
$163$	14.6186			1.14502			0.572508	−	0.819899i	$-0.305971\pi$
$163$	14.6186			1.14502			0.572508	+	0.819899i	$0.305971\pi$
$164$	1.39339	+	0.507151i	0.108805	+	0.0396019i
$165$		0			0
$166$	−15.0439	−	12.6233i	−1.16763	−	0.979758i
$167$	−0.377832	+	2.14279i	−0.0292375	+	0.165814i	−0.995930	−	0.0901247i	$-0.971273\pi$
$167$	−0.377832	+	2.14279i	−0.0292375	+	0.165814i	0.966693	+	0.255939i	$0.0823846\pi$
$168$		0			0
$169$	−9.54744	+	8.01125i	−0.734419	+	0.616250i
$170$	−1.79390	−	3.10712i	−0.137586	−	0.238306i
$171$		0			0
$172$	−2.07611	+	3.59593i	−0.158302	+	0.274187i
$173$	3.05048	+	17.3001i	0.231924	+	1.31531i	0.848996	+	0.528399i	$0.177207\pi$
$173$	3.05048	+	17.3001i	0.231924	+	1.31531i	−0.617072	+	0.786906i	$0.711681\pi$
$174$		0			0
$175$	−13.6794	+	4.97890i	−1.03407	+	0.376370i
$176$	8.73473	−	3.17918i	0.658405	−	0.239640i
$177$		0			0
$178$	−1.67214	−	9.48320i	−0.125333	−	0.710796i
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	−0.846646	−	0.532157i	$-0.821382\pi$
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	0.884184	+	0.467138i	$0.154715\pi$
$180$		0			0
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	0.927859	+	0.372932i	$0.121647\pi$
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	−0.140961	+	0.990015i	$0.545019\pi$
$182$	−3.68741	+	3.09411i	−0.273329	+	0.229350i
$183$		0			0
$184$	1.99792	−	11.3308i	0.147289	−	0.835315i
$185$	2.93859	+	2.46577i	0.216050	+	0.181287i
$186$		0			0
$187$	3.32134	+	1.20887i	0.242880	+	0.0884012i
$188$	−1.41045			−0.102868
$189$		0			0
$190$	−5.20776			−0.377811
$191$	−9.23566	−	3.36150i	−0.668269	−	0.243230i	−0.0144664	−	0.999895i	$-0.504605\pi$
$191$	−9.23566	−	3.36150i	−0.668269	−	0.243230i	−0.653802	+	0.756665i	$0.726827\pi$
$192$		0			0
$193$	−8.54606	−	7.17099i	−0.615159	−	0.516179i	0.281119	−	0.959673i	$-0.409294\pi$
$193$	−8.54606	−	7.17099i	−0.615159	−	0.516179i	−0.896278	+	0.443494i	$0.853739\pi$
$194$	0.100228	−	0.568420i	0.00719594	−	0.0408102i
$195$		0			0
$196$	5.23560	−	4.39319i	0.373971	−	0.313799i
$197$	4.54497	+	7.87212i	0.323816	+	0.560865i	0.981272	−	0.192628i	$-0.0617009\pi$
$197$	4.54497	+	7.87212i	0.323816	+	0.560865i	−0.657456	+	0.753493i	$0.728368\pi$
$198$		0			0
$199$	7.34694	−	12.7253i	0.520811	−	0.902071i	−0.478896	−	0.877872i	$-0.658963\pi$
$199$	7.34694	−	12.7253i	0.520811	−	0.902071i	0.999707	−	0.0241994i	$-0.00770367\pi$
$200$	−1.27675	−	7.24081i	−0.0902798	−	0.512002i
$201$		0			0
$202$	27.4876	−	10.0047i	1.93402	−	0.703925i
$203$	19.5411	−	7.11238i	1.37152	−	0.499191i
$204$		0			0
$205$	−0.352339	−	1.99821i	−0.0246084	−	0.139561i
$206$	−13.2901	+	23.0192i	−0.925968	+	1.60382i
$207$		0			0
$208$	−1.82034	−	3.15292i	−0.126218	−	0.218615i
$209$	3.93011	−	3.29775i	0.271851	−	0.228110i
$210$		0			0
$211$	1.36458	−	7.73891i	0.0939415	−	0.532769i	−0.901125	−	0.433559i	$-0.857257\pi$
$211$	1.36458	−	7.73891i	0.0939415	−	0.532769i	0.995067	−	0.0992096i	$-0.0316314\pi$
$212$	−1.79898	−	1.50952i	−0.123555	−	0.103675i
$213$		0			0
$214$	26.1095	+	9.50309i	1.78481	+	0.649618i
$215$	5.68178			0.387494
$216$		0			0
$217$	−5.24030			−0.355735
$218$	−7.45297	−	2.71266i	−0.504779	−	0.183724i
$219$		0			0
$220$	1.33599	+	1.12103i	0.0900725	+	0.0755798i
$221$	0.240390	−	1.36332i	0.0161704	−	0.0917067i
$222$		0			0
$223$	−6.69591	+	5.61853i	−0.448391	+	0.376245i	−0.838838	−	0.544380i	$-0.816765\pi$
$223$	−6.69591	+	5.61853i	−0.448391	+	0.376245i	0.390447	+	0.920625i	$0.372320\pi$
$224$	8.60897	+	14.9112i	0.575211	+	0.996295i
$225$		0			0
$226$	−16.7627	+	29.0339i	−1.11504	+	1.93131i
$227$	−0.706473	−	4.00661i	−0.0468903	−	0.265928i	0.952345	−	0.305022i	$-0.0986639\pi$
$227$	−0.706473	−	4.00661i	−0.0468903	−	0.265928i	−0.999236	+	0.0390942i	$0.987553\pi$
$228$		0			0
$229$	−15.1816	+	5.52563i	−1.00323	+	0.365144i	−0.790827	−	0.612039i	$-0.790349\pi$
$229$	−15.1816	+	5.52563i	−1.00323	+	0.365144i	−0.212398	+	0.977183i	$0.568127\pi$
$230$	10.3976	−	3.78440i	0.685594	−	0.249536i
$231$		0			0
$232$	1.82384	+	10.3435i	0.119741	+	0.679086i
$233$	8.60658	−	14.9070i	0.563836	−	0.976592i	−0.433321	−	0.901240i	$-0.642658\pi$
$233$	8.60658	−	14.9070i	0.563836	−	0.976592i	0.997157	−	0.0753527i	$-0.0240083\pi$
$234$		0			0
$235$	0.965013	+	1.67145i	0.0629505	+	0.109034i
$236$	7.12022	−	5.97457i	0.463487	−	0.388911i
$237$		0			0
$238$	−2.15602	+	12.2274i	−0.139754	+	0.792583i
$239$	1.17621	+	0.986962i	0.0760830	+	0.0638412i	0.680036	−	0.733179i	$-0.261964\pi$
$239$	1.17621	+	0.986962i	0.0760830	+	0.0638412i	−0.603953	+	0.797020i	$0.706409\pi$
$240$		0			0
$241$	5.18868	+	1.88852i	0.334232	+	0.121650i	0.503684	−	0.863888i	$-0.331978\pi$
$241$	5.18868	+	1.88852i	0.334232	+	0.121650i	−0.169452	+	0.985538i	$0.554200\pi$
$242$	12.6092			0.810549
$243$		0			0
$244$	4.31792			0.276427
$245$	−8.78825	−	3.19866i	−0.561461	−	0.204355i
$246$		0			0
$247$	−1.53930	−	1.29162i	−0.0979432	−	0.0821841i
$248$	0.459600	−	2.60652i	0.0291847	−	0.165514i
$249$		0			0
$250$	12.6889	−	10.6473i	0.802517	−	0.673392i
$251$	−10.7204	−	18.5683i	−0.676668	−	1.17202i	−0.975978	−	0.217868i	$-0.930090\pi$
$251$	−10.7204	−	18.5683i	−0.676668	−	1.17202i	0.299310	−	0.954156i	$-0.403244\pi$
$252$		0			0
$253$	−5.45023	+	9.44007i	−0.342653	+	0.593492i
$254$	−0.312161	−	1.77035i	−0.0195867	−	0.111082i
$255$		0			0
$256$	−15.8814	+	5.78037i	−0.992590	+	0.361273i
$257$	−13.8947	+	5.05727i	−0.866730	+	0.315464i	−0.736842	−	0.676065i	$-0.763684\pi$
$257$	−13.8947	+	5.05727i	−0.866730	+	0.315464i	−0.129888	+	0.991529i	$0.541462\pi$
$258$		0			0
$259$	−2.30520	−	13.0735i	−0.143238	−	0.812346i
$260$	0.341537	−	0.591560i	0.0211812	−	0.0366870i
$261$		0			0
$262$	−6.42133	−	11.1221i	−0.396711	−	0.687124i
$263$	−2.14704	+	1.80158i	−0.132392	+	0.111090i	−0.706579	−	0.707634i	$-0.749763\pi$
$263$	−2.14704	+	1.80158i	−0.132392	+	0.111090i	0.574187	+	0.818724i	$0.305318\pi$
$264$		0			0
$265$	−0.558016	+	3.16467i	−0.0342787	+	0.194404i
$266$	13.8057	+	11.5844i	0.846483	+	0.710284i
$267$		0			0
$268$	1.46529	+	0.533322i	0.0895068	+	0.0325778i
$269$	0.356528			0.0217379			0.0108689	−	0.999941i	$-0.496540\pi$
$269$	0.356528			0.0217379			0.0108689	+	0.999941i	$0.496540\pi$
$270$		0			0
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	−8.82433	−	3.21179i	−0.535054	−	0.194744i
$273$		0			0
$274$	20.1524	+	16.9099i	1.21745	+	1.02156i
$275$	−1.20960	+	6.85999i	−0.0729418	+	0.413673i
$276$		0			0
$277$	19.1434	−	16.0632i	1.15022	−	0.965146i	0.150492	−	0.988611i	$-0.451914\pi$
$277$	19.1434	−	16.0632i	1.15022	−	0.965146i	0.999725	+	0.0234648i	$0.00746978\pi$
$278$	7.27577	+	12.6020i	0.436372	+	0.755818i
$279$		0			0
$280$	4.35854	−	7.54921i	0.260473	−	0.451152i
$281$	−1.27160	−	7.21162i	−0.0758575	−	0.430209i	−0.998958	−	0.0456492i	$-0.985464\pi$
$281$	−1.27160	−	7.21162i	−0.0758575	−	0.430209i	0.923100	−	0.384560i	$-0.125647\pi$
$282$		0			0
$283$	13.5204	−	4.92102i	0.803703	−	0.292524i	0.0926830	−	0.995696i	$-0.470456\pi$
$283$	13.5204	−	4.92102i	0.803703	−	0.292524i	0.711020	+	0.703172i	$0.248233\pi$
$284$	−9.45083	+	3.43982i	−0.560804	+	0.204116i
$285$		0			0
$286$	0.399971	+	2.26835i	0.0236508	+	0.134130i
$287$	−3.51086	+	6.08099i	−0.207240	+	0.358950i
$288$		0			0
$289$	6.71462	+	11.6301i	0.394978	+	0.684122i
$290$	−7.73764	+	6.49265i	−0.454370	+	0.381262i
$291$		0			0
$292$	1.41731	−	8.03794i	0.0829416	−	0.470385i
$293$	11.0429	+	9.26611i	0.645134	+	0.541332i	0.905590	−	0.424154i	$-0.139428\pi$
$293$	11.0429	+	9.26611i	0.645134	+	0.541332i	−0.260456	+	0.965486i	$0.583873\pi$
$294$		0			0
$295$	−11.9517	−	4.35006i	−0.695854	−	0.253270i
$296$	6.70491			0.389715
$297$		0			0
$298$	−4.14147			−0.239909
$299$	4.01189	+	1.46021i	0.232013	+	0.0844460i
$300$		0			0
$301$	−15.0623	−	12.6388i	−0.868178	−	0.728488i
$302$	3.06873	−	17.4036i	0.176586	−	1.00147i
$303$		0			0
$304$	−10.4417	+	8.76166i	−0.598875	+	0.502516i
$305$	−2.95426	−	5.11693i	−0.169161	−	0.292995i
$306$		0			0
$307$	15.2163	−	26.3554i	0.868440	−	1.50418i	0.00484869	−	0.999988i	$-0.498457\pi$
$307$	15.2163	−	26.3554i	0.868440	−	1.50418i	0.863591	−	0.504193i	$-0.168210\pi$
$308$	−1.04803	−	5.94367i	−0.0597171	−	0.338672i
$309$		0			0
$310$	2.39185	−	0.870561i	0.135848	−	0.0494446i
$311$	−13.1516	+	4.78678i	−0.745757	+	0.271433i	−0.686819	−	0.726828i	$-0.740994\pi$
$311$	−13.1516	+	4.78678i	−0.745757	+	0.271433i	−0.0589378	+	0.998262i	$0.518771\pi$
$312$		0			0
$313$	3.83547	+	21.7520i	0.216793	+	1.22950i	0.877767	+	0.479087i	$0.159032\pi$
$313$	3.83547	+	21.7520i	0.216793	+	1.22950i	−0.660974	+	0.750409i	$0.729857\pi$
$314$	0.302521	−	0.523982i	0.0170722	−	0.0295700i
$315$		0			0
$316$	−5.09844	−	8.83075i	−0.286810	−	0.496769i
$317$	−13.3205	+	11.1773i	−0.748156	+	0.627777i	−0.935014	−	0.354610i	$-0.884614\pi$
$317$	−13.3205	+	11.1773i	−0.748156	+	0.627777i	0.186859	+	0.982387i	$0.440169\pi$
$318$		0			0
$319$	1.72792	−	9.79953i	0.0967450	−	0.548668i
$320$	2.19351	+	1.84058i	0.122621	+	0.102891i
$321$		0			0
$322$	−35.9820	−	13.0964i	−2.00520	−	0.729832i
$323$	−5.18302			−0.288391
$324$		0			0
$325$	2.72829			0.151338
$326$	23.0906	+	8.40430i	1.27887	+	0.465471i
$327$		0			0
$328$	−2.71676	−	2.27963i	−0.150008	−	0.125872i
$329$	1.15981	−	6.57762i	0.0639425	−	0.362636i
$330$		0			0
$331$	0.661975	−	0.555463i	0.0363855	−	0.0305310i	−0.624414	−	0.781094i	$-0.714662\pi$
$331$	0.661975	−	0.555463i	0.0363855	−	0.0305310i	0.660799	+	0.750563i	$0.270218\pi$
$332$	−4.82203	−	8.35199i	−0.264643	−	0.458375i
$333$		0			0
$334$	−1.82870	+	3.16741i	−0.100062	+	0.173313i
$335$	−0.370520	−	2.10132i	−0.0202437	−	0.114808i
$336$		0			0
$337$	−0.393289	+	0.143145i	−0.0214238	+	0.00779762i	−0.352710	−	0.935733i	$-0.614740\pi$
$337$	−0.393289	+	0.143145i	−0.0214238	+	0.00779762i	0.331286	+	0.943530i	$0.392517\pi$
$338$	−19.6863	+	7.16522i	−1.07079	+	0.389737i
$339$		0			0
$340$	−0.305951	−	1.73514i	−0.0165925	−	0.0941010i
$341$	−1.25377	+	2.17159i	−0.0678953	+	0.117598i
$342$		0			0
$343$	2.50108	+	4.33199i	0.135046	+	0.233906i
$344$	7.60757	−	6.38351i	0.410173	−	0.344176i
$345$		0			0
$346$	−5.12759	+	29.0800i	−0.275661	+	1.56335i
$347$	−17.9329	−	15.0475i	−0.962689	−	0.807792i	0.0186996	−	0.999825i	$-0.494047\pi$
$347$	−17.9329	−	15.0475i	−0.962689	−	0.807792i	−0.981388	+	0.192033i	$0.938492\pi$
$348$		0			0
$349$	−19.8993	−	7.24276i	−1.06519	−	0.387696i	−0.250811	−	0.968036i	$-0.580697\pi$
$349$	−19.8993	−	7.24276i	−1.06519	−	0.387696i	−0.814374	+	0.580340i	$0.802920\pi$
$350$	−24.4696			−1.30796
$351$		0			0
$352$	8.23894			0.439137
$353$	22.1246	+	8.05268i	1.17757	+	0.428601i	0.855344	−	0.518061i	$-0.173346\pi$
$353$	22.1246	+	8.05268i	1.17757	+	0.428601i	0.322228	+	0.946662i	$0.395568\pi$
$354$		0			0
$355$	10.5425	+	8.84618i	0.559536	+	0.469507i
$356$	0.821160	−	4.65703i	0.0435214	−	0.246822i
$357$		0			0
$358$	1.29341	−	1.08530i	0.0683589	−	0.0573599i
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	0.694347	−	0.719640i	$-0.255693\pi$
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	−0.970400	+	0.241502i	$0.922360\pi$
$360$		0			0
$361$	5.73837	−	9.93915i	0.302019	−	0.523113i
$362$	6.18020	+	35.0497i	0.324824	+	1.84217i
$363$		0			0
$364$	−2.22130	+	0.808488i	−0.116428	+	0.0423763i
$365$	−10.4950	+	3.81988i	−0.549335	+	0.199941i
$366$		0			0
$367$	3.69146	+	20.9353i	0.192693	+	1.09281i	0.915666	+	0.401939i	$0.131664\pi$
$367$	3.69146	+	20.9353i	0.192693	+	1.09281i	−0.722974	+	0.690875i	$0.757225\pi$
$368$	14.4805	−	25.0809i	0.754848	−	1.30743i
$369$		0			0
$370$	3.22404	+	5.58420i	0.167610	+	0.290309i
$371$	8.51892	−	7.14822i	0.442280	−	0.371117i
$372$		0			0
$373$	0.401142	−	2.27499i	0.0207704	−	0.117795i	−0.972660	−	0.232235i	$-0.925396\pi$
$373$	0.401142	−	2.27499i	0.0207704	−	0.117795i	0.993430	+	0.114440i	$0.0365074\pi$
$374$	4.55120	+	3.81891i	0.235337	+	0.197471i
$375$		0			0
$376$	3.16998	+	1.15378i	0.163479	+	0.0595016i
$377$	−3.89737			−0.200725
$378$		0			0
$379$	12.5539			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$379$	12.5539			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$380$	−2.40321	−	0.874696i	−0.123282	−	0.0448709i
$381$		0			0
$382$	−12.6555	−	10.6193i	−0.647514	−	0.543329i
$383$	3.41297	−	19.3559i	0.174395	−	0.989042i	−0.764445	−	0.644689i	$-0.776987\pi$
$383$	3.41297	−	19.3559i	0.174395	−	0.989042i	0.938840	−	0.344353i	$-0.111902\pi$
$384$		0			0
$385$	−6.32647	+	5.30854i	−0.322427	+	0.270548i
$386$	−9.37620	−	16.2401i	−0.477236	−	0.826597i
$387$		0			0
$388$	0.141724	−	0.245472i	0.00719492	−	0.0124620i
$389$	3.27198	+	18.5563i	0.165896	+	0.940843i	0.948136	+	0.317866i	$0.102966\pi$
$389$	3.27198	+	18.5563i	0.165896	+	0.940843i	−0.782240	+	0.622978i	$0.785923\pi$
$390$		0			0
$391$	10.3482	−	3.76642i	0.523329	−	0.190476i
$392$	−15.3607	+	5.59082i	−0.775831	+	0.282379i
$393$		0			0
$394$	2.65324	+	15.0473i	0.133668	+	0.758070i
$395$	−6.97656	+	12.0838i	−0.351029	+	0.608000i
$396$		0			0
$397$	−10.0589	−	17.4225i	−0.504841	−	0.874410i	−0.999984	−	0.00559897i	$-0.998218\pi$
$397$	−10.0589	−	17.4225i	−0.504841	−	0.874410i	0.495143	−	0.868811i	$-0.335116\pi$
$398$	18.9206	−	15.8763i	0.948405	−	0.795807i
$399$		0			0
$400$	3.21374	−	18.2260i	0.160687	−	0.911302i
$401$	23.5985	+	19.8015i	1.17845	+	0.988840i	0.999988	+	0.00489430i	$0.00155791\pi$
$401$	23.5985	+	19.8015i	1.17845	+	0.988840i	0.178466	+	0.983946i	$0.442887\pi$
$402$		0			0
$403$	0.922892	+	0.335905i	0.0459725	+	0.0167326i
$404$	14.3650			0.714684
$405$		0			0
$406$	34.9549			1.73478
$407$	−5.96919	−	2.17261i	−0.295882	−	0.107692i
$408$		0			0
$409$	30.4059	+	25.5136i	1.50347	+	1.26156i	0.875388	+	0.483421i	$0.160606\pi$
$409$	30.4059	+	25.5136i	1.50347	+	1.26156i	0.628086	+	0.778144i	$0.283839\pi$
$410$	0.592250	−	3.35882i	0.0292491	−	0.165880i
$411$		0			0
$412$	−9.99925	+	8.39037i	−0.492628	+	0.413364i
$413$	22.0073	+	38.1178i	1.08291	+	1.87565i
$414$		0			0
$415$	−6.59832	+	11.4286i	−0.323899	+	0.561010i
$416$	−0.560351	−	3.17791i	−0.0274735	−	0.155810i
$417$		0			0
$418$	8.10366	−	2.94949i	0.396363	−	0.144264i
$419$	14.5099	−	5.28118i	0.708856	−	0.258002i	0.0376687	−	0.999290i	$-0.488007\pi$
$419$	14.5099	−	5.28118i	0.708856	−	0.258002i	0.671187	+	0.741288i	$0.265785\pi$
$420$		0			0
$421$	−3.14193	−	17.8188i	−0.153128	−	0.868433i	−0.960477	−	0.278359i	$-0.910210\pi$
$421$	−3.14193	−	17.8188i	−0.153128	−	0.868433i	0.807349	−	0.590074i	$-0.200902\pi$
$422$	6.60456	−	11.4394i	0.321505	−	0.556863i
$423$		0			0
$424$	2.80837	+	4.86424i	0.136386	+	0.236228i
$425$	5.39087	−	4.52348i	0.261496	−	0.219421i
$426$		0			0
$427$	−3.55061	+	20.1365i	−0.171826	+	0.974475i
$428$	10.4525	+	8.77071i	0.505242	+	0.423948i
$429$		0			0
$430$	8.97460	+	3.26649i	0.432794	+	0.157524i
$431$	28.9683			1.39535			0.697677	−	0.716412i	$-0.254217\pi$
$431$	28.9683			1.39535			0.697677	+	0.716412i	$0.254217\pi$
$432$		0			0
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$	−8.27727	−	3.01268i	−0.397322	−	0.144613i
$435$		0			0
$436$	−2.98367	−	2.50360i	−0.142892	−	0.119901i
$437$	2.77569	−	15.7417i	0.132779	−	0.753028i
$438$		0			0
$439$	7.86232	−	6.59727i	0.375248	−	0.314871i	−0.435585	−	0.900147i	$-0.643459\pi$
$439$	7.86232	−	6.59727i	0.375248	−	0.314871i	0.810834	+	0.585277i	$0.199014\pi$
$440$	−2.08560	−	3.61237i	−0.0994272	−	0.172213i
$441$		0			0
$442$	1.16348	−	2.01521i	0.0553413	−	0.0958540i
$443$	−3.80437	−	21.5757i	−0.180751	−	1.02509i	−0.931294	−	0.364269i	$-0.881319\pi$
$443$	−3.80437	−	21.5757i	−0.180751	−	1.02509i	0.750543	−	0.660822i	$-0.229792\pi$
$444$		0			0
$445$	−6.08062	+	2.21316i	−0.288249	+	0.104914i
$446$	−13.8066	+	5.02519i	−0.653761	+	0.237949i
$447$		0			0
$448$	−1.72072	−	9.75869i	−0.0812964	−	0.461055i
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	−0.724069	−	0.689728i	$-0.757730\pi$
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	0.959356	+	0.282198i	$0.0910635\pi$
$450$		0			0
$451$	1.67998	+	2.90981i	0.0791072	+	0.137018i
$452$	−12.6120	+	10.5827i	−0.593217	+	0.497768i
$453$		0			0
$454$	1.18752	−	6.73475i	0.0557330	−	0.316078i
$455$	2.47788	+	2.07919i	0.116165	+	0.0974738i
$456$		0			0
$457$	7.15867	+	2.60554i	0.334869	+	0.121882i	0.503981	−	0.863715i	$-0.331868\pi$
$457$	7.15867	+	2.60554i	0.334869	+	0.121882i	−0.169113	+	0.985597i	$0.554090\pi$
$458$	−27.1566			−1.26894
$459$		0			0
$460$	5.43375			0.253350
$461$	−21.4255	−	7.79824i	−0.997885	−	0.363200i	−0.209116	−	0.977891i	$-0.567059\pi$
$461$	−21.4255	−	7.79824i	−0.997885	−	0.363200i	−0.788768	+	0.614690i	$0.789281\pi$
$462$		0			0
$463$	−6.73792	−	5.65379i	−0.313138	−	0.262754i	0.472650	−	0.881250i	$-0.343298\pi$
$463$	−6.73792	−	5.65379i	−0.313138	−	0.262754i	−0.785787	+	0.618497i	$0.787742\pi$
$464$	−4.59084	+	26.0360i	−0.213125	+	1.20869i
$465$		0			0
$466$	22.1646	−	18.5983i	1.02675	−	0.861549i
$467$	−5.49878	−	9.52416i	−0.254453	−	0.440726i	0.710294	−	0.703905i	$-0.248562\pi$
$467$	−5.49878	−	9.52416i	−0.254453	−	0.440726i	−0.964747	+	0.263180i	$0.915229\pi$
$468$		0			0
$469$	−3.69203	+	6.39479i	−0.170482	+	0.295284i
$470$	0.563350	+	3.19492i	0.0259854	+	0.147371i
$471$		0			0
$472$	−20.8899	+	7.60331i	−0.961536	+	0.349971i
$473$	−8.84127	+	3.21796i	−0.406522	+	0.147962i
$474$		0			0
$475$	−1.77377	−	10.0596i	−0.0813863	−	0.461565i
$476$	−3.04864	+	5.28040i	−0.139734	+	0.242027i
$477$		0			0
$478$	1.29047	+	2.23516i	0.0590247	+	0.102234i
$479$	−19.6816	+	16.5148i	−0.899276	+	0.754582i	−0.970049	−	0.242911i	$-0.921898\pi$
$479$	−19.6816	+	16.5148i	−0.899276	+	0.754582i	0.0707730	+	0.997492i	$0.477453\pi$
$480$		0			0
$481$	−0.432034	+	2.45019i	−0.0196991	+	0.111719i
$482$	7.11000	+	5.96600i	0.323852	+	0.271744i
$483$		0			0
$484$	5.81871	+	2.11784i	0.264487	+	0.0962654i
$485$	−0.387861			−0.0176119
$486$		0			0
$487$	−30.3800			−1.37665			−0.688325	−	0.725402i	$-0.741654\pi$
$487$	−30.3800			−1.37665			−0.688325	+	0.725402i	$0.741654\pi$
$488$	−9.70448	−	3.53214i	−0.439301	−	0.159893i
$489$		0			0
$490$	−12.0425	−	10.1048i	−0.544023	−	0.456490i
$491$	−1.51218	+	8.57597i	−0.0682435	+	0.387028i	0.931486	+	0.363777i	$0.118513\pi$
$491$	−1.51218	+	8.57597i	−0.0682435	+	0.387028i	−0.999730	+	0.0232514i	$0.992598\pi$
$492$		0			0
$493$	−7.70088	+	6.46180i	−0.346830	+	0.291025i
$494$	−1.68882	−	2.92512i	−0.0759837	−	0.131608i
$495$		0			0
$496$	3.33108	−	5.76961i	0.149570	−	0.259063i
$497$	−8.27013	−	46.9023i	−0.370966	−	2.10385i
$498$		0			0
$499$	−10.9338	+	3.97957i	−0.489463	+	0.178150i	−0.574949	−	0.818189i	$-0.694978\pi$
$499$	−10.9338	+	3.97957i	−0.489463	+	0.178150i	0.0854858	+	0.996339i	$0.472756\pi$
$500$	7.64382	−	2.78212i	0.341842	−	0.124420i
$501$		0			0
$502$	−6.25832	−	35.4927i	−0.279323	−	1.58412i
$503$	−18.8996	+	32.7350i	−0.842689	+	1.45958i	0.0449234	+	0.998990i	$0.485696\pi$
$503$	−18.8996	+	32.7350i	−0.842689	+	1.45958i	−0.887613	+	0.460590i	$0.847638\pi$
$504$		0			0
$505$	−9.82831	−	17.0231i	−0.437354	−	0.757519i
$506$	−14.0360	+	11.7776i	−0.623977	+	0.523579i
$507$		0			0
$508$	0.153297	−	0.869388i	0.00680143	−	0.0385729i
$509$	−18.0585	−	15.1528i	−0.800427	−	0.671638i	0.147875	−	0.989006i	$-0.452757\pi$
$509$	−18.0585	−	15.1528i	−0.800427	−	0.671638i	−0.948302	+	0.317368i	$0.897201\pi$
$510$		0			0
$511$	36.3193	+	13.2191i	1.60667	+	0.584780i
$512$	−2.26711			−0.100193
$513$		0			0
$514$	−24.8548			−1.09630
$515$	16.7843	+	6.10899i	0.739605	+	0.269194i
$516$		0			0
$517$	−2.44828	−	2.05435i	−0.107675	−	0.0903503i
$518$	3.87485	−	21.9753i	0.170251	−	0.965541i
$519$		0			0
$520$	−1.25151	+	1.05014i	−0.0548822	+	0.0460517i
$521$	3.93474	+	6.81517i	0.172384	+	0.298578i	0.939253	−	0.343226i	$-0.111520\pi$
$521$	3.93474	+	6.81517i	0.172384	+	0.298578i	−0.766869	+	0.641804i	$0.778186\pi$
$522$		0			0
$523$	−16.6467	+	28.8330i	−0.727911	+	1.26078i	0.229854	+	0.973225i	$0.426175\pi$
$523$	−16.6467	+	28.8330i	−0.727911	+	1.26078i	−0.957765	+	0.287554i	$0.907158\pi$
$524$	−1.09517	−	6.21099i	−0.0478425	−	0.271328i
$525$		0			0
$526$	−4.42707	+	1.61132i	−0.193029	+	0.0702570i
$527$	2.38048	−	0.866425i	0.103695	−	0.0377421i
$528$		0			0
$529$	1.90355	+	10.7955i	0.0827628	+	0.469371i
$530$	−2.70080	+	4.67792i	−0.117315	+	0.203196i
$531$		0			0
$532$	4.42516	+	7.66461i	0.191855	+	0.332303i
$533$	1.00811	−	0.845902i	0.0436659	−	0.0366401i
$534$		0			0
$535$	3.24221	−	18.3875i	0.140173	−	0.794961i
$536$	−2.85695	−	2.39727i	−0.123402	−	0.103546i
$537$		0			0
$538$	0.563150	+	0.204970i	0.0242791	+	0.00883687i
$539$	15.4868			0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	−19.1861	−	6.98318i	−0.824115	−	0.299953i
$543$		0			0
$544$	−6.37614	−	5.35022i	−0.273375	−	0.229389i
$545$	−0.925490	+	5.24872i	−0.0396436	+	0.224830i
$546$		0			0
$547$	−16.0036	+	13.4286i	−0.684262	+	0.574164i	−0.917248	−	0.398316i	$-0.869595\pi$
$547$	−16.0036	+	13.4286i	−0.684262	+	0.574164i	0.232986	+	0.972480i	$0.425150\pi$
$548$	6.45948	+	11.1881i	0.275935	+	0.477934i
$549$		0			0
$550$	−5.85447	+	10.1402i	−0.249635	+	0.432381i
$551$	2.53384	+	14.3701i	0.107945	+	0.612188i
$552$		0			0
$553$	45.3744	−	16.5149i	1.92952	−	0.702286i
$554$	39.4727	−	14.3669i	1.67703	−	0.610390i
$555$		0			0
$556$	1.24089	+	7.03744i	0.0526255	+	0.298454i
$557$	4.28920	−	7.42911i	0.181739	−	0.314782i	−0.760734	−	0.649064i	$-0.775161\pi$
$557$	4.28920	−	7.42911i	0.181739	−	0.314782i	0.942473	+	0.334283i	$0.108494\pi$
$558$		0			0
$559$	1.84254	+	3.19137i	0.0779311	+	0.134981i
$560$	16.8085	−	14.1040i	0.710291	−	0.596005i
$561$		0			0
$562$	2.13745	−	12.1221i	0.0901630	−	0.511340i
$563$	12.0383	+	10.1013i	0.507354	+	0.425720i	0.860197	−	0.509962i	$-0.170341\pi$
$563$	12.0383	+	10.1013i	0.507354	+	0.425720i	−0.352843	+	0.935682i	$0.614785\pi$
$564$		0			0
$565$	21.1699	+	7.70522i	0.890625	+	0.324161i
$566$	24.1851			1.01658
$567$		0			0
$568$	24.0545			1.00930
$569$	11.9085	+	4.33435i	0.499231	+	0.181705i	0.579348	−	0.815080i	$-0.303307\pi$
$569$	11.9085	+	4.33435i	0.499231	+	0.181705i	−0.0801169	+	0.996785i	$0.525529\pi$
$570$		0			0
$571$	−20.1644	−	16.9199i	−0.843852	−	0.708076i	0.114575	−	0.993415i	$-0.463449\pi$
$571$	−20.1644	−	16.9199i	−0.843852	−	0.708076i	−0.958427	+	0.285339i	$0.907894\pi$
$572$	−0.196419	+	1.11394i	−0.00821267	+	0.0465764i
$573$		0			0
$574$	−9.04155	+	7.58676i	−0.377387	+	0.316665i
$575$	10.8516	+	18.7954i	0.452541	+	0.783824i
$576$		0			0
$577$	11.0577	−	19.1525i	0.460338	−	0.797329i	−0.538640	−	0.842536i	$-0.681062\pi$
$577$	11.0577	−	19.1525i	0.460338	−	0.797329i	0.998978	+	0.0452074i	$0.0143949\pi$
$578$	3.91983	+	22.2304i	0.163043	+	0.924665i
$579$		0			0
$580$	−4.66116	+	1.69652i	−0.193544	+	0.0704444i
$581$	42.9144	−	15.6196i	1.78039	−	0.648009i
$582$		0			0
$583$	−0.924041	−	5.24050i	−0.0382699	−	0.217039i
$584$	−9.76057	+	16.9058i	−0.403895	+	0.699567i
$585$		0			0
$586$	12.1156	+	20.9848i	0.500491	+	0.866876i
$587$	−10.9568	+	9.19388i	−0.452237	+	0.379472i	−0.840265	−	0.542176i	$-0.817601\pi$
$587$	−10.9568	+	9.19388i	−0.452237	+	0.379472i	0.388028	+	0.921647i	$0.373156\pi$
$588$		0			0
$589$	0.638517	−	3.62121i	0.0263097	−	0.149209i
$590$	−16.3773	−	13.7422i	−0.674243	−	0.565757i
$591$		0			0
$592$	15.8593	+	5.77231i	0.651813	+	0.237241i
$593$	−47.7300			−1.96004			−0.980018	−	0.198908i	$-0.936260\pi$
$593$	−47.7300			−1.96004			−0.980018	+	0.198908i	$0.936260\pi$
$594$		0			0
$595$	8.34334			0.342044
$596$	−1.91115	−	0.695601i	−0.0782837	−	0.0284929i
$597$		0			0
$598$	5.49746	+	4.61291i	0.224808	+	0.188636i
$599$	0.0867493	−	0.491980i	0.00354448	−	0.0201018i	−0.982984	−	0.183690i	$-0.941196\pi$
$599$	0.0867493	−	0.491980i	0.00354448	−	0.0201018i	0.986529	+	0.163588i	$0.0523069\pi$
$600$		0			0
$601$	−12.9669	+	10.8805i	−0.528931	+	0.443826i	−0.867732	−	0.497032i	$-0.834423\pi$
$601$	−12.9669	+	10.8805i	−0.528931	+	0.443826i	0.338801	+	0.940858i	$0.389979\pi$
$602$	−16.5254	−	28.6229i	−0.673527	−	1.16658i
$603$		0			0
$604$	4.33923	−	7.51577i	0.176561	−	0.305812i
$605$	−1.47135	−	8.34443i	−0.0598188	−	0.339249i
$606$		0			0
$607$	−0.652741	+	0.237578i	−0.0264939	+	0.00964301i	−0.355233	−	0.934778i	$-0.615599\pi$
$607$	−0.652741	+	0.237578i	−0.0264939	+	0.00964301i	0.328739	+	0.944421i	$0.393376\pi$
$608$	−11.3531	+	4.13218i	−0.460427	+	0.167582i
$609$		0			0
$610$	−1.72462	−	9.78083i	−0.0698280	−	0.396014i
$611$	−0.625887	+	1.08407i	−0.0253207	+	0.0438567i
$612$		0			0
$613$	16.3317	+	28.2873i	0.659630	+	1.14251i	0.980711	+	0.195461i	$0.0626204\pi$
$613$	16.3317	+	28.2873i	0.659630	+	1.14251i	−0.321081	+	0.947052i	$0.604046\pi$
$614$	39.1866	−	32.8815i	1.58144	−	1.32699i
$615$		0			0
$616$	−2.50660	+	14.2157i	−0.100994	+	0.572765i
$617$	−17.5305	−	14.7098i	−0.705751	−	0.592195i	0.217652	−	0.976026i	$-0.430160\pi$
$617$	−17.5305	−	14.7098i	−0.705751	−	0.592195i	−0.923403	+	0.383831i	$0.874605\pi$
$618$		0			0
$619$	−7.97398	−	2.90229i	−0.320501	−	0.116653i	0.176759	−	0.984254i	$-0.443439\pi$
$619$	−7.97398	−	2.90229i	−0.320501	−	0.116653i	−0.497261	+	0.867601i	$0.665661\pi$
$620$	1.24998			0.0502002
$621$		0			0
$622$	−23.5254			−0.943282
$623$	21.0427	+	7.65892i	0.843058	+	0.306848i
$624$		0			0
$625$	5.73752	+	4.81435i	0.229501	+	0.192574i
$626$	−6.44708	+	36.5632i	−0.257677	+	1.46136i
$627$		0			0
$628$	0.227611	−	0.190988i	0.00908267	−	0.00762127i
$629$	3.20872	+	5.55767i	0.127940	+	0.221599i
$630$		0			0
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	−0.881432	−	0.472311i	$-0.843420\pi$
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	0.849749	+	0.527187i	$0.176753\pi$
$632$	4.23496	+	24.0176i	0.168458	+	0.955370i
$633$		0			0
$634$	−27.4662	+	9.99688i	−1.09082	+	0.397027i
$635$	−1.13515	+	0.413160i	−0.0450469	+	0.0163957i
$636$		0			0
$637$	−1.05329	−	5.97352i	−0.0417330	−	0.236680i
$638$	8.36313	−	14.4854i	0.331099	−	0.573481i
$639$		0			0
$640$	7.38198	+	12.7860i	0.291798	+	0.505409i
$641$	−16.6038	+	13.9322i	−0.655809	+	0.550289i	−0.908827	−	0.417173i	$-0.863021\pi$
$641$	−16.6038	+	13.9322i	−0.655809	+	0.550289i	0.253019	+	0.967461i	$0.418577\pi$
$642$		0			0
$643$	−1.19853	+	6.79720i	−0.0472654	+	0.268056i	−0.999278	−	0.0380047i	$-0.987900\pi$
$643$	−1.19853	+	6.79720i	−0.0472654	+	0.268056i	0.952012	+	0.306060i	$0.0990109\pi$
$644$	−14.4048	−	12.0871i	−0.567629	−	0.476297i
$645$		0			0
$646$	−8.18679	−	2.97975i	−0.322105	−	0.117237i
$647$	6.18972			0.243343			0.121671	−	0.992570i	$-0.461175\pi$
$647$	6.18972			0.243343			0.121671	+	0.992570i	$0.461175\pi$
$648$		0			0
$649$	21.0614			0.826733
$650$	4.30945	+	1.56851i	0.169030	+	0.0615220i
$651$		0			0
$652$	9.24396	+	7.75660i	0.362021	+	0.303772i
$653$	4.72574	−	26.8010i	0.184933	−	1.04881i	−0.741109	−	0.671384i	$-0.765700\pi$
$653$	4.72574	−	26.8010i	0.184933	−	1.04881i	0.926042	−	0.377421i	$-0.123189\pi$
$654$		0			0
$655$	−6.61100	+	5.54729i	−0.258313	+	0.216751i
$656$	−4.46347	−	7.73096i	−0.174269	−	0.301843i
$657$		0			0
$658$	5.61348	−	9.72283i	0.218836	−	0.379035i
$659$	−0.917209	−	5.20175i	−0.0357294	−	0.202631i	0.961718	−	0.274043i	$-0.0883609\pi$
$659$	−0.917209	−	5.20175i	−0.0357294	−	0.202631i	−0.997447	+	0.0714110i	$0.977250\pi$
$660$		0			0
$661$	−10.9616	+	3.98968i	−0.426355	+	0.155181i	−0.546280	−	0.837602i	$-0.683957\pi$
$661$	−10.9616	+	3.98968i	−0.426355	+	0.155181i	0.119925	+	0.992783i	$0.461734\pi$
$662$	1.36496	−	0.496803i	0.0530505	−	0.0193088i
$663$		0			0
$664$	4.00536	+	22.7155i	0.155438	+	0.881533i
$665$	6.05527	−	10.4880i	0.234813	−	0.406708i
$666$		0			0
$667$	−15.5015	−	26.8494i	−0.600220	−	1.03961i
$668$	−1.37588	+	1.15450i	−0.0532345	+	0.0446690i
$669$		0			0
$670$	0.622812	−	3.53214i	0.0240613	−	0.136459i
$671$	7.49510	+	6.28913i	0.289345	+	0.242789i
$672$		0			0
$673$	−46.1412	−	16.7940i	−1.77861	−	0.647362i	−0.999798	−	0.0201071i	$-0.993599\pi$
$673$	−46.1412	−	16.7940i	−1.77861	−	0.647362i	−0.778814	−	0.627255i	$-0.784178\pi$
$674$	−0.703510			−0.0270982
$675$		0			0
$676$	−10.2880			−0.395693
$677$	−21.2550	−	7.73617i	−0.816894	−	0.297325i	−0.100426	−	0.994945i	$-0.532020\pi$
$677$	−21.2550	−	7.73617i	−0.816894	−	0.297325i	−0.716469	+	0.697619i	$0.754243\pi$
$678$		0			0
$679$	1.02822	+	0.862775i	0.0394593	+	0.0331103i
$680$	−0.731752	+	4.14997i	−0.0280614	+	0.159144i
$681$		0			0
$682$	−3.22884	+	2.70931i	−0.123639	+	0.103745i
$683$	−8.56931	−	14.8425i	−0.327896	−	0.567932i	0.654198	−	0.756323i	$-0.273006\pi$
$683$	−8.56931	−	14.8425i	−0.327896	−	0.567932i	−0.982094	+	0.188391i	$0.939673\pi$
$684$		0			0
$685$	8.83897	−	15.3095i	0.337720	−	0.584947i
$686$	1.46007	+	8.28045i	0.0557456	+	0.316149i
$687$		0			0
$688$	23.4900	−	8.54966i	0.895548	−	0.325953i
$689$	−1.95851	+	0.712838i	−0.0746132	+	0.0271570i
$690$		0			0
$691$	3.17011	+	17.9786i	0.120597	+	0.683937i	0.983826	+	0.179126i	$0.0573268\pi$
$691$	3.17011	+	17.9786i	0.120597	+	0.683937i	−0.863230	+	0.504811i	$0.831562\pi$
$692$	−7.25049	+	12.5582i	−0.275622	+	0.477392i
$693$		0			0
$694$	−19.6749	−	34.0779i	−0.746848	−	1.29358i
$695$	7.49068	−	6.28543i	0.284138	−	0.238420i
$696$		0			0
$697$	0.589436	−	3.34286i	0.0223265	−	0.126620i
$698$	−27.2679	−	22.8805i	−1.03210	−	0.866038i
$699$		0			0
$700$	−11.2919	−	4.10991i	−0.426793	−	0.155340i
$701$	2.92075			0.110315			0.0551575	−	0.998478i	$-0.482434\pi$
$701$	2.92075			0.110315			0.0551575	+	0.998478i	$0.482434\pi$
$702$		0			0
$703$	9.31505			0.351324
$704$	−4.45570	−	1.62174i	−0.167931	−	0.0611218i
$705$		0			0
$706$	30.3171	+	25.4391i	1.14100	+	0.957412i
$707$	−11.8123	+	66.9906i	−0.444246	+	2.51944i
$708$		0			0
$709$	23.0023	−	19.3012i	0.863868	−	0.724872i	−0.0989295	−	0.995094i	$-0.531542\pi$
$709$	23.0023	−	19.3012i	0.863868	−	0.724872i	0.962798	+	0.270223i	$0.0870974\pi$
$710$	11.5665	+	20.0338i	0.434084	+	0.751856i
$711$		0			0
$712$	−5.65509	+	9.79490i	−0.211933	+	0.367079i
$713$	1.35665	+	7.69393i	0.0508068	+	0.288140i
$714$		0			0
$715$	1.45446	−	0.529381i	0.0543938	−	0.0197977i
$716$	0.779152	−	0.283588i	0.0291183	−	0.0105982i
$717$		0			0
$718$	−3.05341	−	17.3168i	−0.113952	−	0.646256i
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	−0.202349	−	0.979314i	$-0.564857\pi$
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	0.949285	−	0.314418i	$-0.101809\pi$
$720$		0			0
$721$	−30.9059	−	53.5306i	−1.15100	−	1.99358i
$722$	14.7781	−	12.4003i	0.549983	−	0.461490i
$723$		0			0
$724$	−3.03499	+	17.2123i	−0.112794	+	0.639689i
$725$	−15.1770	−	12.7350i	−0.563659	−	0.472966i
$726$		0			0
$727$	1.44598	+	0.526294i	0.0536285	+	0.0195192i	0.368695	−	0.929550i	$-0.379805\pi$
$727$	1.44598	+	0.526294i	0.0536285	+	0.0195192i	−0.315067	+	0.949070i	$0.602027\pi$
$728$	5.65371			0.209540
$729$		0			0
$730$	−18.7734			−0.694834
$731$	8.93196	+	3.25097i	0.330361	+	0.120241i
$732$		0			0
$733$	−1.15818	−	0.971827i	−0.0427783	−	0.0358952i	0.621148	−	0.783693i	$-0.286667\pi$
$733$	−1.15818	−	0.971827i	−0.0427783	−	0.0358952i	−0.663926	+	0.747798i	$0.731111\pi$
$734$	−6.20502	+	35.1904i	−0.229031	+	1.29890i
$735$		0			0
$736$	19.6642	−	16.5002i	0.724830	−	0.608205i
$737$	1.76667	+	3.05997i	0.0650762	+	0.112715i
$738$		0			0
$739$	−10.6779	+	18.4946i	−0.392792	+	0.680336i	−0.992817	−	0.119646i	$-0.961824\pi$
$739$	−10.6779	+	18.4946i	−0.392792	+	0.680336i	0.600024	+	0.799982i	$0.295157\pi$
$740$	0.549863	+	3.11843i	0.0202134	+	0.114636i
$741$		0			0
$742$	17.5655	−	6.39333i	0.644851	−	0.234707i
$743$	−19.1028	+	6.95284i	−0.700812	+	0.255075i	−0.667758	−	0.744379i	$-0.732746\pi$
$743$	−19.1028	+	6.95284i	−0.700812	+	0.255075i	−0.0330547	+	0.999454i	$0.510524\pi$
$744$		0			0
$745$	0.483262	+	2.74072i	0.0177054	+	0.100412i
$746$	1.94153	−	3.36282i	0.0710843	−	0.123122i
$747$		0			0
$748$	1.45880	+	2.52672i	0.0533391	+	0.0923860i
$749$	−49.4970	+	41.5329i	−1.80858	+	1.51758i
$750$		0			0
$751$	0.740289	−	4.19839i	0.0270135	−	0.153201i	−0.968317	−	0.249723i	$-0.919661\pi$
$751$	0.740289	−	4.19839i	0.0270135	−	0.153201i	0.995331	+	0.0965214i	$0.0307716\pi$
$752$	6.50474	+	5.45813i	0.237204	+	0.199037i
$753$		0			0
$754$	−6.15606	−	2.24062i	−0.224191	−	0.0815987i
$755$	−11.8754			−0.432189
$756$		0			0
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$	19.8294	+	7.21730i	0.720235	+	0.262144i
$759$		0			0
$760$	4.68566	+	3.93174i	0.169967	+	0.142619i
$761$	−3.15364	+	17.8852i	−0.114319	+	0.648338i	0.872765	+	0.488140i	$0.162324\pi$
$761$	−3.15364	+	17.8852i	−0.114319	+	0.648338i	−0.987085	+	0.160198i	$0.948787\pi$
$762$		0			0
$763$	14.1289	−	11.8556i	0.511502	−	0.429201i
$764$	−4.05650	−	7.02606i	−0.146759	−	0.254194i
$765$		0			0
$766$	16.5188	−	28.6113i	0.596847	−	1.03377i
$767$	−1.43244	−	8.12376i	−0.0517224	−	0.293332i
$768$		0			0
$769$	−23.3558	+	8.50082i	−0.842232	+	0.306547i	−0.726869	−	0.686776i	$-0.759025\pi$
$769$	−23.3558	+	8.50082i	−0.842232	+	0.306547i	−0.115363	+	0.993323i	$0.536803\pi$
$770$	−13.0448	+	4.74793i	−0.470103	+	0.171104i
$771$		0			0
$772$	−1.59912	−	9.06906i	−0.0575536	−	0.326403i
$773$	19.2416	−	33.3274i	0.692071	−	1.19870i	−0.279087	−	0.960266i	$-0.590032\pi$
$773$	19.2416	−	33.3274i	0.692071	−	1.19870i	0.971158	−	0.238437i	$-0.0766350\pi$
$774$		0			0
$775$	2.49629	+	4.32369i	0.0896692	+	0.155312i
$776$	−0.519323	+	0.435764i	−0.0186426	+	0.0156430i
$777$		0			0
$778$	−5.49991	+	31.1916i	−0.197181	+	1.11827i
$779$	−3.77436	−	3.16707i	−0.135231	−	0.113472i
$780$		0			0
$781$	−21.4150	−	7.79443i	−0.766290	−	0.278907i
$782$	18.5107			0.661940
$783$		0			0
$784$	−41.1462			−1.46951
$785$	−0.382058	−	0.139058i	−0.0136362	−	0.00496319i
$786$		0			0
$787$	−0.821566	−	0.689376i	−0.0292857	−	0.0245736i	0.628027	−	0.778191i	$-0.283863\pi$
$787$	−0.821566	−	0.689376i	−0.0292857	−	0.0245736i	−0.657313	+	0.753618i	$0.728307\pi$
$788$	−1.30296	+	7.38944i	−0.0464159	+	0.263238i
$789$		0			0
$790$	−17.9668	+	15.0759i	−0.639229	+	0.536377i
$791$	−38.9814	−	67.5177i	−1.38602	−	2.40065i
$792$		0			0
$793$	1.91607	−	3.31873i	0.0680417	−	0.117852i
$794$	−5.87212	−	33.3025i	−0.208394	−	1.18186i
$795$		0			0
$796$	11.3978	−	4.14846i	0.403985	−	0.147038i
$797$	23.7246	−	8.63505i	0.840369	−	0.305869i	0.114262	−	0.993451i	$-0.463550\pi$
$797$	23.7246	−	8.63505i	0.840369	−	0.305869i	0.726107	+	0.687581i	$0.241328\pi$
$798$		0			0
$799$	0.560674	+	3.17974i	0.0198352	+	0.112491i
$800$	8.20198	−	14.2063i	0.289984	−	0.502267i
$801$		0			0
$802$	25.8908	+	44.8442i	0.914237	+	1.58350i
$803$	14.1676	−	11.8880i	0.499963	−	0.419519i
$804$		0			0
$805$	−4.46815	+	25.3401i	−0.157482	+	0.893122i
$806$	1.26463	+	1.06115i	0.0445448	+	0.0373775i
$807$		0			0
$808$	−32.2851	−	11.7508i	−1.13579	−	0.413392i
$809$	11.7337			0.412536			0.206268	−	0.978495i	$-0.433868\pi$
$809$	11.7337			0.412536			0.206268	+	0.978495i	$0.433868\pi$
$810$		0			0
$811$	−38.4085			−1.34871			−0.674353	−	0.738409i	$-0.735577\pi$
$811$	−38.4085			−1.34871			−0.674353	+	0.738409i	$0.735577\pi$
$812$	16.1305	+	5.87103i	0.566070	+	0.206033i
$813$		0			0
$814$	−8.17953	−	6.86344i	−0.286693	−	0.240564i
$815$	2.86733	−	16.2615i	0.100438	−	0.569614i
$816$		0			0
$817$	10.5691	−	8.86853i	0.369766	−	0.310271i
$818$	33.3594	+	57.7802i	1.16639	+	2.02024i
$819$		0			0
$820$	0.837450	−	1.45051i	0.0292450	−	0.0506539i
$821$	−4.64197	−	26.3259i	−0.162006	−	0.918781i	−0.952098	−	0.305793i	$-0.901078\pi$
$821$	−4.64197	−	26.3259i	−0.162006	−	0.918781i	0.790092	−	0.612988i	$-0.210033\pi$
$822$		0			0
$823$	−4.10107	+	1.49267i	−0.142954	+	0.0520311i	−0.412506	−	0.910955i	$-0.635347\pi$
$823$	−4.10107	+	1.49267i	−0.142954	+	0.0520311i	0.269552	+	0.962986i	$0.413124\pi$
$824$	29.3367	−	10.6777i	1.02199	−	0.371974i
$825$		0			0
$826$	12.8473	+	72.8608i	0.447015	+	2.53515i
$827$	−19.5727	+	33.9009i	−0.680610	+	1.17885i	0.294185	+	0.955748i	$0.404952\pi$
$827$	−19.5727	+	33.9009i	−0.680610	+	1.17885i	−0.974795	+	0.223102i	$0.928382\pi$
$828$		0			0
$829$	16.4433	+	28.4807i	0.571101	+	0.989176i	0.996453	+	0.0841481i	$0.0268169\pi$
$829$	16.4433	+	28.4807i	0.571101	+	0.989176i	−0.425352	+	0.905028i	$0.639850\pi$
$830$	−16.9927	+	14.2586i	−0.589826	+	0.494922i
$831$		0			0
$832$	−0.322492	+	1.82894i	−0.0111804	+	0.0634072i
$833$	−11.9853	−	10.0568i	−0.415264	−	0.348448i
$834$		0			0
$835$	2.30950	+	0.840588i	0.0799234	+	0.0290898i
$836$	4.23496			0.146469
$837$		0			0
$838$	25.9552			0.896607
$839$	29.7322	+	10.8216i	1.02647	+	0.373604i	0.799735	−	0.600353i	$-0.204973\pi$
$839$	29.7322	+	10.8216i	1.02647	+	0.373604i	0.226734	+	0.973957i	$0.427195\pi$
$840$		0			0
$841$	−0.534920	−	0.448851i	−0.0184455	−	0.0154776i
$842$	5.28131	−	29.9518i	0.182006	−	1.03221i
$843$		0			0
$844$	4.96914	−	4.16961i	0.171045	−	0.143524i
$845$	7.03892	+	12.1918i	0.242146	+	0.419410i
$846$		0			0
$847$	−14.6612	+	25.3939i	−0.503764	+	0.872545i
$848$	2.45505	+	13.9233i	0.0843066	+	0.478127i
$849$		0			0
$850$	11.1157	−	4.04577i	0.381264	−	0.138769i
$851$	−18.5980	+	6.76910i	−0.637530	+	0.232042i
$852$		0			0
$853$	−0.982440	−	5.57169i	−0.0336381	−	0.190771i	0.963358	−	0.268217i	$-0.0864345\pi$
$853$	−0.982440	−	5.57169i	−0.0336381	−	0.190771i	−0.996997	+	0.0774461i	$0.975323\pi$
$854$	−17.1849	+	29.7652i	−0.588057	+	1.01854i
$855$		0			0
$856$	−16.3173	−	28.2624i	−0.557715	−	0.965990i
$857$	31.5690	−	26.4895i	1.07838	−	0.904864i	0.0825904	−	0.996584i	$-0.473681\pi$
$857$	31.5690	−	26.4895i	1.07838	−	0.904864i	0.995785	+	0.0917193i	$0.0292362\pi$
$858$		0			0
$859$	6.22605	−	35.3097i	0.212430	−	1.20475i	−0.672880	−	0.739751i	$-0.734943\pi$
$859$	6.22605	−	35.3097i	0.212430	−	1.20475i	0.885311	−	0.465000i	$-0.153946\pi$
$860$	3.59284	+	3.01475i	0.122515	+	0.102802i
$861$		0			0
$862$	45.7566	+	16.6541i	1.55848	+	0.567239i
$863$	−20.9694			−0.713806			−0.356903	−	0.934142i	$-0.616167\pi$
$863$	−20.9694			−0.713806			−0.356903	+	0.934142i	$0.616167\pi$
$864$		0			0
$865$	19.8427			0.674673
$866$	−59.3753	−	21.6108i	−2.01765	−	0.734366i
$867$		0			0
$868$	−3.31367	−	2.78050i	−0.112473	−	0.0943764i
$869$	4.01223	−	22.7545i	0.136106	−	0.771893i
$870$		0			0
$871$	1.06013	−	0.889553i	0.0359210	−	0.0301413i
$872$	4.65778	+	8.06751i	0.157732	+	0.273201i
$873$		0			0
$874$	13.4343	−	23.2689i	0.454422	−	0.787082i
$875$	6.68887	+	37.9345i	0.226125	+	1.28242i
$876$		0			0
$877$	−19.2735	+	7.01498i	−0.650819	+	0.236879i	−0.646268	−	0.763111i	$-0.723671\pi$
$877$	−19.2735	+	7.01498i	−0.650819	+	0.236879i	−0.00455171	+	0.999990i	$0.501449\pi$
$878$	16.2117	−	5.90057i	0.547117	−	0.199134i
$879$		0			0
$880$	−1.82321	−	10.3399i	−0.0614604	−	0.348559i
$881$	−19.1438	+	33.1581i	−0.644972	+	1.11712i	0.339336	+	0.940665i	$0.389798\pi$
$881$	−19.1438	+	33.1581i	−0.644972	+	1.11712i	−0.984308	+	0.176459i	$0.943536\pi$
$882$		0			0
$883$	8.72326	+	15.1091i	0.293561	+	0.508463i	0.974649	−	0.223739i	$-0.0718263\pi$
$883$	8.72326	+	15.1091i	0.293561	+	0.508463i	−0.681088	+	0.732201i	$0.738493\pi$
$884$	0.875384	−	0.734534i	0.0294423	−	0.0247051i
$885$		0			0
$886$	6.39481	−	36.2668i	0.214838	−	1.21841i
$887$	41.5325	+	34.8499i	1.39453	+	1.17015i	0.963468	+	0.267823i	$0.0863041\pi$
$887$	41.5325	+	34.8499i	1.39453	+	1.17015i	0.431058	+	0.902324i	$0.358140\pi$
$888$		0			0
$889$	3.92831	+	1.42979i	0.131751	+	0.0479536i
$890$	−10.8769			−0.364596
$891$		0			0
$892$	−7.21530			−0.241586
$893$	4.40402	+	1.60293i	0.147375	+	0.0536400i
$894$		0			0
$895$	−0.869150	−	0.729303i	−0.0290525	−	0.0243779i
$896$	8.87211	−	50.3162i	0.296396	−	1.68095i
$897$		0			0
$898$	12.8396	−	10.7737i	0.428462	−	0.359523i
$899$	−3.56595	−	6.17641i	−0.118931	−	0.205995i
$900$		0			0
$901$	−2.68796	+	4.65569i	−0.0895491	+	0.155104i
$902$	0.980730	+	5.56200i	0.0326547	+	0.185194i
$903$		0			0
$904$	37.0021	−	13.4677i	1.23067	−	0.447928i
$905$	22.4738	−	8.17979i	0.747054	−	0.271906i
$906$		0			0
$907$	4.98078	+	28.2474i	0.165384	+	0.937939i	0.948668	+	0.316275i	$0.102432\pi$
$907$	4.98078	+	28.2474i	0.165384	+	0.937939i	−0.783284	+	0.621665i	$0.786457\pi$
$908$	1.67917	−	2.90841i	0.0557252	−	0.0965188i
$909$		0			0
$910$	2.71857	+	4.70871i	0.0901198	+	0.156092i
$911$	21.7416	−	18.2433i	0.720330	−	0.604429i	−0.207146	−	0.978310i	$-0.566418\pi$
$911$	21.7416	−	18.2433i	0.720330	−	0.604429i	0.927477	+	0.373881i	$0.121973\pi$
$912$		0			0
$913$	3.79471	−	21.5208i	0.125586	−	0.712236i
$914$	9.80947	+	8.23112i	0.324468	+	0.272261i
$915$		0			0
$916$	−12.5319	−	4.56122i	−0.414064	−	0.150707i
$917$	29.8653			0.986240
$918$		0			0
$919$	37.7786			1.24620			0.623101	−	0.782141i	$-0.285873\pi$
$919$	37.7786			1.24620			0.623101	+	0.782141i	$0.285873\pi$
$920$	−12.2123	−	4.44491i	−0.402627	−	0.146544i
$921$		0			0
$922$	−29.3592	−	24.6353i	−0.966893	−	0.811320i
$923$	−1.54996	+	8.79027i	−0.0510176	+	0.289335i
$924$		0			0
$925$	−9.68860	+	8.12970i	−0.318559	+	0.267303i
$926$	−7.39243	−	12.8041i	−0.242930	−	0.420768i
$927$		0			0
$928$	−11.7166	+	20.2937i	−0.384615	+	0.666173i
$929$	6.00421	+	34.0516i	0.196992	+	1.11720i	0.909554	+	0.415586i	$0.136424\pi$
$929$	6.00421	+	34.0516i	0.196992	+	1.11720i	−0.712562	+	0.701609i	$0.752465\pi$
$930$		0			0
$931$	−21.3404	+	7.76726i	−0.699403	+	0.254562i
$932$	13.3520	−	4.85972i	0.437358	−	0.159185i
$933$		0			0
$934$	−3.21005	−	18.2051i	−0.105036	−	0.595688i
$935$	1.99618	−	3.45749i	0.0652822	−	0.113072i
$936$		0			0
$937$	9.71839	+	16.8328i	0.317486	+	0.549902i	0.979963	−	0.199180i	$-0.0638280\pi$
$937$	9.71839	+	16.8328i	0.317486	+	0.549902i	−0.662477	+	0.749082i	$0.730495\pi$
$938$	−9.50812	+	7.97826i	−0.310451	+	0.260499i
$939$		0			0
$940$	−0.276651	+	1.56897i	−0.00902337	+	0.0511741i
$941$	−7.61330	−	6.38832i	−0.248187	−	0.208253i	0.510204	−	0.860053i	$-0.329570\pi$
$941$	−7.61330	−	6.38832i	−0.248187	−	0.208253i	−0.758391	+	0.651800i	$0.774014\pi$
$942$		0			0
$943$	9.83716	+	3.58043i	0.320342	+	0.116595i
$944$	−55.9572			−1.82125
$945$		0			0
$946$	−15.8152			−0.514195
$947$	15.8909	+	5.78380i	0.516384	+	0.187948i	0.587048	−	0.809552i	$-0.300290\pi$
$947$	15.8909	+	5.78380i	0.516384	+	0.187948i	−0.0706647	+	0.997500i	$0.522512\pi$
$948$		0			0
$949$	−5.54899	−	4.65616i	−0.180128	−	0.151145i
$950$	2.98156	−	16.9093i	0.0967345	−	0.548609i
$951$		0			0
$952$	11.1712	−	9.37379i	0.362062	−	0.303806i
$953$	8.67866	+	15.0319i	0.281129	+	0.486930i	0.971663	−	0.236370i	$-0.0759577\pi$
$953$	8.67866	+	15.0319i	0.281129	+	0.486930i	−0.690534	+	0.723300i	$0.742624\pi$
$954$		0			0
$955$	−5.55079	+	9.61426i	−0.179620	+	0.311110i
$956$	0.220091	+	1.24820i	0.00711825	+	0.0403696i
$957$		0			0
$958$	−40.5824	+	14.7708i	−1.31116	+	0.477222i
$959$	−57.4872	+	20.9236i	−1.85636	+	0.675659i
$960$		0			0
$961$	−5.07101	−	28.7591i	−0.163581	−	0.927714i
$962$	−2.09104	+	3.62179i	−0.0674179	+	0.116771i
$963$		0			0
$964$	2.27898	+	3.94730i	0.0734009	+	0.127134i
$965$	−9.65315	+	8.09995i	−0.310746	+	0.260747i
$966$		0			0
$967$	−2.91440	+	16.5284i	−0.0937207	+	0.531517i	0.901411	+	0.432964i	$0.142532\pi$
$967$	−2.91440	+	16.5284i	−0.0937207	+	0.531517i	−0.995132	+	0.0985525i	$0.968579\pi$
$968$	−11.3451	−	9.51963i	−0.364644	−	0.305973i
$969$		0			0
$970$	−0.612642	−	0.222984i	−0.0196708	−	0.00715957i
$971$	33.4811			1.07446			0.537230	−	0.843436i	$-0.319471\pi$
$971$	33.4811			1.07446			0.537230	+	0.843436i	$0.319471\pi$
$972$		0			0
$973$	−33.8393			−1.08484
$974$	−47.9865	−	17.4657i	−1.53759	−	0.559636i
$975$		0			0
$976$	−19.9134	−	16.7093i	−0.637413	−	0.534853i
$977$	−3.94786	+	22.3894i	−0.126303	+	0.716302i	0.854222	+	0.519909i	$0.174034\pi$
$977$	−3.94786	+	22.3894i	−0.126303	+	0.716302i	−0.980525	+	0.196393i	$0.937077\pi$
$978$		0			0
$979$	8.20843	−	6.88769i	0.262342	−	0.220131i
$980$	−3.85998	−	6.68569i	−0.123303	−	0.213567i
$981$		0			0
$982$	−7.31892	+	12.6767i	−0.233556	+	0.404531i
$983$	−8.18917	−	46.4431i	−0.261194	−	1.48131i	−0.779658	−	0.626206i	$-0.784607\pi$
$983$	−8.18917	−	46.4431i	−0.261194	−	1.48131i	0.518464	−	0.855100i	$-0.326504\pi$
$984$		0			0
$985$	9.64828	−	3.51169i	0.307420	−	0.111892i
$986$	−15.8788	+	5.77940i	−0.505683	+	0.184054i
$987$		0			0
$988$	−0.288030	−	1.63350i	−0.00916346	−	0.0519686i
$989$	−14.6571	+	25.3869i	−0.466069	+	0.807255i
$990$		0			0
$991$	2.18837	+	3.79036i	0.0695158	+	0.120405i	0.898688	−	0.438588i	$-0.144521\pi$
$991$	2.18837	+	3.79036i	0.0695158	+	0.120405i	−0.829172	+	0.558993i	$0.811188\pi$
$992$	4.52353	−	3.79569i	0.143622	−	0.120513i
$993$		0			0
$994$	13.9014	−	78.8386i	0.440925	−	2.50061i
$995$	−12.7143	−	10.6686i	−0.403072	−	0.338217i
$996$		0			0
$997$	2.01517	+	0.733462i	0.0638211	+	0.0232290i	0.373733	−	0.927536i	$-0.378077\pi$
$997$	2.01517	+	0.733462i	0.0638211	+	0.0232290i	−0.309912	+	0.950765i	$0.600300\pi$
$998$	−19.5582			−0.619104
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.e.a.64.2		12
3.2	odd	2		27.2.e.a.4.1	✓	12
9.2	odd	6		243.2.e.c.28.2		12
9.4	even	3		243.2.e.a.109.1		12
9.5	odd	6		243.2.e.d.109.2		12
9.7	even	3		243.2.e.b.28.1		12
12.11	even	2		432.2.u.c.193.1		12
15.2	even	4		675.2.u.b.274.4		24
15.8	even	4		675.2.u.b.274.1		24
15.14	odd	2		675.2.l.c.301.2		12
27.2	odd	18		243.2.e.d.136.2		12
27.4	even	9		729.2.c.b.244.6		12
27.5	odd	18		729.2.c.e.487.1		12
27.7	even	9	inner	81.2.e.a.19.2		12
27.11	odd	18		243.2.e.c.217.2		12
27.13	even	9		729.2.a.d.1.1		6
27.14	odd	18		729.2.a.a.1.6		6
27.16	even	9		243.2.e.b.217.1		12
27.20	odd	18		27.2.e.a.7.1	yes	12
27.22	even	9		729.2.c.b.487.6		12
27.23	odd	18		729.2.c.e.244.1		12
27.25	even	9		243.2.e.a.136.1		12
108.47	even	18		432.2.u.c.385.1		12
135.47	even	36		675.2.u.b.574.1		24
135.74	odd	18		675.2.l.c.601.2		12
135.128	even	36		675.2.u.b.574.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.1	✓	12	3.2	odd	2
27.2.e.a.7.1	yes	12	27.20	odd	18
81.2.e.a.19.2		12	27.7	even	9	inner
81.2.e.a.64.2		12	1.1	even	1	trivial
243.2.e.a.109.1		12	9.4	even	3
243.2.e.a.136.1		12	27.25	even	9
243.2.e.b.28.1		12	9.7	even	3
243.2.e.b.217.1		12	27.16	even	9
243.2.e.c.28.2		12	9.2	odd	6
243.2.e.c.217.2		12	27.11	odd	18
243.2.e.d.109.2		12	9.5	odd	6
243.2.e.d.136.2		12	27.2	odd	18
432.2.u.c.193.1		12	12.11	even	2
432.2.u.c.385.1		12	108.47	even	18
675.2.l.c.301.2		12	15.14	odd	2
675.2.l.c.601.2		12	135.74	odd	18
675.2.u.b.274.1		24	15.8	even	4
675.2.u.b.274.4		24	15.2	even	4
675.2.u.b.574.1		24	135.47	even	36
675.2.u.b.574.4		24	135.128	even	36
729.2.a.a.1.6		6	27.14	odd	18
729.2.a.d.1.1		6	27.13	even	9
729.2.c.b.244.6		12	27.4	even	9
729.2.c.b.487.6		12	27.22	even	9
729.2.c.e.244.1		12	27.23	odd	18
729.2.c.e.487.1		12	27.5	odd	18

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.57954 + 0.574906i) q^{2} +(0.632343 + 0.530599i) q^{4} +(0.196143 - 1.11238i) q^{5} +(-2.99441 + 2.51261i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})\)	\(q+(1.57954 + 0.574906i) q^{2} +(0.632343 + 0.530599i) q^{4} +(0.196143 - 1.11238i) q^{5} +(-2.99441 + 2.51261i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(0.324801 + 1.84204i) q^{11} +(0.688417 - 0.250563i) q^{13} +(-6.17430 + 2.24726i) q^{14} +(-0.862951 - 4.89404i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(0.714260 - 0.599335i) q^{20} +(-0.545962 + 3.09631i) q^{22} +(4.46428 + 3.74597i) q^{23} +(3.49954 + 1.27373i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(-4.99910 - 1.81953i) q^{29} +(1.02696 + 0.861722i) q^{31} +(0.764882 - 4.33786i) q^{32} +(2.43321 - 2.04170i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(-0.800605 - 4.54046i) q^{38} +(-2.09556 + 0.762721i) q^{40} +(1.68800 - 0.614382i) q^{41} +(0.873477 + 4.95373i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(-1.30892 + 1.09832i) q^{47} +(1.43775 - 8.15389i) q^{49} +(4.79539 + 4.02381i) q^{50} +(0.568265 + 0.206831i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(7.25193 + 2.63949i) q^{56} +(-6.85023 - 5.74803i) q^{58} +(1.95529 - 11.0890i) q^{59} +(4.00710 - 3.36235i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(-0.143694 - 0.814930i) q^{65} +(1.77511 - 0.646086i) q^{67} +(1.46577 - 0.533495i) q^{68} +(1.28877 + 7.30898i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(-4.37302 + 3.66940i) q^{74} +(0.393163 - 2.22974i) q^{76} +(-5.60091 - 4.69972i) q^{77} +(-11.6079 - 4.22493i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(-10.9786 - 3.99588i) q^{83} +(-1.63507 - 1.37199i) q^{85} +(-1.46824 + 8.32679i) q^{86} +(2.82886 - 2.37370i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(0.835346 + 4.73748i) q^{92} +(-2.69893 + 0.982329i) q^{94} +(-2.91133 + 1.05964i) q^{95} +(-0.0596270 - 0.338162i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Introduction

L-functions

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