LMFDB - Embedded newform 486.2.e.c.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(55,486)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("486.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.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:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	486.271
Dual form			486.2.e.c.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(0.113341 + 0.0412527i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(0.113341 + 0.0412527i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.673648 - 1.16679i) q^{10} +(-2.84730 + 2.38917i) q^{11} +(-1.05303 + 5.97205i) q^{13} +(-0.0209445 + 0.118782i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-2.58512 + 4.47756i) q^{17} +(2.96064 + 5.12797i) q^{19} +(1.26604 + 0.460802i) q^{20} +(-2.84730 - 2.38917i) q^{22} +(-4.47178 + 1.62760i) q^{23} +(-0.553033 - 3.13641i) q^{25} -6.06418 q^{26} -0.120615 q^{28} +(-1.03209 - 5.85327i) q^{29} +(4.73783 - 1.72443i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-4.85844 - 1.76833i) q^{34} +(-0.0812519 - 0.140732i) q^{35} +(-0.145430 + 0.251892i) q^{37} +(-4.53596 + 3.80612i) q^{38} +(-0.233956 + 1.32683i) q^{40} +(-1.00727 + 5.71253i) q^{41} +(0.347296 - 0.291416i) q^{43} +(1.85844 - 3.21891i) q^{44} +(-2.37939 - 4.12122i) q^{46} +(-0.726682 - 0.264490i) q^{47} +(-5.35117 - 4.49016i) q^{49} +(2.99273 - 1.08926i) q^{50} +(-1.05303 - 5.97205i) q^{52} +7.29086 q^{53} +5.00774 q^{55} +(-0.0209445 - 0.118782i) q^{56} +(5.58512 - 2.03282i) q^{58} +(1.14156 + 0.957882i) q^{59} +(3.55303 + 1.29320i) q^{61} +(2.52094 + 4.36640i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(6.25877 - 5.25173i) q^{65} +(-1.15270 + 6.53731i) q^{67} +(0.897804 - 5.09170i) q^{68} +(0.124485 - 0.104455i) q^{70} +(2.87211 - 4.97464i) q^{71} +(-5.20961 - 9.02330i) q^{73} +(-0.273318 - 0.0994798i) q^{74} +(-4.53596 - 3.80612i) q^{76} +(-0.421274 + 0.153331i) q^{77} +(2.42989 + 13.7806i) q^{79} -1.34730 q^{80} -5.80066 q^{82} +(0.411474 + 2.33359i) q^{83} +(6.54576 - 2.38246i) q^{85} +(0.347296 + 0.291416i) q^{86} +(3.49273 + 1.27125i) q^{88} +(-1.08512 - 1.87949i) q^{89} +(-0.365715 + 0.633436i) q^{91} +(3.64543 - 3.05888i) q^{92} +(0.134285 - 0.761570i) q^{94} +(1.38532 - 7.85651i) q^{95} +(-2.62449 + 2.20220i) q^{97} +(3.49273 - 6.04958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8	$ 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8} + 3 q^{10} - 15 q^{11} + 6 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} - 12 q^{23} + 9 q^{25} - 18 q^{26} - 12 q^{28} + 3 q^{29} + 9 q^{31} - 21 q^{34} - 3 q^{35} + 15 q^{37} + 6 q^{38} - 6 q^{40} - 24 q^{41} + 3 q^{44} - 3 q^{46} + 9 q^{47} - 6 q^{49} + 6 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 12 q^{58} + 15 q^{59} + 9 q^{61} + 12 q^{62} - 3 q^{64} + 15 q^{65} - 9 q^{67} + 6 q^{68} - 12 q^{70} - 12 q^{71} + 3 q^{73} - 15 q^{74} + 6 q^{76} + 15 q^{77} + 6 q^{79} - 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{85} + 3 q^{88} + 15 q^{89} - 12 q^{91} + 6 q^{92} - 9 q^{94} + 24 q^{95} - 3 q^{97} + 3 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8 + 3 * q^10 - 15 * q^11 + 6 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 - 12 * q^23 + 9 * q^25 - 18 * q^26 - 12 * q^28 + 3 * q^29 + 9 * q^31 - 21 * q^34 - 3 * q^35 + 15 * q^37 + 6 * q^38 - 6 * q^40 - 24 * q^41 + 3 * q^44 - 3 * q^46 + 9 * q^47 - 6 * q^49 + 6 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 12 * q^58 + 15 * q^59 + 9 * q^61 + 12 * q^62 - 3 * q^64 + 15 * q^65 - 9 * q^67 + 6 * q^68 - 12 * q^70 - 12 * q^71 + 3 * q^73 - 15 * q^74 + 6 * q^76 + 15 * q^77 + 6 * q^79 - 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^85 + 3 * q^88 + 15 * q^89 - 12 * q^91 + 6 * q^92 - 9 * q^94 + 24 * q^95 - 3 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.03209	−	0.866025i	−0.461564	−	0.387298i	0.382142	−	0.924104i	$-0.375187\pi$
$5$	−1.03209	−	0.866025i	−0.461564	−	0.387298i	−0.843706	+	0.536805i	$0.819631\pi$
$6$		0			0
$7$	0.113341	+	0.0412527i	0.0428388	+	0.0155920i	0.363351	−	0.931652i	$-0.381633\pi$
$7$	0.113341	+	0.0412527i	0.0428388	+	0.0155920i	−0.320512	+	0.947244i	$0.603855\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	0.673648	−	1.16679i	0.213026	−	0.368972i
$11$	−2.84730	+	2.38917i	−0.858492	+	0.720360i	−0.961643	−	0.274305i	$-0.911552\pi$
$11$	−2.84730	+	2.38917i	−0.858492	+	0.720360i	0.103151	+	0.994666i	$0.467108\pi$
$12$		0			0
$13$	−1.05303	+	5.97205i	−0.292059	+	1.65635i	0.386862	+	0.922137i	$0.373559\pi$
$13$	−1.05303	+	5.97205i	−0.292059	+	1.65635i	−0.678921	+	0.734211i	$0.737552\pi$
$14$	−0.0209445	+	0.118782i	−0.00559766	+	0.0317459i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.58512	+	4.47756i	−0.626984	+	1.08597i	0.361169	+	0.932500i	$0.382378\pi$
$17$	−2.58512	+	4.47756i	−0.626984	+	1.08597i	−0.988154	+	0.153468i	$0.950956\pi$
$18$		0			0
$19$	2.96064	+	5.12797i	0.679217	+	1.17644i	0.975217	+	0.221250i	$0.0710137\pi$
$19$	2.96064	+	5.12797i	0.679217	+	1.17644i	−0.296000	+	0.955188i	$0.595653\pi$
$20$	1.26604	+	0.460802i	0.283096	+	0.103039i
$21$		0			0
$22$	−2.84730	−	2.38917i	−0.607046	−	0.509372i
$23$	−4.47178	+	1.62760i	−0.932431	+	0.339377i	−0.763173	−	0.646195i	$-0.776359\pi$
$23$	−4.47178	+	1.62760i	−0.932431	+	0.339377i	−0.169258	+	0.985572i	$0.554137\pi$
$24$		0			0
$25$	−0.553033	−	3.13641i	−0.110607	−	0.627282i
$26$	−6.06418			−1.18928
$27$		0			0
$28$	−0.120615			−0.0227940
$29$	−1.03209	−	5.85327i	−0.191654	−	1.08692i	−0.917104	−	0.398649i	$-0.869479\pi$
$29$	−1.03209	−	5.85327i	−0.191654	−	1.08692i	0.725449	−	0.688275i	$-0.241632\pi$
$30$		0			0
$31$	4.73783	−	1.72443i	0.850939	−	0.309716i	0.120516	−	0.992711i	$-0.461545\pi$
$31$	4.73783	−	1.72443i	0.850939	−	0.309716i	0.730423	+	0.682995i	$0.239323\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$		0			0
$34$	−4.85844	−	1.76833i	−0.833216	−	0.303266i
$35$	−0.0812519	−	0.140732i	−0.0137341	−	0.0237881i
$36$		0			0
$37$	−0.145430	+	0.251892i	−0.0239085	+	0.0414107i	−0.877732	−	0.479152i	$-0.840944\pi$
$37$	−0.145430	+	0.251892i	−0.0239085	+	0.0414107i	0.853824	+	0.520562i	$0.174278\pi$
$38$	−4.53596	+	3.80612i	−0.735830	+	0.617434i
$39$		0			0
$40$	−0.233956	+	1.32683i	−0.0369916	+	0.209790i
$41$	−1.00727	+	5.71253i	−0.157310	+	0.892148i	0.799334	+	0.600887i	$0.205186\pi$
$41$	−1.00727	+	5.71253i	−0.157310	+	0.892148i	−0.956644	+	0.291261i	$0.905925\pi$
$42$		0			0
$43$	0.347296	−	0.291416i	0.0529622	−	0.0444406i	−0.615922	−	0.787807i	$-0.711216\pi$
$43$	0.347296	−	0.291416i	0.0529622	−	0.0444406i	0.668885	+	0.743366i	$0.266772\pi$
$44$	1.85844	−	3.21891i	0.280170	−	0.485270i
$45$		0			0
$46$	−2.37939	−	4.12122i	−0.350821	−	0.607640i
$47$	−0.726682	−	0.264490i	−0.105997	−	0.0385799i	0.288477	−	0.957487i	$-0.406851\pi$
$47$	−0.726682	−	0.264490i	−0.105997	−	0.0385799i	−0.394474	+	0.918907i	$0.629073\pi$
$48$		0			0
$49$	−5.35117	−	4.49016i	−0.764452	−	0.641452i
$50$	2.99273	−	1.08926i	0.423235	−	0.154045i
$51$		0			0
$52$	−1.05303	−	5.97205i	−0.146029	−	0.828174i
$53$	7.29086			1.00148			0.500738	−	0.865599i	$-0.333062\pi$
$53$	7.29086			1.00148			0.500738	+	0.865599i	$0.333062\pi$
$54$		0			0
$55$	5.00774			0.675244
$56$	−0.0209445	−	0.118782i	−0.00279883	−	0.0158730i
$57$		0			0
$58$	5.58512	−	2.03282i	0.733362	−	0.266922i
$59$	1.14156	+	0.957882i	0.148618	+	0.124706i	0.714065	−	0.700079i	$-0.246852\pi$
$59$	1.14156	+	0.957882i	0.148618	+	0.124706i	−0.565447	+	0.824785i	$0.691296\pi$
$60$		0			0
$61$	3.55303	+	1.29320i	0.454919	+	0.165577i	0.559309	−	0.828959i	$-0.311067\pi$
$61$	3.55303	+	1.29320i	0.454919	+	0.165577i	−0.104389	+	0.994536i	$0.533289\pi$
$62$	2.52094	+	4.36640i	0.320160	+	0.554534i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	6.25877	−	5.25173i	0.776305	−	0.651397i
$66$		0			0
$67$	−1.15270	+	6.53731i	−0.140825	+	0.798659i	0.829800	+	0.558061i	$0.188455\pi$
$67$	−1.15270	+	6.53731i	−0.140825	+	0.798659i	−0.970625	+	0.240598i	$0.922656\pi$
$68$	0.897804	−	5.09170i	0.108875	−	0.617459i
$69$		0			0
$70$	0.124485	−	0.104455i	0.0148788	−	0.0124848i
$71$	2.87211	−	4.97464i	0.340857	−	0.590381i	−0.643735	−	0.765248i	$-0.722616\pi$
$71$	2.87211	−	4.97464i	0.340857	−	0.590381i	0.984592	+	0.174867i	$0.0559495\pi$
$72$		0			0
$73$	−5.20961	−	9.02330i	−0.609738	−	1.05610i	−0.991283	−	0.131748i	$-0.957941\pi$
$73$	−5.20961	−	9.02330i	−0.609738	−	1.05610i	0.381545	−	0.924350i	$-0.375392\pi$
$74$	−0.273318	−	0.0994798i	−0.0317726	−	0.0115643i
$75$		0			0
$76$	−4.53596	−	3.80612i	−0.520310	−	0.436592i
$77$	−0.421274	+	0.153331i	−0.0480087	+	0.0174737i
$78$		0			0
$79$	2.42989	+	13.7806i	0.273384	+	1.55044i	0.744048	+	0.668126i	$0.232903\pi$
$79$	2.42989	+	13.7806i	0.273384	+	1.55044i	−0.470664	+	0.882313i	$0.655985\pi$
$80$	−1.34730			−0.150632
$81$		0			0
$82$	−5.80066			−0.640576
$83$	0.411474	+	2.33359i	0.0451652	+	0.256144i	0.999027	−	0.0441014i	$-0.0140425\pi$
$83$	0.411474	+	2.33359i	0.0451652	+	0.256144i	−0.953862	+	0.300246i	$0.902931\pi$
$84$		0			0
$85$	6.54576	−	2.38246i	0.709987	−	0.258414i
$86$	0.347296	+	0.291416i	0.0374499	+	0.0314242i
$87$		0			0
$88$	3.49273	+	1.27125i	0.372326	+	0.135516i
$89$	−1.08512	−	1.87949i	−0.115023	−	0.199225i	0.802766	−	0.596294i	$-0.203361\pi$
$89$	−1.08512	−	1.87949i	−0.115023	−	0.199225i	−0.917789	+	0.397069i	$0.870027\pi$
$90$		0			0
$91$	−0.365715	+	0.633436i	−0.0383373	+	0.0664022i
$92$	3.64543	−	3.05888i	0.380062	−	0.318910i
$93$		0			0
$94$	0.134285	−	0.761570i	0.0138505	−	0.0785499i
$95$	1.38532	−	7.85651i	0.142130	−	0.806061i
$96$		0			0
$97$	−2.62449	+	2.20220i	−0.266476	+	0.223600i	−0.766228	−	0.642568i	$-0.777869\pi$
$97$	−2.62449	+	2.20220i	−0.266476	+	0.223600i	0.499752	+	0.866168i	$0.333424\pi$
$98$	3.49273	−	6.04958i	0.352819	−	0.611100i
$99$		0			0
$100$	1.59240	+	2.75811i	0.159240	+	0.275811i
$101$	8.09879	+	2.94772i	0.805860	+	0.293309i	0.711913	−	0.702268i	$-0.247829\pi$
$101$	8.09879	+	2.94772i	0.805860	+	0.293309i	0.0939474	+	0.995577i	$0.470051\pi$
$102$		0			0
$103$	−1.67365	−	1.40436i	−0.164909	−	0.138375i	0.556598	−	0.830782i	$-0.312106\pi$
$103$	−1.67365	−	1.40436i	−0.164909	−	0.138375i	−0.721508	+	0.692406i	$0.756551\pi$
$104$	5.69846	−	2.07407i	0.558780	−	0.203379i
$105$		0			0
$106$	1.26604	+	7.18009i	0.122969	+	0.697392i
$107$	10.2909			0.994855			0.497427	−	0.867506i	$-0.334278\pi$
$107$	10.2909			0.994855			0.497427	+	0.867506i	$0.334278\pi$
$108$		0			0
$109$	−11.0915			−1.06237			−0.531187	−	0.847254i	$-0.678254\pi$
$109$	−11.0915			−1.06237			−0.531187	+	0.847254i	$0.678254\pi$
$110$	0.869585	+	4.93166i	0.0829117	+	0.470216i
$111$		0			0
$112$	0.113341	−	0.0412527i	0.0107097	−	0.00389801i
$113$	−4.53802	−	3.80785i	−0.426901	−	0.358212i	0.403880	−	0.914812i	$-0.367661\pi$
$113$	−4.53802	−	3.80785i	−0.426901	−	0.358212i	−0.830781	+	0.556600i	$0.812106\pi$
$114$		0			0
$115$	6.02481	+	2.19285i	0.561817	+	0.204485i
$116$	2.97178	+	5.14728i	0.275923	+	0.477913i
$117$		0			0
$118$	−0.745100	+	1.29055i	−0.0685920	+	0.118805i
$119$	−0.477711	+	0.400847i	−0.0437917	+	0.0367456i
$120$		0			0
$121$	0.488856	−	2.77244i	0.0444414	−	0.252040i
$122$	−0.656574	+	3.72362i	−0.0594434	+	0.337120i
$123$		0			0
$124$	−3.86231	+	3.24086i	−0.346846	+	0.291038i
$125$	−5.51367	+	9.54996i	−0.493158	+	0.854174i
$126$		0			0
$127$	2.86959	+	4.97027i	0.254634	+	0.441040i	0.964796	−	0.262999i	$-0.0847115\pi$
$127$	2.86959	+	4.97027i	0.254634	+	0.441040i	−0.710162	+	0.704039i	$0.751378\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$		0			0
$130$	6.25877	+	5.25173i	0.548930	+	0.460607i
$131$	16.1814	−	5.88954i	1.41377	−	0.514572i	0.481539	−	0.876425i	$-0.340078\pi$
$131$	16.1814	−	5.88954i	1.41377	−	0.514572i	0.932235	+	0.361853i	$0.117856\pi$
$132$		0			0
$133$	0.124018	+	0.703343i	0.0107538	+	0.0609876i
$134$	−6.63816			−0.573449
$135$		0			0
$136$	5.17024			0.443345
$137$	−0.0150147	−	0.0851529i	−0.00128280	−	0.00727510i	0.984160	−	0.177285i	$-0.0567313\pi$
$137$	−0.0150147	−	0.0851529i	−0.00128280	−	0.00727510i	−0.985442	+	0.170009i	$0.945620\pi$
$138$		0			0
$139$	17.2554	−	6.28044i	1.46358	−	0.532700i	0.517232	−	0.855845i	$-0.326963\pi$
$139$	17.2554	−	6.28044i	1.46358	−	0.532700i	0.946349	+	0.323145i	$0.104740\pi$
$140$	0.124485	+	0.104455i	0.0105209	+	0.00882810i
$141$		0			0
$142$	5.39780	+	1.96464i	0.452974	+	0.164869i
$143$	−11.2699	−	19.5201i	−0.942438	−	1.63235i
$144$		0			0
$145$	−4.00387	+	6.93491i	−0.332503	+	0.575913i
$146$	7.98158	−	6.69734i	0.660560	−	0.554276i
$147$		0			0
$148$	0.0505072	−	0.286441i	0.00415167	−	0.0235453i
$149$	0.851167	−	4.82721i	0.0697303	−	0.395460i	−0.929888	−	0.367842i	$-0.880097\pi$
$149$	0.851167	−	4.82721i	0.0697303	−	0.395460i	0.999619	−	0.0276180i	$-0.00879221\pi$
$150$		0			0
$151$	1.32635	−	1.11294i	0.107937	−	0.0905699i	−0.587222	−	0.809426i	$-0.699778\pi$
$151$	1.32635	−	1.11294i	0.107937	−	0.0905699i	0.695159	+	0.718856i	$0.255334\pi$
$152$	2.96064	−	5.12797i	0.240139	−	0.415934i
$153$		0			0
$154$	−0.224155	−	0.388249i	−0.0180630	−	0.0312860i
$155$	−6.38326	−	2.32332i	−0.512715	−	0.186613i
$156$		0			0
$157$	−4.45471	−	3.73794i	−0.355524	−	0.298320i	0.447479	−	0.894294i	$-0.352322\pi$
$157$	−4.45471	−	3.73794i	−0.355524	−	0.298320i	−0.803004	+	0.595974i	$0.796766\pi$
$158$	−13.1493	+	4.78595i	−1.04610	+	0.380750i
$159$		0			0
$160$	−0.233956	−	1.32683i	−0.0184958	−	0.104895i
$161$	−0.573978			−0.0452358
$162$		0			0
$163$	−2.70914			−0.212196			−0.106098	−	0.994356i	$-0.533836\pi$
$163$	−2.70914			−0.212196			−0.106098	+	0.994356i	$0.533836\pi$
$164$	−1.00727	−	5.71253i	−0.0786549	−	0.446074i
$165$		0			0
$166$	−2.22668	+	0.810446i	−0.172824	+	0.0629028i
$167$	18.8478	+	15.8152i	1.45848	+	1.22381i	0.926083	+	0.377321i	$0.123155\pi$
$167$	18.8478	+	15.8152i	1.45848	+	1.22381i	0.532401	+	0.846492i	$0.321290\pi$
$168$		0			0
$169$	−22.3405	−	8.13127i	−1.71850	−	0.625483i
$170$	3.48293	+	6.03260i	0.267128	+	0.462680i
$171$		0			0
$172$	−0.226682	+	0.392624i	−0.0172843	+	0.0299373i
$173$	8.21348	−	6.89193i	0.624459	−	0.523983i	−0.274743	−	0.961518i	$-0.588593\pi$
$173$	8.21348	−	6.89193i	0.624459	−	0.523983i	0.899202	+	0.437534i	$0.144148\pi$
$174$		0			0
$175$	0.0667040	−	0.378297i	0.00504235	−	0.0285966i
$176$	−0.645430	+	3.66041i	−0.0486511	+	0.275914i
$177$		0			0
$178$	1.66250	−	1.39501i	0.124610	−	0.104560i
$179$	−6.92262	+	11.9903i	−0.517421	+	0.896199i	0.482374	+	0.875965i	$0.339774\pi$
$179$	−6.92262	+	11.9903i	−0.517421	+	0.896199i	−0.999795	+	0.0202340i	$0.993559\pi$
$180$		0			0
$181$	−1.75490	−	3.03958i	−0.130441	−	0.225930i	0.793406	−	0.608693i	$-0.208306\pi$
$181$	−1.75490	−	3.03958i	−0.130441	−	0.225930i	−0.923847	+	0.382763i	$0.874973\pi$
$182$	−0.687319	−	0.250164i	−0.0509475	−	0.0185434i
$183$		0			0
$184$	3.64543	+	3.05888i	0.268745	+	0.225504i
$185$	0.368241	−	0.134029i	0.0270736	−	0.00985399i
$186$		0			0
$187$	−3.33703	−	18.9252i	−0.244028	−	1.38395i
$188$	0.773318			0.0564000
$189$		0			0
$190$	7.97771			0.578764
$191$	3.80154	+	21.5596i	0.275070	+	1.56000i	0.738741	+	0.673990i	$0.235421\pi$
$191$	3.80154	+	21.5596i	0.275070	+	1.56000i	−0.463671	+	0.886007i	$0.653468\pi$
$192$		0			0
$193$	−24.0672	+	8.75973i	−1.73239	+	0.630539i	−0.998797	−	0.0490460i	$-0.984382\pi$
$193$	−24.0672	+	8.75973i	−1.73239	+	0.630539i	−0.733596	+	0.679585i	$0.762160\pi$
$194$	−2.62449	−	2.20220i	−0.188427	−	0.158109i
$195$		0			0
$196$	6.56418	+	2.38917i	0.468870	+	0.170655i
$197$	6.84255	+	11.8516i	0.487511	+	0.844395i	0.999897	−	0.0143611i	$-0.00457142\pi$
$197$	6.84255	+	11.8516i	0.487511	+	0.844395i	−0.512385	+	0.858756i	$0.671238\pi$
$198$		0			0
$199$	6.19981	−	10.7384i	0.439493	−	0.761224i	−0.558158	−	0.829735i	$-0.688492\pi$
$199$	6.19981	−	10.7384i	0.439493	−	0.761224i	0.997650	+	0.0685113i	$0.0218249\pi$
$200$	−2.43969	+	2.04715i	−0.172512	+	0.144755i
$201$		0			0
$202$	−1.49660	+	8.48762i	−0.105300	+	0.597187i
$203$	0.124485	−	0.705990i	0.00873714	−	0.0495508i
$204$		0			0
$205$	5.98680	−	5.02352i	0.418136	−	0.350858i
$206$	1.09240	−	1.89209i	0.0761109	−	0.131828i
$207$		0			0
$208$	3.03209	+	5.25173i	0.210238	+	0.364142i
$209$	−20.6814	−	7.52741i	−1.43056	−	0.520682i
$210$		0			0
$211$	11.3701	+	9.54061i	0.782747	+	0.656802i	0.943939	−	0.330121i	$-0.107089\pi$
$211$	11.3701	+	9.54061i	0.782747	+	0.656802i	−0.161192	+	0.986923i	$0.551534\pi$
$212$	−6.85117	+	2.49362i	−0.470540	+	0.171263i
$213$		0			0
$214$	1.78699	+	10.1345i	0.122156	+	0.692781i
$215$	−0.610815			−0.0416572
$216$		0			0
$217$	0.608126			0.0412823
$218$	−1.92602	−	10.9230i	−0.130447	−	0.739800i
$219$		0			0
$220$	−4.70574	+	1.71275i	−0.317261	+	0.115473i
$221$	−24.0180	−	20.1535i	−1.61563	−	1.35567i
$222$		0			0
$223$	6.32547	+	2.30228i	0.423585	+	0.154172i	0.545012	−	0.838428i	$-0.316525\pi$
$223$	6.32547	+	2.30228i	0.423585	+	0.154172i	−0.121427	+	0.992600i	$0.538747\pi$
$224$	0.0603074	+	0.104455i	0.00402946	+	0.00697922i
$225$		0			0
$226$	2.96198	−	5.13030i	0.197028	−	0.341263i
$227$	−11.1040	+	9.31737i	−0.736999	+	0.618415i	−0.932030	−	0.362382i	$-0.881964\pi$
$227$	−11.1040	+	9.31737i	−0.736999	+	0.618415i	0.195031	+	0.980797i	$0.437519\pi$
$228$		0			0
$229$	4.47787	−	25.3953i	0.295906	−	1.67817i	−0.367590	−	0.929988i	$-0.619817\pi$
$229$	4.47787	−	25.3953i	0.295906	−	1.67817i	0.663496	−	0.748180i	$-0.269072\pi$
$230$	−1.11334	+	6.31407i	−0.0734115	+	0.416337i
$231$		0			0
$232$	−4.55303	+	3.82045i	−0.298921	+	0.250825i
$233$	5.19846	−	9.00400i	0.340563	−	0.589872i	−0.643975	−	0.765047i	$-0.722716\pi$
$233$	5.19846	−	9.00400i	0.340563	−	0.589872i	0.984537	+	0.175175i	$0.0560491\pi$
$234$		0			0
$235$	0.520945	+	0.902302i	0.0339827	+	0.0588597i
$236$	−1.40033	−	0.509678i	−0.0911537	−	0.0331772i
$237$		0			0
$238$	−0.477711	−	0.400847i	−0.0309654	−	0.0259831i
$239$	−21.5326	+	7.83721i	−1.39283	+	0.506947i	−0.926041	−	0.377424i	$-0.876810\pi$
$239$	−21.5326	+	7.83721i	−1.39283	+	0.506947i	−0.466785	+	0.884371i	$0.654588\pi$
$240$		0			0
$241$	−2.09714	−	11.8935i	−0.135089	−	0.766127i	−0.974798	−	0.223090i	$-0.928385\pi$
$241$	−2.09714	−	11.8935i	−0.135089	−	0.766127i	0.839709	−	0.543037i	$-0.182726\pi$
$242$	2.81521			0.180968
$243$		0			0
$244$	−3.78106			−0.242058
$245$	1.63429	+	9.26849i	0.104411	+	0.592142i
$246$		0			0
$247$	−33.7422	+	12.2811i	−2.14696	+	0.781430i
$248$	−3.86231	−	3.24086i	−0.245257	−	0.205795i
$249$		0			0
$250$	−10.3623	−	3.77157i	−0.655370	−	0.238535i
$251$	−7.02347	−	12.1650i	−0.443318	−	0.767849i	0.554616	−	0.832107i	$-0.312865\pi$
$251$	−7.02347	−	12.1650i	−0.443318	−	0.767849i	−0.997933	+	0.0642581i	$0.979532\pi$
$252$		0			0
$253$	8.84389	−	15.3181i	0.556011	−	0.963039i
$254$	−4.39646	+	3.68907i	−0.275858	+	0.231473i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.15048	+	17.8673i	−0.196522	+	1.11453i	0.713713	+	0.700438i	$0.247012\pi$
$257$	−3.15048	+	17.8673i	−0.196522	+	1.11453i	−0.910235	+	0.414092i	$0.864099\pi$
$258$		0			0
$259$	−0.0268743	+	0.0225502i	−0.00166989	+	0.00140120i
$260$	−4.08512	+	7.07564i	−0.253349	+	0.438813i
$261$		0			0
$262$	8.60994	+	14.9128i	0.531924	+	0.921319i
$263$	4.01589	+	1.46167i	0.247631	+	0.0901301i	0.462853	−	0.886435i	$-0.346826\pi$
$263$	4.01589	+	1.46167i	0.247631	+	0.0901301i	−0.215223	+	0.976565i	$0.569048\pi$
$264$		0			0
$265$	−7.52481	−	6.31407i	−0.462246	−	0.387870i
$266$	−0.671122	+	0.244268i	−0.0411491	+	0.0149771i
$267$		0			0
$268$	−1.15270	−	6.53731i	−0.0704126	−	0.399330i
$269$	−13.0615			−0.796373			−0.398187	−	0.917304i	$-0.630360\pi$
$269$	−13.0615			−0.796373			−0.398187	+	0.917304i	$0.630360\pi$
$270$		0			0
$271$	8.48751			0.515580			0.257790	−	0.966201i	$-0.417006\pi$
$271$	8.48751			0.515580			0.257790	+	0.966201i	$0.417006\pi$
$272$	0.897804	+	5.09170i	0.0544373	+	0.308729i
$273$		0			0
$274$	0.0812519	−	0.0295733i	0.00490861	−	0.00178659i
$275$	9.06805	+	7.60900i	0.546824	+	0.458840i
$276$		0			0
$277$	−6.21466	−	2.26195i	−0.373403	−	0.135907i	0.148500	−	0.988912i	$-0.452555\pi$
$277$	−6.21466	−	2.26195i	−0.373403	−	0.135907i	−0.521903	+	0.853005i	$0.674778\pi$
$278$	9.18139	+	15.9026i	0.550663	+	0.953776i
$279$		0			0
$280$	−0.0812519	+	0.140732i	−0.00485573	+	0.00841037i
$281$	−22.7704	+	19.1066i	−1.35837	+	1.13981i	−0.381884	+	0.924210i	$0.624725\pi$
$281$	−22.7704	+	19.1066i	−1.35837	+	1.13981i	−0.976483	+	0.215595i	$0.930831\pi$
$282$		0			0
$283$	−0.488856	+	2.77244i	−0.0290595	+	0.164804i	−0.995884	−	0.0906371i	$-0.971110\pi$
$283$	−0.488856	+	2.77244i	−0.0290595	+	0.164804i	0.966825	+	0.255441i	$0.0822208\pi$
$284$	−0.997474	+	5.65695i	−0.0591892	+	0.335679i
$285$		0			0
$286$	17.2665	−	14.4883i	1.02099	−	0.856713i
$287$	−0.349823	+	0.605910i	−0.0206494	+	0.0357658i
$288$		0			0
$289$	−4.86571	−	8.42767i	−0.286219	−	0.495745i
$290$	−7.52481	−	2.73881i	−0.441872	−	0.160828i
$291$		0			0
$292$	7.98158	+	6.69734i	0.467087	+	0.391932i
$293$	9.24257	−	3.36402i	0.539957	−	0.196528i	−0.0576218	−	0.998338i	$-0.518352\pi$
$293$	9.24257	−	3.36402i	0.539957	−	0.196528i	0.597579	+	0.801810i	$0.296130\pi$
$294$		0			0
$295$	−0.348641	−	1.97724i	−0.0202986	−	0.115119i
$296$	0.290859			0.0169059
$297$		0			0
$298$	4.90167			0.283946
$299$	−5.01114	−	28.4196i	−0.289802	−	1.64355i
$300$		0			0
$301$	0.0513845	−	0.0187024i	0.00296176	−	0.00107799i
$302$	1.32635	+	1.11294i	0.0763230	+	0.0640426i
$303$		0			0
$304$	5.56418	+	2.02520i	0.319127	+	0.116153i
$305$	−2.54710	−	4.41171i	−0.145847	−	0.252614i
$306$		0			0
$307$	−6.78106	+	11.7451i	−0.387015	+	0.670330i	−0.992047	−	0.125871i	$-0.959827\pi$
$307$	−6.78106	+	11.7451i	−0.387015	+	0.670330i	0.605031	+	0.796202i	$0.293161\pi$
$308$	0.343426	−	0.288169i	0.0195685	−	0.0164199i
$309$		0			0
$310$	1.17958	−	6.68972i	0.0669955	−	0.379951i
$311$	1.83662	−	10.4160i	0.104145	−	0.590636i	−0.887413	−	0.460975i	$-0.847500\pi$
$311$	1.83662	−	10.4160i	0.104145	−	0.590636i	0.991558	−	0.129661i	$-0.0413890\pi$
$312$		0			0
$313$	−8.19640	+	6.87760i	−0.463288	+	0.388745i	−0.844339	−	0.535809i	$-0.820007\pi$
$313$	−8.19640	+	6.87760i	−0.463288	+	0.388745i	0.381051	+	0.924554i	$0.375562\pi$
$314$	2.90760	−	5.03612i	0.164086	−	0.284205i
$315$		0			0
$316$	−6.99660	−	12.1185i	−0.393589	−	0.681717i
$317$	27.4209	+	9.98038i	1.54011	+	0.560554i	0.966071	−	0.258275i	$-0.0831541\pi$
$317$	27.4209	+	9.98038i	1.54011	+	0.560554i	0.574038	+	0.818829i	$0.305376\pi$
$318$		0			0
$319$	16.9231	+	14.2002i	0.947511	+	0.795056i
$320$	1.26604	−	0.460802i	0.0707740	−	0.0257596i
$321$		0			0
$322$	−0.0996702	−	0.565258i	−0.00555440	−	0.0315006i
$323$	−30.6144			−1.70343
$324$		0			0
$325$	19.3131			1.07130
$326$	−0.470437	−	2.66798i	−0.0260551	−	0.147766i
$327$		0			0
$328$	5.45084	−	1.98394i	0.300972	−	0.109545i
$329$	−0.0714517	−	0.0599551i	−0.00393926	−	0.00330543i
$330$		0			0
$331$	6.85844	+	2.49627i	0.376974	+	0.137207i	0.523556	−	0.851991i	$-0.324605\pi$
$331$	6.85844	+	2.49627i	0.376974	+	0.137207i	−0.146582	+	0.989199i	$0.546827\pi$
$332$	−1.18479	−	2.05212i	−0.0650239	−	0.112625i
$333$		0			0
$334$	−12.3020	+	21.3077i	−0.673136	+	1.16591i
$335$	6.85117	−	5.74881i	0.374319	−	0.314091i
$336$		0			0
$337$	−0.281937	+	1.59894i	−0.0153581	+	0.0870999i	−0.991523	−	0.129928i	$-0.958525\pi$
$337$	−0.281937	+	1.59894i	−0.0153581	+	0.0870999i	0.976165	+	0.217028i	$0.0696364\pi$
$338$	4.12836	−	23.4131i	0.224553	−	1.27350i
$339$		0			0
$340$	−5.33615	+	4.47756i	−0.289393	+	0.242830i
$341$	−9.37005	+	16.2294i	−0.507417	+	0.878872i
$342$		0			0
$343$	−0.843426	−	1.46086i	−0.0455407	−	0.0788788i
$344$	−0.426022	−	0.155059i	−0.0229696	−	0.00836024i
$345$		0			0
$346$	8.21348	+	6.89193i	0.441559	+	0.370512i
$347$	−5.13903	+	1.87046i	−0.275878	+	0.100411i	−0.476254	−	0.879308i	$-0.658006\pi$
$347$	−5.13903	+	1.87046i	−0.275878	+	0.100411i	0.200376	+	0.979719i	$0.435784\pi$
$348$		0			0
$349$	0.538019	+	3.05126i	0.0287995	+	0.163330i	0.995816	−	0.0913851i	$-0.0291294\pi$
$349$	0.538019	+	3.05126i	0.0287995	+	0.163330i	−0.967016	+	0.254715i	$0.918018\pi$
$350$	0.384133			0.0205328
$351$		0			0
$352$	−3.71688			−0.198110
$353$	−0.0530334	−	0.300767i	−0.00282268	−	0.0160082i	0.983364	−	0.181647i	$-0.0581427\pi$
$353$	−0.0530334	−	0.300767i	−0.00282268	−	0.0160082i	−0.986187	+	0.165638i	$0.947032\pi$
$354$		0			0
$355$	−7.27244	+	2.64695i	−0.385981	+	0.140486i
$356$	1.66250	+	1.39501i	0.0881125	+	0.0739352i
$357$		0			0
$358$	−13.0103	−	4.73535i	−0.687614	−	0.250271i
$359$	5.28493	+	9.15377i	0.278928	+	0.483117i	0.971119	−	0.238597i	$-0.0766876\pi$
$359$	5.28493	+	9.15377i	0.278928	+	0.483117i	−0.692191	+	0.721715i	$0.743354\pi$
$360$		0			0
$361$	−8.03074	+	13.9097i	−0.422671	+	0.732087i
$362$	2.68866	−	2.25606i	0.141313	−	0.118576i
$363$		0			0
$364$	0.127011	−	0.720317i	0.00665720	−	0.0377549i
$365$	−2.43763	+	13.8245i	−0.127592	+	0.723608i
$366$		0			0
$367$	2.05303	−	1.72270i	0.107167	−	0.0899242i	−0.587629	−	0.809130i	$-0.699939\pi$
$367$	2.05303	−	1.72270i	0.107167	−	0.0899242i	0.694797	+	0.719206i	$0.255494\pi$
$368$	−2.37939	+	4.12122i	−0.124034	+	0.214833i
$369$		0			0
$370$	0.195937	+	0.339373i	0.0101863	+	0.0176431i
$371$	0.826352	+	0.300767i	0.0429020	+	0.0156151i
$372$		0			0
$373$	18.6689	+	15.6651i	0.966639	+	0.811106i	0.982020	−	0.188775i	$-0.0604518\pi$
$373$	18.6689	+	15.6651i	0.966639	+	0.811106i	−0.0153813	+	0.999882i	$0.504896\pi$
$374$	18.0582	−	6.57266i	0.933770	−	0.339864i
$375$		0			0
$376$	0.134285	+	0.761570i	0.00692524	+	0.0392750i
$377$	36.0428			1.85630
$378$		0			0
$379$	−4.08647			−0.209908			−0.104954	−	0.994477i	$-0.533469\pi$
$379$	−4.08647			−0.209908			−0.104954	+	0.994477i	$0.533469\pi$
$380$	1.38532	+	7.85651i	0.0710652	+	0.403031i
$381$		0			0
$382$	−20.5719	+	7.48757i	−1.05255	+	0.383097i
$383$	12.5556	+	10.5354i	0.641559	+	0.538332i	0.904497	−	0.426481i	$-0.140247\pi$
$383$	12.5556	+	10.5354i	0.641559	+	0.538332i	−0.262937	+	0.964813i	$0.584691\pi$
$384$		0			0
$385$	0.567581	+	0.206583i	0.0289266	+	0.0105284i
$386$	−12.8059	−	22.1804i	−0.651802	−	1.12895i
$387$		0			0
$388$	1.71301	−	2.96702i	0.0869650	−	0.150628i
$389$	21.3799	−	17.9398i	1.08400	−	0.909585i	0.0877546	−	0.996142i	$-0.472031\pi$
$389$	21.3799	−	17.9398i	1.08400	−	0.909585i	0.996247	+	0.0865568i	$0.0275864\pi$
$390$		0			0
$391$	4.27244	−	24.2302i	0.216067	−	1.22537i
$392$	−1.21301	+	6.87933i	−0.0612663	+	0.347459i
$393$		0			0
$394$	−10.4834	+	8.79661i	−0.528146	+	0.443167i
$395$	9.42649	−	16.3272i	0.474298	−	0.821508i
$396$		0			0
$397$	16.2469	+	28.1405i	0.815409	+	1.41233i	0.909034	+	0.416722i	$0.136821\pi$
$397$	16.2469	+	28.1405i	0.815409	+	1.41233i	−0.0936247	+	0.995608i	$0.529845\pi$
$398$	11.6518	+	4.24092i	0.584053	+	0.212578i
$399$		0			0
$400$	−2.43969	−	2.04715i	−0.121985	−	0.102357i
$401$	14.4538	−	5.26076i	0.721790	−	0.262710i	0.0451044	−	0.998982i	$-0.485638\pi$
$401$	14.4538	−	5.26076i	0.721790	−	0.262710i	0.676685	+	0.736272i	$0.263416\pi$
$402$		0			0
$403$	5.30928	+	30.1104i	0.264474	+	1.49991i
$404$	−8.61856			−0.428789
$405$		0			0
$406$	0.716881			0.0355782
$407$	−0.187729	−	1.06467i	−0.00930539	−	0.0527735i
$408$		0			0
$409$	8.97343	−	3.26606i	0.443708	−	0.161496i	−0.110498	−	0.993876i	$-0.535244\pi$
$409$	8.97343	−	3.26606i	0.443708	−	0.161496i	0.554205	+	0.832380i	$0.313022\pi$
$410$	5.98680	+	5.02352i	0.295667	+	0.248094i
$411$		0			0
$412$	2.05303	+	0.747243i	0.101146	+	0.0368140i
$413$	0.0898700	+	0.155659i	0.00442222	+	0.00765950i
$414$		0			0
$415$	1.59627	−	2.76481i	0.0783576	−	0.135719i
$416$	−4.64543	+	3.89798i	−0.227761	+	0.191114i
$417$		0			0
$418$	3.82177	−	21.6743i	0.186929	−	1.06013i
$419$	5.89915	−	33.4557i	0.288192	−	1.63442i	−0.405463	−	0.914112i	$-0.632890\pi$
$419$	5.89915	−	33.4557i	0.288192	−	1.63442i	0.693655	−	0.720308i	$-0.255999\pi$
$420$		0			0
$421$	−9.63816	+	8.08737i	−0.469735	+	0.394154i	−0.846698	−	0.532074i	$-0.821413\pi$
$421$	−9.63816	+	8.08737i	−0.469735	+	0.394154i	0.376963	+	0.926228i	$0.376968\pi$
$422$	−7.42127	+	12.8540i	−0.361262	+	0.625724i
$423$		0			0
$424$	−3.64543	−	6.31407i	−0.177038	−	0.306638i
$425$	15.4731	+	5.63176i	0.750557	+	0.273180i
$426$		0			0
$427$	0.349356	+	0.293144i	0.0169065	+	0.0141862i
$428$	−9.67024	+	3.51968i	−0.467429	+	0.170130i
$429$		0			0
$430$	−0.106067	−	0.601535i	−0.00511500	−	0.0290086i
$431$	7.77601			0.374557			0.187279	−	0.982307i	$-0.440033\pi$
$431$	7.77601			0.374557			0.187279	+	0.982307i	$0.440033\pi$
$432$		0			0
$433$	−40.6536			−1.95369			−0.976845	−	0.213950i	$-0.931367\pi$
$433$	−40.6536			−1.95369			−0.976845	+	0.213950i	$0.931367\pi$
$434$	0.105600	+	0.598887i	0.00506896	+	0.0287475i
$435$		0			0
$436$	10.4226	−	3.79352i	0.499153	−	0.181677i
$437$	−21.5856	−	18.1125i	−1.03258	−	0.866436i
$438$		0			0
$439$	16.6284	+	6.05223i	0.793628	+	0.288857i	0.706843	−	0.707370i	$-0.250119\pi$
$439$	16.6284	+	6.05223i	0.793628	+	0.288857i	0.0867847	+	0.996227i	$0.472341\pi$
$440$	−2.50387	−	4.33683i	−0.119367	−	0.206750i
$441$		0			0
$442$	15.6766	−	27.1527i	0.745662	−	1.29152i
$443$	−11.0123	+	9.24044i	−0.523211	+	0.439027i	−0.865750	−	0.500477i	$-0.833158\pi$
$443$	−11.0123	+	9.24044i	−0.523211	+	0.439027i	0.342538	+	0.939504i	$0.388713\pi$
$444$		0			0
$445$	−0.507741	+	2.87954i	−0.0240692	+	0.136503i
$446$	−1.16890	+	6.62916i	−0.0553490	+	0.313900i
$447$		0			0
$448$	−0.0923963	+	0.0775297i	−0.00436531	+	0.00366293i
$449$	13.9859	−	24.2243i	0.660036	−	1.14322i	−0.320569	−	0.947225i	$-0.603874\pi$
$449$	13.9859	−	24.2243i	0.660036	−	1.14322i	0.980606	−	0.195991i	$-0.0627925\pi$
$450$		0			0
$451$	−10.7802	−	18.6718i	−0.507619	−	0.879222i
$452$	5.56670	+	2.02611i	0.261836	+	0.0953004i
$453$		0			0
$454$	−11.1040	−	9.31737i	−0.521137	−	0.437286i
$455$	0.926022	−	0.337044i	0.0434126	−	0.0158009i
$456$		0			0
$457$	1.48087	+	8.39841i	0.0692720	+	0.392861i	0.999655	+	0.0262717i	$0.00836350\pi$
$457$	1.48087	+	8.39841i	0.0692720	+	0.392861i	−0.930383	+	0.366589i	$0.880525\pi$
$458$	25.7870			1.20495
$459$		0			0
$460$	−6.41147			−0.298937
$461$	−3.77110	−	21.3870i	−0.175637	−	0.996090i	−0.937405	−	0.348240i	$-0.886779\pi$
$461$	−3.77110	−	21.3870i	−0.175637	−	0.996090i	0.761768	−	0.647850i	$-0.224332\pi$
$462$		0			0
$463$	18.6091	−	6.77314i	0.864836	−	0.314775i	0.128762	−	0.991676i	$-0.458900\pi$
$463$	18.6091	−	6.77314i	0.864836	−	0.314775i	0.736074	+	0.676901i	$0.236677\pi$
$464$	−4.55303	−	3.82045i	−0.211369	−	0.177360i
$465$		0			0
$466$	9.76991	+	3.55596i	0.452583	+	0.164727i
$467$	18.4927	+	32.0303i	0.855741	+	1.48219i	0.875956	+	0.482392i	$0.160232\pi$
$467$	18.4927	+	32.0303i	0.855741	+	1.48219i	−0.0202143	+	0.999796i	$0.506435\pi$
$468$		0			0
$469$	−0.400330	+	0.693392i	−0.0184855	+	0.0320178i
$470$	−0.798133	+	0.669713i	−0.0368151	+	0.0308916i
$471$		0			0
$472$	0.258770	−	1.46756i	0.0119109	−	0.0675499i
$473$	−0.292614	+	1.65950i	−0.0134544	+	0.0763037i
$474$		0			0
$475$	14.4461	−	12.1217i	0.662832	−	0.556182i
$476$	0.311804	−	0.540060i	0.0142915	−	0.0247536i
$477$		0			0
$478$	−11.4572	−	19.8445i	−0.524042	−	0.907667i
$479$	−10.6677	−	3.88273i	−0.487420	−	0.177407i	0.0866070	−	0.996243i	$-0.472398\pi$
$479$	−10.6677	−	3.88273i	−0.487420	−	0.177407i	−0.574028	+	0.818836i	$0.694620\pi$
$480$		0			0
$481$	−1.35117	−	1.13376i	−0.0616079	−	0.0516952i
$482$	11.3486	−	4.13057i	0.516916	−	0.188142i
$483$		0			0
$484$	0.488856	+	2.77244i	0.0222207	+	0.126020i
$485$	4.61587			0.209596
$486$		0			0
$487$	1.13785			0.0515610			0.0257805	−	0.999668i	$-0.491793\pi$
$487$	1.13785			0.0515610			0.0257805	+	0.999668i	$0.491793\pi$
$488$	−0.656574	−	3.72362i	−0.0297217	−	0.168560i
$489$		0			0
$490$	−8.84389	+	3.21891i	−0.399526	+	0.145416i
$491$	11.7292	+	9.84197i	0.529332	+	0.444162i	0.867871	−	0.496790i	$-0.165488\pi$
$491$	11.7292	+	9.84197i	0.529332	+	0.444162i	−0.338539	+	0.940952i	$0.609933\pi$
$492$		0			0
$493$	28.8764	+	10.5102i	1.30053	+	0.473354i
$494$	−17.9538	−	31.0969i	−0.807781	−	1.39912i
$495$		0			0
$496$	2.52094	−	4.36640i	0.113194	−	0.196057i
$497$	0.530745	−	0.445348i	0.0238072	−	0.0199766i
$498$		0			0
$499$	0.402551	−	2.28298i	0.0180207	−	0.102200i	−0.974471	−	0.224514i	$-0.927920\pi$
$499$	0.402551	−	2.28298i	0.0180207	−	0.102200i	0.992491	+	0.122314i	$0.0390315\pi$
$500$	1.91488	−	10.8598i	0.0856359	−	0.485666i
$501$		0			0
$502$	10.7606	−	9.02920i	0.480268	−	0.402993i
$503$	4.02869	−	6.97789i	0.179630	−	0.311129i	−0.762124	−	0.647431i	$-0.775843\pi$
$503$	4.02869	−	6.97789i	0.179630	−	0.311129i	0.941754	+	0.336303i	$0.109177\pi$
$504$		0			0
$505$	−5.80587	−	10.0561i	−0.258358	−	0.447489i
$506$	16.6211	+	6.04958i	0.738897	+	0.268937i
$507$		0			0
$508$	−4.39646	−	3.68907i	−0.195061	−	0.163676i
$509$	6.76130	−	2.46091i	0.299689	−	0.109078i	−0.187799	−	0.982207i	$-0.560135\pi$
$509$	6.76130	−	2.46091i	0.299689	−	0.109078i	0.487488	+	0.873130i	$0.337913\pi$
$510$		0			0
$511$	−0.218226	−	1.23762i	−0.00965373	−	0.0547490i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.1429			−0.800249
$515$	0.511144	+	2.89884i	0.0225237	+	0.127738i
$516$		0			0
$517$	2.70099	−	0.983080i	0.118789	−	0.0432358i
$518$	−0.0268743	−	0.0225502i	−0.00118079	−	0.000990800i
$519$		0			0
$520$	−7.67752	−	2.79439i	−0.336681	−	0.122542i
$521$	4.84343	+	8.38906i	0.212194	+	0.367531i	0.952401	−	0.304848i	$-0.0986057\pi$
$521$	4.84343	+	8.38906i	0.212194	+	0.367531i	−0.740207	+	0.672379i	$0.765272\pi$
$522$		0			0
$523$	−7.29339	+	12.6325i	−0.318917	+	0.552381i	−0.980262	−	0.197701i	$-0.936653\pi$
$523$	−7.29339	+	12.6325i	−0.318917	+	0.552381i	0.661345	+	0.750082i	$0.269986\pi$
$524$	−13.1912	+	11.0687i	−0.576260	+	0.483539i
$525$		0			0
$526$	−0.742107	+	4.20870i	−0.0323574	+	0.183508i
$527$	−4.52663	+	25.6718i	−0.197183	+	1.11828i
$528$		0			0
$529$	−0.271259	+	0.227613i	−0.0117939	+	0.00989623i
$530$	4.91147	−	8.50692i	0.213341	−	0.369517i
$531$		0			0
$532$	−0.357097	−	0.618509i	−0.0154821	−	0.0268158i
$533$	−33.0548	−	12.0310i	−1.43176	−	0.521120i
$534$		0			0
$535$	−10.6211	−	8.91215i	−0.459189	−	0.385306i
$536$	6.23783	−	2.27038i	0.269433	−	0.0980656i
$537$		0			0
$538$	−2.26810	−	12.8631i	−0.0977849	−	0.554566i
$539$	25.9641			1.11835
$540$		0			0
$541$	23.9786			1.03092			0.515461	−	0.856913i	$-0.327621\pi$
$541$	23.9786			1.03092			0.515461	+	0.856913i	$0.327621\pi$
$542$	1.47384	+	8.35857i	0.0633069	+	0.359031i
$543$		0			0
$544$	−4.85844	+	1.76833i	−0.208304	+	0.0758164i
$545$	11.4474	+	9.60554i	0.490354	+	0.411456i
$546$		0			0
$547$	−37.5702	−	13.6744i	−1.60638	−	0.584676i	−0.625664	−	0.780093i	$-0.715172\pi$
$547$	−37.5702	−	13.6744i	−1.60638	−	0.584676i	−0.980720	+	0.195417i	$0.937394\pi$
$548$	0.0432332	+	0.0748822i	0.00184683	+	0.00319881i
$549$		0			0
$550$	−5.91875	+	10.2516i	−0.252376	+	0.437129i
$551$	26.9598	−	22.6219i	1.14852	−	0.963726i
$552$		0			0
$553$	−0.293081	+	1.66214i	−0.0124631	+	0.0706816i
$554$	1.14842	−	6.51303i	0.0487918	−	0.276712i
$555$		0			0
$556$	−14.0667	+	11.8034i	−0.596561	+	0.500574i
$557$	1.17958	−	2.04309i	0.0499803	−	0.0865685i	−0.839953	−	0.542659i	$-0.817417\pi$
$557$	1.17958	−	2.04309i	0.0499803	−	0.0865685i	0.889933	+	0.456091i	$0.150751\pi$
$558$		0			0
$559$	1.37464	+	2.38094i	0.0581410	+	0.100703i
$560$	−0.152704	−	0.0555796i	−0.00645291	−	0.00234867i
$561$		0			0
$562$	−22.7704	−	19.1066i	−0.960511	−	0.805964i
$563$	−40.9013	+	14.8868i	−1.72378	+	0.627406i	−0.998157	−	0.0606840i	$-0.980672\pi$
$563$	−40.9013	+	14.8868i	−1.72378	+	0.627406i	−0.725626	+	0.688090i	$0.758450\pi$
$564$		0			0
$565$	1.38594	+	7.86008i	0.0583071	+	0.330676i
$566$	−2.81521			−0.118332
$567$		0			0
$568$	−5.74422			−0.241022
$569$	−2.54307	−	14.4225i	−0.106611	−	0.604622i	−0.990565	−	0.137047i	$-0.956239\pi$
$569$	−2.54307	−	14.4225i	−0.106611	−	0.604622i	0.883954	−	0.467575i	$-0.154872\pi$
$570$		0			0
$571$	13.9153	−	5.06477i	0.582339	−	0.211954i	−0.0340176	−	0.999421i	$-0.510830\pi$
$571$	13.9153	−	5.06477i	0.582339	−	0.211954i	0.616357	+	0.787467i	$0.288608\pi$
$572$	17.2665	+	14.4883i	0.721949	+	0.605787i
$573$		0			0
$574$	−0.657451	−	0.239293i	−0.0274415	−	0.00998789i
$575$	7.57785	+	13.1252i	0.316018	+	0.547359i
$576$		0			0
$577$	16.0706	−	27.8351i	0.669027	−	1.15879i	−0.309150	−	0.951013i	$-0.600044\pi$
$577$	16.0706	−	27.8351i	0.669027	−	1.15879i	0.978177	−	0.207775i	$-0.0666222\pi$
$578$	7.45471	−	6.25524i	0.310075	−	0.260184i
$579$		0			0
$580$	1.39053	−	7.88609i	0.0577386	−	0.327452i
$581$	−0.0496299	+	0.281465i	−0.00205899	+	0.0116771i
$582$		0			0
$583$	−20.7592	+	17.4191i	−0.859760	+	0.721424i
$584$	−5.20961	+	9.02330i	−0.215575	+	0.373387i
$585$		0			0
$586$	4.91787	+	8.51800i	0.203155	+	0.351875i
$587$	25.7542	+	9.37376i	1.06299	+	0.386896i	0.813550	−	0.581494i	$-0.197532\pi$
$587$	25.7542	+	9.37376i	1.06299	+	0.386896i	0.249438	+	0.968391i	$0.419754\pi$
$588$		0			0
$589$	22.8698	+	19.1900i	0.942334	+	0.790712i
$590$	1.88666	−	0.686688i	0.0776725	−	0.0282705i
$591$		0			0
$592$	0.0505072	+	0.286441i	0.00207583	+	0.0117726i
$593$	−36.2377			−1.48810			−0.744052	−	0.668121i	$-0.767099\pi$
$593$	−36.2377			−1.48810			−0.744052	+	0.668121i	$0.767099\pi$
$594$		0			0
$595$	0.840185			0.0344442
$596$	0.851167	+	4.82721i	0.0348651	+	0.197730i
$597$		0			0
$598$	27.1177	−	9.87003i	1.10892	−	0.403615i
$599$	−35.2527	−	29.5805i	−1.44039	−	1.20863i	−0.939239	−	0.343264i	$-0.888467\pi$
$599$	−35.2527	−	29.5805i	−1.44039	−	1.20863i	−0.501147	−	0.865362i	$-0.667088\pi$
$600$		0			0
$601$	−1.59462	−	0.580393i	−0.0650458	−	0.0236747i	0.309292	−	0.950967i	$-0.399908\pi$
$601$	−1.59462	−	0.580393i	−0.0650458	−	0.0236747i	−0.374338	+	0.927292i	$0.622130\pi$
$602$	0.0273411	+	0.0473563i	0.00111434	+	0.00193010i
$603$		0			0
$604$	−0.865715	+	1.49946i	−0.0352254	+	0.0610122i
$605$	−2.90554	+	2.43804i	−0.118127	+	0.0991205i
$606$		0			0
$607$	−2.44315	+	13.8558i	−0.0991645	+	0.562390i	0.894227	+	0.447614i	$0.147726\pi$
$607$	−2.44315	+	13.8558i	−0.0991645	+	0.562390i	−0.993391	+	0.114776i	$0.963385\pi$
$608$	−1.02822	+	5.83132i	−0.0416998	+	0.236491i
$609$		0			0
$610$	3.90239	−	3.27449i	0.158003	−	0.132580i
$611$	2.34477	−	4.06126i	0.0948592	−	0.164301i
$612$		0			0
$613$	12.8314	+	22.2246i	0.518256	+	0.897645i	0.999775	+	0.0212096i	$0.00675172\pi$
$613$	12.8314	+	22.2246i	0.518256	+	0.897645i	−0.481520	+	0.876435i	$0.659915\pi$
$614$	−12.7442	−	4.63852i	−0.514315	−	0.187195i
$615$		0			0
$616$	0.343426	+	0.288169i	0.0138370	+	0.0116106i
$617$	29.5911	−	10.7703i	1.19129	−	0.433595i	0.331116	−	0.943590i	$-0.392575\pi$
$617$	29.5911	−	10.7703i	1.19129	−	0.433595i	0.860177	+	0.509995i	$0.170353\pi$
$618$		0			0
$619$	−0.550097	−	3.11975i	−0.0221103	−	0.125393i	0.971755	−	0.235993i	$-0.0758341\pi$
$619$	−0.550097	−	3.11975i	−0.0221103	−	0.125393i	−0.993865	+	0.110599i	$0.964723\pi$
$620$	6.79292			0.272810
$621$		0			0
$622$	10.5767			0.424086
$623$	−0.0454548	−	0.257787i	−0.00182111	−	0.0103280i
$624$		0			0
$625$	−1.00253	+	0.364890i	−0.0401010	+	0.0145956i
$626$	−8.19640	−	6.87760i	−0.327594	−	0.274884i
$627$		0			0
$628$	5.46451	+	1.98892i	0.218058	+	0.0793665i
$629$	−0.751907	−	1.30234i	−0.0299805	−	0.0519277i
$630$		0			0
$631$	−11.2961	+	19.5654i	−0.449690	+	0.778885i	−0.998366	−	0.0571498i	$-0.981799\pi$
$631$	−11.2961	+	19.5654i	−0.449690	+	0.778885i	0.548676	+	0.836035i	$0.315132\pi$
$632$	10.7194	−	8.99465i	0.426395	−	0.357788i
$633$		0			0
$634$	−5.06717	+	28.7374i	−0.201243	+	1.14131i
$635$	1.34271	−	7.61489i	0.0532839	−	0.302188i
$636$		0			0
$637$	32.4504	−	27.2291i	1.28573	−	1.07886i
$638$	−11.0458	+	19.1318i	−0.437306	+	0.757436i
$639$		0			0
$640$	0.673648	+	1.16679i	0.0266283	+	0.0461215i
$641$	−16.4684	−	5.99400i	−0.650462	−	0.236749i	−0.00434887	−	0.999991i	$-0.501384\pi$
$641$	−16.4684	−	5.99400i	−0.650462	−	0.236749i	−0.646113	+	0.763242i	$0.723607\pi$
$642$		0			0
$643$	−21.5967	−	18.1218i	−0.851692	−	0.714654i	0.108470	−	0.994100i	$-0.465405\pi$
$643$	−21.5967	−	18.1218i	−0.851692	−	0.714654i	−0.960162	+	0.279445i	$0.909849\pi$
$644$	0.539363	−	0.196312i	0.0212539	−	0.00773578i
$645$		0			0
$646$	−5.31614	−	30.1493i	−0.209161	−	1.18621i
$647$	−32.3492			−1.27178			−0.635888	−	0.771781i	$-0.719366\pi$
$647$	−32.3492			−1.27178			−0.635888	+	0.771781i	$0.719366\pi$
$648$		0			0
$649$	−5.53890			−0.217421
$650$	3.35369	+	19.0197i	0.131543	+	0.746016i
$651$		0			0
$652$	2.54576	−	0.926581i	0.0996996	−	0.0362877i
$653$	21.1407	+	17.7391i	0.827299	+	0.694186i	0.954669	−	0.297669i	$-0.0962092\pi$
$653$	21.1407	+	17.7391i	0.827299	+	0.694186i	−0.127370	+	0.991855i	$0.540654\pi$
$654$		0			0
$655$	−21.8011	−	7.93496i	−0.851840	−	0.310045i
$656$	2.90033	+	5.02352i	0.113239	+	0.196135i
$657$		0			0
$658$	0.0466368	−	0.0807773i	0.00181809	−	0.00314903i
$659$	3.99866	−	3.35527i	0.155766	−	0.130703i	−0.561574	−	0.827426i	$-0.689804\pi$
$659$	3.99866	−	3.35527i	0.155766	−	0.130703i	0.717340	+	0.696724i	$0.245360\pi$
$660$		0			0
$661$	−8.32588	+	47.2184i	−0.323839	+	1.83658i	0.193869	+	0.981027i	$0.437896\pi$
$661$	−8.32588	+	47.2184i	−0.323839	+	1.83658i	−0.517709	+	0.855557i	$0.673215\pi$
$662$	−1.26739	+	7.18772i	−0.0492585	+	0.279359i
$663$		0			0
$664$	1.81521	−	1.52314i	0.0704437	−	0.0591093i
$665$	0.481115	−	0.833315i	0.0186568	−	0.0323146i
$666$		0			0
$667$	14.1420	+	24.4947i	0.547581	+	0.948439i
$668$	−23.1202	−	8.41507i	−0.894548	−	0.325589i
$669$		0			0
$670$	6.85117	+	5.74881i	0.264684	+	0.222096i
$671$	−13.2062	+	4.80667i	−0.509820	+	0.185559i
$672$		0			0
$673$	−1.93124	−	10.9526i	−0.0744437	−	0.422191i	−0.999139	−	0.0414836i	$-0.986792\pi$
$673$	−1.93124	−	10.9526i	−0.0744437	−	0.422191i	0.924695	−	0.380708i	$-0.124320\pi$
$674$	−1.62361			−0.0625390
$675$		0			0
$676$	23.7743			0.914394
$677$	8.37702	+	47.5084i	0.321955	+	1.82590i	0.530261	+	0.847834i	$0.322094\pi$
$677$	8.37702	+	47.5084i	0.321955	+	1.82590i	−0.208306	+	0.978064i	$0.566795\pi$
$678$		0			0
$679$	−0.388308	+	0.141333i	−0.0149019	+	0.00542385i
$680$	−5.33615	−	4.47756i	−0.204632	−	0.171707i
$681$		0			0
$682$	−17.6099	−	6.40949i	−0.674319	−	0.245432i
$683$	6.60401	+	11.4385i	0.252695	+	0.437681i	0.964267	−	0.264932i	$-0.0853496\pi$
$683$	6.60401	+	11.4385i	0.252695	+	0.437681i	−0.711572	+	0.702614i	$0.752016\pi$
$684$		0			0
$685$	−0.0582480	+	0.100888i	−0.00222554	+	0.00385475i
$686$	1.29220	−	1.08429i	0.0493366	−	0.0413983i
$687$		0			0
$688$	0.0787257	−	0.446476i	0.00300139	−	0.0170217i
$689$	−7.67752	+	43.5414i	−0.292490	+	1.65879i
$690$		0			0
$691$	−7.64022	+	6.41090i	−0.290647	+	0.243882i	−0.776439	−	0.630193i	$-0.782976\pi$
$691$	−7.64022	+	6.41090i	−0.290647	+	0.243882i	0.485791	+	0.874075i	$0.338531\pi$
$692$	−5.36097	+	9.28547i	−0.203793	+	0.352980i
$693$		0			0
$694$	−2.73442	−	4.73616i	−0.103797	−	0.179782i
$695$	−23.2481	−	8.46161i	−0.881850	−	0.320967i
$696$		0			0
$697$	−22.9743	−	19.2777i	−0.870214	−	0.730196i
$698$	−2.91147	+	1.05969i	−0.110201	+	0.0401099i
$699$		0			0
$700$	0.0667040	+	0.378297i	0.00252117	+	0.0142983i
$701$	−46.7588			−1.76605			−0.883027	−	0.469322i	$-0.844498\pi$
$701$	−46.7588			−1.76605			−0.883027	+	0.469322i	$0.844498\pi$
$702$		0			0
$703$	−1.72226			−0.0649562
$704$	−0.645430	−	3.66041i	−0.0243255	−	0.137957i
$705$		0			0
$706$	0.286989	−	0.104455i	0.0108010	−	0.00393123i
$707$	0.796322	+	0.668194i	0.0299488	+	0.0251300i
$708$		0			0
$709$	35.5483	+	12.9385i	1.33505	+	0.485917i	0.908249	−	0.418430i	$-0.137420\pi$
$709$	35.5483	+	12.9385i	1.33505	+	0.485917i	0.426797	+	0.904347i	$0.359642\pi$
$710$	−3.86959	−	6.70232i	−0.145223	−	0.251534i
$711$		0			0
$712$	−1.08512	+	1.87949i	−0.0406667	+	0.0704368i
$713$	−18.3799	+	15.4225i	−0.688331	+	0.577578i
$714$		0			0
$715$	−5.27332	+	29.9065i	−0.197211	+	1.11844i
$716$	2.40420	−	13.6349i	0.0898492	−	0.509560i
$717$		0			0
$718$	−8.09698	+	6.79417i	−0.302177	+	0.253556i
$719$	1.65048	−	2.85872i	0.0615526	−	0.106612i	−0.833607	−	0.552358i	$-0.813728\pi$
$719$	1.65048	−	2.85872i	0.0615526	−	0.106612i	0.895160	+	0.445746i	$0.147061\pi$
$720$		0			0
$721$	−0.131759	−	0.228213i	−0.00490697	−	0.00849911i
$722$	−15.0929	−	5.49335i	−0.561698	−	0.204441i
$723$		0			0
$724$	2.68866	+	2.25606i	0.0999234	+	0.0838457i
$725$	−17.7875	+	6.47410i	−0.660610	+	0.240442i
$726$		0			0
$727$	−3.63934	−	20.6397i	−0.134976	−	0.765484i	−0.974877	−	0.222745i	$-0.928498\pi$
$727$	−3.63934	−	20.6397i	−0.134976	−	0.765484i	0.839901	−	0.542739i	$-0.182613\pi$
$728$	0.731429			0.0271086
$729$		0			0
$730$	−14.0378			−0.519561
$731$	0.407031	+	2.30839i	0.0150546	+	0.0853788i
$732$		0			0
$733$	16.8807	−	6.14408i	0.623504	−	0.226937i	−0.0108975	−	0.999941i	$-0.503469\pi$
$733$	16.8807	−	6.14408i	0.623504	−	0.226937i	0.634401	+	0.773004i	$0.281247\pi$
$734$	2.05303	+	1.72270i	0.0757788	+	0.0635860i
$735$		0			0
$736$	−4.47178	−	1.62760i	−0.164832	−	0.0599940i
$737$	−12.3366	−	21.3677i	−0.454425	−	0.787088i
$738$		0			0
$739$	19.6630	−	34.0573i	0.723314	−	1.25282i	−0.236350	−	0.971668i	$-0.575951\pi$
$739$	19.6630	−	34.0573i	0.723314	−	1.25282i	0.959664	−	0.281149i	$-0.0907154\pi$
$740$	−0.300193	+	0.251892i	−0.0110353	+	0.00925972i
$741$		0			0
$742$	−0.152704	+	0.866025i	−0.00560593	+	0.0317928i
$743$	8.11422	−	46.0180i	0.297682	−	1.68824i	−0.358416	−	0.933562i	$-0.616683\pi$
$743$	8.11422	−	46.0180i	0.297682	−	1.68824i	0.656098	−	0.754676i	$-0.272206\pi$
$744$		0			0
$745$	−5.05896	+	4.24497i	−0.185346	+	0.155524i
$746$	−12.1853	+	21.1055i	−0.446134	+	0.772727i
$747$		0			0
$748$	9.60859	+	16.6426i	0.351325	+	0.608513i
$749$	1.16637	+	0.424525i	0.0426184	+	0.0155118i
$750$		0			0
$751$	−25.5310	−	21.4230i	−0.931638	−	0.781737i	0.0444727	−	0.999011i	$-0.485839\pi$
$751$	−25.5310	−	21.4230i	−0.931638	−	0.781737i	−0.976111	+	0.217273i	$0.930284\pi$
$752$	−0.726682	+	0.264490i	−0.0264994	+	0.00964498i
$753$		0			0
$754$	6.25877	+	35.4953i	0.227931	+	1.29266i
$755$	−2.33275			−0.0848974
$756$		0			0
$757$	32.3354			1.17525			0.587626	−	0.809133i	$-0.300063\pi$
$757$	32.3354			1.17525			0.587626	+	0.809133i	$0.300063\pi$
$758$	−0.709607	−	4.02438i	−0.0257741	−	0.146172i
$759$		0			0
$760$	−7.49660	+	2.72854i	−0.271930	+	0.0989745i
$761$	−1.47977	−	1.24168i	−0.0536416	−	0.0450107i	0.615573	−	0.788080i	$-0.288925\pi$
$761$	−1.47977	−	1.24168i	−0.0536416	−	0.0450107i	−0.669214	+	0.743069i	$0.733369\pi$
$762$		0			0
$763$	−1.25712	−	0.457555i	−0.0455109	−	0.0165646i
$764$	−10.9461	−	18.9592i	−0.396016	−	0.685919i
$765$		0			0
$766$	−8.19506	+	14.1943i	−0.296100	+	0.512859i
$767$	−6.92262	+	5.80877i	−0.249961	+	0.209742i
$768$		0			0
$769$	−0.830060	+	4.70750i	−0.0299327	+	0.169757i	−0.996110	−	0.0881235i	$-0.971913\pi$
$769$	−0.830060	+	4.70750i	−0.0299327	+	0.169757i	0.966177	+	0.257880i	$0.0830241\pi$
$770$	−0.104885	+	0.594831i	−0.00377979	+	0.0214362i
$771$		0			0
$772$	19.6197	−	16.4629i	0.706130	−	0.592513i
$773$	−2.95336	+	5.11538i	−0.106225	+	0.183987i	−0.914238	−	0.405177i	$-0.867210\pi$
$773$	−2.95336	+	5.11538i	−0.106225	+	0.183987i	0.808013	+	0.589165i	$0.200543\pi$
$774$		0			0
$775$	−8.02869	−	13.9061i	−0.288399	−	0.499522i
$776$	3.21941	+	1.17177i	0.115570	+	0.0420640i
$777$		0			0
$778$	21.3799	+	17.9398i	0.766505	+	0.643174i
$779$	−32.2759	+	11.7475i	−1.15640	+	0.420897i
$780$		0			0
$781$	3.70749	+	21.0262i	0.132664	+	0.752378i
$782$	24.6040			0.879838
$783$		0			0
$784$	−6.98545			−0.249480
$785$	1.36050	+	7.71578i	0.0485583	+	0.275388i
$786$		0			0
$787$	−12.4042	+	4.51476i	−0.442162	+	0.160934i	−0.553501	−	0.832849i	$-0.686708\pi$
$787$	−12.4042	+	4.51476i	−0.442162	+	0.160934i	0.111339	+	0.993783i	$0.464486\pi$
$788$	−10.4834	−	8.79661i	−0.373455	−	0.313366i
$789$		0			0
$790$	17.7160	+	6.44810i	0.630307	+	0.229413i
$791$	−0.357259	−	0.618790i	−0.0127027	−	0.0220016i
$792$		0			0
$793$	−11.4645	+	19.8571i	−0.407117	+	0.705147i
$794$	−24.8917	+	20.8866i	−0.883374	+	0.741239i
$795$		0			0
$796$	−2.15317	+	12.2112i	−0.0763171	+	0.432816i
$797$	−1.55721	+	8.83137i	−0.0551592	+	0.312823i	−0.999887	−	0.0150325i	$-0.995215\pi$
$797$	−1.55721	+	8.83137i	−0.0551592	+	0.312823i	0.944728	+	0.327856i	$0.106326\pi$
$798$		0			0
$799$	3.06283	−	2.57002i	0.108355	−	0.0909209i
$800$	1.59240	−	2.75811i	0.0562997	−	0.0975140i
$801$		0			0
$802$	7.69072	+	13.3207i	0.271569	+	0.470371i
$803$	36.3915	+	13.2454i	1.28423	+	0.467420i
$804$		0			0
$805$	0.592396	+	0.497079i	0.0208792	+	0.0175197i
$806$	−28.7310	+	10.4572i	−1.01201	+	0.368340i
$807$		0			0
$808$	−1.49660	−	8.48762i	−0.0526501	−	0.298593i
$809$	−14.9804			−0.526683			−0.263341	−	0.964703i	$-0.584825\pi$
$809$	−14.9804			−0.526683			−0.263341	+	0.964703i	$0.584825\pi$
$810$		0			0
$811$	41.7529			1.46614			0.733071	−	0.680152i	$-0.238086\pi$
$811$	41.7529			1.46614			0.733071	+	0.680152i	$0.238086\pi$
$812$	0.124485	+	0.705990i	0.00436857	+	0.0247754i
$813$		0			0
$814$	1.01589	−	0.369754i	0.0356070	−	0.0129599i
$815$	2.79607	+	2.34618i	0.0979422	+	0.0821833i
$816$		0			0
$817$	2.52259	+	0.918149i	0.0882544	+	0.0321220i
$818$	4.77466	+	8.26996i	0.166942	+	0.289152i
$819$		0			0
$820$	−3.90760	+	6.76817i	−0.136459	+	0.236355i
$821$	−5.98957	+	5.02585i	−0.209037	+	0.175403i	−0.741295	−	0.671179i	$-0.765788\pi$
$821$	−5.98957	+	5.02585i	−0.209037	+	0.175403i	0.532258	+	0.846582i	$0.321344\pi$
$822$		0			0
$823$	−2.37211	+	13.4529i	−0.0826866	+	0.468939i	0.915145	+	0.403124i	$0.132076\pi$
$823$	−2.37211	+	13.4529i	−0.0826866	+	0.468939i	−0.997832	+	0.0658148i	$0.979035\pi$
$824$	−0.379385	+	2.15160i	−0.0132165	+	0.0749546i
$825$		0			0
$826$	−0.137689	+	0.115535i	−0.00479081	+	0.00401997i
$827$	−10.0679	+	17.4381i	−0.350095	+	0.606382i	−0.986266	−	0.165166i	$-0.947184\pi$
$827$	−10.0679	+	17.4381i	−0.350095	+	0.606382i	0.636171	+	0.771548i	$0.280517\pi$
$828$		0			0
$829$	−20.9491	−	36.2849i	−0.727592	−	1.26023i	−0.957898	−	0.287108i	$-0.907306\pi$
$829$	−20.9491	−	36.2849i	−0.727592	−	1.26023i	0.230307	−	0.973118i	$-0.426027\pi$
$830$	3.00000	+	1.09191i	0.104132	+	0.0379008i
$831$		0			0
$832$	−4.64543	−	3.89798i	−0.161051	−	0.135138i
$833$	33.9384	−	12.3526i	1.17590	−	0.427991i
$834$		0			0
$835$	−5.75624	−	32.6453i	−0.199203	−	1.12974i
$836$	22.0087			0.761186
$837$		0			0
$838$	33.9718			1.17354
$839$	6.81134	+	38.6290i	0.235153	+	1.33362i	0.842290	+	0.539024i	$0.181207\pi$
$839$	6.81134	+	38.6290i	0.235153	+	1.33362i	−0.607137	+	0.794597i	$0.707682\pi$
$840$		0			0
$841$	−5.94444	+	2.16360i	−0.204981	+	0.0746069i
$842$	−9.63816	−	8.08737i	−0.332153	−	0.278709i
$843$		0			0
$844$	−13.9474	−	5.07645i	−0.480090	−	0.174739i
$845$	16.0155	+	27.7396i	0.550949	+	0.954272i
$846$		0			0
$847$	0.169778	−	0.294064i	0.00583363	−	0.0101041i
$848$	5.58512	−	4.68647i	0.191794	−	0.160934i
$849$		0			0
$850$	−2.85932	+	16.2160i	−0.0980738	+	0.556204i
$851$	0.240352	−	1.36310i	0.00823917	−	0.0467266i
$852$		0			0
$853$	−4.99344	+	4.18999i	−0.170972	+	0.143463i	−0.724259	−	0.689528i	$-0.757818\pi$
$853$	−4.99344	+	4.18999i	−0.170972	+	0.143463i	0.553287	+	0.832991i	$0.313373\pi$
$854$	−0.228026	+	0.394952i	−0.00780288	+	0.0135150i
$855$		0			0
$856$	−5.14543	−	8.91215i	−0.175867	−	0.304611i
$857$	−17.5069	−	6.37198i	−0.598023	−	0.217663i	0.0252315	−	0.999682i	$-0.491968\pi$
$857$	−17.5069	−	6.37198i	−0.598023	−	0.217663i	−0.623255	+	0.782019i	$0.714190\pi$
$858$		0			0
$859$	−42.5565	−	35.7091i	−1.45201	−	1.21838i	−0.931098	−	0.364769i	$-0.881148\pi$
$859$	−42.5565	−	35.7091i	−1.45201	−	1.21838i	−0.520911	−	0.853611i	$-0.674408\pi$
$860$	0.573978	−	0.208911i	0.0195725	−	0.00712380i
$861$		0			0
$862$	1.35029	+	7.65787i	0.0459910	+	0.260828i
$863$	36.1625			1.23099			0.615493	−	0.788142i	$-0.288957\pi$
$863$	36.1625			1.23099			0.615493	+	0.788142i	$0.288957\pi$
$864$		0			0
$865$	−14.4456			−0.491166
$866$	−7.05943	−	40.0360i	−0.239889	−	1.36048i
$867$		0			0
$868$	−0.571452	+	0.207991i	−0.0193963	+	0.00705969i
$869$	−39.8428	−	33.4321i	−1.35157	−	1.13410i
$870$		0			0
$871$	−37.8273	−	13.7680i	−1.28173	−	0.466511i
$872$	5.54576	+	9.60554i	0.187803	+	0.325285i
$873$		0			0
$874$	14.0890	−	24.4029i	0.476567	−	0.825439i
$875$	−1.01889	+	0.854946i	−0.0344446	+	0.0289025i
$876$		0			0
$877$	−3.37118	+	19.1189i	−0.113837	+	0.645599i	0.873483	+	0.486855i	$0.161856\pi$
$877$	−3.37118	+	19.1189i	−0.113837	+	0.645599i	−0.987320	+	0.158745i	$0.949255\pi$
$878$	−3.07280	+	17.4267i	−0.103702	+	0.588122i
$879$		0			0
$880$	3.83615	−	3.21891i	0.129317	−	0.108510i
$881$	22.9957	−	39.8298i	0.774745	−	1.34190i	−0.160192	−	0.987086i	$-0.551211\pi$
$881$	22.9957	−	39.8298i	0.774745	−	1.34190i	0.934937	−	0.354813i	$-0.115455\pi$
$882$		0			0
$883$	−11.9081	−	20.6254i	−0.400738	−	0.694099i	0.593077	−	0.805146i	$-0.297913\pi$
$883$	−11.9081	−	20.6254i	−0.400738	−	0.694099i	−0.993815	+	0.111047i	$0.964580\pi$
$884$	29.4624	+	10.7235i	0.990929	+	0.360669i
$885$		0			0
$886$	−11.0123	−	9.24044i	−0.369966	−	0.310439i
$887$	24.7729	−	9.01660i	0.831793	−	0.302748i	0.109198	−	0.994020i	$-0.465172\pi$
$887$	24.7729	−	9.01660i	0.831793	−	0.302748i	0.722595	+	0.691272i	$0.242949\pi$
$888$		0			0
$889$	0.120204	+	0.681712i	0.00403152	+	0.0228639i
$890$	−2.92396			−0.0980115
$891$		0			0
$892$	−6.73143			−0.225385
$893$	−0.795140	−	4.50946i	−0.0266084	−	0.150903i
$894$		0			0
$895$	17.5287	−	6.37992i	0.585919	−	0.213257i
$896$	−0.0923963	−	0.0775297i	−0.00308674	−	0.00259008i
$897$		0			0
$898$	26.2849	+	9.56693i	0.877139	+	0.319253i
$899$	−14.9834	−	25.9520i	−0.499724	−	0.865548i
$900$		0			0
$901$	−18.8478	+	32.6453i	−0.627910	+	1.08757i
$902$	16.5162	−	13.8587i	0.549929	−	0.461445i
$903$		0			0
$904$	−1.02869	+	5.83396i	−0.0342136	+	0.194035i
$905$	−0.821137	+	4.65690i	−0.0272955	+	0.154801i
$906$		0			0
$907$	−1.62764	+	1.36575i	−0.0540449	+	0.0453491i	−0.669410	−	0.742893i	$-0.733453\pi$
$907$	−1.62764	+	1.36575i	−0.0540449	+	0.0453491i	0.615365	+	0.788242i	$0.289009\pi$
$908$	7.24763	−	12.5533i	0.240521	−	0.416594i
$909$		0			0
$910$	0.492726	+	0.853427i	0.0163337	+	0.0282908i
$911$	−47.1156	−	17.1487i	−1.56101	−	0.568161i	−0.590042	−	0.807372i	$-0.700889\pi$
$911$	−47.1156	−	17.1487i	−1.56101	−	0.568161i	−0.970968	+	0.239211i	$0.923111\pi$
$912$		0			0
$913$	−6.74691	−	5.66133i	−0.223290	−	0.187363i
$914$	−8.01367	+	2.91674i	−0.265069	+	0.0964771i
$915$		0			0
$916$	4.47787	+	25.3953i	0.147953	+	0.839084i
$917$	2.07697			0.0685876
$918$		0			0
$919$	−56.9469			−1.87850			−0.939252	−	0.343229i	$-0.888479\pi$
$919$	−56.9469			−1.87850			−0.939252	+	0.343229i	$0.888479\pi$
$920$	−1.11334	−	6.31407i	−0.0367058	−	0.208169i
$921$		0			0
$922$	20.4072	−	7.42761i	0.672075	−	0.244615i
$923$	26.6844	+	22.3909i	0.878327	+	0.737004i
$924$		0			0
$925$	0.870462	+	0.316822i	0.0286206	+	0.0104171i
$926$	9.90167	+	17.1502i	0.325389	+	0.563591i
$927$		0			0
$928$	2.97178	−	5.14728i	0.0975535	−	0.168968i
$929$	−0.192533	+	0.161555i	−0.00631681	+	0.00530044i	−0.645941	−	0.763388i	$-0.723535\pi$
$929$	−0.192533	+	0.161555i	−0.00631681	+	0.00530044i	0.639624	+	0.768688i	$0.279090\pi$
$930$		0			0
$931$	7.18257	−	40.7344i	0.235399	−	1.33502i
$932$	−1.80541	+	10.2390i	−0.0591381	+	0.335389i
$933$		0			0
$934$	−28.3325	+	23.7738i	−0.927068	+	0.777902i
$935$	−12.9456	+	22.4225i	−0.423367	+	0.733293i
$936$		0			0
$937$	18.4662	+	31.9843i	0.603263	+	1.04488i	0.992323	+	0.123670i	$0.0394664\pi$
$937$	18.4662	+	31.9843i	0.603263	+	1.04488i	−0.389060	+	0.921212i	$0.627200\pi$
$938$	−0.752374	−	0.273842i	−0.0245659	−	0.00894125i
$939$		0			0
$940$	−0.798133	−	0.669713i	−0.0260322	−	0.0218436i
$941$	40.5925	−	14.7744i	1.32328	−	0.481633i	0.418769	−	0.908093i	$-0.362462\pi$
$941$	40.5925	−	14.7744i	1.32328	−	0.481633i	0.904507	+	0.426459i	$0.140239\pi$
$942$		0			0
$943$	−4.79339	−	27.1846i	−0.156094	−	0.885254i
$944$	1.49020			0.0485019
$945$		0			0
$946$	−1.68510			−0.0547872
$947$	−8.24129	−	46.7387i	−0.267806	−	1.51880i	−0.760925	−	0.648840i	$-0.775254\pi$
$947$	−8.24129	−	46.7387i	−0.267806	−	1.51880i	0.493119	−	0.869962i	$-0.335857\pi$
$948$		0			0
$949$	59.3735	−	21.6102i	1.92735	−	0.701496i
$950$	14.4461	+	12.1217i	0.468693	+	0.393280i
$951$		0			0
$952$	0.586000	+	0.213286i	0.0189924	+	0.00691265i
$953$	−22.6575	−	39.2440i	−0.733949	−	1.27124i	−0.955183	−	0.296016i	$-0.904342\pi$
$953$	−22.6575	−	39.2440i	−0.733949	−	1.27124i	0.221234	−	0.975221i	$-0.428991\pi$
$954$		0			0
$955$	14.7476	−	25.5436i	0.477222	−	0.826573i
$956$	17.5535	−	14.7291i	0.567721	−	0.476374i
$957$		0			0
$958$	1.97131	−	11.1799i	0.0636903	−	0.361206i
$959$	0.00181100	−	0.0102707i	5.84802e−5	−	0.000331658i
$960$		0			0
$961$	−4.27403	+	3.58634i	−0.137872	+	0.115688i
$962$	0.881911	−	1.52752i	0.0284340	−	0.0492491i
$963$		0			0
$964$	6.03849	+	10.4590i	0.194487	+	0.336861i
$965$	32.4256	+	11.8020i	1.04382	+	0.379918i
$966$		0			0
$967$	34.3658	+	28.8363i	1.10513	+	0.927313i	0.997759	−	0.0669061i	$-0.0213128\pi$
$967$	34.3658	+	28.8363i	1.10513	+	0.927313i	0.107369	+	0.994219i	$0.465757\pi$
$968$	−2.64543	+	0.962858i	−0.0850273	+	0.0309474i
$969$		0			0
$970$	0.801537	+	4.54574i	0.0257358	+	0.145955i
$971$	6.55438			0.210340			0.105170	−	0.994454i	$-0.466461\pi$
$971$	6.55438			0.210340			0.105170	+	0.994454i	$0.466461\pi$
$972$		0			0
$973$	2.21482			0.0710039
$974$	0.197586	+	1.12056i	0.00633106	+	0.0359052i
$975$		0			0
$976$	3.55303	−	1.29320i	0.113730	−	0.0413943i
$977$	36.1903	+	30.3673i	1.15783	+	0.971535i	0.999873	−	0.0159107i	$-0.00506474\pi$
$977$	36.1903	+	30.3673i	1.15783	+	0.971535i	0.157957	+	0.987446i	$0.449509\pi$
$978$		0			0
$979$	7.58007	+	2.75892i	0.242260	+	0.0881755i
$980$	−4.70574	−	8.15058i	−0.150319	−	0.260361i
$981$		0			0
$982$	−7.65570	+	13.2601i	−0.244303	+	0.423145i
$983$	24.0646	−	20.1926i	0.767543	−	0.644045i	−0.172535	−	0.985003i	$-0.555196\pi$
$983$	24.0646	−	20.1926i	0.767543	−	0.644045i	0.940078	+	0.340958i	$0.110751\pi$
$984$		0			0
$985$	3.20170	−	18.1578i	0.102015	−	0.578555i
$986$	−5.33615	+	30.2628i	−0.169938	+	0.963765i
$987$		0			0
$988$	27.5069	−	23.0810i	0.875110	−	0.734304i
$989$	−1.07873	+	1.86841i	−0.0343015	+	0.0594119i
$990$		0			0
$991$	−23.2126	−	40.2054i	−0.737373	−	1.27717i	−0.953675	−	0.300840i	$-0.902733\pi$
$991$	−23.2126	−	40.2054i	−0.737373	−	1.27717i	0.216302	−	0.976327i	$-0.430600\pi$
$992$	4.73783	+	1.72443i	0.150426	+	0.0547506i
$993$		0			0
$994$	0.530745	+	0.445348i	0.0168342	+	0.0141256i
$995$	−15.6985	+	5.71377i	−0.497675	+	0.181139i
$996$		0			0
$997$	−4.66503	−	26.4567i	−0.147743	−	0.837892i	−0.965124	−	0.261794i	$-0.915686\pi$
$997$	−4.66503	−	26.4567i	−0.147743	−	0.837892i	0.817381	−	0.576098i	$-0.195425\pi$
$998$	2.31820			0.0733814
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.c.271.1		6
3.2	odd	2		486.2.e.b.271.1		6
9.2	odd	6		54.2.e.a.49.1	yes	6
9.4	even	3		486.2.e.a.433.1		6
9.5	odd	6		486.2.e.d.433.1		6
9.7	even	3		162.2.e.a.37.1		6
27.2	odd	18		486.2.e.b.217.1		6
27.4	even	9		1458.2.c.a.487.2		6
27.5	odd	18		1458.2.a.a.1.2		3
27.7	even	9		162.2.e.a.127.1		6
27.11	odd	18		486.2.e.d.55.1		6
27.13	even	9		1458.2.c.a.973.2		6
27.14	odd	18		1458.2.c.d.973.2		6
27.16	even	9		486.2.e.a.55.1		6
27.20	odd	18		54.2.e.a.43.1	✓	6
27.22	even	9		1458.2.a.d.1.2		3
27.23	odd	18		1458.2.c.d.487.2		6
27.25	even	9	inner	486.2.e.c.217.1		6
36.11	even	6		432.2.u.a.49.1		6
108.47	even	18		432.2.u.a.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.43.1	✓	6	27.20	odd	18
54.2.e.a.49.1	yes	6	9.2	odd	6
162.2.e.a.37.1		6	9.7	even	3
162.2.e.a.127.1		6	27.7	even	9
432.2.u.a.49.1		6	36.11	even	6
432.2.u.a.97.1		6	108.47	even	18
486.2.e.a.55.1		6	27.16	even	9
486.2.e.a.433.1		6	9.4	even	3
486.2.e.b.217.1		6	27.2	odd	18
486.2.e.b.271.1		6	3.2	odd	2
486.2.e.c.217.1		6	27.25	even	9	inner
486.2.e.c.271.1		6	1.1	even	1	trivial
486.2.e.d.55.1		6	27.11	odd	18
486.2.e.d.433.1		6	9.5	odd	6
1458.2.a.a.1.2		3	27.5	odd	18
1458.2.a.d.1.2		3	27.22	even	9
1458.2.c.a.487.2		6	27.4	even	9
1458.2.c.a.973.2		6	27.13	even	9
1458.2.c.d.487.2		6	27.23	odd	18
1458.2.c.d.973.2		6	27.14	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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(0.113341 + 0.0412527i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(0.113341 + 0.0412527i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.673648 - 1.16679i) q^{10} +(-2.84730 + 2.38917i) q^{11} +(-1.05303 + 5.97205i) q^{13} +(-0.0209445 + 0.118782i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-2.58512 + 4.47756i) q^{17} +(2.96064 + 5.12797i) q^{19} +(1.26604 + 0.460802i) q^{20} +(-2.84730 - 2.38917i) q^{22} +(-4.47178 + 1.62760i) q^{23} +(-0.553033 - 3.13641i) q^{25} -6.06418 q^{26} -0.120615 q^{28} +(-1.03209 - 5.85327i) q^{29} +(4.73783 - 1.72443i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-4.85844 - 1.76833i) q^{34} +(-0.0812519 - 0.140732i) q^{35} +(-0.145430 + 0.251892i) q^{37} +(-4.53596 + 3.80612i) q^{38} +(-0.233956 + 1.32683i) q^{40} +(-1.00727 + 5.71253i) q^{41} +(0.347296 - 0.291416i) q^{43} +(1.85844 - 3.21891i) q^{44} +(-2.37939 - 4.12122i) q^{46} +(-0.726682 - 0.264490i) q^{47} +(-5.35117 - 4.49016i) q^{49} +(2.99273 - 1.08926i) q^{50} +(-1.05303 - 5.97205i) q^{52} +7.29086 q^{53} +5.00774 q^{55} +(-0.0209445 - 0.118782i) q^{56} +(5.58512 - 2.03282i) q^{58} +(1.14156 + 0.957882i) q^{59} +(3.55303 + 1.29320i) q^{61} +(2.52094 + 4.36640i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(6.25877 - 5.25173i) q^{65} +(-1.15270 + 6.53731i) q^{67} +(0.897804 - 5.09170i) q^{68} +(0.124485 - 0.104455i) q^{70} +(2.87211 - 4.97464i) q^{71} +(-5.20961 - 9.02330i) q^{73} +(-0.273318 - 0.0994798i) q^{74} +(-4.53596 - 3.80612i) q^{76} +(-0.421274 + 0.153331i) q^{77} +(2.42989 + 13.7806i) q^{79} -1.34730 q^{80} -5.80066 q^{82} +(0.411474 + 2.33359i) q^{83} +(6.54576 - 2.38246i) q^{85} +(0.347296 + 0.291416i) q^{86} +(3.49273 + 1.27125i) q^{88} +(-1.08512 - 1.87949i) q^{89} +(-0.365715 + 0.633436i) q^{91} +(3.64543 - 3.05888i) q^{92} +(0.134285 - 0.761570i) q^{94} +(1.38532 - 7.85651i) q^{95} +(-2.62449 + 2.20220i) q^{97} +(3.49273 - 6.04958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8	\( 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8} + 3 q^{10} - 15 q^{11} + 6 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} - 12 q^{23} + 9 q^{25} - 18 q^{26} - 12 q^{28} + 3 q^{29} + 9 q^{31} - 21 q^{34} - 3 q^{35} + 15 q^{37} + 6 q^{38} - 6 q^{40} - 24 q^{41} + 3 q^{44} - 3 q^{46} + 9 q^{47} - 6 q^{49} + 6 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 12 q^{58} + 15 q^{59} + 9 q^{61} + 12 q^{62} - 3 q^{64} + 15 q^{65} - 9 q^{67} + 6 q^{68} - 12 q^{70} - 12 q^{71} + 3 q^{73} - 15 q^{74} + 6 q^{76} + 15 q^{77} + 6 q^{79} - 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{85} + 3 q^{88} + 15 q^{89} - 12 q^{91} + 6 q^{92} - 9 q^{94} + 24 q^{95} - 3 q^{97} + 3 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8 + 3 * q^10 - 15 * q^11 + 6 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 - 12 * q^23 + 9 * q^25 - 18 * q^26 - 12 * q^28 + 3 * q^29 + 9 * q^31 - 21 * q^34 - 3 * q^35 + 15 * q^37 + 6 * q^38 - 6 * q^40 - 24 * q^41 + 3 * q^44 - 3 * q^46 + 9 * q^47 - 6 * q^49 + 6 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 12 * q^58 + 15 * q^59 + 9 * q^61 + 12 * q^62 - 3 * q^64 + 15 * q^65 - 9 * q^67 + 6 * q^68 - 12 * q^70 - 12 * q^71 + 3 * q^73 - 15 * q^74 + 6 * q^76 + 15 * q^77 + 6 * q^79 - 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^85 + 3 * q^88 + 15 * q^89 - 12 * q^91 + 6 * q^92 - 9 * q^94 + 24 * q^95 - 3 * q^97 + 3 * q^98

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