LMFDB - Embedded newform 585.2.bu.c.316.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(316,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("585.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bu (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.2
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	585.316
Dual form			585.2.bu.c.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05628 - 0.609843i) q^{2} +(-0.256182 - 0.443720i) q^{4} -1.00000i q^{5} +(3.11786 - 1.80010i) q^{7} +3.06430i q^{8} +O(q^{10})$	\(q+(-1.05628 - 0.609843i) q^{2} +(-0.256182 - 0.443720i) q^{4} -1.00000i q^{5} +(3.11786 - 1.80010i) q^{7} +3.06430i q^{8} +(-0.609843 + 1.05628i) q^{10} +(4.65213 + 2.68591i) q^{11} +(1.81988 + 3.11256i) q^{13} -4.39111 q^{14} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-0.443720 + 0.256182i) q^{20} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} -1.00000 q^{25} +(-0.0241312 - 4.39758i) q^{26} +(-1.59748 - 0.922305i) q^{28} +(-0.0123639 + 0.0214150i) q^{29} -5.46410i q^{31} +(2.44209 - 1.40994i) q^{32} -1.38051i q^{34} +(-1.80010 - 3.11786i) q^{35} +(7.53794 + 4.35203i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-3.23205 - 1.86603i) q^{41} +(-0.565928 - 0.980215i) q^{43} -2.75232i q^{44} +(-4.11196 + 2.37404i) q^{46} -2.58535i q^{47} +(2.98070 - 5.16273i) q^{49} +(1.05628 + 0.609843i) q^{50} +(0.914884 - 1.60490i) q^{52} +4.43937 q^{53} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +(0.0261196 - 0.0150801i) q^{58} +(0.148458 - 0.0857123i) q^{59} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} -8.86488 q^{64} +(3.11256 - 1.81988i) q^{65} +(5.54239 + 3.19990i) q^{67} +(0.289961 - 0.502227i) q^{68} +4.39111i q^{70} +(-9.35076 + 5.39866i) q^{71} -4.70308i q^{73} +(-5.30812 - 9.19393i) q^{74} +(1.00633 + 0.581008i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-2.34932 - 1.35638i) q^{80} +(2.27597 + 3.94209i) q^{82} -12.1286i q^{83} +(0.980215 - 0.565928i) q^{85} +1.38051i q^{86} +(-8.23042 + 14.2555i) q^{88} +(-13.9898 - 8.07702i) q^{89} +(11.2771 + 6.42856i) q^{91} -1.99457 q^{92} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +(-10.5379 + 6.08408i) q^{97} +(-6.29692 + 3.63553i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^7	$ 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.05628	−	0.609843i	−0.746903	−	0.431224i	0.0776710	−	0.996979i	$-0.475252\pi$
$2$	−1.05628	−	0.609843i	−0.746903	−	0.431224i	−0.824574	+	0.565755i	$0.808585\pi$
$3$		0			0
$3$		0			0
$4$	−0.256182	−	0.443720i	−0.128091	−	0.221860i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	3.11786	−	1.80010i	1.17844	−	0.680373i	0.222787	−	0.974867i	$-0.428484\pi$
$7$	3.11786	−	1.80010i	1.17844	−	0.680373i	0.955653	+	0.294494i	$0.0951511\pi$
$8$			3.06430i			1.08339i
$9$		0			0
$10$	−0.609843	+	1.05628i	−0.192849	+	0.334025i
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.994666	−	0.103149i	$-0.0328917\pi$
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.408004	+	0.912980i	$0.366225\pi$
$12$		0			0
$13$	1.81988	+	3.11256i	0.504745	+	0.863269i
$13$	1.81988	+	3.11256i	0.504745	+	0.863269i
$14$	−4.39111			−1.17357
$15$		0			0
$16$	1.35638	−	2.34932i	0.339094	−	0.587329i
$17$	0.565928	+	0.980215i	0.137258	+	0.237737i	0.926458	−	0.376399i	$-0.122838\pi$
$17$	0.565928	+	0.980215i	0.137258	+	0.237737i	−0.789200	+	0.614136i	$0.789505\pi$
$18$		0			0
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	−0.708082	−	0.706130i	$-0.750439\pi$
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	0.257486	+	0.966282i	$0.417106\pi$
$20$	−0.443720	+	0.256182i	−0.0992188	+	0.0572840i
$21$		0			0
$22$	−3.27597	−	5.67414i	−0.698438	−	1.20973i
$23$	1.94644	−	3.37133i	0.405860	−	0.702970i	−0.588561	−	0.808453i	$-0.700305\pi$
$23$	1.94644	−	3.37133i	0.405860	−	0.702970i	0.994421	+	0.105483i	$0.0336387\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.0241312	−	4.39758i	−0.00473251	−	0.862436i
$27$		0			0
$28$	−1.59748	−	0.922305i	−0.301895	−	0.174299i
$29$	−0.0123639	+	0.0214150i	−0.00229593	+	0.00397666i	−0.867171	−	0.498010i	$-0.834064\pi$
$29$	−0.0123639	+	0.0214150i	−0.00229593	+	0.00397666i	0.864875	+	0.501987i	$0.167397\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	2.44209	−	1.40994i	0.431705	−	0.249245i
$33$		0			0
$34$		−	1.38051i		−	0.236755i
$35$	−1.80010	−	3.11786i	−0.304272	−	0.527015i
$36$		0			0
$37$	7.53794	+	4.35203i	1.23923	+	0.715470i	0.968937	−	0.247309i	$-0.0795462\pi$
$37$	7.53794	+	4.35203i	1.23923	+	0.715470i	0.270293	+	0.962778i	$0.412879\pi$
$38$	2.76619			0.448735
$39$		0			0
$40$	3.06430			0.484508
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	0.225916	−	0.974147i	$-0.427462\pi$
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	−0.730678	+	0.682723i	$0.760796\pi$
$42$		0			0
$43$	−0.565928	−	0.980215i	−0.0863031	−	0.149481i	0.819643	−	0.572875i	$-0.194172\pi$
$43$	−0.565928	−	0.980215i	−0.0863031	−	0.149481i	−0.905946	+	0.423394i	$0.860839\pi$
$44$		−	2.75232i		−	0.414929i
$45$		0			0
$46$	−4.11196	+	2.37404i	−0.606276	+	0.350034i
$47$		−	2.58535i		−	0.377113i	−0.982062	−	0.188556i	$-0.939619\pi$
$47$		−	2.58535i		−	0.377113i	0.982062	−	0.188556i	$-0.0603808\pi$
$48$		0			0
$49$	2.98070	−	5.16273i	0.425815	−	0.737533i
$50$	1.05628	+	0.609843i	0.149381	+	0.0862449i
$51$		0			0
$52$	0.914884	−	1.60490i	0.126872	−	0.222560i
$53$	4.43937			0.609795			0.304897	−	0.952385i	$-0.401378\pi$
$53$	4.43937			0.609795			0.304897	+	0.952385i	$0.401378\pi$
$54$		0			0
$55$	2.68591	−	4.65213i	0.362168	−	0.627293i
$56$	5.51603	+	9.55405i	0.737111	+	1.27671i
$57$		0			0
$58$	0.0261196	−	0.0150801i	0.00342967	−	0.00198012i
$59$	0.148458	−	0.0857123i	0.0193276	−	0.0111588i	−0.490305	−	0.871551i	$-0.663115\pi$
$59$	0.148458	−	0.0857123i	0.0193276	−	0.0111588i	0.509633	+	0.860392i	$0.329781\pi$
$60$		0			0
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	0.738192	−	0.674591i	$-0.235680\pi$
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	−0.953309	+	0.301997i	$0.902347\pi$
$62$	−3.33225	+	5.77162i	−0.423196	+	0.732997i
$63$		0			0
$64$	−8.86488			−1.10811
$65$	3.11256	−	1.81988i	0.386066	−	0.225729i
$66$		0			0
$67$	5.54239	+	3.19990i	0.677111	+	0.390930i	0.798766	−	0.601642i	$-0.205487\pi$
$67$	5.54239	+	3.19990i	0.677111	+	0.390930i	−0.121655	+	0.992572i	$0.538820\pi$
$68$	0.289961	−	0.502227i	0.0351629	−	0.0609040i
$69$		0			0
$70$			4.39111i			0.524838i
$71$	−9.35076	+	5.39866i	−1.10973	+	0.640703i	−0.938760	−	0.344573i	$-0.888024\pi$
$71$	−9.35076	+	5.39866i	−1.10973	+	0.640703i	−0.170971	+	0.985276i	$0.554691\pi$
$72$		0			0
$73$		−	4.70308i		−	0.550454i	−0.961379	−	0.275227i	$-0.911247\pi$
$73$		−	4.70308i		−	0.550454i	0.961379	−	0.275227i	$-0.0887531\pi$
$74$	−5.30812	−	9.19393i	−0.617056	−	1.06877i
$75$		0			0
$76$	1.00633	+	0.581008i	0.115435	+	0.0666462i
$77$	19.3396			2.20395
$78$		0			0
$79$	−11.9826			−1.34815			−0.674075	−	0.738663i	$-0.735457\pi$
$79$	−11.9826			−1.34815			−0.674075	+	0.738663i	$0.735457\pi$
$80$	−2.34932	−	1.35638i	−0.262661	−	0.151648i
$81$		0			0
$82$	2.27597	+	3.94209i	0.251338	+	0.435331i
$83$		−	12.1286i		−	1.33129i	−0.746270	−	0.665643i	$-0.768157\pi$
$83$		−	12.1286i		−	1.33129i	0.746270	−	0.665643i	$-0.231843\pi$
$84$		0			0
$85$	0.980215	−	0.565928i	0.106319	−	0.0613835i
$86$			1.38051i			0.148864i
$87$		0			0
$88$	−8.23042	+	14.2555i	−0.877366	+	1.51964i
$89$	−13.9898	−	8.07702i	−1.48292	−	0.856162i	−0.483105	−	0.875562i	$-0.660491\pi$
$89$	−13.9898	−	8.07702i	−1.48292	−	0.856162i	−0.999812	+	0.0194001i	$0.993824\pi$
$90$		0			0
$91$	11.2771	+	6.42856i	1.18216	+	0.673896i
$92$	−1.99457			−0.207948
$93$		0			0
$94$	−1.57666	+	2.73086i	−0.162620	+	0.281666i
$95$	1.13397	+	1.96410i	0.116343	+	0.201513i
$96$		0			0
$97$	−10.5379	+	6.08408i	−1.06997	+	0.617745i	−0.928172	−	0.372151i	$-0.878620\pi$
$97$	−10.5379	+	6.08408i	−1.06997	+	0.617745i	−0.141794	+	0.989896i	$0.545287\pi$
$98$	−6.29692	+	3.63553i	−0.636085	+	0.367244i
$99$		0			0
$100$	0.256182	+	0.443720i	0.0256182	+	0.0443720i
$101$	2.02721	−	3.51122i	0.201714	−	0.349380i	−0.747366	−	0.664412i	$-0.768682\pi$
$101$	2.02721	−	3.51122i	0.201714	−	0.349380i	0.949081	+	0.315032i	$0.102015\pi$
$102$		0			0
$103$	17.9035			1.76408			0.882041	−	0.471173i	$-0.156169\pi$
$103$	17.9035			1.76408			0.882041	+	0.471173i	$0.156169\pi$
$104$	−9.53781	+	5.57666i	−0.935259	+	0.546837i
$105$		0			0
$106$	−4.68922	−	2.70732i	−0.455457	−	0.262958i
$107$	−4.56593	+	7.90842i	−0.441405	+	0.764536i	−0.997794	−	0.0663862i	$-0.978853\pi$
$107$	−4.56593	+	7.90842i	−0.441405	+	0.764536i	0.556389	+	0.830922i	$0.312186\pi$
$108$		0			0
$109$		−	7.37605i		−	0.706498i	−0.935529	−	0.353249i	$-0.885077\pi$
$109$		−	7.37605i		−	0.706498i	0.935529	−	0.353249i	$-0.114923\pi$
$110$	−5.67414	+	3.27597i	−0.541008	+	0.312351i
$111$		0			0
$112$		−	9.76645i		−	0.922843i
$113$	3.53794	+	6.12789i	0.332821	+	0.576463i	0.983064	−	0.183263i	$-0.0586661\pi$
$113$	3.53794	+	6.12789i	0.332821	+	0.576463i	−0.650243	+	0.759727i	$0.725333\pi$
$114$		0			0
$115$	−3.37133	−	1.94644i	−0.314378	−	0.181506i
$116$	0.0126697			0.00117635
$117$		0			0
$118$	−0.209084			−0.0192478
$119$	3.52897	+	2.03745i	0.323500	+	0.186773i
$120$		0			0
$121$	8.92820	+	15.4641i	0.811655	+	1.40583i
$122$			4.09843i			0.371055i
$123$		0			0
$124$	−2.42453	+	1.39980i	−0.217729	+	0.125706i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−5.71806	+	9.90396i	−0.507395	+	0.878835i	0.492568	+	0.870274i	$0.336058\pi$
$127$	−5.71806	+	9.90396i	−0.507395	+	0.878835i	−0.999963	+	0.00856072i	$0.997275\pi$
$128$	4.47962	+	2.58631i	0.395946	+	0.228600i
$129$		0			0
$130$	−4.39758	+	0.0241312i	−0.385693	+	0.00211644i
$131$	10.5680			0.923328			0.461664	−	0.887055i	$-0.347253\pi$
$131$	10.5680			0.923328			0.461664	+	0.887055i	$0.347253\pi$
$132$		0			0
$133$	−4.08253	+	7.07115i	−0.354000	+	0.613146i
$134$	−3.90288	−	6.75998i	−0.337157	−	0.583974i
$135$		0			0
$136$	−3.00367	+	1.73417i	−0.257563	+	0.148704i
$137$	−3.27940	+	1.89336i	−0.280178	+	0.161761i	−0.633504	−	0.773739i	$-0.718384\pi$
$137$	−3.27940	+	1.89336i	−0.280178	+	0.161761i	0.353326	+	0.935500i	$0.385051\pi$
$138$		0			0
$139$	−1.00693	−	1.74406i	−0.0854068	−	0.147929i	0.820158	−	0.572138i	$-0.193886\pi$
$139$	−1.00693	−	1.74406i	−0.0854068	−	0.147929i	−0.905564	+	0.424209i	$0.860552\pi$
$140$	−0.922305	+	1.59748i	−0.0779490	+	0.135012i
$141$		0			0
$142$	13.1694			1.10515
$143$	0.106280	+	19.3681i	0.00888757	+	1.61964i
$144$		0			0
$145$	0.0214150	+	0.0123639i	0.00177842	+	0.00102677i
$146$	−2.86814	+	4.96777i	−0.237369	+	0.411136i
$147$		0			0
$148$		−	4.45965i		−	0.366581i
$149$	−4.77855	+	2.75890i	−0.391474	+	0.226018i	−0.682799	−	0.730607i	$-0.739237\pi$
$149$	−4.77855	+	2.75890i	−0.391474	+	0.226018i	0.291324	+	0.956624i	$0.405904\pi$
$150$		0			0
$151$		−	4.88961i		−	0.397911i	−0.980009	−	0.198956i	$-0.936245\pi$
$151$		−	4.88961i		−	0.397911i	0.980009	−	0.198956i	$-0.0637549\pi$
$152$	−3.47484	−	6.01859i	−0.281846	−	0.488172i
$153$		0			0
$154$	−20.4280	−	11.7941i	−1.64614	−	0.950397i
$155$	−5.46410			−0.438887
$156$		0			0
$157$	10.0405			0.801323			0.400661	−	0.916226i	$-0.368780\pi$
$157$	10.0405			0.801323			0.400661	+	0.916226i	$0.368780\pi$
$158$	12.6570	+	7.30752i	1.00694	+	0.581355i
$159$		0			0
$160$	−1.40994	−	2.44209i	−0.111466	−	0.193064i
$161$		−	14.0151i		−	1.10454i
$162$		0			0
$163$	5.87273	−	3.39062i	0.459988	−	0.265574i	−0.252051	−	0.967714i	$-0.581105\pi$
$163$	5.87273	−	3.39062i	0.459988	−	0.265574i	0.712039	+	0.702140i	$0.247772\pi$
$164$			1.91217i			0.149315i
$165$		0			0
$166$	−7.39654	+	12.8112i	−0.574083	+	0.994341i
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	0.808455	−	0.588559i	$-0.200304\pi$
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	−0.105479	+	0.994421i	$0.533638\pi$
$168$		0			0
$169$	−6.37605	+	11.3290i	−0.490466	+	0.871460i
$170$	−1.38051			−0.105880
$171$		0			0
$172$	−0.289961	+	0.502227i	−0.0221093	+	0.0382944i
$173$	2.22923	+	3.86113i	0.169485	+	0.293557i	0.938239	−	0.345988i	$-0.112456\pi$
$173$	2.22923	+	3.86113i	0.169485	+	0.293557i	−0.768754	+	0.639545i	$0.779123\pi$
$174$		0			0
$175$	−3.11786	+	1.80010i	−0.235688	+	0.136075i
$176$	12.6201	−	7.28621i	0.951275	−	0.549219i
$177$		0			0
$178$	9.85143	+	17.0632i	0.738396	+	1.27894i
$179$	−9.31564	+	16.1352i	−0.696284	+	1.20600i	0.273462	+	0.961883i	$0.411831\pi$
$179$	−9.31564	+	16.1352i	−0.696284	+	1.20600i	−0.969746	+	0.244116i	$0.921502\pi$
$180$		0			0
$181$	−18.0900			−1.34462			−0.672310	−	0.740270i	$-0.734698\pi$
$181$	−18.0900			−1.34462			−0.672310	+	0.740270i	$0.734698\pi$
$182$	−7.99131	−	13.6676i	−0.592355	−	1.01311i
$183$		0			0
$184$	10.3307	+	5.96446i	0.761593	+	0.439706i
$185$	4.35203	−	7.53794i	0.319968	−	0.554200i
$186$		0			0
$187$			6.08012i			0.444622i
$188$	−1.14717	+	0.662321i	−0.0836662	+	0.0483047i
$189$		0			0
$190$		−	2.76619i		−	0.200680i
$191$	13.6682	+	23.6740i	0.988994	+	1.71299i	0.622632	+	0.782515i	$0.286063\pi$
$191$	13.6682	+	23.6740i	0.988994	+	1.71299i	0.366361	+	0.930473i	$0.380603\pi$
$192$		0			0
$193$	−18.8511	−	10.8837i	−1.35693	−	0.783425i	−0.367723	−	0.929935i	$-0.619863\pi$
$193$	−18.8511	−	10.8837i	−1.35693	−	0.783425i	−0.989209	+	0.146510i	$0.953196\pi$
$194$	14.8413			1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	1.46940	+	0.848360i	0.104691	+	0.0604432i	0.551431	−	0.834220i	$-0.314082\pi$
$197$	1.46940	+	0.848360i	0.104691	+	0.0604432i	−0.446741	+	0.894664i	$0.647415\pi$
$198$		0			0
$199$	12.6627	+	21.9325i	0.897637	+	1.55475i	0.830506	+	0.557009i	$0.188051\pi$
$199$	12.6627	+	21.9325i	0.897637	+	1.55475i	0.0671309	+	0.997744i	$0.478615\pi$
$200$		−	3.06430i		−	0.216679i
$201$		0			0
$202$	−4.28259	+	2.47256i	−0.301322	+	0.173968i
$203$			0.0890252i			0.00624834i
$204$		0			0
$205$	−1.86603	+	3.23205i	−0.130329	+	0.225736i
$206$	−18.9111	−	10.9183i	−1.31760	−	0.760715i
$207$		0			0
$208$	9.78083	−	0.0536711i	0.678179	−	0.00372142i
$209$	−12.1830			−0.842716
$210$		0			0
$211$	0.167753	−	0.290558i	0.0115486	−	0.0200028i	−0.860193	−	0.509968i	$-0.829657\pi$
$211$	0.167753	−	0.290558i	0.0115486	−	0.0200028i	0.871742	+	0.489965i	$0.162991\pi$
$212$	−1.13729	−	1.96984i	−0.0781092	−	0.135289i
$213$		0			0
$214$	9.64579	−	5.56900i	0.659373	−	0.380689i
$215$	−0.980215	+	0.565928i	−0.0668501	+	0.0385959i
$216$		0			0
$217$	−9.83592	−	17.0363i	−0.667706	−	1.15650i
$218$	−4.49824	+	7.79118i	−0.304659	+	0.527685i
$219$		0			0
$220$	−2.75232			−0.185562
$221$	−2.02106	+	3.54536i	−0.135951	+	0.238487i
$222$		0			0
$223$	−10.6493	−	6.14838i	−0.713130	−	0.411726i	0.0990887	−	0.995079i	$-0.468407\pi$
$223$	−10.6493	−	6.14838i	−0.713130	−	0.411726i	−0.812219	+	0.583353i	$0.801741\pi$
$224$	5.07606	−	8.79200i	0.339159	−	0.587440i
$225$		0			0
$226$		−	8.63036i		−	0.574083i
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	−0.703048	−	0.711143i	$-0.748178\pi$
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	0.264344	+	0.964428i	$0.414845\pi$
$228$		0			0
$229$		−	14.4008i		−	0.951631i	−0.879545	−	0.475815i	$-0.842153\pi$
$229$		−	14.4008i		−	0.951631i	0.879545	−	0.475815i	$-0.157847\pi$
$230$	2.37404	+	4.11196i	0.156540	+	0.271135i
$231$		0			0
$232$	−0.0656218	−	0.0378868i	−0.00430828	−	0.00248739i
$233$	9.49617			0.622115			0.311057	−	0.950391i	$-0.399317\pi$
$233$	9.49617			0.622115			0.311057	+	0.950391i	$0.399317\pi$
$234$		0			0
$235$	−2.58535			−0.168650
$236$	−0.0760645	−	0.0439159i	−0.00495138	−	0.00285868i
$237$		0			0
$238$	−2.48505	−	4.30423i	−0.161082	−	0.279002i
$239$		−	19.9143i		−	1.28815i	−0.764962	−	0.644076i	$-0.777242\pi$
$239$		−	19.9143i		−	1.28815i	0.764962	−	0.644076i	$-0.222758\pi$
$240$		0			0
$241$	20.1493	−	11.6332i	1.29793	−	0.749360i	0.317883	−	0.948130i	$-0.397028\pi$
$241$	20.1493	−	11.6332i	1.29793	−	0.749360i	0.980046	+	0.198770i	$0.0636947\pi$
$242$		−	21.7792i		−	1.40002i
$243$		0			0
$244$	−0.860832	+	1.49100i	−0.0551091	+	0.0954518i
$245$	−5.16273	−	2.98070i	−0.329835	−	0.190430i
$246$		0			0
$247$	−7.10400	−	4.04968i	−0.452017	−	0.257675i
$248$	16.7436			1.06322
$249$		0			0
$250$	0.609843	−	1.05628i	0.0385699	−	0.0668050i
$251$	−5.92008	−	10.2539i	−0.373672	−	0.647219i	0.616455	−	0.787390i	$-0.288568\pi$
$251$	−5.92008	−	10.2539i	−0.373672	−	0.647219i	−0.990127	+	0.140171i	$0.955235\pi$
$252$		0			0
$253$	18.1101	−	10.4559i	1.13858	−	0.657357i
$254$	12.0797	−	6.97424i	0.757950	−	0.437603i
$255$		0			0
$256$	5.71040	+	9.89070i	0.356900	+	0.618169i
$257$	2.77501	−	4.80646i	0.173100	−	0.299819i	−0.766402	−	0.642361i	$-0.777955\pi$
$257$	2.77501	−	4.80646i	0.173100	−	0.299819i	0.939502	+	0.342543i	$0.111288\pi$
$258$		0			0
$259$	31.3363			1.94714
$260$	−1.60490	−	0.914884i	−0.0995317	−	0.0567387i
$261$		0			0
$262$	−11.1627	−	6.44481i	−0.689636	−	0.398161i
$263$	3.42983	−	5.94065i	0.211493	−	0.366316i	−0.740689	−	0.671848i	$-0.765501\pi$
$263$	3.42983	−	5.94065i	0.211493	−	0.366316i	0.952182	+	0.305532i	$0.0988342\pi$
$264$		0			0
$265$		−	4.43937i		−	0.272709i
$266$	8.62459	−	4.97941i	0.528807	−	0.305307i
$267$		0			0
$268$		−	3.27903i		−	0.200299i
$269$	−0.710994	−	1.23148i	−0.0433501	−	0.0750845i	0.843536	−	0.537072i	$-0.180470\pi$
$269$	−0.710994	−	1.23148i	−0.0433501	−	0.0750845i	−0.886886	+	0.461988i	$0.847136\pi$
$270$		0			0
$271$	8.63381	+	4.98473i	0.524467	+	0.302801i	0.738760	−	0.673968i	$-0.235412\pi$
$271$	8.63381	+	4.98473i	0.524467	+	0.302801i	−0.214294	+	0.976769i	$0.568745\pi$
$272$	3.07045			0.186173
$273$		0			0
$274$	4.61862			0.279021
$275$	−4.65213	−	2.68591i	−0.280534	−	0.161966i
$276$		0			0
$277$	−8.76187	−	15.1760i	−0.526449	−	0.911837i	−0.999525	−	0.0308154i	$-0.990190\pi$
$277$	−8.76187	−	15.1760i	−0.526449	−	0.911837i	0.473076	−	0.881022i	$-0.343144\pi$
$278$			2.45628i			0.147318i
$279$		0			0
$280$	9.55405	−	5.51603i	0.570964	−	0.329646i
$281$		−	10.7352i		−	0.640406i	−0.947349	−	0.320203i	$-0.896249\pi$
$281$		−	10.7352i		−	0.640406i	0.947349	−	0.320203i	$-0.103751\pi$
$282$		0			0
$283$	0.659192	−	1.14175i	0.0391849	−	0.0678702i	−0.845768	−	0.533551i	$-0.820857\pi$
$283$	0.659192	−	1.14175i	0.0391849	−	0.0678702i	0.884953	+	0.465681i	$0.154191\pi$
$284$	4.79099	+	2.76608i	0.284293	+	0.164137i
$285$		0			0
$286$	11.6992	−	20.5229i	0.691790	−	1.21355i
$287$	−13.4361			−0.793109
$288$		0			0
$289$	7.85945	−	13.6130i	0.462321	−	0.800763i
$290$	−0.0150801	−	0.0261196i	−0.000885536	−	0.00153379i
$291$		0			0
$292$	−2.08685	+	1.20485i	−0.122124	+	0.0705082i
$293$	−16.2316	+	9.37133i	−0.948261	+	0.547479i	−0.892540	−	0.450968i	$-0.851079\pi$
$293$	−16.2316	+	9.37133i	−0.948261	+	0.547479i	−0.0557207	+	0.998446i	$0.517746\pi$
$294$		0			0
$295$	−0.0857123	−	0.148458i	−0.00499036	−	0.00864356i
$296$	−13.3359	+	23.0985i	−0.775134	+	1.34257i
$297$		0			0
$298$	6.72998			0.389857
$299$	14.0357	−	0.0770194i	0.811708	−	0.00445415i
$300$		0			0
$301$	−3.52897	−	2.03745i	−0.203406	−	0.117437i
$302$	−2.98190	+	5.16480i	−0.171589	+	0.297201i
$303$		0			0
$304$			6.15239i			0.352864i
$305$	−2.91005	+	1.68012i	−0.166629	+	0.0962032i
$306$		0			0
$307$			14.3043i			0.816387i	0.912895	+	0.408194i	$0.133841\pi$
$307$			14.3043i			0.816387i	−0.912895	+	0.408194i	$0.866159\pi$
$308$	−4.95445	−	8.58137i	−0.282306	−	0.488969i
$309$		0			0
$310$	5.77162	+	3.33225i	0.327806	+	0.189259i
$311$	2.76102			0.156563			0.0782815	−	0.996931i	$-0.475057\pi$
$311$	2.76102			0.156563			0.0782815	+	0.996931i	$0.475057\pi$
$312$		0			0
$313$	−16.3858			−0.926179			−0.463090	−	0.886311i	$-0.653259\pi$
$313$	−16.3858			−0.926179			−0.463090	+	0.886311i	$0.653259\pi$
$314$	−10.6056	−	6.12316i	−0.598510	−	0.345550i
$315$		0			0
$316$	3.06973	+	5.31693i	0.172686	+	0.299101i
$317$			1.78575i			0.100297i	0.998742	+	0.0501487i	$0.0159695\pi$
$317$			1.78575i			0.100297i	−0.998742	+	0.0501487i	$0.984030\pi$
$318$		0			0
$319$	−0.115037	+	0.0664168i	−0.00644085	+	0.00371863i
$320$			8.86488i			0.495562i
$321$		0			0
$322$	−8.54702	+	14.8039i	−0.476307	+	0.824987i
$323$	−2.22308	−	1.28349i	−0.123695	−	0.0714156i
$324$		0			0
$325$	−1.81988	−	3.11256i	−0.100949	−	0.172654i
$326$	−8.27099			−0.458088
$327$		0			0
$328$	5.71806	−	9.90396i	0.315727	−	0.546855i
$329$	−4.65389	−	8.06077i	−0.256577	−	0.444405i
$330$		0			0
$331$	−6.25652	+	3.61220i	−0.343889	+	0.198545i	−0.661991	−	0.749512i	$-0.730288\pi$
$331$	−6.25652	+	3.61220i	−0.343889	+	0.198545i	0.318101	+	0.948057i	$0.396955\pi$
$332$	−5.38170	+	3.10713i	−0.295359	+	0.170526i
$333$		0			0
$334$	−6.39714	−	11.0802i	−0.350036	−	0.606280i
$335$	3.19990	−	5.54239i	0.174829	−	0.302813i
$336$		0			0
$337$	4.36219			0.237624			0.118812	−	0.992917i	$-0.462091\pi$
$337$	4.36219			0.237624			0.118812	+	0.992917i	$0.462091\pi$
$338$	13.6438	−	8.07818i	0.742125	−	0.439395i
$339$		0			0
$340$	−0.502227	−	0.289961i	−0.0272371	−	0.0157253i
$341$	14.6761	−	25.4197i	0.794754	−	1.37655i
$342$		0			0
$343$			3.73913i			0.201894i
$344$	3.00367	−	1.73417i	0.161947	−	0.0935002i
$345$		0			0
$346$		−	5.43792i		−	0.292344i
$347$	−13.3536	−	23.1291i	−0.716858	−	1.24163i	−0.962239	−	0.272207i	$-0.912246\pi$
$347$	−13.3536	−	23.1291i	−0.716858	−	1.24163i	0.245381	−	0.969427i	$-0.421087\pi$
$348$		0			0
$349$	−20.4131	−	11.7855i	−1.09269	−	0.630865i	−0.158399	−	0.987375i	$-0.550633\pi$
$349$	−20.4131	−	11.7855i	−1.09269	−	0.630865i	−0.934292	+	0.356510i	$0.883967\pi$
$350$	4.39111			0.234715
$351$		0			0
$352$	15.1479			0.807385
$353$	−4.96862	−	2.86863i	−0.264453	−	0.152682i	0.361911	−	0.932213i	$-0.382124\pi$
$353$	−4.96862	−	2.86863i	−0.264453	−	0.152682i	−0.626364	+	0.779531i	$0.715458\pi$
$354$		0			0
$355$	5.39866	+	9.35076i	0.286531	+	0.496287i
$356$			8.27675i			0.438667i
$357$		0			0
$358$	19.6799	−	11.3622i	1.04011	−	0.600509i
$359$			24.7583i			1.30669i	0.757059	+	0.653347i	$0.226636\pi$
$359$			24.7583i			1.30669i	−0.757059	+	0.653347i	$0.773364\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	19.1081	+	11.0321i	1.00430	+	0.579833i
$363$		0			0
$364$	−0.0364951	−	6.65074i	−0.00191286	−	0.348593i
$365$	−4.70308			−0.246171
$366$		0			0
$367$	−13.0268	+	22.5630i	−0.679992	+	1.17778i	0.294991	+	0.955500i	$0.404683\pi$
$367$	−13.0268	+	22.5630i	−0.679992	+	1.17778i	−0.974983	+	0.222280i	$0.928650\pi$
$368$	−5.28021	−	9.14558i	−0.275250	−	0.476747i
$369$		0			0
$370$	−9.19393	+	5.30812i	−0.477969	+	0.275956i
$371$	13.8413	−	7.99131i	0.718607	−	0.414888i
$372$		0			0
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	0.642926	−	0.765929i	$-0.277720\pi$
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	−0.984776	+	0.173826i	$0.944387\pi$
$374$	3.70792	−	6.42231i	0.191732	−	0.332089i
$375$		0			0
$376$	7.92229			0.408561
$377$	−0.0891563		0.000489234i	−0.00459178		2.51968e-5i
$378$		0			0
$379$	22.5147	+	12.9989i	1.15650	+	0.667707i	0.950463	−	0.310837i	$-0.100609\pi$
$379$	22.5147	+	12.9989i	1.15650	+	0.667707i	0.206039	+	0.978544i	$0.433943\pi$
$380$	0.581008	−	1.00633i	0.0298051	−	0.0516239i
$381$		0			0
$382$		−	33.3418i		−	1.70591i
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	−0.697140	−	0.716935i	$-0.745544\pi$
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	0.272314	+	0.962208i	$0.412211\pi$
$384$		0			0
$385$		−	19.3396i		−	0.985637i
$386$	13.2747	+	22.9924i	0.675664	+	1.17028i
$387$		0			0
$388$	5.39926	+	3.11726i	0.274106	+	0.158255i
$389$	5.63129			0.285518			0.142759	−	0.989758i	$-0.454403\pi$
$389$	5.63129			0.285518			0.142759	+	0.989758i	$0.454403\pi$
$390$		0			0
$391$	4.40617			0.222829
$392$	15.8201	+	9.13376i	0.799038	+	0.461325i
$393$		0			0
$394$	−1.03473	−	1.79221i	−0.0521291	−	0.0902903i
$395$			11.9826i			0.602911i
$396$		0			0
$397$	−14.5196	+	8.38291i	−0.728719	+	0.420726i	−0.817953	−	0.575285i	$-0.804891\pi$
$397$	−14.5196	+	8.38291i	−0.728719	+	0.420726i	0.0892344	+	0.996011i	$0.471558\pi$
$398$		−	30.8891i		−	1.54833i
$399$		0			0
$400$	−1.35638	+	2.34932i	−0.0678189	+	0.117466i
$401$	−12.0187	−	6.93902i	−0.600187	−	0.346518i	0.168928	−	0.985628i	$-0.445969\pi$
$401$	−12.0187	−	6.93902i	−0.600187	−	0.346518i	−0.769115	+	0.639110i	$0.779303\pi$
$402$		0			0
$403$	17.0073	−	9.94402i	0.847196	−	0.495347i
$404$	−2.07733			−0.103351
$405$		0			0
$406$	0.0542914	−	0.0940355i	0.00269444	−	0.00466690i
$407$	23.3783	+	40.4924i	1.15882	+	2.00713i
$408$		0			0
$409$	−25.4829	+	14.7125i	−1.26005	+	0.727489i	−0.973083	−	0.230453i	$-0.925979\pi$
$409$	−25.4829	+	14.7125i	−1.26005	+	0.727489i	−0.286964	+	0.957941i	$0.592646\pi$
$410$	3.94209	−	2.27597i	0.194686	−	0.112402i
$411$		0			0
$412$	−4.58655	−	7.94413i	−0.225963	−	0.391379i
$413$	0.308581	−	0.534478i	0.0151843	−	0.0262999i
$414$		0			0
$415$	−12.1286			−0.595369
$416$	8.83284	+	5.03522i	0.433066	+	0.246872i
$417$		0			0
$418$	12.8687	+	7.42973i	0.629427	+	0.363400i
$419$	3.48397	−	6.03440i	0.170203	−	0.294800i	−0.768288	−	0.640104i	$-0.778891\pi$
$419$	3.48397	−	6.03440i	0.170203	−	0.294800i	0.938491	+	0.345305i	$0.112224\pi$
$420$		0			0
$421$		−	7.12125i		−	0.347069i	−0.984828	−	0.173534i	$-0.944481\pi$
$421$		−	7.12125i		−	0.347069i	0.984828	−	0.173534i	$-0.0555188\pi$
$422$	−0.354389	+	0.204607i	−0.0172514	+	0.00996010i
$423$		0			0
$424$			13.6036i			0.660647i
$425$	−0.565928	−	0.980215i	−0.0274515	−	0.0475474i
$426$		0			0
$427$	−10.4767	−	6.04875i	−0.507005	−	0.292720i
$428$	4.67883			0.226160
$429$		0			0
$430$	1.38051			0.0665740
$431$	−26.1664	−	15.1072i	−1.26039	−	0.727687i	−0.287241	−	0.957858i	$-0.592738\pi$
$431$	−26.1664	−	15.1072i	−1.26039	−	0.727687i	−0.973150	+	0.230171i	$0.926071\pi$
$432$		0			0
$433$	0.600065	+	1.03934i	0.0288373	+	0.0499476i	0.880084	−	0.474818i	$-0.157486\pi$
$433$	0.600065	+	1.03934i	0.0288373	+	0.0499476i	−0.851247	+	0.524766i	$0.824153\pi$
$434$			23.9935i			1.15172i
$435$		0			0
$436$	−3.27290	+	1.88961i	−0.156744	+	0.0904960i
$437$			8.82884i			0.422341i
$438$		0			0
$439$	−8.27705	+	14.3363i	−0.395042	+	0.684233i	−0.993107	−	0.117215i	$-0.962603\pi$
$439$	−8.27705	+	14.3363i	−0.395042	+	0.684233i	0.598064	+	0.801448i	$0.295937\pi$
$440$	14.2555	+	8.23042i	0.679605	+	0.392370i
$441$		0			0
$442$	4.29692	−	2.51236i	0.204383	−	0.119501i
$443$	−4.55949			−0.216628			−0.108314	−	0.994117i	$-0.534545\pi$
$443$	−4.55949			−0.216628			−0.108314	+	0.994117i	$0.534545\pi$
$444$		0			0
$445$	−8.07702	+	13.9898i	−0.382887	+	0.663180i
$446$	7.49910	+	12.9888i	0.355093	+	0.615038i
$447$		0			0
$448$	−27.6395	+	15.9577i	−1.30584	+	0.753929i
$449$	−11.9963	+	6.92608i	−0.566142	+	0.326862i	−0.755607	−	0.655025i	$-0.772658\pi$
$449$	−11.9963	+	6.92608i	−0.566142	+	0.326862i	0.189465	+	0.981887i	$0.439325\pi$
$450$		0			0
$451$	−10.0239	−	17.3620i	−0.472009	−	0.817544i
$452$	1.81271	−	3.13971i	0.0852628	−	0.147680i
$453$		0			0
$454$	9.30897			0.436892
$455$	6.42856	−	11.2771i	0.301376	−	0.528676i
$456$		0			0
$457$	34.7402	+	20.0573i	1.62508	+	0.938240i	0.985532	+	0.169489i	$0.0542117\pi$
$457$	34.7402	+	20.0573i	1.62508	+	0.938240i	0.639548	+	0.768751i	$0.279122\pi$
$458$	−8.78222	+	15.2113i	−0.410366	+	0.710775i
$459$		0			0
$460$			1.99457i			0.0929972i
$461$	−6.52897	+	3.76950i	−0.304084	+	0.175563i	−0.644276	−	0.764793i	$-0.722841\pi$
$461$	−6.52897	+	3.76950i	−0.304084	+	0.175563i	0.340192	+	0.940356i	$0.389508\pi$
$462$		0			0
$463$			23.3031i			1.08299i	0.840705	+	0.541494i	$0.182141\pi$
$463$			23.3031i			1.08299i	−0.840705	+	0.541494i	$0.817859\pi$
$464$	0.0335403	+	0.0580936i	0.00155707	+	0.00269693i
$465$		0			0
$466$	−10.0306	−	5.79118i	−0.464659	−	0.268271i
$467$	−22.6297			−1.04718			−0.523589	−	0.851971i	$-0.675407\pi$
$467$	−22.6297			−1.04718			−0.523589	+	0.851971i	$0.675407\pi$
$468$		0			0
$469$	23.0405			1.06391
$470$	2.73086	+	1.57666i	0.125965	+	0.0727260i
$471$		0			0
$472$	0.262648	+	0.454919i	0.0120893	+	0.0209394i
$473$		−	6.08012i		−	0.279564i
$474$		0			0
$475$	1.96410	−	1.13397i	0.0901192	−	0.0520303i
$476$		−	2.08783i		−	0.0956956i
$477$		0			0
$478$	−12.1446	+	21.0351i	−0.555482	+	0.962124i
$479$	17.8789	+	10.3224i	0.816910	+	0.471643i	0.849350	−	0.527831i	$-0.176994\pi$
$479$	17.8789	+	10.3224i	0.816910	+	0.471643i	−0.0324399	+	0.999474i	$0.510328\pi$
$480$		0			0
$481$	0.172207	+	31.3825i	0.00785198	+	1.43092i
$482$	−28.3777			−1.29257
$483$		0			0
$484$	4.57449	−	7.92325i	0.207931	−	0.360148i
$485$	6.08408	+	10.5379i	0.276264	+	0.478503i
$486$		0			0
$487$	−2.62929	+	1.51802i	−0.119145	+	0.0687882i	−0.558388	−	0.829580i	$-0.688580\pi$
$487$	−2.62929	+	1.51802i	−0.119145	+	0.0687882i	0.439243	+	0.898368i	$0.355247\pi$
$488$	8.91725	−	5.14838i	0.403665	−	0.233056i
$489$		0			0
$490$	3.63553	+	6.29692i	0.164236	+	0.284466i
$491$	−5.33401	+	9.23877i	−0.240720	+	0.416940i	−0.960920	−	0.276827i	$-0.910717\pi$
$491$	−5.33401	+	9.23877i	−0.240720	+	0.416940i	0.720199	+	0.693767i	$0.244050\pi$
$492$		0			0
$493$	−0.0279884			−0.00126053
$494$	5.03414	+	8.60992i	0.226497	+	0.387379i
$495$		0			0
$496$	−12.8369	−	7.41139i	−0.576394	−	0.332781i
$497$	−19.4362	+	33.6646i	−0.871835	+	1.51006i
$498$		0			0
$499$		−	33.9143i		−	1.51821i	−0.650966	−	0.759107i	$-0.725636\pi$
$499$		−	33.9143i		−	1.51821i	0.650966	−	0.759107i	$-0.274364\pi$
$500$	0.443720	−	0.256182i	0.0198438	−	0.0114568i
$501$		0			0
$502$			14.4413i			0.644546i
$503$	−6.31380	−	10.9358i	−0.281518	−	0.487604i	0.690241	−	0.723580i	$-0.257505\pi$
$503$	−6.31380	−	10.9358i	−0.281518	−	0.487604i	−0.971759	+	0.235976i	$0.924171\pi$
$504$		0			0
$505$	−3.51122	−	2.02721i	−0.156247	−	0.0902095i
$506$	−25.5058			−1.13387
$507$		0			0
$508$	5.85945			0.259971
$509$	20.9168	+	12.0763i	0.927120	+	0.535273i	0.885899	−	0.463877i	$-0.153542\pi$
$509$	20.9168	+	12.0763i	0.927120	+	0.535273i	0.0412201	+	0.999150i	$0.486876\pi$
$510$		0			0
$511$	−8.46601	−	14.6636i	−0.374514	−	0.648678i
$512$		−	24.2750i		−	1.07281i
$513$		0			0
$514$	−5.86238	+	3.38465i	−0.258578	+	0.149290i
$515$		−	17.9035i		−	0.788921i
$516$		0			0
$517$	6.94402	−	12.0274i	0.305398	−	0.528964i
$518$	−33.0999	−	19.1103i	−1.45433	−	0.839656i
$519$		0			0
$520$	5.57666	+	9.53781i	0.244553	+	0.418261i
$521$	24.7521			1.08441			0.542205	−	0.840246i	$-0.317590\pi$
$521$	24.7521			1.08441			0.542205	+	0.840246i	$0.317590\pi$
$522$		0			0
$523$	−18.5163	+	32.0712i	−0.809662	+	1.40238i	0.103436	+	0.994636i	$0.467016\pi$
$523$	−18.5163	+	32.0712i	−0.809662	+	1.40238i	−0.913098	+	0.407739i	$0.866317\pi$
$524$	−2.70732	−	4.68922i	−0.118270	−	0.204850i
$525$		0			0
$526$	−7.24573	+	4.18332i	−0.315929	+	0.182402i
$527$	5.35600	−	3.09229i	0.233311	−	0.134702i
$528$		0			0
$529$	3.92277	+	6.79444i	0.170555	+	0.295410i
$530$	−2.70732	+	4.68922i	−0.117599	+	0.203687i
$531$		0			0
$532$	4.18348			0.181377
$533$	−0.0738376	−	13.4559i	−0.00319826	−	0.582840i
$534$		0			0
$535$	7.90842	+	4.56593i	0.341911	+	0.197402i
$536$	−9.80545	+	16.9835i	−0.423531	+	0.733577i
$537$		0			0
$538$			1.73438i			0.0747744i
$539$	27.7332	−	16.0118i	1.19456	−	0.689677i
$540$		0			0
$541$		−	8.38144i		−	0.360346i	−0.983635	−	0.180173i	$-0.942334\pi$
$541$		−	8.38144i		−	0.360346i	0.983635	−	0.180173i	$-0.0576658\pi$
$542$	−6.07981	−	10.5305i	−0.261150	−	0.452326i
$543$		0			0
$544$	2.76409	+	1.59585i	0.118509	+	0.0684215i
$545$	−7.37605			−0.315955
$546$		0			0
$547$	−22.7842			−0.974181			−0.487091	−	0.873351i	$-0.661942\pi$
$547$	−22.7842			−0.974181			−0.487091	+	0.873351i	$0.661942\pi$
$548$	1.68025	+	0.970090i	0.0717765	+	0.0414402i
$549$		0			0
$550$	3.27597	+	5.67414i	0.139688	+	0.241946i
$551$		−	0.0560816i		−	0.00238915i
$552$		0			0
$553$	−37.3601	+	21.5699i	−1.58871	+	0.917245i
$554$			21.3735i			0.908071i
$555$		0			0
$556$	−0.515915	+	0.893592i	−0.0218797	+	0.0378967i
$557$	−24.3810	−	14.0764i	−1.03306	−	0.596435i	−0.115197	−	0.993343i	$-0.536750\pi$
$557$	−24.3810	−	14.0764i	−1.03306	−	0.596435i	−0.917858	+	0.396908i	$0.870083\pi$
$558$		0			0
$559$	2.02106	−	3.54536i	0.0854816	−	0.149953i
$560$	−9.76645			−0.412708
$561$		0			0
$562$	−6.54676	+	11.3393i	−0.276159	+	0.478321i
$563$	9.06514	+	15.7013i	0.382050	+	0.661731i	0.991355	−	0.131206i	$-0.0418848\pi$
$563$	9.06514	+	15.7013i	0.382050	+	0.661731i	−0.609305	+	0.792936i	$0.708551\pi$
$564$		0			0
$565$	6.12789	−	3.53794i	0.257802	−	0.148842i
$566$	−1.39258	+	0.804007i	−0.0585346	+	0.0337950i
$567$		0			0
$568$	−16.5431	−	28.6535i	−0.694133	−	1.20227i
$569$	−20.2992	+	35.1593i	−0.850988	+	1.47395i	0.0293292	+	0.999570i	$0.490663\pi$
$569$	−20.2992	+	35.1593i	−0.850988	+	1.47395i	−0.880317	+	0.474385i	$0.842670\pi$
$570$		0			0
$571$	−24.7159			−1.03433			−0.517164	−	0.855886i	$-0.673012\pi$
$571$	−24.7159			−1.03433			−0.517164	+	0.855886i	$0.673012\pi$
$572$	8.56677	−	5.00891i	0.358195	−	0.209433i
$573$		0			0
$574$	14.1923	+	8.19393i	0.592375	+	0.342008i
$575$	−1.94644	+	3.37133i	−0.0811720	+	0.140594i
$576$		0			0
$577$		−	23.0691i		−	0.960379i	−0.877165	−	0.480189i	$-0.840568\pi$
$577$		−	23.0691i		−	0.960379i	0.877165	−	0.480189i	$-0.159432\pi$
$578$	−16.6036	+	9.58607i	−0.690617	+	0.398728i
$579$		0			0
$580$		−	0.0126697i		−	0.000526079i
$581$	−21.8327	−	37.8153i	−0.905771	−	1.56884i
$582$		0			0
$583$	20.6525	+	11.9237i	0.855341	+	0.493831i
$584$	14.4116			0.596358
$585$		0			0
$586$	22.8602			0.944345
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	0.817502	−	0.575926i	$-0.195358\pi$
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	−0.0900152	+	0.995940i	$0.528692\pi$
$588$		0			0
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$			0.209084i			0.00860786i
$591$		0			0
$592$	20.4486	−	11.8060i	0.840432	−	0.485223i
$593$		−	10.3834i		−	0.426395i	−0.977009	−	0.213198i	$-0.931612\pi$
$593$		−	10.3834i		−	0.426395i	0.977009	−	0.213198i	$-0.0683878\pi$
$594$		0			0
$595$	2.03745	−	3.52897i	0.0835273	−	0.144674i
$596$	2.44836	+	1.41356i	0.100289	+	0.0579017i
$597$		0			0
$598$	−14.8726	−	8.47825i	−0.608187	−	0.346701i
$599$	31.5965			1.29100			0.645499	−	0.763761i	$-0.276649\pi$
$599$	31.5965			1.29100			0.645499	+	0.763761i	$0.276649\pi$
$600$		0			0
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.0612928	−	0.998120i	$-0.480478\pi$
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.833751	−	0.552141i	$-0.186189\pi$
$602$	2.48505	+	4.30423i	0.101283	+	0.175428i
$603$		0			0
$604$	−2.16962	+	1.25263i	−0.0882806	+	0.0509688i
$605$	15.4641	−	8.92820i	0.628705	−	0.362983i
$606$		0			0
$607$	−1.08770	−	1.88395i	−0.0441484	−	0.0764673i	0.843107	−	0.537746i	$-0.180724\pi$
$607$	−1.08770	−	1.88395i	−0.0441484	−	0.0764673i	−0.887255	+	0.461279i	$0.847391\pi$
$608$	−3.19768	+	5.53854i	−0.129683	+	0.224617i
$609$		0			0
$610$	4.09843			0.165941
$611$	8.04707	−	4.70504i	0.325550	−	0.190346i
$612$		0			0
$613$	−12.7843	−	7.38100i	−0.516352	−	0.298116i	0.219089	−	0.975705i	$-0.429691\pi$
$613$	−12.7843	−	7.38100i	−0.516352	−	0.298116i	−0.735441	+	0.677589i	$0.763025\pi$
$614$	8.72336	−	15.1093i	0.352046	−	0.609762i
$615$		0			0
$616$			59.2622i			2.38774i
$617$	−17.5779	+	10.1486i	−0.707659	+	0.408567i	−0.810194	−	0.586162i	$-0.800638\pi$
$617$	−17.5779	+	10.1486i	−0.707659	+	0.408567i	0.102535	+	0.994729i	$0.467305\pi$
$618$		0			0
$619$			9.94207i			0.399605i	0.979836	+	0.199803i	$0.0640301\pi$
$619$			9.94207i			0.399605i	−0.979836	+	0.199803i	$0.935970\pi$
$620$	1.39980	+	2.42453i	0.0562175	+	0.0973716i
$621$		0			0
$622$	−2.91641	−	1.68379i	−0.116937	−	0.0675138i
$623$	−58.1577			−2.33004
$624$		0			0
$625$	1.00000			0.0400000
$626$	17.3080	+	9.99276i	0.691766	+	0.399391i
$627$		0			0
$628$	−2.57221	−	4.45519i	−0.102642	−	0.177782i
$629$			9.85174i			0.392815i
$630$		0			0
$631$	0.843006	−	0.486710i	0.0335596	−	0.0193756i	−0.483126	−	0.875551i	$-0.660499\pi$
$631$	0.843006	−	0.486710i	0.0335596	−	0.0193756i	0.516686	+	0.856175i	$0.327165\pi$
$632$		−	36.7183i		−	1.46058i
$633$		0			0
$634$	1.08903	−	1.88625i	0.0432507	−	0.0749124i
$635$	9.90396	+	5.71806i	0.393027	+	0.226914i
$636$		0			0
$637$	21.4938	−	0.117945i	0.851617	−	0.00467314i
$638$	0.162015			0.00641425
$639$		0			0
$640$	2.58631	−	4.47962i	0.102233	−	0.177072i
$641$	6.31047	+	10.9301i	0.249249	+	0.431711i	0.963318	−	0.268364i	$-0.0864830\pi$
$641$	6.31047	+	10.9301i	0.249249	+	0.431711i	−0.714069	+	0.700075i	$0.753150\pi$
$642$		0			0
$643$	−8.62599	+	4.98022i	−0.340176	+	0.196401i	−0.660350	−	0.750958i	$-0.729592\pi$
$643$	−8.62599	+	4.98022i	−0.340176	+	0.196401i	0.320174	+	0.947359i	$0.396259\pi$
$644$	−6.21878	+	3.59042i	−0.245054	+	0.141482i
$645$		0			0
$646$	1.56546	+	2.71146i	0.0615923	+	0.106681i
$647$	18.1381	−	31.4162i	0.713084	−	1.23510i	−0.250610	−	0.968088i	$-0.580631\pi$
$647$	18.1381	−	31.4162i	0.713084	−	1.23510i	0.963694	−	0.267009i	$-0.0860354\pi$
$648$		0			0
$649$	0.920861			0.0361470
$650$	0.0241312	+	4.39758i	0.000946502	+	0.172487i
$651$		0			0
$652$	−3.00898	−	1.73723i	−0.117841	−	0.0680353i
$653$	6.87769	−	11.9125i	0.269145	−	0.466172i	−0.699497	−	0.714636i	$-0.746592\pi$
$653$	6.87769	−	11.9125i	0.269145	−	0.466172i	0.968641	+	0.248464i	$0.0799257\pi$
$654$		0			0
$655$		−	10.5680i		−	0.412925i
$656$	−8.76776	+	5.06207i	−0.342324	+	0.197641i
$657$		0			0
$658$			11.3526i			0.442570i
$659$	−1.29092	−	2.23593i	−0.0502869	−	0.0870995i	0.839786	−	0.542917i	$-0.182680\pi$
$659$	−1.29092	−	2.23593i	−0.0502869	−	0.0870995i	−0.890073	+	0.455818i	$0.849347\pi$
$660$		0			0
$661$	−21.5437	−	12.4382i	−0.837951	−	0.483791i	0.0186163	−	0.999827i	$-0.494074\pi$
$661$	−21.5437	−	12.4382i	−0.837951	−	0.483791i	−0.856567	+	0.516036i	$0.827407\pi$
$662$	8.81151			0.342469
$663$		0			0
$664$	37.1656			1.44231
$665$	7.07115	+	4.08253i	0.274207	+	0.158314i
$666$		0			0
$667$	0.0481312	+	0.0833657i	0.00186365	+	0.00322793i
$668$		−	5.37460i		−	0.207949i
$669$		0			0
$670$	−6.75998	+	3.90288i	−0.261161	+	0.150781i
$671$		−	18.0506i		−	0.696834i
$672$		0			0
$673$	21.6611	−	37.5181i	0.834974	−	1.44622i	−0.0590774	−	0.998253i	$-0.518816\pi$
$673$	21.6611	−	37.5181i	0.834974	−	1.44622i	0.894052	−	0.447964i	$-0.147851\pi$
$674$	−4.60770	−	2.66025i	−0.177482	−	0.102469i
$675$		0			0
$676$	6.66033	−	0.0730977i	0.256167	−	0.00281145i
$677$	41.3625			1.58969			0.794845	−	0.606813i	$-0.207552\pi$
$677$	41.3625			1.58969			0.794845	+	0.606813i	$0.207552\pi$
$678$		0			0
$679$	−21.9039	+	37.9386i	−0.840594	+	1.45595i
$680$	1.73417	+	3.00367i	0.0665024	+	0.115186i
$681$		0			0
$682$	−31.0041	+	17.9002i	−1.18721	+	0.685435i
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	−0.542892	−	0.839802i	$-0.682671\pi$
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	0.455844	+	0.890060i	$0.349338\pi$
$684$		0			0
$685$	1.89336	+	3.27940i	0.0723416	+	0.125299i
$686$	2.28028	−	3.94957i	0.0870617	−	0.150795i
$687$		0			0
$688$	−3.07045			−0.117060
$689$	8.07914	+	13.8178i	0.307791	+	0.526417i
$690$		0			0
$691$	−13.2288	−	7.63765i	−0.503247	−	0.290550i	0.226806	−	0.973940i	$-0.427172\pi$
$691$	−13.2288	−	7.63765i	−0.503247	−	0.290550i	−0.730053	+	0.683390i	$0.760505\pi$
$692$	1.14218	−	1.97831i	0.0434190	−	0.0752039i
$693$		0			0
$694$			32.5744i			1.23651i
$695$	−1.74406	+	1.00693i	−0.0661558	+	0.0381951i
$696$		0			0
$697$		−	4.22414i		−	0.160001i
$698$	14.3747	+	24.8976i	0.544089	+	0.942390i
$699$		0			0
$700$	1.59748	+	0.922305i	0.0603790	+	0.0348599i
$701$	−48.1947			−1.82029			−0.910144	−	0.414292i	$-0.864029\pi$
$701$	−48.1947			−1.82029			−0.910144	+	0.414292i	$0.864029\pi$
$702$		0			0
$703$	−19.7404			−0.744522
$704$	−41.2406	−	23.8103i	−1.55431	−	0.897383i
$705$		0			0
$706$	3.49884	+	6.06016i	0.131680	+	0.228077i
$707$		−	14.5967i		−	0.548964i
$708$		0			0
$709$	−33.6624	+	19.4350i	−1.26422	+	0.729896i	−0.973887	−	0.227031i	$-0.927098\pi$
$709$	−33.6624	+	19.4350i	−1.26422	+	0.729896i	−0.290329	+	0.956927i	$0.593765\pi$
$710$		−	13.1694i		−	0.494237i
$711$		0			0
$712$	24.7504	−	42.8689i	0.927560	−	1.60658i
$713$	−18.4213	−	10.6355i	−0.689882	−	0.398304i
$714$		0			0
$715$	19.3681	−	0.106280i	0.724325	−	0.00397464i
$716$	9.54600			0.356751
$717$		0			0
$718$	15.0987	−	26.1517i	0.563478	−	0.975973i
$719$	−3.30830	−	5.73015i	−0.123379	−	0.213698i	0.797719	−	0.603029i	$-0.206040\pi$
$719$	−3.30830	−	5.73015i	−0.123379	−	0.213698i	−0.921098	+	0.389331i	$0.872706\pi$
$720$		0			0
$721$	55.8205	−	32.2280i	2.07887	−	1.20023i
$722$	14.6362	−	8.45024i	0.544705	−	0.314485i
$723$		0			0
$724$	4.63433	+	8.02690i	0.172234	+	0.298317i
$725$	0.0123639	−	0.0214150i	0.000459185	−	0.000795332i
$726$		0			0
$727$	18.3735			0.681435			0.340717	−	0.940166i	$-0.389330\pi$
$727$	18.3735			0.681435			0.340717	+	0.940166i	$0.389330\pi$
$728$	−19.6990	+	34.5562i	−0.730094	+	1.28074i
$729$		0			0
$730$	4.96777	+	2.86814i	0.183866	+	0.106155i
$731$	0.640548	−	1.10946i	0.0236915	−	0.0410349i
$732$		0			0
$733$		−	0.791131i		−	0.0292211i	−0.999893	−	0.0146105i	$-0.995349\pi$
$733$		−	0.791131i		−	0.0292211i	0.999893	−	0.0146105i	$-0.00465084\pi$
$734$	27.5198	−	15.8886i	1.01578	−	0.586458i
$735$		0			0
$736$		−	10.9774i		−	0.404634i
$737$	17.1893	+	29.7727i	0.633175	+	1.09669i
$738$		0			0
$739$	−27.0073	−	15.5926i	−0.993478	−	0.573585i	−0.0871658	−	0.996194i	$-0.527781\pi$
$739$	−27.0073	−	15.5926i	−0.993478	−	0.573585i	−0.906312	+	0.422609i	$0.861114\pi$
$740$	−4.45965			−0.163940
$741$		0			0
$742$	−19.4938			−0.715639
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	0.409017	−	0.912527i	$-0.365872\pi$
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	−0.585763	+	0.810483i	$0.699205\pi$
$744$		0			0
$745$	2.75890	+	4.77855i	0.101078	+	0.175073i
$746$			16.1053i			0.589658i
$747$		0			0
$748$	2.69787	−	1.55762i	0.0986439	−	0.0569521i
$749$			32.8765i			1.20128i
$750$		0			0
$751$	−17.6048	+	30.4925i	−0.642410	+	1.11269i	0.342483	+	0.939524i	$0.388732\pi$
$751$	−17.6048	+	30.4925i	−0.642410	+	1.11269i	−0.984893	+	0.173163i	$0.944601\pi$
$752$	−6.07381	−	3.50672i	−0.221489	−	0.127877i
$753$		0			0
$754$	0.0944723	+	0.0538546i	0.00344048	+	0.00196127i
$755$	−4.88961			−0.177951
$756$		0			0
$757$	−25.0223	+	43.3399i	−0.909451	+	1.57522i	−0.0946237	+	0.995513i	$0.530165\pi$
$757$	−25.0223	+	43.3399i	−0.909451	+	1.57522i	−0.814828	+	0.579703i	$0.803169\pi$
$758$	−15.8545	−	27.4609i	−0.575863	−	0.997424i
$759$		0			0
$760$	−6.01859	+	3.47484i	−0.218317	+	0.126046i
$761$	−38.8161	+	22.4105i	−1.40708	+	0.812379i	−0.995106	−	0.0988165i	$-0.968494\pi$
$761$	−38.8161	+	22.4105i	−1.40708	+	0.812379i	−0.411975	+	0.911195i	$0.635161\pi$
$762$		0			0
$763$	−13.2776	−	22.9975i	−0.480682	−	0.832566i
$764$	7.00307	−	12.1297i	0.253362	−	0.438836i
$765$		0			0
$766$	11.7092			0.423072
$767$	0.536961	+	0.306098i	0.0193885	+	0.0110526i
$768$		0			0
$769$	−34.0897	−	19.6817i	−1.22930	−	0.709739i	−0.262420	−	0.964954i	$-0.584521\pi$
$769$	−34.0897	−	19.6817i	−1.22930	−	0.709739i	−0.966884	+	0.255215i	$0.917854\pi$
$770$	−11.7941	+	20.4280i	−0.425031	+	0.736175i
$771$		0			0
$772$			11.1528i			0.401399i
$773$	42.2452	−	24.3902i	1.51945	−	0.877256i	0.519715	−	0.854340i	$-0.326038\pi$
$773$	42.2452	−	24.3902i	1.51945	−	0.877256i	0.999737	−	0.0229167i	$-0.00729525\pi$
$774$		0			0
$775$			5.46410i			0.196276i
$776$	−18.6434	−	32.2914i	−0.669260	−	1.15919i
$777$		0			0
$778$	−5.94822	−	3.43420i	−0.213254	−	0.123122i
$779$	8.46410			0.303258
$780$		0			0
$781$	−58.0013			−2.07545
$782$	−4.65415	−	2.68707i	−0.166432	−	0.0960895i
$783$		0			0
$784$	−8.08592	−	14.0052i	−0.288783	−	0.500187i
$785$		−	10.0405i		−	0.358363i
$786$		0			0
$787$	34.5204	−	19.9304i	1.23052	−	0.710442i	0.263382	−	0.964692i	$-0.415162\pi$
$787$	34.5204	−	19.9304i	1.23052	−	0.710442i	0.967139	+	0.254250i	$0.0818286\pi$
$788$		−	0.869338i		−	0.0309689i
$789$		0			0
$790$	7.30752	−	12.6570i	0.259990	−	0.450316i
$791$	22.0616	+	12.7373i	0.784420	+	0.452885i
$792$		0			0
$793$	6.00008	−	10.5254i	0.213069	−	0.373768i
$794$	20.4490			0.725709
$795$		0			0
$796$	6.48793	−	11.2374i	0.229958	−	0.398300i
$797$	−13.1059	−	22.7001i	−0.464235	−	0.804079i	0.534932	−	0.844895i	$-0.320337\pi$
$797$	−13.1059	−	22.7001i	−0.464235	−	0.804079i	−0.999167	+	0.0408167i	$0.987004\pi$
$798$		0			0
$799$	2.53420	−	1.46312i	0.0896537	−	0.0517616i
$800$	−2.44209	+	1.40994i	−0.0863409	+	0.0498490i
$801$		0			0
$802$	8.46343	+	14.6591i	0.298854	+	0.517630i
$803$	12.6321	−	21.8794i	0.445775	−	0.772106i
$804$		0			0
$805$	−14.0151			−0.493968
$806$	−24.0288	+	0.131855i	−0.846379	+	0.00464440i
$807$		0			0
$808$	10.7594	+	6.21196i	0.378515	+	0.218536i
$809$	11.1068	−	19.2376i	0.390495	−	0.676357i	−0.602020	−	0.798481i	$-0.705637\pi$
$809$	11.1068	−	19.2376i	0.390495	−	0.676357i	0.992515	+	0.122124i	$0.0389705\pi$
$810$		0			0
$811$		−	19.0950i		−	0.670515i	−0.942127	−	0.335257i	$-0.891177\pi$
$811$		−	19.0950i		−	0.670515i	0.942127	−	0.335257i	$-0.108823\pi$
$812$	0.0395023	−	0.0228066i	0.00138626	−	0.000800356i
$813$		0			0
$814$		−	57.0284i		−	1.99885i
$815$	−3.39062	−	5.87273i	−0.118768	−	0.205713i
$816$		0			0
$817$	2.22308	+	1.28349i	0.0777757	+	0.0449038i
$818$	35.8894			1.25484
$819$		0			0
$820$	1.91217			0.0667758
$821$	29.5820	+	17.0792i	1.03242	+	0.596068i	0.917677	−	0.397327i	$-0.130062\pi$
$821$	29.5820	+	17.0792i	1.03242	+	0.596068i	0.114743	+	0.993395i	$0.463396\pi$
$822$		0			0
$823$	2.03970	+	3.53286i	0.0710995	+	0.123148i	0.899383	−	0.437161i	$-0.144016\pi$
$823$	2.03970	+	3.53286i	0.0710995	+	0.123148i	−0.828284	+	0.560309i	$0.810683\pi$
$824$			54.8616i			1.91119i
$825$		0			0
$826$	−0.651896	+	0.376372i	−0.0226824	+	0.0130957i
$827$			54.8780i			1.90830i	0.299337	+	0.954148i	$0.403235\pi$
$827$			54.8780i			1.90830i	−0.299337	+	0.954148i	$0.596765\pi$
$828$		0			0
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	−0.786548	−	0.617529i	$-0.788134\pi$
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	0.928070	+	0.372406i	$0.121467\pi$
$830$	12.8112	+	7.39654i	0.444683	+	0.256738i
$831$		0			0
$832$	−16.1330	−	27.5925i	−0.559313	−	0.956597i
$833$	6.74745			0.233785
$834$		0			0
$835$	5.24490	−	9.08444i	0.181507	−	0.314380i
$836$	3.12107	+	5.40585i	0.107944	+	0.186965i
$837$		0			0
$838$	−7.36008	+	4.24935i	−0.254250	+	0.146791i
$839$	18.9543	−	10.9433i	0.654374	−	0.377803i	−0.135756	−	0.990742i	$-0.543346\pi$
$839$	18.9543	−	10.9433i	0.654374	−	0.377803i	0.790130	+	0.612939i	$0.210013\pi$
$840$		0			0
$841$	14.4997	+	25.1142i	0.499989	+	0.866007i
$842$	−4.34285	+	7.52204i	−0.149664	+	0.259226i
$843$		0			0
$844$	−0.171902			−0.00591710
$845$	11.3290	+	6.37605i	0.389729	+	0.219343i
$846$		0			0
$847$	55.6738	+	32.1433i	1.91297	+	1.10446i
$848$	6.02147	−	10.4295i	0.206778	−	0.358150i
$849$		0			0
$850$			1.38051i			0.0473511i
$851$	29.3442	−	16.9419i	1.00591	−	0.580761i
$852$		0			0
$853$		−	19.2240i		−	0.658217i	−0.944292	−	0.329108i	$-0.893252\pi$
$853$		−	19.2240i		−	0.658217i	0.944292	−	0.329108i	$-0.106748\pi$
$854$	7.37758	+	12.7783i	0.252456	+	0.437266i
$855$		0			0
$856$	−24.2337	−	13.9914i	−0.828292	−	0.478215i
$857$	−27.8197			−0.950302			−0.475151	−	0.879904i	$-0.657607\pi$
$857$	−27.8197			−0.950302			−0.475151	+	0.879904i	$0.657607\pi$
$858$		0			0
$859$	45.7355			1.56048			0.780238	−	0.625482i	$-0.215098\pi$
$859$	45.7355			1.56048			0.780238	+	0.625482i	$0.215098\pi$
$860$	0.502227	+	0.289961i	0.0171258	+	0.00988758i
$861$		0			0
$862$	18.4260	+	31.9148i	0.627593	+	1.08702i
$863$			54.8186i			1.86605i	0.359814	+	0.933024i	$0.382840\pi$
$863$			54.8186i			1.86605i	−0.359814	+	0.933024i	$0.617160\pi$
$864$		0			0
$865$	3.86113	−	2.22923i	0.131283	−	0.0757960i
$866$		−	1.46378i		−	0.0497413i
$867$		0			0
$868$	−5.03957	+	8.72879i	−0.171054	+	0.296274i
$869$	−55.7447	−	32.1842i	−1.89101	−	1.09177i
$870$		0			0
$871$	0.126618	+	23.0745i	0.00429030	+	0.781849i
$872$	22.6024			0.765415
$873$		0			0
$874$	5.38421	−	9.32572i	0.182124	−	0.315447i
$875$	1.80010	+	3.11786i	0.0608544	+	0.105403i
$876$		0			0
$877$	23.7113	−	13.6897i	0.800673	−	0.462269i	−0.0430336	−	0.999074i	$-0.513702\pi$
$877$	23.7113	−	13.6897i	0.800673	−	0.462269i	0.843706	+	0.536805i	$0.180369\pi$
$878$	17.4858	−	10.0954i	0.590116	−	0.340704i
$879$		0			0
$880$	−7.28621	−	12.6201i	−0.245618	−	0.425423i
$881$	17.2213	−	29.8282i	0.580200	−	1.00494i	−0.415255	−	0.909705i	$-0.636308\pi$
$881$	17.2213	−	29.8282i	0.580200	−	1.00494i	0.995455	−	0.0952310i	$-0.0303590\pi$
$882$		0			0
$883$	17.3592			0.584183			0.292092	−	0.956390i	$-0.405649\pi$
$883$	17.3592			0.584183			0.292092	+	0.956390i	$0.405649\pi$
$884$	2.09091	−	0.0114736i	0.0703248	−	0.000385899i
$885$		0			0
$886$	4.81610	+	2.78058i	0.161800	+	0.0934153i
$887$	−15.5714	+	26.9704i	−0.522835	+	0.905577i	0.476812	+	0.879005i	$0.341792\pi$
$887$	−15.5714	+	26.9704i	−0.522835	+	0.905577i	−0.999647	+	0.0265716i	$0.991541\pi$
$888$		0			0
$889$			41.1722i			1.38087i
$890$	17.0632	−	9.85143i	0.571959	−	0.330221i
$891$		0			0
$892$			6.30042i			0.210954i
$893$	2.93173	+	5.07790i	0.0981065	+	0.169925i
$894$		0			0
$895$	16.1352	+	9.31564i	0.539339	+	0.311388i
$896$	18.6224			0.622132
$897$		0			0
$898$	16.8953			0.563804
$899$	0.117014	+	0.0675578i	0.00390262	+	0.00225318i
$900$		0			0
$901$	2.51236	+	4.35154i	0.0836990	+	0.144971i
$902$			24.4521i			0.814167i
$903$		0			0
$904$	−18.7777	+	10.8413i	−0.624536	+	0.360576i
$905$			18.0900i			0.601332i
$906$		0			0
$907$	8.80284	−	15.2470i	0.292294	−	0.506267i	−0.682058	−	0.731298i	$-0.738915\pi$
$907$	8.80284	−	15.2470i	0.292294	−	0.506267i	0.974352	+	0.225031i	$0.0722482\pi$
$908$	3.38659	+	1.95525i	0.112388	+	0.0648872i
$909$		0			0
$910$	−13.6676	+	7.99131i	−0.453076	+	0.264909i
$911$	−50.0232			−1.65734			−0.828671	−	0.559737i	$-0.810902\pi$
$911$	−50.0232			−1.65734			−0.828671	+	0.559737i	$0.810902\pi$
$912$		0			0
$913$	32.5763	−	56.4238i	1.07812	−	1.86735i
$914$	−24.4636	−	42.3722i	−0.809184	−	1.40155i
$915$		0			0
$916$	−6.38992	+	3.68922i	−0.211129	+	0.121895i
$917$	32.9495	−	19.0234i	1.08809	−	0.628207i
$918$		0			0
$919$	3.80778	+	6.59527i	0.125607	+	0.217558i	0.921970	−	0.387261i	$-0.126579\pi$
$919$	3.80778	+	6.59527i	0.125607	+	0.217558i	−0.796363	+	0.604819i	$0.793245\pi$
$920$	5.96446	−	10.3307i	0.196642	−	0.340595i
$921$		0			0
$922$	9.19522			0.302828
$923$	−33.8209	−	19.2799i	−1.11323	−	0.634604i
$924$		0			0
$925$	−7.53794	−	4.35203i	−0.247846	−	0.143094i
$926$	14.2113	−	24.6146i	0.467011	−	0.808887i
$927$		0			0
$928$			0.0697297i			0.00228899i
$929$	−12.2317	+	7.06196i	−0.401308	+	0.231695i	−0.687048	−	0.726612i	$-0.741094\pi$
$929$	−12.2317	+	7.06196i	−0.401308	+	0.231695i	0.285740	+	0.958307i	$0.407761\pi$
$930$		0			0
$931$			13.5202i			0.443106i
$932$	−2.43275	−	4.21364i	−0.0796873	−	0.138022i
$933$		0			0
$934$	23.9033	+	13.8006i	0.782140	+	0.451569i
$935$	6.08012			0.198841
$936$		0			0
$937$	−23.9317			−0.781815			−0.390908	−	0.920430i	$-0.627839\pi$
$937$	−23.9317			−0.781815			−0.390908	+	0.920430i	$0.627839\pi$
$938$	−24.3373	−	14.0511i	−0.794640	−	0.458786i
$939$		0			0
$940$	0.662321	+	1.14717i	0.0216025	+	0.0374167i
$941$		−	25.3591i		−	0.826683i	−0.910576	−	0.413342i	$-0.864362\pi$
$941$		−	25.3591i		−	0.826683i	0.910576	−	0.413342i	$-0.135638\pi$
$942$		0			0
$943$	−12.5820	+	7.26420i	−0.409725	+	0.236555i
$944$		−	0.465033i		−	0.0151355i
$945$		0			0
$946$	−3.70792	+	6.42231i	−0.120555	+	0.208807i
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.952665	−	0.304022i	$-0.0983296\pi$
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.213042	+	0.977043i	$0.431663\pi$
$948$		0			0
$949$	14.6386	−	8.55906i	0.475190	−	0.277839i
$950$	−2.76619			−0.0897470
$951$		0			0
$952$	−6.24335	+	10.8138i	−0.202348	+	0.350477i
$953$	−12.1513	−	21.0466i	−0.393619	−	0.681767i	0.599305	−	0.800521i	$-0.295444\pi$
$953$	−12.1513	−	21.0466i	−0.393619	−	0.681767i	−0.992924	+	0.118753i	$0.962110\pi$
$954$		0			0
$955$	23.6740	−	13.6682i	0.766071	−	0.442291i
$956$	−8.83639	+	5.10169i	−0.285789	+	0.165001i
$957$		0			0
$958$	−12.5901	−	21.8067i	−0.406768	−	0.704543i
$959$	−6.81647	+	11.8065i	−0.220115	+	0.381251i
$960$		0			0
$961$	1.14359			0.0368901
$962$	18.9565	−	33.2537i	0.611182	−	1.07214i
$963$		0			0
$964$	−10.3238	−	5.96043i	−0.332506	−	0.191972i
$965$	−10.8837	+	18.8511i	−0.350358	+	0.606839i
$966$		0			0
$967$		−	23.6784i		−	0.761445i	−0.924689	−	0.380722i	$-0.875675\pi$
$967$		−	23.6784i		−	0.761445i	0.924689	−	0.380722i	$-0.124325\pi$
$968$	−47.3866	+	27.3587i	−1.52306	+	0.879341i
$969$		0			0
$970$		−	14.8413i		−	0.476527i
$971$	−8.48609	−	14.6983i	−0.272332	−	0.471692i	0.697127	−	0.716948i	$-0.254461\pi$
$971$	−8.48609	−	14.6983i	−0.272332	−	0.471692i	−0.969458	+	0.245256i	$0.921128\pi$
$972$		0			0
$973$	−6.27895	−	3.62515i	−0.201294	−	0.116217i
$974$	3.70303			0.118653
$975$		0			0
$976$	−9.11550			−0.291780
$977$	−21.6501	−	12.4997i	−0.692649	−	0.399901i	0.111955	−	0.993713i	$-0.464289\pi$
$977$	−21.6501	−	12.4997i	−0.692649	−	0.399901i	−0.804604	+	0.593812i	$0.797622\pi$
$978$		0			0
$979$	−43.3883	−	75.1507i	−1.38669	−	2.40183i
$980$			3.05441i			0.0975696i
$981$		0			0
$982$	11.2684	−	6.50582i	0.359589	−	0.207609i
$983$			27.3418i			0.872068i	0.899930	+	0.436034i	$0.143617\pi$
$983$			27.3418i			0.872068i	−0.899930	+	0.436034i	$0.856383\pi$
$984$		0			0
$985$	0.848360	−	1.46940i	0.0270310	−	0.0468191i
$986$	0.0295635	+	0.0170685i	0.000941495	+	0.000543573i
$987$		0			0
$988$	0.0229901	+	4.18964i	0.000731414	+	0.133290i
$989$	−4.40617			−0.140108
$990$		0			0
$991$	−8.03802	+	13.9223i	−0.255336	+	0.442255i	−0.964987	−	0.262299i	$-0.915519\pi$
$991$	−8.03802	+	13.9223i	−0.255336	+	0.442255i	0.709651	+	0.704554i	$0.248853\pi$
$992$	−7.70406	−	13.3438i	−0.244604	−	0.423667i
$993$		0			0
$994$	41.0602	−	23.7061i	1.30235	−	0.751913i
$995$	21.9325	−	12.6627i	0.695307	−	0.401436i
$996$		0			0
$997$	17.2806	+	29.9309i	0.547282	+	0.947920i	0.998459	+	0.0554858i	$0.0176708\pi$
$997$	17.2806	+	29.9309i	0.547282	+	0.947920i	−0.451178	+	0.892434i	$0.648996\pi$
$998$	−20.6824	+	35.8230i	−0.654691	+	1.13396i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.c.316.2		8
3.2	odd	2		65.2.m.a.56.3	yes	8
12.11	even	2		1040.2.da.b.641.4		8
13.6	odd	12		7605.2.a.cj.1.3		4
13.7	odd	12		7605.2.a.cf.1.2		4
13.10	even	6	inner	585.2.bu.c.361.2		8
15.2	even	4		325.2.m.b.199.2		8
15.8	even	4		325.2.m.c.199.3		8
15.14	odd	2		325.2.n.d.251.2		8
39.2	even	12		845.2.e.n.146.3		8
39.5	even	4		845.2.e.n.191.3		8
39.8	even	4		845.2.e.m.191.2		8
39.11	even	12		845.2.e.m.146.2		8
39.17	odd	6		845.2.c.g.506.6		8
39.20	even	12		845.2.a.m.1.3		4
39.23	odd	6		65.2.m.a.36.3	✓	8
39.29	odd	6		845.2.m.g.361.2		8
39.32	even	12		845.2.a.l.1.2		4
39.35	odd	6		845.2.c.g.506.3		8
39.38	odd	2		845.2.m.g.316.2		8
156.23	even	6		1040.2.da.b.881.4		8
195.23	even	12		325.2.m.b.49.2		8
195.59	even	12		4225.2.a.bi.1.2		4
195.62	even	12		325.2.m.c.49.3		8
195.149	even	12		4225.2.a.bl.1.3		4
195.179	odd	6		325.2.n.d.101.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	39.23	odd	6
65.2.m.a.56.3	yes	8	3.2	odd	2
325.2.m.b.49.2		8	195.23	even	12
325.2.m.b.199.2		8	15.2	even	4
325.2.m.c.49.3		8	195.62	even	12
325.2.m.c.199.3		8	15.8	even	4
325.2.n.d.101.2		8	195.179	odd	6
325.2.n.d.251.2		8	15.14	odd	2
585.2.bu.c.316.2		8	1.1	even	1	trivial
585.2.bu.c.361.2		8	13.10	even	6	inner
845.2.a.l.1.2		4	39.32	even	12
845.2.a.m.1.3		4	39.20	even	12
845.2.c.g.506.3		8	39.35	odd	6
845.2.c.g.506.6		8	39.17	odd	6
845.2.e.m.146.2		8	39.11	even	12
845.2.e.m.191.2		8	39.8	even	4
845.2.e.n.146.3		8	39.2	even	12
845.2.e.n.191.3		8	39.5	even	4
845.2.m.g.316.2		8	39.38	odd	2
845.2.m.g.361.2		8	39.29	odd	6
1040.2.da.b.641.4		8	12.11	even	2
1040.2.da.b.881.4		8	156.23	even	6
4225.2.a.bi.1.2		4	195.59	even	12
4225.2.a.bl.1.3		4	195.149	even	12
7605.2.a.cf.1.2		4	13.7	odd	12
7605.2.a.cj.1.3		4	13.6	odd	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05628 - 0.609843i) q^{2} +(-0.256182 - 0.443720i) q^{4} -1.00000i q^{5} +(3.11786 - 1.80010i) q^{7} +3.06430i q^{8} +O(q^{10})\)	\(q+(-1.05628 - 0.609843i) q^{2} +(-0.256182 - 0.443720i) q^{4} -1.00000i q^{5} +(3.11786 - 1.80010i) q^{7} +3.06430i q^{8} +(-0.609843 + 1.05628i) q^{10} +(4.65213 + 2.68591i) q^{11} +(1.81988 + 3.11256i) q^{13} -4.39111 q^{14} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-0.443720 + 0.256182i) q^{20} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} -1.00000 q^{25} +(-0.0241312 - 4.39758i) q^{26} +(-1.59748 - 0.922305i) q^{28} +(-0.0123639 + 0.0214150i) q^{29} -5.46410i q^{31} +(2.44209 - 1.40994i) q^{32} -1.38051i q^{34} +(-1.80010 - 3.11786i) q^{35} +(7.53794 + 4.35203i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-3.23205 - 1.86603i) q^{41} +(-0.565928 - 0.980215i) q^{43} -2.75232i q^{44} +(-4.11196 + 2.37404i) q^{46} -2.58535i q^{47} +(2.98070 - 5.16273i) q^{49} +(1.05628 + 0.609843i) q^{50} +(0.914884 - 1.60490i) q^{52} +4.43937 q^{53} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +(0.0261196 - 0.0150801i) q^{58} +(0.148458 - 0.0857123i) q^{59} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} -8.86488 q^{64} +(3.11256 - 1.81988i) q^{65} +(5.54239 + 3.19990i) q^{67} +(0.289961 - 0.502227i) q^{68} +4.39111i q^{70} +(-9.35076 + 5.39866i) q^{71} -4.70308i q^{73} +(-5.30812 - 9.19393i) q^{74} +(1.00633 + 0.581008i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-2.34932 - 1.35638i) q^{80} +(2.27597 + 3.94209i) q^{82} -12.1286i q^{83} +(0.980215 - 0.565928i) q^{85} +1.38051i q^{86} +(-8.23042 + 14.2555i) q^{88} +(-13.9898 - 8.07702i) q^{89} +(11.2771 + 6.42856i) q^{91} -1.99457 q^{92} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +(-10.5379 + 6.08408i) q^{97} +(-6.29692 + 3.63553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^7	\( 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

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