LMFDB - Embedded newform 585.2.bu.c.361.2

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			361.2
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	585.361
Dual form			585.2.bu.c.316.2

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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	−0.824574	−	0.565755i	$-0.808585\pi$
$2$	−1.05628	+	0.609843i	−0.746903	+	0.431224i	0.0776710	+	0.996979i	$0.475252\pi$
$3$		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	0.955653	−	0.294494i	$-0.0951511\pi$
$7$	3.11786	+	1.80010i	1.17844	+	0.680373i	0.222787	+	0.974867i	$0.428484\pi$
$8$		−	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	0.408004	−	0.912980i	$-0.366225\pi$
$11$	4.65213	−	2.68591i	1.40267	−	0.809832i	0.994666	+	0.103149i	$0.0328917\pi$
$12$		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	−0.789200	−	0.614136i	$-0.789505\pi$
$17$	0.565928	−	0.980215i	0.137258	−	0.237737i	0.926458	+	0.376399i	$0.122838\pi$
$18$		0			0
$19$	−1.96410	−	1.13397i	−0.450596	−	0.260152i	0.257486	−	0.966282i	$-0.417106\pi$
$19$	−1.96410	−	1.13397i	−0.450596	−	0.260152i	−0.708082	+	0.706130i	$0.750439\pi$
$20$	−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	0.994421	−	0.105483i	$-0.0336387\pi$
$23$	1.94644	+	3.37133i	0.405860	+	0.702970i	−0.588561	+	0.808453i	$0.700305\pi$
$24$		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	0.864875	−	0.501987i	$-0.167397\pi$
$29$	−0.0123639	−	0.0214150i	−0.00229593	−	0.00397666i	−0.867171	+	0.498010i	$0.834064\pi$
$30$		0			0
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	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	0.270293	−	0.962778i	$-0.412879\pi$
$37$	7.53794	−	4.35203i	1.23923	−	0.715470i	0.968937	+	0.247309i	$0.0795462\pi$
$38$	2.76619			0.448735
$39$		0			0
$40$	3.06430			0.484508
$41$	−3.23205	+	1.86603i	−0.504762	+	0.291424i	−0.730678	−	0.682723i	$-0.760796\pi$
$41$	−3.23205	+	1.86603i	−0.504762	+	0.291424i	0.225916	+	0.974147i	$0.427462\pi$
$42$		0			0
$43$	−0.565928	+	0.980215i	−0.0863031	+	0.149481i	−0.905946	−	0.423394i	$-0.860839\pi$
$43$	−0.565928	+	0.980215i	−0.0863031	+	0.149481i	0.819643	+	0.572875i	$0.194172\pi$
$44$			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	$0.0603808\pi$
$47$			2.58535i			0.377113i	−0.982062	+	0.188556i	$0.939619\pi$
$48$		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	0.509633	−	0.860392i	$-0.329781\pi$
$59$	0.148458	+	0.0857123i	0.0193276	+	0.0111588i	−0.490305	+	0.871551i	$0.663115\pi$
$60$		0			0
$61$	−1.68012	+	2.91005i	−0.215117	+	0.372594i	−0.953309	−	0.301997i	$-0.902347\pi$
$61$	−1.68012	+	2.91005i	−0.215117	+	0.372594i	0.738192	+	0.674591i	$0.235680\pi$
$62$	−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	−0.121655	−	0.992572i	$-0.538820\pi$
$67$	5.54239	−	3.19990i	0.677111	−	0.390930i	0.798766	+	0.601642i	$0.205487\pi$
$68$	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	−0.170971	−	0.985276i	$-0.554691\pi$
$71$	−9.35076	−	5.39866i	−1.10973	−	0.640703i	−0.938760	+	0.344573i	$0.888024\pi$
$72$		0			0
$73$			4.70308i			0.550454i	0.961379	+	0.275227i	$0.0887531\pi$
$73$			4.70308i			0.550454i	−0.961379	+	0.275227i	$0.911247\pi$
$74$	−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	$0.231843\pi$
$83$			12.1286i			1.33129i	−0.746270	+	0.665643i	$0.768157\pi$
$84$		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	−0.999812	−	0.0194001i	$-0.993824\pi$
$89$	−13.9898	+	8.07702i	−1.48292	+	0.856162i	−0.483105	+	0.875562i	$0.660491\pi$
$90$		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	−0.141794	−	0.989896i	$-0.545287\pi$
$97$	−10.5379	−	6.08408i	−1.06997	−	0.617745i	−0.928172	+	0.372151i	$0.878620\pi$
$98$	−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	0.949081	−	0.315032i	$-0.102015\pi$
$101$	2.02721	+	3.51122i	0.201714	+	0.349380i	−0.747366	+	0.664412i	$0.768682\pi$
$102$		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	0.556389	−	0.830922i	$-0.312186\pi$
$107$	−4.56593	−	7.90842i	−0.441405	−	0.764536i	−0.997794	+	0.0663862i	$0.978853\pi$
$108$		0			0
$109$			7.37605i			0.706498i	0.935529	+	0.353249i	$0.114923\pi$
$109$			7.37605i			0.706498i	−0.935529	+	0.353249i	$0.885077\pi$
$110$	−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	−0.650243	−	0.759727i	$-0.725333\pi$
$113$	3.53794	−	6.12789i	0.332821	−	0.576463i	0.983064	+	0.183263i	$0.0586661\pi$
$114$		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	−0.999963	−	0.00856072i	$-0.997275\pi$
$127$	−5.71806	−	9.90396i	−0.507395	−	0.878835i	0.492568	−	0.870274i	$-0.336058\pi$
$128$	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	0.353326	−	0.935500i	$-0.385051\pi$
$137$	−3.27940	−	1.89336i	−0.280178	−	0.161761i	−0.633504	+	0.773739i	$0.718384\pi$
$138$		0			0
$139$	−1.00693	+	1.74406i	−0.0854068	+	0.147929i	−0.905564	−	0.424209i	$-0.860552\pi$
$139$	−1.00693	+	1.74406i	−0.0854068	+	0.147929i	0.820158	+	0.572138i	$0.193886\pi$
$140$	−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	0.291324	−	0.956624i	$-0.405904\pi$
$149$	−4.77855	−	2.75890i	−0.391474	−	0.226018i	−0.682799	+	0.730607i	$0.739237\pi$
$150$		0			0
$151$			4.88961i			0.397911i	0.980009	+	0.198956i	$0.0637549\pi$
$151$			4.88961i			0.397911i	−0.980009	+	0.198956i	$0.936245\pi$
$152$	−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	0.712039	−	0.702140i	$-0.247772\pi$
$163$	5.87273	+	3.39062i	0.459988	+	0.265574i	−0.252051	+	0.967714i	$0.581105\pi$
$164$		−	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	−0.105479	−	0.994421i	$-0.533638\pi$
$167$	9.08444	−	5.24490i	0.702975	−	0.405863i	0.808455	+	0.588559i	$0.200304\pi$
$168$		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	−0.768754	−	0.639545i	$-0.779123\pi$
$173$	2.22923	−	3.86113i	0.169485	−	0.293557i	0.938239	+	0.345988i	$0.112456\pi$
$174$		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	−0.969746	−	0.244116i	$-0.921502\pi$
$179$	−9.31564	−	16.1352i	−0.696284	−	1.20600i	0.273462	−	0.961883i	$-0.411831\pi$
$180$		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	0.366361	−	0.930473i	$-0.380603\pi$
$191$	13.6682	−	23.6740i	0.988994	−	1.71299i	0.622632	−	0.782515i	$-0.286063\pi$
$192$		0			0
$193$	−18.8511	+	10.8837i	−1.35693	+	0.783425i	−0.989209	−	0.146510i	$-0.953196\pi$
$193$	−18.8511	+	10.8837i	−1.35693	+	0.783425i	−0.367723	+	0.929935i	$0.619863\pi$
$194$	14.8413			1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	1.46940	−	0.848360i	0.104691	−	0.0604432i	−0.446741	−	0.894664i	$-0.647415\pi$
$197$	1.46940	−	0.848360i	0.104691	−	0.0604432i	0.551431	+	0.834220i	$0.314082\pi$
$198$		0			0
$199$	12.6627	−	21.9325i	0.897637	−	1.55475i	0.0671309	−	0.997744i	$-0.478615\pi$
$199$	12.6627	−	21.9325i	0.897637	−	1.55475i	0.830506	−	0.557009i	$-0.188051\pi$
$200$			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	0.871742	−	0.489965i	$-0.162991\pi$
$211$	0.167753	+	0.290558i	0.0115486	+	0.0200028i	−0.860193	+	0.509968i	$0.829657\pi$
$212$	−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	−0.812219	−	0.583353i	$-0.801741\pi$
$223$	−10.6493	+	6.14838i	−0.713130	+	0.411726i	0.0990887	+	0.995079i	$0.468407\pi$
$224$	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	0.264344	−	0.964428i	$-0.414845\pi$
$227$	−6.60974	−	3.81613i	−0.438704	−	0.253286i	−0.703048	+	0.711143i	$0.748178\pi$
$228$		0			0
$229$			14.4008i			0.951631i	0.879545	+	0.475815i	$0.157847\pi$
$229$			14.4008i			0.951631i	−0.879545	+	0.475815i	$0.842153\pi$
$230$	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	$0.222758\pi$
$239$			19.9143i			1.28815i	−0.764962	+	0.644076i	$0.777242\pi$
$240$		0			0
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.980046	−	0.198770i	$-0.0636947\pi$
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.317883	+	0.948130i	$0.397028\pi$
$242$			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	−0.990127	−	0.140171i	$-0.955235\pi$
$251$	−5.92008	+	10.2539i	−0.373672	+	0.647219i	0.616455	+	0.787390i	$0.288568\pi$
$252$		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	0.939502	−	0.342543i	$-0.111288\pi$
$257$	2.77501	+	4.80646i	0.173100	+	0.299819i	−0.766402	+	0.642361i	$0.777955\pi$
$258$		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	0.952182	−	0.305532i	$-0.0988342\pi$
$263$	3.42983	+	5.94065i	0.211493	+	0.366316i	−0.740689	+	0.671848i	$0.765501\pi$
$264$		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	−0.886886	−	0.461988i	$-0.847136\pi$
$269$	−0.710994	+	1.23148i	−0.0433501	+	0.0750845i	0.843536	+	0.537072i	$0.180470\pi$
$270$		0			0
$271$	8.63381	−	4.98473i	0.524467	−	0.302801i	−0.214294	−	0.976769i	$-0.568745\pi$
$271$	8.63381	−	4.98473i	0.524467	−	0.302801i	0.738760	+	0.673968i	$0.235412\pi$
$272$	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	0.473076	+	0.881022i	$0.343144\pi$
$277$	−8.76187	+	15.1760i	−0.526449	+	0.911837i	−0.999525	+	0.0308154i	$0.990190\pi$
$278$		−	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	$0.103751\pi$
$281$			10.7352i			0.640406i	−0.947349	+	0.320203i	$0.896249\pi$
$282$		0			0
$283$	0.659192	+	1.14175i	0.0391849	+	0.0678702i	0.884953	−	0.465681i	$-0.154191\pi$
$283$	0.659192	+	1.14175i	0.0391849	+	0.0678702i	−0.845768	+	0.533551i	$0.820857\pi$
$284$	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	−0.0557207	−	0.998446i	$-0.517746\pi$
$293$	−16.2316	−	9.37133i	−0.948261	−	0.547479i	−0.892540	+	0.450968i	$0.851079\pi$
$294$		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	$-0.866159\pi$
$307$		−	14.3043i		−	0.816387i	0.912895	−	0.408194i	$-0.133841\pi$
$308$	−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	$-0.984030\pi$
$317$		−	1.78575i		−	0.100297i	0.998742	−	0.0501487i	$-0.0159695\pi$
$318$		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	0.318101	−	0.948057i	$-0.396955\pi$
$331$	−6.25652	−	3.61220i	−0.343889	−	0.198545i	−0.661991	+	0.749512i	$0.730288\pi$
$332$	−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	0.245381	+	0.969427i	$0.421087\pi$
$347$	−13.3536	+	23.1291i	−0.716858	+	1.24163i	−0.962239	+	0.272207i	$0.912246\pi$
$348$		0			0
$349$	−20.4131	+	11.7855i	−1.09269	+	0.630865i	−0.934292	−	0.356510i	$-0.883967\pi$
$349$	−20.4131	+	11.7855i	−1.09269	+	0.630865i	−0.158399	+	0.987375i	$0.550633\pi$
$350$	4.39111			0.234715
$351$		0			0
$352$	15.1479			0.807385
$353$	−4.96862	+	2.86863i	−0.264453	+	0.152682i	−0.626364	−	0.779531i	$-0.715458\pi$
$353$	−4.96862	+	2.86863i	−0.264453	+	0.152682i	0.361911	+	0.932213i	$0.382124\pi$
$354$		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	$-0.773364\pi$
$359$		−	24.7583i		−	1.30669i	0.757059	−	0.653347i	$-0.226636\pi$
$360$		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	−0.974983	−	0.222280i	$-0.928650\pi$
$367$	−13.0268	−	22.5630i	−0.679992	−	1.17778i	0.294991	−	0.955500i	$-0.404683\pi$
$368$	−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	−0.984776	−	0.173826i	$-0.944387\pi$
$373$	−6.60224	+	11.4354i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$374$	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	0.206039	−	0.978544i	$-0.433943\pi$
$379$	22.5147	−	12.9989i	1.15650	−	0.667707i	0.950463	+	0.310837i	$0.100609\pi$
$380$	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	0.272314	−	0.962208i	$-0.412211\pi$
$383$	−8.31401	−	4.80010i	−0.424826	−	0.245274i	−0.697140	+	0.716935i	$0.745544\pi$
$384$		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	0.0892344	−	0.996011i	$-0.471558\pi$
$397$	−14.5196	−	8.38291i	−0.728719	−	0.420726i	−0.817953	+	0.575285i	$0.804891\pi$
$398$			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	−0.769115	−	0.639110i	$-0.779303\pi$
$401$	−12.0187	+	6.93902i	−0.600187	+	0.346518i	0.168928	+	0.985628i	$0.445969\pi$
$402$		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	−0.286964	−	0.957941i	$-0.592646\pi$
$409$	−25.4829	−	14.7125i	−1.26005	−	0.727489i	−0.973083	+	0.230453i	$0.925979\pi$
$410$	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	0.938491	−	0.345305i	$-0.112224\pi$
$419$	3.48397	+	6.03440i	0.170203	+	0.294800i	−0.768288	+	0.640104i	$0.778891\pi$
$420$		0			0
$421$			7.12125i			0.347069i	0.984828	+	0.173534i	$0.0555188\pi$
$421$			7.12125i			0.347069i	−0.984828	+	0.173534i	$0.944481\pi$
$422$	−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	−0.973150	−	0.230171i	$-0.926071\pi$
$431$	−26.1664	+	15.1072i	−1.26039	+	0.727687i	−0.287241	+	0.957858i	$0.592738\pi$
$432$		0			0
$433$	0.600065	−	1.03934i	0.0288373	−	0.0499476i	−0.851247	−	0.524766i	$-0.824153\pi$
$433$	0.600065	−	1.03934i	0.0288373	−	0.0499476i	0.880084	+	0.474818i	$0.157486\pi$
$434$		−	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	0.598064	−	0.801448i	$-0.295937\pi$
$439$	−8.27705	−	14.3363i	−0.395042	−	0.684233i	−0.993107	+	0.117215i	$0.962603\pi$
$440$	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	0.189465	−	0.981887i	$-0.439325\pi$
$449$	−11.9963	−	6.92608i	−0.566142	−	0.326862i	−0.755607	+	0.655025i	$0.772658\pi$
$450$		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	0.639548	−	0.768751i	$-0.279122\pi$
$457$	34.7402	−	20.0573i	1.62508	−	0.938240i	0.985532	−	0.169489i	$-0.0542117\pi$
$458$	−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	0.340192	−	0.940356i	$-0.389508\pi$
$461$	−6.52897	−	3.76950i	−0.304084	−	0.175563i	−0.644276	+	0.764793i	$0.722841\pi$
$462$		0			0
$463$		−	23.3031i		−	1.08299i	−0.840705	−	0.541494i	$-0.817859\pi$
$463$		−	23.3031i		−	1.08299i	0.840705	−	0.541494i	$-0.182141\pi$
$464$	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	−0.0324399	−	0.999474i	$-0.510328\pi$
$479$	17.8789	−	10.3224i	0.816910	−	0.471643i	0.849350	+	0.527831i	$0.176994\pi$
$480$		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	0.439243	−	0.898368i	$-0.355247\pi$
$487$	−2.62929	−	1.51802i	−0.119145	−	0.0687882i	−0.558388	+	0.829580i	$0.688580\pi$
$488$	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	0.720199	−	0.693767i	$-0.244050\pi$
$491$	−5.33401	−	9.23877i	−0.240720	−	0.416940i	−0.960920	+	0.276827i	$0.910717\pi$
$492$		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	$0.274364\pi$
$499$			33.9143i			1.51821i	−0.650966	+	0.759107i	$0.725636\pi$
$500$	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	−0.971759	−	0.235976i	$-0.924171\pi$
$503$	−6.31380	+	10.9358i	−0.281518	+	0.487604i	0.690241	+	0.723580i	$0.257505\pi$
$504$		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	0.0412201	−	0.999150i	$-0.486876\pi$
$509$	20.9168	−	12.0763i	0.927120	−	0.535273i	0.885899	+	0.463877i	$0.153542\pi$
$510$		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	−0.913098	−	0.407739i	$-0.866317\pi$
$523$	−18.5163	−	32.0712i	−0.809662	−	1.40238i	0.103436	−	0.994636i	$-0.467016\pi$
$524$	−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	$0.0576658\pi$
$541$			8.38144i			0.360346i	−0.983635	+	0.180173i	$0.942334\pi$
$542$	−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	−0.917858	−	0.396908i	$-0.870083\pi$
$557$	−24.3810	+	14.0764i	−1.03306	+	0.596435i	−0.115197	+	0.993343i	$0.536750\pi$
$558$		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	−0.609305	−	0.792936i	$-0.708551\pi$
$563$	9.06514	−	15.7013i	0.382050	−	0.661731i	0.991355	+	0.131206i	$0.0418848\pi$
$564$		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	−0.880317	−	0.474385i	$-0.842670\pi$
$569$	−20.2992	−	35.1593i	−0.850988	−	1.47395i	0.0293292	−	0.999570i	$-0.490663\pi$
$570$		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	$0.159432\pi$
$577$			23.0691i			0.960379i	−0.877165	+	0.480189i	$0.840568\pi$
$578$	−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	−0.0900152	−	0.995940i	$-0.528692\pi$
$587$	17.6256	−	10.1762i	0.727487	−	0.420015i	0.817502	+	0.575926i	$0.195358\pi$
$588$		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	$0.0683878\pi$
$593$			10.3834i			0.426395i	−0.977009	+	0.213198i	$0.931612\pi$
$594$		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	0.833751	+	0.552141i	$0.186189\pi$
$601$	21.9423	+	38.0051i	0.895044	+	1.55026i	0.0612928	+	0.998120i	$0.480478\pi$
$602$	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	−0.887255	−	0.461279i	$-0.847391\pi$
$607$	−1.08770	+	1.88395i	−0.0441484	+	0.0764673i	0.843107	+	0.537746i	$0.180724\pi$
$608$	−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	−0.735441	−	0.677589i	$-0.763025\pi$
$613$	−12.7843	+	7.38100i	−0.516352	+	0.298116i	0.219089	+	0.975705i	$0.429691\pi$
$614$	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	0.102535	−	0.994729i	$-0.467305\pi$
$617$	−17.5779	−	10.1486i	−0.707659	−	0.408567i	−0.810194	+	0.586162i	$0.800638\pi$
$618$		0			0
$619$		−	9.94207i		−	0.399605i	−0.979836	−	0.199803i	$-0.935970\pi$
$619$		−	9.94207i		−	0.399605i	0.979836	−	0.199803i	$-0.0640301\pi$
$620$	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	0.516686	−	0.856175i	$-0.327165\pi$
$631$	0.843006	+	0.486710i	0.0335596	+	0.0193756i	−0.483126	+	0.875551i	$0.660499\pi$
$632$			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	−0.714069	−	0.700075i	$-0.753150\pi$
$641$	6.31047	−	10.9301i	0.249249	−	0.431711i	0.963318	+	0.268364i	$0.0864830\pi$
$642$		0			0
$643$	−8.62599	−	4.98022i	−0.340176	−	0.196401i	0.320174	−	0.947359i	$-0.396259\pi$
$643$	−8.62599	−	4.98022i	−0.340176	−	0.196401i	−0.660350	+	0.750958i	$0.729592\pi$
$644$	−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	0.963694	+	0.267009i	$0.0860354\pi$
$647$	18.1381	+	31.4162i	0.713084	+	1.23510i	−0.250610	+	0.968088i	$0.580631\pi$
$648$		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	0.968641	−	0.248464i	$-0.0799257\pi$
$653$	6.87769	+	11.9125i	0.269145	+	0.466172i	−0.699497	+	0.714636i	$0.746592\pi$
$654$		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	−0.890073	−	0.455818i	$-0.849347\pi$
$659$	−1.29092	+	2.23593i	−0.0502869	+	0.0870995i	0.839786	+	0.542917i	$0.182680\pi$
$660$		0			0
$661$	−21.5437	+	12.4382i	−0.837951	+	0.483791i	−0.856567	−	0.516036i	$-0.827407\pi$
$661$	−21.5437	+	12.4382i	−0.837951	+	0.483791i	0.0186163	+	0.999827i	$0.494074\pi$
$662$	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	0.894052	+	0.447964i	$0.147851\pi$
$673$	21.6611	+	37.5181i	0.834974	+	1.44622i	−0.0590774	+	0.998253i	$0.518816\pi$
$674$	−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	0.455844	−	0.890060i	$-0.349338\pi$
$683$	−2.27495	−	1.31344i	−0.0870484	−	0.0502574i	−0.542892	+	0.839802i	$0.682671\pi$
$684$		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	−0.730053	−	0.683390i	$-0.760505\pi$
$691$	−13.2288	+	7.63765i	−0.503247	+	0.290550i	0.226806	+	0.973940i	$0.427172\pi$
$692$	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	−0.290329	−	0.956927i	$-0.593765\pi$
$709$	−33.6624	−	19.4350i	−1.26422	−	0.729896i	−0.973887	+	0.227031i	$0.927098\pi$
$710$			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	−0.921098	−	0.389331i	$-0.872706\pi$
$719$	−3.30830	+	5.73015i	−0.123379	+	0.213698i	0.797719	+	0.603029i	$0.206040\pi$
$720$		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	$0.00465084\pi$
$733$			0.791131i			0.0292211i	−0.999893	+	0.0146105i	$0.995349\pi$
$734$	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	−0.906312	−	0.422609i	$-0.861114\pi$
$739$	−27.0073	+	15.5926i	−0.993478	+	0.573585i	−0.0871658	+	0.996194i	$0.527781\pi$
$740$	−4.45965			−0.163940
$741$		0			0
$742$	−19.4938			−0.715639
$743$	−4.81773	+	2.78152i	−0.176745	+	0.102044i	−0.585763	−	0.810483i	$-0.699205\pi$
$743$	−4.81773	+	2.78152i	−0.176745	+	0.102044i	0.409017	+	0.912527i	$0.365872\pi$
$744$		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	−0.984893	−	0.173163i	$-0.944601\pi$
$751$	−17.6048	−	30.4925i	−0.642410	−	1.11269i	0.342483	−	0.939524i	$-0.388732\pi$
$752$	−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	−0.814828	−	0.579703i	$-0.803169\pi$
$757$	−25.0223	−	43.3399i	−0.909451	−	1.57522i	−0.0946237	−	0.995513i	$-0.530165\pi$
$758$	−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	−0.411975	−	0.911195i	$-0.635161\pi$
$761$	−38.8161	−	22.4105i	−1.40708	−	0.812379i	−0.995106	+	0.0988165i	$0.968494\pi$
$762$		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	−0.966884	−	0.255215i	$-0.917854\pi$
$769$	−34.0897	+	19.6817i	−1.22930	+	0.709739i	−0.262420	+	0.964954i	$0.584521\pi$
$770$	−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	0.999737	+	0.0229167i	$0.00729525\pi$
$773$	42.2452	+	24.3902i	1.51945	+	0.877256i	0.519715	+	0.854340i	$0.326038\pi$
$774$		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	0.967139	−	0.254250i	$-0.0818286\pi$
$787$	34.5204	+	19.9304i	1.23052	+	0.710442i	0.263382	+	0.964692i	$0.415162\pi$
$788$			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	−0.999167	−	0.0408167i	$-0.987004\pi$
$797$	−13.1059	+	22.7001i	−0.464235	+	0.804079i	0.534932	+	0.844895i	$0.320337\pi$
$798$		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	0.992515	−	0.122124i	$-0.0389705\pi$
$809$	11.1068	+	19.2376i	0.390495	+	0.676357i	−0.602020	+	0.798481i	$0.705637\pi$
$810$		0			0
$811$			19.0950i			0.670515i	0.942127	+	0.335257i	$0.108823\pi$
$811$			19.0950i			0.670515i	−0.942127	+	0.335257i	$0.891177\pi$
$812$	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	0.114743	−	0.993395i	$-0.463396\pi$
$821$	29.5820	−	17.0792i	1.03242	−	0.596068i	0.917677	+	0.397327i	$0.130062\pi$
$822$		0			0
$823$	2.03970	−	3.53286i	0.0710995	−	0.123148i	−0.828284	−	0.560309i	$-0.810683\pi$
$823$	2.03970	−	3.53286i	0.0710995	−	0.123148i	0.899383	+	0.437161i	$0.144016\pi$
$824$		−	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	$-0.596765\pi$
$827$		−	54.8780i		−	1.90830i	0.299337	−	0.954148i	$-0.403235\pi$
$828$		0			0
$829$	4.07475	+	7.05768i	0.141522	+	0.245123i	0.928070	−	0.372406i	$-0.121467\pi$
$829$	4.07475	+	7.05768i	0.141522	+	0.245123i	−0.786548	+	0.617529i	$0.788134\pi$
$830$	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	0.790130	−	0.612939i	$-0.210013\pi$
$839$	18.9543	+	10.9433i	0.654374	+	0.377803i	−0.135756	+	0.990742i	$0.543346\pi$
$840$		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	$0.106748\pi$
$853$			19.2240i			0.658217i	−0.944292	+	0.329108i	$0.893252\pi$
$854$	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	$-0.617160\pi$
$863$		−	54.8186i		−	1.86605i	0.359814	−	0.933024i	$-0.382840\pi$
$864$		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	0.843706	−	0.536805i	$-0.180369\pi$
$877$	23.7113	+	13.6897i	0.800673	+	0.462269i	−0.0430336	+	0.999074i	$0.513702\pi$
$878$	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	0.995455	+	0.0952310i	$0.0303590\pi$
$881$	17.2213	+	29.8282i	0.580200	+	1.00494i	−0.415255	+	0.909705i	$0.636308\pi$
$882$		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	−0.999647	−	0.0265716i	$-0.991541\pi$
$887$	−15.5714	−	26.9704i	−0.522835	−	0.905577i	0.476812	−	0.879005i	$-0.341792\pi$
$888$		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	0.974352	−	0.225031i	$-0.0722482\pi$
$907$	8.80284	+	15.2470i	0.292294	+	0.506267i	−0.682058	+	0.731298i	$0.738915\pi$
$908$	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	−0.796363	−	0.604819i	$-0.793245\pi$
$919$	3.80778	−	6.59527i	0.125607	−	0.217558i	0.921970	+	0.387261i	$0.126579\pi$
$920$	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	0.285740	−	0.958307i	$-0.407761\pi$
$929$	−12.2317	−	7.06196i	−0.401308	−	0.231695i	−0.687048	+	0.726612i	$0.741094\pi$
$930$		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	$0.135638\pi$
$941$			25.3591i			0.826683i	−0.910576	+	0.413342i	$0.864362\pi$
$942$		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	0.213042	−	0.977043i	$-0.431663\pi$
$947$	35.8727	−	20.7111i	1.16571	−	0.673021i	0.952665	+	0.304022i	$0.0983296\pi$
$948$		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	−0.992924	−	0.118753i	$-0.962110\pi$
$953$	−12.1513	+	21.0466i	−0.393619	+	0.681767i	0.599305	+	0.800521i	$0.295444\pi$
$954$		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	$0.124325\pi$
$967$			23.6784i			0.761445i	−0.924689	+	0.380722i	$0.875675\pi$
$968$	−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	−0.969458	−	0.245256i	$-0.921128\pi$
$971$	−8.48609	+	14.6983i	−0.272332	+	0.471692i	0.697127	+	0.716948i	$0.254461\pi$
$972$		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	−0.804604	−	0.593812i	$-0.797622\pi$
$977$	−21.6501	+	12.4997i	−0.692649	+	0.399901i	0.111955	+	0.993713i	$0.464289\pi$
$978$		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	$-0.856383\pi$
$983$		−	27.3418i		−	0.872068i	0.899930	−	0.436034i	$-0.143617\pi$
$984$		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	0.709651	−	0.704554i	$-0.248853\pi$
$991$	−8.03802	−	13.9223i	−0.255336	−	0.442255i	−0.964987	+	0.262299i	$0.915519\pi$
$992$	−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	−0.451178	−	0.892434i	$-0.648996\pi$
$997$	17.2806	−	29.9309i	0.547282	−	0.947920i	0.998459	−	0.0554858i	$-0.0176708\pi$
$998$	−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.361.2		8
3.2	odd	2		65.2.m.a.36.3	✓	8
12.11	even	2		1040.2.da.b.881.4		8
13.2	odd	12		7605.2.a.cf.1.2		4
13.4	even	6	inner	585.2.bu.c.316.2		8
13.11	odd	12		7605.2.a.cj.1.3		4
15.2	even	4		325.2.m.c.49.3		8
15.8	even	4		325.2.m.b.49.2		8
15.14	odd	2		325.2.n.d.101.2		8
39.2	even	12		845.2.a.m.1.3		4
39.5	even	4		845.2.e.m.146.2		8
39.8	even	4		845.2.e.n.146.3		8
39.11	even	12		845.2.a.l.1.2		4
39.17	odd	6		65.2.m.a.56.3	yes	8
39.20	even	12		845.2.e.n.191.3		8
39.23	odd	6		845.2.c.g.506.3		8
39.29	odd	6		845.2.c.g.506.6		8
39.32	even	12		845.2.e.m.191.2		8
39.35	odd	6		845.2.m.g.316.2		8
39.38	odd	2		845.2.m.g.361.2		8
156.95	even	6		1040.2.da.b.641.4		8
195.17	even	12		325.2.m.b.199.2		8
195.89	even	12		4225.2.a.bl.1.3		4
195.119	even	12		4225.2.a.bi.1.2		4
195.134	odd	6		325.2.n.d.251.2		8
195.173	even	12		325.2.m.c.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	3.2	odd	2
65.2.m.a.56.3	yes	8	39.17	odd	6
325.2.m.b.49.2		8	15.8	even	4
325.2.m.b.199.2		8	195.17	even	12
325.2.m.c.49.3		8	15.2	even	4
325.2.m.c.199.3		8	195.173	even	12
325.2.n.d.101.2		8	15.14	odd	2
325.2.n.d.251.2		8	195.134	odd	6
585.2.bu.c.316.2		8	13.4	even	6	inner
585.2.bu.c.361.2		8	1.1	even	1	trivial
845.2.a.l.1.2		4	39.11	even	12
845.2.a.m.1.3		4	39.2	even	12
845.2.c.g.506.3		8	39.23	odd	6
845.2.c.g.506.6		8	39.29	odd	6
845.2.e.m.146.2		8	39.5	even	4
845.2.e.m.191.2		8	39.32	even	12
845.2.e.n.146.3		8	39.8	even	4
845.2.e.n.191.3		8	39.20	even	12
845.2.m.g.316.2		8	39.35	odd	6
845.2.m.g.361.2		8	39.38	odd	2
1040.2.da.b.641.4		8	156.95	even	6
1040.2.da.b.881.4		8	12.11	even	2
4225.2.a.bi.1.2		4	195.119	even	12
4225.2.a.bl.1.3		4	195.89	even	12
7605.2.a.cf.1.2		4	13.2	odd	12
7605.2.a.cj.1.3		4	13.11	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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