LMFDB - Embedded newform 585.2.bu.b.361.3

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:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$0.500000 - 0.564882i$ of defining polynomial
Character	$\chi$	$=$	585.361
Dual form			585.2.bu.b.316.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.260797 + 0.150571i) q^{2} +(-0.954656 + 1.65351i) q^{4} -1.00000i q^{5} +(2.97125 + 1.71545i) q^{7} -1.17726i q^{8} +O(q^{10})$	\(q+(-0.260797 + 0.150571i) q^{2} +(-0.954656 + 1.65351i) q^{4} -1.00000i q^{5} +(2.97125 + 1.71545i) q^{7} -1.17726i q^{8} +(0.150571 + 0.260797i) q^{10} +(-2.28749 + 1.32068i) q^{11} +(0.572034 + 3.55988i) q^{13} -1.03319 q^{14} +(-1.73205 - 3.00000i) q^{16} +(-0.0403455 + 0.0698805i) q^{17} +(0.824892 + 0.476251i) q^{19} +(1.65351 + 0.954656i) q^{20} +(0.397714 - 0.688861i) q^{22} +(-0.110226 - 0.190917i) q^{23} -1.00000 q^{25} +(-0.685202 - 0.842277i) q^{26} +(-5.67305 + 3.27534i) q^{28} +(4.82362 + 8.35476i) q^{29} +1.57498i q^{31} +(2.94251 + 1.69886i) q^{32} -0.0242995i q^{34} +(1.71545 - 2.97125i) q^{35} +(-2.47841 + 1.43091i) q^{37} -0.286840 q^{38} -1.17726 q^{40} +(-6.89590 + 3.98135i) q^{41} +(-4.46704 + 7.73715i) q^{43} -5.04319i q^{44} +(0.0574933 + 0.0331938i) q^{46} +8.52159i q^{47} +(2.38556 + 4.13192i) q^{49} +(0.260797 - 0.150571i) q^{50} +(-6.43241 - 2.45260i) q^{52} -5.28273 q^{53} +(1.32068 + 2.28749i) q^{55} +(2.01954 - 3.49794i) q^{56} +(-2.51598 - 1.45260i) q^{58} +(8.37841 + 4.83728i) q^{59} +(6.49373 - 11.2475i) q^{61} +(-0.237147 - 0.410750i) q^{62} +5.90501 q^{64} +(3.55988 - 0.572034i) q^{65} +(2.17001 - 1.25286i) q^{67} +(-0.0770322 - 0.133424i) q^{68} +1.03319i q^{70} +(-4.58363 - 2.64636i) q^{71} -14.3591i q^{73} +(0.430908 - 0.746354i) q^{74} +(-1.57498 + 0.909313i) q^{76} -9.06228 q^{77} +11.8661 q^{79} +(-3.00000 + 1.73205i) q^{80} +(1.19895 - 2.07665i) q^{82} -9.58956i q^{83} +(0.0698805 + 0.0403455i) q^{85} -2.69044i q^{86} +(1.55479 + 2.69297i) q^{88} +(9.17319 - 5.29614i) q^{89} +(-4.40716 + 11.5586i) q^{91} +0.420912 q^{92} +(-1.28311 - 2.22241i) q^{94} +(0.476251 - 0.824892i) q^{95} +(-4.05202 - 2.33943i) q^{97} +(-1.24430 - 0.718396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 4 q^{4} + 6 q^{7}+O(q^{10}) $ 8 * q - 6 * q^2 + 4 * q^4 + 6 * q^7	$ 8 q - 6 q^{2} + 4 q^{4} + 6 q^{7} + 2 q^{10} - 12 q^{11} + 6 q^{13} + 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 4 q^{26} - 12 q^{28} + 6 q^{29} - 12 q^{32} + 6 q^{35} - 12 q^{37} + 16 q^{38} + 30 q^{41} + 6 q^{43} + 36 q^{46} - 8 q^{49} + 6 q^{50} - 20 q^{52} + 32 q^{53} - 8 q^{55} - 4 q^{56} + 12 q^{58} + 30 q^{59} + 30 q^{62} + 32 q^{64} + 6 q^{65} + 30 q^{67} - 16 q^{68} - 18 q^{71} - 12 q^{74} + 8 q^{77} + 56 q^{79} - 24 q^{80} - 24 q^{82} + 6 q^{85} + 8 q^{88} + 18 q^{89} - 16 q^{91} - 40 q^{92} - 16 q^{94} - 6 q^{97} + 12 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 + 4 * q^4 + 6 * q^7 + 2 * q^10 - 12 * q^11 + 6 * q^13 + 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 4 * q^26 - 12 * q^28 + 6 * q^29 - 12 * q^32 + 6 * q^35 - 12 * q^37 + 16 * q^38 + 30 * q^41 + 6 * q^43 + 36 * q^46 - 8 * q^49 + 6 * q^50 - 20 * q^52 + 32 * q^53 - 8 * q^55 - 4 * q^56 + 12 * q^58 + 30 * q^59 + 30 * q^62 + 32 * q^64 + 6 * q^65 + 30 * q^67 - 16 * q^68 - 18 * q^71 - 12 * q^74 + 8 * q^77 + 56 * q^79 - 24 * q^80 - 24 * q^82 + 6 * q^85 + 8 * q^88 + 18 * q^89 - 16 * q^91 - 40 * q^92 - 16 * q^94 - 6 * q^97 + 12 * 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 $

$2$	−0.260797	+	0.150571i	−0.184412	+	0.106470i	−0.589364	−	0.807868i	$-0.700622\pi$
$2$	−0.260797	+	0.150571i	−0.184412	+	0.106470i	0.404952	+	0.914338i	$0.367288\pi$
$3$		0			0
$3$		0			0
$4$	−0.954656	+	1.65351i	−0.477328	+	0.826757i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	2.97125	+	1.71545i	1.12303	+	0.648381i	0.942172	−	0.335129i	$-0.108780\pi$
$7$	2.97125	+	1.71545i	1.12303	+	0.648381i	0.180856	+	0.983510i	$0.442113\pi$
$8$		−	1.17726i		−	0.416225i
$9$		0			0
$10$	0.150571	+	0.260797i	0.0476149	+	0.0824714i
$11$	−2.28749	+	1.32068i	−0.689704	+	0.398201i	−0.803501	−	0.595303i	$-0.797032\pi$
$11$	−2.28749	+	1.32068i	−0.689704	+	0.398201i	0.113797	+	0.993504i	$0.463699\pi$
$12$		0			0
$13$	0.572034	+	3.55988i	0.158654	+	0.987334i
$13$	0.572034	+	3.55988i	0.158654	+	0.987334i
$14$	−1.03319			−0.276133
$15$		0			0
$16$	−1.73205	−	3.00000i	−0.433013	−	0.750000i
$17$	−0.0403455	+	0.0698805i	−0.00978522	+	0.0169485i	−0.870877	−	0.491502i	$-0.836448\pi$
$17$	−0.0403455	+	0.0698805i	−0.00978522	+	0.0169485i	0.861091	+	0.508450i	$0.169781\pi$
$18$		0			0
$19$	0.824892	+	0.476251i	0.189243	+	0.109260i	0.591628	−	0.806211i	$-0.298485\pi$
$19$	0.824892	+	0.476251i	0.189243	+	0.109260i	−0.402385	+	0.915471i	$0.631819\pi$
$20$	1.65351	+	0.954656i	0.369737	+	0.213468i
$21$		0			0
$22$	0.397714	−	0.688861i	0.0847929	−	0.146866i
$23$	−0.110226	−	0.190917i	−0.0229837	−	0.0398089i	0.854305	−	0.519772i	$-0.173983\pi$
$23$	−0.110226	−	0.190917i	−0.0229837	−	0.0398089i	−0.877288	+	0.479963i	$0.840650\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.685202	−	0.842277i	−0.134379	−	0.165184i
$27$		0			0
$28$	−5.67305	+	3.27534i	−1.07211	+	0.618981i
$29$	4.82362	+	8.35476i	0.895724	+	1.55144i	0.832905	+	0.553415i	$0.186676\pi$
$29$	4.82362	+	8.35476i	0.895724	+	1.55144i	0.0628190	+	0.998025i	$0.479991\pi$
$30$		0			0
$31$			1.57498i			0.282874i	0.989947	+	0.141437i	$0.0451723\pi$
$31$			1.57498i			0.282874i	−0.989947	+	0.141437i	$0.954828\pi$
$32$	2.94251	+	1.69886i	0.520167	+	0.300318i
$33$		0			0
$34$		−	0.0242995i		−	0.00416734i
$35$	1.71545	−	2.97125i	0.289965	−	0.502233i
$36$		0			0
$37$	−2.47841	+	1.43091i	−0.407447	+	0.235240i	−0.689692	−	0.724103i	$-0.742254\pi$
$37$	−2.47841	+	1.43091i	−0.407447	+	0.235240i	0.282245	+	0.959342i	$0.408921\pi$
$38$	−0.286840			−0.0465315
$39$		0			0
$40$	−1.17726			−0.186141
$41$	−6.89590	+	3.98135i	−1.07696	+	0.621782i	−0.930074	−	0.367372i	$-0.880258\pi$
$41$	−6.89590	+	3.98135i	−1.07696	+	0.621782i	−0.146884	+	0.989154i	$0.546924\pi$
$42$		0			0
$43$	−4.46704	+	7.73715i	−0.681218	+	1.17990i	0.293392	+	0.955992i	$0.405216\pi$
$43$	−4.46704	+	7.73715i	−0.681218	+	1.17990i	−0.974609	+	0.223911i	$0.928117\pi$
$44$		−	5.04319i		−	0.760289i
$45$		0			0
$46$	0.0574933	+	0.0331938i	0.00847693	+	0.00489416i
$47$			8.52159i			1.24300i	0.783413	+	0.621501i	$0.213477\pi$
$47$			8.52159i			1.24300i	−0.783413	+	0.621501i	$0.786523\pi$
$48$		0			0
$49$	2.38556	+	4.13192i	0.340795	+	0.590274i
$50$	0.260797	−	0.150571i	0.0368823	−	0.0212940i
$51$		0			0
$52$	−6.43241	−	2.45260i	−0.892015	−	0.340114i
$53$	−5.28273			−0.725638			−0.362819	−	0.931860i	$-0.618186\pi$
$53$	−5.28273			−0.725638			−0.362819	+	0.931860i	$0.618186\pi$
$54$		0			0
$55$	1.32068	+	2.28749i	0.178081	+	0.308445i
$56$	2.01954	−	3.49794i	0.269872	−	0.467432i
$57$		0			0
$58$	−2.51598	−	1.45260i	−0.330364	−	0.190736i
$59$	8.37841	+	4.83728i	1.09078	+	0.629760i	0.933783	−	0.357840i	$-0.116487\pi$
$59$	8.37841	+	4.83728i	1.09078	+	0.629760i	0.156993	+	0.987600i	$0.449820\pi$
$60$		0			0
$61$	6.49373	−	11.2475i	0.831437	−	1.44009i	−0.0654609	−	0.997855i	$-0.520852\pi$
$61$	6.49373	−	11.2475i	0.831437	−	1.44009i	0.896898	−	0.442237i	$-0.145815\pi$
$62$	−0.237147	−	0.410750i	−0.0301176	−	0.0521653i
$63$		0			0
$64$	5.90501			0.738126
$65$	3.55988	−	0.572034i	0.441549	−	0.0709521i
$66$		0			0
$67$	2.17001	−	1.25286i	0.265109	−	0.153061i	−0.361554	−	0.932351i	$-0.617754\pi$
$67$	2.17001	−	1.25286i	0.265109	−	0.153061i	0.626663	+	0.779290i	$0.284420\pi$
$68$	−0.0770322	−	0.133424i	−0.00934153	−	0.0161800i
$69$		0			0
$70$			1.03319i			0.123490i
$71$	−4.58363	−	2.64636i	−0.543977	−	0.314065i	0.202712	−	0.979238i	$-0.435024\pi$
$71$	−4.58363	−	2.64636i	−0.543977	−	0.314065i	−0.746689	+	0.665173i	$0.768358\pi$
$72$		0			0
$73$		−	14.3591i		−	1.68061i	−0.542116	−	0.840303i	$-0.682377\pi$
$73$		−	14.3591i		−	1.68061i	0.542116	−	0.840303i	$-0.317623\pi$
$74$	0.430908	−	0.746354i	0.0500920	−	0.0867619i
$75$		0			0
$76$	−1.57498	+	0.909313i	−0.180662	+	0.104305i
$77$	−9.06228			−1.03274
$78$		0			0
$79$	11.8661			1.33504			0.667522	−	0.744590i	$-0.267355\pi$
$79$	11.8661			1.33504			0.667522	+	0.744590i	$0.267355\pi$
$80$	−3.00000	+	1.73205i	−0.335410	+	0.193649i
$81$		0			0
$82$	1.19895	−	2.07665i	0.132402	−	0.229328i
$83$		−	9.58956i		−	1.05259i	−0.850302	−	0.526295i	$-0.823581\pi$
$83$		−	9.58956i		−	1.05259i	0.850302	−	0.526295i	$-0.176419\pi$
$84$		0			0
$85$	0.0698805	+	0.0403455i	0.00757960	+	0.00437608i
$86$		−	2.69044i		−	0.290117i
$87$		0			0
$88$	1.55479	+	2.69297i	0.165741	+	0.287072i
$89$	9.17319	−	5.29614i	0.972356	−	0.561390i	0.0724026	−	0.997375i	$-0.476933\pi$
$89$	9.17319	−	5.29614i	0.972356	−	0.561390i	0.899954	+	0.435985i	$0.143600\pi$
$90$		0			0
$91$	−4.40716	+	11.5586i	−0.461996	+	1.21167i
$92$	0.420912			0.0438831
$93$		0			0
$94$	−1.28311	−	2.22241i	−0.132343	−	0.229224i
$95$	0.476251	−	0.824892i	0.0488624	−	0.0846321i
$96$		0			0
$97$	−4.05202	−	2.33943i	−0.411420	−	0.237533i	0.279980	−	0.960006i	$-0.409672\pi$
$97$	−4.05202	−	2.33943i	−0.411420	−	0.237533i	−0.691400	+	0.722473i	$0.743006\pi$
$98$	−1.24430	−	0.718396i	−0.125693	−	0.0725689i
$99$		0			0
$100$	0.954656	−	1.65351i	0.0954656	−	0.165351i
$101$	3.40137	+	5.89135i	0.338449	+	0.586211i	0.984141	−	0.177387i	$-0.0567643\pi$
$101$	3.40137	+	5.89135i	0.338449	+	0.586211i	−0.645692	+	0.763598i	$0.723431\pi$
$102$		0			0
$103$	4.67456			0.460598			0.230299	−	0.973120i	$-0.426030\pi$
$103$	4.67456			0.460598			0.230299	+	0.973120i	$0.426030\pi$
$104$	4.19092	−	0.673434i	0.410953	−	0.0660357i
$105$		0			0
$106$	1.37772	−	0.795428i	0.133816	−	0.0772588i
$107$	−6.66217	−	11.5392i	−0.644056	−	1.11554i	−0.984519	−	0.175280i	$-0.943917\pi$
$107$	−6.66217	−	11.5392i	−0.644056	−	1.11554i	0.340462	−	0.940258i	$-0.389416\pi$
$108$		0			0
$109$		−	5.12976i		−	0.491342i	−0.969353	−	0.245671i	$-0.920992\pi$
$109$		−	5.12976i		−	0.491342i	0.969353	−	0.245671i	$-0.0790083\pi$
$110$	−0.688861	−	0.397714i	−0.0656803	−	0.0379205i
$111$		0			0
$112$		−	11.8850i		−	1.12303i
$113$	4.08658	−	7.07816i	0.384433	−	0.665857i	−0.607258	−	0.794505i	$-0.707730\pi$
$113$	4.08658	−	7.07816i	0.384433	−	0.665857i	0.991690	+	0.128648i	$0.0410638\pi$
$114$		0			0
$115$	−0.190917	+	0.110226i	−0.0178031	+	0.0102786i
$116$	−18.4196			−1.71022
$117$		0			0
$118$	−2.91342			−0.268203
$119$	−0.239753	+	0.138422i	−0.0219782	+	0.0126891i
$120$		0			0
$121$	−2.01160	+	3.48419i	−0.182873	+	0.316745i
$122$			3.91108i			0.354093i
$123$		0			0
$124$	−2.60424	−	1.50356i	−0.233868	−	0.135024i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	10.4744	+	18.1422i	0.929456	+	1.60986i	0.784234	+	0.620465i	$0.213056\pi$
$127$	10.4744	+	18.1422i	0.929456	+	1.60986i	0.145222	+	0.989399i	$0.453610\pi$
$128$	−7.42502	+	4.28684i	−0.656286	+	0.378907i
$129$		0			0
$130$	−0.842277	+	0.685202i	−0.0738726	+	0.0600962i
$131$	17.0250			1.48748			0.743739	−	0.668470i	$-0.233050\pi$
$131$	17.0250			1.48748			0.743739	+	0.668470i	$0.233050\pi$
$132$		0			0
$133$	1.63397	+	2.83013i	0.141684	+	0.245403i
$134$	−0.377289	+	0.653484i	−0.0325928	+	0.0564524i
$135$		0			0
$136$	0.0822676	+	0.0474972i	0.00705439	+	0.00407285i
$137$	−12.9233	−	7.46126i	−1.10411	−	0.637458i	−0.166813	−	0.985989i	$-0.553347\pi$
$137$	−12.9233	−	7.46126i	−1.10411	−	0.637458i	−0.937297	+	0.348530i	$0.886681\pi$
$138$		0			0
$139$	4.05479	−	7.02310i	0.343923	−	0.595692i	−0.641235	−	0.767345i	$-0.721578\pi$
$139$	4.05479	−	7.02310i	0.343923	−	0.595692i	0.985157	+	0.171653i	$0.0549109\pi$
$140$	3.27534	+	5.67305i	0.276817	+	0.479460i
$141$		0			0
$142$	1.59387			0.133754
$143$	−6.01000	−	7.38772i	−0.502581	−	0.617792i
$144$		0			0
$145$	8.35476	−	4.82362i	0.693825	−	0.400580i
$146$	2.16207	+	3.74482i	0.178934	+	0.309923i
$147$		0			0
$148$		−	5.46410i		−	0.449146i
$149$	18.8471	+	10.8814i	1.54401	+	0.891435i	0.998580	+	0.0532800i	$0.0169676\pi$
$149$	18.8471	+	10.8814i	1.54401	+	0.891435i	0.545432	+	0.838155i	$0.316366\pi$
$150$		0			0
$151$		−	14.1688i		−	1.15304i	−0.817082	−	0.576522i	$-0.804409\pi$
$151$		−	14.1688i		−	1.15304i	0.817082	−	0.576522i	$-0.195591\pi$
$152$	0.560673	−	0.971114i	0.0454766	−	0.0787677i
$153$		0			0
$154$	2.36342	−	1.36452i	0.190450	−	0.109956i
$155$	1.57498			0.126505
$156$		0			0
$157$	−6.03449			−0.481605			−0.240802	−	0.970574i	$-0.577411\pi$
$157$	−6.03449			−0.481605			−0.240802	+	0.970574i	$0.577411\pi$
$158$	−3.09465	+	1.78670i	−0.246198	+	0.142142i
$159$		0			0
$160$	1.69886	−	2.94251i	0.134306	−	0.232626i
$161$		−	0.756350i		−	0.0596088i
$162$		0			0
$163$	−17.7138	−	10.2271i	−1.38745	−	0.801045i	−0.394423	−	0.918929i	$-0.629055\pi$
$163$	−17.7138	−	10.2271i	−1.38745	−	0.801045i	−0.993027	+	0.117885i	$0.962389\pi$
$164$		−	15.2033i		−	1.18718i
$165$		0			0
$166$	1.44391	+	2.50093i	0.112069	+	0.194110i
$167$	14.6704	−	8.46999i	1.13523	−	0.655427i	0.189987	−	0.981787i	$-0.439155\pi$
$167$	14.6704	−	8.46999i	1.13523	−	0.655427i	0.945246	+	0.326359i	$0.105822\pi$
$168$		0			0
$169$	−12.3456	+	4.07275i	−0.949658	+	0.313289i
$170$	−0.0242995			−0.00186369
$171$		0			0
$172$	−8.52898	−	14.7726i	−0.650329	−	1.12640i
$173$	−9.40534	+	16.2905i	−0.715075	+	1.23855i	0.247856	+	0.968797i	$0.420274\pi$
$173$	−9.40534	+	16.2905i	−0.715075	+	1.23855i	−0.962931	+	0.269749i	$0.913059\pi$
$174$		0			0
$175$	−2.97125	−	1.71545i	−0.224606	−	0.129676i
$176$	7.92409	+	4.57498i	0.597301	+	0.344852i
$177$		0			0
$178$	−1.59490	+	2.76244i	−0.119543	+	0.207054i
$179$	−5.13842	−	8.90001i	−0.384064	−	0.665218i	0.607575	−	0.794262i	$-0.292142\pi$
$179$	−5.13842	−	8.90001i	−0.384064	−	0.665218i	−0.991639	+	0.129044i	$0.958809\pi$
$180$		0			0
$181$	−15.0970			−1.12215			−0.561077	−	0.827763i	$-0.689613\pi$
$181$	−15.0970			−1.12215			−0.561077	+	0.827763i	$0.689613\pi$
$182$	−0.591022	−	3.67805i	−0.0438095	−	0.272635i
$183$		0			0
$184$	−0.224759	+	0.129765i	−0.0165695	+	0.00956639i
$185$	1.43091	+	2.47841i	0.105202	+	0.182216i
$186$		0			0
$187$		−	0.213134i		−	0.0155859i
$188$	−14.0906	−	8.13520i	−1.02766	−	0.593320i
$189$		0			0
$190$			0.286840i			0.0208095i
$191$	5.75659	−	9.97070i	0.416532	−	0.721455i	−0.579056	−	0.815288i	$-0.696579\pi$
$191$	5.75659	−	9.97070i	0.416532	−	0.721455i	0.995588	+	0.0938332i	$0.0299120\pi$
$192$		0			0
$193$	14.6819	−	8.47659i	1.05682	−	0.610158i	0.132273	−	0.991213i	$-0.457773\pi$
$193$	14.6819	−	8.47659i	1.05682	−	0.610158i	0.924552	+	0.381055i	$0.124439\pi$
$194$	1.40901			0.101161
$195$		0			0
$196$	−9.10958			−0.650684
$197$	10.1868	−	5.88135i	0.725780	−	0.419029i	−0.0910965	−	0.995842i	$-0.529037\pi$
$197$	10.1868	−	5.88135i	0.725780	−	0.419029i	0.816876	+	0.576813i	$0.195704\pi$
$198$		0			0
$199$	4.15724	−	7.20056i	0.294699	−	0.510434i	−0.680216	−	0.733012i	$-0.738114\pi$
$199$	4.15724	−	7.20056i	0.294699	−	0.510434i	0.974915	+	0.222578i	$0.0714472\pi$
$200$			1.17726i			0.0832450i
$201$		0			0
$202$	−1.77414	−	1.02430i	−0.124828	−	0.0720695i
$203$			33.0988i			2.32308i
$204$		0			0
$205$	3.98135	+	6.89590i	0.278069	+	0.481630i
$206$	−1.21911	+	0.703855i	−0.0849396	+	0.0490399i
$207$		0			0
$208$	9.68886	−	7.88200i	0.671802	−	0.546519i
$209$	−2.51591			−0.174029
$210$		0			0
$211$	8.21775	+	14.2336i	0.565733	+	0.979878i	0.996981	+	0.0776450i	$0.0247401\pi$
$211$	8.21775	+	14.2336i	0.565733	+	0.979878i	−0.431248	+	0.902233i	$0.641927\pi$
$212$	5.04319	−	8.73506i	0.346368	−	0.599926i
$213$		0			0
$214$	3.47495	+	2.00627i	0.237543	+	0.137146i
$215$	7.73715	+	4.46704i	0.527669	+	0.304650i
$216$		0			0
$217$	−2.70180	+	4.67965i	−0.183410	+	0.317676i
$218$	0.772396	+	1.33783i	0.0523133	+	0.0906093i
$219$		0			0
$220$	−5.04319			−0.340012
$221$	−0.271845	−	0.103651i	−0.0182863	−	0.00697234i
$222$		0			0
$223$	−1.97139	+	1.13818i	−0.132014	+	0.0762185i	−0.564553	−	0.825397i	$-0.690951\pi$
$223$	−1.97139	+	1.13818i	−0.132014	+	0.0762185i	0.432538	+	0.901615i	$0.357618\pi$
$224$	5.82862	+	10.0955i	0.389441	+	0.674532i
$225$		0			0
$226$			2.46129i			0.163722i
$227$	17.0113	+	9.82147i	1.12908	+	0.651874i	0.943703	−	0.330794i	$-0.107316\pi$
$227$	17.0113	+	9.82147i	1.12908	+	0.651874i	0.185376	+	0.982668i	$0.440650\pi$
$228$		0			0
$229$			6.38800i			0.422131i	0.977472	+	0.211065i	$0.0676933\pi$
$229$			6.38800i			0.422131i	−0.977472	+	0.211065i	$0.932307\pi$
$230$	0.0331938	−	0.0574933i	0.00218873	−	0.00379100i
$231$		0			0
$232$	9.83574	−	5.67867i	0.645748	−	0.372823i
$233$	−20.0391			−1.31280			−0.656402	−	0.754411i	$-0.727922\pi$
$233$	−20.0391			−1.31280			−0.656402	+	0.754411i	$0.727922\pi$
$234$		0			0
$235$	8.52159			0.555888
$236$	−15.9970	+	9.23588i	−1.04132	+	0.601204i
$237$		0			0
$238$	0.0416847	−	0.0722001i	0.00270202	−	0.00468004i
$239$		−	4.47998i		−	0.289786i	−0.989447	−	0.144893i	$-0.953716\pi$
$239$		−	4.47998i		−	0.289786i	0.989447	−	0.144893i	$-0.0462838\pi$
$240$		0			0
$241$	−0.535517	−	0.309181i	−0.0344957	−	0.0199161i	0.482653	−	0.875812i	$-0.339673\pi$
$241$	−0.535517	−	0.309181i	−0.0344957	−	0.0199161i	−0.517149	+	0.855896i	$0.673007\pi$
$242$		−	1.21156i		−	0.0778819i
$243$		0			0
$244$	12.3986	+	21.4750i	0.793737	+	1.37479i
$245$	4.13192	−	2.38556i	0.263979	−	0.152408i
$246$		0			0
$247$	−1.22353	+	3.20895i	−0.0778516	+	0.204181i
$248$	1.85416			0.117739
$249$		0			0
$250$	−0.150571	−	0.260797i	−0.00952298	−	0.0164943i
$251$	9.01543	−	15.6152i	0.569049	−	0.985621i	−0.427612	−	0.903963i	$-0.640645\pi$
$251$	9.01543	−	15.6152i	0.569049	−	0.985621i	0.996660	−	0.0816587i	$-0.0260217\pi$
$252$		0			0
$253$	0.504281	+	0.291147i	0.0317039	+	0.0183042i
$254$	−5.46341	−	3.15430i	−0.342805	−	0.197918i
$255$		0			0
$256$	−4.61405	+	7.99178i	−0.288378	+	0.499486i
$257$	3.80193	+	6.58514i	0.237158	+	0.410770i	0.959898	−	0.280351i	$-0.0904508\pi$
$257$	3.80193	+	6.58514i	0.237158	+	0.410770i	−0.722740	+	0.691120i	$0.757117\pi$
$258$		0			0
$259$	−9.81863			−0.610100
$260$	−2.45260	+	6.43241i	−0.152104	+	0.398921i
$261$		0			0
$262$	−4.44007	+	2.56347i	−0.274308	+	0.158372i
$263$	1.48713	+	2.57579i	0.0917006	+	0.158830i	0.908227	−	0.418478i	$-0.137436\pi$
$263$	1.48713	+	2.57579i	0.0917006	+	0.158830i	−0.816526	+	0.577308i	$0.804103\pi$
$264$		0			0
$265$			5.28273i			0.324515i
$266$	−0.852273	−	0.492060i	−0.0522562	−	0.0301701i
$267$		0			0
$268$			4.78419i			0.292241i
$269$	−14.0536	+	24.3416i	−0.856864	+	1.48413i	0.0180404	+	0.999837i	$0.494257\pi$
$269$	−14.0536	+	24.3416i	−0.856864	+	1.48413i	−0.874905	+	0.484295i	$0.839076\pi$
$270$		0			0
$271$	16.3350	−	9.43101i	0.992279	−	0.572893i	0.0863245	−	0.996267i	$-0.472488\pi$
$271$	16.3350	−	9.43101i	0.992279	−	0.572893i	0.905955	+	0.423374i	$0.139154\pi$
$272$	0.279522			0.0169485
$273$		0			0
$274$	4.49381			0.271481
$275$	2.28749	−	1.32068i	0.137941	−	0.0796401i
$276$		0			0
$277$	−10.7668	+	18.6487i	−0.646916	+	1.12049i	0.336940	+	0.941526i	$0.390608\pi$
$277$	−10.7668	+	18.6487i	−0.646916	+	1.12049i	−0.983856	+	0.178965i	$0.942725\pi$
$278$			2.44214i			0.146470i
$279$		0			0
$280$	−3.49794	−	2.01954i	−0.209042	−	0.120691i
$281$		−	18.5104i		−	1.10424i	−0.833766	−	0.552118i	$-0.813820\pi$
$281$		−	18.5104i		−	1.10424i	0.833766	−	0.552118i	$-0.186180\pi$
$282$		0			0
$283$	5.07672	+	8.79313i	0.301780	+	0.522698i	0.976539	−	0.215340i	$-0.0690860\pi$
$283$	5.07672	+	8.79313i	0.301780	+	0.522698i	−0.674760	+	0.738038i	$0.735753\pi$
$284$	8.75159	−	5.05273i	0.519311	−	0.299825i
$285$		0			0
$286$	2.67977	+	1.02176i	0.158458	+	0.0604182i
$287$	−27.3193			−1.61261
$288$		0			0
$289$	8.49674	+	14.7168i	0.499808	+	0.865694i
$290$	−1.45260	+	2.51598i	−0.0852996	+	0.147743i
$291$		0			0
$292$	23.7430	+	13.7080i	1.38945	+	0.802201i
$293$	−14.6080	−	8.43395i	−0.853410	−	0.492716i	0.00838997	−	0.999965i	$-0.497329\pi$
$293$	−14.6080	−	8.43395i	−0.853410	−	0.492716i	−0.861800	+	0.507248i	$0.830663\pi$
$294$		0			0
$295$	4.83728	−	8.37841i	0.281637	−	0.487810i
$296$	1.68455	+	2.91773i	0.0979127	+	0.169590i
$297$		0			0
$298$	−6.55369			−0.379645
$299$	0.616589	−	0.501603i	0.0356583	−	0.0290084i
$300$		0			0
$301$	−26.5454	+	15.3260i	−1.53005	+	0.883377i
$302$	2.13342	+	3.69520i	0.122765	+	0.212635i
$303$		0			0
$304$		−	3.29957i		−	0.189243i
$305$	−11.2475	−	6.49373i	−0.644029	−	0.371830i
$306$		0			0
$307$			6.94155i			0.396175i	0.980184	+	0.198088i	$0.0634730\pi$
$307$			6.94155i			0.396175i	−0.980184	+	0.198088i	$0.936527\pi$
$308$	8.65136	−	14.9846i	0.492957	−	0.853827i
$309$		0			0
$310$	−0.410750	+	0.237147i	−0.0233290	+	0.0134690i
$311$	−13.9341			−0.790130			−0.395065	−	0.918653i	$-0.629278\pi$
$311$	−13.9341			−0.790130			−0.395065	+	0.918653i	$0.629278\pi$
$312$		0			0
$313$	−9.02908			−0.510354			−0.255177	−	0.966894i	$-0.582134\pi$
$313$	−9.02908			−0.510354			−0.255177	+	0.966894i	$0.582134\pi$
$314$	1.57378	−	0.908622i	0.0888135	−	0.0512765i
$315$		0			0
$316$	−11.3281	+	19.6208i	−0.637254	+	1.10376i
$317$		−	0.496821i		−	0.0279042i	−0.999903	−	0.0139521i	$-0.995559\pi$
$317$		−	0.496821i		−	0.0279042i	0.999903	−	0.0139521i	$-0.00444124\pi$
$318$		0			0
$319$	−22.0680	−	12.7409i	−1.23557	−	0.713356i
$320$		−	5.90501i		−	0.330100i
$321$		0			0
$322$	0.113885	+	0.197254i	0.00634655	+	0.0109925i
$323$	−0.0665613	+	0.0384292i	−0.00370357	+	0.00213826i
$324$		0			0
$325$	−0.572034	−	3.55988i	−0.0317307	−	0.197467i
$326$	6.15961			0.341149
$327$		0			0
$328$	4.68709	+	8.11828i	0.258801	+	0.448257i
$329$	−14.6184	+	25.3198i	−0.805939	+	1.39593i
$330$		0			0
$331$	22.5350	+	13.0106i	1.23863	+	0.715126i	0.968815	−	0.247786i	$-0.0797028\pi$
$331$	22.5350	+	13.0106i	1.23863	+	0.715126i	0.269819	+	0.962911i	$0.413036\pi$
$332$	15.8565	+	9.15473i	0.870237	+	0.502431i
$333$		0			0
$334$	−2.55068	+	4.41790i	−0.139567	+	0.241737i
$335$	−1.25286	−	2.17001i	−0.0684509	−	0.118560i
$336$		0			0
$337$	−1.60276			−0.0873079			−0.0436540	−	0.999047i	$-0.513900\pi$
$337$	−1.60276			−0.0873079			−0.0436540	+	0.999047i	$0.513900\pi$
$338$	2.60645	−	2.92105i	0.141772	−	0.158884i
$339$		0			0
$340$	−0.133424	+	0.0770322i	−0.00723592	+	0.00417766i
$341$	−2.08004	−	3.60274i	−0.112641	−	0.195099i
$342$		0			0
$343$		−	7.64705i		−	0.412902i
$344$	9.10865	+	5.25888i	0.491105	+	0.283540i
$345$		0			0
$346$		−	5.66470i		−	0.304536i
$347$	−15.4789	+	26.8102i	−0.830950	+	1.43925i	0.0663361	+	0.997797i	$0.478869\pi$
$347$	−15.4789	+	26.8102i	−0.830950	+	1.43925i	−0.897286	+	0.441450i	$0.854464\pi$
$348$		0			0
$349$	−14.1851	+	8.18979i	−0.759313	+	0.438389i	−0.829049	−	0.559176i	$-0.811118\pi$
$349$	−14.1851	+	8.18979i	−0.759313	+	0.438389i	0.0697363	+	0.997565i	$0.477784\pi$
$350$	1.03319			0.0552265
$351$		0			0
$352$	−8.97460			−0.478348
$353$	17.6768	−	10.2057i	0.940840	−	0.543194i	0.0506166	−	0.998718i	$-0.483881\pi$
$353$	17.6768	−	10.2057i	0.940840	−	0.543194i	0.890224	+	0.455524i	$0.150548\pi$
$354$		0			0
$355$	−2.64636	+	4.58363i	−0.140454	+	0.243274i
$356$			20.2240i			1.07187i
$357$		0			0
$358$	2.68017	+	1.54740i	0.141652	+	0.0817826i
$359$		−	27.7823i		−	1.46629i	−0.680071	−	0.733146i	$-0.738051\pi$
$359$		−	27.7823i		−	1.46629i	0.680071	−	0.733146i	$-0.261949\pi$
$360$		0			0
$361$	−9.04637	−	15.6688i	−0.476125	−	0.824672i
$362$	3.93727	−	2.27318i	0.206938	−	0.119476i
$363$		0			0
$364$	−14.9050	−	18.3218i	−0.781235	−	0.960324i
$365$	−14.3591			−0.751590
$366$		0			0
$367$	−2.83998	−	4.91900i	−0.148246	−	0.256769i	0.782333	−	0.622860i	$-0.214029\pi$
$367$	−2.83998	−	4.91900i	−0.148246	−	0.256769i	−0.930579	+	0.366091i	$0.880696\pi$
$368$	−0.381834	+	0.661356i	−0.0199045	+	0.0344756i
$369$		0			0
$370$	−0.746354	−	0.430908i	−0.0388011	−	0.0224018i
$371$	−15.6963	−	9.06228i	−0.814912	−	0.470490i
$372$		0			0
$373$	1.99014	−	3.44703i	0.103046	−	0.178480i	−0.809892	−	0.586579i	$-0.800475\pi$
$373$	1.99014	−	3.44703i	0.103046	−	0.178480i	0.912938	+	0.408098i	$0.133808\pi$
$374$	0.0320920	+	0.0555849i	0.00165944	+	0.00287423i
$375$		0			0
$376$	10.0322			0.517369
$377$	−26.9827	+	21.9508i	−1.38968	+	1.13052i
$378$		0			0
$379$	23.5846	−	13.6166i	1.21146	−	0.699437i	0.248383	−	0.968662i	$-0.420101\pi$
$379$	23.5846	−	13.6166i	1.21146	−	0.699437i	0.963077	+	0.269225i	$0.0867675\pi$
$380$	0.909313	+	1.57498i	0.0466468	+	0.0807946i
$381$		0			0
$382$			3.46711i			0.177393i
$383$	10.4776	+	6.04924i	0.535380	+	0.309102i	0.743204	−	0.669064i	$-0.233305\pi$
$383$	10.4776	+	6.04924i	0.535380	+	0.309102i	−0.207825	+	0.978166i	$0.566638\pi$
$384$		0			0
$385$			9.06228i			0.461856i
$386$	−2.55266	+	4.42134i	−0.129927	+	0.225041i
$387$		0			0
$388$	7.73657	−	4.46671i	0.392765	−	0.226763i
$389$	38.7373			1.96406			0.982030	−	0.188726i	$-0.0604359\pi$
$389$	38.7373			1.96406			0.982030	+	0.188726i	$0.0604359\pi$
$390$		0			0
$391$	0.0177885			0.000899603
$392$	4.86435	−	2.80843i	0.245687	−	0.141847i
$393$		0			0
$394$	−1.77113	+	3.06768i	−0.0892282	+	0.154548i
$395$		−	11.8661i		−	0.597049i
$396$		0			0
$397$	2.32709	+	1.34354i	0.116793	+	0.0674306i	0.557259	−	0.830339i	$-0.311853\pi$
$397$	2.32709	+	1.34354i	0.116793	+	0.0674306i	−0.440465	+	0.897770i	$0.645187\pi$
$398$			2.50385i			0.125507i
$399$		0			0
$400$	1.73205	+	3.00000i	0.0866025	+	0.150000i
$401$	5.93978	−	3.42933i	0.296618	−	0.171253i	−0.344304	−	0.938858i	$-0.611885\pi$
$401$	5.93978	−	3.42933i	0.296618	−	0.171253i	0.640923	+	0.767605i	$0.278552\pi$
$402$		0			0
$403$	−5.60673	+	0.900940i	−0.279291	+	0.0448790i
$404$	−12.9886			−0.646206
$405$		0			0
$406$	−4.98374	−	8.63209i	−0.247339	−	0.428403i
$407$	3.77955	−	6.54637i	0.187345	−	0.324491i
$408$		0			0
$409$	0.360959	+	0.208400i	0.0178483	+	0.0103047i	0.508898	−	0.860827i	$-0.330053\pi$
$409$	0.360959	+	0.208400i	0.0178483	+	0.0103047i	−0.491049	+	0.871132i	$0.663387\pi$
$410$	−2.07665	−	1.19895i	−0.102558	−	0.0592122i
$411$		0			0
$412$	−4.46260	+	7.72944i	−0.219856	+	0.380802i
$413$	16.5963	+	28.7456i	0.816648	+	1.41448i
$414$		0			0
$415$	−9.58956			−0.470733
$416$	−4.36452	+	11.4468i	−0.213988	+	0.561225i
$417$		0			0
$418$	0.656142	−	0.378824i	0.0320930	−	0.0185289i
$419$	−5.31726	−	9.20977i	−0.259765	−	0.449926i	0.706414	−	0.707799i	$-0.250312\pi$
$419$	−5.31726	−	9.20977i	−0.259765	−	0.449926i	−0.966179	+	0.257873i	$0.916978\pi$
$420$		0			0
$421$		−	26.1373i		−	1.27385i	−0.770925	−	0.636926i	$-0.780205\pi$
$421$		−	26.1373i		−	1.27385i	0.770925	−	0.636926i	$-0.219795\pi$
$422$	−4.28634	−	2.47472i	−0.208656	−	0.120467i
$423$		0			0
$424$			6.21915i			0.302029i
$425$	0.0403455	−	0.0698805i	0.00195704	−	0.00338970i
$426$		0			0
$427$	38.5891	−	22.2794i	1.86746	−	1.07818i
$428$	25.4403			1.22971
$429$		0			0
$430$	−2.69044			−0.129744
$431$	14.6870	−	8.47953i	0.707447	−	0.408445i	−0.102668	−	0.994716i	$-0.532738\pi$
$431$	14.6870	−	8.47953i	0.707447	−	0.408445i	0.810115	+	0.586271i	$0.199405\pi$
$432$		0			0
$433$	−17.9671	+	31.1200i	−0.863446	+	1.49553i	0.00513654	+	0.999987i	$0.498365\pi$
$433$	−17.9671	+	31.1200i	−0.863446	+	1.49553i	−0.868582	+	0.495545i	$0.834968\pi$
$434$		−	1.62726i		−	0.0781108i
$435$		0			0
$436$	8.48214	+	4.89716i	0.406221	+	0.234532i
$437$		−	0.209981i		−	0.0100448i
$438$		0			0
$439$	1.89125	+	3.27575i	0.0902646	+	0.156343i	0.907622	−	0.419787i	$-0.137895\pi$
$439$	1.89125	+	3.27575i	0.0902646	+	0.156343i	−0.817358	+	0.576130i	$0.804562\pi$
$440$	2.69297	−	1.55479i	0.128382	−	0.0741216i
$441$		0			0
$442$	0.0865035	−	0.0139002i	0.00411455	−	0.000661163i
$443$	33.5683			1.59488			0.797440	−	0.603399i	$-0.206187\pi$
$443$	33.5683			1.59488			0.797440	+	0.603399i	$0.206187\pi$
$444$		0			0
$445$	−5.29614	−	9.17319i	−0.251061	−	0.434851i
$446$	0.342756	−	0.593671i	0.0162300	−	0.0281111i
$447$		0			0
$448$	17.5453	+	10.1298i	0.828936	+	0.478586i
$449$	−15.2743	−	8.81863i	−0.720839	−	0.416177i	0.0942223	−	0.995551i	$-0.469964\pi$
$449$	−15.2743	−	8.81863i	−0.720839	−	0.416177i	−0.815061	+	0.579374i	$0.803297\pi$
$450$		0			0
$451$	10.5162	−	18.2146i	0.495188	−	0.857691i
$452$	7.80255	+	13.5144i	0.367001	+	0.635665i
$453$		0			0
$454$	−5.91533			−0.277620
$455$	11.5586	+	4.40716i	0.541876	+	0.206611i
$456$		0			0
$457$	−18.2930	+	10.5615i	−0.855710	+	0.494044i	−0.862573	−	0.505932i	$-0.831149\pi$
$457$	−18.2930	+	10.5615i	−0.855710	+	0.494044i	0.00686344	+	0.999976i	$0.497815\pi$
$458$	−0.961850	−	1.66597i	−0.0449443	−	0.0778458i
$459$		0			0
$460$		−	0.420912i		−	0.0196251i
$461$	20.8786	+	12.0543i	0.972413	+	0.561423i	0.899971	−	0.435949i	$-0.143587\pi$
$461$	20.8786	+	12.0543i	0.972413	+	0.561423i	0.0724423	+	0.997373i	$0.476921\pi$
$462$		0			0
$463$		−	19.0861i		−	0.887006i	−0.896273	−	0.443503i	$-0.853736\pi$
$463$		−	19.0861i		−	0.887006i	0.896273	−	0.443503i	$-0.146264\pi$
$464$	16.7095	−	28.9417i	0.775720	−	1.34359i
$465$		0			0
$466$	5.22614	−	3.01731i	0.242096	−	0.139774i
$467$	13.7080			0.634332			0.317166	−	0.948370i	$-0.397269\pi$
$467$	13.7080			0.634332			0.317166	+	0.948370i	$0.397269\pi$
$468$		0			0
$469$	8.59688			0.396967
$470$	−2.22241	+	1.28311i	−0.102512	+	0.0591854i
$471$		0			0
$472$	5.69474	−	9.86359i	0.262122	−	0.454008i
$473$		−	23.5982i		−	1.08505i
$474$		0			0
$475$	−0.824892	−	0.476251i	−0.0378486	−	0.0218519i
$476$		−	0.528581i		−	0.0242275i
$477$		0			0
$478$	0.674557	+	1.16837i	0.0308535	+	0.0534399i
$479$	−30.3652	+	17.5314i	−1.38742	+	0.801029i	−0.993024	−	0.117910i	$-0.962380\pi$
$479$	−30.3652	+	17.5314i	−1.38742	+	0.801029i	−0.394399	+	0.918939i	$0.629047\pi$
$480$		0			0
$481$	−6.51160	−	8.00431i	−0.296903	−	0.364965i
$482$	0.186215			0.00848187
$483$		0			0
$484$	−3.84077	−	6.65241i	−0.174581	−	0.302382i
$485$	−2.33943	+	4.05202i	−0.106228	+	0.183993i
$486$		0			0
$487$	−2.61331	−	1.50880i	−0.118420	−	0.0683701i	0.439620	−	0.898184i	$-0.355113\pi$
$487$	−2.61331	−	1.50880i	−0.118420	−	0.0683701i	−0.558040	+	0.829814i	$0.688447\pi$
$488$	−13.2412	−	7.64483i	−0.599402	−	0.346065i
$489$		0			0
$490$	−0.718396	+	1.24430i	−0.0324538	+	0.0562117i
$491$	−1.10047	−	1.90607i	−0.0496634	−	0.0860195i	0.840125	−	0.542393i	$-0.182482\pi$
$491$	−1.10047	−	1.90607i	−0.0496634	−	0.0860195i	−0.889788	+	0.456373i	$0.849148\pi$
$492$		0			0
$493$	−0.778446			−0.0350595
$494$	−0.164082	−	1.02112i	−0.00738240	−	0.0459422i
$495$		0			0
$496$	4.72493	−	2.72794i	0.212156	−	0.122488i
$497$	−9.07942	−	15.7260i	−0.407268	−	0.705409i
$498$		0			0
$499$		−	8.68475i		−	0.388783i	−0.980924	−	0.194391i	$-0.937727\pi$
$499$		−	8.68475i		−	0.388783i	0.980924	−	0.194391i	$-0.0622732\pi$
$500$	−1.65351	−	0.954656i	−0.0739474	−	0.0426935i
$501$		0			0
$502$			5.42986i			0.242347i
$503$	7.93251	−	13.7395i	0.353693	−	0.612615i	−0.633200	−	0.773988i	$-0.718259\pi$
$503$	7.93251	−	13.7395i	0.353693	−	0.612615i	0.986893	+	0.161373i	$0.0515924\pi$
$504$		0			0
$505$	5.89135	−	3.40137i	0.262162	−	0.151359i
$506$	−0.175354			−0.00779542
$507$		0			0
$508$	−39.9979			−1.77462
$509$	−36.9324	+	21.3229i	−1.63700	+	0.945122i	−0.655141	+	0.755506i	$0.727391\pi$
$509$	−36.9324	+	21.3229i	−1.63700	+	0.945122i	−0.981858	+	0.189616i	$0.939276\pi$
$510$		0			0
$511$	24.6324	−	42.6646i	1.08967	−	1.88737i
$512$		−	19.9263i		−	0.880628i
$513$		0			0
$514$	−1.98307	−	1.14492i	−0.0874694	−	0.0505005i
$515$		−	4.67456i		−	0.205986i
$516$		0			0
$517$	−11.2543	−	19.4930i	−0.494964	−	0.857303i
$518$	2.56067	−	1.47841i	0.112509	−	0.0649574i
$519$		0			0
$520$	−0.673434	−	4.19092i	−0.0295320	−	0.183784i
$521$	5.40996			0.237015			0.118507	−	0.992953i	$-0.462189\pi$
$521$	5.40996			0.237015			0.118507	+	0.992953i	$0.462189\pi$
$522$		0			0
$523$	8.80021	+	15.2424i	0.384806	+	0.666504i	0.991742	−	0.128247i	$-0.0409349\pi$
$523$	8.80021	+	15.2424i	0.384806	+	0.666504i	−0.606936	+	0.794751i	$0.707602\pi$
$524$	−16.2530	+	28.1510i	−0.710015	+	1.22978i
$525$		0			0
$526$	−0.775681	−	0.447840i	−0.0338213	−	0.0195267i
$527$	−0.110060	−	0.0635432i	−0.00479429	−	0.00276799i
$528$		0			0
$529$	11.4757	−	19.8765i	0.498943	−	0.864195i
$530$	−0.795428	−	1.37772i	−0.0345512	−	0.0598444i
$531$		0			0
$532$	−6.23954			−0.270518
$533$	−18.1178	−	22.2711i	−0.784770	−	0.964669i
$534$		0			0
$535$	−11.5392	+	6.66217i	−0.498884	+	0.288031i
$536$	−1.47494	−	2.55467i	−0.0637078	−	0.110345i
$537$		0			0
$538$		−	8.46430i		−	0.364922i
$539$	−10.9139	−	6.30114i	−0.470095	−	0.271409i
$540$		0			0
$541$		−	2.26288i		−	0.0972887i	−0.998816	−	0.0486444i	$-0.984510\pi$
$541$		−	2.26288i		−	0.0972887i	0.998816	−	0.0486444i	$-0.0154901\pi$
$542$	−2.84008	+	4.91916i	−0.121992	+	0.211296i
$543$		0			0
$544$	−0.237434	+	0.137082i	−0.0101799	+	0.00587736i
$545$	−5.12976			−0.219735
$546$		0			0
$547$	0.320033			0.0136836			0.00684182	−	0.999977i	$-0.497822\pi$
$547$	0.320033			0.0136836			0.00684182	+	0.999977i	$0.497822\pi$
$548$	24.6746	−	14.2459i	1.05405	−	0.608554i
$549$		0			0
$550$	−0.397714	+	0.688861i	−0.0169586	+	0.0293731i
$551$			9.18903i			0.391466i
$552$		0			0
$553$	35.2573	+	20.3558i	1.49929	+	0.865616i
$554$		−	6.48471i		−	0.275509i
$555$		0			0
$556$	7.74186	+	13.4093i	0.328328	+	0.568681i
$557$	13.8305	−	7.98505i	0.586017	−	0.338337i	−0.177504	−	0.984120i	$-0.556802\pi$
$557$	13.8305	−	7.98505i	0.586017	−	0.338337i	0.763521	+	0.645783i	$0.223469\pi$
$558$		0			0
$559$	−30.0986	−	11.4762i	−1.27304	−	0.485394i
$560$	−11.8850			−0.502233
$561$		0			0
$562$	2.78713	+	4.82746i	0.117568	+	0.203634i
$563$	−6.15426	+	10.6595i	−0.259371	+	0.449244i	−0.966074	−	0.258267i	$-0.916849\pi$
$563$	−6.15426	+	10.6595i	−0.259371	+	0.449244i	0.706702	+	0.707511i	$0.250182\pi$
$564$		0			0
$565$	−7.07816	−	4.08658i	−0.297780	−	0.171924i
$566$	−2.64799	−	1.52882i	−0.111303	−	0.0642610i
$567$		0			0
$568$	−3.11546	+	5.39614i	−0.130722	+	0.226417i
$569$	−13.8416	−	23.9743i	−0.580269	−	1.00506i	−0.995447	−	0.0953158i	$-0.969614\pi$
$569$	−13.8416	−	23.9743i	−0.580269	−	1.00506i	0.415178	−	0.909740i	$-0.363719\pi$
$570$		0			0
$571$	−19.9502			−0.834892			−0.417446	−	0.908702i	$-0.637075\pi$
$571$	−19.9502			−0.834892			−0.417446	+	0.908702i	$0.637075\pi$
$572$	17.9532	−	2.88488i	0.750660	−	0.120623i
$573$		0			0
$574$	7.12480	−	4.11350i	0.297383	−	0.171694i
$575$	0.110226	+	0.190917i	0.00459674	+	0.00796179i
$576$		0			0
$577$		−	24.1623i		−	1.00589i	−0.864318	−	0.502946i	$-0.832250\pi$
$577$		−	24.1623i		−	1.00589i	0.864318	−	0.502946i	$-0.167750\pi$
$578$	−4.43186	−	2.55873i	−0.184341	−	0.106429i
$579$		0			0
$580$			18.4196i			0.764833i
$581$	16.4504	−	28.4930i	0.682480	−	1.18209i
$582$		0			0
$583$	12.0842	−	6.97680i	0.500475	−	0.288950i
$584$	−16.9044			−0.699511
$585$		0			0
$586$	5.07965			0.209838
$587$	−9.55436	+	5.51622i	−0.394351	+	0.227679i	−0.684044	−	0.729441i	$-0.739780\pi$
$587$	−9.55436	+	5.51622i	−0.394351	+	0.227679i	0.289693	+	0.957120i	$0.406447\pi$
$588$		0			0
$589$	−0.750085	+	1.29918i	−0.0309067	+	0.0535320i
$590$			2.91342i			0.119944i
$591$		0			0
$592$	8.58545	+	4.95681i	0.352860	+	0.203724i
$593$		−	1.72909i		−	0.0710053i	−0.999370	−	0.0355027i	$-0.988697\pi$
$593$		−	1.72909i		−	0.0710053i	0.999370	−	0.0355027i	$-0.0113032\pi$
$594$		0			0
$595$	0.138422	+	0.239753i	0.00567474	+	0.00982893i
$596$	−35.9849	+	20.7759i	−1.47400	+	0.851014i
$597$		0			0
$598$	−0.0852779	+	0.223658i	−0.00348727	+	0.00914604i
$599$	−15.5218			−0.634203			−0.317102	−	0.948392i	$-0.602710\pi$
$599$	−15.5218			−0.634203			−0.317102	+	0.948392i	$0.602710\pi$
$600$		0			0
$601$	7.39125	+	12.8020i	0.301495	+	0.522206i	0.976475	−	0.215631i	$-0.0691808\pi$
$601$	7.39125	+	12.8020i	0.301495	+	0.522206i	−0.674979	+	0.737837i	$0.735848\pi$
$602$	4.61532	−	7.99397i	0.188106	−	0.325810i
$603$		0			0
$604$	23.4284	+	13.5264i	0.953287	+	0.550380i
$605$	3.48419	+	2.01160i	0.141653	+	0.0817831i
$606$		0			0
$607$	12.4674	−	21.5941i	0.506035	−	0.876479i	−0.493940	−	0.869496i	$-0.664444\pi$
$607$	12.4674	−	21.5941i	0.506035	−	0.876479i	0.999976	−	0.00698303i	$-0.00222279\pi$
$608$	1.61817	+	2.80275i	0.0656253	+	0.113666i
$609$		0			0
$610$	3.91108			0.158355
$611$	−30.3359	+	4.87464i	−1.22726	+	0.197207i
$612$		0			0
$613$	−25.5334	+	14.7417i	−1.03129	+	0.595413i	−0.917353	−	0.398075i	$-0.869678\pi$
$613$	−25.5334	+	14.7417i	−1.03129	+	0.595413i	−0.113933	+	0.993488i	$0.536345\pi$
$614$	−1.04520	−	1.81034i	−0.0421808	−	0.0730593i
$615$		0			0
$616$			10.6687i			0.429853i
$617$	−14.0182	−	8.09339i	−0.564350	−	0.325827i	0.190540	−	0.981679i	$-0.438976\pi$
$617$	−14.0182	−	8.09339i	−0.564350	−	0.325827i	−0.754890	+	0.655852i	$0.772310\pi$
$618$		0			0
$619$			39.3442i			1.58138i	0.612218	+	0.790689i	$0.290278\pi$
$619$			39.3442i			1.58138i	−0.612218	+	0.790689i	$0.709722\pi$
$620$	−1.50356	+	2.60424i	−0.0603845	+	0.104589i
$621$		0			0
$622$	3.63397	−	2.09808i	0.145709	−	0.0841252i
$623$	36.3412			1.45598
$624$		0			0
$625$	1.00000			0.0400000
$626$	2.35476	−	1.35952i	0.0941152	−	0.0543374i
$627$		0			0
$628$	5.76087	−	9.97811i	0.229884	−	0.398170i
$629$		−	0.230923i		−	0.00920750i
$630$		0			0
$631$	18.1035	+	10.4520i	0.720688	+	0.416090i	0.815006	−	0.579453i	$-0.196734\pi$
$631$	18.1035	+	10.4520i	0.720688	+	0.416090i	−0.0943177	+	0.995542i	$0.530067\pi$
$632$		−	13.9695i		−	0.555678i
$633$		0			0
$634$	0.0748070	+	0.129570i	0.00297097	+	0.00514586i
$635$	18.1422	−	10.4744i	0.719953	−	0.415665i
$636$		0			0
$637$	−13.3445	+	10.8559i	−0.528729	+	0.430128i
$638$	7.67369			0.303804
$639$		0			0
$640$	4.28684	+	7.42502i	0.169452	+	0.293500i
$641$	−6.91708	+	11.9807i	−0.273208	+	0.473211i	−0.969682	−	0.244372i	$-0.921418\pi$
$641$	−6.91708	+	11.9807i	−0.273208	+	0.473211i	0.696473	+	0.717583i	$0.254752\pi$
$642$		0			0
$643$	0.133542	+	0.0771004i	0.00526638	+	0.00304054i	0.502631	−	0.864501i	$-0.332365\pi$
$643$	0.133542	+	0.0771004i	0.00526638	+	0.00304054i	−0.497364	+	0.867542i	$0.665699\pi$
$644$	1.25064	+	0.722055i	0.0492819	+	0.0284529i
$645$		0			0
$646$	0.0115727	−	0.0200445i	0.000455321	−	0.000788640i
$647$	6.69998	+	11.6047i	0.263403	+	0.456228i	0.967144	−	0.254229i	$-0.0818216\pi$
$647$	6.69998	+	11.6047i	0.263403	+	0.456228i	−0.703741	+	0.710457i	$0.748488\pi$
$648$		0			0
$649$	−25.5540			−1.00308
$650$	0.685202	+	0.842277i	0.0268758	+	0.0330368i
$651$		0			0
$652$	33.8211	−	19.5266i	1.32454	−	0.764722i
$653$	−2.67870	−	4.63964i	−0.104826	−	0.181563i	0.808841	−	0.588027i	$-0.200095\pi$
$653$	−2.67870	−	4.63964i	−0.104826	−	0.181563i	−0.913667	+	0.406464i	$0.866762\pi$
$654$		0			0
$655$		−	17.0250i		−	0.665221i
$656$	23.8881	+	13.7918i	0.932673	+	0.538479i
$657$		0			0
$658$		−	8.80446i		−	0.343234i
$659$	−6.44138	+	11.1568i	−0.250920	+	0.434607i	−0.963780	−	0.266700i	$-0.914067\pi$
$659$	−6.44138	+	11.1568i	−0.250920	+	0.434607i	0.712859	+	0.701307i	$0.247400\pi$
$660$		0			0
$661$	−5.28132	+	3.04917i	−0.205420	+	0.118599i	−0.599181	−	0.800614i	$-0.704507\pi$
$661$	−5.28132	+	3.04917i	−0.205420	+	0.118599i	0.393761	+	0.919213i	$0.371174\pi$
$662$	−7.83608			−0.304558
$663$		0			0
$664$	−11.2894			−0.438115
$665$	2.83013	−	1.63397i	0.109748	−	0.0633628i
$666$		0			0
$667$	1.06338	−	1.84182i	0.0411741	−	0.0713157i
$668$			32.3437i			1.25142i
$669$		0			0
$670$	0.653484	+	0.377289i	0.0252463	+	0.0145760i
$671$			34.3046i			1.32432i
$672$		0			0
$673$	−10.3388	−	17.9073i	−0.398531	−	0.690276i	0.595014	−	0.803715i	$-0.297146\pi$
$673$	−10.3388	−	17.9073i	−0.398531	−	0.690276i	−0.993545	+	0.113440i	$0.963813\pi$
$674$	0.417996	−	0.241330i	0.0161006	−	0.00929569i
$675$		0			0
$676$	5.05141	−	24.3016i	0.194285	−	0.934678i
$677$	25.5159			0.980656			0.490328	−	0.871538i	$-0.336877\pi$
$677$	25.5159			0.980656			0.490328	+	0.871538i	$0.336877\pi$
$678$		0			0
$679$	−8.02638	−	13.9021i	−0.308024	−	0.533513i
$680$	0.0474972	−	0.0822676i	0.00182144	−	0.00315482i
$681$		0			0
$682$	1.08494	+	0.626390i	0.0415445	+	0.0239857i
$683$	1.38625	+	0.800355i	0.0530436	+	0.0306247i	0.526287	−	0.850307i	$-0.323584\pi$
$683$	1.38625	+	0.800355i	0.0530436	+	0.0306247i	−0.473244	+	0.880932i	$0.656917\pi$
$684$		0			0
$685$	−7.46126	+	12.9233i	−0.285080	+	0.493773i
$686$	1.15143	+	1.99433i	0.0439617	+	0.0761439i
$687$		0			0
$688$	30.9486			1.17990
$689$	−3.02190	−	18.8059i	−0.115125	−	0.716448i
$690$		0			0
$691$	−22.8052	+	13.1666i	−0.867551	+	0.500881i	−0.866534	−	0.499119i	$-0.833657\pi$
$691$	−22.8052	+	13.1666i	−0.867551	+	0.500881i	−0.00101729	+	0.999999i	$0.500324\pi$
$692$	−17.9577	−	31.1037i	−0.682651	−	1.18239i
$693$		0			0
$694$		−	9.32271i		−	0.353885i
$695$	−7.02310	−	4.05479i	−0.266401	−	0.153807i
$696$		0			0
$697$		−	0.642518i		−	0.0243371i
$698$	2.46630	−	4.27175i	0.0933507	−	0.161688i
$699$		0			0
$700$	5.67305	−	3.27534i	0.214421	−	0.123796i
$701$	39.3777			1.48728			0.743638	−	0.668582i	$-0.233099\pi$
$701$	39.3777			1.48728			0.743638	+	0.668582i	$0.233099\pi$
$702$		0			0
$703$	−2.72589			−0.102809
$704$	−13.5076	+	7.79863i	−0.509088	+	0.293922i
$705$		0			0
$706$	−3.07337	+	5.32324i	−0.115668	+	0.200343i
$707$			23.3396i			0.877776i
$708$		0			0
$709$	−15.5842	−	8.99756i	−0.585278	−	0.337911i	0.177950	−	0.984040i	$-0.443053\pi$
$709$	−15.5842	−	8.99756i	−0.585278	−	0.337911i	−0.763228	+	0.646129i	$0.776387\pi$
$710$		−	1.59387i		−	0.0598167i
$711$		0			0
$712$	−6.23495	−	10.7993i	−0.233665	−	0.404719i
$713$	0.300690	−	0.173603i	0.0112609	−	0.00650149i
$714$		0			0
$715$	−7.38772	+	6.01000i	−0.276285	+	0.224761i
$716$	19.6217			0.733298
$717$		0			0
$718$	4.18322	+	7.24555i	0.156116	+	0.270401i
$719$	10.1016	−	17.4964i	0.376725	−	0.652507i	−0.613859	−	0.789416i	$-0.710384\pi$
$719$	10.1016	−	17.4964i	0.376725	−	0.652507i	0.990584	+	0.136909i	$0.0437169\pi$
$720$		0			0
$721$	13.8893	+	8.01899i	0.517264	+	0.298643i
$722$	4.71854	+	2.72425i	0.175606	+	0.101386i
$723$		0			0
$724$	14.4125	−	24.9632i	0.535636	−	0.927749i
$725$	−4.82362	−	8.35476i	−0.179145	−	0.310288i
$726$		0			0
$727$	−21.8795			−0.811466			−0.405733	−	0.913992i	$-0.632984\pi$
$727$	−21.8795			−0.811466			−0.405733	+	0.913992i	$0.632984\pi$
$728$	13.6075	+	5.18838i	0.504328	+	0.192294i
$729$		0			0
$730$	3.74482	−	2.16207i	0.138602	−	0.0800219i
$731$	−0.360450	−	0.624318i	−0.0133317	−	0.0230912i
$732$		0			0
$733$		−	26.2697i		−	0.970294i	−0.874433	−	0.485147i	$-0.838766\pi$
$733$		−	26.2697i		−	0.970294i	0.874433	−	0.485147i	$-0.161234\pi$
$734$	1.48132	+	0.855241i	0.0546766	+	0.0315675i
$735$		0			0
$736$		−	0.749033i		−	0.0276097i
$737$	−3.30925	+	5.73179i	−0.121898	+	0.211133i
$738$		0			0
$739$	−36.1172	+	20.8523i	−1.32859	+	0.767064i	−0.985082	−	0.172084i	$-0.944950\pi$
$739$	−36.1172	+	20.8523i	−1.32859	+	0.767064i	−0.343512	+	0.939148i	$0.611617\pi$
$740$	−5.46410			−0.200864
$741$		0			0
$742$	5.45808			0.200372
$743$	9.06081	−	5.23126i	0.332409	−	0.191916i	−0.324501	−	0.945885i	$-0.605196\pi$
$743$	9.06081	−	5.23126i	0.332409	−	0.191916i	0.656910	+	0.753969i	$0.271863\pi$
$744$		0			0
$745$	10.8814	−	18.8471i	0.398662	−	0.690503i
$746$			1.19864i			0.0438852i
$747$		0			0
$748$	0.352420	+	0.203470i	0.0128858	+	0.00743960i
$749$		−	45.7146i		−	1.67037i
$750$		0			0
$751$	14.3155	+	24.7952i	0.522381	+	0.904791i	0.999661	+	0.0260396i	$0.00828961\pi$
$751$	14.3155	+	24.7952i	0.522381	+	0.904791i	−0.477279	+	0.878752i	$0.658377\pi$
$752$	25.5648	−	14.7598i	0.932252	−	0.538236i
$753$		0			0
$754$	3.73186	−	9.78753i	0.135906	−	0.356441i
$755$	−14.1688			−0.515657
$756$		0			0
$757$	4.66717	+	8.08377i	0.169631	+	0.293810i	0.938290	−	0.345849i	$-0.112409\pi$
$757$	4.66717	+	8.08377i	0.169631	+	0.293810i	−0.768659	+	0.639659i	$0.779076\pi$
$758$	−4.10054	+	7.10234i	−0.148938	+	0.257969i
$759$		0			0
$760$	−0.971114	−	0.560673i	−0.0352260	−	0.0203377i
$761$	−0.754600	−	0.435668i	−0.0273542	−	0.0157930i	0.486261	−	0.873814i	$-0.338361\pi$
$761$	−0.754600	−	0.435668i	−0.0273542	−	0.0157930i	−0.513615	+	0.858021i	$0.671694\pi$
$762$		0			0
$763$	8.79988	−	15.2418i	0.318577	−	0.551791i
$764$	10.9911	+	19.0372i	0.397645	+	0.688741i
$765$		0			0
$766$	−3.64337			−0.131640
$767$	−12.4274	+	32.5933i	−0.448728	+	1.17687i
$768$		0			0
$769$	−30.0008	+	17.3209i	−1.08186	+	0.624609i	−0.931396	−	0.364007i	$-0.881408\pi$
$769$	−30.0008	+	17.3209i	−1.08186	+	0.624609i	−0.150459	+	0.988616i	$0.548075\pi$
$770$	−1.36452	−	2.36342i	−0.0491739	−	0.0851717i
$771$		0			0
$772$			32.3689i			1.16498i
$773$	−23.3874	−	13.5027i	−0.841187	−	0.485659i	0.0164808	−	0.999864i	$-0.494754\pi$
$773$	−23.3874	−	13.5027i	−0.841187	−	0.485659i	−0.857667	+	0.514205i	$0.828087\pi$
$774$		0			0
$775$		−	1.57498i		−	0.0565748i
$776$	−2.75413	+	4.77028i	−0.0988673	+	0.171243i
$777$		0			0
$778$	−10.1026	+	5.83273i	−0.362195	+	0.209114i
$779$	−7.58449			−0.271742
$780$		0			0
$781$	13.9800			0.500244
$782$	−0.00463919	+	0.00267844i	−0.000165897	+	9.57808e-5i
$783$		0			0
$784$	8.26384	−	14.3134i	0.295137	−	0.511192i
$785$			6.03449i			0.215380i
$786$		0			0
$787$	−21.0283	−	12.1407i	−0.749577	−	0.432768i	0.0759643	−	0.997111i	$-0.475796\pi$
$787$	−21.0283	−	12.1407i	−0.749577	−	0.432768i	−0.825541	+	0.564342i	$0.809130\pi$
$788$			22.4587i			0.800058i
$789$		0			0
$790$	1.78670	+	3.09465i	0.0635679	+	0.110103i
$791$	24.2845	−	14.0207i	0.863457	−	0.498517i
$792$		0			0
$793$	43.7544	+	16.6830i	1.55376	+	0.592431i
$794$	−0.809198			−0.0287174
$795$		0			0
$796$	7.93748	+	13.7481i	0.281336	+	0.487289i
$797$	5.49209	−	9.51258i	0.194540	−	0.336953i	−0.752210	−	0.658924i	$-0.771012\pi$
$797$	5.49209	−	9.51258i	0.194540	−	0.336953i	0.946750	+	0.321971i	$0.104345\pi$
$798$		0			0
$799$	−0.595493	−	0.343808i	−0.0210670	−	0.0121631i
$800$	−2.94251	−	1.69886i	−0.104033	−	0.0600637i
$801$		0			0
$802$	−1.03272	+	1.78872i	−0.0364666	+	0.0631620i
$803$	18.9638	+	32.8463i	0.669219	+	1.15912i
$804$		0			0
$805$	−0.756350			−0.0266578
$806$	1.32657	−	1.07918i	0.0467263	−	0.0380124i
$807$		0			0
$808$	6.93566	−	4.00431i	0.243996	−	0.140871i
$809$	25.3218	+	43.8587i	0.890267	+	1.54199i	0.839555	+	0.543275i	$0.182816\pi$
$809$	25.3218	+	43.8587i	0.890267	+	1.54199i	0.0507123	+	0.998713i	$0.483851\pi$
$810$		0			0
$811$		−	7.67073i		−	0.269356i	−0.990889	−	0.134678i	$-0.957000\pi$
$811$		−	7.67073i		−	0.269356i	0.990889	−	0.134678i	$-0.0430000\pi$
$812$	−54.7293	−	31.5980i	−1.92062	−	1.10887i
$813$		0			0
$814$			2.27637i			0.0797867i
$815$	−10.2271	+	17.7138i	−0.358238	+	0.620486i
$816$		0			0
$817$	−7.36965	+	4.25487i	−0.257832	+	0.148859i
$818$	−0.125516			−0.00438857
$819$		0			0
$820$	−15.2033			−0.530921
$821$	30.3041	−	17.4961i	1.05762	−	0.610617i	0.132846	−	0.991137i	$-0.457588\pi$
$821$	30.3041	−	17.4961i	1.05762	−	0.610617i	0.924773	+	0.380520i	$0.124255\pi$
$822$		0			0
$823$	−8.10657	+	14.0410i	−0.282577	+	0.489438i	−0.972019	−	0.234903i	$-0.924523\pi$
$823$	−8.10657	+	14.0410i	−0.282577	+	0.489438i	0.689442	+	0.724341i	$0.257856\pi$
$824$		−	5.50318i		−	0.191712i
$825$		0			0
$826$	−8.65652	−	4.99785i	−0.301199	−	0.173897i
$827$			26.9634i			0.937611i	0.883301	+	0.468805i	$0.155315\pi$
$827$			26.9634i			0.937611i	−0.883301	+	0.468805i	$0.844685\pi$
$828$		0			0
$829$	1.08254	+	1.87501i	0.0375981	+	0.0651219i	0.884212	−	0.467086i	$-0.154696\pi$
$829$	1.08254	+	1.87501i	0.0375981	+	0.0651219i	−0.846614	+	0.532207i	$0.821363\pi$
$830$	2.50093	−	1.44391i	0.0868086	−	0.0501190i
$831$		0			0
$832$	3.37786	+	21.0211i	0.117106	+	0.728777i
$833$	−0.384987			−0.0133390
$834$		0			0
$835$	−8.46999	−	14.6704i	−0.293116	−	0.507692i
$836$	2.40183	−	4.16008i	0.0830689	−	0.143880i
$837$		0			0
$838$	2.77346	+	1.60126i	0.0958074	+	0.0553145i
$839$	6.71524	+	3.87705i	0.231836	+	0.133851i	0.611419	−	0.791307i	$-0.290599\pi$
$839$	6.71524	+	3.87705i	0.231836	+	0.133851i	−0.379583	+	0.925158i	$0.623932\pi$
$840$		0			0
$841$	−32.0347	+	55.4857i	−1.10464	+	1.91330i
$842$	3.93553	+	6.81654i	0.135627	+	0.234913i
$843$		0			0
$844$	−31.3805			−1.08016
$845$	4.07275	+	12.3456i	0.140107	+	0.424700i
$846$		0			0
$847$	−11.9539	+	6.90161i	−0.410742	+	0.237142i
$848$	9.14995	+	15.8482i	0.314211	+	0.544229i
$849$		0			0
$850$			0.0242995i			0.000833467i
$851$	0.546369	+	0.315446i	0.0187293	+	0.0108134i
$852$		0			0
$853$		−	14.4459i		−	0.494618i	−0.968937	−	0.247309i	$-0.920454\pi$
$853$		−	14.4459i		−	0.494618i	0.968937	−	0.247309i	$-0.0795462\pi$
$854$	−6.70929	+	11.6208i	−0.229587	+	0.397656i
$855$		0			0
$856$	−13.5847	+	7.84312i	−0.464315	+	0.268072i
$857$	−1.52830			−0.0522058			−0.0261029	−	0.999659i	$-0.508310\pi$
$857$	−1.52830			−0.0522058			−0.0261029	+	0.999659i	$0.508310\pi$
$858$		0			0
$859$	49.1152			1.67579			0.837894	−	0.545833i	$-0.183787\pi$
$859$	49.1152			1.67579			0.837894	+	0.545833i	$0.183787\pi$
$860$	−14.7726	+	8.52898i	−0.503743	+	0.290836i
$861$		0			0
$862$	−2.55355	+	4.42288i	−0.0869743	+	0.150644i
$863$			9.73540i			0.331397i	0.986176	+	0.165698i	$0.0529878\pi$
$863$			9.73540i			0.331397i	−0.986176	+	0.165698i	$0.947012\pi$
$864$		0			0
$865$	16.2905	+	9.40534i	0.553895	+	0.319791i
$866$		−	10.8214i		−	0.367725i
$867$		0			0
$868$	−5.15858	−	8.93492i	−0.175094	−	0.303271i
$869$	−27.1436	+	15.6714i	−0.920784	+	0.531615i
$870$		0			0
$871$	5.70135	+	7.00832i	0.193183	+	0.237468i
$872$	−6.03908			−0.204509
$873$		0			0
$874$	0.0316172	+	0.0547625i	0.00106947	+	0.00185237i
$875$	−1.71545	+	2.97125i	−0.0579929	+	0.100447i
$876$		0			0
$877$	−42.3637	−	24.4587i	−1.43052	−	0.825911i	−0.433360	−	0.901221i	$-0.642672\pi$
$877$	−42.3637	−	24.4587i	−1.43052	−	0.825911i	−0.997160	+	0.0753094i	$0.976006\pi$
$878$	−0.986468	−	0.569538i	−0.0332917	−	0.0192210i
$879$		0			0
$880$	4.57498	−	7.92409i	0.154222	−	0.267121i
$881$	−0.353227	−	0.611807i	−0.0119005	−	0.0206123i	0.860014	−	0.510271i	$-0.170455\pi$
$881$	−0.353227	−	0.611807i	−0.0119005	−	0.0206123i	−0.871914	+	0.489658i	$0.837121\pi$
$882$		0			0
$883$	6.46965			0.217721			0.108860	−	0.994057i	$-0.465280\pi$
$883$	6.46965			0.217721			0.108860	+	0.994057i	$0.465280\pi$
$884$	0.430908	−	0.350549i	0.0144930	−	0.0117902i
$885$		0			0
$886$	−8.75453	+	5.05443i	−0.294114	+	0.169807i
$887$	−20.8317	−	36.0815i	−0.699459	−	1.21150i	−0.968654	−	0.248413i	$-0.920091\pi$
$887$	−20.8317	−	36.0815i	−0.699459	−	1.21150i	0.269196	−	0.963086i	$-0.413242\pi$
$888$		0			0
$889$			71.8736i			2.41056i
$890$	2.76244	+	1.59490i	0.0925973	+	0.0534611i
$891$		0			0
$892$		−	4.34630i		−	0.145525i
$893$	−4.05842	+	7.02939i	−0.135810	+	0.235230i
$894$		0			0
$895$	−8.90001	+	5.13842i	−0.297494	+	0.171758i
$896$	−29.4155			−0.982703
$897$		0			0
$898$	5.31133			0.177242
$899$	−13.1586	+	7.59709i	−0.438862	+	0.253377i
$900$		0			0
$901$	0.213134	−	0.369159i	0.00710053	−	0.0122985i
$902$			6.33375i			0.210891i
$903$		0			0
$904$	−8.33284	−	4.81097i	−0.277146	−	0.160010i
$905$			15.0970i			0.501843i
$906$		0			0
$907$	25.1044	+	43.4822i	0.833579	+	1.44380i	0.895182	+	0.445701i	$0.147045\pi$
$907$	25.1044	+	43.4822i	0.833579	+	1.44380i	−0.0616030	+	0.998101i	$0.519621\pi$
$908$	−32.4799	+	18.7523i	−1.07788	+	0.622316i
$909$		0			0
$910$	−3.67805	+	0.591022i	−0.121926	+	0.0195922i
$911$	−6.06993			−0.201106			−0.100553	−	0.994932i	$-0.532061\pi$
$911$	−6.06993			−0.201106			−0.100553	+	0.994932i	$0.532061\pi$
$912$		0			0
$913$	12.6648	+	21.9360i	0.419142	+	0.725976i
$914$	3.18051	−	5.50880i	0.105202	−	0.182215i
$915$		0			0
$916$	−10.5626	−	6.09834i	−0.348999	−	0.201495i
$917$	50.5855	+	29.2056i	1.67048	+	0.964452i
$918$		0			0
$919$	9.61032	−	16.6456i	0.317015	−	0.549087i	−0.662849	−	0.748754i	$-0.730653\pi$
$919$	9.61032	−	16.6456i	0.317015	−	0.549087i	0.979864	+	0.199667i	$0.0639860\pi$
$920$	0.129765	+	0.224759i	0.00427822	+	0.00741010i
$921$		0			0
$922$	−7.26012			−0.239099
$923$	6.79875	−	17.8310i	0.223783	−	0.586915i
$924$		0			0
$925$	2.47841	−	1.43091i	0.0814895	−	0.0470480i
$926$	2.87382	+	4.97760i	0.0944396	+	0.163574i
$927$		0			0
$928$			32.7786i			1.07601i
$929$	5.33864	+	3.08227i	0.175155	+	0.101126i	0.585014	−	0.811023i	$-0.301089\pi$
$929$	5.33864	+	3.08227i	0.175155	+	0.101126i	−0.409859	+	0.912149i	$0.634422\pi$
$930$		0			0
$931$			4.54451i			0.148940i
$932$	19.1304	−	33.1349i	0.626638	−	1.08537i
$933$		0			0
$934$	−3.57502	+	2.06404i	−0.116978	+	0.0675374i
$935$	−0.213134			−0.00697024
$936$		0			0
$937$	7.89678			0.257977			0.128988	−	0.991646i	$-0.458827\pi$
$937$	7.89678			0.257977			0.128988	+	0.991646i	$0.458827\pi$
$938$	−2.24204	+	1.29444i	−0.0732053	+	0.0422651i
$939$		0			0
$940$	−8.13520	+	14.0906i	−0.265341	+	0.459584i
$941$		−	38.9659i		−	1.27025i	−0.772409	−	0.635126i	$-0.780948\pi$
$941$		−	38.9659i		−	1.27025i	0.772409	−	0.635126i	$-0.219052\pi$
$942$		0			0
$943$	1.52021	+	0.877696i	0.0495050	+	0.0285817i
$944$		−	33.5137i		−	1.09078i
$945$		0			0
$946$	3.55321	+	6.15434i	0.115525	+	0.200095i
$947$	17.5175	−	10.1137i	0.569243	−	0.328652i	−0.187604	−	0.982245i	$-0.560072\pi$
$947$	17.5175	−	10.1137i	0.569243	−	0.328652i	0.756847	+	0.653592i	$0.226739\pi$
$948$		0			0
$949$	51.1168	−	8.21390i	1.65932	−	0.266635i
$950$	0.286840			0.00930630
$951$		0			0
$952$	0.162959	+	0.282253i	0.00528152	+	0.00914786i
$953$	7.18379	−	12.4427i	0.232706	−	0.403059i	−0.725898	−	0.687803i	$-0.758575\pi$
$953$	7.18379	−	12.4427i	0.232706	−	0.403059i	0.958604	+	0.284744i	$0.0919087\pi$
$954$		0			0
$955$	−9.97070	−	5.75659i	−0.322644	−	0.186279i
$956$	7.40771	+	4.27684i	0.239582	+	0.138323i
$957$		0			0
$958$	5.27945	−	9.14428i	0.170571	−	0.295438i
$959$	−25.5989	−	44.3386i	−0.826631	−	1.43177i
$960$		0			0
$961$	28.5195			0.919982
$962$	2.90343	+	1.10704i	0.0936103	+	0.0356925i
$963$		0			0
$964$	1.02247	−	0.590323i	0.0329315	−	0.0190130i
$965$	−8.47659	−	14.6819i	−0.272871	−	0.472626i
$966$		0			0
$967$		−	3.30779i		−	0.106371i	−0.998585	−	0.0531857i	$-0.983062\pi$
$967$		−	3.30779i		−	0.106371i	0.998585	−	0.0531857i	$-0.0169375\pi$
$968$	4.10181	+	2.36818i	0.131837	+	0.0761162i
$969$		0			0
$970$		−	1.40901i		−	0.0452405i
$971$	−14.6341	+	25.3469i	−0.469630	+	0.813422i	−0.999397	−	0.0347206i	$-0.988946\pi$
$971$	−14.6341	+	25.3469i	−0.469630	+	0.813422i	0.529767	+	0.848143i	$0.322279\pi$
$972$		0			0
$973$	24.0956	−	13.9116i	0.772470	−	0.445986i
$974$	0.908727			0.0291175
$975$		0			0
$976$	−44.9899			−1.44009
$977$	−43.8512	+	25.3175i	−1.40292	+	0.809979i	−0.994692	−	0.102900i	$-0.967188\pi$
$977$	−43.8512	+	25.3175i	−1.40292	+	0.809979i	−0.408232	+	0.912878i	$0.633855\pi$
$978$		0			0
$979$	−13.9890	+	24.2297i	−0.447092	+	0.774386i
$980$			9.10958i			0.290995i
$981$		0			0
$982$	0.573998	+	0.331398i	0.0183170	+	0.0105753i
$983$		−	29.1032i		−	0.928248i	−0.885770	−	0.464124i	$-0.846369\pi$
$983$		−	29.1032i		−	0.928248i	0.885770	−	0.464124i	$-0.153631\pi$
$984$		0			0
$985$	−5.88135	−	10.1868i	−0.187396	−	0.324579i
$986$	0.203017	−	0.117212i	0.00646537	−	0.00373278i
$987$		0			0
$988$	−4.13799	−	5.08658i	−0.131647	−	0.161826i
$989$	1.96954			0.0626276
$990$		0			0
$991$	−9.67671	−	16.7606i	−0.307391	−	0.532417i	0.670400	−	0.742000i	$-0.266123\pi$
$991$	−9.67671	−	16.7606i	−0.307391	−	0.532417i	−0.977791	+	0.209583i	$0.932789\pi$
$992$	−2.67566	+	4.63438i	−0.0849523	+	0.147142i
$993$		0			0
$994$	4.73578	+	2.73420i	0.150210	+	0.0867237i
$995$	−7.20056	−	4.15724i	−0.228273	−	0.131793i
$996$		0			0
$997$	−30.8483	+	53.4309i	−0.976976	+	1.69217i	−0.303723	+	0.952760i	$0.598230\pi$
$997$	−30.8483	+	53.4309i	−0.976976	+	1.69217i	−0.673253	+	0.739412i	$0.735104\pi$
$998$	1.30768	+	2.26496i	0.0413937	+	0.0716961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.b.361.3		8
3.2	odd	2		195.2.bb.c.166.2	yes	8
13.2	odd	12		7605.2.a.cg.1.3		4
13.4	even	6	inner	585.2.bu.b.316.3		8
13.11	odd	12		7605.2.a.ck.1.2		4
15.2	even	4		975.2.w.j.49.2		8
15.8	even	4		975.2.w.g.49.3		8
15.14	odd	2		975.2.bc.i.751.3		8
39.2	even	12		2535.2.a.bl.1.2		4
39.11	even	12		2535.2.a.bi.1.3		4
39.17	odd	6		195.2.bb.c.121.2	✓	8
195.17	even	12		975.2.w.g.199.3		8
195.134	odd	6		975.2.bc.i.901.3		8
195.173	even	12		975.2.w.j.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.2	✓	8	39.17	odd	6
195.2.bb.c.166.2	yes	8	3.2	odd	2
585.2.bu.b.316.3		8	13.4	even	6	inner
585.2.bu.b.361.3		8	1.1	even	1	trivial
975.2.w.g.49.3		8	15.8	even	4
975.2.w.g.199.3		8	195.17	even	12
975.2.w.j.49.2		8	15.2	even	4
975.2.w.j.199.2		8	195.173	even	12
975.2.bc.i.751.3		8	15.14	odd	2
975.2.bc.i.901.3		8	195.134	odd	6
2535.2.a.bi.1.3		4	39.11	even	12
2535.2.a.bl.1.2		4	39.2	even	12
7605.2.a.cg.1.3		4	13.2	odd	12
7605.2.a.ck.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.260797 + 0.150571i) q^{2} +(-0.954656 + 1.65351i) q^{4} -1.00000i q^{5} +(2.97125 + 1.71545i) q^{7} -1.17726i q^{8} +O(q^{10})\)	\(q+(-0.260797 + 0.150571i) q^{2} +(-0.954656 + 1.65351i) q^{4} -1.00000i q^{5} +(2.97125 + 1.71545i) q^{7} -1.17726i q^{8} +(0.150571 + 0.260797i) q^{10} +(-2.28749 + 1.32068i) q^{11} +(0.572034 + 3.55988i) q^{13} -1.03319 q^{14} +(-1.73205 - 3.00000i) q^{16} +(-0.0403455 + 0.0698805i) q^{17} +(0.824892 + 0.476251i) q^{19} +(1.65351 + 0.954656i) q^{20} +(0.397714 - 0.688861i) q^{22} +(-0.110226 - 0.190917i) q^{23} -1.00000 q^{25} +(-0.685202 - 0.842277i) q^{26} +(-5.67305 + 3.27534i) q^{28} +(4.82362 + 8.35476i) q^{29} +1.57498i q^{31} +(2.94251 + 1.69886i) q^{32} -0.0242995i q^{34} +(1.71545 - 2.97125i) q^{35} +(-2.47841 + 1.43091i) q^{37} -0.286840 q^{38} -1.17726 q^{40} +(-6.89590 + 3.98135i) q^{41} +(-4.46704 + 7.73715i) q^{43} -5.04319i q^{44} +(0.0574933 + 0.0331938i) q^{46} +8.52159i q^{47} +(2.38556 + 4.13192i) q^{49} +(0.260797 - 0.150571i) q^{50} +(-6.43241 - 2.45260i) q^{52} -5.28273 q^{53} +(1.32068 + 2.28749i) q^{55} +(2.01954 - 3.49794i) q^{56} +(-2.51598 - 1.45260i) q^{58} +(8.37841 + 4.83728i) q^{59} +(6.49373 - 11.2475i) q^{61} +(-0.237147 - 0.410750i) q^{62} +5.90501 q^{64} +(3.55988 - 0.572034i) q^{65} +(2.17001 - 1.25286i) q^{67} +(-0.0770322 - 0.133424i) q^{68} +1.03319i q^{70} +(-4.58363 - 2.64636i) q^{71} -14.3591i q^{73} +(0.430908 - 0.746354i) q^{74} +(-1.57498 + 0.909313i) q^{76} -9.06228 q^{77} +11.8661 q^{79} +(-3.00000 + 1.73205i) q^{80} +(1.19895 - 2.07665i) q^{82} -9.58956i q^{83} +(0.0698805 + 0.0403455i) q^{85} -2.69044i q^{86} +(1.55479 + 2.69297i) q^{88} +(9.17319 - 5.29614i) q^{89} +(-4.40716 + 11.5586i) q^{91} +0.420912 q^{92} +(-1.28311 - 2.22241i) q^{94} +(0.476251 - 0.824892i) q^{95} +(-4.05202 - 2.33943i) q^{97} +(-1.24430 - 0.718396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 4 q^{4} + 6 q^{7}+O(q^{10}) \) 8 * q - 6 * q^2 + 4 * q^4 + 6 * q^7	\( 8 q - 6 q^{2} + 4 q^{4} + 6 q^{7} + 2 q^{10} - 12 q^{11} + 6 q^{13} + 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 4 q^{26} - 12 q^{28} + 6 q^{29} - 12 q^{32} + 6 q^{35} - 12 q^{37} + 16 q^{38} + 30 q^{41} + 6 q^{43} + 36 q^{46} - 8 q^{49} + 6 q^{50} - 20 q^{52} + 32 q^{53} - 8 q^{55} - 4 q^{56} + 12 q^{58} + 30 q^{59} + 30 q^{62} + 32 q^{64} + 6 q^{65} + 30 q^{67} - 16 q^{68} - 18 q^{71} - 12 q^{74} + 8 q^{77} + 56 q^{79} - 24 q^{80} - 24 q^{82} + 6 q^{85} + 8 q^{88} + 18 q^{89} - 16 q^{91} - 40 q^{92} - 16 q^{94} - 6 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 + 4 * q^4 + 6 * q^7 + 2 * q^10 - 12 * q^11 + 6 * q^13 + 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 4 * q^26 - 12 * q^28 + 6 * q^29 - 12 * q^32 + 6 * q^35 - 12 * q^37 + 16 * q^38 + 30 * q^41 + 6 * q^43 + 36 * q^46 - 8 * q^49 + 6 * q^50 - 20 * q^52 + 32 * q^53 - 8 * q^55 - 4 * q^56 + 12 * q^58 + 30 * q^59 + 30 * q^62 + 32 * q^64 + 6 * q^65 + 30 * q^67 - 16 * q^68 - 18 * q^71 - 12 * q^74 + 8 * q^77 + 56 * q^79 - 24 * q^80 - 24 * q^82 + 6 * q^85 + 8 * q^88 + 18 * q^89 - 16 * q^91 - 40 * q^92 - 16 * q^94 - 6 * q^97 + 12 * q^98

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