LMFDB - Embedded newform 1170.2.bs.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.e.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.401924 + 0.232051i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.464102 - 0.267949i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.232051 - 0.401924i) q^{22} +(0.133975 + 0.232051i) q^{23} -1.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} +(1.73205 - 1.00000i) q^{28} +(1.86603 + 3.23205i) q^{29} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(1.03590 - 0.598076i) q^{37} +0.535898 q^{38} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(0.964102 - 1.66987i) q^{43} +0.464102i q^{44} +(-0.232051 - 0.133975i) q^{46} +10.4641i q^{47} +(-1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.50000 + 0.866025i) q^{52} +12.9282 q^{53} +(0.232051 + 0.401924i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(-3.23205 - 1.86603i) q^{58} +(1.33013 + 0.767949i) q^{59} +(-5.19615 + 9.00000i) q^{61} +(-0.866025 - 1.50000i) q^{62} -1.00000 q^{64} +(3.46410 - 1.00000i) q^{65} +(3.92820 - 2.26795i) q^{67} +(2.00000 + 3.46410i) q^{68} +2.00000i q^{70} +(7.26795 + 4.19615i) q^{71} +2.00000i q^{73} +(-0.598076 + 1.03590i) q^{74} +(-0.464102 + 0.267949i) q^{76} -0.928203 q^{77} -0.0717968 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-1.00000 + 1.73205i) q^{82} +4.92820i q^{83} +(3.46410 + 2.00000i) q^{85} +1.92820i q^{86} +(-0.232051 - 0.401924i) q^{88} +(-6.46410 + 3.73205i) q^{89} +(-1.73205 + 7.00000i) q^{91} +0.267949 q^{92} +(-5.23205 - 9.06218i) q^{94} +(-0.267949 + 0.464102i) q^{95} +(-6.46410 - 3.73205i) q^{97} +(2.59808 + 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} + 2 q^{10} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 2 q^{16} - 8 q^{17} + 12 q^{19} - 6 q^{22} + 4 q^{23} - 4 q^{25} + 4 q^{29} + 4 q^{35} + 18 q^{37} + 16 q^{38} + 4 q^{40} - 10 q^{43} + 6 q^{46} - 6 q^{49} + 14 q^{52} + 24 q^{53} - 6 q^{55} - 4 q^{56} - 6 q^{58} - 12 q^{59} - 4 q^{64} - 12 q^{67} + 8 q^{68} + 36 q^{71} + 8 q^{74} + 12 q^{76} + 24 q^{77} - 28 q^{79} - 4 q^{82} + 6 q^{88} - 12 q^{89} + 8 q^{92} - 14 q^{94} - 8 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^10 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 2 * q^16 - 8 * q^17 + 12 * q^19 - 6 * q^22 + 4 * q^23 - 4 * q^25 + 4 * q^29 + 4 * q^35 + 18 * q^37 + 16 * q^38 + 4 * q^40 - 10 * q^43 + 6 * q^46 - 6 * q^49 + 14 * q^52 + 24 * q^53 - 6 * q^55 - 4 * q^56 - 6 * q^58 - 12 * q^59 - 4 * q^64 - 12 * q^67 + 8 * q^68 + 36 * q^71 + 8 * q^74 + 12 * q^76 + 24 * q^77 - 28 * q^79 - 4 * q^82 + 6 * q^88 - 12 * q^89 + 8 * q^92 - 14 * q^94 - 8 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.401924	+	0.232051i	−0.121185	+	0.0699660i	−0.559367	−	0.828920i	$-0.688956\pi$
$11$	−0.401924	+	0.232051i	−0.121185	+	0.0699660i	0.438182	+	0.898886i	$0.355622\pi$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	−0.464102	−	0.267949i	−0.106472	−	0.0614718i	0.445818	−	0.895123i	$-0.352913\pi$
$19$	−0.464102	−	0.267949i	−0.106472	−	0.0614718i	−0.552291	+	0.833652i	$0.686246\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	0.232051	−	0.401924i	0.0494734	−	0.0856904i
$23$	0.133975	+	0.232051i	0.0279356	+	0.0483859i	0.879655	−	0.475612i	$-0.157773\pi$
$23$	0.133975	+	0.232051i	0.0279356	+	0.0483859i	−0.851720	+	0.523998i	$0.824440\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−2.59808	−	2.50000i	−0.509525	−	0.490290i
$27$		0			0
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	1.86603	+	3.23205i	0.346512	+	0.600177i	0.985627	−	0.168934i	$-0.0540326\pi$
$29$	1.86603	+	3.23205i	0.346512	+	0.600177i	−0.639115	+	0.769111i	$0.720699\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	4.00000i		−	0.685994i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$		0			0
$37$	1.03590	−	0.598076i	0.170301	−	0.0983231i	−0.412427	−	0.910991i	$-0.635319\pi$
$37$	1.03590	−	0.598076i	0.170301	−	0.0983231i	0.582728	+	0.812668i	$0.301985\pi$
$38$	0.535898			0.0869342
$39$		0			0
$40$	1.00000			0.158114
$41$	1.73205	−	1.00000i	0.270501	−	0.156174i	−0.358614	−	0.933486i	$-0.616751\pi$
$41$	1.73205	−	1.00000i	0.270501	−	0.156174i	0.629115	+	0.777312i	$0.283417\pi$
$42$		0			0
$43$	0.964102	−	1.66987i	0.147024	−	0.254653i	−0.783102	−	0.621893i	$-0.786364\pi$
$43$	0.964102	−	1.66987i	0.147024	−	0.254653i	0.930126	+	0.367240i	$0.119697\pi$
$44$			0.464102i			0.0699660i
$45$		0			0
$46$	−0.232051	−	0.133975i	−0.0342140	−	0.0197535i
$47$			10.4641i			1.52635i	0.646194	+	0.763173i	$0.276360\pi$
$47$			10.4641i			1.52635i	−0.646194	+	0.763173i	$0.723640\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	12.9282			1.77583			0.887913	−	0.460012i	$-0.152155\pi$
$53$	12.9282			1.77583			0.887913	+	0.460012i	$0.152155\pi$
$54$		0			0
$55$	0.232051	+	0.401924i	0.0312897	+	0.0541954i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$		0			0
$58$	−3.23205	−	1.86603i	−0.424389	−	0.245021i
$59$	1.33013	+	0.767949i	0.173168	+	0.0999785i	0.584079	−	0.811697i	$-0.301456\pi$
$59$	1.33013	+	0.767949i	0.173168	+	0.0999785i	−0.410911	+	0.911676i	$0.634789\pi$
$60$		0			0
$61$	−5.19615	+	9.00000i	−0.665299	+	1.15233i	0.313905	+	0.949454i	$0.398363\pi$
$61$	−5.19615	+	9.00000i	−0.665299	+	1.15233i	−0.979204	+	0.202878i	$0.934971\pi$
$62$	−0.866025	−	1.50000i	−0.109985	−	0.190500i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.46410	−	1.00000i	0.429669	−	0.124035i
$66$		0			0
$67$	3.92820	−	2.26795i	0.479906	−	0.277074i	−0.240471	−	0.970656i	$-0.577302\pi$
$67$	3.92820	−	2.26795i	0.479906	−	0.277074i	0.720377	+	0.693582i	$0.243969\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$			2.00000i			0.239046i
$71$	7.26795	+	4.19615i	0.862547	+	0.497992i	0.864864	−	0.502006i	$-0.167404\pi$
$71$	7.26795	+	4.19615i	0.862547	+	0.497992i	−0.00231747	+	0.999997i	$0.500738\pi$
$72$		0			0
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	−0.598076	+	1.03590i	−0.0695249	+	0.120421i
$75$		0			0
$76$	−0.464102	+	0.267949i	−0.0532361	+	0.0307359i
$77$	−0.928203			−0.105779
$78$		0			0
$79$	−0.0717968			−0.00807777			−0.00403888	−	0.999992i	$-0.501286\pi$
$79$	−0.0717968			−0.00807777			−0.00403888	+	0.999992i	$0.501286\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$		0			0
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$			4.92820i			0.540941i	0.962728	+	0.270470i	$0.0871792\pi$
$83$			4.92820i			0.540941i	−0.962728	+	0.270470i	$0.912821\pi$
$84$		0			0
$85$	3.46410	+	2.00000i	0.375735	+	0.216930i
$86$			1.92820i			0.207924i
$87$		0			0
$88$	−0.232051	−	0.401924i	−0.0247367	−	0.0428452i
$89$	−6.46410	+	3.73205i	−0.685193	+	0.395597i	−0.801809	−	0.597581i	$-0.796129\pi$
$89$	−6.46410	+	3.73205i	−0.685193	+	0.395597i	0.116615	+	0.993177i	$0.462795\pi$
$90$		0			0
$91$	−1.73205	+	7.00000i	−0.181568	+	0.733799i
$92$	0.267949			0.0279356
$93$		0			0
$94$	−5.23205	−	9.06218i	−0.539645	−	0.934692i
$95$	−0.267949	+	0.464102i	−0.0274910	+	0.0476158i
$96$		0			0
$97$	−6.46410	−	3.73205i	−0.656330	−	0.378932i	0.134547	−	0.990907i	$-0.457042\pi$
$97$	−6.46410	−	3.73205i	−0.656330	−	0.378932i	−0.790877	+	0.611975i	$0.790375\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−5.46410	−	9.46410i	−0.543698	−	0.941713i	−0.998688	−	0.0512163i	$-0.983690\pi$
$101$	−5.46410	−	9.46410i	−0.543698	−	0.941713i	0.454989	−	0.890497i	$-0.349643\pi$
$102$		0			0
$103$	15.8564			1.56238			0.781189	−	0.624295i	$-0.214613\pi$
$103$	15.8564			1.56238			0.781189	+	0.624295i	$0.214613\pi$
$104$	−3.46410	+	1.00000i	−0.339683	+	0.0980581i
$105$		0			0
$106$	−11.1962	+	6.46410i	−1.08747	+	0.627849i
$107$	9.92820	+	17.1962i	0.959796	+	1.66241i	0.722991	+	0.690858i	$0.242767\pi$
$107$	9.92820	+	17.1962i	0.959796	+	1.66241i	0.236805	+	0.971557i	$0.423900\pi$
$108$		0			0
$109$			11.8564i			1.13564i	0.823154	+	0.567819i	$0.192213\pi$
$109$			11.8564i			1.13564i	−0.823154	+	0.567819i	$0.807787\pi$
$110$	−0.401924	−	0.232051i	−0.0383219	−	0.0221252i
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$	5.59808	−	9.69615i	0.526623	−	0.912137i	−0.472896	−	0.881118i	$-0.656791\pi$
$113$	5.59808	−	9.69615i	0.526623	−	0.912137i	0.999519	−	0.0310191i	$-0.00987527\pi$
$114$		0			0
$115$	0.232051	−	0.133975i	0.0216388	−	0.0124932i
$116$	3.73205			0.346512
$117$		0			0
$118$	−1.53590			−0.141391
$119$	−6.92820	+	4.00000i	−0.635107	+	0.366679i
$120$		0			0
$121$	−5.39230	+	9.33975i	−0.490210	+	0.849068i
$122$		−	10.3923i		−	0.940875i
$123$		0			0
$124$	1.50000	+	0.866025i	0.134704	+	0.0777714i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−4.46410	−	7.73205i	−0.396125	−	0.686109i	0.597119	−	0.802153i	$-0.296312\pi$
$127$	−4.46410	−	7.73205i	−0.396125	−	0.686109i	−0.993244	+	0.116044i	$0.962979\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.50000	+	2.59808i	−0.219265	+	0.227866i
$131$	1.33975			0.117054			0.0585271	−	0.998286i	$-0.481360\pi$
$131$	1.33975			0.117054			0.0585271	+	0.998286i	$0.481360\pi$
$132$		0			0
$133$	−0.535898	−	0.928203i	−0.0464683	−	0.0804854i
$134$	−2.26795	+	3.92820i	−0.195921	+	0.339345i
$135$		0			0
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	3.86603	+	2.23205i	0.330297	+	0.190697i	0.655973	−	0.754784i	$-0.272259\pi$
$137$	3.86603	+	2.23205i	0.330297	+	0.190697i	−0.325676	+	0.945481i	$0.605592\pi$
$138$		0			0
$139$	−0.464102	+	0.803848i	−0.0393646	+	0.0681815i	−0.885036	−	0.465522i	$-0.845867\pi$
$139$	−0.464102	+	0.803848i	−0.0393646	+	0.0681815i	0.845672	+	0.533703i	$0.179200\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$		0			0
$142$	−8.39230			−0.704267
$143$	−1.20577	−	1.16025i	−0.100832	−	0.0970253i
$144$		0			0
$145$	3.23205	−	1.86603i	0.268407	−	0.154965i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$		−	1.19615i		−	0.0983231i
$149$	−17.7224	−	10.2321i	−1.45188	−	0.838242i	−0.453290	−	0.891363i	$-0.649750\pi$
$149$	−17.7224	−	10.2321i	−1.45188	−	0.838242i	−0.998588	+	0.0531208i	$0.983083\pi$
$150$		0			0
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	0.267949	−	0.464102i	0.0217335	−	0.0376436i
$153$		0			0
$154$	0.803848	−	0.464102i	0.0647759	−	0.0373984i
$155$	1.73205			0.139122
$156$		0			0
$157$	−5.00000			−0.399043			−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000			−0.399043			−0.199522	+	0.979893i	$0.563939\pi$
$158$	0.0621778	−	0.0358984i	0.00494660	−	0.00285592i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			0.535898i			0.0422347i
$162$		0			0
$163$	19.9641	+	11.5263i	1.56371	+	0.902808i	0.996877	+	0.0789748i	$0.0251647\pi$
$163$	19.9641	+	11.5263i	1.56371	+	0.902808i	0.566833	+	0.823833i	$0.308169\pi$
$164$		−	2.00000i		−	0.156174i
$165$		0			0
$166$	−2.46410	−	4.26795i	−0.191251	−	0.331257i
$167$	−15.8660	+	9.16025i	−1.22775	+	0.708842i	−0.966559	−	0.256445i	$-0.917449\pi$
$167$	−15.8660	+	9.16025i	−1.22775	+	0.708842i	−0.261191	+	0.965287i	$0.584115\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−0.964102	−	1.66987i	−0.0735121	−	0.127327i
$173$	−1.46410	+	2.53590i	−0.111314	+	0.192801i	−0.916300	−	0.400492i	$-0.868839\pi$
$173$	−1.46410	+	2.53590i	−0.111314	+	0.192801i	0.804987	+	0.593293i	$0.202172\pi$
$174$		0			0
$175$	−1.73205	−	1.00000i	−0.130931	−	0.0755929i
$176$	0.401924	+	0.232051i	0.0302961	+	0.0174915i
$177$		0			0
$178$	3.73205	−	6.46410i	0.279729	−	0.484505i
$179$	−8.13397	−	14.0885i	−0.607962	−	1.05302i	−0.991576	−	0.129527i	$-0.958654\pi$
$179$	−8.13397	−	14.0885i	−0.607962	−	1.05302i	0.383614	−	0.923494i	$-0.374679\pi$
$180$		0			0
$181$	10.9282			0.812287			0.406143	−	0.913809i	$-0.366873\pi$
$181$	10.9282			0.812287			0.406143	+	0.913809i	$0.366873\pi$
$182$	−2.00000	−	6.92820i	−0.148250	−	0.513553i
$183$		0			0
$184$	−0.232051	+	0.133975i	−0.0171070	+	0.00987674i
$185$	−0.598076	−	1.03590i	−0.0439714	−	0.0761608i
$186$		0			0
$187$		−	1.85641i		−	0.135754i
$188$	9.06218	+	5.23205i	0.660927	+	0.381587i
$189$		0			0
$190$		−	0.535898i		−	0.0388782i
$191$	7.26795	−	12.5885i	0.525890	−	0.910869i	−0.473655	−	0.880711i	$-0.657066\pi$
$191$	7.26795	−	12.5885i	0.525890	−	0.910869i	0.999545	−	0.0301582i	$-0.00960111\pi$
$192$		0			0
$193$	20.1962	−	11.6603i	1.45375	−	0.839323i	0.455059	−	0.890461i	$-0.349618\pi$
$193$	20.1962	−	11.6603i	1.45375	−	0.839323i	0.998692	+	0.0511377i	$0.0162847\pi$
$194$	7.46410			0.535891
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−14.1962	+	8.19615i	−1.01143	+	0.583952i	−0.911611	−	0.411054i	$-0.865161\pi$
$197$	−14.1962	+	8.19615i	−1.01143	+	0.583952i	−0.0998228	+	0.995005i	$0.531828\pi$
$198$		0			0
$199$	9.46410	−	16.3923i	0.670892	−	1.16202i	−0.306759	−	0.951787i	$-0.599245\pi$
$199$	9.46410	−	16.3923i	0.670892	−	1.16202i	0.977651	−	0.210232i	$-0.0674221\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	9.46410	+	5.46410i	0.665892	+	0.384453i
$203$			7.46410i			0.523877i
$204$		0			0
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	−13.7321	+	7.92820i	−0.956757	+	0.552384i
$207$		0			0
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	0.248711			0.0172037
$210$		0			0
$211$	−11.6603	−	20.1962i	−0.802725	−	1.39036i	−0.917816	−	0.397006i	$-0.870049\pi$
$211$	−11.6603	−	20.1962i	−0.802725	−	1.39036i	0.115091	−	0.993355i	$-0.463284\pi$
$212$	6.46410	−	11.1962i	0.443956	−	0.768955i
$213$		0			0
$214$	−17.1962	−	9.92820i	−1.17550	−	0.678678i
$215$	−1.66987	−	0.964102i	−0.113884	−	0.0657512i
$216$		0			0
$217$	−1.73205	+	3.00000i	−0.117579	+	0.203653i
$218$	−5.92820	−	10.2679i	−0.401509	−	0.695433i
$219$		0			0
$220$	0.464102			0.0312897
$221$	−14.0000	−	3.46410i	−0.941742	−	0.233021i
$222$		0			0
$223$	23.7846	−	13.7321i	1.59274	−	0.919566i	0.599900	−	0.800075i	$-0.295207\pi$
$223$	23.7846	−	13.7321i	1.59274	−	0.919566i	0.992835	−	0.119491i	$-0.0381263\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$			11.1962i			0.744757i
$227$	3.80385	+	2.19615i	0.252470	+	0.145764i	0.620895	−	0.783894i	$-0.286769\pi$
$227$	3.80385	+	2.19615i	0.252470	+	0.145764i	−0.368425	+	0.929658i	$0.620103\pi$
$228$		0			0
$229$			19.8564i			1.31215i	0.754696	+	0.656074i	$0.227784\pi$
$229$			19.8564i			1.31215i	−0.754696	+	0.656074i	$0.772216\pi$
$230$	−0.133975	+	0.232051i	−0.00883402	+	0.0153010i
$231$		0			0
$232$	−3.23205	+	1.86603i	−0.212195	+	0.122511i
$233$	18.1244			1.18737			0.593683	−	0.804699i	$-0.297673\pi$
$233$	18.1244			1.18737			0.593683	+	0.804699i	$0.297673\pi$
$234$		0			0
$235$	10.4641			0.682603
$236$	1.33013	−	0.767949i	0.0865839	−	0.0499892i
$237$		0			0
$238$	4.00000	−	6.92820i	0.259281	−	0.449089i
$239$		−	4.39230i		−	0.284115i	−0.989858	−	0.142057i	$-0.954628\pi$
$239$		−	4.39230i		−	0.284115i	0.989858	−	0.142057i	$-0.0453717\pi$
$240$		0			0
$241$	−12.3564	−	7.13397i	−0.795946	−	0.459540i	0.0461056	−	0.998937i	$-0.485319\pi$
$241$	−12.3564	−	7.13397i	−0.795946	−	0.459540i	−0.842052	+	0.539397i	$0.818652\pi$
$242$		−	10.7846i		−	0.693261i
$243$		0			0
$244$	5.19615	+	9.00000i	0.332650	+	0.576166i
$245$	−2.59808	+	1.50000i	−0.165985	+	0.0958315i
$246$		0			0
$247$	0.464102	−	1.87564i	0.0295301	−	0.119344i
$248$	−1.73205			−0.109985
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	6.13397	−	10.6244i	0.387173	−	0.670603i	−0.604895	−	0.796305i	$-0.706785\pi$
$251$	6.13397	−	10.6244i	0.387173	−	0.670603i	0.992068	+	0.125702i	$0.0401183\pi$
$252$		0			0
$253$	−0.107695	−	0.0621778i	−0.00677074	−	0.00390909i
$254$	7.73205	+	4.46410i	0.485152	+	0.280103i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.3301	−	19.6244i	−0.706754	−	1.22413i	−0.966055	−	0.258337i	$-0.916825\pi$
$257$	−11.3301	−	19.6244i	−0.706754	−	1.22413i	0.259301	−	0.965797i	$-0.416508\pi$
$258$		0			0
$259$	2.39230			0.148651
$260$	0.866025	−	3.50000i	0.0537086	−	0.217061i
$261$		0			0
$262$	−1.16025	+	0.669873i	−0.0716807	+	0.0413849i
$263$	−9.06218	−	15.6962i	−0.558798	−	0.967866i	−0.997597	−	0.0692812i	$-0.977929\pi$
$263$	−9.06218	−	15.6962i	−0.558798	−	0.967866i	0.438799	−	0.898585i	$-0.355404\pi$
$264$		0			0
$265$		−	12.9282i		−	0.794173i
$266$	0.928203	+	0.535898i	0.0569118	+	0.0328580i
$267$		0			0
$268$		−	4.53590i		−	0.277074i
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	−0.623082	−	0.782157i	$-0.714120\pi$
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	0.988908	+	0.148527i	$0.0474530\pi$
$270$		0			0
$271$	7.96410	−	4.59808i	0.483785	−	0.279313i	−0.238208	−	0.971214i	$-0.576560\pi$
$271$	7.96410	−	4.59808i	0.483785	−	0.279313i	0.721992	+	0.691901i	$0.243227\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−4.46410			−0.269686
$275$	0.401924	−	0.232051i	0.0242369	−	0.0139932i
$276$		0			0
$277$	−4.96410	+	8.59808i	−0.298264	+	0.516608i	−0.975739	−	0.218938i	$-0.929741\pi$
$277$	−4.96410	+	8.59808i	−0.298264	+	0.516608i	0.677475	+	0.735546i	$0.263074\pi$
$278$		−	0.928203i		−	0.0556699i
$279$		0			0
$280$	1.73205	+	1.00000i	0.103510	+	0.0597614i
$281$		−	4.92820i		−	0.293992i	−0.989137	−	0.146996i	$-0.953040\pi$
$281$		−	4.92820i		−	0.293992i	0.989137	−	0.146996i	$-0.0469604\pi$
$282$		0			0
$283$	−1.96410	−	3.40192i	−0.116754	−	0.202223i	0.801726	−	0.597692i	$-0.203915\pi$
$283$	−1.96410	−	3.40192i	−0.116754	−	0.202223i	−0.918479	+	0.395469i	$0.870582\pi$
$284$	7.26795	−	4.19615i	0.431273	−	0.248996i
$285$		0			0
$286$	1.62436	+	0.401924i	0.0960502	+	0.0237663i
$287$	4.00000			0.236113
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−1.86603	+	3.23205i	−0.109577	+	0.189793i
$291$		0			0
$292$	1.73205	+	1.00000i	0.101361	+	0.0585206i
$293$	−3.58846	−	2.07180i	−0.209640	−	0.121036i	0.391504	−	0.920176i	$-0.371955\pi$
$293$	−3.58846	−	2.07180i	−0.209640	−	0.121036i	−0.601144	+	0.799141i	$0.705288\pi$
$294$		0			0
$295$	0.767949	−	1.33013i	0.0447117	−	0.0774430i
$296$	0.598076	+	1.03590i	0.0347625	+	0.0602104i
$297$		0			0
$298$	20.4641			1.18545
$299$	−0.669873	+	0.696152i	−0.0387398	+	0.0402595i
$300$		0			0
$301$	3.33975	−	1.92820i	0.192500	−	0.111140i
$302$	−5.19615	−	9.00000i	−0.299005	−	0.517892i
$303$		0			0
$304$			0.535898i			0.0307359i
$305$	9.00000	+	5.19615i	0.515339	+	0.297531i
$306$		0			0
$307$			12.5359i			0.715462i	0.933825	+	0.357731i	$0.116449\pi$
$307$			12.5359i			0.715462i	−0.933825	+	0.357731i	$0.883551\pi$
$308$	−0.464102	+	0.803848i	−0.0264446	+	0.0458035i
$309$		0			0
$310$	−1.50000	+	0.866025i	−0.0851943	+	0.0491869i
$311$	7.60770			0.431393			0.215696	−	0.976460i	$-0.430798\pi$
$311$	7.60770			0.431393			0.215696	+	0.976460i	$0.430798\pi$
$312$		0			0
$313$	−28.0000			−1.58265			−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000			−1.58265			−0.791327	+	0.611393i	$0.790609\pi$
$314$	4.33013	−	2.50000i	0.244363	−	0.141083i
$315$		0			0
$316$	−0.0358984	+	0.0621778i	−0.00201944	+	0.00349778i
$317$		−	21.4641i		−	1.20554i	−0.797913	−	0.602772i	$-0.794063\pi$
$317$		−	21.4641i		−	1.20554i	0.797913	−	0.602772i	$-0.205937\pi$
$318$		0			0
$319$	−1.50000	−	0.866025i	−0.0839839	−	0.0484881i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−0.267949	−	0.464102i	−0.0149322	−	0.0258634i
$323$	1.85641	−	1.07180i	0.103293	−	0.0596364i
$324$		0			0
$325$	−1.00000	−	3.46410i	−0.0554700	−	0.192154i
$326$	−23.0526			−1.27676
$327$		0			0
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$	−10.4641	+	18.1244i	−0.576905	+	0.999228i
$330$		0			0
$331$	−21.4641	−	12.3923i	−1.17977	−	0.681143i	−0.223812	−	0.974632i	$-0.571850\pi$
$331$	−21.4641	−	12.3923i	−1.17977	−	0.681143i	−0.955962	+	0.293490i	$0.905183\pi$
$332$	4.26795	+	2.46410i	0.234234	+	0.135235i
$333$		0			0
$334$	9.16025	−	15.8660i	0.501227	−	0.868150i
$335$	−2.26795	−	3.92820i	−0.123911	−	0.214621i
$336$		0			0
$337$	−25.3205			−1.37930			−0.689648	−	0.724145i	$-0.742235\pi$
$337$	−25.3205			−1.37930			−0.689648	+	0.724145i	$0.742235\pi$
$338$	6.06218	−	11.5000i	0.329739	−	0.625518i
$339$		0			0
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	−0.401924	−	0.696152i	−0.0217654	−	0.0376988i
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$	1.66987	+	0.964102i	0.0900335	+	0.0519809i
$345$		0			0
$346$		−	2.92820i		−	0.157421i
$347$	11.1962	−	19.3923i	0.601041	−	1.04103i	−0.391623	−	0.920126i	$-0.628086\pi$
$347$	11.1962	−	19.3923i	0.601041	−	1.04103i	0.992664	−	0.120908i	$-0.0385805\pi$
$348$		0			0
$349$	−12.5885	+	7.26795i	−0.673845	+	0.389044i	−0.797532	−	0.603277i	$-0.793861\pi$
$349$	−12.5885	+	7.26795i	−0.673845	+	0.389044i	0.123687	+	0.992321i	$0.460528\pi$
$350$	2.00000			0.106904
$351$		0			0
$352$	−0.464102			−0.0247367
$353$	1.73205	−	1.00000i	0.0921878	−	0.0532246i	−0.453197	−	0.891410i	$-0.649717\pi$
$353$	1.73205	−	1.00000i	0.0921878	−	0.0532246i	0.545385	+	0.838186i	$0.316383\pi$
$354$		0			0
$355$	4.19615	−	7.26795i	0.222709	−	0.385743i
$356$			7.46410i			0.395597i
$357$		0			0
$358$	14.0885	+	8.13397i	0.744598	+	0.429894i
$359$		−	18.9282i		−	0.998992i	−0.866316	−	0.499496i	$-0.833518\pi$
$359$		−	18.9282i		−	0.998992i	0.866316	−	0.499496i	$-0.166482\pi$
$360$		0			0
$361$	−9.35641	−	16.2058i	−0.492442	−	0.852935i
$362$	−9.46410	+	5.46410i	−0.497422	+	0.287187i
$363$		0			0
$364$	5.19615	+	5.00000i	0.272352	+	0.262071i
$365$	2.00000			0.104685
$366$		0			0
$367$	−18.1962	−	31.5167i	−0.949831	−	1.64516i	−0.745776	−	0.666197i	$-0.767921\pi$
$367$	−18.1962	−	31.5167i	−0.949831	−	1.64516i	−0.204056	−	0.978959i	$-0.565412\pi$
$368$	0.133975	−	0.232051i	0.00698391	−	0.0120965i
$369$		0			0
$370$	1.03590	+	0.598076i	0.0538538	+	0.0310925i
$371$	22.3923	+	12.9282i	1.16255	+	0.671199i
$372$		0			0
$373$	−12.8923	+	22.3301i	−0.667538	+	1.15621i	0.311052	+	0.950393i	$0.399319\pi$
$373$	−12.8923	+	22.3301i	−0.667538	+	1.15621i	−0.978590	+	0.205817i	$0.934015\pi$
$374$	0.928203	+	1.60770i	0.0479962	+	0.0831319i
$375$		0			0
$376$	−10.4641			−0.539645
$377$	−9.33013	+	9.69615i	−0.480526	+	0.499377i
$378$		0			0
$379$	−0.124356	+	0.0717968i	−0.00638772	+	0.00368795i	−0.503190	−	0.864176i	$-0.667841\pi$
$379$	−0.124356	+	0.0717968i	−0.00638772	+	0.00368795i	0.496803	+	0.867863i	$0.334507\pi$
$380$	0.267949	+	0.464102i	0.0137455	+	0.0238079i
$381$		0			0
$382$			14.5359i			0.743721i
$383$	3.99038	+	2.30385i	0.203899	+	0.117721i	0.598473	−	0.801143i	$-0.295774\pi$
$383$	3.99038	+	2.30385i	0.203899	+	0.117721i	−0.394574	+	0.918864i	$0.629108\pi$
$384$		0			0
$385$			0.928203i			0.0473056i
$386$	−11.6603	+	20.1962i	−0.593491	+	1.02796i
$387$		0			0
$388$	−6.46410	+	3.73205i	−0.328165	+	0.189466i
$389$	20.2679			1.02763			0.513813	−	0.857902i	$-0.328233\pi$
$389$	20.2679			1.02763			0.513813	+	0.857902i	$0.328233\pi$
$390$		0			0
$391$	−1.07180			−0.0542031
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$		0			0
$394$	8.19615	−	14.1962i	0.412916	−	0.715192i
$395$			0.0717968i			0.00361249i
$396$		0			0
$397$	10.5000	+	6.06218i	0.526980	+	0.304252i	0.739786	−	0.672843i	$-0.234927\pi$
$397$	10.5000	+	6.06218i	0.526980	+	0.304252i	−0.212806	+	0.977095i	$0.568260\pi$
$398$			18.9282i			0.948785i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−27.7128	+	16.0000i	−1.38391	+	0.799002i	−0.992620	−	0.121265i	$-0.961305\pi$
$401$	−27.7128	+	16.0000i	−1.38391	+	0.799002i	−0.391292	+	0.920267i	$0.627972\pi$
$402$		0			0
$403$	−6.00000	+	1.73205i	−0.298881	+	0.0862796i
$404$	−10.9282			−0.543698
$405$		0			0
$406$	−3.73205	−	6.46410i	−0.185219	−	0.320808i
$407$	−0.277568	+	0.480762i	−0.0137585	+	0.0238305i
$408$		0			0
$409$	−3.46410	−	2.00000i	−0.171289	−	0.0988936i	0.411905	−	0.911227i	$-0.364864\pi$
$409$	−3.46410	−	2.00000i	−0.171289	−	0.0988936i	−0.583193	+	0.812333i	$0.698197\pi$
$410$	1.73205	+	1.00000i	0.0855399	+	0.0493865i
$411$		0			0
$412$	7.92820	−	13.7321i	0.390595	−	0.676530i
$413$	1.53590	+	2.66025i	0.0755766	+	0.130903i
$414$		0			0
$415$	4.92820			0.241916
$416$	−0.866025	+	3.50000i	−0.0424604	+	0.171602i
$417$		0			0
$418$	−0.215390	+	0.124356i	−0.0105351	+	0.00608243i
$419$	0.803848	+	1.39230i	0.0392705	+	0.0680185i	0.884993	−	0.465605i	$-0.154163\pi$
$419$	0.803848	+	1.39230i	0.0392705	+	0.0680185i	−0.845722	+	0.533624i	$0.820830\pi$
$420$		0			0
$421$		−	16.3923i		−	0.798912i	−0.916752	−	0.399456i	$-0.869199\pi$
$421$		−	16.3923i		−	0.798912i	0.916752	−	0.399456i	$-0.130801\pi$
$422$	20.1962	+	11.6603i	0.983133	+	0.567612i
$423$		0			0
$424$			12.9282i			0.627849i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	−18.0000	+	10.3923i	−0.871081	+	0.502919i
$428$	19.8564			0.959796
$429$		0			0
$430$	1.92820			0.0929862
$431$	6.58846	−	3.80385i	0.317355	−	0.183225i	−0.332858	−	0.942977i	$-0.608013\pi$
$431$	6.58846	−	3.80385i	0.317355	−	0.183225i	0.650213	+	0.759752i	$0.274680\pi$
$432$		0			0
$433$	7.66025	−	13.2679i	0.368128	−	0.637617i	−0.621145	−	0.783696i	$-0.713332\pi$
$433$	7.66025	−	13.2679i	0.368128	−	0.637617i	0.989273	+	0.146079i	$0.0466654\pi$
$434$		−	3.46410i		−	0.166282i
$435$		0			0
$436$	10.2679	+	5.92820i	0.491746	+	0.283909i
$437$		−	0.143594i		−	0.00686901i
$438$		0			0
$439$	−4.92820	−	8.53590i	−0.235210	−	0.407396i	0.724123	−	0.689670i	$-0.242245\pi$
$439$	−4.92820	−	8.53590i	−0.235210	−	0.407396i	−0.959334	+	0.282274i	$0.908911\pi$
$440$	−0.401924	+	0.232051i	−0.0191610	+	0.0110626i
$441$		0			0
$442$	13.8564	−	4.00000i	0.659082	−	0.190261i
$443$	4.39230			0.208685			0.104342	−	0.994541i	$-0.466726\pi$
$443$	4.39230			0.208685			0.104342	+	0.994541i	$0.466726\pi$
$444$		0			0
$445$	3.73205	+	6.46410i	0.176916	+	0.306428i
$446$	−13.7321	+	23.7846i	−0.650231	+	1.12623i
$447$		0			0
$448$	−1.73205	−	1.00000i	−0.0818317	−	0.0472456i
$449$	34.3923	+	19.8564i	1.62307	+	0.937082i	0.986092	+	0.166203i	$0.0531506\pi$
$449$	34.3923	+	19.8564i	1.62307	+	0.937082i	0.636982	+	0.770879i	$0.280183\pi$
$450$		0			0
$451$	−0.464102	+	0.803848i	−0.0218537	+	0.0378517i
$452$	−5.59808	−	9.69615i	−0.263311	−	0.456069i
$453$		0			0
$454$	−4.39230			−0.206141
$455$	7.00000	+	1.73205i	0.328165	+	0.0811998i
$456$		0			0
$457$	−27.2487	+	15.7321i	−1.27464	+	0.735914i	−0.975858	−	0.218407i	$-0.929914\pi$
$457$	−27.2487	+	15.7321i	−1.27464	+	0.735914i	−0.298783	+	0.954321i	$0.596581\pi$
$458$	−9.92820	−	17.1962i	−0.463914	−	0.803523i
$459$		0			0
$460$		−	0.267949i		−	0.0124932i
$461$	−5.59808	−	3.23205i	−0.260728	−	0.150532i	0.363938	−	0.931423i	$-0.381432\pi$
$461$	−5.59808	−	3.23205i	−0.260728	−	0.150532i	−0.624667	+	0.780891i	$0.714765\pi$
$462$		0			0
$463$			20.9282i			0.972616i	0.873787	+	0.486308i	$0.161657\pi$
$463$			20.9282i			0.972616i	−0.873787	+	0.486308i	$0.838343\pi$
$464$	1.86603	−	3.23205i	0.0866281	−	0.150044i
$465$		0			0
$466$	−15.6962	+	9.06218i	−0.727110	+	0.419797i
$467$	−11.8564			−0.548649			−0.274325	−	0.961637i	$-0.588454\pi$
$467$	−11.8564			−0.548649			−0.274325	+	0.961637i	$0.588454\pi$
$468$		0			0
$469$	9.07180			0.418897
$470$	−9.06218	+	5.23205i	−0.418007	+	0.241337i
$471$		0			0
$472$	−0.767949	+	1.33013i	−0.0353477	+	0.0612241i
$473$			0.894882i			0.0411467i
$474$		0			0
$475$	0.464102	+	0.267949i	0.0212944	+	0.0122944i
$476$			8.00000i			0.366679i
$477$		0			0
$478$	2.19615	+	3.80385i	0.100450	+	0.173984i
$479$	−1.26795	+	0.732051i	−0.0579341	+	0.0334483i	−0.528687	−	0.848817i	$-0.677316\pi$
$479$	−1.26795	+	0.732051i	−0.0579341	+	0.0334483i	0.470753	+	0.882265i	$0.343982\pi$
$480$		0			0
$481$	3.10770	+	2.99038i	0.141699	+	0.136350i
$482$	14.2679			0.649887
$483$		0			0
$484$	5.39230	+	9.33975i	0.245105	+	0.424534i
$485$	−3.73205	+	6.46410i	−0.169464	+	0.293520i
$486$		0			0
$487$	33.9282	+	19.5885i	1.53743	+	0.887638i	0.998988	+	0.0449775i	$0.0143216\pi$
$487$	33.9282	+	19.5885i	1.53743	+	0.887638i	0.538446	+	0.842660i	$0.319012\pi$
$488$	−9.00000	−	5.19615i	−0.407411	−	0.235219i
$489$		0			0
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	8.66025	+	15.0000i	0.390832	+	0.676941i	0.992559	−	0.121761i	$-0.0388541\pi$
$491$	8.66025	+	15.0000i	0.390832	+	0.676941i	−0.601728	+	0.798701i	$0.705521\pi$
$492$		0			0
$493$	−14.9282			−0.672332
$494$	0.535898	+	1.85641i	0.0241112	+	0.0835237i
$495$		0			0
$496$	1.50000	−	0.866025i	0.0673520	−	0.0388857i
$497$	8.39230	+	14.5359i	0.376446	+	0.652024i
$498$		0			0
$499$			13.4641i			0.602736i	0.953508	+	0.301368i	$0.0974433\pi$
$499$			13.4641i			0.602736i	−0.953508	+	0.301368i	$0.902557\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$			12.2679i			0.547545i
$503$	15.5885	−	27.0000i	0.695055	−	1.20387i	−0.275107	−	0.961414i	$-0.588713\pi$
$503$	15.5885	−	27.0000i	0.695055	−	1.20387i	0.970162	−	0.242457i	$-0.0779533\pi$
$504$		0			0
$505$	−9.46410	+	5.46410i	−0.421147	+	0.243149i
$506$	0.124356			0.00552828
$507$		0			0
$508$	−8.92820			−0.396125
$509$	−16.7942	+	9.69615i	−0.744391	+	0.429774i	−0.823664	−	0.567079i	$-0.808074\pi$
$509$	−16.7942	+	9.69615i	−0.744391	+	0.429774i	0.0792726	+	0.996853i	$0.474740\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	19.6244	+	11.3301i	0.865593	+	0.499750i
$515$		−	15.8564i		−	0.698717i
$516$		0			0
$517$	−2.42820	−	4.20577i	−0.106792	−	0.184970i
$518$	−2.07180	+	1.19615i	−0.0910295	+	0.0525559i
$519$		0			0
$520$	1.00000	+	3.46410i	0.0438529	+	0.151911i
$521$	−17.3205			−0.758825			−0.379413	−	0.925228i	$-0.623874\pi$
$521$	−17.3205			−0.758825			−0.379413	+	0.925228i	$0.623874\pi$
$522$		0			0
$523$	14.8923	+	25.7942i	0.651195	+	1.12790i	0.982833	+	0.184496i	$0.0590653\pi$
$523$	14.8923	+	25.7942i	0.651195	+	1.12790i	−0.331638	+	0.943407i	$0.607601\pi$
$524$	0.669873	−	1.16025i	0.0292635	−	0.0506859i
$525$		0			0
$526$	15.6962	+	9.06218i	0.684385	+	0.395130i
$527$	−6.00000	−	3.46410i	−0.261364	−	0.150899i
$528$		0			0
$529$	11.4641	−	19.8564i	0.498439	−	0.863322i
$530$	6.46410	+	11.1962i	0.280783	+	0.486330i
$531$		0			0
$532$	−1.07180			−0.0464683
$533$	5.19615	+	5.00000i	0.225070	+	0.216574i
$534$		0			0
$535$	17.1962	−	9.92820i	0.743455	−	0.429234i
$536$	2.26795	+	3.92820i	0.0979605	+	0.169673i
$537$		0			0
$538$			12.0000i			0.517357i
$539$	1.20577	+	0.696152i	0.0519362	+	0.0299854i
$540$		0			0
$541$			13.0718i			0.562000i	0.959708	+	0.281000i	$0.0906662\pi$
$541$			13.0718i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$542$	−4.59808	+	7.96410i	−0.197504	+	0.342087i
$543$		0			0
$544$	−3.46410	+	2.00000i	−0.148522	+	0.0857493i
$545$	11.8564			0.507873
$546$		0			0
$547$	9.07180			0.387882			0.193941	−	0.981013i	$-0.437873\pi$
$547$	9.07180			0.387882			0.193941	+	0.981013i	$0.437873\pi$
$548$	3.86603	−	2.23205i	0.165148	−	0.0953485i
$549$		0			0
$550$	−0.232051	+	0.401924i	−0.00989468	+	0.0171381i
$551$		−	2.00000i		−	0.0852029i
$552$		0			0
$553$	−0.124356	−	0.0717968i	−0.00528814	−	0.00305311i
$554$		−	9.92820i		−	0.421809i
$555$		0			0
$556$	0.464102	+	0.803848i	0.0196823	+	0.0340907i
$557$	−32.6603	+	18.8564i	−1.38386	+	0.798972i	−0.992614	−	0.121315i	$-0.961289\pi$
$557$	−32.6603	+	18.8564i	−1.38386	+	0.798972i	−0.391245	+	0.920286i	$0.627956\pi$
$558$		0			0
$559$	6.74871	+	1.66987i	0.285440	+	0.0706281i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	2.46410	+	4.26795i	0.103942	+	0.180033i
$563$	−19.6603	+	34.0526i	−0.828581	+	1.43514i	0.0705706	+	0.997507i	$0.477518\pi$
$563$	−19.6603	+	34.0526i	−0.828581	+	1.43514i	−0.899152	+	0.437637i	$0.855815\pi$
$564$		0			0
$565$	−9.69615	−	5.59808i	−0.407920	−	0.235513i
$566$	3.40192	+	1.96410i	0.142994	+	0.0825573i
$567$		0			0
$568$	−4.19615	+	7.26795i	−0.176067	+	0.304956i
$569$	−2.66025	−	4.60770i	−0.111524	−	0.193165i	0.804861	−	0.593463i	$-0.202240\pi$
$569$	−2.66025	−	4.60770i	−0.111524	−	0.193165i	−0.916385	+	0.400299i	$0.868906\pi$
$570$		0			0
$571$	45.1769			1.89060			0.945298	−	0.326209i	$-0.105771\pi$
$571$	45.1769			1.89060			0.945298	+	0.326209i	$0.105771\pi$
$572$	−1.60770	+	0.464102i	−0.0672211	+	0.0194051i
$573$		0			0
$574$	−3.46410	+	2.00000i	−0.144589	+	0.0834784i
$575$	−0.133975	−	0.232051i	−0.00558713	−	0.00967719i
$576$		0			0
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$	−0.866025	−	0.500000i	−0.0360219	−	0.0207973i
$579$		0			0
$580$		−	3.73205i		−	0.154965i
$581$	−4.92820	+	8.53590i	−0.204456	+	0.354129i
$582$		0			0
$583$	−5.19615	+	3.00000i	−0.215203	+	0.124247i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	4.14359			0.171170
$587$	15.9282	−	9.19615i	0.657427	−	0.379566i	−0.133869	−	0.990999i	$-0.542740\pi$
$587$	15.9282	−	9.19615i	0.657427	−	0.379566i	0.791296	+	0.611433i	$0.209407\pi$
$588$		0			0
$589$	0.464102	−	0.803848i	0.0191230	−	0.0331220i
$590$			1.53590i			0.0632319i
$591$		0			0
$592$	−1.03590	−	0.598076i	−0.0425752	−	0.0245808i
$593$			31.1051i			1.27733i	0.769483	+	0.638667i	$0.220514\pi$
$593$			31.1051i			1.27733i	−0.769483	+	0.638667i	$0.779486\pi$
$594$		0			0
$595$	4.00000	+	6.92820i	0.163984	+	0.284029i
$596$	−17.7224	+	10.2321i	−0.725939	+	0.419121i
$597$		0			0
$598$	0.232051	−	0.937822i	0.00948926	−	0.0383504i
$599$	−10.3923			−0.424618			−0.212309	−	0.977203i	$-0.568098\pi$
$599$	−10.3923			−0.424618			−0.212309	+	0.977203i	$0.568098\pi$
$600$		0			0
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$	−1.92820	+	3.33975i	−0.0785877	+	0.136118i
$603$		0			0
$604$	9.00000	+	5.19615i	0.366205	+	0.211428i
$605$	9.33975	+	5.39230i	0.379715	+	0.219228i
$606$		0			0
$607$	−21.5885	+	37.3923i	−0.876248	+	1.51771i	−0.0208216	+	0.999783i	$0.506628\pi$
$607$	−21.5885	+	37.3923i	−0.876248	+	1.51771i	−0.855427	+	0.517924i	$0.826705\pi$
$608$	−0.267949	−	0.464102i	−0.0108668	−	0.0188218i
$609$		0			0
$610$	−10.3923			−0.420772
$611$	−36.2487	+	10.4641i	−1.46647	+	0.423332i
$612$		0			0
$613$	0.820508	−	0.473721i	0.0331400	−	0.0191334i	−0.483338	−	0.875434i	$-0.660576\pi$
$613$	0.820508	−	0.473721i	0.0331400	−	0.0191334i	0.516478	+	0.856300i	$0.327243\pi$
$614$	−6.26795	−	10.8564i	−0.252954	−	0.438129i
$615$		0			0
$616$		−	0.928203i		−	0.0373984i
$617$	−13.4545	−	7.76795i	−0.541657	−	0.312726i	0.204093	−	0.978951i	$-0.434575\pi$
$617$	−13.4545	−	7.76795i	−0.541657	−	0.312726i	−0.745750	+	0.666226i	$0.767909\pi$
$618$		0			0
$619$			24.2487i			0.974638i	0.873224	+	0.487319i	$0.162025\pi$
$619$			24.2487i			0.974638i	−0.873224	+	0.487319i	$0.837975\pi$
$620$	0.866025	−	1.50000i	0.0347804	−	0.0602414i
$621$		0			0
$622$	−6.58846	+	3.80385i	−0.264173	+	0.152520i
$623$	−14.9282			−0.598086
$624$		0			0
$625$	1.00000			0.0400000
$626$	24.2487	−	14.0000i	0.969173	−	0.559553i
$627$		0			0
$628$	−2.50000	+	4.33013i	−0.0997609	+	0.172791i
$629$			4.78461i			0.190775i
$630$		0			0
$631$	−21.2487	−	12.2679i	−0.845898	−	0.488379i	0.0133668	−	0.999911i	$-0.495745\pi$
$631$	−21.2487	−	12.2679i	−0.845898	−	0.488379i	−0.859265	+	0.511531i	$0.829078\pi$
$632$		−	0.0717968i		−	0.00285592i
$633$		0			0
$634$	10.7321	+	18.5885i	0.426224	+	0.738242i
$635$	−7.73205	+	4.46410i	−0.306837	+	0.177152i
$636$		0			0
$637$	7.50000	−	7.79423i	0.297161	−	0.308819i
$638$	1.73205			0.0685725
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	13.9282	−	24.1244i	0.550131	−	0.952855i	−0.448134	−	0.893967i	$-0.647911\pi$
$641$	13.9282	−	24.1244i	0.550131	−	0.952855i	0.998265	−	0.0588882i	$-0.0187555\pi$
$642$		0			0
$643$	23.7846	+	13.7321i	0.937973	+	0.541539i	0.889324	−	0.457277i	$-0.151175\pi$
$643$	23.7846	+	13.7321i	0.937973	+	0.541539i	0.0486490	+	0.998816i	$0.484508\pi$
$644$	0.464102	+	0.267949i	0.0182882	+	0.0105587i
$645$		0			0
$646$	−1.07180	+	1.85641i	−0.0421693	+	0.0730393i
$647$	10.6603	+	18.4641i	0.419098	+	0.725899i	0.995849	−	0.0910212i	$-0.0290131\pi$
$647$	10.6603	+	18.4641i	0.419098	+	0.725899i	−0.576751	+	0.816920i	$0.695680\pi$
$648$		0			0
$649$	−0.712813			−0.0279804
$650$	2.59808	+	2.50000i	0.101905	+	0.0980581i
$651$		0			0
$652$	19.9641	−	11.5263i	0.781855	−	0.451404i
$653$	−22.1244	−	38.3205i	−0.865793	−	1.49960i	−0.866258	−	0.499597i	$-0.833481\pi$
$653$	−22.1244	−	38.3205i	−0.865793	−	1.49960i	0.000464739	−	1.00000i	$-0.499852\pi$
$654$		0			0
$655$		−	1.33975i		−	0.0523482i
$656$	−1.73205	−	1.00000i	−0.0676252	−	0.0390434i
$657$		0			0
$658$		−	20.9282i		−	0.815866i
$659$	−1.86603	+	3.23205i	−0.0726900	+	0.125903i	−0.900079	−	0.435726i	$-0.856492\pi$
$659$	−1.86603	+	3.23205i	−0.0726900	+	0.125903i	0.827389	+	0.561629i	$0.189825\pi$
$660$		0			0
$661$	37.5167	−	21.6603i	1.45923	−	0.842486i	0.460256	−	0.887786i	$-0.347758\pi$
$661$	37.5167	−	21.6603i	1.45923	−	0.842486i	0.998973	+	0.0453002i	$0.0144244\pi$
$662$	24.7846			0.963281
$663$		0			0
$664$	−4.92820			−0.191251
$665$	−0.928203	+	0.535898i	−0.0359942	+	0.0207812i
$666$		0			0
$667$	−0.500000	+	0.866025i	−0.0193601	+	0.0335326i
$668$			18.3205i			0.708842i
$669$		0			0
$670$	3.92820	+	2.26795i	0.151760	+	0.0876185i
$671$		−	4.82309i		−	0.186193i
$672$		0			0
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	−0.990074	−	0.140548i	$-0.955114\pi$
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	0.373319	−	0.927703i	$-0.378220\pi$
$674$	21.9282	−	12.6603i	0.844643	−	0.487655i
$675$		0			0
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−11.6077			−0.446120			−0.223060	−	0.974805i	$-0.571605\pi$
$677$	−11.6077			−0.446120			−0.223060	+	0.974805i	$0.571605\pi$
$678$		0			0
$679$	−7.46410	−	12.9282i	−0.286446	−	0.496139i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		0			0
$682$	0.696152	+	0.401924i	0.0266571	+	0.0153905i
$683$	0.679492	+	0.392305i	0.0260000	+	0.0150111i	0.512944	−	0.858422i	$-0.328555\pi$
$683$	0.679492	+	0.392305i	0.0260000	+	0.0150111i	−0.486944	+	0.873433i	$0.661888\pi$
$684$		0			0
$685$	2.23205	−	3.86603i	0.0852823	−	0.147713i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$		0			0
$688$	−1.92820			−0.0735121
$689$	12.9282	+	44.7846i	0.492525	+	1.70616i
$690$		0			0
$691$	−30.4641	+	17.5885i	−1.15891	+	0.669096i	−0.951042	−	0.309061i	$-0.899985\pi$
$691$	−30.4641	+	17.5885i	−1.15891	+	0.669096i	−0.207867	+	0.978157i	$0.566652\pi$
$692$	1.46410	+	2.53590i	0.0556568	+	0.0964004i
$693$		0			0
$694$			22.3923i			0.850000i
$695$	0.803848	+	0.464102i	0.0304917	+	0.0176044i
$696$		0			0
$697$			8.00000i			0.303022i
$698$	7.26795	−	12.5885i	0.275096	−	0.476480i
$699$		0			0
$700$	−1.73205	+	1.00000i	−0.0654654	+	0.0377964i
$701$	3.73205			0.140958			0.0704788	−	0.997513i	$-0.477547\pi$
$701$	3.73205			0.140958			0.0704788	+	0.997513i	$0.477547\pi$
$702$		0			0
$703$	−0.641016			−0.0241764
$704$	0.401924	−	0.232051i	0.0151481	−	0.00874574i
$705$		0			0
$706$	−1.00000	+	1.73205i	−0.0376355	+	0.0651866i
$707$		−	21.8564i		−	0.821995i
$708$		0			0
$709$	7.85641	+	4.53590i	0.295054	+	0.170349i	0.640219	−	0.768193i	$-0.278844\pi$
$709$	7.85641	+	4.53590i	0.295054	+	0.170349i	−0.345165	+	0.938542i	$0.612177\pi$
$710$			8.39230i			0.314958i
$711$		0			0
$712$	−3.73205	−	6.46410i	−0.139865	−	0.242252i
$713$	−0.401924	+	0.232051i	−0.0150522	+	0.00869037i
$714$		0			0
$715$	−1.16025	+	1.20577i	−0.0433910	+	0.0450933i
$716$	−16.2679			−0.607962
$717$		0			0
$718$	9.46410	+	16.3923i	0.353197	+	0.611755i
$719$	17.3205	−	30.0000i	0.645946	−	1.11881i	−0.338136	−	0.941097i	$-0.609796\pi$
$719$	17.3205	−	30.0000i	0.645946	−	1.11881i	0.984082	−	0.177714i	$-0.0568702\pi$
$720$		0			0
$721$	27.4641	+	15.8564i	1.02282	+	0.590523i
$722$	16.2058	+	9.35641i	0.603116	+	0.348209i
$723$		0			0
$724$	5.46410	−	9.46410i	0.203072	−	0.351731i
$725$	−1.86603	−	3.23205i	−0.0693024	−	0.120035i
$726$		0			0
$727$	23.7128			0.879460			0.439730	−	0.898130i	$-0.355074\pi$
$727$	23.7128			0.879460			0.439730	+	0.898130i	$0.355074\pi$
$728$	−7.00000	−	1.73205i	−0.259437	−	0.0641941i
$729$		0			0
$730$	−1.73205	+	1.00000i	−0.0641061	+	0.0370117i
$731$	3.85641	+	6.67949i	0.142634	+	0.247050i
$732$		0			0
$733$		−	37.0718i		−	1.36928i	−0.728882	−	0.684639i	$-0.759960\pi$
$733$		−	37.0718i		−	1.36928i	0.728882	−	0.684639i	$-0.240040\pi$
$734$	31.5167	+	18.1962i	1.16330	+	0.671632i
$735$		0			0
$736$			0.267949i			0.00987674i
$737$	−1.05256	+	1.82309i	−0.0387715	+	0.0671542i
$738$		0			0
$739$	−13.2679	+	7.66025i	−0.488069	+	0.281787i	−0.723773	−	0.690038i	$-0.757594\pi$
$739$	−13.2679	+	7.66025i	−0.488069	+	0.281787i	0.235704	+	0.971825i	$0.424260\pi$
$740$	−1.19615			−0.0439714
$741$		0			0
$742$	−25.8564			−0.949219
$743$	−29.0429	+	16.7679i	−1.06548	+	0.615156i	−0.926944	−	0.375201i	$-0.877574\pi$
$743$	−29.0429	+	16.7679i	−1.06548	+	0.615156i	−0.138539	+	0.990357i	$0.544240\pi$
$744$		0			0
$745$	−10.2321	+	17.7224i	−0.374873	+	0.649300i
$746$		−	25.7846i		−	0.944042i
$747$		0			0
$748$	−1.60770	−	0.928203i	−0.0587832	−	0.0339385i
$749$			39.7128i			1.45107i
$750$		0			0
$751$	−13.9641	−	24.1865i	−0.509557	−	0.882579i	−0.999939	−	0.0110712i	$-0.996476\pi$
$751$	−13.9641	−	24.1865i	−0.509557	−	0.882579i	0.490381	−	0.871508i	$-0.336857\pi$
$752$	9.06218	−	5.23205i	0.330464	−	0.190793i
$753$		0			0
$754$	3.23205	−	13.0622i	0.117704	−	0.475696i
$755$	10.3923			0.378215
$756$		0			0
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	−0.654827	+	0.755779i	$0.727258\pi$
$758$	0.0717968	−	0.124356i	0.00260778	−	0.00451680i
$759$		0			0
$760$	−0.464102	−	0.267949i	−0.0168347	−	0.00971954i
$761$	16.3923	+	9.46410i	0.594221	+	0.343073i	0.766765	−	0.641928i	$-0.221865\pi$
$761$	16.3923	+	9.46410i	0.594221	+	0.343073i	−0.172544	+	0.985002i	$0.555199\pi$
$762$		0			0
$763$	−11.8564	+	20.5359i	−0.429231	+	0.743449i
$764$	−7.26795	−	12.5885i	−0.262945	−	0.455434i
$765$		0			0
$766$	−4.60770			−0.166483
$767$	−1.33013	+	5.37564i	−0.0480281	+	0.194103i
$768$		0			0
$769$	−16.9641	+	9.79423i	−0.611741	+	0.353189i	−0.773647	−	0.633617i	$-0.781569\pi$
$769$	−16.9641	+	9.79423i	−0.611741	+	0.353189i	0.161905	+	0.986806i	$0.448236\pi$
$770$	−0.464102	−	0.803848i	−0.0167251	−	0.0289687i
$771$		0			0
$772$		−	23.3205i		−	0.839323i
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	0.00186926	−	0.999998i	$-0.499405\pi$
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	−0.865089	+	0.501618i	$0.832738\pi$
$774$		0			0
$775$		−	1.73205i		−	0.0622171i
$776$	3.73205	−	6.46410i	0.133973	−	0.232048i
$777$		0			0
$778$	−17.5526	+	10.1340i	−0.629290	+	0.363321i
$779$	−1.07180			−0.0384011
$780$		0			0
$781$	−3.89488			−0.139370
$782$	0.928203	−	0.535898i	0.0331925	−	0.0191637i
$783$		0			0
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$			5.00000i			0.178458i
$786$		0			0
$787$	1.50000	+	0.866025i	0.0534692	+	0.0308705i	0.526496	−	0.850177i	$-0.323505\pi$
$787$	1.50000	+	0.866025i	0.0534692	+	0.0308705i	−0.473027	+	0.881048i	$0.656839\pi$
$788$			16.3923i			0.583952i
$789$		0			0
$790$	−0.0358984	−	0.0621778i	−0.00127721	−	0.00221219i
$791$	19.3923	−	11.1962i	0.689511	−	0.398089i
$792$		0			0
$793$	−36.3731	−	9.00000i	−1.29165	−	0.319599i
$794$	−12.1244			−0.430277
$795$		0			0
$796$	−9.46410	−	16.3923i	−0.335446	−	0.581010i
$797$	−18.9282	+	32.7846i	−0.670471	+	1.16129i	0.307299	+	0.951613i	$0.400575\pi$
$797$	−18.9282	+	32.7846i	−0.670471	+	1.16129i	−0.977771	+	0.209678i	$0.932759\pi$
$798$		0			0
$799$	−36.2487	−	20.9282i	−1.28239	−	0.740387i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	16.0000	−	27.7128i	0.564980	−	0.978573i
$803$	−0.464102	−	0.803848i	−0.0163778	−	0.0283672i
$804$		0			0
$805$	0.535898			0.0188879
$806$	4.33013	−	4.50000i	0.152522	−	0.158506i
$807$		0			0
$808$	9.46410	−	5.46410i	0.332946	−	0.192226i
$809$	−0.607695	−	1.05256i	−0.0213654	−	0.0370060i	0.855145	−	0.518389i	$-0.173468\pi$
$809$	−0.607695	−	1.05256i	−0.0213654	−	0.0370060i	−0.876510	+	0.481383i	$0.840135\pi$
$810$		0			0
$811$		−	0.784610i		−	0.0275514i	−0.999905	−	0.0137757i	$-0.995615\pi$
$811$		−	0.784610i		−	0.0275514i	0.999905	−	0.0137757i	$-0.00438508\pi$
$812$	6.46410	+	3.73205i	0.226845	+	0.130969i
$813$		0			0
$814$		−	0.555136i		−	0.0194575i
$815$	11.5263	−	19.9641i	0.403748	−	0.699312i
$816$		0			0
$817$	−0.894882	+	0.516660i	−0.0313080	+	0.0180757i
$818$	4.00000			0.139857
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	30.6506	−	17.6962i	1.06971	−	0.617600i	0.141611	−	0.989922i	$-0.454772\pi$
$821$	30.6506	−	17.6962i	1.06971	−	0.617600i	0.928103	+	0.372322i	$0.121438\pi$
$822$		0			0
$823$	11.5885	−	20.0718i	0.403948	−	0.699659i	−0.590250	−	0.807220i	$-0.700971\pi$
$823$	11.5885	−	20.0718i	0.403948	−	0.699659i	0.994198	+	0.107561i	$0.0343043\pi$
$824$			15.8564i			0.552384i
$825$		0			0
$826$	−2.66025	−	1.53590i	−0.0925621	−	0.0534407i
$827$			17.3205i			0.602293i	0.953578	+	0.301147i	$0.0973693\pi$
$827$			17.3205i			0.602293i	−0.953578	+	0.301147i	$0.902631\pi$
$828$		0			0
$829$	−11.7321	−	20.3205i	−0.407471	−	0.705760i	0.587135	−	0.809489i	$-0.300256\pi$
$829$	−11.7321	−	20.3205i	−0.407471	−	0.705760i	−0.994606	+	0.103729i	$0.966923\pi$
$830$	−4.26795	+	2.46410i	−0.148143	+	0.0855302i
$831$		0			0
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$	12.0000			0.415775
$834$		0			0
$835$	9.16025	+	15.8660i	0.317004	+	0.549066i
$836$	0.124356	−	0.215390i	0.00430093	−	0.00744943i
$837$		0			0
$838$	−1.39230	−	0.803848i	−0.0480964	−	0.0277685i
$839$	34.2679	+	19.7846i	1.18306	+	0.683041i	0.956721	−	0.291008i	$-0.0939905\pi$
$839$	34.2679	+	19.7846i	1.18306	+	0.683041i	0.226340	+	0.974048i	$0.427324\pi$
$840$		0			0
$841$	7.53590	−	13.0526i	0.259859	−	0.450088i
$842$	8.19615	+	14.1962i	0.282458	+	0.489232i
$843$		0			0
$844$	−23.3205			−0.802725
$845$	6.92820	+	11.0000i	0.238337	+	0.378412i
$846$		0			0
$847$	−18.6795	+	10.7846i	−0.641835	+	0.370564i
$848$	−6.46410	−	11.1962i	−0.221978	−	0.384477i
$849$		0			0
$850$			4.00000i			0.137199i
$851$	0.277568	+	0.160254i	0.00951491	+	0.00549344i
$852$		0			0
$853$		−	35.8372i		−	1.22704i	−0.789679	−	0.613521i	$-0.789753\pi$
$853$		−	35.8372i		−	1.22704i	0.789679	−	0.613521i	$-0.210247\pi$
$854$	10.3923	−	18.0000i	0.355617	−	0.615947i
$855$		0			0
$856$	−17.1962	+	9.92820i	−0.587752	+	0.339339i
$857$	20.5167			0.700836			0.350418	−	0.936593i	$-0.386040\pi$
$857$	20.5167			0.700836			0.350418	+	0.936593i	$0.386040\pi$
$858$		0			0
$859$	27.1769			0.927264			0.463632	−	0.886028i	$-0.346546\pi$
$859$	27.1769			0.927264			0.463632	+	0.886028i	$0.346546\pi$
$860$	−1.66987	+	0.964102i	−0.0569422	+	0.0328756i
$861$		0			0
$862$	−3.80385	+	6.58846i	−0.129560	+	0.224404i
$863$		−	42.4641i		−	1.44549i	−0.691112	−	0.722747i	$-0.742879\pi$
$863$		−	42.4641i		−	1.44549i	0.691112	−	0.722747i	$-0.257121\pi$
$864$		0			0
$865$	2.53590	+	1.46410i	0.0862231	+	0.0497809i
$866$			15.3205i			0.520612i
$867$		0			0
$868$	1.73205	+	3.00000i	0.0587896	+	0.101827i
$869$	0.0288568	−	0.0166605i	0.000978901	−	0.000565169i
$870$		0			0
$871$	11.7846	+	11.3397i	0.399306	+	0.384233i
$872$	−11.8564			−0.401509
$873$		0			0
$874$	0.0717968	+	0.124356i	0.00242856	+	0.00420639i
$875$	−1.00000	+	1.73205i	−0.0338062	+	0.0585540i
$876$		0			0
$877$	24.3564	+	14.0622i	0.822457	+	0.474846i	0.851263	−	0.524739i	$-0.175837\pi$
$877$	24.3564	+	14.0622i	0.822457	+	0.474846i	−0.0288057	+	0.999585i	$0.509170\pi$
$878$	8.53590	+	4.92820i	0.288073	+	0.166319i
$879$		0			0
$880$	0.232051	−	0.401924i	0.00782243	−	0.0135488i
$881$	−7.00000	−	12.1244i	−0.235836	−	0.408480i	0.723679	−	0.690136i	$-0.242449\pi$
$881$	−7.00000	−	12.1244i	−0.235836	−	0.408480i	−0.959515	+	0.281656i	$0.909116\pi$
$882$		0			0
$883$	16.0718			0.540859			0.270430	−	0.962740i	$-0.412834\pi$
$883$	16.0718			0.540859			0.270430	+	0.962740i	$0.412834\pi$
$884$	−10.0000	+	10.3923i	−0.336336	+	0.349531i
$885$		0			0
$886$	−3.80385	+	2.19615i	−0.127793	+	0.0737812i
$887$	−5.06218	−	8.76795i	−0.169971	−	0.294399i	0.768438	−	0.639924i	$-0.221034\pi$
$887$	−5.06218	−	8.76795i	−0.169971	−	0.294399i	−0.938410	+	0.345525i	$0.887701\pi$
$888$		0			0
$889$		−	17.8564i		−	0.598885i
$890$	−6.46410	−	3.73205i	−0.216677	−	0.125099i
$891$		0			0
$892$		−	27.4641i		−	0.919566i
$893$	2.80385	−	4.85641i	0.0938272	−	0.162513i
$894$		0			0
$895$	−14.0885	+	8.13397i	−0.470925	+	0.271889i
$896$	2.00000			0.0668153
$897$		0			0
$898$	−39.7128			−1.32523
$899$	−5.59808	+	3.23205i	−0.186706	+	0.107795i
$900$		0			0
$901$	−25.8564	+	44.7846i	−0.861402	+	1.49199i
$902$		−	0.928203i		−	0.0309058i
$903$		0			0
$904$	9.69615	+	5.59808i	0.322489	+	0.186189i
$905$		−	10.9282i		−	0.363266i
$906$		0			0
$907$	−3.42820	−	5.93782i	−0.113832	−	0.197162i	0.803480	−	0.595331i	$-0.202979\pi$
$907$	−3.42820	−	5.93782i	−0.113832	−	0.197162i	−0.917312	+	0.398169i	$0.869646\pi$
$908$	3.80385	−	2.19615i	0.126235	−	0.0728819i
$909$		0			0
$910$	−6.92820	+	2.00000i	−0.229668	+	0.0662994i
$911$	24.2487			0.803396			0.401698	−	0.915772i	$-0.368420\pi$
$911$	24.2487			0.803396			0.401698	+	0.915772i	$0.368420\pi$
$912$		0			0
$913$	−1.14359	−	1.98076i	−0.0378474	−	0.0655537i
$914$	15.7321	−	27.2487i	0.520370	−	0.901307i
$915$		0			0
$916$	17.1962	+	9.92820i	0.568177	+	0.328037i
$917$	2.32051	+	1.33975i	0.0766299	+	0.0442423i
$918$		0			0
$919$	27.3205	−	47.3205i	0.901220	−	1.56096i	0.0753085	−	0.997160i	$-0.476006\pi$
$919$	27.3205	−	47.3205i	0.901220	−	1.56096i	0.825912	−	0.563799i	$-0.190661\pi$
$920$	0.133975	+	0.232051i	0.00441701	+	0.00765049i
$921$		0			0
$922$	6.46410			0.212884
$923$	−7.26795	+	29.3731i	−0.239227	+	0.966826i
$924$		0			0
$925$	−1.03590	+	0.598076i	−0.0340601	+	0.0196646i
$926$	−10.4641	−	18.1244i	−0.343872	−	0.595603i
$927$		0			0
$928$			3.73205i			0.122511i
$929$	−29.3205	−	16.9282i	−0.961975	−	0.555396i	−0.0651944	−	0.997873i	$-0.520767\pi$
$929$	−29.3205	−	16.9282i	−0.961975	−	0.555396i	−0.896780	+	0.442476i	$0.854100\pi$
$930$		0			0
$931$			1.60770i			0.0526901i
$932$	9.06218	−	15.6962i	0.296842	−	0.514145i
$933$		0			0
$934$	10.2679	−	5.92820i	0.335978	−	0.193977i
$935$	−1.85641			−0.0607110
$936$		0			0
$937$	44.6410			1.45836			0.729179	−	0.684323i	$-0.239902\pi$
$937$	44.6410			1.45836			0.729179	+	0.684323i	$0.239902\pi$
$938$	−7.85641	+	4.53590i	−0.256521	+	0.148102i
$939$		0			0
$940$	5.23205	−	9.06218i	0.170651	−	0.295576i
$941$		−	26.7846i		−	0.873153i	−0.899667	−	0.436577i	$-0.856191\pi$
$941$		−	26.7846i		−	0.873153i	0.899667	−	0.436577i	$-0.143809\pi$
$942$		0			0
$943$	0.464102	+	0.267949i	0.0151132	+	0.00872563i
$944$		−	1.53590i		−	0.0499892i
$945$		0			0
$946$	−0.447441	−	0.774991i	−0.0145476	−	0.0251971i
$947$	2.19615	−	1.26795i	0.0713654	−	0.0412028i	−0.463893	−	0.885891i	$-0.653548\pi$
$947$	2.19615	−	1.26795i	0.0713654	−	0.0412028i	0.535258	+	0.844689i	$0.320214\pi$
$948$		0			0
$949$	−6.92820	+	2.00000i	−0.224899	+	0.0649227i
$950$	−0.535898			−0.0173868
$951$		0			0
$952$	−4.00000	−	6.92820i	−0.129641	−	0.224544i
$953$	−7.86603	+	13.6244i	−0.254806	+	0.441336i	−0.964843	−	0.262828i	$-0.915345\pi$
$953$	−7.86603	+	13.6244i	−0.254806	+	0.441336i	0.710037	+	0.704164i	$0.248678\pi$
$954$		0			0
$955$	−12.5885	−	7.26795i	−0.407353	−	0.235185i
$956$	−3.80385	−	2.19615i	−0.123025	−	0.0710286i
$957$		0			0
$958$	0.732051	−	1.26795i	0.0236515	−	0.0409656i
$959$	4.46410	+	7.73205i	0.144153	+	0.249681i
$960$		0			0
$961$	28.0000			0.903226
$962$	−4.18653	−	1.03590i	−0.134979	−	0.0333987i
$963$		0			0
$964$	−12.3564	+	7.13397i	−0.397973	+	0.229770i
$965$	−11.6603	−	20.1962i	−0.375357	−	0.650137i
$966$		0			0
$967$		−	34.5359i		−	1.11060i	−0.831650	−	0.555300i	$-0.812604\pi$
$967$		−	34.5359i		−	1.11060i	0.831650	−	0.555300i	$-0.187396\pi$
$968$	−9.33975	−	5.39230i	−0.300191	−	0.173315i
$969$		0			0
$970$		−	7.46410i		−	0.239658i
$971$	5.73205	−	9.92820i	0.183950	−	0.318611i	−0.759272	−	0.650773i	$-0.774445\pi$
$971$	5.73205	−	9.92820i	0.183950	−	0.318611i	0.943222	+	0.332162i	$0.107778\pi$
$972$		0			0
$973$	−1.60770	+	0.928203i	−0.0515403	+	0.0297568i
$974$	−39.1769			−1.25531
$975$		0			0
$976$	10.3923			0.332650
$977$	28.9186	−	16.6962i	0.925187	−	0.534157i	0.0399012	−	0.999204i	$-0.487296\pi$
$977$	28.9186	−	16.6962i	0.925187	−	0.534157i	0.885286	+	0.465046i	$0.153962\pi$
$978$		0			0
$979$	1.73205	−	3.00000i	0.0553566	−	0.0958804i
$980$			3.00000i			0.0958315i
$981$		0			0
$982$	−15.0000	−	8.66025i	−0.478669	−	0.276360i
$983$			57.3923i			1.83053i	0.402852	+	0.915265i	$0.368019\pi$
$983$			57.3923i			1.83053i	−0.402852	+	0.915265i	$0.631981\pi$
$984$		0			0
$985$	8.19615	+	14.1962i	0.261151	+	0.452327i
$986$	12.9282	−	7.46410i	0.411718	−	0.237705i
$987$		0			0
$988$	−1.39230	−	1.33975i	−0.0442951	−	0.0426230i
$989$	0.516660			0.0164288
$990$		0			0
$991$	12.5718	+	21.7750i	0.399356	+	0.691705i	0.993647	−	0.112545i	$-0.0359003\pi$
$991$	12.5718	+	21.7750i	0.399356	+	0.691705i	−0.594290	+	0.804251i	$0.702567\pi$
$992$	−0.866025	+	1.50000i	−0.0274963	+	0.0476250i
$993$		0			0
$994$	−14.5359	−	8.39230i	−0.461051	−	0.266188i
$995$	−16.3923	−	9.46410i	−0.519671	−	0.300032i
$996$		0			0
$997$	23.7846	−	41.1962i	0.753266	−	1.30470i	−0.192966	−	0.981206i	$-0.561811\pi$
$997$	23.7846	−	41.1962i	0.753266	−	1.30470i	0.946232	−	0.323490i	$-0.104856\pi$
$998$	−6.73205	−	11.6603i	−0.213099	−	0.369099i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.e.361.1		4
3.2	odd	2		390.2.bb.b.361.2	yes	4
13.4	even	6	inner	1170.2.bs.e.901.1		4
15.2	even	4		1950.2.y.f.49.2		4
15.8	even	4		1950.2.y.c.49.1		4
15.14	odd	2		1950.2.bc.b.751.1		4
39.2	even	12		5070.2.a.bg.1.1		2
39.11	even	12		5070.2.a.y.1.2		2
39.17	odd	6		390.2.bb.b.121.2	✓	4
39.23	odd	6		5070.2.b.o.1351.1		4
39.29	odd	6		5070.2.b.o.1351.4		4
195.17	even	12		1950.2.y.c.199.1		4
195.134	odd	6		1950.2.bc.b.901.1		4
195.173	even	12		1950.2.y.f.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.2	✓	4	39.17	odd	6
390.2.bb.b.361.2	yes	4	3.2	odd	2
1170.2.bs.e.361.1		4	1.1	even	1	trivial
1170.2.bs.e.901.1		4	13.4	even	6	inner
1950.2.y.c.49.1		4	15.8	even	4
1950.2.y.c.199.1		4	195.17	even	12
1950.2.y.f.49.2		4	15.2	even	4
1950.2.y.f.199.2		4	195.173	even	12
1950.2.bc.b.751.1		4	15.14	odd	2
1950.2.bc.b.901.1		4	195.134	odd	6
5070.2.a.y.1.2		2	39.11	even	12
5070.2.a.bg.1.1		2	39.2	even	12
5070.2.b.o.1351.1		4	39.23	odd	6
5070.2.b.o.1351.4		4	39.29	odd	6

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.401924 + 0.232051i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.464102 - 0.267949i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.232051 - 0.401924i) q^{22} +(0.133975 + 0.232051i) q^{23} -1.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} +(1.73205 - 1.00000i) q^{28} +(1.86603 + 3.23205i) q^{29} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(1.03590 - 0.598076i) q^{37} +0.535898 q^{38} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(0.964102 - 1.66987i) q^{43} +0.464102i q^{44} +(-0.232051 - 0.133975i) q^{46} +10.4641i q^{47} +(-1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.50000 + 0.866025i) q^{52} +12.9282 q^{53} +(0.232051 + 0.401924i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(-3.23205 - 1.86603i) q^{58} +(1.33013 + 0.767949i) q^{59} +(-5.19615 + 9.00000i) q^{61} +(-0.866025 - 1.50000i) q^{62} -1.00000 q^{64} +(3.46410 - 1.00000i) q^{65} +(3.92820 - 2.26795i) q^{67} +(2.00000 + 3.46410i) q^{68} +2.00000i q^{70} +(7.26795 + 4.19615i) q^{71} +2.00000i q^{73} +(-0.598076 + 1.03590i) q^{74} +(-0.464102 + 0.267949i) q^{76} -0.928203 q^{77} -0.0717968 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-1.00000 + 1.73205i) q^{82} +4.92820i q^{83} +(3.46410 + 2.00000i) q^{85} +1.92820i q^{86} +(-0.232051 - 0.401924i) q^{88} +(-6.46410 + 3.73205i) q^{89} +(-1.73205 + 7.00000i) q^{91} +0.267949 q^{92} +(-5.23205 - 9.06218i) q^{94} +(-0.267949 + 0.464102i) q^{95} +(-6.46410 - 3.73205i) q^{97} +(2.59808 + 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} + 2 q^{10} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 2 q^{16} - 8 q^{17} + 12 q^{19} - 6 q^{22} + 4 q^{23} - 4 q^{25} + 4 q^{29} + 4 q^{35} + 18 q^{37} + 16 q^{38} + 4 q^{40} - 10 q^{43} + 6 q^{46} - 6 q^{49} + 14 q^{52} + 24 q^{53} - 6 q^{55} - 4 q^{56} - 6 q^{58} - 12 q^{59} - 4 q^{64} - 12 q^{67} + 8 q^{68} + 36 q^{71} + 8 q^{74} + 12 q^{76} + 24 q^{77} - 28 q^{79} - 4 q^{82} + 6 q^{88} - 12 q^{89} + 8 q^{92} - 14 q^{94} - 8 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^10 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 2 * q^16 - 8 * q^17 + 12 * q^19 - 6 * q^22 + 4 * q^23 - 4 * q^25 + 4 * q^29 + 4 * q^35 + 18 * q^37 + 16 * q^38 + 4 * q^40 - 10 * q^43 + 6 * q^46 - 6 * q^49 + 14 * q^52 + 24 * q^53 - 6 * q^55 - 4 * q^56 - 6 * q^58 - 12 * q^59 - 4 * q^64 - 12 * q^67 + 8 * q^68 + 36 * q^71 + 8 * q^74 + 12 * q^76 + 24 * q^77 - 28 * q^79 - 4 * q^82 + 6 * q^88 - 12 * q^89 + 8 * q^92 - 14 * q^94 - 8 * q^95 - 12 * q^97

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