LMFDB - Embedded newform 1710.2.l.i.1261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.i.1531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(1.50000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.00000 q^{26} +(-1.50000 + 2.59808i) q^{28} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(-1.50000 - 2.59808i) q^{35} +9.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{41} +(5.00000 + 8.66025i) q^{43} +(0.500000 - 0.866025i) q^{44} +1.00000 q^{46} +2.00000 q^{49} -1.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{55} -3.00000 q^{56} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(1.00000 - 1.73205i) q^{67} -2.00000 q^{68} +(1.50000 - 2.59808i) q^{70} +(4.00000 + 6.92820i) q^{71} +(6.00000 + 10.3923i) q^{73} +(4.50000 + 7.79423i) q^{74} +(-4.00000 - 1.73205i) q^{76} -3.00000 q^{77} +(-7.00000 - 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{85} +(-5.00000 + 8.66025i) q^{86} +1.00000 q^{88} +(-2.50000 + 4.33013i) q^{89} +(-3.00000 + 5.19615i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.50000 - 2.59808i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} + 6 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 + 6 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{5} + 6 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 2 q^{13} + 3 q^{14} - q^{16} + 2 q^{17} + q^{19} + 2 q^{20} - q^{22} + q^{23} - q^{25} - 4 q^{26} - 3 q^{28} + 8 q^{31} + q^{32} - 2 q^{34} - 3 q^{35} + 18 q^{37} - 7 q^{38} + q^{40} + q^{41} + 10 q^{43} + q^{44} + 2 q^{46} + 4 q^{49} - 2 q^{50} - 2 q^{52} + 3 q^{53} + q^{55} - 6 q^{56} + 12 q^{59} + 2 q^{61} + 4 q^{62} + 2 q^{64} + 4 q^{65} + 2 q^{67} - 4 q^{68} + 3 q^{70} + 8 q^{71} + 12 q^{73} + 9 q^{74} - 8 q^{76} - 6 q^{77} - 14 q^{79} - q^{80} - q^{82} - 12 q^{83} + 2 q^{85} - 10 q^{86} + 2 q^{88} - 5 q^{89} - 6 q^{91} + q^{92} + 7 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 + 6 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 2 * q^13 + 3 * q^14 - q^16 + 2 * q^17 + q^19 + 2 * q^20 - q^22 + q^23 - q^25 - 4 * q^26 - 3 * q^28 + 8 * q^31 + q^32 - 2 * q^34 - 3 * q^35 + 18 * q^37 - 7 * q^38 + q^40 + q^41 + 10 * q^43 + q^44 + 2 * q^46 + 4 * q^49 - 2 * q^50 - 2 * q^52 + 3 * q^53 + q^55 - 6 * q^56 + 12 * q^59 + 2 * q^61 + 4 * q^62 + 2 * q^64 + 4 * q^65 + 2 * q^67 - 4 * q^68 + 3 * q^70 + 8 * q^71 + 12 * q^73 + 9 * q^74 - 8 * q^76 - 6 * q^77 - 14 * q^79 - q^80 - q^82 - 12 * q^83 + 2 * q^85 - 10 * q^86 + 2 * q^88 - 5 * q^89 - 6 * q^91 + q^92 + 7 * q^95 - 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$20$	1.00000			0.223607
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$		0			0
$37$	9.00000			1.47959			0.739795	−	0.672832i	$-0.234922\pi$
$37$	9.00000			1.47959			0.739795	+	0.672832i	$0.234922\pi$
$38$	−3.50000	+	2.59808i	−0.567775	+	0.421464i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	0.902424	−	0.430848i	$-0.141786\pi$
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	−0.824338	+	0.566099i	$0.808452\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	1.00000			0.147442
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		0			0
$55$	0.500000	+	0.866025i	0.0674200	+	0.116775i
$56$	−3.00000			−0.400892
$57$		0			0
$58$		0			0
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000			0.248069
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	−2.00000			−0.242536
$69$		0			0
$70$	1.50000	−	2.59808i	0.179284	−	0.310530i
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	0.999581	−	0.0289572i	$-0.00921865\pi$
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	−0.524868	+	0.851184i	$0.675885\pi$
$72$		0			0
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	0.967676	+	0.252197i	$0.0811531\pi$
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	−0.265429	+	0.964130i	$0.585514\pi$
$74$	4.50000	+	7.79423i	0.523114	+	0.906061i
$75$		0			0
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−0.500000	+	0.866025i	−0.0552158	+	0.0956365i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	−5.00000	+	8.66025i	−0.539164	+	0.933859i
$87$		0			0
$88$	1.00000			0.106600
$89$	−2.50000	+	4.33013i	−0.264999	+	0.458993i	−0.967563	−	0.252628i	$-0.918705\pi$
$89$	−2.50000	+	4.33013i	−0.264999	+	0.458993i	0.702564	+	0.711621i	$0.252038\pi$
$90$		0			0
$91$	−3.00000	+	5.19615i	−0.314485	+	0.544705i
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$		0			0
$95$	3.50000	−	2.59808i	0.359092	−	0.266557i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	3.00000			0.291386
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$		0			0
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	0.973176	−	0.230063i	$-0.0738931\pi$
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	−0.685828	+	0.727764i	$0.740560\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$		0			0
$112$	−1.50000	−	2.59808i	−0.141737	−	0.245495i
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$	−1.00000			−0.0932505
$116$		0			0
$117$		0			0
$118$	−6.00000	+	10.3923i	−0.552345	+	0.956689i
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	2.00000			0.181071
$123$		0			0
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.803365	+	0.595487i	$0.203041\pi$
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.114024	+	0.993478i	$0.463626\pi$
$132$		0			0
$133$	1.50000	+	12.9904i	0.130066	+	1.12641i
$134$	2.00000			0.172774
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	−0.767853	−	0.640626i	$-0.778675\pi$
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	0.938725	+	0.344668i	$0.112008\pi$
$138$		0			0
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$	3.00000			0.253546
$141$		0			0
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$		0			0
$145$		0			0
$146$	−6.00000	+	10.3923i	−0.496564	+	0.860073i
$147$		0			0
$148$	−4.50000	+	7.79423i	−0.369898	+	0.640682i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$	−0.500000	−	4.33013i	−0.0405554	−	0.351220i
$153$		0			0
$154$	−1.50000	−	2.59808i	−0.120873	−	0.209359i
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	7.00000	−	12.1244i	0.556890	−	0.964562i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	1.50000	−	2.59808i	0.118217	−	0.204757i
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	−1.00000			−0.0780869
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	−0.802135	−	0.597143i	$-0.796303\pi$
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	2.00000			0.153393
$171$		0			0
$172$	−10.0000			−0.762493
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	0.995754	−	0.0920525i	$-0.0293428\pi$
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	−0.577597	+	0.816322i	$0.696009\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$	−5.00000			−0.374766
$179$	13.0000			0.971666			0.485833	−	0.874052i	$-0.338516\pi$
$179$	13.0000			0.971666			0.485833	+	0.874052i	$0.338516\pi$
$180$		0			0
$181$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$181$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$182$	−6.00000			−0.444750
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−4.50000	−	7.79423i	−0.330847	−	0.573043i
$186$		0			0
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$		0			0
$189$		0			0
$190$	4.00000	+	1.73205i	0.290191	+	0.125656i
$191$	10.0000			0.723575			0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000			0.723575			0.361787	+	0.932261i	$0.382167\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$		0			0
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	−5.00000			−0.356235			−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000			−0.356235			−0.178118	+	0.984009i	$0.557001\pi$
$198$		0			0
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	−0.347879	−	0.937539i	$-0.613098\pi$
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	0.985873	−	0.167497i	$-0.0535685\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−2.00000			−0.140720
$203$		0			0
$204$		0			0
$205$	0.500000	−	0.866025i	0.0349215	−	0.0604858i
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$		0			0
$208$	2.00000			0.138675
$209$	−0.500000	−	4.33013i	−0.0345857	−	0.299521i
$210$		0			0
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$		0			0
$214$	5.00000	+	8.66025i	0.341793	+	0.592003i
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$	12.0000			0.814613
$218$	−3.00000	+	5.19615i	−0.203186	+	0.351928i
$219$		0			0
$220$	−1.00000			−0.0674200
$221$	−4.00000			−0.269069
$222$		0			0
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	0.811422	−	0.584461i	$-0.198694\pi$
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	−0.911869	+	0.410481i	$0.865361\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	−28.0000			−1.85843			−0.929213	−	0.369546i	$-0.879513\pi$
$227$	−28.0000			−1.85843			−0.929213	+	0.369546i	$0.879513\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	−0.500000	−	0.866025i	−0.0329690	−	0.0571040i
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$		0			0
$236$	−12.0000			−0.781133
$237$		0			0
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−5.00000	−	8.66025i	−0.321412	−	0.556702i
$243$		0			0
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$		0			0
$247$	−8.00000	−	3.46410i	−0.509028	−	0.220416i
$248$	−4.00000			−0.254000
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	14.0000	−	24.2487i	0.883672	−	1.53057i	0.0364441	−	0.999336i	$-0.488397\pi$
$251$	14.0000	−	24.2487i	0.883672	−	1.53057i	0.847228	−	0.531229i	$-0.178270\pi$
$252$		0			0
$253$	−0.500000	+	0.866025i	−0.0314347	+	0.0544466i
$254$	1.00000			0.0627456
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	−0.833150	−	0.553047i	$-0.813465\pi$
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	0.895528	+	0.445005i	$0.146798\pi$
$258$		0			0
$259$	27.0000			1.67770
$260$	−1.00000	+	1.73205i	−0.0620174	+	0.107417i
$261$		0			0
$262$	−10.5000	+	18.1865i	−0.648692	+	1.12357i
$263$	−12.5000	−	21.6506i	−0.770783	−	1.33504i	−0.937134	−	0.348969i	$-0.886532\pi$
$263$	−12.5000	−	21.6506i	−0.770783	−	1.33504i	0.166351	−	0.986067i	$-0.446801\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$	−10.5000	+	7.79423i	−0.643796	+	0.477895i
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	4.00000			0.241649
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	22.0000			1.32185			0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000			1.32185			0.660926	+	0.750451i	$0.270164\pi$
$278$	20.0000			1.19952
$279$		0			0
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	0.361895	+	0.932219i	$0.382130\pi$
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	−0.988273	+	0.152699i	$0.951204\pi$
$282$		0			0
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$	2.00000			0.118262
$287$	1.50000	+	2.59808i	0.0885422	+	0.153360i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$	−12.0000			−0.702247
$293$	−1.00000			−0.0584206			−0.0292103	−	0.999573i	$-0.509299\pi$
$293$	−1.00000			−0.0584206			−0.0292103	+	0.999573i	$0.509299\pi$
$294$		0			0
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	−9.00000			−0.523114
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$		0			0
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	−9.00000	−	15.5885i	−0.517892	−	0.897015i
$303$		0			0
$304$	3.50000	−	2.59808i	0.200739	−	0.149010i
$305$	−2.00000			−0.114520
$306$		0			0
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	0.542194	−	0.840254i	$-0.317594\pi$
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	−0.998778	+	0.0494267i	$0.984261\pi$
$308$	1.50000	−	2.59808i	0.0854704	−	0.148039i
$309$		0			0
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$		0			0
$313$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$313$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$		0			0
$316$	14.0000			0.787562
$317$	3.50000	−	6.06218i	0.196580	−	0.340486i	−0.750838	−	0.660487i	$-0.770350\pi$
$317$	3.50000	−	6.06218i	0.196580	−	0.340486i	0.947417	+	0.320001i	$0.103683\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	3.00000			0.167183
$323$	−7.00000	+	5.19615i	−0.389490	+	0.289122i
$324$		0			0
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	1.00000	+	1.73205i	0.0553849	+	0.0959294i
$327$		0			0
$328$	−0.500000	−	0.866025i	−0.0276079	−	0.0478183i
$329$		0			0
$330$		0			0
$331$	13.0000			0.714545			0.357272	−	0.934000i	$-0.383707\pi$
$331$	13.0000			0.714545			0.357272	+	0.934000i	$0.383707\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$		0			0
$334$	3.00000			0.164153
$335$	−2.00000			−0.109272
$336$		0			0
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	0.837503	−	0.546433i	$-0.184015\pi$
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	−0.891976	+	0.452082i	$0.850681\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	−4.00000			−0.216612
$342$		0			0
$343$	−15.0000			−0.809924
$344$	−5.00000	−	8.66025i	−0.269582	−	0.466930i
$345$		0			0
$346$	−5.50000	+	9.52628i	−0.295682	+	0.512136i
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	−3.00000			−0.160357
$351$		0			0
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−26.0000			−1.38384			−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000			−1.38384			−0.691920	+	0.721974i	$0.743235\pi$
$354$		0			0
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	−2.50000	−	4.33013i	−0.132500	−	0.229496i
$357$		0			0
$358$	6.50000	+	11.2583i	0.343536	+	0.595021i
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	0.979791	−	0.200026i	$-0.0641026\pi$
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	−0.663123	+	0.748511i	$0.730769\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$		0			0
$363$		0			0
$364$	−3.00000	−	5.19615i	−0.157243	−	0.272352i
$365$	6.00000	−	10.3923i	0.314054	−	0.543958i
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	4.50000	−	7.79423i	0.233944	−	0.405203i
$371$	4.50000	−	7.79423i	0.233628	−	0.404656i
$372$		0			0
$373$	−37.0000			−1.91579			−0.957894	−	0.287123i	$-0.907301\pi$
$373$	−37.0000			−1.91579			−0.957894	+	0.287123i	$0.907301\pi$
$374$	1.00000	−	1.73205i	0.0517088	−	0.0895622i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	0.500000	+	4.33013i	0.0256495	+	0.222131i
$381$		0			0
$382$	5.00000	+	8.66025i	0.255822	+	0.443097i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		0			0
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	7.00000	−	12.1244i	0.356291	−	0.617113i
$387$		0			0
$388$	8.00000			0.406138
$389$	4.00000	−	6.92820i	0.202808	−	0.351274i	−0.746624	−	0.665246i	$-0.768327\pi$
$389$	4.00000	−	6.92820i	0.202808	−	0.351274i	0.949432	+	0.313972i	$0.101660\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	−2.00000			−0.101015
$393$		0			0
$394$	−2.50000	−	4.33013i	−0.125948	−	0.218149i
$395$	−7.00000	+	12.1244i	−0.352208	+	0.610043i
$396$		0			0
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	0.990538	−	0.137241i	$-0.0438236\pi$
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$398$	18.0000			0.902258
$399$		0			0
$400$	1.00000			0.0500000
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	0.839976	−	0.542623i	$-0.182569\pi$
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	−0.889914	+	0.456129i	$0.849236\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	−1.00000	−	1.73205i	−0.0497519	−	0.0861727i
$405$		0			0
$406$		0			0
$407$	−9.00000			−0.446113
$408$		0			0
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	0.480560	+	0.876962i	$0.340434\pi$
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	−0.999751	+	0.0223042i	$0.992900\pi$
$410$	1.00000			0.0493865
$411$		0			0
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	18.0000	+	31.1769i	0.885722	+	1.53412i
$414$		0			0
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	3.50000	−	2.59808i	0.171191	−	0.127076i
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	11.5000	−	19.9186i	0.559811	−	0.969622i
$423$		0			0
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$	−2.00000			−0.0970143
$426$		0			0
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$	−5.00000	+	8.66025i	−0.241684	+	0.418609i
$429$		0			0
$430$	10.0000			0.482243
$431$	19.0000	−	32.9090i	0.915198	−	1.58517i	0.108586	−	0.994087i	$-0.465368\pi$
$431$	19.0000	−	32.9090i	0.915198	−	1.58517i	0.806611	−	0.591082i	$-0.201299\pi$
$432$		0			0
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	−0.991693	−	0.128624i	$-0.958944\pi$
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	0.607238	+	0.794520i	$0.292277\pi$
$434$	6.00000	+	10.3923i	0.288009	+	0.498847i
$435$		0			0
$436$	−6.00000			−0.287348
$437$	4.00000	+	1.73205i	0.191346	+	0.0828552i
$438$		0			0
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	−0.962607	−	0.270901i	$-0.912678\pi$
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	0.246696	−	0.969093i	$-0.420655\pi$
$440$	−0.500000	−	0.866025i	−0.0238366	−	0.0412861i
$441$		0			0
$442$	−2.00000	−	3.46410i	−0.0951303	−	0.164771i
$443$	11.0000	−	19.0526i	0.522626	−	0.905214i	−0.477028	−	0.878888i	$-0.658286\pi$
$443$	11.0000	−	19.0526i	0.522626	−	0.905214i	0.999653	−	0.0263261i	$-0.00838082\pi$
$444$		0			0
$445$	5.00000			0.237023
$446$	1.50000	−	2.59808i	0.0710271	−	0.123022i
$447$		0			0
$448$	3.00000			0.141737
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	−0.500000	−	0.866025i	−0.0235441	−	0.0407795i
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$		0			0
$454$	−14.0000	−	24.2487i	−0.657053	−	1.13805i
$455$	6.00000			0.281284
$456$		0			0
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$		0			0
$460$	0.500000	−	0.866025i	0.0233126	−	0.0403786i
$461$	11.0000	+	19.0526i	0.512321	+	0.887366i	0.999898	+	0.0142861i	$0.00454755\pi$
$461$	11.0000	+	19.0526i	0.512321	+	0.887366i	−0.487577	+	0.873080i	$0.662119\pi$
$462$		0			0
$463$	−25.0000			−1.16185			−0.580924	−	0.813958i	$-0.697309\pi$
$463$	−25.0000			−1.16185			−0.580924	+	0.813958i	$0.697309\pi$
$464$		0			0
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−32.0000			−1.48078			−0.740392	−	0.672176i	$-0.765360\pi$
$467$	−32.0000			−1.48078			−0.740392	+	0.672176i	$0.765360\pi$
$468$		0			0
$469$	3.00000	−	5.19615i	0.138527	−	0.239936i
$470$		0			0
$471$		0			0
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	−4.00000	−	1.73205i	−0.183533	−	0.0794719i
$476$	−6.00000			−0.275010
$477$		0			0
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	−0.541884	−	0.840453i	$-0.682289\pi$
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	0.998796	+	0.0490589i	$0.0156222\pi$
$480$		0			0
$481$	−9.00000	+	15.5885i	−0.410365	+	0.710772i
$482$	10.0000			0.455488
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−4.00000	+	6.92820i	−0.181631	+	0.314594i
$486$		0			0
$487$	−41.0000			−1.85789			−0.928944	−	0.370221i	$-0.879282\pi$
$487$	−41.0000			−1.85789			−0.928944	+	0.370221i	$0.879282\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$		0			0
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	−0.950365	−	0.311136i	$-0.899290\pi$
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	0.205731	−	0.978609i	$-0.434043\pi$
$492$		0			0
$493$		0			0
$494$	−1.00000	−	8.66025i	−0.0449921	−	0.389643i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$		0			0
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	0.647882	−	0.761741i	$-0.275655\pi$
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	−0.983628	+	0.180212i	$0.942322\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	28.0000			1.24970
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	−0.948736	−	0.316068i	$-0.897637\pi$
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	0.748091	+	0.663596i	$0.230970\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$	−1.00000			−0.0444554
$507$		0			0
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	18.0000	+	31.1769i	0.796273	+	1.37919i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	2.00000			0.0882162
$515$	6.50000	+	11.2583i	0.286424	+	0.496101i
$516$		0			0
$517$		0			0
$518$	13.5000	+	23.3827i	0.593156	+	1.02738i
$519$		0			0
$520$	−2.00000			−0.0877058
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	16.0000	−	27.7128i	0.699631	−	1.21180i	−0.268963	−	0.963150i	$-0.586681\pi$
$523$	16.0000	−	27.7128i	0.699631	−	1.21180i	0.968594	−	0.248646i	$-0.0799857\pi$
$524$	−21.0000			−0.917389
$525$		0			0
$526$	12.5000	−	21.6506i	0.545026	−	0.944013i
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−1.50000	−	2.59808i	−0.0651558	−	0.112853i
$531$		0			0
$532$	−12.0000	−	5.19615i	−0.520266	−	0.225282i
$533$	−2.00000			−0.0866296
$534$		0			0
$535$	−5.00000	−	8.66025i	−0.216169	−	0.374415i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$		0			0
$538$	7.00000	−	12.1244i	0.301791	−	0.522718i
$539$	−2.00000			−0.0861461
$540$		0			0
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	1.00000	−	1.73205i	0.0429537	−	0.0743980i
$543$		0			0
$544$	2.00000			0.0857493
$545$	3.00000	−	5.19615i	0.128506	−	0.222579i
$546$		0			0
$547$	−1.00000	+	1.73205i	−0.0427569	+	0.0740571i	−0.886612	−	0.462514i	$-0.846947\pi$
$547$	−1.00000	+	1.73205i	−0.0427569	+	0.0740571i	0.843855	+	0.536571i	$0.180281\pi$
$548$	2.00000	+	3.46410i	0.0854358	+	0.147979i
$549$		0			0
$550$	1.00000			0.0426401
$551$		0			0
$552$		0			0
$553$	−21.0000	−	36.3731i	−0.893011	−	1.54674i
$554$	11.0000	+	19.0526i	0.467345	+	0.809466i
$555$		0			0
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	16.5000	−	28.5788i	0.699127	−	1.21092i	−0.269642	−	0.962961i	$-0.586905\pi$
$557$	16.5000	−	28.5788i	0.699127	−	1.21092i	0.968769	−	0.247964i	$-0.0797613\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$		0			0
$562$	−21.0000			−0.885832
$563$	−28.0000			−1.18006			−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000			−1.18006			−0.590030	+	0.807382i	$0.700884\pi$
$564$		0			0
$565$	5.00000	+	8.66025i	0.210352	+	0.364340i
$566$	1.00000	−	1.73205i	0.0420331	−	0.0728035i
$567$		0			0
$568$	−4.00000	−	6.92820i	−0.167836	−	0.290701i
$569$	−31.0000			−1.29959			−0.649794	−	0.760111i	$-0.725145\pi$
$569$	−31.0000			−1.29959			−0.649794	+	0.760111i	$0.725145\pi$
$570$		0			0
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	1.00000	+	1.73205i	0.0418121	+	0.0724207i
$573$		0			0
$574$	−1.50000	+	2.59808i	−0.0626088	+	0.108442i
$575$	0.500000	+	0.866025i	0.0208514	+	0.0361158i
$576$		0			0
$577$	42.0000			1.74848			0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000			1.74848			0.874241	+	0.485491i	$0.161359\pi$
$578$	13.0000			0.540729
$579$		0			0
$580$		0			0
$581$	−18.0000			−0.746766
$582$		0			0
$583$	−1.50000	+	2.59808i	−0.0621237	+	0.107601i
$584$	−6.00000	−	10.3923i	−0.248282	−	0.430037i
$585$		0			0
$586$	−0.500000	−	0.866025i	−0.0206548	−	0.0357752i
$587$	−14.0000	−	24.2487i	−0.577842	−	1.00085i	−0.995726	−	0.0923513i	$-0.970562\pi$
$587$	−14.0000	−	24.2487i	−0.577842	−	1.00085i	0.417885	−	0.908500i	$-0.362772\pi$
$588$		0			0
$589$	2.00000	+	17.3205i	0.0824086	+	0.713679i
$590$	12.0000			0.494032
$591$		0			0
$592$	−4.50000	−	7.79423i	−0.184949	−	0.320341i
$593$	−22.0000	+	38.1051i	−0.903432	+	1.56479i	−0.0804231	+	0.996761i	$0.525627\pi$
$593$	−22.0000	+	38.1051i	−0.903432	+	1.56479i	−0.823009	+	0.568029i	$0.807706\pi$
$594$		0			0
$595$	3.00000	−	5.19615i	0.122988	−	0.213021i
$596$	6.00000			0.245770
$597$		0			0
$598$	−1.00000	+	1.73205i	−0.0408930	+	0.0708288i
$599$	17.0000	−	29.4449i	0.694601	−	1.20308i	−0.275714	−	0.961240i	$-0.588914\pi$
$599$	17.0000	−	29.4449i	0.694601	−	1.20308i	0.970315	−	0.241845i	$-0.0777525\pi$
$600$		0			0
$601$	25.0000			1.01977			0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000			1.01977			0.509886	+	0.860242i	$0.329688\pi$
$602$	−15.0000	+	25.9808i	−0.611354	+	1.05890i
$603$		0			0
$604$	9.00000	−	15.5885i	0.366205	−	0.634285i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	−5.00000			−0.202944			−0.101472	−	0.994838i	$-0.532355\pi$
$607$	−5.00000			−0.202944			−0.101472	+	0.994838i	$0.532355\pi$
$608$	4.00000	+	1.73205i	0.162221	+	0.0702439i
$609$		0			0
$610$	−1.00000	−	1.73205i	−0.0404888	−	0.0701287i
$611$		0			0
$612$		0			0
$613$	5.50000	+	9.52628i	0.222143	+	0.384763i	0.955458	−	0.295126i	$-0.0953615\pi$
$613$	5.50000	+	9.52628i	0.222143	+	0.384763i	−0.733316	+	0.679888i	$0.762028\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$		0			0
$616$	3.00000			0.120873
$617$	8.00000	−	13.8564i	0.322068	−	0.557838i	−0.658847	−	0.752277i	$-0.728955\pi$
$617$	8.00000	−	13.8564i	0.322068	−	0.557838i	0.980915	+	0.194439i	$0.0622887\pi$
$618$		0			0
$619$	13.0000			0.522514			0.261257	−	0.965269i	$-0.415863\pi$
$619$	13.0000			0.522514			0.261257	+	0.965269i	$0.415863\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$	8.00000	+	13.8564i	0.320771	+	0.555591i
$623$	−7.50000	+	12.9904i	−0.300481	+	0.520449i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$	7.00000			0.279330
$629$	9.00000	+	15.5885i	0.358854	+	0.621552i
$630$		0			0
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	−0.775356	−	0.631524i	$-0.782430\pi$
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	0.934594	+	0.355716i	$0.115763\pi$
$632$	7.00000	+	12.1244i	0.278445	+	0.482281i
$633$		0			0
$634$	7.00000			0.278006
$635$	−1.00000			−0.0396838
$636$		0			0
$637$	−2.00000	+	3.46410i	−0.0792429	+	0.137253i
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	21.0000	+	36.3731i	0.829450	+	1.43665i	0.898470	+	0.439034i	$0.144679\pi$
$641$	21.0000	+	36.3731i	0.829450	+	1.43665i	−0.0690201	+	0.997615i	$0.521987\pi$
$642$		0			0
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$		0			0
$646$	−8.00000	−	3.46410i	−0.314756	−	0.136293i
$647$	39.0000			1.53325			0.766624	−	0.642096i	$-0.221935\pi$
$647$	39.0000			1.53325			0.766624	+	0.642096i	$0.221935\pi$
$648$		0			0
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	1.00000	−	1.73205i	0.0392232	−	0.0679366i
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	−9.00000			−0.352197			−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000			−0.352197			−0.176099	+	0.984373i	$0.556348\pi$
$654$		0			0
$655$	10.5000	−	18.1865i	0.410269	−	0.710607i
$656$	0.500000	−	0.866025i	0.0195217	−	0.0338126i
$657$		0			0
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$		0			0
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	−0.902297	−	0.431116i	$-0.858120\pi$
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	0.824506	+	0.565854i	$0.191453\pi$
$662$	6.50000	+	11.2583i	0.252630	+	0.437567i
$663$		0			0
$664$	6.00000			0.232845
$665$	10.5000	−	7.79423i	0.407173	−	0.302247i
$666$		0			0
$667$		0			0
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	−1.00000	+	1.73205i	−0.0386046	+	0.0668651i
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	1.00000	−	1.73205i	0.0385186	−	0.0667161i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	39.0000			1.49889			0.749446	−	0.662066i	$-0.230320\pi$
$677$	39.0000			1.49889			0.749446	+	0.662066i	$0.230320\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$	−1.00000	+	1.73205i	−0.0383482	+	0.0664211i
$681$		0			0
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$		0			0
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	23.0000			0.874961			0.437481	−	0.899228i	$-0.355871\pi$
$691$	23.0000			0.874961			0.437481	+	0.899228i	$0.355871\pi$
$692$	−11.0000			−0.418157
$693$		0			0
$694$	−9.00000	+	15.5885i	−0.341635	+	0.591730i
$695$	−20.0000			−0.758643
$696$		0			0
$697$	−1.00000	+	1.73205i	−0.0378777	+	0.0656061i
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$		0			0
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	−21.0000	−	36.3731i	−0.793159	−	1.37379i	−0.924002	−	0.382389i	$-0.875102\pi$
$701$	−21.0000	−	36.3731i	−0.793159	−	1.37379i	0.130843	−	0.991403i	$-0.458232\pi$
$702$		0			0
$703$	4.50000	+	38.9711i	0.169721	+	1.46982i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	−13.0000	−	22.5167i	−0.489261	−	0.847426i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	8.00000			0.300235
$711$		0			0
$712$	2.50000	−	4.33013i	0.0936915	−	0.162278i
$713$	2.00000	−	3.46410i	0.0749006	−	0.129732i
$714$		0			0
$715$	−2.00000			−0.0747958
$716$	−6.50000	+	11.2583i	−0.242916	+	0.420744i
$717$		0			0
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	0.999669	+	0.0257237i	$0.00818900\pi$
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	−0.477557	+	0.878601i	$0.658478\pi$
$720$		0			0
$721$	−39.0000			−1.45244
$722$	−13.0000	−	13.8564i	−0.483810	−	0.515682i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	0.993770	+	0.111454i	$0.0355509\pi$
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	−0.400362	+	0.916357i	$0.631116\pi$
$728$	3.00000	−	5.19615i	0.111187	−	0.192582i
$729$		0			0
$730$	12.0000			0.444140
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$		0			0
$733$	−35.0000			−1.29275			−0.646377	−	0.763018i	$-0.723717\pi$
$733$	−35.0000			−1.29275			−0.646377	+	0.763018i	$0.723717\pi$
$734$		0			0
$735$		0			0
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	−1.00000	+	1.73205i	−0.0368355	+	0.0638009i
$738$		0			0
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	0.794443	−	0.607339i	$-0.207763\pi$
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	−0.923192	+	0.384338i	$0.874430\pi$
$740$	9.00000			0.330847
$741$		0			0
$742$	9.00000			0.330400
$743$	−11.5000	−	19.9186i	−0.421894	−	0.730742i	0.574231	−	0.818694i	$-0.305301\pi$
$743$	−11.5000	−	19.9186i	−0.421894	−	0.730742i	−0.996125	+	0.0879516i	$0.971968\pi$
$744$		0			0
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$	−18.5000	−	32.0429i	−0.677333	−	1.17318i
$747$		0			0
$748$	2.00000			0.0731272
$749$	30.0000			1.09618
$750$		0			0
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.00000	+	15.5885i	0.327544	+	0.567322i
$756$		0			0
$757$	9.50000	+	16.4545i	0.345283	+	0.598048i	0.985405	−	0.170225i	$-0.0544495\pi$
$757$	9.50000	+	16.4545i	0.345283	+	0.598048i	−0.640122	+	0.768273i	$0.721116\pi$
$758$	8.00000	+	13.8564i	0.290573	+	0.503287i
$759$		0			0
$760$	−3.50000	+	2.59808i	−0.126958	+	0.0942421i
$761$	45.0000			1.63125			0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000			1.63125			0.815624	+	0.578582i	$0.196394\pi$
$762$		0			0
$763$	9.00000	+	15.5885i	0.325822	+	0.564340i
$764$	−5.00000	+	8.66025i	−0.180894	+	0.313317i
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−24.0000			−0.866590
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$	−1.50000	+	2.59808i	−0.0540562	+	0.0936282i
$771$		0			0
$772$	14.0000			0.503871
$773$	−22.5000	+	38.9711i	−0.809269	+	1.40169i	0.104102	+	0.994567i	$0.466803\pi$
$773$	−22.5000	+	38.9711i	−0.809269	+	1.40169i	−0.913371	+	0.407128i	$0.866530\pi$
$774$		0			0
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$		0			0
$778$	8.00000			0.286814
$779$	−3.50000	+	2.59808i	−0.125401	+	0.0930857i
$780$		0			0
$781$	−4.00000	−	6.92820i	−0.143131	−	0.247911i
$782$	1.00000	+	1.73205i	0.0357599	+	0.0619380i
$783$		0			0
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	−3.50000	+	6.06218i	−0.124920	+	0.216368i
$786$		0			0
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$	2.50000	−	4.33013i	0.0890588	−	0.154254i
$789$		0			0
$790$	−14.0000			−0.498098
$791$	−30.0000			−1.06668
$792$		0			0
$793$	2.00000	+	3.46410i	0.0710221	+	0.123014i
$794$	−7.50000	+	12.9904i	−0.266165	+	0.461011i
$795$		0			0
$796$	9.00000	+	15.5885i	0.318997	+	0.552518i
$797$	−15.0000			−0.531327			−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000			−0.531327			−0.265664	+	0.964066i	$0.585591\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	1.00000	−	1.73205i	0.0353112	−	0.0611608i
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$		0			0
$805$	−3.00000			−0.105736
$806$	−8.00000			−0.281788
$807$		0			0
$808$	1.00000	−	1.73205i	0.0351799	−	0.0609333i
$809$	−34.0000			−1.19538			−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000			−1.19538			−0.597688	+	0.801729i	$0.703914\pi$
$810$		0			0
$811$	5.50000	−	9.52628i	0.193131	−	0.334513i	−0.753155	−	0.657843i	$-0.771469\pi$
$811$	5.50000	−	9.52628i	0.193131	−	0.334513i	0.946286	+	0.323330i	$0.104802\pi$
$812$		0			0
$813$		0			0
$814$	−4.50000	−	7.79423i	−0.157725	−	0.273188i
$815$	−1.00000	−	1.73205i	−0.0350285	−	0.0606711i
$816$		0			0
$817$	−35.0000	+	25.9808i	−1.22449	+	0.908952i
$818$	−21.0000			−0.734248
$819$		0			0
$820$	0.500000	+	0.866025i	0.0174608	+	0.0302429i
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$		0			0
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	0.819159	+	0.573567i	$0.194441\pi$
$824$	13.0000			0.452876
$825$		0			0
$826$	−18.0000	+	31.1769i	−0.626300	+	1.08478i
$827$	−24.0000	+	41.5692i	−0.834562	+	1.44550i	0.0598250	+	0.998209i	$0.480946\pi$
$827$	−24.0000	+	41.5692i	−0.834562	+	1.44550i	−0.894387	+	0.447295i	$0.852388\pi$
$828$		0			0
$829$	−8.00000			−0.277851			−0.138926	−	0.990303i	$-0.544365\pi$
$829$	−8.00000			−0.277851			−0.138926	+	0.990303i	$0.544365\pi$
$830$	−3.00000	+	5.19615i	−0.104132	+	0.180361i
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	2.00000	+	3.46410i	0.0692959	+	0.120024i
$834$		0			0
$835$	−3.00000			−0.103819
$836$	4.00000	+	1.73205i	0.138343	+	0.0599042i
$837$		0			0
$838$	7.50000	+	12.9904i	0.259083	+	0.448745i
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	−0.999785	−	0.0207443i	$-0.993396\pi$
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	0.481927	−	0.876211i	$-0.339937\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−11.0000	+	19.0526i	−0.379085	+	0.656595i
$843$		0			0
$844$	23.0000			0.791693
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	−30.0000			−1.03081
$848$	−3.00000			−0.103020
$849$		0			0
$850$	−1.00000	−	1.73205i	−0.0342997	−	0.0594089i
$851$	4.50000	−	7.79423i	0.154258	−	0.267183i
$852$		0			0
$853$	−19.0000	−	32.9090i	−0.650548	−	1.12678i	−0.982990	−	0.183658i	$-0.941206\pi$
$853$	−19.0000	−	32.9090i	−0.650548	−	1.12678i	0.332443	−	0.943123i	$-0.392127\pi$
$854$	6.00000			0.205316
$855$		0			0
$856$	−10.0000			−0.341793
$857$	−20.0000	−	34.6410i	−0.683187	−	1.18331i	−0.974003	−	0.226536i	$-0.927260\pi$
$857$	−20.0000	−	34.6410i	−0.683187	−	1.18331i	0.290816	−	0.956779i	$-0.406073\pi$
$858$		0			0
$859$	7.50000	−	12.9904i	0.255897	−	0.443226i	−0.709242	−	0.704965i	$-0.750963\pi$
$859$	7.50000	−	12.9904i	0.255897	−	0.443226i	0.965139	+	0.261739i	$0.0842960\pi$
$860$	5.00000	+	8.66025i	0.170499	+	0.295312i
$861$		0			0
$862$	38.0000			1.29429
$863$	−17.0000			−0.578687			−0.289343	−	0.957225i	$-0.593437\pi$
$863$	−17.0000			−0.578687			−0.289343	+	0.957225i	$0.593437\pi$
$864$		0			0
$865$	5.50000	−	9.52628i	0.187006	−	0.323903i
$866$	−16.0000			−0.543702
$867$		0			0
$868$	−6.00000	+	10.3923i	−0.203653	+	0.352738i
$869$	7.00000	+	12.1244i	0.237459	+	0.411291i
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$	−3.00000	−	5.19615i	−0.101593	−	0.175964i
$873$		0			0
$874$	0.500000	+	4.33013i	0.0169128	+	0.146469i
$875$	3.00000			0.101419
$876$		0			0
$877$	0.500000	+	0.866025i	0.0168838	+	0.0292436i	0.874344	−	0.485307i	$-0.161292\pi$
$877$	0.500000	+	0.866025i	0.0168838	+	0.0292436i	−0.857460	+	0.514551i	$0.827959\pi$
$878$	15.0000	−	25.9808i	0.506225	−	0.876808i
$879$		0			0
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$		0			0
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	−0.882361	−	0.470573i	$-0.844047\pi$
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	0.848709	+	0.528861i	$0.177381\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$		0			0
$886$	22.0000			0.739104
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$		0			0
$889$	1.50000	−	2.59808i	0.0503084	−	0.0871367i
$890$	2.50000	+	4.33013i	0.0838002	+	0.145146i
$891$		0			0
$892$	3.00000			0.100447
$893$		0			0
$894$		0			0
$895$	−6.50000	−	11.2583i	−0.217271	−	0.376324i
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$		0			0
$898$	4.50000	+	7.79423i	0.150167	+	0.260097i
$899$		0			0
$900$		0			0
$901$	6.00000			0.199889
$902$	0.500000	−	0.866025i	0.0166482	−	0.0288355i
$903$		0			0
$904$	10.0000			0.332595
$905$		0			0
$906$		0			0
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	0.997016	−	0.0771920i	$-0.0245954\pi$
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	−0.565358	+	0.824845i	$0.691262\pi$
$908$	14.0000	−	24.2487i	0.464606	−	0.804722i
$909$		0			0
$910$	3.00000	+	5.19615i	0.0994490	+	0.172251i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	6.00000			0.198571
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	31.5000	+	54.5596i	1.04022	+	1.80172i
$918$		0			0
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$	1.00000			0.0329690
$921$		0			0
$922$	−11.0000	+	19.0526i	−0.362266	+	0.627463i
$923$	−16.0000			−0.526646
$924$		0			0
$925$	−4.50000	+	7.79423i	−0.147959	+	0.256273i
$926$	−12.5000	−	21.6506i	−0.410775	−	0.711484i
$927$		0			0
$928$		0			0
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543055\pi$
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$930$		0			0
$931$	1.00000	+	8.66025i	0.0327737	+	0.283828i
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−16.0000	−	27.7128i	−0.523536	−	0.906791i
$935$	−1.00000	+	1.73205i	−0.0327035	+	0.0566441i
$936$		0			0
$937$	−26.0000	+	45.0333i	−0.849383	+	1.47117i	0.0323768	+	0.999476i	$0.489692\pi$
$937$	−26.0000	+	45.0333i	−0.849383	+	1.47117i	−0.881760	+	0.471699i	$0.843641\pi$
$938$	6.00000			0.195907
$939$		0			0
$940$		0			0
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$		0			0
$943$	1.00000			0.0325645
$944$	6.00000	−	10.3923i	0.195283	−	0.338241i
$945$		0			0
$946$	5.00000	−	8.66025i	0.162564	−	0.281569i
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	0.935757	−	0.352646i	$-0.114718\pi$
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	−0.773279	+	0.634066i	$0.781385\pi$
$948$		0			0
$949$	−24.0000			−0.779073
$950$	−0.500000	−	4.33013i	−0.0162221	−	0.140488i
$951$		0			0
$952$	−3.00000	−	5.19615i	−0.0972306	−	0.168408i
$953$	−24.0000	−	41.5692i	−0.777436	−	1.34656i	−0.933415	−	0.358799i	$-0.883186\pi$
$953$	−24.0000	−	41.5692i	−0.777436	−	1.34656i	0.155979	−	0.987760i	$-0.450147\pi$
$954$		0			0
$955$	−5.00000	−	8.66025i	−0.161796	−	0.280239i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	20.0000			0.646171
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−18.0000			−0.580343
$963$		0			0
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	−7.00000	+	12.1244i	−0.225338	+	0.390297i
$966$		0			0
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$	10.0000			0.321412
$969$		0			0
$970$	−8.00000			−0.256865
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$	30.0000	−	51.9615i	0.961756	−	1.66581i
$974$	−20.5000	−	35.5070i	−0.656862	−	1.13772i
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	−8.00000			−0.255943			−0.127971	−	0.991778i	$-0.540847\pi$
$977$	−8.00000			−0.255943			−0.127971	+	0.991778i	$0.540847\pi$
$978$		0			0
$979$	2.50000	−	4.33013i	0.0799003	−	0.138391i
$980$	2.00000			0.0638877
$981$		0			0
$982$	16.5000	−	28.5788i	0.526536	−	0.911987i
$983$	20.5000	+	35.5070i	0.653848	+	1.13250i	0.982181	+	0.187937i	$0.0601800\pi$
$983$	20.5000	+	35.5070i	0.653848	+	1.13250i	−0.328333	+	0.944562i	$0.606487\pi$
$984$		0			0
$985$	2.50000	+	4.33013i	0.0796566	+	0.137969i
$986$		0			0
$987$		0			0
$988$	7.00000	−	5.19615i	0.222700	−	0.165312i
$989$	10.0000			0.317982
$990$		0			0
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	0.979999	−	0.199000i	$-0.0637695\pi$
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	−0.662339	+	0.749204i	$0.730436\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$	−18.0000			−0.570638
$996$		0			0
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	−0.744548	−	0.667568i	$-0.767335\pi$
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	0.950405	+	0.311014i	$0.100668\pi$
$998$	7.50000	−	12.9904i	0.237408	−	0.411203i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.i.1261.1		2
3.2	odd	2		570.2.i.c.121.1	✓	2
19.11	even	3	inner	1710.2.l.i.1531.1		2
57.11	odd	6		570.2.i.c.391.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.c.121.1	✓	2	3.2	odd	2
570.2.i.c.391.1	yes	2	57.11	odd	6
1710.2.l.i.1261.1		2	1.1	even	1	trivial
1710.2.l.i.1531.1		2	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(1.50000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.00000 q^{26} +(-1.50000 + 2.59808i) q^{28} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(-1.50000 - 2.59808i) q^{35} +9.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{41} +(5.00000 + 8.66025i) q^{43} +(0.500000 - 0.866025i) q^{44} +1.00000 q^{46} +2.00000 q^{49} -1.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{55} -3.00000 q^{56} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(1.00000 - 1.73205i) q^{67} -2.00000 q^{68} +(1.50000 - 2.59808i) q^{70} +(4.00000 + 6.92820i) q^{71} +(6.00000 + 10.3923i) q^{73} +(4.50000 + 7.79423i) q^{74} +(-4.00000 - 1.73205i) q^{76} -3.00000 q^{77} +(-7.00000 - 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{85} +(-5.00000 + 8.66025i) q^{86} +1.00000 q^{88} +(-2.50000 + 4.33013i) q^{89} +(-3.00000 + 5.19615i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.50000 - 2.59808i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} + 6 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 + 6 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{5} + 6 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 2 q^{13} + 3 q^{14} - q^{16} + 2 q^{17} + q^{19} + 2 q^{20} - q^{22} + q^{23} - q^{25} - 4 q^{26} - 3 q^{28} + 8 q^{31} + q^{32} - 2 q^{34} - 3 q^{35} + 18 q^{37} - 7 q^{38} + q^{40} + q^{41} + 10 q^{43} + q^{44} + 2 q^{46} + 4 q^{49} - 2 q^{50} - 2 q^{52} + 3 q^{53} + q^{55} - 6 q^{56} + 12 q^{59} + 2 q^{61} + 4 q^{62} + 2 q^{64} + 4 q^{65} + 2 q^{67} - 4 q^{68} + 3 q^{70} + 8 q^{71} + 12 q^{73} + 9 q^{74} - 8 q^{76} - 6 q^{77} - 14 q^{79} - q^{80} - q^{82} - 12 q^{83} + 2 q^{85} - 10 q^{86} + 2 q^{88} - 5 q^{89} - 6 q^{91} + q^{92} + 7 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 + 6 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 2 * q^13 + 3 * q^14 - q^16 + 2 * q^17 + q^19 + 2 * q^20 - q^22 + q^23 - q^25 - 4 * q^26 - 3 * q^28 + 8 * q^31 + q^32 - 2 * q^34 - 3 * q^35 + 18 * q^37 - 7 * q^38 + q^40 + q^41 + 10 * q^43 + q^44 + 2 * q^46 + 4 * q^49 - 2 * q^50 - 2 * q^52 + 3 * q^53 + q^55 - 6 * q^56 + 12 * q^59 + 2 * q^61 + 4 * q^62 + 2 * q^64 + 4 * q^65 + 2 * q^67 - 4 * q^68 + 3 * q^70 + 8 * q^71 + 12 * q^73 + 9 * q^74 - 8 * q^76 - 6 * q^77 - 14 * q^79 - q^80 - q^82 - 12 * q^83 + 2 * q^85 - 10 * q^86 + 2 * q^88 - 5 * q^89 - 6 * q^91 + q^92 + 7 * q^95 - 8 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

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Database

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