LMFDB - Embedded newform 208.2.i.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(81,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, 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("208.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.i (of order $3$, degree $2$, not 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:	$1.66088836204$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	208.81
Dual form			208.2.i.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{3} -3.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.50000 + 0.866025i) q^{13} +(3.00000 + 5.19615i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +8.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} -4.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} -2.00000 q^{31} +(6.00000 - 10.3923i) q^{35} +(3.50000 + 6.06218i) q^{37} +(5.00000 + 5.19615i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(1.50000 - 2.59808i) q^{45} +6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +6.00000 q^{51} +9.00000 q^{53} -4.00000 q^{57} +(-2.50000 + 4.33013i) q^{61} +(-2.00000 - 3.46410i) q^{63} +(10.5000 - 2.59808i) q^{65} +(1.00000 + 1.73205i) q^{67} +(-6.00000 + 10.3923i) q^{69} +(-3.00000 + 5.19615i) q^{71} -1.00000 q^{73} +(-4.00000 - 6.92820i) q^{75} +4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} +(4.50000 - 7.79423i) q^{85} +(-9.00000 + 15.5885i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(4.00000 - 13.8564i) q^{91} +(2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 6 q^{5} - 4 q^{7} - q^{9} - 7 q^{13} + 6 q^{15} - 3 q^{17} + 2 q^{19} + 16 q^{21} - 6 q^{23} + 8 q^{25} - 8 q^{27} - 9 q^{29} - 4 q^{31} + 12 q^{35} + 7 q^{37} + 10 q^{39} - 3 q^{41} - 4 q^{43}+ \cdots - 14 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 6 * q^5 - 4 * q^7 - q^9 - 7 * q^13 + 6 * q^15 - 3 * q^17 + 2 * q^19 + 16 * q^21 - 6 * q^23 + 8 * q^25 - 8 * q^27 - 9 * q^29 - 4 * q^31 + 12 * q^35 + 7 * q^37 + 10 * q^39 - 3 * q^41 - 4 * q^43 + 3 * q^45 + 12 * q^47 - 9 * q^49 + 12 * q^51 + 18 * q^53 - 8 * q^57 - 5 * q^61 - 4 * q^63 + 21 * q^65 + 2 * q^67 - 12 * q^69 - 6 * q^71 - 2 * q^73 - 8 * q^75 + 8 * q^79 + 11 * q^81 - 24 * q^83 + 9 * q^85 - 18 * q^87 - 6 * q^89 + 8 * q^91 + 4 * q^93 - 6 * q^95 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$		0			0
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$		0			0
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$	8.00000			1.74574
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.00000	−	10.3923i	1.01419	−	1.75662i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	5.00000	+	5.19615i	0.800641	+	0.832050i
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$		0			0
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$		0			0
$51$	6.00000			0.840168
$52$		0			0
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$		0			0
$65$	10.5000	−	2.59808i	1.30236	−	0.322252i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$	−6.00000	+	10.3923i	−0.722315	+	1.25109i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$		0			0
$75$	−4.00000	−	6.92820i	−0.461880	−	0.800000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$		0			0
$87$	−9.00000	+	15.5885i	−0.964901	+	1.67126i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	4.00000	−	13.8564i	0.419314	−	1.45255i
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	−2.00000			−0.197066			−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000			−0.197066			−0.0985329	+	0.995134i	$0.531415\pi$
$104$		0			0
$105$	−24.0000			−2.34216
$106$		0			0
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	7.00000	−	12.1244i	0.664411	−	1.15079i
$112$		0			0
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$		0			0
$117$	1.00000	−	3.46410i	0.0924500	−	0.320256i
$118$		0			0
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	0.554281	−	0.832330i	$-0.312993\pi$
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	−0.997959	+	0.0638564i	$0.979660\pi$
$128$		0			0
$129$	8.00000			0.704361
$130$		0			0
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$		0			0
$135$	12.0000			1.03280
$136$		0			0
$137$	−7.50000	+	12.9904i	−0.640768	+	1.10984i	0.344493	+	0.938789i	$0.388051\pi$
$137$	−7.50000	+	12.9904i	−0.640768	+	1.10984i	−0.985262	+	0.171054i	$0.945283\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	13.5000	+	23.3827i	1.12111	+	1.94183i
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$		0			0
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$		0			0
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$		0			0
$161$	24.0000			1.89146
$162$		0			0
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.0000	−	20.7846i	−0.928588	−	1.60836i	−0.785687	−	0.618624i	$-0.787690\pi$
$167$	−12.0000	−	20.7846i	−0.928588	−	1.60836i	−0.142901	−	0.989737i	$-0.545643\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$		0			0
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−8.00000	+	13.8564i	−0.604743	+	1.04745i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	8.00000	−	13.8564i	0.581914	−	1.00791i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$		0			0
$195$	−15.0000	−	15.5885i	−1.07417	−	1.11631i
$196$		0			0
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$		0			0
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.124521	−	0.992217i	$-0.460261\pi$
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.797025	−	0.603947i	$-0.206406\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$		0			0
$203$	36.0000			2.52670
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	0.898392	−	0.439194i	$-0.144736\pi$
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	−0.829549	+	0.558433i	$0.811403\pi$
$212$		0			0
$213$	12.0000			0.822226
$214$		0			0
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$		0			0
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$		0			0
$221$	3.00000	−	10.3923i	0.201802	−	0.699062i
$222$		0			0
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.861435	+	0.507869i	$0.169566\pi$
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.00910984	+	0.999959i	$0.497100\pi$
$224$		0			0
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$		0			0
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$		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			0
$231$		0			0
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		0			0
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$		0			0
$245$	13.5000	+	23.3827i	0.862483	+	1.49387i
$246$		0			0
$247$	−2.00000	+	6.92820i	−0.127257	+	0.440831i
$248$		0			0
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$		0			0
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−18.0000			−1.12720
$256$		0			0
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$		0			0
$259$	−28.0000			−1.73984
$260$		0			0
$261$	9.00000			0.557086
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	−27.0000			−1.65860
$266$		0			0
$267$	−6.00000	+	10.3923i	−0.367194	+	0.635999i
$268$		0			0
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.107031	+	0.994256i	$0.534134\pi$
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.807535	+	0.589819i	$0.799199\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$	−28.0000	+	6.92820i	−1.69464	+	0.419314i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		0			0
$279$	1.00000	−	1.73205i	0.0598684	−	0.103695i
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$		0			0
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	0.524057	−	0.851683i	$-0.324418\pi$
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	−0.999608	+	0.0280052i	$0.991084\pi$
$284$		0			0
$285$	12.0000			0.710819
$286$		0			0
$287$	12.0000			0.708338
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	28.0000			1.64139
$292$		0			0
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15.0000	+	15.5885i	0.867472	+	0.901504i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$		0			0
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$		0			0
$305$	7.50000	−	12.9904i	0.429449	−	0.743827i
$306$		0			0
$307$	−26.0000			−1.48390			−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000			−1.48390			−0.741949	+	0.670456i	$0.766098\pi$
$308$		0			0
$309$	2.00000	+	3.46410i	0.113776	+	0.197066i
$310$		0			0
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	6.00000	+	10.3923i	0.338062	+	0.585540i
$316$		0			0
$317$	−15.0000			−0.842484			−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000			−0.842484			−0.421242	+	0.906948i	$0.638406\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	3.00000	+	5.19615i	0.166924	+	0.289122i
$324$		0			0
$325$	−14.0000	+	3.46410i	−0.776580	+	0.192154i
$326$		0			0
$327$	10.0000	+	17.3205i	0.553001	+	0.957826i
$328$		0			0
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.851957	−	0.523612i	$-0.175416\pi$
$332$		0			0
$333$	−7.00000			−0.383598
$334$		0			0
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$		0			0
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$		0			0
$339$	−18.0000			−0.977626
$340$		0			0
$341$		0			0
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$	18.0000	−	31.1769i	0.969087	−	1.67851i
$346$		0			0
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	−0.516667	−	0.856186i	$-0.672828\pi$
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	0.999813	+	0.0193540i	$0.00616095\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$	14.0000	−	3.46410i	0.747265	−	0.184900i
$352$		0			0
$353$	−13.5000	−	23.3827i	−0.718532	−	1.24453i	−0.961581	−	0.274521i	$-0.911481\pi$
$353$	−13.5000	−	23.3827i	−0.718532	−	1.24453i	0.243049	−	0.970014i	$-0.421853\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$		0			0
$357$	−12.0000	+	20.7846i	−0.635107	+	1.10004i
$358$		0			0
$359$	−36.0000			−1.90001			−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000			−1.90001			−0.950004	+	0.312239i	$0.898921\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−22.0000			−1.15470
$364$		0			0
$365$	3.00000			0.157027
$366$		0			0
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$		0			0
$369$	3.00000			0.156174
$370$		0			0
$371$	−18.0000	+	31.1769i	−0.934513	+	1.61862i
$372$		0			0
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	−0.761074	−	0.648665i	$-0.775328\pi$
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	0.942297	+	0.334777i	$0.108661\pi$
$374$		0			0
$375$	−3.00000	−	5.19615i	−0.154919	−	0.268328i
$376$		0			0
$377$	22.5000	+	23.3827i	1.15881	+	1.20427i
$378$		0			0
$379$	−5.00000	−	8.66025i	−0.256833	−	0.444847i	0.708559	−	0.705652i	$-0.249346\pi$
$379$	−5.00000	−	8.66025i	−0.256833	−	0.444847i	−0.965392	+	0.260804i	$0.916012\pi$
$380$		0			0
$381$	−10.0000	+	17.3205i	−0.512316	+	0.887357i
$382$		0			0
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$		0			0
$389$	21.0000			1.06474			0.532371	−	0.846511i	$-0.321301\pi$
$389$	21.0000			1.06474			0.532371	+	0.846511i	$0.321301\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$	−12.0000			−0.603786
$396$		0			0
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	−0.712843	−	0.701324i	$-0.752593\pi$
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	0.963786	+	0.266678i	$0.0859261\pi$
$398$		0			0
$399$	8.00000	−	13.8564i	0.400501	−	0.693688i
$400$		0			0
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	0.902703	+	0.430263i	$0.141579\pi$
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	−0.0787327	+	0.996896i	$0.525087\pi$
$402$		0			0
$403$	7.00000	−	1.73205i	0.348695	−	0.0862796i
$404$		0			0
$405$	−16.5000	−	28.5788i	−0.819892	−	1.42009i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	30.0000			1.47979
$412$		0			0
$413$		0			0
$414$		0			0
$415$	36.0000			1.76717
$416$		0			0
$417$	32.0000			1.56705
$418$		0			0
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	0.955683	+	0.294398i	$0.0951193\pi$
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	−0.222885	+	0.974845i	$0.571547\pi$
$420$		0			0
$421$	5.00000			0.243685			0.121843	−	0.992549i	$-0.461120\pi$
$421$	5.00000			0.243685			0.121843	+	0.992549i	$0.461120\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	−10.0000	−	17.3205i	−0.483934	−	0.838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	−0.853761	−	0.520665i	$-0.825684\pi$
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	0.877790	+	0.479046i	$0.159017\pi$
$434$		0			0
$435$	27.0000	−	46.7654i	1.29455	−	2.24223i
$436$		0			0
$437$	−12.0000			−0.574038
$438$		0			0
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	0.940963	+	0.338508i	$0.109922\pi$
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	−0.177325	+	0.984152i	$0.556744\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$	18.0000			0.851371
$448$		0			0
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	−0.965637	+	0.259895i	$0.916312\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$		0			0
$455$	−12.0000	+	41.5692i	−0.562569	+	1.94880i
$456$		0			0
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	−0.999014	−	0.0443868i	$-0.985867\pi$
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	0.461067	−	0.887365i	$-0.347467\pi$
$458$		0			0
$459$	6.00000	−	10.3923i	0.280056	−	0.485071i
$460$		0			0
$461$	19.5000	−	33.7750i	0.908206	−	1.57306i	0.0916500	−	0.995791i	$-0.470786\pi$
$461$	19.5000	−	33.7750i	0.908206	−	1.57306i	0.816556	−	0.577267i	$-0.195881\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$		0			0
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$		0			0
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−8.00000			−0.369406
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$		0			0
$477$	−4.50000	+	7.79423i	−0.206041	+	0.356873i
$478$		0			0
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	−17.5000	−	18.1865i	−0.797931	−	0.829235i
$482$		0			0
$483$	−24.0000	−	41.5692i	−1.09204	−	1.89146i
$484$		0			0
$485$	21.0000	−	36.3731i	0.953561	−	1.65162i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$		0			0
$491$	−12.0000	−	20.7846i	−0.541552	−	0.937996i	−0.998815	−	0.0486647i	$-0.984503\pi$
$491$	−12.0000	−	20.7846i	−0.541552	−	0.937996i	0.457263	−	0.889332i	$-0.348830\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$		0			0
$501$	−24.0000	+	41.5692i	−1.07224	+	1.85718i
$502$		0			0
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	−0.700696	−	0.713460i	$-0.747127\pi$
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	0.968223	+	0.250090i	$0.0804603\pi$
$504$		0			0
$505$	13.5000	+	23.3827i	0.600742	+	1.04052i
$506$		0			0
$507$	−22.0000	−	13.8564i	−0.977054	−	0.615385i
$508$		0			0
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		0			0
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$		0			0
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$		0			0
$515$	6.00000			0.264392
$516$		0			0
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$		0			0
$525$	32.0000			1.39659
$526$		0			0
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.50000	+	7.79423i	0.324861	+	0.337606i
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$		0			0
$537$	24.0000	−	41.5692i	1.03568	−	1.79384i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.0000			−0.816874			−0.408437	−	0.912787i	$-0.633926\pi$
$541$	−19.0000			−0.816874			−0.408437	+	0.912787i	$0.633926\pi$
$542$		0			0
$543$	7.00000	+	12.1244i	0.300399	+	0.520306i
$544$		0			0
$545$	30.0000			1.28506
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$		0			0
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$		0			0
$551$	−18.0000			−0.766826
$552$		0			0
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$		0			0
$555$	−21.0000	+	36.3731i	−0.891400	+	1.54395i
$556$		0			0
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$		0			0
$559$	4.00000	−	13.8564i	0.169182	−	0.586064i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$		0			0
$567$	−44.0000			−1.84783
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$	−11.0000	+	19.0526i	−0.457144	+	0.791797i
$580$		0			0
$581$	24.0000	−	41.5692i	0.995688	−	1.72458i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−3.00000	+	10.3923i	−0.124035	+	0.429669i
$586$		0			0
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$	−6.00000	+	10.3923i	−0.246807	+	0.427482i
$592$		0			0
$593$	−9.00000			−0.369586			−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000			−0.369586			−0.184793	+	0.982777i	$0.559161\pi$
$594$		0			0
$595$	18.0000	+	31.1769i	0.737928	+	1.27813i
$596$		0			0
$597$	−52.0000			−2.12822
$598$		0			0
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	0.876043	−	0.482233i	$-0.160174\pi$
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	−0.855648	+	0.517559i	$0.826841\pi$
$602$		0			0
$603$	−2.00000			−0.0814463
$604$		0			0
$605$	−16.5000	+	28.5788i	−0.670820	+	1.16190i
$606$		0			0
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	−0.998154	−	0.0607380i	$-0.980655\pi$
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	0.551678	+	0.834058i	$0.313988\pi$
$608$		0			0
$609$	−36.0000	−	62.3538i	−1.45879	−	2.52670i
$610$		0			0
$611$	−21.0000	+	5.19615i	−0.849569	+	0.210214i
$612$		0			0
$613$	9.50000	+	16.4545i	0.383701	+	0.664590i	0.991588	−	0.129433i	$-0.0413159\pi$
$613$	9.50000	+	16.4545i	0.383701	+	0.664590i	−0.607887	+	0.794024i	$0.707983\pi$
$614$		0			0
$615$	9.00000	−	15.5885i	0.362915	−	0.628587i
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	12.0000	+	20.7846i	0.481543	+	0.834058i
$622$		0			0
$623$	24.0000			0.961540
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	−14.0000	+	24.2487i	−0.557331	+	0.965326i	0.440387	+	0.897808i	$0.354841\pi$
$631$	−14.0000	+	24.2487i	−0.557331	+	0.965326i	−0.997718	+	0.0675178i	$0.978492\pi$
$632$		0			0
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$		0			0
$635$	15.0000	+	25.9808i	0.595257	+	1.03102i
$636$		0			0
$637$	22.5000	+	23.3827i	0.891482	+	0.926456i
$638$		0			0
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	−0.975271	−	0.221013i	$-0.929064\pi$
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	0.679039	+	0.734103i	$0.262397\pi$
$642$		0			0
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	−0.979541	−	0.201243i	$-0.935502\pi$
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	0.664052	+	0.747686i	$0.268835\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$		0			0
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−16.0000			−0.627089
$652$		0			0
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$		0			0
$655$	18.0000			0.703318
$656$		0			0
$657$	0.500000	−	0.866025i	0.0195069	−	0.0337869i
$658$		0			0
$659$	−6.00000	+	10.3923i	−0.233727	+	0.404827i	−0.958902	−	0.283738i	$-0.908425\pi$
$659$	−6.00000	+	10.3923i	−0.233727	+	0.404827i	0.725175	+	0.688565i	$0.241759\pi$
$660$		0			0
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	0.926030	−	0.377450i	$-0.123199\pi$
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	−0.789896	+	0.613241i	$0.789865\pi$
$662$		0			0
$663$	−21.0000	+	5.19615i	−0.815572	+	0.201802i
$664$		0			0
$665$	−12.0000	−	20.7846i	−0.465340	−	0.805993i
$666$		0			0
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$		0			0
$669$	26.0000	−	45.0333i	1.00522	−	1.74109i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	6.50000	+	11.2583i	0.250557	+	0.433977i	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	6.50000	+	11.2583i	0.250557	+	0.433977i	−0.713123	+	0.701039i	$0.752720\pi$
$674$		0			0
$675$	−16.0000			−0.615840
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	−28.0000	−	48.4974i	−1.07454	−	1.86116i
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	−0.917697	−	0.397282i	$-0.869953\pi$
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	0.802905	+	0.596107i	$0.203287\pi$
$684$		0			0
$685$	22.5000	−	38.9711i	0.859681	−	1.48901i
$686$		0			0
$687$	−14.0000	−	24.2487i	−0.534133	−	0.925146i
$688$		0			0
$689$	−31.5000	+	7.79423i	−1.20005	+	0.296936i
$690$		0			0
$691$	−20.0000	−	34.6410i	−0.760836	−	1.31781i	−0.942420	−	0.334431i	$-0.891456\pi$
$691$	−20.0000	−	34.6410i	−0.760836	−	1.31781i	0.181584	−	0.983375i	$-0.441877\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	24.0000	−	41.5692i	0.910372	−	1.57681i
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	18.0000	+	31.1769i	0.680823	+	1.17922i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$	18.0000	+	31.1769i	0.677919	+	1.17419i
$706$		0			0
$707$	36.0000			1.35392
$708$		0			0
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$		0			0
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$		0			0
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.0000	+	41.5692i	0.896296	+	1.55243i
$718$		0			0
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	−0.732185	−	0.681106i	$-0.761499\pi$
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	0.955947	+	0.293538i	$0.0948328\pi$
$720$		0			0
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$		0			0
$723$	−2.00000			−0.0743808
$724$		0			0
$725$	−18.0000	−	31.1769i	−0.668503	−	1.15788i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	29.0000			1.07114			0.535570	−	0.844491i	$-0.320097\pi$
$733$	29.0000			1.07114			0.535570	+	0.844491i	$0.320097\pi$
$734$		0			0
$735$	27.0000	−	46.7654i	0.995910	−	1.72497i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	0.989230	−	0.146369i	$-0.0467586\pi$
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	−0.621374	+	0.783514i	$0.713425\pi$
$740$		0			0
$741$	14.0000	−	3.46410i	0.514303	−	0.127257i
$742$		0			0
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	0.557470	−	0.830197i	$-0.311772\pi$
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	−0.997707	+	0.0676840i	$0.978439\pi$
$744$		0			0
$745$	13.5000	−	23.3827i	0.494602	−	0.856675i
$746$		0			0
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$	−24.0000			−0.876941
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$	12.0000			0.437304
$754$		0			0
$755$	−30.0000			−1.09181
$756$		0			0
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	−0.655515	−	0.755182i	$-0.727548\pi$
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	0.981764	+	0.190101i	$0.0608816\pi$
$762$		0			0
$763$	20.0000	−	34.6410i	0.724049	−	1.25409i
$764$		0			0
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$		0			0
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$		0			0
$775$	−8.00000			−0.287368
$776$		0			0
$777$	28.0000	+	48.4974i	1.00449	+	1.73984i
$778$		0			0
$779$	−6.00000			−0.214972
$780$		0			0
$781$		0			0
$782$		0			0
$783$	18.0000	+	31.1769i	0.643268	+	1.11417i
$784$		0			0
$785$	21.0000			0.749522
$786$		0			0
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	−0.298521	−	0.954403i	$-0.596493\pi$
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	0.975798	−	0.218675i	$-0.0701734\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.0000	+	31.1769i	0.640006	+	1.10852i
$792$		0			0
$793$	5.00000	−	17.3205i	0.177555	−	0.615069i
$794$		0			0
$795$	27.0000	+	46.7654i	0.957591	+	1.65860i
$796$		0			0
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	−0.661441	−	0.749997i	$-0.730055\pi$
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	0.980237	+	0.197826i	$0.0633881\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$		0			0
$801$	6.00000			0.212000
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−72.0000			−2.53767
$806$		0			0
$807$	60.0000			2.11210
$808$		0			0
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	0.703533	−	0.710663i	$-0.251605\pi$
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	−0.967219	+	0.253946i	$0.918272\pi$
$810$		0			0
$811$	10.0000			0.351147			0.175574	−	0.984466i	$-0.443822\pi$
$811$	10.0000			0.351147			0.175574	+	0.984466i	$0.443822\pi$
$812$		0			0
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$		0			0
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$		0			0
$819$	10.0000	+	10.3923i	0.349428	+	0.363137i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	0.982501	−	0.186256i	$-0.0596352\pi$
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	−0.652553	+	0.757743i	$0.726302\pi$
$830$		0			0
$831$	−38.0000			−1.31821
$832$		0			0
$833$	27.0000			0.935495
$834$		0			0
$835$	36.0000	+	62.3538i	1.24583	+	2.15784i
$836$		0			0
$837$	8.00000			0.276520
$838$		0			0
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	−0.233973	−	0.972243i	$-0.575173\pi$
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	0.958974	−	0.283495i	$-0.0914938\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$		0			0
$845$	−34.5000	+	18.1865i	−1.18684	+	0.625636i
$846$		0			0
$847$	22.0000	+	38.1051i	0.755929	+	1.30931i
$848$		0			0
$849$	−16.0000	+	27.7128i	−0.549119	+	0.951101i
$850$		0			0
$851$	21.0000	−	36.3731i	0.719871	−	1.24685i
$852$		0			0
$853$	5.00000			0.171197			0.0855984	−	0.996330i	$-0.472720\pi$
$853$	5.00000			0.171197			0.0855984	+	0.996330i	$0.472720\pi$
$854$		0			0
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$		0			0
$857$	3.00000			0.102478			0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000			0.102478			0.0512390	+	0.998686i	$0.483683\pi$
$858$		0			0
$859$	−2.00000			−0.0682391			−0.0341196	−	0.999418i	$-0.510863\pi$
$859$	−2.00000			−0.0682391			−0.0341196	+	0.999418i	$0.510863\pi$
$860$		0			0
$861$	−12.0000	−	20.7846i	−0.408959	−	0.708338i
$862$		0			0
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−5.00000	−	5.19615i	−0.169419	−	0.176065i
$872$		0			0
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$		0			0
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		0			0
$877$	−2.50000	+	4.33013i	−0.0844190	+	0.146218i	−0.905143	−	0.425106i	$-0.860237\pi$
$877$	−2.50000	+	4.33013i	−0.0844190	+	0.146218i	0.820724	+	0.571324i	$0.193570\pi$
$878$		0			0
$879$	18.0000			0.607125
$880$		0			0
$881$	−25.5000	−	44.1673i	−0.859117	−	1.48803i	−0.872772	−	0.488127i	$-0.837680\pi$
$881$	−25.5000	−	44.1673i	−0.859117	−	1.48803i	0.0136556	−	0.999907i	$-0.495653\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$		0			0
$889$	40.0000			1.34156
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	−36.0000	−	62.3538i	−1.20335	−	2.08426i
$896$		0			0
$897$	12.0000	−	41.5692i	0.400668	−	1.38796i
$898$		0			0
$899$	9.00000	+	15.5885i	0.300167	+	0.519904i
$900$		0			0
$901$	−13.5000	+	23.3827i	−0.449750	+	0.778990i
$902$		0			0
$903$	−16.0000	+	27.7128i	−0.532447	+	0.922225i
$904$		0			0
$905$	21.0000			0.698064
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$		0			0
$909$	9.00000			0.298511
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−30.0000			−0.991769
$916$		0			0
$917$	12.0000	−	20.7846i	0.396275	−	0.686368i
$918$		0			0
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	−0.361447	−	0.932393i	$-0.617717\pi$
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	0.988199	−	0.153174i	$-0.0489495\pi$
$920$		0			0
$921$	26.0000	+	45.0333i	0.856729	+	1.48390i
$922$		0			0
$923$	6.00000	−	20.7846i	0.197492	−	0.684134i
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$		0			0
$927$	1.00000	−	1.73205i	0.0328443	−	0.0568880i
$928$		0			0
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$		0			0
$933$	6.00000	+	10.3923i	0.196431	+	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	47.0000			1.53542			0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000			1.53542			0.767712	+	0.640796i	$0.221395\pi$
$938$		0			0
$939$	−14.0000	−	24.2487i	−0.456873	−	0.791327i
$940$		0			0
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$		0			0
$945$	−24.0000	+	41.5692i	−0.780720	+	1.35225i
$946$		0			0
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$	3.50000	−	0.866025i	0.113615	−	0.0281124i
$950$		0			0
$951$	15.0000	+	25.9808i	0.486408	+	0.842484i
$952$		0			0
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$		0			0
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−30.0000	−	51.9615i	−0.968751	−	1.67793i
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$	−6.00000			−0.193347
$964$		0			0
$965$	16.5000	+	28.5788i	0.531154	+	0.919985i
$966$		0			0
$967$	58.0000			1.86515			0.932577	−	0.360971i	$-0.117555\pi$
$967$	58.0000			1.86515			0.932577	+	0.360971i	$0.117555\pi$
$968$		0			0
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$		0			0
$971$	15.0000	−	25.9808i	0.481373	−	0.833762i	−0.518399	−	0.855139i	$-0.673472\pi$
$971$	15.0000	−	25.9808i	0.481373	−	0.833762i	0.999771	+	0.0213768i	$0.00680496\pi$
$972$		0			0
$973$	−32.0000	−	55.4256i	−1.02587	−	1.77686i
$974$		0			0
$975$	20.0000	+	20.7846i	0.640513	+	0.665640i
$976$		0			0
$977$	−19.5000	−	33.7750i	−0.623860	−	1.08056i	−0.988760	−	0.149511i	$-0.952230\pi$
$977$	−19.5000	−	33.7750i	−0.623860	−	1.08056i	0.364900	−	0.931047i	$-0.381103\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$		0			0
$983$	6.00000			0.191370			0.0956851	−	0.995412i	$-0.469496\pi$
$983$	6.00000			0.191370			0.0956851	+	0.995412i	$0.469496\pi$
$984$		0			0
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$		0			0
$987$	48.0000			1.52786
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	0.881471	−	0.472237i	$-0.156554\pi$
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	−0.849705	+	0.527258i	$0.823220\pi$
$992$		0			0
$993$	−64.0000			−2.03098
$994$		0			0
$995$	−39.0000	+	67.5500i	−1.23638	+	2.14148i
$996$		0			0
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	−0.902895	−	0.429862i	$-0.858562\pi$
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	0.823719	+	0.566999i	$0.191896\pi$
$998$		0			0
$999$	−14.0000	−	24.2487i	−0.442940	−	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.i.a.81.1		2
3.2	odd	2		1872.2.t.m.289.1		2
4.3	odd	2		52.2.e.b.29.1	yes	2
8.3	odd	2		832.2.i.c.705.1		2
8.5	even	2		832.2.i.i.705.1		2
12.11	even	2		468.2.l.d.289.1		2
13.2	odd	12		2704.2.f.i.337.2		2
13.3	even	3		2704.2.a.l.1.1		1
13.9	even	3	inner	208.2.i.a.113.1		2
13.10	even	6		2704.2.a.m.1.1		1
13.11	odd	12		2704.2.f.i.337.1		2
20.3	even	4		1300.2.bb.d.549.1		4
20.7	even	4		1300.2.bb.d.549.2		4
20.19	odd	2		1300.2.i.b.601.1		2
28.3	even	6		2548.2.i.b.1745.1		2
28.11	odd	6		2548.2.i.g.1745.1		2
28.19	even	6		2548.2.l.g.1537.1		2
28.23	odd	6		2548.2.l.b.1537.1		2
28.27	even	2		2548.2.k.a.393.1		2
39.35	odd	6		1872.2.t.m.1153.1		2
52.3	odd	6		676.2.a.a.1.1		1
52.7	even	12		676.2.h.d.485.1		4
52.11	even	12		676.2.d.a.337.1		2
52.15	even	12		676.2.d.a.337.2		2
52.19	even	12		676.2.h.d.485.2		4
52.23	odd	6		676.2.a.b.1.1		1
52.31	even	4		676.2.h.d.361.2		4
52.35	odd	6		52.2.e.b.9.1	✓	2
52.43	odd	6		676.2.e.d.529.1		2
52.47	even	4		676.2.h.d.361.1		4
52.51	odd	2		676.2.e.d.653.1		2
104.35	odd	6		832.2.i.c.321.1		2
104.61	even	6		832.2.i.i.321.1		2
156.11	odd	12		6084.2.b.k.4393.2		2
156.23	even	6		6084.2.a.c.1.1		1
156.35	even	6		468.2.l.d.217.1		2
156.107	even	6		6084.2.a.o.1.1		1
156.119	odd	12		6084.2.b.k.4393.1		2
260.87	even	12		1300.2.bb.d.1049.1		4
260.139	odd	6		1300.2.i.b.1101.1		2
260.243	even	12		1300.2.bb.d.1049.2		4
364.87	even	6		2548.2.l.g.373.1		2
364.139	even	6		2548.2.k.a.1569.1		2
364.191	odd	6		2548.2.i.g.165.1		2
364.243	even	6		2548.2.i.b.165.1		2
364.347	odd	6		2548.2.l.b.373.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.b.9.1	✓	2	52.35	odd	6
52.2.e.b.29.1	yes	2	4.3	odd	2
208.2.i.a.81.1		2	1.1	even	1	trivial
208.2.i.a.113.1		2	13.9	even	3	inner
468.2.l.d.217.1		2	156.35	even	6
468.2.l.d.289.1		2	12.11	even	2
676.2.a.a.1.1		1	52.3	odd	6
676.2.a.b.1.1		1	52.23	odd	6
676.2.d.a.337.1		2	52.11	even	12
676.2.d.a.337.2		2	52.15	even	12
676.2.e.d.529.1		2	52.43	odd	6
676.2.e.d.653.1		2	52.51	odd	2
676.2.h.d.361.1		4	52.47	even	4
676.2.h.d.361.2		4	52.31	even	4
676.2.h.d.485.1		4	52.7	even	12
676.2.h.d.485.2		4	52.19	even	12
832.2.i.c.321.1		2	104.35	odd	6
832.2.i.c.705.1		2	8.3	odd	2
832.2.i.i.321.1		2	104.61	even	6
832.2.i.i.705.1		2	8.5	even	2
1300.2.i.b.601.1		2	20.19	odd	2
1300.2.i.b.1101.1		2	260.139	odd	6
1300.2.bb.d.549.1		4	20.3	even	4
1300.2.bb.d.549.2		4	20.7	even	4
1300.2.bb.d.1049.1		4	260.87	even	12
1300.2.bb.d.1049.2		4	260.243	even	12
1872.2.t.m.289.1		2	3.2	odd	2
1872.2.t.m.1153.1		2	39.35	odd	6
2548.2.i.b.165.1		2	364.243	even	6
2548.2.i.b.1745.1		2	28.3	even	6
2548.2.i.g.165.1		2	364.191	odd	6
2548.2.i.g.1745.1		2	28.11	odd	6
2548.2.k.a.393.1		2	28.27	even	2
2548.2.k.a.1569.1		2	364.139	even	6
2548.2.l.b.373.1		2	364.347	odd	6
2548.2.l.b.1537.1		2	28.23	odd	6
2548.2.l.g.373.1		2	364.87	even	6
2548.2.l.g.1537.1		2	28.19	even	6
2704.2.a.l.1.1		1	13.3	even	3
2704.2.a.m.1.1		1	13.10	even	6
2704.2.f.i.337.1		2	13.11	odd	12
2704.2.f.i.337.2		2	13.2	odd	12
6084.2.a.c.1.1		1	156.23	even	6
6084.2.a.o.1.1		1	156.107	even	6
6084.2.b.k.4393.1		2	156.119	odd	12
6084.2.b.k.4393.2		2	156.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} -3.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.50000 + 0.866025i) q^{13} +(3.00000 + 5.19615i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +8.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} -4.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} -2.00000 q^{31} +(6.00000 - 10.3923i) q^{35} +(3.50000 + 6.06218i) q^{37} +(5.00000 + 5.19615i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(1.50000 - 2.59808i) q^{45} +6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +6.00000 q^{51} +9.00000 q^{53} -4.00000 q^{57} +(-2.50000 + 4.33013i) q^{61} +(-2.00000 - 3.46410i) q^{63} +(10.5000 - 2.59808i) q^{65} +(1.00000 + 1.73205i) q^{67} +(-6.00000 + 10.3923i) q^{69} +(-3.00000 + 5.19615i) q^{71} -1.00000 q^{73} +(-4.00000 - 6.92820i) q^{75} +4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} +(4.50000 - 7.79423i) q^{85} +(-9.00000 + 15.5885i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(4.00000 - 13.8564i) q^{91} +(2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 6 q^{5} - 4 q^{7} - q^{9} - 7 q^{13} + 6 q^{15} - 3 q^{17} + 2 q^{19} + 16 q^{21} - 6 q^{23} + 8 q^{25} - 8 q^{27} - 9 q^{29} - 4 q^{31} + 12 q^{35} + 7 q^{37} + 10 q^{39} - 3 q^{41} - 4 q^{43}+ \cdots - 14 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 6 * q^5 - 4 * q^7 - q^9 - 7 * q^13 + 6 * q^15 - 3 * q^17 + 2 * q^19 + 16 * q^21 - 6 * q^23 + 8 * q^25 - 8 * q^27 - 9 * q^29 - 4 * q^31 + 12 * q^35 + 7 * q^37 + 10 * q^39 - 3 * q^41 - 4 * q^43 + 3 * q^45 + 12 * q^47 - 9 * q^49 + 12 * q^51 + 18 * q^53 - 8 * q^57 - 5 * q^61 - 4 * q^63 + 21 * q^65 + 2 * q^67 - 12 * q^69 - 6 * q^71 - 2 * q^73 - 8 * q^75 + 8 * q^79 + 11 * q^81 - 24 * q^83 + 9 * q^85 - 18 * q^87 - 6 * q^89 + 8 * q^91 + 4 * q^93 - 6 * q^95 - 14 * q^97

Introduction

L-functions

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