LMFDB - Embedded newform 1344.2.q.r.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(193,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1344.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.q (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:	$10.7318940317$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1344.193
Dual form			1344.2.q.r.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{15} +(4.00000 - 6.92820i) q^{17} +(2.00000 + 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.00000 + 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{27} +5.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(0.500000 + 0.866025i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(4.00000 + 6.92820i) q^{37} +4.00000 q^{41} +10.0000 q^{43} +(0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-4.00000 - 6.92820i) q^{51} +(-0.500000 + 0.866025i) q^{53} -1.00000 q^{55} +4.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(2.00000 + 1.73205i) q^{63} +(-1.00000 + 1.73205i) q^{67} +4.00000 q^{69} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(0.500000 - 2.59808i) q^{77} +(-4.50000 - 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} -3.00000 q^{83} +8.00000 q^{85} +(2.50000 - 4.33013i) q^{87} +(3.00000 + 5.19615i) q^{89} +(-3.50000 - 6.06218i) q^{93} +(-2.00000 + 3.46410i) q^{95} -1.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + q^{5} - 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q + q^3 + q^5 - 5 * q^7 - q^9	$ 2 q + q^{3} + q^{5} - 5 q^{7} - q^{9} - q^{11} + 2 q^{15} + 8 q^{17} + 4 q^{19} - q^{21} + 4 q^{23} + 4 q^{25} - 2 q^{27} + 10 q^{29} + 7 q^{31} + q^{33} - 4 q^{35} + 8 q^{37} + 8 q^{41} + 20 q^{43} + q^{45} + 6 q^{47} + 11 q^{49} - 8 q^{51} - q^{53} - 2 q^{55} + 8 q^{57} - 9 q^{59} - 2 q^{61} + 4 q^{63} - 2 q^{67} + 8 q^{69} - 12 q^{71} - 2 q^{73} - 4 q^{75} + q^{77} - 9 q^{79} - q^{81} - 6 q^{83} + 16 q^{85} + 5 q^{87} + 6 q^{89} - 7 q^{93} - 4 q^{95} - 2 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + q^3 + q^5 - 5 * q^7 - q^9 - q^11 + 2 * q^15 + 8 * q^17 + 4 * q^19 - q^21 + 4 * q^23 + 4 * q^25 - 2 * q^27 + 10 * q^29 + 7 * q^31 + q^33 - 4 * q^35 + 8 * q^37 + 8 * q^41 + 20 * q^43 + q^45 + 6 * q^47 + 11 * q^49 - 8 * q^51 - q^53 - 2 * q^55 + 8 * q^57 - 9 * q^59 - 2 * q^61 + 4 * q^63 - 2 * q^67 + 8 * q^69 - 12 * q^71 - 2 * q^73 - 4 * q^75 + q^77 - 9 * q^79 - q^81 - 6 * q^83 + 16 * q^85 + 5 * q^87 + 6 * q^89 - 7 * q^93 - 4 * q^95 - 2 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	4.00000	−	6.92820i	0.970143	−	1.68034i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	4.00000	−	6.92820i	0.970143	−	1.68034i	0.695113	−	0.718900i	$-0.255354\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		0			0
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		0			0
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$		0			0
$35$	−2.00000	−	1.73205i	−0.338062	−	0.292770i
$36$		0			0
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	−4.00000	−	6.92820i	−0.560112	−	0.970143i
$52$		0			0
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$		0			0
$55$	−1.00000			−0.134840
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$	2.00000	+	1.73205i	0.251976	+	0.218218i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$		0			0
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$		0			0
$77$	0.500000	−	2.59808i	0.0569803	−	0.296078i
$78$		0			0
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	−0.999974	−	0.00727784i	$-0.997683\pi$
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	0.493684	−	0.869641i	$-0.335650\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$	8.00000			0.867722
$86$		0			0
$87$	2.50000	−	4.33013i	0.268028	−	0.464238i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.50000	−	6.06218i	−0.362933	−	0.628619i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$		0			0
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$	−2.50000	+	0.866025i	−0.243975	+	0.0845154i
$106$		0			0
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.00000	+	20.7846i	−0.366679	+	1.90532i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	2.00000	−	3.46410i	0.180334	−	0.312348i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$		0			0
$129$	5.00000	−	8.66025i	0.440225	−	0.762493i
$130$		0			0
$131$	9.50000	+	16.4545i	0.830019	+	1.43763i	0.898022	+	0.439950i	$0.145004\pi$
$131$	9.50000	+	16.4545i	0.830019	+	1.43763i	−0.0680035	+	0.997685i	$0.521663\pi$
$132$		0			0
$133$	−8.00000	−	6.92820i	−0.693688	−	0.600751i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$		0			0
$144$		0			0
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$		0			0
$147$	−1.00000	−	6.92820i	−0.0824786	−	0.571429i
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	−0.687741	−	0.725956i	$-0.741398\pi$
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	0.972567	+	0.232623i	$0.0747309\pi$
$152$		0			0
$153$	−8.00000			−0.646762
$154$		0			0
$155$	7.00000			0.562254
$156$		0			0
$157$	10.0000	−	17.3205i	0.798087	−	1.38233i	−0.122774	−	0.992435i	$-0.539179\pi$
$157$	10.0000	−	17.3205i	0.798087	−	1.38233i	0.920860	−	0.389892i	$-0.127488\pi$
$158$		0			0
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$		0			0
$161$	−8.00000	−	6.92820i	−0.630488	−	0.546019i
$162$		0			0
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$		0			0
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$		0			0
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$		0			0
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$		0			0
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$		0			0
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$		0			0
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$		0			0
$185$	−4.00000	+	6.92820i	−0.294086	+	0.509372i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$		0			0
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$		0			0
$201$	1.00000	+	1.73205i	0.0705346	+	0.122169i
$202$		0			0
$203$	−12.5000	+	4.33013i	−0.877328	+	0.303915i
$204$		0			0
$205$	2.00000	+	3.46410i	0.139686	+	0.241943i
$206$		0			0
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$		0			0
$209$	−4.00000			−0.276686
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$		0			0
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	−3.50000	+	18.1865i	−0.237595	+	1.23458i
$218$		0			0
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	−0.958485	−	0.285141i	$-0.907959\pi$
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	0.726182	+	0.687502i	$0.241293\pi$
$228$		0			0
$229$	12.0000	+	20.7846i	0.792982	+	1.37349i	0.924113	+	0.382121i	$0.124806\pi$
$229$	12.0000	+	20.7846i	0.792982	+	1.37349i	−0.131130	+	0.991365i	$0.541861\pi$
$230$		0			0
$231$	−2.00000	−	1.73205i	−0.131590	−	0.113961i
$232$		0			0
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	0.966786	−	0.255586i	$-0.0822686\pi$
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	−0.704737	+	0.709468i	$0.748935\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$	−9.00000			−0.584613
$238$		0			0
$239$	−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
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−1.50000	+	2.59808i	−0.0950586	+	0.164646i
$250$		0			0
$251$	1.00000			0.0631194			0.0315597	−	0.999502i	$-0.489953\pi$
$251$	1.00000			0.0631194			0.0315597	+	0.999502i	$0.489953\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$		0			0
$255$	4.00000	−	6.92820i	0.250490	−	0.433861i
$256$		0			0
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$		0			0
$261$	−2.50000	−	4.33013i	−0.154746	−	0.268028i
$262$		0			0
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$		0			0
$265$	−1.00000			−0.0614295
$266$		0			0
$267$	6.00000			0.367194
$268$		0			0
$269$	−8.50000	+	14.7224i	−0.518254	+	0.897643i	0.481521	+	0.876435i	$0.340085\pi$
$269$	−8.50000	+	14.7224i	−0.518254	+	0.897643i	−0.999775	+	0.0212079i	$0.993249\pi$
$270$		0			0
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	0.983312	−	0.181928i	$-0.0582339\pi$
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	−0.649211	+	0.760609i	$0.724901\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	−12.0000	+	20.7846i	−0.721010	+	1.24883i	0.239585	+	0.970875i	$0.422989\pi$
$277$	−12.0000	+	20.7846i	−0.721010	+	1.24883i	−0.960595	+	0.277951i	$0.910345\pi$
$278$		0			0
$279$	−7.00000			−0.419079
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	3.00000	−	5.19615i	0.178331	−	0.308879i	−0.762978	−	0.646425i	$-0.776263\pi$
$283$	3.00000	−	5.19615i	0.178331	−	0.308879i	0.941309	+	0.337546i	$0.109597\pi$
$284$		0			0
$285$	2.00000	+	3.46410i	0.118470	+	0.205196i
$286$		0			0
$287$	−10.0000	+	3.46410i	−0.590281	+	0.204479i
$288$		0			0
$289$	−23.5000	−	40.7032i	−1.38235	−	2.39431i
$290$		0			0
$291$	−0.500000	+	0.866025i	−0.0293105	+	0.0507673i
$292$		0			0
$293$	−3.00000			−0.175262			−0.0876309	−	0.996153i	$-0.527930\pi$
$293$	−3.00000			−0.175262			−0.0876309	+	0.996153i	$0.527930\pi$
$294$		0			0
$295$	−9.00000			−0.524000
$296$		0			0
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−25.0000	+	8.66025i	−1.44098	+	0.499169i
$302$		0			0
$303$	−1.00000	−	1.73205i	−0.0574485	−	0.0995037i
$304$		0			0
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	14.0000	−	24.2487i	0.793867	−	1.37502i	−0.129689	−	0.991555i	$-0.541398\pi$
$311$	14.0000	−	24.2487i	0.793867	−	1.37502i	0.923556	−	0.383464i	$-0.125269\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$		0			0
$315$	−0.500000	+	2.59808i	−0.0281718	+	0.146385i
$316$		0			0
$317$	−2.50000	−	4.33013i	−0.140414	−	0.243204i	0.787239	−	0.616649i	$-0.211510\pi$
$317$	−2.50000	−	4.33013i	−0.140414	−	0.243204i	−0.927653	+	0.373444i	$0.878177\pi$
$318$		0			0
$319$	−2.50000	+	4.33013i	−0.139973	+	0.242441i
$320$		0			0
$321$	−15.0000			−0.837218
$322$		0			0
$323$	32.0000			1.78053
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.00000	−	8.66025i	−0.276501	−	0.478913i
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$		0			0
$333$	4.00000	−	6.92820i	0.219199	−	0.379663i
$334$		0			0
$335$	−2.00000			−0.109272
$336$		0			0
$337$	1.00000			0.0544735			0.0272367	−	0.999629i	$-0.491329\pi$
$337$	1.00000			0.0544735			0.0272367	+	0.999629i	$0.491329\pi$
$338$		0			0
$339$	2.00000	−	3.46410i	0.108625	−	0.188144i
$340$		0			0
$341$	3.50000	+	6.06218i	0.189536	+	0.328285i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	2.00000	+	3.46410i	0.107676	+	0.186501i
$346$		0			0
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	0.195507	+	0.980702i	$0.437365\pi$
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	−0.947067	+	0.321037i	$0.895969\pi$
$348$		0			0
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$		0			0
$357$	16.0000	+	13.8564i	0.846810	+	0.733359i
$358$		0			0
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$	10.0000			0.524864
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	−1.50000	+	2.59808i	−0.0782994	+	0.135618i	−0.902516	−	0.430656i	$-0.858282\pi$
$367$	−1.50000	+	2.59808i	−0.0782994	+	0.135618i	0.824217	+	0.566274i	$0.191616\pi$
$368$		0			0
$369$	−2.00000	−	3.46410i	−0.104116	−	0.180334i
$370$		0			0
$371$	0.500000	−	2.59808i	0.0259587	−	0.134885i
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		0			0
$375$	4.50000	−	7.79423i	0.232379	−	0.402492i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	−6.50000	+	11.2583i	−0.333005	+	0.576782i
$382$		0			0
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	2.50000	−	0.866025i	0.127412	−	0.0441367i
$386$		0			0
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$		0			0
$389$	−17.0000	+	29.4449i	−0.861934	+	1.49291i	0.00812520	+	0.999967i	$0.497414\pi$
$389$	−17.0000	+	29.4449i	−0.861934	+	1.49291i	−0.870059	+	0.492947i	$0.835920\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$		0			0
$393$	19.0000			0.958423
$394$		0			0
$395$	4.50000	−	7.79423i	0.226420	−	0.392170i
$396$		0			0
$397$	2.00000	+	3.46410i	0.100377	+	0.173858i	0.911840	−	0.410546i	$-0.134662\pi$
$397$	2.00000	+	3.46410i	0.100377	+	0.173858i	−0.811463	+	0.584404i	$0.801328\pi$
$398$		0			0
$399$	−10.0000	+	3.46410i	−0.500626	+	0.173422i
$400$		0			0
$401$	16.0000	+	27.7128i	0.799002	+	1.38391i	0.920267	+	0.391292i	$0.127972\pi$
$401$	16.0000	+	27.7128i	0.799002	+	1.38391i	−0.121265	+	0.992620i	$0.538695\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$		0			0
$411$	9.00000	+	15.5885i	0.443937	+	0.768922i
$412$		0			0
$413$	4.50000	−	23.3827i	0.221431	−	1.15059i
$414$		0			0
$415$	−1.50000	−	2.59808i	−0.0736321	−	0.127535i
$416$		0			0
$417$	5.00000	−	8.66025i	0.244851	−	0.424094i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	−16.0000	−	27.7128i	−0.776114	−	1.34427i
$426$		0			0
$427$	4.00000	+	3.46410i	0.193574	+	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	30.0000			1.44171			0.720854	−	0.693087i	$-0.243750\pi$
$433$	30.0000			1.44171			0.720854	+	0.693087i	$0.243750\pi$
$434$		0			0
$435$	5.00000			0.239732
$436$		0			0
$437$	−8.00000	+	13.8564i	−0.382692	+	0.662842i
$438$		0			0
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	0.998595	−	0.0529862i	$-0.0168739\pi$
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	−0.545185	+	0.838316i	$0.683541\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−14.5000	−	25.1147i	−0.688916	−	1.19324i	−0.972189	−	0.234198i	$-0.924754\pi$
$443$	−14.5000	−	25.1147i	−0.688916	−	1.19324i	0.283273	−	0.959039i	$-0.408580\pi$
$444$		0			0
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$		0			0
$447$	6.00000			0.283790
$448$		0			0
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$		0			0
$451$	−2.00000	+	3.46410i	−0.0941763	+	0.163118i
$452$		0			0
$453$	−3.50000	−	6.06218i	−0.164444	−	0.284826i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.50000	−	12.9904i	−0.350835	−	0.607664i	0.635561	−	0.772051i	$-0.280769\pi$
$457$	−7.50000	−	12.9904i	−0.350835	−	0.607664i	−0.986396	+	0.164386i	$0.947436\pi$
$458$		0			0
$459$	−4.00000	+	6.92820i	−0.186704	+	0.323381i
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$	3.50000	−	6.06218i	0.162309	−	0.281127i
$466$		0			0
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		0			0
$469$	1.00000	−	5.19615i	0.0461757	−	0.239936i
$470$		0			0
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$		0			0
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$		0			0
$475$	16.0000			0.734130
$476$		0			0
$477$	1.00000			0.0457869
$478$		0			0
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−10.0000	+	3.46410i	−0.455016	+	0.157622i
$484$		0			0
$485$	−0.500000	−	0.866025i	−0.0227038	−	0.0393242i
$486$		0			0
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$		0			0
$489$	−20.0000			−0.904431
$490$		0			0
$491$	−27.0000			−1.21849			−0.609246	−	0.792981i	$-0.708528\pi$
$491$	−27.0000			−1.21849			−0.609246	+	0.792981i	$0.708528\pi$
$492$		0			0
$493$	20.0000	−	34.6410i	0.900755	−	1.56015i
$494$		0			0
$495$	0.500000	+	0.866025i	0.0224733	+	0.0389249i
$496$		0			0
$497$	15.0000	−	5.19615i	0.672842	−	0.233079i
$498$		0			0
$499$	−17.0000	−	29.4449i	−0.761025	−	1.31813i	−0.942323	−	0.334705i	$-0.891363\pi$
$499$	−17.0000	−	29.4449i	−0.761025	−	1.31813i	0.181298	−	0.983428i	$-0.441970\pi$
$500$		0			0
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$	−6.50000	+	11.2583i	−0.288675	+	0.500000i
$508$		0			0
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	0.748894	−	0.662690i	$-0.230585\pi$
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	−0.948353	+	0.317217i	$0.897252\pi$
$510$		0			0
$511$	1.00000	−	5.19615i	0.0442374	−	0.229864i
$512$		0			0
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$		0			0
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	−6.00000			−0.263880
$518$		0			0
$519$	−18.0000			−0.790112
$520$		0			0
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$		0			0
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$		0			0
$525$	8.00000	+	6.92820i	0.349149	+	0.302372i
$526$		0			0
$527$	−28.0000	−	48.4974i	−1.21970	−	2.11258i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	9.00000			0.390567
$532$		0			0
$533$		0			0
$534$		0			0
$535$	7.50000	−	12.9904i	0.324253	−	0.561623i
$536$		0			0
$537$	10.0000	+	17.3205i	0.431532	+	0.747435i
$538$		0			0
$539$	1.00000	+	6.92820i	0.0430730	+	0.298419i
$540$		0			0
$541$	11.0000	+	19.0526i	0.472927	+	0.819133i	0.999520	−	0.0309841i	$-0.00986412\pi$
$541$	11.0000	+	19.0526i	0.472927	+	0.819133i	−0.526593	+	0.850118i	$0.676531\pi$
$542$		0			0
$543$	−10.0000	+	17.3205i	−0.429141	+	0.743294i
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	10.0000	+	17.3205i	0.426014	+	0.737878i
$552$		0			0
$553$	18.0000	+	15.5885i	0.765438	+	0.662889i
$554$		0			0
$555$	4.00000	+	6.92820i	0.169791	+	0.294086i
$556$		0			0
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	8.00000			0.337760
$562$		0			0
$563$	−14.5000	+	25.1147i	−0.611102	+	1.05846i	0.379953	+	0.925006i	$0.375940\pi$
$563$	−14.5000	+	25.1147i	−0.611102	+	1.05846i	−0.991055	+	0.133454i	$0.957393\pi$
$564$		0			0
$565$	2.00000	+	3.46410i	0.0841406	+	0.145736i
$566$		0			0
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$		0			0
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	0.963948	−	0.266090i	$-0.0857319\pi$
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	−0.712415	+	0.701758i	$0.752399\pi$
$570$		0			0
$571$	−7.00000	+	12.1244i	−0.292941	+	0.507388i	−0.974504	−	0.224371i	$-0.927967\pi$
$571$	−7.00000	+	12.1244i	−0.292941	+	0.507388i	0.681563	+	0.731760i	$0.261301\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.0000			0.667246
$576$		0			0
$577$	−11.5000	+	19.9186i	−0.478751	+	0.829222i	−0.999703	−	0.0243645i	$-0.992244\pi$
$577$	−11.5000	+	19.9186i	−0.478751	+	0.829222i	0.520952	+	0.853586i	$0.325577\pi$
$578$		0			0
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	7.50000	−	2.59808i	0.311152	−	0.107786i
$582$		0			0
$583$	−0.500000	−	0.866025i	−0.0207079	−	0.0358671i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.0000			0.619116			0.309558	−	0.950881i	$-0.399819\pi$
$587$	15.0000			0.619116			0.309558	+	0.950881i	$0.399819\pi$
$588$		0			0
$589$	28.0000			1.15372
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$		0			0
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	0.952869	+	0.303383i	$0.0981160\pi$
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	−0.213697	+	0.976900i	$0.568551\pi$
$594$		0			0
$595$	−20.0000	+	6.92820i	−0.819920	+	0.284029i
$596$		0			0
$597$	−10.0000	−	17.3205i	−0.409273	−	0.708881i
$598$		0			0
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$		0			0
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$		0			0
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	0.999964	+	0.00851879i	$0.00271165\pi$
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	−0.492604	+	0.870253i	$0.663955\pi$
$608$		0			0
$609$	−2.50000	+	12.9904i	−0.101305	+	0.526397i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	22.0000	−	38.1051i	0.888572	−	1.53905i	0.0470071	−	0.998895i	$-0.485032\pi$
$613$	22.0000	−	38.1051i	0.888572	−	1.53905i	0.841564	−	0.540157i	$-0.181635\pi$
$614$		0			0
$615$	4.00000			0.161296
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$		0			0
$623$	−12.0000	−	10.3923i	−0.480770	−	0.416359i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	−2.00000	+	3.46410i	−0.0798723	+	0.138343i
$628$		0			0
$629$	64.0000			2.55185
$630$		0			0
$631$	−33.0000			−1.31371			−0.656855	−	0.754017i	$-0.728113\pi$
$631$	−33.0000			−1.31371			−0.656855	+	0.754017i	$0.728113\pi$
$632$		0			0
$633$	11.0000	−	19.0526i	0.437211	−	0.757271i
$634$		0			0
$635$	−6.50000	−	11.2583i	−0.257945	−	0.446773i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	−19.0000	+	32.9090i	−0.750455	+	1.29983i	0.197148	+	0.980374i	$0.436832\pi$
$641$	−19.0000	+	32.9090i	−0.750455	+	1.29983i	−0.947602	+	0.319452i	$0.896501\pi$
$642$		0			0
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$		0			0
$645$	10.0000			0.393750
$646$		0			0
$647$	5.00000	−	8.66025i	0.196570	−	0.340470i	−0.750844	−	0.660480i	$-0.770353\pi$
$647$	5.00000	−	8.66025i	0.196570	−	0.340470i	0.947414	+	0.320010i	$0.103686\pi$
$648$		0			0
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$		0			0
$651$	14.0000	+	12.1244i	0.548703	+	0.475191i
$652$		0			0
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	−0.991803	−	0.127780i	$-0.959215\pi$
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	0.385241	−	0.922816i	$-0.374118\pi$
$654$		0			0
$655$	−9.50000	+	16.4545i	−0.371196	+	0.642930i
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	16.0000			0.623272			0.311636	−	0.950202i	$-0.399123\pi$
$659$	16.0000			0.623272			0.311636	+	0.950202i	$0.399123\pi$
$660$		0			0
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	−0.636200	−	0.771524i	$-0.719495\pi$
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	0.986260	+	0.165203i	$0.0528281\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.00000	−	10.3923i	0.0775567	−	0.402996i
$666$		0			0
$667$	10.0000	+	17.3205i	0.387202	+	0.670653i
$668$		0			0
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$	2.00000			0.0772091
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$		0			0
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$		0			0
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$		0			0
$679$	2.50000	−	0.866025i	0.0959412	−	0.0332350i
$680$		0			0
$681$	3.50000	+	6.06218i	0.134120	+	0.232303i
$682$		0			0
$683$	18.5000	−	32.0429i	0.707883	−	1.22609i	−0.257758	−	0.966209i	$-0.582984\pi$
$683$	18.5000	−	32.0429i	0.707883	−	1.22609i	0.965641	−	0.259880i	$-0.0836829\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$	24.0000			0.915657
$688$		0			0
$689$		0			0
$690$		0			0
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	0.957290	−	0.289130i	$-0.0933661\pi$
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	−0.729039	+	0.684472i	$0.760033\pi$
$692$		0			0
$693$	−2.50000	+	0.866025i	−0.0949671	+	0.0328976i
$694$		0			0
$695$	5.00000	+	8.66025i	0.189661	+	0.328502i
$696$		0			0
$697$	16.0000	−	27.7128i	0.606043	−	1.04970i
$698$		0			0
$699$	8.00000			0.302588
$700$		0			0
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$		0			0
$703$	−16.0000	+	27.7128i	−0.603451	+	1.04521i
$704$		0			0
$705$	3.00000	+	5.19615i	0.112987	+	0.195698i
$706$		0			0
$707$	−1.00000	+	5.19615i	−0.0376089	+	0.195421i
$708$		0			0
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	0.967009	−	0.254743i	$-0.0819909\pi$
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	−0.704118	+	0.710083i	$0.748658\pi$
$710$		0			0
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$		0			0
$713$	28.0000			1.04861
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$		0			0
$719$	5.00000	+	8.66025i	0.186469	+	0.322973i	0.944070	−	0.329744i	$-0.106962\pi$
$719$	5.00000	+	8.66025i	0.186469	+	0.322973i	−0.757602	+	0.652717i	$0.773629\pi$
$720$		0			0
$721$	32.0000	+	27.7128i	1.19174	+	1.03208i
$722$		0			0
$723$	7.50000	+	12.9904i	0.278928	+	0.483117i
$724$		0			0
$725$	10.0000	−	17.3205i	0.371391	−	0.643268i
$726$		0			0
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	40.0000	−	69.2820i	1.47945	−	2.56249i
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$		0			0
$735$	5.50000	−	4.33013i	0.202871	−	0.159719i
$736$		0			0
$737$	−1.00000	−	1.73205i	−0.0368355	−	0.0638009i
$738$		0			0
$739$	−17.0000	+	29.4449i	−0.625355	+	1.08315i	0.363117	+	0.931744i	$0.381713\pi$
$739$	−17.0000	+	29.4449i	−0.625355	+	1.08315i	−0.988472	+	0.151403i	$0.951621\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	38.0000			1.39408			0.697042	−	0.717030i	$-0.254499\pi$
$743$	38.0000			1.39408			0.697042	+	0.717030i	$0.254499\pi$
$744$		0			0
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$		0			0
$747$	1.50000	+	2.59808i	0.0548821	+	0.0950586i
$748$		0			0
$749$	30.0000	+	25.9808i	1.09618	+	0.949316i
$750$		0			0
$751$	−3.50000	−	6.06218i	−0.127717	−	0.221212i	0.795075	−	0.606511i	$-0.207432\pi$
$751$	−3.50000	−	6.06218i	−0.127717	−	0.221212i	−0.922792	+	0.385299i	$0.874098\pi$
$752$		0			0
$753$	0.500000	−	0.866025i	0.0182210	−	0.0315597i
$754$		0			0
$755$	7.00000			0.254756
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$		0			0
$759$	−2.00000	+	3.46410i	−0.0725954	+	0.125739i
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$	−5.00000	+	25.9808i	−0.181012	+	0.940567i
$764$		0			0
$765$	−4.00000	−	6.92820i	−0.144620	−	0.250490i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−19.0000			−0.685158			−0.342579	−	0.939489i	$-0.611300\pi$
$769$	−19.0000			−0.685158			−0.342579	+	0.939489i	$0.611300\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$		0			0
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	−14.0000	−	24.2487i	−0.502895	−	0.871039i
$776$		0			0
$777$	−20.0000	+	6.92820i	−0.717496	+	0.248548i
$778$		0			0
$779$	8.00000	+	13.8564i	0.286630	+	0.496457i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$		0			0
$783$	−5.00000			−0.178685
$784$		0			0
$785$	20.0000			0.713831
$786$		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
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$		0			0
$791$	−10.0000	+	3.46410i	−0.355559	+	0.123169i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.500000	+	0.866025i	−0.0177332	+	0.0307148i
$796$		0			0
$797$	51.0000			1.80651			0.903256	−	0.429101i	$-0.141170\pi$
$797$	51.0000			1.80651			0.903256	+	0.429101i	$0.141170\pi$
$798$		0			0
$799$	48.0000			1.69812
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$		0			0
$803$	−1.00000	−	1.73205i	−0.0352892	−	0.0611227i
$804$		0			0
$805$	2.00000	−	10.3923i	0.0704907	−	0.366281i
$806$		0			0
$807$	8.50000	+	14.7224i	0.299214	+	0.518254i
$808$		0			0
$809$	16.0000	−	27.7128i	0.562530	−	0.974331i	−0.434745	−	0.900554i	$-0.643161\pi$
$809$	16.0000	−	27.7128i	0.562530	−	0.974331i	0.997275	−	0.0737769i	$-0.0235053\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	11.0000			0.385787
$814$		0			0
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$		0			0
$817$	20.0000	+	34.6410i	0.699711	+	1.21194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.500000	−	0.866025i	−0.0174501	−	0.0302245i	0.857168	−	0.515036i	$-0.172221\pi$
$821$	−0.500000	−	0.866025i	−0.0174501	−	0.0302245i	−0.874619	+	0.484812i	$0.838888\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$		0			0
$825$	4.00000			0.139262
$826$		0			0
$827$	−43.0000			−1.49526			−0.747628	−	0.664117i	$-0.768807\pi$
$827$	−43.0000			−1.49526			−0.747628	+	0.664117i	$0.768807\pi$
$828$		0			0
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	−0.985771	−	0.168091i	$-0.946240\pi$
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	0.638457	+	0.769657i	$0.279573\pi$
$830$		0			0
$831$	12.0000	+	20.7846i	0.416275	+	0.721010i
$832$		0			0
$833$	−8.00000	−	55.4256i	−0.277184	−	1.92038i
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$		0			0
$837$	−3.50000	+	6.06218i	−0.120978	+	0.209540i
$838$		0			0
$839$	8.00000			0.276191			0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000			0.276191			0.138095	+	0.990419i	$0.455902\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$		0			0
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$		0			0
$845$	−6.50000	−	11.2583i	−0.223607	−	0.387298i
$846$		0			0
$847$	−20.0000	−	17.3205i	−0.687208	−	0.595140i
$848$		0			0
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$		0			0
$851$	−16.0000	+	27.7128i	−0.548473	+	0.949983i
$852$		0			0
$853$	−42.0000			−1.43805			−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000			−1.43805			−0.719026	+	0.694983i	$0.755412\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$		0			0
$859$	9.00000	+	15.5885i	0.307076	+	0.531871i	0.977721	−	0.209907i	$-0.0673161\pi$
$859$	9.00000	+	15.5885i	0.307076	+	0.531871i	−0.670645	+	0.741778i	$0.733983\pi$
$860$		0			0
$861$	−2.00000	+	10.3923i	−0.0681598	+	0.354169i
$862$		0			0
$863$	−23.0000	−	39.8372i	−0.782929	−	1.35607i	−0.930228	−	0.366981i	$-0.880391\pi$
$863$	−23.0000	−	39.8372i	−0.782929	−	1.35607i	0.147299	−	0.989092i	$-0.452942\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$	−47.0000			−1.59620
$868$		0			0
$869$	9.00000			0.305304
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.500000	+	0.866025i	0.0169224	+	0.0293105i
$874$		0			0
$875$	−22.5000	+	7.79423i	−0.760639	+	0.263493i
$876$		0			0
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$		0			0
$879$	−1.50000	+	2.59808i	−0.0505937	+	0.0876309i
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$		0			0
$887$	2.00000	+	3.46410i	0.0671534	+	0.116313i	0.897647	−	0.440715i	$-0.145275\pi$
$887$	2.00000	+	3.46410i	0.0671534	+	0.116313i	−0.830494	+	0.557028i	$0.811942\pi$
$888$		0			0
$889$	32.5000	−	11.2583i	1.09002	−	0.377592i
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$		0			0
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$	−20.0000			−0.668526
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.5000	−	30.3109i	0.583658	−	1.01092i
$900$		0			0
$901$	4.00000	+	6.92820i	0.133259	+	0.230812i
$902$		0			0
$903$	−5.00000	+	25.9808i	−0.166390	+	0.864586i
$904$		0			0
$905$	−10.0000	−	17.3205i	−0.332411	−	0.575753i
$906$		0			0
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$		0			0
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	1.50000	−	2.59808i	0.0496428	−	0.0859838i
$914$		0			0
$915$	−1.00000	−	1.73205i	−0.0330590	−	0.0572598i
$916$		0			0
$917$	−38.0000	−	32.9090i	−1.25487	−	1.08675i
$918$		0			0
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$		0			0
$921$	−2.00000	+	3.46410i	−0.0659022	+	0.114146i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	32.0000			1.05215
$926$		0			0
$927$	−8.00000	+	13.8564i	−0.262754	+	0.455104i
$928$		0			0
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	−0.997684	−	0.0680235i	$-0.978331\pi$
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	0.439932	−	0.898031i	$-0.355003\pi$
$930$		0			0
$931$	26.0000	+	10.3923i	0.852116	+	0.340594i
$932$		0			0
$933$	−14.0000	−	24.2487i	−0.458339	−	0.793867i
$934$		0			0
$935$	−4.00000	+	6.92820i	−0.130814	+	0.226576i
$936$		0			0
$937$	−29.0000			−0.947389			−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000			−0.947389			−0.473694	+	0.880689i	$0.657080\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$		0			0
$941$	−25.5000	+	44.1673i	−0.831276	+	1.43981i	0.0657503	+	0.997836i	$0.479056\pi$
$941$	−25.5000	+	44.1673i	−0.831276	+	1.43981i	−0.897027	+	0.441977i	$0.854277\pi$
$942$		0			0
$943$	8.00000	+	13.8564i	0.260516	+	0.451227i
$944$		0			0
$945$	2.00000	+	1.73205i	0.0650600	+	0.0563436i
$946$		0			0
$947$	−20.0000	−	34.6410i	−0.649913	−	1.12568i	−0.983143	−	0.182836i	$-0.941472\pi$
$947$	−20.0000	−	34.6410i	−0.649913	−	1.12568i	0.333231	−	0.942845i	$-0.391861\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−5.00000			−0.162136
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.50000	+	4.33013i	0.0808135	+	0.139973i
$958$		0			0
$959$	9.00000	−	46.7654i	0.290625	−	1.51013i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	−7.50000	+	12.9904i	−0.241684	+	0.418609i
$964$		0			0
$965$	11.0000			0.354103
$966$		0			0
$967$	−7.00000			−0.225105			−0.112552	−	0.993646i	$-0.535903\pi$
$967$	−7.00000			−0.225105			−0.112552	+	0.993646i	$0.535903\pi$
$968$		0			0
$969$	16.0000	−	27.7128i	0.513994	−	0.890264i
$970$		0			0
$971$	−29.5000	−	51.0955i	−0.946700	−	1.63973i	−0.752311	−	0.658808i	$-0.771061\pi$
$971$	−29.5000	−	51.0955i	−0.946700	−	1.63973i	−0.194389	−	0.980925i	$-0.562272\pi$
$972$		0			0
$973$	−25.0000	+	8.66025i	−0.801463	+	0.277635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.0000	+	43.3013i	−0.799821	+	1.38533i	0.119912	+	0.992785i	$0.461739\pi$
$977$	−25.0000	+	43.3013i	−0.799821	+	1.38533i	−0.919732	+	0.392546i	$0.871594\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$		0			0
$981$	−10.0000			−0.319275
$982$		0			0
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$	−15.0000	+	5.19615i	−0.477455	+	0.165395i
$988$		0			0
$989$	20.0000	+	34.6410i	0.635963	+	1.10152i
$990$		0			0
$991$	−2.50000	+	4.33013i	−0.0794151	+	0.137551i	−0.902998	−	0.429645i	$-0.858639\pi$
$991$	−2.50000	+	4.33013i	−0.0794151	+	0.137551i	0.823583	+	0.567196i	$0.191972\pi$
$992$		0			0
$993$	−20.0000			−0.634681
$994$		0			0
$995$	20.0000			0.634043
$996$		0			0
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$		0			0
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.q.r.193.1		2
4.3	odd	2		1344.2.q.h.193.1		2
7.2	even	3	inner	1344.2.q.r.961.1		2
7.3	odd	6		9408.2.a.cp.1.1		1
7.4	even	3		9408.2.a.o.1.1		1
8.3	odd	2		672.2.q.g.193.1	yes	2
8.5	even	2		672.2.q.b.193.1	✓	2
24.5	odd	2		2016.2.s.i.865.1		2
24.11	even	2		2016.2.s.j.865.1		2
28.3	even	6		9408.2.a.bb.1.1		1
28.11	odd	6		9408.2.a.cg.1.1		1
28.23	odd	6		1344.2.q.h.961.1		2
56.3	even	6		4704.2.a.w.1.1		1
56.11	odd	6		4704.2.a.l.1.1		1
56.37	even	6		672.2.q.b.289.1	yes	2
56.45	odd	6		4704.2.a.f.1.1		1
56.51	odd	6		672.2.q.g.289.1	yes	2
56.53	even	6		4704.2.a.bc.1.1		1
168.107	even	6		2016.2.s.j.289.1		2
168.149	odd	6		2016.2.s.i.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.b.193.1	✓	2	8.5	even	2
672.2.q.b.289.1	yes	2	56.37	even	6
672.2.q.g.193.1	yes	2	8.3	odd	2
672.2.q.g.289.1	yes	2	56.51	odd	6
1344.2.q.h.193.1		2	4.3	odd	2
1344.2.q.h.961.1		2	28.23	odd	6
1344.2.q.r.193.1		2	1.1	even	1	trivial
1344.2.q.r.961.1		2	7.2	even	3	inner
2016.2.s.i.289.1		2	168.149	odd	6
2016.2.s.i.865.1		2	24.5	odd	2
2016.2.s.j.289.1		2	168.107	even	6
2016.2.s.j.865.1		2	24.11	even	2
4704.2.a.f.1.1		1	56.45	odd	6
4704.2.a.l.1.1		1	56.11	odd	6
4704.2.a.w.1.1		1	56.3	even	6
4704.2.a.bc.1.1		1	56.53	even	6
9408.2.a.o.1.1		1	7.4	even	3
9408.2.a.bb.1.1		1	28.3	even	6
9408.2.a.cg.1.1		1	28.11	odd	6
9408.2.a.cp.1.1		1	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{15} +(4.00000 - 6.92820i) q^{17} +(2.00000 + 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.00000 + 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{27} +5.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(0.500000 + 0.866025i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(4.00000 + 6.92820i) q^{37} +4.00000 q^{41} +10.0000 q^{43} +(0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-4.00000 - 6.92820i) q^{51} +(-0.500000 + 0.866025i) q^{53} -1.00000 q^{55} +4.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(2.00000 + 1.73205i) q^{63} +(-1.00000 + 1.73205i) q^{67} +4.00000 q^{69} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(0.500000 - 2.59808i) q^{77} +(-4.50000 - 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} -3.00000 q^{83} +8.00000 q^{85} +(2.50000 - 4.33013i) q^{87} +(3.00000 + 5.19615i) q^{89} +(-3.50000 - 6.06218i) q^{93} +(-2.00000 + 3.46410i) q^{95} -1.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + q^{5} - 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q + q^3 + q^5 - 5 * q^7 - q^9	\( 2 q + q^{3} + q^{5} - 5 q^{7} - q^{9} - q^{11} + 2 q^{15} + 8 q^{17} + 4 q^{19} - q^{21} + 4 q^{23} + 4 q^{25} - 2 q^{27} + 10 q^{29} + 7 q^{31} + q^{33} - 4 q^{35} + 8 q^{37} + 8 q^{41} + 20 q^{43} + q^{45} + 6 q^{47} + 11 q^{49} - 8 q^{51} - q^{53} - 2 q^{55} + 8 q^{57} - 9 q^{59} - 2 q^{61} + 4 q^{63} - 2 q^{67} + 8 q^{69} - 12 q^{71} - 2 q^{73} - 4 q^{75} + q^{77} - 9 q^{79} - q^{81} - 6 q^{83} + 16 q^{85} + 5 q^{87} + 6 q^{89} - 7 q^{93} - 4 q^{95} - 2 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + q^3 + q^5 - 5 * q^7 - q^9 - q^11 + 2 * q^15 + 8 * q^17 + 4 * q^19 - q^21 + 4 * q^23 + 4 * q^25 - 2 * q^27 + 10 * q^29 + 7 * q^31 + q^33 - 4 * q^35 + 8 * q^37 + 8 * q^41 + 20 * q^43 + q^45 + 6 * q^47 + 11 * q^49 - 8 * q^51 - q^53 - 2 * q^55 + 8 * q^57 - 9 * q^59 - 2 * q^61 + 4 * q^63 - 2 * q^67 + 8 * q^69 - 12 * q^71 - 2 * q^73 - 4 * q^75 + q^77 - 9 * q^79 - q^81 - 6 * q^83 + 16 * q^85 + 5 * q^87 + 6 * q^89 - 7 * q^93 - 4 * q^95 - 2 * q^97 + 2 * q^99

Introduction

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