LMFDB - Embedded newform 1456.2.s.e.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(113,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, 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("1456.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.s (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:	$11.6262185343$
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 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1456.113
Dual form			1456.2.s.e.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(2.50000 - 2.59808i) q^{13} +(1.50000 - 2.59808i) q^{15} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{21} +(1.50000 - 2.59808i) q^{23} +4.00000 q^{25} +5.00000 q^{27} +(-3.00000 + 5.19615i) q^{29} +10.0000 q^{31} +(1.50000 + 2.59808i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-1.00000 - 3.46410i) q^{39} +(4.00000 + 6.92820i) q^{43} +(3.00000 + 5.19615i) q^{45} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} -6.00000 q^{51} +12.0000 q^{53} -4.00000 q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.00000 + 1.73205i) q^{63} +(7.50000 - 7.79423i) q^{65} +(1.00000 - 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(-1.50000 - 2.59808i) q^{71} +2.00000 q^{73} +(2.00000 - 3.46410i) q^{75} +4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-9.00000 - 15.5885i) q^{85} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +(3.50000 + 0.866025i) q^{91} +(5.00000 - 8.66025i) q^{93} +(-6.00000 - 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 6 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + 6 * q^5 + q^7 + 2 * q^9	$ 2 q + q^{3} + 6 q^{5} + q^{7} + 2 q^{9} + 5 q^{13} + 3 q^{15} - 6 q^{17} - 4 q^{19} + 2 q^{21} + 3 q^{23} + 8 q^{25} + 10 q^{27} - 6 q^{29} + 20 q^{31} + 3 q^{35} - 8 q^{37} - 2 q^{39} + 8 q^{43} + 6 q^{45} - 12 q^{47} - q^{49} - 12 q^{51} + 24 q^{53} - 8 q^{57} + 3 q^{59} - 11 q^{61} - 2 q^{63} + 15 q^{65} + 2 q^{67} - 3 q^{69} - 3 q^{71} + 4 q^{73} + 4 q^{75} + 8 q^{79} - q^{81} - 18 q^{85} + 6 q^{87} + 6 q^{89} + 7 q^{91} + 10 q^{93} - 12 q^{95} - 2 q^{97}+O(q^{100}) $ 2 * q + q^3 + 6 * q^5 + q^7 + 2 * q^9 + 5 * q^13 + 3 * q^15 - 6 * q^17 - 4 * q^19 + 2 * q^21 + 3 * q^23 + 8 * q^25 + 10 * q^27 - 6 * q^29 + 20 * q^31 + 3 * q^35 - 8 * q^37 - 2 * q^39 + 8 * q^43 + 6 * q^45 - 12 * q^47 - q^49 - 12 * q^51 + 24 * q^53 - 8 * q^57 + 3 * q^59 - 11 * q^61 - 2 * q^63 + 15 * q^65 + 2 * q^67 - 3 * q^69 - 3 * q^71 + 4 * q^73 + 4 * q^75 + 8 * q^79 - q^81 - 18 * q^85 + 6 * q^87 + 6 * q^89 + 7 * q^91 + 10 * q^93 - 12 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	1.50000	−	2.59808i	0.387298	−	0.670820i
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$		0			0
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$	3.00000	+	5.19615i	0.447214	+	0.774597i
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−6.00000			−0.840168
$52$		0			0
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$		0			0
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$		0			0
$63$	−1.00000	+	1.73205i	−0.125988	+	0.218218i
$64$		0			0
$65$	7.50000	−	7.79423i	0.930261	−	0.966755i
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$		0			0
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$		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
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−9.00000	−	15.5885i	−0.976187	−	1.69081i
$86$		0			0
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$		0			0
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	−6.00000	−	10.3923i	−0.615587	−	1.06623i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$	3.00000			0.292770
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$		0			0
$111$	4.00000	+	6.92820i	0.379663	+	0.657596i
$112$		0			0
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	0.884182	+	0.467143i	$0.154717\pi$
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	−0.0375328	+	0.999295i	$0.511950\pi$
$114$		0			0
$115$	4.50000	−	7.79423i	0.419627	−	0.726816i
$116$		0			0
$117$	7.00000	+	1.73205i	0.647150	+	0.160128i
$118$		0			0
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	−0.511859	−	0.859069i	$-0.671043\pi$
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	0.999905	+	0.0137486i	$0.00437646\pi$
$128$		0			0
$129$	8.00000			0.704361
$130$		0			0
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$		0			0
$135$	15.0000			1.29099
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−9.00000	+	15.5885i	−0.747409	+	1.29455i
$146$		0			0
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$		0			0
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	1.00000			0.0813788			0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000			0.0813788			0.0406894	+	0.999172i	$0.487045\pi$
$152$		0			0
$153$	6.00000	−	10.3923i	0.485071	−	0.840168i
$154$		0			0
$155$	30.0000			2.40966
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		0			0
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	4.00000	−	6.92820i	0.305888	−	0.529813i
$172$		0			0
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$		0			0
$177$	3.00000			0.225494
$178$		0			0
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$	−11.0000			−0.813143
$184$		0			0
$185$	−12.0000	+	20.7846i	−0.882258	+	1.52811i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$		0			0
$195$	−3.00000	−	10.3923i	−0.214834	−	0.744208i
$196$		0			0
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$		0			0
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$		0			0
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$		0			0
$203$	−6.00000			−0.421117
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$		0			0
$213$	−3.00000			−0.205557
$214$		0			0
$215$	12.0000	+	20.7846i	0.818393	+	1.41750i
$216$		0			0
$217$	5.00000	+	8.66025i	0.339422	+	0.587896i
$218$		0			0
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$		0			0
$221$	−21.0000	−	5.19615i	−1.41261	−	0.349531i
$222$		0			0
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$		0			0
$225$	4.00000	+	6.92820i	0.266667	+	0.461880i
$226$		0			0
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	0.502204	−	0.864749i	$-0.332523\pi$
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	−0.999997	+	0.00254715i	$0.999189\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		0			0
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$		0			0
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$		0			0
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.825131	+	0.564942i	$0.191101\pi$
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.0766885	+	0.997055i	$0.475565\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$		0			0
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$		0			0
$247$	−14.0000	−	3.46410i	−0.890799	−	0.220416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	0.909475	−	0.415759i	$-0.136484\pi$
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	−0.814795	+	0.579748i	$0.803151\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−18.0000			−1.12720
$256$		0			0
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−8.00000			−0.497096
$260$		0			0
$261$	−12.0000			−0.742781
$262$		0			0
$263$	−13.5000	+	23.3827i	−0.832446	+	1.44184i	0.0636476	+	0.997972i	$0.479727\pi$
$263$	−13.5000	+	23.3827i	−0.832446	+	1.44184i	−0.896093	+	0.443866i	$0.853607\pi$
$264$		0			0
$265$	36.0000			2.21146
$266$		0			0
$267$	−3.00000	−	5.19615i	−0.183597	−	0.317999i
$268$		0			0
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$		0			0
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$		0			0
$273$	2.50000	−	2.59808i	0.151307	−	0.157243i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	0.150210	−	0.988654i	$-0.452005\pi$
$278$		0			0
$279$	10.0000	+	17.3205i	0.598684	+	1.03695i
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.124096	+	0.992270i	$0.539603\pi$
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.797283	+	0.603606i	$0.793730\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−2.00000			−0.117242
$292$		0			0
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	0.940252	−	0.340480i	$-0.110589\pi$
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	−0.764990	+	0.644042i	$0.777256\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.00000	−	10.3923i	−0.173494	−	0.601003i
$300$		0			0
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$		0			0
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$		0			0
$305$	−16.5000	−	28.5788i	−0.944787	−	1.63642i
$306$		0			0
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$	−7.00000	+	12.1244i	−0.398216	+	0.689730i
$310$		0			0
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$		0			0
$313$	8.00000			0.452187			0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000			0.452187			0.226093	+	0.974106i	$0.427405\pi$
$314$		0			0
$315$	−3.00000	+	5.19615i	−0.169031	+	0.292770i
$316$		0			0
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	9.00000	+	15.5885i	0.502331	+	0.870063i
$322$		0			0
$323$	−12.0000	+	20.7846i	−0.667698	+	1.15649i
$324$		0			0
$325$	10.0000	−	10.3923i	0.554700	−	0.576461i
$326$		0			0
$327$	−8.00000	+	13.8564i	−0.442401	+	0.766261i
$328$		0			0
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$		0			0
$333$	−16.0000			−0.876795
$334$		0			0
$335$	3.00000	−	5.19615i	0.163908	−	0.283896i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	18.0000			0.977626
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−4.50000	−	7.79423i	−0.242272	−	0.419627i
$346$		0			0
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	−14.5000	+	25.1147i	−0.776167	+	1.34436i	0.157969	+	0.987444i	$0.449505\pi$
$349$	−14.5000	+	25.1147i	−0.776167	+	1.34436i	−0.934136	+	0.356917i	$0.883828\pi$
$350$		0			0
$351$	12.5000	−	12.9904i	0.667201	−	0.693375i
$352$		0			0
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$		0			0
$357$	−3.00000	−	5.19615i	−0.158777	−	0.275010i
$358$		0			0
$359$	9.00000			0.475002			0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000			0.475002			0.237501	+	0.971387i	$0.423672\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$	11.0000			0.577350
$364$		0			0
$365$	6.00000			0.314054
$366$		0			0
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	−0.966507	−	0.256639i	$-0.917385\pi$
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	0.705509	+	0.708700i	$0.250718\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$		0			0
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$		0			0
$377$	6.00000	+	20.7846i	0.309016	+	1.07046i
$378$		0			0
$379$	−14.0000	+	24.2487i	−0.719132	+	1.24557i	0.242213	+	0.970223i	$0.422127\pi$
$379$	−14.0000	+	24.2487i	−0.719132	+	1.24557i	−0.961344	+	0.275349i	$0.911206\pi$
$380$		0			0
$381$	−5.50000	−	9.52628i	−0.281774	−	0.488046i
$382$		0			0
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	0.779143	−	0.626846i	$-0.215654\pi$
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	−0.932436	+	0.361335i	$0.882321\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.00000	+	13.8564i	−0.406663	+	0.704361i
$388$		0			0
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−7.50000	+	12.9904i	−0.378325	+	0.655278i
$394$		0			0
$395$	12.0000			0.603786
$396$		0			0
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$		0			0
$399$	−2.00000	−	3.46410i	−0.100125	−	0.173422i
$400$		0			0
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$		0			0
$403$	25.0000	−	25.9808i	1.24534	−	1.29419i
$404$		0			0
$405$	−1.50000	+	2.59808i	−0.0745356	+	0.129099i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$		0			0
$411$	−3.00000			−0.147979
$412$		0			0
$413$	−1.50000	+	2.59808i	−0.0738102	+	0.127843i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−16.0000			−0.783523
$418$		0			0
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$		0			0
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$		0			0
$425$	−12.0000	−	20.7846i	−0.582086	−	1.00820i
$426$		0			0
$427$	5.50000	−	9.52628i	0.266164	−	0.461009i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.5000	+	28.5788i	−0.794777	+	1.37659i	0.128204	+	0.991748i	$0.459079\pi$
$431$	−16.5000	+	28.5788i	−0.794777	+	1.37659i	−0.922981	+	0.384846i	$0.874254\pi$
$432$		0			0
$433$	2.00000	+	3.46410i	0.0961139	+	0.166474i	0.910073	−	0.414448i	$-0.136025\pi$
$433$	2.00000	+	3.46410i	0.0961139	+	0.166474i	−0.813959	+	0.580922i	$0.802692\pi$
$434$		0			0
$435$	9.00000	+	15.5885i	0.431517	+	0.747409i
$436$		0			0
$437$	−12.0000			−0.574038
$438$		0			0
$439$	7.00000	−	12.1244i	0.334092	−	0.578664i	−0.649218	−	0.760602i	$-0.724904\pi$
$439$	7.00000	−	12.1244i	0.334092	−	0.578664i	0.983310	+	0.181938i	$0.0582371\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$		0			0
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	0.740087	−	0.672511i	$-0.234784\pi$
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	−0.952455	+	0.304679i	$0.901451\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.500000	−	0.866025i	0.0234920	−	0.0406894i
$454$		0			0
$455$	10.5000	+	2.59808i	0.492248	+	0.121800i
$456$		0			0
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$		0			0
$459$	−15.0000	−	25.9808i	−0.700140	−	1.21268i
$460$		0			0
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	0.510887	−	0.859648i	$-0.329317\pi$
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	−0.999920	+	0.0126168i	$0.995984\pi$
$462$		0			0
$463$	31.0000			1.44069			0.720346	−	0.693615i	$-0.243983\pi$
$463$	31.0000			1.44069			0.720346	+	0.693615i	$0.243983\pi$
$464$		0			0
$465$	15.0000	−	25.9808i	0.695608	−	1.20483i
$466$		0			0
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$		0			0
$469$	2.00000			0.0923514
$470$		0			0
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−8.00000	−	13.8564i	−0.367065	−	0.635776i
$476$		0			0
$477$	12.0000	+	20.7846i	0.549442	+	0.951662i
$478$		0			0
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	−0.287954	−	0.957644i	$-0.592975\pi$
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	0.973321	−	0.229447i	$-0.0736918\pi$
$480$		0			0
$481$	8.00000	+	27.7128i	0.364769	+	1.26360i
$482$		0			0
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$		0			0
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$		0			0
$487$	−6.50000	−	11.2583i	−0.294543	−	0.510164i	0.680335	−	0.732901i	$-0.261834\pi$
$487$	−6.50000	−	11.2583i	−0.294543	−	0.510164i	−0.974879	+	0.222737i	$0.928501\pi$
$488$		0			0
$489$	20.0000			0.904431
$490$		0			0
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$		0			0
$493$	36.0000			1.62136
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.50000	−	2.59808i	0.0672842	−	0.116540i
$498$		0			0
$499$	22.0000			0.984855			0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000			0.984855			0.492428	+	0.870353i	$0.336110\pi$
$500$		0			0
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$		0			0
$503$	21.0000	+	36.3731i	0.936344	+	1.62179i	0.772220	+	0.635355i	$0.219146\pi$
$503$	21.0000	+	36.3731i	0.936344	+	1.62179i	0.164124	+	0.986440i	$0.447520\pi$
$504$		0			0
$505$	9.00000	−	15.5885i	0.400495	−	0.693677i
$506$		0			0
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$		0			0
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$		0			0
$513$	−10.0000	−	17.3205i	−0.441511	−	0.764719i
$514$		0			0
$515$	−42.0000			−1.85074
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−9.00000			−0.395056
$520$		0			0
$521$	−36.0000			−1.57719			−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000			−1.57719			−0.788594	+	0.614914i	$0.789191\pi$
$522$		0			0
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	−0.876750	−	0.480946i	$-0.840293\pi$
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	0.854887	+	0.518815i	$0.173627\pi$
$524$		0			0
$525$	4.00000			0.174574
$526$		0			0
$527$	−30.0000	−	51.9615i	−1.30682	−	2.26348i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−3.00000	+	5.19615i	−0.130189	+	0.225494i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−27.0000	+	46.7654i	−1.16731	+	2.02184i
$536$		0			0
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$		0			0
$543$	2.50000	−	4.33013i	0.107285	−	0.185824i
$544$		0			0
$545$	−48.0000			−2.05609
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$		0			0
$549$	11.0000	−	19.0526i	0.469469	−	0.813143i
$550$		0			0
$551$	24.0000			1.02243
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$		0			0
$555$	12.0000	+	20.7846i	0.509372	+	0.882258i
$556$		0			0
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$		0			0
$559$	28.0000	+	6.92820i	1.18427	+	0.293032i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$		0			0
$565$	27.0000	+	46.7654i	1.13590	+	1.96743i
$566$		0			0
$567$	−1.00000			−0.0419961
$568$		0			0
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.184030	−	0.982921i	$-0.441086\pi$
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.759220	−	0.650835i	$-0.225581\pi$
$570$		0			0
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	6.00000	−	10.3923i	0.250217	−	0.433389i
$576$		0			0
$577$	−28.0000			−1.16566			−0.582828	−	0.812596i	$-0.698054\pi$
$577$	−28.0000			−1.16566			−0.582828	+	0.812596i	$0.698054\pi$
$578$		0			0
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	21.0000	+	5.19615i	0.868243	+	0.214834i
$586$		0			0
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$		0			0
$589$	−20.0000	−	34.6410i	−0.824086	−	1.42736i
$590$		0			0
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	9.00000	−	15.5885i	0.368964	−	0.639064i
$596$		0			0
$597$	14.0000			0.572982
$598$		0			0
$599$	−3.00000			−0.122577			−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000			−0.122577			−0.0612883	+	0.998120i	$0.519521\pi$
$600$		0			0
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	16.5000	+	28.5788i	0.670820	+	1.16190i
$606$		0			0
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	0.746532	−	0.665350i	$-0.231718\pi$
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	−0.949476	+	0.313841i	$0.898384\pi$
$608$		0			0
$609$	−3.00000	+	5.19615i	−0.121566	+	0.210559i
$610$		0			0
$611$	−15.0000	+	15.5885i	−0.606835	+	0.630641i
$612$		0			0
$613$	11.0000	−	19.0526i	0.444286	−	0.769526i	−0.553716	−	0.832705i	$-0.686791\pi$
$613$	11.0000	−	19.0526i	0.444286	−	0.769526i	0.998002	+	0.0631797i	$0.0201241\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	37.0000			1.48716			0.743578	−	0.668649i	$-0.233127\pi$
$619$	37.0000			1.48716			0.743578	+	0.668649i	$0.233127\pi$
$620$		0			0
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$		0			0
$623$	6.00000			0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	48.0000			1.91389
$630$		0			0
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	0.911487	−	0.411328i	$-0.134935\pi$
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	−0.811964	+	0.583707i	$0.801602\pi$
$632$		0			0
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$		0			0
$635$	16.5000	−	28.5788i	0.654783	−	1.13412i
$636$		0			0
$637$	1.00000	+	3.46410i	0.0396214	+	0.137253i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$		0			0
$643$	20.5000	+	35.5070i	0.808441	+	1.40026i	0.913943	+	0.405842i	$0.133022\pi$
$643$	20.5000	+	35.5070i	0.808441	+	1.40026i	−0.105502	+	0.994419i	$0.533645\pi$
$644$		0			0
$645$	24.0000			0.944999
$646$		0			0
$647$	−18.0000	+	31.1769i	−0.707653	+	1.22569i	0.258073	+	0.966126i	$0.416913\pi$
$647$	−18.0000	+	31.1769i	−0.707653	+	1.22569i	−0.965726	+	0.259565i	$0.916421\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	10.0000			0.391931
$652$		0			0
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$		0			0
$655$	−45.0000			−1.75830
$656$		0			0
$657$	2.00000	+	3.46410i	0.0780274	+	0.135147i
$658$		0			0
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	0.918523	−	0.395367i	$-0.129383\pi$
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	−0.801660	+	0.597781i	$0.796049\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$		0			0
$663$	−15.0000	+	15.5885i	−0.582552	+	0.605406i
$664$		0			0
$665$	6.00000	−	10.3923i	0.232670	−	0.402996i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$		0			0
$675$	20.0000			0.769800
$676$		0			0
$677$	−51.0000			−1.96009			−0.980045	−	0.198778i	$-0.936303\pi$
$677$	−51.0000			−1.96009			−0.980045	+	0.198778i	$0.936303\pi$
$678$		0			0
$679$	1.00000	−	1.73205i	0.0383765	−	0.0664700i
$680$		0			0
$681$	−15.0000			−0.574801
$682$		0			0
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$		0			0
$685$	−4.50000	−	7.79423i	−0.171936	−	0.297802i
$686$		0			0
$687$	−11.0000	+	19.0526i	−0.419676	+	0.726900i
$688$		0			0
$689$	30.0000	−	31.1769i	1.14291	−	1.18775i
$690$		0			0
$691$	−0.500000	+	0.866025i	−0.0190209	+	0.0329452i	−0.875379	−	0.483437i	$-0.839388\pi$
$691$	−0.500000	+	0.866025i	−0.0190209	+	0.0329452i	0.856358	+	0.516382i	$0.172722\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.0000	−	41.5692i	−0.910372	−	1.57681i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−1.50000	+	2.59808i	−0.0567352	+	0.0982683i
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$	32.0000			1.20690
$704$		0			0
$705$	−9.00000	+	15.5885i	−0.338960	+	0.587095i
$706$		0			0
$707$	6.00000			0.225653
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$		0			0
$713$	15.0000	−	25.9808i	0.561754	−	0.972987i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.5000	+	18.1865i	−0.392130	+	0.679189i
$718$		0			0
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$		0			0
$721$	−7.00000	−	12.1244i	−0.260694	−	0.451535i
$722$		0			0
$723$	28.0000			1.04133
$724$		0			0
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$		0			0
$727$	52.0000			1.92857			0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000			1.92857			0.964287	+	0.264861i	$0.0853260\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$		0			0
$733$	35.0000			1.29275			0.646377	−	0.763018i	$-0.276283\pi$
$733$	35.0000			1.29275			0.646377	+	0.763018i	$0.276283\pi$
$734$		0			0
$735$	1.50000	+	2.59808i	0.0553283	+	0.0958315i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$	−10.0000	+	10.3923i	−0.367359	+	0.381771i
$742$		0			0
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−18.0000			−0.657706
$750$		0			0
$751$	8.50000	−	14.7224i	0.310169	−	0.537229i	−0.668229	−	0.743955i	$-0.732948\pi$
$751$	8.50000	−	14.7224i	0.310169	−	0.537229i	0.978399	+	0.206726i	$0.0662809\pi$
$752$		0			0
$753$	3.00000			0.109326
$754$		0			0
$755$	3.00000			0.109181
$756$		0			0
$757$	26.0000	−	45.0333i	0.944986	−	1.63676i	0.189207	−	0.981937i	$-0.439408\pi$
$757$	26.0000	−	45.0333i	0.944986	−	1.63676i	0.755779	−	0.654827i	$-0.227258\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		0			0
$763$	−8.00000	−	13.8564i	−0.289619	−	0.501636i
$764$		0			0
$765$	18.0000	−	31.1769i	0.650791	−	1.12720i
$766$		0			0
$767$	10.5000	+	2.59808i	0.379133	+	0.0938111i
$768$		0			0
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$		0			0
$771$	−3.00000	−	5.19615i	−0.108042	−	0.187135i
$772$		0			0
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$		0			0
$775$	40.0000			1.43684
$776$		0			0
$777$	−4.00000	+	6.92820i	−0.143499	+	0.248548i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−15.0000	+	25.9808i	−0.536056	+	0.928477i
$784$		0			0
$785$	6.00000			0.214149
$786$		0			0
$787$	26.5000	+	45.8993i	0.944623	+	1.63614i	0.756504	+	0.653989i	$0.226906\pi$
$787$	26.5000	+	45.8993i	0.944623	+	1.63614i	0.188119	+	0.982146i	$0.439761\pi$
$788$		0			0
$789$	13.5000	+	23.3827i	0.480613	+	0.832446i
$790$		0			0
$791$	−9.00000	+	15.5885i	−0.320003	+	0.554262i
$792$		0			0
$793$	−38.5000	−	9.52628i	−1.36718	−	0.338288i
$794$		0			0
$795$	18.0000	−	31.1769i	0.638394	−	1.10573i
$796$		0			0
$797$	7.50000	+	12.9904i	0.265664	+	0.460143i	0.967737	−	0.251961i	$-0.0810756\pi$
$797$	7.50000	+	12.9904i	0.265664	+	0.460143i	−0.702074	+	0.712104i	$0.747742\pi$
$798$		0			0
$799$	18.0000	+	31.1769i	0.636794	+	1.10296i
$800$		0			0
$801$	12.0000			0.423999
$802$		0			0
$803$		0			0
$804$		0			0
$805$	9.00000			0.317208
$806$		0			0
$807$	−9.00000			−0.316815
$808$		0			0
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	−0.214930	−	0.976629i	$-0.568952\pi$
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	0.953251	−	0.302180i	$-0.0977142\pi$
$810$		0			0
$811$	19.0000			0.667180			0.333590	−	0.942718i	$-0.391740\pi$
$811$	19.0000			0.667180			0.333590	+	0.942718i	$0.391740\pi$
$812$		0			0
$813$	−1.00000	−	1.73205i	−0.0350715	−	0.0607457i
$814$		0			0
$815$	30.0000	+	51.9615i	1.05085	+	1.82013i
$816$		0			0
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$		0			0
$819$	2.00000	+	6.92820i	0.0698857	+	0.242091i
$820$		0			0
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	−0.951526	−	0.307568i	$-0.900485\pi$
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	0.742125	+	0.670262i	$0.233818\pi$
$822$		0			0
$823$	−6.50000	−	11.2583i	−0.226576	−	0.392441i	0.730215	−	0.683217i	$-0.239420\pi$
$823$	−6.50000	−	11.2583i	−0.226576	−	0.392441i	−0.956791	+	0.290776i	$0.906086\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$	−26.0000			−0.901930
$832$		0			0
$833$	6.00000			0.207888
$834$		0			0
$835$	−18.0000	+	31.1769i	−0.622916	+	1.07892i
$836$		0			0
$837$	50.0000			1.72825
$838$		0			0
$839$	−27.0000	−	46.7654i	−0.932144	−	1.61452i	−0.779650	−	0.626215i	$-0.784603\pi$
$839$	−27.0000	−	46.7654i	−0.932144	−	1.61452i	−0.152493	−	0.988304i	$-0.548730\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	9.00000	−	15.5885i	0.309976	−	0.536895i
$844$		0			0
$845$	−1.50000	−	38.9711i	−0.0516016	−	1.34065i
$846$		0			0
$847$	−5.50000	+	9.52628i	−0.188982	+	0.327327i
$848$		0			0
$849$	15.5000	+	26.8468i	0.531959	+	0.921379i
$850$		0			0
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$	17.0000			0.582069			0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000			0.582069			0.291034	+	0.956713i	$0.406001\pi$
$854$		0			0
$855$	12.0000	−	20.7846i	0.410391	−	0.710819i
$856$		0			0
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	57.0000			1.94030			0.970151	−	0.242500i	$-0.0779676\pi$
$863$	57.0000			1.94030			0.970151	+	0.242500i	$0.0779676\pi$
$864$		0			0
$865$	−13.5000	−	23.3827i	−0.459014	−	0.795035i
$866$		0			0
$867$	9.50000	+	16.4545i	0.322637	+	0.558824i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−2.00000	−	6.92820i	−0.0677674	−	0.234753i
$872$		0			0
$873$	2.00000	−	3.46410i	0.0676897	−	0.117242i
$874$		0			0
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	6.00000			0.202375
$880$		0			0
$881$	3.00000	−	5.19615i	0.101073	−	0.175063i	−0.811054	−	0.584971i	$-0.801106\pi$
$881$	3.00000	−	5.19615i	0.101073	−	0.175063i	0.912127	+	0.409908i	$0.134439\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	9.00000			0.302532
$886$		0			0
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$		0			0
$889$	11.0000			0.368928
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$	9.00000	−	15.5885i	0.300837	−	0.521065i
$896$		0			0
$897$	−10.5000	−	2.59808i	−0.350585	−	0.0867472i
$898$		0			0
$899$	−30.0000	+	51.9615i	−1.00056	+	1.73301i
$900$		0			0
$901$	−36.0000	−	62.3538i	−1.19933	−	2.07731i
$902$		0			0
$903$	4.00000	+	6.92820i	0.133112	+	0.230556i
$904$		0			0
$905$	15.0000			0.498617
$906$		0			0
$907$	7.00000	−	12.1244i	0.232431	−	0.402583i	−0.726092	−	0.687598i	$-0.758665\pi$
$907$	7.00000	−	12.1244i	0.232431	−	0.402583i	0.958523	+	0.285015i	$0.0919986\pi$
$908$		0			0
$909$	12.0000			0.398015
$910$		0			0
$911$	−21.0000			−0.695761			−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000			−0.695761			−0.347881	+	0.937539i	$0.613099\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−33.0000			−1.09095
$916$		0			0
$917$	−7.50000	−	12.9904i	−0.247672	−	0.428980i
$918$		0			0
$919$	−3.50000	−	6.06218i	−0.115454	−	0.199973i	0.802507	−	0.596643i	$-0.203499\pi$
$919$	−3.50000	−	6.06218i	−0.115454	−	0.199973i	−0.917961	+	0.396670i	$0.870166\pi$
$920$		0			0
$921$	6.50000	−	11.2583i	0.214182	−	0.370975i
$922$		0			0
$923$	−10.5000	−	2.59808i	−0.345612	−	0.0855167i
$924$		0			0
$925$	−16.0000	+	27.7128i	−0.526077	+	0.911192i
$926$		0			0
$927$	−14.0000	−	24.2487i	−0.459820	−	0.796432i
$928$		0			0
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	4.00000			0.131095
$932$		0			0
$933$	3.00000	−	5.19615i	0.0982156	−	0.170114i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$		0			0
$939$	4.00000	−	6.92820i	0.130535	−	0.226093i
$940$		0			0
$941$	15.0000			0.488986			0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000			0.488986			0.244493	+	0.969651i	$0.421378\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	7.50000	+	12.9904i	0.243975	+	0.422577i
$946$		0			0
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$948$		0			0
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$		0			0
$951$	−6.00000	+	10.3923i	−0.194563	+	0.336994i
$952$		0			0
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	0.961553	−	0.274620i	$-0.0885520\pi$
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	−0.718604	+	0.695419i	$0.755219\pi$
$954$		0			0
$955$	−36.0000	−	62.3538i	−1.16493	−	2.01772i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.50000	−	2.59808i	0.0484375	−	0.0838963i
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	−36.0000			−1.16008
$964$		0			0
$965$	−7.50000	+	12.9904i	−0.241434	+	0.418175i
$966$		0			0
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$		0			0
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$		0			0
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	0.889090	−	0.457732i	$-0.151338\pi$
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	−0.840953	+	0.541108i	$0.818005\pi$
$972$		0			0
$973$	8.00000	−	13.8564i	0.256468	−	0.444216i
$974$		0			0
$975$	−4.00000	−	13.8564i	−0.128103	−	0.443760i
$976$		0			0
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	0.364900	+	0.931047i	$0.381103\pi$
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	−0.988760	+	0.149511i	$0.952230\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−16.0000	−	27.7128i	−0.510841	−	0.884802i
$982$		0			0
$983$	30.0000			0.956851			0.478426	−	0.878128i	$-0.341208\pi$
$983$	30.0000			0.956851			0.478426	+	0.878128i	$0.341208\pi$
$984$		0			0
$985$	−18.0000	+	31.1769i	−0.573528	+	0.993379i
$986$		0			0
$987$	−6.00000			−0.190982
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	0.968864	+	0.247592i	$0.0796392\pi$
$992$		0			0
$993$	−10.0000			−0.317340
$994$		0			0
$995$	21.0000	+	36.3731i	0.665745	+	1.15310i
$996$		0			0
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	−0.997963	−	0.0637961i	$-0.979679\pi$
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	0.443732	−	0.896159i	$-0.353654\pi$
$998$		0			0
$999$	−20.0000	+	34.6410i	−0.632772	+	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.e.113.1		2
4.3	odd	2		182.2.g.b.113.1	yes	2
12.11	even	2		1638.2.r.c.1387.1		2
13.3	even	3	inner	1456.2.s.e.1121.1		2
28.3	even	6		1274.2.h.i.373.1		2
28.11	odd	6		1274.2.h.j.373.1		2
28.19	even	6		1274.2.e.i.165.1		2
28.23	odd	6		1274.2.e.d.165.1		2
28.27	even	2		1274.2.g.g.295.1		2
52.3	odd	6		182.2.g.b.29.1	✓	2
52.7	even	12		2366.2.d.f.337.1		2
52.19	even	12		2366.2.d.f.337.2		2
52.35	odd	6		2366.2.a.f.1.1		1
52.43	odd	6		2366.2.a.n.1.1		1
156.107	even	6		1638.2.r.c.757.1		2
364.3	even	6		1274.2.e.i.471.1		2
364.55	even	6		1274.2.g.g.393.1		2
364.107	odd	6		1274.2.h.j.263.1		2
364.159	even	6		1274.2.h.i.263.1		2
364.263	odd	6		1274.2.e.d.471.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.b.29.1	✓	2	52.3	odd	6
182.2.g.b.113.1	yes	2	4.3	odd	2
1274.2.e.d.165.1		2	28.23	odd	6
1274.2.e.d.471.1		2	364.263	odd	6
1274.2.e.i.165.1		2	28.19	even	6
1274.2.e.i.471.1		2	364.3	even	6
1274.2.g.g.295.1		2	28.27	even	2
1274.2.g.g.393.1		2	364.55	even	6
1274.2.h.i.263.1		2	364.159	even	6
1274.2.h.i.373.1		2	28.3	even	6
1274.2.h.j.263.1		2	364.107	odd	6
1274.2.h.j.373.1		2	28.11	odd	6
1456.2.s.e.113.1		2	1.1	even	1	trivial
1456.2.s.e.1121.1		2	13.3	even	3	inner
1638.2.r.c.757.1		2	156.107	even	6
1638.2.r.c.1387.1		2	12.11	even	2
2366.2.a.f.1.1		1	52.35	odd	6
2366.2.a.n.1.1		1	52.43	odd	6
2366.2.d.f.337.1		2	52.7	even	12
2366.2.d.f.337.2		2	52.19	even	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(2.50000 - 2.59808i) q^{13} +(1.50000 - 2.59808i) q^{15} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{21} +(1.50000 - 2.59808i) q^{23} +4.00000 q^{25} +5.00000 q^{27} +(-3.00000 + 5.19615i) q^{29} +10.0000 q^{31} +(1.50000 + 2.59808i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-1.00000 - 3.46410i) q^{39} +(4.00000 + 6.92820i) q^{43} +(3.00000 + 5.19615i) q^{45} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} -6.00000 q^{51} +12.0000 q^{53} -4.00000 q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.00000 + 1.73205i) q^{63} +(7.50000 - 7.79423i) q^{65} +(1.00000 - 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(-1.50000 - 2.59808i) q^{71} +2.00000 q^{73} +(2.00000 - 3.46410i) q^{75} +4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-9.00000 - 15.5885i) q^{85} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +(3.50000 + 0.866025i) q^{91} +(5.00000 - 8.66025i) q^{93} +(-6.00000 - 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 6 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + 6 * q^5 + q^7 + 2 * q^9	\( 2 q + q^{3} + 6 q^{5} + q^{7} + 2 q^{9} + 5 q^{13} + 3 q^{15} - 6 q^{17} - 4 q^{19} + 2 q^{21} + 3 q^{23} + 8 q^{25} + 10 q^{27} - 6 q^{29} + 20 q^{31} + 3 q^{35} - 8 q^{37} - 2 q^{39} + 8 q^{43} + 6 q^{45} - 12 q^{47} - q^{49} - 12 q^{51} + 24 q^{53} - 8 q^{57} + 3 q^{59} - 11 q^{61} - 2 q^{63} + 15 q^{65} + 2 q^{67} - 3 q^{69} - 3 q^{71} + 4 q^{73} + 4 q^{75} + 8 q^{79} - q^{81} - 18 q^{85} + 6 q^{87} + 6 q^{89} + 7 q^{91} + 10 q^{93} - 12 q^{95} - 2 q^{97}+O(q^{100}) \) 2 * q + q^3 + 6 * q^5 + q^7 + 2 * q^9 + 5 * q^13 + 3 * q^15 - 6 * q^17 - 4 * q^19 + 2 * q^21 + 3 * q^23 + 8 * q^25 + 10 * q^27 - 6 * q^29 + 20 * q^31 + 3 * q^35 - 8 * q^37 - 2 * q^39 + 8 * q^43 + 6 * q^45 - 12 * q^47 - q^49 - 12 * q^51 + 24 * q^53 - 8 * q^57 + 3 * q^59 - 11 * q^61 - 2 * q^63 + 15 * q^65 + 2 * q^67 - 3 * q^69 - 3 * q^71 + 4 * q^73 + 4 * q^75 + 8 * q^79 - q^81 - 18 * q^85 + 6 * q^87 + 6 * q^89 + 7 * q^91 + 10 * q^93 - 12 * q^95 - 2 * q^97

Introduction

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