LMFDB - Embedded newform 1456.2.s.a.1121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(113,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [2,0,-2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1456.1121
Dual form			1456.2.s.a.113.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{3} -3.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(2.50000 - 2.59808i) q^{13} +(3.00000 + 5.19615i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.00000 + 3.46410i) q^{19} -2.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +10.0000 q^{31} +(-6.00000 + 10.3923i) q^{33} +(-1.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-7.00000 - 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{45} +(-0.500000 - 0.866025i) q^{49} -6.00000 q^{51} -9.00000 q^{53} +(9.00000 + 15.5885i) q^{55} +8.00000 q^{57} +(-3.00000 + 5.19615i) q^{59} +(3.50000 - 6.06218i) q^{61} +(0.500000 + 0.866025i) q^{63} +(-7.50000 + 7.79423i) q^{65} +(1.00000 + 1.73205i) q^{67} +(-6.00000 + 10.3923i) q^{69} -7.00000 q^{73} +(-4.00000 - 6.92820i) q^{75} -6.00000 q^{77} -14.0000 q^{79} +(5.50000 + 9.52628i) q^{81} +18.0000 q^{83} +(-4.50000 + 7.79423i) q^{85} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(-1.00000 - 3.46410i) q^{91} +(-10.0000 - 17.3205i) q^{93} +(6.00000 - 10.3923i) q^{95} +(-1.00000 + 1.73205i) q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 6 q^{5} + q^{7} - q^{9} - 6 q^{11} + 5 q^{13} + 6 q^{15} + 3 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} + 8 q^{25} - 8 q^{27} - 3 q^{29} + 20 q^{31} - 12 q^{33} - 3 q^{35} + q^{37} - 14 q^{39}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 6 * q^5 + q^7 - q^9 - 6 * q^11 + 5 * q^13 + 6 * q^15 + 3 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 + 8 * q^25 - 8 * q^27 - 3 * q^29 + 20 * q^31 - 12 * q^33 - 3 * q^35 + q^37 - 14 * q^39 + 3 * q^41 - 10 * q^43 + 3 * q^45 - q^49 - 12 * q^51 - 18 * q^53 + 18 * q^55 + 16 * q^57 - 6 * q^59 + 7 * q^61 + q^63 - 15 * q^65 + 2 * q^67 - 12 * q^69 - 14 * q^73 - 8 * q^75 - 12 * q^77 - 28 * q^79 + 11 * q^81 + 36 * q^83 - 9 * q^85 - 6 * q^87 + 6 * q^89 - 2 * q^91 - 20 * q^93 + 12 * q^95 - 2 * q^97 + 12 * q^99

Character values

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

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

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
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$		0			0
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		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
$33$	−6.00000	+	10.3923i	−1.04447	+	1.80907i
$34$		0			0
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−7.00000	−	1.73205i	−1.12090	−	0.277350i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$		0			0
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−6.00000			−0.840168
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	9.00000	+	15.5885i	1.21356	+	2.10195i
$56$		0			0
$57$	8.00000			1.05963
$58$		0			0
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$		0			0
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$		0			0
$65$	−7.50000	+	7.79423i	−0.930261	+	0.966755i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$	−6.00000	+	10.3923i	−0.722315	+	1.25109i
$70$		0			0
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$		0			0
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$		0			0
$75$	−4.00000	−	6.92820i	−0.461880	−	0.800000i
$76$		0			0
$77$	−6.00000			−0.683763
$78$		0			0
$79$	−14.0000			−1.57512			−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$		0			0
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$		0			0
$93$	−10.0000	−	17.3205i	−1.03695	−	1.79605i
$94$		0			0
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	6.00000			0.585540
$106$		0			0
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	1.00000	−	1.73205i	0.0949158	−	0.164399i
$112$		0			0
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$		0			0
$117$	1.00000	+	3.46410i	0.0924500	+	0.320256i
$118$		0			0
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	10.0000	+	17.3205i	0.887357	+	1.53695i	0.842989	+	0.537931i	$0.180794\pi$
$127$	10.0000	+	17.3205i	0.887357	+	1.53695i	0.0443678	+	0.999015i	$0.485873\pi$
$128$		0			0
$129$	20.0000			1.76090
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$		0			0
$135$	12.0000			1.03280
$136$		0			0
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	−0.820495	−	0.571654i	$-0.806302\pi$
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	0.905314	+	0.424743i	$0.139635\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−21.0000	−	5.19615i	−1.75611	−	0.434524i
$144$		0			0
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$		0			0
$147$	−1.00000	+	1.73205i	−0.0824786	+	0.142857i
$148$		0			0
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	−0.0115483	−	0.999933i	$-0.503676\pi$
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	0.871742	−	0.489966i	$-0.162991\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$		0			0
$155$	−30.0000			−2.40966
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$		0			0
$159$	9.00000	+	15.5885i	0.713746	+	1.23625i
$160$		0			0
$161$	−6.00000			−0.472866
$162$		0			0
$163$	1.00000	−	1.73205i	0.0783260	−	0.135665i	−0.824202	−	0.566296i	$-0.808376\pi$
$163$	1.00000	−	1.73205i	0.0783260	−	0.135665i	0.902528	+	0.430632i	$0.141709\pi$
$164$		0			0
$165$	18.0000	−	31.1769i	1.40130	−	2.42712i
$166$		0			0
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	0.726293	−	0.687386i	$-0.241242\pi$
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	−0.958440	+	0.285295i	$0.907908\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$		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
$183$	−14.0000			−1.03491
$184$		0			0
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$		0			0
$187$	−18.0000			−1.31629
$188$		0			0
$189$	−2.00000	+	3.46410i	−0.145479	+	0.251976i
$190$		0			0
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$		0			0
$193$	−11.5000	−	19.9186i	−0.827788	−	1.43377i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−11.5000	−	19.9186i	−0.827788	−	1.43377i	0.0719816	−	0.997406i	$-0.477068\pi$
$194$		0			0
$195$	21.0000	+	5.19615i	1.50384	+	0.372104i
$196$		0			0
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	0.343937	−	0.938993i	$-0.388239\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$		0			0
$203$	−3.00000			−0.210559
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$	24.0000			1.66011
$210$		0			0
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	−0.944237	−	0.329266i	$-0.893199\pi$
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	0.186966	−	0.982366i	$-0.440135\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.0000	−	25.9808i	1.02299	−	1.77187i
$216$		0			0
$217$	5.00000	−	8.66025i	0.339422	−	0.587896i
$218$		0			0
$219$	7.00000	+	12.1244i	0.473016	+	0.819288i
$220$		0			0
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$		0			0
$223$	−14.0000	−	24.2487i	−0.937509	−	1.62381i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−14.0000	−	24.2487i	−0.937509	−	1.62381i	−0.167412	−	0.985887i	$-0.553541\pi$
$224$		0			0
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$		0			0
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$	6.00000	+	10.3923i	0.394771	+	0.683763i
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	14.0000	+	24.2487i	0.909398	+	1.57512i
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$		0			0
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$		0			0
$247$	4.00000	+	13.8564i	0.254514	+	0.881662i
$248$		0			0
$249$	−18.0000	−	31.1769i	−1.14070	−	1.97576i
$250$		0			0
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$		0			0
$253$	−18.0000	+	31.1769i	−1.13165	+	1.96008i
$254$		0			0
$255$	18.0000			1.12720
$256$		0			0
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	−0.981901	−	0.189396i	$-0.939347\pi$
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	0.326929	−	0.945049i	$-0.393986\pi$
$258$		0			0
$259$	1.00000			0.0621370
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	0.758585	−	0.651575i	$-0.225891\pi$
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	−0.943572	+	0.331166i	$0.892558\pi$
$264$		0			0
$265$	27.0000			1.65860
$266$		0			0
$267$	6.00000	−	10.3923i	0.367194	−	0.635999i
$268$		0			0
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$		0			0
$273$	−5.00000	+	5.19615i	−0.302614	+	0.314485i
$274$		0			0
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$		0			0
$279$	−5.00000	+	8.66025i	−0.299342	+	0.518476i
$280$		0			0
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$		0			0
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	−0.982173	−	0.187980i	$-0.939806\pi$
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	0.328291	−	0.944577i	$-0.393527\pi$
$284$		0			0
$285$	−24.0000			−1.42164
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	4.00000			0.234484
$292$		0			0
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$		0			0
$295$	9.00000	−	15.5885i	0.524000	−	0.907595i
$296$		0			0
$297$	12.0000	+	20.7846i	0.696311	+	1.20605i
$298$		0			0
$299$	−21.0000	−	5.19615i	−1.21446	−	0.300501i
$300$		0			0
$301$	5.00000	+	8.66025i	0.288195	+	0.499169i
$302$		0			0
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$		0			0
$305$	−10.5000	+	18.1865i	−0.601228	+	1.04136i
$306$		0			0
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$		0			0
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$		0			0
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$	−1.50000	−	2.59808i	−0.0845154	−	0.146385i
$316$		0			0
$317$	−9.00000			−0.505490			−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000			−0.505490			−0.252745	+	0.967533i	$0.581333\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.00000	+	10.3923i	0.333849	+	0.578243i
$324$		0			0
$325$	10.0000	−	10.3923i	0.554700	−	0.576461i
$326$		0			0
$327$	−2.00000	−	3.46410i	−0.110600	−	0.191565i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$		0			0
$333$	−1.00000			−0.0547997
$334$		0			0
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$		0			0
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$		0			0
$341$	−30.0000	−	51.9615i	−1.62459	−	2.81387i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	18.0000	−	31.1769i	0.969087	−	1.67851i
$346$		0			0
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$		0			0
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$		0			0
$351$	−10.0000	+	10.3923i	−0.533761	+	0.554700i
$352$		0			0
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.00000	+	5.19615i	−0.158777	+	0.275010i
$358$		0			0
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$	50.0000			2.62432
$364$		0			0
$365$	21.0000			1.09919
$366$		0			0
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$		0			0
$369$	−3.00000			−0.156174
$370$		0			0
$371$	−4.50000	+	7.79423i	−0.233628	+	0.404656i
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$		0			0
$375$	−3.00000	−	5.19615i	−0.154919	−	0.268328i
$376$		0			0
$377$	−10.5000	−	2.59808i	−0.540778	−	0.133808i
$378$		0			0
$379$	13.0000	+	22.5167i	0.667765	+	1.15660i	0.978528	+	0.206116i	$0.0660823\pi$
$379$	13.0000	+	22.5167i	0.667765	+	1.15660i	−0.310763	+	0.950488i	$0.600584\pi$
$380$		0			0
$381$	20.0000	−	34.6410i	1.02463	−	1.77471i
$382$		0			0
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$		0			0
$385$	18.0000			0.917365
$386$		0			0
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$		0			0
$389$	−33.0000			−1.67317			−0.836583	−	0.547840i	$-0.815450\pi$
$389$	−33.0000			−1.67317			−0.836583	+	0.547840i	$0.815450\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$		0			0
$394$		0			0
$395$	42.0000			2.11325
$396$		0			0
$397$	17.0000	−	29.4449i	0.853206	−	1.47780i	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	17.0000	−	29.4449i	0.853206	−	1.47780i	0.878300	−	0.478110i	$-0.158678\pi$
$398$		0			0
$399$	4.00000	−	6.92820i	0.200250	−	0.346844i
$400$		0			0
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$		0			0
$403$	25.0000	−	25.9808i	1.24534	−	1.29419i
$404$		0			0
$405$	−16.5000	−	28.5788i	−0.819892	−	1.42009i
$406$		0			0
$407$	3.00000	−	5.19615i	0.148704	−	0.257564i
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	6.00000			0.295958
$412$		0			0
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$		0			0
$415$	−54.0000			−2.65076
$416$		0			0
$417$	−4.00000			−0.195881
$418$		0			0
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	0.929954	−	0.367677i	$-0.119847\pi$
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	−0.783394	+	0.621525i	$0.786513\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−3.50000	−	6.06218i	−0.169377	−	0.293369i
$428$		0			0
$429$	12.0000	+	41.5692i	0.579365	+	2.00698i
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	−2.50000	+	4.33013i	−0.120142	+	0.208093i	−0.919824	−	0.392332i	$-0.871668\pi$
$433$	−2.50000	+	4.33013i	−0.120142	+	0.208093i	0.799681	+	0.600425i	$0.205002\pi$
$434$		0			0
$435$	9.00000	−	15.5885i	0.431517	−	0.747409i
$436$		0			0
$437$	24.0000			1.14808
$438$		0			0
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	−0.999576	−	0.0291138i	$-0.990731\pi$
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	0.474575	−	0.880215i	$-0.342602\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		0			0
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$		0			0
$447$	−42.0000			−1.98653
$448$		0			0
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	−0.965637	+	0.259895i	$0.916312\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$		0			0
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$		0			0
$455$	3.00000	+	10.3923i	0.140642	+	0.487199i
$456$		0			0
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$		0			0
$459$	−6.00000	+	10.3923i	−0.280056	+	0.485071i
$460$		0			0
$461$	−16.5000	+	28.5788i	−0.768482	+	1.33105i	0.169904	+	0.985461i	$0.445654\pi$
$461$	−16.5000	+	28.5788i	−0.768482	+	1.33105i	−0.938386	+	0.345589i	$0.887679\pi$
$462$		0			0
$463$	22.0000			1.02243			0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000			1.02243			0.511213	+	0.859454i	$0.329196\pi$
$464$		0			0
$465$	30.0000	+	51.9615i	1.39122	+	2.40966i
$466$		0			0
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$	2.00000			0.0923514
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$		0			0
$473$	60.0000			2.75880
$474$		0			0
$475$	−8.00000	+	13.8564i	−0.367065	+	0.635776i
$476$		0			0
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$		0			0
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.723681	+	0.690134i	$0.242449\pi$
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.235833	+	0.971794i	$0.424218\pi$
$480$		0			0
$481$	3.50000	+	0.866025i	0.159586	+	0.0394874i
$482$		0			0
$483$	6.00000	+	10.3923i	0.273009	+	0.472866i
$484$		0			0
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$		0			0
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	−0.233933	−	0.972253i	$-0.575160\pi$
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	0.958962	−	0.283535i	$-0.0915071\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$		0			0
$495$	−18.0000			−0.809040
$496$		0			0
$497$		0			0
$498$		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
$503$	−9.00000	+	15.5885i	−0.401290	+	0.695055i	−0.993882	−	0.110448i	$-0.964771\pi$
$503$	−9.00000	+	15.5885i	−0.401290	+	0.695055i	0.592592	+	0.805503i	$0.298105\pi$
$504$		0			0
$505$	−4.50000	−	7.79423i	−0.200247	−	0.346839i
$506$		0			0
$507$	−22.0000	+	13.8564i	−0.977054	+	0.615385i
$508$		0			0
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	0.533815	−	0.845601i	$-0.320758\pi$
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	−0.999220	+	0.0394971i	$0.987424\pi$
$510$		0			0
$511$	−3.50000	+	6.06218i	−0.154831	+	0.268175i
$512$		0			0
$513$	8.00000	−	13.8564i	0.353209	−	0.611775i
$514$		0			0
$515$	−12.0000			−0.528783
$516$		0			0
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	−39.0000			−1.70862			−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000			−1.70862			−0.854311	+	0.519763i	$0.826020\pi$
$522$		0			0
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	−0.990873	−	0.134801i	$-0.956961\pi$
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	0.378695	−	0.925521i	$-0.376373\pi$
$524$		0			0
$525$	−8.00000			−0.349149
$526$		0			0
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−3.00000	−	5.19615i	−0.130189	−	0.225494i
$532$		0			0
$533$	10.5000	+	2.59808i	0.454805	+	0.112535i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$		0			0
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$		0			0
$545$	−6.00000			−0.257012
$546$		0			0
$547$	34.0000			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$548$		0			0
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$		0			0
$551$	12.0000			0.511217
$552$		0			0
$553$	−7.00000	+	12.1244i	−0.297670	+	0.515580i
$554$		0			0
$555$	−3.00000	+	5.19615i	−0.127343	+	0.220564i
$556$		0			0
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	0.945473	−	0.325701i	$-0.105600\pi$
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	−0.754802	+	0.655953i	$0.772267\pi$
$558$		0			0
$559$	10.0000	+	34.6410i	0.422955	+	1.46516i
$560$		0			0
$561$	18.0000	+	31.1769i	0.759961	+	1.31629i
$562$		0			0
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$		0			0
$567$	11.0000			0.461957
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	−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
$573$	−36.0000			−1.50392
$574$		0			0
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$		0			0
$577$	−19.0000			−0.790980			−0.395490	−	0.918470i	$-0.629425\pi$
$577$	−19.0000			−0.790980			−0.395490	+	0.918470i	$0.629425\pi$
$578$		0			0
$579$	−23.0000	+	39.8372i	−0.955847	+	1.65558i
$580$		0			0
$581$	9.00000	−	15.5885i	0.373383	−	0.646718i
$582$		0			0
$583$	27.0000	+	46.7654i	1.11823	+	1.93682i
$584$		0			0
$585$	−3.00000	−	10.3923i	−0.124035	−	0.429669i
$586$		0			0
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	−0.951151	−	0.308725i	$-0.900098\pi$
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	0.208212	−	0.978084i	$-0.433236\pi$
$588$		0			0
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$		0			0
$593$	−15.0000			−0.615976			−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000			−0.615976			−0.307988	+	0.951390i	$0.599656\pi$
$594$		0			0
$595$	4.50000	+	7.79423i	0.184482	+	0.319532i
$596$		0			0
$597$	8.00000			0.327418
$598$		0			0
$599$	−36.0000			−1.47092			−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000			−1.47092			−0.735460	+	0.677568i	$0.763034\pi$
$600$		0			0
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$		0			0
$603$	−2.00000			−0.0814463
$604$		0			0
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$		0			0
$607$	22.0000	−	38.1051i	0.892952	−	1.54664i	0.0566340	−	0.998395i	$-0.481963\pi$
$607$	22.0000	−	38.1051i	0.892952	−	1.54664i	0.836318	−	0.548244i	$-0.184703\pi$
$608$		0			0
$609$	3.00000	+	5.19615i	0.121566	+	0.210559i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	6.50000	+	11.2583i	0.262533	+	0.454720i	0.966914	−	0.255102i	$-0.0821090\pi$
$613$	6.50000	+	11.2583i	0.262533	+	0.454720i	−0.704382	+	0.709821i	$0.748776\pi$
$614$		0			0
$615$	−9.00000	+	15.5885i	−0.362915	+	0.628587i
$616$		0			0
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.0859976	−	0.996295i	$-0.472592\pi$
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.819818	−	0.572624i	$-0.194074\pi$
$618$		0			0
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$		0			0
$621$	12.0000	+	20.7846i	0.481543	+	0.834058i
$622$		0			0
$623$	6.00000			0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$	−24.0000	−	41.5692i	−0.958468	−	1.66011i
$628$		0			0
$629$	3.00000			0.119618
$630$		0			0
$631$	−2.00000	+	3.46410i	−0.0796187	+	0.137904i	−0.903085	−	0.429461i	$-0.858704\pi$
$631$	−2.00000	+	3.46410i	−0.0796187	+	0.137904i	0.823467	+	0.567365i	$0.192037\pi$
$632$		0			0
$633$	−22.0000	+	38.1051i	−0.874421	+	1.51454i
$634$		0			0
$635$	−30.0000	−	51.9615i	−1.19051	−	2.06203i
$636$		0			0
$637$	−3.50000	−	0.866025i	−0.138675	−	0.0343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	−20.0000	+	34.6410i	−0.788723	+	1.36611i	0.138027	+	0.990429i	$0.455924\pi$
$643$	−20.0000	+	34.6410i	−0.788723	+	1.36611i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$	−60.0000			−2.36250
$646$		0			0
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	0.527710	−	0.849425i	$-0.323051\pi$
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	−0.999478	+	0.0322975i	$0.989718\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$		0			0
$651$	−20.0000			−0.783862
$652$		0			0
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.50000	−	6.06218i	0.136548	−	0.236508i
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		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
$669$	−28.0000	+	48.4974i	−1.08254	+	1.87502i
$670$		0			0
$671$	−42.0000			−1.62139
$672$		0			0
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$		0			0
$675$	−16.0000			−0.615840
$676$		0			0
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$	1.00000	+	1.73205i	0.0383765	+	0.0664700i
$680$		0			0
$681$	12.0000			0.459841
$682$		0			0
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	−0.998917	−	0.0465244i	$-0.985185\pi$
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	0.539750	+	0.841825i	$0.318519\pi$
$684$		0			0
$685$	4.50000	−	7.79423i	0.171936	−	0.297802i
$686$		0			0
$687$	−14.0000	−	24.2487i	−0.534133	−	0.925146i
$688$		0			0
$689$	−22.5000	+	23.3827i	−0.857182	+	0.890809i
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$		0			0
$693$	3.00000	−	5.19615i	0.113961	−	0.197386i
$694$		0			0
$695$	−3.00000	+	5.19615i	−0.113796	+	0.197101i
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	18.0000	+	31.1769i	0.680823	+	1.17922i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−4.00000			−0.150863
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.00000			0.112827
$708$		0			0
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	−0.856484	−	0.516174i	$-0.827356\pi$
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	0.875262	+	0.483650i	$0.160689\pi$
$710$		0			0
$711$	7.00000	−	12.1244i	0.262521	−	0.454699i
$712$		0			0
$713$	−30.0000	−	51.9615i	−1.12351	−	1.94597i
$714$		0			0
$715$	63.0000	+	15.5885i	2.35607	+	0.582975i
$716$		0			0
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	2.00000	−	3.46410i	0.0744839	−	0.129010i
$722$		0			0
$723$	34.0000			1.26447
$724$		0			0
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		0			0
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	15.0000	+	25.9808i	0.554795	+	0.960933i
$732$		0			0
$733$	17.0000			0.627909			0.313955	−	0.949438i	$-0.398346\pi$
$733$	17.0000			0.627909			0.313955	+	0.949438i	$0.398346\pi$
$734$		0			0
$735$	3.00000	−	5.19615i	0.110657	−	0.191663i
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	20.0000	−	20.7846i	0.734718	−	0.763542i
$742$		0			0
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	−31.5000	+	54.5596i	−1.15407	+	1.99891i
$746$		0			0
$747$	−9.00000	+	15.5885i	−0.329293	+	0.570352i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−23.0000	−	39.8372i	−0.839282	−	1.45368i	−0.890496	−	0.454991i	$-0.849642\pi$
$751$	−23.0000	−	39.8372i	−0.839282	−	1.45368i	0.0512140	−	0.998688i	$-0.483691\pi$
$752$		0			0
$753$	24.0000			0.874609
$754$		0			0
$755$	24.0000			0.873449
$756$		0			0
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	0.847280	−	0.531146i	$-0.178238\pi$
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	−0.883626	+	0.468193i	$0.844905\pi$
$758$		0			0
$759$	72.0000			2.61343
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$		0			0
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$		0			0
$767$	6.00000	+	20.7846i	0.216647	+	0.750489i
$768$		0			0
$769$	23.0000	+	39.8372i	0.829401	+	1.43657i	0.898509	+	0.438956i	$0.144652\pi$
$769$	23.0000	+	39.8372i	0.829401	+	1.43657i	−0.0691074	+	0.997609i	$0.522015\pi$
$770$		0			0
$771$	−21.0000	+	36.3731i	−0.756297	+	1.30994i
$772$		0			0
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	40.0000			1.43684
$776$		0			0
$777$	−1.00000	−	1.73205i	−0.0358748	−	0.0621370i
$778$		0			0
$779$	−12.0000			−0.429945
$780$		0			0
$781$		0			0
$782$		0			0
$783$	6.00000	+	10.3923i	0.214423	+	0.371391i
$784$		0			0
$785$	21.0000			0.749522
$786$		0			0
$787$	−5.00000	+	8.66025i	−0.178231	+	0.308705i	−0.941275	−	0.337642i	$-0.890371\pi$
$787$	−5.00000	+	8.66025i	−0.178231	+	0.308705i	0.763044	+	0.646347i	$0.223704\pi$
$788$		0			0
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	1.50000	+	2.59808i	0.0533339	+	0.0923770i
$792$		0			0
$793$	−7.00000	−	24.2487i	−0.248577	−	0.861097i
$794$		0			0
$795$	−27.0000	−	46.7654i	−0.957591	−	1.65860i
$796$		0			0
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	−0.914255	−	0.405140i	$-0.867223\pi$
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	0.807989	+	0.589197i	$0.200556\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$	21.0000	+	36.3731i	0.741074	+	1.28358i
$804$		0			0
$805$	18.0000			0.634417
$806$		0			0
$807$	36.0000			1.26726
$808$		0			0
$809$	−25.5000	−	44.1673i	−0.896532	−	1.55284i	−0.831897	−	0.554930i	$-0.812745\pi$
$809$	−25.5000	−	44.1673i	−0.896532	−	1.55284i	−0.0646355	−	0.997909i	$-0.520588\pi$
$810$		0			0
$811$	−26.0000			−0.912983			−0.456492	−	0.889728i	$-0.650894\pi$
$811$	−26.0000			−0.912983			−0.456492	+	0.889728i	$0.650894\pi$
$812$		0			0
$813$	2.00000	−	3.46410i	0.0701431	−	0.121491i
$814$		0			0
$815$	−3.00000	+	5.19615i	−0.105085	+	0.182013i
$816$		0			0
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$		0			0
$819$	3.50000	+	0.866025i	0.122300	+	0.0302614i
$820$		0			0
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	−0.898776	−	0.438408i	$-0.855543\pi$
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	0.829060	+	0.559159i	$0.188876\pi$
$824$		0			0
$825$	−24.0000	+	41.5692i	−0.835573	+	1.44725i
$826$		0			0
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$		0			0
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	0.920383	−	0.391018i	$-0.127877\pi$
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	−2.00000			−0.0693792
$832$		0			0
$833$	−3.00000			−0.103944
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$		0			0
$837$	−40.0000			−1.38260
$838$		0			0
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	−27.0000	−	46.7654i	−0.929929	−	1.61068i
$844$		0			0
$845$	1.50000	+	38.9711i	0.0516016	+	1.34065i
$846$		0			0
$847$	12.5000	+	21.6506i	0.429505	+	0.743925i
$848$		0			0
$849$	−22.0000	+	38.1051i	−0.755038	+	1.30776i
$850$		0			0
$851$	3.00000	−	5.19615i	0.102839	−	0.178122i
$852$		0			0
$853$	−19.0000			−0.650548			−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000			−0.650548			−0.325274	+	0.945620i	$0.605456\pi$
$854$		0			0
$855$	6.00000	+	10.3923i	0.205196	+	0.355409i
$856$		0			0
$857$	33.0000			1.12726			0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000			1.12726			0.563629	+	0.826028i	$0.309405\pi$
$858$		0			0
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$		0			0
$861$	−3.00000	−	5.19615i	−0.102240	−	0.177084i
$862$		0			0
$863$	−54.0000			−1.83818			−0.919091	−	0.394046i	$-0.871075\pi$
$863$	−54.0000			−1.83818			−0.919091	+	0.394046i	$0.871075\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$		0			0
$869$	42.0000	+	72.7461i	1.42475	+	2.46774i
$870$		0			0
$871$	7.00000	+	1.73205i	0.237186	+	0.0586883i
$872$		0			0
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	24.5000	−	42.4352i	0.827306	−	1.43294i	−0.0728377	−	0.997344i	$-0.523206\pi$
$877$	24.5000	−	42.4352i	0.827306	−	1.43294i	0.900144	−	0.435593i	$-0.143461\pi$
$878$		0			0
$879$	−6.00000			−0.202375
$880$		0			0
$881$	−22.5000	−	38.9711i	−0.758044	−	1.31297i	−0.943847	−	0.330384i	$-0.892822\pi$
$881$	−22.5000	−	38.9711i	−0.758044	−	1.31297i	0.185802	−	0.982587i	$-0.440512\pi$
$882$		0			0
$883$	−38.0000			−1.27880			−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000			−1.27880			−0.639401	+	0.768874i	$0.720818\pi$
$884$		0			0
$885$	−36.0000			−1.21013
$886$		0			0
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$	20.0000			0.670778
$890$		0			0
$891$	33.0000	−	57.1577i	1.10554	−	1.91485i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	12.0000	+	41.5692i	0.400668	+	1.38796i
$898$		0			0
$899$	−15.0000	−	25.9808i	−0.500278	−	0.866507i
$900$		0			0
$901$	−13.5000	+	23.3827i	−0.449750	+	0.778990i
$902$		0			0
$903$	10.0000	−	17.3205i	0.332779	−	0.576390i
$904$		0			0
$905$	−15.0000			−0.498617
$906$		0			0
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	0.958523	−	0.285015i	$-0.0919986\pi$
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	−0.726092	+	0.687598i	$0.758665\pi$
$908$		0			0
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−54.0000	−	93.5307i	−1.78714	−	3.09542i
$914$		0			0
$915$	42.0000			1.38848
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	−22.0000	−	38.1051i	−0.724925	−	1.25561i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$		0			0
$927$	−2.00000	+	3.46410i	−0.0656886	+	0.113776i
$928$		0			0
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	0.457480	+	0.889220i	$0.348752\pi$
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	−0.998827	+	0.0484211i	$0.984581\pi$
$930$		0			0
$931$	4.00000			0.131095
$932$		0			0
$933$	−18.0000	−	31.1769i	−0.589294	−	1.02069i
$934$		0			0
$935$	54.0000			1.76599
$936$		0			0
$937$	−19.0000			−0.620703			−0.310351	−	0.950622i	$-0.600447\pi$
$937$	−19.0000			−0.620703			−0.310351	+	0.950622i	$0.600447\pi$
$938$		0			0
$939$	10.0000	+	17.3205i	0.326338	+	0.565233i
$940$		0			0
$941$	30.0000			0.977972			0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000			0.977972			0.488986	+	0.872292i	$0.337367\pi$
$942$		0			0
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$		0			0
$945$	6.00000	−	10.3923i	0.195180	−	0.338062i
$946$		0			0
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927599\pi$
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	0.291835	−	0.956469i	$-0.405734\pi$
$948$		0			0
$949$	−17.5000	+	18.1865i	−0.568074	+	0.590360i
$950$		0			0
$951$	9.00000	+	15.5885i	0.291845	+	0.505490i
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$		0			0
$955$	−27.0000	+	46.7654i	−0.873699	+	1.51329i
$956$		0			0
$957$	36.0000			1.16371
$958$		0			0
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$		0			0
$964$		0			0
$965$	34.5000	+	59.7558i	1.11059	+	1.92361i
$966$		0			0
$967$	34.0000			1.09337			0.546683	−	0.837340i	$-0.315890\pi$
$967$	34.0000			1.09337			0.546683	+	0.837340i	$0.315890\pi$
$968$		0			0
$969$	12.0000	−	20.7846i	0.385496	−	0.667698i
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	−1.00000	−	1.73205i	−0.0320585	−	0.0555270i
$974$		0			0
$975$	−28.0000	−	6.92820i	−0.896718	−	0.221880i
$976$		0			0
$977$	−25.5000	−	44.1673i	−0.815817	−	1.41304i	−0.908740	−	0.417364i	$-0.862954\pi$
$977$	−25.5000	−	44.1673i	−0.815817	−	1.41304i	0.0929223	−	0.995673i	$-0.470379\pi$
$978$		0			0
$979$	18.0000	−	31.1769i	0.575282	−	0.996419i
$980$		0			0
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$		0			0
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		0			0
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	60.0000			1.90789
$990$		0			0
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$		0			0
$993$	20.0000			0.634681
$994$		0			0
$995$	6.00000	−	10.3923i	0.190213	−	0.329458i
$996$		0			0
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$		0			0
$999$	−2.00000	−	3.46410i	−0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.a.1121.1		2
4.3	odd	2		182.2.g.c.29.1	✓	2
12.11	even	2		1638.2.r.m.757.1		2
13.9	even	3	inner	1456.2.s.a.113.1		2
28.3	even	6		1274.2.e.b.471.1		2
28.11	odd	6		1274.2.e.k.471.1		2
28.19	even	6		1274.2.h.l.263.1		2
28.23	odd	6		1274.2.h.e.263.1		2
28.27	even	2		1274.2.g.c.393.1		2
52.3	odd	6		2366.2.a.a.1.1		1
52.11	even	12		2366.2.d.a.337.1		2
52.15	even	12		2366.2.d.a.337.2		2
52.23	odd	6		2366.2.a.k.1.1		1
52.35	odd	6		182.2.g.c.113.1	yes	2
156.35	even	6		1638.2.r.m.1387.1		2
364.87	even	6		1274.2.h.l.373.1		2
364.139	even	6		1274.2.g.c.295.1		2
364.191	odd	6		1274.2.e.k.165.1		2
364.243	even	6		1274.2.e.b.165.1		2
364.347	odd	6		1274.2.h.e.373.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.c.29.1	✓	2	4.3	odd	2
182.2.g.c.113.1	yes	2	52.35	odd	6
1274.2.e.b.165.1		2	364.243	even	6
1274.2.e.b.471.1		2	28.3	even	6
1274.2.e.k.165.1		2	364.191	odd	6
1274.2.e.k.471.1		2	28.11	odd	6
1274.2.g.c.295.1		2	364.139	even	6
1274.2.g.c.393.1		2	28.27	even	2
1274.2.h.e.263.1		2	28.23	odd	6
1274.2.h.e.373.1		2	364.347	odd	6
1274.2.h.l.263.1		2	28.19	even	6
1274.2.h.l.373.1		2	364.87	even	6
1456.2.s.a.113.1		2	13.9	even	3	inner
1456.2.s.a.1121.1		2	1.1	even	1	trivial
1638.2.r.m.757.1		2	12.11	even	2
1638.2.r.m.1387.1		2	156.35	even	6
2366.2.a.a.1.1		1	52.3	odd	6
2366.2.a.k.1.1		1	52.23	odd	6
2366.2.d.a.337.1		2	52.11	even	12
2366.2.d.a.337.2		2	52.15	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} -3.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(2.50000 - 2.59808i) q^{13} +(3.00000 + 5.19615i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.00000 + 3.46410i) q^{19} -2.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +10.0000 q^{31} +(-6.00000 + 10.3923i) q^{33} +(-1.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-7.00000 - 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{45} +(-0.500000 - 0.866025i) q^{49} -6.00000 q^{51} -9.00000 q^{53} +(9.00000 + 15.5885i) q^{55} +8.00000 q^{57} +(-3.00000 + 5.19615i) q^{59} +(3.50000 - 6.06218i) q^{61} +(0.500000 + 0.866025i) q^{63} +(-7.50000 + 7.79423i) q^{65} +(1.00000 + 1.73205i) q^{67} +(-6.00000 + 10.3923i) q^{69} -7.00000 q^{73} +(-4.00000 - 6.92820i) q^{75} -6.00000 q^{77} -14.0000 q^{79} +(5.50000 + 9.52628i) q^{81} +18.0000 q^{83} +(-4.50000 + 7.79423i) q^{85} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(-1.00000 - 3.46410i) q^{91} +(-10.0000 - 17.3205i) q^{93} +(6.00000 - 10.3923i) q^{95} +(-1.00000 + 1.73205i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 6 q^{5} + q^{7} - q^{9} - 6 q^{11} + 5 q^{13} + 6 q^{15} + 3 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} + 8 q^{25} - 8 q^{27} - 3 q^{29} + 20 q^{31} - 12 q^{33} - 3 q^{35} + q^{37} - 14 q^{39}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 6 * q^5 + q^7 - q^9 - 6 * q^11 + 5 * q^13 + 6 * q^15 + 3 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 + 8 * q^25 - 8 * q^27 - 3 * q^29 + 20 * q^31 - 12 * q^33 - 3 * q^35 + q^37 - 14 * q^39 + 3 * q^41 - 10 * q^43 + 3 * q^45 - q^49 - 12 * q^51 - 18 * q^53 + 18 * q^55 + 16 * q^57 - 6 * q^59 + 7 * q^61 + q^63 - 15 * q^65 + 2 * q^67 - 12 * q^69 - 14 * q^73 - 8 * q^75 - 12 * q^77 - 28 * q^79 + 11 * q^81 + 36 * q^83 - 9 * q^85 - 6 * q^87 + 6 * q^89 - 2 * q^91 - 20 * q^93 + 12 * q^95 - 2 * q^97 + 12 * q^99

Introduction

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