LMFDB - Embedded newform 1456.2.s.k.113.1

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 = [4,0,-1,0,-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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	1456.113
Dual form			1456.2.s.k.1121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39564 + 2.41733i) q^{3} +0.791288 q^{5} +(0.500000 + 0.866025i) q^{7} +(-2.39564 - 4.14938i) q^{9} +(0.395644 - 0.685275i) q^{11} +(2.50000 - 2.59808i) q^{13} +(-1.10436 + 1.91280i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-3.18693 - 5.51993i) q^{19} -2.79129 q^{21} +(3.00000 - 5.19615i) q^{23} -4.37386 q^{25} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +1.00000 q^{31} +(1.10436 + 1.91280i) q^{33} +(0.395644 + 0.685275i) q^{35} +(2.00000 - 3.46410i) q^{37} +(2.79129 + 9.66930i) q^{39} +(-3.79129 + 6.56670i) q^{41} +(-4.68693 - 8.11800i) q^{43} +(-1.89564 - 3.28335i) q^{45} -6.16515 q^{47} +(-0.500000 + 0.866025i) q^{49} +8.37386 q^{51} -1.41742 q^{53} +(0.313068 - 0.542250i) q^{55} +17.7913 q^{57} +(-4.50000 - 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(2.39564 - 4.14938i) q^{63} +(1.97822 - 2.05583i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(8.37386 + 14.5040i) q^{69} +(-0.791288 - 1.37055i) q^{71} +14.0000 q^{73} +(6.10436 - 10.5731i) q^{75} +0.791288 q^{77} +4.00000 q^{79} +(0.208712 - 0.361500i) q^{81} +9.00000 q^{83} +(-1.18693 - 2.05583i) q^{85} +(9.47822 + 16.4168i) q^{87} +(-4.18693 + 7.25198i) q^{89} +(3.50000 + 0.866025i) q^{91} +(-1.39564 + 2.41733i) q^{93} +(-2.52178 - 4.36785i) q^{95} +(2.31307 + 4.00635i) q^{97} -3.79129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 6 q^{5} + 2 q^{7} - 5 q^{9} - 3 q^{11} + 10 q^{13} - 9 q^{15} - 6 q^{17} + q^{19} - 2 q^{21} + 12 q^{23} + 10 q^{25} + 20 q^{27} + 9 q^{29} + 4 q^{31} + 9 q^{33} - 3 q^{35} + 8 q^{37} + 2 q^{39}+ \cdots - 6 q^{99}+O(q^{100}) $ 4 * q - q^3 - 6 * q^5 + 2 * q^7 - 5 * q^9 - 3 * q^11 + 10 * q^13 - 9 * q^15 - 6 * q^17 + q^19 - 2 * q^21 + 12 * q^23 + 10 * q^25 + 20 * q^27 + 9 * q^29 + 4 * q^31 + 9 * q^33 - 3 * q^35 + 8 * q^37 + 2 * q^39 - 6 * q^41 - 5 * q^43 - 3 * q^45 + 12 * q^47 - 2 * q^49 + 6 * q^51 - 24 * q^53 + 15 * q^55 + 62 * q^57 - 18 * q^59 - 4 * q^61 + 5 * q^63 - 15 * q^65 - 14 * q^67 + 6 * q^69 + 6 * q^71 + 56 * q^73 + 29 * q^75 - 6 * q^77 + 16 * q^79 + 10 * q^81 + 36 * q^83 + 9 * q^85 + 15 * q^87 - 3 * q^89 + 14 * q^91 - q^93 - 33 * q^95 + 23 * q^97 - 6 * q^99

Character values

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

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

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
$3$	−1.39564	+	2.41733i	−0.805775	+	1.39564i	0.109991	+	0.993933i	$0.464918\pi$
$3$	−1.39564	+	2.41733i	−0.805775	+	1.39564i	−0.915766	+	0.401711i	$0.868416\pi$
$4$		0			0
$5$	0.791288			0.353875			0.176937	−	0.984222i	$-0.443381\pi$
$5$	0.791288			0.353875			0.176937	+	0.984222i	$0.443381\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	−2.39564	−	4.14938i	−0.798548	−	1.38313i
$10$		0			0
$11$	0.395644	−	0.685275i	0.119291	−	0.206618i	−0.800196	−	0.599739i	$-0.795271\pi$
$11$	0.395644	−	0.685275i	0.119291	−	0.206618i	0.919487	+	0.393121i	$0.128604\pi$
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	−1.10436	+	1.91280i	−0.285144	+	0.493883i
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−3.18693	−	5.51993i	−0.731132	−	1.26636i	−0.956400	−	0.292061i	$-0.905659\pi$
$19$	−3.18693	−	5.51993i	−0.731132	−	1.26636i	0.225267	−	0.974297i	$-0.427674\pi$
$20$		0			0
$21$	−2.79129			−0.609109
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−4.37386			−0.874773
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	−0.356883	−	0.934149i	$-0.616161\pi$
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	0.987438	−	0.158005i	$-0.0505061\pi$
$30$		0			0
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$		0			0
$33$	1.10436	+	1.91280i	0.192244	+	0.332976i
$34$		0			0
$35$	0.395644	+	0.685275i	0.0668760	+	0.115833i
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$		0			0
$39$	2.79129	+	9.66930i	0.446964	+	1.54833i
$40$		0			0
$41$	−3.79129	+	6.56670i	−0.592100	+	1.02555i	0.401849	+	0.915706i	$0.368368\pi$
$41$	−3.79129	+	6.56670i	−0.592100	+	1.02555i	−0.993949	+	0.109841i	$0.964966\pi$
$42$		0			0
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	−0.963056	−	0.269302i	$-0.913207\pi$
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	0.248305	−	0.968682i	$-0.420126\pi$
$44$		0			0
$45$	−1.89564	−	3.28335i	−0.282586	−	0.489453i
$46$		0			0
$47$	−6.16515			−0.899280			−0.449640	−	0.893210i	$-0.648448\pi$
$47$	−6.16515			−0.899280			−0.449640	+	0.893210i	$0.648448\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	8.37386			1.17258
$52$		0			0
$53$	−1.41742			−0.194698			−0.0973491	−	0.995250i	$-0.531036\pi$
$53$	−1.41742			−0.194698			−0.0973491	+	0.995250i	$0.531036\pi$
$54$		0			0
$55$	0.313068	−	0.542250i	0.0422141	−	0.0731170i
$56$		0			0
$57$	17.7913			2.35651
$58$		0			0
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$	2.39564	−	4.14938i	0.301823	−	0.522772i
$64$		0			0
$65$	1.97822	−	2.05583i	0.245368	−	0.254994i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$		0			0
$69$	8.37386	+	14.5040i	1.00809	+	1.74607i
$70$		0			0
$71$	−0.791288	−	1.37055i	−0.0939086	−	0.162654i	0.815244	−	0.579118i	$-0.196603\pi$
$71$	−0.791288	−	1.37055i	−0.0939086	−	0.162654i	−0.909153	+	0.416463i	$0.863269\pi$
$72$		0			0
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$		0			0
$75$	6.10436	−	10.5731i	0.704870	−	1.22087i
$76$		0			0
$77$	0.791288			0.0901756
$78$		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
$81$	0.208712	−	0.361500i	0.0231902	−	0.0401667i
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	−1.18693	−	2.05583i	−0.128741	−	0.222986i
$86$		0			0
$87$	9.47822	+	16.4168i	1.01617	+	1.76006i
$88$		0			0
$89$	−4.18693	+	7.25198i	−0.443814	+	0.768708i	−0.997969	−	0.0637054i	$-0.979708\pi$
$89$	−4.18693	+	7.25198i	−0.443814	+	0.768708i	0.554155	+	0.832414i	$0.313042\pi$
$90$		0			0
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$		0			0
$93$	−1.39564	+	2.41733i	−0.144722	+	0.250665i
$94$		0			0
$95$	−2.52178	−	4.36785i	−0.258729	−	0.448132i
$96$		0			0
$97$	2.31307	+	4.00635i	0.234856	+	0.406783i	0.959231	−	0.282623i	$-0.0912046\pi$
$97$	2.31307	+	4.00635i	0.234856	+	0.406783i	−0.724374	+	0.689407i	$0.757871\pi$
$98$		0			0
$99$	−3.79129			−0.381039
$100$		0			0
$101$	−8.76951	+	15.1892i	−0.872599	+	1.51139i	−0.0132996	+	0.999912i	$0.504234\pi$
$101$	−8.76951	+	15.1892i	−0.872599	+	1.51139i	−0.859299	+	0.511474i	$0.829100\pi$
$102$		0			0
$103$	1.00000			0.0985329			0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000			0.0985329			0.0492665	+	0.998786i	$0.484312\pi$
$104$		0			0
$105$	−2.20871			−0.215548
$106$		0			0
$107$	7.18693	−	12.4481i	0.694787	−	1.20341i	−0.275466	−	0.961311i	$-0.588832\pi$
$107$	7.18693	−	12.4481i	0.694787	−	1.20341i	0.970252	−	0.242095i	$-0.0778347\pi$
$108$		0			0
$109$	9.74773			0.933663			0.466831	−	0.884346i	$-0.345395\pi$
$109$	9.74773			0.933663			0.466831	+	0.884346i	$0.345395\pi$
$110$		0			0
$111$	5.58258	+	9.66930i	0.529875	+	0.917770i
$112$		0			0
$113$	−3.08258	−	5.33918i	−0.289984	−	0.502268i	0.683821	−	0.729649i	$-0.260317\pi$
$113$	−3.08258	−	5.33918i	−0.289984	−	0.502268i	−0.973806	+	0.227382i	$0.926983\pi$
$114$		0			0
$115$	2.37386	−	4.11165i	0.221364	−	0.383414i
$116$		0			0
$117$	−16.7695	−	4.14938i	−1.55034	−	0.383610i
$118$		0			0
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$		0			0
$121$	5.18693	+	8.98403i	0.471539	+	0.816730i
$122$		0			0
$123$	−10.5826	−	18.3296i	−0.954199	−	1.65272i
$124$		0			0
$125$	−7.41742			−0.663435
$126$		0			0
$127$	−7.68693	+	13.3142i	−0.682105	+	1.18144i	0.292232	+	0.956347i	$0.405602\pi$
$127$	−7.68693	+	13.3142i	−0.682105	+	1.18144i	−0.974337	+	0.225093i	$0.927731\pi$
$128$		0			0
$129$	26.1652			2.30371
$130$		0			0
$131$	18.9564			1.65623			0.828116	−	0.560557i	$-0.189413\pi$
$131$	18.9564			1.65623			0.828116	+	0.560557i	$0.189413\pi$
$132$		0			0
$133$	3.18693	−	5.51993i	0.276342	−	0.478638i
$134$		0			0
$135$	3.95644			0.340516
$136$		0			0
$137$	1.18693	+	2.05583i	0.101406	+	0.175641i	0.912264	−	0.409602i	$-0.134332\pi$
$137$	1.18693	+	2.05583i	0.101406	+	0.175641i	−0.810858	+	0.585243i	$0.800999\pi$
$138$		0			0
$139$	6.68693	+	11.5821i	0.567178	+	0.982381i	0.996843	+	0.0793931i	$0.0252982\pi$
$139$	6.68693	+	11.5821i	0.567178	+	0.982381i	−0.429665	+	0.902988i	$0.641368\pi$
$140$		0			0
$141$	8.60436	−	14.9032i	0.724617	−	1.25507i
$142$		0			0
$143$	−0.791288	−	2.74110i	−0.0661708	−	0.229222i
$144$		0			0
$145$	2.68693	−	4.65390i	0.223138	−	0.386486i
$146$		0			0
$147$	−1.39564	−	2.41733i	−0.115111	−	0.199378i
$148$		0			0
$149$	−10.9782	−	19.0148i	−0.899371	−	1.55776i	−0.828300	−	0.560285i	$-0.810692\pi$
$149$	−10.9782	−	19.0148i	−0.899371	−	1.55776i	−0.0710706	−	0.997471i	$-0.522642\pi$
$150$		0			0
$151$	7.00000			0.569652			0.284826	−	0.958579i	$-0.408064\pi$
$151$	7.00000			0.569652			0.284826	+	0.958579i	$0.408064\pi$
$152$		0			0
$153$	−7.18693	+	12.4481i	−0.581029	+	1.00637i
$154$		0			0
$155$	0.791288			0.0635578
$156$		0			0
$157$	−4.62614			−0.369206			−0.184603	−	0.982813i	$-0.559100\pi$
$157$	−4.62614			−0.369206			−0.184603	+	0.982813i	$0.559100\pi$
$158$		0			0
$159$	1.97822	−	3.42638i	0.156883	−	0.271729i
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−10.3739	−	17.9681i	−0.812544	−	1.40737i	−0.911078	−	0.412233i	$-0.864749\pi$
$163$	−10.3739	−	17.9681i	−0.812544	−	1.40737i	0.0985346	−	0.995134i	$-0.468584\pi$
$164$		0			0
$165$	0.873864	+	1.51358i	0.0680302	+	0.117832i
$166$		0			0
$167$	−9.08258	+	15.7315i	−0.702831	+	1.21734i	0.264638	+	0.964348i	$0.414748\pi$
$167$	−9.08258	+	15.7315i	−0.702831	+	1.21734i	−0.967469	+	0.252991i	$0.918586\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−15.2695	+	26.4476i	−1.16769	+	2.02250i
$172$		0			0
$173$	−7.66515	−	13.2764i	−0.582771	−	1.00939i	−0.995149	−	0.0983759i	$-0.968635\pi$
$173$	−7.66515	−	13.2764i	−0.582771	−	1.00939i	0.412379	−	0.911013i	$-0.364698\pi$
$174$		0			0
$175$	−2.18693	−	3.78788i	−0.165317	−	0.286337i
$176$		0			0
$177$	25.1216			1.88825
$178$		0			0
$179$	−2.29129	+	3.96863i	−0.171259	+	0.296629i	−0.938860	−	0.344298i	$-0.888117\pi$
$179$	−2.29129	+	3.96863i	−0.171259	+	0.296629i	0.767601	+	0.640928i	$0.221450\pi$
$180$		0			0
$181$	−2.74773			−0.204237			−0.102118	−	0.994772i	$-0.532562\pi$
$181$	−2.74773			−0.204237			−0.102118	+	0.994772i	$0.532562\pi$
$182$		0			0
$183$	5.58258			0.412676
$184$		0			0
$185$	1.58258	−	2.74110i	0.116353	−	0.201530i
$186$		0			0
$187$	−2.37386			−0.173594
$188$		0			0
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$		0			0
$191$	−5.76951	−	9.99308i	−0.417467	−	0.723074i	0.578217	−	0.815883i	$-0.303749\pi$
$191$	−5.76951	−	9.99308i	−0.417467	−	0.723074i	−0.995684	+	0.0928091i	$0.970415\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$		0			0
$195$	2.20871	+	7.65120i	0.158169	+	0.547914i
$196$		0			0
$197$	0.395644	−	0.685275i	0.0281885	−	0.0488238i	−0.851587	−	0.524213i	$-0.824359\pi$
$197$	0.395644	−	0.685275i	0.0281885	−	0.0488238i	0.879775	+	0.475389i	$0.157693\pi$
$198$		0			0
$199$	7.87386	+	13.6379i	0.558163	+	0.966767i	0.997650	+	0.0685181i	$0.0218271\pi$
$199$	7.87386	+	13.6379i	0.558163	+	0.966767i	−0.439486	+	0.898249i	$0.644840\pi$
$200$		0			0
$201$	−9.76951	−	16.9213i	−0.689088	−	1.19354i
$202$		0			0
$203$	6.79129			0.476655
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	−28.7477			−1.99811
$208$		0			0
$209$	−5.04356			−0.348870
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$		0			0
$213$	4.41742			0.302677
$214$		0			0
$215$	−3.70871	−	6.42368i	−0.252932	−	0.438091i
$216$		0			0
$217$	0.500000	+	0.866025i	0.0339422	+	0.0587896i
$218$		0			0
$219$	−19.5390	+	33.8426i	−1.32032	+	2.28687i
$220$		0			0
$221$	−10.5000	−	2.59808i	−0.706306	−	0.174766i
$222$		0			0
$223$	4.31307	−	7.47045i	0.288824	−	0.500259i	−0.684705	−	0.728820i	$-0.740069\pi$
$223$	4.31307	−	7.47045i	0.288824	−	0.500259i	0.973529	+	0.228562i	$0.0734023\pi$
$224$		0			0
$225$	10.4782	+	18.1488i	0.698548	+	1.20992i
$226$		0			0
$227$	−6.87386	−	11.9059i	−0.456234	−	0.790221i	0.542524	−	0.840040i	$-0.317469\pi$
$227$	−6.87386	−	11.9059i	−0.456234	−	0.790221i	−0.998758	+	0.0498193i	$0.984135\pi$
$228$		0			0
$229$	−26.7477			−1.76754			−0.883770	−	0.467922i	$-0.845003\pi$
$229$	−26.7477			−1.76754			−0.883770	+	0.467922i	$0.845003\pi$
$230$		0			0
$231$	−1.10436	+	1.91280i	−0.0726613	+	0.125853i
$232$		0			0
$233$	−27.9564			−1.83149			−0.915744	−	0.401763i	$-0.868398\pi$
$233$	−27.9564			−1.83149			−0.915744	+	0.401763i	$0.868398\pi$
$234$		0			0
$235$	−4.87841			−0.318232
$236$		0			0
$237$	−5.58258	+	9.66930i	−0.362627	+	0.628089i
$238$		0			0
$239$	24.4955			1.58448			0.792240	−	0.610210i	$-0.208915\pi$
$239$	24.4955			1.58448			0.792240	+	0.610210i	$0.208915\pi$
$240$		0			0
$241$	1.68693	+	2.92185i	0.108665	+	0.188213i	0.915230	−	0.402933i	$-0.132009\pi$
$241$	1.68693	+	2.92185i	0.108665	+	0.188213i	−0.806565	+	0.591146i	$0.798676\pi$
$242$		0			0
$243$	8.08258	+	13.9994i	0.518497	+	0.898064i
$244$		0			0
$245$	−0.395644	+	0.685275i	−0.0252768	+	0.0437806i
$246$		0			0
$247$	−22.3085	−	5.51993i	−1.41946	−	0.351225i
$248$		0			0
$249$	−12.5608	+	21.7559i	−0.796008	+	1.37873i
$250$		0			0
$251$	2.20871	+	3.82560i	0.139413	+	0.241470i	0.927274	−	0.374382i	$-0.122145\pi$
$251$	2.20871	+	3.82560i	0.139413	+	0.241470i	−0.787862	+	0.615852i	$0.788812\pi$
$252$		0			0
$253$	−2.37386	−	4.11165i	−0.149244	−	0.258497i
$254$		0			0
$255$	6.62614			0.414945
$256$		0			0
$257$	0.313068	−	0.542250i	0.0195287	−	0.0338246i	−0.856096	−	0.516817i	$-0.827117\pi$
$257$	0.313068	−	0.542250i	0.0195287	−	0.0338246i	0.875625	+	0.482992i	$0.160450\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$		0			0
$261$	−32.5390			−2.01411
$262$		0			0
$263$	−5.29129	+	9.16478i	−0.326275	+	0.565125i	−0.981770	−	0.190075i	$-0.939127\pi$
$263$	−5.29129	+	9.16478i	−0.326275	+	0.565125i	0.655495	+	0.755200i	$0.272460\pi$
$264$		0			0
$265$	−1.12159			−0.0688988
$266$		0			0
$267$	−11.6869	−	20.2424i	−0.715229	−	1.23881i
$268$		0			0
$269$	11.6869	+	20.2424i	0.712565	+	1.23420i	0.963891	+	0.266296i	$0.0857999\pi$
$269$	11.6869	+	20.2424i	0.712565	+	1.23420i	−0.251326	+	0.967902i	$0.580867\pi$
$270$		0			0
$271$	1.87386	−	3.24563i	0.113829	−	0.197158i	−0.803482	−	0.595329i	$-0.797022\pi$
$271$	1.87386	−	3.24563i	0.113829	−	0.197158i	0.917311	+	0.398171i	$0.130355\pi$
$272$		0			0
$273$	−6.97822	+	7.25198i	−0.422341	+	0.438910i
$274$		0			0
$275$	−1.73049	+	2.99730i	−0.104353	+	0.180744i
$276$		0			0
$277$	−16.2477	−	28.1419i	−0.976231	−	1.69088i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	−16.2477	−	28.1419i	−0.976231	−	1.69088i	−0.300421	−	0.953807i	$-0.597127\pi$
$278$		0			0
$279$	−2.39564	−	4.14938i	−0.143423	−	0.248417i
$280$		0			0
$281$	−22.7477			−1.35702			−0.678508	−	0.734593i	$-0.737373\pi$
$281$	−22.7477			−1.35702			−0.678508	+	0.734593i	$0.737373\pi$
$282$		0			0
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	0.936039	−	0.351895i	$-0.114463\pi$
$284$		0			0
$285$	14.0780			0.833911
$286$		0			0
$287$	−7.58258			−0.447585
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−12.9129			−0.756966
$292$		0			0
$293$	6.79129	+	11.7629i	0.396751	+	0.687193i	0.993323	−	0.115366i	$-0.0368042\pi$
$293$	6.79129	+	11.7629i	0.396751	+	0.687193i	−0.596572	+	0.802560i	$0.703471\pi$
$294$		0			0
$295$	−3.56080	−	6.16748i	−0.207318	−	0.359084i
$296$		0			0
$297$	1.97822	−	3.42638i	0.114788	−	0.198819i
$298$		0			0
$299$	−6.00000	−	20.7846i	−0.346989	−	1.20201i
$300$		0			0
$301$	4.68693	−	8.11800i	0.270150	−	0.467914i
$302$		0			0
$303$	−24.4782	−	42.3975i	−1.40624	−	2.43567i
$304$		0			0
$305$	−0.791288	−	1.37055i	−0.0453090	−	0.0784775i
$306$		0			0
$307$	14.1216			0.805962			0.402981	−	0.915208i	$-0.367974\pi$
$307$	14.1216			0.805962			0.402981	+	0.915208i	$0.367974\pi$
$308$		0			0
$309$	−1.39564	+	2.41733i	−0.0793954	+	0.137517i
$310$		0			0
$311$	−18.9564			−1.07492			−0.537461	−	0.843289i	$-0.680616\pi$
$311$	−18.9564			−1.07492			−0.537461	+	0.843289i	$0.680616\pi$
$312$		0			0
$313$	6.74773			0.381404			0.190702	−	0.981648i	$-0.438924\pi$
$313$	6.74773			0.381404			0.190702	+	0.981648i	$0.438924\pi$
$314$		0			0
$315$	1.89564	−	3.28335i	0.106807	−	0.184996i
$316$		0			0
$317$	−16.5826			−0.931370			−0.465685	−	0.884950i	$-0.654192\pi$
$317$	−16.5826			−0.931370			−0.465685	+	0.884950i	$0.654192\pi$
$318$		0			0
$319$	−2.68693	−	4.65390i	−0.150439	−	0.260569i
$320$		0			0
$321$	20.0608	+	34.7463i	1.11968	+	1.93935i
$322$		0			0
$323$	−9.56080	+	16.5598i	−0.531977	+	0.921411i
$324$		0			0
$325$	−10.9347	+	11.3636i	−0.606546	+	0.630341i
$326$		0			0
$327$	−13.6044	+	23.5634i	−0.752323	+	1.30306i
$328$		0			0
$329$	−3.08258	−	5.33918i	−0.169948	−	0.294358i
$330$		0			0
$331$	13.5608	+	23.4880i	0.745369	+	1.29102i	0.950022	+	0.312182i	$0.101060\pi$
$331$	13.5608	+	23.4880i	0.745369	+	1.29102i	−0.204654	+	0.978834i	$0.565607\pi$
$332$		0			0
$333$	−19.1652			−1.05024
$334$		0			0
$335$	−2.76951	+	4.79693i	−0.151314	+	0.262084i
$336$		0			0
$337$	−6.37386			−0.347206			−0.173603	−	0.984816i	$-0.555541\pi$
$337$	−6.37386			−0.347206			−0.173603	+	0.984816i	$0.555541\pi$
$338$		0			0
$339$	17.2087			0.934649
$340$		0			0
$341$	0.395644	−	0.685275i	0.0214253	−	0.0371097i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	6.62614	+	11.4768i	0.356739	+	0.617890i
$346$		0			0
$347$	2.37386	+	4.11165i	0.127436	+	0.220725i	0.922682	−	0.385561i	$-0.125992\pi$
$347$	2.37386	+	4.11165i	0.127436	+	0.220725i	−0.795247	+	0.606286i	$0.792659\pi$
$348$		0			0
$349$	14.8739	−	25.7623i	0.796180	−	1.37902i	−0.125908	−	0.992042i	$-0.540184\pi$
$349$	14.8739	−	25.7623i	0.796180	−	1.37902i	0.922087	−	0.386982i	$-0.126482\pi$
$350$		0			0
$351$	12.5000	−	12.9904i	0.667201	−	0.693375i
$352$		0			0
$353$	7.35208	−	12.7342i	0.391312	−	0.677772i	−0.601311	−	0.799015i	$-0.705355\pi$
$353$	7.35208	−	12.7342i	0.391312	−	0.677772i	0.992623	+	0.121243i	$0.0386880\pi$
$354$		0			0
$355$	−0.626136	−	1.08450i	−0.0332319	−	0.0575593i
$356$		0			0
$357$	4.18693	+	7.25198i	0.221596	+	0.383815i
$358$		0			0
$359$	24.9564			1.31715			0.658575	−	0.752515i	$-0.271159\pi$
$359$	24.9564			1.31715			0.658575	+	0.752515i	$0.271159\pi$
$360$		0			0
$361$	−10.8131	+	18.7288i	−0.569109	+	0.985725i
$362$		0			0
$363$	−28.9564			−1.51982
$364$		0			0
$365$	11.0780			0.579851
$366$		0			0
$367$	1.00000	−	1.73205i	0.0521996	−	0.0904123i	−0.838745	−	0.544524i	$-0.816710\pi$
$367$	1.00000	−	1.73205i	0.0521996	−	0.0904123i	0.890945	+	0.454112i	$0.150043\pi$
$368$		0			0
$369$	36.3303			1.89128
$370$		0			0
$371$	−0.708712	−	1.22753i	−0.0367945	−	0.0637299i
$372$		0			0
$373$	7.68693	+	13.3142i	0.398014	+	0.689381i	0.993481	−	0.113999i	$-0.0363661\pi$
$373$	7.68693	+	13.3142i	0.398014	+	0.689381i	−0.595467	+	0.803380i	$0.703033\pi$
$374$		0			0
$375$	10.3521	−	17.9303i	0.534579	−	0.925918i
$376$		0			0
$377$	−6.79129	−	23.5257i	−0.349769	−	1.21164i
$378$		0			0
$379$	2.81307	−	4.87238i	0.144498	−	0.250277i	−0.784688	−	0.619891i	$-0.787177\pi$
$379$	2.81307	−	4.87238i	0.144498	−	0.250277i	0.929185	+	0.369614i	$0.120510\pi$
$380$		0			0
$381$	−21.4564	−	37.1636i	−1.09925	−	1.90395i
$382$		0			0
$383$	−19.2695	−	33.3758i	−0.984626	−	1.70542i	−0.643587	−	0.765373i	$-0.722555\pi$
$383$	−19.2695	−	33.3758i	−0.984626	−	1.70542i	−0.341038	−	0.940049i	$-0.610779\pi$
$384$		0			0
$385$	0.626136			0.0319109
$386$		0			0
$387$	−22.4564	+	38.8957i	−1.14152	+	1.97718i
$388$		0			0
$389$	24.3303			1.23360			0.616798	−	0.787122i	$-0.288430\pi$
$389$	24.3303			1.23360			0.616798	+	0.787122i	$0.288430\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−26.4564	+	45.8239i	−1.33455	+	2.31151i
$394$		0			0
$395$	3.16515			0.159256
$396$		0			0
$397$	15.7477	+	27.2759i	0.790356	+	1.36894i	0.925747	+	0.378144i	$0.123438\pi$
$397$	15.7477	+	27.2759i	0.790356	+	1.36894i	−0.135391	+	0.990792i	$0.543229\pi$
$398$		0			0
$399$	8.89564	+	15.4077i	0.445339	+	0.771350i
$400$		0			0
$401$	12.5608	−	21.7559i	0.627256	−	1.08644i	−0.360844	−	0.932626i	$-0.617511\pi$
$401$	12.5608	−	21.7559i	0.627256	−	1.08644i	0.988100	−	0.153813i	$-0.0491554\pi$
$402$		0			0
$403$	2.50000	−	2.59808i	0.124534	−	0.129419i
$404$		0			0
$405$	0.165151	−	0.286051i	0.00820644	−	0.0142140i
$406$		0			0
$407$	−1.58258	−	2.74110i	−0.0784454	−	0.135871i
$408$		0			0
$409$	14.5608	+	25.2200i	0.719985	+	1.24705i	0.961005	+	0.276530i	$0.0891847\pi$
$409$	14.5608	+	25.2200i	0.719985	+	1.24705i	−0.241020	+	0.970520i	$0.577482\pi$
$410$		0			0
$411$	−6.62614			−0.326843
$412$		0			0
$413$	4.50000	−	7.79423i	0.221431	−	0.383529i
$414$		0			0
$415$	7.12159			0.349585
$416$		0			0
$417$	−37.3303			−1.82807
$418$		0			0
$419$	−0.708712	+	1.22753i	−0.0346229	+	0.0599685i	−0.882818	−	0.469716i	$-0.844356\pi$
$419$	−0.708712	+	1.22753i	−0.0346229	+	0.0599685i	0.848195	+	0.529684i	$0.177690\pi$
$420$		0			0
$421$	23.4955			1.14510			0.572549	−	0.819870i	$-0.305955\pi$
$421$	23.4955			1.14510			0.572549	+	0.819870i	$0.305955\pi$
$422$		0			0
$423$	14.7695	+	25.5815i	0.718118	+	1.24382i
$424$		0			0
$425$	6.56080	+	11.3636i	0.318245	+	0.551217i
$426$		0			0
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$		0			0
$429$	7.73049	+	1.91280i	0.373232	+	0.0923509i
$430$		0			0
$431$	4.26951	−	7.39500i	0.205655	−	0.356205i	−0.744686	−	0.667415i	$-0.767401\pi$
$431$	4.26951	−	7.39500i	0.205655	−	0.356205i	0.950341	+	0.311210i	$0.100734\pi$
$432$		0			0
$433$	11.2477	+	19.4816i	0.540531	+	0.936228i	0.998874	+	0.0474518i	$0.0151101\pi$
$433$	11.2477	+	19.4816i	0.540531	+	0.936228i	−0.458342	+	0.888776i	$0.651557\pi$
$434$		0			0
$435$	7.50000	+	12.9904i	0.359597	+	0.622841i
$436$		0			0
$437$	−38.2432			−1.82942
$438$		0			0
$439$	−4.68693	+	8.11800i	−0.223695	+	0.387451i	−0.955927	−	0.293604i	$-0.905145\pi$
$439$	−4.68693	+	8.11800i	−0.223695	+	0.387451i	0.732232	+	0.681055i	$0.238479\pi$
$440$		0			0
$441$	4.79129			0.228157
$442$		0			0
$443$	13.5826			0.645328			0.322664	−	0.946514i	$-0.395422\pi$
$443$	13.5826			0.645328			0.322664	+	0.946514i	$0.395422\pi$
$444$		0			0
$445$	−3.31307	+	5.73840i	−0.157054	+	0.272026i
$446$		0			0
$447$	61.2867			2.89876
$448$		0			0
$449$	1.41742	+	2.45505i	0.0668924	+	0.115861i	0.897532	−	0.440950i	$-0.145358\pi$
$449$	1.41742	+	2.45505i	0.0668924	+	0.115861i	−0.830639	+	0.556811i	$0.812025\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$		0			0
$453$	−9.76951	+	16.9213i	−0.459012	+	0.795031i
$454$		0			0
$455$	2.76951	+	0.685275i	0.129837	+	0.0321262i
$456$		0			0
$457$	−8.74773	+	15.1515i	−0.409201	+	0.708758i	−0.994800	−	0.101843i	$-0.967526\pi$
$457$	−8.74773	+	15.1515i	−0.409201	+	0.708758i	0.585599	+	0.810601i	$0.300859\pi$
$458$		0			0
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	−12.3956	−	21.4699i	−0.577323	−	0.999952i	−0.995785	−	0.0917181i	$-0.970764\pi$
$461$	−12.3956	−	21.4699i	−0.577323	−	0.999952i	0.418462	−	0.908234i	$-0.362569\pi$
$462$		0			0
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$		0			0
$465$	−1.10436	+	1.91280i	−0.0512133	+	0.0887040i
$466$		0			0
$467$	−42.1652			−1.95117			−0.975585	−	0.219621i	$-0.929518\pi$
$467$	−42.1652			−1.95117			−0.975585	+	0.219621i	$0.929518\pi$
$468$		0			0
$469$	−7.00000			−0.323230
$470$		0			0
$471$	6.45644	−	11.1829i	0.297497	−	0.515280i
$472$		0			0
$473$	−7.41742			−0.341054
$474$		0			0
$475$	13.9392	+	24.1434i	0.639575	+	1.10778i
$476$		0			0
$477$	3.39564	+	5.88143i	0.155476	+	0.269292i
$478$		0			0
$479$	11.1434	−	19.3009i	0.509154	−	0.881880i	−0.490790	−	0.871278i	$-0.663292\pi$
$479$	11.1434	−	19.3009i	0.509154	−	0.881880i	0.999944	−	0.0106021i	$-0.00337483\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$		0			0
$483$	−8.37386	+	14.5040i	−0.381024	+	0.659953i
$484$		0			0
$485$	1.83030	+	3.17018i	0.0831098	+	0.143950i
$486$		0			0
$487$	9.06080	+	15.6938i	0.410584	+	0.711152i	0.994954	−	0.100335i	$-0.0319916\pi$
$487$	9.06080	+	15.6938i	0.410584	+	0.711152i	−0.584370	+	0.811487i	$0.698658\pi$
$488$		0			0
$489$	57.9129			2.61891
$490$		0			0
$491$	−4.89564	+	8.47950i	−0.220937	+	0.382675i	−0.955093	−	0.296307i	$-0.904245\pi$
$491$	−4.89564	+	8.47950i	−0.220937	+	0.382675i	0.734156	+	0.678981i	$0.237578\pi$
$492$		0			0
$493$	−20.3739			−0.917593
$494$		0			0
$495$	−3.00000			−0.134840
$496$		0			0
$497$	0.791288	−	1.37055i	0.0354941	−	0.0614776i
$498$		0			0
$499$	20.1216			0.900766			0.450383	−	0.892835i	$-0.351287\pi$
$499$	20.1216			0.900766			0.450383	+	0.892835i	$0.351287\pi$
$500$		0			0
$501$	−25.3521	−	43.9111i	−1.13265	−	1.96180i
$502$		0			0
$503$	−8.60436	−	14.9032i	−0.383649	−	0.664500i	0.607932	−	0.793989i	$-0.292000\pi$
$503$	−8.60436	−	14.9032i	−0.383649	−	0.664500i	−0.991581	+	0.129489i	$0.958666\pi$
$504$		0			0
$505$	−6.93920	+	12.0191i	−0.308791	+	0.534841i
$506$		0			0
$507$	32.0998	+	16.9213i	1.42560	+	0.751501i
$508$		0			0
$509$	−0.873864	+	1.51358i	−0.0387333	+	0.0670881i	−0.884742	−	0.466081i	$-0.845666\pi$
$509$	−0.873864	+	1.51358i	−0.0387333	+	0.0670881i	0.846009	+	0.533169i	$0.178999\pi$
$510$		0			0
$511$	7.00000	+	12.1244i	0.309662	+	0.536350i
$512$		0			0
$513$	−15.9347	−	27.5996i	−0.703532	−	1.21855i
$514$		0			0
$515$	0.791288			0.0348683
$516$		0			0
$517$	−2.43920	+	4.22483i	−0.107276	+	0.185808i
$518$		0			0
$519$	42.7913			1.87833
$520$		0			0
$521$	31.5826			1.38366			0.691829	−	0.722061i	$-0.256805\pi$
$521$	31.5826			1.38366			0.691829	+	0.722061i	$0.256805\pi$
$522$		0			0
$523$	−13.3739	+	23.1642i	−0.584798	+	1.01290i	0.410102	+	0.912040i	$0.365493\pi$
$523$	−13.3739	+	23.1642i	−0.584798	+	1.01290i	−0.994901	+	0.100861i	$0.967840\pi$
$524$		0			0
$525$	12.2087			0.532832
$526$		0			0
$527$	−1.50000	−	2.59808i	−0.0653410	−	0.113174i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−21.5608	+	37.3444i	−0.935659	+	1.62061i
$532$		0			0
$533$	7.58258	+	26.2668i	0.328438	+	1.13774i
$534$		0			0
$535$	5.68693	−	9.85005i	0.245868	−	0.425855i
$536$		0			0
$537$	−6.39564	−	11.0776i	−0.275992	−	0.478033i
$538$		0			0
$539$	0.395644	+	0.685275i	0.0170416	+	0.0295169i
$540$		0			0
$541$	39.1216			1.68197			0.840984	−	0.541060i	$-0.181977\pi$
$541$	39.1216			1.68197			0.840984	+	0.541060i	$0.181977\pi$
$542$		0			0
$543$	3.83485	−	6.64215i	0.164569	−	0.285042i
$544$		0			0
$545$	7.71326			0.330400
$546$		0			0
$547$	41.7477			1.78500			0.892502	−	0.451044i	$-0.148948\pi$
$547$	41.7477			1.78500			0.892502	+	0.451044i	$0.148948\pi$
$548$		0			0
$549$	−4.79129	+	8.29875i	−0.204487	+	0.354182i
$550$		0			0
$551$	−43.2867			−1.84408
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$		0			0
$555$	4.41742	+	7.65120i	0.187509	+	0.324775i
$556$		0			0
$557$	10.1044	−	17.5013i	0.428135	−	0.741552i	−0.568572	−	0.822633i	$-0.692504\pi$
$557$	10.1044	−	17.5013i	0.428135	−	0.741552i	0.996707	+	0.0810813i	$0.0258373\pi$
$558$		0			0
$559$	−32.8085	−	8.11800i	−1.38765	−	0.343355i
$560$		0			0
$561$	3.31307	−	5.73840i	0.139878	−	0.242276i
$562$		0			0
$563$	−19.7477	−	34.2041i	−0.832267	−	1.44153i	−0.896236	−	0.443578i	$-0.853709\pi$
$563$	−19.7477	−	34.2041i	−0.832267	−	1.44153i	0.0639685	−	0.997952i	$-0.479624\pi$
$564$		0			0
$565$	−2.43920	−	4.22483i	−0.102618	−	0.177740i
$566$		0			0
$567$	0.417424			0.0175302
$568$		0			0
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		0			0
$571$	−15.1216			−0.632819			−0.316409	−	0.948623i	$-0.602477\pi$
$571$	−15.1216			−0.632819			−0.316409	+	0.948623i	$0.602477\pi$
$572$		0			0
$573$	32.2087			1.34554
$574$		0			0
$575$	−13.1216	+	22.7273i	−0.547208	+	0.947792i
$576$		0			0
$577$	26.4955			1.10302			0.551510	−	0.834168i	$-0.314052\pi$
$577$	26.4955			1.10302			0.551510	+	0.834168i	$0.314052\pi$
$578$		0			0
$579$	13.9564	+	24.1733i	0.580010	+	1.00461i
$580$		0			0
$581$	4.50000	+	7.79423i	0.186691	+	0.323359i
$582$		0			0
$583$	−0.560795	+	0.971326i	−0.0232258	+	0.0402282i
$584$		0			0
$585$	−13.2695	−	3.28335i	−0.548627	−	0.135750i
$586$		0			0
$587$	8.85208	−	15.3323i	0.365365	−	0.632830i	−0.623470	−	0.781847i	$-0.714278\pi$
$587$	8.85208	−	15.3323i	0.365365	−	0.632830i	0.988835	+	0.149017i	$0.0476110\pi$
$588$		0			0
$589$	−3.18693	−	5.51993i	−0.131315	−	0.227445i
$590$		0			0
$591$	1.10436	+	1.91280i	0.0454271	+	0.0786821i
$592$		0			0
$593$	−6.95644			−0.285667			−0.142833	−	0.989747i	$-0.545621\pi$
$593$	−6.95644			−0.285667			−0.142833	+	0.989747i	$0.545621\pi$
$594$		0			0
$595$	1.18693	−	2.05583i	0.0486595	−	0.0842807i
$596$		0			0
$597$	−43.9564			−1.79902
$598$		0			0
$599$	−36.9564			−1.51000			−0.755000	−	0.655725i	$-0.772363\pi$
$599$	−36.9564			−1.51000			−0.755000	+	0.655725i	$0.772363\pi$
$600$		0			0
$601$	6.18693	−	10.7161i	0.252370	−	0.437118i	−0.711808	−	0.702374i	$-0.752123\pi$
$601$	6.18693	−	10.7161i	0.252370	−	0.437118i	0.964178	+	0.265256i	$0.0854566\pi$
$602$		0			0
$603$	33.5390			1.36581
$604$		0			0
$605$	4.10436	+	7.10895i	0.166866	+	0.289020i
$606$		0			0
$607$	10.8739	+	18.8341i	0.441357	+	0.764452i	0.997790	−	0.0664400i	$-0.0211641\pi$
$607$	10.8739	+	18.8341i	0.441357	+	0.764452i	−0.556434	+	0.830892i	$0.687831\pi$
$608$		0			0
$609$	−9.47822	+	16.4168i	−0.384077	+	0.665241i
$610$		0			0
$611$	−15.4129	+	16.0175i	−0.623538	+	0.648000i
$612$		0			0
$613$	10.0608	−	17.4258i	0.406352	−	0.703822i	−0.588126	−	0.808769i	$-0.700134\pi$
$613$	10.0608	−	17.4258i	0.406352	−	0.703822i	0.994478	+	0.104947i	$0.0334674\pi$
$614$		0			0
$615$	−8.37386	−	14.5040i	−0.337667	−	0.584856i
$616$		0			0
$617$	−1.33485	−	2.31203i	−0.0537390	−	0.0930786i	0.837905	−	0.545817i	$-0.183781\pi$
$617$	−1.33485	−	2.31203i	−0.0537390	−	0.0930786i	−0.891644	+	0.452738i	$0.850447\pi$
$618$		0			0
$619$	34.0000			1.36658			0.683288	−	0.730149i	$-0.260549\pi$
$619$	34.0000			1.36658			0.683288	+	0.730149i	$0.260549\pi$
$620$		0			0
$621$	15.0000	−	25.9808i	0.601929	−	1.04257i
$622$		0			0
$623$	−8.37386			−0.335492
$624$		0			0
$625$	16.0000			0.640000
$626$		0			0
$627$	7.03901	−	12.1919i	0.281111	−	0.486899i
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−14.5608	−	25.2200i	−0.579656	−	1.00399i	−0.995519	−	0.0945663i	$-0.969854\pi$
$631$	−14.5608	−	25.2200i	−0.579656	−	1.00399i	0.415862	−	0.909428i	$-0.363480\pi$
$632$		0			0
$633$	−18.1434	−	31.4252i	−0.721134	−	1.24904i
$634$		0			0
$635$	−6.08258	+	10.5353i	−0.241380	+	0.418082i
$636$		0			0
$637$	1.00000	+	3.46410i	0.0396214	+	0.137253i
$638$		0			0
$639$	−3.79129	+	6.56670i	−0.149981	+	0.259775i
$640$		0			0
$641$	−20.0608	−	34.7463i	−0.792354	−	1.37240i	−0.924506	−	0.381168i	$-0.875522\pi$
$641$	−20.0608	−	34.7463i	−0.792354	−	1.37240i	0.132152	−	0.991229i	$-0.457811\pi$
$642$		0			0
$643$	−11.8739	−	20.5661i	−0.468259	−	0.811049i	0.531083	−	0.847320i	$-0.321785\pi$
$643$	−11.8739	−	20.5661i	−0.468259	−	0.811049i	−0.999342	+	0.0362709i	$0.988452\pi$
$644$		0			0
$645$	20.7042			0.815226
$646$		0			0
$647$	−9.79129	+	16.9590i	−0.384935	+	0.666727i	−0.991760	−	0.128108i	$-0.959110\pi$
$647$	−9.79129	+	16.9590i	−0.384935	+	0.666727i	0.606825	+	0.794835i	$0.292443\pi$
$648$		0			0
$649$	−7.12159			−0.279547
$650$		0			0
$651$	−2.79129			−0.109399
$652$		0			0
$653$	0.313068	−	0.542250i	0.0122513	−	0.0212199i	−0.859835	−	0.510572i	$-0.829434\pi$
$653$	0.313068	−	0.542250i	0.0122513	−	0.0212199i	0.872086	+	0.489353i	$0.162767\pi$
$654$		0			0
$655$	15.0000			0.586098
$656$		0			0
$657$	−33.5390	−	58.0913i	−1.30848	−	2.26636i
$658$		0			0
$659$	10.5826	+	18.3296i	0.412239	+	0.714018i	0.995134	−	0.0985288i	$-0.0314137\pi$
$659$	10.5826	+	18.3296i	0.412239	+	0.714018i	−0.582896	+	0.812547i	$0.698080\pi$
$660$		0			0
$661$	−9.37386	+	16.2360i	−0.364601	+	0.631508i	−0.988712	−	0.149828i	$-0.952128\pi$
$661$	−9.37386	+	16.2360i	−0.364601	+	0.631508i	0.624111	+	0.781336i	$0.285461\pi$
$662$		0			0
$663$	20.9347	−	21.7559i	0.813035	−	0.844931i
$664$		0			0
$665$	2.52178	−	4.36785i	0.0977904	−	0.169378i
$666$		0			0
$667$	−20.3739	−	35.2886i	−0.788879	−	1.36638i
$668$		0			0
$669$	12.0390	+	20.8522i	0.465455	+	0.806192i
$670$		0			0
$671$	−1.58258			−0.0610947
$672$		0			0
$673$	−10.2477	+	17.7496i	−0.395021	+	0.684196i	−0.993104	−	0.117238i	$-0.962596\pi$
$673$	−10.2477	+	17.7496i	−0.395021	+	0.684196i	0.598083	+	0.801434i	$0.295929\pi$
$674$		0			0
$675$	−21.8693			−0.841750
$676$		0			0
$677$	14.0436			0.539738			0.269869	−	0.962897i	$-0.413020\pi$
$677$	14.0436			0.539738			0.269869	+	0.962897i	$0.413020\pi$
$678$		0			0
$679$	−2.31307	+	4.00635i	−0.0887674	+	0.153750i
$680$		0			0
$681$	38.3739			1.47049
$682$		0			0
$683$	−15.8739	−	27.4943i	−0.607397	−	1.05204i	−0.991668	−	0.128821i	$-0.958881\pi$
$683$	−15.8739	−	27.4943i	−0.607397	−	1.05204i	0.384271	−	0.923220i	$-0.374453\pi$
$684$		0			0
$685$	0.939205	+	1.62675i	0.0358852	+	0.0621549i
$686$		0			0
$687$	37.3303	−	64.6580i	1.42424	−	2.46686i
$688$		0			0
$689$	−3.54356	+	3.68258i	−0.134999	+	0.140295i
$690$		0			0
$691$	2.81307	−	4.87238i	0.107014	−	0.185354i	−0.807545	−	0.589806i	$-0.799204\pi$
$691$	2.81307	−	4.87238i	0.107014	−	0.185354i	0.914559	+	0.404452i	$0.132538\pi$
$692$		0			0
$693$	−1.89564	−	3.28335i	−0.0720096	−	0.124724i
$694$		0			0
$695$	5.29129	+	9.16478i	0.200710	+	0.347640i
$696$		0			0
$697$	22.7477			0.861632
$698$		0			0
$699$	39.0172	−	67.5798i	1.47577	−	2.55610i
$700$		0			0
$701$	−34.7477			−1.31240			−0.656202	−	0.754585i	$-0.727838\pi$
$701$	−34.7477			−1.31240			−0.656202	+	0.754585i	$0.727838\pi$
$702$		0			0
$703$	−25.4955			−0.961579
$704$		0			0
$705$	6.80852	−	11.7927i	0.256424	−	0.444139i
$706$		0			0
$707$	−17.5390			−0.659623
$708$		0			0
$709$	12.8131	+	22.1929i	0.481205	+	0.833471i	0.999767	−	0.0215684i	$-0.00686598\pi$
$709$	12.8131	+	22.1929i	0.481205	+	0.833471i	−0.518562	+	0.855040i	$0.673533\pi$
$710$		0			0
$711$	−9.58258	−	16.5975i	−0.359375	−	0.622455i
$712$		0			0
$713$	3.00000	−	5.19615i	0.112351	−	0.194597i
$714$		0			0
$715$	−0.626136	−	2.16900i	−0.0234162	−	0.0811160i
$716$		0			0
$717$	−34.1869	+	59.2135i	−1.27673	+	2.21137i
$718$		0			0
$719$	24.4129	+	42.2843i	0.910447	+	1.57694i	0.813434	+	0.581657i	$0.197595\pi$
$719$	24.4129	+	42.2843i	0.910447	+	1.57694i	0.0970125	+	0.995283i	$0.469071\pi$
$720$		0			0
$721$	0.500000	+	0.866025i	0.0186210	+	0.0322525i
$722$		0			0
$723$	−9.41742			−0.350238
$724$		0			0
$725$	−14.8521	+	25.7246i	−0.551593	+	0.955386i
$726$		0			0
$727$	28.4955			1.05684			0.528419	−	0.848984i	$-0.322785\pi$
$727$	28.4955			1.05684			0.528419	+	0.848984i	$0.322785\pi$
$728$		0			0
$729$	−43.8693			−1.62479
$730$		0			0
$731$	−14.0608	+	24.3540i	−0.520057	+	0.900766i
$732$		0			0
$733$	−30.8693			−1.14018			−0.570092	−	0.821581i	$-0.693093\pi$
$733$	−30.8693			−1.14018			−0.570092	+	0.821581i	$0.693093\pi$
$734$		0			0
$735$	−1.10436	−	1.91280i	−0.0407348	−	0.0705547i
$736$		0			0
$737$	2.76951	+	4.79693i	0.102016	+	0.176697i
$738$		0			0
$739$	21.3739	−	37.0206i	0.786250	−	1.36183i	−0.141999	−	0.989867i	$-0.545353\pi$
$739$	21.3739	−	37.0206i	0.786250	−	1.36183i	0.928249	−	0.371959i	$-0.121314\pi$
$740$		0			0
$741$	44.4782	−	46.2231i	1.63395	−	1.69805i
$742$		0			0
$743$	−13.8956	+	24.0680i	−0.509782	+	0.882968i	0.490154	+	0.871636i	$0.336941\pi$
$743$	−13.8956	+	24.0680i	−0.509782	+	0.882968i	−0.999936	+	0.0113320i	$0.996393\pi$
$744$		0			0
$745$	−8.68693	−	15.0462i	−0.318265	−	0.551250i
$746$		0			0
$747$	−21.5608	−	37.3444i	−0.788868	−	1.36636i
$748$		0			0
$749$	14.3739			0.525210
$750$		0			0
$751$	2.50000	−	4.33013i	0.0912263	−	0.158009i	−0.816801	−	0.576919i	$-0.804255\pi$
$751$	2.50000	−	4.33013i	0.0912263	−	0.158009i	0.908027	+	0.418911i	$0.137588\pi$
$752$		0			0
$753$	−12.3303			−0.449341
$754$		0			0
$755$	5.53901			0.201585
$756$		0			0
$757$	2.00000	−	3.46410i	0.0726912	−	0.125905i	−0.827389	−	0.561630i	$-0.810175\pi$
$757$	2.00000	−	3.46410i	0.0726912	−	0.125905i	0.900080	+	0.435725i	$0.143508\pi$
$758$		0			0
$759$	13.2523			0.481027
$760$		0			0
$761$	10.2695	+	17.7873i	0.372269	+	0.644789i	0.989914	−	0.141668i	$-0.0452464\pi$
$761$	10.2695	+	17.7873i	0.372269	+	0.644789i	−0.617645	+	0.786457i	$0.711913\pi$
$762$		0			0
$763$	4.87386	+	8.44178i	0.176446	+	0.305613i
$764$		0			0
$765$	−5.68693	+	9.85005i	−0.205611	+	0.356129i
$766$		0			0
$767$	−31.5000	−	7.79423i	−1.13740	−	0.281433i
$768$		0			0
$769$	−17.5000	+	30.3109i	−0.631066	+	1.09304i	0.356268	+	0.934384i	$0.384049\pi$
$769$	−17.5000	+	30.3109i	−0.631066	+	1.09304i	−0.987334	+	0.158655i	$0.949284\pi$
$770$		0			0
$771$	0.873864	+	1.51358i	0.0314714	+	0.0545101i
$772$		0			0
$773$	21.2477	+	36.8021i	0.764228	+	1.32368i	0.940654	+	0.339367i	$0.110213\pi$
$773$	21.2477	+	36.8021i	0.764228	+	1.32368i	−0.176426	+	0.984314i	$0.556454\pi$
$774$		0			0
$775$	−4.37386			−0.157114
$776$		0			0
$777$	−5.58258	+	9.66930i	−0.200274	+	0.346884i
$778$		0			0
$779$	48.3303			1.73161
$780$		0			0
$781$	−1.25227			−0.0448098
$782$		0			0
$783$	16.9782	−	29.4071i	0.606752	−	1.05093i
$784$		0			0
$785$	−3.66061			−0.130653
$786$		0			0
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	0.963394	−	0.268091i	$-0.0863928\pi$
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	−0.713871	+	0.700278i	$0.753059\pi$
$788$		0			0
$789$	−14.7695	−	25.5815i	−0.525808	−	0.910727i
$790$		0			0
$791$	3.08258	−	5.33918i	0.109604	−	0.189839i
$792$		0			0
$793$	−7.00000	−	1.73205i	−0.248577	−	0.0615069i
$794$		0			0
$795$	1.56534	−	2.71125i	0.0555169	−	0.0961581i
$796$		0			0
$797$	−24.9564	−	43.2258i	−0.884002	−	1.53114i	−0.846853	−	0.531827i	$-0.821506\pi$
$797$	−24.9564	−	43.2258i	−0.884002	−	1.53114i	−0.0371497	−	0.999310i	$-0.511828\pi$
$798$		0			0
$799$	9.24773	+	16.0175i	0.327161	+	0.566660i
$800$		0			0
$801$	40.1216			1.41763
$802$		0			0
$803$	5.53901	−	9.59386i	0.195468	−	0.338560i
$804$		0			0
$805$	4.74773			0.167335
$806$		0			0
$807$	−65.2432			−2.29667
$808$		0			0
$809$	−3.08258	+	5.33918i	−0.108378	+	0.187715i	−0.915113	−	0.403197i	$-0.867899\pi$
$809$	−3.08258	+	5.33918i	−0.108378	+	0.187715i	0.806736	+	0.590913i	$0.201232\pi$
$810$		0			0
$811$	−25.8693			−0.908395			−0.454197	−	0.890901i	$-0.650074\pi$
$811$	−25.8693			−0.908395			−0.454197	+	0.890901i	$0.650074\pi$
$812$		0			0
$813$	5.23049	+	9.05948i	0.183441	+	0.317730i
$814$		0			0
$815$	−8.20871	−	14.2179i	−0.287539	−	0.498032i
$816$		0			0
$817$	−29.8739	+	51.7430i	−1.04515	+	1.81026i
$818$		0			0
$819$	−4.79129	−	16.5975i	−0.167421	−	0.579964i
$820$		0			0
$821$	−16.5000	+	28.5788i	−0.575854	+	0.997408i	0.420094	+	0.907480i	$0.361997\pi$
$821$	−16.5000	+	28.5788i	−0.575854	+	0.997408i	−0.995948	+	0.0899279i	$0.971336\pi$
$822$		0			0
$823$	9.12614	+	15.8069i	0.318117	+	0.550995i	0.980095	−	0.198528i	$-0.0636161\pi$
$823$	9.12614	+	15.8069i	0.318117	+	0.550995i	−0.661978	+	0.749523i	$0.730283\pi$
$824$		0			0
$825$	−4.83030	−	8.36633i	−0.168170	−	0.291278i
$826$		0			0
$827$	−4.12159			−0.143322			−0.0716609	−	0.997429i	$-0.522830\pi$
$827$	−4.12159			−0.143322			−0.0716609	+	0.997429i	$0.522830\pi$
$828$		0			0
$829$	21.1869	−	36.6968i	0.735853	−	1.27453i	−0.218496	−	0.975838i	$-0.570115\pi$
$829$	21.1869	−	36.6968i	0.735853	−	1.27453i	0.954348	−	0.298696i	$-0.0965517\pi$
$830$		0			0
$831$	90.7042			3.14649
$832$		0			0
$833$	3.00000			0.103944
$834$		0			0
$835$	−7.18693	+	12.4481i	−0.248714	+	0.430785i
$836$		0			0
$837$	5.00000			0.172825
$838$		0			0
$839$	13.0218	+	22.5544i	0.449562	+	0.778664i	0.998357	−	0.0572927i	$-0.0182468\pi$
$839$	13.0218	+	22.5544i	0.449562	+	0.778664i	−0.548796	+	0.835957i	$0.684913\pi$
$840$		0			0
$841$	−8.56080	−	14.8277i	−0.295200	−	0.511301i
$842$		0			0
$843$	31.7477	−	54.9887i	1.09345	−	1.89391i
$844$		0			0
$845$	−0.395644	−	10.2791i	−0.0136106	−	0.353613i
$846$		0			0
$847$	−5.18693	+	8.98403i	−0.178225	+	0.308695i
$848$		0			0
$849$	36.2867	+	62.8505i	1.24536	+	2.15702i
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$		0			0
$853$	9.74773			0.333756			0.166878	−	0.985978i	$-0.446631\pi$
$853$	9.74773			0.333756			0.166878	+	0.985978i	$0.446631\pi$
$854$		0			0
$855$	−12.0826	+	20.9276i	−0.413215	+	0.715710i
$856$		0			0
$857$	20.2087			0.690316			0.345158	−	0.938545i	$-0.387825\pi$
$857$	20.2087			0.690316			0.345158	+	0.938545i	$0.387825\pi$
$858$		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
$861$	10.5826	−	18.3296i	0.360653	−	0.624670i
$862$		0			0
$863$	2.83485			0.0964994			0.0482497	−	0.998835i	$-0.484636\pi$
$863$	2.83485			0.0964994			0.0482497	+	0.998835i	$0.484636\pi$
$864$		0			0
$865$	−6.06534	−	10.5055i	−0.206228	−	0.357197i
$866$		0			0
$867$	11.1652	+	19.3386i	0.379188	+	0.656774i
$868$		0			0
$869$	1.58258	−	2.74110i	0.0536852	−	0.0929855i
$870$		0			0
$871$	7.00000	+	24.2487i	0.237186	+	0.821636i
$872$		0			0
$873$	11.0826	−	19.1956i	0.375088	−	0.649672i
$874$		0			0
$875$	−3.70871	−	6.42368i	−0.125377	−	0.217160i
$876$		0			0
$877$	11.8739	+	20.5661i	0.400952	+	0.694469i	0.993841	−	0.110815i	$-0.0353461\pi$
$877$	11.8739	+	20.5661i	0.400952	+	0.694469i	−0.592889	+	0.805284i	$0.702013\pi$
$878$		0			0
$879$	−37.9129			−1.27877
$880$		0			0
$881$	3.70871	−	6.42368i	0.124950	−	0.216419i	−0.796764	−	0.604291i	$-0.793456\pi$
$881$	3.70871	−	6.42368i	0.124950	−	0.216419i	0.921713	+	0.387872i	$0.126790\pi$
$882$		0			0
$883$	29.7477			1.00109			0.500545	−	0.865710i	$-0.333133\pi$
$883$	29.7477			1.00109			0.500545	+	0.865710i	$0.333133\pi$
$884$		0			0
$885$	19.8784			0.668205
$886$		0			0
$887$	−12.6261	+	21.8691i	−0.423944	+	0.734293i	−0.996321	−	0.0856977i	$-0.972688\pi$
$887$	−12.6261	+	21.8691i	−0.423944	+	0.734293i	0.572377	+	0.819991i	$0.306021\pi$
$888$		0			0
$889$	−15.3739			−0.515623
$890$		0			0
$891$	−0.165151	−	0.286051i	−0.00553278	−	0.00958306i
$892$		0			0
$893$	19.6479	+	34.0312i	0.657492	+	1.13881i
$894$		0			0
$895$	−1.81307	+	3.14033i	−0.0606042	+	0.104970i
$896$		0			0
$897$	58.6170	+	14.5040i	1.95717	+	0.484273i
$898$		0			0
$899$	3.39564	−	5.88143i	0.113251	−	0.196157i
$900$		0			0
$901$	2.12614	+	3.68258i	0.0708319	+	0.122684i
$902$		0			0
$903$	13.0826	+	22.6597i	0.435361	+	0.754067i
$904$		0			0
$905$	−2.17424			−0.0722743
$906$		0			0
$907$	25.4955	−	44.1594i	0.846563	−	1.46629i	−0.0376945	−	0.999289i	$-0.512001\pi$
$907$	25.4955	−	44.1594i	0.846563	−	1.46629i	0.884257	−	0.467000i	$-0.154665\pi$
$908$		0			0
$909$	84.0345			2.78725
$910$		0			0
$911$	−32.3739			−1.07259			−0.536297	−	0.844029i	$-0.680177\pi$
$911$	−32.3739			−1.07259			−0.536297	+	0.844029i	$0.680177\pi$
$912$		0			0
$913$	3.56080	−	6.16748i	0.117845	−	0.204114i
$914$		0			0
$915$	4.41742			0.146036
$916$		0			0
$917$	9.47822	+	16.4168i	0.312998	+	0.542129i
$918$		0			0
$919$	5.74773	+	9.95536i	0.189600	+	0.328397i	0.945117	−	0.326732i	$-0.105948\pi$
$919$	5.74773	+	9.95536i	0.189600	+	0.328397i	−0.755517	+	0.655129i	$0.772614\pi$
$920$		0			0
$921$	−19.7087	+	34.1365i	−0.649424	+	1.12484i
$922$		0			0
$923$	−5.53901	−	1.37055i	−0.182319	−	0.0451122i
$924$		0			0
$925$	−8.74773	+	15.1515i	−0.287623	+	0.498179i
$926$		0			0
$927$	−2.39564	−	4.14938i	−0.0786833	−	0.136283i
$928$		0			0
$929$	−23.2913	−	40.3417i	−0.764162	−	1.32357i	−0.940688	−	0.339272i	$-0.889819\pi$
$929$	−23.2913	−	40.3417i	−0.764162	−	1.32357i	0.176526	−	0.984296i	$-0.443514\pi$
$930$		0			0
$931$	6.37386			0.208895
$932$		0			0
$933$	26.4564	−	45.8239i	0.866145	−	1.50021i
$934$		0			0
$935$	−1.87841			−0.0614306
$936$		0			0
$937$	−17.7477			−0.579793			−0.289896	−	0.957058i	$-0.593621\pi$
$937$	−17.7477			−0.579793			−0.289896	+	0.957058i	$0.593621\pi$
$938$		0			0
$939$	−9.41742	+	16.3115i	−0.307326	+	0.532304i
$940$		0			0
$941$	38.0780			1.24131			0.620654	−	0.784084i	$-0.286867\pi$
$941$	38.0780			1.24131			0.620654	+	0.784084i	$0.286867\pi$
$942$		0			0
$943$	22.7477	+	39.4002i	0.740768	+	1.28305i
$944$		0			0
$945$	1.97822	+	3.42638i	0.0643515	+	0.111460i
$946$		0			0
$947$	−16.1869	+	28.0366i	−0.526005	+	0.911067i	0.473536	+	0.880774i	$0.342977\pi$
$947$	−16.1869	+	28.0366i	−0.526005	+	0.911067i	−0.999541	+	0.0302925i	$0.990356\pi$
$948$		0			0
$949$	35.0000	−	36.3731i	1.13615	−	1.18072i
$950$		0			0
$951$	23.1434	−	40.0855i	0.750475	−	1.29986i
$952$		0			0
$953$	−4.33485	−	7.50818i	−0.140420	−	0.243214i	0.787235	−	0.616653i	$-0.211512\pi$
$953$	−4.33485	−	7.50818i	−0.140420	−	0.243214i	−0.927655	+	0.373439i	$0.878178\pi$
$954$		0			0
$955$	−4.56534	−	7.90740i	−0.147731	−	0.255878i
$956$		0			0
$957$	15.0000			0.484881
$958$		0			0
$959$	−1.18693	+	2.05583i	−0.0383280	+	0.0663861i
$960$		0			0
$961$	−30.0000			−0.967742
$962$		0			0
$963$	−68.8693			−2.21928
$964$		0			0
$965$	3.95644	−	6.85275i	0.127362	−	0.220598i
$966$		0			0
$967$	−3.74773			−0.120519			−0.0602594	−	0.998183i	$-0.519193\pi$
$967$	−3.74773			−0.120519			−0.0602594	+	0.998183i	$0.519193\pi$
$968$		0			0
$969$	−26.6869	−	46.2231i	−0.857308	−	1.48490i
$970$		0			0
$971$	−15.7087	−	27.2083i	−0.504117	−	0.873156i	−0.999989	−	0.00475994i	$-0.998485\pi$
$971$	−15.7087	−	27.2083i	−0.504117	−	0.873156i	0.495872	−	0.868396i	$-0.334848\pi$
$972$		0			0
$973$	−6.68693	+	11.5821i	−0.214373	+	0.371305i
$974$		0			0
$975$	−12.2087	−	42.2922i	−0.390992	−	1.35444i
$976$		0			0
$977$	24.4129	−	42.2843i	0.781037	−	1.35280i	−0.150301	−	0.988640i	$-0.548024\pi$
$977$	24.4129	−	42.2843i	0.781037	−	1.35280i	0.931338	−	0.364156i	$-0.118642\pi$
$978$		0			0
$979$	3.31307	+	5.73840i	0.105886	+	0.183400i
$980$		0			0
$981$	−23.3521	−	40.4470i	−0.745575	−	1.29137i
$982$		0			0
$983$	14.5390			0.463723			0.231861	−	0.972749i	$-0.425518\pi$
$983$	14.5390			0.463723			0.231861	+	0.972749i	$0.425518\pi$
$984$		0			0
$985$	0.313068	−	0.542250i	0.00997518	−	0.0172775i
$986$		0			0
$987$	17.2087			0.547759
$988$		0			0
$989$	−56.2432			−1.78843
$990$		0			0
$991$	11.8131	−	20.4608i	0.375254	−	0.649960i	−0.615111	−	0.788441i	$-0.710889\pi$
$991$	11.8131	−	20.4608i	0.375254	−	0.649960i	0.990365	+	0.138481i	$0.0442220\pi$
$992$		0			0
$993$	−75.7042			−2.40240
$994$		0			0
$995$	6.23049	+	10.7915i	0.197520	+	0.342114i
$996$		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
$999$	10.0000	−	17.3205i	0.316386	−	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.k.113.1		4
4.3	odd	2		364.2.k.d.113.2	yes	4
12.11	even	2		3276.2.z.e.3025.1		4
13.3	even	3	inner	1456.2.s.k.1121.1		4
28.3	even	6		2548.2.l.l.373.2		4
28.11	odd	6		2548.2.l.j.373.1		4
28.19	even	6		2548.2.i.i.165.1		4
28.23	odd	6		2548.2.i.k.165.2		4
28.27	even	2		2548.2.k.e.1569.1		4
52.3	odd	6		364.2.k.d.29.2	✓	4
52.7	even	12		4732.2.g.e.337.2		4
52.19	even	12		4732.2.g.e.337.1		4
52.35	odd	6		4732.2.a.g.1.1		2
52.43	odd	6		4732.2.a.h.1.1		2
156.107	even	6		3276.2.z.e.757.1		4
364.3	even	6		2548.2.i.i.1745.1		4
364.55	even	6		2548.2.k.e.393.1		4
364.107	odd	6		2548.2.l.j.1537.1		4
364.159	even	6		2548.2.l.l.1537.2		4
364.263	odd	6		2548.2.i.k.1745.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.k.d.29.2	✓	4	52.3	odd	6
364.2.k.d.113.2	yes	4	4.3	odd	2
1456.2.s.k.113.1		4	1.1	even	1	trivial
1456.2.s.k.1121.1		4	13.3	even	3	inner
2548.2.i.i.165.1		4	28.19	even	6
2548.2.i.i.1745.1		4	364.3	even	6
2548.2.i.k.165.2		4	28.23	odd	6
2548.2.i.k.1745.2		4	364.263	odd	6
2548.2.k.e.393.1		4	364.55	even	6
2548.2.k.e.1569.1		4	28.27	even	2
2548.2.l.j.373.1		4	28.11	odd	6
2548.2.l.j.1537.1		4	364.107	odd	6
2548.2.l.l.373.2		4	28.3	even	6
2548.2.l.l.1537.2		4	364.159	even	6
3276.2.z.e.757.1		4	156.107	even	6
3276.2.z.e.3025.1		4	12.11	even	2
4732.2.a.g.1.1		2	52.35	odd	6
4732.2.a.h.1.1		2	52.43	odd	6
4732.2.g.e.337.1		4	52.19	even	12
4732.2.g.e.337.2		4	52.7	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)

\(f(q)\)	\(=\)	\(q+(-1.39564 + 2.41733i) q^{3} +0.791288 q^{5} +(0.500000 + 0.866025i) q^{7} +(-2.39564 - 4.14938i) q^{9} +(0.395644 - 0.685275i) q^{11} +(2.50000 - 2.59808i) q^{13} +(-1.10436 + 1.91280i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-3.18693 - 5.51993i) q^{19} -2.79129 q^{21} +(3.00000 - 5.19615i) q^{23} -4.37386 q^{25} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +1.00000 q^{31} +(1.10436 + 1.91280i) q^{33} +(0.395644 + 0.685275i) q^{35} +(2.00000 - 3.46410i) q^{37} +(2.79129 + 9.66930i) q^{39} +(-3.79129 + 6.56670i) q^{41} +(-4.68693 - 8.11800i) q^{43} +(-1.89564 - 3.28335i) q^{45} -6.16515 q^{47} +(-0.500000 + 0.866025i) q^{49} +8.37386 q^{51} -1.41742 q^{53} +(0.313068 - 0.542250i) q^{55} +17.7913 q^{57} +(-4.50000 - 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(2.39564 - 4.14938i) q^{63} +(1.97822 - 2.05583i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(8.37386 + 14.5040i) q^{69} +(-0.791288 - 1.37055i) q^{71} +14.0000 q^{73} +(6.10436 - 10.5731i) q^{75} +0.791288 q^{77} +4.00000 q^{79} +(0.208712 - 0.361500i) q^{81} +9.00000 q^{83} +(-1.18693 - 2.05583i) q^{85} +(9.47822 + 16.4168i) q^{87} +(-4.18693 + 7.25198i) q^{89} +(3.50000 + 0.866025i) q^{91} +(-1.39564 + 2.41733i) q^{93} +(-2.52178 - 4.36785i) q^{95} +(2.31307 + 4.00635i) q^{97} -3.79129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 6 q^{5} + 2 q^{7} - 5 q^{9} - 3 q^{11} + 10 q^{13} - 9 q^{15} - 6 q^{17} + q^{19} - 2 q^{21} + 12 q^{23} + 10 q^{25} + 20 q^{27} + 9 q^{29} + 4 q^{31} + 9 q^{33} - 3 q^{35} + 8 q^{37} + 2 q^{39}+ \cdots - 6 q^{99}+O(q^{100}) \) 4 * q - q^3 - 6 * q^5 + 2 * q^7 - 5 * q^9 - 3 * q^11 + 10 * q^13 - 9 * q^15 - 6 * q^17 + q^19 - 2 * q^21 + 12 * q^23 + 10 * q^25 + 20 * q^27 + 9 * q^29 + 4 * q^31 + 9 * q^33 - 3 * q^35 + 8 * q^37 + 2 * q^39 - 6 * q^41 - 5 * q^43 - 3 * q^45 + 12 * q^47 - 2 * q^49 + 6 * q^51 - 24 * q^53 + 15 * q^55 + 62 * q^57 - 18 * q^59 - 4 * q^61 + 5 * q^63 - 15 * q^65 - 14 * q^67 + 6 * q^69 + 6 * q^71 + 56 * q^73 + 29 * q^75 - 6 * q^77 + 16 * q^79 + 10 * q^81 + 36 * q^83 + 9 * q^85 + 15 * q^87 - 3 * q^89 + 14 * q^91 - q^93 - 33 * q^95 + 23 * q^97 - 6 * q^99

Introduction

L-functions

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