LMFDB - Embedded newform 1680.2.di.g.289.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(289,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.di (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,2,0,0,0,12,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.12
Character	$\chi$	$=$	1680.289
Dual form			1680.2.di.g.529.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +(2.23316 - 0.114055i) q^{5} +(0.262488 + 2.63270i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.01478 - 3.48970i) q^{11} +6.03388i q^{13} +(1.87694 - 1.21535i) q^{15} +(-0.815983 + 0.471108i) q^{17} +(-4.30486 + 7.45623i) q^{19} +(1.54367 + 2.14874i) q^{21} +(4.28008 + 2.47111i) q^{23} +(4.97398 - 0.509406i) q^{25} -1.00000i q^{27} +5.99068 q^{29} +(1.93071 + 3.34408i) q^{31} +(-3.48970 - 2.01478i) q^{33} +(0.886450 + 5.84929i) q^{35} +(4.61567 + 2.66486i) q^{37} +(3.01694 + 5.22550i) q^{39} +6.24670 q^{41} -5.03947i q^{43} +(1.01780 - 1.99100i) q^{45} +(-10.1585 - 5.86499i) q^{47} +(-6.86220 + 1.38210i) q^{49} +(-0.471108 + 0.815983i) q^{51} +(4.38958 - 2.53432i) q^{53} +(-4.89734 - 7.56325i) q^{55} +8.60971i q^{57} +(-2.18367 - 3.78222i) q^{59} +(-0.759024 + 1.31467i) q^{61} +(2.41123 + 1.08903i) q^{63} +(0.688195 + 13.4746i) q^{65} +(8.28111 - 4.78110i) q^{67} +4.94222 q^{69} -8.93194 q^{71} +(-5.91012 + 3.41221i) q^{73} +(4.05289 - 2.92815i) q^{75} +(8.65847 - 6.22031i) q^{77} +(3.43708 - 5.95320i) q^{79} +(-0.500000 - 0.866025i) q^{81} +16.3602i q^{83} +(-1.76849 + 1.14513i) q^{85} +(5.18808 - 2.99534i) q^{87} +(-2.39902 + 4.15523i) q^{89} +(-15.8854 + 1.58382i) q^{91} +(3.34408 + 1.93071i) q^{93} +(-8.76300 + 17.1419i) q^{95} -18.6629i q^{97} -4.02956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5} + 12 q^{9} + 8 q^{11} - 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} - 4 q^{31} - 30 q^{35} - 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} + 20 q^{51} - 12 q^{55} + 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots + 16 q^{99}+O(q^{100}) $ 24 * q + 2 * q^5 + 12 * q^9 + 8 * q^11 - 8 * q^19 + 12 * q^21 + 2 * q^25 - 24 * q^29 - 4 * q^31 - 30 * q^35 - 4 * q^39 + 32 * q^41 - 2 * q^45 - 12 * q^49 + 20 * q^51 - 12 * q^55 + 4 * q^59 + 32 * q^61 + 22 * q^65 + 56 * q^69 - 72 * q^71 + 16 * q^75 - 20 * q^79 - 12 * q^81 + 8 * q^85 + 24 * q^89 - 8 * q^91 + 18 * q^95 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	2.23316	−	0.114055i	0.998698	−	0.0510070i
$5$	2.23316	−	0.114055i	0.998698	−	0.0510070i
$6$		0			0
$7$	0.262488	+	2.63270i	0.0992112	+	0.995066i
$7$	0.262488	+	2.63270i	0.0992112	+	0.995066i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.01478	−	3.48970i	−0.607479	−	1.05218i	−0.991654	−	0.128924i	$-0.958848\pi$
$11$	−2.01478	−	3.48970i	−0.607479	−	1.05218i	0.384176	−	0.923260i	$-0.374486\pi$
$12$		0			0
$13$			6.03388i			1.67350i	0.547587	+	0.836749i	$0.315547\pi$
$13$			6.03388i			1.67350i	−0.547587	+	0.836749i	$0.684453\pi$
$14$		0			0
$15$	1.87694	−	1.21535i	0.484625	−	0.313803i
$16$		0			0
$17$	−0.815983	+	0.471108i	−0.197905	+	0.114260i	−0.595678	−	0.803223i	$-0.703117\pi$
$17$	−0.815983	+	0.471108i	−0.197905	+	0.114260i	0.397773	+	0.917484i	$0.369783\pi$
$18$		0			0
$19$	−4.30486	+	7.45623i	−0.987602	+	1.71058i	−0.357853	+	0.933778i	$0.616491\pi$
$19$	−4.30486	+	7.45623i	−0.987602	+	1.71058i	−0.629749	+	0.776799i	$0.716842\pi$
$20$		0			0
$21$	1.54367	+	2.14874i	0.336857	+	0.468893i
$22$		0			0
$23$	4.28008	+	2.47111i	0.892459	+	0.515262i	0.874746	−	0.484581i	$-0.161028\pi$
$23$	4.28008	+	2.47111i	0.892459	+	0.515262i	0.0177132	+	0.999843i	$0.494361\pi$
$24$		0			0
$25$	4.97398	−	0.509406i	0.994797	−	0.101881i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	5.99068			1.11244			0.556221	−	0.831035i	$-0.312251\pi$
$29$	5.99068			1.11244			0.556221	+	0.831035i	$0.312251\pi$
$30$		0			0
$31$	1.93071	+	3.34408i	0.346765	+	0.600615i	0.985673	−	0.168669i	$-0.0539468\pi$
$31$	1.93071	+	3.34408i	0.346765	+	0.600615i	−0.638908	+	0.769283i	$0.720613\pi$
$32$		0			0
$33$	−3.48970	−	2.01478i	−0.607479	−	0.350728i
$34$		0			0
$35$	0.886450	+	5.84929i	0.149837	+	0.988711i
$36$		0			0
$37$	4.61567	+	2.66486i	0.758812	+	0.438100i	0.828869	−	0.559443i	$-0.188985\pi$
$37$	4.61567	+	2.66486i	0.758812	+	0.438100i	−0.0700572	+	0.997543i	$0.522318\pi$
$38$		0			0
$39$	3.01694	+	5.22550i	0.483097	+	0.836749i
$40$		0			0
$41$	6.24670			0.975571			0.487786	−	0.872964i	$-0.337805\pi$
$41$	6.24670			0.975571			0.487786	+	0.872964i	$0.337805\pi$
$42$		0			0
$43$		−	5.03947i		−	0.768512i	−0.923227	−	0.384256i	$-0.874458\pi$
$43$		−	5.03947i		−	0.768512i	0.923227	−	0.384256i	$-0.125542\pi$
$44$		0			0
$45$	1.01780	−	1.99100i	0.151725	−	0.296801i
$46$		0			0
$47$	−10.1585	−	5.86499i	−1.48176	−	0.855497i	−0.481978	−	0.876183i	$-0.660082\pi$
$47$	−10.1585	−	5.86499i	−1.48176	−	0.855497i	−0.999786	+	0.0206860i	$0.993415\pi$
$48$		0			0
$49$	−6.86220	+	1.38210i	−0.980314	+	0.197443i
$50$		0			0
$51$	−0.471108	+	0.815983i	−0.0659683	+	0.114260i
$52$		0			0
$53$	4.38958	−	2.53432i	0.602955	−	0.348116i	−0.167248	−	0.985915i	$-0.553488\pi$
$53$	4.38958	−	2.53432i	0.602955	−	0.348116i	0.770203	+	0.637799i	$0.220155\pi$
$54$		0			0
$55$	−4.89734	−	7.56325i	−0.660357	−	1.01983i
$56$		0			0
$57$			8.60971i			1.14038i
$58$		0			0
$59$	−2.18367	−	3.78222i	−0.284289	−	0.492404i	0.688147	−	0.725571i	$-0.258424\pi$
$59$	−2.18367	−	3.78222i	−0.284289	−	0.492404i	−0.972437	+	0.233167i	$0.925091\pi$
$60$		0			0
$61$	−0.759024	+	1.31467i	−0.0971830	+	0.168326i	−0.910518	−	0.413470i	$-0.864317\pi$
$61$	−0.759024	+	1.31467i	−0.0971830	+	0.168326i	0.813335	+	0.581796i	$0.197650\pi$
$62$		0			0
$63$	2.41123	+	1.08903i	0.303786	+	0.137205i
$64$		0			0
$65$	0.688195	+	13.4746i	0.0853600	+	1.67132i
$66$		0			0
$67$	8.28111	−	4.78110i	1.01170	−	0.584105i	0.100010	−	0.994986i	$-0.468112\pi$
$67$	8.28111	−	4.78110i	1.01170	−	0.584105i	0.911689	+	0.410882i	$0.134779\pi$
$68$		0			0
$69$	4.94222			0.594973
$70$		0			0
$71$	−8.93194			−1.06003			−0.530013	−	0.847989i	$-0.677813\pi$
$71$	−8.93194			−1.06003			−0.530013	+	0.847989i	$0.677813\pi$
$72$		0			0
$73$	−5.91012	+	3.41221i	−0.691727	+	0.399369i	−0.804259	−	0.594279i	$-0.797437\pi$
$73$	−5.91012	+	3.41221i	−0.691727	+	0.399369i	0.112532	+	0.993648i	$0.464104\pi$
$74$		0			0
$75$	4.05289	−	2.92815i	0.467988	−	0.338114i
$76$		0			0
$77$	8.65847	−	6.22031i	0.986724	−	0.708870i
$78$		0			0
$79$	3.43708	−	5.95320i	0.386702	−	0.669787i	−0.605302	−	0.795996i	$-0.706948\pi$
$79$	3.43708	−	5.95320i	0.386702	−	0.669787i	0.992004	+	0.126209i	$0.0402810\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			16.3602i			1.79577i	0.440232	+	0.897884i	$0.354896\pi$
$83$			16.3602i			1.79577i	−0.440232	+	0.897884i	$0.645104\pi$
$84$		0			0
$85$	−1.76849	+	1.14513i	−0.191819	+	0.124206i
$86$		0			0
$87$	5.18808	−	2.99534i	0.556221	−	0.321134i
$88$		0			0
$89$	−2.39902	+	4.15523i	−0.254296	+	0.440453i	−0.964704	−	0.263337i	$-0.915177\pi$
$89$	−2.39902	+	4.15523i	−0.254296	+	0.440453i	0.710408	+	0.703790i	$0.248510\pi$
$90$		0			0
$91$	−15.8854	+	1.58382i	−1.66524	+	0.166030i
$92$		0			0
$93$	3.34408	+	1.93071i	0.346765	+	0.200205i
$94$		0			0
$95$	−8.76300	+	17.1419i	−0.899065	+	1.75872i
$96$		0			0
$97$		−	18.6629i		−	1.89493i	−0.319862	−	0.947464i	$-0.603637\pi$
$97$		−	18.6629i		−	1.89493i	0.319862	−	0.947464i	$-0.396363\pi$
$98$		0			0
$99$	−4.02956			−0.404986
$100$		0			0
$101$	−6.23013	−	10.7909i	−0.619921	−	1.07374i	−0.989500	−	0.144536i	$-0.953831\pi$
$101$	−6.23013	−	10.7909i	−0.619921	−	1.07374i	0.369578	−	0.929200i	$-0.379502\pi$
$102$		0			0
$103$	4.65554	+	2.68788i	0.458724	+	0.264845i	0.711508	−	0.702678i	$-0.248013\pi$
$103$	4.65554	+	2.68788i	0.458724	+	0.264845i	−0.252783	+	0.967523i	$0.581346\pi$
$104$		0			0
$105$	3.69233	+	4.62241i	0.360335	+	0.451101i
$106$		0			0
$107$	6.24409	+	3.60503i	0.603639	+	0.348511i	0.770472	−	0.637474i	$-0.220021\pi$
$107$	6.24409	+	3.60503i	0.603639	+	0.348511i	−0.166833	+	0.985985i	$0.553354\pi$
$108$		0			0
$109$	2.64168	+	4.57553i	0.253027	+	0.438256i	0.964358	−	0.264601i	$-0.0852404\pi$
$109$	2.64168	+	4.57553i	0.253027	+	0.438256i	−0.711330	+	0.702858i	$0.751907\pi$
$110$		0			0
$111$	5.32972			0.505874
$112$		0			0
$113$			0.356111i			0.0335001i	0.999860	+	0.0167500i	$0.00533195\pi$
$113$			0.356111i			0.0335001i	−0.999860	+	0.0167500i	$0.994668\pi$
$114$		0			0
$115$	9.83994	+	5.03021i	0.917580	+	0.469069i
$116$		0			0
$117$	5.22550	+	3.01694i	0.483097	+	0.278916i
$118$		0			0
$119$	−1.45447	−	2.02458i	−0.133331	−	0.185593i
$120$		0			0
$121$	−2.61867	+	4.53566i	−0.238060	+	0.412333i
$122$		0			0
$123$	5.40980	−	3.12335i	0.487786	−	0.281623i
$124$		0			0
$125$	11.0496	−	1.70489i	0.988305	−	0.152490i
$126$		0			0
$127$		−	8.24238i		−	0.731393i	−0.930734	−	0.365696i	$-0.880831\pi$
$127$		−	8.24238i		−	0.731393i	0.930734	−	0.365696i	$-0.119169\pi$
$128$		0			0
$129$	−2.51973	−	4.36431i	−0.221850	−	0.384256i
$130$		0			0
$131$	3.49102	−	6.04663i	0.305012	−	0.528297i	−0.672252	−	0.740322i	$-0.734673\pi$
$131$	3.49102	−	6.04663i	0.305012	−	0.528297i	0.977264	+	0.212026i	$0.0680061\pi$
$132$		0			0
$133$	−20.7600	−	9.37622i	−1.80012	−	0.813021i
$134$		0			0
$135$	−0.114055	−	2.23316i	−0.00981629	−	0.192200i
$136$		0			0
$137$	10.0810	−	5.82027i	0.861278	−	0.497259i	−0.00316232	−	0.999995i	$-0.501007\pi$
$137$	10.0810	−	5.82027i	0.861278	−	0.497259i	0.864440	+	0.502736i	$0.167673\pi$
$138$		0			0
$139$	17.6122			1.49385			0.746923	−	0.664910i	$-0.231530\pi$
$139$	17.6122			1.49385			0.746923	+	0.664910i	$0.231530\pi$
$140$		0			0
$141$	−11.7300			−0.987843
$142$		0			0
$143$	21.0564	−	12.1569i	1.76083	−	1.01661i
$144$		0			0
$145$	13.3781	−	0.683267i	1.11099	−	0.0567422i
$146$		0			0
$147$	−5.25179	+	4.62804i	−0.433160	+	0.381714i
$148$		0			0
$149$	−0.0837612	+	0.145079i	−0.00686199	+	0.0118853i	−0.869436	−	0.494046i	$-0.835518\pi$
$149$	−0.0837612	+	0.145079i	−0.00686199	+	0.0118853i	0.862574	+	0.505931i	$0.168851\pi$
$150$		0			0
$151$	−4.46708	−	7.73720i	−0.363526	−	0.629645i	0.625013	−	0.780615i	$-0.285094\pi$
$151$	−4.46708	−	7.73720i	−0.363526	−	0.629645i	−0.988538	+	0.150970i	$0.951760\pi$
$152$		0			0
$153$			0.942216i			0.0761736i
$154$		0			0
$155$	4.69298	+	7.24765i	0.376949	+	0.582146i
$156$		0			0
$157$	0.326196	−	0.188329i	0.0260332	−	0.0150303i	−0.486927	−	0.873443i	$-0.661882\pi$
$157$	0.326196	−	0.188329i	0.0260332	−	0.0150303i	0.512960	+	0.858412i	$0.328549\pi$
$158$		0			0
$159$	2.53432	−	4.38958i	0.200985	−	0.348116i
$160$		0			0
$161$	−5.38221	+	11.9168i	−0.424178	+	0.939176i
$162$		0			0
$163$	10.5436	+	6.08734i	0.825837	+	0.476797i	0.852425	−	0.522849i	$-0.175131\pi$
$163$	10.5436	+	6.08734i	0.825837	+	0.476797i	−0.0265880	+	0.999646i	$0.508464\pi$
$164$		0			0
$165$	−8.02284	−	4.10130i	−0.624577	−	0.319286i
$166$		0			0
$167$			2.43840i			0.188689i	0.995540	+	0.0943447i	$0.0300756\pi$
$167$			2.43840i			0.188689i	−0.995540	+	0.0943447i	$0.969924\pi$
$168$		0			0
$169$	−23.4077			−1.80060
$170$		0			0
$171$	4.30486	+	7.45623i	0.329201	+	0.570192i
$172$		0			0
$173$	−4.91112	−	2.83544i	−0.373385	−	0.215574i	0.301551	−	0.953450i	$-0.402496\pi$
$173$	−4.91112	−	2.83544i	−0.373385	−	0.215574i	−0.674936	+	0.737876i	$0.735829\pi$
$174$		0			0
$175$	2.64672	+	12.9613i	0.200073	+	0.979781i
$176$		0			0
$177$	−3.78222	−	2.18367i	−0.284289	−	0.164135i
$178$		0			0
$179$	−0.252651	−	0.437604i	−0.0188840	−	0.0327081i	0.856429	−	0.516265i	$-0.172678\pi$
$179$	−0.252651	−	0.437604i	−0.0188840	−	0.0327081i	−0.875313	+	0.483557i	$0.839345\pi$
$180$		0			0
$181$	−26.1722			−1.94536			−0.972681	−	0.232145i	$-0.925426\pi$
$181$	−26.1722			−1.94536			−0.972681	+	0.232145i	$0.925426\pi$
$182$		0			0
$183$			1.51805i			0.112217i
$184$		0			0
$185$	10.6115	+	5.42461i	0.780170	+	0.398825i
$186$		0			0
$187$	3.28805	+	1.89836i	0.240446	+	0.138822i
$188$		0			0
$189$	2.63270	−	0.262488i	0.191501	−	0.0190932i
$190$		0			0
$191$	8.67308	−	15.0222i	0.627562	−	1.08697i	−0.360477	−	0.932768i	$-0.617386\pi$
$191$	8.67308	−	15.0222i	0.627562	−	1.08697i	0.988039	−	0.154202i	$-0.0492806\pi$
$192$		0			0
$193$	−3.36126	+	1.94062i	−0.241949	+	0.139689i	−0.616072	−	0.787690i	$-0.711277\pi$
$193$	−3.36126	+	1.94062i	−0.241949	+	0.139689i	0.374123	+	0.927379i	$0.377944\pi$
$194$		0			0
$195$	7.33330	+	11.3253i	0.525148	+	0.811018i
$196$		0			0
$197$			8.60444i			0.613041i	0.951864	+	0.306520i	$0.0991648\pi$
$197$			8.60444i			0.613041i	−0.951864	+	0.306520i	$0.900835\pi$
$198$		0			0
$199$	3.95389	+	6.84834i	0.280284	+	0.485466i	0.971455	−	0.237226i	$-0.0762381\pi$
$199$	3.95389	+	6.84834i	0.280284	+	0.485466i	−0.691171	+	0.722692i	$0.742905\pi$
$200$		0			0
$201$	4.78110	−	8.28111i	0.337233	−	0.584105i
$202$		0			0
$203$	1.57248	+	15.7716i	0.110367	+	1.10695i
$204$		0			0
$205$	13.9499	−	0.712468i	0.974301	−	0.0497609i
$206$		0			0
$207$	4.28008	−	2.47111i	0.297486	−	0.171754i
$208$		0			0
$209$	34.6933			2.39979
$210$		0			0
$211$	−18.3347			−1.26221			−0.631105	−	0.775697i	$-0.717398\pi$
$211$	−18.3347			−1.26221			−0.631105	+	0.775697i	$0.717398\pi$
$212$		0			0
$213$	−7.73529	+	4.46597i	−0.530013	+	0.306003i
$214$		0			0
$215$	−0.574777	−	11.2539i	−0.0391994	−	0.767511i
$216$		0			0
$217$	−8.29717	+	5.96075i	−0.563249	+	0.404642i
$218$		0			0
$219$	−3.41221	+	5.91012i	−0.230576	+	0.399369i
$220$		0			0
$221$	−2.84261	−	4.92355i	−0.191215	−	0.331193i
$222$		0			0
$223$			2.95434i			0.197837i	0.995096	+	0.0989186i	$0.0315383\pi$
$223$			2.95434i			0.197837i	−0.995096	+	0.0989186i	$0.968462\pi$
$224$		0			0
$225$	2.04583	−	4.56230i	0.136389	−	0.304153i
$226$		0			0
$227$	−14.3495	+	8.28468i	−0.952409	+	0.549874i	−0.893828	−	0.448409i	$-0.851991\pi$
$227$	−14.3495	+	8.28468i	−0.952409	+	0.549874i	−0.0585806	+	0.998283i	$0.518657\pi$
$228$		0			0
$229$	−12.0536	+	20.8775i	−0.796525	+	1.37962i	0.125342	+	0.992114i	$0.459997\pi$
$229$	−12.0536	+	20.8775i	−0.796525	+	1.37962i	−0.921866	+	0.387508i	$0.873336\pi$
$230$		0			0
$231$	4.38830	−	9.71618i	0.288729	−	0.639278i
$232$		0			0
$233$	8.93499	+	5.15862i	0.585350	+	0.337952i	0.763257	−	0.646095i	$-0.223599\pi$
$233$	8.93499	+	5.15862i	0.585350	+	0.337952i	−0.177906	+	0.984047i	$0.556932\pi$
$234$		0			0
$235$	−23.3544	−	11.9388i	−1.52347	−	0.778803i
$236$		0			0
$237$		−	6.87416i		−	0.446525i
$238$		0			0
$239$	21.4416			1.38694			0.693472	−	0.720483i	$-0.256080\pi$
$239$	21.4416			1.38694			0.693472	+	0.720483i	$0.256080\pi$
$240$		0			0
$241$	−9.79026	−	16.9572i	−0.630646	−	1.09231i	−0.987420	−	0.158120i	$-0.949457\pi$
$241$	−9.79026	−	16.9572i	−0.630646	−	1.09231i	0.356774	−	0.934191i	$-0.383877\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−15.1667	+	3.86912i	−0.968967	+	0.247189i
$246$		0			0
$247$	−44.9900	−	25.9750i	−2.86265	−	1.65275i
$248$		0			0
$249$	8.18011	+	14.1684i	0.518394	+	0.897884i
$250$		0			0
$251$	−3.07240			−0.193928			−0.0969640	−	0.995288i	$-0.530913\pi$
$251$	−3.07240			−0.193928			−0.0969640	+	0.995288i	$0.530913\pi$
$252$		0			0
$253$		−	19.9149i		−	1.25204i
$254$		0			0
$255$	−0.958991	+	1.87595i	−0.0600544	+	0.117477i
$256$		0			0
$257$	−22.9987	−	13.2783i	−1.43462	−	0.828279i	−0.437152	−	0.899388i	$-0.644013\pi$
$257$	−22.9987	−	13.2783i	−1.43462	−	0.828279i	−0.997469	+	0.0711089i	$0.977346\pi$
$258$		0			0
$259$	−5.80421	+	12.8512i	−0.360656	+	0.798532i
$260$		0			0
$261$	2.99534	−	5.18808i	0.185407	−	0.321134i
$262$		0			0
$263$	16.7003	−	9.64190i	1.02978	−	0.594545i	0.112860	−	0.993611i	$-0.463999\pi$
$263$	16.7003	−	9.64190i	1.02978	−	0.594545i	0.916922	+	0.399066i	$0.130666\pi$
$264$		0			0
$265$	9.51356	−	6.16020i	0.584414	−	0.378418i
$266$		0			0
$267$			4.79804i			0.293635i
$268$		0			0
$269$	−2.89650	−	5.01688i	−0.176603	−	0.305885i	0.764112	−	0.645083i	$-0.223177\pi$
$269$	−2.89650	−	5.01688i	−0.176603	−	0.305885i	−0.940715	+	0.339199i	$0.889844\pi$
$270$		0			0
$271$	−2.79958	+	4.84901i	−0.170062	+	0.294557i	−0.938441	−	0.345438i	$-0.887730\pi$
$271$	−2.79958	+	4.84901i	−0.170062	+	0.294557i	0.768379	+	0.639995i	$0.221064\pi$
$272$		0			0
$273$	−12.9652	+	9.31433i	−0.784692	+	0.563729i
$274$		0			0
$275$	−11.7991	−	16.3314i	−0.711515	−	0.984818i
$276$		0			0
$277$	4.09578	−	2.36470i	0.246091	−	0.142081i	−0.371882	−	0.928280i	$-0.621287\pi$
$277$	4.09578	−	2.36470i	0.246091	−	0.142081i	0.617973	+	0.786199i	$0.287954\pi$
$278$		0			0
$279$	3.86141			0.231177
$280$		0			0
$281$	−13.5939			−0.810942			−0.405471	−	0.914108i	$-0.632893\pi$
$281$	−13.5939			−0.810942			−0.405471	+	0.914108i	$0.632893\pi$
$282$		0			0
$283$	6.80740	−	3.93026i	0.404658	−	0.233629i	−0.283834	−	0.958873i	$-0.591606\pi$
$283$	6.80740	−	3.93026i	0.404658	−	0.233629i	0.688492	+	0.725244i	$0.258273\pi$
$284$		0			0
$285$	0.981981	+	19.2268i	0.0581675	+	1.13890i
$286$		0			0
$287$	1.63969	+	16.4457i	0.0967876	+	0.970758i
$288$		0			0
$289$	−8.05611	+	13.9536i	−0.473889	+	0.820800i
$290$		0			0
$291$	−9.33144	−	16.1625i	−0.547019	−	0.947464i
$292$		0			0
$293$		−	12.6210i		−	0.737325i	−0.929563	−	0.368662i	$-0.879816\pi$
$293$		−	12.6210i		−	0.737325i	0.929563	−	0.368662i	$-0.120184\pi$
$294$		0			0
$295$	−5.30786	−	8.19724i	−0.309035	−	0.477262i
$296$		0			0
$297$	−3.48970	+	2.01478i	−0.202493	+	0.116909i
$298$		0			0
$299$	−14.9104	+	25.8255i	−0.862289	+	1.49353i
$300$		0			0
$301$	13.2674	−	1.32280i	0.764720	−	0.0762450i
$302$		0			0
$303$	−10.7909	−	6.23013i	−0.619921	−	0.357912i
$304$		0			0
$305$	−1.54507	+	3.02243i	−0.0884707	+	0.173064i
$306$		0			0
$307$			21.1967i			1.20976i	0.796316	+	0.604880i	$0.206779\pi$
$307$			21.1967i			1.20976i	−0.796316	+	0.604880i	$0.793221\pi$
$308$		0			0
$309$	5.37576			0.305816
$310$		0			0
$311$	3.00794	+	5.20990i	0.170565	+	0.295427i	0.938617	−	0.344960i	$-0.112108\pi$
$311$	3.00794	+	5.20990i	0.170565	+	0.295427i	−0.768053	+	0.640387i	$0.778774\pi$
$312$		0			0
$313$	−15.8248	−	9.13644i	−0.894470	−	0.516422i	−0.0190678	−	0.999818i	$-0.506070\pi$
$313$	−15.8248	−	9.13644i	−0.894470	−	0.516422i	−0.875402	+	0.483396i	$0.839403\pi$
$314$		0			0
$315$	5.50886	+	2.15696i	0.310389	+	0.121531i
$316$		0			0
$317$	11.1698	+	6.44888i	0.627358	+	0.362205i	0.779728	−	0.626118i	$-0.215357\pi$
$317$	11.1698	+	6.44888i	0.627358	+	0.362205i	−0.152370	+	0.988324i	$0.548691\pi$
$318$		0			0
$319$	−12.0699	−	20.9057i	−0.675784	−	1.17049i
$320$		0			0
$321$	7.21006			0.402426
$322$		0			0
$323$		−	8.11221i		−	0.451375i
$324$		0			0
$325$	3.07369	+	30.0124i	0.170498	+	1.66479i
$326$		0			0
$327$	4.57553	+	2.64168i	0.253027	+	0.146085i
$328$		0			0
$329$	12.7743	−	28.2837i	0.704269	−	1.55933i
$330$		0			0
$331$	1.06329	−	1.84167i	0.0584438	−	0.101228i	−0.835323	−	0.549759i	$-0.814719\pi$
$331$	1.06329	−	1.84167i	0.0584438	−	0.101228i	0.893767	+	0.448532i	$0.148053\pi$
$332$		0			0
$333$	4.61567	−	2.66486i	0.252937	−	0.146033i
$334$		0			0
$335$	17.9477	−	11.6215i	0.980588	−	0.634948i
$336$		0			0
$337$			9.24557i			0.503639i	0.967774	+	0.251819i	$0.0810289\pi$
$337$			9.24557i			0.503639i	−0.967774	+	0.251819i	$0.918971\pi$
$338$		0			0
$339$	0.178055	+	0.308401i	0.00967064	+	0.0167500i
$340$		0			0
$341$	7.77989	−	13.4752i	0.421305	−	0.729721i
$342$		0			0
$343$	−5.43991	−	17.7033i	−0.293728	−	0.955889i
$344$		0			0
$345$	11.0367	−	0.563685i	0.594198	−	0.0303478i
$346$		0			0
$347$	−5.66332	+	3.26972i	−0.304023	+	0.175528i	−0.644249	−	0.764816i	$-0.722830\pi$
$347$	−5.66332	+	3.26972i	−0.304023	+	0.175528i	0.340226	+	0.940344i	$0.389497\pi$
$348$		0			0
$349$	12.0217			0.643508			0.321754	−	0.946823i	$-0.395728\pi$
$349$	12.0217			0.643508			0.321754	+	0.946823i	$0.395728\pi$
$350$		0			0
$351$	6.03388			0.322065
$352$		0			0
$353$	−10.1811	+	5.87805i	−0.541884	+	0.312857i	−0.745842	−	0.666123i	$-0.767953\pi$
$353$	−10.1811	+	5.87805i	−0.541884	+	0.312857i	0.203958	+	0.978980i	$0.434619\pi$
$354$		0			0
$355$	−19.9464	+	1.01873i	−1.05865	+	0.0540687i
$356$		0			0
$357$	−2.27190	−	1.02610i	−0.120242	−	0.0543069i
$358$		0			0
$359$	10.3181	−	17.8714i	0.544567	−	0.943217i	−0.454068	−	0.890967i	$-0.650028\pi$
$359$	10.3181	−	17.8714i	0.544567	−	0.943217i	0.998634	−	0.0522496i	$-0.0166391\pi$
$360$		0			0
$361$	−27.5636	−	47.7415i	−1.45072	−	2.51271i
$362$		0			0
$363$			5.23733i			0.274889i
$364$		0			0
$365$	−12.8090	+	8.29408i	−0.670456	+	0.434132i
$366$		0			0
$367$	17.0552	−	9.84685i	0.890276	−	0.514001i	0.0162435	−	0.999868i	$-0.494829\pi$
$367$	17.0552	−	9.84685i	0.890276	−	0.514001i	0.874033	+	0.485867i	$0.161496\pi$
$368$		0			0
$369$	3.12335	−	5.40980i	0.162595	−	0.281623i
$370$		0			0
$371$	7.82432	+	10.8912i	0.406219	+	0.565443i
$372$		0			0
$373$	5.34658	+	3.08685i	0.276835	+	0.159831i	0.631990	−	0.774977i	$-0.282238\pi$
$373$	5.34658	+	3.08685i	0.276835	+	0.159831i	−0.355155	+	0.934808i	$0.615572\pi$
$374$		0			0
$375$	8.71678	−	7.00127i	0.450132	−	0.361544i
$376$		0			0
$377$			36.1471i			1.86167i
$378$		0			0
$379$	19.0333			0.977675			0.488838	−	0.872375i	$-0.337421\pi$
$379$	19.0333			0.977675			0.488838	+	0.872375i	$0.337421\pi$
$380$		0			0
$381$	−4.12119	−	7.13811i	−0.211135	−	0.365696i
$382$		0			0
$383$	−22.9300	−	13.2387i	−1.17167	−	0.676464i	−0.217597	−	0.976039i	$-0.569822\pi$
$383$	−22.9300	−	13.2387i	−1.17167	−	0.676464i	−0.954073	+	0.299575i	$0.903155\pi$
$384$		0			0
$385$	18.6263	−	14.8785i	0.949282	−	0.758277i
$386$		0			0
$387$	−4.36431	−	2.51973i	−0.221850	−	0.128085i
$388$		0			0
$389$	−11.4088	−	19.7606i	−0.578448	−	1.00190i	−0.995658	−	0.0930910i	$-0.970325\pi$
$389$	−11.4088	−	19.7606i	−0.578448	−	1.00190i	0.417210	−	0.908810i	$-0.363008\pi$
$390$		0			0
$391$	−4.65663			−0.235496
$392$		0			0
$393$		−	6.98205i		−	0.352198i
$394$		0			0
$395$	6.99655	−	13.6864i	0.352034	−	0.688639i
$396$		0			0
$397$	−8.74349	−	5.04806i	−0.438823	−	0.253355i	0.264275	−	0.964447i	$-0.414867\pi$
$397$	−8.74349	−	5.04806i	−0.438823	−	0.253355i	−0.703098	+	0.711093i	$0.748201\pi$
$398$		0			0
$399$	−22.6668	+	2.25995i	−1.13476	+	0.113139i
$400$		0			0
$401$	−6.01833	+	10.4241i	−0.300541	+	0.520552i	−0.976259	−	0.216608i	$-0.930501\pi$
$401$	−6.01833	+	10.4241i	−0.300541	+	0.520552i	0.675718	+	0.737161i	$0.263834\pi$
$402$		0			0
$403$	−20.1778	+	11.6497i	−1.00513	+	0.580311i
$404$		0			0
$405$	−1.21535	−	1.87694i	−0.0603914	−	0.0932661i
$406$		0			0
$407$		−	21.4764i		−	1.06455i
$408$		0			0
$409$	−14.2036	−	24.6013i	−0.702322	−	1.21646i	−0.967649	−	0.252300i	$-0.918813\pi$
$409$	−14.2036	−	24.6013i	−0.702322	−	1.21646i	0.265327	−	0.964159i	$-0.414520\pi$
$410$		0			0
$411$	5.82027	−	10.0810i	0.287093	−	0.497259i
$412$		0			0
$413$	9.38427	−	6.74173i	0.461770	−	0.331739i
$414$		0			0
$415$	1.86597	+	36.5350i	0.0915967	+	1.79343i
$416$		0			0
$417$	15.2526	−	8.80609i	0.746923	−	0.431236i
$418$		0			0
$419$	−23.3941			−1.14288			−0.571439	−	0.820645i	$-0.693614\pi$
$419$	−23.3941			−1.14288			−0.571439	+	0.820645i	$0.693614\pi$
$420$		0			0
$421$	37.7341			1.83905			0.919524	−	0.393033i	$-0.128574\pi$
$421$	37.7341			1.83905			0.919524	+	0.393033i	$0.128574\pi$
$422$		0			0
$423$	−10.1585	+	5.86499i	−0.493921	+	0.285166i
$424$		0			0
$425$	−3.81870	+	2.75895i	−0.185234	+	0.133829i
$426$		0			0
$427$	−3.66036	−	1.65320i	−0.177137	−	0.0800037i
$428$		0			0
$429$	12.1569	−	21.0564i	0.586942	−	1.01661i
$430$		0			0
$431$	−6.67013	−	11.5530i	−0.321289	−	0.556488i	0.659466	−	0.751735i	$-0.270783\pi$
$431$	−6.67013	−	11.5530i	−0.321289	−	0.556488i	−0.980754	+	0.195247i	$0.937449\pi$
$432$		0			0
$433$		−	2.73860i		−	0.131609i	−0.997833	−	0.0658044i	$-0.979039\pi$
$433$		−	2.73860i		−	0.131609i	0.997833	−	0.0658044i	$-0.0209613\pi$
$434$		0			0
$435$	11.2442	−	7.28079i	0.539116	−	0.349087i
$436$		0			0
$437$	−36.8503	+	21.2755i	−1.76279	+	1.01775i
$438$		0			0
$439$	11.2670	−	19.5150i	0.537745	−	0.931401i	−0.461280	−	0.887254i	$-0.652610\pi$
$439$	11.2670	−	19.5150i	0.537745	−	0.931401i	0.999025	−	0.0441467i	$-0.0140569\pi$
$440$		0			0
$441$	−2.23416	+	6.63389i	−0.106389	+	0.315900i
$442$		0			0
$443$	28.2480	+	16.3090i	1.34210	+	0.774863i	0.987116	−	0.160008i	$-0.0511521\pi$
$443$	28.2480	+	16.3090i	1.34210	+	0.774863i	0.354986	+	0.934871i	$0.384485\pi$
$444$		0			0
$445$	−4.88347	+	9.55290i	−0.231499	+	0.452851i
$446$		0			0
$447$			0.167522i			0.00792354i
$448$		0			0
$449$	24.4718			1.15490			0.577448	−	0.816427i	$-0.304049\pi$
$449$	24.4718			1.15490			0.577448	+	0.816427i	$0.304049\pi$
$450$		0			0
$451$	−12.5857	−	21.7991i	−0.592639	−	1.02648i
$452$		0			0
$453$	−7.73720	−	4.46708i	−0.363526	−	0.209882i
$454$		0			0
$455$	−35.2939	+	5.34873i	−1.65461	+	0.250753i
$456$		0			0
$457$	5.20589	+	3.00562i	0.243521	+	0.140597i	0.616794	−	0.787125i	$-0.288431\pi$
$457$	5.20589	+	3.00562i	0.243521	+	0.140597i	−0.373273	+	0.927722i	$0.621764\pi$
$458$		0			0
$459$	0.471108	+	0.815983i	0.0219894	+	0.0380868i
$460$		0			0
$461$	12.6005			0.586863			0.293432	−	0.955980i	$-0.405203\pi$
$461$	12.6005			0.586863			0.293432	+	0.955980i	$0.405203\pi$
$462$		0			0
$463$		−	15.1538i		−	0.704258i	−0.935951	−	0.352129i	$-0.885458\pi$
$463$		−	15.1538i		−	0.704258i	0.935951	−	0.352129i	$-0.114542\pi$
$464$		0			0
$465$	7.68807	+	3.93016i	0.356526	+	0.182257i
$466$		0			0
$467$	−6.26188	−	3.61530i	−0.289765	−	0.167296i	0.348071	−	0.937468i	$-0.386837\pi$
$467$	−6.26188	−	3.61530i	−0.289765	−	0.167296i	−0.637836	+	0.770172i	$0.720170\pi$
$468$		0			0
$469$	14.7609	+	20.5467i	0.681595	+	0.948758i
$470$		0			0
$471$	0.188329	−	0.326196i	0.00867775	−	0.0150303i
$472$		0			0
$473$	−17.5862	+	10.1534i	−0.808616	+	0.466854i
$474$		0			0
$475$	−17.6140	+	39.2801i	−0.808188	+	1.80229i
$476$		0			0
$477$		−	5.06865i		−	0.232077i
$478$		0			0
$479$	−11.3323	−	19.6282i	−0.517788	−	0.896835i	−0.999786	−	0.0206632i	$-0.993422\pi$
$479$	−11.3323	−	19.6282i	−0.517788	−	0.896835i	0.481998	−	0.876172i	$-0.339911\pi$
$480$		0			0
$481$	−16.0794	+	27.8504i	−0.733160	+	1.26987i
$482$		0			0
$483$	1.29727	+	13.0114i	0.0590280	+	0.592038i
$484$		0			0
$485$	−2.12860	−	41.6771i	−0.0966545	−	1.89246i
$486$		0			0
$487$	−1.35472	+	0.782149i	−0.0613883	+	0.0354425i	−0.530380	−	0.847760i	$-0.677951\pi$
$487$	−1.35472	+	0.782149i	−0.0613883	+	0.0354425i	0.468992	+	0.883203i	$0.344617\pi$
$488$		0			0
$489$	12.1747			0.550558
$490$		0			0
$491$	−26.6626			−1.20327			−0.601633	−	0.798773i	$-0.705483\pi$
$491$	−26.6626			−1.20327			−0.601633	+	0.798773i	$0.705483\pi$
$492$		0			0
$493$	−4.88829	+	2.82226i	−0.220158	+	0.127108i
$494$		0			0
$495$	−8.99863	+	0.459591i	−0.404459	+	0.0206571i
$496$		0			0
$497$	−2.34453	−	23.5151i	−0.105167	−	1.05480i
$498$		0			0
$499$	−7.79416	+	13.4999i	−0.348914	+	0.604338i	−0.986057	−	0.166408i	$-0.946783\pi$
$499$	−7.79416	+	13.4999i	−0.348914	+	0.604338i	0.637142	+	0.770746i	$0.280116\pi$
$500$		0			0
$501$	1.21920	+	2.11172i	0.0544699	+	0.0943447i
$502$		0			0
$503$			3.45014i			0.153834i	0.997037	+	0.0769171i	$0.0245077\pi$
$503$			3.45014i			0.153834i	−0.997037	+	0.0769171i	$0.975492\pi$
$504$		0			0
$505$	−15.1436	−	23.3872i	−0.673882	−	1.04072i
$506$		0			0
$507$	−20.2717	+	11.7039i	−0.900298	+	0.519787i
$508$		0			0
$509$	−8.62103	+	14.9321i	−0.382121	+	0.661852i	−0.991365	−	0.131130i	$-0.958139\pi$
$509$	−8.62103	+	14.9321i	−0.382121	+	0.661852i	0.609245	+	0.792982i	$0.291473\pi$
$510$		0			0
$511$	−10.5347	−	14.6639i	−0.466026	−	0.648692i
$512$		0			0
$513$	7.45623	+	4.30486i	0.329201	+	0.190064i
$514$		0			0
$515$	10.7031	+	5.47147i	0.471636	+	0.241102i
$516$		0			0
$517$			47.2666i			2.07878i
$518$		0			0
$519$	−5.67087			−0.248924
$520$		0			0
$521$	−12.0109	−	20.8034i	−0.526205	−	0.911415i	−0.999534	−	0.0305286i	$-0.990281\pi$
$521$	−12.0109	−	20.8034i	−0.526205	−	0.911415i	0.473328	−	0.880886i	$-0.343052\pi$
$522$		0			0
$523$	−11.2726	−	6.50827i	−0.492918	−	0.284587i	0.232866	−	0.972509i	$-0.425190\pi$
$523$	−11.2726	−	6.50827i	−0.492918	−	0.284587i	−0.725784	+	0.687922i	$0.758523\pi$
$524$		0			0
$525$	8.77277	+	9.90144i	0.382875	+	0.432134i
$526$		0			0
$527$	−3.15085	−	1.81914i	−0.137253	−	0.0792431i
$528$		0			0
$529$	0.712749	+	1.23452i	0.0309891	+	0.0536747i
$530$		0			0
$531$	−4.36734			−0.189526
$532$		0			0
$533$			37.6919i			1.63262i
$534$		0			0
$535$	14.3552	+	7.33842i	0.620630	+	0.317268i
$536$		0			0
$537$	−0.437604	−	0.252651i	−0.0188840	−	0.0109027i
$538$		0			0
$539$	18.6489	+	21.1624i	0.803267	+	0.911528i
$540$		0			0
$541$	2.92211	−	5.06124i	0.125631	−	0.217600i	−0.796348	−	0.604838i	$-0.793238\pi$
$541$	2.92211	−	5.06124i	0.125631	−	0.217600i	0.921980	+	0.387239i	$0.126571\pi$
$542$		0			0
$543$	−22.6658	+	13.0861i	−0.972681	+	0.561578i
$544$		0			0
$545$	6.42116	+	9.91658i	0.275052	+	0.424780i
$546$		0			0
$547$			0.494131i			0.0211275i	0.999944	+	0.0105638i	$0.00336261\pi$
$547$			0.494131i			0.0211275i	−0.999944	+	0.0105638i	$0.996637\pi$
$548$		0			0
$549$	0.759024	+	1.31467i	0.0323943	+	0.0561087i
$550$		0			0
$551$	−25.7890	+	44.6679i	−1.09865	+	1.90292i
$552$		0			0
$553$	16.5752	+	7.48615i	0.704848	+	0.318343i
$554$		0			0
$555$	11.9021	−	0.607881i	0.505216	−	0.0258031i
$556$		0			0
$557$	20.2502	−	11.6914i	0.858027	−	0.495382i	−0.00532420	−	0.999986i	$-0.501695\pi$
$557$	20.2502	−	11.6914i	0.858027	−	0.495382i	0.863351	+	0.504604i	$0.168361\pi$
$558$		0			0
$559$	30.4076			1.28610
$560$		0			0
$561$	3.79671			0.160297
$562$		0			0
$563$	35.9025	−	20.7283i	1.51311	−	0.873594i	0.513227	−	0.858253i	$-0.328450\pi$
$563$	35.9025	−	20.7283i	1.51311	−	0.873594i	0.999882	−	0.0153411i	$-0.00488342\pi$
$564$		0			0
$565$	0.0406162	+	0.795251i	0.00170874	+	0.0334565i
$566$		0			0
$567$	2.14874	−	1.54367i	0.0902386	−	0.0648281i
$568$		0			0
$569$	−13.3499	+	23.1227i	−0.559656	+	0.969352i	0.437869	+	0.899039i	$0.355733\pi$
$569$	−13.3499	+	23.1227i	−0.559656	+	0.969352i	−0.997525	+	0.0703134i	$0.977600\pi$
$570$		0			0
$571$	−7.93378	−	13.7417i	−0.332019	−	0.575073i	0.650889	−	0.759173i	$-0.274396\pi$
$571$	−7.93378	−	13.7417i	−0.332019	−	0.575073i	−0.982908	+	0.184100i	$0.941063\pi$
$572$		0			0
$573$		−	17.3462i		−	0.724647i
$574$		0			0
$575$	22.5479	+	10.1109i	0.940311	+	0.421656i
$576$		0			0
$577$	37.9174	−	21.8916i	1.57852	−	0.911359i	0.583454	−	0.812146i	$-0.301701\pi$
$577$	37.9174	−	21.8916i	1.57852	−	0.911359i	0.995066	−	0.0992127i	$-0.0316324\pi$
$578$		0			0
$579$	−1.94062	+	3.36126i	−0.0806496	+	0.139689i
$580$		0			0
$581$	−43.0715	+	4.29437i	−1.78691	+	0.178160i
$582$		0			0
$583$	−17.6881	−	10.2122i	−0.732564	−	0.422946i
$584$		0			0
$585$	12.0135	+	6.14131i	0.496695	+	0.253912i
$586$		0			0
$587$		−	11.9428i		−	0.492933i	−0.969151	−	0.246467i	$-0.920730\pi$
$587$		−	11.9428i		−	0.492933i	0.969151	−	0.246467i	$-0.0792696\pi$
$588$		0			0
$589$	−33.2457			−1.36986
$590$		0			0
$591$	4.30222	+	7.45166i	0.176970	+	0.306520i
$592$		0			0
$593$	39.6083	+	22.8678i	1.62652	+	0.939070i	0.985122	+	0.171859i	$0.0549774\pi$
$593$	39.6083	+	22.8678i	1.62652	+	0.939070i	0.641395	+	0.767211i	$0.278356\pi$
$594$		0			0
$595$	−3.47898	−	4.35531i	−0.142624	−	0.178550i
$596$		0			0
$597$	6.84834	+	3.95389i	0.280284	+	0.161822i
$598$		0			0
$599$	−1.00358	−	1.73825i	−0.0410052	−	0.0710230i	0.844794	−	0.535091i	$-0.179723\pi$
$599$	−1.00358	−	1.73825i	−0.0410052	−	0.0710230i	−0.885800	+	0.464068i	$0.846389\pi$
$600$		0			0
$601$	41.7743			1.70401			0.852004	−	0.523535i	$-0.175387\pi$
$601$	41.7743			1.70401			0.852004	+	0.523535i	$0.175387\pi$
$602$		0			0
$603$		−	9.56220i		−	0.389403i
$604$		0			0
$605$	−5.33058	+	10.4275i	−0.216719	+	0.423939i
$606$		0			0
$607$	21.4763	+	12.3993i	0.871695	+	0.503273i	0.867911	−	0.496720i	$-0.165462\pi$
$607$	21.4763	+	12.3993i	0.871695	+	0.503273i	0.00378381	+	0.999993i	$0.498796\pi$
$608$		0			0
$609$	9.24763	+	12.8724i	0.374733	+	0.521616i
$610$		0			0
$611$	35.3887	−	61.2950i	1.43167	−	2.47973i
$612$		0			0
$613$	−12.0834	+	6.97638i	−0.488045	+	0.281773i	−0.723763	−	0.690048i	$-0.757589\pi$
$613$	−12.0834	+	6.97638i	−0.488045	+	0.281773i	0.235718	+	0.971822i	$0.424256\pi$
$614$		0			0
$615$	11.7247	−	7.59195i	0.472786	−	0.306137i
$616$		0			0
$617$		−	10.0319i		−	0.403867i	−0.979399	−	0.201934i	$-0.935277\pi$
$617$		−	10.0319i		−	0.403867i	0.979399	−	0.201934i	$-0.0647226\pi$
$618$		0			0
$619$	−4.81213	−	8.33486i	−0.193416	−	0.335006i	0.752964	−	0.658061i	$-0.228623\pi$
$619$	−4.81213	−	8.33486i	−0.193416	−	0.335006i	−0.946380	+	0.323055i	$0.895290\pi$
$620$		0			0
$621$	2.47111	−	4.28008i	0.0991621	−	0.171754i
$622$		0			0
$623$	−11.5692	−	5.22520i	−0.463509	−	0.209343i
$624$		0			0
$625$	24.4810	−	5.06755i	0.979240	−	0.202702i
$626$		0			0
$627$	30.0453	−	17.3467i	1.19989	−	0.692759i
$628$		0			0
$629$	−5.02175			−0.200230
$630$		0			0
$631$	−19.5975			−0.780166			−0.390083	−	0.920780i	$-0.627554\pi$
$631$	−19.5975			−0.780166			−0.390083	+	0.920780i	$0.627554\pi$
$632$		0			0
$633$	−15.8783	+	9.16733i	−0.631105	+	0.364369i
$634$		0			0
$635$	−0.940084	−	18.4065i	−0.0373061	−	0.730441i
$636$		0			0
$637$	−8.33946	−	41.4057i	−0.330421	−	1.64055i
$638$		0			0
$639$	−4.46597	+	7.73529i	−0.176671	+	0.306003i
$640$		0			0
$641$	−21.1952	−	36.7112i	−0.837160	−	1.45000i	−0.892259	−	0.451524i	$-0.850881\pi$
$641$	−21.1952	−	36.7112i	−0.837160	−	1.45000i	0.0550987	−	0.998481i	$-0.482453\pi$
$642$		0			0
$643$		−	9.64930i		−	0.380531i	−0.981733	−	0.190266i	$-0.939065\pi$
$643$		−	9.64930i		−	0.380531i	0.981733	−	0.190266i	$-0.0609349\pi$
$644$		0			0
$645$	−6.12473	−	9.45880i	−0.241161	−	0.372440i
$646$		0			0
$647$	9.61266	−	5.54987i	0.377913	−	0.218188i	−0.298997	−	0.954254i	$-0.596652\pi$
$647$	9.61266	−	5.54987i	0.377913	−	0.218188i	0.676910	+	0.736066i	$0.263319\pi$
$648$		0			0
$649$	−8.79922	+	15.2407i	−0.345399	+	0.598249i
$650$		0			0
$651$	−4.20519	+	9.31075i	−0.164814	+	0.364917i
$652$		0			0
$653$	−3.64945	−	2.10701i	−0.142814	−	0.0824536i	0.426891	−	0.904303i	$-0.359609\pi$
$653$	−3.64945	−	2.10701i	−0.142814	−	0.0824536i	−0.569704	+	0.821850i	$0.692942\pi$
$654$		0			0
$655$	7.10636	−	13.9012i	0.277668	−	0.543167i
$656$		0			0
$657$			6.82442i			0.266246i
$658$		0			0
$659$	−6.52405			−0.254141			−0.127070	−	0.991894i	$-0.540557\pi$
$659$	−6.52405			−0.254141			−0.127070	+	0.991894i	$0.540557\pi$
$660$		0			0
$661$	−6.36675	−	11.0275i	−0.247638	−	0.428922i	0.715232	−	0.698887i	$-0.246321\pi$
$661$	−6.36675	−	11.0275i	−0.247638	−	0.428922i	−0.962870	+	0.269965i	$0.912988\pi$
$662$		0			0
$663$	−4.92355	−	2.84261i	−0.191215	−	0.110398i
$664$		0			0
$665$	−47.4297	−	18.5708i	−1.83925	−	0.720144i
$666$		0			0
$667$	25.6406	+	14.8036i	0.992808	+	0.573198i
$668$		0			0
$669$	1.47717	+	2.55853i	0.0571107	+	0.0989186i
$670$		0			0
$671$	6.11706			0.236146
$672$		0			0
$673$		−	36.7489i		−	1.41656i	−0.705929	−	0.708282i	$-0.749470\pi$
$673$		−	36.7489i		−	1.41656i	0.705929	−	0.708282i	$-0.250530\pi$
$674$		0			0
$675$	−0.509406	−	4.97398i	−0.0196070	−	0.191449i
$676$		0			0
$677$	−12.2576	−	7.07691i	−0.471097	−	0.271988i	0.245602	−	0.969371i	$-0.421014\pi$
$677$	−12.2576	−	7.07691i	−0.471097	−	0.271988i	−0.716699	+	0.697383i	$0.754348\pi$
$678$		0			0
$679$	49.1337	−	4.89879i	1.88558	−	0.187998i
$680$		0			0
$681$	−8.28468	+	14.3495i	−0.317470	+	0.549874i
$682$		0			0
$683$	−19.2195	+	11.0964i	−0.735413	+	0.424591i	−0.820399	−	0.571791i	$-0.806249\pi$
$683$	−19.2195	+	11.0964i	−0.735413	+	0.424591i	0.0849862	+	0.996382i	$0.472915\pi$
$684$		0			0
$685$	21.8486	−	14.1474i	0.834793	−	0.540543i
$686$		0			0
$687$			24.1072i			0.919748i
$688$		0			0
$689$	15.2918	+	26.4862i	0.582572	+	1.00904i
$690$		0			0
$691$	−24.2439	+	41.9916i	−0.922280	+	1.59744i	−0.126401	+	0.991979i	$0.540343\pi$
$691$	−24.2439	+	41.9916i	−0.922280	+	1.59744i	−0.795879	+	0.605456i	$0.792991\pi$
$692$		0			0
$693$	−1.05771	−	10.6086i	−0.0401791	−	0.402988i
$694$		0			0
$695$	39.3308	−	2.00876i	1.49190	−	0.0761965i
$696$		0			0
$697$	−5.09720	+	2.94287i	−0.193070	+	0.111469i
$698$		0			0
$699$	10.3172			0.390234
$700$		0			0
$701$	−0.122295			−0.00461901			−0.00230950	−	0.999997i	$-0.500735\pi$
$701$	−0.122295			−0.00461901			−0.00230950	+	0.999997i	$0.500735\pi$
$702$		0			0
$703$	−39.7396	+	22.9437i	−1.49881	+	0.865337i
$704$		0			0
$705$	−26.1949	+	1.33786i	−0.986557	+	0.0503869i
$706$		0			0
$707$	26.7739	−	19.2345i	1.00693	−	0.723389i
$708$		0			0
$709$	11.9545	−	20.7058i	0.448960	−	0.777621i	−0.549359	−	0.835587i	$-0.685128\pi$
$709$	11.9545	−	20.7058i	0.448960	−	0.777621i	0.998319	+	0.0579652i	$0.0184613\pi$
$710$		0			0
$711$	−3.43708	−	5.95320i	−0.128901	−	0.223262i
$712$		0			0
$713$			19.0839i			0.714699i
$714$		0			0
$715$	45.6358	−	29.5499i	1.70668	−	1.10511i
$716$		0			0
$717$	18.5690	−	10.7208i	0.693472	−	0.400376i
$718$		0			0
$719$	−3.19471	+	5.53340i	−0.119143	+	0.206361i	−0.919428	−	0.393258i	$-0.871348\pi$
$719$	−3.19471	+	5.53340i	−0.119143	+	0.206361i	0.800286	+	0.599619i	$0.204681\pi$
$720$		0			0
$721$	−5.85435	+	12.9622i	−0.218027	+	0.482737i
$722$		0			0
$723$	−16.9572	−	9.79026i	−0.630646	−	0.364104i
$724$		0			0
$725$	29.7975	−	3.05169i	1.10665	−	0.113337i
$726$		0			0
$727$			43.7937i			1.62422i	0.583505	+	0.812110i	$0.301681\pi$
$727$			43.7937i			1.62422i	−0.583505	+	0.812110i	$0.698319\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	2.37413	+	4.11212i	0.0878105	+	0.152092i
$732$		0			0
$733$	29.1319	+	16.8193i	1.07601	+	0.621235i	0.929817	−	0.368021i	$-0.119965\pi$
$733$	29.1319	+	16.8193i	1.07601	+	0.621235i	0.146193	+	0.989256i	$0.453298\pi$
$734$		0			0
$735$	−11.2002	+	10.9341i	−0.413126	+	0.403311i
$736$		0			0
$737$	−33.3692	−	19.2657i	−1.22917	−	0.709662i
$738$		0			0
$739$	5.00246	+	8.66452i	0.184019	+	0.318730i	0.943245	−	0.332097i	$-0.107756\pi$
$739$	5.00246	+	8.66452i	0.184019	+	0.318730i	−0.759227	+	0.650826i	$0.774423\pi$
$740$		0			0
$741$	−51.9500			−1.90843
$742$		0			0
$743$			43.8326i			1.60806i	0.594587	+	0.804031i	$0.297316\pi$
$743$			43.8326i			1.60806i	−0.594587	+	0.804031i	$0.702684\pi$
$744$		0			0
$745$	−0.170505	+	0.333537i	−0.00624682	+	0.0122198i
$746$		0			0
$747$	14.1684	+	8.18011i	0.518394	+	0.299295i
$748$		0			0
$749$	−7.85195	+	17.3851i	−0.286904	+	0.635237i
$750$		0			0
$751$	14.0538	−	24.3418i	0.512829	−	0.888246i	−0.487060	−	0.873368i	$-0.661931\pi$
$751$	14.0538	−	24.3418i	0.512829	−	0.888246i	0.999889	−	0.0148777i	$-0.00473591\pi$
$752$		0			0
$753$	−2.66077	+	1.53620i	−0.0969640	+	0.0559822i
$754$		0			0
$755$	−10.8582	−	16.7689i	−0.395169	−	0.610283i
$756$		0			0
$757$			4.04902i			0.147164i	0.997289	+	0.0735821i	$0.0234431\pi$
$757$			4.04902i			0.147164i	−0.997289	+	0.0735821i	$0.976557\pi$
$758$		0			0
$759$	−9.95747	−	17.2468i	−0.361433	−	0.626021i
$760$		0			0
$761$	1.84389	−	3.19371i	0.0668409	−	0.115772i	−0.830668	−	0.556768i	$-0.812041\pi$
$761$	1.84389	−	3.19371i	0.0668409	−	0.115772i	0.897509	+	0.440996i	$0.145375\pi$
$762$		0			0
$763$	−11.3526	+	8.15578i	−0.410991	+	0.295259i
$764$		0			0
$765$	0.107464	+	2.10412i	0.00388539	+	0.0760745i
$766$		0			0
$767$	22.8215	−	13.1760i	0.824037	−	0.475758i
$768$		0			0
$769$	−32.7377			−1.18055			−0.590275	−	0.807202i	$-0.700981\pi$
$769$	−32.7377			−1.18055			−0.590275	+	0.807202i	$0.700981\pi$
$770$		0			0
$771$	−26.5566			−0.956414
$772$		0			0
$773$	34.4737	−	19.9034i	1.23993	−	0.715876i	0.270853	−	0.962621i	$-0.412694\pi$
$773$	34.4737	−	19.9034i	1.23993	−	0.715876i	0.969080	+	0.246745i	$0.0793611\pi$
$774$		0			0
$775$	11.3068	+	15.6499i	0.406152	+	0.562161i
$776$		0			0
$777$	1.39899	+	14.0315i	0.0501884	+	0.503379i
$778$		0			0
$779$	−26.8912	+	46.5769i	−0.963476	+	1.66879i
$780$		0			0
$781$	17.9959	+	31.1698i	0.643943	+	1.11534i
$782$		0			0
$783$		−	5.99068i		−	0.214089i
$784$		0			0
$785$	0.706966	−	0.457773i	0.0252327	−	0.0163386i
$786$		0			0
$787$	−1.32740	+	0.766373i	−0.0473166	+	0.0273183i	−0.523472	−	0.852043i	$-0.675363\pi$
$787$	−1.32740	+	0.766373i	−0.0473166	+	0.0273183i	0.476155	+	0.879361i	$0.342030\pi$
$788$		0			0
$789$	9.64190	−	16.7003i	0.343261	−	0.594545i
$790$		0			0
$791$	−0.937532	+	0.0934748i	−0.0333348	+	0.00332358i
$792$		0			0
$793$	−7.93255	−	4.57986i	−0.281693	−	0.162636i
$794$		0			0
$795$	5.15889	−	10.0917i	0.182967	−	0.357915i
$796$		0			0
$797$			24.0075i			0.850388i	0.905102	+	0.425194i	$0.139794\pi$
$797$			24.0075i			0.850388i	−0.905102	+	0.425194i	$0.860206\pi$
$798$		0			0
$799$	11.0522			0.390998
$800$		0			0
$801$	2.39902	+	4.15523i	0.0847653	+	0.146818i
$802$		0			0
$803$	23.8152	+	13.7497i	0.840419	+	0.485216i
$804$		0			0
$805$	−10.6601	+	27.2260i	−0.375721	+	0.959589i
$806$		0			0
$807$	−5.01688	−	2.89650i	−0.176603	−	0.101962i
$808$		0			0
$809$	−5.42064	−	9.38882i	−0.190580	−	0.330093i	0.754863	−	0.655883i	$-0.227703\pi$
$809$	−5.42064	−	9.38882i	−0.190580	−	0.330093i	−0.945442	+	0.325789i	$0.894370\pi$
$810$		0			0
$811$	14.0911			0.494805			0.247402	−	0.968913i	$-0.420423\pi$
$811$	14.0911			0.494805			0.247402	+	0.968913i	$0.420423\pi$
$812$		0			0
$813$			5.59916i			0.196371i
$814$		0			0
$815$	24.2398	+	12.3914i	0.849082	+	0.434053i
$816$		0			0
$817$	37.5754	+	21.6942i	1.31460	+	0.758984i
$818$		0			0
$819$	−6.57106	+	14.5491i	−0.229612	+	0.508385i
$820$		0			0
$821$	−20.3827	+	35.3039i	−0.711361	+	1.23211i	0.252985	+	0.967470i	$0.418588\pi$
$821$	−20.3827	+	35.3039i	−0.711361	+	1.23211i	−0.964346	+	0.264644i	$0.914746\pi$
$822$		0			0
$823$	8.82720	−	5.09639i	0.307697	−	0.177649i	−0.338198	−	0.941075i	$-0.609818\pi$
$823$	8.82720	−	5.09639i	0.307697	−	0.177649i	0.645895	+	0.763426i	$0.276484\pi$
$824$		0			0
$825$	−18.3840	−	8.24380i	−0.640050	−	0.287012i
$826$		0			0
$827$			12.2847i			0.427180i	0.976923	+	0.213590i	$0.0685157\pi$
$827$			12.2847i			0.427180i	−0.976923	+	0.213590i	$0.931484\pi$
$828$		0			0
$829$	16.7079	+	28.9390i	0.580290	+	1.00509i	0.995445	+	0.0953412i	$0.0303942\pi$
$829$	16.7079	+	28.9390i	0.580290	+	1.00509i	−0.415154	+	0.909751i	$0.636272\pi$
$830$		0			0
$831$	2.36470	−	4.09578i	0.0820305	−	0.142081i
$832$		0			0
$833$	4.94832	−	4.36061i	0.171449	−	0.151086i
$834$		0			0
$835$	0.278112	+	5.44534i	0.00962447	+	0.188444i
$836$		0			0
$837$	3.34408	−	1.93071i	0.115588	−	0.0667350i
$838$		0			0
$839$	21.8245			0.753464			0.376732	−	0.926322i	$-0.377048\pi$
$839$	21.8245			0.753464			0.376732	+	0.926322i	$0.377048\pi$
$840$		0			0
$841$	6.88823			0.237525
$842$		0			0
$843$	−11.7726	+	6.79693i	−0.405471	+	0.234099i
$844$		0			0
$845$	−52.2732	+	2.66977i	−1.79825	+	0.0918429i
$846$		0			0
$847$	−12.6284	−	5.70360i	−0.433917	−	0.195978i
$848$		0			0
$849$	3.93026	−	6.80740i	0.134886	−	0.233629i
$850$		0			0
$851$	13.1703	+	22.8116i	0.451472	+	0.781973i
$852$		0			0
$853$			3.88967i			0.133180i	0.997780	+	0.0665899i	$0.0212119\pi$
$853$			3.88967i			0.133180i	−0.997780	+	0.0665899i	$0.978788\pi$
$854$		0			0
$855$	10.4638	+	16.1599i	0.357856	+	0.552658i
$856$		0			0
$857$	−1.38779	+	0.801241i	−0.0474060	+	0.0273699i	−0.523516	−	0.852016i	$-0.675380\pi$
$857$	−1.38779	+	0.801241i	−0.0474060	+	0.0273699i	0.476110	+	0.879386i	$0.342047\pi$
$858$		0			0
$859$	9.09518	−	15.7533i	0.310324	−	0.537496i	−0.668109	−	0.744064i	$-0.732896\pi$
$859$	9.09518	−	15.7533i	0.310324	−	0.537496i	0.978432	+	0.206567i	$0.0662293\pi$
$860$		0			0
$861$	9.64285	+	13.4225i	0.328627	+	0.457439i
$862$		0			0
$863$	1.10842	+	0.639947i	0.0377311	+	0.0217840i	0.518747	−	0.854928i	$-0.326399\pi$
$863$	1.10842	+	0.639947i	0.0377311	+	0.0217840i	−0.481016	+	0.876712i	$0.659732\pi$
$864$		0			0
$865$	−11.2907	−	5.77184i	−0.383895	−	0.196248i
$866$		0			0
$867$			16.1122i			0.547200i
$868$		0			0
$869$	−27.6998			−0.939652
$870$		0			0
$871$	28.8486	+	49.9673i	0.977498	+	1.69308i
$872$		0			0
$873$	−16.1625	−	9.33144i	−0.547019	−	0.315821i
$874$		0			0
$875$	7.38885	+	28.6427i	0.249789	+	0.968300i
$876$		0			0
$877$	−33.1825	−	19.1579i	−1.12049	−	0.646918i	−0.178967	−	0.983855i	$-0.557276\pi$
$877$	−33.1825	−	19.1579i	−1.12049	−	0.646918i	−0.941527	+	0.336937i	$0.890609\pi$
$878$		0			0
$879$	−6.31048	−	10.9301i	−0.212847	−	0.368662i
$880$		0			0
$881$	18.3756			0.619090			0.309545	−	0.950885i	$-0.399823\pi$
$881$	18.3756			0.619090			0.309545	+	0.950885i	$0.399823\pi$
$882$		0			0
$883$			10.9195i			0.367470i	0.982976	+	0.183735i	$0.0588188\pi$
$883$			10.9195i			0.367470i	−0.982976	+	0.183735i	$0.941181\pi$
$884$		0			0
$885$	−8.69536	−	4.44509i	−0.292291	−	0.149420i
$886$		0			0
$887$	7.39462	+	4.26929i	0.248287	+	0.143349i	0.618980	−	0.785407i	$-0.287546\pi$
$887$	7.39462	+	4.26929i	0.248287	+	0.143349i	−0.370693	+	0.928756i	$0.620880\pi$
$888$		0			0
$889$	21.6997	−	2.16353i	0.727784	−	0.0725624i
$890$		0			0
$891$	−2.01478	+	3.48970i	−0.0674976	+	0.116909i
$892$		0			0
$893$	87.4615	−	50.4959i	2.92679	−	1.68978i
$894$		0			0
$895$	−0.614121	−	0.948423i	−0.0205278	−	0.0317023i
$896$		0			0
$897$			29.8208i			0.995686i
$898$		0			0
$899$	11.5662	+	20.0333i	0.385756	+	0.668149i
$900$		0			0
$901$	−2.38788	+	4.13593i	−0.0795518	+	0.137788i
$902$		0			0
$903$	10.8285	−	7.77928i	0.360350	−	0.258878i
$904$		0			0
$905$	−58.4466	+	2.98507i	−1.94283	+	0.0992270i
$906$		0			0
$907$	8.05971	−	4.65327i	0.267618	−	0.154509i	−0.360187	−	0.932880i	$-0.617287\pi$
$907$	8.05971	−	4.65327i	0.267618	−	0.154509i	0.627805	+	0.778371i	$0.283954\pi$
$908$		0			0
$909$	−12.4603			−0.413281
$910$		0			0
$911$	−49.8087			−1.65024			−0.825119	−	0.564959i	$-0.808892\pi$
$911$	−49.8087			−1.65024			−0.825119	+	0.564959i	$0.808892\pi$
$912$		0			0
$913$	57.0923	−	32.9622i	1.88948	−	1.09089i
$914$		0			0
$915$	0.173141	+	3.39004i	0.00572386	+	0.112071i
$916$		0			0
$917$	16.8353	+	7.60364i	0.555951	+	0.251094i
$918$		0			0
$919$	2.13941	−	3.70556i	0.0705725	−	0.122235i	−0.828580	−	0.559871i	$-0.810851\pi$
$919$	2.13941	−	3.70556i	0.0705725	−	0.122235i	0.899152	+	0.437636i	$0.144184\pi$
$920$		0			0
$921$	10.5984	+	18.3569i	0.349228	+	0.604880i
$922$		0			0
$923$		−	53.8943i		−	1.77395i
$924$		0			0
$925$	24.3158	+	10.9037i	0.799497	+	0.358512i
$926$		0			0
$927$	4.65554	−	2.68788i	0.152908	−	0.0882815i
$928$		0			0
$929$	−0.111327	+	0.192825i	−0.00365254	+	0.00632638i	−0.867846	−	0.496833i	$-0.834496\pi$
$929$	−0.111327	+	0.192825i	−0.00365254	+	0.00632638i	0.864193	+	0.503160i	$0.167829\pi$
$930$		0			0
$931$	19.2355	−	57.1159i	0.630418	−	1.87190i
$932$		0			0
$933$	5.20990	+	3.00794i	0.170565	+	0.0984755i
$934$		0			0
$935$	7.55925	+	3.86431i	0.247214	+	0.126376i
$936$		0			0
$937$			30.1325i			0.984387i	0.870486	+	0.492194i	$0.163805\pi$
$937$			30.1325i			0.984387i	−0.870486	+	0.492194i	$0.836195\pi$
$938$		0			0
$939$	−18.2729			−0.596313
$940$		0			0
$941$	16.2555	+	28.1553i	0.529914	+	0.917838i	0.999391	+	0.0348933i	$0.0111091\pi$
$941$	16.2555	+	28.1553i	0.529914	+	0.917838i	−0.469477	+	0.882945i	$0.655558\pi$
$942$		0			0
$943$	26.7364	+	15.4363i	0.870657	+	0.502674i
$944$		0			0
$945$	5.84929	−	0.886450i	0.190277	−	0.0288362i
$946$		0			0
$947$	−17.4042	−	10.0483i	−0.565560	−	0.326526i	0.189814	−	0.981820i	$-0.439211\pi$
$947$	−17.4042	−	10.0483i	−0.565560	−	0.326526i	−0.755374	+	0.655294i	$0.772545\pi$
$948$		0			0
$949$	−20.5889	−	35.6610i	−0.668343	−	1.15760i
$950$		0			0
$951$	12.8978			0.418239
$952$		0			0
$953$			12.8274i			0.415519i	0.978180	+	0.207760i	$0.0666172\pi$
$953$			12.8274i			0.415519i	−0.978180	+	0.207760i	$0.933383\pi$
$954$		0			0
$955$	17.6550	−	34.5362i	0.571302	−	1.11756i
$956$		0			0
$957$	−20.9057	−	12.0699i	−0.675784	−	0.390164i
$958$		0			0
$959$	17.9691	+	25.0125i	0.580254	+	0.807695i
$960$		0			0
$961$	8.04475	−	13.9339i	0.259508	−	0.449481i
$962$		0			0
$963$	6.24409	−	3.60503i	0.201213	−	0.116170i
$964$		0			0
$965$	−7.28488	+	4.71709i	−0.234509	+	0.151848i
$966$		0			0
$967$			0.279633i			0.00899239i	0.999990	+	0.00449619i	$0.00143119\pi$
$967$			0.279633i			0.00899239i	−0.999990	+	0.00449619i	$0.998569\pi$
$968$		0			0
$969$	−4.05610	−	7.02538i	−0.130301	−	0.225688i
$970$		0			0
$971$	20.2390	−	35.0550i	0.649501	−	1.12497i	−0.333741	−	0.942665i	$-0.608311\pi$
$971$	20.2390	−	35.0550i	0.649501	−	1.12497i	0.983242	−	0.182305i	$-0.0583557\pi$
$972$		0			0
$973$	4.62299	+	46.3676i	0.148206	+	1.48648i
$974$		0			0
$975$	17.6681	+	24.4547i	0.565832	+	0.783177i
$976$		0			0
$977$	−6.16126	+	3.55720i	−0.197116	+	0.113805i	−0.595310	−	0.803496i	$-0.702971\pi$
$977$	−6.16126	+	3.55720i	−0.197116	+	0.113805i	0.398193	+	0.917301i	$0.369637\pi$
$978$		0			0
$979$	19.3340			0.617917
$980$		0			0
$981$	5.28337			0.168685
$982$		0			0
$983$	−13.9886	+	8.07634i	−0.446168	+	0.257595i	−0.706210	−	0.708002i	$-0.749597\pi$
$983$	−13.9886	+	8.07634i	−0.446168	+	0.257595i	0.260042	+	0.965597i	$0.416263\pi$
$984$		0			0
$985$	0.981379	+	19.2151i	0.0312693	+	0.612243i
$986$		0			0
$987$	−3.07898	−	30.8815i	−0.0980051	−	0.982969i
$988$		0			0
$989$	12.4531	−	21.5693i	0.395985	−	0.685865i
$990$		0			0
$991$	7.75931	+	13.4395i	0.246483	+	0.426920i	0.962547	−	0.271113i	$-0.0873919\pi$
$991$	7.75931	+	13.4395i	0.246483	+	0.426920i	−0.716065	+	0.698034i	$0.754059\pi$
$992$		0			0
$993$		−	2.12658i		−	0.0674851i
$994$		0			0
$995$	9.61075	+	14.8425i	0.304681	+	0.470538i
$996$		0			0
$997$	−39.8042	+	22.9810i	−1.26061	+	0.727815i	−0.973193	−	0.229990i	$-0.926131\pi$
$997$	−39.8042	+	22.9810i	−1.26061	+	0.727815i	−0.287419	+	0.957805i	$0.592797\pi$
$998$		0			0
$999$	2.66486	−	4.61567i	0.0843124	−	0.146033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.di.g.289.12		24
4.3	odd	2		840.2.cc.c.289.6	✓	24
5.4	even	2	inner	1680.2.di.g.289.3		24
7.4	even	3	inner	1680.2.di.g.529.2		24
20.19	odd	2		840.2.cc.c.289.8	yes	24
28.11	odd	6		840.2.cc.c.529.8	yes	24
35.4	even	6	inner	1680.2.di.g.529.12		24
140.39	odd	6		840.2.cc.c.529.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cc.c.289.6	✓	24	4.3	odd	2
840.2.cc.c.289.8	yes	24	20.19	odd	2
840.2.cc.c.529.6	yes	24	140.39	odd	6
840.2.cc.c.529.8	yes	24	28.11	odd	6
1680.2.di.g.289.3		24	5.4	even	2	inner
1680.2.di.g.289.12		24	1.1	even	1	trivial
1680.2.di.g.529.2		24	7.4	even	3	inner
1680.2.di.g.529.12		24	35.4	even	6	inner

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.di (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(2.23316 - 0.114055i) q^{5} +(0.262488 + 2.63270i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.01478 - 3.48970i) q^{11} +6.03388i q^{13} +(1.87694 - 1.21535i) q^{15} +(-0.815983 + 0.471108i) q^{17} +(-4.30486 + 7.45623i) q^{19} +(1.54367 + 2.14874i) q^{21} +(4.28008 + 2.47111i) q^{23} +(4.97398 - 0.509406i) q^{25} -1.00000i q^{27} +5.99068 q^{29} +(1.93071 + 3.34408i) q^{31} +(-3.48970 - 2.01478i) q^{33} +(0.886450 + 5.84929i) q^{35} +(4.61567 + 2.66486i) q^{37} +(3.01694 + 5.22550i) q^{39} +6.24670 q^{41} -5.03947i q^{43} +(1.01780 - 1.99100i) q^{45} +(-10.1585 - 5.86499i) q^{47} +(-6.86220 + 1.38210i) q^{49} +(-0.471108 + 0.815983i) q^{51} +(4.38958 - 2.53432i) q^{53} +(-4.89734 - 7.56325i) q^{55} +8.60971i q^{57} +(-2.18367 - 3.78222i) q^{59} +(-0.759024 + 1.31467i) q^{61} +(2.41123 + 1.08903i) q^{63} +(0.688195 + 13.4746i) q^{65} +(8.28111 - 4.78110i) q^{67} +4.94222 q^{69} -8.93194 q^{71} +(-5.91012 + 3.41221i) q^{73} +(4.05289 - 2.92815i) q^{75} +(8.65847 - 6.22031i) q^{77} +(3.43708 - 5.95320i) q^{79} +(-0.500000 - 0.866025i) q^{81} +16.3602i q^{83} +(-1.76849 + 1.14513i) q^{85} +(5.18808 - 2.99534i) q^{87} +(-2.39902 + 4.15523i) q^{89} +(-15.8854 + 1.58382i) q^{91} +(3.34408 + 1.93071i) q^{93} +(-8.76300 + 17.1419i) q^{95} -18.6629i q^{97} -4.02956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5} + 12 q^{9} + 8 q^{11} - 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} - 4 q^{31} - 30 q^{35} - 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} + 20 q^{51} - 12 q^{55} + 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots + 16 q^{99}+O(q^{100}) \) 24 * q + 2 * q^5 + 12 * q^9 + 8 * q^11 - 8 * q^19 + 12 * q^21 + 2 * q^25 - 24 * q^29 - 4 * q^31 - 30 * q^35 - 4 * q^39 + 32 * q^41 - 2 * q^45 - 12 * q^49 + 20 * q^51 - 12 * q^55 + 4 * q^59 + 32 * q^61 + 22 * q^65 + 56 * q^69 - 72 * q^71 + 16 * q^75 - 20 * q^79 - 12 * q^81 + 8 * q^85 + 24 * q^89 - 8 * q^91 + 18 * q^95 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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