LMFDB - Embedded newform 1824.2.bb.a.31.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(31,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	1824.31
Dual form			1824.2.bb.a.1471.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.382920 - 0.663237i) q^{5} -3.54100i q^{7} +(-0.500000 + 0.866025i) q^{9} +4.98498i q^{11} +(-2.08447 - 1.20347i) q^{13} +(-0.382920 + 0.663237i) q^{15} +(-2.29338 - 3.97225i) q^{17} +(3.53104 - 2.55573i) q^{19} +(-3.06659 + 1.77050i) q^{21} +(5.25150 + 3.03196i) q^{23} +(2.20674 - 3.82219i) q^{25} +1.00000 q^{27} +(-8.74320 - 5.04789i) q^{29} -7.61199 q^{31} +(4.31712 - 2.49249i) q^{33} +(-2.34852 + 1.35592i) q^{35} -0.475666i q^{37} +2.40693i q^{39} +(-6.27830 + 3.62478i) q^{41} +(0.234413 - 0.135339i) q^{43} +0.765841 q^{45} +(-10.2613 - 5.92434i) q^{47} -5.53865 q^{49} +(-2.29338 + 3.97225i) q^{51} +(6.18663 + 3.57185i) q^{53} +(3.30622 - 1.90885i) q^{55} +(-3.97885 - 1.78010i) q^{57} +(5.27481 + 9.13624i) q^{59} +(-1.45406 + 2.51851i) q^{61} +(3.06659 + 1.77050i) q^{63} +1.84333i q^{65} +(-6.84499 + 11.8559i) q^{67} -6.06391i q^{69} +(1.51989 + 2.63253i) q^{71} +(-4.04820 - 7.01168i) q^{73} -4.41349 q^{75} +17.6518 q^{77} +(-4.67819 - 8.10286i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.4299i q^{83} +(-1.75636 + 3.04211i) q^{85} +10.0958i q^{87} +(-3.70055 - 2.13651i) q^{89} +(-4.26147 + 7.38109i) q^{91} +(3.80599 + 6.59217i) q^{93} +(-3.04716 - 1.36328i) q^{95} +(-13.1814 + 7.61030i) q^{97} +(-4.31712 - 2.49249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) $ 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−0.382920	−	0.663237i	−0.171247	−	0.296609i	0.767609	−	0.640918i	$-0.221446\pi$
$5$	−0.382920	−	0.663237i	−0.171247	−	0.296609i	−0.938856	+	0.344310i	$0.888113\pi$
$6$		0			0
$7$		−	3.54100i		−	1.33837i	−0.743096	−	0.669185i	$-0.766643\pi$
$7$		−	3.54100i		−	1.33837i	0.743096	−	0.669185i	$-0.233357\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			4.98498i			1.50303i	0.659718	+	0.751514i	$0.270676\pi$
$11$			4.98498i			1.50303i	−0.659718	+	0.751514i	$0.729324\pi$
$12$		0			0
$13$	−2.08447	−	1.20347i	−0.578127	−	0.333782i	0.182262	−	0.983250i	$-0.441658\pi$
$13$	−2.08447	−	1.20347i	−0.578127	−	0.333782i	−0.760389	+	0.649468i	$0.774992\pi$
$14$		0			0
$15$	−0.382920	+	0.663237i	−0.0988696	+	0.171247i
$16$		0			0
$17$	−2.29338	−	3.97225i	−0.556226	−	0.963412i	−0.997807	−	0.0661906i	$-0.978915\pi$
$17$	−2.29338	−	3.97225i	−0.556226	−	0.963412i	0.441581	−	0.897221i	$-0.354418\pi$
$18$		0			0
$19$	3.53104	−	2.55573i	0.810076	−	0.586325i
$19$	3.53104	−	2.55573i	0.810076	−	0.586325i
$20$		0			0
$21$	−3.06659	+	1.77050i	−0.669185	+	0.386354i
$22$		0			0
$23$	5.25150	+	3.03196i	1.09501	+	0.632207i	0.934907	−	0.354893i	$-0.115483\pi$
$23$	5.25150	+	3.03196i	1.09501	+	0.632207i	0.160107	+	0.987100i	$0.448816\pi$
$24$		0			0
$25$	2.20674	−	3.82219i	0.441349	−	0.764439i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−8.74320	−	5.04789i	−1.62357	−	0.937369i	−0.985954	−	0.167016i	$-0.946587\pi$
$29$	−8.74320	−	5.04789i	−1.62357	−	0.937369i	−0.637617	−	0.770353i	$-0.720080\pi$
$30$		0			0
$31$	−7.61199			−1.36715			−0.683577	−	0.729879i	$-0.739576\pi$
$31$	−7.61199			−1.36715			−0.683577	+	0.729879i	$0.739576\pi$
$32$		0			0
$33$	4.31712	−	2.49249i	0.751514	−	0.433887i
$34$		0			0
$35$	−2.34852	+	1.35592i	−0.396973	+	0.229192i
$36$		0			0
$37$		−	0.475666i		−	0.0781991i	−0.999235	−	0.0390995i	$-0.987551\pi$
$37$		−	0.475666i		−	0.0781991i	0.999235	−	0.0390995i	$-0.0124489\pi$
$38$		0			0
$39$			2.40693i			0.385418i
$40$		0			0
$41$	−6.27830	+	3.62478i	−0.980505	+	0.566095i	−0.902423	−	0.430852i	$-0.858213\pi$
$41$	−6.27830	+	3.62478i	−0.980505	+	0.566095i	−0.0780825	+	0.996947i	$0.524880\pi$
$42$		0			0
$43$	0.234413	−	0.135339i	0.0357477	−	0.0206389i	−0.482020	−	0.876160i	$-0.660097\pi$
$43$	0.234413	−	0.135339i	0.0357477	−	0.0206389i	0.517767	+	0.855521i	$0.326763\pi$
$44$		0			0
$45$	0.765841			0.114165
$46$		0			0
$47$	−10.2613	−	5.92434i	−1.49676	−	0.864153i	−0.496764	−	0.867885i	$-0.665479\pi$
$47$	−10.2613	−	5.92434i	−1.49676	−	0.864153i	−0.999993	+	0.00373220i	$0.998812\pi$
$48$		0			0
$49$	−5.53865			−0.791236
$50$		0			0
$51$	−2.29338	+	3.97225i	−0.321137	+	0.556226i
$52$		0			0
$53$	6.18663	+	3.57185i	0.849799	+	0.490632i	0.860583	−	0.509310i	$-0.170099\pi$
$53$	6.18663	+	3.57185i	0.849799	+	0.490632i	−0.0107838	+	0.999942i	$0.503433\pi$
$54$		0			0
$55$	3.30622	−	1.90885i	0.445811	−	0.257389i
$56$		0			0
$57$	−3.97885	−	1.78010i	−0.527011	−	0.235780i
$58$		0			0
$59$	5.27481	+	9.13624i	0.686722	+	1.18944i	0.972892	+	0.231259i	$0.0742843\pi$
$59$	5.27481	+	9.13624i	0.686722	+	1.18944i	−0.286170	+	0.958179i	$0.592382\pi$
$60$		0			0
$61$	−1.45406	+	2.51851i	−0.186174	+	0.322463i	−0.943971	−	0.330027i	$-0.892942\pi$
$61$	−1.45406	+	2.51851i	−0.186174	+	0.322463i	0.757798	+	0.652490i	$0.226275\pi$
$62$		0			0
$63$	3.06659	+	1.77050i	0.386354	+	0.223062i
$64$		0			0
$65$			1.84333i			0.228637i
$66$		0			0
$67$	−6.84499	+	11.8559i	−0.836249	+	1.44842i	0.0567613	+	0.998388i	$0.481923\pi$
$67$	−6.84499	+	11.8559i	−0.836249	+	1.44842i	−0.893010	+	0.450037i	$0.851411\pi$
$68$		0			0
$69$		−	6.06391i		−	0.730009i
$70$		0			0
$71$	1.51989	+	2.63253i	0.180378	+	0.312424i	0.942009	−	0.335587i	$-0.108935\pi$
$71$	1.51989	+	2.63253i	0.180378	+	0.312424i	−0.761631	+	0.648011i	$0.775601\pi$
$72$		0			0
$73$	−4.04820	−	7.01168i	−0.473806	−	0.820655i	0.525745	−	0.850642i	$-0.323787\pi$
$73$	−4.04820	−	7.01168i	−0.473806	−	0.820655i	−0.999550	+	0.0299871i	$0.990453\pi$
$74$		0			0
$75$	−4.41349			−0.509626
$76$		0			0
$77$	17.6518			2.01161
$78$		0			0
$79$	−4.67819	−	8.10286i	−0.526338	−	0.911643i	−0.999529	−	0.0306839i	$-0.990231\pi$
$79$	−4.67819	−	8.10286i	−0.526338	−	0.911643i	0.473192	−	0.880960i	$-0.343102\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			14.4299i			1.58388i	0.610596	+	0.791942i	$0.290930\pi$
$83$			14.4299i			1.58388i	−0.610596	+	0.791942i	$0.709070\pi$
$84$		0			0
$85$	−1.75636	+	3.04211i	−0.190504	+	0.329963i
$86$		0			0
$87$			10.0958i			1.08238i
$88$		0			0
$89$	−3.70055	−	2.13651i	−0.392257	−	0.226470i	0.290881	−	0.956759i	$-0.406052\pi$
$89$	−3.70055	−	2.13651i	−0.392257	−	0.226470i	−0.683138	+	0.730290i	$0.739385\pi$
$90$		0			0
$91$	−4.26147	+	7.38109i	−0.446724	+	0.773748i
$92$		0			0
$93$	3.80599	+	6.59217i	0.394663	+	0.683577i
$94$		0			0
$95$	−3.04716	−	1.36328i	−0.312632	−	0.139869i
$96$		0			0
$97$	−13.1814	+	7.61030i	−1.33837	+	0.772709i	−0.986566	−	0.163364i	$-0.947765\pi$
$97$	−13.1814	+	7.61030i	−1.33837	+	0.772709i	−0.351806	+	0.936073i	$0.614432\pi$
$98$		0			0
$99$	−4.31712	−	2.49249i	−0.433887	−	0.250505i
$100$		0			0
$101$	5.37611	−	9.31169i	0.534943	−	0.926548i	−0.464224	−	0.885718i	$-0.653667\pi$
$101$	5.37611	−	9.31169i	0.534943	−	0.926548i	0.999166	−	0.0408297i	$-0.0130001\pi$
$102$		0			0
$103$	17.2697			1.70163			0.850816	−	0.525465i	$-0.176108\pi$
$103$	17.2697			1.70163			0.850816	+	0.525465i	$0.176108\pi$
$104$		0			0
$105$	2.34852	+	1.35592i	0.229192	+	0.132324i
$106$		0			0
$107$	−8.85989			−0.856518			−0.428259	−	0.903656i	$-0.640873\pi$
$107$	−8.85989			−0.856518			−0.428259	+	0.903656i	$0.640873\pi$
$108$		0			0
$109$	−11.7211	+	6.76719i	−1.12268	+	0.648180i	−0.942084	−	0.335378i	$-0.891136\pi$
$109$	−11.7211	+	6.76719i	−1.12268	+	0.648180i	−0.180596	+	0.983557i	$0.557803\pi$
$110$		0			0
$111$	−0.411939	+	0.237833i	−0.0390995	+	0.0225741i
$112$		0			0
$113$		−	6.70795i		−	0.631031i	−0.948920	−	0.315515i	$-0.897823\pi$
$113$		−	6.70795i		−	0.631031i	0.948920	−	0.315515i	$-0.102177\pi$
$114$		0			0
$115$		−	4.64399i		−	0.433054i
$116$		0			0
$117$	2.08447	−	1.20347i	0.192709	−	0.111261i
$118$		0			0
$119$	−14.0657	+	8.12085i	−1.28940	+	0.744437i
$120$		0			0
$121$	−13.8500			−1.25909
$122$		0			0
$123$	6.27830	+	3.62478i	0.566095	+	0.326835i
$124$		0			0
$125$	−7.20923			−0.644813
$126$		0			0
$127$	3.39784	−	5.88524i	0.301510	−	0.522230i	−0.674968	−	0.737847i	$-0.735843\pi$
$127$	3.39784	−	5.88524i	0.301510	−	0.522230i	0.976478	+	0.215616i	$0.0691761\pi$
$128$		0			0
$129$	−0.234413	−	0.135339i	−0.0206389	−	0.0119159i
$130$		0			0
$131$	9.40891	−	5.43224i	0.822060	−	0.474617i	−0.0290662	−	0.999577i	$-0.509253\pi$
$131$	9.40891	−	5.43224i	0.822060	−	0.474617i	0.851126	+	0.524961i	$0.175920\pi$
$132$		0			0
$133$	−9.04984	−	12.5034i	−0.784720	−	1.08418i
$134$		0			0
$135$	−0.382920	−	0.663237i	−0.0329565	−	0.0570824i
$136$		0			0
$137$	−8.06122	+	13.9624i	−0.688717	+	1.19289i	0.283537	+	0.958961i	$0.408492\pi$
$137$	−8.06122	+	13.9624i	−0.688717	+	1.19289i	−0.972253	+	0.233931i	$0.924841\pi$
$138$		0			0
$139$	−13.1833	−	7.61138i	−1.11819	−	0.645589i	−0.177254	−	0.984165i	$-0.556721\pi$
$139$	−13.1833	−	7.61138i	−1.11819	−	0.645589i	−0.940939	+	0.338576i	$0.890055\pi$
$140$		0			0
$141$			11.8487i			0.997838i
$142$		0			0
$143$	5.99926	−	10.3910i	0.501683	−	0.868941i
$144$		0			0
$145$			7.73176i			0.642087i
$146$		0			0
$147$	2.76933	+	4.79661i	0.228410	+	0.395618i
$148$		0			0
$149$	1.73688	+	3.00836i	0.142291	+	0.246455i	0.928359	−	0.371685i	$-0.121220\pi$
$149$	1.73688	+	3.00836i	0.142291	+	0.246455i	−0.786068	+	0.618140i	$0.787887\pi$
$150$		0			0
$151$	−12.5900			−1.02456			−0.512278	−	0.858820i	$-0.671198\pi$
$151$	−12.5900			−1.02456			−0.512278	+	0.858820i	$0.671198\pi$
$152$		0			0
$153$	4.58676			0.370817
$154$		0			0
$155$	2.91478	+	5.04855i	0.234121	+	0.405510i
$156$		0			0
$157$	−7.94583	−	13.7626i	−0.634146	−	1.09837i	−0.986695	−	0.162580i	$-0.948018\pi$
$157$	−7.94583	−	13.7626i	−0.634146	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$158$		0			0
$159$		−	7.14371i		−	0.566533i
$160$		0			0
$161$	10.7361	−	18.5956i	0.846127	−	1.46553i
$162$		0			0
$163$			17.7591i			1.39100i	0.718527	+	0.695499i	$0.244817\pi$
$163$			17.7591i			1.39100i	−0.718527	+	0.695499i	$0.755183\pi$
$164$		0			0
$165$	−3.30622	−	1.90885i	−0.257389	−	0.148604i
$166$		0			0
$167$	8.67278	−	15.0217i	0.671120	−	1.16241i	−0.306467	−	0.951881i	$-0.599147\pi$
$167$	8.67278	−	15.0217i	0.671120	−	1.16241i	0.977587	−	0.210533i	$-0.0675199\pi$
$168$		0			0
$169$	−3.60333	−	6.24115i	−0.277179	−	0.480089i
$170$		0			0
$171$	0.447809	+	4.33584i	0.0342448	+	0.331570i
$172$		0			0
$173$	−1.01105	+	0.583733i	−0.0768691	+	0.0443804i	−0.537942	−	0.842982i	$-0.680798\pi$
$173$	−1.01105	+	0.583733i	−0.0768691	+	0.0443804i	0.461073	+	0.887362i	$0.347465\pi$
$174$		0			0
$175$	−13.5344	−	7.81407i	−1.02310	−	0.590688i
$176$		0			0
$177$	5.27481	−	9.13624i	0.396479	−	0.686722i
$178$		0			0
$179$	1.89972			0.141992			0.0709960	−	0.997477i	$-0.477382\pi$
$179$	1.89972			0.141992			0.0709960	+	0.997477i	$0.477382\pi$
$180$		0			0
$181$	−12.9164	−	7.45728i	−0.960068	−	0.554295i	−0.0638737	−	0.997958i	$-0.520345\pi$
$181$	−12.9164	−	7.45728i	−0.960068	−	0.554295i	−0.896194	+	0.443663i	$0.853679\pi$
$182$		0			0
$183$	2.90813			0.214975
$184$		0			0
$185$	−0.315480	+	0.182142i	−0.0231945	+	0.0133914i
$186$		0			0
$187$	19.8016	−	11.4324i	1.44803	−	0.836023i
$188$		0			0
$189$		−	3.54100i		−	0.257570i
$190$		0			0
$191$		−	14.7805i		−	1.06948i	−0.845017	−	0.534739i	$-0.820410\pi$
$191$		−	14.7805i		−	1.06948i	0.845017	−	0.534739i	$-0.179590\pi$
$192$		0			0
$193$	22.1644	−	12.7966i	1.59543	−	0.921122i	0.603078	−	0.797682i	$-0.293941\pi$
$193$	22.1644	−	12.7966i	1.59543	−	0.921122i	0.992352	−	0.123440i	$-0.0393927\pi$
$194$		0			0
$195$	1.59637	−	0.921664i	0.114318	−	0.0660017i
$196$		0			0
$197$	9.86493			0.702847			0.351424	−	0.936217i	$-0.385698\pi$
$197$	9.86493			0.702847			0.351424	+	0.936217i	$0.385698\pi$
$198$		0			0
$199$	1.43983	+	0.831285i	0.102067	+	0.0589282i	0.550164	−	0.835056i	$-0.314565\pi$
$199$	1.43983	+	0.831285i	0.102067	+	0.0589282i	−0.448098	+	0.893985i	$0.647898\pi$
$200$		0			0
$201$	13.6900			0.965617
$202$		0			0
$203$	−17.8746	+	30.9596i	−1.25455	+	2.17294i
$204$		0			0
$205$	4.80817	+	2.77600i	0.335817	+	0.193884i
$206$		0			0
$207$	−5.25150	+	3.03196i	−0.365005	+	0.210736i
$208$		0			0
$209$	12.7403	+	17.6021i	0.881263	+	1.21757i
$210$		0			0
$211$	−9.54849	−	16.5385i	−0.657345	−	1.13855i	−0.981300	−	0.192483i	$-0.938346\pi$
$211$	−9.54849	−	16.5385i	−0.657345	−	1.13855i	0.323955	−	0.946072i	$-0.394987\pi$
$212$		0			0
$213$	1.51989	−	2.63253i	0.104141	−	0.180378i
$214$		0			0
$215$	−0.179523	−	0.103648i	−0.0122434	−	0.00706872i
$216$		0			0
$217$			26.9540i			1.82976i
$218$		0			0
$219$	−4.04820	+	7.01168i	−0.273552	+	0.473806i
$220$		0			0
$221$			11.0400i			0.742633i
$222$		0			0
$223$	9.09785	+	15.7579i	0.609237	+	1.05523i	0.991366	+	0.131121i	$0.0418577\pi$
$223$	9.09785	+	15.7579i	0.609237	+	1.05523i	−0.382129	+	0.924109i	$0.624809\pi$
$224$		0			0
$225$	2.20674	+	3.82219i	0.147116	+	0.254813i
$226$		0			0
$227$	5.83589			0.387342			0.193671	−	0.981067i	$-0.437961\pi$
$227$	5.83589			0.387342			0.193671	+	0.981067i	$0.437961\pi$
$228$		0			0
$229$	−5.15561			−0.340692			−0.170346	−	0.985384i	$-0.554489\pi$
$229$	−5.15561			−0.340692			−0.170346	+	0.985384i	$0.554489\pi$
$230$		0			0
$231$	−8.82589	−	15.2869i	−0.580701	−	1.00580i
$232$		0			0
$233$	4.65031	+	8.05457i	0.304652	+	0.527673i	0.977184	−	0.212396i	$-0.0681265\pi$
$233$	4.65031	+	8.05457i	0.304652	+	0.527673i	−0.672532	+	0.740068i	$0.734793\pi$
$234$		0			0
$235$			9.07420i			0.591935i
$236$		0			0
$237$	−4.67819	+	8.10286i	−0.303881	+	0.526338i
$238$		0			0
$239$			19.3585i			1.25219i	0.779745	+	0.626097i	$0.215349\pi$
$239$			19.3585i			1.25219i	−0.779745	+	0.626097i	$0.784651\pi$
$240$		0			0
$241$	−0.322595	−	0.186250i	−0.0207802	−	0.0119974i	0.489574	−	0.871962i	$-0.337152\pi$
$241$	−0.322595	−	0.186250i	−0.0207802	−	0.0119974i	−0.510354	+	0.859964i	$0.670486\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	2.12086	+	3.67344i	0.135497	+	0.234688i
$246$		0			0
$247$	−10.4361	+	1.07785i	−0.664031	+	0.0685818i
$248$		0			0
$249$	12.4966	−	7.21494i	0.791942	−	0.457228i
$250$		0			0
$251$	−14.7418	−	8.51119i	−0.930495	−	0.537221i	−0.0435267	−	0.999052i	$-0.513859\pi$
$251$	−14.7418	−	8.51119i	−0.930495	−	0.537221i	−0.886968	+	0.461831i	$0.847193\pi$
$252$		0			0
$253$	−15.1142	+	26.1786i	−0.950224	+	1.64584i
$254$		0			0
$255$	3.51273			0.219975
$256$		0			0
$257$	−22.3631	−	12.9113i	−1.39497	−	0.805387i	−0.401111	−	0.916029i	$-0.631376\pi$
$257$	−22.3631	−	12.9113i	−1.39497	−	0.805387i	−0.993860	+	0.110642i	$0.964709\pi$
$258$		0			0
$259$	−1.68433			−0.104659
$260$		0			0
$261$	8.74320	−	5.04789i	0.541190	−	0.312456i
$262$		0			0
$263$	−5.19782	+	3.00096i	−0.320511	+	0.185047i	−0.651621	−	0.758545i	$-0.725911\pi$
$263$	−5.19782	+	3.00096i	−0.320511	+	0.185047i	0.331109	+	0.943592i	$0.392577\pi$
$264$		0			0
$265$		−	5.47094i		−	0.336077i
$266$		0			0
$267$			4.27302i			0.261505i
$268$		0			0
$269$	18.3179	−	10.5758i	1.11686	−	0.644821i	0.176264	−	0.984343i	$-0.443599\pi$
$269$	18.3179	−	10.5758i	1.11686	−	0.644821i	0.940598	+	0.339522i	$0.110265\pi$
$270$		0			0
$271$	18.6166	−	10.7483i	1.13088	−	0.652912i	0.186721	−	0.982413i	$-0.440214\pi$
$271$	18.6166	−	10.7483i	1.13088	−	0.652912i	0.944155	+	0.329501i	$0.106881\pi$
$272$		0			0
$273$	8.52295			0.515832
$274$		0			0
$275$	19.0535	+	11.0006i	1.14897	+	0.663359i
$276$		0			0
$277$	14.2720			0.857523			0.428761	−	0.903418i	$-0.358950\pi$
$277$	14.2720			0.857523			0.428761	+	0.903418i	$0.358950\pi$
$278$		0			0
$279$	3.80599	−	6.59217i	0.227859	−	0.394663i
$280$		0			0
$281$	11.0259	+	6.36583i	0.657752	+	0.379753i	0.791420	−	0.611273i	$-0.209342\pi$
$281$	11.0259	+	6.36583i	0.657752	+	0.379753i	−0.133668	+	0.991026i	$0.542676\pi$
$282$		0			0
$283$	22.1454	−	12.7857i	1.31641	−	0.760029i	0.333260	−	0.942835i	$-0.391851\pi$
$283$	22.1454	−	12.7857i	1.31641	−	0.760029i	0.983149	+	0.182806i	$0.0585180\pi$
$284$		0			0
$285$	0.342951	+	3.32056i	0.0203146	+	0.196693i
$286$		0			0
$287$	12.8353	+	22.2314i	0.757645	+	1.31228i
$288$		0			0
$289$	−2.01918	+	3.49732i	−0.118775	+	0.205725i
$290$		0			0
$291$	13.1814	+	7.61030i	0.772709	+	0.446124i
$292$		0			0
$293$		−	4.30275i		−	0.251369i	−0.992070	−	0.125685i	$-0.959887\pi$
$293$		−	4.30275i		−	0.251369i	0.992070	−	0.125685i	$-0.0401128\pi$
$294$		0			0
$295$	4.03967	−	6.99691i	0.235198	−	0.407376i
$296$		0			0
$297$			4.98498i			0.289258i
$298$		0			0
$299$	−7.29772	−	12.6400i	−0.422038	−	0.730992i
$300$		0			0
$301$	−0.479233	−	0.830057i	−0.0276226	−	0.0478437i
$302$		0			0
$303$	−10.7522			−0.617699
$304$		0			0
$305$	2.22716			0.127527
$306$		0			0
$307$	−10.4130	−	18.0358i	−0.594301	−	1.02936i	−0.993645	−	0.112559i	$-0.964095\pi$
$307$	−10.4130	−	18.0358i	−0.594301	−	1.02936i	0.399344	−	0.916801i	$-0.369238\pi$
$308$		0			0
$309$	−8.63483	−	14.9560i	−0.491219	−	0.850816i
$310$		0			0
$311$		−	16.7501i		−	0.949810i	−0.880037	−	0.474905i	$-0.842482\pi$
$311$		−	16.7501i		−	0.949810i	0.880037	−	0.474905i	$-0.157518\pi$
$312$		0			0
$313$	9.15253	−	15.8527i	0.517332	−	0.896045i	−0.482466	−	0.875915i	$-0.660259\pi$
$313$	9.15253	−	15.8527i	0.517332	−	0.896045i	0.999797	−	0.0201299i	$-0.00640799\pi$
$314$		0			0
$315$		−	2.71184i		−	0.152795i
$316$		0			0
$317$	−0.570292	−	0.329258i	−0.0320308	−	0.0184930i	0.483899	−	0.875124i	$-0.339220\pi$
$317$	−0.570292	−	0.329258i	−0.0320308	−	0.0184930i	−0.515930	+	0.856631i	$0.672553\pi$
$318$		0			0
$319$	25.1636	−	43.5847i	1.40889	−	2.44027i
$320$		0			0
$321$	4.42995	+	7.67289i	0.247255	+	0.428259i
$322$		0			0
$323$	−18.2500	−	8.16490i	−1.01546	−	0.454307i
$324$		0			0
$325$	−9.19977	+	5.31149i	−0.510311	+	0.294628i
$326$		0			0
$327$	11.7211	+	6.76719i	0.648180	+	0.374227i
$328$		0			0
$329$	−20.9781	+	36.3351i	−1.15656	+	2.00322i
$330$		0			0
$331$	8.95321			0.492113			0.246057	−	0.969255i	$-0.420865\pi$
$331$	8.95321			0.492113			0.246057	+	0.969255i	$0.420865\pi$
$332$		0			0
$333$	0.411939	+	0.237833i	0.0225741	+	0.0130332i
$334$		0			0
$335$	10.4843			0.572821
$336$		0			0
$337$	8.02081	−	4.63082i	0.436921	−	0.252257i	−0.265369	−	0.964147i	$-0.585494\pi$
$337$	8.02081	−	4.63082i	0.436921	−	0.252257i	0.702291	+	0.711890i	$0.252161\pi$
$338$		0			0
$339$	−5.80925	+	3.35397i	−0.315515	+	0.182163i
$340$		0			0
$341$		−	37.9456i		−	2.05487i
$342$		0			0
$343$		−	5.17462i		−	0.279403i
$344$		0			0
$345$	−4.02181	+	2.32200i	−0.216527	+	0.125012i
$346$		0			0
$347$	17.0068	−	9.81887i	0.912972	−	0.527104i	0.0315856	−	0.999501i	$-0.489944\pi$
$347$	17.0068	−	9.81887i	0.912972	−	0.527104i	0.881386	+	0.472397i	$0.156611\pi$
$348$		0			0
$349$	−5.77191			−0.308963			−0.154482	−	0.987996i	$-0.549371\pi$
$349$	−5.77191			−0.308963			−0.154482	+	0.987996i	$0.549371\pi$
$350$		0			0
$351$	−2.08447	−	1.20347i	−0.111261	−	0.0642363i
$352$		0			0
$353$	−10.3931			−0.553169			−0.276584	−	0.960990i	$-0.589203\pi$
$353$	−10.3931			−0.553169			−0.276584	+	0.960990i	$0.589203\pi$
$354$		0			0
$355$	1.16399	−	2.01610i	0.0617784	−	0.107003i
$356$		0			0
$357$	14.0657	+	8.12085i	0.744437	+	0.429801i
$358$		0			0
$359$	−4.26980	+	2.46517i	−0.225352	+	0.130107i	−0.608426	−	0.793611i	$-0.708199\pi$
$359$	−4.26980	+	2.46517i	−0.225352	+	0.130107i	0.383074	+	0.923718i	$0.374865\pi$
$360$		0			0
$361$	5.93647	−	18.0488i	0.312446	−	0.949936i
$362$		0			0
$363$	6.92500	+	11.9945i	0.363468	+	0.629545i
$364$		0			0
$365$	−3.10027	+	5.36983i	−0.162276	+	0.281070i
$366$		0			0
$367$	−26.1587	−	15.1027i	−1.36547	−	0.788355i	−0.375126	−	0.926974i	$-0.622400\pi$
$367$	−26.1587	−	15.1027i	−1.36547	−	0.788355i	−0.990346	+	0.138619i	$0.955734\pi$
$368$		0			0
$369$		−	7.24955i		−	0.377397i
$370$		0			0
$371$	12.6479	−	21.9068i	0.656647	−	1.13735i
$372$		0			0
$373$			11.5519i			0.598137i	0.954232	+	0.299069i	$0.0966759\pi$
$373$			11.5519i			0.598137i	−0.954232	+	0.299069i	$0.903324\pi$
$374$		0			0
$375$	3.60462	+	6.24338i	0.186142	+	0.322407i
$376$		0			0
$377$	12.1499	+	21.0443i	0.625754	+	1.08384i
$378$		0			0
$379$	4.03187			0.207103			0.103552	−	0.994624i	$-0.466979\pi$
$379$	4.03187			0.207103			0.103552	+	0.994624i	$0.466979\pi$
$380$		0			0
$381$	−6.79569			−0.348154
$382$		0			0
$383$	5.88659	+	10.1959i	0.300791	+	0.520985i	0.976315	−	0.216353i	$-0.0694160\pi$
$383$	5.88659	+	10.1959i	0.300791	+	0.520985i	−0.675524	+	0.737338i	$0.736083\pi$
$384$		0			0
$385$	−6.75923	−	11.7073i	−0.344482	−	0.596661i
$386$		0			0
$387$			0.270677i			0.0137593i
$388$		0			0
$389$	−1.96964	+	3.41152i	−0.0998648	+	0.172971i	−0.911629	−	0.411015i	$-0.865174\pi$
$389$	−1.96964	+	3.41152i	−0.0998648	+	0.172971i	0.811764	+	0.583986i	$0.198508\pi$
$390$		0			0
$391$		−	27.8137i		−	1.40660i
$392$		0			0
$393$	−9.40891	−	5.43224i	−0.474617	−	0.274020i
$394$		0			0
$395$	−3.58275	+	6.20550i	−0.180268	+	0.312233i
$396$		0			0
$397$	−5.62893	−	9.74958i	−0.282508	−	0.489318i	0.689494	−	0.724291i	$-0.257833\pi$
$397$	−5.62893	−	9.74958i	−0.282508	−	0.489318i	−0.972002	+	0.234974i	$0.924500\pi$
$398$		0			0
$399$	−6.30334	+	14.0891i	−0.315562	+	0.705337i
$400$		0			0
$401$	4.76362	−	2.75028i	0.237884	−	0.137342i	−0.376320	−	0.926490i	$-0.622811\pi$
$401$	4.76362	−	2.75028i	0.237884	−	0.137342i	0.614204	+	0.789147i	$0.289477\pi$
$402$		0			0
$403$	15.8669	+	9.16078i	0.790388	+	0.456331i
$404$		0			0
$405$	−0.382920	+	0.663237i	−0.0190275	+	0.0329565i
$406$		0			0
$407$	2.37119			0.117535
$408$		0			0
$409$	−2.43327	−	1.40485i	−0.120317	−	0.0694652i	0.438634	−	0.898666i	$-0.355463\pi$
$409$	−2.43327	−	1.40485i	−0.120317	−	0.0694652i	−0.558951	+	0.829201i	$0.688796\pi$
$410$		0			0
$411$	16.1224			0.795262
$412$		0			0
$413$	32.3514	−	18.6781i	1.59191	−	0.919089i
$414$		0			0
$415$	9.57043	−	5.52549i	0.469794	−	0.271236i
$416$		0			0
$417$			15.2228i			0.745462i
$418$		0			0
$419$		−	12.0614i		−	0.589236i	−0.955615	−	0.294618i	$-0.904808\pi$
$419$		−	12.0614i		−	0.589236i	0.955615	−	0.294618i	$-0.0951924\pi$
$420$		0			0
$421$	−27.6787	+	15.9803i	−1.34898	+	0.778832i	−0.988105	−	0.153783i	$-0.950854\pi$
$421$	−27.6787	+	15.9803i	−1.34898	+	0.778832i	−0.360872	+	0.932615i	$0.617521\pi$
$422$		0			0
$423$	10.2613	−	5.92434i	0.498919	−	0.288051i
$424$		0			0
$425$	−20.2436			−0.981959
$426$		0			0
$427$	8.91804	+	5.14884i	0.431574	+	0.249170i
$428$		0			0
$429$	−11.9985			−0.579294
$430$		0			0
$431$	7.77716	−	13.4704i	0.374612	−	0.648848i	−0.615656	−	0.788015i	$-0.711109\pi$
$431$	7.77716	−	13.4704i	0.374612	−	0.648848i	0.990269	+	0.139167i	$0.0444424\pi$
$432$		0			0
$433$	13.6152	+	7.86077i	0.654307	+	0.377764i	0.790104	−	0.612972i	$-0.210026\pi$
$433$	13.6152	+	7.86077i	0.654307	+	0.377764i	−0.135797	+	0.990737i	$0.543360\pi$
$434$		0			0
$435$	6.69590	−	3.86588i	0.321044	−	0.185355i
$436$		0			0
$437$	26.2921	−	2.71548i	1.25772	−	0.129899i
$438$		0			0
$439$	−11.5520	−	20.0086i	−0.551346	−	0.954959i	−0.998178	−	0.0603409i	$-0.980781\pi$
$439$	−11.5520	−	20.0086i	−0.551346	−	0.954959i	0.446832	−	0.894618i	$-0.352552\pi$
$440$		0			0
$441$	2.76933	−	4.79661i	0.131873	−	0.228410i
$442$		0			0
$443$	1.52977	+	0.883216i	0.0726818	+	0.0419628i	0.535900	−	0.844281i	$-0.319972\pi$
$443$	1.52977	+	0.883216i	0.0726818	+	0.0419628i	−0.463219	+	0.886244i	$0.653306\pi$
$444$		0			0
$445$			3.27245i			0.155129i
$446$		0			0
$447$	1.73688	−	3.00836i	0.0821516	−	0.142291i
$448$		0			0
$449$		−	9.28909i		−	0.438379i	−0.975682	−	0.219190i	$-0.929659\pi$
$449$		−	9.28909i		−	0.438379i	0.975682	−	0.219190i	$-0.0703413\pi$
$450$		0			0
$451$	−18.0694	−	31.2972i	−0.850856	−	1.47373i
$452$		0			0
$453$	6.29498	+	10.9032i	0.295764	+	0.512278i
$454$		0			0
$455$	6.52722			0.306001
$456$		0			0
$457$	18.6288			0.871417			0.435709	−	0.900088i	$-0.356498\pi$
$457$	18.6288			0.871417			0.435709	+	0.900088i	$0.356498\pi$
$458$		0			0
$459$	−2.29338	−	3.97225i	−0.107046	−	0.185409i
$460$		0			0
$461$	15.4501	+	26.7604i	0.719585	+	1.24636i	0.961164	+	0.275976i	$0.0890012\pi$
$461$	15.4501	+	26.7604i	0.719585	+	1.24636i	−0.241580	+	0.970381i	$0.577665\pi$
$462$		0			0
$463$			9.51105i			0.442016i	0.975272	+	0.221008i	$0.0709347\pi$
$463$			9.51105i			0.442016i	−0.975272	+	0.221008i	$0.929065\pi$
$464$		0			0
$465$	2.91478	−	5.04855i	0.135170	−	0.234121i
$466$		0			0
$467$			21.0377i			0.973511i	0.873538	+	0.486755i	$0.161820\pi$
$467$			21.0377i			0.973511i	−0.873538	+	0.486755i	$0.838180\pi$
$468$		0			0
$469$	41.9816	+	24.2381i	1.93853	+	1.11921i
$470$		0			0
$471$	−7.94583	+	13.7626i	−0.366125	+	0.634146i
$472$		0			0
$473$	0.674660	+	1.16855i	0.0310209	+	0.0537298i
$474$		0			0
$475$	−1.97640	−	19.1362i	−0.0906835	−	0.878027i
$476$		0			0
$477$	−6.18663	+	3.57185i	−0.283266	+	0.163544i
$478$		0			0
$479$	−4.85569	−	2.80343i	−0.221862	−	0.128092i	0.384950	−	0.922937i	$-0.374219\pi$
$479$	−4.85569	−	2.80343i	−0.221862	−	0.128092i	−0.606812	+	0.794845i	$0.707552\pi$
$480$		0			0
$481$	−0.572449	+	0.991511i	−0.0261014	+	0.0452090i
$482$		0			0
$483$	−21.4723			−0.977023
$484$		0			0
$485$	10.0949	+	5.82828i	0.458385	+	0.264648i
$486$		0			0
$487$	−4.92392			−0.223124			−0.111562	−	0.993757i	$-0.535585\pi$
$487$	−4.92392			−0.223124			−0.111562	+	0.993757i	$0.535585\pi$
$488$		0			0
$489$	15.3798	−	8.87954i	0.695499	−	0.401547i
$490$		0			0
$491$	19.6305	−	11.3336i	0.885910	−	0.511480i	0.0133075	−	0.999911i	$-0.495764\pi$
$491$	19.6305	−	11.3336i	0.885910	−	0.511480i	0.872602	+	0.488431i	$0.162431\pi$
$492$		0			0
$493$			46.3069i			2.08556i
$494$		0			0
$495$			3.81770i			0.171593i
$496$		0			0
$497$	9.32177	−	5.38193i	0.418139	−	0.241412i
$498$		0			0
$499$	−4.67366	+	2.69834i	−0.209222	+	0.120794i	−0.600950	−	0.799287i	$-0.705211\pi$
$499$	−4.67366	+	2.69834i	−0.209222	+	0.120794i	0.391728	+	0.920081i	$0.371877\pi$
$500$		0			0
$501$	−17.3456			−0.774943
$502$		0			0
$503$	5.80937	+	3.35404i	0.259027	+	0.149549i	0.623891	−	0.781512i	$-0.285551\pi$
$503$	5.80937	+	3.35404i	0.259027	+	0.149549i	−0.364864	+	0.931061i	$0.618884\pi$
$504$		0			0
$505$	−8.23448			−0.366430
$506$		0			0
$507$	−3.60333	+	6.24115i	−0.160030	+	0.277179i
$508$		0			0
$509$	−15.6116	−	9.01337i	−0.691973	−	0.399511i	0.112378	−	0.993666i	$-0.464153\pi$
$509$	−15.6116	−	9.01337i	−0.691973	−	0.399511i	−0.804351	+	0.594155i	$0.797487\pi$
$510$		0			0
$511$	−24.8283	+	14.3346i	−1.09834	+	0.634127i
$512$		0			0
$513$	3.53104	−	2.55573i	0.155899	−	0.112838i
$514$		0			0
$515$	−6.61291	−	11.4539i	−0.291400	−	0.504719i
$516$		0			0
$517$	29.5327	−	51.1521i	1.29885	−	2.24967i
$518$		0			0
$519$	1.01105	+	0.583733i	0.0443804	+	0.0256230i
$520$		0			0
$521$		−	2.18624i		−	0.0957808i	−0.998853	−	0.0478904i	$-0.984750\pi$
$521$		−	2.18624i		−	0.0957808i	0.998853	−	0.0478904i	$-0.0152498\pi$
$522$		0			0
$523$	−1.75609	+	3.04164i	−0.0767884	+	0.133001i	−0.901863	−	0.432023i	$-0.857800\pi$
$523$	−1.75609	+	3.04164i	−0.0767884	+	0.133001i	0.825074	+	0.565024i	$0.191133\pi$
$524$		0			0
$525$			15.6281i			0.682068i
$526$		0			0
$527$	17.4572	+	30.2367i	0.760446	+	1.31713i
$528$		0			0
$529$	6.88552	+	11.9261i	0.299371	+	0.518525i
$530$		0			0
$531$	−10.5496			−0.457815
$532$		0			0
$533$	17.4492			0.755809
$534$		0			0
$535$	3.39263	+	5.87621i	0.146676	+	0.254051i
$536$		0			0
$537$	−0.949862	−	1.64521i	−0.0409896	−	0.0709960i
$538$		0			0
$539$		−	27.6101i		−	1.18925i
$540$		0			0
$541$	7.40522	−	12.8262i	0.318375	−	0.551442i	−0.661774	−	0.749704i	$-0.730196\pi$
$541$	7.40522	−	12.8262i	0.318375	−	0.551442i	0.980149	+	0.198261i	$0.0635294\pi$
$542$		0			0
$543$			14.9146i			0.640045i
$544$		0			0
$545$	8.97651	+	5.18259i	0.384512	+	0.221998i
$546$		0			0
$547$	−9.33681	+	16.1718i	−0.399213	+	0.691458i	−0.993629	−	0.112700i	$-0.964050\pi$
$547$	−9.33681	+	16.1718i	−0.399213	+	0.691458i	0.594416	+	0.804158i	$0.297383\pi$
$548$		0			0
$549$	−1.45406	−	2.51851i	−0.0620579	−	0.107488i
$550$		0			0
$551$	−43.7736	+	4.52098i	−1.86482	+	0.192600i
$552$		0			0
$553$	−28.6922	+	16.5655i	−1.22012	+	0.704435i
$554$		0			0
$555$	0.315480	+	0.182142i	0.0133914	+	0.00773151i
$556$		0			0
$557$	9.53546	−	16.5159i	0.404031	−	0.699801i	−0.590178	−	0.807273i	$-0.700942\pi$
$557$	9.53546	−	16.5159i	0.404031	−	0.699801i	0.994208	+	0.107472i	$0.0342756\pi$
$558$		0			0
$559$	−0.651502			−0.0275556
$560$		0			0
$561$	−19.8016	−	11.4324i	−0.836023	−	0.482678i
$562$		0			0
$563$	−22.4464			−0.946004			−0.473002	−	0.881061i	$-0.656830\pi$
$563$	−22.4464			−0.946004			−0.473002	+	0.881061i	$0.656830\pi$
$564$		0			0
$565$	−4.44896	+	2.56861i	−0.187169	+	0.108062i
$566$		0			0
$567$	−3.06659	+	1.77050i	−0.128785	+	0.0743539i
$568$		0			0
$569$			28.8173i			1.20808i	0.796953	+	0.604041i	$0.206444\pi$
$569$			28.8173i			1.20808i	−0.796953	+	0.604041i	$0.793556\pi$
$570$		0			0
$571$			38.0508i			1.59238i	0.605048	+	0.796189i	$0.293154\pi$
$571$			38.0508i			1.59238i	−0.605048	+	0.796189i	$0.706846\pi$
$572$		0			0
$573$	−12.8003	+	7.39024i	−0.534739	+	0.308732i
$574$		0			0
$575$	23.1774	−	13.3815i	0.966566	−	0.558047i
$576$		0			0
$577$	30.8624			1.28482			0.642410	−	0.766361i	$-0.277935\pi$
$577$	30.8624			1.28482			0.642410	+	0.766361i	$0.277935\pi$
$578$		0			0
$579$	−22.1644	−	12.7966i	−0.921122	−	0.531810i
$580$		0			0
$581$	51.0961			2.11982
$582$		0			0
$583$	−17.8056	+	30.8402i	−0.737433	+	1.27727i
$584$		0			0
$585$	−1.59637	−	0.921664i	−0.0660017	−	0.0381061i
$586$		0			0
$587$	8.10606	−	4.68004i	0.334573	−	0.193166i	−0.323297	−	0.946298i	$-0.604791\pi$
$587$	8.10606	−	4.68004i	0.334573	−	0.193166i	0.657870	+	0.753132i	$0.271458\pi$
$588$		0			0
$589$	−26.8782	+	19.4542i	−1.10750	+	0.801596i
$590$		0			0
$591$	−4.93247	−	8.54328i	−0.202895	−	0.351424i
$592$		0			0
$593$	3.60213	−	6.23907i	0.147922	−	0.256208i	−0.782537	−	0.622604i	$-0.786075\pi$
$593$	3.60213	−	6.23907i	0.147922	−	0.256208i	0.930459	+	0.366396i	$0.119408\pi$
$594$		0			0
$595$	10.7721	+	6.21928i	0.441613	+	0.254965i
$596$		0			0
$597$		−	1.66257i		−	0.0680445i
$598$		0			0
$599$	0.462423	−	0.800940i	0.0188941	−	0.0327255i	−0.856424	−	0.516274i	$-0.827319\pi$
$599$	0.462423	−	0.800940i	0.0188941	−	0.0327255i	0.875318	+	0.483548i	$0.160652\pi$
$600$		0			0
$601$			32.3262i			1.31861i	0.751874	+	0.659307i	$0.229150\pi$
$601$			32.3262i			1.31861i	−0.751874	+	0.659307i	$0.770850\pi$
$602$		0			0
$603$	−6.84499	−	11.8559i	−0.278750	−	0.482808i
$604$		0			0
$605$	5.30345	+	9.18584i	0.215616	+	0.373457i
$606$		0			0
$607$	16.2659			0.660213			0.330106	−	0.943944i	$-0.392915\pi$
$607$	16.2659			0.660213			0.330106	+	0.943944i	$0.392915\pi$
$608$		0			0
$609$	35.7491			1.44863
$610$		0			0
$611$	14.2595	+	24.6982i	0.576877	+	0.999181i
$612$		0			0
$613$	−22.6606	−	39.2493i	−0.915254	−	1.58527i	−0.806529	−	0.591194i	$-0.798657\pi$
$613$	−22.6606	−	39.2493i	−0.915254	−	1.58527i	−0.108724	−	0.994072i	$-0.534677\pi$
$614$		0			0
$615$		−	5.55200i		−	0.223878i
$616$		0			0
$617$	4.21726	−	7.30450i	0.169780	−	0.294068i	−0.768562	−	0.639775i	$-0.779028\pi$
$617$	4.21726	−	7.30450i	0.169780	−	0.294068i	0.938343	+	0.345707i	$0.112361\pi$
$618$		0			0
$619$			5.23372i			0.210361i	0.994453	+	0.105180i	$0.0335420\pi$
$619$			5.23372i			0.210361i	−0.994453	+	0.105180i	$0.966458\pi$
$620$		0			0
$621$	5.25150	+	3.03196i	0.210736	+	0.121668i
$622$		0			0
$623$	−7.56538	+	13.1036i	−0.303101	+	0.524985i
$624$		0			0
$625$	−8.27316	−	14.3295i	−0.330926	−	0.573181i
$626$		0			0
$627$	8.87378	−	19.8345i	0.354384	−	0.792112i
$628$		0			0
$629$	−1.88947	+	1.09088i	−0.0753379	+	0.0434964i
$630$		0			0
$631$	29.8529	+	17.2356i	1.18842	+	0.686137i	0.957948	−	0.286942i	$-0.0926386\pi$
$631$	29.8529	+	17.2356i	1.18842	+	0.686137i	0.230475	+	0.973078i	$0.425972\pi$
$632$		0			0
$633$	−9.54849	+	16.5385i	−0.379518	+	0.657345i
$634$		0			0
$635$	−5.20441			−0.206531
$636$		0			0
$637$	11.5451	+	6.66559i	0.457435	+	0.264100i
$638$		0			0
$639$	−3.03978			−0.120252
$640$		0			0
$641$	−21.3314	+	12.3157i	−0.842538	+	0.486440i	−0.858126	−	0.513439i	$-0.828371\pi$
$641$	−21.3314	+	12.3157i	−0.842538	+	0.486440i	0.0155879	+	0.999879i	$0.495038\pi$
$642$		0			0
$643$	35.6236	−	20.5673i	1.40486	−	0.811096i	0.409973	−	0.912098i	$-0.365538\pi$
$643$	35.6236	−	20.5673i	1.40486	−	0.811096i	0.994886	+	0.101002i	$0.0322048\pi$
$644$		0			0
$645$			0.207296i			0.00816226i
$646$		0			0
$647$			22.0336i			0.866229i	0.901339	+	0.433115i	$0.142585\pi$
$647$			22.0336i			0.866229i	−0.901339	+	0.433115i	$0.857415\pi$
$648$		0			0
$649$	−45.5440	+	26.2948i	−1.78776	+	1.03216i
$650$		0			0
$651$	23.3429	−	13.4770i	0.914879	−	0.528206i
$652$		0			0
$653$	−16.3470			−0.639708			−0.319854	−	0.947467i	$-0.603634\pi$
$653$	−16.3470			−0.639708			−0.319854	+	0.947467i	$0.603634\pi$
$654$		0			0
$655$	−7.20572	−	4.16023i	−0.281551	−	0.162554i
$656$		0			0
$657$	8.09639			0.315870
$658$		0			0
$659$	12.9432	−	22.4182i	0.504194	−	0.873290i	−0.495794	−	0.868440i	$-0.665123\pi$
$659$	12.9432	−	22.4182i	0.504194	−	0.873290i	0.999988	−	0.00484954i	$-0.00154366\pi$
$660$		0			0
$661$	22.4003	+	12.9328i	0.871272	+	0.503029i	0.867771	−	0.496965i	$-0.165552\pi$
$661$	22.4003	+	12.9328i	0.871272	+	0.503029i	0.00350098	+	0.999994i	$0.498886\pi$
$662$		0			0
$663$	9.56095	−	5.52002i	0.371316	−	0.214380i
$664$		0			0
$665$	−4.82735	+	10.7900i	−0.187197	+	0.418418i
$666$		0			0
$667$	−30.6100	−	53.0180i	−1.18522	−	2.05287i
$668$		0			0
$669$	9.09785	−	15.7579i	0.351743	−	0.609237i
$670$		0			0
$671$	−12.5547	−	7.24848i	−0.484670	−	0.279824i
$672$		0			0
$673$		−	36.3544i		−	1.40136i	−0.713476	−	0.700679i	$-0.752880\pi$
$673$		−	36.3544i		−	1.40136i	0.713476	−	0.700679i	$-0.247120\pi$
$674$		0			0
$675$	2.20674	−	3.82219i	0.0849376	−	0.147116i
$676$		0			0
$677$			11.0217i			0.423599i	0.977313	+	0.211800i	$0.0679324\pi$
$677$			11.0217i			0.423599i	−0.977313	+	0.211800i	$0.932068\pi$
$678$		0			0
$679$	26.9480	+	46.6754i	1.03417	+	1.79124i
$680$		0			0
$681$	−2.91795	−	5.05403i	−0.111816	−	0.193671i
$682$		0			0
$683$	−14.5509			−0.556773			−0.278386	−	0.960469i	$-0.589800\pi$
$683$	−14.5509			−0.556773			−0.278386	+	0.960469i	$0.589800\pi$
$684$		0			0
$685$	12.3472			0.471763
$686$		0			0
$687$	2.57781	+	4.46489i	0.0983494	+	0.170346i
$688$		0			0
$689$	−8.59722	−	14.8908i	−0.327528	−	0.567295i
$690$		0			0
$691$		−	24.7586i		−	0.941861i	−0.882170	−	0.470931i	$-0.843918\pi$
$691$		−	24.7586i		−	0.941861i	0.882170	−	0.470931i	$-0.156082\pi$
$692$		0			0
$693$	−8.82589	+	15.2869i	−0.335268	+	0.580701i
$694$		0			0
$695$			11.6582i			0.442221i
$696$		0			0
$697$	28.7970	+	16.6260i	1.09077	+	0.629754i
$698$		0			0
$699$	4.65031	−	8.05457i	0.175891	−	0.304652i
$700$		0			0
$701$	−13.1949	−	22.8543i	−0.498366	−	0.863196i	0.501632	−	0.865081i	$-0.332733\pi$
$701$	−13.1949	−	22.8543i	−0.498366	−	0.863196i	−0.999998	+	0.00188540i	$0.999400\pi$
$702$		0			0
$703$	−1.21568	−	1.67960i	−0.0458501	−	0.0633472i
$704$		0			0
$705$	7.85848	−	4.53710i	0.295968	−	0.170877i
$706$		0			0
$707$	−32.9727	−	19.0368i	−1.24006	−	0.715952i
$708$		0			0
$709$	−8.64831	+	14.9793i	−0.324794	+	0.562560i	−0.981471	−	0.191612i	$-0.938628\pi$
$709$	−8.64831	+	14.9793i	−0.324794	+	0.562560i	0.656677	+	0.754172i	$0.271962\pi$
$710$		0			0
$711$	9.35638			0.350892
$712$		0			0
$713$	−39.9744	−	23.0792i	−1.49705	−	0.864323i
$714$		0			0
$715$	−9.18895			−0.343647
$716$		0			0
$717$	16.7649	−	9.67923i	0.626097	−	0.361478i
$718$		0			0
$719$	−13.3898	+	7.73061i	−0.499356	+	0.288303i	−0.728448	−	0.685102i	$-0.759758\pi$
$719$	−13.3898	+	7.73061i	−0.499356	+	0.288303i	0.229092	+	0.973405i	$0.426424\pi$
$720$		0			0
$721$		−	61.1518i		−	2.27741i
$722$		0			0
$723$			0.372501i			0.0138535i
$724$		0			0
$725$	−38.5880	+	22.2788i	−1.43312	+	0.827414i
$726$		0			0
$727$	5.19985	−	3.00213i	0.192852	−	0.111343i	−0.400465	−	0.916312i	$-0.631151\pi$
$727$	5.19985	−	3.00213i	0.192852	−	0.111343i	0.593317	+	0.804969i	$0.297818\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.07520	−	0.620766i	−0.0397676	−	0.0229598i
$732$		0			0
$733$	−15.5147			−0.573048			−0.286524	−	0.958073i	$-0.592500\pi$
$733$	−15.5147			−0.573048			−0.286524	+	0.958073i	$0.592500\pi$
$734$		0			0
$735$	2.12086	−	3.67344i	0.0782292	−	0.135497i
$736$		0			0
$737$	−59.1012	−	34.1221i	−2.17702	−	1.25690i
$738$		0			0
$739$	−9.81188	+	5.66489i	−0.360936	+	0.208386i	−0.669491	−	0.742820i	$-0.733488\pi$
$739$	−9.81188	+	5.66489i	−0.360936	+	0.208386i	0.308555	+	0.951206i	$0.400154\pi$
$740$		0			0
$741$	6.15148	+	8.49898i	0.225980	+	0.312218i
$742$		0			0
$743$	−8.03831	−	13.9228i	−0.294897	−	0.510776i	0.680064	−	0.733153i	$-0.261952\pi$
$743$	−8.03831	−	13.9228i	−0.294897	−	0.510776i	−0.974961	+	0.222376i	$0.928619\pi$
$744$		0			0
$745$	1.33017	−	2.30393i	0.0487338	−	0.0844093i
$746$		0			0
$747$	−12.4966	−	7.21494i	−0.457228	−	0.263981i
$748$		0			0
$749$			31.3728i			1.14634i
$750$		0			0
$751$	−12.5509	+	21.7389i	−0.457990	+	0.793263i	−0.998855	−	0.0478472i	$-0.984764\pi$
$751$	−12.5509	+	21.7389i	−0.457990	+	0.793263i	0.540864	+	0.841110i	$0.318097\pi$
$752$		0			0
$753$			17.0224i			0.620330i
$754$		0			0
$755$	4.82095	+	8.35013i	0.175452	+	0.303892i
$756$		0			0
$757$	−20.2757	−	35.1185i	−0.736931	−	1.27640i	−0.953871	−	0.300217i	$-0.902941\pi$
$757$	−20.2757	−	35.1185i	−0.736931	−	1.27640i	0.216940	−	0.976185i	$-0.430392\pi$
$758$		0			0
$759$	30.2285			1.09722
$760$		0			0
$761$	−38.2420			−1.38627			−0.693136	−	0.720807i	$-0.743771\pi$
$761$	−38.2420			−1.38627			−0.693136	+	0.720807i	$0.743771\pi$
$762$		0			0
$763$	23.9626	+	41.5045i	0.867505	+	1.50256i
$764$		0			0
$765$	−1.75636	−	3.04211i	−0.0635014	−	0.109988i
$766$		0			0
$767$		−	25.3923i		−	0.916861i
$768$		0			0
$769$	22.4975	−	38.9668i	0.811280	−	1.40518i	−0.100688	−	0.994918i	$-0.532104\pi$
$769$	22.4975	−	38.9668i	0.811280	−	1.40518i	0.911968	−	0.410261i	$-0.134562\pi$
$770$		0			0
$771$			25.8227i			0.929981i
$772$		0			0
$773$	−24.3891	−	14.0810i	−0.877214	−	0.506460i	−0.00747514	−	0.999972i	$-0.502379\pi$
$773$	−24.3891	−	14.0810i	−0.877214	−	0.506460i	−0.869739	+	0.493512i	$0.835713\pi$
$774$		0			0
$775$	−16.7977	+	29.0945i	−0.603391	+	1.04510i
$776$		0			0
$777$	0.842166	+	1.45868i	0.0302126	+	0.0523297i
$778$		0			0
$779$	−12.9050	+	28.8449i	−0.462368	+	1.03347i
$780$		0			0
$781$	−13.1231	+	7.57662i	−0.469581	+	0.271113i
$782$		0			0
$783$	−8.74320	−	5.04789i	−0.312456	−	0.180397i
$784$		0			0
$785$	−6.08524	+	10.5399i	−0.217192	+	0.376187i
$786$		0			0
$787$	−33.8028			−1.20494			−0.602470	−	0.798142i	$-0.705817\pi$
$787$	−33.8028			−1.20494			−0.602470	+	0.798142i	$0.705817\pi$
$788$		0			0
$789$	5.19782	+	3.00096i	0.185047	+	0.106837i
$790$		0			0
$791$	−23.7528			−0.844553
$792$		0			0
$793$	6.06190	−	3.49984i	0.215264	−	0.124283i
$794$		0			0
$795$	−4.73797	+	2.73547i	−0.168039	+	0.0970172i
$796$		0			0
$797$		−	13.9616i		−	0.494546i	−0.968946	−	0.247273i	$-0.920466\pi$
$797$		−	13.9616i		−	0.494546i	0.968946	−	0.247273i	$-0.0795344\pi$
$798$		0			0
$799$			54.3470i			1.92266i
$800$		0			0
$801$	3.70055	−	2.13651i	0.130752	−	0.0754899i
$802$		0			0
$803$	34.9531	−	20.1802i	1.23347	−	0.712143i
$804$		0			0
$805$	−16.4444			−0.579587
$806$		0			0
$807$	−18.3179	−	10.5758i	−0.644821	−	0.372287i
$808$		0			0
$809$	41.3510			1.45382			0.726911	−	0.686731i	$-0.240955\pi$
$809$	41.3510			1.45382			0.726911	+	0.686731i	$0.240955\pi$
$810$		0			0
$811$	7.65969	−	13.2670i	0.268968	−	0.465866i	−0.699628	−	0.714508i	$-0.746651\pi$
$811$	7.65969	−	13.2670i	0.268968	−	0.465866i	0.968596	+	0.248641i	$0.0799841\pi$
$812$		0			0
$813$	−18.6166	−	10.7483i	−0.652912	−	0.376959i
$814$		0			0
$815$	11.7785	−	6.80031i	0.412582	−	0.238205i
$816$		0			0
$817$	0.481833	−	1.07698i	0.0168572	−	0.0376789i
$818$		0			0
$819$	−4.26147	−	7.38109i	−0.148908	−	0.257916i
$820$		0			0
$821$	13.6553	−	23.6517i	0.476575	−	0.825451i	−0.523065	−	0.852293i	$-0.675212\pi$
$821$	13.6553	−	23.6517i	0.476575	−	0.825451i	0.999640	+	0.0268413i	$0.00854489\pi$
$822$		0			0
$823$	−3.63942	−	2.10122i	−0.126862	−	0.0732438i	0.435226	−	0.900321i	$-0.356668\pi$
$823$	−3.63942	−	2.10122i	−0.126862	−	0.0732438i	−0.562088	+	0.827077i	$0.690002\pi$
$824$		0			0
$825$		−	22.0011i		−	0.765981i
$826$		0			0
$827$	0.981304	−	1.69967i	0.0341233	−	0.0591033i	−0.848459	−	0.529260i	$-0.822469\pi$
$827$	0.981304	−	1.69967i	0.0341233	−	0.0591033i	0.882583	+	0.470157i	$0.155803\pi$
$828$		0			0
$829$			9.57003i			0.332381i	0.986094	+	0.166190i	$0.0531466\pi$
$829$			9.57003i			0.332381i	−0.986094	+	0.166190i	$0.946853\pi$
$830$		0			0
$831$	−7.13601	−	12.3599i	−0.247546	−	0.428761i
$832$		0			0
$833$	12.7022	+	22.0009i	0.440106	+	0.762287i
$834$		0			0
$835$	−13.2839			−0.459710
$836$		0			0
$837$	−7.61199			−0.263109
$838$		0			0
$839$	7.08677	+	12.2746i	0.244662	+	0.423768i	0.962037	−	0.272920i	$-0.0879895\pi$
$839$	7.08677	+	12.2746i	0.244662	+	0.423768i	−0.717374	+	0.696688i	$0.754656\pi$
$840$		0			0
$841$	36.4624	+	63.1547i	1.25732	+	2.17775i
$842$		0			0
$843$		−	12.7317i		−	0.438501i
$844$		0			0
$845$	−2.75958	+	4.77973i	−0.0949324	+	0.164428i
$846$		0			0
$847$			49.0428i			1.68513i
$848$		0			0
$849$	−22.1454	−	12.7857i	−0.760029	−	0.438803i
$850$		0			0
$851$	1.44220	−	2.49796i	0.0494380	−	0.0856291i
$852$		0			0
$853$	6.49133	+	11.2433i	0.222259	+	0.384964i	0.955494	−	0.295012i	$-0.0953237\pi$
$853$	6.49133	+	11.2433i	0.222259	+	0.384964i	−0.733235	+	0.679976i	$0.761990\pi$
$854$		0			0
$855$	2.70421	−	1.95728i	0.0924821	−	0.0669377i
$856$		0			0
$857$	−6.91087	+	3.98999i	−0.236071	+	0.136296i	−0.613369	−	0.789796i	$-0.710186\pi$
$857$	−6.91087	+	3.98999i	−0.236071	+	0.136296i	0.377299	+	0.926092i	$0.376853\pi$
$858$		0			0
$859$	−19.4044	−	11.2032i	−0.662071	−	0.382247i	0.130995	−	0.991383i	$-0.458183\pi$
$859$	−19.4044	−	11.2032i	−0.662071	−	0.382247i	−0.793066	+	0.609136i	$0.791516\pi$
$860$		0			0
$861$	12.8353	−	22.2314i	0.437426	−	0.757645i
$862$		0			0
$863$	12.1588			0.413891			0.206945	−	0.978352i	$-0.433648\pi$
$863$	12.1588			0.413891			0.206945	+	0.978352i	$0.433648\pi$
$864$		0			0
$865$	0.774307	+	0.447046i	0.0263272	+	0.0152000i
$866$		0			0
$867$	4.03836			0.137150
$868$		0			0
$869$	40.3926	−	23.3207i	1.37022	−	0.791100i
$870$		0			0
$871$	28.5363	−	16.4754i	0.966916	−	0.558249i
$872$		0			0
$873$		−	15.2206i		−	0.515139i
$874$		0			0
$875$			25.5279i			0.862999i
$876$		0			0
$877$	−5.01764	+	2.89694i	−0.169434	+	0.0978227i	−0.582319	−	0.812960i	$-0.697854\pi$
$877$	−5.01764	+	2.89694i	−0.169434	+	0.0978227i	0.412885	+	0.910783i	$0.364521\pi$
$878$		0			0
$879$	−3.72629	+	2.15137i	−0.125685	+	0.0725641i
$880$		0			0
$881$	35.6938			1.20255			0.601277	−	0.799041i	$-0.294659\pi$
$881$	35.6938			1.20255			0.601277	+	0.799041i	$0.294659\pi$
$882$		0			0
$883$	15.9300	+	9.19717i	0.536086	+	0.309510i	0.743491	−	0.668746i	$-0.233168\pi$
$883$	15.9300	+	9.19717i	0.536086	+	0.309510i	−0.207405	+	0.978255i	$0.566502\pi$
$884$		0			0
$885$	−8.07933			−0.271584
$886$		0			0
$887$	−1.90551	+	3.30044i	−0.0639808	+	0.110818i	−0.896241	−	0.443567i	$-0.853713\pi$
$887$	−1.90551	+	3.30044i	−0.0639808	+	0.110818i	0.832261	+	0.554385i	$0.187046\pi$
$888$		0			0
$889$	−20.8396	−	12.0317i	−0.698938	−	0.403532i
$890$		0			0
$891$	4.31712	−	2.49249i	0.144629	−	0.0835015i
$892$		0			0
$893$	−51.3739	+	5.30595i	−1.71916	+	0.177557i
$894$		0			0
$895$	−0.727443	−	1.25997i	−0.0243157	−	0.0421161i
$896$		0			0
$897$	−7.29772	+	12.6400i	−0.243664	+	0.422038i
$898$		0			0
$899$	66.5531	+	38.4245i	2.21967	+	1.28153i
$900$		0			0
$901$		−	32.7665i		−	1.09161i
$902$		0			0
$903$	−0.479233	+	0.830057i	−0.0159479	+	0.0276226i
$904$		0			0
$905$			11.4222i			0.379686i
$906$		0			0
$907$	7.73022	+	13.3891i	0.256678	+	0.444579i	0.965350	−	0.260959i	$-0.0840388\pi$
$907$	7.73022	+	13.3891i	0.256678	+	0.444579i	−0.708672	+	0.705538i	$0.750705\pi$
$908$		0			0
$909$	5.37611	+	9.31169i	0.178314	+	0.308849i
$910$		0			0
$911$	−16.9523			−0.561655			−0.280827	−	0.959758i	$-0.590609\pi$
$911$	−16.9523			−0.561655			−0.280827	+	0.959758i	$0.590609\pi$
$912$		0			0
$913$	−71.9326			−2.38062
$914$		0			0
$915$	−1.11358	−	1.92878i	−0.0368139	−	0.0637635i
$916$		0			0
$917$	−19.2355	−	33.3169i	−0.635213	−	1.10022i
$918$		0			0
$919$			2.52503i			0.0832930i	0.999132	+	0.0416465i	$0.0132603\pi$
$919$			2.52503i			0.0832930i	−0.999132	+	0.0416465i	$0.986740\pi$
$920$		0			0
$921$	−10.4130	+	18.0358i	−0.343120	+	0.594301i
$922$		0			0
$923$		−	7.31656i		−	0.240827i
$924$		0			0
$925$	−1.81809	−	1.04967i	−0.0597784	−	0.0345131i
$926$		0			0
$927$	−8.63483	+	14.9560i	−0.283605	+	0.491219i
$928$		0			0
$929$	−8.66440	−	15.0072i	−0.284270	−	0.492370i	0.688162	−	0.725557i	$-0.258418\pi$
$929$	−8.66440	−	15.0072i	−0.284270	−	0.492370i	−0.972432	+	0.233187i	$0.925085\pi$
$930$		0			0
$931$	−19.5572	+	14.1553i	−0.640961	+	0.463922i
$932$		0			0
$933$	−14.5060	+	8.37504i	−0.474905	+	0.274187i
$934$		0			0
$935$	−15.1649	−	8.75543i	−0.495944	−	0.286333i
$936$		0			0
$937$	16.1887	−	28.0396i	0.528861	−	0.916015i	−0.470572	−	0.882361i	$-0.655952\pi$
$937$	16.1887	−	28.0396i	0.528861	−	0.916015i	0.999434	−	0.0336533i	$-0.0107142\pi$
$938$		0			0
$939$	−18.3051			−0.597363
$940$		0			0
$941$	−0.547543	−	0.316124i	−0.0178494	−	0.0103053i	0.491049	−	0.871132i	$-0.336614\pi$
$941$	−0.547543	−	0.316124i	−0.0178494	−	0.0103053i	−0.508898	+	0.860827i	$0.669947\pi$
$942$		0			0
$943$	−43.9607			−1.43156
$944$		0			0
$945$	−2.34852	+	1.35592i	−0.0763974	+	0.0441081i
$946$		0			0
$947$	−23.0392	+	13.3017i	−0.748672	+	0.432246i	−0.825214	−	0.564820i	$-0.808945\pi$
$947$	−23.0392	+	13.3017i	−0.748672	+	0.432246i	0.0765417	+	0.997066i	$0.475612\pi$
$948$		0			0
$949$			19.4875i			0.632591i
$950$		0			0
$951$			0.658516i			0.0213538i
$952$		0			0
$953$	4.93313	−	2.84815i	0.159800	−	0.0922605i	−0.417968	−	0.908462i	$-0.637257\pi$
$953$	4.93313	−	2.84815i	0.159800	−	0.0922605i	0.577767	+	0.816201i	$0.303924\pi$
$954$		0			0
$955$	−9.80296	+	5.65974i	−0.317216	+	0.183145i
$956$		0			0
$957$	−50.3272			−1.62685
$958$		0			0
$959$	49.4410	+	28.5448i	1.59653	+	0.921758i
$960$		0			0
$961$	26.9423			0.869108
$962$		0			0
$963$	4.42995	−	7.67289i	0.142753	−	0.247255i
$964$		0			0
$965$	−16.9744	−	9.80019i	−0.546426	−	0.315479i
$966$		0			0
$967$	−32.3670	+	18.6871i	−1.04085	+	0.600937i	−0.920075	−	0.391743i	$-0.871872\pi$
$967$	−32.3670	+	18.6871i	−1.04085	+	0.600937i	−0.120778	+	0.992680i	$0.538539\pi$
$968$		0			0
$969$	2.05399	+	19.8874i	0.0659838	+	0.638876i
$970$		0			0
$971$	−7.63248	−	13.2198i	−0.244938	−	0.424245i	0.717176	−	0.696892i	$-0.245434\pi$
$971$	−7.63248	−	13.2198i	−0.244938	−	0.424245i	−0.962114	+	0.272647i	$0.912101\pi$
$972$		0			0
$973$	−26.9519	+	46.6820i	−0.864037	+	1.49656i
$974$		0			0
$975$	9.19977	+	5.31149i	0.294628	+	0.170104i
$976$		0			0
$977$			12.2300i			0.391274i	0.980676	+	0.195637i	$0.0626774\pi$
$977$			12.2300i			0.391274i	−0.980676	+	0.195637i	$0.937323\pi$
$978$		0			0
$979$	10.6505	−	18.4471i	0.340390	−	0.589573i
$980$		0			0
$981$		−	13.5344i		−	0.432120i
$982$		0			0
$983$	−5.41249	−	9.37471i	−0.172632	−	0.299007i	0.766707	−	0.641997i	$-0.221894\pi$
$983$	−5.41249	−	9.37471i	−0.172632	−	0.299007i	−0.939339	+	0.342990i	$0.888560\pi$
$984$		0			0
$985$	−3.77748	−	6.54279i	−0.120361	−	0.208471i
$986$		0			0
$987$	41.9561			1.33548
$988$		0			0
$989$	1.64136			0.0521923
$990$		0			0
$991$	6.73008	+	11.6568i	0.213788	+	0.370292i	0.952897	−	0.303294i	$-0.0980864\pi$
$991$	6.73008	+	11.6568i	0.213788	+	0.370292i	−0.739109	+	0.673586i	$0.764753\pi$
$992$		0			0
$993$	−4.47661	−	7.75371i	−0.142061	−	0.246057i
$994$		0			0
$995$		−	1.27326i		−	0.0403652i
$996$		0			0
$997$	15.9323	−	27.5955i	0.504581	−	0.873960i	−0.495405	−	0.868662i	$-0.664980\pi$
$997$	15.9323	−	27.5955i	0.504581	−	0.873960i	0.999986	−	0.00529757i	$-0.00168628\pi$
$998$		0			0
$999$		−	0.475666i		−	0.0150494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.bb.a.31.8	✓	40
4.3	odd	2		1824.2.bb.b.31.8	yes	40
19.8	odd	6		1824.2.bb.b.1471.8	yes	40
76.27	even	6	inner	1824.2.bb.a.1471.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.bb.a.31.8	✓	40	1.1	even	1	trivial
1824.2.bb.a.1471.8	yes	40	76.27	even	6	inner
1824.2.bb.b.31.8	yes	40	4.3	odd	2
1824.2.bb.b.1471.8	yes	40	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.382920 - 0.663237i) q^{5} -3.54100i q^{7} +(-0.500000 + 0.866025i) q^{9} +4.98498i q^{11} +(-2.08447 - 1.20347i) q^{13} +(-0.382920 + 0.663237i) q^{15} +(-2.29338 - 3.97225i) q^{17} +(3.53104 - 2.55573i) q^{19} +(-3.06659 + 1.77050i) q^{21} +(5.25150 + 3.03196i) q^{23} +(2.20674 - 3.82219i) q^{25} +1.00000 q^{27} +(-8.74320 - 5.04789i) q^{29} -7.61199 q^{31} +(4.31712 - 2.49249i) q^{33} +(-2.34852 + 1.35592i) q^{35} -0.475666i q^{37} +2.40693i q^{39} +(-6.27830 + 3.62478i) q^{41} +(0.234413 - 0.135339i) q^{43} +0.765841 q^{45} +(-10.2613 - 5.92434i) q^{47} -5.53865 q^{49} +(-2.29338 + 3.97225i) q^{51} +(6.18663 + 3.57185i) q^{53} +(3.30622 - 1.90885i) q^{55} +(-3.97885 - 1.78010i) q^{57} +(5.27481 + 9.13624i) q^{59} +(-1.45406 + 2.51851i) q^{61} +(3.06659 + 1.77050i) q^{63} +1.84333i q^{65} +(-6.84499 + 11.8559i) q^{67} -6.06391i q^{69} +(1.51989 + 2.63253i) q^{71} +(-4.04820 - 7.01168i) q^{73} -4.41349 q^{75} +17.6518 q^{77} +(-4.67819 - 8.10286i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.4299i q^{83} +(-1.75636 + 3.04211i) q^{85} +10.0958i q^{87} +(-3.70055 - 2.13651i) q^{89} +(-4.26147 + 7.38109i) q^{91} +(3.80599 + 6.59217i) q^{93} +(-3.04716 - 1.36328i) q^{95} +(-13.1814 + 7.61030i) q^{97} +(-4.31712 - 2.49249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) \) 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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