LMFDB - Embedded newform 1456.2.cc.c.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.1
Root			$0.759479 + 1.19298i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.c.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41289 + 2.44719i) q^{3} +0.518957i q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})$	\(q+(-1.41289 + 2.44719i) q^{3} +0.518957i q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.49250 - 4.31714i) q^{9} +(-1.40656 - 0.812080i) q^{11} +(1.42641 - 3.31140i) q^{13} +(-1.26999 - 0.733228i) q^{15} +(0.974127 + 1.68724i) q^{17} +(-2.15740 + 1.24558i) q^{19} +2.82577i q^{21} +(4.57029 - 7.91598i) q^{23} +4.73068 q^{25} +5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} -5.79391i q^{31} +(3.97463 - 2.29475i) q^{33} +(0.259479 + 0.449430i) q^{35} +(-8.85879 - 5.11463i) q^{37} +(6.08826 + 8.16934i) q^{39} +(3.64513 + 2.10452i) q^{41} +(0.498655 + 0.863697i) q^{43} +(2.24041 - 1.29350i) q^{45} -4.51725i q^{47} +(0.500000 - 0.866025i) q^{49} -5.50532 q^{51} -8.89651 q^{53} +(0.421434 - 0.729946i) q^{55} -7.03944i q^{57} +(5.37392 - 3.10263i) q^{59} +(6.73536 + 11.6660i) q^{61} +(-4.31714 - 2.49250i) q^{63} +(1.71847 + 0.740247i) q^{65} +(7.25094 + 4.18633i) q^{67} +(12.9146 + 22.3688i) q^{69} +(4.50168 - 2.59905i) q^{71} +11.8395i q^{73} +(-6.68392 + 11.5769i) q^{75} -1.62416 q^{77} -0.982310 q^{79} +(-0.447609 + 0.775281i) q^{81} +8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(7.38934 + 12.7987i) q^{87} +(-10.4087 - 6.00949i) q^{89} +(-0.420388 - 3.58096i) q^{91} +(14.1788 + 8.18614i) q^{93} +(-0.646401 - 1.11960i) q^{95} +(3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^9	$ 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	−1.41289	+	2.44719i	−0.815731	+	1.41289i	0.0930713	+	0.995659i	$0.470332\pi$
$3$	−1.41289	+	2.44719i	−0.815731	+	1.41289i	−0.908802	+	0.417228i	$0.863002\pi$
$4$		0			0
$5$			0.518957i			0.232085i	0.993244	+	0.116042i	$0.0370208\pi$
$5$			0.518957i			0.232085i	−0.993244	+	0.116042i	$0.962979\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		0			0
$9$	−2.49250	−	4.31714i	−0.830833	−	1.43905i
$10$		0			0
$11$	−1.40656	−	0.812080i	−0.424095	−	0.244851i	0.272733	−	0.962090i	$-0.412072\pi$
$11$	−1.40656	−	0.812080i	−0.424095	−	0.244851i	−0.696828	+	0.717239i	$0.745406\pi$
$12$		0			0
$13$	1.42641	−	3.31140i	0.395616	−	0.918416i
$13$	1.42641	−	3.31140i	0.395616	−	0.918416i
$14$		0			0
$15$	−1.26999	−	0.733228i	−0.327909	−	0.189319i
$16$		0			0
$17$	0.974127	+	1.68724i	0.236260	+	0.409215i	0.959638	−	0.281237i	$-0.0907448\pi$
$17$	0.974127	+	1.68724i	0.236260	+	0.409215i	−0.723378	+	0.690452i	$0.757411\pi$
$18$		0			0
$19$	−2.15740	+	1.24558i	−0.494942	+	0.285755i	−0.726622	−	0.687037i	$-0.758911\pi$
$19$	−2.15740	+	1.24558i	−0.494942	+	0.285755i	0.231680	+	0.972792i	$0.425578\pi$
$20$		0			0
$21$			2.82577i			0.616634i
$22$		0			0
$23$	4.57029	−	7.91598i	0.952971	−	1.65059i	0.214028	−	0.976828i	$-0.431342\pi$
$23$	4.57029	−	7.91598i	0.952971	−	1.65059i	0.738943	−	0.673767i	$-0.235325\pi$
$24$		0			0
$25$	4.73068			0.946137
$26$		0			0
$27$	5.60916			1.07948
$28$		0			0
$29$	2.61498	−	4.52928i	0.485589	−	0.841065i	−0.514274	−	0.857626i	$-0.671938\pi$
$29$	2.61498	−	4.52928i	0.485589	−	0.841065i	0.999863	+	0.0165608i	$0.00527172\pi$
$30$		0			0
$31$		−	5.79391i		−	1.04062i	−0.853978	−	0.520308i	$-0.825817\pi$
$31$		−	5.79391i		−	1.04062i	0.853978	−	0.520308i	$-0.174183\pi$
$32$		0			0
$33$	3.97463	−	2.29475i	0.691894	−	0.399465i
$34$		0			0
$35$	0.259479	+	0.449430i	0.0438599	+	0.0759675i
$36$		0			0
$37$	−8.85879	−	5.11463i	−1.45638	−	0.840840i	−0.457546	−	0.889186i	$-0.651272\pi$
$37$	−8.85879	−	5.11463i	−1.45638	−	0.840840i	−0.998831	+	0.0483462i	$0.984605\pi$
$38$		0			0
$39$	6.08826	+	8.16934i	0.974902	+	1.30814i
$40$		0			0
$41$	3.64513	+	2.10452i	0.569273	+	0.328670i	0.756859	−	0.653578i	$-0.226733\pi$
$41$	3.64513	+	2.10452i	0.569273	+	0.328670i	−0.187586	+	0.982248i	$0.560066\pi$
$42$		0			0
$43$	0.498655	+	0.863697i	0.0760442	+	0.131712i	0.901540	−	0.432696i	$-0.142438\pi$
$43$	0.498655	+	0.863697i	0.0760442	+	0.131712i	−0.825496	+	0.564408i	$0.809104\pi$
$44$		0			0
$45$	2.24041	−	1.29350i	0.333980	−	0.192824i
$46$		0			0
$47$		−	4.51725i		−	0.658909i	−0.944171	−	0.329455i	$-0.893135\pi$
$47$		−	4.51725i		−	0.658909i	0.944171	−	0.329455i	$-0.106865\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−5.50532			−0.770899
$52$		0			0
$53$	−8.89651			−1.22203			−0.611015	−	0.791619i	$-0.709238\pi$
$53$	−8.89651			−1.22203			−0.611015	+	0.791619i	$0.709238\pi$
$54$		0			0
$55$	0.421434	−	0.729946i	0.0568262	−	0.0984259i
$56$		0			0
$57$		−	7.03944i		−	0.932397i
$58$		0			0
$59$	5.37392	−	3.10263i	0.699624	−	0.403928i	−0.107583	−	0.994196i	$-0.534311\pi$
$59$	5.37392	−	3.10263i	0.699624	−	0.403928i	0.807207	+	0.590268i	$0.200978\pi$
$60$		0			0
$61$	6.73536	+	11.6660i	0.862375	+	1.49368i	0.869630	+	0.493703i	$0.164357\pi$
$61$	6.73536	+	11.6660i	0.862375	+	1.49368i	−0.00725571	+	0.999974i	$0.502310\pi$
$62$		0			0
$63$	−4.31714	−	2.49250i	−0.543908	−	0.314025i
$64$		0			0
$65$	1.71847	+	0.740247i	0.213150	+	0.0918164i
$66$		0			0
$67$	7.25094	+	4.18633i	0.885843	+	0.511442i	0.872580	−	0.488470i	$-0.162445\pi$
$67$	7.25094	+	4.18633i	0.885843	+	0.511442i	0.0132624	+	0.999912i	$0.495778\pi$
$68$		0			0
$69$	12.9146	+	22.3688i	1.55474	+	2.69288i
$70$		0			0
$71$	4.50168	−	2.59905i	0.534251	−	0.308450i	−0.208495	−	0.978023i	$-0.566856\pi$
$71$	4.50168	−	2.59905i	0.534251	−	0.308450i	0.742746	+	0.669573i	$0.233523\pi$
$72$		0			0
$73$			11.8395i			1.38571i	0.721076	+	0.692856i	$0.243648\pi$
$73$			11.8395i			1.38571i	−0.721076	+	0.692856i	$0.756352\pi$
$74$		0			0
$75$	−6.68392	+	11.5769i	−0.771793	+	1.33678i
$76$		0			0
$77$	−1.62416			−0.185090
$78$		0			0
$79$	−0.982310			−0.110518			−0.0552592	−	0.998472i	$-0.517599\pi$
$79$	−0.982310			−0.110518			−0.0552592	+	0.998472i	$0.517599\pi$
$80$		0			0
$81$	−0.447609	+	0.775281i	−0.0497343	+	0.0861423i
$82$		0			0
$83$			8.91851i			0.978934i	0.872022	+	0.489467i	$0.162809\pi$
$83$			8.91851i			0.978934i	−0.872022	+	0.489467i	$0.837191\pi$
$84$		0			0
$85$	−0.875603	+	0.505530i	−0.0949725	+	0.0548324i
$86$		0			0
$87$	7.38934	+	12.7987i	0.792220	+	1.37217i
$88$		0			0
$89$	−10.4087	−	6.00949i	−1.10332	−	0.637005i	−0.166233	−	0.986087i	$-0.553160\pi$
$89$	−10.4087	−	6.00949i	−1.10332	−	0.637005i	−0.937092	+	0.349082i	$0.886494\pi$
$90$		0			0
$91$	−0.420388	−	3.58096i	−0.0440686	−	0.375387i
$92$		0			0
$93$	14.1788	+	8.18614i	1.47027	+	0.848863i
$94$		0			0
$95$	−0.646401	−	1.11960i	−0.0663194	−	0.114869i
$96$		0			0
$97$	3.82981	−	2.21114i	0.388858	−	0.224507i	−0.292807	−	0.956172i	$-0.594589\pi$
$97$	3.82981	−	2.21114i	0.388858	−	0.224507i	0.681665	+	0.731664i	$0.261256\pi$
$98$		0			0
$99$			8.09643i			0.813722i
$100$		0			0
$101$	9.15132	−	15.8506i	0.910591	−	1.57719i	0.0973594	−	0.995249i	$-0.468960\pi$
$101$	9.15132	−	15.8506i	0.910591	−	1.57719i	0.813231	−	0.581940i	$-0.197706\pi$
$102$		0			0
$103$	5.02046			0.494680			0.247340	−	0.968929i	$-0.420444\pi$
$103$	5.02046			0.494680			0.247340	+	0.968929i	$0.420444\pi$
$104$		0			0
$105$	−1.46646			−0.143111
$106$		0			0
$107$	3.07228	−	5.32134i	0.297008	−	0.514434i	−0.678442	−	0.734654i	$-0.737344\pi$
$107$	3.07228	−	5.32134i	0.297008	−	0.514434i	0.975450	+	0.220221i	$0.0706777\pi$
$108$		0			0
$109$			11.8962i			1.13945i	0.821834	+	0.569727i	$0.192951\pi$
$109$			11.8962i			1.13945i	−0.821834	+	0.569727i	$0.807049\pi$
$110$		0			0
$111$	25.0330	−	14.4528i	2.37602	−	1.37180i
$112$		0			0
$113$	−1.77806	−	3.07969i	−0.167266	−	0.289713i	0.770192	−	0.637812i	$-0.220161\pi$
$113$	−1.77806	−	3.07969i	−0.167266	−	0.289713i	−0.937458	+	0.348099i	$0.886827\pi$
$114$		0			0
$115$	4.10805	+	2.37178i	0.383078	+	0.221170i
$116$		0			0
$117$	−17.8511	+	2.09563i	−1.65033	+	0.193741i
$118$		0			0
$119$	1.68724	+	0.974127i	0.154669	+	0.0892980i
$120$		0			0
$121$	−4.18105	−	7.24180i	−0.380096	−	0.658345i
$122$		0			0
$123$	−10.3003	+	5.94689i	−0.928748	+	0.536213i
$124$		0			0
$125$			5.04981i			0.451668i
$126$		0			0
$127$	0.711749	−	1.23279i	0.0631575	−	0.109392i	−0.832718	−	0.553698i	$-0.813216\pi$
$127$	0.711749	−	1.23279i	0.0631575	−	0.109392i	0.895875	+	0.444306i	$0.146550\pi$
$128$		0			0
$129$	−2.81818			−0.248127
$130$		0			0
$131$	−8.67374			−0.757828			−0.378914	−	0.925432i	$-0.623702\pi$
$131$	−8.67374			−0.757828			−0.378914	+	0.925432i	$0.623702\pi$
$132$		0			0
$133$	−1.24558	+	2.15740i	−0.108005	+	0.187071i
$134$		0			0
$135$			2.91091i			0.250531i
$136$		0			0
$137$	7.37667	−	4.25892i	0.630231	−	0.363864i	−0.150611	−	0.988593i	$-0.548124\pi$
$137$	7.37667	−	4.25892i	0.630231	−	0.363864i	0.780842	+	0.624729i	$0.214791\pi$
$138$		0			0
$139$	−2.51922	−	4.36342i	−0.213677	−	0.370100i	0.739185	−	0.673502i	$-0.235211\pi$
$139$	−2.51922	−	4.36342i	−0.213677	−	0.370100i	−0.952863	+	0.303402i	$0.901877\pi$
$140$		0			0
$141$	11.0546	+	6.38237i	0.930964	+	0.537493i
$142$		0			0
$143$	−4.69546	+	3.49933i	−0.392654	+	0.292628i
$144$		0			0
$145$	2.35050	+	1.35706i	0.195198	+	0.112698i
$146$		0			0
$147$	1.41289	+	2.44719i	0.116533	+	0.201841i
$148$		0			0
$149$	2.91409	−	1.68245i	0.238732	−	0.137832i	−0.375862	−	0.926676i	$-0.622653\pi$
$149$	2.91409	−	1.68245i	0.238732	−	0.137832i	0.614594	+	0.788844i	$0.289320\pi$
$150$		0			0
$151$			12.6566i			1.02998i	0.857196	+	0.514991i	$0.172205\pi$
$151$			12.6566i			1.02998i	−0.857196	+	0.514991i	$0.827795\pi$
$152$		0			0
$153$	4.85602	−	8.41087i	0.392586	−	0.679979i
$154$		0			0
$155$	3.00679			0.241511
$156$		0			0
$157$	10.3691			0.827547			0.413773	−	0.910380i	$-0.364211\pi$
$157$	10.3691			0.827547			0.413773	+	0.910380i	$0.364211\pi$
$158$		0			0
$159$	12.5698	−	21.7715i	0.996847	−	1.72659i
$160$		0			0
$161$		−	9.14058i		−	0.720379i
$162$		0			0
$163$	−13.6428	+	7.87669i	−1.06859	+	0.616950i	−0.927796	−	0.373089i	$-0.878299\pi$
$163$	−13.6428	+	7.87669i	−1.06859	+	0.616950i	−0.140794	+	0.990039i	$0.544965\pi$
$164$		0			0
$165$	1.19088	+	2.06266i	0.0927098	+	0.160578i
$166$		0			0
$167$	14.2016	+	8.19930i	1.09895	+	0.634481i	0.935946	−	0.352144i	$-0.114547\pi$
$167$	14.2016	+	8.19930i	1.09895	+	0.634481i	0.163007	+	0.986625i	$0.447881\pi$
$168$		0			0
$169$	−8.93069	−	9.44684i	−0.686976	−	0.726680i
$170$		0			0
$171$	10.7547	+	6.20920i	0.822429	+	0.474830i
$172$		0			0
$173$	−0.150677	−	0.260981i	−0.0114558	−	0.0198420i	0.860241	−	0.509888i	$-0.170313\pi$
$173$	−0.150677	−	0.260981i	−0.0114558	−	0.0198420i	−0.871696	+	0.490046i	$0.836980\pi$
$174$		0			0
$175$	4.09689	−	2.36534i	0.309696	−	0.178803i
$176$		0			0
$177$			17.5347i			1.31799i
$178$		0			0
$179$	4.90791	−	8.50075i	0.366834	−	0.635376i	−0.622234	−	0.782831i	$-0.713775\pi$
$179$	4.90791	−	8.50075i	0.366834	−	0.635376i	0.989069	+	0.147455i	$0.0471083\pi$
$180$		0			0
$181$	12.4320			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$181$	12.4320			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$182$		0			0
$183$	−38.0652			−2.81386
$184$		0			0
$185$	2.65427	−	4.59733i	0.195146	−	0.338003i
$186$		0			0
$187$		−	3.16427i		−	0.231395i
$188$		0			0
$189$	4.85767	−	2.80458i	0.353344	−	0.204003i
$190$		0			0
$191$	−6.12346	−	10.6061i	−0.443078	−	0.767434i	0.554838	−	0.831958i	$-0.312780\pi$
$191$	−6.12346	−	10.6061i	−0.443078	−	0.767434i	−0.997916	+	0.0645248i	$0.979447\pi$
$192$		0			0
$193$	−10.0752	−	5.81692i	−0.725229	−	0.418711i	0.0914452	−	0.995810i	$-0.470851\pi$
$193$	−10.0752	−	5.81692i	−0.725229	−	0.418711i	−0.816674	+	0.577099i	$0.804185\pi$
$194$		0			0
$195$	−4.23953	+	3.15955i	−0.303599	+	0.226260i
$196$		0			0
$197$	−1.55984	−	0.900572i	−0.111134	−	0.0641631i	0.443403	−	0.896322i	$-0.353771\pi$
$197$	−1.55984	−	0.900572i	−0.111134	−	0.0641631i	−0.554537	+	0.832159i	$0.687104\pi$
$198$		0			0
$199$	−3.29657	−	5.70982i	−0.233687	−	0.404759i	0.725203	−	0.688535i	$-0.241746\pi$
$199$	−3.29657	−	5.70982i	−0.233687	−	0.404759i	−0.958890	+	0.283777i	$0.908413\pi$
$200$		0			0
$201$	−20.4895	+	11.8296i	−1.44522	+	0.834397i
$202$		0			0
$203$		−	5.22996i		−	0.367071i
$204$		0			0
$205$	−1.09215	+	1.89166i	−0.0762793	+	0.132120i
$206$		0			0
$207$	−45.5658			−3.16704
$208$		0			0
$209$	4.04603			0.279870
$210$		0			0
$211$	5.35996	−	9.28373i	0.368995	−	0.639118i	−0.620414	−	0.784275i	$-0.713035\pi$
$211$	5.35996	−	9.28373i	0.368995	−	0.639118i	0.989409	+	0.145157i	$0.0463686\pi$
$212$		0			0
$213$			14.6886i			1.00645i
$214$		0			0
$215$	−0.448221	+	0.258781i	−0.0305684	+	0.0176487i
$216$		0			0
$217$	−2.89695	−	5.01767i	−0.196658	−	0.340622i
$218$		0			0
$219$	−28.9736	−	16.7279i	−1.95785	−	1.13037i
$220$		0			0
$221$	6.97662	−	0.819021i	0.469298	−	0.0550933i
$222$		0			0
$223$	11.1612	+	6.44392i	0.747409	+	0.431517i	0.824757	−	0.565487i	$-0.191312\pi$
$223$	11.1612	+	6.44392i	0.747409	+	0.431517i	−0.0773480	+	0.997004i	$0.524645\pi$
$224$		0			0
$225$	−11.7912	−	20.4230i	−0.786082	−	1.36153i
$226$		0			0
$227$	0.605486	−	0.349577i	0.0401875	−	0.0232023i	−0.479772	−	0.877393i	$-0.659280\pi$
$227$	0.605486	−	0.349577i	0.0401875	−	0.0232023i	0.519959	+	0.854191i	$0.325947\pi$
$228$		0			0
$229$		−	18.2868i		−	1.20843i	−0.796822	−	0.604214i	$-0.793487\pi$
$229$		−	18.2868i		−	1.20843i	0.796822	−	0.604214i	$-0.206513\pi$
$230$		0			0
$231$	2.29475	−	3.97463i	0.150984	−	0.261511i
$232$		0			0
$233$	−26.7796			−1.75439			−0.877194	−	0.480137i	$-0.840587\pi$
$233$	−26.7796			−1.75439			−0.877194	+	0.480137i	$0.840587\pi$
$234$		0			0
$235$	2.34426			0.152923
$236$		0			0
$237$	1.38789	−	2.40390i	0.0901533	−	0.156150i
$238$		0			0
$239$			16.6177i			1.07491i	0.843293	+	0.537454i	$0.180614\pi$
$239$			16.6177i			1.07491i	−0.843293	+	0.537454i	$0.819386\pi$
$240$		0			0
$241$	15.0800	−	8.70643i	0.971387	−	0.560830i	0.0717279	−	0.997424i	$-0.477149\pi$
$241$	15.0800	−	8.70643i	0.971387	−	0.560830i	0.899659	+	0.436594i	$0.143815\pi$
$242$		0			0
$243$	7.14890	+	12.3823i	0.458602	+	0.794322i
$244$		0			0
$245$	0.449430	+	0.259479i	0.0287130	+	0.0165775i
$246$		0			0
$247$	1.04725	+	8.92073i	0.0666350	+	0.567612i
$248$		0			0
$249$	−21.8253	−	12.6008i	−1.38312	−	0.798546i
$250$		0			0
$251$	3.22491	+	5.58571i	0.203554	+	0.352567i	0.949671	−	0.313249i	$-0.101417\pi$
$251$	3.22491	+	5.58571i	0.203554	+	0.352567i	−0.746117	+	0.665815i	$0.768084\pi$
$252$		0			0
$253$	−12.8568	+	7.42288i	−0.808300	+	0.466672i
$254$		0			0
$255$		−	2.85703i		−	0.178914i
$256$		0			0
$257$	−1.83578	+	3.17966i	−0.114513	+	0.198342i	−0.917585	−	0.397540i	$-0.869864\pi$
$257$	−1.83578	+	3.17966i	−0.114513	+	0.198342i	0.803072	+	0.595882i	$0.203197\pi$
$258$		0			0
$259$	−10.2293			−0.635615
$260$		0			0
$261$	−26.0713			−1.61377
$262$		0			0
$263$	9.15964	−	15.8650i	0.564807	−	0.978275i	−0.432260	−	0.901749i	$-0.642284\pi$
$263$	9.15964	−	15.8650i	0.564807	−	0.978275i	0.997068	−	0.0765263i	$-0.0243829\pi$
$264$		0			0
$265$		−	4.61690i		−	0.283614i
$266$		0			0
$267$	29.4128	−	16.9815i	1.80003	−	1.03925i
$268$		0			0
$269$	−13.7715	−	23.8529i	−0.839661	−	1.45434i	−0.890178	−	0.455613i	$-0.849420\pi$
$269$	−13.7715	−	23.8529i	−0.839661	−	1.45434i	0.0505171	−	0.998723i	$-0.483913\pi$
$270$		0			0
$271$	−5.64582	−	3.25961i	−0.342959	−	0.198007i	0.318621	−	0.947882i	$-0.396780\pi$
$271$	−5.64582	−	3.25961i	−0.342959	−	0.198007i	−0.661580	+	0.749875i	$0.730114\pi$
$272$		0			0
$273$	9.35726	+	4.03072i	0.566327	+	0.243950i
$274$		0			0
$275$	−6.65401	−	3.84169i	−0.401252	−	0.231663i
$276$		0			0
$277$	2.72093	+	4.71279i	0.163485	+	0.283164i	0.936116	−	0.351691i	$-0.114393\pi$
$277$	2.72093	+	4.71279i	0.163485	+	0.283164i	−0.772631	+	0.634855i	$0.781060\pi$
$278$		0			0
$279$	−25.0131	+	14.4413i	−1.49749	+	0.864579i
$280$		0			0
$281$		−	3.54237i		−	0.211320i	−0.994402	−	0.105660i	$-0.966304\pi$
$281$		−	3.54237i		−	0.211320i	0.994402	−	0.105660i	$-0.0336955\pi$
$282$		0			0
$283$	7.06956	−	12.2448i	0.420242	−	0.727880i	−0.575721	−	0.817646i	$-0.695279\pi$
$283$	7.06956	−	12.2448i	0.420242	−	0.727880i	0.995963	+	0.0897658i	$0.0286119\pi$
$284$		0			0
$285$	3.65317			0.216395
$286$		0			0
$287$	4.20903			0.248451
$288$		0			0
$289$	6.60215	−	11.4353i	0.388362	−	0.672663i
$290$		0			0
$291$			12.4964i			0.732551i
$292$		0			0
$293$	−7.23071	+	4.17465i	−0.422423	+	0.243886i	−0.696113	−	0.717932i	$-0.745089\pi$
$293$	−7.23071	+	4.17465i	−0.422423	+	0.243886i	0.273691	+	0.961818i	$0.411756\pi$
$294$		0			0
$295$	1.61013	+	2.78883i	0.0937455	+	0.162372i
$296$		0			0
$297$	−7.88964	−	4.55508i	−0.457803	−	0.264313i
$298$		0			0
$299$	−19.6938	−	26.4255i	−1.13892	−	1.52823i
$300$		0			0
$301$	0.863697	+	0.498655i	0.0497826	+	0.0287420i
$302$		0			0
$303$	25.8596	+	44.7901i	1.48559	+	2.57312i
$304$		0			0
$305$	−6.05415	+	3.49536i	−0.346659	+	0.200144i
$306$		0			0
$307$		−	8.33362i		−	0.475625i	−0.971311	−	0.237813i	$-0.923570\pi$
$307$		−	8.33362i		−	0.475625i	0.971311	−	0.237813i	$-0.0764304\pi$
$308$		0			0
$309$	−7.09334	+	12.2860i	−0.403526	+	0.698927i
$310$		0			0
$311$	−14.6227			−0.829176			−0.414588	−	0.910009i	$-0.636074\pi$
$311$	−14.6227			−0.829176			−0.414588	+	0.910009i	$0.636074\pi$
$312$		0			0
$313$	17.1328			0.968404			0.484202	−	0.874956i	$-0.339110\pi$
$313$	17.1328			0.968404			0.484202	+	0.874956i	$0.339110\pi$
$314$		0			0
$315$	1.29350	−	2.24041i	0.0728805	−	0.126233i
$316$		0			0
$317$		−	14.0000i		−	0.786320i	−0.919470	−	0.393160i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786320i	0.919470	−	0.393160i	$-0.128618\pi$
$318$		0			0
$319$	−7.35627	+	4.24714i	−0.411872	+	0.237794i
$320$		0			0
$321$	8.68157	+	15.0369i	0.484558	+	0.839279i
$322$		0			0
$323$	−4.20317	−	2.42670i	−0.233871	−	0.135025i
$324$		0			0
$325$	6.74791	−	15.6652i	0.374307	−	0.868947i
$326$		0			0
$327$	−29.1124	−	16.8081i	−1.60992	−	0.929487i
$328$		0			0
$329$	−2.25863	−	3.91206i	−0.124522	−	0.215679i
$330$		0			0
$331$	−5.99286	+	3.45998i	−0.329397	+	0.190178i	−0.655574	−	0.755131i	$-0.727573\pi$
$331$	−5.99286	+	3.45998i	−0.329397	+	0.190178i	0.326176	+	0.945309i	$0.394240\pi$
$332$		0			0
$333$			50.9928i			2.79439i
$334$		0			0
$335$	−2.17253	+	3.76292i	−0.118698	+	0.205591i
$336$		0			0
$337$	11.1559			0.607703			0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559			0.607703			0.303852	+	0.952719i	$0.401727\pi$
$338$		0			0
$339$	10.0488			0.545776
$340$		0			0
$341$	−4.70512	+	8.14950i	−0.254796	+	0.441320i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	−11.6084	+	6.70213i	−0.624977	+	0.360830i
$346$		0			0
$347$	−2.46255	−	4.26527i	−0.132197	−	0.228971i	0.792326	−	0.610097i	$-0.208870\pi$
$347$	−2.46255	−	4.26527i	−0.132197	−	0.228971i	−0.924523	+	0.381126i	$0.875536\pi$
$348$		0			0
$349$	1.31926	+	0.761675i	0.0706183	+	0.0407715i	0.534893	−	0.844920i	$-0.320352\pi$
$349$	1.31926	+	0.761675i	0.0706183	+	0.0407715i	−0.464275	+	0.885691i	$0.653685\pi$
$350$		0			0
$351$	8.00098	−	18.5741i	0.427061	−	0.991415i
$352$		0			0
$353$	15.5261	+	8.96401i	0.826372	+	0.477106i	0.852609	−	0.522550i	$-0.175019\pi$
$353$	15.5261	+	8.96401i	0.826372	+	0.477106i	−0.0262367	+	0.999656i	$0.508352\pi$
$354$		0			0
$355$	1.34879	+	2.33618i	0.0715865	+	0.123991i
$356$		0			0
$357$	−4.76775	+	2.75266i	−0.252336	+	0.145686i
$358$		0			0
$359$		−	20.0014i		−	1.05563i	−0.849359	−	0.527816i	$-0.823011\pi$
$359$		−	20.0014i		−	1.05563i	0.849359	−	0.527816i	$-0.176989\pi$
$360$		0			0
$361$	−6.39707	+	11.0801i	−0.336688	+	0.583161i
$362$		0			0
$363$	23.6294			1.24022
$364$		0			0
$365$	−6.14421			−0.321602
$366$		0			0
$367$	13.7078	−	23.7427i	0.715544	−	1.23936i	−0.247206	−	0.968963i	$-0.579512\pi$
$367$	13.7078	−	23.7427i	0.715544	−	1.23936i	0.962749	−	0.270395i	$-0.0871543\pi$
$368$		0			0
$369$		−	20.9820i		−	1.09228i
$370$		0			0
$371$	−7.70460	+	4.44825i	−0.400003	+	0.230942i
$372$		0			0
$373$	7.94643	+	13.7636i	0.411451	+	0.712653i	0.995049	−	0.0993893i	$-0.0316889\pi$
$373$	7.94643	+	13.7636i	0.411451	+	0.712653i	−0.583598	+	0.812043i	$0.698356\pi$
$374$		0			0
$375$	−12.3578	−	7.13481i	−0.638156	−	0.368440i
$376$		0			0
$377$	−11.2682	−	15.1199i	−0.580341	−	0.778712i
$378$		0			0
$379$	−7.60284	−	4.38950i	−0.390532	−	0.225474i	0.291859	−	0.956461i	$-0.405726\pi$
$379$	−7.60284	−	4.38950i	−0.390532	−	0.225474i	−0.682390	+	0.730988i	$0.739060\pi$
$380$		0			0
$381$	2.01124	+	3.48357i	0.103039	+	0.178469i
$382$		0			0
$383$	−6.89562	+	3.98119i	−0.352349	+	0.203429i	−0.665720	−	0.746202i	$-0.731875\pi$
$383$	−6.89562	+	3.98119i	−0.352349	+	0.203429i	0.313370	+	0.949631i	$0.398542\pi$
$384$		0			0
$385$		−	0.842869i		−	0.0429566i
$386$		0			0
$387$	2.48580	−	4.30553i	0.126360	−	0.218862i
$388$		0			0
$389$	−32.0434			−1.62467			−0.812333	−	0.583194i	$-0.801803\pi$
$389$	−32.0434			−1.62467			−0.812333	+	0.583194i	$0.801803\pi$
$390$		0			0
$391$	17.8082			0.900598
$392$		0			0
$393$	12.2550	−	21.2263i	0.618184	−	1.07073i
$394$		0			0
$395$		−	0.509777i		−	0.0256496i
$396$		0			0
$397$	5.57251	−	3.21729i	0.279676	−	0.161471i	−0.353601	−	0.935396i	$-0.615043\pi$
$397$	5.57251	−	3.21729i	0.279676	−	0.161471i	0.633277	+	0.773925i	$0.281710\pi$
$398$		0			0
$399$	−3.51972	−	6.09633i	−0.176206	−	0.305198i
$400$		0			0
$401$	−0.462092	−	0.266789i	−0.0230758	−	0.0133228i	0.488418	−	0.872610i	$-0.337574\pi$
$401$	−0.462092	−	0.266789i	−0.0230758	−	0.0133228i	−0.511494	+	0.859287i	$0.670908\pi$
$402$		0			0
$403$	−19.1859	−	8.26451i	−0.955719	−	0.411685i
$404$		0			0
$405$	−0.402337	−	0.232290i	−0.0199923	−	0.0115426i
$406$		0			0
$407$	8.30697	+	14.3881i	0.411761	+	0.713191i
$408$		0			0
$409$	−34.4269	+	19.8764i	−1.70230	+	0.982824i	−0.758877	+	0.651234i	$0.774252\pi$
$409$	−34.4269	+	19.8764i	−1.70230	+	0.982824i	−0.943424	+	0.331590i	$0.892415\pi$
$410$		0			0
$411$			24.0695i			1.18726i
$412$		0			0
$413$	3.10263	−	5.37392i	0.152671	−	0.264433i
$414$		0			0
$415$	−4.62832			−0.227195
$416$		0			0
$417$	14.2375			0.697213
$418$		0			0
$419$	11.9088	−	20.6266i	0.581783	−	1.00768i	−0.413485	−	0.910511i	$-0.635689\pi$
$419$	11.9088	−	20.6266i	0.581783	−	1.00768i	0.995268	−	0.0971665i	$-0.0309779\pi$
$420$		0			0
$421$			23.2419i			1.13274i	0.824151	+	0.566370i	$0.191653\pi$
$421$			23.2419i			1.13274i	−0.824151	+	0.566370i	$0.808347\pi$
$422$		0			0
$423$	−19.5016	+	11.2593i	−0.948200	+	0.547444i
$424$		0			0
$425$	4.60828	+	7.98178i	0.223535	+	0.387173i
$426$		0			0
$427$	11.6660	+	6.73536i	0.564557	+	0.325947i
$428$		0			0
$429$	−1.92937	−	16.4348i	−0.0931510	−	0.793482i
$430$		0			0
$431$	2.34424	+	1.35345i	0.112918	+	0.0651932i	0.555395	−	0.831586i	$-0.312567\pi$
$431$	2.34424	+	1.35345i	0.112918	+	0.0651932i	−0.442477	+	0.896780i	$0.645900\pi$
$432$		0			0
$433$	−2.90945	−	5.03932i	−0.139819	−	0.242174i	0.787609	−	0.616176i	$-0.211319\pi$
$433$	−2.90945	−	5.03932i	−0.139819	−	0.242174i	−0.927428	+	0.374002i	$0.877985\pi$
$434$		0			0
$435$	−6.64198	+	3.83475i	−0.318459	+	0.183862i
$436$		0			0
$437$			22.7706i			1.08927i
$438$		0			0
$439$	−19.0851	+	33.0563i	−0.910882	+	1.57769i	−0.0980599	+	0.995181i	$0.531264\pi$
$439$	−19.0851	+	33.0563i	−0.910882	+	1.57769i	−0.812822	+	0.582513i	$0.802070\pi$
$440$		0			0
$441$	−4.98500			−0.237381
$442$		0			0
$443$	31.6740			1.50488			0.752440	−	0.658661i	$-0.228877\pi$
$443$	31.6740			1.50488			0.752440	+	0.658661i	$0.228877\pi$
$444$		0			0
$445$	3.11867	−	5.40169i	0.147839	−	0.256065i
$446$		0			0
$447$			9.50845i			0.449734i
$448$		0			0
$449$	27.1975	−	15.7025i	1.28353	−	0.741045i	0.306036	−	0.952020i	$-0.400997\pi$
$449$	27.1975	−	15.7025i	1.28353	−	0.741045i	0.977491	+	0.210975i	$0.0676638\pi$
$450$		0			0
$451$	−3.41807	−	5.92027i	−0.160951	−	0.278775i
$452$		0			0
$453$	−30.9732	−	17.8824i	−1.45525	−	0.840187i
$454$		0			0
$455$	1.85836	−	0.218163i	0.0871215	−	0.0102276i
$456$		0			0
$457$	27.5640	+	15.9141i	1.28939	+	0.744429i	0.978545	−	0.206032i	$-0.0660551\pi$
$457$	27.5640	+	15.9141i	1.28939	+	0.744429i	0.310844	+	0.950461i	$0.399388\pi$
$458$		0			0
$459$	5.46403	+	9.46398i	0.255039	+	0.441741i
$460$		0			0
$461$	1.01005	−	0.583153i	0.0470427	−	0.0271601i	−0.476294	−	0.879286i	$-0.658020\pi$
$461$	1.01005	−	0.583153i	0.0470427	−	0.0271601i	0.523337	+	0.852126i	$0.324687\pi$
$462$		0			0
$463$			20.3441i			0.945469i	0.881205	+	0.472734i	$0.156733\pi$
$463$			20.3441i			0.945469i	−0.881205	+	0.472734i	$0.843267\pi$
$464$		0			0
$465$	−4.24825	+	7.35819i	−0.197008	+	0.341228i
$466$		0			0
$467$	−1.56939			−0.0726229			−0.0363114	−	0.999341i	$-0.511561\pi$
$467$	−1.56939			−0.0726229			−0.0363114	+	0.999341i	$0.511561\pi$
$468$		0			0
$469$	8.37266			0.386614
$470$		0			0
$471$	−14.6504	+	25.3753i	−0.675055	+	1.16923i
$472$		0			0
$473$		−	1.61979i		−	0.0744781i
$474$		0			0
$475$	−10.2060	+	5.89243i	−0.468283	+	0.270363i
$476$		0			0
$477$	22.1745	+	38.4074i	1.01530	+	1.75856i
$478$		0			0
$479$	−6.68501	−	3.85959i	−0.305446	−	0.176349i	0.339441	−	0.940627i	$-0.389762\pi$
$479$	−6.68501	−	3.85959i	−0.305446	−	0.176349i	−0.644887	+	0.764278i	$0.723095\pi$
$480$		0			0
$481$	−29.5729	+	22.0394i	−1.34841	+	1.00491i
$482$		0			0
$483$	22.3688	+	12.9146i	1.01781	+	0.587635i
$484$		0			0
$485$	1.14749	+	1.98751i	0.0521047	+	0.0902481i
$486$		0			0
$487$	0.0659739	−	0.0380900i	0.00298956	−	0.00172602i	−0.498504	−	0.866887i	$-0.666117\pi$
$487$	0.0659739	−	0.0380900i	0.00298956	−	0.00172602i	0.501494	+	0.865161i	$0.332784\pi$
$488$		0			0
$489$		−	44.5155i		−	2.01306i
$490$		0			0
$491$	−0.893574	+	1.54772i	−0.0403264	+	0.0698474i	−0.885484	−	0.464670i	$-0.846173\pi$
$491$	−0.893574	+	1.54772i	−0.0403264	+	0.0698474i	0.845158	+	0.534517i	$0.179506\pi$
$492$		0			0
$493$	10.1893			0.458902
$494$		0			0
$495$	−4.20170			−0.188852
$496$		0			0
$497$	2.59905	−	4.50168i	0.116583	−	0.201928i
$498$		0			0
$499$		−	8.33493i		−	0.373123i	−0.982443	−	0.186561i	$-0.940266\pi$
$499$		−	8.33493i		−	0.373123i	0.982443	−	0.186561i	$-0.0597343\pi$
$500$		0			0
$501$	−40.1305	+	23.1694i	−1.79290	+	1.03513i
$502$		0			0
$503$	0.720238	+	1.24749i	0.0321138	+	0.0556228i	0.881636	−	0.471931i	$-0.156443\pi$
$503$	0.720238	+	1.24749i	0.0321138	+	0.0556228i	−0.849522	+	0.527554i	$0.823109\pi$
$504$		0			0
$505$	8.22576	+	4.74914i	0.366041	+	0.211334i
$506$		0			0
$507$	35.7363	−	8.50779i	1.58710	−	0.377844i
$508$		0			0
$509$	12.8394	+	7.41282i	0.569096	+	0.328568i	0.756788	−	0.653660i	$-0.226767\pi$
$509$	12.8394	+	7.41282i	0.569096	+	0.328568i	−0.187692	+	0.982228i	$0.560101\pi$
$510$		0			0
$511$	5.91976	+	10.2533i	0.261875	+	0.453581i
$512$		0			0
$513$	−12.1012	+	6.98664i	−0.534282	+	0.308468i
$514$		0			0
$515$			2.60540i			0.114808i
$516$		0			0
$517$	−3.66837	+	6.35380i	−0.161335	+	0.279440i
$518$		0			0
$519$	0.851561			0.0373794
$520$		0			0
$521$	−0.334388			−0.0146498			−0.00732489	−	0.999973i	$-0.502332\pi$
$521$	−0.334388			−0.0146498			−0.00732489	+	0.999973i	$0.502332\pi$
$522$		0			0
$523$	−16.2533	+	28.1515i	−0.710705	+	1.23098i	0.253887	+	0.967234i	$0.418291\pi$
$523$	−16.2533	+	28.1515i	−0.710705	+	1.23098i	−0.964593	+	0.263744i	$0.915043\pi$
$524$		0			0
$525$			13.3678i			0.583420i
$526$		0			0
$527$	9.77570	−	5.64400i	0.425836	−	0.245857i
$528$		0			0
$529$	−30.2751	−	52.4380i	−1.31631	−	2.27991i
$530$		0			0
$531$	−26.7890	−	15.4666i	−1.16254	−	0.671194i
$532$		0			0
$533$	12.1683	−	9.06855i	0.527070	−	0.392803i
$534$		0			0
$535$	2.76155	+	1.59438i	0.119392	+	0.0689311i
$536$		0			0
$537$	13.8686	+	24.0212i	0.598476	+	1.03659i
$538$		0			0
$539$	−1.40656	+	0.812080i	−0.0605850	+	0.0349787i
$540$		0			0
$541$		−	10.6015i		−	0.455796i	−0.973685	−	0.227898i	$-0.926815\pi$
$541$		−	10.6015i		−	0.455796i	0.973685	−	0.227898i	$-0.0731852\pi$
$542$		0			0
$543$	−17.5650	+	30.4235i	−0.753786	+	1.30560i
$544$		0			0
$545$	−6.17364			−0.264450
$546$		0			0
$547$	−10.2327			−0.437519			−0.218760	−	0.975779i	$-0.570201\pi$
$547$	−10.2327			−0.437519			−0.218760	+	0.975779i	$0.570201\pi$
$548$		0			0
$549$	33.5758	−	58.1549i	1.43298	−	2.48199i
$550$		0			0
$551$			13.0286i			0.555038i
$552$		0			0
$553$	−0.850705	+	0.491155i	−0.0361757	+	0.0208860i
$554$		0			0
$555$	7.50037	+	12.9910i	0.318373	+	0.551438i
$556$		0			0
$557$	27.7067	+	15.9965i	1.17397	+	0.677793i	0.954612	−	0.297851i	$-0.0962700\pi$
$557$	27.7067	+	15.9965i	1.17397	+	0.677793i	0.219359	+	0.975644i	$0.429603\pi$
$558$		0			0
$559$	3.57133	−	0.419257i	0.151051	−	0.0177327i
$560$		0			0
$561$	7.74359	+	4.47076i	0.326934	+	0.188756i
$562$		0			0
$563$	−5.39566	−	9.34556i	−0.227400	−	0.393868i	0.729637	−	0.683835i	$-0.239689\pi$
$563$	−5.39566	−	9.34556i	−0.227400	−	0.393868i	−0.957037	+	0.289967i	$0.906356\pi$
$564$		0			0
$565$	1.59823	−	0.922737i	0.0672380	−	0.0388199i
$566$		0			0
$567$			0.895217i			0.0375956i
$568$		0			0
$569$	−12.3007	+	21.3054i	−0.515672	+	0.893170i	0.484163	+	0.874978i	$0.339124\pi$
$569$	−12.3007	+	21.3054i	−0.515672	+	0.893170i	−0.999835	+	0.0181917i	$0.994209\pi$
$570$		0			0
$571$	16.5724			0.693534			0.346767	−	0.937951i	$-0.387279\pi$
$571$	16.5724			0.693534			0.346767	+	0.937951i	$0.387279\pi$
$572$		0			0
$573$	34.6070			1.44573
$574$		0			0
$575$	21.6206	−	37.4480i	0.901641	−	1.56169i
$576$		0			0
$577$			14.6611i			0.610348i	0.952297	+	0.305174i	$0.0987147\pi$
$577$			14.6611i			0.610348i	−0.952297	+	0.305174i	$0.901285\pi$
$578$		0			0
$579$	28.4702	−	16.4373i	1.18318	−	0.683111i
$580$		0			0
$581$	4.45926	+	7.72366i	0.185001	+	0.320431i
$582$		0			0
$583$	12.5135	+	7.22467i	0.518256	+	0.299215i
$584$		0			0
$585$	−1.08754	−	9.26394i	−0.0449644	−	0.383017i
$586$		0			0
$587$	−30.5998	−	17.6668i	−1.26299	−	0.729186i	−0.289336	−	0.957227i	$-0.593435\pi$
$587$	−30.5998	−	17.6668i	−1.26299	−	0.729186i	−0.973652	+	0.228041i	$0.926768\pi$
$588$		0			0
$589$	7.21676	+	12.4998i	0.297362	+	0.515045i
$590$		0			0
$591$	4.40775	−	2.54481i	0.181310	−	0.104680i
$592$		0			0
$593$		−	16.4294i		−	0.674675i	−0.941384	−	0.337338i	$-0.890474\pi$
$593$		−	16.4294i		−	0.674675i	0.941384	−	0.337338i	$-0.109526\pi$
$594$		0			0
$595$	−0.505530	+	0.875603i	−0.0207247	+	0.0358962i
$596$		0			0
$597$	18.6307			0.762504
$598$		0			0
$599$	−12.0819			−0.493653			−0.246826	−	0.969060i	$-0.579388\pi$
$599$	−12.0819			−0.493653			−0.246826	+	0.969060i	$0.579388\pi$
$600$		0			0
$601$	−3.90743	+	6.76787i	−0.159387	+	0.276067i	−0.934648	−	0.355574i	$-0.884285\pi$
$601$	−3.90743	+	6.76787i	−0.159387	+	0.276067i	0.775261	+	0.631642i	$0.217619\pi$
$602$		0			0
$603$		−	41.7377i		−	1.69969i
$604$		0			0
$605$	3.75818	−	2.16979i	0.152792	−	0.0882144i
$606$		0			0
$607$	17.7825	+	30.8001i	0.721768	+	1.25014i	0.960291	+	0.279002i	$0.0900035\pi$
$607$	17.7825	+	30.8001i	0.721768	+	1.25014i	−0.238523	+	0.971137i	$0.576663\pi$
$608$		0			0
$609$	12.7987	+	7.38934i	0.518630	+	0.299431i
$610$		0			0
$611$	−14.9584	−	6.44347i	−0.605153	−	0.260675i
$612$		0			0
$613$	−10.3376	−	5.96839i	−0.417530	−	0.241061i	0.276490	−	0.961017i	$-0.410829\pi$
$613$	−10.3376	−	5.96839i	−0.417530	−	0.241061i	−0.694020	+	0.719956i	$0.744162\pi$
$614$		0			0
$615$	−3.08618	−	5.34542i	−0.124447	−	0.215548i
$616$		0			0
$617$	−20.4124	+	11.7851i	−0.821772	+	0.474450i	−0.851027	−	0.525122i	$-0.824020\pi$
$617$	−20.4124	+	11.7851i	−0.821772	+	0.474450i	0.0292550	+	0.999572i	$0.490687\pi$
$618$		0			0
$619$			28.5571i			1.14781i	0.818923	+	0.573904i	$0.194572\pi$
$619$			28.5571i			1.14781i	−0.818923	+	0.573904i	$0.805428\pi$
$620$		0			0
$621$	25.6355	−	44.4020i	1.02872	−	1.78179i
$622$		0			0
$623$	−12.0190			−0.481530
$624$		0			0
$625$	21.0328			0.841311
$626$		0			0
$627$	−5.71659	+	9.90142i	−0.228298	+	0.395425i
$628$		0			0
$629$		−	19.9292i		−	0.794628i
$630$		0			0
$631$	38.9646	−	22.4962i	1.55116	−	0.895561i	0.553109	−	0.833109i	$-0.313441\pi$
$631$	38.9646	−	22.4962i	1.55116	−	0.895561i	0.998048	−	0.0624526i	$-0.0198922\pi$
$632$		0			0
$633$	15.1460	+	26.2337i	0.602001	+	1.04270i
$634$		0			0
$635$	0.639763	+	0.369367i	0.0253882	+	0.0146579i
$636$		0			0
$637$	−2.15455	−	2.89101i	−0.0853662	−	0.114546i
$638$		0			0
$639$	−22.4409	−	12.9562i	−0.887747	−	0.512541i
$640$		0			0
$641$	−1.26650	−	2.19364i	−0.0500238	−	0.0866437i	0.839929	−	0.542696i	$-0.182596\pi$
$641$	−1.26650	−	2.19364i	−0.0500238	−	0.0866437i	−0.889953	+	0.456052i	$0.849263\pi$
$642$		0			0
$643$	−15.9150	+	9.18853i	−0.627627	+	0.362360i	−0.779832	−	0.625988i	$-0.784696\pi$
$643$	−15.9150	+	9.18853i	−0.627627	+	0.362360i	0.152206	+	0.988349i	$0.451362\pi$
$644$		0			0
$645$		−	1.46251i		−	0.0575863i
$646$		0			0
$647$	−10.4643	+	18.1248i	−0.411396	+	0.712558i	−0.995043	−	0.0994494i	$-0.968292\pi$
$647$	−10.4643	+	18.1248i	−0.411396	+	0.712558i	0.583647	+	0.812008i	$0.301625\pi$
$648$		0			0
$649$	−10.0783			−0.395609
$650$		0			0
$651$	16.3723			0.641680
$652$		0			0
$653$	24.0580	−	41.6696i	0.941461	−	1.63066i	0.178775	−	0.983890i	$-0.442786\pi$
$653$	24.0580	−	41.6696i	0.941461	−	1.63066i	0.762686	−	0.646769i	$-0.223880\pi$
$654$		0			0
$655$		−	4.50130i		−	0.175880i
$656$		0			0
$657$	51.1129	−	29.5100i	1.99410	−	1.15130i
$658$		0			0
$659$	−1.10819	−	1.91944i	−0.0431690	−	0.0747708i	0.843634	−	0.536919i	$-0.180412\pi$
$659$	−1.10819	−	1.91944i	−0.0431690	−	0.0747708i	−0.886803	+	0.462148i	$0.847079\pi$
$660$		0			0
$661$	−0.552034	−	0.318717i	−0.0214716	−	0.0123966i	0.489226	−	0.872157i	$-0.337279\pi$
$661$	−0.552034	−	0.318717i	−0.0214716	−	0.0123966i	−0.510697	+	0.859761i	$0.670613\pi$
$662$		0			0
$663$	−7.85287	+	18.2303i	−0.304980	+	0.708006i
$664$		0			0
$665$	−1.11960	−	0.646401i	−0.0434162	−	0.0250664i
$666$		0			0
$667$	−23.9024	−	41.4002i	−0.925506	−	1.60302i
$668$		0			0
$669$	−31.5390	+	18.2091i	−1.21937	+	0.704003i
$670$		0			0
$671$		−	21.8786i		−	0.844614i
$672$		0			0
$673$	7.70343	−	13.3427i	0.296945	−	0.514324i	−0.678490	−	0.734609i	$-0.737365\pi$
$673$	7.70343	−	13.3427i	0.296945	−	0.514324i	0.975436	+	0.220285i	$0.0706988\pi$
$674$		0			0
$675$	26.5352			1.02134
$676$		0			0
$677$	−11.6812			−0.448945			−0.224473	−	0.974480i	$-0.572066\pi$
$677$	−11.6812			−0.448945			−0.224473	+	0.974480i	$0.572066\pi$
$678$		0			0
$679$	2.21114	−	3.82981i	0.0848559	−	0.146975i
$680$		0			0
$681$			1.97565i			0.0757072i
$682$		0			0
$683$	−19.8419	+	11.4557i	−0.759227	+	0.438340i	−0.829018	−	0.559221i	$-0.811100\pi$
$683$	−19.8419	+	11.4557i	−0.759227	+	0.438340i	0.0697909	+	0.997562i	$0.477767\pi$
$684$		0			0
$685$	2.21020	+	3.82817i	0.0844473	+	0.146267i
$686$		0			0
$687$	44.7514	+	25.8372i	1.70737	+	0.985752i
$688$		0			0
$689$	−12.6901	+	29.4599i	−0.483454	+	1.12233i
$690$		0			0
$691$	40.9046	+	23.6163i	1.55608	+	0.898405i	0.997625	+	0.0688729i	$0.0219403\pi$
$691$	40.9046	+	23.6163i	1.55608	+	0.898405i	0.558458	+	0.829533i	$0.311393\pi$
$692$		0			0
$693$	4.04822	+	7.01172i	0.153779	+	0.266353i
$694$		0			0
$695$	2.26443	−	1.30737i	0.0858946	−	0.0495913i
$696$		0			0
$697$			8.20026i			0.310607i
$698$		0			0
$699$	37.8365	−	65.5347i	1.43111	−	2.47875i
$700$		0			0
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$		0			0
$703$	25.4827			0.961097
$704$		0			0
$705$	−3.31218	+	5.73686i	−0.124744	+	0.216063i
$706$		0			0
$707$		−	18.3026i		−	0.688342i
$708$		0			0
$709$	−15.4910	+	8.94374i	−0.581777	+	0.335889i	−0.761839	−	0.647766i	$-0.775703\pi$
$709$	−15.4910	+	8.94374i	−0.581777	+	0.335889i	0.180062	+	0.983655i	$0.442370\pi$
$710$		0			0
$711$	2.44841	+	4.24076i	0.0918224	+	0.159041i
$712$		0			0
$713$	−45.8644	−	26.4798i	−1.71764	−	0.991678i
$714$		0			0
$715$	−1.81600	−	2.43674i	−0.0679146	−	0.0911290i
$716$		0			0
$717$	−40.6667	−	23.4789i	−1.51872	−	0.876836i
$718$		0			0
$719$	−4.56317	−	7.90364i	−0.170178	−	0.294756i	0.768304	−	0.640085i	$-0.221101\pi$
$719$	−4.56317	−	7.90364i	−0.170178	−	0.294756i	−0.938482	+	0.345329i	$0.887767\pi$
$720$		0			0
$721$	4.34784	−	2.51023i	0.161922	−	0.0934858i
$722$		0			0
$723$			49.2048i			1.82995i
$724$		0			0
$725$	12.3706	−	21.4266i	0.459434	−	0.795763i
$726$		0			0
$727$	−33.6859			−1.24934			−0.624670	−	0.780889i	$-0.714767\pi$
$727$	−33.6859			−1.24934			−0.624670	+	0.780889i	$0.714767\pi$
$728$		0			0
$729$	−43.0880			−1.59585
$730$		0			0
$731$	−0.971507	+	1.68270i	−0.0359325	+	0.0622369i
$732$		0			0
$733$			46.4344i			1.71509i	0.514406	+	0.857547i	$0.328013\pi$
$733$			46.4344i			1.71509i	−0.514406	+	0.857547i	$0.671987\pi$
$734$		0			0
$735$	−1.26999	+	0.733228i	−0.0468442	+	0.0270455i
$736$		0			0
$737$	−6.79927	−	11.7767i	−0.250454	−	0.433799i
$738$		0			0
$739$	1.60237	+	0.925127i	0.0589440	+	0.0340314i	0.529182	−	0.848508i	$-0.322499\pi$
$739$	1.60237	+	0.925127i	0.0589440	+	0.0340314i	−0.470238	+	0.882539i	$0.655832\pi$
$740$		0			0
$741$	−23.3104	−	10.0412i	−0.856328	−	0.368871i
$742$		0			0
$743$	−28.7095	−	16.5755i	−1.05325	−	0.608094i	−0.129693	−	0.991554i	$-0.541399\pi$
$743$	−28.7095	−	16.5755i	−1.05325	−	0.608094i	−0.923558	+	0.383460i	$0.874732\pi$
$744$		0			0
$745$	0.873120	+	1.51229i	0.0319886	+	0.0554059i
$746$		0			0
$747$	38.5024	−	22.2294i	1.40873	−	0.813331i
$748$		0			0
$749$		−	6.14456i		−	0.224517i
$750$		0			0
$751$	10.3871	−	17.9910i	0.379032	−	0.656503i	−0.611890	−	0.790943i	$-0.709590\pi$
$751$	10.3871	−	17.9910i	0.379032	−	0.656503i	0.990922	+	0.134441i	$0.0429237\pi$
$752$		0			0
$753$	−18.2257			−0.664182
$754$		0			0
$755$	−6.56824			−0.239043
$756$		0			0
$757$	−21.8075	+	37.7717i	−0.792607	+	1.37283i	0.131741	+	0.991284i	$0.457943\pi$
$757$	−21.8075	+	37.7717i	−0.792607	+	1.37283i	−0.924348	+	0.381551i	$0.875390\pi$
$758$		0			0
$759$		−	41.9508i		−	1.52272i
$760$		0			0
$761$	10.7302	−	6.19511i	0.388971	−	0.224573i	−0.292743	−	0.956191i	$-0.594568\pi$
$761$	10.7302	−	6.19511i	0.388971	−	0.224573i	0.681714	+	0.731619i	$0.261235\pi$
$762$		0			0
$763$	5.94812	+	10.3025i	0.215337	+	0.372974i
$764$		0			0
$765$	4.36488	+	2.52007i	0.157813	+	0.0911132i
$766$		0			0
$767$	−2.60862	−	22.2208i	−0.0941917	−	0.802347i
$768$		0			0
$769$	−4.80955	−	2.77680i	−0.173437	−	0.100134i	0.410769	−	0.911740i	$-0.365260\pi$
$769$	−4.80955	−	2.77680i	−0.173437	−	0.100134i	−0.584205	+	0.811606i	$0.698594\pi$
$770$		0			0
$771$	−5.18750	−	8.98501i	−0.186823	−	0.323587i
$772$		0			0
$773$	37.9355	−	21.9021i	1.36445	−	0.787764i	0.374235	−	0.927334i	$-0.377905\pi$
$773$	37.9355	−	21.9021i	1.36445	−	0.787764i	0.990212	+	0.139570i	$0.0445721\pi$
$774$		0			0
$775$		−	27.4092i		−	0.984566i
$776$		0			0
$777$	14.4528	−	25.0330i	0.518491	−	0.898052i
$778$		0			0
$779$	−10.4853			−0.375677
$780$		0			0
$781$	−8.44253			−0.302098
$782$		0			0
$783$	14.6678	−	25.4054i	0.524185	−	0.907916i
$784$		0			0
$785$			5.38113i			0.192061i
$786$		0			0
$787$	−21.4782	+	12.4005i	−0.765616	+	0.442029i	−0.831309	−	0.555811i	$-0.812408\pi$
$787$	−21.4782	+	12.4005i	−0.765616	+	0.442029i	0.0656923	+	0.997840i	$0.479074\pi$
$788$		0			0
$789$	25.8831	+	44.8308i	0.921462	+	1.59602i
$790$		0			0
$791$	−3.07969	−	1.77806i	−0.109501	−	0.0632206i
$792$		0			0
$793$	48.2381	−	5.66293i	1.71299	−	0.201096i
$794$		0			0
$795$	11.2985	+	6.52316i	0.400715	+	0.231353i
$796$		0			0
$797$	−8.23575	−	14.2647i	−0.291725	−	0.505283i	0.682492	−	0.730893i	$-0.260896\pi$
$797$	−8.23575	−	14.2647i	−0.291725	−	0.505283i	−0.974218	+	0.225610i	$0.927563\pi$
$798$		0			0
$799$	7.62168	−	4.40038i	0.269636	−	0.155674i
$800$		0			0
$801$			59.9146i			2.11698i
$802$		0			0
$803$	9.61464	−	16.6530i	0.339293	−	0.587673i
$804$		0			0
$805$	4.74357			0.167189
$806$		0			0
$807$	77.8301			2.73975
$808$		0			0
$809$	−0.690968	+	1.19679i	−0.0242932	+	0.0420770i	−0.877916	−	0.478814i	$-0.841067\pi$
$809$	−0.690968	+	1.19679i	−0.0242932	+	0.0420770i	0.853623	+	0.520891i	$0.174400\pi$
$810$		0			0
$811$			6.83571i			0.240034i	0.992772	+	0.120017i	$0.0382950\pi$
$811$			6.83571i			0.240034i	−0.992772	+	0.120017i	$0.961705\pi$
$812$		0			0
$813$	15.9538	−	9.21093i	0.559524	−	0.323041i
$814$		0			0
$815$	−4.08767	−	7.08004i	−0.143185	−	0.248003i
$816$		0			0
$817$	−2.15160	−	1.24223i	−0.0752750	−	0.0434601i
$818$		0			0
$819$	−14.4117	+	10.7404i	−0.503585	+	0.375300i
$820$		0			0
$821$	−9.13009	−	5.27126i	−0.318642	−	0.183968i	0.332145	−	0.943228i	$-0.392228\pi$
$821$	−9.13009	−	5.27126i	−0.318642	−	0.183968i	−0.650787	+	0.759260i	$0.725561\pi$
$822$		0			0
$823$	−7.41652	−	12.8458i	−0.258524	−	0.447776i	0.707323	−	0.706891i	$-0.249903\pi$
$823$	−7.41652	−	12.8458i	−0.258524	−	0.447776i	−0.965847	+	0.259114i	$0.916569\pi$
$824$		0			0
$825$	18.8027	−	10.8558i	0.654627	−	0.377949i
$826$		0			0
$827$			55.6758i			1.93604i	0.250879	+	0.968018i	$0.419280\pi$
$827$			55.6758i			1.93604i	−0.250879	+	0.968018i	$0.580720\pi$
$828$		0			0
$829$	−0.0232424	+	0.0402570i	−0.000807242	+	0.00139818i	−0.866429	−	0.499301i	$-0.833590\pi$
$829$	−0.0232424	+	0.0402570i	−0.000807242	+	0.00139818i	0.865622	+	0.500699i	$0.166924\pi$
$830$		0			0
$831$	−15.3775			−0.533438
$832$		0			0
$833$	1.94825			0.0675030
$834$		0			0
$835$	−4.25508	+	7.37002i	−0.147253	+	0.255050i
$836$		0			0
$837$		−	32.4990i		−	1.12333i
$838$		0			0
$839$	−22.1248	+	12.7738i	−0.763833	+	0.440999i	−0.830670	−	0.556765i	$-0.812043\pi$
$839$	−22.1248	+	12.7738i	−0.763833	+	0.440999i	0.0668370	+	0.997764i	$0.478709\pi$
$840$		0			0
$841$	0.823775	+	1.42682i	0.0284060	+	0.0492007i
$842$		0			0
$843$	8.66886	+	5.00497i	0.298572	+	0.172380i
$844$		0			0
$845$	4.90250	−	4.63464i	0.168651	−	0.159437i
$846$		0			0
$847$	−7.24180	−	4.18105i	−0.248831	−	0.143663i
$848$		0			0
$849$	19.9770	+	34.6012i	0.685609	+	1.18751i
$850$		0			0
$851$	−80.9745	+	46.7507i	−2.77577	+	1.60259i
$852$		0			0
$853$			22.6671i			0.776105i	0.921637	+	0.388053i	$0.126852\pi$
$853$			22.6671i			0.776105i	−0.921637	+	0.388053i	$0.873148\pi$
$854$		0			0
$855$	−3.22231	+	5.58120i	−0.110201	+	0.190873i
$856$		0			0
$857$	37.0535			1.26572			0.632862	−	0.774264i	$-0.281880\pi$
$857$	37.0535			1.26572			0.632862	+	0.774264i	$0.281880\pi$
$858$		0			0
$859$	4.24339			0.144782			0.0723912	−	0.997376i	$-0.476937\pi$
$859$	4.24339			0.144782			0.0723912	+	0.997376i	$0.476937\pi$
$860$		0			0
$861$	−5.94689	+	10.3003i	−0.202669	+	0.351034i
$862$		0			0
$863$			7.50051i			0.255320i	0.991818	+	0.127660i	$0.0407467\pi$
$863$			7.50051i			0.255320i	−0.991818	+	0.127660i	$0.959253\pi$
$864$		0			0
$865$	0.135438	−	0.0781951i	0.00460503	−	0.00265871i
$866$		0			0
$867$	18.6562	+	32.3135i	0.633598	+	1.09742i
$868$		0			0
$869$	1.38168	+	0.797714i	0.0468703	+	0.0270606i
$870$		0			0
$871$	24.2054	−	18.0393i	0.820170	−	0.611238i
$872$		0			0
$873$	−19.0916	−	11.0225i	−0.646153	−	0.373057i
$874$		0			0
$875$	2.52490	+	4.37326i	0.0853573	+	0.147843i
$876$		0			0
$877$	−24.4996	+	14.1448i	−0.827291	+	0.477637i	−0.852924	−	0.522035i	$-0.825173\pi$
$877$	−24.4996	+	14.1448i	−0.827291	+	0.477637i	0.0256330	+	0.999671i	$0.491840\pi$
$878$		0			0
$879$		−	23.5933i		−	0.795781i
$880$		0			0
$881$	−19.7860	+	34.2704i	−0.666609	+	1.15460i	0.312238	+	0.950004i	$0.398921\pi$
$881$	−19.7860	+	34.2704i	−0.666609	+	1.15460i	−0.978846	+	0.204596i	$0.934412\pi$
$882$		0			0
$883$	28.3609			0.954419			0.477209	−	0.878790i	$-0.341648\pi$
$883$	28.3609			0.954419			0.477209	+	0.878790i	$0.341648\pi$
$884$		0			0
$885$	−9.09974			−0.305884
$886$		0			0
$887$	−21.8593	+	37.8614i	−0.733963	+	1.27126i	0.221214	+	0.975225i	$0.428998\pi$
$887$	−21.8593	+	37.8614i	−0.733963	+	1.27126i	−0.955177	+	0.296036i	$0.904335\pi$
$888$		0			0
$889$		−	1.42350i		−	0.0477426i
$890$		0			0
$891$	1.25918	−	0.726988i	0.0421841	−	0.0243550i
$892$		0			0
$893$	5.62659	+	9.74554i	0.188287	+	0.326122i
$894$		0			0
$895$	4.41152	+	2.54699i	0.147461	+	0.0851366i
$896$		0			0
$897$	92.4934	−	10.8583i	3.08826	−	0.362547i
$898$		0			0
$899$	−26.2422	−	15.1509i	−0.875227	−	0.505312i
$900$		0			0
$901$	−8.66632	−	15.0105i	−0.288717	−	0.500073i
$902$		0			0
$903$	−2.44061	+	1.40909i	−0.0812185	+	0.0468915i
$904$		0			0
$905$			6.45167i			0.214461i
$906$		0			0
$907$	18.3493	−	31.7818i	0.609277	−	1.05530i	−0.382083	−	0.924128i	$-0.624793\pi$
$907$	18.3493	−	31.7818i	0.609277	−	1.05530i	0.991360	−	0.131171i	$-0.0418736\pi$
$908$		0			0
$909$	−91.2387			−3.02620
$910$		0			0
$911$	35.5211			1.17686			0.588432	−	0.808546i	$-0.299745\pi$
$911$	35.5211			1.17686			0.588432	+	0.808546i	$0.299745\pi$
$912$		0			0
$913$	7.24254	−	12.5444i	0.239693	−	0.415161i
$914$		0			0
$915$		−	19.7542i		−	0.653054i
$916$		0			0
$917$	−7.51168	+	4.33687i	−0.248057	+	0.143216i
$918$		0			0
$919$	10.9667	+	18.9949i	0.361758	+	0.626583i	0.988250	−	0.152844i	$-0.0488434\pi$
$919$	10.9667	+	18.9949i	0.361758	+	0.626583i	−0.626492	+	0.779428i	$0.715510\pi$
$920$		0			0
$921$	20.3940	+	11.7745i	0.672005	+	0.387982i
$922$		0			0
$923$	−2.18521	−	18.6142i	−0.0719272	−	0.612693i
$924$		0			0
$925$	−41.9082	−	24.1957i	−1.37793	−	0.795549i
$926$		0			0
$927$	−12.5135	−	21.6740i	−0.410997	−	0.711867i
$928$		0			0
$929$	−13.4383	+	7.75858i	−0.440895	+	0.254551i	−0.703977	−	0.710223i	$-0.748594\pi$
$929$	−13.4383	+	7.75858i	−0.440895	+	0.254551i	0.263082	+	0.964773i	$0.415261\pi$
$930$		0			0
$931$			2.49115i			0.0816443i
$932$		0			0
$933$	20.6602	−	35.7845i	0.676385	−	1.17153i
$934$		0			0
$935$	1.64212			0.0537031
$936$		0			0
$937$	40.8110			1.33324			0.666618	−	0.745399i	$-0.267741\pi$
$937$	40.8110			1.33324			0.666618	+	0.745399i	$0.267741\pi$
$938$		0			0
$939$	−24.2067	+	41.9273i	−0.789957	+	1.36825i
$940$		0			0
$941$		−	51.5936i		−	1.68190i	−0.541109	−	0.840952i	$-0.681996\pi$
$941$		−	51.5936i		−	1.68190i	0.541109	−	0.840952i	$-0.318004\pi$
$942$		0			0
$943$	33.3186	−	19.2365i	1.08500	−	0.626427i
$944$		0			0
$945$	1.45546	+	2.52092i	0.0473460	+	0.0820057i
$946$		0			0
$947$	4.31462	+	2.49105i	0.140206	+	0.0809482i	0.568462	−	0.822709i	$-0.307539\pi$
$947$	4.31462	+	2.49105i	0.140206	+	0.0809482i	−0.428256	+	0.903657i	$0.640872\pi$
$948$		0			0
$949$	39.2054	+	16.8881i	1.27266	+	0.548210i
$950$		0			0
$951$	34.2608	+	19.7805i	1.11098	+	0.641426i
$952$		0			0
$953$	15.1163	+	26.1822i	0.489664	+	0.848123i	0.999929	−	0.0118941i	$-0.00378608\pi$
$953$	15.1163	+	26.1822i	0.489664	+	0.848123i	−0.510265	+	0.860017i	$0.670453\pi$
$954$		0			0
$955$	5.50413	−	3.17781i	0.178110	−	0.102832i
$956$		0			0
$957$		−	24.0029i		−	0.775904i
$958$		0			0
$959$	4.25892	−	7.37667i	0.137528	−	0.238205i
$960$		0			0
$961$	−2.56939			−0.0828835
$962$		0			0
$963$	−30.6306			−0.987058
$964$		0			0
$965$	3.01873	−	5.22860i	0.0971764	−	0.168315i
$966$		0			0
$967$			29.9990i			0.964703i	0.875978	+	0.482352i	$0.160217\pi$
$967$			29.9990i			0.964703i	−0.875978	+	0.482352i	$0.839783\pi$
$968$		0			0
$969$	11.8772	−	6.85731i	0.381551	−	0.220288i
$970$		0			0
$971$	22.0620	+	38.2125i	0.708003	+	1.22630i	0.965597	+	0.260044i	$0.0837371\pi$
$971$	22.0620	+	38.2125i	0.708003	+	1.22630i	−0.257594	+	0.966253i	$0.582930\pi$
$972$		0			0
$973$	−4.36342	−	2.51922i	−0.139885	−	0.0807625i
$974$		0			0
$975$	28.8016	+	38.6465i	0.922391	+	1.23768i
$976$		0			0
$977$	−12.9925	−	7.50121i	−0.415666	−	0.239985i	0.277555	−	0.960710i	$-0.410476\pi$
$977$	−12.9925	−	7.50121i	−0.415666	−	0.239985i	−0.693221	+	0.720725i	$0.743809\pi$
$978$		0			0
$979$	9.76037	+	16.9055i	0.311943	+	0.540301i
$980$		0			0
$981$	51.3577	−	29.6514i	1.63973	−	0.946696i
$982$		0			0
$983$		−	6.01856i		−	0.191962i	−0.995383	−	0.0959812i	$-0.969401\pi$
$983$		−	6.01856i		−	0.191962i	0.995383	−	0.0959812i	$-0.0305989\pi$
$984$		0			0
$985$	0.467358	−	0.809488i	0.0148913	−	0.0257924i
$986$		0			0
$987$	12.7647			0.406306
$988$		0			0
$989$	9.11600			0.289872
$990$		0			0
$991$	16.9200	−	29.3063i	0.537482	−	0.930946i	−0.461557	−	0.887111i	$-0.652709\pi$
$991$	16.9200	−	29.3063i	0.537482	−	0.930946i	0.999039	−	0.0438356i	$-0.0139578\pi$
$992$		0			0
$993$		−	19.5542i		−	0.620535i
$994$		0			0
$995$	2.96315	−	1.71078i	0.0939382	−	0.0542353i
$996$		0			0
$997$	−13.1608	−	22.7951i	−0.416805	−	0.721928i	0.578811	−	0.815462i	$-0.303517\pi$
$997$	−13.1608	−	22.7951i	−0.416805	−	0.721928i	−0.995616	+	0.0935340i	$0.970184\pi$
$998$		0			0
$999$	−49.6904	−	28.6888i	−1.57213	−	0.907672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.c.225.1		12
4.3	odd	2		91.2.q.a.43.2	yes	12
12.11	even	2		819.2.ct.a.316.5		12
13.10	even	6	inner	1456.2.cc.c.673.1		12
28.3	even	6		637.2.u.i.30.5		12
28.11	odd	6		637.2.u.h.30.5		12
28.19	even	6		637.2.k.g.459.5		12
28.23	odd	6		637.2.k.h.459.5		12
28.27	even	2		637.2.q.h.589.2		12
52.7	even	12		1183.2.a.p.1.1		6
52.19	even	12		1183.2.a.m.1.6		6
52.23	odd	6		91.2.q.a.36.2	✓	12
52.35	odd	6		1183.2.c.i.337.10		12
52.43	odd	6		1183.2.c.i.337.3		12
156.23	even	6		819.2.ct.a.127.5		12
364.23	odd	6		637.2.u.h.361.5		12
364.75	even	6		637.2.u.i.361.5		12
364.111	odd	12		8281.2.a.ch.1.1		6
364.179	odd	6		637.2.k.h.569.2		12
364.279	odd	12		8281.2.a.by.1.6		6
364.283	even	6		637.2.k.g.569.2		12
364.335	even	6		637.2.q.h.491.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	52.23	odd	6
91.2.q.a.43.2	yes	12	4.3	odd	2
637.2.k.g.459.5		12	28.19	even	6
637.2.k.g.569.2		12	364.283	even	6
637.2.k.h.459.5		12	28.23	odd	6
637.2.k.h.569.2		12	364.179	odd	6
637.2.q.h.491.2		12	364.335	even	6
637.2.q.h.589.2		12	28.27	even	2
637.2.u.h.30.5		12	28.11	odd	6
637.2.u.h.361.5		12	364.23	odd	6
637.2.u.i.30.5		12	28.3	even	6
637.2.u.i.361.5		12	364.75	even	6
819.2.ct.a.127.5		12	156.23	even	6
819.2.ct.a.316.5		12	12.11	even	2
1183.2.a.m.1.6		6	52.19	even	12
1183.2.a.p.1.1		6	52.7	even	12
1183.2.c.i.337.3		12	52.43	odd	6
1183.2.c.i.337.10		12	52.35	odd	6
1456.2.cc.c.225.1		12	1.1	even	1	trivial
1456.2.cc.c.673.1		12	13.10	even	6	inner
8281.2.a.by.1.6		6	364.279	odd	12
8281.2.a.ch.1.1		6	364.111	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41289 + 2.44719i) q^{3} +0.518957i q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})\)	\(q+(-1.41289 + 2.44719i) q^{3} +0.518957i q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.49250 - 4.31714i) q^{9} +(-1.40656 - 0.812080i) q^{11} +(1.42641 - 3.31140i) q^{13} +(-1.26999 - 0.733228i) q^{15} +(0.974127 + 1.68724i) q^{17} +(-2.15740 + 1.24558i) q^{19} +2.82577i q^{21} +(4.57029 - 7.91598i) q^{23} +4.73068 q^{25} +5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} -5.79391i q^{31} +(3.97463 - 2.29475i) q^{33} +(0.259479 + 0.449430i) q^{35} +(-8.85879 - 5.11463i) q^{37} +(6.08826 + 8.16934i) q^{39} +(3.64513 + 2.10452i) q^{41} +(0.498655 + 0.863697i) q^{43} +(2.24041 - 1.29350i) q^{45} -4.51725i q^{47} +(0.500000 - 0.866025i) q^{49} -5.50532 q^{51} -8.89651 q^{53} +(0.421434 - 0.729946i) q^{55} -7.03944i q^{57} +(5.37392 - 3.10263i) q^{59} +(6.73536 + 11.6660i) q^{61} +(-4.31714 - 2.49250i) q^{63} +(1.71847 + 0.740247i) q^{65} +(7.25094 + 4.18633i) q^{67} +(12.9146 + 22.3688i) q^{69} +(4.50168 - 2.59905i) q^{71} +11.8395i q^{73} +(-6.68392 + 11.5769i) q^{75} -1.62416 q^{77} -0.982310 q^{79} +(-0.447609 + 0.775281i) q^{81} +8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(7.38934 + 12.7987i) q^{87} +(-10.4087 - 6.00949i) q^{89} +(-0.420388 - 3.58096i) q^{91} +(14.1788 + 8.18614i) q^{93} +(-0.646401 - 1.11960i) q^{95} +(3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^9	\( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Introduction

L-functions

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Database

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