LMFDB - Embedded newform 1320.2.bw.e.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7 x^{10} - 6 x^{9} + 130 x^{8} - 768 x^{7} + 3132 x^{6} - 7488 x^{5} + 18450 x^{4} + \cdots + 9801 $ x^12 - 2x^11 + 7x^10 - 6x^9 + 130x^8 - 768x^7 + 3132x^6 - 7488x^5 + 18450x^4 - 35046x^3 + 44847x^2 - 19602*x + 9801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			961.1
Root			$0.176245 + 0.542427i$ of defining polynomial
Character	$\chi$	$=$	1320.961
Dual form			1320.2.bw.e.1081.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.25654 - 3.86723i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.25654 - 3.86723i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-0.495215 + 3.27945i) q^{11} +(2.46563 + 1.79139i) q^{13} +(-0.309017 - 0.951057i) q^{15} +(-5.92380 + 4.30389i) q^{17} +(2.03312 - 6.25731i) q^{19} +4.06625 q^{21} +8.23914 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-2.19833 - 6.76576i) q^{29} +(-4.32961 - 3.14565i) q^{31} +(-2.96591 - 1.48438i) q^{33} +(3.28966 + 2.39008i) q^{35} +(-3.08098 - 9.48230i) q^{37} +(-2.46563 + 1.79139i) q^{39} +(2.19167 - 6.74528i) q^{41} +7.76770 q^{43} +1.00000 q^{45} +(0.533019 - 1.64046i) q^{47} +(-7.71346 + 5.60416i) q^{49} +(-2.26269 - 6.96384i) q^{51} +(-5.10005 - 3.70540i) q^{53} +(-1.52697 - 2.94421i) q^{55} +(5.32279 + 3.86723i) q^{57} +(-1.01350 - 3.11922i) q^{59} +(7.05002 - 5.12214i) q^{61} +(-1.25654 + 3.86723i) q^{63} -3.04769 q^{65} +1.56190 q^{67} +(-2.54603 + 7.83588i) q^{69} +(7.31954 - 5.31795i) q^{71} +(1.22849 + 3.78092i) q^{73} +(0.809017 + 0.587785i) q^{75} +(13.3046 - 2.20564i) q^{77} +(-0.511044 - 0.371295i) q^{79} +(0.309017 + 0.951057i) q^{81} +(8.84492 - 6.42621i) q^{83} +(2.26269 - 6.96384i) q^{85} +7.11394 q^{87} -5.13820 q^{89} +(3.82955 - 11.7861i) q^{91} +(4.32961 - 3.14565i) q^{93} +(2.03312 + 6.25731i) q^{95} +(-4.54553 - 3.30252i) q^{97} +(2.32825 - 2.36205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9} + 6 q^{11} + 12 q^{13} + 3 q^{15} - 13 q^{17} + 20 q^{23} - 3 q^{25} + 3 q^{27} - 3 q^{29} - 3 q^{31} - q^{33} + 5 q^{35} + 5 q^{37} - 12 q^{39} + q^{41} + 6 q^{43} + 12 q^{45} - 10 q^{47} - 12 q^{51} - 3 q^{53} + q^{55} + 5 q^{57} + 23 q^{59} - 7 q^{61} - 5 q^{63} - 28 q^{65} + 44 q^{67} + 5 q^{69} - 9 q^{71} - 27 q^{73} + 3 q^{75} + 65 q^{77} - q^{79} - 3 q^{81} - 21 q^{83} + 12 q^{85} + 28 q^{87} + 32 q^{89} - 19 q^{91} + 3 q^{93} + 5 q^{97} - 4 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9 + 6 * q^11 + 12 * q^13 + 3 * q^15 - 13 * q^17 + 20 * q^23 - 3 * q^25 + 3 * q^27 - 3 * q^29 - 3 * q^31 - q^33 + 5 * q^35 + 5 * q^37 - 12 * q^39 + q^41 + 6 * q^43 + 12 * q^45 - 10 * q^47 - 12 * q^51 - 3 * q^53 + q^55 + 5 * q^57 + 23 * q^59 - 7 * q^61 - 5 * q^63 - 28 * q^65 + 44 * q^67 + 5 * q^69 - 9 * q^71 - 27 * q^73 + 3 * q^75 + 65 * q^77 - q^79 - 3 * q^81 - 21 * q^83 + 12 * q^85 + 28 * q^87 + 32 * q^89 - 19 * q^91 + 3 * q^93 + 5 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−1.25654	−	3.86723i	−0.474927	−	1.46168i	−0.846056	−	0.533094i	$-0.821029\pi$
$7$	−1.25654	−	3.86723i	−0.474927	−	1.46168i	0.371129	−	0.928581i	$-0.378971\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−0.495215	+	3.27945i	−0.149313	+	0.988790i
$11$	−0.495215	+	3.27945i	−0.149313	+	0.988790i
$12$		0			0
$13$	2.46563	+	1.79139i	0.683844	+	0.496842i	0.874631	−	0.484790i	$-0.161104\pi$
$13$	2.46563	+	1.79139i	0.683844	+	0.496842i	−0.190787	+	0.981632i	$0.561104\pi$
$14$		0			0
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$		0			0
$17$	−5.92380	+	4.30389i	−1.43673	+	1.04385i	−0.448020	+	0.894024i	$0.647871\pi$
$17$	−5.92380	+	4.30389i	−1.43673	+	1.04385i	−0.988713	+	0.149824i	$0.952129\pi$
$18$		0			0
$19$	2.03312	−	6.25731i	0.466431	−	1.43553i	−0.390744	−	0.920499i	$-0.627782\pi$
$19$	2.03312	−	6.25731i	0.466431	−	1.43553i	0.857174	−	0.515026i	$-0.172218\pi$
$20$		0			0
$21$	4.06625			0.887328
$22$		0			0
$23$	8.23914			1.71798			0.858989	−	0.511993i	$-0.171093\pi$
$23$	8.23914			1.71798			0.858989	+	0.511993i	$0.171093\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	−2.19833	−	6.76576i	−0.408219	−	1.25637i	−0.918177	−	0.396170i	$-0.870339\pi$
$29$	−2.19833	−	6.76576i	−0.408219	−	1.25637i	0.509958	−	0.860199i	$-0.329661\pi$
$30$		0			0
$31$	−4.32961	−	3.14565i	−0.777621	−	0.564975i	0.126643	−	0.991948i	$-0.459580\pi$
$31$	−4.32961	−	3.14565i	−0.777621	−	0.564975i	−0.904264	+	0.426973i	$0.859580\pi$
$32$		0			0
$33$	−2.96591	−	1.48438i	−0.516298	−	0.258398i
$34$		0			0
$35$	3.28966	+	2.39008i	0.556055	+	0.403997i
$36$		0			0
$37$	−3.08098	−	9.48230i	−0.506511	−	1.55888i	−0.798216	−	0.602372i	$-0.794223\pi$
$37$	−3.08098	−	9.48230i	−0.506511	−	1.55888i	0.291705	−	0.956508i	$-0.405777\pi$
$38$		0			0
$39$	−2.46563	+	1.79139i	−0.394818	+	0.286852i
$40$		0			0
$41$	2.19167	−	6.74528i	0.342282	−	1.05344i	−0.620741	−	0.784016i	$-0.713168\pi$
$41$	2.19167	−	6.74528i	0.342282	−	1.05344i	0.963023	−	0.269420i	$-0.0868319\pi$
$42$		0			0
$43$	7.76770			1.18456			0.592282	−	0.805731i	$-0.298227\pi$
$43$	7.76770			1.18456			0.592282	+	0.805731i	$0.298227\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	0.533019	−	1.64046i	0.0777488	−	0.239286i	−0.904627	−	0.426205i	$-0.859850\pi$
$47$	0.533019	−	1.64046i	0.0777488	−	0.239286i	0.982375	+	0.186919i	$0.0598502\pi$
$48$		0			0
$49$	−7.71346	+	5.60416i	−1.10192	+	0.800594i
$50$		0			0
$51$	−2.26269	−	6.96384i	−0.316840	−	0.975133i
$52$		0			0
$53$	−5.10005	−	3.70540i	−0.700545	−	0.508976i	0.179565	−	0.983746i	$-0.442531\pi$
$53$	−5.10005	−	3.70540i	−0.700545	−	0.508976i	−0.880110	+	0.474770i	$0.842531\pi$
$54$		0			0
$55$	−1.52697	−	2.94421i	−0.205897	−	0.396997i
$56$		0			0
$57$	5.32279	+	3.86723i	0.705020	+	0.512227i
$58$		0			0
$59$	−1.01350	−	3.11922i	−0.131946	−	0.406088i	0.863157	−	0.504936i	$-0.168484\pi$
$59$	−1.01350	−	3.11922i	−0.131946	−	0.406088i	−0.995102	+	0.0988486i	$0.968484\pi$
$60$		0			0
$61$	7.05002	−	5.12214i	0.902662	−	0.655823i	−0.0364860	−	0.999334i	$-0.511616\pi$
$61$	7.05002	−	5.12214i	0.902662	−	0.655823i	0.939148	+	0.343511i	$0.111616\pi$
$62$		0			0
$63$	−1.25654	+	3.86723i	−0.158309	+	0.487225i
$64$		0			0
$65$	−3.04769			−0.378020
$66$		0			0
$67$	1.56190			0.190817			0.0954085	−	0.995438i	$-0.469584\pi$
$67$	1.56190			0.190817			0.0954085	+	0.995438i	$0.469584\pi$
$68$		0			0
$69$	−2.54603	+	7.83588i	−0.306506	+	0.943330i
$70$		0			0
$71$	7.31954	−	5.31795i	0.868669	−	0.631125i	−0.0615604	−	0.998103i	$-0.519608\pi$
$71$	7.31954	−	5.31795i	0.868669	−	0.631125i	0.930229	+	0.366978i	$0.119608\pi$
$72$		0			0
$73$	1.22849	+	3.78092i	0.143784	+	0.442523i	0.996853	−	0.0792765i	$-0.0252610\pi$
$73$	1.22849	+	3.78092i	0.143784	+	0.442523i	−0.853068	+	0.521799i	$0.825261\pi$
$74$		0			0
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$		0			0
$77$	13.3046	−	2.20564i	1.51620	−	0.251356i
$78$		0			0
$79$	−0.511044	−	0.371295i	−0.0574970	−	0.0417740i	0.558666	−	0.829393i	$-0.311314\pi$
$79$	−0.511044	−	0.371295i	−0.0574970	−	0.0417740i	−0.616163	+	0.787619i	$0.711314\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	8.84492	−	6.42621i	0.970856	−	0.705368i	0.0152092	−	0.999884i	$-0.495159\pi$
$83$	8.84492	−	6.42621i	0.970856	−	0.705368i	0.955646	+	0.294516i	$0.0951586\pi$
$84$		0			0
$85$	2.26269	−	6.96384i	0.245423	−	0.755335i
$86$		0			0
$87$	7.11394			0.762694
$88$		0			0
$89$	−5.13820			−0.544648			−0.272324	−	0.962206i	$-0.587792\pi$
$89$	−5.13820			−0.544648			−0.272324	+	0.962206i	$0.587792\pi$
$90$		0			0
$91$	3.82955	−	11.7861i	0.401445	−	1.23552i
$92$		0			0
$93$	4.32961	−	3.14565i	0.448960	−	0.326188i
$94$		0			0
$95$	2.03312	+	6.25731i	0.208594	+	0.641987i
$96$		0			0
$97$	−4.54553	−	3.30252i	−0.461528	−	0.335320i	0.332602	−	0.943067i	$-0.392073\pi$
$97$	−4.54553	−	3.30252i	−0.461528	−	0.335320i	−0.794131	+	0.607747i	$0.792073\pi$
$98$		0			0
$99$	2.32825	−	2.36205i	0.233998	−	0.237395i
$100$		0			0
$101$	10.6574	+	7.74304i	1.06045	+	0.770462i	0.974171	−	0.225809i	$-0.0725027\pi$
$101$	10.6574	+	7.74304i	1.06045	+	0.770462i	0.0862780	+	0.996271i	$0.472503\pi$
$102$		0			0
$103$	5.06260	+	15.5811i	0.498833	+	1.53525i	0.810897	+	0.585188i	$0.198979\pi$
$103$	5.06260	+	15.5811i	0.498833	+	1.53525i	−0.312065	+	0.950061i	$0.601021\pi$
$104$		0			0
$105$	−3.28966	+	2.39008i	−0.321038	+	0.233248i
$106$		0			0
$107$	−1.05551	+	3.24853i	−0.102040	+	0.314047i	−0.989024	−	0.147752i	$-0.952796\pi$
$107$	−1.05551	+	3.24853i	−0.102040	+	0.314047i	0.886984	+	0.461800i	$0.152796\pi$
$108$		0			0
$109$	−6.75525			−0.647035			−0.323518	−	0.946222i	$-0.604865\pi$
$109$	−6.75525			−0.647035			−0.323518	+	0.946222i	$0.604865\pi$
$110$		0			0
$111$	9.97028			0.946337
$112$		0			0
$113$	−0.565983	+	1.74192i	−0.0532432	+	0.163866i	−0.974142	−	0.225935i	$-0.927456\pi$
$113$	−0.565983	+	1.74192i	−0.0532432	+	0.163866i	0.920899	+	0.389801i	$0.127456\pi$
$114$		0			0
$115$	−6.66560	+	4.84284i	−0.621571	+	0.451597i
$116$		0			0
$117$	−0.941789	−	2.89853i	−0.0870684	−	0.267969i
$118$		0			0
$119$	24.0876	+	17.5007i	2.20811	+	1.60429i
$120$		0			0
$121$	−10.5095	−	3.24806i	−0.955411	−	0.295278i
$122$		0			0
$123$	5.73788	+	4.16881i	0.517367	+	0.375889i
$124$		0			0
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	1.90569	−	1.38456i	0.169102	−	0.122860i	−0.500015	−	0.866017i	$-0.666672\pi$
$127$	1.90569	−	1.38456i	0.169102	−	0.122860i	0.669118	+	0.743157i	$0.266672\pi$
$128$		0			0
$129$	−2.40035	+	7.38752i	−0.211339	+	0.650435i
$130$		0			0
$131$	−8.74734			−0.764259			−0.382129	−	0.924109i	$-0.624809\pi$
$131$	−8.74734			−0.764259			−0.382129	+	0.924109i	$0.624809\pi$
$132$		0			0
$133$	−26.7532			−2.31979
$134$		0			0
$135$	−0.309017	+	0.951057i	−0.0265959	+	0.0818539i
$136$		0			0
$137$	−16.7865	+	12.1961i	−1.43417	+	1.04198i	−0.444946	+	0.895557i	$0.646777\pi$
$137$	−16.7865	+	12.1961i	−1.43417	+	1.04198i	−0.989222	+	0.146427i	$0.953223\pi$
$138$		0			0
$139$	−5.61926	−	17.2943i	−0.476619	−	1.46688i	−0.843762	−	0.536718i	$-0.819664\pi$
$139$	−5.61926	−	17.2943i	−0.476619	−	1.46688i	0.367143	−	0.930165i	$-0.380336\pi$
$140$		0			0
$141$	1.39546	+	1.01386i	0.117519	+	0.0853826i
$142$		0			0
$143$	−7.09578	+	7.19879i	−0.593379	+	0.601993i
$144$		0			0
$145$	5.75530	+	4.18147i	0.477951	+	0.347252i
$146$		0			0
$147$	−2.94628	−	9.06772i	−0.243005	−	0.747893i
$148$		0			0
$149$	16.5902	−	12.0535i	1.35912	−	0.987460i	0.360621	−	0.932712i	$-0.382565\pi$
$149$	16.5902	−	12.0535i	1.35912	−	0.987460i	0.998500	−	0.0547475i	$-0.0174354\pi$
$150$		0			0
$151$	4.58732	−	14.1183i	0.373311	−	1.14893i	−0.571301	−	0.820741i	$-0.693561\pi$
$151$	4.58732	−	14.1183i	0.373311	−	1.14893i	0.944611	−	0.328191i	$-0.106439\pi$
$152$		0			0
$153$	7.32222			0.591966
$154$		0			0
$155$	5.35170			0.429858
$156$		0			0
$157$	−1.43995	+	4.43171i	−0.114920	+	0.353689i	−0.991930	−	0.126783i	$-0.959535\pi$
$157$	−1.43995	+	4.43171i	−0.114920	+	0.353689i	0.877010	+	0.480472i	$0.159535\pi$
$158$		0			0
$159$	5.10005	−	3.70540i	0.404460	−	0.293857i
$160$		0			0
$161$	−10.3528	−	31.8626i	−0.815915	−	2.51113i
$162$		0			0
$163$	−11.0890	−	8.05664i	−0.868559	−	0.631045i	0.0616408	−	0.998098i	$-0.480367\pi$
$163$	−11.0890	−	8.05664i	−0.868559	−	0.631045i	−0.930200	+	0.367053i	$0.880367\pi$
$164$		0			0
$165$	3.27197	−	0.542427i	0.254722	−	0.0422279i
$166$		0			0
$167$	−7.39854	−	5.37536i	−0.572516	−	0.415958i	0.263502	−	0.964659i	$-0.415122\pi$
$167$	−7.39854	−	5.37536i	−0.572516	−	0.415958i	−0.836018	+	0.548701i	$0.815122\pi$
$168$		0			0
$169$	−1.14694	−	3.52992i	−0.0882261	−	0.271532i
$170$		0			0
$171$	−5.32279	+	3.86723i	−0.407044	+	0.295735i
$172$		0			0
$173$	−4.68784	+	14.4277i	−0.356410	+	1.09692i	0.598778	+	0.800915i	$0.295653\pi$
$173$	−4.68784	+	14.4277i	−0.356410	+	1.09692i	−0.955188	+	0.296001i	$0.904347\pi$
$174$		0			0
$175$	−4.06625			−0.307379
$176$		0			0
$177$	3.27974			0.246520
$178$		0			0
$179$	4.02219	−	12.3790i	0.300632	−	0.925251i	−0.680639	−	0.732619i	$-0.738298\pi$
$179$	4.02219	−	12.3790i	0.300632	−	0.925251i	0.981271	−	0.192632i	$-0.0617024\pi$
$180$		0			0
$181$	−6.99819	+	5.08448i	−0.520171	+	0.377927i	−0.816668	−	0.577107i	$-0.804182\pi$
$181$	−6.99819	+	5.08448i	−0.520171	+	0.377927i	0.296497	+	0.955034i	$0.404182\pi$
$182$		0			0
$183$	2.69287	+	8.28779i	0.199063	+	0.612651i
$184$		0			0
$185$	8.06612	+	5.86038i	0.593033	+	0.430864i
$186$		0			0
$187$	−11.1808	−	21.5581i	−0.817623	−	1.57649i
$188$		0			0
$189$	−3.28966	−	2.39008i	−0.239288	−	0.173853i
$190$		0			0
$191$	1.34038	+	4.12526i	0.0969863	+	0.298493i	0.987766	−	0.155942i	$-0.0498412\pi$
$191$	1.34038	+	4.12526i	0.0969863	+	0.298493i	−0.890780	+	0.454435i	$0.849841\pi$
$192$		0			0
$193$	−12.8891	+	9.36451i	−0.927780	+	0.674072i	−0.945448	−	0.325772i	$-0.894376\pi$
$193$	−12.8891	+	9.36451i	−0.927780	+	0.674072i	0.0176681	+	0.999844i	$0.494376\pi$
$194$		0			0
$195$	0.941789	−	2.89853i	0.0674429	−	0.207568i
$196$		0			0
$197$	−0.516397			−0.0367917			−0.0183959	−	0.999831i	$-0.505856\pi$
$197$	−0.516397			−0.0367917			−0.0183959	+	0.999831i	$0.505856\pi$
$198$		0			0
$199$	−2.45883			−0.174302			−0.0871508	−	0.996195i	$-0.527776\pi$
$199$	−2.45883			−0.174302			−0.0871508	+	0.996195i	$0.527776\pi$
$200$		0			0
$201$	−0.482655	+	1.48546i	−0.0340439	+	0.104776i
$202$		0			0
$203$	−23.4025	+	17.0029i	−1.64253	+	1.19337i
$204$		0			0
$205$	2.19167	+	6.74528i	0.153073	+	0.471111i
$206$		0			0
$207$	−6.66560	−	4.84284i	−0.463291	−	0.336601i
$208$		0			0
$209$	19.5137	+	9.76623i	1.34979	+	0.675544i
$210$		0			0
$211$	7.65982	+	5.56519i	0.527324	+	0.383123i	0.819356	−	0.573285i	$-0.194331\pi$
$211$	7.65982	+	5.56519i	0.527324	+	0.383123i	−0.292032	+	0.956409i	$0.594331\pi$
$212$		0			0
$213$	2.79581	+	8.60463i	0.191566	+	0.589580i
$214$		0			0
$215$	−6.28420	+	4.56574i	−0.428579	+	0.311381i
$216$		0			0
$217$	−6.72462	+	20.6962i	−0.456497	+	1.40495i
$218$		0			0
$219$	−3.97549			−0.268639
$220$		0			0
$221$	−22.3159			−1.50113
$222$		0			0
$223$	−0.530487	+	1.63267i	−0.0355240	+	0.109332i	−0.967246	−	0.253840i	$-0.918306\pi$
$223$	−0.530487	+	1.63267i	−0.0355240	+	0.109332i	0.931722	+	0.363172i	$0.118306\pi$
$224$		0			0
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$		0			0
$227$	2.21750	+	6.82477i	0.147181	+	0.452976i	0.997285	−	0.0736388i	$-0.0234612\pi$
$227$	2.21750	+	6.82477i	0.147181	+	0.452976i	−0.850104	+	0.526614i	$0.823461\pi$
$228$		0			0
$229$	4.49370	+	3.26486i	0.296952	+	0.215748i	0.726278	−	0.687402i	$-0.241249\pi$
$229$	4.49370	+	3.26486i	0.296952	+	0.215748i	−0.429326	+	0.903150i	$0.641249\pi$
$230$		0			0
$231$	−2.01366	+	13.3350i	−0.132489	+	0.877381i
$232$		0			0
$233$	8.53199	+	6.19885i	0.558949	+	0.406100i	0.831074	−	0.556162i	$-0.187726\pi$
$233$	8.53199	+	6.19885i	0.558949	+	0.406100i	−0.272125	+	0.962262i	$0.587726\pi$
$234$		0			0
$235$	0.533019	+	1.64046i	0.0347703	+	0.107012i
$236$		0			0
$237$	0.511044	−	0.371295i	0.0331959	−	0.0241182i
$238$		0			0
$239$	5.82158	−	17.9170i	0.376566	−	1.15895i	−0.565849	−	0.824509i	$-0.691452\pi$
$239$	5.82158	−	17.9170i	0.376566	−	1.15895i	0.942416	−	0.334444i	$-0.108548\pi$
$240$		0			0
$241$	7.47045			0.481214			0.240607	−	0.970623i	$-0.422654\pi$
$241$	7.47045			0.481214			0.240607	+	0.970623i	$0.422654\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.94628	−	9.06772i	0.188231	−	0.579315i
$246$		0			0
$247$	16.2222	−	11.7861i	1.03219	−	0.749933i
$248$		0			0
$249$	3.37846	+	10.3978i	0.214101	+	0.658935i
$250$		0			0
$251$	−16.1462	−	11.7309i	−1.01914	−	0.740449i	−0.0530337	−	0.998593i	$-0.516889\pi$
$251$	−16.1462	−	11.7309i	−1.01914	−	0.740449i	−0.966106	+	0.258144i	$0.916889\pi$
$252$		0			0
$253$	−4.08014	+	27.0198i	−0.256516	+	1.69872i
$254$		0			0
$255$	5.92380	+	4.30389i	0.370963	+	0.269520i
$256$		0			0
$257$	5.79662	+	17.8402i	0.361583	+	1.11284i	0.952093	+	0.305809i	$0.0989268\pi$
$257$	5.79662	+	17.8402i	0.361583	+	1.11284i	−0.590510	+	0.807031i	$0.701073\pi$
$258$		0			0
$259$	−32.7988	+	23.8298i	−2.03802	+	1.48071i
$260$		0			0
$261$	−2.19833	+	6.76576i	−0.136073	+	0.418790i
$262$		0			0
$263$	5.89770			0.363668			0.181834	−	0.983329i	$-0.441797\pi$
$263$	5.89770			0.363668			0.181834	+	0.983329i	$0.441797\pi$
$264$		0			0
$265$	6.30400			0.387252
$266$		0			0
$267$	1.58779	−	4.88672i	0.0971712	−	0.299062i
$268$		0			0
$269$	−23.6793	+	17.2040i	−1.44375	+	1.04895i	−0.456510	+	0.889718i	$0.650901\pi$
$269$	−23.6793	+	17.2040i	−1.44375	+	1.04895i	−0.987242	+	0.159229i	$0.949099\pi$
$270$		0			0
$271$	3.32224	+	10.2248i	0.201812	+	0.621113i	0.999829	+	0.0184785i	$0.00588223\pi$
$271$	3.32224	+	10.2248i	0.201812	+	0.621113i	−0.798017	+	0.602634i	$0.794118\pi$
$272$		0			0
$273$	10.0259	+	7.28423i	0.606794	+	0.440862i
$274$		0			0
$275$	2.96591	+	1.48438i	0.178851	+	0.0895116i
$276$		0			0
$277$	2.04817	+	1.48808i	0.123062	+	0.0894101i	0.647614	−	0.761969i	$-0.275767\pi$
$277$	2.04817	+	1.48808i	0.123062	+	0.0894101i	−0.524552	+	0.851379i	$0.675767\pi$
$278$		0			0
$279$	1.65376	+	5.08976i	0.0990083	+	0.304716i
$280$		0			0
$281$	17.1906	−	12.4897i	1.02550	−	0.745072i	0.0580995	−	0.998311i	$-0.481496\pi$
$281$	17.1906	−	12.4897i	1.02550	−	0.745072i	0.967404	+	0.253239i	$0.0814959\pi$
$282$		0			0
$283$	8.26394	−	25.4338i	0.491240	−	1.51188i	−0.331495	−	0.943457i	$-0.607553\pi$
$283$	8.26394	−	25.4338i	0.491240	−	1.51188i	0.822735	−	0.568425i	$-0.192447\pi$
$284$		0			0
$285$	−6.57933			−0.389726
$286$		0			0
$287$	−28.8395			−1.70234
$288$		0			0
$289$	11.3146	−	34.8228i	0.665566	−	2.04840i
$290$		0			0
$291$	4.54553	−	3.30252i	0.266464	−	0.193597i
$292$		0			0
$293$	−3.26549	−	10.0502i	−0.190772	−	0.587137i	0.809228	−	0.587495i	$-0.199886\pi$
$293$	−3.26549	−	10.0502i	−0.190772	−	0.587137i	−1.00000		0.000358582i	$0.999886\pi$
$294$		0			0
$295$	2.65337	+	1.92778i	0.154485	+	0.112240i
$296$		0			0
$297$	1.52697	+	2.94421i	0.0886039	+	0.170840i
$298$		0			0
$299$	20.3147	+	14.7595i	1.17483	+	0.853564i
$300$		0			0
$301$	−9.76042	−	30.0395i	−0.562581	−	1.73145i
$302$		0			0
$303$	−10.6574	+	7.74304i	−0.612251	+	0.444826i
$304$		0			0
$305$	−2.69287	+	8.28779i	−0.154193	+	0.474558i
$306$		0			0
$307$	21.0922			1.20380			0.601898	−	0.798573i	$-0.294411\pi$
$307$	21.0922			1.20380			0.601898	+	0.798573i	$0.294411\pi$
$308$		0			0
$309$	−16.3829			−0.931991
$310$		0			0
$311$	−5.10511	+	15.7119i	−0.289484	+	0.890940i	0.695535	+	0.718492i	$0.255168\pi$
$311$	−5.10511	+	15.7119i	−0.289484	+	0.890940i	−0.985019	+	0.172448i	$0.944832\pi$
$312$		0			0
$313$	16.3794	−	11.9003i	0.925819	−	0.672647i	−0.0191466	−	0.999817i	$-0.506095\pi$
$313$	16.3794	−	11.9003i	0.925819	−	0.672647i	0.944966	+	0.327170i	$0.106095\pi$
$314$		0			0
$315$	−1.25654	−	3.86723i	−0.0707980	−	0.217894i
$316$		0			0
$317$	1.91326	+	1.39007i	0.107459	+	0.0780739i	0.640217	−	0.768194i	$-0.278844\pi$
$317$	1.91326	+	1.39007i	0.107459	+	0.0780739i	−0.532758	+	0.846268i	$0.678844\pi$
$318$		0			0
$319$	23.2766	−	3.85879i	1.30324	−	0.216051i
$320$		0			0
$321$	−2.76337	−	2.00770i	−0.154236	−	0.112059i
$322$		0			0
$323$	14.8870	+	45.8174i	0.828334	+	2.54935i
$324$		0			0
$325$	2.46563	−	1.79139i	0.136769	−	0.0993684i
$326$		0			0
$327$	2.08749	−	6.42462i	0.115438	−	0.355282i
$328$		0			0
$329$	−7.01381			−0.386684
$330$		0			0
$331$	−11.3984			−0.626511			−0.313256	−	0.949669i	$-0.601420\pi$
$331$	−11.3984			−0.626511			−0.313256	+	0.949669i	$0.601420\pi$
$332$		0			0
$333$	−3.08098	+	9.48230i	−0.168837	+	0.519627i
$334$		0			0
$335$	−1.26361	+	0.918065i	−0.0690382	+	0.0501592i
$336$		0			0
$337$	−3.21911	−	9.90740i	−0.175356	−	0.539691i	0.824293	−	0.566163i	$-0.191573\pi$
$337$	−3.21911	−	9.90740i	−0.175356	−	0.539691i	−0.999650	+	0.0264721i	$0.991573\pi$
$338$		0			0
$339$	−1.48176	−	1.07656i	−0.0804783	−	0.0584709i
$340$		0			0
$341$	12.4601	−	12.6410i	0.674750	−	0.684546i
$342$		0			0
$343$	8.33721	+	6.05733i	0.450167	+	0.327065i
$344$		0			0
$345$	−2.54603	−	7.83588i	−0.137074	−	0.421870i
$346$		0			0
$347$	−12.2382	+	8.89154i	−0.656978	+	0.477323i	−0.865641	−	0.500665i	$-0.833089\pi$
$347$	−12.2382	+	8.89154i	−0.656978	+	0.477323i	0.208663	+	0.977988i	$0.433089\pi$
$348$		0			0
$349$	−9.60882	+	29.5729i	−0.514348	+	1.58300i	0.270116	+	0.962828i	$0.412938\pi$
$349$	−9.60882	+	29.5729i	−0.514348	+	1.58300i	−0.784465	+	0.620174i	$0.787062\pi$
$350$		0			0
$351$	3.04769			0.162674
$352$		0			0
$353$	−17.9074			−0.953113			−0.476556	−	0.879144i	$-0.658115\pi$
$353$	−17.9074			−0.953113			−0.476556	+	0.879144i	$0.658115\pi$
$354$		0			0
$355$	−2.79581	+	8.60463i	−0.148386	+	0.456686i
$356$		0			0
$357$	−24.0876	+	17.5007i	−1.27485	+	0.926235i
$358$		0			0
$359$	10.2900	+	31.6693i	0.543085	+	1.67144i	0.725500	+	0.688222i	$0.241609\pi$
$359$	10.2900	+	31.6693i	0.543085	+	1.67144i	−0.182415	+	0.983222i	$0.558391\pi$
$360$		0			0
$361$	−19.6490	−	14.2759i	−1.03416	−	0.751361i
$362$		0			0
$363$	6.33671	−	8.99145i	0.332591	−	0.471929i
$364$		0			0
$365$	−3.21624	−	2.33673i	−0.168346	−	0.122310i
$366$		0			0
$367$	−1.68267	−	5.17873i	−0.0878347	−	0.270327i	0.897485	−	0.441044i	$-0.145392\pi$
$367$	−1.68267	−	5.17873i	−0.0878347	−	0.270327i	−0.985320	+	0.170717i	$0.945392\pi$
$368$		0			0
$369$	−5.73788	+	4.16881i	−0.298702	+	0.217020i
$370$		0			0
$371$	−7.92123	+	24.3790i	−0.411250	+	1.26570i
$372$		0			0
$373$	33.9464			1.75768			0.878840	−	0.477116i	$-0.158318\pi$
$373$	33.9464			1.75768			0.878840	+	0.477116i	$0.158318\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	6.69983	−	20.6199i	0.345059	−	1.06198i
$378$		0			0
$379$	−24.0157	+	17.4484i	−1.23360	+	0.896264i	−0.997155	−	0.0753808i	$-0.975983\pi$
$379$	−24.0157	+	17.4484i	−1.23360	+	0.896264i	−0.236446	+	0.971645i	$0.575983\pi$
$380$		0			0
$381$	0.727908	+	2.24027i	0.0372919	+	0.114773i
$382$		0			0
$383$	−25.3545	−	18.4211i	−1.29556	−	0.941276i	−0.295654	−	0.955295i	$-0.595538\pi$
$383$	−25.3545	−	18.4211i	−1.29556	−	0.941276i	−0.999902	+	0.0140188i	$0.995538\pi$
$384$		0			0
$385$	−9.46723	+	9.60467i	−0.482495	+	0.489499i
$386$		0			0
$387$	−6.28420	−	4.56574i	−0.319444	−	0.232090i
$388$		0			0
$389$	−0.105707	−	0.325331i	−0.00535954	−	0.0164950i	0.948341	−	0.317253i	$-0.102760\pi$
$389$	−0.105707	−	0.325331i	−0.00535954	−	0.0164950i	−0.953701	+	0.300758i	$0.902760\pi$
$390$		0			0
$391$	−48.8070	+	35.4604i	−2.46828	+	1.79331i
$392$		0			0
$393$	2.70308	−	8.31922i	0.136352	−	0.419649i
$394$		0			0
$395$	0.631686			0.0317836
$396$		0			0
$397$	9.35666			0.469597			0.234799	−	0.972044i	$-0.424557\pi$
$397$	9.35666			0.469597			0.234799	+	0.972044i	$0.424557\pi$
$398$		0			0
$399$	8.26718	−	25.4438i	0.413877	−	1.27378i
$400$		0			0
$401$	8.47784	−	6.15951i	0.423363	−	0.307591i	−0.355626	−	0.934628i	$-0.615732\pi$
$401$	8.47784	−	6.15951i	0.423363	−	0.307591i	0.778990	+	0.627037i	$0.215732\pi$
$402$		0			0
$403$	−5.04017	−	15.5120i	−0.251069	−	0.772710i
$404$		0			0
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$		0			0
$407$	32.6224	−	5.40815i	1.61703	−	0.268072i
$408$		0			0
$409$	−18.9725	−	13.7843i	−0.938130	−	0.681591i	0.00983996	−	0.999952i	$-0.496868\pi$
$409$	−18.9725	−	13.7843i	−0.938130	−	0.681591i	−0.947970	+	0.318360i	$0.896868\pi$
$410$		0			0
$411$	−6.41187	−	19.7337i	−0.316274	−	0.973393i
$412$		0			0
$413$	−10.7892	+	7.83885i	−0.530904	+	0.385724i
$414$		0			0
$415$	−3.37846	+	10.3978i	−0.165842	+	0.510409i
$416$		0			0
$417$	18.1843			0.890489
$418$		0			0
$419$	2.15086			0.105077			0.0525383	−	0.998619i	$-0.483269\pi$
$419$	2.15086			0.105077			0.0525383	+	0.998619i	$0.483269\pi$
$420$		0			0
$421$	4.55590	−	14.0216i	0.222041	−	0.683371i	−0.776538	−	0.630071i	$-0.783026\pi$
$421$	4.55590	−	14.0216i	0.222041	−	0.683371i	0.998579	−	0.0533006i	$-0.0169742\pi$
$422$		0			0
$423$	−1.39546	+	1.01386i	−0.0678497	+	0.0492957i
$424$		0			0
$425$	2.26269	+	6.96384i	0.109757	+	0.337796i
$426$		0			0
$427$	−28.6671	−	20.8279i	−1.38730	−	1.00793i
$428$		0			0
$429$	−4.65374	−	8.97304i	−0.224685	−	0.433222i
$430$		0			0
$431$	7.44452	+	5.40876i	0.358590	+	0.260531i	0.752464	−	0.658634i	$-0.228865\pi$
$431$	7.44452	+	5.40876i	0.358590	+	0.260531i	−0.393874	+	0.919165i	$0.628865\pi$
$432$		0			0
$433$	10.8787	+	33.4813i	0.522798	+	1.60901i	0.768630	+	0.639694i	$0.220939\pi$
$433$	10.8787	+	33.4813i	0.522798	+	1.60901i	−0.245832	+	0.969312i	$0.579061\pi$
$434$		0			0
$435$	−5.75530	+	4.18147i	−0.275945	+	0.200486i
$436$		0			0
$437$	16.7512	−	51.5548i	0.801318	−	2.46620i
$438$		0			0
$439$	−16.1403			−0.770336			−0.385168	−	0.922846i	$-0.625857\pi$
$439$	−16.1403			−0.770336			−0.385168	+	0.922846i	$0.625857\pi$
$440$		0			0
$441$	9.53436			0.454017
$442$		0			0
$443$	−1.36423	+	4.19868i	−0.0648167	+	0.199485i	−0.978220	−	0.207570i	$-0.933444\pi$
$443$	−1.36423	+	4.19868i	−0.0648167	+	0.199485i	0.913403	+	0.407056i	$0.133444\pi$
$444$		0			0
$445$	4.15689	−	3.02016i	0.197056	−	0.143169i
$446$		0			0
$447$	6.33689	+	19.5029i	0.299725	+	0.922458i
$448$		0			0
$449$	−4.56090	−	3.31369i	−0.215242	−	0.156383i	0.474940	−	0.880018i	$-0.342470\pi$
$449$	−4.56090	−	3.31369i	−0.215242	−	0.156383i	−0.690182	+	0.723636i	$0.742470\pi$
$450$		0			0
$451$	21.0354	+	10.5278i	0.990519	+	0.495736i
$452$		0			0
$453$	12.0098	+	8.72560i	0.564267	+	0.409964i
$454$		0			0
$455$	3.82955	+	11.7861i	0.179532	+	0.552542i
$456$		0			0
$457$	−15.0029	+	10.9003i	−0.701808	+	0.509893i	−0.880520	−	0.474008i	$-0.842807\pi$
$457$	−15.0029	+	10.9003i	−0.701808	+	0.509893i	0.178713	+	0.983901i	$0.442807\pi$
$458$		0			0
$459$	−2.26269	+	6.96384i	−0.105613	+	0.325044i
$460$		0			0
$461$	14.9437			0.695996			0.347998	−	0.937495i	$-0.386862\pi$
$461$	14.9437			0.695996			0.347998	+	0.937495i	$0.386862\pi$
$462$		0			0
$463$	21.6943			1.00822			0.504110	−	0.863639i	$-0.331821\pi$
$463$	21.6943			1.00822			0.504110	+	0.863639i	$0.331821\pi$
$464$		0			0
$465$	−1.65376	+	5.08976i	−0.0766915	+	0.236032i
$466$		0			0
$467$	23.1950	−	16.8521i	1.07333	−	0.779823i	0.0968258	−	0.995301i	$-0.469131\pi$
$467$	23.1950	−	16.8521i	1.07333	−	0.779823i	0.976509	+	0.215478i	$0.0691310\pi$
$468$		0			0
$469$	−1.96259	−	6.04025i	−0.0906242	−	0.278913i
$470$		0			0
$471$	−3.76983	−	2.73894i	−0.173705	−	0.126204i
$472$		0			0
$473$	−3.84668	+	25.4738i	−0.176871	+	1.17128i
$474$		0			0
$475$	−5.32279	−	3.86723i	−0.244226	−	0.177441i
$476$		0			0
$477$	1.94804	+	5.99546i	0.0891948	+	0.274513i
$478$		0			0
$479$	10.0227	−	7.28192i	0.457949	−	0.332719i	−0.334777	−	0.942297i	$-0.608661\pi$
$479$	10.0227	−	7.28192i	0.457949	−	0.332719i	0.792726	+	0.609578i	$0.208661\pi$
$480$		0			0
$481$	9.38989	−	28.8991i	0.428142	−	1.31769i
$482$		0			0
$483$	33.5024			1.52441
$484$		0			0
$485$	5.61858			0.255127
$486$		0			0
$487$	−5.26351	+	16.1994i	−0.238512	+	0.734066i	0.758124	+	0.652111i	$0.226116\pi$
$487$	−5.26351	+	16.1994i	−0.238512	+	0.734066i	−0.996636	+	0.0819548i	$0.973884\pi$
$488$		0			0
$489$	11.0890	−	8.05664i	0.501463	−	0.364334i
$490$		0			0
$491$	−2.77192	−	8.53109i	−0.125095	−	0.385003i	0.868823	−	0.495122i	$-0.164877\pi$
$491$	−2.77192	−	8.53109i	−0.125095	−	0.385003i	−0.993918	+	0.110119i	$0.964877\pi$
$492$		0			0
$493$	42.1416	+	30.6176i	1.89796	+	1.37895i
$494$		0			0
$495$	−0.495215	+	3.27945i	−0.0222582	+	0.147400i
$496$		0			0
$497$	−29.7630	−	21.6241i	−1.33505	−	0.969974i
$498$		0			0
$499$	−8.76672	−	26.9812i	−0.392452	−	1.20784i	−0.930928	−	0.365203i	$-0.881000\pi$
$499$	−8.76672	−	26.9812i	−0.392452	−	1.20784i	0.538476	−	0.842641i	$-0.319000\pi$
$500$		0			0
$501$	7.39854	−	5.37536i	0.330543	−	0.240153i
$502$		0			0
$503$	−6.16607	+	18.9772i	−0.274931	+	0.846152i	0.714306	+	0.699833i	$0.246742\pi$
$503$	−6.16607	+	18.9772i	−0.274931	+	0.846152i	−0.989238	+	0.146318i	$0.953258\pi$
$504$		0			0
$505$	−13.1733			−0.586202
$506$		0			0
$507$	3.71157			0.164837
$508$		0			0
$509$	6.95337	−	21.4003i	0.308203	−	0.948550i	−0.670260	−	0.742126i	$-0.733817\pi$
$509$	6.95337	−	21.4003i	0.308203	−	0.948550i	0.978463	−	0.206424i	$-0.0661826\pi$
$510$		0			0
$511$	13.0780	−	9.50174i	0.578538	−	0.420332i
$512$		0			0
$513$	−2.03312	−	6.25731i	−0.0897646	−	0.276267i
$514$		0			0
$515$	−13.2541	−	9.62964i	−0.584043	−	0.424332i
$516$		0			0
$517$	5.11585	+	2.56039i	0.224995	+	0.112606i
$518$		0			0
$519$	−12.2729	−	8.91680i	−0.538721	−	0.391404i
$520$		0			0
$521$	2.58773	+	7.96423i	0.113371	+	0.348919i	0.991604	−	0.129314i	$-0.0412775\pi$
$521$	2.58773	+	7.96423i	0.113371	+	0.348919i	−0.878233	+	0.478233i	$0.841277\pi$
$522$		0			0
$523$	−30.8536	+	22.4165i	−1.34913	+	0.980203i	−0.350080	+	0.936720i	$0.613846\pi$
$523$	−30.8536	+	22.4165i	−1.34913	+	0.980203i	−0.999054	+	0.0434834i	$0.986154\pi$
$524$		0			0
$525$	1.25654	−	3.86723i	0.0548399	−	0.168780i
$526$		0			0
$527$	39.1863			1.70698
$528$		0			0
$529$	44.8834			1.95145
$530$		0			0
$531$	−1.01350	+	3.11922i	−0.0439820	+	0.135363i
$532$		0			0
$533$	17.4873	−	12.7053i	0.757458	−	0.550326i
$534$		0			0
$535$	−1.05551	−	3.24853i	−0.0456337	−	0.140446i
$536$		0			0
$537$	10.5302	+	7.65065i	0.454413	+	0.330150i
$538$		0			0
$539$	−14.5587	−	28.0711i	−0.627088	−	1.20911i
$540$		0			0
$541$	−5.54255	−	4.02690i	−0.238293	−	0.173130i	0.462230	−	0.886760i	$-0.347050\pi$
$541$	−5.54255	−	4.02690i	−0.238293	−	0.173130i	−0.700522	+	0.713630i	$0.747050\pi$
$542$		0			0
$543$	−2.67307	−	8.22687i	−0.114712	−	0.353049i
$544$		0			0
$545$	5.46511	−	3.97063i	0.234100	−	0.170083i
$546$		0			0
$547$	−6.28906	+	19.3557i	−0.268901	+	0.827591i	0.721868	+	0.692031i	$0.243284\pi$
$547$	−6.28906	+	19.3557i	−0.268901	+	0.827591i	−0.990769	+	0.135561i	$0.956716\pi$
$548$		0			0
$549$	−8.71430			−0.371917
$550$		0			0
$551$	−46.8049			−1.99396
$552$		0			0
$553$	−0.793738	+	2.44287i	−0.0337532	+	0.103882i
$554$		0			0
$555$	−8.06612	+	5.86038i	−0.342388	+	0.248759i
$556$		0			0
$557$	4.22200	+	12.9940i	0.178892	+	0.550573i	0.999790	−	0.0205022i	$-0.00652650\pi$
$557$	4.22200	+	12.9940i	0.178892	+	0.550573i	−0.820898	+	0.571075i	$0.806526\pi$
$558$		0			0
$559$	19.1523	+	13.9150i	0.810057	+	0.588541i
$560$		0			0
$561$	23.9581	−	3.97177i	1.01151	−	0.167688i
$562$		0			0
$563$	−27.7002	−	20.1253i	−1.16742	−	0.848182i	−0.176724	−	0.984260i	$-0.556550\pi$
$563$	−27.7002	−	20.1253i	−1.16742	−	0.848182i	−0.990698	+	0.136078i	$0.956550\pi$
$564$		0			0
$565$	−0.565983	−	1.74192i	−0.0238111	−	0.0732830i
$566$		0			0
$567$	3.28966	−	2.39008i	0.138153	−	0.100374i
$568$		0			0
$569$	−8.28183	+	25.4889i	−0.347192	+	1.06855i	0.613207	+	0.789922i	$0.289879\pi$
$569$	−8.28183	+	25.4889i	−0.347192	+	1.06855i	−0.960400	+	0.278626i	$0.910121\pi$
$570$		0			0
$571$	34.1852			1.43061			0.715303	−	0.698814i	$-0.246289\pi$
$571$	34.1852			1.43061			0.715303	+	0.698814i	$0.246289\pi$
$572$		0			0
$573$	−4.33755			−0.181204
$574$		0			0
$575$	2.54603	−	7.83588i	0.106177	−	0.326779i
$576$		0			0
$577$	7.55622	−	5.48991i	0.314569	−	0.228548i	−0.419285	−	0.907855i	$-0.637719\pi$
$577$	7.55622	−	5.48991i	0.314569	−	0.228548i	0.733855	+	0.679306i	$0.237719\pi$
$578$		0			0
$579$	−4.92321	−	15.1521i	−0.204602	−	0.629699i
$580$		0			0
$581$	−35.9656	−	26.1305i	−1.49211	−	1.08408i
$582$		0			0
$583$	14.6773	−	14.8904i	0.607871	−	0.616695i
$584$		0			0
$585$	2.46563	+	1.79139i	0.101941	+	0.0740648i
$586$		0			0
$587$	5.14482	+	15.8341i	0.212349	+	0.653544i	0.999331	+	0.0365678i	$0.0116425\pi$
$587$	5.14482	+	15.8341i	0.212349	+	0.653544i	−0.786982	+	0.616976i	$0.788358\pi$
$588$		0			0
$589$	−28.4859	+	20.6962i	−1.17374	+	0.852774i
$590$		0			0
$591$	0.159575	−	0.491122i	0.00656405	−	0.0202021i
$592$		0			0
$593$	−30.0023			−1.23205			−0.616023	−	0.787728i	$-0.711257\pi$
$593$	−30.0023			−1.23205			−0.616023	+	0.787728i	$0.711257\pi$
$594$		0			0
$595$	−29.7740			−1.22061
$596$		0			0
$597$	0.759819	−	2.33848i	0.0310973	−	0.0957078i
$598$		0			0
$599$	16.8812	−	12.2649i	0.689746	−	0.501130i	−0.186831	−	0.982392i	$-0.559822\pi$
$599$	16.8812	−	12.2649i	0.689746	−	0.501130i	0.876577	+	0.481262i	$0.159822\pi$
$600$		0			0
$601$	4.97961	+	15.3257i	0.203122	+	0.625147i	0.999785	+	0.0207227i	$0.00659671\pi$
$601$	4.97961	+	15.3257i	0.203122	+	0.625147i	−0.796663	+	0.604424i	$0.793403\pi$
$602$		0			0
$603$	−1.26361	−	0.918065i	−0.0514581	−	0.0373865i
$604$		0			0
$605$	10.4115	−	3.54961i	0.423290	−	0.144312i
$606$		0			0
$607$	35.1814	+	25.5608i	1.42797	+	1.03748i	0.990390	+	0.138302i	$0.0441645\pi$
$607$	35.1814	+	25.5608i	1.42797	+	1.03748i	0.437581	+	0.899179i	$0.355835\pi$
$608$		0			0
$609$	−8.93895	−	27.5112i	−0.362224	−	1.11481i
$610$		0			0
$611$	4.25294	−	3.08994i	0.172055	−	0.125006i
$612$		0			0
$613$	0.852605	−	2.62405i	0.0344364	−	0.105984i	−0.932361	−	0.361529i	$-0.882255\pi$
$613$	0.852605	−	2.62405i	0.0344364	−	0.105984i	0.966797	+	0.255545i	$0.0822548\pi$
$614$		0			0
$615$	−7.09240			−0.285993
$616$		0			0
$617$	−13.4008			−0.539494			−0.269747	−	0.962931i	$-0.586940\pi$
$617$	−13.4008			−0.539494			−0.269747	+	0.962931i	$0.586940\pi$
$618$		0			0
$619$	12.6645	−	38.9775i	0.509031	−	1.56664i	−0.284855	−	0.958571i	$-0.591946\pi$
$619$	12.6645	−	38.9775i	0.509031	−	1.56664i	0.793886	−	0.608066i	$-0.208054\pi$
$620$		0			0
$621$	6.66560	−	4.84284i	0.267481	−	0.194337i
$622$		0			0
$623$	6.45635	+	19.8706i	0.258668	+	0.796099i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−15.3183	+	15.5407i	−0.611754	+	0.620635i
$628$		0			0
$629$	59.0619	+	42.9110i	2.35495	+	1.71097i
$630$		0			0
$631$	−9.87278	−	30.3853i	−0.393029	−	1.20962i	−0.930486	−	0.366328i	$-0.880615\pi$
$631$	−9.87278	−	30.3853i	−0.393029	−	1.20962i	0.537456	−	0.843292i	$-0.319385\pi$
$632$		0			0
$633$	−7.65982	+	5.56519i	−0.304451	+	0.221196i
$634$		0			0
$635$	−0.727908	+	2.24027i	−0.0288861	+	0.0889024i
$636$		0			0
$637$	−29.0578			−1.15131
$638$		0			0
$639$	−9.04744			−0.357911
$640$		0			0
$641$	−2.06141	+	6.34437i	−0.0814208	+	0.250588i	−0.983478	−	0.181030i	$-0.942057\pi$
$641$	−2.06141	+	6.34437i	−0.0814208	+	0.250588i	0.902057	+	0.431617i	$0.142057\pi$
$642$		0			0
$643$	22.1655	−	16.1042i	0.874121	−	0.635086i	−0.0575685	−	0.998342i	$-0.518335\pi$
$643$	22.1655	−	16.1042i	0.874121	−	0.635086i	0.931690	+	0.363255i	$0.118335\pi$
$644$		0			0
$645$	−2.40035	−	7.38752i	−0.0945138	−	0.290883i
$646$		0			0
$647$	−20.5250	−	14.9123i	−0.806923	−	0.586264i	0.106014	−	0.994365i	$-0.466191\pi$
$647$	−20.5250	−	14.9123i	−0.806923	−	0.586264i	−0.912937	+	0.408101i	$0.866191\pi$
$648$		0			0
$649$	10.7312	−	1.77902i	0.421237	−	0.0698327i
$650$		0			0
$651$	−17.6053	−	12.7910i	−0.690005	−	0.501318i
$652$		0			0
$653$	−9.09518	−	27.9921i	−0.355922	−	1.09542i	−0.955473	−	0.295079i	$-0.904654\pi$
$653$	−9.09518	−	27.9921i	−0.355922	−	1.09542i	0.599551	−	0.800336i	$-0.295346\pi$
$654$		0			0
$655$	7.07675	−	5.14156i	0.276511	−	0.200897i
$656$		0			0
$657$	1.22849	−	3.78092i	0.0479281	−	0.147508i
$658$		0			0
$659$	−2.32173			−0.0904417			−0.0452208	−	0.998977i	$-0.514399\pi$
$659$	−2.32173			−0.0904417			−0.0452208	+	0.998977i	$0.514399\pi$
$660$		0			0
$661$	−13.5631			−0.527542			−0.263771	−	0.964585i	$-0.584966\pi$
$661$	−13.5631			−0.527542			−0.263771	+	0.964585i	$0.584966\pi$
$662$		0			0
$663$	6.89598	−	21.2237i	0.267818	−	0.824258i
$664$		0			0
$665$	21.6438	−	15.7251i	0.839309	−	0.609794i
$666$		0			0
$667$	−18.1123	−	55.7440i	−0.701312	−	2.15842i
$668$		0			0
$669$	−1.38883	−	1.00905i	−0.0536954	−	0.0390120i
$670$		0			0
$671$	13.3065	+	25.6567i	0.513692	+	0.990466i
$672$		0			0
$673$	22.4034	+	16.2770i	0.863586	+	0.627432i	0.928858	−	0.370435i	$-0.120791\pi$
$673$	22.4034	+	16.2770i	0.863586	+	0.627432i	−0.0652719	+	0.997868i	$0.520791\pi$
$674$		0			0
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$		0			0
$677$	26.8288	−	19.4923i	1.03112	−	0.749149i	0.0625835	−	0.998040i	$-0.480066\pi$
$677$	26.8288	−	19.4923i	1.03112	−	0.749149i	0.968532	+	0.248891i	$0.0800660\pi$
$678$		0			0
$679$	−7.05997	+	21.7283i	−0.270937	+	0.833857i
$680$		0			0
$681$	−7.17598			−0.274984
$682$		0			0
$683$	31.6611			1.21148			0.605739	−	0.795664i	$-0.292878\pi$
$683$	31.6611			1.21148			0.605739	+	0.795664i	$0.292878\pi$
$684$		0			0
$685$	6.41187	−	19.7337i	0.244985	−	0.753987i
$686$		0			0
$687$	−4.49370	+	3.26486i	−0.171445	+	0.124562i
$688$		0			0
$689$	−5.93704	−	18.2723i	−0.226183	−	0.696120i
$690$		0			0
$691$	32.6763	+	23.7407i	1.24307	+	0.903140i	0.997799	−	0.0663150i	$-0.0211242\pi$
$691$	32.6763	+	23.7407i	1.24307	+	0.903140i	0.245267	+	0.969455i	$0.421124\pi$
$692$		0			0
$693$	−12.0601	−	6.03586i	−0.458126	−	0.229283i
$694$		0			0
$695$	14.7114	+	10.6885i	0.558035	+	0.405436i
$696$		0			0
$697$	16.0479	+	49.3904i	0.607858	+	1.87079i
$698$		0			0
$699$	−8.53199	+	6.19885i	−0.322709	+	0.234462i
$700$		0			0
$701$	9.80026	−	30.1621i	0.370151	−	1.13921i	−0.576542	−	0.817068i	$-0.695598\pi$
$701$	9.80026	−	30.1621i	0.370151	−	1.13921i	0.946692	−	0.322139i	$-0.104402\pi$
$702$		0			0
$703$	−65.5977			−2.47406
$704$		0			0
$705$	−1.72489			−0.0649630
$706$		0			0
$707$	16.5527	−	50.9440i	0.622529	−	1.91595i
$708$		0			0
$709$	7.32463	−	5.32165i	0.275082	−	0.199859i	−0.441687	−	0.897169i	$-0.645620\pi$
$709$	7.32463	−	5.32165i	0.275082	−	0.199859i	0.716770	+	0.697310i	$0.245620\pi$
$710$		0			0
$711$	0.195202	+	0.600769i	0.00732063	+	0.0225306i
$712$		0			0
$713$	−35.6723	−	25.9174i	−1.33594	−	0.970615i
$714$		0			0
$715$	1.50926	−	9.99474i	0.0564432	−	0.373782i
$716$		0			0
$717$	15.2411	+	11.0733i	0.569189	+	0.413540i
$718$		0			0
$719$	−1.41262	−	4.34760i	−0.0526819	−	0.162138i	0.921254	−	0.388961i	$-0.127166\pi$
$719$	−1.41262	−	4.34760i	−0.0526819	−	0.162138i	−0.973936	+	0.226823i	$0.927166\pi$
$720$		0			0
$721$	53.8943	−	39.1565i	2.00713	−	1.45826i
$722$		0			0
$723$	−2.30850	+	7.10482i	−0.0858539	+	0.264231i
$724$		0			0
$725$	−7.11394			−0.264205
$726$		0			0
$727$	21.4548			0.795715			0.397858	−	0.917447i	$-0.369754\pi$
$727$	21.4548			0.795715			0.397858	+	0.917447i	$0.369754\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−46.0143	+	33.4314i	−1.70190	+	1.23650i
$732$		0			0
$733$	−13.7768	−	42.4005i	−0.508856	−	1.56610i	−0.794190	−	0.607669i	$-0.792105\pi$
$733$	−13.7768	−	42.4005i	−0.508856	−	1.56610i	0.285334	−	0.958428i	$-0.407895\pi$
$734$		0			0
$735$	7.71346	+	5.60416i	0.284515	+	0.206713i
$736$		0			0
$737$	−0.773478	+	5.12218i	−0.0284914	+	0.188678i
$738$		0			0
$739$	3.80964	+	2.76786i	0.140140	+	0.101818i	0.655646	−	0.755068i	$-0.272396\pi$
$739$	3.80964	+	2.76786i	0.140140	+	0.101818i	−0.515507	+	0.856886i	$0.672396\pi$
$740$		0			0
$741$	6.19633	+	19.0704i	0.227628	+	0.700567i
$742$		0			0
$743$	−21.4107	+	15.5558i	−0.785483	+	0.570687i	−0.906620	−	0.421949i	$-0.861346\pi$
$743$	−21.4107	+	15.5558i	−0.785483	+	0.570687i	0.121136	+	0.992636i	$0.461346\pi$
$744$		0			0
$745$	−6.33689	+	19.5029i	−0.232166	+	0.714533i
$746$		0			0
$747$	−10.9329			−0.400015
$748$		0			0
$749$	13.8891			0.507497
$750$		0			0
$751$	−2.64421	+	8.13805i	−0.0964887	+	0.296962i	−0.987639	−	0.156747i	$-0.949899\pi$
$751$	−2.64421	+	8.13805i	−0.0964887	+	0.296962i	0.891150	+	0.453709i	$0.149899\pi$
$752$		0			0
$753$	16.1462	−	11.7309i	0.588401	−	0.427498i
$754$		0			0
$755$	4.58732	+	14.1183i	0.166950	+	0.513818i
$756$		0			0
$757$	−8.52618	−	6.19464i	−0.309889	−	0.225148i	0.421960	−	0.906615i	$-0.361342\pi$
$757$	−8.52618	−	6.19464i	−0.309889	−	0.225148i	−0.731849	+	0.681467i	$0.761342\pi$
$758$		0			0
$759$	−24.4365	−	12.2300i	−0.886990	−	0.443922i
$760$		0			0
$761$	−8.91113	−	6.47432i	−0.323028	−	0.234694i	0.414438	−	0.910077i	$-0.363978\pi$
$761$	−8.91113	−	6.47432i	−0.323028	−	0.234694i	−0.737467	+	0.675384i	$0.763978\pi$
$762$		0			0
$763$	8.48823	+	26.1241i	0.307295	+	0.945756i
$764$		0			0
$765$	−5.92380	+	4.30389i	−0.214175	+	0.155608i
$766$		0			0
$767$	3.08882	−	9.50642i	0.111531	−	0.343257i
$768$		0			0
$769$	−18.1683			−0.655164			−0.327582	−	0.944823i	$-0.606234\pi$
$769$	−18.1683			−0.655164			−0.327582	+	0.944823i	$0.606234\pi$
$770$		0			0
$771$	−18.7583			−0.675562
$772$		0			0
$773$	12.4069	−	38.1846i	0.446246	−	1.37340i	−0.434866	−	0.900495i	$-0.643204\pi$
$773$	12.4069	−	38.1846i	0.446246	−	1.37340i	0.881112	−	0.472908i	$-0.156796\pi$
$774$		0			0
$775$	−4.32961	+	3.14565i	−0.155524	+	0.112995i
$776$		0			0
$777$	−12.5280	−	38.5574i	−0.449441	−	1.38324i
$778$		0			0
$779$	−37.7514	−	27.4280i	−1.35258	−	0.982709i
$780$		0			0
$781$	13.8152	+	26.6375i	0.494347	+	0.953166i
$782$		0			0
$783$	−5.75530	−	4.18147i	−0.205678	−	0.149433i
$784$		0			0
$785$	−1.43995	−	4.43171i	−0.0513940	−	0.158174i
$786$		0			0
$787$	25.9724	−	18.8700i	0.925815	−	0.672644i	−0.0191499	−	0.999817i	$-0.506096\pi$
$787$	25.9724	−	18.8700i	0.925815	−	0.672644i	0.944964	+	0.327173i	$0.106096\pi$
$788$		0			0
$789$	−1.82249	+	5.60905i	−0.0648824	+	0.199687i
$790$		0			0
$791$	7.44758			0.264805
$792$		0			0
$793$	26.5585			0.943120
$794$		0			0
$795$	−1.94804	+	5.99546i	−0.0690900	+	0.212637i
$796$		0			0
$797$	−41.6389	+	30.2524i	−1.47493	+	1.07160i	−0.495778	+	0.868449i	$0.665117\pi$
$797$	−41.6389	+	30.2524i	−1.47493	+	1.07160i	−0.979148	+	0.203147i	$0.934883\pi$
$798$		0			0
$799$	3.90288	+	12.0118i	0.138074	+	0.424948i
$800$		0			0
$801$	4.15689	+	3.02016i	0.146877	+	0.106712i
$802$		0			0
$803$	−13.0077	+	2.15641i	−0.459031	+	0.0760982i
$804$		0			0
$805$	27.1040	+	19.6922i	0.955290	+	0.694059i
$806$		0			0
$807$	−9.04469	−	27.8367i	−0.318388	−	0.979898i
$808$		0			0
$809$	32.6349	−	23.7106i	1.14738	−	0.833621i	0.159251	−	0.987238i	$-0.449092\pi$
$809$	32.6349	−	23.7106i	1.14738	−	0.833621i	0.988131	+	0.153617i	$0.0490921\pi$
$810$		0			0
$811$	−9.48355	+	29.1874i	−0.333012	+	1.02491i	0.634680	+	0.772775i	$0.281132\pi$
$811$	−9.48355	+	29.1874i	−0.333012	+	1.02491i	−0.967693	+	0.252132i	$0.918868\pi$
$812$		0			0
$813$	−10.7510			−0.377054
$814$		0			0
$815$	13.7068			0.480128
$816$		0			0
$817$	15.7927	−	48.6049i	0.552517	−	1.70047i
$818$		0			0
$819$	−10.0259	+	7.28423i	−0.350333	+	0.254532i
$820$		0			0
$821$	9.33298	+	28.7240i	0.325723	+	1.00247i	0.971113	+	0.238620i	$0.0766949\pi$
$821$	9.33298	+	28.7240i	0.325723	+	1.00247i	−0.645390	+	0.763853i	$0.723305\pi$
$822$		0			0
$823$	−10.3294	−	7.50473i	−0.360059	−	0.261598i	0.393017	−	0.919531i	$-0.371431\pi$
$823$	−10.3294	−	7.50473i	−0.360059	−	0.261598i	−0.753077	+	0.657933i	$0.771431\pi$
$824$		0			0
$825$	−2.32825	+	2.36205i	−0.0810591	+	0.0822359i
$826$		0			0
$827$	−24.0825	−	17.4970i	−0.837430	−	0.608429i	0.0842213	−	0.996447i	$-0.473160\pi$
$827$	−24.0825	−	17.4970i	−0.837430	−	0.608429i	−0.921652	+	0.388018i	$0.873160\pi$
$828$		0			0
$829$	8.30598	+	25.5632i	0.288478	+	0.887845i	0.985334	+	0.170634i	$0.0545817\pi$
$829$	8.30598	+	25.5632i	0.288478	+	0.887845i	−0.696856	+	0.717211i	$0.745418\pi$
$830$		0			0
$831$	−2.04817	+	1.48808i	−0.0710501	+	0.0516209i
$832$		0			0
$833$	21.5733	−	66.3958i	0.747471	−	2.30048i
$834$		0			0
$835$	9.14510			0.316479
$836$		0			0
$837$	−5.35170			−0.184982
$838$		0			0
$839$	−5.73195	+	17.6411i	−0.197889	+	0.609040i	0.802042	+	0.597268i	$0.203747\pi$
$839$	−5.73195	+	17.6411i	−0.197889	+	0.609040i	−0.999931	+	0.0117716i	$0.996253\pi$
$840$		0			0
$841$	−17.4813	+	12.7009i	−0.602805	+	0.437963i
$842$		0			0
$843$	6.56621	+	20.2087i	0.226152	+	0.696025i
$844$		0			0
$845$	3.00273	+	2.18161i	0.103297	+	0.0750496i
$846$		0			0
$847$	0.644640	+	44.7241i	0.0221501	+	1.53674i
$848$		0			0
$849$	21.6353	+	15.7190i	0.742521	+	0.539473i
$850$		0			0
$851$	−25.3847	−	78.1259i	−0.870175	−	2.67812i
$852$		0			0
$853$	15.0449	−	10.9308i	0.515129	−	0.374263i	−0.299637	−	0.954053i	$-0.596865\pi$
$853$	15.0449	−	10.9308i	0.515129	−	0.374263i	0.814766	+	0.579790i	$0.196865\pi$
$854$		0			0
$855$	2.03312	−	6.25731i	0.0695314	−	0.213996i
$856$		0			0
$857$	−24.1981			−0.826591			−0.413295	−	0.910597i	$-0.635622\pi$
$857$	−24.1981			−0.826591			−0.413295	+	0.910597i	$0.635622\pi$
$858$		0			0
$859$	4.32264			0.147486			0.0737432	−	0.997277i	$-0.476505\pi$
$859$	4.32264			0.147486			0.0737432	+	0.997277i	$0.476505\pi$
$860$		0			0
$861$	8.91189	−	27.4280i	0.303716	−	0.934743i
$862$		0			0
$863$	−23.6458	+	17.1797i	−0.804914	+	0.584804i	−0.912352	−	0.409408i	$-0.865735\pi$
$863$	−23.6458	+	17.1797i	−0.804914	+	0.584804i	0.107438	+	0.994212i	$0.465735\pi$
$864$		0			0
$865$	−4.68784	−	14.4277i	−0.159391	−	0.490556i
$866$		0			0
$867$	29.6221	+	21.5217i	1.00602	+	0.730915i
$868$		0			0
$869$	1.47072	−	1.49207i	0.0498908	−	0.0506150i
$870$		0			0
$871$	3.85109	+	2.79798i	0.130489	+	0.0948059i
$872$		0			0
$873$	1.73624	+	5.34359i	0.0587627	+	0.180853i
$874$		0			0
$875$	3.28966	−	2.39008i	0.111211	−	0.0807995i
$876$		0			0
$877$	−5.99885	+	18.4626i	−0.202567	+	0.623436i	0.797238	+	0.603665i	$0.206294\pi$
$877$	−5.99885	+	18.4626i	−0.202567	+	0.623436i	−0.999805	+	0.0197709i	$0.993706\pi$
$878$		0			0
$879$	10.5674			0.356428
$880$		0			0
$881$	−32.8828			−1.10785			−0.553925	−	0.832567i	$-0.686871\pi$
$881$	−32.8828			−1.10785			−0.553925	+	0.832567i	$0.686871\pi$
$882$		0			0
$883$	1.72885	−	5.32086i	0.0581805	−	0.179061i	−0.917743	−	0.397175i	$-0.869991\pi$
$883$	1.72885	−	5.32086i	0.0581805	−	0.179061i	0.975923	+	0.218114i	$0.0699905\pi$
$884$		0			0
$885$	−2.65337	+	1.92778i	−0.0891920	+	0.0648017i
$886$		0			0
$887$	−11.1619	−	34.3526i	−0.374778	−	1.15345i	−0.943628	−	0.331008i	$-0.892611\pi$
$887$	−11.1619	−	34.3526i	−0.374778	−	1.15345i	0.568850	−	0.822441i	$-0.307389\pi$
$888$		0			0
$889$	−7.74900	−	5.62998i	−0.259893	−	0.188823i
$890$		0			0
$891$	−3.27197	+	0.542427i	−0.109615	+	0.0181720i
$892$		0			0
$893$	−9.18120	−	6.67053i	−0.307237	−	0.223221i
$894$		0			0
$895$	4.02219	+	12.3790i	0.134447	+	0.413785i
$896$		0			0
$897$	−20.3147	+	14.7595i	−0.678288	+	0.492805i
$898$		0			0
$899$	−11.7648	+	36.2083i	−0.392377	+	1.20761i
$900$		0			0
$901$	46.1593			1.53779
$902$		0			0
$903$	31.5854			1.05110
$904$		0			0
$905$	2.67307	−	8.22687i	0.0888559	−	0.273470i
$906$		0			0
$907$	−18.0159	+	13.0893i	−0.598208	+	0.434624i	−0.845242	−	0.534383i	$-0.820544\pi$
$907$	−18.0159	+	13.0893i	−0.598208	+	0.434624i	0.247034	+	0.969007i	$0.420544\pi$
$908$		0			0
$909$	−4.07076	−	12.5285i	−0.135019	−	0.415544i
$910$		0			0
$911$	−6.89416	−	5.00890i	−0.228414	−	0.165952i	0.467692	−	0.883891i	$-0.345086\pi$
$911$	−6.89416	−	5.00890i	−0.228414	−	0.165952i	−0.696106	+	0.717939i	$0.745086\pi$
$912$		0			0
$913$	16.6943	+	32.1888i	0.552500	+	1.06529i
$914$		0			0
$915$	−7.05002	−	5.12214i	−0.233066	−	0.169333i
$916$		0			0
$917$	10.9914	+	33.8280i	0.362967	+	1.11710i
$918$		0			0
$919$	26.9749	−	19.5984i	0.889820	−	0.646492i	−0.0460113	−	0.998941i	$-0.514651\pi$
$919$	26.9749	−	19.5984i	0.889820	−	0.646492i	0.935831	+	0.352449i	$0.114651\pi$
$920$		0			0
$921$	−6.51785	+	20.0599i	−0.214771	+	0.660996i
$922$		0			0
$923$	27.5738			0.907603
$924$		0			0
$925$	−9.97028			−0.327821
$926$		0			0
$927$	5.06260	−	15.5811i	0.166278	−	0.511750i
$928$		0			0
$929$	−29.9734	+	21.7769i	−0.983394	+	0.714478i	−0.958465	−	0.285211i	$-0.907936\pi$
$929$	−29.9734	+	21.7769i	−0.983394	+	0.714478i	−0.0249297	+	0.999689i	$0.507936\pi$
$930$		0			0
$931$	19.3845	+	59.6595i	0.635303	+	1.95526i
$932$		0			0
$933$	−13.3653	−	9.71049i	−0.437562	−	0.317907i
$934$		0			0
$935$	21.7170	+	10.8690i	0.710223	+	0.355453i
$936$		0			0
$937$	33.5077	+	24.3448i	1.09465	+	0.795310i	0.980178	−	0.198117i	$-0.0634825\pi$
$937$	33.5077	+	24.3448i	1.09465	+	0.795310i	0.114472	+	0.993427i	$0.463482\pi$
$938$		0			0
$939$	6.25638	+	19.2551i	0.204169	+	0.628368i
$940$		0			0
$941$	2.12133	−	1.54124i	0.0691534	−	0.0502429i	−0.552671	−	0.833399i	$-0.686392\pi$
$941$	2.12133	−	1.54124i	0.0691534	−	0.0502429i	0.621825	+	0.783156i	$0.286392\pi$
$942$		0			0
$943$	18.0575	−	55.5753i	0.588033	−	1.80978i
$944$		0			0
$945$	4.06625			0.132275
$946$		0			0
$947$	19.1970			0.623817			0.311909	−	0.950112i	$-0.399032\pi$
$947$	19.1970			0.623817			0.311909	+	0.950112i	$0.399032\pi$
$948$		0			0
$949$	−3.74407	+	11.5231i	−0.121538	+	0.374055i
$950$		0			0
$951$	−1.91326	+	1.39007i	−0.0620418	+	0.0450760i
$952$		0			0
$953$	−0.357215	−	1.09939i	−0.0115713	−	0.0356129i	0.945104	−	0.326769i	$-0.105960\pi$
$953$	−0.357215	−	1.09939i	−0.0115713	−	0.0356129i	−0.956675	+	0.291156i	$0.905960\pi$
$954$		0			0
$955$	−3.50915	−	2.54955i	−0.113554	−	0.0825015i
$956$		0			0
$957$	−3.52293	+	23.3298i	−0.113880	+	0.754145i
$958$		0			0
$959$	68.2581	+	49.5924i	2.20417	+	1.60142i
$960$		0			0
$961$	−0.729082	−	2.24389i	−0.0235188	−	0.0723834i
$962$		0			0
$963$	2.76337	−	2.00770i	0.0890482	−	0.0646973i
$964$		0			0
$965$	4.92321	−	15.1521i	0.158484	−	0.487763i
$966$		0			0
$967$	56.7505			1.82497			0.912486	−	0.409107i	$-0.134160\pi$
$967$	56.7505			1.82497			0.912486	+	0.409107i	$0.134160\pi$
$968$		0			0
$969$	−48.1753			−1.54761
$970$		0			0
$971$	2.19886	−	6.76741i	0.0705649	−	0.217176i	−0.909555	−	0.415584i	$-0.863577\pi$
$971$	2.19886	−	6.76741i	0.0705649	−	0.217176i	0.980120	+	0.198408i	$0.0635771\pi$
$972$		0			0
$973$	−59.8202	+	43.4619i	−1.91775	+	1.39333i
$974$		0			0
$975$	0.941789	+	2.89853i	0.0301614	+	0.0928272i
$976$		0			0
$977$	18.1288	+	13.1713i	0.579990	+	0.421388i	0.838721	−	0.544562i	$-0.183304\pi$
$977$	18.1288	+	13.1713i	0.579990	+	0.421388i	−0.258730	+	0.965950i	$0.583304\pi$
$978$		0			0
$979$	2.54451	−	16.8504i	0.0813230	−	0.538543i
$980$		0			0
$981$	5.46511	+	3.97063i	0.174488	+	0.126773i
$982$		0			0
$983$	−12.2639	−	37.7444i	−0.391157	−	1.20386i	−0.931914	−	0.362680i	$-0.881862\pi$
$983$	−12.2639	−	37.7444i	−0.391157	−	1.20386i	0.540756	−	0.841179i	$-0.318138\pi$
$984$		0			0
$985$	0.417774	−	0.303530i	0.0133114	−	0.00967128i
$986$		0			0
$987$	2.16739	−	6.67053i	0.0689887	−	0.212325i
$988$		0			0
$989$	63.9992			2.03505
$990$		0			0
$991$	−2.21449			−0.0703457			−0.0351728	−	0.999381i	$-0.511198\pi$
$991$	−2.21449			−0.0703457			−0.0351728	+	0.999381i	$0.511198\pi$
$992$		0			0
$993$	3.52229	−	10.8405i	0.111777	−	0.344013i
$994$		0			0
$995$	1.98923	−	1.44526i	0.0630629	−	0.0458179i
$996$		0			0
$997$	4.79751	+	14.7652i	0.151939	+	0.467619i	0.997838	−	0.0657237i	$-0.0209356\pi$
$997$	4.79751	+	14.7652i	0.151939	+	0.467619i	−0.845899	+	0.533343i	$0.820936\pi$
$998$		0			0
$999$	−8.06612	−	5.86038i	−0.255201	−	0.185414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.e.961.1	✓	12
11.3	even	5	inner	1320.2.bw.e.1081.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.e.961.1	✓	12	1.1	even	1	trivial
1320.2.bw.e.1081.1	yes	12	11.3	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.25654 - 3.86723i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.25654 - 3.86723i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-0.495215 + 3.27945i) q^{11} +(2.46563 + 1.79139i) q^{13} +(-0.309017 - 0.951057i) q^{15} +(-5.92380 + 4.30389i) q^{17} +(2.03312 - 6.25731i) q^{19} +4.06625 q^{21} +8.23914 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-2.19833 - 6.76576i) q^{29} +(-4.32961 - 3.14565i) q^{31} +(-2.96591 - 1.48438i) q^{33} +(3.28966 + 2.39008i) q^{35} +(-3.08098 - 9.48230i) q^{37} +(-2.46563 + 1.79139i) q^{39} +(2.19167 - 6.74528i) q^{41} +7.76770 q^{43} +1.00000 q^{45} +(0.533019 - 1.64046i) q^{47} +(-7.71346 + 5.60416i) q^{49} +(-2.26269 - 6.96384i) q^{51} +(-5.10005 - 3.70540i) q^{53} +(-1.52697 - 2.94421i) q^{55} +(5.32279 + 3.86723i) q^{57} +(-1.01350 - 3.11922i) q^{59} +(7.05002 - 5.12214i) q^{61} +(-1.25654 + 3.86723i) q^{63} -3.04769 q^{65} +1.56190 q^{67} +(-2.54603 + 7.83588i) q^{69} +(7.31954 - 5.31795i) q^{71} +(1.22849 + 3.78092i) q^{73} +(0.809017 + 0.587785i) q^{75} +(13.3046 - 2.20564i) q^{77} +(-0.511044 - 0.371295i) q^{79} +(0.309017 + 0.951057i) q^{81} +(8.84492 - 6.42621i) q^{83} +(2.26269 - 6.96384i) q^{85} +7.11394 q^{87} -5.13820 q^{89} +(3.82955 - 11.7861i) q^{91} +(4.32961 - 3.14565i) q^{93} +(2.03312 + 6.25731i) q^{95} +(-4.54553 - 3.30252i) q^{97} +(2.32825 - 2.36205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9} + 6 q^{11} + 12 q^{13} + 3 q^{15} - 13 q^{17} + 20 q^{23} - 3 q^{25} + 3 q^{27} - 3 q^{29} - 3 q^{31} - q^{33} + 5 q^{35} + 5 q^{37} - 12 q^{39} + q^{41} + 6 q^{43} + 12 q^{45} - 10 q^{47} - 12 q^{51} - 3 q^{53} + q^{55} + 5 q^{57} + 23 q^{59} - 7 q^{61} - 5 q^{63} - 28 q^{65} + 44 q^{67} + 5 q^{69} - 9 q^{71} - 27 q^{73} + 3 q^{75} + 65 q^{77} - q^{79} - 3 q^{81} - 21 q^{83} + 12 q^{85} + 28 q^{87} + 32 q^{89} - 19 q^{91} + 3 q^{93} + 5 q^{97} - 4 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9 + 6 * q^11 + 12 * q^13 + 3 * q^15 - 13 * q^17 + 20 * q^23 - 3 * q^25 + 3 * q^27 - 3 * q^29 - 3 * q^31 - q^33 + 5 * q^35 + 5 * q^37 - 12 * q^39 + q^41 + 6 * q^43 + 12 * q^45 - 10 * q^47 - 12 * q^51 - 3 * q^53 + q^55 + 5 * q^57 + 23 * q^59 - 7 * q^61 - 5 * q^63 - 28 * q^65 + 44 * q^67 + 5 * q^69 - 9 * q^71 - 27 * q^73 + 3 * q^75 + 65 * q^77 - q^79 - 3 * q^81 - 21 * q^83 + 12 * q^85 + 28 * q^87 + 32 * q^89 - 19 * q^91 + 3 * q^93 + 5 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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