LMFDB - Embedded newform 1920.2.y.j.1567.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(223,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.223"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,16,0,4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1567.3
Root			$1.28040 + 0.600471i$ of defining polynomial
Character	$\chi$	$=$	1920.1567
Dual form			1920.2.y.j.223.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-1.45639 + 1.69674i) q^{5} +(-1.12791 - 1.12791i) q^{7} +1.00000 q^{9} +(-4.05250 + 4.05250i) q^{11} -1.51085i q^{13} +(-1.45639 + 1.69674i) q^{15} +(-1.61725 - 1.61725i) q^{17} +(3.09584 - 3.09584i) q^{19} +(-1.12791 - 1.12791i) q^{21} +(-1.55774 + 1.55774i) q^{23} +(-0.757876 - 4.94223i) q^{25} +1.00000 q^{27} +(-0.425907 - 0.425907i) q^{29} -9.02889i q^{31} +(-4.05250 + 4.05250i) q^{33} +(3.55644 - 0.271100i) q^{35} -7.76193i q^{37} -1.51085i q^{39} -7.27238i q^{41} +9.30484i q^{43} +(-1.45639 + 1.69674i) q^{45} +(1.13932 - 1.13932i) q^{47} -4.45565i q^{49} +(-1.61725 - 1.61725i) q^{51} +8.27183 q^{53} +(-0.974046 - 12.7781i) q^{55} +(3.09584 - 3.09584i) q^{57} +(-9.12504 - 9.12504i) q^{59} +(-4.89881 + 4.89881i) q^{61} +(-1.12791 - 1.12791i) q^{63} +(2.56353 + 2.20039i) q^{65} +2.17068i q^{67} +(-1.55774 + 1.55774i) q^{69} -13.5937 q^{71} +(-1.11750 - 1.11750i) q^{73} +(-0.757876 - 4.94223i) q^{75} +9.14169 q^{77} -1.68922 q^{79} +1.00000 q^{81} -5.64544 q^{83} +(5.09941 - 0.388718i) q^{85} +(-0.425907 - 0.425907i) q^{87} +10.4975 q^{89} +(-1.70410 + 1.70410i) q^{91} -9.02889i q^{93} +(0.744106 + 9.76158i) q^{95} +(-6.26114 - 6.26114i) q^{97} +(-4.05250 + 4.05250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.45639	+	1.69674i	−0.651316	+	0.758807i
$5$	−1.45639	+	1.69674i	−0.651316	+	0.758807i
$6$		0			0
$7$	−1.12791	−	1.12791i	−0.426309	−	0.426309i	0.461060	−	0.887369i	$-0.347469\pi$
$7$	−1.12791	−	1.12791i	−0.426309	−	0.426309i	−0.887369	+	0.461060i	$0.847469\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−4.05250	+	4.05250i	−1.22188	+	1.22188i	−0.254911	+	0.966965i	$0.582046\pi$
$11$	−4.05250	+	4.05250i	−1.22188	+	1.22188i	−0.966965	+	0.254911i	$0.917954\pi$
$12$		0			0
$13$		−	1.51085i		−	0.419036i	−0.977805	−	0.209518i	$-0.932811\pi$
$13$		−	1.51085i		−	0.419036i	0.977805	−	0.209518i	$-0.0671894\pi$
$14$		0			0
$15$	−1.45639	+	1.69674i	−0.376037	+	0.438097i
$16$		0			0
$17$	−1.61725	−	1.61725i	−0.392241	−	0.392241i	0.483244	−	0.875486i	$-0.339458\pi$
$17$	−1.61725	−	1.61725i	−0.392241	−	0.392241i	−0.875486	+	0.483244i	$0.839458\pi$
$18$		0			0
$19$	3.09584	−	3.09584i	0.710234	−	0.710234i	−0.256350	−	0.966584i	$-0.582520\pi$
$19$	3.09584	−	3.09584i	0.710234	−	0.710234i	0.966584	+	0.256350i	$0.0825200\pi$
$20$		0			0
$21$	−1.12791	−	1.12791i	−0.246130	−	0.246130i
$22$		0			0
$23$	−1.55774	+	1.55774i	−0.324810	+	0.324810i	−0.850609	−	0.525799i	$-0.823767\pi$
$23$	−1.55774	+	1.55774i	−0.324810	+	0.324810i	0.525799	+	0.850609i	$0.323767\pi$
$24$		0			0
$25$	−0.757876	−	4.94223i	−0.151575	−	0.988446i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.425907	−	0.425907i	−0.0790889	−	0.0790889i	0.666456	−	0.745545i	$-0.267811\pi$
$29$	−0.425907	−	0.425907i	−0.0790889	−	0.0790889i	−0.745545	+	0.666456i	$0.767811\pi$
$30$		0			0
$31$		−	9.02889i		−	1.62164i	−0.585298	−	0.810818i	$-0.699022\pi$
$31$		−	9.02889i		−	1.62164i	0.585298	−	0.810818i	$-0.300978\pi$
$32$		0			0
$33$	−4.05250	+	4.05250i	−0.705450	+	0.705450i
$34$		0			0
$35$	3.55644	−	0.271100i	0.601148	−	0.0458243i
$36$		0			0
$37$		−	7.76193i		−	1.27605i	−0.770014	−	0.638027i	$-0.779751\pi$
$37$		−	7.76193i		−	1.27605i	0.770014	−	0.638027i	$-0.220249\pi$
$38$		0			0
$39$		−	1.51085i		−	0.241930i
$40$		0			0
$41$		−	7.27238i		−	1.13576i	−0.823113	−	0.567878i	$-0.807765\pi$
$41$		−	7.27238i		−	1.13576i	0.823113	−	0.567878i	$-0.192235\pi$
$42$		0			0
$43$			9.30484i			1.41897i	0.704718	+	0.709487i	$0.251073\pi$
$43$			9.30484i			1.41897i	−0.704718	+	0.709487i	$0.748927\pi$
$44$		0			0
$45$	−1.45639	+	1.69674i	−0.217105	+	0.252936i
$46$		0			0
$47$	1.13932	−	1.13932i	0.166187	−	0.166187i	−0.619114	−	0.785301i	$-0.712508\pi$
$47$	1.13932	−	1.13932i	0.166187	−	0.166187i	0.785301	+	0.619114i	$0.212508\pi$
$48$		0			0
$49$		−	4.45565i		−	0.636522i
$50$		0			0
$51$	−1.61725	−	1.61725i	−0.226461	−	0.226461i
$52$		0			0
$53$	8.27183			1.13622			0.568112	−	0.822952i	$-0.307674\pi$
$53$	8.27183			1.13622			0.568112	+	0.822952i	$0.307674\pi$
$54$		0			0
$55$	−0.974046	−	12.7781i	−0.131340	−	1.72299i
$56$		0			0
$57$	3.09584	−	3.09584i	0.410054	−	0.410054i
$58$		0			0
$59$	−9.12504	−	9.12504i	−1.18798	−	1.18798i	−0.977625	−	0.210354i	$-0.932538\pi$
$59$	−9.12504	−	9.12504i	−1.18798	−	1.18798i	−0.210354	−	0.977625i	$-0.567462\pi$
$60$		0			0
$61$	−4.89881	+	4.89881i	−0.627229	+	0.627229i	−0.947370	−	0.320141i	$-0.896270\pi$
$61$	−4.89881	+	4.89881i	−0.627229	+	0.627229i	0.320141	+	0.947370i	$0.396270\pi$
$62$		0			0
$63$	−1.12791	−	1.12791i	−0.142103	−	0.142103i
$64$		0			0
$65$	2.56353	+	2.20039i	0.317967	+	0.272925i
$66$		0			0
$67$			2.17068i			0.265191i	0.991170	+	0.132596i	$0.0423312\pi$
$67$			2.17068i			0.265191i	−0.991170	+	0.132596i	$0.957669\pi$
$68$		0			0
$69$	−1.55774	+	1.55774i	−0.187529	+	0.187529i
$70$		0			0
$71$	−13.5937			−1.61328			−0.806641	−	0.591042i	$-0.798717\pi$
$71$	−13.5937			−1.61328			−0.806641	+	0.591042i	$0.798717\pi$
$72$		0			0
$73$	−1.11750	−	1.11750i	−0.130793	−	0.130793i	0.638680	−	0.769473i	$-0.279481\pi$
$73$	−1.11750	−	1.11750i	−0.130793	−	0.130793i	−0.769473	+	0.638680i	$0.779481\pi$
$74$		0			0
$75$	−0.757876	−	4.94223i	−0.0875120	−	0.570679i
$76$		0			0
$77$	9.14169			1.04179
$78$		0			0
$79$	−1.68922			−0.190052			−0.0950261	−	0.995475i	$-0.530293\pi$
$79$	−1.68922			−0.190052			−0.0950261	+	0.995475i	$0.530293\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.64544			−0.619668			−0.309834	−	0.950791i	$-0.600273\pi$
$83$	−5.64544			−0.619668			−0.309834	+	0.950791i	$0.600273\pi$
$84$		0			0
$85$	5.09941	−	0.388718i	0.553109	−	0.0421624i
$86$		0			0
$87$	−0.425907	−	0.425907i	−0.0456620	−	0.0456620i
$88$		0			0
$89$	10.4975			1.11273			0.556365	−	0.830938i	$-0.312196\pi$
$89$	10.4975			1.11273			0.556365	+	0.830938i	$0.312196\pi$
$90$		0			0
$91$	−1.70410	+	1.70410i	−0.178639	+	0.178639i
$92$		0			0
$93$		−	9.02889i		−	0.936252i
$94$		0			0
$95$	0.744106	+	9.76158i	0.0763436	+	1.00152i
$96$		0			0
$97$	−6.26114	−	6.26114i	−0.635722	−	0.635722i	0.313775	−	0.949497i	$-0.398406\pi$
$97$	−6.26114	−	6.26114i	−0.635722	−	0.635722i	−0.949497	+	0.313775i	$0.898406\pi$
$98$		0			0
$99$	−4.05250	+	4.05250i	−0.407292	+	0.407292i
$100$		0			0
$101$	−1.36593	−	1.36593i	−0.135915	−	0.135915i	0.635876	−	0.771791i	$-0.280639\pi$
$101$	−1.36593	−	1.36593i	−0.135915	−	0.135915i	−0.771791	+	0.635876i	$0.780639\pi$
$102$		0			0
$103$	0.00181474	−	0.00181474i	0.000178812	−	0.000178812i	−0.707017	−	0.707196i	$-0.749960\pi$
$103$	0.00181474	−	0.00181474i	0.000178812	−	0.000178812i	0.707196	+	0.707017i	$0.249960\pi$
$104$		0			0
$105$	3.55644	−	0.271100i	0.347073	−	0.0264567i
$106$		0			0
$107$	−14.5410			−1.40573			−0.702863	−	0.711325i	$-0.748096\pi$
$107$	−14.5410			−1.40573			−0.702863	+	0.711325i	$0.748096\pi$
$108$		0			0
$109$	11.1313	+	11.1313i	1.06619	+	1.06619i	0.997649	+	0.0685378i	$0.0218334\pi$
$109$	11.1313	+	11.1313i	1.06619	+	1.06619i	0.0685378	+	0.997649i	$0.478167\pi$
$110$		0			0
$111$		−	7.76193i		−	0.736730i
$112$		0			0
$113$	9.54820	−	9.54820i	0.898219	−	0.898219i	−0.0970594	−	0.995279i	$-0.530944\pi$
$113$	9.54820	−	9.54820i	0.898219	−	0.898219i	0.995279	+	0.0970594i	$0.0309437\pi$
$114$		0			0
$115$	−0.374412	−	4.91174i	−0.0349141	−	0.458023i
$116$		0			0
$117$		−	1.51085i		−	0.139679i
$118$		0			0
$119$			3.64822i			0.334432i
$120$		0			0
$121$		−	21.8455i		−	1.98596i
$122$		0			0
$123$		−	7.27238i		−	0.655729i
$124$		0			0
$125$	9.48945	+	5.91187i	0.848763	+	0.528774i
$126$		0			0
$127$	−7.29219	+	7.29219i	−0.647077	+	0.647077i	−0.952286	−	0.305209i	$-0.901274\pi$
$127$	−7.29219	+	7.29219i	−0.647077	+	0.647077i	0.305209	+	0.952286i	$0.401274\pi$
$128$		0			0
$129$			9.30484i			0.819246i
$130$		0			0
$131$	−2.59824	−	2.59824i	−0.227009	−	0.227009i	0.584433	−	0.811442i	$-0.301317\pi$
$131$	−2.59824	−	2.59824i	−0.227009	−	0.227009i	−0.811442	+	0.584433i	$0.801317\pi$
$132$		0			0
$133$	−6.98363			−0.605558
$134$		0			0
$135$	−1.45639	+	1.69674i	−0.125346	+	0.146032i
$136$		0			0
$137$	−13.6691	+	13.6691i	−1.16783	+	1.16783i	−0.185115	+	0.982717i	$0.559266\pi$
$137$	−13.6691	+	13.6691i	−1.16783	+	1.16783i	−0.982717	+	0.185115i	$0.940734\pi$
$138$		0			0
$139$	−4.06432	−	4.06432i	−0.344731	−	0.344731i	0.513412	−	0.858143i	$-0.328381\pi$
$139$	−4.06432	−	4.06432i	−0.344731	−	0.344731i	−0.858143	+	0.513412i	$0.828381\pi$
$140$		0			0
$141$	1.13932	−	1.13932i	0.0959479	−	0.0959479i
$142$		0			0
$143$	6.12274	+	6.12274i	0.512009	+	0.512009i
$144$		0			0
$145$	1.34294	−	0.102370i	0.111525	−	0.00850133i
$146$		0			0
$147$		−	4.45565i		−	0.367496i
$148$		0			0
$149$	7.44842	−	7.44842i	0.610199	−	0.610199i	−0.332799	−	0.942998i	$-0.607993\pi$
$149$	7.44842	−	7.44842i	0.610199	−	0.610199i	0.942998	+	0.332799i	$0.107993\pi$
$150$		0			0
$151$	7.91377			0.644013			0.322007	−	0.946737i	$-0.395643\pi$
$151$	7.91377			0.644013			0.322007	+	0.946737i	$0.395643\pi$
$152$		0			0
$153$	−1.61725	−	1.61725i	−0.130747	−	0.130747i
$154$		0			0
$155$	15.3197	+	13.1496i	1.23051	+	1.05620i
$156$		0			0
$157$	−9.30731			−0.742804			−0.371402	−	0.928472i	$-0.621123\pi$
$157$	−9.30731			−0.742804			−0.371402	+	0.928472i	$0.621123\pi$
$158$		0			0
$159$	8.27183			0.655999
$160$		0			0
$161$	3.51396			0.276939
$162$		0			0
$163$	−3.08826			−0.241891			−0.120946	−	0.992659i	$-0.538593\pi$
$163$	−3.08826			−0.241891			−0.120946	+	0.992659i	$0.538593\pi$
$164$		0			0
$165$	−0.974046	−	12.7781i	−0.0758294	−	0.994771i
$166$		0			0
$167$	4.67681	+	4.67681i	0.361902	+	0.361902i	0.864513	−	0.502611i	$-0.167627\pi$
$167$	4.67681	+	4.67681i	0.361902	+	0.361902i	−0.502611	+	0.864513i	$0.667627\pi$
$168$		0			0
$169$	10.7173			0.824409
$170$		0			0
$171$	3.09584	−	3.09584i	0.236745	−	0.236745i
$172$		0			0
$173$		−	22.7032i		−	1.72609i	−0.505124	−	0.863047i	$-0.668553\pi$
$173$		−	22.7032i		−	1.72609i	0.505124	−	0.863047i	$-0.331447\pi$
$174$		0			0
$175$	−4.71956	+	6.42919i	−0.356765	+	0.486001i
$176$		0			0
$177$	−9.12504	−	9.12504i	−0.685880	−	0.685880i
$178$		0			0
$179$	5.21450	−	5.21450i	0.389750	−	0.389750i	−0.484848	−	0.874598i	$-0.661125\pi$
$179$	5.21450	−	5.21450i	0.389750	−	0.389750i	0.874598	+	0.484848i	$0.161125\pi$
$180$		0			0
$181$	−14.5282	−	14.5282i	−1.07987	−	1.07987i	−0.996520	−	0.0833500i	$-0.973438\pi$
$181$	−14.5282	−	14.5282i	−1.07987	−	1.07987i	−0.0833500	−	0.996520i	$-0.526562\pi$
$182$		0			0
$183$	−4.89881	+	4.89881i	−0.362131	+	0.362131i
$184$		0			0
$185$	13.1700	+	11.3044i	0.968278	+	0.831114i
$186$		0			0
$187$	13.1078			0.958540
$188$		0			0
$189$	−1.12791	−	1.12791i	−0.0820432	−	0.0820432i
$190$		0			0
$191$			21.5118i			1.55654i	0.627929	+	0.778271i	$0.283903\pi$
$191$			21.5118i			1.55654i	−0.627929	+	0.778271i	$0.716097\pi$
$192$		0			0
$193$	−14.7523	+	14.7523i	−1.06189	+	1.06189i	−0.0639410	+	0.997954i	$0.520367\pi$
$193$	−14.7523	+	14.7523i	−1.06189	+	1.06189i	−0.997954	+	0.0639410i	$0.979633\pi$
$194$		0			0
$195$	2.56353	+	2.20039i	0.183578	+	0.157573i
$196$		0			0
$197$			6.41499i			0.457049i	0.973538	+	0.228524i	$0.0733901\pi$
$197$			6.41499i			0.457049i	−0.973538	+	0.228524i	$0.926610\pi$
$198$		0			0
$199$			9.01442i			0.639015i	0.947584	+	0.319508i	$0.103518\pi$
$199$			9.01442i			0.639015i	−0.947584	+	0.319508i	$0.896482\pi$
$200$		0			0
$201$			2.17068i			0.153108i
$202$		0			0
$203$			0.960767i			0.0674326i
$204$		0			0
$205$	12.3394	+	10.5914i	0.861819	+	0.739736i
$206$		0			0
$207$	−1.55774	+	1.55774i	−0.108270	+	0.108270i
$208$		0			0
$209$			25.0918i			1.73563i
$210$		0			0
$211$	−12.1263	−	12.1263i	−0.834809	−	0.834809i	0.153361	−	0.988170i	$-0.450990\pi$
$211$	−12.1263	−	12.1263i	−0.834809	−	0.834809i	−0.988170	+	0.153361i	$0.950990\pi$
$212$		0			0
$213$	−13.5937			−0.931428
$214$		0			0
$215$	−15.7879	−	13.5514i	−1.07673	−	0.924201i
$216$		0			0
$217$	−10.1837	+	10.1837i	−0.691318	+	0.691318i
$218$		0			0
$219$	−1.11750	−	1.11750i	−0.0755134	−	0.0755134i
$220$		0			0
$221$	−2.44343	+	2.44343i	−0.164363	+	0.164363i
$222$		0			0
$223$	−9.07927	−	9.07927i	−0.607993	−	0.607993i	0.334428	−	0.942421i	$-0.391457\pi$
$223$	−9.07927	−	9.07927i	−0.607993	−	0.607993i	−0.942421	+	0.334428i	$0.891457\pi$
$224$		0			0
$225$	−0.757876	−	4.94223i	−0.0505251	−	0.329482i
$226$		0			0
$227$		−	0.580888i		−	0.0385549i	−0.999814	−	0.0192774i	$-0.993863\pi$
$227$		−	0.580888i		−	0.0385549i	0.999814	−	0.0192774i	$-0.00613658\pi$
$228$		0			0
$229$	−8.27674	+	8.27674i	−0.546942	+	0.546942i	−0.925555	−	0.378613i	$-0.876401\pi$
$229$	−8.27674	+	8.27674i	−0.546942	+	0.546942i	0.378613	+	0.925555i	$0.376401\pi$
$230$		0			0
$231$	9.14169			0.601479
$232$		0			0
$233$	10.8812	+	10.8812i	0.712852	+	0.712852i	0.967131	−	0.254279i	$-0.0818382\pi$
$233$	10.8812	+	10.8812i	0.712852	+	0.712852i	−0.254279	+	0.967131i	$0.581838\pi$
$234$		0			0
$235$	0.273843	+	3.59242i	0.0178635	+	0.234344i
$236$		0			0
$237$	−1.68922			−0.109727
$238$		0			0
$239$	10.3831			0.671628			0.335814	−	0.941928i	$-0.390989\pi$
$239$	10.3831			0.671628			0.335814	+	0.941928i	$0.390989\pi$
$240$		0			0
$241$	22.4691			1.44736			0.723680	−	0.690136i	$-0.242449\pi$
$241$	22.4691			1.44736			0.723680	+	0.690136i	$0.242449\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	7.56010	+	6.48915i	0.482997	+	0.414577i
$246$		0			0
$247$	−4.67736	−	4.67736i	−0.297613	−	0.297613i
$248$		0			0
$249$	−5.64544			−0.357765
$250$		0			0
$251$	−16.2297	+	16.2297i	−1.02441	+	1.02441i	−0.0247152	+	0.999695i	$0.507868\pi$
$251$	−16.2297	+	16.2297i	−1.02441	+	1.02441i	−0.999695	+	0.0247152i	$0.992132\pi$
$252$		0			0
$253$		−	12.6255i		−	0.793756i
$254$		0			0
$255$	5.09941	−	0.388718i	0.319337	−	0.0243424i
$256$		0			0
$257$	−0.223380	−	0.223380i	−0.0139341	−	0.0139341i	0.700105	−	0.714039i	$-0.253136\pi$
$257$	−0.223380	−	0.223380i	−0.0139341	−	0.0139341i	−0.714039	+	0.700105i	$0.753136\pi$
$258$		0			0
$259$	−8.75474	+	8.75474i	−0.543993	+	0.543993i
$260$		0			0
$261$	−0.425907	−	0.425907i	−0.0263630	−	0.0263630i
$262$		0			0
$263$	1.01264	−	1.01264i	0.0624420	−	0.0624420i	−0.675196	−	0.737638i	$-0.735941\pi$
$263$	1.01264	−	1.01264i	0.0624420	−	0.0624420i	0.737638	+	0.675196i	$0.235941\pi$
$264$		0			0
$265$	−12.0470	+	14.0352i	−0.740040	+	0.862174i
$266$		0			0
$267$	10.4975			0.642435
$268$		0			0
$269$	−12.5052	−	12.5052i	−0.762455	−	0.762455i	0.214310	−	0.976766i	$-0.431250\pi$
$269$	−12.5052	−	12.5052i	−0.762455	−	0.762455i	−0.976766	+	0.214310i	$0.931250\pi$
$270$		0			0
$271$		−	25.2641i		−	1.53469i	−0.641237	−	0.767343i	$-0.721578\pi$
$271$		−	25.2641i		−	1.53469i	0.641237	−	0.767343i	$-0.278422\pi$
$272$		0			0
$273$	−1.70410	+	1.70410i	−0.103137	+	0.103137i
$274$		0			0
$275$	23.0997	+	16.9571i	1.39296	+	1.02255i
$276$		0			0
$277$			13.1100i			0.787706i	0.919174	+	0.393853i	$0.128858\pi$
$277$			13.1100i			0.787706i	−0.919174	+	0.393853i	$0.871142\pi$
$278$		0			0
$279$		−	9.02889i		−	0.540546i
$280$		0			0
$281$			2.34999i			0.140189i	0.997540	+	0.0700944i	$0.0223301\pi$
$281$			2.34999i			0.140189i	−0.997540	+	0.0700944i	$0.977670\pi$
$282$		0			0
$283$		−	16.1614i		−	0.960695i	−0.877078	−	0.480348i	$-0.840510\pi$
$283$		−	16.1614i		−	0.960695i	0.877078	−	0.480348i	$-0.159490\pi$
$284$		0			0
$285$	0.744106	+	9.76158i	0.0440770	+	0.578226i
$286$		0			0
$287$	−8.20257	+	8.20257i	−0.484183	+	0.484183i
$288$		0			0
$289$		−	11.7690i		−	0.692293i
$290$		0			0
$291$	−6.26114	−	6.26114i	−0.367035	−	0.367035i
$292$		0			0
$293$	−15.9522			−0.931939			−0.465969	−	0.884801i	$-0.654294\pi$
$293$	−15.9522			−0.931939			−0.465969	+	0.884801i	$0.654294\pi$
$294$		0			0
$295$	28.7724	−	2.19327i	1.67520	−	0.127697i
$296$		0			0
$297$	−4.05250	+	4.05250i	−0.235150	+	0.235150i
$298$		0			0
$299$	2.35351	+	2.35351i	0.136107	+	0.136107i
$300$		0			0
$301$	10.4950	−	10.4950i	0.604921	−	0.604921i
$302$		0			0
$303$	−1.36593	−	1.36593i	−0.0784705	−	0.0784705i
$304$		0			0
$305$	−1.17746	−	15.4466i	−0.0674213	−	0.884469i
$306$		0			0
$307$			24.9902i			1.42627i	0.701029	+	0.713133i	$0.252724\pi$
$307$			24.9902i			1.42627i	−0.701029	+	0.713133i	$0.747276\pi$
$308$		0			0
$309$	0.00181474	−	0.00181474i	0.000103237	−	0.000103237i
$310$		0			0
$311$	−5.55703			−0.315111			−0.157555	−	0.987510i	$-0.550361\pi$
$311$	−5.55703			−0.315111			−0.157555	+	0.987510i	$0.550361\pi$
$312$		0			0
$313$	3.12705	+	3.12705i	0.176751	+	0.176751i	0.789938	−	0.613187i	$-0.210113\pi$
$313$	3.12705	+	3.12705i	0.176751	+	0.176751i	−0.613187	+	0.789938i	$0.710113\pi$
$314$		0			0
$315$	3.55644	−	0.271100i	0.200383	−	0.0152748i
$316$		0			0
$317$	−33.8169			−1.89935			−0.949674	−	0.313240i	$-0.898586\pi$
$317$	−33.8169			−1.89935			−0.949674	+	0.313240i	$0.898586\pi$
$318$		0			0
$319$	3.45198			0.193274
$320$		0			0
$321$	−14.5410			−0.811597
$322$		0			0
$323$	−10.0135			−0.557166
$324$		0			0
$325$	−7.46699	+	1.14504i	−0.414194	+	0.0635154i
$326$		0			0
$327$	11.1313	+	11.1313i	0.615563	+	0.615563i
$328$		0			0
$329$	−2.57009			−0.141694
$330$		0			0
$331$	13.0748	−	13.0748i	0.718658	−	0.718658i	−0.249672	−	0.968330i	$-0.580323\pi$
$331$	13.0748	−	13.0748i	0.718658	−	0.718658i	0.968330	+	0.249672i	$0.0803229\pi$
$332$		0			0
$333$		−	7.76193i		−	0.425351i
$334$		0			0
$335$	−3.68309	−	3.16136i	−0.201229	−	0.172723i
$336$		0			0
$337$	−4.71773	−	4.71773i	−0.256991	−	0.256991i	0.566838	−	0.823829i	$-0.308167\pi$
$337$	−4.71773	−	4.71773i	−0.256991	−	0.256991i	−0.823829	+	0.566838i	$0.808167\pi$
$338$		0			0
$339$	9.54820	−	9.54820i	0.518587	−	0.518587i
$340$		0			0
$341$	36.5896	+	36.5896i	1.98144	+	1.98144i
$342$		0			0
$343$	−12.9209	+	12.9209i	−0.697664	+	0.697664i
$344$		0			0
$345$	−0.374412	−	4.91174i	−0.0201577	−	0.264439i
$346$		0			0
$347$	26.4531			1.42008			0.710039	−	0.704163i	$-0.248677\pi$
$347$	26.4531			1.42008			0.710039	+	0.704163i	$0.248677\pi$
$348$		0			0
$349$	7.72146	+	7.72146i	0.413320	+	0.413320i	0.882893	−	0.469573i	$-0.155592\pi$
$349$	7.72146	+	7.72146i	0.413320	+	0.413320i	−0.469573	+	0.882893i	$0.655592\pi$
$350$		0			0
$351$		−	1.51085i		−	0.0806434i
$352$		0			0
$353$	17.1761	−	17.1761i	0.914189	−	0.914189i	−0.0824092	−	0.996599i	$-0.526261\pi$
$353$	17.1761	−	17.1761i	0.914189	−	0.914189i	0.996599	+	0.0824092i	$0.0262615\pi$
$354$		0			0
$355$	19.7978	−	23.0651i	1.05076	−	1.22417i
$356$		0			0
$357$			3.64822i			0.193084i
$358$		0			0
$359$		−	13.3611i		−	0.705173i	−0.935779	−	0.352587i	$-0.885302\pi$
$359$		−	13.3611i		−	0.705173i	0.935779	−	0.352587i	$-0.114698\pi$
$360$		0			0
$361$		−	0.168423i		−	0.00886435i
$362$		0			0
$363$		−	21.8455i		−	1.14659i
$364$		0			0
$365$	3.52361	−	0.268598i	0.184434	−	0.0140591i
$366$		0			0
$367$	2.07421	−	2.07421i	0.108273	−	0.108273i	−0.650895	−	0.759168i	$-0.725606\pi$
$367$	2.07421	−	2.07421i	0.108273	−	0.108273i	0.759168	+	0.650895i	$0.225606\pi$
$368$		0			0
$369$		−	7.27238i		−	0.378585i
$370$		0			0
$371$	−9.32985	−	9.32985i	−0.484382	−	0.484382i
$372$		0			0
$373$	31.6636			1.63948			0.819739	−	0.572737i	$-0.194118\pi$
$373$	31.6636			1.63948			0.819739	+	0.572737i	$0.194118\pi$
$374$		0			0
$375$	9.48945	+	5.91187i	0.490033	+	0.305288i
$376$		0			0
$377$	−0.643483	+	0.643483i	−0.0331411	+	0.0331411i
$378$		0			0
$379$	−5.09306	−	5.09306i	−0.261613	−	0.261613i	0.564096	−	0.825709i	$-0.309225\pi$
$379$	−5.09306	−	5.09306i	−0.261613	−	0.261613i	−0.825709	+	0.564096i	$0.809225\pi$
$380$		0			0
$381$	−7.29219	+	7.29219i	−0.373590	+	0.373590i
$382$		0			0
$383$	3.20359	+	3.20359i	0.163696	+	0.163696i	0.784202	−	0.620506i	$-0.213073\pi$
$383$	3.20359	+	3.20359i	0.163696	+	0.163696i	−0.620506	+	0.784202i	$0.713073\pi$
$384$		0			0
$385$	−13.3138	+	15.5111i	−0.678536	+	0.790519i
$386$		0			0
$387$			9.30484i			0.472992i
$388$		0			0
$389$	1.34936	−	1.34936i	0.0684155	−	0.0684155i	−0.672071	−	0.740487i	$-0.734595\pi$
$389$	1.34936	−	1.34936i	0.0684155	−	0.0684155i	0.740487	+	0.672071i	$0.234595\pi$
$390$		0			0
$391$	5.03851			0.254808
$392$		0			0
$393$	−2.59824	−	2.59824i	−0.131064	−	0.131064i
$394$		0			0
$395$	2.46016	−	2.86617i	0.123784	−	0.144213i
$396$		0			0
$397$	−24.4680			−1.22801			−0.614007	−	0.789301i	$-0.710443\pi$
$397$	−24.4680			−1.22801			−0.614007	+	0.789301i	$0.710443\pi$
$398$		0			0
$399$	−6.98363			−0.349619
$400$		0			0
$401$	28.5323			1.42484			0.712419	−	0.701755i	$-0.247600\pi$
$401$	28.5323			1.42484			0.712419	+	0.701755i	$0.247600\pi$
$402$		0			0
$403$	−13.6413			−0.679523
$404$		0			0
$405$	−1.45639	+	1.69674i	−0.0723684	+	0.0843119i
$406$		0			0
$407$	31.4552	+	31.4552i	1.55918	+	1.55918i
$408$		0			0
$409$	−15.1016			−0.746726			−0.373363	−	0.927685i	$-0.621795\pi$
$409$	−15.1016			−0.746726			−0.373363	+	0.927685i	$0.621795\pi$
$410$		0			0
$411$	−13.6691	+	13.6691i	−0.674248	+	0.674248i
$412$		0			0
$413$			20.5844i			1.01289i
$414$		0			0
$415$	8.22194	−	9.57886i	0.403599	−	0.470208i
$416$		0			0
$417$	−4.06432	−	4.06432i	−0.199030	−	0.199030i
$418$		0			0
$419$	1.93018	−	1.93018i	0.0942953	−	0.0942953i	−0.658386	−	0.752681i	$-0.728760\pi$
$419$	1.93018	−	1.93018i	0.0942953	−	0.0942953i	0.752681	+	0.658386i	$0.228760\pi$
$420$		0			0
$421$	−11.3334	−	11.3334i	−0.552355	−	0.552355i	0.374765	−	0.927120i	$-0.377723\pi$
$421$	−11.3334	−	11.3334i	−0.552355	−	0.552355i	−0.927120	+	0.374765i	$0.877723\pi$
$422$		0			0
$423$	1.13932	−	1.13932i	0.0553956	−	0.0553956i
$424$		0			0
$425$	−6.76716	+	9.21851i	−0.328255	+	0.447164i
$426$		0			0
$427$	11.0508			0.534786
$428$		0			0
$429$	6.12274	+	6.12274i	0.295609	+	0.295609i
$430$		0			0
$431$		−	23.3060i		−	1.12261i	−0.827609	−	0.561305i	$-0.810299\pi$
$431$		−	23.3060i		−	1.12261i	0.827609	−	0.561305i	$-0.189701\pi$
$432$		0			0
$433$	2.27419	−	2.27419i	0.109291	−	0.109291i	−0.650347	−	0.759637i	$-0.725376\pi$
$433$	2.27419	−	2.27419i	0.109291	−	0.109291i	0.759637	+	0.650347i	$0.225376\pi$
$434$		0			0
$435$	1.34294	−	0.102370i	0.0643890	−	0.00490825i
$436$		0			0
$437$			9.64500i			0.461383i
$438$		0			0
$439$			9.72340i			0.464073i	0.972707	+	0.232036i	$0.0745388\pi$
$439$			9.72340i			0.464073i	−0.972707	+	0.232036i	$0.925461\pi$
$440$		0			0
$441$		−	4.45565i		−	0.212174i
$442$		0			0
$443$			16.8029i			0.798332i	0.916879	+	0.399166i	$0.130700\pi$
$443$			16.8029i			0.798332i	−0.916879	+	0.399166i	$0.869300\pi$
$444$		0			0
$445$	−15.2884	+	17.8115i	−0.724738	+	0.844347i
$446$		0			0
$447$	7.44842	−	7.44842i	0.352298	−	0.352298i
$448$		0			0
$449$			14.6889i			0.693212i	0.938011	+	0.346606i	$0.112666\pi$
$449$			14.6889i			0.693212i	−0.938011	+	0.346606i	$0.887334\pi$
$450$		0			0
$451$	29.4713	+	29.4713i	1.38775	+	1.38775i
$452$		0			0
$453$	7.91377			0.371821
$454$		0			0
$455$	−0.409593	−	5.37326i	−0.0192020	−	0.251902i
$456$		0			0
$457$	−10.8605	+	10.8605i	−0.508034	+	0.508034i	−0.913922	−	0.405889i	$-0.866962\pi$
$457$	−10.8605	+	10.8605i	−0.508034	+	0.508034i	0.405889	+	0.913922i	$0.366962\pi$
$458$		0			0
$459$	−1.61725	−	1.61725i	−0.0754869	−	0.0754869i
$460$		0			0
$461$	12.2300	−	12.2300i	0.569608	−	0.569608i	−0.362411	−	0.932019i	$-0.618046\pi$
$461$	12.2300	−	12.2300i	0.569608	−	0.569608i	0.932019	+	0.362411i	$0.118046\pi$
$462$		0			0
$463$	25.4819	+	25.4819i	1.18424	+	1.18424i	0.978634	+	0.205609i	$0.0659176\pi$
$463$	25.4819	+	25.4819i	1.18424	+	1.18424i	0.205609	+	0.978634i	$0.434082\pi$
$464$		0			0
$465$	15.3197	+	13.1496i	0.710435	+	0.609796i
$466$		0			0
$467$			34.3316i			1.58868i	0.607475	+	0.794339i	$0.292182\pi$
$467$			34.3316i			1.58868i	−0.607475	+	0.794339i	$0.707818\pi$
$468$		0			0
$469$	2.44833	−	2.44833i	0.113053	−	0.113053i
$470$		0			0
$471$	−9.30731			−0.428858
$472$		0			0
$473$	−37.7079	−	37.7079i	−1.73381	−	1.73381i
$474$		0			0
$475$	−17.6466	−	12.9541i	−0.809682	−	0.594374i
$476$		0			0
$477$	8.27183			0.378741
$478$		0			0
$479$	−8.65519			−0.395466			−0.197733	−	0.980256i	$-0.563358\pi$
$479$	−8.65519			−0.395466			−0.197733	+	0.980256i	$0.563358\pi$
$480$		0			0
$481$	−11.7271			−0.534712
$482$		0			0
$483$	3.51396			0.159891
$484$		0			0
$485$	19.7422	−	1.50491i	0.896447	−	0.0683343i
$486$		0			0
$487$	7.87838	+	7.87838i	0.357004	+	0.357004i	0.862707	−	0.505704i	$-0.168767\pi$
$487$	7.87838	+	7.87838i	0.357004	+	0.357004i	−0.505704	+	0.862707i	$0.668767\pi$
$488$		0			0
$489$	−3.08826			−0.139656
$490$		0			0
$491$	−5.87690	+	5.87690i	−0.265221	+	0.265221i	−0.827171	−	0.561950i	$-0.810051\pi$
$491$	−5.87690	+	5.87690i	−0.265221	+	0.265221i	0.561950	+	0.827171i	$0.310051\pi$
$492$		0			0
$493$			1.37760i			0.0620439i
$494$		0			0
$495$	−0.974046	−	12.7781i	−0.0437801	−	0.574331i
$496$		0			0
$497$	15.3325	+	15.3325i	0.687756	+	0.687756i
$498$		0			0
$499$	4.52232	−	4.52232i	0.202447	−	0.202447i	−0.598601	−	0.801048i	$-0.704276\pi$
$499$	4.52232	−	4.52232i	0.202447	−	0.202447i	0.801048	+	0.598601i	$0.204276\pi$
$500$		0			0
$501$	4.67681	+	4.67681i	0.208944	+	0.208944i
$502$		0			0
$503$	−7.49454	+	7.49454i	−0.334165	+	0.334165i	−0.854166	−	0.520001i	$-0.825932\pi$
$503$	−7.49454	+	7.49454i	−0.334165	+	0.334165i	0.520001	+	0.854166i	$0.325932\pi$
$504$		0			0
$505$	4.30695	−	0.328310i	0.191657	−	0.0146096i
$506$		0			0
$507$	10.7173			0.475973
$508$		0			0
$509$	−2.39069	−	2.39069i	−0.105965	−	0.105965i	0.652136	−	0.758102i	$-0.273873\pi$
$509$	−2.39069	−	2.39069i	−0.105965	−	0.105965i	−0.758102	+	0.652136i	$0.773873\pi$
$510$		0			0
$511$			2.52086i			0.111516i
$512$		0			0
$513$	3.09584	−	3.09584i	0.136685	−	0.136685i
$514$		0			0
$515$	0.000436186		0.00572212i	1.92206e−5		0.000252147i
$516$		0			0
$517$			9.23418i			0.406119i
$518$		0			0
$519$		−	22.7032i		−	0.996561i
$520$		0			0
$521$			27.6569i			1.21167i	0.795590	+	0.605835i	$0.207161\pi$
$521$			27.6569i			1.21167i	−0.795590	+	0.605835i	$0.792839\pi$
$522$		0			0
$523$			5.69218i			0.248902i	0.992226	+	0.124451i	$0.0397169\pi$
$523$			5.69218i			0.248902i	−0.992226	+	0.124451i	$0.960283\pi$
$524$		0			0
$525$	−4.71956	+	6.42919i	−0.205979	+	0.280593i
$526$		0			0
$527$	−14.6020	+	14.6020i	−0.636073	+	0.636073i
$528$		0			0
$529$			18.1469i			0.788996i
$530$		0			0
$531$	−9.12504	−	9.12504i	−0.395993	−	0.395993i
$532$		0			0
$533$	−10.9875			−0.475922
$534$		0			0
$535$	21.1772	−	24.6723i	0.915572	−	1.06668i
$536$		0			0
$537$	5.21450	−	5.21450i	0.225022	−	0.225022i
$538$		0			0
$539$	18.0565	+	18.0565i	0.777750	+	0.777750i
$540$		0			0
$541$	−8.91173	+	8.91173i	−0.383145	+	0.383145i	−0.872234	−	0.489089i	$-0.837329\pi$
$541$	−8.91173	+	8.91173i	−0.383145	+	0.383145i	0.489089	+	0.872234i	$0.337329\pi$
$542$		0			0
$543$	−14.5282	−	14.5282i	−0.623463	−	0.623463i
$544$		0			0
$545$	−35.0985	+	2.67549i	−1.50345	+	0.114605i
$546$		0			0
$547$			16.9775i			0.725904i	0.931808	+	0.362952i	$0.118231\pi$
$547$			16.9775i			0.725904i	−0.931808	+	0.362952i	$0.881769\pi$
$548$		0			0
$549$	−4.89881	+	4.89881i	−0.209076	+	0.209076i
$550$		0			0
$551$	−2.63708			−0.112343
$552$		0			0
$553$	1.90528	+	1.90528i	0.0810209	+	0.0810209i
$554$		0			0
$555$	13.1700	+	11.3044i	0.559035	+	0.479844i
$556$		0			0
$557$	−5.77429			−0.244665			−0.122332	−	0.992489i	$-0.539037\pi$
$557$	−5.77429			−0.244665			−0.122332	+	0.992489i	$0.539037\pi$
$558$		0			0
$559$	14.0583			0.594601
$560$		0			0
$561$	13.1078			0.553414
$562$		0			0
$563$	−8.76839			−0.369544			−0.184772	−	0.982781i	$-0.559155\pi$
$563$	−8.76839			−0.369544			−0.184772	+	0.982781i	$0.559155\pi$
$564$		0			0
$565$	2.29497	+	30.1067i	0.0965503	+	1.26660i
$566$		0			0
$567$	−1.12791	−	1.12791i	−0.0473676	−	0.0473676i
$568$		0			0
$569$	−6.53649			−0.274024			−0.137012	−	0.990569i	$-0.543750\pi$
$569$	−6.53649			−0.274024			−0.137012	+	0.990569i	$0.543750\pi$
$570$		0			0
$571$	8.51080	−	8.51080i	0.356166	−	0.356166i	−0.506232	−	0.862397i	$-0.668962\pi$
$571$	8.51080	−	8.51080i	0.356166	−	0.356166i	0.862397	+	0.506232i	$0.168962\pi$
$572$		0			0
$573$			21.5118i			0.898670i
$574$		0			0
$575$	8.87926	+	6.51812i	0.370291	+	0.271824i
$576$		0			0
$577$	−2.50352	−	2.50352i	−0.104223	−	0.104223i	0.653072	−	0.757295i	$-0.273480\pi$
$577$	−2.50352	−	2.50352i	−0.104223	−	0.104223i	−0.757295	+	0.653072i	$0.773480\pi$
$578$		0			0
$579$	−14.7523	+	14.7523i	−0.613085	+	0.613085i
$580$		0			0
$581$	6.36753	+	6.36753i	0.264170	+	0.264170i
$582$		0			0
$583$	−33.5216	+	33.5216i	−1.38832	+	1.38832i
$584$		0			0
$585$	2.56353	+	2.20039i	0.105989	+	0.0909749i
$586$		0			0
$587$	−28.0515			−1.15781			−0.578904	−	0.815396i	$-0.696519\pi$
$587$	−28.0515			−1.15781			−0.578904	+	0.815396i	$0.696519\pi$
$588$		0			0
$589$	−27.9520	−	27.9520i	−1.15174	−	1.15174i
$590$		0			0
$591$			6.41499i			0.263877i
$592$		0			0
$593$	10.3023	−	10.3023i	0.423066	−	0.423066i	−0.463192	−	0.886258i	$-0.653296\pi$
$593$	10.3023	−	10.3023i	0.423066	−	0.423066i	0.886258	+	0.463192i	$0.153296\pi$
$594$		0			0
$595$	−6.19010	−	5.31322i	−0.253769	−	0.217821i
$596$		0			0
$597$			9.01442i			0.368936i
$598$		0			0
$599$			16.5177i			0.674893i	0.941345	+	0.337447i	$0.109563\pi$
$599$			16.5177i			0.674893i	−0.941345	+	0.337447i	$0.890437\pi$
$600$		0			0
$601$		−	28.1393i		−	1.14783i	−0.818916	−	0.573913i	$-0.805425\pi$
$601$		−	28.1393i		−	1.14783i	0.818916	−	0.573913i	$-0.194575\pi$
$602$		0			0
$603$			2.17068i			0.0883971i
$604$		0			0
$605$	37.0663	+	31.8156i	1.50696	+	1.29349i
$606$		0			0
$607$	7.05215	−	7.05215i	0.286238	−	0.286238i	−0.549353	−	0.835591i	$-0.685126\pi$
$607$	7.05215	−	7.05215i	0.286238	−	0.286238i	0.835591	+	0.549353i	$0.185126\pi$
$608$		0			0
$609$			0.960767i			0.0389322i
$610$		0			0
$611$	−1.72134	−	1.72134i	−0.0696381	−	0.0696381i
$612$		0			0
$613$	−9.16257			−0.370073			−0.185036	−	0.982732i	$-0.559240\pi$
$613$	−9.16257			−0.370073			−0.185036	+	0.982732i	$0.559240\pi$
$614$		0			0
$615$	12.3394	+	10.5914i	0.497571	+	0.427087i
$616$		0			0
$617$	1.80126	−	1.80126i	0.0725161	−	0.0725161i	−0.669919	−	0.742435i	$-0.733671\pi$
$617$	1.80126	−	1.80126i	0.0725161	−	0.0725161i	0.742435	+	0.669919i	$0.233671\pi$
$618$		0			0
$619$	22.8596	+	22.8596i	0.918804	+	0.918804i	0.996943	−	0.0781384i	$-0.0248976\pi$
$619$	22.8596	+	22.8596i	0.918804	+	0.918804i	−0.0781384	+	0.996943i	$0.524898\pi$
$620$		0			0
$621$	−1.55774	+	1.55774i	−0.0625098	+	0.0625098i
$622$		0			0
$623$	−11.8402	−	11.8402i	−0.474366	−	0.474366i
$624$		0			0
$625$	−23.8512	+	7.49119i	−0.954050	+	0.299648i
$626$		0			0
$627$			25.0918i			1.00207i
$628$		0			0
$629$	−12.5530	+	12.5530i	−0.500521	+	0.500521i
$630$		0			0
$631$	5.25748			0.209297			0.104648	−	0.994509i	$-0.466628\pi$
$631$	5.25748			0.209297			0.104648	+	0.994509i	$0.466628\pi$
$632$		0			0
$633$	−12.1263	−	12.1263i	−0.481977	−	0.481977i
$634$		0			0
$635$	−1.75273	−	22.9932i	−0.0695548	−	0.912458i
$636$		0			0
$637$	−6.73184			−0.266725
$638$		0			0
$639$	−13.5937			−0.537760
$640$		0			0
$641$	−13.7980			−0.544989			−0.272494	−	0.962157i	$-0.587849\pi$
$641$	−13.7980			−0.544989			−0.272494	+	0.962157i	$0.587849\pi$
$642$		0			0
$643$	−10.3483			−0.408098			−0.204049	−	0.978961i	$-0.565410\pi$
$643$	−10.3483			−0.408098			−0.204049	+	0.978961i	$0.565410\pi$
$644$		0			0
$645$	−15.7879	−	13.5514i	−0.621649	−	0.533588i
$646$		0			0
$647$	−5.33727	−	5.33727i	−0.209830	−	0.209830i	0.594365	−	0.804195i	$-0.297403\pi$
$647$	−5.33727	−	5.33727i	−0.209830	−	0.209830i	−0.804195	+	0.594365i	$0.797403\pi$
$648$		0			0
$649$	73.9585			2.90312
$650$		0			0
$651$	−10.1837	+	10.1837i	−0.399133	+	0.399133i
$652$		0			0
$653$			30.3415i			1.18735i	0.804703	+	0.593677i	$0.202324\pi$
$653$			30.3415i			1.18735i	−0.804703	+	0.593677i	$0.797676\pi$
$654$		0			0
$655$	8.19258	−	0.624504i	0.320110	−	0.0244014i
$656$		0			0
$657$	−1.11750	−	1.11750i	−0.0435977	−	0.0435977i
$658$		0			0
$659$	22.0703	−	22.0703i	0.859738	−	0.859738i	−0.131569	−	0.991307i	$-0.542002\pi$
$659$	22.0703	−	22.0703i	0.859738	−	0.859738i	0.991307	+	0.131569i	$0.0420016\pi$
$660$		0			0
$661$	−12.8058	−	12.8058i	−0.498089	−	0.498089i	0.412753	−	0.910843i	$-0.364567\pi$
$661$	−12.8058	−	12.8058i	−0.498089	−	0.498089i	−0.910843	+	0.412753i	$0.864567\pi$
$662$		0			0
$663$	−2.44343	+	2.44343i	−0.0948951	+	0.0948951i
$664$		0			0
$665$	10.1709	−	11.8494i	0.394409	−	0.459501i
$666$		0			0
$667$	1.32690			0.0513778
$668$		0			0
$669$	−9.07927	−	9.07927i	−0.351025	−	0.351025i
$670$		0			0
$671$		−	39.7049i		−	1.53279i
$672$		0			0
$673$	5.19258	−	5.19258i	0.200159	−	0.200159i	−0.599909	−	0.800068i	$-0.704797\pi$
$673$	5.19258	−	5.19258i	0.200159	−	0.200159i	0.800068	+	0.599909i	$0.204797\pi$
$674$		0			0
$675$	−0.757876	−	4.94223i	−0.0291707	−	0.190226i
$676$		0			0
$677$		−	34.5001i		−	1.32595i	−0.748643	−	0.662973i	$-0.769294\pi$
$677$		−	34.5001i		−	1.32595i	0.748643	−	0.662973i	$-0.230706\pi$
$678$		0			0
$679$			14.1240i			0.542028i
$680$		0			0
$681$		−	0.580888i		−	0.0222597i
$682$		0			0
$683$			16.4252i			0.628494i	0.949341	+	0.314247i	$0.101752\pi$
$683$			16.4252i			0.628494i	−0.949341	+	0.314247i	$0.898248\pi$
$684$		0			0
$685$	−3.28547	−	43.1005i	−0.125531	−	1.64679i
$686$		0			0
$687$	−8.27674	+	8.27674i	−0.315777	+	0.315777i
$688$		0			0
$689$		−	12.4975i		−	0.476118i
$690$		0			0
$691$	−9.38248	−	9.38248i	−0.356926	−	0.356926i	0.505752	−	0.862679i	$-0.331215\pi$
$691$	−9.38248	−	9.38248i	−0.356926	−	0.356926i	−0.862679	+	0.505752i	$0.831215\pi$
$692$		0			0
$693$	9.14169			0.347264
$694$		0			0
$695$	12.8153	−	0.976886i	0.486113	−	0.0370554i
$696$		0			0
$697$	−11.7613	+	11.7613i	−0.445490	+	0.445490i
$698$		0			0
$699$	10.8812	+	10.8812i	0.411565	+	0.411565i
$700$		0			0
$701$	9.83481	−	9.83481i	0.371455	−	0.371455i	−0.496552	−	0.868007i	$-0.665401\pi$
$701$	9.83481	−	9.83481i	0.371455	−	0.371455i	0.868007	+	0.496552i	$0.165401\pi$
$702$		0			0
$703$	−24.0297	−	24.0297i	−0.906296	−	0.906296i
$704$		0			0
$705$	0.273843	+	3.59242i	0.0103135	+	0.135298i
$706$		0			0
$707$			3.08128i			0.115883i
$708$		0			0
$709$	23.8550	−	23.8550i	0.895894	−	0.895894i	−0.0991761	−	0.995070i	$-0.531621\pi$
$709$	23.8550	−	23.8550i	0.895894	−	0.895894i	0.995070	+	0.0991761i	$0.0316207\pi$
$710$		0			0
$711$	−1.68922			−0.0633507
$712$		0			0
$713$	14.0646	+	14.0646i	0.526724	+	0.526724i
$714$		0			0
$715$	−19.3058	+	1.47164i	−0.721996	+	0.0550363i
$716$		0			0
$717$	10.3831			0.387765
$718$		0			0
$719$	15.7928			0.588971			0.294485	−	0.955656i	$-0.404852\pi$
$719$	15.7928			0.588971			0.294485	+	0.955656i	$0.404852\pi$
$720$		0			0
$721$	−0.00409372			−0.000152458
$722$		0			0
$723$	22.4691			0.835634
$724$		0			0
$725$	−1.78214	+	2.42771i	−0.0661872	+	0.0901630i
$726$		0			0
$727$	−2.18456	−	2.18456i	−0.0810208	−	0.0810208i	0.665435	−	0.746456i	$-0.268246\pi$
$727$	−2.18456	−	2.18456i	−0.0810208	−	0.0810208i	−0.746456	+	0.665435i	$0.768246\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.0483	−	15.0483i	0.556581	−	0.556581i
$732$		0			0
$733$		−	27.2805i		−	1.00763i	−0.863812	−	0.503815i	$-0.831929\pi$
$733$		−	27.2805i		−	1.00763i	0.863812	−	0.503815i	$-0.168071\pi$
$734$		0			0
$735$	7.56010	+	6.48915i	0.278858	+	0.239356i
$736$		0			0
$737$	−8.79670	−	8.79670i	−0.324031	−	0.324031i
$738$		0			0
$739$	35.5998	−	35.5998i	1.30956	−	1.30956i	0.387826	−	0.921733i	$-0.373226\pi$
$739$	35.5998	−	35.5998i	1.30956	−	1.30956i	0.921733	−	0.387826i	$-0.126774\pi$
$740$		0			0
$741$	−4.67736	−	4.67736i	−0.171827	−	0.171827i
$742$		0			0
$743$	25.0052	−	25.0052i	0.917352	−	0.917352i	−0.0794841	−	0.996836i	$-0.525327\pi$
$743$	25.0052	−	25.0052i	0.917352	−	0.917352i	0.996836	+	0.0794841i	$0.0253273\pi$
$744$		0			0
$745$	1.79028	+	23.4858i	0.0655907	+	0.860455i
$746$		0			0
$747$	−5.64544			−0.206556
$748$		0			0
$749$	16.4008	+	16.4008i	0.599274	+	0.599274i
$750$		0			0
$751$			35.0837i			1.28022i	0.768283	+	0.640111i	$0.221112\pi$
$751$			35.0837i			1.28022i	−0.768283	+	0.640111i	$0.778888\pi$
$752$		0			0
$753$	−16.2297	+	16.2297i	−0.591443	+	0.591443i
$754$		0			0
$755$	−11.5255	+	13.4276i	−0.419456	+	0.488682i
$756$		0			0
$757$			18.8071i			0.683554i	0.939781	+	0.341777i	$0.111029\pi$
$757$			18.8071i			0.683554i	−0.939781	+	0.341777i	$0.888971\pi$
$758$		0			0
$759$		−	12.6255i		−	0.458275i
$760$		0			0
$761$		−	0.986222i		−	0.0357505i	−0.999840	−	0.0178753i	$-0.994310\pi$
$761$		−	0.986222i		−	0.0357505i	0.999840	−	0.0178753i	$-0.00569017\pi$
$762$		0			0
$763$		−	25.1102i		−	0.909049i
$764$		0			0
$765$	5.09941	−	0.388718i	0.184370	−	0.0140541i
$766$		0			0
$767$	−13.7866	+	13.7866i	−0.497806	+	0.497806i
$768$		0			0
$769$		−	43.7365i		−	1.57718i	−0.614921	−	0.788589i	$-0.710812\pi$
$769$		−	43.7365i		−	1.57718i	0.614921	−	0.788589i	$-0.289188\pi$
$770$		0			0
$771$	−0.223380	−	0.223380i	−0.00804485	−	0.00804485i
$772$		0			0
$773$	−33.7211			−1.21286			−0.606431	−	0.795136i	$-0.707399\pi$
$773$	−33.7211			−1.21286			−0.606431	+	0.795136i	$0.707399\pi$
$774$		0			0
$775$	−44.6228	+	6.84278i	−1.60290	+	0.245800i
$776$		0			0
$777$	−8.75474	+	8.75474i	−0.314074	+	0.314074i
$778$		0			0
$779$	−22.5141	−	22.5141i	−0.806652	−	0.806652i
$780$		0			0
$781$	55.0887	−	55.0887i	1.97123	−	1.97123i
$782$		0			0
$783$	−0.425907	−	0.425907i	−0.0152207	−	0.0152207i
$784$		0			0
$785$	13.5550	−	15.7921i	0.483800	−	0.563645i
$786$		0			0
$787$		−	27.5235i		−	0.981106i	−0.871411	−	0.490553i	$-0.836795\pi$
$787$		−	27.5235i		−	0.981106i	0.871411	−	0.490553i	$-0.163205\pi$
$788$		0			0
$789$	1.01264	−	1.01264i	0.0360509	−	0.0360509i
$790$		0			0
$791$	−21.5390			−0.765838
$792$		0			0
$793$	7.40139	+	7.40139i	0.262831	+	0.262831i
$794$		0			0
$795$	−12.0470	+	14.0352i	−0.427262	+	0.497776i
$796$		0			0
$797$	−21.0022			−0.743937			−0.371969	−	0.928245i	$-0.621317\pi$
$797$	−21.0022			−0.743937			−0.371969	+	0.928245i	$0.621317\pi$
$798$		0			0
$799$	−3.68513			−0.130371
$800$		0			0
$801$	10.4975			0.370910
$802$		0			0
$803$	9.05731			0.319626
$804$		0			0
$805$	−5.11769	+	5.96229i	−0.180375	+	0.210143i
$806$		0			0
$807$	−12.5052	−	12.5052i	−0.440204	−	0.440204i
$808$		0			0
$809$	−17.2682			−0.607117			−0.303559	−	0.952813i	$-0.598175\pi$
$809$	−17.2682			−0.607117			−0.303559	+	0.952813i	$0.598175\pi$
$810$		0			0
$811$	12.8011	−	12.8011i	0.449507	−	0.449507i	−0.445683	−	0.895191i	$-0.647039\pi$
$811$	12.8011	−	12.8011i	0.449507	−	0.449507i	0.895191	+	0.445683i	$0.147039\pi$
$812$		0			0
$813$		−	25.2641i		−	0.886052i
$814$		0			0
$815$	4.49770	−	5.23999i	0.157548	−	0.183549i
$816$		0			0
$817$	28.8063	+	28.8063i	1.00780	+	1.00780i
$818$		0			0
$819$	−1.70410	+	1.70410i	−0.0595462	+	0.0595462i
$820$		0			0
$821$	−25.3693	−	25.3693i	−0.885395	−	0.885395i	0.108682	−	0.994077i	$-0.465337\pi$
$821$	−25.3693	−	25.3693i	−0.885395	−	0.885395i	−0.994077	+	0.108682i	$0.965337\pi$
$822$		0			0
$823$	12.8031	−	12.8031i	0.446288	−	0.446288i	−0.447830	−	0.894119i	$-0.647803\pi$
$823$	12.8031	−	12.8031i	0.446288	−	0.446288i	0.894119	+	0.447830i	$0.147803\pi$
$824$		0			0
$825$	23.0997	+	16.9571i	0.804228	+	0.590370i
$826$		0			0
$827$	−22.8624			−0.795005			−0.397502	−	0.917601i	$-0.630123\pi$
$827$	−22.8624			−0.795005			−0.397502	+	0.917601i	$0.630123\pi$
$828$		0			0
$829$	32.1620	+	32.1620i	1.11703	+	1.11703i	0.992175	+	0.124857i	$0.0398471\pi$
$829$	32.1620	+	32.1620i	1.11703	+	1.11703i	0.124857	+	0.992175i	$0.460153\pi$
$830$		0			0
$831$			13.1100i			0.454782i
$832$		0			0
$833$	−7.20592	+	7.20592i	−0.249670	+	0.249670i
$834$		0			0
$835$	−14.7466	+	1.12410i	−0.510326	+	0.0389012i
$836$		0			0
$837$		−	9.02889i		−	0.312084i
$838$		0			0
$839$		−	19.2953i		−	0.666147i	−0.942901	−	0.333073i	$-0.891914\pi$
$839$		−	19.2953i		−	0.666147i	0.942901	−	0.333073i	$-0.108086\pi$
$840$		0			0
$841$		−	28.6372i		−	0.987490i
$842$		0			0
$843$			2.34999i			0.0809381i
$844$		0			0
$845$	−15.6086	+	18.1845i	−0.536951	+	0.625567i
$846$		0			0
$847$	−24.6397	+	24.6397i	−0.846631	+	0.846631i
$848$		0			0
$849$		−	16.1614i		−	0.554658i
$850$		0			0
$851$	12.0910	+	12.0910i	0.414475	+	0.414475i
$852$		0			0
$853$	42.4336			1.45290			0.726449	−	0.687220i	$-0.241169\pi$
$853$	42.4336			1.45290			0.726449	+	0.687220i	$0.241169\pi$
$854$		0			0
$855$	0.744106	+	9.76158i	0.0254479	+	0.333839i
$856$		0			0
$857$	7.60830	−	7.60830i	0.259894	−	0.259894i	−0.565117	−	0.825011i	$-0.691169\pi$
$857$	7.60830	−	7.60830i	0.259894	−	0.259894i	0.825011	+	0.565117i	$0.191169\pi$
$858$		0			0
$859$	11.8598	+	11.8598i	0.404651	+	0.404651i	0.879869	−	0.475217i	$-0.157631\pi$
$859$	11.8598	+	11.8598i	0.404651	+	0.404651i	−0.475217	+	0.879869i	$0.657631\pi$
$860$		0			0
$861$	−8.20257	+	8.20257i	−0.279543	+	0.279543i
$862$		0			0
$863$	−5.07126	−	5.07126i	−0.172628	−	0.172628i	0.615505	−	0.788133i	$-0.288952\pi$
$863$	−5.07126	−	5.07126i	−0.172628	−	0.172628i	−0.788133	+	0.615505i	$0.788952\pi$
$864$		0			0
$865$	38.5215	+	33.0647i	1.30977	+	1.12423i
$866$		0			0
$867$		−	11.7690i		−	0.399696i
$868$		0			0
$869$	6.84557	−	6.84557i	0.232220	−	0.232220i
$870$		0			0
$871$	3.27959			0.111125
$872$		0			0
$873$	−6.26114	−	6.26114i	−0.211907	−	0.211907i
$874$		0			0
$875$	−4.03518	−	17.3713i	−0.136414	−	0.587256i
$876$		0			0
$877$	−10.2891			−0.347437			−0.173719	−	0.984795i	$-0.555578\pi$
$877$	−10.2891			−0.347437			−0.173719	+	0.984795i	$0.555578\pi$
$878$		0			0
$879$	−15.9522			−0.538055
$880$		0			0
$881$	−11.5441			−0.388932			−0.194466	−	0.980909i	$-0.562297\pi$
$881$	−11.5441			−0.388932			−0.194466	+	0.980909i	$0.562297\pi$
$882$		0			0
$883$	−38.5099			−1.29596			−0.647981	−	0.761657i	$-0.724386\pi$
$883$	−38.5099			−1.29596			−0.647981	+	0.761657i	$0.724386\pi$
$884$		0			0
$885$	28.7724	−	2.19327i	0.967175	−	0.0737258i
$886$		0			0
$887$	5.56002	+	5.56002i	0.186687	+	0.186687i	0.794262	−	0.607575i	$-0.207858\pi$
$887$	5.56002	+	5.56002i	0.186687	+	0.186687i	−0.607575	+	0.794262i	$0.707858\pi$
$888$		0			0
$889$	16.4498			0.551709
$890$		0			0
$891$	−4.05250	+	4.05250i	−0.135764	+	0.135764i
$892$		0			0
$893$		−	7.05429i		−	0.236063i
$894$		0			0
$895$	1.25334	+	16.4420i	0.0418945	+	0.549595i
$896$		0			0
$897$	2.35351	+	2.35351i	0.0785815	+	0.0785815i
$898$		0			0
$899$	−3.84547	+	3.84547i	−0.128253	+	0.128253i
$900$		0			0
$901$	−13.3776	−	13.3776i	−0.445674	−	0.445674i
$902$		0			0
$903$	10.4950	−	10.4950i	0.349252	−	0.349252i
$904$		0			0
$905$	45.8092	−	3.49194i	1.52275	−	0.116076i
$906$		0			0
$907$	−30.0758			−0.998649			−0.499325	−	0.866415i	$-0.666419\pi$
$907$	−30.0758			−0.998649			−0.499325	+	0.866415i	$0.666419\pi$
$908$		0			0
$909$	−1.36593	−	1.36593i	−0.0453049	−	0.0453049i
$910$		0			0
$911$			39.1493i			1.29707i	0.761183	+	0.648537i	$0.224619\pi$
$911$			39.1493i			1.29707i	−0.761183	+	0.648537i	$0.775381\pi$
$912$		0			0
$913$	22.8782	−	22.8782i	0.757157	−	0.757157i
$914$		0			0
$915$	−1.17746	−	15.4466i	−0.0389257	−	0.510649i
$916$		0			0
$917$			5.86114i			0.193552i
$918$		0			0
$919$		−	49.7130i		−	1.63988i	−0.572448	−	0.819941i	$-0.694006\pi$
$919$		−	49.7130i		−	1.63988i	0.572448	−	0.819941i	$-0.305994\pi$
$920$		0			0
$921$			24.9902i			0.823455i
$922$		0			0
$923$			20.5382i			0.676022i
$924$		0			0
$925$	−38.3612	+	5.88258i	−1.26131	+	0.193418i
$926$		0			0
$927$	0.00181474	−	0.00181474i	5.96040e−5	−	5.96040e-5i
$928$		0			0
$929$			0.175895i			0.00577094i	0.999996	+	0.00288547i	$0.000918475\pi$
$929$			0.175895i			0.00577094i	−0.999996	+	0.00288547i	$0.999082\pi$
$930$		0			0
$931$	−13.7940	−	13.7940i	−0.452079	−	0.452079i
$932$		0			0
$933$	−5.55703			−0.181929
$934$		0			0
$935$	−19.0901	+	22.2406i	−0.624313	+	0.727347i
$936$		0			0
$937$	−30.8310	+	30.8310i	−1.00720	+	1.00720i	−0.00722969	+	0.999974i	$0.502301\pi$
$937$	−30.8310	+	30.8310i	−1.00720	+	1.00720i	−0.999974	+	0.00722969i	$0.997699\pi$
$938$		0			0
$939$	3.12705	+	3.12705i	0.102048	+	0.102048i
$940$		0			0
$941$	38.5292	−	38.5292i	1.25602	−	1.25602i	0.303037	−	0.952979i	$-0.402000\pi$
$941$	38.5292	−	38.5292i	1.25602	−	1.25602i	0.952979	−	0.303037i	$-0.0980005\pi$
$942$		0			0
$943$	11.3285	+	11.3285i	0.368905	+	0.368905i
$944$		0			0
$945$	3.55644	−	0.271100i	0.115691	−	0.00881889i
$946$		0			0
$947$		−	57.6451i		−	1.87321i	−0.350382	−	0.936607i	$-0.613948\pi$
$947$		−	57.6451i		−	1.87321i	0.350382	−	0.936607i	$-0.386052\pi$
$948$		0			0
$949$	−1.68837	+	1.68837i	−0.0548070	+	0.0548070i
$950$		0			0
$951$	−33.8169			−1.09659
$952$		0			0
$953$	−31.1076	−	31.1076i	−1.00767	−	1.00767i	−0.999970	−	0.00770207i	$-0.997548\pi$
$953$	−31.1076	−	31.1076i	−1.00767	−	1.00767i	−0.00770207	−	0.999970i	$-0.502452\pi$
$954$		0			0
$955$	−36.5001	−	31.3296i	−1.18111	−	1.01380i
$956$		0			0
$957$	3.45198			0.111587
$958$		0			0
$959$	30.8350			0.995714
$960$		0			0
$961$	−50.5209			−1.62971
$962$		0			0
$963$	−14.5410			−0.468576
$964$		0			0
$965$	−3.54582	−	46.5160i	−0.114144	−	1.49740i
$966$		0			0
$967$	−37.9194	−	37.9194i	−1.21941	−	1.21941i	−0.967840	−	0.251567i	$-0.919054\pi$
$967$	−37.9194	−	37.9194i	−1.21941	−	1.21941i	−0.251567	−	0.967840i	$-0.580946\pi$
$968$		0			0
$969$	−10.0135			−0.321680
$970$		0			0
$971$	26.9668	−	26.9668i	0.865404	−	0.865404i	−0.126555	−	0.991960i	$-0.540392\pi$
$971$	26.9668	−	26.9668i	0.865404	−	0.865404i	0.991960	+	0.126555i	$0.0403921\pi$
$972$		0			0
$973$			9.16835i			0.293924i
$974$		0			0
$975$	−7.46699	+	1.14504i	−0.239135	+	0.0366706i
$976$		0			0
$977$	−13.1778	−	13.1778i	−0.421596	−	0.421596i	0.464157	−	0.885753i	$-0.346357\pi$
$977$	−13.1778	−	13.1778i	−0.421596	−	0.421596i	−0.885753	+	0.464157i	$0.846357\pi$
$978$		0			0
$979$	−42.5410	+	42.5410i	−1.35962	+	1.35962i
$980$		0			0
$981$	11.1313	+	11.1313i	0.355395	+	0.355395i
$982$		0			0
$983$	33.1704	−	33.1704i	1.05797	−	1.05797i	0.0597600	−	0.998213i	$-0.480966\pi$
$983$	33.1704	−	33.1704i	1.05797	−	1.05797i	0.998213	−	0.0597600i	$-0.0190335\pi$
$984$		0			0
$985$	−10.8846	−	9.34270i	−0.346812	−	0.297683i
$986$		0			0
$987$	−2.57009			−0.0818069
$988$		0			0
$989$	−14.4945	−	14.4945i	−0.460898	−	0.460898i
$990$		0			0
$991$			10.3297i			0.328135i	0.986449	+	0.164067i	$0.0524615\pi$
$991$			10.3297i			0.328135i	−0.986449	+	0.164067i	$0.947539\pi$
$992$		0			0
$993$	13.0748	−	13.0748i	0.414917	−	0.414917i
$994$		0			0
$995$	−15.2952	−	13.1285i	−0.484889	−	0.416201i
$996$		0			0
$997$		−	37.9110i		−	1.20065i	−0.799755	−	0.600327i	$-0.795037\pi$
$997$		−	37.9110i		−	1.20065i	0.799755	−	0.600327i	$-0.204963\pi$
$998$		0			0
$999$		−	7.76193i		−	0.245577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.j.1567.3		16
4.3	odd	2		1920.2.y.i.1567.3		16
5.3	odd	4		1920.2.bc.j.1183.7		16
8.3	odd	2		240.2.y.e.187.6	yes	16
8.5	even	2		960.2.y.e.847.6		16
16.3	odd	4		1920.2.bc.j.607.7		16
16.5	even	4		240.2.bc.e.67.2	yes	16
16.11	odd	4		960.2.bc.e.367.2		16
16.13	even	4		1920.2.bc.i.607.7		16
20.3	even	4		1920.2.bc.i.1183.7		16
24.11	even	2		720.2.z.f.667.3		16
40.3	even	4		240.2.bc.e.43.2	yes	16
40.13	odd	4		960.2.bc.e.463.2		16
48.5	odd	4		720.2.bd.f.307.7		16
80.3	even	4	inner	1920.2.y.j.223.3		16
80.13	odd	4		1920.2.y.i.223.3		16
80.43	even	4		960.2.y.e.943.6		16
80.53	odd	4		240.2.y.e.163.6	✓	16
120.83	odd	4		720.2.bd.f.523.7		16
240.53	even	4		720.2.z.f.163.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.6	✓	16	80.53	odd	4
240.2.y.e.187.6	yes	16	8.3	odd	2
240.2.bc.e.43.2	yes	16	40.3	even	4
240.2.bc.e.67.2	yes	16	16.5	even	4
720.2.z.f.163.3		16	240.53	even	4
720.2.z.f.667.3		16	24.11	even	2
720.2.bd.f.307.7		16	48.5	odd	4
720.2.bd.f.523.7		16	120.83	odd	4
960.2.y.e.847.6		16	8.5	even	2
960.2.y.e.943.6		16	80.43	even	4
960.2.bc.e.367.2		16	16.11	odd	4
960.2.bc.e.463.2		16	40.13	odd	4
1920.2.y.i.223.3		16	80.13	odd	4
1920.2.y.i.1567.3		16	4.3	odd	2
1920.2.y.j.223.3		16	80.3	even	4	inner
1920.2.y.j.1567.3		16	1.1	even	1	trivial
1920.2.bc.i.607.7		16	16.13	even	4
1920.2.bc.i.1183.7		16	20.3	even	4
1920.2.bc.j.607.7		16	16.3	odd	4
1920.2.bc.j.1183.7		16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-1.45639 + 1.69674i) q^{5} +(-1.12791 - 1.12791i) q^{7} +1.00000 q^{9} +(-4.05250 + 4.05250i) q^{11} -1.51085i q^{13} +(-1.45639 + 1.69674i) q^{15} +(-1.61725 - 1.61725i) q^{17} +(3.09584 - 3.09584i) q^{19} +(-1.12791 - 1.12791i) q^{21} +(-1.55774 + 1.55774i) q^{23} +(-0.757876 - 4.94223i) q^{25} +1.00000 q^{27} +(-0.425907 - 0.425907i) q^{29} -9.02889i q^{31} +(-4.05250 + 4.05250i) q^{33} +(3.55644 - 0.271100i) q^{35} -7.76193i q^{37} -1.51085i q^{39} -7.27238i q^{41} +9.30484i q^{43} +(-1.45639 + 1.69674i) q^{45} +(1.13932 - 1.13932i) q^{47} -4.45565i q^{49} +(-1.61725 - 1.61725i) q^{51} +8.27183 q^{53} +(-0.974046 - 12.7781i) q^{55} +(3.09584 - 3.09584i) q^{57} +(-9.12504 - 9.12504i) q^{59} +(-4.89881 + 4.89881i) q^{61} +(-1.12791 - 1.12791i) q^{63} +(2.56353 + 2.20039i) q^{65} +2.17068i q^{67} +(-1.55774 + 1.55774i) q^{69} -13.5937 q^{71} +(-1.11750 - 1.11750i) q^{73} +(-0.757876 - 4.94223i) q^{75} +9.14169 q^{77} -1.68922 q^{79} +1.00000 q^{81} -5.64544 q^{83} +(5.09941 - 0.388718i) q^{85} +(-0.425907 - 0.425907i) q^{87} +10.4975 q^{89} +(-1.70410 + 1.70410i) q^{91} -9.02889i q^{93} +(0.744106 + 9.76158i) q^{95} +(-6.26114 - 6.26114i) q^{97} +(-4.05250 + 4.05250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

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