LMFDB - Embedded newform 855.2.n.c.818.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, degree $2$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			818.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	855.818
Dual form			855.2.n.c.647.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 + 1.41421i) q^{2} +2.00000i q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.36603 - 2.36603i) q^{7} +(-3.73205 + 2.46410i) q^{10} +1.55291i q^{11} +(0.732051 + 0.732051i) q^{13} +6.69213 q^{14} +4.00000 q^{16} +(4.57081 + 4.57081i) q^{17} +1.00000i q^{19} +(-4.38134 - 0.896575i) q^{20} +(-2.19615 + 2.19615i) q^{22} +(-2.44949 + 2.44949i) q^{23} +(-4.59808 - 1.96410i) q^{25} +2.07055i q^{26} +(4.73205 + 4.73205i) q^{28} -8.76268 q^{29} -0.535898 q^{31} +(5.65685 + 5.65685i) q^{32} +12.9282i q^{34} +(4.12252 + 6.24384i) q^{35} +(3.46410 - 3.46410i) q^{37} +(-1.41421 + 1.41421i) q^{38} -2.82843i q^{41} +(-3.09808 - 3.09808i) q^{43} -3.10583 q^{44} -6.92820 q^{46} +(-2.63896 - 2.63896i) q^{47} -4.19615i q^{49} +(-3.72500 - 9.28032i) q^{50} +(-1.46410 + 1.46410i) q^{52} +(4.24264 - 4.24264i) q^{53} +(-3.40192 - 0.696152i) q^{55} +(-12.3923 - 12.3923i) q^{58} +13.3843 q^{59} -12.8564 q^{61} +(-0.757875 - 0.757875i) q^{62} +8.00000i q^{64} +(-1.93185 + 1.27551i) q^{65} +(9.46410 - 9.46410i) q^{67} +(-9.14162 + 9.14162i) q^{68} +(-3.00000 + 14.6603i) q^{70} -0.757875i q^{71} +(-3.90192 - 3.90192i) q^{73} +9.79796 q^{74} -2.00000 q^{76} +(3.67423 + 3.67423i) q^{77} +13.4641i q^{79} +(-1.79315 + 8.76268i) q^{80} +(4.00000 - 4.00000i) q^{82} +(-0.757875 + 0.757875i) q^{83} +(-12.0622 + 7.96410i) q^{85} -8.76268i q^{86} +8.76268 q^{89} +3.46410 q^{91} +(-4.89898 - 4.89898i) q^{92} -7.46410i q^{94} +(-2.19067 - 0.448288i) q^{95} +(-5.66025 + 5.66025i) q^{97} +(5.93426 - 5.93426i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{7} - 16 q^{10} - 8 q^{13} + 32 q^{16} + 24 q^{22} - 16 q^{25} + 24 q^{28} - 32 q^{31} - 4 q^{43} + 16 q^{52} - 48 q^{55} - 16 q^{58} + 8 q^{61} + 48 q^{67} - 24 q^{70} - 52 q^{73} - 16 q^{76}+ \cdots + 24 q^{97}+O(q^{100}) $ 8 * q + 12 * q^7 - 16 * q^10 - 8 * q^13 + 32 * q^16 + 24 * q^22 - 16 * q^25 + 24 * q^28 - 32 * q^31 - 4 * q^43 + 16 * q^52 - 48 * q^55 - 16 * q^58 + 8 * q^61 + 48 * q^67 - 24 * q^70 - 52 * q^73 - 16 * q^76 + 32 * q^82 - 48 * q^85 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.41421	+	1.41421i	1.00000	+	1.00000i	1.00000			$0$
$2$	1.41421	+	1.41421i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	−0.448288	+	2.19067i	−0.200480	+	0.979698i
$5$	−0.448288	+	2.19067i	−0.200480	+	0.979698i
$6$		0			0
$7$	2.36603	−	2.36603i	0.894274	−	0.894274i	−0.100649	−	0.994922i	$-0.532092\pi$
$7$	2.36603	−	2.36603i	0.894274	−	0.894274i	0.994922	+	0.100649i	$0.0320918\pi$
$8$		0			0
$9$		0			0
$10$	−3.73205	+	2.46410i	−1.18018	+	0.779217i
$11$			1.55291i			0.468221i	0.972210	+	0.234111i	$0.0752178\pi$
$11$			1.55291i			0.468221i	−0.972210	+	0.234111i	$0.924782\pi$
$12$		0			0
$13$	0.732051	+	0.732051i	0.203034	+	0.203034i	0.801299	−	0.598264i	$-0.204143\pi$
$13$	0.732051	+	0.732051i	0.203034	+	0.203034i	−0.598264	+	0.801299i	$0.704143\pi$
$14$	6.69213			1.78855
$15$		0			0
$16$	4.00000			1.00000
$17$	4.57081	+	4.57081i	1.10858	+	1.10858i	0.993337	+	0.115247i	$0.0367661\pi$
$17$	4.57081	+	4.57081i	1.10858	+	1.10858i	0.115247	+	0.993337i	$0.463234\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−4.38134	−	0.896575i	−0.979698	−	0.200480i
$21$		0			0
$22$	−2.19615	+	2.19615i	−0.468221	+	0.468221i
$23$	−2.44949	+	2.44949i	−0.510754	+	0.510754i	−0.914757	−	0.404004i	$-0.867618\pi$
$23$	−2.44949	+	2.44949i	−0.510754	+	0.510754i	0.404004	+	0.914757i	$0.367618\pi$
$24$		0			0
$25$	−4.59808	−	1.96410i	−0.919615	−	0.392820i
$26$			2.07055i			0.406069i
$27$		0			0
$28$	4.73205	+	4.73205i	0.894274	+	0.894274i
$29$	−8.76268			−1.62719			−0.813595	−	0.581432i	$-0.802492\pi$
$29$	−8.76268			−1.62719			−0.813595	+	0.581432i	$0.802492\pi$
$30$		0			0
$31$	−0.535898			−0.0962502			−0.0481251	−	0.998841i	$-0.515325\pi$
$31$	−0.535898			−0.0962502			−0.0481251	+	0.998841i	$0.515325\pi$
$32$	5.65685	+	5.65685i	1.00000	+	1.00000i
$33$		0			0
$34$			12.9282i			2.21717i
$35$	4.12252	+	6.24384i	0.696833	+	1.05540i
$36$		0			0
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	−0.362492	−	0.931987i	$-0.618074\pi$
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	0.931987	+	0.362492i	$0.118074\pi$
$38$	−1.41421	+	1.41421i	−0.229416	+	0.229416i
$39$		0			0
$40$		0			0
$41$		−	2.82843i		−	0.441726i	−0.975305	−	0.220863i	$-0.929113\pi$
$41$		−	2.82843i		−	0.441726i	0.975305	−	0.220863i	$-0.0708874\pi$
$42$		0			0
$43$	−3.09808	−	3.09808i	−0.472452	−	0.472452i	0.430255	−	0.902707i	$-0.358424\pi$
$43$	−3.09808	−	3.09808i	−0.472452	−	0.472452i	−0.902707	+	0.430255i	$0.858424\pi$
$44$	−3.10583			−0.468221
$45$		0			0
$46$	−6.92820			−1.02151
$47$	−2.63896	−	2.63896i	−0.384932	−	0.384932i	0.487944	−	0.872875i	$-0.337747\pi$
$47$	−2.63896	−	2.63896i	−0.384932	−	0.384932i	−0.872875	+	0.487944i	$0.837747\pi$
$48$		0			0
$49$		−	4.19615i		−	0.599450i
$50$	−3.72500	−	9.28032i	−0.526795	−	1.31244i
$51$		0			0
$52$	−1.46410	+	1.46410i	−0.203034	+	0.203034i
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	−0.352892	−	0.935664i	$-0.614802\pi$
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	0.935664	+	0.352892i	$0.114802\pi$
$54$		0			0
$55$	−3.40192	−	0.696152i	−0.458715	−	0.0938692i
$56$		0			0
$57$		0			0
$58$	−12.3923	−	12.3923i	−1.62719	−	1.62719i
$59$	13.3843			1.74248			0.871241	−	0.490855i	$-0.163316\pi$
$59$	13.3843			1.74248			0.871241	+	0.490855i	$0.163316\pi$
$60$		0			0
$61$	−12.8564			−1.64609			−0.823047	−	0.567973i	$-0.807728\pi$
$61$	−12.8564			−1.64609			−0.823047	+	0.567973i	$0.807728\pi$
$62$	−0.757875	−	0.757875i	−0.0962502	−	0.0962502i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−1.93185	+	1.27551i	−0.239617	+	0.158208i
$66$		0			0
$67$	9.46410	−	9.46410i	1.15622	−	1.15622i	0.170943	−	0.985281i	$-0.445319\pi$
$67$	9.46410	−	9.46410i	1.15622	−	1.15622i	0.985281	−	0.170943i	$-0.0546814\pi$
$68$	−9.14162	+	9.14162i	−1.10858	+	1.10858i
$69$		0			0
$70$	−3.00000	+	14.6603i	−0.358569	+	1.75224i
$71$		−	0.757875i		−	0.0899432i	−0.998988	−	0.0449716i	$-0.985680\pi$
$71$		−	0.757875i		−	0.0899432i	0.998988	−	0.0449716i	$-0.0143197\pi$
$72$		0			0
$73$	−3.90192	−	3.90192i	−0.456686	−	0.456686i	0.440880	−	0.897566i	$-0.354666\pi$
$73$	−3.90192	−	3.90192i	−0.456686	−	0.456686i	−0.897566	+	0.440880i	$0.854666\pi$
$74$	9.79796			1.13899
$75$		0			0
$76$	−2.00000			−0.229416
$77$	3.67423	+	3.67423i	0.418718	+	0.418718i
$78$		0			0
$79$			13.4641i			1.51483i	0.652934	+	0.757415i	$0.273538\pi$
$79$			13.4641i			1.51483i	−0.652934	+	0.757415i	$0.726462\pi$
$80$	−1.79315	+	8.76268i	−0.200480	+	0.979698i
$81$		0			0
$82$	4.00000	−	4.00000i	0.441726	−	0.441726i
$83$	−0.757875	+	0.757875i	−0.0831876	+	0.0831876i	−0.747476	−	0.664289i	$-0.768735\pi$
$83$	−0.757875	+	0.757875i	−0.0831876	+	0.0831876i	0.664289	+	0.747476i	$0.268735\pi$
$84$		0			0
$85$	−12.0622	+	7.96410i	−1.30833	+	0.863828i
$86$		−	8.76268i		−	0.944904i
$87$		0			0
$88$		0			0
$89$	8.76268			0.928843			0.464421	−	0.885614i	$-0.346262\pi$
$89$	8.76268			0.928843			0.464421	+	0.885614i	$0.346262\pi$
$90$		0			0
$91$	3.46410			0.363137
$92$	−4.89898	−	4.89898i	−0.510754	−	0.510754i
$93$		0			0
$94$		−	7.46410i		−	0.769863i
$95$	−2.19067	−	0.448288i	−0.224758	−	0.0459934i
$96$		0			0
$97$	−5.66025	+	5.66025i	−0.574712	+	0.574712i	−0.933441	−	0.358730i	$-0.883210\pi$
$97$	−5.66025	+	5.66025i	−0.574712	+	0.574712i	0.358730	+	0.933441i	$0.383210\pi$
$98$	5.93426	−	5.93426i	0.599450	−	0.599450i
$99$		0			0
$100$	3.92820	−	9.19615i	0.392820	−	0.919615i
$101$		−	18.9396i		−	1.88456i	−0.334828	−	0.942279i	$-0.608678\pi$
$101$		−	18.9396i		−	1.88456i	0.334828	−	0.942279i	$-0.391322\pi$
$102$		0			0
$103$	1.80385	+	1.80385i	0.177738	+	0.177738i	0.790369	−	0.612631i	$-0.209889\pi$
$103$	1.80385	+	1.80385i	0.177738	+	0.177738i	−0.612631	+	0.790369i	$0.709889\pi$
$104$		0			0
$105$		0			0
$106$	12.0000			1.16554
$107$	−0.378937	−	0.378937i	−0.0366333	−	0.0366333i	0.688553	−	0.725186i	$-0.258246\pi$
$107$	−0.378937	−	0.378937i	−0.0366333	−	0.0366333i	−0.725186	+	0.688553i	$0.758246\pi$
$108$		0			0
$109$		−	8.39230i		−	0.803837i	−0.915675	−	0.401919i	$-0.868344\pi$
$109$		−	8.39230i		−	0.803837i	0.915675	−	0.401919i	$-0.131656\pi$
$110$	−3.82654	−	5.79555i	−0.364846	−	0.552584i
$111$		0			0
$112$	9.46410	−	9.46410i	0.894274	−	0.894274i
$113$	−10.9348	+	10.9348i	−1.02866	+	1.02866i	−0.0290796	+	0.999577i	$0.509258\pi$
$113$	−10.9348	+	10.9348i	−1.02866	+	1.02866i	−0.999577	+	0.0290796i	$0.990742\pi$
$114$		0			0
$115$	−4.26795	−	6.46410i	−0.397988	−	0.602781i
$116$		−	17.5254i		−	1.62719i
$117$		0			0
$118$	18.9282	+	18.9282i	1.74248	+	1.74248i
$119$	21.6293			1.98276
$120$		0			0
$121$	8.58846			0.780769
$122$	−18.1817	−	18.1817i	−1.64609	−	1.64609i
$123$		0			0
$124$		−	1.07180i		−	0.0962502i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$		0			0
$127$	−1.26795	+	1.26795i	−0.112512	+	0.112512i	−0.761122	−	0.648609i	$-0.775351\pi$
$127$	−1.26795	+	1.26795i	−0.112512	+	0.112512i	0.648609	+	0.761122i	$0.275351\pi$
$128$		0			0
$129$		0			0
$130$	−4.53590	−	0.928203i	−0.397825	−	0.0814088i
$131$		−	12.8666i		−	1.12416i	−0.827082	−	0.562081i	$-0.810001\pi$
$131$		−	12.8666i		−	1.12416i	0.827082	−	0.562081i	$-0.189999\pi$
$132$		0			0
$133$	2.36603	+	2.36603i	0.205160	+	0.205160i
$134$	26.7685			2.31245
$135$		0			0
$136$		0			0
$137$	−1.08604	−	1.08604i	−0.0927870	−	0.0927870i	0.659190	−	0.751977i	$-0.270899\pi$
$137$	−1.08604	−	1.08604i	−0.0927870	−	0.0927870i	−0.751977	+	0.659190i	$0.770899\pi$
$138$		0			0
$139$		−	9.73205i		−	0.825462i	−0.910853	−	0.412731i	$-0.864575\pi$
$139$		−	9.73205i		−	0.825462i	0.910853	−	0.412731i	$-0.135425\pi$
$140$	−12.4877	+	8.24504i	−1.05540	+	0.696833i
$141$		0			0
$142$	1.07180	−	1.07180i	0.0899432	−	0.0899432i
$143$	−1.13681	+	1.13681i	−0.0950650	+	0.0950650i
$144$		0			0
$145$	3.92820	−	19.1962i	0.326220	−	1.59415i
$146$		−	11.0363i		−	0.913371i
$147$		0			0
$148$	6.92820	+	6.92820i	0.569495	+	0.569495i
$149$	−24.3562			−1.99534			−0.997669	−	0.0682436i	$-0.978261\pi$
$149$	−24.3562			−1.99534			−0.997669	+	0.0682436i	$0.978261\pi$
$150$		0			0
$151$	1.07180			0.0872216			0.0436108	−	0.999049i	$-0.486114\pi$
$151$	1.07180			0.0872216			0.0436108	+	0.999049i	$0.486114\pi$
$152$		0			0
$153$		0			0
$154$			10.3923i			0.837436i
$155$	0.240237	−	1.17398i	0.0192963	−	0.0942961i
$156$		0			0
$157$	−0.0717968	+	0.0717968i	−0.00573001	+	0.00573001i	−0.709966	−	0.704236i	$-0.751290\pi$
$157$	−0.0717968	+	0.0717968i	−0.00573001	+	0.00573001i	0.704236	+	0.709966i	$0.251290\pi$
$158$	−19.0411	+	19.0411i	−1.51483	+	1.51483i
$159$		0			0
$160$	−14.9282	+	9.85641i	−1.18018	+	0.779217i
$161$			11.5911i			0.913507i
$162$		0			0
$163$	−9.19615	−	9.19615i	−0.720298	−	0.720298i	0.248368	−	0.968666i	$-0.420106\pi$
$163$	−9.19615	−	9.19615i	−0.720298	−	0.720298i	−0.968666	+	0.248368i	$0.920106\pi$
$164$	5.65685			0.441726
$165$		0			0
$166$	−2.14359			−0.166375
$167$	14.0406	+	14.0406i	1.08649	+	1.08649i	0.995887	+	0.0906075i	$0.0288809\pi$
$167$	14.0406	+	14.0406i	1.08649	+	1.08649i	0.0906075	+	0.995887i	$0.471119\pi$
$168$		0			0
$169$		−	11.9282i		−	0.917554i
$170$	−28.3214	−	5.79555i	−2.17215	−	0.444499i
$171$		0			0
$172$	6.19615	−	6.19615i	0.472452	−	0.472452i
$173$	−8.10634	+	8.10634i	−0.616314	+	0.616314i	−0.944584	−	0.328270i	$-0.893534\pi$
$173$	−8.10634	+	8.10634i	−0.616314	+	0.616314i	0.328270	+	0.944584i	$0.393534\pi$
$174$		0			0
$175$	−15.5263	+	6.23205i	−1.17368	+	0.471099i
$176$			6.21166i			0.468221i
$177$		0			0
$178$	12.3923	+	12.3923i	0.928843	+	0.928843i
$179$	−5.17638			−0.386901			−0.193450	−	0.981110i	$-0.561968\pi$
$179$	−5.17638			−0.386901			−0.193450	+	0.981110i	$0.561968\pi$
$180$		0			0
$181$	18.3923			1.36709			0.683545	−	0.729909i	$-0.260437\pi$
$181$	18.3923			1.36709			0.683545	+	0.729909i	$0.260437\pi$
$182$	4.89898	+	4.89898i	0.363137	+	0.363137i
$183$		0			0
$184$		0			0
$185$	6.03579	+	9.14162i	0.443760	+	0.672105i
$186$		0			0
$187$	−7.09808	+	7.09808i	−0.519063	+	0.519063i
$188$	5.27792	−	5.27792i	0.384932	−	0.384932i
$189$		0			0
$190$	−2.46410	−	3.73205i	−0.178765	−	0.270751i
$191$			2.58819i			0.187275i	0.995606	+	0.0936374i	$0.0298495\pi$
$191$			2.58819i			0.187275i	−0.995606	+	0.0936374i	$0.970151\pi$
$192$		0			0
$193$	−11.4641	−	11.4641i	−0.825204	−	0.825204i	0.161645	−	0.986849i	$-0.448320\pi$
$193$	−11.4641	−	11.4641i	−0.825204	−	0.825204i	−0.986849	+	0.161645i	$0.948320\pi$
$194$	−16.0096			−1.14942
$195$		0			0
$196$	8.39230			0.599450
$197$	−9.79796	−	9.79796i	−0.698076	−	0.698076i	0.265920	−	0.963995i	$-0.414324\pi$
$197$	−9.79796	−	9.79796i	−0.698076	−	0.698076i	−0.963995	+	0.265920i	$0.914324\pi$
$198$		0			0
$199$		−	9.73205i		−	0.689887i	−0.938623	−	0.344943i	$-0.887898\pi$
$199$		−	9.73205i		−	0.689887i	0.938623	−	0.344943i	$-0.112102\pi$
$200$		0			0
$201$		0			0
$202$	26.7846	−	26.7846i	1.88456	−	1.88456i
$203$	−20.7327	+	20.7327i	−1.45515	+	1.45515i
$204$		0			0
$205$	6.19615	+	1.26795i	0.432758	+	0.0885574i
$206$			5.10205i			0.355477i
$207$		0			0
$208$	2.92820	+	2.92820i	0.203034	+	0.203034i
$209$	−1.55291			−0.107417
$210$		0			0
$211$	−5.85641			−0.403172			−0.201586	−	0.979471i	$-0.564609\pi$
$211$	−5.85641			−0.403172			−0.201586	+	0.979471i	$0.564609\pi$
$212$	8.48528	+	8.48528i	0.582772	+	0.582772i
$213$		0			0
$214$		−	1.07180i		−	0.0732665i
$215$	8.17569	−	5.39804i	0.557578	−	0.368143i
$216$		0			0
$217$	−1.26795	+	1.26795i	−0.0860740	+	0.0860740i
$218$	11.8685	−	11.8685i	0.803837	−	0.803837i
$219$		0			0
$220$	1.39230	−	6.80385i	0.0938692	−	0.458715i
$221$			6.69213i			0.450161i
$222$		0			0
$223$	−4.92820	−	4.92820i	−0.330017	−	0.330017i	0.522576	−	0.852593i	$-0.324971\pi$
$223$	−4.92820	−	4.92820i	−0.330017	−	0.330017i	−0.852593	+	0.522576i	$0.824971\pi$
$224$	26.7685			1.78855
$225$		0			0
$226$	−30.9282			−2.05731
$227$	−17.1464	−	17.1464i	−1.13805	−	1.13805i	−0.988800	−	0.149249i	$-0.952314\pi$
$227$	−17.1464	−	17.1464i	−1.13805	−	1.13805i	−0.149249	−	0.988800i	$-0.547686\pi$
$228$		0			0
$229$		−	12.6603i		−	0.836613i	−0.908306	−	0.418307i	$-0.862624\pi$
$229$		−	12.6603i		−	0.836613i	0.908306	−	0.418307i	$-0.137376\pi$
$230$	3.10583	−	15.1774i	0.204792	−	1.00077i
$231$		0			0
$232$		0			0
$233$	−5.46739	+	5.46739i	−0.358180	+	0.358180i	−0.863142	−	0.504962i	$-0.831507\pi$
$233$	−5.46739	+	5.46739i	−0.358180	+	0.358180i	0.504962	+	0.863142i	$0.331507\pi$
$234$		0			0
$235$	6.96410	−	4.59808i	0.454288	−	0.299945i
$236$			26.7685i			1.74248i
$237$		0			0
$238$	30.5885	+	30.5885i	1.98276	+	1.98276i
$239$	8.14351			0.526760			0.263380	−	0.964692i	$-0.415163\pi$
$239$	8.14351			0.526760			0.263380	+	0.964692i	$0.415163\pi$
$240$		0			0
$241$	28.3923			1.82891			0.914455	−	0.404689i	$-0.132620\pi$
$241$	28.3923			1.82891			0.914455	+	0.404689i	$0.132620\pi$
$242$	12.1459	+	12.1459i	0.780769	+	0.780769i
$243$		0			0
$244$		−	25.7128i		−	1.64609i
$245$	9.19239	+	1.88108i	0.587280	+	0.120178i
$246$		0			0
$247$	−0.732051	+	0.732051i	−0.0465793	+	0.0465793i
$248$		0			0
$249$		0			0
$250$	22.0000	−	4.00000i	1.39140	−	0.252982i
$251$			15.0387i			0.949235i	0.880192	+	0.474618i	$0.157414\pi$
$251$			15.0387i			0.949235i	−0.880192	+	0.474618i	$0.842586\pi$
$252$		0			0
$253$	−3.80385	−	3.80385i	−0.239146	−	0.239146i
$254$	−3.58630			−0.225025
$255$		0			0
$256$	16.0000			1.00000
$257$	−18.5606	−	18.5606i	−1.15778	−	1.15778i	−0.984952	−	0.172829i	$-0.944709\pi$
$257$	−18.5606	−	18.5606i	−1.15778	−	1.15778i	−0.172829	−	0.984952i	$-0.555291\pi$
$258$		0			0
$259$		−	16.3923i		−	1.01857i
$260$	−2.55103	−	3.86370i	−0.158208	−	0.239617i
$261$		0			0
$262$	18.1962	−	18.1962i	1.12416	−	1.12416i
$263$	−12.9546	+	12.9546i	−0.798812	+	0.798812i	−0.982908	−	0.184096i	$-0.941064\pi$
$263$	−12.9546	+	12.9546i	−0.798812	+	0.798812i	0.184096	+	0.982908i	$0.441064\pi$
$264$		0			0
$265$	7.39230	+	11.1962i	0.454106	+	0.687774i
$266$			6.69213i			0.410321i
$267$		0			0
$268$	18.9282	+	18.9282i	1.15622	+	1.15622i
$269$	−16.4901			−1.00542			−0.502709	−	0.864456i	$-0.667663\pi$
$269$	−16.4901			−1.00542			−0.502709	+	0.864456i	$0.667663\pi$
$270$		0			0
$271$	19.4641			1.18236			0.591180	−	0.806540i	$-0.298662\pi$
$271$	19.4641			1.18236			0.591180	+	0.806540i	$0.298662\pi$
$272$	18.2832	+	18.2832i	1.10858	+	1.10858i
$273$		0			0
$274$		−	3.07180i		−	0.185574i
$275$	3.05008	−	7.14042i	0.183927	−	0.430583i
$276$		0			0
$277$	−9.16987	+	9.16987i	−0.550964	+	0.550964i	−0.926719	−	0.375755i	$-0.877383\pi$
$277$	−9.16987	+	9.16987i	−0.550964	+	0.550964i	0.375755	+	0.926719i	$0.377383\pi$
$278$	13.7632	−	13.7632i	0.825462	−	0.825462i
$279$		0			0
$280$		0			0
$281$			3.10583i			0.185278i	0.995700	+	0.0926391i	$0.0295303\pi$
$281$			3.10583i			0.185278i	−0.995700	+	0.0926391i	$0.970470\pi$
$282$		0			0
$283$	0.633975	+	0.633975i	0.0376859	+	0.0376859i	0.725699	−	0.688013i	$-0.241517\pi$
$283$	0.633975	+	0.633975i	0.0376859	+	0.0376859i	−0.688013	+	0.725699i	$0.741517\pi$
$284$	1.51575			0.0899432
$285$		0			0
$286$	−3.21539			−0.190130
$287$	−6.69213	−	6.69213i	−0.395024	−	0.395024i
$288$		0			0
$289$			24.7846i			1.45792i
$290$	32.7028	−	21.5921i	1.92037	−	1.26793i
$291$		0			0
$292$	7.80385	−	7.80385i	0.456686	−	0.456686i
$293$	−10.2784	+	10.2784i	−0.600472	+	0.600472i	−0.940438	−	0.339965i	$-0.889585\pi$
$293$	−10.2784	+	10.2784i	−0.600472	+	0.600472i	0.339965	+	0.940438i	$0.389585\pi$
$294$		0			0
$295$	−6.00000	+	29.3205i	−0.349334	+	1.70711i
$296$		0			0
$297$		0			0
$298$	−34.4449	−	34.4449i	−1.99534	−	1.99534i
$299$	−3.58630			−0.207401
$300$		0			0
$301$	−14.6603			−0.845003
$302$	1.51575	+	1.51575i	0.0872216	+	0.0872216i
$303$		0			0
$304$			4.00000i			0.229416i
$305$	5.76337	−	28.1642i	0.330010	−	1.61267i
$306$		0			0
$307$	−18.3923	+	18.3923i	−1.04970	+	1.04970i	−0.0510059	+	0.998698i	$0.516243\pi$
$307$	−18.3923	+	18.3923i	−1.04970	+	1.04970i	−0.998698	+	0.0510059i	$0.983757\pi$
$308$	−7.34847	+	7.34847i	−0.418718	+	0.418718i
$309$		0			0
$310$	2.00000	−	1.32051i	0.113592	−	0.0749998i
$311$		−	9.65926i		−	0.547726i	−0.961769	−	0.273863i	$-0.911698\pi$
$311$		−	9.65926i		−	0.547726i	0.961769	−	0.273863i	$-0.0883015\pi$
$312$		0			0
$313$	22.3205	+	22.3205i	1.26163	+	1.26163i	0.950303	+	0.311327i	$0.100773\pi$
$313$	22.3205	+	22.3205i	1.26163	+	1.26163i	0.311327	+	0.950303i	$0.399227\pi$
$314$	−0.203072			−0.0114600
$315$		0			0
$316$	−26.9282			−1.51483
$317$	7.45001	+	7.45001i	0.418434	+	0.418434i	0.884664	−	0.466230i	$-0.154388\pi$
$317$	7.45001	+	7.45001i	0.418434	+	0.418434i	−0.466230	+	0.884664i	$0.654388\pi$
$318$		0			0
$319$		−	13.6077i		−	0.761885i
$320$	−17.5254	−	3.58630i	−0.979698	−	0.200480i
$321$		0			0
$322$	−16.3923	+	16.3923i	−0.913507	+	0.913507i
$323$	−4.57081	+	4.57081i	−0.254327	+	0.254327i
$324$		0			0
$325$	−1.92820	−	4.80385i	−0.106957	−	0.266470i
$326$		−	26.0106i		−	1.44060i
$327$		0			0
$328$		0			0
$329$	−12.4877			−0.688468
$330$		0			0
$331$	2.14359			0.117823			0.0589113	−	0.998263i	$-0.481237\pi$
$331$	2.14359			0.117823			0.0589113	+	0.998263i	$0.481237\pi$
$332$	−1.51575	−	1.51575i	−0.0831876	−	0.0831876i
$333$		0			0
$334$			39.7128i			2.17299i
$335$	16.4901	+	24.9754i	0.900950	+	1.36455i
$336$		0			0
$337$	3.66025	−	3.66025i	0.199387	−	0.199387i	−0.600350	−	0.799737i	$-0.704972\pi$
$337$	3.66025	−	3.66025i	0.199387	−	0.199387i	0.799737	+	0.600350i	$0.204972\pi$
$338$	16.8690	−	16.8690i	0.917554	−	0.917554i
$339$		0			0
$340$	−15.9282	−	24.1244i	−0.863828	−	1.30833i
$341$		−	0.832204i		−	0.0450664i
$342$		0			0
$343$	6.63397	+	6.63397i	0.358201	+	0.358201i
$344$		0			0
$345$		0			0
$346$	−22.9282			−1.23263
$347$	24.1667	+	24.1667i	1.29734	+	1.29734i	0.930145	+	0.367193i	$0.119681\pi$
$347$	24.1667	+	24.1667i	1.29734	+	1.29734i	0.367193	+	0.930145i	$0.380319\pi$
$348$		0			0
$349$		−	11.3397i		−	0.607003i	−0.952831	−	0.303501i	$-0.901844\pi$
$349$		−	11.3397i		−	0.607003i	0.952831	−	0.303501i	$-0.0981557\pi$
$350$	−30.7709	−	13.1440i	−1.64478	−	0.702578i
$351$		0			0
$352$	−8.78461	+	8.78461i	−0.468221	+	0.468221i
$353$	12.6264	−	12.6264i	0.672035	−	0.672035i	−0.286150	−	0.958185i	$-0.592376\pi$
$353$	12.6264	−	12.6264i	0.672035	−	0.672035i	0.958185	+	0.286150i	$0.0923756\pi$
$354$		0			0
$355$	1.66025	+	0.339746i	0.0881171	+	0.0180318i
$356$			17.5254i			0.928843i
$357$		0			0
$358$	−7.32051	−	7.32051i	−0.386901	−	0.386901i
$359$	0.517638			0.0273199			0.0136599	−	0.999907i	$-0.495652\pi$
$359$	0.517638			0.0273199			0.0136599	+	0.999907i	$0.495652\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	26.0106	+	26.0106i	1.36709	+	1.36709i
$363$		0			0
$364$			6.92820i			0.363137i
$365$	10.2970	−	6.79865i	0.538970	−	0.355857i
$366$		0			0
$367$	−13.7321	+	13.7321i	−0.716807	+	0.716807i	−0.967950	−	0.251143i	$-0.919194\pi$
$367$	−13.7321	+	13.7321i	−0.716807	+	0.716807i	0.251143	+	0.967950i	$0.419194\pi$
$368$	−9.79796	+	9.79796i	−0.510754	+	0.510754i
$369$		0			0
$370$	−4.39230	+	21.4641i	−0.228345	+	1.11587i
$371$		−	20.0764i		−	1.04231i
$372$		0			0
$373$	−3.46410	−	3.46410i	−0.179364	−	0.179364i	0.611714	−	0.791079i	$-0.290480\pi$
$373$	−3.46410	−	3.46410i	−0.179364	−	0.179364i	−0.791079	+	0.611714i	$0.790480\pi$
$374$	−20.0764			−1.03813
$375$		0			0
$376$		0			0
$377$	−6.41473	−	6.41473i	−0.330375	−	0.330375i
$378$		0			0
$379$			20.9282i			1.07501i	0.843261	+	0.537505i	$0.180633\pi$
$379$			20.9282i			1.07501i	−0.843261	+	0.537505i	$0.819367\pi$
$380$	0.896575	−	4.38134i	0.0459934	−	0.224758i
$381$		0			0
$382$	−3.66025	+	3.66025i	−0.187275	+	0.187275i
$383$	−14.0406	+	14.0406i	−0.717441	+	0.717441i	−0.968081	−	0.250639i	$-0.919359\pi$
$383$	−14.0406	+	14.0406i	−0.717441	+	0.717441i	0.250639	+	0.968081i	$0.419359\pi$
$384$		0			0
$385$	−9.69615	+	6.40192i	−0.494162	+	0.326272i
$386$		−	32.4254i		−	1.65041i
$387$		0			0
$388$	−11.3205	−	11.3205i	−0.574712	−	0.574712i
$389$	−11.0735			−0.561447			−0.280724	−	0.959789i	$-0.590574\pi$
$389$	−11.0735			−0.561447			−0.280724	+	0.959789i	$0.590574\pi$
$390$		0			0
$391$	−22.3923			−1.13243
$392$		0			0
$393$		0			0
$394$		−	27.7128i		−	1.39615i
$395$	−29.4954	−	6.03579i	−1.48408	−	0.303694i
$396$		0			0
$397$	23.2224	−	23.2224i	1.16550	−	1.16550i	0.182248	−	0.983253i	$-0.441663\pi$
$397$	23.2224	−	23.2224i	1.16550	−	1.16550i	0.983253	−	0.182248i	$-0.0583373\pi$
$398$	13.7632	−	13.7632i	0.689887	−	0.689887i
$399$		0			0
$400$	−18.3923	−	7.85641i	−0.919615	−	0.392820i
$401$			19.0411i			0.950868i	0.879751	+	0.475434i	$0.157709\pi$
$401$			19.0411i			0.950868i	−0.879751	+	0.475434i	$0.842291\pi$
$402$		0			0
$403$	−0.392305	−	0.392305i	−0.0195421	−	0.0195421i
$404$	37.8792			1.88456
$405$		0			0
$406$	−58.6410			−2.91030
$407$	5.37945	+	5.37945i	0.266650	+	0.266650i
$408$		0			0
$409$			11.8564i			0.586262i	0.956072	+	0.293131i	$0.0946971\pi$
$409$			11.8564i			0.586262i	−0.956072	+	0.293131i	$0.905303\pi$
$410$	6.96953	+	10.5558i	0.344201	+	0.521315i
$411$		0			0
$412$	−3.60770	+	3.60770i	−0.177738	+	0.177738i
$413$	31.6675	−	31.6675i	1.55826	−	1.55826i
$414$		0			0
$415$	−1.32051	−	2.00000i	−0.0648212	−	0.0981761i
$416$			8.28221i			0.406069i
$417$		0			0
$418$	−2.19615	−	2.19615i	−0.107417	−	0.107417i
$419$	29.9759			1.46442			0.732209	−	0.681080i	$-0.238489\pi$
$419$	29.9759			1.46442			0.732209	+	0.681080i	$0.238489\pi$
$420$		0			0
$421$	9.60770			0.468250			0.234125	−	0.972206i	$-0.424777\pi$
$421$	9.60770			0.468250			0.234125	+	0.972206i	$0.424777\pi$
$422$	−8.28221	−	8.28221i	−0.403172	−	0.403172i
$423$		0			0
$424$		0			0
$425$	−12.0394	−	29.9945i	−0.583997	−	1.45495i
$426$		0			0
$427$	−30.4186	+	30.4186i	−1.47206	+	1.47206i
$428$	0.757875	−	0.757875i	0.0366333	−	0.0366333i
$429$		0			0
$430$	19.1962	+	3.92820i	0.925721	+	0.189435i
$431$			8.76268i			0.422084i	0.977477	+	0.211042i	$0.0676856\pi$
$431$			8.76268i			0.422084i	−0.977477	+	0.211042i	$0.932314\pi$
$432$		0			0
$433$	−4.73205	−	4.73205i	−0.227408	−	0.227408i	0.584201	−	0.811609i	$-0.301408\pi$
$433$	−4.73205	−	4.73205i	−0.227408	−	0.227408i	−0.811609	+	0.584201i	$0.801408\pi$
$434$	−3.58630			−0.172148
$435$		0			0
$436$	16.7846			0.803837
$437$	−2.44949	−	2.44949i	−0.117175	−	0.117175i
$438$		0			0
$439$			31.8564i			1.52042i	0.649675	+	0.760212i	$0.274905\pi$
$439$			31.8564i			1.52042i	−0.649675	+	0.760212i	$0.725095\pi$
$440$		0			0
$441$		0			0
$442$	−9.46410	+	9.46410i	−0.450161	+	0.450161i
$443$	−22.4379	+	22.4379i	−1.06606	+	1.06606i	−0.0684012	+	0.997658i	$0.521790\pi$
$443$	−22.4379	+	22.4379i	−1.06606	+	1.06606i	−0.997658	+	0.0684012i	$0.978210\pi$
$444$		0			0
$445$	−3.92820	+	19.1962i	−0.186215	+	0.909985i
$446$		−	13.9391i		−	0.660034i
$447$		0			0
$448$	18.9282	+	18.9282i	0.894274	+	0.894274i
$449$	−6.41473			−0.302730			−0.151365	−	0.988478i	$-0.548367\pi$
$449$	−6.41473			−0.302730			−0.151365	+	0.988478i	$0.548367\pi$
$450$		0			0
$451$	4.39230			0.206826
$452$	−21.8695	−	21.8695i	−1.02866	−	1.02866i
$453$		0			0
$454$		−	48.4974i		−	2.27610i
$455$	−1.55291	+	7.58871i	−0.0728017	+	0.355764i
$456$		0			0
$457$	0.0262794	−	0.0262794i	0.00122930	−	0.00122930i	−0.706492	−	0.707721i	$-0.749723\pi$
$457$	0.0262794	−	0.0262794i	0.00122930	−	0.00122930i	0.707721	+	0.706492i	$0.249723\pi$
$458$	17.9043	−	17.9043i	0.836613	−	0.836613i
$459$		0			0
$460$	12.9282	−	8.53590i	0.602781	−	0.397988i
$461$		−	17.5897i		−	0.819236i	−0.912257	−	0.409618i	$-0.865662\pi$
$461$		−	17.5897i		−	0.819236i	0.912257	−	0.409618i	$-0.134338\pi$
$462$		0			0
$463$	9.97372	+	9.97372i	0.463518	+	0.463518i	0.899807	−	0.436289i	$-0.143707\pi$
$463$	9.97372	+	9.97372i	0.463518	+	0.463518i	−0.436289	+	0.899807i	$0.643707\pi$
$464$	−35.0507			−1.62719
$465$		0			0
$466$	−15.4641			−0.716361
$467$	−7.91688	−	7.91688i	−0.366349	−	0.366349i	0.499795	−	0.866144i	$-0.333409\pi$
$467$	−7.91688	−	7.91688i	−0.366349	−	0.366349i	−0.866144	+	0.499795i	$0.833409\pi$
$468$		0			0
$469$		−	44.7846i		−	2.06796i
$470$	16.3514	+	3.34607i	0.754233	+	0.154342i
$471$		0			0
$472$		0			0
$473$	4.81105	−	4.81105i	0.221212	−	0.221212i
$474$		0			0
$475$	1.96410	−	4.59808i	0.0901192	−	0.210974i
$476$			43.2586i			1.98276i
$477$		0			0
$478$	11.5167	+	11.5167i	0.526760	+	0.526760i
$479$	−23.7642			−1.08582			−0.542908	−	0.839792i	$-0.682677\pi$
$479$	−23.7642			−1.08582			−0.542908	+	0.839792i	$0.682677\pi$
$480$		0			0
$481$	5.07180			0.231254
$482$	40.1528	+	40.1528i	1.82891	+	1.82891i
$483$		0			0
$484$			17.1769i			0.780769i
$485$	−9.86233	−	14.9372i	−0.447825	−	0.678262i
$486$		0			0
$487$	−26.9282	+	26.9282i	−1.22023	+	1.22023i	−0.252685	+	0.967549i	$0.581314\pi$
$487$	−26.9282	+	26.9282i	−1.22023	+	1.22023i	−0.967549	+	0.252685i	$0.918686\pi$
$488$		0			0
$489$		0			0
$490$	10.3397	+	15.6603i	0.467102	+	0.707458i
$491$			37.7033i			1.70153i	0.525550	+	0.850763i	$0.323860\pi$
$491$			37.7033i			1.70153i	−0.525550	+	0.850763i	$0.676140\pi$
$492$		0			0
$493$	−40.0526	−	40.0526i	−1.80388	−	1.80388i
$494$	−2.07055			−0.0931586
$495$		0			0
$496$	−2.14359			−0.0962502
$497$	−1.79315	−	1.79315i	−0.0804338	−	0.0804338i
$498$		0			0
$499$		−	41.7321i		−	1.86818i	−0.357033	−	0.934092i	$-0.616212\pi$
$499$		−	41.7321i		−	1.86818i	0.357033	−	0.934092i	$-0.383788\pi$
$500$	18.3848	+	12.7279i	0.822192	+	0.569210i
$501$		0			0
$502$	−21.2679	+	21.2679i	−0.949235	+	0.949235i
$503$	−2.07055	+	2.07055i	−0.0923214	+	0.0923214i	−0.751759	−	0.659438i	$-0.770794\pi$
$503$	−2.07055	+	2.07055i	−0.0923214	+	0.0923214i	0.659438	+	0.751759i	$0.270794\pi$
$504$		0			0
$505$	41.4904	+	8.49038i	1.84630	+	0.377817i
$506$		−	10.7589i		−	0.478292i
$507$		0			0
$508$	−2.53590	−	2.53590i	−0.112512	−	0.112512i
$509$	−11.0363			−0.489176			−0.244588	−	0.969627i	$-0.578653\pi$
$509$	−11.0363			−0.489176			−0.244588	+	0.969627i	$0.578653\pi$
$510$		0			0
$511$	−18.4641			−0.816804
$512$	22.6274	+	22.6274i	1.00000	+	1.00000i
$513$		0			0
$514$		−	52.4974i		−	2.31556i
$515$	−4.76028	+	3.14299i	−0.209763	+	0.138497i
$516$		0			0
$517$	4.09808	−	4.09808i	0.180233	−	0.180233i
$518$	23.1822	−	23.1822i	1.01857	−	1.01857i
$519$		0			0
$520$		0			0
$521$			5.65685i			0.247831i	0.992293	+	0.123916i	$0.0395452\pi$
$521$			5.65685i			0.247831i	−0.992293	+	0.123916i	$0.960455\pi$
$522$		0			0
$523$	25.6603	+	25.6603i	1.12204	+	1.12204i	0.991434	+	0.130611i	$0.0416938\pi$
$523$	25.6603	+	25.6603i	1.12204	+	1.12204i	0.130611	+	0.991434i	$0.458306\pi$
$524$	25.7332			1.12416
$525$		0			0
$526$	−36.6410			−1.59762
$527$	−2.44949	−	2.44949i	−0.106701	−	0.106701i
$528$		0			0
$529$			11.0000i			0.478261i
$530$	−5.37945	+	26.2880i	−0.233668	+	1.14188i
$531$		0			0
$532$	−4.73205	+	4.73205i	−0.205160	+	0.205160i
$533$	2.07055	−	2.07055i	0.0896856	−	0.0896856i
$534$		0			0
$535$	1.00000	−	0.660254i	0.0432338	−	0.0285453i
$536$		0			0
$537$		0			0
$538$	−23.3205	−	23.3205i	−1.00542	−	1.00542i
$539$	6.51626			0.280675
$540$		0			0
$541$	29.1962			1.25524			0.627620	−	0.778520i	$-0.284029\pi$
$541$	29.1962			1.25524			0.627620	+	0.778520i	$0.284029\pi$
$542$	27.5264	+	27.5264i	1.18236	+	1.18236i
$543$		0			0
$544$			51.7128i			2.21717i
$545$	18.3848	+	3.76217i	0.787517	+	0.161154i
$546$		0			0
$547$	−22.0526	+	22.0526i	−0.942899	+	0.942899i	−0.998456	−	0.0555562i	$-0.982307\pi$
$547$	−22.0526	+	22.0526i	−0.942899	+	0.942899i	0.0555562	+	0.998456i	$0.482307\pi$
$548$	2.17209	−	2.17209i	0.0927870	−	0.0927870i
$549$		0			0
$550$	14.4115	−	5.78461i	0.614510	−	0.246657i
$551$		−	8.76268i		−	0.373303i
$552$		0			0
$553$	31.8564	+	31.8564i	1.35467	+	1.35467i
$554$	−25.9363			−1.10193
$555$		0			0
$556$	19.4641			0.825462
$557$	15.0895	+	15.0895i	0.639362	+	0.639362i	0.950398	−	0.311036i	$-0.100676\pi$
$557$	15.0895	+	15.0895i	0.639362	+	0.639362i	−0.311036	+	0.950398i	$0.600676\pi$
$558$		0			0
$559$		−	4.53590i		−	0.191848i
$560$	16.4901	+	24.9754i	0.696833	+	1.05540i
$561$		0			0
$562$	−4.39230	+	4.39230i	−0.185278	+	0.185278i
$563$	28.2843	−	28.2843i	1.19204	−	1.19204i	0.215546	−	0.976494i	$-0.430847\pi$
$563$	28.2843	−	28.2843i	1.19204	−	1.19204i	0.976494	−	0.215546i	$-0.0691532\pi$
$564$		0			0
$565$	−19.0526	−	28.8564i	−0.801547	−	1.21400i
$566$			1.79315i			0.0753718i
$567$		0			0
$568$		0			0
$569$	−17.4510			−0.731585			−0.365793	−	0.930696i	$-0.619202\pi$
$569$	−17.4510			−0.731585			−0.365793	+	0.930696i	$0.619202\pi$
$570$		0			0
$571$	−42.3923			−1.77406			−0.887031	−	0.461709i	$-0.847236\pi$
$571$	−42.3923			−1.77406			−0.887031	+	0.461709i	$0.847236\pi$
$572$	−2.27362	−	2.27362i	−0.0950650	−	0.0950650i
$573$		0			0
$574$		−	18.9282i		−	0.790048i
$575$	16.0740	−	6.45189i	0.670332	−	0.269063i
$576$		0			0
$577$	14.8301	−	14.8301i	0.617386	−	0.617386i	−0.327474	−	0.944860i	$-0.606197\pi$
$577$	14.8301	−	14.8301i	0.617386	−	0.617386i	0.944860	+	0.327474i	$0.106197\pi$
$578$	−35.0507	+	35.0507i	−1.45792	+	1.45792i
$579$		0			0
$580$	38.3923	+	7.85641i	1.59415	+	0.326220i
$581$			3.58630i			0.148785i
$582$		0			0
$583$	6.58846	+	6.58846i	0.272866	+	0.272866i
$584$		0			0
$585$		0			0
$586$	−29.0718			−1.20094
$587$	24.6844	+	24.6844i	1.01883	+	1.01883i	0.999819	+	0.0190136i	$0.00605258\pi$
$587$	24.6844	+	24.6844i	1.01883	+	1.01883i	0.0190136	+	0.999819i	$0.493947\pi$
$588$		0			0
$589$		−	0.535898i		−	0.0220813i
$590$	−49.9507	+	32.9802i	−2.05644	+	1.35777i
$591$		0			0
$592$	13.8564	−	13.8564i	0.569495	−	0.569495i
$593$	−5.00052	+	5.00052i	−0.205347	+	0.205347i	−0.802286	−	0.596940i	$-0.796383\pi$
$593$	−5.00052	+	5.00052i	−0.205347	+	0.205347i	0.596940	+	0.802286i	$0.296383\pi$
$594$		0			0
$595$	−9.69615	+	47.3827i	−0.397503	+	1.94250i
$596$		−	48.7124i		−	1.99534i
$597$		0			0
$598$	−5.07180	−	5.07180i	−0.207401	−	0.207401i
$599$	23.3853			0.955497			0.477749	−	0.878497i	$-0.341453\pi$
$599$	23.3853			0.955497			0.477749	+	0.878497i	$0.341453\pi$
$600$		0			0
$601$	16.0000			0.652654			0.326327	−	0.945257i	$-0.394189\pi$
$601$	16.0000			0.652654			0.326327	+	0.945257i	$0.394189\pi$
$602$	−20.7327	−	20.7327i	−0.845003	−	0.845003i
$603$		0			0
$604$			2.14359i			0.0872216i
$605$	−3.85010	+	18.8145i	−0.156529	+	0.764917i
$606$		0			0
$607$	−11.5167	+	11.5167i	−0.467447	+	0.467447i	−0.901086	−	0.433640i	$-0.857229\pi$
$607$	−11.5167	+	11.5167i	−0.467447	+	0.467447i	0.433640	+	0.901086i	$0.357229\pi$
$608$	−5.65685	+	5.65685i	−0.229416	+	0.229416i
$609$		0			0
$610$	47.9808	−	31.6795i	1.94268	−	1.28267i
$611$		−	3.86370i		−	0.156309i
$612$		0			0
$613$	13.1506	+	13.1506i	0.531149	+	0.531149i	0.920914	−	0.389765i	$-0.127444\pi$
$613$	13.1506	+	13.1506i	0.531149	+	0.531149i	−0.389765	+	0.920914i	$0.627444\pi$
$614$	−52.0213			−2.09941
$615$		0			0
$616$		0			0
$617$	−28.5109	−	28.5109i	−1.14781	−	1.14781i	−0.986983	−	0.160822i	$-0.948585\pi$
$617$	−28.5109	−	28.5109i	−1.14781	−	1.14781i	−0.160822	−	0.986983i	$-0.551415\pi$
$618$		0			0
$619$		−	36.2487i		−	1.45696i	−0.685068	−	0.728479i	$-0.740227\pi$
$619$		−	36.2487i		−	1.45696i	0.685068	−	0.728479i	$-0.259773\pi$
$620$	2.34795	+	0.480473i	0.0942961	+	0.0192963i
$621$		0			0
$622$	13.6603	−	13.6603i	0.547726	−	0.547726i
$623$	20.7327	−	20.7327i	0.830639	−	0.830639i
$624$		0			0
$625$	17.2846	+	18.0622i	0.691384	+	0.722487i
$626$			63.1319i			2.52326i
$627$		0			0
$628$	−0.143594	−	0.143594i	−0.00573001	−	0.00573001i
$629$	31.6675			1.26267
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$		0			0
$633$		0			0
$634$			21.0718i			0.836868i
$635$	−2.20925	−	3.34607i	−0.0876715	−	0.132785i
$636$		0			0
$637$	3.07180	−	3.07180i	0.121709	−	0.121709i
$638$	19.2442	−	19.2442i	0.761885	−	0.761885i
$639$		0			0
$640$		0			0
$641$			12.5521i			0.495776i	0.968789	+	0.247888i	$0.0797366\pi$
$641$			12.5521i			0.495776i	−0.968789	+	0.247888i	$0.920263\pi$
$642$		0			0
$643$	−8.24167	−	8.24167i	−0.325020	−	0.325020i	0.525669	−	0.850689i	$-0.323815\pi$
$643$	−8.24167	−	8.24167i	−0.325020	−	0.325020i	−0.850689	+	0.525669i	$0.823815\pi$
$644$	−23.1822			−0.913507
$645$		0			0
$646$	−12.9282			−0.508653
$647$	−22.1977	−	22.1977i	−0.872682	−	0.872682i	0.120082	−	0.992764i	$-0.461684\pi$
$647$	−22.1977	−	22.1977i	−0.872682	−	0.872682i	−0.992764	+	0.120082i	$0.961684\pi$
$648$		0			0
$649$			20.7846i			0.815867i
$650$	4.06678	−	9.52056i	0.159512	−	0.373427i
$651$		0			0
$652$	18.3923	−	18.3923i	0.720298	−	0.720298i
$653$	−13.7124	+	13.7124i	−0.536609	+	0.536609i	−0.922531	−	0.385922i	$-0.873883\pi$
$653$	−13.7124	+	13.7124i	−0.536609	+	0.536609i	0.385922	+	0.922531i	$0.373883\pi$
$654$		0			0
$655$	28.1865	+	5.76795i	1.10134	+	0.225372i
$656$		−	11.3137i		−	0.441726i
$657$		0			0
$658$	−17.6603	−	17.6603i	−0.688468	−	0.688468i
$659$	−12.9038			−0.502660			−0.251330	−	0.967901i	$-0.580868\pi$
$659$	−12.9038			−0.502660			−0.251330	+	0.967901i	$0.580868\pi$
$660$		0			0
$661$	37.5692			1.46127			0.730637	−	0.682767i	$-0.239223\pi$
$661$	37.5692			1.46127			0.730637	+	0.682767i	$0.239223\pi$
$662$	3.03150	+	3.03150i	0.117823	+	0.117823i
$663$		0			0
$664$		0			0
$665$	−6.24384	+	4.12252i	−0.242126	+	0.159865i
$666$		0			0
$667$	21.4641	−	21.4641i	0.831093	−	0.831093i
$668$	−28.0812	+	28.0812i	−1.08649	+	1.08649i
$669$		0			0
$670$	−12.0000	+	58.6410i	−0.463600	+	2.26550i
$671$		−	19.9649i		−	0.770736i
$672$		0			0
$673$	6.92820	+	6.92820i	0.267063	+	0.267063i	0.827915	−	0.560853i	$-0.189527\pi$
$673$	6.92820	+	6.92820i	0.267063	+	0.267063i	−0.560853	+	0.827915i	$0.689527\pi$
$674$	10.3528			0.398773
$675$		0			0
$676$	23.8564			0.917554
$677$	12.2474	+	12.2474i	0.470708	+	0.470708i	0.902144	−	0.431436i	$-0.141993\pi$
$677$	12.2474	+	12.2474i	0.470708	+	0.470708i	−0.431436	+	0.902144i	$0.641993\pi$
$678$		0			0
$679$			26.7846i			1.02790i
$680$		0			0
$681$		0			0
$682$	1.17691	−	1.17691i	0.0450664	−	0.0450664i
$683$	21.2132	−	21.2132i	0.811701	−	0.811701i	−0.173188	−	0.984889i	$-0.555407\pi$
$683$	21.2132	−	21.2132i	0.811701	−	0.811701i	0.984889	+	0.173188i	$0.0554069\pi$
$684$		0			0
$685$	2.86603	−	1.89230i	0.109505	−	0.0723013i
$686$			18.7637i			0.716402i
$687$		0			0
$688$	−12.3923	−	12.3923i	−0.472452	−	0.472452i
$689$	6.21166			0.236645
$690$		0			0
$691$	30.5167			1.16091			0.580454	−	0.814293i	$-0.302875\pi$
$691$	30.5167			1.16091			0.580454	+	0.814293i	$0.302875\pi$
$692$	−16.2127	−	16.2127i	−0.616314	−	0.616314i
$693$		0			0
$694$			68.3538i			2.59468i
$695$	21.3197	+	4.36276i	0.808703	+	0.165489i
$696$		0			0
$697$	12.9282	−	12.9282i	0.489691	−	0.489691i
$698$	16.0368	−	16.0368i	0.607003	−	0.607003i
$699$		0			0
$700$	−12.4641	−	31.0526i	−0.471099	−	1.17368i
$701$			42.8797i			1.61954i	0.586745	+	0.809771i	$0.300409\pi$
$701$			42.8797i			1.61954i	−0.586745	+	0.809771i	$0.699591\pi$
$702$		0			0
$703$	3.46410	+	3.46410i	0.130651	+	0.130651i
$704$	−12.4233			−0.468221
$705$		0			0
$706$	35.7128			1.34407
$707$	−44.8115	−	44.8115i	−1.68531	−	1.68531i
$708$		0			0
$709$		−	29.8564i		−	1.12128i	−0.828059	−	0.560640i	$-0.810555\pi$
$709$		−	29.8564i		−	1.12128i	0.828059	−	0.560640i	$-0.189445\pi$
$710$	1.86748	+	2.82843i	0.0700853	+	0.106149i
$711$		0			0
$712$		0			0
$713$	1.31268	−	1.31268i	0.0491602	−	0.0491602i
$714$		0			0
$715$	−1.98076	−	3.00000i	−0.0740763	−	0.112194i
$716$		−	10.3528i		−	0.386901i
$717$		0			0
$718$	0.732051	+	0.732051i	0.0273199	+	0.0273199i
$719$	20.4182			0.761469			0.380735	−	0.924684i	$-0.375671\pi$
$719$	20.4182			0.761469			0.380735	+	0.924684i	$0.375671\pi$
$720$		0			0
$721$	8.53590			0.317893
$722$	−1.41421	−	1.41421i	−0.0526316	−	0.0526316i
$723$		0			0
$724$			36.7846i			1.36709i
$725$	40.2915	+	17.2108i	1.49639	+	0.639193i
$726$		0			0
$727$	8.95448	−	8.95448i	0.332103	−	0.332103i	−0.521281	−	0.853385i	$-0.674546\pi$
$727$	8.95448	−	8.95448i	0.332103	−	0.332103i	0.853385	+	0.521281i	$0.174546\pi$
$728$		0			0
$729$		0			0
$730$	24.1769	+	4.94744i	0.894828	+	0.183113i
$731$		−	28.3214i		−	1.04751i
$732$		0			0
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	0.649529	−	0.760337i	$-0.274966\pi$
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	−0.760337	+	0.649529i	$0.774966\pi$
$734$	−38.8401			−1.43361
$735$		0			0
$736$	−27.7128			−1.02151
$737$	14.6969	+	14.6969i	0.541369	+	0.541369i
$738$		0			0
$739$			3.78461i			0.139219i	0.997574	+	0.0696096i	$0.0221753\pi$
$739$			3.78461i			0.139219i	−0.997574	+	0.0696096i	$0.977825\pi$
$740$	−18.2832	+	12.0716i	−0.672105	+	0.443760i
$741$		0			0
$742$	28.3923	−	28.3923i	1.04231	−	1.04231i
$743$	−8.76268	+	8.76268i	−0.321472	+	0.321472i	−0.849331	−	0.527860i	$-0.822995\pi$
$743$	−8.76268	+	8.76268i	−0.321472	+	0.321472i	0.527860	+	0.849331i	$0.322995\pi$
$744$		0			0
$745$	10.9186	−	53.3564i	0.400026	−	1.95483i
$746$		−	9.79796i		−	0.358729i
$747$		0			0
$748$	−14.1962	−	14.1962i	−0.519063	−	0.519063i
$749$	−1.79315			−0.0655203
$750$		0			0
$751$	−40.1051			−1.46346			−0.731728	−	0.681596i	$-0.761286\pi$
$751$	−40.1051			−1.46346			−0.731728	+	0.681596i	$0.761286\pi$
$752$	−10.5558	−	10.5558i	−0.384932	−	0.384932i
$753$		0			0
$754$		−	18.1436i		−	0.660751i
$755$	−0.480473	+	2.34795i	−0.0174862	+	0.0854508i
$756$		0			0
$757$	−5.43782	+	5.43782i	−0.197641	+	0.197641i	−0.798988	−	0.601347i	$-0.794631\pi$
$757$	−5.43782	+	5.43782i	−0.197641	+	0.197641i	0.601347	+	0.798988i	$0.294631\pi$
$758$	−29.5969	+	29.5969i	−1.07501	+	1.07501i
$759$		0			0
$760$		0			0
$761$		−	17.7656i		−	0.644003i	−0.946739	−	0.322001i	$-0.895644\pi$
$761$		−	17.7656i		−	0.644003i	0.946739	−	0.322001i	$-0.104356\pi$
$762$		0			0
$763$	−19.8564	−	19.8564i	−0.718850	−	0.718850i
$764$	−5.17638			−0.187275
$765$		0			0
$766$	−39.7128			−1.43488
$767$	9.79796	+	9.79796i	0.353784	+	0.353784i
$768$		0			0
$769$		−	10.8038i		−	0.389597i	−0.980843	−	0.194798i	$-0.937595\pi$
$769$		−	10.8038i		−	0.389597i	0.980843	−	0.194798i	$-0.0624052\pi$
$770$	−22.7661	−	4.65874i	−0.820434	−	0.167889i
$771$		0			0
$772$	22.9282	−	22.9282i	0.825204	−	0.825204i
$773$	21.6665	−	21.6665i	0.779289	−	0.779289i	−0.200421	−	0.979710i	$-0.564231\pi$
$773$	21.6665	−	21.6665i	0.779289	−	0.779289i	0.979710	+	0.200421i	$0.0642310\pi$
$774$		0			0
$775$	2.46410	+	1.05256i	0.0885131	+	0.0378090i
$776$		0			0
$777$		0			0
$778$	−15.6603	−	15.6603i	−0.561447	−	0.561447i
$779$	2.82843			0.101339
$780$		0			0
$781$	1.17691			0.0421133
$782$	−31.6675	−	31.6675i	−1.13243	−	1.13243i
$783$		0			0
$784$		−	16.7846i		−	0.599450i
$785$	−0.125097	−	0.189469i	−0.00446492	−	0.00676243i
$786$		0			0
$787$	−9.46410	+	9.46410i	−0.337359	+	0.337359i	−0.855372	−	0.518014i	$-0.826672\pi$
$787$	−9.46410	+	9.46410i	−0.337359	+	0.337359i	0.518014	+	0.855372i	$0.326672\pi$
$788$	19.5959	−	19.5959i	0.698076	−	0.698076i
$789$		0			0
$790$	−33.1769	−	50.2487i	−1.18038	−	1.78777i
$791$			51.7439i			1.83980i
$792$		0			0
$793$	−9.41154	−	9.41154i	−0.334214	−	0.334214i
$794$	65.6830			2.33100
$795$		0			0
$796$	19.4641			0.689887
$797$	−15.6579	−	15.6579i	−0.554631	−	0.554631i	0.373143	−	0.927774i	$-0.378280\pi$
$797$	−15.6579	−	15.6579i	−0.554631	−	0.554631i	−0.927774	+	0.373143i	$0.878280\pi$
$798$		0			0
$799$		−	24.1244i		−	0.853458i
$800$	−14.9000	−	37.1213i	−0.526795	−	1.31244i
$801$		0			0
$802$	−26.9282	+	26.9282i	−0.950868	+	0.950868i
$803$	6.05935	−	6.05935i	0.213830	−	0.213830i
$804$		0			0
$805$	−25.3923	−	5.19615i	−0.894961	−	0.183140i
$806$		−	1.10961i		−	0.0390842i
$807$		0			0
$808$		0			0
$809$	0.314566			0.0110596			0.00552978	−	0.999985i	$-0.498240\pi$
$809$	0.314566			0.0110596			0.00552978	+	0.999985i	$0.498240\pi$
$810$		0			0
$811$	39.8564			1.39955			0.699774	−	0.714364i	$-0.253284\pi$
$811$	39.8564			1.39955			0.699774	+	0.714364i	$0.253284\pi$
$812$	−41.4655	−	41.4655i	−1.45515	−	1.45515i
$813$		0			0
$814$			15.2154i			0.533299i
$815$	24.2683	−	16.0232i	0.850080	−	0.561269i
$816$		0			0
$817$	3.09808	−	3.09808i	0.108388	−	0.108388i
$818$	−16.7675	+	16.7675i	−0.586262	+	0.586262i
$819$		0			0
$820$	−2.53590	+	12.3923i	−0.0885574	+	0.432758i
$821$		−	33.7752i		−	1.17876i	−0.807855	−	0.589382i	$-0.799371\pi$
$821$		−	33.7752i		−	1.17876i	0.807855	−	0.589382i	$-0.200629\pi$
$822$		0			0
$823$	12.6340	+	12.6340i	0.440393	+	0.440393i	0.892144	−	0.451751i	$-0.149201\pi$
$823$	12.6340	+	12.6340i	0.440393	+	0.440393i	−0.451751	+	0.892144i	$0.649201\pi$
$824$		0			0
$825$		0			0
$826$	89.5692			3.11651
$827$	39.1918	+	39.1918i	1.36283	+	1.36283i	0.870285	+	0.492549i	$0.163935\pi$
$827$	39.1918	+	39.1918i	1.36283	+	1.36283i	0.492549	+	0.870285i	$0.336065\pi$
$828$		0			0
$829$			16.6795i			0.579303i	0.957132	+	0.289651i	$0.0935394\pi$
$829$			16.6795i			0.579303i	−0.957132	+	0.289651i	$0.906461\pi$
$830$	0.960947	−	4.69591i	0.0333549	−	0.162997i
$831$		0			0
$832$	−5.85641	+	5.85641i	−0.203034	+	0.203034i
$833$	19.1798	−	19.1798i	0.664541	−	0.664541i
$834$		0			0
$835$	−37.0526	+	24.4641i	−1.28226	+	0.846615i
$836$		−	3.10583i		−	0.107417i
$837$		0			0
$838$	42.3923	+	42.3923i	1.46442	+	1.46442i
$839$	−21.5921			−0.745443			−0.372722	−	0.927943i	$-0.621575\pi$
$839$	−21.5921			−0.745443			−0.372722	+	0.927943i	$0.621575\pi$
$840$		0			0
$841$	47.7846			1.64775
$842$	13.5873	+	13.5873i	0.468250	+	0.468250i
$843$		0			0
$844$		−	11.7128i		−	0.403172i
$845$	26.1308	+	5.34727i	0.898926	+	0.183952i
$846$		0			0
$847$	20.3205	−	20.3205i	0.698221	−	0.698221i
$848$	16.9706	−	16.9706i	0.582772	−	0.582772i
$849$		0			0
$850$	25.3923	−	59.4449i	0.870949	−	2.03894i
$851$			16.9706i			0.581743i
$852$		0			0
$853$	−24.7128	−	24.7128i	−0.846151	−	0.846151i	0.143500	−	0.989650i	$-0.454164\pi$
$853$	−24.7128	−	24.7128i	−0.846151	−	0.846151i	−0.989650	+	0.143500i	$0.954164\pi$
$854$	−86.0367			−2.94412
$855$		0			0
$856$		0			0
$857$	−4.62158	−	4.62158i	−0.157870	−	0.157870i	0.623752	−	0.781622i	$-0.285607\pi$
$857$	−4.62158	−	4.62158i	−0.157870	−	0.157870i	−0.781622	+	0.623752i	$0.785607\pi$
$858$		0			0
$859$		−	28.5692i		−	0.974769i	−0.873187	−	0.487385i	$-0.837951\pi$
$859$		−	28.5692i		−	0.974769i	0.873187	−	0.487385i	$-0.162049\pi$
$860$	10.7961	+	16.3514i	0.368143	+	0.557578i
$861$		0			0
$862$	−12.3923	+	12.3923i	−0.422084	+	0.422084i
$863$	−11.5911	+	11.5911i	−0.394566	+	0.394566i	−0.876311	−	0.481745i	$-0.840003\pi$
$863$	−11.5911	+	11.5911i	−0.394566	+	0.394566i	0.481745	+	0.876311i	$0.340003\pi$
$864$		0			0
$865$	−14.1244	−	21.3923i	−0.480242	−	0.727360i
$866$		−	13.3843i		−	0.454816i
$867$		0			0
$868$	−2.53590	−	2.53590i	−0.0860740	−	0.0860740i
$869$	−20.9086			−0.709276
$870$		0			0
$871$	13.8564			0.469506
$872$		0			0
$873$		0			0
$874$		−	6.92820i		−	0.234350i
$875$	−6.69213	−	36.8067i	−0.226235	−	1.24429i
$876$		0			0
$877$	−17.2679	+	17.2679i	−0.583097	+	0.583097i	−0.935753	−	0.352656i	$-0.885279\pi$
$877$	−17.2679	+	17.2679i	−0.583097	+	0.583097i	0.352656	+	0.935753i	$0.385279\pi$
$878$	−45.0518	+	45.0518i	−1.52042	+	1.52042i
$879$		0			0
$880$	−13.6077	−	2.78461i	−0.458715	−	0.0938692i
$881$			30.0131i			1.01117i	0.862778	+	0.505583i	$0.168722\pi$
$881$			30.0131i			1.01117i	−0.862778	+	0.505583i	$0.831278\pi$
$882$		0			0
$883$	−24.6340	−	24.6340i	−0.828999	−	0.828999i	0.158379	−	0.987378i	$-0.449373\pi$
$883$	−24.6340	−	24.6340i	−0.828999	−	0.828999i	−0.987378	+	0.158379i	$0.949373\pi$
$884$	−13.3843			−0.450161
$885$		0			0
$886$	−63.4641			−2.13212
$887$	16.2127	+	16.2127i	0.544369	+	0.544369i	0.924807	−	0.380438i	$-0.124227\pi$
$887$	16.2127	+	16.2127i	0.544369	+	0.544369i	−0.380438	+	0.924807i	$0.624227\pi$
$888$		0			0
$889$			6.00000i			0.201234i
$890$	−32.7028	+	21.5921i	−1.09620	+	0.723770i
$891$		0			0
$892$	9.85641	−	9.85641i	0.330017	−	0.330017i
$893$	2.63896	−	2.63896i	0.0883094	−	0.0883094i
$894$		0			0
$895$	2.32051	−	11.3397i	0.0775660	−	0.379046i
$896$		0			0
$897$		0			0
$898$	−9.07180	−	9.07180i	−0.302730	−	0.302730i
$899$	4.69591			0.156617
$900$		0			0
$901$	38.7846			1.29210
$902$	6.21166	+	6.21166i	0.206826	+	0.206826i
$903$		0			0
$904$		0			0
$905$	−8.24504	+	40.2915i	−0.274075	+	1.33933i
$906$		0			0
$907$	−6.33975	+	6.33975i	−0.210508	+	0.210508i	−0.804483	−	0.593975i	$-0.797558\pi$
$907$	−6.33975	+	6.33975i	−0.210508	+	0.210508i	0.593975	+	0.804483i	$0.297558\pi$
$908$	34.2929	−	34.2929i	1.13805	−	1.13805i
$909$		0			0
$910$	−12.9282	+	8.53590i	−0.428566	+	0.282962i
$911$		−	57.4007i		−	1.90177i	−0.309542	−	0.950886i	$-0.600176\pi$
$911$		−	57.4007i		−	1.90177i	0.309542	−	0.950886i	$-0.399824\pi$
$912$		0			0
$913$	−1.17691	−	1.17691i	−0.0389502	−	0.0389502i
$914$	0.0743295			0.00245860
$915$		0			0
$916$	25.3205			0.836613
$917$	−30.4428	−	30.4428i	−1.00531	−	1.00531i
$918$		0			0
$919$			43.7128i			1.44195i	0.692960	+	0.720976i	$0.256306\pi$
$919$			43.7128i			1.44195i	−0.692960	+	0.720976i	$0.743694\pi$
$920$		0			0
$921$		0			0
$922$	24.8756	−	24.8756i	0.819236	−	0.819236i
$923$	0.554803	−	0.554803i	0.0182616	−	0.0182616i
$924$		0			0
$925$	−22.7321	+	9.12436i	−0.747425	+	0.300007i
$926$			28.2099i			0.927036i
$927$		0			0
$928$	−49.5692	−	49.5692i	−1.62719	−	1.62719i
$929$	−5.00052			−0.164062			−0.0820308	−	0.996630i	$-0.526141\pi$
$929$	−5.00052			−0.164062			−0.0820308	+	0.996630i	$0.526141\pi$
$930$		0			0
$931$	4.19615			0.137523
$932$	−10.9348	−	10.9348i	−0.358180	−	0.358180i
$933$		0			0
$934$		−	22.3923i		−	0.732699i
$935$	−12.3676	−	18.7315i	−0.404463	−	0.612586i
$936$		0			0
$937$	−13.7583	+	13.7583i	−0.449465	+	0.449465i	−0.895177	−	0.445712i	$-0.852951\pi$
$937$	−13.7583	+	13.7583i	−0.449465	+	0.449465i	0.445712	+	0.895177i	$0.352951\pi$
$938$	63.3350	−	63.3350i	2.06796	−	2.06796i
$939$		0			0
$940$	9.19615	+	13.9282i	0.299945	+	0.454288i
$941$		−	37.6018i		−	1.22578i	−0.790167	−	0.612891i	$-0.790006\pi$
$941$		−	37.6018i		−	1.22578i	0.790167	−	0.612891i	$-0.209994\pi$
$942$		0			0
$943$	6.92820	+	6.92820i	0.225613	+	0.225613i
$944$	53.5370			1.74248
$945$		0			0
$946$	13.6077			0.442424
$947$	−31.6675	−	31.6675i	−1.02906	−	1.02906i	−0.999565	−	0.0294905i	$-0.990612\pi$
$947$	−31.6675	−	31.6675i	−1.02906	−	1.02906i	−0.0294905	−	0.999565i	$-0.509388\pi$
$948$		0			0
$949$		−	5.71281i		−	0.185446i
$950$	9.28032	−	3.72500i	0.301093	−	0.120855i
$951$		0			0
$952$		0			0
$953$	34.9764	−	34.9764i	1.13300	−	1.13300i	0.143320	−	0.989676i	$-0.454222\pi$
$953$	34.9764	−	34.9764i	1.13300	−	1.13300i	0.989676	−	0.143320i	$-0.0457780\pi$
$954$		0			0
$955$	−5.66987	−	1.16025i	−0.183473	−	0.0375449i
$956$			16.2870i			0.526760i
$957$		0			0
$958$	−33.6077	−	33.6077i	−1.08582	−	1.08582i
$959$	−5.13922			−0.165954
$960$		0			0
$961$	−30.7128			−0.990736
$962$	7.17260	+	7.17260i	0.231254	+	0.231254i
$963$		0			0
$964$			56.7846i			1.82891i
$965$	30.2533	−	19.9749i	0.973888	−	0.643013i
$966$		0			0
$967$	−25.9808	+	25.9808i	−0.835485	+	0.835485i	−0.988261	−	0.152776i	$-0.951179\pi$
$967$	−25.9808	+	25.9808i	−0.835485	+	0.835485i	0.152776	+	0.988261i	$0.451179\pi$
$968$		0			0
$969$		0			0
$970$	7.17691	−	35.0718i	0.230437	−	1.12609i
$971$			26.0106i			0.834721i	0.908741	+	0.417361i	$0.137045\pi$
$971$			26.0106i			0.834721i	−0.908741	+	0.417361i	$0.862955\pi$
$972$		0			0
$973$	−23.0263	−	23.0263i	−0.738189	−	0.738189i
$974$	−76.1645			−2.44047
$975$		0			0
$976$	−51.4256			−1.64609
$977$	2.24642	+	2.24642i	0.0718693	+	0.0718693i	0.742128	−	0.670258i	$-0.233817\pi$
$977$	2.24642	+	2.24642i	0.0718693	+	0.0718693i	−0.670258	+	0.742128i	$0.733817\pi$
$978$		0			0
$979$			13.6077i			0.434904i
$980$	−3.76217	+	18.3848i	−0.120178	+	0.587280i
$981$		0			0
$982$	−53.3205	+	53.3205i	−1.70153	+	1.70153i
$983$	−13.9391	+	13.9391i	−0.444587	+	0.444587i	−0.893550	−	0.448963i	$-0.851793\pi$
$983$	−13.9391	+	13.9391i	−0.444587	+	0.444587i	0.448963	+	0.893550i	$0.351793\pi$
$984$		0			0
$985$	25.8564	−	17.0718i	0.823854	−	0.543953i
$986$		−	113.286i		−	3.60775i
$987$		0			0
$988$	−1.46410	−	1.46410i	−0.0465793	−	0.0465793i
$989$	15.1774			0.482614
$990$		0			0
$991$	26.1436			0.830479			0.415239	−	0.909712i	$-0.363698\pi$
$991$	26.1436			0.830479			0.415239	+	0.909712i	$0.363698\pi$
$992$	−3.03150	−	3.03150i	−0.0962502	−	0.0962502i
$993$		0			0
$994$		−	5.07180i		−	0.160868i
$995$	21.3197	+	4.36276i	0.675881	+	0.138309i
$996$		0			0
$997$	−16.3660	+	16.3660i	−0.518317	+	0.518317i	−0.917062	−	0.398745i	$-0.869446\pi$
$997$	−16.3660	+	16.3660i	−0.518317	+	0.518317i	0.398745	+	0.917062i	$0.369446\pi$
$998$	59.0180	−	59.0180i	1.86818	−	1.86818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.c.818.4	yes	8
3.2	odd	2	inner	855.2.n.c.818.1	yes	8
5.2	odd	4	inner	855.2.n.c.647.1	✓	8
15.2	even	4	inner	855.2.n.c.647.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.c.647.1	✓	8	5.2	odd	4	inner
855.2.n.c.647.4	yes	8	15.2	even	4	inner
855.2.n.c.818.1	yes	8	3.2	odd	2	inner
855.2.n.c.818.4	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 1.41421i) q^{2} +2.00000i q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.36603 - 2.36603i) q^{7} +(-3.73205 + 2.46410i) q^{10} +1.55291i q^{11} +(0.732051 + 0.732051i) q^{13} +6.69213 q^{14} +4.00000 q^{16} +(4.57081 + 4.57081i) q^{17} +1.00000i q^{19} +(-4.38134 - 0.896575i) q^{20} +(-2.19615 + 2.19615i) q^{22} +(-2.44949 + 2.44949i) q^{23} +(-4.59808 - 1.96410i) q^{25} +2.07055i q^{26} +(4.73205 + 4.73205i) q^{28} -8.76268 q^{29} -0.535898 q^{31} +(5.65685 + 5.65685i) q^{32} +12.9282i q^{34} +(4.12252 + 6.24384i) q^{35} +(3.46410 - 3.46410i) q^{37} +(-1.41421 + 1.41421i) q^{38} -2.82843i q^{41} +(-3.09808 - 3.09808i) q^{43} -3.10583 q^{44} -6.92820 q^{46} +(-2.63896 - 2.63896i) q^{47} -4.19615i q^{49} +(-3.72500 - 9.28032i) q^{50} +(-1.46410 + 1.46410i) q^{52} +(4.24264 - 4.24264i) q^{53} +(-3.40192 - 0.696152i) q^{55} +(-12.3923 - 12.3923i) q^{58} +13.3843 q^{59} -12.8564 q^{61} +(-0.757875 - 0.757875i) q^{62} +8.00000i q^{64} +(-1.93185 + 1.27551i) q^{65} +(9.46410 - 9.46410i) q^{67} +(-9.14162 + 9.14162i) q^{68} +(-3.00000 + 14.6603i) q^{70} -0.757875i q^{71} +(-3.90192 - 3.90192i) q^{73} +9.79796 q^{74} -2.00000 q^{76} +(3.67423 + 3.67423i) q^{77} +13.4641i q^{79} +(-1.79315 + 8.76268i) q^{80} +(4.00000 - 4.00000i) q^{82} +(-0.757875 + 0.757875i) q^{83} +(-12.0622 + 7.96410i) q^{85} -8.76268i q^{86} +8.76268 q^{89} +3.46410 q^{91} +(-4.89898 - 4.89898i) q^{92} -7.46410i q^{94} +(-2.19067 - 0.448288i) q^{95} +(-5.66025 + 5.66025i) q^{97} +(5.93426 - 5.93426i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{7} - 16 q^{10} - 8 q^{13} + 32 q^{16} + 24 q^{22} - 16 q^{25} + 24 q^{28} - 32 q^{31} - 4 q^{43} + 16 q^{52} - 48 q^{55} - 16 q^{58} + 8 q^{61} + 48 q^{67} - 24 q^{70} - 52 q^{73} - 16 q^{76}+ \cdots + 24 q^{97}+O(q^{100}) \) 8 * q + 12 * q^7 - 16 * q^10 - 8 * q^13 + 32 * q^16 + 24 * q^22 - 16 * q^25 + 24 * q^28 - 32 * q^31 - 4 * q^43 + 16 * q^52 - 48 * q^55 - 16 * q^58 + 8 * q^61 + 48 * q^67 - 24 * q^70 - 52 * q^73 - 16 * q^76 + 32 * q^82 - 48 * q^85 + 24 * q^97

Introduction

L-functions

Modular forms

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