LMFDB - Embedded newform 1638.2.bc.b.881.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(251,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1638.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bc (of order $6$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.18
Character	$\chi$	$=$	1638.881
Dual form			1638.2.bc.b.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.05770i q^{5} +(-1.82998 + 1.91080i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.05770i q^{5} +(-1.82998 + 1.91080i) q^{7} -1.00000 q^{8} +(-2.64804 + 1.52885i) q^{10} +(-0.612072 - 1.06014i) q^{11} +(0.0126145 + 3.60553i) q^{13} +(-2.56979 - 0.629412i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.789002 - 1.36659i) q^{17} +(0.675572 - 1.17012i) q^{19} +(-2.64804 - 1.52885i) q^{20} +(0.612072 - 1.06014i) q^{22} +(-2.87424 + 1.65944i) q^{23} -4.34951 q^{25} +(-3.11617 + 1.81369i) q^{26} +(-0.739810 - 2.54021i) q^{28} +(-8.83351 + 5.10003i) q^{29} +6.68216 q^{31} +(0.500000 - 0.866025i) q^{32} +1.57800 q^{34} +(-5.84265 - 5.59554i) q^{35} +(0.00898792 - 0.00518918i) q^{37} +1.35114 q^{38} -3.05770i q^{40} +(-1.33437 + 0.770398i) q^{41} +(1.77949 - 3.08217i) q^{43} +1.22414 q^{44} +(-2.87424 - 1.65944i) q^{46} -0.262559i q^{47} +(-0.302320 - 6.99347i) q^{49} +(-2.17476 - 3.76679i) q^{50} +(-3.12879 - 1.79184i) q^{52} -12.3299i q^{53} +(3.24159 - 1.87153i) q^{55} +(1.82998 - 1.91080i) q^{56} +(-8.83351 - 5.10003i) q^{58} +(5.61418 + 3.24135i) q^{59} +(-7.31734 - 4.22467i) q^{61} +(3.34108 + 5.78692i) q^{62} +1.00000 q^{64} +(-11.0246 + 0.0385714i) q^{65} +(8.47580 - 4.89351i) q^{67} +(0.789002 + 1.36659i) q^{68} +(1.92455 - 7.85765i) q^{70} +(-5.54292 + 9.60061i) q^{71} -11.5599 q^{73} +(0.00898792 + 0.00518918i) q^{74} +(0.675572 + 1.17012i) q^{76} +(3.14580 + 0.770491i) q^{77} +5.47379 q^{79} +(2.64804 - 1.52885i) q^{80} +(-1.33437 - 0.770398i) q^{82} -0.716433i q^{83} +(4.17862 + 2.41253i) q^{85} +3.55898 q^{86} +(0.612072 + 1.06014i) q^{88} +(-1.66426 + 0.960864i) q^{89} +(-6.91253 - 6.57396i) q^{91} -3.31889i q^{92} +(0.227383 - 0.131280i) q^{94} +(3.57789 + 2.06569i) q^{95} +(-1.79666 + 3.11190i) q^{97} +(5.90536 - 3.75855i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{2} - 20 q^{4} - 40 q^{8}+O(q^{10}) $ 40 * q + 20 * q^2 - 20 * q^4 - 40 * q^8	$ 40 q + 20 q^{2} - 20 q^{4} - 40 q^{8} - 20 q^{16} - 12 q^{23} - 56 q^{25} + 20 q^{32} + 48 q^{35} + 24 q^{37} + 12 q^{43} - 12 q^{46} + 4 q^{49} - 28 q^{50} + 40 q^{64} - 48 q^{65} - 12 q^{67} - 12 q^{71} + 24 q^{74} + 48 q^{79} + 48 q^{85} + 24 q^{86} + 24 q^{95} - 4 q^{98}+O(q^{100}) $ 40 * q + 20 * q^2 - 20 * q^4 - 40 * q^8 - 20 * q^16 - 12 * q^23 - 56 * q^25 + 20 * q^32 + 48 * q^35 + 24 * q^37 + 12 * q^43 - 12 * q^46 + 4 * q^49 - 28 * q^50 + 40 * q^64 - 48 * q^65 - 12 * q^67 - 12 * q^71 + 24 * q^74 + 48 * q^79 + 48 * q^85 + 24 * q^86 + 24 * q^95 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			3.05770i			1.36744i	0.729743	+	0.683722i	$0.239640\pi$
$5$			3.05770i			1.36744i	−0.729743	+	0.683722i	$0.760360\pi$
$6$		0			0
$7$	−1.82998	+	1.91080i	−0.691669	+	0.722215i
$7$	−1.82998	+	1.91080i	−0.691669	+	0.722215i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.64804	+	1.52885i	−0.837385	+	0.483464i
$11$	−0.612072	−	1.06014i	−0.184547	−	0.319644i	0.758877	−	0.651234i	$-0.225748\pi$
$11$	−0.612072	−	1.06014i	−0.184547	−	0.319644i	−0.943424	+	0.331590i	$0.892415\pi$
$12$		0			0
$13$	0.0126145	+	3.60553i	0.00349864	+	0.999994i
$13$	0.0126145	+	3.60553i	0.00349864	+	0.999994i
$14$	−2.56979	−	0.629412i	−0.686806	−	0.168217i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.789002	−	1.36659i	0.191361	−	0.331447i	−0.754340	−	0.656483i	$-0.772043\pi$
$17$	0.789002	−	1.36659i	0.191361	−	0.331447i	0.945702	+	0.325036i	$0.105377\pi$
$18$		0			0
$19$	0.675572	−	1.17012i	0.154987	−	0.268445i	−0.778067	−	0.628181i	$-0.783800\pi$
$19$	0.675572	−	1.17012i	0.154987	−	0.268445i	0.933054	+	0.359736i	$0.117133\pi$
$20$	−2.64804	−	1.52885i	−0.592120	−	0.341861i
$21$		0			0
$22$	0.612072	−	1.06014i	0.130494	−	0.226023i
$23$	−2.87424	+	1.65944i	−0.599321	+	0.346018i	−0.768774	−	0.639520i	$-0.779133\pi$
$23$	−2.87424	+	1.65944i	−0.599321	+	0.346018i	0.169454	+	0.985538i	$0.445800\pi$
$24$		0			0
$25$	−4.34951			−0.869902
$26$	−3.11617	+	1.81369i	−0.611132	+	0.355694i
$27$		0			0
$28$	−0.739810	−	2.54021i	−0.139811	−	0.480055i
$29$	−8.83351	+	5.10003i	−1.64034	+	0.947051i	−0.659630	+	0.751591i	$0.729287\pi$
$29$	−8.83351	+	5.10003i	−1.64034	+	0.947051i	−0.980712	+	0.195461i	$0.937380\pi$
$30$		0			0
$31$	6.68216			1.20015			0.600076	−	0.799943i	$-0.295137\pi$
$31$	6.68216			1.20015			0.600076	+	0.799943i	$0.295137\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	1.57800			0.270625
$35$	−5.84265	−	5.59554i	−0.987588	−	0.945818i
$36$		0			0
$37$	0.00898792	−	0.00518918i	0.00147760	−	0.000853095i	−0.499261	−	0.866452i	$-0.666395\pi$
$37$	0.00898792	−	0.00518918i	0.00147760	−	0.000853095i	0.500739	+	0.865599i	$0.333062\pi$
$38$	1.35114			0.219184
$39$		0			0
$40$		−	3.05770i		−	0.483464i
$41$	−1.33437	+	0.770398i	−0.208393	+	0.120316i	−0.600564	−	0.799576i	$-0.705057\pi$
$41$	−1.33437	+	0.770398i	−0.208393	+	0.120316i	0.392171	+	0.919892i	$0.371724\pi$
$42$		0			0
$43$	1.77949	−	3.08217i	0.271370	−	0.470026i	−0.697843	−	0.716251i	$-0.745857\pi$
$43$	1.77949	−	3.08217i	0.271370	−	0.470026i	0.969213	+	0.246225i	$0.0791901\pi$
$44$	1.22414			0.184547
$45$		0			0
$46$	−2.87424	−	1.65944i	−0.423784	−	0.244672i
$47$		−	0.262559i		−	0.0382982i	−0.999817	−	0.0191491i	$-0.993904\pi$
$47$		−	0.262559i		−	0.0382982i	0.999817	−	0.0191491i	$-0.00609572\pi$
$48$		0			0
$49$	−0.302320	−	6.99347i	−0.0431885	−	0.999067i
$50$	−2.17476	−	3.76679i	−0.307557	−	0.532704i
$51$		0			0
$52$	−3.12879	−	1.79184i	−0.433885	−	0.248484i
$53$		−	12.3299i		−	1.69364i	−0.531882	−	0.846819i	$-0.678515\pi$
$53$		−	12.3299i		−	1.69364i	0.531882	−	0.846819i	$-0.321485\pi$
$54$		0			0
$55$	3.24159	−	1.87153i	0.437096	−	0.252357i
$56$	1.82998	−	1.91080i	0.244542	−	0.255341i
$57$		0			0
$58$	−8.83351	−	5.10003i	−1.15990	−	0.669666i
$59$	5.61418	+	3.24135i	0.730904	+	0.421988i	0.818753	−	0.574146i	$-0.194666\pi$
$59$	5.61418	+	3.24135i	0.730904	+	0.421988i	−0.0878486	+	0.996134i	$0.527999\pi$
$60$		0			0
$61$	−7.31734	−	4.22467i	−0.936890	−	0.540914i	−0.0479058	−	0.998852i	$-0.515255\pi$
$61$	−7.31734	−	4.22467i	−0.936890	−	0.540914i	−0.888984	+	0.457938i	$0.848588\pi$
$62$	3.34108	+	5.78692i	0.424318	+	0.734940i
$63$		0			0
$64$	1.00000			0.125000
$65$	−11.0246	+	0.0385714i	−1.36744	+	0.00478420i
$66$		0			0
$67$	8.47580	−	4.89351i	1.03548	−	0.597837i	0.116933	−	0.993140i	$-0.462694\pi$
$67$	8.47580	−	4.89351i	1.03548	−	0.597837i	0.918551	+	0.395303i	$0.129360\pi$
$68$	0.789002	+	1.36659i	0.0956805	+	0.165724i
$69$		0			0
$70$	1.92455	−	7.85765i	0.230028	−	0.939169i
$71$	−5.54292	+	9.60061i	−0.657823	+	1.13938i	0.323355	+	0.946278i	$0.395189\pi$
$71$	−5.54292	+	9.60061i	−0.657823	+	1.13938i	−0.981178	+	0.193105i	$0.938144\pi$
$72$		0			0
$73$	−11.5599			−1.35298			−0.676490	−	0.736452i	$-0.736500\pi$
$73$	−11.5599			−1.35298			−0.676490	+	0.736452i	$0.736500\pi$
$74$	0.00898792	+	0.00518918i	0.00104482	+	0.000603230i
$75$		0			0
$76$	0.675572	+	1.17012i	0.0774934	+	0.134222i
$77$	3.14580	+	0.770491i	0.358497	+	0.0878056i
$78$		0			0
$79$	5.47379			0.615850			0.307925	−	0.951411i	$-0.400365\pi$
$79$	5.47379			0.615850			0.307925	+	0.951411i	$0.400365\pi$
$80$	2.64804	−	1.52885i	0.296060	−	0.170930i
$81$		0			0
$82$	−1.33437	−	0.770398i	−0.147356	−	0.0850762i
$83$		−	0.716433i		−	0.0786387i	−0.999227	−	0.0393194i	$-0.987481\pi$
$83$		−	0.716433i		−	0.0786387i	0.999227	−	0.0393194i	$-0.0125190\pi$
$84$		0			0
$85$	4.17862	+	2.41253i	0.453235	+	0.261675i
$86$	3.55898			0.383775
$87$		0			0
$88$	0.612072	+	1.06014i	0.0652471	+	0.113011i
$89$	−1.66426	+	0.960864i	−0.176412	+	0.101851i	−0.585606	−	0.810596i	$-0.699143\pi$
$89$	−1.66426	+	0.960864i	−0.176412	+	0.101851i	0.409194	+	0.912447i	$0.365810\pi$
$90$		0			0
$91$	−6.91253	−	6.57396i	−0.724630	−	0.689138i
$92$		−	3.31889i		−	0.346018i
$93$		0			0
$94$	0.227383	−	0.131280i	0.0234528	−	0.0135405i
$95$	3.57789	+	2.06569i	0.367083	+	0.211936i
$96$		0			0
$97$	−1.79666	+	3.11190i	−0.182423	+	0.315966i	−0.942705	−	0.333627i	$-0.891727\pi$
$97$	−1.79666	+	3.11190i	−0.182423	+	0.315966i	0.760282	+	0.649593i	$0.225061\pi$
$98$	5.90536	−	3.75855i	0.596532	−	0.379671i
$99$		0			0
$100$	2.17476	−	3.76679i	0.217476	−	0.376679i
$101$	4.64764	+	8.04996i	0.462458	+	0.801001i	0.999083	−	0.0428204i	$-0.0136343\pi$
$101$	4.64764	+	8.04996i	0.462458	+	0.801001i	−0.536625	+	0.843821i	$0.680301\pi$
$102$		0			0
$103$			7.55911i			0.744821i	0.928068	+	0.372410i	$0.121469\pi$
$103$			7.55911i			0.744821i	−0.928068	+	0.372410i	$0.878531\pi$
$104$	−0.0126145	−	3.60553i	−0.00123696	−	0.353551i
$105$		0			0
$106$	10.6780	−	6.16493i	1.03714	−	0.598791i
$107$	−14.3627	+	8.29233i	−1.38850	+	0.801650i	−0.993146	−	0.116879i	$-0.962711\pi$
$107$	−14.3627	+	8.29233i	−1.38850	+	0.801650i	−0.395353	+	0.918529i	$0.629378\pi$
$108$		0			0
$109$			3.01209i			0.288506i	0.989541	+	0.144253i	$0.0460780\pi$
$109$			3.01209i			0.288506i	−0.989541	+	0.144253i	$0.953922\pi$
$110$	3.24159	+	1.87153i	0.309073	+	0.178444i
$111$		0			0
$112$	2.56979	+	0.629412i	0.242823	+	0.0594738i
$113$	−5.84378	−	3.37391i	−0.549736	−	0.317390i	0.199279	−	0.979943i	$-0.436140\pi$
$113$	−5.84378	−	3.37391i	−0.549736	−	0.317390i	−0.749016	+	0.662552i	$0.769473\pi$
$114$		0			0
$115$	−5.07408	−	8.78856i	−0.473160	−	0.819537i
$116$		−	10.2001i		−	0.947051i
$117$		0			0
$118$			6.48270i			0.596781i
$119$	1.16742	+	4.00846i	0.107018	+	0.367455i
$120$		0			0
$121$	4.75073	−	8.22851i	0.431885	−	0.748047i
$122$		−	8.44934i		−	0.764967i
$123$		0			0
$124$	−3.34108	+	5.78692i	−0.300038	+	0.519681i
$125$			1.98900i			0.177901i
$126$		0			0
$127$	2.46108	+	4.26271i	0.218385	+	0.378254i	0.954314	−	0.298804i	$-0.0965878\pi$
$127$	2.46108	+	4.26271i	0.218385	+	0.378254i	−0.735929	+	0.677058i	$0.763254\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−5.54571	−	9.52831i	−0.486391	−	0.835688i
$131$	−14.3135			−1.25058			−0.625288	−	0.780394i	$-0.715019\pi$
$131$	−14.3135			−1.25058			−0.625288	+	0.780394i	$0.715019\pi$
$132$		0			0
$133$	0.999590	+	3.43219i	0.0866754	+	0.297609i
$134$	8.47580	+	4.89351i	0.732198	+	0.422735i
$135$		0			0
$136$	−0.789002	+	1.36659i	−0.0676563	+	0.117184i
$137$	−5.14303	+	8.90798i	−0.439398	+	0.761060i	−0.997643	−	0.0686160i	$-0.978142\pi$
$137$	−5.14303	+	8.90798i	−0.439398	+	0.761060i	0.558245	+	0.829676i	$0.311475\pi$
$138$		0			0
$139$	12.3914	+	7.15418i	1.05102	+	0.606809i	0.922936	−	0.384953i	$-0.125782\pi$
$139$	12.3914	+	7.15418i	1.05102	+	0.606809i	0.128089	+	0.991763i	$0.459116\pi$
$140$	7.76720	−	2.26212i	0.656448	−	0.191184i
$141$		0			0
$142$	−11.0858			−0.930302
$143$	3.81465	−	2.22022i	0.318997	−	0.185664i
$144$		0			0
$145$	−15.5943	−	27.0102i	−1.29504	−	2.24307i
$146$	−5.77993	−	10.0111i	−0.478350	−	0.828527i
$147$		0			0
$148$			0.0103784i			0.000853095i
$149$	8.08473	−	14.0032i	0.662327	−	1.14718i	−0.317676	−	0.948199i	$-0.602902\pi$
$149$	8.08473	−	14.0032i	0.662327	−	1.14718i	0.980003	−	0.198985i	$-0.0637643\pi$
$150$		0			0
$151$		−	17.9312i		−	1.45922i	−0.683864	−	0.729609i	$-0.739702\pi$
$151$		−	17.9312i		−	1.45922i	0.683864	−	0.729609i	$-0.260298\pi$
$152$	−0.675572	+	1.17012i	−0.0547961	+	0.0949096i
$153$		0			0
$154$	0.905635	+	3.10959i	0.0729781	+	0.250578i
$155$			20.4320i			1.64114i
$156$		0			0
$157$			9.34255i			0.745617i	0.927908	+	0.372808i	$0.121605\pi$
$157$			9.34255i			0.745617i	−0.927908	+	0.372808i	$0.878395\pi$
$158$	2.73690	+	4.74044i	0.217736	+	0.377129i
$159$		0			0
$160$	2.64804	+	1.52885i	0.209346	+	0.120866i
$161$	2.08895	−	8.52886i	0.164632	−	0.672168i
$162$		0			0
$163$	19.6902	+	11.3682i	1.54226	+	0.890423i	0.998696	+	0.0510543i	$0.0162582\pi$
$163$	19.6902	+	11.3682i	1.54226	+	0.890423i	0.543562	+	0.839369i	$0.317075\pi$
$164$		−	1.54080i		−	0.120316i
$165$		0			0
$166$	0.620449	−	0.358216i	0.0481562	−	0.0278030i
$167$	−19.4643	+	11.2377i	−1.50619	+	0.869602i	−0.506220	+	0.862404i	$0.668958\pi$
$167$	−19.4643	+	11.2377i	−1.50619	+	0.869602i	−0.999974	+	0.00719734i	$0.997709\pi$
$168$		0			0
$169$	−12.9997	+	0.0909641i	−0.999976	+	0.00699724i
$170$			4.82506i			0.370065i
$171$		0			0
$172$	1.77949	+	3.08217i	0.135685	+	0.235013i
$173$	−10.1117	+	17.5139i	−0.768775	+	1.33156i	0.169453	+	0.985538i	$0.445800\pi$
$173$	−10.1117	+	17.5139i	−0.768775	+	1.33156i	−0.938228	+	0.346018i	$0.887533\pi$
$174$		0			0
$175$	7.95953	−	8.31105i	0.601684	−	0.628256i
$176$	−0.612072	+	1.06014i	−0.0461367	+	0.0799111i
$177$		0			0
$178$	−1.66426	−	0.960864i	−0.124742	−	0.0720198i
$179$	−1.71871	+	0.992298i	−0.128463	+	0.0741679i	−0.562854	−	0.826556i	$-0.690297\pi$
$179$	−1.71871	+	0.992298i	−0.128463	+	0.0741679i	0.434392	+	0.900724i	$0.356963\pi$
$180$		0			0
$181$			19.9459i			1.48257i	0.671190	+	0.741285i	$0.265783\pi$
$181$			19.9459i			1.48257i	−0.671190	+	0.741285i	$0.734217\pi$
$182$	2.23695	−	9.27341i	0.165813	−	0.687391i
$183$		0			0
$184$	2.87424	−	1.65944i	0.211892	−	0.122336i
$185$	0.0158669	+	0.0274823i	0.00116656	+	0.00202054i
$186$		0			0
$187$	−1.93170			−0.141260
$188$	0.227383	+	0.131280i	0.0165836	+	0.00957456i
$189$		0			0
$190$			4.13139i			0.299722i
$191$	3.91500	+	2.26033i	0.283279	+	0.163551i	0.634907	−	0.772589i	$-0.281038\pi$
$191$	3.91500	+	2.26033i	0.283279	+	0.163551i	−0.351628	+	0.936140i	$0.614372\pi$
$192$		0			0
$193$	−7.06211	+	4.07731i	−0.508342	+	0.293491i	−0.732152	−	0.681142i	$-0.761484\pi$
$193$	−7.06211	+	4.07731i	−0.508342	+	0.293491i	0.223810	+	0.974633i	$0.428151\pi$
$194$	−3.59331			−0.257985
$195$		0			0
$196$	6.20768	+	3.23492i	0.443406	+	0.231066i
$197$	5.60656	+	9.71084i	0.399451	+	0.691869i	0.993658	−	0.112443i	$-0.0358675\pi$
$197$	5.60656	+	9.71084i	0.399451	+	0.691869i	−0.594207	+	0.804312i	$0.702534\pi$
$198$		0			0
$199$	14.5580	+	8.40505i	1.03199	+	0.595818i	0.917553	−	0.397613i	$-0.130161\pi$
$199$	14.5580	+	8.40505i	1.03199	+	0.595818i	0.114434	+	0.993431i	$0.463495\pi$
$200$	4.34951			0.307557
$201$		0			0
$202$	−4.64764	+	8.04996i	−0.327007	+	0.566393i
$203$	6.42004	−	26.2120i	0.450598	−	1.83972i
$204$		0			0
$205$	−2.35564	−	4.08009i	−0.164525	−	0.284966i
$206$	−6.54638	+	3.77955i	−0.456108	+	0.263334i
$207$		0			0
$208$	3.11617	−	1.81369i	0.216068	−	0.125757i
$209$	−1.65400			−0.114409
$210$		0			0
$211$	2.05863	+	3.56566i	0.141722	+	0.245470i	0.928145	−	0.372218i	$-0.121403\pi$
$211$	2.05863	+	3.56566i	0.141722	+	0.245470i	−0.786423	+	0.617688i	$0.788069\pi$
$212$	10.6780	+	6.16493i	0.733367	+	0.423409i
$213$		0			0
$214$	−14.3627	−	8.29233i	−0.981817	−	0.566852i
$215$	9.42433	+	5.44114i	0.642734	+	0.371083i
$216$		0			0
$217$	−12.2282	+	12.7683i	−0.830107	+	0.866767i
$218$	−2.60855	+	1.50605i	−0.176673	+	0.102002i
$219$		0			0
$220$			3.74306i			0.252357i
$221$	4.93724	+	2.82753i	0.332115	+	0.190200i
$222$		0			0
$223$	−3.30868	−	5.73079i	−0.221565	−	0.383762i	0.733718	−	0.679454i	$-0.237783\pi$
$223$	−3.30868	−	5.73079i	−0.221565	−	0.383762i	−0.955283	+	0.295692i	$0.904450\pi$
$224$	0.739810	+	2.54021i	0.0494306	+	0.169725i
$225$		0			0
$226$		−	6.74781i		−	0.448858i
$227$	5.12560	+	2.95927i	0.340198	+	0.196413i	0.660360	−	0.750950i	$-0.270404\pi$
$227$	5.12560	+	2.95927i	0.340198	+	0.196413i	−0.320162	+	0.947363i	$0.603737\pi$
$228$		0			0
$229$	−9.70258			−0.641164			−0.320582	−	0.947221i	$-0.603879\pi$
$229$	−9.70258			−0.641164			−0.320582	+	0.947221i	$0.603879\pi$
$230$	5.07408	−	8.78856i	0.334575	−	0.579500i
$231$		0			0
$232$	8.83351	−	5.10003i	0.579948	−	0.334833i
$233$		−	14.3427i		−	0.939619i	−0.882768	−	0.469809i	$-0.844323\pi$
$233$		−	14.3427i		−	0.939619i	0.882768	−	0.469809i	$-0.155677\pi$
$234$		0			0
$235$	0.802827			0.0523707
$236$	−5.61418	+	3.24135i	−0.365452	+	0.210994i
$237$		0			0
$238$	−2.88772	+	3.01525i	−0.187183	+	0.195450i
$239$	14.5214			0.939310			0.469655	−	0.882850i	$-0.344378\pi$
$239$	14.5214			0.939310			0.469655	+	0.882850i	$0.344378\pi$
$240$		0			0
$241$	7.73852	−	13.4035i	0.498482	−	0.863396i	−0.501517	−	0.865148i	$-0.667224\pi$
$241$	7.73852	−	13.4035i	0.498482	−	0.863396i	0.999998	+	0.00175205i	$0.000557696\pi$
$242$	9.50147			0.610778
$243$		0			0
$244$	7.31734	−	4.22467i	0.468445	−	0.270457i
$245$	21.3839	−	0.924401i	1.36617	−	0.0590578i
$246$		0			0
$247$	4.22744	+	2.42103i	0.268986	+	0.154047i
$248$	−6.68216			−0.424318
$249$		0			0
$250$	−1.72252	+	0.994499i	−0.108942	+	0.0628976i
$251$	10.0125	−	17.3421i	0.631982	−	1.09462i	−0.355164	−	0.934804i	$-0.615575\pi$
$251$	10.0125	−	17.3421i	0.631982	−	1.09462i	0.987146	−	0.159821i	$-0.0510916\pi$
$252$		0			0
$253$	3.51849	+	2.03140i	0.221205	+	0.127713i
$254$	−2.46108	+	4.26271i	−0.154422	+	0.267466i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.37478	+	4.11324i	0.148135	+	0.256577i	0.930538	−	0.366195i	$-0.119340\pi$
$257$	2.37478	+	4.11324i	0.148135	+	0.256577i	−0.782403	+	0.622772i	$0.786006\pi$
$258$		0			0
$259$	−0.00653226	+	0.0266702i	−0.000405895	+	0.00165721i
$260$	5.47890	−	9.56688i	0.339787	−	0.593313i
$261$		0			0
$262$	−7.15675	−	12.3959i	−0.442146	−	0.765819i
$263$	−20.1741	+	11.6475i	−1.24399	+	0.718219i	−0.969904	−	0.243486i	$-0.921709\pi$
$263$	−20.1741	+	11.6475i	−1.24399	+	0.718219i	−0.274087	+	0.961705i	$0.588376\pi$
$264$		0			0
$265$	37.7010			2.31595
$266$	−2.47257	+	2.58177i	−0.151603	+	0.158298i
$267$		0			0
$268$			9.78701i			0.597837i
$269$	0.149998	−	0.259803i	0.00914551	−	0.0158405i	−0.861416	−	0.507899i	$-0.830422\pi$
$269$	0.149998	−	0.259803i	0.00914551	−	0.0158405i	0.870562	+	0.492059i	$0.163756\pi$
$270$		0			0
$271$	−5.56431	−	9.63766i	−0.338007	−	0.585446i	0.646050	−	0.763295i	$-0.276420\pi$
$271$	−5.56431	−	9.63766i	−0.338007	−	0.585446i	−0.984058	+	0.177849i	$0.943086\pi$
$272$	−1.57800			−0.0956805
$273$		0			0
$274$	−10.2861			−0.621403
$275$	2.66222	+	4.61109i	0.160538	+	0.278059i
$276$		0			0
$277$	−7.34099	+	12.7150i	−0.441077	+	0.763968i	−0.997770	−	0.0667505i	$-0.978737\pi$
$277$	−7.34099	+	12.7150i	−0.441077	+	0.763968i	0.556692	+	0.830719i	$0.312070\pi$
$278$			14.3084i			0.858158i
$279$		0			0
$280$	5.84265	+	5.59554i	0.349165	+	0.334397i
$281$	−12.9823			−0.774461			−0.387231	−	0.921983i	$-0.626568\pi$
$281$	−12.9823			−0.774461			−0.387231	+	0.921983i	$0.626568\pi$
$282$		0			0
$283$	−24.2843	+	14.0205i	−1.44355	+	0.833435i	−0.998085	−	0.0618638i	$-0.980296\pi$
$283$	−24.2843	+	14.0205i	−1.44355	+	0.833435i	−0.445467	+	0.895299i	$0.646962\pi$
$284$	−5.54292	−	9.60061i	−0.328912	−	0.569692i
$285$		0			0
$286$	3.83009	+	2.19347i	0.226478	+	0.129703i
$287$	0.969795	−	3.95953i	0.0572452	−	0.233723i
$288$		0			0
$289$	7.25495	+	12.5659i	0.426762	+	0.739173i
$290$	15.5943	−	27.0102i	0.915731	−	1.58609i
$291$		0			0
$292$	5.77993	−	10.0111i	0.338245	−	0.585857i
$293$	14.7145	+	8.49543i	0.859631	+	0.496308i	0.863889	−	0.503683i	$-0.168022\pi$
$293$	14.7145	+	8.49543i	0.859631	+	0.496308i	−0.00425750	+	0.999991i	$0.501355\pi$
$294$		0			0
$295$	−9.91107	+	17.1665i	−0.577045	+	0.999470i
$296$	−0.00898792	+	0.00518918i	−0.000522412	+	0.000301615i
$297$		0			0
$298$	16.1695			0.936672
$299$	−6.01943	−	10.3422i	−0.348113	−	0.598106i
$300$		0			0
$301$	2.63297	+	9.04056i	0.151762	+	0.521089i
$302$	15.5289	−	8.96559i	0.893585	−	0.515912i
$303$		0			0
$304$	−1.35114			−0.0774934
$305$	12.9178	−	22.3742i	0.739669	−	1.28114i
$306$		0			0
$307$	18.0907			1.03249			0.516245	−	0.856441i	$-0.327329\pi$
$307$	18.0907			1.03249			0.516245	+	0.856441i	$0.327329\pi$
$308$	−2.24017	+	2.33910i	−0.127645	+	0.133282i
$309$		0			0
$310$	−17.6946	+	10.2160i	−1.00499	+	0.580230i
$311$	19.4006			1.10011			0.550053	−	0.835130i	$-0.314607\pi$
$311$	19.4006			1.10011			0.550053	+	0.835130i	$0.314607\pi$
$312$		0			0
$313$			7.59423i			0.429251i	0.976696	+	0.214626i	$0.0688531\pi$
$313$			7.59423i			0.429251i	−0.976696	+	0.214626i	$0.931147\pi$
$314$	−8.09089	+	4.67127i	−0.456595	+	0.263615i
$315$		0			0
$316$	−2.73690	+	4.74044i	−0.153962	+	0.266671i
$317$	23.3470			1.31130			0.655649	−	0.755066i	$-0.272395\pi$
$317$	23.3470			1.31130			0.655649	+	0.755066i	$0.272395\pi$
$318$		0			0
$319$	10.8135	+	6.24317i	0.605439	+	0.349551i
$320$			3.05770i			0.170930i
$321$		0			0
$322$	8.43068	−	2.45535i	0.469823	−	0.136831i
$323$	−1.06605	−	1.84646i	−0.0593169	−	0.102740i
$324$		0			0
$325$	−0.0548671	−	15.6823i	−0.00304348	−	0.869897i
$326$			22.7363i			1.25925i
$327$		0			0
$328$	1.33437	−	0.770398i	0.0736781	−	0.0425381i
$329$	0.501699	+	0.480479i	0.0276595	+	0.0264897i
$330$		0			0
$331$	4.00207	+	2.31059i	0.219973	+	0.127002i	0.605938	−	0.795512i	$-0.292798\pi$
$331$	4.00207	+	2.31059i	0.219973	+	0.127002i	−0.385965	+	0.922514i	$0.626131\pi$
$332$	0.620449	+	0.358216i	0.0340516	+	0.0196597i
$333$		0			0
$334$	−19.4643	−	11.2377i	−1.06504	−	0.614901i
$335$	14.9629	+	25.9164i	0.817508	+	1.41597i
$336$		0			0
$337$	11.0560			0.602257			0.301129	−	0.953583i	$-0.402637\pi$
$337$	11.0560			0.602257			0.301129	+	0.953583i	$0.402637\pi$
$338$	−6.57862	−	11.2126i	−0.357830	−	0.609884i
$339$		0			0
$340$	−4.17862	+	2.41253i	−0.226618	+	0.130838i
$341$	−4.08997	−	7.08403i	−0.221484	−	0.383622i
$342$		0			0
$343$	13.9164	+	12.2203i	0.751413	+	0.659832i
$344$	−1.77949	+	3.08217i	−0.0959436	+	0.166179i
$345$		0			0
$346$	−20.2233			−1.08721
$347$	−1.22028	−	0.704528i	−0.0655079	−	0.0378210i	0.466888	−	0.884316i	$-0.345375\pi$
$347$	−1.22028	−	0.704528i	−0.0655079	−	0.0378210i	−0.532396	+	0.846495i	$0.678708\pi$
$348$		0			0
$349$	8.04728	+	13.9383i	0.430761	+	0.746100i	0.996939	−	0.0781828i	$-0.0249118\pi$
$349$	8.04728	+	13.9383i	0.430761	+	0.746100i	−0.566178	+	0.824283i	$0.691578\pi$
$350$	11.1773	+	2.73763i	0.597454	+	0.146333i
$351$		0			0
$352$	−1.22414			−0.0652471
$353$	−16.9434	+	9.78227i	−0.901806	+	0.520658i	−0.877786	−	0.479054i	$-0.840980\pi$
$353$	−16.9434	+	9.78227i	−0.901806	+	0.520658i	−0.0240202	+	0.999711i	$0.507647\pi$
$354$		0			0
$355$	−29.3558	−	16.9486i	−1.55804	−	0.899536i
$356$		−	1.92173i		−	0.101851i
$357$		0			0
$358$	−1.71871	−	0.992298i	−0.0908367	−	0.0524446i
$359$	21.9223			1.15702			0.578509	−	0.815676i	$-0.303635\pi$
$359$	21.9223			1.15702			0.578509	+	0.815676i	$0.303635\pi$
$360$		0			0
$361$	8.58721	+	14.8735i	0.451958	+	0.782815i
$362$	−17.2737	+	9.97297i	−0.907885	+	0.524168i
$363$		0			0
$364$	9.14948	−	2.69945i	0.479563	−	0.141490i
$365$		−	35.3465i		−	1.85012i
$366$		0			0
$367$	13.3950	−	7.73359i	0.699212	−	0.403690i	−0.107842	−	0.994168i	$-0.534394\pi$
$367$	13.3950	−	7.73359i	0.699212	−	0.403690i	0.807054	+	0.590478i	$0.201061\pi$
$368$	2.87424	+	1.65944i	0.149830	+	0.0865045i
$369$		0			0
$370$	−0.0158669	+	0.0274823i	−0.000824883	+	0.00142874i
$371$	23.5599	+	22.5635i	1.22317	+	1.17144i
$372$		0			0
$373$	−0.207371	+	0.359178i	−0.0107373	+	0.0185975i	−0.871344	−	0.490672i	$-0.836751\pi$
$373$	−0.207371	+	0.359178i	−0.0107373	+	0.0185975i	0.860607	+	0.509270i	$0.170085\pi$
$374$	−0.965852	−	1.67291i	−0.0499430	−	0.0865039i
$375$		0			0
$376$			0.262559i			0.0135405i
$377$	−18.4997	−	31.7851i	−0.952785	−	1.63702i
$378$		0			0
$379$	−23.9912	+	13.8513i	−1.23234	+	0.711494i	−0.967518	−	0.252802i	$-0.918648\pi$
$379$	−23.9912	+	13.8513i	−1.23234	+	0.711494i	−0.264826	+	0.964296i	$0.585315\pi$
$380$	−3.57789	+	2.06569i	−0.183542	+	0.105968i
$381$		0			0
$382$			4.52065i			0.231297i
$383$	−5.39475	−	3.11466i	−0.275659	−	0.159152i	0.355798	−	0.934563i	$-0.384209\pi$
$383$	−5.39475	−	3.11466i	−0.275659	−	0.159152i	−0.631457	+	0.775411i	$0.717543\pi$
$384$		0			0
$385$	−2.35593	+	9.61890i	−0.120069	+	0.490225i
$386$	−7.06211	−	4.07731i	−0.359452	−	0.207530i
$387$		0			0
$388$	−1.79666	−	3.11190i	−0.0912115	−	0.157983i
$389$		−	0.387161i		−	0.0196298i	−0.999952	−	0.00981492i	$-0.996876\pi$
$389$		−	0.387161i		−	0.0196298i	0.999952	−	0.00981492i	$-0.00312424\pi$
$390$		0			0
$391$			5.23722i			0.264857i
$392$	0.302320	+	6.99347i	0.0152694	+	0.353224i
$393$		0			0
$394$	−5.60656	+	9.71084i	−0.282454	+	0.489225i
$395$			16.7372i			0.842140i
$396$		0			0
$397$	−14.7473	+	25.5430i	−0.740144	+	1.28197i	0.212286	+	0.977208i	$0.431909\pi$
$397$	−14.7473	+	25.5430i	−0.740144	+	1.28197i	−0.952430	+	0.304759i	$0.901424\pi$
$398$			16.8101i			0.842614i
$399$		0			0
$400$	2.17476	+	3.76679i	0.108738	+	0.188339i
$401$	−11.0249	−	19.0958i	−0.550559	−	0.953597i	−0.998234	−	0.0594004i	$-0.981081\pi$
$401$	−11.0249	−	19.0958i	−0.550559	−	0.953597i	0.447675	−	0.894196i	$-0.352252\pi$
$402$		0			0
$403$	0.0842923	+	24.0927i	0.00419890	+	1.20014i
$404$	−9.29529			−0.462458
$405$		0			0
$406$	25.9103	−	7.54611i	1.28591	−	0.374507i
$407$	−0.0110025	−	0.00635230i	−0.000545374	−	0.000314872i
$408$		0			0
$409$	12.6832	−	21.9679i	0.627144	−	1.08624i	−0.360978	−	0.932574i	$-0.617557\pi$
$409$	12.6832	−	21.9679i	0.627144	−	1.08624i	0.988122	−	0.153671i	$-0.0491095\pi$
$410$	2.35564	−	4.08009i	0.116337	−	0.201501i
$411$		0			0
$412$	−6.54638	−	3.77955i	−0.322517	−	0.186205i
$413$	−16.4674	+	4.79597i	−0.810310	+	0.235994i
$414$		0			0
$415$	2.19063			0.107534
$416$	3.12879	+	1.79184i	0.153401	+	0.0878522i
$417$		0			0
$418$	−0.826998	−	1.43240i	−0.0404498	−	0.0700611i
$419$	−5.59563	−	9.69191i	−0.273364	−	0.473481i	0.696357	−	0.717696i	$-0.254803\pi$
$419$	−5.59563	−	9.69191i	−0.273364	−	0.473481i	−0.969721	+	0.244215i	$0.921470\pi$
$420$		0			0
$421$		−	37.4059i		−	1.82305i	−0.411244	−	0.911525i	$-0.634905\pi$
$421$		−	37.4059i		−	1.82305i	0.411244	−	0.911525i	$-0.365095\pi$
$422$	−2.05863	+	3.56566i	−0.100213	+	0.173573i
$423$		0			0
$424$			12.3299i			0.598791i
$425$	−3.43177	+	5.94400i	−0.166465	+	0.288327i
$426$		0			0
$427$	21.4631	−	6.25091i	1.03867	−	0.302503i
$428$		−	16.5847i		−	0.801650i
$429$		0			0
$430$			10.8823i			0.524790i
$431$	5.35039	+	9.26714i	0.257719	+	0.446383i	0.965631	−	0.259919i	$-0.0836958\pi$
$431$	5.35039	+	9.26714i	0.257719	+	0.446383i	−0.707911	+	0.706301i	$0.750362\pi$
$432$		0			0
$433$	26.9384	+	15.5529i	1.29458	+	0.747425i	0.979462	−	0.201627i	$-0.0646230\pi$
$433$	26.9384	+	15.5529i	1.29458	+	0.747425i	0.315117	+	0.949053i	$0.397956\pi$
$434$	−17.1718	−	4.20583i	−0.824271	−	0.201886i
$435$		0			0
$436$	−2.60855	−	1.50605i	−0.124927	−	0.0721266i
$437$			4.48429i			0.214513i
$438$		0			0
$439$	−17.8736	+	10.3194i	−0.853063	+	0.492516i	−0.861683	−	0.507447i	$-0.830589\pi$
$439$	−17.8736	+	10.3194i	−0.853063	+	0.492516i	0.00862037	+	0.999963i	$0.497256\pi$
$440$	−3.24159	+	1.87153i	−0.154537	+	0.0892218i
$441$		0			0
$442$	0.0199058	+	5.68954i	0.000946821	+	0.270624i
$443$			19.2442i			0.914319i	0.889385	+	0.457160i	$0.151133\pi$
$443$			19.2442i			0.914319i	−0.889385	+	0.457160i	$0.848867\pi$
$444$		0			0
$445$	−2.93803	−	5.08882i	−0.139276	−	0.241233i
$446$	3.30868	−	5.73079i	0.156670	−	0.271361i
$447$		0			0
$448$	−1.82998	+	1.91080i	−0.0864586	+	0.0902769i
$449$	8.21166	−	14.2230i	0.387532	−	0.671226i	−0.604585	−	0.796541i	$-0.706661\pi$
$449$	8.21166	−	14.2230i	0.387532	−	0.671226i	0.992117	+	0.125315i	$0.0399942\pi$
$450$		0			0
$451$	1.63346	+	0.943078i	0.0769166	+	0.0444078i
$452$	5.84378	−	3.37391i	0.274868	−	0.158695i
$453$		0			0
$454$			5.91853i			0.277771i
$455$	20.1012	−	21.1364i	0.942357	−	0.990891i
$456$		0			0
$457$	−29.6453	+	17.1158i	−1.38675	+	0.800641i	−0.992948	−	0.118554i	$-0.962174\pi$
$457$	−29.6453	+	17.1158i	−1.38675	+	0.800641i	−0.393803	+	0.919195i	$0.628841\pi$
$458$	−4.85129	−	8.40268i	−0.226686	−	0.392631i
$459$		0			0
$460$	10.1482			0.473160
$461$	−22.3419	−	12.8991i	−1.04057	−	0.600772i	−0.120574	−	0.992704i	$-0.538473\pi$
$461$	−22.3419	−	12.8991i	−1.04057	−	0.600772i	−0.919994	+	0.391932i	$0.871807\pi$
$462$		0			0
$463$		−	1.88388i		−	0.0875511i	−0.999041	−	0.0437755i	$-0.986061\pi$
$463$		−	1.88388i		−	0.0875511i	0.999041	−	0.0437755i	$-0.0139386\pi$
$464$	8.83351	+	5.10003i	0.410085	+	0.236763i
$465$		0			0
$466$	12.4211	−	7.17133i	0.575397	−	0.332205i
$467$	−21.1626			−0.979290			−0.489645	−	0.871922i	$-0.662874\pi$
$467$	−21.1626			−0.979290			−0.489645	+	0.871922i	$0.662874\pi$
$468$		0			0
$469$	−6.16006	+	25.1506i	−0.284445	+	1.16135i
$470$	0.401414	+	0.695269i	0.0185158	+	0.0320703i
$471$		0			0
$472$	−5.61418	−	3.24135i	−0.258414	−	0.149195i
$473$	−4.35671			−0.200322
$474$		0			0
$475$	−2.93841	+	5.08947i	−0.134823	+	0.233521i
$476$	−4.05514	−	0.993214i	−0.185867	−	0.0455239i
$477$		0			0
$478$	7.26069	+	12.5759i	0.332096	+	0.575208i
$479$	−6.60511	+	3.81346i	−0.301795	+	0.174242i	−0.643249	−	0.765657i	$-0.722414\pi$
$479$	−6.60511	+	3.81346i	−0.301795	+	0.174242i	0.341454	+	0.939899i	$0.389081\pi$
$480$		0			0
$481$	0.0188231	+	0.0323407i	0.000858260	+	0.00147461i
$482$	15.4770			0.704960
$483$		0			0
$484$	4.75073	+	8.22851i	0.215942	+	0.374023i
$485$	−9.51525	−	5.49363i	−0.432065	−	0.249453i
$486$		0			0
$487$	20.8565	+	12.0415i	0.945096	+	0.545651i	0.891554	−	0.452914i	$-0.149616\pi$
$487$	20.8565	+	12.0415i	0.945096	+	0.545651i	0.0535419	+	0.998566i	$0.482949\pi$
$488$	7.31734	+	4.22467i	0.331241	+	0.191242i
$489$		0			0
$490$	11.4925	+	18.0568i	0.519179	+	0.815723i
$491$	21.2582	−	12.2734i	0.959368	−	0.553891i	0.0633897	−	0.997989i	$-0.479809\pi$
$491$	21.2582	−	12.2734i	0.959368	−	0.553891i	0.895979	+	0.444097i	$0.146476\pi$
$492$		0			0
$493$			16.0957i			0.724915i
$494$	0.0170440	+	4.87159i	0.000766848	+	0.219183i
$495$		0			0
$496$	−3.34108	−	5.78692i	−0.150019	−	0.259840i
$497$	−8.20141	−	28.1604i	−0.367884	−	1.26317i
$498$		0			0
$499$			25.8071i			1.15529i	0.816289	+	0.577643i	$0.196028\pi$
$499$			25.8071i			1.15529i	−0.816289	+	0.577643i	$0.803972\pi$
$500$	−1.72252	−	0.994499i	−0.0770336	−	0.0444754i
$501$		0			0
$502$	20.0249			0.893757
$503$	1.64331	−	2.84630i	0.0732716	−	0.126910i	−0.827062	−	0.562111i	$-0.809989\pi$
$503$	1.64331	−	2.84630i	0.0732716	−	0.126910i	0.900333	+	0.435201i	$0.143323\pi$
$504$		0			0
$505$	−24.6143	+	14.2111i	−1.09532	+	0.632385i
$506$			4.06280i			0.180613i
$507$		0			0
$508$	−4.92215			−0.218385
$509$	−9.30274	+	5.37094i	−0.412337	+	0.238063i	−0.691793	−	0.722096i	$-0.743179\pi$
$509$	−9.30274	+	5.37094i	−0.412337	+	0.238063i	0.279457	+	0.960158i	$0.409846\pi$
$510$		0			0
$511$	21.1544	−	22.0886i	0.935813	−	0.977142i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−2.37478	+	4.11324i	−0.104747	+	0.181427i
$515$	−23.1135			−1.01850
$516$		0			0
$517$	−0.278350	+	0.160705i	−0.0122418	+	0.00706781i
$518$	−0.0263632	+	0.00767801i	−0.00115833	+	0.000337353i
$519$		0			0
$520$	11.0246	−	0.0385714i	0.483461	−	0.00169147i
$521$	−39.5713			−1.73365			−0.866824	−	0.498614i	$-0.833842\pi$
$521$	−39.5713			−1.73365			−0.866824	+	0.498614i	$0.833842\pi$
$522$		0			0
$523$	−1.19351	+	0.689072i	−0.0521884	+	0.0301310i	−0.525867	−	0.850567i	$-0.676259\pi$
$523$	−1.19351	+	0.689072i	−0.0521884	+	0.0301310i	0.473679	+	0.880698i	$0.342926\pi$
$524$	7.15675	−	12.3959i	0.312644	−	0.541516i
$525$		0			0
$526$	−20.1741	−	11.6475i	−0.879634	−	0.507857i
$527$	5.27224	−	9.13178i	0.229662	−	0.397787i
$528$		0			0
$529$	−5.99249	+	10.3793i	−0.260543	+	0.451274i
$530$	18.8505	+	32.6500i	0.818813	+	1.41823i
$531$		0			0
$532$	−3.47216	−	0.850426i	−0.150537	−	0.0368706i
$533$	−2.79452	−	4.80138i	−0.121044	−	0.207971i
$534$		0			0
$535$	−25.3554	−	43.9169i	−1.09621	−	1.89869i
$536$	−8.47580	+	4.89351i	−0.366099	+	0.211367i
$537$		0			0
$538$	0.299995			0.0129337
$539$	−7.22902	+	4.60101i	−0.311376	+	0.198180i
$540$		0			0
$541$		−	40.2236i		−	1.72935i	−0.502333	−	0.864675i	$-0.667525\pi$
$541$		−	40.2236i		−	1.72935i	0.502333	−	0.864675i	$-0.332475\pi$
$542$	5.56431	−	9.63766i	0.239007	−	0.413973i
$543$		0			0
$544$	−0.789002	−	1.36659i	−0.0338282	−	0.0585921i
$545$	−9.21007			−0.394516
$546$		0			0
$547$	12.6370			0.540318			0.270159	−	0.962816i	$-0.412924\pi$
$547$	12.6370			0.540318			0.270159	+	0.962816i	$0.412924\pi$
$548$	−5.14303	−	8.90798i	−0.219699	−	0.380530i
$549$		0			0
$550$	−2.66222	+	4.61109i	−0.113517	+	0.196618i
$551$			13.7817i			0.587122i
$552$		0			0
$553$	−10.0169	+	10.4593i	−0.425964	+	0.444776i
$554$	−14.6820			−0.623777
$555$		0			0
$556$	−12.3914	+	7.15418i	−0.525512	+	0.303405i
$557$	17.5694	+	30.4311i	0.744438	+	1.28941i	0.950457	+	0.310857i	$0.100616\pi$
$557$	17.5694	+	30.4311i	0.744438	+	1.28941i	−0.206018	+	0.978548i	$0.566051\pi$
$558$		0			0
$559$	11.1353	+	6.37712i	0.470972	+	0.269723i
$560$	−1.92455	+	7.85765i	−0.0813271	+	0.332046i
$561$		0			0
$562$	−6.49117	−	11.2430i	−0.273813	−	0.474259i
$563$	−10.1326	+	17.5501i	−0.427037	+	0.739650i	−0.996608	−	0.0822918i	$-0.973776\pi$
$563$	−10.1326	+	17.5501i	−0.427037	+	0.739650i	0.569571	+	0.821942i	$0.307109\pi$
$564$		0			0
$565$	10.3164	−	17.8685i	0.434014	−	0.751733i
$566$	−24.2843	−	14.0205i	−1.02074	−	0.589327i
$567$		0			0
$568$	5.54292	−	9.60061i	0.232576	−	0.402833i
$569$	−4.38484	+	2.53159i	−0.183822	+	0.106130i	−0.589087	−	0.808070i	$-0.700513\pi$
$569$	−4.38484	+	2.53159i	−0.183822	+	0.106130i	0.405265	+	0.914199i	$0.367179\pi$
$570$		0			0
$571$	−4.23236			−0.177119			−0.0885594	−	0.996071i	$-0.528226\pi$
$571$	−4.23236			−0.177119			−0.0885594	+	0.996071i	$0.528226\pi$
$572$	0.0154420	+	4.41369i	0.000645663	+	0.184546i
$573$		0			0
$574$	3.91395	−	1.13990i	0.163365	−	0.0475783i
$575$	12.5015	−	7.21777i	0.521350	−	0.301002i
$576$		0			0
$577$	33.1502			1.38006			0.690030	−	0.723781i	$-0.257598\pi$
$577$	33.1502			1.38006			0.690030	+	0.723781i	$0.257598\pi$
$578$	−7.25495	+	12.5659i	−0.301766	+	0.522674i
$579$		0			0
$580$	31.1887			1.29504
$581$	1.36896	+	1.31106i	0.0567941	+	0.0543920i
$582$		0			0
$583$	−13.0714	+	7.54677i	−0.541362	+	0.312555i
$584$	11.5599			0.478350
$585$		0			0
$586$			16.9909i			0.701886i
$587$	31.2791	−	18.0590i	1.29103	−	0.745375i	0.312191	−	0.950019i	$-0.398937\pi$
$587$	31.2791	−	18.0590i	1.29103	−	0.745375i	0.978836	+	0.204644i	$0.0656037\pi$
$588$		0			0
$589$	4.51428	−	7.81896i	0.186008	−	0.322175i
$590$	−19.8221			−0.816064
$591$		0			0
$592$	−0.00898792	−	0.00518918i	−0.000369401	−	0.000213274i
$593$			4.36184i			0.179119i	0.995981	+	0.0895597i	$0.0285460\pi$
$593$			4.36184i			0.179119i	−0.995981	+	0.0895597i	$0.971454\pi$
$594$		0			0
$595$	−12.2567	+	3.56963i	−0.502475	+	0.146340i
$596$	8.08473	+	14.0032i	0.331163	+	0.573592i
$597$		0			0
$598$	5.94692	−	10.3841i	0.243187	−	0.424637i
$599$			31.6014i			1.29120i	0.763676	+	0.645599i	$0.223392\pi$
$599$			31.6014i			1.29120i	−0.763676	+	0.645599i	$0.776608\pi$
$600$		0			0
$601$	−11.0117	+	6.35762i	−0.449178	+	0.259333i	−0.707483	−	0.706731i	$-0.750169\pi$
$601$	−11.0117	+	6.35762i	−0.449178	+	0.259333i	0.258305	+	0.966063i	$0.416836\pi$
$602$	−6.51287	+	6.80050i	−0.265445	+	0.277168i
$603$		0			0
$604$	15.5289	+	8.96559i	0.631860	+	0.364805i
$605$	25.1603	+	14.5263i	1.02291	+	0.590578i
$606$		0			0
$607$	−37.3636	−	21.5719i	−1.51654	−	0.875577i	−0.999811	−	0.0194294i	$-0.993815\pi$
$607$	−37.3636	−	21.5719i	−1.51654	−	0.875577i	−0.516732	−	0.856147i	$-0.672852\pi$
$608$	−0.675572	−	1.17012i	−0.0273980	−	0.0474548i
$609$		0			0
$610$	25.8355			1.04605
$611$	0.946666	−	0.00331206i	0.0382980	−	0.000133992i
$612$		0			0
$613$	−12.3394	+	7.12413i	−0.498382	+	0.287741i	−0.728045	−	0.685529i	$-0.759571\pi$
$613$	−12.3394	+	7.12413i	−0.498382	+	0.287741i	0.229663	+	0.973270i	$0.426238\pi$
$614$	9.04534	+	15.6670i	0.365040	+	0.632268i
$615$		0			0
$616$	−3.14580	−	0.770491i	−0.126748	−	0.0310440i
$617$	13.6335	−	23.6139i	0.548865	−	0.950662i	−0.449488	−	0.893286i	$-0.648394\pi$
$617$	13.6335	−	23.6139i	0.548865	−	0.950662i	0.998353	−	0.0573752i	$-0.0182731\pi$
$618$		0			0
$619$	−20.8345			−0.837411			−0.418706	−	0.908122i	$-0.637516\pi$
$619$	−20.8345			−0.837411			−0.418706	+	0.908122i	$0.637516\pi$
$620$	−17.6946	−	10.2160i	−0.710634	−	0.410285i
$621$		0			0
$622$	9.70029	+	16.8014i	0.388946	+	0.673675i
$623$	1.20956	−	4.93844i	0.0484599	−	0.197855i
$624$		0			0
$625$	−27.8293			−1.11317
$626$	−6.57679	+	3.79711i	−0.262862	+	0.151763i
$627$		0			0
$628$	−8.09089	−	4.67127i	−0.322861	−	0.186404i
$629$		−	0.0163771i		−	0.000652997i
$630$		0			0
$631$	−9.96607	−	5.75391i	−0.396743	−	0.229060i	0.288335	−	0.957530i	$-0.406898\pi$
$631$	−9.96607	−	5.75391i	−0.396743	−	0.229060i	−0.685078	+	0.728470i	$0.740232\pi$
$632$	−5.47379			−0.217736
$633$		0			0
$634$	11.6735	+	20.2191i	0.463614	+	0.803002i
$635$	−13.0341	+	7.52522i	−0.517241	+	0.298629i
$636$		0			0
$637$	25.2113	−	1.17824i	0.998910	−	0.0466836i
$638$			12.4863i			0.494339i
$639$		0			0
$640$	−2.64804	+	1.52885i	−0.104673	+	0.0604330i
$641$	−15.9775	−	9.22464i	−0.631075	−	0.364351i	0.150093	−	0.988672i	$-0.452043\pi$
$641$	−15.9775	−	9.22464i	−0.631075	−	0.364351i	−0.781168	+	0.624320i	$0.785376\pi$
$642$		0			0
$643$	8.16863	−	14.1485i	0.322139	−	0.557962i	−0.658790	−	0.752327i	$-0.728931\pi$
$643$	8.16863	−	14.1485i	0.322139	−	0.557962i	0.980929	+	0.194365i	$0.0622647\pi$
$644$	6.34173	+	6.07351i	0.249899	+	0.239330i
$645$		0			0
$646$	1.06605	−	1.84646i	0.0419434	−	0.0726480i
$647$	0.389873	+	0.675279i	0.0153275	+	0.0265480i	0.873587	−	0.486667i	$-0.161788\pi$
$647$	0.389873	+	0.675279i	0.0153275	+	0.0265480i	−0.858260	+	0.513215i	$0.828454\pi$
$648$		0			0
$649$		−	7.93576i		−	0.311506i
$650$	13.5538	−	7.88866i	0.531625	−	0.309419i
$651$		0			0
$652$	−19.6902	+	11.3682i	−0.771129	+	0.445212i
$653$	35.7099	−	20.6171i	1.39744	−	0.806810i	0.403313	−	0.915062i	$-0.367859\pi$
$653$	35.7099	−	20.6171i	1.39744	−	0.806810i	0.994124	+	0.108252i	$0.0345253\pi$
$654$		0			0
$655$		−	43.7664i		−	1.71009i
$656$	1.33437	+	0.770398i	0.0520983	+	0.0300790i
$657$		0			0
$658$	−0.165258	+	0.674723i	−0.00644243	+	0.0263035i
$659$	42.8855	+	24.7600i	1.67058	+	0.964511i	0.967312	+	0.253588i	$0.0816106\pi$
$659$	42.8855	+	24.7600i	1.67058	+	0.964511i	0.703270	+	0.710923i	$0.251723\pi$
$660$		0			0
$661$	−8.60759	−	14.9088i	−0.334796	−	0.579884i	0.648649	−	0.761087i	$-0.275334\pi$
$661$	−8.60759	−	14.9088i	−0.334796	−	0.579884i	−0.983446	+	0.181203i	$0.942001\pi$
$662$			4.62119i			0.179608i
$663$		0			0
$664$			0.716433i			0.0278030i
$665$	−10.4946	+	3.05644i	−0.406963	+	0.118524i
$666$		0			0
$667$	16.9264	−	29.3174i	0.655394	−	1.13518i
$668$		−	22.4755i		−	0.869602i
$669$		0			0
$670$	−14.9629	+	25.9164i	−0.578066	+	1.00124i
$671$			10.3432i			0.399295i
$672$		0			0
$673$	−17.6865	−	30.6339i	−0.681764	−	1.18085i	−0.974442	−	0.224638i	$-0.927880\pi$
$673$	−17.6865	−	30.6339i	−0.681764	−	1.18085i	0.292678	−	0.956211i	$-0.405453\pi$
$674$	5.52799	+	9.57476i	0.212930	+	0.368806i
$675$		0			0
$676$	6.42106	−	11.3035i	0.246964	−	0.434751i
$677$	39.9702			1.53618			0.768089	−	0.640343i	$-0.221208\pi$
$677$	39.9702			1.53618			0.768089	+	0.640343i	$0.221208\pi$
$678$		0			0
$679$	−2.65837	−	9.12778i	−0.102019	−	0.350292i
$680$	−4.17862	−	2.41253i	−0.160243	−	0.0925162i
$681$		0			0
$682$	4.08997	−	7.08403i	0.156613	−	0.271261i
$683$	22.9733	−	39.7909i	0.879048	−	1.52256i	0.0266605	−	0.999645i	$-0.491513\pi$
$683$	22.9733	−	39.7909i	0.879048	−	1.52256i	0.852387	−	0.522911i	$-0.175154\pi$
$684$		0			0
$685$	−27.2379	−	15.7258i	−1.04071	−	0.600853i
$686$	−3.62487	+	18.1621i	−0.138398	+	0.693431i
$687$		0			0
$688$	−3.55898			−0.135685
$689$	44.4557	−	0.155536i	1.69363	−	0.00592543i
$690$		0			0
$691$	−25.3023	−	43.8249i	−0.962546	−	1.66718i	−0.716068	−	0.698031i	$-0.754060\pi$
$691$	−25.3023	−	43.8249i	−0.962546	−	1.66718i	−0.246479	−	0.969148i	$-0.579273\pi$
$692$	−10.1117	−	17.5139i	−0.384387	−	0.665778i
$693$		0			0
$694$		−	1.40906i		−	0.0534870i
$695$	−21.8753	+	37.8891i	−0.829778	+	1.43722i
$696$		0			0
$697$			2.43138i			0.0920951i
$698$	−8.04728	+	13.9383i	−0.304594	+	0.527573i
$699$		0			0
$700$	3.21781	+	11.0487i	0.121622	+	0.417601i
$701$		−	2.25551i		−	0.0851895i	−0.999092	−	0.0425948i	$-0.986438\pi$
$701$		−	2.25551i		−	0.0851895i	0.999092	−	0.0425948i	$-0.0135624\pi$
$702$		0			0
$703$		−	0.0140226i		−	0.000528874i
$704$	−0.612072	−	1.06014i	−0.0230683	−	0.0399555i
$705$		0			0
$706$	−16.9434	−	9.78227i	−0.637673	−	0.368161i
$707$	−23.8870	−	5.85057i	−0.898362	−	0.220033i
$708$		0			0
$709$	−26.7670	−	15.4540i	−1.00526	−	0.580386i	−0.0954577	−	0.995433i	$-0.530431\pi$
$709$	−26.7670	−	15.4540i	−1.00526	−	0.580386i	−0.909800	+	0.415048i	$0.863765\pi$
$710$		−	33.8971i		−	1.27214i
$711$		0			0
$712$	1.66426	−	0.960864i	0.0623710	−	0.0360099i
$713$	−19.2061	+	11.0887i	−0.719275	+	0.415274i
$714$		0			0
$715$	6.78875	+	11.6640i	0.253885	+	0.436210i
$716$		−	1.98460i		−	0.0741679i
$717$		0			0
$718$	10.9612	+	18.9853i	0.409067	+	0.708525i
$719$	−5.86881	+	10.1651i	−0.218870	+	0.379093i	−0.954463	−	0.298330i	$-0.903570\pi$
$719$	−5.86881	+	10.1651i	−0.218870	+	0.379093i	0.735593	+	0.677424i	$0.236904\pi$
$720$		0			0
$721$	−14.4439	−	13.8330i	−0.537921	−	0.515169i
$722$	−8.58721	+	14.8735i	−0.319583	+	0.553533i
$723$		0			0
$724$	−17.2737	−	9.97297i	−0.641972	−	0.370643i
$725$	38.4214	−	22.1826i	1.42694	−	0.823842i
$726$		0			0
$727$			44.2271i			1.64029i	0.572154	+	0.820146i	$0.306108\pi$
$727$			44.2271i			1.64029i	−0.572154	+	0.820146i	$0.693892\pi$
$728$	6.91253	+	6.57396i	0.256196	+	0.243647i
$729$		0			0
$730$	30.6110	−	17.6733i	1.13296	−	0.654117i
$731$	−2.80804	−	4.86367i	−0.103859	−	0.179889i
$732$		0			0
$733$	−20.8094			−0.768613			−0.384307	−	0.923205i	$-0.625559\pi$
$733$	−20.8094			−0.768613			−0.384307	+	0.923205i	$0.625559\pi$
$734$	13.3950	+	7.73359i	0.494418	+	0.285452i
$735$		0			0
$736$			3.31889i			0.122336i
$737$	−10.3756	−	5.99036i	−0.382191	−	0.220658i
$738$		0			0
$739$	37.1516	−	21.4495i	1.36664	−	0.789032i	0.376146	−	0.926560i	$-0.377249\pi$
$739$	37.1516	−	21.4495i	1.36664	−	0.789032i	0.990498	+	0.137528i	$0.0439158\pi$
$740$	−0.0317339			−0.00116656
$741$		0			0
$742$	−7.76057	+	31.6852i	−0.284899	+	1.16320i
$743$	−11.2928	−	19.5597i	−0.414292	−	0.717575i	0.581062	−	0.813859i	$-0.302637\pi$
$743$	−11.2928	−	19.5597i	−0.414292	−	0.717575i	−0.995354	+	0.0962847i	$0.969304\pi$
$744$		0			0
$745$	42.8174	+	24.7207i	1.56871	+	0.905695i
$746$	−0.414743			−0.0151848
$747$		0			0
$748$	0.965852	−	1.67291i	0.0353151	−	0.0611675i
$749$	10.4386	−	42.6192i	0.381418	−	1.55727i
$750$		0			0
$751$	−2.78046	−	4.81589i	−0.101460	−	0.175734i	0.810826	−	0.585287i	$-0.199018\pi$
$751$	−2.78046	−	4.81589i	−0.101460	−	0.175734i	−0.912286	+	0.409553i	$0.865685\pi$
$752$	−0.227383	+	0.131280i	−0.00829181	+	0.00478728i
$753$		0			0
$754$	18.2769	−	31.9138i	0.665604	−	1.16223i
$755$	54.8281			1.99540
$756$		0			0
$757$	−1.00594	−	1.74235i	−0.0365616	−	0.0633266i	0.847166	−	0.531329i	$-0.178307\pi$
$757$	−1.00594	−	1.74235i	−0.0365616	−	0.0633266i	−0.883727	+	0.468002i	$0.844974\pi$
$758$	−23.9912	−	13.8513i	−0.871399	−	0.503102i
$759$		0			0
$760$	−3.57789	−	2.06569i	−0.129784	−	0.0749306i
$761$	9.45932	+	5.46134i	0.342900	+	0.197973i	0.661554	−	0.749898i	$-0.269897\pi$
$761$	9.45932	+	5.46134i	0.342900	+	0.197973i	−0.318654	+	0.947871i	$0.603231\pi$
$762$		0			0
$763$	−5.75551	−	5.51208i	−0.208364	−	0.199551i
$764$	−3.91500	+	2.26033i	−0.141640	+	0.0817757i
$765$		0			0
$766$		−	6.22932i		−	0.225075i
$767$	−11.6160	+	20.2830i	−0.419428	+	0.732376i
$768$		0			0
$769$	−18.4480	−	31.9529i	−0.665252	−	1.15225i	−0.979217	−	0.202816i	$-0.934991\pi$
$769$	−18.4480	−	31.9529i	−0.665252	−	1.15225i	0.313964	−	0.949435i	$-0.398343\pi$
$770$	−9.50818	+	2.76916i	−0.342651	+	0.0997935i
$771$		0			0
$772$		−	8.15462i		−	0.293491i
$773$	1.10778	+	0.639577i	0.0398441	+	0.0230040i	0.519790	−	0.854294i	$-0.326010\pi$
$773$	1.10778	+	0.639577i	0.0398441	+	0.0230040i	−0.479946	+	0.877298i	$0.659344\pi$
$774$		0			0
$775$	−29.0641			−1.04401
$776$	1.79666	−	3.11190i	0.0644962	−	0.111711i
$777$		0			0
$778$	0.335291	−	0.193580i	0.0120208	−	0.00694020i
$779$			2.08184i			0.0745895i
$780$		0			0
$781$	13.5707			0.485597
$782$	−4.53556	+	2.61861i	−0.162191	+	0.0936412i
$783$		0			0
$784$	−5.90536	+	3.75855i	−0.210906	+	0.134234i
$785$	−28.5667			−1.01959
$786$		0			0
$787$	11.1783	−	19.3614i	0.398464	−	0.690159i	−0.595073	−	0.803672i	$-0.702877\pi$
$787$	11.1783	−	19.3614i	0.398464	−	0.690159i	0.993537	+	0.113512i	$0.0362102\pi$
$788$	−11.2131			−0.399451
$789$		0			0
$790$	−14.4948	+	8.36860i	−0.515703	+	0.297741i
$791$	17.1409	−	4.99210i	0.609460	−	0.177499i
$792$		0			0
$793$	15.1399	−	26.4362i	0.537632	−	0.938777i
$794$	−29.4945			−1.04672
$795$		0			0
$796$	−14.5580	+	8.40505i	−0.515994	+	0.297909i
$797$	5.16411	−	8.94451i	0.182922	−	0.316831i	−0.759952	−	0.649979i	$-0.774778\pi$
$797$	5.16411	−	8.94451i	0.182922	−	0.316831i	0.942874	+	0.333148i	$0.108111\pi$
$798$		0			0
$799$	−0.358811	−	0.207160i	−0.0126938	−	0.00732879i
$800$	−2.17476	+	3.76679i	−0.0768892	+	0.133176i
$801$		0			0
$802$	11.0249	−	19.0958i	0.389304	−	0.674295i
$803$	7.07547	+	12.2551i	0.249688	+	0.432472i
$804$		0			0
$805$	26.0787	+	6.38737i	0.919152	+	0.225125i
$806$	−20.8228	+	12.1194i	−0.733450	+	0.426886i
$807$		0			0
$808$	−4.64764	−	8.04996i	−0.163504	−	0.283196i
$809$	7.36433	−	4.25180i	0.258916	−	0.149485i	−0.364924	−	0.931037i	$-0.618905\pi$
$809$	7.36433	−	4.25180i	0.258916	−	0.149485i	0.623840	+	0.781552i	$0.285572\pi$
$810$		0			0
$811$	49.0043			1.72077			0.860387	−	0.509640i	$-0.170222\pi$
$811$	49.0043			1.72077			0.860387	+	0.509640i	$0.170222\pi$
$812$	19.4903	+	18.6659i	0.683975	+	0.655046i
$813$		0			0
$814$		−	0.0127046i		−	0.000445296i
$815$	−34.7604	+	60.2068i	−1.21760	+	2.10895i
$816$		0			0
$817$	−2.40435	−	4.16445i	−0.0841174	−	0.145696i
$818$	25.3664			0.886915
$819$		0			0
$820$	4.71129			0.164525
$821$	−3.99874	−	6.92603i	−0.139557	−	0.241720i	0.787772	−	0.615967i	$-0.211235\pi$
$821$	−3.99874	−	6.92603i	−0.139557	−	0.241720i	−0.927329	+	0.374247i	$0.877901\pi$
$822$		0			0
$823$	11.4714	−	19.8691i	0.399869	−	0.692594i	−0.593840	−	0.804583i	$-0.702389\pi$
$823$	11.4714	−	19.8691i	0.399869	−	0.692594i	0.993709	+	0.111989i	$0.0357222\pi$
$824$		−	7.55911i		−	0.263334i
$825$		0			0
$826$	−12.3871	−	11.8632i	−0.431004	−	0.412775i
$827$	15.6206			0.543182			0.271591	−	0.962413i	$-0.412450\pi$
$827$	15.6206			0.543182			0.271591	+	0.962413i	$0.412450\pi$
$828$		0			0
$829$	−37.6566	+	21.7411i	−1.30787	+	0.755098i	−0.981740	−	0.190228i	$-0.939077\pi$
$829$	−37.6566	+	21.7411i	−1.30787	+	0.755098i	−0.326128	+	0.945326i	$0.605744\pi$
$830$	1.09532	+	1.89715i	0.0380190	+	0.0658509i
$831$		0			0
$832$	0.0126145	+	3.60553i	0.000437330	+	0.124999i
$833$	−9.79574	−	5.10471i	−0.339402	−	0.176868i
$834$		0			0
$835$	−34.3616	−	59.5160i	−1.18913	−	2.05964i
$836$	0.826998	−	1.43240i	0.0286023	−	0.0495407i
$837$		0			0
$838$	5.59563	−	9.69191i	0.193298	−	0.334801i
$839$	20.8997	+	12.0665i	0.721539	+	0.416581i	0.815319	−	0.579012i	$-0.196562\pi$
$839$	20.8997	+	12.0665i	0.721539	+	0.416581i	−0.0937801	+	0.995593i	$0.529895\pi$
$840$		0			0
$841$	37.5206	−	64.9875i	1.29381	−	2.24095i
$842$	32.3944	−	18.7029i	1.11639	−	0.644546i
$843$		0			0
$844$	−4.11726			−0.141722
$845$	−0.278141	−	39.7491i	−0.00956833	−	1.36741i
$846$		0			0
$847$	7.02928	+	24.1358i	0.241529	+	0.829314i
$848$	−10.6780	+	6.16493i	−0.366683	+	0.211705i
$849$		0			0
$850$	−6.86354			−0.235418
$851$	−0.0172223	+	0.0298299i	−0.000590373	+	0.00102256i
$852$		0			0
$853$	36.2991			1.24286			0.621429	−	0.783471i	$-0.286553\pi$
$853$	36.2991			1.24286			0.621429	+	0.783471i	$0.286553\pi$
$854$	16.1450	+	15.4622i	0.552471	+	0.529104i
$855$		0			0
$856$	14.3627	−	8.29233i	0.490908	−	0.283426i
$857$	−5.77225			−0.197176			−0.0985882	−	0.995128i	$-0.531433\pi$
$857$	−5.77225			−0.197176			−0.0985882	+	0.995128i	$0.531433\pi$
$858$		0			0
$859$			44.7219i			1.52589i	0.646462	+	0.762946i	$0.276248\pi$
$859$			44.7219i			1.52589i	−0.646462	+	0.762946i	$0.723752\pi$
$860$	−9.42433	+	5.44114i	−0.321367	+	0.185541i
$861$		0			0
$862$	−5.35039	+	9.26714i	−0.182235	+	0.315640i
$863$	15.2040			0.517550			0.258775	−	0.965938i	$-0.416681\pi$
$863$	15.2040			0.517550			0.258775	+	0.965938i	$0.416681\pi$
$864$		0			0
$865$	−53.5522	−	30.9184i	−1.82083	−	1.05126i
$866$			31.1058i			1.05702i
$867$		0			0
$868$	−4.94353	−	16.9741i	−0.167794	−	0.576139i
$869$	−3.35036	−	5.80299i	−0.113653	−	0.196853i
$870$		0			0
$871$	17.7506	+	30.4980i	0.601456	+	1.03339i
$872$		−	3.01209i		−	0.102002i
$873$		0			0
$874$	−3.88351	+	2.24215i	−0.131362	+	0.0758417i
$875$	−3.80058	−	3.63983i	−0.128483	−	0.123049i
$876$		0			0
$877$	23.9157	+	13.8077i	0.807575	+	0.466253i	0.846113	−	0.533004i	$-0.178937\pi$
$877$	23.9157	+	13.8077i	0.807575	+	0.466253i	−0.0385382	+	0.999257i	$0.512270\pi$
$878$	−17.8736	−	10.3194i	−0.603206	−	0.348261i
$879$		0			0
$880$	−3.24159	−	1.87153i	−0.109274	−	0.0630893i
$881$	13.0960	+	22.6829i	0.441214	+	0.764205i	0.997780	−	0.0665983i	$-0.0212146\pi$
$881$	13.0960	+	22.6829i	0.441214	+	0.764205i	−0.556566	+	0.830804i	$0.687881\pi$
$882$		0			0
$883$	−11.2225			−0.377668			−0.188834	−	0.982009i	$-0.560471\pi$
$883$	−11.2225			−0.377668			−0.188834	+	0.982009i	$0.560471\pi$
$884$	−4.91733	+	2.86201i	−0.165388	+	0.0962597i
$885$		0			0
$886$	−16.6660	+	9.62210i	−0.559904	+	0.323261i
$887$	−26.6020	−	46.0759i	−0.893206	−	1.54708i	−0.836009	−	0.548716i	$-0.815117\pi$
$887$	−26.6020	−	46.0759i	−0.893206	−	1.54708i	−0.0571970	−	0.998363i	$-0.518216\pi$
$888$		0			0
$889$	−12.6489	−	3.09806i	−0.424231	−	0.103906i
$890$	2.93803	−	5.08882i	0.0984830	−	0.170578i
$891$		0			0
$892$	6.61735			0.221565
$893$	−0.307227	−	0.177378i	−0.0102810	−	0.00593572i
$894$		0			0
$895$	−3.03415	−	5.25530i	−0.101420	−	0.175665i
$896$	−2.56979	−	0.629412i	−0.0858508	−	0.0210272i
$897$		0			0
$898$	16.4233			0.548054
$899$	−59.0269	+	34.0792i	−1.96866	+	1.13660i
$900$		0			0
$901$	−16.8499	−	9.72829i	−0.561351	−	0.324096i
$902$			1.88616i			0.0628021i
$903$		0			0
$904$	5.84378	+	3.37391i	0.194361	+	0.112214i
$905$	−60.9887			−2.02733
$906$		0			0
$907$	9.13624	+	15.8244i	0.303364	+	0.525442i	0.976896	−	0.213717i	$-0.0685569\pi$
$907$	9.13624	+	15.8244i	0.303364	+	0.525442i	−0.673532	+	0.739158i	$0.735224\pi$
$908$	−5.12560	+	2.95927i	−0.170099	+	0.0982067i
$909$		0			0
$910$	28.3553	+	6.83990i	0.939968	+	0.226741i
$911$			11.1562i			0.369622i	0.982774	+	0.184811i	$0.0591673\pi$
$911$			11.1562i			0.369622i	−0.982774	+	0.184811i	$0.940833\pi$
$912$		0			0
$913$	−0.759520	+	0.438509i	−0.0251364	+	0.0145125i
$914$	−29.6453	−	17.1158i	−0.980581	−	0.566139i
$915$		0			0
$916$	4.85129	−	8.40268i	0.160291	−	0.277632i
$917$	26.1935	−	27.3503i	0.864985	−	0.903185i
$918$		0			0
$919$	3.77850	−	6.54456i	0.124641	−	0.215885i	−0.796951	−	0.604044i	$-0.793555\pi$
$919$	3.77850	−	6.54456i	0.124641	−	0.215885i	0.921593	+	0.388158i	$0.126889\pi$
$920$	5.07408	+	8.78856i	0.167287	+	0.289750i
$921$		0			0
$922$		−	25.7983i		−	0.849620i
$923$	−34.6852	−	19.8640i	−1.14168	−	0.653833i
$924$		0			0
$925$	−0.0390931	+	0.0225704i	−0.00128537	+	0.000742110i
$926$	1.63148	−	0.941938i	0.0536139	−	0.0309540i
$927$		0			0
$928$			10.2001i			0.334833i
$929$	−11.6312	−	6.71530i	−0.381609	−	0.220322i	0.296909	−	0.954906i	$-0.404044\pi$
$929$	−11.6312	−	6.71530i	−0.381609	−	0.220322i	−0.678518	+	0.734584i	$0.737377\pi$
$930$		0			0
$931$	−8.38747	−	4.37084i	−0.274888	−	0.143248i
$932$	12.4211	+	7.17133i	0.406867	+	0.234905i
$933$		0			0
$934$	−10.5813	−	18.3274i	−0.346231	−	0.599690i
$935$		−	5.90657i		−	0.193165i
$936$		0			0
$937$		−	30.6584i		−	1.00157i	−0.865573	−	0.500783i	$-0.833045\pi$
$937$		−	30.6584i		−	1.00157i	0.865573	−	0.500783i	$-0.166955\pi$
$938$	−24.8611	+	7.24053i	−0.811744	+	0.236412i
$939$		0			0
$940$	−0.401414	+	0.695269i	−0.0130927	+	0.0226772i
$941$			28.5812i			0.931720i	0.884858	+	0.465860i	$0.154255\pi$
$941$			28.5812i			0.931720i	−0.884858	+	0.465860i	$0.845745\pi$
$942$		0			0
$943$	2.55686	−	4.42862i	0.0832629	−	0.144216i
$944$		−	6.48270i		−	0.210994i
$945$		0			0
$946$	−2.17835	−	3.77302i	−0.0708244	−	0.122671i
$947$	22.2575	+	38.5512i	0.723273	+	1.25275i	0.959681	+	0.281091i	$0.0906964\pi$
$947$	22.2575	+	38.5512i	0.723273	+	1.25275i	−0.236408	+	0.971654i	$0.575970\pi$
$948$		0			0
$949$	−0.145822	−	41.6794i	−0.00473359	−	1.35297i
$950$	−5.87681			−0.190669
$951$		0			0
$952$	−1.16742	−	4.00846i	−0.0378364	−	0.129915i
$953$	−48.0563	−	27.7453i	−1.55669	−	0.898758i	−0.997570	−	0.0696751i	$-0.977804\pi$
$953$	−48.0563	−	27.7453i	−1.55669	−	0.898758i	−0.559125	−	0.829083i	$-0.688863\pi$
$954$		0			0
$955$	−6.91139	+	11.9709i	−0.223647	+	0.387369i
$956$	−7.26069	+	12.5759i	−0.234827	+	0.406733i
$957$		0			0
$958$	−6.60511	−	3.81346i	−0.213401	−	0.123207i
$959$	−7.60973	−	26.1288i	−0.245731	−	0.843742i
$960$		0			0
$961$	13.6513			0.440363
$962$	−0.0185964	+	0.0324717i	−0.000599570	+	0.00104693i
$963$		0			0
$964$	7.73852	+	13.4035i	0.249241	+	0.431698i
$965$	−12.4672	−	21.5938i	−0.401333	−	0.695129i
$966$		0			0
$967$			15.5253i			0.499260i	0.968341	+	0.249630i	$0.0803090\pi$
$967$			15.5253i			0.499260i	−0.968341	+	0.249630i	$0.919691\pi$
$968$	−4.75073	+	8.22851i	−0.152694	+	0.264474i
$969$		0			0
$970$		−	10.9873i		−	0.352780i
$971$	2.81459	−	4.87501i	0.0903244	−	0.156446i	−0.817323	−	0.576179i	$-0.804543\pi$
$971$	2.81459	−	4.87501i	0.0903244	−	0.156446i	0.907648	+	0.419733i	$0.137876\pi$
$972$		0			0
$973$	−36.3463	+	10.5855i	−1.16521	+	0.339354i
$974$			24.0830i			0.771668i
$975$		0			0
$976$			8.44934i			0.270457i
$977$	4.69491	+	8.13182i	0.150203	+	0.260160i	0.931302	−	0.364248i	$-0.118674\pi$
$977$	4.69491	+	8.13182i	0.150203	+	0.260160i	−0.781099	+	0.624408i	$0.785340\pi$
$978$		0			0
$979$	2.03730	+	1.17624i	0.0651124	+	0.0375927i
$980$	−9.89140	+	18.9812i	−0.315969	+	0.606332i
$981$		0			0
$982$	21.2582	+	12.2734i	0.678376	+	0.391660i
$983$		−	54.0282i		−	1.72323i	−0.507562	−	0.861615i	$-0.669453\pi$
$983$		−	54.0282i		−	1.72323i	0.507562	−	0.861615i	$-0.330547\pi$
$984$		0			0
$985$	−29.6928	+	17.1432i	−0.946092	+	0.546226i
$986$	−13.9393	+	8.04786i	−0.443918	+	0.256296i
$987$		0			0
$988$	−4.21040	+	2.45055i	−0.133951	+	0.0779625i
$989$			11.8119i			0.375595i
$990$		0			0
$991$	−28.6873	−	49.6879i	−0.911283	−	1.57839i	−0.812254	−	0.583303i	$-0.801760\pi$
$991$	−28.6873	−	49.6879i	−0.911283	−	1.57839i	−0.0990284	−	0.995085i	$-0.531573\pi$
$992$	3.34108	−	5.78692i	0.106079	−	0.183735i
$993$		0			0
$994$	20.2869	−	21.1828i	0.643461	−	0.671878i
$995$	−25.7001	+	44.5139i	−0.814748	+	1.41118i
$996$		0			0
$997$	−12.9269	−	7.46336i	−0.409400	−	0.236367i	0.281132	−	0.959669i	$-0.409290\pi$
$997$	−12.9269	−	7.46336i	−0.409400	−	0.236367i	−0.690532	+	0.723302i	$0.742623\pi$
$998$	−22.3496	+	12.9036i	−0.707466	+	0.408456i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bc.b.881.18	yes	40
3.2	odd	2		1638.2.bc.a.881.3	yes	40
7.6	odd	2	inner	1638.2.bc.b.881.3	yes	40
13.4	even	6		1638.2.bc.a.251.3	✓	40
21.20	even	2		1638.2.bc.a.881.18	yes	40
39.17	odd	6	inner	1638.2.bc.b.251.18	yes	40
91.69	odd	6		1638.2.bc.a.251.18	yes	40
273.251	even	6	inner	1638.2.bc.b.251.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bc.a.251.3	✓	40	13.4	even	6
1638.2.bc.a.251.18	yes	40	91.69	odd	6
1638.2.bc.a.881.3	yes	40	3.2	odd	2
1638.2.bc.a.881.18	yes	40	21.20	even	2
1638.2.bc.b.251.3	yes	40	273.251	even	6	inner
1638.2.bc.b.251.18	yes	40	39.17	odd	6	inner
1638.2.bc.b.881.3	yes	40	7.6	odd	2	inner
1638.2.bc.b.881.18	yes	40	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.05770i q^{5} +(-1.82998 + 1.91080i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.05770i q^{5} +(-1.82998 + 1.91080i) q^{7} -1.00000 q^{8} +(-2.64804 + 1.52885i) q^{10} +(-0.612072 - 1.06014i) q^{11} +(0.0126145 + 3.60553i) q^{13} +(-2.56979 - 0.629412i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.789002 - 1.36659i) q^{17} +(0.675572 - 1.17012i) q^{19} +(-2.64804 - 1.52885i) q^{20} +(0.612072 - 1.06014i) q^{22} +(-2.87424 + 1.65944i) q^{23} -4.34951 q^{25} +(-3.11617 + 1.81369i) q^{26} +(-0.739810 - 2.54021i) q^{28} +(-8.83351 + 5.10003i) q^{29} +6.68216 q^{31} +(0.500000 - 0.866025i) q^{32} +1.57800 q^{34} +(-5.84265 - 5.59554i) q^{35} +(0.00898792 - 0.00518918i) q^{37} +1.35114 q^{38} -3.05770i q^{40} +(-1.33437 + 0.770398i) q^{41} +(1.77949 - 3.08217i) q^{43} +1.22414 q^{44} +(-2.87424 - 1.65944i) q^{46} -0.262559i q^{47} +(-0.302320 - 6.99347i) q^{49} +(-2.17476 - 3.76679i) q^{50} +(-3.12879 - 1.79184i) q^{52} -12.3299i q^{53} +(3.24159 - 1.87153i) q^{55} +(1.82998 - 1.91080i) q^{56} +(-8.83351 - 5.10003i) q^{58} +(5.61418 + 3.24135i) q^{59} +(-7.31734 - 4.22467i) q^{61} +(3.34108 + 5.78692i) q^{62} +1.00000 q^{64} +(-11.0246 + 0.0385714i) q^{65} +(8.47580 - 4.89351i) q^{67} +(0.789002 + 1.36659i) q^{68} +(1.92455 - 7.85765i) q^{70} +(-5.54292 + 9.60061i) q^{71} -11.5599 q^{73} +(0.00898792 + 0.00518918i) q^{74} +(0.675572 + 1.17012i) q^{76} +(3.14580 + 0.770491i) q^{77} +5.47379 q^{79} +(2.64804 - 1.52885i) q^{80} +(-1.33437 - 0.770398i) q^{82} -0.716433i q^{83} +(4.17862 + 2.41253i) q^{85} +3.55898 q^{86} +(0.612072 + 1.06014i) q^{88} +(-1.66426 + 0.960864i) q^{89} +(-6.91253 - 6.57396i) q^{91} -3.31889i q^{92} +(0.227383 - 0.131280i) q^{94} +(3.57789 + 2.06569i) q^{95} +(-1.79666 + 3.11190i) q^{97} +(5.90536 - 3.75855i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{2} - 20 q^{4} - 40 q^{8}+O(q^{10}) \) 40 * q + 20 * q^2 - 20 * q^4 - 40 * q^8	\( 40 q + 20 q^{2} - 20 q^{4} - 40 q^{8} - 20 q^{16} - 12 q^{23} - 56 q^{25} + 20 q^{32} + 48 q^{35} + 24 q^{37} + 12 q^{43} - 12 q^{46} + 4 q^{49} - 28 q^{50} + 40 q^{64} - 48 q^{65} - 12 q^{67} - 12 q^{71} + 24 q^{74} + 48 q^{79} + 48 q^{85} + 24 q^{86} + 24 q^{95} - 4 q^{98}+O(q^{100}) \) 40 * q + 20 * q^2 - 20 * q^4 - 40 * q^8 - 20 * q^16 - 12 * q^23 - 56 * q^25 + 20 * q^32 + 48 * q^35 + 24 * q^37 + 12 * q^43 - 12 * q^46 + 4 * q^49 - 28 * q^50 + 40 * q^64 - 48 * q^65 - 12 * q^67 - 12 * q^71 + 24 * q^74 + 48 * q^79 + 48 * q^85 + 24 * q^86 + 24 * q^95 - 4 * q^98

Introduction

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